Properties

Label 175.4.x.a.117.43
Level $175$
Weight $4$
Character 175.117
Analytic conductor $10.325$
Analytic rank $0$
Dimension $928$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [175,4,Mod(3,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([21, 10]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 175.x (of order \(60\), degree \(16\), 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: \(10.3253342510\)
Analytic rank: \(0\)
Dimension: \(928\)
Relative dimension: \(58\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 117.43
Character \(\chi\) \(=\) 175.117
Dual form 175.4.x.a.3.43

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.66660 + 2.56634i) q^{2} +(3.28687 + 8.56260i) q^{3} +(-0.554650 + 1.24576i) q^{4} +(5.95503 - 9.46244i) q^{5} +(-16.4966 + 22.7057i) q^{6} +(16.8267 + 7.73716i) q^{7} +(20.0573 - 3.17676i) q^{8} +(-42.4496 + 38.2218i) q^{9} +(34.2085 - 0.487482i) q^{10} +(-18.2776 + 20.2994i) q^{11} +(-12.4900 - 0.654575i) q^{12} +(-30.7491 + 15.6674i) q^{13} +(8.18715 + 56.0777i) q^{14} +(100.596 + 19.8887i) q^{15} +(48.8798 + 54.2865i) q^{16} +(-33.3321 - 41.1617i) q^{17} +(-168.837 - 45.2397i) q^{18} +(17.3924 - 7.74361i) q^{19} +(8.48500 + 12.6669i) q^{20} +(-10.9431 + 169.511i) q^{21} +(-82.5567 - 13.0757i) q^{22} +(91.8109 - 59.6227i) q^{23} +(93.1269 + 161.301i) q^{24} +(-54.0754 - 112.698i) q^{25} +(-91.4544 - 52.8012i) q^{26} +(-246.157 - 125.423i) q^{27} +(-18.9716 + 16.6706i) q^{28} +(-142.281 - 195.833i) q^{29} +(116.613 + 291.311i) q^{30} +(112.275 + 11.8006i) q^{31} +(-15.8073 + 58.9935i) q^{32} +(-233.892 - 89.7826i) q^{33} +(50.0836 - 154.141i) q^{34} +(173.416 - 113.146i) q^{35} +(-24.0707 - 74.0819i) q^{36} +(9.15272 - 174.644i) q^{37} +(48.8590 + 31.7294i) q^{38} +(-235.222 - 211.795i) q^{39} +(89.3816 - 208.708i) q^{40} +(-190.983 - 62.0541i) q^{41} +(-453.260 + 254.423i) q^{42} +(-131.557 + 131.557i) q^{43} +(-15.1505 - 34.0287i) q^{44} +(108.883 + 629.289i) q^{45} +(306.024 + 136.251i) q^{46} +(440.124 + 356.405i) q^{47} +(-304.172 + 596.971i) q^{48} +(223.273 + 260.381i) q^{49} +(199.100 - 326.598i) q^{50} +(242.893 - 420.702i) q^{51} +(-2.46296 - 46.9960i) q^{52} +(-275.106 + 105.603i) q^{53} +(-88.3668 - 840.754i) q^{54} +(83.2378 + 293.834i) q^{55} +(362.076 + 101.732i) q^{56} +(123.472 + 123.472i) q^{57} +(265.448 - 691.516i) q^{58} +(425.060 - 90.3494i) q^{59} +(-80.5723 + 114.288i) q^{60} +(14.1121 - 66.3922i) q^{61} +(156.833 + 307.803i) q^{62} +(-1010.01 + 314.706i) q^{63} +(378.053 - 122.837i) q^{64} +(-34.8594 + 384.261i) q^{65} +(-159.391 - 749.877i) q^{66} +(594.519 - 481.432i) q^{67} +(69.7653 - 18.6936i) q^{68} +(812.296 + 590.168i) q^{69} +(579.386 + 256.474i) q^{70} +(-785.349 + 570.590i) q^{71} +(-730.001 + 901.477i) q^{72} +(-540.459 + 28.3242i) q^{73} +(463.451 - 267.573i) q^{74} +(787.249 - 833.450i) q^{75} +25.9618i q^{76} +(-464.611 + 200.154i) q^{77} +(151.517 - 956.638i) q^{78} +(-708.371 + 74.4528i) q^{79} +(804.763 - 139.244i) q^{80} +(103.650 - 986.161i) q^{81} +(-159.040 - 593.546i) q^{82} +(-185.606 - 1171.87i) q^{83} +(-205.101 - 107.652i) q^{84} +(-587.983 + 70.2837i) q^{85} +(-556.874 - 118.367i) q^{86} +(1209.18 - 1861.97i) q^{87} +(-302.113 + 465.214i) q^{88} +(819.936 + 174.283i) q^{89} +(-1433.50 + 1328.20i) q^{90} +(-638.626 + 25.7202i) q^{91} +(23.3529 + 147.444i) q^{92} +(267.990 + 1000.15i) q^{93} +(-181.146 + 1723.49i) q^{94} +(30.2990 - 210.688i) q^{95} +(-557.094 + 58.5530i) q^{96} +(223.240 - 1409.48i) q^{97} +(-296.119 + 1006.95i) q^{98} -1560.31i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.66660 + 2.56634i 0.589232 + 0.907338i 0.999990 0.00440625i \(-0.00140256\pi\)
−0.410758 + 0.911744i \(0.634736\pi\)
\(3\) 3.28687 + 8.56260i 0.632559 + 1.64787i 0.755257 + 0.655428i \(0.227512\pi\)
−0.122698 + 0.992444i \(0.539155\pi\)
\(4\) −0.554650 + 1.24576i −0.0693312 + 0.155720i
\(5\) 5.95503 9.46244i 0.532634 0.846346i
\(6\) −16.4966 + 22.7057i −1.12245 + 1.54492i
\(7\) 16.8267 + 7.73716i 0.908554 + 0.417767i
\(8\) 20.0573 3.17676i 0.886414 0.140394i
\(9\) −42.4496 + 38.2218i −1.57221 + 1.41562i
\(10\) 34.2085 0.487482i 1.08177 0.0154155i
\(11\) −18.2776 + 20.2994i −0.500993 + 0.556409i −0.939602 0.342269i \(-0.888805\pi\)
0.438609 + 0.898678i \(0.355471\pi\)
\(12\) −12.4900 0.654575i −0.300463 0.0157466i
\(13\) −30.7491 + 15.6674i −0.656020 + 0.334259i −0.750118 0.661304i \(-0.770003\pi\)
0.0940979 + 0.995563i \(0.470003\pi\)
\(14\) 8.18715 + 56.0777i 0.156293 + 1.07053i
\(15\) 100.596 + 19.8887i 1.73159 + 0.342349i
\(16\) 48.8798 + 54.2865i 0.763747 + 0.848227i
\(17\) −33.3321 41.1617i −0.475542 0.587246i 0.481772 0.876297i \(-0.339994\pi\)
−0.957314 + 0.289051i \(0.906660\pi\)
\(18\) −168.837 45.2397i −2.21084 0.592394i
\(19\) 17.3924 7.74361i 0.210005 0.0935003i −0.299038 0.954241i \(-0.596666\pi\)
0.509044 + 0.860741i \(0.329999\pi\)
\(20\) 8.48500 + 12.6669i 0.0948652 + 0.141620i
\(21\) −10.9431 + 169.511i −0.113713 + 1.76144i
\(22\) −82.5567 13.0757i −0.800052 0.126716i
\(23\) 91.8109 59.6227i 0.832343 0.540530i −0.0566797 0.998392i \(-0.518051\pi\)
0.889023 + 0.457862i \(0.151385\pi\)
\(24\) 93.1269 + 161.301i 0.792061 + 1.37189i
\(25\) −54.0754 112.698i −0.432603 0.901585i
\(26\) −91.4544 52.8012i −0.689834 0.398276i
\(27\) −246.157 125.423i −1.75455 0.893990i
\(28\) −18.9716 + 16.6706i −0.128046 + 0.112516i
\(29\) −142.281 195.833i −0.911065 1.25397i −0.966802 0.255528i \(-0.917751\pi\)
0.0557366 0.998446i \(-0.482249\pi\)
\(30\) 116.613 + 291.311i 0.709684 + 1.77286i
\(31\) 112.275 + 11.8006i 0.650491 + 0.0683693i 0.424026 0.905650i \(-0.360617\pi\)
0.226465 + 0.974019i \(0.427283\pi\)
\(32\) −15.8073 + 58.9935i −0.0873237 + 0.325896i
\(33\) −233.892 89.7826i −1.23380 0.473611i
\(34\) 50.0836 154.141i 0.252626 0.777501i
\(35\) 173.416 113.146i 0.837502 0.546434i
\(36\) −24.0707 74.0819i −0.111438 0.342972i
\(37\) 9.15272 174.644i 0.0406675 0.775983i −0.899842 0.436216i \(-0.856318\pi\)
0.940510 0.339767i \(-0.110348\pi\)
\(38\) 48.8590 + 31.7294i 0.208578 + 0.135452i
\(39\) −235.222 211.795i −0.965788 0.869599i
\(40\) 89.3816 208.708i 0.353312 0.824991i
\(41\) −190.983 62.0541i −0.727476 0.236371i −0.0782144 0.996937i \(-0.524922\pi\)
−0.649261 + 0.760565i \(0.724922\pi\)
\(42\) −453.260 + 254.423i −1.66523 + 0.934723i
\(43\) −131.557 + 131.557i −0.466565 + 0.466565i −0.900800 0.434235i \(-0.857019\pi\)
0.434235 + 0.900800i \(0.357019\pi\)
\(44\) −15.1505 34.0287i −0.0519098 0.116591i
\(45\) 108.883 + 629.289i 0.360695 + 2.08464i
\(46\) 306.024 + 136.251i 0.980887 + 0.436719i
\(47\) 440.124 + 356.405i 1.36593 + 1.10611i 0.983257 + 0.182223i \(0.0583291\pi\)
0.382671 + 0.923885i \(0.375004\pi\)
\(48\) −304.172 + 596.971i −0.914654 + 1.79511i
\(49\) 223.273 + 260.381i 0.650941 + 0.759128i
\(50\) 199.100 326.598i 0.563139 0.923760i
\(51\) 242.893 420.702i 0.666897 1.15510i
\(52\) −2.46296 46.9960i −0.00656828 0.125330i
\(53\) −275.106 + 105.603i −0.712994 + 0.273693i −0.687708 0.725987i \(-0.741383\pi\)
−0.0252861 + 0.999680i \(0.508050\pi\)
\(54\) −88.3668 840.754i −0.222689 2.11874i
\(55\) 83.2378 + 293.834i 0.204069 + 0.720375i
\(56\) 362.076 + 101.732i 0.864007 + 0.242759i
\(57\) 123.472 + 123.472i 0.286917 + 0.286917i
\(58\) 265.448 691.516i 0.600949 1.56553i
\(59\) 425.060 90.3494i 0.937935 0.199364i 0.286510 0.958077i \(-0.407505\pi\)
0.651425 + 0.758713i \(0.274172\pi\)
\(60\) −80.5723 + 114.288i −0.173364 + 0.245909i
\(61\) 14.1121 66.3922i 0.0296208 0.139355i −0.960852 0.277061i \(-0.910640\pi\)
0.990473 + 0.137706i \(0.0439729\pi\)
\(62\) 156.833 + 307.803i 0.321256 + 0.630500i
\(63\) −1010.01 + 314.706i −2.01984 + 0.629353i
\(64\) 378.053 122.837i 0.738385 0.239916i
\(65\) −34.8594 + 384.261i −0.0665197 + 0.733258i
\(66\) −159.391 749.877i −0.297269 1.39854i
\(67\) 594.519 481.432i 1.08406 0.877855i 0.0910462 0.995847i \(-0.470979\pi\)
