Properties

Label 22.9.b.a.21.1
Level $22$
Weight $9$
Character 22.21
Analytic conductor $8.962$
Analytic rank $0$
Dimension $8$
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] = [22,9,Mod(21,22)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(22, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("22.21");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 22.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: \(8.96232942134\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 7944x^{6} + 15215349x^{4} + 1757611988x^{2} + 38177252100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{16}\cdot 11^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 21.1
Root \(-9.64354i\) of defining polynomial
Character \(\chi\) \(=\) 22.21
Dual form 22.9.b.a.21.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-11.3137i q^{2} -143.261 q^{3} -128.000 q^{4} -309.991 q^{5} +1620.81i q^{6} -1256.92i q^{7} +1448.15i q^{8} +13962.6 q^{9} +O(q^{10})\) \(q-11.3137i q^{2} -143.261 q^{3} -128.000 q^{4} -309.991 q^{5} +1620.81i q^{6} -1256.92i q^{7} +1448.15i q^{8} +13962.6 q^{9} +3507.15i q^{10} +(2859.33 + 14359.1i) q^{11} +18337.4 q^{12} -38587.8i q^{13} -14220.5 q^{14} +44409.6 q^{15} +16384.0 q^{16} +31930.4i q^{17} -157969. i q^{18} +196632. i q^{19} +39678.9 q^{20} +180068. i q^{21} +(162454. - 32349.6i) q^{22} +293331. q^{23} -207464. i q^{24} -294530. q^{25} -436571. q^{26} -1.06036e6 q^{27} +160886. i q^{28} +368541. i q^{29} -502437. i q^{30} -433548. q^{31} -185364. i q^{32} +(-409629. - 2.05709e6i) q^{33} +361252. q^{34} +389635. i q^{35} -1.78722e6 q^{36} +2.92200e6 q^{37} +2.22463e6 q^{38} +5.52812e6i q^{39} -448915. i q^{40} -3.66432e6i q^{41} +2.03724e6 q^{42} +5.40993e6i q^{43} +(-365994. - 1.83796e6i) q^{44} -4.32829e6 q^{45} -3.31867e6i q^{46} +3.98014e6 q^{47} -2.34718e6 q^{48} +4.18494e6 q^{49} +3.33223e6i q^{50} -4.57438e6i q^{51} +4.93924e6i q^{52} +4.85507e6 q^{53} +1.19967e7i q^{54} +(-886366. - 4.45119e6i) q^{55} +1.82022e6 q^{56} -2.81696e7i q^{57} +4.16956e6 q^{58} +761371. q^{59} -5.68442e6 q^{60} +1.65487e7i q^{61} +4.90503e6i q^{62} -1.75500e7i q^{63} -2.09715e6 q^{64} +1.19619e7i q^{65} +(-2.32733e7 + 4.63443e6i) q^{66} -3.56044e7 q^{67} -4.08710e6i q^{68} -4.20229e7 q^{69} +4.40822e6 q^{70} +6.40846e6 q^{71} +2.02201e7i q^{72} +1.18845e7i q^{73} -3.30587e7i q^{74} +4.21947e7 q^{75} -2.51688e7i q^{76} +(1.80483e7 - 3.59396e6i) q^{77} +6.25435e7 q^{78} +5.34827e7i q^{79} -5.07889e6 q^{80} +6.02997e7 q^{81} -4.14570e7 q^{82} +1.61252e7i q^{83} -2.30487e7i q^{84} -9.89815e6i q^{85} +6.12063e7 q^{86} -5.27974e7i q^{87} +(-2.07942e7 + 4.14075e6i) q^{88} -1.55356e6 q^{89} +4.89691e7i q^{90} -4.85019e7 q^{91} -3.75464e7 q^{92} +6.21104e7 q^{93} -4.50302e7i q^{94} -6.09540e7i q^{95} +2.65554e7i q^{96} -1.42492e8 q^{97} -4.73472e7i q^{98} +(3.99237e7 + 2.00491e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 182 q^{3} - 1024 q^{4} - 1410 q^{5} + 44582 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 182 q^{3} - 1024 q^{4} - 1410 q^{5} + 44582 q^{9} + 5808 q^{11} - 23296 q^{12} + 12288 q^{14} + 87958 q^{15} + 131072 q^{16} + 180480 q^{20} + 359040 q^{22} - 802026 q^{23} + 999558 q^{25} - 1321728 q^{26} - 1561354 q^{27} + 196726 q^{31} - 4286722 q^{33} - 701952 q^{34} - 5706496 q^{36} + 8627998 q^{37} + 9288960 q^{38} + 4366848 q^{42} - 743424 q^{44} + 1146988 q^{45} - 14335392 q^{47} + 2981888 q^{48} - 6714712 q^{49} + 55946352 q^{53} - 10078442 q^{55} - 1572864 q^{56} - 23226624 q^{58} + 21793110 q^{59} - 11258624 q^{60} - 16777216 q^{64} - 44242176 q^{66} - 113809034 q^{67} - 171636914 q^{69} + 137817600 q^{70} + 16741974 q^{71} + 346496844 q^{75} - 137074080 q^{77} - 57993216 q^{78} - 23101440 q^{80} + 85282724 q^{81} + 47480832 q^{82} + 49839360 q^{86} - 45957120 q^{88} + 42055422 q^{89} - 146801952 q^{91} + 102659328 q^{92} + 253251118 q^{93} + 100034782 q^{97} - 333541978 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).

\(n\) \(13\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.3137i 0.707107i
\(3\) −143.261 −1.76865 −0.884326 0.466871i \(-0.845381\pi\)
−0.884326 + 0.466871i \(0.845381\pi\)
\(4\) −128.000 −0.500000
\(5\) −309.991 −0.495986 −0.247993 0.968762i \(-0.579771\pi\)
−0.247993 + 0.968762i \(0.579771\pi\)
\(6\) 1620.81i 1.25063i
\(7\) 1256.92i 0.523500i −0.965136 0.261750i \(-0.915700\pi\)
0.965136 0.261750i \(-0.0842997\pi\)
\(8\) 1448.15i 0.353553i
\(9\) 13962.6 2.12813
\(10\) 3507.15i 0.350715i
\(11\) 2859.33 + 14359.1i 0.195296 + 0.980744i
\(12\) 18337.4 0.884326
\(13\) 38587.8i 1.35107i −0.737330 0.675533i \(-0.763914\pi\)
0.737330 0.675533i \(-0.236086\pi\)
\(14\) −14220.5 −0.370171
\(15\) 44409.6 0.877226
\(16\) 16384.0 0.250000
\(17\) 31930.4i 0.382304i 0.981560 + 0.191152i \(0.0612224\pi\)
−0.981560 + 0.191152i \(0.938778\pi\)
\(18\) 157969.i 1.50481i
\(19\) 196632.i 1.50882i 0.656401 + 0.754412i \(0.272078\pi\)
−0.656401 + 0.754412i \(0.727922\pi\)
\(20\) 39678.9 0.247993
\(21\) 180068.i 0.925890i
\(22\) 162454. 32349.6i 0.693491 0.138095i
\(23\) 293331. 1.04821 0.524104 0.851654i \(-0.324400\pi\)
0.524104 + 0.851654i \(0.324400\pi\)
\(24\) 207464.i 0.625313i
\(25\) −294530. −0.753998
\(26\) −436571. −0.955348
\(27\) −1.06036e6 −1.99526
\(28\) 160886.i 0.261750i
\(29\) 368541.i 0.521067i 0.965465 + 0.260533i \(0.0838984\pi\)
−0.965465 + 0.260533i \(0.916102\pi\)
\(30\) 502437.i 0.620292i
\(31\) −433548. −0.469451 −0.234725 0.972062i \(-0.575419\pi\)
−0.234725 + 0.972062i \(0.575419\pi\)
\(32\) 185364.i 0.176777i
\(33\) −409629. 2.05709e6i −0.345410 1.73459i
\(34\) 361252. 0.270330
\(35\) 389635.i 0.259649i
\(36\) −1.78722e6 −1.06406
\(37\) 2.92200e6 1.55910 0.779550 0.626340i \(-0.215448\pi\)
0.779550 + 0.626340i \(0.215448\pi\)
\(38\) 2.22463e6 1.06690
\(39\) 5.52812e6i 2.38956i
\(40\) 448915.i 0.175357i
\(41\) 3.66432e6i 1.29675i −0.761319 0.648377i \(-0.775448\pi\)
0.761319 0.648377i \(-0.224552\pi\)
\(42\) 2.03724e6 0.654703
\(43\) 5.40993e6i 1.58240i 0.611555 + 0.791202i \(0.290545\pi\)
