Properties

Label 105.4.x.a.2.19
Level $105$
Weight $4$
Character 105.2
Analytic conductor $6.195$
Analytic rank $0$
Dimension $176$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,4,Mod(2,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.2");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.x (of order \(12\), degree \(4\), 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: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(176\)
Relative dimension: \(44\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 2.19
Character \(\chi\) \(=\) 105.2
Dual form 105.4.x.a.53.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.212644 - 0.793597i) q^{2} +(5.02395 - 1.32663i) q^{3} +(6.34362 - 3.66249i) q^{4} +(10.8037 - 2.87737i) q^{5} +(-2.12112 - 3.70489i) q^{6} +(4.51416 + 17.9617i) q^{7} +(-8.90311 - 8.90311i) q^{8} +(23.4801 - 13.3299i) q^{9} +O(q^{10})\) \(q+(-0.212644 - 0.793597i) q^{2} +(5.02395 - 1.32663i) q^{3} +(6.34362 - 3.66249i) q^{4} +(10.8037 - 2.87737i) q^{5} +(-2.12112 - 3.70489i) q^{6} +(4.51416 + 17.9617i) q^{7} +(-8.90311 - 8.90311i) q^{8} +(23.4801 - 13.3299i) q^{9} +(-4.58082 - 7.96196i) q^{10} +(-36.3672 + 20.9966i) q^{11} +(27.0113 - 26.8158i) q^{12} +(-35.7320 + 35.7320i) q^{13} +(13.2944 - 7.40187i) q^{14} +(50.4602 - 28.7883i) q^{15} +(24.1277 - 41.7903i) q^{16} +(-43.2578 - 11.5909i) q^{17} +(-15.5714 - 15.7992i) q^{18} +(-14.4788 - 8.35932i) q^{19} +(57.9965 - 57.8216i) q^{20} +(46.5075 + 84.2500i) q^{21} +(24.3961 + 24.3961i) q^{22} +(62.4977 - 16.7462i) q^{23} +(-56.5399 - 32.9176i) q^{24} +(108.441 - 62.1727i) q^{25} +(35.9550 + 20.7586i) q^{26} +(100.279 - 98.1179i) q^{27} +(94.4207 + 97.4091i) q^{28} -159.202 q^{29} +(-33.5764 - 33.9234i) q^{30} +(-101.058 - 175.037i) q^{31} +(-135.590 - 36.3313i) q^{32} +(-154.852 + 153.732i) q^{33} +36.7940i q^{34} +(100.452 + 181.064i) q^{35} +(100.128 - 170.555i) q^{36} +(-160.362 + 42.9689i) q^{37} +(-3.55511 + 13.2679i) q^{38} +(-132.112 + 226.919i) q^{39} +(-121.804 - 70.5693i) q^{40} +386.741i q^{41} +(56.9710 - 54.8234i) q^{42} +(231.567 - 231.567i) q^{43} +(-153.800 + 266.389i) q^{44} +(215.318 - 211.573i) q^{45} +(-26.5795 - 46.0370i) q^{46} +(90.3055 + 337.025i) q^{47} +(65.7757 - 241.961i) q^{48} +(-302.245 + 162.164i) q^{49} +(-72.3995 - 72.8382i) q^{50} +(-232.702 - 0.844857i) q^{51} +(-95.8022 + 357.539i) q^{52} +(-103.768 + 387.266i) q^{53} +(-99.1898 - 58.7169i) q^{54} +(-332.487 + 331.484i) q^{55} +(119.725 - 200.105i) q^{56} +(-83.8303 - 22.7888i) q^{57} +(33.8534 + 126.343i) q^{58} +(-304.751 - 527.843i) q^{59} +(214.663 - 367.433i) q^{60} +(177.870 - 308.079i) q^{61} +(-117.420 + 117.420i) q^{62} +(345.420 + 361.569i) q^{63} -270.713i q^{64} +(-283.225 + 488.853i) q^{65} +(154.930 + 90.2002i) q^{66} +(-4.36445 + 16.2884i) q^{67} +(-316.863 + 84.9031i) q^{68} +(291.769 - 167.043i) q^{69} +(122.332 - 118.221i) q^{70} -38.2179i q^{71} +(-327.723 - 90.3686i) q^{72} +(1017.83 + 272.726i) q^{73} +(68.2000 + 118.126i) q^{74} +(462.324 - 456.214i) q^{75} -122.464 q^{76} +(-541.302 - 558.435i) q^{77} +(208.175 + 56.5912i) q^{78} +(-206.647 - 119.308i) q^{79} +(140.423 - 520.916i) q^{80} +(373.630 - 625.973i) q^{81} +(306.917 - 82.2381i) q^{82} +(783.711 + 783.711i) q^{83} +(603.591 + 364.117i) q^{84} +(-500.697 - 0.756243i) q^{85} +(-233.012 - 134.530i) q^{86} +(-799.825 + 211.203i) q^{87} +(510.716 + 136.846i) q^{88} +(448.039 - 776.027i) q^{89} +(-213.690 - 125.886i) q^{90} +(-803.107 - 480.507i) q^{91} +(335.129 - 335.129i) q^{92} +(-739.920 - 745.312i) q^{93} +(248.259 - 143.332i) q^{94} +(-180.478 - 48.6511i) q^{95} +(-729.396 - 2.64818i) q^{96} +(569.267 + 569.267i) q^{97} +(192.963 + 205.377i) q^{98} +(-574.024 + 977.773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 176 q - 2 q^{3} + 4 q^{7} - 28 q^{10} - 94 q^{12} - 16 q^{13} - 176 q^{15} + 1016 q^{16} + 14 q^{18} - 148 q^{21} - 32 q^{22} - 76 q^{25} - 32 q^{27} + 776 q^{28} - 500 q^{30} - 296 q^{31} - 430 q^{33} - 880 q^{36} + 212 q^{37} - 1296 q^{40} - 910 q^{42} - 1360 q^{43} + 490 q^{45} + 1000 q^{46} + 1604 q^{48} - 268 q^{51} + 68 q^{52} + 1240 q^{55} + 3548 q^{57} - 1572 q^{58} - 470 q^{60} - 608 q^{61} - 2974 q^{63} - 92 q^{66} - 1012 q^{67} - 6720 q^{70} + 866 q^{72} + 2804 q^{73} + 4086 q^{75} - 8256 q^{76} + 6888 q^{78} - 2992 q^{81} - 1112 q^{82} + 4736 q^{85} - 52 q^{87} + 1284 q^{88} - 5724 q^{90} - 4192 q^{91} + 3034 q^{93} - 1824 q^{96} + 7496 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.212644 0.793597i −0.0751809 0.280579i 0.918093 0.396364i \(-0.129728\pi\)
−0.993274 + 0.115785i \(0.963062\pi\)
\(3\) 5.02395 1.32663i 0.966859 0.255310i
\(4\) 6.34362 3.66249i 0.792953 0.457812i
\(5\) 10.8037 2.87737i 0.966316 0.257360i
\(6\) −2.12112 3.70489i −0.144324 0.252086i
\(7\) 4.51416 + 17.9617i 0.243742 + 0.969840i
\(8\) −8.90311 8.90311i −0.393465 0.393465i
\(9\) 23.4801 13.3299i 0.869633 0.493698i
\(10\) −4.58082 7.96196i −0.144858 0.251779i
\(11\) −36.3672 + 20.9966i −0.996830 + 0.575520i −0.907309 0.420465i \(-0.861867\pi\)
−0.0895211 + 0.995985i \(0.528534\pi\)
\(12\) 27.0113 26.8158i 0.649790 0.645089i
\(13\) −35.7320 + 35.7320i −0.762329 + 0.762329i −0.976743 0.214414i \(-0.931216\pi\)
0.214414 + 0.976743i \(0.431216\pi\)
\(14\) 13.2944 7.40187i 0.253792 0.141302i
\(15\) 50.4602 28.7883i 0.868584 0.495541i
\(16\) 24.1277 41.7903i 0.376995 0.652974i
\(17\) −43.2578 11.5909i −0.617151 0.165365i −0.0633185 0.997993i \(-0.520168\pi\)
−0.553832 + 0.832628i \(0.686835\pi\)
\(18\) −15.5714 15.7992i −0.203901 0.206884i
\(19\) −14.4788 8.35932i −0.174824 0.100935i 0.410035 0.912070i \(-0.365517\pi\)
−0.584859 + 0.811135i \(0.698850\pi\)
\(20\) 57.9965 57.8216i 0.648421 0.646465i
\(21\) 46.5075 + 84.2500i 0.483274 + 0.875469i
\(22\) 24.3961 + 24.3961i 0.236421 + 0.236421i
\(23\) 62.4977 16.7462i 0.566594 0.151818i 0.0358601 0.999357i \(-0.488583\pi\)
0.530734 + 0.847538i \(0.321916\pi\)
\(24\) −56.5399 32.9176i −0.480881 0.279970i
\(25\) 108.441 62.1727i 0.867532 0.497382i
\(26\) 35.9550 + 20.7586i 0.271206 + 0.156581i
\(27\) 100.279 98.1179i 0.714766 0.699363i
\(28\) 94.4207 + 97.4091i 0.637280 + 0.657450i
\(29\) −159.202 −1.01942 −0.509710 0.860347i \(-0.670247\pi\)
−0.509710 + 0.860347i \(0.670247\pi\)
\(30\) −33.5764 33.9234i −0.204339 0.206451i
\(31\) −101.058 175.037i −0.585501 1.01412i −0.994813 0.101723i \(-0.967564\pi\)
0.409311 0.912395i \(-0.365769\pi\)
\(32\) −135.590 36.3313i −0.749037 0.200704i
\(33\) −154.852 + 153.732i −0.816858 + 0.810948i
\(34\) 36.7940i 0.185592i
\(35\) 100.452 + 181.064i 0.485129 + 0.874442i
\(36\) 100.128 170.555i 0.463557 0.789608i
\(37\) −160.362 + 42.9689i −0.712523 + 0.190920i −0.596833 0.802365i \(-0.703575\pi\)
−0.115690 + 0.993285i \(0.536908\pi\)
\(38\) −3.55511 + 13.2679i −0.0151767 + 0.0566403i
\(39\) −132.112 + 226.919i −0.542434 + 0.931695i
\(40\) −121.804 70.5693i −0.481474 0.278950i
\(41\) 386.741i 1.47314i 0.676360 + 0.736571i \(0.263556\pi\)
−0.676360 + 0.736571i \(0.736444\pi\)
\(42\) 56.9710 54.8234i 0.209305 0.201415i
\(43\) 231.567 231.567i 0.821246 0.821246i −0.165040 0.986287i \(-0.552775\pi\)
0.986287 + 0.165040i \(0.0527755\pi\)
\(44\) −153.800 + 266.389i −0.526960 + 0.912721i
\(45\) 215.318 211.573i 0.713282 0.700877i
\(46\) −26.5795 46.0370i −0.0851942 0.147561i
\(47\) 90.3055 + 337.025i 0.280264 + 1.04596i 0.952231 + 0.305379i \(0.0987831\pi\)
−0.671967 + 0.740581i \(0.734550\pi\)
\(48\) 65.7757 241.961i 0.197790 0.727584i
\(49\) −302.245 + 162.164i −0.881180 + 0.472781i
\(50\) −72.3995 72.8382i −0.204777 0.206018i
\(51\) −232.702 0.844857i −0.638917 0.00231968i
\(52\) −95.8022 + 357.539i −0.255488 + 0.953494i
\(53\) −103.768 + 387.266i −0.268935 + 1.00368i 0.690862 + 0.722986i \(0.257231\pi\)
−0.959797 + 0.280694i \(0.909436\pi\)
\(54\) −99.1898 58.7169i −0.249963 0.147970i
\(55\) −332.487 + 331.484i −0.815137 + 0.812678i
\(56\) 119.725 200.105i 0.285695 0.477503i
\(57\) −83.8303 22.7888i −0.194800 0.0529552i
