Properties

Label 75.9.d.d.74.14
Level $75$
Weight $9$
Character 75.74
Analytic conductor $30.553$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [75,9,Mod(74,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.74");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 75.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(30.5533957546\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 3278 x^{18} + 4245491 x^{16} + 2854629536 x^{14} + 1117319469691 x^{12} + 266849787342054 x^{10} + \cdots + 89\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{21}\cdot 3^{22}\cdot 5^{26} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 74.14
Root \(-12.7835i\) of defining polynomial
Character \(\chi\) \(=\) 75.74
Dual form 75.9.d.d.74.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+16.2639 q^{2} +(-22.8278 + 77.7167i) q^{3} +8.51375 q^{4} +(-371.269 + 1263.98i) q^{6} +569.895i q^{7} -4025.09 q^{8} +(-5518.78 - 3548.20i) q^{9} +O(q^{10})\) \(q+16.2639 q^{2} +(-22.8278 + 77.7167i) q^{3} +8.51375 q^{4} +(-371.269 + 1263.98i) q^{6} +569.895i q^{7} -4025.09 q^{8} +(-5518.78 - 3548.20i) q^{9} -6582.70i q^{11} +(-194.350 + 661.661i) q^{12} -28214.2i q^{13} +9268.70i q^{14} -67643.0 q^{16} +151139. q^{17} +(-89756.8 - 57707.6i) q^{18} -41572.9 q^{19} +(-44290.4 - 13009.4i) q^{21} -107060. i q^{22} -173241. q^{23} +(91883.9 - 312817. i) q^{24} -458873. i q^{26} +(401737. - 347904. i) q^{27} +4851.94i q^{28} -783419. i q^{29} -215271. q^{31} -69716.1 q^{32} +(511586. + 150269. i) q^{33} +2.45811e6 q^{34} +(-46985.6 - 30208.5i) q^{36} -2.71385e6i q^{37} -676137. q^{38} +(2.19272e6 + 644068. i) q^{39} +676092. i q^{41} +(-720333. - 211584. i) q^{42} -4.21531e6i q^{43} -56043.5i q^{44} -2.81758e6 q^{46} -8.87092e6 q^{47} +(1.54414e6 - 5.25700e6i) q^{48} +5.44002e6 q^{49} +(-3.45018e6 + 1.17461e7i) q^{51} -240209. i q^{52} -6.53406e6 q^{53} +(6.53379e6 - 5.65827e6i) q^{54} -2.29387e6i q^{56} +(949019. - 3.23091e6i) q^{57} -1.27414e7i q^{58} +1.54958e7i q^{59} -8.68344e6 q^{61} -3.50114e6 q^{62} +(2.02210e6 - 3.14512e6i) q^{63} +1.61828e7 q^{64} +(8.32037e6 + 2.44395e6i) q^{66} -2.87523e7i q^{67} +1.28676e6 q^{68} +(3.95472e6 - 1.34638e7i) q^{69} -3.73955e7i q^{71} +(2.22136e7 + 1.42818e7i) q^{72} +3.75089e7i q^{73} -4.41378e7i q^{74} -353942. q^{76} +3.75145e6 q^{77} +(3.56621e7 + 1.04751e7i) q^{78} -4.22725e7 q^{79} +(1.78672e7 + 3.91635e7i) q^{81} +1.09959e7i q^{82} -7.28474e7 q^{83} +(-377077. - 110759. i) q^{84} -6.85572e7i q^{86} +(6.08847e7 + 1.78837e7i) q^{87} +2.64959e7i q^{88} +5.99236e7i q^{89} +1.60791e7 q^{91} -1.47494e6 q^{92} +(4.91416e6 - 1.67302e7i) q^{93} -1.44276e8 q^{94} +(1.59146e6 - 5.41811e6i) q^{96} +1.15177e7i q^{97} +8.84758e7 q^{98} +(-2.33568e7 + 3.63285e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 3108 q^{4} + 4514 q^{6} + 22414 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 3108 q^{4} + 4514 q^{6} + 22414 q^{9} + 89268 q^{16} + 287868 q^{19} + 1346856 q^{21} + 2033718 q^{24} - 6028120 q^{31} - 9954292 q^{34} + 9001054 q^{36} + 15026564 q^{39} - 27877272 q^{46} - 17907092 q^{49} + 12418574 q^{51} + 17772544 q^{54} + 3040440 q^{61} + 9073996 q^{64} + 20930590 q^{66} - 22789956 q^{69} - 59058092 q^{76} - 17099792 q^{79} + 45225890 q^{81} + 273766584 q^{84} - 214448528 q^{91} - 712237192 q^{94} + 1050848002 q^{96} + 764842670 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 16.2639 1.01649 0.508246 0.861212i \(-0.330294\pi\)
0.508246 + 0.861212i \(0.330294\pi\)
\(3\) −22.8278 + 77.7167i −0.281825 + 0.959466i
\(4\) 8.51375 0.0332569
\(5\) 0 0
\(6\) −371.269 + 1263.98i −0.286473 + 0.975290i
\(7\) 569.895i 0.237357i 0.992933 + 0.118679i \(0.0378658\pi\)
−0.992933 + 0.118679i \(0.962134\pi\)
\(8\) −4025.09 −0.982687
\(9\) −5518.78 3548.20i −0.841150 0.540802i
\(10\) 0 0
\(11\) 6582.70i 0.449607i −0.974404 0.224804i \(-0.927826\pi\)
0.974404 0.224804i \(-0.0721741\pi\)
\(12\) −194.350 + 661.661i −0.00937260 + 0.0319088i
\(13\) 28214.2i 0.987858i −0.869502 0.493929i \(-0.835560\pi\)
0.869502 0.493929i \(-0.164440\pi\)
\(14\) 9268.70i 0.241272i
\(15\) 0 0
\(16\) −67643.0 −1.03215
\(17\) 151139. 1.80960 0.904798 0.425840i \(-0.140021\pi\)
0.904798 + 0.425840i \(0.140021\pi\)
\(18\) −89756.8 57707.6i −0.855022 0.549721i
\(19\) −41572.9 −0.319004 −0.159502 0.987198i \(-0.550989\pi\)
−0.159502 + 0.987198i \(0.550989\pi\)
\(20\) 0 0
\(21\) −44290.4 13009.4i −0.227736 0.0668931i
\(22\) 107060.i 0.457022i
\(23\) −173241. −0.619071 −0.309536 0.950888i \(-0.600174\pi\)
−0.309536 + 0.950888i \(0.600174\pi\)
\(24\) 91883.9 312817.i 0.276945 0.942855i
\(25\) 0 0
\(26\) 458873.i 1.00415i
\(27\) 401737. 347904.i 0.755938 0.654643i
\(28\) 4851.94i 0.00789375i
\(29\) 783419.i 1.10765i −0.832634 0.553824i \(-0.813168\pi\)
0.832634 0.553824i \(-0.186832\pi\)
\(30\) 0 0
\(31\) −215271. −0.233098 −0.116549 0.993185i \(-0.537183\pi\)
−0.116549 + 0.993185i \(0.537183\pi\)
\(32\) −69716.1 −0.0664864
\(33\) 511586. + 150269.i 0.431383 + 0.126710i
\(34\) 2.45811e6 1.83944
\(35\) 0 0
\(36\) −46985.6 30208.5i −0.0279740 0.0179854i
\(37\) 2.71385e6i 1.44804i −0.689781 0.724018i \(-0.742293\pi\)
0.689781 0.724018i \(-0.257707\pi\)
\(38\) −676137. −0.324265
\(39\) 2.19272e6 + 644068.i 0.947816 + 0.278403i
\(40\) 0 0
\(41\) 676092.i 0.239260i 0.992819 + 0.119630i \(0.0381709\pi\)
−0.992819 + 0.119630i \(0.961829\pi\)
\(42\) −720333. 211584.i −0.231492 0.0679963i
\(43\) 4.21531e6i 1.23298i −0.787364 0.616489i \(-0.788555\pi\)
0.787364 0.616489i \(-0.211445\pi\)
\(44\) 56043.5i 0.0149525i
\(45\) 0 0
\(46\) −2.81758e6 −0.629281
\(47\) −8.87092e6 −1.81793 −0.908965 0.416872i \(-0.863126\pi\)
−0.908965 + 0.416872i \(0.863126\pi\)
\(48\) 1.54414e6 5.25700e6i 0.290886 0.990314i
\(49\) 5.44002e6 0.943662
\(50\) 0 0
\(51\) −3.45018e6 + 1.17461e7i −0.509989 + 1.73625i
\(52\) 240209.i 0.0328531i
\(53\) −6.53406e6 −0.828094 −0.414047 0.910255i \(-0.635885\pi\)
−0.414047 + 0.910255i \(0.635885\pi\)
\(54\) 6.53379e6 5.65827e6i 0.768405 0.665440i
\(55\) 0 0
\(56\) 2.29387e6i 0.233248i