−0.611555 + 0.791202i \(0.709455\pi\)
\(44\) −365994. 1.83796e6i −0.0976479 0.490372i
\(45\) −4.32829e6 −1.05552
\(46\) 3.31867e6i 0.741195i
\(47\) 3.98014e6 0.815656 0.407828 0.913059i \(-0.366286\pi\)
0.407828 + 0.913059i \(0.366286\pi\)
\(48\) −2.34718e6 −0.442163
\(49\) 4.18494e6 0.725947
\(50\) 3.33223e6i 0.533157i
\(51\) 4.57438e6i 0.676163i
\(52\) 4.93924e6i 0.675533i
\(53\) 4.85507e6 0.615307 0.307654 0.951498i \(-0.400456\pi\)
0.307654 + 0.951498i \(0.400456\pi\)
\(54\) 1.19967e7i 1.41086i
\(55\) −886366. 4.45119e6i −0.0968640 0.486435i
\(56\) 1.82022e6 0.185085
\(57\) 2.81696e7i 2.66858i
\(58\) 4.16956e6 0.368450
\(59\) 761371. 0.0628330 0.0314165 0.999506i \(-0.489998\pi\)
0.0314165 + 0.999506i \(0.489998\pi\)
\(60\) −5.68442e6 −0.438613
\(61\) 1.65487e7i 1.19521i 0.801789 + 0.597607i \(0.203882\pi\)
−0.801789 + 0.597607i \(0.796118\pi\)
\(62\) 4.90503e6i 0.331952i
\(63\) 1.75500e7i 1.11408i
\(64\) −2.09715e6 −0.125000
\(65\) 1.19619e7i 0.670110i
\(66\) −2.32733e7 + 4.63443e6i −1.22654 + 0.244242i
\(67\) −3.56044e7 −1.76687 −0.883434 0.468555i \(-0.844775\pi\)
−0.883434 + 0.468555i \(0.844775\pi\)
\(68\) 4.08710e6i 0.191152i
\(69\) −4.20229e7 −1.85391
\(70\) 4.40822e6 0.183599
\(71\) 6.40846e6 0.252186 0.126093 0.992018i \(-0.459756\pi\)
0.126093 + 0.992018i \(0.459756\pi\)
\(72\) 2.02201e7i 0.752406i
\(73\) 1.18845e7i 0.418493i 0.977863 + 0.209246i \(0.0671011\pi\)
−0.977863 + 0.209246i \(0.932899\pi\)
\(74\) 3.30587e7i 1.10245i
\(75\) 4.21947e7 1.33356
\(76\) 2.51688e7i 0.754412i
\(77\) 1.80483e7 3.59396e6i 0.513420 0.102237i
\(78\) 6.25435e7 1.68968
\(79\) 5.34827e7i 1.37311i 0.727079 + 0.686554i \(0.240877\pi\)
−0.727079 + 0.686554i \(0.759123\pi\)
\(80\) −5.07889e6 −0.123996
\(81\) 6.02997e7 1.40080
\(82\) −4.14570e7 −0.916944
\(83\) 1.61252e7i 0.339776i 0.985463 + 0.169888i \(0.0543406\pi\)
−0.985463 + 0.169888i \(0.945659\pi\)
\(84\) 2.30487e7i 0.462945i
\(85\) 9.89815e6i 0.189618i
\(86\) 6.12063e7 1.11893
\(87\) 5.27974e7i 0.921585i
\(88\) −2.07942e7 + 4.14075e6i −0.346746 + 0.0690475i
\(89\) −1.55356e6 −0.0247610 −0.0123805 0.999923i \(-0.503941\pi\)
−0.0123805 + 0.999923i \(0.503941\pi\)
\(90\) 4.89691e7i 0.746366i
\(91\) −4.85019e7 −0.707284
\(92\) −3.75464e7 −0.524104
\(93\) 6.21104e7 0.830295
\(94\) 4.50302e7i 0.576756i
\(95\) 6.09540e7i 0.748356i
\(96\) 2.65554e7i 0.312656i
\(97\) −1.42492e8 −1.60955 −0.804776 0.593579i \(-0.797714\pi\)
−0.804776 + 0.593579i \(0.797714\pi\)
\(98\) 4.73472e7i 0.513322i
\(99\) 3.99237e7 + 2.00491e8i 0.415614 + 2.08715i
\(100\) 3.76999e7 0.376999
\(101\) 5.11231e7i 0.491283i 0.969361 + 0.245642i \(0.0789986\pi\)
−0.969361 + 0.245642i \(0.921001\pi\)
\(102\) −5.17532e7 −0.478119
\(103\) 1.62007e8 1.43942 0.719708 0.694277i \(-0.244276\pi\)
0.719708 + 0.694277i \(0.244276\pi\)
\(104\) 5.58811e7 0.477674
\(105\) 5.58195e7i 0.459228i
\(106\) 5.49288e7i 0.435088i
\(107\) 1.98786e8i 1.51653i 0.651946 + 0.758266i \(0.273953\pi\)
−0.651946 + 0.758266i \(0.726047\pi\)
\(108\) 1.35727e8 0.997631
\(109\) 1.49606e8i 1.05984i −0.848046 0.529922i \(-0.822221\pi\)
0.848046 0.529922i \(-0.177779\pi\)
\(110\) −5.03594e7 + 1.00281e7i −0.343962 + 0.0684932i
\(111\) −4.18609e8 −2.75750
\(112\) 2.05935e7i 0.130875i
\(113\) 9.52975e7 0.584477 0.292239 0.956345i \(-0.405600\pi\)
0.292239 + 0.956345i \(0.405600\pi\)
\(114\) −3.18702e8 −1.88697
\(115\) −9.09301e7 −0.519896
\(116\) 4.71732e7i 0.260533i
\(117\) 5.38788e8i 2.87524i
\(118\) 8.61393e6i 0.0444297i
\(119\) 4.01342e7 0.200136
\(120\) 6.43119e7i 0.310146i
\(121\) −1.98007e8 + 8.21146e7i −0.923719 + 0.383071i
\(122\) 1.87228e8 0.845144
\(123\) 5.24953e8i 2.29351i
\(124\) 5.54941e7 0.234725
\(125\) 2.12392e8 0.869958
\(126\) −1.98555e8 −0.787770
\(127\) 8.11193e7i 0.311824i 0.987771 + 0.155912i \(0.0498316\pi\)
−0.987771 + 0.155912i \(0.950168\pi\)
\(128\) 2.37266e7i 0.0883883i
\(129\) 7.75030e8i 2.79872i
\(130\) 1.35333e8 0.473839
\(131\) 2.71103e7i 0.0920553i −0.998940 0.0460276i \(-0.985344\pi\)
0.998940 0.0460276i \(-0.0146562\pi\)
\(132\) 5.24325e7 + 2.63308e8i 0.172705 + 0.867297i
\(133\) 2.47151e8 0.789870
\(134\) 4.02818e8i 1.24936i
\(135\) 3.28704e8 0.989622
\(136\) −4.62402e7 −0.135165
\(137\) 6.89037e8 1.95596 0.977981 0.208692i \(-0.0669207\pi\)
0.977981 + 0.208692i \(0.0669207\pi\)
\(138\) 4.75435e8i 1.31091i
\(139\) 3.22285e7i 0.0863339i 0.999068 + 0.0431669i \(0.0137447\pi\)
−0.999068 + 0.0431669i \(0.986255\pi\)
\(140\) 4.98733e7i 0.129824i
\(141\) −5.70198e8 −1.44261
\(142\) 7.25035e7i 0.178322i
\(143\) 5.54085e8 1.10335e8i 1.32505 0.263858i
\(144\) 2.28764e8 0.532032
\(145\) 1.14244e8i 0.258442i
\(146\) 1.34457e8 0.295919
\(147\) −5.99538e8 −1.28395
\(148\) −3.74017e8 −0.779550
\(149\) 7.59825e8i 1.54159i 0.637084 + 0.770794i \(0.280140\pi\)
−0.637084 + 0.770794i \(0.719860\pi\)
\(150\) 4.77378e8i 0.942969i
\(151\) 4.11446e8i 0.791416i −0.918376 0.395708i \(-0.870499\pi\)
0.918376 0.395708i \(-0.129501\pi\)
\(152\) −2.84753e8 −0.533450
\(153\) 4.45833e8i 0.813592i
\(154\) −4.06610e7 2.04193e8i −0.0722928 0.363043i
\(155\) 1.34396e8 0.232841
\(156\) 7.07599e8i 1.19478i
\(157\) −4.67385e8 −0.769265 −0.384632 0.923070i \(-0.625672\pi\)
−0.384632 + 0.923070i \(0.625672\pi\)
\(158\) 6.05087e8 0.970934
\(159\) −6.95541e8 −1.08826
\(160\) 5.74611e7i 0.0876787i
\(161\) 3.68695e8i 0.548737i
\(162\) 6.82213e8i 0.990513i
\(163\) 2.51220e8 0.355880 0.177940 0.984041i \(-0.443057\pi\)
0.177940 + 0.984041i \(0.443057\pi\)
\(164\) 4.69033e8i 0.648377i
\(165\) 1.26981e8 + 6.37680e8i 0.171319 + 0.860334i
\(166\) 1.82436e8 0.240258
\(167\) 1.37596e9i 1.76905i −0.466490 0.884526i \(-0.654482\pi\)
0.466490 0.884526i \(-0.345518\pi\)
\(168\) −2.60766e8 −0.327351
\(169\) −6.73287e8 −0.825379
\(170\) −1.11985e8 −0.134080
\(171\) 2.74550e9i 3.21097i
\(172\) 6.92471e8i 0.791202i
\(173\) 2.76459e8i 0.308636i −0.988021 0.154318i \(-0.950682\pi\)
0.988021 0.154318i \(-0.0493181\pi\)
\(174\) −5.97334e8 −0.651659
\(175\) 3.70203e8i 0.394718i