\(58\) 33.8534 + 126.343i 0.0766409 + 0.286028i
\(59\) −304.751 527.843i −0.672460 1.16473i −0.977204 0.212301i \(-0.931904\pi\)
0.304744 0.952434i \(-0.401429\pi\)
\(60\) 214.663 367.433i 0.461882 0.790589i
\(61\) 177.870 308.079i 0.373342 0.646648i −0.616735 0.787171i \(-0.711545\pi\)
0.990077 + 0.140523i \(0.0448783\pi\)
\(62\) −117.420 + 117.420i −0.240522 + 0.240522i
\(63\) 345.420 + 361.569i 0.690775 + 0.723070i
\(64\) 270.713i 0.528736i
\(65\) −283.225 + 488.853i −0.540457 + 0.932843i
\(66\) 154.930 + 90.2002i 0.288947 + 0.168225i
\(67\) −4.36445 + 16.2884i −0.00795825 + 0.0297006i −0.969791 0.243938i \(-0.921561\pi\)
0.961833 + 0.273639i \(0.0882273\pi\)
\(68\) −316.863 + 84.9031i −0.565077 + 0.151412i
\(69\) 291.769 167.043i 0.509056 0.291445i
\(70\) 122.332 118.221i 0.208878 0.201859i
\(71\) 38.2179i 0.0638821i −0.999490 0.0319410i \(-0.989831\pi\)
0.999490 0.0319410i \(-0.0101689\pi\)
\(72\) −327.723 90.3686i −0.536424 0.147917i
\(73\) 1017.83 + 272.726i 1.63188 + 0.437262i 0.954462 0.298332i \(-0.0964302\pi\)
0.677423 + 0.735594i \(0.263097\pi\)
\(74\) 68.2000 + 118.126i 0.107136 + 0.185566i
\(75\) 462.324 456.214i 0.711794 0.702388i
\(76\) −122.464 −0.184836
\(77\) −541.302 558.435i −0.801132 0.826487i
\(78\) 208.175 + 56.5912i 0.302195 + 0.0821499i
\(79\) −206.647 119.308i −0.294299 0.169914i 0.345580 0.938389i \(-0.387682\pi\)
−0.639879 + 0.768476i \(0.721016\pi\)
\(80\) 140.423 520.916i 0.196247 0.728002i
\(81\) 373.630 625.973i 0.512524 0.858673i
\(82\) 306.917 82.2381i 0.413333 0.110752i
\(83\) 783.711 + 783.711i 1.03643 + 1.03643i 0.999311 + 0.0371156i \(0.0118170\pi\)
0.0371156 + 0.999311i \(0.488183\pi\)
\(84\) 603.591 + 364.117i 0.784014 + 0.472957i
\(85\) −500.697 0.756243i −0.638921 0.000965012i
\(86\) −233.012 134.530i −0.292167 0.168682i
\(87\) −799.825 + 211.203i −0.985635 + 0.260268i
\(88\) 510.716 + 136.846i 0.618665 + 0.165771i
\(89\) 448.039 776.027i 0.533619 0.924255i −0.465610 0.884990i \(-0.654165\pi\)
0.999229 0.0392649i \(-0.0125016\pi\)
\(90\) −213.690 125.886i −0.250277 0.147439i
\(91\) −803.107 480.507i −0.925148 0.553526i
\(92\) 335.129 335.129i 0.379778 0.379778i
\(93\) −739.920 745.312i −0.825012 0.831025i
\(94\) 248.259 143.332i 0.272404 0.157272i
\(95\) −180.478 48.6511i −0.194912 0.0525421i
\(96\) −729.396 2.64818i −0.775455 0.00281540i
\(97\) 569.267 + 569.267i 0.595880 + 0.595880i 0.939213 0.343334i \(-0.111556\pi\)
−0.343334 + 0.939213i \(0.611556\pi\)
\(98\) 192.963 + 205.377i 0.198900 + 0.211696i
\(99\) −574.024 + 977.773i −0.582743 + 0.992625i
\(100\) 460.205 791.566i 0.460205 0.791566i
\(101\) 1369.68 790.784i 1.34939 0.779069i 0.361224 0.932479i \(-0.382359\pi\)
0.988163 + 0.153410i \(0.0490256\pi\)
\(102\) 48.8121 + 184.851i 0.0473835 + 0.179441i
\(103\) 268.902 + 1003.56i 0.257240 + 0.960033i 0.966830 + 0.255419i \(0.0822134\pi\)
−0.709590 + 0.704615i \(0.751120\pi\)
\(104\) 636.251 0.599900
\(105\) 744.873 + 776.395i 0.692306 + 0.721604i
\(106\) 329.399 0.301830
\(107\) −42.6284 159.091i −0.0385144 0.143738i 0.943991 0.329970i \(-0.107039\pi\)
−0.982506 + 0.186233i \(0.940372\pi\)
\(108\) 276.776 989.694i 0.246600 0.881791i
\(109\) −1396.54 + 806.290i −1.22719 + 0.708519i −0.966441 0.256887i \(-0.917303\pi\)
−0.260750 + 0.965406i \(0.583970\pi\)
\(110\) 333.766 + 193.373i 0.289303 + 0.167612i
\(111\) −748.647 + 428.615i −0.640166 + 0.366507i
\(112\) 859.541 + 244.725i 0.725170 + 0.206467i
\(113\) −524.716 524.716i −0.436824 0.436824i 0.454118 0.890942i \(-0.349955\pi\)
−0.890942 + 0.454118i \(0.849955\pi\)
\(114\) −0.259131 + 71.3734i −0.000212893 + 0.0586380i
\(115\) 627.024 360.751i 0.508437 0.292523i
\(116\) −1009.92 + 583.078i −0.808351 + 0.466702i
\(117\) −362.688 + 1315.29i −0.286586 + 1.03931i
\(118\) −354.092 + 354.092i −0.276244 + 0.276244i
\(119\) 12.9193 829.307i 0.00995219 0.638844i
\(120\) −705.558 192.947i −0.536736 0.146780i
\(121\) 216.216 374.498i 0.162447 0.281366i
\(122\) −282.314 75.6458i −0.209504 0.0561365i
\(123\) 513.063 + 1942.97i 0.376108 + 1.42432i
\(124\) −1282.15 740.248i −0.928550 0.536099i
\(125\) 992.679 983.724i 0.710304 0.703896i
\(126\) 213.489 351.010i 0.150945 0.248178i
\(127\) −761.790 761.790i −0.532267 0.532267i 0.388979 0.921246i \(-0.372828\pi\)
−0.921246 + 0.388979i \(0.872828\pi\)
\(128\) −1299.56 + 348.216i −0.897389 + 0.240455i
\(129\) 856.175 1470.58i 0.584357 1.00370i
\(130\) 448.179 + 120.815i 0.302368 + 0.0815090i
\(131\) −156.855 90.5600i −0.104614 0.0603990i 0.446780 0.894644i \(-0.352571\pi\)
−0.551394 + 0.834245i \(0.685904\pi\)
\(132\) −419.282 + 1542.36i −0.276469 + 1.01701i
\(133\) 84.7880 297.798i 0.0552786 0.194153i
\(134\) 13.8545 0.00893167
\(135\) 801.066 1348.58i 0.510702 0.859758i
\(136\) 281.934 + 488.324i 0.177762 + 0.307893i
\(137\) 1269.16 + 340.070i 0.791470 + 0.212074i 0.631836 0.775102i \(-0.282302\pi\)
0.159634 + 0.987176i \(0.448968\pi\)
\(138\) −194.608 196.026i −0.120045 0.120919i
\(139\) 602.119i 0.367418i −0.982981 0.183709i \(-0.941190\pi\)
0.982981 0.183709i \(-0.0588103\pi\)
\(140\) 1300.38 + 780.699i 0.785015 + 0.471294i
\(141\) 900.798 + 1573.39i 0.538020 + 0.939742i
\(142\) −30.3296 + 8.12679i −0.0179240 + 0.00480271i
\(143\) 549.222 2049.72i 0.321177 1.19865i
\(144\) 9.46055 1302.86i 0.00547486 0.753969i
\(145\) −1719.98 + 458.084i −0.985081 + 0.262358i
\(146\) 865.738i 0.490746i
\(147\) −1303.33 + 1215.67i −0.731271 + 0.682087i
\(148\) −859.903 + 859.903i −0.477592 + 0.477592i
\(149\) −1608.31 + 2785.68i −0.884281 + 1.53162i −0.0377462 + 0.999287i \(0.512018\pi\)
−0.846535 + 0.532333i \(0.821315\pi\)
\(150\) −460.361 269.888i −0.250589 0.146908i
\(151\) −34.5817 59.8973i −0.0186372 0.0322806i 0.856556 0.516053i \(-0.172599\pi\)
−0.875194 + 0.483773i \(0.839266\pi\)
\(152\) 54.4821 + 203.330i 0.0290729 + 0.108501i
\(153\) −1170.20 + 304.465i −0.618335 + 0.160879i
\(154\) −328.068 + 548.324i −0.171665 + 0.286917i
\(155\) −1595.45 1600.28i −0.826772 0.829274i
\(156\) −6.98299 + 1923.35i −0.00358389 + 0.987123i
\(157\) −196.714 + 734.145i −0.0999966 + 0.373192i −0.997730 0.0673477i \(-0.978546\pi\)
0.897733 + 0.440540i \(0.145213\pi\)
\(158\) −50.7401 + 189.365i −0.0255485 + 0.0953484i
\(159\) −7.56359 + 2083.26i −0.00377253 + 1.03908i
\(160\) −1569.42 2.37042i −0.775460 0.00117124i
\(161\) 582.915 + 1046.97i 0.285342 + 0.512501i
\(162\) −576.220 163.402i −0.279458 0.0792476i
\(163\) −562.417 2098.97i −0.270257 1.00861i −0.958953 0.283563i \(-0.908483\pi\)
0.688696 0.725050i \(-0.258183\pi\)
\(164\) 1416.44 + 2453.34i 0.674421 + 1.16813i
\(165\) −1230.64 + 2106.45i −0.580637 + 0.993858i
\(166\) 455.299 788.602i 0.212880 0.368719i
\(167\) 1622.86 1622.86i 0.751982 0.751982i −0.222867 0.974849i \(-0.571541\pi\)
0.974849 + 0.222867i \(0.0715414\pi\)
\(168\) 336.025 1164.15i 0.154315 0.534618i
\(169\) 356.551i 0.162290i
\(170\) 105.870 + 397.513i 0.0477639 + 0.179340i
\(171\) −451.391 3.27772i −0.201864 0.00146581i
\(172\) 620.861 2317.08i 0.275234 1.02719i
\(173\) −1074.10 + 287.805i −0.472038 + 0.126482i −0.486993 0.873406i \(-0.661906\pi\)
0.0149547 + 0.999888i \(0.495240\pi\)
\(174\) 337.688 + 589.828i 0.147127 + 0.256981i
\(175\) 1606.25 + 1667.13i 0.693835 + 0.720134i
\(176\) 2026.40i 0.867872i
\(177\) −2231.30 2247.57i −0.947543 0.954449i
\(178\) −711.126 190.546i −0.299445 0.0802359i
\(179\) −1608.61 2786.20i −0.671696 1.16341i −0.977423 0.211292i \(-0.932233\pi\)
0.305728 0.952119i \(-0.401100\pi\)
\(180\) 591.010 2130.74i 0.244729 0.882311i
\(181\) 3642.53 1.49584 0.747921 0.663788i \(-0.231052\pi\)
0.747921 + 0.663788i \(0.231052\pi\)
\(182\) −210.553 + 739.520i −0.0857541 + 0.301192i
\(183\) 484.900 1783.74i 0.195874 0.720536i
\(184\) −705.517 407.330i −0.282671 0.163200i
\(185\) −1608.87 + 925.645i −0.639387 + 0.367864i
\(186\) −434.139 + 745.685i −0.171143 + 0.293958i
\(187\) 1816.54 486.739i 0.710365 0.190342i
\(188\) 1807.22 + 1807.22i 0.701089 + 0.701089i
