Properties

Label 930.2.bs.a.107.5
Level $930$
Weight $2$
Character 930.107
Analytic conductor $7.426$
Analytic rank $0$
Dimension $1024$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(107,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([30, 15, 44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bs (of order \(60\), degree \(16\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(1024\)
Relative dimension: \(64\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 107.5
Character \(\chi\) \(=\) 930.107
Dual form 930.2.bs.a.113.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.453990 - 0.891007i) q^{2} +(-1.61622 - 0.622763i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.949618 + 2.02441i) q^{5} +(0.178863 + 1.72279i) q^{6} +(0.463591 - 0.375409i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.22433 + 2.01304i) q^{9} +O(q^{10})\) \(q+(-0.453990 - 0.891007i) q^{2} +(-1.61622 - 0.622763i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.949618 + 2.02441i) q^{5} +(0.178863 + 1.72279i) q^{6} +(0.463591 - 0.375409i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.22433 + 2.01304i) q^{9} +(2.23488 - 0.0729461i) q^{10} +(-0.839446 - 1.88543i) q^{11} +(1.45382 - 0.941498i) q^{12} +(1.28984 - 0.837629i) q^{13} +(-0.544957 - 0.242631i) q^{14} +(2.79552 - 2.68050i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.43780 - 0.551919i) q^{17} +(0.783809 - 2.89580i) q^{18} +(-0.0719150 - 0.338333i) q^{19} +(-1.07961 - 1.95817i) q^{20} +(-0.983055 + 0.318035i) q^{21} +(-1.29883 + 1.60392i) q^{22} +(-3.89805 - 0.617391i) q^{23} +(-1.49890 - 0.867928i) q^{24} +(-3.19645 - 3.84483i) q^{25} +(-1.33191 - 0.768976i) q^{26} +(-2.34136 - 4.63875i) q^{27} +(0.0312200 + 0.595712i) q^{28} +(-2.11711 + 6.51581i) q^{29} +(-3.65748 - 1.27390i) q^{30} +(-3.18205 + 4.56887i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.182556 + 3.57004i) q^{33} +(-1.14451 - 1.03052i) q^{34} +(0.319746 + 1.29499i) q^{35} +(-2.93602 + 0.616286i) q^{36} +(-0.559713 + 2.08888i) q^{37} +(-0.268809 + 0.217677i) q^{38} +(-2.60630 + 0.550531i) q^{39} +(-1.25461 + 1.85093i) q^{40} +(-3.71846 + 3.34811i) q^{41} +(0.729669 + 0.731524i) q^{42} +(2.76977 - 4.26508i) q^{43} +(2.01876 + 0.429100i) q^{44} +(-6.18749 + 2.59133i) q^{45} +(1.21958 + 3.75348i) q^{46} +(-3.84537 - 1.95931i) q^{47} +(-0.0928433 + 1.72956i) q^{48} +(-1.38140 + 6.49896i) q^{49} +(-1.97461 + 4.59357i) q^{50} +(-2.66751 - 0.00338488i) q^{51} +(-0.0804902 + 1.53584i) q^{52} +(1.04873 - 1.29507i) q^{53} +(-3.07020 + 4.19212i) q^{54} +(4.61403 + 0.0910539i) q^{55} +(0.516610 - 0.298265i) q^{56} +(-0.0944711 + 0.591607i) q^{57} +(6.76678 - 