\(176\) 4.68472e7 + 2.35259e8i 0.0488240 + 0.245186i
\(177\) −1.09075e8 −0.111130
\(178\) 1.75765e7i 0.0175087i
\(179\) 4.07962e8 0.397381 0.198690 0.980062i \(-0.436331\pi\)
0.198690 + 0.980062i \(0.436331\pi\)
\(180\) 5.54022e8 0.527760
\(181\) 3.39618e8 0.316429 0.158215 0.987405i \(-0.449426\pi\)
0.158215 + 0.987405i \(0.449426\pi\)
\(182\) 5.48737e8i 0.500125i
\(183\) 2.37078e9i 2.11392i
\(184\) 4.24789e8i 0.370597i
\(185\) −9.05796e8 −0.773292
\(186\) 7.02699e8i 0.587107i
\(187\) −4.58492e8 + 9.12995e7i −0.374943 + 0.0746624i
\(188\) −5.09458e8 −0.407828
\(189\) 1.33280e9i 1.04452i
\(190\) −6.89616e8 −0.529167
\(191\) −7.22044e8 −0.542538 −0.271269 0.962504i \(-0.587443\pi\)
−0.271269 + 0.962504i \(0.587443\pi\)
\(192\) 3.00440e8 0.221081
\(193\) 1.18124e9i 0.851354i 0.904875 + 0.425677i \(0.139964\pi\)
−0.904875 + 0.425677i \(0.860036\pi\)
\(194\) 1.61212e9i 1.13812i
\(195\) 1.71367e9i 1.18519i
\(196\) −5.35673e8 −0.362974
\(197\) 8.48888e8i 0.563619i −0.959470 0.281809i \(-0.909065\pi\)
0.959470 0.281809i \(-0.0909346\pi\)
\(198\) 2.26829e9 4.51686e8i 1.47584 0.293884i
\(199\) −7.90352e7 −0.0503974 −0.0251987 0.999682i \(-0.508022\pi\)
−0.0251987 + 0.999682i \(0.508022\pi\)
\(200\) 4.26526e8i 0.266579i
\(201\) 5.10071e9 3.12497
\(202\) 5.78392e8 0.347390
\(203\) 4.63228e8 0.272779
\(204\) 5.85520e8i 0.338081i
\(205\) 1.13591e9i 0.643172i
\(206\) 1.83291e9i 1.01782i
\(207\) 4.09568e9 2.23072
\(208\) 6.32222e8i 0.337767i
\(209\) −2.82345e9 + 5.62234e8i −1.47977 + 0.294667i
\(210\) −6.31525e8 −0.324723
\(211\) 1.77494e9i 0.895477i 0.894165 + 0.447738i \(0.147770\pi\)
−0.894165 + 0.447738i \(0.852230\pi\)
\(212\) −6.21449e8 −0.307654
\(213\) −9.18081e8 −0.446028
\(214\) 2.24901e9 1.07235
\(215\) 1.67703e9i 0.784850i
\(216\) 1.53557e9i 0.705432i
\(217\) 5.44937e8i 0.245758i
\(218\) −1.69260e9 −0.749423
\(219\) 1.70258e9i 0.740168i
\(220\) 1.13455e8 + 5.69752e8i 0.0484320 + 0.243218i
\(221\) 1.23213e9 0.516518
\(222\) 4.73601e9i 1.94985i
\(223\) −2.44670e9 −0.989374 −0.494687 0.869071i \(-0.664717\pi\)
−0.494687 + 0.869071i \(0.664717\pi\)
\(224\) −2.32988e8 −0.0925427
\(225\) −4.11242e9 −1.60460
\(226\) 1.07817e9i 0.413288i
\(227\) 2.04022e9i 0.768377i −0.923255 0.384188i \(-0.874481\pi\)
0.923255 0.384188i \(-0.125519\pi\)
\(228\) 3.60571e9i 1.33429i
\(229\) 1.18977e9 0.432635 0.216317 0.976323i \(-0.430595\pi\)
0.216317 + 0.976323i \(0.430595\pi\)
\(230\) 1.02876e9i 0.367622i
\(231\) −2.58561e9 + 5.14873e8i −0.908061 + 0.180822i
\(232\) −5.33704e8 −0.184225
\(233\) 2.48427e7i 0.00842898i 0.999991 + 0.00421449i \(0.00134152\pi\)
−0.999991 + 0.00421449i \(0.998658\pi\)
\(234\) −6.09568e9 −2.03310
\(235\) −1.23381e9 −0.404554
\(236\) −9.74554e7 −0.0314165
\(237\) 7.66197e9i 2.42855i
\(238\) 4.54066e8i 0.141518i
\(239\) 2.28556e9i 0.700487i 0.936659 + 0.350244i \(0.113901\pi\)
−0.936659 + 0.350244i \(0.886099\pi\)
\(240\) 7.27606e8 0.219306
\(241\) 4.44393e8i 0.131734i 0.997828 + 0.0658672i \(0.0209814\pi\)
−0.997828 + 0.0658672i \(0.979019\pi\)
\(242\) 9.29020e8 + 2.24020e9i 0.270872 + 0.653168i
\(243\) −1.68153e9 −0.482258
\(244\) 2.11824e9i 0.597607i
\(245\) −1.29729e9 −0.360060
\(246\) 5.93917e9 1.62175
\(247\) 7.58758e9 2.03852
\(248\) 6.27844e8i 0.165976i
\(249\) 2.31011e9i 0.600945i
\(250\) 2.40294e9i 0.615153i
\(251\) −1.07101e9 −0.269834 −0.134917 0.990857i \(-0.543077\pi\)
−0.134917 + 0.990857i \(0.543077\pi\)
\(252\) 2.24640e9i 0.557038i
\(253\) 8.38730e8 + 4.21197e9i 0.204711 + 1.02802i
\(254\) 9.17760e8 0.220493
\(255\) 1.41802e9i 0.335367i
\(256\) 2.68435e8 0.0625000
\(257\) 1.65767e9 0.379983 0.189992 0.981786i \(-0.439154\pi\)
0.189992 + 0.981786i \(0.439154\pi\)
\(258\) −8.76846e9 −1.97900
\(259\) 3.67274e9i 0.816190i
\(260\) 1.53112e9i 0.335055i
\(261\) 5.14580e9i 1.10890i
\(262\) −3.06718e8 −0.0650929
\(263\) 2.52475e9i 0.527711i −0.964562 0.263855i \(-0.915006\pi\)
0.964562 0.263855i \(-0.0849942\pi\)
\(264\) 2.97899e9 5.93206e8i 0.613272 0.122121i
\(265\) −1.50503e9 −0.305184
\(266\) 2.79619e9i 0.558523i
\(267\) 2.22564e8 0.0437935
\(268\) 4.55736e9 0.883434
\(269\) −3.95184e9 −0.754728 −0.377364 0.926065i \(-0.623169\pi\)
−0.377364 + 0.926065i \(0.623169\pi\)
\(270\) 3.71886e9i 0.699768i
\(271\) 8.79271e9i 1.63022i 0.579308 + 0.815109i \(0.303323\pi\)
−0.579308 + 0.815109i \(0.696677\pi\)
\(272\) 5.23148e8i 0.0955761i
\(273\) 6.94842e9 1.25094
\(274\) 7.79557e9i 1.38307i
\(275\) −8.42159e8 4.22919e9i −0.147253 0.739479i
\(276\) 5.37893e9 0.926957
\(277\) 6.17521e9i 1.04890i 0.851442 + 0.524449i \(0.175728\pi\)
−0.851442 + 0.524449i \(0.824272\pi\)
\(278\) 3.64624e8 0.0610473
\(279\) −6.05347e9 −0.999051
\(280\) −5.64252e8 −0.0917997
\(281\) 8.95370e9i 1.43607i 0.696005 + 0.718037i \(0.254959\pi\)
−0.696005 + 0.718037i \(0.745041\pi\)
\(282\) 6.45106e9i 1.02008i
\(283\) 2.92082e9i 0.455364i −0.973736 0.227682i \(-0.926885\pi\)
0.973736 0.227682i \(-0.0731146\pi\)
\(284\) −8.20283e8 −0.126093
\(285\) 8.73232e9i 1.32358i
\(286\) −1.24830e9 6.26876e9i −0.186575 0.936952i
\(287\) −4.60577e9 −0.678852
\(288\) 2.58817e9i 0.376203i
\(289\) 5.95620e9 0.853843
\(290\) −1.29253e9 −0.182746
\(291\) 2.04136e10 2.84673
\(292\) 1.52121e9i 0.209246i
\(293\) 1.20314e10i 1.63248i 0.577714 + 0.816239i \(0.303945\pi\)
−0.577714 + 0.816239i \(0.696055\pi\)
\(294\) 6.78300e9i 0.907888i
\(295\) −2.36018e8 −0.0311643
\(296\) 4.23151e9i 0.551225i
\(297\) −3.03193e9 1.52259e10i −0.389666 1.95684i
\(298\) 8.59644e9 1.09007
\(299\) 1.13190e10i 1.41620i
\(300\) −5.40092e9 −0.666780
\(301\) 6.79987e9 0.828389
\(302\) −4.65498e9 −0.559616
\(303\) 7.32394e9i 0.868909i
\(304\) 3.22161e9i 0.377206i
\(305\) 5.12996e9i 0.592809i
\(306\) 5.04403e9 0.575296
\(307\) 3.80612e9i 0.428478i −0.976781 0.214239i \(-0.931273\pi\)
0.976781 0.214239i \(-0.0687272\pi\)
\(308\) −2.31018e9 + 4.60027e8i −0.256710 + 0.0511187i
\(309\) −2.32093e10 −2.54582
\(310\) 1.52052e9i 0.164643i
\(311\) −4.35112e9 −0.465114 −0.232557 0.972583i \(-0.574709\pi\)
