Properties

Label 13.15.d.a.8.13
Level $13$
Weight $15$
Character 13.8
Analytic conductor $16.163$
Analytic rank $0$
Dimension $32$
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] = [13,15,Mod(5,13)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(13, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("13.5");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 13 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 13.d (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(16.1627658597\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.13
Character \(\chi\) \(=\) 13.8
Dual form 13.15.d.a.5.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(100.811 + 100.811i) q^{2} -1095.41 q^{3} +3941.67i q^{4} +(-6132.14 - 6132.14i) q^{5} +(-110429. - 110429. i) q^{6} +(-84903.1 + 84903.1i) q^{7} +(1.25432e6 - 1.25432e6i) q^{8} -3.58306e6 q^{9} +O(q^{10})\) \(q+(100.811 + 100.811i) q^{2} -1095.41 q^{3} +3941.67i q^{4} +(-6132.14 - 6132.14i) q^{5} +(-110429. - 110429. i) q^{6} +(-84903.1 + 84903.1i) q^{7} +(1.25432e6 - 1.25432e6i) q^{8} -3.58306e6 q^{9} -1.23637e6i q^{10} +(2.64072e7 - 2.64072e7i) q^{11} -4.31773e6i q^{12} +(1.43089e7 - 6.10953e7i) q^{13} -1.71183e7 q^{14} +(6.71718e6 + 6.71718e6i) q^{15} +3.17479e8 q^{16} +2.93214e8i q^{17} +(-3.61211e8 - 3.61211e8i) q^{18} +(5.26914e8 + 5.26914e8i) q^{19} +(2.41709e7 - 2.41709e7i) q^{20} +(9.30034e7 - 9.30034e7i) q^{21} +5.32426e9 q^{22} -4.39854e9i q^{23} +(-1.37399e9 + 1.37399e9i) q^{24} -6.02831e9i q^{25} +(7.60156e9 - 4.71657e9i) q^{26} +9.16419e9 q^{27} +(-3.34661e8 - 3.34661e8i) q^{28} -1.36510e10 q^{29} +1.35433e9i q^{30} +(-6.49603e9 - 6.49603e9i) q^{31} +(1.14545e10 + 1.14545e10i) q^{32} +(-2.89265e10 + 2.89265e10i) q^{33} +(-2.95592e10 + 2.95592e10i) q^{34} +1.04128e9 q^{35} -1.41232e10i q^{36} +(-5.07123e10 + 5.07123e10i) q^{37} +1.06237e11i q^{38} +(-1.56741e10 + 6.69241e10i) q^{39} -1.53834e10 q^{40} +(-2.46469e11 - 2.46469e11i) q^{41} +1.87515e10 q^{42} -1.06941e11i q^{43} +(1.04088e11 + 1.04088e11i) q^{44} +(2.19718e10 + 2.19718e10i) q^{45} +(4.43420e11 - 4.43420e11i) q^{46} +(-4.88003e10 + 4.88003e10i) q^{47} -3.47768e11 q^{48} +6.63806e11i q^{49} +(6.07719e11 - 6.07719e11i) q^{50} -3.21189e11i q^{51} +(2.40818e11 + 5.64011e10i) q^{52} +1.06455e12 q^{53} +(9.23850e11 + 9.23850e11i) q^{54} -3.23865e11 q^{55} +2.12992e11i q^{56} +(-5.77184e11 - 5.77184e11i) q^{57} +(-1.37617e12 - 1.37617e12i) q^{58} +(-1.64153e12 + 1.64153e12i) q^{59} +(-2.64769e10 + 2.64769e10i) q^{60} +4.56945e12 q^{61} -1.30974e12i q^{62} +(3.04213e11 - 3.04213e11i) q^{63} -2.89209e12i q^{64} +(-4.62389e11 + 2.86900e11i) q^{65} -5.83222e12 q^{66} +(-1.08953e12 - 1.08953e12i) q^{67} -1.15576e12 q^{68} +4.81818e12i q^{69} +(1.04972e11 + 1.04972e11i) q^{70} +(2.36495e12 + 2.36495e12i) q^{71} +(-4.49431e12 + 4.49431e12i) q^{72} +(-3.90739e12 + 3.90739e12i) q^{73} -1.02247e13 q^{74} +6.60344e12i q^{75} +(-2.07692e12 + 2.07692e12i) q^{76} +4.48410e12i q^{77} +(-8.32680e12 + 5.16656e12i) q^{78} +1.49060e13 q^{79} +(-1.94683e12 - 1.94683e12i) q^{80} +7.09914e12 q^{81} -4.96936e13i q^{82} +(2.76010e13 + 2.76010e13i) q^{83} +(3.66589e11 + 3.66589e11i) q^{84} +(1.79803e12 - 1.79803e12i) q^{85} +(1.07809e13 - 1.07809e13i) q^{86} +1.49534e13 q^{87} -6.62461e13i q^{88} +(2.88589e13 - 2.88589e13i) q^{89} +4.42999e12i q^{90} +(3.97231e12 + 6.40205e12i) q^{91} +1.73376e13 q^{92} +(7.11578e12 + 7.11578e12i) q^{93} -9.83921e12 q^{94} -6.46222e12i q^{95} +(-1.25474e13 - 1.25474e13i) q^{96} +(1.40159e13 + 1.40159e13i) q^{97} +(-6.69189e13 + 6.69189e13i) q^{98} +(-9.46183e13 + 9.46183e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 126 q^{2} - 4 q^{3} + 40308 q^{5} - 215296 q^{6} - 342172 q^{7} + 2132400 q^{8} + 51018332 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 126 q^{2} - 4 q^{3} + 40308 q^{5} - 215296 q^{6} - 342172 q^{7} + 2132400 q^{8} + 51018332 q^{9} - 19776228 q^{11} + 42276320 q^{13} + 504176460 q^{14} + 206094692 q^{15} - 2531526316 q^{16} + 2815918046 q^{18} - 3946163104 q^{19} - 716259684 q^{20} - 3367522672 q^{21} - 14762241344 q^{22} + 29491821240 q^{24} - 4794721266 q^{26} + 13386727964 q^{27} + 21253870460 q^{28} + 51981667512 q^{29} - 81106252408 q^{31} - 46362860004 q^{32} + 105153523412 q^{33} - 182529279768 q^{34} - 370063477908 q^{35} + 362625318836 q^{37} - 384840090244 q^{39} + 1418885544444 q^{40} - 271128165276 q^{41} + 282362729116 q^{42} + 371212733148 q^{44} - 45612965524 q^{45} - 2243149012284 q^{46} - 186355978644 q^{47} + 4851512979332 q^{48} + 584922885822 q^{50} - 4161984175620 q^{52} - 7014914206728 q^{53} - 16155068308552 q^{54} + 10809637665184 q^{55} + 10539677371976 q^{57} + 1379941218100 q^{58} - 346563818376 q^{59} - 10818733483076 q^{60} + 10463189375104 q^{61} + 20564799781280 q^{63} - 36771299231364 q^{65} + 42566898217168 q^{66} - 33242476172548 q^{67} + 73991369730132 q^{68} + 15425582685208 q^{70} - 32475992326884 q^{71} - 94516161515148 q^{72} - 46644619387444 q^{73} + 19517335633512 q^{74} + 153247499250952 q^{76} - 161936899980568 q^{78} + 50555071999360 q^{79} - 164927157279648 q^{80} + 180616513188704 q^{81} + 40646195239884 q^{83} - 8563943720152 q^{84} + 8377594459896 q^{85} - 50876984146272 q^{86} + 82858002231808 q^{87} + 43433785559052 q^{89} - 4834418011540 q^{91} + 2835746550840 q^{92} - 161211565737376 q^{93} - 30798863063804 q^{94} + 114745181636288 q^{96} + 131071048977944 q^{97} - 160069892052210 q^{98} - 66089157162136 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 100.811 + 100.811i 0.787585 + 0.787585i 0.981098 0.193513i \(-0.0619881\pi\)
−0.193513 + 0.981098i \(0.561988\pi\)
\(3\) −1095.41 −0.500871 −0.250436 0.968133i \(-0.580574\pi\)
−0.250436 + 0.968133i \(0.580574\pi\)
\(4\) 3941.67i 0.240581i
\(5\) −6132.14 6132.14i −0.0784914 0.0784914i 0.666771 0.745263i \(-0.267676\pi\)
−0.745263 + 0.666771i \(0.767676\pi\)
\(6\) −110429. 110429.i −0.394479 0.394479i
\(7\) −84903.1 + 84903.1i −0.103095 + 0.103095i −0.756773 0.653678i \(-0.773225\pi\)
0.653678 + 0.756773i \(0.273225\pi\)
\(8\) 1.25432e6 1.25432e6i 0.598107 0.598107i
\(9\) −3.58306e6 −0.749128
\(10\) 1.23637e6i 0.123637i
\(11\) 2.64072e7 2.64072e7i 1.35510 1.35510i 0.475258 0.879847i \(-0.342355\pi\)
0.879847 0.475258i \(-0.157645\pi\)
\(12\) 4.31773e6i 0.120500i
\(13\) 1.43089e7 6.10953e7i 0.228036 0.973653i
\(14\) −1.71183e7 −0.162392
\(15\) 6.71718e6 + 6.71718e6i 0.0393141 + 0.0393141i
\(16\) 3.17479e8 1.18270
\(17\) 2.93214e8i 0.714567i 0.933996 + 0.357283i \(0.116297\pi\)
−0.933996 + 0.357283i \(0.883703\pi\)
\(18\) −3.61211e8 3.61211e8i −0.590002 0.590002i
\(19\) 5.26914e8 + 5.26914e8i 0.589474 + 0.589474i 0.937489 0.348015i \(-0.113144\pi\)
−0.348015 + 0.937489i \(0.613144\pi\)
\(20\) 2.41709e7 2.41709e7i 0.0188835 0.0188835i
\(21\) 9.30034e7 9.30034e7i 0.0516373 0.0516373i
\(22\) 5.32426e9 2.13452
\(23\) 4.39854e9i 1.29185i −0.763399 0.645927i \(-0.776471\pi\)
0.763399 0.645927i \(-0.223529\pi\)
\(24\) −1.37399e9 + 1.37399e9i −0.299575 + 0.299575i
\(25\) 6.02831e9i 0.987678i
\(26\) 7.60156e9 4.71657e9i 0.946432 0.587237i
\(27\) 9.16419e9 0.876088
\(28\) −3.34661e8 3.34661e8i −0.0248027 0.0248027i
\(29\) −1.36510e10 −0.791368 −0.395684 0.918387i \(-0.629492\pi\)
−0.395684 + 0.918387i \(0.629492\pi\)
\(30\) 1.35433e9i 0.0619264i
\(31\) −6.49603e9 6.49603e9i −0.236111 0.236111i 0.579127 0.815238i \(-0.303394\pi\)
−0.815238 + 0.579127i \(0.803394\pi\)
\(32\) 1.14545e10 + 1.14545e10i 0.333371 + 0.333371i
\(33\) −2.89265e10 + 2.89265e10i −0.678733 + 0.678733i
\(34\) −2.95592e10 + 2.95592e10i −0.562782 + 0.562782i
\(35\) 1.04128e9 0.0161841
