Properties

Label 8.22.b.a.5.16
Level $8$
Weight $22$
Character 8.5
Analytic conductor $22.358$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8,22,Mod(5,8)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 22, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8.5");
 
S:= CuspForms(chi, 22);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 8.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: \(22.3581875430\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 10 x^{19} + 8499037025 x^{18} - 76491332940 x^{17} + \cdots + 35\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{190}\cdot 3^{14}\cdot 5^{4}\cdot 7^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.16
Root \(0.500000 + 44665.4i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.22.b.a.5.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1174.53 + 847.130i) q^{2} -178662. i q^{3} +(661894. + 1.98996e6i) q^{4} +3.12530e7i q^{5} +(1.51350e8 - 2.09844e8i) q^{6} +2.98846e8 q^{7} +(-9.08340e8 + 2.89798e9i) q^{8} -2.14596e10 q^{9} +O(q^{10})\) \(q+(1174.53 + 847.130i) q^{2} -178662. i q^{3} +(661894. + 1.98996e6i) q^{4} +3.12530e7i q^{5} +(1.51350e8 - 2.09844e8i) q^{6} +2.98846e8 q^{7} +(-9.08340e8 + 2.89798e9i) q^{8} -2.14596e10 q^{9} +(-2.64753e10 + 3.67076e10i) q^{10} -1.69327e10i q^{11} +(3.55530e11 - 1.18255e11i) q^{12} +5.06807e11i q^{13} +(3.51004e11 + 2.53161e11i) q^{14} +5.58370e12 q^{15} +(-3.52184e12 + 2.63429e12i) q^{16} +9.27906e12 q^{17} +(-2.52050e13 - 1.81791e13i) q^{18} +5.18928e13i q^{19} +(-6.21921e13 + 2.06861e13i) q^{20} -5.33923e13i q^{21} +(1.43442e13 - 1.98880e13i) q^{22} +2.52326e14 q^{23} +(5.17758e14 + 1.62285e14i) q^{24} -4.99910e14 q^{25} +(-4.29332e14 + 5.95261e14i) q^{26} +1.96515e15i q^{27} +(1.97804e14 + 5.94691e14i) q^{28} -3.59359e14i q^{29} +(6.55823e15 + 4.73012e15i) q^{30} +7.41345e14 q^{31} +(-6.36809e15 + 1.10596e14i) q^{32} -3.02522e15 q^{33} +(1.08985e16 + 7.86057e15i) q^{34} +9.33981e15i q^{35} +(-1.42040e16 - 4.27038e16i) q^{36} -3.56134e16i q^{37} +(-4.39599e16 + 6.09497e16i) q^{38} +9.05470e16 q^{39} +(-9.05704e16 - 2.83883e16i) q^{40} -4.38833e16 q^{41} +(4.52302e16 - 6.27109e16i) q^{42} +6.67420e16i q^{43} +(3.36954e16 - 1.12077e16i) q^{44} -6.70677e17i q^{45} +(2.96364e17 + 2.13752e17i) q^{46} -1.54355e17 q^{47} +(4.70646e17 + 6.29218e17i) q^{48} -4.69237e17 q^{49} +(-5.87160e17 - 4.23489e17i) q^{50} -1.65781e18i q^{51} +(-1.00853e18 + 3.35453e17i) q^{52} +1.64102e18i q^{53} +(-1.66474e18 + 2.30813e18i) q^{54} +5.29197e17 q^{55} +(-2.71454e17 + 8.66049e17i) q^{56} +9.27125e18 q^{57} +(3.04424e17 - 4.22079e17i) q^{58} -4.37549e18i q^{59} +(3.69582e18 + 1.11114e19i) q^{60} +3.59042e17i q^{61} +(8.70733e17 + 6.28016e17i) q^{62} -6.41312e18 q^{63} +(-7.57321e18 - 5.26470e18i) q^{64} -1.58392e19 q^{65} +(-3.55322e18 - 2.56276e18i) q^{66} -1.04612e19i q^{67} +(6.14176e18 + 1.84650e19i) q^{68} -4.50809e19i q^{69} +(-7.91203e18 + 1.09699e19i) q^{70} +2.52620e19 q^{71} +(1.94926e19 - 6.21896e19i) q^{72} -9.66939e18 q^{73} +(3.01692e19 - 4.18291e19i) q^{74} +8.93147e19i q^{75} +(-1.03265e20 + 3.43475e19i) q^{76} -5.06027e18i q^{77} +(1.06350e20 + 7.67051e19i) q^{78} -5.47438e19 q^{79} +(-8.23292e19 - 1.10068e20i) q^{80} +1.26622e20 q^{81} +(-5.15423e19 - 3.71749e19i) q^{82} +1.31783e20i q^{83} +(1.06249e20 - 3.53400e19i) q^{84} +2.89998e20i q^{85} +(-5.65391e19 + 7.83905e19i) q^{86} -6.42038e19 q^{87} +(4.90706e19 + 1.53806e19i) q^{88} -2.00107e20 q^{89} +(5.68150e20 - 7.87731e20i) q^{90} +1.51457e20i q^{91} +(1.67013e20 + 5.02118e20i) q^{92} -1.32450e20i q^{93} +(-1.81295e20 - 1.30759e20i) q^{94} -1.62180e21 q^{95} +(1.97593e19 + 1.13773e21i) q^{96} +1.40141e21 q^{97} +(-5.51133e20 - 3.97505e20i) q^{98} +3.63370e20i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 286 q^{2} + 409876 q^{4} + 118236748 q^{6} + 564950496 q^{7} + 3649699336 q^{8} - 62762119220 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 286 q^{2} + 409876 q^{4} + 118236748 q^{6} + 564950496 q^{7} + 3649699336 q^{8} - 62762119220 q^{9} - 51269339528 q^{10} + 65316900136 q^{12} - 1924309104464 q^{14} - 2285680856096 q^{15} + 7793508571920 q^{16} + 1740714497000 q^{17} - 41325344023822 q^{18} - 78999934156016 q^{20} + 294957216952508 q^{22} + 335749622520224 q^{23} + 786737698607504 q^{24} - 16\!\cdots\!04 q^{25}+ \cdots + 13\!\cdots\!30 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1174.53 + 847.130i 0.811054 + 0.584972i
\(3\) 178662.i 1.74686i −0.486949 0.873430i \(-0.661890\pi\)
0.486949 0.873430i \(-0.338110\pi\)
\(4\) 661894. + 1.98996e6i 0.315616 + 0.948887i
\(5\) 3.12530e7i 1.43122i 0.698501 + 0.715609i \(0.253851\pi\)
−0.698501 + 0.715609i \(0.746149\pi\)
\(6\) 1.51350e8 2.09844e8i 1.02186 1.41680i
\(7\) 2.98846e8 0.399869 0.199934 0.979809i \(-0.435927\pi\)
0.199934 + 0.979809i \(0.435927\pi\)
\(8\) −9.08340e8 + 2.89798e9i −0.299091 + 0.954225i
\(9\) −2.14596e10 −2.05152
\(10\) −2.64753e10 + 3.67076e10i −0.837223 + 1.16079i
\(11\) 1.69327e10i 0.196835i −0.995145 0.0984177i \(-0.968622\pi\)
0.995145 0.0984177i \(-0.0313781\pi\)
\(12\) 3.55530e11 1.18255e11i 1.65757 0.551337i
\(13\) 5.06807e11i 1.01962i 0.860288 + 0.509809i \(0.170284\pi\)
−0.860288 + 0.509809i \(0.829716\pi\)
\(14\) 3.51004e11 + 2.53161e11i 0.324315 + 0.233912i
\(15\) 5.58370e12 2.50014
\(16\) −3.52184e12 + 2.63429e12i −0.800773 + 0.598967i
\(17\) 9.27906e12 1.11632 0.558162 0.829732i \(-0.311507\pi\)
0.558162 + 0.829732i \(0.311507\pi\)
\(18\) −2.52050e13 1.81791e13i −1.66389 1.20008i
\(19\) 5.18928e13i 1.94175i 0.239577 + 0.970877i \(0.422991\pi\)
−0.239577 + 0.970877i \(0.577009\pi\)
\(20\) −6.21921e13 + 2.06861e13i −1.35806 + 0.451715i
\(21\) 5.33923e13i 0.698515i
\(22\) 1.43442e13 1.98880e13i 0.115143 0.159644i
\(23\) 2.52326e14 1.27004 0.635022 0.772494i \(-0.280991\pi\)
0.635022 + 0.772494i \(0.280991\pi\)
\(24\) 5.17758e14 + 1.62285e14i 1.66690 + 0.522470i
\(25\) −4.99910e14 −1.04839
\(26\) −4.29332e14 + 5.95261e14i −0.596448 + 0.826965i
\(27\) 1.96515e15i 1.83686i
\(28\) 1.97804e14 + 5.94691e14i 0.126205 + 0.379431i
\(29\) 3.59359e14i 0.158617i −0.996850 0.0793086i \(-0.974729\pi\)
0.996850 0.0793086i \(-0.0252712\pi\)
\(30\) 6.55823e15 + 4.73012e15i 2.02775 + 1.46251i
\(31\) 7.41345e14 0.162451 0.0812256 0.996696i \(-0.474117\pi\)
0.0812256 + 0.996696i \(0.474117\pi\)
\(32\) −6.36809e15 + 1.10596e14i −0.999849 + 0.0173646i
\(33\) −3.02522e15 −0.343844
\(34\) 1.08985e16 + 7.86057e15i 0.905399 + 0.653019i
\(35\) 9.33981e15i 0.572300i
\(36\) −1.42040e16 4.27038e16i −0.647492 1.94666i
\(37\) 3.56134e16i 1.21757i −0.793334 0.608787i \(-0.791656\pi\)
0.793334 0.608787i \(-0.208344\pi\)
\(38\) −4.39599e16 + 6.09497e16i −1.13587 + 1.57487i
\(39\) 9.05470e16 1.78113
\(40\) −9.05704e16 2.83883e16i −1.36570 0.428065i
\(41\) −4.38833e16 −0.510586 −0.255293 0.966864i \(-0.582172\pi\)
−0.255293 + 0.966864i \(0.582172\pi\)
\(42\) 4.52302e16 6.27109e16i 0.408612 0.566533i
\(43\) 6.67420e16i 0.470956i 0.971880 + 0.235478i \(0.0756655\pi\)
−0.971880 + 0.235478i \(0.924334\pi\)
\(44\) 3.36954e16 1.12077e16i 0.186774 0.0621243i
\(45\) 6.70677e17i 2.93618i
\(46\) 2.96364e17 + 2.13752e17i 1.03007 + 0.742940i
\(47\) −1.54355e17 −0.428048 −0.214024 0.976828i \(-0.568657\pi\)
−0.214024 + 0.976828i \(0.568657\pi\)
