Properties

Label 230.6.b.a.139.17
Level $230$
Weight $6$
Character 230.139
Analytic conductor $36.888$
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] = [230,6,Mod(139,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("230.139");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 230.b (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: \(36.8882785570\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 139.17
Character \(\chi\) \(=\) 230.139
Dual form 230.6.b.a.139.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000i q^{2} -14.1507i q^{3} -16.0000 q^{4} +(55.0409 - 9.77250i) q^{5} +56.6028 q^{6} -1.53351i q^{7} -64.0000i q^{8} +42.7574 q^{9} +O(q^{10})\) \(q+4.00000i q^{2} -14.1507i q^{3} -16.0000 q^{4} +(55.0409 - 9.77250i) q^{5} +56.6028 q^{6} -1.53351i q^{7} -64.0000i q^{8} +42.7574 q^{9} +(39.0900 + 220.164i) q^{10} +219.251 q^{11} +226.411i q^{12} +629.810i q^{13} +6.13404 q^{14} +(-138.288 - 778.868i) q^{15} +256.000 q^{16} +655.144i q^{17} +171.030i q^{18} +390.169 q^{19} +(-880.654 + 156.360i) q^{20} -21.7003 q^{21} +877.003i q^{22} +529.000i q^{23} -905.645 q^{24} +(2934.00 - 1075.77i) q^{25} -2519.24 q^{26} -4043.67i q^{27} +24.5362i q^{28} +4018.71 q^{29} +(3115.47 - 553.151i) q^{30} -7093.23 q^{31} +1024.00i q^{32} -3102.56i q^{33} -2620.57 q^{34} +(-14.9862 - 84.4058i) q^{35} -684.118 q^{36} +2921.35i q^{37} +1560.68i q^{38} +8912.26 q^{39} +(-625.440 - 3522.62i) q^{40} +13254.6 q^{41} -86.8011i q^{42} +11785.5i q^{43} -3508.01 q^{44} +(2353.40 - 417.846i) q^{45} -2116.00 q^{46} -17941.7i q^{47} -3622.58i q^{48} +16804.6 q^{49} +(4303.10 + 11736.0i) q^{50} +9270.75 q^{51} -10077.0i q^{52} -32881.8i q^{53} +16174.7 q^{54} +(12067.8 - 2142.63i) q^{55} -98.1447 q^{56} -5521.17i q^{57} +16074.8i q^{58} +28442.8 q^{59} +(2212.60 + 12461.9i) q^{60} +46727.3 q^{61} -28372.9i q^{62} -65.5689i q^{63} -4096.00 q^{64} +(6154.82 + 34665.3i) q^{65} +12410.2 q^{66} +11017.7i q^{67} -10482.3i q^{68} +7485.73 q^{69} +(337.623 - 59.9449i) q^{70} -39807.8 q^{71} -2736.47i q^{72} +53911.2i q^{73} -11685.4 q^{74} +(-15223.0 - 41518.1i) q^{75} -6242.71 q^{76} -336.224i q^{77} +35649.1i q^{78} +102235. q^{79} +(14090.5 - 2501.76i) q^{80} -46830.8 q^{81} +53018.5i q^{82} +29815.3i q^{83} +347.204 q^{84} +(6402.39 + 36059.7i) q^{85} -47141.9 q^{86} -56867.6i q^{87} -14032.1i q^{88} -72771.4 q^{89} +(1671.39 + 9413.62i) q^{90} +965.821 q^{91} -8464.00i q^{92} +100374. i q^{93} +71766.6 q^{94} +(21475.3 - 3812.93i) q^{95} +14490.3 q^{96} -55084.5i q^{97} +67218.6i q^{98} +9374.59 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26} + 16084 q^{29} - 6200 q^{30} + 418 q^{31} + 3320 q^{34} - 3160 q^{35} + 22400 q^{36} + 71296 q^{39} - 1280 q^{40} - 35826 q^{41} + 21024 q^{44} - 83960 q^{45} - 55016 q^{46} + 53532 q^{49} - 20800 q^{50} - 25430 q^{51} + 98736 q^{54} - 110390 q^{55} - 12928 q^{56} + 126992 q^{59} - 20480 q^{60} - 63662 q^{61} - 106496 q^{64} - 88520 q^{65} - 18664 q^{66} - 9522 q^{69} - 116520 q^{70} - 106514 q^{71} + 183536 q^{74} - 44200 q^{75} - 106080 q^{76} + 324676 q^{79} - 7680 q^{80} - 170702 q^{81} + 160960 q^{84} + 120780 q^{85} - 42768 q^{86} + 465200 q^{89} + 61360 q^{90} - 468838 q^{91} + 107152 q^{94} + 309670 q^{95} - 18432 q^{96} + 523850 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000i 0.707107i
\(3\) 14.1507i 0.907769i −0.891061 0.453884i \(-0.850038\pi\)
0.891061 0.453884i \(-0.149962\pi\)
\(4\) −16.0000 −0.500000
\(5\) 55.0409 9.77250i 0.984601 0.174816i
\(6\) 56.6028 0.641889
\(7\) 1.53351i 0.0118288i −0.999983 0.00591441i \(-0.998117\pi\)
0.999983 0.00591441i \(-0.00188263\pi\)
\(8\) 64.0000i 0.353553i
\(9\) 42.7574 0.175956
\(10\) 39.0900 + 220.164i 0.123613 + 0.696218i
\(11\) 219.251 0.546336 0.273168 0.961966i \(-0.411929\pi\)
0.273168 + 0.961966i \(0.411929\pi\)
\(12\) 226.411i 0.453884i
\(13\) 629.810i 1.03360i 0.856107 + 0.516799i \(0.172876\pi\)
−0.856107 + 0.516799i \(0.827124\pi\)
\(14\) 6.13404 0.00836425
\(15\) −138.288 778.868i −0.158692 0.893790i
\(16\) 256.000 0.250000
\(17\) 655.144i 0.549812i 0.961471 + 0.274906i \(0.0886467\pi\)
−0.961471 + 0.274906i \(0.911353\pi\)
\(18\) 171.030i 0.124420i
\(19\) 390.169 0.247953 0.123976 0.992285i \(-0.460435\pi\)
0.123976 + 0.992285i \(0.460435\pi\)
\(20\) −880.654 + 156.360i −0.492301 + 0.0874079i
\(21\) −21.7003 −0.0107378
\(22\) 877.003i 0.386318i
\(23\) 529.000i 0.208514i
\(24\) −905.645 −0.320945
\(25\) 2934.00 1075.77i 0.938879 0.344248i
\(26\) −2519.24 −0.730864
\(27\) 4043.67i 1.06750i
\(28\) 24.5362i 0.00591441i
\(29\) 4018.71 0.887344 0.443672 0.896189i \(-0.353676\pi\)
0.443672 + 0.896189i \(0.353676\pi\)
\(30\) 3115.47 553.151i 0.632005 0.112212i
\(31\) −7093.23 −1.32568 −0.662842 0.748760i \(-0.730650\pi\)
−0.662842 + 0.748760i \(0.730650\pi\)
\(32\) 1024.00i 0.176777i
\(33\) 3102.56i 0.495946i
\(34\) −2620.57 −0.388776
\(35\) −14.9862 84.4058i −0.00206787 0.0116467i
\(36\) −684.118 −0.0879782
\(37\) 2921.35i 0.350815i 0.984496 + 0.175408i \(0.0561243\pi\)
−0.984496 + 0.175408i \(0.943876\pi\)
\(38\) 1560.68i 0.175329i
\(39\) 8912.26 0.938267
\(40\) −625.440 3522.62i −0.0618067 0.348109i
\(41\) 13254.6 1.23142 0.615712 0.787971i \(-0.288868\pi\)
0.615712 + 0.787971i \(0.288868\pi\)
\(42\) 86.8011i 0.00759280i
\(43\) 11785.5i 0.972022i 0.873953 + 0.486011i \(0.161548\pi\)
−0.873953 + 0.486011i \(0.838452\pi\)
\(44\) −3508.01 −0.273168
\(45\) 2353.40 417.846i 0.173247 0.0307599i
\(46\) −2116.00 −0.147442
\(47\) 17941.7i 1.18473i −0.805671 0.592363i \(-0.798195\pi\)
0.805671 0.592363i \(-0.201805\pi\)
\(48\) 3622.58i 0.226942i
\(49\) 16804.6 0.999860
\(50\) 4303.10 + 11736.0i 0.243420 + 0.663888i
\(51\) 9270.75 0.499102
\(52\) 10077.0i 0.516799i
\(53\) 32881.8i 1.60793i −0.594680 0.803963i \(-0.702721\pi\)
0.594680 0.803963i \(-0.297279\pi\)
\(54\) 16174.7 0.754834
\(55\) 12067.8 2142.63i 0.537923 0.0955081i
\(56\) −98.1447 −0.00418212
\(57\) 5521.17i 0.225084i
\(58\) 16074.8i 0.627447i
\(59\) 28442.8 1.06376 0.531878 0.846821i \(-0.321486\pi\)
