Properties

Label 7.9.b.b.6.2
Level $7$
Weight $9$
Character 7.6
Analytic conductor $2.852$
Analytic rank $0$
Dimension $4$
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] = [7,9,Mod(6,7)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7, 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("7.6");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 7.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: \(2.85165027043\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1016x^{2} + 51570 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4}\cdot 3\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 6.2
Root \(31.0228i\) of defining polynomial
Character \(\chi\) \(=\) 7.6
Dual form 7.9.b.b.6.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.56466 q^{2} +53.0420i q^{3} -225.035 q^{4} +1090.79i q^{5} -295.161i q^{6} +(-1257.19 - 2045.55i) q^{7} +2676.79 q^{8} +3747.55 q^{9} +O(q^{10})\) \(q-5.56466 q^{2} +53.0420i q^{3} -225.035 q^{4} +1090.79i q^{5} -295.161i q^{6} +(-1257.19 - 2045.55i) q^{7} +2676.79 q^{8} +3747.55 q^{9} -6069.88i q^{10} -4619.60 q^{11} -11936.3i q^{12} +34774.3i q^{13} +(6995.86 + 11382.8i) q^{14} -57857.7 q^{15} +42713.4 q^{16} +11872.7i q^{17} -20853.8 q^{18} +70683.5i q^{19} -245466. i q^{20} +(108500. - 66684.1i) q^{21} +25706.5 q^{22} +308189. q^{23} +141983. i q^{24} -799200. q^{25} -193507. i q^{26} +546786. i q^{27} +(282912. + 460319. i) q^{28} -51871.9 q^{29} +321959. q^{30} -492602. i q^{31} -922945. q^{32} -245033. i q^{33} -66067.6i q^{34} +(2.23126e6 - 1.37134e6i) q^{35} -843327. q^{36} +1.27573e6 q^{37} -393330. i q^{38} -1.84450e6 q^{39} +2.91982e6i q^{40} -1.22535e6i q^{41} +(-603765. + 371074. i) q^{42} -918567. q^{43} +1.03957e6 q^{44} +4.08779e6i q^{45} -1.71497e6 q^{46} -5.57969e6i q^{47} +2.26560e6i q^{48} +(-2.60372e6 + 5.14330e6i) q^{49} +4.44728e6 q^{50} -629753. q^{51} -7.82542e6i q^{52} +6.83969e6 q^{53} -3.04268e6i q^{54} -5.03902e6i q^{55} +(-3.36525e6 - 5.47551e6i) q^{56} -3.74920e6 q^{57} +288649. q^{58} +8.16175e6i q^{59} +1.30200e7 q^{60} +1.94292e7i q^{61} +2.74116e6i q^{62} +(-4.71139e6 - 7.66578e6i) q^{63} -5.79876e6 q^{64} -3.79315e7 q^{65} +1.36353e6i q^{66} +2.53838e7 q^{67} -2.67177e6i q^{68} +1.63470e7i q^{69} +(-1.24162e7 + 7.63102e6i) q^{70} +2.99440e7 q^{71} +1.00314e7 q^{72} -3.30065e7i q^{73} -7.09901e6 q^{74} -4.23912e7i q^{75} -1.59062e7i q^{76} +(5.80774e6 + 9.44962e6i) q^{77} +1.02640e7 q^{78} -6.23959e6 q^{79} +4.65914e7i q^{80} -4.41498e6 q^{81} +6.81868e6i q^{82} -9.62572e6i q^{83} +(-2.44162e7 + 1.50062e7i) q^{84} -1.29507e7 q^{85} +5.11151e6 q^{86} -2.75139e6i q^{87} -1.23657e7 q^{88} +9.84326e7i q^{89} -2.27472e7i q^{90} +(7.11325e7 - 4.37181e7i) q^{91} -6.93532e7 q^{92} +2.61286e7 q^{93} +3.10491e7i q^{94} -7.71010e7 q^{95} -4.89548e7i q^{96} +4.75670e6i q^{97} +(1.44888e7 - 2.86207e7i) q^{98} -1.73122e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 32 q^{2} - 32 q^{4} + 1428 q^{7} + 3328 q^{8} - 8124 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 32 q^{2} - 32 q^{4} + 1428 q^{7} + 3328 q^{8} - 8124 q^{9} - 22168 q^{11} + 99008 q^{14} + 72960 q^{15} - 65280 q^{16} - 378528 q^{18} + 545664 q^{21} - 227392 q^{22} + 908072 q^{23} - 2055740 q^{25} + 1389920 q^{28} - 1473016 q^{29} + 4712640 q^{30} - 4577280 q^{32} + 2304960 q^{35} - 4951584 q^{36} + 6715272 q^{37} - 9276288 q^{39} + 5880000 q^{42} + 5748072 q^{43} - 623424 q^{44} + 2860352 q^{46} - 1194620 q^{49} - 967840 q^{50} - 21727872 q^{51} + 6749576 q^{53} - 10723328 q^{56} + 33733440 q^{57} - 28950592 q^{58} + 65479680 q^{60} - 40211052 q^{63} - 31918080 q^{64} - 39184320 q^{65} + 70027112 q^{67} - 71359680 q^{70} + 49900712 q^{71} + 35881728 q^{72} + 75593152 q^{74} - 13869688 q^{77} - 99960000 q^{78} - 82167256 q^{79} - 75422268 q^{81} + 19869696 q^{84} + 108466560 q^{85} + 173795392 q^{86} - 11637248 q^{88} + 206157504 q^{91} - 77732160 q^{92} - 90960000 q^{93} - 424874880 q^{95} + 115512992 q^{98} + 66343656 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.56466 −0.347791 −0.173896 0.984764i \(-0.555636\pi\)
−0.173896 + 0.984764i \(0.555636\pi\)
\(3\) 53.0420i 0.654840i 0.944879 + 0.327420i \(0.106179\pi\)
−0.944879 + 0.327420i \(0.893821\pi\)
\(4\) −225.035 −0.879041
\(5\) 1090.79i 1.74527i 0.488377 + 0.872633i \(0.337589\pi\)
−0.488377 + 0.872633i \(0.662411\pi\)
\(6\) 295.161i 0.227747i
\(7\) −1257.19 2045.55i −0.523613 0.851956i
\(8\) 2676.79 0.653514
\(9\) 3747.55 0.571185
\(10\) 6069.88i 0.606988i
\(11\) −4619.60 −0.315525 −0.157763 0.987477i \(-0.550428\pi\)
−0.157763 + 0.987477i \(0.550428\pi\)
\(12\) 11936.3i 0.575631i
\(13\) 34774.3i 1.21754i 0.793345 + 0.608772i \(0.208338\pi\)
−0.793345 + 0.608772i \(0.791662\pi\)
\(14\) 6995.86 + 11382.8i 0.182108 + 0.296303i
\(15\) −57857.7 −1.14287
\(16\) 42713.4 0.651755
\(17\) 11872.7i 0.142152i 0.997471 + 0.0710762i \(0.0226434\pi\)
−0.997471 + 0.0710762i \(0.977357\pi\)
\(18\) −20853.8 −0.198653
\(19\) 70683.5i 0.542380i 0.962526 + 0.271190i \(0.0874172\pi\)
−0.962526 + 0.271190i \(0.912583\pi\)
\(20\) 245466.i 1.53416i
\(21\) 108500. 66684.1i 0.557895 0.342882i
\(22\) 25706.5 0.109737
\(23\) 308189. 1.10130 0.550650 0.834736i \(-0.314380\pi\)
0.550650 + 0.834736i \(0.314380\pi\)
\(24\) 141983.i 0.427947i
\(25\) −799200. −2.04595
\(26\) 193507.i 0.423451i
\(27\) 546786.i 1.02887i
\(28\) 282912. + 460319.i 0.460277 + 0.748905i
\(29\) −51871.9 −0.0733398 −0.0366699 0.999327i \(-0.511675\pi\)
−0.0366699 + 0.999327i \(0.511675\pi\)
\(30\) 321959. 0.397480
\(31\) 492602.i 0.533395i −0.963780 0.266698i \(-0.914067\pi\)
0.963780 0.266698i \(-0.0859325\pi\)
\(32\) −922945. −0.880189
\(33\) 245033.i 0.206618i
\(34\) 66067.6i 0.0494394i
\(35\) 2.23126e6 1.37134e6i 1.48689 0.913843i
\(36\) −843327. −0.502095
\(37\) 1.27573e6 0.680694 0.340347 0.940300i \(-0.389455\pi\)
0.340347 + 0.940300i \(0.389455\pi\)
\(38\) 393330.i 0.188635i
\(39\) −1.84450e6 −0.797297
\(40\) 2.91982e6i 1.14056i
\(41\) 1.22535e6i 0.433637i −0.976212 0.216818i \(-0.930432\pi\)
0.976212 0.216818i \(-0.0695679\pi\)
\(42\) −603765. + 371074.i −0.194031 + 0.119252i
\(43\) −918567. −0.268681 −0.134340 0.990935i \(-0.542892\pi\)
−0.134340 + 0.990935i \(0.542892\pi\)
\(44\) 1.03957e6 0.277360
