Properties

Label 75.9.f.e.43.6
Level $75$
Weight $9$
Character 75.43
Analytic conductor $30.553$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [75,9,Mod(7,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.7");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 75.f (of order \(4\), degree \(2\), 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: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4140 x^{13} + 1109893 x^{12} - 3063780 x^{11} + 8569800 x^{10} - 2336277960 x^{9} + 311176823556 x^{8} - 1727244961920 x^{7} + \cdots + 66\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{20}\cdot 5^{8} \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.6
Root \(-8.66090 + 8.66090i\) of defining polynomial
Character \(\chi\) \(=\) 75.43
Dual form 75.9.f.e.7.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(11.1104 - 11.1104i) q^{2} +(-33.0681 - 33.0681i) q^{3} +9.11845i q^{4} -734.799 q^{6} +(1159.26 - 1159.26i) q^{7} +(2945.57 + 2945.57i) q^{8} +2187.00i q^{9} +O(q^{10})\) \(q+(11.1104 - 11.1104i) q^{2} +(-33.0681 - 33.0681i) q^{3} +9.11845i q^{4} -734.799 q^{6} +(1159.26 - 1159.26i) q^{7} +(2945.57 + 2945.57i) q^{8} +2187.00i q^{9} -24937.9 q^{11} +(301.530 - 301.530i) q^{12} +(-15387.3 - 15387.3i) q^{13} -25759.6i q^{14} +63118.5 q^{16} +(-68599.4 + 68599.4i) q^{17} +(24298.4 + 24298.4i) q^{18} +159765. i q^{19} -76668.9 q^{21} +(-277069. + 277069. i) q^{22} +(112884. + 112884. i) q^{23} -194809. i q^{24} -341917. q^{26} +(72320.0 - 72320.0i) q^{27} +(10570.6 + 10570.6i) q^{28} +824755. i q^{29} +343482. q^{31} +(-52794.3 + 52794.3i) q^{32} +(824648. + 824648. i) q^{33} +1.52433e6i q^{34} -19942.1 q^{36} +(-564458. + 564458. i) q^{37} +(1.77505e6 + 1.77505e6i) q^{38} +1.01766e6i q^{39} +3.69004e6 q^{41} +(-851821. + 851821. i) q^{42} +(-2.72005e6 - 2.72005e6i) q^{43} -227395. i q^{44} +2.50836e6 q^{46} +(-2.57514e6 + 2.57514e6i) q^{47} +(-2.08721e6 - 2.08721e6i) q^{48} +3.07705e6i q^{49} +4.53690e6 q^{51} +(140308. - 140308. i) q^{52} +(-993857. - 993857. i) q^{53} -1.60701e6i q^{54} +6.82934e6 q^{56} +(5.28311e6 - 5.28311e6i) q^{57} +(9.16335e6 + 9.16335e6i) q^{58} +8.43553e6i q^{59} -2.18751e7 q^{61} +(3.81622e6 - 3.81622e6i) q^{62} +(2.53529e6 + 2.53529e6i) q^{63} +1.73315e7i q^{64} +1.83243e7 q^{66} +(-1.90919e7 + 1.90919e7i) q^{67} +(-625520. - 625520. i) q^{68} -7.46570e6i q^{69} +6.06339e6 q^{71} +(-6.44196e6 + 6.44196e6i) q^{72} +(-7.87654e6 - 7.87654e6i) q^{73} +1.25427e7i q^{74} -1.45681e6 q^{76} +(-2.89094e7 + 2.89094e7i) q^{77} +(1.13066e7 + 1.13066e7i) q^{78} -2.50449e7i q^{79} -4.78297e6 q^{81} +(4.09978e7 - 4.09978e7i) q^{82} +(4.76305e7 + 4.76305e7i) q^{83} -699101. i q^{84} -6.04417e7 q^{86} +(2.72731e7 - 2.72731e7i) q^{87} +(-7.34562e7 - 7.34562e7i) q^{88} -6.58613e7i q^{89} -3.56756e7 q^{91} +(-1.02932e6 + 1.02932e6i) q^{92} +(-1.13583e7 - 1.13583e7i) q^{93} +5.72216e7i q^{94} +3.49161e6 q^{96} +(-2.70869e7 + 2.70869e7i) q^{97} +(3.41872e7 + 3.41872e7i) q^{98} -5.45391e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8} - 23616 q^{11} - 22680 q^{12} - 133420 q^{13} - 471380 q^{16} - 573300 q^{17} + 163944 q^{21} + 234700 q^{22} - 651480 q^{23} - 448848 q^{26} + 3567940 q^{28} + 1311776 q^{31} - 641460 q^{32} + 3815100 q^{33} + 5519988 q^{36} + 3607340 q^{37} - 8139840 q^{38} - 14740104 q^{41} + 9643860 q^{42} + 4805480 q^{43} + 14024216 q^{46} - 26529600 q^{47} - 3661200 q^{48} - 6168312 q^{51} + 15861080 q^{52} - 16612140 q^{53} + 10752000 q^{56} - 4714200 q^{57} - 63562980 q^{58} - 12550600 q^{61} + 35190840 q^{62} - 9928980 q^{63} + 46958616 q^{66} - 46836760 q^{67} + 197811840 q^{68} - 85681968 q^{71} + 38185020 q^{72} + 50835800 q^{73} + 101166648 q^{76} - 97175880 q^{77} - 131709240 q^{78} - 76527504 q^{81} + 181542400 q^{82} + 208234800 q^{83} - 187512576 q^{86} + 74298060 q^{87} - 138207420 q^{88} + 38623856 q^{91} - 652331400 q^{92} - 159787080 q^{93} + 531512604 q^{96} + 138370520 q^{97} + 50186520 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.1104 11.1104i 0.694399 0.694399i −0.268797 0.963197i \(-0.586626\pi\)
0.963197 + 0.268797i \(0.0866262\pi\)
\(3\) −33.0681 33.0681i −0.408248 0.408248i
\(4\) 9.11845i 0.0356190i
\(5\) 0 0
\(6\) −734.799 −0.566975
\(7\) 1159.26 1159.26i 0.482822 0.482822i −0.423209 0.906032i \(-0.639097\pi\)
0.906032 + 0.423209i \(0.139097\pi\)
\(8\) 2945.57 + 2945.57i 0.719133 + 0.719133i
\(9\) 2187.00i 0.333333i
\(10\) 0 0
\(11\) −24937.9 −1.70329 −0.851644 0.524120i \(-0.824394\pi\)
−0.851644 + 0.524120i \(0.824394\pi\)
\(12\) 301.530 301.530i 0.0145414 0.0145414i
\(13\) −15387.3 15387.3i −0.538751 0.538751i 0.384411 0.923162i \(-0.374405\pi\)
−0.923162 + 0.384411i \(0.874405\pi\)
\(14\) 25759.6i 0.670543i
\(15\) 0 0
\(16\) 63118.5 0.963112
\(17\) −68599.4 + 68599.4i −0.821343 + 0.821343i −0.986301 0.164958i \(-0.947251\pi\)
0.164958 + 0.986301i \(0.447251\pi\)
\(18\) 24298.4 + 24298.4i 0.231466 + 0.231466i
\(19\) 159765.i 1.22593i 0.790110 + 0.612965i \(0.210024\pi\)
−0.790110 + 0.612965i \(0.789976\pi\)
\(20\) 0 0
\(21\) −76668.9 −0.394223
\(22\) −277069. + 277069.i −1.18276 + 1.18276i
\(23\) 112884. + 112884.i 0.403385 + 0.403385i 0.879424 0.476039i \(-0.157928\pi\)
−0.476039 + 0.879424i \(0.657928\pi\)
\(24\) 194809.i 0.587170i
\(25\) 0 0
\(26\) −341917. −0.748217
\(27\) 72320.0 72320.0i 0.136083 0.136083i
\(28\) 10570.6 + 10570.6i 0.0171976 + 0.0171976i
\(29\) 824755.i 1.16609i 0.812439 + 0.583046i \(0.198139\pi\)
−0.812439 + 0.583046i \(0.801861\pi\)
\(30\) 0 0
\(31\) 343482. 0.371926 0.185963 0.982557i \(-0.440459\pi\)
0.185963 + 0.982557i \(0.440459\pi\)
\(32\) −52794.3 + 52794.3i −0.0503486 + 0.0503486i
\(33\) 824648. + 824648.i 0.695365 + 0.695365i
\(34\) 1.52433e6i 1.14068i
\(35\) 0 0
\(36\) −19942.1 −0.0118730
\(37\) −564458. + 564458.i −0.301179 + 0.301179i −0.841475 0.540296i \(-0.818312\pi\)
0.540296 + 0.841475i \(0.318312\pi\)
\(38\) 1.77505e6 + 1.77505e6i 0.851286 + 0.851286i
\(39\) 1.01766e6i 0.439889i
\(40\) 0 0
\(41\) 3.69004e6 1.30586 0.652929 0.757420i \(-0.273540\pi\)
0.652929 + 0.757420i \(0.273540\pi\)
\(42\) −851821. + 851821.i −0.273748 + 0.273748i
\(43\) −2.72005e6 2.72005e6i −0.795617 0.795617i 0.186784 0.982401i \(-0.440193\pi\)
−0.982401 + 0.186784i \(0.940193\pi\)
\(44\) 227395.i 0.0606694i
\(45\) 0 0
\(46\) 2.50836e6 0.560220
\(47\) −2.57514e6 + 2.57514e6i −0.527727 + 0.527727i −0.919894 0.392167i \(-0.871725\pi\)
0.392167 + 0.919894i \(0.371725\pi\)
\(48\) −2.08721e6 2.08721e6i −0.393189 0.393189i
