Properties

Label 165.6.c.b.34.26
Level $165$
Weight $6$
Character 165.34
Analytic conductor $26.463$
Analytic rank $0$
Dimension $26$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [165,6,Mod(34,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.34");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 165.c (of order \(2\), degree \(1\), 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: \(26.4633302691\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 34.26
Character \(\chi\) \(=\) 165.34
Dual form 165.6.c.b.34.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+10.7531i q^{2} -9.00000i q^{3} -83.6283 q^{4} +(8.68170 - 55.2234i) q^{5} +96.7775 q^{6} +41.3813i q^{7} -555.162i q^{8} -81.0000 q^{9} +O(q^{10})\) \(q+10.7531i q^{2} -9.00000i q^{3} -83.6283 q^{4} +(8.68170 - 55.2234i) q^{5} +96.7775 q^{6} +41.3813i q^{7} -555.162i q^{8} -81.0000 q^{9} +(593.821 + 93.3549i) q^{10} +121.000 q^{11} +752.654i q^{12} +13.6514i q^{13} -444.975 q^{14} +(-497.011 - 78.1353i) q^{15} +3293.58 q^{16} +1143.92i q^{17} -870.998i q^{18} +1425.16 q^{19} +(-726.036 + 4618.24i) q^{20} +372.432 q^{21} +1301.12i q^{22} +2533.88i q^{23} -4996.46 q^{24} +(-2974.26 - 958.867i) q^{25} -146.795 q^{26} +729.000i q^{27} -3460.65i q^{28} -8594.21 q^{29} +(840.194 - 5344.39i) q^{30} +434.427 q^{31} +17650.9i q^{32} -1089.00i q^{33} -12300.6 q^{34} +(2285.22 + 359.260i) q^{35} +6773.89 q^{36} +14403.2i q^{37} +15324.8i q^{38} +122.863 q^{39} +(-30657.9 - 4819.75i) q^{40} +12386.5 q^{41} +4004.78i q^{42} +2699.39i q^{43} -10119.0 q^{44} +(-703.218 + 4473.10i) q^{45} -27246.9 q^{46} -1691.93i q^{47} -29642.3i q^{48} +15094.6 q^{49} +(10310.8 - 31982.4i) q^{50} +10295.3 q^{51} -1141.65i q^{52} +9465.19i q^{53} -7838.98 q^{54} +(1050.49 - 6682.04i) q^{55} +22973.3 q^{56} -12826.4i q^{57} -92414.0i q^{58} +41470.4 q^{59} +(41564.2 + 6534.32i) q^{60} -17867.3 q^{61} +4671.41i q^{62} -3351.88i q^{63} -84406.7 q^{64} +(753.880 + 118.518i) q^{65} +11710.1 q^{66} +51700.6i q^{67} -95664.1i q^{68} +22804.9 q^{69} +(-3863.15 + 24573.1i) q^{70} -16645.8 q^{71} +44968.1i q^{72} +49707.4i q^{73} -154878. q^{74} +(-8629.80 + 26768.3i) q^{75} -119184. q^{76} +5007.14i q^{77} +1321.15i q^{78} -71497.6 q^{79} +(28593.9 - 181883. i) q^{80} +6561.00 q^{81} +133193. i q^{82} +33539.3i q^{83} -31145.8 q^{84} +(63171.2 + 9931.17i) q^{85} -29026.7 q^{86} +77347.9i q^{87} -67174.6i q^{88} +76978.3 q^{89} +(-48099.5 - 7561.74i) q^{90} -564.914 q^{91} -211904. i q^{92} -3909.84i q^{93} +18193.4 q^{94} +(12372.8 - 78702.1i) q^{95} +158858. q^{96} +17713.7i q^{97} +162313. i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.7531i 1.90089i 0.310892 + 0.950445i \(0.399372\pi\)
−0.310892 + 0.950445i \(0.600628\pi\)
\(3\) 9.00000i 0.577350i
\(4\) −83.6283 −2.61338
\(5\) 8.68170 55.2234i 0.155303 0.987867i
\(6\) 96.7775 1.09748
\(7\) 41.3813i 0.319197i 0.987182 + 0.159599i \(0.0510200\pi\)
−0.987182 + 0.159599i \(0.948980\pi\)
\(8\) 555.162i 3.06687i
\(9\) −81.0000 −0.333333
\(10\) 593.821 + 93.3549i 1.87783 + 0.295214i
\(11\) 121.000 0.301511
\(12\) 752.654i 1.50884i
\(13\) 13.6514i 0.0224037i 0.999937 + 0.0112019i \(0.00356574\pi\)
−0.999937 + 0.0112019i \(0.996434\pi\)
\(14\) −444.975 −0.606759
\(15\) −497.011 78.1353i −0.570345 0.0896643i
\(16\) 3293.58 3.21639
\(17\) 1143.92i 0.960005i 0.877267 + 0.480002i \(0.159364\pi\)
−0.877267 + 0.480002i \(0.840636\pi\)
\(18\) 870.998i 0.633630i
\(19\) 1425.16 0.905689 0.452844 0.891590i \(-0.350409\pi\)
0.452844 + 0.891590i \(0.350409\pi\)
\(20\) −726.036 + 4618.24i −0.405866 + 2.58168i
\(21\) 372.432 0.184289
\(22\) 1301.12i 0.573140i
\(23\) 2533.88i 0.998770i 0.866380 + 0.499385i \(0.166441\pi\)
−0.866380 + 0.499385i \(0.833559\pi\)
\(24\) −4996.46 −1.77066
\(25\) −2974.26 958.867i −0.951762 0.306837i
\(26\) −146.795 −0.0425870
\(27\) 729.000i 0.192450i
\(28\) 3460.65i 0.834185i
\(29\) −8594.21 −1.89763 −0.948814 0.315837i \(-0.897715\pi\)
−0.948814 + 0.315837i \(0.897715\pi\)
\(30\) 840.194 5344.39i 0.170442 1.08416i
\(31\) 434.427 0.0811918 0.0405959 0.999176i \(-0.487074\pi\)
0.0405959 + 0.999176i \(0.487074\pi\)
\(32\) 17650.9i 3.04714i
\(33\) 1089.00i 0.174078i
\(34\) −12300.6 −1.82486
\(35\) 2285.22 + 359.260i 0.315324 + 0.0495723i
\(36\) 6773.89 0.871128
\(37\) 14403.2i 1.72963i 0.502090 + 0.864815i \(0.332564\pi\)
−0.502090 + 0.864815i \(0.667436\pi\)
\(38\) 15324.8i 1.72162i
\(39\) 122.863 0.0129348
\(40\) −30657.9 4819.75i −3.02965 0.476293i
\(41\) 12386.5 1.15077 0.575387 0.817881i \(-0.304851\pi\)
0.575387 + 0.817881i \(0.304851\pi\)
\(42\) 4004.78i 0.350312i
\(43\) 2699.39i 0.222635i 0.993785 + 0.111318i \(0.0355071\pi\)
−0.993785 + 0.111318i \(0.964493\pi\)
\(44\) −10119.0 −0.787965
\(45\) −703.218 + 4473.10i −0.0517677 + 0.329289i
\(46\) −27246.9 −1.89855
\(47\) 1691.93i 0.111722i −0.998439 0.0558608i \(-0.982210\pi\)
0.998439 0.0558608i \(-0.0177903\pi\)
\(48\) 29642.3i 1.85698i
\(49\) 15094.6 0.898113
\(50\) 10310.8 31982.4i 0.583264 1.80919i
\(51\) 10295.3 0.554259
\(52\) 1141.65i 0.0585495i
\(53\) 9465.19i 0.462850i 0.972853 + 0.231425i \(0.0743387\pi\)
−0.972853 + 0.231425i \(0.925661\pi\)
\(54\) −7838.98 −0.365826
\(55\) 1050.49 6682.04i 0.0468256 0.297853i
\(56\) 22973.3 0.978935
\(57\) 12826.4i 0.522900i
\(58\) 92414.0i 3.60718i
\(59\) 41470.4 1.55099 0.775493 0.631356i \(-0.217501\pi\)
0.775493 + 0.631356i \(0.217501\pi\)
\(60\) 41564.2 + 6534.32i 1.49053 + 0.234327i
\(61\) −17867.3 −0.614802 −0.307401 0.951580i \(-0.599459\pi\)
−0.307401 + 0.951580i \(0.599459\pi\)
\(62\) 4671.41i 0.154337i
\(63\) 3351.88i 0.106399i
\(64\) −84406.7 −2.57589
\(65\) 753.880 + 118.518i 0.0221319 + 0.00347937i
\(66\) 11710.1 0.330903
\(67\) 51700.6i 1.40705i 0.710672 + 0.703523i \(0.248391\pi\)
−0.710672 + 0.703523i \(0.751609\pi\)
\(68\) 95664.1i 2.50886i
\(69\) 22804.9 0.576640
\(70\) −3863.15 + 24573.1i −0.0942315 + 0.599397i