0.993015 + 0.117992i \(0.0376456\pi\)
\(68\) 69.7653 18.6936i 0.124416 0.0333372i
\(69\) 812.296 + 590.168i 1.41723 + 1.02968i
\(70\) 579.386 + 256.474i 0.989284 + 0.437921i
\(71\) −785.349 + 570.590i −1.31273 + 0.953754i −0.312738 + 0.949840i \(0.601246\pi\)
−0.999992 + 0.00391469i \(0.998754\pi\)
\(72\) −730.001 + 901.477i −1.19488 + 1.47556i
\(73\) −540.459 + 28.3242i −0.866519 + 0.0454123i −0.480413 0.877042i \(-0.659513\pi\)
−0.386106 + 0.922455i \(0.626180\pi\)
\(74\) 463.451 267.573i 0.728041 0.420335i
\(75\) 787.249 833.450i 1.21205 1.28318i
\(76\) 25.9618i 0.0391846i
\(77\) −464.611 + 200.154i −0.687628 + 0.296229i
\(78\) 151.517 956.638i 0.219947 1.38869i
\(79\) −708.371 + 74.4528i −1.00883 + 0.106033i −0.594503 0.804093i \(-0.702651\pi\)
−0.414332 + 0.910126i \(0.635985\pi\)
\(80\) 804.763 139.244i 1.12469 0.194600i
\(81\) 103.650 986.161i 0.142181 1.35276i
\(82\) −159.040 593.546i −0.214184 0.799344i
\(83\) −185.606 1171.87i −0.245457 1.54976i −0.735176 0.677876i \(-0.762901\pi\)
0.489719 0.871880i \(-0.337099\pi\)
\(84\) −205.101 107.652i −0.266409 0.139830i
\(85\) −587.983 + 70.2837i −0.750303 + 0.0896864i
\(86\) −556.874 118.367i −0.698247 0.148417i
\(87\) 1209.18 1861.97i 1.49009 2.29453i
\(88\) −302.113 + 465.214i −0.365970 + 0.563545i
\(89\) 819.936 + 174.283i 0.976551 + 0.207572i 0.668430 0.743775i \(-0.266967\pi\)
0.308121 + 0.951347i \(0.400300\pi\)
\(90\) −1433.50 + 1328.20i −1.67894 + 1.55561i
\(91\) −638.626 + 25.7202i −0.735672 + 0.0296287i
\(92\) 23.3529 + 147.444i 0.0264642 + 0.167088i
\(93\) 267.990 + 1000.15i 0.298810 + 1.11517i
\(94\) −181.146 + 1723.49i −0.198764 + 1.89111i
\(95\) 30.2990 210.688i 0.0327222 0.227538i
\(96\) −557.094 + 58.5530i −0.592273 + 0.0622504i
\(97\) 223.240 1409.48i 0.233677 1.47538i −0.539930 0.841710i \(-0.681549\pi\)
0.773607 0.633666i \(-0.218451\pi\)
\(98\) −296.119 + 1006.95i −0.305230 + 1.03793i
\(99\) 1560.31i 1.58401i
\(100\) 170.388 4.85715i 0.170388 0.00485715i
\(101\) 1570.92 906.968i 1.54764 0.893532i 0.549321 0.835611i \(-0.314886\pi\)
0.998321 0.0579208i \(-0.0184471\pi\)
\(102\) 1484.47 77.7978i 1.44102 0.0755209i
\(103\) −1185.60 + 1464.09i −1.13418 + 1.40060i −0.230136 + 0.973158i \(0.573917\pi\)
−0.904044 + 0.427438i \(0.859416\pi\)
\(104\) −566.971 + 411.928i −0.534577 + 0.388393i
\(105\) 1538.82 + 1112.99i 1.43022 + 1.03444i
\(106\) −729.505 530.017i −0.668451 0.485658i
\(107\) 637.456 170.806i 0.575936 0.154322i 0.0409184 0.999162i \(-0.486972\pi\)
0.535018 + 0.844841i \(0.320305\pi\)
\(108\) 292.779 237.088i 0.260858 0.211239i
\(109\) −37.4402 176.142i −0.0329002 0.154783i 0.958631 0.284651i \(-0.0918779\pi\)
−0.991531 + 0.129868i \(0.958545\pi\)
\(110\) −615.355 + 703.321i −0.533380 + 0.609627i
\(111\) 1525.49 495.663i 1.30444 0.423840i
\(112\) 402.460 + 1291.65i 0.339544 + 1.08973i
\(113\) 164.007 + 321.883i 0.136536 + 0.267966i 0.949143 0.314845i \(-0.101953\pi\)
−0.812607 + 0.582811i \(0.801953\pi\)
\(114\) −111.093 + 522.650i −0.0912701 + 0.429392i
\(115\) −17.4397 1223.81i −0.0141414 0.992355i
\(116\) 322.877 68.6297i 0.258434 0.0549319i
\(117\) 706.449 1840.36i 0.558216 1.45420i
\(118\) 940.273 + 940.273i 0.733552 + 0.733552i
\(119\) −242.393 950.509i −0.186724 0.732210i
\(120\) 2080.87 + 79.3414i 1.58297 + 0.0603571i
\(121\) 61.1348 + 581.659i 0.0459315 + 0.437009i
\(122\) 193.904 74.4329i 0.143896 0.0552363i
\(123\) −96.3922 1839.27i −0.0706617 1.34831i
\(124\) −76.9741 + 133.323i −0.0557458 + 0.0965545i
\(125\) −1388.42 159.435i −0.993471 0.114083i
\(126\) −2490.93 2067.55i −1.76119 1.46184i
\(127\) −283.770 + 556.929i −0.198272 + 0.389130i −0.968640 0.248469i \(-0.920072\pi\)
0.770368 + 0.637599i \(0.220072\pi\)
\(128\) 1325.02 + 1072.98i 0.914969 + 0.740927i
\(129\) −1558.88 694.059i −1.06397 0.473709i
\(130\) −1044.24 + 550.949i −0.704508 + 0.371703i
\(131\) −135.548 304.447i −0.0904040 0.203051i 0.862684 0.505742i \(-0.168781\pi\)
−0.953089 + 0.302692i \(0.902115\pi\)
\(132\) 241.576 241.576i 0.159291 0.159291i
\(133\) 352.570 + 4.26888i 0.229862 + 0.00278315i
\(134\) 2226.34 + 723.383i 1.43527 + 0.466349i
\(135\) −2652.68 + 1582.35i −1.69116 + 1.00879i
\(136\) −799.310 719.702i −0.503973 0.453779i
\(137\) −167.619 108.853i −0.104531 0.0678830i 0.491315 0.870982i \(-0.336516\pi\)
−0.595846 + 0.803099i \(0.703183\pi\)
\(138\) −160.798 + 3068.20i −0.0991884 + 1.89263i
\(139\) 504.857 + 1553.79i 0.308068 + 0.948136i 0.978515 + 0.206178i \(0.0661025\pi\)
−0.670447 + 0.741958i \(0.733897\pi\)
\(140\) 44.7686 + 278.791i 0.0270260 + 0.168301i
\(141\) −1605.12 + 4940.06i −0.958693 + 2.95055i
\(142\) −2773.19 1064.53i −1.63888 0.629107i
\(143\) 243.982 910.551i 0.142677 0.532476i
\(144\) −4149.86 436.167i −2.40154 0.252412i
\(145\) −2700.34 + 180.134i −1.54656 + 0.103168i
\(146\) −973.418 1339.80i −0.551785 0.759467i
\(147\) −1495.67 + 2767.63i −0.839188 + 1.55286i
\(148\) 212.489 + 108.269i 0.118017 + 0.0601326i
\(149\) −1059.60 611.762i −0.582591 0.336359i 0.179572 0.983745i \(-0.442529\pi\)
−0.762162 + 0.647386i \(0.775862\pi\)
\(150\) 3450.95 + 631.322i 1.87846 + 0.343648i
\(151\) −1089.16 1886.48i −0.586984 1.01669i −0.994625 0.103544i \(-0.966982\pi\)
0.407641 0.913142i \(-0.366352\pi\)
\(152\) 324.245 210.567i 0.173025 0.112363i
\(153\) 2988.21 + 473.286i 1.57897 + 0.250084i
\(154\) −1287.98 858.774i −0.673953 0.449363i
\(155\) 780.264 992.123i 0.404337 0.514124i
\(156\) 394.313 175.559i 0.202374 0.0901025i
\(157\) 2070.11 + 554.685i 1.05231 + 0.281966i 0.743207 0.669062i \(-0.233304\pi\)
0.309105 + 0.951028i \(0.399970\pi\)
\(158\) −1371.64 1693.84i −0.690646 0.852876i
\(159\) −1808.48 2008.52i −0.902022 1.00180i
\(160\) 464.090 + 500.883i 0.229310 + 0.247489i
\(161\) 2006.18 292.896i 0.982045 0.143375i
\(162\) 2703.57 1377.54i 1.31119 0.668083i
\(163\) −2437.41 127.739i −1.17124 0.0613823i −0.543229 0.839584i \(-0.682799\pi\)
−0.628014 + 0.778202i \(0.716132\pi\)
\(164\) 183.233 203.501i 0.0872446 0.0968949i
\(165\) −2242.39 + 1678.53i −1.05800 + 0.791959i
\(166\) 2698.09 2429.37i 1.26152 1.13588i
\(167\) 2484.70 393.537i 1.15133 0.182352i 0.448547 0.893759i \(-0.351942\pi\)
0.702780 + 0.711407i \(0.251942\pi\)
\(168\) 319.007 + 3434.69i 0.146500 + 1.57733i
\(169\) −591.327 + 813.891i −0.269152 + 0.370456i
\(170\) −1160.30 1391.83i −0.523478 0.627932i
\(171\) −442.327 + 993.483i −0.197811 + 0.444290i
\(172\) −90.9209 236.857i −0.0403061 0.105001i
\(173\) 1793.77 + 2762.17i 0.788312 + 1.21389i 0.972934 + 0.231085i \(0.0742274\pi\)
−0.184621 + 0.982810i \(0.559106\pi\)
\(174\) 6793.67 2.95992
\(175\) −37.9449 2314.72i −0.0163907 0.999866i
\(176\) −1995.39 −0.854592
\(177\) 2170.74 + 3342.65i 0.921826 + 1.41949i
\(178\) 919.237 + 2394.69i 0.387077 + 1.00837i
\(179\) −85.5285 + 192.100i −0.0357134 + 0.0802136i −0.930521 0.366238i \(-0.880646\pi\)
0.894808 + 0.446451i \(0.147312\pi\)
\(180\) −844.336 213.392i −0.349628 0.0883629i
\(181\) −1993.91 + 2744.38i −0.818819 + 1.12701i 0.171083 + 0.985257i \(0.445273\pi\)
−0.989902 + 0.141751i \(0.954727\pi\)
\(182\) −1130.34 1596.07i −0.460365 0.650045i
\(183\) 614.874 97.3865i 0.248376 0.0393389i
\(184\) 1652.07 1487.53i 0.661913 0.595990i
\(185\) −1598.06 1126.62i −0.635089 0.447733i
\(186\) −2120.10 + 2354.61i −0.835771 + 0.928218i
\(187\) 1444.79 + 75.7182i 0.564991 + 0.0296099i
\(188\) −688.111 + 350.610i −0.266945 + 0.136015i
\(189\) −3171.58 4015.01i −1.22063 1.54523i
\(190\) 591.194 273.376i 0.225735 0.104383i
\(191\) −1972.86 2191.08i −0.747389 0.830059i 0.242759 0.970087i \(-0.421948\pi\)
−0.990148 + 0.140027i \(0.955281\pi\)
\(192\) 2294.42 + 2833.37i 0.862423 + 1.06500i
\(193\) −3830.73 1026.44i −1.42871 0.382823i −0.540147 0.841571i \(-0.681631\pi\)
−0.888566 + 0.458748i \(0.848298\pi\)
\(194\) 3989.27 1776.14i 1.47635 0.657315i
\(195\) −3404.85 + 964.531i −1.25039 + 0.354213i
\(196\) −448.211 + 133.725i −0.163342 + 0.0487336i