\(49\) 3.07705e6i 0.533765i
\(50\) 0 0
\(51\) 4.53690e6 0.670623
\(52\) 140308. 140308.i 0.0191898 0.0191898i
\(53\) −993857. 993857.i −0.125957 0.125957i 0.641318 0.767275i \(-0.278388\pi\)
−0.767275 + 0.641318i \(0.778388\pi\)
\(54\) 1.60701e6i 0.188992i
\(55\) 0 0
\(56\) 6.82934e6 0.694427
\(57\) 5.28311e6 5.28311e6i 0.500484 0.500484i
\(58\) 9.16335e6 + 9.16335e6i 0.809734 + 0.809734i
\(59\) 8.43553e6i 0.696152i 0.937466 + 0.348076i \(0.113165\pi\)
−0.937466 + 0.348076i \(0.886835\pi\)
\(60\) 0 0
\(61\) −2.18751e7 −1.57990 −0.789952 0.613169i \(-0.789895\pi\)
−0.789952 + 0.613169i \(0.789895\pi\)
\(62\) 3.81622e6 3.81622e6i 0.258265 0.258265i
\(63\) 2.53529e6 + 2.53529e6i 0.160941 + 0.160941i
\(64\) 1.73315e7i 1.03304i
\(65\) 0 0
\(66\) 1.83243e7 0.965722
\(67\) −1.90919e7 + 1.90919e7i −0.947437 + 0.947437i −0.998686 0.0512494i \(-0.983680\pi\)
0.0512494 + 0.998686i \(0.483680\pi\)
\(68\) −625520. 625520.i −0.0292554 0.0292554i
\(69\) 7.46570e6i 0.329362i
\(70\) 0 0
\(71\) 6.06339e6 0.238607 0.119303 0.992858i \(-0.461934\pi\)
0.119303 + 0.992858i \(0.461934\pi\)
\(72\) −6.44196e6 + 6.44196e6i −0.239711 + 0.239711i
\(73\) −7.87654e6 7.87654e6i −0.277360 0.277360i 0.554694 0.832054i \(-0.312835\pi\)
−0.832054 + 0.554694i \(0.812835\pi\)
\(74\) 1.25427e7i 0.418277i
\(75\) 0 0
\(76\) −1.45681e6 −0.0436664
\(77\) −2.89094e7 + 2.89094e7i −0.822386 + 0.822386i
\(78\) 1.13066e7 + 1.13066e7i 0.305458 + 0.305458i
\(79\) 2.50449e7i 0.643000i −0.946910 0.321500i \(-0.895813\pi\)
0.946910 0.321500i \(-0.104187\pi\)
\(80\) 0 0
\(81\) −4.78297e6 −0.111111
\(82\) 4.09978e7 4.09978e7i 0.906786 0.906786i
\(83\) 4.76305e7 + 4.76305e7i 1.00363 + 1.00363i 0.999993 + 0.00363460i \(0.00115693\pi\)
0.00363460 + 0.999993i \(0.498843\pi\)
\(84\) 699101.i 0.0140418i
\(85\) 0 0
\(86\) −6.04417e7 −1.10495
\(87\) 2.72731e7 2.72731e7i 0.476055 0.476055i
\(88\) −7.34562e7 7.34562e7i −1.22489 1.22489i
\(89\) 6.58613e7i 1.04971i −0.851191 0.524856i \(-0.824119\pi\)
0.851191 0.524856i \(-0.175881\pi\)
\(90\) 0 0
\(91\) −3.56756e7 −0.520242
\(92\) −1.02932e6 + 1.02932e6i −0.0143681 + 0.0143681i
\(93\) −1.13583e7 1.13583e7i −0.151838 0.151838i
\(94\) 5.72216e7i 0.732906i
\(95\) 0 0
\(96\) 3.49161e6 0.0411094
\(97\) −2.70869e7 + 2.70869e7i −0.305965 + 0.305965i −0.843342 0.537377i \(-0.819415\pi\)
0.537377 + 0.843342i \(0.319415\pi\)
\(98\) 3.41872e7 + 3.41872e7i 0.370646 + 0.370646i
\(99\) 5.45391e7i 0.567763i
\(100\) 0 0
\(101\) −4.42884e7 −0.425603 −0.212801 0.977095i \(-0.568259\pi\)
−0.212801 + 0.977095i \(0.568259\pi\)
\(102\) 5.04068e7 5.04068e7i 0.465680 0.465680i
\(103\) −7.81171e7 7.81171e7i −0.694061 0.694061i 0.269062 0.963123i \(-0.413286\pi\)
−0.963123 + 0.269062i \(0.913286\pi\)
\(104\) 9.06486e7i 0.774868i
\(105\) 0 0
\(106\) −2.20843e7 −0.174928
\(107\) 1.05407e8 1.05407e8i 0.804143 0.804143i −0.179597 0.983740i \(-0.557480\pi\)
0.983740 + 0.179597i \(0.0574795\pi\)
\(108\) 659446. + 659446.i 0.00484713 + 0.00484713i
\(109\) 2.01252e8i 1.42572i −0.701307 0.712859i \(-0.747400\pi\)
0.701307 0.712859i \(-0.252600\pi\)
\(110\) 0 0
\(111\) 3.73312e7 0.245912
\(112\) 7.31706e7 7.31706e7i 0.465012 0.465012i
\(113\) −1.56470e8 1.56470e8i −0.959658 0.959658i 0.0395594 0.999217i \(-0.487405\pi\)
−0.999217 + 0.0395594i \(0.987405\pi\)
\(114\) 1.17395e8i 0.695072i
\(115\) 0 0
\(116\) −7.52049e6 −0.0415350
\(117\) 3.36520e7 3.36520e7i 0.179584 0.179584i
\(118\) 9.37220e7 + 9.37220e7i 0.483408 + 0.483408i
\(119\) 1.59049e8i 0.793125i
\(120\) 0 0
\(121\) 4.07537e8 1.90119
\(122\) −2.43041e8 + 2.43041e8i −1.09708 + 1.09708i
\(123\) −1.22023e8 1.22023e8i −0.533114 0.533114i
\(124\) 3.13202e6i 0.0132476i
\(125\) 0 0
\(126\) 5.63362e7 0.223514
\(127\) 2.87409e8 2.87409e8i 1.10480 1.10480i 0.110982 0.993822i \(-0.464600\pi\)
0.993822 0.110982i \(-0.0353995\pi\)
\(128\) 1.79044e8 + 1.79044e8i 0.666991 + 0.666991i
\(129\) 1.79894e8i 0.649618i
\(130\) 0 0
\(131\) −3.75848e8 −1.27622 −0.638112 0.769944i \(-0.720284\pi\)
−0.638112 + 0.769944i \(0.720284\pi\)
\(132\) −7.51951e6 + 7.51951e6i −0.0247682 + 0.0247682i
\(133\) 1.85208e8 + 1.85208e8i 0.591907 + 0.591907i
\(134\) 4.24237e8i 1.31580i
\(135\) 0 0
\(136\) −4.04128e8 −1.18131
\(137\) −3.94996e8 + 3.94996e8i −1.12127 + 1.12127i −0.129721 + 0.991551i \(0.541408\pi\)
−0.991551 + 0.129721i \(0.958592\pi\)
\(138\) −8.29468e7 8.29468e7i −0.228709 0.228709i
\(139\) 3.91457e8i 1.04863i −0.851523 0.524317i \(-0.824321\pi\)
0.851523 0.524317i \(-0.175679\pi\)
\(140\) 0 0
\(141\) 1.70310e8 0.430887
\(142\) 6.73667e7 6.73667e7i 0.165688 0.165688i
\(143\) 3.83726e8 + 3.83726e8i 0.917649 + 0.917649i
\(144\) 1.38040e8i 0.321037i
\(145\) 0 0
\(146\) −1.75023e8 −0.385197
\(147\) 1.01752e8 1.01752e8i 0.217909 0.217909i
\(148\) −5.14699e6 5.14699e6i −0.0107277 0.0107277i
\(149\) 3.71759e8i 0.754251i 0.926162 + 0.377125i \(0.123087\pi\)
−0.926162 + 0.377125i \(0.876913\pi\)
\(150\) 0 0
\(151\) 5.50632e8 1.05914 0.529570 0.848266i \(-0.322353\pi\)
0.529570 + 0.848266i \(0.322353\pi\)
\(152\) −4.70598e8 + 4.70598e8i −0.881608 + 0.881608i
\(153\) −1.50027e8 1.50027e8i −0.273781 0.273781i
\(154\) 6.42389e8i 1.14213i
\(155\) 0 0
\(156\) −9.27945e6 −0.0156684
\(157\) −5.44897e8 + 5.44897e8i −0.896842 + 0.896842i −0.995156 0.0983132i \(-0.968655\pi\)
0.0983132 + 0.995156i \(0.468655\pi\)
\(158\) −2.78259e8 2.78259e8i −0.446499 0.446499i
\(159\) 6.57300e7i 0.102843i
\(160\) 0 0
\(161\) 2.61722e8 0.389527
\(162\) −5.31407e7 + 5.31407e7i −0.0771555 + 0.0771555i
\(163\) 2.88245e8 + 2.88245e8i 0.408330 + 0.408330i 0.881156 0.472826i \(-0.156766\pi\)
−0.472826 + 0.881156i \(0.656766\pi\)
\(164\) 3.36475e7i 0.0465133i
\(165\) 0 0
\(166\) 1.05839e9 1.39384
\(167\) −2.32402e8 + 2.32402e8i −0.298795 + 0.298795i −0.840542 0.541747i \(-0.817763\pi\)
0.541747 + 0.840542i \(0.317763\pi\)
\(168\) −2.25833e8 2.25833e8i −0.283499 0.283499i
\(169\) 3.42194e8i 0.419494i
\(170\) 0 0
\(171\) −3.49405e8 −0.408644
\(172\) 2.48027e7 2.48027e7i 0.0283390 0.0283390i
\(173\) 6.25257e8 + 6.25257e8i 0.698031 + 0.698031i 0.963985 0.265955i \(-0.0856872\pi\)
−0.265955 + 0.963985i \(0.585687\pi\)
\(174\) 6.06029e8i 0.661145i
\(175\) 0 0
\(176\) −1.57404e9 −1.64046
\(177\) 2.78947e8 2.78947e8i 0.284203 0.284203i
\(178\) −7.31745e8 7.31745e8i −0.728920 0.728920i
\(179\) 6.97348e8i 0.679263i 0.940559 + 0.339631i \(0.110302\pi\)
−0.940559 + 0.339631i \(0.889698\pi\)
\(180\) 0 0
\(181\) 1.10377e9 1.02840 0.514202 0.857669i \(-0.328088\pi\)
0.514202 + 0.857669i \(0.328088\pi\)