\(36\) 1.41232e10i 0.180226i
\(37\) −5.07123e10 + 5.07123e10i −0.534197 + 0.534197i −0.921819 0.387622i \(-0.873297\pi\)
0.387622 + 0.921819i \(0.373297\pi\)
\(38\) 1.06237e11i 0.928521i
\(39\) −1.56741e10 + 6.69241e10i −0.114217 + 0.487675i
\(40\) −1.53834e10 −0.0938926
\(41\) −2.46469e11 2.46469e11i −1.26554 1.26554i −0.948368 0.317171i \(-0.897267\pi\)
−0.317171 0.948368i \(-0.602733\pi\)
\(42\) 1.87515e10 0.0813376
\(43\) 1.06941e11i 0.393430i −0.980461 0.196715i \(-0.936973\pi\)
0.980461 0.196715i \(-0.0630273\pi\)
\(44\) 1.04088e11 + 1.04088e11i 0.326012 + 0.326012i
\(45\) 2.19718e10 + 2.19718e10i 0.0588001 + 0.0588001i
\(46\) 4.43420e11 4.43420e11i 1.01744 1.01744i
\(47\) −4.88003e10 + 4.88003e10i −0.0963247 + 0.0963247i −0.753627 0.657302i \(-0.771697\pi\)
0.657302 + 0.753627i \(0.271697\pi\)
\(48\) −3.47768e11 −0.592381
\(49\) 6.63806e11i 0.978743i
\(50\) 6.07719e11 6.07719e11i 0.777881 0.777881i
\(51\) 3.21189e11i 0.357906i
\(52\) 2.40818e11 + 5.64011e10i 0.234242 + 0.0548611i
\(53\) 1.06455e12 0.906225 0.453112 0.891453i \(-0.350314\pi\)
0.453112 + 0.891453i \(0.350314\pi\)
\(54\) 9.23850e11 + 9.23850e11i 0.689994 + 0.689994i
\(55\) −3.23865e11 −0.212728
\(56\) 2.12992e11i 0.123324i
\(57\) −5.77184e11 5.77184e11i −0.295251 0.295251i
\(58\) −1.37617e12 1.37617e12i −0.623270 0.623270i
\(59\) −1.64153e12 + 1.64153e12i −0.659608 + 0.659608i −0.955287 0.295679i \(-0.904454\pi\)
0.295679 + 0.955287i \(0.404454\pi\)
\(60\) −2.64769e10 + 2.64769e10i −0.00945822 + 0.00945822i
\(61\) 4.56945e12 1.45397 0.726985 0.686654i \(-0.240921\pi\)
0.726985 + 0.686654i \(0.240921\pi\)
\(62\) 1.30974e12i 0.371915i
\(63\) 3.04213e11 3.04213e11i 0.0772313 0.0772313i
\(64\) 2.89209e12i 0.657586i
\(65\) −4.62389e11 + 2.86900e11i −0.0943223 + 0.0585245i
\(66\) −5.83222e12 −1.06912
\(67\) −1.08953e12 1.08953e12i −0.179769 0.179769i 0.611486 0.791255i \(-0.290572\pi\)
−0.791255 + 0.611486i \(0.790572\pi\)
\(68\) −1.15576e12 −0.171911
\(69\) 4.81818e12i 0.647053i
\(70\) 1.04972e11 + 1.04972e11i 0.0127464 + 0.0127464i
\(71\) 2.36495e12 + 2.36495e12i 0.260024 + 0.260024i 0.825064 0.565040i \(-0.191139\pi\)
−0.565040 + 0.825064i \(0.691139\pi\)
\(72\) −4.49431e12 + 4.49431e12i −0.448059 + 0.448059i
\(73\) −3.90739e12 + 3.90739e12i −0.353693 + 0.353693i −0.861482 0.507789i \(-0.830463\pi\)
0.507789 + 0.861482i \(0.330463\pi\)
\(74\) −1.02247e13 −0.841451
\(75\) 6.60344e12i 0.494700i
\(76\) −2.07692e12 + 2.07692e12i −0.141816 + 0.141816i
\(77\) 4.48410e12i 0.279409i
\(78\) −8.32680e12 + 5.16656e12i −0.474041 + 0.294130i
\(79\) 1.49060e13 0.776196 0.388098 0.921618i \(-0.373132\pi\)
0.388098 + 0.921618i \(0.373132\pi\)
\(80\) −1.94683e12 1.94683e12i −0.0928319 0.0928319i
\(81\) 7.09914e12 0.310320
\(82\) 4.96936e13i 1.99344i
\(83\) 2.76010e13 + 2.76010e13i 1.01713 + 1.01713i 0.999851 + 0.0172828i \(0.00550155\pi\)
0.0172828 + 0.999851i \(0.494498\pi\)
\(84\) 3.66589e11 + 3.66589e11i 0.0124229 + 0.0124229i
\(85\) 1.79803e12 1.79803e12i 0.0560874 0.0560874i
\(86\) 1.07809e13 1.07809e13i 0.309859 0.309859i
\(87\) 1.49534e13 0.396373
\(88\) 6.62461e13i 1.62100i
\(89\) 2.88589e13 2.88589e13i 0.652453 0.652453i −0.301130 0.953583i \(-0.597364\pi\)
0.953583 + 0.301130i \(0.0973639\pi\)
\(90\) 4.42999e12i 0.0926202i
\(91\) 3.97231e12 + 6.40205e12i 0.0768693 + 0.123888i
\(92\) 1.73376e13 0.310795
\(93\) 7.11578e12 + 7.11578e12i 0.118261 + 0.118261i
\(94\) −9.83921e12 −0.151728
\(95\) 6.46222e12i 0.0925373i
\(96\) −1.25474e13 1.25474e13i −0.166976 0.166976i
\(97\) 1.40159e13 + 1.40159e13i 0.173468 + 0.173468i 0.788501 0.615033i \(-0.210857\pi\)
−0.615033 + 0.788501i \(0.710857\pi\)
\(98\) −6.69189e13 + 6.69189e13i −0.770843 + 0.770843i
\(99\) −9.46183e13 + 9.46183e13i −1.01515 + 1.01515i
\(100\) 2.37616e13 0.237616
\(101\) 1.86753e14i 1.74188i 0.491389 + 0.870940i \(0.336489\pi\)
−0.491389 + 0.870940i \(0.663511\pi\)
\(102\) 3.23793e13 3.23793e13i 0.281882 0.281882i
\(103\) 8.21341e13i 0.667826i −0.942604 0.333913i \(-0.891631\pi\)
0.942604 0.333913i \(-0.108369\pi\)
\(104\) −5.86851e13 9.45811e13i −0.445959 0.718739i
\(105\) −1.14062e12 −0.00810617
\(106\) 1.07318e14 + 1.07318e14i 0.713729 + 0.713729i
\(107\) −2.79271e14 −1.73916 −0.869580 0.493792i \(-0.835610\pi\)
−0.869580 + 0.493792i \(0.835610\pi\)
\(108\) 3.61223e13i 0.210770i
\(109\) −5.80489e13 5.80489e13i −0.317548 0.317548i 0.530277 0.847824i \(-0.322088\pi\)
−0.847824 + 0.530277i \(0.822088\pi\)
\(110\) −3.26491e13 3.26491e13i −0.167542 0.167542i
\(111\) 5.55506e13 5.55506e13i 0.267564 0.267564i
\(112\) −2.69550e13 + 2.69550e13i −0.121931 + 0.121931i
\(113\) 2.55335e14 1.08533 0.542664 0.839950i \(-0.317416\pi\)
0.542664 + 0.839950i \(0.317416\pi\)
\(114\) 1.16373e14i 0.465070i
\(115\) −2.69725e13 + 2.69725e13i −0.101399 + 0.101399i
\(116\) 5.38078e13i 0.190388i
\(117\) −5.12697e13 + 2.18908e14i −0.170828 + 0.729390i
\(118\) −3.30969e14 −1.03900
\(119\) −2.48948e13 2.48948e13i −0.0736683 0.0736683i
\(120\) 1.68510e13 0.0470281
\(121\) 1.01493e15i 2.67262i
\(122\) 4.60651e14 + 4.60651e14i 1.14512 + 1.14512i
\(123\) 2.69984e14 + 2.69984e14i 0.633872 + 0.633872i
\(124\) 2.56052e13 2.56052e13i 0.0568037 0.0568037i
\(125\) −7.43941e13 + 7.43941e13i −0.156016 + 0.156016i
\(126\) 6.13359e13 0.121652
\(127\) 5.08541e14i 0.954333i 0.878813 + 0.477166i \(0.158336\pi\)
−0.878813 + 0.477166i \(0.841664\pi\)
\(128\) 4.79226e14 4.79226e14i 0.851276 0.851276i
\(129\) 1.17144e14i 0.197058i
\(130\) −7.55366e13 1.76912e13i −0.120380 0.0281938i
\(131\) 1.46006e14 0.220533 0.110266 0.993902i \(-0.464830\pi\)
0.110266 + 0.993902i \(0.464830\pi\)
\(132\) −1.14019e14 1.14019e14i −0.163290 0.163290i
\(133\) −8.94733e13 −0.121544
\(134\) 2.19672e14i 0.283166i
\(135\) −5.61961e13 5.61961e13i −0.0687654 0.0687654i
\(136\) 3.67785e14 + 3.67785e14i 0.427388 + 0.427388i
\(137\) 3.15098e14 3.15098e14i 0.347858 0.347858i −0.511453 0.859311i \(-0.670893\pi\)
0.859311 + 0.511453i \(0.170893\pi\)
\(138\) −4.85725e14 + 4.85725e14i −0.509609 + 0.509609i
\(139\) 9.08367e14 0.906062 0.453031 0.891495i \(-0.350343\pi\)
0.453031 + 0.891495i \(0.350343\pi\)
\(140\) 4.10437e12i 0.00389359i
\(141\) 5.34561e13 5.34561e13i 0.0482463 0.0482463i
\(142\) 4.76826e14i 0.409582i
\(143\) −1.23549e15 1.99121e15i −1.01039 1.62841i
\(144\) −1.13755e15 −0.885995
\(145\) 8.37099e13 + 8.37099e13i 0.0621156 + 0.0621156i
\(146\) −7.87815e14 −0.557127
\(147\) 7.27137e14i 0.490224i
\(148\) −1.99891e14 1.99891e14i −0.128517 0.128517i
\(149\) 1.28650e15 + 1.28650e15i 0.789053 + 0.789053i 0.981339 0.192286i \(-0.0615902\pi\)
−0.192286 + 0.981339i \(0.561590\pi\)
\(150\) −6.65699e14 + 6.65699e14i −0.389618 + 0.389618i
\(151\) −1.61734e15 + 1.61734e15i −0.903573 + 0.903573i −0.995743 0.0921706i \(-0.970619\pi\)
0.0921706 + 0.995743i \(0.470619\pi\)
\(152\) 1.32184e15 0.705137
\(153\) 1.05060e15i 0.535302i
\(154\) −4.52046e14 + 4.52046e14i −0.220058 + 0.220058i
\(155\) 7.96691e13i 0.0370653i
\(156\) −2.63793e14 6.17821e13i −0.117325 0.0274783i
\(157\) −1.98697e15 −0.845073 −0.422537 0.906346i \(-0.638860\pi\)
−0.422537 + 0.906346i \(0.638860\pi\)
\(158\) 1.50269e15 + 1.50269e15i 0.611320 + 0.611320i
\(159\) −1.16612e15 −0.453902
\(160\) 1.40482e14i 0.0523335i
\(161\) 3.73450e14 + 3.73450e14i 0.133184 + 0.133184i
\(162\) 7.15670e14 + 7.15670e14i 0.244404 + 0.244404i
\(163\) −1.91657e15 + 1.91657e15i −0.626920 + 0.626920i −0.947292 0.320372i \(-0.896192\pi\)
0.320372 + 0.947292i \(0.396192\pi\)
\(164\) 9.71501e14 9.71501e14i 0.304464 0.304464i
\(165\) 3.54763e14 0.106549
\(166\) 5.56496e15i 1.60216i