\(71\) −16645.8 −0.391885 −0.195943 0.980615i \(-0.562777\pi\)
−0.195943 + 0.980615i \(0.562777\pi\)
\(72\) 44968.1i 1.02229i
\(73\) 49707.4i 1.09173i 0.837874 + 0.545863i \(0.183798\pi\)
−0.837874 + 0.545863i \(0.816202\pi\)
\(74\) −154878. −3.28784
\(75\) −8629.80 + 26768.3i −0.177153 + 0.549500i
\(76\) −119184. −2.36691
\(77\) 5007.14i 0.0962416i
\(78\) 1321.15i 0.0245876i
\(79\) −71497.6 −1.28891 −0.644456 0.764641i \(-0.722916\pi\)
−0.644456 + 0.764641i \(0.722916\pi\)
\(80\) 28593.9 181883.i 0.499515 3.17737i
\(81\) 6561.00 0.111111
\(82\) 133193.i 2.18750i
\(83\) 33539.3i 0.534390i 0.963642 + 0.267195i \(0.0860969\pi\)
−0.963642 + 0.267195i \(0.913903\pi\)
\(84\) −31145.8 −0.481617
\(85\) 63171.2 + 9931.17i 0.948357 + 0.149092i
\(86\) −29026.7 −0.423205
\(87\) 77347.9i 1.09560i
\(88\) 67174.6i 0.924695i
\(89\) 76978.3 1.03013 0.515066 0.857150i \(-0.327767\pi\)
0.515066 + 0.857150i \(0.327767\pi\)
\(90\) −48099.5 7561.74i −0.625942 0.0984047i
\(91\) −564.914 −0.00715120
\(92\) 211904.i 2.61017i
\(93\) 3909.84i 0.0468761i
\(94\) 18193.4 0.212371
\(95\) 12372.8 78702.1i 0.140656 0.894700i
\(96\) 158858. 1.75927
\(97\) 17713.7i 0.191152i 0.995422 + 0.0955761i \(0.0304693\pi\)
−0.995422 + 0.0955761i \(0.969531\pi\)
\(98\) 162313.i 1.70721i
\(99\) −9801.00 −0.100504
\(100\) 248732. + 80188.4i 2.48732 + 0.801884i
\(101\) −2788.38 −0.0271987 −0.0135994 0.999908i \(-0.504329\pi\)
−0.0135994 + 0.999908i \(0.504329\pi\)
\(102\) 110706.i 1.05359i
\(103\) 3106.69i 0.0288539i −0.999896 0.0144269i \(-0.995408\pi\)
0.999896 0.0144269i \(-0.00459240\pi\)
\(104\) 7578.76 0.0687092
\(105\) 3233.34 20567.0i 0.0286206 0.182053i
\(106\) −101780. −0.879826
\(107\) 21599.2i 0.182381i −0.995833 0.0911904i \(-0.970933\pi\)
0.995833 0.0911904i \(-0.0290672\pi\)
\(108\) 60965.0i 0.502946i
\(109\) −190632. −1.53684 −0.768421 0.639945i \(-0.778957\pi\)
−0.768421 + 0.639945i \(0.778957\pi\)
\(110\) 71852.3 + 11295.9i 0.566186 + 0.0890104i
\(111\) 129628. 0.998603
\(112\) 136293.i 1.02666i
\(113\) 239503.i 1.76447i 0.470808 + 0.882236i \(0.343962\pi\)
−0.470808 + 0.882236i \(0.656038\pi\)
\(114\) 137923. 0.993975
\(115\) 139929. + 21998.4i 0.986652 + 0.155112i
\(116\) 718719. 4.95923
\(117\) 1105.77i 0.00746791i
\(118\) 445934.i 2.94826i
\(119\) −47336.9 −0.306431
\(120\) −43377.8 + 275922.i −0.274988 + 1.74917i
\(121\) 14641.0 0.0909091
\(122\) 192129.i 1.16867i
\(123\) 111479.i 0.664400i
\(124\) −36330.3 −0.212185
\(125\) −78773.5 + 155924.i −0.450926 + 0.892561i
\(126\) 36043.0 0.202253
\(127\) 112217.i 0.617373i −0.951164 0.308687i \(-0.900111\pi\)
0.951164 0.308687i \(-0.0998894\pi\)
\(128\) 342801.i 1.84934i
\(129\) 24294.5 0.128539
\(130\) −1274.43 + 8106.51i −0.00661389 + 0.0420703i
\(131\) 334801. 1.70455 0.852273 0.523097i \(-0.175224\pi\)
0.852273 + 0.523097i \(0.175224\pi\)
\(132\) 91071.2i 0.454932i
\(133\) 58974.9i 0.289093i
\(134\) −555939. −2.67464
\(135\) 40257.9 + 6328.96i 0.190115 + 0.0298881i
\(136\) 635061. 2.94420
\(137\) 913.914i 0.00416010i 0.999998 + 0.00208005i \(0.000662101\pi\)
−0.999998 + 0.00208005i \(0.999338\pi\)
\(138\) 245222.i 1.09613i
\(139\) −270355. −1.18685 −0.593427 0.804888i \(-0.702226\pi\)
−0.593427 + 0.804888i \(0.702226\pi\)
\(140\) −191109. 30044.3i −0.824063 0.129551i
\(141\) −15227.4 −0.0645025
\(142\) 178993.i 0.744931i
\(143\) 1651.82i 0.00675498i
\(144\) −266780. −1.07213
\(145\) −74612.4 + 474602.i −0.294707 + 1.87460i
\(146\) −534507. −2.07525
\(147\) 135851.i 0.518526i
\(148\) 1.20451e6i 4.52019i
\(149\) 533592. 1.96899 0.984496 0.175407i \(-0.0561242\pi\)
0.984496 + 0.175407i \(0.0561242\pi\)
\(150\) −287841. 92796.8i −1.04454 0.336748i
\(151\) −109266. −0.389980 −0.194990 0.980805i \(-0.562467\pi\)
−0.194990 + 0.980805i \(0.562467\pi\)
\(152\) 791193.i 2.77763i
\(153\) 92657.5i 0.320002i
\(154\) −53842.0 −0.182945
\(155\) 3771.56 23990.5i 0.0126093 0.0802067i
\(156\) −10274.8 −0.0338036
\(157\) 362759.i 1.17454i −0.809390 0.587272i \(-0.800202\pi\)
0.809390 0.587272i \(-0.199798\pi\)
\(158\) 768818.i 2.45008i
\(159\) 85186.7 0.267226
\(160\) 974744. + 153240.i 3.01017 + 0.473230i
\(161\) −104855. −0.318805
\(162\) 70550.8i 0.211210i
\(163\) 339033.i 0.999478i −0.866176 0.499739i \(-0.833429\pi\)
0.866176 0.499739i \(-0.166571\pi\)
\(164\) −1.03586e6 −3.00742
\(165\) −60138.3 9454.38i −0.171966 0.0270348i
\(166\) −360650. −1.01582
\(167\) 459806.i 1.27580i 0.770118 + 0.637901i \(0.220197\pi\)
−0.770118 + 0.637901i \(0.779803\pi\)
\(168\) 206760.i 0.565188i
\(169\) 371107. 0.999498
\(170\) −106791. + 679284.i −0.283407 + 1.80272i
\(171\) −115438. −0.301896
\(172\) 225745.i 0.581831i
\(173\) 527699.i 1.34051i 0.742130 + 0.670256i \(0.233816\pi\)
−0.742130 + 0.670256i \(0.766184\pi\)
\(174\) −831726. −2.08261
\(175\) 39679.2 123079.i 0.0979416 0.303800i
\(176\) 398524. 0.969778
\(177\) 373234.i 0.895463i
\(178\) 827752.i 1.95817i
\(179\) −789810. −1.84243 −0.921213 0.389059i \(-0.872800\pi\)
−0.921213 + 0.389059i \(0.872800\pi\)
\(180\) 58808.9 374078.i 0.135289 0.860558i
\(181\) −375428. −0.851786 −0.425893 0.904773i \(-0.640040\pi\)
−0.425893 + 0.904773i \(0.640040\pi\)
\(182\) 6074.56i 0.0135937i
\(183\) 160806.i 0.354956i
\(184\) 1.40671e6 3.06309
\(185\) 795392. + 125044.i 1.70864 + 0.268617i
\(186\) 42042.7 0.0891063
\(187\) 138414.i 0.289452i
\(188\) 141493.i 0.291972i
\(189\) −30167.0 −0.0614295
\(190\) 846289. + 133045.i 1.70073 + 0.267372i
\(191\) 339151. 0.672681 0.336341 0.941740i \(-0.390811\pi\)
0.336341 + 0.941740i \(0.390811\pi\)
\(192\) 759660.i 1.48719i
\(193\) 359337.i 0.694398i −0.937792 0.347199i \(-0.887133\pi\)
0.937792 0.347199i \(-0.112867\pi\)
\(194\) −190476. −0.363359
\(195\) 1066.66 6784.92i 0.00200881 0.0127779i
\(196\) −1.26233e6 −2.34711
\(197\) 604048.i 1.10893i −0.832206 0.554467i \(-0.812922\pi\)
0.832206 0.554467i \(-0.187078\pi\)
\(198\) 105391.i 0.191047i
\(199\) 1.03446e6 1.85174 0.925868 0.377846i \(-0.123335\pi\)