\(182\) −3.96370e8 + 3.96370e8i −0.361256 + 0.361256i
\(183\) 7.23368e8 + 7.23368e8i 0.644993 + 0.644993i
\(184\) 6.65013e8i 0.580175i
\(185\) 0 0
\(186\) −2.52390e8 −0.210873
\(187\) 1.71072e9 1.71072e9i 1.39898 1.39898i
\(188\) −2.34813e7 2.34813e7i −0.0187971 0.0187971i
\(189\) 1.67675e8i 0.131408i
\(190\) 0 0
\(191\) 1.04416e9 0.784573 0.392287 0.919843i \(-0.371684\pi\)
0.392287 + 0.919843i \(0.371684\pi\)
\(192\) 5.73119e8 5.73119e8i 0.421735 0.421735i
\(193\) −3.34003e8 3.34003e8i −0.240725 0.240725i 0.576425 0.817150i \(-0.304447\pi\)
−0.817150 + 0.576425i \(0.804447\pi\)
\(194\) 6.01891e8i 0.424924i
\(195\) 0 0
\(196\) −2.80579e7 −0.0190122
\(197\) 1.08026e9 1.08026e9i 0.717240 0.717240i −0.250799 0.968039i \(-0.580693\pi\)
0.968039 + 0.250799i \(0.0806933\pi\)
\(198\) −6.05950e8 6.05950e8i −0.394254 0.394254i
\(199\) 7.03684e8i 0.448710i −0.974508 0.224355i \(-0.927973\pi\)
0.974508 0.224355i \(-0.0720275\pi\)
\(200\) 0 0
\(201\) 1.26267e9 0.773579
\(202\) −4.92062e8 + 4.92062e8i −0.295538 + 0.295538i
\(203\) 9.56103e8 + 9.56103e8i 0.563016 + 0.563016i
\(204\) 4.13695e7i 0.0238869i
\(205\) 0 0
\(206\) −1.73582e9 −0.963911
\(207\) −2.46876e8 + 2.46876e8i −0.134462 + 0.134462i
\(208\) −9.71222e8 9.71222e8i −0.518878 0.518878i
\(209\) 3.98418e9i 2.08811i
\(210\) 0 0
\(211\) −2.56752e9 −1.29534 −0.647671 0.761920i \(-0.724257\pi\)
−0.647671 + 0.761920i \(0.724257\pi\)
\(212\) 9.06244e6 9.06244e6i 0.00448644 0.00448644i
\(213\) −2.00505e8 2.00505e8i −0.0974107 0.0974107i
\(214\) 2.34222e9i 1.11679i
\(215\) 0 0
\(216\) 4.26047e8 0.195723
\(217\) 3.98184e8 3.98184e8i 0.179574 0.179574i
\(218\) −2.23598e9 2.23598e9i −0.990018 0.990018i
\(219\) 5.20925e8i 0.226464i
\(220\) 0 0
\(221\) 2.11111e9 0.884999
\(222\) 4.14764e8 4.14764e8i 0.170761 0.170761i
\(223\) 9.21336e8 + 9.21336e8i 0.372562 + 0.372562i 0.868410 0.495848i \(-0.165143\pi\)
−0.495848 + 0.868410i \(0.665143\pi\)
\(224\) 1.22404e8i 0.0486188i
\(225\) 0 0
\(226\) −3.47688e9 −1.33277
\(227\) −2.31382e9 + 2.31382e9i −0.871415 + 0.871415i −0.992627 0.121211i \(-0.961322\pi\)
0.121211 + 0.992627i \(0.461322\pi\)
\(228\) 4.81738e7 + 4.81738e7i 0.0178267 + 0.0178267i
\(229\) 1.33331e9i 0.484830i 0.970173 + 0.242415i \(0.0779395\pi\)
−0.970173 + 0.242415i \(0.922060\pi\)
\(230\) 0 0
\(231\) 1.91196e9 0.671475
\(232\) −2.42937e9 + 2.42937e9i −0.838576 + 0.838576i
\(233\) −1.72769e8 1.72769e8i −0.0586194 0.0586194i 0.677189 0.735809i \(-0.263198\pi\)
−0.735809 + 0.677189i \(0.763198\pi\)
\(234\) 7.47773e8i 0.249406i
\(235\) 0 0
\(236\) −7.69189e7 −0.0247962
\(237\) −8.28188e8 + 8.28188e8i −0.262504 + 0.262504i
\(238\) 1.76709e9 + 1.76709e9i 0.550746 + 0.550746i
\(239\) 3.60567e9i 1.10508i 0.833486 + 0.552541i \(0.186342\pi\)
−0.833486 + 0.552541i \(0.813658\pi\)
\(240\) 0 0
\(241\) −5.36725e9 −1.59105 −0.795525 0.605921i \(-0.792805\pi\)
−0.795525 + 0.605921i \(0.792805\pi\)
\(242\) 4.52790e9 4.52790e9i 1.32019 1.32019i
\(243\) 1.58164e8 + 1.58164e8i 0.0453609 + 0.0453609i
\(244\) 1.99467e8i 0.0562745i
\(245\) 0 0
\(246\) −2.71144e9 −0.740388
\(247\) 2.45834e9 2.45834e9i 0.660472 0.660472i
\(248\) 1.01175e9 + 1.01175e9i 0.267465 + 0.267465i
\(249\) 3.15010e9i 0.819459i
\(250\) 0 0
\(251\) 6.83207e8 0.172130 0.0860652 0.996290i \(-0.472571\pi\)
0.0860652 + 0.996290i \(0.472571\pi\)
\(252\) −2.31180e7 + 2.31180e7i −0.00573254 + 0.00573254i
\(253\) −2.81507e9 2.81507e9i −0.687081 0.687081i
\(254\) 6.38645e9i 1.53435i
\(255\) 0 0
\(256\) −4.58358e8 −0.106720
\(257\) 3.17797e9 3.17797e9i 0.728479 0.728479i −0.241838 0.970317i \(-0.577750\pi\)
0.970317 + 0.241838i \(0.0777501\pi\)
\(258\) 1.99869e9 + 1.99869e9i 0.451094 + 0.451094i
\(259\) 1.30870e9i 0.290832i
\(260\) 0 0
\(261\) −1.80374e9 −0.388697
\(262\) −4.17581e9 + 4.17581e9i −0.886209 + 0.886209i
\(263\) 1.32078e9 + 1.32078e9i 0.276063 + 0.276063i 0.831535 0.555472i \(-0.187462\pi\)
−0.555472 + 0.831535i \(0.687462\pi\)
\(264\) 4.85811e9i 1.00012i
\(265\) 0 0
\(266\) 4.11547e9 0.822040
\(267\) −2.17791e9 + 2.17791e9i −0.428543 + 0.428543i
\(268\) −1.74089e8 1.74089e8i −0.0337467 0.0337467i
\(269\) 7.27142e8i 0.138871i 0.997586 + 0.0694353i \(0.0221197\pi\)
−0.997586 + 0.0694353i \(0.977880\pi\)
\(270\) 0 0
\(271\) 8.56757e9 1.58847 0.794237 0.607607i \(-0.207871\pi\)
0.794237 + 0.607607i \(0.207871\pi\)
\(272\) −4.32989e9 + 4.32989e9i −0.791045 + 0.791045i
\(273\) 1.17972e9 + 1.17972e9i 0.212388 + 0.212388i
\(274\) 8.77712e9i 1.55722i
\(275\) 0 0
\(276\) 6.80756e7 0.0117315
\(277\) −1.36868e9 + 1.36868e9i −0.232478 + 0.232478i −0.813726 0.581248i \(-0.802564\pi\)
0.581248 + 0.813726i \(0.302564\pi\)
\(278\) −4.34923e9 4.34923e9i −0.728172 0.728172i
\(279\) 7.51195e8i 0.123975i
\(280\) 0 0
\(281\) 4.39746e9 0.705304 0.352652 0.935754i \(-0.385280\pi\)
0.352652 + 0.935754i \(0.385280\pi\)
\(282\) 1.89221e9 1.89221e9i 0.299208 0.299208i
\(283\) −5.43431e8 5.43431e8i −0.0847225 0.0847225i 0.663475 0.748198i \(-0.269081\pi\)
−0.748198 + 0.663475i \(0.769081\pi\)
\(284\) 5.52888e7i 0.00849892i
\(285\) 0 0
\(286\) 8.52668e9 1.27443
\(287\) 4.27770e9 4.27770e9i 0.630497 0.630497i
\(288\) −1.15461e8 1.15461e8i −0.0167829 0.0167829i
\(289\) 2.43598e9i 0.349207i
\(290\) 0 0
\(291\) 1.79142e9 0.249819
\(292\) 7.18218e7 7.18218e7i 0.00987928 0.00987928i
\(293\) 1.75807e9 + 1.75807e9i 0.238543 + 0.238543i 0.816246 0.577704i \(-0.196051\pi\)
−0.577704 + 0.816246i \(0.696051\pi\)
\(294\) 2.26101e9i 0.302631i
\(295\) 0 0
\(296\) −3.32530e9 −0.433176
\(297\) −1.80350e9 + 1.80350e9i −0.231788 + 0.231788i
\(298\) 4.13038e9 + 4.13038e9i 0.523751 + 0.523751i
\(299\) 3.47394e9i 0.434648i
\(300\) 0 0
\(301\) −6.30648e9 −0.768283
\(302\) 6.11773e9 6.11773e9i 0.735466 0.735466i
\(303\) 1.46453e9 + 1.46453e9i 0.173752 + 0.173752i
\(304\) 1.00841e10i 1.18071i
\(305\) 0 0
\(306\) −3.33371e9 −0.380227
\(307\) −3.73647e9 + 3.73647e9i −0.420637 + 0.420637i −0.885423 0.464786i \(-0.846131\pi\)
0.464786 + 0.885423i \(0.346131\pi\)
\(308\) −2.63609e8 2.63609e8i −0.0292925 0.0292925i
\(309\) 5.16637e9i 0.566698i
\(310\) 0 0
\(311\) 7.09667e9 0.758601 0.379300 0.925274i \(-0.376165\pi\)
0.379300 + 0.925274i \(0.376165\pi\)
\(312\) −2.99758e9 + 2.99758e9i −0.316338 + 0.316338i
\(313\) −2.46148e9 2.46148e9i −0.256459 0.256459i 0.567153 0.823612i \(-0.308045\pi\)
−0.823612 + 0.567153i \(0.808045\pi\)
\(314\) 1.21080e10i 1.24553i
\(315\) 0 0
\(316\) 2.28371e8 0.0229030
\(317\) −2.29391e9 + 2.29391e9i −0.227164 + 0.227164i −0.811507 0.584343i \(-0.801352\pi\)