\(197\) −2206.19 349.426i −0.797890 0.126373i −0.255840 0.966719i \(-0.582352\pi\)
−0.542051 + 0.840346i \(0.682352\pi\)
\(198\) 4004.27 2600.41i 1.43723 0.933348i
\(199\) 1251.41 + 2167.51i 0.445781 + 0.772116i 0.998106 0.0615132i \(-0.0195926\pi\)
−0.552325 + 0.833629i \(0.686259\pi\)
\(200\) −1442.62 2088.63i −0.510042 0.738442i
\(201\) 6076.42 + 3508.22i 2.13233 + 1.23110i
\(202\) 4945.68 + 2519.95i 1.72266 + 0.877737i
\(203\) −878.922 4396.06i −0.303883 1.51992i
\(204\) 389.375 + 535.929i 0.133636 + 0.183934i
\(205\) −1724.49 + 1437.63i −0.587530 + 0.489797i
\(206\) −5733.28 602.592i −1.93911 0.203809i
\(207\) −1618.45 + 6040.14i −0.543430 + 2.02811i
\(208\) −2353.54 903.439i −0.784561 0.301165i
\(209\) −160.702 + 494.591i −0.0531866 + 0.163692i
\(210\) −291.712 + 5804.04i −0.0958573 + 1.90722i
\(211\) 566.141 + 1742.40i 0.184714 + 0.568492i 0.999943 0.0106464i \(-0.00338893\pi\)
−0.815229 + 0.579139i \(0.803389\pi\)
\(212\) 21.0307 401.289i 0.00681318 0.130003i
\(213\) −7467.07 4849.17i −2.40204 1.55991i
\(214\) 1500.73 + 1351.26i 0.479382 + 0.431637i
\(215\) 461.425 + 2028.28i 0.146367 + 0.643383i
\(216\) −5335.68 1733.67i −1.68077 0.546116i
\(217\) 1797.91 + 1067.25i 0.562443 + 0.333871i
\(218\) 389.643 389.643i 0.121055 0.121055i
\(219\) −2018.95 4534.63i −0.622958 1.39919i
\(220\) −412.216 59.2806i −0.126325 0.0181668i
\(221\) 1669.83 + 743.456i 0.508257 + 0.226291i
\(222\) 3814.43 + 3088.86i 1.15319 + 0.933832i
\(223\) −352.484 + 691.789i −0.105848 + 0.207738i −0.937856 0.347026i \(-0.887192\pi\)
0.832008 + 0.554764i \(0.187192\pi\)
\(224\) −722.426 + 870.361i −0.215487 + 0.259614i
\(225\) 6603.00 + 2717.13i 1.95644 + 0.805076i
\(226\) −552.726 + 957.349i −0.162685 + 0.281778i
\(227\) 86.8784 + 1657.74i 0.0254023 + 0.484705i 0.981477 + 0.191581i \(0.0613614\pi\)
−0.956075 + 0.293124i \(0.905305\pi\)
\(228\) −222.301 + 85.3333i −0.0645712 + 0.0247866i
\(229\) 36.9237 + 351.305i 0.0106550 + 0.101375i 0.998557 0.0537051i \(-0.0171031\pi\)
−0.987902 + 0.155080i \(0.950436\pi\)
\(230\) 3111.65 2084.36i 0.892069 0.597559i
\(231\) −3240.95 3320.40i −0.923113 0.945741i
\(232\) −3475.88 3475.88i −0.983631 0.983631i
\(233\) 1318.26 3434.18i 0.370652 0.965581i −0.613727 0.789518i \(-0.710330\pi\)
0.984379 0.176063i \(-0.0563363\pi\)
\(234\) 5900.36 1254.16i 1.64837 0.350372i
\(235\) 5993.41 2042.24i 1.66369 0.566898i
\(236\) −123.206 + 579.637i −0.0339831 + 0.159878i
\(237\) −2965.83 5820.78i −0.812876 1.59536i
\(238\) 2035.36 2206.18i 0.554339 0.600864i
\(239\) −1695.61 + 550.937i −0.458912 + 0.149109i −0.529344 0.848407i \(-0.677562\pi\)
0.0704327 + 0.997517i \(0.477562\pi\)
\(240\) 3837.45 + 6433.18i 1.03211 + 1.73025i
\(241\) −518.048 2437.22i −0.138466 0.651433i −0.991557 0.129671i \(-0.958608\pi\)
0.853091 0.521763i \(-0.174725\pi\)
\(242\) −1390.85 + 1126.29i −0.369450 + 0.299175i
\(243\) 1579.70 423.278i 0.417027 0.111742i
\(244\) 74.8817 + 54.4047i 0.0196468 + 0.0142742i
\(245\) 3793.43 562.130i 0.989198 0.146584i
\(246\) 4559.55 3312.71i 1.18173 0.858579i
\(247\) −413.479 + 510.604i −0.106514 + 0.131534i
\(248\) 2289.42 119.983i 0.586202 0.0307216i
\(249\) 9424.21 5441.07i 2.39853 1.38479i
\(250\) −1904.77 3828.87i −0.481874 0.968636i
\(251\) 6750.43i 1.69754i 0.528759 + 0.848772i \(0.322658\pi\)
−0.528759 + 0.848772i \(0.677342\pi\)
\(252\) 168.154 1432.79i 0.0420346 0.358164i
\(253\) −467.783 + 2953.47i −0.116242 + 0.733925i
\(254\) −1902.20 + 199.929i −0.469900 + 0.0493885i
\(255\) −2534.44 4803.65i −0.622402 1.17967i
\(256\) −212.943 + 2026.02i −0.0519880 + 0.494633i
\(257\) −1866.88 6967.30i −0.453124 1.69108i −0.693544 0.720414i \(-0.743952\pi\)
0.240420 0.970669i \(-0.422715\pi\)
\(258\) −816.843 5157.34i −0.197110 1.24450i
\(259\) 1505.26 2867.86i 0.361129 0.688033i
\(260\) −459.364 256.557i −0.109571 0.0611961i
\(261\) 13524.8 + 2874.80i 3.20754 + 0.681783i
\(262\) 555.409 855.255i 0.130967 0.201671i
\(263\) −1640.55 + 2526.22i −0.384640 + 0.592294i −0.976964 0.213406i \(-0.931544\pi\)
0.592323 + 0.805700i \(0.298211\pi\)
\(264\) −4976.44 1057.78i −1.16015 0.246597i
\(265\) −638.998 + 3232.04i −0.148126 + 0.749218i
\(266\) 576.638 + 911.929i 0.132917 + 0.210203i
\(267\) 1202.71 + 7593.63i 0.275673 + 1.74053i
\(268\) 270.001 + 1007.66i 0.0615407 + 0.229673i
\(269\) 692.994 6593.40i 0.157073 1.49445i −0.577764 0.816204i \(-0.696075\pi\)
0.734837 0.678244i \(-0.237259\pi\)
\(270\) −8481.80 4170.54i −1.91180 0.940042i
\(271\) −2490.61 + 261.774i −0.558280 + 0.0586776i −0.379467 0.925205i \(-0.623893\pi\)
−0.178814 + 0.983883i \(0.557226\pi\)
\(272\) 605.259 3821.46i 0.134924 0.851874i
\(273\) −2319.31 5383.76i −0.514180 1.19355i
\(274\) 611.583i 0.134843i
\(275\) 3276.07 + 962.159i 0.718380 + 0.210983i
\(276\) −1185.75 + 684.592i −0.258600 + 0.149303i
\(277\) −5733.71 + 300.491i −1.24370 + 0.0651796i −0.662801 0.748795i \(-0.730633\pi\)
−0.580900 + 0.813975i \(0.697299\pi\)
\(278\) −3146.16 + 3885.18i −0.678756 + 0.838194i
\(279\) −5217.08 + 3790.43i −1.11949 + 0.813358i
\(280\) 3118.80 2820.30i 0.665657 0.601947i
\(281\) 736.192 + 534.875i 0.156290 + 0.113551i 0.663182 0.748458i \(-0.269206\pi\)
−0.506892 + 0.862010i \(0.669206\pi\)
\(282\) −15353.0 + 4113.82i −3.24204 + 0.868703i
\(283\) 1381.64 1118.83i 0.290212 0.235009i −0.473147 0.880983i \(-0.656882\pi\)
0.763359 + 0.645974i \(0.223549\pi\)
\(284\) −275.226 1294.84i −0.0575059 0.270544i
\(285\) 1903.63 433.067i 0.395653 0.0900095i
\(286\) 2743.40 891.386i 0.567206 0.184296i
\(287\) −2733.48 2521.83i −0.562203 0.518671i
\(288\) −1583.83 3108.44i −0.324055 0.635994i
\(289\) 438.213 2061.63i 0.0891946 0.419628i
\(290\) −4962.67 6629.78i −1.00489 1.34246i
\(291\) 12802.6 2721.28i 2.57905 0.548193i
\(292\) 264.480 688.993i 0.0530052 0.138083i
\(293\) 3115.70 + 3115.70i 0.621233 + 0.621233i 0.945847 0.324614i \(-0.105234\pi\)
−0.324614 + 0.945847i \(0.605234\pi\)
\(294\) −9595.37 + 774.150i −1.90345 + 0.153569i
\(295\) 1676.32 4560.14i 0.330845 0.900005i
\(296\) −371.224 3531.96i −0.0728952 0.693551i
\(297\) 7045.19 2704.40i 1.37644 0.528367i
\(298\) −195.945 3738.86i −0.0380900 0.726800i
\(299\) −1888.97 + 3271.79i −0.365357 + 0.632817i
\(300\) 601.633 + 1443.00i 0.115784 + 0.277705i
\(301\) −3231.55 + 1195.79i −0.618814 + 0.228984i
\(302\) 3026.16 5939.17i 0.576608 1.13166i
\(303\) 12929.4 + 10470.0i 2.45140 + 1.98511i
\(304\) 1270.51 + 565.668i 0.239700 + 0.106721i
\(305\) −544.194 528.902i −0.102165 0.0992946i
\(306\) 3765.54 + 8457.53i 0.703469 + 1.58002i
\(307\) −6748.13 + 6748.13i −1.25451 + 1.25451i −0.300840 + 0.953675i \(0.597267\pi\)
−0.953675 + 0.300840i \(0.902733\pi\)
\(308\) 8.35216 689.811i 0.00154516 0.127616i
\(309\) −16433.4 5339.52i −3.02544 0.983025i
\(310\) 3846.51 + 348.948i 0.704733 + 0.0639320i
\(311\) −3449.68 3106.11i −0.628982 0.566338i 0.291769 0.956489i \(-0.405756\pi\)
−0.920751 + 0.390151i \(0.872423\pi\)
\(312\) −5390.74 3500.78i −0.978174 0.635234i
\(313\) −324.413 + 6190.17i −0.0585844 + 1.11786i 0.798270 + 0.602299i \(0.205749\pi\)
−0.856855 + 0.515558i \(0.827585\pi\)
\(314\) 2026.54 + 6237.05i 0.364218 + 1.12095i
\(315\) −3036.77 + 11431.3i −0.543183 + 2.04469i
\(316\) 300.147 923.758i 0.0534322 0.164448i
\(317\) −4787.54 1837.77i −0.848250 0.325613i −0.104873 0.994486i \(-0.533444\pi\)
−0.743377 + 0.668873i \(0.766777\pi\)
\(318\) 2140.53 7988.56i 0.377468 1.40873i
\(319\) 6575.84 + 691.149i 1.15416 + 0.121307i
\(320\) 1088.98 4308.80i 0.190237 0.752717i
\(321\) 3557.78 + 4896.86i 0.618616 + 0.851452i
\(322\) 4095.17 + 4660.40i 0.708742 + 0.806565i
\(323\) −898.466 457.791i −0.154774 0.0788612i
\(324\) 1171.03 + 676.097i 0.200795 + 0.115929i
\(325\) 3428.46 + 2618.14i 0.585159 + 0.446856i
\(326\) −3734.37 6468.11i −0.634440 1.09888i
\(327\) 1385.17 899.542i 0.234252 0.152125i
\(328\) −4027.72 637.928i −0.678030 0.107389i
\(329\) 4648.25 + 9402.41i 0.778925 + 1.57560i
