Properties

Label 38.2.e.a.17.1
Level $38$
Weight $2$
Character 38.17
Analytic conductor $0.303$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [38,2,Mod(5,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 38.e (of order \(9\), degree \(6\), 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: \(0.303431527681\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 17.1
Root \(-0.173648 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 38.17
Dual form 38.2.e.a.9.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.173648 - 0.984808i) q^{2} +(0.266044 + 0.223238i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.87939 + 0.684040i) q^{5} +(0.266044 - 0.223238i) q^{6} +(0.879385 + 1.52314i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.500000 - 2.83564i) q^{9} +O(q^{10})\) \(q+(0.173648 - 0.984808i) q^{2} +(0.266044 + 0.223238i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.87939 + 0.684040i) q^{5} +(0.266044 - 0.223238i) q^{6} +(0.879385 + 1.52314i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.500000 - 2.83564i) q^{9} +(0.347296 + 1.96962i) q^{10} +(-2.11334 + 3.66041i) q^{11} +(-0.173648 - 0.300767i) q^{12} +(0.815207 - 0.684040i) q^{13} +(1.65270 - 0.601535i) q^{14} +(-0.652704 - 0.237565i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.23783 - 7.02006i) q^{17} -2.87939 q^{18} +(3.93969 - 1.86516i) q^{19} +2.00000 q^{20} +(-0.106067 + 0.601535i) q^{21} +(3.23783 + 2.71686i) q^{22} +(-3.53209 - 1.28558i) q^{23} +(-0.326352 + 0.118782i) q^{24} +(-0.766044 + 0.642788i) q^{25} +(-0.532089 - 0.921605i) q^{26} +(1.02094 - 1.76833i) q^{27} +(-0.305407 - 1.73205i) q^{28} +(1.10607 + 6.27282i) q^{29} +(-0.347296 + 0.601535i) q^{30} +(4.41147 + 7.64090i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-1.37939 + 0.502055i) q^{33} +(-6.69846 - 2.43804i) q^{34} +(-2.69459 - 2.26103i) q^{35} +(-0.500000 + 2.83564i) q^{36} -6.45336 q^{37} +(-1.15270 - 4.20372i) q^{38} +0.369585 q^{39} +(0.347296 - 1.96962i) q^{40} +(1.43969 + 1.20805i) q^{41} +(0.573978 + 0.208911i) q^{42} +(-3.47178 + 1.26363i) q^{43} +(3.23783 - 2.71686i) q^{44} +(2.87939 + 4.98724i) q^{45} +(-1.87939 + 3.25519i) q^{46} +(-0.638156 - 3.61916i) q^{47} +(0.0603074 + 0.342020i) q^{48} +(1.95336 - 3.38332i) q^{49} +(0.500000 + 0.866025i) q^{50} +(1.89646 - 1.59132i) q^{51} +(-1.00000 + 0.363970i) q^{52} +(9.29086 + 3.38160i) q^{53} +(-1.56418 - 1.31250i) q^{54} +(1.46791 - 8.32494i) q^{55} -1.75877 q^{56} +(1.46451 + 0.383273i) q^{57} +6.36959 q^{58} +(-1.26604 + 7.18009i) q^{59} +(0.532089 + 0.446476i) q^{60} +(-4.98545 - 1.81456i) q^{61} +(8.29086 - 3.01763i) q^{62} +(3.87939 - 3.25519i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.06418 + 1.84321i) q^{65} +(0.254900 + 1.44561i) q^{66} +(-2.02094 - 11.4613i) q^{67} +(-3.56418 + 6.17334i) q^{68} +(-0.652704 - 1.13052i) q^{69} +(-2.69459 + 2.26103i) q^{70} +(-2.65270 + 0.965505i) q^{71} +(2.70574 + 0.984808i) q^{72} +(0.607411 + 0.509678i) q^{73} +(-1.12061 + 6.35532i) q^{74} -0.347296 q^{75} +(-4.34002 + 0.405223i) q^{76} -7.43376 q^{77} +(0.0641778 - 0.363970i) q^{78} +(-5.12836 - 4.30320i) q^{79} +(-1.87939 - 0.684040i) q^{80} +(-7.45084 + 2.71188i) q^{81} +(1.43969 - 1.20805i) q^{82} +(-0.754900 - 1.30753i) q^{83} +(0.305407 - 0.528981i) q^{84} +(2.47565 + 14.0401i) q^{85} +(0.641559 + 3.63846i) q^{86} +(-1.10607 + 1.91576i) q^{87} +(-2.11334 - 3.66041i) q^{88} +(9.12108 - 7.65350i) q^{89} +(5.41147 - 1.96962i) q^{90} +(1.75877 + 0.640140i) q^{91} +(2.87939 + 2.41609i) q^{92} +(-0.532089 + 3.01763i) q^{93} -3.67499 q^{94} +(-6.12836 + 6.20026i) q^{95} +0.347296 q^{96} +(0.326352 - 1.85083i) q^{97} +(-2.99273 - 2.51120i) q^{98} +(11.4363 + 4.16247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{3} - 3 q^{6} - 6 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{3} - 3 q^{6} - 6 q^{7} - 3 q^{8} - 3 q^{9} - 6 q^{11} + 12 q^{13} + 12 q^{14} - 6 q^{15} - 12 q^{17} - 6 q^{18} + 18 q^{19} + 12 q^{20} + 24 q^{21} - 12 q^{23} - 3 q^{24} + 6 q^{26} + 3 q^{27} - 6 q^{28} - 18 q^{29} + 6 q^{31} + 3 q^{33} - 12 q^{34} - 12 q^{35} - 3 q^{36} - 12 q^{37} - 9 q^{38} - 12 q^{39} + 3 q^{41} - 12 q^{42} - 6 q^{43} + 6 q^{45} + 30 q^{47} + 6 q^{48} - 15 q^{49} + 3 q^{50} + 21 q^{51} - 6 q^{52} + 24 q^{53} + 9 q^{54} + 18 q^{55} + 12 q^{56} - 24 q^{57} + 24 q^{58} - 3 q^{59} - 6 q^{60} + 6 q^{61} + 18 q^{62} + 12 q^{63} - 3 q^{64} + 12 q^{65} + 3 q^{66} - 9 q^{67} - 3 q^{68} - 6 q^{69} - 12 q^{70} - 18 q^{71} + 6 q^{72} - 30 q^{73} - 18 q^{74} - 6 q^{76} - 12 q^{77} - 18 q^{78} + 6 q^{79} - 33 q^{81} + 3 q^{82} - 6 q^{83} + 6 q^{84} - 24 q^{85} + 12 q^{86} + 18 q^{87} - 6 q^{88} + 12 q^{90} - 12 q^{91} + 6 q^{92} + 6 q^{93} - 12 q^{94} + 3 q^{97} + 21 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.173648 0.984808i 0.122788 0.696364i
\(3\) 0.266044 + 0.223238i 0.153601 + 0.128886i 0.716349 0.697742i \(-0.245812\pi\)
−0.562749 + 0.826628i \(0.690256\pi\)
\(4\) −0.939693 0.342020i −0.469846 0.171010i
\(5\) −1.87939 + 0.684040i −0.840487 + 0.305912i −0.726155 0.687531i \(-0.758695\pi\)
−0.114331 + 0.993443i \(0.536473\pi\)
\(6\) 0.266044 0.223238i 0.108612 0.0911364i
\(7\) 0.879385 + 1.52314i 0.332376 + 0.575693i 0.982977 0.183727i \(-0.0588162\pi\)
−0.650601 + 0.759420i \(0.725483\pi\)
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) −0.500000 2.83564i −0.166667 0.945214i
\(10\) 0.347296 + 1.96962i 0.109825 + 0.622847i
\(11\) −2.11334 + 3.66041i −0.637196 + 1.10366i 0.348849 + 0.937179i \(0.386573\pi\)
−0.986045 + 0.166477i \(0.946761\pi\)
\(12\) −0.173648 0.300767i −0.0501279 0.0868241i
\(13\) 0.815207 0.684040i 0.226098 0.189719i −0.522701 0.852516i \(-0.675075\pi\)
0.748799 + 0.662798i \(0.230631\pi\)
\(14\) 1.65270 0.601535i 0.441704 0.160767i
\(15\) −0.652704 0.237565i −0.168527 0.0613389i
\(16\) 0.766044 + 0.642788i 0.191511 + 0.160697i
\(17\) 1.23783 7.02006i 0.300217 1.70261i −0.344990 0.938606i \(-0.612118\pi\)
0.645207 0.764008i \(-0.276771\pi\)
\(18\) −2.87939 −0.678678
\(19\) 3.93969 1.86516i 0.903827 0.427897i
\(20\) 2.00000 0.447214
\(21\) −0.106067 + 0.601535i −0.0231457 + 0.131266i
\(22\) 3.23783 + 2.71686i 0.690307 + 0.579236i
\(23\) −3.53209 1.28558i −0.736491 0.268061i −0.0535814 0.998563i \(-0.517064\pi\)
−0.682910 + 0.730503i \(0.739286\pi\)
\(24\) −0.326352 + 0.118782i −0.0666163 + 0.0242463i
\(25\) −0.766044 + 0.642788i −0.153209 + 0.128558i
\(26\) −0.532089 0.921605i −0.104351 0.180742i
\(27\) 1.02094 1.76833i 0.196481 0.340315i
\(28\) −0.305407 1.73205i −0.0577166 0.327327i
\(29\) 1.10607 + 6.27282i 0.205391 + 1.16483i 0.896823 + 0.442390i \(0.145869\pi\)
−0.691431 + 0.722442i \(0.743019\pi\)
\(30\) −0.347296 + 0.601535i −0.0634073 + 0.109825i
\(31\) 4.41147 + 7.64090i 0.792324 + 1.37235i 0.924524 + 0.381123i \(0.124462\pi\)
−0.132200 + 0.991223i \(0.542204\pi\)
\(32\) 0.766044 0.642788i 0.135419 0.113630i
\(33\) −1.37939 + 0.502055i −0.240120 + 0.0873966i
\(34\) −6.69846 2.43804i −1.14878 0.418121i
\(35\) −2.69459 2.26103i −0.455469 0.382184i
\(36\) −0.500000 + 2.83564i −0.0833333 + 0.472607i
\(37\) −6.45336 −1.06093 −0.530463 0.847708i \(-0.677982\pi\)
−0.530463 + 0.847708i \(0.677982\pi\)
\(38\) −1.15270 4.20372i −0.186993 0.681934i
\(39\) 0.369585 0.0591810
\(40\) 0.347296 1.96962i 0.0549124 0.311424i
\(41\) 1.43969 + 1.20805i 0.224842 + 0.188665i 0.748249 0.663418i \(-0.230895\pi\)
−0.523407 + 0.852083i \(0.675339\pi\)
\(42\) 0.573978 + 0.208911i 0.0885667 + 0.0322357i
\(43\) −3.47178 + 1.26363i −0.529442 + 0.192701i −0.592889 0.805284i \(-0.702013\pi\)
0.0634473 + 0.997985i \(0.479791\pi\)
\(44\) 3.23783 2.71686i 0.488121 0.409582i
\(45\) 2.87939 + 4.98724i 0.429233 + 0.743454i
\(46\) −1.87939 + 3.25519i −0.277100 + 0.479952i
\(47\) −0.638156 3.61916i −0.0930846 0.527909i −0.995317 0.0966598i \(-0.969184\pi\)
0.902233 0.431249i \(-0.141927\pi\)
\(48\) 0.0603074 + 0.342020i 0.00870462 + 0.0493664i
\(49\) 1.95336 3.38332i 0.279052 0.483332i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) 1.89646 1.59132i 0.265557 0.222829i
\(52\) −1.00000 + 0.363970i −0.138675 + 0.0504736i
\(53\) 9.29086 + 3.38160i 1.27620 + 0.464498i 0.889173 0.457571i \(-0.151281\pi\)