1.07175i) q^{58} +(2.24166 - 2.48961i) q^{59} +(0.525407 + 3.83718i) q^{60} -8.05452 q^{61} +(5.51551 + 0.761005i) q^{62} +(1.78689 + 0.0981951i) q^{63} +(0.951057 + 0.309017i) q^{64} +(0.470851 + 3.40658i) q^{65} +(3.09805 - 1.78342i) q^{66} +(-6.46480 + 1.73224i) q^{67} +(-0.398605 + 1.48761i) q^{68} +(5.91562 + 3.42540i) q^{69} +(1.00868 - 0.872809i) q^{70} +(-11.2306 + 1.18038i) q^{71} +(1.88204 + 2.33622i) q^{72} +(-0.119430 + 0.311127i) q^{73} +(2.11531 - 0.449623i) q^{74} +(2.77175 + 8.20472i) q^{75} +(0.315988 + 0.140687i) q^{76} +(-1.09697 - 0.558932i) q^{77} +(1.67376 + 2.07230i) q^{78} +(-6.17323 + 13.8653i) q^{79} +(2.21877 + 0.277564i) q^{80} +(0.895313 + 8.95536i) q^{81} +(4.67133 + 1.79316i) q^{82} +(0.448678 - 8.56129i) q^{83} +(0.320529 - 0.982245i) q^{84} +(-0.248050 + 3.43480i) q^{85} +(-5.05766 - 0.531582i) q^{86} +(7.47952 - 9.21252i) q^{87} +(-0.534166 - 1.99353i) q^{88} +(5.96446 + 4.33343i) q^{89} +(5.11796 + 4.33665i) q^{90} +(0.283503 - 0.872532i) q^{91} +(2.79070 - 2.79070i) q^{92} +(7.98821 - 5.40263i) q^{93} +4.31576i q^{94} +(0.753217 + 0.175702i) q^{95} +(1.58320 - 0.702480i) q^{96} +(1.58980 + 10.0376i) q^{97} +(6.41776 - 1.71963i) q^{98} +(1.92824 - 5.88366i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(e\left(\frac{11}{15}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.453990 0.891007i −0.321020 0.630037i
\(3\) −1.61622 0.622763i −0.933125 0.359552i
\(4\) −0.587785 + 0.809017i −0.293893 + 0.404508i
\(5\) −0.949618 + 2.02441i −0.424682 + 0.905343i
\(6\) 0.178863 + 1.72279i 0.0730204 + 0.703326i
\(7\) 0.463591 0.375409i 0.175221 0.141891i −0.537698 0.843137i \(-0.680706\pi\)
0.712919 + 0.701246i \(0.247373\pi\)
\(8\) 0.987688 + 0.156434i 0.349201 + 0.0553079i
\(9\) 2.22433 + 2.01304i 0.741444 + 0.671014i
\(10\) 2.23488 0.0729461i 0.706730 0.0230676i
\(11\) −0.839446 1.88543i −0.253103 0.568478i 0.741650 0.670787i \(-0.234044\pi\)
−0.994753 + 0.102309i \(0.967377\pi\)
\(12\) 1.45382 0.941498i 0.419680 0.271787i
\(13\) 1.28984 0.837629i 0.357736 0.232316i −0.353240 0.935533i \(-0.614920\pi\)
0.710976 + 0.703216i \(0.248253\pi\)
\(14\) −0.544957 0.242631i −0.145646 0.0648458i
\(15\) 2.79552 2.68050i 0.721799 0.692102i
\(16\) −0.309017 0.951057i −0.0772542 0.237764i
\(17\) 1.43780 0.551919i 0.348717 0.133860i −0.177704 0.984084i \(-0.556867\pi\)
0.526421 + 0.850224i \(0.323534\pi\)
\(18\) 0.783809 2.89580i 0.184745 0.682546i
\(19\) −0.0719150 0.338333i −0.0164984 0.0776190i 0.969128 0.246557i \(-0.0792994\pi\)
−0.985627 + 0.168938i \(0.945966\pi\)
\(20\) −1.07961 1.95817i −0.241408 0.437861i
\(21\) −0.983055 + 0.318035i −0.214520 + 0.0694010i
