Properties

Label 24.8.d.a.13.1
Level $24$
Weight $8$
Character 24.13
Analytic conductor $7.497$
Analytic rank $0$
Dimension $14$
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] = [24,8,Mod(13,24)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(24, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("24.13");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 24.d (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: \(7.49724061162\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 6 x^{13} - 52 x^{12} + 300 x^{11} - 1005 x^{10} - 23250 x^{9} + 349930 x^{8} + 2867784 x^{7} - 20463993 x^{6} - 78987210 x^{5} + 94608296 x^{4} + \cdots + 3813237677250 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{37}\cdot 3^{16} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 13.1
Root \(-4.99225 + 5.30027i\) of defining polynomial
Character \(\chi\) \(=\) 24.13
Dual form 24.8.d.a.13.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-11.2925 - 0.691979i) q^{2} -27.0000i q^{3} +(127.042 + 15.6284i) q^{4} +124.215i q^{5} +(-18.6834 + 304.898i) q^{6} +646.373 q^{7} +(-1423.81 - 264.394i) q^{8} -729.000 q^{9} +O(q^{10})\) \(q+(-11.2925 - 0.691979i) q^{2} -27.0000i q^{3} +(127.042 + 15.6284i) q^{4} +124.215i q^{5} +(-18.6834 + 304.898i) q^{6} +646.373 q^{7} +(-1423.81 - 264.394i) q^{8} -729.000 q^{9} +(85.9543 - 1402.70i) q^{10} -5132.96i q^{11} +(421.966 - 3430.14i) q^{12} -13479.3i q^{13} +(-7299.18 - 447.276i) q^{14} +3353.81 q^{15} +(15895.5 + 3970.93i) q^{16} -21363.6 q^{17} +(8232.25 + 504.453i) q^{18} -12292.3i q^{19} +(-1941.28 + 15780.6i) q^{20} -17452.1i q^{21} +(-3551.90 + 57964.0i) q^{22} -15142.2 q^{23} +(-7138.65 + 38443.0i) q^{24} +62695.6 q^{25} +(-9327.39 + 152215. i) q^{26} +19683.0i q^{27} +(82116.7 + 10101.8i) q^{28} -132704. i q^{29} +(-37873.0 - 2320.77i) q^{30} +81021.1 q^{31} +(-176753. - 55841.2i) q^{32} -138590. q^{33} +(241249. + 14783.1i) q^{34} +80289.3i q^{35} +(-92613.9 - 11393.1i) q^{36} -429188. i q^{37} +(-8506.01 + 138811. i) q^{38} -363941. q^{39} +(32841.8 - 176859. i) q^{40} +314662. q^{41} +(-12076.5 + 197078. i) q^{42} +686180. i q^{43} +(80219.8 - 652103. i) q^{44} -90552.9i q^{45} +(170994. + 10478.1i) q^{46} +351245. q^{47} +(107215. - 429179. i) q^{48} -405745. q^{49} +(-707991. - 43384.0i) q^{50} +576817. i q^{51} +(210660. - 1.71244e6i) q^{52} -602657. i q^{53} +(13620.2 - 222271. i) q^{54} +637591. q^{55} +(-920315. - 170897. i) q^{56} -331892. q^{57} +(-91828.1 + 1.49856e6i) q^{58} +2.99946e6i q^{59} +(426076. + 52414.6i) q^{60} +372829. i q^{61} +(-914933. - 56064.9i) q^{62} -471206. q^{63} +(1.95734e6 + 752897. i) q^{64} +1.67433e6 q^{65} +(1.56503e6 + 95901.2i) q^{66} +1.57142e6i q^{67} +(-2.71408e6 - 333878. i) q^{68} +408840. i q^{69} +(55558.5 - 906669. i) q^{70} +3.21138e6 q^{71} +(1.03796e6 + 192744. i) q^{72} -3.96716e6 q^{73} +(-296989. + 4.84661e6i) q^{74} -1.69278e6i q^{75} +(192109. - 1.56164e6i) q^{76} -3.31780e6i q^{77} +(4.10981e6 + 251839. i) q^{78} -5.94163e6 q^{79} +(-493250. + 1.97446e6i) q^{80} +531441. q^{81} +(-3.55332e6 - 217739. i) q^{82} -9.26430e6i q^{83} +(272747. - 2.21715e6i) q^{84} -2.65368e6i q^{85} +(474822. - 7.74870e6i) q^{86} -3.58300e6 q^{87} +(-1.35712e6 + 7.30838e6i) q^{88} +1.28258e7 q^{89} +(-62660.7 + 1.02257e6i) q^{90} -8.71265e6i q^{91} +(-1.92370e6 - 236648. i) q^{92} -2.18757e6i q^{93} +(-3.96644e6 - 243054. i) q^{94} +1.52689e6 q^{95} +(-1.50771e6 + 4.77232e6i) q^{96} -1.36350e7 q^{97} +(4.58189e6 + 280767. i) q^{98} +3.74192e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9} + 5020 q^{10} + 7668 q^{12} + 4636 q^{14} - 13500 q^{15} - 43336 q^{16} - 2908 q^{17} + 10206 q^{18} + 175096 q^{20} - 128480 q^{22} - 143416 q^{23} - 29268 q^{24} - 202626 q^{25} + 424984 q^{26} + 567520 q^{28} - 250668 q^{30} - 89468 q^{31} - 893944 q^{32} + 1109820 q^{34} + 151632 q^{36} - 823816 q^{38} + 474552 q^{39} - 860888 q^{40} - 441284 q^{41} + 427788 q^{42} + 1275264 q^{44} - 2167992 q^{46} - 1056408 q^{47} - 233280 q^{48} + 2158134 q^{49} + 324610 q^{50} - 2059248 q^{52} + 39366 q^{54} + 4757504 q^{55} + 1643704 q^{56} + 1551096 q^{57} - 5494676 q^{58} - 3203712 q^{60} + 5767172 q^{62} - 1000188 q^{63} + 3852224 q^{64} - 2520464 q^{65} - 3615840 q^{66} - 3735840 q^{68} + 12890312 q^{70} + 5172696 q^{71} + 312012 q^{72} - 5446196 q^{73} - 6468800 q^{74} - 9084624 q^{76} + 3542184 q^{78} - 14373548 q^{79} + 14369088 q^{80} + 7440174 q^{81} - 7935708 q^{82} - 2775816 q^{84} + 4738312 q^{86} + 7902036 q^{87} + 12598720 q^{88} - 11952620 q^{89} - 3659580 q^{90} + 11004480 q^{92} - 15440088 q^{94} - 69327376 q^{95} + 1341576 q^{96} + 133732 q^{97} + 53030538 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(13\) \(17\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11.2925 0.691979i −0.998128 0.0611629i
\(3\) 27.0000i 0.577350i
\(4\) 127.042 + 15.6284i 0.992518 + 0.122097i
\(5\) 124.215i 0.444406i 0.975000 + 0.222203i \(0.0713248\pi\)
−0.975000 + 0.222203i \(0.928675\pi\)
\(6\) −18.6834 + 304.898i −0.0353124 + 0.576269i
\(7\) 646.373 0.712262 0.356131 0.934436i \(-0.384096\pi\)
0.356131 + 0.934436i \(0.384096\pi\)
\(8\) −1423.81 264.394i −0.983192 0.182573i
\(9\) −729.000 −0.333333
\(10\) 85.9543 1402.70i 0.0271811 0.443574i
\(11\) 5132.96i 1.16277i −0.813629 0.581384i \(-0.802511\pi\)
0.813629 0.581384i \(-0.197489\pi\)
\(12\) 421.966 3430.14i 0.0704926 0.573031i
\(13\) 13479.3i 1.70163i −0.525464 0.850816i \(-0.676108\pi\)
0.525464 0.850816i \(-0.323892\pi\)
\(14\) −7299.18 447.276i −0.710929 0.0435640i
\(15\) 3353.81 0.256578
\(16\) 15895.5 + 3970.93i 0.970185 + 0.242366i
\(17\) −21363.6 −1.05464 −0.527318 0.849668i \(-0.676802\pi\)
−0.527318 + 0.849668i \(0.676802\pi\)
\(18\) 8232.25 + 504.453i 0.332709 + 0.0203876i
\(19\) 12292.3i 0.411145i −0.978642 0.205573i \(-0.934094\pi\)
0.978642 0.205573i \(-0.0659057\pi\)
\(20\) −1941.28 + 15780.6i −0.0542605 + 0.441081i
\(21\) 17452.1i 0.411225i
\(22\) −3551.90 + 57964.0i −0.0711182 + 1.16059i
\(23\) −15142.2 −0.259503 −0.129752 0.991547i \(-0.541418\pi\)
−0.129752 + 0.991547i \(0.541418\pi\)
\(24\) −7138.65 + 38443.0i −0.105409 + 0.567646i
\(25\) 62695.6 0.802503
\(26\) −9327.39 + 152215.i −0.104077 + 1.69845i
\(27\) 19683.0i 0.192450i
\(28\) 82116.7 + 10101.8i 0.706933 + 0.0869648i
\(29\) 132704.i 1.01039i −0.863005 0.505196i \(-0.831420\pi\)
0.863005 0.505196i \(-0.168580\pi\)
\(30\) −37873.0 2320.77i −0.256098 0.0156930i
\(31\) 81021.1 0.488463 0.244232 0.969717i \(-0.421464\pi\)
0.244232 + 0.969717i \(0.421464\pi\)
\(32\) −176753. 55841.2i −0.953545 0.301252i
\(33\) −138590. −0.671324
\(34\) 241249. + 14783.1i 1.05266 + 0.0645046i
\(35\) 80289.3i 0.316533i
\(36\) −92613.9 11393.1i −0.330839 0.0406989i
\(37\) 429188.i 1.39297i −0.717572 0.696484i \(-0.754747\pi\)
0.717572 0.696484i \(-0.245253\pi\)
\(38\) −8506.01 + 138811.i −0.0251468 + 0.410376i
\(39\) −363941. −0.982437
\(40\) 32841.8 176859.i 0.0811367 0.436936i
\(41\) 314662. 0.713018 0.356509 0.934292i \(-0.383967\pi\)
0.356509 + 0.934292i \(0.383967\pi\)
\(42\) −12076.5 + 197078.i −0.0251517 + 0.410455i
\(43\) 686180.i 1.31613i 0.752962 + 0.658064i \(0.228624\pi\)
−0.752962 + 0.658064i \(0.771376\pi\)
\(44\) 80219.8 652103.i 0.141970 1.15407i
