Properties

Label 38.3.f.a.15.2
Level $38$
Weight $3$
Character 38.15
Analytic conductor $1.035$
Analytic rank $0$
Dimension $24$
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] = [38,3,Mod(3,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([13]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.3");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 38.f (of order \(18\), degree \(6\), 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: \(1.03542500457\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 15.2
Character \(\chi\) \(=\) 38.15
Dual form 38.3.f.a.33.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.483690 + 1.32893i) q^{2} +(3.64826 - 0.643286i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(0.297798 - 0.249882i) q^{5} +(-0.909744 + 5.15941i) q^{6} +(-2.96431 + 5.13434i) q^{7} +(2.44949 - 1.41421i) q^{8} +(4.43872 - 1.61556i) q^{9} +O(q^{10})\) \(q+(-0.483690 + 1.32893i) q^{2} +(3.64826 - 0.643286i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(0.297798 - 0.249882i) q^{5} +(-0.909744 + 5.15941i) q^{6} +(-2.96431 + 5.13434i) q^{7} +(2.44949 - 1.41421i) q^{8} +(4.43872 - 1.61556i) q^{9} +(0.188033 + 0.516617i) q^{10} +(-8.13043 - 14.0823i) q^{11} +(-6.41645 - 3.70454i) q^{12} +(1.76528 + 0.311267i) q^{13} +(-5.38935 - 6.42278i) q^{14} +(0.925699 - 1.10320i) q^{15} +(0.694593 + 3.93923i) q^{16} +(-24.3446 - 8.86071i) q^{17} +6.68017i q^{18} +(18.6700 - 3.52570i) q^{19} -0.777496 q^{20} +(-7.51173 + 20.6383i) q^{21} +(22.6470 - 3.99327i) q^{22} +(32.3354 + 27.1326i) q^{23} +(8.02662 - 6.73514i) q^{24} +(-4.31496 + 24.4714i) q^{25} +(-1.26750 + 2.19538i) q^{26} +(-13.7197 + 7.92106i) q^{27} +(11.1422 - 4.05542i) q^{28} +(-9.40038 - 25.8273i) q^{29} +(1.01833 + 1.76379i) q^{30} +(17.4291 + 10.0627i) q^{31} +(-5.57091 - 0.982302i) q^{32} +(-38.7208 - 46.1457i) q^{33} +(23.5505 - 28.0663i) q^{34} +(0.400214 + 2.26973i) q^{35} +(-8.87745 - 3.23113i) q^{36} +19.4424i q^{37} +(-4.34510 + 26.5164i) q^{38} +6.64044 q^{39} +(0.376067 - 1.03323i) q^{40} +(-18.6213 + 3.28344i) q^{41} +(-23.7934 - 19.9651i) q^{42} +(37.5820 - 31.5350i) q^{43} +(-5.64734 + 32.0276i) q^{44} +(0.918143 - 1.59027i) q^{45} +(-51.6975 + 29.8476i) q^{46} +(52.0500 - 18.9446i) q^{47} +(5.06810 + 13.9245i) q^{48} +(6.92569 + 11.9956i) q^{49} +(-30.4335 - 17.5708i) q^{50} +(-94.5153 - 16.6656i) q^{51} +(-2.30441 - 2.74629i) q^{52} +(-9.03932 + 10.7726i) q^{53} +(-3.89044 - 22.0638i) q^{54} +(-5.94015 - 2.16204i) q^{55} +16.7687i q^{56} +(65.8450 - 24.8728i) q^{57} +38.8695 q^{58} +(7.58069 - 20.8278i) q^{59} +(-2.83651 + 0.500152i) q^{60} +(-10.9255 - 9.16757i) q^{61} +(-21.8028 + 18.2948i) q^{62} +(-4.86291 + 27.5790i) q^{63} +(4.00000 - 6.92820i) q^{64} +(0.603479 - 0.348419i) q^{65} +(80.0531 - 29.1369i) q^{66} +(12.7327 + 34.9828i) q^{67} +(25.9070 + 44.8722i) q^{68} +(135.422 + 78.1858i) q^{69} +(-3.20988 - 0.565989i) q^{70} +(-20.3418 - 24.2424i) q^{71} +(8.58785 - 10.2346i) q^{72} +(-12.9628 - 73.5160i) q^{73} +(-25.8376 - 9.40410i) q^{74} +92.0536i q^{75} +(-33.1367 - 18.6000i) q^{76} +96.4045 q^{77} +(-3.21191 + 8.82466i) q^{78} +(-147.140 + 25.9447i) q^{79} +(1.19119 + 0.999530i) q^{80} +(-77.5237 + 65.0501i) q^{81} +(4.64349 - 26.3345i) q^{82} +(29.0689 - 50.3489i) q^{83} +(38.0407 - 21.9628i) q^{84} +(-9.46392 + 3.44458i) q^{85} +(23.7297 + 65.1969i) q^{86} +(-50.9094 - 88.1776i) q^{87} +(-39.8308 - 22.9963i) q^{88} +(-91.8814 - 16.2012i) q^{89} +(1.66926 + 1.98934i) q^{90} +(-6.83101 + 8.14088i) q^{91} +(-14.6597 - 83.1391i) q^{92} +(70.0590 + 25.4994i) q^{93} +78.3339i q^{94} +(4.67889 - 5.71526i) q^{95} -20.9560 q^{96} +(41.6935 - 114.552i) q^{97} +(-19.2912 + 3.40156i) q^{98} +(-58.8396 - 49.3723i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9} + 30 q^{11} - 36 q^{12} - 90 q^{13} - 48 q^{14} - 114 q^{15} + 18 q^{17} - 12 q^{19} + 24 q^{20} + 90 q^{21} + 84 q^{22} + 120 q^{23} - 24 q^{24} + 252 q^{25} + 48 q^{26} + 126 q^{27} + 72 q^{28} - 210 q^{29} - 108 q^{31} - 132 q^{33} - 24 q^{34} - 66 q^{35} - 12 q^{36} + 84 q^{38} + 120 q^{39} + 54 q^{41} + 72 q^{42} + 90 q^{43} - 48 q^{44} - 144 q^{45} - 360 q^{46} - 246 q^{47} - 48 q^{48} + 54 q^{49} - 432 q^{50} - 342 q^{51} + 36 q^{52} - 174 q^{53} - 42 q^{55} - 12 q^{57} + 48 q^{58} + 228 q^{59} + 132 q^{60} + 12 q^{61} + 204 q^{62} + 174 q^{63} + 96 q^{64} + 630 q^{65} + 696 q^{66} + 72 q^{67} - 48 q^{68} + 702 q^{69} + 528 q^{70} + 432 q^{71} + 96 q^{72} - 144 q^{74} + 72 q^{76} - 144 q^{77} - 708 q^{78} - 246 q^{79} - 642 q^{81} - 384 q^{82} - 126 q^{83} - 540 q^{84} - 684 q^{85} - 12 q^{86} - 324 q^{87} - 12 q^{89} - 336 q^{90} + 372 q^{91} - 132 q^{92} - 168 q^{93} - 570 q^{95} + 72 q^{97} + 384 q^{98} - 204 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{11}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.483690 + 1.32893i −0.241845 + 0.664463i
\(3\) 3.64826 0.643286i 1.21609 0.214429i 0.471446 0.881895i \(-0.343732\pi\)
0.744640 + 0.667466i \(0.232621\pi\)
\(4\) −1.53209 1.28558i −0.383022 0.321394i
\(5\) 0.297798 0.249882i 0.0595597 0.0499765i −0.612522 0.790454i \(-0.709845\pi\)
0.672082 + 0.740477i \(0.265400\pi\)
\(6\) −0.909744 + 5.15941i −0.151624 + 0.859902i
\(7\) −2.96431 + 5.13434i −0.423473 + 0.733477i −0.996277 0.0862156i \(-0.972523\pi\)
0.572803 + 0.819693i \(0.305856\pi\)
\(8\) 2.44949 1.41421i 0.306186 0.176777i
\(9\) 4.43872 1.61556i 0.493191 0.179507i
\(10\) 0.188033 + 0.516617i 0.0188033 + 0.0516617i
\(11\) −8.13043 14.0823i −0.739130 1.28021i −0.952888 0.303324i \(-0.901904\pi\)
0.213758 0.976887i \(-0.431430\pi\)
\(12\) −6.41645 3.70454i −0.534704 0.308711i
\(13\) 1.76528 + 0.311267i 0.135791 + 0.0239436i 0.241131 0.970493i \(-0.422482\pi\)
−0.105339 + 0.994436i \(0.533593\pi\)
\(14\) −5.38935 6.42278i −0.384954 0.458770i
\(15\) 0.925699 1.10320i 0.0617132 0.0735470i
\(16\) 0.694593 + 3.93923i 0.0434120 + 0.246202i
\(17\) −24.3446 8.86071i −1.43204 0.521218i −0.494521 0.869166i \(-0.664657\pi\)
−0.937514 + 0.347947i \(0.886879\pi\)
\(18\) 6.68017i 0.371120i
\(19\) 18.6700 3.52570i 0.982632 0.185563i
\(20\) −0.777496 −0.0388748
\(21\) −7.51173 + 20.6383i −0.357701 + 0.982776i
\(22\) 22.6470 3.99327i 1.02941 0.181512i
\(23\) 32.3354 + 27.1326i 1.40589 + 1.17968i 0.958415 + 0.285379i \(0.0921196\pi\)
0.447471 + 0.894299i \(0.352325\pi\)
\(24\) 8.02662 6.73514i 0.334443 0.280631i
\(25\) −4.31496 + 24.4714i −0.172598 + 0.978855i
\(26\) −1.26750 + 2.19538i −0.0487500 + 0.0844375i
\(27\) −13.7197 + 7.92106i −0.508136 + 0.293373i
\(28\) 11.1422 4.05542i 0.397935 0.144836i
\(29\) −9.40038 25.8273i −0.324151 0.890598i −0.989560 0.144119i \(-0.953965\pi\)
0.665409 0.746479i \(-0.268257\pi\)
\(30\) 1.01833 + 1.76379i 0.0339442 + 0.0587931i
\(31\) 17.4291 + 10.0627i 0.562229 + 0.324603i 0.754040 0.656829i \(-0.228103\pi\)
−0.191811 + 0.981432i \(0.561436\pi\)
\(32\) −5.57091 0.982302i −0.174091 0.0306970i
\(33\) −38.7208 46.1457i −1.17336 1.39835i
\(34\) 23.5505 28.0663i 0.692660 0.825481i
\(35\) 0.400214 + 2.26973i 0.0114347 + 0.0648494i
\(36\) −8.87745 3.23113i −0.246596 0.0897535i
\(37\) 19.4424i 0.525471i 0.964868 + 0.262736i \(0.0846247\pi\)
−0.964868 + 0.262736i \(0.915375\pi\)
\(38\) −4.34510 + 26.5164i −0.114345 + 0.697800i
\(39\) 6.64044 0.170268
\(40\) 0.376067 1.03323i 0.00940167 0.0258309i
\(41\) −18.6213 + 3.28344i −0.454179 + 0.0800839i −0.396058 0.918226i \(-0.629622\pi\)
−0.0581209 + 0.998310i \(0.518511\pi\)
\(42\) −23.7934 19.9651i −0.566510 0.475358i
\(43\) 37.5820 31.5350i 0.874000 0.733373i −0.0909364 0.995857i \(-0.528986\pi\)
0.964936 + 0.262484i \(0.0845416\pi\)
\(44\) −5.64734 + 32.0276i −0.128349 + 0.727901i
\(45\) 0.918143 1.59027i 0.0204032 0.0353394i
\(46\) −51.6975 + 29.8476i −1.12386 + 0.648860i
\(47\) 52.0500 18.9446i 1.10745 0.403077i 0.277390 0.960757i \(-0.410531\pi\)
0.830056 + 0.557680i \(0.188308\pi\)
\(48\) 5.06810 + 13.9245i 0.105586 + 0.290094i
\(49\) 6.92569 + 11.9956i 0.141341 + 0.244809i
