Properties

Label 950.2.u.b.549.1
Level $950$
Weight $2$
Character 950.549
Analytic conductor $7.586$
Analytic rank $0$
Dimension $12$
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] = [950,2,Mod(99,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 549.1
Root \(0.642788 + 0.766044i\) of defining polynomial
Character \(\chi\) \(=\) 950.549
Dual form 950.2.u.b.199.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.984808 0.173648i −0.696364 0.122788i
\(3\) −0.223238 + 0.266044i −0.128886 + 0.153601i −0.826628 0.562749i \(-0.809744\pi\)
0.697742 + 0.716349i \(0.254188\pi\)
\(4\) 0.939693 + 0.342020i 0.469846 + 0.171010i
\(5\) 0 0
\(6\) 0.266044 0.223238i 0.108612 0.0911364i
\(7\) 1.52314 0.879385i 0.575693 0.332376i −0.183727 0.982977i \(-0.558816\pi\)
0.759420 + 0.650601i \(0.225483\pi\)
\(8\) −0.866025 0.500000i −0.306186 0.176777i
\(9\) 0.500000 + 2.83564i 0.166667 + 0.945214i
\(10\) 0 0
\(11\) −2.11334 + 3.66041i −0.637196 + 1.10366i 0.348849 + 0.937179i \(0.386573\pi\)
−0.986045 + 0.166477i \(0.946761\pi\)
\(12\) −0.300767 + 0.173648i −0.0868241 + 0.0501279i
\(13\) 0.684040 + 0.815207i 0.189719 + 0.226098i 0.852516 0.522701i \(-0.175075\pi\)
−0.662798 + 0.748799i \(0.730631\pi\)
\(14\) −1.65270 + 0.601535i −0.441704 + 0.160767i
\(15\) 0 0
\(16\) 0.766044 + 0.642788i 0.191511 + 0.160697i
\(17\) −7.02006 1.23783i −1.70261 0.300217i −0.764008 0.645207i \(-0.776771\pi\)
−0.938606 + 0.344990i \(0.887882\pi\)
\(18\) 2.87939i 0.678678i
\(19\) −3.93969 + 1.86516i −0.903827 + 0.427897i
\(20\) 0 0
\(21\) −0.106067 + 0.601535i −0.0231457 + 0.131266i
\(22\) 2.71686 3.23783i 0.579236 0.690307i
\(23\) 1.28558 3.53209i 0.268061 0.736491i −0.730503 0.682910i \(-0.760714\pi\)
0.998563 0.0535814i \(-0.0170637\pi\)
\(24\) 0.326352 0.118782i 0.0666163 0.0242463i
\(25\) 0 0
\(26\) −0.532089 0.921605i −0.104351 0.180742i
\(27\) −1.76833 1.02094i −0.340315 0.196481i
\(28\) 1.73205 0.305407i 0.327327 0.0577166i
\(29\) −1.10607 6.27282i −0.205391 1.16483i −0.896823 0.442390i \(-0.854131\pi\)
0.691431 0.722442i \(-0.256981\pi\)
\(30\) 0 0
\(31\) 4.41147 + 7.64090i 0.792324 + 1.37235i 0.924524 + 0.381123i \(0.124462\pi\)
−0.132200 + 0.991223i \(0.542204\pi\)
\(32\) −0.642788 0.766044i −0.113630 0.135419i
\(33\) −0.502055 1.37939i −0.0873966 0.240120i
\(34\) 6.69846 + 2.43804i 1.14878 + 0.418121i
\(35\) 0 0
\(36\) −0.500000 + 2.83564i −0.0833333 + 0.472607i
\(37\) 6.45336i 1.06093i 0.847708 + 0.530463i \(0.177982\pi\)
−0.847708 + 0.530463i \(0.822018\pi\)
\(38\) 4.20372 1.15270i 0.681934 0.186993i
\(39\) −0.369585 −0.0591810
\(40\) 0 0
\(41\) 1.43969 + 1.20805i 0.224842 + 0.188665i 0.748249 0.663418i \(-0.230895\pi\)
−0.523407 + 0.852083i \(0.675339\pi\)
\(42\) 0.208911 0.573978i 0.0322357 0.0885667i
\(43\) −1.26363 3.47178i −0.192701 0.529442i 0.805284 0.592889i \(-0.202013\pi\)
−0.997985 + 0.0634473i \(0.979791\pi\)
\(44\) −3.23783 + 2.71686i −0.488121 + 0.409582i
\(45\) 0 0
\(46\) −1.87939 + 3.25519i −0.277100 + 0.479952i
\(47\) −3.61916 + 0.638156i −0.527909 + 0.0930846i −0.431249 0.902233i \(-0.641927\pi\)
−0.0966598 + 0.995317i \(0.530816\pi\)
\(48\) −0.342020 + 0.0603074i −0.0493664 + 0.00870462i
\(49\) −1.95336 + 3.38332i −0.279052 + 0.483332i
\(50\) 0 0
\(51\) 1.89646 1.59132i 0.265557 0.222829i
\(52\) 0.363970 + 1.00000i 0.0504736 + 0.138675i
\(53\) −3.38160 + 9.29086i −0.464498 + 1.27620i 0.457571 + 0.889173i \(0.348719\pi\)
−0.922069 + 0.387025i \(0.873503\pi\)
\(54\) 1.56418 + 1.31250i 0.212858 + 0.178609i
\(55\) 0 0
\(56\) −1.75877 −0.235026
\(57\) 0.383273 1.46451i 0.0507657 0.193979i
\(58\) 6.36959i 0.836367i
\(59\) 1.26604 7.18009i 0.164825 0.934769i −0.784420 0.620230i \(-0.787039\pi\)
0.949245 0.314538i \(-0.101850\pi\)
\(60\) 0 0
\(61\) −4.98545 1.81456i −0.638322 0.232330i 0.00252758 0.999997i \(-0.499195\pi\)
−0.640849 + 0.767667i \(0.721418\pi\)
\(62\) −3.01763 8.29086i −0.383239 1.05294i
\(63\) 3.25519 + 3.87939i 0.410115 + 0.488757i
\(64\) 0.500000 + 0.866025i 0.0625000 + 0.108253i
\(65\) 0 0
\(66\) 0.254900 + 1.44561i 0.0313760 + 0.177942i
\(67\) −11.4613 + 2.02094i −1.40023 + 0.246898i −0.822236 0.569146i \(-0.807274\pi\)
−0.577990 + 0.816044i \(0.696163\pi\)
\(68\) −6.17334 3.56418i −0.748627 0.432220i
\(69\) 0.652704 + 1.13052i 0.0785763 + 0.136098i
\(70\) 0 0
\(71\) −2.65270 + 0.965505i −0.314818 + 0.114584i −0.494596 0.869123i \(-0.664684\pi\)
0.179778 + 0.983707i \(0.442462\pi\)
\(72\) 0.984808 2.70574i 0.116061 0.318874i
\(73\) −0.509678 + 0.607411i −0.0596533 + 0.0710921i −0.795046 0.606549i \(-0.792553\pi\)
0.735393 + 0.677641i \(0.236998\pi\)
\(74\) 1.12061 6.35532i 0.130269 0.738791i
\(75\) 0 0
\(76\) −4.34002 + 0.405223i −0.497835 + 0.0464823i
\(77\) 7.43376i 0.847156i
\(78\) 0.363970 + 0.0641778i 0.0412115 + 0.00726670i
\(79\) 5.12836 + 4.30320i 0.576985 + 0.484148i 0.883955 0.467571i \(-0.154871\pi\)
−0.306970 + 0.951719i \(0.599315\pi\)
\(80\) 0 0
\(81\) −7.45084 + 2.71188i −0.827871 + 0.301320i
\(82\) −1.20805 1.43969i −0.133406 0.158987i
\(83\) 1.30753 0.754900i 0.143520 0.0828610i −0.426521 0.904478i \(-0.640261\pi\)
0.570040 + 0.821617i \(0.306928\pi\)
\(84\) −0.305407 + 0.528981i −0.0333227 + 0.0577166i
\(85\) 0 0
\(86\) 0.641559 + 3.63846i 0.0691811 + 0.392346i
\(87\) 1.91576 + 1.10607i 0.205391 + 0.118583i
\(88\) 3.66041 2.11334i 0.390201 0.225283i
\(89\) −9.12108 + 7.65350i −0.966833 + 0.811269i −0.982051 0.188615i \(-0.939600\pi\)
0.0152184 + 0.999884i \(0.495156\pi\)
\(90\) 0 0
\(91\) 1.75877 + 0.640140i 0.184369 + 0.0671049i
\(92\) 2.41609 2.87939i 0.251895 0.300197i
\(93\) −3.01763 0.532089i −0.312913 0.0551750i
\(94\) 3.67499 0.379047
\(95\) 0 0
\(96\) 0.347296 0.0354458
\(97\) −1.85083 0.326352i −0.187924 0.0331360i 0.0788942 0.996883i \(-0.474861\pi\)
−0.266818 + 0.963747i \(0.585972\pi\)
\(98\) 2.51120 2.99273i 0.253669 0.302311i
\(99\) −11.4363 4.16247i −1.14939 0.418344i
\(100\) 0 0
\(101\) −1.87939 + 1.57699i −0.187006 + 0.156917i −0.731484 0.681858i \(-0.761172\pi\)
0.544478 + 0.838775i \(0.316728\pi\)
\(102\) −2.14398 + 1.23783i −0.212285 + 0.122563i
\(103\) 6.43783 + 3.71688i 0.634338 + 0.366235i 0.782430 0.622738i \(-0.213980\pi\)
−0.148092 + 0.988974i \(0.547313\pi\)
\(104\) −0.184793 1.04801i −0.0181204 0.102766i
\(105\) 0 0
\(106\) 4.94356 8.56250i 0.480161 0.831664i
\(107\) 0.153331 0.0885259i 0.0148231 0.00855812i −0.492570 0.870273i \(-0.663942\pi\)
0.507393 + 0.861715i \(0.330609\pi\)
\(108\) −1.31250 1.56418i −0.126295 0.150513i
\(109\) 3.98545 1.45059i 0.381737 0.138941i −0.144022 0.989574i \(-0.546004\pi\)
0.525759 + 0.850634i \(0.323781\pi\)
\(110\) 0 0
\(111\) −1.71688 1.44063i −0.162959 0.136739i
\(112\) 1.73205 + 0.305407i 0.163663 + 0.0288583i
\(113\) 10.4388i 0.982001i 0.871159 + 0.491001i \(0.163369\pi\)
