Properties

Label 3.15.b.a.2.4
Level $3$
Weight $15$
Character 3.2
Analytic conductor $3.730$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3,15,Mod(2,3)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 3.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.72986904456\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.1929141760.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 364x^{2} + 3640 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{10}\cdot 3^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.4
Root \(18.8072i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.15.b.a.2.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+225.686i q^{2} +(1922.67 + 1042.26i) q^{3} -34550.1 q^{4} -23159.5i q^{5} +(-235223. + 433920. i) q^{6} +478389. q^{7} -4.09983e6i q^{8} +(2.61037e6 + 4.00784e6i) q^{9} +O(q^{10})\) \(q+225.686i q^{2} +(1922.67 + 1042.26i) q^{3} -34550.1 q^{4} -23159.5i q^{5} +(-235223. + 433920. i) q^{6} +478389. q^{7} -4.09983e6i q^{8} +(2.61037e6 + 4.00784e6i) q^{9} +5.22678e6 q^{10} +1.60910e7i q^{11} +(-6.64285e7 - 3.60101e7i) q^{12} +3.37094e7 q^{13} +1.07966e8i q^{14} +(2.41382e7 - 4.45282e7i) q^{15} +3.59205e8 q^{16} -6.70754e8i q^{17} +(-9.04512e8 + 5.89124e8i) q^{18} +3.92753e8 q^{19} +8.00165e8i q^{20} +(9.19786e8 + 4.98604e8i) q^{21} -3.63152e9 q^{22} -3.24506e7i q^{23} +(4.27308e9 - 7.88264e9i) q^{24} +5.56715e9 q^{25} +7.60773e9i q^{26} +(8.41689e8 + 1.04264e10i) q^{27} -1.65284e10 q^{28} -2.47510e10i q^{29} +(1.00494e10 + 5.44765e9i) q^{30} -3.17682e10 q^{31} +1.38959e10i q^{32} +(-1.67710e10 + 3.09378e10i) q^{33} +1.51380e11 q^{34} -1.10793e10i q^{35} +(-9.01885e10 - 1.38471e11i) q^{36} -4.38690e10 q^{37} +8.86387e10i q^{38} +(6.48121e10 + 3.51338e10i) q^{39} -9.49502e10 q^{40} +1.11156e11i q^{41} +(-1.12528e11 + 2.07583e11i) q^{42} +1.00533e11 q^{43} -5.55947e11i q^{44} +(9.28197e10 - 6.04550e10i) q^{45} +7.32365e9 q^{46} -2.14354e11i q^{47} +(6.90634e11 + 3.74384e11i) q^{48} -4.49367e11 q^{49} +1.25643e12i q^{50} +(6.99098e11 - 1.28964e12i) q^{51} -1.16466e12 q^{52} +5.81823e11i q^{53} +(-2.35310e12 + 1.89957e11i) q^{54} +3.72661e11 q^{55} -1.96132e12i q^{56} +(7.55135e11 + 4.09349e11i) q^{57} +5.58594e12 q^{58} +2.31936e12i q^{59} +(-8.33977e11 + 1.53845e12i) q^{60} -4.22999e12 q^{61} -7.16964e12i q^{62} +(1.24877e12 + 1.91731e12i) q^{63} +2.74911e12 q^{64} -7.80694e11i q^{65} +(-6.98222e12 - 3.78498e12i) q^{66} -2.32014e12 q^{67} +2.31746e13i q^{68} +(3.38219e10 - 6.23919e10i) q^{69} +2.50044e12 q^{70} -1.42262e13i q^{71} +(1.64315e13 - 1.07021e13i) q^{72} -1.06676e13 q^{73} -9.90062e12i q^{74} +(1.07038e13 + 5.80240e12i) q^{75} -1.35696e13 q^{76} +7.69778e12i q^{77} +(-7.92921e12 + 1.46272e13i) q^{78} +3.21572e13 q^{79} -8.31903e12i q^{80} +(-9.24873e12 + 2.09239e13i) q^{81} -2.50864e13 q^{82} -1.21884e13i q^{83} +(-3.17787e13 - 1.72268e13i) q^{84} -1.55344e13 q^{85} +2.26889e13i q^{86} +(2.57969e13 - 4.75880e13i) q^{87} +6.59706e13 q^{88} +3.00312e13i q^{89} +(1.36438e13 + 2.09481e13i) q^{90} +1.61262e13 q^{91} +1.12117e12i q^{92} +(-6.10799e13 - 3.31107e13i) q^{93} +4.83768e13 q^{94} -9.09597e12i q^{95} +(-1.44831e13 + 2.67173e13i) q^{96} -5.28428e13 q^{97} -1.01416e14i q^{98} +(-6.44903e13 + 4.20035e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2196 q^{3} - 39296 q^{4} - 314496 q^{6} + 825608 q^{7} - 1624860 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2196 q^{3} - 39296 q^{4} - 314496 q^{6} + 825608 q^{7} - 1624860 q^{9} + 19918080 q^{10} - 157435776 q^{12} + 201696872 q^{13} - 449729280 q^{15} + 1113997312 q^{16} - 2066238720 q^{18} + 1314947240 q^{19} + 1947743784 q^{21} - 6769002240 q^{22} + 13425205248 q^{24} - 6882482780 q^{25} + 20862898164 q^{27} - 35011502848 q^{28} + 12293648640 q^{30} - 34970710072 q^{31} - 59537237760 q^{33} + 278847249408 q^{34} - 282390924672 q^{36} + 55576789928 q^{37} + 18888686856 q^{39} + 106207395840 q^{40} - 235283892480 q^{42} - 323678929048 q^{43} + 1007022481920 q^{45} - 273460142592 q^{46} + 1055038980096 q^{48} - 2246577120564 q^{49} + 2656416881664 q^{51} - 328297944832 q^{52} - 5027863591296 q^{54} - 832322050560 q^{55} + 1073653456968 q^{57} + 12943993870080 q^{58} - 9089286635520 q^{60} - 4171641626392 q^{61} + 2946514688712 q^{63} + 9874081841152 q^{64} - 14371860222720 q^{66} - 10964239937752 q^{67} + 15227331485184 q^{69} + 4380138846720 q^{70} + 24815696855040 q^{72} - 44644130922808 q^{73} + 36265563003060 q^{75} - 19249495285504 q^{76} - 5388124734720 q^{78} + 41215442578760 q^{79} - 17388818777916 q^{81} - 42500400284160 q^{82} - 61945380290304 q^{84} + 45292279818240 q^{85} - 41651639527680 q^{87} + 147397549178880 q^{88} - 5107487374080 q^{90} + 23445744391888 q^{91} - 145717264072728 q^{93} + 50952237493248 q^{94} + 81817830162432 q^{96} + 70529980615688 q^{97} - 86105375516160 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 225.686i 1.76317i 0.472025 + 0.881585i \(0.343523\pi\)
−0.472025 + 0.881585i \(0.656477\pi\)
\(3\) 1922.67 + 1042.26i 0.879137 + 0.476569i
\(4\) −34550.1 −2.10877
\(5\) 23159.5i 0.296442i −0.988954 0.148221i \(-0.952645\pi\)
0.988954 0.148221i \(-0.0473547\pi\)
\(6\) −235223. + 433920.i −0.840273 + 1.55007i
\(7\) 478389. 0.580892 0.290446 0.956891i \(-0.406196\pi\)
0.290446 + 0.956891i \(0.406196\pi\)
\(8\) 4.09983e6i 1.95495i
\(9\) 2.61037e6 + 4.00784e6i 0.545763 + 0.837939i
\(10\) 5.22678e6 0.522678
\(11\) 1.60910e7i 0.825725i 0.910793 + 0.412862i \(0.135471\pi\)
−0.910793 + 0.412862i \(0.864529\pi\)
\(12\) −6.64285e7 3.60101e7i −1.85390 1.00498i
\(13\) 3.37094e7 0.537214 0.268607 0.963250i \(-0.413437\pi\)
0.268607 + 0.963250i \(0.413437\pi\)
\(14\) 1.07966e8i 1.02421i
\(15\) 2.41382e7 4.45282e7i 0.141275 0.260613i
\(16\) 3.59205e8 1.33814
\(17\) 6.70754e8i 1.63464i −0.576187 0.817318i \(-0.695460\pi\)
0.576187 0.817318i \(-0.304540\pi\)
\(18\) −9.04512e8 + 5.89124e8i −1.47743 + 0.962274i
\(19\) 3.92753e8 0.439384 0.219692 0.975569i \(-0.429495\pi\)
0.219692 + 0.975569i \(0.429495\pi\)
\(20\) 8.00165e8i 0.625129i
\(21\) 9.19786e8 + 4.98604e8i 0.510683 + 0.276835i
\(22\) −3.63152e9 −1.45589
\(23\) 3.24506e7i 0.00953077i −0.999989 0.00476539i \(-0.998483\pi\)
0.999989 0.00476539i \(-0.00151688\pi\)
\(24\) 4.27308e9 7.88264e9i 0.931670 1.71867i
\(25\) 5.56715e9 0.912122
\(26\) 7.60773e9i 0.947200i
\(27\) 8.41689e8 + 1.04264e10i 0.0804647 + 0.996757i
\(28\) −1.65284e10 −1.22497
\(29\) 2.47510e10i 1.43485i −0.696637 0.717424i \(-0.745321\pi\)
0.696637 0.717424i \(-0.254679\pi\)
\(30\) 1.00494e10 + 5.44765e9i 0.459506 + 0.249092i
\(31\) −3.17682e10 −1.15468 −0.577340 0.816504i \(-0.695909\pi\)
−0.577340 + 0.816504i \(0.695909\pi\)
\(32\) 1.38959e10i 0.404424i
\(33\) −1.67710e10 + 3.09378e10i −0.393515 + 0.725925i
\(34\) 1.51380e11 2.88214
\(35\) 1.10793e10i 0.172201i
\(36\) −9.01885e10 1.38471e11i −1.15089 1.76702i
\(37\) −4.38690e10 −0.462111 −0.231055 0.972941i \(-0.574218\pi\)
