Properties

Label 4.15.b.a.3.3
Level $4$
Weight $15$
Character 4.3
Analytic conductor $4.973$
Analytic rank $0$
Dimension $6$
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] = [4,15,Mod(3,4)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4.3");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 4.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: \(4.97315872608\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 88x^{4} - 1824x^{3} + 325632x^{2} + 21572352x + 982333440 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{30}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.3
Root \(-4.07037 - 30.9656i\) of defining polynomial
Character \(\chi\) \(=\) 4.3
Dual form 4.15.b.a.3.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-32.2815 - 123.862i) q^{2} +2369.41i q^{3} +(-14299.8 + 7996.93i) q^{4} +113343. q^{5} +(293481. - 76488.1i) q^{6} +697667. i q^{7} +(1.45214e6 + 1.51306e6i) q^{8} -831139. q^{9} +O(q^{10})\) \(q+(-32.2815 - 123.862i) q^{2} +2369.41i q^{3} +(-14299.8 + 7996.93i) q^{4} +113343. q^{5} +(293481. - 76488.1i) q^{6} +697667. i q^{7} +(1.45214e6 + 1.51306e6i) q^{8} -831139. q^{9} +(-3.65890e6 - 1.40390e7i) q^{10} +2.00895e7i q^{11} +(-1.89480e7 - 3.38821e7i) q^{12} -6.13899e7 q^{13} +(8.64148e7 - 2.25217e7i) q^{14} +2.68557e8i q^{15} +(1.40534e8 - 2.28709e8i) q^{16} +3.44542e8 q^{17} +(2.68304e7 + 1.02947e8i) q^{18} -3.17454e8i q^{19} +(-1.62079e9 + 9.06399e8i) q^{20} -1.65306e9 q^{21} +(2.48833e9 - 6.48519e8i) q^{22} -5.79264e9i q^{23} +(-3.58505e9 + 3.44071e9i) q^{24} +6.74323e9 q^{25} +(1.98176e9 + 7.60390e9i) q^{26} +9.36351e9i q^{27} +(-5.57919e9 - 9.97651e9i) q^{28} -3.72362e9 q^{29} +(3.32642e10 - 8.66943e9i) q^{30} +8.57575e8i q^{31} +(-3.28651e10 - 1.00238e10i) q^{32} -4.76003e10 q^{33} +(-1.11223e10 - 4.26758e10i) q^{34} +7.90760e10i q^{35} +(1.18851e10 - 6.64656e9i) q^{36} +9.83497e10 q^{37} +(-3.93207e10 + 1.02479e10i) q^{38} -1.45458e11i q^{39} +(1.64590e11 + 1.71495e11i) q^{40} -8.26198e9 q^{41} +(5.33632e10 + 2.04752e11i) q^{42} -1.16363e11i q^{43} +(-1.60654e11 - 2.87276e11i) q^{44} -9.42042e10 q^{45} +(-7.17490e11 + 1.86995e11i) q^{46} -3.17697e11i q^{47} +(5.41906e11 + 3.32982e11i) q^{48} +1.91484e11 q^{49} +(-2.17681e11 - 8.35233e11i) q^{50} +8.16362e11i q^{51} +(8.77864e11 - 4.90930e11i) q^{52} -6.36538e11 q^{53} +(1.15979e12 - 3.02268e11i) q^{54} +2.27701e12i q^{55} +(-1.05561e12 + 1.01311e12i) q^{56} +7.52180e11 q^{57} +(1.20204e11 + 4.61217e11i) q^{58} -2.87412e12i q^{59} +(-2.14763e12 - 3.84032e12i) q^{60} +8.45647e11 q^{61} +(1.06221e11 - 2.76838e10i) q^{62} -5.79859e11i q^{63} +(-1.80638e11 + 4.39434e12i) q^{64} -6.95814e12 q^{65} +(1.53661e12 + 5.89589e12i) q^{66} -6.82161e12i q^{67} +(-4.92689e12 + 2.75528e12i) q^{68} +1.37251e13 q^{69} +(9.79455e12 - 2.55269e12i) q^{70} +3.28972e12i q^{71} +(-1.20693e12 - 1.25756e12i) q^{72} +6.25122e10 q^{73} +(-3.17487e12 - 1.21818e13i) q^{74} +1.59775e13i q^{75} +(2.53866e12 + 4.53954e12i) q^{76} -1.40158e13 q^{77} +(-1.80168e13 + 4.69560e12i) q^{78} -1.05071e13i q^{79} +(1.59286e13 - 2.59227e13i) q^{80} -2.61613e13 q^{81} +(2.66709e11 + 1.02335e12i) q^{82} +2.38301e13i q^{83} +(2.36384e13 - 1.32194e13i) q^{84} +3.90516e13 q^{85} +(-1.44130e13 + 3.75636e12i) q^{86} -8.82279e12i q^{87} +(-3.03966e13 + 2.91727e13i) q^{88} +3.23837e13 q^{89} +(3.04105e12 + 1.16684e13i) q^{90} -4.28297e13i q^{91} +(4.63233e13 + 8.28336e13i) q^{92} -2.03195e12 q^{93} +(-3.93507e13 + 1.02557e13i) q^{94} -3.59814e13i q^{95} +(2.37505e13 - 7.78709e13i) q^{96} -1.34788e14 q^{97} +(-6.18138e12 - 2.37176e13i) q^{98} -1.66972e13i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 92 q^{2} - 1392 q^{4} + 8060 q^{5} + 50784 q^{6} + 446272 q^{8} - 2998698 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 92 q^{2} - 1392 q^{4} + 8060 q^{5} + 50784 q^{6} + 446272 q^{8} - 2998698 q^{9} + 5796840 q^{10} + 193920 q^{12} - 80775396 q^{13} + 175232064 q^{14} - 353013504 q^{16} - 120131764 q^{17} + 1599402372 q^{18} - 5047343200 q^{20} + 1226658048 q^{21} + 9916985760 q^{22} - 24092176896 q^{24} + 3942973410 q^{25} + 39549467048 q^{26} - 65094731520 q^{28} - 8035796644 q^{29} + 99698873280 q^{30} - 85711465472 q^{32} - 37769804160 q^{33} + 98089165512 q^{34} - 27478990320 q^{36} + 31334118396 q^{37} - 165268841760 q^{38} + 435607171200 q^{40} + 83362750892 q^{41} - 830203906560 q^{42} + 915657452160 q^{44} + 271078769820 q^{45} - 1712365889856 q^{46} + 2292961843200 q^{48} - 551978693658 q^{49} - 1639579094580 q^{50} + 1057159118496 q^{52} + 76712275004 q^{53} + 445471858368 q^{54} - 560223046656 q^{56} - 2647253865600 q^{57} + 4483777382184 q^{58} - 9544013748480 q^{60} + 6210000787932 q^{61} + 10375644284160 q^{62} - 14398852657152 q^{64} - 7189912943720 q^{65} + 15071210499840 q^{66} - 18507298307296 q^{68} + 19348372347648 q^{69} + 12679529923200 q^{70} - 5286233111232 q^{72} - 29882649313236 q^{73} - 1536652566808 q^{74} + 21457134000000 q^{76} + 37339673521920 q^{77} - 29727224255040 q^{78} + 57843429624320 q^{80} - 98651978873946 q^{81} - 71900577251064 q^{82} + 102961968764928 q^{84} + 151199882653560 q^{85} - 100164269733216 q^{86} + 51557990330880 q^{88} - 180966014731924 q^{89} - 84934442792280 q^{90} + 82241452266240 q^{92} + 295002300748800 q^{93} - 40381697410176 q^{94} - 82703070928896 q^{96} - 345459072299124 q^{97} + 121406102961892 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −32.2815 123.862i −0.252199 0.967675i
\(3\) 2369.41i 1.08341i 0.840570 + 0.541703i \(0.182220\pi\)
−0.840570 + 0.541703i \(0.817780\pi\)
\(4\) −14299.8 + 7996.93i −0.872791 + 0.488094i
\(5\) 113343. 1.45080 0.725398 0.688329i \(-0.241656\pi\)
0.725398 + 0.688329i \(0.241656\pi\)
\(6\) 293481. 76488.1i 1.04839 0.273234i
\(7\) 697667.i 0.847153i 0.905860 + 0.423577i \(0.139226\pi\)
−0.905860 + 0.423577i \(0.860774\pi\)
\(8\) 1.45214e6 + 1.51306e6i 0.692433 + 0.721482i
\(9\) −831139. −0.173771
\(10\) −3.65890e6 1.40390e7i −0.365890 1.40390i
\(11\) 2.00895e7i 1.03091i 0.856917 + 0.515454i \(0.172377\pi\)
−0.856917 + 0.515454i \(0.827623\pi\)
\(12\) −1.89480e7 3.38821e7i −0.528804 0.945588i
\(13\) −6.13899e7 −0.978348 −0.489174 0.872186i \(-0.662702\pi\)
−0.489174 + 0.872186i \(0.662702\pi\)
\(14\) 8.64148e7 2.25217e7i 0.819769 0.213651i
\(15\) 2.68557e8i 1.57180i
\(16\) 1.40534e8 2.28709e8i 0.523529 0.852008i
\(17\) 3.44542e8 0.839653 0.419827 0.907604i \(-0.362091\pi\)
0.419827 + 0.907604i \(0.362091\pi\)
\(18\) 2.68304e7 + 1.02947e8i 0.0438248 + 0.168154i
\(19\) 3.17454e8i 0.355145i −0.984108 0.177573i \(-0.943176\pi\)
0.984108 0.177573i \(-0.0568245\pi\)
\(20\) −1.62079e9 + 9.06399e8i −1.26624 + 0.708125i
\(21\) −1.65306e9 −0.917812
\(22\) 2.48833e9 6.48519e8i 0.997585 0.259994i
\(23\) 5.79264e9i 1.70130i −0.525731 0.850651i \(-0.676208\pi\)
0.525731 0.850651i \(-0.323792\pi\)
\(24\) −3.58505e9 + 3.44071e9i −0.781659 + 0.750187i
\(25\) 6.74323e9 1.10481
\(26\) 1.98176e9 + 7.60390e9i 0.246738 + 0.946723i
\(27\) 9.36351e9i 0.895143i
\(28\) −5.57919e9 9.97651e9i −0.413490 0.739388i
\(29\) −3.72362e9 −0.215864 −0.107932 0.994158i \(-0.534423\pi\)
−0.107932 + 0.994158i \(0.534423\pi\)
\(30\) 3.32642e10 8.66943e9i 1.52100 0.396407i
\(31\) 8.57575e8i 0.0311702i 0.999879 + 0.0155851i \(0.00496110\pi\)
−0.999879 + 0.0155851i \(0.995039\pi\)
\(32\) −3.28651e10 1.00238e10i −0.956500 0.291731i
\(33\) −4.76003e10 −1.11689
\(34\) −1.11223e10 4.26758e10i −0.211760 0.812512i
\(35\) 7.90760e10i 1.22905i
