Properties

Label 91.10.u.a.30.19
Level $91$
Weight $10$
Character 91.30
Analytic conductor $46.868$
Analytic rank $0$
Dimension $164$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [91,10,Mod(30,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.30");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 91.u (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(46.8682610909\)
Analytic rank: \(0\)
Dimension: \(164\)
Relative dimension: \(82\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 30.19
Character \(\chi\) \(=\) 91.30
Dual form 91.10.u.a.88.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-23.7092 + 13.6885i) q^{2} -252.262 q^{3} +(118.751 - 205.683i) q^{4} +(-1023.39 - 590.853i) q^{5} +(5980.94 - 3453.10i) q^{6} +(5001.22 + 3916.81i) q^{7} -7514.94i q^{8} +43953.3 q^{9} +O(q^{10})\) \(q+(-23.7092 + 13.6885i) q^{2} -252.262 q^{3} +(118.751 - 205.683i) q^{4} +(-1023.39 - 590.853i) q^{5} +(5980.94 - 3453.10i) q^{6} +(5001.22 + 3916.81i) q^{7} -7514.94i q^{8} +43953.3 q^{9} +32351.6 q^{10} -90197.3i q^{11} +(-29956.4 + 51886.0i) q^{12} +(-78918.7 + 66153.9i) q^{13} +(-172190. - 24405.2i) q^{14} +(258162. + 149050. i) q^{15} +(163669. + 283483. i) q^{16} +(100819. - 174624. i) q^{17} +(-1.04210e6 + 601655. i) q^{18} +1.04004e6i q^{19} +(-243057. + 140329. i) q^{20} +(-1.26162e6 - 988064. i) q^{21} +(1.23467e6 + 2.13851e6i) q^{22} +(-631911. - 1.09450e6i) q^{23} +1.89574e6i q^{24} +(-278347. - 482111. i) q^{25} +(965549. - 2.64874e6i) q^{26} -6.12248e6 q^{27} +(1.39952e6 - 563539. i) q^{28} +(-1.88485e6 + 3.26465e6i) q^{29} -8.16110e6 q^{30} +(985061. - 568726. i) q^{31} +(-4.42876e6 - 2.55694e6i) q^{32} +2.27534e7i q^{33} +5.52025e6i q^{34} +(-2.80393e6 - 6.96341e6i) q^{35} +(5.21950e6 - 9.04043e6i) q^{36} +(3.43634e6 - 1.98397e6i) q^{37} +(-1.42367e7 - 2.46586e7i) q^{38} +(1.99082e7 - 1.66882e7i) q^{39} +(-4.44023e6 + 7.69070e6i) q^{40} +(8.18221e6 + 4.72400e6i) q^{41} +(4.34371e7 + 6.15652e6i) q^{42} +(1.35008e7 + 2.33841e7i) q^{43} +(-1.85520e7 - 1.07110e7i) q^{44} +(-4.49813e7 - 2.59700e7i) q^{45} +(2.99642e7 + 1.72998e7i) q^{46} +(-4.67496e7 - 2.69909e7i) q^{47} +(-4.12875e7 - 7.15121e7i) q^{48} +(9.67077e6 + 3.91777e7i) q^{49} +(1.31988e7 + 7.62032e6i) q^{50} +(-2.54328e7 + 4.40510e7i) q^{51} +(4.23506e6 + 2.40880e7i) q^{52} +(1.68826e7 + 2.92416e7i) q^{53} +(1.45159e8 - 8.38077e7i) q^{54} +(-5.32934e7 + 9.23068e7i) q^{55} +(2.94346e7 - 3.75839e7i) q^{56} -2.62364e8i q^{57} -1.03203e8i q^{58} +(7.01181e7 + 4.04827e7i) q^{59} +(6.13140e7 - 3.53997e7i) q^{60} +1.00389e8 q^{61} +(-1.55700e7 + 2.69681e7i) q^{62} +(2.19820e8 + 1.72157e8i) q^{63} -2.75939e7 q^{64} +(1.19852e8 - 2.10718e7i) q^{65} +(-3.11460e8 - 5.39465e8i) q^{66} -6.20288e7i q^{67} +(-2.39447e7 - 4.14734e7i) q^{68} +(1.59407e8 + 2.76102e8i) q^{69} +(1.61798e8 + 1.26715e8i) q^{70} +(-4.41361e7 + 2.54820e7i) q^{71} -3.30307e8i q^{72} +(4.14534e7 - 2.39331e7i) q^{73} +(-5.43153e7 + 9.40769e7i) q^{74} +(7.02165e7 + 1.21619e8i) q^{75} +(2.13919e8 + 1.23506e8i) q^{76} +(3.53286e8 - 4.51096e8i) q^{77} +(-2.43572e8 + 6.68177e8i) q^{78} +(-2.21735e8 + 3.84056e8i) q^{79} -3.86817e8i q^{80} +6.79339e8 q^{81} -2.58658e8 q^{82} +1.90644e8i q^{83} +(-3.53046e8 + 1.42160e8i) q^{84} +(-2.06354e8 + 1.19138e8i) q^{85} +(-6.40187e8 - 3.69612e8i) q^{86} +(4.75475e8 - 8.23548e8i) q^{87} -6.77828e8 q^{88} +(-5.33163e8 + 3.07822e8i) q^{89} +1.42196e9 q^{90} +(-6.53802e8 + 2.17408e7i) q^{91} -3.00160e8 q^{92} +(-2.48494e8 + 1.43468e8i) q^{93} +1.47786e9 q^{94} +(6.14514e8 - 1.06437e9i) q^{95} +(1.11721e9 + 6.45021e8i) q^{96} +(4.05942e8 - 2.34370e8i) q^{97} +(-7.65570e8 - 7.96493e8i) q^{98} -3.96447e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 164 q - 3 q^{2} + 322 q^{3} + 20481 q^{4} - 6 q^{6} + 1023 q^{7} + 1021818 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 164 q - 3 q^{2} + 322 q^{3} + 20481 q^{4} - 6 q^{6} + 1023 q^{7} + 1021818 q^{9} - 82050 q^{10} + 43064 q^{12} - 232462 q^{13} + 82708 q^{14} + 338445 q^{15} - 4712643 q^{16} + 638795 q^{17} - 1176873 q^{18} + 571062 q^{20} + 1367523 q^{21} - 1417332 q^{22} + 1074033 q^{23} + 29660776 q^{25} - 4350684 q^{26} + 7350574 q^{27} - 5807904 q^{28} + 996812 q^{29} + 18354032 q^{30} + 21474090 q^{31} + 786429 q^{32} - 14921172 q^{35} + 131881331 q^{36} + 6476901 q^{37} - 8950274 q^{38} + 27439160 q^{39} - 7901342 q^{40} + 24649770 q^{41} + 107058858 q^{42} + 15892214 q^{43} + 1176612 q^{44} + 20834727 q^{45} + 277543272 q^{46} + 69222114 q^{47} - 15455476 q^{48} - 69917499 q^{49} + 309166224 q^{50} + 52823362 q^{51} - 95118408 q^{52} - 155327528 q^{53} + 82174923 q^{54} - 77925569 q^{55} - 282686919 q^{56} - 216056427 q^{59} + 290928939 q^{60} + 937523074 q^{61} + 238770500 q^{62} - 521903604 q^{63} - 2035250696 q^{64} + 418729590 q^{65} - 154929237 q^{66} - 598026797 q^{68} + 127053056 q^{69} + 1180478502 q^{70} - 269829840 q^{71} + 35353098 q^{73} - 460031457 q^{74} + 803288072 q^{75} + 1140965370 q^{76} - 1032378781 q^{77} - 835494667 q^{78} - 683323974 q^{79} + 3448679004 q^{81} + 649989068 q^{82} + 2491042464 q^{84} - 196261605 q^{85} - 572477022 q^{86} - 1849967933 q^{87} - 74806442 q^{88} - 207815607 q^{89} - 9086462948 q^{90} - 1222123653 q^{91} - 2683122798 q^{92} + 389990277 q^{93} + 5123642528 q^{94} + 198982451 q^{95} - 392112 q^{96} + 6155159124 q^{97} + 1935772011 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −23.7092 + 13.6885i −1.04781 + 0.604953i −0.922035 0.387106i \(-0.873475\pi\)
−0.125774 + 0.992059i \(0.540141\pi\)
\(3\) −252.262 −1.79807 −0.899035 0.437876i \(-0.855731\pi\)
−0.899035 + 0.437876i \(0.855731\pi\)
\(4\) 118.751 205.683i 0.231935 0.401724i
\(5\) −1023.39 590.853i −0.732277 0.422780i 0.0869777 0.996210i \(-0.472279\pi\)
−0.819255 + 0.573430i \(0.805612\pi\)
\(6\) 5980.94 3453.10i 1.88403 1.08775i
\(7\) 5001.22 + 3916.81i 0.787290 + 0.616583i
\(8\) 7514.94i 0.648666i
\(9\) 43953.3 2.23306
\(10\) 32351.6 1.02305
\(11\) 90197.3i 1.85749i −0.370719 0.928745i \(-0.620889\pi\)
0.370719 0.928745i \(-0.379111\pi\)
\(12\) −29956.4 + 51886.0i −0.417036 + 0.722328i
\(13\) −78918.7 + 66153.9i −0.766363 + 0.642408i
\(14\) −172190. 24405.2i −1.19793 0.169788i
\(15\) 258162. + 149050.i 1.31669 + 0.760189i
\(16\) 163669. + 283483.i 0.624347 + 1.08140i
\(17\) 100819. 174624.i 0.292767 0.507087i −0.681696 0.731636i \(-0.738757\pi\)
0.974463 + 0.224548i \(0.0720906\pi\)
\(18\) −1.04210e6 + 601655.i −2.33982 + 1.35090i
\(19\) 1.04004e6i 1.83088i 0.402451 + 0.915442i \(0.368158\pi\)
−0.402451 + 0.915442i \(0.631842\pi\)
\(20\) −243057. + 140329.i −0.339682 + 0.196115i
\(21\) −1.26162e6 988064.i −1.41560 1.10866i
\(22\) 1.23467e6 + 2.13851e6i 1.12369 + 1.94629i
\(23\) −631911. 1.09450e6i −0.470848 0.815532i 0.528596 0.848873i \(-0.322719\pi\)
−0.999444 + 0.0333410i \(0.989385\pi\)
\(24\) 1.89574e6i 1.16635i
\(25\) −278347. 482111.i −0.142514 0.246841i
\(26\) 965549. 2.64874e6i 0.414376 1.13673i
\(27\) −6.12248e6 −2.21713
\(28\) 1.39952e6 563539.i 0.430297 0.173266i
\(29\) −1.88485e6 + 3.26465e6i −0.494863 + 0.857127i −0.999982 0.00592200i \(-0.998115\pi\)
0.505120 + 0.863049i \(0.331448\pi\)
\(30\) −8.16110e6 −1.83951
\(31\) 985061. 568726.i 0.191574 0.110605i −0.401145 0.916014i \(-0.631388\pi\)
0.592719 + 0.805409i \(0.298054\pi\)
\(32\) −4.42876e6 2.55694e6i −0.746632 0.431068i
\(33\) 2.27534e7i 3.33990i
\(34\) 5.52025e6i 0.708441i
\(35\) −2.80393e6 6.96341e6i −0.315835 0.784360i
\(36\) 5.21950e6 9.04043e6i 0.517925 0.897073i
\(37\) 3.43634e6 1.98397e6i 0.301432 0.174032i −0.341654 0.939826i \(-0.610987\pi\)
0.643086 + 0.765794i \(0.277654\pi\)
\(38\) −1.42367e7 2.46586e7i −1.10760 1.91842i
\(39\) 1.99082e7 1.66882e7i 1.37798 1.15509i
\(40\) −4.44023e6 + 7.69070e6i −0.274243 + 0.475003i
\(41\) 8.18221e6 + 4.72400e6i 0.452213 + 0.261085i 0.708764 0.705445i \(-0.249253\pi\)
−0.256551 + 0.966531i \(0.582586\pi\)
\(42\) 4.34371e7 + 6.15652e6i 2.15397 + 0.305291i
\(43\) 1.35008e7 + 2.33841e7i 0.602215 + 1.04307i 0.992485 + 0.122367i \(0.0390485\pi\)
−0.390270 + 0.920701i \(0.627618\pi\)