\(167\) 4.73787e15 4.73787e15i 1.30788 1.30788i 0.384935 0.922944i \(-0.374224\pi\)
0.922944 0.384935i \(-0.125776\pi\)
\(168\) 2.33312e14i 0.0617693i
\(169\) −3.52789e15 1.74842e15i −0.895999 0.444056i
\(170\) 3.62523e14 0.0883472
\(171\) −1.88796e15 1.88796e15i −0.441591 0.441591i
\(172\) 4.21529e14 0.0946516
\(173\) 3.06016e15i 0.659813i −0.944014 0.329907i \(-0.892983\pi\)
0.944014 0.329907i \(-0.107017\pi\)
\(174\) 1.50746e15 + 1.50746e15i 0.312178 + 0.312178i
\(175\) 5.11822e14 + 5.11822e14i 0.101825 + 0.101825i
\(176\) 8.38372e15 8.38372e15i 1.60268 1.60268i
\(177\) 1.79815e15 1.79815e15i 0.330379 0.330379i
\(178\) 5.81857e15 1.02772
\(179\) 1.66702e15i 0.283120i −0.989930 0.141560i \(-0.954788\pi\)
0.989930 0.141560i \(-0.0452118\pi\)
\(180\) −8.66057e13 + 8.66057e13i −0.0141462 + 0.0141462i
\(181\) 2.40808e14i 0.0378374i 0.999821 + 0.0189187i \(0.00602238\pi\)
−0.999821 + 0.0189187i \(0.993978\pi\)
\(182\) −2.44945e14 + 1.04585e15i −0.0370313 + 0.158114i
\(183\) −5.00540e15 −0.728252
\(184\) −5.51718e15 5.51718e15i −0.772667 0.772667i
\(185\) 6.21950e14 0.0838598
\(186\) 1.43470e15i 0.186281i
\(187\) 7.74296e15 + 7.74296e15i 0.968313 + 0.968313i
\(188\) −1.92355e14 1.92355e14i −0.0231739 0.0231739i
\(189\) −7.78069e14 + 7.78069e14i −0.0903203 + 0.0903203i
\(190\) 6.51462e14 6.51462e14i 0.0728810 0.0728810i
\(191\) 1.37073e15 0.147815 0.0739074 0.997265i \(-0.476453\pi\)
0.0739074 + 0.997265i \(0.476453\pi\)
\(192\) 3.16801e15i 0.329366i
\(193\) −1.00953e16 + 1.00953e16i −1.01209 + 1.01209i −0.0121646 + 0.999926i \(0.503872\pi\)
−0.999926 + 0.0121646i \(0.996128\pi\)
\(194\) 2.82591e15i 0.273241i
\(195\) 5.06504e14 3.14272e14i 0.0472433 0.0293132i
\(196\) −2.61651e15 −0.235467
\(197\) 1.41171e15 + 1.41171e15i 0.122598 + 0.122598i 0.765744 0.643146i \(-0.222371\pi\)
−0.643146 + 0.765744i \(0.722371\pi\)
\(198\) −1.90771e16 −1.59903
\(199\) 5.21957e15i 0.422341i 0.977449 + 0.211171i \(0.0677275\pi\)
−0.977449 + 0.211171i \(0.932272\pi\)
\(200\) −7.56144e15 7.56144e15i −0.590738 0.590738i
\(201\) 1.19347e15 + 1.19347e15i 0.0900409 + 0.0900409i
\(202\) −1.88268e16 + 1.88268e16i −1.37188 + 1.37188i
\(203\) 1.15901e15 1.15901e15i 0.0815860 0.0815860i
\(204\) 1.26602e15 0.0861053
\(205\) 3.02277e15i 0.198668i
\(206\) 8.28002e15 8.28002e15i 0.525970 0.525970i
\(207\) 1.57602e16i 0.967764i
\(208\) 4.54279e15 1.93965e16i 0.269699 1.15154i
\(209\) 2.78286e16 1.59760
\(210\) −1.14987e14 1.14987e14i −0.00638430 0.00638430i
\(211\) 1.32849e14 0.00713477 0.00356738 0.999994i \(-0.498864\pi\)
0.00356738 + 0.999994i \(0.498864\pi\)
\(212\) 4.19612e15i 0.218020i
\(213\) −2.59058e15 2.59058e15i −0.130239 0.130239i
\(214\) −2.81536e16 2.81536e16i −1.36974 1.36974i
\(215\) −6.55780e14 + 6.55780e14i −0.0308808 + 0.0308808i
\(216\) 1.14948e16 1.14948e16i 0.523995 0.523995i
\(217\) 1.10307e15 0.0486837
\(218\) 1.17039e16i 0.500191i
\(219\) 4.28018e15 4.28018e15i 0.177155 0.177155i
\(220\) 1.27657e15i 0.0511783i
\(221\) 1.79140e16 + 4.19558e15i 0.695740 + 0.162947i
\(222\) 1.12002e16 0.421459
\(223\) −7.52643e15 7.52643e15i −0.274445 0.274445i 0.556442 0.830887i \(-0.312166\pi\)
−0.830887 + 0.556442i \(0.812166\pi\)
\(224\) −1.94505e15 −0.0687377
\(225\) 2.15998e16i 0.739897i
\(226\) 2.57406e16 + 2.57406e16i 0.854789 + 0.854789i
\(227\) −4.94179e15 4.94179e15i −0.159112 0.159112i 0.623061 0.782173i \(-0.285889\pi\)
−0.782173 + 0.623061i \(0.785889\pi\)
\(228\) 2.27507e15 2.27507e15i 0.0710316 0.0710316i
\(229\) 3.62744e16 3.62744e16i 1.09838 1.09838i 0.103777 0.994601i \(-0.466907\pi\)
0.994601 0.103777i \(-0.0330930\pi\)
\(230\) −5.43823e15 −0.159721
\(231\) 4.91191e15i 0.139948i
\(232\) −1.71227e16 + 1.71227e16i −0.473323 + 0.473323i
\(233\) 3.79238e16i 1.01723i 0.860993 + 0.508617i \(0.169843\pi\)
−0.860993 + 0.508617i \(0.830157\pi\)
\(234\) −2.72368e16 + 1.68997e16i −0.708999 + 0.439915i
\(235\) 5.98501e14 0.0151213
\(236\) −6.47040e15 6.47040e15i −0.158689 0.158689i
\(237\) −1.63281e16 −0.388774
\(238\) 5.01934e15i 0.116040i
\(239\) 2.53393e16 + 2.53393e16i 0.568866 + 0.568866i 0.931811 0.362945i \(-0.118229\pi\)
−0.362945 + 0.931811i \(0.618229\pi\)
\(240\) 2.13256e15 + 2.13256e15i 0.0464969 + 0.0464969i
\(241\) −3.37486e15 + 3.37486e15i −0.0714722 + 0.0714722i −0.741939 0.670467i \(-0.766094\pi\)
0.670467 + 0.741939i \(0.266094\pi\)
\(242\) 1.02316e17 1.02316e17i 2.10491 2.10491i
\(243\) −5.16085e16 −1.03152
\(244\) 1.80113e16i 0.349797i
\(245\) 4.07055e15 4.07055e15i 0.0768229 0.0768229i
\(246\) 5.44346e16i 0.998457i
\(247\) 3.97315e16 2.46524e16i 0.708364 0.439521i
\(248\) −1.62962e16 −0.282439
\(249\) −3.02343e16 3.02343e16i −0.509453 0.509453i
\(250\) −1.49995e16 −0.245751
\(251\) 6.72375e16i 1.07126i 0.844452 + 0.535631i \(0.179926\pi\)
−0.844452 + 0.535631i \(0.820074\pi\)
\(252\) 1.19911e15 + 1.19911e15i 0.0185804 + 0.0185804i
\(253\) −1.16153e17 1.16153e17i −1.75060 1.75060i
\(254\) −5.12665e16 + 5.12665e16i −0.751618 + 0.751618i
\(255\) −1.96958e15 + 1.96958e15i −0.0280926 + 0.0280926i
\(256\) 4.92383e16 0.683318
\(257\) 8.23263e15i 0.111175i −0.998454 0.0555874i \(-0.982297\pi\)
0.998454 0.0555874i \(-0.0177032\pi\)
\(258\) −1.18094e16 + 1.18094e16i −0.155200 + 0.155200i
\(259\) 8.61127e15i 0.110146i
\(260\) −1.13087e15 1.82259e15i −0.0140799 0.0226921i
\(261\) 4.89123e16 0.592836
\(262\) 1.47190e16 + 1.47190e16i 0.173688 + 0.173688i
\(263\) −1.36769e17 −1.57144 −0.785720 0.618582i \(-0.787707\pi\)
−0.785720 + 0.618582i \(0.787707\pi\)
\(264\) 7.25664e16i 0.811910i
\(265\) −6.52799e15 6.52799e15i −0.0711309 0.0711309i
\(266\) −9.01988e15 9.01988e15i −0.0957259 0.0957259i
\(267\) −3.16121e16 + 3.16121e16i −0.326795 + 0.326795i
\(268\) 4.29456e15 4.29456e15i 0.0432489 0.0432489i
\(269\) 1.33505e17 1.30988 0.654939 0.755682i \(-0.272694\pi\)
0.654939 + 0.755682i \(0.272694\pi\)
\(270\) 1.13304e16i 0.108317i
\(271\) −5.84550e16 + 5.84550e16i −0.544549 + 0.544549i −0.924859 0.380310i \(-0.875817\pi\)
0.380310 + 0.924859i \(0.375817\pi\)
\(272\) 9.30894e16i 0.845119i
\(273\) −4.35129e15 7.01284e15i −0.0385016 0.0620520i
\(274\) 6.35307e16 0.547936
\(275\) −1.59190e17 1.59190e17i −1.33841 1.33841i
\(276\) −1.89917e16 −0.155668
\(277\) 1.35119e17i 1.07983i 0.841719 + 0.539917i \(0.181544\pi\)
−0.841719 + 0.539917i \(0.818456\pi\)
\(278\) 9.15733e16 + 9.15733e16i 0.713601 + 0.713601i
\(279\) 2.32756e16 + 2.32756e16i 0.176877 + 0.176877i
\(280\) 1.30610e15 1.30610e15i 0.00967985 0.00967985i
\(281\) 1.76695e17 1.76695e17i 1.27726 1.27726i 0.335066 0.942195i \(-0.391241\pi\)
0.942195 0.335066i \(-0.108759\pi\)
\(282\) 1.07779e16 0.0759961
\(283\) 9.09025e16i 0.625275i 0.949873 + 0.312637i \(0.101212\pi\)
−0.949873 + 0.312637i \(0.898788\pi\)
\(284\) −9.32187e15 + 9.32187e15i −0.0625568 + 0.0625568i
\(285\) 7.07875e15i 0.0463493i
\(286\) 7.61844e16 3.25287e17i 0.486748 2.07828i
\(287\) 4.18520e16 0.260941
\(288\) −4.10422e16 4.10422e16i −0.249737 0.249737i
\(289\) 8.24031e16 0.489394
\(290\) 1.68777e16i 0.0978426i
\(291\) −1.53531e16 1.53531e16i −0.0868851 0.0868851i
\(292\) −1.54017e16 1.54017e16i −0.0850918 0.0850918i
\(293\) 8.64610e16 8.64610e16i 0.466388 0.466388i −0.434354 0.900742i \(-0.643023\pi\)
0.900742 + 0.434354i \(0.143023\pi\)
\(294\) 7.33033e16 7.33033e16i 0.386093 0.386093i
\(295\) 2.01322e16 0.103547
\(296\) 1.27219e17i 0.639014i
\(297\) 2.42000e17 2.42000e17i 1.18719 1.18719i
\(298\) 2.59387e17i 1.24289i
\(299\) −2.68730e17 6.29384e16i −1.25782 0.294589i
\(300\) −2.60286e16 −0.119015
\(301\) 9.07967e15 + 9.07967e15i 0.0405606 + 0.0405606i
\(302\) −3.26091e17 −1.42328
\(303\) 2.04570e17i 0.872458i