0.925868 + 0.377846i \(0.123335\pi\)
\(200\) −532326. + 1.65119e6i −0.941029 + 2.91893i
\(201\) 465305. 0.812358
\(202\) 29983.6i 0.0517018i
\(203\) 355639.i 0.605717i
\(204\) −860976. −1.44849
\(205\) 107536. 684027.i 0.178719 1.13681i
\(206\) 33406.4 0.0548481
\(207\) 205244.i 0.332923i
\(208\) 44962.2i 0.0720591i
\(209\) 172444. 0.273075
\(210\) 221158. + 34768.3i 0.346062 + 0.0544046i
\(211\) −758371. −1.17267 −0.586335 0.810069i \(-0.699430\pi\)
−0.586335 + 0.810069i \(0.699430\pi\)
\(212\) 791558.i 1.20960i
\(213\) 149812.i 0.226255i
\(214\) 232258. 0.346686
\(215\) 149069. + 23435.3i 0.219934 + 0.0345759i
\(216\) 404713. 0.590218
\(217\) 17977.1i 0.0259162i
\(218\) 2.04988e6i 2.92137i
\(219\) 447367. 0.630309
\(220\) −87850.3 + 558807.i −0.122373 + 0.778404i
\(221\) −15616.2 −0.0215077
\(222\) 1.39390e6i 1.89823i
\(223\) 1.08373e6i 1.45935i 0.683792 + 0.729677i \(0.260329\pi\)
−0.683792 + 0.729677i \(0.739671\pi\)
\(224\) −730418. −0.972638
\(225\) 240915. + 77668.2i 0.317254 + 0.102279i
\(226\) −2.57539e6 −3.35407
\(227\) 635159.i 0.818122i −0.912507 0.409061i \(-0.865856\pi\)
0.912507 0.409061i \(-0.134144\pi\)
\(228\) 1.07265e6i 1.36654i
\(229\) −622829. −0.784838 −0.392419 0.919787i \(-0.628362\pi\)
−0.392419 + 0.919787i \(0.628362\pi\)
\(230\) −236550. + 1.50467e6i −0.294851 + 1.87552i
\(231\) 45064.2 0.0555651
\(232\) 4.77118e6i 5.81977i
\(233\) 1.31801e6i 1.59048i −0.606296 0.795239i \(-0.707345\pi\)
0.606296 0.795239i \(-0.292655\pi\)
\(234\) 11890.4 0.0141957
\(235\) −93434.1 14688.8i −0.110366 0.0173507i
\(236\) −3.46810e6 −4.05332
\(237\) 643478.i 0.744154i
\(238\) 509016.i 0.582491i
\(239\) 240029. 0.271812 0.135906 0.990722i \(-0.456605\pi\)
0.135906 + 0.990722i \(0.456605\pi\)
\(240\) −1.63695e6 257345.i −1.83445 0.288395i
\(241\) 659027. 0.730904 0.365452 0.930830i \(-0.380914\pi\)
0.365452 + 0.930830i \(0.380914\pi\)
\(242\) 157436.i 0.172808i
\(243\) 59049.0i 0.0641500i
\(244\) 1.49422e6 1.60671
\(245\) 131047. 833575.i 0.139480 0.887216i
\(246\) 1.19874e6 1.26295
\(247\) 19455.5i 0.0202908i
\(248\) 241177.i 0.249004i
\(249\) 301854. 0.308530
\(250\) −1.67666e6 847057.i −1.69666 0.857161i
\(251\) 1.72716e6 1.73040 0.865202 0.501424i \(-0.167190\pi\)
0.865202 + 0.501424i \(0.167190\pi\)
\(252\) 280312.i 0.278062i
\(253\) 306599.i 0.301141i
\(254\) 1.20667e6 1.17356
\(255\) 89380.6 568541.i 0.0860781 0.547534i
\(256\) 985142. 0.939505
\(257\) 889184.i 0.839767i −0.907578 0.419883i \(-0.862071\pi\)
0.907578 0.419883i \(-0.137929\pi\)
\(258\) 261240.i 0.244338i
\(259\) −596021. −0.552093
\(260\) −63045.7 9911.44i −0.0578391 0.00909292i
\(261\) 696131. 0.632542
\(262\) 3.60014e6i 3.24015i
\(263\) 352666.i 0.314394i 0.987567 + 0.157197i \(0.0502458\pi\)
−0.987567 + 0.157197i \(0.949754\pi\)
\(264\) −604571. −0.533873
\(265\) 522701. + 82174.0i 0.457234 + 0.0718819i
\(266\) −634160. −0.549535
\(267\) 692804.i 0.594747i
\(268\) 4.32363e6i 3.67715i
\(269\) 506736. 0.426973 0.213487 0.976946i \(-0.431518\pi\)
0.213487 + 0.976946i \(0.431518\pi\)
\(270\) −68055.7 + 432895.i −0.0568140 + 0.361388i
\(271\) −1.33528e6 −1.10446 −0.552230 0.833691i \(-0.686223\pi\)
−0.552230 + 0.833691i \(0.686223\pi\)
\(272\) 3.76760e6i 3.08775i
\(273\) 5084.23i 0.00412875i
\(274\) −9827.37 −0.00790790
\(275\) −359885. 116023.i −0.286967 0.0925150i
\(276\) −1.90713e6 −1.50698
\(277\) 1.72199e6i 1.34844i −0.738532 0.674218i \(-0.764481\pi\)
0.738532 0.674218i \(-0.235519\pi\)
\(278\) 2.90714e6i 2.25608i
\(279\) −35188.5 −0.0270639
\(280\) 199448. 1.26867e6i 0.152032 0.967057i
\(281\) −1.20590e6 −0.911061 −0.455530 0.890220i \(-0.650550\pi\)
−0.455530 + 0.890220i \(0.650550\pi\)
\(282\) 163741.i 0.122612i
\(283\) 920183.i 0.682980i −0.939885 0.341490i \(-0.889068\pi\)
0.939885 0.341490i \(-0.110932\pi\)
\(284\) 1.39206e6 1.02415
\(285\) −708319. 111355.i −0.516555 0.0812079i
\(286\) −17762.2 −0.0128405
\(287\) 512571.i 0.367324i
\(288\) 1.42972e6i 1.01571i
\(289\) 111304. 0.0783911
\(290\) −5.10342e6 802311.i −3.56341 0.560206i
\(291\) 159423. 0.110362
\(292\) 4.15694e6i 2.85310i
\(293\) 125447.i 0.0853674i 0.999089 + 0.0426837i \(0.0135908\pi\)
−0.999089 + 0.0426837i \(0.986409\pi\)
\(294\) 1.46082e6 0.985661
\(295\) 360034. 2.29014e6i 0.240873 1.53217i
\(296\) 7.99608e6 5.30454
\(297\) 88209.0i 0.0580259i
\(298\) 5.73775e6i 3.74284i
\(299\) −34591.1 −0.0223762
\(300\) 721696. 2.23859e6i 0.462968 1.43605i
\(301\) −111704. −0.0710646
\(302\) 1.17494e6i 0.741310i
\(303\) 25095.4i 0.0157032i
\(304\) 4.69388e6 2.91305
\(305\) −155119. + 986696.i −0.0954807 + 0.607343i
\(306\) 996352. 0.608288
\(307\) 922678.i 0.558733i 0.960185 + 0.279366i \(0.0901244\pi\)
−0.960185 + 0.279366i \(0.909876\pi\)
\(308\) 418738.i 0.251516i
\(309\) −27960.2 −0.0166588
\(310\) 257972. + 40555.8i 0.152464 + 0.0239690i
\(311\) −1.60136e6 −0.938831 −0.469416 0.882977i \(-0.655535\pi\)
−0.469416 + 0.882977i \(0.655535\pi\)
\(312\) 68208.9i 0.0396693i
\(313\) 177127.i 0.102193i −0.998694 0.0510967i \(-0.983728\pi\)
0.998694 0.0510967i \(-0.0162717\pi\)
\(314\) 3.90077e6 2.23268
\(315\) −185103. 29100.1i −0.105108 0.0165241i
\(316\) 5.97922e6 3.36842
\(317\) 578254.i 0.323199i 0.986856 + 0.161600i \(0.0516653\pi\)
−0.986856 + 0.161600i \(0.948335\pi\)
\(318\) 916018.i 0.507968i
\(319\) −1.03990e6 −0.572156
\(320\) −732794. + 4.66123e6i −0.400043 + 2.54463i
\(321\) −194393. −0.105298
\(322\) 1.12751e6i 0.606013i
\(323\) 1.63027e6i 0.869466i
\(324\) −548685. −0.290376
\(325\) 13089.9 40602.9i 0.00687430 0.0213230i
\(326\) 3.64565e6 1.89990
\(327\) 1.71569e6i 0.887296i
\(328\) 6.87653e6i 3.52927i
\(329\) 70014.2 0.0356612
\(330\) 101663. 646671.i 0.0513902 0.326888i
\(331\) −3.23768e6 −1.62429 −0.812145 0.583456i \(-0.801700\pi\)
−0.812145 + 0.583456i \(0.801700\pi\)
\(332\) 2.80483e6i 1.39657i
\(333\) 1.16666e6i 0.576543i
\(334\) −4.94432e6 −2.42516
\(335\) 2.85508e6 + 448849.i 1.38997 + 0.218519i
\(336\) 1.22663e6 0.592744
