Properties

Label 210.2.x.a.107.1
Level $210$
Weight $2$
Character 210.107
Analytic conductor $1.677$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,2,Mod(23,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.x (of order \(12\), degree \(4\), 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: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 107.1
Character \(\chi\) \(=\) 210.107
Dual form 210.2.x.a.53.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(-1.69017 - 0.378582i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.593376 + 2.15590i) q^{5} +(0.0717662 + 1.73056i) q^{6} +(2.64334 + 0.113038i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.71335 + 1.27974i) q^{9} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(-1.69017 - 0.378582i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.593376 + 2.15590i) q^{5} +(0.0717662 + 1.73056i) q^{6} +(2.64334 + 0.113038i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.71335 + 1.27974i) q^{9} +(1.92886 - 1.13115i) q^{10} +(-3.54004 + 2.04384i) q^{11} +(1.65302 - 0.517224i) q^{12} +(3.69641 - 3.69641i) q^{13} +(-0.574959 - 2.58252i) q^{14} +(-0.186722 - 3.86848i) q^{15} +(0.500000 - 0.866025i) q^{16} +(7.20783 + 1.93133i) q^{17} +(0.533863 - 2.95212i) q^{18} +(2.12380 + 1.22618i) q^{19} +(-1.59183 - 1.57038i) q^{20} +(-4.42489 - 1.19177i) q^{21} +(2.89043 + 2.89043i) q^{22} +(-1.06215 + 0.284603i) q^{23} +(-0.927433 - 1.46283i) q^{24} +(-4.29581 + 2.55852i) q^{25} +(-4.52715 - 2.61375i) q^{26} +(-4.10154 - 3.19020i) q^{27} +(-2.34571 + 1.22377i) q^{28} -1.48870 q^{29} +(-3.68834 + 1.18160i) q^{30} +(2.62194 + 4.54133i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(6.75703 - 2.11425i) q^{33} -7.46210i q^{34} +(1.32479 + 5.76584i) q^{35} +(-2.98970 + 0.248392i) q^{36} +(-5.34010 + 1.43087i) q^{37} +(0.634717 - 2.36880i) q^{38} +(-7.64695 + 4.84816i) q^{39} +(-1.10487 + 1.94403i) q^{40} +6.74278i q^{41} +(-0.00591784 + 4.58257i) q^{42} +(1.27352 - 1.27352i) q^{43} +(2.04384 - 3.54004i) q^{44} +(-1.14894 + 6.60908i) q^{45} +(0.549811 + 0.952300i) q^{46} +(-0.796909 - 2.97410i) q^{47} +(-1.17295 + 1.27444i) q^{48} +(6.97444 + 0.597597i) q^{49} +(3.58318 + 3.48724i) q^{50} +(-11.4513 - 5.99303i) q^{51} +(-1.35298 + 5.04938i) q^{52} +(1.47542 - 5.50634i) q^{53} +(-2.01994 + 4.78747i) q^{54} +(-6.50689 - 6.41920i) q^{55} +(1.78919 + 1.94905i) q^{56} +(-3.12538 - 2.87649i) q^{57} +(0.385303 + 1.43797i) q^{58} +(-5.09134 - 8.81846i) q^{59} +(2.09595 + 3.25684i) q^{60} +(-0.814929 + 1.41150i) q^{61} +(3.70798 - 3.70798i) q^{62} +(7.02764 + 3.68948i) q^{63} +1.00000i q^{64} +(10.1624 + 5.77572i) q^{65} +(-3.79105 - 5.97958i) q^{66} +(0.909261 - 3.39341i) q^{67} +(-7.20783 + 1.93133i) q^{68} +(1.90296 - 0.0789157i) q^{69} +(5.22649 - 2.77196i) q^{70} -5.89777i q^{71} +(1.01372 + 2.82354i) q^{72} +(-5.38514 - 1.44294i) q^{73} +(2.76424 + 4.78780i) q^{74} +(8.22926 - 2.69802i) q^{75} -2.45236 q^{76} +(-9.58854 + 5.00240i) q^{77} +(6.66214 + 6.13159i) q^{78} +(-8.18814 - 4.72742i) q^{79} +(2.16375 + 0.564071i) q^{80} +(5.72455 + 6.94475i) q^{81} +(6.51303 - 1.74516i) q^{82} +(-6.31379 - 6.31379i) q^{83} +(4.42796 - 1.18034i) q^{84} +(0.113194 + 16.6854i) q^{85} +(-1.55973 - 0.900511i) q^{86} +(2.51615 + 0.563594i) q^{87} +(-3.94840 - 1.05797i) q^{88} +(6.71062 - 11.6231i) q^{89} +(6.68125 - 0.600760i) q^{90} +(10.1887 - 9.35301i) q^{91} +(0.777550 - 0.777550i) q^{92} +(-2.71226 - 8.66824i) q^{93} +(-2.66651 + 1.53951i) q^{94} +(-1.38331 + 5.30630i) q^{95} +(1.53459 + 0.803130i) q^{96} +(-5.21514 - 5.21514i) q^{97} +(-1.22788 - 6.89147i) q^{98} +(-12.2209 + 1.01535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 0.965926i −0.183013 0.683013i
\(3\) −1.69017 0.378582i −0.975820 0.218574i
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) 0.593376 + 2.15590i 0.265366 + 0.964148i
\(6\) 0.0717662 + 1.73056i 0.0292984 + 0.706500i
\(7\) 2.64334 + 0.113038i 0.999087 + 0.0427245i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 2.71335 + 1.27974i 0.904450 + 0.426579i
\(10\) 1.92886 1.13115i 0.609960 0.357700i
\(11\) −3.54004 + 2.04384i −1.06736 + 0.616242i −0.927459 0.373924i \(-0.878012\pi\)
−0.139902 + 0.990165i \(0.544679\pi\)
\(12\) 1.65302 0.517224i 0.477186 0.149310i
\(13\) 3.69641 3.69641i 1.02520 1.02520i 0.0255244 0.999674i \(-0.491874\pi\)
0.999674 0.0255244i \(-0.00812556\pi\)
\(14\) −0.574959 2.58252i −0.153664 0.690208i
\(15\) −0.186722 3.86848i −0.0482114 0.998837i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 7.20783 + 1.93133i 1.74816 + 0.468417i 0.984231 0.176888i \(-0.0566032\pi\)
0.763925 + 0.645305i \(0.223270\pi\)
\(18\) 0.533863 2.95212i 0.125833 0.695820i
\(19\) 2.12380 + 1.22618i 0.487234 + 0.281305i 0.723426 0.690402i \(-0.242566\pi\)
−0.236192 + 0.971706i \(0.575899\pi\)
\(20\) −1.59183 1.57038i −0.355944 0.351147i
\(21\) −4.42489 1.19177i −0.965591 0.260066i
\(22\) 2.89043 + 2.89043i 0.616242 + 0.616242i
\(23\) −1.06215 + 0.284603i −0.221474 + 0.0593438i −0.367850 0.929885i \(-0.619906\pi\)
0.146376 + 0.989229i \(0.453239\pi\)
\(24\) −0.927433 1.46283i −0.189311 0.298599i
\(25\) −4.29581 + 2.55852i −0.859162 + 0.511704i
\(26\) −4.52715 2.61375i −0.887848 0.512599i
\(27\) −4.10154 3.19020i −0.789342 0.613954i
\(28\) −2.34571 + 1.22377i −0.443298 + 0.231271i
\(29\) −1.48870 −0.276444 −0.138222 0.990401i \(-0.544139\pi\)
−0.138222 + 0.990401i \(0.544139\pi\)
\(30\) −3.68834 + 1.18160i −0.673395 + 0.215729i
\(31\) 2.62194 + 4.54133i 0.470914 + 0.815647i 0.999447 0.0332663i \(-0.0105909\pi\)
−0.528533 + 0.848913i \(0.677258\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) 6.75703 2.11425i 1.17625 0.368043i
\(34\) 7.46210i 1.27974i
\(35\) 1.32479 + 5.76584i 0.223931 + 0.974605i
\(36\) −2.98970 + 0.248392i −0.498283 + 0.0413987i
\(37\) −5.34010 + 1.43087i −0.877906 + 0.235234i −0.669504 0.742809i \(-0.733493\pi\)
−0.208403 + 0.978043i \(0.566826\pi\)
\(38\) 0.634717 2.36880i 0.102965 0.384269i
\(39\) −7.64695 + 4.84816i −1.22449 + 0.776328i
\(40\) −1.10487 + 1.94403i −0.174695 + 0.307378i
\(41\) 6.74278i 1.05305i 0.850161 + 0.526523i \(0.176505\pi\)
−0.850161 + 0.526523i \(0.823495\pi\)
\(42\) −0.00591784 + 4.58257i −0.000913142 + 0.707106i
\(43\) 1.27352 1.27352i 0.194209 0.194209i −0.603303 0.797512i \(-0.706149\pi\)
0.797512 + 0.603303i \(0.206149\pi\)
\(44\) 2.04384 3.54004i 0.308121 0.533681i
\(45\) −1.14894 + 6.60908i −0.171275 + 0.985223i
\(46\) 0.549811 + 0.952300i 0.0810651 + 0.140409i
\(47\) −0.796909 2.97410i −0.116241 0.433818i 0.883136 0.469118i \(-0.155428\pi\)
−0.999377 + 0.0353000i \(0.988761\pi\)
\(48\) −1.17295 + 1.27444i −0.169300 + 0.183949i
\(49\) 6.97444 + 0.597597i 0.996349 + 0.0853710i
\(50\) 3.58318 + 3.48724i 0.506738 + 0.493170i
\(51\) −11.4513 5.99303i −1.60350 0.839193i
\(52\) −1.35298 + 5.04938i −0.187624 + 0.700224i
\(53\) 1.47542 5.50634i 0.202665 0.756355i −0.787484 0.616335i \(-0.788617\pi\)
0.990149 0.140020i \(-0.0447166\pi\)
\(54\) −2.01994 + 4.78747i −0.274879 + 0.651492i
\(55\) −6.50689 6.41920i −0.877389 0.865565i
\(56\) 1.78919 + 1.94905i 0.239091 + 0.260453i
\(57\) −3.12538 2.87649i −0.413967 0.381000i
\(58\) 0.385303 + 1.43797i 0.0505928 + 0.188815i
\(59\) −5.09134 8.81846i −0.662836 1.14807i −0.979867 0.199651i \(-0.936019\pi\)
0.317031 0.948415i \(-0.397314\pi\)
\(60\) 2.09595 + 3.25684i 0.270585 + 0.420456i
\(61\) −0.814929 + 1.41150i −0.104341 + 0.180724i −0.913469 0.406909i \(-0.866607\pi\)
0.809128 + 0.587633i \(0.199940\pi\)
\(62\) 3.70798 3.70798i 0.470914 0.470914i
\(63\) 7.02764 + 3.68948i 0.885399 + 0.464831i
\(64\) 1.00000i 0.125000i
\(65\) 10.1624 + 5.77572i 1.26050 + 0.716390i
\(66\) −3.79105 5.97958i −0.466646 0.736036i
\(67\) 0.909261 3.39341i 0.111084 0.414571i −0.887880 0.460075i \(-0.847823\pi\)
0.998964 + 0.0455037i \(0.0144893\pi\)
\(68\) −7.20783 + 1.93133i −0.874078 + 0.234208i