\(57\) 949019. 3.23091e6i 0.0899032 0.306074i
\(58\) 1.27414e7i 1.12592i
\(59\) 1.54958e7i 1.27881i 0.768871 + 0.639403i \(0.220819\pi\)
−0.768871 + 0.639403i \(0.779181\pi\)
\(60\) 0 0
\(61\) −8.68344e6 −0.627152 −0.313576 0.949563i \(-0.601527\pi\)
−0.313576 + 0.949563i \(0.601527\pi\)
\(62\) −3.50114e6 −0.236942
\(63\) 2.02210e6 3.14512e6i 0.128363 0.199653i
\(64\) 1.61828e7 0.964568
\(65\) 0 0
\(66\) 8.32037e6 + 2.44395e6i 0.438497 + 0.128800i
\(67\) 2.87523e7i 1.42684i −0.700739 0.713418i \(-0.747146\pi\)
0.700739 0.713418i \(-0.252854\pi\)
\(68\) 1.28676e6 0.0601815
\(69\) 3.95472e6 1.34638e7i 0.174470 0.593978i
\(70\) 0 0
\(71\) 3.73955e7i 1.47159i −0.677207 0.735793i \(-0.736810\pi\)
0.677207 0.735793i \(-0.263190\pi\)
\(72\) 2.22136e7 + 1.42818e7i 0.826587 + 0.531439i
\(73\) 3.75089e7i 1.32082i 0.750907 + 0.660408i \(0.229617\pi\)
−0.750907 + 0.660408i \(0.770383\pi\)
\(74\) 4.41378e7i 1.47192i
\(75\) 0 0
\(76\) −353942. −0.0106091
\(77\) 3.75145e6 0.106718
\(78\) 3.56621e7 + 1.04751e7i 0.963448 + 0.282994i
\(79\) −4.22725e7 −1.08530 −0.542649 0.839959i \(-0.682579\pi\)
−0.542649 + 0.839959i \(0.682579\pi\)
\(80\) 0 0
\(81\) 1.78672e7 + 3.91635e7i 0.415066 + 0.909791i
\(82\) 1.09959e7i 0.243206i
\(83\) −7.28474e7 −1.53498 −0.767488 0.641064i \(-0.778493\pi\)
−0.767488 + 0.641064i \(0.778493\pi\)
\(84\) −377077. 110759.i −0.00757379 0.00222465i
\(85\) 0 0
\(86\) 6.85572e7i 1.25331i
\(87\) 6.08847e7 + 1.78837e7i 1.06275 + 0.312163i
\(88\) 2.64959e7i 0.441823i
\(89\) 5.99236e7i 0.955077i 0.878611 + 0.477538i \(0.158471\pi\)
−0.878611 + 0.477538i \(0.841529\pi\)
\(90\) 0 0
\(91\) 1.60791e7 0.234475
\(92\) −1.47494e6 −0.0205884
\(93\) 4.91416e6 1.67302e7i 0.0656928 0.223650i
\(94\) −1.44276e8 −1.84791
\(95\) 0 0
\(96\) 1.59146e6 5.41811e6i 0.0187375 0.0637915i
\(97\) 1.15177e7i 0.130100i 0.997882 + 0.0650500i \(0.0207207\pi\)
−0.997882 + 0.0650500i \(0.979279\pi\)
\(98\) 8.84758e7 0.959225
\(99\) −2.33568e7 + 3.63285e7i −0.243149 + 0.378187i
\(100\) 0 0
\(101\) 9.81566e7i 0.943266i 0.881795 + 0.471633i \(0.156335\pi\)
−0.881795 + 0.471633i \(0.843665\pi\)
\(102\) −5.61133e7 + 1.91036e8i −0.518400 + 1.76488i
\(103\) 1.66920e7i 0.148306i 0.997247 + 0.0741529i \(0.0236253\pi\)
−0.997247 + 0.0741529i \(0.976375\pi\)
\(104\) 1.13565e8i 0.970755i
\(105\) 0 0
\(106\) −1.06269e8 −0.841751
\(107\) −4.28172e7 −0.326651 −0.163325 0.986572i \(-0.552222\pi\)
−0.163325 + 0.986572i \(0.552222\pi\)
\(108\) 3.42029e6 2.96197e6i 0.0251401 0.0217714i
\(109\) −1.49703e8 −1.06053 −0.530266 0.847831i \(-0.677908\pi\)
−0.530266 + 0.847831i \(0.677908\pi\)
\(110\) 0 0
\(111\) 2.10912e8 + 6.19513e7i 1.38934 + 0.408092i
\(112\) 3.85494e7i 0.244988i
\(113\) −1.27819e7 −0.0783937 −0.0391969 0.999232i \(-0.512480\pi\)
−0.0391969 + 0.999232i \(0.512480\pi\)
\(114\) 1.54347e7 5.25472e7i 0.0913860 0.311122i
\(115\) 0 0
\(116\) 6.66983e6i 0.0368369i
\(117\) −1.00110e8 + 1.55708e8i −0.534236 + 0.830937i
\(118\) 2.52021e8i 1.29990i
\(119\) 8.61335e7i 0.429521i
\(120\) 0 0
\(121\) 1.71027e8 0.797853
\(122\) −1.41226e8 −0.637495
\(123\) −5.25437e7 1.54337e7i −0.229562 0.0674295i
\(124\) −1.83276e6 −0.00775211
\(125\) 0 0
\(126\) 3.28872e7 5.11519e7i 0.130480 0.202946i
\(127\) 2.68115e8i 1.03064i −0.856998 0.515320i \(-0.827673\pi\)
0.856998 0.515320i \(-0.172327\pi\)
\(128\) 2.81042e8 1.04696
\(129\) 3.27600e8 + 9.62261e7i 1.18300 + 0.347484i
\(130\) 0 0
\(131\) 5.50651e6i 0.0186978i −0.999956 0.00934892i \(-0.997024\pi\)
0.999956 0.00934892i \(-0.00297590\pi\)
\(132\) 4.35552e6 + 1.27935e6i 0.0143464 + 0.00421399i
\(133\) 2.36922e7i 0.0757179i
\(134\) 4.67624e8i 1.45037i
\(135\) 0 0
\(136\) −6.08349e8 −1.77827
\(137\) 5.57045e8 1.58128 0.790639 0.612283i \(-0.209749\pi\)
0.790639 + 0.612283i \(0.209749\pi\)
\(138\) 6.43191e7 2.18973e8i 0.177347 0.603774i
\(139\) 3.34413e7 0.0895827 0.0447914 0.998996i \(-0.485738\pi\)
0.0447914 + 0.998996i \(0.485738\pi\)
\(140\) 0 0
\(141\) 2.02504e8 6.89419e8i 0.512338 1.74424i
\(142\) 6.08195e8i 1.49586i
\(143\) −1.85726e8 −0.444148
\(144\) 3.73307e8 + 2.40011e8i 0.868193 + 0.558190i
\(145\) 0 0
\(146\) 6.10040e8i 1.34260i
\(147\) −1.24184e8 + 4.22781e8i −0.265947 + 0.905411i
\(148\) 2.31051e7i 0.0481571i
\(149\) 4.46572e8i 0.906037i −0.891501 0.453019i \(-0.850347\pi\)
0.891501 0.453019i \(-0.149653\pi\)
\(150\) 0 0
\(151\) −2.41495e8 −0.464515 −0.232257 0.972654i \(-0.574611\pi\)
−0.232257 + 0.972654i \(0.574611\pi\)
\(152\) 1.67335e8 0.313481
\(153\) −8.34105e8 5.36273e8i −1.52214 0.978634i
\(154\) 6.10130e7 0.108478
\(155\) 0 0
\(156\) 1.86683e7 + 5.48344e6i 0.0315214 + 0.00925880i
\(157\) 1.12488e9i 1.85143i −0.378226 0.925713i \(-0.623466\pi\)
0.378226 0.925713i \(-0.376534\pi\)
\(158\) −6.87514e8 −1.10320
\(159\) 1.49158e8 5.07806e8i 0.233377 0.794528i
\(160\) 0 0
\(161\) 9.87294e7i 0.146941i
\(162\) 2.90590e8 + 6.36951e8i 0.421911 + 0.924796i
\(163\) 1.05083e9i 1.48861i −0.667838 0.744307i \(-0.732780\pi\)
0.667838 0.744307i \(-0.267220\pi\)
\(164\) 5.75609e6i 0.00795705i
\(165\) 0 0
\(166\) −1.18478e9 −1.56029
\(167\) −1.52565e8 −0.196150 −0.0980751 0.995179i \(-0.531269\pi\)
−0.0980751 + 0.995179i \(0.531269\pi\)
\(168\) 1.78272e8 + 5.23641e7i 0.223793 + 0.0657350i
\(169\) 1.96888e7 0.0241364
\(170\) 0 0
\(171\) 2.29432e8 + 1.47509e8i 0.268330 + 0.172518i
\(172\) 3.58881e7i 0.0410050i
\(173\) 1.48867e9 1.66193 0.830967 0.556321i \(-0.187788\pi\)
0.830967 + 0.556321i \(0.187788\pi\)
\(174\) 9.90222e8 + 2.90859e8i 1.08028 + 0.317311i
\(175\) 0 0
\(176\) 4.45274e8i 0.464063i
\(177\) −1.20428e9 3.53734e8i −1.22697 0.360399i
\(178\) 9.74591e8i 0.970828i
\(179\) 6.73543e8i 0.656074i 0.944665 + 0.328037i \(0.106387\pi\)
−0.944665 + 0.328037i \(0.893613\pi\)
\(180\) 0 0
\(181\) 9.31938e8 0.868306 0.434153 0.900839i \(-0.357048\pi\)
0.434153 + 0.900839i \(0.357048\pi\)
\(182\) 2.61509e8 0.238342
\(183\) 1.98224e8 6.74849e8i 0.176747 0.601731i
\(184\) 6.97312e8 0.608353
\(185\) 0 0
\(186\) 7.99233e7 2.72097e8i 0.0667762 0.227338i
\(187\) 9.94905e8i 0.813608i
\(188\) −7.55248e7 −0.0604586