\(36\) 1.18851e10 6.64656e9i 0.151665 0.0848163i
\(37\) 9.83497e10 1.03600 0.518002 0.855380i \(-0.326676\pi\)
0.518002 + 0.855380i \(0.326676\pi\)
\(38\) −3.93207e10 + 1.02479e10i −0.343665 + 0.0895673i
\(39\) 1.45458e11i 1.05995i
\(40\) 1.64590e11 + 1.71495e11i 1.00458 + 1.04672i
\(41\) −8.26198e9 −0.0424226 −0.0212113 0.999775i \(-0.506752\pi\)
−0.0212113 + 0.999775i \(0.506752\pi\)
\(42\) 5.33632e10 + 2.04752e11i 0.231471 + 0.888144i
\(43\) 1.16363e11i 0.428089i −0.976824 0.214045i \(-0.931336\pi\)
0.976824 0.214045i \(-0.0686638\pi\)
\(44\) −1.60654e11 2.87276e11i −0.503180 0.899768i
\(45\) −9.42042e10 −0.252106
\(46\) −7.17490e11 + 1.86995e11i −1.64631 + 0.429067i
\(47\) 3.17697e11i 0.627087i −0.949574 0.313543i \(-0.898484\pi\)
0.949574 0.313543i \(-0.101516\pi\)
\(48\) 5.41906e11 + 3.32982e11i 0.923071 + 0.567195i
\(49\) 1.91484e11 0.282332
\(50\) −2.17681e11 8.35233e11i −0.278632 1.06910i
\(51\) 8.16362e11i 0.909686i
\(52\) 8.77864e11 4.90930e11i 0.853894 0.477525i
\(53\) −6.36538e11 −0.541867 −0.270934 0.962598i \(-0.587332\pi\)
−0.270934 + 0.962598i \(0.587332\pi\)
\(54\) 1.15979e12 3.02268e11i 0.866208 0.225754i
\(55\) 2.27701e12i 1.49564i
\(56\) −1.05561e12 + 1.01311e12i −0.611206 + 0.586597i
\(57\) 7.52180e11 0.384767
\(58\) 1.20204e11 + 4.61217e11i 0.0544406 + 0.208886i
\(59\) 2.87412e12i 1.15489i −0.816429 0.577445i \(-0.804050\pi\)
0.816429 0.577445i \(-0.195950\pi\)
\(60\) −2.14763e12 3.84032e12i −0.767187 1.37186i
\(61\) 8.45647e11 0.269079 0.134540 0.990908i \(-0.457044\pi\)
0.134540 + 0.990908i \(0.457044\pi\)
\(62\) 1.06221e11 2.76838e10i 0.0301627 0.00786110i
\(63\) 5.79859e11i 0.147210i
\(64\) −1.80638e11 + 4.39434e12i −0.0410723 + 0.999156i
\(65\) −6.95814e12 −1.41938
\(66\) 1.53661e12 + 5.89589e12i 0.281680 + 1.08079i
\(67\) 6.82161e12i 1.12555i −0.826611 0.562773i \(-0.809734\pi\)
0.826611 0.562773i \(-0.190266\pi\)
\(68\) −4.92689e12 + 2.75528e12i −0.732842 + 0.409829i
\(69\) 1.37251e13 1.84320
\(70\) 9.79455e12 2.55269e12i 1.18932 0.309964i
\(71\) 3.28972e12i 0.361702i 0.983511 + 0.180851i \(0.0578851\pi\)
−0.983511 + 0.180851i \(0.942115\pi\)
\(72\) −1.20693e12 1.25756e12i −0.120325 0.125372i
\(73\) 6.25122e10 0.00565854 0.00282927 0.999996i \(-0.499099\pi\)
0.00282927 + 0.999996i \(0.499099\pi\)
\(74\) −3.17487e12 1.21818e13i −0.261279 1.00251i
\(75\) 1.59775e13i 1.19696i
\(76\) 2.53866e12 + 4.53954e12i 0.173344 + 0.309968i
\(77\) −1.40158e13 −0.873338
\(78\) −1.80168e13 + 4.69560e12i −1.02569 + 0.267318i
\(79\) 1.05071e13i 0.547135i −0.961853 0.273568i \(-0.911796\pi\)
0.961853 0.273568i \(-0.0882037\pi\)
\(80\) 1.59286e13 2.59227e13i 0.759535 1.23609i
\(81\) −2.61613e13 −1.14357
\(82\) 2.66709e11 + 1.02335e12i 0.0106989 + 0.0410513i
\(83\) 2.38301e13i 0.878171i 0.898445 + 0.439086i \(0.144698\pi\)
−0.898445 + 0.439086i \(0.855302\pi\)
\(84\) 2.36384e13 1.32194e13i 0.801058 0.447978i
\(85\) 3.90516e13 1.21817
\(86\) −1.44130e13 + 3.75636e12i −0.414251 + 0.107964i
\(87\) 8.82279e12i 0.233868i
\(88\) −3.03966e13 + 2.91727e13i −0.743782 + 0.713836i
\(89\) 3.23837e13 0.732143 0.366071 0.930587i \(-0.380703\pi\)
0.366071 + 0.930587i \(0.380703\pi\)
\(90\) 3.04105e12 + 1.16684e13i 0.0635808 + 0.243957i
\(91\) 4.28297e13i 0.828811i
\(92\) 4.63233e13 + 8.28336e13i 0.830395 + 1.48488i
\(93\) −2.03195e12 −0.0337701
\(94\) −3.93507e13 + 1.02557e13i −0.606816 + 0.158151i
\(95\) 3.59814e13i 0.515243i
\(96\) 2.37505e13 7.78709e13i 0.316063 1.03628i
\(97\) −1.34788e14 −1.66820 −0.834101 0.551612i \(-0.814013\pi\)
−0.834101 + 0.551612i \(0.814013\pi\)
\(98\) −6.18138e12 2.37176e13i −0.0712037 0.273205i
\(99\) 1.66972e13i 0.179142i
\(100\) −9.64269e13 + 5.39251e13i −0.964269 + 0.539251i
\(101\) 1.79994e14 1.67884 0.839419 0.543485i \(-0.182896\pi\)
0.839419 + 0.543485i \(0.182896\pi\)
\(102\) 1.01117e14 2.63534e13i 0.880281 0.229422i
\(103\) 5.09045e12i 0.0413900i 0.999786 + 0.0206950i \(0.00658790\pi\)
−0.999786 + 0.0206950i \(0.993412\pi\)
\(104\) −8.91466e13 9.28864e13i −0.677441 0.705860i
\(105\) −1.87364e14 −1.33156
\(106\) 2.05484e13 + 7.88431e13i 0.136658 + 0.524352i
\(107\) 2.79523e14i 1.74073i 0.492407 + 0.870365i \(0.336117\pi\)
−0.492407 + 0.870365i \(0.663883\pi\)
\(108\) −7.48793e13 1.33896e14i −0.436913 0.781273i
\(109\) 2.45434e14 1.34261 0.671305 0.741182i \(-0.265734\pi\)
0.671305 + 0.741182i \(0.265734\pi\)
\(110\) 2.82036e14 7.35054e13i 1.44729 0.377199i
\(111\) 2.33031e14i 1.12241i
\(112\) 1.59563e14 + 9.80458e13i 0.721781 + 0.443509i
\(113\) −2.38170e14 −1.01237 −0.506184 0.862426i \(-0.668944\pi\)
−0.506184 + 0.862426i \(0.668944\pi\)
\(114\) −2.42815e13 9.31668e13i −0.0970378 0.372329i
\(115\) 6.56558e14i 2.46824i
\(116\) 5.32471e13 2.97775e13i 0.188404 0.105362i
\(117\) 5.10236e13 0.170008
\(118\) −3.55995e14 + 9.27808e13i −1.11756 + 0.291262i
\(119\) 2.40376e14i 0.711315i
\(120\) −4.06343e14 + 3.89982e14i −1.13403 + 1.08837i
\(121\) −2.38380e13 −0.0627730
\(122\) −2.72987e13 1.04744e14i −0.0678616 0.260381i
\(123\) 1.95760e13i 0.0459609i
\(124\) −6.85796e12 1.22632e13i −0.0152140 0.0272051i
\(125\) 7.25076e13 0.152060
\(126\) −7.18227e13 + 1.87187e13i −0.142452 + 0.0371263i
\(127\) 9.50007e14i 1.78279i −0.453225 0.891396i \(-0.649727\pi\)
0.453225 0.891396i \(-0.350273\pi\)
\(128\) 5.50124e14 1.19481e14i 0.977217 0.212242i
\(129\) 2.75711e14 0.463795
\(130\) 2.24619e14 + 8.61853e14i 0.357967 + 1.37350i
\(131\) 3.13334e14i 0.473270i 0.971599 + 0.236635i \(0.0760445\pi\)
−0.971599 + 0.236635i \(0.923955\pi\)
\(132\) 6.80675e14 3.80656e14i 0.974815 0.545149i
\(133\) 2.21477e14 0.300862
\(134\) −8.44942e14 + 2.20212e14i −1.08916 + 0.283862i
\(135\) 1.06129e15i 1.29867i
\(136\) 5.00323e14 + 5.21312e14i 0.581404 + 0.605794i
\(137\) −1.05928e15 −1.16941 −0.584704 0.811247i \(-0.698789\pi\)
−0.584704 + 0.811247i \(0.698789\pi\)
\(138\) −4.43068e14 1.70003e15i −0.464854 1.78362i
\(139\) 1.02367e15i 1.02108i 0.859855 + 0.510538i \(0.170554\pi\)
−0.859855 + 0.510538i \(0.829446\pi\)
\(140\) −6.32365e14 1.13077e15i −0.599890 1.07270i
\(141\) 7.52754e14 0.679390
\(142\) 4.07473e14 1.06197e14i 0.350010 0.0912208i
\(143\) 1.23329e15i 1.00859i
\(144\) −1.16803e14 + 1.90089e14i −0.0909740 + 0.148054i
\(145\) −4.22048e14 −0.313174
\(146\) −2.01799e12 7.74291e12i −0.00142708 0.00547563i
\(147\) 4.53704e14i 0.305880i
\(148\) −1.40638e15 + 7.86495e14i −0.904215 + 0.505667i
\(149\) −9.53793e14 −0.584993 −0.292496 0.956267i \(-0.594486\pi\)
−0.292496 + 0.956267i \(0.594486\pi\)
\(150\) 1.97901e15 5.15777e14i 1.15827 0.301872i
\(151\) 2.50228e14i 0.139797i −0.997554 0.0698984i \(-0.977732\pi\)
0.997554 0.0698984i \(-0.0222675\pi\)
\(152\) 4.80326e14 4.60987e14i 0.256231 0.245914i
\(153\) −2.86363e14 −0.145907
\(154\) 4.52450e14 + 1.73603e15i 0.220255 + 0.845107i
\(155\) 9.72005e13i 0.0452217i
\(156\) 1.16322e15 + 2.08002e15i 0.517354 + 0.925114i
\(157\) 2.72276e15 1.15801 0.579005 0.815324i \(-0.303441\pi\)
0.579005 + 0.815324i \(0.303441\pi\)
\(158\) −1.30144e15 + 3.39186e14i −0.529449 + 0.137987i
\(159\) 1.50822e15i 0.587063i
\(160\) −3.72505e15 1.13613e15i −1.38769 0.423242i
\(161\) 4.04133e15 1.44126
\(162\) 8.44526e14 + 3.24040e15i 0.288408 + 1.10661i
\(163\) 4.12649e15i 1.34979i −0.737912 0.674897i \(-0.764188\pi\)
0.737912 0.674897i \(-0.235812\pi\)
\(164\) 1.18145e14 6.60705e13i 0.0370261 0.0207062i
\(165\) −5.39518e15 −1.62039
\(166\) 2.95166e15 7.69271e14i 0.849785 0.221474i
\(167\) 3.19518e15i 0.882024i 0.897501 + 0.441012i \(0.145380\pi\)
