Properties

Label 84.12.b.a.55.12
Level $84$
Weight $12$
Character 84.55
Analytic conductor $64.541$
Analytic rank $0$
Dimension $44$
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] = [84,12,Mod(55,84)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(84, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.55");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 84.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(64.5408271670\)
Analytic rank: \(0\)
Dimension: \(44\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.12
Character \(\chi\) \(=\) 84.55
Dual form 84.12.b.a.55.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-32.5648 + 31.4250i) q^{2} -243.000 q^{3} +(72.9330 - 2046.70i) q^{4} +4483.20i q^{5} +(7913.25 - 7636.29i) q^{6} +(44244.4 - 4445.20i) q^{7} +(61942.6 + 68942.3i) q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+(-32.5648 + 31.4250i) q^{2} -243.000 q^{3} +(72.9330 - 2046.70i) q^{4} +4483.20i q^{5} +(7913.25 - 7636.29i) q^{6} +(44244.4 - 4445.20i) q^{7} +(61942.6 + 68942.3i) q^{8} +59049.0 q^{9} +(-140885. - 145994. i) q^{10} +407222. i q^{11} +(-17722.7 + 497348. i) q^{12} +1.73481e6i q^{13} +(-1.30112e6 + 1.53514e6i) q^{14} -1.08942e6i q^{15} +(-4.18367e6 - 298544. i) q^{16} -5.93548e6i q^{17} +(-1.92292e6 + 1.85562e6i) q^{18} +1.52535e7 q^{19} +(9.17576e6 + 326973. i) q^{20} +(-1.07514e7 + 1.08018e6i) q^{21} +(-1.27970e7 - 1.32611e7i) q^{22} -2.31359e6i q^{23} +(-1.50521e7 - 1.67530e7i) q^{24} +2.87291e7 q^{25} +(-5.45165e7 - 5.64937e7i) q^{26} -1.43489e7 q^{27} +(-5.87113e6 - 9.08793e7i) q^{28} -1.10429e8 q^{29} +(3.42350e7 + 3.54767e7i) q^{30} +9.60969e7 q^{31} +(1.45622e8 - 1.21750e8i) q^{32} -9.89550e7i q^{33} +(1.86523e8 + 1.93288e8i) q^{34} +(1.99287e7 + 1.98356e8i) q^{35} +(4.30662e6 - 1.20856e8i) q^{36} +6.26376e8 q^{37} +(-4.96729e8 + 4.79343e8i) q^{38} -4.21559e8i q^{39} +(-3.09082e8 + 2.77701e8i) q^{40} -9.25635e8i q^{41} +(3.16172e8 - 3.73039e8i) q^{42} -1.26922e9i q^{43} +(8.33462e8 + 2.96999e7i) q^{44} +2.64728e8i q^{45} +(7.27046e7 + 7.53415e7i) q^{46} -3.43921e8 q^{47} +(1.01663e9 + 7.25462e7i) q^{48} +(1.93781e9 - 3.93351e8i) q^{49} +(-9.35556e8 + 9.02812e8i) q^{50} +1.44232e9i q^{51} +(3.55064e9 + 1.26525e8i) q^{52} +3.23392e9 q^{53} +(4.67269e8 - 4.50915e8i) q^{54} -1.82566e9 q^{55} +(3.04708e9 + 2.77496e9i) q^{56} -3.70661e9 q^{57} +(3.59609e9 - 3.47023e9i) q^{58} -4.88844e9 q^{59} +(-2.22971e9 - 7.94545e7i) q^{60} +1.28488e9i q^{61} +(-3.12938e9 + 3.01985e9i) q^{62} +(2.61259e9 - 2.62485e8i) q^{63} +(-9.16158e8 + 8.54094e9i) q^{64} -7.77750e9 q^{65} +(3.10966e9 + 3.22245e9i) q^{66} +1.47138e10i q^{67} +(-1.21482e10 - 4.32893e8i) q^{68} +5.62202e8i q^{69} +(-6.88233e9 - 5.83318e9i) q^{70} -6.23819e9i q^{71} +(3.65765e9 + 4.07098e9i) q^{72} -7.64640e9i q^{73} +(-2.03978e10 + 1.96839e10i) q^{74} -6.98116e9 q^{75} +(1.11249e9 - 3.12194e10i) q^{76} +(1.81019e9 + 1.80173e10i) q^{77} +(1.32475e10 + 1.37280e10i) q^{78} +5.20281e10i q^{79} +(1.33843e9 - 1.87562e10i) q^{80} +3.48678e9 q^{81} +(2.90881e10 + 3.01431e10i) q^{82} -3.89227e10 q^{83} +(1.42668e9 + 2.20837e10i) q^{84} +2.66099e10 q^{85} +(3.98852e10 + 4.13318e10i) q^{86} +2.68342e10 q^{87} +(-2.80748e10 + 2.52244e10i) q^{88} -6.32910e10i q^{89} +(-8.31910e9 - 8.62083e9i) q^{90} +(7.71158e9 + 7.67556e10i) q^{91} +(-4.73522e9 - 1.68737e8i) q^{92} -2.33516e10 q^{93} +(1.11997e10 - 1.08077e10i) q^{94} +6.83846e10i q^{95} +(-3.53861e10 + 2.95852e10i) q^{96} -5.71799e10i q^{97} +(-5.07432e10 + 7.37051e10i) q^{98} +2.40461e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9} - 828424 q^{10} - 374463 q^{12} + 4198365 q^{14} - 4412759 q^{16} - 1358127 q^{18} + 6983052 q^{19} - 44417108 q^{20} + 32562 q^{21} - 17991462 q^{22} + 4542885 q^{24} - 453628696 q^{25} - 98243700 q^{26} - 631351908 q^{27} + 197028053 q^{28} - 77673208 q^{29} + 201307032 q^{30} + 363408768 q^{31} - 193132863 q^{32} + 244149820 q^{34} - 387281676 q^{35} + 90994509 q^{36} + 341371884 q^{37} - 414182420 q^{38} - 770410876 q^{40} - 1020202695 q^{42} - 880133666 q^{44} - 1775052978 q^{46} - 1792699304 q^{47} + 1072300437 q^{48} - 819617000 q^{49} + 2158233149 q^{50} - 4514138716 q^{52} + 1914807152 q^{53} + 330024861 q^{54} + 1785927092 q^{55} - 16112780167 q^{56} - 1696881636 q^{57} + 5084833750 q^{58} + 3729062416 q^{59} + 10793357244 q^{60} - 18353275776 q^{62} - 7912566 q^{63} - 12067108399 q^{64} - 5624825000 q^{65} + 4371925266 q^{66} + 885261520 q^{68} + 34763977928 q^{70} - 1103921055 q^{72} - 40922634778 q^{74} + 110231773128 q^{75} + 82420472236 q^{76} - 2093349112 q^{77} + 23873219100 q^{78} - 62176412340 q^{80} + 153418513644 q^{81} - 5083269068 q^{82} + 34205636344 q^{83} - 47877816879 q^{84} + 105152127628 q^{85} + 242964863598 q^{86} + 18874589544 q^{87} + 218894674838 q^{88} - 48917608776 q^{90} - 6678724880 q^{91} + 101339859530 q^{92} - 88308330624 q^{93} + 220283048096 q^{94} + 46931285709 q^{96} + 222198095305 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −32.5648 + 31.4250i −0.719587 + 0.694402i
\(3\) −243.000 −0.577350
\(4\) 72.9330 2046.70i 0.0356118 0.999366i
\(5\) 4483.20i 0.641583i 0.947150 + 0.320792i \(0.103949\pi\)
−0.947150 + 0.320792i \(0.896051\pi\)
\(6\) 7913.25 7636.29i 0.415454 0.400913i
\(7\) 44244.4 4445.20i 0.994991 0.0999660i
\(8\) 61942.6 + 68942.3i 0.668336 + 0.743860i
\(9\) 59049.0 0.333333
\(10\) −140885. 145994.i −0.445516 0.461675i
\(11\) 407222.i 0.762380i 0.924497 + 0.381190i \(0.124486\pi\)
−0.924497 + 0.381190i \(0.875514\pi\)
\(12\) −17722.7 + 497348.i −0.0205605 + 0.576984i
\(13\) 1.73481e6i 1.29588i 0.761693 + 0.647938i \(0.224368\pi\)
−0.761693 + 0.647938i \(0.775632\pi\)
\(14\) −1.30112e6 + 1.53514e6i −0.646566 + 0.762858i
\(15\) 1.08942e6i 0.370418i
\(16\) −4.18367e6 298544.i −0.997464 0.0711785i
\(17\) 5.93548e6i 1.01388i −0.861981 0.506940i \(-0.830776\pi\)
0.861981 0.506940i \(-0.169224\pi\)
\(18\) −1.92292e6 + 1.85562e6i −0.239862 + 0.231467i
\(19\) 1.52535e7 1.41327 0.706636 0.707577i \(-0.250212\pi\)
0.706636 + 0.707577i \(0.250212\pi\)
\(20\) 9.17576e6 + 326973.i 0.641176 + 0.0228479i
\(21\) −1.07514e7 + 1.08018e6i −0.574458 + 0.0577154i
\(22\) −1.27970e7 1.32611e7i −0.529398 0.548599i
\(23\) 2.31359e6i 0.0749519i −0.999298 0.0374760i \(-0.988068\pi\)
0.999298 0.0374760i \(-0.0119318\pi\)
\(24\) −1.50521e7 1.67530e7i −0.385864 0.429468i
\(25\) 2.87291e7 0.588371
\(26\) −5.45165e7 5.64937e7i −0.899859 0.932496i
\(27\) −1.43489e7 −0.192450
\(28\) −5.87113e6 9.08793e7i −0.0644692 0.997920i
\(29\) −1.10429e8 −0.999753 −0.499877 0.866097i \(-0.666621\pi\)
−0.499877 + 0.866097i \(0.666621\pi\)
\(30\) 3.42350e7 + 3.54767e7i 0.257219 + 0.266548i
\(31\) 9.60969e7 0.602865 0.301433 0.953487i \(-0.402535\pi\)
0.301433 + 0.953487i \(0.402535\pi\)
\(32\) 1.45622e8 1.21750e8i 0.767189 0.641422i
\(33\) 9.89550e7i 0.440160i
\(34\) 1.86523e8 + 1.93288e8i 0.704041 + 0.729576i
\(35\) 1.99287e7 + 1.98356e8i 0.0641365 + 0.638369i
\(36\) 4.30662e6 1.20856e8i 0.0118706 0.333122i
\(37\) 6.26376e8 1.48500 0.742499 0.669848i \(-0.233641\pi\)
0.742499 + 0.669848i \(0.233641\pi\)
\(38\) −4.96729e8 + 4.79343e8i −1.01697 + 0.981379i
\(39\) 4.21559e8i 0.748174i
\(40\) −3.09082e8 + 2.77701e8i −0.477248 + 0.428793i
\(41\) 9.25635e8i 1.24775i −0.781523 0.623876i \(-0.785557\pi\)
0.781523 0.623876i \(-0.214443\pi\)
\(42\) 3.16172e8 3.73039e8i 0.373295 0.440436i
\(43\) 1.26922e9i 1.31662i −0.752748 0.658309i \(-0.771272\pi\)
0.752748 0.658309i \(-0.228728\pi\)
\(44\) 8.33462e8 + 2.96999e7i 0.761897 + 0.0271497i
\(45\) 2.64728e8i 0.213861i
\(46\) 7.27046e7 + 7.53415e7i 0.0520468 + 0.0539345i