\(50\) −30.4335 17.5708i −0.608671 0.351416i
\(51\) −94.5153 16.6656i −1.85324 0.326776i
\(52\) −2.30441 2.74629i −0.0443157 0.0528134i
\(53\) −9.03932 + 10.7726i −0.170553 + 0.203257i −0.844550 0.535477i \(-0.820132\pi\)
0.673997 + 0.738734i \(0.264576\pi\)
\(54\) −3.89044 22.0638i −0.0720451 0.408588i
\(55\) −5.94015 2.16204i −0.108003 0.0393098i
\(56\) 16.7687i 0.299441i
\(57\) 65.8450 24.8728i 1.15517 0.436365i
\(58\) 38.8695 0.670163
\(59\) 7.58069 20.8278i 0.128486 0.353013i −0.858724 0.512439i \(-0.828742\pi\)
0.987210 + 0.159426i \(0.0509643\pi\)
\(60\) −2.83651 + 0.500152i −0.0472751 + 0.00833587i
\(61\) −10.9255 9.16757i −0.179106 0.150288i 0.548827 0.835936i \(-0.315075\pi\)
−0.727933 + 0.685648i \(0.759519\pi\)
\(62\) −21.8028 + 18.2948i −0.351659 + 0.295077i
\(63\) −4.86291 + 27.5790i −0.0771891 + 0.437761i
\(64\) 4.00000 6.92820i 0.0625000 0.108253i
\(65\) 0.603479 0.348419i 0.00928429 0.00536029i
\(66\) 80.0531 29.1369i 1.21293 0.441469i
\(67\) 12.7327 + 34.9828i 0.190040 + 0.522131i 0.997720 0.0674903i \(-0.0214992\pi\)
−0.807680 + 0.589621i \(0.799277\pi\)
\(68\) 25.9070 + 44.8722i 0.380985 + 0.659885i
\(69\) 135.422 + 78.1858i 1.96263 + 1.13313i
\(70\) −3.20988 0.565989i −0.0458554 0.00808555i
\(71\) −20.3418 24.2424i −0.286505 0.341443i 0.603526 0.797343i \(-0.293762\pi\)
−0.890031 + 0.455900i \(0.849317\pi\)
\(72\) 8.58785 10.2346i 0.119276 0.142147i
\(73\) −12.9628 73.5160i −0.177573 1.00707i −0.935132 0.354301i \(-0.884719\pi\)
0.757558 0.652767i \(-0.226392\pi\)
\(74\) −25.8376 9.40410i −0.349156 0.127082i
\(75\) 92.0536i 1.22738i
\(76\) −33.1367 18.6000i −0.436009 0.244737i
\(77\) 96.4045 1.25201
\(78\) −3.21191 + 8.82466i −0.0411784 + 0.113137i
\(79\) −147.140 + 25.9447i −1.86253 + 0.328414i −0.987741 0.156099i \(-0.950108\pi\)
−0.874785 + 0.484512i \(0.838997\pi\)
\(80\) 1.19119 + 0.999530i 0.0148899 + 0.0124941i
\(81\) −77.5237 + 65.0501i −0.957083 + 0.803088i
\(82\) 4.64349 26.3345i 0.0566279 0.321153i
\(83\) 29.0689 50.3489i 0.350228 0.606613i −0.636061 0.771639i \(-0.719437\pi\)
0.986289 + 0.165026i \(0.0527707\pi\)
\(84\) 38.0407 21.9628i 0.452866 0.261462i
\(85\) −9.46392 + 3.44458i −0.111340 + 0.0405245i
\(86\) 23.7297 + 65.1969i 0.275927 + 0.758103i
\(87\) −50.9094 88.1776i −0.585165 1.01354i
\(88\) −39.8308 22.9963i −0.452623 0.261322i
\(89\) −91.8814 16.2012i −1.03238 0.182036i −0.368304 0.929705i \(-0.620062\pi\)
−0.664071 + 0.747670i \(0.731173\pi\)
\(90\) 1.66926 + 1.98934i 0.0185473 + 0.0221038i
\(91\) −6.83101 + 8.14088i −0.0750660 + 0.0894602i
\(92\) −14.6597 83.1391i −0.159344 0.903686i
\(93\) 70.0590 + 25.4994i 0.753322 + 0.274187i
\(94\) 78.3339i 0.833339i
\(95\) 4.67889 5.71526i 0.0492515 0.0601606i
\(96\) −20.9560 −0.218292
\(97\) 41.6935 114.552i 0.429830 1.18095i −0.516086 0.856537i \(-0.672612\pi\)
0.945916 0.324411i \(-0.105166\pi\)
\(98\) −19.2912 + 3.40156i −0.196849 + 0.0347098i
\(99\) −58.8396 49.3723i −0.594339 0.498710i
\(100\) 38.0707 31.9451i 0.380707 0.319451i
\(101\) −23.4332 + 132.896i −0.232012 + 1.31580i 0.616805 + 0.787116i \(0.288427\pi\)
−0.848816 + 0.528688i \(0.822684\pi\)
\(102\) 67.8634 117.543i 0.665328 1.15238i
\(103\) −92.3597 + 53.3239i −0.896697 + 0.517708i −0.876127 0.482080i \(-0.839881\pi\)
−0.0205696 + 0.999788i \(0.506548\pi\)
\(104\) 4.76424 1.73404i 0.0458100 0.0166735i
\(105\) 2.92017 + 8.02310i 0.0278111 + 0.0764105i
\(106\) −9.94382 17.2232i −0.0938096 0.162483i
\(107\) 6.51505 + 3.76147i 0.0608883 + 0.0351539i 0.530135 0.847913i \(-0.322141\pi\)
−0.469247 + 0.883067i \(0.655475\pi\)
\(108\) 31.2029 + 5.50191i 0.288916 + 0.0509436i
\(109\) −9.26982 11.0473i −0.0850442 0.101352i 0.721844 0.692055i \(-0.243295\pi\)
−0.806889 + 0.590704i \(0.798850\pi\)
\(110\) 5.74638 6.84827i 0.0522398 0.0622570i
\(111\) 12.5070 + 70.9310i 0.112676 + 0.639018i
\(112\) −22.2843 8.11084i −0.198967 0.0724182i
\(113\) 141.490i 1.25212i −0.779774 0.626061i \(-0.784666\pi\)
0.779774 0.626061i \(-0.215334\pi\)
\(114\) 1.20560 + 99.5338i 0.0105754 + 0.873104i
\(115\) 16.4094 0.142690
\(116\) −18.8008 + 51.6547i −0.162076 + 0.445299i
\(117\) 8.33848 1.47030i 0.0712690 0.0125667i
\(118\) 24.0119 + 20.1483i 0.203490 + 0.170749i
\(119\) 117.659 98.7276i 0.988731 0.829643i
\(120\) 0.707322 4.01142i 0.00589435 0.0334285i
\(121\) −71.7077 + 124.201i −0.592626 + 1.02646i
\(122\) 17.4676 10.0849i 0.143177 0.0826631i
\(123\) −65.8232 + 23.9577i −0.535148 + 0.194778i
\(124\) −13.7666 37.8233i −0.111021 0.305027i
\(125\) 9.68933 + 16.7824i 0.0775146 + 0.134259i
\(126\) −34.2983 19.8021i −0.272208 0.157160i
\(127\) 92.1323 + 16.2454i 0.725451 + 0.127917i 0.524166 0.851616i \(-0.324377\pi\)
0.201285 + 0.979533i \(0.435488\pi\)
\(128\) 7.27231 + 8.66680i 0.0568149 + 0.0677094i
\(129\) 116.823 139.224i 0.905602 1.07926i
\(130\) 0.171126 + 0.970505i 0.00131636 + 0.00746542i
\(131\) 155.637 + 56.6473i 1.18807 + 0.432422i 0.859046 0.511899i \(-0.171058\pi\)
0.329025 + 0.944321i \(0.393280\pi\)
\(132\) 120.478i 0.912711i
\(133\) −37.2416 + 106.310i −0.280012 + 0.799320i
\(134\) −52.6482 −0.392897
\(135\) −2.10636 + 5.78718i −0.0156027 + 0.0428680i
\(136\) −72.1628 + 12.7242i −0.530609 + 0.0935606i
\(137\) 100.767 + 84.5537i 0.735526 + 0.617180i 0.931632 0.363403i \(-0.118385\pi\)
−0.196106 + 0.980583i \(0.562830\pi\)
\(138\) −169.405 + 142.148i −1.22757 + 1.03006i
\(139\) −20.5435 + 116.508i −0.147795 + 0.838188i 0.817285 + 0.576234i \(0.195478\pi\)
−0.965080 + 0.261955i \(0.915633\pi\)
\(140\) 2.30474 3.99193i 0.0164624 0.0285138i
\(141\) 177.705 102.598i 1.26032 0.727645i
\(142\) 42.0555 15.3070i 0.296166 0.107796i
\(143\) −9.96915 27.3900i −0.0697143 0.191539i
\(144\) 9.44718 + 16.3630i 0.0656054 + 0.113632i
\(145\) −9.25321 5.34235i −0.0638153 0.0368438i
\(146\) 103.967 + 18.3322i 0.712105 + 0.125563i
\(147\) 32.9833 + 39.3080i 0.224376 + 0.267401i
\(148\) 24.9947 29.7875i 0.168883 0.201267i
\(149\) −22.4518 127.331i −0.150683 0.854568i −0.962627 0.270832i \(-0.912701\pi\)
0.811943 0.583736i \(-0.198410\pi\)
\(150\) −122.332 44.5253i −0.815549 0.296836i
\(151\) 288.719i 1.91204i −0.293294 0.956022i \(-0.594751\pi\)
0.293294 0.956022i \(-0.405249\pi\)
\(152\) 40.7459 35.0395i 0.268065 0.230523i
\(153\) −122.374 −0.799830
\(154\) −46.6299 + 128.115i −0.302791 + 0.831912i
\(155\) 7.70484 1.35857i 0.0497087 0.00876498i
\(156\) −10.1737 8.53679i −0.0652163 0.0547230i
\(157\) 89.0151 74.6926i 0.566975 0.475749i −0.313665 0.949534i \(-0.601557\pi\)
0.880641 + 0.473785i \(0.157113\pi\)
\(158\) 36.6913 208.087i 0.232223 1.31700i
\(159\) −26.0479 + 45.1162i −0.163823 + 0.283750i
\(160\) −1.90447 + 1.09955i −0.0119029 + 0.00687216i
\(161\) −235.160 + 85.5913i −1.46062 + 0.531623i
\(162\) −48.9494 134.487i −0.302157 0.830169i
\(163\) −90.4066 156.589i −0.554642 0.960668i −0.997931 0.0642894i \(-0.979522\pi\)
0.443289 0.896379i \(-0.353811\pi\)
\(164\) 32.7506 + 18.9086i 0.199699 + 0.115296i
\(165\) −23.0620 4.06645i −0.139770 0.0246452i
\(166\) 52.8496 + 62.9837i 0.318371 + 0.379420i
\(167\) −134.977 + 160.860i −0.808247 + 0.963232i −0.999834 0.0182441i \(-0.994192\pi\)
0.191586 + 0.981476i \(0.438637\pi\)
\(168\) 10.7871 + 61.1765i 0.0642087 + 0.364146i
\(169\) −155.789 56.7025i −0.921827 0.335517i
\(170\) 14.2430i 0.0837821i
\(171\) 77.1750 45.8122i 0.451316 0.267907i
\(172\) −98.1196 −0.570463
\(173\) −82.3903 + 226.365i −0.476244 + 1.30847i 0.436413 + 0.899746i \(0.356249\pi\)
−0.912658 + 0.408725i \(0.865974\pi\)
\(174\) 141.806 25.0042i 0.814976 0.143702i
\(175\) −112.853 94.6953i −0.644877 0.541116i
\(176\) 49.8262 41.8091i 0.283103 0.237552i
\(177\) 14.2581 80.8616i 0.0805541 0.456845i
\(178\) 65.9722 114.267i 0.370630 0.641951i
\(179\) 7.69927 4.44517i 0.0430127 0.0248334i −0.478339 0.878175i \(-0.658761\pi\)
0.521352 + 0.853342i \(0.325428\pi\)
\(180\) −3.45109 + 1.25609i −0.0191727 + 0.00697830i
\(181\) 46.2352 + 127.030i 0.255443 + 0.701824i 0.999434 + 0.0336348i \(0.0107083\pi\)