\(44\) −1.85520e7 1.07110e7i −0.746198 0.430818i
\(45\) −4.49813e7 2.59700e7i −1.63522 0.944093i
\(46\) 2.99642e7 + 1.72998e7i 0.986717 + 0.569681i
\(47\) −4.67496e7 2.69909e7i −1.39745 0.806821i −0.403329 0.915055i \(-0.632147\pi\)
−0.994125 + 0.108234i \(0.965480\pi\)
\(48\) −4.12875e7 7.15121e7i −1.12262 1.94444i
\(49\) 9.67077e6 + 3.91777e7i 0.239651 + 0.970859i
\(50\) 1.31988e7 + 7.62032e6i 0.298654 + 0.172428i
\(51\) −2.54328e7 + 4.40510e7i −0.526416 + 0.911779i
\(52\) 4.23506e6 + 2.40880e7i 0.0803238 + 0.456863i
\(53\) 1.68826e7 + 2.92416e7i 0.293899 + 0.509049i 0.974728 0.223394i \(-0.0717136\pi\)
−0.680829 + 0.732443i \(0.738380\pi\)
\(54\) 1.45159e8 8.38077e7i 2.32313 1.34126i
\(55\) −5.32934e7 + 9.23068e7i −0.785310 + 1.36020i
\(56\) 2.94346e7 3.75839e7i 0.399956 0.510688i
\(57\) 2.62364e8i 3.29206i
\(58\) 1.03203e8i 1.19747i
\(59\) 7.01181e7 + 4.04827e7i 0.753348 + 0.434946i 0.826902 0.562345i \(-0.190101\pi\)
−0.0735541 + 0.997291i \(0.523434\pi\)
\(60\) 6.13140e7 3.53997e7i 0.610772 0.352629i
\(61\) 1.00389e8 0.928333 0.464166 0.885748i \(-0.346354\pi\)
0.464166 + 0.885748i \(0.346354\pi\)
\(62\) −1.55700e7 + 2.69681e7i −0.133822 + 0.231786i
\(63\) 2.19820e8 + 1.72157e8i 1.75806 + 1.37687i
\(64\) −2.75939e7 −0.205591
\(65\) 1.19852e8 2.10718e7i 0.832787 0.146417i
\(66\) −3.11460e8 5.39465e8i −2.02048 3.49958i
\(67\) 6.20288e7i 0.376059i −0.982163 0.188030i \(-0.939790\pi\)
0.982163 0.188030i \(-0.0602101\pi\)
\(68\) −2.39447e7 4.14734e7i −0.135806 0.235223i
\(69\) 1.59407e8 + 2.76102e8i 0.846618 + 1.46639i
\(70\) 1.61798e8 + 1.26715e8i 0.805435 + 0.630794i
\(71\) −4.41361e7 + 2.54820e7i −0.206125 + 0.119006i −0.599509 0.800368i \(-0.704638\pi\)
0.393384 + 0.919374i \(0.371304\pi\)
\(72\) 3.30307e8i 1.44851i
\(73\) 4.14534e7 2.39331e7i 0.170847 0.0986385i −0.412138 0.911121i \(-0.635218\pi\)
0.582985 + 0.812483i \(0.301885\pi\)
\(74\) −5.43153e7 + 9.40769e7i −0.210562 + 0.364704i
\(75\) 7.02165e7 + 1.21619e8i 0.256250 + 0.443838i
\(76\) 2.13919e8 + 1.23506e8i 0.735509 + 0.424647i
\(77\) 3.53286e8 4.51096e8i 1.14530 1.46238i
\(78\) −2.43572e8 + 6.68177e8i −0.745077 + 2.04393i
\(79\) −2.21735e8 + 3.84056e8i −0.640489 + 1.10936i 0.344835 + 0.938663i \(0.387935\pi\)
−0.985324 + 0.170696i \(0.945398\pi\)
\(80\) 3.86817e8i 1.05585i
\(81\) 6.79339e8 1.75349
\(82\) −2.58658e8 −0.631777
\(83\) 1.90644e8i 0.440933i 0.975395 + 0.220466i \(0.0707580\pi\)
−0.975395 + 0.220466i \(0.929242\pi\)
\(84\) −3.53046e8 + 1.42160e8i −0.773704 + 0.311544i
\(85\) −2.06354e8 + 1.19138e8i −0.428773 + 0.247552i
\(86\) −6.40187e8 3.69612e8i −1.26201 0.728623i
\(87\) 4.75475e8 8.23548e8i 0.889798 1.54118i
\(88\) −6.77828e8 −1.20489
\(89\) −5.33163e8 + 3.07822e8i −0.900751 + 0.520049i −0.877444 0.479679i \(-0.840753\pi\)
−0.0233076 + 0.999728i \(0.507420\pi\)
\(90\) 1.42196e9 2.28453
\(91\) −6.53802e8 + 2.17408e7i −0.999448 + 0.0332345i
\(92\) −3.00160e8 −0.436825
\(93\) −2.48494e8 + 1.43468e8i −0.344463 + 0.198876i
\(94\) 1.47786e9 1.95235
\(95\) 6.14514e8 1.06437e9i 0.774061 1.34071i
\(96\) 1.11721e9 + 6.45021e8i 1.34250 + 0.775092i
\(97\) 4.05942e8 2.34370e8i 0.465576 0.268801i −0.248810 0.968552i \(-0.580039\pi\)
0.714386 + 0.699752i \(0.246706\pi\)
\(98\) −7.65570e8 7.96493e8i −0.838432 0.872297i
\(99\) 3.96447e9i 4.14789i
\(100\) −1.32216e8 −0.132216
\(101\) −1.52599e8 −0.145917 −0.0729584 0.997335i \(-0.523244\pi\)
−0.0729584 + 0.997335i \(0.523244\pi\)
\(102\) 1.39255e9i 1.27383i
\(103\) 1.73506e8 3.00522e8i 0.151897 0.263092i −0.780028 0.625744i \(-0.784795\pi\)
0.931925 + 0.362652i \(0.118129\pi\)
\(104\) 4.97143e8 + 5.93069e8i 0.416708 + 0.497113i
\(105\) 7.07325e8 + 1.75661e9i 0.567894 + 1.41034i
\(106\) −8.00548e8 4.62196e8i −0.615901 0.355591i
\(107\) 5.94234e8 + 1.02924e9i 0.438259 + 0.759086i 0.997555 0.0698812i \(-0.0222620\pi\)
−0.559297 + 0.828968i \(0.688929\pi\)
\(108\) −7.27051e8 + 1.25929e9i −0.514230 + 0.890673i
\(109\) 4.62090e8 2.66788e8i 0.313550 0.181028i −0.334964 0.942231i \(-0.608724\pi\)
0.648514 + 0.761203i \(0.275391\pi\)
\(110\) 2.91803e9i 1.90030i
\(111\) −8.66860e8 + 5.00482e8i −0.541996 + 0.312921i
\(112\) −2.91805e8 + 2.05882e9i −0.175231 + 1.23634i
\(113\) −1.47317e8 2.55161e8i −0.0849965 0.147218i 0.820393 0.571800i \(-0.193755\pi\)
−0.905390 + 0.424581i \(0.860421\pi\)
\(114\) 3.59137e9 + 6.22044e9i 1.99154 + 3.44945i
\(115\) 1.49347e9i 0.796261i
\(116\) 4.47654e8 + 7.75360e8i 0.229552 + 0.397596i
\(117\) −3.46874e9 + 2.90768e9i −1.71133 + 1.43453i
\(118\) −2.21659e9 −1.05249
\(119\) 1.18819e9 4.78442e8i 0.543154 0.218710i
\(120\) 1.12010e9 1.94008e9i 0.493108 0.854089i
\(121\) −5.77761e9 −2.45027
\(122\) −2.38015e9 + 1.37418e9i −0.972715 + 0.561597i
\(123\) −2.06406e9 1.19169e9i −0.813111 0.469450i
\(124\) 2.70147e8i 0.102613i
\(125\) 2.96587e9i 1.08657i
\(126\) −7.56833e9 1.07269e9i −2.67505 0.379147i
\(127\) 2.23365e9 3.86880e9i 0.761902 1.31965i −0.179967 0.983673i \(-0.557599\pi\)
0.941869 0.335980i \(-0.109068\pi\)
\(128\) 2.92175e9 1.68687e9i 0.962052 0.555441i
\(129\) −3.40575e9 5.89893e9i −1.08283 1.87551i
\(130\) −2.55315e9 + 2.14019e9i −0.784026 + 0.657214i
\(131\) −2.11902e9 + 3.67025e9i −0.628658 + 1.08887i 0.359163 + 0.933275i \(0.383062\pi\)
−0.987821 + 0.155593i \(0.950271\pi\)
\(132\) 4.67998e9 + 2.70199e9i 1.34172 + 0.774641i
\(133\) −4.07366e9 + 5.20149e9i −1.12889 + 1.44144i
\(134\) 8.49082e8 + 1.47065e9i 0.227498 + 0.394038i
\(135\) 6.26568e9 + 3.61749e9i 1.62355 + 0.937358i
\(136\) −1.31229e9 7.57649e8i −0.328930 0.189908i
\(137\) −5.60185e9 3.23423e9i −1.35859 0.784383i −0.369158 0.929367i \(-0.620354\pi\)
−0.989434 + 0.144984i \(0.953687\pi\)
\(138\) −7.55884e9 4.36410e9i −1.77419 1.02433i
\(139\) 9.04003e8 + 1.56578e9i 0.205401 + 0.355766i 0.950261 0.311456i \(-0.100817\pi\)
−0.744859 + 0.667222i \(0.767483\pi\)
\(140\) −1.76522e9 2.50192e8i −0.388350 0.0550424i
\(141\) 1.17932e10 + 6.80879e9i 2.51272 + 1.45072i
\(142\) 6.97620e8 1.20831e9i 0.143986 0.249392i
\(143\) 5.96691e9 + 7.11825e9i 1.19327 + 1.42351i
\(144\) 7.19379e9 + 1.24600e10i 1.39420 + 2.41483i
\(145\) 3.85786e9 2.22733e9i 0.724753 0.418436i
\(146\) −6.55218e8 + 1.13487e9i −0.119343 + 0.206709i
\(147\) −2.43957e9 9.88305e9i −0.430909 1.74567i
\(148\) 9.42395e8i 0.161456i
\(149\) 3.30580e9i 0.549463i 0.961521 + 0.274731i \(0.0885889\pi\)
−0.961521 + 0.274731i \(0.911411\pi\)
\(150\) −3.32956e9 1.92232e9i −0.537002 0.310038i
\(151\) 5.64867e9 3.26126e9i 0.884199 0.510492i 0.0121583 0.999926i \(-0.496130\pi\)
0.872041 + 0.489434i \(0.162796\pi\)
\(152\) 7.81587e9 1.18763
\(153\) 4.43133e9 7.67528e9i 0.653766 1.13236i
\(154\) −2.20129e9 + 1.55311e10i −0.315379 + 2.22515i
\(155\) −1.34413e9 −0.187047
\(156\) −1.06835e9 6.07651e9i −0.144428 0.821473i
\(157\) 5.08563e8 + 8.80857e8i 0.0668030 + 0.115706i 0.897492 0.441030i \(-0.145387\pi\)
−0.830689 + 0.556736i \(0.812053\pi\)
\(158\) 1.21409e10i 1.54986i
\(159\) −4.25885e9 7.37655e9i −0.528452 0.915306i
\(160\) 3.02156e9 + 5.23349e9i 0.364494 + 0.631323i
\(161\) 1.12663e9 7.94892e9i 0.132150 0.932377i
\(162\) −1.61066e10 + 9.29915e9i −1.83733 + 1.06078i
\(163\) 5.63785e9i 0.625561i −0.949825 0.312780i \(-0.898740\pi\)
0.949825 0.312780i \(-0.101260\pi\)
\(164\) 1.94329e9 1.12196e9i 0.209768 0.121110i
\(165\) 1.34439e10 2.32855e10i 1.41204 2.44573i
\(166\) −2.60964e9 4.52003e9i −0.266744 0.462013i
\(167\) −2.16595e9 1.25051e9i −0.215489 0.124412i 0.388371 0.921503i \(-0.373038\pi\)
−0.603860 + 0.797091i \(0.706371\pi\)
\(168\) −7.42525e9 + 9.48100e9i −0.719150 + 0.918253i
\(169\) 1.85181e9 1.04416e10i 0.174625 0.984635i
\(170\) 3.26166e9 5.64936e9i 0.299515 0.518775i
\(171\) 4.57134e10i 4.08847i
\(172\) 6.41293e9 0.558700
\(173\) −1.08703e9 −0.0922643 −0.0461321 0.998935i \(-0.514690\pi\)
−0.0461321 + 0.998935i \(0.514690\pi\)
\(174\) 2.60342e10i 2.15314i
\(175\) 4.96265e8 3.50138e9i 0.0399984 0.282207i
\(176\) 2.55694e10 1.47625e10i 2.00869 1.15972i
\(177\) −1.76881e10 1.02123e10i −1.35457 0.782064i
\(178\) 8.42725e9 1.45964e10i 0.629210 1.08982i
\(179\) 6.14908e8 0.0447684 0.0223842 0.999749i \(-0.492874\pi\)
