Properties

Label 35.10.k.a.3.2
Level $35$
Weight $10$
Character 35.3
Analytic conductor $18.026$
Analytic rank $0$
Dimension $136$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,10,Mod(3,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.3");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 35.k (of order \(12\), degree \(4\), 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: \(18.0262542657\)
Analytic rank: \(0\)
Dimension: \(136\)
Relative dimension: \(34\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 3.2
Character \(\chi\) \(=\) 35.3
Dual form 35.10.k.a.12.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-39.0059 - 10.4516i) q^{2} +(-2.23944 - 8.35771i) q^{3} +(968.820 + 559.349i) q^{4} +(42.9502 - 1396.88i) q^{5} +349.406i q^{6} +(6351.67 - 99.7449i) q^{7} +(-17323.8 - 17323.8i) q^{8} +(16981.1 - 9804.07i) q^{9} +(-16275.0 + 54037.8i) q^{10} +(-36572.6 + 63345.5i) q^{11} +(2505.26 - 9349.75i) q^{12} +(-83277.2 + 83277.2i) q^{13} +(-248795. - 62494.4i) q^{14} +(-11770.9 + 2769.27i) q^{15} +(208283. + 360757. i) q^{16} +(204019. - 54666.7i) q^{17} +(-764833. + 204936. i) q^{18} +(470064. + 814174. i) q^{19} +(822955. - 1.32930e6i) q^{20} +(-15057.8 - 52862.0i) q^{21} +(2.08861e6 - 2.08861e6i) q^{22} +(514101. - 1.91865e6i) q^{23} +(-105992. + 183583. i) q^{24} +(-1.94944e6 - 119993. i) q^{25} +(4.11868e6 - 2.37792e6i) q^{26} +(-240394. - 240394. i) q^{27} +(6.20941e6 + 3.45616e6i) q^{28} +3.47419e6i q^{29} +(488079. + 15007.1i) q^{30} +(1.49660e6 + 864063. i) q^{31} +(-1.10722e6 - 4.13219e6i) q^{32} +(611326. + 163804. i) q^{33} -8.52929e6 q^{34} +(133474. - 8.87681e6i) q^{35} +2.19356e7 q^{36} +(1.43384e7 + 3.84196e6i) q^{37} +(-9.82583e6 - 3.66705e7i) q^{38} +(882501. + 509512. i) q^{39} +(-2.49434e7 + 2.34553e7i) q^{40} +1.48704e7i q^{41} +(34851.4 + 2.21931e6i) q^{42} +(1.16590e7 + 1.16590e7i) q^{43} +(-7.08645e7 + 4.09136e7i) q^{44} +(-1.29658e7 - 2.41417e7i) q^{45} +(-4.01060e7 + 6.94656e7i) q^{46} +(1.43658e7 - 5.36138e7i) q^{47} +(2.54866e6 - 2.54866e6i) q^{48} +(4.03337e7 - 1.26709e6i) q^{49} +(7.47854e7 + 2.50552e7i) q^{50} +(-913776. - 1.58271e6i) q^{51} +(-1.27262e8 + 3.40997e7i) q^{52} +(2.53675e6 - 679719. i) q^{53} +(6.86428e6 + 1.18893e7i) q^{54} +(8.69155e7 + 5.38083e7i) q^{55} +(-1.11763e8 - 1.08307e8i) q^{56} +(5.75195e6 - 5.75195e6i) q^{57} +(3.63109e7 - 1.35514e8i) q^{58} +(2.62607e7 - 4.54848e7i) q^{59} +(-1.29529e7 - 3.90112e6i) q^{60} +(-2.12248e7 + 1.22542e7i) q^{61} +(-4.93454e7 - 4.93454e7i) q^{62} +(1.06881e8 - 6.39659e7i) q^{63} -4.05301e7i q^{64} +(1.12752e8 + 1.19905e8i) q^{65} +(-2.21333e7 - 1.27787e7i) q^{66} +(1.15942e7 + 4.32701e7i) q^{67} +(2.28235e8 + 6.11554e7i) q^{68} -1.71868e7 q^{69} +(-9.79832e7 + 3.44853e8i) q^{70} +1.14914e8 q^{71} +(-4.64022e8 - 1.24334e8i) q^{72} +(-6.20080e6 - 2.31417e7i) q^{73} +(-5.19127e8 - 2.99718e8i) q^{74} +(3.36278e6 + 1.65615e7i) q^{75} +1.05172e9i q^{76} +(-2.25978e8 + 4.05998e8i) q^{77} +(-2.90975e7 - 2.90975e7i) q^{78} +(1.54149e8 - 8.89979e7i) q^{79} +(5.12881e8 - 2.75452e8i) q^{80} +(1.91503e8 - 3.31692e8i) q^{81} +(1.55419e8 - 5.80033e8i) q^{82} +(1.56076e8 - 1.56076e8i) q^{83} +(1.49800e7 - 5.96364e7i) q^{84} +(-6.76002e7 - 2.87338e8i) q^{85} +(-3.32916e8 - 5.76627e8i) q^{86} +(2.90363e7 - 7.78025e6i) q^{87} +(1.73096e9 - 4.63810e8i) q^{88} +(-1.36058e8 - 2.35659e8i) q^{89} +(2.53422e8 + 1.07718e9i) q^{90} +(-5.20643e8 + 5.37255e8i) q^{91} +(1.57127e9 - 1.57127e9i) q^{92} +(3.87004e6 - 1.44432e7i) q^{93} +(-1.12070e9 + 1.94111e9i) q^{94} +(1.15749e9 - 6.21655e8i) q^{95} +(-3.20561e7 + 1.85076e7i) q^{96} +(-3.93410e8 - 3.93410e8i) q^{97} +(-1.58650e9 - 3.72128e8i) q^{98} +1.43424e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 136 q - 2 q^{2} - 6 q^{3} - 1710 q^{5} + 5940 q^{7} - 3484 q^{8} + 153786 q^{10} - 87752 q^{11} + 3066 q^{12} - 318872 q^{15} + 3132804 q^{16} - 1578678 q^{17} - 239036 q^{18} - 5745396 q^{21} + 2132088 q^{22}+ \cdots + 5117393178 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −39.0059 10.4516i −1.72383 0.461900i −0.745086 0.666968i \(-0.767592\pi\)
−0.978748 + 0.205068i \(0.934258\pi\)
\(3\) −2.23944 8.35771i −0.0159623 0.0595719i 0.957485 0.288482i \(-0.0931505\pi\)
−0.973448 + 0.228910i \(0.926484\pi\)
\(4\) 968.820 + 559.349i 1.89223 + 1.09248i
\(5\) 42.9502 1396.88i 0.0307327 0.999528i
\(6\) 349.406i 0.110065i
\(7\) 6351.67 99.7449i 0.999877 0.0157018i
\(8\) −17323.8 17323.8i −1.49534 1.49534i
\(9\) 16981.1 9804.07i 0.862731 0.498098i
\(10\) −16275.0 + 54037.8i −0.514660 + 1.70882i
\(11\) −36572.6 + 63345.5i −0.753162 + 1.30451i 0.193121 + 0.981175i \(0.438139\pi\)
−0.946283 + 0.323340i \(0.895194\pi\)
\(12\) 2505.26 9349.75i 0.0348768 0.130162i
\(13\) −83277.2 + 83277.2i −0.808688 + 0.808688i −0.984435 0.175747i \(-0.943766\pi\)
0.175747 + 0.984435i \(0.443766\pi\)
\(14\) −248795. 62494.4i −1.73087 0.434776i
\(15\) −11770.9 + 2769.27i −0.0600344 + 0.0141239i
\(16\) 208283. + 360757.i 0.794537 + 1.37618i
\(17\) 204019. 54666.7i 0.592448 0.158746i 0.0498760 0.998755i \(-0.484117\pi\)
0.542572 + 0.840010i \(0.317451\pi\)
\(18\) −764833. + 204936.i −1.71728 + 0.460143i
\(19\) 470064. + 814174.i 0.827495 + 1.43326i 0.899997 + 0.435895i \(0.143568\pi\)
−0.0725025 + 0.997368i \(0.523099\pi\)
\(20\) 822955. 1.32930e6i 1.15011 1.85776i
\(21\) −15057.8 52862.0i −0.0168957 0.0593140i
\(22\) 2.08861e6 2.08861e6i 1.90088 1.90088i
\(23\) 514101. 1.91865e6i 0.383066 1.42962i −0.458128 0.888886i \(-0.651480\pi\)
0.841193 0.540735i \(-0.181854\pi\)
\(24\) −105992. + 183583.i −0.0652111 + 0.112949i
\(25\) −1.94944e6 119993.i −0.998111 0.0614363i
\(26\) 4.11868e6 2.37792e6i 1.76758 1.02051i
\(27\) −240394. 240394.i −0.0870535 0.0870535i
\(28\) 6.20941e6 + 3.45616e6i 1.90915 + 1.06263i
\(29\) 3.47419e6i 0.912143i 0.889943 + 0.456072i \(0.150744\pi\)
−0.889943 + 0.456072i \(0.849256\pi\)
\(30\) 488079. + 15007.1i 0.110013 + 0.00338260i
\(31\) 1.49660e6 + 864063.i 0.291057 + 0.168042i 0.638418 0.769689i \(-0.279589\pi\)
−0.347361 + 0.937731i \(0.612922\pi\)
\(32\) −1.10722e6 4.13219e6i −0.186663 0.696634i
\(33\) 611326. + 163804.i 0.0897346 + 0.0240443i
\(34\) −8.52929e6 −1.09461
\(35\) 133474. 8.87681e6i 0.0150345 0.999887i
\(36\) 2.19356e7 2.17664
\(37\) 1.43384e7 + 3.84196e6i 1.25774 + 0.337011i 0.825323 0.564661i \(-0.190993\pi\)
0.432421 + 0.901672i \(0.357660\pi\)
\(38\) −9.82583e6 3.66705e7i −0.764440 2.85293i
\(39\) 882501. + 509512.i 0.0610836 + 0.0352666i
\(40\) −2.49434e7 + 2.34553e7i −1.54058 + 1.44867i
\(41\) 1.48704e7i 0.821854i 0.911668 + 0.410927i \(0.134795\pi\)
−0.911668 + 0.410927i \(0.865205\pi\)
\(42\) 34851.4 + 2.21931e6i 0.00172822 + 0.110052i
\(43\) 1.16590e7 + 1.16590e7i 0.520061 + 0.520061i 0.917590 0.397528i \(-0.130132\pi\)
−0.397528 + 0.917590i \(0.630132\pi\)
\(44\) −7.08645e7 + 4.09136e7i −2.85031 + 1.64563i
\(45\) −1.29658e7 2.41417e7i −0.471349 0.877632i
\(46\) −4.01060e7 + 6.94656e7i −1.32068 + 2.28749i
\(47\) 1.43658e7 5.36138e7i 0.429426 1.60264i −0.324638 0.945838i \(-0.605242\pi\)
0.754064 0.656801i \(-0.228091\pi\)
\(48\) 2.54866e6 2.54866e6i 0.0692990 0.0692990i
\(49\) 4.03337e7 1.26709e6i 0.999507 0.0313997i
\(50\) 7.47854e7 + 2.50552e7i 1.69220 + 0.566933i
\(51\) −913776. 1.58271e6i −0.0189136 0.0327593i
\(52\) −1.27262e8 + 3.40997e7i −2.41370 + 0.646748i
\(53\) 2.53675e6 679719.i 0.0441607 0.0118328i −0.236671 0.971590i \(-0.576056\pi\)
0.280832 + 0.959757i \(0.409390\pi\)
\(54\) 6.86428e6 + 1.18893e7i 0.109856 + 0.190276i
\(55\) 8.69155e7 + 5.38083e7i 1.28075 + 0.792897i
\(56\) −1.11763e8 1.08307e8i −1.51863 1.47167i
\(57\) 5.75195e6 5.75195e6i 0.0721736 0.0721736i
\(58\) 3.63109e7 1.35514e8i 0.421319 1.57238i
\(59\) 2.62607e7 4.54848e7i 0.282145 0.488689i −0.689768 0.724030i \(-0.742288\pi\)
0.971913 + 0.235342i \(0.0756209\pi\)
\(60\) −1.29529e7 3.90112e6i −0.129029 0.0388606i
\(61\) −2.12248e7 + 1.22542e7i −0.196273 + 0.113318i −0.594916 0.803788i \(-0.702815\pi\)
0.398643 + 0.917106i \(0.369481\pi\)
\(62\) −4.93454e7 4.93454e7i −0.424116 0.424116i
\(63\) 1.06881e8 6.39659e7i 0.854804 0.511583i
\(64\) 4.05301e7i 0.301973i
\(65\) 1.12752e8 + 1.19905e8i 0.783453 + 0.833159i
\(66\) −2.21333e7 1.27787e7i −0.143582 0.0828968i
\(67\) 1.15942e7 + 4.32701e7i 0.0702917 + 0.262332i 0.992125 0.125256i \(-0.0399751\pi\)
−0.921833 + 0.387588i \(0.873308\pi\)