\(45\) 90552.9i 0.148135i
\(46\) 170994. + 10478.1i 0.259017 + 0.0158719i
\(47\) 351245. 0.493477 0.246739 0.969082i \(-0.420641\pi\)
0.246739 + 0.969082i \(0.420641\pi\)
\(48\) 107215. 429179.i 0.139930 0.560136i
\(49\) −405745. −0.492683
\(50\) −707991. 43384.0i −0.801001 0.0490834i
\(51\) 576817.i 0.608895i
\(52\) 210660. 1.71244e6i 0.207764 1.68890i
\(53\) 602657.i 0.556039i −0.960575 0.278019i \(-0.910322\pi\)
0.960575 0.278019i \(-0.0896779\pi\)
\(54\) 13620.2 222271.i 0.0117708 0.192090i
\(55\) 637591. 0.516741
\(56\) −920315. 170897.i −0.700290 0.130040i
\(57\) −331892. −0.237375
\(58\) −91828.1 + 1.49856e6i −0.0617984 + 1.00850i
\(59\) 2.99946e6i 1.90134i 0.310197 + 0.950672i \(0.399605\pi\)
−0.310197 + 0.950672i \(0.600395\pi\)
\(60\) 426076. + 52414.6i 0.254658 + 0.0313273i
\(61\) 372829.i 0.210308i 0.994456 + 0.105154i \(0.0335335\pi\)
−0.994456 + 0.105154i \(0.966467\pi\)
\(62\) −914933. 56064.9i −0.487549 0.0298758i
\(63\) −471206. −0.237421
\(64\) 1.95734e6 + 752897.i 0.933334 + 0.359009i
\(65\) 1.67433e6 0.756215
\(66\) 1.56503e6 + 95901.2i 0.670068 + 0.0410601i
\(67\) 1.57142e6i 0.638309i 0.947703 + 0.319155i \(0.103399\pi\)
−0.947703 + 0.319155i \(0.896601\pi\)
\(68\) −2.71408e6 333878.i −1.04675 0.128768i
\(69\) 408840.i 0.149824i
\(70\) 55558.5 906669.i 0.0193601 0.315941i
\(71\) 3.21138e6 1.06485 0.532423 0.846478i \(-0.321282\pi\)
0.532423 + 0.846478i \(0.321282\pi\)
\(72\) 1.03796e6 + 192744.i 0.327731 + 0.0608578i
\(73\) −3.96716e6 −1.19357 −0.596787 0.802400i \(-0.703556\pi\)
−0.596787 + 0.802400i \(0.703556\pi\)
\(74\) −296989. + 4.84661e6i −0.0851979 + 1.39036i
\(75\) 1.69278e6i 0.463326i
\(76\) 192109. 1.56164e6i 0.0501995 0.408069i
\(77\) 3.31780e6i 0.828195i
\(78\) 4.10981e6 + 251839.i 0.980598 + 0.0600887i
\(79\) −5.94163e6 −1.35585 −0.677923 0.735133i \(-0.737120\pi\)
−0.677923 + 0.735133i \(0.737120\pi\)
\(80\) −493250. + 1.97446e6i −0.107709 + 0.431156i
\(81\) 531441. 0.111111
\(82\) −3.55332e6 217739.i −0.711683 0.0436102i
\(83\) 9.26430e6i 1.77844i −0.457480 0.889220i \(-0.651248\pi\)
0.457480 0.889220i \(-0.348752\pi\)
\(84\) 272747. 2.21715e6i 0.0502092 0.408148i
\(85\) 2.65368e6i 0.468687i
\(86\) 474822. 7.74870e6i 0.0804982 1.31366i
\(87\) −3.58300e6 −0.583350
\(88\) −1.35712e6 + 7.30838e6i −0.212290 + 1.14322i
\(89\) 1.28258e7 1.92850 0.964250 0.264993i \(-0.0853697\pi\)
0.964250 + 0.264993i \(0.0853697\pi\)
\(90\) −62660.7 + 1.02257e6i −0.00906038 + 0.147858i
\(91\) 8.71265e6i 1.21201i
\(92\) −1.92370e6 236648.i −0.257561 0.0316845i
\(93\) 2.18757e6i 0.282014i
\(94\) −3.96644e6 243054.i −0.492553 0.0301825i
\(95\) 1.52689e6 0.182715
\(96\) −1.50771e6 + 4.77232e6i −0.173928 + 0.550529i
\(97\) −1.36350e7 −1.51690 −0.758448 0.651734i \(-0.774042\pi\)
−0.758448 + 0.651734i \(0.774042\pi\)
\(98\) 4.58189e6 + 280767.i 0.491760 + 0.0301339i
\(99\) 3.74192e6i 0.387589i
\(100\) 7.96499e6 + 979830.i 0.796499 + 0.0979830i
\(101\) 1.15744e7i 1.11782i 0.829228 + 0.558910i \(0.188780\pi\)
−0.829228 + 0.558910i \(0.811220\pi\)
\(102\) 399145. 6.51372e6i 0.0372417 0.607755i
\(103\) 1.54055e7 1.38914 0.694571 0.719424i \(-0.255594\pi\)
0.694571 + 0.719424i \(0.255594\pi\)
\(104\) −3.56385e6 + 1.91920e7i −0.310673 + 1.67303i
\(105\) 2.16781e6 0.182751
\(106\) −417026. + 6.80553e6i −0.0340089 + 0.554998i
\(107\) 3.25844e6i 0.257138i −0.991701 0.128569i \(-0.958962\pi\)
0.991701 0.128569i \(-0.0410383\pi\)
\(108\) −307613. + 2.50057e6i −0.0234975 + 0.191010i
\(109\) 2.19394e7i 1.62268i 0.584577 + 0.811338i \(0.301261\pi\)
−0.584577 + 0.811338i \(0.698739\pi\)
\(110\) −7.20002e6 441200.i −0.515774 0.0316054i
\(111\) −1.15881e7 −0.804230
\(112\) 1.02744e7 + 2.56670e6i 0.691026 + 0.172628i
\(113\) −2.56062e6 −0.166944 −0.0834721 0.996510i \(-0.526601\pi\)
−0.0834721 + 0.996510i \(0.526601\pi\)
\(114\) 3.74790e6 + 229662.i 0.236931 + 0.0145185i
\(115\) 1.88090e6i 0.115325i
\(116\) 2.07394e6 1.68590e7i 0.123365 1.00283i
\(117\) 9.82641e6i 0.567211i
\(118\) 2.07556e6 3.38715e7i 0.116292 1.89778i
\(119\) −1.38088e7 −0.751177
\(120\) −4.77521e6 886729.i −0.252265 0.0468443i
\(121\) −6.86006e6 −0.352029
\(122\) 257990. 4.21018e6i 0.0128630 0.209914i
\(123\) 8.49586e6i 0.411661i
\(124\) 1.02931e7 + 1.26623e6i 0.484809 + 0.0596398i
\(125\) 1.74921e7i 0.801043i
\(126\) 5.32110e6 + 326064.i 0.236976 + 0.0145213i
\(127\) 3.97514e7 1.72203 0.861013 0.508583i \(-0.169831\pi\)
0.861013 + 0.508583i \(0.169831\pi\)
\(128\) −2.15824e7 9.85655e6i −0.909629 0.415423i
\(129\) 1.85268e7 0.759867
\(130\) −1.89075e7 1.15860e6i −0.754799 0.0462523i
\(131\) 1.09930e7i 0.427233i 0.976918 + 0.213617i \(0.0685243\pi\)
−0.976918 + 0.213617i \(0.931476\pi\)
\(132\) −1.76068e7 2.16593e6i −0.666302 0.0819665i
\(133\) 7.94540e6i 0.292843i
\(134\) 1.08739e6 1.77453e7i 0.0390408 0.637114i
\(135\) −2.44493e6 −0.0855260
\(136\) 3.04178e7 + 5.64841e6i 1.03691 + 0.192548i
\(137\) −6.84719e6 −0.227505 −0.113752 0.993509i \(-0.536287\pi\)
−0.113752 + 0.993509i \(0.536287\pi\)
\(138\) 282909. 4.61684e6i 0.00916367 0.149544i
\(139\) 5.55412e6i 0.175414i 0.996146 + 0.0877068i \(0.0279539\pi\)
−0.996146 + 0.0877068i \(0.972046\pi\)
\(140\) −1.25479e6 + 1.02001e7i −0.0386477 + 0.314165i
\(141\) 9.48360e6i 0.284909i
\(142\) −3.62645e7 2.22220e6i −1.06285 0.0651290i
\(143\) −6.91886e7 −1.97860
\(144\) −1.15878e7 2.89481e6i −0.323395 0.0807888i
\(145\) 1.64838e7 0.449024
\(146\) 4.47992e7 + 2.74519e6i 1.19134 + 0.0730024i
\(147\) 1.09551e7i 0.284451i
\(148\) 6.70751e6 5.45250e7i 0.170077 1.38255i
\(149\) 3.66701e7i 0.908154i −0.890962 0.454077i \(-0.849969\pi\)
0.890962 0.454077i \(-0.150031\pi\)
\(150\) −1.17137e6 + 1.91158e7i −0.0283383 + 0.462458i
\(151\) 4.09127e7 0.967027 0.483513 0.875337i \(-0.339360\pi\)
0.483513 + 0.875337i \(0.339360\pi\)
\(152\) −3.25002e6 + 1.75020e7i −0.0750642 + 0.404235i
\(153\) 1.55740e7 0.351545
\(154\) −2.29585e6 + 3.74664e7i −0.0506548 + 0.826645i
\(155\) 1.00641e7i 0.217076i
\(156\) −4.62359e7 5.68781e6i −0.975087 0.119952i
\(157\) 1.97881e7i 0.408088i −0.978962 0.204044i \(-0.934591\pi\)
0.978962 0.204044i \(-0.0654086\pi\)
\(158\) 6.70960e7 + 4.11148e6i 1.35331 + 0.0829274i
\(159\) −1.62718e7 −0.321029
\(160\) 6.93633e6 2.19554e7i 0.133878 0.423761i
\(161\) −9.78752e6 −0.184834
\(162\) −6.00131e6 367746.i −0.110903 0.00679587i
\(163\) 1.94325e7i 0.351457i −0.984439 0.175728i \(-0.943772\pi\)
0.984439 0.175728i \(-0.0562280\pi\)
\(164\) 3.99753e7 + 4.91765e6i 0.707683 + 0.0870571i
\(165\) 1.72150e7i 0.298341i
\(166\) −6.41070e6 + 1.04617e8i −0.108774 + 1.77511i
\(167\) 1.44338e7 0.239813 0.119906 0.992785i \(-0.461741\pi\)
0.119906 + 0.992785i \(0.461741\pi\)
\(168\) −4.61423e6 + 2.48485e7i −0.0750787 + 0.404313i
\(169\) −1.18943e8 −1.89555
\(170\) −1.83629e6 + 2.99668e7i −0.0286662 + 0.467809i
\(171\) 8.96109e6i 0.137048i
\(172\) −1.07239e7 + 8.71738e7i −0.160695 + 1.30628i
\(173\) 5.75803e7i 0.845498i −0.906247 0.422749i \(-0.861065\pi\)
0.906247 0.422749i \(-0.138935\pi\)
\(174\) 4.04611e7 + 2.47936e6i 0.582258 + 0.0356793i
\(175\) 4.05247e7 0.571593
\(176\) 2.03826e7 8.15909e7i 0.281816 1.12810i
\(177\) 8.09854e7 1.09774
\(178\) −1.44836e8 8.87519e6i −1.92489 0.117953i
\(179\) 6.92684e7i 0.902713i 0.892344 + 0.451357i \(0.149060\pi\)