−0.231055 + 0.972941i \(0.574218\pi\)
\(38\) 8.86387e10i 0.774709i
\(39\) 6.48121e10 + 3.51338e10i 0.472285 + 0.256020i
\(40\) −9.49502e10 −0.579530
\(41\) 1.11156e11i 0.570751i 0.958416 + 0.285376i \(0.0921184\pi\)
−0.958416 + 0.285376i \(0.907882\pi\)
\(42\) −1.12528e11 + 2.07583e11i −0.488107 + 0.900422i
\(43\) 1.00533e11 0.369853 0.184927 0.982752i \(-0.440795\pi\)
0.184927 + 0.982752i \(0.440795\pi\)
\(44\) 5.55947e11i 1.74126i
\(45\) 9.28197e10 6.04550e10i 0.248401 0.161787i
\(46\) 7.32365e9 0.0168044
\(47\) 2.14354e11i 0.423104i −0.977367 0.211552i \(-0.932148\pi\)
0.977367 0.211552i \(-0.0678518\pi\)
\(48\) 6.90634e11 + 3.74384e11i 1.17641 + 0.637718i
\(49\) −4.49367e11 −0.662565
\(50\) 1.25643e12i 1.60823i
\(51\) 6.99098e11 1.28964e12i 0.779017 1.43707i
\(52\) −1.16466e12 −1.13286
\(53\) 5.81823e11i 0.495290i 0.968851 + 0.247645i \(0.0796567\pi\)
−0.968851 + 0.247645i \(0.920343\pi\)
\(54\) −2.35310e12 + 1.89957e11i −1.75745 + 0.141873i
\(55\) 3.72661e11 0.244780
\(56\) 1.96132e12i 1.13562i
\(57\) 7.55135e11 + 4.09349e11i 0.386278 + 0.209397i
\(58\) 5.58594e12 2.52988
\(59\) 2.31936e12i 0.931973i 0.884792 + 0.465986i \(0.154300\pi\)
−0.884792 + 0.465986i \(0.845700\pi\)
\(60\) −8.33977e11 + 1.53845e12i −0.297917 + 0.549574i
\(61\) −4.22999e12 −1.34595 −0.672977 0.739663i \(-0.734985\pi\)
−0.672977 + 0.739663i \(0.734985\pi\)
\(62\) 7.16964e12i 2.03590i
\(63\) 1.24877e12 + 1.91731e12i 0.317029 + 0.486752i
\(64\) 2.74911e12 0.625076
\(65\) 7.80694e11i 0.159253i
\(66\) −6.98222e12 3.78498e12i −1.27993 0.693834i
\(67\) −2.32014e12 −0.382817 −0.191408 0.981510i \(-0.561305\pi\)
−0.191408 + 0.981510i \(0.561305\pi\)
\(68\) 2.31746e13i 3.44707i
\(69\) 3.38219e10 6.23919e10i 0.00454207 0.00837886i
\(70\) 2.50044e12 0.303619
\(71\) 1.42262e13i 1.56415i −0.623182 0.782077i \(-0.714160\pi\)
0.623182 0.782077i \(-0.285840\pi\)
\(72\) 1.64315e13 1.07021e13i 1.63813 1.06694i
\(73\) −1.06676e13 −0.965622 −0.482811 0.875725i \(-0.660384\pi\)
−0.482811 + 0.875725i \(0.660384\pi\)
\(74\) 9.90062e12i 0.814780i
\(75\) 1.07038e13 + 5.80240e12i 0.801880 + 0.434689i
\(76\) −1.35696e13 −0.926560
\(77\) 7.69778e12i 0.479656i
\(78\) −7.92921e12 + 1.46272e13i −0.451406 + 0.832718i
\(79\) 3.21572e13 1.67451 0.837256 0.546812i \(-0.184159\pi\)
0.837256 + 0.546812i \(0.184159\pi\)
\(80\) 8.31903e12i 0.396682i
\(81\) −9.24873e12 + 2.09239e13i −0.404284 + 0.914633i
\(82\) −2.50864e13 −1.00633
\(83\) 1.21884e13i 0.449159i −0.974456 0.224580i \(-0.927899\pi\)
0.974456 0.224580i \(-0.0721009\pi\)
\(84\) −3.17787e13 1.72268e13i −1.07691 0.583782i
\(85\) −1.55344e13 −0.484575
\(86\) 2.26889e13i 0.652114i
\(87\) 2.57969e13 4.75880e13i 0.683805 1.26143i
\(88\) 6.59706e13 1.61425
\(89\) 3.00312e13i 0.678957i 0.940614 + 0.339479i \(0.110251\pi\)
−0.940614 + 0.339479i \(0.889749\pi\)
\(90\) 1.36438e13 + 2.09481e13i 0.285259 + 0.437973i
\(91\) 1.61262e13 0.312063
\(92\) 1.12117e12i 0.0200982i
\(93\) −6.10799e13 3.31107e13i −1.01512 0.550285i
\(94\) 4.83768e13 0.746005
\(95\) 9.09597e12i 0.130252i
\(96\) −1.44831e13 + 2.67173e13i −0.192736 + 0.355544i
\(97\) −5.28428e13 −0.654009 −0.327004 0.945023i \(-0.606039\pi\)
−0.327004 + 0.945023i \(0.606039\pi\)
\(98\) 1.01416e14i 1.16822i
\(99\) −6.44903e13 + 4.20035e13i −0.691907 + 0.450650i
\(100\) −1.92346e14 −1.92346
\(101\) 9.00471e13i 0.839886i 0.907551 + 0.419943i \(0.137950\pi\)
−0.907551 + 0.419943i \(0.862050\pi\)
\(102\) 2.91054e14 + 1.57777e14i 2.53380 + 1.37354i
\(103\) 9.84098e13 0.800162 0.400081 0.916480i \(-0.368982\pi\)
0.400081 + 0.916480i \(0.368982\pi\)
\(104\) 1.38203e14i 1.05023i
\(105\) 1.15475e13 2.13018e13i 0.0820656 0.151388i
\(106\) −1.31309e14 −0.873281
\(107\) 1.29015e14i 0.803440i 0.915763 + 0.401720i \(0.131587\pi\)
−0.915763 + 0.401720i \(0.868413\pi\)
\(108\) −2.90804e13 3.60234e14i −0.169682 2.10193i
\(109\) 1.17591e14 0.643265 0.321633 0.946865i \(-0.395768\pi\)
0.321633 + 0.946865i \(0.395768\pi\)
\(110\) 8.41043e13i 0.431588i
\(111\) −8.43458e13 4.57228e13i −0.406259 0.220228i
\(112\) 1.71840e14 0.777317
\(113\) 2.84987e14i 1.21137i −0.795705 0.605684i \(-0.792899\pi\)
0.795705 0.605684i \(-0.207101\pi\)
\(114\) −9.23843e13 + 1.70423e14i −0.369202 + 0.681075i
\(115\) −7.51542e11 −0.00282532
\(116\) 8.55148e14i 3.02577i
\(117\) 8.79939e13 + 1.35102e14i 0.293192 + 0.450153i
\(118\) −5.23446e14 −1.64323
\(119\) 3.20882e14i 0.949546i
\(120\) −1.82558e14 9.89626e13i −0.509487 0.276186i
\(121\) 1.20828e14 0.318179
\(122\) 9.54649e14i 2.37315i
\(123\) −1.15853e14 + 2.13717e14i −0.272003 + 0.501769i
\(124\) 1.09760e15 2.43495
\(125\) 2.70287e14i 0.566834i
\(126\) −4.32709e14 + 2.81830e14i −0.858227 + 0.558977i
\(127\) −1.21233e14 −0.227506 −0.113753 0.993509i \(-0.536287\pi\)
−0.113753 + 0.993509i \(0.536287\pi\)
\(128\) 8.48106e14i 1.50654i
\(129\) 1.93292e14 + 1.04781e14i 0.325152 + 0.176261i
\(130\) 1.76192e14 0.280790
\(131\) 4.29478e14i 0.648697i 0.945938 + 0.324348i \(0.105145\pi\)
−0.945938 + 0.324348i \(0.894855\pi\)
\(132\) 5.79440e14 1.06890e15i 0.829833 1.53081i
\(133\) 1.87889e14 0.255234
\(134\) 5.23623e14i 0.674971i
\(135\) 2.41471e14 1.94931e13i 0.295481 0.0238531i
\(136\) −2.74998e15 −3.19564
\(137\) 7.44475e14i 0.821876i 0.911663 + 0.410938i \(0.134799\pi\)
−0.911663 + 0.410938i \(0.865201\pi\)
\(138\) 1.40810e13 + 7.63312e12i 0.0147734 + 0.00800845i
\(139\) −1.29615e15 −1.29286 −0.646431 0.762972i \(-0.723739\pi\)
−0.646431 + 0.762972i \(0.723739\pi\)
\(140\) 3.82790e14i 0.363132i
\(141\) 2.23412e14 4.12133e14i 0.201639 0.371967i
\(142\) 3.21065e15 2.75787
\(143\) 5.42419e14i 0.443591i
\(144\) 9.37659e14 + 1.43964e15i 0.730310 + 1.12128i
\(145\) −5.73221e14 −0.425349
\(146\) 2.40753e15i 1.70256i
\(147\) −8.63985e14 4.68356e14i −0.582485 0.315758i
\(148\) 1.51568e15 0.974486
\(149\) 9.69877e14i 0.594857i −0.954744 0.297429i \(-0.903871\pi\)
0.954744 0.297429i \(-0.0961290\pi\)
\(150\) −1.30952e15 + 2.41570e15i −0.766432 + 1.41385i
\(151\) −1.01305e15 −0.565966 −0.282983 0.959125i \(-0.591324\pi\)
−0.282983 + 0.959125i \(0.591324\pi\)
\(152\) 1.61022e15i 0.858974i
\(153\) 2.68827e15 1.75092e15i 1.36973 0.892125i
\(154\) −1.73728e15 −0.845716
\(155\) 7.35738e14i 0.342296i
\(156\) −2.23926e15 1.21388e15i −0.995940 0.539887i
\(157\) 1.64534e15 0.699776 0.349888 0.936792i \(-0.386220\pi\)
0.349888 + 0.936792i \(0.386220\pi\)
\(158\) 7.25742e15i 2.95245i
\(159\) −6.06409e14 + 1.11865e15i −0.236040 + 0.435428i
\(160\) 3.21823e14 0.119888
\(161\) 1.55240e13i 0.00553635i
\(162\) −4.72222e15 2.08731e15i −1.61265 0.712823i
\(163\) 2.55006e15 0.834137 0.417068 0.908875i \(-0.363058\pi\)
0.417068 + 0.908875i \(0.363058\pi\)
\(164\) 3.84046e15i 1.20358i
\(165\) 7.16505e14 + 3.88409e14i 0.215195 + 0.116654i
\(166\) 2.75075e15 0.791945
\(167\) 8.83395e14i 0.243859i 0.992539 + 0.121930i \(0.0389082\pi\)
−0.992539 + 0.121930i \(0.961092\pi\)
\(168\) 2.04419e15 3.77097e15i 0.541199 0.998361i