\(189\) 1.98269e8 + 2.28947e8i 0.155384 + 0.179427i
\(190\) 0 0
\(191\) 6.44104e7i 0.0483974i 0.999707 + 0.0241987i \(0.00770344\pi\)
−0.999707 + 0.0241987i \(0.992297\pi\)
\(192\) −3.69417e8 + 1.25767e9i −0.271839 + 0.925470i
\(193\) 9.15124e8i 0.659554i 0.944059 + 0.329777i \(0.106974\pi\)
−0.944059 + 0.329777i \(0.893026\pi\)
\(194\) 1.87322e8i 0.132246i
\(195\) 0 0
\(196\) 4.63150e7 0.0313832
\(197\) −1.99042e9 −1.32154 −0.660769 0.750589i \(-0.729770\pi\)
−0.660769 + 0.750589i \(0.729770\pi\)
\(198\) −3.79872e8 + 5.90842e8i −0.247159 + 0.384424i
\(199\) −2.33793e9 −1.49080 −0.745400 0.666618i \(-0.767741\pi\)
−0.745400 + 0.666618i \(0.767741\pi\)
\(200\) 0 0
\(201\) 2.23454e9 + 6.56352e8i 1.36900 + 0.402117i
\(202\) 1.59641e9i 0.958823i
\(203\) 4.46466e8 0.262908
\(204\) −2.93740e7 + 1.00003e8i −0.0169606 + 0.0577421i
\(205\) 0 0
\(206\) 2.71476e8i 0.150752i
\(207\) 9.56082e8 + 6.14696e8i 0.520732 + 0.334795i
\(208\) 1.90850e9i 1.01962i
\(209\) 2.73662e8i 0.143427i
\(210\) 0 0
\(211\) −3.72705e7 −0.0188034 −0.00940168 0.999956i \(-0.502993\pi\)
−0.00940168 + 0.999956i \(0.502993\pi\)
\(212\) −5.56294e7 −0.0275398
\(213\) 2.90625e9 + 8.53656e8i 1.41194 + 0.414729i
\(214\) −6.96374e8 −0.332038
\(215\) 0 0
\(216\) −1.61702e9 + 1.40034e9i −0.742851 + 0.643309i
\(217\) 1.22682e8i 0.0553275i
\(218\) −2.43475e9 −1.07802
\(219\) −2.91507e9 8.56245e8i −1.26728 0.372239i
\(220\) 0 0
\(221\) 4.26428e9i 1.78762i
\(222\) 3.43024e9 + 1.00757e9i 1.41225 + 0.414823i
\(223\) 2.51046e9i 1.01516i −0.861606 0.507578i \(-0.830541\pi\)
0.861606 0.507578i \(-0.169459\pi\)
\(224\) 3.97308e7i 0.0157810i
\(225\) 0 0
\(226\) −2.07883e8 −0.0796866
\(227\) 1.11767e9 0.420930 0.210465 0.977601i \(-0.432502\pi\)
0.210465 + 0.977601i \(0.432502\pi\)
\(228\) 8.07971e6 2.75072e7i 0.00298990 0.0101790i
\(229\) −3.29155e9 −1.19690 −0.598450 0.801160i \(-0.704217\pi\)
−0.598450 + 0.801160i \(0.704217\pi\)
\(230\) 0 0
\(231\) −8.56372e7 + 2.91550e8i −0.0300756 + 0.102392i
\(232\) 3.15333e9i 1.08847i
\(233\) −1.74654e9 −0.592591 −0.296296 0.955096i \(-0.595751\pi\)
−0.296296 + 0.955096i \(0.595751\pi\)
\(234\) −1.62817e9 + 2.53242e9i −0.543047 + 0.844641i
\(235\) 0 0
\(236\) 1.31927e8i 0.0425291i
\(237\) 9.64988e8 3.28528e9i 0.305864 1.04131i
\(238\) 1.40086e9i 0.436605i
\(239\) 3.20404e9i 0.981988i 0.871163 + 0.490994i \(0.163366\pi\)
−0.871163 + 0.490994i \(0.836634\pi\)
\(240\) 0 0
\(241\) 2.32540e9 0.689334 0.344667 0.938725i \(-0.387992\pi\)
0.344667 + 0.938725i \(0.387992\pi\)
\(242\) 2.78156e9 0.811012
\(243\) −3.45153e9 + 4.94565e8i −0.989890 + 0.141840i
\(244\) −7.39287e7 −0.0208571
\(245\) 0 0
\(246\) −8.54564e8 2.51012e8i −0.233348 0.0685415i
\(247\) 1.17295e9i 0.315131i
\(248\) 8.66484e8 0.229062
\(249\) 1.66294e9 5.66146e9i 0.432594 1.47276i
\(250\) 0 0
\(251\) 3.38503e9i 0.852840i −0.904525 0.426420i \(-0.859775\pi\)
0.904525 0.426420i \(-0.140225\pi\)
\(252\) 1.72157e7 2.67768e7i 0.00426896 0.00663983i
\(253\) 1.14040e9i 0.278339i
\(254\) 4.36059e9i 1.04764i
\(255\) 0 0
\(256\) 4.28043e8 0.0996614
\(257\) 9.71066e8 0.222595 0.111298 0.993787i \(-0.464499\pi\)
0.111298 + 0.993787i \(0.464499\pi\)
\(258\) 5.32804e9 + 1.56501e9i 1.20251 + 0.353214i
\(259\) 1.54661e9 0.343702
\(260\) 0 0
\(261\) −2.77973e9 + 4.32352e9i −0.599019 + 0.931698i
\(262\) 8.95573e7i 0.0190062i
\(263\) 2.06605e8 0.0431835 0.0215918 0.999767i \(-0.493127\pi\)
0.0215918 + 0.999767i \(0.493127\pi\)
\(264\) −2.05918e9 6.04844e8i −0.423914 0.124517i
\(265\) 0 0
\(266\) 3.85327e8i 0.0769667i
\(267\) −4.65707e9 1.36792e9i −0.916363 0.269164i
\(268\) 2.44790e8i 0.0474520i
\(269\) 3.12793e9i 0.597376i 0.954351 + 0.298688i \(0.0965489\pi\)
−0.954351 + 0.298688i \(0.903451\pi\)
\(270\) 0 0
\(271\) 4.61051e9 0.854814 0.427407 0.904059i \(-0.359427\pi\)
0.427407 + 0.904059i \(0.359427\pi\)
\(272\) −1.02235e10 −1.86778
\(273\) −3.67051e8 + 1.24962e9i −0.0660809 + 0.224971i
\(274\) 9.05972e9 1.60736
\(275\) 0 0
\(276\) 3.36695e7 1.14627e8i 0.00580231 0.0197538i
\(277\) 1.77445e9i 0.301401i 0.988579 + 0.150700i \(0.0481529\pi\)
−0.988579 + 0.150700i \(0.951847\pi\)
\(278\) 5.43886e8 0.0910602
\(279\) 1.18803e9 + 7.63825e8i 0.196070 + 0.126060i
\(280\) 0 0
\(281\) 7.80582e7i 0.0125197i −0.999980 0.00625984i \(-0.998007\pi\)
0.999980 0.00625984i \(-0.00199258\pi\)
\(282\) 3.29349e9 1.12126e10i 0.520787 1.77301i
\(283\) 8.12145e9i 1.26616i −0.774088 0.633079i \(-0.781791\pi\)
0.774088 0.633079i \(-0.218209\pi\)
\(284\) 3.18376e8i 0.0489403i
\(285\) 0 0
\(286\) −3.02062e9 −0.451473
\(287\) −3.85301e8 −0.0567902
\(288\) 3.84748e8 + 2.47367e8i 0.0559250 + 0.0359560i
\(289\) 1.58673e10 2.27464
\(290\) 0 0
\(291\) −8.95115e8 2.62923e8i −0.124826 0.0366654i
\(292\) 3.19341e8i 0.0439262i
\(293\) 2.52625e9 0.342773 0.171386 0.985204i \(-0.445175\pi\)
0.171386 + 0.985204i \(0.445175\pi\)
\(294\) −2.01971e9 + 6.87605e9i −0.270333 + 0.920344i
\(295\) 0 0
\(296\) 1.09235e10i 1.42297i
\(297\) −2.29015e9 2.64451e9i −0.294332 0.339875i
\(298\) 7.26299e9i 0.920980i
\(299\) 4.88787e9i 0.611554i
\(300\) 0 0
\(301\) 2.40228e9 0.292656
\(302\) −3.92764e9 −0.472176
\(303\) −7.62841e9 2.24070e9i −0.905032 0.265836i
\(304\) 2.81212e9 0.329260
\(305\) 0 0
\(306\) −1.35658e10 8.72188e9i −1.54725 0.994774i
\(307\) 1.03150e10i 1.16123i 0.814180 + 0.580613i \(0.197187\pi\)
−0.814180 + 0.580613i \(0.802813\pi\)
\(308\) 3.19389e7 0.00354909
\(309\) −1.29724e9 3.81040e8i −0.142294 0.0417962i
\(310\) 0 0
\(311\) 1.72354e10i 1.84239i 0.389106 + 0.921193i \(0.372784\pi\)
−0.389106 + 0.921193i \(0.627216\pi\)
\(312\) −8.82587e9 2.59243e9i −0.931407 0.273583i
\(313\) 5.42800e9i 0.565539i −0.959188 0.282770i \(-0.908747\pi\)
0.959188 0.282770i \(-0.0912532\pi\)
\(314\) 1.82949e10i 1.88196i
\(315\) 0 0
\(316\) −3.59897e8 −0.0360936
\(317\) 1.16981e10 1.15845 0.579226 0.815167i \(-0.303355\pi\)
0.579226 + 0.815167i \(0.303355\pi\)
\(318\) 2.42589e9 8.25889e9i 0.237226 0.807632i
\(319\) −5.15701e9 −0.498007
\(320\) 0 0
\(321\) 9.77423e8 3.32761e9i 0.0920582 0.313410i
\(322\) 1.60572e9i 0.149364i