−0.892344 + 0.451357i \(0.850940\pi\)
\(180\) 1.41520e6 1.15041e7i 0.0180868 0.147027i
\(181\) 8.27698e7i 1.03752i −0.854920 0.518761i \(-0.826394\pi\)
0.854920 0.518761i \(-0.173606\pi\)
\(182\) −6.02897e6 + 9.83878e7i −0.0741298 + 1.20974i
\(183\) 1.00664e7 0.121421
\(184\) 2.15597e7 + 4.00352e6i 0.255141 + 0.0473783i
\(185\) 5.33116e7 0.619043
\(186\) −1.51375e6 + 2.47032e7i −0.0172488 + 0.281487i
\(187\) 1.09658e8i 1.22630i
\(188\) 4.46229e7 + 5.48938e6i 0.489785 + 0.0602519i
\(189\) 1.27226e7i 0.137075i
\(190\) −1.72425e7 1.05658e6i −0.182373 0.0111754i
\(191\) −7.12908e7 −0.740316 −0.370158 0.928969i \(-0.620696\pi\)
−0.370158 + 0.928969i \(0.620696\pi\)
\(192\) 2.03282e7 5.28483e7i 0.207274 0.538861i
\(193\) −8.45423e7 −0.846493 −0.423247 0.906015i \(-0.639110\pi\)
−0.423247 + 0.906015i \(0.639110\pi\)
\(194\) 1.53974e8 + 9.43516e6i 1.51406 + 0.0927777i
\(195\) 4.52070e7i 0.436601i
\(196\) −5.15469e7 6.34114e6i −0.488997 0.0601549i
\(197\) 4.53519e7i 0.422634i −0.977418 0.211317i \(-0.932225\pi\)
0.977418 0.211317i \(-0.0677752\pi\)
\(198\) 2.58933e6 4.22558e7i 0.0237061 0.386864i
\(199\) 8.78225e7 0.789987 0.394993 0.918684i \(-0.370747\pi\)
0.394993 + 0.918684i \(0.370747\pi\)
\(200\) −8.92669e7 1.65764e7i −0.789015 0.146516i
\(201\) 4.24284e7 0.368528
\(202\) 8.00921e6 1.30704e8i 0.0683691 1.11573i
\(203\) 8.57760e7i 0.719664i
\(204\) −9.01471e6 + 7.32801e7i −0.0743440 + 0.604339i
\(205\) 3.90858e7i 0.316869i
\(206\) −1.73967e8 1.06603e7i −1.38654 0.0849639i
\(207\) 1.10387e7 0.0865010
\(208\) 5.35254e7 2.14260e8i 0.412418 1.65090i
\(209\) −6.30958e7 −0.478067
\(210\) −2.44801e7 1.50008e6i −0.182409 0.0111776i
\(211\) 7.44392e7i 0.545523i −0.962082 0.272761i \(-0.912063\pi\)
0.962082 0.272761i \(-0.0879369\pi\)
\(212\) 9.41856e6 7.65630e7i 0.0678905 0.551878i
\(213\) 8.67071e7i 0.614789i
\(214\) −2.25477e6 + 3.67960e7i −0.0157273 + 0.256656i
\(215\) −8.52339e7 −0.584895
\(216\) 5.20408e6 2.80249e7i 0.0351363 0.189215i
\(217\) 5.23698e7 0.347914
\(218\) 1.51816e7 2.47751e8i 0.0992476 1.61964i
\(219\) 1.07113e8i 0.689110i
\(220\) 8.10011e7 + 9.96452e6i 0.512875 + 0.0630924i
\(221\) 2.87966e8i 1.79460i
\(222\) 1.30859e8 + 8.01869e6i 0.802725 + 0.0491890i
\(223\) −8.46115e7 −0.510931 −0.255466 0.966818i \(-0.582229\pi\)
−0.255466 + 0.966818i \(0.582229\pi\)
\(224\) −1.14248e8 3.60942e7i −0.679174 0.214570i
\(225\) −4.57051e7 −0.267501
\(226\) 2.89159e7 + 1.77190e6i 0.166632 + 0.0102108i
\(227\) 8.23087e7i 0.467041i 0.972352 + 0.233521i \(0.0750247\pi\)
−0.972352 + 0.233521i \(0.924975\pi\)
\(228\) −4.21643e7 5.18693e6i −0.235599 0.0289827i
\(229\) 2.13102e8i 1.17264i 0.810081 + 0.586318i \(0.199423\pi\)
−0.810081 + 0.586318i \(0.800577\pi\)
\(230\) −1.30154e6 + 2.12401e7i −0.00705359 + 0.115109i
\(231\) −8.95806e7 −0.478159
\(232\) −3.50861e7 + 1.88945e8i −0.184471 + 0.993409i
\(233\) 1.70596e8 0.883536 0.441768 0.897129i \(-0.354351\pi\)
0.441768 + 0.897129i \(0.354351\pi\)
\(234\) 6.79967e6 1.10965e8i 0.0346922 0.566149i
\(235\) 4.36299e7i 0.219304i
\(236\) −4.68767e7 + 3.81058e8i −0.232148 + 1.88712i
\(237\) 1.60424e8i 0.782798i
\(238\) 1.55937e8 + 9.55542e6i 0.749771 + 0.0459442i
\(239\) 3.87765e8 1.83728 0.918642 0.395090i \(-0.129287\pi\)
0.918642 + 0.395090i \(0.129287\pi\)
\(240\) 5.33105e7 + 1.33178e7i 0.248928 + 0.0621859i
\(241\) 1.12927e8 0.519683 0.259841 0.965651i \(-0.416330\pi\)
0.259841 + 0.965651i \(0.416330\pi\)
\(242\) 7.74674e7 + 4.74701e6i 0.351370 + 0.0215311i
\(243\) 1.43489e7i 0.0641500i
\(244\) −5.82671e6 + 4.73650e7i −0.0256779 + 0.208734i
\(245\) 5.03998e7i 0.218951i
\(246\) −5.87896e6 + 9.59398e7i −0.0251784 + 0.410890i
\(247\) −1.65692e8 −0.699618
\(248\) −1.15359e8 2.14215e7i −0.480253 0.0891804i
\(249\) −2.50136e8 −1.02678
\(250\) 1.21041e7 1.97530e8i 0.0489941 0.799543i
\(251\) 1.91451e8i 0.764187i −0.924124 0.382093i \(-0.875203\pi\)
0.924124 0.382093i \(-0.124797\pi\)
\(252\) −5.98631e7 7.36418e6i −0.235644 0.0289883i
\(253\) 7.77244e7i 0.301742i
\(254\) −4.48894e8 2.75071e7i −1.71880 0.105324i
\(255\) −7.16494e7 −0.270596
\(256\) 2.36899e8 + 1.26240e8i 0.882517 + 0.470280i
\(257\) 1.62153e8 0.595880 0.297940 0.954585i \(-0.403701\pi\)
0.297940 + 0.954585i \(0.403701\pi\)
\(258\) −2.09215e8 1.28202e7i −0.758444 0.0464756i
\(259\) 2.77415e8i 0.992158i
\(260\) 2.12711e8 + 2.61671e7i 0.750557 + 0.0923314i
\(261\) 9.67409e7i 0.336797i
\(262\) 7.60689e6 1.24138e8i 0.0261308 0.426433i
\(263\) −8.57486e6 −0.0290658 −0.0145329 0.999894i \(-0.504626\pi\)
−0.0145329 + 0.999894i \(0.504626\pi\)
\(264\) 1.97326e8 + 3.66424e7i 0.660041 + 0.122566i
\(265\) 7.48592e7 0.247107
\(266\) −5.49805e6 + 8.97237e7i −0.0179111 + 0.292295i
\(267\) 3.46297e8i 1.11342i
\(268\) −2.45588e7 + 1.99637e8i −0.0779354 + 0.633534i
\(269\) 2.35872e7i 0.0738828i 0.999317 + 0.0369414i \(0.0117615\pi\)
−0.999317 + 0.0369414i \(0.988239\pi\)
\(270\) 2.76094e7 + 1.69184e6i 0.0853658 + 0.00523101i
\(271\) 2.51796e7 0.0768522 0.0384261 0.999261i \(-0.487766\pi\)
0.0384261 + 0.999261i \(0.487766\pi\)
\(272\) −3.39585e8 8.48333e7i −1.02319 0.255608i
\(273\) −2.35242e8 −0.699753
\(274\) 7.73221e7 + 4.73811e6i 0.227079 + 0.0139148i
\(275\) 3.21814e8i 0.933125i
\(276\) −6.38951e6 + 5.19400e7i −0.0182930 + 0.148703i
\(277\) 3.44675e8i 0.974384i −0.873295 0.487192i \(-0.838021\pi\)
0.873295 0.487192i \(-0.161979\pi\)
\(278\) 3.84333e6 6.27200e7i 0.0107288 0.175085i
\(279\) −5.90644e7 −0.162821
\(280\) 2.12281e7 1.14317e8i 0.0577906 0.311213i
\(281\) −3.37409e8 −0.907162 −0.453581 0.891215i \(-0.649854\pi\)
−0.453581 + 0.891215i \(0.649854\pi\)
\(282\) −6.56245e6 + 1.07094e8i −0.0174259 + 0.284376i
\(283\) 3.95114e8i 1.03626i −0.855301 0.518131i \(-0.826628\pi\)
0.855301 0.518131i \(-0.173372\pi\)
\(284\) 4.07981e8 + 5.01886e7i 1.05688 + 0.130014i
\(285\) 4.12260e7i 0.105491i
\(286\) 7.81315e8 + 4.78771e7i 1.97490 + 0.121017i
\(287\) 2.03389e8 0.507855
\(288\) 1.28853e8 + 4.07082e7i 0.317848 + 0.100417i
\(289\) 4.60637e7 0.112258
\(290\) −1.86144e8 1.14064e7i −0.448183 0.0274636i
\(291\) 3.68146e8i 0.875780i
\(292\) −5.03997e8 6.20002e7i −1.18464 0.145731i
\(293\) 6.01628e8i 1.39731i −0.715461 0.698653i \(-0.753783\pi\)
0.715461 0.698653i \(-0.246217\pi\)
\(294\) 7.58072e6 1.23711e8i 0.0173978 0.283918i
\(295\) −3.72578e8 −0.844969
\(296\) −1.13475e8 + 6.11083e8i −0.254319 + 1.36956i
\(297\) 1.01032e8 0.223775
\(298\) −2.53749e7 + 4.14098e8i −0.0555453 + 0.906454i
\(299\) 2.04107e8i 0.441579i
\(300\) 2.64554e7 2.15055e8i 0.0565705 0.459859i
\(301\) 4.43528e8i 0.937428i
\(302\) −4.62007e8 2.83107e7i −0.965216 0.0591461i
\(303\) 3.12508e8 0.645374
\(304\) 4.88119e7 1.95392e8i 0.0996478 0.398887i
\(305\) −4.63110e7 −0.0934620
\(306\) −1.75870e8 1.07769e7i −0.350887 0.0215015i
\(307\) 5.80663e8i 1.14535i 0.819781 + 0.572677i \(0.194095\pi\)
−0.819781 + 0.572677i \(0.805905\pi\)
\(308\) 5.18519e7 4.21501e8i 0.101120 0.821999i
\(309\) 4.15950e8i 0.802022i
\(310\) 6.96411e6 1.13649e8i 0.0132770 0.216670i
\(311\) 3.05489e8 0.575883 0.287942 0.957648i \(-0.407029\pi\)
0.287942 + 0.957648i \(0.407029\pi\)
\(312\) 5.18185e8 + 9.62240e7i 0.965925 + 0.179367i
\(313\) 4.78994e8 0.882928 0.441464 0.897279i \(-0.354459\pi\)
0.441464 + 0.897279i \(0.354459\pi\)