\(169\) −2.80105e15 −0.711401
\(170\) 3.50589e15i 0.854388i
\(171\) 1.02523e15 + 1.57409e15i 0.239800 + 0.368177i
\(172\) −3.47343e15 −0.779936
\(173\) 8.97288e14i 0.193468i −0.995310 0.0967340i \(-0.969160\pi\)
0.995310 0.0967340i \(-0.0308396\pi\)
\(174\) 1.07399e16 + 5.82199e15i 2.22411 + 1.20566i
\(175\) 2.66326e15 0.529844
\(176\) 5.77999e15i 1.10494i
\(177\) −2.41736e15 + 4.45936e15i −0.444150 + 0.819332i
\(178\) −6.77761e15 −1.19712
\(179\) 1.09489e16i 1.85951i −0.368178 0.929755i \(-0.620018\pi\)
0.368178 0.929755i \(-0.379982\pi\)
\(180\) −3.20693e15 + 2.08873e15i −0.523820 + 0.341172i
\(181\) −6.47973e15 −1.01814 −0.509070 0.860725i \(-0.670010\pi\)
−0.509070 + 0.860725i \(0.670010\pi\)
\(182\) 3.63945e15i 0.550220i
\(183\) −8.13289e15 4.40874e15i −1.18328 0.641441i
\(184\) −1.33042e14 −0.0186322
\(185\) 1.01599e15i 0.136989i
\(186\) 7.47261e15 1.37849e16i 0.970246 1.78983i
\(187\) 1.07931e16 1.34976
\(188\) 7.40597e15i 0.892230i
\(189\) 4.02655e14 + 4.98789e15i 0.0467413 + 0.579008i
\(190\) 2.05283e15 0.229656
\(191\) 1.10814e16i 1.19498i 0.801877 + 0.597490i \(0.203835\pi\)
−0.801877 + 0.597490i \(0.796165\pi\)
\(192\) 5.28564e15 + 2.86528e15i 0.549527 + 0.297892i
\(193\) −9.76570e15 −0.979044 −0.489522 0.871991i \(-0.662829\pi\)
−0.489522 + 0.871991i \(0.662829\pi\)
\(194\) 1.19259e16i 1.15313i
\(195\) 8.13683e14 1.50102e15i 0.0758950 0.140005i
\(196\) 1.55257e16 1.39720
\(197\) 1.03403e16i 0.897984i 0.893536 + 0.448992i \(0.148217\pi\)
−0.893536 + 0.448992i \(0.851783\pi\)
\(198\) −9.47961e15 1.45545e16i −0.794573 1.21995i
\(199\) 1.32910e16 1.07544 0.537721 0.843123i \(-0.319285\pi\)
0.537721 + 0.843123i \(0.319285\pi\)
\(200\) 2.28244e16i 1.78316i
\(201\) −4.46087e15 2.41818e15i −0.336548 0.182439i
\(202\) −2.03224e16 −1.48086
\(203\) 1.18406e16i 0.833491i
\(204\) −2.41539e16 + 4.45572e16i −1.64277 + 3.03045i
\(205\) 2.57433e15 0.169195
\(206\) 2.22097e16i 1.41082i
\(207\) 1.30057e14 8.47081e13i 0.00798621 0.00520155i
\(208\) 1.21086e16 0.718870
\(209\) 6.31980e15i 0.362810i
\(210\) 4.80752e15 + 2.60610e15i 0.266923 + 0.144696i
\(211\) 1.38905e16 0.746003 0.373001 0.927831i \(-0.378329\pi\)
0.373001 + 0.927831i \(0.378329\pi\)
\(212\) 2.01020e16i 1.04445i
\(213\) 1.48273e16 2.73523e16i 0.745428 1.37511i
\(214\) −2.91168e16 −1.41660
\(215\) 2.32830e15i 0.109640i
\(216\) 4.27466e16 3.45078e15i 1.94861 0.157305i
\(217\) −1.51976e16 −0.670743
\(218\) 2.65387e16i 1.13419i
\(219\) −2.05103e16 1.11184e16i −0.848914 0.460186i
\(220\) −1.28755e16 −0.516184
\(221\) 2.26107e16i 0.878149i
\(222\) 1.03190e16 1.90357e16i 0.388299 0.716303i
\(223\) −1.51743e14 −0.00553317 −0.00276659 0.999996i \(-0.500881\pi\)
−0.00276659 + 0.999996i \(0.500881\pi\)
\(224\) 6.64765e15i 0.234926i
\(225\) 1.45323e16 + 2.23122e16i 0.497803 + 0.764303i
\(226\) 6.43176e16 2.13585
\(227\) 5.26622e16i 1.69558i 0.530332 + 0.847790i \(0.322067\pi\)
−0.530332 + 0.847790i \(0.677933\pi\)
\(228\) −2.60900e16 1.41431e16i −0.814573 0.441570i
\(229\) −1.16961e16 −0.354154 −0.177077 0.984197i \(-0.556664\pi\)
−0.177077 + 0.984197i \(0.556664\pi\)
\(230\) 1.69612e14i 0.00498153i
\(231\) −8.02306e15 + 1.48003e16i −0.228589 + 0.421684i
\(232\) −1.01475e17 −2.80506
\(233\) 8.01172e14i 0.0214899i −0.999942 0.0107450i \(-0.996580\pi\)
0.999942 0.0107450i \(-0.00342029\pi\)
\(234\) −3.04905e16 + 1.98590e16i −0.793696 + 0.516947i
\(235\) −4.96435e15 −0.125426
\(236\) 8.01340e16i 1.96532i
\(237\) 6.18277e16 + 3.35160e16i 1.47212 + 0.798021i
\(238\) 7.24184e16 1.67421
\(239\) 6.36561e16i 1.42907i −0.699598 0.714536i \(-0.746638\pi\)
0.699598 0.714536i \(-0.253362\pi\)
\(240\) 8.67057e15 1.59948e16i 0.189047 0.348738i
\(241\) −6.17574e16 −1.30789 −0.653943 0.756544i \(-0.726886\pi\)
−0.653943 + 0.756544i \(0.726886\pi\)
\(242\) 2.72693e16i 0.561004i
\(243\) −3.95903e16 + 3.05902e16i −0.791308 + 0.611418i
\(244\) 1.46147e17 2.83831
\(245\) 1.04071e16i 0.196412i
\(246\) −4.82329e16 2.61465e16i −0.884704 0.479587i
\(247\) 1.32394e16 0.236043
\(248\) 1.30244e17i 2.25734i
\(249\) 1.27035e16 2.34343e16i 0.214056 0.394873i
\(250\) 6.10000e16 0.999424
\(251\) 3.71900e16i 0.592530i −0.955106 0.296265i \(-0.904259\pi\)
0.955106 0.296265i \(-0.0957411\pi\)
\(252\) −4.31452e16 6.62431e16i −0.668542 1.02645i
\(253\) 5.22164e14 0.00786979
\(254\) 2.73605e16i 0.401132i
\(255\) −2.98675e16 1.61908e16i −0.426008 0.230934i
\(256\) −1.46364e17 −2.03121
\(257\) 1.85887e15i 0.0251025i −0.999921 0.0125512i \(-0.996005\pi\)
0.999921 0.0125512i \(-0.00399529\pi\)
\(258\) −2.36476e16 + 4.36233e16i −0.310778 + 0.573298i
\(259\) −2.09865e16 −0.268436
\(260\) 2.69730e16i 0.335828i
\(261\) 9.91978e16 6.46091e16i 1.20232 0.783088i
\(262\) −9.69271e16 −1.14376
\(263\) 8.73906e16i 1.00409i 0.864840 + 0.502047i \(0.167420\pi\)
−0.864840 + 0.502047i \(0.832580\pi\)
\(264\) 1.26840e17 + 6.87583e16i 1.41915 + 0.769303i
\(265\) 1.34747e16 0.146825
\(266\) 4.24038e16i 0.450022i
\(267\) −3.13002e16 + 5.77401e16i −0.323570 + 0.596896i
\(268\) 8.01611e16 0.807273
\(269\) 1.26379e17i 1.23996i −0.784616 0.619982i \(-0.787140\pi\)
0.784616 0.619982i \(-0.212860\pi\)
\(270\) 4.39932e15 + 5.44967e16i 0.0420571 + 0.520983i
\(271\) 5.86413e16 0.546284 0.273142 0.961974i \(-0.411937\pi\)
0.273142 + 0.961974i \(0.411937\pi\)
\(272\) 2.40939e17i 2.18738i
\(273\) 3.10054e16 + 1.68076e16i 0.274346 + 0.148720i
\(274\) −1.68017e17 −1.44911
\(275\) 8.95812e16i 0.753162i
\(276\) −1.16855e15 + 2.15565e15i −0.00957819 + 0.0176691i
\(277\) 1.76150e17 1.40774 0.703872 0.710327i \(-0.251453\pi\)
0.703872 + 0.710327i \(0.251453\pi\)
\(278\) 2.92523e17i 2.27954i
\(279\) −8.29269e16 1.27322e17i −0.630182 0.967551i
\(280\) −4.54232e16 −0.336644
\(281\) 1.87231e17i 1.35342i 0.736249 + 0.676711i \(0.236595\pi\)
−0.736249 + 0.676711i \(0.763405\pi\)
\(282\) 9.30127e16 + 5.04210e16i 0.655841 + 0.355523i
\(283\) −1.05273e16 −0.0724121 −0.0362060 0.999344i \(-0.511527\pi\)
−0.0362060 + 0.999344i \(0.511527\pi\)
\(284\) 4.91516e17i 3.29844i
\(285\) 9.48034e15 1.74886e16i 0.0620740 0.114509i
\(286\) −1.22416e17 −0.782126
\(287\) 5.31760e16i 0.331545i
\(288\) −5.56925e16 + 3.62734e16i −0.338883 + 0.220720i
\(289\) −2.81534e17 −1.67203
\(290\) 1.29368e17i 0.749964i
\(291\) −1.01599e17 5.50758e16i −0.574963 0.311680i
\(292\) 3.68567e17 2.03627
\(293\) 2.07675e17i 1.12024i −0.828411 0.560121i \(-0.810755\pi\)
0.828411 0.560121i \(-0.189245\pi\)
\(294\) 1.05701e17 1.94989e17i 0.556736 1.02702i
\(295\) 5.37152e16 0.276276
\(296\) 1.79856e17i 0.903405i
\(297\) −1.67772e17 + 1.35436e16i −0.823047 + 0.0664417i
\(298\) 2.18887e17 1.04883
\(299\) 1.09389e15i 0.00512006i
\(300\) −3.69818e17 2.00474e17i −1.69098 0.916660i
\(301\) 4.80939e16 0.214845
\(302\) 2.28630e17i 0.997895i
\(303\) −9.38523e16 + 1.73131e17i −0.400264 + 0.738375i
\(304\) 1.41079e17 0.587959
\(305\) 9.79646e16i 0.398998i
\(306\) 3.95157e17 + 6.06706e17i 1.57297 + 2.41506i