\(304\) 1.67284e17 + 1.67284e17i 0.697172 + 0.697172i
\(305\) −2.80205e16 2.80205e16i −0.114124 0.114124i
\(306\) 1.05912e17 1.05912e17i 0.421596 0.421596i
\(307\) 7.72770e16 7.72770e16i 0.300664 0.300664i −0.540610 0.841274i \(-0.681806\pi\)
0.841274 + 0.540610i \(0.181806\pi\)
\(308\) −1.76749e16 −0.0672204
\(309\) 8.99702e16i 0.334495i
\(310\) −8.03151e15 + 8.03151e15i −0.0291921 + 0.0291921i
\(311\) 3.17755e17i 1.12920i 0.825366 + 0.564598i \(0.190969\pi\)
−0.825366 + 0.564598i \(0.809031\pi\)
\(312\) 6.42840e16 + 1.03605e17i 0.223368 + 0.359996i
\(313\) −2.79974e17 −0.951277 −0.475638 0.879641i \(-0.657783\pi\)
−0.475638 + 0.879641i \(0.657783\pi\)
\(314\) −2.00309e17 2.00309e17i −0.665567 0.665567i
\(315\) −3.73095e15 −0.0121240
\(316\) 5.87546e16i 0.186738i
\(317\) 2.62369e17 + 2.62369e17i 0.815640 + 0.815640i 0.985473 0.169833i \(-0.0543228\pi\)
−0.169833 + 0.985473i \(0.554323\pi\)
\(318\) −1.17557e17 1.17557e17i −0.357487 0.357487i
\(319\) −3.60484e17 + 3.60484e17i −1.07239 + 1.07239i
\(320\) −1.77347e16 + 1.77347e16i −0.0516148 + 0.0516148i
\(321\) 3.05915e17 0.871096
\(322\) 7.52956e16i 0.209787i
\(323\) −1.54499e17 + 1.54499e17i −0.421218 + 0.421218i
\(324\) 2.79825e16i 0.0746571i
\(325\) −3.68301e17 8.62586e16i −0.961656 0.225226i
\(326\) −3.86423e17 −0.987506
\(327\) 6.35871e16 + 6.35871e16i 0.159050 + 0.159050i
\(328\) −6.18303e17 −1.51386
\(329\) 8.28660e15i 0.0198612i
\(330\) 3.57640e16 + 3.57640e16i 0.0839167 + 0.0839167i
\(331\) 4.67857e17 + 4.67857e17i 1.07477 + 1.07477i 0.996969 + 0.0778045i \(0.0247910\pi\)
0.0778045 + 0.996969i \(0.475209\pi\)
\(332\) −1.08794e17 + 1.08794e17i −0.244703 + 0.244703i
\(333\) 1.81705e17 1.81705e17i 0.400182 0.400182i
\(334\) 9.55257e17 2.06013
\(335\) 1.33623e16i 0.0282206i
\(336\) 2.95266e16 2.95266e16i 0.0610715 0.0610715i
\(337\) 3.03989e17i 0.615812i −0.951417 0.307906i \(-0.900372\pi\)
0.951417 0.307906i \(-0.0996282\pi\)
\(338\) −1.79390e17 5.31909e17i −0.355944 1.05541i
\(339\) −2.79695e17 −0.543610
\(340\) 7.08726e15 + 7.08726e15i 0.0134935 + 0.0134935i
\(341\) −3.43083e17 −0.639910
\(342\) 3.80654e17i 0.695581i
\(343\) −1.13942e17 1.13942e17i −0.203998 0.203998i
\(344\) −1.34139e17 1.34139e17i −0.235313 0.235313i
\(345\) 2.95458e16 2.95458e16i 0.0507881 0.0507881i
\(346\) 3.08497e17 3.08497e17i 0.519659 0.519659i
\(347\) 9.68427e16 0.159868 0.0799339 0.996800i \(-0.474529\pi\)
0.0799339 + 0.996800i \(0.474529\pi\)
\(348\) 5.89414e16i 0.0953598i
\(349\) 6.60094e17 6.60094e17i 1.04671 1.04671i 0.0478593 0.998854i \(-0.484760\pi\)
0.998854 0.0478593i \(-0.0152399\pi\)
\(350\) 1.03195e17i 0.160391i
\(351\) 1.31130e17 5.59889e17i 0.199780 0.853005i
\(352\) 6.04963e17 0.903505
\(353\) 6.67572e17 + 6.67572e17i 0.977406 + 0.977406i 0.999750 0.0223445i \(-0.00711306\pi\)
−0.0223445 + 0.999750i \(0.507113\pi\)
\(354\) 3.62546e17 0.520403
\(355\) 2.90044e16i 0.0408193i
\(356\) 1.13752e17 + 1.13752e17i 0.156968 + 0.156968i
\(357\) 2.72699e16 + 2.72699e16i 0.0368983 + 0.0368983i
\(358\) 1.68054e17 1.68054e17i 0.222981 0.222981i
\(359\) −6.85110e17 + 6.85110e17i −0.891454 + 0.891454i −0.994660 0.103206i \(-0.967090\pi\)
0.103206 + 0.994660i \(0.467090\pi\)
\(360\) 5.51194e16 0.0703376
\(361\) 2.43730e17i 0.305041i
\(362\) −2.42761e16 + 2.42761e16i −0.0298002 + 0.0298002i
\(363\) 1.11175e18i 1.33864i
\(364\) −2.52348e16 + 1.56575e16i −0.0298051 + 0.0184933i
\(365\) 4.79213e16 0.0555238
\(366\) −5.04599e17 5.04599e17i −0.573560 0.573560i
\(367\) −1.24504e18 −1.38842 −0.694211 0.719771i \(-0.744247\pi\)
−0.694211 + 0.719771i \(0.744247\pi\)
\(368\) 1.39644e18i 1.52788i
\(369\) 8.83113e17 + 8.83113e17i 0.948051 + 0.948051i
\(370\) 6.26994e16 + 6.26994e16i 0.0660467 + 0.0660467i
\(371\) −9.03839e16 + 9.03839e16i −0.0934272 + 0.0934272i
\(372\) −2.80481e16 + 2.80481e16i −0.0284513 + 0.0284513i
\(373\) 7.60754e17 0.757325 0.378663 0.925535i \(-0.376384\pi\)
0.378663 + 0.925535i \(0.376384\pi\)
\(374\) 1.56115e18i 1.52526i
\(375\) 8.14917e16 8.14917e16i 0.0781438 0.0781438i
\(376\) 1.22423e17i 0.115225i
\(377\) −1.95331e17 + 8.34011e17i −0.180460 + 0.770517i
\(378\) −1.56876e17 −0.142270
\(379\) −1.19975e18 1.19975e18i −1.06811 1.06811i −0.997504 0.0706038i \(-0.977507\pi\)
−0.0706038 0.997504i \(-0.522493\pi\)
\(380\) 2.54720e16 0.0222627
\(381\) 5.57059e17i 0.477998i
\(382\) 1.38184e17 + 1.38184e17i 0.116417 + 0.116417i
\(383\) −1.80601e17 1.80601e17i −0.149393 0.149393i 0.628454 0.777847i \(-0.283688\pi\)
−0.777847 + 0.628454i \(0.783688\pi\)
\(384\) −5.24946e17 + 5.24946e17i −0.426380 + 0.426380i
\(385\) 2.74971e16 2.74971e16i 0.0219312 0.0219312i
\(386\) −2.03544e18 −1.59422
\(387\) 3.83177e17i 0.294729i
\(388\) −5.52461e16 + 5.52461e16i −0.0417330 + 0.0417330i
\(389\) 1.70230e18i 1.26296i −0.775392 0.631480i \(-0.782448\pi\)
0.775392 0.631480i \(-0.217552\pi\)
\(390\) 8.27432e16 + 1.93790e16i 0.0602948 + 0.0141215i
\(391\) 1.28971e18 0.923116
\(392\) 8.32626e17 + 8.32626e17i 0.585393 + 0.585393i
\(393\) −1.59936e17 −0.110458
\(394\) 2.84632e17i 0.193112i
\(395\) −9.14056e16 9.14056e16i −0.0609247 0.0609247i
\(396\) −3.72954e17 3.72954e17i −0.244225 0.244225i
\(397\) 3.84862e17 3.84862e17i 0.247612 0.247612i −0.572378 0.819990i \(-0.693979\pi\)
0.819990 + 0.572378i \(0.193979\pi\)
\(398\) −5.26190e17 + 5.26190e17i −0.332629 + 0.332629i
\(399\) 9.80095e16 0.0608777
\(400\) 1.91386e18i 1.16813i
\(401\) 4.58433e17 4.58433e17i 0.274957 0.274957i −0.556135 0.831092i \(-0.687716\pi\)
0.831092 + 0.556135i \(0.187716\pi\)
\(402\) 2.40630e17i 0.141830i
\(403\) −4.89828e17 + 3.03925e17i −0.283732 + 0.176048i
\(404\) −7.36120e17 −0.419063
\(405\) −4.35329e16 4.35329e16i −0.0243575 0.0243575i
\(406\) 2.33682e17 0.128512
\(407\) 2.67834e18i 1.44779i
\(408\) −4.02874e17 4.02874e17i −0.214066 0.214066i
\(409\) 4.25730e16 + 4.25730e16i 0.0222368 + 0.0222368i 0.718138 0.695901i \(-0.244995\pi\)
−0.695901 + 0.718138i \(0.744995\pi\)
\(410\) −3.04728e17 + 3.04728e17i −0.156468 + 0.156468i
\(411\) −3.45160e17 + 3.45160e17i −0.174232 + 0.174232i
\(412\) 3.23746e17 0.160666
\(413\) 2.78743e17i 0.136005i
\(414\) −1.58880e18 + 1.58880e18i −0.762196 + 0.762196i
\(415\) 3.38506e17i 0.159672i
\(416\) 8.63720e17 5.35916e17i 0.400608 0.248567i
\(417\) −9.95031e17 −0.453820
\(418\) 2.80543e18 + 2.80543e18i 1.25824 + 1.25824i
\(419\) 2.22931e18 0.983267 0.491633 0.870802i \(-0.336400\pi\)
0.491633 + 0.870802i \(0.336400\pi\)
\(420\) 4.49595e15i 0.00195019i
\(421\) −2.33481e18 2.33481e18i −0.996041 0.996041i 0.00395089 0.999992i \(-0.498742\pi\)
−0.999992 + 0.00395089i \(0.998742\pi\)
\(422\) 1.33926e16 + 1.33926e16i 0.00561924 + 0.00561924i
\(423\) 1.74854e17 1.74854e17i 0.0721595 0.0721595i
\(424\) 1.33529e18 1.33529e18i 0.542020 0.542020i
\(425\) 1.76759e18 0.705762
\(426\) 5.22318e17i 0.205148i
\(427\) −3.87961e17 + 3.87961e17i −0.149897 + 0.149897i
\(428\) 1.10080e18i 0.418408i
\(429\) 1.35337e18 + 2.18118e18i 0.506075 + 0.815626i
\(430\) −1.32220e17 −0.0486426
\(431\) −2.61335e18 2.61335e18i −0.945926 0.945926i 0.0526854 0.998611i \(-0.483222\pi\)
−0.998611 + 0.0526854i \(0.983222\pi\)
\(432\) 2.90944e18 1.03615
\(433\) 2.16540e18i 0.758793i 0.925234 + 0.379396i \(0.123868\pi\)
−0.925234 + 0.379396i \(0.876132\pi\)
\(434\) 1.11201e17 + 1.11201e17i 0.0383425 + 0.0383425i
\(435\) −9.16962e16 9.16962e16i −0.0311119 0.0311119i
\(436\) 2.28810e17 2.28810e17i 0.0763958 0.0763958i
\(437\) 2.31765e18 2.31765e18i 0.761514 0.761514i
\(438\) 8.62977e17 0.279049
\(439\) 3.89405e18i 1.23922i −0.784909 0.619611i \(-0.787290\pi\)
0.784909 0.619611i \(-0.212710\pi\)
\(440\) −4.06231e17 + 4.06231e17i −0.127234 + 0.127234i