\(69\) 1.90296 0.0789157i 0.229090 0.00950033i
\(70\) 5.22649 2.77196i 0.624685 0.331313i
\(71\) 5.89777i 0.699937i −0.936761 0.349969i \(-0.886192\pi\)
0.936761 0.349969i \(-0.113808\pi\)
\(72\) 1.01372 + 2.82354i 0.119468 + 0.332757i
\(73\) −5.38514 1.44294i −0.630283 0.168884i −0.0704850 0.997513i \(-0.522455\pi\)
−0.559798 + 0.828629i \(0.689121\pi\)
\(74\) 2.76424 + 4.78780i 0.321336 + 0.556570i
\(75\) 8.22926 2.69802i 0.950233 0.311540i
\(76\) −2.45236 −0.281305
\(77\) −9.58854 + 5.00240i −1.09272 + 0.570076i
\(78\) 6.66214 + 6.13159i 0.754339 + 0.694266i
\(79\) −8.18814 4.72742i −0.921238 0.531877i −0.0372080 0.999308i \(-0.511846\pi\)
−0.884030 + 0.467431i \(0.845180\pi\)
\(80\) 2.16375 + 0.564071i 0.241915 + 0.0630651i
\(81\) 5.72455 + 6.94475i 0.636061 + 0.771638i
\(82\) 6.51303 1.74516i 0.719243 0.192721i
\(83\) −6.31379 6.31379i −0.693029 0.693029i 0.269868 0.962897i \(-0.413020\pi\)
−0.962897 + 0.269868i \(0.913020\pi\)
\(84\) 4.42796 1.18034i 0.483130 0.128786i
\(85\) 0.113194 + 16.6854i 0.0122776 + 1.80978i
\(86\) −1.55973 0.900511i −0.168190 0.0971046i
\(87\) 2.51615 + 0.563594i 0.269760 + 0.0604236i
\(88\) −3.94840 1.05797i −0.420901 0.112780i
\(89\) 6.71062 11.6231i 0.711325 1.23205i −0.253035 0.967457i \(-0.581429\pi\)
0.964360 0.264594i \(-0.0852378\pi\)
\(90\) 6.68125 0.600760i 0.704265 0.0633257i
\(91\) 10.1887 9.35301i 1.06806 0.980461i
\(92\) 0.777550 0.777550i 0.0810651 0.0810651i
\(93\) −2.71226 8.66824i −0.281248 0.898854i
\(94\) −2.66651 + 1.53951i −0.275029 + 0.158788i
\(95\) −1.38331 + 5.30630i −0.141924 + 0.544414i
\(96\) 1.53459 + 0.803130i 0.156624 + 0.0819691i
\(97\) −5.21514 5.21514i −0.529518 0.529518i 0.390911 0.920429i \(-0.372160\pi\)
−0.920429 + 0.390911i \(0.872160\pi\)
\(98\) −1.22788 6.89147i −0.124035 0.696143i
\(99\) −12.2209 + 1.01535i −1.22825 + 0.102046i
\(100\) 2.44102 4.36365i 0.244102 0.436365i
\(101\) −2.56058 + 1.47835i −0.254787 + 0.147101i −0.621954 0.783054i \(-0.713661\pi\)
0.367167 + 0.930155i \(0.380328\pi\)
\(102\) −2.82501 + 12.6122i −0.279718 + 1.24880i
\(103\) 2.68295 + 10.0129i 0.264359 + 0.986601i 0.962642 + 0.270779i \(0.0872813\pi\)
−0.698283 + 0.715822i \(0.746052\pi\)
\(104\) 5.22751 0.512599
\(105\) −0.0562816 10.2468i −0.00549252 0.999985i
\(106\) −5.70059 −0.553690
\(107\) 0.329519 + 1.22978i 0.0318558 + 0.118887i 0.980023 0.198885i \(-0.0637320\pi\)
−0.948167 + 0.317772i \(0.897065\pi\)
\(108\) 5.14714 + 0.712021i 0.495284 + 0.0685143i
\(109\) 2.57800 1.48841i 0.246927 0.142564i −0.371429 0.928461i \(-0.621132\pi\)
0.618356 + 0.785898i \(0.287799\pi\)
\(110\) −4.51637 + 7.94659i −0.430619 + 0.757677i
\(111\) 9.56737 0.396758i 0.908095 0.0376586i
\(112\) 1.41956 2.23268i 0.134136 0.210968i
\(113\) −2.76230 2.76230i −0.259856 0.259856i 0.565140 0.824995i \(-0.308822\pi\)
−0.824995 + 0.565140i \(0.808822\pi\)
\(114\) −1.96956 + 3.76338i −0.184467 + 0.352473i
\(115\) −1.24383 2.12102i −0.115988 0.197786i
\(116\) 1.28925 0.744349i 0.119704 0.0691110i
\(117\) 14.7601 5.29923i 1.36457 0.489914i
\(118\) −7.20025 + 7.20025i −0.662836 + 0.662836i
\(119\) 18.8344 + 5.91992i 1.72655 + 0.542678i
\(120\) 2.60340 2.86746i 0.237656 0.261762i
\(121\) 2.85458 4.94428i 0.259507 0.449480i
\(122\) 1.57432 + 0.421838i 0.142532 + 0.0381914i
\(123\) 2.55269 11.3964i 0.230169 1.02758i
\(124\) −4.54133 2.62194i −0.407823 0.235457i
\(125\) −8.06494 7.74317i −0.721350 0.692570i
\(126\) 1.74488 7.74309i 0.155446 0.689809i
\(127\) 5.50671 + 5.50671i 0.488642 + 0.488642i 0.907877 0.419236i \(-0.137702\pi\)
−0.419236 + 0.907877i \(0.637702\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) −2.63459 + 1.67033i −0.231963 + 0.147064i
\(130\) 2.94869 11.3110i 0.258617 0.992043i
\(131\) 12.5406 + 7.24030i 1.09567 + 0.632588i 0.935082 0.354433i \(-0.115326\pi\)
0.160593 + 0.987021i \(0.448659\pi\)
\(132\) −4.79464 + 5.20951i −0.417320 + 0.453429i
\(133\) 5.47532 + 3.48127i 0.474771 + 0.301865i
\(134\) −3.51312 −0.303487
\(135\) 4.44399 10.7355i 0.382478 0.923965i
\(136\) 3.73105 + 6.46236i 0.319935 + 0.554143i
\(137\) −11.5861 3.10449i −0.989868 0.265234i −0.272673 0.962107i \(-0.587908\pi\)
−0.717195 + 0.696872i \(0.754574\pi\)
\(138\) −0.568750 1.81770i −0.0484152 0.154733i
\(139\) 7.25394i 0.615271i 0.951504 + 0.307636i \(0.0995378\pi\)
−0.951504 + 0.307636i \(0.900462\pi\)
\(140\) −4.03022 4.33097i −0.340616 0.366034i
\(141\) 0.220970 + 5.32844i 0.0186090 + 0.448735i
\(142\) −5.69681 + 1.52646i −0.478066 + 0.128097i
\(143\) −5.53055 + 20.6403i −0.462488 + 1.72603i
\(144\) 2.46496 1.70996i 0.205413 0.142497i
\(145\) −0.883357 3.20948i −0.0733588 0.266533i
\(146\) 5.57511i 0.461399i
\(147\) −11.5618 3.65044i −0.953598 0.301083i
\(148\) 3.90922 3.90922i 0.321336 0.321336i
\(149\) −5.71976 + 9.90691i −0.468581 + 0.811606i −0.999355 0.0359074i \(-0.988568\pi\)
0.530774 + 0.847513i \(0.321901\pi\)
\(150\) −4.73597 7.25056i −0.386691 0.592005i
\(151\) −6.75854 11.7061i −0.550002 0.952632i −0.998274 0.0587343i \(-0.981294\pi\)
0.448271 0.893897i \(-0.352040\pi\)
\(152\) 0.634717 + 2.36880i 0.0514824 + 0.192135i
\(153\) 17.0858 + 14.4645i 1.38130 + 1.16939i
\(154\) 7.31365 + 7.96710i 0.589350 + 0.642008i
\(155\) −8.23486 + 8.34735i −0.661440 + 0.670475i
\(156\) 4.19837 8.02211i 0.336139 0.642283i
\(157\) 2.57312 9.60302i 0.205358 0.766405i −0.783983 0.620783i \(-0.786815\pi\)
0.989340 0.145622i \(-0.0465184\pi\)
\(158\) −2.44710 + 9.13268i −0.194680 + 0.726557i
\(159\) −4.57831 + 8.74809i −0.363084 + 0.693769i
\(160\) −0.0151692 2.23602i −0.00119923 0.176773i
\(161\) −2.83980 + 0.632237i −0.223807 + 0.0498272i
\(162\) 5.22649 7.32693i 0.410632 0.575658i
\(163\) 3.00701 + 11.2223i 0.235527 + 0.879000i 0.977910 + 0.209024i \(0.0670288\pi\)
−0.742383 + 0.669976i \(0.766305\pi\)
\(164\) −3.37139 5.83942i −0.263261 0.455982i
\(165\) 8.56756 + 13.3129i 0.666984 + 1.03641i
\(166\) −4.46453 + 7.73279i −0.346514 + 0.600181i
\(167\) 15.6944 15.6944i 1.21447 1.21447i 0.244931 0.969541i \(-0.421235\pi\)
0.969541 0.244931i \(-0.0787652\pi\)
\(168\) −2.28616 3.97158i −0.176381 0.306414i
\(169\) 14.3268i 1.10206i
\(170\) 16.0875 4.42783i 1.23386 0.339599i
\(171\) 4.19344 + 6.04496i 0.320681 + 0.462270i
\(172\) −0.466139 + 1.73965i −0.0355428 + 0.132647i
\(173\) −1.05488 + 0.282653i −0.0802007 + 0.0214897i −0.298696 0.954348i \(-0.596552\pi\)
0.218496 + 0.975838i \(0.429885\pi\)
\(174\) −0.106838 2.57629i −0.00809938 0.195308i
\(175\) −11.6445 + 6.27743i −0.880240 + 0.474529i
\(176\) 4.08768i 0.308121i
\(177\) 5.26673 + 16.8322i 0.395871 + 1.26519i
\(178\) −12.9639 3.47367i −0.971688 0.260363i
\(179\) 2.65439 + 4.59754i 0.198399 + 0.343637i 0.948009 0.318242i \(-0.103093\pi\)
−0.749611 + 0.661879i \(0.769759\pi\)
\(180\) −2.30952 6.29810i −0.172142 0.469433i
\(181\) −13.7484 −1.02191 −0.510957 0.859607i \(-0.670709\pi\)
−0.510957 + 0.859607i \(0.670709\pi\)
\(182\) −11.6713 7.42077i −0.865137 0.550064i
\(183\) 1.91174 2.07716i 0.141320 0.153548i
\(184\) −0.952300 0.549811i −0.0702045 0.0405326i
\(185\) −6.25351 10.6637i −0.459767 0.784008i
\(186\) −7.67089 + 4.86334i −0.562457 + 0.356598i
\(187\) −29.4633 + 7.89468i −2.15457 + 0.577316i
\(188\) 2.17720 + 2.17720i 0.158788 + 0.158788i
\(189\) −10.4811 8.89639i −0.762390 0.647117i
\(190\) 5.48351 0.0372003i 0.397816 0.00269880i
\(191\) −1.45963 0.842720i −0.105615 0.0609771i 0.446262 0.894902i \(-0.352755\pi\)
−0.551877 + 0.833925i \(0.686088\pi\)
\(192\) 0.378582 1.69017i 0.0273218 0.121978i
\(193\) −3.28843 0.881131i −0.236706 0.0634252i 0.138516 0.990360i \(-0.455767\pi\)
−0.375222 + 0.926935i \(0.622433\pi\)
\(194\) −3.68766 + 6.38722i −0.264759 + 0.458576i
\(195\) −14.9897 13.6093i −1.07343 0.974580i
\(196\) −6.33884 + 2.96969i −0.452775 + 0.212121i
\(197\) 11.9821 11.9821i 0.853688 0.853688i −0.136897 0.990585i \(-0.543713\pi\)