\(48\) 4.70646e17 + 6.29218e17i 1.04631 + 1.39884i
\(49\) −4.69237e17 −0.840105
\(50\) −5.87160e17 4.23489e17i −0.850298 0.613277i
\(51\) 1.65781e18i 1.95006i
\(52\) −1.00853e18 + 3.35453e17i −0.967503 + 0.321808i
\(53\) 1.64102e18i 1.28890i 0.764648 + 0.644448i \(0.222913\pi\)
−0.764648 + 0.644448i \(0.777087\pi\)
\(54\) −1.66474e18 + 2.30813e18i −1.07451 + 1.48979i
\(55\) 5.29197e17 0.281714
\(56\) −2.71454e17 + 8.66049e17i −0.119597 + 0.381565i
\(57\) 9.27125e18 3.39197
\(58\) 3.04424e17 4.22079e17i 0.0927866 0.128647i
\(59\) 4.37549e18i 1.11450i −0.830344 0.557251i \(-0.811856\pi\)
0.830344 0.557251i \(-0.188144\pi\)
\(60\) 3.69582e18 + 1.11114e19i 0.789083 + 2.37235i
\(61\) 3.59042e17i 0.0644439i 0.999481 + 0.0322219i \(0.0102583\pi\)
−0.999481 + 0.0322219i \(0.989742\pi\)
\(62\) 8.70733e17 + 6.28016e17i 0.131757 + 0.0950294i
\(63\) −6.41312e18 −0.820340
\(64\) −7.57321e18 5.26470e18i −0.821089 0.570800i
\(65\) −1.58392e19 −1.45930
\(66\) −3.55322e18 2.56276e18i −0.278876 0.201139i
\(67\) 1.04612e19i 0.701127i −0.936539 0.350564i \(-0.885990\pi\)
0.936539 0.350564i \(-0.114010\pi\)
\(68\) 6.14176e18 + 1.84650e19i 0.352330 + 1.05927i
\(69\) 4.50809e19i 2.21859i
\(70\) −7.91203e18 + 1.09699e19i −0.334779 + 0.464166i
\(71\) 2.52620e19 0.920989 0.460494 0.887663i \(-0.347672\pi\)
0.460494 + 0.887663i \(0.347672\pi\)
\(72\) 1.94926e19 6.21896e19i 0.613592 1.95761i
\(73\) −9.66939e18 −0.263335 −0.131668 0.991294i \(-0.542033\pi\)
−0.131668 + 0.991294i \(0.542033\pi\)
\(74\) 3.01692e19 4.18291e19i 0.712247 0.987518i
\(75\) 8.93147e19i 1.83139i
\(76\) −1.03265e20 + 3.43475e19i −1.84251 + 0.612848i
\(77\) 5.06027e18i 0.0787083i
\(78\) 1.06350e20 + 7.67051e19i 1.44459 + 1.04191i
\(79\) −5.47438e19 −0.650505 −0.325253 0.945627i \(-0.605449\pi\)
−0.325253 + 0.945627i \(0.605449\pi\)
\(80\) −8.23292e19 1.10068e20i −0.857253 1.14608i
\(81\) 1.26622e20 1.15722
\(82\) −5.15423e19 3.71749e19i −0.414113 0.298679i
\(83\) 1.31783e20i 0.932264i 0.884715 + 0.466132i \(0.154353\pi\)
−0.884715 + 0.466132i \(0.845647\pi\)
\(84\) 1.06249e20 3.53400e19i 0.662812 0.220462i
\(85\) 2.89998e20i 1.59770i
\(86\) −5.65391e19 + 7.83905e19i −0.275496 + 0.381970i
\(87\) −6.42038e19 −0.277082
\(88\) 4.90706e19 + 1.53806e19i 0.187825 + 0.0588717i
\(89\) −2.00107e20 −0.680247 −0.340123 0.940381i \(-0.610469\pi\)
−0.340123 + 0.940381i \(0.610469\pi\)
\(90\) 5.68150e20 7.87731e20i 1.71758 2.38140i
\(91\) 1.51457e20i 0.407714i
\(92\) 1.67013e20 + 5.02118e20i 0.400846 + 1.20513i
\(93\) 1.32450e20i 0.283779i
\(94\) −1.81295e20 1.30759e20i −0.347170 0.250396i
\(95\) −1.62180e21 −2.77908
\(96\) 1.97593e19 + 1.13773e21i 0.0303335 + 1.74660i
\(97\) 1.40141e21 1.92957 0.964786 0.263036i \(-0.0847238\pi\)
0.964786 + 0.263036i \(0.0847238\pi\)
\(98\) −5.51133e20 3.97505e20i −0.681370 0.491438i
\(99\) 3.63370e20i 0.403812i
\(100\) −3.30887e20 9.94801e20i −0.330887 0.994801i
\(101\) 7.48916e20i 0.674619i −0.941394 0.337310i \(-0.890483\pi\)
0.941394 0.337310i \(-0.109517\pi\)
\(102\) 1.40438e21 1.94715e21i 1.14073 1.58161i
\(103\) 1.85952e21 1.36336 0.681679 0.731651i \(-0.261250\pi\)
0.681679 + 0.731651i \(0.261250\pi\)
\(104\) −1.46872e21 4.60353e20i −0.972945 0.304959i
\(105\) 1.66867e21 0.999728
\(106\) −1.39016e21 + 1.92743e21i −0.753968 + 1.04536i
\(107\) 1.84717e21i 0.907773i −0.891060 0.453886i \(-0.850037\pi\)
0.891060 0.453886i \(-0.149963\pi\)
\(108\) −3.91057e21 + 1.30072e21i −1.74297 + 0.579742i
\(109\) 3.16859e21i 1.28200i −0.767540 0.641000i \(-0.778520\pi\)
0.767540 0.641000i \(-0.221480\pi\)
\(110\) 6.21558e20 + 4.48298e20i 0.228485 + 0.164795i
\(111\) −6.36275e21 −2.12693
\(112\) −1.05249e21 + 7.87245e20i −0.320204 + 0.239508i
\(113\) −1.05802e20 −0.0293203 −0.0146602 0.999893i \(-0.504667\pi\)
−0.0146602 + 0.999893i \(0.504667\pi\)
\(114\) 1.08894e22 + 7.85396e21i 2.75107 + 1.98421i
\(115\) 7.88592e21i 1.81771i
\(116\) 7.15111e20 2.37858e20i 0.150510 0.0500621i
\(117\) 1.08759e22i 2.09177i
\(118\) 3.70661e21 5.13915e21i 0.651952 0.903920i
\(119\) 2.77301e21 0.446384
\(120\) −5.07190e21 + 1.61815e22i −0.747769 + 2.38569i
\(121\) 7.11353e21 0.961256
\(122\) −3.04155e20 + 4.21706e20i −0.0376979 + 0.0522674i
\(123\) 7.84027e21i 0.891923i
\(124\) 4.90692e20 + 1.47525e21i 0.0512721 + 0.154148i
\(125\) 7.21089e20i 0.0692522i
\(126\) −7.53241e21 5.43275e21i −0.665339 0.479876i
\(127\) 2.41309e21 0.196171 0.0980855 0.995178i \(-0.468728\pi\)
0.0980855 + 0.995178i \(0.468728\pi\)
\(128\) −4.43508e21 1.25990e22i −0.332045 0.943263i
\(129\) 1.19242e22 0.822694
\(130\) −1.86037e22 1.34179e22i −1.18357 0.853648i
\(131\) 1.00194e22i 0.588154i −0.955782 0.294077i \(-0.904988\pi\)
0.955782 0.294077i \(-0.0950123\pi\)
\(132\) −2.00238e21 6.02008e21i −0.108523 0.326269i
\(133\) 1.55079e22i 0.776447i
\(134\) 8.86201e21 1.22870e22i 0.410140 0.568652i
\(135\) −6.14167e22 −2.62895
\(136\) −8.42854e21 + 2.68905e22i −0.333883 + 1.06522i
\(137\) 1.16848e22 0.428604 0.214302 0.976767i \(-0.431252\pi\)
0.214302 + 0.976767i \(0.431252\pi\)
\(138\) 3.81894e22 5.29489e22i 1.29781 1.79940i
\(139\) 2.54754e22i 0.802538i −0.915960 0.401269i \(-0.868569\pi\)
0.915960 0.401269i \(-0.131431\pi\)
\(140\) −1.85859e22 + 6.18197e21i −0.543048 + 0.180627i
\(141\) 2.75773e22i 0.747741i
\(142\) 2.96710e22 + 2.14002e22i 0.746971 + 0.538753i
\(143\) 8.58161e21 0.200697
\(144\) 7.55774e22 5.65308e22i 1.64280 1.22879i
\(145\) 1.12310e22 0.227016
\(146\) −1.13570e22 8.19122e21i −0.213579 0.154044i
\(147\) 8.38347e22i 1.46755i
\(148\) 7.08693e22 2.35723e22i 1.15534 0.384286i
\(149\) 3.66823e22i 0.557187i 0.960409 + 0.278594i \(0.0898683\pi\)
−0.960409 + 0.278594i \(0.910132\pi\)
\(150\) −7.56612e22 + 1.04903e23i −1.07131 + 1.48535i
\(151\) 3.98226e22 0.525862 0.262931 0.964815i \(-0.415311\pi\)
0.262931 + 0.964815i \(0.415311\pi\)
\(152\) −1.50384e23 4.71363e22i −1.85287 0.580761i
\(153\) −1.99125e23 −2.29016
\(154\) 4.28670e21 5.94344e21i 0.0460422 0.0638367i
\(155\) 2.31692e22i 0.232503i
\(156\) 5.99325e22 + 1.80185e23i 0.562153 + 1.69009i
\(157\) 1.00324e23i 0.879953i −0.898009 0.439977i \(-0.854987\pi\)
0.898009 0.439977i \(-0.145013\pi\)
\(158\) −6.42983e22 4.63751e22i −0.527595 0.380527i
\(159\) 2.93188e23 2.25152
\(160\) −3.45645e21 1.99022e23i −0.0248525 1.43100i
\(161\) 7.54064e22 0.507851
\(162\) 1.48721e23 + 1.07265e23i 0.938565 + 0.676940i
\(163\) 1.66045e23i 0.982326i 0.871068 + 0.491163i \(0.163428\pi\)
−0.871068 + 0.491163i \(0.836572\pi\)
\(164\) −2.90461e22 8.73261e22i −0.161149 0.484489i
\(165\) 9.45472e22i 0.492116i
\(166\) −1.11637e23 + 1.54783e23i −0.545348 + 0.756116i
\(167\) 3.63488e22 0.166712 0.0833561 0.996520i \(-0.473436\pi\)
0.0833561 + 0.996520i \(0.473436\pi\)
\(168\) 1.54730e23 + 4.84983e22i 0.666540 + 0.208920i
\(169\) −9.78904e21 −0.0396214
\(170\) −2.45666e23 + 3.40612e23i −0.934612 + 1.29582i
\(171\) 1.11360e24i 3.98355i
\(172\) −1.32814e23 + 4.41761e22i −0.446884 + 0.148641i
\(173\) 4.44315e23i 1.40672i 0.710835 + 0.703358i \(0.248317\pi\)
−0.710835 + 0.703358i \(0.751683\pi\)
\(174\) −7.54093e22 5.43889e22i −0.224728 0.162085i
\(175\) −1.49396e23 −0.419217
\(176\) 4.46056e22 + 5.96342e22i 0.117898 + 0.157620i
\(177\) −7.81732e23 −1.94688
\(178\) −2.35032e23 1.69516e23i −0.551717 0.397925i
\(179\) 3.32159e23i 0.735173i −0.929989 0.367587i \(-0.880184\pi\)