\(314\) −1.36929e7 + 2.23457e8i −0.0249599 + 0.407324i
\(315\) 5.85309e7i 0.105511i
\(316\) −7.54838e8 9.28580e7i −1.34570 0.165544i
\(317\) 8.73052e8i 1.53933i 0.638446 + 0.769666i \(0.279577\pi\)
−0.638446 + 0.769666i \(0.720423\pi\)
\(318\) 1.83749e8 + 1.12597e7i 0.320428 + 0.0196351i
\(319\) −6.81162e8 −1.17485
\(320\) −9.35213e7 + 2.43132e8i −0.159546 + 0.414779i
\(321\) −8.79778e7 −0.148459
\(322\) 1.10526e8 + 6.77276e6i 0.184488 + 0.0113050i
\(323\) 2.62607e8i 0.433609i
\(324\) 6.75155e7 + 8.30556e6i 0.110280 + 0.0135663i
\(325\) 8.45092e8i 1.36557i
\(326\) −1.34469e7 + 2.19442e8i −0.0214961 + 0.350799i
\(327\) 5.92364e8 0.936853
\(328\) −4.48020e8 8.31948e7i −0.701033 0.130178i
\(329\) 2.27035e8 0.351485
\(330\) −1.19124e7 + 1.94400e8i −0.0182474 + 0.297782i
\(331\) 9.94404e8i 1.50718i 0.657346 + 0.753589i \(0.271679\pi\)
−0.657346 + 0.753589i \(0.728321\pi\)
\(332\) 1.44786e8 1.17696e9i 0.217142 1.76513i
\(333\) 3.12878e8i 0.464323i
\(334\) −1.62994e8 9.98787e6i −0.239364 0.0146676i
\(335\) −1.95195e8 −0.283668
\(336\) 6.93009e7 2.77409e8i 0.0996670 0.398964i
\(337\) 2.60603e8 0.370916 0.185458 0.982652i \(-0.440623\pi\)
0.185458 + 0.982652i \(0.440623\pi\)
\(338\) 1.34317e9 + 8.23060e7i 1.89200 + 0.115937i
\(339\) 6.91369e7i 0.0963853i
\(340\) 4.14727e7 3.37130e8i 0.0572251 0.465180i
\(341\) 4.15878e8i 0.567970i
\(342\) 6.20088e6 1.01193e8i 0.00838228 0.136792i
\(343\) −7.94578e8 −1.06318
\(344\) 1.81422e8 9.76992e8i 0.240290 1.29401i
\(345\) −5.07842e7 −0.0665827
\(346\) −3.98443e7 + 6.50227e8i −0.0517130 + 0.843915i
\(347\) 1.06575e9i 1.36931i 0.728865 + 0.684657i \(0.240048\pi\)
−0.728865 + 0.684657i \(0.759952\pi\)
\(348\) −4.55192e8 5.59964e7i −0.578985 0.0712251i
\(349\) 4.25455e8i 0.535754i 0.963453 + 0.267877i \(0.0863220\pi\)
−0.963453 + 0.267877i \(0.913678\pi\)
\(350\) −4.57626e8 2.80422e7i −0.570523 0.0349602i
\(351\) 2.65313e8 0.327479
\(352\) −2.86630e8 + 9.07263e8i −0.350286 + 1.10875i
\(353\) −8.81730e8 −1.06690 −0.533451 0.845831i \(-0.679105\pi\)
−0.533451 + 0.845831i \(0.679105\pi\)
\(354\) −9.14530e8 5.60402e7i −1.09569 0.0671410i
\(355\) 3.98902e8i 0.473224i
\(356\) 1.62942e9 + 2.00447e8i 1.91407 + 0.235464i
\(357\) 3.72838e8i 0.433692i
\(358\) 4.79323e7 7.82216e8i 0.0552125 0.901023i
\(359\) 2.70320e8 0.308353 0.154176 0.988043i \(-0.450728\pi\)
0.154176 + 0.988043i \(0.450728\pi\)
\(360\) −2.39417e7 + 1.28931e8i −0.0270456 + 0.145645i
\(361\) 7.42771e8 0.830959
\(362\) −5.72750e7 + 9.34680e8i −0.0634578 + 1.03558i
\(363\) 1.85222e8i 0.203244i
\(364\) 1.36165e8 1.10688e9i 0.147982 1.20294i
\(365\) 4.92781e8i 0.530431i
\(366\) −1.13675e8 6.96572e6i −0.121194 0.00742647i
\(367\) 3.82422e8 0.403842 0.201921 0.979402i \(-0.435282\pi\)
0.201921 + 0.979402i \(0.435282\pi\)
\(368\) −2.40693e8 6.01288e7i −0.251766 0.0628948i
\(369\) −2.29388e8 −0.237673
\(370\) −6.02023e8 3.68905e7i −0.617884 0.0378625i
\(371\) 3.89541e8i 0.396045i
\(372\) 3.41882e7 2.77914e8i 0.0344330 0.279905i
\(373\) 1.28178e9i 1.27889i −0.768838 0.639443i \(-0.779165\pi\)
0.768838 0.639443i \(-0.220835\pi\)
\(374\) 7.58812e7 1.23832e9i 0.0750038 1.22400i
\(375\) 4.72286e8 0.462483
\(376\) −5.00107e8 9.28671e7i −0.485183 0.0900958i
\(377\) −1.78875e9 −1.71931
\(378\) 8.80374e6 1.43670e8i 0.00838389 0.136818i
\(379\) 9.91369e8i 0.935402i −0.883887 0.467701i \(-0.845082\pi\)
0.883887 0.467701i \(-0.154918\pi\)
\(380\) 1.93980e8 + 2.38628e7i 0.181348 + 0.0223090i
\(381\) 1.07329e9i 0.994212i
\(382\) 8.05054e8 + 4.93317e7i 0.738930 + 0.0452798i
\(383\) 2.86442e8 0.260520 0.130260 0.991480i \(-0.458419\pi\)
0.130260 + 0.991480i \(0.458419\pi\)
\(384\) −2.66127e8 + 5.82724e8i −0.239844 + 0.525174i
\(385\) 4.12121e8 0.368055
\(386\) 9.54696e8 + 5.85015e7i 0.844908 + 0.0517739i
\(387\) 5.00225e8i 0.438709i
\(388\) −1.73223e9 2.13094e8i −1.50555 0.185208i
\(389\) 8.13802e8i 0.700963i −0.936570 0.350481i \(-0.886018\pi\)
0.936570 0.350481i \(-0.113982\pi\)
\(390\) −3.12823e7 + 5.10502e8i −0.0267038 + 0.435784i
\(391\) 3.23492e8 0.273681
\(392\) 5.77706e8 + 1.07277e8i 0.484402 + 0.0899508i
\(393\) 2.96810e8 0.246663
\(394\) −3.13826e7 + 5.12138e8i −0.0258495 + 0.421842i
\(395\) 7.38041e8i 0.602546i
\(396\) −5.84802e7 + 4.75383e8i −0.0473234 + 0.384689i
\(397\) 1.88070e9i 1.50853i 0.656571 + 0.754265i \(0.272006\pi\)
−0.656571 + 0.754265i \(0.727994\pi\)
\(398\) −9.91737e8 6.07713e7i −0.788508 0.0483178i
\(399\) −2.14526e8 −0.169073
\(400\) 9.96578e8 + 2.48960e8i 0.778577 + 0.194500i
\(401\) 1.34747e9 1.04355 0.521776 0.853083i \(-0.325270\pi\)
0.521776 + 0.853083i \(0.325270\pi\)
\(402\) −4.79124e8 2.93596e7i −0.367838 0.0225402i
\(403\) 1.09211e9i 0.831185i
\(404\) −1.80888e8 + 1.47043e9i −0.136482 + 1.10946i
\(405\) 6.60131e7i 0.0493784i
\(406\) −5.93552e7 + 9.68627e8i −0.0440167 + 0.718316i
\(407\) −2.20300e9 −1.61970
\(408\) 1.52507e8 8.21280e8i 0.111168 0.598660i
\(409\) −2.51620e8 −0.181850 −0.0909250 0.995858i \(-0.528982\pi\)
−0.0909250 + 0.995858i \(0.528982\pi\)
\(410\) 2.70465e7 4.41377e8i 0.0193806 0.316276i
\(411\) 1.84874e8i 0.131350i
\(412\) 1.95716e9 + 2.40764e8i 1.37875 + 0.169610i
\(413\) 1.93877e9i 1.35426i
\(414\) −1.24655e8 7.63854e6i −0.0863391 0.00529065i
\(415\) 1.15077e9 0.790349
\(416\) −7.52700e8 + 2.38250e9i −0.512620 + 1.62258i
\(417\) 1.49961e8 0.101275
\(418\) 7.12511e8 + 4.36610e7i 0.477172 + 0.0292399i
\(419\) 3.20953e8i 0.213153i −0.994304 0.106577i \(-0.966011\pi\)
0.994304 0.106577i \(-0.0339889\pi\)
\(420\) 2.75404e8 + 3.38794e7i 0.181383 + 0.0223133i
\(421\) 1.60605e9i 1.04899i −0.851414 0.524494i \(-0.824254\pi\)
0.851414 0.524494i \(-0.175746\pi\)
\(422\) −5.15103e7 + 8.40606e8i −0.0333657 + 0.544501i
\(423\) −2.56057e8 −0.164492
\(424\) −1.59339e8 + 8.58072e8i −0.101518 + 0.546693i
\(425\) −1.33940e9 −0.846349
\(426\) −5.99995e7 + 9.79143e8i −0.0376023 + 0.613638i
\(427\) 2.40986e8i 0.149794i
\(428\) 5.09241e7 4.13959e8i 0.0313957 0.255214i
\(429\) 1.86809e9i 1.14235i
\(430\) 9.62507e8 + 5.89801e7i 0.583800 + 0.0357739i
\(431\) −1.54536e9 −0.929735 −0.464868 0.885380i \(-0.653898\pi\)
−0.464868 + 0.885380i \(0.653898\pi\)
\(432\) −7.81598e7 + 3.12871e8i −0.0466434 + 0.186712i
\(433\) 1.64675e9 0.974811 0.487405 0.873176i \(-0.337943\pi\)
0.487405 + 0.873176i \(0.337943\pi\)
\(434\) −5.91387e8 3.62388e7i −0.347263 0.0212794i
\(435\) 4.45063e8i 0.259244i
\(436\) −3.42877e8 + 2.78723e9i −0.198123 + 1.61054i
\(437\) 1.86133e8i 0.106693i
\(438\) 7.41201e7 1.20958e9i 0.0421479 0.687820i
\(439\) 1.90299e9 1.07352 0.536762 0.843734i \(-0.319647\pi\)
0.536762 + 0.843734i \(0.319647\pi\)
\(440\) −9.07812e8 1.68576e8i −0.508056 0.0943431i
\(441\) 2.95788e8 0.164228
\(442\) 1.99266e8 3.25186e9i 0.109763 1.79124i
\(443\) 1.07338e9i 0.586598i −0.956021 0.293299i \(-0.905247\pi\)
0.956021 0.293299i \(-0.0947531\pi\)
\(444\) −1.47217e9 1.81103e8i −0.798213 0.0981939i
\(445\) 1.59316e9i 0.857037i
\(446\) 9.55478e8 + 5.85494e7i 0.509975 + 0.0312500i
\(447\) −9.90091e8 −0.524323
\(448\) 1.26517e9 + 4.86652e8i 0.664778 + 0.255709i
\(449\) 1.87557e8 0.0977850 0.0488925 0.998804i \(-0.484431\pi\)
0.0488925 + 0.998804i \(0.484431\pi\)
\(450\) 5.16126e8 + 3.16269e7i 0.267000 + 0.0163611i
\(451\) 1.61514e9i 0.829074i