0.531878 + 0.846821i \(0.321486\pi\)
\(60\) 2212.60 + 12461.9i 0.0793461 + 0.446895i
\(61\) 46727.3 1.60785 0.803927 0.594729i \(-0.202740\pi\)
0.803927 + 0.594729i \(0.202740\pi\)
\(62\) 28372.9i 0.937400i
\(63\) 65.5689i 0.00208136i
\(64\) −4096.00 −0.125000
\(65\) 6154.82 + 34665.3i 0.180689 + 1.01768i
\(66\) 12410.2 0.350687
\(67\) 11017.7i 0.299851i 0.988697 + 0.149926i \(0.0479034\pi\)
−0.988697 + 0.149926i \(0.952097\pi\)
\(68\) 10482.3i 0.274906i
\(69\) 7485.73 0.189283
\(70\) 337.623 59.9449i 0.00823545 0.00146220i
\(71\) −39807.8 −0.937178 −0.468589 0.883416i \(-0.655238\pi\)
−0.468589 + 0.883416i \(0.655238\pi\)
\(72\) 2736.47i 0.0622099i
\(73\) 53911.2i 1.18406i 0.805917 + 0.592028i \(0.201673\pi\)
−0.805917 + 0.592028i \(0.798327\pi\)
\(74\) −11685.4 −0.248064
\(75\) −15223.0 41518.1i −0.312497 0.852285i
\(76\) −6242.71 −0.123976
\(77\) 336.224i 0.00646251i
\(78\) 35649.1i 0.663455i
\(79\) 102235. 1.84304 0.921518 0.388336i \(-0.126950\pi\)
0.921518 + 0.388336i \(0.126950\pi\)
\(80\) 14090.5 2501.76i 0.246150 0.0437039i
\(81\) −46830.8 −0.793083
\(82\) 53018.5i 0.870749i
\(83\) 29815.3i 0.475055i 0.971381 + 0.237528i \(0.0763371\pi\)
−0.971381 + 0.237528i \(0.923663\pi\)
\(84\) 347.204 0.00536892
\(85\) 6402.39 + 36059.7i 0.0961158 + 0.541346i
\(86\) −47141.9 −0.687323
\(87\) 56867.6i 0.805503i
\(88\) 14032.1i 0.193159i
\(89\) −72771.4 −0.973835 −0.486918 0.873448i \(-0.661879\pi\)
−0.486918 + 0.873448i \(0.661879\pi\)
\(90\) 1671.39 + 9413.62i 0.0217506 + 0.122504i
\(91\) 965.821 0.0122262
\(92\) 8464.00i 0.104257i
\(93\) 100374.i 1.20341i
\(94\) 71766.6 0.837727
\(95\) 21475.3 3812.93i 0.244135 0.0433461i
\(96\) 14490.3 0.160472
\(97\) 55084.5i 0.594429i −0.954811 0.297215i \(-0.903942\pi\)
0.954811 0.297215i \(-0.0960577\pi\)
\(98\) 67218.6i 0.707008i
\(99\) 9374.59 0.0961312
\(100\) −46943.9 + 17212.4i −0.469439 + 0.172124i
\(101\) 82683.6 0.806522 0.403261 0.915085i \(-0.367877\pi\)
0.403261 + 0.915085i \(0.367877\pi\)
\(102\) 37083.0i 0.352918i
\(103\) 5305.74i 0.0492779i 0.999696 + 0.0246390i \(0.00784362\pi\)
−0.999696 + 0.0246390i \(0.992156\pi\)
\(104\) 40307.9 0.365432
\(105\) −1194.40 + 212.066i −0.0105725 + 0.00187714i
\(106\) 131527. 1.13697
\(107\) 4491.44i 0.0379251i −0.999820 0.0189625i \(-0.993964\pi\)
0.999820 0.0189625i \(-0.00603633\pi\)
\(108\) 64698.7i 0.533748i
\(109\) −38228.6 −0.308193 −0.154096 0.988056i \(-0.549247\pi\)
−0.154096 + 0.988056i \(0.549247\pi\)
\(110\) 8570.51 + 48271.0i 0.0675344 + 0.380369i
\(111\) 41339.1 0.318459
\(112\) 392.579i 0.00295721i
\(113\) 24756.8i 0.182389i −0.995833 0.0911944i \(-0.970932\pi\)
0.995833 0.0911944i \(-0.0290685\pi\)
\(114\) 22084.7 0.159158
\(115\) 5169.65 + 29116.6i 0.0364516 + 0.205304i
\(116\) −64299.4 −0.443672
\(117\) 26929.0i 0.181868i
\(118\) 113771.i 0.752190i
\(119\) 1004.67 0.00650363
\(120\) −49847.5 + 8850.42i −0.316002 + 0.0561062i
\(121\) −112980. −0.701517
\(122\) 186909.i 1.13692i
\(123\) 187562.i 1.11785i
\(124\) 113492. 0.662842
\(125\) 150977. 87884.0i 0.864241 0.503077i
\(126\) 262.276 0.00147174
\(127\) 240110.i 1.32099i −0.750829 0.660497i \(-0.770346\pi\)
0.750829 0.660497i \(-0.229654\pi\)
\(128\) 16384.0i 0.0883883i
\(129\) 166773. 0.882371
\(130\) −138661. + 24619.3i −0.719609 + 0.127766i
\(131\) −3138.28 −0.0159777 −0.00798884 0.999968i \(-0.502543\pi\)
−0.00798884 + 0.999968i \(0.502543\pi\)
\(132\) 49640.9i 0.247973i
\(133\) 598.329i 0.00293299i
\(134\) −44071.0 −0.212027
\(135\) −39516.8 222567.i −0.186615 1.05106i
\(136\) 41929.2 0.194388
\(137\) 182339.i 0.829999i −0.909822 0.414999i \(-0.863782\pi\)
0.909822 0.414999i \(-0.136218\pi\)
\(138\) 29942.9i 0.133843i
\(139\) −100800. −0.442509 −0.221255 0.975216i \(-0.571015\pi\)
−0.221255 + 0.975216i \(0.571015\pi\)
\(140\) 239.780 + 1350.49i 0.00103393 + 0.00582334i
\(141\) −253887. −1.07546
\(142\) 159231.i 0.662685i
\(143\) 138086.i 0.564691i
\(144\) 10945.9 0.0439891
\(145\) 221193. 39272.9i 0.873680 0.155122i
\(146\) −215645. −0.837254
\(147\) 237798.i 0.907642i
\(148\) 46741.5i 0.175408i
\(149\) −137943. −0.509018 −0.254509 0.967070i \(-0.581914\pi\)
−0.254509 + 0.967070i \(0.581914\pi\)
\(150\) 166073. 60891.9i 0.602656 0.220969i
\(151\) −15161.0 −0.0541108 −0.0270554 0.999634i \(-0.508613\pi\)
−0.0270554 + 0.999634i \(0.508613\pi\)
\(152\) 24970.8i 0.0876646i
\(153\) 28012.2i 0.0967429i
\(154\) 1344.89 0.00456969
\(155\) −390418. + 69318.6i −1.30527 + 0.231750i
\(156\) −142596. −0.469134
\(157\) 146002.i 0.472726i −0.971665 0.236363i \(-0.924045\pi\)
0.971665 0.236363i \(-0.0759554\pi\)
\(158\) 408942.i 1.30322i
\(159\) −465301. −1.45962
\(160\) 10007.0 + 56361.9i 0.0309034 + 0.174055i
\(161\) 811.227 0.00246648
\(162\) 187323.i 0.560794i
\(163\) 73666.6i 0.217171i −0.994087 0.108585i \(-0.965368\pi\)
0.994087 0.108585i \(-0.0346321\pi\)
\(164\) −212074. −0.615712
\(165\) −30319.7 170767.i −0.0866992 0.488309i
\(166\) −119261. −0.335915
\(167\) 599597.i 1.66367i −0.555020 0.831837i \(-0.687289\pi\)
0.555020 0.831837i \(-0.312711\pi\)
\(168\) 1388.82i 0.00379640i
\(169\) −25367.9 −0.0683232
\(170\) −144239. + 25609.6i −0.382789 + 0.0679641i
\(171\) 16682.6 0.0436289
\(172\) 188568.i 0.486011i
\(173\) 92162.8i 0.234121i 0.993125 + 0.117061i \(0.0373472\pi\)
−0.993125 + 0.117061i \(0.962653\pi\)
\(174\) 227471. 0.569576
\(175\) −1649.71 4499.32i −0.00407205 0.0111058i
\(176\) 56128.2 0.136584
\(177\) 402486.i 0.965645i
\(178\) 291085.i 0.688605i
\(179\) −307154. −0.716512 −0.358256 0.933623i \(-0.616629\pi\)
−0.358256 + 0.933623i \(0.616629\pi\)
\(180\) −37654.5 + 6685.54i −0.0866234 + 0.0153800i
\(181\) 150578. 0.341637 0.170818 0.985303i \(-0.445359\pi\)
0.170818 + 0.985303i \(0.445359\pi\)
\(182\) 3863.28i 0.00864526i
\(183\) 661225.i 1.45956i
\(184\) 33856.0 0.0737210
\(185\) 28548.8 + 160793.i 0.0613281 + 0.345413i
\(186\) −401497. −0.850942
\(187\) 143641.i 0.300382i
\(188\) 287066.i 0.592363i
\(189\) −6201.01 −0.0126272
\(190\) 15251.7 + 85901.1i 0.0306503 + 0.172629i