\(330\) −8044.85 2957.31i −1.34198 0.493317i
\(331\) 5044.28 2245.86i 0.837639 0.372941i 0.0573456 0.998354i \(-0.481736\pi\)
0.780294 + 0.625413i \(0.215070\pi\)
\(332\) 1562.82 + 418.757i 0.258346 + 0.0692237i
\(333\) 6286.69 + 7763.42i 1.03456 + 1.27758i
\(334\) 5150.95 + 5720.71i 0.843855 + 0.937195i
\(335\) −1015.14 8492.54i −0.165562 1.38507i
\(336\) −9737.05 + 7691.60i −1.58095 + 1.24884i
\(337\) −1968.79 + 1003.15i −0.318240 + 0.162152i −0.605813 0.795607i \(-0.707152\pi\)
0.287572 + 0.957759i \(0.407152\pi\)
\(338\) −3074.23 161.113i −0.494722 0.0259273i
\(339\) −2217.08 + 2462.32i −0.355207 + 0.394498i
\(340\) 238.568 771.470i 0.0380534 0.123055i
\(341\) −2291.67 + 2063.43i −0.363932 + 0.327686i
\(342\) −3286.80 + 520.578i −0.519678 + 0.0823088i
\(343\) 1742.33 + 6108.84i 0.274277 + 0.961651i
\(344\) −2220.75 + 3056.60i −0.348066 + 0.479072i
\(345\) 10421.7 4171.84i 1.62633 0.651026i
\(346\) −4099.16 + 9206.86i −0.636914 + 1.43053i
\(347\) −27.5805 71.8497i −0.00426686 0.0111155i 0.931430 0.363919i \(-0.118562\pi\)
−0.935697 + 0.352804i \(0.885228\pi\)
\(348\) 1648.90 + 2539.09i 0.253996 + 0.391119i
\(349\) 1764.87 0.270691 0.135346 0.990798i \(-0.456786\pi\)
0.135346 + 0.990798i \(0.456786\pi\)
\(350\) 5877.12 3955.10i 0.897558 0.604025i
\(351\) 9534.17 1.44985
\(352\) −908.613 1399.14i −0.137583 0.211859i
\(353\) −2532.22 6596.66i −0.381803 0.994631i −0.980996 0.194027i \(-0.937845\pi\)
0.599193 0.800604i \(-0.295488\pi\)
\(354\) −4960.62 + 11141.7i −0.744785 + 1.67282i
\(355\) 722.393 + 10829.2i 0.108002 + 1.61903i
\(356\) −671.892 + 924.781i −0.100029 + 0.137678i
\(357\) 7342.11 5199.72i 1.08848 0.770863i
\(358\) −635.536 + 100.659i −0.0938244 + 0.0148603i
\(359\) −4369.88 + 3934.66i −0.642433 + 0.578449i −0.924611 0.380913i \(-0.875610\pi\)
0.282178 + 0.959362i \(0.408943\pi\)
\(360\) 4182.99 + 12275.9i 0.612397 + 1.79721i
\(361\) −4347.03 + 4827.87i −0.633771 + 0.703874i
\(362\) −10366.1 543.263i −1.50505 0.0788764i
\(363\) −4779.57 + 2435.31i −0.691080 + 0.352123i
\(364\) 322.172 809.842i 0.0463912 0.116613i
\(365\) −2950.43 + 5282.73i −0.423103 + 0.757563i
\(366\) 1274.68 + 1415.67i 0.182045 + 0.202181i
\(367\) 4615.84 + 5700.09i 0.656525 + 0.810741i 0.991309 0.131554i \(-0.0419966\pi\)
−0.334784 + 0.942295i \(0.608663\pi\)
\(368\) 7724.41 + 2069.75i 1.09419 + 0.293188i
\(369\) 10479.0 4665.54i 1.47836 0.658206i
\(370\) 227.965 5978.78i 0.0320306 0.840059i
\(371\) −5446.18 351.587i −0.762134 0.0492008i
\(372\) −1394.60 220.882i −0.194372 0.0307855i
\(373\) −4602.81 + 2989.10i −0.638939 + 0.414932i −0.823046 0.567974i \(-0.807727\pi\)
0.184107 + 0.982906i \(0.441061\pi\)
\(374\) 2213.57 + 3834.01i 0.306045 + 0.530085i
\(375\) −3198.37 12412.5i −0.440436 1.70928i
\(376\) 9959.89 + 5750.34i 1.36607 + 0.788700i
\(377\) 7443.20 + 3792.50i 1.01683 + 0.518100i
\(378\) 5018.12 14830.8i 0.682816 2.01802i
\(379\) 4603.39 + 6336.02i 0.623905 + 0.858732i 0.997630 0.0688075i \(-0.0219194\pi\)
−0.373724 + 0.927540i \(0.621919\pi\)
\(380\) 245.662 + 154.603i 0.0331637 + 0.0208710i
\(381\) −5701.48 599.249i −0.766655 0.0805787i
\(382\) 2335.10 8714.70i 0.312759 1.16723i
\(383\) −4696.28 1802.73i −0.626551 0.240510i 0.0243137 0.999704i \(-0.492260\pi\)
−0.650864 + 0.759194i \(0.725593\pi\)
\(384\) −4832.31 + 14872.3i −0.642182 + 1.97643i
\(385\) −872.829 + 5588.27i −0.115542 + 0.739753i
\(386\) −3750.10 11541.6i −0.494495 1.52190i
\(387\) 556.199 10612.9i 0.0730573 1.39402i
\(388\) 1632.06 + 1059.87i 0.213545 + 0.138678i
\(389\) 6258.30 + 5635.00i 0.815703 + 0.734462i 0.967206 0.253995i \(-0.0817445\pi\)
−0.151503 + 0.988457i \(0.548411\pi\)
\(390\) −8149.84 7130.52i −1.05816 0.925815i
\(391\) −5514.42 1791.74i −0.713238 0.231745i
\(392\) 5305.41 + 4513.24i 0.683580 + 0.581513i
\(393\) 2161.33 2161.33i 0.277416 0.277416i
\(394\) −2780.09 6244.18i −0.355479 0.798420i
\(395\) −3513.86 + 7146.28i −0.447599 + 0.910300i
\(396\) 1943.77 + 865.423i 0.246662 + 0.109821i
\(397\) −6445.97 5219.84i −0.814896 0.659890i 0.128444 0.991717i \(-0.459002\pi\)
−0.943340 + 0.331827i \(0.892335\pi\)
\(398\) −3476.97 + 6823.94i −0.437901 + 0.859430i
\(399\) 1122.30 + 3032.95i 0.140815 + 0.380544i
\(400\) 3474.79 8444.22i 0.434349 1.05553i
\(401\) 6898.24 11948.1i 0.859056 1.48793i −0.0137742 0.999905i \(-0.504385\pi\)
0.872830 0.488024i \(-0.162282\pi\)
\(402\) 1123.67 + 21441.0i 0.139412 + 2.66014i
\(403\) −3637.24 + 1396.21i −0.449588 + 0.172581i
\(404\) 258.560 + 2460.04i 0.0318412 + 0.302949i
\(405\) −8714.25 6853.39i −1.06917 0.840859i
\(406\) 9816.97 9582.09i 1.20002 1.17131i
\(407\) 3377.88 + 3377.88i 0.411389 + 0.411389i
\(408\) 3535.29 9209.74i 0.428978 1.11753i
\(409\) 3719.13 790.525i 0.449631 0.0955720i 0.0224698 0.999748i \(-0.492847\pi\)
0.427161 + 0.904176i \(0.359514\pi\)
\(410\) −6563.48 2029.67i −0.790603 0.244484i
\(411\) 381.123 1793.04i 0.0457407 0.215193i
\(412\) −1166.32 2289.04i −0.139467 0.273720i
\(413\) 7851.39 + 1768.48i 0.935452 + 0.210705i
\(414\) −18198.4 + 5913.01i −2.16039 + 0.701953i
\(415\) −12194.1 5222.24i −1.44237 0.617710i
\(416\) −438.219 2061.66i −0.0516477 0.242983i
\(417\) −11645.1 + 9430.00i −1.36754 + 1.10741i
\(418\) −1537.11 + 411.868i −0.179863 + 0.0481941i
\(419\) −5512.16 4004.82i −0.642689 0.466941i 0.218084 0.975930i \(-0.430019\pi\)
−0.860773 + 0.508989i \(0.830019\pi\)
\(420\) −2240.03 + 1299.69i −0.260243 + 0.150996i
\(421\) 3390.32 2463.21i 0.392479 0.285153i −0.373991 0.927432i \(-0.622011\pi\)
0.766471 + 0.642279i \(0.222011\pi\)
\(422\) −3528.06 + 4356.80i −0.406975 + 0.502572i
\(423\) −32305.5 + 1693.06i −3.71335 + 0.194609i
\(424\) −5182.39 + 2992.05i −0.593583 + 0.342705i
\(425\) −2836.40 + 5982.29i −0.323731 + 0.682785i
\(426\) 27244.7i 3.09861i
\(427\) 751.146 1007.97i 0.0851300 0.114237i
\(428\) −140.781 + 888.856i −0.0158993 + 0.100384i
\(429\) 8598.62 903.751i 0.967705 0.101710i
\(430\) −4436.24 + 4564.50i −0.497522 + 0.511906i
\(431\) 891.091 8478.16i 0.0995878 0.947515i −0.824636 0.565664i \(-0.808620\pi\)
0.924224 0.381851i \(-0.124713\pi\)
\(432\) −5223.32 19493.7i −0.581729 2.17104i
\(433\) 835.023 + 5272.13i 0.0926759 + 0.585133i 0.989701 + 0.143152i \(0.0457239\pi\)
−0.897025 + 0.441980i \(0.854276\pi\)
\(434\) 257.463 + 6392.74i 0.0284761 + 0.707054i
\(435\) −10418.1 22529.9i −1.14830 2.48327i
\(436\) 240.198 + 51.0556i 0.0263839 + 0.00560807i
\(437\) 1135.12 1747.93i 0.124257 0.191338i
\(438\) 8272.62 12738.7i 0.902469 1.38968i
\(439\) −5179.27 1100.89i −0.563083 0.119687i −0.0824282 0.996597i \(-0.526268\pi\)
−0.480654 + 0.876910i \(0.659601\pi\)
\(440\) 2602.96 + 5629.08i 0.282026 + 0.609900i
\(441\) −19430.1 2519.18i −2.09805 0.272020i
\(442\) 874.978 + 5524.39i 0.0941594 + 0.594499i
\(443\) 1001.83 + 3738.89i 0.107446 + 0.400993i 0.998611 0.0526853i \(-0.0167780\pi\)
−0.891165 + 0.453679i \(0.850111\pi\)
\(444\) −228.636 + 2175.32i −0.0244382 + 0.232514i
\(445\) 6531.88 6720.73i 0.695822 0.715940i
\(446\) −2362.82 + 248.342i −0.250858 + 0.0263662i
\(447\) 1755.49 11083.7i 0.185754 1.17280i
\(448\) 7311.78 + 858.122i 0.771092 + 0.0904965i
\(449\) 7849.27i 0.825011i 0.910955 + 0.412506i \(0.135346\pi\)
−0.910955 + 0.412506i \(0.864654\pi\)
\(450\) 4031.48 + 21473.9i 0.422324 + 2.24953i
\(451\) 4750.38 2742.63i 0.495979 0.286354i
\(452\) −491.956 + 25.7823i −0.0511940 + 0.00268296i
\(453\) 12573.2 15526.7i 1.30407 1.61039i
\(454\) −4109.53 + 2985.75i −0.424823 + 0.308652i
\(455\) −3559.66 + 6196.12i −0.366768 + 0.638414i
\(456\) 2868.75 + 2084.27i 0.294609 + 0.214046i
\(457\) −4232.53 + 1134.10i −0.433237 + 0.116085i −0.468845 0.883280i \(-0.655330\pi\)
0.0356084 + 0.999366i \(0.488663\pi\)
\(458\) −840.032 + 680.244i −0.0857033 + 0.0694011i
\(459\) 3042.29 + 14312.9i 0.309373 + 1.45548i
\(460\) 1534.25 + 657.060i 0.155510 + 0.0665991i
\(461\) 13749.4 4467.45i 1.38909 0.451344i 0.483446 0.875374i \(-0.339385\pi\)