\(452\) −3.25308e8 4.00184e7i −0.165695 0.0203833i
\(453\) 1.10464e9i 0.558313i
\(454\) 5.69559e7 9.29474e8i 0.0285656 0.466167i
\(455\) 1.08224e9 0.538623
\(456\) 4.72553e8 + 8.77504e7i 0.233385 + 0.0433383i
\(457\) −1.01128e9 −0.495640 −0.247820 0.968806i \(-0.579714\pi\)
−0.247820 + 0.968806i \(0.579714\pi\)
\(458\) 1.47462e8 2.40646e9i 0.0717218 1.17044i
\(459\) 4.20499e8i 0.202965i
\(460\) 2.93953e7 2.38953e8i 0.0140808 0.114462i
\(461\) 1.15008e9i 0.546734i 0.961910 + 0.273367i \(0.0881373\pi\)
−0.961910 + 0.273367i \(0.911863\pi\)
\(462\) 1.01159e9 + 6.19879e7i 0.477264 + 0.0292456i
\(463\) −3.01661e9 −1.41249 −0.706245 0.707967i \(-0.749612\pi\)
−0.706245 + 0.707967i \(0.749612\pi\)
\(464\) 5.26957e8 2.10939e9i 0.244885 0.980267i
\(465\) 2.71729e8 0.125329
\(466\) −1.92647e9 1.18049e8i −0.881882 0.0540396i
\(467\) 1.34443e9i 0.610843i 0.952217 + 0.305421i \(0.0987974\pi\)
−0.952217 + 0.305421i \(0.901203\pi\)
\(468\) −1.53571e8 + 1.24837e9i −0.0692545 + 0.562967i
\(469\) 1.01572e9i 0.454643i
\(470\) 3.01910e7 4.92692e8i 0.0134133 0.218894i
\(471\) −5.34277e8 −0.235610
\(472\) 7.93040e8 4.27067e9i 0.347135 1.86939i
\(473\) 3.52213e9 1.53035
\(474\) 1.11010e8 1.81159e9i 0.0478782 0.781333i
\(475\) 7.70673e8i 0.329946i
\(476\) −1.75431e9 2.15810e8i −0.745557 0.0917163i
\(477\) 4.39337e8i 0.185346i
\(478\) −4.37885e9 2.68325e8i −1.83384 0.112374i
\(479\) 3.13761e9 1.30444 0.652220 0.758030i \(-0.273838\pi\)
0.652220 + 0.758030i \(0.273838\pi\)
\(480\) −5.92795e8 1.87281e8i −0.244658 0.0772946i
\(481\) −5.78515e9 −2.37032
\(482\) −1.27523e9 7.81431e7i −0.518710 0.0317853i
\(483\) 2.64263e8i 0.106714i
\(484\) −8.71518e8 1.07212e8i −0.349396 0.0429816i
\(485\) 1.69368e9i 0.674117i
\(486\) −9.92914e6 + 1.62035e8i −0.00392360 + 0.0640299i
\(487\) 3.33575e9 1.30871 0.654354 0.756189i \(-0.272941\pi\)
0.654354 + 0.756189i \(0.272941\pi\)
\(488\) 9.85739e7 5.30839e8i 0.0383966 0.206773i
\(489\) −5.24677e8 −0.202914
\(490\) −3.48756e7 + 5.69141e8i −0.0133917 + 0.218541i
\(491\) 2.38332e9i 0.908649i −0.890836 0.454325i \(-0.849881\pi\)
0.890836 0.454325i \(-0.150119\pi\)
\(492\) 1.32777e8 1.07933e9i 0.0502624 0.408581i
\(493\) 2.83502e9i 1.06560i
\(494\) 1.87108e9 + 1.14655e8i 0.698308 + 0.0427906i
\(495\) −4.64804e8 −0.172247
\(496\) 1.28787e9 + 3.21729e8i 0.473900 + 0.118387i
\(497\) 2.07575e9 0.758450
\(498\) 2.82467e9 + 1.73089e8i 1.02486 + 0.0628010i
\(499\) 3.49696e9i 1.25991i 0.776633 + 0.629954i \(0.216926\pi\)
−0.776633 + 0.629954i \(0.783074\pi\)
\(500\) −2.73373e8 + 2.22223e9i −0.0978047 + 0.795050i
\(501\) 3.89712e8i 0.138456i
\(502\) −1.32480e8 + 2.16196e9i −0.0467398 + 0.762756i
\(503\) 1.55596e9 0.545142 0.272571 0.962136i \(-0.412126\pi\)
0.272571 + 0.962136i \(0.412126\pi\)
\(504\) 6.70909e8 + 1.24584e8i 0.233430 + 0.0433467i
\(505\) −1.43771e9 −0.496766
\(506\) 5.37836e7 8.77705e8i 0.0184554 0.301177i
\(507\) 3.21146e9i 1.09440i
\(508\) 5.05011e9 + 6.21250e8i 1.70914 + 0.210254i
\(509\) 3.55919e9i 1.19630i 0.801385 + 0.598149i \(0.204097\pi\)
−0.801385 + 0.598149i \(0.795903\pi\)
\(510\) 8.09103e8 + 4.95799e7i 0.270090 + 0.0165504i
\(511\) −2.56426e9 −0.850137
\(512\) −2.58783e9 1.58950e9i −0.852101 0.523377i
\(513\) 2.41949e8 0.0791250
\(514\) −1.83112e9 1.12206e8i −0.594764 0.0364457i
\(515\) 1.91360e9i 0.617343i
\(516\) 2.35369e9 + 2.89545e8i 0.754182 + 0.0927772i
\(517\) 1.80292e9i 0.573799i
\(518\) −1.91965e8 + 3.13272e9i −0.0606832 + 0.990301i
\(519\) −1.55467e9 −0.488148
\(520\) −2.38394e9 4.42685e8i −0.743505 0.138065i
\(521\) 4.88706e9 1.51396 0.756982 0.653436i \(-0.226673\pi\)
0.756982 + 0.653436i \(0.226673\pi\)
\(522\) 6.69427e7 1.09245e9i 0.0205995 0.336167i
\(523\) 2.25480e9i 0.689212i 0.938747 + 0.344606i \(0.111987\pi\)
−0.938747 + 0.344606i \(0.888013\pi\)
\(524\) −1.71802e8 + 1.39657e9i −0.0521638 + 0.424037i
\(525\) 1.09417e9i 0.330009i
\(526\) 9.68318e7 + 5.93362e6i 0.0290113 + 0.00177775i
\(527\) −1.73090e9 −0.515151
\(528\) −2.20295e9 5.50330e8i −0.651309 0.162706i
\(529\) −3.17554e9 −0.932658
\(530\) −8.45350e8 5.18010e7i −0.246644 0.0151138i
\(531\) 2.18661e9i 0.633781i
\(532\) 1.24174e8 1.00940e9i 0.0357552 0.290652i
\(533\) 4.24142e9i 1.21329i
\(534\) −2.39630e8 + 3.91057e9i −0.0681000 + 1.11134i
\(535\) 4.04747e8 0.114274
\(536\) 4.15475e8 2.23741e9i 0.116538 0.627581i
\(537\) 1.87025e9 0.521182
\(538\) 1.63218e7 2.66359e8i 0.00451888 0.0737445i
\(539\) 2.08267e9i 0.572876i
\(540\) −3.10609e8 3.82103e7i −0.0848861 0.0104424i
\(541\) 6.18666e9i 1.67983i −0.542718 0.839915i \(-0.682605\pi\)
0.542718 0.839915i \(-0.317395\pi\)
\(542\) −2.84341e8 1.74238e7i −0.0767084 0.00470050i
\(543\) −2.23479e9 −0.599013
\(544\) 3.77607e9 + 1.19297e9i 1.00564 + 0.317711i
\(545\) −2.72521e9 −0.721127
\(546\) 2.65647e9 + 1.62782e8i 0.698443 + 0.0427989i
\(547\) 1.78927e9i 0.467433i 0.972305 + 0.233717i \(0.0750888\pi\)
−0.972305 + 0.233717i \(0.924911\pi\)
\(548\) −8.69883e8 1.07010e8i −0.225803 0.0277776i
\(549\) 2.71792e8i 0.0701025i
\(550\) −2.22688e8 + 3.63409e9i −0.0570726 + 0.931378i
\(551\) −1.63123e9 −0.415418
\(552\) 1.08095e8 5.82113e8i 0.0273539 0.147306i
\(553\) −3.84050e9 −0.965718
\(554\) −2.38508e8 + 3.89225e9i −0.0595961 + 0.972560i
\(555\) 1.43941e9i 0.357405i
\(556\) −8.68018e7 + 7.05608e8i −0.0214174 + 0.174101i
\(557\) 3.18701e9i 0.781430i −0.920512 0.390715i \(-0.872228\pi\)
0.920512 0.390715i \(-0.127772\pi\)
\(558\) 6.66986e8 + 4.08713e7i 0.162516 + 0.00995861i
\(559\) 9.24922e9 2.23957
\(560\) −3.18823e8 + 1.27624e9i −0.0767171 + 0.307096i
\(561\) 2.96077e9 0.708003
\(562\) 3.81020e9 + 2.33480e8i 0.905464 + 0.0554846i
\(563\) 1.15604e9i 0.273020i −0.990639 0.136510i \(-0.956411\pi\)
0.990639 0.136510i \(-0.0435886\pi\)
\(564\) 1.48213e8 1.20482e9i 0.0347865 0.282778i
\(565\) 3.18069e8i 0.0741910i
\(566\) −2.73410e8 + 4.46183e9i −0.0633807 + 1.03432i
\(567\) 3.43509e8 0.0791402
\(568\) −4.57240e9 8.49070e8i −1.04695 0.194413i
\(569\) 5.86706e8 0.133514 0.0667571 0.997769i \(-0.478735\pi\)
0.0667571 + 0.997769i \(0.478735\pi\)
\(570\) −2.85276e7 + 4.65546e8i −0.00645212 + 0.105293i
\(571\) 5.83720e9i 1.31213i −0.754702 0.656067i \(-0.772219\pi\)
0.754702 0.656067i \(-0.227781\pi\)
\(572\) −8.78989e9 1.08131e9i −1.96380 0.241581i
\(573\) 1.92485e9i 0.427421i
\(574\) −2.29677e9 1.40741e8i −0.506905 0.0310619i
\(575\) −9.49351e8 −0.208252
\(576\) −1.42690e9 5.48862e8i −0.311111 0.119670i
\(577\) 5.04159e9 1.09258 0.546289 0.837597i \(-0.316040\pi\)
0.546289 + 0.837597i \(0.316040\pi\)
\(578\) −5.20175e8 3.18751e7i −0.112047 0.00686600i
\(579\) 2.28264e9i 0.488723i
\(580\) 2.09414e9 + 2.57615e8i 0.445665 + 0.0548244i
\(581\) 5.98819e9i 1.26672i
\(582\) 2.54749e8 4.15730e9i 0.0535652 0.874140i
\(583\) −3.09341e9 −0.646544
\(584\) 5.64849e9 + 1.04889e9i 1.17351 + 0.217915i
\(585\) −1.22059e9 −0.252072
\(586\) −4.16314e8 + 6.79390e9i −0.0854632 + 1.39469i
\(587\) 5.71937e9i 1.16712i 0.812071 + 0.583559i \(0.198340\pi\)
−0.812071 + 0.583559i \(0.801660\pi\)
\(588\) −1.71211e8 + 1.39177e9i −0.0347305 + 0.282322i
\(589\) 9.95935e8i 0.200830i
\(590\) 4.20735e9 + 2.57816e8i 0.843387 + 0.0516807i
\(591\) −1.22450e9 −0.244008
\(592\) 1.70427e9 6.82215e9i 0.337609 1.35144i
\(593\) 2.07985e9 0.409581 0.204791 0.978806i \(-0.434349\pi\)