\(191\) −580954. −1.15228 −0.576140 0.817351i \(-0.695442\pi\)
−0.576140 + 0.817351i \(0.695442\pi\)
\(192\) 57961.3i 0.113471i
\(193\) 882560.i 1.70550i 0.522322 + 0.852748i \(0.325066\pi\)
−0.522322 + 0.852748i \(0.674934\pi\)
\(194\) 220338. 0.420325
\(195\) 490539. 87095.1i 0.923819 0.164024i
\(196\) −268874. −0.499930
\(197\) 640956.i 1.17669i 0.808609 + 0.588346i \(0.200221\pi\)
−0.808609 + 0.588346i \(0.799779\pi\)
\(198\) 37498.4i 0.0679750i
\(199\) −968212. −1.73316 −0.866578 0.499041i \(-0.833686\pi\)
−0.866578 + 0.499041i \(0.833686\pi\)
\(200\) −68849.5 187776.i −0.121710 0.331944i
\(201\) 155909. 0.272195
\(202\) 330734.i 0.570297i
\(203\) 6162.74i 0.0104962i
\(204\) −148332. −0.249551
\(205\) 729546. 129531.i 1.21246 0.215272i
\(206\) −21222.9 −0.0348448
\(207\) 22618.7i 0.0366894i
\(208\) 161231.i 0.258399i
\(209\) 85545.0 0.135466
\(210\) −848.263 4777.61i −0.00132734 0.00747588i
\(211\) 256429. 0.396516 0.198258 0.980150i \(-0.436472\pi\)
0.198258 + 0.980150i \(0.436472\pi\)
\(212\) 526109.i 0.803963i
\(213\) 563309.i 0.850741i
\(214\) 17965.8 0.0268171
\(215\) 115174. + 648683.i 0.169925 + 0.957054i
\(216\) −258795. −0.377417
\(217\) 10877.5i 0.0156813i
\(218\) 152915.i 0.217925i
\(219\) 762882. 1.07485
\(220\) −193084. + 34282.1i −0.268961 + 0.0477540i
\(221\) −412616. −0.568284
\(222\) 165356.i 0.225185i
\(223\) 1.36647e6i 1.84008i 0.391819 + 0.920042i \(0.371846\pi\)
−0.391819 + 0.920042i \(0.628154\pi\)
\(224\) 1570.32 0.00209106
\(225\) 125450. 45997.3i 0.165202 0.0605725i
\(226\) 99027.1 0.128968
\(227\) 1.30150e6i 1.67640i 0.545361 + 0.838201i \(0.316392\pi\)
−0.545361 + 0.838201i \(0.683608\pi\)
\(228\) 88338.8i 0.112542i
\(229\) 452685. 0.570436 0.285218 0.958463i \(-0.407934\pi\)
0.285218 + 0.958463i \(0.407934\pi\)
\(230\) −116466. + 20678.6i −0.145172 + 0.0257752i
\(231\) −4757.80 −0.00586646
\(232\) 257198.i 0.313723i
\(233\) 979540.i 1.18204i −0.806657 0.591020i \(-0.798725\pi\)
0.806657 0.591020i \(-0.201275\pi\)
\(234\) −107716. −0.128600
\(235\) −175335. 987524.i −0.207109 1.16648i
\(236\) −455085. −0.531878
\(237\) 1.44670e6i 1.67305i
\(238\) 4018.68i 0.00459876i
\(239\) 692403. 0.784087 0.392043 0.919947i \(-0.371768\pi\)
0.392043 + 0.919947i \(0.371768\pi\)
\(240\) −35401.7 199390.i −0.0396731 0.223447i
\(241\) −1.68954e6 −1.87382 −0.936908 0.349575i \(-0.886326\pi\)
−0.936908 + 0.349575i \(0.886326\pi\)
\(242\) 451920.i 0.496048i
\(243\) 319923.i 0.347560i
\(244\) −747637. −0.803927
\(245\) 924943. 164223.i 0.984463 0.174791i
\(246\) 750250. 0.790438
\(247\) 245733.i 0.256283i
\(248\) 453967.i 0.468700i
\(249\) 421908. 0.431240
\(250\) 351536. + 603907.i 0.355729 + 0.611111i
\(251\) −554814. −0.555857 −0.277928 0.960602i \(-0.589648\pi\)
−0.277928 + 0.960602i \(0.589648\pi\)
\(252\) 1049.10i 0.00104068i
\(253\) 115984.i 0.113919i
\(254\) 960439. 0.934083
\(255\) 510270. 90598.4i 0.491416 0.0872509i
\(256\) 65536.0 0.0625000
\(257\) 1.94048e6i 1.83263i 0.400453 + 0.916317i \(0.368853\pi\)
−0.400453 + 0.916317i \(0.631147\pi\)
\(258\) 667092.i 0.623930i
\(259\) 4479.91 0.00414973
\(260\) −98477.1 554645.i −0.0903445 0.508841i
\(261\) 171830. 0.156134
\(262\) 12553.1i 0.0112979i
\(263\) 1.03518e6i 0.922844i −0.887181 0.461422i \(-0.847339\pi\)
0.887181 0.461422i \(-0.152661\pi\)
\(264\) −198564. −0.175344
\(265\) −321337. 1.80984e6i −0.281091 1.58317i
\(266\) 2393.32 0.00207394
\(267\) 1.02977e6i 0.884017i
\(268\) 176284.i 0.149926i
\(269\) −577562. −0.486652 −0.243326 0.969945i \(-0.578238\pi\)
−0.243326 + 0.969945i \(0.578238\pi\)
\(270\) 890269. 158067.i 0.743210 0.131957i
\(271\) −1.10989e6 −0.918033 −0.459017 0.888428i \(-0.651798\pi\)
−0.459017 + 0.888428i \(0.651798\pi\)
\(272\) 167717.i 0.137453i
\(273\) 13667.1i 0.0110986i
\(274\) 729355. 0.586898
\(275\) 643281. 235864.i 0.512943 0.188075i
\(276\) −119772. −0.0946414
\(277\) 1.78721e6i 1.39951i 0.714381 + 0.699757i \(0.246708\pi\)
−0.714381 + 0.699757i \(0.753292\pi\)
\(278\) 403199.i 0.312901i
\(279\) −303288. −0.233262
\(280\) −5401.97 + 959.119i −0.00411772 + 0.000731101i
\(281\) 14269.1 0.0107803 0.00539016 0.999985i \(-0.498284\pi\)
0.00539016 + 0.999985i \(0.498284\pi\)
\(282\) 1.01555e6i 0.760463i
\(283\) 593348.i 0.440396i −0.975455 0.220198i \(-0.929330\pi\)
0.975455 0.220198i \(-0.0706703\pi\)
\(284\) 636925. 0.468589
\(285\) −53955.7 303890.i −0.0393482 0.221618i
\(286\) −552346. −0.399297
\(287\) 20326.1i 0.0145663i
\(288\) 43783.6i 0.0311050i
\(289\) 990644. 0.697707
\(290\) 157091. + 884774.i 0.109688 + 0.617785i
\(291\) −779485. −0.539604
\(292\) 862580.i 0.592028i
\(293\) 1.19558e6i 0.813601i 0.913517 + 0.406800i \(0.133356\pi\)
−0.913517 + 0.406800i \(0.866644\pi\)
\(294\) 951191. 0.641799
\(295\) 1.56552e6 277957.i 1.04738 0.185961i
\(296\) 186966. 0.124032
\(297\) 886578.i 0.583211i
\(298\) 551771.i 0.359930i
\(299\) −333170. −0.215520
\(300\) 243567. + 664290.i 0.156249 + 0.426142i
\(301\) 18073.2 0.0114979
\(302\) 60643.8i 0.0382621i
\(303\) 1.17003e6i 0.732135i
\(304\) 99883.4 0.0619882
\(305\) 2.57191e6 456643.i 1.58309 0.281078i
\(306\) −112049. −0.0684076
\(307\) 1.41410e6i 0.856315i −0.903704 0.428157i \(-0.859163\pi\)
0.903704 0.428157i \(-0.140837\pi\)
\(308\) 5379.58i 0.00323126i
\(309\) 75079.9 0.0447330
\(310\) −277274. 1.56167e6i −0.163872 0.922965i
\(311\) 2.67249e6 1.56680 0.783402 0.621516i \(-0.213483\pi\)
0.783402 + 0.621516i \(0.213483\pi\)
\(312\) 570385.i 0.331727i
\(313\) 398469.i 0.229897i −0.993371 0.114949i \(-0.963330\pi\)
0.993371 0.114949i \(-0.0366704\pi\)
\(314\) 584008. 0.334268
\(315\) −640.772 3608.97i −0.000363854 0.00204931i
\(316\) −1.63577e6 −0.921518
\(317\) 1.27652e6i 0.713477i 0.934204 + 0.356738i \(0.116111\pi\)
−0.934204 + 0.356738i \(0.883889\pi\)
\(318\) 1.86120e6i 1.03211i
\(319\) 881106. 0.484788
\(320\) −225447. + 40028.2i −0.123075 + 0.0218520i
\(321\) −63557.1 −0.0344272
\(322\) 3244.91i 0.00174407i
\(323\) 255617.i 0.136327i
\(324\) 749292. 0.396542
\(325\) 677533. + 1.84786e6i 0.355813 + 0.970423i