−0.871159 + 0.491001i \(0.836631\pi\)
\(114\) −0.631759 + 1.37570i −0.0591697 + 0.128846i
\(115\) 0 0
\(116\) 1.10607 6.27282i 0.102696 0.582416i
\(117\) −1.96962 + 2.34730i −0.182091 + 0.217008i
\(118\) −2.49362 + 6.85117i −0.229556 + 0.630701i
\(119\) −11.7811 + 4.28795i −1.07997 + 0.393076i
\(120\) 0 0
\(121\) −3.43242 5.94512i −0.312038 0.540466i
\(122\) 4.59462 + 2.65270i 0.415977 + 0.240165i
\(123\) −0.642788 + 0.113341i −0.0579582 + 0.0102196i
\(124\) 1.53209 + 8.68891i 0.137586 + 0.780287i
\(125\) 0 0
\(126\) −2.53209 4.38571i −0.225576 0.390710i
\(127\) 14.1513 + 16.8648i 1.25572 + 1.49651i 0.791986 + 0.610539i \(0.209047\pi\)
0.463737 + 0.885973i \(0.346508\pi\)
\(128\) −0.342020 0.939693i −0.0302306 0.0830579i
\(129\) 1.20574 + 0.438852i 0.106159 + 0.0386388i
\(130\) 0 0
\(131\) −1.32888 + 7.53644i −0.116105 + 0.658462i 0.870093 + 0.492888i \(0.164059\pi\)
−0.986197 + 0.165574i \(0.947052\pi\)
\(132\) 1.46791i 0.127765i
\(133\) −4.36051 + 6.30541i −0.378104 + 0.546748i
\(134\) 11.6382 1.00538
\(135\) 0 0
\(136\) 5.46064 + 4.58202i 0.468246 + 0.392905i
\(137\) 1.96199 5.39053i 0.167624 0.460544i −0.827230 0.561864i \(-0.810084\pi\)
0.994854 + 0.101320i \(0.0323066\pi\)
\(138\) −0.446476 1.22668i −0.0380065 0.104422i
\(139\) 14.8589 12.4681i 1.26032 1.05753i 0.264668 0.964340i \(-0.414738\pi\)
0.995648 0.0931911i \(-0.0297068\pi\)
\(140\) 0 0
\(141\) 0.638156 1.10532i 0.0537424 0.0930846i
\(142\) 2.78006 0.490200i 0.233298 0.0411367i
\(143\) −4.42961 + 0.781059i −0.370422 + 0.0653155i
\(144\) −1.43969 + 2.49362i −0.119974 + 0.207802i
\(145\) 0 0
\(146\) 0.607411 0.509678i 0.0502697 0.0421813i
\(147\) −0.464050 1.27497i −0.0382742 0.105158i
\(148\) −2.20718 + 6.06418i −0.181429 + 0.498472i
\(149\) 3.96585 + 3.32774i 0.324895 + 0.272619i 0.790616 0.612312i \(-0.209760\pi\)
−0.465721 + 0.884932i \(0.654205\pi\)
\(150\) 0 0
\(151\) 22.1830 1.80523 0.902615 0.430449i \(-0.141645\pi\)
0.902615 + 0.430449i \(0.141645\pi\)
\(152\) 4.34445 + 0.354570i 0.352382 + 0.0287595i
\(153\) 20.5253i 1.65937i
\(154\) 1.29086 7.32083i 0.104020 0.589929i
\(155\) 0 0
\(156\) −0.347296 0.126406i −0.0278060 0.0101205i
\(157\) −0.965505 2.65270i −0.0770557 0.211709i 0.895184 0.445698i \(-0.147044\pi\)
−0.972239 + 0.233989i \(0.924822\pi\)
\(158\) −4.30320 5.12836i −0.342344 0.407990i
\(159\) −1.71688 2.97373i −0.136158 0.235832i
\(160\) 0 0
\(161\) −1.14796 6.51038i −0.0904716 0.513090i
\(162\) 7.80856 1.37686i 0.613498 0.108176i
\(163\) −1.92166 1.10947i −0.150516 0.0869004i 0.422851 0.906199i \(-0.361030\pi\)
−0.573366 + 0.819299i \(0.694363\pi\)
\(164\) 0.939693 + 1.62760i 0.0733777 + 0.127094i
\(165\) 0 0
\(166\) −1.41875 + 0.516382i −0.110116 + 0.0400790i
\(167\) −1.33943 + 3.68004i −0.103648 + 0.284770i −0.980667 0.195686i \(-0.937307\pi\)
0.877019 + 0.480456i \(0.159529\pi\)
\(168\) 0.392624 0.467911i 0.0302916 0.0361001i
\(169\) 2.06077 11.6872i 0.158521 0.899018i
\(170\) 0 0
\(171\) −7.25877 10.2390i −0.555092 0.782994i
\(172\) 3.69459i 0.281710i
\(173\) 7.43199 + 1.31046i 0.565043 + 0.0996324i 0.448871 0.893597i \(-0.351826\pi\)
0.116173 + 0.993229i \(0.462937\pi\)
\(174\) −1.69459 1.42193i −0.128467 0.107796i
\(175\) 0 0
\(176\) −3.97178 + 1.44561i −0.299384 + 0.108967i
\(177\) 1.62760 + 1.93969i 0.122338 + 0.145796i
\(178\) 10.3115 5.95336i 0.772882 0.446223i
\(179\) −5.49407 + 9.51601i −0.410646 + 0.711260i −0.994961 0.100267i \(-0.968030\pi\)
0.584314 + 0.811527i \(0.301363\pi\)
\(180\) 0 0
\(181\) −2.61081 14.8067i −0.194060 1.10057i −0.913751 0.406276i \(-0.866827\pi\)
0.719690 0.694295i \(-0.244284\pi\)
\(182\) −1.62089 0.935822i −0.120148 0.0693678i
\(183\) 1.59569 0.921274i 0.117957 0.0681026i
\(184\) −2.87939 + 2.41609i −0.212271 + 0.178117i
\(185\) 0 0
\(186\) 2.87939 + 1.04801i 0.211127 + 0.0768439i
\(187\) 19.3667 23.0804i 1.41624 1.68780i
\(188\) −3.61916 0.638156i −0.263954 0.0465423i
\(189\) −3.59121 −0.261222
\(190\) 0 0
\(191\) 4.53714 0.328296 0.164148 0.986436i \(-0.447513\pi\)
0.164148 + 0.986436i \(0.447513\pi\)
\(192\) −0.342020 0.0603074i −0.0246832 0.00435231i
\(193\) −14.1387 + 16.8498i −1.01772 + 1.21288i −0.0408274 + 0.999166i \(0.512999\pi\)
−0.976897 + 0.213711i \(0.931445\pi\)
\(194\) 1.76604 + 0.642788i 0.126795 + 0.0461495i
\(195\) 0 0
\(196\) −2.99273 + 2.51120i −0.213766 + 0.179371i
\(197\) −13.7973 + 7.96585i −0.983014 + 0.567543i −0.903179 0.429265i \(-0.858773\pi\)
−0.0798353 + 0.996808i \(0.525439\pi\)
\(198\) 10.5397 + 6.08512i 0.749027 + 0.432451i
\(199\) 0.568926 + 3.22654i 0.0403301 + 0.228723i 0.998310 0.0581118i \(-0.0185080\pi\)
−0.957980 + 0.286835i \(0.907397\pi\)
\(200\) 0 0
\(201\) 2.02094 3.50038i 0.142546 0.246898i
\(202\) 2.12467 1.22668i 0.149492 0.0863090i
\(203\) −7.20092 8.58172i −0.505405 0.602319i
\(204\) 2.32635 0.846723i 0.162877 0.0592825i
\(205\) 0 0
\(206\) −5.69459 4.77833i −0.396761 0.332922i
\(207\) 10.6585 + 1.87939i 0.740819 + 0.130626i
\(208\) 1.06418i 0.0737875i
\(209\) 1.49866 18.3626i 0.103664 1.27017i
\(210\) 0 0
\(211\) 1.99154 11.2946i 0.137104 0.777553i −0.836268 0.548321i \(-0.815267\pi\)
0.973372 0.229232i \(-0.0736215\pi\)
\(212\) −6.35532 + 7.57398i −0.436485 + 0.520183i
\(213\) 0.335316 0.921274i 0.0229755 0.0631247i
\(214\) −0.166374 + 0.0605553i −0.0113731 + 0.00413947i
\(215\) 0 0
\(216\) 1.02094 + 1.76833i 0.0694665 + 0.120319i
\(217\) 13.4386 + 7.75877i 0.912271 + 0.526700i
\(218\) −4.17680 + 0.736482i −0.282888 + 0.0498808i
\(219\) −0.0478189 0.271194i −0.00323130 0.0183256i
\(220\) 0 0
\(221\) −3.79292 6.56953i −0.255139 0.441914i
\(222\) 1.44063 + 1.71688i 0.0966891 + 0.115230i
\(223\) −3.82807 10.5175i −0.256347 0.704307i −0.999385 0.0350581i \(-0.988838\pi\)
0.743039 0.669249i \(-0.233384\pi\)
\(224\) −1.65270 0.601535i −0.110426 0.0401917i
\(225\) 0 0
\(226\) 1.81268 10.2802i 0.120578 0.683830i
\(227\) 3.39693i 0.225462i 0.993626 + 0.112731i \(0.0359598\pi\)
−0.993626 + 0.112731i \(0.964040\pi\)
\(228\) 0.861050 1.24510i 0.0570244 0.0824588i
\(229\) −4.25671 −0.281291 −0.140646 0.990060i \(-0.544918\pi\)
−0.140646 + 0.990060i \(0.544918\pi\)
\(230\) 0 0
\(231\) −1.97771 1.65950i −0.130124 0.109187i
\(232\) −2.17853 + 5.98545i −0.143027 + 0.392964i
\(233\) −2.27211 6.24257i −0.148851 0.408965i 0.842749 0.538307i \(-0.180936\pi\)
−0.991600 + 0.129342i \(0.958714\pi\)
\(234\) 2.34730 1.96962i 0.153448 0.128758i
\(235\) 0 0
\(236\) 3.64543 6.31407i 0.237297 0.411011i
\(237\) −2.28969 + 0.403733i −0.148731 + 0.0262253i
\(238\) 12.3467 2.17705i 0.800316 0.141117i
\(239\) 8.00774 13.8698i 0.517978 0.897164i −0.481804 0.876279i \(-0.660018\pi\)
0.999782 0.0208848i \(-0.00664831\pi\)
\(240\) 0 0
\(241\) −6.59105 + 5.53055i −0.424567 + 0.356254i −0.829897 0.557916i \(-0.811601\pi\)
