Properties

Label 126.9.n.b.19.1
Level $126$
Weight $9$
Character 126.19
Analytic conductor $51.330$
Analytic rank $0$
Dimension $12$
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] = [126,9,Mod(19,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.19");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 126.n (of order \(6\), 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: \(51.3297048677\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} + 1771 x^{10} + 26038 x^{9} + 2442597 x^{8} + 26522276 x^{7} + 1175865280 x^{6} + 6901058684 x^{5} + 370996492174 x^{4} + \cdots + 36\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{24}\cdot 3^{10}\cdot 7^{3} \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.1
Root \(20.6104 - 35.6982i\) of defining polynomial
Character \(\chi\) \(=\) 126.19
Dual form 126.9.n.b.73.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.65685 + 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(-928.109 - 535.844i) q^{5} +(2212.86 + 931.703i) q^{7} +1448.15 q^{8} +O(q^{10})\) \(q+(-5.65685 + 9.79796i) q^{2} +(-64.0000 - 110.851i) q^{4} +(-928.109 - 535.844i) q^{5} +(2212.86 + 931.703i) q^{7} +1448.15 q^{8} +(10500.4 - 6062.38i) q^{10} +(-312.559 - 541.368i) q^{11} +43334.3i q^{13} +(-21646.6 + 16411.0i) q^{14} +(-8192.00 + 14189.0i) q^{16} +(-91086.4 + 52588.8i) q^{17} +(-138800. - 80136.4i) q^{19} +137176. i q^{20} +7072.40 q^{22} +(12272.7 - 21256.9i) q^{23} +(378945. + 656351. i) q^{25} +(-424587. - 245136. i) q^{26} +(-38342.4 - 304927. i) q^{28} +201272. q^{29} +(757712. - 437465. i) q^{31} +(-92681.9 - 160530. i) q^{32} -1.18995e6i q^{34} +(-1.55452e6 - 2.05047e6i) q^{35} +(830325. - 1.43817e6i) q^{37} +(1.57035e6 - 906640. i) q^{38} +(-1.34404e6 - 775985. i) q^{40} -464024. i q^{41} -2.94357e6 q^{43} +(-40007.5 + 69295.1i) q^{44} +(138849. + 240494. i) q^{46} +(2.19794e6 + 1.26898e6i) q^{47} +(4.02866e6 + 4.12345e6i) q^{49} -8.57454e6 q^{50} +(4.80366e6 - 2.77339e6i) q^{52} +(1.79237e6 + 3.10447e6i) q^{53} +669931. i q^{55} +(3.20456e6 + 1.34925e6i) q^{56} +(-1.13857e6 + 1.97206e6i) q^{58} +(-5.42785e6 + 3.13377e6i) q^{59} +(-1.03573e7 - 5.97980e6i) q^{61} +9.89870e6i q^{62} +2.09715e6 q^{64} +(2.32204e7 - 4.02189e7i) q^{65} +(-5.34103e6 - 9.25093e6i) q^{67} +(1.16591e7 + 6.73136e6i) q^{68} +(2.88841e7 - 3.63197e6i) q^{70} +2.25839e7 q^{71} +(4.20899e7 - 2.43006e7i) q^{73} +(9.39406e6 + 1.62710e7i) q^{74} +2.05149e7i q^{76} +(-187254. - 1.48918e6i) q^{77} +(2.70859e7 - 4.69142e7i) q^{79} +(1.52061e7 - 8.77926e6i) q^{80} +(4.54649e6 + 2.62492e6i) q^{82} -2.28950e7i q^{83} +1.12717e8 q^{85} +(1.66513e7 - 2.88409e7i) q^{86} +(-452634. - 783985. i) q^{88} +(-7.46258e7 - 4.30852e7i) q^{89} +(-4.03747e7 + 9.58925e7i) q^{91} -3.14181e6 q^{92} +(-2.48669e7 + 1.43569e7i) q^{94} +(8.58812e7 + 1.48751e8i) q^{95} -1.34358e8i q^{97} +(-6.31909e7 + 1.61469e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 768 q^{4} - 1674 q^{5} - 1308 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 768 q^{4} - 1674 q^{5} - 1308 q^{7} + 17664 q^{10} - 10302 q^{11} - 56832 q^{14} - 98304 q^{16} - 173178 q^{17} + 405978 q^{19} - 941568 q^{22} - 158934 q^{23} + 838668 q^{25} - 1958400 q^{26} - 255744 q^{28} + 4355256 q^{29} + 4520250 q^{31} + 5270790 q^{35} + 134214 q^{37} - 1278720 q^{38} - 2260992 q^{40} - 12961896 q^{43} - 1318656 q^{44} + 2345472 q^{46} - 18385002 q^{47} - 3659172 q^{49} - 2970624 q^{50} - 3369984 q^{52} + 16540506 q^{53} - 4325376 q^{56} + 9176064 q^{58} - 31163922 q^{59} - 85390158 q^{61} + 25165824 q^{64} + 46506264 q^{65} - 37750362 q^{67} + 22166784 q^{68} + 92031744 q^{70} - 45506424 q^{71} + 9414786 q^{73} - 58837248 q^{74} + 100614066 q^{77} + 59730294 q^{79} + 27426816 q^{80} - 93259776 q^{82} - 64652220 q^{85} + 15144960 q^{86} + 60260352 q^{88} - 323014482 q^{89} - 266861424 q^{91} + 40687104 q^{92} - 443440128 q^{94} + 175918350 q^{95} - 472166400 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.65685 + 9.79796i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −64.0000 110.851i −0.250000 0.433013i
\(5\) −928.109 535.844i −1.48497 0.857350i −0.485120 0.874448i \(-0.661224\pi\)
−0.999854 + 0.0170975i \(0.994557\pi\)
\(6\) 0 0
\(7\) 2212.86 + 931.703i 0.921639 + 0.388048i
\(8\) 1448.15 0.353553
\(9\) 0 0
\(10\) 10500.4 6062.38i 1.05004 0.606238i
\(11\) −312.559 541.368i −0.0213482 0.0369762i 0.855154 0.518374i \(-0.173463\pi\)
−0.876502 + 0.481398i \(0.840129\pi\)
\(12\) 0 0
\(13\) 43334.3i 1.51725i 0.651526 + 0.758626i \(0.274129\pi\)
−0.651526 + 0.758626i \(0.725871\pi\)
\(14\) −21646.6 + 16411.0i −0.563478 + 0.427191i
\(15\) 0 0
\(16\) −8192.00 + 14189.0i −0.125000 + 0.216506i
\(17\) −91086.4 + 52588.8i −1.09058 + 0.629647i −0.933731 0.357975i \(-0.883467\pi\)
−0.156850 + 0.987622i \(0.550134\pi\)
\(18\) 0 0
\(19\) −138800. 80136.4i −1.06506 0.614915i −0.138236 0.990399i \(-0.544143\pi\)
−0.926829 + 0.375484i \(0.877476\pi\)
\(20\) 137176.i 0.857350i
\(21\) 0 0
\(22\) 7072.40 0.0301909
\(23\) 12272.7 21256.9i 0.0438559 0.0759606i −0.843264 0.537499i \(-0.819369\pi\)
0.887120 + 0.461539i \(0.152702\pi\)
\(24\) 0 0
\(25\) 378945. + 656351.i 0.970098 + 1.68026i
\(26\) −424587. 245136.i −0.929124 0.536430i
\(27\) 0 0
\(28\) −38342.4 304927.i −0.0623802 0.496093i
\(29\) 201272. 0.284572 0.142286 0.989826i \(-0.454555\pi\)
0.142286 + 0.989826i \(0.454555\pi\)
\(30\) 0 0
\(31\) 757712. 437465.i 0.820459 0.473692i −0.0301154 0.999546i \(-0.509587\pi\)
0.850575 + 0.525854i \(0.176254\pi\)
\(32\) −92681.9 160530.i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 1.18995e6i 0.890456i
\(35\) −1.55452e6 2.05047e6i −1.03592 1.36641i
\(36\) 0 0
\(37\) 830325. 1.43817e6i 0.443038 0.767365i −0.554875 0.831934i \(-0.687234\pi\)
0.997913 + 0.0645689i \(0.0205672\pi\)
\(38\) 1.57035e6 906640.i 0.753114 0.434811i
\(39\) 0 0
\(40\) −1.34404e6 775985.i −0.525018 0.303119i
\(41\) 464024.i 0.164212i −0.996624 0.0821060i \(-0.973835\pi\)
0.996624 0.0821060i \(-0.0261646\pi\)
\(42\) 0 0
\(43\) −2.94357e6 −0.860994 −0.430497 0.902592i \(-0.641662\pi\)
−0.430497 + 0.902592i \(0.641662\pi\)
\(44\) −40007.5 + 69295.1i −0.0106741 + 0.0184881i
\(45\) 0 0
\(46\) 138849. + 240494.i 0.0310108 + 0.0537123i
\(47\) 2.19794e6 + 1.26898e6i 0.450427 + 0.260054i 0.708011 0.706202i \(-0.249593\pi\)
−0.257583 + 0.966256i \(0.582926\pi\)
\(48\) 0 0
\(49\) 4.02866e6 + 4.12345e6i 0.698838 + 0.715280i
\(50\) −8.57454e6 −1.37193
\(51\) 0 0