\(326\) 294667. 0.153563
\(327\) 540962.i 0.279768i
\(328\) 848296.i 0.435374i
\(329\) −27513.7 −0.0140139
\(330\) 683070. 121279.i 0.345287 0.0613056i
\(331\) −2.72461e6 −1.36689 −0.683446 0.730001i \(-0.739520\pi\)
−0.683446 + 0.730001i \(0.739520\pi\)
\(332\) 477045.i 0.237528i
\(333\) 124909.i 0.0617282i
\(334\) 2.39839e6 1.17640
\(335\) 107671. + 606426.i 0.0524187 + 0.295234i
\(336\) −5555.27 −0.00268446
\(337\) 1.69907e6i 0.814959i 0.913214 + 0.407479i \(0.133592\pi\)
−0.913214 + 0.407479i \(0.866408\pi\)
\(338\) 101472.i 0.0483118i
\(339\) −350326. −0.165567
\(340\) −102438. 576955.i −0.0480579 0.270673i
\(341\) −1.55520e6 −0.724268
\(342\) 66730.5i 0.0308503i
\(343\) 51543.8i 0.0236560i
\(344\) 754271. 0.343662
\(345\) 412021. 73154.2i 0.186368 0.0330896i
\(346\) −368651. −0.165549
\(347\) 2.53603e6i 1.13066i 0.824866 + 0.565329i \(0.191251\pi\)
−0.824866 + 0.565329i \(0.808749\pi\)
\(348\) 909882.i 0.402751i
\(349\) 1.87884e6 0.825708 0.412854 0.910797i \(-0.364532\pi\)
0.412854 + 0.910797i \(0.364532\pi\)
\(350\) 17997.3 6598.84i 0.00785301 0.00287937i
\(351\) 2.54674e6 1.10336
\(352\) 224513.i 0.0965794i
\(353\) 30316.4i 0.0129491i −0.999979 0.00647457i \(-0.997939\pi\)
0.999979 0.00647457i \(-0.00206093\pi\)
\(354\) 1.60994e6 0.682814
\(355\) −2.19106e6 + 389022.i −0.922747 + 0.163834i
\(356\) 1.16434e6 0.486918
\(357\) 14216.8i 0.00590379i
\(358\) 1.22862e6i 0.506651i
\(359\) 1.85159e6 0.758243 0.379122 0.925347i \(-0.376226\pi\)
0.379122 + 0.925347i \(0.376226\pi\)
\(360\) −26742.2 150618.i −0.0108753 0.0612520i
\(361\) −2.32387e6 −0.938519
\(362\) 602311.i 0.241574i
\(363\) 1.59875e6i 0.636815i
\(364\) −15453.1 −0.00611312
\(365\) 526848. + 2.96732e6i 0.206992 + 1.16582i
\(366\) 2.64490e6 1.03206
\(367\) 1.43933e6i 0.557820i −0.960317 0.278910i \(-0.910027\pi\)
0.960317 0.278910i \(-0.0899732\pi\)
\(368\) 135424.i 0.0521286i
\(369\) 566733. 0.216677
\(370\) −643174. + 114195.i −0.244244 + 0.0433655i
\(371\) −50424.6 −0.0190199
\(372\) 1.60599e6i 0.601707i
\(373\) 1.32778e6i 0.494144i 0.968997 + 0.247072i \(0.0794684\pi\)
−0.968997 + 0.247072i \(0.920532\pi\)
\(374\) −574563. −0.212402
\(375\) −1.24362e6 2.13643e6i −0.456678 0.784531i
\(376\) −1.14827e6 −0.418864
\(377\) 2.53103e6i 0.917156i
\(378\) 24804.0i 0.00892880i
\(379\) −2.94089e6 −1.05167 −0.525837 0.850585i \(-0.676248\pi\)
−0.525837 + 0.850585i \(0.676248\pi\)
\(380\) −343604. + 61006.9i −0.122067 + 0.0216730i
\(381\) −3.39773e6 −1.19916
\(382\) 2.32382e6i 0.814786i
\(383\) 2.29361e6i 0.798957i 0.916743 + 0.399478i \(0.130809\pi\)
−0.916743 + 0.399478i \(0.869191\pi\)
\(384\) −231845. −0.0802362
\(385\) −3285.74 18506.0i −0.00112975 0.00636300i
\(386\) −3.53024e6 −1.20597
\(387\) 503916.i 0.171033i
\(388\) 881352.i 0.297215i
\(389\) 762957. 0.255639 0.127819 0.991797i \(-0.459202\pi\)
0.127819 + 0.991797i \(0.459202\pi\)
\(390\) 348380. + 1.96216e6i 0.115982 + 0.653239i
\(391\) −346571. −0.114644
\(392\) 1.07550e6i 0.353504i
\(393\) 44408.9i 0.0145040i
\(394\) −2.56382e6 −0.832047
\(395\) 5.62713e6 999096.i 1.81466 0.322192i
\(396\) −149993. −0.0480656
\(397\) 1.78568e6i 0.568628i 0.958731 + 0.284314i \(0.0917658\pi\)
−0.958731 + 0.284314i \(0.908234\pi\)
\(398\) 3.87285e6i 1.22553i
\(399\) −8466.78 −0.00266248
\(400\) 751103. 275398.i 0.234720 0.0860619i
\(401\) 2.25925e6 0.701621 0.350810 0.936446i \(-0.385906\pi\)
0.350810 + 0.936446i \(0.385906\pi\)
\(402\) 623636.i 0.192471i
\(403\) 4.46739e6i 1.37022i
\(404\) −1.32294e6 −0.403261
\(405\) −2.57761e6 + 457654.i −0.780871 + 0.138643i
\(406\) 24651.0 0.00742196
\(407\) 640507.i 0.191663i
\(408\) 593328.i 0.176459i
\(409\) −4.05322e6 −1.19810 −0.599048 0.800713i \(-0.704454\pi\)
−0.599048 + 0.800713i \(0.704454\pi\)
\(410\) 518123. + 2.91819e6i 0.152221 + 0.857340i
\(411\) −2.58022e6 −0.753447
\(412\) 84891.8i 0.0246390i
\(413\) 43617.4i 0.0125830i
\(414\) −90474.6 −0.0259433
\(415\) 291370. + 1.64106e6i 0.0830472 + 0.467740i
\(416\) −644926. −0.182716
\(417\) 1.42639e6i 0.401696i
\(418\) 342180.i 0.0957886i
\(419\) 741313. 0.206284 0.103142 0.994667i \(-0.467110\pi\)
0.103142 + 0.994667i \(0.467110\pi\)
\(420\) 19110.4 3393.05i 0.00528624 0.000938572i
\(421\) −5.67332e6 −1.56003 −0.780013 0.625763i \(-0.784788\pi\)
−0.780013 + 0.625763i \(0.784788\pi\)
\(422\) 1.02572e6i 0.280379i
\(423\) 767138.i 0.208460i
\(424\) −2.10444e6 −0.568487
\(425\) 704786. + 1.92219e6i 0.189271 + 0.516207i
\(426\) −2.25323e6 −0.601565
\(427\) 71656.9i 0.0190190i
\(428\) 71863.1i 0.0189625i
\(429\) 1.95402e6 0.512609
\(430\) −2.59473e6 + 460694.i −0.676739 + 0.120155i
\(431\) −746537. −0.193579 −0.0967895 0.995305i \(-0.530857\pi\)
−0.0967895 + 0.995305i \(0.530857\pi\)
\(432\) 1.03518e6i 0.266874i
\(433\) 3.52859e6i 0.904444i −0.891905 0.452222i \(-0.850631\pi\)
0.891905 0.452222i \(-0.149369\pi\)
\(434\) −43510.2 −0.0110883
\(435\) −555739. 3.13004e6i −0.140815 0.793099i
\(436\) 611658. 0.154096
\(437\) 206400.i 0.0517018i
\(438\) 3.05153e6i 0.760033i
\(439\) 2.08705e6 0.516859 0.258430 0.966030i \(-0.416795\pi\)
0.258430 + 0.966030i \(0.416795\pi\)
\(440\) −137128. 772337.i −0.0337672 0.190184i
\(441\) 718523. 0.175932
\(442\) 1.65046e6i 0.401838i
\(443\) 4.61691e6i 1.11774i −0.829254 0.558872i \(-0.811234\pi\)
0.829254 0.558872i \(-0.188766\pi\)
\(444\) −661426. −0.159230
\(445\) −4.00540e6 + 711158.i −0.958839 + 0.170242i
\(446\) −5.46588e6 −1.30114
\(447\) 1.95199e6i 0.462070i
\(448\) 6281.26i 0.00147860i
\(449\) −2.13634e6 −0.500098 −0.250049 0.968233i \(-0.580447\pi\)
−0.250049 + 0.968233i \(0.580447\pi\)
\(450\) 183989. + 501800.i 0.0428313 + 0.116815i
\(451\) 2.90609e6 0.672771
\(452\) 396108.i 0.0911944i
\(453\) 214538.i 0.0491201i
\(454\) −5.20598e6 −1.18540
\(455\) 53159.6 9438.48i 0.0120380 0.00213734i
\(456\) −353355. −0.0795792
\(457\) 100158.i 0.0224335i 0.999937 + 0.0112168i \(0.00357048\pi\)
−0.999937 + 0.0112168i \(0.996430\pi\)
\(458\) 1.81074e6i 0.403359i
\(459\) 2.64918e6 0.586922
\(460\) −82714.4 465866.i −0.0182258 0.102652i