\(189\) 2215.04 + 1358.26i 0.852489 + 0.522745i
\(190\) −0.231952 + 153.572i −8.85660e−5 + 0.0586383i
\(191\) −1748.09 1009.26i −0.662238 0.382343i 0.130891 0.991397i \(-0.458216\pi\)
−0.793129 + 0.609053i \(0.791550\pi\)
\(192\) −359.136 1360.05i −0.134992 0.511213i
\(193\) −3269.37 876.026i −1.21935 0.326724i −0.408926 0.912568i \(-0.634097\pi\)
−0.810424 + 0.585844i \(0.800763\pi\)
\(194\) 330.718 572.820i 0.122393 0.211990i
\(195\) −774.379 + 2831.71i −0.284382 + 1.03991i
\(196\) −1323.40 + 2135.68i −0.482289 + 0.778308i
\(197\) 2403.13 2403.13i 0.869118 0.869118i −0.123257 0.992375i \(-0.539334\pi\)
0.992375 + 0.123257i \(0.0393339\pi\)
\(198\) 898.020 + 247.626i 0.322321 + 0.0888790i
\(199\) 1551.01 895.479i 0.552505 0.318989i −0.197627 0.980277i \(-0.563323\pi\)
0.750132 + 0.661288i \(0.229990\pi\)
\(200\) −1519.00 411.936i −0.537046 0.145641i
\(201\) −0.318124 + 87.6219i −0.000111635 + 0.0307481i
\(202\) −918.817 918.817i −0.320038 0.320038i
\(203\) −718.666 2859.55i −0.248475 0.988674i
\(204\) −1479.27 + 846.909i −0.507693 + 0.290664i
\(205\) 1112.80 + 4178.25i 0.379128 + 1.42352i
\(206\) 739.240 426.800i 0.250026 0.144352i
\(207\) 1244.23 1226.29i 0.417777 0.411753i
\(208\) 631.122 + 2355.38i 0.210387 + 0.785174i
\(209\) 702.070 0.232360
\(210\) 457.753 756.225i 0.150419 0.248497i
\(211\) 3789.41 1.23637 0.618185 0.786033i \(-0.287868\pi\)
0.618185 + 0.786033i \(0.287868\pi\)
\(212\) 760.096 + 2836.72i 0.246243 + 0.918993i
\(213\) −50.7010 192.005i −0.0163098 0.0617650i
\(214\) −117.190 + 67.6595i −0.0374342 + 0.0216127i
\(215\) 1835.48 3168.09i 0.582227 1.00494i
\(216\) −1766.35 19.2396i −0.556411 0.00606060i
\(217\) 2687.78 2605.32i 0.840821 0.815026i
\(218\) 936.834 + 936.834i 0.291057 + 0.291057i
\(219\) 5475.31 + 19.8789i 1.68944 + 0.00613375i
\(220\) −895.114 + 3320.54i −0.274312 + 1.01759i
\(221\) 1959.85 1131.52i 0.596534 0.344409i
\(222\) 499.343 + 502.982i 0.150963 + 0.152063i
\(223\) 645.045 645.045i 0.193701 0.193701i −0.603592 0.797293i \(-0.706264\pi\)
0.797293 + 0.603592i \(0.206264\pi\)
\(224\) 40.4951 2599.44i 0.0120790 0.775366i
\(225\) 1717.46 2905.33i 0.508878 0.860839i
\(226\) −304.835 + 527.990i −0.0897228 + 0.155404i
\(227\) −3473.70 930.775i −1.01567 0.272149i −0.287675 0.957728i \(-0.592882\pi\)
−0.727998 + 0.685580i \(0.759549\pi\)
\(228\) −615.251 + 162.464i −0.178711 + 0.0471906i
\(229\) −1407.32 812.518i −0.406107 0.234466i 0.283009 0.959117i \(-0.408668\pi\)
−0.689116 + 0.724651i \(0.742001\pi\)
\(230\) −419.623 420.893i −0.120301 0.120665i
\(231\) −3460.31 2087.44i −0.985592 0.594560i
\(232\) 1417.40 + 1417.40i 0.401106 + 0.401106i
\(233\) 5095.30 1365.28i 1.43264 0.383874i 0.542688 0.839934i \(-0.317407\pi\)
0.889949 + 0.456060i \(0.150740\pi\)
\(234\) 1120.94 + 8.13955i 0.313153 + 0.00227393i
\(235\) 1945.38 + 3381.29i 0.540012 + 0.938599i
\(236\) −3866.45 2232.29i −1.06646 0.615720i
\(237\) −1196.46 325.251i −0.327926 0.0891449i
\(238\) −660.883 + 166.094i −0.179994 + 0.0452365i
\(239\) 876.196 0.237140 0.118570 0.992946i \(-0.462169\pi\)
0.118570 + 0.992946i \(0.462169\pi\)
\(240\) 14.4121 2803.34i 0.00387624 0.753979i
\(241\) −2914.92 5048.79i −0.779114 1.34946i −0.932453 0.361291i \(-0.882336\pi\)
0.153339 0.988174i \(-0.450997\pi\)
\(242\) −343.178 91.9542i −0.0911582 0.0244258i
\(243\) 1046.66 3640.52i 0.276310 0.961069i
\(244\) 2605.79i 0.683682i
\(245\) −2798.77 + 2621.65i −0.729823 + 0.683636i
\(246\) 1432.83 820.325i 0.371358 0.212610i
\(247\) 816.050 218.660i 0.210219 0.0563279i
\(248\) −658.648 + 2458.11i −0.168646 + 0.629395i
\(249\) 4977.02 + 2897.63i 1.26669 + 0.737468i
\(250\) −991.768 578.605i −0.250900 0.146377i
\(251\) 1089.28i 0.273923i 0.990576 + 0.136961i \(0.0437336\pi\)
−0.990576 + 0.136961i \(0.956266\pi\)
\(252\) 3515.46 + 1028.56i 0.878782 + 0.257116i
\(253\) −1921.25 + 1921.25i −0.477424 + 0.477424i
\(254\) −442.564 + 766.544i −0.109327 + 0.189359i
\(255\) −2516.48 + 660.442i −0.617993 + 0.162190i
\(256\) −530.165 918.273i −0.129435 0.224188i
\(257\) 412.775 + 1540.50i 0.100188 + 0.373905i 0.997755 0.0669725i \(-0.0213340\pi\)
−0.897567 + 0.440878i \(0.854667\pi\)
\(258\) −1349.11 366.748i −0.325550 0.0884990i
\(259\) −1495.69 2686.40i −0.358834 0.644498i
\(260\) −6.25057 + 4138.41i −0.00149094 + 0.987128i
\(261\) −3738.09 + 2122.15i −0.886521 + 0.503286i
\(262\) −38.5141 + 143.736i −0.00908170 + 0.0338934i
\(263\) 783.363 2923.55i 0.183666 0.685452i −0.811246 0.584705i \(-0.801210\pi\)
0.994912 0.100747i \(-0.0321232\pi\)
\(264\) 2747.36 + 9.97467i 0.640485 + 0.00232537i
\(265\) −6.77027 + 4482.50i −0.00156941 + 1.03908i
\(266\) −254.362 3.96256i −0.0586312 0.000913383i
\(267\) 1221.42 4493.10i 0.279962 1.02986i
\(268\) 31.9695 + 119.312i 0.00728676 + 0.0271945i
\(269\) 3480.31 + 6028.07i 0.788840 + 1.36631i 0.926678 + 0.375857i \(0.122651\pi\)
−0.137838 + 0.990455i \(0.544015\pi\)
\(270\) −1240.57 348.956i −0.279625 0.0786549i
\(271\) −976.514 + 1691.37i −0.218889 + 0.379127i −0.954469 0.298311i \(-0.903577\pi\)
0.735579 + 0.677439i \(0.236910\pi\)
\(272\) −1528.10 + 1528.10i −0.340641 + 0.340641i
\(273\) −4672.22 1348.61i −1.03581 0.298981i
\(274\) 1079.51i 0.238014i
\(275\) −2638.30 + 4537.95i −0.578529 + 0.995087i
\(276\) 1239.08 2128.26i 0.270231 0.464154i
\(277\) −952.787 + 3555.85i −0.206669 + 0.771301i 0.782265 + 0.622946i \(0.214064\pi\)
−0.988934 + 0.148355i \(0.952602\pi\)
\(278\) −477.840 + 128.037i −0.103090 + 0.0276228i
\(279\) −4706.07 2762.81i −1.00984 0.592850i
\(280\) 717.699 2506.37i 0.153181 0.534944i
\(281\) 3555.52i 0.754821i 0.926046 + 0.377410i \(0.123185\pi\)
−0.926046 + 0.377410i \(0.876815\pi\)
\(282\) 1057.09 1049.44i 0.223223 0.221608i
\(283\) −3103.82 831.665i −0.651953 0.174690i −0.0823415 0.996604i \(-0.526240\pi\)
−0.569612 + 0.821914i \(0.692906\pi\)
\(284\) −139.973 242.440i −0.0292460 0.0506555i
\(285\) −971.252 4.99325i −0.201867 0.00103781i
\(286\) −1743.44 −0.360462
\(287\) −6946.52 + 1745.81i −1.42871 + 0.359066i
\(288\) −3667.96 + 954.336i −0.750475 + 0.195260i
\(289\) −2517.89 1453.71i −0.512496 0.295890i
\(290\) 729.278 + 1267.56i 0.147671 + 0.256669i
\(291\) 3615.18 + 2104.76i 0.728266 + 0.423997i
\(292\) 7455.56 1997.71i 1.49419 0.400367i
\(293\) −2955.83 2955.83i −0.589357 0.589357i 0.348100 0.937457i \(-0.386827\pi\)
−0.937457 + 0.348100i \(0.886827\pi\)
\(294\) 1241.90 + 775.814i 0.246357 + 0.153899i
\(295\) −4811.25 4825.80i −0.949565 0.952437i
\(296\) 1810.28 + 1045.16i 0.355474 + 0.205233i
\(297\) −1586.72 + 5673.80i −0.310003 + 1.10851i
\(298\) 2552.70 + 683.994i 0.496222 + 0.132962i
\(299\) −1634.79 + 2831.54i −0.316195 + 0.547667i
\(300\) 1261.93 4587.31i 0.242858 0.882828i
\(301\) 5204.66 + 3114.00i 0.996650 + 0.596306i
\(302\) −40.1807 + 40.1807i −0.00765610 + 0.00765610i
\(303\) 5832.11 5789.92i 1.10576 1.09776i
\(304\) −698.677 + 403.381i −0.131815 + 0.0761036i
\(305\) 1035.20 3840.21i 0.194345 0.720949i
\(306\) 490.459 + 863.927i 0.0916264 + 0.161397i
\(307\) −2416.45 2416.45i −0.449231 0.449231i 0.445868 0.895099i \(-0.352895\pi\)
−0.895099 + 0.445868i \(0.852895\pi\)
\(308\) −5479.08 1559.98i −1.01364 0.288598i
\(309\) 2682.30 + 4685.08i 0.493822 + 0.862541i
\(310\) −930.714 + 1606.43i −0.170519 + 0.294321i
\(311\) −2136.82 + 1233.69i −0.389608 + 0.224940i −0.681990 0.731361i \(-0.738885\pi\)
0.292382 + 0.956301i \(0.405552\pi\)
\(312\) 3196.49 844.071i 0.580019 0.153161i
\(313\) 1228.64 + 4585.35i 0.221875 + 0.828050i 0.983632 + 0.180187i \(0.0576703\pi\)
−0.761757 + 0.647863i \(0.775663\pi\)
\(314\) 624.446 0.112228
\(315\) 4772.19 + 2912.40i 0.853595 + 0.520936i
\(316\) −1747.86 −0.311154
\(317\) 1640.04 + 6120.71i 0.290580 + 1.08446i 0.944665 + 0.328037i \(0.106387\pi\)
−0.654085 + 0.756421i \(0.726946\pi\)
\(318\) 1654.88 436.991i 0.291827 0.0770604i
\(319\) 5789.75 3342.71i 1.01619 0.586696i
\(320\) −778.941 2924.71i −0.136075 0.510926i
\(321\) −425.218 742.714i −0.0739357 0.129141i