0.990585 + 0.136897i \(0.0437130\pi\)
\(198\) 4.14377 + 11.5417i 0.294485 + 0.820236i
\(199\) −3.65684 + 2.11128i −0.259226 + 0.149664i −0.623982 0.781439i \(-0.714486\pi\)
0.364755 + 0.931103i \(0.381153\pi\)
\(200\) −4.84674 1.22845i −0.342716 0.0868646i
\(201\) −2.82149 + 5.39121i −0.199013 + 0.380267i
\(202\) 2.09070 + 2.09070i 0.147101 + 0.147101i
\(203\) −3.93513 0.168280i −0.276192 0.0118109i
\(204\) 12.9136 0.535527i 0.904135 0.0374944i
\(205\) −14.5368 + 4.00100i −1.01529 + 0.279442i
\(206\) 8.97733 5.18306i 0.625480 0.361121i
\(207\) −3.24621 0.587047i −0.225627 0.0408026i
\(208\) −1.35298 5.04938i −0.0938122 0.350112i
\(209\) −10.0245 −0.693407
\(210\) −9.88308 + 2.70643i −0.681997 + 0.186761i
\(211\) −1.74688 −0.120260 −0.0601302 0.998191i \(-0.519152\pi\)
−0.0601302 + 0.998191i \(0.519152\pi\)
\(212\) 1.47542 + 5.50634i 0.101332 + 0.378177i
\(213\) −2.23279 + 9.96824i −0.152988 + 0.683013i
\(214\) 1.10259 0.636581i 0.0753715 0.0435158i
\(215\) 3.50125 + 1.98990i 0.238783 + 0.135710i
\(216\) −0.644418 5.15604i −0.0438471 0.350824i
\(217\) 6.41732 + 12.3006i 0.435636 + 0.835021i
\(218\) −2.10493 2.10493i −0.142564 0.142564i
\(219\) 8.55554 + 4.47754i 0.578130 + 0.302564i
\(220\) 8.84474 + 2.30575i 0.596312 + 0.155453i
\(221\) 33.7821 19.5041i 2.27243 1.31199i
\(222\) −2.85946 9.13869i −0.191914 0.613348i
\(223\) 5.26364 5.26364i 0.352480 0.352480i −0.508552 0.861031i \(-0.669819\pi\)
0.861031 + 0.508552i \(0.169819\pi\)
\(224\) −2.52401 0.793332i −0.168642 0.0530067i
\(225\) −14.9303 + 1.44466i −0.995351 + 0.0963106i
\(226\) −1.95324 + 3.38312i −0.129928 + 0.225042i
\(227\) −6.84424 1.83391i −0.454268 0.121721i 0.0244277 0.999702i \(-0.492224\pi\)
−0.478696 + 0.877981i \(0.658890\pi\)
\(228\) 4.14490 + 0.928418i 0.274503 + 0.0614860i
\(229\) −2.52452 1.45753i −0.166825 0.0963164i 0.414263 0.910157i \(-0.364039\pi\)
−0.581088 + 0.813841i \(0.697373\pi\)
\(230\) −1.72682 + 1.75041i −0.113863 + 0.115419i
\(231\) 18.1001 4.82486i 1.19090 0.317453i
\(232\) −1.05267 1.05267i −0.0691110 0.0691110i
\(233\) −26.8253 + 7.18782i −1.75738 + 0.470890i −0.986177 0.165694i \(-0.947014\pi\)
−0.771207 + 0.636584i \(0.780347\pi\)
\(234\) −8.93885 12.8856i −0.584351 0.842358i
\(235\) 5.93901 3.48282i 0.387418 0.227194i
\(236\) 8.81846 + 5.09134i 0.574033 + 0.331418i
\(237\) 12.0496 + 11.0900i 0.782708 + 0.720375i
\(238\) 0.843503 19.7248i 0.0546762 1.27857i
\(239\) 6.40772 0.414481 0.207240 0.978290i \(-0.433552\pi\)
0.207240 + 0.978290i \(0.433552\pi\)
\(240\) −3.44356 1.77253i −0.222281 0.114417i
\(241\) 6.89013 + 11.9341i 0.443832 + 0.768740i 0.997970 0.0636847i \(-0.0202852\pi\)
−0.554138 + 0.832425i \(0.686952\pi\)
\(242\) −5.51463 1.47764i −0.354494 0.0949863i
\(243\) −7.04631 13.9050i −0.452021 0.892007i
\(244\) 1.62986i 0.104341i
\(245\) 2.85011 + 15.3908i 0.182087 + 0.983282i
\(246\) −11.6688 + 0.483904i −0.743976 + 0.0308526i
\(247\) 12.3829 3.31799i 0.787905 0.211119i
\(248\) −1.35721 + 5.06519i −0.0861832 + 0.321640i
\(249\) 8.28110 + 13.0617i 0.524793 + 0.827750i
\(250\) −5.39197 + 9.79422i −0.341018 + 0.619441i
\(251\) 15.7442i 0.993767i 0.867817 + 0.496884i \(0.165522\pi\)
−0.867817 + 0.496884i \(0.834478\pi\)
\(252\) −7.93086 + 0.318633i −0.499597 + 0.0200720i
\(253\) 3.17838 3.17838i 0.199823 0.199823i
\(254\) 3.89384 6.74432i 0.244321 0.423176i
\(255\) 6.12546 28.2440i 0.383591 1.76871i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.65924 24.8526i −0.415392 1.55026i −0.784049 0.620699i \(-0.786849\pi\)
0.368656 0.929566i \(-0.379818\pi\)
\(258\) 2.29529 + 2.11250i 0.142899 + 0.131519i
\(259\) −14.2774 + 3.17865i −0.887155 + 0.197511i
\(260\) −11.6888 + 0.0792971i −0.724908 + 0.00491780i
\(261\) −4.03936 1.90514i −0.250030 0.117925i
\(262\) 3.74786 13.9872i 0.231543 0.864131i
\(263\) −0.236555 + 0.882836i −0.0145866 + 0.0544380i −0.972836 0.231497i \(-0.925638\pi\)
0.958249 + 0.285935i \(0.0923042\pi\)
\(264\) 6.27294 + 3.28294i 0.386073 + 0.202051i
\(265\) 12.7466 0.0864734i 0.783018 0.00531202i
\(266\) 1.94553 6.18978i 0.119288 0.379520i
\(267\) −15.7424 + 17.1046i −0.963420 + 1.04678i
\(268\) 0.909261 + 3.39341i 0.0555420 + 0.207285i
\(269\) 4.05903 + 7.03044i 0.247483 + 0.428654i 0.962827 0.270119i \(-0.0870631\pi\)
−0.715344 + 0.698773i \(0.753730\pi\)
\(270\) −11.5199 1.51401i −0.701078 0.0921399i
\(271\) −0.143382 + 0.248344i −0.00870982 + 0.0150858i −0.870347 0.492438i \(-0.836106\pi\)
0.861638 + 0.507524i \(0.169439\pi\)
\(272\) 5.27650 5.27650i 0.319935 0.319935i
\(273\) −20.7615 + 11.9509i −1.25654 + 0.723303i
\(274\) 11.9948i 0.724634i
\(275\) 9.97812 17.8372i 0.601704 1.07562i
\(276\) −1.60856 + 1.01982i −0.0968238 + 0.0613862i
\(277\) 8.33301 31.0992i 0.500682 1.86857i 0.00514027 0.999987i \(-0.498364\pi\)
0.495542 0.868584i \(-0.334970\pi\)
\(278\) 7.00677 1.87746i 0.420238 0.112602i
\(279\) 1.30254 + 15.6776i 0.0779808 + 0.938594i
\(280\) −3.14030 + 5.01384i −0.187669 + 0.299634i
\(281\) 6.43714i 0.384007i −0.981394 0.192004i \(-0.938501\pi\)
0.981394 0.192004i \(-0.0614986\pi\)
\(282\) 5.08969 1.59254i 0.303086 0.0948345i
\(283\) 1.89667 + 0.508211i 0.112745 + 0.0302100i 0.314751 0.949174i \(-0.398079\pi\)
−0.202005 + 0.979384i \(0.564746\pi\)
\(284\) 2.94889 + 5.10762i 0.174984 + 0.303082i
\(285\) 4.34689 8.44485i 0.257487 0.500230i
\(286\) 21.3684 1.26354
\(287\) −0.762193 + 17.8234i −0.0449908 + 1.05208i
\(288\) −2.28968 1.93840i −0.134920 0.114221i
\(289\) 33.5003 + 19.3414i 1.97061 + 1.13773i
\(290\) −2.87149 + 1.68393i −0.168620 + 0.0988839i
\(291\) 6.84012 + 10.7888i 0.400975 + 0.632453i
\(292\) 5.38514 1.44294i 0.315142 0.0844419i
\(293\) −1.37301 1.37301i −0.0802121 0.0802121i 0.665862 0.746075i \(-0.268064\pi\)
−0.746075 + 0.665862i \(0.768064\pi\)
\(294\) −0.533649 + 12.1126i −0.0311231 + 0.706422i
\(295\) 15.9906 16.2091i 0.931011 0.943730i
\(296\) −4.78780 2.76424i −0.278285 0.160668i
\(297\) 21.0399 + 2.91052i 1.22086 + 0.168885i
\(298\) 11.0497 + 2.96076i 0.640093 + 0.171512i
\(299\) −2.87414 + 4.97815i −0.166216 + 0.287894i
\(300\) −5.77774 + 6.45118i −0.333578 + 0.372459i
\(301\) 3.51028 3.22237i 0.202329 0.185734i
\(302\) −9.55802 + 9.55802i −0.550002 + 0.550002i
\(303\) 4.88749 1.52928i 0.280779 0.0878546i
\(304\) 2.12380 1.22618i 0.121809 0.0703262i
\(305\) −3.52661 0.919356i −0.201933 0.0526422i
\(306\) 9.54951 20.2473i 0.545909 1.15746i
\(307\) 10.0236 + 10.0236i 0.572077 + 0.572077i 0.932708 0.360631i \(-0.117439\pi\)
−0.360631 + 0.932708i \(0.617439\pi\)
\(308\) 5.80272 9.12648i 0.330641 0.520029i
\(309\) −0.743938 17.9392i −0.0423212 1.02053i
\(310\) 10.1943 + 5.79381i 0.578995 + 0.329066i
\(311\) −3.26860 + 1.88713i −0.185345 + 0.107009i −0.589802 0.807548i \(-0.700794\pi\)
0.404456 + 0.914557i \(0.367461\pi\)
\(312\) −8.83538 1.97904i −0.500205 0.112041i
\(313\) −7.00492 26.1427i −0.395941 1.47767i −0.820171 0.572119i \(-0.806122\pi\)
0.424229 0.905555i \(-0.360545\pi\)
\(314\) −9.94178 −0.561047
\(315\) −3.78413 + 17.3401i −0.213211 + 0.977006i
\(316\) 9.45485 0.531877
\(317\) 5.50111 + 20.5304i 0.308973 + 1.15310i 0.929471 + 0.368895i \(0.120264\pi\)
−0.620498 + 0.784208i \(0.713069\pi\)
\(318\) 9.63496 + 2.15814i 0.540302 + 0.121022i
\(319\) 5.27005 3.04266i 0.295066 0.170356i
\(320\) −2.15590 + 0.593376i −0.120518 + 0.0331707i
\(321\) −0.0913700 2.20329i −0.00509978 0.122976i
\(322\) 1.34569 + 2.57940i 0.0749922 + 0.143744i
\(323\) 12.9399 + 12.9399i 0.719993 + 0.719993i
\(324\) −8.42998 3.15205i −0.468332 0.175114i
\(325\) −6.42173 + 25.3364i −0.356214 + 1.40541i
\(326\) 10.0617 5.80910i 0.557264 0.321736i
\(327\) −4.92074 + 1.53968i −0.272117 + 0.0851444i
\(328\) −4.76787 + 4.76787i −0.263261 + 0.263261i
\(329\) −1.77031 7.95164i −0.0976003 0.438388i
\(330\) 10.6419 11.7213i 0.585815 0.645235i
\(331\) 2.05157 3.55342i 0.112764 0.195313i −0.804120 0.594468i \(-0.797363\pi\)