\(68\) 2.28235e8 + 6.11554e7i 1.29447 + 0.346853i
\(69\) −1.71868e7 −0.0912799
\(70\) −9.79832e7 + 3.44853e8i −0.487765 + 1.71669i
\(71\) 1.14914e8 0.536673 0.268336 0.963325i \(-0.413526\pi\)
0.268336 + 0.963325i \(0.413526\pi\)
\(72\) −4.64022e8 1.24334e8i −2.03490 0.545249i
\(73\) −6.20080e6 2.31417e7i −0.0255561 0.0953767i 0.951970 0.306192i \(-0.0990549\pi\)
−0.977526 + 0.210815i \(0.932388\pi\)
\(74\) −5.19127e8 2.99718e8i −2.01248 1.16190i
\(75\) 3.36278e6 + 1.65615e7i 0.0122722 + 0.0604401i
\(76\) 1.05172e9i 3.61608i
\(77\) −2.25978e8 + 4.05998e8i −0.732586 + 1.31618i
\(78\) −2.90975e7 2.90975e7i −0.0890083 0.0890083i
\(79\) 1.54149e8 8.89979e7i 0.445265 0.257074i −0.260563 0.965457i \(-0.583908\pi\)
0.705828 + 0.708383i \(0.250575\pi\)
\(80\) 5.12881e8 2.75452e8i 1.39995 0.751868i
\(81\) 1.91503e8 3.31692e8i 0.494302 0.856156i
\(82\) 1.55419e8 5.80033e8i 0.379615 1.41674i
\(83\) 1.56076e8 1.56076e8i 0.360982 0.360982i −0.503192 0.864175i \(-0.667841\pi\)
0.864175 + 0.503192i \(0.167841\pi\)
\(84\) 1.49800e7 5.96364e7i 0.0328287 0.130694i
\(85\) −6.76002e7 2.87338e8i −0.140463 0.597047i
\(86\) −3.32916e8 5.76627e8i −0.656283 1.13672i
\(87\) 2.90363e7 7.78025e6i 0.0543381 0.0145599i
\(88\) 1.73096e9 4.63810e8i 3.07692 0.824457i
\(89\) −1.36058e8 2.35659e8i −0.229863 0.398134i 0.727905 0.685678i \(-0.240494\pi\)
−0.957767 + 0.287545i \(0.907161\pi\)
\(90\) 2.53422e8 + 1.07718e9i 0.407149 + 1.73061i
\(91\) −5.20643e8 + 5.37255e8i −0.795891 + 0.821286i
\(92\) 1.57127e9 1.57127e9i 2.28668 2.28668i
\(93\) 3.87004e6 1.44432e7i 0.00536465 0.0200212i
\(94\) −1.12070e9 + 1.94111e9i −1.48052 + 2.56433i
\(95\) 1.15749e9 6.21655e8i 1.45802 0.783056i
\(96\) −3.20561e7 + 1.85076e7i −0.0385203 + 0.0222397i
\(97\) −3.93410e8 3.93410e8i −0.451203 0.451203i 0.444550 0.895754i \(-0.353363\pi\)
−0.895754 + 0.444550i \(0.853363\pi\)
\(98\) −1.58650e9 3.72128e8i −1.73749 0.407544i
\(99\) 1.43424e9i 1.50059i
\(100\) −1.82153e9 1.20667e9i −1.82153 1.20667i
\(101\) 1.05845e9 + 6.11096e8i 1.01210 + 0.584337i 0.911806 0.410620i \(-0.134688\pi\)
0.100295 + 0.994958i \(0.468021\pi\)
\(102\) 1.91009e7 + 7.12854e7i 0.0174724 + 0.0652078i
\(103\) 4.10057e8 + 1.09874e8i 0.358985 + 0.0961898i 0.433804 0.901007i \(-0.357171\pi\)
−0.0748185 + 0.997197i \(0.523838\pi\)
\(104\) 2.88536e9 2.41852
\(105\) −7.44887e7 + 1.87636e7i −0.0598052 + 0.0150648i
\(106\) −1.06052e8 −0.0815912
\(107\) −1.10910e9 2.97183e8i −0.817984 0.219178i −0.174519 0.984654i \(-0.555837\pi\)
−0.643465 + 0.765476i \(0.722504\pi\)
\(108\) −9.84344e7 3.67362e8i −0.0696210 0.259829i
\(109\) −2.72971e8 1.57600e8i −0.185224 0.106939i 0.404521 0.914529i \(-0.367438\pi\)
−0.589745 + 0.807590i \(0.700772\pi\)
\(110\) −2.82783e9 3.00725e9i −1.84156 1.95840i
\(111\) 1.28440e8i 0.0803057i
\(112\) 1.35893e9 + 2.27063e9i 0.816048 + 1.36353i
\(113\) 3.68340e8 + 3.68340e8i 0.212518 + 0.212518i 0.805336 0.592818i \(-0.201985\pi\)
−0.592818 + 0.805336i \(0.701985\pi\)
\(114\) −2.84477e8 + 1.64243e8i −0.157752 + 0.0910783i
\(115\) −2.65805e9 8.00545e8i −1.41717 0.426821i
\(116\) −1.94329e9 + 3.36587e9i −0.996496 + 1.72598i
\(117\) −5.97687e8 + 2.23060e9i −0.294875 + 1.10049i
\(118\) −1.49971e9 + 1.49971e9i −0.712096 + 0.712096i
\(119\) 1.29041e9 3.67574e8i 0.589882 0.168029i
\(120\) 2.51892e8 + 1.55943e8i 0.110891 + 0.0686515i
\(121\) −1.49613e9 2.59138e9i −0.634506 1.09900i
\(122\) 9.55970e8 2.56151e8i 0.390683 0.104683i
\(123\) 1.24282e8 3.33014e7i 0.0489595 0.0131186i
\(124\) 9.66624e8 + 1.67424e9i 0.367164 + 0.635947i
\(125\) −2.51345e8 + 2.71798e9i −0.0920820 + 0.995751i
\(126\) −4.83752e9 + 1.37798e9i −1.70984 + 0.487051i
\(127\) 1.68604e9 1.68604e9i 0.575112 0.575112i −0.358441 0.933553i \(-0.616691\pi\)
0.933553 + 0.358441i \(0.116691\pi\)
\(128\) −9.90499e8 + 3.69659e9i −0.326144 + 1.21719i
\(129\) 7.13331e7 1.23553e8i 0.0226797 0.0392824i
\(130\) −3.14478e9 5.85545e9i −0.965707 1.79811i
\(131\) 2.20166e9 1.27113e9i 0.653174 0.377110i −0.136497 0.990640i \(-0.543584\pi\)
0.789671 + 0.613530i \(0.210251\pi\)
\(132\) 5.00641e8 + 5.00641e8i 0.143530 + 0.143530i
\(133\) 3.06690e9 + 5.12447e9i 0.849898 + 1.42009i
\(134\) 1.80897e9i 0.484685i
\(135\) −3.46127e8 + 3.25477e8i −0.0896878 + 0.0843370i
\(136\) −4.48142e9 2.58735e9i −1.12329 0.648530i
\(137\) 1.03214e9 + 3.85200e9i 0.250320 + 0.934208i 0.970634 + 0.240560i \(0.0773310\pi\)
−0.720314 + 0.693648i \(0.756002\pi\)
\(138\) 6.70388e8 + 1.79630e8i 0.157351 + 0.0421622i
\(139\) 1.11876e9 0.254198 0.127099 0.991890i \(-0.459433\pi\)
0.127099 + 0.991890i \(0.459433\pi\)
\(140\) 5.09455e9 8.52538e9i 1.12080 1.87559i
\(141\) −4.80260e8 −0.102327
\(142\) −4.48232e9 1.20103e9i −0.925134 0.247889i
\(143\) −2.22958e9 8.32090e9i −0.445872 1.66402i
\(144\) 7.07377e9 + 4.08404e9i 1.37094 + 0.791515i
\(145\) 4.85304e9 + 1.49217e8i 0.911712 + 0.0280326i
\(146\) 9.67471e8i 0.176218i
\(147\) −1.00915e8 3.34260e8i −0.0178249 0.0590413i
\(148\) 1.17423e10 + 1.17423e10i 2.01176 + 2.01176i
\(149\) 5.12506e9 2.95896e9i 0.851846 0.491813i −0.00942735 0.999956i \(-0.503001\pi\)
0.861273 + 0.508142i \(0.169668\pi\)
\(150\) 4.19262e7 6.81144e8i 0.00676200 0.109857i
\(151\) −3.51842e9 + 6.09408e9i −0.550746 + 0.953920i 0.447475 + 0.894296i \(0.352323\pi\)
−0.998221 + 0.0596234i \(0.981010\pi\)
\(152\) 5.96131e9 2.22479e10i 0.905827 3.38059i
\(153\) 2.92852e9 2.92852e9i 0.432052 0.432052i
\(154\) 1.30578e10 1.34745e10i 1.87080 1.93049i
\(155\) 1.27127e9 2.05346e9i 0.176907 0.285755i
\(156\) 5.69990e8 + 9.87252e8i 0.0770560 + 0.133465i
\(157\) 4.72348e9 1.26565e9i 0.620460 0.166252i 0.0651229 0.997877i \(-0.479256\pi\)
0.555337 + 0.831626i \(0.312589\pi\)
\(158\) −6.94289e9 + 1.86034e9i −0.886305 + 0.237485i
\(159\) −1.13618e7 1.96792e7i −0.00140981 0.00244186i
\(160\) −5.81973e9 + 1.36917e9i −0.702042 + 0.165165i
\(161\) 3.07402e9 1.22379e10i 0.360571 1.43546i
\(162\) −1.09365e10 + 1.09365e10i −1.24755 + 1.24755i
\(163\) −2.92896e9 + 1.09310e10i −0.324989 + 1.21288i 0.589333 + 0.807890i \(0.299391\pi\)
−0.914323 + 0.404987i \(0.867276\pi\)
\(164\) −8.31773e9 + 1.44067e10i −0.897858 + 1.55514i
\(165\) 2.55072e8 8.46915e8i 0.0267907 0.0889533i
\(166\) −7.71915e9 + 4.45666e9i −0.789011 + 0.455536i
\(167\) −2.55209e9 2.55209e9i −0.253905 0.253905i 0.568664 0.822570i \(-0.307460\pi\)
−0.822570 + 0.568664i \(0.807460\pi\)
\(168\) −6.54913e8 + 1.17663e9i −0.0634296 + 0.113959i
\(169\) 3.26569e9i 0.307953i
\(170\) −3.66335e8 + 1.19144e10i −0.0336402 + 1.09409i
\(171\) 1.59644e10 + 9.21707e9i 1.42781 + 0.824348i
\(172\) 4.77404e9 + 1.78170e10i 0.415919 + 1.55223i
\(173\) −1.48349e10 3.97500e9i −1.25915 0.337388i −0.433285 0.901257i \(-0.642646\pi\)
−0.825865 + 0.563868i \(0.809312\pi\)
\(174\) −1.21390e9 −0.100395
\(175\) −1.23941e10 5.67708e8i −0.998953 0.0457566i
\(176\) −3.04698e10 −2.39366
\(177\) −4.38958e8 1.17618e8i −0.0336158 0.00900732i
\(178\) 2.84404e9 + 1.06141e10i 0.212347 + 0.792490i
\(179\) 7.27026e9 + 4.19749e9i 0.529312 + 0.305598i 0.740736 0.671796i \(-0.234477\pi\)
−0.211424 + 0.977394i \(0.567810\pi\)
\(180\) 9.42138e8 3.06414e10i 0.0668941 2.17562i
\(181\) 6.25708e9i 0.433330i 0.976246 + 0.216665i \(0.0695179\pi\)
−0.976246 + 0.216665i \(0.930482\pi\)
\(182\) 2.59233e10 1.55146e10i 1.75134 1.04814i
\(183\) 1.49949e8 + 1.49949e8i 0.00988354 + 0.00988354i
\(184\) −4.21446e10 + 2.43322e10i −2.71057 + 1.56495i
\(185\) 5.98260e9 1.98640e10i 0.375506 1.24679i
\(186\) −3.01909e8 + 5.22921e8i −0.0184955 + 0.0320352i
\(187\) −3.99860e9 + 1.49230e10i −0.239123 + 0.892418i
\(188\) 4.39066e10 4.39066e10i 2.56342 2.56342i
\(189\) −1.55088e9 1.50292e9i −0.0884097 0.0856759i
\(190\) −5.16464e10 + 1.21505e10i −2.87507 + 0.676401i
\(191\) 3.26030e9 + 5.64701e9i 0.177259 + 0.307021i 0.940941 0.338571i \(-0.109944\pi\)
−0.763682 + 0.645593i \(0.776610\pi\)
\(192\) −3.38739e8 + 9.07649e7i −0.0179891 + 0.00482017i
\(193\) 1.48534e10 3.97996e9i 0.770580 0.206476i 0.147952 0.988994i \(-0.452732\pi\)
0.622628 + 0.782518i \(0.286065\pi\)
\(194\) 1.12335e10 + 1.94571e10i 0.569389 + 0.986211i
\(195\) 7.49632e8 1.21087e9i 0.0371272 0.0599709i
\(196\) 3.97849e10 + 2.13330e10i 1.92560 + 1.03252i
\(197\) −9.59171e9 + 9.59171e9i −0.453731 + 0.453731i −0.896591 0.442860i \(-0.853964\pi\)
0.442860 + 0.896591i \(0.353964\pi\)
\(198\) 1.49901e10 5.59438e10i 0.693124 2.58678i