\(52\) 4.80366e6 2.77339e6i 0.656990 0.379313i
\(53\) 1.79237e6 + 3.10447e6i 0.227156 + 0.393445i 0.956964 0.290207i \(-0.0937240\pi\)
−0.729808 + 0.683652i \(0.760391\pi\)
\(54\) 0 0
\(55\) 669931.i 0.0732115i
\(56\) 3.20456e6 + 1.34925e6i 0.325849 + 0.137196i
\(57\) 0 0
\(58\) −1.13857e6 + 1.97206e6i −0.100611 + 0.174264i
\(59\) −5.42785e6 + 3.13377e6i −0.447940 + 0.258618i −0.706960 0.707254i \(-0.749934\pi\)
0.259020 + 0.965872i \(0.416600\pi\)
\(60\) 0 0
\(61\) −1.03573e7 5.97980e6i −0.748045 0.431884i 0.0769420 0.997036i \(-0.475484\pi\)
−0.824987 + 0.565152i \(0.808818\pi\)
\(62\) 9.89870e6i 0.669902i
\(63\) 0 0
\(64\) 2.09715e6 0.125000
\(65\) 2.32204e7 4.02189e7i 1.30082 2.25308i
\(66\) 0 0
\(67\) −5.34103e6 9.25093e6i −0.265049 0.459078i 0.702528 0.711656i \(-0.252055\pi\)
−0.967576 + 0.252579i \(0.918721\pi\)
\(68\) 1.16591e7 + 6.73136e6i 0.545291 + 0.314824i
\(69\) 0 0
\(70\) 2.88841e7 3.63197e6i 1.20300 0.151269i
\(71\) 2.25839e7 0.888721 0.444361 0.895848i \(-0.353431\pi\)
0.444361 + 0.895848i \(0.353431\pi\)
\(72\) 0 0
\(73\) 4.20899e7 2.43006e7i 1.48213 0.855709i 0.482337 0.875986i \(-0.339788\pi\)
0.999794 + 0.0202769i \(0.00645479\pi\)
\(74\) 9.39406e6 + 1.62710e7i 0.313275 + 0.542609i
\(75\) 0 0
\(76\) 2.05149e7i 0.614915i
\(77\) −187254. 1.48918e6i −0.00532682 0.0423628i
\(78\) 0 0
\(79\) 2.70859e7 4.69142e7i 0.695401 1.20447i −0.274645 0.961546i \(-0.588560\pi\)
0.970045 0.242924i \(-0.0781064\pi\)
\(80\) 1.52061e7 8.77926e6i 0.371243 0.214338i
\(81\) 0 0
\(82\) 4.54649e6 + 2.62492e6i 0.100559 + 0.0580577i
\(83\) 2.28950e7i 0.482424i −0.970472 0.241212i \(-0.922455\pi\)
0.970472 0.241212i \(-0.0775449\pi\)
\(84\) 0 0
\(85\) 1.12717e8 2.15931
\(86\) 1.66513e7 2.88409e7i 0.304407 0.527249i
\(87\) 0 0
\(88\) −452634. 783985.i −0.00754773 0.0130730i
\(89\) −7.46258e7 4.30852e7i −1.18940 0.686702i −0.231232 0.972899i \(-0.574276\pi\)
−0.958171 + 0.286197i \(0.907609\pi\)
\(90\) 0 0
\(91\) −4.03747e7 + 9.58925e7i −0.588767 + 1.39836i
\(92\) −3.14181e6 −0.0438559
\(93\) 0 0
\(94\) −2.48669e7 + 1.43569e7i −0.318500 + 0.183886i
\(95\) 8.58812e7 + 1.48751e8i 1.05440 + 1.82627i
\(96\) 0 0
\(97\) 1.34358e8i 1.51766i −0.651287 0.758831i \(-0.725771\pi\)
0.651287 0.758831i \(-0.274229\pi\)
\(98\) −6.31909e7 + 1.61469e7i −0.685094 + 0.175059i
\(99\) 0 0
\(100\) 4.85049e7 8.40130e7i 0.485049 0.840130i
\(101\) 3.28253e7 1.89517e7i 0.315445 0.182122i −0.333915 0.942603i \(-0.608370\pi\)
0.649360 + 0.760481i \(0.275037\pi\)
\(102\) 0 0
\(103\) 1.02126e8 + 5.89624e7i 0.907375 + 0.523873i 0.879586 0.475741i \(-0.157820\pi\)
0.0277893 + 0.999614i \(0.491153\pi\)
\(104\) 6.27547e7i 0.536430i
\(105\) 0 0
\(106\) −4.05567e7 −0.321247
\(107\) 2.25483e7 3.90548e7i 0.172020 0.297947i −0.767106 0.641520i \(-0.778304\pi\)
0.939126 + 0.343573i \(0.111637\pi\)
\(108\) 0 0
\(109\) 722053. + 1.25063e6i 0.00511520 + 0.00885979i 0.868572 0.495564i \(-0.165038\pi\)
−0.863456 + 0.504423i \(0.831705\pi\)
\(110\) −6.56396e6 3.78970e6i −0.0448327 0.0258842i
\(111\) 0 0
\(112\) −3.13476e7 + 2.37656e7i −0.199220 + 0.151035i
\(113\) 2.56178e8 1.57119 0.785594 0.618742i \(-0.212357\pi\)
0.785594 + 0.618742i \(0.212357\pi\)
\(114\) 0 0
\(115\) −2.27808e7 + 1.31525e7i −0.130250 + 0.0751997i
\(116\) −1.28814e7 2.23113e7i −0.0711430 0.123223i
\(117\) 0 0
\(118\) 7.09091e7i 0.365741i
\(119\) −2.50558e8 + 3.15059e7i −1.24946 + 0.157110i
\(120\) 0 0
\(121\) 1.06984e8 1.85302e8i 0.499089 0.864447i
\(122\) 1.17180e8 6.76537e7i 0.528948 0.305388i
\(123\) 0 0
\(124\) −9.69871e7 5.59955e7i −0.410230 0.236846i
\(125\) 3.93593e8i 1.61215i
\(126\) 0 0
\(127\) −1.98954e8 −0.764783 −0.382391 0.924000i \(-0.624899\pi\)
−0.382391 + 0.924000i \(0.624899\pi\)
\(128\) −1.18633e7 + 2.05478e7i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 2.62709e8 + 4.55025e8i 0.919816 + 1.59317i
\(131\) −3.13374e8 1.80926e8i −1.06409 0.614351i −0.137527 0.990498i \(-0.543915\pi\)
−0.926560 + 0.376147i \(0.877249\pi\)
\(132\) 0 0
\(133\) −2.32482e8 3.06651e8i −0.742989 0.980026i
\(134\) 1.20854e8 0.374836
\(135\) 0 0
\(136\) −1.31907e8 + 7.61567e7i −0.385579 + 0.222614i
\(137\) −8.75137e6 1.51578e7i −0.0248424 0.0430283i 0.853337 0.521360i \(-0.174575\pi\)
−0.878179 + 0.478332i \(0.841242\pi\)
\(138\) 0 0
\(139\) 5.04614e8i 1.35176i 0.737011 + 0.675881i \(0.236237\pi\)
−0.737011 + 0.675881i \(0.763763\pi\)
\(140\) −1.27807e8 + 3.03551e8i −0.332693 + 0.790167i
\(141\) 0 0
\(142\) −1.27754e8 + 2.21276e8i −0.314210 + 0.544229i
\(143\) 2.34598e7 1.35445e7i 0.0561022 0.0323906i
\(144\) 0 0
\(145\) −1.86803e8 1.07850e8i −0.422582 0.243978i
\(146\) 5.49860e8i 1.21016i
\(147\) 0 0
\(148\) −2.12563e8 −0.443038
\(149\) 1.33029e8 2.30412e8i 0.269898 0.467477i −0.698937 0.715183i \(-0.746343\pi\)
0.968835 + 0.247706i \(0.0796767\pi\)
\(150\) 0 0
\(151\) −3.14108e8 5.44051e8i −0.604187 1.04648i −0.992179 0.124820i \(-0.960165\pi\)
0.387992 0.921663i \(-0.373169\pi\)
\(152\) −2.01004e8 1.16050e8i −0.376557 0.217405i
\(153\) 0 0
\(154\) 1.56502e7 + 6.58938e6i 0.0278251 + 0.0117155i
\(155\) −9.37652e8 −1.62448
\(156\) 0 0
\(157\) −1.35298e8 + 7.81141e7i −0.222685 + 0.128567i −0.607193 0.794554i \(-0.707705\pi\)
0.384508 + 0.923122i \(0.374371\pi\)
\(158\) 3.06442e8 + 5.30773e8i 0.491723 + 0.851688i
\(159\) 0 0
\(160\) 1.98652e8i 0.303119i
\(161\) 4.69628e7 3.56040e7i 0.0698957 0.0529901i
\(162\) 0 0
\(163\) 3.22381e8 5.58380e8i 0.456687 0.791005i −0.542096 0.840316i \(-0.682369\pi\)
0.998783 + 0.0493110i \(0.0157025\pi\)
\(164\) −5.14376e7 + 2.96975e7i −0.0711059 + 0.0410530i
\(165\) 0 0
\(166\) 2.24325e8 + 1.29514e8i 0.295423 + 0.170563i
\(167\) 4.01008e8i 0.515569i −0.966202 0.257785i \(-0.917007\pi\)
0.966202 0.257785i \(-0.0829925\pi\)
\(168\) 0 0
\(169\) −1.06213e9 −1.30206
\(170\) −6.37626e8 + 1.10440e9i −0.763432 + 1.32230i
\(171\) 0 0
\(172\) 1.88388e8 + 3.26298e8i 0.215248 + 0.372821i
\(173\) 6.72494e8 + 3.88265e8i 0.750765 + 0.433454i 0.825970 0.563714i \(-0.190628\pi\)
−0.0752052 + 0.997168i \(0.523961\pi\)
\(174\) 0 0
\(175\) 2.27025e8 + 1.80547e9i 0.242060 + 1.92504i
\(176\) 1.02419e7 0.0106741
\(177\) 0 0
\(178\) 8.44295e8 4.87454e8i 0.841035 0.485572i
\(179\) −1.31349e8 2.27504e8i −0.127943 0.221604i 0.794937 0.606693i \(-0.207504\pi\)
−0.922879 + 0.385089i \(0.874171\pi\)
\(180\) 0 0
\(181\) 6.26304e8i 0.583540i 0.956488 + 0.291770i \(0.0942442\pi\)
−0.956488 + 0.291770i \(0.905756\pi\)
\(182\) −7.11157e8 9.38039e8i −0.648157 0.854939i