0.0223842 + 0.999749i \(0.492874\pi\)
\(180\) −1.06831e10 + 6.16791e9i −0.758530 + 0.437937i
\(181\) 2.75898e9 0.191071 0.0955355 0.995426i \(-0.469544\pi\)
0.0955355 + 0.995426i \(0.469544\pi\)
\(182\) 1.52035e10 9.46504e9i 1.02712 0.639442i
\(183\) −2.53245e10 −1.66921
\(184\) −8.22512e9 + 4.74878e9i −0.529008 + 0.305423i
\(185\) −4.68895e9 −0.294309
\(186\) 3.92773e9 6.80303e9i 0.240621 0.416768i
\(187\) −1.57506e10 9.09360e9i −0.941910 0.543812i
\(188\) −1.11031e10 + 6.41039e9i −0.648238 + 0.374261i
\(189\) −3.06199e10 2.39806e10i −1.74552 1.36704i
\(190\) 3.36471e10i 1.87308i
\(191\) 3.61726e10 1.96666 0.983330 0.181828i \(-0.0582015\pi\)
0.983330 + 0.181828i \(0.0582015\pi\)
\(192\) 6.96091e9 0.369667
\(193\) 2.23809e10i 1.16110i −0.814225 0.580549i \(-0.802838\pi\)
0.814225 0.580549i \(-0.197162\pi\)
\(194\) −6.41637e9 + 1.11135e10i −0.325223 + 0.563303i
\(195\) −3.02341e10 + 5.31562e9i −1.49741 + 0.263268i
\(196\) 9.20658e9 + 2.66327e9i 0.445601 + 0.128903i
\(197\) −2.81017e10 1.62245e10i −1.32933 0.767491i −0.344137 0.938920i \(-0.611828\pi\)
−0.985197 + 0.171429i \(0.945162\pi\)
\(198\) 5.42677e10 + 9.39944e10i 2.50927 + 4.34619i
\(199\) 1.07970e10 1.87009e10i 0.488048 0.845324i −0.511857 0.859070i \(-0.671042\pi\)
0.999906 + 0.0137463i \(0.00437572\pi\)
\(200\) −3.62304e9 + 2.09176e9i −0.160117 + 0.0924438i
\(201\) 1.56475e10i 0.676181i
\(202\) 3.61800e9 2.08885e9i 0.152893 0.0882728i
\(203\) −2.22135e10 + 8.94463e9i −0.918090 + 0.369684i
\(204\) 6.04034e9 + 1.04622e10i 0.244189 + 0.422948i
\(205\) −5.58238e9 9.66897e9i −0.220763 0.382374i
\(206\) 9.50018e9i 0.367561i
\(207\) −2.77746e10 4.81070e10i −1.05143 1.82113i
\(208\) −3.16700e10 1.15447e10i −1.17318 0.427661i
\(209\) 9.38092e10 3.40085
\(210\) −4.08154e10 3.19655e10i −1.44823 1.13421i
\(211\) 2.20586e10 3.82066e10i 0.766137 1.32699i −0.173506 0.984833i \(-0.555509\pi\)
0.939643 0.342156i \(-0.111157\pi\)
\(212\) 8.01931e9 0.272663
\(213\) 1.11339e10 6.42814e9i 0.370628 0.213982i
\(214\) −2.81776e10 1.62684e10i −0.918423 0.530252i
\(215\) 3.19080e10i 1.01842i
\(216\) 4.60101e10i 1.43817i
\(217\) 7.15410e9 + 1.01398e9i 0.219021 + 0.0310428i
\(218\) −7.30386e9 + 1.26507e10i −0.219027 + 0.379366i
\(219\) −1.04571e10 + 6.03743e9i −0.307195 + 0.177359i
\(220\) 1.26573e10 + 2.19230e10i 0.364282 + 0.630956i
\(221\) 3.59554e9 + 2.04506e10i 0.101391 + 0.576689i
\(222\) 1.37017e10 2.37321e10i 0.378605 0.655763i
\(223\) 4.27411e10 + 2.46766e10i 1.15737 + 0.668210i 0.950673 0.310194i \(-0.100394\pi\)
0.206700 + 0.978404i \(0.433727\pi\)
\(224\) −1.21341e10 3.01344e10i −0.322027 0.799737i
\(225\) −1.22343e10 2.11904e10i −0.318242 0.551211i
\(226\) 6.98556e9 + 4.03312e9i 0.178120 + 0.102838i
\(227\) 2.16068e10 + 1.24747e10i 0.540100 + 0.311827i 0.745119 0.666931i \(-0.232392\pi\)
−0.205019 + 0.978758i \(0.565726\pi\)
\(228\) −5.39637e10 3.11560e10i −1.32250 0.763545i
\(229\) −1.77700e10 1.02595e10i −0.427000 0.246529i 0.271068 0.962560i \(-0.412623\pi\)
−0.698068 + 0.716032i \(0.745957\pi\)
\(230\) −2.04433e10 3.54089e10i −0.481700 0.834329i
\(231\) −8.91207e10 + 1.13795e11i −2.05933 + 2.62947i
\(232\) 2.45336e10 + 1.41645e10i 0.555989 + 0.321000i
\(233\) 1.64970e10 2.85737e10i 0.366694 0.635133i −0.622352 0.782737i \(-0.713823\pi\)
0.989047 + 0.147604i \(0.0471562\pi\)
\(234\) 4.24391e10 1.16421e11i 0.925326 2.53839i
\(235\) 3.18953e10 + 5.52443e10i 0.682216 + 1.18163i
\(236\) 1.66532e10 9.61471e9i 0.349456 0.201759i
\(237\) 5.59353e10 9.68828e10i 1.15164 1.99471i
\(238\) −2.16218e10 + 2.76080e10i −0.436812 + 0.557748i
\(239\) 5.53506e10i 1.09732i 0.836047 + 0.548658i \(0.184861\pi\)
−0.836047 + 0.548658i \(0.815139\pi\)
\(240\) 9.75794e10i 1.89849i
\(241\) 2.36447e10 + 1.36513e10i 0.451499 + 0.260673i 0.708463 0.705748i \(-0.249389\pi\)
−0.256964 + 0.966421i \(0.582722\pi\)
\(242\) 1.36982e11 7.90869e10i 2.56741 1.48230i
\(243\) −5.08629e10 −0.935779
\(244\) 1.19213e10 2.06484e10i 0.215313 0.372933i
\(245\) 1.32513e10 4.58080e10i 0.234969 0.812257i
\(246\) 6.52497e10 1.13598
\(247\) −6.88030e10 8.20789e10i −1.17617 1.40312i
\(248\) −4.27394e9 7.40268e9i −0.0717457 0.124267i
\(249\) 4.80924e10i 0.792829i
\(250\) −4.05984e10 7.03184e10i −0.657322 1.13852i
\(251\) −1.82822e10 3.16657e10i −0.290735 0.503568i 0.683249 0.730186i \(-0.260566\pi\)
−0.973984 + 0.226618i \(0.927233\pi\)
\(252\) 6.15135e10 2.47694e10i 0.960878 0.386913i
\(253\) −9.87211e10 + 5.69967e10i −1.51484 + 0.874595i
\(254\) 1.22302e11i 1.84366i
\(255\) 5.20553e10 3.00541e10i 0.770964 0.445116i
\(256\) −3.91176e10 + 6.77536e10i −0.569236 + 0.985945i
\(257\) 4.35796e10 + 7.54822e10i 0.623139 + 1.07931i 0.988898 + 0.148598i \(0.0474761\pi\)
−0.365759 + 0.930710i \(0.619191\pi\)
\(258\) 1.61495e11 + 9.32392e10i 2.26919 + 1.31012i
\(259\) 2.49568e10 + 3.53723e9i 0.344619 + 0.0488443i
\(260\) 9.89839e9 2.71537e10i 0.134334 0.368510i
\(261\) −8.28452e10 + 1.43492e11i −1.10506 + 1.91402i
\(262\) 1.16025e11i 1.52123i
\(263\) −1.15471e11 −1.48823 −0.744116 0.668050i \(-0.767129\pi\)
−0.744116 + 0.668050i \(0.767129\pi\)
\(264\) 1.70990e11 2.16648
\(265\) 3.99006e10i 0.497020i
\(266\) 2.53825e10 1.79085e11i 0.310862 2.19327i
\(267\) 1.34497e11 7.76519e10i 1.61962 0.935085i
\(268\) −1.27582e10 7.36597e9i −0.151072 0.0872215i
\(269\) 2.86011e10 4.95386e10i 0.333041 0.576844i −0.650065 0.759878i \(-0.725259\pi\)
0.983107 + 0.183034i \(0.0585919\pi\)
\(270\) −1.98072e11 −2.26823
\(271\) 1.25465e11 7.24372e10i 1.41306 0.815831i 0.417385 0.908730i \(-0.362947\pi\)
0.995676 + 0.0928991i \(0.0296134\pi\)
\(272\) 6.60037e10 0.731153
\(273\) 1.64930e11 5.48439e9i 1.79708 0.0597581i
\(274\) 1.77087e11 1.89806
\(275\) −4.34852e10 + 2.51062e10i −0.458505 + 0.264718i
\(276\) 7.57191e10 0.785443
\(277\) −4.12484e10 + 7.14443e10i −0.420967 + 0.729136i −0.996034 0.0889702i \(-0.971642\pi\)
0.575068 + 0.818106i \(0.304976\pi\)
\(278\) −4.28664e10 2.47489e10i −0.430443 0.248516i
\(279\) 4.32967e10 2.49974e10i 0.427795 0.246988i
\(280\) −5.23296e10 + 2.10713e10i −0.508787 + 0.204871i
\(281\) 1.64703e11i 1.57588i −0.615753 0.787940i \(-0.711148\pi\)
0.615753 0.787940i \(-0.288852\pi\)
\(282\) −3.72809e11 −3.51047
\(283\) −1.51597e11 −1.40492 −0.702460 0.711723i \(-0.747915\pi\)
−0.702460 + 0.711723i \(0.747915\pi\)
\(284\) 1.21040e10i 0.110407i
\(285\) −1.55019e11 + 2.68500e11i −1.39182 + 2.41070i
\(286\) −2.38909e11 8.70899e10i −2.11147 0.769699i
\(287\) 2.24180e10 + 5.56739e10i 0.195042 + 0.484377i
\(288\) −1.94658e11 1.12386e11i −1.66727 0.962601i
\(289\) 3.89650e10 + 6.74894e10i 0.328575 + 0.569109i
\(290\) −6.09778e10 + 1.05617e11i −0.506268 + 0.876882i
\(291\) −1.02404e11 + 5.91229e10i −0.837139 + 0.483322i
\(292\) 1.13683e10i 0.0915110i
\(293\) −9.60887e10 + 5.54769e10i −0.761672 + 0.439752i −0.829896 0.557918i \(-0.811600\pi\)
0.0682236 + 0.997670i \(0.478267\pi\)
\(294\) 1.93125e11 + 2.00925e11i 1.50756 + 1.56845i
\(295\) −4.78387e10 8.28590e10i −0.367773 0.637002i
\(296\) −1.49095e10 2.58239e10i −0.112888 0.195528i
\(297\) 5.52232e11i 4.11829i
\(298\) −4.52515e10 7.83779e10i −0.332399 0.575732i
\(299\) 1.22275e11 + 4.45732e10i 0.884745 + 0.322518i
\(300\) 3.33531e10 0.237734
\(301\) −2.40706e10 + 1.69829e11i −0.169020 + 1.19251i
\(302\) −8.92837e10 + 1.54644e11i −0.617648 + 1.06980i
\(303\) 3.84950e10 0.262369
\(304\) −2.94835e11 + 1.70223e11i −1.97992 + 1.14311i
\(305\) −1.02737e11 5.93154e10i −0.679796 0.392481i
\(306\) 2.42633e11i 1.58199i
\(307\) 7.34189e10i 0.471721i 0.971787 + 0.235860i \(0.0757908\pi\)
−0.971787 + 0.235860i \(0.924209\pi\)
\(308\) −5.08297e10 1.26233e11i −0.321839 0.799272i
\(309\) −4.37691e10 + 7.58103e10i −0.273121 + 0.473059i
\(310\) 3.18683e10 1.83992e10i 0.195989 0.113154i
\(311\) 1.43571e10 + 2.48671e10i 0.0870249 + 0.150732i 0.906252 0.422737i \(-0.138931\pi\)
−0.819227 + 0.573469i \(0.805597\pi\)
\(312\) −1.25411e11 1.49609e11i −0.749270 0.893845i
\(313\) 5.72582e9 9.91741e9i 0.0337200 0.0584048i −0.848673 0.528918i \(-0.822598\pi\)
0.882393 + 0.470513i \(0.155931\pi\)
\(314\) −2.41152e10 1.39229e10i −0.139994 0.0808254i