\(47\) −3.43921e8 −0.218736 −0.109368 0.994001i \(-0.534883\pi\)
−0.109368 + 0.994001i \(0.534883\pi\)
\(48\) 1.01663e9 + 7.25462e7i 0.575886 + 0.0410949i
\(49\) 1.93781e9 3.93351e8i 0.980014 0.198931i
\(50\) −9.35556e8 + 9.02812e8i −0.423384 + 0.408566i
\(51\) 1.44232e9i 0.585364i
\(52\) 3.55064e9 + 1.26525e8i 1.29505 + 0.0461485i
\(53\) 3.23392e9 1.06222 0.531108 0.847304i \(-0.321776\pi\)
0.531108 + 0.847304i \(0.321776\pi\)
\(54\) 4.67269e8 4.50915e8i 0.138485 0.133638i
\(55\) −1.82566e9 −0.489130
\(56\) 3.04708e9 + 2.77496e9i 0.739349 + 0.673323i
\(57\) −3.70661e9 −0.815953
\(58\) 3.59609e9 3.47023e9i 0.719410 0.694231i
\(59\) −4.88844e9 −0.890194 −0.445097 0.895482i \(-0.646831\pi\)
−0.445097 + 0.895482i \(0.646831\pi\)
\(60\) −2.22971e9 7.94545e7i −0.370183 0.0131913i
\(61\) 1.28488e9i 0.194781i 0.995246 + 0.0973906i \(0.0310496\pi\)
−0.995246 + 0.0973906i \(0.968950\pi\)
\(62\) −3.12938e9 + 3.01985e9i −0.433814 + 0.418631i
\(63\) 2.61259e9 2.62485e8i 0.331664 0.0333220i
\(64\) −9.16158e8 + 8.54094e9i −0.106655 + 0.994296i
\(65\) −7.77750e9 −0.831412
\(66\) 3.10966e9 + 3.22245e9i 0.305648 + 0.316734i
\(67\) 1.47138e10i 1.33141i 0.746214 + 0.665706i \(0.231870\pi\)
−0.746214 + 0.665706i \(0.768130\pi\)
\(68\) −1.21482e10 4.32893e8i −1.01324 0.0361061i
\(69\) 5.62202e8i 0.0432735i
\(70\) −6.88233e9 5.83318e9i −0.489437 0.414826i
\(71\) 6.23819e9i 0.410334i −0.978727 0.205167i \(-0.934226\pi\)
0.978727 0.205167i \(-0.0657738\pi\)
\(72\) 3.65765e9 + 4.07098e9i 0.222779 + 0.247953i
\(73\) 7.64640e9i 0.431699i −0.976427 0.215850i \(-0.930748\pi\)
0.976427 0.215850i \(-0.0692521\pi\)
\(74\) −2.03978e10 + 1.96839e10i −1.06859 + 1.03118i
\(75\) −6.98116e9 −0.339696
\(76\) 1.11249e9 3.12194e10i 0.0503292 1.41238i
\(77\) 1.81019e9 + 1.80173e10i 0.0762121 + 0.758561i
\(78\) 1.32475e10 + 1.37280e10i 0.519534 + 0.538377i
\(79\) 5.20281e10i 1.90234i 0.308661 + 0.951172i \(0.400119\pi\)
−0.308661 + 0.951172i \(0.599881\pi\)
\(80\) 1.33843e9 1.87562e10i 0.0456669 0.639956i
\(81\) 3.48678e9 0.111111
\(82\) 2.90881e10 + 3.01431e10i 0.866442 + 0.897867i
\(83\) −3.89227e10 −1.08461 −0.542304 0.840182i \(-0.682448\pi\)
−0.542304 + 0.840182i \(0.682448\pi\)
\(84\) 1.42668e9 + 2.20837e10i 0.0372213 + 0.576149i
\(85\) 2.66099e10 0.650489
\(86\) 3.98852e10 + 4.13318e10i 0.914262 + 0.947421i
\(87\) 2.68342e10 0.577208
\(88\) −2.80748e10 + 2.52244e10i −0.567104 + 0.509526i
\(89\) 6.32910e10i 1.20143i −0.799465 0.600713i \(-0.794883\pi\)
0.799465 0.600713i \(-0.205117\pi\)
\(90\) −8.31910e9 8.62083e9i −0.148505 0.153892i
\(91\) 7.71158e9 + 7.67556e10i 0.129544 + 1.28938i
\(92\) −4.73522e9 1.68737e8i −0.0749044 0.00266917i
\(93\) −2.33516e10 −0.348064
\(94\) 1.11997e10 1.08077e10i 0.157400 0.151891i
\(95\) 6.83846e10i 0.906731i
\(96\) −3.53861e10 + 2.95852e10i −0.442937 + 0.370325i
\(97\) 5.71799e10i 0.676081i −0.941132 0.338040i \(-0.890236\pi\)
0.941132 0.338040i \(-0.109764\pi\)
\(98\) −5.07432e10 + 7.37051e10i −0.567068 + 0.823671i
\(99\) 2.40461e10i 0.254127i
\(100\) 2.09530e9 5.87998e10i 0.0209530 0.587998i
\(101\) 1.30879e11i 1.23909i 0.784962 + 0.619544i \(0.212682\pi\)
−0.784962 + 0.619544i \(0.787318\pi\)
\(102\) −4.53250e10 4.69689e10i −0.406478 0.421221i
\(103\) 1.08228e11 0.919884 0.459942 0.887949i \(-0.347870\pi\)
0.459942 + 0.887949i \(0.347870\pi\)
\(104\) −1.19602e11 + 1.07459e11i −0.963950 + 0.866080i
\(105\) −4.84268e9 4.82006e10i −0.0370292 0.368563i
\(106\) −1.05312e11 + 1.01626e11i −0.764357 + 0.737604i
\(107\) 2.22083e11i 1.53075i 0.643584 + 0.765376i \(0.277447\pi\)
−0.643584 + 0.765376i \(0.722553\pi\)
\(108\) −1.04651e9 + 2.93679e10i −0.00685350 + 0.192328i
\(109\) −1.37011e11 −0.852923 −0.426461 0.904506i \(-0.640240\pi\)
−0.426461 + 0.904506i \(0.640240\pi\)
\(110\) 5.94522e10 5.73714e10i 0.351972 0.339653i
\(111\) −1.52209e11 −0.857363
\(112\) −1.86431e11 + 5.38834e9i −0.999583 + 0.0288906i
\(113\) 2.93672e11 1.49945 0.749723 0.661752i \(-0.230187\pi\)
0.749723 + 0.661752i \(0.230187\pi\)
\(114\) 1.20705e11 1.16480e11i 0.587149 0.566599i
\(115\) 1.03723e10 0.0480879
\(116\) −8.05389e9 + 2.26014e11i −0.0356030 + 0.999119i
\(117\) 1.02439e11i 0.431959i
\(118\) 1.59191e11 1.53620e11i 0.640572 0.618152i
\(119\) −2.63844e10 2.62612e11i −0.101354 1.00880i
\(120\) 7.51070e10 6.74813e10i 0.275539 0.247564i
\(121\) 1.19482e11 0.418777
\(122\) −4.03773e10 4.18417e10i −0.135256 0.140162i
\(123\) 2.24929e11i 0.720390i
\(124\) 7.00864e9 1.96682e11i 0.0214691 0.602483i
\(125\) 3.47704e11i 1.01907i
\(126\) −7.68298e10 + 9.06485e10i −0.215522 + 0.254286i
\(127\) 1.57348e11i 0.422612i 0.977420 + 0.211306i \(0.0677716\pi\)
−0.977420 + 0.211306i \(0.932228\pi\)
\(128\) −2.38565e11 3.06924e11i −0.613694 0.789544i
\(129\) 3.08420e11i 0.760150i
\(130\) 2.53273e11 2.44408e11i 0.598274 0.577334i
\(131\) 7.46145e11 1.68978 0.844892 0.534938i \(-0.179665\pi\)
0.844892 + 0.534938i \(0.179665\pi\)
\(132\) −2.02531e11 7.21708e9i −0.439881 0.0156749i
\(133\) 6.74884e11 6.78051e10i 1.40619 0.141279i
\(134\) −4.62381e11 4.79151e11i −0.924535 0.958067i
\(135\) 6.43290e10i 0.123473i
\(136\) 4.09206e11 3.67659e11i 0.754185 0.677613i
\(137\) −6.37133e10 −0.112789 −0.0563946 0.998409i \(-0.517960\pi\)
−0.0563946 + 0.998409i \(0.517960\pi\)
\(138\) −1.76672e10 1.83080e10i −0.0300492 0.0311391i
\(139\) 6.10597e10 0.0998099 0.0499049 0.998754i \(-0.484108\pi\)
0.0499049 + 0.998754i \(0.484108\pi\)
\(140\) 4.07430e11 2.63214e10i 0.640248 0.0413623i
\(141\) 8.35728e10 0.126287
\(142\) 1.96035e11 + 2.03145e11i 0.284937 + 0.295271i
\(143\) −7.06453e11 −0.987950
\(144\) −2.47041e11 1.76287e10i −0.332488 0.0237262i
\(145\) 4.95074e11i 0.641425i
\(146\) 2.40289e11 + 2.49004e11i 0.299773 + 0.310645i
\(147\) −4.70887e11 + 9.55842e10i −0.565811 + 0.114853i
\(148\) 4.56835e10 1.28200e12i 0.0528834 1.48406i
\(149\) 1.20132e12 1.34009 0.670045 0.742321i \(-0.266275\pi\)
0.670045 + 0.742321i \(0.266275\pi\)
\(150\) 2.27340e11 2.19383e11i 0.244441 0.235886i
\(151\) 1.22900e11i 0.127403i 0.997969 + 0.0637015i \(0.0202906\pi\)
−0.997969 + 0.0637015i \(0.979709\pi\)
\(152\) 9.44844e11 + 1.05161e12i 0.944540 + 1.05128i
\(153\) 3.50484e11i 0.337960i
\(154\) −6.25143e11 5.29845e11i −0.581588 0.492929i
\(155\) 4.30822e11i 0.386788i
\(156\) −8.62805e11 3.07455e10i −0.747700 0.0266438i
\(157\) 9.32421e11i 0.780124i −0.920789 0.390062i \(-0.872454\pi\)
0.920789 0.390062i \(-0.127546\pi\)
\(158\) −1.63499e12 1.69429e12i −1.32099 1.36890i
\(159\) −7.85844e11 −0.613270
\(160\) 5.45829e11 + 6.52852e11i 0.411525 + 0.492215i
\(161\) −1.02844e10 1.02363e11i −0.00749265 0.0745765i
\(162\) −1.13546e11 + 1.09572e11i −0.0799541 + 0.0771558i
\(163\) 3.01539e11i 0.205263i 0.994719 + 0.102632i \(0.0327263\pi\)
−0.994719 + 0.102632i \(0.967274\pi\)
\(164\) −1.89450e12 6.75093e10i −1.24696 0.0444347i
\(165\) 4.43635e11 0.282399
\(166\) 1.26751e12 1.22315e12i 0.780471 0.753154i
\(167\) −1.81605e12 −1.08190 −0.540951 0.841054i \(-0.681935\pi\)
−0.540951 + 0.841054i \(0.681935\pi\)
\(168\) −7.40440e11 6.74316e11i −0.426863 0.388743i
\(169\) −1.21740e12 −0.679294
\(170\) −8.66547e11 + 8.36219e11i −0.468083 + 0.451701i
\(171\) 9.00706e11 0.471091
\(172\) −2.59771e12 9.25679e10i −1.31578 0.0468872i
\(173\) 7.08521e11i 0.347616i 0.984780 + 0.173808i \(0.0556072\pi\)
−0.984780 + 0.173808i \(0.944393\pi\)
\(174\) −8.73849e11 + 8.43265e11i −0.415351 + 0.400814i
\(175\) 1.27110e12 1.27707e11i 0.585424 0.0588171i
\(176\) 1.21574e11 1.70368e12i 0.0542650 0.760446i
\(177\) 1.18789e12 0.513954
\(178\) 1.98892e12 + 2.06106e12i 0.834273 + 0.864531i
\(179\) 6.20432e11i 0.252350i 0.992008 + 0.126175i \(0.0402700\pi\)