\(307\) 3.26458e17 1.27016 0.635081 0.772446i \(-0.280967\pi\)
0.635081 + 0.772446i \(0.280967\pi\)
\(308\) 2.65959e17i 1.01149i
\(309\) 1.89210e17 + 1.02568e17i 0.703452 + 0.381333i
\(310\) −1.66046e17 −0.603526
\(311\) 3.94473e17i 1.40183i −0.713245 0.700915i \(-0.752775\pi\)
0.713245 0.700915i \(-0.247225\pi\)
\(312\) 1.44043e17 2.65719e17i 0.500506 0.923294i
\(313\) −4.19357e17 −1.42486 −0.712432 0.701741i \(-0.752406\pi\)
−0.712432 + 0.701741i \(0.752406\pi\)
\(314\) 3.71331e17i 1.23382i
\(315\) 4.44039e16 2.89210e16i 0.144294 0.0939809i
\(316\) −1.11103e18 −3.53116
\(317\) 3.68072e17i 1.14424i 0.820170 + 0.572120i \(0.193879\pi\)
−0.820170 + 0.572120i \(0.806121\pi\)
\(318\) −2.52465e17 1.36858e17i −0.767734 0.416179i
\(319\) 3.98268e17 1.18479
\(320\) 6.36682e16i 0.185299i
\(321\) −1.34467e17 + 2.48053e17i −0.382895 + 0.706334i
\(322\) 3.50355e15 0.00976152
\(323\) 2.63441e17i 0.718232i
\(324\) 3.19545e17 7.22922e17i 0.852543 1.92875i
\(325\) 1.87665e17 0.490005
\(326\) 5.75513e17i 1.47073i
\(327\) 2.26090e17 + 1.22561e17i 0.565518 + 0.306561i
\(328\) 4.55722e17 1.11579
\(329\) 1.02545e17i 0.245778i
\(330\) −8.76583e16 + 1.61705e17i −0.205682 + 0.379425i
\(331\) 1.46374e17 0.336255 0.168127 0.985765i \(-0.446228\pi\)
0.168127 + 0.985765i \(0.446228\pi\)
\(332\) 4.21111e17i 0.947174i
\(333\) −1.14514e17 1.75820e17i −0.252203 0.387221i
\(334\) −1.99370e17 −0.429966
\(335\) 5.37334e16i 0.113483i
\(336\) 3.30392e17 + 1.79101e17i 0.683368 + 0.370445i
\(337\) −5.56586e17 −1.12752 −0.563758 0.825940i \(-0.690645\pi\)
−0.563758 + 0.825940i \(0.690645\pi\)
\(338\) 6.32158e17i 1.25432i
\(339\) 2.97030e17 5.47937e17i 0.577301 1.06496i
\(340\) 5.36714e17 1.02186
\(341\) 5.11184e17i 0.953447i
\(342\) −3.55250e17 + 2.31380e17i −0.649159 + 0.422808i
\(343\) −5.39427e17 −0.965770
\(344\) 4.12169e17i 0.723046i
\(345\) −1.44497e15 7.83299e14i −0.00248385 0.00134646i
\(346\) 2.02505e17 0.341117
\(347\) 5.48397e16i 0.0905292i −0.998975 0.0452646i \(-0.985587\pi\)
0.998975 0.0452646i \(-0.0144131\pi\)
\(348\) −8.91284e17 + 1.64417e18i −1.44199 + 2.66006i
\(349\) 5.77040e17 0.915014 0.457507 0.889206i \(-0.348742\pi\)
0.457507 + 0.889206i \(0.348742\pi\)
\(350\) 6.01061e17i 0.934205i
\(351\) 2.83728e16 + 3.51469e17i 0.0432267 + 0.535472i
\(352\) −2.23599e17 −0.333943
\(353\) 8.97000e17i 1.31332i 0.754188 + 0.656658i \(0.228031\pi\)
−0.754188 + 0.656658i \(0.771969\pi\)
\(354\) −1.00641e18 5.45565e17i −1.44462 0.783112i
\(355\) −3.29472e17 −0.463681
\(356\) 1.03758e18i 1.43177i
\(357\) 3.34441e17 6.16950e17i 0.452525 0.834781i
\(358\) 2.47101e18 3.27863
\(359\) 1.18291e18i 1.53918i 0.638540 + 0.769589i \(0.279539\pi\)
−0.638540 + 0.769589i \(0.720461\pi\)
\(360\) −2.47855e17 3.80545e17i −0.316286 0.485611i
\(361\) −6.44752e17 −0.806942
\(362\) 1.46238e18i 1.79515i
\(363\) 2.32313e17 + 1.25934e17i 0.279723 + 0.151634i
\(364\) −5.57162e17 −0.658069
\(365\) 2.47057e17i 0.286251i
\(366\) 9.94989e17 1.83548e18i 1.13097 2.08632i
\(367\) −1.25177e18 −1.39592 −0.697962 0.716135i \(-0.745909\pi\)
−0.697962 + 0.716135i \(0.745909\pi\)
\(368\) 1.16564e16i 0.0127535i
\(369\) −4.45496e17 + 2.90159e17i −0.478255 + 0.311495i
\(370\) −2.29294e17 −0.241535
\(371\) 2.78338e17i 0.287710i
\(372\) 2.11032e18 + 1.14398e18i 2.14066 + 1.16042i
\(373\) 1.64900e18 1.64157 0.820783 0.571240i \(-0.193538\pi\)
0.820783 + 0.571240i \(0.193538\pi\)
\(374\) 2.43586e18i 2.37986i
\(375\) 2.81709e17 5.19674e17i 0.270135 0.498324i
\(376\) −8.78817e17 −0.827149
\(377\) 8.34339e17i 0.770820i
\(378\) −1.12570e18 + 9.08735e16i −1.02089 + 0.0824128i
\(379\) −2.49403e17 −0.222038 −0.111019 0.993818i \(-0.535411\pi\)
−0.111019 + 0.993818i \(0.535411\pi\)
\(380\) 3.14267e17i 0.274671i
\(381\) −2.33091e17 1.26356e17i −0.200009 0.108422i
\(382\) −2.50091e18 −2.10695
\(383\) 7.17438e17i 0.593462i −0.954961 0.296731i \(-0.904104\pi\)
0.954961 0.296731i \(-0.0958965\pi\)
\(384\) −8.83944e17 + 1.63063e18i −0.717970 + 1.32445i
\(385\) 1.78277e17 0.142190
\(386\) 2.20398e18i 1.72622i
\(387\) 2.62428e17 + 4.02920e17i 0.201852 + 0.309915i
\(388\) 1.82572e18 1.37915
\(389\) 2.36642e18i 1.75568i −0.478958 0.877838i \(-0.658985\pi\)
0.478958 0.877838i \(-0.341015\pi\)
\(390\) 3.38759e17 + 1.83637e17i 0.246853 + 0.133816i
\(391\) −2.17664e16 −0.0155793
\(392\) 1.84233e18i 1.29528i
\(393\) −4.47626e17 + 8.25745e17i −0.309149 + 0.570293i
\(394\) −2.33365e18 −1.58330
\(395\) 7.44745e17i 0.496396i
\(396\) 2.22815e18 1.45123e18i 1.45907 0.950318i
\(397\) 9.86307e17 0.634569 0.317284 0.948330i \(-0.397229\pi\)
0.317284 + 0.948330i \(0.397229\pi\)
\(398\) 2.99960e18i 1.89619i
\(399\) 3.61248e17 + 1.95828e17i 0.224386 + 0.121637i
\(400\) 1.99975e18 1.22055
\(401\) 2.15290e18i 1.29126i 0.763651 + 0.645629i \(0.223405\pi\)
−0.763651 + 0.645629i \(0.776595\pi\)
\(402\) 5.45750e17 1.00676e18i 0.321671 0.593392i
\(403\) −1.07089e18 −0.620310
\(404\) 3.11114e18i 1.77113i
\(405\) 4.84587e17 + 2.14196e17i 0.271136 + 0.119847i
\(406\) 2.67225e18 1.46959
\(407\) 7.05898e17i 0.381576i
\(408\) −5.28731e18 2.86619e18i −2.80940 1.52294i
\(409\) 3.32383e18 1.73610 0.868052 0.496474i \(-0.165372\pi\)
0.868052 + 0.496474i \(0.165372\pi\)
\(410\) 5.80990e17i 0.298319i
\(411\) −7.75934e17 + 1.43138e18i −0.391681 + 0.722541i
\(412\) −3.40007e18 −1.68736
\(413\) 1.10955e18i 0.541375i
\(414\) 1.91174e16 + 2.93520e16i 0.00917122 + 0.0140811i
\(415\) −2.82278e17 −0.133150
\(416\) 4.68422e17i 0.217262i
\(417\) −2.49208e18 1.35092e18i −1.13660 0.616139i
\(418\) −1.42629e18 −0.639696
\(419\) 2.14089e18i 0.944272i 0.881526 + 0.472136i \(0.156517\pi\)
−0.881526 + 0.472136i \(0.843483\pi\)
\(420\) −3.98966e17 + 7.35980e17i −0.173058 + 0.319243i
\(421\) 8.73440e17 0.372613 0.186307 0.982492i \(-0.440348\pi\)
0.186307 + 0.982492i \(0.440348\pi\)
\(422\) 3.13489e18i 1.31533i
\(423\) 8.59098e17 5.59544e17i 0.354536 0.230915i
\(424\) 2.38538e18 0.968269
\(425\) 3.73419e18i 1.49099i
\(426\) 6.17302e18 + 3.34632e18i 2.42455 + 1.31432i
\(427\) −2.02358e18 −0.781854
\(428\) 4.45748e18i 1.69427i
\(429\) −5.65340e17 + 1.04289e18i −0.211402 + 0.389977i
\(430\) 5.25464e17 0.193314
\(431\) 5.74588e17i 0.207977i 0.994578 + 0.103989i \(0.0331605\pi\)
−0.994578 + 0.103989i \(0.966839\pi\)
\(432\) 3.02339e17 + 3.74523e18i 0.107673 + 1.33381i
\(433\) −1.73636e18 −0.608450 −0.304225 0.952600i \(-0.598398\pi\)
−0.304225 + 0.952600i \(0.598398\pi\)
\(434\) 3.42988e18i 1.18264i
\(435\) −1.10212e18 5.97443e17i −0.373940 0.202708i
\(436\) −4.06280e18 −1.35650
\(437\) 1.27451e16i 0.00418767i
\(438\) 2.50926e18 4.62889e18i 0.811386 1.49678i
\(439\) 2.13182e17 0.0678419 0.0339209 0.999425i \(-0.489201\pi\)
0.0339209 + 0.999425i \(0.489201\pi\)
\(440\) 1.52785e18i 0.478532i
\(441\) −1.17301e18 1.80099e18i −0.361604 0.555189i
\(442\) 5.10292e18 1.54833
\(443\) 1.81656e18i 0.542530i 0.962505 + 0.271265i \(0.0874420\pi\)
−0.962505 + 0.271265i \(0.912558\pi\)