0.584343 + 0.811507i \(0.301352\pi\)
\(318\) 7.30286e8 + 7.30286e8i 0.0714142 + 0.0714142i
\(319\) 2.05676e10i 1.98619i
\(320\) 0 0
\(321\) −6.97120e9 −0.656580
\(322\) 2.90784e9 2.90784e9i 0.270487 0.270487i
\(323\) −1.09597e10 1.09597e10i −1.00691 1.00691i
\(324\) 4.36133e7i 0.00395766i
\(325\) 0 0
\(326\) 6.40503e9 0.567089
\(327\) −6.65501e9 + 6.65501e9i −0.582047 + 0.582047i
\(328\) 1.08693e10 + 1.08693e10i 0.939085 + 0.939085i
\(329\) 5.97049e9i 0.509597i
\(330\) 0 0
\(331\) −6.33975e9 −0.528153 −0.264077 0.964502i \(-0.585067\pi\)
−0.264077 + 0.964502i \(0.585067\pi\)
\(332\) −4.34316e8 + 4.34316e8i −0.0357482 + 0.0357482i
\(333\) −1.23447e9 1.23447e9i −0.100393 0.100393i
\(334\) 5.16415e9i 0.414967i
\(335\) 0 0
\(336\) −4.83923e9 −0.379681
\(337\) −3.37261e9 + 3.37261e9i −0.261485 + 0.261485i −0.825657 0.564172i \(-0.809195\pi\)
0.564172 + 0.825657i \(0.309195\pi\)
\(338\) −3.80191e9 3.80191e9i −0.291297 0.291297i
\(339\) 1.03483e10i 0.783557i
\(340\) 0 0
\(341\) −8.56570e9 −0.633498
\(342\) −3.88203e9 + 3.88203e9i −0.283762 + 0.283762i
\(343\) 1.02500e10 + 1.02500e10i 0.740536 + 0.740536i
\(344\) 1.60242e10i 1.14431i
\(345\) 0 0
\(346\) 1.38937e10 0.969424
\(347\) −7.51385e9 + 7.51385e9i −0.518256 + 0.518256i −0.917043 0.398787i \(-0.869431\pi\)
0.398787 + 0.917043i \(0.369431\pi\)
\(348\) 2.48688e8 + 2.48688e8i 0.0169566 + 0.0169566i
\(349\) 3.35120e9i 0.225891i −0.993601 0.112945i \(-0.963972\pi\)
0.993601 0.112945i \(-0.0360285\pi\)
\(350\) 0 0
\(351\) −2.22561e9 −0.146630
\(352\) 1.31658e9 1.31658e9i 0.0857581 0.0857581i
\(353\) 4.76890e9 + 4.76890e9i 0.307128 + 0.307128i 0.843795 0.536666i \(-0.180317\pi\)
−0.536666 + 0.843795i \(0.680317\pi\)
\(354\) 6.19842e9i 0.394701i
\(355\) 0 0
\(356\) 6.00553e8 0.0373897
\(357\) 5.25943e9 5.25943e9i 0.323792 0.323792i
\(358\) 7.74781e9 + 7.74781e9i 0.471679 + 0.471679i
\(359\) 1.11490e10i 0.671209i 0.942003 + 0.335604i \(0.108941\pi\)
−0.942003 + 0.335604i \(0.891059\pi\)
\(360\) 0 0
\(361\) −8.54115e9 −0.502907
\(362\) 1.22633e10 1.22633e10i 0.714123 0.714123i
\(363\) −1.34765e10 1.34765e10i −0.776159 0.776159i
\(364\) 3.25306e8i 0.0185305i
\(365\) 0 0
\(366\) 1.60738e10 0.895766
\(367\) −2.39212e9 + 2.39212e9i −0.131862 + 0.131862i −0.769957 0.638096i \(-0.779722\pi\)
0.638096 + 0.769957i \(0.279722\pi\)
\(368\) 7.12505e9 + 7.12505e9i 0.388505 + 0.388505i
\(369\) 8.07012e9i 0.435286i
\(370\) 0 0
\(371\) −2.30427e9 −0.121629
\(372\) 1.03570e8 1.03570e8i 0.00540832 0.00540832i
\(373\) −1.75464e10 1.75464e10i −0.906470 0.906470i 0.0895152 0.995985i \(-0.471468\pi\)
−0.995985 + 0.0895152i \(0.971468\pi\)
\(374\) 3.80135e10i 1.94291i
\(375\) 0 0
\(376\) −1.51705e10 −0.759012
\(377\) 1.26907e10 1.26907e10i 0.628234 0.628234i
\(378\) −1.86293e9 1.86293e9i −0.0912494 0.0912494i
\(379\) 5.61785e9i 0.272278i 0.990690 + 0.136139i \(0.0434694\pi\)
−0.990690 + 0.136139i \(0.956531\pi\)
\(380\) 0 0
\(381\) −1.90081e10 −0.902069
\(382\) 1.16010e10 1.16010e10i 0.544807 0.544807i
\(383\) −1.04233e10 1.04233e10i −0.484408 0.484408i 0.422128 0.906536i \(-0.361283\pi\)
−0.906536 + 0.422128i \(0.861283\pi\)
\(384\) 1.18413e10i 0.544596i
\(385\) 0 0
\(386\) −7.42181e9 −0.334319
\(387\) 5.94876e9 5.94876e9i 0.265206 0.265206i
\(388\) −2.46990e8 2.46990e8i −0.0108982 0.0108982i
\(389\) 4.20782e9i 0.183763i 0.995770 + 0.0918817i \(0.0292882\pi\)
−0.995770 + 0.0918817i \(0.970712\pi\)
\(390\) 0 0
\(391\) −1.54875e10 −0.662634
\(392\) −9.06366e9 + 9.06366e9i −0.383848 + 0.383848i
\(393\) 1.24286e10 + 1.24286e10i 0.521016 + 0.521016i
\(394\) 2.40043e10i 0.996102i
\(395\) 0 0
\(396\) 4.97312e8 0.0202231
\(397\) 1.76294e10 1.76294e10i 0.709700 0.709700i −0.256772 0.966472i \(-0.582659\pi\)
0.966472 + 0.256772i \(0.0826589\pi\)
\(398\) −7.81821e9 7.81821e9i −0.311584 0.311584i
\(399\) 1.22490e10i 0.483290i
\(400\) 0 0
\(401\) −1.84488e10 −0.713496 −0.356748 0.934201i \(-0.616114\pi\)
−0.356748 + 0.934201i \(0.616114\pi\)
\(402\) 1.40287e10 1.40287e10i 0.537173 0.537173i
\(403\) −5.28525e9 5.28525e9i −0.200376 0.200376i
\(404\) 4.03842e8i 0.0151595i
\(405\) 0 0
\(406\) 2.12453e10 0.781915
\(407\) 1.40764e10 1.40764e10i 0.512995 0.512995i
\(408\) 1.33638e10 + 1.33638e10i 0.482268 + 0.482268i
\(409\) 2.03359e10i 0.726724i −0.931648 0.363362i \(-0.881629\pi\)
0.931648 0.363362i \(-0.118371\pi\)
\(410\) 0 0
\(411\) 2.61236e10 0.915514
\(412\) 7.12307e8 7.12307e8i 0.0247217 0.0247217i
\(413\) 9.77894e9 + 9.77894e9i 0.336118 + 0.336118i
\(414\) 5.48579e9i 0.186740i
\(415\) 0 0
\(416\) 1.62472e9 0.0542507
\(417\) −1.29447e10 + 1.29447e10i −0.428103 + 0.428103i
\(418\) −4.42658e10 4.42658e10i −1.44999 1.44999i
\(419\) 3.97862e10i 1.29085i 0.763823 + 0.645426i \(0.223320\pi\)
−0.763823 + 0.645426i \(0.776680\pi\)
\(420\) 0 0
\(421\) 5.52423e10 1.75850 0.879252 0.476356i \(-0.158043\pi\)
0.879252 + 0.476356i \(0.158043\pi\)
\(422\) −2.85262e10 + 2.85262e10i −0.899485 + 0.899485i
\(423\) −5.63183e9 5.63183e9i −0.175909 0.175909i
\(424\) 5.85495e9i 0.181159i
\(425\) 0 0
\(426\) −4.45538e9 −0.135284
\(427\) −2.53589e10 + 2.53589e10i −0.762813 + 0.762813i
\(428\) 9.61146e8 + 9.61146e8i 0.0286427 + 0.0286427i
\(429\) 2.53782e10i 0.749257i
\(430\) 0 0
\(431\) 6.79307e9 0.196860 0.0984299 0.995144i \(-0.468618\pi\)
0.0984299 + 0.995144i \(0.468618\pi\)
\(432\) 4.56473e9 4.56473e9i 0.131063 0.131063i
\(433\) −2.64633e10 2.64633e10i −0.752822 0.752822i 0.222183 0.975005i \(-0.428682\pi\)
−0.975005 + 0.222183i \(0.928682\pi\)
\(434\) 8.84795e9i 0.249393i
\(435\) 0 0
\(436\) 1.83510e9 0.0507826
\(437\) −1.80348e10 + 1.80348e10i −0.494522 + 0.494522i
\(438\) 5.78767e9 + 5.78767e9i 0.157256 + 0.157256i
\(439\) 4.93784e10i 1.32947i 0.747079 + 0.664735i \(0.231456\pi\)
−0.747079 + 0.664735i \(0.768544\pi\)
\(440\) 0 0
\(441\) −6.72951e9 −0.177922
\(442\) 2.34553e10 2.34553e10i 0.614542 0.614542i
\(443\) 3.77217e10 + 3.77217e10i 0.979437 + 0.979437i 0.999793 0.0203558i \(-0.00647990\pi\)
−0.0203558 + 0.999793i \(0.506480\pi\)
\(444\) 3.40402e8i 0.00875912i
\(445\) 0 0
\(446\) 2.04728e10 0.517414
\(447\) 1.22934e10 1.22934e10i 0.307922 0.307922i
\(448\) 2.00916e10 + 2.00916e10i 0.498773 + 0.498773i
\(449\) 4.14653e10i 1.02023i −0.860106 0.510116i \(-0.829602\pi\)
0.860106 0.510116i \(-0.170398\pi\)
\(450\) 0 0
\(451\) −9.20217e10 −2.22425
\(452\) 1.42676e9 1.42676e9i 0.0341820 0.0341820i
\(453\) −1.82083e10 1.82083e10i −0.432392 0.432392i
\(454\) 5.14148e10i 1.21022i
\(455\) 0 0
\(456\) 3.11235e10 0.719830