\(323\) −6.28331e9 −0.577269
\(324\) 1.52117e8 + 3.33429e8i 0.0138038 + 0.0302568i
\(325\) 0 0
\(326\) 1.70906e10i 1.51316i
\(327\) 3.41738e9 1.16344e10i 0.298884 1.01754i
\(328\) 2.72133e9i 0.235118i
\(329\) 5.05549e9i 0.431499i
\(330\) 0 0
\(331\) −6.03632e9 −0.502875 −0.251438 0.967873i \(-0.580903\pi\)
−0.251438 + 0.967873i \(0.580903\pi\)
\(332\) −6.20205e8 −0.0510485
\(333\) −9.62930e9 + 1.49772e10i −0.783101 + 1.21801i
\(334\) −2.48130e9 −0.199385
\(335\) 0 0
\(336\) 2.99593e9 + 8.79998e8i 0.235058 + 0.0690438i
\(337\) 1.35475e9i 0.105037i 0.998620 + 0.0525183i \(0.0167248\pi\)
−0.998620 + 0.0525183i \(0.983275\pi\)
\(338\) 3.20216e8 0.0245345
\(339\) 2.91782e8 9.93367e8i 0.0220933 0.0752161i
\(340\) 0 0
\(341\) 1.41706e9i 0.104803i
\(342\) 3.73146e9 + 2.39907e9i 0.272756 + 0.175363i
\(343\) 6.38557e9i 0.461342i
\(344\) 1.69670e10i 1.21163i
\(345\) 0 0
\(346\) 2.42115e10 1.68934
\(347\) 2.47345e10 1.70602 0.853012 0.521891i \(-0.174773\pi\)
0.853012 + 0.521891i \(0.174773\pi\)
\(348\) 5.18358e8 + 1.52258e8i 0.0353437 + 0.0103815i
\(349\) 9.08306e9 0.612253 0.306126 0.951991i \(-0.400967\pi\)
0.306126 + 0.951991i \(0.400967\pi\)
\(350\) 0 0
\(351\) −9.81584e9 1.13347e10i −0.646694 0.746760i
\(352\) 4.58920e8i 0.0298928i
\(353\) 1.66294e10 1.07097 0.535485 0.844545i \(-0.320129\pi\)
0.535485 + 0.844545i \(0.320129\pi\)
\(354\) −1.95863e10 5.75309e9i −1.24721 0.366343i
\(355\) 0 0
\(356\) 5.10175e8i 0.0317628i
\(357\) −6.69401e9 1.96624e9i −0.412111 0.121050i
\(358\) 1.09544e10i 0.666894i
\(359\) 6.51832e9i 0.392426i −0.980561 0.196213i \(-0.937136\pi\)
0.980561 0.196213i \(-0.0628644\pi\)
\(360\) 0 0
\(361\) −1.52553e10 −0.898236
\(362\) 1.51569e10 0.882626
\(363\) −3.90417e9 + 1.32917e10i −0.224855 + 0.765513i
\(364\) 1.36894e8 0.00779791
\(365\) 0 0
\(366\) 3.22389e9 1.09757e10i 0.179662 0.611655i
\(367\) 1.72068e10i 0.948498i 0.880391 + 0.474249i \(0.157280\pi\)
−0.880391 + 0.474249i \(0.842720\pi\)
\(368\) 1.17186e10 0.638975
\(369\) 2.39891e9 3.73121e9i 0.129393 0.201254i
\(370\) 0 0
\(371\) 3.72373e9i 0.196554i
\(372\) 4.18380e7 1.42436e8i 0.00218474 0.00743789i
\(373\) 1.47580e10i 0.762418i 0.924489 + 0.381209i \(0.124492\pi\)
−0.924489 + 0.381209i \(0.875508\pi\)
\(374\) 1.61810e10i 0.827026i
\(375\) 0 0
\(376\) 3.57062e10 1.78646
\(377\) −2.21035e10 −1.09420
\(378\) 3.22462e9 + 3.72357e9i 0.157947 + 0.182387i
\(379\) −3.28781e10 −1.59349 −0.796746 0.604315i \(-0.793447\pi\)
−0.796746 + 0.604315i \(0.793447\pi\)
\(380\) 0 0
\(381\) 2.08370e10 + 6.12048e9i 0.988863 + 0.290460i
\(382\) 1.04756e9i 0.0491956i
\(383\) 1.11696e10 0.519089 0.259544 0.965731i \(-0.416428\pi\)
0.259544 + 0.965731i \(0.416428\pi\)
\(384\) −6.41557e9 + 2.18417e10i −0.295060 + 1.00452i
\(385\) 0 0
\(386\) 1.48835e10i 0.670432i
\(387\) −1.49568e10 + 2.32634e10i −0.666797 + 1.03712i
\(388\) 9.80585e7i 0.00432672i
\(389\) 3.14195e10i 1.37215i 0.727533 + 0.686073i \(0.240667\pi\)
−0.727533 + 0.686073i \(0.759333\pi\)
\(390\) 0 0
\(391\) −2.61836e10 −1.12027
\(392\) −2.18966e10 −0.927324
\(393\) 4.27948e8 + 1.25702e8i 0.0179399 + 0.00526951i
\(394\) −3.23719e10 −1.34333
\(395\) 0 0
\(396\) −1.98854e8 + 3.09292e8i −0.00808636 + 0.0125773i
\(397\) 8.73430e9i 0.351614i 0.984425 + 0.175807i \(0.0562534\pi\)
−0.984425 + 0.175807i \(0.943747\pi\)
\(398\) −3.80238e10 −1.51539
\(399\) 1.84128e9 + 5.40841e8i 0.0726488 + 0.0213392i
\(400\) 0 0
\(401\) 1.27867e9i 0.0494516i 0.999694 + 0.0247258i \(0.00787127\pi\)
−0.999694 + 0.0247258i \(0.992129\pi\)
\(402\) 3.63422e10 + 1.06748e10i 1.39158 + 0.408749i
\(403\) 6.07370e9i 0.230268i
\(404\) 8.35682e8i 0.0313701i
\(405\) 0 0
\(406\) 7.26127e9 0.267244
\(407\) −1.78645e10 −0.651047
\(408\) 1.38873e10 4.72789e10i 0.501160 1.70619i
\(409\) −1.02810e10 −0.367401 −0.183701 0.982982i \(-0.558808\pi\)
−0.183701 + 0.982982i \(0.558808\pi\)
\(410\) 0 0
\(411\) −1.27161e10 + 4.32917e10i −0.445643 + 1.51718i
\(412\) 1.42111e8i 0.00493219i
\(413\) −8.83095e9 −0.303534
\(414\) 1.55496e10 + 9.99734e9i 0.529320 + 0.340317i
\(415\) 0 0
\(416\) 1.96698e9i 0.0656792i
\(417\) −7.63392e8 + 2.59895e9i −0.0252466 + 0.0859516i
\(418\) 4.45081e9i 0.145792i
\(419\) 3.60565e10i 1.16984i 0.811090 + 0.584922i \(0.198875\pi\)
−0.811090 + 0.584922i \(0.801125\pi\)
\(420\) 0 0
\(421\) −3.63986e10 −1.15866 −0.579331 0.815092i \(-0.696686\pi\)
−0.579331 + 0.815092i \(0.696686\pi\)
\(422\) −6.06163e8 −0.0191135
\(423\) 4.89567e10 + 3.14758e10i 1.52915 + 0.983141i
\(424\) 2.63002e10 0.813757
\(425\) 0 0
\(426\) 4.72670e10 + 1.38838e10i 1.43522 + 0.421569i
\(427\) 4.94865e9i 0.148859i
\(428\) −3.64535e8 −0.0108634
\(429\) 4.23971e9 1.44340e10i 0.125172 0.426145i
\(430\) 0 0
\(431\) 3.03555e10i 0.879686i −0.898075 0.439843i \(-0.855034\pi\)
0.898075 0.439843i \(-0.144966\pi\)
\(432\) −2.71747e10 + 2.35333e10i −0.780242 + 0.675690i
\(433\) 3.45811e10i 0.983757i −0.870664 0.491878i \(-0.836310\pi\)
0.870664 0.491878i \(-0.163690\pi\)
\(434\) 1.99528e9i 0.0562400i
\(435\) 0 0
\(436\) −1.27453e9 −0.0352700
\(437\) 7.20216e9 0.197486
\(438\) −4.74103e10 1.39259e10i −1.28818 0.378378i
\(439\) 1.76997e9 0.0476549 0.0238275 0.999716i \(-0.492415\pi\)
0.0238275 + 0.999716i \(0.492415\pi\)
\(440\) 0 0
\(441\) −3.00223e10 1.93023e10i −0.793761 0.510334i
\(442\) 6.93537e10i 1.81711i
\(443\) 3.19676e10 0.830033 0.415017 0.909814i \(-0.363776\pi\)
0.415017 + 0.909814i \(0.363776\pi\)
\(444\) 1.79565e9 + 5.27438e8i 0.0462051 + 0.0135719i
\(445\) 0 0
\(446\) 4.08297e10i 1.03190i
\(447\) 3.47061e10 + 1.01942e10i 0.869312 + 0.255344i
\(448\) 9.22247e9i 0.228947i
\(449\) 8.00746e10i 1.97020i −0.171994 0.985098i \(-0.555021\pi\)
0.171994 0.985098i \(-0.444979\pi\)
\(450\) 0 0
\(451\) 4.45051e9 0.107573
\(452\) −1.08822e8 −0.00260713
\(453\) 5.51279e9 1.87682e10i 0.130912 0.445686i
\(454\) 1.81777e10 0.427873
\(455\) 0 0
\(456\) −3.81988e9 + 1.30047e10i −0.0883468 + 0.300775i
\(457\) 5.45219e10i 1.24999i −0.780629 0.624994i \(-0.785101\pi\)
0.780629 0.624994i \(-0.214899\pi\)
\(458\) −5.35333e10 −1.21664
\(459\) 6.07182e10 5.25820e10i 1.36794 1.18464i