\(444\) 2.91416e18 + 1.57973e18i 0.856707 + 0.464410i
\(445\) 6.95508e17 0.201272
\(446\) 3.42462e16i 0.00975593i
\(447\) 1.01086e18 1.86476e18i 0.283491 0.522961i
\(448\) 1.31515e18 0.363101
\(449\) 4.45737e18i 1.21158i 0.795623 + 0.605792i \(0.207144\pi\)
−0.795623 + 0.605792i \(0.792856\pi\)
\(450\) −5.03556e18 + 3.27974e18i −1.34760 + 0.877711i
\(451\) −1.78862e18 −0.471283
\(452\) 9.84634e18i 2.55450i
\(453\) −1.94775e18 1.05585e18i −0.497562 0.269722i
\(454\) −1.18851e19 −2.98960
\(455\) 3.73475e17i 0.0925086i
\(456\) 1.67826e18 3.09593e18i 0.409361 0.755156i
\(457\) 1.94241e18 0.466581 0.233290 0.972407i \(-0.425051\pi\)
0.233290 + 0.972407i \(0.425051\pi\)
\(458\) 2.63964e18i 0.624434i
\(459\) 6.99358e18 5.64567e17i 1.62934 0.131530i
\(460\) 2.59658e16 0.00595796
\(461\) 1.12266e18i 0.253713i 0.991921 + 0.126856i \(0.0404888\pi\)
−0.991921 + 0.126856i \(0.959511\pi\)
\(462\) −3.34022e18 1.81069e18i −0.743500 0.403042i
\(463\) 3.87736e18 0.850098 0.425049 0.905170i \(-0.360257\pi\)
0.425049 + 0.905170i \(0.360257\pi\)
\(464\) 8.89068e18i 1.92003i
\(465\) −7.66828e17 + 1.41458e18i −0.163128 + 0.300925i
\(466\) 1.80813e17 0.0378904
\(467\) 2.71349e18i 0.560156i −0.959977 0.280078i \(-0.909640\pi\)
0.959977 0.280078i \(-0.0903604\pi\)
\(468\) −3.04020e18 4.66778e18i −0.618274 0.949269i
\(469\) −1.10993e18 −0.222375
\(470\) 1.12038e18i 0.221147i
\(471\) 3.16346e18 + 1.71487e18i 0.615199 + 0.333492i
\(472\) 9.50897e18 1.82196
\(473\) 1.61768e18i 0.305397i
\(474\) −7.56409e18 + 1.39536e19i −1.40705 + 2.59561i
\(475\) 2.18651e18 0.400772
\(476\) 1.10865e19i 2.00238i
\(477\) −2.33185e18 + 1.51877e18i −0.415023 + 0.270311i
\(478\) 1.43663e19 2.51970
\(479\) 9.98368e18i 1.72561i −0.505538 0.862804i \(-0.668706\pi\)
0.505538 0.862804i \(-0.331294\pi\)
\(480\) 6.18760e17 + 3.35422e17i 0.105398 + 0.0571351i
\(481\) −1.47880e18 −0.248252
\(482\) 1.39378e19i 2.30603i
\(483\) 1.61800e16 2.98476e16i 0.00263845 0.00486721i
\(484\) −4.17463e18 −0.670967
\(485\) 1.22381e18i 0.193876i
\(486\) −6.90378e18 8.93498e18i −1.07803 1.39521i
\(487\) −7.04157e18 −1.08384 −0.541922 0.840429i \(-0.682303\pi\)
−0.541922 + 0.840429i \(0.682303\pi\)
\(488\) 1.73423e19i 2.63128i
\(489\) 4.90293e18 + 2.65782e18i 0.733320 + 0.397524i
\(490\) −2.34874e18 −0.346308
\(491\) 3.57849e18i 0.520151i −0.965588 0.260076i \(-0.916253\pi\)
0.965588 0.260076i \(-0.0837475\pi\)
\(492\) 4.00275e18 7.38395e18i 0.573591 1.05812i
\(493\) −1.66018e19 −2.34545
\(494\) 2.98796e18i 0.416184i
\(495\) 9.72783e17 + 1.49356e18i 0.133592 + 0.205110i
\(496\) −1.14113e19 −1.54513
\(497\) 6.80564e18i 0.908604i
\(498\) 5.28880e18 + 2.86699e18i 0.696228 + 0.377416i
\(499\) 1.27672e19 1.65726 0.828629 0.559797i \(-0.189121\pi\)
0.828629 + 0.559797i \(0.189121\pi\)
\(500\) 9.33845e18i 1.19532i
\(501\) −9.20724e17 + 1.69848e18i −0.116216 + 0.214386i
\(502\) 8.39326e18 1.04473
\(503\) 1.14021e19i 1.39962i 0.714330 + 0.699809i \(0.246731\pi\)
−0.714330 + 0.699809i \(0.753269\pi\)
\(504\) 7.86063e18 5.11976e18i 0.951577 0.619777i
\(505\) 2.08545e18 0.248978
\(506\) 1.17845e17i 0.0138758i
\(507\) −5.38551e18 2.91942e18i −0.625419 0.339032i
\(508\) 4.18860e18 0.479759
\(509\) 5.16333e18i 0.583319i 0.956522 + 0.291659i \(0.0942073\pi\)
−0.956522 + 0.291659i \(0.905793\pi\)
\(510\) 3.65403e18 6.74067e18i 0.407175 0.751124i
\(511\) −5.10327e18 −0.560921
\(512\) 1.91369e19i 2.07483i
\(513\) 3.30576e17 + 4.09501e18i 0.0353549 + 0.437959i
\(514\) 4.19520e17 0.0442599
\(515\) 2.27913e18i 0.237202i
\(516\) −6.67826e18 3.62020e18i −0.685670 0.371693i
\(517\) 3.44919e18 0.349368
\(518\) 4.73635e18i 0.473299i
\(519\) 9.35205e17 1.72519e18i 0.0922009 0.170085i
\(520\) −3.20071e18 −0.311332
\(521\) 1.00727e19i 0.966675i −0.875434 0.483338i \(-0.839424\pi\)
0.875434 0.483338i \(-0.160576\pi\)
\(522\) 1.45814e19 + 2.23875e19i 1.38072 + 2.11989i
\(523\) −7.35018e18 −0.686730 −0.343365 0.939202i \(-0.611567\pi\)
−0.343365 + 0.939202i \(0.611567\pi\)
\(524\) 1.48385e19i 1.36795i
\(525\) 5.12059e18 + 2.77581e18i 0.465805 + 0.252507i
\(526\) −1.97228e19 −1.77039
\(527\) 2.13087e19i 1.88748i
\(528\) −6.02423e18 + 1.11130e19i −0.526580 + 0.971392i
\(529\) 1.15918e19 0.999909
\(530\) 3.04106e18i 0.258877i
\(531\) −9.29560e18 + 6.05438e18i −0.780937 + 0.508637i
\(532\) −6.49157e18 −0.538231
\(533\) 3.74701e18i 0.306616i
\(534\) −1.30311e19 7.06401e18i −1.05243 0.570509i
\(535\) 2.98793e18 0.238173
\(536\) 9.51219e18i 0.748388i
\(537\) 1.14115e19 2.10511e19i 0.886185 1.63476i
\(538\) 2.85220e19 2.18627
\(539\) 7.23078e18i 0.547096i
\(540\) −8.34286e18 + 6.73490e17i −0.623102 + 0.0503008i
\(541\) −3.58953e18 −0.264640 −0.132320 0.991207i \(-0.542243\pi\)
−0.132320 + 0.991207i \(0.542243\pi\)
\(542\) 1.32345e19i 0.963192i
\(543\) −1.24584e19 6.75355e18i −0.895084 0.485214i
\(544\) 9.32074e18 0.661086
\(545\) 2.72336e18i 0.190691i
\(546\) −3.79325e18 + 6.99748e18i −0.262218 + 0.483719i
\(547\) 4.53669e18 0.309619 0.154809 0.987944i \(-0.450524\pi\)
0.154809 + 0.987944i \(0.450524\pi\)
\(548\) 2.57217e19i 1.73315i
\(549\) −1.10418e19 1.69531e19i −0.734573 1.12783i
\(550\) −2.02172e19 −1.32795
\(551\) 9.72100e18i 0.630449i
\(552\) −2.55796e17 1.38664e17i −0.0163803 0.00887954i
\(553\) 1.53836e19 0.972709
\(554\) 3.97545e19i 2.48209i
\(555\) −1.05892e18 + 1.95341e18i −0.0652848 + 0.120432i
\(556\) 4.47822e19 2.72635
\(557\) 6.89338e18i 0.414425i 0.978296 + 0.207212i \(0.0664391\pi\)
−0.978296 + 0.207212i \(0.933561\pi\)
\(558\) 2.87348e19 1.87154e19i 1.70596 1.11112i
\(559\) 3.38890e18 0.198690
\(560\) 3.97973e18i 0.230429i
\(561\) 2.07517e19 + 1.12492e19i 1.18662 + 0.643254i
\(562\) −4.22554e19 −2.38631
\(563\) 1.45922e18i 0.0813883i −0.999172 0.0406942i \(-0.987043\pi\)
0.999172 0.0406942i \(-0.0129569\pi\)
\(564\) −7.71892e18 + 1.42393e19i −0.425210 + 0.784393i
\(565\) −6.60018e18 −0.359101
\(566\) 2.37586e18i 0.127675i
\(567\) −4.42449e18 + 1.00098e19i −0.234845 + 0.531303i
\(568\) −5.83249e19 −3.05785
\(569\) 4.36385e18i 0.225987i 0.993596 + 0.112994i \(0.0360440\pi\)
−0.993596 + 0.112994i \(0.963956\pi\)
\(570\) 3.94692e18 + 2.13958e18i 0.201899 + 0.109447i
\(571\) 1.61706e19 0.817099 0.408549 0.912736i \(-0.366035\pi\)
0.408549 + 0.912736i \(0.366035\pi\)
\(572\) 1.87406e19i 0.935431i
\(573\) −1.15496e19 + 2.13059e19i −0.569490 + 1.05055i
\(574\) −1.20011e19 −0.584570
\(575\) 1.80658e17i 0.00869323i
\(576\) 7.17620e18 + 1.10180e19i 0.341143 + 0.523775i
\(577\) 8.26639e17 0.0388227 0.0194113 0.999812i \(-0.493821\pi\)
0.0194113 + 0.999812i \(0.493821\pi\)
\(578\) 6.35381e19i 2.94808i
\(579\) −1.87762e19 1.01784e19i −0.860714 0.466582i
\(580\) 1.98048e19 0.896965
\(581\) 5.83080e18i 0.260913i
\(582\) 1.24298e19 2.29295e19i 0.549546 1.01376i
\(583\) −9.36213e18 −0.408973
\(584\) 4.37354e19i 1.88774i
\(585\) 3.12889e18 2.03790e18i 0.133444 0.0869144i
\(586\) 4.68694e19 1.97518
\(587\) 3.82350e19i 1.59219i 0.605172 + 0.796095i \(0.293104\pi\)