−0.743991 + 0.668190i \(0.767069\pi\)
\(182\) −7.51454 13.0156i −0.0412887 0.0715141i
\(183\) −45.7563 26.4174i −0.250035 0.144357i
\(184\) 117.576 + 20.7319i 0.639002 + 0.112673i
\(185\) 4.85832 + 5.78992i 0.0262612 + 0.0312969i
\(186\) −67.7736 + 80.7694i −0.364374 + 0.434244i
\(187\) 73.1527 + 414.870i 0.391191 + 2.21855i
\(188\) −104.100 37.8893i −0.553723 0.201539i
\(189\) 93.9220i 0.496942i
\(190\) 5.33202 + 8.98231i 0.0280633 + 0.0472753i
\(191\) −109.638 −0.574020 −0.287010 0.957928i \(-0.592661\pi\)
−0.287010 + 0.957928i \(0.592661\pi\)
\(192\) 10.1362 27.8490i 0.0527928 0.145047i
\(193\) 311.671 54.9559i 1.61487 0.284746i 0.708020 0.706192i \(-0.249589\pi\)
0.906853 + 0.421446i \(0.138477\pi\)
\(194\) 132.064 + 110.815i 0.680744 + 0.571212i
\(195\) 1.97751 1.65933i 0.0101411 0.00850938i
\(196\) 4.81053 27.2819i 0.0245435 0.139193i
\(197\) −92.7151 + 160.587i −0.470635 + 0.815164i −0.999436 0.0335821i \(-0.989308\pi\)
0.528801 + 0.848746i \(0.322642\pi\)
\(198\) 94.0722 54.3126i 0.475112 0.274306i
\(199\) 44.3698 16.1493i 0.222964 0.0811521i −0.228123 0.973632i \(-0.573259\pi\)
0.451087 + 0.892480i \(0.351037\pi\)
\(200\) 24.0383 + 66.0446i 0.120191 + 0.330223i
\(201\) 68.9561 + 119.435i 0.343065 + 0.594206i
\(202\) −165.275 95.4215i −0.818192 0.472384i
\(203\) 160.472 + 28.2955i 0.790503 + 0.139387i
\(204\) 123.381 + 147.040i 0.604809 + 0.720783i
\(205\) −4.72492 + 5.63094i −0.0230484 + 0.0274680i
\(206\) −26.1901 148.531i −0.127136 0.721027i
\(207\) 187.362 + 68.1942i 0.905131 + 0.329441i
\(208\) 7.17007i 0.0344715i
\(209\) −201.445 234.252i −0.963853 1.12082i
\(210\) −12.0746 −0.0574979
\(211\) 83.5213 229.473i 0.395835 1.08755i −0.568458 0.822712i \(-0.692460\pi\)
0.964293 0.264837i \(-0.0853180\pi\)
\(212\) 27.6981 4.88392i 0.130651 0.0230374i
\(213\) −89.8070 75.3570i −0.421629 0.353789i
\(214\) −8.14997 + 6.83864i −0.0380840 + 0.0319563i
\(215\) 3.31180 18.7822i 0.0154037 0.0873589i
\(216\) −22.4041 + 38.8051i −0.103723 + 0.179653i
\(217\) −103.331 + 59.6579i −0.476178 + 0.274921i
\(218\) 19.1648 6.97542i 0.0879120 0.0319973i
\(219\) −94.5836 259.866i −0.431889 1.18660i
\(220\) 6.32138 + 10.9489i 0.0287335 + 0.0497679i
\(221\) −40.2171 23.2193i −0.181978 0.105065i
\(222\) −100.312 17.6876i −0.451854 0.0796740i
\(223\) 161.214 + 192.127i 0.722933 + 0.861558i 0.994912 0.100745i \(-0.0321227\pi\)
−0.271979 + 0.962303i \(0.587678\pi\)
\(224\) 21.5574 25.6911i 0.0962384 0.114693i
\(225\) 20.3821 + 115.593i 0.0905872 + 0.513745i
\(226\) 188.030 + 68.4372i 0.831989 + 0.302819i
\(227\) 0.891777i 0.00392853i 0.999998 + 0.00196427i \(0.000625246\pi\)
−0.999998 + 0.00196427i \(0.999375\pi\)
\(228\) −132.856 46.5413i −0.582703 0.204129i
\(229\) 289.709 1.26510 0.632552 0.774518i \(-0.282007\pi\)
0.632552 + 0.774518i \(0.282007\pi\)
\(230\) −7.93704 + 21.8068i −0.0345089 + 0.0948124i
\(231\) 351.708 62.0157i 1.52255 0.268466i
\(232\) −59.5515 49.9696i −0.256687 0.215386i
\(233\) −192.719 + 161.710i −0.827118 + 0.694034i −0.954627 0.297803i \(-0.903746\pi\)
0.127509 + 0.991837i \(0.459302\pi\)
\(234\) −2.07932 + 11.7924i −0.00888597 + 0.0503948i
\(235\) 10.7665 18.6480i 0.0458147 0.0793534i
\(236\) −38.3900 + 22.1645i −0.162669 + 0.0939172i
\(237\) −520.113 + 189.306i −2.19457 + 0.798758i
\(238\) 74.2912 + 204.114i 0.312148 + 0.857620i
\(239\) 104.580 + 181.137i 0.437572 + 0.757897i 0.997502 0.0706430i \(-0.0225051\pi\)
−0.559929 + 0.828540i \(0.689172\pi\)
\(240\) 4.98876 + 2.88026i 0.0207865 + 0.0120011i
\(241\) −49.6606 8.75651i −0.206061 0.0363341i 0.0696649 0.997570i \(-0.477807\pi\)
−0.275726 + 0.961236i \(0.588918\pi\)
\(242\) −130.370 155.369i −0.538720 0.642021i
\(243\) −149.332 + 177.967i −0.614537 + 0.732377i
\(244\) 4.95321 + 28.0911i 0.0203000 + 0.115127i
\(245\) 5.05996 + 1.84167i 0.0206529 + 0.00751704i
\(246\) 99.0622i 0.402692i
\(247\) 34.0553 0.412493i 0.137876 0.00167001i
\(248\) 56.9232 0.229529
\(249\) 73.6622 202.385i 0.295832 0.812792i
\(250\) −26.9892 + 4.75892i −0.107957 + 0.0190357i
\(251\) 35.2847 + 29.6073i 0.140576 + 0.117958i 0.710364 0.703834i \(-0.248530\pi\)
−0.569788 + 0.821792i \(0.692975\pi\)
\(252\) 42.9052 36.0018i 0.170259 0.142864i
\(253\) 119.189 675.956i 0.471104 2.67176i
\(254\) −66.1523 + 114.579i −0.260442 + 0.451099i
\(255\) −32.3109 + 18.6547i −0.126710 + 0.0731558i
\(256\) −15.0351 + 5.47232i −0.0587308 + 0.0213763i
\(257\) −29.1491 80.0866i −0.113421 0.311621i 0.869975 0.493096i \(-0.164135\pi\)
−0.983396 + 0.181475i \(0.941913\pi\)
\(258\) 128.512 + 222.590i 0.498110 + 0.862752i
\(259\) −99.8241 57.6335i −0.385421 0.222523i
\(260\) −1.37250 0.242009i −0.00527885 0.000930804i
\(261\) −83.4514 99.4535i −0.319737 0.381048i
\(262\) −150.560 + 179.431i −0.574657 + 0.684850i
\(263\) −13.4824 76.4625i −0.0512639 0.290732i 0.948388 0.317112i \(-0.102713\pi\)
−0.999652 + 0.0263800i \(0.991602\pi\)
\(264\) −160.106 58.2739i −0.606463 0.220734i
\(265\) 5.46684i 0.0206296i
\(266\) −123.264 100.912i −0.463399 0.379369i
\(267\) −345.629 −1.29449
\(268\) 25.4654 69.9656i 0.0950201 0.261066i
\(269\) −313.463 + 55.2719i −1.16529 + 0.205472i −0.722641 0.691224i \(-0.757072\pi\)
−0.442648 + 0.896695i \(0.645961\pi\)
\(270\) −6.67191 5.59840i −0.0247108 0.0207348i
\(271\) 85.7299 71.9360i 0.316347 0.265446i −0.470763 0.882260i \(-0.656021\pi\)
0.787109 + 0.616814i \(0.211577\pi\)
\(272\) 17.9948 102.054i 0.0661574 0.375197i
\(273\) −19.6844 + 34.0943i −0.0721039 + 0.124888i
\(274\) −161.106 + 93.0143i −0.587977 + 0.339468i
\(275\) 379.696 138.198i 1.38071 0.502538i
\(276\) −106.964 293.882i −0.387552 1.06479i
\(277\) 86.2411 + 149.374i 0.311340 + 0.539256i 0.978653 0.205521i \(-0.0658890\pi\)
−0.667313 + 0.744777i \(0.732556\pi\)
\(278\) −144.894 83.6546i −0.521202 0.300916i
\(279\) 93.6198 + 16.5077i 0.335555 + 0.0591674i
\(280\) 4.19020 + 4.99369i 0.0149650 + 0.0178346i
\(281\) −5.93324 + 7.07097i −0.0211147 + 0.0251636i −0.776498 0.630119i \(-0.783006\pi\)
0.755384 + 0.655283i \(0.227450\pi\)
\(282\) 50.3911 + 285.782i 0.178692 + 1.01341i
\(283\) 133.243 + 48.4965i 0.470824 + 0.171366i 0.566525 0.824044i \(-0.308287\pi\)
−0.0957017 + 0.995410i \(0.530510\pi\)
\(284\) 63.2925i 0.222861i
\(285\) 13.3932 23.8606i 0.0469938 0.0837213i
\(286\) 41.2213 0.144130
\(287\) 38.3411 105.341i 0.133593 0.367043i
\(288\) −26.3147 + 4.63999i −0.0913705 + 0.0161111i
\(289\) 292.760 + 245.655i 1.01301 + 0.850018i
\(290\) 11.5753 9.71280i 0.0399147 0.0334924i
\(291\) 78.4189 444.736i 0.269481 1.52830i
\(292\) −74.6501 + 129.298i −0.255651 + 0.442800i
\(293\) 362.249 209.145i 1.23634 0.713804i 0.268000 0.963419i \(-0.413637\pi\)
0.968345 + 0.249615i \(0.0803041\pi\)
\(294\) −68.1911 + 24.8195i −0.231943 + 0.0844202i
\(295\) −2.94698 8.09676i −0.00998976 0.0274466i
\(296\) 27.4958 + 47.6240i 0.0928911 + 0.160892i
\(297\) 223.094 + 128.803i 0.751157 + 0.433681i
\(298\) 180.073 + 31.7517i 0.604271 + 0.106549i
\(299\) 48.6356 + 57.9617i 0.162661 + 0.193852i
\(300\) 118.342 141.034i 0.394473 0.470114i
\(301\) 50.5069 + 286.439i 0.167797 + 0.951623i
\(302\) 383.686 + 139.650i 1.27048 + 0.462418i
\(303\) 499.914i 1.64988i
\(304\) 26.8566 + 71.0966i 0.0883440 + 0.233870i
\(305\) −5.54440 −0.0181784
\(306\) 59.1910 162.626i 0.193435 0.531457i
\(307\) −396.123 + 69.8472i −1.29030 + 0.227515i −0.776350 0.630302i \(-0.782931\pi\)
−0.513954 + 0.857818i \(0.671820\pi\)
\(308\) −147.700 123.935i −0.479547 0.402387i
\(309\) −302.649 + 253.953i −0.979448 + 0.821855i
\(310\) −1.92131 + 10.8963i −0.00619778 + 0.0351493i
\(311\) 1.92896 3.34106i 0.00620244 0.0107429i −0.862908 0.505362i \(-0.831359\pi\)
0.869110 + 0.494619i \(0.164692\pi\)
\(312\) 16.2657 9.39100i 0.0521336 0.0300994i
\(313\) 317.780 115.663i 1.01527 0.369529i 0.219817 0.975541i \(-0.429454\pi\)
0.795455 + 0.606012i \(0.207232\pi\)
\(314\) 56.2052 + 154.423i 0.178997 + 0.491792i
\(315\) 5.44333 + 9.42812i 0.0172804 + 0.0299305i