−0.992008 + 0.126175i \(0.959730\pi\)
\(180\) 5.41820e11 + 1.93074e10i 0.213725 + 0.00761598i
\(181\) 1.37684e12i 0.526806i −0.964686 0.263403i \(-0.915155\pi\)
0.964686 0.263403i \(-0.0848449\pi\)
\(182\) −2.66318e12 2.25719e12i −0.988569 0.837870i
\(183\) 3.12225e11i 0.112457i
\(184\) 1.59504e11 1.43310e11i 0.0557537 0.0500931i
\(185\) 2.80817e12i 0.952749i
\(186\) 7.60439e11 7.33824e11i 0.250463 0.241697i
\(187\) 2.41706e12 0.772963
\(188\) −2.50832e10 + 7.03903e11i −0.00778959 + 0.218597i
\(189\) −6.34859e11 + 6.37838e10i −0.191486 + 0.0192385i
\(190\) −2.14899e12 2.22693e12i −0.629636 0.652472i
\(191\) 3.17158e12i 0.902801i 0.892321 + 0.451400i \(0.149075\pi\)
−0.892321 + 0.451400i \(0.850925\pi\)
\(192\) 2.22626e11 2.07545e12i 0.0615772 0.574057i
\(193\) 6.82500e12 1.83458 0.917291 0.398217i \(-0.130371\pi\)
0.917291 + 0.398217i \(0.130371\pi\)
\(194\) 1.79688e12 + 1.86205e12i 0.469472 + 0.486499i
\(195\) 1.88993e12 0.480016
\(196\) −6.63741e11 3.99480e12i −0.163904 0.986476i
\(197\) 7.97874e11 0.191589 0.0957944 0.995401i \(-0.469461\pi\)
0.0957944 + 0.995401i \(0.469461\pi\)
\(198\) −7.55648e11 7.83055e11i −0.176466 0.182866i
\(199\) 1.81743e11 0.0412826 0.0206413 0.999787i \(-0.493429\pi\)
0.0206413 + 0.999787i \(0.493429\pi\)
\(200\) 1.77955e12 + 1.98065e12i 0.393230 + 0.437666i
\(201\) 3.57545e12i 0.768691i
\(202\) −4.11287e12 4.26204e12i −0.860425 0.891631i
\(203\) −4.88585e12 + 4.90878e11i −0.994745 + 0.0999414i
\(204\) 2.95200e12 + 1.05193e11i 0.584993 + 0.0208459i
\(205\) 4.14980e12 0.800537
\(206\) −3.52441e12 + 3.40105e12i −0.661937 + 0.638769i
\(207\) 1.36615e11i 0.0249840i
\(208\) 5.17917e11 7.25786e12i 0.0922385 1.29259i
\(209\) 6.21158e12i 1.07745i
\(210\) 1.67241e12 + 1.41746e12i 0.282576 + 0.239500i
\(211\) 5.60576e12i 0.922743i 0.887207 + 0.461371i \(0.152642\pi\)
−0.887207 + 0.461371i \(0.847358\pi\)
\(212\) 2.35860e11 6.61888e12i 0.0378274 1.06154i
\(213\) 1.51588e12i 0.236906i
\(214\) −6.97897e12 7.23209e12i −1.06296 1.10151i
\(215\) 5.69016e12 0.844720
\(216\) −8.88809e11 9.89247e11i −0.128621 0.143156i
\(217\) 4.25175e12 4.27170e11i 0.599845 0.0602660i
\(218\) 4.46174e12 4.30558e12i 0.613752 0.592271i
\(219\) 1.85808e12i 0.249242i
\(220\) −1.33151e11 + 3.73657e12i −0.0174188 + 0.488820i
\(221\) 1.02969e13 1.31386
\(222\) 4.95667e12 4.78319e12i 0.616948 0.595355i
\(223\) −1.41028e13 −1.71249 −0.856247 0.516567i \(-0.827210\pi\)
−0.856247 + 0.516567i \(0.827210\pi\)
\(224\) 5.90176e12 6.03407e12i 0.699225 0.714901i
\(225\) 1.69642e12 0.196124
\(226\) −9.56336e12 + 9.22865e12i −1.07898 + 1.04122i
\(227\) 1.45948e12 0.160715 0.0803574 0.996766i \(-0.474394\pi\)
0.0803574 + 0.996766i \(0.474394\pi\)
\(228\) −2.70334e11 + 7.58632e12i −0.0290576 + 0.815435i
\(229\) 9.59476e12i 1.00679i 0.864056 + 0.503395i \(0.167916\pi\)
−0.864056 + 0.503395i \(0.832084\pi\)
\(230\) −3.37771e11 + 3.25949e11i −0.0346034 + 0.0333923i
\(231\) −4.39875e11 4.37820e12i −0.0440011 0.437956i
\(232\) −6.84024e12 7.61321e12i −0.668171 0.743676i
\(233\) −1.11640e13 −1.06503 −0.532515 0.846420i \(-0.678753\pi\)
−0.532515 + 0.846420i \(0.678753\pi\)
\(234\) −3.21914e12 3.33590e12i −0.299953 0.310832i
\(235\) 1.54186e12i 0.140337i
\(236\) −3.56529e11 + 1.00052e13i −0.0317014 + 0.889629i
\(237\) 1.26428e13i 1.09832i
\(238\) 9.11179e12 + 7.72277e12i 0.773447 + 0.655541i
\(239\) 9.38444e12i 0.778431i 0.921147 + 0.389215i \(0.127254\pi\)
−0.921147 + 0.389215i \(0.872746\pi\)
\(240\) −3.25239e11 + 4.55776e12i −0.0263658 + 0.369479i
\(241\) 6.47684e12i 0.513179i −0.966520 0.256590i \(-0.917401\pi\)
0.966520 0.256590i \(-0.0825989\pi\)
\(242\) −3.89090e12 + 3.75472e12i −0.301346 + 0.290799i
\(243\) −8.47289e11 −0.0641500
\(244\) 2.62976e12 + 9.37099e10i 0.194658 + 0.00693651i
\(245\) 1.76347e12 + 8.68757e12i 0.127630 + 0.628760i
\(246\) −7.06841e12 7.32478e12i −0.500241 0.518384i
\(247\) 2.64620e13i 1.83143i
\(248\) 5.95250e12 + 6.62515e12i 0.402916 + 0.448447i
\(249\) 9.45821e12 0.626199
\(250\) −1.09266e13 1.13229e13i −0.707646 0.733311i
\(251\) 1.68995e13 1.07070 0.535350 0.844630i \(-0.320180\pi\)
0.535350 + 0.844630i \(0.320180\pi\)
\(252\) −3.46684e11 5.36633e12i −0.0214897 0.332640i
\(253\) 9.42144e11 0.0571419
\(254\) −4.94468e12 5.12402e12i −0.293463 0.304106i
\(255\) −6.46622e12 −0.375560
\(256\) 1.74139e13 + 2.49802e12i 0.989867 + 0.141996i
\(257\) 1.83480e13i 1.02084i −0.859926 0.510418i \(-0.829491\pi\)
0.859926 0.510418i \(-0.170509\pi\)
\(258\) −9.69211e12 1.00436e13i −0.527849 0.546994i
\(259\) 2.77136e13 2.78437e12i 1.47756 0.148449i
\(260\) −5.67236e11 + 1.59182e13i −0.0296081 + 0.830885i
\(261\) −6.52070e12 −0.333251
\(262\) −2.42981e13 + 2.34476e13i −1.21595 + 1.17339i
\(263\) 2.32492e13i 1.13934i 0.821875 + 0.569668i \(0.192928\pi\)
−0.821875 + 0.569668i \(0.807072\pi\)
\(264\) 6.82219e12 6.12953e12i 0.327418 0.294175i
\(265\) 1.44983e13i 0.681499i
\(266\) −1.98467e13 + 2.34163e13i −0.913774 + 1.07813i
\(267\) 1.53797e13i 0.693644i
\(268\) 3.01147e13 + 1.07312e12i 1.33057 + 0.0474140i
\(269\) 3.93209e13i 1.70210i 0.525084 + 0.851051i \(0.324034\pi\)
−0.525084 + 0.851051i \(0.675966\pi\)
\(270\) 2.02154e12 + 2.09486e12i 0.0857397 + 0.0888494i
\(271\) −1.91685e13 −0.796633 −0.398316 0.917248i \(-0.630405\pi\)
−0.398316 + 0.917248i \(0.630405\pi\)
\(272\) −1.77200e12 + 2.48321e13i −0.0721665 + 1.01131i
\(273\) −1.87391e12 1.86516e13i −0.0747920 0.744427i
\(274\) 2.07481e12 2.00219e12i 0.0811616 0.0783210i
\(275\) 1.16991e13i 0.448563i
\(276\) 1.15066e12 + 4.10031e10i 0.0432461 + 0.00154105i
\(277\) −3.04162e13 −1.12064 −0.560320 0.828276i \(-0.689322\pi\)
−0.560320 + 0.828276i \(0.689322\pi\)
\(278\) −1.98840e12 + 1.91880e12i −0.0718219 + 0.0693082i
\(279\) 5.67443e12 0.200955
\(280\) −1.24407e13 + 1.36606e13i −0.431992 + 0.474354i
\(281\) 9.27444e12 0.315793 0.157897 0.987456i \(-0.449529\pi\)
0.157897 + 0.987456i \(0.449529\pi\)
\(282\) −2.72153e12 + 2.62628e12i −0.0908747 + 0.0876941i
\(283\) −4.46834e13 −1.46326 −0.731628 0.681704i \(-0.761239\pi\)
−0.731628 + 0.681704i \(0.761239\pi\)
\(284\) −1.27677e13 4.54970e11i −0.410074 0.0146127i
\(285\) 1.66175e13i 0.523502i
\(286\) 2.30055e13 2.22003e13i 0.710916 0.686034i
\(287\) −4.11464e12 4.09542e13i −0.124733 1.24150i
\(288\) 8.59883e12 7.18921e12i 0.255730 0.213807i
\(289\) −9.58052e11 −0.0279544
\(290\) 1.55577e13 + 1.61220e13i 0.445407 + 0.461561i
\(291\) 1.38947e13i 0.390335i
\(292\) −1.56499e13 5.57675e11i −0.431426 0.0153736i
\(293\) 2.42007e13i 0.654721i 0.944900 + 0.327360i \(0.106159\pi\)
−0.944900 + 0.327360i \(0.893841\pi\)
\(294\) 1.23306e13 1.79103e13i 0.327397 0.475547i
\(295\) 2.19159e13i 0.571133i
\(296\) 3.87994e13 + 4.31838e13i 0.992477 + 1.10463i
\(297\) 5.84319e12i 0.146720i
\(298\) −3.91207e13 + 3.77515e13i −0.964311 + 0.930561i
\(299\) 4.01363e12 0.0971284
\(300\) −5.09157e11 + 1.42884e13i −0.0120972 + 0.339481i
\(301\) −5.64193e12 5.61558e13i −0.131617 1.31002i
\(302\) −3.86215e12 4.00222e12i −0.0884689 0.0916776i
\(303\) 3.18036e13i 0.715387i
\(304\) −6.38157e13 4.55385e12i −1.40969 0.100595i
\(305\) −5.76035e12 −0.124968
\(306\) 1.10140e13 + 1.14135e13i 0.234680 + 0.243192i
\(307\) 5.66237e13 1.18505 0.592526 0.805552i \(-0.298131\pi\)
0.592526 + 0.805552i \(0.298131\pi\)
\(308\) 3.70080e13 2.39085e12i 0.760794 0.0491500i
\(309\) −2.62993e13 −0.531095
\(310\) −1.35386e13 1.40296e13i −0.268586 0.278328i
\(311\) −4.87454e13 −0.950062 −0.475031 0.879969i \(-0.657563\pi\)
−0.475031 + 0.879969i \(0.657563\pi\)
\(312\) 2.90632e13 2.61125e13i 0.556537 0.500032i
\(313\) 4.59284e13i 0.864147i −0.901838 0.432074i \(-0.857782\pi\)