\(322\) 706.919 685.231i 0.122345 0.118591i
\(323\) 529.427 + 529.427i 0.0912016 + 0.0912016i
\(324\) 77.5462 5339.35i 0.0132967 0.915527i
\(325\) −1653.28 + 6096.39i −0.282176 + 1.04051i
\(326\) −1546.14 + 892.666i −0.262678 + 0.151657i
\(327\) −5946.47 + 5903.45i −1.00563 + 0.998353i
\(328\) 3443.20 3443.20i 0.579630 0.579630i
\(329\) −5645.88 + 3143.42i −0.946102 + 0.526756i
\(330\) 1933.36 + 528.709i 0.322509 + 0.0881954i
\(331\) 2174.35 3766.08i 0.361067 0.625386i −0.627070 0.778963i \(-0.715746\pi\)
0.988137 + 0.153577i \(0.0490793\pi\)
\(332\) 7841.90 + 2101.23i 1.29633 + 0.347349i
\(333\) −3192.55 + 3146.52i −0.525377 + 0.517802i
\(334\) −1632.99 942.809i −0.267525 0.154456i
\(335\) −0.284757 + 188.533i −4.64415e−5 + 0.0307483i
\(336\) 4642.95 + 89.1918i 0.753850 + 0.0144816i
\(337\) −2708.79 2708.79i −0.437855 0.437855i 0.453435 0.891290i \(-0.350199\pi\)
−0.891290 + 0.453435i \(0.850199\pi\)
\(338\) −282.958 + 75.8183i −0.0455351 + 0.0122011i
\(339\) −3332.25 1940.04i −0.533873 0.310821i
\(340\) −3179.01 + 1829.00i −0.507076 + 0.291740i
\(341\) 7350.39 + 4243.75i 1.16729 + 0.673936i
\(342\) 93.3843 + 358.920i 0.0147650 + 0.0567490i
\(343\) −4277.12 4696.79i −0.673303 0.739367i
\(344\) −4123.33 −0.646264
\(345\) 2671.55 2644.22i 0.416903 0.412638i
\(346\) 456.803 + 791.206i 0.0709765 + 0.122935i
\(347\) −9097.19 2437.58i −1.40739 0.377108i −0.526394 0.850241i \(-0.676456\pi\)
−0.880991 + 0.473133i \(0.843123\pi\)
\(348\) −4300.26 + 4269.15i −0.662408 + 0.657616i
\(349\) 1487.28i 0.228116i 0.993474 + 0.114058i \(0.0363850\pi\)
−0.993474 + 0.114058i \(0.963615\pi\)
\(350\) 981.475 1629.22i 0.149892 0.248816i
\(351\) −77.2169 + 7089.12i −0.0117423 + 1.07803i
\(352\) 5693.87 1525.67i 0.862172 0.231018i
\(353\) −2990.62 + 11161.2i −0.450920 + 1.68286i 0.248894 + 0.968531i \(0.419933\pi\)
−0.699814 + 0.714326i \(0.746734\pi\)
\(354\) −1309.19 + 2248.69i −0.196561 + 0.337617i
\(355\) −109.967 412.896i −0.0164407 0.0617302i
\(356\) 6563.76i 0.977188i
\(357\) −1035.28 4183.53i −0.153481 0.620213i
\(358\) −1869.06 + 1869.06i −0.275930 + 0.275930i
\(359\) 4412.19 7642.14i 0.648654 1.12350i −0.334791 0.942292i \(-0.608666\pi\)
0.983445 0.181209i \(-0.0580009\pi\)
\(360\) −3800.66 33.3388i −0.556423 0.00488086i
\(361\) −3289.74 5698.00i −0.479624 0.830734i
\(362\) −774.562 2890.70i −0.112459 0.419702i
\(363\) 589.439 2168.30i 0.0852274 0.313515i
\(364\) −6854.46 106.782i −0.987010 0.0153761i
\(365\) 11781.1 + 17.7939i 1.68945 + 0.00255171i
\(366\) −1518.68 5.51380i −0.216893 0.000787462i
\(367\) 255.708 954.316i 0.0363702 0.135735i −0.945354 0.326047i \(-0.894283\pi\)
0.981724 + 0.190312i \(0.0609499\pi\)
\(368\) 808.093 3015.84i 0.114469 0.427206i
\(369\) 5155.20 + 9080.72i 0.727288 + 1.28109i
\(370\) 1076.71 + 1079.96i 0.151285 + 0.151742i
\(371\) −7424.37 115.660i −1.03896 0.0161854i
\(372\) −7423.48 2018.03i −1.03465 0.281263i
\(373\) 1713.23 + 6393.88i 0.237823 + 0.887567i 0.976856 + 0.213898i \(0.0686160\pi\)
−0.739033 + 0.673669i \(0.764717\pi\)
\(374\) −772.550 1338.10i −0.106812 0.185003i
\(375\) 3682.13 6259.10i 0.507052 0.861916i
\(376\) 2196.57 3804.57i 0.301275 0.521823i
\(377\) 5688.62 5688.62i 0.777132 0.777132i
\(378\) 606.896 2046.68i 0.0825804 0.278491i
\(379\) 13698.5i 1.85658i 0.371859 + 0.928289i \(0.378720\pi\)
−0.371859 + 0.928289i \(0.621280\pi\)
\(380\) −1323.07 + 352.374i −0.178610 + 0.0475694i
\(381\) −4837.81 2816.58i −0.650520 0.378734i
\(382\) −429.226 + 1601.89i −0.0574899 + 0.214555i
\(383\) 7368.17 1974.30i 0.983018 0.263399i 0.268703 0.963223i \(-0.413405\pi\)
0.714315 + 0.699824i \(0.246738\pi\)
\(384\) −6066.96 + 3473.45i −0.806259 + 0.461599i
\(385\) −7454.91 4475.65i −0.986851 0.592469i
\(386\) 2780.85i 0.366687i
\(387\) 2350.46 8523.96i 0.308735 1.11963i
\(388\) 5696.15 + 1526.28i 0.745305 + 0.199704i
\(389\) −2576.08 4461.89i −0.335764 0.581560i 0.647867 0.761753i \(-0.275661\pi\)
−0.983631 + 0.180193i \(0.942328\pi\)
\(390\) 2411.90 + 12.3997i 0.313158 + 0.00160996i
\(391\) −2897.62 −0.374779
\(392\) 4134.68 + 1247.15i 0.532737 + 0.160691i
\(393\) −908.169 246.881i −0.116568 0.0316882i
\(394\) −2418.13 1396.11i −0.309197 0.178515i
\(395\) −2575.85 694.370i −0.328115 0.0884495i
\(396\) −60.3056 + 8304.98i −0.00765271 + 1.05389i
\(397\) −13851.0 + 3711.36i −1.75104 + 0.469189i −0.984847 0.173425i \(-0.944516\pi\)
−0.766190 + 0.642614i \(0.777850\pi\)
\(398\) −1040.46 1040.46i −0.131039 0.131039i
\(399\) 30.9016 1608.61i 0.00387723 0.201832i
\(400\) 18.2209 6031.89i 0.00227761 0.753986i
\(401\) 1835.49 + 1059.72i 0.228579 + 0.131970i 0.609916 0.792466i \(-0.291203\pi\)
−0.381337 + 0.924436i \(0.624536\pi\)
\(402\) 69.6041 18.3798i 0.00863567 0.00228035i
\(403\) 9865.44 + 2643.44i 1.21944 + 0.326747i
\(404\) 5792.48 10032.9i 0.713333 1.23553i
\(405\) 2235.44 7837.92i 0.274272 0.961652i
\(406\) −2116.51 + 1178.40i −0.258720 + 0.144046i
\(407\) 4929.72 4929.72i 0.600386 0.600386i
\(408\) 2064.25 + 2079.29i 0.250479 + 0.252304i
\(409\) 1348.31 778.444i 0.163006 0.0941115i −0.416278 0.909237i \(-0.636666\pi\)
0.579284 + 0.815126i \(0.303332\pi\)
\(410\) 3079.22 1771.59i 0.370907 0.213397i
\(411\) 6827.32 + 24.7876i 0.819385 + 0.00297489i
\(412\) 5381.34 + 5381.34i 0.643494 + 0.643494i
\(413\) 8105.27 7856.61i 0.965700 0.936073i
\(414\) −1237.76 726.653i −0.146938 0.0862634i
\(415\) 10722.0 + 6211.98i 1.26825 + 0.734781i
\(416\) 6143.10 3546.72i 0.724015 0.418010i
\(417\) −798.790 3025.01i −0.0938055 0.355241i
\(418\) −149.291 557.161i −0.0174690 0.0651953i
\(419\) 7947.94 0.926688 0.463344 0.886179i \(-0.346649\pi\)
0.463344 + 0.886179i \(0.346649\pi\)
\(420\) 7568.73 + 2197.07i 0.879325 + 0.255252i
\(421\) 16800.8 1.94494 0.972469 0.233031i \(-0.0748643\pi\)
0.972469 + 0.233031i \(0.0748643\pi\)
\(422\) −805.795 3007.27i −0.0929514 0.346899i
\(423\) 6612.88 + 6709.62i 0.760116 + 0.771236i
\(424\) 4371.72 2524.01i 0.500730 0.289097i
\(425\) −5411.58 + 1432.52i −0.617647 + 0.163500i
\(426\) −141.593 + 81.0648i −0.0161038 + 0.00921972i
\(427\) 6336.56 + 1804.12i 0.718144 + 0.204467i
\(428\) −853.089 853.089i −0.0963449 0.0963449i
\(429\) 40.0326 11026.3i 0.00450535 1.24092i
\(430\) −2904.49 782.960i −0.325737 0.0878085i
\(431\) 2178.88 1257.98i 0.243511 0.140591i −0.373279 0.927719i \(-0.621766\pi\)
0.616789 + 0.787128i \(0.288433\pi\)
\(432\) −1680.88 6558.05i −0.187203 0.730380i
\(433\) 6032.13 6032.13i 0.669482 0.669482i −0.288114 0.957596i \(-0.593028\pi\)
0.957596 + 0.288114i \(0.0930282\pi\)
\(434\) −2639.11 1579.01i −0.291893 0.174642i
\(435\) −8033.39 + 4583.17i −0.885452 + 0.505164i
\(436\) −5906.06 + 10229.6i −0.648737 + 1.12364i
\(437\) −1044.88 279.974i −0.114378 0.0306475i
\(438\) −1148.52 4349.42i −0.125293 0.474483i
\(439\) 657.119 + 379.388i 0.0714410 + 0.0412465i 0.535295 0.844665i \(-0.320200\pi\)
−0.463854 + 0.885912i \(0.653534\pi\)
\(440\) 5911.40 + 8.92846i 0.640489 + 0.000967381i
\(441\) −4935.11 + 7836.50i −0.532892 + 0.846183i
\(442\) −1314.72 1314.72i −0.141482 0.141482i
\(443\) −12898.1 + 3456.04i −1.38331 + 0.370657i −0.872323 0.488930i \(-0.837387\pi\)
−0.510989 + 0.859587i \(0.670721\pi\)
\(444\) −3179.33 + 5460.88i −0.339830 + 0.583698i
\(445\) 2607.58 9673.17i 0.277778 1.03045i
\(446\) −649.070 374.741i −0.0689111 0.0397859i
\(447\) −4384.50 + 16128.7i −0.463937 + 1.70663i
\(448\) 4862.46 1222.04i 0.512789 0.128875i
\(449\) 214.586 0.0225545 0.0112772 0.999936i \(-0.496410\pi\)
0.0112772 + 0.999936i \(0.496410\pi\)
\(450\) −2670.87 745.174i −0.279791 0.0780618i
\(451\) −8120.26 14064.7i −0.847823 1.46847i
\(452\) −5250.37 1406.83i −0.546364 0.146398i
\(453\) −253.198 255.043i −0.0262611 0.0264525i
\(454\) 2954.64i 0.305437i
\(455\) −10059.2 2880.43i −1.03644 0.296784i
\(456\) 543.459 + 949.241i 0.0558109 + 0.0974830i
\(457\) −5653.98 + 1514.98i −0.578735 + 0.155072i −0.536300 0.844028i \(-0.680178\pi\)
−0.0424354 + 0.999099i \(0.513512\pi\)
\(458\) −345.554 + 1289.62i −0.0352548 + 0.131573i