0.916884 + 0.399154i \(0.130696\pi\)
\(332\) 8.62480 + 2.31101i 0.473348 + 0.126833i
\(333\) −16.3207 2.95145i −0.894369 0.161738i
\(334\) −19.2217 11.0976i −1.05176 0.607236i
\(335\) 7.85539 0.0532912i 0.429186 0.00291161i
\(336\) −3.24455 + 3.23618i −0.177005 + 0.176548i
\(337\) 11.5744 + 11.5744i 0.630498 + 0.630498i 0.948193 0.317695i \(-0.102909\pi\)
−0.317695 + 0.948193i \(0.602909\pi\)
\(338\) −13.8387 + 3.70806i −0.752724 + 0.201692i
\(339\) 3.62301 + 5.71452i 0.196775 + 0.310370i
\(340\) −8.44071 14.3934i −0.457762 0.780589i
\(341\) −18.5635 10.7177i −1.00527 0.580393i
\(342\) 4.75364 5.61511i 0.257048 0.303630i
\(343\) 18.3682 + 2.36803i 0.991792 + 0.127862i
\(344\) 1.80102 0.0971046
\(345\) 1.29931 + 4.05577i 0.0699524 + 0.218356i
\(346\) 0.546044 + 0.945776i 0.0293555 + 0.0508452i
\(347\) −30.2063 8.09375i −1.62156 0.434495i −0.670099 0.742272i \(-0.733748\pi\)
−0.951459 + 0.307776i \(0.900415\pi\)
\(348\) −2.46085 + 0.769989i −0.131915 + 0.0412758i
\(349\) 26.4465i 1.41565i 0.706387 + 0.707826i \(0.250324\pi\)
−0.706387 + 0.707826i \(0.749676\pi\)
\(350\) 9.07735 + 9.62298i 0.485205 + 0.514370i
\(351\) −26.9532 + 3.36870i −1.43866 + 0.179808i
\(352\) 3.94840 1.05797i 0.210450 0.0563900i
\(353\) 5.15317 19.2319i 0.274276 1.02361i −0.682049 0.731306i \(-0.738911\pi\)
0.956325 0.292305i \(-0.0944223\pi\)
\(354\) 14.8955 9.44376i 0.791688 0.501930i
\(355\) 12.7150 3.49960i 0.674843 0.185739i
\(356\) 13.4212i 0.711325i
\(357\) −29.5922 17.1360i −1.56618 0.906935i
\(358\) 3.75388 3.75388i 0.198399 0.198399i
\(359\) 14.1219 24.4599i 0.745327 1.29094i −0.204715 0.978822i \(-0.565627\pi\)
0.950042 0.312122i \(-0.101040\pi\)
\(360\) −5.48575 + 3.86090i −0.289124 + 0.203487i
\(361\) −6.49297 11.2462i −0.341735 0.591903i
\(362\) 3.55836 + 13.2800i 0.187023 + 0.697980i
\(363\) −6.69655 + 7.27599i −0.351478 + 0.381890i
\(364\) −4.14715 + 13.1943i −0.217370 + 0.691568i
\(365\) −0.0845700 12.4660i −0.00442660 0.652502i
\(366\) −2.50117 1.30899i −0.130738 0.0684219i
\(367\) −5.67214 + 21.1687i −0.296084 + 1.10500i 0.644269 + 0.764799i \(0.277162\pi\)
−0.940353 + 0.340200i \(0.889505\pi\)
\(368\) −0.284603 + 1.06215i −0.0148360 + 0.0553685i
\(369\) −8.62898 + 18.2955i −0.449207 + 0.952428i
\(370\) −8.68178 + 8.80038i −0.451344 + 0.457510i
\(371\) 4.52246 14.3883i 0.234794 0.747005i
\(372\) 6.68300 + 6.15079i 0.346497 + 0.318903i
\(373\) −1.05918 3.95292i −0.0548423 0.204674i 0.933068 0.359700i \(-0.117121\pi\)
−0.987911 + 0.155025i \(0.950454\pi\)
\(374\) 15.2513 + 26.4161i 0.788628 + 1.36594i
\(375\) 10.6997 + 16.1405i 0.552530 + 0.833493i
\(376\) 1.53951 2.66651i 0.0793942 0.137515i
\(377\) −5.50283 + 5.50283i −0.283410 + 0.283410i
\(378\) −5.88054 + 12.4266i −0.302462 + 0.639153i
\(379\) 12.0806i 0.620537i −0.950649 0.310269i \(-0.899581\pi\)
0.950649 0.310269i \(-0.100419\pi\)
\(380\) −1.45517 5.28704i −0.0746487 0.271219i
\(381\) −7.22254 11.3920i −0.370022 0.583631i
\(382\) −0.436224 + 1.62801i −0.0223192 + 0.0832962i
\(383\) 31.3832 8.40909i 1.60360 0.429684i 0.657476 0.753476i \(-0.271624\pi\)
0.946129 + 0.323791i \(0.104958\pi\)
\(384\) −1.73056 + 0.0717662i −0.0883124 + 0.00366231i
\(385\) −16.4743 17.7036i −0.839607 0.902261i
\(386\) 3.40443i 0.173281i
\(387\) 5.08526 1.82573i 0.258498 0.0928072i
\(388\) 7.12402 + 1.90888i 0.361667 + 0.0969085i
\(389\) 0.0153183 + 0.0265320i 0.000776666 + 0.00134523i 0.866413 0.499327i \(-0.166419\pi\)
−0.865637 + 0.500672i \(0.833086\pi\)
\(390\) −9.26594 + 18.0013i −0.469199 + 0.911529i
\(391\) −8.20548 −0.414969
\(392\) 4.50911 + 5.35424i 0.227745 + 0.270430i
\(393\) −18.4546 16.9850i −0.930914 0.856779i
\(394\) −14.6750 8.47261i −0.739316 0.426844i
\(395\) 5.33321 20.4580i 0.268343 1.02935i
\(396\) 10.0760 6.98979i 0.506337 0.351250i
\(397\) −22.1678 + 5.93984i −1.11257 + 0.298112i −0.767873 0.640603i \(-0.778685\pi\)
−0.344696 + 0.938714i \(0.612018\pi\)
\(398\) 2.98580 + 2.98580i 0.149664 + 0.149664i
\(399\) −7.93628 7.95680i −0.397311 0.398338i
\(400\) 0.0678372 + 4.99954i 0.00339186 + 0.249977i
\(401\) −14.5458 8.39801i −0.726382 0.419377i 0.0907151 0.995877i \(-0.471085\pi\)
−0.817097 + 0.576500i \(0.804418\pi\)
\(402\) 5.93776 + 1.33000i 0.296149 + 0.0663345i
\(403\) 26.4783 + 7.09485i 1.31898 + 0.353420i
\(404\) 1.47835 2.56058i 0.0735507 0.127393i
\(405\) −11.5754 + 16.4624i −0.575185 + 0.818024i
\(406\) 0.855940 + 3.84459i 0.0424796 + 0.190804i
\(407\) 15.9797 15.9797i 0.792083 0.792083i
\(408\) −3.85957 12.3350i −0.191077 0.610674i
\(409\) 24.6188 14.2137i 1.21732 0.702822i 0.252979 0.967472i \(-0.418590\pi\)
0.964345 + 0.264650i \(0.0852563\pi\)
\(410\) 7.62706 + 13.0059i 0.376674 + 0.642315i
\(411\) 18.4072 + 9.63341i 0.907960 + 0.475181i
\(412\) −7.32996 7.32996i −0.361121 0.361121i
\(413\) −12.4613 23.8857i −0.613181 1.17534i
\(414\) 0.273137 + 3.28754i 0.0134240 + 0.161574i
\(415\) 9.86545 17.3584i 0.484276 0.852088i
\(416\) −4.52715 + 2.61375i −0.221962 + 0.128150i
\(417\) 2.74621 12.2604i 0.134483 0.600394i
\(418\) 2.59452 + 9.68289i 0.126902 + 0.473606i
\(419\) −20.1095 −0.982415 −0.491207 0.871043i \(-0.663444\pi\)
−0.491207 + 0.871043i \(0.663444\pi\)
\(420\) 5.17214 + 8.84585i 0.252375 + 0.431633i
\(421\) 0.466628 0.0227420 0.0113710 0.999935i \(-0.496380\pi\)
0.0113710 + 0.999935i \(0.496380\pi\)
\(422\) 0.452127 + 1.68736i 0.0220092 + 0.0821394i
\(423\) 1.64377 9.08962i 0.0799230 0.441953i
\(424\) 4.93685 2.85029i 0.239755 0.138422i
\(425\) −35.9048 + 10.1447i −1.74164 + 0.492092i
\(426\) 10.2065 0.423261i 0.494505 0.0205071i
\(427\) −2.31368 + 3.63895i −0.111967 + 0.176101i
\(428\) −0.900261 0.900261i −0.0435158 0.0435158i
\(429\) 17.1616 32.7918i 0.828570 1.58321i
\(430\) 1.01591 3.89697i 0.0489913 0.187928i
\(431\) −12.1781 + 7.03102i −0.586598 + 0.338672i −0.763751 0.645511i \(-0.776645\pi\)
0.177153 + 0.984183i \(0.443311\pi\)
\(432\) −4.81356 + 1.95694i −0.231593 + 0.0941533i
\(433\) −7.91330 + 7.91330i −0.380289 + 0.380289i −0.871206 0.490917i \(-0.836662\pi\)
0.490917 + 0.871206i \(0.336662\pi\)
\(434\) 10.2206 9.38229i 0.490603 0.450364i
\(435\) 0.277972 + 5.75900i 0.0133277 + 0.276123i
\(436\) −1.48841 + 2.57800i −0.0712818 + 0.123464i
\(437\) −2.60478 0.697948i −0.124603 0.0333874i
\(438\) 2.11064 9.42289i 0.100850 0.450243i
\(439\) −1.69708 0.979808i −0.0809971 0.0467637i 0.458954 0.888460i \(-0.348224\pi\)
−0.539952 + 0.841696i \(0.681557\pi\)
\(440\) −0.0620069 9.14013i −0.00295606 0.435739i
\(441\) 18.1594 + 10.5469i 0.864731 + 0.502235i
\(442\) −27.5829 27.5829i −1.31199 1.31199i
\(443\) −24.7782 + 6.63929i −1.17725 + 0.315442i −0.793834 0.608135i \(-0.791918\pi\)
−0.383413 + 0.923577i \(0.625251\pi\)
\(444\) −8.08721 + 5.12729i −0.383802 + 0.243330i
\(445\) 29.0403 + 7.57054i 1.37664 + 0.358878i
\(446\) −6.44662 3.72196i −0.305256 0.176240i
\(447\) 13.4179 14.5790i 0.634647 0.689562i
\(448\) −0.113038 + 2.64334i −0.00534056 + 0.124886i
\(449\) 4.51616 0.213131 0.106565 0.994306i \(-0.466015\pi\)
0.106565 + 0.994306i \(0.466015\pi\)
\(450\) 5.25967 + 14.0476i 0.247943 + 0.662212i
\(451\) −13.7812 23.8697i −0.648930 1.12398i
\(452\) 3.77338 + 1.01107i 0.177485 + 0.0475569i
\(453\) 6.99135 + 22.3440i 0.328482 + 1.04981i
\(454\) 7.08568i 0.332547i
\(455\) 26.2099 + 16.4159i 1.22874 + 0.769590i
\(456\) −0.175997 4.24396i −0.00824179 0.198742i
\(457\) −27.9253 + 7.48257i −1.30629 + 0.350020i −0.843826 0.536617i \(-0.819702\pi\)
−0.462466 + 0.886637i \(0.653035\pi\)
\(458\) −0.754474 + 2.81574i −0.0352543 + 0.131571i
\(459\) −23.4019 30.9158i −1.09231 1.44303i
\(460\) 2.13770 + 1.21494i 0.0996707 + 0.0566469i
\(461\) 28.5763i 1.33093i 0.746428 + 0.665466i \(0.231767\pi\)
−0.746428 + 0.665466i \(0.768233\pi\)
\(462\) −9.34510 16.2346i −0.434774 0.755301i
\(463\) −26.2518 + 26.2518i −1.22002 + 1.22002i −0.252401 + 0.967623i \(0.581220\pi\)