0.387025 + 0.922069i \(0.373503\pi\)
\(54\) −1.56418 1.31250i −0.212858 0.178609i
\(55\) 1.46791 8.32494i 0.197933 1.12253i
\(56\) −1.75877 −0.235026
\(57\) 1.46451 + 0.383273i 0.193979 + 0.0507657i
\(58\) 6.36959 0.836367
\(59\) −1.26604 + 7.18009i −0.164825 + 0.934769i 0.784420 + 0.620230i \(0.212961\pi\)
−0.949245 + 0.314538i \(0.898150\pi\)
\(60\) 0.532089 + 0.446476i 0.0686924 + 0.0576398i
\(61\) −4.98545 1.81456i −0.638322 0.232330i 0.00252758 0.999997i \(-0.499195\pi\)
−0.640849 + 0.767667i \(0.721418\pi\)
\(62\) 8.29086 3.01763i 1.05294 0.383239i
\(63\) 3.87939 3.25519i 0.488757 0.410115i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) −1.06418 + 1.84321i −0.131995 + 0.228622i
\(66\) 0.254900 + 1.44561i 0.0313760 + 0.177942i
\(67\) −2.02094 11.4613i −0.246898 1.40023i −0.816044 0.577990i \(-0.803837\pi\)
0.569146 0.822236i \(-0.307274\pi\)
\(68\) −3.56418 + 6.17334i −0.432220 + 0.748627i
\(69\) −0.652704 1.13052i −0.0785763 0.136098i
\(70\) −2.69459 + 2.26103i −0.322065 + 0.270245i
\(71\) −2.65270 + 0.965505i −0.314818 + 0.114584i −0.494596 0.869123i \(-0.664684\pi\)
0.179778 + 0.983707i \(0.442462\pi\)
\(72\) 2.70574 + 0.984808i 0.318874 + 0.116061i
\(73\) 0.607411 + 0.509678i 0.0710921 + 0.0596533i 0.677641 0.735393i \(-0.263002\pi\)
−0.606549 + 0.795046i \(0.707447\pi\)
\(74\) −1.12061 + 6.35532i −0.130269 + 0.738791i
\(75\) −0.347296 −0.0401023
\(76\) −4.34002 + 0.405223i −0.497835 + 0.0464823i
\(77\) −7.43376 −0.847156
\(78\) 0.0641778 0.363970i 0.00726670 0.0412115i
\(79\) −5.12836 4.30320i −0.576985 0.484148i 0.306970 0.951719i \(-0.400685\pi\)
−0.883955 + 0.467571i \(0.845129\pi\)
\(80\) −1.87939 0.684040i −0.210122 0.0764780i
\(81\) −7.45084 + 2.71188i −0.827871 + 0.301320i
\(82\) 1.43969 1.20805i 0.158987 0.133406i
\(83\) −0.754900 1.30753i −0.0828610 0.143520i 0.821617 0.570040i \(-0.193072\pi\)
−0.904478 + 0.426521i \(0.859739\pi\)
\(84\) 0.305407 0.528981i 0.0333227 0.0577166i
\(85\) 2.47565 + 14.0401i 0.268522 + 1.52286i
\(86\) 0.641559 + 3.63846i 0.0691811 + 0.392346i
\(87\) −1.10607 + 1.91576i −0.118583 + 0.205391i
\(88\) −2.11334 3.66041i −0.225283 0.390201i
\(89\) 9.12108 7.65350i 0.966833 0.811269i −0.0152184 0.999884i \(-0.504844\pi\)
0.982051 + 0.188615i \(0.0603999\pi\)
\(90\) 5.41147 1.96962i 0.570419 0.207616i
\(91\) 1.75877 + 0.640140i 0.184369 + 0.0671049i
\(92\) 2.87939 + 2.41609i 0.300197 + 0.251895i
\(93\) −0.532089 + 3.01763i −0.0551750 + 0.312913i
\(94\) −3.67499 −0.379047
\(95\) −6.12836 + 6.20026i −0.628756 + 0.636134i
\(96\) 0.347296 0.0354458
\(97\) 0.326352 1.85083i 0.0331360 0.187924i −0.963747 0.266818i \(-0.914028\pi\)
0.996883 + 0.0788942i \(0.0251389\pi\)
\(98\) −2.99273 2.51120i −0.302311 0.253669i
\(99\) 11.4363 + 4.16247i 1.14939 + 0.418344i
\(100\) 0.939693 0.342020i 0.0939693 0.0342020i
\(101\) −1.87939 + 1.57699i −0.187006 + 0.156917i −0.731484 0.681858i \(-0.761172\pi\)
0.544478 + 0.838775i \(0.316728\pi\)
\(102\) −1.23783 2.14398i −0.122563 0.212285i
\(103\) 3.71688 6.43783i 0.366235 0.634338i −0.622738 0.782430i \(-0.713980\pi\)
0.988974 + 0.148092i \(0.0473132\pi\)
\(104\) 0.184793 + 1.04801i 0.0181204 + 0.102766i
\(105\) −0.212134 1.20307i −0.0207021 0.117408i
\(106\) 4.94356 8.56250i 0.480161 0.831664i
\(107\) 0.0885259 + 0.153331i 0.00855812 + 0.0148231i 0.870273 0.492570i \(-0.163942\pi\)
−0.861715 + 0.507393i \(0.830609\pi\)
\(108\) −1.56418 + 1.31250i −0.150513 + 0.126295i
\(109\) −3.98545 + 1.45059i −0.381737 + 0.138941i −0.525759 0.850634i \(-0.676219\pi\)
0.144022 + 0.989574i \(0.453996\pi\)
\(110\) −7.94356 2.89122i −0.757389 0.275667i
\(111\) −1.71688 1.44063i −0.162959 0.136739i
\(112\) −0.305407 + 1.73205i −0.0288583 + 0.163663i
\(113\) 10.4388 0.982001 0.491001 0.871159i \(-0.336631\pi\)
0.491001 + 0.871159i \(0.336631\pi\)
\(114\) 0.631759 1.37570i 0.0591697 0.128846i
\(115\) 7.51754 0.701014
\(116\) 1.10607 6.27282i 0.102696 0.582416i
\(117\) −2.34730 1.96962i −0.217008 0.182091i
\(118\) 6.85117 + 2.49362i 0.630701 + 0.229556i
\(119\) 11.7811 4.28795i 1.07997 0.393076i
\(120\) 0.532089 0.446476i 0.0485728 0.0407575i
\(121\) −3.43242 5.94512i −0.312038 0.540466i
\(122\) −2.65270 + 4.59462i −0.240165 + 0.415977i
\(123\) 0.113341 + 0.642788i 0.0102196 + 0.0579582i
\(124\) −1.53209 8.68891i −0.137586 0.780287i
\(125\) 6.00000 10.3923i 0.536656 0.929516i
\(126\) −2.53209 4.38571i −0.225576 0.390710i
\(127\) −16.8648 + 14.1513i −1.49651 + 1.25572i −0.610539 + 0.791986i \(0.709047\pi\)
−0.885973 + 0.463737i \(0.846508\pi\)
\(128\) −0.939693 + 0.342020i −0.0830579 + 0.0302306i
\(129\) −1.20574 0.438852i −0.106159 0.0386388i
\(130\) 1.63041 + 1.36808i 0.142997 + 0.119989i
\(131\) −1.32888 + 7.53644i −0.116105 + 0.658462i 0.870093 + 0.492888i \(0.164059\pi\)
−0.986197 + 0.165574i \(0.947052\pi\)
\(132\) 1.46791 0.127765
\(133\) 6.30541 + 4.36051i 0.546748 + 0.378104i
\(134\) −11.6382 −1.00538
\(135\) −0.709141 + 4.02174i −0.0610331 + 0.346136i
\(136\) 5.46064 + 4.58202i 0.468246 + 0.392905i
\(137\) 5.39053 + 1.96199i 0.460544 + 0.167624i 0.561864 0.827230i \(-0.310084\pi\)
−0.101320 + 0.994854i \(0.532307\pi\)
\(138\) −1.22668 + 0.446476i −0.104422 + 0.0380065i
\(139\) −14.8589 + 12.4681i −1.26032 + 1.05753i −0.264668 + 0.964340i \(0.585262\pi\)
−0.995648 + 0.0931911i \(0.970293\pi\)
\(140\) 1.75877 + 3.04628i 0.148643 + 0.257458i
\(141\) 0.638156 1.10532i 0.0537424 0.0930846i
\(142\) 0.490200 + 2.78006i 0.0411367 + 0.233298i
\(143\) 0.781059 + 4.42961i 0.0653155 + 0.370422i
\(144\) 1.43969 2.49362i 0.119974 0.207802i
\(145\) −6.36959 11.0324i −0.528965 0.916195i
\(146\) 0.607411 0.509678i 0.0502697 0.0421813i
\(147\) 1.27497 0.464050i 0.105158 0.0382742i
\(148\) 6.06418 + 2.20718i 0.498472 + 0.181429i
\(149\) −3.96585 3.32774i −0.324895 0.272619i 0.465721 0.884932i \(-0.345795\pi\)
−0.790616 + 0.612312i \(0.790240\pi\)
\(150\) −0.0603074 + 0.342020i −0.00492408 + 0.0279258i
\(151\) 22.1830 1.80523 0.902615 0.430449i \(-0.141645\pi\)
0.902615 + 0.430449i \(0.141645\pi\)
\(152\) −0.354570 + 4.34445i −0.0287595 + 0.352382i
\(153\) −20.5253 −1.65937
\(154\) −1.29086 + 7.32083i −0.104020 + 0.589929i
\(155\) −13.5175 11.3426i −1.08576 0.911057i
\(156\) −0.347296 0.126406i −0.0278060 0.0101205i
\(157\) 2.65270 0.965505i 0.211709 0.0770557i −0.233989 0.972239i \(-0.575178\pi\)
0.445698 + 0.895184i \(0.352956\pi\)
\(158\) −5.12836 + 4.30320i −0.407990 + 0.342344i
\(159\) 1.71688 + 2.97373i 0.136158 + 0.235832i
\(160\) −1.00000 + 1.73205i −0.0790569 + 0.136931i
\(161\) −1.14796 6.51038i −0.0904716 0.513090i
\(162\) 1.37686 + 7.80856i 0.108176 + 0.613498i
\(163\) −1.10947 + 1.92166i −0.0869004 + 0.150516i −0.906199 0.422851i \(-0.861030\pi\)
0.819299 + 0.573366i \(0.194363\pi\)
\(164\) −0.939693 1.62760i −0.0733777 0.127094i
\(165\) 2.24897 1.88711i 0.175082 0.146911i
\(166\) −1.41875 + 0.516382i −0.110116 + 0.0400790i
\(167\) −3.68004 1.33943i −0.284770 0.103648i 0.195686 0.980667i \(-0.437307\pi\)
−0.480456 + 0.877019i \(0.659529\pi\)
\(168\) −0.467911 0.392624i −0.0361001 0.0302916i
\(169\) −2.06077 + 11.6872i −0.158521 + 0.899018i
\(170\) 14.2567 1.09344
\(171\) −7.25877 10.2390i −0.555092 0.782994i
\(172\) 3.69459 0.281710
\(173\) 1.31046 7.43199i 0.0996324 0.565043i −0.893597 0.448871i \(-0.851826\pi\)
0.993229 0.116173i \(-0.0370626\pi\)
\(174\) 1.69459 + 1.42193i 0.128467 + 0.107796i
\(175\) −1.65270 0.601535i −0.124933 0.0454718i
\(176\) −3.97178 + 1.44561i −0.299384 + 0.108967i
\(177\) −1.93969 + 1.62760i −0.145796 + 0.122338i
\(178\) −5.95336 10.3115i −0.446223 0.772882i
\(179\) 5.49407 9.51601i 0.410646 0.711260i −0.584314 0.811527i \(-0.698637\pi\)
0.994961 + 0.100267i \(0.0319698\pi\)
\(180\) −1.00000 5.67128i −0.0745356 0.422712i
\(181\) −2.61081 14.8067i −0.194060 1.10057i −0.913751 0.406276i \(-0.866827\pi\)
0.719690 0.694295i \(-0.244284\pi\)
\(182\) 0.935822 1.62089i 0.0693678 0.120148i
\(183\) −0.921274 1.59569i −0.0681026 0.117957i
\(184\) 2.87939 2.41609i 0.212271 0.178117i
\(185\) 12.1284 4.41436i 0.891694 0.324550i
\(186\) 2.87939 + 1.04801i 0.211127 + 0.0768439i
\(187\) 23.0804 + 19.3667i 1.68780 + 1.41624i