\(183\) 0 0
\(184\) 1.77727e7 3.07833e7i 0.0155054 0.0268561i
\(185\) −1.54126e9 + 8.89849e8i −1.31580 + 0.759678i
\(186\) 0 0
\(187\) 5.69398e7 + 3.28742e7i 0.0465639 + 0.0268837i
\(188\) 3.24859e8i 0.260054i
\(189\) 0 0
\(190\) −1.94327e9 −1.49114
\(191\) 1.19335e9 2.06694e9i 0.896673 1.55308i 0.0649528 0.997888i \(-0.479310\pi\)
0.831720 0.555195i \(-0.187356\pi\)
\(192\) 0 0
\(193\) −2.37008e8 4.10510e8i −0.170818 0.295865i 0.767888 0.640584i \(-0.221308\pi\)
−0.938706 + 0.344719i \(0.887974\pi\)
\(194\) 1.31643e9 + 7.60041e8i 0.929375 + 0.536575i
\(195\) 0 0
\(196\) 1.99255e8 7.10483e8i 0.135016 0.481426i
\(197\) 2.00834e9 1.33343 0.666717 0.745311i \(-0.267699\pi\)
0.666717 + 0.745311i \(0.267699\pi\)
\(198\) 0 0
\(199\) −8.10273e8 + 4.67811e8i −0.516677 + 0.298303i −0.735574 0.677444i \(-0.763087\pi\)
0.218897 + 0.975748i \(0.429754\pi\)
\(200\) 5.48770e8 + 9.50498e8i 0.342982 + 0.594061i
\(201\) 0 0
\(202\) 4.28828e8i 0.257560i
\(203\) 4.45386e8 + 1.87526e8i 0.262273 + 0.110427i
\(204\) 0 0
\(205\) −2.48644e8 + 4.30665e8i −0.140787 + 0.243851i
\(206\) −1.15542e9 + 6.67083e8i −0.641611 + 0.370434i
\(207\) 0 0
\(208\) −6.14868e8 3.54994e8i −0.328495 0.189657i
\(209\) 1.00189e8i 0.0525093i
\(210\) 0 0
\(211\) 1.34825e9 0.680205 0.340103 0.940388i \(-0.389538\pi\)
0.340103 + 0.940388i \(0.389538\pi\)
\(212\) 2.29423e8 3.97373e8i 0.113578 0.196723i
\(213\) 0 0
\(214\) 2.55105e8 + 4.41854e8i 0.121636 + 0.210680i
\(215\) 2.73195e9 + 1.57729e9i 1.27855 + 0.738173i
\(216\) 0 0
\(217\) 2.08429e9 2.62085e8i 0.939983 0.118196i
\(218\) −1.63382e7 −0.00723399
\(219\) 0 0
\(220\) 7.42627e7 4.28756e7i 0.0317015 0.0183029i
\(221\) −2.27890e9 3.94716e9i −0.955334 1.65469i
\(222\) 0 0
\(223\) 2.27893e9i 0.921533i −0.887521 0.460767i \(-0.847575\pi\)
0.887521 0.460767i \(-0.152425\pi\)
\(224\) −5.55257e7 4.41581e8i −0.0220547 0.175396i
\(225\) 0 0
\(226\) −1.44916e9 + 2.51002e9i −0.555499 + 0.962153i
\(227\) −2.55953e9 + 1.47774e9i −0.963954 + 0.556539i −0.897388 0.441243i \(-0.854538\pi\)
−0.0665664 + 0.997782i \(0.521204\pi\)
\(228\) 0 0
\(229\) 1.42462e8 + 8.22504e7i 0.0518032 + 0.0299086i 0.525678 0.850684i \(-0.323812\pi\)
−0.473875 + 0.880592i \(0.657145\pi\)
\(230\) 2.97607e8i 0.106348i
\(231\) 0 0
\(232\) 2.91473e8 0.100611
\(233\) −2.52459e9 + 4.37272e9i −0.856579 + 1.48364i 0.0185942 + 0.999827i \(0.494081\pi\)
−0.875173 + 0.483811i \(0.839252\pi\)
\(234\) 0 0
\(235\) −1.35995e9 2.35551e9i −0.445915 0.772347i
\(236\) 6.94765e8 + 4.01123e8i 0.223970 + 0.129309i
\(237\) 0 0
\(238\) 1.10868e9 2.63318e9i 0.345539 0.820679i
\(239\) −5.80584e8 −0.177940 −0.0889699 0.996034i \(-0.528358\pi\)
−0.0889699 + 0.996034i \(0.528358\pi\)
\(240\) 0 0
\(241\) −3.79705e9 + 2.19223e9i −1.12559 + 0.649857i −0.942821 0.333300i \(-0.891838\pi\)
−0.182765 + 0.983157i \(0.558505\pi\)
\(242\) 1.21039e9 + 2.09645e9i 0.352909 + 0.611256i
\(243\) 0 0
\(244\) 1.53083e9i 0.431884i
\(245\) −1.52951e9 5.98574e9i −0.424510 1.66132i
\(246\) 0 0
\(247\) 3.47265e9 6.01481e9i 0.932982 1.61597i
\(248\) 1.09728e9 6.33517e8i 0.290076 0.167476i
\(249\) 0 0
\(250\) 3.85640e9 + 2.22650e9i 0.987239 + 0.569983i
\(251\) 4.01412e9i 1.01134i −0.862728 0.505668i \(-0.831246\pi\)
0.862728 0.505668i \(-0.168754\pi\)
\(252\) 0 0
\(253\) −1.53437e7 −0.00374498
\(254\) 1.12545e9 1.94935e9i 0.270392 0.468332i
\(255\) 0 0
\(256\) −1.34218e8 2.32472e8i −0.0312500 0.0541266i
\(257\) 5.04886e9 + 2.91496e9i 1.15734 + 0.668190i 0.950665 0.310220i \(-0.100403\pi\)
0.206674 + 0.978410i \(0.433736\pi\)
\(258\) 0 0
\(259\) 3.17733e9 2.40884e9i 0.706096 0.535314i
\(260\) −5.94442e9 −1.30082
\(261\) 0 0
\(262\) 3.54542e9 2.04695e9i 0.752423 0.434412i
\(263\) −4.65172e6 8.05701e6i −0.000972278 0.00168403i 0.865539 0.500842i \(-0.166976\pi\)
−0.866511 + 0.499158i \(0.833643\pi\)
\(264\) 0 0
\(265\) 3.84172e9i 0.779008i
\(266\) 4.31967e9 5.43167e8i 0.862827 0.108494i
\(267\) 0 0
\(268\) −6.83652e8 + 1.18412e9i −0.132524 + 0.229539i
\(269\) 2.50581e9 1.44673e9i 0.478563 0.276298i −0.241255 0.970462i \(-0.577559\pi\)
0.719817 + 0.694164i \(0.244226\pi\)
\(270\) 0 0
\(271\) 3.08901e9 + 1.78344e9i 0.572719 + 0.330660i 0.758235 0.651982i \(-0.226062\pi\)
−0.185515 + 0.982641i \(0.559395\pi\)
\(272\) 1.72323e9i 0.314824i
\(273\) 0 0
\(274\) 1.98021e8 0.0351325
\(275\) 2.36885e8 4.10297e8i 0.0414197 0.0717410i
\(276\) 0 0
\(277\) 4.37953e9 + 7.58557e9i 0.743890 + 1.28846i 0.950712 + 0.310076i \(0.100355\pi\)
−0.206822 + 0.978379i \(0.566312\pi\)
\(278\) −4.94419e9 2.85453e9i −0.827782 0.477920i
\(279\) 0 0
\(280\) −2.25119e9 2.96939e9i −0.366252 0.483098i
\(281\) −1.01410e9 −0.162650 −0.0813251 0.996688i \(-0.525915\pi\)
−0.0813251 + 0.996688i \(0.525915\pi\)
\(282\) 0 0
\(283\) 1.88672e9 1.08930e9i 0.294145 0.169825i −0.345665 0.938358i \(-0.612347\pi\)
0.639810 + 0.768534i \(0.279013\pi\)
\(284\) −1.44537e9 2.50345e9i −0.222180 0.384828i
\(285\) 0 0
\(286\) 3.06477e8i 0.0458072i
\(287\) 4.32332e8 1.02682e9i 0.0637221 0.151344i
\(288\) 0 0
\(289\) 2.04328e9 3.53906e9i 0.292912 0.507338i
\(290\) 2.11343e9 1.22019e9i 0.298810 0.172518i
\(291\) 0 0
\(292\) −5.38751e9 3.11048e9i −0.741066 0.427854i
\(293\) 5.77278e9i 0.783275i 0.920120 + 0.391637i \(0.128091\pi\)
−0.920120 + 0.391637i \(0.871909\pi\)
\(294\) 0 0
\(295\) 6.71684e9 0.886905
\(296\) 1.20244e9 2.08269e9i 0.156638 0.271304i
\(297\) 0 0
\(298\) 1.50505e9 + 2.60682e9i 0.190847 + 0.330556i
\(299\) 9.21152e8 + 5.31827e8i 0.115251 + 0.0665405i
\(300\) 0 0
\(301\) −6.51369e9 2.74253e9i −0.793525 0.334107i
\(302\) 7.10746e9 0.854449
\(303\) 0 0
\(304\) 2.27410e9 1.31295e9i 0.266266 0.153729i
\(305\) 6.40847e9 + 1.10998e10i 0.740552 + 1.28267i
\(306\) 0 0
\(307\) 8.41085e9i 0.946862i 0.880831 + 0.473431i \(0.156985\pi\)
−0.880831 + 0.473431i \(0.843015\pi\)
\(308\) −1.53093e8 + 1.16065e8i −0.0170119 + 0.0128973i
\(309\) 0 0
\(310\) 5.30416e9 9.18707e9i 0.574341 0.994787i
\(311\) −1.22281e10 + 7.05989e9i −1.30713 + 0.754669i −0.981615 0.190869i \(-0.938869\pi\)
−0.325510 + 0.945539i \(0.605536\pi\)
\(312\) 0 0
\(313\) 4.89621e9 + 2.82683e9i 0.510132 + 0.294525i 0.732888 0.680349i \(-0.238172\pi\)
−0.222756 + 0.974874i \(0.571505\pi\)
\(314\) 1.76752e9i 0.181822i
\(315\) 0 0
\(316\) −6.93399e9 −0.695401
\(317\) −1.02907e9 + 1.78241e9i −0.101908 + 0.176510i −0.912471 0.409142i \(-0.865828\pi\)
0.810563 + 0.585652i \(0.199161\pi\)
\(318\) 0 0
\(319\) −6.29094e7 1.08962e8i −0.00607509 0.0105224i