0.405330 + 0.914170i \(0.367157\pi\)
\(242\) 2.34791 + 6.45084i 0.150930 + 0.414676i
\(243\) 3.03693 8.34389i 0.194819 0.535261i
\(244\) −4.06418 3.41025i −0.260182 0.218319i
\(245\) 0 0
\(246\) 0.652704 0.0416149
\(247\) −4.21540 1.93582i −0.268220 0.123173i
\(248\) 8.82295i 0.560258i
\(249\) −0.0910521 + 0.516382i −0.00577019 + 0.0327244i
\(250\) 0 0
\(251\) 18.7087 + 6.80942i 1.18088 + 0.429807i 0.856514 0.516123i \(-0.172625\pi\)
0.324370 + 0.945930i \(0.394848\pi\)
\(252\) 1.73205 + 4.75877i 0.109109 + 0.299774i
\(253\) 10.2120 + 12.1702i 0.642026 + 0.765137i
\(254\) −11.0077 19.0660i −0.690687 1.19631i
\(255\) 0 0
\(256\) 0.173648 + 0.984808i 0.0108530 + 0.0615505i
\(257\) 26.0161 4.58734i 1.62284 0.286151i 0.713018 0.701146i \(-0.247328\pi\)
0.909823 + 0.414996i \(0.136217\pi\)
\(258\) −1.11121 0.641559i −0.0691811 0.0399417i
\(259\) 5.67499 + 9.82938i 0.352627 + 0.610768i
\(260\) 0 0
\(261\) 17.2344 6.27282i 1.06678 0.388278i
\(262\) 2.61738 7.19119i 0.161702 0.444273i
\(263\) 17.9606 21.4047i 1.10750 1.31987i 0.164763 0.986333i \(-0.447314\pi\)
0.942738 0.333535i \(-0.108242\pi\)
\(264\) −0.254900 + 1.44561i −0.0156880 + 0.0889712i
\(265\) 0 0
\(266\) 5.38919 5.45242i 0.330432 0.334309i
\(267\) 4.13516i 0.253068i
\(268\) −11.4613 2.02094i −0.700113 0.123449i
\(269\) −11.1702 9.37295i −0.681062 0.571479i 0.235255 0.971934i \(-0.424408\pi\)
−0.916316 + 0.400455i \(0.868852\pi\)
\(270\) 0 0
\(271\) 17.1284 6.23421i 1.04047 0.378701i 0.235414 0.971895i \(-0.424355\pi\)
0.805060 + 0.593194i \(0.202133\pi\)
\(272\) −4.58202 5.46064i −0.277826 0.331100i
\(273\) −0.562930 + 0.325008i −0.0340701 + 0.0196704i
\(274\) −2.86824 + 4.96794i −0.173277 + 0.300124i
\(275\) 0 0
\(276\) 0.226682 + 1.28558i 0.0136446 + 0.0773825i
\(277\) −14.2624 8.23442i −0.856947 0.494758i 0.00604184 0.999982i \(-0.498077\pi\)
−0.862989 + 0.505223i \(0.831410\pi\)
\(278\) −16.7982 + 9.69846i −1.00749 + 0.581675i
\(279\) −19.4611 + 16.3298i −1.16511 + 0.977640i
\(280\) 0 0
\(281\) 6.73783 + 2.45237i 0.401945 + 0.146296i 0.535079 0.844802i \(-0.320282\pi\)
−0.133134 + 0.991098i \(0.542504\pi\)
\(282\) −0.820397 + 0.977711i −0.0488539 + 0.0582219i
\(283\) 20.6187 + 3.63563i 1.22565 + 0.216116i 0.748757 0.662844i \(-0.230651\pi\)
0.476896 + 0.878960i \(0.341762\pi\)
\(284\) −2.82295 −0.167511
\(285\) 0 0
\(286\) 4.49794 0.265969
\(287\) 3.25519 + 0.573978i 0.192148 + 0.0338808i
\(288\) 1.85083 2.20574i 0.109061 0.129974i
\(289\) 31.7743 + 11.5649i 1.86907 + 0.680287i
\(290\) 0 0
\(291\) 0.500000 0.419550i 0.0293105 0.0245944i
\(292\) −0.686688 + 0.396459i −0.0401854 + 0.0232010i
\(293\) −8.20848 4.73917i −0.479545 0.276865i 0.240682 0.970604i \(-0.422629\pi\)
−0.720227 + 0.693739i \(0.755962\pi\)
\(294\) 0.235604 + 1.33618i 0.0137407 + 0.0779275i
\(295\) 0 0
\(296\) 3.22668 5.58878i 0.187547 0.324841i
\(297\) 7.47416 4.31521i 0.433695 0.250394i
\(298\) −3.32774 3.96585i −0.192771 0.229736i
\(299\) 3.75877 1.36808i 0.217375 0.0791181i
\(300\) 0 0
\(301\) −4.97771 4.17680i −0.286911 0.240747i
\(302\) −21.8460 3.85204i −1.25710 0.221660i
\(303\) 0.852044i 0.0489487i
\(304\) −4.21688 1.10359i −0.241855 0.0632952i
\(305\) 0 0
\(306\) −3.56418 + 20.2135i −0.203750 + 1.15553i
\(307\) 0.854946 1.01889i 0.0487944 0.0581508i −0.741095 0.671400i \(-0.765693\pi\)
0.789890 + 0.613249i \(0.210138\pi\)
\(308\) −2.54250 + 6.98545i −0.144872 + 0.398033i
\(309\) −2.42602 + 0.883000i −0.138012 + 0.0502321i
\(310\) 0 0
\(311\) −3.73917 6.47643i −0.212029 0.367245i 0.740320 0.672254i \(-0.234674\pi\)
−0.952349 + 0.305009i \(0.901340\pi\)
\(312\) 0.320070 + 0.184793i 0.0181204 + 0.0104618i
\(313\) −28.8535 + 5.08765i −1.63090 + 0.287571i −0.912810 0.408384i \(-0.866092\pi\)
−0.718085 + 0.695955i \(0.754981\pi\)
\(314\) 0.490200 + 2.78006i 0.0276636 + 0.156888i
\(315\) 0 0
\(316\) 3.34730 + 5.79769i 0.188300 + 0.326145i
\(317\) −3.60046 4.29086i −0.202222 0.240999i 0.655397 0.755285i \(-0.272501\pi\)
−0.857619 + 0.514286i \(0.828057\pi\)
\(318\) 1.17442 + 3.22668i 0.0658580 + 0.180943i
\(319\) 25.2986 + 9.20794i 1.41645 + 0.515546i
\(320\) 0 0
\(321\) −0.0106775 + 0.0605553i −0.000595961 + 0.00337987i
\(322\) 6.61081i 0.368406i
\(323\) 29.9656 8.21688i 1.66733 0.457200i
\(324\) −7.92902 −0.440501
\(325\) 0 0
\(326\) 1.69981 + 1.42631i 0.0941436 + 0.0789959i
\(327\) −0.503783 + 1.38413i −0.0278593 + 0.0765427i
\(328\) −0.642788 1.76604i −0.0354920 0.0975135i
\(329\) −4.95130 + 4.15464i −0.272974 + 0.229053i
\(330\) 0 0
\(331\) −11.4880 + 19.8978i −0.631436 + 1.09368i 0.355822 + 0.934554i \(0.384201\pi\)
−0.987258 + 0.159126i \(0.949132\pi\)
\(332\) 1.48686 0.262174i 0.0816022 0.0143887i
\(333\) −18.2994 + 3.22668i −1.00280 + 0.176821i
\(334\) 1.95811 3.39155i 0.107143 0.185577i
\(335\) 0 0
\(336\) −0.467911 + 0.392624i −0.0255266 + 0.0214194i
\(337\) 0.448804 + 1.23308i 0.0244479 + 0.0671701i 0.951316 0.308217i \(-0.0997322\pi\)
−0.926868 + 0.375387i \(0.877510\pi\)
\(338\) −4.05893 + 11.1518i −0.220777 + 0.606579i
\(339\) −2.77719 2.33034i −0.150836 0.126567i
\(340\) 0 0
\(341\) −37.2918 −2.01946
\(342\) 5.37051 + 11.3439i 0.290404 + 0.613407i
\(343\) 19.1824i 1.03575i
\(344\) −0.641559 + 3.63846i −0.0345906 + 0.196173i
\(345\) 0 0
\(346\) −7.09152 2.58110i −0.381242 0.138761i
\(347\) 0.826501 + 2.27079i 0.0443689 + 0.121903i 0.959898 0.280349i \(-0.0904501\pi\)
−0.915529 + 0.402251i \(0.868228\pi\)
\(348\) 1.42193 + 1.69459i 0.0762236 + 0.0908397i
\(349\) −4.24897 7.35943i −0.227442 0.393941i 0.729607 0.683866i \(-0.239703\pi\)
−0.957049 + 0.289925i \(0.906370\pi\)
\(350\) 0 0
\(351\) −0.377326 2.13992i −0.0201402 0.114221i
\(352\) 4.16247 0.733956i 0.221860 0.0391200i
\(353\) 3.32570 + 1.92009i 0.177009 + 0.102196i 0.585887 0.810393i \(-0.300746\pi\)
−0.408878 + 0.912589i \(0.634080\pi\)
\(354\) −1.26604 2.19285i −0.0672895 0.116549i
\(355\) 0 0
\(356\) −11.1887 + 4.07234i −0.592998 + 0.215834i
\(357\) 1.48919 4.09152i 0.0788164 0.216546i
\(358\) 7.06304 8.41740i 0.373293 0.444874i
\(359\) 4.15476 23.5628i 0.219280 1.24360i −0.654043 0.756457i \(-0.726929\pi\)
0.873323 0.487141i \(-0.161960\pi\)
\(360\) 0 0
\(361\) 12.0424 14.6963i 0.633808 0.773490i
\(362\) 15.0351i 0.790226i
\(363\) 2.34791 + 0.414000i 0.123233 + 0.0217294i
\(364\) 1.43376 + 1.20307i 0.0751496 + 0.0630580i
\(365\) 0 0
\(366\) −1.73143 + 0.630189i −0.0905033 + 0.0329405i
\(367\) −10.9973 13.1061i −0.574054 0.684131i 0.398404 0.917210i \(-0.369564\pi\)
−0.972458 + 0.233079i \(0.925120\pi\)
\(368\) 3.25519 1.87939i 0.169689 0.0979697i
\(369\) −2.70574 + 4.68647i −0.140855 + 0.243968i
\(370\) 0 0
\(371\) 3.01960 + 17.1250i 0.156770 + 0.889086i
\(372\) −2.65366 1.53209i −0.137586 0.0794351i
\(373\) −3.43015 + 1.98040i −0.177607 + 0.102541i −0.586168 0.810190i \(-0.699364\pi\)