\(337\) 1.82330e6i 0.874546i 0.899329 + 0.437273i \(0.144056\pi\)
−0.899329 + 0.437273i \(0.855944\pi\)
\(338\) 3.99053e6i 1.89994i
\(339\) 2.15553e6 1.01872
\(340\) −5.28290e6 830527.i −2.47842 0.389634i
\(341\) 52565.6 0.0244802
\(342\) 1.24131e6i 0.573872i
\(343\) 1.32013e6i 0.605872i
\(344\) 1.49860e6 0.682792
\(345\) 197985. 1.25936e6i 0.0895540 0.569644i
\(346\) −5.67438e6 −2.54817
\(347\) 564150.i 0.251519i 0.992061 + 0.125759i \(0.0401368\pi\)
−0.992061 + 0.125759i \(0.959863\pi\)
\(348\) 6.46847e6i 2.86321i
\(349\) −2.72653e6 −1.19825 −0.599124 0.800657i \(-0.704484\pi\)
−0.599124 + 0.800657i \(0.704484\pi\)
\(350\) 1.32347e6 + 426672.i 0.577490 + 0.186176i
\(351\) −9951.90 −0.00431160
\(352\) 2.13576e6i 0.918747i
\(353\) 694975.i 0.296847i −0.988924 0.148423i \(-0.952580\pi\)
0.988924 0.148423i \(-0.0474198\pi\)
\(354\) 4.01340e6 1.70218
\(355\) −144514. + 919239.i −0.0608610 + 0.387130i
\(356\) −6.43756e6 −2.69213
\(357\) 426032.i 0.176918i
\(358\) 8.49287e6i 3.50225i
\(359\) 306112. 0.125356 0.0626779 0.998034i \(-0.480036\pi\)
0.0626779 + 0.998034i \(0.480036\pi\)
\(360\) 2.48329e6 + 390400.i 1.00988 + 0.158764i
\(361\) −445023. −0.179728
\(362\) 4.03700e6i 1.61915i
\(363\) 131769.i 0.0524864i
\(364\) 47242.8 0.0186888
\(365\) 2.74501e6 + 431545.i 1.07848 + 0.169548i
\(366\) −1.72916e6 −0.674733
\(367\) 1.51571e6i 0.587423i 0.955894 + 0.293712i \(0.0948906\pi\)
−0.955894 + 0.293712i \(0.905109\pi\)
\(368\) 8.34553e6i 3.21244i
\(369\) −1.00331e6 −0.383592
\(370\) −1.34460e6 + 8.55289e6i −0.510611 + 3.24795i
\(371\) −391682. −0.147740
\(372\) 326973.i 0.122505i
\(373\) 1.05811e6i 0.393783i −0.980425 0.196892i \(-0.936915\pi\)
0.980425 0.196892i \(-0.0630847\pi\)
\(374\) −1.48838e6 −0.550217
\(375\) 1.40332e6 + 708962.i 0.515321 + 0.260342i
\(376\) −939294. −0.342635
\(377\) 117323.i 0.0425139i
\(378\) 324387.i 0.116771i
\(379\) −812383. −0.290511 −0.145256 0.989394i \(-0.546400\pi\)
−0.145256 + 0.989394i \(0.546400\pi\)
\(380\) −1.03472e6 + 6.58172e6i −0.367589 + 2.33819i
\(381\) −1.00995e6 −0.356441
\(382\) 3.64691e6i 1.27869i
\(383\) 1.22178e6i 0.425593i 0.977096 + 0.212797i \(0.0682572\pi\)
−0.977096 + 0.212797i \(0.931743\pi\)
\(384\) −3.08521e6 −1.06772
\(385\) 276511. + 43470.5i 0.0950738 + 0.0149466i
\(386\) 3.86397e6 1.31997
\(387\) 218650.i 0.0742118i
\(388\) 1.48136e6i 0.499554i
\(389\) 4.08811e6 1.36977 0.684887 0.728649i \(-0.259852\pi\)
0.684887 + 0.728649i \(0.259852\pi\)
\(390\) 72958.6 + 11469.9i 0.0242893 + 0.00381853i
\(391\) −2.89855e6 −0.958824
\(392\) 8.37994e6i 2.75439i
\(393\) 3.01321e6i 0.984120i
\(394\) 6.49536e6 2.10796
\(395\) −620721. + 3.94834e6i −0.200172 + 1.27327i
\(396\) 819641. 0.262655
\(397\) 15256.4i 0.00485822i 0.999997 + 0.00242911i \(0.000773210\pi\)
−0.999997 + 0.00242911i \(0.999227\pi\)
\(398\) 1.11236e7i 3.51995i
\(399\) 530774. 0.166908
\(400\) −9.79596e6 3.15811e6i −3.06124 0.986909i
\(401\) −4.75411e6 −1.47642 −0.738208 0.674574i \(-0.764328\pi\)
−0.738208 + 0.674574i \(0.764328\pi\)
\(402\) 5.00345e6i 1.54420i
\(403\) 5930.55i 0.00181900i
\(404\) 233188. 0.0710807
\(405\) 56960.7 362321.i 0.0172559 0.109763i
\(406\) 3.82421e6 1.15140
\(407\) 1.74278e6i 0.521503i
\(408\) 5.71555e6i 1.69984i
\(409\) 6.12814e6 1.81143 0.905713 0.423891i \(-0.139336\pi\)
0.905713 + 0.423891i \(0.139336\pi\)
\(410\) 7.35538e6 + 1.15634e6i 2.16095 + 0.339725i
\(411\) 8225.23 0.00240184
\(412\) 259807.i 0.0754063i
\(413\) 1.71610e6i 0.495071i
\(414\) 2.20700e6 0.632851
\(415\) 1.85215e6 + 291178.i 0.527907 + 0.0829925i
\(416\) −240961. −0.0682673
\(417\) 2.43320e6i 0.685231i
\(418\) 1.85430e6i 0.519086i
\(419\) 3.61815e6 1.00682 0.503410 0.864048i \(-0.332079\pi\)
0.503410 + 0.864048i \(0.332079\pi\)
\(420\) −270399. + 1.71998e6i −0.0747965 + 0.475773i
\(421\) −1.49527e6 −0.411164 −0.205582 0.978640i \(-0.565909\pi\)
−0.205582 + 0.978640i \(0.565909\pi\)
\(422\) 8.15481e6i 2.22912i
\(423\) 137046.i 0.0372406i
\(424\) 5.25471e6 1.41950
\(425\) 1.09687e6 3.40231e6i 0.294565 0.913696i
\(426\) −1.61094e6 −0.430086
\(427\) 739374.i 0.196243i
\(428\) 1.80631e6i 0.476631i
\(429\) 14866.4 0.00389999
\(430\) −252001. + 1.60295e6i −0.0657251 + 0.418070i
\(431\) 538580. 0.139655 0.0698276 0.997559i \(-0.477755\pi\)
0.0698276 + 0.997559i \(0.477755\pi\)
\(432\) 2.40102e6i 0.618995i
\(433\) 5.50572e6i 1.41122i 0.708600 + 0.705610i \(0.249327\pi\)
−0.708600 + 0.705610i \(0.750673\pi\)
\(434\) −193309. −0.0492638
\(435\) 4.27142e6 + 671511.i 1.08230 + 0.170149i
\(436\) 1.59422e7 4.01636
\(437\) 3.61117e6i 0.904575i
\(438\) 4.81056e6i 1.19815i
\(439\) −4.55179e6 −1.12725 −0.563626 0.826030i \(-0.690594\pi\)
−0.563626 + 0.826030i \(0.690594\pi\)
\(440\) −3.70961e6 583190.i −0.913475 0.143608i
\(441\) −1.22266e6 −0.299371
\(442\) 167921.i 0.0408837i
\(443\) 1.92800e6i 0.466764i 0.972385 + 0.233382i \(0.0749793\pi\)
−0.972385 + 0.233382i \(0.925021\pi\)
\(444\) −1.08406e7 −2.60973
\(445\) 668303. 4.25100e6i 0.159983 1.01763i
\(446\) −1.16535e7 −2.77407
\(447\) 4.80233e6i 1.13680i
\(448\) 3.49286e6i 0.822216i
\(449\) −2.25763e6 −0.528491 −0.264246 0.964455i \(-0.585123\pi\)
−0.264246 + 0.964455i \(0.585123\pi\)
\(450\) −835171. + 2.59057e6i −0.194421 + 0.603065i
\(451\) 1.49877e6 0.346972
\(452\) 2.00292e7i 4.61124i
\(453\) 983394.i 0.225155i
\(454\) 6.82991e6 1.55516
\(455\) −4904.42 + 31196.5i −0.00111060 + 0.00706444i
\(456\) −7.12074e6 −1.60366
\(457\) 1.40364e6i 0.314388i −0.987568 0.157194i \(-0.949755\pi\)
0.987568 0.157194i \(-0.0502448\pi\)
\(458\) 6.69732e6i 1.49189i
\(459\) −833918. −0.184753
\(460\) −1.17020e7 1.83968e6i −2.57850 0.405367i
\(461\) 1.28230e6 0.281021 0.140510 0.990079i \(-0.455126\pi\)
0.140510 + 0.990079i \(0.455126\pi\)
\(462\) 484578.i 0.105623i
\(463\) 5.16733e6i 1.12025i 0.828409 + 0.560124i \(0.189246\pi\)
−0.828409 + 0.560124i \(0.810754\pi\)
\(464\) −2.83057e7 −6.10351
\(465\) −215915. 33944.1i −0.0463073 0.00728000i