0.929989 0.367587i \(-0.119816\pi\)
\(180\) 1.33462e24 4.43917e23i 2.78610 0.926703i
\(181\) 2.07408e23i 0.408507i −0.978918 0.204254i \(-0.934523\pi\)
0.978918 0.204254i \(-0.0654768\pi\)
\(182\) −1.28304e23 + 1.77891e23i −0.238501 + 0.330678i
\(183\) 6.41470e22 0.112574
\(184\) −2.29197e23 + 7.31234e23i −0.379859 + 1.21191i
\(185\) 1.11302e24 1.74262
\(186\) 1.12202e23 1.55567e23i 0.166003 0.230160i
\(187\) 1.57120e23i 0.219732i
\(188\) −1.02167e23 3.07160e23i −0.135099 0.406170i
\(189\) 5.87277e23i 0.734504i
\(190\) −1.90486e24 1.37388e24i −2.25398 1.62568i
\(191\) 5.53919e23 0.620292 0.310146 0.950689i \(-0.399622\pi\)
0.310146 + 0.950689i \(0.399622\pi\)
\(192\) −9.40600e23 + 1.35304e24i −0.997108 + 1.43433i
\(193\) −4.76903e23 −0.478716 −0.239358 0.970931i \(-0.576937\pi\)
−0.239358 + 0.970931i \(0.576937\pi\)
\(194\) 1.64600e24 + 1.18717e24i 1.56499 + 1.12875i
\(195\) 2.82986e24i 2.54919i
\(196\) −3.10585e23 9.33763e23i −0.265150 0.797165i
\(197\) 1.38831e24i 1.12355i 0.827290 + 0.561775i \(0.189881\pi\)
−0.827290 + 0.561775i \(0.810119\pi\)
\(198\) −3.07821e23 + 4.26789e23i −0.236219 + 0.327513i
\(199\) 2.31118e24 1.68220 0.841099 0.540881i \(-0.181909\pi\)
0.841099 + 0.540881i \(0.181909\pi\)
\(200\) 4.54088e23 1.44873e24i 0.313563 1.00040i
\(201\) −1.86902e24 −1.22477
\(202\) 6.34429e23 8.79625e23i 0.394633 0.547152i
\(203\) 1.07393e23i 0.0634261i
\(204\) 3.29898e24 1.09730e24i 1.85039 0.615471i
\(205\) 1.37148e24i 0.730760i
\(206\) 2.18406e24 + 1.57526e24i 1.10576 + 0.797526i
\(207\) −5.41481e24 −2.60552
\(208\) −1.33508e24 1.78489e24i −0.610718 0.816483i
\(209\) 8.78685e23 0.382206
\(210\) 1.95990e24 + 1.41358e24i 0.810833 + 0.584813i
\(211\) 5.53529e23i 0.217858i 0.994050 + 0.108929i \(0.0347422\pi\)
−0.994050 + 0.108929i \(0.965258\pi\)
\(212\) −3.26557e24 + 1.08618e24i −1.22302 + 0.406796i
\(213\) 4.51334e24i 1.60884i
\(214\) 1.56479e24 2.16956e24i 0.531021 0.736252i
\(215\) −2.08588e24 −0.674041
\(216\) −5.69497e24 1.78502e24i −1.75278 0.549389i
\(217\) 2.21548e23 0.0649592
\(218\) 2.68421e24 3.72161e24i 0.749935 1.03977i
\(219\) 1.72755e24i 0.460010i
\(220\) 3.50272e23 + 1.05308e24i 0.0889135 + 0.267315i
\(221\) 4.70270e24i 1.13822i
\(222\) −7.47325e24 5.39008e24i −1.72506 1.24420i
\(223\) 3.17162e24 0.698361 0.349180 0.937056i \(-0.386460\pi\)
0.349180 + 0.937056i \(0.386460\pi\)
\(224\) −1.90308e24 + 3.30512e22i −0.399809 + 0.00694356i
\(225\) 1.07279e25 2.15079
\(226\) −1.24267e23 8.96277e22i −0.0237803 0.0171516i
\(227\) 9.35215e23i 0.170860i −0.996344 0.0854299i \(-0.972774\pi\)
0.996344 0.0854299i \(-0.0272264\pi\)
\(228\) 6.13659e24 + 1.84494e25i 1.07056 + 3.21860i
\(229\) 1.00652e25i 1.67707i −0.544850 0.838533i \(-0.683413\pi\)
0.544850 0.838533i \(-0.316587\pi\)
\(230\) −6.68040e24 + 9.26225e24i −1.06331 + 1.47426i
\(231\) −9.04075e23 −0.137492
\(232\) 1.04142e24 + 3.26420e23i 0.151356 + 0.0474410i
\(233\) 4.28113e24 0.594732 0.297366 0.954764i \(-0.403892\pi\)
0.297366 + 0.954764i \(0.403892\pi\)
\(234\) 9.21330e24 1.27741e25i 1.22363 1.69654i
\(235\) 4.82405e24i 0.612631i
\(236\) 8.70705e24 2.89611e24i 1.05754 0.351754i
\(237\) 9.78063e24i 1.13634i
\(238\) 3.25699e24 + 2.34910e24i 0.362041 + 0.261122i
\(239\) −1.01975e25 −1.08471 −0.542356 0.840149i \(-0.682468\pi\)
−0.542356 + 0.840149i \(0.682468\pi\)
\(240\) −1.96649e25 + 1.47091e25i −2.00205 + 1.49750i
\(241\) −7.47572e24 −0.728575 −0.364287 0.931287i \(-0.618687\pi\)
−0.364287 + 0.931287i \(0.618687\pi\)
\(242\) 8.35507e24 + 6.02609e24i 0.779630 + 0.562308i
\(243\) 2.06626e24i 0.184637i
\(244\) −7.14479e23 + 2.37648e23i −0.0611500 + 0.0203395i
\(245\) 1.46650e25i 1.20237i
\(246\) −6.64172e24 + 9.20864e24i −0.521750 + 0.723397i
\(247\) −2.62996e25 −1.97985
\(248\) −6.73393e23 + 2.14840e24i −0.0485877 + 0.155015i
\(249\) 2.35445e25 1.62854
\(250\) 6.10856e23 8.46942e23i 0.0405106 0.0561673i
\(251\) 1.08621e25i 0.690783i 0.938459 + 0.345391i \(0.112254\pi\)
−0.938459 + 0.345391i \(0.887746\pi\)
\(252\) −4.24481e24 1.27619e25i −0.258912 0.778410i
\(253\) 4.27255e24i 0.249990i
\(254\) 2.83425e24 + 2.04420e24i 0.159105 + 0.114755i
\(255\) 5.18116e25 2.79097
\(256\) 5.46389e24 1.85551e25i 0.282476 0.959274i
\(257\) −2.46308e25 −1.22231 −0.611153 0.791512i \(-0.709294\pi\)
−0.611153 + 0.791512i \(0.709294\pi\)
\(258\) 1.40054e25 + 1.01014e25i 0.667249 + 0.481253i
\(259\) 1.06429e25i 0.486870i
\(260\) −1.04839e25 3.15194e25i −0.460577 1.38471i
\(261\) 7.71172e24i 0.325406i
\(262\) 8.48770e24 1.17680e25i 0.344054 0.477025i
\(263\) 1.97728e25 0.770074 0.385037 0.922901i \(-0.374189\pi\)
0.385037 + 0.922901i \(0.374189\pi\)
\(264\) 2.74793e24 8.76704e24i 0.102841 0.328104i
\(265\) −5.12868e25 −1.84469
\(266\) −1.31372e25 + 1.82146e25i −0.454200 + 0.629740i
\(267\) 3.57514e25i 1.18830i
\(268\) 2.08174e25 6.92422e24i 0.665290 0.221287i
\(269\) 2.42083e25i 0.743987i 0.928235 + 0.371993i \(0.121326\pi\)
−0.928235 + 0.371993i \(0.878674\pi\)
\(270\) −7.21359e25 5.20279e25i −2.13222 1.53786i
\(271\) −1.14270e25 −0.324904 −0.162452 0.986716i \(-0.551940\pi\)
−0.162452 + 0.986716i \(0.551940\pi\)
\(272\) −3.26794e25 + 2.44437e25i −0.893923 + 0.668642i
\(273\) 2.70596e25 0.712219
\(274\) 1.37242e25 + 9.89856e24i 0.347621 + 0.250721i
\(275\) 8.46482e24i 0.206360i
\(276\) 8.97092e25 2.98388e25i 2.10519 0.700222i
\(277\) 7.54507e25i 1.70461i −0.523043 0.852307i \(-0.675203\pi\)
0.523043 0.852307i \(-0.324797\pi\)
\(278\) 2.15810e25 2.99217e25i 0.469462 0.650902i
\(279\) −1.59090e25 −0.333272
\(280\) −2.70666e25 8.48372e24i −0.546103 0.171170i
\(281\) −5.69982e25 −1.10776 −0.553879 0.832597i \(-0.686853\pi\)
−0.553879 + 0.832597i \(0.686853\pi\)
\(282\) −2.33616e25 + 3.23904e25i −0.437407 + 0.606458i
\(283\) 9.95326e24i 0.179559i −0.995962 0.0897797i \(-0.971384\pi\)
0.995962 0.0897797i \(-0.0286163\pi\)
\(284\) 1.67207e25 + 5.02703e25i 0.290679 + 0.873914i
\(285\) 2.89754e26i 4.85466i
\(286\) 1.00794e25 + 7.26974e24i 0.162776 + 0.117402i
\(287\) −1.31143e25 −0.204168
\(288\) 1.36657e26 2.37335e24i 2.05121 0.0356238i
\(289\) 1.70091e25 0.246181
\(290\) 1.31912e25 + 9.51415e24i 0.184122 + 0.132798i
\(291\) 2.50378e26i 3.37069i
\(292\) −6.40011e24 1.92417e25i −0.0831127 0.249875i
\(293\) 5.05103e25i 0.632805i −0.948625 0.316402i \(-0.897525\pi\)
0.948625 0.316402i \(-0.102475\pi\)
\(294\) −7.10189e25 + 9.84664e25i −0.858473 + 1.19026i
\(295\) 1.36747e26 1.59510
\(296\) 1.03207e26 + 3.23491e25i 1.16184 + 0.364166i
\(297\) 3.32753e25 0.361559
\(298\) −3.10747e25 + 4.30846e25i −0.325939 + 0.451909i
\(299\) 1.27880e26i 1.29496i
\(300\) −1.77733e26 + 5.91169e25i −1.73778 + 0.578014i
\(301\) 1.99456e25i 0.188321i
\(302\) 4.67729e25 + 3.37349e25i 0.426502 + 0.307614i
\(303\) −1.33803e26 −1.17847
\(304\) −1.36700e26 1.82758e26i −1.16305 1.55491i
\(305\) −1.12211e25 −0.0922333
\(306\) −2.33879e26 1.68685e26i −1.85745 1.33968i
\(307\) 3.58137e24i 0.0274850i 0.999906 + 0.0137425i \(0.00437452\pi\)
−0.999906 + 0.0137425i \(0.995625\pi\)
\(308\) 1.00697e25 3.34936e24i 0.0746853 0.0248416i
\(309\) 3.32225e26i 2.38160i
\(310\) −1.96273e25 + 2.72130e25i −0.136008 + 0.188572i
\(311\) 2.92172e26 1.95728 0.978642 0.205571i \(-0.0659051\pi\)
0.978642 + 0.205571i \(0.0659051\pi\)
\(312\) −8.22475e25 + 2.62403e26i −0.532720 + 1.69960i