\(315\) −1.23242e11 3.06065e11i −0.705278 1.75152i
\(316\) 5.26624e10 + 9.12139e10i 0.297104 + 0.514600i
\(317\) −1.14225e11 6.59479e10i −0.635324 0.366804i 0.147487 0.989064i \(-0.452881\pi\)
−0.782811 + 0.622260i \(0.786215\pi\)
\(318\) 2.01948e11 + 1.16595e11i 1.10743 + 0.639377i
\(319\) 2.94462e11 + 1.70008e11i 1.59211 + 0.919202i
\(320\) 2.82393e10 + 1.63040e10i 0.150549 + 0.0869198i
\(321\) −1.49903e11 2.59639e11i −0.788020 1.36489i
\(322\) 8.20973e10 + 2.03884e11i 0.425576 + 1.05690i
\(323\) 1.81616e11 + 1.04856e11i 0.928418 + 0.536022i
\(324\) 8.06722e10 1.39728e11i 0.406697 0.704420i
\(325\) 5.38604e10 + 1.96338e10i 0.267790 + 0.0976180i
\(326\) 7.71738e10 + 1.33669e11i 0.378435 + 0.655468i
\(327\) −1.16568e11 + 6.73005e10i −0.563786 + 0.325502i
\(328\) 3.55006e10 6.14888e10i 0.169357 0.293335i
\(329\) −1.28087e11 3.18097e11i −0.602730 1.49685i
\(330\) 7.36109e11i 3.41688i
\(331\) 1.88741e11i 0.864251i −0.901814 0.432125i \(-0.857764\pi\)
0.901814 0.432125i \(-0.142236\pi\)
\(332\) 3.92122e10 + 2.26392e10i 0.177133 + 0.102268i
\(333\) 1.51039e11 8.72022e10i 0.673115 0.388623i
\(334\) 6.84706e10 0.301055
\(335\) −3.66499e10 + 6.34795e10i −0.158990 + 0.275380i
\(336\) 7.36114e10 5.19363e11i 0.315078 2.22302i
\(337\) −5.70876e10 −0.241106 −0.120553 0.992707i \(-0.538467\pi\)
−0.120553 + 0.992707i \(0.538467\pi\)
\(338\) 9.90246e10 + 2.72910e11i 0.412684 + 1.13735i
\(339\) 3.71627e10 + 6.43676e10i 0.152830 + 0.264709i
\(340\) 5.65912e10i 0.229664i
\(341\) −5.12975e10 8.88499e10i −0.205448 0.355846i
\(342\) −6.25748e11 1.08383e12i −2.47333 4.28393i
\(343\) −1.05086e11 + 2.33815e11i −0.409941 + 0.912112i
\(344\) 1.75730e11 1.01458e11i 0.676602 0.390636i
\(345\) 3.76745e11i 1.43173i
\(346\) 2.57726e10 1.48798e10i 0.0966753 0.0558155i
\(347\) 2.54857e10 4.41426e10i 0.0943657 0.163446i −0.814978 0.579492i \(-0.803251\pi\)
0.909344 + 0.416046i \(0.136584\pi\)
\(348\) −1.12926e11 1.95594e11i −0.412751 0.714906i
\(349\) −2.51330e11 1.45105e11i −0.906838 0.523563i −0.0274257 0.999624i \(-0.508731\pi\)
−0.879412 + 0.476061i \(0.842064\pi\)
\(350\) 3.61626e10 + 8.98080e10i 0.128811 + 0.319896i
\(351\) 4.83178e11 4.05026e11i 1.69912 1.42430i
\(352\) −2.30629e11 + 3.99462e11i −0.800705 + 1.38686i
\(353\) 5.16421e11i 1.77018i −0.465419 0.885090i \(-0.654096\pi\)
0.465419 0.885090i \(-0.345904\pi\)
\(354\) 5.59163e11 1.89245
\(355\) 6.02244e10 0.201254
\(356\) 1.46216e11i 0.482471i
\(357\) −2.99734e11 + 1.20693e11i −0.976629 + 0.393255i
\(358\) −1.45790e10 + 8.41718e9i −0.0469087 + 0.0270828i
\(359\) 1.24716e11 + 7.20049e10i 0.396276 + 0.228790i 0.684876 0.728660i \(-0.259856\pi\)
−0.288600 + 0.957450i \(0.593190\pi\)
\(360\) −1.95163e11 + 3.38032e11i −0.612401 + 1.06071i
\(361\) −7.59004e11 −2.35213
\(362\) −6.54132e10 + 3.77663e10i −0.200206 + 0.115589i
\(363\) 1.45747e12 4.40576
\(364\) −7.31679e10 + 1.37057e11i −0.218456 + 0.409210i
\(365\) −5.65639e10 −0.166810
\(366\) 6.00423e11 3.46654e11i 1.74901 1.00979i
\(367\) −1.67449e11 −0.481820 −0.240910 0.970547i \(-0.577446\pi\)
−0.240910 + 0.970547i \(0.577446\pi\)
\(368\) 2.06848e11 3.58272e11i 0.587945 1.01835i
\(369\) 3.59635e11 + 2.07635e11i 1.00982 + 0.583019i
\(370\) 1.11171e11 6.41848e10i 0.308379 0.178043i
\(371\) −3.01000e10 + 2.12370e11i −0.0824868 + 0.581982i
\(372\) 6.81479e10i 0.184505i
\(373\) −3.39297e11 −0.907592 −0.453796 0.891106i \(-0.649930\pi\)
−0.453796 + 0.891106i \(0.649930\pi\)
\(374\) 4.97912e11 1.31592
\(375\) 7.48177e11i 1.95373i
\(376\) −2.02835e11 + 3.51321e11i −0.523357 + 0.906481i
\(377\) −6.72199e10 3.82332e11i −0.171381 0.974774i
\(378\) 1.05423e12 + 1.49421e11i 2.65597 + 0.376442i
\(379\) 1.45117e11 + 8.37832e10i 0.361278 + 0.208584i 0.669641 0.742685i \(-0.266448\pi\)
−0.308363 + 0.951269i \(0.599781\pi\)
\(380\) −1.45948e11 2.52790e11i −0.359064 0.621918i
\(381\) −5.63467e11 + 9.75953e11i −1.36995 + 2.37283i
\(382\) −8.57623e11 + 4.95149e11i −2.06068 + 1.18974i
\(383\) 6.06739e11i 1.44081i −0.693553 0.720406i \(-0.743955\pi\)
0.693553 0.720406i \(-0.256045\pi\)
\(384\) −7.37048e11 + 4.25535e11i −1.72984 + 0.998723i
\(385\) −6.28080e11 + 2.52907e11i −1.45694 + 0.586660i
\(386\) 3.06361e11 + 5.30632e11i 0.702409 + 1.21661i
\(387\) 5.93405e11 + 1.02781e12i 1.34478 + 2.32923i
\(388\) 1.11327e11i 0.249377i
\(389\) −3.69657e11 6.40265e11i −0.818514 1.41771i −0.906777 0.421610i \(-0.861465\pi\)
0.0882632 0.996097i \(-0.471868\pi\)
\(390\) 6.44063e11 5.39889e11i 1.40973 1.18172i
\(391\) −2.54834e11 −0.551395
\(392\) 2.94418e11 7.26753e10i 0.629763 0.155453i
\(393\) 5.34549e11 9.25867e11i 1.13037 1.95786i
\(394\) 8.88357e11 1.85718
\(395\) 4.53841e11 2.62025e11i 0.938031 0.541572i
\(396\) −8.15423e11 4.70784e11i −1.66630 0.962041i
\(397\) 1.91585e11i 0.387083i −0.981092 0.193541i \(-0.938003\pi\)
0.981092 0.193541i \(-0.0619973\pi\)
\(398\) 5.91177e11i 1.18098i
\(399\) 1.02763e12 1.31214e12i 2.02983 2.59180i
\(400\) 9.11136e10 1.57813e11i 0.177956 0.308229i
\(401\) −7.21991e11 + 4.16841e11i −1.39438 + 0.805047i −0.993797 0.111212i \(-0.964527\pi\)
−0.400586 + 0.916259i \(0.631193\pi\)
\(402\) −2.14191e11 3.70990e11i −0.409058 0.708509i
\(403\) −4.01163e10 + 1.10049e11i −0.0757614 + 0.207832i
\(404\) −1.81213e10 + 3.13870e10i −0.0338433 + 0.0586183i
\(405\) −6.95228e11 4.01390e11i −1.28404 0.741343i
\(406\) 4.04226e11 5.16140e11i 0.738342 0.942759i
\(407\) −1.78949e11 3.09949e11i −0.323262 0.559906i
\(408\) 3.31041e11 + 1.91126e11i 0.591440 + 0.341468i
\(409\) −8.77292e9 5.06505e9i −0.0155021 0.00895012i 0.492229 0.870466i \(-0.336182\pi\)
−0.507731 + 0.861516i \(0.669516\pi\)
\(410\) 2.64708e11 + 1.52829e11i 0.462636 + 0.267103i
\(411\) 1.41314e12 + 8.15874e11i 2.44284 + 1.41038i
\(412\) −4.12081e10 7.13745e10i −0.0704604 0.122041i
\(413\) 1.92113e11 + 4.77102e11i 0.324923 + 0.806930i
\(414\) 1.31703e12 + 7.60385e11i 2.20340 + 1.27213i
\(415\) 1.12643e11 1.95103e11i 0.186418 0.322885i
\(416\) 5.18663e11 9.11891e10i 0.849113 0.149287i
\(417\) −2.28046e11 3.94987e11i −0.369326 0.639692i
\(418\) −2.22414e12 + 1.28411e12i −3.56344 + 2.05735i
\(419\) −5.59106e11 + 9.68400e11i −0.886199 + 1.53494i −0.0418654 + 0.999123i \(0.513330\pi\)
−0.844333 + 0.535818i \(0.820003\pi\)
\(420\) 4.45299e11 + 6.31140e10i 0.698280 + 0.0989701i
\(421\) 7.87081e10i 0.122110i −0.998134 0.0610548i \(-0.980554\pi\)
0.998134 0.0610548i \(-0.0194464\pi\)
\(422\) 1.20780e12i 1.85391i
\(423\) −2.05480e12 1.18634e12i −3.12060 1.80168i
\(424\) 2.19749e11 1.26872e11i 0.330202 0.190642i
\(425\) −1.12251e11 −0.166893
\(426\) −1.75983e11 + 3.04812e11i −0.258898 + 0.448424i
\(427\) 5.02069e11 + 3.93206e11i 0.730867 + 0.572394i
\(428\) 2.82263e11 0.406591
\(429\) −1.50523e12 1.79567e12i −2.14558 2.55958i
\(430\) 4.36773e11 + 7.56513e11i 0.616095 + 1.06711i
\(431\) 2.58806e11i 0.361266i −0.983551 0.180633i \(-0.942185\pi\)
0.983551 0.180633i \(-0.0578146\pi\)
\(432\) −1.00206e12 1.73562e12i −1.38426 2.39760i
\(433\) −9.10029e10 1.57622e11i −0.124411 0.215487i 0.797091 0.603859i \(-0.206371\pi\)
−0.921503 + 0.388372i \(0.873038\pi\)
\(434\) −1.83498e11 + 7.38883e10i −0.248272 + 0.0999706i
\(435\) −9.73192e11 + 5.61873e11i −1.30316 + 0.752378i
\(436\) 1.26725e11i 0.167948i
\(437\) 1.13833e12 6.57215e11i 1.49314 0.862067i
\(438\) 1.65287e11 2.86285e11i 0.214588 0.371677i
\(439\) 3.30437e11 + 5.72333e11i 0.424617 + 0.735459i 0.996385 0.0849569i \(-0.0270753\pi\)
−0.571767 + 0.820416i \(0.693742\pi\)
\(440\) 6.93681e11 + 4.00497e11i 0.882313 + 0.509404i
\(441\) 4.25062e11 + 1.72199e12i 0.535154 + 2.16799i
\(442\) −3.65186e11 4.35651e11i −0.455108 0.542923i
\(443\) 4.90188e10 8.49031e10i 0.0604709 0.104739i −0.834205 0.551454i \(-0.814073\pi\)
0.894676 + 0.446716i \(0.147406\pi\)
\(444\) 2.37731e11i 0.290310i
\(445\) 7.27510e11 0.879466
\(446\) −1.35114e12 −1.61694
\(447\) 8.33929e11i 0.987973i
\(448\) −1.38003e11 1.08080e11i −0.161860 0.126764i
\(449\) 5.05575e11 2.91894e11i 0.587053 0.338935i −0.176879 0.984233i \(-0.556600\pi\)
0.763931 + 0.645298i \(0.223267\pi\)
\(450\) 5.80130e11 + 3.34938e11i 0.666913 + 0.385042i