0.901838 0.432074i \(-0.142218\pi\)
\(314\) 2.93014e13 + 3.03641e13i 0.541720 + 0.561368i
\(315\) 1.17677e12 + 1.17127e13i 0.0213788 + 0.212790i
\(316\) 1.06486e14 + 3.79457e12i 1.90114 + 0.0677459i
\(317\) −4.78681e13 −0.839886 −0.419943 0.907550i \(-0.637950\pi\)
−0.419943 + 0.907550i \(0.637950\pi\)
\(318\) 2.55908e13 2.46952e13i 0.441302 0.425856i
\(319\) 4.49690e13i 0.762192i
\(320\) −3.82907e13 4.10732e12i −0.637923 0.0684279i
\(321\) 5.39662e13i 0.883780i
\(322\) 3.55168e12 + 3.01025e12i 0.0571777 + 0.0484614i
\(323\) 9.05371e13i 1.43289i
\(324\) 2.54302e11 7.13640e12i 0.00395687 0.111041i
\(325\) 4.98395e13i 0.762456i
\(326\) −9.47588e12 9.81956e12i −0.142535 0.147705i
\(327\) 3.32937e13 0.492435
\(328\) 6.38154e13 5.73363e13i 0.928153 0.833918i
\(329\) −1.52166e13 + 1.52880e12i −0.217640 + 0.0218662i
\(330\) −1.44469e13 + 1.39412e13i −0.203211 + 0.196099i
\(331\) 1.26897e14i 1.75548i −0.479133 0.877742i \(-0.659049\pi\)
0.479133 0.877742i \(-0.340951\pi\)
\(332\) −2.83875e12 + 7.96631e13i −0.0386249 + 1.08392i
\(333\) 3.69869e13 0.494999
\(334\) 5.91394e13 5.70695e13i 0.778522 0.751274i
\(335\) −6.59647e13 −0.854211
\(336\) 4.53027e13 1.30937e12i 0.577109 0.0166800i
\(337\) −1.28175e14 −1.60635 −0.803175 0.595743i \(-0.796858\pi\)
−0.803175 + 0.595743i \(0.796858\pi\)
\(338\) 3.96445e13 3.82570e13i 0.488812 0.471703i
\(339\) −7.13622e13 −0.865705
\(340\) 1.94074e12 5.44626e13i 0.0231651 0.650076i
\(341\) 3.91328e13i 0.459612i
\(342\) −2.93313e13 + 2.83047e13i −0.338991 + 0.327126i
\(343\) 8.39886e13 2.60175e13i 0.955218 0.295902i
\(344\) 8.75029e13 7.86187e13i 0.979379 0.879943i
\(345\) −2.52046e12 −0.0277636
\(346\) −2.22653e13 2.30729e13i −0.241385 0.250140i
\(347\) 1.11509e14i 1.18986i −0.803777 0.594931i \(-0.797179\pi\)
0.803777 0.594931i \(-0.202821\pi\)
\(348\) 1.95710e12 5.49215e13i 0.0205554 0.576842i
\(349\) 4.63058e13i 0.478735i 0.970929 + 0.239367i \(0.0769401\pi\)
−0.970929 + 0.239367i \(0.923060\pi\)
\(350\) −3.73799e13 + 4.41031e13i −0.380421 + 0.448844i
\(351\) 2.48926e13i 0.249391i
\(352\) 4.95792e13 + 5.93005e13i 0.489007 + 0.584889i
\(353\) 1.52616e14i 1.48197i 0.671524 + 0.740983i \(0.265640\pi\)
−0.671524 + 0.740983i \(0.734360\pi\)
\(354\) −3.86835e13 + 3.73295e13i −0.369834 + 0.356890i
\(355\) 2.79670e13 0.263263
\(356\) −1.29538e14 4.61601e12i −1.20066 0.0427850i
\(357\) 6.41142e12 + 6.38147e13i 0.0585166 + 0.582432i
\(358\) −1.94971e13 2.02042e13i −0.175232 0.181588i
\(359\) 1.12167e14i 0.992762i −0.868105 0.496381i \(-0.834662\pi\)
0.868105 0.496381i \(-0.165338\pi\)
\(360\) −1.82510e13 + 1.63980e13i −0.159083 + 0.142931i
\(361\) 1.16180e14 0.997338
\(362\) 4.32672e13 + 4.48365e13i 0.365815 + 0.379083i
\(363\) −2.90341e13 −0.241781
\(364\) 1.57658e14 1.01853e13i 1.29318 0.0835441i
\(365\) 3.42803e13 0.276971
\(366\) 9.81168e12 + 1.01675e13i 0.0780904 + 0.0809226i
\(367\) 2.01020e14 1.57607 0.788036 0.615630i \(-0.211098\pi\)
0.788036 + 0.615630i \(0.211098\pi\)
\(368\) −6.90708e11 + 9.67928e12i −0.00533496 + 0.0747618i
\(369\) 5.46578e13i 0.415918i
\(370\) −8.82468e13 9.14474e13i −0.661591 0.685586i
\(371\) 1.43083e14 1.43755e13i 1.05689 0.106185i
\(372\) −1.70310e12 + 4.77936e13i −0.0123952 + 0.347844i
\(373\) −6.67376e13 −0.478599 −0.239299 0.970946i \(-0.576918\pi\)
−0.239299 + 0.970946i \(0.576918\pi\)
\(374\) −7.87111e13 + 7.59562e13i −0.556214 + 0.536747i
\(375\) 8.44921e13i 0.588361i
\(376\) −2.13034e13 2.37107e13i −0.146189 0.162709i
\(377\) 1.91573e14i 1.29556i
\(378\) 1.86696e13 2.20276e13i 0.124432 0.146812i
\(379\) 1.48535e14i 0.975696i 0.872929 + 0.487848i \(0.162218\pi\)
−0.872929 + 0.487848i \(0.837782\pi\)
\(380\) 1.39963e14 + 4.98750e12i 0.906156 + 0.0322904i
\(381\) 3.82356e13i 0.243995i
\(382\) −9.96670e13 1.03282e14i −0.626907 0.649644i
\(383\) 1.16834e14 0.724394 0.362197 0.932101i \(-0.382027\pi\)
0.362197 + 0.932101i \(0.382027\pi\)
\(384\) 5.79713e13 + 7.45826e13i 0.354316 + 0.455844i
\(385\) −8.07751e13 + 8.11542e12i −0.486680 + 0.0488964i
\(386\) −2.22255e14 + 2.14476e14i −1.32014 + 1.27394i
\(387\) 7.49461e13i 0.438873i
\(388\) −1.17030e14 4.17030e12i −0.675652 0.0240765i
\(389\) −2.51101e14 −1.42931 −0.714654 0.699478i \(-0.753416\pi\)
−0.714654 + 0.699478i \(0.753416\pi\)
\(390\) −6.15452e13 + 5.93912e13i −0.345413 + 0.333324i
\(391\) −1.37323e13 −0.0759923
\(392\) 1.47151e14 + 1.09232e14i 0.802955 + 0.596040i
\(393\) −1.81313e14 −0.975597
\(394\) −2.59826e13 + 2.50732e13i −0.137865 + 0.133040i
\(395\) −2.33252e14 −1.22051
\(396\) 4.92151e13 + 1.75375e12i 0.253966 + 0.00904991i
\(397\) 1.93283e14i 0.983662i −0.870691 0.491831i \(-0.836328\pi\)
0.870691 0.491831i \(-0.163672\pi\)
\(398\) −5.91844e12 + 5.71129e12i −0.0297064 + 0.0286667i
\(399\) −1.63997e14 + 1.64766e13i −0.811866 + 0.0815676i
\(400\) −1.20193e14 8.57689e12i −0.586879 0.0418794i
\(401\) −5.07447e13 −0.244398 −0.122199 0.992506i \(-0.538995\pi\)
−0.122199 + 0.992506i \(0.538995\pi\)
\(402\) 1.12359e14 + 1.16434e14i 0.533781 + 0.553140i
\(403\) 1.66710e14i 0.781238i
\(404\) 2.67870e14 + 9.54539e12i 1.23830 + 0.0441261i
\(405\) 1.56319e13i 0.0712870i
\(406\) 1.43681e14 1.69523e14i 0.646407 0.762670i
\(407\) 2.55074e14i 1.13213i
\(408\) −9.94371e13 + 8.93412e13i −0.435429 + 0.391220i
\(409\) 2.92527e14i 1.26383i 0.775039 + 0.631913i \(0.217730\pi\)
−0.775039 + 0.631913i \(0.782270\pi\)
\(410\) −1.35138e14 + 1.30408e14i −0.576056 + 0.555894i
\(411\) 1.54823e13 0.0651188
\(412\) 7.89336e12 2.21509e14i 0.0327587 0.919300i
\(413\) −2.16286e14 + 2.17301e13i −0.885735 + 0.0889891i
\(414\) 4.29313e12 + 4.44884e12i 0.0173489 + 0.0179782i
\(415\) 1.74498e14i 0.695867i
\(416\) 2.11213e14 + 2.52626e14i 0.831203 + 0.994181i
\(417\) −1.48375e13 −0.0576253
\(418\) −1.95199e14 2.02279e14i −0.748184 0.775320i
\(419\) −1.59383e14 −0.602925 −0.301463 0.953478i \(-0.597475\pi\)
−0.301463 + 0.953478i \(0.597475\pi\)
\(420\) −9.90054e13 + 6.39611e12i −0.369648 + 0.0238806i
\(421\) 2.67679e14 0.986423 0.493212 0.869909i \(-0.335823\pi\)
0.493212 + 0.869909i \(0.335823\pi\)
\(422\) −1.76161e14 1.82550e14i −0.640754 0.663994i
\(423\) −2.03082e13 −0.0729120
\(424\) 2.00318e14 + 2.22954e14i 0.709916 + 0.790139i
\(425\) 1.70521e14i 0.596538i
\(426\) −4.76366e13 4.93643e13i −0.164508 0.170475i
\(427\) 5.71154e12 + 5.68486e13i 0.0194715 + 0.193806i
\(428\) 4.54538e14 + 1.61972e13i 1.52978 + 0.0545128i
\(429\) 1.71668e14 0.570393
\(430\) −1.85299e14 + 1.78813e14i −0.607850 + 0.586575i
\(431\) 4.08490e14i 1.32299i 0.749950 + 0.661494i \(0.230077\pi\)
−0.749950 + 0.661494i \(0.769923\pi\)
\(432\) 6.00310e13 + 4.28378e12i 0.191962 + 0.0136983i
\(433\) 3.45919e13i 0.109217i 0.998508 + 0.0546085i \(0.0173911\pi\)
−0.998508 + 0.0546085i \(0.982609\pi\)
\(434\) −1.25034e14 + 1.47522e14i −0.389792 + 0.459900i
\(435\) 1.20303e14i 0.370327i
\(436\) −9.99262e12 + 2.80421e14i −0.0303741 + 0.852382i
\(437\) 3.52904e13i 0.105927i
\(438\) −5.83901e13 6.05079e13i −0.173074 0.179351i
\(439\) 9.72822e12 0.0284760 0.0142380 0.999899i \(-0.495468\pi\)
0.0142380 + 0.999899i \(0.495468\pi\)
\(440\) −1.13086e14 1.25865e14i −0.326903 0.363844i
\(441\) 1.14426e14 2.32270e13i 0.326671 0.0663102i
\(442\) −3.35318e14 + 3.23582e14i −0.945440 + 0.912350i
\(443\) 2.37670e14i 0.661840i 0.943659 + 0.330920i \(0.107359\pi\)
−0.943659 + 0.330920i \(0.892641\pi\)
\(444\) −1.11011e13 + 3.11527e14i −0.0305323 + 0.856820i
\(445\) 2.83746e14 0.770815
\(446\) 4.59255e14 4.43182e14i 1.23229 1.18916i
\(447\) −2.91920e14 −0.773701
\(448\) −2.56864e12 + 3.81961e14i −0.00672471 + 0.999977i
\(449\) 6.77274e14 1.75150 0.875748 0.482768i \(-0.160369\pi\)