\(316\) 258.785 + 149.409i 0.818939 + 0.472815i
\(317\) 10.5173 + 1.85448i 0.0331775 + 0.00585009i 0.190212 0.981743i \(-0.439082\pi\)
−0.157035 + 0.987593i \(0.550193\pi\)
\(318\) −47.3570 56.4379i −0.148922 0.177478i
\(319\) −287.279 + 342.366i −0.900563 + 1.07325i
\(320\) −0.540043 3.06274i −0.00168763 0.00957105i
\(321\) 26.1883 + 9.53175i 0.0815834 + 0.0296939i
\(322\) 353.910i 1.09910i
\(323\) −485.754 79.5979i −1.50388 0.246433i
\(324\) 202.400 0.624691
\(325\) −15.2343 + 41.8558i −0.0468747 + 0.128787i
\(326\) 251.824 44.4033i 0.772466 0.136207i
\(327\) −40.9253 34.3404i −0.125154 0.105016i
\(328\) −40.9693 + 34.3773i −0.124906 + 0.104809i
\(329\) −57.0242 + 323.400i −0.173326 + 0.982979i
\(330\) 16.5589 28.6808i 0.0501784 0.0869115i
\(331\) −148.405 + 85.6815i −0.448353 + 0.258857i −0.707134 0.707079i \(-0.750012\pi\)
0.258782 + 0.965936i \(0.416679\pi\)
\(332\) −109.263 + 39.7686i −0.329107 + 0.119785i
\(333\) 31.4105 + 86.2996i 0.0943258 + 0.259158i
\(334\) −148.484 257.181i −0.444561 0.770003i
\(335\) 12.5334 + 7.23614i 0.0374130 + 0.0216004i
\(336\) −86.5166 15.2552i −0.257490 0.0454024i
\(337\) −3.21424 3.83059i −0.00953782 0.0113667i 0.761254 0.648453i \(-0.224584\pi\)
−0.770792 + 0.637087i \(0.780139\pi\)
\(338\) 150.707 179.605i 0.445878 0.531377i
\(339\) −91.0185 516.191i −0.268491 1.52269i
\(340\) 18.9278 + 6.88917i 0.0556701 + 0.0202623i
\(341\) 327.256i 0.959695i
\(342\) 23.5522 + 124.719i 0.0688662 + 0.364675i
\(343\) −372.622 −1.08636
\(344\) 47.4594 130.394i 0.137963 0.379052i
\(345\) 59.8656 10.5559i 0.173523 0.0305969i
\(346\) −260.972 218.981i −0.754253 0.632894i
\(347\) 32.3482 27.1434i 0.0932226 0.0782231i −0.594985 0.803737i \(-0.702842\pi\)
0.688208 + 0.725514i \(0.258398\pi\)
\(348\) −35.3613 + 200.544i −0.101613 + 0.576275i
\(349\) 68.5275 118.693i 0.196354 0.340095i −0.750990 0.660314i \(-0.770423\pi\)
0.947344 + 0.320219i \(0.103757\pi\)
\(350\) 180.429 104.171i 0.515512 0.297631i
\(351\) −26.6847 + 9.71243i −0.0760248 + 0.0276707i
\(352\) 31.4608 + 86.4379i 0.0893773 + 0.245562i
\(353\) 179.947 + 311.677i 0.509765 + 0.882938i 0.999936 + 0.0113122i \(0.00360086\pi\)
−0.490171 + 0.871626i \(0.663066\pi\)
\(354\) 100.563 + 58.0598i 0.284075 + 0.164011i
\(355\) −12.1155 2.13629i −0.0341282 0.00601773i
\(356\) 119.943 + 142.942i 0.336918 + 0.401523i
\(357\) 365.740 435.872i 1.02448 1.22093i
\(358\) 2.18325 + 12.3818i 0.00609847 + 0.0345861i
\(359\) −322.462 117.367i −0.898224 0.326927i −0.148683 0.988885i \(-0.547503\pi\)
−0.749541 + 0.661958i \(0.769726\pi\)
\(360\) 5.19380i 0.0144272i
\(361\) 336.139 131.650i 0.931133 0.364680i
\(362\) −191.177 −0.528114
\(363\) −181.711 + 499.247i −0.500581 + 1.37534i
\(364\) 20.9314 3.69077i 0.0575039 0.0101395i
\(365\) −22.2307 18.6537i −0.0609059 0.0511061i
\(366\) 57.2386 48.0289i 0.156390 0.131227i
\(367\) −31.2479 + 177.216i −0.0851441 + 0.482876i 0.912181 + 0.409787i \(0.134397\pi\)
−0.997325 + 0.0730895i \(0.976714\pi\)
\(368\) −84.4216 + 146.223i −0.229407 + 0.397344i
\(369\) −77.3503 + 44.6582i −0.209621 + 0.121025i
\(370\) −10.0443 + 3.65583i −0.0271468 + 0.00988061i
\(371\) −28.5150 78.3444i −0.0768600 0.211171i
\(372\) −74.5552 129.133i −0.200417 0.347133i
\(373\) −614.242 354.633i −1.64676 0.950757i −0.978348 0.206966i \(-0.933641\pi\)
−0.668412 0.743791i \(-0.733026\pi\)
\(374\) −586.714 103.454i −1.56875 0.276614i
\(375\) 46.1450 + 54.9935i 0.123053 + 0.146649i
\(376\) 100.704 120.014i 0.267830 0.319187i
\(377\) −8.55514 48.5186i −0.0226927 0.128697i
\(378\) 124.815 + 45.4291i 0.330199 + 0.120183i
\(379\) 36.9284i 0.0974365i 0.998813 + 0.0487183i \(0.0155136\pi\)
−0.998813 + 0.0487183i \(0.984486\pi\)
\(380\) −14.5159 + 2.74122i −0.0381996 + 0.00721373i
\(381\) 346.572 0.909639
\(382\) 53.0307 145.701i 0.138824 0.381415i
\(383\) 289.583 51.0612i 0.756090 0.133319i 0.217701 0.976015i \(-0.430144\pi\)
0.538389 + 0.842696i \(0.319033\pi\)
\(384\) 32.1065 + 26.9405i 0.0836106 + 0.0701577i
\(385\) 28.7091 24.0898i 0.0745691 0.0625709i
\(386\) −77.7194 + 440.769i −0.201346 + 1.14189i
\(387\) 115.869 200.691i 0.299404 0.518582i
\(388\) −211.143 + 121.904i −0.544184 + 0.314185i
\(389\) −29.3487 + 10.6820i −0.0754464 + 0.0274602i −0.379468 0.925205i \(-0.623893\pi\)
0.304021 + 0.952665i \(0.401671\pi\)
\(390\) 1.24862 + 3.43057i 0.00320160 + 0.00879633i
\(391\) −546.777 947.046i −1.39841 2.42211i
\(392\) 33.9288 + 19.5888i 0.0865531 + 0.0499715i
\(393\) 604.245 + 106.545i 1.53752 + 0.271106i
\(394\) −168.563 200.886i −0.427826 0.509863i
\(395\) −37.3348 + 44.4939i −0.0945185 + 0.112643i
\(396\) 26.6757 + 151.285i 0.0673629 + 0.382034i
\(397\) −383.480 139.575i −0.965945 0.351575i −0.189585 0.981864i \(-0.560714\pi\)
−0.776361 + 0.630289i \(0.782936\pi\)
\(398\) 66.7754i 0.167777i
\(399\) −67.4796 + 411.801i −0.169122 + 1.03208i
\(400\) −99.3955 −0.248489
\(401\) −85.5142 + 234.948i −0.213252 + 0.585906i −0.999487 0.0320219i \(-0.989805\pi\)
0.786235 + 0.617928i \(0.212028\pi\)
\(402\) −192.074 + 33.8679i −0.477796 + 0.0842484i
\(403\) 27.6351 + 23.1886i 0.0685735 + 0.0575400i
\(404\) 206.750 173.484i 0.511757 0.429415i
\(405\) −6.83155 + 38.7436i −0.0168680 + 0.0956633i
\(406\) −115.221 + 199.569i −0.283796 + 0.491550i
\(407\) 273.794 158.075i 0.672714 0.388391i
\(408\) −255.083 + 92.8426i −0.625203 + 0.227555i
\(409\) 226.429 + 622.110i 0.553617 + 1.52105i 0.828735 + 0.559641i \(0.189061\pi\)
−0.275118 + 0.961410i \(0.588717\pi\)
\(410\) −5.19771 9.00270i −0.0126773 0.0219578i
\(411\) 422.016 + 243.651i 1.02680 + 0.592826i
\(412\) 210.055 + 37.0384i 0.509843 + 0.0898991i
\(413\) 84.4654 + 100.662i 0.204517 + 0.243733i
\(414\) −181.250 + 216.006i −0.437802 + 0.521753i
\(415\) −3.92462 22.2576i −0.00945691 0.0536328i
\(416\) −9.52849 3.46809i −0.0229050 0.00833674i
\(417\) 438.267i 1.05100i
\(418\) 408.740 154.401i 0.977847 0.369380i
\(419\) 587.978 1.40329 0.701645 0.712527i \(-0.252449\pi\)
0.701645 + 0.712527i \(0.252449\pi\)
\(420\) 5.84034 16.0462i 0.0139056 0.0382052i
\(421\) −641.015 + 113.028i −1.52260 + 0.268476i −0.871455 0.490476i \(-0.836823\pi\)
−0.651147 + 0.758952i \(0.725712\pi\)
\(422\) 264.554 + 221.987i 0.626905 + 0.526036i
\(423\) 200.429 168.180i 0.473828 0.397589i
\(424\) −6.90690 + 39.1710i −0.0162899 + 0.0923844i
\(425\) 321.880 557.512i 0.757364 1.31179i
\(426\) 143.583 82.8975i 0.337048 0.194595i
\(427\) 79.4560 28.9196i 0.186080 0.0677274i
\(428\) −5.14599 14.1385i −0.0120233 0.0330338i
\(429\) −53.9896 93.5128i −0.125850 0.217979i
\(430\) 23.3582 + 13.4859i 0.0543215 + 0.0313625i
\(431\) −216.189 38.1199i −0.501599 0.0884453i −0.0828765 0.996560i \(-0.526411\pi\)
−0.418722 + 0.908114i \(0.637522\pi\)
\(432\) −40.7325 48.5431i −0.0942881 0.112368i
\(433\) 178.919 213.227i 0.413207 0.492441i −0.518793 0.854900i \(-0.673618\pi\)
0.932000 + 0.362459i \(0.118063\pi\)
\(434\) −29.3011 166.175i −0.0675140 0.382891i
\(435\) −37.1947 13.5378i −0.0855052 0.0311213i
\(436\) 28.8425i 0.0661526i
\(437\) 699.363 + 392.561i 1.60037 + 0.898309i
\(438\) 391.092 0.892904
\(439\) −126.632 + 347.918i −0.288455 + 0.792525i 0.707828 + 0.706385i \(0.249675\pi\)
−0.996283 + 0.0861396i \(0.972547\pi\)
\(440\) −17.6079 + 3.10475i −0.0400180 + 0.00705625i
\(441\) 50.1209 + 42.0565i 0.113653 + 0.0953661i
\(442\) 50.3094 42.2146i 0.113822 0.0955081i
\(443\) −97.2235 + 551.382i −0.219466 + 1.24465i 0.653520 + 0.756909i \(0.273292\pi\)
−0.872986 + 0.487745i \(0.837820\pi\)
\(444\) 72.0252 124.751i 0.162219 0.280971i
\(445\) −31.4105 + 18.1349i −0.0705854 + 0.0407525i
\(446\) −333.301 + 121.312i −0.747311 + 0.271999i
\(447\) −163.820 450.092i −0.366488 1.00692i
\(448\) 23.7145 + 41.0747i 0.0529342 + 0.0916847i
\(449\) −127.703 73.7296i −0.284417 0.164208i 0.351004 0.936374i \(-0.385840\pi\)
−0.635422 + 0.772165i \(0.719174\pi\)
\(450\) −163.473 28.8247i −0.363273 0.0640548i
\(451\) 197.638 + 235.536i 0.438221 + 0.522252i
\(452\) −181.896 + 216.775i −0.402425 + 0.479591i