−0.232557 + 0.972583i \(0.574709\pi\)
\(312\) −8.00557e9 −0.844839
\(313\) −7.40132e9 −0.771137 −0.385569 0.922679i \(-0.625995\pi\)
−0.385569 + 0.922679i \(0.625995\pi\)
\(314\) 5.28785e9i 0.543952i
\(315\) 5.44034e9i 0.552565i
\(316\) 6.84578e9i 0.686554i
\(317\) −1.24891e10 −1.23678 −0.618392 0.785870i \(-0.712215\pi\)
−0.618392 + 0.785870i \(0.712215\pi\)
\(318\) 7.86915e9i 0.769519i
\(319\) −5.29190e9 + 1.05378e9i −0.511033 + 0.101762i
\(320\) 6.50099e8 0.0619982
\(321\) 2.84783e10i 2.68221i
\(322\) −4.17131e9 −0.388016
\(323\) −6.27853e9 −0.576830
\(324\) −7.71836e9 −0.700398
\(325\) 1.13653e10i 1.01870i
\(326\) 2.84223e9i 0.251645i
\(327\) 2.14326e10i 1.87450i
\(328\) 5.30650e9 0.458472
\(329\) 5.00274e9i 0.426996i
\(330\) 7.21453e9 1.43663e9i 0.608348 0.121141i
\(331\) −2.09868e9 −0.174837 −0.0874187 0.996172i \(-0.527862\pi\)
−0.0874187 + 0.996172i \(0.527862\pi\)
\(332\) 2.06403e9i 0.169888i
\(333\) 4.07989e10 3.31796
\(334\) −1.55672e10 −1.25091
\(335\) 1.10370e10 0.876342
\(336\) 2.95023e9i 0.231472i
\(337\) 3.34750e9i 0.259538i 0.991544 + 0.129769i \(0.0414235\pi\)
−0.991544 + 0.129769i \(0.958576\pi\)
\(338\) 7.61738e9i 0.583631i
\(339\) −1.36524e10 −1.03374
\(340\) 1.26696e9i 0.0948088i
\(341\) −1.23965e9 6.22535e9i −0.0916818 0.460411i
\(342\) 3.10617e10 2.27050
\(343\) 1.25061e10i 0.903534i
\(344\) −7.83441e9 −0.559465
\(345\) 1.30267e10 0.919515
\(346\) −3.12778e9 −0.218239
\(347\) 9.26936e9i 0.639340i −0.947529 0.319670i \(-0.896428\pi\)
0.947529 0.319670i \(-0.103572\pi\)
\(348\) 6.75807e9i 0.460793i
\(349\) 4.31190e9i 0.290648i 0.989384 + 0.145324i \(0.0464224\pi\)
−0.989384 + 0.145324i \(0.953578\pi\)
\(350\) 4.18836e9 0.279108
\(351\) 4.09171e10i 2.69573i
\(352\) 2.66165e9 5.30016e8i 0.173373 0.0345238i
\(353\) 1.11945e10 0.720954 0.360477 0.932768i \(-0.382614\pi\)
0.360477 + 0.932768i \(0.382614\pi\)
\(354\) 1.23404e9i 0.0785806i
\(355\) −1.98657e9 −0.125081
\(356\) 1.98856e8 0.0123805
\(357\) −5.74965e9 −0.353972
\(358\) 4.61556e9i 0.280991i
\(359\) 1.51798e10i 0.913877i 0.889498 + 0.456939i \(0.151054\pi\)
−0.889498 + 0.456939i \(0.848946\pi\)
\(360\) 6.26804e9i 0.373183i
\(361\) −2.16804e10 −1.27655
\(362\) 3.84234e9i 0.223749i
\(363\) 2.83667e10 1.17638e10i 1.63374 0.677518i
\(364\) 6.20825e9 0.353642
\(365\) 3.68408e9i 0.207567i
\(366\) −2.68224e10 −1.49476
\(367\) −1.69081e9 −0.0932034 −0.0466017 0.998914i \(-0.514839\pi\)
−0.0466017 + 0.998914i \(0.514839\pi\)
\(368\) 4.80594e9 0.262052
\(369\) 5.11636e10i 2.75966i
\(370\) 1.02479e10i 0.546800i
\(371\) 6.10246e9i 0.322114i
\(372\) −7.95013e9 −0.415147
\(373\) 2.28601e10i 1.18098i −0.807044 0.590491i \(-0.798934\pi\)
0.807044 0.590491i \(-0.201066\pi\)
\(374\) 1.03294e9 + 5.18724e9i 0.0527943 + 0.265125i
\(375\) −3.04275e10 −1.53865
\(376\) 5.76386e9i 0.288378i
\(377\) 1.42212e10 0.703995
\(378\) 1.50789e10 0.738588
\(379\) 2.27992e9 0.110500 0.0552500 0.998473i \(-0.482404\pi\)
0.0552500 + 0.998473i \(0.482404\pi\)
\(380\) 7.80212e9i 0.374178i
\(381\) 1.16212e10i 0.551507i
\(382\) 8.16899e9i 0.383632i
\(383\) 3.47039e10 1.61281 0.806405 0.591364i \(-0.201410\pi\)
0.806405 + 0.591364i \(0.201410\pi\)
\(384\) 3.39909e9i 0.156328i
\(385\) −5.59481e9 + 1.11409e9i −0.254649 + 0.0507083i
\(386\) 1.33642e10 0.601998
\(387\) 7.55369e10i 3.36756i
\(388\) 1.82390e10 0.804776
\(389\) 2.33533e10 1.01988 0.509942 0.860209i \(-0.329667\pi\)
0.509942 + 0.860209i \(0.329667\pi\)
\(390\) −1.93879e10 −0.838056
\(391\) 9.36620e9i 0.400734i
\(392\) 6.06044e9i 0.256661i
\(393\) 3.88384e9i 0.162814i
\(394\) −9.60407e9 −0.398539
\(395\) 1.65792e10i 0.681042i
\(396\) −5.11024e9 2.56628e10i −0.207807 1.04357i
\(397\) −1.07914e10 −0.434427 −0.217213 0.976124i \(-0.569697\pi\)
−0.217213 + 0.976124i \(0.569697\pi\)
\(398\) 8.94181e8i 0.0356363i
\(399\) −3.54070e10 −1.39701
\(400\) −4.82559e9 −0.188500
\(401\) −5.21695e9 −0.201762 −0.100881 0.994898i \(-0.532166\pi\)
−0.100881 + 0.994898i \(0.532166\pi\)
\(402\) 5.77079e10i 2.20969i
\(403\) 1.67297e10i 0.634259i
\(404\) 6.54376e9i 0.245642i
\(405\) −1.86924e10 −0.694775
\(406\) 5.24082e9i 0.192884i
\(407\) 8.35496e9 + 4.19573e10i 0.304486 + 1.52908i
\(408\) 6.62441e9 0.239060
\(409\) 2.36701e10i 0.845877i 0.906158 + 0.422939i \(0.139001\pi\)
−0.906158 + 0.422939i \(0.860999\pi\)
\(410\) 1.28513e10 0.454791
\(411\) −9.87120e10 −3.45942
\(412\) −2.07370e10 −0.719708
\(413\) 9.56985e8i 0.0328931i
\(414\) 4.63373e10i 1.57736i
\(415\) 4.99867e9i 0.168524i
\(416\) −7.15278e9 −0.238837
\(417\) 4.61708e9i 0.152695i
\(418\) 6.36095e9 + 3.19437e10i 0.208361 + 1.04636i
\(419\) −1.41556e10 −0.459273 −0.229637 0.973276i \(-0.573754\pi\)
−0.229637 + 0.973276i \(0.573754\pi\)
\(420\) 7.14489e9i 0.229614i
\(421\) 1.60760e10 0.511742 0.255871 0.966711i \(-0.417638\pi\)
0.255871 + 0.966711i \(0.417638\pi\)
\(422\) 2.00812e10 0.633198
\(423\) 5.55733e10 1.73582
\(424\) 7.03089e9i 0.217544i
\(425\) 9.40449e9i 0.288257i
\(426\) 1.03869e10i 0.315390i
\(427\) 2.08005e10 0.625695
\(428\) 2.54447e10i 0.758266i
\(429\) −7.93787e10 + 1.58067e10i −2.34355 + 0.466672i
\(430\) −1.89734e10 −0.554973
\(431\) 5.69466e10i 1.65028i −0.564926 0.825142i \(-0.691095\pi\)
0.564926 0.825142i \(-0.308905\pi\)
\(432\) −1.73730e10 −0.498816
\(433\) 3.63016e9 0.103270 0.0516350 0.998666i \(-0.483557\pi\)
0.0516350 + 0.998666i \(0.483557\pi\)
\(434\) 6.16526e9 0.173777
\(435\) 1.63667e10i 0.457093i
\(436\) 1.91495e10i 0.529922i
\(437\) 5.76782e10i 1.58156i
\(438\) −1.92625e10 −0.523378
\(439\) 4.75630e10i 1.28059i −0.768128 0.640296i \(-0.778812\pi\)
0.768128 0.640296i \(-0.221188\pi\)
\(440\) 6.44601e9 1.28359e9i 0.171981 0.0342466i
\(441\) 5.84328e10 1.54491
\(442\) 1.39399e10i 0.365234i
\(443\) 6.68171e10 1.73489 0.867446 0.497531i \(-0.165760\pi\)
0.867446 + 0.497531i \(0.165760\pi\)
\(444\) 5.35819e10 1.37875
\(445\) 4.81590e8 0.0122811
\(446\) 2.76812e10i 0.699593i
\(447\) 1.08853e11i 2.72653i
\(448\) 2.63596e9i 0.0654375i
\(449\) 3.66527e10 0.901822 0.450911 0.892569i \(-0.351099\pi\)