\(45\) 4.08779e6i 0.996870i
\(46\) −1.71497e6 −0.383023
\(47\) 5.57969e6i 1.14345i −0.820444 0.571727i \(-0.806274\pi\)
0.820444 0.571727i \(-0.193726\pi\)
\(48\) 2.26560e6i 0.426795i
\(49\) −2.60372e6 + 5.14330e6i −0.451659 + 0.892191i
\(50\) 4.44728e6 0.711564
\(51\) −629753. −0.0930871
\(52\) 7.82542e6i 1.07027i
\(53\) 6.83969e6 0.866828 0.433414 0.901195i \(-0.357309\pi\)
0.433414 + 0.901195i \(0.357309\pi\)
\(54\) 3.04268e6i 0.357833i
\(55\) 5.03902e6i 0.550675i
\(56\) −3.36525e6 5.47551e6i −0.342188 0.556765i
\(57\) −3.74920e6 −0.355172
\(58\) 288649. 0.0255070
\(59\) 8.16175e6i 0.673559i 0.941584 + 0.336779i \(0.109338\pi\)
−0.941584 + 0.336779i \(0.890662\pi\)
\(60\) 1.30200e7 1.00463
\(61\) 1.94292e7i 1.40325i 0.712547 + 0.701625i \(0.247542\pi\)
−0.712547 + 0.701625i \(0.752458\pi\)
\(62\) 2.74116e6i 0.185510i
\(63\) −4.71139e6 7.66578e6i −0.299080 0.486625i
\(64\) −5.79876e6 −0.345633
\(65\) −3.79315e7 −2.12494
\(66\) 1.36353e6i 0.0718601i
\(67\) 2.53838e7 1.25967 0.629837 0.776728i \(-0.283122\pi\)
0.629837 + 0.776728i \(0.283122\pi\)
\(68\) 2.67177e6i 0.124958i
\(69\) 1.63470e7i 0.721175i
\(70\) −1.24162e7 + 7.63102e6i −0.517127 + 0.317827i
\(71\) 2.99440e7 1.17836 0.589178 0.808003i \(-0.299452\pi\)
0.589178 + 0.808003i \(0.299452\pi\)
\(72\) 1.00314e7 0.373277
\(73\) 3.30065e7i 1.16227i −0.813806 0.581137i \(-0.802608\pi\)
0.813806 0.581137i \(-0.197392\pi\)
\(74\) −7.09901e6 −0.236739
\(75\) 4.23912e7i 1.33977i
\(76\) 1.59062e7i 0.476775i
\(77\) 5.80774e6 + 9.44962e6i 0.165213 + 0.268814i
\(78\) 1.02640e7 0.277293
\(79\) −6.23959e6 −0.160195 −0.0800973 0.996787i \(-0.525523\pi\)
−0.0800973 + 0.996787i \(0.525523\pi\)
\(80\) 4.65914e7i 1.13749i
\(81\) −4.41498e6 −0.102563
\(82\) 6.81868e6i 0.150815i
\(83\) 9.62572e6i 0.202825i −0.994844 0.101412i \(-0.967664\pi\)
0.994844 0.101412i \(-0.0323361\pi\)
\(84\) −2.44162e7 + 1.50062e7i −0.490413 + 0.301408i
\(85\) −1.29507e7 −0.248094
\(86\) 5.11151e6 0.0934449
\(87\) 2.75139e6i 0.0480258i
\(88\) −1.23657e7 −0.206200
\(89\) 9.84326e7i 1.56884i 0.620229 + 0.784421i \(0.287040\pi\)
−0.620229 + 0.784421i \(0.712960\pi\)
\(90\) 2.27472e7i 0.346703i
\(91\) 7.11325e7 4.37181e7i 1.03730 0.637522i
\(92\) −6.93532e7 −0.968088
\(93\) 2.61286e7 0.349288
\(94\) 3.10491e7i 0.397683i
\(95\) −7.71010e7 −0.946597
\(96\) 4.89548e7i 0.576382i
\(97\) 4.75670e6i 0.0537302i 0.999639 + 0.0268651i \(0.00855246\pi\)
−0.999639 + 0.0268651i \(0.991448\pi\)
\(98\) 1.44888e7 2.86207e7i 0.157083 0.310296i
\(99\) −1.73122e7 −0.180223
\(100\) 1.79848e8 1.79848
\(101\) 9.65936e7i 0.928246i −0.885771 0.464123i \(-0.846370\pi\)
0.885771 0.464123i \(-0.153630\pi\)
\(102\) 3.50436e6 0.0323749
\(103\) 1.13982e8i 1.01272i −0.862323 0.506358i \(-0.830992\pi\)
0.862323 0.506358i \(-0.169008\pi\)
\(104\) 9.30836e7i 0.795683i
\(105\) 7.27384e7 + 1.18351e8i 0.598421 + 0.973674i
\(106\) −3.80605e7 −0.301475
\(107\) −1.90137e7 −0.145054 −0.0725272 0.997366i \(-0.523106\pi\)
−0.0725272 + 0.997366i \(0.523106\pi\)
\(108\) 1.23046e8i 0.904423i
\(109\) −2.50660e8 −1.77574 −0.887869 0.460096i \(-0.847815\pi\)
−0.887869 + 0.460096i \(0.847815\pi\)
\(110\) 2.80404e7i 0.191520i
\(111\) 6.76673e7i 0.445746i
\(112\) −5.36991e7 8.73723e7i −0.341267 0.555267i
\(113\) 1.89409e8 1.16168 0.580839 0.814018i \(-0.302724\pi\)
0.580839 + 0.814018i \(0.302724\pi\)
\(114\) 2.08630e7 0.123526
\(115\) 3.36170e8i 1.92206i
\(116\) 1.16730e7 0.0644687
\(117\) 1.30318e8i 0.695443i
\(118\) 4.54174e7i 0.234258i
\(119\) 2.42862e7 1.49263e7i 0.121108 0.0744329i
\(120\) −1.54873e8 −0.746881
\(121\) −1.93018e8 −0.900444
\(122\) 1.08117e8i 0.488038i
\(123\) 6.49952e7 0.283962
\(124\) 1.10852e8i 0.468876i
\(125\) 4.45670e8i 1.82546i
\(126\) 2.62173e7 + 4.26575e7i 0.104017 + 0.169244i
\(127\) 1.14559e8 0.440368 0.220184 0.975458i \(-0.429334\pi\)
0.220184 + 0.975458i \(0.429334\pi\)
\(128\) 2.68542e8 1.00040
\(129\) 4.87226e7i 0.175943i
\(130\) 2.11076e8 0.739035
\(131\) 2.36265e8i 0.802257i −0.916022 0.401128i \(-0.868618\pi\)
0.916022 0.401128i \(-0.131382\pi\)
\(132\) 5.51409e7i 0.181626i
\(133\) 1.44586e8 8.88630e7i 0.462084 0.283997i
\(134\) −1.41252e8 −0.438103
\(135\) −5.96429e8 −1.79566
\(136\) 3.17808e7i 0.0928987i
\(137\) 4.33194e8 1.22970 0.614851 0.788643i \(-0.289216\pi\)
0.614851 + 0.788643i \(0.289216\pi\)
\(138\) 9.09653e7i 0.250818i
\(139\) 5.35069e8i 1.43334i 0.697410 + 0.716672i \(0.254336\pi\)
−0.697410 + 0.716672i \(0.745664\pi\)
\(140\) −5.02112e8 + 3.08598e8i −1.30704 + 0.803306i
\(141\) 2.95958e8 0.748779
\(142\) −1.66628e8 −0.409822
\(143\) 1.60643e8i 0.384166i
\(144\) 1.60070e8 0.372273
\(145\) 5.65814e7i 0.127997i
\(146\) 1.83670e8i 0.404229i
\(147\) −2.72811e8 1.38107e8i −0.584242 0.295764i
\(148\) −2.87083e8 −0.598358
\(149\) −4.22768e7 −0.0857743 −0.0428871 0.999080i \(-0.513656\pi\)
−0.0428871 + 0.999080i \(0.513656\pi\)
\(150\) 2.35892e8i 0.465960i
\(151\) 1.14410e8 0.220068 0.110034 0.993928i \(-0.464904\pi\)
0.110034 + 0.993928i \(0.464904\pi\)
\(152\) 1.89205e8i 0.354453i
\(153\) 4.44935e7i 0.0811954i
\(154\) −3.23181e7 5.25839e7i −0.0574596 0.0934910i
\(155\) 5.37325e8 0.930916
\(156\) 4.15076e8 0.700857
\(157\) 4.34094e8i 0.714472i −0.934014 0.357236i \(-0.883719\pi\)
0.934014 0.357236i \(-0.116281\pi\)
\(158\) 3.47212e7 0.0557142
\(159\) 3.62791e8i 0.567633i
\(160\) 1.00674e9i 1.53616i
\(161\) −3.87453e8 6.30415e8i −0.576655 0.938260i
\(162\) 2.45679e7 0.0356704
\(163\) −2.23602e8 −0.316756 −0.158378 0.987379i \(-0.550626\pi\)
−0.158378 + 0.987379i \(0.550626\pi\)
\(164\) 2.75747e8i 0.381184i
\(165\) 2.67280e8 0.360604
\(166\) 5.35638e7i 0.0705406i
\(167\) 2.88063e8i 0.370358i 0.982705 + 0.185179i \(0.0592865\pi\)
−0.982705 + 0.185179i \(0.940714\pi\)
\(168\) 2.90432e8 1.78500e8i 0.364592 0.224079i
\(169\) −3.93521e8 −0.482416
\(170\) 7.20660e7 0.0862849
\(171\) 2.64890e8i 0.309799i
\(172\) 2.06709e8 0.236182
\(173\) 1.75344e8i 0.195752i −0.995199 0.0978762i \(-0.968795\pi\)
0.995199 0.0978762i \(-0.0312049\pi\)
\(174\) 1.53105e7i 0.0167030i
\(175\) 1.00475e9 + 1.63480e9i 1.07129 + 1.74306i
\(176\) −1.97319e8 −0.205645
\(177\) −4.32916e8 −0.441073
\(178\) 5.47744e8i 0.545629i
\(179\) −1.46595e9 −1.42793 −0.713964 0.700182i \(-0.753102\pi\)