−0.897501 + 0.441012i \(0.854620\pi\)
\(168\) −2.40047e15 2.50117e15i −0.635523 0.662184i
\(169\) −1.68658e14 −0.0428351
\(170\) −1.26064e15 4.83703e15i −0.307220 1.17879i
\(171\) 2.63849e14i 0.0617138i
\(172\) 9.30543e14 + 1.66396e15i 0.208948 + 0.373632i
\(173\) −7.49126e15 −1.61522 −0.807611 0.589716i \(-0.799240\pi\)
−0.807611 + 0.589716i \(0.799240\pi\)
\(174\) −1.09281e15 + 2.84813e14i −0.226309 + 0.0589814i
\(175\) 4.70453e15i 0.935944i
\(176\) 4.59465e15 + 2.82325e15i 0.878342 + 0.539711i
\(177\) 6.80997e15 1.25122
\(178\) −1.04539e15 4.01112e15i −0.184646 0.708476i
\(179\) 1.06547e15i 0.180955i 0.995899 + 0.0904773i \(0.0288393\pi\)
−0.995899 + 0.0904773i \(0.971161\pi\)
\(180\) 1.34710e15 7.53344e14i 0.220036 0.123051i
\(181\) 7.52697e14 0.118269 0.0591344 0.998250i \(-0.481166\pi\)
0.0591344 + 0.998250i \(0.481166\pi\)
\(182\) −5.30499e15 + 1.38261e15i −0.802020 + 0.209025i
\(183\) 2.00369e15i 0.291522i
\(184\) 8.76459e15 8.41171e15i 1.22746 1.17804i
\(185\) 1.11473e16 1.50303
\(186\) 6.55943e13 + 2.51682e14i 0.00851678 + 0.0326785i
\(187\) 6.92168e15i 0.865606i
\(188\) 2.54060e15 + 4.54300e15i 0.306077 + 0.547316i
\(189\) −6.53261e15 −0.758323
\(190\) −4.45674e15 + 1.16153e15i −0.498588 + 0.129944i
\(191\) 9.65360e15i 1.04101i −0.853858 0.520506i \(-0.825743\pi\)
0.853858 0.520506i \(-0.174257\pi\)
\(192\) −1.04120e16 4.28005e14i −1.08249 0.0444980i
\(193\) −1.80058e16 −1.80515 −0.902573 0.430538i \(-0.858324\pi\)
−0.902573 + 0.430538i \(0.858324\pi\)
\(194\) 4.35115e15 + 1.66951e16i 0.420719 + 1.61428i
\(195\) 1.64867e16i 1.53777i
\(196\) −2.73818e15 + 1.53128e15i −0.246416 + 0.137804i
\(197\) 4.30570e15 0.373921 0.186961 0.982367i \(-0.440136\pi\)
0.186961 + 0.982367i \(0.440136\pi\)
\(198\) −2.06815e15 + 5.39009e14i −0.173351 + 0.0451794i
\(199\) 3.57983e15i 0.289662i −0.989456 0.144831i \(-0.953736\pi\)
0.989456 0.144831i \(-0.0462638\pi\)
\(200\) 9.79210e15 + 1.02029e16i 0.765008 + 0.797101i
\(201\) 1.61632e16 1.21942
\(202\) −5.81048e15 2.22945e16i −0.423401 1.62457i
\(203\) 2.59785e15i 0.182870i
\(204\) −6.52839e15 1.16738e16i −0.444012 0.793966i
\(205\) −9.36442e14 −0.0615466
\(206\) 6.30516e14 1.64327e14i 0.0400521 0.0104385i
\(207\) 4.81449e15i 0.295636i
\(208\) −8.62736e15 + 1.40404e16i −0.512194 + 0.833560i
\(209\) 6.37750e15 0.366122
\(210\) 6.04837e15 + 2.32073e16i 0.335818 + 1.28852i
\(211\) 3.54222e16i 1.90238i 0.308599 + 0.951192i \(0.400140\pi\)
−0.308599 + 0.951192i \(0.599860\pi\)
\(212\) 9.10237e15 5.09034e15i 0.472937 0.264482i
\(213\) −7.79470e15 −0.391870
\(214\) 3.46224e16 9.02343e15i 1.68446 0.439011i
\(215\) 1.31889e16i 0.621070i
\(216\) −1.41675e16 + 1.35971e16i −0.645829 + 0.619827i
\(217\) −5.98302e14 −0.0264060
\(218\) −7.92298e15 3.04001e16i −0.338605 1.29921i
\(219\) 1.48117e14i 0.00613051i
\(220\) −1.82091e16 3.25609e16i −0.730012 1.30538i
\(221\) −2.11514e16 −0.821473
\(222\) 2.88638e16 7.52258e15i 1.08613 0.283071i
\(223\) 1.98330e16i 0.723194i 0.932335 + 0.361597i \(0.117768\pi\)
−0.932335 + 0.361597i \(0.882232\pi\)
\(224\) 6.99327e15 2.29289e16i 0.247141 0.810302i
\(225\) −5.60457e15 −0.191984
\(226\) 7.68849e15 + 2.95003e16i 0.255318 + 0.979643i
\(227\) 1.14566e16i 0.368870i 0.982845 + 0.184435i \(0.0590455\pi\)
−0.982845 + 0.184435i \(0.940955\pi\)
\(228\) −1.07560e16 + 6.01512e15i −0.335821 + 0.187802i
\(229\) 1.23732e16 0.374657 0.187328 0.982297i \(-0.440017\pi\)
0.187328 + 0.982297i \(0.440017\pi\)
\(230\) −8.13228e16 + 2.11947e16i −2.38846 + 0.622489i
\(231\) 3.32091e16i 0.946180i
\(232\) −5.40721e15 5.63406e15i −0.149471 0.155742i
\(233\) 3.86944e15 0.103790 0.0518951 0.998653i \(-0.483474\pi\)
0.0518951 + 0.998653i \(0.483474\pi\)
\(234\) −1.64712e15 6.31990e15i −0.0428759 0.164513i
\(235\) 3.60088e16i 0.909775i
\(236\) 2.29841e16 + 4.10994e16i 0.563695 + 1.00798i
\(237\) 2.48957e16 0.592770
\(238\) 2.97735e16 7.75968e15i 0.688322 0.179393i
\(239\) 1.42837e16i 0.320668i 0.987063 + 0.160334i \(0.0512572\pi\)
−0.987063 + 0.160334i \(0.948743\pi\)
\(240\) 6.14215e16 + 3.77414e16i 1.33919 + 0.822885i
\(241\) −4.35287e15 −0.0921841 −0.0460921 0.998937i \(-0.514677\pi\)
−0.0460921 + 0.998937i \(0.514677\pi\)
\(242\) 7.69527e14 + 2.95264e15i 0.0158313 + 0.0607439i
\(243\) 1.72015e16i 0.343814i
\(244\) −1.20926e16 + 6.76258e15i −0.234850 + 0.131336i
\(245\) 2.17034e16 0.409606
\(246\) −2.42474e15 + 6.31943e14i −0.0444753 + 0.0115913i
\(247\) 1.94885e16i 0.347456i
\(248\) −1.29756e15 + 1.24532e15i −0.0224888 + 0.0215833i
\(249\) −5.64633e16 −0.951417
\(250\) −2.34065e15 8.98097e15i −0.0383493 0.147144i
\(251\) 1.03484e17i 1.64876i −0.566040 0.824378i \(-0.691525\pi\)
0.566040 0.824378i \(-0.308475\pi\)
\(252\) 4.63709e15 + 8.29187e15i 0.0718524 + 0.128484i
\(253\) 1.16371e17 1.75389
\(254\) −1.17670e17 + 3.06676e16i −1.72516 + 0.449618i
\(255\) 9.25293e16i 1.31977i
\(256\) −3.25581e16 6.42827e16i −0.451834 0.892102i
\(257\) −1.39119e17 −1.87868 −0.939342 0.342981i \(-0.888563\pi\)
−0.939342 + 0.342981i \(0.888563\pi\)
\(258\) −8.90035e15 3.41502e16i −0.116969 0.448803i
\(259\) 6.86154e16i 0.877653i
\(260\) 9.95002e16 5.56438e16i 1.23883 0.692792i
\(261\) 3.09485e15 0.0375108
\(262\) 3.88103e16 1.01149e16i 0.457972 0.119358i
\(263\) 2.95629e16i 0.339669i 0.985473 + 0.169835i \(0.0543234\pi\)
−0.985473 + 0.169835i \(0.945677\pi\)
\(264\) −6.91222e16 7.20219e16i −0.773374 0.805819i
\(265\) −7.21474e16 −0.786139
\(266\) −7.14962e15 2.74327e16i −0.0758772 0.291137i
\(267\) 7.67302e16i 0.793209i
\(268\) 5.45519e16 + 9.75478e16i 0.549372 + 0.982367i
\(269\) 8.72957e16 0.856499 0.428249 0.903661i \(-0.359130\pi\)
0.428249 + 0.903661i \(0.359130\pi\)
\(270\) 1.31454e17 3.42601e16i 1.25669 0.327523i
\(271\) 1.77937e17i 1.65760i −0.559543 0.828801i \(-0.689023\pi\)
0.559543 0.828801i \(-0.310977\pi\)
\(272\) 4.84198e16 7.87999e16i 0.439583 0.715391i
\(273\) 1.01481e17 0.897939
\(274\) 3.41950e16 + 1.31205e17i 0.294923 + 1.13161i
\(275\) 1.35468e17i 1.13896i
\(276\) −1.96267e17 + 1.09759e17i −1.60873 + 0.899655i
\(277\) −1.24976e17 −0.998778 −0.499389 0.866378i \(-0.666442\pi\)
−0.499389 + 0.866378i \(0.666442\pi\)
\(278\) 1.26795e17 3.30457e16i 0.988071 0.257515i
\(279\) 7.12764e14i 0.00541647i
\(280\) −1.19647e17 + 1.14829e17i −0.886735 + 0.851033i
\(281\) 9.16435e16 0.662457 0.331228 0.943551i \(-0.392537\pi\)
0.331228 + 0.943551i \(0.392537\pi\)
\(282\) −2.43000e16 9.32379e16i −0.171342 0.657429i
\(283\) 7.61168e16i 0.523571i −0.965126 0.261785i \(-0.915689\pi\)
0.965126 0.261785i \(-0.0843112\pi\)
\(284\) −2.63077e16 4.70424e16i −0.176544 0.315690i
\(285\) 8.52547e16 0.558218
\(286\) −1.52759e17 + 3.98125e16i −0.975985 + 0.254365i
\(287\) 5.76411e15i 0.0359384i
\(288\) 2.73155e16 + 8.33117e15i 0.166212 + 0.0506942i
\(289\) −4.96686e16 −0.294983
\(290\) 1.36243e16 + 5.22760e16i 0.0789823 + 0.303051i
\(291\) 3.19368e17i 1.80734i
\(292\) −8.93913e14 + 4.99905e14i −0.00493873 + 0.00276190i
\(293\) −8.23784e16 −0.444365 −0.222183 0.975005i \(-0.571318\pi\)
−0.222183 + 0.975005i \(0.571318\pi\)
\(294\) 5.61968e16 1.46462e16i 0.295992 0.0771426i
\(295\) 3.25763e17i 1.67551i
\(296\) 1.42817e17 + 1.48809e17i 0.717363 + 0.747458i
\(297\) −1.88108e17 −0.922810
\(298\) 3.07899e16 + 1.18139e17i 0.147535 + 0.566083i
\(299\) 3.55609e17i 1.66447i
\(300\) −1.27771e17 2.28475e17i −0.584229 1.04470i
\(301\) 8.11823e16 0.362657
\(302\) −3.09938e16 + 8.07773e15i −0.135278 + 0.0352566i
\(303\) 4.26480e17i 1.81886i
\(304\) −7.26047e16 4.46131e16i −0.302586 0.185929i