0.875748 + 0.482768i \(0.160369\pi\)
\(450\) −5.52437e13 + 5.33102e13i −0.141128 + 0.136189i
\(451\) 3.76939e14 0.951262
\(452\) 2.14184e13 6.01058e14i 0.0533980 1.49849i
\(453\) 2.98648e13i 0.0735561i
\(454\) −4.75277e13 + 4.58642e13i −0.115648 + 0.111601i
\(455\) −3.44111e14 + 3.45726e13i −0.827247 + 0.0831130i
\(456\) −2.29597e14 2.55542e14i −0.545331 0.606955i
\(457\) −4.00602e14 −0.940099 −0.470050 0.882640i \(-0.655764\pi\)
−0.470050 + 0.882640i \(0.655764\pi\)
\(458\) −3.01516e14 3.12451e14i −0.699117 0.724473i
\(459\) 8.51677e13i 0.195121i
\(460\) 7.56481e11 2.12289e13i 0.00171250 0.0480574i
\(461\) 6.40102e14i 1.43184i −0.698183 0.715919i \(-0.746008\pi\)
0.698183 0.715919i \(-0.253992\pi\)
\(462\) 1.51910e14 + 1.28752e14i 0.335780 + 0.284593i
\(463\) 1.45973e14i 0.318843i −0.987211 0.159422i \(-0.949037\pi\)
0.987211 0.159422i \(-0.0509630\pi\)
\(464\) 4.61997e14 + 3.29678e13i 0.997218 + 0.0711609i
\(465\) 1.04690e14i 0.223312i
\(466\) 3.63553e14 3.50829e14i 0.766383 0.739559i
\(467\) 4.94883e11 0.00103100 0.000515501 1.00000i \(-0.499836\pi\)
0.000515501 1.00000i \(0.499836\pi\)
\(468\) 2.09662e14 + 7.47117e12i 0.431685 + 0.0153828i
\(469\) 6.54057e13 + 6.51002e14i 0.133096 + 1.32474i
\(470\) 4.84532e13 + 5.02105e13i 0.0974505 + 0.100985i
\(471\) 2.26578e14i 0.450405i
\(472\) −3.02803e14 3.37021e14i −0.594948 0.662179i
\(473\) 5.16854e14 1.00376
\(474\) 3.97302e14 + 4.11711e14i 0.762675 + 0.790336i
\(475\) 4.38220e14 0.831529
\(476\) −5.39412e14 + 3.48480e13i −1.01177 + 0.0653641i
\(477\) 1.90960e14 0.354072
\(478\) −2.94907e14 3.05603e14i −0.540544 0.560149i
\(479\) −2.28739e14 −0.414472 −0.207236 0.978291i \(-0.566447\pi\)
−0.207236 + 0.978291i \(0.566447\pi\)
\(480\) −1.32636e14 1.58643e14i −0.237594 0.284181i
\(481\) 1.08664e15i 1.92437i
\(482\) 2.03535e14 + 2.10917e14i 0.356353 + 0.369277i
\(483\) 2.49910e12 + 2.48743e13i 0.00432588 + 0.0430568i
\(484\) 8.71417e12 2.44544e14i 0.0149134 0.418511i
\(485\) 2.56349e14 0.433762
\(486\) 2.75918e13 2.66261e13i 0.0461615 0.0445459i
\(487\) 1.05789e15i 1.74998i 0.484142 + 0.874990i \(0.339132\pi\)
−0.484142 + 0.874990i \(0.660868\pi\)
\(488\) −8.85824e13 + 7.95886e13i −0.144890 + 0.130179i
\(489\) 7.32740e13i 0.118509i
\(490\) −3.30434e14 2.27492e14i −0.528453 0.363821i
\(491\) 6.23073e14i 0.985350i −0.870213 0.492675i \(-0.836019\pi\)
0.870213 0.492675i \(-0.163981\pi\)
\(492\) 4.60363e14 + 1.64048e13i 0.719934 + 0.0256544i
\(493\) 6.55447e14i 1.01363i
\(494\) −8.31569e14 8.61729e14i −1.27175 1.31787i
\(495\) −1.07803e14 −0.163043
\(496\) −4.02037e14 2.86892e13i −0.601336 0.0429110i
\(497\) −2.77300e13 2.76005e14i −0.0410195 0.408279i
\(498\) −3.08005e14 + 2.97225e14i −0.450605 + 0.434834i
\(499\) 4.39882e14i 0.636477i 0.948011 + 0.318239i \(0.103091\pi\)
−0.948011 + 0.318239i \(0.896909\pi\)
\(500\) 7.11647e14 + 2.53591e13i 1.01843 + 0.0362910i
\(501\) 4.41301e14 0.624636
\(502\) −5.50328e14 + 5.31067e14i −0.770462 + 0.743496i
\(503\) −1.26286e13 −0.0174876 −0.00874381 0.999962i \(-0.502783\pi\)
−0.00874381 + 0.999962i \(0.502783\pi\)
\(504\) 1.79927e14 + 1.63859e14i 0.246450 + 0.224441i
\(505\) −5.86756e14 −0.794977
\(506\) −3.06807e13 + 2.96069e13i −0.0411186 + 0.0396794i
\(507\) 2.95829e14 0.392191
\(508\) 3.22045e14 + 1.14759e13i 0.422344 + 0.0150500i
\(509\) 1.30789e15i 1.69678i −0.529374 0.848389i \(-0.677573\pi\)
0.529374 0.848389i \(-0.322427\pi\)
\(510\) 2.10571e14 2.03201e14i 0.270248 0.260789i
\(511\) −3.39898e13 3.38311e14i −0.0431553 0.429537i
\(512\) −6.45581e14 + 4.65886e14i −0.810898 + 0.585187i
\(513\) −2.18872e14 −0.271984
\(514\) 5.76586e14 + 5.97499e14i 0.708871 + 0.734581i
\(515\) 4.85205e14i 0.590182i
\(516\) 6.31243e14 + 2.24940e13i 0.759667 + 0.0270703i
\(517\) 1.40052e14i 0.166760i
\(518\) −8.14990e14 + 9.61575e14i −0.960149 + 1.13284i
\(519\) 1.72171e14i 0.200696i
\(520\) −4.81758e14 5.36199e14i −0.555662 0.618454i
\(521\) 8.44201e14i 0.963470i −0.876317 0.481735i \(-0.840007\pi\)
0.876317 0.481735i \(-0.159993\pi\)
\(522\) 2.12345e14 2.04913e14i 0.239803 0.231410i
\(523\) 9.87674e14 1.10371 0.551854 0.833940i \(-0.313920\pi\)
0.551854 + 0.833940i \(0.313920\pi\)
\(524\) 5.44186e13 1.52714e15i 0.0601763 1.68871i
\(525\) −3.08877e14 + 3.10327e13i −0.337995 + 0.0339581i
\(526\) −7.30608e14 7.57107e14i −0.791158 0.819852i
\(527\) 5.70382e14i 0.611233i
\(528\) −2.95424e13 + 4.13994e14i −0.0313299 + 0.439044i
\(529\) 9.47457e14 0.994382
\(530\) −4.55610e14 4.72135e14i −0.473234 0.490398i
\(531\) −2.88658e14 −0.296731
\(532\) −8.95555e13 1.38623e15i −0.0911125 1.41033i
\(533\) 1.60580e15 1.61693
\(534\) −4.83309e14 5.00838e14i −0.481668 0.499137i
\(535\) −9.95642e14 −0.982104
\(536\) −1.01440e15 + 9.11409e14i −0.990384 + 0.889830i
\(537\) 1.50765e14i 0.145694i
\(538\) −1.23566e15 1.28048e15i −1.18194 1.22481i
\(539\) 1.60181e14 + 7.89118e14i 0.151661 + 0.747143i
\(540\) −1.31662e14 4.69171e12i −0.123394 0.00439709i
\(541\) −4.87158e13 −0.0451944 −0.0225972 0.999745i \(-0.507194\pi\)
−0.0225972 + 0.999745i \(0.507194\pi\)
\(542\) 6.24220e14 6.02372e14i 0.573247 0.553183i
\(543\) 3.34572e14i 0.304152i
\(544\) −7.22644e14 8.64337e14i −0.650325 0.777838i
\(545\) 6.14247e14i 0.547221i
\(546\) 6.47152e14 + 5.48498e14i 0.570751 + 0.483744i
\(547\) 2.49278e14i 0.217647i 0.994061 + 0.108824i \(0.0347084\pi\)
−0.994061 + 0.108824i \(0.965292\pi\)
\(548\) −4.64681e12 + 1.30402e14i −0.00401663 + 0.112718i
\(549\) 7.58706e13i 0.0649271i
\(550\) −3.67645e14 3.80979e14i −0.311483 0.322780i
\(551\) −1.68443e15 −1.41292
\(552\) −3.87595e13 + 3.48243e13i −0.0321894 + 0.0289212i
\(553\) 2.31276e14 + 2.30195e15i 0.190170 + 1.89281i
\(554\) 9.90498e14 9.55831e14i 0.806399 0.778175i
\(555\) 6.82385e14i 0.550070i
\(556\) 4.45327e12 1.24971e14i 0.00355441 0.0997466i
\(557\) −1.07858e15 −0.852414 −0.426207 0.904626i \(-0.640150\pi\)
−0.426207 + 0.904626i \(0.640150\pi\)
\(558\) −1.84787e14 + 1.78319e14i −0.144605 + 0.139544i
\(559\) 2.20185e15 1.70617
\(560\) −2.41570e13 8.35806e14i −0.0185357 0.641315i
\(561\) −5.87345e14 −0.446270
\(562\) −3.02020e14 + 2.91450e14i −0.227241 + 0.219288i
\(563\) 1.47824e15 1.10141 0.550706 0.834699i \(-0.314358\pi\)
0.550706 + 0.834699i \(0.314358\pi\)
\(564\) 6.09521e12 1.71048e14i 0.00449732 0.126207i
\(565\) 1.31659e15i 0.962019i
\(566\) 1.45511e15 1.40418e15i 1.05294 1.01609i
\(567\) 1.54271e14 1.54995e13i 0.110555 0.0111073i
\(568\) 4.30075e14 3.86410e14i 0.305231 0.274241i
\(569\) 1.04040e15 0.731276 0.365638 0.930757i \(-0.380851\pi\)
0.365638 + 0.930757i \(0.380851\pi\)
\(570\) 5.22205e14 + 5.41144e14i 0.363521 + 0.376705i
\(571\) 1.47971e15i 1.02018i −0.860120 0.510091i \(-0.829612\pi\)
0.860120 0.510091i \(-0.170388\pi\)
\(572\) −5.15237e13 + 1.44590e15i −0.0351827 + 0.987323i
\(573\) 7.70694e14i 0.521232i
\(574\) 1.42098e15 + 1.20436e15i 0.951858 + 0.806755i
\(575\) 6.64672e13i 0.0440996i
\(576\) −5.40982e13 + 5.04334e14i −0.0355516 + 0.331432i
\(577\) 2.78366e15i 1.81196i 0.423320 + 0.905980i \(0.360865\pi\)
−0.423320 + 0.905980i \(0.639135\pi\)
\(578\) 3.11988e13 3.01068e13i 0.0201157 0.0194116i
\(579\) −1.65847e15 −1.05920
\(580\) −1.01327e15 3.61072e13i −0.641018 0.0228423i
\(581\) −1.72211e15 + 1.73019e14i −1.07918 + 0.108424i
\(582\) −4.36642e14 4.52478e14i −0.271050 0.280880i
\(583\) 1.31693e15i 0.809812i
\(584\) 5.27161e14 4.73638e14i 0.321124 0.288520i
\(585\) −4.59253e14 −0.277137
\(586\) −7.60508e14 7.88091e14i −0.454639 0.471129i
\(587\) −8.72225e14 −0.516558 −0.258279 0.966070i \(-0.583155\pi\)
−0.258279 + 0.966070i \(0.583155\pi\)
\(588\) 1.61289e14 + 9.70736e14i 0.0946302 + 0.569542i