\(466\) 1.41726e7 3.02332
\(467\) 1.85528e6i 0.393657i 0.980438 + 0.196828i \(0.0630642\pi\)
−0.980438 + 0.196828i \(0.936936\pi\)
\(468\) 92473.4i 0.0195165i
\(469\) −2.13944e6 −0.449125
\(470\) 157950. 1.00470e6i 0.0329818 0.209794i
\(471\) −3.26483e6 −0.678123
\(472\) 2.30228e7i 4.75667i
\(473\) 326626.i 0.0671271i
\(474\) −6.91936e6 −1.41456
\(475\) −4.23879e6 1.36654e6i −0.862000 0.277899i
\(476\) 3.95870e6 0.800821
\(477\) 766681.i 0.154283i
\(478\) 2.58104e6i 0.516685i
\(479\) −2.77689e6 −0.552993 −0.276497 0.961015i \(-0.589173\pi\)
−0.276497 + 0.961015i \(0.589173\pi\)
\(480\) 1.37916e6 8.77270e6i 0.273220 1.73792i
\(481\) −196624. −0.0387502
\(482\) 7.08655e6i 1.38937i
\(483\) 943695.i 0.184062i
\(484\) −1.22440e6 −0.237580
\(485\) 978210. + 153785.i 0.188833 + 0.0296865i
\(486\) 634957. 0.121942
\(487\) 8.55421e6i 1.63440i 0.576356 + 0.817198i \(0.304474\pi\)
−0.576356 + 0.817198i \(0.695526\pi\)
\(488\) 9.91927e6i 1.88552i
\(489\) −3.05130e6 −0.577049
\(490\) 8.96348e6 + 1.40915e6i 1.68650 + 0.265136i
\(491\) −9.34368e6 −1.74910 −0.874550 0.484936i \(-0.838843\pi\)
−0.874550 + 0.484936i \(0.838843\pi\)
\(492\) 9.32278e6i 1.73633i
\(493\) 9.83109e6i 1.82173i
\(494\) −209206. −0.0385706
\(495\) −85089.4 + 541245.i −0.0156085 + 0.0992844i
\(496\) 1.43082e6 0.261144
\(497\) 688825.i 0.125089i
\(498\) 3.24585e6i 0.586483i
\(499\) −1.03633e7 −1.86314 −0.931569 0.363564i \(-0.881560\pi\)
−0.931569 + 0.363564i \(0.881560\pi\)
\(500\) 6.58770e6 1.30397e7i 1.17844 2.33261i
\(501\) 4.13825e6 0.736585
\(502\) 1.85722e7i 3.28931i
\(503\) 5.19173e6i 0.914938i −0.889225 0.457469i \(-0.848756\pi\)
0.889225 0.457469i \(-0.151244\pi\)
\(504\) −1.86084e6 −0.326312
\(505\) −24207.9 + 153984.i −0.00422405 + 0.0268687i
\(506\) −3.29688e6 −0.572435
\(507\) 3.33996e6i 0.577060i
\(508\) 9.38448e6i 1.61343i
\(509\) −591024. −0.101114 −0.0505569 0.998721i \(-0.516100\pi\)
−0.0505569 + 0.998721i \(0.516100\pi\)
\(510\) 6.11355e6 + 961115.i 1.04080 + 0.163625i
\(511\) −2.05696e6 −0.348476
\(512\) 376329.i 0.0634444i
\(513\) 1.03894e6i 0.174300i
\(514\) 9.56145e6 1.59630
\(515\) −171562. 26971.3i −0.0285038 0.00448110i
\(516\) −2.03171e6 −0.335921
\(517\) 204723.i 0.0336854i
\(518\) 6.40905e6i 1.04947i
\(519\) 4.74929e6 0.773945
\(520\) 65796.6 418525.i 0.0106707 0.0678755i
\(521\) 4.41573e6 0.712702 0.356351 0.934352i \(-0.384021\pi\)
0.356351 + 0.934352i \(0.384021\pi\)
\(522\) 7.48554e6i 1.20239i
\(523\) 7.91473e6i 1.26527i −0.774452 0.632633i \(-0.781974\pi\)
0.774452 0.632633i \(-0.218026\pi\)
\(524\) −2.79988e7 −4.45463
\(525\) −1.10771e6 357112.i −0.175399 0.0565466i
\(526\) −3.79224e6 −0.597629
\(527\) 496949.i 0.0779445i
\(528\) 3.58671e6i 0.559902i
\(529\) 15819.3 0.00245780
\(530\) −883622. + 5.62063e6i −0.136640 + 0.869151i
\(531\) −3.35910e6 −0.516996
\(532\) 4.93197e6i 0.755512i
\(533\) 169094.i 0.0257816i
\(534\) 7.44977e6 1.13055
\(535\) −1.19278e6 187518.i −0.180168 0.0283243i
\(536\) 2.87022e7 4.31522
\(537\) 7.10829e6i 1.06372i
\(538\) 5.44896e6i 0.811629i
\(539\) 1.82645e6 0.270791
\(540\) −3.36670e6 529280.i −0.496844 0.0781090i
\(541\) 1.37134e6 0.201443 0.100722 0.994915i \(-0.467885\pi\)
0.100722 + 0.994915i \(0.467885\pi\)
\(542\) 1.43584e7i 2.09946i
\(543\) 3.37886e6i 0.491779i
\(544\) −2.01912e7 −2.92527
\(545\) −1.65501e6 + 1.05273e7i −0.238676 + 1.51820i
\(546\) −54671.0 −0.00784830
\(547\) 7.82390e6i 1.11803i 0.829156 + 0.559017i \(0.188821\pi\)
−0.829156 + 0.559017i \(0.811179\pi\)
\(548\) 76429.1i 0.0108719i
\(549\) 1.44726e6 0.204934
\(550\) 1.24760e6 3.86986e6i 0.175861 0.545493i
\(551\) −1.22481e7 −1.71866
\(552\) 1.26604e7i 1.76848i
\(553\) 2.95866e6i 0.411417i
\(554\) 1.85166e7 2.56323
\(555\) 1.12540e6 7.15853e6i 0.155086 0.986486i
\(556\) 2.26093e7 3.10171
\(557\) 8.25549e6i 1.12747i 0.825956 + 0.563735i \(0.190636\pi\)
−0.825956 + 0.563735i \(0.809364\pi\)
\(558\) 378385.i 0.0514456i
\(559\) −36850.5 −0.00498786
\(560\) 7.52655e6 + 1.18325e6i 1.01421 + 0.159444i
\(561\) 1.24573e6 0.167115
\(562\) 1.29672e7i 1.73183i
\(563\) 1.20969e7i 1.60843i −0.594340 0.804214i \(-0.702587\pi\)
0.594340 0.804214i \(-0.297413\pi\)
\(564\) 1.27344e6 0.168570
\(565\) 1.32262e7 + 2.07929e6i 1.74306 + 0.274028i
\(566\) 9.89478e6 1.29827
\(567\) 271503.i 0.0354663i
\(568\) 9.24112e6i 1.20186i
\(569\) 7.97678e6 1.03287 0.516437 0.856325i \(-0.327258\pi\)
0.516437 + 0.856325i \(0.327258\pi\)
\(570\) 1.19741e6 7.61660e6i 0.154367 0.981915i
\(571\) −8.94027e6 −1.14752 −0.573760 0.819023i \(-0.694516\pi\)
−0.573760 + 0.819023i \(0.694516\pi\)
\(572\) 138139.i 0.0176533i
\(573\) 3.05236e6i 0.388373i
\(574\) −5.51171e6 −0.698242
\(575\) 2.42965e6 7.53639e6i 0.306460 0.950592i
\(576\) 6.83694e6 0.858629
\(577\) 4.92430e6i 0.615751i −0.951427 0.307875i \(-0.900382\pi\)
0.951427 0.307875i \(-0.0996180\pi\)
\(578\) 1.19686e6i 0.149013i
\(579\) −3.23403e6 −0.400911
\(580\) 6.23970e6 3.96901e7i 0.770183 4.89906i
\(581\) −1.38790e6 −0.170576
\(582\) 1.71428e6i 0.209786i
\(583\) 1.14529e6i 0.139554i
\(584\) 2.75957e7 3.34818
\(585\) −61064.3 9599.94i −0.00737730 0.00115979i
\(586\) −1.34894e6 −0.162274
\(587\) 1.22885e7i 1.47199i 0.676989 + 0.735993i \(0.263285\pi\)
−0.676989 + 0.735993i \(0.736715\pi\)
\(588\) 1.13610e7i 1.35511i
\(589\) 619126. 0.0735345
\(590\) 2.46260e7 + 3.87146e6i 2.91248 + 0.457873i
\(591\) −5.43643e6 −0.640244
\(592\) 4.74380e7i 5.56317i
\(593\) 8.20846e6i 0.958572i 0.877659 + 0.479286i \(0.159104\pi\)
−0.877659 + 0.479286i \(0.840896\pi\)
\(594\) −948517. −0.110301
\(595\) −410965. + 2.61411e6i −0.0475896 + 0.302713i
\(596\) −4.46234e7 −5.14573
\(597\) 9.31010e6i 1.06910i
\(598\) 371960.i 0.0425347i
\(599\) 2.00442e6 0.228256 0.114128 0.993466i \(-0.463593\pi\)
0.114128 + 0.993466i \(0.463593\pi\)
\(600\) 1.48607e7 + 4.79094e6i 1.68524 + 0.543303i
\(601\) −871399. −0.0984081 −0.0492041 0.998789i \(-0.515668\pi\)
−0.0492041 + 0.998789i \(0.515668\pi\)