\(453\) −185.729 1053.32i −0.409997 2.32521i
\(454\) −1.18511 0.431343i −0.00261037 0.000950095i
\(455\) 4.13129i 0.00907975i
\(456\) 126.111 154.045i 0.276559 0.337817i
\(457\) −448.874 −0.982219 −0.491110 0.871098i \(-0.663409\pi\)
−0.491110 + 0.871098i \(0.663409\pi\)
\(458\) −140.129 + 385.002i −0.305959 + 0.840615i
\(459\) 404.186 71.2689i 0.880580 0.155270i
\(460\) −25.1406 21.0955i −0.0546535 0.0458597i
\(461\) −93.2749 + 78.2670i −0.202332 + 0.169776i −0.738324 0.674447i \(-0.764382\pi\)
0.535992 + 0.844223i \(0.319938\pi\)
\(462\) −87.7034 + 497.391i −0.189834 + 1.07660i
\(463\) 309.579 536.206i 0.668636 1.15811i −0.309649 0.950851i \(-0.600212\pi\)
0.978286 0.207261i \(-0.0664551\pi\)
\(464\) 95.2104 54.9697i 0.205195 0.118469i
\(465\) 27.2353 9.91284i 0.0585705 0.0213179i
\(466\) −121.685 334.326i −0.261126 0.717438i
\(467\) 161.988 + 280.572i 0.346870 + 0.600796i 0.985692 0.168558i \(-0.0539112\pi\)
−0.638822 + 0.769355i \(0.720578\pi\)
\(468\) −14.6655 8.46711i −0.0313365 0.0180921i
\(469\) −217.357 38.3259i −0.463448 0.0817184i
\(470\) 19.5743 + 23.3277i 0.0416474 + 0.0496334i
\(471\) 276.701 329.760i 0.587476 0.700127i
\(472\) −10.8861 61.7381i −0.0230638 0.130801i
\(473\) −749.644 272.848i −1.58487 0.576846i
\(474\) 782.757i 1.65139i
\(475\) 5.71821 + 472.094i 0.0120383 + 0.993882i
\(476\) −307.186 −0.645348
\(477\) −22.7192 + 62.4204i −0.0476292 + 0.130860i
\(478\) −291.302 + 51.3645i −0.609419 + 0.107457i
\(479\) 56.2520 + 47.2011i 0.117436 + 0.0985408i 0.699615 0.714520i \(-0.253355\pi\)
−0.582178 + 0.813061i \(0.697799\pi\)
\(480\) −6.24067 + 5.23654i −0.0130014 + 0.0109095i
\(481\) −6.05179 + 34.3214i −0.0125817 + 0.0713543i
\(482\) 35.6571 61.7599i 0.0739774 0.128133i
\(483\) −802.865 + 463.534i −1.66225 + 0.959698i
\(484\) 269.533 98.1019i 0.556886 0.202690i
\(485\) −16.2083 44.5319i −0.0334191 0.0918183i
\(486\) −164.275 284.533i −0.338015 0.585458i
\(487\) −16.2303 9.37057i −0.0333271 0.0192414i 0.483244 0.875486i \(-0.339458\pi\)
−0.516571 + 0.856244i \(0.672792\pi\)
\(488\) −39.7267 7.00490i −0.0814073 0.0143543i
\(489\) −430.558 513.119i −0.880487 1.04932i
\(490\) −4.89490 + 5.83351i −0.00998959 + 0.0119051i
\(491\) −58.4551 331.515i −0.119053 0.675184i −0.984663 0.174465i \(-0.944180\pi\)
0.865610 0.500718i \(-0.166931\pi\)
\(492\) 131.646 + 47.9153i 0.267574 + 0.0973889i
\(493\) 712.050i 1.44432i
\(494\) −15.9240 + 45.4565i −0.0322349 + 0.0920172i
\(495\) −29.8596 −0.0603224
\(496\) −27.5331 + 75.6467i −0.0555104 + 0.152513i
\(497\) 184.769 32.5797i 0.371768 0.0655527i
\(498\) 233.325 + 195.783i 0.468525 + 0.393139i
\(499\) 234.470 196.743i 0.469879 0.394275i −0.376872 0.926266i \(-0.623000\pi\)
0.846750 + 0.531990i \(0.178556\pi\)
\(500\) 6.73014 38.1685i 0.0134603 0.0763370i
\(501\) −388.953 + 673.686i −0.776353 + 1.34468i
\(502\) −56.4128 + 32.5699i −0.112376 + 0.0648804i
\(503\) 466.415 169.761i 0.927267 0.337498i 0.166141 0.986102i \(-0.446869\pi\)
0.761126 + 0.648604i \(0.224647\pi\)
\(504\) 27.0909 + 74.4316i 0.0537517 + 0.147682i
\(505\) 26.2301 + 45.4318i 0.0519407 + 0.0899640i
\(506\) 840.645 + 485.347i 1.66135 + 0.959183i
\(507\) −604.833 106.648i −1.19296 0.210352i
\(508\) −120.270 143.332i −0.236752 0.282150i
\(509\) 277.084 330.215i 0.544369 0.648753i −0.421793 0.906692i \(-0.638599\pi\)
0.966161 + 0.257939i \(0.0830434\pi\)
\(510\) −9.16229 51.9619i −0.0179653 0.101886i
\(511\) 415.882 + 151.369i 0.813859 + 0.296221i
\(512\) 22.6274i 0.0441942i
\(513\) −228.219 + 196.258i −0.444872 + 0.382569i
\(514\) 120.528 0.234491
\(515\) −14.1799 + 38.9589i −0.0275337 + 0.0756483i
\(516\) −357.966 + 63.1190i −0.693732 + 0.122324i
\(517\) −689.973 578.956i −1.33457 1.11984i
\(518\) 124.875 104.782i 0.241070 0.202282i
\(519\) −154.963 + 878.840i −0.298580 + 1.69333i
\(520\) 0.985477 1.70690i 0.00189515 0.00328249i
\(521\) 15.6249 9.02106i 0.0299903 0.0173149i −0.484930 0.874553i \(-0.661155\pi\)
0.514920 + 0.857238i \(0.327822\pi\)
\(522\) 172.531 62.7961i 0.330519 0.120299i
\(523\) 43.7031 + 120.073i 0.0835624 + 0.229586i 0.974436 0.224666i \(-0.0721290\pi\)
−0.890874 + 0.454251i \(0.849907\pi\)
\(524\) −165.626 286.872i −0.316080 0.547466i
\(525\) −472.634 272.876i −0.900256 0.519763i
\(526\) 108.134 + 19.0670i 0.205579 + 0.0362490i
\(527\) −335.142 399.406i −0.635942 0.757887i
\(528\) 154.883 184.583i 0.293340 0.349589i
\(529\) 217.538 + 1233.72i 0.411226 + 2.33218i
\(530\) −7.26503 2.64425i −0.0137076 0.00498916i
\(531\) 104.696i 0.197167i
\(532\) 193.726 114.999i 0.364147 0.216163i
\(533\) −33.8939 −0.0635909
\(534\) 167.177 459.315i 0.313066 0.860141i
\(535\) 2.88010 0.507838i 0.00538336 0.000949231i
\(536\) 80.6617 + 67.6832i 0.150488 + 0.126275i
\(537\) 25.2294 21.1700i 0.0469821 0.0394226i
\(538\) 78.1663 443.303i 0.145291 0.823984i
\(539\) 112.618 195.059i 0.208938 0.361891i
\(540\) 10.6670 6.15859i 0.0197537 0.0114048i
\(541\) 640.195 233.012i 1.18335 0.430706i 0.325969 0.945380i \(-0.394309\pi\)
0.857386 + 0.514675i \(0.172087\pi\)
\(542\) 54.1309 + 148.723i 0.0998725 + 0.274397i
\(543\) 250.395 + 433.696i 0.461132 + 0.798704i
\(544\) 126.918 + 73.2760i 0.233305 + 0.134699i
\(545\) −5.52107 0.973514i −0.0101304 0.00178626i
\(546\) −35.7877 42.6501i −0.0655452 0.0781137i
\(547\) 181.686 216.525i 0.332151 0.395842i −0.573959 0.818884i \(-0.694593\pi\)
0.906110 + 0.423042i \(0.139038\pi\)
\(548\) −45.6841 259.087i −0.0833652 0.472787i
\(549\) −63.3060 23.0415i −0.115311 0.0419699i
\(550\) 571.433i 1.03897i
\(551\) −266.565 449.054i −0.483783 0.814980i
\(552\) 442.285 0.801242
\(553\) 302.959 832.373i 0.547846 1.50520i
\(554\) −240.221 + 42.3574i −0.433611 + 0.0764574i
\(555\) 21.4490 + 17.9978i 0.0386468 + 0.0324285i
\(556\) 181.255 152.091i 0.325997 0.273544i
\(557\) −23.2813 + 132.035i −0.0417977 + 0.237047i −0.998548 0.0538627i \(-0.982847\pi\)
0.956751 + 0.290909i \(0.0939578\pi\)
\(558\) −67.2204 + 116.429i −0.120467 + 0.208655i
\(559\) 76.1587 43.9703i 0.136241 0.0786588i
\(560\) −8.66300 + 3.15307i −0.0154696 + 0.00563049i
\(561\) 533.760 + 1466.49i 0.951443 + 2.61407i
\(562\) −6.52694 11.3050i −0.0116138 0.0201157i
\(563\) −65.0895 37.5795i −0.115612 0.0667486i 0.441079 0.897468i \(-0.354596\pi\)
−0.556691 + 0.830720i \(0.687929\pi\)
\(564\) −404.157 71.2637i −0.716590 0.126354i
\(565\) −35.3558 42.1354i −0.0625767 0.0745760i
\(566\) −128.897 + 153.613i −0.227733 + 0.271401i
\(567\) −104.185 590.862i −0.183748 1.04208i
\(568\) −84.1111 30.6139i −0.148083 0.0538978i
\(569\) 184.239i 0.323794i −0.986808 0.161897i \(-0.948239\pi\)
0.986808 0.161897i \(-0.0517612\pi\)
\(570\) 25.2308 + 29.3397i 0.0442645 + 0.0514732i
\(571\) 90.1138 0.157818 0.0789088 0.996882i \(-0.474856\pi\)
0.0789088 + 0.996882i \(0.474856\pi\)
\(572\) −19.9383 + 54.7800i −0.0348572 + 0.0957693i
\(573\) −399.987 + 70.5285i −0.698058 + 0.123086i
\(574\) 121.446 + 101.905i 0.211578 + 0.177535i
\(575\) −803.497 + 674.214i −1.39739 + 1.17255i
\(576\) 6.56194 37.2146i 0.0113923 0.0646087i
\(577\) 162.882 282.120i 0.282291 0.488943i −0.689657 0.724136i \(-0.742239\pi\)
0.971949 + 0.235193i \(0.0755722\pi\)
\(578\) −468.063 + 270.236i −0.809797 + 0.467537i
\(579\) 1101.70 400.987i 1.90277 0.692550i
\(580\) 7.30876 + 20.0806i 0.0126013 + 0.0346218i
\(581\) 172.339 + 298.500i 0.296625 + 0.513769i
\(582\) 553.091 + 319.327i 0.950327 + 0.548672i
\(583\) 225.197 + 39.7083i 0.386273 + 0.0681104i
\(584\) −135.720 161.744i −0.232397 0.276960i
\(585\) 2.11578 2.52149i 0.00361672 0.00431024i
\(586\) 102.722 + 582.563i 0.175293 + 0.994135i
\(587\) 835.717 + 304.176i 1.42371 + 0.518188i 0.935121 0.354327i \(-0.115290\pi\)
0.488587 + 0.872515i \(0.337512\pi\)
\(588\) 102.626i 0.174534i
\(589\) 360.879 + 126.421i 0.612699 + 0.214637i
\(590\) 12.1854 0.0206532
\(591\) −234.945 + 645.506i −0.397538 + 1.09223i
\(592\) −76.5882 + 13.5046i −0.129372 + 0.0228118i
\(593\) −267.026 224.062i −0.450297 0.377844i 0.389249 0.921133i \(-0.372735\pi\)