−0.967623 + 0.252401i \(0.918780\pi\)
\(464\) −0.744349 + 1.28925i −0.0345555 + 0.0598519i
\(465\) 17.0785 10.9909i 0.791995 0.509690i
\(466\) 13.8858 + 24.0509i 0.643247 + 1.11414i
\(467\) 8.06394 + 30.0950i 0.373154 + 1.39263i 0.856023 + 0.516938i \(0.172928\pi\)
−0.482868 + 0.875693i \(0.660405\pi\)
\(468\) −10.1330 + 11.9693i −0.468397 + 0.553281i
\(469\) 2.78707 8.86714i 0.128695 0.409446i
\(470\) −4.90127 4.83522i −0.226079 0.223032i
\(471\) −7.98455 + 15.2566i −0.367908 + 0.702987i
\(472\) 2.63547 9.83572i 0.121307 0.452726i
\(473\) −1.90543 + 7.11116i −0.0876117 + 0.326971i
\(474\) 7.59348 14.5094i 0.348780 0.666437i
\(475\) −12.2607 + 0.166361i −0.562558 + 0.00763317i
\(476\) −19.2710 + 4.29040i −0.883286 + 0.196650i
\(477\) 11.0500 13.0525i 0.505945 0.597633i
\(478\) −1.65844 6.18938i −0.0758552 0.283096i
\(479\) 3.35100 + 5.80410i 0.153111 + 0.265196i 0.932370 0.361506i \(-0.117737\pi\)
−0.779258 + 0.626703i \(0.784404\pi\)
\(480\) −0.820877 + 3.78499i −0.0374677 + 0.172760i
\(481\) −14.4501 + 25.0283i −0.658867 + 1.14119i
\(482\) 9.74412 9.74412i 0.443832 0.443832i
\(483\) 5.03909 + 0.00650738i 0.229287 + 0.000296096i
\(484\) 5.70916i 0.259507i
\(485\) 8.14879 14.3379i 0.370017 0.651049i
\(486\) −11.6075 + 10.4051i −0.526527 + 0.471985i
\(487\) −1.79725 + 6.70741i −0.0814409 + 0.303942i −0.994616 0.103625i \(-0.966956\pi\)
0.913176 + 0.407567i \(0.133623\pi\)
\(488\) −1.57432 + 0.421838i −0.0712662 + 0.0190957i
\(489\) −0.833794 20.1060i −0.0377055 0.909226i
\(490\) 14.1287 6.73643i 0.638270 0.304321i
\(491\) 18.8686i 0.851527i 0.904835 + 0.425763i \(0.139994\pi\)
−0.904835 + 0.425763i \(0.860006\pi\)
\(492\) 3.48753 + 11.1460i 0.157230 + 0.502499i
\(493\) −10.7303 2.87517i −0.483267 0.129491i
\(494\) −6.40986 11.1022i −0.288393 0.499512i
\(495\) −9.44061 25.7447i −0.424324 1.15714i
\(496\) 5.24387 0.235457
\(497\) 0.666675 15.5898i 0.0299045 0.699298i
\(498\) 10.4733 11.3795i 0.469320 0.509929i
\(499\) −33.7931 19.5105i −1.51279 0.873408i −0.999888 0.0149599i \(-0.995238\pi\)
−0.512900 0.858449i \(-0.671429\pi\)
\(500\) 10.8560 + 2.67331i 0.485496 + 0.119554i
\(501\) −32.4679 + 20.5846i −1.45056 + 0.919653i
\(502\) 15.2078 4.07491i 0.678756 0.181872i
\(503\) 23.7568 + 23.7568i 1.05926 + 1.05926i 0.998130 + 0.0611349i \(0.0194720\pi\)
0.0611349 + 0.998130i \(0.480528\pi\)
\(504\) 2.36043 + 7.57815i 0.105142 + 0.337558i
\(505\) −4.70656 4.64313i −0.209439 0.206617i
\(506\) −3.89270 2.24745i −0.173052 0.0999114i
\(507\) −5.42388 + 24.2148i −0.240883 + 1.07542i
\(508\) −7.52231 2.01560i −0.333749 0.0894277i
\(509\) 9.24940 16.0204i 0.409972 0.710093i −0.584914 0.811095i \(-0.698872\pi\)
0.994886 + 0.101002i \(0.0322050\pi\)
\(510\) −28.8670 + 1.39334i −1.27825 + 0.0616979i
\(511\) −14.0716 4.42291i −0.622492 0.195658i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −4.79912 11.8046i −0.211886 0.521185i
\(514\) −22.2823 + 12.8647i −0.982829 + 0.567436i
\(515\) −19.9948 + 11.7256i −0.881078 + 0.516691i
\(516\) 1.44646 2.76384i 0.0636767 0.121671i
\(517\) 8.89969 + 8.89969i 0.391408 + 0.391408i
\(518\) 6.76560 + 12.9682i 0.297263 + 0.569791i
\(519\) 1.88993 0.0783751i 0.0829586 0.00344028i
\(520\) 3.10188 + 11.2700i 0.136026 + 0.494222i
\(521\) −25.4519 + 14.6946i −1.11507 + 0.643784i −0.940137 0.340797i \(-0.889303\pi\)
−0.174929 + 0.984581i \(0.555970\pi\)
\(522\) −0.794760 + 4.39481i −0.0347857 + 0.192356i
\(523\) 5.14665 + 19.2076i 0.225047 + 0.839888i 0.982386 + 0.186865i \(0.0598327\pi\)
−0.757338 + 0.653023i \(0.773501\pi\)
\(524\) −14.4806 −0.632588
\(525\) 22.0577 6.20154i 0.962676 0.270657i
\(526\) 0.913979 0.0398514
\(527\) 10.1277 + 37.7970i 0.441168 + 1.64646i
\(528\) 1.54752 6.90888i 0.0673473 0.300671i
\(529\) −18.8714 + 10.8954i −0.820496 + 0.473714i
\(530\) −3.38259 12.2899i −0.146930 0.533839i
\(531\) −2.52930 30.4432i −0.109762 1.32112i
\(532\) −6.48241 0.277211i −0.281048 0.0120186i
\(533\) 24.9241 + 24.9241i 1.07958 + 1.07958i
\(534\) 20.5962 + 10.7790i 0.891284 + 0.466453i
\(535\) −2.45575 + 1.44013i −0.106172 + 0.0622623i
\(536\) 3.04245 1.75656i 0.131414 0.0758718i
\(537\) −2.74583 8.77554i −0.118491 0.378692i
\(538\) 5.74033 5.74033i 0.247483 0.247483i
\(539\) −25.9112 + 12.1391i −1.11607 + 0.522870i
\(540\) 1.51914 + 11.5192i 0.0653734 + 0.495708i
\(541\) 8.30525 14.3851i 0.357071 0.618465i −0.630399 0.776271i \(-0.717109\pi\)
0.987470 + 0.157806i \(0.0504422\pi\)
\(542\) 0.276992 + 0.0742198i 0.0118978 + 0.00318801i
\(543\) 23.2372 + 5.20491i 0.997204 + 0.223364i
\(544\) −6.46236 3.73105i −0.277072 0.159967i
\(545\) 4.73858 + 4.67472i 0.202978 + 0.200243i
\(546\) 16.9172 + 16.9609i 0.723988 + 0.725860i
\(547\) 3.70807 + 3.70807i 0.158545 + 0.158545i 0.781922 0.623376i \(-0.214240\pi\)
−0.623376 + 0.781922i \(0.714240\pi\)
\(548\) 11.5861 3.10449i 0.494934 0.132617i
\(549\) −4.01753 + 2.78700i −0.171464 + 0.118946i
\(550\) −19.8120 5.02152i −0.844785 0.214118i
\(551\) −3.16170 1.82541i −0.134693 0.0777651i
\(552\) 1.40140 + 1.28980i 0.0596476 + 0.0548974i
\(553\) −21.1096 13.4217i −0.897672 0.570751i
\(554\) −32.1963 −1.36789
\(555\) 6.53242 + 20.3909i 0.277286 + 0.865545i
\(556\) −3.62697 6.28210i −0.153818 0.266420i
\(557\) 36.4006 + 9.75350i 1.54234 + 0.413269i 0.927022 0.375008i \(-0.122360\pi\)
0.615320 + 0.788277i \(0.289027\pi\)
\(558\) 14.8063 5.31582i 0.626800 0.225036i
\(559\) 9.41486i 0.398206i
\(560\) 5.65576 + 1.73562i 0.239000 + 0.0733432i
\(561\) 52.7868 2.18906i 2.22866 0.0924223i
\(562\) −6.21780 + 1.66605i −0.262282 + 0.0702782i
\(563\) 9.51495 35.5103i 0.401007 1.49658i −0.410295 0.911953i \(-0.634574\pi\)
0.811302 0.584627i \(-0.198759\pi\)
\(564\) −2.85558 4.50408i −0.120242 0.189656i
\(565\) 4.31617 7.59433i 0.181582 0.319496i
\(566\) 1.96358i 0.0825353i
\(567\) 14.3469 + 19.0044i 0.602513 + 0.798109i
\(568\) 4.17036 4.17036i 0.174984 0.174984i
\(569\) −9.38493 + 16.2552i −0.393437 + 0.681452i −0.992900 0.118950i \(-0.962047\pi\)
0.599464 + 0.800402i \(0.295381\pi\)
\(570\) −9.28216 2.01308i −0.388787 0.0843188i
\(571\) −16.9888 29.4255i −0.710960 1.23142i −0.964497 0.264093i \(-0.914928\pi\)
0.253538 0.967326i \(-0.418406\pi\)
\(572\) −5.53055 20.6403i −0.231244 0.863014i
\(573\) 2.14799 + 1.97693i 0.0897336 + 0.0825875i
\(574\) 17.4134 3.87682i 0.726821 0.161815i
\(575\) 3.83464 3.94014i 0.159916 0.164315i
\(576\) −1.27974 + 2.71335i −0.0533223 + 0.113056i
\(577\) 5.97184 22.2872i 0.248611 0.927829i −0.722923 0.690929i \(-0.757202\pi\)
0.971534 0.236900i \(-0.0761315\pi\)
\(578\) 10.0119 37.3648i 0.416439 1.55417i
\(579\) 5.22442 + 2.73420i 0.217119 + 0.113629i
\(580\) 2.36975 + 2.33781i 0.0983986 + 0.0970725i
\(581\) −15.9758 17.4032i −0.662787 0.722005i
\(582\) 8.65087 9.39941i 0.358590 0.389618i
\(583\) 6.03105 + 22.5082i 0.249781 + 0.932194i
\(584\) −2.78756 4.82819i −0.115350 0.199792i
\(585\) 20.1829 + 28.6768i 0.834459 + 1.18564i
\(586\) −0.970865 + 1.68159i −0.0401061 + 0.0694657i
\(587\) 21.5670 21.5670i 0.890166 0.890166i −0.104372 0.994538i \(-0.533283\pi\)
0.994538 + 0.104372i \(0.0332834\pi\)
\(588\) 11.8380 2.61951i 0.488191 0.108027i
\(589\) 12.8599i 0.529881i
\(590\) −19.7955 11.2506i −0.814966 0.463178i
\(591\) −24.7880 + 15.7156i −1.01964 + 0.646452i
\(592\) −1.43087 + 5.34010i −0.0588086 + 0.219477i
\(593\) −2.59375 + 0.694994i −0.106513 + 0.0285400i −0.311682 0.950187i \(-0.600892\pi\)
0.205169 + 0.978727i \(0.434226\pi\)
\(594\) −2.63418 21.0763i −0.108082 0.864769i
\(595\) −1.58688 + 44.1178i −0.0650556 + 1.80865i
\(596\) 11.4395i 0.468581i
\(597\) 6.97997 2.18400i 0.285671 0.0893854i
\(598\) 5.55241 + 1.48776i 0.227055 + 0.0608392i
\(599\) 8.81980 + 15.2764i 0.360367 + 0.624175i 0.988021 0.154318i \(-0.0493180\pi\)
−0.627654 + 0.778493i \(0.715985\pi\)
\(600\) 7.72675 + 3.91118i 0.315443 + 0.159673i
\(601\) −25.1426 −1.02559 −0.512794 0.858512i \(-0.671390\pi\)