\(188\) −0.638156 + 3.61916i −0.0465423 + 0.263954i
\(189\) 3.59121 0.261222
\(190\) 5.04189 + 7.11192i 0.365777 + 0.515953i
\(191\) 4.53714 0.328296 0.164148 0.986436i \(-0.447513\pi\)
0.164148 + 0.986436i \(0.447513\pi\)
\(192\) 0.0603074 0.342020i 0.00435231 0.0246832i
\(193\) 16.8498 + 14.1387i 1.21288 + 1.01772i 0.999166 + 0.0408274i \(0.0129994\pi\)
0.213711 + 0.976897i \(0.431445\pi\)
\(194\) −1.76604 0.642788i −0.126795 0.0461495i
\(195\) −0.694593 + 0.252811i −0.0497408 + 0.0181042i
\(196\) −2.99273 + 2.51120i −0.213766 + 0.179371i
\(197\) −7.96585 13.7973i −0.567543 0.983014i −0.996808 0.0798353i \(-0.974561\pi\)
0.429265 0.903179i \(-0.358773\pi\)
\(198\) 6.08512 10.5397i 0.432451 0.749027i
\(199\) −0.568926 3.22654i −0.0403301 0.228723i 0.957980 0.286835i \(-0.0926031\pi\)
−0.998310 + 0.0581118i \(0.981492\pi\)
\(200\) −0.173648 0.984808i −0.0122788 0.0696364i
\(201\) 2.02094 3.50038i 0.142546 0.246898i
\(202\) 1.22668 + 2.12467i 0.0863090 + 0.149492i
\(203\) −8.58172 + 7.20092i −0.602319 + 0.505405i
\(204\) −2.32635 + 0.846723i −0.162877 + 0.0592825i
\(205\) −3.53209 1.28558i −0.246692 0.0897885i
\(206\) −5.69459 4.77833i −0.396761 0.332922i
\(207\) −1.87939 + 10.6585i −0.130626 + 0.740819i
\(208\) 1.06418 0.0737875
\(209\) −1.49866 + 18.3626i −0.103664 + 1.27017i
\(210\) −1.22163 −0.0843004
\(211\) 1.99154 11.2946i 0.137104 0.777553i −0.836268 0.548321i \(-0.815267\pi\)
0.973372 0.229232i \(-0.0736215\pi\)
\(212\) −7.57398 6.35532i −0.520183 0.436485i
\(213\) −0.921274 0.335316i −0.0631247 0.0229755i
\(214\) 0.166374 0.0605553i 0.0113731 0.00413947i
\(215\) 5.66044 4.74968i 0.386039 0.323925i
\(216\) 1.02094 + 1.76833i 0.0694665 + 0.120319i
\(217\) −7.75877 + 13.4386i −0.526700 + 0.912271i
\(218\) 0.736482 + 4.17680i 0.0498808 + 0.282888i
\(219\) 0.0478189 + 0.271194i 0.00323130 + 0.0183256i
\(220\) −4.22668 + 7.32083i −0.284963 + 0.493570i
\(221\) −3.79292 6.56953i −0.255139 0.441914i
\(222\) −1.71688 + 1.44063i −0.115230 + 0.0966891i
\(223\) −10.5175 + 3.82807i −0.704307 + 0.256347i −0.669249 0.743039i \(-0.733384\pi\)
−0.0350581 + 0.999385i \(0.511162\pi\)
\(224\) 1.65270 + 0.601535i 0.110426 + 0.0401917i
\(225\) 2.20574 + 1.85083i 0.147049 + 0.123389i
\(226\) 1.81268 10.2802i 0.120578 0.683830i
\(227\) −3.39693 −0.225462 −0.112731 0.993626i \(-0.535960\pi\)
−0.112731 + 0.993626i \(0.535960\pi\)
\(228\) −1.24510 0.861050i −0.0824588 0.0570244i
\(229\) 4.25671 0.281291 0.140646 0.990060i \(-0.455082\pi\)
0.140646 + 0.990060i \(0.455082\pi\)
\(230\) 1.30541 7.40333i 0.0860760 0.488161i
\(231\) −1.97771 1.65950i −0.130124 0.109187i
\(232\) −5.98545 2.17853i −0.392964 0.143027i
\(233\) −6.24257 + 2.27211i −0.408965 + 0.148851i −0.538307 0.842749i \(-0.680936\pi\)
0.129342 + 0.991600i \(0.458714\pi\)
\(234\) −2.34730 + 1.96962i −0.153448 + 0.128758i
\(235\) 3.67499 + 6.36527i 0.239730 + 0.415225i
\(236\) 3.64543 6.31407i 0.237297 0.411011i
\(237\) −0.403733 2.28969i −0.0262253 0.148731i
\(238\) −2.17705 12.3467i −0.141117 0.800316i
\(239\) −8.00774 + 13.8698i −0.517978 + 0.897164i 0.481804 + 0.876279i \(0.339982\pi\)
−0.999782 + 0.0208848i \(0.993352\pi\)
\(240\) −0.347296 0.601535i −0.0224179 0.0388289i
\(241\) −6.59105 + 5.53055i −0.424567 + 0.356254i −0.829897 0.557916i \(-0.811601\pi\)
0.405330 + 0.914170i \(0.367157\pi\)
\(242\) −6.45084 + 2.34791i −0.414676 + 0.150930i
\(243\) −8.34389 3.03693i −0.535261 0.194819i
\(244\) 4.06418 + 3.41025i 0.260182 + 0.218319i
\(245\) −1.35679 + 7.69475i −0.0866823 + 0.491599i
\(246\) 0.652704 0.0416149
\(247\) 1.93582 4.21540i 0.123173 0.268220i
\(248\) −8.82295 −0.560258
\(249\) 0.0910521 0.516382i 0.00577019 0.0327244i
\(250\) −9.19253 7.71345i −0.581387 0.487841i
\(251\) 18.7087 + 6.80942i 1.18088 + 0.429807i 0.856514 0.516123i \(-0.172625\pi\)
0.324370 + 0.945930i \(0.394848\pi\)
\(252\) −4.75877 + 1.73205i −0.299774 + 0.109109i
\(253\) 12.1702 10.2120i 0.765137 0.642026i
\(254\) 11.0077 + 19.0660i 0.690687 + 1.19631i
\(255\) −2.47565 + 4.28795i −0.155031 + 0.268522i
\(256\) 0.173648 + 0.984808i 0.0108530 + 0.0615505i
\(257\) 4.58734 + 26.0161i 0.286151 + 1.62284i 0.701146 + 0.713018i \(0.252672\pi\)
−0.414996 + 0.909823i \(0.636217\pi\)
\(258\) −0.641559 + 1.11121i −0.0399417 + 0.0691811i
\(259\) −5.67499 9.82938i −0.352627 0.610768i
\(260\) 1.63041 1.36808i 0.101114 0.0848448i
\(261\) 17.2344 6.27282i 1.06678 0.388278i
\(262\) 7.19119 + 2.61738i 0.444273 + 0.161702i
\(263\) −21.4047 17.9606i −1.31987 1.10750i −0.986333 0.164763i \(-0.947314\pi\)
−0.333535 0.942738i \(-0.608242\pi\)
\(264\) 0.254900 1.44561i 0.0156880 0.0889712i
\(265\) −19.7743 −1.21472
\(266\) 5.38919 5.45242i 0.330432 0.334309i
\(267\) 4.13516 0.253068
\(268\) −2.02094 + 11.4613i −0.123449 + 0.700113i
\(269\) 11.1702 + 9.37295i 0.681062 + 0.571479i 0.916316 0.400455i \(-0.131148\pi\)
−0.235255 + 0.971934i \(0.575592\pi\)
\(270\) 3.83750 + 1.39673i 0.233543 + 0.0850025i
\(271\) 17.1284 6.23421i 1.04047 0.378701i 0.235414 0.971895i \(-0.424355\pi\)
0.805060 + 0.593194i \(0.202133\pi\)
\(272\) 5.46064 4.58202i 0.331100 0.277826i
\(273\) 0.325008 + 0.562930i 0.0196704 + 0.0340701i
\(274\) 2.86824 4.96794i 0.173277 0.300124i
\(275\) −0.733956 4.16247i −0.0442592 0.251006i
\(276\) 0.226682 + 1.28558i 0.0136446 + 0.0773825i
\(277\) 8.23442 14.2624i 0.494758 0.856947i −0.505223 0.862989i \(-0.668590\pi\)
0.999982 + 0.00604184i \(0.00192319\pi\)
\(278\) 9.69846 + 16.7982i 0.581675 + 1.00749i
\(279\) 19.4611 16.3298i 1.16511 0.977640i
\(280\) 3.30541 1.20307i 0.197536 0.0718972i
\(281\) 6.73783 + 2.45237i 0.401945 + 0.146296i 0.535079 0.844802i \(-0.320282\pi\)
−0.133134 + 0.991098i \(0.542504\pi\)
\(282\) −0.977711 0.820397i −0.0582219 0.0488539i
\(283\) 3.63563 20.6187i 0.216116 1.22565i −0.662844 0.748757i \(-0.730651\pi\)
0.878960 0.476896i \(-0.158238\pi\)
\(284\) 2.82295 0.167511
\(285\) −3.01455 + 0.281465i −0.178566 + 0.0166725i
\(286\) 4.49794 0.265969
\(287\) −0.573978 + 3.25519i −0.0338808 + 0.192148i
\(288\) −2.20574 1.85083i −0.129974 0.109061i
\(289\) −31.7743 11.5649i −1.86907 0.680287i
\(290\) −11.9709 + 4.35705i −0.702956 + 0.255855i
\(291\) 0.500000 0.419550i 0.0293105 0.0245944i
\(292\) −0.396459 0.686688i −0.0232010 0.0401854i
\(293\) −4.73917 + 8.20848i −0.276865 + 0.479545i −0.970604 0.240682i \(-0.922629\pi\)
0.693739 + 0.720227i \(0.255962\pi\)
\(294\) −0.235604 1.33618i −0.0137407 0.0779275i
\(295\) −2.53209 14.3602i −0.147424 0.836083i
\(296\) 3.22668 5.58878i 0.187547 0.324841i
\(297\) 4.31521 + 7.47416i 0.250394 + 0.433695i
\(298\) −3.96585 + 3.32774i −0.229736 + 0.192771i
\(299\) −3.75877 + 1.36808i −0.217375 + 0.0791181i
\(300\) 0.326352 + 0.118782i 0.0188419 + 0.00685790i
\(301\) −4.97771 4.17680i −0.286911 0.240747i
\(302\) 3.85204 21.8460i 0.221660 1.25710i
\(303\) −0.852044 −0.0489487
\(304\) 4.21688 + 1.10359i 0.241855 + 0.0632952i
\(305\) 10.6108 0.607573
\(306\) −3.56418 + 20.2135i −0.203750 + 1.15553i
\(307\) 1.01889 + 0.854946i 0.0581508 + 0.0487944i 0.671400 0.741095i \(-0.265693\pi\)
−0.613249 + 0.789890i \(0.710138\pi\)
\(308\) 6.98545 + 2.54250i 0.398033 + 0.144872i
\(309\) 2.42602 0.883000i 0.138012 0.0502321i
\(310\) −13.5175 + 11.3426i −0.767745 + 0.644214i
\(311\) −3.73917 6.47643i −0.212029 0.367245i 0.740320 0.672254i \(-0.234674\pi\)
−0.952349 + 0.305009i \(0.901340\pi\)
\(312\) −0.184793 + 0.320070i −0.0104618 + 0.0181204i
\(313\) 5.08765 + 28.8535i 0.287571 + 1.63090i 0.695955 + 0.718085i \(0.254981\pi\)
−0.408384 + 0.912810i \(0.633908\pi\)
\(314\) −0.490200 2.78006i −0.0276636 0.156888i
\(315\) −5.06418 + 8.77141i −0.285334 + 0.494213i
\(316\) 3.34730 + 5.79769i 0.188300 + 0.326145i
\(317\) 4.29086 3.60046i 0.240999 0.202222i −0.514286 0.857619i \(-0.671943\pi\)
0.755285 + 0.655397i \(0.227499\pi\)
\(318\) 3.22668 1.17442i 0.180943 0.0658580i
\(319\) −25.2986 9.20794i −1.41645 0.515546i
\(320\) 1.53209 + 1.28558i 0.0856464 + 0.0718658i
\(321\) −0.0106775 + 0.0605553i −0.000595961 + 0.00337987i
\(322\) −6.61081 −0.368406
\(323\) −8.21688 29.9656i −0.457200 1.66733i
\(324\) 7.92902 0.440501
\(325\) −0.184793 + 1.04801i −0.0102504 + 0.0581332i