0.450911 + 0.892569i \(0.351099\pi\)
\(450\) 4.65268e10i 1.13463i
\(451\) 5.26162e10 1.04775e10i 1.27179 0.253251i
\(452\) −1.21981e10 −0.292239
\(453\) 5.89441e10i 1.39974i
\(454\) −2.30825e10 −0.543324
\(455\) 1.50352e10 0.350803
\(456\) 4.07939e10 0.943487
\(457\) 8.74858e9i 0.200573i −0.994959 0.100287i \(-0.968024\pi\)
0.994959 0.100287i \(-0.0319759\pi\)
\(458\) 1.34607e10i 0.305919i
\(459\) 3.38579e10i 0.762798i
\(460\) 1.16391e10 0.259948
\(461\) 7.45105e9i 0.164973i 0.996592 + 0.0824867i \(0.0262862\pi\)
−0.996592 + 0.0824867i \(0.973714\pi\)
\(462\) 5.82512e9 + 2.92528e10i 0.127861 + 0.642096i
\(463\) −2.66604e10 −0.580153 −0.290077 0.957003i \(-0.593681\pi\)
−0.290077 + 0.957003i \(0.593681\pi\)
\(464\) 6.03817e9i 0.130267i
\(465\) −1.92537e10 −0.411815
\(466\) 2.81063e8 0.00596019
\(467\) −5.56014e10 −1.16901 −0.584504 0.811390i \(-0.698711\pi\)
−0.584504 + 0.811390i \(0.698711\pi\)
\(468\) 6.89648e10i 1.43762i
\(469\) 4.47520e10i 0.924956i
\(470\) 1.39590e10i 0.286063i
\(471\) 6.69579e10 1.36056
\(472\) 1.10258e9i 0.0222148i
\(473\) −7.76816e10 + 1.54687e10i −1.55193 + 0.309037i
\(474\) −8.66853e10 −1.71724
\(475\) 5.79140e10i 1.13765i
\(476\) −5.13717e9 −0.100068
\(477\) 6.77896e10 1.30945
\(478\) 2.58581e10 0.495319
\(479\) 3.43852e10i 0.653175i 0.945167 + 0.326588i \(0.105899\pi\)
−0.945167 + 0.326588i \(0.894101\pi\)
\(480\) 8.23192e9i 0.155073i
\(481\) 1.12754e11i 2.10645i
\(482\) 5.02773e9 0.0931503
\(483\) 5.28196e10i 0.970524i
\(484\) 2.53449e10 1.05107e10i 0.461860 0.191535i
\(485\) 4.41714e10 0.798315
\(486\) 1.90243e10i 0.341008i
\(487\) −9.31385e10 −1.65582 −0.827911 0.560860i \(-0.810471\pi\)
−0.827911 + 0.560860i \(0.810471\pi\)
\(488\) −2.39651e10 −0.422572
\(489\) −3.59899e10 −0.629428
\(490\) 1.46772e10i 0.254601i
\(491\) 7.76972e10i 1.33684i 0.743784 + 0.668420i \(0.233029\pi\)
−0.743784 + 0.668420i \(0.766971\pi\)
\(492\) 6.71940e10i 1.14675i
\(493\) −1.17677e10 −0.199206
\(494\) 8.58437e10i 1.44145i
\(495\) −1.23760e10 6.21503e10i −0.206139 1.03520i
\(496\) −7.10325e9 −0.117363
\(497\) 8.05495e9i 0.132019i
\(498\) −2.61359e10 −0.424933
\(499\) −5.94257e10 −0.958457 −0.479228 0.877690i \(-0.659083\pi\)
−0.479228 + 0.877690i \(0.659083\pi\)
\(500\) −2.71862e10 −0.434979
\(501\) 1.97121e11i 3.12884i
\(502\) 1.21170e10i 0.190801i
\(503\) 8.94434e10i 1.39726i −0.715485 0.698629i \(-0.753794\pi\)
0.715485 0.698629i \(-0.246206\pi\)
\(504\) 2.54151e10 0.393885
\(505\) 1.58477e10i 0.243670i
\(506\) 4.76530e10 9.48915e9i 0.726922 0.144752i
\(507\) 9.64557e10 1.45981
\(508\) 1.03833e10i 0.155912i
\(509\) −5.73817e10 −0.854875 −0.427437 0.904045i \(-0.640584\pi\)
−0.427437 + 0.904045i \(0.640584\pi\)
\(510\) 1.60430e10 0.237140
\(511\) 1.49379e10 0.219081
\(512\) 3.03700e9i 0.0441942i
\(513\) 2.08501e11i 3.01050i
\(514\) 1.87544e10i 0.268689i
\(515\) −5.02209e10 −0.713930
\(516\) 9.92038e10i 1.39936i
\(517\) 1.13805e10 + 5.71512e10i 0.159294 + 0.799950i
\(518\) −4.15523e10 −0.577133
\(519\) 3.96058e10i 0.545870i
\(520\) −1.73226e10 −0.236920
\(521\) 8.04784e10 1.09227 0.546133 0.837698i \(-0.316099\pi\)
0.546133 + 0.837698i \(0.316099\pi\)
\(522\) 5.82181e10 0.784108
\(523\) 7.86300e10i 1.05095i 0.850809 + 0.525475i \(0.176112\pi\)
−0.850809 + 0.525475i \(0.823888\pi\)
\(524\) 3.47011e9i 0.0460276i
\(525\) 5.30355e10i 0.698119i
\(526\) −2.85643e10 −0.373148
\(527\) 1.38434e10i 0.179473i
\(528\) −6.71136e9 3.37034e10i −0.0863525 0.433649i
\(529\) 7.73235e9 0.0987390
\(530\) 1.70275e10i 0.215797i
\(531\) 1.06307e10 0.133717
\(532\) −3.16353e10 −0.394935
\(533\) −1.41398e11 −1.75200
\(534\) 2.51803e9i 0.0309667i
\(535\) 6.16220e10i 0.752178i
\(536\) 5.15607e10i 0.624682i
\(537\) −5.84449e10 −0.702828
\(538\) 4.47100e10i 0.533673i
\(539\) 1.19661e10 + 6.00919e10i 0.141774 + 0.711969i
\(540\) −4.20741e10 −0.494811
\(541\) 1.17136e11i 1.36741i −0.729756 0.683707i \(-0.760367\pi\)
0.729756 0.683707i \(-0.239633\pi\)
\(542\) 9.94781e10 1.15274
\(543\) −4.86539e10 −0.559653
\(544\) 5.91875e9 0.0675825
\(545\) 4.63764e10i 0.525668i
\(546\) 7.86125e10i 0.884547i
\(547\) 4.84298e10i 0.540958i 0.962726 + 0.270479i \(0.0871821\pi\)
−0.962726 + 0.270479i \(0.912818\pi\)
\(548\) −8.81968e10 −0.977981
\(549\) 2.31064e11i 2.54357i
\(550\) −4.78478e10 + 9.52794e9i −0.522891 + 0.104123i
\(551\) −7.24667e10 −0.786198
\(552\) 6.08556e10i 0.655457i
\(553\) 6.72237e10 0.718823
\(554\) 6.98646e10 0.741682
\(555\) 1.29765e11 1.36768
\(556\) 4.12525e9i 0.0431669i
\(557\) 6.78924e10i 0.705343i 0.935747 + 0.352671i \(0.114727\pi\)
−0.935747 + 0.352671i \(0.885273\pi\)
\(558\) 6.84872e10i 0.706436i
\(559\) 2.08757e11 2.13793
\(560\) 6.38379e9i 0.0649122i
\(561\) 6.56839e10 1.30796e10i 0.663143 0.132052i
\(562\) 1.01300e11 1.01546
\(563\) 4.05432e10i 0.403538i 0.979433 + 0.201769i \(0.0646691\pi\)
−0.979433 + 0.201769i \(0.935331\pi\)
\(564\) 7.29854e10 0.721306
\(565\) −2.95414e10 −0.289892
\(566\) −3.30453e10 −0.321991
\(567\) 7.57922e10i 0.733318i
\(568\) 9.28044e9i 0.0891611i
\(569\) 8.62637e10i 0.822961i 0.911419 + 0.411480i \(0.134988\pi\)
−0.911419 + 0.411480i \(0.865012\pi\)
\(570\) 9.87949e10 0.935913
\(571\) 4.01160e10i 0.377375i −0.982037 0.188688i \(-0.939577\pi\)
0.982037 0.188688i \(-0.0604234\pi\)
\(572\) −7.09229e10 + 1.41229e10i −0.662525 + 0.131929i
\(573\) 1.03441e11 0.959560
\(574\) 5.21084e10i 0.480021i
\(575\) −8.63951e10 −0.790346
\(576\) −2.92818e10 −0.266016
\(577\) 5.13949e10 0.463679 0.231839 0.972754i \(-0.425526\pi\)
0.231839 + 0.972754i \(0.425526\pi\)
\(578\) 6.73868e10i 0.603758i
\(579\) 1.69226e11i 1.50575i
\(580\) 1.46233e10i 0.129221i
\(581\) 2.02682e10 0.177873
\(582\) 2.30953e11i 2.01295i
\(583\) 1.38822e10 + 6.97143e10i 0.120167 + 0.603459i
\(584\) −1.72105e10 −0.147960
\(585\) 1.67019e11i 1.42608i
\(586\) 1.36120e11 1.15434
\(587\) −4.03753e10 −0.340066 −0.170033 0.985438i \(-0.554387\pi\)
−0.170033 + 0.985438i \(0.554387\pi\)
\(588\) 7.67408e10 0.641974
\(589\) 8.52492e10i 0.708319i
\(590\) 2.67024e9i 0.0220365i