\(461\) −3.77604e6 −0.827532 −0.413766 0.910383i \(-0.635787\pi\)
−0.413766 + 0.910383i \(0.635787\pi\)
\(462\) 19031.2i 0.00414822i
\(463\) 2.32618e6i 0.504303i −0.967688 0.252151i \(-0.918862\pi\)
0.967688 0.252151i \(-0.0811381\pi\)
\(464\) 1.02879e6 0.221836
\(465\) 980907. + 5.52469e6i 0.210376 + 1.18488i
\(466\) 3.91816e6 0.835829
\(467\) 4.72960e6i 1.00353i −0.865003 0.501767i \(-0.832683\pi\)
0.865003 0.501767i \(-0.167317\pi\)
\(468\) 430865.i 0.0909340i
\(469\) 16895.8 0.00354689
\(470\) 3.95010e6 701339.i 0.824827 0.146448i
\(471\) −2.06603e6 −0.429126
\(472\) 1.82034e6i 0.376095i
\(473\) 2.58398e6i 0.531050i
\(474\) 5.78682e6 1.18303
\(475\) 1.14476e6 419734.i 0.232798 0.0853572i
\(476\) −16074.7 −0.00325182
\(477\) 1.40594e6i 0.282925i
\(478\) 2.76961e6i 0.554433i
\(479\) 6.65405e6 1.32510 0.662548 0.749020i \(-0.269475\pi\)
0.662548 + 0.749020i \(0.269475\pi\)
\(480\) 797560. 141607.i 0.158001 0.0280531i
\(481\) −1.83989e6 −0.362602
\(482\) 6.75818e6i 1.32499i
\(483\) 11479.4i 0.00223899i
\(484\) 1.80768e6 0.350759
\(485\) −538313. 3.03190e6i −0.103916 0.585276i
\(486\) 1.27969e6 0.245762
\(487\) 752137.i 0.143706i −0.997415 0.0718529i \(-0.977109\pi\)
0.997415 0.0718529i \(-0.0228912\pi\)
\(488\) 2.99055e6i 0.568462i
\(489\) −1.04244e6 −0.197141
\(490\) 656894. + 3.69977e6i 0.123596 + 0.696121i
\(491\) −8.71020e6 −1.63051 −0.815256 0.579100i \(-0.803404\pi\)
−0.815256 + 0.579100i \(0.803404\pi\)
\(492\) 3.00100e6i 0.558924i
\(493\) 2.63283e6i 0.487872i
\(494\) −982931. −0.181220
\(495\) 515986. 91613.2i 0.0946509 0.0168053i
\(496\) −1.81587e6 −0.331421
\(497\) 61045.7i 0.0110857i
\(498\) 1.68763e6i 0.304933i
\(499\) −15775.8 −0.00283623 −0.00141811 0.999999i \(-0.500451\pi\)
−0.00141811 + 0.999999i \(0.500451\pi\)
\(500\) −2.41563e6 + 1.40614e6i −0.432121 + 0.251539i
\(501\) −8.48472e6 −1.51023
\(502\) 2.21926e6i 0.393050i
\(503\) 937195.i 0.165162i −0.996584 0.0825810i \(-0.973684\pi\)
0.996584 0.0825810i \(-0.0263163\pi\)
\(504\) −4196.41 −0.000735871
\(505\) 4.55098e6 808026.i 0.794102 0.140993i
\(506\) −463935. −0.0805528
\(507\) 358974.i 0.0620217i
\(508\) 3.84176e6i 0.660497i
\(509\) −746746. −0.127755 −0.0638776 0.997958i \(-0.520347\pi\)
−0.0638776 + 0.997958i \(0.520347\pi\)
\(510\) 362393. + 2.04108e6i 0.0616957 + 0.347484i
\(511\) 82673.5 0.0140060
\(512\) 262144.i 0.0441942i
\(513\) 1.57772e6i 0.264689i
\(514\) −7.76191e6 −1.29587
\(515\) 51850.3 + 292032.i 0.00861456 + 0.0485191i
\(516\) −2.66837e6 −0.441185
\(517\) 3.93372e6i 0.647258i
\(518\) 17919.7i 0.00293431i
\(519\) 1.30417e6 0.212528
\(520\) 2.21858e6 393908.i 0.359805 0.0638832i
\(521\) −199402. −0.0321836 −0.0160918 0.999871i \(-0.505122\pi\)
−0.0160918 + 0.999871i \(0.505122\pi\)
\(522\) 687318.i 0.110403i
\(523\) 8.65539e6i 1.38367i −0.722055 0.691835i \(-0.756802\pi\)
0.722055 0.691835i \(-0.243198\pi\)
\(524\) 50212.5 0.00798884
\(525\) −63668.5 + 23344.6i −0.0100815 + 0.00369648i
\(526\) 4.14074e6 0.652549
\(527\) 4.64708e6i 0.728877i
\(528\) 794254.i 0.123987i
\(529\) −279841. −0.0434783
\(530\) 7.23937e6 1.28535e6i 1.11947 0.198761i
\(531\) 1.21614e6 0.187175
\(532\) 9573.26i 0.00146650i
\(533\) 8.34790e6i 1.27280i
\(534\) −4.11907e6 −0.625094
\(535\) −43892.6 247213.i −0.00662990 0.0373411i
\(536\) 705135. 0.106013
\(537\) 4.34645e6i 0.650427i
\(538\) 2.31025e6i 0.344115i
\(539\) 3.68443e6 0.546259
\(540\) 632268. + 3.56107e6i 0.0933076 + 0.525529i
\(541\) 2.46716e6 0.362413 0.181207 0.983445i \(-0.442000\pi\)
0.181207 + 0.983445i \(0.442000\pi\)
\(542\) 4.43958e6i 0.649148i
\(543\) 2.13078e6i 0.310127i
\(544\) −670867. −0.0971939
\(545\) −2.10414e6 + 373589.i −0.303447 + 0.0538770i
\(546\) 54668.2 0.00784790
\(547\) 1.56237e6i 0.223263i −0.993750 0.111631i \(-0.964392\pi\)
0.993750 0.111631i \(-0.0356075\pi\)
\(548\) 2.91742e6i 0.414999i
\(549\) 1.99794e6 0.282912
\(550\) 943457. + 2.57313e6i 0.132989 + 0.362706i
\(551\) 1.56798e6 0.220019
\(552\) 479086.i 0.0669216i
\(553\) 156779.i 0.0218010i
\(554\) −7.14886e6 −0.989606
\(555\) 2.27534e6 403986.i 0.313555 0.0556717i
\(556\) 1.61280e6 0.221255
\(557\) 7.59477e6i 1.03723i 0.855007 + 0.518617i \(0.173553\pi\)
−0.855007 + 0.518617i \(0.826447\pi\)
\(558\) 1.21315e6i 0.164941i
\(559\) −7.42261e6 −1.00468
\(560\) −3836.48 21607.9i −0.000516966 0.00291167i
\(561\) 2.03262e6 0.272677
\(562\) 57076.5i 0.00762283i
\(563\) 7.58578e6i 1.00862i −0.863522 0.504312i \(-0.831746\pi\)
0.863522 0.504312i \(-0.168254\pi\)
\(564\) 4.06219e6 0.537728
\(565\) −241936. 1.36263e6i −0.0318844 0.179580i
\(566\) 2.37339e6 0.311407
\(567\) 71815.5i 0.00938124i
\(568\) 2.54770e6i 0.331343i
\(569\) −6.86354e6 −0.888725 −0.444362 0.895847i \(-0.646570\pi\)
−0.444362 + 0.895847i \(0.646570\pi\)
\(570\) 1.21556e6 215823.i 0.156707 0.0278234i
\(571\) −1.08414e7 −1.39154 −0.695770 0.718264i \(-0.744937\pi\)
−0.695770 + 0.718264i \(0.744937\pi\)
\(572\) 2.20938e6i 0.282346i
\(573\) 8.22091e6i 1.04600i
\(574\) 81304.4 0.0102999
\(575\) 569084. + 1.55208e6i 0.0717806 + 0.195770i
\(576\) −175134. −0.0219945
\(577\) 5.00533e6i 0.625883i −0.949772 0.312941i \(-0.898686\pi\)
0.949772 0.312941i \(-0.101314\pi\)
\(578\) 3.96258e6i 0.493353i
\(579\) 1.24888e7 1.54820
\(580\) −3.53910e6 + 628366.i −0.436840 + 0.0775608i
\(581\) 45722.1 0.00561935
\(582\) 3.11794e6i 0.381558i
\(583\) 7.20936e6i 0.878467i
\(584\) 3.45032e6 0.418627
\(585\) 263164. + 1.48220e6i 0.0317934 + 0.179067i
\(586\) −4.78234e6 −0.575303
\(587\) 257953.i 0.0308991i 0.999881 + 0.0154496i \(0.00491794\pi\)
−0.999881 + 0.0154496i \(0.995082\pi\)
\(588\) 3.80476e6i 0.453821i
\(589\) −2.76756e6 −0.328707
\(590\) 1.11183e6 + 6.26207e6i 0.131495 + 0.740607i
\(591\) 9.06998e6 1.06816
\(592\) 747864.i 0.0877038i
\(593\) 1.08797e7i 1.27051i −0.772301 0.635257i \(-0.780894\pi\)
0.772301 0.635257i \(-0.219106\pi\)
\(594\) 3.54631e6 0.412393
\(595\) 55297.9 9818.13i 0.00640348 0.00113694i
\(596\) 2.20708e6 0.254509
\(597\) 1.37009e7i 1.57330i
\(598\) 1.33268e6i 0.152396i