\(451\) 4.26092e11 7.38013e11i 0.484963 0.839981i
\(452\) −6.99763e10 −0.0788548
\(453\) −1.42495e12 + 8.22694e11i −1.58985 + 0.917902i
\(454\) −6.83040e11 −0.754562
\(455\) 6.81939e11 + 3.64052e11i 0.745923 + 0.398210i
\(456\) −1.97165e12 −2.13544
\(457\) 4.24855e11 2.45290e11i 0.455635 0.263061i −0.254572 0.967054i \(-0.581935\pi\)
0.710207 + 0.703993i \(0.248601\pi\)
\(458\) 5.61750e11 0.596553
\(459\) −6.17263e11 + 1.06913e12i −0.649102 + 1.12428i
\(460\) 3.07180e11 + 1.77351e11i 0.319877 + 0.184681i
\(461\) −7.09341e11 + 4.09538e11i −0.731478 + 0.422319i −0.818963 0.573847i \(-0.805450\pi\)
0.0874848 + 0.996166i \(0.472117\pi\)
\(462\) 5.55302e11 3.91791e12i 0.567075 4.00097i
\(463\) 2.99451e11i 0.302839i −0.988470 0.151419i \(-0.951616\pi\)
0.988470 0.151419i \(-0.0483844\pi\)
\(464\) −1.23396e12 −1.23586
\(465\) 3.39074e11 0.336323
\(466\) 9.03279e11i 0.887331i
\(467\) 6.03249e11 1.04486e12i 0.586909 1.01656i −0.407726 0.913105i \(-0.633678\pi\)
0.994634 0.103452i \(-0.0329887\pi\)
\(468\) 1.86145e11 + 1.05875e12i 0.179368 + 1.02020i
\(469\) 2.42955e11 3.10219e11i 0.231872 0.296068i
\(470\) −1.51243e12 8.73200e11i −1.42966 0.825416i
\(471\) −1.28291e11 2.22207e11i −0.120117 0.208048i
\(472\) 3.04225e11 5.26933e11i 0.282134 0.488671i
\(473\) 2.10918e12 1.21774e12i 1.93749 1.11861i
\(474\) 3.06269e12i 2.78676i
\(475\) 5.01417e11 2.89493e11i 0.451937 0.260926i
\(476\) 4.26910e10 3.01205e11i 0.0381158 0.268924i
\(477\) 7.42048e11 + 1.28526e12i 0.656295 + 1.13674i
\(478\) −7.57668e11 1.31232e12i −0.663824 1.14978i
\(479\) 7.64456e11i 0.663503i −0.943367 0.331751i \(-0.892360\pi\)
0.943367 0.331751i \(-0.107640\pi\)
\(480\) −7.62225e11 1.32021e12i −0.655387 1.13516i
\(481\) −1.39944e11 + 3.83900e11i −0.119207 + 0.327013i
\(482\) −7.47462e11 −0.630779
\(483\) −2.84207e11 + 2.00521e12i −0.237614 + 1.67648i
\(484\) −6.86096e11 + 1.18835e12i −0.568304 + 0.984332i
\(485\) −5.53914e11 −0.454574
\(486\) 1.20592e12 6.96238e11i 0.980517 0.566102i
\(487\) 8.08672e11 + 4.66887e11i 0.651466 + 0.376124i 0.789018 0.614370i \(-0.210590\pi\)
−0.137552 + 0.990495i \(0.543923\pi\)
\(488\) 7.54421e11i 0.602177i
\(489\) 1.42222e12i 1.12480i
\(490\) 3.12865e11 + 1.26746e12i 0.245174 + 0.993236i
\(491\) 4.42971e11 7.67249e11i 0.343961 0.595758i −0.641204 0.767371i \(-0.721565\pi\)
0.985164 + 0.171613i \(0.0548979\pi\)
\(492\) −4.90219e11 + 2.83028e11i −0.377179 + 0.217764i
\(493\) 3.80056e11 + 6.58277e11i 0.289759 + 0.501877i
\(494\) 2.75480e12 + 1.00421e12i 2.08123 + 0.758674i
\(495\) −2.34242e12 + 4.05719e12i −1.75364 + 3.03740i
\(496\) 3.22448e11 + 1.86165e11i 0.239217 + 0.138112i
\(497\) −3.20542e11 4.54318e10i −0.235658 0.0334007i
\(498\) 6.58314e11 + 1.14023e12i 0.479624 + 0.830733i
\(499\) 1.22625e12 + 7.07977e11i 0.885375 + 0.511172i 0.872427 0.488745i \(-0.162545\pi\)
0.0129482 + 0.999916i \(0.495878\pi\)
\(500\) 6.10028e11 + 3.52200e11i 0.436501 + 0.252014i
\(501\) 5.46388e11 + 3.15457e11i 0.387464 + 0.223702i
\(502\) 8.66914e11 + 5.00513e11i 0.609269 + 0.351762i
\(503\) −2.85571e11 4.94624e11i −0.198911 0.344524i 0.749265 0.662271i \(-0.230407\pi\)
−0.948176 + 0.317747i \(0.897074\pi\)
\(504\) 1.29375e12 1.65194e12i 0.893126 1.14040i
\(505\) 1.56168e11 + 9.01636e10i 0.106852 + 0.0616908i
\(506\) 1.56040e12 2.70269e12i 1.05818 1.83282i
\(507\) −4.67142e11 + 2.63401e12i −0.313988 + 1.77044i
\(508\) −5.30497e11 9.18848e11i −0.353424 0.612149i
\(509\) −4.05958e11 + 2.34380e11i −0.268072 + 0.154771i −0.628011 0.778204i \(-0.716131\pi\)
0.359939 + 0.932976i \(0.382797\pi\)
\(510\) −8.22793e11 + 1.42512e12i −0.538549 + 0.932794i
\(511\) 3.01059e11 + 4.26703e10i 0.195325 + 0.0276842i
\(512\) 4.14486e11i 0.266560i
\(513\) 6.36765e12i 4.05930i
\(514\) −2.06648e12 1.19308e12i −1.30586 0.753939i
\(515\) −3.55129e11 + 2.05034e11i −0.222461 + 0.128438i
\(516\) −1.61774e12 −1.00458
\(517\) −2.43451e12 + 4.21669e12i −1.49866 + 2.59576i
\(518\) −6.40124e11 + 2.57756e11i −0.390643 + 0.157299i
\(519\) 2.74217e11 0.165898
\(520\) −1.58353e11 9.00679e11i −0.0949757 0.540200i
\(521\) −4.69332e10 8.12907e10i −0.0279068 0.0483360i 0.851735 0.523973i \(-0.175551\pi\)
−0.879642 + 0.475637i \(0.842218\pi\)
\(522\) 4.53611e12i 2.67403i
\(523\) −1.41830e12 2.45656e12i −0.828914 1.43572i −0.898891 0.438173i \(-0.855626\pi\)
0.0699767 0.997549i \(-0.477707\pi\)
\(524\) 5.03271e11 + 8.71692e11i 0.291616 + 0.505094i
\(525\) −1.25189e11 + 8.83266e11i −0.0719199 + 0.507428i
\(526\) 2.73772e12 1.58062e12i 1.55938 0.900310i
\(527\) 2.29353e11i 0.129526i
\(528\) −6.45020e12 + 3.72402e12i −3.61177 + 2.08526i
\(529\) 1.01954e11 1.76589e11i 0.0566046 0.0980421i
\(530\) 5.46181e11 + 9.46013e11i 0.300673 + 0.520781i
\(531\) 3.08192e12 + 1.77935e12i 1.68227 + 0.971260i
\(532\) 5.86105e11 + 1.45556e12i 0.317229 + 0.787823i
\(533\) −9.58240e11 + 1.68474e11i −0.514283 + 0.0904190i
\(534\) −2.12588e12 + 3.68213e12i −1.13136 + 1.95958i
\(535\) 1.40442e12i 0.741149i
\(536\) −4.66143e11 −0.243937
\(537\) −1.55118e11 −0.0804968
\(538\) 1.56603e12i 0.805896i
\(539\) 3.53372e12 8.72278e11i 1.80336 0.445149i
\(540\) 1.48811e12 8.59161e11i 0.753118 0.434813i
\(541\) 1.93909e12 + 1.11953e12i 0.973218 + 0.561888i 0.900216 0.435444i \(-0.143409\pi\)
0.0730025 + 0.997332i \(0.476742\pi\)
\(542\) −1.98312e12 + 3.43486e12i −0.987078 + 1.70967i
\(543\) −6.95987e11 −0.343559
\(544\) −8.93005e11 + 5.15577e11i −0.437179 + 0.252405i
\(545\) −6.30530e11 −0.306141
\(546\) −3.83528e12 + 2.38767e12i −1.84684 + 1.14976i
\(547\) −5.80050e11 −0.277027 −0.138514 0.990361i \(-0.544232\pi\)
−0.138514 + 0.990361i \(0.544232\pi\)
\(548\) −1.33045e12 + 7.68136e11i −0.630211 + 0.363852i
\(549\) 4.41245e12 2.07302
\(550\) 6.87332e11 1.19049e12i 0.320284 0.554747i
\(551\) −3.39538e12 1.96032e12i −1.56930 0.906036i
\(552\) 2.07489e12 1.19794e12i 0.951193 0.549172i
\(553\) −2.61322e12 + 1.05225e12i −1.18826 + 0.478473i
\(554\) 2.25852e12i 1.01866i
\(555\) 1.18285e12 0.529188
\(556\) 4.29405e11 0.190559
\(557\) 1.39868e12i 0.615701i −0.951435 0.307850i \(-0.900390\pi\)
0.951435 0.307850i \(-0.0996096\pi\)
\(558\) −6.84354e11 + 1.18534e12i −0.298832 + 0.517592i
\(559\) −2.61242e12 9.52309e11i −1.13159 0.412501i
\(560\) 1.51509e12 1.93456e12i 0.651017 0.831258i
\(561\) 3.97328e12 + 2.29397e12i 1.69362 + 0.977812i
\(562\) 2.25454e12 + 3.90498e12i 0.953332 + 1.65122i
\(563\) −6.87910e11 + 1.19150e12i −0.288565 + 0.499810i −0.973467 0.228825i \(-0.926512\pi\)
0.684902 + 0.728635i \(0.259845\pi\)
\(564\) 2.80090e12 1.61710e12i 1.16558 0.672947i
\(565\) 3.48172e11i 0.143739i
\(566\) 3.59424e12 2.07514e12i 1.47209 0.849910i
\(567\) 3.39753e12 + 2.66085e12i 1.38051 + 1.08117i
\(568\) 1.91496e11 + 3.31680e11i 0.0771953 + 0.133706i
\(569\) 2.98509e10 + 5.17033e10i 0.0119386 + 0.0206782i 0.871933 0.489625i \(-0.162866\pi\)
−0.859994 + 0.510303i \(0.829533\pi\)
\(570\) 8.48790e12i 3.36793i
\(571\) −2.15976e12 3.74081e12i −0.850241 1.47266i −0.880990 0.473134i \(-0.843123\pi\)
0.0307491 0.999527i \(-0.490211\pi\)
\(572\) 2.17268e12 3.81991e11i 0.848619 0.149201i
\(573\) −9.12498e12 −3.53620
\(574\) −1.29361e12 1.01312e12i −0.497392 0.389543i
\(575\) −3.51781e11 + 6.09303e11i −0.134205 + 0.232449i
\(576\) −1.21284e12 −0.459097
\(577\) −1.99967e11 + 1.15451e11i −0.0751047 + 0.0433617i −0.537082 0.843530i \(-0.680473\pi\)
0.461977 + 0.886892i \(0.347140\pi\)
\(578\) −1.84766e12 1.06675e12i −0.688567 0.397545i
\(579\) 5.64585e12i 2.08774i
\(580\) 1.05799e12i 0.388201i
\(581\) −7.46718e11 + 9.53454e11i −0.271872 + 0.347142i
\(582\) 1.61861e12 2.80351e12i 0.584774 1.01286i
\(583\) 2.63751e12 1.52277e12i 0.945553 0.545915i
\(584\) −1.79856e11 3.11520e11i −0.0639834 0.110823i
\(585\) 5.26788e12 9.26175e11i 1.85966 0.326958i
\(586\) 1.51879e12 2.63062e12i 0.532058 0.921551i
\(587\) 2.48065e12 + 1.43220e12i 0.862370 + 0.497889i 0.864805 0.502108i \(-0.167442\pi\)
−0.00243544 + 0.999997i \(0.500775\pi\)
\(588\) −2.32247e12 6.71844e11i −0.801222 0.231777i
\(589\) 5.91500e11 + 1.02451e12i 0.202505 + 0.350749i
\(590\) 2.26843e12 + 1.30968e12i 0.770712 + 0.444971i