\(199\) −2.01507e9 + 3.49020e9i −0.0910858 + 0.157765i −0.907968 0.419039i \(-0.862367\pi\)
0.816882 + 0.576804i \(0.195700\pi\)
\(200\) 3.16929e10 + 3.58504e10i 1.40064 + 1.58438i
\(201\) 3.35675e8 1.93802e8i 0.0145056 0.00837483i
\(202\) −3.48989e10 3.48989e10i −1.47479 1.47479i
\(203\) 3.46533e8 + 2.20669e10i 0.0143223 + 0.912031i
\(204\) 2.04448e9i 0.0826507i
\(205\) 2.07722e10 + 6.38687e8i 0.821466 + 0.0252578i
\(206\) −1.48463e10 8.57150e9i −0.574401 0.331631i
\(207\) −1.00806e10 3.76212e10i −0.381609 1.42418i
\(208\) −4.73881e10 1.26976e10i −1.75543 0.470367i
\(209\) −6.87657e10 −2.49295
\(210\) 3.10161e9 + 4.66365e7i 0.110053 + 0.00165478i
\(211\) −1.00183e10 −0.347955 −0.173977 0.984750i \(-0.555662\pi\)
−0.173977 + 0.984750i \(0.555662\pi\)
\(212\) 2.83785e9 + 7.60400e8i 0.0964891 + 0.0258542i
\(213\) −2.57343e8 9.60416e8i −0.00856650 0.0319706i
\(214\) 4.01555e10 + 2.31838e10i 1.30883 + 0.755654i
\(215\) 1.67871e10 1.57855e10i 0.535799 0.503833i
\(216\) 8.32907e9i 0.260348i
\(217\) 9.59209e9 + 5.33896e9i 0.293660 + 0.163451i
\(218\) 9.00031e9 + 9.00031e9i 0.269900 + 0.269900i
\(219\) −1.79525e8 + 1.03649e8i −0.00527384 + 0.00304485i
\(220\) 5.41079e10 + 1.00747e11i 1.55725 + 2.89953i
\(221\) −1.24376e10 + 2.15426e10i −0.350730 + 0.607481i
\(222\) −1.34240e9 + 5.00991e9i −0.0370932 + 0.138434i
\(223\) 2.76355e10 2.76355e10i 0.748333 0.748333i −0.225833 0.974166i \(-0.572510\pi\)
0.974166 + 0.225833i \(0.0725105\pi\)
\(224\) −7.44483e9 2.61358e10i −0.197578 0.693618i
\(225\) −3.42801e10 + 1.70748e10i −0.891703 + 0.444154i
\(226\) −1.05177e10 1.82172e10i −0.268184 0.464508i
\(227\) −7.35250e10 + 1.97010e10i −1.83789 + 0.492460i −0.998681 0.0513520i \(-0.983647\pi\)
−0.839207 + 0.543812i \(0.816980\pi\)
\(228\) 8.78995e9 2.35526e9i 0.215417 0.0577208i
\(229\) −2.52046e10 4.36556e10i −0.605647 1.04901i −0.991949 0.126639i \(-0.959581\pi\)
0.386302 0.922372i \(-0.373752\pi\)
\(230\) 9.53127e10 + 5.90069e10i 2.24582 + 1.39036i
\(231\) 3.89928e9 + 9.79453e8i 0.0901011 + 0.0226324i
\(232\) 6.01863e10 6.01863e10i 1.36396 1.36396i
\(233\) −1.61470e10 + 6.02615e10i −0.358914 + 1.33949i 0.516573 + 0.856243i \(0.327208\pi\)
−0.875487 + 0.483242i \(0.839459\pi\)
\(234\) 4.66266e10 8.07597e10i 1.01663 1.76085i
\(235\) −7.42751e10 2.23700e10i −1.58869 0.478477i
\(236\) 5.08837e10 2.93777e10i 1.06776 0.616473i
\(237\) −1.08903e9 1.08903e9i −0.0224218 0.0224218i
\(238\) −5.41752e10 + 8.50753e8i −1.09447 + 0.0171873i
\(239\) 3.18362e10i 0.631147i −0.948901 0.315574i \(-0.897803\pi\)
0.948901 0.315574i \(-0.102197\pi\)
\(240\) −3.45072e9 3.66965e9i −0.0671366 0.0713960i
\(241\) 1.98688e10 + 1.14713e10i 0.379398 + 0.219045i 0.677556 0.735471i \(-0.263039\pi\)
−0.298158 + 0.954516i \(0.596372\pi\)
\(242\) 3.12739e10 + 1.16716e11i 0.586156 + 2.18757i
\(243\) −9.66463e9 2.58963e9i −0.177810 0.0476441i
\(244\) −2.74174e10 −0.495190
\(245\) −3.76365e7 5.63959e10i −0.000667363 1.00000i
\(246\) −5.19580e9 −0.0904575
\(247\) −1.06948e11 2.86566e10i −1.82825 0.489878i
\(248\) −1.09580e10 4.08957e10i −0.183949 0.686507i
\(249\) −1.65397e9 9.54918e8i −0.0272665 0.0157423i
\(250\) 3.82112e10 1.03390e11i 0.618672 1.67398i
\(251\) 6.67930e9i 0.106218i 0.998589 + 0.0531091i \(0.0169131\pi\)
−0.998589 + 0.0531091i \(0.983087\pi\)
\(252\) 1.39327e11 2.18796e9i 2.17638 0.0341772i
\(253\) 1.02736e11 + 1.02736e11i 1.57645 + 1.57645i
\(254\) −8.33876e10 + 4.81438e10i −1.25704 + 0.725753i
\(255\) −2.25010e9 + 1.20846e9i −0.0333251 + 0.0178979i
\(256\) 6.68949e10 1.15865e11i 0.973450 1.68606i
\(257\) −2.07643e10 + 7.74933e10i −0.296905 + 1.10807i 0.642787 + 0.766045i \(0.277778\pi\)
−0.939692 + 0.342020i \(0.888889\pi\)
\(258\) −4.07374e9 + 4.07374e9i −0.0572406 + 0.0572406i
\(259\) 9.14558e10 + 2.29726e10i 1.26288 + 0.317221i
\(260\) 4.21673e10 + 1.79234e11i 0.572263 + 2.43243i
\(261\) 3.40612e10 + 5.89958e10i 0.454337 + 0.786934i
\(262\) −9.91630e10 + 2.65707e10i −1.30015 + 0.348375i
\(263\) −1.17394e11 + 3.14557e10i −1.51303 + 0.405414i −0.917439 0.397876i \(-0.869747\pi\)
−0.595588 + 0.803290i \(0.703081\pi\)
\(264\) −7.75278e9 1.34282e10i −0.0982290 0.170138i
\(265\) −8.40534e8 3.57273e9i −0.0104701 0.0445035i
\(266\) −6.60681e10 2.31939e11i −0.809142 2.84057i
\(267\) −1.66488e9 + 1.66488e9i −0.0200485 + 0.0200485i
\(268\) −1.29704e10 + 4.84062e10i −0.153584 + 0.573184i
\(269\) 4.77454e10 8.26975e10i 0.555964 0.962958i −0.441864 0.897082i \(-0.645683\pi\)
0.997828 0.0658756i \(-0.0209840\pi\)
\(270\) 1.69027e10 9.07794e9i 0.193562 0.103956i
\(271\) 9.81082e10 5.66428e10i 1.10495 0.637944i 0.167435 0.985883i \(-0.446452\pi\)
0.937517 + 0.347939i \(0.113118\pi\)
\(272\) 6.22151e10 + 6.22151e10i 0.689184 + 0.689184i
\(273\) 5.65617e9 + 3.14823e9i 0.0616298 + 0.0343032i
\(274\) 1.61038e11i 1.72604i
\(275\) 7.88969e10 1.19100e11i 0.831884 1.25578i
\(276\) −1.66510e10 9.61343e9i −0.172722 0.0997212i
\(277\) −1.35836e10 5.06945e10i −0.138629 0.517371i −0.999957 0.00932078i \(-0.997033\pi\)
0.861327 0.508050i \(-0.169634\pi\)
\(278\) −4.36384e10 1.16929e10i −0.438195 0.117414i
\(279\) 3.38853e10 0.334805
\(280\) −1.56093e11 + 1.51468e11i −1.51765 + 1.47268i
\(281\) 6.33592e10 0.606222 0.303111 0.952955i \(-0.401975\pi\)
0.303111 + 0.952955i \(0.401975\pi\)
\(282\) 1.87330e10 + 5.01948e9i 0.176395 + 0.0472648i
\(283\) −4.73693e10 1.76785e11i −0.438994 1.63835i −0.731325 0.682029i \(-0.761098\pi\)
0.292331 0.956317i \(-0.405569\pi\)
\(284\) 1.11331e11 + 6.42768e10i 1.01551 + 0.586303i
\(285\) −7.78775e9 8.28185e9i −0.0699214 0.0743576i
\(286\) 3.47867e11i 3.07444i
\(287\) 1.48324e9 + 9.44517e10i 0.0129046 + 0.821753i
\(288\) −5.93140e10 5.93140e10i −0.508032 0.508032i
\(289\) −6.40649e10 + 3.69879e10i −0.540231 + 0.311903i
\(290\) −1.87738e11 5.65424e10i −1.55869 0.469443i
\(291\) −2.40699e9 + 4.16902e9i −0.0196768 + 0.0340813i
\(292\) 6.93682e9 2.58886e10i 0.0558390 0.208394i
\(293\) −5.78945e10 + 5.78945e10i −0.458916 + 0.458916i −0.898300 0.439384i \(-0.855197\pi\)
0.439384 + 0.898300i \(0.355197\pi\)
\(294\) 4.42729e8 + 1.40928e10i 0.00345601 + 0.110011i
\(295\) −6.24090e10 3.86366e10i −0.479787 0.297030i
\(296\) −1.81838e11 3.14953e11i −1.37680 2.38469i
\(297\) 2.40197e10 6.43606e9i 0.179128 0.0479972i
\(298\) −2.30834e11 + 6.18517e10i −1.69561 + 0.454337i
\(299\) 1.16967e11 + 2.02593e11i 0.846337 + 1.46590i
\(300\) −6.00574e9 + 1.79261e10i −0.0428076 + 0.127773i
\(301\) 7.52172e10 + 7.28914e10i 0.528163 + 0.511831i
\(302\) 2.00932e11 2.00932e11i 1.39001 1.39001i
\(303\) 2.73703e9 1.02147e10i 0.0186547 0.0696202i
\(304\) −1.95813e11 + 3.39157e11i −1.31495 + 2.27756i
\(305\) 1.62060e10 + 3.01749e10i 0.107233 + 0.199663i
\(306\) −1.44837e11 + 8.36218e10i −0.944351 + 0.545221i
\(307\) 1.12857e11 + 1.12857e11i 0.725110 + 0.725110i 0.969641 0.244531i \(-0.0786340\pi\)
−0.244531 + 0.969641i \(0.578634\pi\)
\(308\) −4.46027e11 + 2.66938e11i −2.82412 + 1.69018i
\(309\) 3.67319e9i 0.0229209i
\(310\) −7.10491e10 + 6.68103e10i −0.436949 + 0.410881i
\(311\) 1.23031e11 + 7.10320e10i 0.745749 + 0.430559i 0.824156 0.566363i \(-0.191650\pi\)
−0.0784067 + 0.996921i \(0.524983\pi\)
\(312\) −6.46159e9 2.41150e10i −0.0386050 0.144076i
\(313\) 8.15479e10 + 2.18507e10i 0.480245 + 0.128681i 0.490817 0.871263i \(-0.336698\pi\)
−0.0105716 + 0.999944i \(0.503365\pi\)
\(314\) −1.97472e11 −1.14636
\(315\) −8.47623e10 1.52047e11i −0.485071 0.870123i
\(316\) 1.99123e11 1.12339
\(317\) 1.99515e11 + 5.34600e10i 1.10971 + 0.297346i 0.766713 0.641990i \(-0.221891\pi\)
0.342998 + 0.939336i \(0.388558\pi\)
\(318\) 2.37498e8 + 8.86354e8i 0.00130238 + 0.00486055i
\(319\) −2.20075e11 1.27060e11i −1.18990 0.686991i
\(320\) −5.66158e10 1.74078e9i −0.301830 0.00928044i
\(321\) 9.93509e9i 0.0522275i
\(322\) −2.47811e11 + 4.45223e11i −1.28460 + 2.30795i
\(323\) 1.40410e11 + 1.40410e11i 0.717772 + 0.717772i
\(324\) 3.71063e11 2.14233e11i 1.87066 1.08003i
\(325\) 1.72336e11 1.52351e11i 0.856843 0.757478i
\(326\) 2.28493e11 3.95762e11i 1.12046 1.94069i
\(327\) −7.05871e8 + 2.63435e9i −0.00341398 + 0.0127411i
\(328\) 2.57612e11 2.57612e11i 1.22895 1.22895i
\(329\) 8.58988e10 3.41970e11i 0.404209 1.60918i
\(330\) −1.88009e10 + 3.03688e10i −0.0872703 + 0.140966i
\(331\) −1.51185e11 2.61860e11i −0.692281 1.19907i −0.971089 0.238719i \(-0.923273\pi\)
0.278808 0.960347i \(-0.410061\pi\)
\(332\) 2.38511e11 6.39089e10i 1.07743 0.288695i