\(589\) 1.46582e15 0.852013
\(590\) 6.88707e14 + 7.13686e14i 0.396596 + 0.410980i
\(591\) −1.93883e14 −0.110614
\(592\) −2.62055e15 1.87001e14i −1.48123 0.105700i
\(593\) 9.68246e14i 0.542232i −0.962547 0.271116i \(-0.912607\pi\)
0.962547 0.271116i \(-0.0873926\pi\)
\(594\) 1.83623e14 + 1.90282e14i 0.101883 + 0.105578i
\(595\) 1.17734e15 1.18287e14i 0.647230 0.0650268i
\(596\) 8.76158e13 2.45874e15i 0.0477230 1.33924i
\(597\) −4.41636e13 −0.0238345
\(598\) −1.30703e14 + 1.26129e14i −0.0698924 + 0.0674462i
\(599\) 1.22290e15i 0.647952i −0.946065 0.323976i \(-0.894980\pi\)
0.946065 0.323976i \(-0.105020\pi\)
\(600\) −4.32432e14 4.81298e14i −0.227031 0.252686i
\(601\) 2.89149e15i 1.50422i −0.659037 0.752111i \(-0.729036\pi\)
0.659037 0.752111i \(-0.270964\pi\)
\(602\) 1.94843e15 + 1.65140e15i 1.00439 + 0.851281i
\(603\) 8.68833e14i 0.443804i
\(604\) 2.51540e14 + 8.96348e12i 0.127322 + 0.00453705i
\(605\) 5.35661e14i 0.268680i
\(606\) 9.99428e14 + 1.03568e15i 0.496766 + 0.514784i
\(607\) −1.35219e15 −0.666041 −0.333021 0.942920i \(-0.608068\pi\)
−0.333021 + 0.942920i \(0.608068\pi\)
\(608\) 2.22125e15 1.85712e15i 1.08425 0.906503i
\(609\) 1.18726e15 1.19283e14i 0.574317 0.0577012i
\(610\) 1.87585e14 1.81019e14i 0.0899256 0.0867783i
\(611\) 5.96637e14i 0.283455i
\(612\) −7.17337e14 2.55619e13i −0.337746 0.0120354i
\(613\) −1.65146e15 −0.770610 −0.385305 0.922789i \(-0.625904\pi\)
−0.385305 + 0.922789i \(0.625904\pi\)
\(614\) −1.84394e15 + 1.77940e15i −0.852748 + 0.822902i
\(615\) −1.00840e15 −0.462190
\(616\) −1.13003e15 + 1.24084e15i −0.513328 + 0.563665i
\(617\) −1.85421e15 −0.834815 −0.417408 0.908719i \(-0.637061\pi\)
−0.417408 + 0.908719i \(0.637061\pi\)
\(618\) 8.56431e14 8.26456e14i 0.382169 0.368794i
\(619\) 2.67968e15 1.18518 0.592590 0.805504i \(-0.298105\pi\)
0.592590 + 0.805504i \(0.298105\pi\)
\(620\) 8.81763e14 + 3.14211e13i 0.386543 + 0.0137742i
\(621\) 3.31975e13i 0.0144245i
\(622\) 1.58739e15 1.53183e15i 0.683652 0.659725i
\(623\) −2.81342e14 2.80027e15i −0.120102 1.19541i
\(624\) −1.25854e14 + 1.76366e15i −0.0532539 + 0.746277i
\(625\) −1.56040e14 −0.0654480
\(626\) 1.44330e15 + 1.49565e15i 0.600065 + 0.621829i
\(627\) 1.50941e15i 0.622066i
\(628\) −1.90839e15 6.80042e13i −0.779629 0.0277816i
\(629\) 3.71784e15i 1.50561i
\(630\) −4.06395e14 3.44443e14i −0.163146 0.138275i
\(631\) 1.95571e15i 0.778293i −0.921176 0.389146i \(-0.872770\pi\)
0.921176 0.389146i \(-0.127230\pi\)
\(632\) −3.58694e15 + 3.22276e15i −1.41508 + 1.27140i
\(633\) 1.36220e15i 0.532746i
\(634\) 1.55882e15 1.50426e15i 0.604371 0.583219i
\(635\) −7.05424e14 −0.271141
\(636\) −5.73139e13 + 1.60839e15i −0.0218397 + 0.612881i
\(637\) 6.82389e14 + 3.36173e15i 0.257789 + 1.26998i
\(638\) 1.41315e15 + 1.46441e15i 0.529268 + 0.548464i
\(639\) 3.68359e14i 0.136778i
\(640\) 1.37600e15 1.06953e15i 0.506558 0.393735i
\(641\) 7.90913e14 0.288675 0.144338 0.989528i \(-0.453895\pi\)
0.144338 + 0.989528i \(0.453895\pi\)
\(642\) 1.69589e15 + 1.75740e15i 0.613698 + 0.635957i
\(643\) 2.36334e15 0.847943 0.423972 0.905675i \(-0.360636\pi\)
0.423972 + 0.905675i \(0.360636\pi\)
\(644\) −2.10257e14 + 1.35834e13i −0.0747960 + 0.00483209i
\(645\) −1.38271e15 −0.487699
\(646\) 2.84513e15 + 2.94832e15i 0.995001 + 1.03109i
\(647\) −2.45880e15 −0.852608 −0.426304 0.904580i \(-0.640185\pi\)
−0.426304 + 0.904580i \(0.640185\pi\)
\(648\) 2.15981e14 + 2.40387e14i 0.0742595 + 0.0826511i
\(649\) 1.99068e15i 0.678666i
\(650\) −1.56621e15 1.62301e15i −0.529451 0.548654i
\(651\) −1.03318e15 + 1.03802e14i −0.346321 + 0.0347946i
\(652\) 6.17160e14 + 2.19921e13i 0.205133 + 0.00730980i
\(653\) 1.51415e15 0.499053 0.249526 0.968368i \(-0.419725\pi\)
0.249526 + 0.968368i \(0.419725\pi\)
\(654\) −1.08420e15 + 1.04626e15i −0.354350 + 0.341948i
\(655\) 3.34511e15i 1.08414i
\(656\) −2.76343e14 + 3.87255e15i −0.0888131 + 1.24459i
\(657\) 4.51513e14i 0.143900i
\(658\) 4.47482e14 5.27966e14i 0.141427 0.166864i
\(659\) 4.30335e15i 1.34877i 0.738381 + 0.674384i \(0.235591\pi\)
−0.738381 + 0.674384i \(0.764409\pi\)
\(660\) 3.23556e13 9.07987e14i 0.0100568 0.282220i
\(661\) 3.33418e15i 1.02774i −0.857869 0.513868i \(-0.828212\pi\)
0.857869 0.513868i \(-0.171788\pi\)
\(662\) 3.98774e15 + 4.13237e15i 1.21901 + 1.26322i
\(663\) −2.50215e15 −0.758560
\(664\) −2.41097e15 2.68342e15i −0.724883 0.806797i
\(665\) 3.03984e14 + 3.02564e15i 0.0906423 + 0.902189i
\(666\) −1.20447e15 + 1.16231e15i −0.356195 + 0.343728i
\(667\) 2.55486e14i 0.0749335i
\(668\) −1.32450e14 + 3.71691e15i −0.0385285 + 1.08122i
\(669\) 3.42698e15 0.988709
\(670\) 2.14813e15 2.07294e15i 0.614680 0.593166i
\(671\) −5.23230e14 −0.148497
\(672\) −1.43413e15 + 1.46628e15i −0.403698 + 0.412749i
\(673\) −5.15623e15 −1.43963 −0.719813 0.694168i \(-0.755773\pi\)
−0.719813 + 0.694168i \(0.755773\pi\)
\(674\) 4.17401e15 4.02792e15i 1.15591 1.11545i
\(675\) −4.12231e14 −0.113232
\(676\) −8.87890e13 + 2.49166e15i −0.0241909 + 0.678864i
\(677\) 1.76720e15i 0.477581i −0.971071 0.238791i \(-0.923249\pi\)
0.971071 0.238791i \(-0.0767509\pi\)
\(678\) 2.32390e15 2.24256e15i 0.622951 0.601148i
\(679\) −2.54176e14 2.52989e15i −0.0675851 0.672694i
\(680\) 1.64829e15 + 1.83455e15i 0.434745 + 0.483872i
\(681\) −3.54653e14 −0.0927887
\(682\) −1.22975e15 1.27435e15i −0.319156 0.330731i
\(683\) 5.30298e14i 0.136523i −0.997667 0.0682616i \(-0.978255\pi\)
0.997667 0.0682616i \(-0.0217452\pi\)
\(684\) 6.56912e13 1.84348e15i 0.0167764 0.470792i
\(685\) 2.85639e14i 0.0723636i
\(686\) −1.91747e15 + 3.48660e15i −0.481888 + 0.876233i
\(687\) 2.33153e15i 0.581271i
\(688\) −3.78918e14 + 5.30998e15i −0.0937148 + 1.31328i
\(689\) 5.61024e15i 1.37650i
\(690\) 8.20784e13 7.92056e13i 0.0199783 0.0192791i
\(691\) 1.60339e15 0.387177 0.193589 0.981083i \(-0.437987\pi\)
0.193589 + 0.981083i \(0.437987\pi\)
\(692\) 1.45013e15 + 5.16746e13i 0.347395 + 0.0123792i
\(693\) 1.06890e14 + 1.06390e15i 0.0254040 + 0.252854i
\(694\) 3.50416e15 + 3.63126e15i 0.826242 + 0.856209i
\(695\) 2.73743e14i 0.0640363i
\(696\) 1.66218e15 + 1.85001e15i 0.385769 + 0.429362i
\(697\) −5.49409e15 −1.26507
\(698\) −1.45516e15 1.50794e15i −0.332434 0.344492i
\(699\) 2.71285e15 0.614896
\(700\) −1.68672e14 2.61088e15i −0.0379318 0.587147i
\(701\) −6.57181e15 −1.46634 −0.733172 0.680043i \(-0.761961\pi\)
−0.733172 + 0.680043i \(0.761961\pi\)
\(702\) 7.82252e14 + 8.10623e14i 0.173178 + 0.179459i
\(703\) 9.55445e15 2.09871
\(704\) −3.47806e15 3.73080e14i −0.758032 0.0813115i
\(705\) 3.74673e14i 0.0810238i
\(706\) −4.79595e15 4.96990e15i −1.02908 1.06640i
\(707\) 5.81783e14 + 5.79066e15i 0.123867 + 1.23288i
\(708\) 8.66365e13 2.43126e15i 0.0183028 0.513628i
\(709\) −5.81764e15 −1.21953 −0.609765 0.792582i \(-0.708736\pi\)
−0.609765 + 0.792582i \(0.708736\pi\)
\(710\) −9.10741e14 + 8.78865e14i −0.189441 + 0.182811i
\(711\) 3.07221e15i 0.634115i
\(712\) 4.36343e15 3.92041e15i 0.893693 0.802956i
\(713\) 2.22329e14i 0.0451859i
\(714\) −2.21417e15 1.87663e15i −0.446550 0.378477i
\(715\) 3.16717e15i 0.633852i
\(716\) 1.26984e15 + 4.52500e13i 0.252189 + 0.00898663i
\(717\) 2.28042e15i 0.449427i
\(718\) 3.52485e15 + 3.65269e15i 0.689376 + 0.714379i
\(719\) 6.95565e14 0.134998 0.0674992 0.997719i \(-0.478498\pi\)
0.0674992 + 0.997719i \(0.478498\pi\)
\(720\) 7.90331e13 1.10753e15i 0.0152223 0.213319i
\(721\) 4.78846e15 4.81093e14i 0.915276 0.0919571i
\(722\) −3.78338e15 + 3.65097e15i −0.717672 + 0.692554i
\(723\) 1.57387e15i 0.296284i
\(724\) −2.81798e15 1.00417e14i −0.526472 0.0187605i
\(725\) −3.17251e15 −0.588226
\(726\) 9.45489e14 9.12398e14i 0.173982 0.167893i