\(459\) −5475.12 + 3082.04i −0.556769 + 0.313415i
\(460\) 2656.36 4584.94i 0.269246 0.464725i
\(461\) 6147.78i 0.621108i −0.950556 0.310554i \(-0.899485\pi\)
0.950556 0.310554i \(-0.100515\pi\)
\(462\) −920.771 + 3189.97i −0.0927232 + 0.321236i
\(463\) −8434.34 + 8434.34i −0.846602 + 0.846602i −0.989707 0.143105i \(-0.954291\pi\)
0.143105 + 0.989707i \(0.454291\pi\)
\(464\) −3841.18 + 6653.12i −0.384315 + 0.665654i
\(465\) −10138.4 5923.14i −1.01109 0.590707i
\(466\) −2166.97 3753.30i −0.215414 0.373108i
\(467\) −34.9103 130.287i −0.00345922 0.0129100i 0.964175 0.265268i \(-0.0854605\pi\)
−0.967634 + 0.252358i \(0.918794\pi\)
\(468\) 2516.49 + 9672.07i 0.248558 + 0.955324i
\(469\) −312.268 4.86465i −0.0307446 0.000478952i
\(470\) 2269.71 2262.86i 0.222753 0.222081i
\(471\) −14.3384 + 3949.27i −0.00140272 + 0.386355i
\(472\) −1986.22 + 7412.67i −0.193693 + 0.722873i
\(473\) −3559.32 + 13283.6i −0.345999 + 1.29129i
\(474\) −3.69843 + 1018.67i −0.000358385 + 0.0987113i
\(475\) −2089.82 6.31285i −0.201868 0.000609797i
\(476\) −2955.37 5308.13i −0.284578 0.511129i
\(477\) 2725.73 + 10476.2i 0.261640 + 1.00561i
\(478\) −186.318 695.347i −0.0178284 0.0665365i
\(479\) 5160.88 + 8938.91i 0.492290 + 0.852671i 0.999961 0.00888027i \(-0.00282671\pi\)
−0.507671 + 0.861551i \(0.669493\pi\)
\(480\) −7887.83 + 2070.13i −0.750059 + 0.196850i
\(481\) 4194.69 7265.42i 0.397633 0.688721i
\(482\) −3386.86 + 3386.86i −0.320057 + 0.320057i
\(483\) 4317.48 + 4486.60i 0.406733 + 0.422666i
\(484\) 3167.57i 0.297480i
\(485\) 7788.21 + 4512.22i 0.729163 + 0.422452i
\(486\) −3111.68 56.4929i −0.290429 0.00527277i
\(487\) −4145.60 + 15471.6i −0.385739 + 1.43960i 0.451260 + 0.892393i \(0.350975\pi\)
−0.836999 + 0.547205i \(0.815692\pi\)
\(488\) −4326.46 + 1159.27i −0.401331 + 0.107536i
\(489\) −5610.11 9798.99i −0.518810 0.906188i
\(490\) 2675.67 + 1663.62i 0.246683 + 0.153377i
\(491\) 18850.4i 1.73260i −0.499527 0.866298i \(-0.666493\pi\)
0.499527 0.866298i \(-0.333507\pi\)
\(492\) 10370.8 + 10446.4i 0.950307 + 0.957232i
\(493\) 6886.75 + 1845.30i 0.629135 + 0.168576i
\(494\) −347.056 601.118i −0.0316089 0.0547482i
\(495\) −3388.19 + 12215.3i −0.307652 + 1.10916i
\(496\) −9753.16 −0.882923
\(497\) 686.458 172.522i 0.0619554 0.0155707i
\(498\) 1241.22 4565.91i 0.111687 0.410850i
\(499\) −15111.1 8724.39i −1.35564 0.782680i −0.366609 0.930375i \(-0.619481\pi\)
−0.989033 + 0.147695i \(0.952815\pi\)
\(500\) 2694.30 9876.06i 0.240986 0.883341i
\(501\) 6000.24 10306.1i 0.535072 0.919050i
\(502\) 864.448 231.628i 0.0768570 0.0205938i
\(503\) 11471.6 + 11471.6i 1.01688 + 1.01688i 0.999855 + 0.0170292i \(0.00542083\pi\)
0.0170292 + 0.999855i \(0.494579\pi\)
\(504\) 143.779 6294.40i 0.0127072 0.556299i
\(505\) 12522.3 12484.5i 1.10343 1.10010i
\(506\) 1933.24 + 1116.16i 0.169848 + 0.0980619i
\(507\) −473.012 1791.29i −0.0414343 0.156911i
\(508\) −7622.56 2042.46i −0.665741 0.178385i
\(509\) −6171.68 + 10689.7i −0.537436 + 0.930867i 0.461605 + 0.887086i \(0.347274\pi\)
−0.999041 + 0.0437814i \(0.986059\pi\)
\(510\) 1059.24 + 1856.63i 0.0919684 + 0.161202i
\(511\) −303.982 + 19513.0i −0.0263158 + 1.68925i
\(512\) −8226.75 + 8226.75i −0.710106 + 0.710106i
\(513\) −2272.11 + 582.363i −0.195548 + 0.0501208i
\(514\) 1134.76 655.154i 0.0973777 0.0562210i
\(515\) 5792.76 + 10068.4i 0.495649 + 0.861492i
\(516\) 45.2544 12464.6i 0.00386088 1.06341i
\(517\) −10360.5 10360.5i −0.881347 0.881347i
\(518\) −1813.87 + 1758.23i −0.153855 + 0.149135i
\(519\) −5014.43 + 2870.86i −0.424102 + 0.242807i
\(520\) 6873.89 1830.73i 0.579693 0.154390i
\(521\) 3591.05 2073.29i 0.301971 0.174343i −0.341357 0.939934i \(-0.610887\pi\)
0.643328 + 0.765591i \(0.277553\pi\)
\(522\) 2479.01 + 2515.28i 0.207861 + 0.210902i
\(523\) 148.431 + 553.950i 0.0124100 + 0.0463147i 0.971853 0.235587i \(-0.0757014\pi\)
−0.959443 + 0.281902i \(0.909035\pi\)
\(524\) −1326.70 −0.110605
\(525\) 10281.4 + 6244.69i 0.854698 + 0.519125i
\(526\) −2486.70 −0.206132
\(527\) 2342.70 + 8743.09i 0.193643 + 0.722685i
\(528\) 2688.28 + 10180.5i 0.221577 + 0.839110i
\(529\) −6911.41 + 3990.30i −0.568045 + 0.327961i
\(530\) 3558.74 947.802i 0.291663 0.0776790i
\(531\) −14191.6 8331.53i −1.15982 0.680900i
\(532\) −552.821 2199.66i −0.0450523 0.179262i
\(533\) −13819.0 13819.0i −1.12302 1.12302i
\(534\) −3825.44 13.8888i −0.310006 0.00112552i
\(535\) −918.310 1596.12i −0.0742094 0.128984i
\(536\) 183.874 106.160i 0.0148174 0.00855486i
\(537\) −11777.9 11863.7i −0.946466 0.953363i
\(538\) 4043.79 4043.79i 0.324053 0.324053i
\(539\) 7586.90 12243.6i 0.606291 0.978419i
\(540\) 142.494 11488.8i 0.0113555 0.915553i
\(541\) −2615.70 + 4530.53i −0.207870 + 0.360042i −0.951043 0.309057i \(-0.899987\pi\)
0.743173 + 0.669099i \(0.233320\pi\)
\(542\) 1549.92 + 415.299i 0.122831 + 0.0329126i
\(543\) 18299.9 4832.30i 1.44627 0.381904i
\(544\) 5444.22 + 3143.22i 0.429079 + 0.247729i
\(545\) −12767.8 + 12729.3i −1.00351 + 1.00048i
\(546\) −76.7377 + 3994.64i −0.00601478 + 0.313104i
\(547\) 5874.72 + 5874.72i 0.459205 + 0.459205i 0.898394 0.439190i \(-0.144734\pi\)
−0.439190 + 0.898394i \(0.644734\pi\)
\(548\) 9296.56 2491.00i 0.724688 0.194180i
\(549\) 69.7435 9604.71i 0.00542182 0.746665i
\(550\) 4162.33 + 1128.78i 0.322695 + 0.0875114i
\(551\) 2305.05 + 1330.82i 0.178219 + 0.102895i
\(552\) −4084.86 1110.44i −0.314969 0.0856226i
\(553\) 1210.13 4250.31i 0.0930561 0.326838i
\(554\) 3024.52 0.231949
\(555\) −6854.90 + 6784.77i −0.524278 + 0.518915i
\(556\) −2205.26 3819.61i −0.168208 0.291345i
\(557\) −313.931 84.1176i −0.0238810 0.00639888i 0.246859 0.969051i \(-0.420602\pi\)
−0.270740 + 0.962653i \(0.587268\pi\)
\(558\) −1191.84 + 4322.22i −0.0904205 + 0.327911i
\(559\) 16548.7i 1.25212i
\(560\) 9990.42 + 170.728i 0.753879 + 0.0128832i
\(561\) 8480.46 4855.23i 0.638227 0.365397i
\(562\) 2821.65 756.059i 0.211787 0.0567481i
\(563\) 32.0863 119.748i 0.00240192 0.00896407i −0.964714 0.263298i \(-0.915190\pi\)
0.967116 + 0.254334i \(0.0818563\pi\)
\(564\) 11476.9 + 6681.85i 0.856850 + 0.498859i
\(565\) −7178.69 4159.09i −0.534531 0.309689i
\(566\) 2640.03i 0.196058i
\(567\) 12930.2 + 3885.28i 0.957699 + 0.287771i
\(568\) −340.258 + 340.258i −0.0251354 + 0.0251354i
\(569\) −3195.10 + 5534.08i −0.235405 + 0.407734i −0.959390 0.282082i \(-0.908975\pi\)
0.723985 + 0.689816i \(0.242308\pi\)
\(570\) 202.568 + 771.845i 0.0148853 + 0.0567176i
\(571\) 327.200 + 566.728i 0.0239806 + 0.0415356i 0.877767 0.479088i \(-0.159033\pi\)
−0.853786 + 0.520624i \(0.825699\pi\)
\(572\) −4023.04 15014.2i −0.294077 1.09751i
\(573\) −10121.2 2751.40i −0.737907 0.200596i
\(574\) 2862.61 + 5141.51i 0.208158 + 0.373872i
\(575\) 5736.18 5701.63i 0.416027 0.413521i
\(576\) −3608.56 6356.36i −0.261036 0.459806i
\(577\) 2844.13 10614.4i 0.205204 0.765832i −0.784183 0.620529i \(-0.786918\pi\)
0.989387 0.145302i \(-0.0464155\pi\)
\(578\) −618.243 + 2307.32i −0.0444905 + 0.166041i
\(579\) −17587.3 63.8533i −1.26236 0.00458316i
\(580\) −9233.18 + 9205.34i −0.661012 + 0.659019i
\(581\) −10539.0 + 17614.6i −0.752548 + 1.25779i
\(582\) 901.588 3316.56i 0.0642131 0.236213i
\(583\) −4357.54 16262.5i −0.309555 1.15528i
\(584\) −6633.71 11489.9i −0.470043 0.814138i
\(585\) −133.803 + 15253.7i −0.00945653 + 1.07805i
\(586\) −1717.20 + 2974.28i −0.121053 + 0.209670i
\(587\) 8930.91 8930.91i 0.627970 0.627970i −0.319587 0.947557i \(-0.603544\pi\)
0.947557 + 0.319587i \(0.103544\pi\)
\(588\) −3815.45 + 12485.2i −0.267596 + 0.875647i
\(589\) 3379.10i 0.236390i
\(590\) −2806.66 + 4844.37i −0.195845 + 0.338033i
\(591\) 8885.15 15261.3i 0.618420 1.06221i
\(592\) −2073.48 + 7738.32i −0.143952 + 0.537235i
\(593\) 7443.34 1994.44i 0.515449 0.138114i 0.00828853 0.999966i \(-0.497362\pi\)
0.507161 + 0.861851i \(0.330695\pi\)
\(594\) 4840.12 + 52.7200i 0.334331 + 0.00364163i
\(595\) −2246.65 8996.78i −0.154796 0.619886i
\(596\) 23561.7i 1.61934i
\(597\) 6604.25 6556.46i 0.452753 0.449478i