\(457\) −2.09923e10 + 2.09923e10i −0.481278 + 0.481278i −0.905540 0.424262i \(-0.860534\pi\)
0.424262 + 0.905540i \(0.360534\pi\)
\(458\) 1.48136e10 + 1.48136e10i 0.336666 + 0.336666i
\(459\) 9.92220e9i 0.223541i
\(460\) 0 0
\(461\) −5.33896e10 −1.18210 −0.591049 0.806636i \(-0.701286\pi\)
−0.591049 + 0.806636i \(0.701286\pi\)
\(462\) 2.12426e10 2.12426e10i 0.466272 0.466272i
\(463\) 5.09927e10 + 5.09927e10i 1.10964 + 1.10964i 0.993197 + 0.116447i \(0.0371506\pi\)
0.116447 + 0.993197i \(0.462849\pi\)
\(464\) 5.20573e10i 1.12308i
\(465\) 0 0
\(466\) −3.83906e9 −0.0814106
\(467\) −1.84770e10 + 1.84770e10i −0.388475 + 0.388475i −0.874143 0.485668i \(-0.838576\pi\)
0.485668 + 0.874143i \(0.338576\pi\)
\(468\) 3.06854e8 + 3.06854e8i 0.00639659 + 0.00639659i
\(469\) 4.42648e10i 0.914887i
\(470\) 0 0
\(471\) 3.60375e10 0.732269
\(472\) −2.48474e10 + 2.48474e10i −0.500626 + 0.500626i
\(473\) 6.78323e10 + 6.78323e10i 1.35516 + 1.35516i
\(474\) 1.84030e10i 0.364565i
\(475\) 0 0
\(476\) −1.45028e9 −0.0282503
\(477\) 2.17357e9 2.17357e9i 0.0419855 0.0419855i
\(478\) 4.00604e10 + 4.00604e10i 0.767368 + 0.767368i
\(479\) 7.28099e10i 1.38308i 0.722337 + 0.691542i \(0.243068\pi\)
−0.722337 + 0.691542i \(0.756932\pi\)
\(480\) 0 0
\(481\) 1.73710e10 0.324521
\(482\) −5.96322e10 + 5.96322e10i −1.10482 + 1.10482i
\(483\) −8.65466e9 8.65466e9i −0.159024 0.159024i
\(484\) 3.71611e9i 0.0677185i
\(485\) 0 0
\(486\) 3.51452e9 0.0629972
\(487\) −4.95995e9 + 4.95995e9i −0.0881783 + 0.0881783i −0.749820 0.661642i \(-0.769860\pi\)
0.661642 + 0.749820i \(0.269860\pi\)
\(488\) −6.44346e10 6.44346e10i −1.13616 1.13616i
\(489\) 1.90634e10i 0.333400i
\(490\) 0 0
\(491\) 8.34792e10 1.43632 0.718162 0.695876i \(-0.244984\pi\)
0.718162 + 0.695876i \(0.244984\pi\)
\(492\) 1.11266e9 1.11266e9i 0.0189890 0.0189890i
\(493\) −5.65777e10 5.65777e10i −0.957761 0.957761i
\(494\) 5.46262e10i 0.917262i
\(495\) 0 0
\(496\) 2.16801e10 0.358207
\(497\) 7.02903e9 7.02903e9i 0.115205 0.115205i
\(498\) −3.49989e10 3.49989e10i −0.569032 0.569032i
\(499\) 6.77551e10i 1.09280i −0.837525 0.546399i \(-0.815998\pi\)
0.837525 0.546399i \(-0.184002\pi\)
\(500\) 0 0
\(501\) 1.53702e10 0.243965
\(502\) 7.59070e9 7.59070e9i 0.119527 0.119527i
\(503\) 1.13594e10 + 1.13594e10i 0.177453 + 0.177453i 0.790245 0.612792i \(-0.209953\pi\)
−0.612792 + 0.790245i \(0.709953\pi\)
\(504\) 1.49358e10i 0.231476i
\(505\) 0 0
\(506\) −6.25532e10 −0.954217
\(507\) −1.13157e10 + 1.13157e10i −0.171258 + 0.171258i
\(508\) 2.62072e9 + 2.62072e9i 0.0393520 + 0.0393520i
\(509\) 1.19786e11i 1.78458i 0.451468 + 0.892288i \(0.350901\pi\)
−0.451468 + 0.892288i \(0.649099\pi\)
\(510\) 0 0
\(511\) −1.82619e10 −0.267831
\(512\) −5.09278e10 + 5.09278e10i −0.741097 + 0.741097i
\(513\) 1.15542e10 + 1.15542e10i 0.166828 + 0.166828i
\(514\) 7.06169e10i 1.01171i
\(515\) 0 0
\(516\) −1.64036e9 −0.0231387
\(517\) 6.42184e10 6.42184e10i 0.898871 0.898871i
\(518\) 1.45402e10 + 1.45402e10i 0.201954 + 0.201954i
\(519\) 4.13522e10i 0.569940i
\(520\) 0 0
\(521\) 5.94713e10 0.807154 0.403577 0.914946i \(-0.367767\pi\)
0.403577 + 0.914946i \(0.367767\pi\)
\(522\) −2.00402e10 + 2.00402e10i −0.269911 + 0.269911i
\(523\) −2.63261e10 2.63261e10i −0.351868 0.351868i 0.508936 0.860804i \(-0.330039\pi\)
−0.860804 + 0.508936i \(0.830039\pi\)
\(524\) 3.42715e9i 0.0454577i
\(525\) 0 0
\(526\) 2.93488e10 0.383396
\(527\) −2.35626e10 + 2.35626e10i −0.305479 + 0.305479i
\(528\) 5.20505e10 + 5.20505e10i 0.669714 + 0.669714i
\(529\) 5.28256e10i 0.674561i
\(530\) 0 0
\(531\) −1.84485e10 −0.232051
\(532\) −1.68881e9 + 1.68881e9i −0.0210831 + 0.0210831i
\(533\) −5.67797e10 5.67797e10i −0.703532 0.703532i
\(534\) 4.83948e10i 0.595160i
\(535\) 0 0
\(536\) −1.12473e11 −1.36267
\(537\) 2.30600e10 2.30600e10i 0.277308 0.277308i
\(538\) 8.07884e9 + 8.07884e9i 0.0964317 + 0.0964317i
\(539\) 7.67350e10i 0.909156i
\(540\) 0 0
\(541\) 1.20878e11 1.41110 0.705550 0.708660i \(-0.250700\pi\)
0.705550 + 0.708660i \(0.250700\pi\)
\(542\) 9.51890e10 9.51890e10i 1.10304 1.10304i
\(543\) −3.64995e10 3.64995e10i −0.419844 0.419844i
\(544\) 7.24331e9i 0.0827068i
\(545\) 0 0
\(546\) 2.62144e10 0.294964
\(547\) 7.50251e10 7.50251e10i 0.838025 0.838025i −0.150574 0.988599i \(-0.548112\pi\)
0.988599 + 0.150574i \(0.0481120\pi\)
\(548\) −3.60175e9 3.60175e9i −0.0399385 0.0399385i
\(549\) 4.78408e10i 0.526635i
\(550\) 0 0
\(551\) −1.31767e11 −1.42955
\(552\) 2.19907e10 2.19907e10i 0.236855 0.236855i
\(553\) −2.90335e10 2.90335e10i −0.310455 0.310455i
\(554\) 3.04131e10i 0.322865i
\(555\) 0 0
\(556\) 3.56948e9 0.0373513
\(557\) 6.33690e10 6.33690e10i 0.658348 0.658348i −0.296641 0.954989i \(-0.595866\pi\)
0.954989 + 0.296641i \(0.0958664\pi\)
\(558\) 8.34606e9 + 8.34606e9i 0.0860885 + 0.0860885i
\(559\) 8.37084e10i 0.857279i
\(560\) 0 0
\(561\) −1.13141e11 −1.14227
\(562\) 4.88575e10 4.88575e10i 0.489763 0.489763i
\(563\) 1.07781e10 + 1.07781e10i 0.107277 + 0.107277i 0.758708 0.651431i \(-0.225831\pi\)
−0.651431 + 0.758708i \(0.725831\pi\)
\(564\) 1.55296e9i 0.0153477i
\(565\) 0 0
\(566\) −1.20755e10 −0.117663
\(567\) −5.54469e9 + 5.54469e9i −0.0536469 + 0.0536469i
\(568\) 1.78602e10 + 1.78602e10i 0.171590 + 0.171590i
\(569\) 2.03427e11i 1.94071i −0.241685 0.970355i \(-0.577700\pi\)
0.241685 0.970355i \(-0.422300\pi\)
\(570\) 0 0
\(571\) 3.50525e10 0.329742 0.164871 0.986315i \(-0.447279\pi\)
0.164871 + 0.986315i \(0.447279\pi\)
\(572\) −3.49898e9 + 3.49898e9i −0.0326857 + 0.0326857i
\(573\) −3.45284e10 3.45284e10i −0.320301 0.320301i
\(574\) 9.50539e10i 0.875634i
\(575\) 0 0
\(576\) −3.79039e10 −0.344345
\(577\) −8.96159e10 + 8.96159e10i −0.808504 + 0.808504i −0.984407 0.175904i \(-0.943715\pi\)
0.175904 + 0.984407i \(0.443715\pi\)
\(578\) −2.70647e10 2.70647e10i −0.242489 0.242489i
\(579\) 2.20897e10i 0.196551i
\(580\) 0 0
\(581\) 1.10432e11 0.969148
\(582\) 1.99034e10 1.99034e10i 0.173474 0.173474i
\(583\) 2.47847e10 + 2.47847e10i 0.214540 + 0.214540i
\(584\) 4.64018e10i 0.398918i
\(585\) 0 0
\(586\) 3.90657e10 0.331288
\(587\) 3.59120e10 3.59120e10i 0.302474 0.302474i −0.539507 0.841981i \(-0.681389\pi\)
0.841981 + 0.539507i \(0.181389\pi\)
\(588\) 9.27823e8 + 9.27823e8i 0.00776168 + 0.00776168i
\(589\) 5.48762e10i 0.455956i
\(590\) 0 0
\(591\) −7.14445e10 −0.585624
\(592\) −3.56278e10 + 3.56278e10i −0.290069 + 0.290069i
\(593\) 7.94062e10 + 7.94062e10i 0.642148 + 0.642148i 0.951083 0.308935i \(-0.0999725\pi\)
−0.308935 + 0.951083i \(0.599973\pi\)
\(594\) 4.00753e10i 0.321907i
\(595\) 0 0
\(596\) −3.38986e9 −0.0268656