\(305\) 9.58486e16 0.390379
\(306\) 9.24421e15 + 3.54696e16i 0.0367976 + 0.141191i
\(307\) 1.52343e17i 0.592726i 0.955075 + 0.296363i \(0.0957738\pi\)
−0.955075 + 0.296363i \(0.904226\pi\)
\(308\) 2.00423e17 1.12083e17i 0.762242 0.426271i
\(309\) −1.20614e16 −0.0448422
\(310\) 1.20395e16 3.13778e15i 0.0437599 0.0114049i
\(311\) 1.11654e16i 0.0396781i 0.999803 + 0.0198390i \(0.00631538\pi\)
−0.999803 + 0.0198390i \(0.993685\pi\)
\(312\) 2.20086e17 2.11225e17i 0.764734 0.733944i
\(313\) 4.49996e17 1.52897 0.764483 0.644644i \(-0.222994\pi\)
0.764483 + 0.644644i \(0.222994\pi\)
\(314\) −8.78948e16 3.37248e17i −0.292049 1.12058i
\(315\) 6.57232e16i 0.213572i
\(316\) 8.40248e16 + 1.50250e17i 0.267053 + 0.477535i
\(317\) 2.34027e16 0.0727531 0.0363766 0.999338i \(-0.488418\pi\)
0.0363766 + 0.999338i \(0.488418\pi\)
\(318\) −1.86812e17 + 4.86875e16i −0.568086 + 0.148057i
\(319\) 7.48057e16i 0.222536i
\(320\) −2.04741e16 + 4.98069e17i −0.0595875 + 1.44957i
\(321\) −6.62306e17 −1.88592
\(322\) −1.30460e17 5.00569e17i −0.363485 1.39468i
\(323\) 1.09376e17i 0.298199i
\(324\) 3.74102e17 2.09210e17i 0.998102 0.558171i
\(325\) −4.13966e17 −1.08089
\(326\) −5.11117e17 + 1.33209e17i −1.30616 + 0.340417i
\(327\) 5.81535e17i 1.45459i
\(328\) −1.19975e16 1.25009e16i −0.0293748 0.0306071i
\(329\) 2.21646e17 0.531239
\(330\) 1.74164e17 + 6.68260e17i 0.408660 + 1.56801i
\(331\) 4.74292e17i 1.08956i −0.838580 0.544778i \(-0.816614\pi\)
0.838580 0.544778i \(-0.183386\pi\)
\(332\) −1.90568e17 3.40766e17i −0.428630 0.766460i
\(333\) −8.17423e16 −0.180027
\(334\) 3.95763e17 1.03145e17i 0.853513 0.222446i
\(335\) 7.73185e17i 1.63294i
\(336\) −2.32311e17 + 3.78070e17i −0.480501 + 0.781983i
\(337\) 6.48884e17 1.31449 0.657245 0.753677i \(-0.271722\pi\)
0.657245 + 0.753677i \(0.271722\pi\)
\(338\) 5.44452e15 + 2.08904e16i 0.0108030 + 0.0414504i
\(339\) 5.64323e17i 1.09681i
\(340\) −5.58431e17 + 3.12293e17i −1.06320 + 0.594579i
\(341\) −1.72282e16 −0.0321337
\(342\) 3.26810e16 8.51743e15i 0.0597189 0.0155642i
\(343\) 6.06766e17i 1.08633i
\(344\) 1.76063e17 1.68975e17i 0.308859 0.296423i
\(345\) 1.55565e18 2.67411
\(346\) 2.41829e17 + 9.27885e17i 0.407357 + 1.56301i
\(347\) 7.04504e17i 1.16299i 0.813549 + 0.581496i \(0.197532\pi\)
−0.813549 + 0.581496i \(0.802468\pi\)
\(348\) 7.05552e16 + 1.26164e17i 0.114150 + 0.204118i
\(349\) −9.26668e17 −1.46942 −0.734711 0.678381i \(-0.762682\pi\)
−0.734711 + 0.678381i \(0.762682\pi\)
\(350\) 5.82715e17 1.51869e17i 0.905690 0.236044i
\(351\) 5.74825e17i 0.875761i
\(352\) 2.01373e17 6.60243e17i 0.300748 0.986065i
\(353\) −1.15975e18 −1.69801 −0.849005 0.528385i \(-0.822798\pi\)
−0.849005 + 0.528385i \(0.822798\pi\)
\(354\) −2.19836e17 8.43500e17i −0.315556 1.21077i
\(355\) 3.72868e17i 0.524756i
\(356\) −4.63080e17 + 2.58970e17i −0.639008 + 0.357354i
\(357\) −5.69549e17 −0.770643
\(358\) 1.31972e17 3.43949e16i 0.175105 0.0456366i
\(359\) 8.35881e16i 0.108764i 0.998520 + 0.0543818i \(0.0173188\pi\)
−0.998520 + 0.0543818i \(0.982681\pi\)
\(360\) −1.36798e17 1.42536e17i −0.174566 0.181890i
\(361\) 6.98229e17 0.873872
\(362\) −2.42982e16 9.32309e16i −0.0298273 0.114446i
\(363\) 5.64821e16i 0.0680087i
\(364\) 3.42506e17 + 6.12457e17i 0.404537 + 0.723379i
\(365\) 7.08535e15 0.00820940
\(366\) 2.48181e17 6.46819e16i 0.282099 0.0735217i
\(367\) 8.77749e17i 0.978831i 0.872051 + 0.489416i \(0.162790\pi\)
−0.872051 + 0.489416i \(0.837210\pi\)
\(368\) −1.32483e18 8.14061e17i −1.44952 0.890681i
\(369\) 6.86686e15 0.00737180
\(370\) −3.59851e17 1.38073e18i −0.379063 1.45445i
\(371\) 4.44091e17i 0.459045i
\(372\) 2.90565e16 1.62493e16i 0.0294742 0.0164829i
\(373\) −5.51683e17 −0.549196 −0.274598 0.961559i \(-0.588545\pi\)
−0.274598 + 0.961559i \(0.588545\pi\)
\(374\) 8.57336e17 2.23442e17i 0.837625 0.218305i
\(375\) 1.71800e17i 0.164742i
\(376\) 4.80693e17 4.61339e17i 0.452432 0.434216i
\(377\) 2.28593e17 0.211190
\(378\) 2.10882e17 + 8.09145e17i 0.191248 + 0.733810i
\(379\) 1.91257e18i 1.70272i 0.524580 + 0.851361i \(0.324222\pi\)
−0.524580 + 0.851361i \(0.675778\pi\)
\(380\) 2.87740e17 + 5.14527e17i 0.251487 + 0.449700i
\(381\) 2.25096e18 1.93149
\(382\) −1.19572e18 + 3.11632e17i −1.00736 + 0.262542i
\(383\) 1.96195e18i 1.62291i −0.584412 0.811457i \(-0.698675\pi\)
0.584412 0.811457i \(-0.301325\pi\)
\(384\) 2.83101e17 + 1.30347e18i 0.229944 + 1.05872i
\(385\) −1.58860e18 −1.26704
\(386\) 5.81255e17 + 2.23025e18i 0.455256 + 1.74679i
\(387\) 9.67135e16i 0.0743893i
\(388\) 1.92744e18 1.07789e18i 1.45599 0.814239i
\(389\) −2.25076e17 −0.166987 −0.0834933 0.996508i \(-0.526608\pi\)
−0.0834933 + 0.996508i \(0.526608\pi\)
\(390\) −2.04208e18 + 5.32215e17i −1.48806 + 0.387824i
\(391\) 1.99581e18i 1.42850i
\(392\) 2.78061e17 + 2.89726e17i 0.195496 + 0.203697i
\(393\) −7.42418e17 −0.512744
\(394\) −1.38994e17 5.33314e17i −0.0943026 0.361834i
\(395\) 1.19092e18i 0.793782i
\(396\) 1.33526e17 + 2.38766e17i 0.0874379 + 0.156353i
\(397\) 2.10584e18 1.35485 0.677427 0.735590i \(-0.263095\pi\)
0.677427 + 0.735590i \(0.263095\pi\)
\(398\) −4.43407e17 + 1.15562e17i −0.280299 + 0.0730524i
\(399\) 5.24771e17i 0.325956i
\(400\) 9.47652e17 1.54224e18i 0.578401 0.941308i
\(401\) 1.01874e18 0.611014 0.305507 0.952190i \(-0.401174\pi\)
0.305507 + 0.952190i \(0.401174\pi\)
\(402\) −5.21772e17 2.00201e18i −0.307538 1.18001i
\(403\) 5.26464e16i 0.0304953i
\(404\) −2.57388e18 + 1.43940e18i −1.46527 + 0.819430i
\(405\) −2.96521e18 −1.65909
\(406\) −3.21776e17 + 8.38624e16i −0.176958 + 0.0461196i
\(407\) 1.97580e18i 1.06802i
\(408\) −1.23520e18 + 1.18547e18i −0.656322 + 0.629897i
\(409\) −5.09887e17 −0.266324 −0.133162 0.991094i \(-0.542513\pi\)
−0.133162 + 0.991094i \(0.542513\pi\)
\(410\) 3.02297e16 + 1.15990e17i 0.0155220 + 0.0595571i
\(411\) 2.50986e18i 1.26694i
\(412\) −4.07080e16 7.27925e16i −0.0202022 0.0361249i
\(413\) 2.00518e18 0.978369
\(414\) 5.96334e17 1.55419e17i 0.286080 0.0745592i
\(415\) 2.70099e18i 1.27405i
\(416\) 2.01759e18 + 6.15360e17i 0.935790 + 0.285414i
\(417\) −2.42551e18 −1.10624
\(418\) −2.05875e17 7.89932e17i −0.0923357 0.354288i
\(419\) 1.48939e18i 0.656917i 0.944518 + 0.328459i \(0.106529\pi\)
−0.944518 + 0.328459i \(0.893471\pi\)
\(420\) 2.67926e18 1.49833e18i 1.16217 0.649925i
\(421\) −3.84687e17 −0.164109 −0.0820546 0.996628i \(-0.526148\pi\)
−0.0820546 + 0.996628i \(0.526148\pi\)
\(422\) 4.38748e18 1.14348e18i 1.84089 0.479780i
\(423\) 2.64050e17i 0.108969i
\(424\) −9.24340e17 9.63118e17i −0.375207 0.390948i
\(425\) 2.32333e18 0.927658
\(426\) 2.51624e17 + 9.65471e17i 0.0988293 + 0.379203i
\(427\) 5.89980e17i 0.227951i
\(428\) −2.23533e18 3.99713e18i −0.849640 1.51929i
\(429\) 2.92218e18 1.09271
\(430\) −1.63361e18 + 4.25759e17i −0.600994 + 0.156633i
\(431\) 3.54760e18i 1.28408i 0.766669 + 0.642042i \(0.221913\pi\)
−0.766669 + 0.642042i \(0.778087\pi\)
\(432\) 2.14152e18 + 1.31589e18i 0.762668 + 0.468633i
\(433\) −2.75629e18 −0.965849 −0.482925 0.875662i \(-0.660426\pi\)
−0.482925 + 0.875662i \(0.660426\pi\)
\(434\) 1.93141e16 + 7.41071e16i 0.00665956 + 0.0255524i
\(435\) 1.00001e18i 0.339295i
\(436\) −3.50966e18 + 1.96272e18i −1.17182 + 0.655319i
\(437\) −1.83890e18 −0.604209
\(438\) 1.83461e16 4.78144e15i 0.00593234 0.00154611i
\(439\) 3.70584e18i 1.17933i −0.807648 0.589665i \(-0.799260\pi\)
0.807648 0.589665i \(-0.200740\pi\)
\(440\) −3.44525e18 + 3.30654e18i −1.07908 + 1.03563i
\(441\) −1.59150e17 −0.0490609
\(442\) 6.82799e17 + 2.61986e18i 0.207175 + 0.794919i