\(22\) −1.29883 + 1.60392i −0.276911 + 0.341957i
\(23\) −3.89805 0.617391i −0.812800 0.128735i −0.263822 0.964571i \(-0.584983\pi\)
−0.548978 + 0.835837i \(0.684983\pi\)
\(24\) −1.49890 0.867928i −0.305962 0.177165i
\(25\) −3.19645 3.84483i −0.639290 0.768965i
\(26\) −1.33191 0.768976i −0.261208 0.150809i
\(27\) −2.34136 4.63875i −0.450595 0.892728i
\(28\) 0.0312200 + 0.595712i 0.00590002 + 0.112579i
\(29\) −2.11711 + 6.51581i −0.393138 + 1.20995i 0.537264 + 0.843414i \(0.319458\pi\)
−0.930402 + 0.366541i \(0.880542\pi\)
\(30\) −3.65748 1.27390i −0.667762 0.232582i
\(31\) −3.18205 + 4.56887i −0.571513 + 0.820593i
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0.182556 + 3.57004i 0.0317789 + 0.621464i
\(34\) −1.14451 1.03052i −0.196282 0.176733i
\(35\) 0.319746 + 1.29499i 0.0540469 + 0.218894i
\(36\) −2.93602 + 0.616286i −0.489336 + 0.102714i
\(37\) −0.559713 + 2.08888i −0.0920163 + 0.343410i −0.996550 0.0829922i \(-0.973552\pi\)
0.904534 + 0.426402i \(0.140219\pi\)
\(38\) −0.268809 + 0.217677i −0.0436065 + 0.0353119i
\(39\) −2.60630 + 0.550531i −0.417342 + 0.0881555i
\(40\) −1.25461 + 1.85093i −0.198372 + 0.292658i
\(41\) −3.71846 + 3.34811i −0.580725 + 0.522887i −0.906303 0.422628i \(-0.861108\pi\)
0.325578 + 0.945515i \(0.394441\pi\)
\(42\) 0.729669 + 0.731524i 0.112590 + 0.112877i
\(43\) 2.76977 4.26508i 0.422387 0.650418i −0.561857 0.827234i \(-0.689913\pi\)
0.984244 + 0.176816i \(0.0565797\pi\)
\(44\) 2.01876 + 0.429100i 0.304339 + 0.0646893i
\(45\) −6.18749 + 2.59133i −0.922376 + 0.386293i
\(46\) 1.21958 + 3.75348i 0.179817 + 0.553420i
\(47\) −3.84537 1.95931i −0.560905 0.285795i 0.150462 0.988616i \(-0.451924\pi\)
−0.711367 + 0.702820i \(0.751924\pi\)
\(48\) −0.0928433 + 1.72956i −0.0134008 + 0.249641i
\(49\) −1.38140 + 6.49896i −0.197342 + 0.928423i
\(50\) −1.97461 + 4.59357i −0.279252 + 0.649630i
\(51\) −2.66751 0.00338488i −0.373526 0.000473978i
\(52\) −0.0804902 + 1.53584i −0.0111620 + 0.212983i
\(53\) 1.04873 1.29507i 0.144054 0.177892i −0.700012 0.714131i \(-0.746822\pi\)
0.844066 + 0.536239i \(0.180156\pi\)
\(54\) −3.07020 + 4.19212i −0.417802 + 0.570475i
\(55\) 4.61403 + 0.0910539i 0.622155 + 0.0122777i
\(56\) 0.516610 0.298265i 0.0690349 0.0398573i
\(57\) −0.0944711 + 0.591607i −0.0125130 + 0.0783603i
\(58\) 6.76678 1.07175i 0.888521 0.140728i
\(59\) 2.24166 2.48961i 0.291839 0.324120i −0.579340 0.815086i \(-0.696689\pi\)
0.871179 + 0.490966i \(0.163356\pi\)
\(60\) 0.525407 + 3.83718i 0.0678298 + 0.495378i
\(61\) −8.05452 −1.03128 −0.515638 0.856807i \(-0.672445\pi\)
−0.515638 + 0.856807i \(0.672445\pi\)
\(62\) 5.51551 + 0.761005i 0.700471 + 0.0966478i
\(63\) 1.78689 + 0.0981951i 0.225127 + 0.0123714i