−0.512794 + 0.858512i \(0.671390\pi\)
\(602\) −4.02110 2.55666i −0.163888 0.104202i
\(603\) 6.80981 8.04390i 0.277317 0.327573i
\(604\) 11.7061 + 6.75854i 0.476316 + 0.275001i
\(605\) 12.3532 + 3.22038i 0.502230 + 0.130927i
\(606\) −2.74214 4.32515i −0.111392 0.175697i
\(607\) 41.5761 11.1403i 1.68752 0.452170i 0.717773 0.696277i \(-0.245161\pi\)
0.969748 + 0.244107i \(0.0784947\pi\)
\(608\) −1.73408 1.73408i −0.0703262 0.0703262i
\(609\) 6.58733 + 1.77419i 0.266932 + 0.0718938i
\(610\) 0.0247237 + 3.64439i 0.00100103 + 0.147557i
\(611\) −13.9392 8.04780i −0.563920 0.325579i
\(612\) −22.0290 3.98373i −0.890468 0.161033i
\(613\) −28.4761 7.63014i −1.15014 0.308178i −0.367117 0.930175i \(-0.619655\pi\)
−0.783020 + 0.621996i \(0.786322\pi\)
\(614\) 7.08776 12.2764i 0.286039 0.495433i
\(615\) 26.0843 1.25902i 1.05182 0.0507687i
\(616\) −10.3174 3.24289i −0.415698 0.130660i
\(617\) −21.8338 + 21.8338i −0.878994 + 0.878994i −0.993431 0.114437i \(-0.963494\pi\)
0.114437 + 0.993431i \(0.463494\pi\)
\(618\) −17.1354 + 5.36161i −0.689288 + 0.215675i
\(619\) 22.7455 13.1321i 0.914221 0.527826i 0.0324339 0.999474i \(-0.489674\pi\)
0.881787 + 0.471648i \(0.156341\pi\)
\(620\) 2.95792 11.3464i 0.118793 0.455684i
\(621\) 5.26440 + 2.22117i 0.211253 + 0.0891323i
\(622\) 2.66880 + 2.66880i 0.107009 + 0.107009i
\(623\) 19.0523 29.9653i 0.763314 1.20053i
\(624\) 0.375159 + 9.04653i 0.0150184 + 0.362151i
\(625\) 11.9080 21.9818i 0.476319 0.879273i
\(626\) −23.4389 + 13.5325i −0.936807 + 0.540866i
\(627\) 16.9431 + 3.79508i 0.676641 + 0.151561i
\(628\) 2.57312 + 9.60302i 0.102679 + 0.383202i
\(629\) −41.2540 −1.64490
\(630\) 17.7287 0.832773i 0.706328 0.0331785i
\(631\) 29.2208 1.16326 0.581631 0.813452i \(-0.302415\pi\)
0.581631 + 0.813452i \(0.302415\pi\)
\(632\) −2.44710 9.13268i −0.0973402 0.363279i
\(633\) 2.95253 + 0.661339i 0.117353 + 0.0262858i
\(634\) 18.4071 10.6273i 0.731038 0.422065i
\(635\) −8.60437 + 15.1395i −0.341454 + 0.600792i
\(636\) −0.409110 9.86523i −0.0162223 0.391182i
\(637\) 27.9893 23.5714i 1.10898 0.933934i
\(638\) −4.30297 4.30297i −0.170356 0.170356i
\(639\) 7.54759 16.0027i 0.298578 0.633058i
\(640\) 1.13115 + 1.92886i 0.0447124 + 0.0762450i
\(641\) 40.0771 23.1385i 1.58295 0.913916i 0.588522 0.808481i \(-0.299710\pi\)
0.994426 0.105435i \(-0.0336235\pi\)
\(642\) −2.10456 + 0.658509i −0.0830605 + 0.0259893i
\(643\) 26.7885 26.7885i 1.05644 1.05644i 0.0581268 0.998309i \(-0.481487\pi\)
0.998309 0.0581268i \(-0.0185128\pi\)
\(644\) 2.14322 1.96743i 0.0844546 0.0775277i
\(645\) −5.16436 4.68878i −0.203347 0.184620i
\(646\) 9.14987 15.8480i 0.359997 0.623532i
\(647\) −1.85517 0.497092i −0.0729343 0.0195427i 0.222167 0.975009i \(-0.428687\pi\)
−0.295102 + 0.955466i \(0.595354\pi\)
\(648\) −0.862807 + 8.95855i −0.0338943 + 0.351925i
\(649\) 36.0471 + 20.8118i 1.41497 + 0.816935i
\(650\) 26.1351 0.354619i 1.02510 0.0139093i
\(651\) −6.18956 23.2196i −0.242588 0.910050i
\(652\) −8.21531 8.21531i −0.321736 0.321736i
\(653\) 47.9356 12.8443i 1.87586 0.502636i 0.876073 0.482179i \(-0.160155\pi\)
0.999791 0.0204570i \(-0.00651211\pi\)
\(654\) 2.76080 + 4.35457i 0.107956 + 0.170277i
\(655\) −8.16809 + 31.3324i −0.319154 + 1.22426i
\(656\) 5.83942 + 3.37139i 0.227991 + 0.131631i
\(657\) −12.7652 10.8068i −0.498018 0.421612i
\(658\) −7.22250 + 3.76802i −0.281562 + 0.146893i
\(659\) 23.0084 0.896279 0.448139 0.893964i \(-0.352087\pi\)
0.448139 + 0.893964i \(0.352087\pi\)
\(660\) −14.0762 7.24556i −0.547915 0.282033i
\(661\) 15.1551 + 26.2494i 0.589465 + 1.02098i 0.994303 + 0.106594i \(0.0339947\pi\)
−0.404838 + 0.914389i \(0.632672\pi\)
\(662\) −3.96332 1.06197i −0.154039 0.0412746i
\(663\) −64.4813 + 20.1759i −2.50425 + 0.783569i
\(664\) 8.92905i 0.346514i
\(665\) −4.25635 + 13.8700i −0.165054 + 0.537854i
\(666\) 1.37323 + 16.5285i 0.0532115 + 0.640465i
\(667\) 1.58122 0.423688i 0.0612252 0.0164052i
\(668\) −5.74456 + 21.4390i −0.222264 + 0.829499i
\(669\) −10.8892 + 6.90373i −0.421000 + 0.266914i
\(670\) −2.08460 7.57393i −0.0805351 0.292606i
\(671\) 6.66235i 0.257197i
\(672\) 3.96566 + 2.29641i 0.152979 + 0.0885860i
\(673\) −15.1720 + 15.1720i −0.584839 + 0.584839i −0.936229 0.351390i \(-0.885709\pi\)
0.351390 + 0.936229i \(0.385709\pi\)
\(674\) 8.18434 14.1757i 0.315249 0.546027i
\(675\) 25.7816 + 3.21061i 0.992335 + 0.123576i
\(676\) 7.16342 + 12.4074i 0.275516 + 0.477208i
\(677\) 6.87791 + 25.6687i 0.264340 + 0.986529i 0.962653 + 0.270737i \(0.0872675\pi\)
−0.698314 + 0.715792i \(0.746066\pi\)
\(678\) 4.58210 4.97858i 0.175975 0.191201i
\(679\) −13.1959 14.3749i −0.506411 0.551658i
\(680\) −11.7183 + 11.8784i −0.449376 + 0.455515i
\(681\) 10.8736 + 5.69072i 0.416679 + 0.218069i
\(682\) −5.54787 + 20.7049i −0.212439 + 0.792832i
\(683\) −5.07317 + 18.9333i −0.194119 + 0.724464i 0.798374 + 0.602163i \(0.205694\pi\)
−0.992493 + 0.122301i \(0.960973\pi\)
\(684\) −6.65411 3.13837i −0.254426 0.119999i
\(685\) −0.181952 26.8206i −0.00695203 1.02476i
\(686\) −2.46671 18.3553i −0.0941795 0.700807i
\(687\) 3.71507 + 3.41922i 0.141739 + 0.130451i
\(688\) −0.466139 1.73965i −0.0177714 0.0663237i
\(689\) −14.8999 25.8074i −0.567642 0.983185i
\(690\) 3.58129 2.30475i 0.136337 0.0877402i
\(691\) 17.1906 29.7749i 0.653960 1.13269i −0.328194 0.944610i \(-0.606440\pi\)
0.982154 0.188081i \(-0.0602267\pi\)
\(692\) 0.772223 0.772223i 0.0293555 0.0293555i
\(693\) −32.4188 + 1.30247i −1.23149 + 0.0494768i
\(694\) 31.2718i 1.18706i
\(695\) −15.6388 + 4.30432i −0.593213 + 0.163272i
\(696\) 1.38067 + 2.17771i 0.0523341 + 0.0825459i
\(697\) −13.0226 + 48.6008i −0.493264 + 1.84089i
\(698\) 25.5454 6.84487i 0.966908 0.259082i
\(699\) 48.0605 1.99306i 1.81782 0.0753846i
\(700\) 6.94570 11.2587i 0.262523 0.425537i
\(701\) 13.1621i 0.497124i 0.968616 + 0.248562i \(0.0799581\pi\)
−0.968616 + 0.248562i \(0.920042\pi\)
\(702\) 10.2299 + 25.1629i 0.386104 + 0.949714i
\(703\) −13.0958 3.50902i −0.493919 0.132345i
\(704\) −2.04384 3.54004i −0.0770302 0.133420i
\(705\) −11.3565 + 3.63816i −0.427709 + 0.137021i
\(706\) −19.9103 −0.749335
\(707\) −6.93558 + 3.61833i −0.260839 + 0.136081i
\(708\) −12.9772 11.9437i −0.487714 0.448874i
\(709\) 6.02363 + 3.47774i 0.226222 + 0.130609i 0.608828 0.793302i \(-0.291640\pi\)
−0.382606 + 0.923912i \(0.624973\pi\)
\(710\) −6.67124 11.3760i −0.250367 0.426934i
\(711\) −16.1674 23.3058i −0.606327 0.874037i
\(712\) 12.9639 3.47367i 0.485844 0.130181i
\(713\) −4.07737 4.07737i −0.152699 0.152699i
\(714\) −8.89312 + 33.0190i −0.332817 + 1.23570i
\(715\) −47.7801 + 0.324142i −1.78687 + 0.0121222i
\(716\) −4.59754 2.65439i −0.171818 0.0991993i
\(717\) −10.8301 2.42585i −0.404459 0.0905949i
\(718\) −27.2815 7.31005i −1.01814 0.272808i
\(719\) −8.04406 + 13.9327i −0.299993 + 0.519603i −0.976134 0.217169i \(-0.930318\pi\)
0.676141 + 0.736772i \(0.263651\pi\)
\(720\) 5.14916 + 4.29955i 0.191898 + 0.160235i
\(721\) 5.96010 + 26.7708i 0.221966 + 0.996995i
\(722\) −9.18245 + 9.18245i −0.341735 + 0.341735i
\(723\) −7.12748 22.7791i −0.265074 0.847163i
\(724\) 11.9065 6.87422i 0.442501 0.255478i
\(725\) 6.39516 3.80886i 0.237510 0.141458i
\(726\) 8.76126 + 4.58520i 0.325161 + 0.170173i
\(727\) −15.0421 15.0421i −0.557879 0.557879i 0.370824 0.928703i \(-0.379075\pi\)
−0.928703 + 0.370824i \(0.879075\pi\)
\(728\) 13.8181 + 0.590909i 0.512131 + 0.0219005i
\(729\) 6.64528 + 26.1695i 0.246122 + 0.969239i
\(730\) −12.0194 + 3.30814i −0.444857 + 0.122440i
\(731\) 11.6389 6.71970i 0.430479 0.248537i
\(732\) −0.617035 + 2.75474i −0.0228063 + 0.101818i
\(733\) −1.94770 7.26892i −0.0719400 0.268484i 0.920582 0.390549i \(-0.127715\pi\)
−0.992522 + 0.122066i \(0.961048\pi\)
\(734\) 21.9155 0.808915
\(735\) 1.00951 27.0921i 0.0372363 0.999306i
\(736\) 1.09962 0.0405326
\(737\) 3.71677 + 13.8712i 0.136909 + 0.510952i
\(738\) 19.9055 + 3.59972i 0.732731 + 0.132508i