\(591\) 1.21612e11i 0.996845i
\(592\) 4.78741e10 0.389775
\(593\) 1.97480e11i 1.59700i −0.601996 0.798499i \(-0.705628\pi\)
0.601996 0.798499i \(-0.294372\pi\)
\(594\) −1.72261e11 + 3.43023e10i −1.38370 + 0.275536i
\(595\) −1.24412e10 −0.0992648
\(596\) 9.72576e10i 0.770794i
\(597\) 1.13226e10 0.0891354
\(598\) −1.28060e11 −1.00140
\(599\) 9.12212e10 0.708580 0.354290 0.935136i \(-0.384723\pi\)
0.354290 + 0.935136i \(0.384723\pi\)
\(600\) 6.11044e10i 0.471484i
\(601\) 1.40799e11i 1.07920i 0.841922 + 0.539599i \(0.181424\pi\)
−0.841922 + 0.539599i \(0.818576\pi\)
\(602\) 7.69317e10i 0.585760i
\(603\) −4.97131e11 −3.76012
\(604\) 5.26651e10i 0.395708i
\(605\) 6.13805e10 2.54548e10i 0.458152 0.189998i
\(606\) −8.28609e10 −0.614411
\(607\) 1.46613e11i 1.07999i 0.841669 + 0.539994i \(0.181573\pi\)
−0.841669 + 0.539994i \(0.818427\pi\)
\(608\) 3.64484e10 0.266725
\(609\) −6.63623e10 −0.482450
\(610\) −5.80389e10 −0.419179
\(611\) 1.53585e11i 1.10201i
\(612\) 5.70667e10i 0.406796i
\(613\) 1.42880e11i 1.01188i −0.862569 0.505939i \(-0.831146\pi\)
0.862569 0.505939i \(-0.168854\pi\)
\(614\) −4.30613e10 −0.302980
\(615\) 1.62731e11i 1.13755i
\(616\) 5.20461e9 + 2.61367e10i 0.0361464 + 0.181521i
\(617\) −1.69764e11 −1.17140 −0.585700 0.810528i \(-0.699180\pi\)
−0.585700 + 0.810528i \(0.699180\pi\)
\(618\) 2.62583e11i 1.80017i
\(619\) −7.20916e10 −0.491046 −0.245523 0.969391i \(-0.578960\pi\)
−0.245523 + 0.969391i \(0.578960\pi\)
\(620\) −1.72027e10 −0.116421
\(621\) −3.11038e11 −2.09145
\(622\) 4.92273e10i 0.328885i
\(623\) 1.95271e9i 0.0129624i
\(624\) 9.05727e10i 0.597391i
\(625\) 4.92113e10 0.322511
\(626\) 8.37364e10i 0.545277i
\(627\) 4.04489e11 8.05460e10i 2.61720 0.521163i
\(628\) 5.98252e10 0.384632
\(629\) 9.33009e10i 0.596051i
\(630\) 6.15504e10 0.390723
\(631\) 2.64546e11 1.66872 0.834362 0.551218i \(-0.185837\pi\)
0.834362 + 0.551218i \(0.185837\pi\)
\(632\) −7.74512e10 −0.485467
\(633\) 2.54279e11i 1.58379i
\(634\) 1.41298e11i 0.874538i
\(635\) 2.51463e10i 0.154660i
\(636\) 8.90292e10 0.544132
\(637\) 1.61488e11i 0.980803i
\(638\) 1.19221e10 + 5.98710e10i 0.0719567 + 0.361355i
\(639\) 8.94790e10 0.536683
\(640\) 7.35503e9i 0.0438394i
\(641\) 7.40418e10 0.438576 0.219288 0.975660i \(-0.429627\pi\)
0.219288 + 0.975660i \(0.429627\pi\)
\(642\) −3.22195e11 −1.89661
\(643\) −7.98961e9 −0.0467393 −0.0233696 0.999727i \(-0.507439\pi\)
−0.0233696 + 0.999727i \(0.507439\pi\)
\(644\) 4.71930e10i 0.274369i
\(645\) 2.40252e11i 1.38813i
\(646\) 7.10335e10i 0.407881i
\(647\) −1.94844e11 −1.11191 −0.555957 0.831211i \(-0.687648\pi\)
−0.555957 + 0.831211i \(0.687648\pi\)
\(648\) 8.73233e10i 0.495256i
\(649\) 2.17701e9 + 1.09326e10i 0.0122710 + 0.0616232i
\(650\) 1.28584e11 0.720331
\(651\) 7.80681e10i 0.434660i
\(652\) −3.21561e10 −0.177940
\(653\) 1.05032e11 0.577657 0.288828 0.957381i \(-0.406734\pi\)
0.288828 + 0.957381i \(0.406734\pi\)
\(654\) 2.42482e11 1.32547
\(655\) 8.40394e9i 0.0456581i
\(656\) 6.00362e10i 0.324189i
\(657\) 1.65938e11i 0.890606i
\(658\) −5.65995e10 −0.301932
\(659\) 1.21988e11i 0.646810i −0.946261 0.323405i \(-0.895172\pi\)
0.946261 0.323405i \(-0.104828\pi\)
\(660\) −1.62536e10 8.16231e10i −0.0856593 0.430167i
\(661\) −4.46559e10 −0.233923 −0.116962 0.993136i \(-0.537315\pi\)
−0.116962 + 0.993136i \(0.537315\pi\)
\(662\) 2.37439e10i 0.123629i
\(663\) −1.76515e11 −0.913541
\(664\) −2.33518e10 −0.120129
\(665\) −7.66146e10 −0.391765
\(666\) 4.61587e11i 2.34615i
\(667\) 1.08105e11i 0.546186i
\(668\) 1.76123e11i 0.884526i
\(669\) 3.50515e11 1.74986
\(670\) 1.24870e11i 0.619667i
\(671\) −2.37625e11 + 4.73182e10i −1.17220 + 0.233420i
\(672\) 3.33781e10 0.163676
\(673\) 3.68652e11i 1.79703i −0.438941 0.898516i \(-0.644646\pi\)
0.438941 0.898516i \(-0.355354\pi\)
\(674\) 3.78726e10 0.183521
\(675\) 3.12310e11 1.50442
\(676\) 8.61808e10 0.412690
\(677\) 1.82453e10i 0.0868554i −0.999057 0.0434277i \(-0.986172\pi\)
0.999057 0.0434277i \(-0.0138278\pi\)
\(678\) 1.54459e11i 0.730962i
\(679\) 1.79102e11i 0.842601i
\(680\) 1.43341e10 0.0670399
\(681\) 2.92284e11i 1.35899i
\(682\) −7.04318e10 + 1.40251e10i −0.325560 + 0.0648288i
\(683\) 3.48602e11 1.60194 0.800972 0.598702i \(-0.204317\pi\)
0.800972 + 0.598702i \(0.204317\pi\)
\(684\) 3.51423e11i 1.60549i
\(685\) −2.13595e11 −0.970130
\(686\) −1.41490e11 −0.638895
\(687\) −1.70447e11 −0.765180
\(688\) 8.86362e10i 0.395601i
\(689\) 1.87346e11i 0.831321i
\(690\) 1.47381e11i 0.650195i
\(691\) −2.99034e11 −1.31162 −0.655811 0.754925i \(-0.727673\pi\)
−0.655811 + 0.754925i \(0.727673\pi\)
\(692\) 3.53868e10i 0.154318i
\(693\) 2.52002e11 5.01811e10i 1.09262 0.217574i
\(694\) −1.04871e11 −0.452082
\(695\) 9.99056e9i 0.0428204i
\(696\) 7.64588e10 0.325830
\(697\) 1.17003e11 0.495755
\(698\) 4.87836e10 0.205519
\(699\) 3.55898e9i 0.0149079i
\(700\) 4.73859e10i 0.197359i
\(701\) 1.73386e11i 0.718030i 0.933332 + 0.359015i \(0.116887\pi\)
−0.933332 + 0.359015i \(0.883113\pi\)
\(702\) 4.62924e11 1.90617
\(703\) 5.74558e11i 2.35241i
\(704\) −5.99644e9 3.01132e10i −0.0244120 0.122593i
\(705\) 1.76756e11 0.715515
\(706\) 1.26652e11i 0.509791i
\(707\) 6.42579e10 0.257187
\(708\) 1.39615e10 0.0555649
\(709\) 2.62470e11 1.03871 0.519356 0.854558i \(-0.326172\pi\)
0.519356 + 0.854558i \(0.326172\pi\)
\(710\) 2.24754e10i 0.0884453i
\(711\) 7.46759e11i 2.92215i
\(712\) 2.24979e9i 0.00875433i
\(713\) −1.27173e11 −0.492082
\(714\) 6.50498e10i 0.250296i
\(715\) −1.71762e11 + 3.42029e10i −0.657206 + 0.130870i
\(716\) −5.22191e10 −0.198690
\(717\) 3.27430e11i 1.23892i
\(718\) 1.71740e11 0.646209
\(719\) 3.75789e11 1.40614 0.703069 0.711121i \(-0.251812\pi\)
0.703069 + 0.711121i \(0.251812\pi\)
\(720\) −7.09148e10 −0.263880
\(721\) 2.03631e11i 0.753535i
\(722\) 2.45286e11i 0.902659i
\(723\) 6.36641e10i 0.232992i
\(724\) −4.34711e10 −0.158215
\(725\) 1.08546e11i 0.392883i
\(726\) −1.33092e11 3.20932e11i −0.479078 1.15523i
\(727\) −5.04234e11 −1.80507 −0.902536 0.430613i \(-0.858297\pi\)
−0.902536 + 0.430613i \(0.858297\pi\)