\(326\) 1.69981 + 1.42631i 0.0941436 + 0.0789959i
\(327\) −1.38413 0.503783i −0.0765427 0.0278593i
\(328\) −1.76604 + 0.642788i −0.0975135 + 0.0354920i
\(329\) 4.95130 4.15464i 0.272974 0.229053i
\(330\) −1.46791 2.54250i −0.0808058 0.139960i
\(331\) −11.4880 + 19.8978i −0.631436 + 1.09368i 0.355822 + 0.934554i \(0.384201\pi\)
−0.987258 + 0.159126i \(0.949132\pi\)
\(332\) 0.262174 + 1.48686i 0.0143887 + 0.0816022i
\(333\) 3.22668 + 18.2994i 0.176821 + 1.00280i
\(334\) −1.95811 + 3.39155i −0.107143 + 0.185577i
\(335\) 11.6382 + 20.1579i 0.635860 + 1.10134i
\(336\) −0.467911 + 0.392624i −0.0255266 + 0.0214194i
\(337\) −1.23308 + 0.448804i −0.0671701 + 0.0244479i −0.375387 0.926868i \(-0.622490\pi\)
0.308217 + 0.951316i \(0.400268\pi\)
\(338\) 11.1518 + 4.05893i 0.606579 + 0.220777i
\(339\) 2.77719 + 2.33034i 0.150836 + 0.126567i
\(340\) 2.47565 14.0401i 0.134261 0.761432i
\(341\) −37.2918 −2.01946
\(342\) −11.3439 + 5.37051i −0.613407 + 0.290404i
\(343\) 19.1824 1.03575
\(344\) 0.641559 3.63846i 0.0345906 0.196173i
\(345\) 2.00000 + 1.67820i 0.107676 + 0.0903512i
\(346\) −7.09152 2.58110i −0.381242 0.138761i
\(347\) −2.27079 + 0.826501i −0.121903 + 0.0443689i −0.402251 0.915529i \(-0.631772\pi\)
0.280349 + 0.959898i \(0.409550\pi\)
\(348\) 1.69459 1.42193i 0.0908397 0.0762236i
\(349\) 4.24897 + 7.35943i 0.227442 + 0.393941i 0.957049 0.289925i \(-0.0936304\pi\)
−0.729607 + 0.683866i \(0.760297\pi\)
\(350\) −0.879385 + 1.52314i −0.0470051 + 0.0814153i
\(351\) −0.377326 2.13992i −0.0201402 0.114221i
\(352\) 0.733956 + 4.16247i 0.0391200 + 0.221860i
\(353\) 1.92009 3.32570i 0.102196 0.177009i −0.810393 0.585887i \(-0.800746\pi\)
0.912589 + 0.408878i \(0.134080\pi\)
\(354\) 1.26604 + 2.19285i 0.0672895 + 0.116549i
\(355\) 4.32501 3.62911i 0.229548 0.192613i
\(356\) −11.1887 + 4.07234i −0.592998 + 0.215834i
\(357\) 4.09152 + 1.48919i 0.216546 + 0.0788164i
\(358\) −8.41740 7.06304i −0.444874 0.373293i
\(359\) −4.15476 + 23.5628i −0.219280 + 1.24360i 0.654043 + 0.756457i \(0.273071\pi\)
−0.873323 + 0.487141i \(0.838040\pi\)
\(360\) −5.75877 −0.303514
\(361\) 12.0424 14.6963i 0.633808 0.773490i
\(362\) −15.0351 −0.790226
\(363\) 0.414000 2.34791i 0.0217294 0.123233i
\(364\) −1.43376 1.20307i −0.0751496 0.0630580i
\(365\) −1.49020 0.542388i −0.0780006 0.0283899i
\(366\) −1.73143 + 0.630189i −0.0905033 + 0.0329405i
\(367\) 13.1061 10.9973i 0.684131 0.574054i −0.233079 0.972458i \(-0.574880\pi\)
0.917210 + 0.398404i \(0.130436\pi\)
\(368\) −1.87939 3.25519i −0.0979697 0.169689i
\(369\) 2.70574 4.68647i 0.140855 0.243968i
\(370\) −2.24123 12.7106i −0.116516 0.660795i
\(371\) 3.01960 + 17.1250i 0.156770 + 0.889086i
\(372\) 1.53209 2.65366i 0.0794351 0.137586i
\(373\) 1.98040 + 3.43015i 0.102541 + 0.177607i 0.912731 0.408561i \(-0.133969\pi\)
−0.810190 + 0.586168i \(0.800636\pi\)
\(374\) 23.0804 19.3667i 1.19346 1.00143i
\(375\) 3.91622 1.42539i 0.202233 0.0736067i
\(376\) 3.45336 + 1.25692i 0.178094 + 0.0648208i
\(377\) 5.19253 + 4.35705i 0.267429 + 0.224400i
\(378\) 0.623608 3.53666i 0.0320749 0.181906i
\(379\) −27.2918 −1.40189 −0.700943 0.713218i \(-0.747237\pi\)
−0.700943 + 0.713218i \(0.747237\pi\)
\(380\) 7.87939 3.73032i 0.404204 0.191361i
\(381\) −7.64590 −0.391711
\(382\) 0.787866 4.46821i 0.0403107 0.228614i
\(383\) 4.90941 + 4.11949i 0.250859 + 0.210496i 0.759542 0.650458i \(-0.225423\pi\)
−0.508683 + 0.860954i \(0.669867\pi\)
\(384\) −0.326352 0.118782i −0.0166541 0.00606159i
\(385\) 13.9709 5.08499i 0.712023 0.259155i
\(386\) 16.8498 14.1387i 0.857633 0.719640i
\(387\) 5.31908 + 9.21291i 0.270384 + 0.468319i
\(388\) −0.939693 + 1.62760i −0.0477057 + 0.0826286i
\(389\) −4.41653 25.0474i −0.223927 1.26995i −0.864726 0.502244i \(-0.832508\pi\)
0.640799 0.767708i \(-0.278603\pi\)
\(390\) 0.128356 + 0.727940i 0.00649954 + 0.0368607i
\(391\) −13.3969 + 23.2042i −0.677512 + 1.17348i
\(392\) 1.95336 + 3.38332i 0.0986597 + 0.170884i
\(393\) −2.03596 + 1.70837i −0.102701 + 0.0861760i
\(394\) −14.9709 + 5.44896i −0.754223 + 0.274515i
\(395\) 12.5817 + 4.57937i 0.633055 + 0.230413i
\(396\) −9.32295 7.82288i −0.468496 0.393115i
\(397\) 3.92127 22.2387i 0.196803 1.11613i −0.713024 0.701139i \(-0.752675\pi\)
0.909827 0.414987i \(-0.136214\pi\)
\(398\) −3.27631 −0.164227
\(399\) 0.704088 + 2.56769i 0.0352485 + 0.128546i
\(400\) −1.00000 −0.0500000
\(401\) 0.132636 0.752219i 0.00662355 0.0375640i −0.981317 0.192399i \(-0.938373\pi\)
0.987940 + 0.154835i \(0.0494845\pi\)
\(402\) −3.09627 2.59808i −0.154428 0.129580i
\(403\) 8.82295 + 3.21129i 0.439502 + 0.159966i
\(404\) 2.30541 0.839100i 0.114698 0.0417468i
\(405\) 12.1480 10.1933i 0.603637 0.506511i
\(406\) 5.60132 + 9.70177i 0.277989 + 0.481491i
\(407\) 13.6382 23.6220i 0.676018 1.17090i
\(408\) 0.429892 + 2.43804i 0.0212828 + 0.120701i
\(409\) −2.92144 16.5683i −0.144456 0.819249i −0.967803 0.251711i \(-0.919007\pi\)
0.823347 0.567539i \(-0.192104\pi\)
\(410\) −1.87939 + 3.25519i −0.0928162 + 0.160762i
\(411\) 0.996130 + 1.72535i 0.0491354 + 0.0851051i
\(412\) −5.69459 + 4.77833i −0.280552 + 0.235411i
\(413\) −12.0496 + 4.38571i −0.592924 + 0.215807i
\(414\) 10.1702 + 3.70167i 0.499840 + 0.181927i
\(415\) 2.31315 + 1.94096i 0.113548 + 0.0952781i
\(416\) 0.184793 1.04801i 0.00906020 0.0513829i
\(417\) −6.73648 −0.329887
\(418\) 17.8234 + 4.66452i 0.871772 + 0.228149i
\(419\) 35.8931 1.75349 0.876747 0.480953i \(-0.159709\pi\)
0.876747 + 0.480953i \(0.159709\pi\)
\(420\) −0.212134 + 1.20307i −0.0103511 + 0.0587038i
\(421\) 15.8648 + 13.3122i 0.773205 + 0.648796i 0.941528 0.336936i \(-0.109391\pi\)
−0.168323 + 0.985732i \(0.553835\pi\)
\(422\) −10.7772 3.92258i −0.524625 0.190948i
\(423\) −9.94356 + 3.61916i −0.483473 + 0.175970i
\(424\) −7.57398 + 6.35532i −0.367825 + 0.308642i
\(425\) 3.56418 + 6.17334i 0.172888 + 0.299451i
\(426\) −0.490200 + 0.849051i −0.0237503 + 0.0411367i
\(427\) −1.62031 9.18923i −0.0784123 0.444698i
\(428\) −0.0307447 0.174362i −0.00148610 0.00842810i
\(429\) −0.781059 + 1.35283i −0.0377099 + 0.0653155i
\(430\) −3.69459 6.39922i −0.178169 0.308598i
\(431\) −14.0378 + 11.7791i −0.676176 + 0.567379i −0.914886 0.403712i \(-0.867720\pi\)
0.238710 + 0.971091i \(0.423275\pi\)
\(432\) 1.91875 0.698367i 0.0923158 0.0336002i
\(433\) −4.78611 1.74200i −0.230006 0.0837153i 0.224446 0.974486i \(-0.427943\pi\)
−0.454452 + 0.890771i \(0.650165\pi\)
\(434\) 11.8871 + 9.97448i 0.570600 + 0.478791i
\(435\) 0.768266 4.35705i 0.0368355 0.208905i
\(436\) 4.24123 0.203118
\(437\) −16.3131 + 1.52314i −0.780364 + 0.0728617i
\(438\) 0.275378 0.0131581
\(439\) −1.79055 + 10.1547i −0.0854585 + 0.484659i 0.911798 + 0.410639i \(0.134694\pi\)
−0.997257 + 0.0740207i \(0.976417\pi\)
\(440\) 6.47565 + 5.43372i 0.308715 + 0.259042i
\(441\) −10.5706 3.84737i −0.503361 0.183208i
\(442\) −7.12836 + 2.59451i −0.339061 + 0.123408i
\(443\) −6.75356 + 5.66691i −0.320871 + 0.269243i −0.788968 0.614434i \(-0.789384\pi\)
0.468097 + 0.883677i \(0.344940\pi\)
\(444\) 1.12061 + 1.94096i 0.0531820 + 0.0921140i
\(445\) −11.9067 + 20.6231i −0.564433 + 0.977627i
\(446\) 1.94356 + 11.0225i 0.0920304 + 0.521930i
\(447\) −0.312214 1.77066i −0.0147672 0.0837492i
\(448\) 0.879385 1.52314i 0.0415470 0.0719616i
\(449\) −6.03849 10.4590i −0.284974 0.493589i 0.687629 0.726062i \(-0.258652\pi\)
−0.972603 + 0.232473i \(0.925318\pi\)
\(450\) 2.20574 1.85083i 0.103979 0.0872491i
\(451\) −7.46451 + 2.71686i −0.351490 + 0.127932i
\(452\) −9.80928 3.57029i −0.461390 0.167932i
\(453\) 5.90167 + 4.95209i 0.277285 + 0.232670i
\(454\) −0.589870 + 3.34532i −0.0276840 + 0.157004i
\(455\) −3.74329 −0.175488
\(456\) −1.06418 + 1.07666i −0.0498347 + 0.0504194i
\(457\) −0.731429 −0.0342148 −0.0171074 0.999854i \(-0.505446\pi\)
−0.0171074 + 0.999854i \(0.505446\pi\)
\(458\) 0.739170 4.19204i 0.0345392 0.195881i
\(459\) −11.1500 9.35597i −0.520438 0.436699i
\(460\) −7.06418 2.57115i −0.329369 0.119881i
\(461\) −21.6878 + 7.89371i −1.01010 + 0.367647i −0.793472 0.608607i \(-0.791729\pi\)
−0.216629 + 0.976254i \(0.569506\pi\)
\(462\) −1.97771 + 1.65950i −0.0920115 + 0.0772068i
\(463\) −9.02229 15.6271i −0.419301 0.726251i 0.576568 0.817049i \(-0.304392\pi\)