0.905648 + 0.424030i \(0.139385\pi\)
\(462\) 3119.89 13851.2i 0.314179 1.39484i
\(463\) 1904.54 + 3737.88i 0.191170 + 0.375192i 0.966619 0.256218i \(-0.0824765\pi\)
−0.775449 + 0.631410i \(0.782477\pi\)
\(464\) 3676.42 17296.2i 0.367831 1.73051i
\(465\) 11059.8 + 3420.10i 1.10298 + 0.341082i
\(466\) 11010.3 2340.31i 1.09451 0.232645i
\(467\) 3034.90 7906.19i 0.300725 0.783415i −0.697067 0.717006i \(-0.745512\pi\)
0.997792 0.0664099i \(-0.0211545\pi\)
\(468\) 1900.82 + 1900.82i 0.187747 + 0.187747i
\(469\) 13728.7 3501.01i 1.35167 0.344694i
\(470\) 15229.7 + 11977.5i 1.49467 + 1.17549i
\(471\) 2054.65 + 19548.7i 0.201005 + 1.91244i
\(472\) 8238.53 3162.47i 0.803409 0.308400i
\(473\) −265.974 5075.08i −0.0258552 0.493346i
\(474\) 9995.23 17312.2i 0.968557 1.67759i
\(475\) −1813.19 1541.36i −0.175147 0.148889i
\(476\) 1318.55 + 225.235i 0.126966 + 0.0216883i
\(477\) 7641.79 14997.9i 0.733529 1.43963i
\(478\) −4239.79 3433.32i −0.405698 0.328528i
\(479\) 7401.51 + 3295.37i 0.706020 + 0.314340i 0.728153 0.685415i \(-0.240379\pi\)
−0.0221328 + 0.999755i \(0.507046\pi\)
\(480\) −2763.46 + 5620.15i −0.262779 + 0.534424i
\(481\) 2454.79 + 5513.55i 0.232700 + 0.522654i
\(482\) 5391.37 5391.37i 0.509482 0.509482i
\(483\) 9102.01 + 16215.4i 0.857465 + 1.52759i
\(484\) −758.517 246.457i −0.0712357 0.0231459i
\(485\) −12007.8 10505.9i −1.12421 0.983606i
\(486\) 3719.00 + 3348.60i 0.347114 + 0.312542i
\(487\) −4114.91 2672.26i −0.382884 0.248648i 0.338818 0.940852i \(-0.389973\pi\)
−0.721702 + 0.692204i \(0.756640\pi\)
\(488\) 72.1381 1376.48i 0.00669167 0.127685i
\(489\) −6917.68 21290.4i −0.639730 1.96889i
\(490\) 7764.75 + 8798.39i 0.715869 + 0.811165i
\(491\) 2152.10 6623.47i 0.197806 0.608785i −0.802126 0.597154i \(-0.796298\pi\)
0.999932 0.0116301i \(-0.00370206\pi\)
\(492\) 2344.76 + 900.070i 0.214858 + 0.0824762i
\(493\) −3318.29 + 12384.0i −0.303141 + 1.13134i
\(494\) −1999.49 210.155i −0.182108 0.0191403i
\(495\) −14764.3 9291.66i −1.34062 0.843695i
\(496\) 4847.37 + 6671.84i 0.438817 + 0.603980i
\(497\) −17629.5 + 3524.75i −1.59113 + 0.318122i
\(498\) 29670.0 + 15117.6i 2.66977 + 1.36032i
\(499\) −3544.05 2046.16i −0.317943 0.183564i 0.332533 0.943092i \(-0.392097\pi\)
−0.650475 + 0.759528i \(0.725430\pi\)
\(500\) 968.704 1641.21i 0.0866435 0.146794i
\(501\) 11536.6 + 19982.0i 1.02878 + 1.78189i
\(502\) −17323.9 + 11250.3i −1.54025 + 1.00025i
\(503\) 2257.20 + 357.506i 0.200087 + 0.0316907i 0.255673 0.966763i \(-0.417703\pi\)
−0.0555864 + 0.998454i \(0.517703\pi\)
\(504\) −19258.3 + 9520.70i −1.70205 + 0.841440i
\(505\) 772.711 20265.7i 0.0680894 1.78577i
\(506\) −8359.21 + 3721.76i −0.734411 + 0.326981i
\(507\) −8912.64 2388.13i −0.780718 0.209193i
\(508\) −536.409 662.410i −0.0468491 0.0578538i
\(509\) 14583.4 + 16196.5i 1.26994 + 1.41041i 0.869386 + 0.494133i \(0.164515\pi\)
0.400551 + 0.916275i \(0.368819\pi\)
\(510\) 8103.90 14510.0i 0.703621 1.25983i
\(511\) −9313.26 3705.01i −0.806251 0.320744i
\(512\) 6598.83 3362.27i 0.569589 0.290220i
\(513\) −5252.50 275.272i −0.452054 0.0236911i
\(514\) 14769.1 16402.8i 1.26739 1.40758i
\(515\) 6793.62 + 19937.4i 0.581286 + 1.70591i
\(516\) 1729.27 1557.04i 0.147532 0.132839i
\(517\) −15279.2 + 2419.99i −1.29977 + 0.205863i
\(518\) 9868.58 916.576i 0.837067 0.0777452i
\(519\) −17755.4 + 24438.2i −1.50169 + 2.06690i
\(520\) 521.520 + 7817.96i 0.0439811 + 0.659309i
\(521\) −1917.25 + 4306.21i −0.161221 + 0.362109i −0.976035 0.217614i \(-0.930173\pi\)
0.814814 + 0.579723i \(0.196839\pi\)
\(522\) 15162.8 + 39500.5i 1.27138 + 3.31205i
\(523\) 3854.41 + 5935.27i 0.322259 + 0.496236i 0.962257 0.272141i \(-0.0877316\pi\)
−0.639998 + 0.768376i \(0.721065\pi\)
\(524\) 454.451 0.0378870
\(525\) 19695.3 7933.10i 1.63728 0.659484i
\(526\) −9217.27 −0.764054
\(527\) −3256.63 5014.77i −0.269186 0.414510i
\(528\) −6558.59 17085.7i −0.540580 1.40826i
\(529\) −74.3878 + 167.078i −0.00611390 + 0.0137320i
\(530\) −9359.47 + 3746.63i −0.767074 + 0.307063i
\(531\) −14590.3 + 20081.9i −1.19240 + 1.64120i
\(532\) −200.871 + 436.851i −0.0163700 + 0.0356013i
\(533\) 6844.78 1084.11i 0.556248 0.0881010i
\(534\) −17483.4 + 15742.1i −1.41682 + 1.27571i
\(535\) 2179.83 7049.03i 0.176153 0.569638i
\(536\) 10395.0 11544.8i 0.837681 0.930339i
\(537\) −1926.00 100.937i −0.154773 0.00811129i
\(538\) 18075.8 9210.10i 1.44852 0.738059i
\(539\) −9366.48 226.850i −0.748502 0.0181282i
\(540\) −499.921 4182.26i −0.0398392 0.333289i
\(541\) 7325.54 + 8135.84i 0.582162 + 0.646556i 0.960226 0.279223i \(-0.0900769\pi\)
−0.378064 + 0.925779i \(0.623410\pi\)
\(542\) −4822.66 5955.49i −0.382197 0.471974i
\(543\) −30052.8 8052.62i −2.37512 0.636411i
\(544\) 2955.16 1315.72i 0.232907 0.103697i
\(545\) −1889.69 694.656i −0.148524 0.0545978i
\(546\) 9951.18 14924.7i 0.779984 1.16981i
\(547\) −1042.25 165.077i −0.0814690 0.0129034i 0.115567 0.993300i \(-0.463132\pi\)
−0.197036 + 0.980396i \(0.563132\pi\)
\(548\) 228.575 148.439i 0.0178180 0.0115711i
\(549\) 1938.58 + 3357.71i 0.150704 + 0.261027i
\(550\) 2990.68 + 10011.0i 0.231860 + 0.776132i
\(551\) −3991.06 2304.24i −0.308575 0.178156i
\(552\) 18167.2 + 9256.67i 1.40081 + 0.713750i
\(553\) −12495.6 4227.98i −0.960878 0.325121i
\(554\) −10327.0 14213.9i −0.791969 1.09005i
\(555\) 4394.17 17386.6i 0.336076 1.32976i
\(556\) −2215.67 232.877i −0.169003 0.0177629i
\(557\) 1532.09 5717.86i 0.116547 0.434961i −0.882851 0.469654i \(-0.844379\pi\)
0.999398 + 0.0346929i \(0.0110453\pi\)
\(558\) −18422.3 7071.66i −1.39763 0.536501i
\(559\) 1984.10 6106.43i 0.150122 0.462029i
\(560\) 14618.8 + 3883.56i 1.10314 + 0.293054i
\(561\) 4100.49 + 12620.0i 0.308597 + 0.949764i
\(562\) −145.732 + 2780.74i −0.0109383 + 0.208716i
\(563\) 8009.46 + 5201.40i 0.599571 + 0.389366i 0.808441 0.588577i \(-0.200312\pi\)
−0.208870 + 0.977943i \(0.566978\pi\)
\(564\) −5263.86 4739.60i −0.392994 0.353853i
\(565\) 4022.46 + 364.910i 0.299516 + 0.0271715i
\(566\) 5173.94 + 1681.12i 0.384235 + 0.124845i
\(567\) 9374.16 15791.8i 0.694317 1.16966i
\(568\) −13939.3 + 13939.3i −1.02972 + 1.02972i
\(569\) 8680.04 + 19495.7i 0.639518 + 1.43638i 0.884354 + 0.466817i \(0.154599\pi\)
−0.244835 + 0.969565i \(0.578734\pi\)
\(570\) 4283.98 + 4163.60i 0.314801 + 0.305955i
\(571\) 13951.5 + 6211.62i 1.02251 + 0.455251i 0.848333 0.529463i \(-0.177607\pi\)
0.174178 + 0.984714i \(0.444273\pi\)
\(572\) 999.007 + 808.980i 0.0730255 + 0.0591349i
\(573\) 12276.8 24094.6i 0.895064 1.75666i
\(574\) 1916.24 11217.9i 0.139342 0.815726i
\(575\) −11684.1 7122.79i −0.847408 0.516593i
\(576\) −11353.2 + 19664.3i −0.821265 + 1.42247i
\(577\) −191.744 3658.70i −0.0138343 0.263975i −0.996786 0.0801107i \(-0.974473\pi\)
0.982952 0.183864i \(-0.0588607\pi\)
\(578\) 6021.17 2311.31i 0.433301 0.166329i
\(579\) −3802.12 36174.7i −0.272903 2.59650i
\(580\) 1273.34 3463.90i 0.0911595 0.247984i
\(581\) 5943.83 21154.8i 0.424426 1.51058i
\(582\) 28320.6 + 28320.6i 2.01705 + 2.01705i
\(583\) 2884.61 7514.66i 0.204920 0.533834i
\(584\) −10750.1 + 2285.01i −0.761719 + 0.161908i
\(585\) −13207.4 17644.1i −0.933433 1.24700i
\(586\) −2803.32 + 13188.6i −0.197618 + 0.929719i
\(587\) 3265.42 + 6408.75i 0.229605 + 0.450626i 0.976851 0.213923i \(-0.0686240\pi\)
−0.747245 + 0.664548i \(0.768624\pi\)
\(588\) −2618.25 3398.31i −0.183630 0.238340i
\(589\) 2044.12 664.174i 0.142999 0.0464632i
\(590\) 14496.6 3297.92i 1.01155 0.230124i
\(591\) −4259.47 20039.2i −0.296465 1.39476i
\(592\) 9928.21 8039.71i 0.689269 0.558159i
\(593\) 12162.3 3258.87i 0.842233 0.225676i 0.188189 0.982133i \(-0.439738\pi\)
0.654043 + 0.756457i \(0.273071\pi\)
\(594\) 18681.9 + 13573.2i 1.29045 + 0.937568i
\(595\) −10437.6 3366.68i −0.719158 0.231967i
\(596\) 1349.82 980.700i 0.0927696 0.0674011i
\(597\) −14446.3 + 17839.7i −0.990365 + 1.22300i
\(598\) −11544.7 + 605.030i −0.789459 + 0.0413738i
\(599\) 11590.3 6691.66i 0.790596 0.456451i −0.0495765 0.998770i \(-0.515787\pi\)