\(599\) 4.82031e6 0.548918 0.274459 0.961599i \(-0.411501\pi\)
0.274459 + 0.961599i \(0.411501\pi\)
\(600\) −2.65716e6 + 974270.i −0.301328 + 0.110484i
\(601\) −1.41939e7 −1.60294 −0.801469 0.598036i \(-0.795948\pi\)
−0.801469 + 0.598036i \(0.795948\pi\)
\(602\) 72292.6i 0.00813023i
\(603\) 471090.i 0.0527607i
\(604\) 242575. 0.0270554
\(605\) −6.21852e6 + 1.10410e6i −0.690715 + 0.122636i
\(606\) 4.68013e6 0.517698
\(607\) 1.18194e7i 1.30203i −0.759064 0.651016i \(-0.774343\pi\)
0.759064 0.651016i \(-0.225657\pi\)
\(608\) 399533.i 0.0438323i
\(609\) −87207.1 −0.00952815
\(610\) 1.82657e6 + 1.02877e7i 0.198752 + 1.11942i
\(611\) 1.12998e7 1.22453
\(612\) 448196.i 0.0483714i
\(613\) 6.80804e6i 0.731763i −0.930661 0.365882i \(-0.880767\pi\)
0.930661 0.365882i \(-0.119233\pi\)
\(614\) 5.65639e6 0.605506
\(615\) −1.83295e6 1.03236e7i −0.195418 1.10063i
\(616\) −21518.3 −0.00228484
\(617\) 2.44923e6i 0.259010i 0.991579 + 0.129505i \(0.0413388\pi\)
−0.991579 + 0.129505i \(0.958661\pi\)
\(618\) 300320.i 0.0316310i
\(619\) −5.31393e6 −0.557429 −0.278714 0.960374i \(-0.589908\pi\)
−0.278714 + 0.960374i \(0.589908\pi\)
\(620\) 6.24668e6 1.10910e6i 0.652635 0.115875i
\(621\) 2.13910e6 0.222588
\(622\) 1.06899e7i 1.10790i
\(623\) 111596.i 0.0115193i
\(624\) 2.28154e6 0.234567
\(625\) 7.45105e6 6.31263e6i 0.762987 0.646414i
\(626\) 1.59388e6 0.162562
\(627\) 1.21052e6i 0.122971i
\(628\) 2.33603e6i 0.236363i
\(629\) −1.91390e6 −0.192882
\(630\) 14435.9 2563.09i 0.00144908 0.000257284i
\(631\) 1.10479e7 1.10460 0.552302 0.833644i \(-0.313749\pi\)
0.552302 + 0.833644i \(0.313749\pi\)
\(632\) 6.54307e6i 0.651612i
\(633\) 3.62865e6i 0.359945i
\(634\) −5.10609e6 −0.504504
\(635\) −2.34647e6 1.32159e7i −0.230930 1.30065i
\(636\) 7.44481e6 0.729812
\(637\) 1.05837e7i 1.03345i
\(638\) 3.52442e6i 0.342797i
\(639\) −1.70208e6 −0.164902
\(640\) −160113. 901790.i −0.0154517 0.0870273i
\(641\) 1.96723e7 1.89108 0.945542 0.325501i \(-0.105533\pi\)
0.945542 + 0.325501i \(0.105533\pi\)
\(642\) 254229.i 0.0243437i
\(643\) 1.58115e7i 1.50816i 0.656784 + 0.754079i \(0.271916\pi\)
−0.656784 + 0.754079i \(0.728084\pi\)
\(644\) −12979.6 −0.00123324
\(645\) 9.17933e6 1.62979e6i 0.868783 0.154252i
\(646\) −1.02247e6 −0.0963981
\(647\) 4.14517e6i 0.389297i 0.980873 + 0.194649i \(0.0623567\pi\)
−0.980873 + 0.194649i \(0.937643\pi\)
\(648\) 2.99717e6i 0.280397i
\(649\) 6.23611e6 0.581168
\(650\) −7.39144e6 + 2.71013e6i −0.686192 + 0.251598i
\(651\) 153925. 0.0142350
\(652\) 1.17867e6i 0.108585i
\(653\) 3.24380e6i 0.297695i 0.988860 + 0.148847i \(0.0475563\pi\)
−0.988860 + 0.148847i \(0.952444\pi\)
\(654\) −2.16385e6 −0.197826
\(655\) −172734. + 30668.8i −0.0157316 + 0.00279315i
\(656\) 3.39318e6 0.307856
\(657\) 2.30510e6i 0.208342i
\(658\) 110055.i 0.00990933i
\(659\) −1.16821e7 −1.04787 −0.523935 0.851759i \(-0.675536\pi\)
−0.523935 + 0.851759i \(0.675536\pi\)
\(660\) 485115. + 2.73228e6i 0.0433496 + 0.244155i
\(661\) 9.90399e6 0.881671 0.440836 0.897588i \(-0.354682\pi\)
0.440836 + 0.897588i \(0.354682\pi\)
\(662\) 1.08984e7i 0.966539i
\(663\) 5.83881e6i 0.515870i
\(664\) 1.90818e6 0.167957
\(665\) −5847.17 32932.6i −0.000512733 0.00288783i
\(666\) −499636. −0.0436484
\(667\) 2.12590e6i 0.185024i
\(668\) 9.59355e6i 0.831837i
\(669\) 1.93365e7 1.67037
\(670\) −2.42570e6 + 430683.i −0.208762 + 0.0370656i
\(671\) 1.02450e7 0.878428
\(672\) 22221.1i 0.00189820i
\(673\) 3.59697e6i 0.306126i 0.988216 + 0.153063i \(0.0489137\pi\)
−0.988216 + 0.153063i \(0.951086\pi\)
\(674\) −6.79627e6 −0.576263
\(675\) −4.35007e6 1.18641e7i −0.367483 1.00225i
\(676\) 405887. 0.0341616
\(677\) 1.04284e7i 0.874473i 0.899346 + 0.437237i \(0.144043\pi\)
−0.899346 + 0.437237i \(0.855957\pi\)
\(678\) 1.40130e6i 0.117073i
\(679\) −84472.7 −0.00703140
\(680\) 2.30782e6 409753.i 0.191395 0.0339821i
\(681\) 1.84171e7 1.52179
\(682\) 6.22079e6i 0.512135i
\(683\) 1.57875e7i 1.29498i −0.762074 0.647490i \(-0.775819\pi\)
0.762074 0.647490i \(-0.224181\pi\)
\(684\) −266922. −0.0218144
\(685\) −1.78190e6 1.00361e7i −0.145097 0.817218i
\(686\) 206175. 0.0167273
\(687\) 6.40581e6i 0.517824i
\(688\) 3.01708e6i 0.243005i
\(689\) 2.07093e7 1.66195
\(690\) 292617. + 1.64808e6i 0.0233979 + 0.131782i
\(691\) 1.13676e7 0.905680 0.452840 0.891592i \(-0.350411\pi\)
0.452840 + 0.891592i \(0.350411\pi\)
\(692\) 1.47461e6i 0.117061i
\(693\) 14376.0i 0.00113712i
\(694\) −1.01441e7 −0.799496
\(695\) −5.54811e6 + 985065.i −0.435695 + 0.0773576i
\(696\) −3.63953e6 −0.284788
\(697\) 8.68368e6i 0.677052i
\(698\) 7.51537e6i 0.583864i
\(699\) −1.38612e7 −1.07302
\(700\) 26395.4 + 71989.0i 0.00203602 + 0.00555292i
\(701\) −2.10664e7 −1.61918 −0.809591 0.586994i \(-0.800311\pi\)
−0.809591 + 0.586994i \(0.800311\pi\)
\(702\) 1.01870e7i 0.780194i
\(703\) 1.13982e6i 0.0869857i
\(704\) −898052. −0.0682920
\(705\) −1.39742e7 + 2.48111e6i −1.05890 + 0.188007i
\(706\) 121266. 0.00915643
\(707\) 126796.i 0.00954021i
\(708\) 6.43977e6i 0.482823i
\(709\) 1.63858e7 1.22420 0.612100 0.790781i \(-0.290325\pi\)
0.612100 + 0.790781i \(0.290325\pi\)
\(710\) −1.55609e6 8.76422e6i −0.115848 0.652481i
\(711\) 4.37132e6 0.324294
\(712\) 4.65737e6i 0.344303i
\(713\) 3.75232e6i 0.276424i
\(714\) 56867.2 0.00417461
\(715\) 1.34945e6 + 7.60040e6i 0.0987169 + 0.555995i
\(716\) 4.91446e6 0.358256
\(717\) 9.79799e6i 0.711769i
\(718\) 7.40636e6i 0.536159i
\(719\) 1.60559e7 1.15827 0.579137 0.815230i \(-0.303390\pi\)
0.579137 + 0.815230i \(0.303390\pi\)
\(720\) 602471. 106969.i 0.0433117 0.00768998i
\(721\) 8136.40 0.000582900
\(722\) 9.29547e6i 0.663633i
\(723\) 2.39083e7i 1.70099i
\(724\) −2.40924e6 −0.170818
\(725\) 1.17909e7 4.32322e6i 0.833108 0.305466i
\(726\) −6.39499e6 −0.450296
\(727\) 6.39709e6i 0.448897i −0.974486 0.224448i \(-0.927942\pi\)
0.974486 0.224448i \(-0.0720580\pi\)
\(728\) 61812.5i 0.00432263i
\(729\) −1.59070e7 −1.10859
\(730\) −1.18693e7 + 2.10739e6i −0.824361 + 0.146365i
\(731\) −7.72118e6 −0.534429
\(732\) 1.05796e7i 0.729779i