\(597\) −2.32695e10 + 2.32695e10i −0.183185 + 0.183185i
\(598\) −3.85969e10 3.85969e10i −0.301819 0.301819i
\(599\) 6.17729e10i 0.479834i 0.970793 + 0.239917i \(0.0771202\pi\)
−0.970793 + 0.239917i \(0.922880\pi\)
\(600\) 0 0
\(601\) −6.64109e10 −0.509028 −0.254514 0.967069i \(-0.581916\pi\)
−0.254514 + 0.967069i \(0.581916\pi\)
\(602\) −7.00675e10 + 7.00675e10i −0.533495 + 0.533495i
\(603\) −4.17540e10 4.17540e10i −0.315812 0.315812i
\(604\) 5.02091e9i 0.0377255i
\(605\) 0 0
\(606\) 3.25431e10 0.241306
\(607\) −9.40030e10 + 9.40030e10i −0.692448 + 0.692448i −0.962770 0.270322i \(-0.912870\pi\)
0.270322 + 0.962770i \(0.412870\pi\)
\(608\) −8.43466e9 8.43466e9i −0.0617239 0.0617239i
\(609\) 6.32330e10i 0.459700i
\(610\) 0 0
\(611\) 7.92487e10 0.568627
\(612\) 1.36801e9 1.36801e9i 0.00975179 0.00975179i
\(613\) 6.90775e10 + 6.90775e10i 0.489209 + 0.489209i 0.908057 0.418848i \(-0.137566\pi\)
−0.418848 + 0.908057i \(0.637566\pi\)
\(614\) 8.30273e10i 0.584181i
\(615\) 0 0
\(616\) −1.70309e11 −1.18281
\(617\) 3.90224e10 3.90224e10i 0.269261 0.269261i −0.559542 0.828802i \(-0.689023\pi\)
0.828802 + 0.559542i \(0.189023\pi\)
\(618\) 5.74004e10 + 5.74004e10i 0.393515 + 0.393515i
\(619\) 1.05074e11i 0.715701i −0.933779 0.357850i \(-0.883510\pi\)
0.933779 0.357850i \(-0.116490\pi\)
\(620\) 0 0
\(621\) 1.63275e10 0.109787
\(622\) 7.88468e10 7.88468e10i 0.526772 0.526772i
\(623\) −7.63502e10 7.63502e10i −0.506825 0.506825i
\(624\) 6.42330e10i 0.423662i
\(625\) 0 0
\(626\) −5.46959e10 −0.356170
\(627\) −1.31749e11 + 1.31749e11i −0.852469 + 0.852469i
\(628\) −4.96862e9 4.96862e9i −0.0319446 0.0319446i
\(629\) 7.74430e10i 0.494743i
\(630\) 0 0
\(631\) 1.43175e11 0.903128 0.451564 0.892239i \(-0.350866\pi\)
0.451564 + 0.892239i \(0.350866\pi\)
\(632\) 7.37715e10 7.37715e10i 0.462403 0.462403i
\(633\) 8.49031e10 + 8.49031e10i 0.528821 + 0.528821i
\(634\) 5.09726e10i 0.315486i
\(635\) 0 0
\(636\) −5.99356e8 −0.00366316
\(637\) 4.73474e10 4.73474e10i 0.287566 0.287566i
\(638\) −2.28514e11 2.28514e11i −1.37921 1.37921i
\(639\) 1.32606e10i 0.0795355i
\(640\) 0 0
\(641\) −1.98847e11 −1.17784 −0.588920 0.808191i \(-0.700447\pi\)
−0.588920 + 0.808191i \(0.700447\pi\)
\(642\) −7.74528e10 + 7.74528e10i −0.455929 + 0.455929i
\(643\) 1.71558e11 + 1.71558e11i 1.00362 + 1.00362i 0.999993 + 0.00362360i \(0.00115343\pi\)
0.00362360 + 0.999993i \(0.498847\pi\)
\(644\) 2.38650e9i 0.0138745i
\(645\) 0 0
\(646\) −2.43534e11 −1.39839
\(647\) 6.30833e9 6.30833e9i 0.0359996 0.0359996i −0.688878 0.724877i \(-0.741896\pi\)
0.724877 + 0.688878i \(0.241896\pi\)
\(648\) −1.40886e10 1.40886e10i −0.0799037 0.0799037i
\(649\) 2.10364e11i 1.18575i
\(650\) 0 0
\(651\) −2.63344e10 −0.146622
\(652\) −2.62835e9 + 2.62835e9i −0.0145443 + 0.0145443i
\(653\) 1.17079e9 + 1.17079e9i 0.00643912 + 0.00643912i 0.710319 0.703880i \(-0.248551\pi\)
−0.703880 + 0.710319i \(0.748551\pi\)
\(654\) 1.47880e11i 0.808346i
\(655\) 0 0
\(656\) 2.32910e11 1.25769
\(657\) 1.72260e10 1.72260e10i 0.0924534 0.0924534i
\(658\) 6.63345e10 + 6.63345e10i 0.353864 + 0.353864i
\(659\) 1.23390e11i 0.654243i 0.944982 + 0.327122i \(0.106079\pi\)
−0.944982 + 0.327122i \(0.893921\pi\)
\(660\) 0 0
\(661\) −2.02550e11 −1.06103 −0.530514 0.847676i \(-0.678001\pi\)
−0.530514 + 0.847676i \(0.678001\pi\)
\(662\) −7.04371e10 + 7.04371e10i −0.366749 + 0.366749i
\(663\) −6.98105e10 6.98105e10i −0.361299 0.361299i
\(664\) 2.80598e11i 1.44348i
\(665\) 0 0
\(666\) −2.74309e10 −0.139426
\(667\) −9.31013e10 + 9.31013e10i −0.470384 + 0.470384i
\(668\) −2.11915e9 2.11915e9i −0.0106428 0.0106428i
\(669\) 6.09337e10i 0.304196i
\(670\) 0 0
\(671\) 5.45518e11 2.69103
\(672\) 4.04768e9 4.04768e9i 0.0198486 0.0198486i
\(673\) −9.90515e9 9.90515e9i −0.0482837 0.0482837i 0.682553 0.730836i \(-0.260870\pi\)
−0.730836 + 0.682553i \(0.760870\pi\)
\(674\) 7.49420e10i 0.363149i
\(675\) 0 0
\(676\) 3.12028e9 0.0149419
\(677\) 2.62761e11 2.62761e11i 1.25086 1.25086i 0.295518 0.955337i \(-0.404508\pi\)
0.955337 0.295518i \(-0.0954922\pi\)
\(678\) 1.14974e11 + 1.14974e11i 0.544102 + 0.544102i
\(679\) 6.28013e10i 0.295454i
\(680\) 0 0
\(681\) 1.53027e11 0.711508
\(682\) −9.51682e10 + 9.51682e10i −0.439901 + 0.439901i
\(683\) 1.89021e11 + 1.89021e11i 0.868613 + 0.868613i 0.992319 0.123706i \(-0.0394781\pi\)
−0.123706 + 0.992319i \(0.539478\pi\)
\(684\) 3.18603e9i 0.0145555i
\(685\) 0 0
\(686\) 2.27762e11 1.02846
\(687\) 4.40901e10 4.40901e10i 0.197931 0.197931i
\(688\) −1.71686e11 1.71686e11i −0.766268 0.766268i
\(689\) 3.05855e10i 0.135718i
\(690\) 0 0
\(691\) 2.60447e11 1.14237 0.571186 0.820821i \(-0.306483\pi\)
0.571186 + 0.820821i \(0.306483\pi\)
\(692\) −5.70138e9 + 5.70138e9i −0.0248631 + 0.0248631i
\(693\) −6.32248e10 6.32248e10i −0.274129 0.274129i
\(694\) 1.66964e11i 0.719753i
\(695\) 0 0
\(696\) 1.60670e11 0.684694
\(697\) −2.53134e11 + 2.53134e11i −1.07256 + 1.07256i
\(698\) −3.72331e10 3.72331e10i −0.156858 0.156858i
\(699\) 1.14263e10i 0.0478626i
\(700\) 0 0
\(701\) −2.55285e11 −1.05719 −0.528594 0.848875i \(-0.677281\pi\)
−0.528594 + 0.848875i \(0.677281\pi\)
\(702\) −2.47274e10 + 2.47274e10i −0.101819 + 0.101819i
\(703\) −9.01804e10 9.01804e10i −0.369225 0.369225i
\(704\) 4.32210e11i 1.75956i
\(705\) 0 0
\(706\) 1.05969e11 0.426539
\(707\) −5.13416e10 + 5.13416e10i −0.205491 + 0.205491i
\(708\) 2.54356e9 + 2.54356e9i 0.0101230 + 0.0101230i
\(709\) 2.98420e11i 1.18098i 0.807044 + 0.590491i \(0.201066\pi\)
−0.807044 + 0.590491i \(0.798934\pi\)
\(710\) 0 0
\(711\) 5.47732e10 0.214333
\(712\) 1.93999e11 1.93999e11i 0.754883 0.754883i
\(713\) 3.87735e10 + 3.87735e10i 0.150029 + 0.150029i
\(714\) 1.16869e11i 0.449682i
\(715\) 0 0
\(716\) −6.35874e9 −0.0241946
\(717\) 1.19233e11 1.19233e11i 0.451148 0.451148i
\(718\) 1.23870e11 + 1.23870e11i 0.466087 + 0.466087i
\(719\) 5.68269e10i 0.212637i 0.994332 + 0.106318i \(0.0339063\pi\)
−0.994332 + 0.106318i \(0.966094\pi\)
\(720\) 0 0
\(721\) −1.81116e11 −0.670216
\(722\) −9.48955e10 + 9.48955e10i −0.349218 + 0.349218i
\(723\) 1.77485e11 + 1.77485e11i 0.649543 + 0.649543i
\(724\) 1.00647e10i 0.0366307i
\(725\) 0 0
\(726\) −2.99458e11 −1.07793
\(727\) −2.45376e11 + 2.45376e11i −0.878404 + 0.878404i −0.993369 0.114966i \(-0.963324\pi\)
0.114966 + 0.993369i \(0.463324\pi\)
\(728\) −1.05085e11 1.05085e11i −0.374124 0.374124i
\(729\) 1.04604e10i 0.0370370i
\(730\) 0 0
\(731\) 3.73188e11 1.30695
\(732\) −6.59600e9 + 6.59600e9i −0.0229740 + 0.0229740i
\(733\) −1.90055e11 1.90055e11i −0.658361 0.658361i 0.296631 0.954992i \(-0.404137\pi\)