\(333\) 2.81149e11 7.53336e10i 1.25296 0.335730i
\(334\) 7.28731e10 + 1.26220e11i 0.320411 + 0.554969i
\(335\) 6.09413e10 1.43373e10i 0.264369 0.0621963i
\(336\) 1.59341e10 1.64425e10i 0.0682024 0.0703786i
\(337\) −1.54585e11 + 1.54585e11i −0.652878 + 0.652878i −0.953685 0.300807i \(-0.902744\pi\)
0.300807 + 0.953685i \(0.402744\pi\)
\(338\) −3.41317e10 + 1.27381e11i −0.142244 + 0.530860i
\(339\) 2.25360e9 3.90336e9i 0.00926785 0.0160524i
\(340\) 9.52297e10 3.16191e11i 0.386471 1.28320i
\(341\) −1.09469e11 + 6.32020e10i −0.438426 + 0.253126i
\(342\) −5.26374e11 5.26374e11i −2.08054 2.08054i
\(343\) 2.56060e11 1.20712e10i 0.998891 0.0470899i
\(344\) 4.03958e11i 1.55533i
\(345\) −7.38179e8 + 2.40080e10i −0.00280528 + 0.0912368i
\(346\) 5.37104e11 + 3.10097e11i 2.01473 + 1.16320i
\(347\) −1.62024e10 6.04683e10i −0.0599926 0.223895i 0.929420 0.369023i \(-0.120308\pi\)
−0.989413 + 0.145127i \(0.953641\pi\)
\(348\) 3.24828e10 + 8.70375e9i 0.118726 + 0.0318126i
\(349\) 5.17296e11 1.86649 0.933243 0.359245i \(-0.116966\pi\)
0.933243 + 0.359245i \(0.116966\pi\)
\(350\) 4.77511e11 + 1.51683e11i 1.70089 + 0.540293i
\(351\) 4.00386e10 0.140798
\(352\) 3.02249e11 + 8.09874e10i 1.04936 + 0.281174i
\(353\) −8.21978e9 3.06766e10i −0.0281757 0.105153i 0.950406 0.311012i \(-0.100668\pi\)
−0.978582 + 0.205859i \(0.934001\pi\)
\(354\) 1.58927e10 + 9.17563e9i 0.0537876 + 0.0310543i
\(355\) 4.93557e9 1.60521e11i 0.0164934 0.536419i
\(356\) 3.04415e11i 1.00448i
\(357\) −5.96187e9 9.96168e9i −0.0194256 0.0324583i
\(358\) −2.39713e11 2.39713e11i −0.771290 0.771290i
\(359\) −5.12777e11 + 2.96052e11i −1.62931 + 0.940682i −0.645010 + 0.764174i \(0.723147\pi\)
−0.984299 + 0.176507i \(0.943520\pi\)
\(360\) −1.93610e11 + 6.42844e11i −0.607529 + 2.01718i
\(361\) −2.80576e11 + 4.85971e11i −0.869496 + 1.50601i
\(362\) 6.53965e10 2.44063e11i 0.200155 0.746988i
\(363\) −1.83075e10 + 1.83075e10i −0.0553412 + 0.0553412i
\(364\) −8.04922e11 + 2.29283e11i −2.40324 + 0.684567i
\(365\) −3.25926e10 + 7.66785e9i −0.0961171 + 0.0226129i
\(366\) −4.28168e9 7.41608e9i −0.0124724 0.0216028i
\(367\) −3.71699e11 + 9.95965e10i −1.06953 + 0.286580i −0.750301 0.661096i \(-0.770091\pi\)
−0.319232 + 0.947677i \(0.603425\pi\)
\(368\) 7.99246e11 2.14157e11i 2.27177 0.608720i
\(369\) 1.45790e11 + 2.52516e11i 0.409364 + 0.709040i
\(370\) −4.40967e11 + 7.12286e11i −1.22320 + 1.97582i
\(371\) 1.60448e10 4.57038e9i 0.0439694 0.0125248i
\(372\) 1.18281e10 1.18281e10i 0.0320238 0.0320238i
\(373\) −7.32956e10 + 2.73543e11i −0.196060 + 0.731705i 0.795930 + 0.605388i \(0.206982\pi\)
−0.991990 + 0.126316i \(0.959685\pi\)
\(374\) 3.11938e11 5.40293e11i 0.824416 1.42793i
\(375\) 2.32789e10 3.98609e9i 0.0607887 0.0104089i
\(376\) −1.17766e12 + 6.79925e11i −3.03862 + 1.75435i
\(377\) −2.89321e11 2.89321e11i −0.737639 0.737639i
\(378\) 4.47855e10 + 7.48320e10i 0.112830 + 0.188527i
\(379\) 1.05524e11i 0.262708i 0.991336 + 0.131354i \(0.0419324\pi\)
−0.991336 + 0.131354i \(0.958068\pi\)
\(380\) 1.46913e12 + 4.51715e10i 3.61437 + 0.111132i
\(381\) −1.78673e10 1.03157e10i −0.0434406 0.0250804i
\(382\) −6.81508e10 2.54342e11i −0.163752 0.611130i
\(383\) −4.11220e10 1.10186e10i −0.0976517 0.0261657i 0.209662 0.977774i \(-0.432764\pi\)
−0.307314 + 0.951608i \(0.599430\pi\)
\(384\) 3.31132e10 0.0777161
\(385\) 5.57425e11 + 3.33103e11i 1.29304 + 0.772690i
\(386\) −6.20967e11 −1.42372
\(387\) 3.12290e11 + 8.36778e10i 0.707715 + 0.189632i
\(388\) −1.61090e11 6.01197e11i −0.360850 1.34671i
\(389\) −7.14031e11 4.12246e11i −1.58104 0.912816i −0.994708 0.102747i \(-0.967237\pi\)
−0.586335 0.810068i \(-0.699430\pi\)
\(390\) −4.18956e10 + 3.93961e10i −0.0917018 + 0.0862308i
\(391\) 4.19545e11i 0.907786i
\(392\) −7.20685e11 6.76783e11i −1.54155 1.44765i
\(393\) −1.55542e10 1.55542e10i −0.0328913 0.0328913i
\(394\) 4.74382e11 2.73885e11i 0.991734 0.572578i
\(395\) −1.17699e11 2.19150e11i −0.243268 0.452955i
\(396\) −8.02240e11 + 1.38952e12i −1.63937 + 2.83946i
\(397\) 3.92796e10 1.46593e11i 0.0793614 0.296181i −0.914825 0.403850i \(-0.867672\pi\)
0.994187 + 0.107669i \(0.0343386\pi\)
\(398\) 1.15078e11 1.15078e11i 0.229889 0.229889i
\(399\) 3.59607e10 3.71082e10i 0.0710314 0.0732979i
\(400\) −3.62746e11 7.28265e11i −0.708489 1.42239i
\(401\) 2.57062e11 + 4.45244e11i 0.496464 + 0.859901i 0.999992 0.00407832i \(-0.00129817\pi\)
−0.503528 + 0.863979i \(0.667965\pi\)
\(402\) −1.51188e10 + 4.05108e9i −0.0288736 + 0.00773666i
\(403\) −1.96589e11 + 5.26760e10i −0.371268 + 0.0994809i
\(404\) 6.83632e11 + 1.18409e12i 1.27675 + 2.21140i
\(405\) −4.55110e11 2.81753e11i −0.840560 0.520380i
\(406\) 2.17118e11 8.64362e11i 0.396578 1.57880i
\(407\) −7.67762e11 + 7.67762e11i −1.38692 + 1.38692i
\(408\) −1.15884e10 + 4.32486e10i −0.0207040 + 0.0772683i
\(409\) −2.64051e10 + 4.57350e10i −0.0466587 + 0.0808153i −0.888412 0.459048i \(-0.848191\pi\)
0.841753 + 0.539863i \(0.181524\pi\)
\(410\) −8.03563e11 2.42015e11i −1.40440 0.422975i
\(411\) 2.98825e10 1.72527e10i 0.0516569 0.0298241i
\(412\) 3.35813e11 + 3.35813e11i 0.574196 + 0.574196i
\(413\) 1.62262e11 2.91524e11i 0.274436 0.493059i
\(414\) 1.57281e12i 2.63132i
\(415\) −2.11317e11 2.24724e11i −0.349718 0.371906i
\(416\) 4.36323e11 + 2.51911e11i 0.714312 + 0.412408i
\(417\) −2.50541e9 9.35030e9i −0.00405757 0.0151430i
\(418\) 2.68227e12 + 7.18712e11i 4.29743 + 1.15149i
\(419\) −1.00043e12 −1.58572 −0.792858 0.609407i \(-0.791408\pi\)
−0.792858 + 0.609407i \(0.791408\pi\)
\(420\) −8.26616e10 2.34866e10i −0.129623 0.0368298i
\(421\) 1.25128e12 1.94126 0.970632 0.240569i \(-0.0773340\pi\)
0.970632 + 0.240569i \(0.0773340\pi\)
\(422\) 3.90773e11 + 1.04707e11i 0.599816 + 0.160720i
\(423\) −2.81686e11 1.05127e12i −0.427793 1.59654i
\(424\) −5.57215e10 3.21708e10i −0.0837291 0.0483410i
\(425\) −4.04281e11 + 8.20884e10i −0.601081 + 0.122048i
\(426\) 4.01515e10i 0.0590689i
\(427\) −1.33591e11 + 7.99514e10i −0.194469 + 0.116386i
\(428\) −9.08292e11 9.08292e11i −1.30836 1.30836i
\(429\) −6.45507e10 + 3.72683e10i −0.0920117 + 0.0531230i
\(430\) −8.19779e11 + 4.40278e11i −1.15635 + 0.621039i
\(431\) −3.38727e10 + 5.86692e10i −0.0472826 + 0.0818959i −0.888698 0.458493i \(-0.848389\pi\)
0.841415 + 0.540389i \(0.181723\pi\)
\(432\) 3.66538e10 1.36794e11i 0.0506339 0.188968i
\(433\) 1.32923e11 1.32923e11i 0.181721 0.181721i −0.610384 0.792105i \(-0.708985\pi\)
0.792105 + 0.610384i \(0.208985\pi\)
\(434\) −3.18348e11 3.08504e11i −0.430723 0.417404i
\(435\) −9.62098e9 4.08945e10i −0.0128830 0.0547599i
\(436\) −1.76306e11 3.05372e11i −0.233657 0.404706i
\(437\) 1.80378e12 4.83320e11i 2.36601 0.633970i
\(438\) 8.08585e9 2.16660e9i 0.0104976 0.00281284i
\(439\) −1.54008e11 2.66750e11i −0.197903 0.342779i 0.749945 0.661500i \(-0.230080\pi\)
−0.947848 + 0.318721i \(0.896747\pi\)
\(440\) −5.73543e11 2.43787e12i −0.729506 3.10080i
\(441\) 6.72490e11 4.16951e11i 0.846666 0.524942i
\(442\) 7.10296e11 7.10296e11i 0.885195 0.885195i
\(443\) −2.22734e11 + 8.31256e11i −0.274771 + 1.02546i 0.681224 + 0.732075i \(0.261448\pi\)
−0.955995 + 0.293383i \(0.905219\pi\)
\(444\) 7.18426e10 1.24435e11i 0.0877322 0.151957i
\(445\) −3.35032e11 + 1.79935e11i −0.405010 + 0.217518i
\(446\) −1.36678e12 + 7.89111e11i −1.63566 + 0.944346i
\(447\) −3.62074e10 3.62074e10i −0.0428957 0.0428957i
\(448\) −4.04267e9 2.57434e11i −0.00474152 0.301936i
\(449\) 9.98153e11i 1.15901i 0.814967 + 0.579507i \(0.196755\pi\)
−0.814967 + 0.579507i \(0.803245\pi\)
\(450\) 1.51558e12 3.07736e11i 1.74230 0.353771i
\(451\) −9.41973e11 5.43848e11i −1.07212 0.618989i
\(452\) 1.50825e11 + 5.62886e11i 0.169961 + 0.634304i
\(453\) 5.88118e10 + 1.57586e10i 0.0656180 + 0.0175823i
\(454\) 3.07382e12 3.39568
\(455\) 7.28121e11 + 7.50352e11i 0.796439 + 0.820755i
\(456\) −1.99291e11 −0.215847
\(457\) 6.57872e11 + 1.76276e11i 0.705535 + 0.189047i 0.593708 0.804680i \(-0.297663\pi\)
0.111826 + 0.993728i \(0.464330\pi\)
\(458\) 5.26856e11 + 1.96625e12i 0.559497 + 2.08807i
\(459\) −6.21864e10 3.59033e10i −0.0653940 0.0377553i
\(460\) −2.12739e12 2.26236e12i −2.21532 2.35587i
\(461\) 1.79010e12i 1.84596i 0.384846 + 0.922981i \(0.374255\pi\)
−0.384846 + 0.922981i \(0.625745\pi\)
\(462\) −1.41858e11 7.89582e10i −0.144865 0.0806321i
\(463\) −5.36805e11 5.36805e11i −0.542877 0.542877i 0.381494 0.924371i \(-0.375410\pi\)
−0.924371 + 0.381494i \(0.875410\pi\)
\(464\) −1.25334e12 + 7.23616e11i −1.25527 + 0.724732i