−0.839546 + 0.543288i \(0.817179\pi\)
\(594\) −279.078 + 234.174i −0.469828 + 0.394233i
\(595\) 10.3683 58.8018i 0.0174258 0.0988266i
\(596\) −129.295 + 223.945i −0.216938 + 0.375747i
\(597\) 151.484 87.4592i 0.253742 0.146498i
\(598\) −100.551 + 36.5977i −0.168146 + 0.0612001i
\(599\) −392.697 1078.93i −0.655588 1.80121i −0.595993 0.802990i \(-0.703241\pi\)
−0.0595953 0.998223i \(-0.518981\pi\)
\(600\) 130.183 + 225.484i 0.216972 + 0.375807i
\(601\) 197.455 + 114.000i 0.328543 + 0.189685i 0.655194 0.755460i \(-0.272587\pi\)
−0.326651 + 0.945145i \(0.605920\pi\)
\(602\) −405.085 71.4275i −0.672899 0.118650i
\(603\) 113.034 + 134.708i 0.187452 + 0.223397i
\(604\) −371.170 + 442.343i −0.614519 + 0.732356i
\(605\) 9.68131 + 54.9055i 0.0160022 + 0.0907528i
\(606\) −664.348 241.803i −1.09628 0.399015i
\(607\) 1077.82i 1.77566i 0.460174 + 0.887829i \(0.347787\pi\)
−0.460174 + 0.887829i \(0.652213\pi\)
\(608\) −107.472 + 1.30175i −0.176764 + 0.00214104i
\(609\) 603.645 0.991207
\(610\) 2.68177 7.36810i 0.00439634 0.0120789i
\(611\) 97.7798 17.2412i 0.160032 0.0282180i
\(612\) 187.488 + 157.321i 0.306353 + 0.257060i
\(613\) 664.095 557.242i 1.08335 0.909041i 0.0871583 0.996194i \(-0.472221\pi\)
0.996195 + 0.0871532i \(0.0277770\pi\)
\(614\) 98.7789 560.203i 0.160878 0.912383i
\(615\) −13.6154 + 23.5826i −0.0221389 + 0.0383457i
\(616\) 236.142 136.337i 0.383347 0.221326i
\(617\) −572.032 + 208.203i −0.927119 + 0.337444i −0.761067 0.648673i \(-0.775324\pi\)
−0.166052 + 0.986117i \(0.553102\pi\)
\(618\) −191.096 525.033i −0.309218 0.849568i
\(619\) 91.1210 + 157.826i 0.147207 + 0.254970i 0.930194 0.367068i \(-0.119638\pi\)
−0.782987 + 0.622038i \(0.786305\pi\)
\(620\) −13.5511 7.82370i −0.0218565 0.0126189i
\(621\) −658.549 116.120i −1.06047 0.186989i
\(622\) 3.50700 + 4.17948i 0.00563826 + 0.00671942i
\(623\) 355.548 423.725i 0.570702 0.680137i
\(624\) 4.61240 + 26.1582i 0.00739167 + 0.0419202i
\(625\) −576.679 209.894i −0.922686 0.335830i
\(626\) 478.251i 0.763979i
\(627\) −885.614 725.023i −1.41246 1.15634i
\(628\) −232.402 −0.370067
\(629\) 172.274 473.318i 0.273885 0.752493i
\(630\) −15.1622 + 2.67350i −0.0240669 + 0.00424365i
\(631\) 205.728 + 172.626i 0.326035 + 0.273576i 0.791082 0.611710i \(-0.209518\pi\)
−0.465047 + 0.885286i \(0.653963\pi\)
\(632\) −323.726 + 271.638i −0.512224 + 0.429807i
\(633\) 157.090 890.904i 0.248168 1.40743i
\(634\) −7.55156 + 13.0797i −0.0119110 + 0.0206304i
\(635\) 31.4963 18.1844i 0.0496004 0.0286368i
\(636\) 97.9079 35.6356i 0.153943 0.0560308i
\(637\) 8.49196 + 23.3315i 0.0133312 + 0.0366271i
\(638\) −316.025 547.372i −0.495338 0.857950i
\(639\) −129.457 74.7420i −0.202593 0.116967i
\(640\) 4.33136 + 0.763736i 0.00676776 + 0.00119334i
\(641\) −786.917 937.811i −1.22764 1.46304i −0.841196 0.540730i \(-0.818148\pi\)
−0.386443 0.922313i \(-0.626296\pi\)
\(642\) −25.3340 + 30.1919i −0.0394610 + 0.0470278i
\(643\) −73.9991 419.670i −0.115084 0.652675i −0.986709 0.162500i \(-0.948044\pi\)
0.871624 0.490174i \(-0.163067\pi\)
\(644\) 470.320 + 171.183i 0.730311 + 0.265811i
\(645\) 70.6526i 0.109539i
\(646\) 340.734 607.031i 0.527452 0.939676i
\(647\) 546.821 0.845163 0.422582 0.906325i \(-0.361124\pi\)
0.422582 + 0.906325i \(0.361124\pi\)
\(648\) −97.8988 + 268.975i −0.151078 + 0.415084i
\(649\) −354.937 + 62.5850i −0.546899 + 0.0964330i
\(650\) −48.2546 40.4904i −0.0742379 0.0622930i
\(651\) −338.599 + 284.119i −0.520122 + 0.436434i
\(652\) −62.7958 + 356.133i −0.0963126 + 0.546216i
\(653\) −485.458 + 840.838i −0.743428 + 1.28765i 0.207498 + 0.978235i \(0.433468\pi\)
−0.950926 + 0.309419i \(0.899865\pi\)
\(654\) 65.4309 37.7766i 0.100047 0.0577623i
\(655\) 60.5037 22.0215i 0.0923720 0.0336207i
\(656\) −25.8685 71.0730i −0.0394336 0.108343i
\(657\) −176.308 305.375i −0.268353 0.464802i
\(658\) −402.193 232.206i −0.611235 0.352897i
\(659\) 57.2312 + 10.0914i 0.0868456 + 0.0153132i 0.216902 0.976193i \(-0.430405\pi\)
−0.130056 + 0.991507i \(0.541516\pi\)
\(660\) 30.1053 + 35.8781i 0.0456141 + 0.0543608i
\(661\) −675.405 + 804.917i −1.02179 + 1.21773i −0.0460205 + 0.998940i \(0.514654\pi\)
−0.975773 + 0.218786i \(0.929790\pi\)
\(662\) −42.0826 238.662i −0.0635689 0.360517i
\(663\) −161.659 58.8390i −0.243829 0.0887466i
\(664\) 164.439i 0.247649i
\(665\) 15.4744 + 40.9648i 0.0232697 + 0.0616012i
\(666\) −129.879 −0.195013
\(667\) 396.798 1090.19i 0.594899 1.63447i
\(668\) 413.594 72.9279i 0.619153 0.109173i
\(669\) 711.743 + 597.223i 1.06389 + 0.892710i
\(670\) −15.6785 + 13.1559i −0.0234008 + 0.0196356i
\(671\) −40.2717 + 228.392i −0.0600175 + 0.340376i
\(672\) 62.1202 107.595i 0.0924408 0.160112i
\(673\) −561.669 + 324.280i −0.834576 + 0.481842i −0.855417 0.517940i \(-0.826699\pi\)
0.0208412 + 0.999783i \(0.493366\pi\)
\(674\) 6.64526 2.41868i 0.00985944 0.00358854i
\(675\) −134.639 369.918i −0.199466 0.548027i
\(676\) 165.787 + 287.151i 0.245247 + 0.424780i
\(677\) −291.669 168.395i −0.430826 0.248737i 0.268873 0.963176i \(-0.413349\pi\)
−0.699698 + 0.714438i \(0.746682\pi\)
\(678\) 730.005 + 128.720i 1.07670 + 0.189852i
\(679\) 464.556 + 553.637i 0.684177 + 0.815371i
\(680\) −18.3104 + 21.8215i −0.0269270 + 0.0320904i
\(681\) 0.573668 + 3.25343i 0.000842390 + 0.00477743i
\(682\) 434.899 + 158.290i 0.637682 + 0.232097i
\(683\) 914.053i 1.33829i 0.743131 + 0.669146i \(0.233340\pi\)
−0.743131 + 0.669146i \(0.766660\pi\)
\(684\) −177.134 29.0260i −0.258968 0.0424357i
\(685\) 51.1368 0.0746522
\(686\) 180.234 495.188i 0.262731 0.721848i
\(687\) 1056.93 186.366i 1.53847 0.271275i
\(688\) 150.328 + 126.140i 0.218500 + 0.183343i
\(689\) −19.3101 + 16.2031i −0.0280263 + 0.0235169i
\(690\) −14.9283 + 84.6627i −0.0216353 + 0.122700i
\(691\) −112.767 + 195.319i −0.163195 + 0.282661i −0.936013 0.351966i \(-0.885513\pi\)
0.772818 + 0.634628i \(0.218846\pi\)
\(692\) 417.239 240.893i 0.602947 0.348111i
\(693\) 427.913 155.748i 0.617479 0.224744i
\(694\) 20.4251 + 56.1174i 0.0294309 + 0.0808608i
\(695\) 22.9955 + 39.8294i 0.0330871 + 0.0573085i
\(696\) −249.404 143.993i −0.358339 0.206887i
\(697\) 482.422 + 85.0641i 0.692141 + 0.122043i
\(698\) 124.588 + 148.479i 0.178493 + 0.212720i
\(699\) −599.061 + 713.933i −0.857025 + 1.02136i
\(700\) 51.1636 + 290.163i 0.0730909 + 0.414519i
\(701\) 597.024 + 217.299i 0.851674 + 0.309984i 0.730723 0.682674i \(-0.239183\pi\)
0.120951 + 0.992658i \(0.461405\pi\)
\(702\) 40.1598i 0.0572077i
\(703\) 68.5481 + 362.991i 0.0975080 + 0.516345i
\(704\) −130.087 −0.184782
\(705\) 27.2828 74.9588i 0.0386990 0.106325i
\(706\) −501.234 + 88.3811i −0.709964 + 0.125186i
\(707\) −612.871 514.260i −0.866862 0.727383i
\(708\) −125.798 + 105.557i −0.177681 + 0.149092i
\(709\) 119.189 675.954i 0.168108 0.953390i −0.777693 0.628644i \(-0.783610\pi\)
0.945801 0.324746i \(-0.105279\pi\)
\(710\) 8.69913 15.0673i 0.0122523 0.0212216i
\(711\) −611.196 + 352.874i −0.859629 + 0.496307i
\(712\) −247.974 + 90.2553i −0.348279 + 0.126763i
\(713\) 290.549 + 798.277i 0.407502 + 1.11960i
\(714\) 402.337 + 696.868i 0.563497 + 0.976005i
\(715\) −9.81308 5.66558i −0.0137246 0.00792389i
\(716\) −17.5106 3.08758i −0.0244561 0.00431227i
\(717\) 498.057 + 593.561i 0.694640 + 0.827840i
\(718\) 311.943 371.760i 0.434462 0.517771i
\(719\) 146.800 + 832.545i 0.204173 + 1.15792i 0.898736 + 0.438490i \(0.144486\pi\)
−0.694564 + 0.719431i \(0.744402\pi\)
\(720\) 6.90218 + 2.51219i 0.00958636 + 0.00348915i
\(721\) 632.275i 0.876942i
\(722\) 12.3657 + 510.381i 0.0171271 + 0.706899i
\(723\) −186.808 −0.258379
\(724\) 92.4704 254.060i 0.127722 0.350912i
\(725\) 672.592 118.596i 0.927713 0.163581i
\(726\) −575.571 482.961i −0.792797 0.665236i
\(727\) 697.047 584.892i 0.958799 0.804528i −0.0219584 0.999759i \(-0.506990\pi\)
0.980757 + 0.195231i \(0.0625457\pi\)
\(728\) −5.21954 + 29.6015i −0.00716970 + 0.0406614i
\(729\) 25.0810 43.4415i 0.0344046 0.0595905i
\(730\) 35.5422 20.5203i 0.0486879 0.0281100i