\(320\) −1.94638e9 1.12375e9i −0.185622 0.107169i
\(321\) 0 0
\(322\) 8.31846e7 + 6.61546e8i 0.00773784 + 0.0615370i
\(323\) 1.68571e10 1.54872
\(324\) 0 0
\(325\) −2.84425e10 + 1.64213e10i −2.54938 + 1.47188i
\(326\) 3.64732e9 + 6.31735e9i 0.322927 + 0.559325i
\(327\) 0 0
\(328\) 6.71978e8i 0.0580577i
\(329\) 3.68141e9 + 4.85590e9i 0.314218 + 0.414463i
\(330\) 0 0
\(331\) −1.84939e9 + 3.20323e9i −0.154069 + 0.266856i −0.932720 0.360602i \(-0.882571\pi\)
0.778650 + 0.627458i \(0.215905\pi\)
\(332\) −2.53794e9 + 1.46528e9i −0.208896 + 0.120606i
\(333\) 0 0
\(334\) 3.92906e9 + 2.26844e9i 0.315720 + 0.182281i
\(335\) 1.14478e10i 0.908958i
\(336\) 0 0
\(337\) 1.14169e10 0.885171 0.442586 0.896726i \(-0.354061\pi\)
0.442586 + 0.896726i \(0.354061\pi\)
\(338\) 6.00830e9 1.04067e10i 0.460346 0.797343i
\(339\) 0 0
\(340\) −7.21392e9 1.24949e10i −0.539828 0.935010i
\(341\) −4.73659e8 2.73467e8i −0.0350307 0.0202250i
\(342\) 0 0
\(343\) 5.07302e9 + 1.28781e10i 0.366513 + 0.930413i
\(344\) −4.26274e9 −0.304407
\(345\) 0 0
\(346\) −7.60840e9 + 4.39271e9i −0.530871 + 0.306499i
\(347\) −5.05429e9 8.75429e9i −0.348612 0.603814i 0.637391 0.770540i \(-0.280014\pi\)
−0.986003 + 0.166727i \(0.946680\pi\)
\(348\) 0 0
\(349\) 2.23530e9i 0.150672i −0.997158 0.0753362i \(-0.975997\pi\)
0.997158 0.0753362i \(-0.0240030\pi\)
\(350\) −1.89742e10 7.98892e9i −1.26442 0.532373i
\(351\) 0 0
\(352\) −5.79371e7 + 1.00350e8i −0.00377386 + 0.00653652i
\(353\) 1.12278e10 6.48240e9i 0.723098 0.417481i −0.0927937 0.995685i \(-0.529580\pi\)
0.815892 + 0.578204i \(0.196246\pi\)
\(354\) 0 0
\(355\) −2.09603e10 1.21014e10i −1.31973 0.761945i
\(356\) 1.10298e10i 0.686702i
\(357\) 0 0
\(358\) 2.97210e9 0.180939
\(359\) 1.51567e10 2.62522e10i 0.912488 1.58048i 0.101950 0.994790i \(-0.467492\pi\)
0.810538 0.585686i \(-0.199175\pi\)
\(360\) 0 0
\(361\) 4.35190e9 + 7.53770e9i 0.256242 + 0.443823i
\(362\) −6.13650e9 3.54291e9i −0.357344 0.206313i
\(363\) 0 0
\(364\) 1.32138e10 1.66154e9i 0.752699 0.0946465i
\(365\) −5.20854e10 −2.93457
\(366\) 0 0
\(367\) −4.69235e9 + 2.70913e9i −0.258658 + 0.149336i −0.623722 0.781646i \(-0.714380\pi\)
0.365064 + 0.930982i \(0.381047\pi\)
\(368\) 2.01076e8 + 3.48273e8i 0.0109640 + 0.0189902i
\(369\) 0 0
\(370\) 2.01350e10i 1.07435i
\(371\) 1.07381e9 + 8.53971e9i 0.0566801 + 0.450762i
\(372\) 0 0
\(373\) 3.95213e9 6.84529e9i 0.204172 0.353636i −0.745697 0.666286i \(-0.767883\pi\)
0.949869 + 0.312649i \(0.101217\pi\)
\(374\) −6.44200e8 + 3.71929e8i −0.0329256 + 0.0190096i
\(375\) 0 0
\(376\) 3.18296e9 + 1.83768e9i 0.159250 + 0.0919431i
\(377\) 8.72198e9i 0.431767i
\(378\) 0 0
\(379\) −1.84501e10 −0.894216 −0.447108 0.894480i \(-0.647546\pi\)
−0.447108 + 0.894480i \(0.647546\pi\)
\(380\) 1.09928e10 1.90401e10i 0.527198 0.913133i
\(381\) 0 0
\(382\) 1.35012e10 + 2.33848e10i 0.634044 + 1.09820i
\(383\) 8.39027e9 + 4.84413e9i 0.389925 + 0.225123i 0.682128 0.731233i \(-0.261055\pi\)
−0.292203 + 0.956356i \(0.594388\pi\)
\(384\) 0 0
\(385\) −6.24177e8 + 1.48246e9i −0.0284096 + 0.0674746i
\(386\) 5.36287e9 0.241573
\(387\) 0 0
\(388\) −1.48937e10 + 8.59888e9i −0.657167 + 0.379416i
\(389\) 1.29668e10 + 2.24592e10i 0.566285 + 0.980834i 0.996929 + 0.0783124i \(0.0249532\pi\)
−0.430644 + 0.902522i \(0.641714\pi\)
\(390\) 0 0
\(391\) 2.58162e9i 0.110455i
\(392\) 5.83412e9 + 5.97139e9i 0.247076 + 0.252890i
\(393\) 0 0
\(394\) −1.13609e10 + 1.96776e10i −0.471440 + 0.816558i
\(395\) −5.02773e10 + 2.90276e10i −2.06530 + 1.19240i
\(396\) 0 0
\(397\) −3.43145e10 1.98115e10i −1.38139 0.797545i −0.389065 0.921210i \(-0.627202\pi\)
−0.992324 + 0.123665i \(0.960535\pi\)
\(398\) 1.05854e10i 0.421865i
\(399\) 0 0
\(400\) −1.24173e10 −0.485049
\(401\) 1.82067e9 3.15349e9i 0.0704131 0.121959i −0.828669 0.559738i \(-0.810902\pi\)
0.899082 + 0.437779i \(0.144235\pi\)
\(402\) 0 0
\(403\) 1.89572e10 + 3.28349e10i 0.718711 + 1.24484i
\(404\) −4.20164e9 2.42582e9i −0.157723 0.0910611i
\(405\) 0 0
\(406\) −4.35686e9 + 3.30307e9i −0.160350 + 0.121566i
\(407\) −1.03810e9 −0.0378323
\(408\) 0 0
\(409\) 3.30558e10 1.90847e10i 1.18128 0.682014i 0.224972 0.974365i \(-0.427771\pi\)
0.956311 + 0.292352i \(0.0944377\pi\)
\(410\) −2.81309e9 4.87241e9i −0.0995516 0.172428i
\(411\) 0 0
\(412\) 1.50944e10i 0.523873i
\(413\) −1.49308e10 + 1.87744e9i −0.513195 + 0.0645306i
\(414\) 0 0
\(415\) −1.22682e10 + 2.12491e10i −0.413606 + 0.716387i
\(416\) 6.95644e9 4.01630e9i 0.232281 0.134107i
\(417\) 0 0
\(418\) −9.81651e8 5.66757e8i −0.0321553 0.0185649i
\(419\) 1.70754e10i 0.554007i 0.960869 + 0.277004i \(0.0893414\pi\)
−0.960869 + 0.277004i \(0.910659\pi\)
\(420\) 0 0
\(421\) −2.86510e10 −0.912033 −0.456017 0.889971i \(-0.650724\pi\)
−0.456017 + 0.889971i \(0.650724\pi\)
\(422\) −7.62684e9 + 1.32101e10i −0.240489 + 0.416539i
\(423\) 0 0
\(424\) 2.59563e9 + 4.49576e9i 0.0803117 + 0.139104i
\(425\) −6.90334e10 3.98565e10i −2.11594 1.22164i
\(426\) 0 0
\(427\) −1.73478e10 2.28824e10i −0.521836 0.688319i
\(428\) −5.77236e9 −0.172020
\(429\) 0 0
\(430\) −3.09085e10 + 1.78450e10i −0.904073 + 0.521967i
\(431\) 2.28785e10 + 3.96268e10i 0.663009 + 1.14836i 0.979821 + 0.199876i \(0.0640541\pi\)
−0.316813 + 0.948488i \(0.602613\pi\)
\(432\) 0 0
\(433\) 1.41731e10i 0.403193i −0.979469 0.201597i \(-0.935387\pi\)
0.979469 0.201597i \(-0.0646130\pi\)
\(434\) −9.22265e9 + 2.19044e10i −0.259954 + 0.617408i
\(435\) 0 0
\(436\) 9.24228e7 1.60081e8i 0.00255760 0.00442990i
\(437\) −3.40690e9 + 1.96698e9i −0.0934187 + 0.0539353i
\(438\) 0 0
\(439\) −8.46361e9 4.88647e9i −0.227875 0.131564i 0.381716 0.924280i \(-0.375333\pi\)
−0.609592 + 0.792716i \(0.708667\pi\)
\(440\) 9.70164e8i 0.0258842i
\(441\) 0 0
\(442\) 5.15655e10 1.35105
\(443\) 2.55450e10 4.42452e10i 0.663270 1.14882i −0.316481 0.948599i \(-0.602501\pi\)
0.979751 0.200219i \(-0.0641653\pi\)
\(444\) 0 0
\(445\) 4.61739e10 + 7.99755e10i 1.17749 + 2.03947i
\(446\) 2.23288e10 + 1.28916e10i 0.564321 + 0.325811i
\(447\) 0 0
\(448\) 4.64070e9 + 1.95392e9i 0.115205 + 0.0485060i
\(449\) 2.61180e10 0.642620 0.321310 0.946974i \(-0.395877\pi\)
0.321310 + 0.946974i \(0.395877\pi\)
\(450\) 0 0
\(451\) −2.51208e8 + 1.45035e8i −0.00607193 + 0.00350563i
\(452\) −1.63954e10 2.83977e10i −0.392797 0.680345i
\(453\) 0 0
\(454\) 3.34375e10i 0.787065i
\(455\) 8.88554e10 6.73641e10i 2.07319 1.57175i
\(456\) 0 0
\(457\) 3.19803e10 5.53914e10i 0.733191 1.26992i −0.222322 0.974973i \(-0.571363\pi\)
0.955513 0.294951i \(-0.0953032\pi\)