\(441\) 2.37845e18i 0.733204i
\(442\) 1.38297e18 + 2.22889e18i 0.419620 + 0.676289i
\(443\) 4.07893e18 1.21821 0.609103 0.793091i \(-0.291530\pi\)
0.609103 + 0.793091i \(0.291530\pi\)
\(444\) 2.18962e17 + 2.18962e17i 0.0643707 + 0.0643707i
\(445\) −3.53933e17 −0.102424
\(446\) 1.51749e18i 0.432297i
\(447\) −1.40924e18 1.40924e18i −0.395214 0.395214i
\(448\) 2.45548e17 + 2.45548e17i 0.0677938 + 0.0677938i
\(449\) 7.62760e17 7.62760e17i 0.207331 0.207331i −0.595801 0.803132i \(-0.703165\pi\)
0.803132 + 0.595801i \(0.203165\pi\)
\(450\) −2.17749e18 + 2.17749e18i −0.582732 + 0.582732i
\(451\) −1.30171e19 −3.42988
\(452\) 1.00645e18i 0.261109i
\(453\) 1.77164e18 1.77164e18i 0.452574 0.452574i
\(454\) 9.96373e17i 0.250629i
\(455\) 1.48995e16 6.36170e16i 0.00369057 0.0157577i
\(456\) −1.44795e18 −0.353183
\(457\) 1.65256e18 + 1.65256e18i 0.396956 + 0.396956i 0.877158 0.480202i \(-0.159437\pi\)
−0.480202 + 0.877158i \(0.659437\pi\)
\(458\) 7.31371e18 1.73013
\(459\) 2.68707e18i 0.626024i
\(460\) −1.06317e17 1.06317e17i −0.0243948 0.0243948i
\(461\) −8.83635e17 8.83635e17i −0.199695 0.199695i 0.600174 0.799869i \(-0.295098\pi\)
−0.799869 + 0.600174i \(0.795098\pi\)
\(462\) 4.95174e17 4.95174e17i 0.110221 0.110221i
\(463\) −5.31532e18 + 5.31532e18i −1.16537 + 1.16537i −0.182083 + 0.983283i \(0.558284\pi\)
−0.983283 + 0.182083i \(0.941716\pi\)
\(464\) −4.33391e18 −0.935952
\(465\) 8.72700e16i 0.0185650i
\(466\) −3.82314e18 + 3.82314e18i −0.801158 + 0.801158i
\(467\) 5.02545e18i 1.03742i 0.854949 + 0.518712i \(0.173588\pi\)
−0.854949 + 0.518712i \(0.826412\pi\)
\(468\) −8.62863e17 2.02088e17i −0.175477 0.0410980i
\(469\) 1.85008e17 0.0370665
\(470\) 6.03354e16 + 6.03354e16i 0.0119093 + 0.0119093i
\(471\) 2.17654e18 0.423273
\(472\) 4.11803e18i 0.789033i
\(473\) −2.82402e18 2.82402e18i −0.533138 0.533138i
\(474\) −1.64605e18 1.64605e18i −0.306193 0.306193i
\(475\) 3.17640e18 3.17640e18i 0.582210 0.582210i
\(476\) 9.81273e16 9.81273e16i 0.0177232 0.0177232i
\(477\) −3.81435e18 −0.678878
\(478\) 5.10896e18i 0.896061i
\(479\) −3.30952e18 + 3.30952e18i −0.572026 + 0.572026i −0.932694 0.360668i \(-0.882549\pi\)
0.360668 + 0.932694i \(0.382549\pi\)
\(480\) 1.53884e17i 0.0262124i
\(481\) 2.37264e18 + 3.82392e18i 0.398306 + 0.641939i
\(482\) −6.80446e17 −0.112581
\(483\) −4.09079e17 4.09079e17i −0.0667079 0.0667079i
\(484\) 4.00051e18 0.642980
\(485\) 1.71895e17i 0.0272315i
\(486\) −5.20270e18 5.20270e18i −0.812409 0.812409i
\(487\) 6.01603e18 + 6.01603e18i 0.925993 + 0.925993i 0.997444 0.0714514i \(-0.0227631\pi\)
−0.0714514 + 0.997444i \(0.522763\pi\)
\(488\) 5.73156e18 5.73156e18i 0.869630 0.869630i
\(489\) 2.09943e18 2.09943e18i 0.314006 0.314006i
\(490\) 8.20712e17 0.121009
\(491\) 1.06187e19i 1.54347i −0.635942 0.771737i \(-0.719388\pi\)
0.635942 0.771737i \(-0.280612\pi\)
\(492\) −1.06419e18 + 1.06419e18i −0.152497 + 0.152497i
\(493\) 4.00267e18i 0.565485i
\(494\) 6.49060e18 + 1.52014e18i 0.904057 + 0.211736i
\(495\) 1.16043e18 0.159361
\(496\) −2.06235e18 2.06235e18i −0.279249 0.279249i
\(497\) −4.01584e17 −0.0536144
\(498\) 6.09589e18i 0.802475i
\(499\) −2.78129e18 2.78129e18i −0.361029 0.361029i 0.503163 0.864192i \(-0.332170\pi\)
−0.864192 + 0.503163i \(0.832170\pi\)
\(500\) −2.93237e17 2.93237e17i −0.0375344 0.0375344i
\(501\) −5.18989e18 + 5.18989e18i −0.655079 + 0.655079i
\(502\) −6.77827e18 + 6.77827e18i −0.843710 + 0.843710i
\(503\) 1.40706e19 1.72717 0.863586 0.504202i \(-0.168213\pi\)
0.863586 + 0.504202i \(0.168213\pi\)
\(504\) 7.63161e17i 0.0923852i
\(505\) 1.14520e18 1.14520e18i 0.136723 0.136723i
\(506\) 2.34189e19i 2.75749i
\(507\) 3.86447e18 + 1.91522e18i 0.448780 + 0.222415i
\(508\) −2.00450e18 −0.229594
\(509\) 9.50188e18 + 9.50188e18i 1.07346 + 1.07346i 0.997079 + 0.0763797i \(0.0243361\pi\)
0.0763797 + 0.997079i \(0.475664\pi\)
\(510\) −3.97109e17 −0.0442506
\(511\) 6.63499e17i 0.0729280i
\(512\) −2.88788e18 2.88788e18i −0.313104 0.313104i
\(513\) 4.82874e18 + 4.82874e18i 0.516431 + 0.516431i
\(514\) 8.29939e17 8.29939e17i 0.0875597 0.0875597i
\(515\) −5.03658e17 + 5.03658e17i −0.0524186 + 0.0524186i
\(516\) −4.61745e17 −0.0474083
\(517\) 2.57735e18i 0.261060i
\(518\) 8.68110e17 8.68110e17i 0.0867494 0.0867494i
\(519\) 3.35211e18i 0.330482i
\(520\) −2.20119e17 + 9.39851e17i −0.0214109 + 0.0914188i
\(521\) 6.10865e18 0.586248 0.293124 0.956074i \(-0.405305\pi\)
0.293124 + 0.956074i \(0.405305\pi\)
\(522\) 4.93089e18 + 4.93089e18i 0.466909 + 0.466909i
\(523\) 8.20567e18 0.766659 0.383330 0.923612i \(-0.374777\pi\)
0.383330 + 0.923612i \(0.374777\pi\)
\(524\) 5.75509e17i 0.0530559i
\(525\) −5.60653e17 5.60653e17i −0.0510011 0.0510011i
\(526\) −1.37878e19 1.37878e19i −1.23764 1.23764i
\(527\) 1.90473e18 1.90473e18i 0.168717 0.168717i
\(528\) −9.18357e18 + 9.18357e18i −0.802739 + 0.802739i
\(529\) −7.75429e18 −0.668886
\(530\) 1.31618e18i 0.112043i
\(531\) 5.88171e18 5.88171e18i 0.494131 0.494131i
\(532\) 3.52675e17i 0.0292410i
\(533\) −1.85848e19 + 1.15314e19i −1.52078 + 0.943607i
\(534\) −6.37370e18 −0.514758
\(535\) 1.71253e18 + 1.71253e18i 0.136509 + 0.136509i
\(536\) −2.73323e18 −0.215042
\(537\) 1.82607e18i 0.141807i
\(538\) 1.34587e19 + 1.34587e19i 1.03164 + 1.03164i
\(539\) 1.75292e19 + 1.75292e19i 1.32630 + 1.32630i
\(540\) 2.21507e17 2.21507e17i 0.0165436 0.0165436i
\(541\) −5.17154e17 + 5.17154e17i −0.0381276 + 0.0381276i −0.725914 0.687786i \(-0.758583\pi\)
0.687786 + 0.725914i \(0.258583\pi\)
\(542\) −1.17858e19 −0.857757
\(543\) 2.63783e17i 0.0189517i
\(544\) −3.35864e18 + 3.35864e18i −0.238216 + 0.238216i
\(545\) 7.11929e17i 0.0498495i
\(546\) 2.68314e17 1.14563e18i 0.0185479 0.0791945i
\(547\) −1.28317e19 −0.875732 −0.437866 0.899040i \(-0.644266\pi\)
−0.437866 + 0.899040i \(0.644266\pi\)
\(548\) 1.24201e18 + 1.24201e18i 0.0836879 + 0.0836879i
\(549\) −1.63726e19 −1.08921
\(550\) 3.20963e19i 2.10822i
\(551\) −7.19290e18 7.19290e18i −0.466491 0.466491i
\(552\) 6.04355e18 + 6.04355e18i 0.387007 + 0.387007i
\(553\) −1.26557e18 + 1.26557e18i −0.0800219 + 0.0800219i
\(554\) −1.36214e19 + 1.36214e19i −0.850460 + 0.850460i
\(555\) −6.81288e17 −0.0420030
\(556\) 3.58049e18i 0.217981i
\(557\) 6.06968e18 6.06968e18i 0.364905 0.364905i −0.500710 0.865615i \(-0.666928\pi\)
0.865615 + 0.500710i \(0.166928\pi\)
\(558\) 4.69287e18i 0.278612i
\(559\) −6.53362e18 1.53022e18i −0.383064 0.0897162i
\(560\) 3.30583e17 0.0191410
\(561\) −8.48168e18 8.48168e18i −0.485000 0.485000i
\(562\) 3.56255e19 2.01190
\(563\) 1.83779e19i 1.02503i −0.858678 0.512516i \(-0.828713\pi\)
0.858678 0.512516i \(-0.171287\pi\)
\(564\) 2.10707e17 + 2.10707e17i 0.0116071 + 0.0116071i
\(565\) −1.56575e18 1.56575e18i −0.0851890 0.0851890i
\(566\) −9.16397e18 + 9.16397e18i −0.492457 + 0.492457i
\(567\) −6.02739e17 + 6.02739e17i −0.0319925 + 0.0319925i
\(568\) 5.93282e18 0.311045
\(569\) 3.29569e18i 0.170671i 0.996352 + 0.0853355i \(0.0271962\pi\)
−0.996352 + 0.0853355i \(0.972804\pi\)
\(570\) −7.13616e17 + 7.13616e17i −0.0365040 + 0.0365040i
\(571\) 1.15752e19i 0.584892i −0.956282 0.292446i \(-0.905531\pi\)
0.956282 0.292446i \(-0.0944691\pi\)
\(572\) 7.84870e18 4.86991e18i 0.391765 0.243080i
\(573\) −1.50150e18 −0.0740362
\(574\) 4.21914e18 + 4.21914e18i 0.205514 + 0.205514i
\(575\) −2.65157e19 −1.27594
\(576\) 1.03625e19i 0.492616i
\(577\) 5.57983e18 + 5.57983e18i 0.262054 + 0.262054i 0.825888 0.563834i \(-0.190674\pi\)
−0.563834 + 0.825888i \(0.690674\pi\)
\(578\) 8.30713e18 + 8.30713e18i 0.385440 + 0.385440i
\(579\) 1.10585e19 1.10585e19i 0.506927 0.506927i
\(580\) −3.29957e17 + 3.29957e17i −0.0149438 + 0.0149438i