0.204791 + 0.978806i \(0.434349\pi\)
\(594\) −1.14091e9 6.99120e7i −0.223356 0.0136867i
\(595\) 1.71527e9i 0.333828i
\(596\) 5.73093e8 4.65865e9i 0.110883 0.901360i
\(597\) 2.37121e9i 0.456099i
\(598\) 1.41237e8 2.30488e9i 0.0270082 0.440752i
\(599\) −6.32006e9 −1.20151 −0.600755 0.799433i \(-0.705133\pi\)
−0.600755 + 0.799433i \(0.705133\pi\)
\(600\) −4.47562e8 + 2.41021e9i −0.0845909 + 0.455538i
\(601\) −3.92467e9 −0.737466 −0.368733 0.929535i \(-0.620208\pi\)
−0.368733 + 0.929535i \(0.620208\pi\)
\(602\) 3.06912e8 5.00855e9i 0.0573358 0.935673i
\(603\) 1.14557e9i 0.212770i
\(604\) 5.19764e9 + 6.39398e8i 0.959791 + 0.118071i
\(605\) 8.52123e8i 0.156444i
\(606\) −3.52900e9 2.16249e8i −0.644166 0.0394729i
\(607\) −3.19677e8 −0.0580164 −0.0290082 0.999579i \(-0.509235\pi\)
−0.0290082 + 0.999579i \(0.509235\pi\)
\(608\) −6.86417e8 + 2.17270e9i −0.123858 + 0.392046i
\(609\) −2.31595e9 −0.415498
\(610\) 5.22968e8 + 3.20462e7i 0.0932870 + 0.00571640i
\(611\) 4.73453e9i 0.839716i
\(612\) 1.97856e9 + 2.43397e8i 0.348915 + 0.0429225i
\(613\) 1.39750e9i 0.245043i 0.992466 + 0.122521i \(0.0390980\pi\)
−0.992466 + 0.122521i \(0.960902\pi\)
\(614\) 4.01806e8 6.55715e9i 0.0700531 1.14321i
\(615\) 1.05532e9 0.182945
\(616\) −8.77208e8 + 4.72393e9i −0.151206 + 0.814275i
\(617\) −5.55555e9 −0.952202 −0.476101 0.879391i \(-0.657950\pi\)
−0.476101 + 0.879391i \(0.657950\pi\)
\(618\) −2.87828e8 + 4.69712e9i −0.0490539 + 0.800520i
\(619\) 1.48636e9i 0.251887i 0.992037 + 0.125944i \(0.0401959\pi\)
−0.992037 + 0.125944i \(0.959804\pi\)
\(620\) −1.57285e8 + 1.27856e9i −0.0265043 + 0.215452i
\(621\) 2.98045e8i 0.0499414i
\(622\) −3.44974e9 2.11392e8i −0.574805 0.0352227i
\(623\) 8.29025e9 1.37360
\(624\) −5.78503e9 1.44518e9i −0.953146 0.238110i
\(625\) 2.72531e9 0.446515
\(626\) −5.40906e9 3.31454e8i −0.881275 0.0540024i
\(627\) 1.70359e9i 0.276012i
\(628\) 3.09255e8 2.51392e9i 0.0498263 0.405035i
\(629\) 9.16898e9i 1.46907i
\(630\) −4.05022e7 + 6.60962e8i −0.00645336 + 0.105314i
\(631\) 7.72780e9 1.22448 0.612242 0.790670i \(-0.290268\pi\)
0.612242 + 0.790670i \(0.290268\pi\)
\(632\) 8.45977e9 + 1.57093e9i 1.33306 + 0.247541i
\(633\) −2.00986e9 −0.314958
\(634\) 6.04133e8 9.85896e9i 0.0941500 1.53645i
\(635\) 4.93773e9i 0.765278i
\(636\) −2.06720e9 2.54301e8i −0.318627 0.0391966i
\(637\) 5.46916e9i 0.838365i
\(638\) 7.69204e9 + 4.71349e8i 1.17265 + 0.0718572i
\(639\) −2.34109e9 −0.354949
\(640\) 1.22433e9 2.68086e9i 0.184616 0.404244i
\(641\) −6.28895e9 −0.943137 −0.471569 0.881829i \(-0.656312\pi\)
−0.471569 + 0.881829i \(0.656312\pi\)
\(642\) 9.93491e8 + 6.08787e7i 0.148181 + 0.00908015i
\(643\) 7.19728e9i 1.06765i 0.845594 + 0.533826i \(0.179246\pi\)
−0.845594 + 0.533826i \(0.820754\pi\)
\(644\) −1.24343e9 1.52963e8i −0.183451 0.0225676i
\(645\) 2.30132e9i 0.337689i
\(646\) 1.81719e8 2.96550e9i 0.0265208 0.432797i
\(647\) −8.28399e9 −1.20247 −0.601235 0.799072i \(-0.705325\pi\)
−0.601235 + 0.799072i \(0.705325\pi\)
\(648\) −7.56673e8 1.40510e8i −0.109244 0.0202859i
\(649\) 1.53961e10 2.21082
\(650\) −5.84786e8 + 9.54323e9i −0.0835219 + 1.36301i
\(651\) 1.41398e9i 0.200868i
\(652\) 3.03698e8 2.46875e9i 0.0429117 0.348827i
\(653\) 9.71933e9i 1.36597i 0.730434 + 0.682983i \(0.239318\pi\)
−0.730434 + 0.682983i \(0.760682\pi\)
\(654\) −6.68929e9 4.09903e8i −0.935099 0.0573006i
\(655\) −1.36549e9 −0.189865
\(656\) 5.00171e9 + 1.24950e9i 0.691759 + 0.172812i
\(657\) 2.89206e9 0.397858
\(658\) −2.56380e9 1.57103e8i −0.350827 0.0214978i
\(659\) 9.81337e9i 1.33573i −0.744282 0.667866i \(-0.767208\pi\)
0.744282 0.667866i \(-0.232792\pi\)
\(660\) 2.69042e8 2.18703e9i 0.0364264 0.296108i
\(661\) 4.59313e9i 0.618591i 0.950966 + 0.309295i \(0.100093\pi\)
−0.950966 + 0.309295i \(0.899907\pi\)
\(662\) 6.88106e8 1.12293e10i 0.0921833 1.50436i
\(663\) 7.77508e9 1.03611
\(664\) −2.44943e9 + 1.31906e10i −0.324696 + 1.74855i
\(665\) 9.86940e8 0.130141
\(666\) 2.16505e8 3.53318e9i 0.0283993 0.463453i
\(667\) 2.00943e9i 0.262200i
\(668\) 1.83370e9 + 2.25576e8i 0.238019 + 0.0292803i
\(669\) 2.28451e9i 0.294986i
\(670\) 2.20424e9 + 1.35071e8i 0.283137 + 0.0173500i
\(671\) 1.91371e9 0.244539
\(672\) −9.74544e8 + 3.08470e9i −0.123882 + 0.392121i
\(673\) −7.01118e8 −0.0886622 −0.0443311 0.999017i \(-0.514116\pi\)
−0.0443311 + 0.999017i \(0.514116\pi\)
\(674\) −2.94287e9 1.80332e8i −0.370221 0.0226863i
\(675\) 1.23404e9i 0.154442i
\(676\) −1.51108e10 1.85889e9i −1.88137 0.231440i
\(677\) 1.33165e10i 1.64941i 0.565560 + 0.824707i \(0.308660\pi\)
−0.565560 + 0.824707i \(0.691340\pi\)
\(678\) 4.78412e7 7.80730e8i 0.00589520 0.0962048i
\(679\) −8.81332e9 −1.08043
\(680\) −7.01619e8 + 3.77835e9i −0.0855697 + 0.460809i
\(681\) 2.22234e9 0.269647
\(682\) −2.87778e8 + 4.69631e9i −0.0347386 + 0.566906i
\(683\) 2.68818e9i 0.322839i −0.986886 0.161419i \(-0.948393\pi\)
0.986886 0.161419i \(-0.0516072\pi\)
\(684\) −1.40047e8 + 1.13844e9i −0.0167332 + 0.136023i
\(685\) 8.50525e8i 0.101104i
\(686\) 8.97280e9 + 5.49831e8i 1.06119 + 0.0650272i
\(687\) 5.75376e9 0.677022
\(688\) −2.72477e9 + 1.09072e10i −0.318985 + 1.27689i
\(689\) −8.12340e9 −0.946173
\(690\) 5.73482e8 + 3.51416e7i 0.0664581 + 0.00407239i
\(691\) 1.41484e10i 1.63131i −0.578541 0.815653i \(-0.696378\pi\)
0.578541 0.815653i \(-0.303622\pi\)
\(692\) 8.99886e8 7.31513e9i 0.103232 0.839172i
\(693\) 2.41868e9i 0.276065i
\(694\) 7.37478e8 1.20350e10i 0.0837512 1.36675i
\(695\) −6.89906e8 −0.0779548
\(696\) 5.10152e9 + 9.47325e8i 0.573545 + 0.106504i
\(697\) −6.72230e9 −0.751974
\(698\) 2.94406e8 4.80447e9i 0.0327682 0.534751i
\(699\) 4.60610e9i 0.510110i
\(700\) 5.14835e9 + 6.33335e8i 0.567316 + 0.0697896i
\(701\) 1.53529e10i 1.68337i −0.539972 0.841683i \(-0.681565\pi\)
0.539972 0.841683i \(-0.318435\pi\)
\(702\) −2.99605e9 1.83591e8i −0.326866 0.0200296i
\(703\) −5.27570e9 −0.572712
\(704\) 3.86459e9 1.00470e10i 0.417445 1.08525i
\(705\) 1.17801e9 0.126615
\(706\) 9.95696e9 + 6.10139e8i 1.06490 + 0.0652547i
\(707\) 7.48135e9i 0.796181i
\(708\) 1.02886e10 + 1.26567e9i 1.08953 + 0.134031i
\(709\) 5.59636e8i 0.0589717i −0.999565 0.0294859i \(-0.990613\pi\)
0.999565 0.0294859i \(-0.00938700\pi\)
\(710\) 2.76032e8 4.50461e9i 0.0289437 0.472338i
\(711\) 4.33145e9 0.451949
\(712\) −1.82616e10 3.39107e9i −1.89609 0.352093i
\(713\) −1.22684e9 −0.126758
\(714\) 2.57996e8 4.21029e9i 0.0265259 0.432880i
\(715\) 8.59428e9i 0.879303i
\(716\) −1.08255e9 + 8.80002e9i −0.110218 + 0.895959i
\(717\) 1.04697e10i 1.06076i
\(718\) −3.05260e9 1.87056e8i −0.307776 0.0188598i
\(719\) −7.25097e9 −0.727520 −0.363760 0.931493i \(-0.618507\pi\)
−0.363760 + 0.931493i \(0.618507\pi\)
\(720\) 3.59579e8 1.43938e9i 0.0359030 0.143719i
\(721\) 9.95772e9 0.989433
\(722\) −8.38776e9 5.13982e8i −0.829404 0.0508239i
\(723\) 3.04903e9i 0.300039i
\(724\) 1.29356e9 1.05153e10i 0.126678 1.02976i
\(725\) 8.31993e9i 0.810843i
\(726\) 1.28169e8 2.09162e9i 0.0124310 0.202864i
\(727\) −3.30176e9 −0.318695 −0.159347 0.987223i \(-0.550939\pi\)
−0.159347 + 0.987223i \(0.550939\pi\)
\(728\) −2.30358e9 + 1.24052e10i −0.221280 + 1.19164i
\(729\) −3.87420e8 −0.0370370
\(730\) −3.40994e8 + 5.56475e9i −0.0324427 + 0.529438i
\(731\) 1.46592e10i 1.38804i