0.408561 + 0.912731i \(0.366031\pi\)
\(374\) −23.0804 + 19.3667i −1.19346 + 1.00143i
\(375\) 0 0
\(376\) 3.45336 + 1.25692i 0.178094 + 0.0648208i
\(377\) 4.35705 5.19253i 0.224400 0.267429i
\(378\) 3.53666 + 0.623608i 0.181906 + 0.0320749i
\(379\) 27.2918 1.40189 0.700943 0.713218i \(-0.252763\pi\)
0.700943 + 0.713218i \(0.252763\pi\)
\(380\) 0 0
\(381\) −7.64590 −0.391711
\(382\) −4.46821 0.787866i −0.228614 0.0403107i
\(383\) −4.11949 + 4.90941i −0.210496 + 0.250859i −0.860954 0.508683i \(-0.830133\pi\)
0.650458 + 0.759542i \(0.274577\pi\)
\(384\) 0.326352 + 0.118782i 0.0166541 + 0.00606159i
\(385\) 0 0
\(386\) 16.8498 14.1387i 0.857633 0.719640i
\(387\) 9.21291 5.31908i 0.468319 0.270384i
\(388\) −1.62760 0.939693i −0.0826286 0.0477057i
\(389\) 4.41653 + 25.0474i 0.223927 + 1.26995i 0.864726 + 0.502244i \(0.167492\pi\)
−0.640799 + 0.767708i \(0.721397\pi\)
\(390\) 0 0
\(391\) −13.3969 + 23.2042i −0.677512 + 1.17348i
\(392\) 3.38332 1.95336i 0.170884 0.0986597i
\(393\) −1.70837 2.03596i −0.0861760 0.102701i
\(394\) 14.9709 5.44896i 0.754223 0.274515i
\(395\) 0 0
\(396\) −9.32295 7.82288i −0.468496 0.393115i
\(397\) −22.2387 3.92127i −1.11613 0.196803i −0.414987 0.909827i \(-0.636214\pi\)
−0.701139 + 0.713024i \(0.747325\pi\)
\(398\) 3.27631i 0.164227i
\(399\) −0.704088 2.56769i −0.0352485 0.128546i
\(400\) 0 0
\(401\) 0.132636 0.752219i 0.00662355 0.0375640i −0.981317 0.192399i \(-0.938373\pi\)
0.987940 + 0.154835i \(0.0494845\pi\)
\(402\) −2.59808 + 3.09627i −0.129580 + 0.154428i
\(403\) −3.21129 + 8.82295i −0.159966 + 0.439502i
\(404\) −2.30541 + 0.839100i −0.114698 + 0.0417468i
\(405\) 0 0
\(406\) 5.60132 + 9.70177i 0.277989 + 0.481491i
\(407\) −23.6220 13.6382i −1.17090 0.676018i
\(408\) −2.43804 + 0.429892i −0.120701 + 0.0212828i
\(409\) 2.92144 + 16.5683i 0.144456 + 0.819249i 0.967803 + 0.251711i \(0.0809931\pi\)
−0.823347 + 0.567539i \(0.807896\pi\)
\(410\) 0 0
\(411\) 0.996130 + 1.72535i 0.0491354 + 0.0851051i
\(412\) 4.77833 + 5.69459i 0.235411 + 0.280552i
\(413\) −4.38571 12.0496i −0.215807 0.592924i
\(414\) −10.1702 3.70167i −0.499840 0.181927i
\(415\) 0 0
\(416\) 0.184793 1.04801i 0.00906020 0.0513829i
\(417\) 6.73648i 0.329887i
\(418\) −4.66452 + 17.8234i −0.228149 + 0.871772i
\(419\) −35.8931 −1.75349 −0.876747 0.480953i \(-0.840291\pi\)
−0.876747 + 0.480953i \(0.840291\pi\)
\(420\) 0 0
\(421\) 15.8648 + 13.3122i 0.773205 + 0.648796i 0.941528 0.336936i \(-0.109391\pi\)
−0.168323 + 0.985732i \(0.553835\pi\)
\(422\) −3.92258 + 10.7772i −0.190948 + 0.524625i
\(423\) −3.61916 9.94356i −0.175970 0.483473i
\(424\) 7.57398 6.35532i 0.367825 0.308642i
\(425\) 0 0
\(426\) −0.490200 + 0.849051i −0.0237503 + 0.0411367i
\(427\) −9.18923 + 1.62031i −0.444698 + 0.0784123i
\(428\) 0.174362 0.0307447i 0.00842810 0.00148610i
\(429\) 0.781059 1.35283i 0.0377099 0.0653155i
\(430\) 0 0
\(431\) −14.0378 + 11.7791i −0.676176 + 0.567379i −0.914886 0.403712i \(-0.867720\pi\)
0.238710 + 0.971091i \(0.423275\pi\)
\(432\) −0.698367 1.91875i −0.0336002 0.0923158i
\(433\) 1.74200 4.78611i 0.0837153 0.230006i −0.890771 0.454452i \(-0.849835\pi\)
0.974486 + 0.224446i \(0.0720573\pi\)
\(434\) −11.8871 9.97448i −0.570600 0.478791i
\(435\) 0 0
\(436\) 4.24123 0.203118
\(437\) 1.52314 + 16.3131i 0.0728617 + 0.780364i
\(438\) 0.275378i 0.0131581i
\(439\) 1.79055 10.1547i 0.0854585 0.484659i −0.911798 0.410639i \(-0.865306\pi\)
0.997257 0.0740207i \(-0.0235831\pi\)
\(440\) 0 0
\(441\) −10.5706 3.84737i −0.503361 0.183208i
\(442\) 2.59451 + 7.12836i 0.123408 + 0.339061i
\(443\) −5.66691 6.75356i −0.269243 0.320871i 0.614434 0.788968i \(-0.289384\pi\)
−0.883677 + 0.468097i \(0.844940\pi\)
\(444\) −1.12061 1.94096i −0.0531820 0.0921140i
\(445\) 0 0
\(446\) 1.94356 + 11.0225i 0.0920304 + 0.521930i
\(447\) −1.77066 + 0.312214i −0.0837492 + 0.0147672i
\(448\) 1.52314 + 0.879385i 0.0719616 + 0.0415470i
\(449\) 6.03849 + 10.4590i 0.284974 + 0.493589i 0.972603 0.232473i \(-0.0746818\pi\)
−0.687629 + 0.726062i \(0.741348\pi\)
\(450\) 0 0
\(451\) −7.46451 + 2.71686i −0.351490 + 0.127932i
\(452\) −3.57029 + 9.80928i −0.167932 + 0.461390i
\(453\) −4.95209 + 5.90167i −0.232670 + 0.277285i
\(454\) 0.589870 3.34532i 0.0276840 0.157004i
\(455\) 0 0
\(456\) −1.06418 + 1.07666i −0.0498347 + 0.0504194i
\(457\) 0.731429i 0.0342148i 0.999854 + 0.0171074i \(0.00544572\pi\)
−0.999854 + 0.0171074i \(0.994554\pi\)
\(458\) 4.19204 + 0.739170i 0.195881 + 0.0345392i
\(459\) 11.1500 + 9.35597i 0.520438 + 0.436699i
\(460\) 0 0
\(461\) −21.6878 + 7.89371i −1.01010 + 0.367647i −0.793472 0.608607i \(-0.791729\pi\)
−0.216629 + 0.976254i \(0.569506\pi\)
\(462\) 1.65950 + 1.97771i 0.0772068 + 0.0920115i
\(463\) 15.6271 9.02229i 0.726251 0.419301i −0.0907980 0.995869i \(-0.528942\pi\)
0.817049 + 0.576568i \(0.195608\pi\)
\(464\) 3.18479 5.51622i 0.147850 0.256084i
\(465\) 0 0
\(466\) 1.15358 + 6.54228i 0.0534386 + 0.303065i
\(467\) 9.50260 + 5.48633i 0.439728 + 0.253877i 0.703482 0.710713i \(-0.251627\pi\)
−0.263754 + 0.964590i \(0.584961\pi\)
\(468\) −2.65366 + 1.53209i −0.122665 + 0.0708208i
\(469\) −15.6800 + 13.1571i −0.724037 + 0.607539i
\(470\) 0 0
\(471\) 0.921274 + 0.335316i 0.0424501 + 0.0154506i
\(472\) −4.68647 + 5.58512i −0.215712 + 0.257076i
\(473\) 15.3786 + 2.71167i 0.707110 + 0.124683i
\(474\) 2.32501 0.106791
\(475\) 0 0
\(476\) −12.5371 −0.574639
\(477\) −28.0363 4.94356i −1.28370 0.226350i
\(478\) −10.2946 + 12.2686i −0.470862 + 0.561151i
\(479\) 21.0351 + 7.65614i 0.961117 + 0.349818i 0.774471 0.632609i \(-0.218016\pi\)
0.186646 + 0.982427i \(0.440238\pi\)
\(480\) 0 0
\(481\) −5.26083 + 4.41436i −0.239873 + 0.201278i
\(482\) 7.45129 4.30200i 0.339397 0.195951i
\(483\) 1.98832 + 1.14796i 0.0904716 + 0.0522338i
\(484\) −1.19207 6.76055i −0.0541848 0.307298i
\(485\) 0 0
\(486\) −4.43969 + 7.68977i −0.201389 + 0.348815i
\(487\) 32.7017 18.8803i 1.48185 0.855549i 0.482066 0.876135i \(-0.339887\pi\)
0.999788 + 0.0205859i \(0.00655317\pi\)
\(488\) 3.41025 + 4.06418i 0.154375 + 0.183977i
\(489\) 0.724155 0.263571i 0.0327474 0.0119191i
\(490\) 0 0
\(491\) −0.958578 0.804342i −0.0432600 0.0362995i 0.620901 0.783889i \(-0.286767\pi\)
−0.664161 + 0.747589i \(0.731211\pi\)
\(492\) −0.642788 0.113341i −0.0289791 0.00510980i
\(493\) 45.4047i 2.04492i
\(494\) 3.81521 + 2.63841i 0.171654 + 0.118708i
\(495\) 0 0
\(496\) −1.53209 + 8.68891i −0.0687928 + 0.390143i
\(497\) −3.19139 + 3.80335i −0.143153 + 0.170603i
\(498\) 0.179338 0.492726i 0.00803631 0.0220796i
\(499\) −8.76739 + 3.19107i −0.392482 + 0.142852i −0.530720 0.847547i \(-0.678078\pi\)
0.138238 + 0.990399i \(0.455856\pi\)
\(500\) 0 0
\(501\) −0.680045 1.17787i −0.0303822 0.0526234i
\(502\) −17.2421 9.95471i −0.769551 0.444300i
\(503\) 9.54325 1.68273i 0.425513 0.0750294i 0.0432089 0.999066i \(-0.486242\pi\)