\(465\) −2.00092e10 6.02632e9i −0.0198468 0.00597742i
\(466\) 1.25966e12 2.18179e12i 1.23742 2.14327i
\(467\) 2.31286e11 8.63172e11i 0.225021 0.839791i −0.757375 0.652981i \(-0.773518\pi\)
0.982396 0.186811i \(-0.0598151\pi\)
\(468\) −1.82673e12 + 1.82673e12i −1.76023 + 1.76023i
\(469\) 7.79585e10 + 2.73681e11i 0.0744021 + 0.261196i
\(470\) 2.66337e12 + 1.64886e12i 2.51762 + 1.55863i
\(471\) −2.11559e10 3.66431e10i −0.0198079 0.0343082i
\(472\) −1.24291e12 + 3.33035e11i −1.15265 + 0.308853i
\(473\) −1.16495e12 + 3.12147e11i −1.07012 + 0.286737i
\(474\) 3.10964e10 + 5.38605e10i 0.0282949 + 0.0490081i
\(475\) −8.18664e11 1.64358e12i −0.737877 1.48139i
\(476\) 1.45577e12 + 3.65674e11i 1.29976 + 0.326484i
\(477\) 3.64128e10 3.64128e10i 0.0322049 0.0322049i
\(478\) −3.32739e11 + 1.24180e12i −0.291527 + 1.08799i
\(479\) 8.34044e11 1.44461e12i 0.723901 1.25383i −0.235523 0.971869i \(-0.575680\pi\)
0.959425 0.281965i \(-0.0909862\pi\)
\(480\) 2.44761e10 + 4.55735e10i 0.0210454 + 0.0391856i
\(481\) −1.51401e12 + 8.74112e11i −1.28966 + 0.744585i
\(482\) −6.55108e11 6.55108e11i −0.552842 0.552842i
\(483\) −1.09165e11 + 1.71430e9i −0.0912686 + 0.00143326i
\(484\) 3.34744e12i 2.77273i
\(485\) −5.66444e11 + 5.32650e11i −0.464857 + 0.437124i
\(486\) 3.49912e11 + 2.02022e11i 0.284509 + 0.164261i
\(487\) −7.20374e10 2.68847e11i −0.0580334 0.216584i 0.930820 0.365479i \(-0.119095\pi\)
−0.988853 + 0.148896i \(0.952428\pi\)
\(488\) 5.79984e11 + 1.55406e11i 0.462942 + 0.124045i
\(489\) 9.79176e10 0.0774410
\(490\) −5.87959e11 + 2.20017e12i −0.460749 + 1.72414i
\(491\) −1.73175e12 −1.34468 −0.672339 0.740244i \(-0.734710\pi\)
−0.672339 + 0.740244i \(0.734710\pi\)
\(492\) 1.39034e11 + 3.72541e10i 0.106974 + 0.0286637i
\(493\) 1.89923e11 + 7.08801e11i 0.144799 + 0.540397i
\(494\) 3.87209e12 + 2.23555e12i 2.92532 + 1.68894i
\(495\) 2.00346e12 + 6.16009e10i 1.49989 + 0.0461173i
\(496\) 7.19879e11i 0.534062i
\(497\) 7.29894e11 1.14621e10i 0.536606 0.00842672i
\(498\) 5.45340e10 + 5.45340e10i 0.0397316 + 0.0397316i
\(499\) −5.23630e11 + 3.02318e11i −0.378070 + 0.218279i −0.676978 0.736003i \(-0.736711\pi\)
0.298908 + 0.954282i \(0.403378\pi\)
\(500\) −1.76381e12 + 2.49264e12i −1.26208 + 1.78359i
\(501\) −1.56144e10 + 2.70449e10i −0.0110727 + 0.0191785i
\(502\) 6.98094e10 2.60532e11i 0.0490622 0.183103i
\(503\) 8.52175e11 8.52175e11i 0.593572 0.593572i −0.345023 0.938594i \(-0.612129\pi\)
0.938594 + 0.345023i \(0.112129\pi\)
\(504\) −2.95971e12 7.43446e11i −2.04321 0.513230i
\(505\) 8.99090e11 1.45228e12i 0.615166 0.993665i
\(506\) −2.93356e12 5.08107e12i −1.98938 3.44570i
\(507\) −2.72937e10 + 7.31332e9i −0.0183454 + 0.00491562i
\(508\) 2.57656e12 6.90387e11i 1.71654 0.459945i
\(509\) −2.85483e11 4.94471e11i −0.188517 0.326521i 0.756239 0.654296i \(-0.227035\pi\)
−0.944756 + 0.327774i \(0.893701\pi\)
\(510\) 1.00398e11 2.36199e10i 0.0657140 0.0154601i
\(511\) −4.16937e10 1.46370e11i −0.0270506 0.0949637i
\(512\) −2.43476e12 + 2.43476e12i −1.56582 + 1.56582i
\(513\) 8.27220e10 3.08723e11i 0.0527343 0.196807i
\(514\) 1.61986e12 2.80568e12i 1.02363 1.77298i
\(515\) 1.71094e11 5.68082e11i 0.107177 0.355860i
\(516\) 1.38218e11 7.98002e10i 0.0858303 0.0495542i
\(517\) 2.87080e12 + 2.87080e12i 1.76724 + 1.76724i
\(518\) −3.32721e12 1.85193e12i −2.03047 1.13016i
\(519\) 1.32888e11i 0.0803955i
\(520\) 1.23927e11 4.03051e12i 0.0743276 2.41738i
\(521\) 1.76380e12 + 1.01833e12i 1.04877 + 0.605506i 0.922304 0.386466i \(-0.126304\pi\)
0.126463 + 0.991971i \(0.459638\pi\)
\(522\) −7.11989e11 2.65718e12i −0.419716 1.56640i
\(523\) 1.94222e12 + 5.20417e11i 1.13512 + 0.304154i 0.776987 0.629517i \(-0.216747\pi\)
0.358132 + 0.933671i \(0.383414\pi\)
\(524\) 2.84402e12 1.64794
\(525\) 2.30112e10 + 1.04858e11i 0.0132197 + 0.0602399i
\(526\) 4.90784e12 2.79547
\(527\) 3.52570e11 + 9.44708e10i 0.199112 + 0.0533519i
\(528\) 6.82353e10 + 2.54658e11i 0.0382082 + 0.142595i
\(529\) −1.85708e12 1.07219e12i −1.03105 0.595278i
\(530\) −4.55497e9 + 1.48143e11i −0.00250752 + 0.0815527i
\(531\) 1.02985e12i 0.562143i
\(532\) 1.04903e11 + 6.68016e12i 0.0567789 + 3.61563i
\(533\) −1.23836e12 1.23836e12i −0.664624 0.664624i
\(534\) 8.23406e10 4.75394e10i 0.0438206 0.0252999i
\(535\) −4.62766e11 + 1.53652e12i −0.244213 + 0.810862i
\(536\) 5.48748e11 9.50460e11i 0.287165 0.497384i
\(537\) 1.88001e10 7.01628e10i 0.00975607 0.0364102i
\(538\) −2.72668e12 + 2.72668e12i −1.40318 + 1.40318i
\(539\) −1.39484e12 + 2.60130e12i −0.711829 + 1.32752i
\(540\) −5.17389e11 + 1.21723e11i −0.261846 + 0.0616028i
\(541\) −1.59265e12 2.75855e12i −0.799343 1.38450i −0.920045 0.391813i \(-0.871848\pi\)
0.120702 0.992689i \(-0.461485\pi\)
\(542\) −4.41881e12 + 1.18402e12i −2.19942 + 0.589333i
\(543\) 5.22949e10 1.40124e10i 0.0258143 0.00691692i
\(544\) −4.51786e11 7.82516e11i −0.221176 0.383087i
\(545\) −2.31873e11 + 3.74539e11i −0.112581 + 0.181850i
\(546\) −1.87720e11 1.81916e11i −0.0903950 0.0875998i
\(547\) 9.09916e11 9.09916e11i 0.434569 0.434569i −0.455611 0.890179i \(-0.650579\pi\)
0.890179 + 0.455611i \(0.150579\pi\)
\(548\) −1.15465e12 + 4.30922e12i −0.546939 + 2.04120i
\(549\) −2.40281e11 + 4.16179e11i −0.112887 + 0.195526i
\(550\) −4.32223e12 + 3.82099e12i −2.01407 + 1.78051i
\(551\) −2.82860e12 + 1.63309e12i −1.30734 + 0.754794i
\(552\) 2.97742e11 + 2.97742e11i 0.136494 + 0.136494i
\(553\) 9.70225e11 5.80661e11i 0.441174 0.264034i
\(554\) 2.11936e12i 0.955895i
\(555\) −1.79415e11 5.51652e9i −0.0802677 0.00246801i
\(556\) 1.08388e12 + 6.25779e11i 0.481000 + 0.277705i
\(557\) 1.68036e11 + 6.27117e11i 0.0739695 + 0.276058i 0.992998 0.118134i \(-0.0376912\pi\)
−0.919028 + 0.394192i \(0.871025\pi\)
\(558\) −1.32173e12 3.54156e11i −0.577149 0.154647i
\(559\) −1.94186e12 −0.841135
\(560\) 3.23017e12 1.80074e12i 1.38797 0.773757i
\(561\) 1.33677e11 0.0569800
\(562\) −2.47138e12 6.62205e11i −1.04503 0.280014i
\(563\) −1.06421e12 3.97167e12i −0.446414 1.66604i −0.712177 0.702000i \(-0.752290\pi\)
0.265763 0.964038i \(-0.414376\pi\)
\(564\) −4.65285e11 2.68633e11i −0.193626 0.111790i
\(565\) 5.30348e11 4.98708e11i 0.218949 0.205887i
\(566\) 7.39073e12i 3.02701i
\(567\) 1.18328e12 2.12590e12i 0.480798 0.863812i
\(568\) −1.99074e12 1.99074e12i −0.802506 0.802506i
\(569\) −3.08914e12 + 1.78351e12i −1.23547 + 0.713299i −0.968165 0.250314i \(-0.919466\pi\)
−0.267304 + 0.963612i \(0.586133\pi\)
\(570\) 2.17210e11 + 4.04435e11i 0.0861871 + 0.160477i
\(571\) −3.87173e11 + 6.70603e11i −0.152420 + 0.263999i −0.932117 0.362158i \(-0.882040\pi\)
0.779697 + 0.626158i \(0.215373\pi\)
\(572\) 2.49422e12 9.30857e12i 0.974211 3.63581i
\(573\) 3.98948e10 3.98948e10i 0.0154604 0.0154604i
\(574\) 9.29317e11 3.69968e12i 0.357322 1.42253i
\(575\) −1.23243e12 + 3.67860e12i −0.470173 + 1.40339i
\(576\) −3.97360e11 6.88248e11i −0.150412 0.260522i
\(577\) 1.59356e12 4.26993e11i 0.598518 0.160372i 0.0531745 0.998585i \(-0.483066\pi\)
0.545343 + 0.838213i \(0.316399\pi\)
\(578\) 2.88549e12 7.73165e11i 1.07534 0.288136i
\(579\) −6.65266e10 1.15228e11i −0.0246004 0.0426091i
\(580\) 4.61826e12 + 2.85911e12i 1.69454 + 1.04907i
\(581\) 9.75778e11 1.00691e12i 0.355270 0.366606i
\(582\) 1.37460e11 1.37460e11i 0.0496617 0.0496617i
\(583\) −4.97182e10 + 1.85551e11i −0.0178241 + 0.0665203i
\(584\) −2.93481e11 + 5.08324e11i −0.104405 + 0.180835i
\(585\) 3.09021e12 + 9.30703e11i 1.09090 + 0.328556i
\(586\) 2.86332e12 1.65314e12i 1.00307 0.579122i
\(587\) −6.29587e11 6.29587e11i −0.218869 0.218869i 0.589153 0.808022i \(-0.299462\pi\)
−0.808022 + 0.589153i \(0.799462\pi\)
\(588\) 8.91993e10 3.80284e11i 0.0307726 0.131193i
\(589\) 1.62466e12i 0.556215i
\(590\) 2.03051e12 + 2.15933e12i 0.689875 + 0.733644i
\(591\) 1.01645e11 + 5.86847e10i 0.0342722 + 0.0197870i
\(592\) 1.60043e12 + 5.97288e12i 0.535536 + 1.99865i
\(593\) 6.03000e10 + 1.61573e10i 0.0200249 + 0.00536567i 0.268818 0.963191i \(-0.413367\pi\)
−0.248793 + 0.968557i \(0.580034\pi\)
\(594\) −1.00418e12 −0.330957
\(595\) −4.58035e11 1.81833e12i −0.149821 0.594767i
\(596\) 6.62035e12 2.14918
\(597\) 3.36827e10 + 9.02525e9i 0.0108523 + 0.00290787i
\(598\) −2.44499e12 9.12481e12i −0.781846 2.91789i
\(599\) 1.08217e12 + 6.24793e11i 0.343460 + 0.198297i 0.661801 0.749680i \(-0.269792\pi\)
−0.318341 + 0.947976i \(0.603126\pi\)
\(600\) 2.28653e11 3.45165e11i 0.0720271 0.108729i