−0.995869 + 0.0907980i \(0.971058\pi\)
\(464\) −3.18479 + 5.51622i −0.147850 + 0.256084i
\(465\) −1.06418 6.03525i −0.0493501 0.279878i
\(466\) 1.15358 + 6.54228i 0.0534386 + 0.303065i
\(467\) −5.48633 + 9.50260i −0.253877 + 0.439728i −0.964590 0.263754i \(-0.915039\pi\)
0.710713 + 0.703482i \(0.248373\pi\)
\(468\) 1.53209 + 2.65366i 0.0708208 + 0.122665i
\(469\) 15.6800 13.1571i 0.724037 0.607539i
\(470\) 6.90673 2.51384i 0.318584 0.115955i
\(471\) 0.921274 + 0.335316i 0.0424501 + 0.0154506i
\(472\) −5.58512 4.68647i −0.257076 0.215712i
\(473\) 2.71167 15.3786i 0.124683 0.707110i
\(474\) −2.32501 −0.106791
\(475\) −1.81908 + 3.96118i −0.0834650 + 0.181751i
\(476\) −12.5371 −0.574639
\(477\) 4.94356 28.0363i 0.226350 1.28370i
\(478\) 12.2686 + 10.2946i 0.561151 + 0.470862i
\(479\) −21.0351 7.65614i −0.961117 0.349818i −0.186646 0.982427i \(-0.559762\pi\)
−0.774471 + 0.632609i \(0.781984\pi\)
\(480\) −0.652704 + 0.237565i −0.0297917 + 0.0108433i
\(481\) −5.26083 + 4.41436i −0.239873 + 0.201278i
\(482\) 4.30200 + 7.45129i 0.195951 + 0.339397i
\(483\) 1.14796 1.98832i 0.0522338 0.0904716i
\(484\) 1.19207 + 6.76055i 0.0541848 + 0.307298i
\(485\) 0.652704 + 3.70167i 0.0296377 + 0.168084i
\(486\) −4.43969 + 7.68977i −0.201389 + 0.348815i
\(487\) 18.8803 + 32.7017i 0.855549 + 1.48185i 0.876135 + 0.482066i \(0.160113\pi\)
−0.0205859 + 0.999788i \(0.506553\pi\)
\(488\) 4.06418 3.41025i 0.183977 0.154375i
\(489\) −0.724155 + 0.263571i −0.0327474 + 0.0119191i
\(490\) 7.34224 + 2.67236i 0.331689 + 0.120725i
\(491\) −0.958578 0.804342i −0.0432600 0.0362995i 0.620901 0.783889i \(-0.286767\pi\)
−0.664161 + 0.747589i \(0.731211\pi\)
\(492\) 0.113341 0.642788i 0.00510980 0.0289791i
\(493\) 45.4047 2.04492
\(494\) −3.81521 2.63841i −0.171654 0.118708i
\(495\) −24.3405 −1.09402
\(496\) −1.53209 + 8.68891i −0.0687928 + 0.390143i
\(497\) −3.80335 3.19139i −0.170603 0.143153i
\(498\) −0.492726 0.179338i −0.0220796 0.00803631i
\(499\) 8.76739 3.19107i 0.392482 0.142852i −0.138238 0.990399i \(-0.544144\pi\)
0.530720 + 0.847547i \(0.321922\pi\)
\(500\) −9.19253 + 7.71345i −0.411103 + 0.344956i
\(501\) −0.680045 1.17787i −0.0303822 0.0526234i
\(502\) 9.95471 17.2421i 0.444300 0.769551i
\(503\) −1.68273 9.54325i −0.0750294 0.425513i −0.999066 0.0432089i \(-0.986242\pi\)
0.924037 0.382304i \(-0.124869\pi\)
\(504\) 0.879385 + 4.98724i 0.0391709 + 0.222149i
\(505\) 2.45336 4.24935i 0.109173 0.189094i
\(506\) −7.94356 13.7587i −0.353134 0.611647i
\(507\) −3.15729 + 2.64928i −0.140220 + 0.117659i
\(508\) 20.6878 7.52974i 0.917872 0.334078i
\(509\) −27.2053 9.90193i −1.20585 0.438895i −0.340591 0.940212i \(-0.610627\pi\)
−0.865264 + 0.501316i \(0.832849\pi\)
\(510\) 3.79292 + 3.18264i 0.167953 + 0.140930i
\(511\) −0.242163 + 1.37338i −0.0107127 + 0.0607546i
\(512\) 1.00000 0.0441942
\(513\) 0.723993 8.87089i 0.0319651 0.391659i
\(514\) 26.4175 1.16522
\(515\) −2.58172 + 14.6417i −0.113764 + 0.645188i
\(516\) 0.982926 + 0.824773i 0.0432709 + 0.0363086i
\(517\) 14.5963 + 5.31261i 0.641943 + 0.233648i
\(518\) −10.6655 + 3.88192i −0.468615 + 0.170562i
\(519\) 2.00774 1.68469i 0.0881300 0.0739499i
\(520\) −1.06418 1.84321i −0.0466673 0.0808301i
\(521\) 1.08037 1.87126i 0.0473321 0.0819815i −0.841389 0.540430i \(-0.818261\pi\)
0.888721 + 0.458449i \(0.151595\pi\)
\(522\) −3.18479 18.0619i −0.139395 0.790546i
\(523\) 2.49794 + 14.1665i 0.109227 + 0.619459i 0.989447 + 0.144893i \(0.0462838\pi\)
−0.880220 + 0.474566i \(0.842605\pi\)
\(524\) 3.82635 6.62744i 0.167155 0.289521i
\(525\) −0.305407 0.528981i −0.0133291 0.0230866i
\(526\) −21.4047 + 17.9606i −0.933288 + 0.783121i
\(527\) 59.1002 21.5107i 2.57444 0.937021i
\(528\) −1.37939 0.502055i −0.0600300 0.0218491i
\(529\) −6.79607 5.70258i −0.295481 0.247938i
\(530\) −3.43376 + 19.4738i −0.149153 + 0.845889i
\(531\) 20.9932 0.911027
\(532\) −4.43376 6.25411i −0.192228 0.271150i
\(533\) 2.00000 0.0866296
\(534\) 0.718063 4.07234i 0.0310736 0.176227i
\(535\) −0.271259 0.227613i −0.0117275 0.00984058i
\(536\) 10.9363 + 3.98048i 0.472376 + 0.171931i
\(537\) 3.58600 1.30520i 0.154747 0.0563234i
\(538\) 11.1702 9.37295i 0.481583 0.404096i
\(539\) 8.25624 + 14.3002i 0.355622 + 0.615955i
\(540\) 2.04189 3.53666i 0.0878689 0.152193i
\(541\) 2.24897 + 12.7545i 0.0966908 + 0.548361i 0.994216 + 0.107398i \(0.0342518\pi\)
−0.897525 + 0.440963i \(0.854637\pi\)
\(542\) −3.16519 17.9507i −0.135957 0.771048i
\(543\) 2.61081 4.52206i 0.112041 0.194060i
\(544\) −3.56418 6.17334i −0.152813 0.264680i
\(545\) 6.49794 5.45242i 0.278341 0.233556i
\(546\) 0.610815 0.222318i 0.0261405 0.00951435i
\(547\) −1.31433 0.478377i −0.0561967 0.0204539i 0.313769 0.949499i \(-0.398408\pi\)
−0.369966 + 0.929045i \(0.620631\pi\)
\(548\) −4.39440 3.68734i −0.187719 0.157515i
\(549\) −2.65270 + 15.0442i −0.113215 + 0.642072i
\(550\) −4.22668 −0.180226
\(551\) 16.0574 + 22.6500i 0.684067 + 0.964922i
\(552\) 1.30541 0.0555618
\(553\) 2.04458 11.5954i 0.0869443 0.493085i
\(554\) −12.6159 10.5860i −0.535997 0.449755i
\(555\) 4.21213 + 1.53309i 0.178795 + 0.0650761i
\(556\) 18.2271 6.63414i 0.773003 0.281350i
\(557\) −22.7178 + 19.0625i −0.962585 + 0.807704i −0.981372 0.192119i \(-0.938464\pi\)
0.0187869 + 0.999824i \(0.494020\pi\)
\(558\) −12.7023 22.0011i −0.537733 0.931380i
\(559\) −1.96585 + 3.40496i −0.0831467 + 0.144014i
\(560\) −0.610815 3.46410i −0.0258116 0.146385i
\(561\) 1.81702 + 10.3048i 0.0767146 + 0.435070i
\(562\) 3.58512 6.20961i 0.151229 0.261937i
\(563\) −21.0646 36.4850i −0.887769 1.53766i −0.842507 0.538686i \(-0.818921\pi\)
−0.0452621 0.998975i \(-0.514412\pi\)
\(564\) −0.977711 + 0.820397i −0.0411691 + 0.0345450i
\(565\) −19.6186 + 7.14057i −0.825359 + 0.300406i
\(566\) −19.6741 7.16079i −0.826965 0.300991i
\(567\) −10.6827 8.96388i −0.448633 0.376447i
\(568\) 0.490200 2.78006i 0.0205683 0.116649i
\(569\) 5.08915 0.213348 0.106674 0.994294i \(-0.465980\pi\)
0.106674 + 0.994294i \(0.465980\pi\)
\(570\) −0.246282 + 3.01763i −0.0103156 + 0.126394i
\(571\) −12.6486 −0.529327 −0.264663 0.964341i \(-0.585261\pi\)
−0.264663 + 0.964341i \(0.585261\pi\)
\(572\) 0.781059 4.42961i 0.0326577 0.185211i
\(573\) 1.20708 + 1.01286i 0.0504265 + 0.0423129i
\(574\) 3.10607 + 1.13052i 0.129645 + 0.0471868i
\(575\) 3.53209 1.28558i 0.147298 0.0536122i
\(576\) −2.20574 + 1.85083i −0.0919057 + 0.0771180i
\(577\) −5.00727 8.67285i −0.208456 0.361056i 0.742773 0.669544i \(-0.233510\pi\)
−0.951228 + 0.308488i \(0.900177\pi\)
\(578\) −16.9067 + 29.2833i −0.703227 + 1.21803i
\(579\) 1.32651 + 7.52303i 0.0551280 + 0.312647i
\(580\) 2.21213 + 12.5456i 0.0918539 + 0.520929i
\(581\) 1.32770 2.29964i 0.0550821 0.0954050i
\(582\) −0.326352 0.565258i −0.0135277 0.0234307i
\(583\) −32.0128 + 26.8619i −1.32583 + 1.11251i
\(584\) −0.745100 + 0.271194i −0.0308325 + 0.0112221i
\(585\) 5.75877 + 2.09602i 0.238096 + 0.0866598i
\(586\) 7.26083 + 6.09256i 0.299942 + 0.251681i
\(587\) 0.769915 4.36640i 0.0317778 0.180221i −0.964788 0.263030i \(-0.915278\pi\)
0.996565 + 0.0828093i \(0.0263893\pi\)
\(588\) −1.35679 −0.0559532
\(589\) 31.6313 + 21.8747i 1.30335 + 0.901331i
\(590\) −14.5817 −0.600320
\(591\) 0.960799 5.44896i 0.0395220 0.224140i
\(592\) −4.94356 4.14814i −0.203179 0.170488i
\(593\) 22.5758 + 8.21692i 0.927077 + 0.337428i 0.761050 0.648693i \(-0.224684\pi\)
0.166026 + 0.986121i \(0.446906\pi\)
\(594\) 8.10994 2.95178i 0.332755 0.121113i
\(595\) −19.2080 + 16.1174i −0.787452 + 0.660751i
\(596\) 2.58853 + 4.48346i 0.106030 + 0.183650i
\(597\) 0.568926 0.985408i 0.0232846 0.0403301i
\(598\) 0.694593 + 3.93923i 0.0284040 + 0.161087i
\(599\) −5.89992 33.4601i −0.241064 1.36714i −0.829458 0.558569i \(-0.811351\pi\)
0.588394 0.808574i \(-0.299760\pi\)
\(600\) 0.173648 0.300767i 0.00708916 0.0122788i
\(601\) −8.07145 13.9802i −0.329241 0.570263i 0.653120 0.757254i \(-0.273460\pi\)
−0.982362 + 0.186991i \(0.940126\pi\)
\(602\) −4.97771 + 4.17680i −0.202876 + 0.170233i
\(603\) −31.4898 + 11.4613i −1.28236 + 0.466742i
\(604\) −20.8452 7.58705i −0.848181 0.308713i
\(605\) 10.5175 + 8.82526i 0.427599 + 0.358798i
\(606\) −0.147956 + 0.839100i −0.00601030 + 0.0340861i