\(727\) −1.04179e15 −0.190257 −0.0951287 0.995465i \(-0.530326\pi\)
−0.0951287 + 0.995465i \(0.530326\pi\)
\(728\) −4.81404e15 + 5.28610e15i −0.872543 + 0.958104i
\(729\) 2.05891e14 0.0370370
\(730\) −1.11633e15 + 1.07726e15i −0.199305 + 0.192329i
\(731\) −7.53342e15 −1.33489
\(732\) −6.39031e14 2.27715e13i −0.112386 0.00400480i
\(733\) 4.26471e15i 0.744420i 0.928149 + 0.372210i \(0.121400\pi\)
−0.928149 + 0.372210i \(0.878600\pi\)
\(734\) −6.54618e15 + 6.31706e15i −1.13412 + 1.09443i
\(735\) −4.28523e14 2.11108e15i −0.0736875 0.363015i
\(736\) −2.81679e14 3.36909e14i −0.0480758 0.0575023i
\(737\) −5.99177e15 −1.01504
\(738\) 1.71762e15 + 1.77992e15i 0.288814 + 0.299289i
\(739\) 1.18750e16i 1.98193i −0.134124 0.990965i \(-0.542822\pi\)
0.134124 0.990965i \(-0.457178\pi\)
\(740\) 5.74748e15 + 2.04808e14i 0.952145 + 0.0339291i
\(741\) 6.43026e15i 1.05737i
\(742\) −4.20772e15 + 4.96452e15i −0.686792 + 0.810319i
\(743\) 2.39150e15i 0.387464i −0.981054 0.193732i \(-0.937941\pi\)
0.981054 0.193732i \(-0.0620593\pi\)
\(744\) −1.44646e15 1.60991e15i −0.232624 0.258911i
\(745\) 5.38575e15i 0.859778i
\(746\) 2.17330e15 2.09723e15i 0.344394 0.332340i
\(747\) −2.29834e15 −0.361536
\(748\) 1.76283e14 4.94700e15i 0.0275266 0.772472i
\(749\) 9.87205e14 + 9.82593e15i 0.153023 + 1.52308i
\(750\) 2.65517e15 + 2.75147e15i 0.408559 + 0.423377i
\(751\) 1.10256e16i 1.68415i 0.539359 + 0.842076i \(0.318666\pi\)
−0.539359 + 0.842076i \(0.681334\pi\)
\(752\) 1.43885e15 + 1.02676e14i 0.218181 + 0.0155693i
\(753\) −4.10657e15 −0.618169
\(754\) 6.02018e15 + 6.23853e15i 0.899637 + 0.932266i
\(755\) −5.50986e14 −0.0817396
\(756\) 8.42442e13 + 1.30402e15i 0.0124071 + 0.192050i
\(757\) 1.11914e16 1.63628 0.818139 0.575021i \(-0.195006\pi\)
0.818139 + 0.575021i \(0.195006\pi\)
\(758\) −4.66773e15 4.83703e15i −0.677525 0.702098i
\(759\) −2.28941e14 −0.0329909
\(760\) −4.71460e15 + 4.23592e15i −0.674481 + 0.606001i
\(761\) 3.49689e15i 0.496668i −0.968674 0.248334i \(-0.920117\pi\)
0.968674 0.248334i \(-0.0798831\pi\)
\(762\) 1.20156e15 + 1.24514e15i 0.169431 + 0.175576i
\(763\) −6.06197e15 + 6.09042e14i −0.848650 + 0.0852633i
\(764\) 6.49127e15 + 2.31313e14i 0.902228 + 0.0321504i
\(765\) 1.57129e15 0.216830
\(766\) −3.80467e15 + 3.67151e15i −0.521265 + 0.503021i
\(767\) 8.48052e15i 1.15358i
\(768\) −4.23158e15 6.07018e14i −0.571500 0.0819813i
\(769\) 6.15624e15i 0.825507i −0.910843 0.412753i \(-0.864567\pi\)
0.910843 0.412753i \(-0.135433\pi\)
\(770\) 2.37540e15 2.80264e15i 0.316255 0.373137i
\(771\) 4.45856e15i 0.589380i
\(772\) 4.97768e14 1.39687e16i 0.0653328 1.83342i
\(773\) 6.51219e15i 0.848673i 0.905505 + 0.424336i \(0.139493\pi\)
−0.905505 + 0.424336i \(0.860507\pi\)
\(774\) 2.35518e15 + 2.44060e15i 0.304754 + 0.315807i
\(775\) 2.76077e15 0.354709
\(776\) 3.94211e15 3.54187e15i 0.502909 0.451849i
\(777\) −6.73441e15 + 6.76602e14i −0.853069 + 0.0857072i
\(778\) 8.17706e15 7.89087e15i 1.02851 0.992515i
\(779\) 1.41192e16i 1.76341i
\(780\) 1.37838e14 3.86812e15i 0.0170942 0.479711i
\(781\) 2.54033e15 0.312831
\(782\) 4.47188e14 4.31537e14i 0.0546831 0.0527692i
\(783\) 1.58453e15 0.192403
\(784\) −8.22457e15 + 1.06713e15i −0.991687 + 0.128670i
\(785\) 4.18023e15 0.500514
\(786\) 5.90443e15 5.69778e15i 0.702027 0.677456i
\(787\) 8.41526e14 0.0993588 0.0496794 0.998765i \(-0.484180\pi\)
0.0496794 + 0.998765i \(0.484180\pi\)
\(788\) 5.81913e13 1.63301e15i 0.00682282 0.191467i
\(789\) 5.64957e15i 0.657796i
\(790\) 7.59582e15 7.32996e15i 0.878265 0.847526i
\(791\) 1.29933e16 1.30543e15i 1.49193 0.149894i
\(792\) −1.65779e15 + 1.48948e15i −0.189035 + 0.169842i
\(793\) −2.22902e15 −0.252412
\(794\) 6.07392e15 + 6.29422e15i 0.683057 + 0.707830i
\(795\) 3.52309e15i 0.393464i
\(796\) 1.32551e13 3.71974e14i 0.00147015 0.0412564i
\(797\) 2.83110e14i 0.0311842i 0.999878 + 0.0155921i \(0.00496331\pi\)
−0.999878 + 0.0155921i \(0.995037\pi\)
\(798\) 4.82274e15 5.69016e15i 0.527568 0.622456i
\(799\) 2.04134e15i 0.221772i
\(800\) 4.18358e15 3.49776e15i 0.451392 0.377394i
\(801\) 3.73727e15i 0.400476i
\(802\) 1.65249e15 1.59466e15i 0.175865 0.169710i
\(803\) 3.11378e15 0.329119
\(804\) −7.31787e15 2.60768e14i −0.768204 0.0273745i
\(805\) 4.58915e14 4.61069e13i 0.0478470 0.00480716i
\(806\) −5.23887e15 5.42888e15i −0.542494 0.562169i
\(807\) 9.55497e15i 0.982709i
\(808\) −9.02309e15 + 8.10698e15i −0.921707 + 0.828126i
\(809\) 1.24272e16 1.26083 0.630416 0.776258i \(-0.282884\pi\)
0.630416 + 0.776258i \(0.282884\pi\)
\(810\) −4.91235e14 5.09051e14i −0.0495018 0.0512972i
\(811\) −1.07557e16 −1.07653 −0.538263 0.842777i \(-0.680919\pi\)
−0.538263 + 0.842777i \(0.680919\pi\)
\(812\) 6.48341e14 + 1.00357e16i 0.0644533 + 0.997674i
\(813\) 4.65796e15 0.459936
\(814\) −8.01572e15 8.30644e15i −0.786155 0.814668i
\(815\) −1.35186e15 −0.131694
\(816\) 4.30597e14 6.03419e15i 0.0416653 0.583880i
\(817\) 1.93601e16i 1.86074i
\(818\) −9.19267e15 9.52608e15i −0.877604 0.909434i
\(819\) 4.55361e14 + 4.53234e15i 0.0431812 + 0.429795i
\(820\) 3.02658e14 8.49341e15i 0.0285086 0.800029i
\(821\) 1.66989e16 1.56243 0.781214 0.624263i \(-0.214601\pi\)
0.781214 + 0.624263i \(0.214601\pi\)
\(822\) −5.04179e14 + 4.86533e14i −0.0468587 + 0.0452186i
\(823\) 4.63913e15i 0.428289i 0.976802 + 0.214145i \(0.0686964\pi\)
−0.976802 + 0.214145i \(0.931304\pi\)
\(824\) 6.70390e15 + 7.46146e15i 0.614791 + 0.684265i
\(825\) 2.84288e15i 0.258978i
\(826\) 6.36045e15 7.50444e15i 0.575569 0.679091i
\(827\) 2.17176e15i 0.195223i −0.995225 0.0976117i \(-0.968880\pi\)
0.995225 0.0976117i \(-0.0311203\pi\)
\(828\) −2.79610e14 9.96375e12i −0.0249681 0.000889725i
\(829\) 6.24017e15i 0.553537i 0.960937 + 0.276768i \(0.0892635\pi\)
−0.960937 + 0.276768i \(0.910737\pi\)
\(830\) 5.48361e15 + 5.68249e15i 0.483211 + 0.500737i
\(831\) 7.39114e15 0.647002
\(832\) −1.48169e16 1.58936e15i −1.28848 0.138211i
\(833\) −2.33473e15 1.15018e16i −0.201692 0.993617i
\(834\) 4.83181e14 4.66270e14i 0.0414664 0.0400151i
\(835\) 8.14172e15i 0.694129i
\(836\) 1.27132e16 + 4.53029e14i 1.07677 + 0.0383700i
\(837\) −1.37889e15 −0.116021
\(838\) 5.19026e15 5.00860e15i 0.433857 0.418673i
\(839\) 9.67165e15 0.803175 0.401587 0.915821i \(-0.368459\pi\)
0.401587 + 0.915821i \(0.368459\pi\)
\(840\) 3.02309e15 3.31954e15i 0.249411 0.273868i
\(841\) −6.01842e12 −0.000493293
\(842\) −8.71693e15 + 8.41184e15i −0.709818 + 0.684974i
\(843\) −2.25369e15 −0.182323
\(844\) 1.14733e16 + 4.08845e14i 0.922158 + 0.0328606i
\(845\) 5.45787e15i 0.435824i
\(846\) 6.61332e14 6.38186e14i 0.0524665 0.0506302i
\(847\) 5.28640e15 5.31121e14i 0.416679 0.0418634i
\(848\) −1.35297e16 9.65469e14i −1.05952 0.0756068i
\(849\) 1.08581e16 0.844812
\(850\) 5.35863e15 + 5.55298e15i 0.414237 + 0.429261i
\(851\) 1.44918e15i 0.111303i
\(852\) 3.10255e15 + 1.10558e14i 0.236756 + 0.00843667i
\(853\) 1.74669e16i 1.32433i 0.749358 + 0.662165i \(0.230362\pi\)
−0.749358 + 0.662165i \(0.769638\pi\)
\(854\) −1.97246e15 1.67178e15i −0.148590 0.125939i
\(855\) 4.03804e15i 0.302244i
\(856\) −1.53109e16 + 1.37564e16i −1.13866 + 1.02306i
\(857\) 2.51032e16i 1.85496i 0.373873 + 0.927480i \(0.378029\pi\)
−0.373873 + 0.927480i \(0.621971\pi\)
\(858\) −5.59034e15 + 5.39468e15i −0.410448 + 0.396082i
\(859\) −1.76987e16 −1.29115 −0.645577 0.763695i \(-0.723383\pi\)
−0.645577 + 0.763695i \(0.723383\pi\)
\(860\) 4.15000e14 1.16460e16i 0.0300820 0.844184i
\(861\) 9.99857e14 + 9.95186e15i 0.0720146 + 0.716782i
\(862\) −1.28368e16 1.33024e16i −0.918686 0.952006i
\(863\) 2.26334e16i 1.60950i 0.593615 + 0.804749i \(0.297700\pi\)
−0.593615 + 0.804749i \(0.702300\pi\)
\(864\) −2.08952e15 + 1.74698e15i −0.147646 + 0.123442i