\(313\) 6.40749e25 0.401303 0.200652 0.979663i \(-0.435694\pi\)
0.200652 + 0.979663i \(0.435694\pi\)
\(314\) 8.49877e25 1.17834e26i 0.514748 0.713689i
\(315\) 2.00429e26i 1.17409i
\(316\) −3.62346e25 1.08938e26i −0.205310 0.617256i
\(317\) 2.40904e26i 1.32045i −0.751069 0.660224i \(-0.770461\pi\)
0.751069 0.660224i \(-0.229539\pi\)
\(318\) 3.44358e26 + 2.48368e26i 1.82611 + 1.31708i
\(319\) −6.08493e24 −0.0312215
\(320\) 1.64537e26 2.36685e26i 0.816940 1.17516i
\(321\) −3.30018e26 −1.58575
\(322\) 8.85672e25 + 6.38790e25i 0.411895 + 0.297079i
\(323\) 4.81517e26i 2.16763i
\(324\) 8.38101e25 + 2.51972e26i 0.365236 + 1.09807i
\(325\) 2.53358e26i 1.06895i
\(326\) −1.40662e26 + 1.95025e26i −0.574633 + 0.796719i
\(327\) −5.66106e26 −2.23948
\(328\) 3.98610e25 1.27173e26i 0.152712 0.487214i
\(329\) −4.61283e25 −0.171163
\(330\) 8.00937e25 1.11049e26i 0.287874 0.399132i
\(331\) 1.09753e25i 0.0382140i −0.999817 0.0191070i \(-0.993918\pi\)
0.999817 0.0191070i \(-0.00608232\pi\)
\(332\) −2.62243e26 + 8.72263e25i −0.884614 + 0.294237i
\(333\) 7.64251e26i 2.49788i
\(334\) 4.26928e25 + 3.07922e25i 0.135213 + 0.0975220i
\(335\) 3.26944e26 1.00347
\(336\) 1.40651e26 + 1.88039e26i 0.418388 + 0.559352i
\(337\) 5.36457e26 1.54675 0.773377 0.633947i \(-0.218566\pi\)
0.773377 + 0.633947i \(0.218566\pi\)
\(338\) −1.14975e25 8.29258e24i −0.0321351 0.0231774i
\(339\) 1.89027e25i 0.0512185i
\(340\) −5.77085e26 + 1.91948e26i −1.51604 + 0.504261i
\(341\) 1.25530e25i 0.0319761i
\(342\) 9.43364e26 1.30796e27i 2.33027 3.23087i
\(343\) −3.07149e26 −0.735801
\(344\) −1.93417e26 6.06244e25i −0.449398 0.140859i
\(345\) 1.40891e27 3.17529
\(346\) −3.76392e26 + 5.21861e26i −0.822890 + 1.14092i
\(347\) 1.78294e26i 0.378161i 0.981962 + 0.189080i \(0.0605507\pi\)
−0.981962 + 0.189080i \(0.939449\pi\)
\(348\) −4.24961e25 1.27763e26i −0.0874514 0.262920i
\(349\) 5.73446e26i 1.14505i 0.819886 + 0.572527i \(0.194037\pi\)
−0.819886 + 0.572527i \(0.805963\pi\)
\(350\) −1.75470e26 1.26558e26i −0.340008 0.245230i
\(351\) −9.95952e26 −1.87290
\(352\) 1.87269e24 + 1.07829e26i 0.00341797 + 0.196806i
\(353\) −2.84034e26 −0.503195 −0.251597 0.967832i \(-0.580956\pi\)
−0.251597 + 0.967832i \(0.580956\pi\)
\(354\) −9.18169e26 6.62229e26i −1.57902 1.13887i
\(355\) 7.89511e26i 1.31814i
\(356\) −1.32449e26 3.98204e26i −0.214697 0.645478i
\(357\) 4.95430e26i 0.779770i
\(358\) 2.81382e26 3.90132e26i 0.430056 0.596265i
\(359\) −4.61851e26 −0.685504 −0.342752 0.939426i \(-0.611359\pi\)
−0.342752 + 0.939426i \(0.611359\pi\)
\(360\) 1.94361e27 + 6.09203e26i 2.80177 + 0.878184i
\(361\) −1.97865e27 −2.77041
\(362\) 1.75701e26 2.43607e26i 0.238965 0.331321i
\(363\) 1.27092e27i 1.67918i
\(364\) −3.01394e26 + 1.00249e26i −0.386874 + 0.128681i
\(365\) 3.02197e26i 0.376890i
\(366\) 7.53426e25 + 5.43408e25i 0.0913039 + 0.0658529i
\(367\) 1.47117e27 1.73249 0.866243 0.499623i \(-0.166528\pi\)
0.866243 + 0.499623i \(0.166528\pi\)
\(368\) −8.88650e26 + 6.64698e26i −1.01702 + 0.760715i
\(369\) 9.41720e26 1.04748
\(370\) 1.30728e27 + 9.42876e26i 1.41335 + 1.01938i
\(371\) 4.90413e26i 0.515390i
\(372\) 2.63570e26 8.76679e25i 0.269275 0.0895653i
\(373\) 1.34633e27i 1.33724i −0.743603 0.668621i \(-0.766885\pi\)
0.743603 0.668621i \(-0.233115\pi\)
\(374\) 1.33101e26 1.84542e26i 0.128537 0.178215i
\(375\) −1.28831e26 −0.120974
\(376\) 1.40207e26 4.47317e26i 0.128025 0.408454i
\(377\) 1.82126e26 0.161729
\(378\) −4.97500e26 + 6.89775e26i −0.429664 + 0.595722i
\(379\) 1.00783e27i 0.846597i 0.905990 + 0.423299i \(0.139128\pi\)
−0.905990 + 0.423299i \(0.860872\pi\)
\(380\) −1.07346e27 3.22732e27i −0.877120 2.63703i
\(381\) 4.31127e26i 0.342683i
\(382\) 6.50595e26 + 4.69242e26i 0.503090 + 0.362853i
\(383\) −2.67432e26 −0.201199 −0.100600 0.994927i \(-0.532076\pi\)
−0.100600 + 0.994927i \(0.532076\pi\)
\(384\) −2.25097e27 + 7.92379e26i −1.64775 + 0.580037i
\(385\) 1.58148e26 0.112649
\(386\) −5.60137e26 4.03998e26i −0.388264 0.280035i
\(387\) 1.43226e27i 0.966176i
\(388\) 9.27583e26 + 2.78874e27i 0.609003 + 1.83095i
\(389\) 1.00027e27i 0.639212i 0.947551 + 0.319606i \(0.103550\pi\)
−0.947551 + 0.319606i \(0.896450\pi\)
\(390\) −2.39726e27 + 3.32376e27i −1.49120 + 2.06753i
\(391\) 2.34134e27 1.41778
\(392\) 4.26227e26 1.35984e27i 0.251268 0.801649i
\(393\) −1.79008e27 −1.02742
\(394\) −1.17608e27 + 1.63062e27i −0.657245 + 0.911259i
\(395\) 1.71091e27i 0.931015i
\(396\) −7.23091e26 + 2.40512e26i −0.383172 + 0.127449i
\(397\) 4.09541e25i 0.0211347i 0.999944 + 0.0105674i \(0.00336376\pi\)
−0.999944 + 0.0105674i \(0.996636\pi\)
\(398\) 2.71456e27 + 1.95787e27i 1.36435 + 0.984039i
\(399\) 2.77068e27 1.35635
\(400\) 1.76060e27 1.31691e27i 0.839520 0.627950i
\(401\) −9.84276e26 −0.457195 −0.228597 0.973521i \(-0.573414\pi\)
−0.228597 + 0.973521i \(0.573414\pi\)
\(402\) −2.19522e27 1.58330e27i −0.993355 0.716457i
\(403\) 3.75719e26i 0.165638i
\(404\) 1.49031e27 4.95703e26i 0.640137 0.212920i
\(405\) 3.95730e27i 1.65623i
\(406\) 9.09759e25 1.26136e26i 0.0371025 0.0514419i
\(407\) −6.03031e26 −0.239662
\(408\) 4.80431e27 + 1.50586e27i 1.86080 + 0.583247i
\(409\) 3.41873e27 1.29054 0.645268 0.763956i \(-0.276746\pi\)
0.645268 + 0.763956i \(0.276746\pi\)
\(410\) 1.16182e27 1.61085e27i 0.427474 0.592686i
\(411\) 2.08763e27i 0.748711i
\(412\) 1.23081e27 + 3.70037e27i 0.430297 + 1.29367i
\(413\) 1.30760e27i 0.445655i
\(414\) −6.35987e27 4.58705e27i −2.11322 1.52416i
\(415\) −4.11860e27 −1.33427
\(416\) −5.60509e25 3.22739e27i −0.0177053 1.01946i
\(417\) −4.55148e27 −1.40192
\(418\) 1.03204e27 + 7.44360e26i 0.309989 + 0.223580i
\(419\) 1.46751e27i 0.429865i −0.976629 0.214933i \(-0.931047\pi\)
0.976629 0.214933i \(-0.0689532\pi\)
\(420\) 1.10448e27 + 3.32058e27i 0.315530 + 0.948629i
\(421\) 1.09266e27i 0.304455i 0.988345 + 0.152228i \(0.0486447\pi\)
−0.988345 + 0.152228i \(0.951355\pi\)
\(422\) −4.68911e26 + 6.50137e26i −0.127441 + 0.176695i
\(423\) 3.31240e27 0.878150
\(424\) −4.75565e27 1.49061e27i −1.22990 0.385498i
\(425\) −4.63870e27 −1.17034
\(426\) 3.82339e27 5.30106e27i 0.941126 1.30485i
\(427\) 1.07298e26i 0.0257691i
\(428\) 3.67579e27 1.22263e27i 0.861374 0.286507i
\(429\) 1.53321e27i 0.350589i
\(430\) −2.44993e27 1.76701e27i −0.546683 0.394295i
\(431\) −6.19140e27 −1.34827 −0.674136 0.738608i \(-0.735484\pi\)
−0.674136 + 0.738608i \(0.735484\pi\)
\(432\) −5.17677e27 6.92094e27i −1.10022 1.47091i
\(433\) −2.24766e26 −0.0466237 −0.0233119 0.999728i \(-0.507421\pi\)
−0.0233119 + 0.999728i \(0.507421\pi\)
\(434\) 2.60215e26 + 1.87680e26i 0.0526854 + 0.0379993i
\(435\) 2.00656e27i 0.396565i
\(436\) 6.30538e27 2.09727e27i 1.21647 0.404620i
\(437\) 1.30939e28i 2.46611i
\(438\) −1.46346e27 + 2.02906e27i −0.269093 + 0.373093i
\(439\) 6.04486e27 1.08520 0.542599 0.839992i \(-0.317440\pi\)
0.542599 + 0.839992i \(0.317440\pi\)
\(440\) −4.80691e26 + 1.53360e27i −0.0842583 + 0.268819i
\(441\) 1.00697e28 1.72349
\(442\) −3.98379e27 + 5.52346e27i −0.665830 + 0.923161i
\(443\) 1.14428e28i 1.86764i 0.357742 + 0.933820i \(0.383547\pi\)
−0.357742 + 0.933820i \(0.616453\pi\)
\(444\) −4.21147e27 1.26616e28i −0.671293 2.01822i
\(445\) 6.25393e27i 0.973582i
\(446\) 3.72516e27 + 2.68677e27i 0.566408 + 0.408521i
\(447\) 6.55373e27 0.973329
\(448\) −2.26322e27 1.57333e27i −0.328328 0.228245i
\(449\) 5.23182e27 0.741423 0.370712 0.928748i \(-0.379114\pi\)