0.382304 + 0.924037i \(0.375131\pi\)
\(504\) −0.879385 4.98724i −0.0391709 0.222149i
\(505\) 0 0
\(506\) −7.94356 13.7587i −0.353134 0.611647i
\(507\) 2.64928 + 3.15729i 0.117659 + 0.140220i
\(508\) 7.52974 + 20.6878i 0.334078 + 0.917872i
\(509\) 27.2053 + 9.90193i 1.20585 + 0.438895i 0.865264 0.501316i \(-0.167151\pi\)
0.340591 + 0.940212i \(0.389373\pi\)
\(510\) 0 0
\(511\) −0.242163 + 1.37338i −0.0107127 + 0.0607546i
\(512\) 1.00000i 0.0441942i
\(513\) 8.87089 + 0.723993i 0.391659 + 0.0319651i
\(514\) −26.4175 −1.16522
\(515\) 0 0
\(516\) 0.982926 + 0.824773i 0.0432709 + 0.0363086i
\(517\) 5.31261 14.5963i 0.233648 0.641943i
\(518\) −3.88192 10.6655i −0.170562 0.468615i
\(519\) −2.00774 + 1.68469i −0.0881300 + 0.0739499i
\(520\) 0 0
\(521\) 1.08037 1.87126i 0.0473321 0.0819815i −0.841389 0.540430i \(-0.818261\pi\)
0.888721 + 0.458449i \(0.151595\pi\)
\(522\) −18.0619 + 3.18479i −0.790546 + 0.139395i
\(523\) −14.1665 + 2.49794i −0.619459 + 0.109227i −0.474566 0.880220i \(-0.657395\pi\)
−0.144893 + 0.989447i \(0.546284\pi\)
\(524\) −3.82635 + 6.62744i −0.167155 + 0.289521i
\(525\) 0 0
\(526\) −21.4047 + 17.9606i −0.933288 + 0.783121i
\(527\) −21.5107 59.1002i −0.937021 2.57444i
\(528\) 0.502055 1.37939i 0.0218491 0.0600300i
\(529\) 6.79607 + 5.70258i 0.295481 + 0.247938i
\(530\) 0 0
\(531\) 20.9932 0.911027
\(532\) −6.25411 + 4.43376i −0.271150 + 0.192228i
\(533\) 2.00000i 0.0866296i
\(534\) −0.718063 + 4.07234i −0.0310736 + 0.176227i
\(535\) 0 0
\(536\) 10.9363 + 3.98048i 0.472376 + 0.171931i
\(537\) −1.30520 3.58600i −0.0563234 0.154747i
\(538\) 9.37295 + 11.1702i 0.404096 + 0.481583i
\(539\) −8.25624 14.3002i −0.355622 0.615955i
\(540\) 0 0
\(541\) 2.24897 + 12.7545i 0.0966908 + 0.548361i 0.994216 + 0.107398i \(0.0342518\pi\)
−0.897525 + 0.440963i \(0.854637\pi\)
\(542\) −17.9507 + 3.16519i −0.771048 + 0.135957i
\(543\) 4.52206 + 2.61081i 0.194060 + 0.112041i
\(544\) 3.56418 + 6.17334i 0.152813 + 0.264680i
\(545\) 0 0
\(546\) 0.610815 0.222318i 0.0261405 0.00951435i
\(547\) −0.478377 + 1.31433i −0.0204539 + 0.0561967i −0.949499 0.313769i \(-0.898408\pi\)
0.929045 + 0.369966i \(0.120631\pi\)
\(548\) 3.68734 4.39440i 0.157515 0.187719i
\(549\) 2.65270 15.0442i 0.113215 0.642072i
\(550\) 0 0
\(551\) 16.0574 + 22.6500i 0.684067 + 0.964922i
\(552\) 1.30541i 0.0555618i
\(553\) 11.5954 + 2.04458i 0.493085 + 0.0869443i
\(554\) 12.6159 + 10.5860i 0.535997 + 0.449755i
\(555\) 0 0
\(556\) 18.2271 6.63414i 0.773003 0.281350i
\(557\) 19.0625 + 22.7178i 0.807704 + 0.962585i 0.999824 0.0187869i \(-0.00598041\pi\)
−0.192119 + 0.981372i \(0.561536\pi\)
\(558\) 22.0011 12.7023i 0.931380 0.537733i
\(559\) 1.96585 3.40496i 0.0831467 0.144014i
\(560\) 0 0
\(561\) 1.81702 + 10.3048i 0.0767146 + 0.435070i
\(562\) −6.20961 3.58512i −0.261937 0.151229i
\(563\) 36.4850 21.0646i 1.53766 0.887769i 0.538686 0.842507i \(-0.318921\pi\)
0.998975 0.0452621i \(-0.0144123\pi\)
\(564\) 0.977711 0.820397i 0.0411691 0.0345450i
\(565\) 0 0
\(566\) −19.6741 7.16079i −0.826965 0.300991i
\(567\) −8.96388 + 10.6827i −0.376447 + 0.448633i
\(568\) 2.78006 + 0.490200i 0.116649 + 0.0205683i
\(569\) −5.08915 −0.213348 −0.106674 0.994294i \(-0.534020\pi\)
−0.106674 + 0.994294i \(0.534020\pi\)
\(570\) 0 0
\(571\) −12.6486 −0.529327 −0.264663 0.964341i \(-0.585261\pi\)
−0.264663 + 0.964341i \(0.585261\pi\)
\(572\) −4.42961 0.781059i −0.185211 0.0326577i
\(573\) −1.01286 + 1.20708i −0.0423129 + 0.0504265i
\(574\) −3.10607 1.13052i −0.129645 0.0471868i
\(575\) 0 0
\(576\) −2.20574 + 1.85083i −0.0919057 + 0.0771180i
\(577\) −8.67285 + 5.00727i −0.361056 + 0.208456i −0.669544 0.742773i \(-0.733510\pi\)
0.308488 + 0.951228i \(0.400177\pi\)
\(578\) −29.2833 16.9067i −1.21803 0.703227i
\(579\) −1.32651 7.52303i −0.0551280 0.312647i
\(580\) 0 0
\(581\) 1.32770 2.29964i 0.0550821 0.0954050i
\(582\) −0.565258 + 0.326352i −0.0234307 + 0.0135277i
\(583\) −26.8619 32.0128i −1.11251 1.32583i
\(584\) 0.745100 0.271194i 0.0308325 0.0112221i
\(585\) 0 0
\(586\) 7.26083 + 6.09256i 0.299942 + 0.251681i
\(587\) −4.36640 0.769915i −0.180221 0.0317778i 0.0828093 0.996565i \(-0.473611\pi\)
−0.263030 + 0.964788i \(0.584722\pi\)
\(588\) 1.35679i 0.0559532i
\(589\) −31.6313 21.8747i −1.30335 0.901331i
\(590\) 0 0
\(591\) 0.960799 5.44896i 0.0395220 0.224140i
\(592\) −4.14814 + 4.94356i −0.170488 + 0.203179i
\(593\) −8.21692 + 22.5758i −0.337428 + 0.927077i 0.648693 + 0.761050i \(0.275316\pi\)
−0.986121 + 0.166026i \(0.946906\pi\)
\(594\) −8.10994 + 2.95178i −0.332755 + 0.121113i
\(595\) 0 0
\(596\) 2.58853 + 4.48346i 0.106030 + 0.183650i
\(597\) −0.985408 0.568926i −0.0403301 0.0232846i
\(598\) −3.93923 + 0.694593i −0.161087 + 0.0284040i
\(599\) 5.89992 + 33.4601i 0.241064 + 1.36714i 0.829458 + 0.558569i \(0.188649\pi\)
−0.588394 + 0.808574i \(0.700240\pi\)
\(600\) 0 0
\(601\) −8.07145 13.9802i −0.329241 0.570263i 0.653120 0.757254i \(-0.273460\pi\)
−0.982362 + 0.186991i \(0.940126\pi\)
\(602\) 4.17680 + 4.97771i 0.170233 + 0.202876i
\(603\) −11.4613 31.4898i −0.466742 1.28236i
\(604\) 20.8452 + 7.58705i 0.848181 + 0.308713i
\(605\) 0 0
\(606\) −0.147956 + 0.839100i −0.00601030 + 0.0340861i
\(607\) 8.92221i 0.362141i −0.983470 0.181071i \(-0.942044\pi\)
0.983470 0.181071i \(-0.0579563\pi\)
\(608\) 3.96118 + 1.81908i 0.160647 + 0.0737733i
\(609\) 3.89064 0.157657
\(610\) 0 0
\(611\) −2.99588 2.51384i −0.121200 0.101699i
\(612\) 7.02006 19.2875i 0.283769 0.779649i
\(613\) −8.83402 24.2713i −0.356803 0.980307i −0.980132 0.198347i \(-0.936443\pi\)
0.623329 0.781960i \(-0.285780\pi\)
\(614\) −1.01889 + 0.854946i −0.0411189 + 0.0345028i
\(615\) 0 0
\(616\) 3.71688 6.43783i 0.149757 0.259387i
\(617\) 18.2465 3.21735i 0.734576 0.129526i 0.206169 0.978516i \(-0.433900\pi\)
0.528407 + 0.848991i \(0.322789\pi\)
\(618\) 2.54250 0.448311i 0.102274 0.0180337i
\(619\) −17.6061 + 30.4946i −0.707648 + 1.22568i 0.258080 + 0.966124i \(0.416910\pi\)
−0.965728 + 0.259558i \(0.916423\pi\)
\(620\) 0 0
\(621\) −5.87939 + 4.93339i −0.235932 + 0.197970i
\(622\) 2.55774 + 7.02734i 0.102556 + 0.281771i
\(623\) −7.16231 + 19.6783i −0.286952 + 0.788394i
\(624\) −0.283119 0.237565i −0.0113338 0.00951020i
\(625\) 0 0
\(626\) 29.2986 1.17101
\(627\) 4.55072 + 4.49794i 0.181738 + 0.179630i
\(628\) 2.82295i 0.112648i
\(629\) 7.98814 45.3030i 0.318508 1.80635i
\(630\) 0 0
\(631\) 1.73143 + 0.630189i 0.0689271 + 0.0250874i 0.376254 0.926517i \(-0.377212\pi\)
−0.307326 + 0.951604i \(0.599434\pi\)
\(632\) −2.28969 6.29086i −0.0910788 0.250237i
\(633\) 2.56028 + 3.05122i 0.101762 + 0.121275i
\(634\) 2.80066 + 4.85088i 0.111228 + 0.192653i
\(635\) 0 0
\(636\) −0.596267 3.38160i −0.0236435 0.134089i
\(637\) −4.09429 + 0.721934i −0.162222 + 0.0286041i