\(460\) 0 0
\(461\) 3.66539e8i 0.00811552i 0.999992 + 0.00405776i \(0.00129163\pi\)
−0.999992 + 0.00405776i \(0.998708\pi\)
\(462\) −1.39279e9 + 4.74174e9i −0.0305716 + 0.104081i
\(463\) 3.22822e10i 0.702488i 0.936284 + 0.351244i \(0.114241\pi\)
−0.936284 + 0.351244i \(0.885759\pi\)
\(464\) 5.29928e10i 1.14326i
\(465\) 0 0
\(466\) −2.84055e10 −0.602365
\(467\) −2.11777e10 −0.445258 −0.222629 0.974903i \(-0.571464\pi\)
−0.222629 + 0.974903i \(0.571464\pi\)
\(468\) −8.52310e8 + 1.32566e9i −0.0177670 + 0.0276343i
\(469\) 1.63858e10 0.338670
\(470\) 0 0
\(471\) 8.74218e10 + 2.56785e10i 1.77638 + 0.521778i
\(472\) 6.23718e10i 1.25667i
\(473\) −2.77481e10 −0.554356
\(474\) 1.56944e10 5.34314e10i 0.310908 1.05848i
\(475\) 0 0
\(476\) 7.33319e8i 0.0142845i
\(477\) 3.60601e10 + 2.31842e10i 0.696551 + 0.447835i
\(478\) 5.21101e10i 0.998184i
\(479\) 4.69016e10i 0.890934i −0.895298 0.445467i \(-0.853038\pi\)
0.895298 0.445467i \(-0.146962\pi\)
\(480\) 0 0
\(481\) −7.65692e10 −1.43045
\(482\) 3.78201e10 0.700703
\(483\) 7.67293e9 + 2.25377e9i 0.140985 + 0.0414116i
\(484\) 1.45608e9 0.0265341
\(485\) 0 0
\(486\) −5.61353e10 + 8.04354e9i −1.00622 + 0.144179i
\(487\) 1.34767e10i 0.239590i −0.992799 0.119795i \(-0.961776\pi\)
0.992799 0.119795i \(-0.0382237\pi\)
\(488\) 3.49516e10 0.616294
\(489\) 8.16671e10 + 2.39881e10i 1.42827 + 0.419528i
\(490\) 0 0
\(491\) 8.27160e10i 1.42319i −0.702589 0.711596i \(-0.747973\pi\)
0.702589 0.711596i \(-0.252027\pi\)
\(492\) −4.47344e8 1.31399e8i −0.00763451 0.00224249i
\(493\) 1.18405e11i 2.00440i
\(494\) 1.90767e10i 0.320328i
\(495\) 0 0
\(496\) 1.45616e10 0.240592
\(497\) 2.13115e10 0.349291
\(498\) 2.70459e10 9.20773e10i 0.439728 1.49705i
\(499\) −1.96950e10 −0.317653 −0.158827 0.987307i \(-0.550771\pi\)
−0.158827 + 0.987307i \(0.550771\pi\)
\(500\) 0 0
\(501\) 3.48272e9 1.18569e10i 0.0552800 0.188199i
\(502\) 5.50537e10i 0.866906i
\(503\) −5.14640e10 −0.803955 −0.401978 0.915649i \(-0.631677\pi\)
−0.401978 + 0.915649i \(0.631677\pi\)
\(504\) −8.13914e9 + 1.26594e10i −0.126141 + 0.196196i
\(505\) 0 0
\(506\) 1.85473e10i 0.282929i
\(507\) −4.49452e8 + 1.53015e9i −0.00680223 + 0.0231580i
\(508\) 2.28267e9i 0.0342758i
\(509\) 7.84617e8i 0.0116893i 0.999983 + 0.00584463i \(0.00186041\pi\)
−0.999983 + 0.00584463i \(0.998140\pi\)
\(510\) 0 0
\(511\) −2.13761e10 −0.313505
\(512\) −6.49851e10 −0.945657
\(513\) −1.67014e10 + 1.44634e10i −0.241147 + 0.208834i
\(514\) 1.57933e10 0.226267
\(515\) 0 0
\(516\) 2.78910e9 + 8.19246e8i 0.0393429 + 0.0115562i
\(517\) 5.83946e10i 0.817355i
\(518\) 2.51539e10 0.349370
\(519\) −3.39830e10 + 1.15695e11i −0.468374 + 1.59457i
\(520\) 0 0
\(521\) 1.39001e11i 1.88654i 0.332024 + 0.943271i \(0.392269\pi\)
−0.332024 + 0.943271i \(0.607731\pi\)
\(522\) −4.52092e10 + 7.03172e10i −0.608898 + 0.947064i
\(523\) 9.91022e9i 0.132457i 0.997804 + 0.0662287i \(0.0210967\pi\)
−0.997804 + 0.0662287i \(0.978903\pi\)
\(524\) 4.68811e7i 0.000621831i
\(525\) 0 0
\(526\) 3.36020e9 0.0438957
\(527\) −3.25359e10 −0.421814
\(528\) −3.46052e10 1.01646e10i −0.445252 0.130784i
\(529\) −4.82984e10 −0.616751
\(530\) 0 0
\(531\) 5.49821e10 8.55178e10i 0.691582 1.07567i
\(532\) 2.01710e8i 0.00251814i
\(533\) 1.90754e10 0.236355
\(534\) −7.57420e10 2.22478e10i −0.931477 0.273603i
\(535\) 0 0
\(536\) 1.15731e11i 1.40213i
\(537\) −5.23455e10 1.53755e10i −0.629481 0.184898i
\(538\) 5.08722e10i 0.607228i
\(539\) 3.58100e10i 0.424277i
\(540\) 0 0
\(541\) −2.74155e10 −0.320042 −0.160021 0.987114i \(-0.551156\pi\)
−0.160021 + 0.987114i \(0.551156\pi\)
\(542\) 7.49848e10 0.868912
\(543\) −2.12741e10 + 7.24272e10i −0.244710 + 0.833110i
\(544\) −1.05368e10 −0.120314
\(545\) 0 0
\(546\) −5.96967e9 + 2.03236e10i −0.0671707 + 0.228681i
\(547\) 8.62303e10i 0.963187i 0.876395 + 0.481594i \(0.159942\pi\)
−0.876395 + 0.481594i \(0.840058\pi\)
\(548\) 4.74255e9 0.0525883
\(549\) 4.79220e10 + 3.08106e10i 0.527528 + 0.339165i
\(550\) 0 0
\(551\) 3.25690e10i 0.353344i
\(552\) −1.59181e10 + 5.41928e10i −0.171449 + 0.583694i
\(553\) 2.40909e10i 0.257603i
\(554\) 2.88594e10i 0.306372i
\(555\) 0 0
\(556\) 2.84711e8 0.00297924
\(557\) −6.87189e10 −0.713929 −0.356965 0.934118i \(-0.616188\pi\)
−0.356965 + 0.934118i \(0.616188\pi\)
\(558\) 1.93220e10 + 1.24228e10i 0.199304 + 0.128139i
\(559\) −1.18932e11 −1.21801
\(560\) 0 0
\(561\) 7.73208e10 + 2.27115e10i 0.780629 + 0.229295i
\(562\) 1.26953e9i 0.0127262i
\(563\) 9.04024e10 0.899801 0.449901 0.893079i \(-0.351459\pi\)
0.449901 + 0.893079i \(0.351459\pi\)
\(564\) 1.72407e9 5.86954e9i 0.0170387 0.0580080i
\(565\) 0 0
\(566\) 1.32086e11i 1.28704i
\(567\) −2.23191e10 + 1.01824e10i −0.215946 + 0.0985188i
\(568\) 1.50520e11i 1.44611i
\(569\) 1.77922e11i 1.69739i 0.528886 + 0.848693i \(0.322610\pi\)
−0.528886 + 0.848693i \(0.677390\pi\)
\(570\) 0 0
\(571\) 1.96988e11 1.85309 0.926543 0.376189i \(-0.122766\pi\)
0.926543 + 0.376189i \(0.122766\pi\)
\(572\) −1.58122e9 −0.0147710
\(573\) −5.00576e9 1.47035e9i −0.0464357 0.0136396i
\(574\) −6.26650e9 −0.0577268
\(575\) 0 0
\(576\) −8.93092e10 5.74197e10i −0.811346 0.521641i
\(577\) 2.39252e10i 0.215850i −0.994159 0.107925i \(-0.965579\pi\)
0.994159 0.107925i \(-0.0344206\pi\)
\(578\) 2.58064e11 2.31215
\(579\) −7.11204e10 2.08903e10i −0.632820 0.185879i
\(580\) 0 0
\(581\) 4.15153e10i 0.364337i
\(582\) −1.45580e10 4.27614e9i −0.126885 0.0372701i
\(583\) 4.30118e10i 0.372317i
\(584\) 1.50976e11i 1.29795i
\(585\) 0 0
\(586\) 4.10866e10 0.348426
\(587\) 2.02670e11 1.70701 0.853505 0.521085i \(-0.174472\pi\)
0.853505 + 0.521085i \(0.174472\pi\)
\(588\) −1.05727e9 + 3.59945e9i −0.00884456 + 0.0301111i
\(589\) 8.94945e9 0.0743593
\(590\) 0 0
\(591\) 4.54369e10 1.54689e11i 0.372442 1.26797i
\(592\) 1.83573e11i 1.49459i
\(593\) −1.89947e11 −1.53608 −0.768039 0.640403i \(-0.778767\pi\)
−0.768039 + 0.640403i \(0.778767\pi\)
\(594\) −3.72467e10 4.30100e10i −0.299187 0.345481i
\(595\) 0 0
\(596\) 3.80200e9i 0.0301320i
\(597\) 5.33698e10 1.81696e11i 0.420144 1.43037i
\(598\) 7.94958e10i 0.621640i