\(598\) 2594.73 + 695.257i 0.177436 + 0.0475437i
\(599\) −1495.48 2590.24i −0.102009 0.176685i 0.810503 0.585734i \(-0.199194\pi\)
−0.912512 + 0.409049i \(0.865860\pi\)
\(600\) −8177.84 54.3948i −0.556432 0.00370109i
\(601\) 741.724 0.0503420 0.0251710 0.999683i \(-0.491987\pi\)
0.0251710 + 0.999683i \(0.491987\pi\)
\(602\) 1364.52 4792.58i 0.0923818 0.324470i
\(603\) 114.644 + 440.630i 0.00774238 + 0.0297576i
\(604\) −438.747 253.310i −0.0295569 0.0170647i
\(605\) 1258.38 4668.11i 0.0845625 0.313695i
\(606\) −5835.02 3397.16i −0.391141 0.227723i
\(607\) 665.164 178.230i 0.0444780 0.0119179i −0.236511 0.971629i \(-0.576004\pi\)
0.280989 + 0.959711i \(0.409337\pi\)
\(608\) 1659.47 + 1659.47i 0.110692 + 0.110692i
\(609\) −7404.10 13412.8i −0.492659 0.892470i
\(610\) −3267.71 4.93547i −0.216894 0.000327593i
\(611\) −15269.4 8815.77i −1.01102 0.583712i
\(612\) −6308.22 + 6217.27i −0.416658 + 0.410651i
\(613\) −13373.6 3583.44i −0.881163 0.236107i −0.210254 0.977647i \(-0.567429\pi\)
−0.670909 + 0.741540i \(0.734096\pi\)
\(614\) −1403.84 + 2431.53i −0.0922712 + 0.159818i
\(615\) 11133.6 + 19515.0i 0.730002 + 1.27955i
\(616\) −152.530 + 9791.07i −0.00997661 + 0.640412i
\(617\) 1918.92 1918.92i 0.125207 0.125207i −0.641726 0.766934i \(-0.721782\pi\)
0.766934 + 0.641726i \(0.221782\pi\)
\(618\) 3147.70 3124.92i 0.204885 0.203403i
\(619\) 15934.6 9199.83i 1.03468 0.597370i 0.116355 0.993208i \(-0.462879\pi\)
0.918321 + 0.395837i \(0.129546\pi\)
\(620\) −15981.9 4308.23i −1.03524 0.279069i
\(621\) 4624.10 7811.44i 0.298806 0.504770i
\(622\) 1433.44 + 1433.44i 0.0924045 + 0.0924045i
\(623\) 15961.3 + 4544.43i 1.02644 + 0.292245i
\(624\) 6295.45 + 10996.0i 0.403878 + 0.705439i
\(625\) 7894.11 13484.2i 0.505223 0.862989i
\(626\) 3377.66 1950.09i 0.215653 0.124507i
\(627\) 3527.16 931.388i 0.224659 0.0593238i
\(628\) 1440.92 + 5377.61i 0.0915592 + 0.341704i
\(629\) 7434.96 0.471306
\(630\) 1296.49 4406.50i 0.0819897 0.278665i
\(631\) 20147.0 1.27106 0.635529 0.772077i \(-0.280782\pi\)
0.635529 + 0.772077i \(0.280782\pi\)
\(632\) 777.592 + 2902.01i 0.0489414 + 0.182652i
\(633\) 19037.8 5027.15i 1.19539 0.315658i
\(634\) 4508.63 2603.06i 0.282430 0.163061i
\(635\) −10422.1 6038.22i −0.651322 0.377354i
\(636\) 7581.96 + 13243.1i 0.472711 + 0.825668i
\(637\) 5005.36 16594.2i 0.311334 1.03216i
\(638\) −3883.92 3883.92i −0.241013 0.241013i
\(639\) −509.439 897.359i −0.0315385 0.0555540i
\(640\) −13038.1 + 7501.34i −0.805278 + 0.463307i
\(641\) 8351.63 4821.82i 0.514617 0.297114i −0.220112 0.975475i \(-0.570642\pi\)
0.734730 + 0.678360i \(0.237309\pi\)
\(642\) −498.996 + 495.386i −0.0306757 + 0.0304538i
\(643\) 1306.96 1306.96i 0.0801580 0.0801580i −0.665891 0.746049i \(-0.731948\pi\)
0.746049 + 0.665891i \(0.231948\pi\)
\(644\) 7532.31 + 4506.66i 0.460892 + 0.275756i
\(645\) 5018.48 18351.3i 0.306360 1.12028i
\(646\) 307.573 532.732i 0.0187326 0.0324459i
\(647\) −15542.5 4164.59i −0.944416 0.253055i −0.246425 0.969162i \(-0.579256\pi\)
−0.697991 + 0.716106i \(0.745923\pi\)
\(648\) −8899.57 + 2246.64i −0.539518 + 0.136198i
\(649\) 22165.9 + 12797.5i 1.34066 + 0.774028i
\(650\) 5189.63 + 15.6767i 0.313160 + 0.000945983i
\(651\) 10047.0 16654.7i 0.604871 1.00269i
\(652\) −11255.2 11255.2i −0.676056 0.676056i
\(653\) −13983.8 + 3746.95i −0.838022 + 0.224547i −0.652210 0.758038i \(-0.726158\pi\)
−0.185812 + 0.982585i \(0.559491\pi\)
\(654\) 5949.44 + 3463.77i 0.355721 + 0.207101i
\(655\) −1955.19 527.058i −0.116635 0.0314410i
\(656\) 16162.0 + 9331.16i 0.961923 + 0.555366i
\(657\) 27534.1 7163.86i 1.63502 0.425401i
\(658\) 3695.18 + 3812.13i 0.218925 + 0.225854i
\(659\) −20669.8 −1.22182 −0.610910 0.791700i \(-0.709196\pi\)
−0.610910 + 0.791700i \(0.709196\pi\)
\(660\) −91.8690 + 17869.7i −0.00541818 + 1.05391i
\(661\) 11692.6 + 20252.1i 0.688030 + 1.19170i 0.972474 + 0.233011i \(0.0748577\pi\)
−0.284444 + 0.958693i \(0.591809\pi\)
\(662\) −3451.12 924.724i −0.202616 0.0542907i
\(663\) 8345.09 8284.71i 0.488833 0.485296i
\(664\) 13954.9i 0.815596i
\(665\) 59.1509 3461.30i 0.00344928 0.201840i
\(666\) 3175.94 + 1864.51i 0.184783 + 0.108481i
\(667\) −9949.79 + 2666.04i −0.577597 + 0.154767i
\(668\) 4351.11 16238.6i 0.252020 0.940553i
\(669\) 2384.93 4096.41i 0.137828 0.236736i
\(670\) 149.680 39.8644i 0.00863081 0.00229865i
\(671\) 14938.7i 0.859464i
\(672\) −3245.05 13113.1i −0.186280 0.752754i
\(673\) −20269.6 + 20269.6i −1.16097 + 1.16097i −0.176711 + 0.984263i \(0.556546\pi\)
−0.984263 + 0.176711i \(0.943454\pi\)
\(674\) −1573.68 + 2725.70i −0.0899346 + 0.155771i
\(675\) 4774.14 16874.7i 0.272232 0.962232i
\(676\) −1305.86 2261.82i −0.0742982 0.128688i
\(677\) 1262.44 + 4711.48i 0.0716683 + 0.267470i 0.992457 0.122592i \(-0.0391205\pi\)
−0.920789 + 0.390061i \(0.872454\pi\)
\(678\) −831.028 + 3057.00i −0.0470729 + 0.173161i
\(679\) −7655.24 + 12794.8i −0.432667 + 0.723149i
\(680\) 4451.03 + 4464.49i 0.251013 + 0.251773i
\(681\) −18686.5 67.8439i −1.05149 0.00381760i
\(682\) 1804.81 6735.66i 0.101334 0.378184i
\(683\) −25.6637 + 95.7784i −0.00143777 + 0.00536582i −0.966641 0.256135i \(-0.917551\pi\)
0.965203 + 0.261501i \(0.0842175\pi\)
\(684\) −2875.46 + 1632.42i −0.160740 + 0.0912534i
\(685\) 14690.1 + 22.1877i 0.819389 + 0.00123759i
\(686\) −2817.86 + 4393.06i −0.156831 + 0.244501i
\(687\) −8148.23 2215.05i −0.452510 0.123012i
\(688\) −4090.09 15264.4i −0.226647 0.845858i
\(689\) −10130.0 17545.6i −0.560117 0.970151i
\(690\) −2666.54 1557.86i −0.147121 0.0859516i
\(691\) −4393.41 + 7609.60i −0.241871 + 0.418933i −0.961247 0.275688i \(-0.911095\pi\)
0.719376 + 0.694621i \(0.244428\pi\)
\(692\) −5759.63 + 5759.63i −0.316399 + 0.316399i
\(693\) −20153.7 5896.61i −1.10473 0.323223i
\(694\) 7737.84i 0.423234i
\(695\) −1732.52 6505.13i −0.0945585 0.355041i
\(696\) 9001.29 + 5240.56i 0.490220 + 0.285407i
\(697\) 4482.68 16729.6i 0.243606 0.909150i
\(698\) 1180.30 316.262i 0.0640045 0.0171500i
\(699\) 23787.3 13618.7i 1.28715 0.736919i
\(700\) 16295.3 + 4692.80i 0.879864 + 0.253387i
\(701\) 15231.9i 0.820684i 0.911932 + 0.410342i \(0.134591\pi\)
−0.911932 + 0.410342i \(0.865409\pi\)
\(702\) 5642.32 1446.18i 0.303356 0.0777528i
\(703\) 2681.03 + 718.381i 0.143837 + 0.0385409i
\(704\) 5684.05 + 9845.07i 0.304298 + 0.527060i
\(705\) 14259.2 + 14406.6i 0.761749 + 0.769622i
\(706\) 9493.40 0.506075
\(707\) 20386.8 + 21032.0i 1.08447 + 1.11880i
\(708\) −22386.3 6085.57i −1.18831 0.323037i
\(709\) 17070.3 + 9855.54i 0.904215 + 0.522049i 0.878565 0.477622i \(-0.158501\pi\)
0.0256494 + 0.999671i \(0.491835\pi\)
\(710\) −304.289 + 175.069i −0.0160842 + 0.00925385i
\(711\) −6442.45 46.7811i −0.339818 0.00246755i
\(712\) −10898.0 + 2920.11i −0.573623 + 0.153702i
\(713\) −9247.10 9247.10i −0.485704 0.485704i
\(714\) −3099.89 + 1711.20i −0.162480 + 0.0896918i
\(715\) 35.8337 23725.0i 0.00187427 1.24093i
\(716\) −20408.9 11783.1i −1.06525 0.615020i
\(717\) 4401.96 1162.39i 0.229281 0.0605443i
\(718\) −7003.01 1876.45i −0.363997 0.0975328i
\(719\) −6971.12 + 12074.3i −0.361584 + 0.626282i −0.988222 0.153029i \(-0.951097\pi\)
0.626638 + 0.779311i \(0.284431\pi\)
\(720\) −3646.60 14103.0i −0.188751 0.729981i
\(721\) −16811.7 + 9360.16i −0.868379 + 0.483482i
\(722\) −3822.38 + 3822.38i −0.197028 + 0.197028i
\(723\) −21342.3 21497.8i −1.09783 1.10583i
\(724\) 23106.9 13340.7i 1.18613 0.684814i
\(725\) −17264.1 + 9898.05i −0.884379 + 0.507040i
\(726\) −1846.10 6.70251i −0.0943733 0.000342636i
\(727\) 6196.94 + 6196.94i 0.316137 + 0.316137i 0.847281 0.531144i \(-0.178238\pi\)
−0.531144 + 0.847281i \(0.678238\pi\)
\(728\) 2872.14 + 11428.2i 0.146221 + 0.581807i
\(729\) 428.736 19678.3i 0.0217820 0.999763i
\(730\) −2491.05 9353.20i −0.126298 0.474216i
\(731\) −12701.1 + 7333.00i −0.642638 + 0.371027i
\(732\) −3456.92 13091.3i −0.174551 0.661024i
\(733\) −2511.15 9371.75i −0.126537 0.472242i 0.873353 0.487088i \(-0.161941\pi\)
−0.999890 + 0.0148459i \(0.995274\pi\)