−0.713964 + 0.700182i \(0.753102\pi\)
\(180\) 9.19894e8i 0.876289i
\(181\) 1.47207e8i 0.137156i 0.997646 + 0.0685778i \(0.0218462\pi\)
−0.997646 + 0.0685778i \(0.978154\pi\)
\(182\) −3.95828e8 + 2.43276e8i −0.360762 + 0.221725i
\(183\) −1.03056e9 −0.918903
\(184\) 8.24958e8 0.719715
\(185\) 1.39156e9i 1.18799i
\(186\) −1.45397e8 −0.121479
\(187\) 5.48472e7i 0.0448527i
\(188\) 1.25562e9i 1.00514i
\(189\) 1.11848e9 6.87416e8i 0.876556 0.538732i
\(190\) 4.29041e8 0.329218
\(191\) 9.48564e8 0.712743 0.356372 0.934344i \(-0.384014\pi\)
0.356372 + 0.934344i \(0.384014\pi\)
\(192\) 3.07578e8i 0.226334i
\(193\) −1.41990e9 −1.02336 −0.511681 0.859175i \(-0.670977\pi\)
−0.511681 + 0.859175i \(0.670977\pi\)
\(194\) 2.64694e7i 0.0186869i
\(195\) 2.01196e9i 1.39149i
\(196\) 5.85928e8 1.15742e9i 0.397027 0.784272i
\(197\) 1.85323e9 1.23045 0.615226 0.788351i \(-0.289065\pi\)
0.615226 + 0.788351i \(0.289065\pi\)
\(198\) 9.63363e7 0.0626801
\(199\) 2.41054e9i 1.53710i −0.639789 0.768551i \(-0.720978\pi\)
0.639789 0.768551i \(-0.279022\pi\)
\(200\) −2.13929e9 −1.33706
\(201\) 1.34641e9i 0.824884i
\(202\) 5.37511e8i 0.322836i
\(203\) 6.52130e7 + 1.06106e8i 0.0384017 + 0.0624823i
\(204\) 1.41716e8 0.0818274
\(205\) 1.33660e9 0.756811
\(206\) 6.34271e8i 0.352214i
\(207\) 1.15495e9 0.629046
\(208\) 1.48533e9i 0.793541i
\(209\) 3.26530e8i 0.171135i
\(210\) −4.04765e8 6.58582e8i −0.208126 0.338635i
\(211\) −2.68024e9 −1.35221 −0.676105 0.736806i \(-0.736333\pi\)
−0.676105 + 0.736806i \(0.736333\pi\)
\(212\) −1.53917e9 −0.761977
\(213\) 1.58829e9i 0.771634i
\(214\) 1.05805e8 0.0504486
\(215\) 1.00196e9i 0.468920i
\(216\) 1.46363e9i 0.672384i
\(217\) −1.00764e9 + 6.19296e8i −0.454429 + 0.279293i
\(218\) 1.39484e9 0.617586
\(219\) 1.75073e9 0.761103
\(220\) 1.13395e9i 0.484066i
\(221\) −4.12865e8 −0.173077
\(222\) 3.76546e8i 0.155026i
\(223\) 1.59059e9i 0.643191i 0.946877 + 0.321595i \(0.104219\pi\)
−0.946877 + 0.321595i \(0.895781\pi\)
\(224\) 1.16032e9 + 1.88793e9i 0.460878 + 0.749882i
\(225\) −2.99504e9 −1.16862
\(226\) −1.05399e9 −0.404022
\(227\) 3.14403e9i 1.18408i −0.805907 0.592042i \(-0.798322\pi\)
0.805907 0.592042i \(-0.201678\pi\)
\(228\) 8.43699e8 0.312211
\(229\) 3.13926e9i 1.14152i −0.821115 0.570762i \(-0.806648\pi\)
0.821115 0.570762i \(-0.193352\pi\)
\(230\) 1.87067e9i 0.668476i
\(231\) −5.01227e8 + 3.08054e8i −0.176030 + 0.108188i
\(232\) −1.38850e8 −0.0479286
\(233\) −2.14656e8 −0.0728316 −0.0364158 0.999337i \(-0.511594\pi\)
−0.0364158 + 0.999337i \(0.511594\pi\)
\(234\) 7.25177e8i 0.241869i
\(235\) 6.08628e9 1.99563
\(236\) 1.83668e9i 0.592086i
\(237\) 3.30960e8i 0.104902i
\(238\) −1.35144e8 + 8.30599e7i −0.0421202 + 0.0258871i
\(239\) 4.65634e9 1.42709 0.713547 0.700607i \(-0.247087\pi\)
0.713547 + 0.700607i \(0.247087\pi\)
\(240\) −2.47130e9 −0.744870
\(241\) 4.83663e9i 1.43375i 0.697200 + 0.716877i \(0.254429\pi\)
−0.697200 + 0.716877i \(0.745571\pi\)
\(242\) 1.07408e9 0.313167
\(243\) 3.35328e9i 0.961712i
\(244\) 4.37223e9i 1.23351i
\(245\) −5.61027e9 2.84012e9i −1.55711 0.788265i
\(246\) −3.61676e8 −0.0987596
\(247\) −2.45797e9 −0.660372
\(248\) 1.31859e9i 0.348581i
\(249\) 5.10567e8 0.132818
\(250\) 2.48000e9i 0.634880i
\(251\) 9.65082e8i 0.243147i 0.992582 + 0.121574i \(0.0387941\pi\)
−0.992582 + 0.121574i \(0.961206\pi\)
\(252\) 1.06023e9 + 1.72507e9i 0.262904 + 0.427763i
\(253\) −1.42371e9 −0.347488
\(254\) −6.37484e8 −0.153156
\(255\) 6.86929e8i 0.162462i
\(256\) −9.86300e6 −0.00229641
\(257\) 4.81547e9i 1.10384i 0.833897 + 0.551920i \(0.186105\pi\)
−0.833897 + 0.551920i \(0.813895\pi\)
\(258\) 2.71125e8i 0.0611914i
\(259\) −1.60384e9 2.60957e9i −0.356420 0.579922i
\(260\) 8.53590e9 1.86791
\(261\) −1.94392e8 −0.0418906
\(262\) 1.31473e9i 0.279018i
\(263\) −2.09659e9 −0.438218 −0.219109 0.975700i \(-0.570315\pi\)
−0.219109 + 0.975700i \(0.570315\pi\)
\(264\) 6.55903e8i 0.135028i
\(265\) 7.46067e9i 1.51284i
\(266\) −8.04575e8 + 4.94492e8i −0.160709 + 0.0987718i
\(267\) −5.22107e9 −1.02734
\(268\) −5.71224e9 −1.10730
\(269\) 3.85590e9i 0.736404i −0.929746 0.368202i \(-0.879973\pi\)
0.929746 0.368202i \(-0.120027\pi\)
\(270\) 3.31893e9 0.624514
\(271\) 8.41141e9i 1.55952i −0.626077 0.779761i \(-0.715341\pi\)
0.626077 0.779761i \(-0.284659\pi\)
\(272\) 5.07124e8i 0.0926486i
\(273\) 2.31889e9 + 3.77301e9i 0.417475 + 0.679262i
\(274\) −2.41058e9 −0.427680
\(275\) 3.69199e9 0.645549
\(276\) 3.67863e9i 0.633943i
\(277\) 4.95554e9 0.841728 0.420864 0.907124i \(-0.361727\pi\)
0.420864 + 0.907124i \(0.361727\pi\)
\(278\) 2.97748e9i 0.498505i
\(279\) 1.84605e9i 0.304667i
\(280\) 5.97263e9 3.67078e9i 0.971704 0.597210i
\(281\) 4.41060e9 0.707412 0.353706 0.935357i \(-0.384921\pi\)
0.353706 + 0.935357i \(0.384921\pi\)
\(282\) −1.64691e9 −0.260419
\(283\) 4.90528e9i 0.764747i 0.924008 + 0.382374i \(0.124893\pi\)
−0.924008 + 0.382374i \(0.875107\pi\)
\(284\) −6.73843e9 −1.03582
\(285\) 4.08959e9i 0.619870i
\(286\) 8.93926e8i 0.133610i
\(287\) −2.50652e9 + 1.54051e9i −0.369439 + 0.227058i
\(288\) −3.45878e9 −0.502751
\(289\) 6.83480e9 0.979793
\(290\) 3.14856e8i 0.0445164i
\(291\) −2.52305e8 −0.0351847
\(292\) 7.42761e9i 1.02169i
\(293\) 9.91738e9i 1.34563i −0.739810 0.672816i \(-0.765085\pi\)
0.739810 0.672816i \(-0.234915\pi\)
\(294\) 1.51810e9 + 7.68517e8i 0.203194 + 0.102864i
\(295\) −8.90276e9 −1.17554
\(296\) 3.41487e9 0.444843
\(297\) 2.52593e9i 0.324636i
\(298\) 2.35256e8 0.0298315
\(299\) 1.07171e10i 1.34088i
\(300\) 9.53948e9i 1.17771i
\(301\) 1.15482e9 + 1.87897e9i 0.140685 + 0.228904i
\(302\) −6.36654e8 −0.0765377
\(303\) 5.12352e9 0.607852
\(304\) 3.01913e9i 0.353499i
\(305\) −2.11932e10 −2.44904
\(306\) 2.47591e8i 0.0282390i
\(307\) 1.23430e10i 1.38953i −0.719237 0.694765i \(-0.755508\pi\)
0.719237 0.694765i \(-0.244492\pi\)
\(308\) −1.30694e9 2.12649e9i −0.145229 0.236298i
\(309\) 6.04584e9 0.663166
\(310\) −2.99003e9 −0.323765
\(311\) 1.55097e10i 1.65791i 0.559315 + 0.828955i \(0.311064\pi\)
−0.559315 + 0.828955i \(0.688936\pi\)
\(312\) −4.93734e9 −0.521045
\(313\) 3.48632e8i 0.0363237i 0.999835 + 0.0181619i \(0.00578141\pi\)
−0.999835 + 0.0181619i \(0.994219\pi\)
\(314\) 2.41558e9i 0.248487i
\(315\) 8.36176e9 5.13914e9i 0.849289 0.521974i
\(316\) 1.40412e9 0.140818