\(599\) 3.15053e10i 0.244724i −0.992486 0.122362i \(-0.960953\pi\)
0.992486 0.122362i \(-0.0390469\pi\)
\(600\) 0 0
\(601\) 2.47794e10 0.189930 0.0949649 0.995481i \(-0.469726\pi\)
0.0949649 + 0.995481i \(0.469726\pi\)
\(602\) 3.90704e10 0.297483
\(603\) −1.02019e11 + 1.58678e11i −0.771636 + 1.20018i
\(604\) −2.05603e9 −0.0154483
\(605\) 0 0
\(606\) −1.24068e11 3.64425e10i −0.919958 0.270220i
\(607\) 6.54251e10i 0.481936i −0.970533 0.240968i \(-0.922535\pi\)
0.970533 0.240968i \(-0.0774649\pi\)
\(608\) 2.89830e9 0.0212094
\(609\) −1.01918e10 + 3.46979e10i −0.0740940 + 0.252252i
\(610\) 0 0
\(611\) 2.50286e11i 1.79586i
\(612\) −7.10137e9 4.56570e9i −0.0506216 0.0325463i
\(613\) 1.70377e11i 1.20661i −0.797509 0.603307i \(-0.793849\pi\)
0.797509 0.603307i \(-0.206151\pi\)
\(614\) 1.67762e11i 1.18038i
\(615\) 0 0
\(616\) −1.50999e10 −0.104870
\(617\) 8.96664e10 0.618713 0.309356 0.950946i \(-0.399886\pi\)
0.309356 + 0.950946i \(0.399886\pi\)
\(618\) −2.10982e10 6.19720e9i −0.144641 0.0424856i
\(619\) −1.34052e11 −0.913085 −0.456542 0.889702i \(-0.650912\pi\)
−0.456542 + 0.889702i \(0.650912\pi\)
\(620\) 0 0
\(621\) −6.95974e10 + 6.02714e10i −0.467979 + 0.405271i
\(622\) 2.80315e11i 1.87277i
\(623\) −3.41502e10 −0.226694
\(624\) −1.48322e11 4.35667e10i −0.978289 0.287354i
\(625\) 0 0
\(626\) 8.82804e10i 0.574867i
\(627\) −2.12681e10 6.24711e9i −0.137613 0.0404212i
\(628\) 9.57693e9i 0.0615726i
\(629\) 4.10170e11i 2.62036i
\(630\) 0 0
\(631\) −3.60073e9 −0.0227130 −0.0113565 0.999936i \(-0.503615\pi\)
−0.0113565 + 0.999936i \(0.503615\pi\)
\(632\) 1.70150e11 1.06651
\(633\) 8.50804e8 2.89654e9i 0.00529925 0.0180412i
\(634\) 1.90256e11 1.17756
\(635\) 0 0
\(636\) 1.26990e9 4.32333e9i 0.00776140 0.0264235i
\(637\) 1.53486e11i 0.932204i
\(638\) −8.38730e10 −0.506220
\(639\) −1.32687e11 + 2.06377e11i −0.795837 + 1.23782i
\(640\) 0 0
\(641\) 1.77443e11i 1.05106i −0.850775 0.525530i \(-0.823867\pi\)
0.850775 0.525530i \(-0.176133\pi\)
\(642\) 1.58967e10 5.41199e10i 0.0935764 0.318579i
\(643\) 1.47027e11i 0.860110i −0.902803 0.430055i \(-0.858494\pi\)
0.902803 0.430055i \(-0.141506\pi\)
\(644\) 8.40558e8i 0.00488680i
\(645\) 0 0
\(646\) −1.02191e11 −0.586789
\(647\) −2.73529e11 −1.56094 −0.780471 0.625192i \(-0.785021\pi\)
−0.780471 + 0.625192i \(0.785021\pi\)
\(648\) −7.19171e10 1.57637e11i −0.407880 0.894040i
\(649\) 1.02004e11 0.574961
\(650\) 0 0
\(651\) 9.53443e9 + 2.80055e9i 0.0530849 + 0.0155927i
\(652\) 8.94651e9i 0.0495066i
\(653\) −1.23992e11 −0.681933 −0.340967 0.940075i \(-0.610754\pi\)
−0.340967 + 0.940075i \(0.610754\pi\)
\(654\) 5.55799e10 1.89221e11i 0.303813 1.03433i
\(655\) 0 0
\(656\) 4.57329e10i 0.246953i
\(657\) 1.33089e11 2.07003e11i 0.714301 1.11100i
\(658\) 8.22219e10i 0.438615i
\(659\) 2.37796e11i 1.26085i 0.776251 + 0.630424i \(0.217119\pi\)
−0.776251 + 0.630424i \(0.782881\pi\)
\(660\) 0 0
\(661\) 8.33114e10 0.436414 0.218207 0.975903i \(-0.429979\pi\)
0.218207 + 0.975903i \(0.429979\pi\)
\(662\) −9.81740e10 −0.511169
\(663\) 3.31406e11 + 9.73441e10i 1.71517 + 0.503797i
\(664\) 2.93217e11 1.50840
\(665\) 0 0
\(666\) −1.56610e11 + 2.43587e11i −0.796016 + 1.23810i
\(667\) 1.35721e11i 0.685713i
\(668\) −1.29890e9 −0.00652334
\(669\) 1.95104e11 + 5.73082e10i 0.974008 + 0.286096i
\(670\) 0 0
\(671\) 5.71605e10i 0.281972i
\(672\) 3.08775e9 + 9.06967e8i 0.0151414 + 0.00444748i
\(673\) 3.96318e11i 1.93189i −0.258742 0.965947i \(-0.583308\pi\)
0.258742 0.965947i \(-0.416692\pi\)
\(674\) 2.20335e10i 0.106769i
\(675\) 0 0
\(676\) 1.67626e8 0.000802700
\(677\) −3.22020e11 −1.53295 −0.766474 0.642275i \(-0.777991\pi\)
−0.766474 + 0.642275i \(0.777991\pi\)
\(678\) 4.74551e9 1.61560e10i 0.0224577 0.0764566i
\(679\) −6.56385e9 −0.0308802
\(680\) 0 0
\(681\) −2.55140e10 + 8.68617e10i −0.118629 + 0.403868i
\(682\) 2.30470e10i 0.106531i
\(683\) −3.92810e10 −0.180510 −0.0902548 0.995919i \(-0.528768\pi\)
−0.0902548 + 0.995919i \(0.528768\pi\)
\(684\) 1.95333e9 + 1.25586e9i 0.00892382 + 0.00573741i
\(685\) 0 0
\(686\) 1.03854e11i 0.468951i
\(687\) 7.51387e10 2.55808e11i 0.337316 1.14839i
\(688\) 2.85136e11i 1.27262i
\(689\) 1.84353e11i 0.818039i
\(690\) 0 0
\(691\) 3.54272e10 0.155391 0.0776954 0.996977i \(-0.475244\pi\)
0.0776954 + 0.996977i \(0.475244\pi\)
\(692\) 1.26742e10 0.0552707
\(693\) −2.07034e10 1.33109e10i −0.0897654 0.0577131i
\(694\) 4.02279e11 1.73416
\(695\) 0 0
\(696\) −2.45066e11 7.19835e10i −1.04435 0.306758i
\(697\) 1.02184e11i 0.432965i
\(698\) 1.47726e11 0.622350
\(699\) 3.98697e10 1.35736e11i 0.167007 0.568571i
\(700\) 0 0
\(701\) 3.64764e9i 0.0151057i 0.999971 + 0.00755284i \(0.00240417\pi\)
−0.999971 + 0.00755284i \(0.997596\pi\)
\(702\) −1.59644e11 1.84346e11i −0.657360 0.759075i
\(703\) 1.12823e11i 0.461929i
\(704\) 1.06526e11i 0.433677i
\(705\) 0 0
\(706\) 2.70458e11 1.08863
\(707\) −5.59389e10 −0.223891
\(708\) −1.02529e10 3.01161e9i −0.0408052 0.0119857i
\(709\) 2.79311e11 1.10536 0.552678 0.833395i \(-0.313606\pi\)
0.552678 + 0.833395i \(0.313606\pi\)
\(710\) 0 0
\(711\) 2.33293e11 + 1.49991e11i 0.912899 + 0.586932i
\(712\) 2.41198e11i 0.938541i
\(713\) 3.72939e10 0.144304
\(714\) −1.08871e11 3.19787e10i −0.418907 0.123046i
\(715\) 0 0
\(716\) 5.73438e9i 0.0218190i
\(717\) −2.49008e11 7.31412e10i −0.942184 0.276749i
\(718\) 1.06013e11i 0.398898i
\(719\) 1.75259e11i 0.655789i −0.944714 0.327895i \(-0.893661\pi\)
0.944714 0.327895i \(-0.106339\pi\)
\(720\) 0 0
\(721\) −9.51265e9 −0.0352015
\(722\) −2.48110e11 −0.913050
\(723\) −5.30838e10 + 1.80723e11i −0.194271 + 0.661393i
\(724\) 7.93429e9 0.0288771
\(725\) 0 0
\(726\) −6.34969e10 + 2.16174e11i −0.228563 + 0.778138i
\(727\) 3.76305e11i 1.34711i 0.739137 + 0.673555i \(0.235233\pi\)
−0.739137 + 0.673555i \(0.764767\pi\)
\(728\) −6.47199e10 −0.230416
\(729\) 4.03549e10 2.79532e11i 0.142885 0.989739i
\(730\) 0 0
\(731\) 6.37098e11i 2.23119i
\(732\) 1.68763e9 5.74550e9i 0.00587804 0.0200117i
\(733\) 2.94004e11i 1.01845i −0.860635 0.509223i \(-0.829933\pi\)
0.860635 0.509223i \(-0.170067\pi\)
\(734\) 2.79850e11i 0.964141i
\(735\) 0 0