0.370712 + 0.928748i \(0.379114\pi\)
\(450\) 1.26002e28 + 9.08791e27i 1.74440 + 1.25815i
\(451\) 7.43063e26i 0.100501i
\(452\) −7.00294e25 2.10541e26i −0.00925395 0.0278217i
\(453\) 7.11477e27i 0.918607i
\(454\) 7.92249e26 1.09844e27i 0.0999482 0.138577i
\(455\) −4.73348e27 −0.583527
\(456\) −8.42145e27 + 2.68679e28i −1.01451 + 3.23670i
\(457\) −1.46186e28 −1.72102 −0.860508 0.509438i \(-0.829853\pi\)
−0.860508 + 0.509438i \(0.829853\pi\)
\(458\) 8.52654e27 1.18219e28i 0.981037 1.36019i
\(459\) 1.82348e28i 2.05053i
\(460\) −1.56927e28 + 5.21964e27i −1.72480 + 0.573698i
\(461\) 9.86587e27i 1.05993i −0.848021 0.529963i \(-0.822206\pi\)
0.848021 0.529963i \(-0.177794\pi\)
\(462\) −1.06186e27 7.65869e26i −0.111514 0.0804292i
\(463\) −1.03281e28 −1.06028 −0.530138 0.847911i \(-0.677860\pi\)
−0.530138 + 0.847911i \(0.677860\pi\)
\(464\) 9.46656e26 + 1.26561e27i 0.0950065 + 0.127016i
\(465\) 4.13945e27 0.406150
\(466\) 5.02832e27 + 3.62667e27i 0.482360 + 0.347902i
\(467\) 3.56189e27i 0.334082i −0.985950 0.167041i \(-0.946579\pi\)
0.985950 0.167041i \(-0.0534213\pi\)
\(468\) 2.16426e28 7.19869e27i 1.98485 0.660195i
\(469\) 3.12629e27i 0.280359i
\(470\) 4.08659e27 5.66599e27i 0.358372 0.496876i
\(471\) −1.79241e28 −1.53716
\(472\) 1.26801e28 + 3.97443e27i 1.06348 + 0.333337i
\(473\) 1.13012e27 0.0927007
\(474\) −8.28546e27 + 1.14876e28i −0.664728 + 0.921634i
\(475\) 2.59417e28i 2.03571i
\(476\) 1.83544e27 + 5.51818e27i 0.140886 + 0.423568i
\(477\) 3.52158e28i 2.64420i
\(478\) −1.19772e28 8.63858e27i −0.879759 0.634526i
\(479\) 2.46990e28 1.77483 0.887415 0.460971i \(-0.152499\pi\)
0.887415 + 0.460971i \(0.152499\pi\)
\(480\) −3.55575e28 + 6.17535e26i −2.49976 + 0.0434139i
\(481\) 1.80491e28 1.24146
\(482\) −8.78046e27 6.33291e27i −0.590913 0.426196i
\(483\) 1.34722e28i 0.887145i
\(484\) 4.70841e27 + 1.41557e28i 0.303387 + 0.912123i
\(485\) 4.37981e28i 2.76164i
\(486\) 1.75039e27 2.42689e27i 0.108008 0.149751i
\(487\) −9.98326e27 −0.602862 −0.301431 0.953488i \(-0.597464\pi\)
−0.301431 + 0.953488i \(0.597464\pi\)
\(488\) −1.04050e27 3.26132e26i −0.0614939 0.0192746i
\(489\) 2.96659e28 1.71599
\(490\) 1.24232e28 1.72245e28i 0.703355 0.975189i
\(491\) 2.04646e28i 1.13409i 0.823687 + 0.567045i \(0.191914\pi\)
−0.823687 + 0.567045i \(0.808086\pi\)
\(492\) −1.56018e28 + 5.18943e27i −0.846334 + 0.281505i
\(493\) 3.33452e27i 0.177068i
\(494\) −3.08898e28 2.22792e28i −1.60576 1.15816i
\(495\) −1.13564e28 −0.577943
\(496\) −2.61090e27 + 1.95292e27i −0.130087 + 0.0973029i
\(497\) 7.54943e27 0.368275
\(498\) 2.76538e28 + 1.99453e28i 1.32083 + 0.952648i
\(499\) 2.44867e28i 1.14518i −0.819841 0.572591i \(-0.805938\pi\)
0.819841 0.572591i \(-0.194062\pi\)
\(500\) 1.43494e27 4.77285e26i 0.0657126 0.0218571i
\(501\) 6.49414e27i 0.291223i
\(502\) −9.20164e27 + 1.27579e28i −0.404088 + 0.560262i
\(503\) −3.35320e28 −1.44210 −0.721051 0.692882i \(-0.756341\pi\)
−0.721051 + 0.692882i \(0.756341\pi\)
\(504\) 5.82529e27 1.85851e28i 0.245356 0.782788i
\(505\) 2.34058e28 0.965528
\(506\) 3.61941e27 5.01825e27i 0.146237 0.202755i
\(507\) 1.74893e27i 0.0692130i
\(508\) 1.59721e27 + 4.80196e27i 0.0619146 + 0.186144i
\(509\) 1.11713e28i 0.424195i 0.977249 + 0.212097i \(0.0680294\pi\)
−0.977249 + 0.212097i \(0.931971\pi\)
\(510\) 6.08543e28 + 4.38911e28i 2.26362 + 1.63264i
\(511\) −2.88966e27 −0.105300
\(512\) 2.21361e28 1.71649e28i 0.790252 0.612782i
\(513\) −1.01977e29 −3.56673
\(514\) −2.89296e28 2.08655e28i −0.991356 0.715015i
\(515\) 5.81155e28i 1.95126i
\(516\) 7.89258e27 + 2.37287e28i 0.259655 + 0.780644i
\(517\) 2.61364e27i 0.0842550i
\(518\) 9.01593e27 1.25004e28i 0.284805 0.394878i
\(519\) 7.93820e28 2.45734
\(520\) 1.43874e28 4.59018e28i 0.436463 1.39250i
\(521\) −4.03710e28 −1.20025 −0.600127 0.799905i \(-0.704883\pi\)
−0.600127 + 0.799905i \(0.704883\pi\)
\(522\) −6.53283e27 + 9.05766e27i −0.190354 + 0.263922i
\(523\) 2.77341e28i 0.792038i −0.918242 0.396019i \(-0.870391\pi\)
0.918242 0.396019i \(-0.129609\pi\)
\(524\) 1.99381e28 6.63176e27i 0.558092 0.185631i
\(525\) 2.66913e28i 0.732314i
\(526\) 2.32237e28 + 1.67501e28i 0.624571 + 0.450471i
\(527\) 6.87899e27 0.181348
\(528\) 1.06544e28 7.96931e27i 0.275341 0.205951i
\(529\) 2.41966e28 0.613013
\(530\) −6.02380e28 4.34466e28i −1.49615 1.07909i
\(531\) 9.38964e28i 2.28642i
\(532\) −3.08602e28 + 1.02646e28i −0.736761 + 0.245059i
\(533\) 2.22404e28i 0.520603i
\(534\) −3.02861e28 + 4.19911e28i −0.695120 + 0.963772i
\(535\) 5.77295e28 1.29922
\(536\) 3.03164e28 + 9.50234e27i 0.669033 + 0.209701i
\(537\) −5.93442e28 −1.28425
\(538\) −2.05076e28 + 2.84334e28i −0.435211 + 0.603413i
\(539\) 7.94545e27i 0.165362i
\(540\) −4.06514e28 1.22217e29i −0.829738 2.49458i
\(541\) 1.63598e28i 0.327496i 0.986502 + 0.163748i \(0.0523584\pi\)
−0.986502 + 0.163748i \(0.947642\pi\)
\(542\) −1.34214e28 9.68017e27i −0.263515 0.190060i
\(543\) −3.70558e28 −0.713605
\(544\) −5.90899e28 + 1.02623e27i −1.11616 + 0.0193845i
\(545\) 9.90279e28 1.83482
\(546\) 3.17823e28 + 2.29230e28i 0.577648 + 0.416628i
\(547\) 6.66163e28i 1.18772i −0.804569 0.593859i \(-0.797604\pi\)
0.804569 0.593859i \(-0.202396\pi\)
\(548\) 7.73412e27 + 2.32523e28i 0.135274 + 0.406697i
\(549\) 7.70491e27i 0.132208i
\(550\) −7.17080e27 + 9.94220e27i −0.120715 + 0.167369i
\(551\) 1.86482e28 0.307996
\(552\) 1.30644e29 + 4.09488e28i 2.11703 + 0.663561i
\(553\) −1.63600e28 −0.260117
\(554\) 6.39166e28 8.86192e28i 0.997151 1.38253i
\(555\) 1.98855e29i 3.04411i
\(556\) 5.06951e28 1.68620e28i 0.761518 0.253294i
\(557\) 1.08955e29i 1.60608i 0.595925 + 0.803040i \(0.296786\pi\)
−0.595925 + 0.803040i \(0.703214\pi\)
\(558\) −1.86856e28 1.34770e28i −0.270301 0.194955i
\(559\) −3.38253e28 −0.480195
\(560\) −2.46037e28 3.28933e28i −0.342789 0.458283i
\(561\) −2.80712e28 −0.383841
\(562\) −6.69462e28 4.82849e28i −0.898452 0.648008i
\(563\) 8.28756e28i 1.09166i −0.837895 0.545832i \(-0.816214\pi\)
0.837895 0.545832i \(-0.183786\pi\)
\(564\) −5.48777e28 + 1.82532e28i −0.709521 + 0.235999i
\(565\) 3.30661e27i 0.0419638i
\(566\) 8.43171e27 1.16904e28i 0.105037 0.145632i
\(567\) 3.78403e28 0.462735
\(568\) −2.29464e28 + 7.32087e28i −0.275460 + 0.878830i
\(569\) −1.33952e29 −1.57860 −0.789298 0.614010i \(-0.789556\pi\)
−0.789298 + 0.614010i \(0.789556\pi\)
\(570\) −2.45459e29 + 3.40325e29i −2.83984 + 3.93739i
\(571\) 2.81406e28i 0.319635i −0.987147 0.159817i \(-0.948909\pi\)
0.987147 0.159817i \(-0.0510905\pi\)
\(572\) 5.68012e27 + 1.70771e28i 0.0633431 + 0.190439i
\(573\) 9.89642e28i 1.08356i
\(574\) −1.54032e28 1.11096e28i −0.165591 0.119432i
\(575\) −1.26140e29 −1.33150
\(576\) 1.62518e29 + 1.12979e29i 1.68448 + 1.17101i
\(577\) 4.95811e28 0.504627 0.252313 0.967646i \(-0.418809\pi\)
0.252313 + 0.967646i \(0.418809\pi\)
\(578\) 1.99777e28 + 1.44089e28i 0.199666 + 0.144009i
\(579\) 8.52042e28i 0.836250i
\(580\) 7.43376e27 + 2.23493e28i 0.0716498 + 0.215412i
\(581\) 3.93828e28i 0.372784i
\(582\) 2.12102e29 2.94076e29i 1.97176 2.73381i
\(583\) 2.77870e28 0.253700
\(584\) 8.78309e27 2.80217e28i 0.0787612 0.251281i
\(585\) 3.39904e29 2.99378
\(586\) 4.27888e28 5.93259e28i 0.370173 0.513239i
\(587\) 1.42608e29i 1.21184i 0.795526 + 0.605919i \(0.207194\pi\)
−0.795526 + 0.605919i \(0.792806\pi\)
\(588\) −1.66828e29 + 5.54897e28i −1.39254 + 0.463180i