\(458\) −1.61177e9 + 9.30557e8i −0.0366304 + 0.0211486i
\(459\) 0 0
\(460\) 2.91594e9 + 1.68352e9i 0.0651248 + 0.0375998i
\(461\) 6.21950e10i 1.37706i −0.725210 0.688528i \(-0.758257\pi\)
0.725210 0.688528i \(-0.241743\pi\)
\(462\) 0 0
\(463\) 3.25332e10 0.707951 0.353976 0.935255i \(-0.384830\pi\)
0.353976 + 0.935255i \(0.384830\pi\)
\(464\) −1.64882e9 + 2.85584e9i −0.0355715 + 0.0616116i
\(465\) 0 0
\(466\) −2.85625e10 4.94717e10i −0.605693 1.04909i
\(467\) 7.58397e10 + 4.37861e10i 1.59452 + 0.920594i 0.992518 + 0.122097i \(0.0389619\pi\)
0.601998 + 0.798497i \(0.294371\pi\)
\(468\) 0 0
\(469\) −3.19981e9 2.54472e10i −0.0661352 0.525956i
\(470\) 3.07722e10 0.630619
\(471\) 0 0
\(472\) −7.86036e9 + 4.53818e9i −0.158371 + 0.0914353i
\(473\) 9.20038e8 + 1.59355e9i 0.0183807 + 0.0318362i
\(474\) 0 0
\(475\) 1.21469e11i 2.38611i
\(476\) 1.95282e10 + 2.57583e10i 0.380395 + 0.501753i
\(477\) 0 0
\(478\) 3.28428e9 5.68854e9i 0.0629112 0.108965i
\(479\) 5.86256e10 3.38475e10i 1.11364 0.642960i 0.173870 0.984769i \(-0.444373\pi\)
0.939770 + 0.341808i \(0.111039\pi\)
\(480\) 0 0
\(481\) 6.23218e10 + 3.59815e10i 1.16429 + 0.672201i
\(482\) 4.96045e10i 0.919037i
\(483\) 0 0
\(484\) −2.73879e10 −0.499089
\(485\) −7.19947e10 + 1.24698e11i −1.30117 + 2.25369i
\(486\) 0 0
\(487\) −1.77087e8 3.06724e8i −0.00314826 0.00545295i 0.864447 0.502724i \(-0.167669\pi\)
−0.867595 + 0.497271i \(0.834335\pi\)
\(488\) −1.49990e10 8.65967e9i −0.264474 0.152694i
\(489\) 0 0
\(490\) 6.73003e10 + 1.88744e10i 1.16743 + 0.327407i
\(491\) −3.00967e10 −0.517837 −0.258918 0.965899i \(-0.583366\pi\)
−0.258918 + 0.965899i \(0.583366\pi\)
\(492\) 0 0
\(493\) −1.83332e10 + 1.05847e10i −0.310349 + 0.179180i
\(494\) 3.92886e10 + 6.80498e10i 0.659718 + 1.14266i
\(495\) 0 0
\(496\) 1.43349e10i 0.236846i
\(497\) 4.99749e10 + 2.10415e10i 0.819081 + 0.344866i
\(498\) 0 0
\(499\) −2.64618e10 + 4.58332e10i −0.426793 + 0.739228i −0.996586 0.0825607i \(-0.973690\pi\)
0.569793 + 0.821788i \(0.307023\pi\)
\(500\) −4.36302e10 + 2.51899e10i −0.698084 + 0.403039i
\(501\) 0 0
\(502\) 3.93301e10 + 2.27073e10i 0.619314 + 0.357561i
\(503\) 9.78079e10i 1.52793i −0.645261 0.763963i \(-0.723251\pi\)
0.645261 0.763963i \(-0.276749\pi\)
\(504\) 0 0
\(505\) −4.06206e10 −0.624570
\(506\) 8.67973e7 1.50337e8i 0.00132405 0.00229332i
\(507\) 0 0
\(508\) 1.27331e10 + 2.20543e10i 0.191196 + 0.331161i
\(509\) −1.25561e10 7.24925e9i −0.187061 0.108000i 0.403545 0.914960i \(-0.367778\pi\)
−0.590606 + 0.806960i \(0.701111\pi\)
\(510\) 0 0
\(511\) 1.15780e11 1.45585e10i 1.69805 0.213517i
\(512\) 3.03700e9 0.0441942
\(513\) 0 0
\(514\) −5.71213e10 + 3.29790e10i −0.818362 + 0.472482i
\(515\) −6.31893e10 1.09447e11i −0.898285 1.55588i
\(516\) 0 0
\(517\) 1.58653e9i 0.0222068i
\(518\) 5.62797e9 + 4.47578e10i 0.0781687 + 0.621656i
\(519\) 0 0
\(520\) 3.36267e10 5.82432e10i 0.459908 0.796584i
\(521\) −2.40889e10 + 1.39077e10i −0.326938 + 0.188758i −0.654481 0.756079i \(-0.727113\pi\)
0.327543 + 0.944836i \(0.393779\pi\)
\(522\) 0 0
\(523\) 4.13262e10 + 2.38597e10i 0.552355 + 0.318902i 0.750071 0.661357i \(-0.230019\pi\)
−0.197716 + 0.980259i \(0.563352\pi\)
\(524\) 4.63171e10i 0.614351i
\(525\) 0 0
\(526\) 1.05256e8 0.00137501
\(527\) −4.60115e10 + 7.96942e10i −0.596518 + 1.03320i
\(528\) 0 0
\(529\) 3.88543e10 + 6.72975e10i 0.496153 + 0.859363i
\(530\) 3.76410e10 + 2.17320e10i 0.477043 + 0.275421i
\(531\) 0 0
\(532\) −1.91138e10 + 4.53965e10i −0.238617 + 0.566730i
\(533\) 2.01081e10 0.249151
\(534\) 0 0
\(535\) −4.18545e10 + 2.41647e10i −0.510890 + 0.294962i
\(536\) −7.73464e9 1.33968e10i −0.0937089 0.162309i
\(537\) 0 0
\(538\) 3.27358e10i 0.390745i
\(539\) 9.73109e8 3.46981e9i 0.0115294 0.0411103i
\(540\) 0 0
\(541\) 4.34084e10 7.51855e10i 0.506739 0.877697i −0.493231 0.869899i \(-0.664184\pi\)
0.999970 0.00779894i \(-0.00248250\pi\)
\(542\) −3.49481e10 + 2.01773e10i −0.404974 + 0.233812i
\(543\) 0 0
\(544\) 1.68841e10 + 9.74806e9i 0.192789 + 0.111307i
\(545\) 1.54763e9i 0.0175421i
\(546\) 0 0
\(547\) −8.29408e8 −0.00926443 −0.00463222 0.999989i \(-0.501474\pi\)
−0.00463222 + 0.999989i \(0.501474\pi\)
\(548\) −1.12018e9 + 1.94020e9i −0.0124212 + 0.0215142i
\(549\) 0 0
\(550\) 2.68005e9 + 4.64198e9i 0.0292881 + 0.0507286i
\(551\) −2.79366e10 1.61292e10i −0.303087 0.174988i
\(552\) 0 0
\(553\) 1.03647e11 7.85783e10i 1.10830 0.840238i
\(554\) −9.90975e10 −1.05202
\(555\) 0 0
\(556\) 5.59371e10 3.22953e10i 0.585330 0.337941i
\(557\) −3.13936e10 5.43753e10i −0.326152 0.564913i 0.655593 0.755115i \(-0.272419\pi\)
−0.981745 + 0.190202i \(0.939086\pi\)
\(558\) 0 0
\(559\) 1.27557e11i 1.30634i
\(560\) 4.18286e10 5.25965e9i 0.425326 0.0534817i
\(561\) 0 0
\(562\) 5.73660e9 9.93609e9i 0.0575055 0.0996025i
\(563\) 1.44357e11 8.33443e10i 1.43682 0.829550i 0.439195 0.898392i \(-0.355264\pi\)
0.997628 + 0.0688418i \(0.0219304\pi\)
\(564\) 0 0
\(565\) −2.37761e11 1.37271e11i −2.33317 1.34706i
\(566\) 2.46480e10i 0.240168i
\(567\) 0 0
\(568\) 3.27050e10 0.314210
\(569\) 5.98889e10 1.03731e11i 0.571344 0.989596i −0.425085 0.905154i \(-0.639756\pi\)
0.996428 0.0844427i \(-0.0269110\pi\)
\(570\) 0 0
\(571\) −3.41052e10 5.90720e10i −0.320831 0.555696i 0.659829 0.751416i \(-0.270629\pi\)
−0.980660 + 0.195720i \(0.937296\pi\)
\(572\) −3.00285e9 1.73370e9i −0.0280511 0.0161953i
\(573\) 0 0
\(574\) 7.61508e9 + 1.00445e10i 0.0701499 + 0.0925299i
\(575\) 1.86027e10 0.170178
\(576\) 0 0
\(577\) −1.44054e11 + 8.31694e10i −1.29963 + 0.750344i −0.980341 0.197312i \(-0.936779\pi\)
−0.319293 + 0.947656i \(0.603445\pi\)
\(578\) 2.31171e10 + 4.00399e10i 0.207120 + 0.358742i
\(579\) 0 0
\(580\) 2.76097e10i 0.243978i
\(581\) 2.13314e10 5.06634e10i 0.187204 0.444621i
\(582\) 0 0
\(583\) 1.12044e9 1.94066e9i 0.00969873 0.0167987i
\(584\) 6.09527e10 3.51911e10i 0.524013 0.302539i
\(585\) 0 0
\(586\) −5.65614e10 3.26558e10i −0.479656 0.276930i
\(587\) 1.46339e11i 1.23256i −0.787526 0.616281i \(-0.788639\pi\)
0.787526 0.616281i \(-0.211361\pi\)
\(588\) 0 0
\(589\) −1.40227e11 −1.16512
\(590\) −3.79962e10 + 6.58114e10i −0.313568 + 0.543116i
\(591\) 0 0
\(592\) 1.36040e10 + 2.35629e10i 0.110760 + 0.191841i
\(593\) −1.94527e11 1.12310e11i −1.57312 0.908242i −0.995783 0.0917357i \(-0.970759\pi\)
−0.577337 0.816506i \(-0.695908\pi\)
\(594\) 0 0
\(595\) 2.49428e11 + 1.05019e11i 1.99011 + 0.837917i
\(596\) −3.40553e10 −0.269898
\(597\) 0 0
\(598\) −1.04216e10 + 6.01694e9i −0.0814951 + 0.0470512i