\(317\) 1.67563e10 1.65936 0.829682 0.558237i \(-0.188522\pi\)
0.829682 + 0.558237i \(0.188522\pi\)
\(318\) 2.01881e9i 0.197418i
\(319\) 2.39627e8 0.0231406
\(320\) 6.32523e9i 0.603221i
\(321\) 1.00852e9i 0.0949873i
\(322\) 2.15605e9 + 3.50804e9i 0.200556 + 0.326318i
\(323\) −8.39206e8 −0.0771007
\(324\) 9.93524e8 0.0901567
\(325\) 2.77916e10i 2.49104i
\(326\) 1.24427e9 0.110165
\(327\) 1.32955e10i 1.16282i
\(328\) 3.28002e9i 0.283388i
\(329\) −1.14135e10 + 7.01476e9i −0.974173 + 0.598727i
\(330\) −1.48732e9 −0.125415
\(331\) −5.54002e9 −0.461530 −0.230765 0.973010i \(-0.574123\pi\)
−0.230765 + 0.973010i \(0.574123\pi\)
\(332\) 2.16612e9i 0.178291i
\(333\) 4.78086e9 0.388802
\(334\) 1.60297e9i 0.128807i
\(335\) 2.76885e10i 2.19846i
\(336\) 4.63440e9 2.84831e9i 0.363611 0.223475i
\(337\) 1.42537e9 0.110512 0.0552560 0.998472i \(-0.482403\pi\)
0.0552560 + 0.998472i \(0.482403\pi\)
\(338\) 2.18981e9 0.167780
\(339\) 1.00466e10i 0.760713i
\(340\) 2.91434e9 0.218085
\(341\) 2.27562e9i 0.168300i
\(342\) 1.47402e9i 0.107746i
\(343\) 1.37943e10 1.14009e9i 0.996602 0.0823687i
\(344\) −2.45881e9 −0.175587
\(345\) −1.78311e10 −1.25864
\(346\) 9.75731e8i 0.0680809i
\(347\) −1.75840e9 −0.121283 −0.0606415 0.998160i \(-0.519315\pi\)
−0.0606415 + 0.998160i \(0.519315\pi\)
\(348\) 6.19157e8i 0.0422167i
\(349\) 6.24983e9i 0.421276i 0.977564 + 0.210638i \(0.0675541\pi\)
−0.977564 + 0.210638i \(0.932446\pi\)
\(350\) −5.59109e9 9.09711e9i −0.372584 0.606221i
\(351\) −1.90141e10 −1.25270
\(352\) 4.26364e9 0.277722
\(353\) 3.49131e9i 0.224848i −0.993660 0.112424i \(-0.964138\pi\)
0.993660 0.112424i \(-0.0358616\pi\)
\(354\) 2.40903e9 0.153401
\(355\) 3.26626e10i 2.05654i
\(356\) 2.21507e10i 1.37908i
\(357\) 7.91722e8 + 1.28819e9i 0.0487416 + 0.0793061i
\(358\) 8.15750e9 0.496621
\(359\) −2.24032e10 −1.34875 −0.674376 0.738388i \(-0.735587\pi\)
−0.674376 + 0.738388i \(0.735587\pi\)
\(360\) 1.09422e10i 0.651468i
\(361\) 1.19874e10 0.705824
\(362\) 8.19156e8i 0.0477015i
\(363\) 1.02381e10i 0.589646i
\(364\) −1.60073e10 + 9.83807e9i −0.911825 + 0.560408i
\(365\) 3.60032e10 2.02848
\(366\) 5.73473e9 0.319587
\(367\) 6.13435e9i 0.338146i −0.985604 0.169073i \(-0.945923\pi\)
0.985604 0.169073i \(-0.0540774\pi\)
\(368\) 1.31638e10 0.717778
\(369\) 4.59207e9i 0.247687i
\(370\) 7.74353e9i 0.413173i
\(371\) −8.59882e9 1.39909e10i −0.453882 0.738499i
\(372\) −5.87983e9 −0.307039
\(373\) −1.89260e10 −0.977738 −0.488869 0.872357i \(-0.662590\pi\)
−0.488869 + 0.872357i \(0.662590\pi\)
\(374\) 3.05206e8i 0.0155994i
\(375\) 2.36392e10 1.19539
\(376\) 1.49357e10i 0.747263i
\(377\) 1.80381e9i 0.0892945i
\(378\) −6.22394e9 + 3.82524e9i −0.304858 + 0.187366i
\(379\) −1.23203e9 −0.0597126 −0.0298563 0.999554i \(-0.509505\pi\)
−0.0298563 + 0.999554i \(0.509505\pi\)
\(380\) 1.73504e10 0.832098
\(381\) 6.07646e9i 0.288370i
\(382\) −5.27844e9 −0.247886
\(383\) 2.90499e10i 1.35005i −0.737795 0.675025i \(-0.764133\pi\)
0.737795 0.675025i \(-0.235867\pi\)
\(384\) 1.42440e10i 0.655099i
\(385\) −1.03076e10 + 6.33503e9i −0.469151 + 0.288341i
\(386\) 7.90128e9 0.355917
\(387\) −3.44237e9 −0.153467
\(388\) 1.07042e9i 0.0472311i
\(389\) −1.24931e9 −0.0545598 −0.0272799 0.999628i \(-0.508685\pi\)
−0.0272799 + 0.999628i \(0.508685\pi\)
\(390\) 1.11959e10i 0.483950i
\(391\) 3.65904e9i 0.156553i
\(392\) −6.96963e9 + 1.37676e10i −0.295166 + 0.583059i
\(393\) 1.25319e10 0.525350
\(394\) −1.03126e10 −0.427940
\(395\) 6.80609e9i 0.279582i
\(396\) 3.89584e9 0.158424
\(397\) 1.31642e10i 0.529946i −0.964256 0.264973i \(-0.914637\pi\)
0.964256 0.264973i \(-0.0853631\pi\)
\(398\) 1.34138e10i 0.534590i
\(399\) 4.71347e9 + 7.66916e9i 0.185973 + 0.302591i
\(400\) −3.41365e10 −1.33346
\(401\) −3.42284e9 −0.132376 −0.0661879 0.997807i \(-0.521084\pi\)
−0.0661879 + 0.997807i \(0.521084\pi\)
\(402\) 7.49231e9i 0.286887i
\(403\) 1.71299e10 0.649433
\(404\) 2.17369e10i 0.815966i
\(405\) 4.81582e9i 0.178999i
\(406\) −3.62888e8 5.90446e8i −0.0133558 0.0217308i
\(407\) −5.89337e9 −0.214776
\(408\) −1.68572e9 −0.0608337
\(409\) 3.67295e10i 1.31257i 0.754514 + 0.656284i \(0.227873\pi\)
−0.754514 + 0.656284i \(0.772127\pi\)
\(410\) −7.43775e9 −0.263212
\(411\) 2.29775e10i 0.805258i
\(412\) 2.56499e10i 0.890219i
\(413\) 1.66952e10 1.02609e10i 0.573842 0.352684i
\(414\) −6.42691e9 −0.218777
\(415\) 1.04996e10 0.353983
\(416\) 3.20948e10i 1.07167i
\(417\) −2.83811e10 −0.938611
\(418\) 1.81703e9i 0.0595191i
\(419\) 3.44354e10i 1.11725i −0.829421 0.558623i \(-0.811330\pi\)
0.829421 0.558623i \(-0.188670\pi\)
\(420\) −1.63687e10 2.66330e10i −0.526037 0.855900i
\(421\) −8.91543e9 −0.283801 −0.141900 0.989881i \(-0.545321\pi\)
−0.141900 + 0.989881i \(0.545321\pi\)
\(422\) 1.49146e10 0.470286
\(423\) 2.09101e10i 0.653124i
\(424\) 1.83084e10 0.566484
\(425\) 9.48867e9i 0.290837i
\(426\) 8.83829e9i 0.268367i
\(427\) 3.97433e10 2.44262e10i 1.19551 0.734760i
\(428\) 4.27873e9 0.127509
\(429\) 8.52085e9 0.251567
\(430\) 5.57559e9i 0.163086i
\(431\) 8.63513e9 0.250242 0.125121 0.992141i \(-0.460068\pi\)
0.125121 + 0.992141i \(0.460068\pi\)
\(432\) 2.33551e10i 0.670574i
\(433\) 1.00230e10i 0.285133i 0.989785 + 0.142566i \(0.0455354\pi\)
−0.989785 + 0.142566i \(0.954465\pi\)
\(434\) 5.60717e9 3.44617e9i 0.158047 0.0971355i
\(435\) 3.00119e9 0.0838178
\(436\) 5.64072e10 1.56095
\(437\) 2.17839e10i 0.597323i
\(438\) −9.74224e9 −0.264705
\(439\) 1.95383e10i 0.526052i −0.964789 0.263026i \(-0.915280\pi\)
0.964789 0.263026i \(-0.0847205\pi\)
\(440\) 1.34884e10i 0.359874i
\(441\) −9.75758e9 + 1.92748e10i −0.257981 + 0.509606i
\(442\) 2.29746e9 0.0601947
\(443\) −6.16372e10 −1.60040 −0.800198 0.599735i \(-0.795272\pi\)
−0.800198 + 0.599735i \(0.795272\pi\)
\(444\) 1.52275e10i 0.391829i
\(445\) −1.07369e11 −2.73805
\(446\) 8.85111e9i 0.223696i
\(447\) 2.24245e9i 0.0561684i
\(448\) 7.29017e9 + 1.18616e10i 0.180978 + 0.294464i
\(449\) 4.20875e10 1.03554 0.517772 0.855519i \(-0.326762\pi\)
0.517772 + 0.855519i \(0.326762\pi\)
\(450\) 1.66664e10 0.406435
\(451\) 5.66065e9i 0.136823i
\(452\) −4.26235e10 −1.02116
\(453\) 6.06855e9i 0.144109i
\(454\) 1.74954e10i 0.411814i
\(455\) 4.76873e10 + 7.75907e10i 1.11265 + 1.81036i
\(456\) −1.00358e10 −0.232110
\(457\) 3.52520e10 0.808201 0.404101 0.914715i \(-0.367585\pi\)