\(638\) −23.3153 13.4611i −0.923062 0.532930i
\(639\) −4.06418 7.03936i −0.160776 0.278473i
\(640\) 0 0
\(641\) 4.89945 1.78325i 0.193517 0.0704343i −0.243444 0.969915i \(-0.578277\pi\)
0.436961 + 0.899481i \(0.356055\pi\)
\(642\) 0.0210306 0.0577812i 0.000830012 0.00228044i
\(643\) −3.79504 + 4.52276i −0.149662 + 0.178360i −0.835667 0.549237i \(-0.814918\pi\)
0.686005 + 0.727597i \(0.259363\pi\)
\(644\) 1.14796 6.51038i 0.0452358 0.256545i
\(645\) 0 0
\(646\) −30.9372 + 2.88857i −1.21721 + 0.113649i
\(647\) 42.6810i 1.67796i 0.544160 + 0.838981i \(0.316848\pi\)
−0.544160 + 0.838981i \(0.683152\pi\)
\(648\) 7.80856 + 1.37686i 0.306749 + 0.0540881i
\(649\) 23.6065 + 19.8082i 0.926638 + 0.777541i
\(650\) 0 0
\(651\) −5.06418 + 1.84321i −0.198481 + 0.0722411i
\(652\) −1.42631 1.69981i −0.0558585 0.0665696i
\(653\) 6.71929 3.87939i 0.262946 0.151812i −0.362732 0.931894i \(-0.618156\pi\)
0.625678 + 0.780082i \(0.284822\pi\)
\(654\) 0.736482 1.27562i 0.0287987 0.0498808i
\(655\) 0 0
\(656\) 0.326352 + 1.85083i 0.0127419 + 0.0722629i
\(657\) −1.97724 1.14156i −0.0771394 0.0445365i
\(658\) 5.59753 3.23173i 0.218214 0.125986i
\(659\) −22.2049 + 18.6321i −0.864979 + 0.725803i −0.963035 0.269378i \(-0.913182\pi\)
0.0980561 + 0.995181i \(0.468738\pi\)
\(660\) 0 0
\(661\) 30.7374 + 11.1875i 1.19555 + 0.435143i 0.861668 0.507472i \(-0.169420\pi\)
0.333879 + 0.942616i \(0.391642\pi\)
\(662\) 14.7687 17.6006i 0.574000 0.684067i
\(663\) 2.59451 + 0.457482i 0.100762 + 0.0177671i
\(664\) −1.50980 −0.0585916
\(665\) 0 0
\(666\) 18.5817 0.720027
\(667\) −23.5781 4.15745i −0.912947 0.160977i
\(668\) −2.51730 + 3.00000i −0.0973972 + 0.116073i
\(669\) 3.65270 + 1.32948i 0.141222 + 0.0514005i
\(670\) 0 0
\(671\) 17.1780 14.4140i 0.663149 0.556448i
\(672\) 0.528981 0.305407i 0.0204059 0.0117813i
\(673\) 28.4441 + 16.4222i 1.09644 + 0.633030i 0.935284 0.353899i \(-0.115144\pi\)
0.161156 + 0.986929i \(0.448478\pi\)
\(674\) −0.227864 1.29228i −0.00877698 0.0497767i
\(675\) 0 0
\(676\) 5.93376 10.2776i 0.228222 0.395291i
\(677\) −21.3404 + 12.3209i −0.820178 + 0.473530i −0.850478 0.526011i \(-0.823687\pi\)
0.0302996 + 0.999541i \(0.490354\pi\)
\(678\) 2.33034 + 2.77719i 0.0894961 + 0.106657i
\(679\) −3.10607 + 1.13052i −0.119200 + 0.0433852i
\(680\) 0 0
\(681\) −0.903733 0.758322i −0.0346311 0.0290590i
\(682\) 36.7252 + 6.47565i 1.40628 + 0.247966i
\(683\) 29.9905i 1.14755i 0.819011 + 0.573777i \(0.194523\pi\)
−0.819011 + 0.573777i \(0.805477\pi\)
\(684\) −3.31908 12.1041i −0.126908 0.462813i
\(685\) 0 0
\(686\) 3.33099 18.8910i 0.127178 0.721262i
\(687\) 0.950259 1.13247i 0.0362546 0.0432066i
\(688\) 1.26363 3.47178i 0.0481753 0.132360i
\(689\) −9.88713 + 3.59862i −0.376670 + 0.137096i
\(690\) 0 0
\(691\) −11.2365 19.4622i −0.427456 0.740375i 0.569190 0.822206i \(-0.307257\pi\)
−0.996646 + 0.0818304i \(0.973923\pi\)
\(692\) 6.53558 + 3.77332i 0.248445 + 0.143440i
\(693\) −21.0795 + 3.71688i −0.800743 + 0.141193i
\(694\) −0.419625 2.37981i −0.0159288 0.0903365i
\(695\) 0 0
\(696\) −1.10607 1.91576i −0.0419254 0.0726168i
\(697\) −8.61138 10.2626i −0.326179 0.388725i
\(698\) 2.90647 + 7.98545i 0.110011 + 0.302254i
\(699\) 2.16802 + 0.789096i 0.0820022 + 0.0298463i
\(700\) 0 0
\(701\) −0.837496 + 4.74968i −0.0316318 + 0.179393i −0.996530 0.0832300i \(-0.973476\pi\)
0.964899 + 0.262623i \(0.0845875\pi\)
\(702\) 2.17293i 0.0820121i
\(703\) −12.0366 25.4243i −0.453967 0.958894i
\(704\) −4.22668 −0.159299
\(705\) 0 0
\(706\) −2.94175 2.46842i −0.110714 0.0929003i
\(707\) −1.47578 + 4.05468i −0.0555026 + 0.152492i
\(708\) 0.866025 + 2.37939i 0.0325472 + 0.0894228i
\(709\) 31.6955 26.5957i 1.19035 0.998823i 0.190497 0.981688i \(-0.438990\pi\)
0.999853 0.0171349i \(-0.00545448\pi\)
\(710\) 0 0
\(711\) −9.63816 + 16.6938i −0.361459 + 0.626065i
\(712\) 11.7258 2.06758i 0.439444 0.0774859i
\(713\) 32.6596 5.75877i 1.22311 0.215668i
\(714\) −2.17705 + 3.77076i −0.0814741 + 0.141117i
\(715\) 0 0
\(716\) −8.41740 + 7.06304i −0.314573 + 0.263958i
\(717\) 1.90236 + 5.22668i 0.0710448 + 0.195194i
\(718\) −8.18329 + 22.4834i −0.305398 + 0.839073i
\(719\) −17.4730 14.6616i −0.651632 0.546784i 0.255934 0.966694i \(-0.417617\pi\)
−0.907566 + 0.419910i \(0.862061\pi\)
\(720\) 0 0
\(721\) 13.0743 0.486912
\(722\) −14.4114 + 12.3819i −0.536337 + 0.460807i
\(723\) 2.98814i 0.111130i
\(724\) 2.61081 14.8067i 0.0970302 0.550285i
\(725\) 0 0
\(726\) −2.24035 0.815422i −0.0831473 0.0302631i
\(727\) 3.08672 + 8.48070i 0.114480 + 0.314532i 0.983679 0.179930i \(-0.0575872\pi\)
−0.869199 + 0.494462i \(0.835365\pi\)
\(728\) −1.20307 1.43376i −0.0445887 0.0531388i
\(729\) −10.3516 17.9296i −0.383394 0.664058i
\(730\) 0 0
\(731\) 4.57326 + 25.9363i 0.169148 + 0.959287i
\(732\) 1.81456 0.319955i 0.0670679 0.0118259i
\(733\) −25.0386 14.4561i −0.924822 0.533946i −0.0396520 0.999214i \(-0.512625\pi\)
−0.885170 + 0.465267i \(0.845958\pi\)
\(734\) 8.55438 + 14.8166i 0.315748 + 0.546891i
\(735\) 0 0
\(736\) −3.53209 + 1.28558i −0.130195 + 0.0473869i
\(737\) 16.8242 46.2242i 0.619729 1.70269i
\(738\) 3.47843 4.14543i 0.128043 0.152595i
\(739\) 1.05685 5.99368i 0.0388768 0.220481i −0.959180 0.282797i \(-0.908738\pi\)
0.998056 + 0.0623162i \(0.0198487\pi\)
\(740\) 0 0
\(741\) 1.45605 0.689335i 0.0534894 0.0253234i
\(742\) 17.3892i 0.638377i
\(743\) −28.9526 5.10513i −1.06217 0.187289i −0.384851 0.922979i \(-0.625747\pi\)
−0.677319 + 0.735690i \(0.736858\pi\)
\(744\) 2.34730 + 1.96962i 0.0860561 + 0.0722096i
\(745\) 0 0
\(746\) 3.72193 1.35467i 0.136270 0.0495981i
\(747\) 2.79439 + 3.33022i 0.102241 + 0.121846i
\(748\) 26.0927 15.0646i 0.954045 0.550818i
\(749\) 0.155697 0.269675i 0.00568903 0.00985369i
\(750\) 0 0
\(751\) −6.67736 37.8692i −0.243660 1.38187i −0.823584 0.567195i \(-0.808029\pi\)
0.579924 0.814671i \(-0.303082\pi\)
\(752\) −3.18264 1.83750i −0.116059 0.0670066i
\(753\) −5.98810 + 3.45723i −0.218219 + 0.125989i
\(754\) −5.19253 + 4.35705i −0.189101 + 0.158675i
\(755\) 0 0
\(756\) −3.37464 1.22827i −0.122734 0.0446717i
\(757\) −4.88603 + 5.82295i −0.177586 + 0.211639i −0.847493 0.530806i \(-0.821889\pi\)
0.669907 + 0.742445i \(0.266334\pi\)
\(758\) −26.8772 4.73917i −0.976223 0.172134i
\(759\) −5.51754 −0.200274
\(760\) 0 0
\(761\) −2.89992 −0.105122 −0.0525610 0.998618i \(-0.516738\pi\)
−0.0525610 + 0.998618i \(0.516738\pi\)
\(762\) 7.52974 + 1.32770i 0.272774 + 0.0480974i
\(763\) 4.79478 5.71419i 0.173583 0.206868i
\(764\) 4.26352 + 1.55179i 0.154249 + 0.0561419i
\(765\) 0 0
\(766\) 4.90941 4.11949i 0.177384 0.148843i
\(767\) 6.71929 3.87939i 0.242620 0.140076i
\(768\) −0.300767 0.173648i −0.0108530 0.00626599i
\(769\) 2.94521 + 16.7031i 0.106207 + 0.602330i 0.990731 + 0.135836i \(0.0433720\pi\)
−0.884524 + 0.466494i \(0.845517\pi\)