\(601\) 4.60882e12i 1.44097i −0.693471 0.720485i \(-0.743919\pi\)
0.693471 0.720485i \(-0.256081\pi\)
\(602\) −2.17208e12 3.62933e12i −0.674051 1.12627i
\(603\) 6.21106e11 + 6.21106e11i 0.191310 + 0.191310i
\(604\) −6.81743e12 + 3.93604e12i −2.08427 + 1.20336i
\(605\) −3.68411e12 + 1.97862e12i −1.11798 + 0.600431i
\(606\) −2.13521e11 + 3.69829e11i −0.0643151 + 0.111397i
\(607\) −4.71608e11 + 1.76007e12i −0.141004 + 0.526235i 0.858897 + 0.512149i \(0.171150\pi\)
−0.999901 + 0.0140858i \(0.995516\pi\)
\(608\) 2.84386e12 2.84386e12i 0.843998 0.843998i
\(609\) 1.83653e11 5.23138e10i 0.0541028 0.0154113i
\(610\) −3.16754e11 1.34638e12i −0.0926271 0.393716i
\(611\) 3.26846e12 + 5.66115e12i 0.948764 + 1.64331i
\(612\) 4.47527e12 1.19914e12i 1.28955 0.345533i
\(613\) 2.09070e12 5.60200e11i 0.598024 0.160240i 0.0529062 0.998599i \(-0.483152\pi\)
0.545118 + 0.838359i \(0.316485\pi\)
\(614\) −3.22254e12 5.58161e12i −0.915042 1.58490i
\(615\) −4.11801e10 1.75038e11i −0.0116078 0.0493395i
\(616\) 1.09482e13 3.11862e12i 3.06359 0.872669i
\(617\) 2.58514e12 2.58514e12i 0.718127 0.718127i −0.250095 0.968221i \(-0.580462\pi\)
0.968221 + 0.250095i \(0.0804617\pi\)
\(618\) −3.83908e10 + 1.43276e11i −0.0105871 + 0.0395117i
\(619\) −3.13270e12 + 5.42599e12i −0.857651 + 1.48550i 0.0165122 + 0.999864i \(0.494744\pi\)
−0.874163 + 0.485632i \(0.838590\pi\)
\(620\) 2.38024e12 1.27835e12i 0.646930 0.347446i
\(621\) −5.84819e11 + 3.37645e11i −0.157801 + 0.0911063i
\(622\) −4.05654e12 4.05654e12i −1.08667 1.08667i
\(623\) −8.87699e11 1.48326e12i −0.236086 0.394475i
\(624\) 4.24491e11i 0.112083i
\(625\) 3.78590e12 + 4.67837e11i 0.992451 + 0.122641i
\(626\) −2.95247e12 1.70461e12i −0.768425 0.443650i
\(627\) 1.53997e11 + 5.74724e11i 0.0397931 + 0.148510i
\(628\) 5.28414e12 + 1.41588e12i 1.35568 + 0.363252i
\(629\) 3.13532e12 0.798646
\(630\) 1.71710e12 + 6.81663e12i 0.434273 + 1.72400i
\(631\) −1.59457e12 −0.400416 −0.200208 0.979753i \(-0.564162\pi\)
−0.200208 + 0.979753i \(0.564162\pi\)
\(632\) −4.21223e12 1.12866e12i −1.05023 0.281409i
\(633\) 2.24354e10 + 8.37300e10i 0.00555414 + 0.0207283i
\(634\) −7.22354e12 4.17051e12i −1.77561 1.02515i
\(635\) −2.28279e12 2.42762e12i −0.557165 0.592515i
\(636\) 2.54208e10i 0.00616073i
\(637\) −3.25336e12 + 3.46440e12i −0.782897 + 0.833682i
\(638\) 7.25623e12 + 7.25623e12i 1.73388 + 1.73388i
\(639\) 1.95137e12 1.12662e12i 0.463004 0.267316i
\(640\) 5.12116e12 + 1.54238e12i 1.20659 + 0.363397i
\(641\) −2.50749e12 + 4.34310e12i −0.586649 + 1.01611i 0.408019 + 0.912974i \(0.366220\pi\)
−0.994668 + 0.103132i \(0.967114\pi\)
\(642\) 1.03838e11 3.87527e11i 0.0241239 0.0900315i
\(643\) 5.83268e12 5.83268e12i 1.34561 1.34561i 0.455242 0.890368i \(-0.349553\pi\)
0.890368 0.455242i \(-0.150447\pi\)
\(644\) 9.82344e12 1.01369e13i 2.25049 2.32230i
\(645\) −1.69525e11 1.04951e11i −0.0385668 0.0238763i
\(646\) −4.00931e12 6.94433e12i −0.905781 1.56886i
\(647\) −1.57287e12 + 4.21451e11i −0.352878 + 0.0945534i −0.430904 0.902398i \(-0.641805\pi\)
0.0780254 + 0.996951i \(0.475138\pi\)
\(648\) −9.06373e12 + 2.42862e12i −2.01939 + 0.541093i
\(649\) 1.92084e12 + 3.32699e12i 0.425001 + 0.736123i
\(650\) −8.31444e12 + 4.14140e12i −1.82693 + 0.909990i
\(651\) 2.31405e10 9.21242e10i 0.00504962 0.0201029i
\(652\) −8.95189e12 + 8.95189e12i −1.93999 + 1.93999i
\(653\) 1.70246e11 6.35366e11i 0.0366410 0.136746i −0.945182 0.326543i \(-0.894116\pi\)
0.981823 + 0.189797i \(0.0607829\pi\)
\(654\) 5.50663e10 9.53776e10i 0.0117703 0.0203867i
\(655\) −1.68105e12 3.13005e12i −0.356859 0.664456i
\(656\) −5.36460e12 + 3.09725e12i −1.13102 + 0.652994i
\(657\) −3.32179e11 3.32179e11i −0.0695550 0.0695550i
\(658\) −6.92469e12 + 1.24411e13i −1.44007 + 2.58726i
\(659\) 7.89734e12i 1.63116i −0.578645 0.815580i \(-0.696418\pi\)
0.578645 0.815580i \(-0.303582\pi\)
\(660\) 7.20839e11 6.77834e11i 0.147874 0.139052i
\(661\) 4.54671e12 + 2.62505e12i 0.926384 + 0.534848i 0.885666 0.464323i \(-0.153702\pi\)
0.0407179 + 0.999171i \(0.487036\pi\)
\(662\) 3.16025e12 + 1.17942e13i 0.639529 + 2.38675i
\(663\) 2.07900e11 + 5.57067e10i 0.0417873 + 0.0111969i
\(664\) −5.40768e12 −1.07958
\(665\) 7.29001e12 4.06400e12i 1.44554 0.805853i
\(666\) −1.17538e13 −2.31497
\(667\) 6.66577e12 + 1.78609e12i 1.30402 + 0.349411i
\(668\) −1.04501e12 3.90002e12i −0.203060 0.757832i
\(669\) −2.92857e11 1.69081e11i −0.0565247 0.0326345i
\(670\) −2.52692e12 7.76957e10i −0.484456 0.0148957i
\(671\) 1.79267e12i 0.341388i
\(672\) −2.01763e11 + 1.20751e11i −0.0381663 + 0.0228418i
\(673\) −5.79849e12 5.79849e12i −1.08955 1.08955i −0.995574 0.0939762i \(-0.970042\pi\)
−0.0939762 0.995574i \(-0.529958\pi\)
\(674\) 7.64537e12 4.41406e12i 1.42702 0.823889i
\(675\) 4.39787e11 + 4.97478e11i 0.0815408 + 0.0922373i
\(676\) 1.82666e12 3.16386e12i 0.336432 0.582717i
\(677\) 4.11666e11 1.53636e12i 0.0753176 0.281089i −0.917988 0.396609i \(-0.870187\pi\)
0.993305 + 0.115520i \(0.0368535\pi\)
\(678\) −1.28700e11 + 1.28700e11i −0.0233908 + 0.0233908i
\(679\) −2.53805e12 2.45957e12i −0.458232 0.444063i
\(680\) −3.80670e12 + 6.14889e12i −0.682745 + 1.10282i
\(681\) 3.29310e11 + 5.70382e11i 0.0586736 + 0.101626i
\(682\) 4.93050e12 1.32112e12i 0.872693 0.233837i
\(683\) −6.60965e11 + 1.77105e11i −0.116221 + 0.0311414i −0.316461 0.948606i \(-0.602495\pi\)
0.200240 + 0.979747i \(0.435828\pi\)
\(684\) 1.03111e13 + 1.78594e13i 1.80116 + 3.11970i
\(685\) 5.42512e12 1.27633e12i 0.941460 0.221491i
\(686\) −1.01140e13 2.20539e12i −1.74367 0.380212i
\(687\) −3.08417e11 + 3.08417e11i −0.0528242 + 0.0528242i
\(688\) −1.77770e12 + 6.63446e12i −0.302489 + 1.12891i
\(689\) −1.54648e11 + 2.67858e11i −0.0261432 + 0.0452813i
\(690\) 2.79715e11 9.28738e11i 0.0469781 0.155981i
\(691\) 2.42587e12 1.40058e12i 0.404777 0.233698i −0.283766 0.958894i \(-0.591584\pi\)
0.688543 + 0.725195i \(0.258251\pi\)
\(692\) −1.21489e13 1.21489e13i −2.01401 2.01401i
\(693\) 1.43058e11 + 9.10981e12i 0.0235620 + 1.50041i
\(694\) 2.52796e12i 0.413669i
\(695\) 4.80511e10 1.56278e12i 0.00781218 0.254078i
\(696\) −6.37803e11 3.68236e11i −0.103026 0.0594819i
\(697\) 8.12915e11 + 3.03384e12i 0.130466 + 0.486906i
\(698\) −2.01776e13 5.40657e12i −3.21751 0.862130i
\(699\) 5.39808e11 0.0855248
\(700\) −1.16901e13 7.48265e12i −1.84026 1.17792i
\(701\) −7.79044e12 −1.21851 −0.609257 0.792973i \(-0.708532\pi\)
−0.609257 + 0.792973i \(0.708532\pi\)
\(702\) −1.56174e12 4.18468e11i −0.242713 0.0650347i
\(703\) 3.61193e12 + 1.34799e13i 0.557750 + 2.08155i
\(704\) 2.56740e12 + 1.48229e12i 0.393928 + 0.227435i
\(705\) −2.06273e10 + 6.70866e11i −0.00314478 + 0.102279i
\(706\) 1.28248e12i 0.194281i
\(707\) 6.78387e12 + 3.77591e12i 1.02115 + 0.568373i
\(708\) −3.59482e11 3.59482e11i −0.0537684 0.0537684i
\(709\) 1.81400e12 1.04731e12i 0.269605 0.155657i −0.359103 0.933298i \(-0.616917\pi\)
0.628708 + 0.777641i \(0.283584\pi\)
\(710\) −1.87022e12 + 6.20968e12i −0.276204 + 0.917079i
\(711\) 1.74508e12 3.02257e12i 0.256096 0.443571i
\(712\) −1.72547e12 + 6.43955e12i −0.251622 + 0.939065i
\(713\) 2.42724e12 2.42724e12i 0.351730 0.351730i
\(714\) 1.28433e11 + 4.50876e11i 0.0184941 + 0.0649254i
\(715\) −1.17191e13 + 2.75707e12i −1.67694 + 0.394522i
\(716\) 4.69572e12 + 8.13322e12i 0.667719 + 1.15652i
\(717\) −2.66078e11 + 7.12953e10i −0.0375986 + 0.0100745i
\(718\) 2.30955e13 6.18843e12i 3.24316 0.869002i
\(719\) −2.32097e12 4.02003e12i −0.323883 0.560983i 0.657402 0.753540i \(-0.271655\pi\)
−0.981286 + 0.192557i \(0.938322\pi\)
\(720\) 6.00875e12 9.70582e12i 0.833274 1.34597i
\(721\) 2.61550e12 + 6.56985e11i 0.360451 + 0.0905412i
\(722\) 1.60233e13 1.60233e13i 2.19449 2.19449i
\(723\) 5.13784e10 1.91747e11i 0.00699292 0.0260979i
\(724\) −3.49989e12 + 6.06199e12i −0.473403 + 0.819958i
\(725\) 4.16878e11 6.77272e12i 0.0560387 0.910420i
\(726\) 9.05442e11 5.22757e11i 0.120961 0.0698369i
\(727\) −2.54474e12 2.54474e12i −0.337862 0.337862i 0.517700 0.855562i \(-0.326788\pi\)
−0.855562 + 0.517700i \(0.826788\pi\)
\(728\) 1.83268e13 2.87800e11i 2.41822 0.0379751i
\(729\) 7.45212e12i 0.977251i
\(730\) 1.35144e12 + 4.15531e10i 0.176135 + 0.00541565i
\(731\) 3.01602e12 + 1.74130e12i 0.390667 + 0.225552i
\(732\) 6.13997e10 + 2.29147e11i 0.00790435 + 0.0294994i
\(733\) −9.21754e12 2.46983e12i −1.17936 0.316009i −0.384689 0.923046i \(-0.625691\pi\)
−0.794674 + 0.607037i \(0.792358\pi\)
\(734\) 1.55394e13 1.97607