0.404101 + 0.914715i \(0.367585\pi\)
\(458\) 1.74689e10i 0.397012i
\(459\) −6.49184e9 −0.146257
\(460\) 7.56498e10i 1.68957i
\(461\) 6.35329e10i 1.40668i 0.710854 + 0.703340i \(0.248309\pi\)
−0.710854 + 0.703340i \(0.751691\pi\)
\(462\) 2.78916e9 1.71422e9i 0.0612216 0.0376268i
\(463\) −1.97409e10 −0.429580 −0.214790 0.976660i \(-0.568907\pi\)
−0.214790 + 0.976660i \(0.568907\pi\)
\(464\) −2.21562e9 −0.0477996
\(465\) 2.85008e10i 0.609601i
\(466\) 1.19449e9 0.0253302
\(467\) 2.52130e10i 0.530098i 0.964235 + 0.265049i \(0.0853882\pi\)
−0.964235 + 0.265049i \(0.914612\pi\)
\(468\) 2.93261e10i 0.611323i
\(469\) −3.19124e10 5.19238e10i −0.659581 1.07319i
\(470\) −3.38681e10 −0.694063
\(471\) 2.30252e10 0.467864
\(472\) 2.18473e10i 0.440180i
\(473\) 4.24341e9 0.0847756
\(474\) 1.84168e9i 0.0364839i
\(475\) 5.64903e10i 1.10968i
\(476\) −5.46524e9 + 3.35894e9i −0.106459 + 0.0654296i
\(477\) 2.56320e10 0.495119
\(478\) −2.59109e10 −0.496331
\(479\) 8.60005e10i 1.63365i −0.576886 0.816825i \(-0.695732\pi\)
0.576886 0.816825i \(-0.304268\pi\)
\(480\) 5.33995e10 1.00594
\(481\) 4.43626e10i 0.828776i
\(482\) 2.69142e10i 0.498647i
\(483\) 3.34385e10 2.05513e10i 0.614410 0.377617i
\(484\) 4.34358e10 0.791527
\(485\) −5.18856e9 −0.0937735
\(486\) 1.86599e10i 0.334475i
\(487\) 3.49822e10 0.621915 0.310957 0.950424i \(-0.399350\pi\)
0.310957 + 0.950424i \(0.399350\pi\)
\(488\) 5.20079e10i 0.917043i
\(489\) 1.18603e10i 0.207424i
\(490\) 3.12192e10 + 1.58043e10i 0.541549 + 0.274152i
\(491\) −1.12326e11 −1.93265 −0.966324 0.257327i \(-0.917158\pi\)
−0.966324 + 0.257327i \(0.917158\pi\)
\(492\) −1.46262e10 −0.249615
\(493\) 6.15860e8i 0.0104254i
\(494\) 1.36778e10 0.229672
\(495\) 1.88840e10i 0.314537i
\(496\) 2.10407e10i 0.347643i
\(497\) −3.76454e10 6.12518e10i −0.617002 1.00391i
\(498\) −2.84113e9 −0.0461928
\(499\) 2.70319e10 0.435988 0.217994 0.975950i \(-0.430049\pi\)
0.217994 + 0.975950i \(0.430049\pi\)
\(500\) 1.00291e11i 1.60466i
\(501\) −1.52794e10 −0.242525
\(502\) 5.37035e9i 0.0845645i
\(503\) 9.55454e10i 1.49258i 0.665621 + 0.746290i \(0.268167\pi\)
−0.665621 + 0.746290i \(0.731833\pi\)
\(504\) −1.26114e10 2.05197e10i −0.195453 0.318016i
\(505\) 1.05363e11 1.62004
\(506\) 7.92246e9 0.120853
\(507\) 2.08732e10i 0.315905i
\(508\) −2.57798e10 −0.387101
\(509\) 3.53308e10i 0.526359i −0.964747 0.263180i \(-0.915229\pi\)
0.964747 0.263180i \(-0.0847712\pi\)
\(510\) 3.82252e9i 0.0565027i
\(511\) −6.75165e10 + 4.14957e10i −0.990207 + 0.608582i
\(512\) −6.86919e10 −0.999598
\(513\) −3.86488e10 −0.558041
\(514\) 2.67965e10i 0.383906i
\(515\) 1.24331e11 1.76746
\(516\) 1.09643e10i 0.154661i
\(517\) 2.57760e10i 0.360789i
\(518\) 8.92483e9 + 1.45214e10i 0.123960 + 0.201692i
\(519\) 9.30061e9 0.128186
\(520\) −1.01535e11 −1.38868
\(521\) 4.31721e10i 0.585938i −0.956122 0.292969i \(-0.905357\pi\)
0.956122 0.292969i \(-0.0946433\pi\)
\(522\) 1.08173e9 0.0145692
\(523\) 3.35907e10i 0.448965i 0.974478 + 0.224482i \(0.0720691\pi\)
−0.974478 + 0.224482i \(0.927931\pi\)
\(524\) 5.31677e10i 0.705217i
\(525\) −8.67131e10 + 5.32939e10i −1.14143 + 0.701521i
\(526\) 1.16668e10 0.152408
\(527\) 5.84852e9 0.0758235
\(528\) 1.04662e10i 0.134664i
\(529\) 1.66694e10 0.212862
\(530\) 4.15161e10i 0.526154i
\(531\) 3.05865e10i 0.384727i
\(532\) −3.25370e10 + 1.99972e10i −0.406191 + 0.249645i
\(533\) 4.26108e10 0.527972
\(534\) 2.90535e10 0.357300
\(535\) 2.07399e10i 0.253158i
\(536\) 6.79473e10 0.823214
\(537\) 7.77568e10i 0.935064i
\(538\) 2.14568e10i 0.256115i
\(539\) 1.20282e10 2.37600e10i 0.142510 0.281509i
\(540\) 1.34217e11 1.57846
\(541\) 4.61851e10 0.539154 0.269577 0.962979i \(-0.413116\pi\)
0.269577 + 0.962979i \(0.413116\pi\)
\(542\) 4.68066e10i 0.542388i
\(543\) −7.80815e9 −0.0898150
\(544\) 1.09579e10i 0.125121i
\(545\) 2.73418e11i 3.09914i
\(546\) −1.29039e10 2.09955e10i −0.145194 0.236241i
\(547\) −6.37938e10 −0.712572 −0.356286 0.934377i \(-0.615957\pi\)
−0.356286 + 0.934377i \(0.615957\pi\)
\(548\) −9.74836e10 −1.08096
\(549\) 7.28117e10i 0.801515i
\(550\) −2.05446e10 −0.224516
\(551\) 3.66649e9i 0.0397781i
\(552\) 4.37574e10i 0.471298i
\(553\) 7.84438e9 + 1.27634e10i 0.0838799 + 0.136479i
\(554\) −2.75759e10 −0.292746
\(555\) −7.38109e10 −0.777944
\(556\) 1.20409e11i 1.25997i
\(557\) 1.37758e11 1.43118 0.715591 0.698519i \(-0.246157\pi\)
0.715591 + 0.698519i \(0.246157\pi\)
\(558\) 1.02726e10i 0.105961i
\(559\) 3.19425e10i 0.327131i
\(560\) 9.53049e10 5.85744e10i 0.969088 0.595602i
\(561\) 2.90921e9 0.0293713
\(562\) −2.45435e10 −0.246032
\(563\) 1.49790e11i 1.49090i 0.666561 + 0.745450i \(0.267765\pi\)
−0.666561 + 0.745450i \(0.732235\pi\)
\(564\) −6.66008e10 −0.658208
\(565\) 2.06605e11i 2.02744i
\(566\) 2.72962e10i 0.265972i
\(567\) 5.55049e9 + 9.03105e9i 0.0537031 + 0.0873788i
\(568\) 8.01539e10 0.770072
\(569\) 8.86831e10 0.846042 0.423021 0.906120i \(-0.360970\pi\)
0.423021 + 0.906120i \(0.360970\pi\)
\(570\) 2.27572e10i 0.215585i
\(571\) −3.26006e10 −0.306677 −0.153338 0.988174i \(-0.549002\pi\)
−0.153338 + 0.988174i \(0.549002\pi\)
\(572\) 3.61503e10i 0.337698i
\(573\) 5.03137e10i 0.466733i
\(574\) 1.39479e10 8.57240e9i 0.128488 0.0789687i
\(575\) −2.46305e11 −2.25321
\(576\) −2.17311e10 −0.197420
\(577\) 2.58510e10i 0.233225i −0.993177 0.116612i \(-0.962796\pi\)
0.993177 0.116612i \(-0.0372035\pi\)
\(578\) −3.80333e10 −0.340763
\(579\) 7.53145e10i 0.670138i
\(580\) 1.27328e10i 0.112515i
\(581\) −1.96899e10 + 1.21014e10i −0.172798 + 0.106202i
\(582\) 1.40399e9 0.0122369
\(583\) −3.15966e10 −0.273506
\(584\) 8.83517e10i 0.759563i
\(585\) −1.42150e11 −1.21373
\(586\) 5.51868e10i 0.467999i
\(587\) 1.55628e11i 1.31079i 0.755285 + 0.655396i \(0.227498\pi\)
−0.755285 + 0.655396i \(0.772502\pi\)
\(588\) 6.13919e10 + 3.10788e10i 0.513573 + 0.259989i
\(589\) 3.48188e10 0.289303
\(590\) 4.95409e10 0.408842
\(591\) 9.82991e10i 0.805748i
\(592\) 5.44908e10 0.443646
\(593\) 1.26533e11i 1.02325i −0.859208 0.511627i \(-0.829043\pi\)
0.859208 0.511627i \(-0.170957\pi\)
\(594\) 1.40560e10i 0.112905i
\(595\) 1.62815e10 + 2.64912e10i 0.129905 + 0.211365i
\(596\) 9.51374e9 0.0753991
\(597\) 1.27860e11 1.00655
\(598\) 5.96368e10i 0.466347i
\(599\) −1.90322e10 −0.147836 −0.0739182 0.997264i \(-0.523550\pi\)