\(589\) 3.84705e28i 0.315440i
\(590\) 1.60614e29 + 1.15842e29i 1.29371 + 0.933086i
\(591\) 2.48039e29 1.96269
\(592\) 9.38159e28 + 1.25425e29i 0.729287 + 0.975001i
\(593\) −1.13065e29 −0.863483 −0.431742 0.901997i \(-0.642101\pi\)
−0.431742 + 0.901997i \(0.642101\pi\)
\(594\) 3.90829e28 + 2.81885e28i 0.293244 + 0.211502i
\(595\) 8.66647e28i 0.638873i
\(596\) −7.29964e28 + 2.42798e28i −0.528708 + 0.175857i
\(597\) 4.12920e29i 2.93857i
\(598\) −1.08331e29 + 1.50199e29i −0.757516 + 1.05028i
\(599\) −8.35529e28 −0.574090 −0.287045 0.957917i \(-0.592673\pi\)
−0.287045 + 0.957917i \(0.592673\pi\)
\(600\) −2.58832e29 8.11281e28i −1.74755 0.547751i
\(601\) −1.31030e29 −0.869336 −0.434668 0.900591i \(-0.643134\pi\)
−0.434668 + 0.900591i \(0.643134\pi\)
\(602\) −1.68965e28 + 2.34267e28i −0.110162 + 0.152738i
\(603\) 2.24494e29i 1.43838i
\(604\) 2.63583e28 + 7.92454e28i 0.165970 + 0.498984i
\(605\) 2.22319e29i 1.37577i
\(606\) −1.57155e29 1.13348e29i −0.955799 0.689369i
\(607\) −5.68586e28 −0.339872 −0.169936 0.985455i \(-0.554356\pi\)
−0.169936 + 0.985455i \(0.554356\pi\)
\(608\) −5.73914e27 3.30458e29i −0.0337178 1.94146i
\(609\) −1.91870e28 −0.110796
\(610\) −1.31795e28 9.50574e27i −0.0748061 0.0539539i
\(611\) 7.82282e28i 0.436446i
\(612\) −1.31800e29 3.96252e29i −0.722812 2.17311i
\(613\) 2.41527e29i 1.30206i −0.759052 0.651030i \(-0.774337\pi\)
0.759052 0.651030i \(-0.225663\pi\)
\(614\) −3.03389e27 + 4.20643e27i −0.0160780 + 0.0222918i
\(615\) −2.45031e29 −1.27654
\(616\) 1.46646e28 + 4.59644e27i 0.0751054 + 0.0235410i
\(617\) 2.33971e29 1.17806 0.589032 0.808110i \(-0.299509\pi\)
0.589032 + 0.808110i \(0.299509\pi\)
\(618\) 2.81438e29 3.90209e29i 1.39317 1.93160i
\(619\) 6.73316e28i 0.327693i 0.986486 + 0.163847i \(0.0523902\pi\)
−0.986486 + 0.163847i \(0.947610\pi\)
\(620\) −4.61059e28 + 1.53356e28i −0.220619 + 0.0733816i
\(621\) 4.95857e29i 2.33289i
\(622\) 3.43165e29 + 2.47507e29i 1.58746 + 1.14496i
\(623\) −5.98010e28 −0.272010
\(624\) −3.18892e29 + 2.38527e29i −1.42628 + 1.06684i
\(625\) −2.15839e29 −0.949272
\(626\) 7.52580e28 + 5.42798e28i 0.325478 + 0.234751i
\(627\) 1.56987e29i 0.667660i
\(628\) 1.99641e29 6.64040e28i 0.834976 0.277727i
\(629\) 3.30459e29i 1.35921i
\(630\) 1.69789e29 2.35410e29i 0.686807 0.952246i
\(631\) −1.15456e29 −0.459312 −0.229656 0.973272i \(-0.573760\pi\)
−0.229656 + 0.973272i \(0.573760\pi\)
\(632\) 4.97260e28 1.58647e29i 0.194560 0.620728i
\(633\) 9.88943e28 0.380568
\(634\) 2.04077e29 2.82949e29i 0.772425 1.07095i
\(635\) 7.54162e28i 0.280764i
\(636\) 1.94059e29 + 5.83432e29i 0.710616 + 2.13644i
\(637\) 2.37813e29i 0.856586i
\(638\) −7.14693e27 5.15472e27i −0.0253223 0.0182637i
\(639\) −5.42112e29 −1.88943
\(640\) 3.93757e29 1.38609e29i 1.35002 0.475229i
\(641\) 4.45875e29 1.50385 0.751924 0.659249i \(-0.229126\pi\)
0.751924 + 0.659249i \(0.229126\pi\)
\(642\) −3.87617e29 2.79568e29i −1.28613 0.927620i
\(643\) 3.74184e29i 1.22143i 0.791849 + 0.610717i \(0.209119\pi\)
−0.791849 + 0.610717i \(0.790881\pi\)
\(644\) 4.99111e28 + 1.50056e29i 0.160286 + 0.481894i
\(645\) 3.72667e29i 1.17745i
\(646\) −4.07907e29 + 5.65556e29i −1.26800 + 1.75806i
\(647\) 1.27928e29 0.391264 0.195632 0.980677i \(-0.437324\pi\)
0.195632 + 0.980677i \(0.437324\pi\)
\(648\) −1.15015e29 + 3.66947e29i −0.346113 + 1.10425i
\(649\) −7.40889e28 −0.219373
\(650\) 2.14627e29 2.97577e29i 0.625308 0.866979i
\(651\) 3.95821e28i 0.113475i
\(652\) −3.30423e29 + 1.09904e29i −0.932116 + 0.310037i
\(653\) 2.46770e29i 0.685021i 0.939514 + 0.342510i \(0.111277\pi\)
−0.939514 + 0.342510i \(0.888723\pi\)
\(654\) −6.64909e29 4.79565e29i −1.81634 1.31003i
\(655\) 3.13135e29 0.841778
\(656\) 1.54550e29 1.15601e29i 0.408864 0.305824i
\(657\) 2.07501e29 0.540238
\(658\) −5.41791e28 3.90767e28i −0.138823 0.100126i
\(659\) 3.76657e29i 0.949838i −0.880029 0.474919i \(-0.842477\pi\)
0.880029 0.474919i \(-0.157523\pi\)
\(660\) 1.88145e29 6.25802e28i 0.466962 0.155319i
\(661\) 5.90601e29i 1.44271i 0.692566 + 0.721355i \(0.256480\pi\)
−0.692566 + 0.721355i \(0.743520\pi\)
\(662\) 9.29750e27 1.28908e28i 0.0223541 0.0309936i
\(663\) 8.40192e29 1.98832
\(664\) −3.81904e29 1.19704e29i −0.889589 0.278832i
\(665\) −4.84669e29 −1.11127
\(666\) −6.47420e29 + 8.97636e29i −1.46119 + 2.02591i
\(667\) 9.06756e28i 0.201451i
\(668\) 2.40591e28 + 7.23327e28i 0.0526170 + 0.158191i
\(669\) 5.66646e29i 1.21994i
\(670\) 3.84006e29 + 2.76964e29i 0.813865 + 0.586999i
\(671\) 6.07955e27 0.0126848
\(672\) 5.90497e27 + 3.40007e29i 0.0121294 + 0.698410i
\(673\) 2.15360e29 0.435519 0.217760 0.976002i \(-0.430125\pi\)
0.217760 + 0.976002i \(0.430125\pi\)
\(674\) 6.30086e29 + 4.54449e29i 1.25450 + 0.904807i
\(675\) 9.82398e29i 1.92574i
\(676\) −6.47930e27 1.94798e28i −0.0125051 0.0375962i
\(677\) 8.99548e29i 1.70940i −0.519124 0.854699i \(-0.673742\pi\)
0.519124 0.854699i \(-0.326258\pi\)
\(678\) −1.60130e28 + 2.22018e28i −0.0299614 + 0.0415409i
\(679\) 4.18804e29 0.771576
\(680\) −8.40409e29 2.63417e29i −1.52457 0.477859i
\(681\) −1.67087e29 −0.298468
\(682\) 1.06340e28 1.47439e28i 0.0187051 0.0259343i
\(683\) 5.90620e29i 1.02304i 0.859272 + 0.511518i \(0.170917\pi\)
−0.859272 + 0.511518i \(0.829083\pi\)
\(684\) 2.21602e30 7.37086e29i 3.77994 1.25727i
\(685\) 3.65185e29i 0.613426i
\(686\) −3.60756e29 2.60195e29i −0.596774 0.430423i
\(687\) −1.79827e30 −2.92960
\(688\) −1.75817e29 2.35054e29i −0.282087 0.377129i
\(689\) −8.31683e29 −1.31418
\(690\) 1.65481e30 + 1.19353e30i 2.57533 + 1.85745i
\(691\) 4.03124e28i 0.0617901i 0.999523 + 0.0308951i \(0.00983577\pi\)
−0.999523 + 0.0308951i \(0.990164\pi\)
\(692\) −8.84169e29 + 2.94089e29i −1.33482 + 0.443982i
\(693\) 1.08591e29i 0.161472i
\(694\) −1.51038e29 + 2.09412e29i −0.221214 + 0.306709i
\(695\) 7.96182e29 1.14861
\(696\) 5.83188e28 1.86061e29i 0.0828727 0.264398i
\(697\) −4.07196e29 −0.569980
\(698\) −4.85784e29 + 6.73531e29i −0.669824 + 0.928700i
\(699\) 7.64874e29i 1.03891i
\(700\) −9.88843e28 2.97292e29i −0.132312 0.397790i
\(701\) 1.27766e30i 1.68413i −0.539373 0.842067i \(-0.681339\pi\)
0.539373 0.842067i \(-0.318661\pi\)
\(702\) −1.16978e30 8.43701e29i −1.51902 1.09559i
\(703\) 1.84808e30 2.36423
\(704\) −8.91456e28 + 1.28235e29i −0.112354 + 0.161619i
\(705\) −8.61872e29 −1.07018
\(706\) −3.33607e29 2.40614e29i −0.408118 0.294355i
\(707\) 2.23810e29i 0.269759i
\(708\) −5.17424e29 1.55562e30i −0.614465 1.84737i
\(709\) 8.61111e29i 1.00757i 0.863830 + 0.503783i \(0.168059\pi\)
−0.863830 + 0.503783i \(0.831941\pi\)
\(710\) −6.68818e29 + 9.27305e29i −0.771073 + 1.06908i
\(711\) 1.17478e30 1.33453
\(712\) 1.81765e29 5.79905e29i 0.203456 0.649108i
\(713\) 1.87060e29 0.206320
\(714\) 4.19694e29 5.81898e29i 0.456143 0.632435i
\(715\) 2.68201e29i 0.287241i
\(716\) 6.60984e29 2.19854e29i 0.697597 0.232032i
\(717\) 1.82190e30i 1.89484i
\(718\) −5.42458e29 3.91247e29i −0.555980 0.401000i
\(719\) −7.17709e29 −0.724928 −0.362464 0.931998i \(-0.618064\pi\)
−0.362464 + 0.931998i \(0.618064\pi\)
\(720\) 1.76676e30 + 2.36202e30i 1.75867 + 2.35121i
\(721\) 5.55710e29 0.545165
\(722\) −2.32399e30 1.67618e30i −2.24695 1.62061i
\(723\) 1.33562e30i 1.27272i
\(724\) 4.12733e29 1.37282e29i 0.387627 0.128931i
\(725\) 1.79647e29i 0.166292i
\(726\) 1.07663e30 1.49273e30i 0.982273 1.36190i