\(733\) 2.63593e7i 1.81207i −0.423205 0.906034i \(-0.639095\pi\)
0.423205 0.906034i \(-0.360905\pi\)
\(734\) 5.75731e6 0.394439
\(735\) −2.32388e6 1.30886e7i −0.158670 0.893665i
\(736\) −541696. −0.0368605
\(737\) 2.41565e6i 0.163819i
\(738\) 2.26693e6i 0.153214i
\(739\) −1.89946e7 −1.27944 −0.639719 0.768609i \(-0.720949\pi\)
−0.639719 + 0.768609i \(0.720949\pi\)
\(740\) −456781. 2.57269e6i −0.0306640 0.172707i
\(741\) 3.47729e6 0.232646
\(742\) 201698.i 0.0134491i
\(743\) 1.51089e7i 1.00406i 0.864849 + 0.502032i \(0.167414\pi\)
−0.864849 + 0.502032i \(0.832586\pi\)
\(744\) 6.42395e6 0.425471
\(745\) −7.59249e6 + 1.34804e6i −0.501180 + 0.0889844i
\(746\) −5.31111e6 −0.349412
\(747\) 1.27483e6i 0.0835890i
\(748\) 2.29825e6i 0.150191i
\(749\) −6887.68 −0.000448609
\(750\) 8.54571e6 4.97448e6i 0.554747 0.322920i
\(751\) −7.92257e6 −0.512585 −0.256293 0.966599i \(-0.582501\pi\)
−0.256293 + 0.966599i \(0.582501\pi\)
\(752\) 4.59306e6i 0.296181i
\(753\) 7.85101e6i 0.504589i
\(754\) −1.01241e7 −0.648527
\(755\) −834472. + 148160.i −0.0532776 + 0.00945942i
\(756\) 99216.2 0.00631361
\(757\) 1.90710e7i 1.20958i 0.796385 + 0.604790i \(0.206743\pi\)
−0.796385 + 0.604790i \(0.793257\pi\)
\(758\) 1.17636e7i 0.743646i
\(759\) 1.64125e6 0.103412
\(760\) −244027. 1.37442e6i −0.0153252 0.0863147i
\(761\) −2.86186e6 −0.179138 −0.0895689 0.995981i \(-0.528549\pi\)
−0.0895689 + 0.995981i \(0.528549\pi\)
\(762\) 1.35909e7i 0.847932i
\(763\) 58624.0i 0.00364556i
\(764\) 9.29527e6 0.576140
\(765\) 273749. + 1.54182e6i 0.0169122 + 0.0952532i
\(766\) −9.17445e6 −0.564948
\(767\) 1.79136e7i 1.09950i
\(768\) 927381.i 0.0567355i
\(769\) −3.12303e7 −1.90441 −0.952204 0.305462i \(-0.901189\pi\)
−0.952204 + 0.305462i \(0.901189\pi\)
\(770\) 74024.2 13143.0i 0.00449932 0.000798853i
\(771\) 2.74591e7 1.66361
\(772\) 1.41210e7i 0.852748i
\(773\) 3.81991e6i 0.229934i −0.993369 0.114967i \(-0.963324\pi\)
0.993369 0.114967i \(-0.0366763\pi\)
\(774\) −2.01566e6 −0.120939
\(775\) −2.08115e7 + 7.63071e6i −1.24466 + 0.456363i
\(776\) −3.52541e6 −0.210162
\(777\) 63394.0i 0.00376700i
\(778\) 3.05183e6i 0.180764i
\(779\) 5.17155e6 0.305335
\(780\) −7.84862e6 + 1.39352e6i −0.461909 + 0.0820119i
\(781\) −8.72789e6 −0.512014
\(782\) 1.38628e6i 0.0810654i
\(783\) 1.62503e7i 0.947236i
\(784\) 4.30199e6 0.249965
\(785\) −1.42680e6 8.03608e6i −0.0826400 0.465447i
\(786\) −177636. −0.0102559
\(787\) 8.19748e6i 0.471784i −0.971779 0.235892i \(-0.924199\pi\)
0.971779 0.235892i \(-0.0758012\pi\)
\(788\) 1.02553e7i 0.588346i
\(789\) −1.46486e7 −0.837729
\(790\) 3.99638e6 + 2.25085e7i 0.227824 + 1.28316i
\(791\) −37964.8 −0.00215745
\(792\) 599974.i 0.0339875i
\(793\) 2.94294e7i 1.66187i
\(794\) −7.14273e6 −0.402081
\(795\) −2.56106e7 + 4.54715e6i −1.43715 + 0.255165i
\(796\) 1.54914e7 0.866578
\(797\) 1.25909e6i 0.0702121i −0.999384 0.0351061i \(-0.988823\pi\)
0.999384 0.0351061i \(-0.0111769\pi\)
\(798\) 33867.1i 0.00188266i
\(799\) 1.17544e7 0.651376
\(800\) 1.10159e6 + 3.00441e6i 0.0608550 + 0.165972i
\(801\) −3.11151e6 −0.171352
\(802\) 9.03698e6i 0.496121i
\(803\) 1.18201e7i 0.646892i
\(804\) −2.49454e6 −0.136098
\(805\) 44650.7 7927.72i 0.00242850 0.000431180i
\(806\) 1.78696e7 0.968894
\(807\) 8.17292e6i 0.441767i
\(808\) 5.29175e6i 0.285148i
\(809\) 2.67193e7 1.43534 0.717668 0.696385i \(-0.245209\pi\)
0.717668 + 0.696385i \(0.245209\pi\)
\(810\) −1.83061e6 1.03104e7i −0.0980357 0.552159i
\(811\) −1.69459e7 −0.904717 −0.452359 0.891836i \(-0.649417\pi\)
−0.452359 + 0.891836i \(0.649417\pi\)
\(812\) 98603.8i 0.00524812i
\(813\) 1.57058e7i 0.833362i
\(814\) −2.56203e6 −0.135526
\(815\) −719907. 4.05468e6i −0.0379649 0.213827i
\(816\) 2.37331e6 0.124776
\(817\) 4.59833e6i 0.241016i
\(818\) 1.62129e7i 0.847182i
\(819\) 41296.0 0.00215128
\(820\) −1.16727e7 + 2.07249e6i −0.606231 + 0.107636i
\(821\) 2.66090e7 1.37775 0.688876 0.724879i \(-0.258104\pi\)
0.688876 + 0.724879i \(0.258104\pi\)
\(822\) 1.03209e7i 0.532767i
\(823\) 2.24043e7i 1.15301i −0.817095 0.576504i \(-0.804417\pi\)
0.817095 0.576504i \(-0.195583\pi\)
\(824\) 339567. 0.0174224
\(825\) −3.33765e6 9.10289e6i −0.170728 0.465634i
\(826\) 174469. 0.00889752
\(827\) 1.91344e7i 0.972862i 0.873719 + 0.486431i \(0.161701\pi\)
−0.873719 + 0.486431i \(0.838299\pi\)
\(828\) 361898.i 0.0183447i
\(829\) −5.05760e6 −0.255599 −0.127799 0.991800i \(-0.540791\pi\)
−0.127799 + 0.991800i \(0.540791\pi\)
\(830\) −6.56425e6 + 1.16548e6i −0.330742 + 0.0587232i
\(831\) 2.52903e7 1.27043
\(832\) 2.57970e6i 0.129200i
\(833\) 1.10095e7i 0.549735i
\(834\) −5.70555e6 −0.284042
\(835\) −5.85956e6 3.30023e7i −0.290836 1.63806i
\(836\) −1.36872e6 −0.0677328
\(837\) 2.86827e7i 1.41516i
\(838\) 2.96525e6i 0.145865i
\(839\) −2.20620e7 −1.08203 −0.541015 0.841013i \(-0.681960\pi\)
−0.541015 + 0.841013i \(0.681960\pi\)
\(840\) 13572.2 + 76441.7i 0.000663670 + 0.00373794i
\(841\) −4.36110e6 −0.212621
\(842\) 2.26933e7i 1.10311i
\(843\) 201918.i 0.00978603i
\(844\) −4.10286e6 −0.198258
\(845\) −1.39627e6 + 247908.i −0.0672711 + 0.0119440i
\(846\) 3.06855e6 0.147403
\(847\) 173256.i 0.00829813i
\(848\) 8.41774e6i 0.401981i
\(849\) −8.39629e6 −0.399777
\(850\) −7.68876e6 + 2.81915e6i −0.365013 + 0.133835i
\(851\) −1.54539e6 −0.0731501
\(852\) 9.01294e6i 0.425371i
\(853\) 2.04264e7i 0.961214i −0.876936 0.480607i \(-0.840416\pi\)
0.876936 0.480607i \(-0.159584\pi\)
\(854\) 286627. 0.0134485
\(855\) 918226. 163031.i 0.0429570 0.00762701i
\(856\) −287452. −0.0134085
\(857\) 3.89718e6i 0.181258i 0.995885 + 0.0906292i \(0.0288878\pi\)
−0.995885 + 0.0906292i \(0.971112\pi\)
\(858\) 7.81608e6i 0.362469i
\(859\) −2.90283e7 −1.34227 −0.671133 0.741337i \(-0.734192\pi\)
−0.671133 + 0.741337i \(0.734192\pi\)
\(860\) −1.84278e6 1.03789e7i −0.0849624 0.478527i
\(861\) −287629. −0.0132228
\(862\) 2.98615e6i 0.136881i
\(863\) 5.36756e6i 0.245330i −0.992448 0.122665i \(-0.960856\pi\)
0.992448 0.122665i \(-0.0391440\pi\)
\(864\) 4.14072e6 0.188708
\(865\) 900661. + 5.07272e6i 0.0409281 + 0.230516i
\(866\) 1.41144e7 0.639539