−0.0739182 + 0.997264i \(0.523550\pi\)
\(600\) 1.13472e11i 0.875559i
\(601\) 3.70216e10i 0.283764i 0.989884 + 0.141882i \(0.0453154\pi\)
−0.989884 + 0.141882i \(0.954685\pi\)
\(602\) −6.42616e9 1.04558e10i −0.0489289 0.0796109i
\(603\) 9.51271e10 0.719507
\(604\) −2.57462e10 −0.193449
\(605\) 2.10542e11i 1.57151i
\(606\) −2.85106e10 −0.211406
\(607\) 1.82542e11i 1.34464i −0.740259 0.672322i \(-0.765297\pi\)
0.740259 0.672322i \(-0.234703\pi\)
\(608\) 6.52370e10i 0.477397i
\(609\) −5.62809e9 + 3.45903e9i −0.0409159 + 0.0251469i
\(610\) 1.17933e11 0.851756
\(611\) 1.94030e11 1.39221
\(612\) 1.00126e10i 0.0713741i
\(613\) −2.40596e11 −1.70391 −0.851954 0.523616i \(-0.824583\pi\)
−0.851954 + 0.523616i \(0.824583\pi\)
\(614\) 6.86847e10i 0.483266i
\(615\) 7.08962e10i 0.495590i
\(616\) 1.55461e10 + 2.52947e10i 0.107969 + 0.175673i
\(617\) −6.10078e10 −0.420964 −0.210482 0.977598i \(-0.567503\pi\)
−0.210482 + 0.977598i \(0.567503\pi\)
\(618\) −3.36430e10 −0.230643
\(619\) 1.29814e11i 0.884215i 0.896962 + 0.442108i \(0.145769\pi\)
−0.896962 + 0.442108i \(0.854231\pi\)
\(620\) −1.20917e11 −0.818314
\(621\) 1.68513e11i 1.13310i
\(622\) 8.63060e10i 0.576607i
\(623\) 2.01349e11 1.23749e11i 1.33658 0.821466i
\(624\) −7.87848e10 −0.519642
\(625\) 1.73945e11 1.13997
\(626\) 1.94002e9i 0.0126331i
\(627\) 1.73198e10 0.112066
\(628\) 9.76861e10i 0.628050i
\(629\) 1.51464e10i 0.0967624i
\(630\) −4.65304e10 + 2.85976e10i −0.295375 + 0.181538i
\(631\) −1.95506e11 −1.23323 −0.616614 0.787266i \(-0.711496\pi\)
−0.616614 + 0.787266i \(0.711496\pi\)
\(632\) −1.67021e10 −0.104689
\(633\) 1.42165e11i 0.885480i
\(634\) −9.32432e10 −0.577112
\(635\) 1.24960e11i 0.768559i
\(636\) 8.16404e10i 0.498973i
\(637\) −1.78855e11 9.05427e10i −1.08628 0.549915i
\(638\) −1.33345e9 −0.00804808
\(639\) 1.12216e11 0.673059
\(640\) 2.92923e11i 1.74596i
\(641\) 7.18991e10 0.425884 0.212942 0.977065i \(-0.431695\pi\)
0.212942 + 0.977065i \(0.431695\pi\)
\(642\) 5.61209e9i 0.0330358i
\(643\) 1.33296e11i 0.779784i −0.920861 0.389892i \(-0.872512\pi\)
0.920861 0.389892i \(-0.127488\pi\)
\(644\) 8.71904e10 + 1.41865e11i 0.506903 + 0.824769i
\(645\) 5.31462e10 0.307067
\(646\) 4.66989e9 0.0268149
\(647\) 1.36807e11i 0.780715i 0.920663 + 0.390358i \(0.127649\pi\)
−0.920663 + 0.390358i \(0.872351\pi\)
\(648\) −1.18180e10 −0.0670261
\(649\) 3.77041e10i 0.212525i
\(650\) 1.54651e11i 0.866361i
\(651\) −3.28487e10 5.34473e10i −0.182892 0.297578i
\(652\) 5.03181e10 0.278442
\(653\) −2.96176e11 −1.62891 −0.814454 0.580228i \(-0.802963\pi\)
−0.814454 + 0.580228i \(0.802963\pi\)
\(654\) 7.39850e10i 0.404420i
\(655\) 2.57715e11 1.40015
\(656\) 5.23390e10i 0.282625i
\(657\) 1.23694e11i 0.663874i
\(658\) 6.35124e10 3.90347e10i 0.338809 0.208232i
\(659\) −2.23698e11 −1.18610 −0.593050 0.805166i \(-0.702076\pi\)
−0.593050 + 0.805166i \(0.702076\pi\)
\(660\) −6.01472e10 −0.316986
\(661\) 6.94168e10i 0.363629i −0.983333 0.181815i \(-0.941803\pi\)
0.983333 0.181815i \(-0.0581971\pi\)
\(662\) 3.08283e10 0.160516
\(663\) 2.18992e10i 0.113338i
\(664\) 2.57661e10i 0.132549i
\(665\) 9.69309e10 + 1.57714e11i 0.495651 + 0.806460i
\(666\) −2.66038e10 −0.135222
\(667\) −1.59863e10 −0.0807692
\(668\) 6.48241e10i 0.325560i
\(669\) −8.43683e10 −0.421187
\(670\) 1.54077e11i 0.764607i
\(671\) 8.97551e10i 0.442760i
\(672\) −1.00139e11 + 6.15458e10i −0.491053 + 0.301801i
\(673\) 2.96996e11 1.44774 0.723868 0.689938i \(-0.242362\pi\)
0.723868 + 0.689938i \(0.242362\pi\)
\(674\) −7.93172e9 −0.0384351
\(675\) 4.36991e11i 2.10503i
\(676\) 8.85559e10 0.424063
\(677\) 6.21127e10i 0.295683i 0.989011 + 0.147841i \(0.0472325\pi\)
−0.989011 + 0.147841i \(0.952768\pi\)
\(678\) 5.59060e10i 0.264569i
\(679\) 9.73005e9 5.98010e9i 0.0457758 0.0281338i
\(680\) −3.46662e10 −0.162133
\(681\) 1.66765e11 0.775385
\(682\) 1.26631e10i 0.0585331i
\(683\) 1.74236e11 0.800675 0.400337 0.916368i \(-0.368893\pi\)
0.400337 + 0.916368i \(0.368893\pi\)
\(684\) 5.96093e10i 0.272327i
\(685\) 4.72524e11i 2.14616i
\(686\) −7.67603e10 + 6.34421e9i −0.346609 + 0.0286471i
\(687\) 1.66513e11 0.747515
\(688\) −3.92351e10 −0.175114
\(689\) 2.37845e11i 1.05540i
\(690\) 9.92241e10 0.437745
\(691\) 3.76057e11i 1.64946i −0.565529 0.824729i \(-0.691328\pi\)
0.565529 0.824729i \(-0.308672\pi\)
\(692\) 3.94585e10i 0.172074i
\(693\) 2.17648e10 + 3.54129e10i 0.0943672 + 0.153542i
\(694\) 9.78491e9 0.0421812
\(695\) −5.83648e11 −2.50157
\(696\) 7.36490e9i 0.0313856i
\(697\) 1.45483e10 0.0616425
\(698\) 3.47782e10i 0.146516i
\(699\) 1.13858e10i 0.0476930i
\(700\) −2.26103e11 3.67887e11i −0.941705 1.53222i
\(701\) 5.52623e10 0.228853 0.114426 0.993432i \(-0.463497\pi\)
0.114426 + 0.993432i \(0.463497\pi\)
\(702\) 1.05807e11 0.435678
\(703\) 9.01731e10i 0.369195i
\(704\) 2.67880e10 0.109056
\(705\) 3.22828e11i 1.30682i
\(706\) 1.94280e10i 0.0782003i
\(707\) −1.97587e11 + 1.21437e11i −0.790825 + 0.486041i
\(708\) 9.74210e10 0.387721
\(709\) −1.95876e11 −0.775168 −0.387584 0.921834i \(-0.626690\pi\)
−0.387584 + 0.921834i \(0.626690\pi\)
\(710\) 1.81756e11i 0.715248i
\(711\) −2.33831e10 −0.0915007
\(712\) 2.63484e11i 1.02526i
\(713\) 1.51814e11i 0.587428i
\(714\) −4.40566e9 7.16833e9i −0.0169519 0.0275820i
\(715\) 1.75228e11 0.670472
\(716\) 3.29889e11 1.25521
\(717\) 2.46982e11i 0.934518i
\(718\) 1.24666e11 0.469084
\(719\) 5.03402e11i 1.88365i 0.336107 + 0.941824i \(0.390890\pi\)
−0.336107 + 0.941824i \(0.609110\pi\)
\(720\) 1.74603e11i 0.649714i
\(721\) −2.33156e11 + 1.43298e11i −0.862789 + 0.530271i
\(722\) −6.67058e10 −0.245479
\(723\) −2.56545e11 −0.938879
\(724\) 3.31266e10i 0.120566i
\(725\) 4.14560e10 0.150050
\(726\) 5.69714e10i 0.205074i
\(727\) 3.52126e11i 1.26055i −0.776371 0.630276i \(-0.782942\pi\)
0.776371 0.630276i \(-0.217058\pi\)
\(728\) 1.90407e11 1.17024e11i 0.677887 0.416630i
\(729\) −2.06832e11 −0.732330
\(730\) −2.00346e11 −0.705487
\(731\) 1.09059e10i 0.0381937i
\(732\) 2.31912e11 0.807754
\(733\) 3.13444e11i 1.08579i −0.839802 0.542893i \(-0.817329\pi\)
0.839802 0.542893i \(-0.182671\pi\)
\(734\) 3.41356e10i 0.117604i
\(735\) 1.50646e11 2.97580e11i 0.516187 1.01966i
\(736\) −2.84441e11 −0.969352
\(737\) −1.17263e11 −0.397459
\(738\) 2.55533e10i 0.0861433i