\(727\) −2.93731e29 −0.264143 −0.132071 0.991240i \(-0.542163\pi\)
−0.132071 + 0.991240i \(0.542163\pi\)
\(728\) −4.38920e29 1.37575e29i −0.389050 0.121944i
\(729\) 9.55345e29 0.834682
\(730\) 2.56000e29 3.54940e29i 0.220470 0.305678i
\(731\) 6.19303e29i 0.525740i
\(732\) 4.24585e28 + 1.27650e29i 0.0355303 + 0.106820i
\(733\) 1.28152e30i 1.05714i −0.848890 0.528569i \(-0.822729\pi\)
0.848890 0.528569i \(-0.177271\pi\)
\(734\) 1.72794e30 + 1.24627e30i 1.40514 + 1.01346i
\(735\) −2.62008e30 −2.10038
\(736\) −1.60683e30 + 2.79062e28i −1.26985 + 0.0220538i
\(737\) −1.77137e29 −0.138007
\(738\) 1.10608e30 + 7.97759e29i 0.849561 + 0.612745i
\(739\) 1.95302e29i 0.147891i 0.997262 + 0.0739453i \(0.0235590\pi\)
−0.997262 + 0.0739453i \(0.976441\pi\)
\(740\) 7.36704e29 + 2.21487e30i 0.549997 + 1.65355i
\(741\) 4.69874e30i 3.45852i
\(742\) −4.15443e29 + 5.76005e29i −0.301489 + 0.418009i
\(743\) 7.65776e29 0.547923 0.273961 0.961741i \(-0.411666\pi\)
0.273961 + 0.961741i \(0.411666\pi\)
\(744\) 3.83838e29 + 1.20310e29i 0.270789 + 0.0848759i
\(745\) −1.14643e30 −0.797457
\(746\) 1.14052e30 1.58131e30i 0.782250 1.08458i
\(747\) 2.82801e30i 1.91256i
\(748\) 3.12662e29 1.03997e29i 0.208501 0.0693509i
\(749\) 5.52019e29i 0.362990i
\(750\) −1.51316e29 1.09137e29i −0.0981164 0.0707664i
\(751\) −2.22552e30 −1.42302 −0.711512 0.702674i \(-0.751989\pi\)
−0.711512 + 0.702674i \(0.751989\pi\)
\(752\) 5.43613e29 4.06615e29i 0.342770 0.256387i
\(753\) 1.94065e30 1.20670
\(754\) 2.13913e29 + 1.54284e29i 0.131171 + 0.0946069i
\(755\) 1.24457e30i 0.752623i
\(756\) −1.16866e30 + 3.88715e29i −0.696961 + 0.231821i
\(757\) 5.24409e29i 0.308435i 0.988037 + 0.154217i \(0.0492856\pi\)
−0.988037 + 0.154217i \(0.950714\pi\)
\(758\) −8.53765e29 + 1.18373e30i −0.495236 + 0.686636i
\(759\) −7.63341e29 −0.436697
\(760\) 1.47315e30 4.69995e30i 0.831197 2.65186i
\(761\) 2.82547e30 1.57236 0.786179 0.617999i \(-0.212057\pi\)
0.786179 + 0.617999i \(0.212057\pi\)
\(762\) 3.65221e29 5.06372e29i 0.200460 0.277934i
\(763\) 9.46921e29i 0.512632i
\(764\) 3.66636e29 + 1.10228e30i 0.195774 + 0.588587i
\(765\) 6.22325e30i 3.27772i
\(766\) −3.14107e29 2.26550e29i −0.163183 0.117696i
\(767\) 2.21753e30 1.13637
\(768\) −3.31508e30 9.76187e29i −1.67572 0.493447i
\(769\) −2.60437e30 −1.29860 −0.649300 0.760532i \(-0.724938\pi\)
−0.649300 + 0.760532i \(0.724938\pi\)
\(770\) 1.85750e29 + 1.33972e29i 0.0913642 + 0.0658964i
\(771\) 4.40057e30i 2.13520i
\(772\) −3.15659e29 9.49017e29i −0.151090 0.454247i
\(773\) 2.19908e30i 1.03838i −0.854659 0.519189i \(-0.826234\pi\)
0.854659 0.519189i \(-0.173766\pi\)
\(774\) 1.21331e30 1.68223e30i 0.565186 0.783620i
\(775\) −3.70606e29 −0.170312
\(776\) −1.27295e30 + 4.06125e30i −0.577118 + 1.84125i
\(777\) −1.90148e30 −0.850494
\(778\) −8.47355e29 + 1.17484e30i −0.373921 + 0.518435i
\(779\) 2.27723e30i 0.991433i
\(780\) −5.63131e30 + 1.87307e30i −2.41889 + 0.804564i
\(781\) 4.27753e29i 0.181283i
\(782\) 2.74998e30 + 1.98342e30i 1.14990 + 0.829363i
\(783\) 7.06195e29 0.291358
\(784\) 1.65258e30 1.23610e30i 0.672734 0.503195i
\(785\) 3.13543e30 1.25941
\(786\) −2.10250e30 1.51643e30i −0.833296 0.601014i
\(787\) 2.48348e30i 0.971239i −0.874170 0.485620i \(-0.838594\pi\)
0.874170 0.485620i \(-0.161406\pi\)
\(788\) −2.76269e30 + 9.18917e29i −1.06612 + 0.354610i
\(789\) 3.53264e30i 1.34521i
\(790\) 1.44936e30 2.00951e30i 0.544618 0.755103i
\(791\) −3.16184e28 −0.0117243
\(792\) −1.05304e30 3.30063e29i −0.385327 0.120776i
\(793\) −1.81965e29 −0.0657082
\(794\) −3.46934e28 + 4.81018e28i −0.0123632 + 0.0171414i
\(795\) 9.16299e30i 3.22242i
\(796\) 1.52976e30 + 4.59917e30i 0.530928 + 1.59622i
\(797\) 2.70053e30i 0.924988i −0.886622 0.462494i \(-0.846955\pi\)
0.886622 0.462494i \(-0.153045\pi\)
\(798\) 3.25424e30 + 2.34712e30i 1.10007 + 0.793424i
\(799\) −1.43227e30 −0.477841
\(800\) 3.18347e30 5.52880e28i 1.04823 0.0182048i
\(801\) 4.29422e30 1.39554
\(802\) −1.15606e30 8.33810e29i −0.370809 0.267446i
\(803\) 1.63729e29i 0.0518337i
\(804\) −1.23709e30 3.71927e30i −0.386557 1.16217i
\(805\) 2.35667e30i 0.726846i
\(806\) −3.18283e29 + 4.41294e29i −0.0968937 + 0.134341i
\(807\) 4.32509e30 1.29964
\(808\) 2.17034e30 + 6.80270e29i 0.643738 + 0.201773i
\(809\) −3.79900e29 −0.111227 −0.0556134 0.998452i \(-0.517711\pi\)
−0.0556134 + 0.998452i \(0.517711\pi\)
\(810\) −3.35235e30 + 4.64797e30i −0.968849 + 1.34329i
\(811\) 5.66301e30i 1.61558i −0.589471 0.807790i \(-0.700664\pi\)
0.589471 0.807790i \(-0.299336\pi\)
\(812\) 2.13708e29 7.10828e28i 0.0601842 0.0200183i
\(813\) 2.04157e30i 0.567563i
\(814\) −7.08279e29 5.10846e29i −0.194378 0.140195i
\(815\) −5.18939e30 −1.40592
\(816\) 4.36715e30 + 5.83855e30i 1.16802 + 1.56156i
\(817\) −3.46343e30 −0.914480
\(818\) 4.01541e30 + 2.89611e30i 1.04669 + 0.754928i
\(819\) 3.25022e30i 0.836433i
\(820\) 2.72920e30 9.07777e29i 0.693409 0.230639i
\(821\) 6.44047e30i 1.61553i 0.589507 + 0.807763i \(0.299322\pi\)
−0.589507 + 0.807763i \(0.700678\pi\)
\(822\) 1.76849e30 2.45199e30i 0.437975 0.607245i
\(823\) 3.58633e30 0.876905 0.438452 0.898754i \(-0.355527\pi\)
0.438452 + 0.898754i \(0.355527\pi\)
\(824\) −1.68908e30 + 5.38885e30i −0.407768 + 1.30095i
\(825\) 1.51234e30 0.360481
\(826\) 1.10770e30 1.53581e30i 0.260695 0.361450i
\(827\) 5.93139e30i 1.37831i −0.724612 0.689157i \(-0.757981\pi\)
0.724612 0.689157i \(-0.242019\pi\)
\(828\) −3.58403e30 1.07753e31i −0.822344 2.47235i
\(829\) 6.70193e30i 1.51837i 0.650876 + 0.759184i \(0.274402\pi\)
−0.650876 + 0.759184i \(0.725598\pi\)
\(830\) −4.83743e30 3.48899e30i −1.08217 0.780513i
\(831\) −1.34802e31 −2.97772
\(832\) 2.66819e30 3.83816e30i 0.581998 0.837197i
\(833\) −4.35408e30 −0.937830
\(834\) −5.34585e30 3.85569e30i −1.13703 0.820085i
\(835\) 1.13601e30i 0.238602i
\(836\) 5.81597e29 + 1.74855e30i 0.120630 + 0.362670i
\(837\) 1.45685e30i 0.298400i
\(838\) 1.24317e30 1.72363e30i 0.251459 0.348644i
\(839\) −2.22879e30 −0.445214 −0.222607 0.974908i \(-0.571457\pi\)
−0.222607 + 0.974908i \(0.571457\pi\)
\(840\) −1.51572e30 + 4.83576e30i −0.299010 + 0.953965i
\(841\) 5.00370e30 0.974841
\(842\) −9.25626e29 + 1.28336e30i −0.178098 + 0.246930i
\(843\) 1.01834e31i 1.93510i
\(844\) −1.10150e30 + 3.66377e29i −0.206723 + 0.0687595i
\(845\) 3.05936e29i 0.0567068i
\(846\) 3.89052e30 + 2.80603e30i 0.712227 + 0.513693i
\(847\) 2.12585e30 0.384376
\(848\) −4.32293e30 5.77942e30i −0.772007 1.03211i
\(849\) −1.77827e30 −0.313665
\(850\) −5.44829e30 3.92958e30i −0.949209 0.684616i
\(851\) 8.98617e30i 1.54637i
\(852\) 8.98137e30 2.98736e30i 1.52661 0.507775i
\(853\) 5.01110e30i 0.841334i −0.907215 0.420667i \(-0.861796\pi\)
0.907215 0.420667i \(-0.138204\pi\)
\(854\) −9.08954e28 + 1.26025e29i −0.0150742 + 0.0209001i
\(855\) 3.48033e31 5.70133
\(856\) 5.35306e30 + 1.67786e30i 0.866219 + 0.271507i
\(857\) 7.58197e30 1.21195 0.605973 0.795485i \(-0.292784\pi\)
0.605973 + 0.795485i \(0.292784\pi\)
\(858\) 1.29882e30 1.80080e30i 0.205085 0.284347i
\(859\) 9.10584e30i 1.42034i 0.704031 + 0.710169i \(0.251381\pi\)
−0.704031 + 0.710169i \(0.748619\pi\)
\(860\) −1.38063e30 4.15082e30i −0.212738 0.639589i
\(861\) 2.34303e30i 0.356652i
\(862\) −7.27199e30 5.24492e30i −1.09352 0.788701i
\(863\) −8.75139e30 −1.30006 −0.650030 0.759908i \(-0.725244\pi\)
−0.650030 + 0.759908i \(0.725244\pi\)