\(443\) 1.77582e18i 0.530362i −0.964199 0.265181i \(-0.914568\pi\)
0.964199 0.265181i \(-0.0854317\pi\)
\(444\) −1.86353e18 3.33230e18i −0.547843 0.979632i
\(445\) 3.67048e18 1.06219
\(446\) 2.45657e18 6.40239e17i 0.699817 0.182389i
\(447\) 2.25993e18i 0.633785i
\(448\) −3.06578e18 1.26025e17i −0.846438 0.0347945i
\(449\) −3.86648e18 −1.05097 −0.525486 0.850802i \(-0.676116\pi\)
−0.525486 + 0.850802i \(0.676116\pi\)
\(450\) 1.80924e17 + 6.94195e17i 0.0484181 + 0.185778i
\(451\) 1.65979e17i 0.0437338i
\(452\) 3.40579e18 1.90463e18i 0.883586 0.494130i
\(453\) 5.92893e17 0.151457
\(454\) 1.41904e18 3.69835e17i 0.356946 0.0930286i
\(455\) 4.85447e18i 1.20244i
\(456\) 1.09227e18 + 1.13809e18i 0.266425 + 0.277602i
\(457\) −1.78862e18 −0.429639 −0.214820 0.976654i \(-0.568916\pi\)
−0.214820 + 0.976654i \(0.568916\pi\)
\(458\) −3.99425e17 1.53257e18i −0.0944881 0.362546i
\(459\) 3.22612e18i 0.751609i
\(460\) 5.25044e18 + 9.38865e18i 1.20473 + 2.15426i
\(461\) 3.38458e18 0.764889 0.382444 0.923979i \(-0.375082\pi\)
0.382444 + 0.923979i \(0.375082\pi\)
\(462\) −4.11337e18 + 1.07204e18i −0.915595 + 0.238626i
\(463\) 1.27172e18i 0.278821i −0.990235 0.139410i \(-0.955479\pi\)
0.990235 0.139410i \(-0.0445207\pi\)
\(464\) −5.23295e17 + 8.51626e17i −0.113011 + 0.183918i
\(465\) −2.30308e17 −0.0489935
\(466\) −1.24911e17 4.79278e17i −0.0261758 0.100435i
\(467\) 1.67912e18i 0.346628i 0.984867 + 0.173314i \(0.0554475\pi\)
−0.984867 + 0.173314i \(0.944553\pi\)
\(468\) −7.29627e17 + 4.08032e17i −0.148382 + 0.0829799i
\(469\) 4.75921e18 0.953510
\(470\) −4.46014e18 + 1.16242e18i −0.880367 + 0.229444i
\(471\) 6.45134e18i 1.25460i
\(472\) 4.34871e18 4.17362e18i 0.833232 0.799684i
\(473\) 2.33767e18 0.441321
\(474\) −8.03671e17 3.08365e18i −0.149496 0.573609i
\(475\) 2.14067e18i 0.392368i
\(476\) −1.92227e18 3.43733e18i −0.347188 0.620829i
\(477\) 5.29052e17 0.0941606
\(478\) 1.76922e18 4.61100e17i 0.310303 0.0808722i
\(479\) 2.63877e18i 0.456092i 0.973650 + 0.228046i \(0.0732337\pi\)
−0.973650 + 0.228046i \(0.926766\pi\)
\(480\) 2.69196e18 8.82616e18i 0.458543 1.50343i
\(481\) −6.03768e18 −1.01357
\(482\) 1.40517e17 + 5.39157e17i 0.0232488 + 0.0892043i
\(483\) 9.57558e18i 1.56147i
\(484\) 3.40879e17 1.90631e17i 0.0547877 0.0306391i
\(485\) −1.52773e19 −2.42022
\(486\) −2.13062e18 + 5.55291e17i −0.332700 + 0.0867095i
\(487\) 6.02454e18i 0.927303i −0.886018 0.463651i \(-0.846539\pi\)
0.886018 0.463651i \(-0.153461\pi\)
\(488\) 1.22800e18 + 1.27951e18i 0.186320 + 0.194136i
\(489\) 9.77735e18 1.46238
\(490\) −7.00619e17 2.68824e18i −0.103302 0.396365i
\(491\) 3.04593e18i 0.442741i −0.975190 0.221371i \(-0.928947\pi\)
0.975190 0.221371i \(-0.0710531\pi\)
\(492\) 1.56548e17 + 2.79934e17i 0.0224332 + 0.0401143i
\(493\) −1.28295e18 −0.181251
\(494\) 2.41389e18 6.29117e17i 0.336224 0.0876280i
\(495\) 1.89252e18i 0.259898i
\(496\) 1.96135e17 + 1.20518e17i 0.0265573 + 0.0163185i
\(497\) −2.29513e18 −0.306417
\(498\) 1.82272e18 + 6.99368e18i 0.239946 + 0.920663i
\(499\) 4.15397e18i 0.539212i −0.962971 0.269606i \(-0.913106\pi\)
0.962971 0.269606i \(-0.0868935\pi\)
\(500\) −1.03685e18 + 5.79838e17i −0.132716 + 0.0742193i
\(501\) −7.57070e18 −0.955591
\(502\) −1.28178e19 + 3.34061e18i −1.59546 + 0.415815i
\(503\) 8.28512e18i 1.01700i 0.861061 + 0.508502i \(0.169801\pi\)
−0.861061 + 0.508502i \(0.830199\pi\)
\(504\) 8.77359e17 8.42035e17i 0.106210 0.101933i
\(505\) 2.04012e19 2.43565
\(506\) −3.75663e18 1.44140e19i −0.442329 1.69719i
\(507\) 3.99620e17i 0.0464078i
\(508\) 7.59713e18 + 1.35849e19i 0.870169 + 1.55601i
\(509\) −1.06268e17 −0.0120054 −0.00600270 0.999982i \(-0.501911\pi\)
−0.00600270 + 0.999982i \(0.501911\pi\)
\(510\) 1.14609e19 2.98698e18i 1.27711 0.332845i
\(511\) 4.36127e16i 0.00479365i
\(512\) −6.91119e18 + 6.10787e18i −0.749313 + 0.662216i
\(513\) 2.97249e18 0.317906
\(514\) 4.49096e18 + 1.72316e19i 0.473803 + 1.81796i
\(515\) 5.76970e17i 0.0600485i
\(516\) −3.94261e18 + 2.20484e18i −0.404796 + 0.226375i
\(517\) 6.38237e18 0.646469
\(518\) 8.49887e18 2.21501e18i 0.849284 0.221343i
\(519\) 1.77499e19i 1.74994i
\(520\) −1.01042e19 1.05281e19i −0.982829 1.02406i
\(521\) 5.25175e18 0.504011 0.252006 0.967726i \(-0.418910\pi\)
0.252006 + 0.967726i \(0.418910\pi\)
\(522\) −9.99063e16 3.83336e17i −0.00946018 0.0362983i
\(523\) 1.39466e19i 1.30304i −0.758632 0.651519i \(-0.774132\pi\)
0.758632 0.651519i \(-0.225868\pi\)
\(524\) −2.50571e18 4.48062e18i −0.231000 0.413066i
\(525\) −1.11470e19 −1.01401
\(526\) 3.66173e18 9.54333e17i 0.328690 0.0856643i
\(527\) 2.95471e17i 0.0261722i
\(528\) −6.68945e18 + 1.08866e19i −0.584727 + 0.951602i
\(529\) −2.19618e19 −1.89443
\(530\) 2.32902e18 + 8.93635e18i 0.198264 + 0.760728i
\(531\) 2.38879e18i 0.200686i
\(532\) −3.16708e18 + 1.77114e18i −0.262590 + 0.146849i
\(533\) 5.07202e17 0.0415041
\(534\) 9.50399e18 2.47696e18i 0.767568 0.200046i
\(535\) 3.16821e19i 2.52545i
\(536\) 1.03215e19 9.90592e18i 0.812061 0.779366i
\(537\) −2.52454e18 −0.196048
\(538\) −2.81803e18 1.08127e19i −0.216008 0.828813i
\(539\) 3.84681e18i 0.291058i
\(540\) −8.48708e18 1.51763e19i −0.633873 1.13347i
\(541\) −7.44833e18 −0.549134 −0.274567 0.961568i \(-0.588534\pi\)
−0.274567 + 0.961568i \(0.588534\pi\)
\(542\) −2.20397e19 + 5.74406e18i −1.60402 + 0.418046i
\(543\) 1.78345e18i 0.128133i
\(544\) −1.13234e19 3.45362e18i −0.803129 0.244953i
\(545\) 2.78184e19 1.94785
\(546\) −3.27596e18 1.25697e19i −0.226459 0.868914i
\(547\) 1.84776e19i 1.26106i −0.776167 0.630528i \(-0.782838\pi\)
0.776167 0.630528i \(-0.217162\pi\)
\(548\) 1.51475e19 8.47096e18i 1.02065 0.570780i
\(549\) −7.02851e17 −0.0467581
\(550\) 1.67794e19 4.37311e18i 1.10214 0.287244i
\(551\) 1.18208e18i 0.0766630i
\(552\) 1.99308e19 + 2.07669e19i 1.27629 + 1.32984i
\(553\) 7.33048e18 0.463507
\(554\) 4.03442e18 + 1.54799e19i 0.251891 + 0.966493i
\(555\) 2.64125e19i 1.62839i
\(556\) −8.18625e18 1.46384e19i −0.498381 0.891187i
\(557\) 1.27693e19 0.767683 0.383841 0.923399i \(-0.374601\pi\)
0.383841 + 0.923399i \(0.374601\pi\)
\(558\) −8.82847e16 + 2.30091e16i −0.00524139 + 0.00136603i
\(559\) 7.14349e18i 0.418820i
\(560\) 1.80854e19 + 1.11129e19i 1.04716 + 0.643442i
\(561\) −1.64003e19 −0.937803
\(562\) −2.95839e18 1.13512e19i −0.167071 0.641043i
\(563\) 1.53198e18i 0.0854467i −0.999087 0.0427234i \(-0.986397\pi\)
0.999087 0.0427234i \(-0.0136034\pi\)
\(564\) −1.07642e19 + 6.01972e18i −0.592966 + 0.331606i
\(565\) −2.69950e19 −1.46874
\(566\) −9.42801e18 + 2.45716e18i −0.506646 + 0.132044i
\(567\) 1.82519e19i 0.968783i
\(568\) −4.97754e18 + 4.77713e18i −0.260961 + 0.250454i
\(569\) −1.27708e19 −0.661350 −0.330675 0.943745i \(-0.607276\pi\)
−0.330675 + 0.943745i \(0.607276\pi\)
\(570\) −2.75215e18 1.05599e19i −0.140782 0.540174i
\(571\) 3.30749e19i 1.67127i 0.549286 + 0.835635i \(0.314900\pi\)
−0.549286 + 0.835635i \(0.685100\pi\)
\(572\) 9.86254e18 + 1.76358e19i 0.492285 + 0.880287i
\(573\) 2.28733e19 1.12784
\(574\) −7.13957e17 + 1.86074e17i −0.0347767 + 0.00906364i
\(575\) 3.90611e19i 1.87962i
\(576\) 1.50135e17 3.65231e18i 0.00713715 0.173624i
\(577\) 2.53825e19 1.19207 0.596037 0.802957i \(-0.296741\pi\)
0.596037 + 0.802957i \(0.296741\pi\)
\(578\) 1.60337e18 + 6.15207e18i 0.0743944 + 0.285448i
\(579\) 4.26632e19i 1.95571i
\(580\) 6.03521e18 3.37509e18i 0.273336 0.152858i
\(581\) −1.66255e19 −0.743946
\(582\) −3.95577e19 + 1.03097e19i −1.74892 + 0.455810i
\(583\) 1.27877e19i 0.558616i