\(770\) 0 0
\(771\) −4.58734 + 7.94551i −0.165209 + 0.286151i
\(772\) −19.0490 + 10.9979i −0.685588 + 0.395825i
\(773\) −30.8451 36.7597i −1.10942 1.32215i −0.941751 0.336311i \(-0.890821\pi\)
−0.167669 0.985843i \(-0.553624\pi\)
\(774\) −9.99660 + 3.63846i −0.359320 + 0.130782i
\(775\) 0 0
\(776\) 1.43969 + 1.20805i 0.0516820 + 0.0433663i
\(777\) −3.88192 0.684488i −0.139263 0.0245559i
\(778\) 25.4338i 0.911845i
\(779\) −7.92514 2.07407i −0.283948 0.0743113i
\(780\) 0 0
\(781\) 2.07192 11.7504i 0.0741391 0.420464i
\(782\) 17.2228 20.5253i 0.615885 0.733983i
\(783\) −4.44831 + 12.2216i −0.158970 + 0.436765i
\(784\) −3.67112 + 1.33618i −0.131111 + 0.0477207i
\(785\) 0 0
\(786\) 1.32888 + 2.30168i 0.0473995 + 0.0820984i
\(787\) 43.8059 + 25.2913i 1.56151 + 0.901538i 0.997105 + 0.0760408i \(0.0242279\pi\)
0.564406 + 0.825498i \(0.309105\pi\)
\(788\) −15.6897 + 2.76651i −0.558921 + 0.0985529i
\(789\) 1.68510 + 9.55666i 0.0599910 + 0.340226i
\(790\) 0 0
\(791\) 9.17974 + 15.8998i 0.326394 + 0.565331i
\(792\) 7.82288 + 9.32295i 0.277974 + 0.331277i
\(793\) −1.93101 5.30541i −0.0685722 0.188401i
\(794\) 21.2199 + 7.72340i 0.753065 + 0.274093i
\(795\) 0 0
\(796\) −0.568926 + 3.22654i −0.0201650 + 0.114362i
\(797\) 3.87702i 0.137331i 0.997640 + 0.0686656i \(0.0218741\pi\)
−0.997640 + 0.0686656i \(0.978126\pi\)
\(798\) 0.247516 + 2.65095i 0.00876197 + 0.0938426i
\(799\) 26.1967 0.926771
\(800\) 0 0
\(801\) −26.2631 22.0374i −0.927961 0.778652i
\(802\) −0.261243 + 0.717759i −0.00922480 + 0.0253449i
\(803\) −1.14625 3.14930i −0.0404503 0.111136i
\(804\) 3.09627 2.59808i 0.109197 0.0916271i
\(805\) 0 0
\(806\) 4.69459 8.13127i 0.165360 0.286412i
\(807\) 4.98724 0.879385i 0.175559 0.0309558i
\(808\) 2.41609 0.426022i 0.0849978 0.0149874i
\(809\) −8.65317 + 14.9877i −0.304229 + 0.526941i −0.977089 0.212829i \(-0.931732\pi\)
0.672860 + 0.739770i \(0.265066\pi\)
\(810\) 0 0
\(811\) 37.5330 31.4939i 1.31796 1.10590i 0.331230 0.943550i \(-0.392536\pi\)
0.986733 0.162352i \(-0.0519080\pi\)
\(812\) −3.83153 10.5270i −0.134460 0.369427i
\(813\) −2.16512 + 5.94862i −0.0759340 + 0.208627i
\(814\) 20.8949 + 17.5329i 0.732365 + 0.614527i
\(815\) 0 0
\(816\) 2.47565 0.0866652
\(817\) 11.4537 + 11.3209i 0.400715 + 0.396068i
\(818\) 16.8239i 0.588233i
\(819\) −0.935822 + 5.30731i −0.0327003 + 0.185452i
\(820\) 0 0
\(821\) 26.8307 + 9.76557i 0.936398 + 0.340821i 0.764742 0.644336i \(-0.222866\pi\)
0.171655 + 0.985157i \(0.445088\pi\)
\(822\) −0.681393 1.87211i −0.0237663 0.0652974i
\(823\) 30.2535 + 36.0547i 1.05457 + 1.25679i 0.965401 + 0.260771i \(0.0839767\pi\)
0.0891689 + 0.996017i \(0.471579\pi\)
\(824\) −3.71688 6.43783i −0.129484 0.224272i
\(825\) 0 0
\(826\) 2.22668 + 12.6281i 0.0774762 + 0.439389i
\(827\) 24.3929 4.30113i 0.848224 0.149565i 0.267392 0.963588i \(-0.413838\pi\)
0.580833 + 0.814023i \(0.302727\pi\)
\(828\) 9.37295 + 5.41147i 0.325732 + 0.188062i
\(829\) −17.2959 29.9574i −0.600712 1.04046i −0.992713 0.120499i \(-0.961551\pi\)
0.392002 0.919965i \(-0.371783\pi\)
\(830\) 0 0
\(831\) 5.37464 1.95621i 0.186444 0.0678601i
\(832\) −0.363970 + 1.00000i −0.0126184 + 0.0346688i
\(833\) 17.9007 21.3332i 0.620222 0.739152i
\(834\) 1.16978 6.63414i 0.0405061 0.229721i
\(835\) 0 0
\(836\) 7.68866 16.7427i 0.265918 0.579057i
\(837\) 18.0155i 0.622706i
\(838\) 35.3478 + 6.23277i 1.22107 + 0.215308i
\(839\) −5.15207 4.32310i −0.177869 0.149250i 0.549506 0.835490i \(-0.314816\pi\)
−0.727376 + 0.686239i \(0.759260\pi\)
\(840\) 0 0
\(841\) −10.8738 + 3.95773i −0.374957 + 0.136473i
\(842\) −13.3122 15.8648i −0.458768 0.546738i
\(843\) −2.15658 + 1.24510i −0.0742764 + 0.0428835i
\(844\) 5.73442 9.93231i 0.197387 0.341884i
\(845\) 0 0
\(846\) 1.83750 + 10.4210i 0.0631744 + 0.358280i
\(847\) −10.4561 6.03684i −0.359276 0.207428i
\(848\) −8.56250 + 4.94356i −0.294038 + 0.169763i
\(849\) −5.57011 + 4.67388i −0.191166 + 0.160407i
\(850\) 0 0
\(851\) 22.7939 + 8.29628i 0.781363 + 0.284393i
\(852\) 0.630189 0.751030i 0.0215899 0.0257299i
\(853\) 21.3270 + 3.76053i 0.730223 + 0.128758i 0.526384 0.850247i \(-0.323547\pi\)
0.203838 + 0.979005i \(0.434658\pi\)
\(854\) 9.33099 0.319300
\(855\) 0 0
\(856\) −0.177052 −0.00605150
\(857\) 37.8911 + 6.68123i 1.29434 + 0.228226i 0.778057 0.628194i \(-0.216206\pi\)
0.516279 + 0.856420i \(0.327317\pi\)
\(858\) −1.00411 + 1.19665i −0.0342798 + 0.0408530i
\(859\) −15.5731 5.66815i −0.531347 0.193395i 0.0623925 0.998052i \(-0.480127\pi\)
−0.593740 + 0.804657i \(0.702349\pi\)
\(860\) 0 0
\(861\) −0.879385 + 0.737892i −0.0299694 + 0.0251473i
\(862\) 15.8699 9.16250i 0.540532 0.312076i
\(863\) 22.3937 + 12.9290i 0.762291 + 0.440109i 0.830118 0.557588i \(-0.188273\pi\)
−0.0678268 + 0.997697i \(0.521607\pi\)
\(864\) 0.354570 + 2.01087i 0.0120627 + 0.0684111i
\(865\) 0 0
\(866\) −2.54664 + 4.41090i −0.0865382 + 0.149889i
\(867\) −10.1700 + 5.87164i −0.345391 + 0.199412i
\(868\) 9.97448 + 11.8871i 0.338556 + 0.403475i
\(869\) −26.5895 + 9.67777i −0.901986 + 0.328296i
\(870\) 0 0
\(871\) −9.48751 7.96097i −0.321472 0.269747i
\(872\) −4.17680 0.736482i −0.141444 0.0249404i
\(873\) 5.41147i 0.183151i
\(874\) 1.33275 16.3298i 0.0450809 0.552364i
\(875\) 0 0
\(876\) 0.0478189 0.271194i 0.00161565 0.00916280i
\(877\) −32.5397 + 38.7793i −1.09879 + 1.30948i −0.151729 + 0.988422i \(0.548484\pi\)
−0.947058 + 0.321062i \(0.895960\pi\)
\(878\) −3.52670 + 9.68954i −0.119021 + 0.327006i
\(879\) 3.09327 1.12586i 0.104334 0.0379743i
\(880\) 0 0
\(881\) −25.4846 44.1406i −0.858597 1.48713i −0.873267 0.487241i \(-0.838003\pi\)
0.0146701 0.999892i \(-0.495330\pi\)
\(882\) 9.74189 + 5.62449i 0.328027 + 0.189386i
\(883\) −37.5380 + 6.61897i −1.26325 + 0.222746i −0.764856 0.644202i \(-0.777190\pi\)
−0.498399 + 0.866948i \(0.666079\pi\)
\(884\) −1.31727 7.47059i −0.0443045 0.251263i
\(885\) 0 0
\(886\) 4.40807 + 7.63500i 0.148092 + 0.256503i
\(887\) 20.2404 + 24.1215i 0.679606 + 0.809922i 0.990057 0.140667i \(-0.0449247\pi\)
−0.310451 + 0.950589i \(0.600480\pi\)
\(888\) 0.766546 + 2.10607i 0.0257236 + 0.0706750i
\(889\) 36.3851 + 13.2431i 1.22032 + 0.444159i
\(890\) 0 0
\(891\) 5.81954 33.0043i 0.194962 1.10568i
\(892\) 11.1925i 0.374754i
\(893\) 13.0681 9.26445i 0.437308 0.310023i
\(894\) 1.79797 0.0601332
\(895\) 0 0
\(896\) −1.34730 1.13052i −0.0450100 0.0377679i
\(897\) −0.475129 + 1.30541i −0.0158641 + 0.0435863i
\(898\) −4.13057 11.3486i −0.137839 0.378709i
\(899\) 43.0506 36.1237i 1.43582 1.20479i
\(900\) 0 0
\(901\) 35.2395 61.0366i 1.17400 2.03342i
\(902\) 7.82288 1.37939i 0.260473 0.0459285i
\(903\) 2.22243 0.391874i 0.0739577 0.0130407i
\(904\) 5.21941 9.04028i 0.173595 0.300675i
\(905\) 0 0
\(906\) 5.90167 4.95209i 0.196070 0.164522i
\(907\) 3.04596 + 8.36871i 0.101139 + 0.277878i 0.979934 0.199322i \(-0.0638739\pi\)