\(736\) 1.20777e10 0.0411598
\(737\) −1.89268e11 −0.641515
\(738\) 3.90156e10 6.06839e10i 0.131527 0.204573i
\(739\) −2.57966e11 −0.864939 −0.432470 0.901649i \(-0.642358\pi\)
−0.432470 + 0.901649i \(0.642358\pi\)
\(740\) 0 0
\(741\) −9.11577e10 2.67758e10i −0.302357 0.0888117i
\(742\) 6.05622e10i 0.199796i
\(743\) 8.70436e10 0.285615 0.142808 0.989750i \(-0.454387\pi\)
0.142808 + 0.989750i \(0.454387\pi\)
\(744\) −1.97799e10 + 6.73403e10i −0.0645555 + 0.219778i
\(745\) 0 0
\(746\) 2.40023e11i 0.774992i
\(747\) 4.02029e11 + 2.58477e11i 1.29114 + 0.830118i
\(748\) 8.47038e9i 0.0270580i
\(749\) 2.44013e10i 0.0775328i
\(750\) 0 0
\(751\) −3.07477e11 −0.966613 −0.483306 0.875451i \(-0.660564\pi\)
−0.483306 + 0.875451i \(0.660564\pi\)
\(752\) 6.00056e11 1.87638
\(753\) 2.63074e11 + 7.72728e10i 0.818271 + 0.240351i
\(754\) −3.59489e11 −1.11225
\(755\) 0 0
\(756\) 1.68801e9 + 1.94920e9i 0.00516759 + 0.00596719i
\(757\) 3.68112e11i 1.12098i −0.828163 0.560488i \(-0.810614\pi\)
0.828163 0.560488i \(-0.189386\pi\)
\(758\) −5.34725e11 −1.61977
\(759\) −8.86279e10 2.60327e10i −0.267057 0.0784428i
\(760\) 0 0
\(761\) 1.79849e11i 0.536252i −0.963384 0.268126i \(-0.913596\pi\)
0.963384 0.268126i \(-0.0864043\pi\)
\(762\) 3.38891e11 + 9.95427e10i 1.00517 + 0.295250i
\(763\) 8.53148e10i 0.251725i
\(764\) 5.48374e8i 0.00160955i
\(765\) 0 0
\(766\) 1.81661e11 0.527650
\(767\) 4.37201e11 1.26328
\(768\) −9.77127e9 + 3.32661e10i −0.0280871 + 0.0956218i
\(769\) 4.66289e11 1.33337 0.666684 0.745341i \(-0.267713\pi\)
0.666684 + 0.745341i \(0.267713\pi\)
\(770\) 0 0
\(771\) −2.21673e10 + 7.54681e10i −0.0627329 + 0.213573i
\(772\) 7.79114e9i 0.0219347i
\(773\) −3.85685e10 −0.108023 −0.0540114 0.998540i \(-0.517201\pi\)
−0.0540114 + 0.998540i \(0.517201\pi\)
\(774\) −2.43255e11 + 3.78352e11i −0.677794 + 1.05422i
\(775\) 0 0
\(776\) 4.63596e10i 0.127848i
\(777\) −3.53057e10 + 1.20197e11i −0.0968636 + 0.329770i
\(778\) 5.11002e11i 1.39478i
\(779\) 2.81072e10i 0.0763250i
\(780\) 0 0
\(781\) −2.46163e11 −0.661636
\(782\) −4.25847e11 −1.13875
\(783\) −2.72555e11 3.14728e11i −0.725114 0.837314i
\(784\) −3.67980e11 −0.974001
\(785\) 0 0
\(786\) 6.96010e9 + 2.04439e9i 0.0182358 + 0.00535642i
\(787\) 5.13745e11i 1.33921i 0.742717 + 0.669605i \(0.233537\pi\)
−0.742717 + 0.669605i \(0.766463\pi\)
\(788\) −1.69459e10 −0.0439502
\(789\) −4.71634e9 + 1.60567e10i −0.0121702 + 0.0414331i
\(790\) 0 0
\(791\) 7.28433e9i 0.0186073i
\(792\) 9.40130e10 1.46225e11i 0.238939 0.371640i
\(793\) 2.44996e11i 0.619537i
\(794\) 1.42054e11i 0.357413i
\(795\) 0 0
\(796\) −1.99046e10 −0.0495793
\(797\) 5.20760e11 1.29064 0.645318 0.763914i \(-0.276725\pi\)
0.645318 + 0.763914i \(0.276725\pi\)
\(798\) 2.99464e10 + 8.79617e9i 0.0738469 + 0.0216911i
\(799\) −1.34074e12 −3.28972
\(800\) 0 0
\(801\) 2.12621e11 3.30706e11i 0.516508 0.803362i
\(802\) 2.07961e10i 0.0502672i
\(803\) 2.46910e11 0.593849
\(804\) 1.90243e10 + 5.58802e9i 0.0455286 + 0.0133732i
\(805\) 0 0
\(806\) 9.87820e10i 0.234066i
\(807\) −2.43092e11 7.14037e10i −0.573162 0.168355i
\(808\) 3.95089e11i 0.926935i
\(809\) 7.88009e11i 1.83966i −0.392320 0.919829i \(-0.628327\pi\)
0.392320 0.919829i \(-0.371673\pi\)
\(810\) 0 0
\(811\) 5.15883e11 1.19253 0.596263 0.802789i \(-0.296651\pi\)
0.596263 + 0.802789i \(0.296651\pi\)
\(812\) 3.80110e9 0.00874350
\(813\) −1.05248e11 + 3.58314e11i −0.240908 + 0.820165i
\(814\) −2.90546e11 −0.661785
\(815\) 0 0
\(816\) 2.33381e11 7.94539e11i 0.526386 1.79207i
\(817\) 1.75243e11i 0.393325i
\(818\) −1.67208e11 −0.373461
\(819\) −8.87372e10 5.70520e10i −0.197229 0.126805i
\(820\) 0 0
\(821\) 5.32514e11i 1.17208i 0.810281 + 0.586041i \(0.199314\pi\)
−0.810281 + 0.586041i \(0.800686\pi\)
\(822\) −2.06813e11 + 7.04092e11i −0.452993 + 1.54220i
\(823\) 6.35863e11i 1.38600i 0.720936 + 0.693002i \(0.243712\pi\)
−0.720936 + 0.693002i \(0.756288\pi\)
\(824\) 6.71865e10i 0.145738i
\(825\) 0 0
\(826\) −1.43626e11 −0.308540
\(827\) 1.67343e10 0.0357756 0.0178878 0.999840i \(-0.494306\pi\)
0.0178878 + 0.999840i \(0.494306\pi\)
\(828\) 8.13985e9 + 5.23337e9i 0.0173179 + 0.0111342i
\(829\) 5.88172e11 1.24534 0.622668 0.782486i \(-0.286049\pi\)
0.622668 + 0.782486i \(0.286049\pi\)
\(830\) 0 0
\(831\) −1.37904e11 4.05068e10i −0.289184 0.0849422i
\(832\) 4.56584e11i 0.952856i
\(833\) 8.22201e11 1.70765
\(834\) −1.24157e10 + 4.22690e10i −0.0256630 + 0.0873691i
\(835\) 0 0
\(836\) 2.32989e9i 0.00476992i
\(837\) −8.64822e10 + 7.48937e10i −0.176208 + 0.152596i
\(838\) 5.86419e11i 1.18914i
\(839\) 9.03790e11i 1.82398i 0.410215 + 0.911989i \(0.365454\pi\)
−0.410215 + 0.911989i \(0.634546\pi\)
\(840\) 0 0
\(841\) −1.13498e11 −0.226885
\(842\) −5.91983e11 −1.17777
\(843\) 6.06643e9 + 1.78190e9i 0.0120122 + 0.00352836i
\(844\) −3.17312e8 −0.000625341
\(845\) 0 0
\(846\) 7.96225e11 + 5.11919e11i 1.55437 + 0.999355i
\(847\) 9.74673e10i 0.189376i
\(848\) 4.41984e11 0.854718
\(849\) 6.31172e11 + 1.85395e11i 1.21483 + 0.356834i
\(850\) 0 0
\(851\) 4.70152e11i 0.896437i
\(852\) 2.47431e10 + 7.26782e9i 0.0469566 + 0.0137926i
\(853\) 2.17472e11i 0.410779i 0.978680 + 0.205389i \(0.0658461\pi\)
−0.978680 + 0.205389i \(0.934154\pi\)
\(854\) 8.04842e10i 0.151314i
\(855\) 0 0
\(856\) 1.72343e11 0.320995
\(857\) 5.72821e10 0.106193 0.0530964 0.998589i \(-0.483091\pi\)
0.0530964 + 0.998589i \(0.483091\pi\)
\(858\) 6.89541e10 2.34753e11i 0.127236 0.433173i
\(859\) −2.59635e11 −0.476860 −0.238430 0.971160i \(-0.576633\pi\)
−0.238430 + 0.971160i \(0.576633\pi\)
\(860\) 0 0
\(861\) 8.79558e9 2.99444e10i 0.0160049 0.0544882i
\(862\) 4.93697e11i 0.894194i
\(863\) −9.75428e10 −0.175854 −0.0879270 0.996127i \(-0.528024\pi\)
−0.0879270 + 0.996127i \(0.528024\pi\)
\(864\) −2.80075e10 + 2.42545e10i −0.0502596 + 0.0435249i
\(865\) 0 0
\(866\) 5.62424e11i 0.999982i
\(867\) −3.62216e11 + 1.23316e12i −0.641050 + 2.18244i
\(868\) 1.04448e9i 0.00184002i
\(869\) 2.78267e11i 0.487958i
\(870\) 0 0
\(871\) −8.11224e11 −1.40951
\(872\) 6.02566e11 1.04217
\(873\) 4.08670e10 6.35634e10i 0.0703584 0.109434i
\(874\) 1.17135e11 0.200743