\(602\) 1.20116e6i 0.135086i
\(603\) 4.18775e6i 0.469015i
\(604\) 9.13773e6 1.01917
\(605\) 127109. 808526.i 0.0141185 0.0898061i
\(606\) −269853. −0.0298501
\(607\) 1.04538e7i 1.15160i −0.817589 0.575802i \(-0.804690\pi\)
0.817589 0.575802i \(-0.195310\pi\)
\(608\) 2.51554e7i 2.75976i
\(609\) −3.20075e6 −0.349711
\(610\) −1.06100e7 1.66800e6i −1.15449 0.181498i
\(611\) 23097.3 0.00250298
\(612\) 7.74879e6i 0.836287i
\(613\) 5.79441e6i 0.622814i 0.950277 + 0.311407i \(0.100800\pi\)
−0.950277 + 0.311407i \(0.899200\pi\)
\(614\) −9.92161e6 −1.06209
\(615\) −6.15624e6 967826.i −0.656339 0.103183i
\(616\) 2.77977e6 0.295160
\(617\) 7.10900e6i 0.751788i 0.926663 + 0.375894i \(0.122664\pi\)
−0.926663 + 0.375894i \(0.877336\pi\)
\(618\) 300657.i 0.0316665i
\(619\) 1.13332e7 1.18885 0.594424 0.804152i \(-0.297380\pi\)
0.594424 + 0.804152i \(0.297380\pi\)
\(620\) −315409. + 2.00629e6i −0.0329530 + 0.209611i
\(621\) −1.84720e6 −0.192213
\(622\) 1.72195e7i 1.78462i
\(623\) 3.18546e6i 0.328815i
\(624\) 404660. 0.0416034
\(625\) 7.92677e6 + 5.70383e6i 0.811702 + 0.584072i
\(626\) 1.90465e6 0.194259
\(627\) 1.55200e6i 0.157660i
\(628\) 3.03369e7i 3.06953i
\(629\) −1.64761e7 −1.66045
\(630\) 312915. 1.99042e6i 0.0314105 0.199799i
\(631\) 3.77282e6 0.377218 0.188609 0.982052i \(-0.439602\pi\)
0.188609 + 0.982052i \(0.439602\pi\)
\(632\) 3.96927e7i 3.95292i
\(633\) 6.82534e6i 0.677041i
\(634\) −6.21800e6 −0.614366
\(635\) −6.19699e6 974231.i −0.609882 0.0958799i
\(636\) −7.12402e6 −0.698365
\(637\) 206063.i 0.0201211i
\(638\) 1.11821e7i 1.08761i
\(639\) 1.34831e6 0.130628
\(640\) −1.89306e7 2.97609e6i −1.82690 0.287208i
\(641\) 1.76552e6 0.169718 0.0848591 0.996393i \(-0.472956\pi\)
0.0848591 + 0.996393i \(0.472956\pi\)
\(642\) 2.09032e6i 0.200159i
\(643\) 3.29197e6i 0.313999i −0.987599 0.157000i \(-0.949818\pi\)
0.987599 0.157000i \(-0.0501822\pi\)
\(644\) 8.76885e6 0.833159
\(645\) 210918. 1.34162e6i 0.0199624 0.126979i
\(646\) −1.75304e7 −1.65276
\(647\) 1.62220e7i 1.52350i 0.647868 + 0.761752i \(0.275661\pi\)
−0.647868 + 0.761752i \(0.724339\pi\)
\(648\) 3.64242e6i 0.340763i
\(649\) 5.01792e6 0.467640
\(650\) 436605. + 140757.i 0.0405327 + 0.0130673i
\(651\) 161794. 0.0149627
\(652\) 2.83528e7i 2.61202i
\(653\) 3.42354e6i 0.314190i −0.987583 0.157095i \(-0.949787\pi\)
0.987583 0.157095i \(-0.0502129\pi\)
\(654\) −1.84489e7 −1.68665
\(655\) 2.90664e6 1.84889e7i 0.264721 1.68386i
\(656\) 4.07961e7 3.70134
\(657\) 4.02630e6i 0.363909i
\(658\) 752867.i 0.0677881i
\(659\) −5.40108e6 −0.484470 −0.242235 0.970218i \(-0.577881\pi\)
−0.242235 + 0.970218i \(0.577881\pi\)
\(660\) 5.02926e6 + 790653.i 0.449412 + 0.0706523i
\(661\) 4.42083e6 0.393550 0.196775 0.980449i \(-0.436953\pi\)
0.196775 + 0.980449i \(0.436953\pi\)
\(662\) 3.48149e7i 3.08760i
\(663\) 140545.i 0.0124175i
\(664\) 1.86197e7 1.63890
\(665\) 3.25680e6 + 512003.i 0.285586 + 0.0448971i
\(666\) 1.25451e7 1.09595
\(667\) 2.17767e7i 1.89529i
\(668\) 3.84528e7i 3.33416i
\(669\) 9.75360e6 0.842558
\(670\) −4.82650e6 + 3.07009e7i −0.415380 + 2.64219i
\(671\) −2.16195e6 −0.185370
\(672\) 6.57376e6i 0.561553i
\(673\) 1.15029e7i 0.978969i −0.872012 0.489484i \(-0.837185\pi\)
0.872012 0.489484i \(-0.162815\pi\)
\(674\) −1.96060e7 −1.66242
\(675\) 699014. 2.16823e6i 0.0590509 0.183167i
\(676\) −3.10350e7 −2.61207
\(677\) 2.08105e7i 1.74506i −0.488560 0.872530i \(-0.662478\pi\)
0.488560 0.872530i \(-0.337522\pi\)
\(678\) 2.31785e7i 1.93647i
\(679\) −733014. −0.0610152
\(680\) 5.51341e6 3.50702e7i 0.457244 2.90848i
\(681\) −5.71643e6 −0.472343
\(682\) 565241.i 0.0465343i
\(683\) 2.29333e7i 1.88111i −0.339638 0.940556i \(-0.610305\pi\)
0.339638 0.940556i \(-0.389695\pi\)
\(684\) 9.65386e6 0.788971
\(685\) 50469.5 + 7934.33i 0.00410963 + 0.000646077i
\(686\) −1.41954e7 −1.15170
\(687\) 5.60546e6i 0.453126i
\(688\) 8.89066e6i 0.716082i
\(689\) −129214. −0.0103696
\(690\) 1.35420e7 + 2.12895e6i 1.08283 + 0.170232i
\(691\) −1.87802e7 −1.49626 −0.748128 0.663554i \(-0.769047\pi\)
−0.748128 + 0.663554i \(0.769047\pi\)
\(692\) 4.41306e7i 3.50327i
\(693\) 405578.i 0.0320805i
\(694\) −6.06634e6 −0.478110
\(695\) −2.34714e6 + 1.49299e7i −0.184322 + 1.17245i
\(696\) 4.29406e7 3.36004
\(697\) 1.41692e7i 1.10475i
\(698\) 2.93185e7i 2.27774i
\(699\) −1.18621e7 −0.918263
\(700\) −3.31830e6 + 1.02928e7i −0.255959 + 0.793945i
\(701\) −4.01030e6 −0.308235 −0.154118 0.988053i \(-0.549253\pi\)
−0.154118 + 0.988053i \(0.549253\pi\)
\(702\) 107013.i 0.00819588i
\(703\) 2.05268e7i 1.56651i
\(704\) −1.02132e7 −0.776659
\(705\) −132199. + 840907.i −0.0100174 + 0.0637199i
\(706\) 7.47310e6 0.564273
\(707\) 115387.i 0.00868176i
\(708\) 3.12129e7i 2.34019i
\(709\) 326851. 0.0244193 0.0122097 0.999925i \(-0.496113\pi\)
0.0122097 + 0.999925i \(0.496113\pi\)
\(710\) −9.88463e6 1.55397e6i −0.735892 0.115690i
\(711\) 5.79130e6 0.429638
\(712\) 4.27354e7i 3.15928i
\(713\) 1.10078e6i 0.0810919i
\(714\) −4.58115e6 −0.336301
\(715\) 91219.4 + 14340.7i 0.00667302 + 0.00104907i
\(716\) 6.60504e7 4.81496
\(717\) 2.16026e6i 0.156931i
\(718\) 3.29164e6i 0.238287i
\(719\) 1.34067e7 0.967161 0.483581 0.875300i \(-0.339336\pi\)
0.483581 + 0.875300i \(0.339336\pi\)
\(720\) −2.31611e6 + 1.47325e7i −0.166505 + 1.05912i
\(721\) 128559. 0.00921008
\(722\) 4.78536e6i 0.341643i
\(723\) 5.93124e6i 0.421988i
\(724\) 3.13964e7 2.22604
\(725\) 2.55614e7 + 8.24070e6i 1.80609 + 0.582263i
\(726\) 1.41692e6 0.0997709
\(727\) 2.14838e7i 1.50756i −0.657127 0.753780i \(-0.728229\pi\)
0.657127 0.753780i \(-0.271771\pi\)
\(728\) 313619.i 0.0219318i
\(729\) −531441. −0.0370370
\(730\) −4.64043e6 + 2.95173e7i −0.322293 + 2.05007i
\(731\) −3.08788e6 −0.213731
\(732\) 1.34479e7i 0.927637i
\(733\) 8.60145e6i 0.591305i −0.955296 0.295653i \(-0.904463\pi\)
0.955296 0.295653i \(-0.0955371\pi\)
\(734\) −1.62985e7 −1.11663
\(735\) −7.50218e6 1.17942e6i −0.512235 0.0805286i
\(736\) −4.47252e7 −3.04339