\(739\) −35.8593 + 20.7034i −1.31911 + 0.761586i −0.983585 0.180446i \(-0.942246\pi\)
−0.335522 + 0.942033i \(0.608913\pi\)
\(740\) 10.7475 + 6.10825i 0.395087 + 0.224544i
\(741\) −22.1853 + 0.920023i −0.814999 + 0.0337979i
\(742\) −15.0686 0.644385i −0.553184 0.0236561i
\(743\) −27.8973 27.8973i −1.02345 1.02345i −0.999718 0.0237355i \(-0.992444\pi\)
−0.0237355 0.999718i \(-0.507556\pi\)
\(744\) 4.21151 8.04722i 0.154402 0.295026i
\(745\) −24.7523 6.45270i −0.906853 0.236409i
\(746\) −3.54409 + 2.04618i −0.129758 + 0.0749160i
\(747\) −9.05155 25.2115i −0.331179 0.922442i
\(748\) 21.5687 21.5687i 0.788628 0.788628i
\(749\) 0.732016 + 3.28797i 0.0267473 + 0.120140i
\(750\) 12.8213 14.5126i 0.468166 0.529925i
\(751\) −23.2055 + 40.1931i −0.846781 + 1.46667i 0.0372844 + 0.999305i \(0.488129\pi\)
−0.884065 + 0.467363i \(0.845204\pi\)
\(752\) −2.97410 0.796909i −0.108454 0.0290603i
\(753\) 5.96048 26.6104i 0.217212 0.969738i
\(754\) 6.73956 + 3.89109i 0.245440 + 0.141705i
\(755\) 21.2269 21.5169i 0.772526 0.783079i
\(756\) 13.5251 + 2.46393i 0.491904 + 0.0896124i
\(757\) −10.4877 10.4877i −0.381181 0.381181i 0.490346 0.871528i \(-0.336870\pi\)
−0.871528 + 0.490346i \(0.836870\pi\)
\(758\) −11.6689 + 3.12668i −0.423835 + 0.113566i
\(759\) −6.57527 + 4.16872i −0.238667 + 0.151315i
\(760\) −4.73026 + 2.77397i −0.171585 + 0.100623i
\(761\) −22.6579 13.0816i −0.821350 0.474207i 0.0295319 0.999564i \(-0.490598\pi\)
−0.850882 + 0.525357i \(0.823932\pi\)
\(762\) −9.13452 + 9.92491i −0.330909 + 0.359542i
\(763\) 6.98276 3.64295i 0.252793 0.131884i
\(764\) 1.68544 0.0609771
\(765\) −21.0457 + 45.4181i −0.760910 + 1.64210i
\(766\) −16.2451 28.1374i −0.586960 1.01664i
\(767\) −51.4163 13.7770i −1.85653 0.497457i
\(768\) 0.517224 + 1.65302i 0.0186637 + 0.0596483i
\(769\) 51.0736i 1.84176i −0.389843 0.920881i \(-0.627471\pi\)
0.389843 0.920881i \(-0.372529\pi\)
\(770\) −12.8365 + 20.4950i −0.462597 + 0.738588i
\(771\) 1.84650 + 44.5263i 0.0665000 + 1.60357i
\(772\) 3.28843 0.881131i 0.118353 0.0317126i
\(773\) −9.45865 + 35.3002i −0.340204 + 1.26966i 0.557912 + 0.829900i \(0.311603\pi\)
−0.898116 + 0.439759i \(0.855064\pi\)
\(774\) −3.07968 4.43945i −0.110697 0.159573i
\(775\) −22.8824 12.8004i −0.821961 0.459804i
\(776\) 7.37533i 0.264759i
\(777\) 25.3346 + 0.0327166i 0.908875 + 0.00117370i
\(778\) 0.0216633 0.0216633i 0.000776666 0.000776666i
\(779\) −8.26786 + 14.3203i −0.296227 + 0.513080i
\(780\) 19.7861 + 4.29114i 0.708455 + 0.153647i
\(781\) 12.0541 + 20.8784i 0.431330 + 0.747086i
\(782\) 2.12373 + 7.92588i 0.0759446 + 0.283429i
\(783\) 6.10595 + 4.74924i 0.218209 + 0.169724i
\(784\) 4.00476 5.74125i 0.143027 0.205045i
\(785\) 22.2300 0.150809i 0.793422 0.00538260i
\(786\) −11.6298 + 22.2219i −0.414822 + 0.792627i
\(787\) −3.54432 + 13.2276i −0.126342 + 0.471513i −0.999884 0.0152350i \(-0.995150\pi\)
0.873542 + 0.486748i \(0.161817\pi\)
\(788\) −4.38575 + 16.3678i −0.156236 + 0.583080i
\(789\) 0.734044 1.40259i 0.0261327 0.0499334i
\(790\) −21.1412 + 0.143423i −0.752170 + 0.00510275i
\(791\) −6.98945 7.61394i −0.248516 0.270721i
\(792\) −9.35947 7.92355i −0.332574 0.281551i
\(793\) 2.20516 + 8.22978i 0.0783076 + 0.292248i
\(794\) 11.4749 + 19.8751i 0.407228 + 0.705340i
\(795\) −21.5767 4.67948i −0.765246 0.165964i
\(796\) 2.11128 3.65684i 0.0748322 0.129613i
\(797\) 0.268242 0.268242i 0.00950163 0.00950163i −0.702340 0.711842i \(-0.747861\pi\)
0.711842 + 0.702340i \(0.247861\pi\)
\(798\) −5.63162 + 9.72523i −0.199357 + 0.344269i
\(799\) 22.9759i 0.812830i
\(800\) 4.81163 1.35950i 0.170117 0.0480656i
\(801\) 33.0828 22.9498i 1.16892 0.810893i
\(802\) −4.34713 + 16.2237i −0.153503 + 0.572879i
\(803\) 22.0128 5.89830i 0.776814 0.208147i
\(804\) −0.252123 6.07967i −0.00889170 0.214413i
\(805\) −3.04811 5.74716i −0.107432 0.202561i
\(806\) 27.4124i 0.965560i
\(807\) −4.19885 13.4193i −0.147807 0.472383i
\(808\) −2.85595 0.765250i −0.100472 0.0269214i
\(809\) 12.6754 + 21.9544i 0.445642 + 0.771875i 0.998097 0.0616679i \(-0.0196420\pi\)
−0.552454 + 0.833543i \(0.686309\pi\)
\(810\) 18.8974 + 6.92016i 0.663987 + 0.243150i
\(811\) 44.0597 1.54714 0.773572 0.633708i \(-0.218468\pi\)
0.773572 + 0.633708i \(0.218468\pi\)
\(812\) 3.49206 1.82183i 0.122547 0.0639336i
\(813\) 0.336358 0.365462i 0.0117966 0.0128173i
\(814\) −19.5710 11.2993i −0.685964 0.396041i
\(815\) −22.4099 + 13.1419i −0.784985 + 0.460340i
\(816\) −10.9158 + 6.92059i −0.382128 + 0.242269i
\(817\) 4.26626 1.14314i 0.149257 0.0399934i
\(818\) −20.1012 20.1012i −0.702822 0.702822i
\(819\) 39.6148 12.3392i 1.38425 0.431166i
\(820\) 10.5887 10.7334i 0.369774 0.374825i
\(821\) 39.8047 + 22.9813i 1.38919 + 0.802051i 0.993224 0.116213i \(-0.0370754\pi\)
0.395969 + 0.918264i \(0.370409\pi\)
\(822\) 4.54102 20.2733i 0.158386 0.707113i
\(823\) 20.0447 + 5.37097i 0.698716 + 0.187220i 0.590655 0.806924i \(-0.298869\pi\)
0.108061 + 0.994144i \(0.465536\pi\)
\(824\) −5.18306 + 8.97733i −0.180561 + 0.312740i
\(825\) −23.6176 + 26.3704i −0.822258 + 0.918099i
\(826\) −19.8466 + 18.2188i −0.690550 + 0.633912i
\(827\) −15.6135 + 15.6135i −0.542934 + 0.542934i −0.924388 0.381454i \(-0.875423\pi\)
0.381454 + 0.924388i \(0.375423\pi\)
\(828\) 3.10482 1.11471i 0.107900 0.0387388i
\(829\) −12.2584 + 7.07737i −0.425751 + 0.245807i −0.697535 0.716551i \(-0.745720\pi\)
0.271784 + 0.962358i \(0.412386\pi\)
\(830\) −19.3203 5.03662i −0.670616 0.174824i
\(831\) −25.8578 + 49.4082i −0.896997 + 1.71395i
\(832\) 3.69641 + 3.69641i 0.128150 + 0.128150i
\(833\) 49.1165 + 17.7773i 1.70178 + 0.615949i
\(834\) −12.5534 + 0.520588i −0.434689 + 0.0180265i
\(835\) 43.1483 + 24.5229i 1.49321 + 0.848651i
\(836\) 8.68144 5.01223i 0.300254 0.173352i
\(837\) 3.73375 26.9909i 0.129057 0.932944i
\(838\) 5.20473 + 19.4243i 0.179794 + 0.671002i
\(839\) −7.87337 −0.271819 −0.135909 0.990721i \(-0.543396\pi\)
−0.135909 + 0.990721i \(0.543396\pi\)
\(840\) 7.20578 7.28538i 0.248623 0.251369i
\(841\) −26.7838 −0.923579
\(842\) −0.120772 0.450728i −0.00416208 0.0155331i
\(843\) −2.43698 + 10.8799i −0.0839342 + 0.374722i
\(844\) 1.51285 0.873442i 0.0520743 0.0300651i
\(845\) 30.8872 8.50120i 1.06255 0.292450i
\(846\) −9.20534 + 0.764804i −0.316486 + 0.0262945i
\(847\) 8.10451 12.7467i 0.278474 0.437982i
\(848\) −4.03092 4.03092i −0.138422 0.138422i
\(849\) −3.01329 1.57701i −0.103416 0.0541228i
\(850\) 19.0919 + 32.0557i 0.654847 + 1.09950i
\(851\) 5.26476 3.03961i 0.180474 0.104197i
\(852\) −3.05047 9.74915i −0.104507 0.334000i
\(853\) 7.40770 7.40770i 0.253635 0.253635i −0.568824 0.822459i \(-0.692602\pi\)
0.822459 + 0.568824i \(0.192602\pi\)
\(854\) 4.11378 + 1.29302i 0.140771 + 0.0442462i
\(855\) −10.5440 + 12.6276i −0.360599 + 0.431854i
\(856\) −0.636581 + 1.10259i −0.0217579 + 0.0376858i
\(857\) −35.1598 9.42103i −1.20103 0.321816i −0.397796 0.917474i \(-0.630225\pi\)
−0.803239 + 0.595657i \(0.796892\pi\)
\(858\) −36.1162 8.08969i −1.23299 0.276177i
\(859\) 18.8699 + 10.8945i 0.643831 + 0.371716i 0.786089 0.618114i \(-0.212103\pi\)
−0.142258 + 0.989830i \(0.545436\pi\)
\(860\) −4.02712 + 0.0273201i −0.137324 + 0.000931607i
\(861\) 8.03586 29.8361i 0.273862 1.01681i
\(862\) 9.94337 + 9.94337i 0.338672 + 0.338672i
\(863\) −29.5289 + 7.91226i −1.00518 + 0.269336i −0.723613 0.690206i \(-0.757520\pi\)
−0.281564 + 0.959542i \(0.590853\pi\)
\(864\) 3.13610 + 4.14305i 0.106692 + 0.140949i
\(865\) −1.23531 2.10649i −0.0420018 0.0716227i
\(866\) 9.69177 + 5.59555i 0.329340 + 0.190144i
\(867\) −49.2990 45.3729i −1.67428 1.54095i
\(868\) −11.7079 7.44400i −0.397391 0.252666i
\(869\) 38.6484 1.31106
\(870\) 5.49082 1.75904i 0.186156 0.0596370i
\(871\) −9.18242 15.9044i −0.311134 0.538901i
\(872\) 2.87538 + 0.770456i 0.0973727 + 0.0260909i
\(873\) −7.47651 20.8245i −0.253042 0.704803i
\(874\) 2.69666i 0.0912161i
\(875\) −20.4431 21.3795i −0.691102 0.722757i