\(735\) −4.71256e11 + 1.26610e11i −0.0595613 + 0.0160020i
\(736\) −8.49745e12 −1.06743
\(737\) −3.16500e12 8.48059e11i −0.395157 0.105882i
\(738\) −3.04748e12 1.13734e13i −0.378171 1.41135i
\(739\) 9.24985e12 + 5.34040e12i 1.14087 + 0.658679i 0.946645 0.322278i \(-0.104449\pi\)
0.194221 + 0.980958i \(0.437782\pi\)
\(740\) 1.69070e13 1.58983e13i 2.07264 1.94898i
\(741\) 9.58013e11i 0.116732i
\(742\) −6.73609e11 + 1.05782e10i −0.0815812 + 0.00128113i
\(743\) 7.33647e11 + 7.33647e11i 0.0883156 + 0.0883156i 0.749884 0.661569i \(-0.230109\pi\)
−0.661569 + 0.749884i \(0.730109\pi\)
\(744\) −3.17255e11 + 1.83167e11i −0.0379603 + 0.0219164i
\(745\) −3.91319e12 7.28620e12i −0.465402 0.866558i
\(746\) 5.71793e12 9.90374e12i 0.675949 1.17078i
\(747\) 1.12017e12 4.18054e12i 0.131626 0.491236i
\(748\) −1.22211e13 + 1.22211e13i −1.42742 + 1.42742i
\(749\) −7.07429e12 1.77698e12i −0.821325 0.206307i
\(750\) −9.49678e11 8.78213e10i −0.109597 0.0101350i
\(751\) 3.29206e12 + 5.70202e12i 0.377649 + 0.654107i 0.990720 0.135921i \(-0.0433993\pi\)
−0.613071 + 0.790028i \(0.710066\pi\)
\(752\) 2.23337e13 5.98429e12i 2.54671 0.682390i
\(753\) 5.58237e10 1.49579e10i 0.00632763 0.00169548i
\(754\) 8.26136e12 + 1.43091e13i 0.930852 + 1.61228i
\(755\) 8.36160e12 + 5.17656e12i 0.936543 + 0.579802i
\(756\) −6.61865e11 2.32354e12i −0.0736922 0.258704i
\(757\) −6.82321e12 + 6.82321e12i −0.755192 + 0.755192i −0.975443 0.220251i \(-0.929312\pi\)
0.220251 + 0.975443i \(0.429312\pi\)
\(758\) 1.10289e12 4.11604e12i 0.121345 0.452865i
\(759\) 6.28567e11 1.08871e12i 0.0687485 0.119076i
\(760\) −3.08217e13 9.28280e12i −3.35116 1.00929i
\(761\) 4.18775e12 2.41780e12i 0.452637 0.261330i −0.256306 0.966596i \(-0.582506\pi\)
0.708943 + 0.705265i \(0.249172\pi\)
\(762\) 5.89114e11 + 5.89114e11i 0.0632997 + 0.0632997i
\(763\) −1.74954e12 9.73794e11i −0.186880 0.104018i
\(764\) 7.29459e12i 0.774605i
\(765\) −3.96501e12 4.21657e12i −0.418570 0.445126i
\(766\) 1.48884e12 + 8.59582e11i 0.156249 + 0.0902106i
\(767\) 1.60093e12 + 5.97476e12i 0.167030 + 0.623364i
\(768\) −1.11818e12 2.99615e11i −0.115981 0.0310769i
\(769\) −1.70913e13 −1.76241 −0.881205 0.472734i \(-0.843267\pi\)
−0.881205 + 0.472734i \(0.843267\pi\)
\(770\) −1.82614e13 1.88190e13i −1.87209 1.92925i
\(771\) 6.94167e11 0.0707489
\(772\) 1.66165e13 + 4.45237e12i 1.68368 + 0.451142i
\(773\) 3.39183e12 + 1.26585e13i 0.341685 + 1.27519i 0.896437 + 0.443170i \(0.146146\pi\)
−0.554752 + 0.832016i \(0.687187\pi\)
\(774\) −1.13066e13 6.52786e12i −1.13239 0.653787i
\(775\) −2.81384e12 1.86402e12i −0.280183 0.185606i
\(776\) 1.36307e13i 1.34940i
\(777\) −1.28112e10 8.15807e11i −0.00126094 0.0802958i
\(778\) 2.35428e13 + 2.35428e13i 2.30383 + 2.30383i
\(779\) −1.21071e13 + 6.99003e12i −1.17793 + 0.680080i
\(780\) 1.40356e12 7.53806e11i 0.135770 0.0729179i
\(781\) −4.20269e12 + 7.27927e12i −0.404201 + 0.700097i
\(782\) −4.38492e12 + 1.63647e13i −0.419306 + 1.56487i
\(783\) 8.35174e11 8.35174e11i 0.0794052 0.0794052i
\(784\) 8.85795e12 + 1.42868e13i 0.837357 + 1.35055i
\(785\) −1.56509e12 6.65250e12i −0.147105 0.625276i
\(786\) 4.44140e11 + 7.69273e11i 0.0415067 + 0.0718917i
\(787\) −8.78992e12 + 2.35525e12i −0.816768 + 0.218852i −0.642933 0.765922i \(-0.722283\pi\)
−0.173835 + 0.984775i \(0.555616\pi\)
\(788\) −1.46578e13 + 3.92753e12i −1.35425 + 0.362871i
\(789\) 5.25796e11 + 9.10705e11i 0.0483026 + 0.0836626i
\(790\) 2.30048e12 + 9.77830e12i 0.210134 + 0.893185i
\(791\) 2.37631e12 + 2.30283e12i 0.215829 + 0.209155i
\(792\) 2.48465e13 2.48465e13i 2.24389 2.24389i
\(793\) 7.47053e11 2.78804e12i 0.0670844 0.250363i
\(794\) −3.06427e12 + 5.30747e12i −0.273612 + 0.473910i
\(795\) −2.79775e10 + 1.50259e10i −0.00248403 + 0.00133410i
\(796\) −3.90447e12 + 2.25425e12i −0.344710 + 0.199018i
\(797\) −1.32697e13 1.32697e13i −1.16493 1.16493i −0.983382 0.181547i \(-0.941890\pi\)
−0.181547 0.983382i \(-0.558110\pi\)
\(798\) −1.79052e12 + 1.07159e12i −0.156303 + 0.0935441i
\(799\) 1.17235e13i 1.01765i
\(800\) 1.66261e12 + 8.18829e12i 0.143511 + 0.706786i
\(801\) −4.62083e12 2.66784e12i −0.396619 0.228988i
\(802\) −5.37341e12 2.00539e13i −0.458633 1.71164i
\(803\) 1.69270e12 + 4.53558e11i 0.143668 + 0.0384958i
\(804\) 4.33611e11 0.0365972
\(805\) −1.69629e13 4.81967e12i −1.42370 0.404516i
\(806\) 8.21870e12 0.685954
\(807\) −7.98085e11 2.13846e11i −0.0662397 0.0177489i
\(808\) −7.74987e12 2.89229e13i −0.639652 2.38721i
\(809\) 1.81753e12 + 1.04935e12i 0.149181 + 0.0861295i 0.572732 0.819742i \(-0.305883\pi\)
−0.423552 + 0.905872i \(0.639217\pi\)
\(810\) 1.48072e13 + 1.57467e13i 1.20862 + 1.28530i
\(811\) 4.28385e12i 0.347728i 0.984770 + 0.173864i \(0.0556254\pi\)
−0.984770 + 0.173864i \(0.944375\pi\)
\(812\) −1.20074e13 + 2.15727e13i −0.969272 + 1.74142i
\(813\) −6.93111e11 6.93111e11i −0.0556411 0.0556411i
\(814\) 3.79716e13 2.19229e13i 3.03144 1.75020i
\(815\) 1.51436e13 + 4.56090e12i 1.20232 + 0.362111i
\(816\) 3.80648e11 6.59303e11i 0.0300551 0.0520570i
\(817\) −4.01200e12 + 1.49730e13i −0.315037 + 1.17573i
\(818\) 1.50796e12 1.50796e12i 0.117761 0.117761i
\(819\) −3.57382e12 + 1.42276e13i −0.277559 + 1.10498i
\(820\) 1.97673e13 + 1.22377e13i 1.52681 + 0.945227i
\(821\) −1.83457e12 3.17757e12i −0.140926 0.244091i 0.786920 0.617055i \(-0.211675\pi\)
−0.927846 + 0.372965i \(0.878341\pi\)
\(822\) −1.34591e12 + 3.60636e11i −0.102824 + 0.0275515i
\(823\) −1.92319e13 + 5.15318e12i −1.46125 + 0.391540i −0.899920 0.436054i \(-0.856376\pi\)
−0.561327 + 0.827594i \(0.689709\pi\)
\(824\) −5.20031e12 9.00720e12i −0.392967 0.680639i
\(825\) −1.17209e12 3.92681e11i −0.0880879 0.0295119i
\(826\) −9.37607e12 + 9.67525e12i −0.700827 + 0.723189i
\(827\) 6.76053e12 6.76053e12i 0.502581 0.502581i −0.409658 0.912239i \(-0.634352\pi\)
0.912239 + 0.409658i \(0.134352\pi\)
\(828\) 1.12771e13 4.20867e13i 0.833798 3.11178i
\(829\) 3.77372e11 6.53627e11i 0.0277507 0.0480656i −0.851817 0.523840i \(-0.824499\pi\)
0.879567 + 0.475775i \(0.157832\pi\)
\(830\) 5.89388e12 + 1.09742e13i 0.431072 + 0.802639i
\(831\) −3.93271e11 + 2.27055e11i −0.0286080 + 0.0165168i
\(832\) 3.37524e12 + 3.37524e12i 0.244202 + 0.244202i
\(833\) 8.15957e12 2.46342e12i 0.587171 0.177270i
\(834\) 3.90902e11i 0.0279783i
\(835\) −3.67458e12 + 3.45535e12i −0.261588 + 0.245982i
\(836\) −6.66216e13 3.84640e13i −4.71723 2.72349i
\(837\) −1.52058e11 5.67489e11i −0.0107089 0.0399662i
\(838\) 3.90228e13 + 1.04561e13i 2.73351 + 0.732442i
\(839\) 2.14353e13 1.49348 0.746742 0.665114i \(-0.231617\pi\)
0.746742 + 0.665114i \(0.231617\pi\)
\(840\) 1.61549e12 + 9.65373e11i 0.111956 + 0.0669019i
\(841\) 2.43713e12 0.167995
\(842\) −4.88073e13 1.30779e13i −3.34642 0.896670i
\(843\) −1.41889e11 5.29538e11i −0.00967666 0.0361138i
\(844\) −9.70593e12 5.60372e12i −0.658410 0.380133i
\(845\) −4.56178e12 1.40262e11i −0.307808 0.00946423i
\(846\) 4.39496e13i 2.94977i
\(847\) −9.76140e12 1.63103e13i −0.651684 1.08890i
\(848\) 7.73575e11 + 7.73575e11i 0.0513714 + 0.0513714i
\(849\) −1.37143e12 + 7.91798e11i −0.0905921 + 0.0523034i
\(850\) 1.66273e13 + 1.02345e12i 1.09254 + 0.0672486i
\(851\) 1.47428e13 2.55352e13i 0.963597 1.66900i
\(852\) 2.87888e11 1.07441e12i 0.0187174 0.0698544i
\(853\) 7.77297e12 7.77297e12i 0.502708 0.502708i −0.409570 0.912279i \(-0.634321\pi\)
0.912279 + 0.409570i \(0.134321\pi\)
\(854\) 6.04645e12 1.72234e12i 0.388992 0.110805i
\(855\) 1.35608e13 2.19046e13i 0.867839 1.40180i
\(856\) 1.40655e13 + 2.43622e13i 0.895416 + 1.55091i
\(857\) −1.43208e13 + 3.83724e12i −0.906887 + 0.243000i −0.681971 0.731379i \(-0.738877\pi\)
−0.224915 + 0.974378i \(0.572210\pi\)
\(858\) 2.90737e12 7.79028e11i 0.183150 0.0490750i
\(859\) −8.45434e12 1.46433e13i −0.529798 0.917637i −0.999396 0.0347567i \(-0.988934\pi\)
0.469598 0.882880i \(-0.344399\pi\)
\(860\) 2.50933e13 5.90353e12i 1.56428 0.368018i
\(861\) 7.86079e11 2.23916e11i 0.0487474 0.0138858i
\(862\) 1.93442e12 1.93442e12i 0.119335 0.119335i
\(863\) −6.10149e12 + 2.27711e13i −0.374444 + 1.39744i 0.479711 + 0.877426i \(0.340741\pi\)
−0.854155 + 0.520018i \(0.825925\pi\)
\(864\) −7.27184e11 + 1.25952e12i −0.0443948 + 0.0768941i
\(865\) −6.18977e12 + 2.05519e13i −0.375926 + 1.24819i
\(866\) −6.57404e12 + 3.79553e12i −0.397193 + 0.229320i
\(867\) 4.52604e11 + 4.52604e11i 0.0272040 + 0.0272040i
\(868\) 6.30667e12 + 1.05378e13i 0.377104 + 0.630103i
\(869\) 1.30195e13i 0.774473i