\(584\) 9.07763e16 + 9.45845e16i 0.00391816 + 0.00408254i
\(585\) 5.78319e18 0.246647
\(586\) 2.65930e18 + 1.02036e19i 0.112068 + 0.430001i
\(587\) 8.66644e18i 0.360889i −0.983585 0.180445i \(-0.942246\pi\)
0.983585 0.180445i \(-0.0577537\pi\)
\(588\) −3.62823e18 6.48788e18i −0.149298 0.266969i
\(589\) 2.72241e17 0.0110700
\(590\) −4.03498e19 + 1.05161e19i −1.62135 + 0.422562i
\(591\) 1.02020e19i 0.405109i
\(592\) 1.38215e19 2.24935e19i 0.542378 0.882683i
\(593\) 1.33237e18 0.0516704 0.0258352 0.999666i \(-0.491775\pi\)
0.0258352 + 0.999666i \(0.491775\pi\)
\(594\) 6.07241e18 + 2.32995e19i 0.232732 + 0.892981i
\(595\) 2.72450e19i 1.03197i
\(596\) 1.36391e19 7.62741e18i 0.510576 0.285531i
\(597\) 8.48210e18 0.313822
\(598\) 4.40466e19 1.14796e19i 1.61066 0.419777i
\(599\) 3.49944e19i 1.26477i 0.774656 + 0.632383i \(0.217923\pi\)
−0.774656 + 0.632383i \(0.782077\pi\)
\(600\) −2.41749e19 + 2.32015e19i −0.863585 + 0.828815i
\(601\) −2.22716e19 −0.786376 −0.393188 0.919458i \(-0.628628\pi\)
−0.393188 + 0.919458i \(0.628628\pi\)
\(602\) −2.62069e18 1.00554e19i −0.0914618 0.350934i
\(603\) 5.66971e18i 0.195587i
\(604\) 2.00105e18 + 3.57821e18i 0.0682339 + 0.122013i
\(605\) −2.70189e18 −0.0910709
\(606\) 5.28249e19 1.37674e19i 1.76007 0.458716i
\(607\) 2.81797e19i 0.928145i −0.885797 0.464073i \(-0.846388\pi\)
0.885797 0.464073i \(-0.153612\pi\)
\(608\) −3.18210e18 + 1.04332e19i −0.103607 + 0.339697i
\(609\) 6.15537e18 0.198122
\(610\) −3.09413e18 1.18720e19i −0.0984533 0.377761i
\(611\) 1.95034e19i 0.613509i
\(612\) 4.09493e18 2.29002e18i 0.127346 0.0712163i
\(613\) 2.19343e19 0.674372 0.337186 0.941438i \(-0.390525\pi\)
0.337186 + 0.941438i \(0.390525\pi\)
\(614\) 1.88696e19 4.91786e18i 0.573566 0.149485i
\(615\) 2.21882e18i 0.0666800i
\(616\) −2.03528e19 2.12067e19i −0.604728 0.630097i
\(617\) −4.07723e19 −1.19776 −0.598879 0.800840i \(-0.704387\pi\)
−0.598879 + 0.800840i \(0.704387\pi\)
\(618\) 3.89359e17 + 1.49395e18i 0.0113092 + 0.0433927i
\(619\) 1.07476e19i 0.308658i 0.988019 + 0.154329i \(0.0493216\pi\)
−0.988019 + 0.154329i \(0.950678\pi\)
\(620\) −7.77305e17 1.38995e18i −0.0220724 0.0394691i
\(621\) 5.42394e19 1.52291
\(622\) 1.38297e18 3.60435e17i 0.0383955 0.0100068i
\(623\) 2.25930e19i 0.620237i
\(624\) −3.32675e19 2.04418e19i −0.903085 0.554914i
\(625\) −3.29391e19 −0.884204
\(626\) −1.45265e19 5.57375e19i −0.385604 1.47954i
\(627\) 1.51109e19i 0.396659i
\(628\) −3.89350e19 + 2.17737e19i −1.01070 + 0.565217i
\(629\) 3.38856e19 0.869883
\(630\) −8.14064e18 + 2.12164e18i −0.206669 + 0.0538627i
\(631\) 6.39901e19i 1.60660i 0.595575 + 0.803300i \(0.296924\pi\)
−0.595575 + 0.803300i \(0.703076\pi\)
\(632\) 1.58979e19 1.52578e19i 0.394748 0.378855i
\(633\) −8.39297e19 −2.06106
\(634\) −7.55475e17 2.89872e18i −0.0183483 0.0704014i
\(635\) 1.07677e20i 2.58647i
\(636\) 1.20611e19 + 2.15673e19i 0.286542 + 0.512383i
\(637\) −1.17552e19 −0.276218
\(638\) −9.26562e18 + 2.41484e18i −0.215342 + 0.0561233i
\(639\) 2.73422e18i 0.0628531i
\(640\) 6.23530e19 1.35424e19i 1.41774 0.307919i
\(641\) 5.57952e18 0.125485 0.0627423 0.998030i \(-0.480015\pi\)
0.0627423 + 0.998030i \(0.480015\pi\)
\(642\) 2.13802e19 + 8.20348e19i 0.475627 + 1.82496i
\(643\) 3.16664e19i 0.696822i −0.937342 0.348411i \(-0.886721\pi\)
0.937342 0.348411i \(-0.113279\pi\)
\(644\) −5.77903e19 + 3.23182e19i −1.25792 + 0.703471i
\(645\) 3.12500e19 0.672872
\(646\) −1.35476e19 + 3.53083e18i −0.288560 + 0.0752054i
\(647\) 4.14438e19i 0.873231i −0.899648 0.436616i \(-0.856177\pi\)
0.899648 0.436616i \(-0.143823\pi\)
\(648\) −3.79898e19 3.95836e19i −0.791849 0.825068i
\(649\) 5.77396e19 1.19059
\(650\) 1.33634e19 + 5.12749e19i 0.272599 + 1.04595i
\(651\) 1.41762e18i 0.0286084i
\(652\) 3.29992e19 + 5.90080e19i 0.658826 + 1.17809i
\(653\) −3.03333e19 −0.599138 −0.299569 0.954075i \(-0.596843\pi\)
−0.299569 + 0.954075i \(0.596843\pi\)
\(654\) 7.20303e19 1.87728e19i 1.40757 0.366847i
\(655\) 3.55144e19i 0.686618i
\(656\) −1.16109e18 + 1.88959e18i −0.0222095 + 0.0361444i
\(657\) −5.19563e16 −0.000983289
\(658\) −7.15508e18 2.74537e19i −0.133978 0.514066i
\(659\) 5.74518e18i 0.106440i 0.998583 + 0.0532201i \(0.0169485\pi\)
−0.998583 + 0.0532201i \(0.983051\pi\)
\(660\) 7.71501e19 4.31449e19i 1.41426 0.790900i
\(661\) 7.51512e19 1.36309 0.681547 0.731775i \(-0.261308\pi\)
0.681547 + 0.731775i \(0.261308\pi\)
\(662\) −5.87469e19 + 1.53108e19i −1.05434 + 0.274785i
\(663\) 5.01164e19i 0.889989i
\(664\) −3.60563e19 + 3.46046e19i −0.633585 + 0.608075i
\(665\) 2.51030e19 0.436490
\(666\) 2.63876e18 + 1.01248e19i 0.0454026 + 0.174208i
\(667\) 2.15696e19i 0.367249i
\(668\) −2.55516e19 4.56905e19i −0.430510 0.769823i
\(669\) −4.69926e19 −0.783513
\(670\) −9.57686e19 + 2.49596e19i −1.58015 + 0.411826i
\(671\) 1.69886e19i 0.277396i
\(672\) 5.43280e19 + 1.65699e19i 0.877887 + 0.267754i
\(673\) −2.08259e19 −0.333041 −0.166521 0.986038i \(-0.553253\pi\)
−0.166521 + 0.986038i \(0.553253\pi\)
\(674\) −2.09469e19 8.03723e19i −0.331513 1.27200i
\(675\) 6.31403e19i 0.988964i
\(676\) 2.41178e18 1.34874e18i 0.0373861 0.0209075i
\(677\) −1.13345e19 −0.173893 −0.0869464 0.996213i \(-0.527711\pi\)
−0.0869464 + 0.996213i \(0.527711\pi\)
\(678\) −6.98984e19 + 1.82172e19i −1.06135 + 0.276614i
\(679\) 9.40370e19i 1.41322i
\(680\) 5.67083e19 + 5.90873e19i 0.843499 + 0.878885i
\(681\) −2.71453e19 −0.399636
\(682\) 5.56153e17 + 2.13393e18i 0.00810408 + 0.0310950i
\(683\) 7.73552e19i 1.11569i 0.829944 + 0.557846i \(0.188372\pi\)
−0.829944 + 0.557846i \(0.811628\pi\)
\(684\) −2.10998e18 3.77299e18i −0.0301221 0.0538633i
\(685\) −1.20062e20 −1.69657
\(686\) 7.51555e19 1.95873e19i 1.05122 0.273972i
\(687\) 2.93172e19i 0.405906i
\(688\) −2.66132e19 1.63529e19i −0.364735 0.224117i
\(689\) 3.90770e19 0.530135
\(690\) −5.02188e19 1.92687e20i −0.674408 2.58767i
\(691\) 7.17459e19i 0.953786i −0.878961 0.476893i \(-0.841763\pi\)
0.878961 0.476893i \(-0.158237\pi\)
\(692\) 1.07124e20 5.99070e19i 1.40975 0.788379i
\(693\) 1.16491e19 0.151760
\(694\) 8.72615e19 2.27424e19i 1.12540 0.293306i
\(695\) 1.16027e20i 1.48137i
\(696\) 1.33494e19 1.28119e19i 0.168732 0.161938i
\(697\) −2.84660e18 −0.0356203
\(698\) 2.99142e19 + 1.14779e20i 0.370587 + 1.42192i
\(699\) 9.16829e18i 0.112447i
\(700\) −3.76218e19 6.72739e19i −0.456828 0.816884i
\(701\) −2.41146e19 −0.289904 −0.144952 0.989439i \(-0.546303\pi\)
−0.144952 + 0.989439i \(0.546303\pi\)
\(702\) −7.11992e19 + 1.85562e19i −0.847452 + 0.220866i
\(703\) 3.12215e19i 0.367932i
\(704\) −8.82800e19 3.62892e18i −1.03004 0.0423418i
\(705\) 8.53198e19 0.985657
\(706\) 3.74383e19 + 1.43649e20i 0.428236 + 1.64312i
\(707\) 1.25576e20i 1.42223i
\(708\) −9.73813e19 + 5.44588e19i −1.09205 + 0.610711i
\(709\) 1.28450e20 1.42630 0.713151 0.701011i \(-0.247268\pi\)
0.713151 + 0.701011i \(0.247268\pi\)
\(710\) 4.61844e19 1.20367e19i 0.507793 0.132343i
\(711\) 8.73289e18i 0.0950760i
\(712\) 4.70255e19 + 4.89983e19i 0.506960 + 0.528228i
\(713\) 4.96762e18 0.0530300
\(714\) 1.83859e19 + 7.05457e19i 0.194356 + 0.745733i
\(715\) 1.39786e20i 1.46326i
\(716\) −8.52048e18 1.52360e19i −0.0883228 0.157936i
\(717\) −3.38440e19 −0.347414
\(718\) 1.03534e19 2.69835e18i 0.105248 0.0274301i
\(719\) 4.82643e19i 0.485874i −0.970042 0.242937i \(-0.921889\pi\)
0.970042 0.242937i \(-0.0781109\pi\)
\(720\) −1.32389e19 + 2.15454e19i −0.131985 + 0.214796i
\(721\) −3.55144e18 −0.0350637
\(722\) −2.25399e19 8.64844e19i −0.220390 0.845624i
\(723\) 1.03137e19i 0.0998729i