\(591\) 7.08899e12 + 4.09283e12i 2.39024 + 1.38000i
\(592\) 1.12485e12 + 6.49430e11i 0.376396 + 0.217312i
\(593\) −1.55535e12 8.97983e11i −0.516515 0.298210i 0.218993 0.975726i \(-0.429723\pi\)
−0.735507 + 0.677517i \(0.763056\pi\)
\(594\) −7.55923e12 1.30930e13i −2.49137 4.31518i
\(595\) −1.49866e12 2.12412e11i −0.490205 0.0694788i
\(596\) 6.79945e11 + 3.92567e11i 0.220732 + 0.127440i
\(597\) −2.72367e12 + 4.71753e12i −0.877545 + 1.51995i
\(598\) −3.50919e12 + 6.16970e11i −1.12215 + 0.197292i
\(599\) 4.00685e11 + 6.94006e11i 0.127169 + 0.220263i 0.922579 0.385809i \(-0.126078\pi\)
−0.795410 + 0.606072i \(0.792744\pi\)
\(600\) 9.13957e11 5.27673e11i 0.287902 0.166220i
\(601\) −1.09595e12 + 1.89824e12i −0.342654 + 0.593495i −0.984925 0.172983i \(-0.944659\pi\)
0.642270 + 0.766478i \(0.277993\pi\)
\(602\) −1.75401e12 4.35600e12i −0.544313 1.35177i
\(603\) 2.72637e12i 0.839763i
\(604\) 1.54911e12i 0.473605i
\(605\) 5.91273e12 + 3.41372e12i 1.79428 + 1.03593i
\(606\) −9.12685e11 + 5.26939e11i −0.274912 + 0.158721i
\(607\) 1.73713e11 0.0519378 0.0259689 0.999663i \(-0.491733\pi\)
0.0259689 + 0.999663i \(0.491733\pi\)
\(608\) 2.65933e12 4.60610e12i 0.789236 1.36700i
\(609\) 5.60364e12 2.25639e12i 1.65079 0.664718i
\(610\) 3.24776e12 0.949729
\(611\) 5.47497e12 9.62586e11i 1.58927 0.279418i
\(612\) −1.05245e12 1.82289e12i −0.303263 0.525267i
\(613\) 9.51581e11i 0.272191i 0.990696 + 0.136095i \(0.0434554\pi\)
−0.990696 + 0.136095i \(0.956545\pi\)
\(614\) −1.00500e12 1.74070e12i −0.285369 0.494273i
\(615\) 1.40822e12 + 2.43912e12i 0.396948 + 0.687535i
\(616\) −3.38997e12 2.65492e12i −0.948598 0.742915i
\(617\) −5.50130e12 + 3.17618e12i −1.52821 + 0.882311i −0.528769 + 0.848765i \(0.677346\pi\)
−0.999437 + 0.0335451i \(0.989320\pi\)
\(618\) 2.39654e12i 0.660900i
\(619\) 3.23123e12 1.86555e12i 0.884626 0.510739i 0.0124450 0.999923i \(-0.496039\pi\)
0.872181 + 0.489184i \(0.162705\pi\)
\(620\) −1.59617e11 + 2.76465e11i −0.0433827 + 0.0751411i
\(621\) 3.86886e12 + 6.70107e12i 1.04393 + 1.80814i
\(622\) −6.80789e11 3.93053e11i −0.182371 0.105292i
\(623\) −3.87215e12 5.48815e11i −1.02981 0.145959i
\(624\) 7.98916e12 + 2.91230e12i 2.10946 + 0.768964i
\(625\) 1.20875e12 2.09361e12i 0.316866 0.548828i
\(626\) 3.13512e11i 0.0815961i
\(627\) −2.36645e13 −6.11496
\(628\) 2.41569e11 0.0619760
\(629\) 8.00089e11i 0.203803i
\(630\) 7.11154e12 + 5.56955e12i 1.79858 + 1.40860i
\(631\) 1.66552e12 9.61589e11i 0.418233 0.241467i −0.276088 0.961132i \(-0.589038\pi\)
0.694321 + 0.719666i \(0.255705\pi\)
\(632\) 2.88616e12 + 1.66632e12i 0.719603 + 0.415463i
\(633\) −5.56455e12 + 9.63809e12i −1.37757 + 2.38602i
\(634\) 3.61092e12 0.887597
\(635\) −4.57179e12 + 2.63952e12i −1.11585 + 0.644234i
\(636\) −2.02297e12 −0.490267
\(637\) −3.35496e12 2.45209e12i −0.807347 0.590077i
\(638\) −9.30863e12 −2.22430
\(639\) −1.93993e12 + 1.12002e12i −0.460290 + 0.265748i
\(640\) −3.98678e12 −0.939318
\(641\) 2.09269e12 3.62465e12i 0.489603 0.848017i −0.510326 0.859981i \(-0.670475\pi\)
0.999928 + 0.0119645i \(0.00380850\pi\)
\(642\) 7.10816e12 + 4.10390e12i 1.65139 + 0.953430i
\(643\) −5.23467e11 + 3.02224e11i −0.120765 + 0.0697235i −0.559166 0.829056i \(-0.688878\pi\)
0.438401 + 0.898780i \(0.355545\pi\)
\(644\) −1.50117e12 1.17567e12i −0.343908 0.269339i
\(645\) 8.04919e12i 1.83119i
\(646\) −5.74130e12 −1.29707
\(647\) −4.36931e11 −0.0980264 −0.0490132 0.998798i \(-0.515608\pi\)
−0.0490132 + 0.998798i \(0.515608\pi\)
\(648\) 5.10520e12i 1.13743i
\(649\) 3.65143e12 6.32446e12i 0.807908 1.39934i
\(650\) −1.54574e12 + 2.71766e11i −0.339647 + 0.0597152i
\(651\) −1.80471e12 2.55789e11i −0.393816 0.0558171i
\(652\) −1.15961e12 6.69500e11i −0.251303 0.145090i
\(653\) −1.57512e12 2.72819e12i −0.339004 0.587173i 0.645241 0.763979i \(-0.276757\pi\)
−0.984246 + 0.176806i \(0.943423\pi\)
\(654\) 1.84249e12 3.19128e12i 0.393826 0.682127i
\(655\) 4.33716e12 2.50406e12i 0.920703 0.531568i
\(656\) 3.09269e12i 0.652032i
\(657\) 1.82201e12 1.05194e12i 0.381511 0.220266i
\(658\) 7.39111e12 + 5.78851e12i 1.53707 + 1.20379i
\(659\) −1.93254e12 3.34725e12i −0.399157 0.691360i 0.594465 0.804121i \(-0.297364\pi\)
−0.993622 + 0.112761i \(0.964030\pi\)
\(660\) −3.19295e12 5.53036e12i −0.655006 1.13450i
\(661\) 1.76284e12i 0.359176i 0.983742 + 0.179588i \(0.0574764\pi\)
−0.983742 + 0.179588i \(0.942524\pi\)
\(662\) 2.58358e12 + 4.47489e12i 0.522831 + 0.905570i
\(663\) −9.07020e11 5.15892e12i −0.182308 1.03693i
\(664\) 1.43268e12 0.286018
\(665\) 7.24225e12 2.91621e12i 1.43607 0.578257i
\(666\) −2.38734e12 + 4.13499e12i −0.470197 + 0.814405i
\(667\) 4.76422e12 0.932020
\(668\) −5.14417e11 + 2.96999e11i −0.0999589 + 0.0577113i
\(669\) −1.07820e13 6.22497e12i −2.08104 1.20149i
\(670\) 2.00673e12i 0.384727i
\(671\) 9.05485e12i 1.72437i
\(672\) 3.06098e12 + 7.60178e12i 0.579027 + 1.43798i
\(673\) 2.34364e12 4.05930e12i 0.440375 0.762752i −0.557342 0.830283i \(-0.688179\pi\)
0.997717 + 0.0675310i \(0.0215121\pi\)
\(674\) 1.35350e12 7.81444e11i 0.252632 0.145857i
\(675\) 1.70418e12 + 2.95172e12i 0.315971 + 0.547278i
\(676\) −1.92774e12 1.62083e12i −0.355050 0.298523i
\(677\) 3.20356e11 5.54873e11i 0.0586117 0.101518i −0.835231 0.549900i \(-0.814666\pi\)
0.893842 + 0.448381i \(0.147999\pi\)
\(678\) −1.76219e12 1.01740e12i −0.320273 0.184910i
\(679\) 2.94819e12 + 4.17859e11i 0.532281 + 0.0754424i
\(680\) 8.95319e11 + 1.55074e12i 0.160579 + 0.278130i
\(681\) −5.45058e12 3.14690e12i −0.971138 0.560687i
\(682\) 2.43245e12 + 1.40437e12i 0.430540 + 0.248572i
\(683\) 5.65717e12 + 3.26617e12i 0.994733 + 0.574309i 0.906686 0.421807i \(-0.138604\pi\)
0.0880470 + 0.996116i \(0.471937\pi\)
\(684\) 9.40245e12 + 5.42851e12i 1.64244 + 0.948261i
\(685\) 3.82191e12 + 6.61974e12i 0.663243 + 1.14877i
\(686\) −7.09072e11 6.98203e12i −0.122245 1.20371i
\(687\) 4.48271e12 + 2.58809e12i 0.767777 + 0.443276i
\(688\) −4.41933e12 + 7.65450e12i −0.751983 + 1.30247i
\(689\) −3.26680e12 1.19085e12i −0.552251 0.201313i
\(690\) 5.15709e12 + 8.93233e12i 0.866131 + 1.50018i
\(691\) 1.00895e13 5.82517e12i 1.68352 0.971979i 0.724226 0.689563i \(-0.242197\pi\)
0.959292 0.282417i \(-0.0911361\pi\)
\(692\) −1.29086e11 + 2.23583e11i −0.0213994 + 0.0370648i
\(693\) 1.55281e13 1.98272e13i 2.55752 3.26559i
\(694\) 1.39545e12i 0.228347i
\(695\) 2.13653e12i 0.347359i
\(696\) −6.18892e12 3.57317e12i −0.999707 0.577181i
\(697\) 1.64984e12 9.52538e11i 0.264786 0.152874i
\(698\) 7.94511e12 1.26692
\(699\) −4.16158e12 + 7.20807e12i −0.659342 + 1.14201i
\(700\) −6.61241e11 5.17865e11i −0.104092 0.0815221i
\(701\) −1.34885e12 −0.210977 −0.105488 0.994421i \(-0.533641\pi\)
−0.105488 + 0.994421i \(0.533641\pi\)
\(702\) −5.91156e12 + 1.62168e13i −0.918724 + 2.52028i
\(703\) 2.06342e12 + 3.57395e12i 0.318632 + 0.551886i
\(704\) 2.48890e12i 0.381883i
\(705\) −8.04599e12 1.39361e13i −1.22667 2.12466i
\(706\) 7.06904e12 + 1.22439e13i 1.07088 + 1.85481i
\(707\) −7.63181e11 5.97701e11i −0.114879 0.0899698i
\(708\) −4.20097e12 + 2.42543e12i −0.628347 + 0.362776i
\(709\) 2.51191e12i 0.373333i 0.982423 + 0.186666i \(0.0597683\pi\)
−0.982423 + 0.186666i \(0.940232\pi\)
\(710\) −1.42787e12 + 8.24383e11i −0.210876 + 0.121749i
\(711\) −9.74597e12 + 1.68805e13i −1.43025 + 2.47727i
\(712\) 2.31326e12 + 4.00669e12i 0.337338 + 0.584286i
\(713\) −1.24494e12 7.18768e11i −0.180404 0.104156i
\(714\) 5.45436e12 6.96445e12i 0.785420 1.00287i
\(715\) −1.90062e12 1.08103e13i −0.271968 1.54689i
\(716\) 7.30209e10 1.26476e11i 0.0103834 0.0179845i
\(717\) 1.39629e13i 1.97305i
\(718\) −3.94256e12 −0.553628
\(719\) −1.34093e13 −1.87123 −0.935616 0.353020i \(-0.885155\pi\)
−0.935616 + 0.353020i \(0.885155\pi\)
\(720\) 1.70019e13i 2.35777i
\(721\) 2.04483e12 8.23383e11i 0.281805 0.113473i
\(722\) 1.79954e13 1.03896e13i 2.46459 1.42293i
\(723\) −5.96466e12 3.44370e12i −0.811827 0.468709i
\(724\) 3.27631e11 5.67474e11i 0.0443161 0.0767578i
\(725\) 2.09857e12 0.282099
\(726\) −3.45555e13 + 1.99506e13i −4.61639 + 2.66528i
\(727\) 5.22725e12 0.694014 0.347007 0.937863i \(-0.387198\pi\)
0.347007 + 0.937863i \(0.387198\pi\)