\(739\) 1.23610e11 0.414453 0.207227 0.978293i \(-0.433556\pi\)
0.207227 + 0.978293i \(0.433556\pi\)
\(740\) 3.13148e11i 1.04429i
\(741\) 1.30376e11i 0.432438i
\(742\) 4.78495e10 + 7.78546e10i 0.157856 + 0.256844i
\(743\) 4.82588e11 1.58351 0.791756 0.610837i \(-0.209167\pi\)
0.791756 + 0.610837i \(0.209167\pi\)
\(744\) 6.99408e10 0.228265
\(745\) 4.61151e10i 0.149699i
\(746\) 1.05317e11 0.340049
\(747\) 3.60728e10i 0.115850i
\(748\) 1.23425e10i 0.0394274i
\(749\) 2.39039e10 + 3.88933e10i 0.0759523 + 0.123580i
\(750\) −1.31544e11 −0.415745
\(751\) 6.28682e11 1.97638 0.988192 0.153223i \(-0.0489653\pi\)
0.988192 + 0.153223i \(0.0489653\pi\)
\(752\) 2.38328e11i 0.745252i
\(753\) −5.11899e10 −0.159222
\(754\) 1.00376e10i 0.0310559i
\(755\) 1.24798e11i 0.384077i
\(756\) −2.51696e11 + 1.54692e11i −0.770529 + 0.473567i
\(757\) −2.63545e11 −0.802548 −0.401274 0.915958i \(-0.631432\pi\)
−0.401274 + 0.915958i \(0.631432\pi\)
\(758\) 6.85585e9 0.0207675
\(759\) 7.55165e10i 0.227549i
\(760\) −2.06383e11 −0.618615
\(761\) 5.81694e11i 1.73443i −0.497937 0.867213i \(-0.665909\pi\)
0.497937 0.867213i \(-0.334091\pi\)
\(762\) 3.38134e10i 0.100293i
\(763\) 3.15128e11 + 5.12737e11i 0.929800 + 1.51285i
\(764\) −2.13460e11 −0.626531
\(765\) −4.85332e10 −0.141707
\(766\) 1.61653e11i 0.469536i
\(767\) −2.83819e11 −0.820088
\(768\) 5.23153e8i 0.00150378i
\(769\) 1.04399e11i 0.298533i 0.988797 + 0.149267i \(0.0476912\pi\)
−0.988797 + 0.149267i \(0.952309\pi\)
\(770\) 5.73580e10 3.52523e10i 0.163167 0.100282i
\(771\) −2.55422e11 −0.722838
\(772\) 3.19527e11 0.899578
\(773\) 1.57883e11i 0.442199i 0.975251 + 0.221100i \(0.0709646\pi\)
−0.975251 + 0.221100i \(0.929035\pi\)
\(774\) 1.91556e10 0.0533743
\(775\) 3.93687e11i 1.09130i
\(776\) 1.27327e10i 0.0351135i
\(777\) 1.38417e11 8.50710e10i 0.379756 0.233398i
\(778\) 6.95200e9 0.0189754
\(779\) 8.66123e10 0.235196
\(780\) 4.52761e11i 1.22318i
\(781\) −1.38329e11 −0.371801
\(782\) 2.03613e10i 0.0544476i
\(783\) 2.83628e10i 0.0754575i
\(784\) −1.11214e11 + 2.19688e11i −0.294371 + 0.581489i
\(785\) 4.73506e11 1.24694
\(786\) −6.97360e10 −0.182712
\(787\) 4.73305e11i 1.23379i −0.787045 0.616896i \(-0.788390\pi\)
0.787045 0.616896i \(-0.211610\pi\)
\(788\) −4.17041e11 −1.08162
\(789\) 1.11207e11i 0.286963i
\(790\) 3.78736e10i 0.0972362i
\(791\) −2.38124e11 3.87444e11i −0.608270 0.989700i
\(792\) −4.63411e10 −0.117778
\(793\) −6.75636e11 −1.70852
\(794\) 7.32542e10i 0.184311i
\(795\) −3.95729e11 −0.990670
\(796\) 5.42455e11i 1.35118i
\(797\) 1.42604e11i 0.353427i 0.984262 + 0.176714i \(0.0565466\pi\)
−0.984262 + 0.176714i \(0.943453\pi\)
\(798\) −2.62289e10 4.26763e10i −0.0646797 0.105239i
\(799\) 6.62461e10 0.162545
\(800\) 7.37617e11 1.80082
\(801\) 3.68881e11i 0.896099i
\(802\) 1.90469e10 0.0460392
\(803\) 1.52477e11i 0.366727i
\(804\) 3.02989e11i 0.725107i
\(805\) 6.87651e11 4.22631e11i 1.63751 1.00642i
\(806\) −9.53220e10 −0.225867
\(807\) 2.04525e11 0.482227
\(808\) 2.58561e11i 0.606622i
\(809\) −8.94669e10 −0.208866 −0.104433 0.994532i \(-0.533303\pi\)
−0.104433 + 0.994532i \(0.533303\pi\)
\(810\) 2.67984e10i 0.0622543i
\(811\) 1.52760e11i 0.353123i 0.984290 + 0.176562i \(0.0564975\pi\)
−0.984290 + 0.176562i \(0.943502\pi\)
\(812\) −1.46752e10 2.38776e10i −0.0337567 0.0549245i
\(813\) 4.46158e11 1.02124
\(814\) 3.27946e10 0.0746973
\(815\) 2.43903e11i 0.552823i
\(816\) −2.68989e10 −0.0606699
\(817\) 6.49275e10i 0.145727i
\(818\) 2.04387e11i 0.456500i
\(819\) 2.66572e11 1.63835e11i 0.592487 0.364143i
\(820\) −3.00782e11 −0.665268
\(821\) 6.73481e11 1.48236 0.741178 0.671309i \(-0.234268\pi\)
0.741178 + 0.671309i \(0.234268\pi\)
\(822\) 1.27862e11i 0.280062i
\(823\) −8.00004e11 −1.74379 −0.871893 0.489697i \(-0.837107\pi\)
−0.871893 + 0.489697i \(0.837107\pi\)
\(824\) 3.05106e11i 0.661824i
\(825\) 1.95830e11i 0.422731i
\(826\) −9.29034e10 + 5.70985e10i −0.199577 + 0.122660i
\(827\) −1.04890e11 −0.224239 −0.112119 0.993695i \(-0.535764\pi\)
−0.112119 + 0.993695i \(0.535764\pi\)
\(828\) −2.59904e11 −0.552958
\(829\) 4.44519e11i 0.941179i −0.882352 0.470589i \(-0.844041\pi\)
0.882352 0.470589i \(-0.155959\pi\)
\(830\) −5.84269e10 −0.123112
\(831\) 2.62852e11i 0.551197i
\(832\) 2.01648e11i 0.420824i
\(833\) −6.10650e10 3.09133e10i −0.126827 0.0642045i
\(834\) 1.57931e11 0.326441
\(835\) −3.14216e11 −0.646373
\(836\) 7.34805e10i 0.150434i
\(837\) 2.69348e11 0.548797
\(838\) 1.91621e11i 0.388569i
\(839\) 3.50412e10i 0.0707181i 0.999375 + 0.0353591i \(0.0112575\pi\)
−0.999375 + 0.0353591i \(0.988743\pi\)
\(840\) 1.94706e11 + 3.16801e11i 0.391077 + 0.636310i
\(841\) −4.97556e11 −0.994621
\(842\) 4.96113e10 0.0987035
\(843\) 2.33947e11i 0.463241i
\(844\) 6.03147e11 1.18865
\(845\) 4.29249e11i 0.841943i
\(846\) 1.16358e11i 0.227151i
\(847\) 2.42661e11 + 3.94828e11i 0.471484 + 0.767139i
\(848\) 2.92146e11 0.564959
\(849\) −2.60186e11 −0.500787
\(850\) 5.28012e10i 0.101151i
\(851\) 3.93166e11 0.749649
\(852\) 3.57420e11i 0.678298i
\(853\) 3.49404e11i 0.659982i 0.943984 + 0.329991i \(0.107046\pi\)
−0.943984 + 0.329991i \(0.892954\pi\)
\(854\) −2.21158e11 + 1.35924e11i −0.415787 + 0.255543i
\(855\) −2.88939e11 −0.540682
\(856\) −5.08957e10 −0.0947950
\(857\) 4.87905e11i 0.904507i 0.891889 + 0.452254i \(0.149380\pi\)
−0.891889 + 0.452254i \(0.850620\pi\)
\(858\) −4.74156e10 −0.0874928
\(859\) 2.43546e11i 0.447309i −0.974668 0.223655i \(-0.928201\pi\)
0.974668 0.223655i \(-0.0717988\pi\)
\(860\) 2.25477e11i 0.412200i
\(861\) −8.17116e10 1.32951e11i −0.148686 0.241924i
\(862\) −4.80516e10 −0.0870319
\(863\) −9.85522e11 −1.77674 −0.888369 0.459130i \(-0.848161\pi\)
−0.888369 + 0.459130i \(0.848161\pi\)
\(864\) 5.04653e11i 0.905603i
\(865\) 1.91264e11 0.341640
\(866\) 5.57747e10i 0.0991667i
\(867\) 3.62531e11i 0.641607i
\(868\) 2.26754e11 1.39363e11i 0.399462 0.245510i
\(869\) 2.88244e10 0.0505454
\(870\) −1.67006e10 −0.0291511
\(871\) 8.82705e11i 1.53371i
\(872\) −6.70965e11 −1.16047
\(873\) 1.78259e10i 0.0306899i
\(874\) 1.21220e11i 0.207744i
\(875\) −9.11638e11 + 5.60293e11i −1.55521 + 0.955836i
\(876\) −3.93976e11 −0.669041
\(877\) 6.65633e11 1.12522 0.562609 0.826723i \(-0.309798\pi\)
0.562609 + 0.826723i \(0.309798\pi\)
\(878\) 1.08724e11i 0.182956i
\(879\) 5.26038e11 0.881173