−0.878795 + 0.477200i \(0.841652\pi\)
\(908\) −1.16182 + 3.19207i −0.0385563 + 0.105932i
\(909\) −5.41147 4.54077i −0.179487 0.150608i
\(910\) 0 0
\(911\) −44.2959 −1.46759 −0.733795 0.679371i \(-0.762253\pi\)
−0.733795 + 0.679371i \(0.762253\pi\)
\(912\) 1.23497 0.875515i 0.0408940 0.0289912i
\(913\) 6.38144i 0.211195i
\(914\) 0.127011 0.720317i 0.00420116 0.0238260i
\(915\) 0 0
\(916\) −4.00000 1.45588i −0.132164 0.0481037i
\(917\) 4.60337 + 12.6477i 0.152017 + 0.417662i
\(918\) −9.35597 11.1500i −0.308793 0.368005i
\(919\) −27.3969 47.4529i −0.903741 1.56533i −0.822598 0.568623i \(-0.807476\pi\)
−0.0811431 0.996702i \(-0.525857\pi\)
\(920\) 0 0
\(921\) 0.0802124 + 0.454907i 0.00264309 + 0.0149897i
\(922\) 22.7290 4.00774i 0.748541 0.131988i
\(923\) −2.60164 1.50206i −0.0856341 0.0494409i
\(924\) −1.29086 2.23583i −0.0424662 0.0735535i
\(925\) 0 0
\(926\) −16.9564 + 6.17161i −0.557220 + 0.202812i
\(927\) −7.32083 + 20.1138i −0.240448 + 0.660624i
\(928\) −4.09429 + 4.87939i −0.134402 + 0.160174i
\(929\) −5.28059 + 29.9477i −0.173251 + 0.982553i 0.766893 + 0.641775i \(0.221802\pi\)
−0.940144 + 0.340778i \(0.889309\pi\)
\(930\) 0 0
\(931\) 1.38521 16.9726i 0.0453984 0.556254i
\(932\) 6.64321i 0.217606i
\(933\) 2.55774 + 0.450999i 0.0837367 + 0.0147650i
\(934\) −8.40554 7.05309i −0.275038 0.230784i
\(935\) 0 0
\(936\) 2.87939 1.04801i 0.0941157 0.0342553i
\(937\) −18.9691 22.6065i −0.619695 0.738523i 0.361323 0.932441i \(-0.382325\pi\)
−0.981018 + 0.193917i \(0.937881\pi\)
\(938\) 17.7265 10.2344i 0.578792 0.334166i
\(939\) 5.08765 8.81207i 0.166029 0.287571i
\(940\) 0 0
\(941\) −2.34905 13.3221i −0.0765769 0.434289i −0.998858 0.0477701i \(-0.984789\pi\)
0.922281 0.386519i \(-0.126323\pi\)
\(942\) −0.849051 0.490200i −0.0276636 0.0159716i
\(943\) 6.11776 3.53209i 0.199222 0.115021i
\(944\) 5.58512 4.68647i 0.181780 0.152532i
\(945\) 0 0
\(946\) −14.6741 5.34094i −0.477097 0.173649i
\(947\) −5.58003 + 6.65002i −0.181326 + 0.216096i −0.849049 0.528313i \(-0.822825\pi\)
0.667723 + 0.744410i \(0.267269\pi\)
\(948\) −2.28969 0.403733i −0.0743655 0.0131126i
\(949\) −0.843807 −0.0273911
\(950\) 0 0
\(951\) 1.94532 0.0630812
\(952\) 12.3467 + 2.17705i 0.400158 + 0.0705587i
\(953\) −26.8930 + 32.0498i −0.871150 + 1.03820i 0.127773 + 0.991803i \(0.459217\pi\)
−0.998923 + 0.0463930i \(0.985227\pi\)
\(954\) 26.7520 + 9.73692i 0.866127 + 0.315244i
\(955\) 0 0
\(956\) 12.2686 10.2946i 0.396794 0.332950i
\(957\) −8.09732 + 4.67499i −0.261749 + 0.151121i
\(958\) −19.3860 11.1925i −0.626334 0.361614i
\(959\) −1.75196 9.93588i −0.0565738 0.320846i
\(960\) 0 0
\(961\) −23.4222 + 40.5685i −0.755555 + 1.30866i
\(962\) 5.94745 3.43376i 0.191754 0.110709i
\(963\) 0.327693 + 0.390530i 0.0105598 + 0.0125846i
\(964\) −8.08512 + 2.94274i −0.260404 + 0.0947794i
\(965\) 0 0
\(966\) −1.75877 1.47578i −0.0565875 0.0474826i
\(967\) 13.8564 + 2.44326i 0.445592 + 0.0785699i 0.391942 0.919990i \(-0.371803\pi\)
0.0536500 + 0.998560i \(0.482914\pi\)
\(968\) 6.86484i 0.220644i
\(969\) −4.50340 + 9.80651i −0.144670 + 0.315030i
\(970\) 0 0
\(971\) 6.49819 36.8531i 0.208537 1.18267i −0.683239 0.730194i \(-0.739429\pi\)
0.891776 0.452477i \(-0.149459\pi\)
\(972\) 5.70756 6.80200i 0.183070 0.218174i
\(973\) 11.6679 32.0574i 0.374057 1.02771i
\(974\) −35.4834 + 12.9149i −1.13696 + 0.413820i
\(975\) 0 0
\(976\) −2.65270 4.59462i −0.0849110 0.147070i
\(977\) 43.0881 + 24.8769i 1.37851 + 0.795883i 0.991980 0.126394i \(-0.0403403\pi\)
0.386530 + 0.922277i \(0.373674\pi\)
\(978\) −0.758922 + 0.133819i −0.0242677 + 0.00427904i
\(979\) −8.73901 49.5614i −0.279300 1.58399i
\(980\) 0 0
\(981\) 6.10607 + 10.5760i 0.194952 + 0.337666i
\(982\) 0.804342 + 0.958578i 0.0256676 + 0.0305894i
\(983\) 7.65430 + 21.0300i 0.244134 + 0.670754i 0.999874 + 0.0158814i \(0.00505541\pi\)
−0.755739 + 0.654872i \(0.772722\pi\)
\(984\) 0.613341 + 0.223238i 0.0195526 + 0.00711656i
\(985\) 0 0
\(986\) 7.88444 44.7149i 0.251092 1.42401i
\(987\) 2.24474i 0.0714508i
\(988\) −3.29909 3.26083i −0.104958 0.103741i
\(989\) −13.8871 −0.441585
\(990\) 0 0
\(991\) 36.8803 + 30.9463i 1.17154 + 0.983040i 0.999998 0.00213601i \(-0.000679914\pi\)
0.171544 + 0.985176i \(0.445124\pi\)
\(992\) 3.01763 8.29086i 0.0958097 0.263235i
\(993\) −2.72914 7.49825i −0.0866066 0.237950i
\(994\) 3.80335 3.19139i 0.120635 0.101225i
\(995\) 0 0
\(996\) −0.262174 + 0.454099i −0.00830730 + 0.0143887i
\(997\) −42.0039 + 7.40642i −1.33028 + 0.234564i −0.793196 0.608967i \(-0.791584\pi\)
−0.537081 + 0.843530i \(0.680473\pi\)
\(998\) 9.18832 1.62015i 0.290851 0.0512849i
\(999\) 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 950.2.u.b.549.1 12
5.2 odd 4 38.2.e.a.17.1 yes 6
5.3 odd 4 950.2.l.d.701.1 6
5.4 even 2 inner 950.2.u.b.549.2 12
15.2 even 4 342.2.u.c.55.1 6
19.9 even 9 inner 950.2.u.b.199.2 12
20.7 even 4 304.2.u.c.17.1 6
95.2 even 36 722.2.c.l.429.2 6
95.7 odd 12 722.2.e.b.415.1 6
95.9 even 18 inner 950.2.u.b.199.1 12
95.12 even 12 722.2.e.l.415.1 6
95.17 odd 36 722.2.c.k.429.2 6
95.22 even 36 722.2.a.k.1.2 3
95.27 even 12 722.2.e.a.423.1 6
95.28 odd 36 950.2.l.d.351.1 6
95.32 even 36 722.2.e.a.99.1 6
95.37 even 4 722.2.e.k.245.1 6
95.42 odd 36 722.2.e.b.595.1 6
95.47 odd 36 38.2.e.a.9.1 6
95.52 even 36 722.2.c.l.653.2 6
95.62 odd 36 722.2.c.k.653.2 6
95.67 even 36 722.2.e.k.389.1 6
95.72 even 36 722.2.e.l.595.1 6
95.82 odd 36 722.2.e.m.99.1 6
95.87 odd 12 722.2.e.m.423.1 6
95.92 odd 36 722.2.a.l.1.2 3
285.47 even 36 342.2.u.c.199.1 6
285.92 even 36 6498.2.a.bl.1.1 3
285.212 odd 36 6498.2.a.bq.1.1 3
380.47 even 36 304.2.u.c.161.1 6
380.187 even 36 5776.2.a.bn.1.2 3
380.307 odd 36 5776.2.a.bo.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.e.a.9.1 6 95.47 odd 36
38.2.e.a.17.1 yes 6 5.2 odd 4
304.2.u.c.17.1 6 20.7 even 4
304.2.u.c.161.1 6 380.47 even 36
342.2.u.c.55.1 6 15.2 even 4
342.2.u.c.199.1 6 285.47 even 36
722.2.a.k.1.2 3 95.22 even 36
722.2.a.l.1.2 3 95.92 odd 36
722.2.c.k.429.2 6 95.17 odd 36
722.2.c.k.653.2 6 95.62 odd 36
722.2.c.l.429.2 6 95.2 even 36
722.2.c.l.653.2 6 95.52 even 36
722.2.e.a.99.1 6 95.32 even 36
722.2.e.a.423.1 6 95.27 even 12
722.2.e.b.415.1 6 95.7 odd 12
722.2.e.b.595.1 6 95.42 odd 36
722.2.e.k.245.1 6 95.37 even 4
722.2.e.k.389.1 6 95.67 even 36
722.2.e.l.415.1 6 95.12 even 12
722.2.e.l.595.1 6 95.72 even 36
722.2.e.m.99.1 6 95.82 odd 36
722.2.e.m.423.1 6 95.87 odd 12
950.2.l.d.351.1 6 95.28 odd 36
950.2.l.d.701.1 6 5.3 odd 4
950.2.u.b.199.1 12 95.9 even 18 inner
950.2.u.b.199.2 12 19.9 even 9 inner
950.2.u.b.549.1 12 1.1 even 1 trivial
950.2.u.b.549.2 12 5.4 even 2 inner
5776.2.a.bn.1.2 3 380.187 even 36
5776.2.a.bo.1.2 3 380.307 odd 36
6498.2.a.bl.1.1 3 285.92 even 36
6498.2.a.bq.1.1 3 285.212 odd 36