−0.954992 + 0.296631i \(0.904137\pi\)
\(734\) 5.31547e10i 0.183129i
\(735\) 0 0
\(736\) −1.19192e10 −0.0406197
\(737\) 4.76111e11 4.76111e11i 1.61376 1.61376i
\(738\) 8.96622e10 + 8.96622e10i 0.302262 + 0.302262i
\(739\) 4.93909e11i 1.65603i 0.560704 + 0.828016i \(0.310531\pi\)
−0.560704 + 0.828016i \(0.689469\pi\)
\(740\) 0 0
\(741\) −1.62585e11 −0.539273
\(742\) −2.56014e10 + 2.56014e10i −0.0844593 + 0.0844593i
\(743\) 1.76600e11 + 1.76600e11i 0.579474 + 0.579474i 0.934758 0.355284i \(-0.115616\pi\)
−0.355284 + 0.934758i \(0.615616\pi\)
\(744\) 6.69133e10i 0.218384i
\(745\) 0 0
\(746\) −3.89895e11 −1.25890
\(747\) −1.04168e11 + 1.04168e11i −0.334543 + 0.334543i
\(748\) 1.55991e10 + 1.55991e10i 0.0498303 + 0.0498303i
\(749\) 2.44387e11i 0.776516i
\(750\) 0 0
\(751\) 1.29096e11 0.405839 0.202920 0.979195i \(-0.434957\pi\)
0.202920 + 0.979195i \(0.434957\pi\)
\(752\) −1.62539e11 + 1.62539e11i −0.508260 + 0.508260i
\(753\) −2.25924e10 2.25924e10i −0.0702719 0.0702719i
\(754\) 2.81998e11i 0.872490i
\(755\) 0 0
\(756\) 1.52893e9 0.00468060
\(757\) 2.24616e11 2.24616e11i 0.684002 0.684002i −0.276897 0.960899i \(-0.589306\pi\)
0.960899 + 0.276897i \(0.0893062\pi\)
\(758\) 6.24165e10 + 6.24165e10i 0.189070 + 0.189070i
\(759\) 1.86178e11i 0.560999i
\(760\) 0 0
\(761\) 7.21683e10 0.215183 0.107591 0.994195i \(-0.465686\pi\)
0.107591 + 0.994195i \(0.465686\pi\)
\(762\) −2.11188e11 + 2.11188e11i −0.626396 + 0.626396i
\(763\) −2.33302e11 2.33302e11i −0.688369 0.688369i
\(764\) 9.52112e9i 0.0279457i
\(765\) 0 0
\(766\) −2.31615e11 −0.672746
\(767\) 1.29800e11 1.29800e11i 0.375053 0.375053i
\(768\) 1.51570e10 + 1.51570e10i 0.0435681 + 0.0435681i
\(769\) 5.91023e11i 1.69005i −0.534729 0.845023i \(-0.679586\pi\)
0.534729 0.845023i \(-0.320414\pi\)
\(770\) 0 0
\(771\) −2.10179e11 −0.594801
\(772\) 3.04559e9 3.04559e9i 0.00857437 0.00857437i
\(773\) −1.90676e11 1.90676e11i −0.534045 0.534045i 0.387729 0.921773i \(-0.373260\pi\)
−0.921773 + 0.387729i \(0.873260\pi\)
\(774\) 1.32186e11i 0.368317i
\(775\) 0 0
\(776\) −1.59573e11 −0.440059
\(777\) 4.32764e10 4.32764e10i 0.118732 0.118732i
\(778\) 4.67506e10 + 4.67506e10i 0.127605 + 0.127605i
\(779\) 5.89538e11i 1.60089i
\(780\) 0 0
\(781\) −1.51208e11 −0.406416
\(782\) −1.72072e11 + 1.72072e11i −0.460133 + 0.460133i
\(783\) 5.96462e10 + 5.96462e10i 0.158685 + 0.158685i
\(784\) 1.94219e11i 0.514076i
\(785\) 0 0
\(786\) 2.76173e11 0.723586
\(787\) −7.13349e10 + 7.13349e10i −0.185953 + 0.185953i −0.793944 0.607991i \(-0.791976\pi\)
0.607991 + 0.793944i \(0.291976\pi\)
\(788\) 9.85033e9 + 9.85033e9i 0.0255473 + 0.0255473i
\(789\) 8.73516e10i 0.225405i
\(790\) 0 0
\(791\) −3.62777e11 −0.926689
\(792\) 1.60649e11 1.60649e11i 0.408297 0.408297i
\(793\) 3.36598e11 + 3.36598e11i 0.851175 + 0.851175i
\(794\) 3.91738e11i 0.985631i
\(795\) 0 0
\(796\) 6.41651e9 0.0159826
\(797\) −4.72991e11 + 4.72991e11i −1.17225 + 1.17225i −0.190577 + 0.981672i \(0.561036\pi\)
−0.981672 + 0.190577i \(0.938964\pi\)
\(798\) −1.36091e11 1.36091e11i −0.335596 0.335596i
\(799\) 3.53306e11i 0.866889i
\(800\) 0 0
\(801\) 1.44039e11 0.349904
\(802\) −2.04974e11 + 2.04974e11i −0.495451 + 0.495451i
\(803\) 1.96424e11 + 1.96424e11i 0.472424 + 0.472424i
\(804\) 1.15136e10i 0.0275541i
\(805\) 0 0
\(806\) −1.17442e11 −0.278282
\(807\) 2.40452e10 2.40452e10i 0.0566937 0.0566937i
\(808\) −1.30455e11 1.30455e11i −0.306065 0.306065i
\(809\) 2.07110e11i 0.483511i 0.970337 + 0.241756i \(0.0777233\pi\)
−0.970337 + 0.241756i \(0.922277\pi\)
\(810\) 0 0
\(811\) −3.53517e11 −0.817197 −0.408598 0.912714i \(-0.633982\pi\)
−0.408598 + 0.912714i \(0.633982\pi\)
\(812\) −8.71818e9 + 8.71818e9i −0.0200540 + 0.0200540i
\(813\) −2.83313e11 2.83313e11i −0.648492 0.648492i
\(814\) 3.12788e11i 0.712447i
\(815\) 0 0
\(816\) 2.86363e11 0.645886
\(817\) 4.34568e11 4.34568e11i 0.975371 0.975371i
\(818\) −2.25939e11 2.25939e11i −0.504636 0.504636i
\(819\) 7.80225e10i 0.173414i
\(820\) 0 0
\(821\) 3.67064e10 0.0807922 0.0403961 0.999184i \(-0.487138\pi\)
0.0403961 + 0.999184i \(0.487138\pi\)
\(822\) 2.90243e11 2.90243e11i 0.635732 0.635732i
\(823\) −2.88642e11 2.88642e11i −0.629158 0.629158i 0.318698 0.947856i \(-0.396754\pi\)
−0.947856 + 0.318698i \(0.896754\pi\)
\(824\) 4.60199e11i 0.998244i
\(825\) 0 0
\(826\) 2.17296e11 0.466800
\(827\) −1.71126e11 + 1.71126e11i −0.365842 + 0.365842i −0.865958 0.500117i \(-0.833290\pi\)
0.500117 + 0.865958i \(0.333290\pi\)
\(828\) −2.25113e9 2.25113e9i −0.00478938 0.00478938i
\(829\) 4.90777e11i 1.03912i −0.854434 0.519561i \(-0.826096\pi\)
0.854434 0.519561i \(-0.173904\pi\)
\(830\) 0 0
\(831\) 9.05191e10 0.189817
\(832\) 2.66684e11 2.66684e11i 0.556550 0.556550i
\(833\) −2.11084e11 2.11084e11i −0.438404 0.438404i
\(834\) 2.87642e11i 0.594550i
\(835\) 0 0
\(836\) 3.63296e10 0.0743765
\(837\) 2.48406e10 2.48406e10i 0.0506128 0.0506128i
\(838\) 4.42040e11 + 4.42040e11i 0.896366 + 0.896366i
\(839\) 4.10905e11i 0.829266i −0.909989 0.414633i \(-0.863910\pi\)
0.909989 0.414633i \(-0.136090\pi\)
\(840\) 0 0
\(841\) −1.79974e11 −0.359771
\(842\) 6.13764e11 6.13764e11i 1.22110 1.22110i
\(843\) −1.45416e11 1.45416e11i −0.287939 0.287939i
\(844\) 2.34118e10i 0.0461387i
\(845\) 0 0
\(846\) −1.25144e11 −0.244302
\(847\) 4.72441e11 4.72441e11i 0.917938 0.917938i
\(848\) −6.27308e10 6.27308e10i −0.121310 0.121310i
\(849\) 3.59405e10i 0.0691756i
\(850\) 0 0
\(851\) −1.27436e11 −0.242982
\(852\) 1.82830e9 1.82830e9i 0.00346967 0.00346967i
\(853\) 3.54583e11 + 3.54583e11i 0.669764 + 0.669764i 0.957661 0.287898i \(-0.0929562\pi\)
−0.287898 + 0.957661i \(0.592956\pi\)
\(854\) 5.63494e11i 1.05939i
\(855\) 0 0
\(856\) 6.20966e11 1.15657
\(857\) −5.99454e11 + 5.99454e11i −1.11130 + 1.11130i −0.118329 + 0.992974i \(0.537754\pi\)
−0.992974 + 0.118329i \(0.962246\pi\)
\(858\) −2.81961e11 2.81961e11i −0.520284 0.520284i
\(859\) 2.91954e11i 0.536218i 0.963389 + 0.268109i \(0.0863988\pi\)
−0.963389 + 0.268109i \(0.913601\pi\)
\(860\) 0 0
\(861\) −2.82911e11 −0.514799
\(862\) 7.54737e10 7.54737e10i 0.136699 0.136699i
\(863\) 2.27449e11 + 2.27449e11i 0.410053 + 0.410053i 0.881757 0.471704i \(-0.156361\pi\)
−0.471704 + 0.881757i \(0.656361\pi\)
\(864\) 7.63616e9i 0.0137031i
\(865\) 0 0
\(866\) −5.88035e11 −1.04552
\(867\) −8.05534e10 + 8.05534e10i −0.142563 + 0.142563i
\(868\) 3.63082e9 + 3.63082e9i 0.00639625 + 0.00639625i
\(869\) 6.24566e11i 1.09522i
\(870\) 0 0
\(871\) 5.87545e11 1.02087
\(872\) 5.92801e11 5.92801e11i 1.02528 1.02528i