\(870\) −5.21374e10 + 1.69568e12i −0.00308541 + 0.100348i
\(871\) −4.56895e12 2.63788e12i −0.268989 0.155301i
\(872\) 1.99867e12 + 7.45913e12i 0.117062 + 0.436882i
\(873\) −1.05376e13 2.82353e12i −0.614011 0.164524i
\(874\) −7.54094e13 −4.37144
\(875\) −1.32535e12 + 1.72888e13i −0.0764355 + 0.997075i
\(876\) −2.31904e11 −0.0133057
\(877\) −9.79815e12 2.62541e12i −0.559301 0.149864i −0.0319160 0.999491i \(-0.510161\pi\)
−0.527385 + 0.849626i \(0.676828\pi\)
\(878\) 3.21926e12 + 1.20145e13i 0.182823 + 0.682306i
\(879\) 6.13517e11 + 3.54214e11i 0.0346638 + 0.0200132i
\(880\) −1.30869e12 + 4.25627e13i −0.0735636 + 2.39253i
\(881\) 2.13671e12i 0.119496i −0.998213 0.0597481i \(-0.980970\pi\)
0.998213 0.0597481i \(-0.0190298\pi\)
\(882\) −3.05889e13 + 9.23496e12i −1.70198 + 0.513838i
\(883\) −1.02436e13 1.02436e13i −0.567062 0.567062i 0.364242 0.931304i \(-0.381328\pi\)
−0.931304 + 0.364242i \(0.881328\pi\)
\(884\) −2.40996e13 + 1.39139e13i −1.32732 + 0.766328i
\(885\) −1.83153e11 + 6.08121e11i −0.0100362 + 0.0333231i
\(886\) 1.73759e13 3.00960e13i 0.947318 1.64080i
\(887\) −4.59508e12 + 1.71491e13i −0.249251 + 0.930217i 0.721948 + 0.691947i \(0.243247\pi\)
−0.971199 + 0.238270i \(0.923420\pi\)
\(888\) −2.22507e12 + 2.22507e12i −0.120084 + 0.120084i
\(889\) 1.05410e13 1.08774e13i 0.566011 0.584071i
\(890\) 1.49488e13 3.51692e12i 0.798642 0.187891i
\(891\) 1.40075e13 + 2.42617e13i 0.744579 + 1.28965i
\(892\) 4.22316e13 1.13159e13i 2.23355 0.598478i
\(893\) 5.04037e13 1.35056e13i 2.65235 0.710696i
\(894\) 1.03388e12 + 1.79073e12i 0.0541315 + 0.0937585i
\(895\) 6.17566e12 9.97542e12i 0.321721 0.519670i
\(896\) −5.92260e12 + 2.35783e13i −0.306992 + 1.22216i
\(897\) 1.43127e12 1.43127e12i 0.0738170 0.0738170i
\(898\) 1.04323e13 3.89339e13i 0.535349 1.99795i
\(899\) −3.00192e12 + 5.19948e12i −0.153278 + 0.265486i
\(900\) −4.27620e13 2.63211e12i −2.17253 0.133725i
\(901\) 4.80386e11 2.77351e11i 0.0242845 0.0140206i
\(902\) 3.10584e13 + 3.10584e13i 1.56225 + 1.56225i
\(903\) 4.40760e11 7.91880e11i 0.0220601 0.0396337i
\(904\) 1.27621e13i 0.635572i
\(905\) 8.74041e12 + 2.68743e11i 0.433125 + 0.0133174i
\(906\) −2.12931e12 1.22936e12i −0.104993 0.0606179i
\(907\) 5.90207e12 + 2.20268e13i 0.289582 + 1.08074i 0.945425 + 0.325838i \(0.105647\pi\)
−0.655843 + 0.754897i \(0.727687\pi\)
\(908\) −8.22522e13 2.20394e13i −4.01570 1.07600i
\(909\) 2.39649e13 1.16423
\(910\) −2.05586e13 3.68782e13i −0.993821 1.78272i
\(911\) −1.69330e13 −0.814521 −0.407260 0.913312i \(-0.633516\pi\)
−0.407260 + 0.913312i \(0.633516\pi\)
\(912\) 3.27309e12 + 8.77022e11i 0.156668 + 0.0419792i
\(913\) 4.17863e12 + 1.55949e13i 0.199029 + 0.742785i
\(914\) −2.38185e13 1.37516e13i −1.12890 0.651773i
\(915\) 2.15901e11 2.03020e11i 0.0101826 0.00957512i
\(916\) 5.63926e13i 2.64662i
\(917\) 1.38574e13 8.29339e12i 0.647173 0.387320i
\(918\) 2.05039e12 + 2.05039e12i 0.0952893 + 0.0952893i
\(919\) 3.17278e13 1.83181e13i 1.46731 0.847150i 0.467976 0.883741i \(-0.344983\pi\)
0.999330 + 0.0365918i \(0.0116501\pi\)
\(920\) 3.21791e13 + 5.99161e13i 1.48091 + 2.75739i
\(921\) 6.90487e11 1.19596e12i 0.0316218 0.0547706i
\(922\) 1.87094e13 6.98244e13i 0.852650 3.18213i
\(923\) −9.56970e12 + 9.56970e12i −0.434001 + 0.434001i
\(924\) 3.22984e12 + 3.12997e12i 0.145766 + 0.141259i
\(925\) −2.74907e13 9.21015e12i −1.23466 0.413646i
\(926\) 1.53281e13 + 2.65490e13i 0.685075 + 1.18659i
\(927\) 8.04045e12 2.15443e12i 0.357620 0.0958239i
\(928\) 1.43560e13 3.84668e12i 0.635430 0.170263i
\(929\) −1.69569e13 2.93703e13i −0.746925 1.29371i −0.949290 0.314402i \(-0.898196\pi\)
0.202365 0.979310i \(-0.435137\pi\)
\(930\) 7.17492e11 + 4.44190e11i 0.0314517 + 0.0194713i
\(931\) 1.99910e13 + 3.22430e13i 0.872091 + 1.40657i
\(932\) −4.93507e13 + 4.93507e13i −2.14250 + 2.14250i
\(933\) 3.18144e11 1.18733e12i 0.0137454 0.0512984i
\(934\) −1.80431e13 + 3.12515e13i −0.775799 + 1.34372i
\(935\) 2.06739e13 + 6.22652e12i 0.884648 + 0.266436i
\(936\) 4.89967e13 2.82882e13i 2.08653 1.20466i
\(937\) −7.02099e12 7.02099e12i −0.297557 0.297557i 0.542499 0.840056i \(-0.317478\pi\)
−0.840056 + 0.542499i \(0.817478\pi\)
\(938\) −1.80435e11 1.14900e13i −0.00761043 0.484625i
\(939\) 7.30487e11i 0.0306632i
\(940\) −5.94466e13 6.32182e13i −2.48343 2.64099i
\(941\) 1.39146e13 + 8.03361e12i 0.578519 + 0.334008i 0.760545 0.649286i \(-0.224932\pi\)
−0.182025 + 0.983294i \(0.558265\pi\)
\(942\) 4.42226e11 + 1.65041e12i 0.0182985 + 0.0682909i
\(943\) 2.85311e13 + 7.64488e12i 1.17494 + 0.314824i
\(944\) 2.18786e13 0.896697
\(945\) −2.16602e12 + 2.10184e12i −0.0883525 + 0.0857348i
\(946\) 4.87023e13 1.97715
\(947\) 4.32244e12 + 1.15819e12i 0.174644 + 0.0467958i 0.345081 0.938573i \(-0.387851\pi\)
−0.170437 + 0.985369i \(0.554518\pi\)
\(948\) −4.45925e11 1.66422e12i −0.0179318 0.0669225i
\(949\) 2.44356e12 + 1.41079e12i 0.0977970 + 0.0564631i
\(950\) 1.47546e13 + 7.26658e13i 0.587722 + 2.89450i
\(951\) 1.78721e12i 0.0708539i
\(952\) −2.87226e13 1.59870e13i −1.13333 0.630812i
\(953\) −3.36282e12 3.36282e12i −0.132064 0.132064i 0.637985 0.770049i \(-0.279768\pi\)
−0.770049 + 0.637985i \(0.779768\pi\)
\(954\) −1.80089e12 + 1.03974e12i −0.0703913 + 0.0406405i
\(955\) 8.02824e12 4.31172e12i 0.312324 0.167740i
\(956\) 1.78075e13 3.08435e13i 0.689514 1.19427i
\(957\) −5.69088e11 + 2.12386e12i −0.0219319 + 0.0818508i
\(958\) −4.76311e13 + 4.76311e13i −1.82703 + 1.82703i
\(959\) 6.94002e12 + 2.43637e13i 0.264958 + 0.930162i
\(960\) 1.12239e11 + 4.77077e11i 0.00426504 + 0.0181288i
\(961\) −1.17266e13 2.03111e13i −0.443524 0.768206i
\(962\) 6.81911e13 1.82718e13i 2.56708 0.687848i
\(963\) −2.17474e13 + 5.82721e12i −0.814873 + 0.218345i
\(964\) 1.28329e13 + 2.22272e13i 0.478605 + 0.828968i
\(965\) −4.92157e12 2.09194e13i −0.182697 0.776562i
\(966\) 4.27600e12 + 1.07408e12i 0.157994 + 0.0396863i
\(967\) −3.94387e12 + 3.94387e12i −0.145045 + 0.145045i −0.775901 0.630855i \(-0.782704\pi\)
0.630855 + 0.775901i \(0.282704\pi\)
\(968\) −1.89738e13 + 7.08112e13i −0.694569 + 2.59217i
\(969\) 8.59066e11 1.48795e12i 0.0313018 0.0542163i
\(970\) 2.76617e13 1.48563e13i 1.00324 0.538811i
\(971\) 3.40006e13 1.96303e13i 1.22744 0.708663i 0.260946 0.965353i \(-0.415965\pi\)
0.966494 + 0.256691i \(0.0826321\pi\)
\(972\) −7.91478e12 7.91478e12i −0.284407 0.284407i
\(973\) 7.10601e12 1.11591e11i 0.254166 0.00399136i
\(974\) 1.12395e13i 0.400160i
\(975\) −1.65924e12 1.09916e12i −0.0588016 0.0389528i
\(976\) −8.84155e12 5.10467e12i −0.311892 0.180071i
\(977\) −7.64637e12 2.85366e13i −0.268491 1.00202i −0.960079 0.279730i \(-0.909755\pi\)
0.691588 0.722293i \(-0.256912\pi\)
\(978\) −3.81936e12 1.02340e12i −0.133495 0.0357700i
\(979\) 1.99039e13 0.692495
\(980\) 3.15085e13 5.46585e13i 1.09121 1.89296i
\(981\) −6.18048e12 −0.213065
\(982\) 6.75484e13 + 1.80995e13i 2.31800 + 0.621106i
\(983\) −4.50234e12 1.68029e13i −0.153797 0.573977i −0.999205 0.0398572i \(-0.987310\pi\)
0.845409 0.534120i \(-0.179357\pi\)
\(984\) −2.72995e12 1.57614e12i −0.0928276 0.0535940i
\(985\) 1.29865e13 + 1.38105e13i 0.439572 + 0.467461i
\(986\) 2.96324e13i 0.998437i
\(987\) −3.05045e12 + 4.79034e10i −0.102314 + 0.00160672i
\(988\) −8.75841e13 8.75841e13i −2.92428 2.92428i
\(989\) 2.83636e13 1.63757e13i 0.942708 0.544273i
\(990\) −7.75031e13 2.33422e13i −2.56425 0.772296i
\(991\) −2.13973e13 + 3.70613e13i −0.704739 + 1.22064i 0.262047 + 0.965055i \(0.415602\pi\)
−0.966786 + 0.255588i \(0.917731\pi\)
\(992\) 1.91341e12 7.14093e12i 0.0627343 0.234128i
\(993\) −1.84998e12 + 1.84998e12i −0.0603803 + 0.0603803i
\(994\) −2.85900e13 7.18147e12i −0.928913 0.233332i
\(995\) 4.78885e12 + 2.96472e12i 0.154891 + 0.0958913i
\(996\) −1.06826e12 1.85029e12i −0.0343963 0.0595761i
\(997\) −5.08668e12 + 1.36297e12i −0.163045 + 0.0436877i −0.339418 0.940636i \(-0.610230\pi\)
0.176373 + 0.984323i \(0.443563\pi\)
\(998\) 2.35844e13 6.31941e12i 0.752553 0.201646i
\(999\) −2.52327e12 4.37044e12i −0.0801530 0.138829i
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 35.10.k.a.3.2 136
5.2 odd 4 inner 35.10.k.a.17.33 yes 136
7.5 odd 6 inner 35.10.k.a.33.33 yes 136
35.12 even 12 inner 35.10.k.a.12.2 yes 136
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.10.k.a.3.2 136 1.1 even 1 trivial
35.10.k.a.12.2 yes 136 35.12 even 12 inner
35.10.k.a.17.33 yes 136 5.2 odd 4 inner
35.10.k.a.33.33 yes 136 7.5 odd 6 inner