\(737\) 6.25577e6i 0.424240i
\(738\) 1.07886e7i 0.729165i
\(739\) 4.69199e6 0.316043 0.158022 0.987436i \(-0.449488\pi\)
0.158022 + 0.987436i \(0.449488\pi\)
\(740\) −6.65172e7 1.04572e7i −4.46534 0.701999i
\(741\) 175099. 0.0117149
\(742\) 4.21178e6i 0.280838i
\(743\) 1.84011e7i 1.22284i 0.791305 + 0.611422i \(0.209402\pi\)
−0.791305 + 0.611422i \(0.790598\pi\)
\(744\) −2.17059e6 −0.143763
\(745\) 4.63249e6 2.94668e7i 0.305790 1.94510i
\(746\) 1.13779e7 0.748539
\(747\) 2.71668e6i 0.178130i
\(748\) 1.15754e7i 0.756450i
\(749\) 893804. 0.0582154
\(750\) −7.62351e6 + 1.50899e7i −0.494882 + 0.979568i
\(751\) 4.90697e6 0.317478 0.158739 0.987321i \(-0.449257\pi\)
0.158739 + 0.987321i \(0.449257\pi\)
\(752\) 5.57251e6i 0.359341i
\(753\) 1.55444e7i 0.999049i
\(754\) 1.26158e6 0.0808143
\(755\) −948615. + 6.03404e6i −0.0605651 + 0.385249i
\(756\) 2.52281e6 0.160539
\(757\) 1.77340e7i 1.12478i 0.826872 + 0.562390i \(0.190118\pi\)
−0.826872 + 0.562390i \(0.809882\pi\)
\(758\) 8.73560e6i 0.552230i
\(759\) 2.75939e6 0.173864
\(760\) −4.36924e7 6.86891e6i −2.74392 0.431374i
\(761\) 7.16267e6 0.448346 0.224173 0.974549i \(-0.428032\pi\)
0.224173 + 0.974549i \(0.428032\pi\)
\(762\) 1.08600e7i 0.677554i
\(763\) 7.88859e6i 0.490556i
\(764\) −2.83626e7 −1.75797
\(765\) −5.11687e6 804425.i −0.316119 0.0496972i
\(766\) −1.31378e7 −0.809006
\(767\) 566131.i 0.0347479i
\(768\) 8.86628e6i 0.542423i
\(769\) 1.90012e7 1.15869 0.579343 0.815084i \(-0.303309\pi\)
0.579343 + 0.815084i \(0.303309\pi\)
\(770\) −467441. + 2.97334e6i −0.0284119 + 0.180725i
\(771\) −8.00265e6 −0.484840
\(772\) 3.00507e7i 1.81473i
\(773\) 6.66234e6i 0.401031i 0.979690 + 0.200516i \(0.0642618\pi\)
−0.979690 + 0.200516i \(0.935738\pi\)
\(774\) 2.35116e6 0.141068
\(775\) −1.29210e6 416557.i −0.0772753 0.0249127i
\(776\) 9.83395e6 0.586238
\(777\) 5.36419e6i 0.318751i
\(778\) 4.39597e7i 2.60379i
\(779\) 1.76528e7 1.04224
\(780\) −89203.0 + 567411.i −0.00524980 + 0.0333934i
\(781\) −2.01414e6 −0.118158
\(782\) 3.11683e7i 1.82262i
\(783\) 6.26518e6i 0.365198i
\(784\) 4.97153e7 2.88868
\(785\) −2.00328e7 3.14937e6i −1.16029 0.182410i
\(786\) 3.24012e7 1.87070
\(787\) 9.20508e6i 0.529774i −0.964279 0.264887i \(-0.914665\pi\)
0.964279 0.264887i \(-0.0853347\pi\)
\(788\) 5.05155e7i 2.89807i
\(789\) 3.17400e6 0.181516
\(790\) −4.24567e7 6.67465e6i −2.42035 0.380505i
\(791\) −9.91094e6 −0.563214
\(792\) 5.44114e6i 0.308232i
\(793\) 243915.i 0.0137739i
\(794\) −164053. −0.00923494
\(795\) 739566. 4.70430e6i 0.0415011 0.263984i
\(796\) −8.65098e7 −4.83930
\(797\) 2.71663e7i 1.51490i −0.652893 0.757450i \(-0.726445\pi\)
0.652893 0.757450i \(-0.273555\pi\)
\(798\) 5.70744e6i 0.317274i
\(799\) 1.93543e6 0.107253
\(800\) 1.69249e7 5.24984e7i 0.934977 2.90015i
\(801\) −6.23524e6 −0.343378
\(802\) 5.11213e7i 2.80650i
\(803\) 6.01460e6i 0.329168i
\(804\) −3.89127e7 −2.12300
\(805\) −910320. + 5.79046e6i −0.0495113 + 0.314937i
\(806\) −63771.6 −0.00345772
\(807\) 4.56062e6i 0.246513i
\(808\) 1.54800e6i 0.0834149i
\(809\) 2.31559e7 1.24392 0.621958 0.783051i \(-0.286338\pi\)
0.621958 + 0.783051i \(0.286338\pi\)
\(810\) 3.89606e6 + 612501.i 0.208647 + 0.0328016i
\(811\) 1.33212e6 0.0711200 0.0355600 0.999368i \(-0.488679\pi\)
0.0355600 + 0.999368i \(0.488679\pi\)
\(812\) 2.97415e7i 1.58297i
\(813\) 1.20176e7i 0.637661i
\(814\) −1.87402e7 −0.991320
\(815\) −1.87226e7 2.94339e6i −0.987352 0.155222i
\(816\) 3.39084e7 1.78271
\(817\) 3.84705e6i 0.201638i
\(818\) 6.58963e7i 3.44332i
\(819\) 45758.1 0.00238373
\(820\) −8.99307e6 + 5.72040e7i −0.467061 + 2.97093i
\(821\) 1.06084e7 0.549277 0.274638 0.961548i \(-0.411442\pi\)
0.274638 + 0.961548i \(0.411442\pi\)
\(822\) 88446.4i 0.00456563i
\(823\) 1.83916e7i 0.946496i −0.880929 0.473248i \(-0.843081\pi\)
0.880929 0.473248i \(-0.156919\pi\)
\(824\) −1.72471e6 −0.0884910
\(825\) −1.04421e6 + 3.23896e6i −0.0534135 + 0.165680i
\(826\) −1.84533e7 −0.941075
\(827\) 1.95386e7i 0.993414i 0.867918 + 0.496707i \(0.165458\pi\)
−0.867918 + 0.496707i \(0.834542\pi\)
\(828\) 1.71642e7i 0.870057i
\(829\) 3.37798e7 1.70714 0.853572 0.520974i \(-0.174431\pi\)
0.853572 + 0.520974i \(0.174431\pi\)
\(830\) −3.13106e6 + 1.99163e7i −0.157760 + 1.00349i
\(831\) −1.54979e7 −0.778520
\(832\) 1.15227e6i 0.0577095i
\(833\) 1.72670e7i 0.862193i
\(834\) −2.61643e7 −1.30255
\(835\) 2.53921e7 + 3.99190e6i 1.26032 + 0.198136i
\(836\) −1.44212e7 −0.713651
\(837\) 316697.i 0.0156254i
\(838\) 3.89062e7i 1.91385i
\(839\) −2.77050e7 −1.35879 −0.679396 0.733772i \(-0.737758\pi\)
−0.679396 + 0.733772i \(0.737758\pi\)
\(840\) −1.14180e7 1.79503e6i −0.558331 0.0877754i
\(841\) 5.33493e7 2.60099
\(842\) 1.60788e7i 0.781578i
\(843\) 1.08531e7i 0.526001i
\(844\) 6.34213e7 3.06463
\(845\) 3.22184e6 2.04938e7i 0.155225 0.987371i
\(846\) −1.47367e6 −0.0707902
\(847\) 605864.i 0.0290179i
\(848\) 3.11744e7i 1.48870i
\(849\) −8.28165e6 −0.394319
\(850\) 3.65852e7 + 1.17947e7i 1.73684 + 0.559936i
\(851\) −3.64958e7 −1.72750
\(852\) 1.25285e7i 0.591291i
\(853\) 1.04555e7i 0.492007i 0.969269 + 0.246003i \(0.0791174\pi\)
−0.969269 + 0.246003i \(0.920883\pi\)
\(854\) 7.95053e6 0.373037
\(855\) −1.00220e6 + 6.37487e6i −0.0468854 + 0.298233i
\(856\) −1.19911e7 −0.559337
\(857\) 2.53866e7i 1.18074i 0.807134 + 0.590369i \(0.201018\pi\)
−0.807134 + 0.590369i \(0.798982\pi\)
\(858\) 159860.i 0.00741345i
\(859\) −1.84775e6 −0.0854396 −0.0427198 0.999087i \(-0.513602\pi\)
−0.0427198 + 0.999087i \(0.513602\pi\)
\(860\) −1.24664e7 1.95985e6i −0.574772 0.0903602i
\(861\) 4.61314e6 0.212075
\(862\) 5.79138e6i 0.265469i
\(863\) 2.89194e7i 1.32179i −0.750479 0.660894i \(-0.770177\pi\)
0.750479 0.660894i \(-0.229823\pi\)
\(864\) −1.28675e7 −0.586422
\(865\) 2.91413e7 + 4.58133e6i 1.32425 + 0.208186i
\(866\) −5.92034e7 −2.68257
\(867\) 1.00174e6i 0.0452591i
\(868\) 1.50340e6i 0.0677289i
\(869\) −8.65121e6 −0.388622
\(870\) −7.22080e6 + 4.59308e7i −0.323435 + 2.05734i