\(728\) 7.02383e10i 0.250063i
\(729\) −1.54729e11 −0.547851
\(730\) −4.16806e10 −0.146772
\(731\) −1.72741e11 −0.604960
\(732\) 3.03460e11i 1.05696i
\(733\) 2.95479e11i 1.02355i −0.859119 0.511776i \(-0.828988\pi\)
0.859119 0.511776i \(-0.171012\pi\)
\(734\) 1.91294e10i 0.0659047i
\(735\) 1.85851e11 0.636820
\(736\) 5.43730e10i 0.185299i
\(737\) −1.01805e11 5.11246e11i −0.345062 1.73285i
\(738\) −5.78850e11 −1.95137
\(739\) 1.70289e11i 0.570964i −0.958384 0.285482i \(-0.907846\pi\)
0.958384 0.285482i \(-0.0921536\pi\)
\(740\) 1.15942e11 0.386646
\(741\) −1.08700e12 −3.60543
\(742\) −6.90414e10 −0.227769
\(743\) 5.05484e11i 1.65864i 0.558774 + 0.829320i \(0.311272\pi\)
−0.558774 + 0.829320i \(0.688728\pi\)
\(744\) 8.99454e10i 0.293554i
\(745\) 2.35539e11i 0.764606i
\(746\) −2.58633e11 −0.835080
\(747\) 2.25150e11i 0.723087i
\(748\) 5.86869e10 1.16863e10i 0.187471 0.0373312i
\(749\) 2.49859e11 0.793905
\(750\) 3.44247e11i 1.08799i
\(751\) −1.53665e11 −0.483077 −0.241538 0.970391i \(-0.577652\pi\)
−0.241538 + 0.970391i \(0.577652\pi\)
\(752\) 6.52107e10 0.203914
\(753\) 1.53433e11 0.477242
\(754\) 1.60894e11i 0.497800i
\(755\) 1.27545e11i 0.392531i
\(756\) 1.70598e11i 0.522260i
\(757\) 1.98576e11 0.604703 0.302352 0.953196i \(-0.402228\pi\)
0.302352 + 0.953196i \(0.402228\pi\)
\(758\) 2.57943e10i 0.0781353i
\(759\) −1.20157e11 6.03410e11i −0.362062 1.81822i
\(760\) 8.82709e10 0.264584
\(761\) 2.65735e11i 0.792338i 0.918178 + 0.396169i \(0.129661\pi\)
−0.918178 + 0.396169i \(0.870339\pi\)
\(762\) −1.31479e11 −0.389975
\(763\) −1.88043e11 −0.554829
\(764\) 9.24216e10 0.271269
\(765\) 1.38204e11i 0.403530i
\(766\) 3.92630e11i 1.14043i
\(767\) 2.93796e10i 0.0848916i
\(768\) −3.84563e10 −0.110541
\(769\) 3.30229e11i 0.944299i 0.881518 + 0.472150i \(0.156522\pi\)
−0.881518 + 0.472150i \(0.843478\pi\)
\(770\) 1.26045e10 + 6.32980e10i 0.0358562 + 0.180064i
\(771\) −2.37478e11 −0.672058
\(772\) 1.51199e11i 0.425677i
\(773\) −8.90645e9 −0.0249452 −0.0124726 0.999922i \(-0.503970\pi\)
−0.0124726 + 0.999922i \(0.503970\pi\)
\(774\) 8.54602e11 2.38122
\(775\) 1.27693e11 0.353965
\(776\) 2.06351e11i 0.569062i
\(777\) 5.26159e11i 1.44355i
\(778\) 2.64213e11i 0.721166i
\(779\) 7.20521e11 1.95658
\(780\) 2.19349e11i 0.592595i
\(781\) 1.83239e10 + 9.20196e10i 0.0492508 + 0.247330i
\(782\) 1.05966e11 0.283362
\(783\) 3.90787e11i 1.03966i
\(784\) 6.85661e10 0.181487
\(785\) 1.44885e11 0.381544
\(786\) 4.39406e10 0.115127
\(787\) 2.31980e11i 0.604717i −0.953194 0.302358i \(-0.902226\pi\)
0.953194 0.302358i \(-0.0977740\pi\)
\(788\) 1.08658e11i 0.281809i
\(789\) 3.61698e11i 0.933336i
\(790\) −1.87572e11 −0.481570
\(791\) 1.19782e11i 0.305974i
\(792\) −2.90341e11 + 5.78158e10i −0.737918 + 0.146942i
\(793\) 6.38579e11 1.61481
\(794\) 1.22091e11i 0.307186i
\(795\) 2.15611e11 0.539763
\(796\) 1.01165e10 0.0251987
\(797\) 2.60242e11 0.644976 0.322488 0.946574i \(-0.395481\pi\)
0.322488 + 0.946574i \(0.395481\pi\)
\(798\) 4.00585e11i 0.987832i
\(799\) 1.27088e11i 0.311829i
\(800\) 5.45953e10i 0.133289i
\(801\) −2.16918e10 −0.0526945
\(802\) 5.90231e10i 0.142667i
\(803\) −1.70650e11 + 3.39816e10i −0.410435 + 0.0817299i
\(804\) −6.52891e11 −1.56249
\(805\) 1.14292e11i 0.272166i
\(806\) 1.89274e11 0.448489
\(807\) 5.66144e11 1.33485
\(808\) −7.40342e10 −0.173695
\(809\) 2.68336e11i 0.626448i 0.949679 + 0.313224i \(0.101409\pi\)
−0.949679 + 0.313224i \(0.898591\pi\)
\(810\) 2.11480e11i 0.491280i
\(811\) 5.22878e11i 1.20870i 0.796721 + 0.604348i \(0.206566\pi\)
−0.796721 + 0.604348i \(0.793434\pi\)
\(812\) −5.92931e10 −0.136389
\(813\) 1.25965e12i 2.88329i
\(814\) 4.74693e11 9.45256e10i 1.08122 0.215304i
\(815\) −7.78759e10 −0.176511
\(816\) 7.49466e10i 0.169041i
\(817\) −1.06376e12 −2.38757
\(818\) 2.67797e11 0.598125
\(819\) −6.77215e11 −1.50519
\(820\) 1.45396e11i 0.321586i
\(821\) 2.21311e11i 0.487115i −0.969887 0.243557i \(-0.921686\pi\)
0.969887 0.243557i \(-0.0783144\pi\)
\(822\) 1.11680e12i 2.44618i
\(823\) 2.08544e11 0.454568 0.227284 0.973829i \(-0.427015\pi\)
0.227284 + 0.973829i \(0.427015\pi\)
\(824\) 2.34612e11i 0.508910i
\(825\) 1.20648e11 + 6.05876e11i 0.260439 + 1.30788i
\(826\) −1.08271e10 −0.0232590
\(827\) 5.24626e11i 1.12157i −0.827960 0.560786i \(-0.810499\pi\)
0.827960 0.560786i \(-0.189501\pi\)
\(828\) −5.24247e11 −1.11536
\(829\) −3.55424e11 −0.752538 −0.376269 0.926511i \(-0.622793\pi\)
−0.376269 + 0.926511i \(0.622793\pi\)
\(830\) −5.65535e10 −0.119165
\(831\) 8.84666e11i 1.85513i
\(832\) 8.09245e10i 0.168883i
\(833\) 1.33627e11i 0.277533i
\(834\) −5.22363e10 −0.107971
\(835\) 4.26536e11i 0.877425i
\(836\) 3.61401e11 7.19659e10i 0.739886 0.147334i
\(837\) 4.59719e11 0.936678
\(838\) 1.60152e11i 0.324755i
\(839\) 3.96702e11 0.800603 0.400301 0.916384i \(-0.368905\pi\)
0.400301 + 0.916384i \(0.368905\pi\)
\(840\) 8.08352e10 0.162362
\(841\) 3.64424e11 0.728490
\(842\) 1.81880e11i 0.361856i
\(843\) 1.28271e12i 2.53992i
\(844\) 2.27193e11i 0.447738i
\(845\) 2.08713e11 0.409377
\(846\) 6.28740e11i 1.22741i
\(847\) 1.03212e11 + 2.48880e11i 0.200538 + 0.483567i
\(848\) 7.95455e10 0.153827
\(849\) 4.18438e11i 0.805380i
\(850\) −1.06400e11 −0.203828
\(851\) 8.57116e11 1.63426
\(852\) 1.17514e11 0.223014
\(853\) 1.59147e11i 0.300609i −0.988640 0.150304i \(-0.951975\pi\)
0.988640 0.150304i \(-0.0480254\pi\)
\(854\) 2.35331e11i 0.442433i
\(855\) 8.51079e11i 1.59260i
\(856\) −2.87873e11 −0.536175
\(857\) 7.79199e11i 1.44453i 0.691619 + 0.722263i \(0.256898\pi\)
−0.691619 + 0.722263i \(0.743102\pi\)
\(858\) 1.78832e11 + 8.98067e11i 0.329987 + 1.65714i
\(859\) 1.95693e11 0.359420 0.179710 0.983720i \(-0.442484\pi\)
0.179710 + 0.983720i \(0.442484\pi\)
\(860\) 2.14660e11i 0.392425i
\(861\) 6.59826e11 1.20065
\(862\) −6.44277e11 −1.16693
\(863\) −9.26945e11 −1.67113 −0.835566 0.549390i \(-0.814860\pi\)
−0.835566 + 0.549390i \(0.814860\pi\)
\(864\) 1.96553e11i 0.352716i
\(865\) 8.56999e10i 0.153079i
\(866\) 4.10706e10i 0.0730229i
\(867\) −8.53290e11 −1.51015