\(864\) −2.17338e29 1.25143e31i −0.0318963 1.83658i
\(865\) −1.38861e31 −2.01332
\(866\) −2.63994e29 1.90406e29i −0.0378143 0.0272736i
\(867\) 3.03887e30i 0.430043i
\(868\) 1.46641e29 + 4.40872e29i 0.0205021 + 0.0616389i
\(869\) 9.26961e29i 0.128042i
\(870\) 1.69981e30 2.35676e30i 0.231979 0.321635i
\(871\) 5.30182e30 0.714882
\(872\) 9.18252e30 + 2.87816e30i 1.22332 + 0.383435i
\(873\) −3.00737e31 −3.95856
\(874\) −1.10922e31 + 1.53792e31i −1.44261 + 2.00015i
\(875\) 2.15494e29i 0.0276918i
\(876\) −3.43775e30 + 1.14345e30i −0.436497 + 0.145186i
\(877\) 1.02617e31i 1.28743i 0.765266 + 0.643715i \(0.222608\pi\)
−0.765266 + 0.643715i \(0.777392\pi\)
\(878\) 7.09988e30 + 5.12078e30i 0.880154 + 0.634811i
\(879\) −9.02425e30 −1.10542
\(880\) −1.86375e30 + 1.39406e30i −0.225589 + 0.168738i
\(881\) 4.73054e30 0.565801 0.282901 0.959149i \(-0.408703\pi\)
0.282901 + 0.959149i \(0.408703\pi\)
\(882\) 1.18271e31 + 8.53031e30i 1.39784 + 1.00819i
\(883\) 1.26828e30i 0.148125i 0.997254 + 0.0740626i \(0.0235965\pi\)
−0.997254 + 0.0740626i \(0.976404\pi\)
\(884\) −9.35818e30 + 3.11269e30i −1.08005 + 0.359242i
\(885\) 2.44314e31i 2.78641i
\(886\) −9.69354e30 + 1.34399e31i −1.09252 + 1.51476i
\(887\) −1.34347e31 −1.49634 −0.748170 0.663507i \(-0.769067\pi\)
−0.748170 + 0.663507i \(0.769067\pi\)
\(888\) 5.77954e30 1.84391e31i 0.636146 2.02957i
\(889\) 7.21142e29 0.0784427
\(890\) 5.29789e30 7.34543e30i 0.569518 0.789627i
\(891\) 2.14405e30i 0.227781i
\(892\) 2.09928e30 + 6.31139e30i 0.220414 + 0.662665i
\(893\) 8.00991e30i 0.831165i
\(894\) 7.69756e30 + 5.55186e30i 0.789422 + 0.569370i
\(895\) 1.03810e31 1.05219
\(896\) −1.32541e30 3.76517e30i −0.132775 0.377182i
\(897\) 2.28473e31 2.26212
\(898\) 6.14493e30 + 4.43203e30i 0.601334 + 0.433712i
\(899\) 2.66409e29i 0.0257675i
\(900\) 7.10072e30 + 2.13481e31i 0.678822 + 2.04085i
\(901\) 1.52272e31i 1.43883i
\(902\) −6.29471e29 + 8.72751e29i −0.0587905 + 0.0815120i
\(903\) 3.56351e30 0.328970
\(904\) 9.61038e28 3.06611e29i 0.00876944 0.0279782i
\(905\) 6.48210e30 0.584663
\(906\) 6.02714e30 8.35652e30i 0.537359 0.745040i
\(907\) 1.68871e31i 1.48826i −0.668033 0.744132i \(-0.732863\pi\)
0.668033 0.744132i \(-0.267137\pi\)
\(908\) 1.86104e30 6.19014e29i 0.162127 0.0539261i
\(909\) 1.60715e31i 1.38400i
\(910\) −5.55962e30 4.00988e30i −0.473272 0.341347i
\(911\) 1.11512e31 0.938379 0.469190 0.883097i \(-0.344546\pi\)
0.469190 + 0.883097i \(0.344546\pi\)
\(912\) −3.26519e31 + 2.44231e31i −2.71620 + 2.03168i
\(913\) 2.23144e30 0.183503
\(914\) −1.71700e31 1.23838e31i −1.39584 1.00675i
\(915\) 2.00478e30i 0.161119i
\(916\) 2.00294e31 6.66210e30i 1.59135 0.529309i
\(917\) 2.99424e30i 0.235185i
\(918\) −1.54472e31 + 2.14173e31i −1.19950 + 1.66309i
\(919\) 1.42554e31 1.09438 0.547189 0.837009i \(-0.315698\pi\)
0.547189 + 0.837009i \(0.315698\pi\)
\(920\) −2.28532e31 7.16309e30i −1.73450 0.543661i
\(921\) 6.39854e29 0.0480125
\(922\) 8.35767e30 1.15878e31i 0.620027 0.859657i
\(923\) 1.28029e31i 0.939057i
\(924\) −5.98402e29 1.79907e30i −0.0433948 0.130465i
\(925\) 1.78035e31i 1.27649i
\(926\) −1.21306e31 8.74922e30i −0.859941 0.620232i
\(927\) −3.99046e31 −2.79696
\(928\) 3.97437e28 + 2.28843e30i 0.00275432 + 0.158593i
\(929\) 1.65266e31 1.13245 0.566226 0.824250i \(-0.308403\pi\)
0.566226 + 0.824250i \(0.308403\pi\)
\(930\) 4.86192e30 + 3.50665e30i 0.329410 + 0.237587i
\(931\) 2.43500e31i 1.63128i
\(932\) 2.83366e30 + 8.51928e30i 0.187707 + 0.564334i
\(933\) 5.21999e31i 3.41910i
\(934\) 3.01739e30 4.18355e30i 0.195429 0.270959i
\(935\) 4.91045e30 0.314485
\(936\) 3.15181e31 + 9.87901e30i 1.99602 + 0.625629i
\(937\) 8.77702e30 0.549644 0.274822 0.961495i \(-0.411381\pi\)
0.274822 + 0.961495i \(0.411381\pi\)
\(938\) 2.64837e30 3.67192e30i 0.164002 0.227386i
\(939\) 1.14477e31i 0.701021i
\(940\) 9.59966e30 3.19301e30i 0.581317 0.193356i
\(941\) 4.85137e30i 0.290518i 0.989394 + 0.145259i \(0.0464015\pi\)
−0.989394 + 0.145259i \(0.953598\pi\)
\(942\) −2.10524e31 1.51840e31i −1.24672 0.899193i
\(943\) −1.10729e31 −0.648467
\(944\) 1.15263e31 + 1.54098e31i 0.667550 + 0.892463i
\(945\) −1.83541e31 −1.05124
\(946\) 1.32736e30 + 9.57360e29i 0.0751852 + 0.0542273i
\(947\) 2.34170e31i 1.31177i 0.754863 + 0.655883i \(0.227704\pi\)
−0.754863 + 0.655883i \(0.772296\pi\)
\(948\) −1.94631e31 + 6.47374e30i −1.07826 + 0.358647i
\(949\) 4.90051e30i 0.268501i
\(950\) 2.19760e31 3.04694e31i 1.19083 1.65107i
\(951\) −4.30402e31 −2.30664
\(952\) −2.51883e30 + 8.03613e30i −0.133509 + 0.425950i
\(953\) −1.62933e31 −0.854151 −0.427076 0.904216i \(-0.640456\pi\)
−0.427076 + 0.904216i \(0.640456\pi\)
\(954\) 2.98323e31 4.13620e31i 1.54678 2.14459i
\(955\) 1.73116e31i 0.887774i
\(956\) −6.74964e30 2.02926e31i −0.342352 1.02927i
\(957\) 1.08714e30i 0.0545395i
\(958\) 2.90098e31 + 2.09233e31i 1.43948 + 1.03823i
\(959\) 3.49196e30 0.171385
\(960\) −4.22866e31 2.93965e31i −2.05284 1.42708i
\(961\) −2.02759e31 −0.973610
\(962\) 2.11993e31 + 1.52900e31i 1.00689 + 0.726220i
\(963\) 3.96396e31i 1.86231i
\(964\) −4.94813e30 1.48764e31i −0.229950 0.691335i
\(965\) 1.49046e31i 0.685147i
\(966\) 1.14127e31 1.58236e31i 0.518955 0.719522i
\(967\) 3.73495e31 1.67999 0.839996 0.542593i \(-0.182557\pi\)
0.839996 + 0.542593i \(0.182557\pi\)
\(968\) −6.46151e30 + 2.06149e31i −0.287503 + 0.917254i
\(969\) 8.60286e31 3.78654
\(970\) −3.71027e31 + 5.14422e31i −1.61548 + 2.23984i
\(971\) 2.84559e30i 0.122566i −0.998120 0.0612830i \(-0.980481\pi\)
0.998120 0.0612830i \(-0.0195192\pi\)
\(972\) 4.11178e30 1.36765e30i 0.175200 0.0582744i
\(973\) 7.61322e30i 0.320910i
\(974\) −1.17256e31 8.45712e30i −0.488954 0.352658i
\(975\) −4.52653e31 −1.86731
\(976\) −9.45819e29 1.26449e30i −0.0385998 0.0516050i
\(977\) −9.12612e30 −0.368463 −0.184231 0.982883i \(-0.558980\pi\)
−0.184231 + 0.982883i \(0.558980\pi\)
\(978\) 3.48435e31 + 2.51308e31i 1.39176 + 1.00380i
\(979\) 3.38835e30i 0.133897i
\(980\) 2.91829e31 9.70671e30i 1.14092 0.379488i
\(981\) 6.79969e31i 2.63005i
\(982\) −1.73362e31 + 2.40363e31i −0.663411 + 0.919808i
\(983\) 4.18979e31 1.58628 0.793141 0.609037i \(-0.208444\pi\)
0.793141 + 0.609037i \(0.208444\pi\)
\(984\) −2.27209e31 7.12163e30i −0.851094 0.266766i
\(985\) −4.33889e31 −1.60805
\(986\) 2.82477e30 3.91650e30i 0.103580 0.143612i
\(987\) 8.24136e30i 0.298998i
\(988\) −1.74076e31 5.23353e31i −0.624871 1.87865i
\(989\) 1.68407e31i 0.598135i
\(990\) −1.33384e31 9.62032e30i −0.468743 0.338080i
\(991\) 4.03029e30 0.140140 0.0700701 0.997542i \(-0.477678\pi\)
0.0700701 + 0.997542i \(0.477678\pi\)
\(992\) −4.72096e30 + 8.19898e28i −0.162427 + 0.00282090i
\(993\) −1.96087e30 −0.0667545
\(994\) 8.86704e30 + 6.39535e30i 0.298691 + 0.215430i
\(995\) 7.22313e31i 2.40759i
\(996\) 1.55840e31 + 4.68527e31i 0.513991 + 1.54530i
\(997\) 6.29686e30i 0.205506i −0.994707 0.102753i \(-0.967235\pi\)
0.994707 0.102753i \(-0.0327651\pi\)
\(998\) 2.07434e31 2.87604e31i 0.669900 0.928804i
\(999\) 6.99857e31 2.23651
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 8.22.b.a.5.16 yes 20
4.3 odd 2 32.22.b.a.17.19 20
8.3 odd 2 32.22.b.a.17.2 20
8.5 even 2 inner 8.22.b.a.5.15 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.22.b.a.5.15 20 8.5 even 2 inner
8.22.b.a.5.16 yes 20 1.1 even 1 trivial
32.22.b.a.17.2 20 8.3 odd 2
32.22.b.a.17.19 20 4.3 odd 2