\(871\) −705788. −0.0315231
\(872\) 1.05832e8i 4.71329i
\(873\) 1.43481e6i 0.0637174i
\(874\) −3.88312e7 −1.71950
\(875\) −6.45234e6 3.25975e6i −0.284903 0.143934i
\(876\) −3.74125e7 −1.64724
\(877\) 2.63977e7i 1.15896i 0.814988 + 0.579478i \(0.196743\pi\)
−0.814988 + 0.579478i \(0.803257\pi\)
\(878\) 4.89457e7i 2.14278i
\(879\) 1.12903e6 0.0492869
\(880\) 3.45986e6 2.20078e7i 0.150610 0.958012i
\(881\) 1.08347e7 0.470304 0.235152 0.971959i \(-0.424441\pi\)
0.235152 + 0.971959i \(0.424441\pi\)
\(882\) 1.31474e7i 0.569072i
\(883\) 2.45316e7i 1.05883i −0.848364 0.529413i \(-0.822412\pi\)
0.848364 0.529413i \(-0.177588\pi\)
\(884\) 1.30595e6 0.0562078
\(885\) −2.06112e7 3.24030e6i −0.884598 0.139068i
\(886\) −2.07319e7 −0.887268
\(887\) 2.84619e7i 1.21466i 0.794450 + 0.607330i \(0.207759\pi\)
−0.794450 + 0.607330i \(0.792241\pi\)
\(888\) 7.19647e7i 3.06258i
\(889\) 4.64367e6 0.197064
\(890\) 4.57113e7 + 7.18630e6i 1.93441 + 0.304110i
\(891\) 793881. 0.0335013
\(892\) 9.06308e7i 3.81385i
\(893\) 2.41127e6i 0.101185i
\(894\) 5.16398e7 2.16093
\(895\) −6.85689e6 + 4.36160e7i −0.286134 + 1.82007i
\(896\) 1.41855e7 0.590304
\(897\) 311320.i 0.0129189i
\(898\) 2.42765e7i 1.00460i
\(899\) −3.73355e6 −0.154072
\(900\) −2.01473e7 6.49526e6i −0.829106 0.267295i
\(901\) −1.08274e7 −0.444338
\(902\) 1.61164e7i 0.659555i
\(903\) 1.00534e6i 0.0410291i
\(904\) 1.32963e8 5.41139
\(905\) −3.25936e6 + 2.07324e7i −0.132285 + 0.841452i
\(906\) −1.05745e7 −0.427995
\(907\) 1.85629e7i 0.749253i 0.927176 + 0.374626i \(0.122229\pi\)
−0.927176 + 0.374626i \(0.877771\pi\)
\(908\) 5.31173e7i 2.13807i
\(909\) 225859. 0.00906625
\(910\) −335458. 52737.5i −0.0134287 0.00211114i
\(911\) 3.93363e7 1.57035 0.785177 0.619271i \(-0.212572\pi\)
0.785177 + 0.619271i \(0.212572\pi\)
\(912\) 4.22449e7i 1.68185i
\(913\) 4.05825e6i 0.161125i
\(914\) 1.50935e7 0.597617
\(915\) 8.88027e6 + 1.39607e6i 0.350650 + 0.0551258i
\(916\) 5.20861e7 2.05108
\(917\) 1.38545e7i 0.544086i
\(918\) 8.96717e6i 0.351195i
\(919\) −2.72458e7 −1.06417 −0.532084 0.846691i \(-0.678591\pi\)
−0.532084 + 0.846691i \(0.678591\pi\)
\(920\) 1.22126e7 7.76834e7i 0.475708 3.02593i
\(921\) 8.30410e6 0.322584
\(922\) 1.37887e7i 0.534190i
\(923\) 227239.i 0.00877969i
\(924\) −3.76864e6 −0.145213
\(925\) 1.38107e7 4.28387e7i 0.530715 1.64620i
\(926\) −5.55646e7 −2.12947
\(927\) 251642.i 0.00961796i
\(928\) 1.51696e8i 5.78233i
\(929\) 2.98863e7 1.13614 0.568071 0.822980i \(-0.307690\pi\)
0.568071 + 0.822980i \(0.307690\pi\)
\(930\) 365003. 2.32174e6i 0.0138385 0.0880252i
\(931\) 2.15122e7 0.813411
\(932\) 1.10223e8i 4.15653i
\(933\) 1.44122e7i 0.542035i
\(934\) −1.99500e7 −0.748298
\(935\) 7.64371e6 + 1.20167e6i 0.285940 + 0.0449528i
\(936\) −613880. −0.0229031
\(937\) 3.91979e7i 1.45852i −0.684234 0.729262i \(-0.739863\pi\)
0.684234 0.729262i \(-0.260137\pi\)
\(938\) 2.30055e7i 0.853737i
\(939\) −1.59414e6 −0.0590014
\(940\) 7.81373e6 + 1.22840e6i 0.288429 + 0.0453441i
\(941\) 2.33041e7 0.857941 0.428971 0.903318i \(-0.358876\pi\)
0.428971 + 0.903318i \(0.358876\pi\)
\(942\) 3.51069e7i 1.28904i
\(943\) 3.13859e7i 1.14936i
\(944\) 1.36586e8 4.98858
\(945\) −261901. + 1.66592e6i −0.00954019 + 0.0606842i
\(946\) −3.51223e6 −0.127601
\(947\) 2.41038e7i 0.873394i 0.899609 + 0.436697i \(0.143852\pi\)
−0.899609 + 0.436697i \(0.856148\pi\)
\(948\) 5.38130e7i 1.94476i
\(949\) −678578. −0.0244587
\(950\) 1.46945e7 4.55799e7i 0.528256 1.63857i
\(951\) 5.20428e6 0.186599
\(952\) 2.62796e7i 0.939782i
\(953\) 3.46893e7i 1.23727i −0.785680 0.618633i \(-0.787687\pi\)
0.785680 0.618633i \(-0.212313\pi\)
\(954\) 8.24416e6 0.293275
\(955\) 2.94441e6 1.87291e7i 0.104469 0.664520i
\(956\) −2.00732e7 −0.710349
\(957\) 9.35909e6i 0.330334i
\(958\) 2.98601e7i 1.05118i
\(959\) −37819.0 −0.00132789
\(960\) 4.19511e7 + 6.59515e6i 1.46915 + 0.230965i
\(961\) −2.84404e7 −0.993408
\(962\) 2.11431e6i 0.0736598i
\(963\) 1.74954e6i 0.0607936i
\(964\) −5.51133e7 −1.91013
\(965\) −1.98438e7 3.11965e6i −0.685973 0.107842i
\(966\) −1.01476e7 −0.349882
\(967\) 3.99380e7i 1.37347i 0.726906 + 0.686737i \(0.240958\pi\)
−0.726906 + 0.686737i \(0.759042\pi\)
\(968\) 8.12813e6i 0.278806i
\(969\) 1.46724e7 0.501986
\(970\) −1.65366e6 + 1.05187e7i −0.0564308 + 0.358951i
\(971\) −3.25227e6 −0.110698 −0.0553488 0.998467i \(-0.517627\pi\)
−0.0553488 + 0.998467i \(0.517627\pi\)
\(972\) 4.93817e6i 0.167649i
\(973\) 1.11876e7i 0.378841i
\(974\) −9.19839e7 −3.10681
\(975\) −365426. 117809.i −0.0123108 0.00396888i
\(976\) −5.88476e7 −1.97744
\(977\) 2.38653e7i 0.799892i 0.916539 + 0.399946i \(0.130971\pi\)
−0.916539 + 0.399946i \(0.869029\pi\)
\(978\) 3.28108e7i 1.09691i
\(979\) 9.31437e6 0.310597
\(980\) −1.09592e7 + 6.97104e7i −0.364514 + 2.31864i
\(981\) 1.54412e7 0.512281
\(982\) 1.00473e8i 3.32485i
\(983\) 2.22870e7i 0.735645i 0.929896 + 0.367823i \(0.119897\pi\)
−0.929896 + 0.367823i \(0.880103\pi\)
\(984\) −6.18888e7 −2.03763
\(985\) −3.33576e7 5.24417e6i −1.09548 0.172221i
\(986\) 1.05714e8 3.46291
\(987\) 630128.i 0.0205890i
\(988\) 1.62703e6i 0.0530277i
\(989\) −6.83991e6 −0.222362
\(990\) −5.82004e6 914971.i −0.188729 0.0296701i
\(991\) −1.74834e7 −0.565513 −0.282756 0.959192i \(-0.591249\pi\)
−0.282756 + 0.959192i \(0.591249\pi\)
\(992\) 7.66803e6i 0.247403i
\(993\) 2.91391e7i 0.937784i
\(994\) 7.40697e6 0.237780
\(995\) 8.98084e6 5.71262e7i 0.287580 1.82927i
\(996\) −2.52435e7 −0.806308
\(997\) 4.50302e7i 1.43472i 0.696705 + 0.717358i \(0.254649\pi\)
−0.696705 + 0.717358i \(0.745351\pi\)
\(998\) 1.11437e8i 3.54162i
\(999\) −1.04999e7 −0.332868
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 165.6.c.b.34.26 yes 26
5.2 odd 4 825.6.a.v.1.1 13
5.3 odd 4 825.6.a.y.1.13 13
5.4 even 2 inner 165.6.c.b.34.1 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.6.c.b.34.1 26 5.4 even 2 inner
165.6.c.b.34.26 yes 26 1.1 even 1 trivial
825.6.a.v.1.1 13 5.2 odd 4
825.6.a.y.1.13 13 5.3 odd 4