\(867\) 1.40183e7i 0.633356i
\(868\) 174041.i 0.00784064i
\(869\) 2.24152e7 1.00692
\(870\) 1.25202e7 2.22296e6i 0.560806 0.0995709i
\(871\) −6.93909e6 −0.309925
\(872\) 2.44663e6i 0.108963i
\(873\) 2.35527e6i 0.104594i
\(874\) −825598. −0.0365587
\(875\) −134771. 231524.i −0.00595082 0.0102230i
\(876\) −1.22061e7 −0.537424
\(877\) 3.29965e7i 1.44867i −0.689450 0.724333i \(-0.742148\pi\)
0.689450 0.724333i \(-0.257852\pi\)
\(878\) 8.34822e6i 0.365475i
\(879\) 1.69184e7 0.738561
\(880\) 3.08935e6 548513.i 0.134481 0.0238770i
\(881\) −3.83926e7 −1.66651 −0.833254 0.552891i \(-0.813525\pi\)
−0.833254 + 0.552891i \(0.813525\pi\)
\(882\) 2.87409e6i 0.124402i
\(883\) 3.89550e6i 0.168136i 0.996460 + 0.0840681i \(0.0267913\pi\)
−0.996460 + 0.0840681i \(0.973209\pi\)
\(884\) 6.60186e6 0.284142
\(885\) −3.93329e6 2.21532e7i −0.168810 0.950775i
\(886\) 1.84677e7 0.790364
\(887\) 3.91229e7i 1.66964i 0.550525 + 0.834819i \(0.314427\pi\)
−0.550525 + 0.834819i \(0.685573\pi\)
\(888\) 2.64570e6i 0.112592i
\(889\) −368211. −0.0156258
\(890\) −2.84463e6 1.60216e7i −0.120379 0.678002i
\(891\) −1.02677e7 −0.433290
\(892\) 2.18635e7i 0.920042i
\(893\) 7.00028e6i 0.293756i
\(894\) −7.80795e6 −0.326733
\(895\) −1.69060e7 + 3.00166e6i −0.705479 + 0.125258i
\(896\) −25125.0 −0.00104553
\(897\) 4.71459e6i 0.195642i
\(898\) 8.54536e6i 0.353622i
\(899\) −2.85056e7 −1.17634
\(900\) −2.00720e6 + 735956.i −0.0826008 + 0.0302863i
\(901\) 2.15423e7 0.884057
\(902\) 1.16244e7i 0.475721i
\(903\) 255748.i 0.0104374i
\(904\) −1.58443e6 −0.0644842
\(905\) 8.28793e6 1.47152e6i 0.336376 0.0597234i
\(906\) −858153. −0.0347332
\(907\) 1.75220e7i 0.707239i 0.935389 + 0.353620i \(0.115049\pi\)
−0.935389 + 0.353620i \(0.884951\pi\)
\(908\) 2.08239e7i 0.838201i
\(909\) 3.53534e6 0.141913
\(910\) 37753.9 + 212639.i 0.00151133 + 0.00851213i
\(911\) −4.85291e6 −0.193734 −0.0968670 0.995297i \(-0.530882\pi\)
−0.0968670 + 0.995297i \(0.530882\pi\)
\(912\) 1.41342e6i 0.0562710i
\(913\) 6.53704e6i 0.259540i
\(914\) −400634. −0.0158629
\(915\) −6.46182e6 3.63944e7i −0.255154 1.43708i
\(916\) −7.24295e6 −0.285218
\(917\) 4812.59i 0.000188997i
\(918\) 1.05967e7i 0.415017i
\(919\) −2.25255e7 −0.879803 −0.439901 0.898046i \(-0.644987\pi\)
−0.439901 + 0.898046i \(0.644987\pi\)
\(920\) 1.86346e6 330858.i 0.0725858 0.0128876i
\(921\) −2.00105e7 −0.777336
\(922\) 1.51042e7i 0.585153i
\(923\) 2.50714e7i 0.968665i
\(924\) 76124.8 0.00293323
\(925\) 3.14271e6 + 8.57122e6i 0.120767 + 0.329373i
\(926\) 9.30473e6 0.356596
\(927\) 226859.i 0.00867076i
\(928\) 4.11516e6i 0.156862i
\(929\) −2.50840e7 −0.953581 −0.476791 0.879017i \(-0.658200\pi\)
−0.476791 + 0.879017i \(0.658200\pi\)
\(930\) −2.20987e7 + 3.92363e6i −0.837838 + 0.148758i
\(931\) 6.55666e6 0.247918
\(932\) 1.56726e7i 0.591020i
\(933\) 3.78176e7i 1.42229i
\(934\) 1.89184e7 0.709606
\(935\) 1.40373e6 + 7.90612e6i 0.0525115 + 0.295756i
\(936\) 1.72346e6 0.0643000
\(937\) 2.23564e6i 0.0831864i −0.999135 0.0415932i \(-0.986757\pi\)
0.999135 0.0415932i \(-0.0132434\pi\)
\(938\) 67583.3i 0.00250803i
\(939\) −5.63863e6 −0.208694
\(940\) 2.80536e6 + 1.58004e7i 0.103554 + 0.583241i
\(941\) −8.87004e6 −0.326551 −0.163276 0.986580i \(-0.552206\pi\)
−0.163276 + 0.986580i \(0.552206\pi\)
\(942\) 8.26413e6i 0.303438i
\(943\) 7.01170e6i 0.256770i
\(944\) 7.28136e6 0.265939
\(945\) −341309. + 60599.4i −0.0124328 + 0.00220744i
\(946\) −1.03359e7 −0.375509
\(947\) 3.36858e7i 1.22060i −0.792171 0.610299i \(-0.791049\pi\)
0.792171 0.610299i \(-0.208951\pi\)
\(948\) 2.31473e7i 0.836525i
\(949\) −3.39539e7 −1.22384
\(950\) 1.67894e6 + 4.57902e6i 0.0603566 + 0.164613i
\(951\) 1.80637e7 0.647672
\(952\) 64298.9i 0.00229938i
\(953\) 3.19415e7i 1.13926i 0.821901 + 0.569631i \(0.192914\pi\)
−0.821901 + 0.569631i \(0.807086\pi\)
\(954\) 5.62376e6 0.200058
\(955\) −3.19762e7 + 5.67737e6i −1.13454 + 0.201437i
\(956\) −1.10784e7 −0.392043
\(957\) 1.24683e7i 0.440075i
\(958\) 2.66162e7i 0.936984i
\(959\) −279618. −0.00981791
\(960\) 566427. + 3.19024e6i 0.0198365 + 0.111724i
\(961\) 2.16848e7 0.757436
\(962\) 7.35957e6i 0.256398i
\(963\) 192042.i 0.00667316i
\(964\) 2.70327e7 0.936908
\(965\) 8.62481e6 + 4.85769e7i 0.298148 + 1.67923i
\(966\) 45917.8 0.00158321
\(967\) 2.60523e7i 0.895942i 0.894048 + 0.447971i \(0.147853\pi\)
−0.894048 + 0.447971i \(0.852147\pi\)
\(968\) 7.23072e6i 0.248024i
\(969\) 3.61716e6 0.123754
\(970\) 1.21276e7 2.15325e6i 0.413852 0.0734794i
\(971\) 5.18849e7 1.76601 0.883005 0.469363i \(-0.155516\pi\)
0.883005 + 0.469363i \(0.155516\pi\)
\(972\) 5.11877e6i 0.173780i
\(973\) 154577.i 0.00523437i
\(974\) 3.00855e6 0.101615
\(975\) 2.61485e7 9.58758e6i 0.880919 0.322996i
\(976\) 1.19622e7 0.401963
\(977\) 3.19273e7i 1.07011i 0.844819 + 0.535053i \(0.179708\pi\)
−0.844819 + 0.535053i \(0.820292\pi\)
\(978\) 4.16974e6i 0.139400i
\(979\) −1.59552e7 −0.532041
\(980\) −1.47991e7 + 2.62757e6i −0.492232 + 0.0873957i
\(981\) −1.63456e6 −0.0542285
\(982\) 3.48408e7i 1.15295i
\(983\) 2.50693e7i 0.827480i −0.910395 0.413740i \(-0.864222\pi\)
0.910395 0.413740i \(-0.135778\pi\)
\(984\) −1.20040e7 −0.395219
\(985\) 6.26374e6 + 3.52788e7i 0.205704 + 1.15857i
\(986\) −1.05313e7 −0.344978
\(987\) 389339.i 0.0127214i
\(988\) 3.93172e6i 0.128142i
\(989\) −6.23452e6 −0.202681
\(990\) 366453. + 2.06394e6i 0.0118831 + 0.0669283i
\(991\) 3.58435e7 1.15938 0.579690 0.814837i \(-0.303174\pi\)
0.579690 + 0.814837i \(0.303174\pi\)
\(992\) 7.26347e6i 0.234350i
\(993\) 3.85552e7i 1.24082i
\(994\) −244183. −0.00783879
\(995\) −5.32912e7 + 9.46185e6i −1.70647 + 0.302983i
\(996\) −6.75053e6 −0.215620
\(997\) 6.94641e6i 0.221321i −0.993858 0.110661i \(-0.964703\pi\)
0.993858 0.110661i \(-0.0352966\pi\)
\(998\) 63103.4i 0.00200552i
\(999\) 1.18130e7 0.374494
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 230.6.b.a.139.17 yes 26
5.4 even 2 inner 230.6.b.a.139.10 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.6.b.a.139.10 26 5.4 even 2 inner
230.6.b.a.139.17 yes 26 1.1 even 1 trivial