0.840172 + 0.542320i \(0.182454\pi\)
\(600\) 13142.4 19217.6i 0.894227 1.30759i
\(601\) 6732.60i 0.456953i −0.973549 0.228476i \(-0.926626\pi\)
0.973549 0.228476i \(-0.0733743\pi\)
\(602\) −8454.50 6300.34i −0.572391 0.426549i
\(603\) −6835.90 + 43160.2i −0.461658 + 2.91479i
\(604\) 2954.21 310.500i 0.199015 0.0209173i
\(605\) 5867.97 + 2885.31i 0.394325 + 0.193892i
\(606\) −5321.49 + 50630.6i −0.356717 + 3.39394i
\(607\) 2374.44 + 8861.55i 0.158774 + 0.592552i 0.998753 + 0.0499327i \(0.0159007\pi\)
−0.839979 + 0.542619i \(0.817433\pi\)
\(608\) 181.896 + 1148.45i 0.0121330 + 0.0766047i
\(609\) 34752.8 21975.1i 2.31240 1.46220i
\(610\) 450.388 2278.06i 0.0298946 0.151206i
\(611\) −19117.4 4063.52i −1.26580 0.269055i
\(612\) −2247.01 + 3460.09i −0.148415 + 0.228539i
\(613\) 14584.5 22458.1i 0.960947 1.47973i 0.0855449 0.996334i \(-0.472737\pi\)
0.875402 0.483395i \(-0.160596\pi\)
\(614\) −28564.4 6071.56i −1.87747 0.399068i
\(615\) −17978.0 10040.8i −1.17877 0.658349i
\(616\) −8682.99 + 5490.49i −0.567934 + 0.359121i
\(617\) 3086.90 + 19489.9i 0.201417 + 1.27169i 0.856504 + 0.516141i \(0.172632\pi\)
−0.655087 + 0.755553i \(0.727368\pi\)
\(618\) −13684.8 51072.4i −0.890751 3.32433i
\(619\) −1038.21 + 9877.93i −0.0674140 + 0.641402i 0.907688 + 0.419645i \(0.137846\pi\)
−0.975102 + 0.221756i \(0.928821\pi\)
\(620\) 803.178 + 1522.30i 0.0520265 + 0.0986084i
\(621\) −30078.0 + 3161.32i −1.94362 + 0.204283i
\(622\) 2222.08 14029.7i 0.143243 0.904404i
\(623\) 12448.3 + 9276.57i 0.800533 + 0.596562i
\(624\) 23121.9i 1.48336i
\(625\) −9776.71 + 12188.4i −0.625710 + 0.780056i
\(626\) −16426.8 + 9483.99i −1.04879 + 0.605521i
\(627\) −4763.19 + 249.628i −0.303387 + 0.0158998i
\(628\) −1839.19 + 2271.21i −0.116866 + 0.144317i
\(629\) −7493.73 + 5444.52i −0.475031 + 0.345131i
\(630\) −34397.6 + 11258.0i −2.17529 + 0.711950i
\(631\) −4423.85 3214.12i −0.279098 0.202777i 0.439426 0.898279i \(-0.355182\pi\)
−0.718524 + 0.695502i \(0.755182\pi\)
\(632\) −13971.5 + 3743.64i −0.879359 + 0.235623i
\(633\) −13058.7 + 10574.7i −0.819960 + 0.663991i
\(634\) −3262.59 15349.3i −0.204376 0.961511i
\(635\) 3580.05 + 6001.68i 0.223732 + 0.375070i
\(636\) 3505.20 1138.91i 0.218538 0.0710074i
\(637\) −10944.9 4508.36i −0.680776 0.280420i
\(638\) 9185.58 + 18027.7i 0.570001 + 1.11869i
\(639\) 11528.8 54238.8i 0.713729 3.35783i
\(640\) 18043.5 6148.28i 1.11442 0.379737i
\(641\) −5799.92 + 1232.81i −0.357384 + 0.0759642i −0.383105 0.923705i \(-0.625145\pi\)
0.0257211 + 0.999669i \(0.491812\pi\)
\(642\) −6637.61 + 17291.6i −0.408046 + 1.06300i
\(643\) −6638.15 6638.15i −0.407128 0.407128i 0.473608 0.880736i \(-0.342951\pi\)
−0.880736 + 0.473608i \(0.842951\pi\)
\(644\) −747.849 + 2661.68i −0.0457599 + 0.162865i
\(645\) −15850.7 + 10617.7i −0.967627 + 0.648172i
\(646\) −322.536 3068.72i −0.0196440 0.186900i
\(647\) −15690.6 + 6023.05i −0.953416 + 0.365982i −0.784834 0.619706i \(-0.787252\pi\)
−0.168581 + 0.985688i \(0.553919\pi\)
\(648\) −1053.87 20109.0i −0.0638885 1.21907i
\(649\) −5935.07 + 10279.8i −0.358970 + 0.621755i
\(650\) −1005.17 + 13162.0i −0.0606552 + 0.794239i
\(651\) −3228.96 + 18902.7i −0.194398 + 1.13803i
\(652\) 1511.04 2965.58i 0.0907622 0.178131i
\(653\) 13128.3 + 10631.1i 0.786755 + 0.637102i 0.936120 0.351680i \(-0.114390\pi\)
−0.149365 + 0.988782i \(0.547723\pi\)
\(654\) 4617.06 + 2055.65i 0.276057 + 0.122909i
\(655\) −3688.00 530.370i −0.220003 0.0316386i
\(656\) −5966.50 13401.0i −0.355111 0.797592i
\(657\) 21859.7 21859.7i 1.29806 1.29806i
\(658\) −16383.0 + 27599.1i −0.970633 + 1.63514i
\(659\) 20563.7 + 6681.56i 1.21555 + 0.394957i 0.845460 0.534038i \(-0.179326\pi\)
0.370092 + 0.928995i \(0.379326\pi\)
\(660\) −847.305 3724.49i −0.0499717 0.219660i
\(661\) 16684.8 + 15023.1i 0.981793 + 0.884010i 0.993258 0.115924i \(-0.0369829\pi\)
−0.0114653 + 0.999934i \(0.503650\pi\)
\(662\) 14170.4 + 9202.38i 0.831948 + 0.540273i
\(663\) −877.396 + 16741.7i −0.0513955 + 0.980685i
\(664\) −7445.51 22914.9i −0.435153 1.33926i
\(665\) 2139.96 3310.75i 0.124788 0.193061i
\(666\) −9446.17 + 29072.3i −0.549597 + 1.69149i
\(667\) −24739.0 9496.42i −1.43613 0.551278i
\(668\) −887.882 + 3313.62i −0.0514269 + 0.191928i
\(669\) −7082.08 744.357i −0.409281 0.0430172i
\(670\) 20102.9 16758.9i 1.15917 0.966346i
\(671\) 1089.79 + 1499.96i 0.0626985 + 0.0862971i
\(672\) −9827.07 3325.07i −0.564118 0.190874i
\(673\) −25098.1 12788.1i −1.43754 0.732462i −0.450473 0.892790i \(-0.648745\pi\)
−0.987064 + 0.160328i \(0.948745\pi\)
\(674\) −5855.61 3380.74i −0.334644 0.193207i
\(675\) −823.933 + 34523.8i −0.0469825 + 1.96862i
\(676\) −685.937 1188.08i −0.0390269 0.0675966i
\(677\) 10357.2 6726.04i 0.587976 0.381836i −0.216093 0.976373i \(-0.569331\pi\)
0.804068 + 0.594537i \(0.202665\pi\)
\(678\) −10014.1 1586.08i −0.567242 0.0898424i
\(679\) 14661.8 21989.7i 0.828671 1.24284i
\(680\) −11570.1 + 3277.58i −0.652487 + 0.184837i
\(681\) −13909.0 + 6192.68i −0.782663 + 0.348464i
\(682\) −9114.76 2442.29i −0.511763 0.137126i
\(683\) 17699.0 + 21856.5i 0.991558 + 1.22447i 0.974447 + 0.224619i \(0.0721138\pi\)
0.0171117 + 0.999854i \(0.494553\pi\)
\(684\) −992.308 1102.07i −0.0554706 0.0616063i
\(685\) −2028.19 + 937.863i −0.113129 + 0.0523123i
\(686\) −12773.6 + 14652.4i −0.710930 + 0.815497i
\(687\) −2886.72 + 1470.86i −0.160313 + 0.0816838i
\(688\) −13572.3 711.292i −0.752090 0.0394153i
\(689\) 6804.72 7557.41i 0.376254 0.417873i
\(690\) 28075.1 + 19792.8i 1.54899 + 1.09202i
\(691\) 11573.4 10420.7i 0.637153 0.573695i −0.285952 0.958244i \(-0.592310\pi\)
0.923105 + 0.384549i \(0.125643\pi\)
\(692\) −4435.92 + 702.581i −0.243683 + 0.0385956i
\(693\) 12072.3 26254.7i 0.661746 1.43916i
\(694\) 138.425 190.526i 0.00757138 0.0104211i
\(695\) 17709.1 + 4475.69i 0.966538 + 0.244277i
\(696\) 18337.8 41187.3i 0.998694 2.24310i
\(697\) 3811.60 + 9929.56i 0.207137 + 0.539611i
\(698\) 2941.33 + 4529.25i 0.159500 + 0.245608i
\(699\) 33738.4 1.82561
\(700\) 2904.64 + 1236.59i 0.156836 + 0.0667695i
\(701\) 660.516 0.0355882 0.0177941 0.999842i \(-0.494336\pi\)
0.0177941 + 0.999842i \(0.494336\pi\)
\(702\) 15889.7 + 24467.9i 0.854297 + 1.31550i
\(703\) −1193.19 3108.37i −0.0640142 0.166763i
\(704\) −4416.41 + 9919.42i −0.236434 + 0.531040i
\(705\) 37186.5 + 44606.6i 1.98656 + 2.38295i
\(706\) 12709.1 17492.5i 0.677496 0.932493i
\(707\) 33450.6 3106.83i 1.77941 0.165268i
\(708\) −5368.16 + 850.233i −0.284954 + 0.0451323i
\(709\) 1822.85 1641.30i 0.0965566 0.0869399i −0.619439 0.785045i \(-0.712640\pi\)
0.715995 + 0.698105i \(0.245973\pi\)
\(710\) −26587.5 + 19901.8i −1.40537 + 1.05198i
\(711\) 27224.3 30235.7i 1.43600 1.59483i
\(712\) 16999.3 + 890.897i 0.894770 + 0.0468929i
\(713\) 11011.7 5610.72i 0.578387 0.294703i
\(714\) 25580.6 + 10176.5i 1.34080 + 0.533398i
\(715\) −7163.12 7731.02i −0.374665 0.404369i
\(716\) −191.873 213.097i −0.0100148 0.0111226i
\(717\) −10290.7 12708.0i −0.536002 0.661907i
\(718\) −17380.5 4657.09i −0.903391 0.242063i
\(719\) −26964.9 + 12005.5i −1.39864 + 0.622714i −0.961028 0.276451i \(-0.910842\pi\)
−0.437610 + 0.899165i \(0.644175\pi\)
\(720\) −28839.7 + 36670.4i −1.49277 + 1.89809i
\(721\) −31277.6 + 15462.6i −1.61559 + 0.798694i
\(722\) −19634.7 3109.83i −1.01209 0.160299i
\(723\) 19166.2 12446.7i 0.985891 0.640245i
\(724\) −2312.93 4006.11i −0.118728 0.205644i
\(725\) −14376.1 + 26624.5i −0.736434 + 1.36387i
\(726\) −14215.5 8207.30i −0.726702 0.419561i
\(727\) −4828.87 2460.43i −0.246345 0.125519i 0.326459 0.945211i \(-0.394144\pi\)
−0.572804 + 0.819692i \(0.694144\pi\)
\(728\) −12727.4 + 2544.64i −0.647950 + 0.129547i
\(729\) −6920.16 9524.78i −0.351581 0.483909i
\(730\) −18474.5 + 1232.39i −0.936672 + 0.0624834i
\(731\) 9800.18 + 1030.04i 0.495859 + 0.0521169i
\(732\) −219.719 + 820.003i −0.0110943 + 0.0414046i
\(733\) −20123.4 7724.66i −1.01402 0.389245i −0.206094 0.978532i \(-0.566075\pi\)