\(868\) 6.97519e10i 0.122879i
\(869\) −7.67962e11 + 1.52924e11i −1.34667 + 0.268162i
\(870\) 1.85168e11 0.323214
\(871\) 1.37389e12i 2.38716i
\(872\) 2.16652e11 0.374712
\(873\) −1.98957e12 −3.42533
\(874\) 6.52555e11 1.11833
\(875\) 2.66961e11i 0.455423i
\(876\) 2.17930e11i 0.370084i
\(877\) 3.79925e11i 0.642244i −0.947038 0.321122i \(-0.895940\pi\)
0.947038 0.321122i \(-0.104060\pi\)
\(878\) −5.38114e11 −0.905516
\(879\) 1.72363e12i 2.88728i
\(880\) −1.45222e10 7.29282e10i −0.0242160 0.121609i
\(881\) 5.59727e11 0.929122 0.464561 0.885541i \(-0.346212\pi\)
0.464561 + 0.885541i \(0.346212\pi\)
\(882\) 6.61092e11i 1.09241i
\(883\) 6.16215e11 1.01365 0.506827 0.862048i \(-0.330818\pi\)
0.506827 + 0.862048i \(0.330818\pi\)
\(884\) −1.57712e11 −0.258259
\(885\) 3.38121e10 0.0551188
\(886\) 7.55949e11i 1.22675i
\(887\) 2.94445e11i 0.475675i −0.971305 0.237838i \(-0.923561\pi\)
0.971305 0.237838i \(-0.0764386\pi\)
\(888\) 6.06210e11i 0.974925i
\(889\) 1.01961e11 0.163240
\(890\) 5.44857e9i 0.00868405i
\(891\) 1.72417e11 + 8.65848e11i 0.273570 + 1.37382i
\(892\) 3.13177e11 0.494687
\(893\) 7.82622e11i 1.23068i
\(894\) −1.23153e12 −1.92795
\(895\) −1.26464e11 −0.197095
\(896\) 2.98225e10 0.0462713
\(897\) 1.62157e12i 2.50476i
\(898\) 4.14678e11i 0.637685i
\(899\) 1.59780e11i 0.244615i
\(900\) 5.26390e11 0.802302
\(901\) 1.55024e11i 0.235235i
\(902\) −1.18539e11 5.95285e11i −0.179075 0.899288i
\(903\) −9.74154e11 −1.46513
\(904\) 1.38005e11i 0.206644i
\(905\) −1.05279e11 −0.156944
\(906\) 6.66876e11 0.989765
\(907\) −6.09734e11 −0.900972 −0.450486 0.892784i \(-0.648749\pi\)
−0.450486 + 0.892784i \(0.648749\pi\)
\(908\) 2.61149e11i 0.384188i
\(909\) 7.13814e11i 1.04551i
\(910\) 1.70104e11i 0.248055i
\(911\) −5.64111e11 −0.819013 −0.409507 0.912307i \(-0.634299\pi\)
−0.409507 + 0.912307i \(0.634299\pi\)
\(912\) 4.61530e11i 0.667146i
\(913\) −2.31543e11 + 4.61072e10i −0.333233 + 0.0663568i
\(914\) −9.89788e10 −0.141827
\(915\) 7.34922e11i 1.04847i
\(916\) −1.52291e11 −0.216317
\(917\) −3.40756e10 −0.0481910
\(918\) −3.83058e11 −0.539379
\(919\) 4.06554e11i 0.569975i −0.958531 0.284988i \(-0.908011\pi\)
0.958531 0.284988i \(-0.0919895\pi\)
\(920\) 1.31681e11i 0.183811i
\(921\) 5.45267e11i 0.757829i
\(922\) 8.42990e10 0.116654
\(923\) 2.47288e11i 0.340719i
\(924\) 3.30958e11 6.59037e10i 0.454030 0.0904112i
\(925\) −8.60619e11 −1.17556
\(926\) 3.01628e11i 0.410230i
\(927\) 2.26205e12 3.06326
\(928\) 6.83141e10 0.0921124
\(929\) 9.63039e11 1.29295 0.646474 0.762936i \(-0.276243\pi\)
0.646474 + 0.762936i \(0.276243\pi\)
\(930\) 2.17830e11i 0.291197i
\(931\) 8.22892e11i 1.09533i
\(932\) 3.17987e9i 0.00421449i
\(933\) 6.23345e11 0.822624
\(934\) 6.29058e11i 0.826614i
\(935\) 1.42128e11 2.83021e10i 0.185966 0.0370315i
\(936\) 7.80248e11 1.01655
\(937\) 2.62286e11i 0.340264i −0.985421 0.170132i \(-0.945581\pi\)
0.985421 0.170132i \(-0.0544194\pi\)
\(938\) 5.06311e11 0.654043
\(939\) 1.06032e12 1.36387
\(940\) 1.57928e11 0.202277
\(941\) 9.14087e11i 1.16581i −0.812539 0.582907i \(-0.801915\pi\)
0.812539 0.582907i \(-0.198085\pi\)
\(942\) 7.57542e11i 0.962062i
\(943\) 1.07486e12i 1.35927i
\(944\) 1.24743e10 0.0157083
\(945\) 4.13156e11i 0.518067i
\(946\) 1.75009e11 + 8.78867e11i 0.218522 + 1.09738i
\(947\) −1.46362e12 −1.81983 −0.909913 0.414800i \(-0.863852\pi\)
−0.909913 + 0.414800i \(0.863852\pi\)
\(948\) 9.80732e11i 1.21427i
\(949\) 4.58595e11 0.565412
\(950\) −6.55222e11 −0.804441
\(951\) 1.78920e12 2.18744
\(952\) 5.81205e10i 0.0707589i
\(953\) 1.45117e12i 1.75933i −0.475593 0.879665i \(-0.657767\pi\)
0.475593 0.879665i \(-0.342233\pi\)
\(954\) 7.66952e11i 0.925922i
\(955\) 2.23827e11 0.269091
\(956\) 2.92551e11i 0.350244i
\(957\) 7.58122e11 1.50965e11i 0.903839 0.179982i
\(958\) 3.89024e11 0.461865
\(959\) 8.66068e11i 1.02395i
\(960\) −9.31336e10 −0.109653
\(961\) −6.64927e11 −0.779616
\(962\) −1.27566e12 −1.48948
\(963\) 2.77558e12i 3.22737i
\(964\) 5.68823e10i 0.0658672i
\(965\) 3.66175e11i 0.422260i
\(966\) 5.97585e11 0.686264
\(967\) 1.58102e12i 1.80814i 0.427386 + 0.904069i \(0.359434\pi\)
−0.427386 + 0.904069i \(0.640566\pi\)
\(968\) −1.18915e11 2.86745e11i −0.135436 0.326584i
\(969\) 8.99467e11 1.02021
\(970\) 4.99742e11i 0.564494i
\(971\) −1.32322e12 −1.48852 −0.744258 0.667892i \(-0.767197\pi\)
−0.744258 + 0.667892i \(0.767197\pi\)
\(972\) 2.15236e11 0.241129
\(973\) 4.05088e10 0.0451958
\(974\) 1.05374e12i 1.17084i
\(975\) 1.62820e12i 1.80173i
\(976\) 2.71134e11i 0.298803i
\(977\) −4.93380e11 −0.541506 −0.270753 0.962649i \(-0.587273\pi\)
−0.270753 + 0.962649i \(0.587273\pi\)
\(978\) 4.07180e11i 0.445072i
\(979\) −4.44213e9 2.23077e10i −0.00483572 0.0242842i
\(980\) 1.66054e11 0.180030
\(981\) 2.08889e12i 2.25548i
\(982\) 8.79044e11 0.945289
\(983\) 3.86926e11 0.414394 0.207197 0.978299i \(-0.433566\pi\)
0.207197 + 0.978299i \(0.433566\pi\)
\(984\) −7.60213e11 −0.810877
\(985\) 2.63148e11i 0.279547i
\(986\) 1.33136e11i 0.140860i
\(987\) 7.16696e11i 0.755208i
\(988\) −9.71210e11 −1.01926
\(989\) 1.58690e12i 1.65869i
\(990\) −7.03151e11 + 1.40019e11i −0.731994 + 0.145762i
\(991\) −5.12465e10 −0.0531337 −0.0265668 0.999647i \(-0.508457\pi\)
−0.0265668 + 0.999647i \(0.508457\pi\)
\(992\) 8.03641e10i 0.0829880i
\(993\) 3.00659e11 0.309226
\(994\) −9.11314e10 −0.0933517
\(995\) 2.45002e10 0.0249964
\(996\) 2.95694e11i 0.300473i
\(997\) 1.50058e12i 1.51872i −0.650670 0.759361i \(-0.725512\pi\)
0.650670 0.759361i \(-0.274488\pi\)
\(998\) 6.72326e11i 0.677731i
\(999\) −3.09839e12 −3.11081
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 22.9.b.a.21.1 8
3.2 odd 2 198.9.d.a.109.7 8
4.3 odd 2 176.9.h.e.65.8 8
11.10 odd 2 inner 22.9.b.a.21.5 yes 8
33.32 even 2 198.9.d.a.109.3 8
44.43 even 2 176.9.h.e.65.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.9.b.a.21.1 8 1.1 even 1 trivial
22.9.b.a.21.5 yes 8 11.10 odd 2 inner
176.9.h.e.65.7 8 44.43 even 2
176.9.h.e.65.8 8 4.3 odd 2
198.9.d.a.109.3 8 33.32 even 2
198.9.d.a.109.7 8 3.2 odd 2