\(731\) −1194.34 + 434.705i −1.63385 + 0.594671i
\(732\) 36.1412 + 99.2970i 0.0493732 + 0.135652i
\(733\) 99.4128 + 172.188i 0.135625 + 0.234909i 0.925836 0.377926i \(-0.123363\pi\)
−0.790211 + 0.612834i \(0.790029\pi\)
\(734\) −220.392 127.244i −0.300262 0.173356i
\(735\) 19.6448 + 3.46390i 0.0267276 + 0.00471279i
\(736\) −153.485 182.916i −0.208540 0.248528i
\(737\) 389.116 463.731i 0.527973 0.629214i
\(738\) −21.9339 124.394i −0.0297208 0.168555i
\(739\) −570.980 207.820i −0.772639 0.281218i −0.0745393 0.997218i \(-0.523749\pi\)
−0.698100 + 0.716000i \(0.745971\pi\)
\(740\) 15.1164i 0.0204276i
\(741\) 123.977 23.4122i 0.167311 0.0315954i
\(742\) 117.906 0.158903
\(743\) −470.492 + 1292.66i −0.633232 + 1.73979i 0.0387762 + 0.999248i \(0.487654\pi\)
−0.672008 + 0.740543i \(0.734568\pi\)
\(744\) 207.670 36.6179i 0.279127 0.0492176i
\(745\) −38.5038 32.3085i −0.0516829 0.0433671i
\(746\) 768.383 644.750i 1.03000 0.864275i
\(747\) 47.6872 270.447i 0.0638382 0.362045i
\(748\) 421.270 729.660i 0.563195 0.975482i
\(749\) −38.6253 + 22.3003i −0.0515692 + 0.0297735i
\(750\) −95.4022 + 34.7236i −0.127203 + 0.0462981i
\(751\) −198.529 545.453i −0.264352 0.726302i −0.998862 0.0477032i \(-0.984810\pi\)
0.734509 0.678599i \(-0.237412\pi\)
\(752\) 110.781 + 191.878i 0.147315 + 0.255157i
\(753\) 147.773 + 85.3171i 0.196246 + 0.113303i
\(754\) 68.6157 + 12.0988i 0.0910022 + 0.0160461i
\(755\) −72.1457 85.9799i −0.0955573 0.113881i
\(756\) −120.744 + 143.897i −0.159714 + 0.190340i
\(757\) 160.240 + 908.768i 0.211678 + 1.20049i 0.886579 + 0.462578i \(0.153075\pi\)
−0.674901 + 0.737909i \(0.735813\pi\)
\(758\) −49.0752 17.8619i −0.0647430 0.0235645i
\(759\) 2542.73i 3.35011i
\(760\) 3.37830 20.6164i 0.00444513 0.0271269i
\(761\) −514.855 −0.676550 −0.338275 0.941047i \(-0.609843\pi\)
−0.338275 + 0.941047i \(0.609843\pi\)
\(762\) −167.633 + 460.569i −0.219991 + 0.604422i
\(763\) 84.1994 14.8466i 0.110353 0.0194582i
\(764\) 167.975 + 140.948i 0.219863 + 0.184487i
\(765\) −36.4428 + 30.5791i −0.0476376 + 0.0399727i
\(766\) −72.2115 + 409.532i −0.0942709 + 0.534637i
\(767\) 19.8651 34.4073i 0.0258997 0.0448596i
\(768\) −51.3316 + 29.6363i −0.0668380 + 0.0385889i
\(769\) −728.967 + 265.322i −0.947941 + 0.345022i −0.769297 0.638891i \(-0.779393\pi\)
−0.178644 + 0.983914i \(0.557171\pi\)
\(770\) 18.1273 + 49.8043i 0.0235419 + 0.0646809i
\(771\) −157.862 273.425i −0.204750 0.354637i
\(772\) −548.157 316.479i −0.710048 0.409946i
\(773\) 1143.59 + 201.645i 1.47941 + 0.260860i 0.854343 0.519710i \(-0.173960\pi\)
0.625069 + 0.780570i \(0.285071\pi\)
\(774\) 210.659 + 251.054i 0.272170 + 0.324359i
\(775\) −321.454 + 383.094i −0.414779 + 0.494314i
\(776\) −59.8731 339.557i −0.0771561 0.437574i
\(777\) −401.259 146.046i −0.516421 0.187962i
\(778\) 44.1690i 0.0567725i
\(779\) −336.084 + 126.955i −0.431430 + 0.162972i
\(780\) −5.16292 −0.00661913
\(781\) −176.002 + 483.561i −0.225355 + 0.619157i
\(782\) 1523.02 268.550i 1.94760 0.343415i
\(783\) 333.550 + 279.882i 0.425990 + 0.357448i
\(784\) −42.4431 + 35.6140i −0.0541366 + 0.0454260i
\(785\) 7.84420 44.4866i 0.00999261 0.0566709i
\(786\) −433.857 + 751.462i −0.551981 + 0.956059i
\(787\) 1036.38 598.354i 1.31687 0.760297i 0.333649 0.942698i \(-0.391720\pi\)
0.983224 + 0.182401i \(0.0583868\pi\)
\(788\) 348.495 126.842i 0.442252 0.160967i
\(789\) −98.3745 270.282i −0.124683 0.342562i
\(790\) −41.0706 71.1364i −0.0519881 0.0900461i
\(791\) 726.457 + 419.420i 0.918404 + 0.530241i
\(792\) −213.950 37.7251i −0.270139 0.0476327i
\(793\) −16.4330 19.5841i −0.0207226 0.0246962i
\(794\) 370.971 442.106i 0.467218 0.556808i
\(795\) 3.51674 + 19.9444i 0.00442358 + 0.0250873i
\(796\) −88.7395 32.2986i −0.111482 0.0405761i
\(797\) 461.365i 0.578877i −0.957197 0.289438i \(-0.906532\pi\)
0.957197 0.289438i \(-0.0934685\pi\)
\(798\) −514.614 288.859i −0.644880 0.361979i
\(799\) −1435.00 −1.79599
\(800\) 48.0766 132.089i 0.0600957 0.165112i
\(801\) −434.010 + 76.5277i −0.541835 + 0.0955402i
\(802\) −270.867 227.284i −0.337739 0.283396i
\(803\) −929.881 + 780.263i −1.15801 + 0.971685i
\(804\) 47.8964 271.634i 0.0595726 0.337853i
\(805\) −48.6425 + 84.2513i −0.0604255 + 0.104660i
\(806\) −44.1828 + 25.5089i −0.0548173 + 0.0316488i
\(807\) −1108.04 + 403.292i −1.37303 + 0.499743i
\(808\) 130.544 + 358.667i 0.161565 + 0.443895i
\(809\) 105.585 + 182.878i 0.130513 + 0.226055i 0.923874 0.382696i \(-0.125004\pi\)
−0.793362 + 0.608751i \(0.791671\pi\)
\(810\) −48.1831 27.8185i −0.0594853 0.0343438i
\(811\) −112.676 19.8677i −0.138934 0.0244978i 0.103749 0.994604i \(-0.466916\pi\)
−0.242683 + 0.970106i \(0.578027\pi\)
\(812\) −209.481 249.650i −0.257982 0.307451i
\(813\) 266.489 317.590i 0.327785 0.390639i
\(814\) 77.6389 + 440.312i 0.0953795 + 0.540924i
\(815\) −66.0518 24.0409i −0.0810451 0.0294980i
\(816\) 383.893i 0.470458i
\(817\) 590.474 721.263i 0.722734 0.882818i
\(818\) −936.260 −1.14457
\(819\) −17.1688 + 47.1710i −0.0209632 + 0.0575959i
\(820\) 14.4780 2.55286i 0.0176561 0.00311325i
\(821\) 579.086 + 485.910i 0.705342 + 0.591852i 0.923288 0.384109i \(-0.125491\pi\)
−0.217946 + 0.975961i \(0.569936\pi\)
\(822\) −527.920 + 442.977i −0.642238 + 0.538902i
\(823\) 80.5969 457.088i 0.0979307 0.555392i −0.895879 0.444298i \(-0.853453\pi\)
0.993810 0.111095i \(-0.0354357\pi\)
\(824\) −150.823 + 261.233i −0.183037 + 0.317030i
\(825\) 1296.33 748.435i 1.57131 0.907194i
\(826\) −174.627 + 63.5591i −0.211413 + 0.0769481i
\(827\) −451.994 1241.84i −0.546546 1.50162i −0.838343 0.545143i \(-0.816475\pi\)
0.291797 0.956480i \(-0.405747\pi\)
\(828\) −199.387 345.348i −0.240805 0.417087i
\(829\) −882.290 509.390i −1.06428 0.614464i −0.137669 0.990478i \(-0.543961\pi\)
−0.926614 + 0.376015i \(0.877294\pi\)
\(830\) 31.4770 + 5.55025i 0.0379241 + 0.00668705i
\(831\) 410.720 + 489.477i 0.494247 + 0.589021i
\(832\) 9.21766 10.9852i 0.0110789 0.0132033i
\(833\) −62.3132 353.396i −0.0748058 0.424245i
\(834\) −582.424 211.985i −0.698351 0.254179i
\(835\) 81.6322i 0.0977631i
\(836\) 7.48388 + 617.867i 0.00895201 + 0.739076i
\(837\) −318.829 −0.380918
\(838\) −284.399 + 781.379i −0.339378 + 0.932434i
\(839\) −495.619 + 87.3910i −0.590726 + 0.104161i −0.461017 0.887391i \(-0.652515\pi\)
−0.129709 + 0.991552i \(0.541404\pi\)
\(840\) 18.4993 + 15.5228i 0.0220230 + 0.0184795i
\(841\) 65.5595 55.0110i 0.0779543 0.0654114i
\(842\) 159.846 906.533i 0.189841 1.07664i
\(843\) −17.0973 + 29.6135i −0.0202815 + 0.0351287i
\(844\) −422.967 + 244.200i −0.501145 + 0.289336i
\(845\) −60.5626 + 22.0430i −0.0716717 + 0.0260864i
\(846\) 126.553 + 347.702i 0.149590 + 0.410996i
\(847\) −425.128 736.344i −0.501922 0.869355i
\(848\) −48.7146 28.1254i −0.0574464 0.0331667i
\(849\) 517.302 + 91.2143i 0.609308 + 0.107437i
\(850\) 585.202 + 697.417i 0.688473 + 0.820491i
\(851\) −527.524 + 628.678i −0.619887 + 0.738752i
\(852\) 40.7152 + 230.907i 0.0477878 + 0.271018i
\(853\) 805.856 + 293.307i 0.944731 + 0.343854i 0.768032 0.640411i \(-0.221236\pi\)
0.176699 + 0.984265i \(0.443458\pi\)
\(854\) 119.579i 0.140022i
\(855\) 11.5349 32.9275i 0.0134912 0.0385117i
\(856\) 21.2781 0.0248576
\(857\) −166.727 + 458.079i −0.194547 + 0.534514i −0.998160 0.0606385i \(-0.980686\pi\)
0.803612 + 0.595153i \(0.202909\pi\)
\(858\) 150.386 26.5171i 0.175275 0.0309057i
\(859\) −29.8375 25.0366i −0.0347351 0.0291462i 0.625255 0.780421i \(-0.284995\pi\)
−0.659990 + 0.751274i \(0.729439\pi\)
\(860\) −29.2199 + 24.5184i −0.0339766 + 0.0285097i
\(861\) 72.1136 408.977i 0.0837557 0.475002i
\(862\) 155.227 268.861i 0.180078 0.311904i
\(863\) 107.887 62.2886i 0.125014 0.0721768i −0.436189 0.899855i \(-0.643672\pi\)
0.561203 + 0.827678i \(0.310339\pi\)
\(864\) 84.2120 30.6507i 0.0974676 0.0354753i
\(865\) 32.0291 + 87.9991i 0.0370278 + 0.101733i
\(866\) 196.822 + 340.905i 0.227277 + 0.393655i
\(867\) 1226.09 + 707.884i 1.41418 + 0.816476i
\(868\) 235.006 + 41.4380i 0.270745 + 0.0477396i