\(728\) 1.63381e11 + 4.91329e12i 0.0215581 + 0.648307i
\(729\) −5.40636e11 −0.0708975
\(730\) 1.34108e12 7.74275e11i 0.174785 0.100912i
\(731\) 5.44455e12 0.705235
\(732\) −3.00730e12 + 5.20880e12i −0.387148 + 0.670561i
\(733\) −1.10390e13 6.37338e12i −1.41241 0.815458i −0.416799 0.908999i \(-0.636848\pi\)
−0.995615 + 0.0935406i \(0.970182\pi\)
\(734\) 3.97008e12 2.29213e12i 0.504855 0.291478i
\(735\) −3.34281e12 + 1.15556e13i −0.422492 + 1.46050i
\(736\) 6.46304e12i 0.811870i
\(737\) −5.59483e12 −0.698527
\(738\) −1.13689e13 −1.41080
\(739\) 2.07917e12i 0.256443i −0.991746 0.128221i \(-0.959073\pi\)
0.991746 0.128221i \(-0.0409268\pi\)
\(740\) −5.56817e11 + 9.64436e11i −0.0682606 + 0.118231i
\(741\) 1.73564e13 + 2.07054e13i 2.11484 + 2.52291i
\(742\) −2.19338e12 5.44714e12i −0.265641 0.659707i
\(743\) 3.62249e12 + 2.09144e12i 0.436071 + 0.251766i 0.701930 0.712246i \(-0.252322\pi\)
−0.265859 + 0.964012i \(0.585655\pi\)
\(744\) 1.07815e12 + 1.86742e12i 0.129004 + 0.223441i
\(745\) 1.95324e12 3.38312e12i 0.232302 0.402359i
\(746\) 8.04446e12 4.64447e12i 0.950982 0.549050i
\(747\) 8.37945e12i 0.984629i
\(748\) −3.74079e12 + 2.15975e12i −0.436924 + 0.252258i
\(749\) −1.05946e12 + 7.47498e12i −0.123003 + 0.867844i
\(750\) 1.02414e13 + 1.77387e13i 1.18191 + 2.04713i
\(751\) 2.08962e10 + 3.61933e10i 0.00239711 + 0.00415191i 0.867221 0.497923i \(-0.165904\pi\)
−0.864824 + 0.502075i \(0.832570\pi\)
\(752\) 1.76703e13i 2.01495i
\(753\) 4.61192e12 + 7.98807e12i 0.522762 + 0.905450i
\(754\) 6.82728e12 + 8.14464e12i 0.769266 + 0.917700i
\(755\) −7.70771e12 −0.863305
\(756\) −8.56854e12 + 3.45026e12i −0.954022 + 0.384152i
\(757\) 1.10725e11 1.91782e11i 0.0122551 0.0212264i −0.859833 0.510576i \(-0.829432\pi\)
0.872088 + 0.489349i \(0.162766\pi\)
\(758\) −4.58747e12 −0.504733
\(759\) 2.49036e13 1.43781e13i 2.72380 1.57258i
\(760\) −7.99867e12 4.61804e12i −0.869675 0.502107i
\(761\) 7.52491e12i 0.813337i −0.913576 0.406668i \(-0.866690\pi\)
0.913576 0.406668i \(-0.133310\pi\)
\(762\) 3.08521e13i 3.31503i
\(763\) 3.35597e12 + 4.75656e11i 0.358474 + 0.0508080i
\(764\) 4.29553e12 7.44007e12i 0.456138 0.790055i
\(765\) −9.06993e12 + 5.23653e12i −0.957475 + 0.552799i
\(766\) 8.30535e12 + 1.43853e13i 0.871623 + 1.50970i
\(767\) −8.21171e12 + 1.44375e12i −0.856751 + 0.150630i
\(768\) 9.86789e12 1.70917e13i 1.02353 1.77280i
\(769\) −8.44648e12 4.87658e12i −0.870978 0.502859i −0.00330487 0.999995i \(-0.501052\pi\)
−0.867673 + 0.497135i \(0.834385\pi\)
\(770\) 1.14294e13 1.45937e13i 1.17169 1.49609i
\(771\) −1.09935e13 1.90413e13i −1.12045 1.94067i
\(772\) −4.60335e12 2.65775e12i −0.466441 0.269300i
\(773\) 6.30827e12 + 3.64208e12i 0.635481 + 0.366895i 0.782872 0.622183i \(-0.213754\pi\)
−0.147391 + 0.989078i \(0.547087\pi\)
\(774\) −2.81383e13 1.62457e13i −2.81815 1.62706i
\(775\) −5.48378e11 3.16606e11i −0.0546038 0.0315255i
\(776\) −1.76128e12 3.05063e12i −0.174362 0.302003i
\(777\) −6.29565e12 8.92309e11i −0.619650 0.0878255i
\(778\) 1.75286e13 + 1.01201e13i 1.71529 + 0.990324i
\(779\) −4.91317e12 + 8.50986e12i −0.478017 + 0.827949i
\(780\) −2.49699e12 + 6.84986e12i −0.241541 + 0.662607i
\(781\) 2.29840e12 + 3.98095e12i 0.221053 + 0.382875i
\(782\) 6.04192e12 3.48831e12i 0.577756 0.333568i
\(783\) 1.15399e13 1.99878e13i 1.09717 1.90036i
\(784\) −9.52339e12 + 9.15366e12i −0.900263 + 0.865312i
\(785\) 1.20194e12i 0.112972i
\(786\) 2.92687e13i 2.73529i
\(787\) 1.45794e13 + 8.41742e12i 1.35473 + 0.782155i 0.988908 0.148529i \(-0.0474538\pi\)
0.365824 + 0.930684i \(0.380787\pi\)
\(788\) −6.67419e12 + 3.85335e12i −0.616639 + 0.356017i
\(789\) 2.91289e13 2.67595
\(790\) −7.17348e12 + 1.24248e13i −0.655251 + 1.13493i
\(791\) 2.62652e11 1.85313e12i 0.0238554 0.168311i
\(792\) −2.97928e13 −2.69059
\(793\) −7.92260e12 + 6.64116e12i −0.711440 + 0.596368i
\(794\) 2.62251e12 + 4.54232e12i 0.234167 + 0.405588i
\(795\) 1.00654e13i 0.893676i
\(796\) −2.56430e12 4.44149e12i −0.226391 0.392121i
\(797\) −3.01642e12 5.22458e12i −0.264807 0.458658i 0.702706 0.711480i \(-0.251975\pi\)
−0.967513 + 0.252822i \(0.918641\pi\)
\(798\) −6.40306e12 + 4.51765e13i −0.558952 + 3.94366i
\(799\) −9.42650e12 + 5.44239e12i −0.818257 + 0.472421i
\(800\) 2.84687e12i 0.245733i
\(801\) −2.34343e13 + 1.35298e13i −2.01143 + 1.16130i
\(802\) 1.14119e13 1.97660e13i 0.974031 1.68707i
\(803\) −2.15870e12 3.73898e12i −0.183220 0.317346i
\(804\) 3.21842e12 + 1.85816e12i 0.271638 + 0.156830i
\(805\) −5.84963e12 + 7.46915e12i −0.490961 + 0.626888i
\(806\) −5.55279e11 3.15830e12i −0.0463451 0.263600i
\(807\) −7.21499e12 + 1.24967e13i −0.598832 + 1.03721i
\(808\) 1.14677e12i 0.0946512i
\(809\) 1.76807e13 1.45121 0.725606 0.688110i \(-0.241559\pi\)
0.725606 + 0.688110i \(0.241559\pi\)
\(810\) 2.19777e13 1.79391
\(811\) 1.82336e13i 1.48006i 0.672573 + 0.740031i \(0.265189\pi\)
−0.672573 + 0.740031i \(0.734811\pi\)
\(812\) −7.98122e11 + 5.63112e12i −0.0644269 + 0.454562i
\(813\) −3.16501e13 + 1.82732e13i −2.54078 + 1.46692i
\(814\) 8.48548e12 + 4.89910e12i 0.677434 + 0.391116i
\(815\) −3.33114e12 + 5.76971e12i −0.264475 + 0.458084i
\(816\) −1.66503e13 −1.31467
\(817\) −2.43205e13 + 1.40414e13i −1.90973 + 1.10259i
\(818\) 2.77332e11 0.0216576
\(819\) −2.87368e13 + 9.55581e11i −2.23183 + 0.0742147i
\(820\) −2.65165e12 −0.204811
\(821\) 1.43421e13 8.28039e12i 1.10171 0.636073i 0.165040 0.986287i \(-0.447225\pi\)
0.936670 + 0.350214i \(0.113891\pi\)
\(822\) −4.46724e13 −3.41284
\(823\) −6.73526e12 + 1.16658e13i −0.511746 + 0.886371i 0.488161 + 0.872754i \(0.337668\pi\)
−0.999907 + 0.0136171i \(0.995665\pi\)
\(824\) −2.25840e12 1.30389e12i −0.170659 0.0985300i
\(825\) 1.09697e13 6.33334e12i 0.824424 0.475982i
\(826\) −1.10857e13 8.68197e12i −0.828612 0.648945i
\(827\) 1.90251e13i 1.41433i −0.707046 0.707167i \(-0.749973\pi\)
0.707046 0.707167i \(-0.250027\pi\)
\(828\) −1.31930e13 −0.975456
\(829\) −1.12966e12 −0.0830714 −0.0415357 0.999137i \(-0.513225\pi\)
−0.0415357 + 0.999137i \(0.513225\pi\)
\(830\) 6.16765e12i 0.451096i
\(831\) 1.04054e13 1.80227e13i 0.756928 1.31104i
\(832\) 2.17768e12 1.82545e12i 0.157557 0.132073i
\(833\) 7.81634e12 + 2.26111e12i 0.562472 + 0.162712i
\(834\) 1.08136e13 + 6.24322e12i 0.773966 + 0.446850i
\(835\) 1.47774e12 + 2.55952e12i 0.105198 + 0.182209i
\(836\) 1.11399e13 1.92949e13i 0.788777 1.36620i
\(837\) −6.03102e12 + 3.48201e12i −0.424743 + 0.245226i
\(838\) 3.06133e13i 2.14443i
\(839\) −2.97293e12 + 1.71642e12i −0.207136 + 0.119590i −0.599980 0.800015i \(-0.704825\pi\)
0.392844 + 0.919605i \(0.371491\pi\)
\(840\) 1.32008e13 5.31551e12i 0.914836 0.368373i
\(841\) 1.48291e11 + 2.56848e11i 0.0102220 + 0.0177050i
\(842\) 1.07740e12 + 1.86611e12i 0.0738705 + 0.127948i
\(843\) 4.15484e13i 2.83354i
\(844\) −5.23896e12 9.07414e12i −0.355389 0.615551i
\(845\) −8.06455e12 + 9.59162e12i −0.544158 + 0.647197i
\(846\) 6.49569e13 4.35972
\(847\) −2.88951e13 2.26298e13i −1.92907 1.51079i
\(848\) −5.52633e12 + 9.57188e12i −0.366991 + 0.635647i
\(849\) 3.82422e13 2.52615
\(850\) 2.66137e12 1.53655e12i 0.174872 0.100963i
\(851\) −4.34293e12 2.50739e12i −0.283857 0.163885i
\(852\) 3.05339e12i 0.198520i
\(853\) 2.62750e13i 1.69931i −0.527342 0.849653i \(-0.676812\pi\)
0.527342 0.849653i \(-0.323188\pi\)
\(854\) −1.72861e13 2.45003e12i −1.11208 0.157620i
\(855\) 2.70099e13 4.67825e13i 1.72852 2.99389i
\(856\) 7.73471e12 4.46564e12i 0.492393 0.284283i
\(857\) −1.45376e13 2.51799e13i −0.920617 1.59456i −0.798463 0.602044i \(-0.794353\pi\)
−0.122154 0.992511i \(-0.538980\pi\)
\(858\) 6.02677e13 + 2.19695e13i 3.79658 + 1.38397i
\(859\) 6.84063e12 1.18483e13i 0.428674 0.742485i −0.568082 0.822972i \(-0.692314\pi\)
0.996756 + 0.0804875i \(0.0256477\pi\)
\(860\) −6.56292e12 3.78910e12i −0.409123 0.236207i
\(861\) −5.65522e12 1.40444e13i −0.350699 0.870944i
\(862\) 3.54267e12 + 6.13609e12i 0.218549 + 0.378538i
\(863\) 2.20709e13 + 1.27426e13i 1.35448 + 0.782007i 0.988873 0.148764i \(-0.0475295\pi\)
0.365603 + 0.930771i \(0.380863\pi\)
\(864\) 2.71150e13 + 1.56548e13i 1.65538 + 0.955734i
\(865\) 1.11245e12 + 6.42275e11i 0.0675630 + 0.0390075i