−0.605172 + 0.796095i \(0.706896\pi\)
\(588\) 2.98508e19 + 1.61817e19i 1.22833 + 0.665862i
\(589\) −1.24771e19 −0.507347
\(590\) 1.21228e19i 0.487122i
\(591\) −1.07772e19 + 1.98810e19i −0.427952 + 0.789451i
\(592\) −1.57580e19 −0.618371
\(593\) 2.10110e19i 0.814826i −0.913244 0.407413i \(-0.866431\pi\)
0.913244 0.407413i \(-0.133569\pi\)
\(594\) −3.05661e18 3.78638e19i −0.117148 1.45117i
\(595\) −7.43147e18 −0.281485
\(596\) 3.35093e19i 1.25442i
\(597\) 2.55543e19 + 1.38527e19i 0.945461 + 0.512523i
\(598\) 2.46876e17 0.00902755
\(599\) 4.94075e19i 1.78569i −0.450367 0.892844i \(-0.648707\pi\)
0.450367 0.892844i \(-0.351293\pi\)
\(600\) 2.37889e19 4.38838e19i 0.849797 1.56764i
\(601\) −2.29665e19 −0.810912 −0.405456 0.914115i \(-0.632887\pi\)
−0.405456 + 0.914115i \(0.632887\pi\)
\(602\) 1.08541e19i 0.378808i
\(603\) −6.05643e18 9.29875e18i −0.208927 0.320777i
\(604\) 3.50008e19 1.19349
\(605\) 2.79833e18i 0.0943217i
\(606\) −3.90733e19 2.11811e19i −1.30188 0.705733i
\(607\) 2.40723e19 0.792862 0.396431 0.918065i \(-0.370249\pi\)
0.396431 + 0.918065i \(0.370249\pi\)
\(608\) 5.45765e18i 0.177697i
\(609\) 1.23409e19 2.27656e19i 0.397216 0.732753i
\(610\) −2.21092e19 −0.703501
\(611\) 7.22575e18i 0.227298i
\(612\) −9.28802e19 + 6.04944e19i −2.88844 + 1.88129i
\(613\) −4.49657e19 −1.38248 −0.691239 0.722626i \(-0.742935\pi\)
−0.691239 + 0.722626i \(0.742935\pi\)
\(614\) 7.36770e19i 2.23951i
\(615\) 4.94959e18 + 2.68311e18i 0.148745 + 0.0806330i
\(616\) 3.15596e19 0.937705
\(617\) 1.15025e18i 0.0337907i 0.999857 + 0.0168954i \(0.00537822\pi\)
−0.999857 + 0.0168954i \(0.994622\pi\)
\(618\) −2.31482e19 + 4.27020e19i −0.672355 + 1.24031i
\(619\) 1.85323e19 0.532224 0.266112 0.963942i \(-0.414261\pi\)
0.266112 + 0.963942i \(0.414261\pi\)
\(620\) 2.54198e19i 0.721823i
\(621\) 3.38344e17 2.73133e16i 0.00949987 0.000766891i
\(622\) 8.90271e19 2.47166
\(623\) 1.43666e19i 0.394400i
\(624\) 2.32808e19 + 1.26203e19i 0.631985 + 0.342591i
\(625\) 2.77195e19 0.744089
\(626\) 9.46430e19i 2.51228i
\(627\) −6.58685e18 + 1.21509e19i −0.172904 + 0.318960i
\(628\) −5.68468e19 −1.47567
\(629\) 2.94254e19i 0.755383i
\(630\) 6.52706e18 + 1.00213e19i 0.165704 + 0.254415i
\(631\) 2.33455e18 0.0586136 0.0293068 0.999570i \(-0.490670\pi\)
0.0293068 + 0.999570i \(0.490670\pi\)
\(632\) 1.31839e20i 3.27359i
\(633\) 2.67069e19 + 1.44775e19i 0.655838 + 0.355522i
\(634\) −8.30685e19 −2.01749
\(635\) 2.80769e18i 0.0674424i
\(636\) 2.09515e19 3.86496e19i 0.497754 0.918217i
\(637\) −1.51479e19 −0.355939
\(638\) 8.98836e19i 2.08899i
\(639\) 5.70162e19 3.71356e19i 1.31067 0.853658i
\(640\) 1.96417e19 0.446602
\(641\) 2.31344e19i 0.520298i 0.965568 + 0.260149i \(0.0837717\pi\)
−0.965568 + 0.260149i \(0.916228\pi\)
\(642\) −5.59821e19 3.03472e19i −1.24539 0.675109i
\(643\) 3.27850e19 0.721438 0.360719 0.932675i \(-0.382531\pi\)
0.360719 + 0.932675i \(0.382531\pi\)
\(644\) 5.36357e17i 0.0116749i
\(645\) 2.42669e18 4.47656e18i 0.0522511 0.0963887i
\(646\) 5.94548e19 1.26637
\(647\) 2.52933e19i 0.532937i 0.963844 + 0.266468i \(0.0858568\pi\)
−0.963844 + 0.266468i \(0.914143\pi\)
\(648\) 8.57844e19 + 3.79183e19i 1.78806 + 0.790357i
\(649\) −3.73208e19 −0.769553
\(650\) 4.23534e19i 0.863962i
\(651\) −2.92200e19 1.58398e19i −0.589675 0.319656i
\(652\) −8.81048e19 −1.75900
\(653\) 2.21595e19i 0.437692i −0.975759 0.218846i \(-0.929771\pi\)
0.975759 0.218846i \(-0.0702292\pi\)
\(654\) −2.76602e19 + 5.10253e19i −0.540519 + 0.997106i
\(655\) 9.94651e18 0.192301
\(656\) 3.99279e19i 0.763748i
\(657\) −2.78464e19 4.27540e19i −0.527001 0.809132i
\(658\) 2.31429e19 0.433348
\(659\) 1.61070e19i 0.298413i 0.988806 + 0.149207i \(0.0476719\pi\)
−0.988806 + 0.149207i \(0.952328\pi\)
\(660\) −2.47553e19 1.34196e19i −0.453796 0.245997i
\(661\) −3.88817e19 −0.705236 −0.352618 0.935767i \(-0.614709\pi\)
−0.352618 + 0.935767i \(0.614709\pi\)
\(662\) 3.30346e19i 0.592875i
\(663\) 2.35662e19 4.34730e19i 0.418499 0.772013i
\(664\) −4.99704e19 −0.878085
\(665\) 4.35141e18i 0.0756622i
\(666\) 3.96801e19 2.58443e19i 0.682736 0.444677i
\(667\) −8.03184e17 −0.0136752
\(668\) 3.05214e19i 0.514244i
\(669\) −2.91752e17 1.58155e17i −0.00486442 0.00263694i
\(670\) −1.21269e19 −0.200090
\(671\) 6.80649e19i 1.11139i
\(672\) −6.92856e18 + 1.27813e19i −0.111959 + 0.206533i
\(673\) −3.72205e19 −0.595219 −0.297609 0.954688i \(-0.596189\pi\)
−0.297609 + 0.954688i \(0.596189\pi\)
\(674\) 1.25614e20i 1.98800i
\(675\) 4.68581e18 + 5.80455e19i 0.0733936 + 0.909164i
\(676\) 9.67767e19 1.50018
\(677\) 8.23009e19i 1.26265i 0.775517 + 0.631326i \(0.217489\pi\)
−0.775517 + 0.631326i \(0.782511\pi\)
\(678\) 1.23662e20 + 6.70355e19i 1.87770 + 1.01788i
\(679\) −2.52794e19 −0.379908
\(680\) 6.36883e19i 0.947321i
\(681\) −5.48876e19 + 1.01252e20i −0.808061 + 1.49065i
\(682\) 1.15367e20 1.68109
\(683\) 6.26033e19i 0.902927i −0.892290 0.451463i \(-0.850902\pi\)
0.892290 0.451463i \(-0.149098\pi\)
\(684\) −3.54218e19 5.43849e19i −0.505682 0.776401i
\(685\) 1.72417e19 0.243639
\(686\) 1.21741e20i 1.70282i
\(687\) −2.24877e19 1.21903e19i −0.311350 0.168779i
\(688\) 3.61120e19 0.494917
\(689\) 1.96129e19i 0.266077i
\(690\) 1.76780e17 3.26109e17i 0.00237404 0.00437944i
\(691\) 2.70281e19 0.359309 0.179655 0.983730i \(-0.442502\pi\)
0.179655 + 0.983730i \(0.442502\pi\)
\(692\) 3.10014e19i 0.407980i
\(693\) −3.08514e19 + 2.00940e19i −0.401923 + 0.261779i
\(694\) 1.23765e19 0.159618
\(695\) 3.00183e19i 0.383259i
\(696\) −1.95103e20 1.05763e20i −2.46603 1.33681i
\(697\) 7.45586e19 0.932971
\(698\) 1.30230e20i 1.61333i
\(699\) 8.35028e17 1.54039e18i 0.0102414 0.0188926i
\(700\) −9.20161e19 −1.11732
\(701\) 9.70271e19i 1.16645i −0.812310 0.583226i \(-0.801790\pi\)
0.812310 0.583226i \(-0.198210\pi\)
\(702\) −7.93215e19 + 6.40334e18i −0.944128 + 0.0762161i
\(703\) −1.72297e19 −0.203044
\(704\) 4.42360e19i 0.516140i
\(705\) −9.54482e18 5.17413e18i −0.110267 0.0597742i
\(706\) −2.02440e20 −2.31560
\(707\) 4.30776e19i 0.487883i
\(708\) 8.35202e19 1.54071e20i 0.936610 1.72778i
\(709\) 1.02481e20 1.13794 0.568968 0.822360i \(-0.307343\pi\)
0.568968 + 0.822360i \(0.307343\pi\)
\(710\) 7.43571e19i 0.817549i
\(711\) 8.39421e19 + 1.28881e20i 0.913887 + 1.40314i
\(712\) 1.23123e20 1.32733
\(713\) 1.03090e18i 0.0110050i
\(714\) 1.39237e20 + 7.54786e19i 1.47186 + 0.797878i
\(715\) 1.25622e19 0.131499
\(716\) 3.78285e20i 3.92128i
\(717\) 6.63460e19 1.22390e20i 0.681052 1.25635i
\(718\) −2.66965e20 −2.71383
\(719\) 1.67928e19i 0.169052i 0.996421 + 0.0845260i \(0.0269376\pi\)
−0.996421 + 0.0845260i \(0.973062\pi\)
\(720\) 3.33413e19 2.17157e19i 0.332396 0.216495i
\(721\) 4.70782e19 0.464807
\(722\) 1.45511e20i 1.42278i
\(723\) −1.18739e20 6.43671e19i −1.14981 0.623298i
\(724\) 2.23875e20 2.14702
\(725\) 1.37792e20i 1.30876i
\(726\) −2.84216e19 + 5.24299e19i −0.267357 + 0.493199i
\(727\) −1.97576e20 −1.84074 −0.920371 0.391047i \(-0.872113\pi\)