\(869\) 1561.67 + 1861.12i 1.79709 + 2.14168i
\(870\) 35.9814 42.8810i 0.0413580 0.0492885i
\(871\) 11.5878 + 65.7178i 0.0133040 + 0.0754510i
\(872\) −38.3296 13.9508i −0.0439560 0.0159987i
\(873\) 575.823i 0.659591i
\(874\) −859.959 + 739.524i −0.983935 + 0.846137i
\(875\) −114.889 −0.131302
\(876\) −189.167 + 519.733i −0.215944 + 0.593302i
\(877\) −90.8962 + 16.0275i −0.103644 + 0.0182753i −0.225230 0.974306i \(-0.572313\pi\)
0.121585 + 0.992581i \(0.461202\pi\)
\(878\) −401.107 336.569i −0.456842 0.383336i
\(879\) 1187.04 996.043i 1.35044 1.13315i
\(880\) 4.39078 24.9014i 0.00498952 0.0282970i
\(881\) 749.201 1297.65i 0.850398 1.47293i −0.0304516 0.999536i \(-0.509695\pi\)
0.880850 0.473396i \(-0.156972\pi\)
\(882\) −80.1329 + 46.2648i −0.0908536 + 0.0524544i
\(883\) 277.285 100.923i 0.314026 0.114296i −0.180199 0.983630i \(-0.557674\pi\)
0.494225 + 0.869334i \(0.335452\pi\)
\(884\) 31.7659 + 87.2762i 0.0359343 + 0.0987287i
\(885\) −15.9599 27.6433i −0.0180337 0.0312354i
\(886\) −685.720 395.900i −0.773950 0.446840i
\(887\) 42.6298 + 7.51679i 0.0480607 + 0.00847439i 0.197627 0.980277i \(-0.436677\pi\)
−0.149566 + 0.988752i \(0.547788\pi\)
\(888\) 130.947 + 156.057i 0.147463 + 0.175740i
\(889\) −356.518 + 424.882i −0.401033 + 0.477933i
\(890\) −8.90696 50.5139i −0.0100078 0.0567572i
\(891\) 1546.36 + 562.828i 1.73553 + 0.631681i
\(892\) 501.609i 0.562342i
\(893\) 904.980 537.209i 1.01342 0.601578i
\(894\) 677.377 0.757692
\(895\) 1.18206 3.24768i 0.00132073 0.00362869i
\(896\) −66.0557 + 11.6474i −0.0737229 + 0.0129993i
\(897\) 214.721 + 180.172i 0.239377 + 0.200861i
\(898\) 159.750 134.046i 0.177895 0.149272i
\(899\) 96.0524 544.740i 0.106844 0.605940i
\(900\) 117.376 203.301i 0.130418 0.225890i
\(901\) 315.512 182.161i 0.350180 0.202176i
\(902\) −408.605 + 148.720i −0.452998 + 0.164878i
\(903\) 368.524 + 1012.51i 0.408111 + 1.12127i
\(904\) −200.097 346.578i −0.221346 0.383383i
\(905\) 45.5114 + 26.2760i 0.0502888 + 0.0290343i
\(906\) 1489.62 + 262.660i 1.64417 + 0.289912i
\(907\) −480.494 572.630i −0.529762 0.631346i 0.433098 0.901347i \(-0.357420\pi\)
−0.962860 + 0.270001i \(0.912976\pi\)
\(908\) 1.14645 1.36628i 0.00126261 0.00150472i
\(909\) 110.689 + 627.747i 0.121770 + 0.690591i
\(910\) −5.49018 1.99826i −0.00603316 0.00219589i
\(911\) 384.631i 0.422207i −0.977464 0.211104i \(-0.932294\pi\)
0.977464 0.211104i \(-0.0677058\pi\)
\(912\) 143.715 + 242.102i 0.157582 + 0.265463i
\(913\) −945.371 −1.03546
\(914\) 217.116 596.521i 0.237545 0.652648i
\(915\) −20.2274 + 3.56664i −0.0221065 + 0.00389796i
\(916\) −443.860 372.443i −0.484563 0.406597i
\(917\) −752.204 + 631.174i −0.820288 + 0.688304i
\(918\) −100.789 + 571.606i −0.109792 + 0.622664i
\(919\) −438.220 + 759.020i −0.476845 + 0.825920i −0.999648 0.0265340i \(-0.991553\pi\)
0.522803 + 0.852453i \(0.324886\pi\)
\(920\) 40.1946 23.2064i 0.0436898 0.0252243i
\(921\) −1400.23 + 509.641i −1.52033 + 0.553356i
\(922\) −58.8949 161.812i −0.0638773 0.175501i
\(923\) −28.3632 49.1265i −0.0307294 0.0532249i
\(924\) −618.575 357.134i −0.669453 0.386509i
\(925\) −475.783 83.8934i −0.514360 0.0906955i
\(926\) 562.838 + 670.764i 0.607817 + 0.724368i
\(927\) −323.811 + 385.903i −0.349311 + 0.416292i
\(928\) 26.9985 + 153.116i 0.0290932 + 0.164996i
\(929\) −851.650 309.975i −0.916739 0.333666i −0.159798 0.987150i \(-0.551084\pi\)
−0.756940 + 0.653484i \(0.773307\pi\)
\(930\) 40.9884i 0.0440736i
\(931\) 171.596 + 199.541i 0.184313 + 0.214330i
\(932\) 503.152 0.539863
\(933\) 4.88808 13.4299i 0.00523910 0.0143943i
\(934\) −451.211 + 79.5607i −0.483096 + 0.0851828i
\(935\) 125.453 + 105.268i 0.134175 + 0.112586i
\(936\) 18.3457 15.3939i 0.0196001 0.0164464i
\(937\) −144.397 + 818.914i −0.154105 + 0.873974i 0.805494 + 0.592604i \(0.201900\pi\)
−0.959599 + 0.281370i \(0.909211\pi\)
\(938\) 156.066 270.314i 0.166381 0.288181i
\(939\) 1084.94 626.390i 1.15542 0.667082i
\(940\) −40.4686 + 14.7294i −0.0430517 + 0.0156696i
\(941\) −474.163 1302.75i −0.503892 1.38443i −0.887445 0.460913i \(-0.847522\pi\)
0.383553 0.923519i \(-0.374700\pi\)
\(942\) 304.389 + 527.217i 0.323130 + 0.559678i
\(943\) −691.215 399.073i −0.732996 0.423196i
\(944\) 87.3109 + 15.3953i 0.0924904 + 0.0163085i
\(945\) −23.4695 27.9698i −0.0248354 0.0295977i
\(946\) 725.190 864.248i 0.766586 0.913581i
\(947\) 2.34633 + 13.3067i 0.00247764 + 0.0140514i 0.986022 0.166618i \(-0.0532847\pi\)
−0.983544 + 0.180669i \(0.942174\pi\)
\(948\) 1040.23 + 378.611i 1.09728 + 0.399379i
\(949\) 133.811i 0.141003i
\(950\) −630.144 220.748i −0.663309 0.232366i
\(951\) 39.5627 0.0416011
\(952\) 148.582 408.227i 0.156074 0.428810i
\(953\) −555.176 + 97.8925i −0.582556 + 0.102720i −0.457157 0.889386i \(-0.651132\pi\)
−0.125399 + 0.992106i \(0.540021\pi\)
\(954\) −71.9630 60.3841i −0.0754329 0.0632957i
\(955\) −32.6500 + 27.3966i −0.0341885 + 0.0286875i
\(956\) 72.6403 411.964i 0.0759836 0.430925i
\(957\) −827.830 + 1433.84i −0.865026 + 1.49827i
\(958\) −89.9352 + 51.9241i −0.0938781 + 0.0542006i
\(959\) −732.833 + 266.729i −0.764163 + 0.278133i
\(960\) −3.94043 10.8262i −0.00410462 0.0112773i
\(961\) −277.984 481.483i −0.289266 0.501023i
\(962\) −42.6834 24.6433i −0.0443695 0.0256167i
\(963\) 34.9954 + 6.17063i 0.0363400 + 0.00640772i
\(964\) 64.8274 + 77.2582i 0.0672483 + 0.0801434i
\(965\) 79.0824 94.2468i 0.0819507 0.0976651i
\(966\) −227.665 1291.15i −0.235678 1.33660i
\(967\) 603.875 + 219.792i 0.624482 + 0.227293i 0.634828 0.772653i \(-0.281071\pi\)
−0.0103456 + 0.999946i \(0.503293\pi\)
\(968\) 405.640i 0.419050i
\(969\) −1823.36 + 22.0853i −1.88169 + 0.0227919i
\(970\) 67.0193 0.0690921
\(971\) 593.190 1629.78i 0.610906 1.67845i −0.117304 0.993096i \(-0.537425\pi\)
0.728210 0.685354i \(-0.240353\pi\)
\(972\) 457.581 80.6839i 0.470763 0.0830081i
\(973\) −537.295 450.844i −0.552205 0.463355i
\(974\) 20.3032 17.0364i 0.0208452 0.0174912i
\(975\) −28.6533 + 162.501i −0.0293880 + 0.166667i
\(976\) 28.5244 49.4057i 0.0292258 0.0506206i
\(977\) −718.452 + 414.798i −0.735365 + 0.424563i −0.820382 0.571816i \(-0.806239\pi\)
0.0850166 + 0.996380i \(0.472906\pi\)
\(978\) 890.154 323.989i 0.910178 0.331278i
\(979\) 518.885 + 1425.63i 0.530015 + 1.45621i
\(980\) −5.38470 9.32657i −0.00549459 0.00951691i
\(981\) −58.9938 34.0601i −0.0601364 0.0347198i
\(982\) 468.833 + 82.6679i 0.477427 + 0.0841832i
\(983\) −123.720 147.444i −0.125860 0.149994i 0.699435 0.714697i \(-0.253435\pi\)
−0.825294 + 0.564703i \(0.808991\pi\)
\(984\) −127.352 + 151.772i −0.129423 + 0.154240i
\(985\) 12.5175 + 70.9905i 0.0127082 + 0.0720716i
\(986\) −946.262 344.411i −0.959698 0.349301i
\(987\) 1216.53i 1.23255i
\(988\) −52.7061 43.1487i −0.0533462 0.0436728i
\(989\) 2070.86 2.09389
\(990\) 14.4428 39.6812i 0.0145887 0.0400820i
\(991\) 1012.91 178.603i 1.02211 0.180225i 0.362618 0.931938i \(-0.381883\pi\)
0.659491 + 0.751712i \(0.270772\pi\)
\(992\) −87.2114 73.1790i −0.0879147 0.0737692i
\(993\) −486.301 + 408.055i −0.489729 + 0.410931i
\(994\) −46.0746 + 261.302i −0.0463527 + 0.262879i
\(995\) 9.17782 15.8965i 0.00922394 0.0159763i
\(996\) −373.038 + 215.374i −0.374537 + 0.216239i
\(997\) −1235.15 + 449.559i −1.23887 + 0.450912i −0.876627 0.481171i \(-0.840211\pi\)
−0.362244 + 0.932083i \(0.617989\pi\)
\(998\) 148.047 + 406.755i 0.148344 + 0.407570i
\(999\) −154.005 266.744i −0.154159 0.267011i
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 38.3.f.a.15.2 24
3.2 odd 2 342.3.z.b.91.3 24
4.3 odd 2 304.3.z.c.129.2 24
19.9 even 9 722.3.b.f.721.4 24
19.10 odd 18 722.3.b.f.721.21 24
19.14 odd 18 inner 38.3.f.a.33.2 yes 24
57.14 even 18 342.3.z.b.109.3 24
76.71 even 18 304.3.z.c.33.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.3.f.a.15.2 24 1.1 even 1 trivial
38.3.f.a.33.2 yes 24 19.14 odd 18 inner
304.3.z.c.33.2 24 76.71 even 18
304.3.z.c.129.2 24 4.3 odd 2
342.3.z.b.91.3 24 3.2 odd 2
342.3.z.b.109.3 24 57.14 even 18
722.3.b.f.721.4 24 19.9 even 9
722.3.b.f.721.21 24 19.10 odd 18