\(865\) −3.17644e15 −0.223024
\(866\) −1.08705e15 1.12648e15i −0.0758405 0.0785912i
\(867\) 2.32807e14 0.0161395
\(868\) −5.64197e14 8.73322e15i −0.0388662 0.601611i
\(869\) −2.11870e16 −1.45031
\(870\) −3.78052e15 3.91764e15i −0.257156 0.266482i
\(871\) −2.55256e16 −1.72534
\(872\) −8.48682e15 9.44586e15i −0.570039 0.634455i
\(873\) 3.37641e15i 0.225360i
\(874\) 1.10900e15 + 1.14923e15i 0.0735563 + 0.0762241i
\(875\) 1.54562e15 + 1.53840e16i 0.101873 + 1.01397i
\(876\) 3.80293e15 + 1.35515e14i 0.249084 + 0.00887595i
\(877\) 7.99857e15 0.520612 0.260306 0.965526i \(-0.416177\pi\)
0.260306 + 0.965526i \(0.416177\pi\)
\(878\) −3.16798e14 + 3.05710e14i −0.0204910 + 0.0197738i
\(879\) 5.88077e15i 0.378003i
\(880\) 7.63794e15 + 5.45039e14i 0.487889 + 0.0348155i
\(881\) 4.50306e15i 0.285851i −0.989733 0.142926i \(-0.954349\pi\)
0.989733 0.142926i \(-0.0456510\pi\)
\(882\) −2.99634e15 + 4.35221e15i −0.189023 + 0.274557i
\(883\) 3.45453e15i 0.216573i 0.994120 + 0.108287i \(0.0345364\pi\)
−0.994120 + 0.108287i \(0.965464\pi\)
\(884\) 7.50986e14 2.10747e16i 0.0467891 1.31303i
\(885\) 5.32555e15i 0.329744i
\(886\) −7.46878e15 7.73966e15i −0.459583 0.476252i
\(887\) −4.50027e15 −0.275207 −0.137603 0.990487i \(-0.543940\pi\)
−0.137603 + 0.990487i \(0.543940\pi\)
\(888\) −9.42825e15 1.04937e16i −0.573007 0.637758i
\(889\) 6.99445e14 + 6.96178e15i 0.0422468 + 0.420495i
\(890\) −9.24014e15 + 8.91674e15i −0.554669 + 0.535255i
\(891\) 1.41990e15i 0.0847089i
\(892\) −1.02856e15 + 2.88642e16i −0.0609850 + 1.71141i
\(893\) −5.24601e15 −0.309133
\(894\) 9.50633e15 9.17361e15i 0.556745 0.537259i
\(895\) −2.78152e15 −0.161903
\(896\) −1.19195e16 1.25192e16i −0.689547 0.724241i
\(897\) −9.75313e14 −0.0560771
\(898\) −2.20553e16 + 2.12834e16i −1.26035 + 1.21624i
\(899\) −1.06119e16 −0.602716
\(900\) 1.23725e14 3.47207e15i 0.00698432 0.195999i
\(901\) 1.91949e16i 1.07696i
\(902\) −1.22749e16 + 1.18453e16i −0.684516 + 0.660558i
\(903\) 1.37099e15 + 1.36459e16i 0.0759892 + 0.756342i
\(904\) 1.81908e16 + 2.02464e16i 1.00213 + 1.11538i
\(905\) 6.17264e15 0.337990
\(906\) 9.38502e14 + 9.72540e14i 0.0510775 + 0.0529301i
\(907\) 3.48914e16i 1.88746i 0.330716 + 0.943730i \(0.392710\pi\)
−0.330716 + 0.943730i \(0.607290\pi\)
\(908\) 1.06444e14 2.98712e15i 0.00572334 0.160613i
\(909\) 7.72826e15i 0.413029i
\(910\) 1.01195e16 1.19395e16i 0.537563 0.634249i
\(911\) 1.76541e16i 0.932167i 0.884741 + 0.466084i \(0.154335\pi\)
−0.884741 + 0.466084i \(0.845665\pi\)
\(912\) 1.55072e16 + 1.10659e15i 0.813883 + 0.0580783i
\(913\) 1.58502e16i 0.826884i
\(914\) 1.30455e16 1.25889e16i 0.676483 0.652807i
\(915\) 1.39977e15 0.0721505
\(916\) 1.96376e16 + 6.99775e14i 1.00615 + 0.0358536i
\(917\) 3.30127e16 3.31677e15i 1.68132 0.168921i
\(918\) −2.67640e15 2.77347e15i −0.135493 0.140407i
\(919\) 1.41179e16i 0.710451i 0.934781 + 0.355226i \(0.115596\pi\)
−0.934781 + 0.355226i \(0.884404\pi\)
\(920\) 6.42486e14 + 7.15089e14i 0.0321389 + 0.0357707i
\(921\) −1.37596e16 −0.684190
\(922\) 2.01152e16 + 2.08448e16i 0.994272 + 1.03033i
\(923\) 1.08221e16 0.531742
\(924\) −8.99295e15 + 5.80977e14i −0.439245 + 0.0283768i
\(925\) 1.79952e16 0.873730
\(926\) 4.58721e15 + 4.75359e15i 0.221406 + 0.229436i
\(927\) 6.39073e15 0.306628
\(928\) −1.60808e16 + 1.34447e16i −0.766999 + 0.641263i
\(929\) 9.39791e15i 0.445600i −0.974864 0.222800i \(-0.928480\pi\)
0.974864 0.222800i \(-0.0715197\pi\)
\(930\) 3.28988e15 + 3.40920e15i 0.155068 + 0.160693i
\(931\) 2.95584e16 5.99999e15i 1.38503 0.281143i
\(932\) −8.14224e14 + 2.28494e16i −0.0379277 + 1.06436i
\(933\) 1.18451e16 0.548518
\(934\) −1.61158e13 + 1.55517e13i −0.000741896 + 0.000715930i
\(935\) 1.08362e16i 0.495920i
\(936\) −7.06237e15 + 6.34533e15i −0.321317 + 0.288693i
\(937\) 6.83842e15i 0.309306i 0.987969 + 0.154653i \(0.0494260\pi\)
−0.987969 + 0.154653i \(0.950574\pi\)
\(938\) −2.25877e16 1.91444e16i −1.01568 0.860846i
\(939\) 1.11606e16i 0.498916i
\(940\) −3.15574e15 1.12453e14i −0.140248 0.00499767i
\(941\) 1.73416e15i 0.0766205i −0.999266 0.0383103i \(-0.987802\pi\)
0.999266 0.0383103i \(-0.0121975\pi\)
\(942\) −7.12023e15 7.37848e15i −0.312762 0.324106i
\(943\) −2.14154e15 −0.0935215
\(944\) 2.04516e16 + 1.45942e15i 0.887936 + 0.0633626i
\(945\) −2.85955e14 2.84620e15i −0.0123431 0.122854i
\(946\) −1.68312e16 + 1.62421e16i −0.722295 + 0.697015i
\(947\) 1.15888e16i 0.494439i 0.968960 + 0.247219i \(0.0795168\pi\)
−0.968960 + 0.247219i \(0.920483\pi\)
\(948\) −2.58761e16 9.22080e14i −1.09762 0.0391131i
\(949\) 1.32651e16 0.559429
\(950\) −1.42705e16 + 1.37711e16i −0.598358 + 0.577415i
\(951\) 1.16320e16 0.484909
\(952\) 1.64708e16 1.80859e16i 0.682669 0.749611i
\(953\) 8.72826e15 0.359680 0.179840 0.983696i \(-0.442442\pi\)
0.179840 + 0.983696i \(0.442442\pi\)
\(954\) −6.21857e15 + 6.00093e15i −0.254786 + 0.245868i
\(955\) −1.42188e16 −0.579222
\(956\) 1.92071e16 + 6.84436e14i 0.777937 + 0.0277213i
\(957\) 1.09275e16i 0.440052i
\(958\) 7.44885e15 7.18814e15i 0.298249 0.287810i
\(959\) −2.81896e15 + 2.83219e14i −0.112224 + 0.0112751i
\(960\) 9.30464e15 + 9.98078e14i 0.368305 + 0.0395069i
\(961\) −1.61739e16 −0.636554
\(962\) −3.41478e16 3.53863e16i −1.33629 1.38475i
\(963\) 1.31138e16i 0.510250i
\(964\) −1.32561e16 4.72375e14i −0.512854 0.0182753i
\(965\) 3.05978e16i 1.17704i
\(966\) −8.63058e14 7.31492e14i −0.0330115 0.0279792i
\(967\) 3.48013e16i 1.32358i −0.749690 0.661790i \(-0.769797\pi\)
0.749690 0.661790i \(-0.230203\pi\)
\(968\) 7.40102e15 + 8.23736e15i 0.279883 + 0.311511i
\(969\) 2.20005e16i 0.827279i
\(970\) −8.34794e15 + 8.05577e15i −0.312130 + 0.301205i
\(971\) −1.59839e16 −0.594262 −0.297131 0.954837i \(-0.596030\pi\)
−0.297131 + 0.954837i \(0.596030\pi\)
\(972\) −6.17953e13 + 1.73415e15i −0.00228450 + 0.0641093i
\(973\) 2.70155e15 2.71423e14i 0.0993099 0.00997760i
\(974\) −3.32444e16 3.44501e16i −1.21519 1.25926i
\(975\) 1.21110e16i 0.440204i
\(976\) 3.83592e14 5.37549e15i 0.0138642 0.194287i
\(977\) −1.92350e16 −0.691310 −0.345655 0.938362i \(-0.612343\pi\)
−0.345655 + 0.938362i \(0.612343\pi\)
\(978\) 2.30264e15 + 2.38615e15i 0.0822928 + 0.0852775i
\(979\) 2.57735e16 0.915944
\(980\) 1.79095e16 2.97568e15i 0.632906 0.105158i
\(981\) −8.09036e15 −0.284308
\(982\) 1.95801e16 + 2.02902e16i 0.684229 + 0.709045i
\(983\) −1.79838e16 −0.624937 −0.312469 0.949928i \(-0.601156\pi\)
−0.312469 + 0.949928i \(0.601156\pi\)
\(984\) −1.55072e16 + 1.39327e16i −0.535870 + 0.481463i
\(985\) 3.57703e15i 0.122920i
\(986\) −2.05975e16 2.13445e16i −0.703867 0.729396i
\(987\) 3.69763e15 3.71498e14i 0.125655 0.0126244i
\(988\) 5.41598e16 + 1.92995e15i 1.83026 + 0.0652204i
\(989\) −2.93645e15 −0.0986831
\(990\) 3.51059e15 3.38772e15i 0.117324 0.113218i
\(991\) 1.42077e15i 0.0472193i 0.999721 + 0.0236097i \(0.00751588\pi\)
−0.999721 + 0.0236097i \(0.992484\pi\)
\(992\) 1.39938e16 1.16998e16i 0.462511 0.386691i
\(993\) 3.08359e16i 1.01353i
\(994\) 9.57649e15 + 8.11663e15i 0.313027 + 0.265308i
\(995\) 8.14791e14i 0.0264862i
\(996\) 6.89816e14 1.93581e16i 0.0223001 0.625802i
\(997\) 5.05628e16i 1.62558i −0.582558 0.812789i \(-0.697948\pi\)
0.582558 0.812789i \(-0.302052\pi\)
\(998\) −1.38233e16 1.43247e16i −0.441971 0.458001i
\(999\) −8.98781e15 −0.285788
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 84.12.b.a.55.12 yes 44
4.3 odd 2 84.12.b.b.55.11 yes 44
7.6 odd 2 84.12.b.b.55.12 yes 44
28.27 even 2 inner 84.12.b.a.55.11 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.12.b.a.55.11 44 28.27 even 2 inner
84.12.b.a.55.12 yes 44 1.1 even 1 trivial
84.12.b.b.55.11 yes 44 4.3 odd 2
84.12.b.b.55.12 yes 44 7.6 odd 2