\(581\) −4.68682e18 −0.209723
\(582\) 3.09552e18i 0.136859i
\(583\) 2.81118e19 2.81118e19i 1.22803 1.22803i
\(584\) 9.80225e18i 0.423093i
\(585\) 1.65677e18 1.02798e18i 0.0706594 0.0438423i
\(586\) 1.74324e19 0.734640
\(587\) 9.50742e18 + 9.50742e18i 0.395909 + 0.395909i 0.876787 0.480878i \(-0.159682\pi\)
−0.480878 + 0.876787i \(0.659682\pi\)
\(588\) 2.86614e18 0.117939
\(589\) 6.84569e18i 0.278362i
\(590\) 2.02955e18 + 2.02955e18i 0.0815522 + 0.0815522i
\(591\) −1.54640e18 1.54640e18i −0.0614056 0.0614056i
\(592\) −1.61001e19 + 1.61001e19i −0.631796 + 0.631796i
\(593\) −3.19617e19 + 3.19617e19i −1.23950 + 1.23950i −0.279299 + 0.960204i \(0.590102\pi\)
−0.960204 + 0.279299i \(0.909898\pi\)
\(594\) 4.87925e19 1.87003
\(595\) 3.05317e17i 0.0115647i
\(596\) −5.07097e18 + 5.07097e18i −0.189831 + 0.189831i
\(597\) 5.71755e18i 0.211539i
\(598\) −2.07460e19 3.34358e19i −0.758624 1.22265i
\(599\) 8.42119e18 0.304359 0.152179 0.988353i \(-0.451371\pi\)
0.152179 + 0.988353i \(0.451371\pi\)
\(600\) 8.28285e18 + 8.28285e18i 0.295884 + 0.295884i
\(601\) −2.60694e19 −0.920469 −0.460234 0.887797i \(-0.652235\pi\)
−0.460234 + 0.887797i \(0.652235\pi\)
\(602\) 1.83066e18i 0.0638899i
\(603\) 3.90383e18 + 3.90383e18i 0.134670 + 0.134670i
\(604\) −6.37503e18 6.37503e18i −0.217382 0.217382i
\(605\) −6.22367e18 + 6.22367e18i −0.209777 + 0.209777i
\(606\) 2.06229e19 2.06229e19i 0.687135 0.687135i
\(607\) 2.78903e19 0.918612 0.459306 0.888278i \(-0.348098\pi\)
0.459306 + 0.888278i \(0.348098\pi\)
\(608\) 1.20711e19i 0.393027i
\(609\) −1.26959e18 + 1.26959e18i −0.0408641 + 0.0408641i
\(610\) 5.64955e18i 0.179765i
\(611\) 2.28319e18 + 3.67975e18i 0.0718213 + 0.115752i
\(612\) 4.14114e18 0.128783
\(613\) −1.33803e19 1.33803e19i −0.411380 0.411380i 0.470839 0.882219i \(-0.343951\pi\)
−0.882219 + 0.470839i \(0.843951\pi\)
\(614\) 1.55807e19 0.473597
\(615\) 3.31116e18i 0.0995071i
\(616\) 5.62451e18 + 5.62451e18i 0.167117 + 0.167117i
\(617\) 2.36469e18 + 2.36469e18i 0.0694668 + 0.0694668i 0.740987 0.671520i \(-0.234358\pi\)
−0.671520 + 0.740987i \(0.734358\pi\)
\(618\) −9.06998e18 + 9.06998e18i −0.263443 + 0.263443i
\(619\) 3.05943e19 3.05943e19i 0.878629 0.878629i −0.114764 0.993393i \(-0.536611\pi\)
0.993393 + 0.114764i \(0.0366113\pi\)
\(620\) −3.14030e17 −0.00891721
\(621\) 4.03090e19i 1.13178i
\(622\) −3.20331e19 + 3.20331e19i −0.889338 + 0.889338i
\(623\) 4.90041e18i 0.134529i
\(624\) −4.97619e18 + 2.12470e19i −0.135084 + 0.576774i
\(625\) −3.58815e19 −0.963186
\(626\) −2.82244e19 2.82244e19i −0.749211 0.749211i
\(627\) −3.04836e19 −0.800190
\(628\) 7.83200e18i 0.203308i
\(629\) −1.48696e19 1.48696e19i −0.381719 0.381719i
\(630\) −3.76120e17 3.76120e17i −0.00954868 0.00954868i
\(631\) 4.28697e19 4.28697e19i 1.07633 1.07633i 0.0794946 0.996835i \(-0.474669\pi\)
0.996835 0.0794946i \(-0.0253306\pi\)
\(632\) 1.86969e19 1.86969e19i 0.464248 0.464248i
\(633\) −1.45523e17 −0.00357360
\(634\) 5.28994e19i 1.28477i
\(635\) 3.11844e18 3.11844e18i 0.0749069 0.0749069i
\(636\) 4.59645e18i 0.109200i
\(637\) 4.05554e19 + 9.49835e18i 0.952956 + 0.223189i
\(638\) −7.26814e19 −1.68919
\(639\) −8.47375e18 8.47375e18i −0.194791 0.194791i
\(640\) −5.87736e18 −0.133636
\(641\) 5.51770e19i 1.24094i 0.784229 + 0.620472i \(0.213059\pi\)
−0.784229 + 0.620472i \(0.786941\pi\)
\(642\) 3.08396e19 + 3.08396e19i 0.686062 + 0.686062i
\(643\) 2.06268e19 + 2.06268e19i 0.453895 + 0.453895i 0.896645 0.442750i \(-0.145997\pi\)
−0.442750 + 0.896645i \(0.645997\pi\)
\(644\) −1.47202e18 + 1.47202e18i −0.0320414 + 0.0320414i
\(645\) 7.18346e17 7.18346e17i 0.0154673 0.0154673i
\(646\) −3.11503e19 −0.663491
\(647\) 7.09991e19i 1.49597i 0.663715 + 0.747985i \(0.268979\pi\)
−0.663715 + 0.747985i \(0.731021\pi\)
\(648\) 8.90460e18 8.90460e18i 0.185605 0.185605i
\(649\) 8.66965e19i 1.78768i
\(650\) −2.84330e19 4.58246e19i −0.580001 0.934770i
\(651\) −1.20830e18 −0.0243843
\(652\) −7.55451e18 7.55451e18i −0.150825 0.150825i
\(653\) −5.96284e19 −1.17777 −0.588885 0.808217i \(-0.700433\pi\)
−0.588885 + 0.808217i \(0.700433\pi\)
\(654\) 1.28206e19i 0.250532i
\(655\) −8.95332e17 8.95332e17i −0.0173099 0.0173099i
\(656\) −7.82488e19 7.82488e19i −1.49676 1.49676i
\(657\) 1.40004e19 1.40004e19i 0.264961 0.264961i
\(658\) 8.35380e17 8.35380e17i 0.0156424 0.0156424i
\(659\) −3.76869e19 −0.698220 −0.349110 0.937082i \(-0.613516\pi\)
−0.349110 + 0.937082i \(0.613516\pi\)
\(660\) 1.39836e18i 0.0256337i
\(661\) −7.96405e18 + 7.96405e18i −0.144452 + 0.144452i −0.775634 0.631182i \(-0.782570\pi\)
0.631182 + 0.775634i \(0.282570\pi\)
\(662\) 9.43301e19i 1.69295i
\(663\) −1.96231e19 4.59587e18i −0.348476 0.0816155i
\(664\) 6.92410e19 1.21671
\(665\) 5.48663e17 + 5.48663e17i 0.00954013 + 0.00954013i
\(666\) 3.66357e19 0.630355
\(667\) 6.00444e19i 1.02233i
\(668\) 1.86751e19 + 1.86751e19i 0.314650 + 0.314650i
\(669\) 8.24450e18 + 8.24450e18i 0.137462 + 0.137462i
\(670\) −1.34706e18 + 1.34706e18i −0.0222261 + 0.0222261i
\(671\) 1.20666e20 1.20666e20i 1.97028 1.97028i
\(672\) 2.13062e18 0.0344288
\(673\) 6.45234e19i 1.03184i −0.856637 0.515919i \(-0.827450\pi\)
0.856637 0.515919i \(-0.172550\pi\)
\(674\) 3.06454e19 3.06454e19i 0.485004 0.485004i
\(675\) 5.52446e19i 0.865293i
\(676\) 6.89168e18 1.39058e19i 0.106831 0.215560i
\(677\) 1.19160e20 1.82815 0.914073 0.405550i \(-0.132920\pi\)
0.914073 + 0.405550i \(0.132920\pi\)
\(678\) −2.81964e19 2.81964e19i −0.428139 0.428139i
\(679\) −2.37999e18 −0.0357673
\(680\) 4.51062e18i 0.0670925i
\(681\) 5.41327e18 + 5.41327e18i 0.0796948 + 0.0796948i
\(682\) −3.45865e19 3.45865e19i −0.503983 0.503983i
\(683\) −6.01411e19 + 6.01411e19i −0.867414 + 0.867414i −0.992185 0.124772i \(-0.960180\pi\)
0.124772 + 0.992185i \(0.460180\pi\)
\(684\) 7.44173e18 7.44173e18i 0.106238 0.106238i
\(685\) −3.86445e18 −0.0546077
\(686\) 2.29733e19i 0.321332i
\(687\) −3.97352e19 + 3.97352e19i −0.550146 + 0.550146i
\(688\) 3.39517e19i 0.465310i
\(689\) 1.52326e19 6.50391e19i 0.206652 0.882348i
\(690\) 5.95707e18 0.0799999
\(691\) 3.90835e19 + 3.90835e19i 0.519574 + 0.519574i 0.917443 0.397868i \(-0.130250\pi\)
−0.397868 + 0.917443i \(0.630250\pi\)
\(692\) 1.20621e19 0.158738
\(693\) 1.60668e19i 0.209313i
\(694\) 9.76280e18 + 9.76280e18i 0.125909 + 0.125909i
\(695\) −5.57024e18 5.57024e18i −0.0711181 0.0711181i
\(696\) 1.87564e19 1.87564e19i 0.237074 0.237074i
\(697\) 7.22683e19 7.22683e19i 0.904312 0.904312i
\(698\) 1.33089e20 1.64875
\(699\) 4.15420e19i 0.509503i
\(700\) −2.01744e18 + 2.01744e18i −0.0244970 + 0.0244970i
\(701\) 8.14488e19i 0.979171i 0.871955 + 0.489586i \(0.162852\pi\)
−0.871955 + 0.489586i \(0.837148\pi\)
\(702\) 6.96622e19 4.32236e19i 0.829158 0.514471i
\(703\) −5.34421e19 −0.629790
\(704\) −7.63719e19 7.63719e19i −0.891097 0.891097i
\(705\) −6.55601e17 −0.00757384
\(706\) 1.34597e20i 1.53958i
\(707\) −1.58559e19 1.58559e19i −0.179579 0.179579i
\(708\) 7.08771e18 + 7.08771e18i 0.0794828 + 0.0794828i
\(709\) −9.76920e19 + 9.76920e19i −1.08476 + 1.08476i −0.0887060 + 0.996058i \(0.528273\pi\)
−0.996058 + 0.0887060i \(0.971727\pi\)
\(710\) 2.92396e18 2.92396e18i 0.0321487 0.0321487i
\(711\) −5.34090e19 −0.581470
\(712\) 7.23966e19i 0.780473i
\(713\) −2.85730e19 + 2.85730e19i −0.305021 + 0.305021i
\(714\) 5.49821e18i 0.0581211i
\(715\) −4.63416e18 + 1.97866e19i −0.0485097 + 0.207123i
\(716\) 6.57087e18 0.0681132
\(717\) −2.77569e19 2.77569e19i −0.284929 0.284929i
\(718\) −1.38133e20 −1.40419
\(719\) 1.07716e20i 1.08437i 0.840258 + 0.542186i \(0.182403\pi\)
−0.840258 + 0.542186i \(0.817597\pi\)
\(720\) 6.97559e18 + 6.97559e18i 0.0695430 + 0.0695430i