\(607\) 8.92221 0.362141 0.181071 0.983470i \(-0.442044\pi\)
0.181071 + 0.983470i \(0.442044\pi\)
\(608\) 1.81908 3.96118i 0.0737733 0.160647i
\(609\) −3.89064 −0.157657
\(610\) 1.84255 10.4496i 0.0746026 0.423092i
\(611\) −2.99588 2.51384i −0.121200 0.101699i
\(612\) 19.2875 + 7.02006i 0.779649 + 0.283769i
\(613\) −24.2713 + 8.83402i −0.980307 + 0.356803i −0.781960 0.623329i \(-0.785780\pi\)
−0.198347 + 0.980132i \(0.563557\pi\)
\(614\) 1.01889 0.854946i 0.0411189 0.0345028i
\(615\) −0.652704 1.13052i −0.0263196 0.0455868i
\(616\) 3.71688 6.43783i 0.149757 0.259387i
\(617\) 3.21735 + 18.2465i 0.129526 + 0.734576i 0.978516 + 0.206169i \(0.0660995\pi\)
−0.848991 + 0.528407i \(0.822789\pi\)
\(618\) −0.448311 2.54250i −0.0180337 0.102274i
\(619\) 17.6061 30.4946i 0.707648 1.22568i −0.258080 0.966124i \(-0.583090\pi\)
0.965728 0.259558i \(-0.0835769\pi\)
\(620\) 8.82295 + 15.2818i 0.354338 + 0.613732i
\(621\) −5.87939 + 4.93339i −0.235932 + 0.197970i
\(622\) −7.02734 + 2.55774i −0.281771 + 0.102556i
\(623\) 19.6783 + 7.16231i 0.788394 + 0.286952i
\(624\) 0.283119 + 0.237565i 0.0113338 + 0.00951020i
\(625\) −3.29932 + 18.7113i −0.131973 + 0.748454i
\(626\) 29.2986 1.17101
\(627\) −4.49794 + 4.55072i −0.179630 + 0.181738i
\(628\) −2.82295 −0.112648
\(629\) −7.98814 + 45.3030i −0.318508 + 1.80635i
\(630\) 7.75877 + 6.51038i 0.309117 + 0.259380i
\(631\) 1.73143 + 0.630189i 0.0689271 + 0.0250874i 0.376254 0.926517i \(-0.377212\pi\)
−0.307326 + 0.951604i \(0.599434\pi\)
\(632\) 6.29086 2.28969i 0.250237 0.0910788i
\(633\) 3.05122 2.56028i 0.121275 0.101762i
\(634\) −2.80066 4.85088i −0.111228 0.192653i
\(635\) 22.0155 38.1319i 0.873658 1.51322i
\(636\) −0.596267 3.38160i −0.0236435 0.134089i
\(637\) −0.721934 4.09429i −0.0286041 0.162222i
\(638\) −13.4611 + 23.3153i −0.532930 + 0.923062i
\(639\) 4.06418 + 7.03936i 0.160776 + 0.278473i
\(640\) 1.53209 1.28558i 0.0605611 0.0508168i
\(641\) 4.89945 1.78325i 0.193517 0.0704343i −0.243444 0.969915i \(-0.578277\pi\)
0.436961 + 0.899481i \(0.356055\pi\)
\(642\) 0.0577812 + 0.0210306i 0.00228044 + 0.000830012i
\(643\) 4.52276 + 3.79504i 0.178360 + 0.149662i 0.727597 0.686005i \(-0.240637\pi\)
−0.549237 + 0.835667i \(0.685082\pi\)
\(644\) −1.14796 + 6.51038i −0.0452358 + 0.256545i
\(645\) 2.56624 0.101045
\(646\) −30.9372 + 2.88857i −1.21721 + 0.113649i
\(647\) −42.6810 −1.67796 −0.838981 0.544160i \(-0.816848\pi\)
−0.838981 + 0.544160i \(0.816848\pi\)
\(648\) 1.37686 7.80856i 0.0540881 0.306749i
\(649\) −23.6065 19.8082i −0.926638 0.777541i
\(650\) 1.00000 + 0.363970i 0.0392232 + 0.0142761i
\(651\) −5.06418 + 1.84321i −0.198481 + 0.0722411i
\(652\) 1.69981 1.42631i 0.0665696 0.0558585i
\(653\) −3.87939 6.71929i −0.151812 0.262946i 0.780082 0.625678i \(-0.215178\pi\)
−0.931894 + 0.362732i \(0.881844\pi\)
\(654\) −0.736482 + 1.27562i −0.0287987 + 0.0498808i
\(655\) −2.65776 15.0729i −0.103847 0.588946i
\(656\) 0.326352 + 1.85083i 0.0127419 + 0.0722629i
\(657\) 1.14156 1.97724i 0.0445365 0.0771394i
\(658\) −3.23173 5.59753i −0.125986 0.218214i
\(659\) 22.2049 18.6321i 0.864979 0.725803i −0.0980561 0.995181i \(-0.531262\pi\)
0.963035 + 0.269378i \(0.0868180\pi\)
\(660\) −2.75877 + 1.00411i −0.107385 + 0.0390849i
\(661\) 30.7374 + 11.1875i 1.19555 + 0.435143i 0.861668 0.507472i \(-0.169420\pi\)
0.333879 + 0.942616i \(0.391642\pi\)
\(662\) 17.6006 + 14.7687i 0.684067 + 0.574000i
\(663\) 0.457482 2.59451i 0.0177671 0.100762i
\(664\) 1.50980 0.0585916
\(665\) −14.8331 3.88192i −0.575201 0.150535i
\(666\) 18.5817 0.720027
\(667\) 4.15745 23.5781i 0.160977 0.912947i
\(668\) 3.00000 + 2.51730i 0.116073 + 0.0973972i
\(669\) −3.65270 1.32948i −0.141222 0.0514005i
\(670\) 21.8726 7.96097i 0.845011 0.307559i
\(671\) 17.1780 14.4140i 0.663149 0.556448i
\(672\) 0.305407 + 0.528981i 0.0117813 + 0.0204059i
\(673\) 16.4222 28.4441i 0.633030 1.09644i −0.353899 0.935284i \(-0.615144\pi\)
0.986929 0.161156i \(-0.0515222\pi\)
\(674\) 0.227864 + 1.29228i 0.00877698 + 0.0497767i
\(675\) 0.354570 + 2.01087i 0.0136474 + 0.0773984i
\(676\) 5.93376 10.2776i 0.228222 0.395291i
\(677\) −12.3209 21.3404i −0.473530 0.820178i 0.526011 0.850478i \(-0.323687\pi\)
−0.999541 + 0.0302996i \(0.990354\pi\)
\(678\) 2.77719 2.33034i 0.106657 0.0894961i
\(679\) 3.10607 1.13052i 0.119200 0.0433852i
\(680\) −13.3969 4.87608i −0.513749 0.186989i
\(681\) −0.903733 0.758322i −0.0346311 0.0290590i
\(682\) −6.47565 + 36.7252i −0.247966 + 1.40628i
\(683\) 29.9905 1.14755 0.573777 0.819011i \(-0.305477\pi\)
0.573777 + 0.819011i \(0.305477\pi\)
\(684\) 3.31908 + 12.1041i 0.126908 + 0.462813i
\(685\) −11.4730 −0.438359
\(686\) 3.33099 18.8910i 0.127178 0.721262i
\(687\) 1.13247 + 0.950259i 0.0432066 + 0.0362546i
\(688\) −3.47178 1.26363i −0.132360 0.0481753i
\(689\) 9.88713 3.59862i 0.376670 0.137096i
\(690\) 2.00000 1.67820i 0.0761387 0.0638880i
\(691\) −11.2365 19.4622i −0.427456 0.740375i 0.569190 0.822206i \(-0.307257\pi\)
−0.996646 + 0.0818304i \(0.973923\pi\)
\(692\) −3.77332 + 6.53558i −0.143440 + 0.248445i
\(693\) 3.71688 + 21.0795i 0.141193 + 0.800743i
\(694\) 0.419625 + 2.37981i 0.0159288 + 0.0903365i
\(695\) 19.3969 33.5965i 0.735767 1.27439i
\(696\) −1.10607 1.91576i −0.0419254 0.0726168i
\(697\) 10.2626 8.61138i 0.388725 0.326179i
\(698\) 7.98545 2.90647i 0.302254 0.110011i
\(699\) −2.16802 0.789096i −0.0820022 0.0298463i
\(700\) 1.34730 + 1.13052i 0.0509230 + 0.0427295i
\(701\) −0.837496 + 4.74968i −0.0316318 + 0.179393i −0.996530 0.0832300i \(-0.973476\pi\)
0.964899 + 0.262623i \(0.0845875\pi\)
\(702\) −2.17293 −0.0820121
\(703\) −25.4243 + 12.0366i −0.958894 + 0.453967i
\(704\) 4.22668 0.159299
\(705\) −0.443258 + 2.51384i −0.0166941 + 0.0946768i
\(706\) −2.94175 2.46842i −0.110714 0.0929003i
\(707\) −4.05468 1.47578i −0.152492 0.0555026i
\(708\) 2.37939 0.866025i 0.0894228 0.0325472i
\(709\) −31.6955 + 26.5957i −1.19035 + 0.998823i −0.190497 + 0.981688i \(0.561010\pi\)
−0.999853 + 0.0171349i \(0.994546\pi\)
\(710\) −2.82295 4.88949i −0.105943 0.183499i
\(711\) −9.63816 + 16.6938i −0.361459 + 0.626065i
\(712\) 2.06758 + 11.7258i 0.0774859 + 0.439444i
\(713\) −5.75877 32.6596i −0.215668 1.22311i
\(714\) 2.17705 3.77076i 0.0814741 0.141117i
\(715\) −4.49794 7.79066i −0.168213 0.291354i
\(716\) −8.41740 + 7.06304i −0.314573 + 0.263958i
\(717\) −5.22668 + 1.90236i −0.195194 + 0.0710448i
\(718\) 22.4834 + 8.18329i 0.839073 + 0.305398i
\(719\) 17.4730 + 14.6616i 0.651632 + 0.546784i 0.907566 0.419910i \(-0.137939\pi\)
−0.255934 + 0.966694i \(0.582383\pi\)
\(720\) −1.00000 + 5.67128i −0.0372678 + 0.211356i
\(721\) 13.0743 0.486912
\(722\) −12.3819 14.4114i −0.460807 0.536337i
\(723\) −2.98814 −0.111130
\(724\) −2.61081 + 14.8067i −0.0970302 + 0.550285i
\(725\) −4.87939 4.09429i −0.181216 0.152058i
\(726\) −2.24035 0.815422i −0.0831473 0.0302631i
\(727\) −8.48070 + 3.08672i −0.314532 + 0.114480i −0.494462 0.869199i \(-0.664635\pi\)
0.179930 + 0.983679i \(0.442413\pi\)
\(728\) −1.43376 + 1.20307i −0.0531388 + 0.0445887i
\(729\) 10.3516 + 17.9296i 0.383394 + 0.664058i
\(730\) −0.792919 + 1.37338i −0.0293472 + 0.0508309i
\(731\) 4.57326 + 25.9363i 0.169148 + 0.959287i
\(732\) 0.319955 + 1.81456i 0.0118259 + 0.0670679i
\(733\) −14.4561 + 25.0386i −0.533946 + 0.924822i 0.465267 + 0.885170i \(0.345958\pi\)
−0.999214 + 0.0396520i \(0.987375\pi\)
\(734\) −8.55438 14.8166i −0.315748 0.546891i
\(735\) −2.07873 + 1.74426i −0.0766750 + 0.0643379i
\(736\) −3.53209 + 1.28558i −0.130195 + 0.0473869i
\(737\) 46.2242 + 16.8242i 1.70269 + 0.619729i
\(738\) −4.14543 3.47843i −0.152595 0.128043i
\(739\) −1.05685 + 5.99368i −0.0388768 + 0.220481i −0.998056 0.0623162i \(-0.980151\pi\)
0.959180 + 0.282797i \(0.0912624\pi\)
\(740\) −12.9067 −0.474461
\(741\) 1.45605 0.689335i 0.0534894 0.0253234i
\(742\) 17.3892 0.638377
\(743\) −5.10513 + 28.9526i −0.187289 + 1.06217i 0.735690 + 0.677319i \(0.236858\pi\)
−0.922979 + 0.384851i \(0.874253\pi\)
\(744\) −2.34730 1.96962i −0.0860561 0.0722096i
\(745\) 9.72967 + 3.54131i 0.356468 + 0.129744i
\(746\) 3.72193 1.35467i 0.136270 0.0495981i
\(747\) −3.33022 + 2.79439i −0.121846 + 0.102241i
\(748\) −15.0646 26.0927i −0.550818 0.954045i