\(876\) −9.64808 + 0.400105i −0.325978 + 0.0135183i
\(877\) −20.2019 + 5.41309i −0.682171 + 0.182787i −0.583231 0.812306i \(-0.698212\pi\)
−0.0989398 + 0.995093i \(0.531545\pi\)
\(878\) −0.507186 + 1.89284i −0.0171167 + 0.0638804i
\(879\) 1.80082 + 2.84042i 0.0607403 + 0.0958049i
\(880\) −8.81264 + 2.42553i −0.297074 + 0.0817647i
\(881\) 42.7328i 1.43971i 0.694127 + 0.719853i \(0.255791\pi\)
−0.694127 + 0.719853i \(0.744209\pi\)
\(882\) 5.48757 20.2703i 0.184776 0.682538i
\(883\) 11.2379 11.2379i 0.378184 0.378184i −0.492263 0.870447i \(-0.663830\pi\)
0.870447 + 0.492263i \(0.163830\pi\)
\(884\) −19.5041 + 33.7821i −0.655993 + 1.13621i
\(885\) −33.1634 + 21.3424i −1.11477 + 0.717415i
\(886\) 12.8261 + 22.2155i 0.430902 + 0.746344i
\(887\) 0.399896 + 1.49243i 0.0134272 + 0.0501110i 0.972314 0.233676i \(-0.0750757\pi\)
−0.958887 + 0.283787i \(0.908409\pi\)
\(888\) 7.04571 + 6.48461i 0.236438 + 0.217609i
\(889\) 13.9336 + 15.1786i 0.467319 + 0.509073i
\(890\) −0.203590 30.0101i −0.00682434 1.00594i
\(891\) −34.4591 12.8846i −1.15442 0.431650i
\(892\) −1.92663 + 7.19027i −0.0645082 + 0.240748i
\(893\) 1.95431 7.29357i 0.0653984 0.244070i
\(894\) −17.5550 9.18742i −0.587128 0.307273i
\(895\) −8.33679 + 8.45068i −0.278668 + 0.282475i
\(896\) 2.58252 0.574959i 0.0862760 0.0192080i
\(897\) 6.74242 7.32583i 0.225123 0.244602i
\(898\) −1.16887 4.36227i −0.0390056 0.145571i
\(899\) −3.90327 6.76066i −0.130181 0.225481i
\(900\) 12.2077 8.71625i 0.406922 0.290542i
\(901\) 21.2692 36.8393i 0.708579 1.22729i
\(902\) −19.4895 + 19.4895i −0.648930 + 0.648930i
\(903\) −7.15291 + 4.11743i −0.238034 + 0.137019i
\(904\) 3.90649i 0.129928i
\(905\) −8.15799 29.6402i −0.271181 0.985275i
\(906\) 19.7732 12.5362i 0.656920 0.416487i
\(907\) −2.23419 + 8.33811i −0.0741851 + 0.276862i −0.993047 0.117716i \(-0.962443\pi\)
0.918862 + 0.394579i \(0.129109\pi\)
\(908\) 6.84424 1.83391i 0.227134 0.0608604i
\(909\) −8.83964 + 0.734421i −0.293192 + 0.0243592i
\(910\) 9.07295 29.5655i 0.300765 0.980088i
\(911\) 49.6817i 1.64603i −0.568020 0.823015i \(-0.692290\pi\)
0.568020 0.823015i \(-0.307710\pi\)
\(912\) −4.05380 + 1.26842i −0.134235 + 0.0420015i
\(913\) 35.2555 + 9.44668i 1.16679 + 0.312639i
\(914\) 14.4552 + 25.0372i 0.478136 + 0.828156i
\(915\) 5.61252 + 2.88898i 0.185544 + 0.0955067i
\(916\) 2.91506 0.0963164
\(917\) 32.3305 + 20.5561i 1.06765 + 0.678822i
\(918\) −23.8056 + 30.6061i −0.785700 + 1.01015i
\(919\) −28.8152 16.6365i −0.950525 0.548786i −0.0572812 0.998358i \(-0.518243\pi\)
−0.893244 + 0.449572i \(0.851576\pi\)
\(920\) 0.620265 2.37931i 0.0204495 0.0784434i
\(921\) −13.1468 20.7363i −0.433203 0.683286i
\(922\) 27.6026 7.39609i 0.909043 0.243577i
\(923\) −21.8006 21.8006i −0.717575 0.717575i
\(924\) −13.2627 + 13.2285i −0.436311 + 0.435186i
\(925\) 19.2791 19.8095i 0.633893 0.651332i
\(926\) 32.1517 + 18.5628i 1.05657 + 0.610012i
\(927\) −5.53409 + 30.6020i −0.181763 + 1.00510i
\(928\) 1.43797 + 0.385303i 0.0472037 + 0.0126482i
\(929\) −12.5625 + 21.7588i −0.412161 + 0.713884i −0.995126 0.0986138i \(-0.968559\pi\)
0.582965 + 0.812497i \(0.301892\pi\)
\(930\) −15.0366 13.6519i −0.493070 0.447663i
\(931\) 14.0796 + 9.82110i 0.461440 + 0.321873i
\(932\) 19.6375 19.6375i 0.643247 0.643247i
\(933\) 6.23893 1.95213i 0.204253 0.0639100i
\(934\) 26.9825 15.5783i 0.882893 0.509738i
\(935\) −34.5030 58.8355i −1.12837 1.92413i
\(936\) 14.1841 + 6.68983i 0.463621 + 0.218664i
\(937\) 8.91661 + 8.91661i 0.291293 + 0.291293i 0.837591 0.546298i \(-0.183963\pi\)
−0.546298 + 0.837591i \(0.683963\pi\)
\(938\) −9.28634 0.397117i −0.303210 0.0129663i
\(939\) 1.94235 + 46.8376i 0.0633861 + 1.52849i
\(940\) −3.40192 + 5.98571i −0.110958 + 0.195232i
\(941\) 32.5006 18.7642i 1.05949 0.611696i 0.134197 0.990955i \(-0.457154\pi\)
0.925291 + 0.379259i \(0.123821\pi\)
\(942\) 16.8033 + 3.76378i 0.547481 + 0.122631i
\(943\) −1.91901 7.16186i −0.0624917 0.233222i
\(944\) −10.1827 −0.331418
\(945\) 12.9605 27.8752i 0.421604 0.906780i
\(946\) 7.36201 0.239360
\(947\) −14.8618 55.4649i −0.482943 1.80237i −0.589149 0.808024i \(-0.700537\pi\)
0.106206 0.994344i \(-0.466130\pi\)
\(948\) −15.9803 3.57943i −0.519016 0.116255i
\(949\) −25.2394 + 14.5720i −0.819305 + 0.473026i
\(950\) 3.33399 + 11.7998i 0.108169 + 0.382837i
\(951\) −1.52537 36.7825i −0.0494634 1.19276i
\(952\) 9.13192 + 17.5039i 0.295967 + 0.567306i
\(953\) 22.8327 + 22.8327i 0.739622 + 0.739622i 0.972505 0.232883i \(-0.0748158\pi\)
−0.232883 + 0.972505i \(0.574816\pi\)
\(954\) −15.4677 7.29525i −0.500785 0.236192i
\(955\) 0.950708 3.64687i 0.0307642 0.118010i
\(956\) −5.54924 + 3.20386i −0.179475 + 0.103620i
\(957\) −10.0592 + 3.14747i −0.325167 + 0.101743i
\(958\) 4.73903 4.73903i 0.153111 0.153111i
\(959\) −30.2751 9.51588i −0.977633 0.307284i
\(960\) 3.86848 0.186722i 0.124855 0.00602642i
\(961\) 1.75089 3.03263i 0.0564803 0.0978268i
\(962\) 27.9154 + 7.47991i 0.900028 + 0.241162i
\(963\) −0.679694 + 3.75852i −0.0219028 + 0.121117i
\(964\) −11.9341 6.89013i −0.384370 0.221916i
\(965\) −0.0516425 7.61236i −0.00166243 0.245051i
\(966\) −1.29793 4.86907i −0.0417601 0.156660i
\(967\) 10.9688 + 10.9688i 0.352734 + 0.352734i 0.861126 0.508392i \(-0.169760\pi\)
−0.508392 + 0.861126i \(0.669760\pi\)
\(968\) 5.51463 1.47764i 0.177247 0.0474932i
\(969\) −16.9718 26.7694i −0.545212 0.859956i
\(970\) −15.9584 4.16021i −0.512393 0.133576i
\(971\) −29.4378 16.9959i −0.944702 0.545424i −0.0532711 0.998580i \(-0.516965\pi\)
−0.891431 + 0.453156i \(0.850298\pi\)
\(972\) 13.0548 + 8.51894i 0.418733 + 0.273245i
\(973\) −0.819974 + 19.1746i −0.0262872 + 0.614710i
\(974\) 6.94402 0.222501
\(975\) 20.4457 40.3917i 0.654787 1.29357i
\(976\) 0.814929 + 1.41150i 0.0260852 + 0.0451810i
\(977\) 23.7906 + 6.37466i 0.761127 + 0.203943i 0.618448 0.785826i \(-0.287762\pi\)
0.142679 + 0.989769i \(0.454428\pi\)
\(978\) −19.2051 + 6.00921i −0.614112 + 0.192153i
\(979\) 54.8618i 1.75339i
\(980\) −10.1637 11.9038i −0.324667 0.380252i
\(981\) 8.89978 0.739417i 0.284148 0.0236078i
\(982\) 18.2256 4.88355i 0.581604 0.155840i
\(983\) −2.73551 + 10.2091i −0.0872492 + 0.325618i −0.995731 0.0923068i \(-0.970576\pi\)
0.908481 + 0.417925i \(0.137243\pi\)
\(984\) 9.86353 6.25348i 0.314438 0.199354i
\(985\) 32.9421 + 18.7223i 1.04962 + 0.596542i
\(986\) 11.1088i 0.353776i
\(987\) −0.0182211 + 14.1098i −0.000579985 + 0.449121i
\(988\) −9.06491 + 9.06491i −0.288393 + 0.288393i
\(989\) −0.990221 + 1.71511i −0.0314872 + 0.0545374i
\(990\) −22.4240 + 15.7821i −0.712682 + 0.501589i
\(991\) 19.0277 + 32.9570i 0.604435 + 1.04691i 0.992140 + 0.125129i \(0.0399346\pi\)
−0.387705 + 0.921784i \(0.626732\pi\)
\(992\) −1.35721 5.06519i −0.0430916 0.160820i
\(993\) −4.81275 + 5.22919i −0.152728 + 0.165943i
\(994\) −15.2311 + 3.39098i −0.483102 + 0.107555i
\(995\) −6.72158 6.63100i −0.213088 0.210217i
\(996\) −13.7025 7.17119i −0.434180 0.227228i
\(997\) 5.07524 18.9410i 0.160734 0.599869i −0.837812 0.545960i \(-0.816165\pi\)
0.998546 0.0539091i \(-0.0171681\pi\)
\(998\) −10.0994 + 37.6913i −0.319690 + 1.19310i
\(999\) 26.4674 + 11.1672i 0.837391 + 0.353314i
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 210.2.x.a.107.1 yes 64
3.2 odd 2 inner 210.2.x.a.107.10 yes 64
5.3 odd 4 inner 210.2.x.a.23.5 64
7.4 even 3 inner 210.2.x.a.137.13 yes 64
15.8 even 4 inner 210.2.x.a.23.13 yes 64
21.11 odd 6 inner 210.2.x.a.137.5 yes 64
35.18 odd 12 inner 210.2.x.a.53.10 yes 64
105.53 even 12 inner 210.2.x.a.53.1 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.x.a.23.5 64 5.3 odd 4 inner
210.2.x.a.23.13 yes 64 15.8 even 4 inner
210.2.x.a.53.1 yes 64 105.53 even 12 inner
210.2.x.a.53.10 yes 64 35.18 odd 12 inner
210.2.x.a.107.1 yes 64 1.1 even 1 trivial
210.2.x.a.107.10 yes 64 3.2 odd 2 inner
210.2.x.a.137.5 yes 64 21.11 odd 6 inner
210.2.x.a.137.13 yes 64 7.4 even 3 inner