\(873\) −5.92390e10 5.92390e10i −0.101988 0.101988i
\(874\) 4.00747e11i 0.686792i
\(875\) 0 0
\(876\) −4.75003e9 −0.00806640
\(877\) 3.12100e11 3.12100e11i 0.527589 0.527589i −0.392264 0.919853i \(-0.628308\pi\)
0.919853 + 0.392264i \(0.128308\pi\)
\(878\) 5.48613e11 + 5.48613e11i 0.923183 + 0.923183i
\(879\) 1.16272e11i 0.194769i
\(880\) 0 0
\(881\) −5.56713e11 −0.924119 −0.462059 0.886849i \(-0.652889\pi\)
−0.462059 + 0.886849i \(0.652889\pi\)
\(882\) −7.47674e10 + 7.47674e10i −0.123549 + 0.123549i
\(883\) 3.44597e11 + 3.44597e11i 0.566851 + 0.566851i 0.931245 0.364394i \(-0.118724\pi\)
−0.364394 + 0.931245i \(0.618724\pi\)
\(884\) 1.92501e10i 0.0315227i
\(885\) 0 0
\(886\) 8.38206e11 1.36024
\(887\) −1.77733e11 + 1.77733e11i −0.287127 + 0.287127i −0.835943 0.548816i \(-0.815079\pi\)
0.548816 + 0.835943i \(0.315079\pi\)
\(888\) 1.09961e11 + 1.09961e11i 0.176843 + 0.176843i
\(889\) 6.66361e11i 1.06685i
\(890\) 0 0
\(891\) 1.19277e11 0.189254
\(892\) −8.40116e9 + 8.40116e9i −0.0132703 + 0.0132703i
\(893\) −4.11416e11 4.11416e11i −0.646956 0.646956i
\(894\) 2.73168e11i 0.427641i
\(895\) 0 0
\(896\) 4.15116e11 0.644077
\(897\) −1.14877e11 + 1.14877e11i −0.177444 + 0.177444i
\(898\) −4.60695e11 4.60695e11i −0.708449 0.708449i
\(899\) 2.83288e11i 0.433700i
\(900\) 0 0
\(901\) 1.36356e11 0.206907
\(902\) −1.02240e12 + 1.02240e12i −1.54452 + 1.54452i
\(903\) 2.08543e11 + 2.08543e11i 0.313650 + 0.313650i
\(904\) 9.21785e11i 1.38024i
\(905\) 0 0
\(906\) −4.04604e11 −0.600506
\(907\) −3.59456e11 + 3.59456e11i −0.531149 + 0.531149i −0.920914 0.389765i \(-0.872556\pi\)
0.389765 + 0.920914i \(0.372556\pi\)
\(908\) −2.10984e10 2.10984e10i −0.0310389 0.0310389i
\(909\) 9.68588e10i 0.141868i
\(910\) 0 0
\(911\) −4.36965e11 −0.634414 −0.317207 0.948356i \(-0.602745\pi\)
−0.317207 + 0.948356i \(0.602745\pi\)
\(912\) 3.33462e11 3.33462e11i 0.482023 0.482023i
\(913\) −1.18780e12 1.18780e12i −1.70947 1.70947i
\(914\) 4.66466e11i 0.668398i
\(915\) 0 0
\(916\) −1.21577e10 −0.0172691
\(917\) −4.35704e11 + 4.35704e11i −0.616189 + 0.616189i
\(918\) 1.10240e11 + 1.10240e11i 0.155227 + 0.155227i
\(919\) 1.18791e12i 1.66542i 0.553713 + 0.832708i \(0.313211\pi\)
−0.553713 + 0.832708i \(0.686789\pi\)
\(920\) 0 0
\(921\) 2.47116e11 0.343449
\(922\) −5.93180e11 + 5.93180e11i −0.820847 + 0.820847i
\(923\) −9.32991e10 9.32991e10i −0.128550 0.128550i
\(924\) 1.74341e10i 0.0239173i
\(925\) 0 0
\(926\) 1.13310e12 1.54107
\(927\) 1.70842e11 1.70842e11i 0.231354 0.231354i
\(928\) −4.35424e10 4.35424e10i −0.0587111 0.0587111i
\(929\) 7.00667e11i 0.940695i −0.882481 0.470347i \(-0.844129\pi\)
0.882481 0.470347i \(-0.155871\pi\)
\(930\) 0 0
\(931\) −4.91603e11 −0.654359
\(932\) 1.57538e9 1.57538e9i 0.00208796 0.00208796i
\(933\) −2.34674e11 2.34674e11i −0.309697 0.309697i
\(934\) 4.10572e11i 0.539513i
\(935\) 0 0
\(936\) 1.98248e11 0.258289
\(937\) 2.56761e11 2.56761e11i 0.333097 0.333097i −0.520664 0.853762i \(-0.674316\pi\)
0.853762 + 0.520664i \(0.174316\pi\)
\(938\) 4.91800e11 + 4.91800e11i 0.635297 + 0.635297i
\(939\) 1.62793e11i 0.209398i
\(940\) 0 0
\(941\) −1.56412e11 −0.199485 −0.0997427 0.995013i \(-0.531802\pi\)
−0.0997427 + 0.995013i \(0.531802\pi\)
\(942\) 4.00390e11 4.00390e11i 0.508487 0.508487i
\(943\) 4.16545e11 + 4.16545e11i 0.526763 + 0.526763i
\(944\) 5.32438e11i 0.670473i
\(945\) 0 0
\(946\) 1.50729e12 1.88205
\(947\) −3.12048e11 + 3.12048e11i −0.387990 + 0.387990i −0.873970 0.485980i \(-0.838463\pi\)
0.485980 + 0.873970i \(0.338463\pi\)
\(948\) −7.55179e9 7.55179e9i −0.00935011 0.00935011i
\(949\) 2.42397e11i 0.298856i
\(950\) 0 0
\(951\) 1.51711e11 0.185479
\(952\) −4.68488e11 + 4.68488e11i −0.570363 + 0.570363i
\(953\) 8.58235e11 + 8.58235e11i 1.04048 + 1.04048i 0.999145 + 0.0413362i \(0.0131615\pi\)
0.0413362 + 0.999145i \(0.486839\pi\)
\(954\) 4.82983e10i 0.0583094i
\(955\) 0 0
\(956\) −3.28781e10 −0.0393619
\(957\) −6.80132e11 + 6.80132e11i −0.810859 + 0.810859i
\(958\) 8.08946e11 + 8.08946e11i 0.960412 + 0.960412i
\(959\) 9.15804e11i 1.08275i
\(960\) 0 0
\(961\) −7.34911e11 −0.861671
\(962\) 1.92998e11 1.92998e11i 0.225347 0.225347i
\(963\) 2.30524e11 + 2.30524e11i 0.268048 + 0.268048i
\(964\) 4.89410e10i 0.0566715i
\(965\) 0 0
\(966\) −1.92313e11 −0.220852
\(967\) −5.46083e11 + 5.46083e11i −0.624529 + 0.624529i −0.946686 0.322157i \(-0.895592\pi\)
0.322157 + 0.946686i \(0.395592\pi\)
\(968\) 1.20043e12 + 1.20043e12i 1.36721 + 1.36721i
\(969\) 7.24836e11i 0.822138i
\(970\) 0 0
\(971\) −1.21655e12 −1.36853 −0.684263 0.729235i \(-0.739876\pi\)
−0.684263 + 0.729235i \(0.739876\pi\)
\(972\) −1.44221e9 + 1.44221e9i −0.00161571 + 0.00161571i
\(973\) −4.53799e11 4.53799e11i −0.506305 0.506305i
\(974\) 1.10214e11i 0.122462i
\(975\) 0 0
\(976\) −1.38072e12 −1.52163
\(977\) −3.20646e11 + 3.20646e11i −0.351923 + 0.351923i −0.860825 0.508902i \(-0.830052\pi\)
0.508902 + 0.860825i \(0.330052\pi\)
\(978\) −2.11802e11 2.11802e11i −0.231513 0.231513i
\(979\) 1.64244e12i 1.78796i
\(980\) 0 0
\(981\) 4.40137e11 0.475239
\(982\) 9.27487e11 9.27487e11i 0.997383 0.997383i
\(983\) −4.05945e11 4.05945e11i −0.434763 0.434763i 0.455482 0.890245i \(-0.349467\pi\)
−0.890245 + 0.455482i \(0.849467\pi\)
\(984\) 7.18852e11i 0.766760i
\(985\) 0 0
\(986\) −1.25720e12 −1.33014
\(987\) 1.97433e11 1.97433e11i 0.208042 0.208042i
\(988\) 2.24163e10 + 2.24163e10i 0.0235253 + 0.0235253i
\(989\) 6.14099e11i 0.641879i
\(990\) 0 0
\(991\) 4.86193e11 0.504097 0.252049 0.967715i \(-0.418896\pi\)
0.252049 + 0.967715i \(0.418896\pi\)
\(992\) −1.81339e10 + 1.81339e10i −0.0187260 + 0.0187260i
\(993\) 2.09644e11 + 2.09644e11i 0.215618 + 0.215618i
\(994\) 1.56191e11i 0.159996i
\(995\) 0 0
\(996\) 2.87241e10 0.0291883
\(997\) −1.27343e11 + 1.27343e11i −0.128883 + 0.128883i −0.768606 0.639723i \(-0.779049\pi\)
0.639723 + 0.768606i \(0.279049\pi\)
\(998\) −7.52785e11 7.52785e11i −0.758838 0.758838i
\(999\) 8.16432e10i 0.0819706i
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.f.e.43.6 16
5.2 odd 4 inner 75.9.f.e.7.6 16
5.3 odd 4 15.9.f.a.7.3 16
5.4 even 2 15.9.f.a.13.3 yes 16
15.8 even 4 45.9.g.c.37.6 16
15.14 odd 2 45.9.g.c.28.6 16
20.3 even 4 240.9.bg.d.97.4 16
20.19 odd 2 240.9.bg.d.193.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.9.f.a.7.3 16 5.3 odd 4
15.9.f.a.13.3 yes 16 5.4 even 2
45.9.g.c.28.6 16 15.14 odd 2
45.9.g.c.37.6 16 15.8 even 4
75.9.f.e.7.6 16 5.2 odd 4 inner
75.9.f.e.43.6 16 1.1 even 1 trivial
240.9.bg.d.97.4 16 20.3 even 4
240.9.bg.d.193.4 16 20.19 odd 2