\(749\) −0.155697 + 0.269675i −0.00568903 + 0.00985369i
\(750\) −0.723689 4.10424i −0.0264254 0.149866i
\(751\) −6.67736 37.8692i −0.243660 1.38187i −0.823584 0.567195i \(-0.808029\pi\)
0.579924 0.814671i \(-0.303082\pi\)
\(752\) 1.83750 3.18264i 0.0670066 0.116059i
\(753\) 3.45723 + 5.98810i 0.125989 + 0.218219i
\(754\) 5.19253 4.35705i 0.189101 0.158675i
\(755\) −41.6905 + 15.1741i −1.51727 + 0.552242i
\(756\) −3.37464 1.22827i −0.122734 0.0446717i
\(757\) −5.82295 4.88603i −0.211639 0.177586i 0.530806 0.847493i \(-0.321889\pi\)
−0.742445 + 0.669907i \(0.766334\pi\)
\(758\) −4.73917 + 26.8772i −0.172134 + 0.976223i
\(759\) 5.51754 0.200274
\(760\) −2.30541 8.40744i −0.0836259 0.304970i
\(761\) −2.89992 −0.105122 −0.0525610 0.998618i \(-0.516738\pi\)
−0.0525610 + 0.998618i \(0.516738\pi\)
\(762\) −1.32770 + 7.52974i −0.0480974 + 0.272774i
\(763\) −5.71419 4.79478i −0.206868 0.173583i
\(764\) −4.26352 1.55179i −0.154249 0.0561419i
\(765\) 38.5749 14.0401i 1.39468 0.507622i
\(766\) 4.90941 4.11949i 0.177384 0.148843i
\(767\) 3.87939 + 6.71929i 0.140076 + 0.242620i
\(768\) −0.173648 + 0.300767i −0.00626599 + 0.0108530i
\(769\) −2.94521 16.7031i −0.106207 0.602330i −0.990731 0.135836i \(-0.956628\pi\)
0.884524 0.466494i \(-0.154483\pi\)
\(770\) −2.58172 14.6417i −0.0930387 0.527649i
\(771\) −4.58734 + 7.94551i −0.165209 + 0.286151i
\(772\) −10.9979 19.0490i −0.395825 0.685588i
\(773\) −36.7597 + 30.8451i −1.32215 + 1.10942i −0.336311 + 0.941751i \(0.609179\pi\)
−0.985843 + 0.167669i \(0.946376\pi\)
\(774\) 9.99660 3.63846i 0.359320 0.130782i
\(775\) −8.29086 3.01763i −0.297816 0.108396i
\(776\) 1.43969 + 1.20805i 0.0516820 + 0.0433663i
\(777\) 0.684488 3.88192i 0.0245559 0.139263i
\(778\) −25.4338 −0.911845
\(779\) 7.92514 + 2.07407i 0.283948 + 0.0743113i
\(780\) 0.739170 0.0264665
\(781\) 2.07192 11.7504i 0.0741391 0.420464i
\(782\) 20.5253 + 17.2228i 0.733983 + 0.615885i
\(783\) 12.2216 + 4.44831i 0.436765 + 0.158970i
\(784\) 3.67112 1.33618i 0.131111 0.0477207i
\(785\) −4.32501 + 3.62911i −0.154366 + 0.129529i
\(786\) 1.32888 + 2.30168i 0.0473995 + 0.0820984i
\(787\) −25.2913 + 43.8059i −0.901538 + 1.56151i −0.0760408 + 0.997105i \(0.524228\pi\)
−0.825498 + 0.564406i \(0.809105\pi\)
\(788\) 2.76651 + 15.6897i 0.0985529 + 0.558921i
\(789\) −1.68510 9.55666i −0.0599910 0.340226i
\(790\) 6.69459 11.5954i 0.238183 0.412545i
\(791\) 9.17974 + 15.8998i 0.326394 + 0.565331i
\(792\) −9.32295 + 7.82288i −0.331277 + 0.277974i
\(793\) −5.30541 + 1.93101i −0.188401 + 0.0685722i
\(794\) −21.2199 7.72340i −0.753065 0.274093i
\(795\) −5.26083 4.41436i −0.186582 0.156561i
\(796\) −0.568926 + 3.22654i −0.0201650 + 0.114362i
\(797\) −3.87702 −0.137331 −0.0686656 0.997640i \(-0.521874\pi\)
−0.0686656 + 0.997640i \(0.521874\pi\)
\(798\) 2.65095 0.247516i 0.0938426 0.00876197i
\(799\) −26.1967 −0.926771
\(800\) −0.173648 + 0.984808i −0.00613939 + 0.0348182i
\(801\) −26.2631 22.0374i −0.927961 0.778652i
\(802\) −0.717759 0.261243i −0.0253449 0.00922480i
\(803\) −3.14930 + 1.14625i −0.111136 + 0.0404503i
\(804\) −3.09627 + 2.59808i −0.109197 + 0.0916271i
\(805\) 6.61081 + 11.4503i 0.233001 + 0.403569i
\(806\) 4.69459 8.13127i 0.165360 0.286412i
\(807\) 0.879385 + 4.98724i 0.0309558 + 0.175559i
\(808\) −0.426022 2.41609i −0.0149874 0.0849978i
\(809\) 8.65317 14.9877i 0.304229 0.526941i −0.672860 0.739770i \(-0.734934\pi\)
0.977089 + 0.212829i \(0.0682678\pi\)
\(810\) −7.92902 13.7335i −0.278597 0.482544i
\(811\) 37.5330 31.4939i 1.31796 1.10590i 0.331230 0.943550i \(-0.392536\pi\)
0.986733 0.162352i \(-0.0519080\pi\)
\(812\) 10.5270 3.83153i 0.369427 0.134460i
\(813\) 5.94862 + 2.16512i 0.208627 + 0.0759340i
\(814\) −20.8949 17.5329i −0.732365 0.614527i
\(815\) 0.770630 4.37046i 0.0269940 0.153091i
\(816\) 2.47565 0.0866652
\(817\) −11.3209 + 11.4537i −0.396068 + 0.400715i
\(818\) −16.8239 −0.588233
\(819\) 0.935822 5.30731i 0.0327003 0.185452i
\(820\) 2.87939 + 2.41609i 0.100552 + 0.0843736i
\(821\) 26.8307 + 9.76557i 0.936398 + 0.340821i 0.764742 0.644336i \(-0.222866\pi\)
0.171655 + 0.985157i \(0.445088\pi\)
\(822\) 1.87211 0.681393i 0.0652974 0.0237663i
\(823\) 36.0547 30.2535i 1.25679 1.05457i 0.260771 0.965401i \(-0.416023\pi\)
0.996017 0.0891689i \(-0.0284211\pi\)
\(824\) 3.71688 + 6.43783i 0.129484 + 0.224272i
\(825\) 0.733956 1.27125i 0.0255531 0.0442592i
\(826\) 2.22668 + 12.6281i 0.0774762 + 0.439389i
\(827\) 4.30113 + 24.3929i 0.149565 + 0.848224i 0.963588 + 0.267392i \(0.0861618\pi\)
−0.814023 + 0.580833i \(0.802727\pi\)
\(828\) 5.41147 9.37295i 0.188062 0.325732i
\(829\) 17.2959 + 29.9574i 0.600712 + 1.04046i 0.992713 + 0.120499i \(0.0384494\pi\)
−0.392002 + 0.919965i \(0.628217\pi\)
\(830\) 2.31315 1.94096i 0.0802905 0.0673718i
\(831\) 5.37464 1.95621i 0.186444 0.0678601i
\(832\) −1.00000 0.363970i −0.0346688 0.0126184i
\(833\) −21.3332 17.9007i −0.739152 0.620222i
\(834\) −1.16978 + 6.63414i −0.0405061 + 0.229721i
\(835\) 7.83244 0.271053
\(836\) 7.68866 16.7427i 0.265918 0.579057i
\(837\) 18.0155 0.622706
\(838\) 6.23277 35.3478i 0.215308 1.22107i
\(839\) 5.15207 + 4.32310i 0.177869 + 0.149250i 0.727376 0.686239i \(-0.240740\pi\)
−0.549506 + 0.835490i \(0.685184\pi\)
\(840\) 1.14796 + 0.417822i 0.0396082 + 0.0144162i
\(841\) −10.8738 + 3.95773i −0.374957 + 0.136473i
\(842\) 15.8648 13.3122i 0.546738 0.458768i
\(843\) 1.24510 + 2.15658i 0.0428835 + 0.0742764i
\(844\) −5.73442 + 9.93231i −0.197387 + 0.341884i
\(845\) −4.12155 23.3745i −0.141786 0.804106i
\(846\) 1.83750 + 10.4210i 0.0631744 + 0.358280i
\(847\) 6.03684 10.4561i 0.207428 0.359276i
\(848\) 4.94356 + 8.56250i 0.169763 + 0.294038i
\(849\) 5.57011 4.67388i 0.191166 0.160407i
\(850\) 6.69846 2.43804i 0.229755 0.0836241i
\(851\) 22.7939 + 8.29628i 0.781363 + 0.284393i
\(852\) 0.751030 + 0.630189i 0.0257299 + 0.0215899i
\(853\) 3.76053 21.3270i 0.128758 0.730223i −0.850247 0.526384i \(-0.823547\pi\)
0.979005 0.203838i \(-0.0653416\pi\)
\(854\) −9.33099 −0.319300
\(855\) 20.6459 + 14.2777i 0.706075 + 0.488287i
\(856\) −0.177052 −0.00605150
\(857\) −6.68123 + 37.8911i −0.228226 + 1.29434i 0.628194 + 0.778057i \(0.283794\pi\)
−0.856420 + 0.516279i \(0.827317\pi\)
\(858\) 1.19665 + 1.00411i 0.0408530 + 0.0342798i
\(859\) 15.5731 + 5.66815i 0.531347 + 0.193395i 0.593740 0.804657i \(-0.297651\pi\)
−0.0623925 + 0.998052i \(0.519873\pi\)
\(860\) −6.94356 + 2.52725i −0.236774 + 0.0861785i
\(861\) −0.879385 + 0.737892i −0.0299694 + 0.0251473i
\(862\) 9.16250 + 15.8699i 0.312076 + 0.540532i
\(863\) 12.9290 22.3937i 0.440109 0.762291i −0.557588 0.830118i \(-0.688273\pi\)
0.997697 + 0.0678268i \(0.0216065\pi\)
\(864\) −0.354570 2.01087i −0.0120627 0.0684111i
\(865\) 2.62092 + 14.8640i 0.0891139 + 0.505390i
\(866\) −2.54664 + 4.41090i −0.0865382 + 0.149889i
\(867\) −5.87164 10.1700i −0.199412 0.345391i
\(868\) 11.8871 9.97448i 0.403475 0.338556i
\(869\) 26.5895 9.67777i 0.901986 0.328296i
\(870\) −4.15745 1.51319i −0.140951 0.0513019i
\(871\) −9.48751 7.96097i −0.321472 0.269747i
\(872\) 0.736482 4.17680i 0.0249404 0.141444i
\(873\) −5.41147 −0.183151
\(874\) −1.33275 + 16.3298i −0.0450809 + 0.552364i
\(875\) 21.1052 0.713488
\(876\) 0.0478189 0.271194i 0.00161565 0.00916280i
\(877\) −38.7793 32.5397i −1.30948 1.09879i −0.988422 0.151729i \(-0.951516\pi\)
−0.321062 0.947058i \(-0.604040\pi\)
\(878\) 9.68954 + 3.52670i 0.327006 + 0.119021i
\(879\) −3.09327 + 1.12586i −0.104334 + 0.0379743i
\(880\) 6.47565 5.43372i 0.218294 0.183171i
\(881\) −25.4846 44.1406i −0.858597 1.48713i −0.873267 0.487241i \(-0.838003\pi\)
0.0146701 0.999892i \(-0.495330\pi\)
\(882\) −5.62449 + 9.74189i −0.189386 + 0.328027i
\(883\) 6.61897 + 37.5380i 0.222746 + 1.26325i 0.866948 + 0.498399i \(0.166079\pi\)
−0.644202 + 0.764856i \(0.722810\pi\)
\(884\) 1.31727 + 7.47059i 0.0443045 + 0.251263i
\(885\) 2.53209 4.38571i 0.0851152 0.147424i
\(886\) 4.40807 + 7.63500i 0.148092 + 0.256503i
\(887\) −24.1215 + 20.2404i −0.809922 + 0.679606i −0.950589 0.310451i \(-0.899520\pi\)
0.140667 + 0.990057i \(0.455075\pi\)
\(888\) 2.10607 0.766546i 0.0706750 0.0257236i
\(889\) −36.3851 13.2431i −1.22032 0.444159i
\(890\) 18.2422 + 15.3070i 0.611479 + 0.513092i