−0.807924 + 0.589287i \(0.799409\pi\)
\(734\) −6935.60 + 21345.6i −0.348771 + 1.07341i
\(735\) 17281.8 + 30634.0i 0.867278 + 1.53735i
\(736\) 2066.07 + 6358.72i 0.103474 + 0.318459i
\(737\) −1093.64 + 20867.8i −0.0546602 + 1.04298i
\(738\) 29437.6 + 19117.0i 1.46831 + 0.953532i
\(739\) −9974.92 8981.46i −0.496527 0.447075i 0.382424 0.923987i \(-0.375089\pi\)
−0.878951 + 0.476912i \(0.841756\pi\)
\(740\) 2289.86 1365.92i 0.113753 0.0678544i
\(741\) −5731.15 1862.16i −0.284128 0.0923188i
\(742\) −8174.31 14562.7i −0.404432 0.720504i
\(743\) 21516.3 21516.3i 1.06239 1.06239i 0.0644734 0.997919i \(-0.479463\pi\)
0.997919 0.0644734i \(-0.0205368\pi\)
\(744\) 8552.40 + 19209.0i 0.421433 + 0.946554i
\(745\) −12098.7 + 6383.36i −0.594983 + 0.313917i
\(746\) −15342.1 6830.73i −0.752967 0.335243i
\(747\) 52670.0 + 42651.3i 2.57978 + 2.08906i
\(748\) −895.678 + 1757.87i −0.0437824 + 0.0859278i
\(749\) 12047.8 + 2058.00i 0.587740 + 0.100398i
\(750\) 26524.3 28894.8i 1.29137 1.40679i
\(751\) 10099.6 17493.1i 0.490734 0.849976i −0.509209 0.860643i \(-0.670062\pi\)
0.999943 + 0.0106666i \(0.00339534\pi\)
\(752\) 2165.16 + 41313.8i 0.104994 + 2.00340i
\(753\) −57801.2 + 22187.8i −2.79734 + 1.07380i
\(754\) 2672.00 + 25422.4i 0.129056 + 1.22789i
\(755\) −24336.7 927.933i −1.17312 0.0447297i
\(756\) 6760.87 1724.12i 0.325252 0.0829438i
\(757\) −7588.97 7588.97i −0.364367 0.364367i 0.501051 0.865418i \(-0.332947\pi\)
−0.865418 + 0.501051i \(0.832947\pi\)
\(758\) −8588.37 + 22373.5i −0.411535 + 1.07209i
\(759\) −26826.9 + 5702.23i −1.28294 + 0.272698i
\(760\) −61.5910 4322.08i −0.00293966 0.206287i
\(761\) 373.440 1756.90i 0.0177887 0.0836891i −0.968358 0.249566i \(-0.919712\pi\)
0.986146 + 0.165877i \(0.0530454\pi\)
\(762\) −7964.21 15630.6i −0.378626 0.743095i
\(763\) 732.847 3253.57i 0.0347717 0.154374i
\(764\) 3823.82 1242.43i 0.181075 0.0588347i
\(765\) 22273.3 25457.3i 1.05267 1.20315i
\(766\) −3200.40 15056.7i −0.150960 0.710210i
\(767\) −11654.7 + 9437.77i −0.548665 + 0.444300i
\(768\) −18047.9 + 4835.92i −0.847978 + 0.227215i
\(769\) −9918.00 7205.85i −0.465088 0.337906i 0.330436 0.943828i \(-0.392804\pi\)
−0.795524 + 0.605922i \(0.792804\pi\)
\(770\) −15796.1 + 7073.44i −0.739287 + 0.331051i
\(771\) 53522.0 38886.0i 2.50006 1.81640i
\(772\) 3403.41 4202.86i 0.158668 0.195938i
\(773\) −11325.3 + 593.532i −0.526961 + 0.0276169i −0.313962 0.949435i \(-0.601657\pi\)
−0.212999 + 0.977052i \(0.568323\pi\)
\(774\) 28163.3 16260.1i 1.30789 0.755111i
\(775\) −4741.41 13291.3i −0.219763 0.616049i
\(776\) 28979.6i 1.34060i
\(777\) 29504.0 + 3462.63i 1.36223 + 0.159873i
\(778\) −4031.24 + 25452.2i −0.185767 + 1.17289i
\(779\) −3802.18 + 399.625i −0.174874 + 0.0183800i
\(780\) 686.923 4776.62i 0.0315331 0.219270i
\(781\) 2771.72 26371.1i 0.126991 1.20824i
\(782\) −4592.11 17138.0i −0.209992 0.783700i
\(783\) 10461.4 + 66051.0i 0.477473 + 3.01465i
\(784\) −3221.64 + 24848.1i −0.146758 + 1.13193i
\(785\) 17576.2 16285.1i 0.799138 0.740435i
\(786\) 9148.76 + 1944.63i 0.415172 + 0.0882476i
\(787\) 6454.62 9939.24i 0.292354 0.450185i −0.661723 0.749749i \(-0.730174\pi\)
0.954076 + 0.299564i \(0.0968411\pi\)
\(788\) 1658.96 2554.58i 0.0749976 0.115486i
\(789\) −27023.3 5743.97i −1.21933 0.259177i
\(790\) −24196.0 + 2892.23i −1.08969 + 0.130254i
\(791\) 269.240 + 6685.16i 0.0121025 + 0.300502i
\(792\) −4956.71 31295.4i −0.222385 1.40408i
\(793\) 606.262 + 2262.60i 0.0271488 + 0.101321i
\(794\) 2653.03 25241.9i 0.118580 1.12821i
\(795\) −29775.0 + 5151.82i −1.32831 + 0.229832i
\(796\) −3394.31 + 356.756i −0.151141 + 0.0158855i
\(797\) 3064.71 19349.8i 0.136208 0.859983i −0.821073 0.570823i \(-0.806624\pi\)
0.957281 0.289160i \(-0.0933759\pi\)
\(798\) −5913.14 + 7934.91i −0.262310 + 0.351996i
\(799\) 29996.0i 1.32814i
\(800\) 7503.24 1408.65i 0.331600 0.0622540i
\(801\) −41467.4 + 23941.2i −1.82919 + 1.05608i
\(802\) 42159.5 2209.48i 1.85624 0.0972813i
\(803\) 9303.35 11488.7i 0.408852 0.504890i
\(804\) −7740.69 + 5623.94i −0.339544 + 0.246693i
\(805\) 9175.35 20727.6i 0.401725 0.907516i
\(806\) −9644.97 7007.48i −0.421501 0.306238i
\(807\) 58734.4 15737.8i 2.56202 0.686490i
\(808\) 28627.0 23181.7i 1.24641 1.00932i
\(809\) 98.1840 + 461.919i 0.00426695 + 0.0200744i 0.980230 0.197864i \(-0.0634003\pi\)
−0.975963 + 0.217938i \(0.930067\pi\)
\(810\) 3064.96 33785.6i 0.132953 1.46556i
\(811\) −39464.3 + 12822.7i −1.70873 + 0.555200i −0.990121 0.140216i \(-0.955220\pi\)
−0.718607 + 0.695416i \(0.755220\pi\)
\(812\) 5963.94 + 1343.34i 0.257750 + 0.0580568i
\(813\) −10427.8 20465.7i −0.449838 0.882858i
\(814\) −3039.21 + 14298.4i −0.130865 + 0.615673i
\(815\) −15723.6 + 22303.1i −0.675794 + 0.958583i
\(816\) 34711.0 7378.05i 1.48913 0.316524i
\(817\) −1269.37 + 3306.83i −0.0543570 + 0.141605i
\(818\) 8227.06 + 8227.06i 0.351653 + 0.351653i
\(819\) 26126.3 25501.2i 1.11469 1.08802i
\(820\) −834.458 2945.69i −0.0355372 0.125449i
\(821\) 4086.66 + 38882.0i 0.173722 + 1.65285i 0.640118 + 0.768277i \(0.278885\pi\)
−0.466396 + 0.884576i \(0.654448\pi\)
\(822\) 5236.74 2010.20i 0.222205 0.0852964i
\(823\) 291.657 + 5565.15i 0.0123530 + 0.235709i 0.997827 + 0.0658845i \(0.0209869\pi\)
−0.985474 + 0.169825i \(0.945680\pi\)
\(824\) −19128.8 + 33132.1i −0.808718 + 1.40074i
\(825\) 2529.45 + 31214.2i 0.106744 + 1.31726i
\(826\) 8546.61 + 23096.7i 0.360018 + 0.972926i
\(827\) 10838.2 21271.2i 0.455721 0.894403i −0.542791 0.839868i \(-0.682632\pi\)
0.998512 0.0545351i \(-0.0173677\pi\)
\(828\) −6626.91 5366.37i −0.278141 0.225234i
\(829\) 4372.51 + 1946.77i 0.183189 + 0.0815609i 0.496282 0.868162i \(-0.334698\pi\)
−0.313093 + 0.949723i \(0.601365\pi\)
\(830\) −6920.58 39997.5i −0.289418 1.67269i
\(831\) −21419.0 48107.8i −0.894122 2.00823i
\(832\) −9700.25 + 9700.25i −0.404202 + 0.404202i
\(833\) 3275.57 17869.3i 0.136245 0.743260i
\(834\) −43608.3 14169.2i −1.81059 0.588296i
\(835\) 11072.6 25854.8i 0.458903 1.07155i
\(836\) −527.009 474.521i −0.0218026 0.0196312i
\(837\) −26157.3 16986.7i −1.08020 0.701490i
\(838\) 1091.16 20820.5i 0.0449802 0.858272i
\(839\) 11671.3 + 35920.5i 0.480258 + 1.47808i 0.838732 + 0.544544i \(0.183297\pi\)
−0.358474 + 0.933540i \(0.616703\pi\)
\(840\) 34400.2 + 17435.1i 1.41300 + 0.716151i
\(841\) −10570.0 + 32531.2i −0.433393 + 1.33385i
\(842\) 11971.7 + 4595.52i 0.489992 + 0.188090i
\(843\) −2160.15 + 8061.78i −0.0882555 + 0.329374i
\(844\) −2484.63 261.145i −0.101332 0.0106505i
\(845\) 4180.03 + 10442.1i 0.170174 + 0.425113i
\(846\) −58185.4 80085.3i −2.36460 3.25460i
\(847\) −3471.69 + 10260.4i −0.140837 + 0.416235i
\(848\) −19179.9 9772.67i −0.776700 0.395749i
\(849\) 14121.4 + 8152.97i 0.570841 + 0.329575i
\(850\) −20079.7 + 2690.93i −0.810270 + 0.108586i
\(851\) −9572.45 16580.0i −0.385593 0.667866i
\(852\) 10182.5 6612.61i 0.409446 0.265897i
\(853\) 12622.4 + 1999.20i 0.506664 + 0.0802477i 0.404533 0.914523i \(-0.367434\pi\)
0.102131 + 0.994771i \(0.467434\pi\)
\(854\) 3838.66 + 247.811i 0.153813 + 0.00992964i
\(855\) 6766.70 + 10101.7i 0.270662 + 0.404060i
\(856\) 12243.0 5450.93i 0.488852 0.217651i
\(857\) 1842.67 + 493.742i 0.0734475 + 0.0196802i 0.295356 0.955387i \(-0.404562\pi\)
−0.221908 + 0.975068i \(0.571229\pi\)
\(858\) 16649.8 + 20560.8i 0.662488 + 0.818105i
\(859\) 219.820 + 244.135i 0.00873127 + 0.00969706i 0.747495 0.664268i \(-0.231257\pi\)
−0.738763 + 0.673965i \(0.764590\pi\)
\(860\) −2782.68 550.157i −0.110336 0.0218142i
\(861\) 12608.8 31694.6i 0.499078 1.25453i
\(862\) 23242.9 11842.9i 0.918397 0.467946i
\(863\) −47514.4 2490.12i −1.87417 0.0982211i −0.918996 0.394266i \(-0.870999\pi\)
−0.955174 + 0.296045i \(0.904332\pi\)
\(864\) 11290.2 12539.1i 0.444562 0.493736i
\(865\) 36818.8 524.680i 1.44726 0.0206239i
\(866\) −12138.4 + 10929.5i −0.476305 + 0.428867i
\(867\) 19093.3 3024.08i 0.747914 0.118458i
\(868\) −2326.76 + 1647.82i −0.0909854 + 0.0644363i