\(866\) 4.31521e12 + 2.49139e12i 0.260718 + 0.150526i
\(867\) −9.82941e12 1.70250e13i −0.590801 1.02330i
\(868\) 1.05811e12 1.35106e12i 0.0632694 0.0807861i
\(869\) 3.46408e13 + 1.99999e13i 2.06062 + 1.18970i
\(870\) 1.53824e13 2.66431e13i 0.910306 1.57670i
\(871\) 4.10345e12 + 4.89523e12i 0.241583 + 0.288198i
\(872\) −2.00490e12 3.47258e12i −0.117427 0.203389i
\(873\) 1.78425e13 1.03014e13i 1.03966 0.600247i
\(874\) −1.79926e13 + 3.11641e13i −1.04302 + 1.80656i
\(875\) −1.16168e13 + 1.48330e13i −0.669960 + 0.855444i
\(876\) 2.86780e12i 0.164543i
\(877\) 2.56926e13i 1.46659i −0.679908 0.733297i \(-0.737980\pi\)
0.679908 0.733297i \(-0.262020\pi\)
\(878\) −1.56688e13 9.04637e12i −0.889836 0.513747i
\(879\) 2.42396e13 1.39947e13i 1.36954 0.790705i
\(880\) −3.48899e13 −1.96123
\(881\) −5.10693e12 + 8.84547e12i −0.285607 + 0.494686i −0.972756 0.231831i \(-0.925529\pi\)
0.687149 + 0.726516i \(0.258862\pi\)
\(882\) −3.36493e13 3.50085e13i −1.87227 1.94789i
\(883\) −1.20548e13 −0.667321 −0.333661 0.942693i \(-0.608284\pi\)
−0.333661 + 0.942693i \(0.608284\pi\)
\(884\) 4.63331e12 + 1.68899e12i 0.255186 + 0.0930234i
\(885\) 1.20679e13 + 2.09022e13i 0.661282 + 1.14537i
\(886\) 2.68398e12i 0.146328i
\(887\) 8.54945e12 + 1.48081e13i 0.463748 + 0.803235i 0.999144 0.0413661i \(-0.0131710\pi\)
−0.535396 + 0.844601i \(0.679838\pi\)
\(888\) 3.76109e12 + 6.51441e12i 0.202981 + 0.351574i
\(889\) 2.63244e13 1.05999e13i 1.41351 0.569174i
\(890\) −1.72487e13 + 9.95853e12i −0.921512 + 0.532035i
\(891\) 6.12746e13i 3.25710i
\(892\) 1.01511e13 5.86073e12i 0.536872 0.309963i
\(893\) 2.80717e13 4.86217e13i 1.47719 2.55858i
\(894\) 1.14152e13 + 1.97718e13i 0.597677 + 1.03521i
\(895\) −6.29290e11 3.63320e11i −0.0327829 0.0189272i
\(896\) 2.12195e13 + 3.00753e12i 1.09989 + 0.155892i
\(897\) −3.08454e13 1.12441e13i −1.59083 0.579910i
\(898\) −7.99119e12 + 1.38411e13i −0.410079 + 0.710278i
\(899\) 4.28784e12i 0.218937i
\(900\) −5.81133e12 −0.295246
\(901\) 6.80836e12 0.344176
\(902\) 2.33303e13i 1.17352i
\(903\) 6.07210e12 4.28415e13i 0.303909 2.14422i
\(904\) −1.91752e12 + 1.10708e12i −0.0954955 + 0.0551343i
\(905\) −2.82351e12 1.63015e12i −0.139917 0.0807811i
\(906\) 2.25229e13 3.90108e13i 1.11057 1.92357i
\(907\) −1.51424e13 −0.742953 −0.371476 0.928442i \(-0.621148\pi\)
−0.371476 + 0.928442i \(0.621148\pi\)
\(908\) 5.13166e12 2.96276e12i 0.250537 0.144647i
\(909\) −6.70723e12 −0.325841
\(910\) −2.11516e13 + 7.03351e11i −1.02248 + 0.0340005i
\(911\) 2.61869e13 1.25965 0.629827 0.776735i \(-0.283126\pi\)
0.629827 + 0.776735i \(0.283126\pi\)
\(912\) 7.43757e13 4.29408e13i 3.56004 2.05539i
\(913\) 1.71956e13 0.819029
\(914\) −6.71531e12 + 1.16313e13i −0.318279 + 0.551276i
\(915\) 2.59168e13 + 1.49630e13i 1.22232 + 0.705708i
\(916\) −4.22041e12 + 2.43666e12i −0.198073 + 0.114357i
\(917\) −2.49734e13 + 1.00559e13i −1.16631 + 0.469635i
\(918\) 3.37976e13i 1.57070i
\(919\) −2.85097e13 −1.31848 −0.659239 0.751934i \(-0.729121\pi\)
−0.659239 + 0.751934i \(0.729121\pi\)
\(920\) 1.12233e13 0.516507
\(921\) 1.85208e13i 0.848187i
\(922\) 1.12119e13 1.94197e13i 0.510966 0.885019i
\(923\) 1.79743e12 4.93078e12i 0.0815161 0.223618i
\(924\) 1.28224e13 + 3.18438e13i 0.578690 + 1.43715i
\(925\) −1.91299e12 1.10447e12i −0.0859163 0.0496038i
\(926\) 4.09904e12 + 7.09975e12i 0.183203 + 0.317317i
\(927\) 7.62618e12 1.32089e13i 0.339194 0.587501i
\(928\) 1.66950e13 9.63888e12i 0.738961 0.426639i
\(929\) 3.21436e13i 1.41587i 0.706278 + 0.707935i \(0.250373\pi\)
−0.706278 + 0.707935i \(0.749627\pi\)
\(930\) −8.03918e12 + 4.64142e12i −0.352402 + 0.203459i
\(931\) −4.07465e13 + 1.00580e13i −1.77753 + 0.438772i
\(932\) −3.91807e12 6.78630e12i −0.170099 0.294620i
\(933\) −3.62174e12 6.27304e12i −0.156477 0.271026i
\(934\) 3.30303e13i 1.42021i
\(935\) 1.07460e13 + 1.86126e13i 0.459826 + 0.796442i
\(936\) 2.18511e13 + 2.60674e13i 0.930533 + 1.11008i
\(937\) −4.87350e12 −0.206544 −0.103272 0.994653i \(-0.532931\pi\)
−0.103272 + 0.994653i \(0.532931\pi\)
\(938\) −1.51383e12 + 1.06807e13i −0.0638504 + 0.450494i
\(939\) −1.44441e12 + 2.50179e12i −0.0606310 + 0.105016i
\(940\) 1.51504e13 0.632920
\(941\) −2.39608e13 + 1.38338e13i −0.996204 + 0.575158i −0.907123 0.420866i \(-0.861726\pi\)
−0.0890808 + 0.996024i \(0.528393\pi\)
\(942\) 6.08337e12 + 3.51223e12i 0.251718 + 0.145330i
\(943\) 1.19406e13i 0.491726i
\(944\) 2.65030e13i 1.08623i
\(945\) 1.71670e13 + 4.26333e13i 0.700247 + 1.73903i
\(946\) −3.33380e13 + 5.77431e13i −1.35341 + 2.34418i
\(947\) −4.59802e12 + 2.65467e12i −0.185779 + 0.107259i −0.590005 0.807400i \(-0.700874\pi\)
0.404226 + 0.914659i \(0.367541\pi\)
\(948\) −1.32847e13 2.30098e13i −0.534214 0.925286i
\(949\) −1.68817e12 + 4.63107e12i −0.0675646 + 0.185346i
\(950\) −7.92547e12 + 1.37273e13i −0.315696 + 0.546801i
\(951\) 2.88147e13 + 1.66362e13i 1.14236 + 0.659540i
\(952\) −3.59546e12 8.92915e12i −0.141869 0.352325i
\(953\) −1.43822e13 2.49107e13i −0.564815 0.978289i −0.997067 0.0765357i \(-0.975614\pi\)
0.432252 0.901753i \(-0.357719\pi\)
\(954\) −3.51867e13 2.03151e13i −1.37534 0.794055i
\(955\) −3.70186e13 2.13727e13i −1.44014 0.831465i
\(956\) 1.13847e13 + 6.57294e12i 0.440818 + 0.254506i
\(957\) −7.42818e13 4.28866e13i −2.86272 1.65279i
\(958\) 1.04643e13 + 1.81246e13i 0.401388 + 0.695224i
\(959\) −1.53482e13 3.81165e13i −0.585968 1.45522i
\(960\) −7.12372e12 4.11288e12i −0.270699 0.156288i
\(961\) −1.25729e13 + 2.17769e13i −0.475533 + 0.823647i
\(962\) −1.93707e12 1.10176e13i −0.0729217 0.414762i
\(963\) 2.61186e13 + 4.52387e13i 0.978658 + 1.69508i
\(964\) 5.61565e12 3.24220e12i 0.209437 0.120919i
\(965\) −1.32238e13 + 2.29043e13i −0.490889 + 0.850245i
\(966\) −2.07101e13 5.14324e13i −0.765217 1.90038i
\(967\) 1.06351e13i 0.391130i −0.980691 0.195565i \(-0.937346\pi\)
0.980691 0.195565i \(-0.0626540\pi\)
\(968\) 4.34184e13i 1.58941i
\(969\) −4.58149e13 2.64513e13i −1.66936 0.963806i
\(970\) 1.31329e13 7.58226e12i 0.476307 0.274996i
\(971\) 1.68726e12 0.0609110 0.0304555 0.999536i \(-0.490304\pi\)
0.0304555 + 0.999536i \(0.490304\pi\)
\(972\) −6.04002e12 + 1.04616e13i −0.217040 + 0.375925i
\(973\) −1.61175e12 + 1.13716e13i −0.0576486 + 0.406738i
\(974\) −2.55639e13 −0.910149
\(975\) −1.35869e13 4.95287e12i −0.481505 0.175524i
\(976\) 1.64306e13 + 2.84587e13i 0.579602 + 1.00390i
\(977\) 1.69087e12i 0.0593725i −0.999559 0.0296862i \(-0.990549\pi\)
0.999559 0.0296862i \(-0.00945081\pi\)
\(978\) −1.94681e13 3.37197e13i −0.680452 1.17858i
\(979\) 2.77647e13 + 4.80899e13i 0.965986 + 1.67314i
\(980\) −7.84830e12 8.16530e12i −0.271805 0.282784i
\(981\) 2.03104e13 1.17262e13i 0.700176 0.404247i
\(982\) 2.42545e13i 0.832320i
\(983\) 4.01134e13 2.31595e13i 1.37025 0.791112i 0.379288 0.925279i \(-0.376169\pi\)
0.990959 + 0.134167i \(0.0428358\pi\)
\(984\) −8.95546e12 + 1.55113e13i −0.304516 + 0.527437i
\(985\) 1.91726e13 + 3.32079e13i 0.648960 + 1.12403i
\(986\) −1.80217e13 1.04048e13i −0.607224 0.350581i
\(987\) 3.23115e13 + 8.02439e13i 1.08375 + 2.69144i
\(988\) −2.50526e13 + 4.40464e12i −0.836464 + 0.147063i
\(989\) 1.70626e13 2.95533e13i 0.567104 0.982252i
\(990\) 1.28257e14i 4.24349i
\(991\) −4.08335e13 −1.34489 −0.672443 0.740149i \(-0.734755\pi\)
−0.672443 + 0.740149i \(0.734755\pi\)
\(992\) −5.81680e12 −0.190713
\(993\) 4.76122e13i 1.55398i
\(994\) 8.22169e12 3.31059e12i 0.267130 0.107564i
\(995\) −2.20990e13 + 1.27588e13i −0.714773 + 0.412674i
\(996\) −9.89177e12 5.71102e12i −0.318498 0.183885i
\(997\) −2.57110e13 + 4.45327e13i −0.824120 + 1.42742i 0.0784698 + 0.996916i \(0.474997\pi\)
−0.902590 + 0.430501i \(0.858337\pi\)
\(998\) −3.87646e13 −1.23694
\(999\) −2.10390e13 + 1.21468e13i −0.668313 + 0.385850i
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 91.10.u.a.30.19 yes 164
7.4 even 3 91.10.k.a.4.19 164
13.10 even 6 91.10.k.a.23.64 yes 164
91.88 even 6 inner 91.10.u.a.88.19 yes 164
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.10.k.a.4.19 164 7.4 even 3
91.10.k.a.23.64 yes 164 13.10 even 6
91.10.u.a.30.19 yes 164 1.1 even 1 trivial
91.10.u.a.88.19 yes 164 91.88 even 6 inner