\(891\) 5.81954 33.0043i 0.194962 1.10568i
\(892\) 11.1925 0.374754
\(893\) −9.26445 13.0681i −0.310023 0.437308i
\(894\) −1.79797 −0.0601332
\(895\) −3.81614 + 21.6424i −0.127560 + 0.723426i
\(896\) −1.34730 1.13052i −0.0450100 0.0377679i
\(897\) −1.30541 0.475129i −0.0435863 0.0158641i
\(898\) −11.3486 + 4.13057i −0.378709 + 0.137839i
\(899\) −43.0506 + 36.1237i −1.43582 + 1.20479i
\(900\) −1.43969 2.49362i −0.0479898 0.0831207i
\(901\) 35.2395 61.0366i 1.17400 2.03342i
\(902\) 1.37939 + 7.82288i 0.0459285 + 0.260473i
\(903\) −0.391874 2.22243i −0.0130407 0.0739577i
\(904\) −5.21941 + 9.04028i −0.173595 + 0.300675i
\(905\) 15.0351 + 26.0415i 0.499783 + 0.865650i
\(906\) 5.90167 4.95209i 0.196070 0.164522i
\(907\) −8.36871 + 3.04596i −0.277878 + 0.101139i −0.477200 0.878795i \(-0.658348\pi\)
0.199322 + 0.979934i \(0.436126\pi\)
\(908\) 3.19207 + 1.16182i 0.105932 + 0.0385563i
\(909\) 5.41147 + 4.54077i 0.179487 + 0.150608i
\(910\) −0.650015 + 3.68642i −0.0215478 + 0.122204i
\(911\) −44.2959 −1.46759 −0.733795 0.679371i \(-0.762253\pi\)
−0.733795 + 0.679371i \(0.762253\pi\)
\(912\) 0.875515 + 1.23497i 0.0289912 + 0.0408940i
\(913\) 6.38144 0.211195
\(914\) −0.127011 + 0.720317i −0.00420116 + 0.0238260i
\(915\) 2.82295 + 2.36873i 0.0933238 + 0.0783080i
\(916\) −4.00000 1.45588i −0.132164 0.0481037i
\(917\) −12.6477 + 4.60337i −0.417662 + 0.152017i
\(918\) −11.1500 + 9.35597i −0.368005 + 0.308793i
\(919\) 27.3969 + 47.4529i 0.903741 + 1.56533i 0.822598 + 0.568623i \(0.192524\pi\)
0.0811431 + 0.996702i \(0.474143\pi\)
\(920\) −3.75877 + 6.51038i −0.123923 + 0.214641i
\(921\) 0.0802124 + 0.454907i 0.00264309 + 0.0149897i
\(922\) 4.00774 + 22.7290i 0.131988 + 0.748541i
\(923\) −1.50206 + 2.60164i −0.0494409 + 0.0856341i
\(924\) 1.29086 + 2.23583i 0.0424662 + 0.0735535i
\(925\) 4.94356 4.14814i 0.162543 0.136390i
\(926\) −16.9564 + 6.17161i −0.557220 + 0.202812i
\(927\) −20.1138 7.32083i −0.660624 0.240448i
\(928\) 4.87939 + 4.09429i 0.160174 + 0.134402i
\(929\) 5.28059 29.9477i 0.173251 0.982553i −0.766893 0.641775i \(-0.778198\pi\)
0.940144 0.340778i \(-0.110691\pi\)
\(930\) −6.12836 −0.200957
\(931\) 1.38521 16.9726i 0.0453984 0.556254i
\(932\) 6.64321 0.217606
\(933\) 0.450999 2.55774i 0.0147650 0.0837367i
\(934\) 8.40554 + 7.05309i 0.275038 + 0.230784i
\(935\) −56.6245 20.6096i −1.85182 0.674008i
\(936\) 2.87939 1.04801i 0.0941157 0.0342553i
\(937\) 22.6065 18.9691i 0.738523 0.619695i −0.193917 0.981018i \(-0.562119\pi\)
0.932441 + 0.361323i \(0.117675\pi\)
\(938\) −10.2344 17.7265i −0.334166 0.578792i
\(939\) −5.08765 + 8.81207i −0.166029 + 0.287571i
\(940\) −1.27631 7.23832i −0.0416287 0.236088i
\(941\) −2.34905 13.3221i −0.0765769 0.434289i −0.998858 0.0477701i \(-0.984789\pi\)
0.922281 0.386519i \(-0.126323\pi\)
\(942\) 0.490200 0.849051i 0.0159716 0.0276636i
\(943\) −3.53209 6.11776i −0.115021 0.199222i
\(944\) −5.58512 + 4.68647i −0.181780 + 0.152532i
\(945\) −6.74928 + 2.45654i −0.219554 + 0.0799111i
\(946\) −14.6741 5.34094i −0.477097 0.173649i
\(947\) −6.65002 5.58003i −0.216096 0.181326i 0.528313 0.849049i \(-0.322825\pi\)
−0.744410 + 0.667723i \(0.767269\pi\)
\(948\) −0.403733 + 2.28969i −0.0131126 + 0.0743655i
\(949\) 0.843807 0.0273911
\(950\) 3.58512 + 2.47929i 0.116317 + 0.0804389i
\(951\) 1.94532 0.0630812
\(952\) −2.17705 + 12.3467i −0.0705587 + 0.400158i
\(953\) 32.0498 + 26.8930i 1.03820 + 0.871150i 0.991803 0.127773i \(-0.0407829\pi\)
0.0463930 + 0.998923i \(0.485227\pi\)
\(954\) −26.7520 9.73692i −0.866127 0.315244i
\(955\) −8.52704 + 3.10359i −0.275928 + 0.100430i
\(956\) 12.2686 10.2946i 0.396794 0.332950i
\(957\) −4.67499 8.09732i −0.151121 0.261749i
\(958\) −11.1925 + 19.3860i −0.361614 + 0.626334i
\(959\) 1.75196 + 9.93588i 0.0565738 + 0.320846i
\(960\) 0.120615 + 0.684040i 0.00389282 + 0.0220773i
\(961\) −23.4222 + 40.5685i −0.755555 + 1.30866i
\(962\) 3.43376 + 5.94745i 0.110709 + 0.191754i
\(963\) 0.390530 0.327693i 0.0125846 0.0105598i
\(964\) 8.08512 2.94274i 0.260404 0.0947794i
\(965\) −41.3387 15.0461i −1.33074 0.484350i
\(966\) −1.75877 1.47578i −0.0565875 0.0474826i
\(967\) −2.44326 + 13.8564i −0.0785699 + 0.445592i 0.919990 + 0.391942i \(0.128197\pi\)
−0.998560 + 0.0536500i \(0.982914\pi\)
\(968\) 6.86484 0.220644
\(969\) 4.50340 9.80651i 0.144670 0.315030i
\(970\) 3.75877 0.120687
\(971\) 6.49819 36.8531i 0.208537 1.18267i −0.683239 0.730194i \(-0.739429\pi\)
0.891776 0.452477i \(-0.149459\pi\)
\(972\) 6.80200 + 5.70756i 0.218174 + 0.183070i
\(973\) −32.0574 11.6679i −1.02771 0.374057i
\(974\) 35.4834 12.9149i 1.13696 0.413820i
\(975\) −0.283119 + 0.237565i −0.00906705 + 0.00760816i
\(976\) −2.65270 4.59462i −0.0849110 0.147070i
\(977\) −24.8769 + 43.0881i −0.795883 + 1.37851i 0.126394 + 0.991980i \(0.459660\pi\)
−0.922277 + 0.386530i \(0.873674\pi\)
\(978\) 0.133819 + 0.758922i 0.00427904 + 0.0242677i
\(979\) 8.73901 + 49.5614i 0.279300 + 1.58399i
\(980\) 3.90673 6.76665i 0.124796 0.216153i
\(981\) 6.10607 + 10.5760i 0.194952 + 0.337666i
\(982\) −0.958578 + 0.804342i −0.0305894 + 0.0256676i
\(983\) 21.0300 7.65430i 0.670754 0.244134i 0.0158814 0.999874i \(-0.494945\pi\)
0.654872 + 0.755739i \(0.272722\pi\)
\(984\) −0.613341 0.223238i −0.0195526 0.00711656i
\(985\) 24.4088 + 20.4814i 0.777729 + 0.652592i
\(986\) 7.88444 44.7149i 0.251092 1.42401i
\(987\) 2.24474 0.0714508
\(988\) −3.26083 + 3.29909i −0.103741 + 0.104958i
\(989\) 13.8871 0.441585
\(990\) −4.22668 + 23.9707i −0.134333 + 0.761839i
\(991\) 36.8803 + 30.9463i 1.17154 + 0.983040i 0.999998 0.00213601i \(-0.000679914\pi\)
0.171544 + 0.985176i \(0.445124\pi\)
\(992\) 8.29086 + 3.01763i 0.263235 + 0.0958097i
\(993\) −7.49825 + 2.72914i −0.237950 + 0.0866066i
\(994\) −3.80335 + 3.19139i −0.120635 + 0.101225i
\(995\) 3.27631 + 5.67474i 0.103866 + 0.179901i
\(996\) −0.262174 + 0.454099i −0.00830730 + 0.0143887i
\(997\) −7.40642 42.0039i −0.234564 1.33028i −0.843530 0.537081i \(-0.819527\pi\)
0.608967 0.793196i \(-0.291584\pi\)
\(998\) −1.62015 9.18832i −0.0512849 0.290851i
\(999\) −6.58853 + 11.4117i −0.208452 + 0.361049i
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 38.2.e.a.17.1 yes 6
3.2 odd 2 342.2.u.c.55.1 6
4.3 odd 2 304.2.u.c.17.1 6
5.2 odd 4 950.2.u.b.549.2 12
5.3 odd 4 950.2.u.b.549.1 12
5.4 even 2 950.2.l.d.701.1 6
19.2 odd 18 722.2.c.l.429.2 6
19.3 odd 18 722.2.a.k.1.2 3
19.4 even 9 722.2.e.b.595.1 6
19.5 even 9 722.2.c.k.653.2 6
19.6 even 9 722.2.e.m.99.1 6
19.7 even 3 722.2.e.b.415.1 6
19.8 odd 6 722.2.e.a.423.1 6
19.9 even 9 inner 38.2.e.a.9.1 6
19.10 odd 18 722.2.e.k.389.1 6
19.11 even 3 722.2.e.m.423.1 6
19.12 odd 6 722.2.e.l.415.1 6
19.13 odd 18 722.2.e.a.99.1 6
19.14 odd 18 722.2.c.l.653.2 6
19.15 odd 18 722.2.e.l.595.1 6
19.16 even 9 722.2.a.l.1.2 3
19.17 even 9 722.2.c.k.429.2 6
19.18 odd 2 722.2.e.k.245.1 6
57.35 odd 18 6498.2.a.bl.1.1 3
57.41 even 18 6498.2.a.bq.1.1 3
57.47 odd 18 342.2.u.c.199.1 6
76.3 even 18 5776.2.a.bo.1.2 3
76.35 odd 18 5776.2.a.bn.1.2 3
76.47 odd 18 304.2.u.c.161.1 6
95.9 even 18 950.2.l.d.351.1 6
95.28 odd 36 950.2.u.b.199.2 12
95.47 odd 36 950.2.u.b.199.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.e.a.9.1 6 19.9 even 9 inner
38.2.e.a.17.1 yes 6 1.1 even 1 trivial
304.2.u.c.17.1 6 4.3 odd 2
304.2.u.c.161.1 6 76.47 odd 18
342.2.u.c.55.1 6 3.2 odd 2
342.2.u.c.199.1 6 57.47 odd 18
722.2.a.k.1.2 3 19.3 odd 18
722.2.a.l.1.2 3 19.16 even 9
722.2.c.k.429.2 6 19.17 even 9
722.2.c.k.653.2 6 19.5 even 9
722.2.c.l.429.2 6 19.2 odd 18
722.2.c.l.653.2 6 19.14 odd 18
722.2.e.a.99.1 6 19.13 odd 18
722.2.e.a.423.1 6 19.8 odd 6
722.2.e.b.415.1 6 19.7 even 3
722.2.e.b.595.1 6 19.4 even 9
722.2.e.k.245.1 6 19.18 odd 2
722.2.e.k.389.1 6 19.10 odd 18
722.2.e.l.415.1 6 19.12 odd 6
722.2.e.l.595.1 6 19.15 odd 18
722.2.e.m.99.1 6 19.6 even 9
722.2.e.m.423.1 6 19.11 even 3
950.2.l.d.351.1 6 95.9 even 18
950.2.l.d.701.1 6 5.4 even 2
950.2.u.b.199.1 12 95.47 odd 36
950.2.u.b.199.2 12 95.28 odd 36
950.2.u.b.549.1 12 5.3 odd 4
950.2.u.b.549.2 12 5.2 odd 4
5776.2.a.bn.1.2 3 76.35 odd 18
5776.2.a.bo.1.2 3 76.3 even 18
6498.2.a.bl.1.1 3 57.35 odd 18
6498.2.a.bq.1.1 3 57.41 even 18