\(869\) 11436.0 15740.3i 0.446421 0.614446i
\(870\) 40456.5 64284.6i 1.57655 2.50512i
\(871\) −10738.1 + 24118.2i −0.417735 + 0.938248i
\(872\) −1310.51 3413.99i −0.0508938 0.132583i
\(873\) 44396.6 + 68364.7i 1.72119 + 2.65040i
\(874\) 6377.58 0.246825
\(875\) −22128.9 13425.2i −0.854962 0.518690i
\(876\) 6768.88 0.261072
\(877\) −19137.3 29468.8i −0.736853 1.13465i −0.986090 0.166212i \(-0.946846\pi\)
0.249237 0.968443i \(-0.419820\pi\)
\(878\) −5806.53 15126.5i −0.223190 0.581430i
\(879\) −16437.6 + 36919.4i −0.630746 + 1.41668i
\(880\) −11882.6 + 18881.2i −0.455184 + 0.723280i
\(881\) −1757.80 + 2419.40i −0.0672210 + 0.0925218i −0.841304 0.540563i \(-0.818211\pi\)
0.774083 + 0.633084i \(0.218211\pi\)
\(882\) −25917.1 54062.6i −0.989427 2.06393i
\(883\) −11837.4 + 1874.87i −0.451145 + 0.0714544i −0.377873 0.925858i \(-0.623344\pi\)
−0.0732726 + 0.997312i \(0.523344\pi\)
\(884\) −1852.34 + 1667.85i −0.0704762 + 0.0634570i
\(885\) 44556.5 634.944i 1.69237 0.0241169i
\(886\) −7925.61 + 8802.28i −0.300526 + 0.333768i
\(887\) −6956.91 364.596i −0.263349 0.0138015i −0.0797953 0.996811i \(-0.525427\pi\)
−0.183553 + 0.983010i \(0.558760\pi\)
\(888\) 29022.6 14787.8i 1.09677 0.558834i
\(889\) −9083.94 + 7175.69i −0.342706 + 0.270714i
\(890\) 28133.7 + 5562.25i 1.05960 + 0.209491i
\(891\) 18124.0 + 20128.7i 0.681455 + 0.756832i
\(892\) −666.300 822.813i −0.0250105 0.0308854i
\(893\) 10414.7 + 2790.61i 0.390273 + 0.104573i
\(894\) 31370.3 13967.0i 1.17358 0.522511i
\(895\) 1308.41 + 1953.27i 0.0488663 + 0.0729504i
\(896\) 13993.8 + 28306.5i 0.521764 + 1.05542i
\(897\) −34223.8 5420.51i −1.27391 0.201768i
\(898\) −20143.9 + 13081.6i −0.748564 + 0.486123i
\(899\) −13663.7 23666.1i −0.506906 0.877987i
\(900\) −7047.26 + 6718.72i −0.261009 + 0.248841i
\(901\) 13516.7 + 7803.84i 0.499783 + 0.288550i
\(902\) 14955.5 + 7620.21i 0.552066 + 0.281292i
\(903\) −20860.7 23740.0i −0.768773 0.874882i
\(904\) 4312.08 + 5935.07i 0.158648 + 0.218360i
\(905\) 14094.8 + 35210.1i 0.517708 + 1.29329i
\(906\) 60801.3 + 6390.47i 2.22957 + 0.234337i
\(907\) −2751.33 + 10268.1i −0.100724 + 0.375906i −0.997825 0.0659191i \(-0.979002\pi\)
0.897101 + 0.441825i \(0.145669\pi\)
\(908\) −2113.34 811.234i −0.0772396 0.0296495i
\(909\) −32018.8 + 98543.7i −1.16831 + 3.59570i
\(910\) −21833.9 + 1191.17i −0.795369 + 0.0433921i
\(911\) −998.375 3072.68i −0.0363092 0.111748i 0.931259 0.364357i \(-0.118711\pi\)
−0.967568 + 0.252609i \(0.918711\pi\)
\(912\) −667.579 + 12738.2i −0.0242388 + 0.462503i
\(913\) 27180.7 + 17651.4i 0.985270 + 0.639842i
\(914\) −9964.42 8972.00i −0.360606 0.324691i
\(915\) 2740.08 6398.15i 0.0989991 0.231165i
\(916\) −458.123 148.853i −0.0165249 0.00536926i
\(917\) 74.7250 6171.58i 0.00269099 0.222250i
\(918\) −31661.4 + 31661.4i −1.13832 + 1.13832i
\(919\) 17554.1 + 39427.1i 0.630093 + 1.41521i 0.892852 + 0.450350i \(0.148701\pi\)
−0.262760 + 0.964861i \(0.584633\pi\)
\(920\) −4237.54 24490.9i −0.151856 0.877652i
\(921\) −79961.7 35601.3i −2.86083 1.27373i
\(922\) 34379.7 + 27840.1i 1.22802 + 0.994432i
\(923\) 15209.1 29849.5i 0.542376 1.06447i
\(924\) 5934.02 2195.80i 0.211272 0.0781782i
\(925\) −20177.0 + 8412.46i −0.717207 + 0.299027i
\(926\) −6418.55 + 11117.2i −0.227782 + 0.394531i
\(927\) −5632.05 107466.i −0.199548 3.80760i
\(928\) 13801.9 5298.07i 0.488223 0.187411i
\(929\) −4486.05 42681.9i −0.158431 1.50737i −0.728084 0.685487i \(-0.759589\pi\)
0.569653 0.821885i \(-0.307078\pi\)
\(930\) 9655.10 + 34083.1i 0.340433 + 1.20175i
\(931\) 5899.55 + 2799.72i 0.207680 + 0.0985576i
\(932\) 3547.00 + 3547.00i 0.124663 + 0.124663i
\(933\) 15257.7 39747.6i 0.535384 1.39472i
\(934\) 25348.0 5387.87i 0.888020 0.188754i
\(935\) 9320.23 13220.3i 0.325994 0.462407i
\(936\) 8323.04 39156.8i 0.290649 1.36739i
\(937\) −4357.77 8552.61i −0.151934 0.298187i 0.802477 0.596683i \(-0.203515\pi\)
−0.954411 + 0.298496i \(0.903515\pi\)
\(938\) 31865.0 + 29397.7i 1.10920 + 1.02331i
\(939\) −54070.2 + 17568.5i −1.87914 + 0.610571i
\(940\) −780.093 + 8599.10i −0.0270679 + 0.298374i
\(941\) −3730.64 17551.3i −0.129241 0.608029i −0.994323 0.106400i \(-0.966068\pi\)
0.865083 0.501629i \(-0.167266\pi\)
\(942\) −46744.4 + 37852.8i −1.61679 + 1.30925i
\(943\) −21234.1 + 5689.67i −0.733275 + 0.196481i
\(944\) 25681.6 + 18658.8i 0.885451 + 0.643318i
\(945\) −56878.6 + 6101.40i −1.95795 + 0.210030i
\(946\) 12581.1 9140.72i 0.432397 0.314155i
\(947\) 31130.3 38442.7i 1.06821 1.31914i 0.123101 0.992394i \(-0.460716\pi\)
0.945114 0.326741i \(-0.105950\pi\)
\(948\) 8896.31 466.236i 0.304788 0.0159732i
\(949\) 16174.8 9338.55i 0.553274 0.319433i
\(950\) 933.775 7222.09i 0.0318902 0.246648i
\(951\) 47034.3i 1.60378i
\(952\) −7881.27 18294.6i −0.268313 0.622826i
\(953\) 4009.11 25312.5i 0.136273 0.860391i −0.820942 0.571012i \(-0.806551\pi\)
0.957215 0.289379i \(-0.0934489\pi\)
\(954\) 51225.4 5384.01i 1.73845 0.182719i
\(955\) −32481.4 + 5620.11i −1.10060 + 0.190432i
\(956\) 254.132 2417.90i 0.00859751 0.0817998i
\(957\) 15695.9 + 58578.0i 0.530175 + 1.97864i
\(958\) 3878.34 + 24486.9i 0.130797 + 0.825819i
\(959\) −1978.26 3128.53i −0.0666124 0.105345i
\(960\) 40473.9 4837.99i 1.36072 0.162651i
\(961\) −16673.5 3544.07i −0.559684 0.118964i
\(962\) −10058.5 + 15488.7i −0.337109 + 0.519102i
\(963\) −20531.2 + 31615.3i −0.687030 + 1.05793i
\(964\) 3323.54 + 706.440i 0.111042 + 0.0236026i
\(965\) −32524.7 + 30135.5i −1.08498 + 1.00528i
\(966\) −26444.8 + 50383.5i −0.880796 + 1.67812i
\(967\) −2334.45 14739.1i −0.0776328 0.490154i −0.995616 0.0935348i \(-0.970183\pi\)
0.917983 0.396619i \(-0.129817\pi\)
\(968\) 3073.98 + 11472.3i 0.102068 + 0.380922i
\(969\) 966.738 9197.90i 0.0320497 0.304932i
\(970\) 6949.62 48325.1i 0.230040 1.59962i
\(971\) 44203.2 4645.95i 1.46092 0.153548i 0.659522 0.751685i \(-0.270759\pi\)
0.801394 + 0.598137i \(0.204092\pi\)
\(972\) −348.873 + 2202.70i −0.0115125 + 0.0726868i
\(973\) −3526.86 + 30051.3i −0.116204 + 0.990133i
\(974\) 15013.8i 0.493917i
\(975\) −11149.2 + 37962.0i −0.366215 + 1.24693i
\(976\) 4294.00 2479.14i 0.140827 0.0813067i
\(977\) 4638.44 243.090i 0.151890 0.00796023i 0.0237608 0.999718i \(-0.492436\pi\)
0.128130 + 0.991757i \(0.459103\pi\)
\(978\) 43109.4 53235.7i 1.40950 1.74058i
\(979\) −18524.3 + 13458.7i −0.604740 + 0.439369i
\(980\) −1403.75 + 5037.50i −0.0457561 + 0.164201i
\(981\) 8321.80 + 6046.14i 0.270840 + 0.196777i
\(982\) 20584.8 5515.67i 0.668927 0.179238i
\(983\) 35867.2 29044.7i 1.16377 0.942403i 0.164736 0.986338i \(-0.447323\pi\)
0.999034 + 0.0439349i \(0.0139894\pi\)
\(984\) −7776.28 36584.5i −0.251930 1.18524i
\(985\) −16444.3 + 18795.1i −0.531939 + 0.607981i
\(986\) −37311.9 + 12123.4i −1.20512 + 0.391569i
\(987\) −65230.9 + 70705.6i −2.10367 + 2.28023i
\(988\) −406.756 798.303i −0.0130978 0.0257059i
\(989\) −4234.59 + 19922.2i −0.136150 + 0.640534i
\(990\) −760.620 53375.7i −0.0244183 1.71353i
\(991\) 36233.8 7701.73i 1.16146 0.246875i 0.413425 0.910538i \(-0.364332\pi\)
0.748032 + 0.663663i \(0.230999\pi\)
\(992\) −2470.92 + 6436.97i −0.0790845 + 0.206022i
\(993\) 35810.3 + 35810.3i 1.14442 + 1.14442i
\(994\) −38427.1 39369.1i −1.22619 1.25625i
\(995\) 27962.2 + 1066.17i 0.890915 + 0.0339697i
\(996\) 1551.15 + 14758.2i 0.0493475 + 0.469510i
\(997\) −11360.6 + 4360.93i −0.360877 + 0.138528i −0.532049 0.846713i \(-0.678578\pi\)
0.171172 + 0.985241i \(0.445245\pi\)
\(998\) −655.378 12505.4i −0.0207872 0.396643i
\(999\) −24157.5 + 41842.0i −0.765074 + 1.32515i
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 175.4.x.a.117.43 yes 928
7.3 odd 6 inner 175.4.x.a.17.16 yes 928
25.3 odd 20 inner 175.4.x.a.103.16 yes 928
175.3 even 60 inner 175.4.x.a.3.43 928
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.4.x.a.3.43 928 175.3 even 60 inner
175.4.x.a.17.16 yes 928 7.3 odd 6 inner
175.4.x.a.103.16 yes 928 25.3 odd 20 inner
175.4.x.a.117.43 yes 928 1.1 even 1 trivial