\(732\) 1.27886e9 + 1.57321e8i 0.120513 + 0.0148251i
\(733\) 1.17975e9i 0.110644i 0.998469 + 0.0553218i \(0.0176185\pi\)
−0.998469 + 0.0553218i \(0.982382\pi\)
\(734\) −4.31851e9 2.64628e8i −0.403086 0.0247001i
\(735\) −1.36079e9 −0.126412
\(736\) 2.67643e9 + 8.45560e8i 0.247448 + 0.0781758i
\(737\) 8.06604e9 0.742206
\(738\) 2.59037e9 + 1.58732e8i 0.237228 + 0.0145367i
\(739\) 4.28180e9i 0.390275i −0.980776 0.195138i \(-0.937485\pi\)
0.980776 0.195138i \(-0.0625153\pi\)
\(740\) 6.77283e9 + 8.33174e8i 0.614412 + 0.0755831i
\(741\) 4.47367e9i 0.403925i
\(742\) −2.69554e8 + 4.39890e9i −0.0242233 + 0.395304i
\(743\) −2.30686e9 −0.206329 −0.103165 0.994664i \(-0.532897\pi\)
−0.103165 + 0.994664i \(0.532897\pi\)
\(744\) −5.78381e8 + 3.11469e9i −0.0514883 + 0.277274i
\(745\) 4.55498e9 0.403589
\(746\) −8.86964e8 + 1.44745e10i −0.0782204 + 1.27649i
\(747\) 6.75367e9i 0.592813i
\(748\) −1.71378e9 + 1.39312e10i −0.149727 + 1.21712i
\(749\) 2.10616e9i 0.183149i
\(750\) −5.33330e9 3.26812e8i −0.461617 0.0282868i
\(751\) −1.92214e10 −1.65594 −0.827972 0.560770i \(-0.810505\pi\)
−0.827972 + 0.560770i \(0.810505\pi\)
\(752\) 5.58321e9 + 1.39477e9i 0.478764 + 0.119602i
\(753\) −5.16917e9 −0.441203
\(754\) 2.01995e10 + 1.23778e9i 1.71610 + 0.105158i
\(755\) 5.08198e9i 0.429752i
\(756\) −1.98833e8 + 1.61630e9i −0.0167364 + 0.136049i
\(757\) 1.11993e9i 0.0938329i −0.998899 0.0469164i \(-0.985061\pi\)
0.998899 0.0469164i \(-0.0149395\pi\)
\(758\) −6.86007e8 + 1.11951e10i −0.0572119 + 0.933651i
\(759\) 2.09856e9 0.174211
\(760\) −2.17401e9 4.03701e8i −0.179644 0.0333590i
\(761\) −1.10491e10 −0.908826 −0.454413 0.890791i \(-0.650151\pi\)
−0.454413 + 0.890791i \(0.650151\pi\)
\(762\) −7.42693e8 + 1.21201e10i −0.0608088 + 0.992350i
\(763\) 1.41810e10i 1.15577i
\(764\) −9.05695e9 1.11416e9i −0.734777 0.0903901i
\(765\) 1.93453e9i 0.156229i
\(766\) −3.23465e9 1.98212e8i −0.260032 0.0159341i
\(767\) 4.04306e10 3.23539
\(768\) 3.40848e9 6.39627e9i 0.271517 0.509521i
\(769\) −3.08275e9 −0.244453 −0.122227 0.992502i \(-0.539003\pi\)
−0.122227 + 0.992502i \(0.539003\pi\)
\(770\) −4.65389e9 2.85179e8i −0.367366 0.0225113i
\(771\) 4.37813e9i 0.344031i
\(772\) −1.07405e10 1.32126e9i −0.840160 0.103354i
\(773\) 1.61813e10i 1.26004i 0.776577 + 0.630022i \(0.216954\pi\)
−0.776577 + 0.630022i \(0.783046\pi\)
\(774\) −3.46145e8 + 5.64880e9i −0.0268327 + 0.437888i
\(775\) 5.07966e9 0.391994
\(776\) 1.94138e10 + 3.60503e9i 1.49140 + 0.276945i
\(777\) −7.49021e9 −0.572823
\(778\) −5.63133e8 + 9.18988e9i −0.0428729 + 0.699650i
\(779\) 3.86791e9i 0.293154i
\(780\) 7.06512e8 5.74321e9i 0.0533075 0.433335i
\(781\) 1.64838e10i 1.23817i
\(782\) −3.65304e9 2.23850e8i −0.273169 0.0167391i
\(783\) 2.61201e9 0.194450
\(784\) −6.44953e9 1.61119e9i −0.477993 0.119410i
\(785\) 2.45798e9 0.181357
\(786\) −3.35173e9 2.05386e8i −0.246201 0.0150866i
\(787\) 1.76252e10i 1.28891i 0.764644 + 0.644453i \(0.222915\pi\)
−0.764644 + 0.644453i \(0.777085\pi\)
\(788\) 7.08777e8 5.76162e9i 0.0516022 0.419472i
\(789\) 2.31521e8i 0.0167811i
\(790\) −5.10708e8 + 8.33434e9i −0.0368535 + 0.601418i
\(791\) −1.65512e9 −0.118908
\(792\) 9.89344e8 5.32781e9i 0.0707635 0.381075i
\(793\) 5.02547e9 0.357866
\(794\) 1.30141e9 2.12379e10i 0.0922660 1.50571i
\(795\) 2.02120e9i 0.142667i
\(796\) 1.11572e10 + 1.37252e9i 0.784076 + 0.0964548i
\(797\) 1.78726e10i 1.25050i −0.780423 0.625251i \(-0.784996\pi\)
0.780423 0.625251i \(-0.215004\pi\)
\(798\) 2.42254e9 + 1.48447e8i 0.168757 + 0.0103410i
\(799\) −7.50384e9 −0.520439
\(800\) −1.10816e10 3.50100e9i −0.765223 0.241756i
\(801\) −9.35002e9 −0.642834
\(802\) −1.52163e10 9.32421e8i −1.04160 0.0638266i
\(803\) 2.03632e10i 1.38785i
\(804\) 5.39020e9 + 6.63087e8i 0.365771 + 0.0449961i
\(805\) 1.21576e9i 0.0821414i
\(806\) −7.55715e8 + 1.23326e10i −0.0508376 + 0.829629i
\(807\) 6.36854e8 0.0426562
\(808\) 3.06020e9 1.64797e10i 0.204084 1.09903i
\(809\) 6.25322e9 0.415225 0.207613 0.978211i \(-0.433431\pi\)
0.207613 + 0.978211i \(0.433431\pi\)
\(810\) 4.56796e7 7.45454e8i 0.00302013 0.0492860i
\(811\) 5.32870e9i 0.350791i 0.984498 + 0.175395i \(0.0561204\pi\)
−0.984498 + 0.175395i \(0.943880\pi\)
\(812\) 1.34054e9 1.08972e10i 0.0878685 0.714279i
\(813\) 6.79850e8i 0.0443707i
\(814\) 2.48774e10 + 1.52443e9i 1.61667 + 0.0990654i
\(815\) 2.41381e9 0.156189
\(816\) −2.29050e9 + 9.16879e9i −0.147576 + 0.590740i
\(817\) 8.43472e9 0.541120
\(818\) 2.84142e9 + 1.74116e8i 0.181509 + 0.0111225i
\(819\) 6.35152e9i 0.404003i
\(820\) −6.10847e8 + 4.96555e9i −0.0386887 + 0.314498i
\(821\) 9.82164e9i 0.619417i −0.950832 0.309708i \(-0.899769\pi\)
0.950832 0.309708i \(-0.100231\pi\)
\(822\) 1.27929e8 2.08770e9i 0.00803374 0.131104i
\(823\) −9.91646e9 −0.620093 −0.310047 0.950721i \(-0.600345\pi\)
−0.310047 + 0.950721i \(0.600345\pi\)
\(824\) −2.19346e10 4.07314e9i −1.36579 0.253620i
\(825\) −8.68897e9 −0.538740
\(826\) 1.34159e9 2.18936e10i 0.0828301 1.35172i
\(827\) 6.85015e9i 0.421144i 0.977578 + 0.210572i \(0.0675327\pi\)
−0.977578 + 0.210572i \(0.932467\pi\)
\(828\) 1.40238e9 + 1.72517e8i 0.0858538 + 0.0105615i
\(829\) 1.40904e9i 0.0858978i 0.999077 + 0.0429489i \(0.0136753\pi\)
−0.999077 + 0.0429489i \(0.986325\pi\)
\(830\) −1.29951e10 7.96306e8i −0.788870 0.0483400i
\(831\) −9.30622e9 −0.562561
\(832\) 1.01485e10 2.63836e10i 0.610902 1.58819i
\(833\) 8.66817e9 0.519601
\(834\) −1.69344e9 1.03770e8i −0.101085 0.00619427i
\(835\) 1.79289e9i 0.106574i
\(836\) −8.01584e9 9.86085e8i −0.474490 0.0583704i
\(837\) 1.59474e9i 0.0940048i
\(838\) −2.22092e8 + 3.62437e9i −0.0130371 + 0.212754i
\(839\) 3.05412e9 0.178533 0.0892667 0.996008i \(-0.471548\pi\)
0.0892667 + 0.996008i \(0.471548\pi\)
\(840\) −3.08656e9 5.73157e8i −0.179679 0.0333654i
\(841\) −3.60372e8 −0.0208913
\(842\) −1.11135e9 + 1.81363e10i −0.0641591 + 1.04702i
\(843\) 9.11005e9i 0.523750i
\(844\) 1.16336e9 9.45692e9i 0.0666065 0.541441i
\(845\) 1.47745e10i 0.842394i
\(846\) 2.89153e9 + 1.77186e8i 0.164184 + 0.0100608i
\(847\) −4.43415e9 −0.250737
\(848\) 2.39311e9 9.57955e9i 0.134765 0.539460i
\(849\) −1.06681e10 −0.598286
\(850\) 1.51252e10 + 9.26837e8i 0.844765 + 0.0517651i
\(851\) 6.49886e9i 0.361479i
\(852\) 1.35509e9 1.10155e10i 0.0750637 0.610190i
\(853\) 1.95266e10i 1.07722i 0.842555 + 0.538610i \(0.181051\pi\)
−0.842555 + 0.538610i \(0.818949\pi\)
\(854\) 1.66757e8 2.72134e9i 0.00916184 0.149514i
\(855\) −1.11310e9 −0.0609052
\(856\) −8.61512e8 + 4.63941e9i −0.0469465 + 0.252816i
\(857\) −8.87348e9 −0.481572 −0.240786 0.970578i \(-0.577405\pi\)
−0.240786 + 0.970578i \(0.577405\pi\)
\(858\) 1.29268e9 2.10955e10i 0.0698692 1.14021i
\(859\) 2.58119e9i 0.138945i −0.997584 0.0694727i \(-0.977868\pi\)
0.997584 0.0694727i \(-0.0221317\pi\)
\(860\) −1.08283e10 1.33207e9i −0.580519 0.0714138i
\(861\) 5.49149e9i 0.293210i
\(862\) 1.74510e10 + 1.06936e9i 0.927994 + 0.0568653i
\(863\) 8.06781e9 0.427285 0.213643 0.976912i \(-0.431467\pi\)
0.213643 + 0.976912i \(0.431467\pi\)
\(864\) 1.09912e9 3.47902e9i 0.0579760 0.183510i
\(865\) 7.15235e9 0.375744
\(866\) −1.85960e10 1.13952e9i −0.972986 0.0596222i
\(867\) 1.24372e9i 0.0648120i
\(868\) 6.65318e9 + 8.18455e8i 0.345311 + 0.0424791i
\(869\) 3.04981e10i 1.57653i
\(870\) −3.07974e8 + 5.02588e9i −0.0158561 + 0.258759i