\(734\) −811.717 −0.0408189
\(735\) −10582.9 + 16883.9i −0.531096 + 0.847311i
\(736\) −9082.49 −0.454871
\(737\) −183.278 684.001i −0.00916026 0.0341866i
\(738\) 6110.21 6022.11i 0.304770 0.300375i
\(739\) −8167.66 + 4715.60i −0.406566 + 0.234731i −0.689313 0.724464i \(-0.742088\pi\)
0.282747 + 0.959194i \(0.408754\pi\)
\(740\) −6815.91 + 11764.4i −0.338592 + 0.584418i
\(741\) 3809.71 2181.13i 0.188871 0.108132i
\(742\) 1486.96 + 5916.56i 0.0735687 + 0.292727i
\(743\) 5590.07 + 5590.07i 0.276016 + 0.276016i 0.831516 0.555500i \(-0.187473\pi\)
−0.555500 + 0.831516i \(0.687473\pi\)
\(744\) −48.0086 + 13223.2i −0.00236570 + 0.651593i
\(745\) −9360.34 + 34723.4i −0.460317 + 1.70761i
\(746\) 4709.86 2719.24i 0.231153 0.133456i
\(747\) 28848.3 + 7954.85i 1.41299 + 0.389629i
\(748\) 9740.74 9740.74i 0.476145 0.476145i
\(749\) 2665.12 1483.84i 0.130015 0.0723877i
\(750\) −5750.18 1591.17i −0.279956 0.0774684i
\(751\) −5677.71 + 9834.09i −0.275876 + 0.477831i −0.970356 0.241681i \(-0.922301\pi\)
0.694480 + 0.719512i \(0.255635\pi\)
\(752\) 16263.2 + 4357.72i 0.788643 + 0.211316i
\(753\) 1445.07 + 5472.48i 0.0699354 + 0.264845i
\(754\) −5724.12 3304.82i −0.276473 0.159622i
\(755\) −545.958 547.610i −0.0263172 0.0263968i
\(756\) 19026.0 + 503.718i 0.915303 + 0.0242329i
\(757\) −8559.38 8559.38i −0.410959 0.410959i 0.471114 0.882073i \(-0.343852\pi\)
−0.882073 + 0.471114i \(0.843852\pi\)
\(758\) 10871.1 2912.89i 0.520917 0.139579i
\(759\) −7103.48 + 12201.1i −0.339710 + 0.583493i
\(760\) 1173.66 + 2039.96i 0.0560175 + 0.0973645i
\(761\) 11916.3 + 6879.87i 0.567628 + 0.327720i 0.756201 0.654339i \(-0.227053\pi\)
−0.188573 + 0.982059i \(0.560386\pi\)
\(762\) −1206.50 + 4438.20i −0.0573580 + 0.210996i
\(763\) −20786.5 21444.4i −0.986268 1.01748i
\(764\) −14785.7 −0.700165
\(765\) −11766.5 + 6656.47i −0.556103 + 0.314595i
\(766\) −3133.59 5427.54i −0.147808 0.256012i
\(767\) 29750.2 + 7971.55i 1.40055 + 0.375275i
\(768\) −3881.73 3910.02i −0.182383 0.183712i
\(769\) 4419.71i 0.207255i −0.994616 0.103627i \(-0.966955\pi\)
0.994616 0.103627i \(-0.0330449\pi\)
\(770\) −1966.63 + 6867.92i −0.0920419 + 0.321432i
\(771\) 4117.43 + 7191.78i 0.192329 + 0.335935i
\(772\) −23948.1 + 6416.88i −1.11647 + 0.299156i
\(773\) 1507.92 5627.65i 0.0701634 0.261853i −0.921930 0.387357i \(-0.873388\pi\)
0.992093 + 0.125504i \(0.0400547\pi\)
\(774\) −7264.40 52.7496i −0.337356 0.00244967i
\(775\) −21841.4 12698.3i −1.01234 0.588562i
\(776\) 10136.5i 0.468916i
\(777\) −11078.2 11512.1i −0.511489 0.531525i
\(778\) −2993.16 + 2993.16i −0.137931 + 0.137931i
\(779\) 3232.89 5599.53i 0.148691 0.257540i
\(780\) 5458.74 + 20799.4i 0.250583 + 0.954795i
\(781\) 802.446 + 1389.88i 0.0367654 + 0.0636796i
\(782\) 616.160 + 2299.54i 0.0281763 + 0.105155i
\(783\) −15964.7 + 15620.6i −0.728647 + 0.712944i
\(784\) −515.570 + 16543.5i −0.0234862 + 0.753623i
\(785\) −12.8345 + 8497.53i −0.000583545 + 0.386357i
\(786\) −2.80728 + 773.218i −0.000127395 + 0.0350888i
\(787\) −6316.95 + 23575.2i −0.286118 + 1.06781i 0.661900 + 0.749592i \(0.269750\pi\)
−0.948018 + 0.318215i \(0.896916\pi\)
\(788\) 6443.12 24046.0i 0.291277 1.08706i
\(789\) 57.0991 15727.0i 0.00257640 0.709628i
\(790\) −3.31052 + 2191.85i −0.000149092 + 0.0987118i
\(791\) 7056.13 11793.4i 0.317177 0.530122i
\(792\) 13815.8 3594.62i 0.619853 0.161274i
\(793\) 4652.65 + 17363.9i 0.208349 + 0.777568i
\(794\) 5890.66 + 10202.9i 0.263289 + 0.456030i
\(795\) 5912.61 + 22528.8i 0.263772 + 1.00505i
\(796\) 6559.37 11361.2i 0.292074 0.505887i
\(797\) −18690.0 + 18690.0i −0.830658 + 0.830658i −0.987607 0.156948i \(-0.949834\pi\)
0.156948 + 0.987607i \(0.449834\pi\)
\(798\) −1283.16 + 317.537i −0.0569213 + 0.0140861i
\(799\) 15625.7i 0.691861i
\(800\) −16962.4 + 4490.19i −0.749640 + 0.198440i
\(801\) 175.678 24193.5i 0.00774941 1.06721i
\(802\) 450.687 1681.99i 0.0198433 0.0740561i
\(803\) −42741.8 + 11452.6i −1.87836 + 0.503306i
\(804\) 318.896 + 557.005i 0.0139883 + 0.0244329i
\(805\) 9310.18 + 9633.92i 0.407628 + 0.421802i
\(806\) 8391.30i 0.366713i
\(807\) 25481.9 + 25667.6i 1.11153 + 1.11963i
\(808\) −19234.8 5153.95i −0.837473 0.224400i
\(809\) 16896.4 + 29265.4i 0.734296 + 1.27184i 0.955032 + 0.296504i \(0.0958208\pi\)
−0.220736 + 0.975334i \(0.570846\pi\)
\(810\) −6695.50 107.357i −0.290439 0.00465698i
\(811\) −26144.2 −1.13199 −0.565996 0.824408i \(-0.691508\pi\)
−0.565996 + 0.824408i \(0.691508\pi\)
\(812\) −15032.0 15507.8i −0.649655 0.670217i
\(813\) −2662.13 + 9792.84i −0.114840 + 0.422447i
\(814\) −4960.49 2863.94i −0.213593 0.123318i
\(815\) −12115.7 21058.4i −0.520730 0.905085i
\(816\) −5649.86 + 9704.30i −0.242383 + 0.416322i
\(817\) −5288.54 + 1417.06i −0.226466 + 0.0606813i
\(818\) −904.480 904.480i −0.0386606 0.0386606i
\(819\) −25262.1 577.047i −1.07781 0.0246199i
\(820\) 22362.0 + 22429.6i 0.952334 + 0.955215i
\(821\) 5871.35 + 3389.82i 0.249588 + 0.144099i 0.619575 0.784937i \(-0.287305\pi\)
−0.369988 + 0.929037i \(0.620638\pi\)
\(822\) −1432.12 5423.42i −0.0607674 0.230126i
\(823\) 20484.7 + 5488.85i 0.867620 + 0.232478i 0.665058 0.746792i \(-0.268407\pi\)
0.202562 + 0.979270i \(0.435073\pi\)
\(824\) 6540.71 11328.8i 0.276525 0.478955i
\(825\) −7234.48 + 26298.5i −0.305300 + 1.10981i
\(826\) −7958.52 4761.66i −0.335245 0.200580i
\(827\) 8077.18 8077.18i 0.339627 0.339627i −0.516600 0.856227i \(-0.672803\pi\)
0.856227 + 0.516600i \(0.172803\pi\)
\(828\) 3401.64 12336.1i 0.142772 0.517764i
\(829\) 32809.9 18942.8i 1.37459 0.793619i 0.383086 0.923713i \(-0.374861\pi\)
0.991502 + 0.130094i \(0.0415279\pi\)
\(830\) 2649.84 9829.91i 0.110816 0.411086i
\(831\) −69.4484 + 19128.4i −0.00289908 + 0.798504i
\(832\) 9673.11 + 9673.11i 0.403071 + 0.403071i
\(833\) 14954.1 3511.57i 0.622002 0.146061i
\(834\) −2230.78 + 1277.17i −0.0926208 + 0.0530272i
\(835\) 12863.4 22202.6i 0.533122 0.920182i
\(836\) 4453.67 2571.33i 0.184250 0.106377i
\(837\) −27308.3 7636.98i −1.12773 0.315379i
\(838\) −1690.08 6307.46i −0.0696693 0.260009i
\(839\) 9131.09 0.375733 0.187867 0.982195i \(-0.439843\pi\)
0.187867 + 0.982195i \(0.439843\pi\)
\(840\) 280.647 13544.0i 0.0115277 0.556325i
\(841\) 956.422 0.0392153
\(842\) −3572.58 13333.0i −0.146222 0.545709i
\(843\) 4716.87 + 17862.8i 0.192714 + 0.729805i
\(844\) 24038.6 13878.7i 0.980383 0.566024i
\(845\) −1025.93 3852.08i −0.0417669 0.156823i
\(846\) 3918.55 6674.72i 0.159246 0.271255i
\(847\) 7702.65 + 2193.07i 0.312475 + 0.0889666i
\(848\) 13680.3 + 13680.3i 0.553990 + 0.553990i
\(849\) −16696.7 60.6199i −0.674947 0.00245049i
\(850\) 2287.58 + 3990.00i 0.0923100 + 0.161007i
\(851\) −9302.69 + 5370.91i −0.374726 + 0.216348i
\(852\) −1024.84 1032.31i −0.0412096 0.0415099i
\(853\) −14868.7 + 14868.7i −0.596829 + 0.596829i −0.939467 0.342639i \(-0.888679\pi\)
0.342639 + 0.939467i \(0.388679\pi\)
\(854\) 84.3154 5412.31i 0.00337847 0.216868i
\(855\) −4886.14 + 1263.41i −0.195442 + 0.0505352i
\(856\) −1036.88 + 1795.93i −0.0414017 + 0.0717099i
\(857\) −16091.3 4311.64i −0.641385 0.171859i −0.0765543 0.997065i \(-0.524392\pi\)
−0.564831 + 0.825207i \(0.691059\pi\)
\(858\) −8758.97 + 2312.91i −0.348516 + 0.0920296i
\(859\) 28765.6 + 16607.8i 1.14257 + 0.659665i 0.947066 0.321038i \(-0.104032\pi\)
0.195506 + 0.980702i \(0.437365\pi\)
\(860\) 40.5078 26819.6i 0.00160617 1.06342i
\(861\) −32582.9 + 17986.3i −1.28969 + 0.711932i
\(862\) −1461.65 1461.65i −0.0577542 0.0577542i
\(863\) 36321.2 9732.24i 1.43266 0.383881i 0.542705 0.839923i \(-0.317400\pi\)
0.889958 + 0.456042i \(0.150733\pi\)
\(864\) −17161.6 + 9660.57i −0.675752 + 0.380393i
\(865\) −10776.2 + 6199.97i −0.423586 + 0.243705i
\(866\) −6069.78 3504.39i −0.238175 0.137510i
\(867\) −14578.3 3963.03i −0.571055 0.155238i
\(868\) 7508.29 26371.1i 0.293603 1.03121i
\(869\) 10020.2 0.391155
\(870\) 5345.44 + 5400.69i 0.208308 + 0.210460i
\(871\) −426.065 737.966i −0.0165748 0.0287084i
\(872\) 19612.0 + 5255.02i 0.761635 + 0.204079i