\(599\) 8.39482e10 + 1.45403e11i 0.652085 + 1.12944i 0.982616 + 0.185649i \(0.0594387\pi\)
−0.330531 + 0.943795i \(0.607228\pi\)
\(600\) 0 0
\(601\) 2.01982e11i 1.54816i 0.633088 + 0.774080i \(0.281787\pi\)
−0.633088 + 0.774080i \(0.718213\pi\)
\(602\) 6.37182e10 4.83067e10i 0.485151 0.367809i
\(603\) 0 0
\(604\) −4.02058e10 + 6.96386e10i −0.302094 + 0.523241i
\(605\) −1.98586e11 + 1.14653e11i −1.48227 + 0.855787i
\(606\) 0 0
\(607\) −1.69808e11 9.80385e10i −1.25084 0.722174i −0.279565 0.960127i \(-0.590190\pi\)
−0.971277 + 0.237953i \(0.923524\pi\)
\(608\) 2.97088e10i 0.217405i
\(609\) 0 0
\(610\) −1.45007e11 −1.04730
\(611\) −5.49904e10 + 9.52461e10i −0.394568 + 0.683412i
\(612\) 0 0
\(613\) 1.21921e10 + 2.11174e10i 0.0863451 + 0.149554i 0.905964 0.423356i \(-0.139148\pi\)
−0.819619 + 0.572910i \(0.805815\pi\)
\(614\) −8.24092e10 4.75790e10i −0.579832 0.334766i
\(615\) 0 0
\(616\) −2.71173e8 2.15656e9i −0.00188331 0.0149775i
\(617\) 6.93902e10 0.478804 0.239402 0.970921i \(-0.423049\pi\)
0.239402 + 0.970921i \(0.423049\pi\)
\(618\) 0 0
\(619\) 2.63983e10 1.52411e10i 0.179810 0.103813i −0.407394 0.913253i \(-0.633562\pi\)
0.587203 + 0.809439i \(0.300229\pi\)
\(620\) 6.00097e10 + 1.03940e11i 0.406120 + 0.703421i
\(621\) 0 0
\(622\) 1.59747e11i 1.06726i
\(623\) −1.24994e11 1.64870e11i −0.829727 1.09444i
\(624\) 0 0
\(625\) −6.28789e10 + 1.08909e11i −0.412083 + 0.713749i
\(626\) −5.53943e10 + 3.19819e10i −0.360718 + 0.208261i
\(627\) 0 0
\(628\) 1.73181e10 + 9.99860e9i 0.111343 + 0.0642837i
\(629\) 1.74663e11i 1.11583i
\(630\) 0 0
\(631\) 7.98314e10 0.503566 0.251783 0.967784i \(-0.418983\pi\)
0.251783 + 0.967784i \(0.418983\pi\)
\(632\) 3.92246e10 6.79390e10i 0.245861 0.425844i
\(633\) 0 0
\(634\) −1.16426e10 2.01656e10i −0.0720600 0.124812i
\(635\) 1.84651e11 + 1.06608e11i 1.13568 + 0.655687i
\(636\) 0 0
\(637\) −1.78687e11 + 1.74579e11i −1.08526 + 1.06031i
\(638\) 1.42348e9 0.00859148
\(639\) 0 0
\(640\) 2.20208e10 1.27137e10i 0.131254 0.0757798i
\(641\) 8.08656e10 + 1.40063e11i 0.478996 + 0.829645i 0.999710 0.0240860i \(-0.00766754\pi\)
−0.520714 + 0.853731i \(0.674334\pi\)
\(642\) 0 0
\(643\) 1.63061e11i 0.953906i −0.878929 0.476953i \(-0.841741\pi\)
0.878929 0.476953i \(-0.158259\pi\)
\(644\) −6.95236e9 2.92723e9i −0.0404193 0.0170182i
\(645\) 0 0
\(646\) −9.53581e10 + 1.65165e11i −0.547555 + 0.948393i
\(647\) −1.56164e11 + 9.01611e10i −0.891174 + 0.514520i −0.874326 0.485338i \(-0.838696\pi\)
−0.0168480 + 0.999858i \(0.505363\pi\)
\(648\) 0 0
\(649\) 3.39305e9 + 1.95898e9i 0.0191254 + 0.0110421i
\(650\) 3.71571e11i 2.08156i
\(651\) 0 0
\(652\) −8.25295e10 −0.456687
\(653\) −9.24573e10 + 1.60141e11i −0.508497 + 0.880743i 0.491454 + 0.870903i \(0.336465\pi\)
−0.999952 + 0.00983959i \(0.996868\pi\)
\(654\) 0 0
\(655\) 1.93897e11 + 3.35839e11i 1.05343 + 1.82459i
\(656\) 6.58402e9 + 3.80128e9i 0.0355529 + 0.0205265i
\(657\) 0 0
\(658\) −6.84031e10 + 8.60120e9i −0.364899 + 0.0458834i
\(659\) 1.54086e11 0.816997 0.408498 0.912759i \(-0.366053\pi\)
0.408498 + 0.912759i \(0.366053\pi\)
\(660\) 0 0
\(661\) −2.25654e11 + 1.30282e11i −1.18206 + 0.682460i −0.956489 0.291768i \(-0.905756\pi\)
−0.225566 + 0.974228i \(0.572423\pi\)
\(662\) −2.09234e10 3.62405e10i −0.108943 0.188696i
\(663\) 0 0
\(664\) 3.31555e10i 0.170563i
\(665\) 5.14513e10 + 4.09179e11i 0.263094 + 2.09231i
\(666\) 0 0
\(667\) 2.47015e9 4.27842e9i 0.0124802 0.0216163i
\(668\) −4.44522e10 + 2.56645e10i −0.223248 + 0.128892i
\(669\) 0 0
\(670\) −1.12165e11 6.47587e10i −0.556621 0.321365i
\(671\) 7.47616e9i 0.0368798i
\(672\) 0 0
\(673\) 1.66660e11 0.812401 0.406201 0.913784i \(-0.366853\pi\)
0.406201 + 0.913784i \(0.366853\pi\)
\(674\) −6.45836e10 + 1.11862e11i −0.312955 + 0.542055i
\(675\) 0 0
\(676\) 6.79762e10 + 1.17738e11i 0.325514 + 0.563807i
\(677\) −2.97264e11 1.71626e11i −1.41510 0.817010i −0.419239 0.907876i \(-0.637703\pi\)
−0.995863 + 0.0908659i \(0.971037\pi\)
\(678\) 0 0
\(679\) 1.25181e11 2.97314e11i 0.588926 1.39874i
\(680\) 1.63232e11 0.763432
\(681\) 0 0
\(682\) 5.35884e9 3.09393e9i 0.0247704 0.0143012i
\(683\) 7.86838e10 + 1.36284e11i 0.361578 + 0.626272i 0.988221 0.153035i \(-0.0489046\pi\)
−0.626642 + 0.779307i \(0.715571\pi\)
\(684\) 0 0
\(685\) 1.87575e10i 0.0851946i
\(686\) −1.54877e11 2.31444e10i −0.699341 0.104508i
\(687\) 0 0
\(688\) 2.41137e10 4.17661e10i 0.107624 0.186411i
\(689\) −1.34530e11 + 7.76710e10i −0.596956 + 0.344653i
\(690\) 0 0
\(691\) 2.95389e10 + 1.70543e10i 0.129564 + 0.0748035i 0.563381 0.826197i \(-0.309500\pi\)
−0.433817 + 0.901001i \(0.642834\pi\)
\(692\) 9.93958e10i 0.433454i
\(693\) 0 0
\(694\) 1.14366e11 0.493012
\(695\) 2.70394e11 4.68337e11i 1.15893 2.00733i
\(696\) 0 0
\(697\) 2.44024e10 + 4.22663e10i 0.103396 + 0.179086i
\(698\) 2.19014e10 + 1.26448e10i 0.0922676 + 0.0532707i
\(699\) 0 0
\(700\) 1.85609e11 1.40716e11i 0.773051 0.586074i
\(701\) 4.82108e10 0.199651 0.0998256 0.995005i \(-0.468172\pi\)
0.0998256 + 0.995005i \(0.468172\pi\)
\(702\) 0 0
\(703\) −2.30499e11 + 1.33078e11i −0.943729 + 0.544862i
\(704\) −6.55484e8 1.13533e9i −0.00266852 0.00462202i
\(705\) 0 0
\(706\) 1.46680e11i 0.590407i
\(707\) 9.02951e10 1.13540e10i 0.361399 0.0454433i
\(708\) 0 0
\(709\) 1.77293e11 3.07080e11i 0.701627 1.21525i −0.266269 0.963899i \(-0.585791\pi\)
0.967895 0.251354i \(-0.0808759\pi\)
\(710\) 2.37139e11 1.36912e11i 0.933189 0.538777i
\(711\) 0 0
\(712\) −1.08070e11 6.23941e10i −0.420517 0.242786i
\(713\) 2.14755e10i 0.0830968i
\(714\) 0 0
\(715\) −2.90310e10 −0.111080
\(716\) −1.68127e10 + 2.91205e10i −0.0639714 + 0.110802i
\(717\) 0 0
\(718\) 1.71479e11 + 2.97010e11i 0.645226 + 1.11756i
\(719\) −3.74314e11 2.16110e11i −1.40062 0.808649i −0.406165 0.913800i \(-0.633134\pi\)
−0.994456 + 0.105151i \(0.966467\pi\)
\(720\) 0 0
\(721\) 1.71054e11 + 2.25626e11i 0.632985 + 0.834927i
\(722\) −9.84722e10 −0.362380
\(723\) 0 0
\(724\) 6.94266e10 4.00835e10i 0.252680 0.145885i
\(725\) 7.62710e10 + 1.32105e11i 0.276063 + 0.478154i
\(726\) 0 0
\(727\) 2.64649e10i 0.0947397i −0.998877 0.0473698i \(-0.984916\pi\)
0.998877 0.0473698i \(-0.0150839\pi\)
\(728\) −5.84687e10 + 1.38867e11i −0.208160 + 0.494395i
\(729\) 0 0
\(730\) 2.94639e11 5.10330e11i 1.03753 1.79705i
\(731\) 2.68119e11 1.54799e11i 0.938983 0.542122i
\(732\) 0 0
\(733\) −3.25895e11 1.88156e11i −1.12892 0.651780i −0.185254 0.982691i \(-0.559311\pi\)
−0.943662 + 0.330910i \(0.892644\pi\)
\(734\) 6.13006e10i 0.211193i