−0.920371 + 0.391047i \(0.872113\pi\)
\(728\) 6.61147e19i 0.610068i
\(729\) −1.08002e20 + 1.75516e19i −0.987051 + 0.160408i
\(730\) −5.57572e19 −0.504709
\(731\) 6.74329e19i 0.604575i
\(732\) 2.80992e20 + 1.52322e20i 2.49526 + 1.35265i
\(733\) 2.03135e20 1.78672 0.893360 0.449341i \(-0.148341\pi\)
0.893360 + 0.449341i \(0.148341\pi\)
\(734\) 2.82506e20i 2.46125i
\(735\) −1.08469e19 + 2.00095e19i −0.0936040 + 0.172673i
\(736\) 4.50931e17 0.00385447
\(737\) 3.73335e19i 0.316101i
\(738\) −6.54848e19 1.00542e20i −0.549219 0.843245i
\(739\) 3.77054e19 0.313251 0.156625 0.987658i \(-0.449938\pi\)
0.156625 + 0.987658i \(0.449938\pi\)
\(740\) 3.51025e19i 0.288879i
\(741\) 2.54551e19 + 1.37989e19i 0.207514 + 0.112491i
\(742\) −6.28169e19 −0.507282
\(743\) 1.51734e20i 1.21384i 0.794764 + 0.606918i \(0.207595\pi\)
−0.794764 + 0.606918i \(0.792405\pi\)
\(744\) −1.35748e20 + 2.50417e20i −1.07578 + 1.98451i
\(745\) −2.24619e19 −0.176341
\(746\) 3.72156e20i 2.89436i
\(747\) 4.88492e19 3.18163e19i 0.376368 0.245135i
\(748\) −3.72904e20 −2.84633
\(749\) 6.17193e19i 0.466711i
\(750\) 1.17283e20 + 6.35777e19i 0.878631 + 0.476295i
\(751\) −1.19860e20 −0.889600 −0.444800 0.895630i \(-0.646725\pi\)
−0.444800 + 0.895630i \(0.646725\pi\)
\(752\) 7.69973e19i 0.566175i
\(753\) 3.87615e19 7.15042e19i 0.282381 0.520915i
\(754\) 1.88299e20 1.35909
\(755\) 2.34617e19i 0.167776i
\(756\) −1.39118e19 1.72332e20i −0.0985666 1.22100i
\(757\) 6.29864e19 0.442156 0.221078 0.975256i \(-0.429042\pi\)
0.221078 + 0.975256i \(0.429042\pi\)
\(758\) 5.62867e19i 0.391491i
\(759\) 1.00395e18 + 5.44229e17i 0.00691863 + 0.00375050i
\(760\) −3.72920e19 −0.254636
\(761\) 7.74499e19i 0.523997i 0.965068 + 0.261998i \(0.0843815\pi\)
−0.965068 + 0.261998i \(0.915619\pi\)
\(762\) 2.85167e19 5.26052e19i 0.191167 0.352650i
\(763\) 5.62545e19 0.373667
\(764\) 3.82863e20i 2.51994i
\(765\) −4.05504e19 6.22592e19i −0.264463 0.406044i
\(766\) 1.61916e20 1.04638
\(767\) 7.81840e19i 0.500669i
\(768\) −2.81410e20 1.52549e20i −1.78571 0.968012i
\(769\) −1.63707e20 −1.02939 −0.514697 0.857372i \(-0.672096\pi\)
−0.514697 + 0.857372i \(0.672096\pi\)
\(770\) 4.02346e19i 0.250706i
\(771\) 1.93742e18 3.57399e18i 0.0119631 0.0220685i
\(772\) 3.37406e20 2.06458
\(773\) 1.95306e20i 1.18430i 0.805829 + 0.592148i \(0.201720\pi\)
−0.805829 + 0.592148i \(0.798280\pi\)
\(774\) −9.09333e19 + 5.92264e19i −0.546432 + 0.355900i
\(775\) −1.76859e20 −1.05321
\(776\) 2.16647e20i 1.27856i
\(777\) −4.03501e19 2.18733e19i −0.235992 0.127928i
\(778\) 5.34067e20 3.09556
\(779\) 4.36569e19i 0.250779i
\(780\) −2.81128e19 + 5.18603e19i −0.160045 + 0.295239i
\(781\) 2.28914e20 1.29156
\(782\) 4.91237e18i 0.0274690i
\(783\) 2.58064e20 2.08326e19i 1.43020 0.115455i
\(784\) −1.61415e20 −0.886608
\(785\) 3.81054e19i 0.207443i
\(786\) −1.86359e20 1.01023e20i −1.00552 0.545082i
\(787\) −1.79888e20 −0.962007 −0.481004 0.876719i \(-0.659728\pi\)
−0.481004 + 0.876719i \(0.659728\pi\)
\(788\) 3.57258e20i 1.89364i
\(789\) −9.10834e19 + 1.68023e20i −0.478520 + 0.882736i
\(790\) 1.68078e20 0.875230
\(791\) 1.36335e20i 0.703674i
\(792\) 1.72208e20 + 2.64399e20i 0.881000 + 1.35265i
\(793\) −1.42590e20 −0.723066
\(794\) 2.22596e20i 1.11885i
\(795\) 2.59075e19 + 1.40442e19i 0.129079 + 0.0699722i
\(796\) −4.59206e20 −2.26786
\(797\) 2.77052e20i 1.35629i −0.734927 0.678146i \(-0.762784\pi\)
0.734927 0.678146i \(-0.237216\pi\)
\(798\) −4.41957e19 + 8.15286e19i −0.214466 + 0.395631i
\(799\) −1.43779e20 −0.691622
\(800\) 7.73606e19i 0.368884i
\(801\) −1.20360e20 + 7.83925e19i −0.568925 + 0.370550i
\(802\) −4.85879e20 −2.27671
\(803\) 1.71653e20i 0.797337i
\(804\) 1.54124e20 + 8.35485e19i 0.709703 + 0.384721i
\(805\) −3.59529e17 −0.00164121
\(806\) 2.41684e20i 1.09371i
\(807\) 1.31719e20 2.42985e20i 0.590929 1.09010i
\(808\) 3.69178e20 1.64194
\(809\) 1.89882e20i 0.837229i 0.908164 + 0.418615i \(0.137484\pi\)
−0.908164 + 0.418615i \(0.862516\pi\)
\(810\) −4.83411e19 + 1.09365e20i −0.211311 + 0.478059i
\(811\) 2.25399e20 0.976802 0.488401 0.872619i \(-0.337580\pi\)
0.488401 + 0.872619i \(0.337580\pi\)
\(812\) 4.09094e20i 1.75764i
\(813\) 1.12748e20 + 6.11193e19i 0.480259 + 0.260342i
\(814\) 1.59311e20 0.672784
\(815\) 5.90582e19i 0.247273i
\(816\) 2.51120e20 4.63246e20i 1.04244 1.92301i
\(817\) 3.94846e19 0.162508
\(818\) 7.50141e20i 3.06105i
\(819\) 4.20953e19 + 6.46312e19i 0.170313 + 0.261490i
\(820\) −8.89433e19 −0.356793
\(821\) 4.00570e20i 1.59322i −0.604492 0.796611i \(-0.706624\pi\)
0.604492 0.796611i \(-0.293376\pi\)
\(822\) −3.23042e20 1.75117e20i −1.27396 0.690600i
\(823\) 1.34324e20 0.525235 0.262617 0.964900i \(-0.415414\pi\)
0.262617 + 0.964900i \(0.415414\pi\)
\(824\) 4.03464e20i 1.56428i
\(825\) −9.33667e19 + 1.72235e20i −0.358934 + 0.662132i
\(826\) −2.50411e20 −0.954537
\(827\) 9.76761e19i 0.369190i 0.982815 + 0.184595i \(0.0590973\pi\)
−0.982815 + 0.184595i \(0.940903\pi\)
\(828\) −4.49348e18 + 2.92667e18i −0.0168411 + 0.0109689i
\(829\) 1.39626e20 0.518900 0.259450 0.965757i \(-0.416459\pi\)
0.259450 + 0.965757i \(0.416459\pi\)
\(830\) 6.37062e19i 0.234766i
\(831\) 3.38678e20 + 1.83593e20i 1.23760 + 0.670888i
\(832\) 9.26708e19 0.335799
\(833\) 3.01415e20i 1.08305i
\(834\) 3.04884e20 5.62426e20i 1.08636 2.00403i
\(835\) 2.04590e19 0.0722902
\(836\) 2.18350e20i 0.765083i
\(837\) −2.67390e19 3.31230e20i −0.0929109 1.15094i
\(838\) −4.83169e20 −1.66491
\(839\) 3.23963e19i 0.110703i −0.998467 0.0553517i \(-0.982372\pi\)
0.998467 0.0553517i \(-0.0176280\pi\)
\(840\) −8.73339e19 4.73426e19i −0.295956 0.160434i
\(841\) −3.15052e20 −1.05879
\(842\) 1.97123e20i 0.656981i
\(843\) −1.95143e20 + 3.59984e20i −0.644999 + 1.18984i
\(844\) −4.79918e20 −1.57315
\(845\) 6.48711e19i 0.210889i
\(846\) 1.26281e20 + 1.93886e20i 0.407142 + 0.625107i
\(847\) 5.78030e19 0.184827
\(848\) 2.08994e20i 0.662770i
\(849\) −2.02405e19 1.09721e19i −0.0636601 0.0345094i
\(850\) 8.42754e20 2.62887
\(851\) 1.42358e18i 0.00440427i
\(852\) −5.12286e20 + 9.45024e20i −1.57194 + 2.89978i
\(853\) −3.08044e19 −0.0937495 −0.0468748 0.998901i \(-0.514926\pi\)
−0.0468748 + 0.998901i \(0.514926\pi\)
\(854\) 4.56694e20i 1.37854i
\(855\) 3.64552e19 2.37439e19i 0.109143 0.0710867i
\(856\) 5.28940e20 1.57069
\(857\) 4.87680e19i 0.143638i −0.997418 0.0718190i \(-0.977120\pi\)
0.997418 0.0718190i \(-0.0228804\pi\)
\(858\) −2.35366e20 1.27589e20i −0.687596 0.372737i
\(859\) 1.49706e20 0.433799 0.216899 0.976194i \(-0.430406\pi\)
0.216899 + 0.976194i \(0.430406\pi\)
\(860\) 8.04430e19i 0.231206i
\(861\) −5.54230e19 + 1.02240e20i −0.158004 + 0.291473i
\(862\) −1.29676e20 −0.366699
\(863\) 3.15069e20i 0.883751i −0.897076 0.441875i \(-0.854313\pi\)
0.897076 0.441875i \(-0.145687\pi\)
\(864\) −1.44885e20 + 1.16960e19i −0.403113 + 0.0325419i
\(865\) −2.07808e19 −0.0573521
\(866\) 3.91872e20i 1.07280i
\(867\) −5.41297e20 2.93430e20i −1.46995 0.796840i
\(868\) 5.25078e20 1.41444
\(869\) 5.17442e20i 1.38269i