\(721\) 6.97345e18 + 6.97345e18i 0.0688495 + 0.0688495i
\(722\) 2.45707e19 2.45707e19i 0.240246 0.240246i
\(723\) 3.69685e18 3.69685e18i 0.0357984 0.0357984i
\(724\) −9.49189e17 −0.00910296
\(725\) 8.22924e19i 0.781617i
\(726\) −1.12077e20 + 1.12077e20i −1.05429 + 1.05429i
\(727\) 1.63428e20i 1.52260i 0.648398 + 0.761302i \(0.275439\pi\)
−0.648398 + 0.761302i \(0.724561\pi\)
\(728\) 1.30128e19 + 3.04768e18i 0.120074 + 0.0281223i
\(729\) 2.25773e19 0.206338
\(730\) 4.83099e18 + 4.83099e18i 0.0437297 + 0.0437297i
\(731\) 3.13568e19 0.281132
\(732\) 1.97297e19i 0.175203i
\(733\) 1.20713e18 + 1.20713e18i 0.0106176 + 0.0106176i 0.712396 0.701778i \(-0.247610\pi\)
−0.701778 + 0.712396i \(0.747610\pi\)
\(734\) −1.25514e20 1.25514e20i −1.09350 1.09350i
\(735\) −4.45891e18 + 4.45891e18i −0.0384784 + 0.0384784i
\(736\) 5.03832e19 5.03832e19i 0.430666 0.430666i
\(737\) −5.75425e19 −0.487210
\(738\) 1.78055e20i 1.49334i
\(739\) 1.41866e20 1.41866e20i 1.17861 1.17861i 0.198505 0.980100i \(-0.436391\pi\)
0.980100 0.198505i \(-0.0636088\pi\)
\(740\) 2.45153e18i 0.0201750i
\(741\) −4.35221e19 + 2.70043e19i −0.354799 + 0.220144i
\(742\) −1.82234e19 −0.147164
\(743\) −2.37536e19 2.37536e19i −0.190024 0.190024i 0.605683 0.795706i \(-0.292900\pi\)
−0.795706 + 0.605683i \(0.792900\pi\)
\(744\) 1.78510e19 0.141466
\(745\) 1.57780e19i 0.123868i
\(746\) 7.66923e19 + 7.66923e19i 0.596458 + 0.596458i
\(747\) −9.88959e19 9.88959e19i −0.761963 0.761963i
\(748\) −3.05202e19 + 3.05202e19i −0.232957 + 0.232957i
\(749\) 2.37110e19 2.37110e19i 0.179299 0.179299i
\(750\) 1.64305e19 0.123090
\(751\) 9.60699e19i 0.713030i −0.934290 0.356515i \(-0.883965\pi\)
0.934290 0.356515i \(-0.116035\pi\)
\(752\) −1.54931e19 + 1.54931e19i −0.113923 + 0.113923i
\(753\) 7.36524e19i 0.536564i
\(754\) −1.03769e20 + 6.43859e19i −0.748976 + 0.464720i
\(755\) 1.98355e19 0.141845
\(756\) −3.06689e18 3.06689e18i −0.0217293 0.0217293i
\(757\) −6.17496e19 −0.433474 −0.216737 0.976230i \(-0.569541\pi\)
−0.216737 + 0.976230i \(0.569541\pi\)
\(758\) 2.41895e20i 1.68245i
\(759\) 1.27234e20 + 1.27234e20i 0.876824 + 0.876824i
\(760\) −8.10571e18 8.10571e18i −0.0553472 0.0553472i
\(761\) 7.60556e19 7.60556e19i 0.514563 0.514563i −0.401358 0.915921i \(-0.631462\pi\)
0.915921 + 0.401358i \(0.131462\pi\)
\(762\) 5.61576e19 5.61576e19i 0.376464 0.376464i
\(763\) 9.85707e18 0.0654751
\(764\) 5.40297e18i 0.0355614i
\(765\) −6.44245e18 + 6.44245e18i −0.0420166 + 0.0420166i
\(766\) 3.64131e19i 0.235319i
\(767\) 7.68014e19 + 1.23779e20i 0.491815 + 0.792644i
\(768\) −5.39359e19 −0.342255
\(769\) −1.15253e20 1.15253e20i −0.724713 0.724713i 0.244848 0.969561i \(-0.421262\pi\)
−0.969561 + 0.244848i \(0.921262\pi\)
\(770\) 5.54402e18 0.0345454
\(771\) 9.01807e18i 0.0556843i
\(772\) −3.97925e19 3.97925e19i −0.243489 0.243489i
\(773\) 1.80432e20 + 1.80432e20i 1.09410 + 1.09410i 0.995086 + 0.0990158i \(0.0315694\pi\)
0.0990158 + 0.995086i \(0.468431\pi\)
\(774\) −3.86284e19 + 3.86284e19i −0.232124 + 0.232124i
\(775\) −3.91600e19 + 3.91600e19i −0.233201 + 0.233201i
\(776\) 3.51609e19 0.207505
\(777\) 9.43283e18i 0.0551690i
\(778\) 1.71611e20 1.71611e20i 0.994689 0.994689i
\(779\) 2.59736e20i 1.49200i
\(780\) 1.23876e18 + 1.99647e18i 0.00705220 + 0.0113658i
\(781\) 1.24903e20 0.704720
\(782\) 1.30017e20 + 1.30017e20i 0.727032 + 0.727032i
\(783\) −1.25100e20 −0.693308
\(784\) 2.10744e20i 1.15756i
\(785\) 1.21844e19 + 1.21844e19i 0.0663310 + 0.0663310i
\(786\) −1.61233e19 1.61233e19i −0.0869954 0.0869954i
\(787\) −8.74950e19 + 8.74950e19i −0.467908 + 0.467908i −0.901236 0.433328i \(-0.857339\pi\)
0.433328 + 0.901236i \(0.357339\pi\)
\(788\) −5.56450e18 + 5.56450e18i −0.0294946 + 0.0294946i
\(789\) 1.49818e20 0.787089
\(790\) 1.84294e19i 0.0959668i
\(791\) −2.16787e19 + 2.16787e19i −0.111892 + 0.111892i
\(792\) 2.37364e20i 1.21433i
\(793\) 6.53840e19 2.79172e20i 0.331558 1.41566i
\(794\) 7.75965e19 0.390030
\(795\) 7.15079e18 + 7.15079e18i 0.0356274 + 0.0356274i
\(796\) −2.05738e19 −0.101607
\(797\) 2.35050e20i 1.15067i −0.817916 0.575337i \(-0.804871\pi\)
0.817916 0.575337i \(-0.195129\pi\)
\(798\) 9.88043e18 + 9.88043e18i 0.0479464 + 0.0479464i
\(799\) −1.43090e19 1.43090e19i −0.0688304 0.0688304i
\(800\) 6.90515e19 6.90515e19i 0.329263 0.329263i
\(801\) −1.03403e20 + 1.03403e20i −0.488770 + 0.488770i
\(802\) 9.24300e19 0.433104
\(803\) 2.06366e20i 0.958582i
\(804\) −4.70428e18 + 4.70428e18i −0.0216621 + 0.0216621i
\(805\) 4.58009e18i 0.0209075i
\(806\) −8.00189e19 1.87410e19i −0.362116 0.0848100i
\(807\) −1.46242e20 −0.656080
\(808\) 2.34249e20 + 2.34249e20i 1.04183 + 1.04183i
\(809\) 1.10721e20 0.488191 0.244095 0.969751i \(-0.421509\pi\)
0.244095 + 0.969751i \(0.421509\pi\)
\(810\) 8.77718e18i 0.0383672i
\(811\) −2.36065e20 2.36065e20i −1.02302 1.02302i −0.999729 0.0232938i \(-0.992585\pi\)
−0.0232938 0.999729i \(-0.507415\pi\)
\(812\) 4.56845e18 + 4.56845e18i 0.0196280 + 0.0196280i
\(813\) 6.40319e19 6.40319e19i 0.272749 0.272749i
\(814\) −2.70005e20 + 2.70005e20i −1.14025 + 1.14025i
\(815\) 2.35054e19 0.0984157
\(816\) 1.01971e20i 0.423296i
\(817\) 5.63490e19 5.63490e19i 0.231916 0.231916i
\(818\) 8.58365e18i 0.0350267i
\(819\) −1.42330e19 2.29389e19i −0.0575849 0.0928080i
\(820\) −1.19148e19 −0.0477957
\(821\) −3.91861e18 3.91861e18i −0.0155858 0.0155858i 0.699271 0.714857i \(-0.253508\pi\)
−0.714857 + 0.699271i \(0.753508\pi\)
\(822\) −6.95919e19 −0.274445
\(823\) 3.14965e20i 1.23158i −0.787910 0.615790i \(-0.788837\pi\)
0.787910 0.615790i \(-0.211163\pi\)
\(824\) −1.03023e20 1.03023e20i −0.399432 0.399432i
\(825\) 1.74378e20 + 1.74378e20i 0.670370 + 0.670370i
\(826\) 2.81003e19 2.81003e19i 0.107115 0.107115i
\(827\) −2.12438e20 + 2.12438e20i −0.802960 + 0.802960i −0.983557 0.180597i \(-0.942197\pi\)
0.180597 + 0.983557i \(0.442197\pi\)
\(828\) −6.21216e19 −0.232825
\(829\) 8.08132e19i 0.300331i 0.988661 + 0.150166i \(0.0479807\pi\)
−0.988661 + 0.150166i \(0.952019\pi\)
\(830\) 3.41251e19 3.41251e19i 0.125756 0.125756i
\(831\) 1.48010e20i 0.540857i
\(832\) −1.76693e20 4.13827e19i −0.640260 0.149953i
\(833\) −1.94637e20 −0.699377
\(834\) −1.00310e20 1.00310e20i −0.357422 0.357422i
\(835\) −5.81065e19 −0.205315
\(836\) 1.09691e20i 0.384351i
\(837\) −5.95308e19 5.95308e19i −0.206854 0.206854i
\(838\) 2.24738e20 + 2.24738e20i 0.774406 + 0.774406i
\(839\) −7.59857e19 + 7.59857e19i −0.259656 + 0.259656i −0.824914 0.565258i \(-0.808777\pi\)
0.565258 + 0.824914i \(0.308777\pi\)
\(840\) −1.43070e18 + 1.43070e18i −0.00484836 + 0.00484836i
\(841\) −1.11209e20 −0.373737
\(842\) 4.70749e20i 1.56893i
\(843\) −1.93552e20 + 1.93552e20i −0.639743 + 0.639743i
\(844\) 5.23646e17i 0.00171649i
\(845\) 1.09120e19 + 3.23550e19i 0.0354737 + 0.105183i
\(846\) 3.52544e19 0.113664
\(847\) 8.61703e19 + 8.61703e19i 0.275533 + 0.275533i
\(848\) 3.37973e20 1.07179
\(849\) 9.95751e19i 0.313182i
\(850\) 1.78192e20 + 1.78192e20i 0.555848 + 0.555848i
\(851\) 2.23060e20 + 2.23060e20i 0.690104 + 0.690104i
\(852\) 1.02112e19 1.02112e19i 0.0313329 0.0313329i
\(853\) −1.24288e19 + 1.24288e19i −0.0378257 + 0.0378257i −0.725767 0.687941i \(-0.758515\pi\)
0.687941 + 0.725767i \(0.258515\pi\)
\(854\) −7.82214e19 −0.236113
\(855\) 2.31545e19i 0.0693222i
\(856\) −3.50296e20 + 3.50296e20i −1.04020 + 1.04020i
\(857\) 2.78492e20i 0.820253i −0.912029 0.410126i \(-0.865485\pi\)
0.912029 0.410126i \(-0.134515\pi\)
\(858\) −8.34528e19 + 3.56321e20i −0.243798 + 1.04095i
\(859\) −4.39133e20 −1.27246 −0.636230 0.771499i \(-0.719507\pi\)
−0.636230 + 0.771499i \(0.719507\pi\)
\(860\) −2.58487e18 2.58487e18i −0.00742934 0.00742934i