\(871\) 2.11817e10 1.08617
\(872\) 5.80066e9 3.12376e10i 0.296258 1.59540i
\(873\) 9.93995e9 0.505632
\(874\) 1.28800e8 2.10191e9i 0.00652568 0.106494i
\(875\) 1.13064e10i 0.570553i
\(876\) −1.67401e9 + 1.36079e10i −0.0841381 + 0.683954i
\(877\) 2.78406e10i 1.39373i −0.717200 0.696867i \(-0.754577\pi\)
0.717200 0.696867i \(-0.245423\pi\)
\(878\) −2.14896e10 1.31683e9i −1.07151 0.0656598i
\(879\) −1.62440e10 −0.806735
\(880\) 1.01348e10 + 2.53183e9i 0.501334 + 0.125241i
\(881\) 8.64505e9 0.425943 0.212972 0.977058i \(-0.431686\pi\)
0.212972 + 0.977058i \(0.431686\pi\)
\(882\) −3.34020e9 2.04679e8i −0.163920 0.0100446i
\(883\) 2.55194e10i 1.24741i −0.781661 0.623704i \(-0.785627\pi\)
0.781661 0.623704i \(-0.214373\pi\)
\(884\) −4.50044e9 + 3.65839e10i −0.219115 + 1.78118i
\(885\) 1.00596e10i 0.487843i
\(886\) −7.42756e8 + 1.21212e10i −0.0358780 + 0.585500i
\(887\) −2.64691e10 −1.27352 −0.636761 0.771061i \(-0.719726\pi\)
−0.636761 + 0.771061i \(0.719726\pi\)
\(888\) 1.64993e10 + 3.06382e9i 0.790713 + 0.146831i
\(889\) 2.56942e10 1.22653
\(890\) 1.10243e9 1.79908e10i 0.0524188 0.855433i
\(891\) 2.72786e9i 0.129196i
\(892\) −1.07492e10 1.32234e9i −0.507109 0.0623830i
\(893\) 4.31760e9i 0.202891i
\(894\) 1.11806e10 + 6.85122e8i 0.523341 + 0.0320691i
\(895\) −8.60420e9 −0.401171
\(896\) −1.39502e10 6.37101e9i −0.647894 0.295890i
\(897\) 5.51088e9 0.254946
\(898\) −2.11800e9 1.29786e8i −0.0976019 0.00598081i
\(899\) 1.07518e10i 0.493539i
\(900\) −5.80648e9 7.14296e8i −0.265500 0.0326610i
\(901\) 1.28749e10i 0.586418i
\(902\) −1.11765e9 + 1.82391e10i −0.0507085 + 0.827522i
\(903\) 1.19752e10 0.541224
\(904\) 3.64585e9 + 6.77015e8i 0.164138 + 0.0304796i
\(905\) 1.02813e10 0.461081
\(906\) −7.64389e8 + 1.24742e10i −0.0341480 + 0.557268i
\(907\) 2.81900e10i 1.25450i 0.778819 + 0.627249i \(0.215819\pi\)
−0.778819 + 0.627249i \(0.784181\pi\)
\(908\) −1.28635e9 + 1.04567e10i −0.0570242 + 0.463547i
\(909\) 8.43771e9i 0.372607i
\(910\) −1.22213e10 7.48890e8i −0.537615 0.0329437i
\(911\) 1.11448e10 0.488381 0.244190 0.969727i \(-0.421478\pi\)
0.244190 + 0.969727i \(0.421478\pi\)
\(912\) −5.27559e9 1.31792e9i −0.230298 0.0575317i
\(913\) −4.75532e10 −2.06791
\(914\) 1.14199e10 + 6.99787e8i 0.494712 + 0.0303147i
\(915\) 1.25040e9i 0.0539603i
\(916\) −3.33044e9 + 2.70730e10i −0.143175 + 1.16386i
\(917\) 7.10554e9i 0.304302i
\(918\) −2.90977e8 + 4.74850e9i −0.0124139 + 0.202585i
\(919\) 3.43901e10 1.46160 0.730801 0.682591i \(-0.239147\pi\)
0.730801 + 0.682591i \(0.239147\pi\)
\(920\) −4.97298e8 + 2.67805e9i −0.0210552 + 0.113386i
\(921\) 1.56779e10 0.661270
\(922\) 7.95833e8 1.29873e10i 0.0334398 0.545710i
\(923\) 4.32871e10i 1.81198i
\(924\) −1.13805e10 1.40000e9i −0.474581 0.0583816i
\(925\) 2.69082e10i 1.11786i
\(926\) 3.40651e10 + 2.08743e9i 1.40985 + 0.0863919i
\(927\) −1.12306e10 −0.463047
\(928\) −7.41033e9 + 2.34557e10i −0.304382 + 0.963453i
\(929\) −2.08357e10 −0.852617 −0.426308 0.904578i \(-0.640186\pi\)
−0.426308 + 0.904578i \(0.640186\pi\)
\(930\) −3.06851e9 1.88031e8i −0.125094 0.00766547i
\(931\) 4.98754e9i 0.202564i
\(932\) 2.16730e10 + 2.66615e9i 0.876926 + 0.107877i
\(933\) 8.24821e9i 0.332486i
\(934\) 9.30318e8 1.51820e10i 0.0373609 0.609699i
\(935\) −1.36212e10 −0.544974
\(936\) 2.59805e9 1.39910e10i 0.103558 0.557677i
\(937\) −3.36470e10 −1.33616 −0.668079 0.744090i \(-0.732883\pi\)
−0.668079 + 0.744090i \(0.732883\pi\)
\(938\) 7.02860e8 1.14701e10i 0.0278073 0.453792i
\(939\) 1.29328e10i 0.509759i
\(940\) −6.81865e8 + 5.54285e9i −0.0267763 + 0.217663i
\(941\) 1.90133e10i 0.743865i 0.928260 + 0.371932i \(0.121305\pi\)
−0.928260 + 0.371932i \(0.878695\pi\)
\(942\) 6.03334e9 + 3.69709e8i 0.235169 + 0.0144106i
\(943\) −4.76468e9 −0.185030
\(944\) −1.19106e10 + 4.76779e10i −0.460822 + 1.84466i
\(945\) −1.58033e9 −0.0609169
\(946\) −3.97737e10 2.43724e9i −1.52749 0.0936007i
\(947\) 3.29218e10i 1.25968i −0.776727 0.629838i \(-0.783121\pi\)
0.776727 0.629838i \(-0.216879\pi\)
\(948\) −2.50717e9 + 2.03806e10i −0.0955771 + 0.776942i
\(949\) 5.34745e10i 2.03102i
\(950\) −5.33289e8 + 8.70284e9i −0.0201804 + 0.329328i
\(951\) 2.35724e10 0.888734
\(952\) 1.96612e10 + 3.65098e9i 0.738552 + 0.137145i
\(953\) 2.39320e10 0.895684 0.447842 0.894113i \(-0.352193\pi\)
0.447842 + 0.894113i \(0.352193\pi\)
\(954\) 3.04012e8 4.96123e9i 0.0113363 0.184999i
\(955\) 8.85541e9i 0.329001i
\(956\) 4.92626e10 + 6.06014e9i 1.82354 + 0.224326i
\(957\) 1.83914e10i 0.678301i
\(958\) −3.54315e10 2.17116e9i −1.30200 0.0797833i
\(959\) −4.42584e9 −0.162043
\(960\) 6.56456e9 + 2.52508e9i 0.239473 + 0.0921139i
\(961\) −2.09482e10 −0.761403
\(962\) 6.53289e10 + 4.00320e9i 2.36588 + 0.144975i
\(963\) 2.37540e9i 0.0857126i
\(964\) 1.43465e10 + 1.76487e9i 0.515795 + 0.0634516i
\(965\) 1.05014e10i 0.376187i
\(966\) 1.82864e8 2.98420e9i 0.00652694 0.106514i
\(967\) 1.73835e9 0.0618221 0.0309110 0.999522i \(-0.490159\pi\)
0.0309110 + 0.999522i \(0.490159\pi\)
\(968\) 9.76745e9 + 1.81376e9i 0.346113 + 0.0642712i
\(969\) 7.09040e9 0.250344
\(970\) −1.17199e9 + 1.91259e10i −0.0412309 + 0.672855i
\(971\) 2.13641e10i 0.748889i 0.927249 + 0.374444i \(0.122167\pi\)
−0.927249 + 0.374444i \(0.877833\pi\)
\(972\) 2.24250e8 1.82292e9i 0.00783251 0.0636701i
\(973\) 3.59003e9i 0.124940i
\(974\) −3.76691e10 2.30827e9i −1.30626 0.0800443i
\(975\) −2.28175e10 −0.788409
\(976\) −1.48048e9 + 5.92630e9i −0.0509715 + 0.204037i
\(977\) 2.02894e10 0.696045 0.348023 0.937486i \(-0.386853\pi\)
0.348023 + 0.937486i \(0.386853\pi\)
\(978\) 5.92493e9 + 3.63065e8i 0.202534 + 0.0124108i
\(979\) 6.58343e10i 2.24240i
\(980\) 7.87667e8 6.40290e9i 0.0267332 0.217313i
\(981\) 1.59938e10i 0.540892i
\(982\) −1.64920e9 + 2.69137e10i −0.0555756 + 0.906948i
\(983\) 2.41614e9 0.0811306 0.0405653 0.999177i \(-0.487084\pi\)
0.0405653 + 0.999177i \(0.487084\pi\)
\(984\) −2.24626e9 + 1.20965e10i −0.0751583 + 0.404742i
\(985\) 5.63340e9 0.187821
\(986\) 1.96178e9 3.20146e10i 0.0651749 1.06360i
\(987\) 6.12994e9i 0.202930i
\(988\) −2.10498e10 2.58949e9i −0.694384 0.0854211i
\(989\) 1.03903e10i 0.341539i
\(990\) 5.24881e9 + 3.21634e8i 0.171925 + 0.0105351i
\(991\) −9.02687e9 −0.294631 −0.147316 0.989090i \(-0.547063\pi\)
−0.147316 + 0.989090i \(0.547063\pi\)
\(992\) −1.43207e10 4.52431e9i −0.465772 0.147151i
\(993\) 2.68489e10 0.870170
\(994\) −2.34404e10 1.43637e9i −0.757030 0.0463889i
\(995\) 1.09089e10i 0.351075i
\(996\) −3.17779e10 3.90922e9i −1.01910 0.125367i
\(997\) 3.77389e9i 0.120602i −0.998180 0.0603012i \(-0.980794\pi\)
0.998180 0.0603012i \(-0.0192061\pi\)
\(998\) 2.41982e9 3.94895e10i 0.0770595 1.25755i
\(999\) 8.44770e9 0.268077
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 24.8.d.a.13.1 14
3.2 odd 2 72.8.d.d.37.14 14
4.3 odd 2 96.8.d.a.49.12 14
8.3 odd 2 96.8.d.a.49.3 14
8.5 even 2 inner 24.8.d.a.13.2 yes 14
12.11 even 2 288.8.d.d.145.5 14
24.5 odd 2 72.8.d.d.37.13 14
24.11 even 2 288.8.d.d.145.10 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
24.8.d.a.13.1 14 1.1 even 1 trivial
24.8.d.a.13.2 yes 14 8.5 even 2 inner
72.8.d.d.37.13 14 24.5 odd 2
72.8.d.d.37.14 14 3.2 odd 2
96.8.d.a.49.3 14 8.3 odd 2
96.8.d.a.49.12 14 4.3 odd 2
288.8.d.d.145.5 14 12.11 even 2
288.8.d.d.145.10 14 24.11 even 2