\(870\) 1.34835e20 2.48732e20i 0.357410 0.659321i
\(871\) −7.82105e19 −0.205654
\(872\) 4.82105e20i 1.25755i
\(873\) −1.37939e20 2.11785e20i −0.356934 0.548020i
\(874\) 2.87638e18 0.00738357
\(875\) 1.29303e20i 0.329269i
\(876\) 7.08633e20 + 3.84141e20i 1.79016 + 0.970426i
\(877\) −3.62517e20 −0.908512 −0.454256 0.890871i \(-0.650095\pi\)
−0.454256 + 0.890871i \(0.650095\pi\)
\(878\) 4.81121e19i 0.119617i
\(879\) 2.16451e20 3.99292e20i 0.533873 0.984846i
\(880\) 1.33862e20 0.327550
\(881\) 1.15407e20i 0.280157i −0.990140 0.140078i \(-0.955265\pi\)
0.990140 0.140078i \(-0.0447355\pi\)
\(882\) 4.06458e20 2.64733e20i 0.978893 0.637569i
\(883\) 3.76570e20 0.899748 0.449874 0.893092i \(-0.351469\pi\)
0.449874 + 0.893092i \(0.351469\pi\)
\(884\) 7.81202e20i 1.85182i
\(885\) 1.03277e20 + 5.59851e19i 0.242884 + 0.131665i
\(886\) −4.09972e20 −0.956573
\(887\) 4.49245e20i 1.03996i 0.854177 + 0.519982i \(0.174061\pi\)
−0.854177 + 0.519982i \(0.825939\pi\)
\(888\) −1.87456e20 + 3.45804e20i −0.430535 + 0.794216i
\(889\) −5.79964e19 −0.132156
\(890\) 1.56966e20i 0.354876i
\(891\) −3.36687e20 1.48822e20i −0.755235 0.333828i
\(892\) 5.24273e18 0.0116682
\(893\) 8.41883e19i 0.185905i
\(894\) 4.20849e20 + 2.28137e20i 0.922069 + 0.499842i
\(895\) −2.53571e20 −0.551237
\(896\) 4.05725e20i 0.875136i
\(897\) 1.14011e18 2.10319e18i 0.00244006 0.00450124i
\(898\) −1.00596e21 −2.13623
\(899\) 7.86294e20i 1.65679i
\(900\) −5.02093e20 7.70890e20i −1.04975 1.61174i
\(901\) 3.90260e20 0.809619
\(902\) 4.03666e20i 0.830953i
\(903\) 9.24688e19 + 5.01262e19i 0.188878 + 0.102388i
\(904\) −1.16840e21 −2.36817
\(905\) 1.50068e20i 0.301819i
\(906\) 2.38291e20 4.39581e20i 0.475566 0.877286i
\(907\) 9.99929e20 1.98024 0.990121 0.140215i \(-0.0447794\pi\)
0.990121 + 0.140215i \(0.0447794\pi\)
\(908\) 1.81949e21i 3.57559i
\(909\) −3.60894e20 + 2.35056e20i −0.703773 + 0.458379i
\(910\) 8.42881e19 0.163108
\(911\) 5.11050e20i 0.981374i −0.871336 0.490687i \(-0.836746\pi\)
0.871336 0.490687i \(-0.163254\pi\)
\(912\) 2.71248e20 + 1.47040e20i 0.516896 + 0.280203i
\(913\) 1.96124e20 0.370882
\(914\) 4.38374e20i 0.822661i
\(915\) −1.02104e20 + 1.88354e20i −0.190150 + 0.350774i
\(916\) 4.04101e20 0.746830
\(917\) 2.05458e20i 0.376822i
\(918\) 1.27415e20 + 1.57835e21i 0.231911 + 2.87280i
\(919\) −4.38250e20 −0.791613 −0.395807 0.918334i \(-0.629535\pi\)
−0.395807 + 0.918334i \(0.629535\pi\)
\(920\) 3.08119e18i 0.00552337i
\(921\) 6.27672e20 + 3.40253e20i 1.11665 + 0.605320i
\(922\) −2.53369e20 −0.447339
\(923\) 4.79555e20i 0.840285i
\(924\) 2.77198e20 5.11352e20i 0.482043 0.889234i
\(925\) −2.44226e20 −0.421501
\(926\) 8.75065e20i 1.49887i
\(927\) 2.56886e20 + 3.94411e20i 0.436699 + 0.670487i
\(928\) 3.43937e20 0.580287
\(929\) 6.29570e20i 1.05423i −0.849795 0.527113i \(-0.823274\pi\)
0.849795 0.527113i \(-0.176726\pi\)
\(930\) −3.19251e20 1.73062e20i −0.530582 0.287622i
\(931\) −1.76490e20 −0.291120
\(932\) 2.76806e19i 0.0453173i
\(933\) 4.11143e20 7.58443e20i 0.668069 1.23240i
\(934\) 6.12395e20 0.987651
\(935\) 2.49964e20i 0.400125i
\(936\) 5.53894e20 3.60760e20i 0.880027 0.573176i
\(937\) 4.29592e20 0.677454 0.338727 0.940885i \(-0.390004\pi\)
0.338727 + 0.940885i \(0.390004\pi\)
\(938\) 2.50496e20i 0.392085i
\(939\) −8.06286e20 4.37078e20i −1.25265 0.679047i
\(940\) 1.71519e20 0.264495
\(941\) 2.95757e20i 0.452697i −0.974046 0.226349i \(-0.927321\pi\)
0.974046 0.226349i \(-0.0726789\pi\)
\(942\) −3.87022e20 + 7.13947e20i −0.588003 + 1.08470i
\(943\) 3.60709e18 0.00543970
\(944\) 8.33125e20i 1.24711i
\(945\) 1.15517e20 9.32530e18i 0.171642 0.0138561i
\(946\) −3.65088e20 −0.538467
\(947\) 1.58610e20i 0.232210i 0.993237 + 0.116105i \(0.0370408\pi\)
−0.993237 + 0.116105i \(0.962959\pi\)
\(948\) −2.13615e21 1.15798e21i −3.10437 1.68284i
\(949\) −3.59598e20 −0.518745
\(950\) 4.93465e20i 0.706629i
\(951\) −3.83625e20 + 7.07681e20i −0.545310 + 1.00594i
\(952\) −1.31556e21 −1.85632
\(953\) 8.31966e20i 1.16535i −0.812707 0.582673i \(-0.802007\pi\)
0.812707 0.582673i \(-0.197993\pi\)
\(954\) −3.42765e20 5.26266e20i −0.476605 0.731756i
\(955\) 2.56640e20 0.354242
\(956\) 2.19932e21i 3.01359i
\(957\) 7.65740e20 + 4.15098e20i 1.04159 + 0.564634i
\(958\) 2.25318e21 3.04254
\(959\) 3.56149e20i 0.477421i
\(960\) 6.63586e19 1.22413e20i 0.0883077 0.162903i
\(961\) 2.52277e20 0.333284
\(962\) 3.33744e20i 0.437711i
\(963\) −5.17071e20 + 3.36777e20i −0.673234 + 0.438488i
\(964\) 2.13372e21 2.75803
\(965\) 2.26169e20i 0.290230i
\(966\) 6.73618e18 + 3.65160e18i 0.00858171 + 0.00465204i
\(967\) −1.46184e21 −1.84890 −0.924452 0.381299i \(-0.875477\pi\)
−0.924452 + 0.381299i \(0.875477\pi\)
\(968\) 4.95376e20i 0.622025i
\(969\) 2.74573e20 5.06510e20i 0.342287 0.631425i
\(970\) −2.76198e20 −0.341836
\(971\) 3.08836e20i 0.379484i 0.981834 + 0.189742i \(0.0607652\pi\)
−0.981834 + 0.189742i \(0.939235\pi\)
\(972\) 1.36785e21 1.05689e21i 1.66869 1.28934i
\(973\) −6.20065e20 −0.751013
\(974\) 1.58918e21i 1.91100i
\(975\) 3.60819e20 + 1.95595e20i 0.430781 + 0.233521i
\(976\) −1.51943e21 −1.80108
\(977\) 2.08527e20i 0.245414i 0.992443 + 0.122707i \(0.0391576\pi\)
−0.992443 + 0.122707i \(0.960842\pi\)
\(978\) −5.99832e20 + 1.10652e21i −0.700902 + 1.29297i
\(979\) −4.83233e20 −0.560632
\(980\) 3.59567e20i 0.414188i
\(981\) 3.06957e20 + 4.71287e20i 0.351071 + 0.539017i
\(982\) 8.07615e20 0.917115
\(983\) 1.09204e21i 1.23130i 0.788020 + 0.615649i \(0.211106\pi\)
−0.788020 + 0.615649i \(0.788894\pi\)
\(984\) 8.76204e20 + 4.74980e20i 0.980934 + 0.531752i
\(985\) 2.39476e20 0.266200
\(986\) 3.74679e21i 4.13544i
\(987\) 1.06878e20 1.97160e20i 0.117130 0.216072i
\(988\) −4.57424e20 −0.497761
\(989\) 3.26236e18i 0.00352499i
\(990\) −3.37076e20 + 2.19543e20i −0.361645 + 0.235545i
\(991\) 5.22556e20 0.556695 0.278347 0.960480i \(-0.410213\pi\)
0.278347 + 0.960480i \(0.410213\pi\)
\(992\) 4.41448e20i 0.466980i
\(993\) 2.81430e20 + 1.52559e20i 0.295614 + 0.160249i
\(994\) 1.53594e21 1.60202
\(995\) 3.07814e20i 0.318806i
\(996\) −4.38906e20 + 8.09658e20i −0.451394 + 0.832696i
\(997\) −8.85987e20 −0.904818 −0.452409 0.891811i \(-0.649435\pi\)
−0.452409 + 0.891811i \(0.649435\pi\)
\(998\) 2.88137e21i 2.92203i
\(999\) −3.69241e19 4.57398e20i −0.0371836 0.460612i
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 3.15.b.a.2.4 yes 4
3.2 odd 2 inner 3.15.b.a.2.1 4
4.3 odd 2 48.15.e.b.17.1 4
5.2 odd 4 75.15.d.b.74.1 8
5.3 odd 4 75.15.d.b.74.8 8
5.4 even 2 75.15.c.d.26.1 4
12.11 even 2 48.15.e.b.17.2 4
15.2 even 4 75.15.d.b.74.7 8
15.8 even 4 75.15.d.b.74.2 8
15.14 odd 2 75.15.c.d.26.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.15.b.a.2.1 4 3.2 odd 2 inner
3.15.b.a.2.4 yes 4 1.1 even 1 trivial
48.15.e.b.17.1 4 4.3 odd 2
48.15.e.b.17.2 4 12.11 even 2
75.15.c.d.26.1 4 5.4 even 2
75.15.c.d.26.4 4 15.14 odd 2
75.15.d.b.74.1 8 5.2 odd 4
75.15.d.b.74.2 8 15.8 even 4
75.15.d.b.74.7 8 15.2 even 4
75.15.d.b.74.8 8 5.3 odd 4