\(880\) 2.15234e11i 0.358905i
\(881\) 6.98615e11i 1.15967i −0.814734 0.579835i \(-0.803117\pi\)
0.814734 0.579835i \(-0.196883\pi\)
\(882\) 5.42976e10 1.07257e11i 0.0897235 0.177236i
\(883\) 7.15472e11 1.17693 0.588464 0.808523i \(-0.299733\pi\)
0.588464 + 0.808523i \(0.299733\pi\)
\(884\) 9.29090e10 0.152142
\(885\) 4.72221e11i 0.769789i
\(886\) 3.42990e11 0.556604
\(887\) 1.12134e12i 1.81152i 0.423787 + 0.905762i \(0.360701\pi\)
−0.423787 + 0.905762i \(0.639299\pi\)
\(888\) 1.81131e11i 0.291301i
\(889\) −1.44023e11 2.34336e11i −0.230582 0.375174i
\(890\) 5.97474e11 0.952268
\(891\) 2.03955e10 0.0323611
\(892\) 3.57939e11i 0.565391i
\(893\) 3.94392e11 0.620187
\(894\) 1.24785e10i 0.0195349i
\(895\) 1.59904e12i 2.49211i
\(896\) −3.37609e11 5.49315e11i −0.523821 0.852294i
\(897\) −5.68454e11 −0.878063
\(898\) −2.34203e11 −0.360153
\(899\) 2.55522e10i 0.0391191i
\(900\) 6.73987e11 1.02726
\(901\) 8.12057e10i 0.123222i
\(902\) 3.14996e10i 0.0475859i
\(903\) −9.96644e10 + 6.12538e10i −0.149896 + 0.0921260i
\(904\) 5.07008e11 0.759173
\(905\) −1.60572e11 −0.239373
\(906\) 3.37694e10i 0.0501199i
\(907\) −5.76730e10 −0.0852203 −0.0426102 0.999092i \(-0.513567\pi\)
−0.0426102 + 0.999092i \(0.513567\pi\)
\(908\) 7.07514e11i 1.04086i
\(909\) 3.61989e11i 0.530200i
\(910\) −2.65363e11 4.31766e11i −0.386968 0.629626i
\(911\) 6.14760e11 0.892548 0.446274 0.894896i \(-0.352751\pi\)
0.446274 + 0.894896i \(0.352751\pi\)
\(912\) −1.60141e11 −0.231485
\(913\) 4.44670e10i 0.0639963i
\(914\) −1.96166e11 −0.281085
\(915\) 1.12413e12i 1.60373i
\(916\) 7.06442e11i 1.00345i
\(917\) −4.83290e11 + 2.97030e11i −0.683488 + 0.420072i
\(918\) 3.61249e10 0.0508669
\(919\) 3.09399e11 0.433768 0.216884 0.976197i \(-0.430411\pi\)
0.216884 + 0.976197i \(0.430411\pi\)
\(920\) 8.99857e11i 1.25609i
\(921\) 6.54698e11 0.909919
\(922\) 3.53539e11i 0.489231i
\(923\) 1.04128e12i 1.43470i
\(924\) 1.12793e11 6.93228e10i 0.154737 0.0951017i
\(925\) −1.01956e12 −1.39267
\(926\) 1.09852e11 0.149404
\(927\) 4.27153e11i 0.578448i
\(928\) 4.78749e10 0.0645529
\(929\) 4.52187e11i 0.607093i 0.952817 + 0.303547i \(0.0981709\pi\)
−0.952817 + 0.303547i \(0.901829\pi\)
\(930\) 1.58597e11i 0.212014i
\(931\) −3.63547e11 1.84040e11i −0.483907 0.244971i
\(932\) 4.83051e10 0.0640220
\(933\) −8.22664e11 −1.08567
\(934\) 1.40302e11i 0.184364i
\(935\) 5.98269e10 0.0782798
\(936\) 3.48835e11i 0.454482i
\(937\) 8.14555e11i 1.05672i 0.849019 + 0.528362i \(0.177194\pi\)
−0.849019 + 0.528362i \(0.822806\pi\)
\(938\) 1.77582e11 + 2.88938e11i 0.229397 + 0.373245i
\(939\) −1.84922e10 −0.0237862
\(940\) −1.36962e12 −1.75424
\(941\) 1.39547e12i 1.77977i −0.456188 0.889883i \(-0.650786\pi\)
0.456188 0.889883i \(-0.349214\pi\)
\(942\) −1.28127e11 −0.162719
\(943\) 3.77640e11i 0.477564i
\(944\) 3.48616e11i 0.438995i
\(945\) 7.49827e11 + 1.22002e12i 0.940230 + 1.52982i
\(946\) −2.36132e10 −0.0294842
\(947\) 5.69289e11 0.707837 0.353918 0.935276i \(-0.384849\pi\)
0.353918 + 0.935276i \(0.384849\pi\)
\(948\) 7.44775e10i 0.0922129i
\(949\) 1.14778e12 1.41512
\(950\) 3.14349e11i 0.385938i
\(951\) 8.88789e11i 1.08662i
\(952\) 6.50092e10 3.99547e10i 0.0791456 0.0486429i
\(953\) 1.65586e11 0.200748 0.100374 0.994950i \(-0.467996\pi\)
0.100374 + 0.994950i \(0.467996\pi\)
\(954\) −1.42634e11 −0.172198
\(955\) 1.03468e12i 1.24393i
\(956\) −1.04784e12 −1.25448
\(957\) 1.27103e10i 0.0151534i
\(958\) 4.78564e11i 0.568169i
\(959\) −5.44609e11 8.86119e11i −0.643888 1.04765i
\(960\) 3.35503e11 0.395013
\(961\) 6.10235e11 0.715489
\(962\) 2.46863e11i 0.288241i
\(963\) −7.12546e10 −0.0828529
\(964\) 1.08841e12i 1.26033i
\(965\) 1.54882e12i 1.78604i
\(966\) −1.86074e11 + 1.14361e11i −0.213686 + 0.131332i
\(967\) −8.88485e11 −1.01612 −0.508059 0.861322i \(-0.669637\pi\)
−0.508059 + 0.861322i \(0.669637\pi\)
\(968\) −5.16670e11 −0.588453
\(969\) 4.45132e10i 0.0504886i
\(970\) 2.88726e10 0.0326136
\(971\) 1.28823e12i 1.44916i −0.689191 0.724580i \(-0.742034\pi\)
0.689191 0.724580i \(-0.257966\pi\)
\(972\) 7.54605e11i 0.845385i
\(973\) 1.09451e12 6.72686e11i 1.22115 0.750517i
\(974\) −1.94664e11 −0.216297
\(975\) 1.47412e12 1.63123
\(976\) 8.29886e11i 0.914575i
\(977\) −4.18373e11 −0.459183 −0.229592 0.973287i \(-0.573739\pi\)
−0.229592 + 0.973287i \(0.573739\pi\)
\(978\) 6.59985e10i 0.0721404i
\(979\) 4.54720e11i 0.495009i
\(980\) 1.26250e12 + 6.39125e11i 1.36876 + 0.692917i
\(981\) −9.39360e11 −1.01428
\(982\) 6.25054e11 0.672158
\(983\) 7.99049e11i 0.855774i −0.903832 0.427887i \(-0.859258\pi\)
0.903832 0.427887i \(-0.140742\pi\)
\(984\) 1.73979e11 0.185573
\(985\) 2.02149e12i 2.14746i
\(986\) 3.42705e9i 0.00362588i
\(987\) −3.72077e11 6.05396e11i −0.392070 0.637927i
\(988\) 5.53128e11 0.580494
\(989\) −2.83092e11 −0.295898
\(990\) 1.05083e11i 0.109393i
\(991\) −1.46398e12 −1.51789 −0.758944 0.651155i \(-0.774285\pi\)
−0.758944 + 0.651155i \(0.774285\pi\)
\(992\) 4.54644e11i 0.469488i
\(993\) 2.93854e11i 0.302228i
\(994\) 2.09484e11 + 3.40846e11i 0.214588 + 0.349150i
\(995\) 2.62940e12 2.68265
\(996\) −1.14895e11 −0.116752
\(997\) 3.58073e11i 0.362402i 0.983446 + 0.181201i \(0.0579985\pi\)
−0.983446 + 0.181201i \(0.942001\pi\)
\(998\) −1.50423e11 −0.151633
\(999\) 6.97552e11i 0.700349i
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 7.9.b.b.6.2 yes 4
3.2 odd 2 63.9.d.c.55.3 4
4.3 odd 2 112.9.c.b.97.2 4
5.2 odd 4 175.9.c.c.174.4 8
5.3 odd 4 175.9.c.c.174.5 8
5.4 even 2 175.9.d.e.76.3 4
7.2 even 3 49.9.d.b.31.3 8
7.3 odd 6 49.9.d.b.19.3 8
7.4 even 3 49.9.d.b.19.4 8
7.5 odd 6 49.9.d.b.31.4 8
7.6 odd 2 inner 7.9.b.b.6.1 4
21.20 even 2 63.9.d.c.55.4 4
28.27 even 2 112.9.c.b.97.3 4
35.13 even 4 175.9.c.c.174.6 8
35.27 even 4 175.9.c.c.174.3 8
35.34 odd 2 175.9.d.e.76.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.9.b.b.6.1 4 7.6 odd 2 inner
7.9.b.b.6.2 yes 4 1.1 even 1 trivial
49.9.d.b.19.3 8 7.3 odd 6
49.9.d.b.19.4 8 7.4 even 3
49.9.d.b.31.3 8 7.2 even 3
49.9.d.b.31.4 8 7.5 odd 6
63.9.d.c.55.3 4 3.2 odd 2
63.9.d.c.55.4 4 21.20 even 2
112.9.c.b.97.2 4 4.3 odd 2
112.9.c.b.97.3 4 28.27 even 2
175.9.c.c.174.3 8 35.27 even 4
175.9.c.c.174.4 8 5.2 odd 4
175.9.c.c.174.5 8 5.3 odd 4
175.9.c.c.174.6 8 35.13 even 4
175.9.d.e.76.3 4 5.4 even 2
175.9.d.e.76.4 4 35.34 odd 2