\(861\) −4.58449e19 −0.130698
\(862\) 5.26909e20i 1.48999i
\(863\) 2.98295e20 + 2.98295e20i 0.836701 + 0.836701i 0.988423 0.151722i \(-0.0484820\pi\)
−0.151722 + 0.988423i \(0.548482\pi\)
\(864\) 1.04972e20 + 1.04972e20i 0.292062 + 0.292062i
\(865\) −1.87653e19 + 1.87653e19i −0.0517897 + 0.0517897i
\(866\) −2.18296e20 + 2.18296e20i −0.597614 + 0.597614i
\(867\) −9.02648e19 −0.245124
\(868\) 4.34793e18i 0.0117124i
\(869\) 3.93625e20 3.93625e20i 1.05183 1.05183i
\(870\) 1.84880e19i 0.0490066i
\(871\) −8.21548e19 + 5.09749e19i −0.216026 + 0.134038i
\(872\) −1.45624e20 −0.379855
\(873\) −5.02198e19 5.02198e19i −0.129950 0.129950i
\(874\) 4.67289e20 1.19951
\(875\) 1.26326e19i 0.0321689i
\(876\) 1.68711e19 + 1.68711e19i 0.0426200 + 0.0426200i
\(877\) −7.29370e19 7.29370e19i −0.182789 0.182789i 0.609781 0.792570i \(-0.291257\pi\)
−0.792570 + 0.609781i \(0.791257\pi\)
\(878\) 3.92562e20 3.92562e20i 0.975993 0.975993i
\(879\) −9.47099e19 + 9.47099e19i −0.233600 + 0.233600i
\(880\) −1.02820e20 −0.251594
\(881\) 5.45347e20i 1.32386i 0.749566 + 0.661930i \(0.230262\pi\)
−0.749566 + 0.661930i \(0.769738\pi\)
\(882\) 2.39774e20 2.39774e20i 0.577460 0.577460i
\(883\) 1.47622e20i 0.352716i −0.984326 0.176358i \(-0.943568\pi\)
0.984326 0.176358i \(-0.0564316\pi\)
\(884\) −1.65376e19 + 7.06112e19i −0.0392019 + 0.167382i
\(885\) −2.20530e19 −0.0518638
\(886\) 4.11201e20 + 4.11201e20i 0.959441 + 0.959441i
\(887\) 4.32237e19 0.100059 0.0500295 0.998748i \(-0.484068\pi\)
0.0500295 + 0.998748i \(0.484068\pi\)
\(888\) 1.39357e20i 0.320064i
\(889\) −4.31767e19 4.31767e19i −0.0983869 0.0983869i
\(890\) −3.56803e19 3.56803e19i −0.0806675 0.0806675i
\(891\) 1.87468e20 1.87468e20i 0.420517 0.420517i
\(892\) 2.96668e19 2.96668e19i 0.0660262 0.0660262i
\(893\) −5.14271e19 −0.113562
\(894\) 2.84133e20i 0.622529i
\(895\) −1.02224e19 + 1.02224e19i −0.0222225 + 0.0222225i
\(896\) 8.13755e19i 0.175524i
\(897\) 2.94368e20 + 6.89430e19i 0.630005 + 0.147551i
\(898\) 1.53789e20 0.326581
\(899\) 8.86772e19 + 8.86772e19i 0.186850 + 0.186850i
\(900\) −8.51392e19 −0.178005
\(901\) 3.12142e20i 0.647558i
\(902\) −1.31227e21 1.31227e21i −2.70132 2.70132i
\(903\) −9.94592e18 9.94592e18i −0.0203157 0.0203157i
\(904\) 3.20272e20 3.20272e20i 0.649143 0.649143i
\(905\) 1.47667e18 1.47667e18i 0.00296991 0.00296991i
\(906\) 3.57202e20 0.712881
\(907\) 7.94126e19i 0.157267i 0.996904 + 0.0786336i \(0.0250557\pi\)
−0.996904 + 0.0786336i \(0.974944\pi\)
\(908\) 1.94789e19 1.94789e19i 0.0382793 0.0382793i
\(909\) 6.69147e20i 1.30489i
\(910\) 7.91533e18 4.91125e18i 0.0153172 0.00950392i
\(911\) 3.51503e20 0.674995 0.337497 0.941327i \(-0.390420\pi\)
0.337497 + 0.941327i \(0.390420\pi\)
\(912\) −1.83244e20 1.83244e20i −0.349193 0.349193i
\(913\) 1.45773e21 2.75664
\(914\) 3.33191e20i 0.625274i
\(915\) 3.06938e19 + 3.06938e19i 0.0571615 + 0.0571615i
\(916\) 1.42982e20 + 1.42982e20i 0.264249 + 0.264249i
\(917\) −1.23964e19 + 1.23964e19i −0.0227358 + 0.0227358i
\(918\) −2.70886e20 + 2.70886e20i −0.493047 + 0.493047i
\(919\) −4.75510e20 −0.858916 −0.429458 0.903087i \(-0.641295\pi\)
−0.429458 + 0.903087i \(0.641295\pi\)
\(920\) 6.76643e19i 0.121296i
\(921\) −8.46497e19 + 8.46497e19i −0.150594 + 0.150594i
\(922\) 1.78160e20i 0.314553i
\(923\) 1.78327e20 1.10647e20i 0.312468 0.193878i
\(924\) 1.93611e19 0.0336688
\(925\) 3.05710e20 + 3.05710e20i 0.527615 + 0.527615i
\(926\) −1.07168e21 −1.83565
\(927\) 2.94291e20i 0.500287i
\(928\) −1.56366e20 1.56366e20i −0.263819 0.263819i
\(929\) −1.10072e20 1.10072e20i −0.184318 0.184318i 0.608916 0.793235i \(-0.291605\pi\)
−0.793235 + 0.608916i \(0.791605\pi\)
\(930\) 8.79777e18 8.79777e18i 0.0146215 0.0146215i
\(931\) −3.49769e20 + 3.49769e20i −0.576943 + 0.576943i
\(932\) −1.49483e20 −0.244727
\(933\) 3.48070e20i 0.565582i
\(934\) −5.06620e20 + 5.06620e20i −0.817060 + 0.817060i
\(935\) 9.49618e19i 0.152008i
\(936\) 2.10272e20 + 3.38889e20i 0.334080 + 0.538427i
\(937\) −8.20987e20 −1.29467 −0.647335 0.762205i \(-0.724117\pi\)
−0.647335 + 0.762205i \(0.724117\pi\)
\(938\) 1.86509e19 + 1.86509e19i 0.0291930 + 0.0291930i
\(939\) 3.06685e20 0.476467
\(940\) 2.35910e18i 0.00363790i
\(941\) 5.54474e20 + 5.54474e20i 0.848700 + 0.848700i 0.989971 0.141271i \(-0.0451190\pi\)
−0.141271 + 0.989971i \(0.545119\pi\)
\(942\) 2.19419e20 + 2.19419e20i 0.333364 + 0.333364i
\(943\) −1.08410e21 + 1.08410e21i −1.63489 + 1.63489i
\(944\) −5.21153e20 + 5.21153e20i −0.780120 + 0.780120i
\(945\) 9.54245e18 0.0141787
\(946\) 5.69384e20i 0.839783i
\(947\) −1.48904e20 + 1.48904e20i −0.218001 + 0.218001i −0.807655 0.589655i \(-0.799264\pi\)
0.589655 + 0.807655i \(0.299264\pi\)
\(948\) 6.43601e19i 0.0935316i
\(949\) 1.82812e20 + 2.94634e20i 0.263720 + 0.425029i
\(950\) 6.40431e20 0.917080
\(951\) −2.87401e20 2.87401e20i −0.408531 0.408531i
\(952\) −6.24523e19 −0.0881230
\(953\) 1.13656e21i 1.59200i 0.605296 + 0.796001i \(0.293055\pi\)
−0.605296 + 0.796001i \(0.706945\pi\)
\(954\) −3.84528e20 3.84528e20i −0.534675 0.534675i
\(955\) −8.40550e18 8.40550e18i −0.0116022 0.0116022i
\(956\) −9.98795e19 + 9.98795e19i −0.136858 + 0.136858i
\(957\) 3.94876e20 3.94876e20i 0.537127 0.537127i
\(958\) −6.67270e20 −0.901038
\(959\) 5.35057e19i 0.0717248i
\(960\) 1.94267e19 1.94267e19i 0.0258524 0.0258524i
\(961\) 6.72547e20i 0.888503i
\(962\) −1.46305e20 + 6.24681e20i −0.191881 + 0.819281i
\(963\) 1.00064e21 1.30285
\(964\) −1.33026e19 1.33026e19i −0.0171948 0.0171948i
\(965\) 1.23812e20 0.158881
\(966\) 8.24792e19i 0.105076i
\(967\) −4.77735e19 4.77735e19i −0.0604229 0.0604229i 0.676250 0.736673i \(-0.263604\pi\)
−0.736673 + 0.676250i \(0.763604\pi\)
\(968\) −1.27304e21 1.27304e21i −1.59851 1.59851i
\(969\) 1.69239e20 1.69239e20i 0.210976 0.210976i
\(970\) 1.73289e19 1.73289e19i 0.0214471 0.0214471i
\(971\) −1.27898e21 −1.57155 −0.785774 0.618513i \(-0.787735\pi\)
−0.785774 + 0.618513i \(0.787735\pi\)
\(972\) 2.03424e20i 0.248163i
\(973\) −7.71232e19 + 7.71232e19i −0.0934104 + 0.0934104i
\(974\) 1.21296e21i 1.45860i
\(975\) 4.03439e20 + 9.44882e19i 0.481666 + 0.112809i
\(976\) 1.45071e21 1.71961
\(977\) −1.93313e20 1.93313e20i −0.227510 0.227510i 0.584142 0.811652i \(-0.301431\pi\)
−0.811652 + 0.584142i \(0.801431\pi\)
\(978\) 4.23290e20 0.494614
\(979\) 1.52416e21i 1.76828i
\(980\) 1.60448e19 + 1.60448e19i 0.0184821 + 0.0184821i
\(981\) 2.07993e20 + 2.07993e20i 0.237884 + 0.237884i
\(982\) 1.07048e21 1.07048e21i 1.21562 1.21562i
\(983\) 2.30700e20 2.30700e20i 0.260120 0.260120i −0.564983 0.825103i \(-0.691117\pi\)
0.825103 + 0.564983i \(0.191117\pi\)
\(984\) 6.77293e20 0.758247
\(985\) 1.73136e19i 0.0192457i
\(986\) 4.03513e20 4.03513e20i 0.445368 0.445368i
\(987\) 9.07719e18i 0.00994790i
\(988\) 9.71716e19 + 1.56609e20i 0.105740 + 0.170419i
\(989\) −4.70386e20 −0.508254
\(990\) 1.16984e20 + 1.16984e20i 0.125510 + 0.125510i
\(991\) 1.64715e21 1.75476 0.877381 0.479795i \(-0.159289\pi\)
0.877381 + 0.479795i \(0.159289\pi\)
\(992\) 1.48818e20i 0.157425i
\(993\) −5.12493e20 5.12493e20i −0.538323 0.538323i
\(994\) −4.04840e19 4.04840e19i −0.0422259 0.0422259i
\(995\) 3.20071e19 3.20071e19i 0.0331501 0.0331501i
\(996\) 1.19174e20 1.19174e20i 0.122565 0.122565i
\(997\) −9.84895e20 −1.00583 −0.502914 0.864336i \(-0.667739\pi\)
−0.502914 + 0.864336i \(0.667739\pi\)
\(998\) 5.60768e20i 0.568682i
\(999\) −4.64737e20 + 4.64737e20i −0.468004 + 0.468004i
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 13.15.d.a.8.13 yes 32
13.5 odd 4 inner 13.15.d.a.5.13 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.15.d.a.5.13 32 13.5 odd 4 inner
13.15.d.a.8.13 yes 32 1.1 even 1 trivial