\(735\) 0 0
\(736\) −4.54982e9 −0.0155054
\(737\) −3.33877e9 + 5.78292e9i −0.0113166 + 0.0196010i
\(738\) 0 0
\(739\) −2.33306e11 4.04098e11i −0.782255 1.35491i −0.930625 0.365974i \(-0.880736\pi\)
0.148370 0.988932i \(-0.452598\pi\)
\(740\) 1.97282e11 + 1.13901e11i 0.657900 + 0.379839i
\(741\) 0 0
\(742\) −8.97461e10 3.77868e10i −0.296074 0.124659i
\(743\) 2.39593e11 0.786175 0.393088 0.919501i \(-0.371407\pi\)
0.393088 + 0.919501i \(0.371407\pi\)
\(744\) 0 0
\(745\) −2.46930e11 + 1.42565e11i −0.801583 + 0.462794i
\(746\) 4.47133e10 + 7.74456e10i 0.144371 + 0.250058i
\(747\) 0 0
\(748\) 8.41579e9i 0.0268837i
\(749\) 8.62835e10 6.54143e10i 0.274158 0.207848i
\(750\) 0 0
\(751\) −1.07451e11 + 1.86111e11i −0.337793 + 0.585075i −0.984017 0.178072i \(-0.943014\pi\)
0.646224 + 0.763148i \(0.276347\pi\)
\(752\) −3.60111e10 + 2.07910e10i −0.112607 + 0.0650136i
\(753\) 0 0
\(754\) −8.54576e10 4.93390e10i −0.264402 0.152653i
\(755\) 6.73252e11i 2.07200i
\(756\) 0 0
\(757\) 3.69943e11 1.12655 0.563276 0.826269i \(-0.309541\pi\)
0.563276 + 0.826269i \(0.309541\pi\)
\(758\) 1.04370e11 1.80774e11i 0.316153 0.547593i
\(759\) 0 0
\(760\) 1.24369e11 + 2.15414e11i 0.372785 + 0.645683i
\(761\) −2.53298e11 1.46242e11i −0.755255 0.436047i 0.0723346 0.997380i \(-0.476955\pi\)
−0.827589 + 0.561334i \(0.810288\pi\)
\(762\) 0 0
\(763\) 4.32581e8 + 3.44021e9i 0.00127635 + 0.0101505i
\(764\) −3.05497e11 −0.896673
\(765\) 0 0
\(766\) −9.49251e10 + 5.48050e10i −0.275719 + 0.159186i
\(767\) −1.35800e11 2.35212e11i −0.392389 0.679638i
\(768\) 0 0
\(769\) 4.88004e10i 0.139546i −0.997563 0.0697732i \(-0.977772\pi\)
0.997563 0.0697732i \(-0.0222275\pi\)
\(770\) −1.09942e10 1.45017e10i −0.0312753 0.0412531i
\(771\) 0 0
\(772\) −3.03370e10 + 5.25452e10i −0.0854090 + 0.147933i
\(773\) −2.18055e11 + 1.25894e11i −0.610729 + 0.352604i −0.773251 0.634101i \(-0.781371\pi\)
0.162522 + 0.986705i \(0.448037\pi\)
\(774\) 0 0
\(775\) 5.74261e11 + 3.31550e11i 1.59185 + 0.919057i
\(776\) 1.94571e11i 0.536575i
\(777\) 0 0
\(778\) −2.93406e11 −0.800848
\(779\) −3.71852e10 + 6.44066e10i −0.100976 + 0.174896i
\(780\) 0 0
\(781\) −7.05880e9 1.22262e10i −0.0189726 0.0328615i
\(782\) −2.52946e10 1.46038e10i −0.0676396 0.0390517i
\(783\) 0 0
\(784\) −9.15102e10 + 2.33832e10i −0.242217 + 0.0618928i
\(785\) 1.67428e11 0.440909
\(786\) 0 0
\(787\) 1.64633e11 9.50509e10i 0.429159 0.247775i −0.269830 0.962908i \(-0.586967\pi\)
0.698988 + 0.715133i \(0.253634\pi\)
\(788\) −1.28533e11 2.22626e11i −0.333358 0.577394i
\(789\) 0 0
\(790\) 6.56820e11i 1.68631i
\(791\) 5.66885e11 + 2.38682e11i 1.44807 + 0.609696i
\(792\) 0 0
\(793\) 2.59130e11 4.48827e11i 0.655277 1.13497i
\(794\) 3.88225e11 2.24142e11i 0.976790 0.563950i
\(795\) 0 0
\(796\) 1.03715e11 + 5.98798e10i 0.258338 + 0.149152i
\(797\) 4.35825e11i 1.08014i −0.841621 0.540069i \(-0.818398\pi\)
0.841621 0.540069i \(-0.181602\pi\)
\(798\) 0 0
\(799\) −2.66937e11 −0.654970
\(800\) 7.02426e10 1.21664e11i 0.171491 0.297031i
\(801\) 0 0
\(802\) 2.05985e10 + 3.56777e10i 0.0497896 + 0.0862381i
\(803\) −2.63112e10 1.51908e10i −0.0632817 0.0365357i
\(804\) 0 0
\(805\) −6.26647e10 + 7.87964e9i −0.149224 + 0.0187639i
\(806\) −4.28953e11 −1.01641
\(807\) 0 0
\(808\) 4.75362e10 2.74450e10i 0.111527 0.0643900i
\(809\) 1.12279e11 + 1.94473e11i 0.262123 + 0.454011i 0.966806 0.255512i \(-0.0822440\pi\)
−0.704683 + 0.709523i \(0.748911\pi\)
\(810\) 0 0
\(811\) 5.24327e10i 0.121204i 0.998162 + 0.0606022i \(0.0193021\pi\)
−0.998162 + 0.0606022i \(0.980698\pi\)
\(812\) −7.71725e9 6.13733e10i −0.0177516 0.141174i
\(813\) 0 0
\(814\) 5.87239e9 1.01713e10i 0.0133757 0.0231674i
\(815\) −5.98409e11 + 3.45492e11i −1.35634 + 0.783082i
\(816\) 0 0
\(817\) 4.08568e11 + 2.35887e11i 0.917014 + 0.529438i
\(818\) 4.31839e11i 0.964513i
\(819\) 0 0
\(820\) 6.36529e10 0.140787
\(821\) 1.49561e10 2.59046e10i 0.0329188 0.0570171i −0.849097 0.528238i \(-0.822853\pi\)
0.882015 + 0.471220i \(0.156186\pi\)
\(822\) 0 0
\(823\) 3.11555e11 + 5.39629e11i 0.679102 + 1.17624i 0.975252 + 0.221098i \(0.0709641\pi\)
−0.296149 + 0.955142i \(0.595703\pi\)
\(824\) 1.47894e11 + 8.53867e10i 0.320805 + 0.185217i
\(825\) 0 0
\(826\) 6.60662e10 1.56912e11i 0.141925 0.337082i
\(827\) 2.57252e11 0.549968 0.274984 0.961449i \(-0.411328\pi\)
0.274984 + 0.961449i \(0.411328\pi\)
\(828\) 0 0
\(829\) 5.81907e10 3.35964e10i 0.123207 0.0711336i −0.437130 0.899398i \(-0.644005\pi\)
0.560337 + 0.828265i \(0.310672\pi\)
\(830\) −1.38798e11 2.40406e11i −0.292464 0.506562i
\(831\) 0 0
\(832\) 9.08785e10i 0.189657i
\(833\) −5.83803e11 1.63728e11i −1.21251 0.340050i
\(834\) 0 0
\(835\) −2.14878e11 + 3.72179e11i −0.442023 + 0.765607i
\(836\) 1.11061e10 6.41212e9i 0.0227372 0.0131273i
\(837\) 0 0
\(838\) −1.67304e11 9.65932e10i −0.339259 0.195871i
\(839\) 4.03627e11i 0.814577i −0.913300 0.407289i \(-0.866474\pi\)
0.913300 0.407289i \(-0.133526\pi\)
\(840\) 0 0
\(841\) −4.59736e11 −0.919019
\(842\) 1.62074e11 2.80721e11i 0.322452 0.558504i
\(843\) 0 0
\(844\) −8.62879e10 1.49455e11i −0.170051 0.294537i
\(845\) 9.85770e11 + 5.69134e11i 1.93352 + 1.11632i
\(846\) 0 0
\(847\) 4.09387e11 3.10369e11i 0.795426 0.603038i
\(848\) −5.87323e10 −0.113578
\(849\) 0 0
\(850\) 7.81024e11 4.50924e11i 1.49620 0.863830i
\(851\) −2.03806e10 3.53003e10i −0.0388597 0.0673069i
\(852\) 0 0
\(853\) 1.87913e11i 0.354945i −0.984126 0.177472i \(-0.943208\pi\)
0.984126 0.177472i \(-0.0567921\pi\)
\(854\) 3.22335e11 4.05313e10i 0.606004 0.0762007i
\(855\) 0 0
\(856\) 3.26534e10 5.65573e10i 0.0608181 0.105340i
\(857\) −5.48475e10 + 3.16662e10i −0.101680 + 0.0587047i −0.549977 0.835179i \(-0.685364\pi\)
0.448298 + 0.893884i \(0.352030\pi\)
\(858\) 0 0
\(859\) 2.97843e11 + 1.71960e11i 0.547034 + 0.315830i 0.747925 0.663783i \(-0.231050\pi\)
−0.200891 + 0.979614i \(0.564384\pi\)
\(860\) 4.03787e11i 0.738173i
\(861\) 0 0
\(862\) −5.17682e11 −0.937636
\(863\) 2.48122e10 4.29760e10i 0.0447324 0.0774789i −0.842792 0.538239i \(-0.819090\pi\)
0.887525 + 0.460760i \(0.152423\pi\)
\(864\) 0 0
\(865\) −4.16098e11 7.20704e11i −0.743244 1.28734i
\(866\) 1.38867e11 + 8.01752e10i 0.246904 + 0.142550i
\(867\) 0 0
\(868\) −1.62447e11 2.14273e11i −0.286176 0.377476i
\(869\) −3.38638e10 −0.0593822
\(870\) 0 0
\(871\) 4.00882e11 2.31450e11i 0.696537 0.402146i
\(872\) 1.04564e9 + 1.81111e9i 0.00180850 + 0.00313241i
\(873\) 0 0
\(874\) 4.45076e10i 0.0762761i
\(875\) 3.66711e11 8.70963e11i 0.625593 1.48583i