\(873\) 20954.7 + 5778.20i 0.812382 + 0.224012i
\(874\) 888.745i 0.0343962i
\(875\) 22150.5 + 13389.5i 0.855797 + 0.517312i
\(876\) 34806.1 19927.2i 1.34245 0.768582i
\(877\) 10288.5 2756.80i 0.396144 0.106147i −0.0552469 0.998473i \(-0.517595\pi\)
0.451391 + 0.892326i \(0.350928\pi\)
\(878\) 161.349 602.162i 0.00620189 0.0231458i
\(879\) −18771.2 10928.6i −0.720294 0.419356i
\(880\) 5830.69 + 21892.7i 0.223355 + 0.838638i
\(881\) 11778.8i 0.450440i −0.974308 0.225220i \(-0.927690\pi\)
0.974308 0.225220i \(-0.0723101\pi\)
\(882\) 7268.45 + 2250.11i 0.277485 + 0.0859014i
\(883\) 19073.4 19073.4i 0.726920 0.726920i −0.243085 0.970005i \(-0.578159\pi\)
0.970005 + 0.243085i \(0.0781594\pi\)
\(884\) 8288.38 14355.9i 0.315349 0.546200i
\(885\) −30573.5 17861.8i −1.16126 0.678439i
\(886\) 5485.40 + 9500.99i 0.207997 + 0.360262i
\(887\) −1223.17 4564.93i −0.0463022 0.172802i 0.938903 0.344183i \(-0.111844\pi\)
−0.985205 + 0.171380i \(0.945177\pi\)
\(888\) 10481.3 + 2849.28i 0.396091 + 0.107675i
\(889\) 10244.2 17121.9i 0.386478 0.645950i
\(890\) −8231.08 12.4321i −0.310007 0.000468229i
\(891\) −444.563 + 30609.9i −0.0167154 + 1.15092i
\(892\) 1729.45 6454.39i 0.0649173 0.242275i
\(893\) 1509.78 5634.59i 0.0565767 0.211147i
\(894\) 13732.0 + 49.8562i 0.513723 + 0.00186514i
\(895\) −25396.0 25472.8i −0.948485 0.951355i
\(896\) −12121.0 21770.4i −0.451934 0.811715i
\(897\) −4456.69 + 16394.3i −0.165891 + 0.610244i
\(898\) −45.6305 170.295i −0.00169567 0.00632831i
\(899\) 16088.7 + 27866.4i 0.596871 + 1.03381i
\(900\) 254.186 24720.5i 0.00941428 0.915575i
\(901\) 8977.51 15549.5i 0.331947 0.574949i
\(902\) −9434.99 + 9434.99i −0.348282 + 0.348282i
\(903\) 30279.1 + 8739.91i 1.11586 + 0.322088i
\(904\) 9343.20i 0.343750i
\(905\) 39353.0 10480.9i 1.44545 0.384969i
\(906\) −148.561 + 255.171i −0.00544768 + 0.00935705i
\(907\) 770.592 2875.89i 0.0282107 0.105284i −0.950385 0.311076i \(-0.899311\pi\)
0.978596 + 0.205793i \(0.0659772\pi\)
\(908\) −25444.8 + 6817.91i −0.929973 + 0.249185i
\(909\) 21619.1 36825.3i 0.788846 1.34369i
\(910\) −146.889 + 8595.42i −0.00535091 + 0.313116i
\(911\) 15023.3i 0.546369i −0.961962 0.273185i \(-0.911923\pi\)
0.961962 0.273185i \(-0.0880770\pi\)
\(912\) −2974.98 + 2953.45i −0.108017 + 0.107235i
\(913\) −44956.6 12046.1i −1.62963 0.436657i
\(914\) 2404.57 + 4164.83i 0.0870197 + 0.150723i
\(915\) 106.247 20666.3i 0.00383869 0.746675i
\(916\) −11903.4 −0.429365
\(917\) 918.544 3226.18i 0.0330785 0.116181i
\(918\) 3610.15 + 3689.67i 0.129796 + 0.132655i
\(919\) 20061.6 + 11582.6i 0.720100 + 0.415750i 0.814790 0.579757i \(-0.196852\pi\)
−0.0946892 + 0.995507i \(0.530186\pi\)
\(920\) −8794.26 2370.66i −0.315150 0.0849546i
\(921\) −15345.8 8934.37i −0.549036 0.319650i
\(922\) −4878.86 + 1307.29i −0.174270 + 0.0466955i
\(923\) 1365.60 + 1365.60i 0.0486991 + 0.0486991i
\(924\) −29596.1 568.547i −1.05372 0.0202422i
\(925\) −14718.4 + 14629.8i −0.523176 + 0.520025i
\(926\) 8486.98 + 4899.96i 0.301187 + 0.173891i
\(927\) 19691.1 + 19979.2i 0.697672 + 0.707878i
\(928\) 21586.3 + 5784.03i 0.763583 + 0.204601i
\(929\) 22910.8 39682.7i 0.809128 1.40145i −0.104341 0.994542i \(-0.533273\pi\)
0.913469 0.406909i \(-0.133393\pi\)
\(930\) −2544.71 + 9305.36i −0.0897250 + 0.328102i
\(931\) 5731.71 + 178.625i 0.201771 + 0.00628809i
\(932\) 27322.3 27322.3i 0.960272 0.960272i
\(933\) −9098.62 + 9032.79i −0.319266 + 0.316956i
\(934\) −95.9720 + 55.4095i −0.00336221 + 0.00194117i
\(935\) 18224.8 10485.5i 0.637451 0.366750i
\(936\) 14939.2 8481.14i 0.521693 0.296170i
\(937\) 11019.0 + 11019.0i 0.384178 + 0.384178i 0.872605 0.488427i \(-0.162429\pi\)
−0.488427 + 0.872605i \(0.662429\pi\)
\(938\) 62.5413 + 248.850i 0.00217702 + 0.00866229i
\(939\) 12255.7 + 21406.6i 0.425932 + 0.743960i
\(940\) 24724.7 + 14324.7i 0.857905 + 0.497041i
\(941\) −4604.68 + 2658.51i −0.159520 + 0.0920988i −0.577635 0.816295i \(-0.696024\pi\)
0.418115 + 0.908394i \(0.362691\pi\)
\(942\) 3137.18 828.410i 0.108508 0.0286529i
\(943\) 6476.45 + 24170.4i 0.223650 + 0.834674i
\(944\) −29411.7 −1.01406
\(945\) 27838.9 + 8300.79i 0.958307 + 0.285740i
\(946\) 11298.7 0.388321
\(947\) −13940.7 52027.3i −0.478364 1.78528i −0.608244 0.793750i \(-0.708126\pi\)
0.129880 0.991530i \(-0.458541\pi\)
\(948\) −8781.14 + 2318.76i −0.300842 + 0.0794408i
\(949\) −46114.0 + 26623.9i −1.57737 + 0.910695i
\(950\) 439.377 + 1659.82i 0.0150056 + 0.0566859i
\(951\) 16359.4 + 28574.4i 0.557823 + 0.974330i
\(952\) −7498.43 + 7268.38i −0.255279 + 0.247447i
\(953\) −18298.9 18298.9i −0.621994 0.621994i 0.324047 0.946041i \(-0.394956\pi\)
−0.946041 + 0.324047i \(0.894956\pi\)
\(954\) 7734.31 4390.84i 0.262482 0.149013i
\(955\) −21789.9 5873.89i −0.738331 0.199031i
\(956\) 5558.26 3209.06i 0.188041 0.108565i
\(957\) 24652.9 24474.5i 0.832721 0.826696i
\(958\) 5996.47 5996.47i 0.202231 0.202231i
\(959\) −379.044 + 24331.3i −0.0127633 + 0.819291i
\(960\) −7793.37 13660.2i −0.262010 0.459252i
\(961\) −5529.91 + 9578.09i −0.185624 + 0.321510i
\(962\) −6657.79 1783.95i −0.223135 0.0597888i
\(963\) −3121.58 3167.25i −0.104456 0.105985i
\(964\) −36982.3 21351.7i −1.23560 0.713375i
\(965\) −37842.1 57.1559i −1.26236 0.00190665i
\(966\) 2642.47 4380.39i 0.0880126 0.145897i
\(967\) −19832.0 19832.0i −0.659518 0.659518i 0.295748 0.955266i \(-0.404431\pi\)
−0.955266 + 0.295748i \(0.904431\pi\)
\(968\) −5259.19 + 1409.20i −0.174625 + 0.0467906i
\(969\) 3362.17 + 1957.46i 0.111464 + 0.0648944i
\(970\) 1924.77 7140.20i 0.0637121 0.236348i
\(971\) −38964.1 22495.9i −1.28776 0.743490i −0.309508 0.950897i \(-0.600164\pi\)
−0.978255 + 0.207406i \(0.933498\pi\)
\(972\) −6693.77 26927.5i −0.220887 0.888580i
\(973\) 10815.1 2718.06i 0.356336 0.0895550i
\(974\) 13159.7 0.432921
\(975\) −218.310 + 32821.2i −0.00717077 + 1.07807i
\(976\) −8583.16 14866.5i −0.281496 0.487566i
\(977\) 12148.6 + 3255.20i 0.397817 + 0.106595i 0.452180 0.891927i \(-0.350646\pi\)
−0.0543635 + 0.998521i \(0.517313\pi\)
\(978\) −6583.50 + 6535.87i −0.215253 + 0.213695i
\(979\) 37629.3i 1.22843i
\(980\) −8152.56 + 26881.2i −0.265739 + 0.876213i
\(981\) −22043.0 + 37547.4i −0.717411 + 1.22201i
\(982\) −14959.6 + 4008.41i −0.486130 + 0.130258i
\(983\) −7870.81 + 29374.3i −0.255381 + 0.953096i 0.712497 + 0.701675i \(0.247564\pi\)
−0.967878 + 0.251420i \(0.919102\pi\)
\(984\) 12730.6 21866.3i 0.412435 0.708407i
\(985\) 19048.1 32877.5i 0.616166 1.06352i
\(986\) 5857.70i 0.189196i
\(987\) −24194.4 + 23282.4i −0.780261 + 0.750848i
\(988\) 4375.87 4375.87i 0.140906 0.140906i
\(989\) 10594.5 18350.2i 0.340633 0.589994i
\(990\) 10414.5 + 91.3544i 0.334338 + 0.00293276i
\(991\) −6881.34 11918.8i −0.220578 0.382053i 0.734405 0.678711i \(-0.237461\pi\)
−0.954984 + 0.296658i \(0.904128\pi\)
\(992\) 7343.13 + 27404.9i 0.235025 + 0.877125i
\(993\) 5927.61 21805.2i 0.189433 0.696844i
\(994\) −282.884 508.085i −0.00902668 0.0162128i
\(995\) 14180.1 14137.4i 0.451799 0.450437i
\(996\) 42184.8 + 153.158i 1.34205 + 0.00487249i
\(997\) 3790.17 14145.1i 0.120397 0.449328i −0.879237 0.476385i \(-0.841947\pi\)
0.999634 + 0.0270568i \(0.00861351\pi\)
\(998\) −3710.37 + 13847.3i −0.117685 + 0.439207i
\(999\) −11864.9 + 20043.3i −0.375765 + 0.634776i
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 105.4.x.a.2.19 176
3.2 odd 2 inner 105.4.x.a.2.26 yes 176
5.3 odd 4 inner 105.4.x.a.23.19 yes 176
7.4 even 3 inner 105.4.x.a.32.26 yes 176
15.8 even 4 inner 105.4.x.a.23.26 yes 176
21.11 odd 6 inner 105.4.x.a.32.19 yes 176
35.18 odd 12 inner 105.4.x.a.53.26 yes 176
105.53 even 12 inner 105.4.x.a.53.19 yes 176
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.x.a.2.19 176 1.1 even 1 trivial
105.4.x.a.2.26 yes 176 3.2 odd 2 inner
105.4.x.a.23.19 yes 176 5.3 odd 4 inner
105.4.x.a.23.26 yes 176 15.8 even 4 inner
105.4.x.a.32.19 yes 176 21.11 odd 6 inner
105.4.x.a.32.26 yes 176 7.4 even 3 inner
105.4.x.a.53.19 yes 176 105.53 even 12 inner
105.4.x.a.53.26 yes 176 35.18 odd 12 inner