\(724\) −1.07634e19 + 6.01926e18i −0.103224 + 0.0577263i
\(725\) −2.51093e19 −0.238489
\(726\) −6.99601e18 + 1.82333e18i −0.0658103 + 0.0171517i
\(727\) 1.76865e20i 1.64779i −0.566743 0.823895i \(-0.691797\pi\)
0.566743 0.823895i \(-0.308203\pi\)
\(728\) 6.48038e19 6.21946e19i 0.597972 0.573896i
\(729\) −8.43712e19 −0.771084
\(730\) −2.28726e17 8.77609e17i −0.00207040 0.00794403i
\(731\) 4.00918e19i 0.359446i
\(732\) −1.60233e19 2.86523e19i −0.142290 0.254438i
\(733\) −6.10273e19 −0.536780 −0.268390 0.963310i \(-0.586492\pi\)
−0.268390 + 0.963310i \(0.586492\pi\)
\(734\) 1.08720e20 2.83350e19i 0.947191 0.246860i
\(735\) 5.14244e19i 0.443770i
\(736\) −5.80642e19 + 1.90376e20i −0.496322 + 1.62730i
\(737\) 1.37043e20 1.16034
\(738\) −2.21672e17 8.50546e17i −0.00185916 0.00713351i
\(739\) 8.22272e19i 0.683131i 0.939858 + 0.341566i \(0.110957\pi\)
−0.939858 + 0.341566i \(0.889043\pi\)
\(740\) −1.59404e20 + 8.91441e19i −1.31183 + 0.733619i
\(741\) −4.61762e19 −0.376436
\(742\) −5.50062e19 + 1.43359e19i −0.444206 + 0.115771i
\(743\) 1.41500e20i 1.13197i −0.824417 0.565983i \(-0.808497\pi\)
0.824417 0.565983i \(-0.191503\pi\)
\(744\) −2.95067e18 3.07445e18i −0.0233835 0.0243645i
\(745\) −1.08106e20 −0.848705
\(746\) 1.78091e19 + 6.83328e19i 0.138507 + 0.531444i
\(747\) 1.98061e19i 0.152600i
\(748\) −5.53521e19 9.89787e19i −0.422497 0.755493i
\(749\) −1.95014e20 −1.47467
\(750\) 2.12796e19 5.54597e18i 0.159417 0.0415479i
\(751\) 1.20048e20i 0.890996i 0.895283 + 0.445498i \(0.146973\pi\)
−0.895283 + 0.445498i \(0.853027\pi\)
\(752\) −7.26601e19 4.46471e19i −0.534283 0.328298i
\(753\) 2.45196e20 1.78627
\(754\) −7.37931e18 2.83141e19i −0.0532619 0.204363i
\(755\) 2.83617e19i 0.202817i
\(756\) 9.34151e19 5.22408e19i 0.661858 0.370133i
\(757\) 1.53107e20 1.07479 0.537395 0.843331i \(-0.319408\pi\)
0.537395 + 0.843331i \(0.319408\pi\)
\(758\) 2.36896e20 6.17407e19i 1.64768 0.429425i
\(759\) 2.75731e20i 1.90017i
\(760\) 5.44419e19 5.22499e19i 0.371739 0.356772i
\(761\) 2.17872e20 1.47404 0.737018 0.675873i \(-0.236233\pi\)
0.737018 + 0.675873i \(0.236233\pi\)
\(762\) −7.26642e19 2.78809e20i −0.487120 1.86905i
\(763\) 1.71231e20i 1.13740i
\(764\) 7.71991e19 + 1.38045e20i 0.508111 + 0.908586i
\(765\) −3.24573e19 −0.211681
\(766\) −2.43011e20 + 6.33345e19i −1.57045 + 0.409297i
\(767\) 1.76442e20i 1.12988i
\(768\) 1.52312e20 7.71435e19i 0.966509 0.489520i
\(769\) −7.62132e19 −0.479232 −0.239616 0.970868i \(-0.577022\pi\)
−0.239616 + 0.970868i \(0.577022\pi\)
\(770\) 5.12823e19 + 1.96768e20i 0.319545 + 1.22608i
\(771\) 3.29630e20i 2.03538i
\(772\) 2.57480e20 1.43991e20i 1.57552 0.881080i
\(773\) −2.83396e20 −1.71845 −0.859226 0.511597i \(-0.829054\pi\)
−0.859226 + 0.511597i \(0.829054\pi\)
\(774\) 1.19792e19 3.12206e18i 0.0719847 0.0187609i
\(775\) 5.78283e18i 0.0344372i
\(776\) −1.95731e20 2.03942e20i −1.15512 1.20358i
\(777\) −1.62578e20 −0.950856
\(778\) 7.26578e18 + 2.78784e19i 0.0421139 + 0.161589i
\(779\) 2.62280e18i 0.0150662i
\(780\) 1.31843e20 + 2.35757e20i 0.750576 + 1.34215i
\(781\) −6.60888e19 −0.372882
\(782\) −2.47206e20 + 6.44276e19i −1.38233 + 0.360267i
\(783\) 3.48662e19i 0.193229i
\(784\) 2.69099e19 4.37941e19i 0.147809 0.240549i
\(785\) 3.08607e20 1.68004
\(786\) 2.39663e19 + 9.19577e19i 0.129313 + 0.496170i
\(787\) 1.63309e20i 0.873345i 0.899621 + 0.436672i \(0.143843\pi\)
−0.899621 + 0.436672i \(0.856157\pi\)
\(788\) −6.15707e19 + 3.44324e19i −0.326355 + 0.182509i
\(789\) −7.00466e19 −0.368000
\(790\) −1.47510e20 + 3.84445e19i −0.768123 + 0.200191i
\(791\) 1.66164e20i 0.857631i
\(792\) 2.52638e19 2.42466e19i 0.129247 0.124044i
\(793\) −5.19142e19 −0.263253
\(794\) −6.79797e19 2.60835e20i −0.341693 1.31106i
\(795\) 1.70947e20i 0.851709i
\(796\) 2.86277e19 + 5.11909e19i 0.141382 + 0.252814i
\(797\) −8.26020e19 −0.404373 −0.202187 0.979347i \(-0.564805\pi\)
−0.202187 + 0.979347i \(0.564805\pi\)
\(798\) 6.49994e19 1.69404e19i 0.315420 0.0822059i
\(799\) 1.09460e20i 0.526535i
\(800\) −2.21617e20 6.75928e19i −1.05675 0.322307i
\(801\) −2.69153e19 −0.127225
\(802\) −3.28863e19 1.26183e20i −0.154097 0.591263i
\(803\) 1.25584e18i 0.00583344i
\(804\) −2.31131e20 + 1.29256e20i −1.06430 + 0.595193i
\(805\) 4.58059e20 2.09098
\(806\) −6.52091e18 + 1.69950e18i −0.0295096 + 0.00769090i
\(807\) 2.06839e20i 0.927937i
\(808\) 2.61376e20 + 2.72341e20i 1.16248 + 1.21125i
\(809\) −2.49148e20 −1.09854 −0.549272 0.835643i \(-0.685095\pi\)
−0.549272 + 0.835643i \(0.685095\pi\)
\(810\) 9.57215e19 + 3.67279e20i 0.418422 + 1.60546i
\(811\) 1.92894e20i 0.835937i −0.908462 0.417968i \(-0.862742\pi\)
0.908462 0.417968i \(-0.137258\pi\)
\(812\) 2.07748e19 + 3.71488e19i 0.0892575 + 0.159607i
\(813\) 4.21605e20 1.79586
\(814\) 2.44727e20 6.37816e19i 1.03350 0.269355i
\(815\) 4.67711e20i 1.95828i
\(816\) 1.86709e20 + 1.14726e20i 0.775059 + 0.476247i
\(817\) −3.69398e19 −0.152034
\(818\) 1.64599e19 + 6.31559e19i 0.0671667 + 0.257715i
\(819\) 3.55975e19i 0.144023i
\(820\) 1.33909e19 7.48866e18i 0.0537173 0.0300405i
\(821\) −1.20724e20 −0.480167 −0.240084 0.970752i \(-0.577175\pi\)
−0.240084 + 0.970752i \(0.577175\pi\)
\(822\) −3.10878e20 + 8.10221e19i −1.22599 + 0.319522i
\(823\) 1.98153e20i 0.774821i 0.921907 + 0.387411i \(0.126630\pi\)
−0.921907 + 0.387411i \(0.873370\pi\)
\(824\) −7.70214e18 + 7.39204e18i −0.0298622 + 0.0286598i
\(825\) −3.20980e20 −1.23396
\(826\) −6.47301e19 2.48366e20i −0.246744 0.946744i
\(827\) 4.73938e20i 1.79136i 0.444699 + 0.895680i \(0.353311\pi\)
−0.444699 + 0.895680i \(0.646689\pi\)
\(828\) −3.85011e19 6.88463e19i −0.144298 0.258029i
\(829\) 6.87626e19 0.255547 0.127773 0.991803i \(-0.459217\pi\)
0.127773 + 0.991803i \(0.459217\pi\)
\(830\) 3.34551e20 8.71919e19i 1.23287 0.321314i
\(831\) 2.96120e20i 1.08208i
\(832\) 1.10893e19 2.69768e20i 0.0401830 0.977523i
\(833\) 6.59742e19 0.237061
\(834\) 7.82989e19 + 3.00429e20i 0.278993 + 1.07048i
\(835\) 3.62153e20i 1.27964i
\(836\) −9.11970e19 + 5.10004e19i −0.319548 + 0.178702i
\(837\) −8.02991e18 −0.0279018
\(838\) 1.84480e20 4.80798e19i 0.635683 0.165674i
\(839\) 9.49839e19i 0.324576i 0.986743 + 0.162288i \(0.0518874\pi\)
−0.986743 + 0.162288i \(0.948113\pi\)
\(840\) −2.72078e20 2.83492e20i −0.922015 0.960695i
\(841\) −2.83693e20 −0.953403
\(842\) 1.24183e19 + 4.76483e19i 0.0413882 + 0.158804i
\(843\) 2.17141e20i 0.717710i
\(844\) −2.83269e20 5.06531e20i −0.928542 1.66038i
\(845\) −1.91163e19 −0.0621450
\(846\) 3.27059e19 8.52393e18i 0.105447 0.0274819i
\(847\) 1.66310e19i 0.0531783i
\(848\) −8.94551e19 + 1.45582e20i −0.283683 + 0.461675i
\(849\) 1.80352e20 0.567240
\(850\) −7.50004e19 2.87773e20i −0.233954 0.897672i
\(851\) 5.69704e20i 1.76255i
\(852\) 1.11463e20 6.23336e19i 0.342021 0.191269i
\(853\) 2.02272e20 0.615593 0.307796 0.951452i \(-0.400408\pi\)
0.307796 + 0.951452i \(0.400408\pi\)
\(854\) 7.30764e19 1.90454e19i 0.220583 0.0574891i
\(855\) 2.99055e19i 0.0895342i
\(856\) −4.22935e20 + 4.05906e20i −1.25591 + 1.20534i
\(857\) 4.20343e19 0.123805 0.0619025 0.998082i \(-0.480283\pi\)
0.0619025 + 0.998082i \(0.480283\pi\)
\(858\) −9.43321e19 3.61948e20i −0.275581 1.05739i
\(859\) 2.14936e20i 0.622811i 0.950277 + 0.311406i \(0.100800\pi\)
−0.950277 + 0.311406i \(0.899200\pi\)
\(860\) 1.05471e20 + 1.88599e20i 0.303140 + 0.542065i
\(861\) 1.36576e19 0.0389360
\(862\) 4.39414e20 1.14522e20i 1.24258 0.323845i
\(863\) 2.61596e20i 0.733762i 0.930268 + 0.366881i \(0.119574\pi\)
−0.930268 + 0.366881i \(0.880426\pi\)