\(876\) 0 0
\(877\) −3.26476e11 + 5.65473e11i −0.551890 + 0.955902i 0.446248 + 0.894909i \(0.352760\pi\)
−0.998138 + 0.0609924i \(0.980573\pi\)
\(878\) 9.57548e10 5.52841e10i 0.161132 0.0930298i
\(879\) 0 0
\(880\) −9.50562e9 5.48807e9i −0.0158508 0.00915144i
\(881\) 8.21158e11i 1.36309i 0.731778 + 0.681543i \(0.238691\pi\)
−0.731778 + 0.681543i \(0.761309\pi\)
\(882\) 0 0
\(883\) 9.78470e11 1.60955 0.804775 0.593580i \(-0.202286\pi\)
0.804775 + 0.593580i \(0.202286\pi\)
\(884\) −2.91699e11 + 5.05237e11i −0.477667 + 0.827344i
\(885\) 0 0
\(886\) 2.89008e11 + 5.00577e11i 0.469003 + 0.812337i
\(887\) 3.32455e11 + 1.91943e11i 0.537080 + 0.310083i 0.743895 0.668297i \(-0.232976\pi\)
−0.206815 + 0.978380i \(0.566310\pi\)
\(888\) 0 0
\(889\) −4.40257e11 1.85366e11i −0.704854 0.296772i
\(890\) −1.04480e12 −1.66522
\(891\) 0 0
\(892\) −2.52622e11 + 1.45851e11i −0.399036 + 0.230383i
\(893\) −2.03383e11 3.52270e11i −0.319823 0.553949i
\(894\) 0 0
\(895\) 2.81531e11i 0.438767i
\(896\) −4.53962e10 + 3.44163e10i −0.0704348 + 0.0533989i
\(897\) 0 0
\(898\) −1.47746e11 + 2.55903e11i −0.227200 + 0.393523i
\(899\) 1.52506e11 8.80496e10i 0.233480 0.134800i
\(900\) 0 0
\(901\) −3.26521e11 1.88517e11i −0.495464 0.286056i
\(902\) 3.28176e9i 0.00495771i
\(903\) 0 0
\(904\) 3.70986e11 0.555499
\(905\) 3.35601e11 5.81278e11i 0.500298 0.866542i
\(906\) 0 0
\(907\) −5.87195e11 1.01705e12i −0.867667 1.50284i −0.864375 0.502848i \(-0.832285\pi\)
−0.00329220 0.999995i \(-0.501048\pi\)
\(908\) 3.27620e11 + 1.89151e11i 0.481977 + 0.278270i
\(909\) 0 0
\(910\) 1.57389e11 + 1.25167e12i 0.229513 + 1.82526i
\(911\) −1.28724e12 −1.86890 −0.934449 0.356096i \(-0.884107\pi\)
−0.934449 + 0.356096i \(0.884107\pi\)
\(912\) 0 0
\(913\) −1.23946e10 + 7.15605e9i −0.0178382 + 0.0102989i
\(914\) 3.61815e11 + 6.26682e11i 0.518444 + 0.897972i
\(915\) 0 0
\(916\) 2.10561e10i 0.0299086i
\(917\) −5.24881e11 6.92335e11i −0.742307 0.979127i
\(918\) 0 0
\(919\) −2.53931e11 + 4.39821e11i −0.356002 + 0.616614i −0.987289 0.158935i \(-0.949194\pi\)
0.631287 + 0.775550i \(0.282527\pi\)
\(920\) −3.29901e10 + 1.90468e10i −0.0460502 + 0.0265871i
\(921\) 0 0
\(922\) 6.09384e11 + 3.51828e11i 0.843271 + 0.486863i
\(923\) 9.78657e11i 1.34842i
\(924\) 0 0
\(925\) 1.25859e12 1.71916
\(926\) −1.84036e11 + 3.18759e11i −0.250298 + 0.433530i
\(927\) 0 0
\(928\) −1.86543e10 3.23102e10i −0.0251528 0.0435660i
\(929\) 1.48512e11 + 8.57434e10i 0.199388 + 0.115117i 0.596370 0.802710i \(-0.296609\pi\)
−0.396982 + 0.917826i \(0.629943\pi\)
\(930\) 0 0
\(931\) −2.28741e11 8.95178e11i −0.304471 1.19155i
\(932\) 6.46295e11 0.856579
\(933\) 0 0
\(934\) −8.58028e11 + 4.95383e11i −1.12749 + 0.650959i
\(935\) −3.52309e10 6.10216e10i −0.0460974 0.0798431i
\(936\) 0 0
\(937\) 9.69345e11i 1.25754i −0.777593 0.628768i \(-0.783560\pi\)
0.777593 0.628768i \(-0.216440\pi\)
\(938\) 2.67432e11 + 1.12600e11i 0.345463 + 0.145454i
\(939\) 0 0
\(940\) −1.74074e11 + 3.01505e11i −0.222957 + 0.386174i
\(941\) −5.54229e11 + 3.19984e11i −0.706856 + 0.408103i −0.809896 0.586574i \(-0.800476\pi\)
0.103040 + 0.994677i \(0.467143\pi\)
\(942\) 0 0
\(943\) −9.86371e9 5.69481e9i −0.0124736 0.00720166i
\(944\) 1.02687e11i 0.129309i
\(945\) 0 0
\(946\) −2.08181e10 −0.0259942
\(947\) −2.62353e11 + 4.54409e11i −0.326202 + 0.564998i −0.981755 0.190151i \(-0.939102\pi\)
0.655553 + 0.755149i \(0.272436\pi\)
\(948\) 0 0
\(949\) 1.05305e12 + 1.82394e12i 1.29833 + 2.24877i
\(950\) 1.19015e12 + 6.87132e11i 1.46119 + 0.843618i
\(951\) 0 0
\(952\) −3.62847e11 + 4.56254e10i −0.441749 + 0.0555468i
\(953\) −3.48057e11 −0.421967 −0.210983 0.977490i \(-0.567667\pi\)
−0.210983 + 0.977490i \(0.567667\pi\)
\(954\) 0 0
\(955\) −2.21512e12 + 1.27890e12i −2.66307 + 1.53753i
\(956\) 3.71574e10 + 6.43584e10i 0.0444850 + 0.0770502i
\(957\) 0 0
\(958\) 7.65881e11i 0.909283i
\(959\) −5.24294e9 4.16957e10i −0.00619870 0.0492966i
\(960\) 0 0
\(961\) −4.36943e10 + 7.56808e10i −0.0512308 + 0.0887344i
\(962\) −7.05091e11 + 4.07084e11i −0.823275 + 0.475318i
\(963\) 0 0
\(964\) 4.86023e11 + 2.80605e11i 0.562793 + 0.324929i
\(965\) 5.07997e11i 0.585803i
\(966\) 0 0
\(967\) −1.63339e12 −1.86803 −0.934013 0.357240i \(-0.883718\pi\)
−0.934013 + 0.357240i \(0.883718\pi\)
\(968\) 1.54929e11 2.68346e11i 0.176454 0.305628i
\(969\) 0 0
\(970\) −8.14527e11 1.41080e12i −0.920065 1.59360i
\(971\) 3.36844e11 + 1.94477e11i 0.378924 + 0.218772i 0.677350 0.735661i \(-0.263128\pi\)
−0.298426 + 0.954433i \(0.596462\pi\)
\(972\) 0 0
\(973\) −4.70151e11 + 1.11664e12i −0.524548 + 1.24584i
\(974\) 4.00702e9 0.00445231
\(975\) 0 0
\(976\) 1.69694e11 9.79730e10i 0.187011 0.107971i
\(977\) −3.10825e11 5.38365e11i −0.341144 0.590879i 0.643501 0.765445i \(-0.277481\pi\)
−0.984645 + 0.174566i \(0.944148\pi\)
\(978\) 0 0
\(979\) 5.38667e10i 0.0586394i
\(980\) −5.65638e11 + 5.52636e11i −0.613245 + 0.599149i
\(981\) 0 0
\(982\) 1.70253e11 2.94886e11i 0.183083 0.317109i
\(983\) 1.22811e12 7.09049e11i 1.31529 0.759385i 0.332326 0.943165i \(-0.392167\pi\)
0.982967 + 0.183780i \(0.0588333\pi\)
\(984\) 0 0
\(985\) −1.86395e12 1.07615e12i −1.98011 1.14322i
\(986\) 2.39504e11i 0.253399i
\(987\) 0 0
\(988\) −8.88999e11 −0.932982
\(989\) −3.61254e10 + 6.25711e10i −0.0377596 + 0.0654016i
\(990\) 0 0
\(991\) −7.91519e11 1.37095e12i −0.820666 1.42144i −0.905187 0.425014i \(-0.860269\pi\)
0.0845208 0.996422i \(-0.473064\pi\)
\(992\) −1.40452e11 8.10902e10i −0.145038 0.0837378i
\(993\) 0 0
\(994\) −4.88865e11 + 3.70624e11i −0.500775 + 0.379654i
\(995\) 1.00269e12 1.02300
\(996\) 0 0
\(997\) 1.14818e12 6.62901e11i 1.16206 0.670916i 0.210263 0.977645i \(-0.432568\pi\)
0.951797 + 0.306729i \(0.0992345\pi\)
\(998\) −2.99381e11 5.18544e11i −0.301788 0.522713i
\(999\) 0 0
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 126.9.n.b.19.1 12
3.2 odd 2 14.9.d.a.5.4 yes 12
7.3 odd 6 inner 126.9.n.b.73.1 12
12.11 even 2 112.9.s.c.33.5 12
21.2 odd 6 98.9.b.c.97.2 12
21.5 even 6 98.9.b.c.97.5 12
21.11 odd 6 98.9.d.b.31.6 12
21.17 even 6 14.9.d.a.3.4 12
21.20 even 2 98.9.d.b.19.6 12
84.59 odd 6 112.9.s.c.17.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.9.d.a.3.4 12 21.17 even 6
14.9.d.a.5.4 yes 12 3.2 odd 2
98.9.b.c.97.2 12 21.2 odd 6
98.9.b.c.97.5 12 21.5 even 6
98.9.d.b.19.6 12 21.20 even 2
98.9.d.b.31.6 12 21.11 odd 6
112.9.s.c.17.5 12 84.59 odd 6
112.9.s.c.33.5 12 12.11 even 2
126.9.n.b.19.1 12 1.1 even 1 trivial
126.9.n.b.73.1 12 7.3 odd 6 inner