\(875\) 0 0
\(876\) −2.48182e10 7.28986e9i −0.0421457 0.0123795i
\(877\) 9.16421e11i 1.54916i −0.632476 0.774580i \(-0.717961\pi\)
0.632476 0.774580i \(-0.282039\pi\)
\(878\) 2.87866e10 0.0484409
\(879\) −5.76688e10 + 1.96332e11i −0.0966018 + 0.328879i
\(880\) 0 0
\(881\) 5.22036e11i 0.866557i 0.901260 + 0.433279i \(0.142643\pi\)
−0.901260 + 0.433279i \(0.857357\pi\)
\(882\) −4.88279e11 3.13930e11i −0.806852 0.518751i
\(883\) 2.66487e11i 0.438363i −0.975684 0.219181i \(-0.929661\pi\)
0.975684 0.219181i \(-0.0703386\pi\)
\(884\) 3.63050e10i 0.0594508i
\(885\) 0 0
\(886\) 5.19917e11 0.843722
\(887\) −4.32506e11 −0.698710 −0.349355 0.936990i \(-0.613599\pi\)
−0.349355 + 0.936990i \(0.613599\pi\)
\(888\) −8.48938e11 2.49359e11i −1.36529 0.401027i
\(889\) 1.52797e11 0.244630
\(890\) 0 0
\(891\) 2.57802e11 1.17615e11i 0.409049 0.186617i
\(892\) 2.13734e10i 0.0337609i
\(893\) 3.68790e11 0.579927
\(894\) 5.64456e11 + 1.65798e11i 0.883649 + 0.259555i
\(895\) 0 0
\(896\) 1.60164e11i 0.248504i
\(897\) −3.79870e11 1.11579e11i −0.586766 0.172351i
\(898\) 1.30232e12i 2.00269i
\(899\) 1.68647e11i 0.258191i
\(900\) 0 0
\(901\) −9.87554e11 −1.49852
\(902\) 7.23826e10 0.109347
\(903\) −5.48388e10 + 1.86697e11i −0.0824777 + 0.280794i
\(904\) 5.14482e10 0.0770365
\(905\) 0 0
\(906\) 8.96593e10 3.05243e11i 0.133071 0.453037i
\(907\) 1.46416e10i 0.0216352i 0.999941 + 0.0108176i \(0.00344341\pi\)
−0.999941 + 0.0108176i \(0.996557\pi\)
\(908\) 9.51557e9 0.0139988
\(909\) 3.48280e11 5.41705e11i 0.510120 0.793428i
\(910\) 0 0
\(911\) 4.82789e11i 0.700944i 0.936573 + 0.350472i \(0.113979\pi\)
−0.936573 + 0.350472i \(0.886021\pi\)
\(912\) −6.41945e10 + 2.18549e11i −0.0927937 + 0.315914i
\(913\) 4.79532e11i 0.690136i
\(914\) 8.86737e11i 1.27060i
\(915\) 0 0
\(916\) −2.80234e10 −0.0398051
\(917\) 3.13813e9 0.00443807
\(918\) 9.87513e11 8.55187e11i 1.39050 1.20418i
\(919\) −2.79672e11 −0.392090 −0.196045 0.980595i \(-0.562810\pi\)
−0.196045 + 0.980595i \(0.562810\pi\)
\(920\) 0 0
\(921\) −8.01650e11 2.35469e11i −1.11416 0.327262i
\(922\) 5.96134e9i 0.00824936i
\(923\) −1.05508e12 −1.45372
\(924\) −7.29094e8 + 2.48219e9i −0.00100022 + 0.00340523i
\(925\) 0 0
\(926\) 5.25034e11i 0.714074i
\(927\) 5.92264e10 9.21193e10i 0.0802041 0.124747i
\(928\) 5.46169e10i 0.0736436i
\(929\) 9.95357e10i 0.133634i −0.997765 0.0668169i \(-0.978716\pi\)
0.997765 0.0668169i \(-0.0212843\pi\)
\(930\) 0 0
\(931\) −2.26158e11 −0.301032
\(932\) −1.48696e10 −0.0197077
\(933\) −1.33948e12 3.93447e11i −1.76771 0.519230i
\(934\) −3.44432e11 −0.452601
\(935\) 0 0
\(936\) 4.02951e11 6.26739e11i 0.524987 0.816551i
\(937\) 8.34167e11i 1.08217i −0.840968 0.541084i \(-0.818014\pi\)
0.840968 0.541084i \(-0.181986\pi\)
\(938\) 2.66497e11 0.344255
\(939\) 4.21847e11 + 1.23909e11i 0.542616 + 0.159383i
\(940\) 0 0
\(941\) 2.45126e11i 0.312630i −0.987707 0.156315i \(-0.950039\pi\)
0.987707 0.156315i \(-0.0499615\pi\)
\(942\) 1.42182e12 + 4.17632e11i 1.80568 + 0.530383i
\(943\) 1.17127e11i 0.148119i
\(944\) 1.04818e12i 1.31992i
\(945\) 0 0
\(946\) −4.51292e11 −0.563498
\(947\) 1.34423e12 1.67137 0.835685 0.549209i \(-0.185071\pi\)
0.835685 + 0.549209i \(0.185071\pi\)
\(948\) 8.21567e9 2.79701e10i 0.0101721 0.0346306i
\(949\) 1.05828e12 1.30478
\(950\) 0 0
\(951\) −2.67042e11 + 9.09137e11i −0.326480 + 1.11149i
\(952\) 3.46695e11i 0.422085i
\(953\) −1.02998e12 −1.24870 −0.624351 0.781144i \(-0.714637\pi\)
−0.624351 + 0.781144i \(0.714637\pi\)
\(954\) 5.86477e11 + 3.77065e11i 0.708039 + 0.455221i
\(955\) 0 0
\(956\) 2.72784e10i 0.0326578i
\(957\) 1.17723e11 4.00786e11i 0.140351 0.477820i
\(958\) 7.62802e11i 0.905628i
\(959\) 3.17457e11i 0.375328i
\(960\) 0 0
\(961\) −8.06549e11 −0.945665
\(962\) −1.24531e12 −1.45405
\(963\) 2.36299e11 + 1.51924e11i 0.274762 + 0.176653i
\(964\) 1.97979e10 0.0229251
\(965\) 0 0
\(966\) 1.24792e11 + 3.66551e10i 0.143310 + 0.0420946i
\(967\) 8.83788e11i 1.01075i −0.862901 0.505373i \(-0.831355\pi\)
0.862901 0.505373i \(-0.168645\pi\)
\(968\) −6.88398e11 −0.784040
\(969\) 1.43434e11 4.88318e11i 0.162689 0.553870i
\(970\) 0 0
\(971\) 1.36295e12i 1.53321i −0.642117 0.766607i \(-0.721943\pi\)
0.642117 0.766607i \(-0.278057\pi\)
\(972\) −2.93855e10 + 4.21060e9i −0.0329206 + 0.00471714i
\(973\) 1.90580e10i 0.0212631i
\(974\) 2.19184e11i 0.243541i
\(975\) 0 0
\(976\) 5.87374e11 0.647315
\(977\) −8.27099e10 −0.0907777 −0.0453888 0.998969i \(-0.514453\pi\)
−0.0453888 + 0.998969i \(0.514453\pi\)
\(978\) 1.32822e12 + 3.90140e11i 1.45183 + 0.426447i
\(979\) 3.94459e11 0.429409
\(980\) 0 0
\(981\) 8.26177e11 + 5.31176e11i 0.892066 + 0.573538i
\(982\) 1.34528e12i 1.44666i
\(983\) 1.05894e12 1.13412 0.567058 0.823678i \(-0.308082\pi\)
0.567058 + 0.823678i \(0.308082\pi\)
\(984\) 2.11493e11 + 6.21220e10i 0.225588 + 0.0662621i
\(985\) 0 0
\(986\) 1.92573e12i 2.03745i
\(987\) 3.92896e11 + 1.15406e11i 0.414008 + 0.121607i
\(988\) 9.98619e9i 0.0104803i
\(989\) 7.30266e11i 0.763301i
\(990\) 0 0
\(991\) 1.36731e11 0.141766 0.0708828 0.997485i \(-0.477418\pi\)
0.0708828 + 0.997485i \(0.477418\pi\)
\(992\) 1.50078e10 0.0154979
\(993\) 1.37796e11 4.69123e11i 0.141723 0.482492i
\(994\) 3.46607e11 0.355052
\(995\) 0 0
\(996\) 1.41579e10 4.82003e10i 0.0143867 0.0489793i
\(997\) 1.12309e12i 1.13667i 0.822798 + 0.568334i \(0.192412\pi\)
−0.822798 + 0.568334i \(0.807588\pi\)
\(998\) −3.20317e11 −0.322892
\(999\) −9.44160e11 1.09025e12i −0.947947 1.09463i
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 75.9.d.d.74.14 20
3.2 odd 2 inner 75.9.d.d.74.8 20
5.2 odd 4 75.9.c.f.26.7 yes 10
5.3 odd 4 75.9.c.e.26.4 10
5.4 even 2 inner 75.9.d.d.74.7 20
15.2 even 4 75.9.c.f.26.4 yes 10
15.8 even 4 75.9.c.e.26.7 yes 10
15.14 odd 2 inner 75.9.d.d.74.13 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.9.c.e.26.4 10 5.3 odd 4
75.9.c.e.26.7 yes 10 15.8 even 4
75.9.c.f.26.4 yes 10 15.2 even 4
75.9.c.f.26.7 yes 10 5.2 odd 4
75.9.d.d.74.7 20 5.4 even 2 inner
75.9.d.d.74.8 20 3.2 odd 2 inner
75.9.d.d.74.13 20 15.14 odd 2 inner
75.9.d.d.74.14 20 1.1 even 1 trivial