\(864\) 9.38579e19 3.07733e20i 0.261141 0.856204i
\(865\) −8.49085e20 −2.34336
\(866\) 8.89771e19 + 3.41401e20i 0.243586 + 0.934629i
\(867\) 1.17685e20i 0.319586i
\(868\) 8.55560e18 4.78457e18i 0.0230469 0.0128886i
\(869\) 2.11083e20 0.564047
\(870\) −1.23863e20 + 3.22817e19i −0.328328 + 0.0855700i
\(871\) 4.18778e20i 1.10118i
\(872\) 3.56404e20 + 3.71356e20i 0.929667 + 0.968668i
\(873\) 1.12027e20 0.289884
\(874\) 5.93623e19 + 2.27770e20i 0.152381 + 0.584678i
\(875\) 5.05862e19i 0.128818i
\(876\) −1.18448e18 2.11805e18i −0.00299226 0.00535065i
\(877\) −3.90992e20 −0.979875 −0.489938 0.871758i \(-0.662980\pi\)
−0.489938 + 0.871758i \(0.662980\pi\)
\(878\) −4.59014e20 + 1.19630e20i −1.14121 + 0.297426i
\(879\) 1.95188e20i 0.481428i
\(880\) 5.20774e20 + 3.19997e20i 1.27430 + 0.783011i
\(881\) 5.40581e20 1.31229 0.656144 0.754636i \(-0.272186\pi\)
0.656144 + 0.754636i \(0.272186\pi\)
\(882\) 5.13759e18 + 1.97127e19i 0.0123731 + 0.0474750i
\(883\) 3.86863e20i 0.924342i −0.886791 0.462171i \(-0.847071\pi\)
0.886791 0.462171i \(-0.152929\pi\)
\(884\) 3.02461e20 1.69146e20i 0.716974 0.400956i
\(885\) 7.71866e20 1.81526
\(886\) −2.19957e20 + 5.73260e19i −0.513218 + 0.133757i
\(887\) 6.78127e20i 1.56981i −0.619619 0.784903i \(-0.712713\pi\)
0.619619 0.784903i \(-0.287287\pi\)
\(888\) −3.52589e20 + 3.38393e20i −0.809801 + 0.777196i
\(889\) 6.62788e20 1.51030
\(890\) −1.18488e20 4.54634e20i −0.267883 1.02786i
\(891\) 5.25568e20i 1.17892i
\(892\) −1.58603e20 2.83608e20i −0.352986 0.631197i
\(893\) −1.00854e20 −0.222707
\(894\) −2.79920e20 + 7.29538e19i −0.613298 + 0.159840i
\(895\) 1.20764e20i 0.262528i
\(896\) 8.33582e19 + 3.83804e20i 0.179801 + 0.827853i
\(897\) −8.42585e20 −1.80329
\(898\) 1.24816e20 + 4.78911e20i 0.265054 + 1.01700i
\(899\) 3.19329e18i 0.00672853i
\(900\) 8.01442e19 4.48193e19i 0.167562 0.0937060i
\(901\) −2.19314e20 −0.454981
\(902\) −2.05586e19 + 5.35805e18i −0.0423202 + 0.0110296i
\(903\) 1.92354e20i 0.392905i
\(904\) −3.45856e20 3.60365e20i −0.700997 0.730405i
\(905\) 8.53133e19 0.171584
\(906\) −1.91395e19 7.34371e19i −0.0381973 0.146561i
\(907\) 9.18773e18i 0.0181952i 0.999959 + 0.00909761i \(0.00289590\pi\)
−0.999959 + 0.00909761i \(0.997104\pi\)
\(908\) −9.16173e19 1.63827e20i −0.180043 0.321946i
\(909\) −1.49600e20 −0.291733
\(910\) −6.01286e20 + 1.56709e20i −1.16357 + 0.303253i
\(911\) 1.02841e21i 1.97486i 0.158046 + 0.987432i \(0.449481\pi\)
−0.158046 + 0.987432i \(0.550519\pi\)
\(912\) 1.05707e20 1.72030e20i 0.201437 0.327824i
\(913\) −4.78735e20 −0.905315
\(914\) 5.77392e19 + 2.21542e20i 0.108355 + 0.415751i
\(915\) 2.27105e20i 0.422940i
\(916\) −1.76934e20 + 9.89476e19i −0.326997 + 0.182868i
\(917\) −2.18603e20 −0.400932
\(918\) 3.99595e20 1.04144e20i 0.727314 0.189555i
\(919\) 8.16694e20i 1.47520i −0.675238 0.737600i \(-0.735959\pi\)
0.675238 0.737600i \(-0.264041\pi\)
\(920\) 9.93409e20 9.53412e20i 1.78079 1.70909i
\(921\) −3.60963e20 −0.642163
\(922\) −1.09259e20 4.19222e20i −0.192904 0.740164i
\(923\) 2.01956e20i 0.353870i
\(924\) 2.65571e20 + 4.74885e20i 0.461824 + 0.825818i
\(925\) 6.63195e20 1.14459
\(926\) −1.57519e20 + 4.10530e19i −0.269808 + 0.0703183i
\(927\) 4.23088e18i 0.00719237i
\(928\) 1.22377e20 + 3.73248e19i 0.206474 + 0.0629741i
\(929\) 7.17263e19 0.120107 0.0600535 0.998195i \(-0.480873\pi\)
0.0600535 + 0.998195i \(0.480873\pi\)
\(930\) 7.43468e18 + 2.85265e19i 0.0123561 + 0.0474098i
\(931\) 6.07873e19i 0.100269i
\(932\) −5.53323e19 + 3.09436e19i −0.0905873 + 0.0506594i
\(933\) −2.64554e19 −0.0429875
\(934\) 2.07980e20 5.42044e19i 0.335423 0.0874191i
\(935\) 7.84527e20i 1.25582i
\(936\) 7.40932e19 + 7.72016e19i 0.117719 + 0.122658i
\(937\) 9.33303e20 1.47179 0.735894 0.677096i \(-0.236762\pi\)
0.735894 + 0.677096i \(0.236762\pi\)
\(938\) −1.53634e20 5.89488e20i −0.240474 0.922688i
\(939\) 1.06622e21i 1.65649i
\(940\) 2.87960e20 + 5.14920e20i 0.444056 + 0.794044i
\(941\) 3.59055e20 0.549583 0.274791 0.961504i \(-0.411391\pi\)
0.274791 + 0.961504i \(0.411391\pi\)
\(942\) 7.99079e20 2.08259e20i 1.21404 0.316408i
\(943\) 4.78587e19i 0.0721737i
\(944\) −6.57337e20 4.03911e20i −0.983975 0.604619i
\(945\) −7.40429e20 −1.10017
\(946\) −7.54633e19 2.89549e20i −0.111301 0.427055i
\(947\) 8.55162e20i 1.25198i 0.779830 + 0.625991i \(0.215305\pi\)
−0.779830 + 0.625991i \(0.784695\pi\)
\(948\) −3.56004e20 + 1.99089e20i −0.517365 + 0.289327i
\(949\) −3.83762e18 −0.00553603
\(950\) −2.65148e20 + 6.91039e19i −0.379685 + 0.0989549i
\(951\) 5.54507e19i 0.0788212i
\(952\) −3.63702e20 + 3.49059e20i −0.513201 + 0.492538i
\(953\) −1.03188e20 −0.144538 −0.0722688 0.997385i \(-0.523024\pi\)
−0.0722688 + 0.997385i \(0.523024\pi\)
\(954\) −1.70786e19 6.55296e19i −0.0237472 0.0911169i
\(955\) 1.09417e21i 1.51030i
\(956\) −1.14226e20 2.04255e20i −0.156516 0.279877i
\(957\) 1.77246e20 0.241097
\(958\) 3.26844e20 8.51834e19i 0.441349 0.115026i
\(959\) 7.39023e20i 0.990667i
\(960\) −1.18013e21 4.85116e19i −1.57048 0.0645575i
\(961\) 7.56209e20 0.999028
\(962\) 1.94905e20 + 7.47842e20i 0.255622 + 0.980808i
\(963\) 2.32323e20i 0.302488i
\(964\) 6.22452e19 3.48096e19i 0.0804575 0.0449945i
\(965\) −2.04084e21 −2.61890
\(966\) 1.18605e21 3.09114e20i 1.51100 0.393802i
\(967\) 8.55095e20i 1.08151i −0.841181 0.540753i \(-0.818139\pi\)
0.841181 0.540753i \(-0.181861\pi\)
\(968\) −3.46161e19 3.60683e19i −0.0434661 0.0452896i
\(969\) 2.59158e20 0.323071
\(970\) 4.93175e20 + 1.89229e21i 0.610377 + 2.34199i
\(971\) 4.99804e20i 0.614136i −0.951688 0.307068i \(-0.900652\pi\)
0.951688 0.307068i \(-0.0993480\pi\)
\(972\) 1.37559e20 + 2.45979e20i 0.167813 + 0.300078i
\(973\) −7.14184e20 −0.865008
\(974\) −7.46215e20 + 1.94481e20i −0.897328 + 0.233865i
\(975\) 9.80856e20i 1.17104i
\(976\) 1.18842e20 1.93407e20i 0.140871 0.229258i
\(977\) 1.26501e21 1.48879 0.744395 0.667739i \(-0.232738\pi\)
0.744395 + 0.667739i \(0.232738\pi\)
\(978\) −3.15627e20 1.21105e21i −0.368810 1.41511i
\(979\) 6.50571e20i 0.754772i
\(980\) −3.10355e20 + 1.73561e20i −0.357500 + 0.199926i
\(981\) −2.03990e20 −0.233306
\(982\) −3.77277e20 + 9.83272e19i −0.428430 + 0.111659i
\(983\) 4.78813e20i 0.539873i −0.962878 0.269936i \(-0.912997\pi\)
0.962878 0.269936i \(-0.0870026\pi\)
\(984\) 2.96197e19 2.84271e19i 0.0331600 0.0318249i
\(985\) 4.88023e20 0.542484
\(986\) 4.14154e19 + 1.58909e20i 0.0457112 + 0.175392i
\(987\) 5.25172e20i 0.575548i
\(988\) −1.55848e20 2.78682e20i −0.169591 0.303256i
\(989\) −6.74046e20 −0.728309
\(990\) −2.34412e20 + 6.10932e19i −0.251497 + 0.0655461i
\(991\) 1.15848e21i 1.23417i 0.786897 + 0.617085i \(0.211686\pi\)
−0.786897 + 0.617085i \(0.788314\pi\)
\(992\) 8.59615e18 2.81843e19i 0.00909332 0.0298143i
\(993\) 1.12379e21 1.18043
\(994\) 7.40902e19 + 2.84280e20i 0.0772780 + 0.296512i
\(995\) 4.05751e20i 0.420240i
\(996\) 8.07415e20 4.51533e20i 0.830388 0.464381i
\(997\) −1.22877e20 −0.125488 −0.0627442 0.998030i \(-0.519985\pi\)
−0.0627442 + 0.998030i \(0.519985\pi\)
\(998\) −5.14521e20 + 1.34096e20i −0.521783 + 0.135989i
\(999\) 9.20898e20i 0.927371i
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 4.15.b.a.3.3 6
3.2 odd 2 36.15.d.c.19.4 6
4.3 odd 2 inner 4.15.b.a.3.4 yes 6
8.3 odd 2 64.15.c.d.63.5 6
8.5 even 2 64.15.c.d.63.2 6
12.11 even 2 36.15.d.c.19.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4.15.b.a.3.3 6 1.1 even 1 trivial
4.15.b.a.3.4 yes 6 4.3 odd 2 inner
36.15.d.c.19.3 6 12.11 even 2
36.15.d.c.19.4 6 3.2 odd 2
64.15.c.d.63.2 6 8.5 even 2
64.15.c.d.63.5 6 8.3 odd 2