\(64\) 0.951057 + 0.309017i 0.118882 + 0.0386271i
\(65\) 0.470851 + 3.40658i 0.0584019 + 0.422534i
\(66\) 3.09805 1.78342i 0.381344 0.219524i
\(67\) −6.46480 + 1.73224i −0.789801 + 0.211627i −0.631101 0.775700i \(-0.717397\pi\)
−0.158700 + 0.987327i \(0.550730\pi\)
\(68\) −0.398605 + 1.48761i −0.0483379 + 0.180400i
\(69\) 5.91562 + 3.42540i 0.712157 + 0.412370i
\(70\) 1.00868 0.872809i 0.120561 0.104321i
\(71\) −11.2306 + 1.18038i −1.33283 + 0.140086i −0.744004 0.668176i \(-0.767075\pi\)
−0.588824 + 0.808261i \(0.700409\pi\)
\(72\) 1.88204 + 2.33622i 0.221800 + 0.275326i
\(73\) −0.119430 + 0.311127i −0.0139783 + 0.0364146i −0.940392 0.340092i \(-0.889542\pi\)
0.926414 + 0.376507i \(0.122875\pi\)
\(74\) 2.11531 0.449623i 0.245900 0.0522676i
\(75\) 2.77175 + 8.20472i 0.320054 + 0.947399i
\(76\) 0.315988 + 0.140687i 0.0362463 + 0.0161379i
\(77\) −1.09697 0.558932i −0.125011 0.0636962i
\(78\) 1.67376 + 2.07230i 0.189516 + 0.234641i
\(79\) −6.17323 + 13.8653i −0.694543 + 1.55997i 0.128323 + 0.991732i \(0.459041\pi\)
−0.822866 + 0.568236i \(0.807626\pi\)
\(80\) 2.21877 + 0.277564i 0.248066 + 0.0310326i
\(81\) 0.895313 + 8.95536i 0.0994792 + 0.995040i
\(82\) 4.67133 + 1.79316i 0.515863 + 0.198021i
\(83\) 0.448678 8.56129i 0.0492488 0.939724i −0.856563 0.516043i \(-0.827404\pi\)
0.905812 0.423681i \(-0.139262\pi\)
\(84\) 0.320529 0.982245i 0.0349726 0.107172i
\(85\) −0.248050 + 3.43480i −0.0269048 + 0.372557i
\(86\) −5.05766 0.531582i −0.545382 0.0573219i
\(87\) 7.47952 9.21252i 0.801889 0.987685i
\(88\) −0.534166 1.99353i −0.0569422 0.212511i
\(89\) 5.96446 + 4.33343i 0.632231 + 0.459343i 0.857172 0.515030i \(-0.172219\pi\)
−0.224941 + 0.974372i \(0.572219\pi\)
\(90\) 5.11796 + 4.33665i 0.539480 + 0.457123i
\(91\) 0.283503 0.872532i 0.0297192 0.0914662i
\(92\) 2.79070 2.79070i 0.290950 0.290950i
\(93\) 7.98821 5.40263i 0.828339 0.560227i
\(94\) 4.31576i 0.445137i
\(95\) 0.753217 + 0.175702i 0.0772784 + 0.0180267i
\(96\) 1.58320 0.702480i 0.161585 0.0716966i
\(97\) 1.58980 + 10.0376i 0.161420 + 1.01917i 0.926791 + 0.375577i \(0.122555\pi\)
−0.765371 + 0.643589i \(0.777445\pi\)
\(98\) 6.41776 1.71963i 0.648291 0.173709i
\(99\) 1.92824 5.88366i 0.193795 0.591330i
\(100\) 4.98936 0.326051i 0.498936 0.0326051i
\(101\) −7.82617 10.7718i −0.778733 1.07183i −0.995421 0.0955930i \(-0.969525\pi\)
0.216688 0.976241i \(-0.430475\pi\)
\(102\) 1.20801 + 2.37831i 0.119611 + 0.235488i
\(103\) −7.77536 0.407489i −0.766129 0.0401511i −0.334732 0.942313i \(-0.608646\pi\)
−0.431397 + 0.902162i \(0.641979\pi\)
\(104\) 1.40499 0.625541i 0.137771 0.0613394i
\(105\) 0.289693 2.29212i 0.0282712 0.223688i
\(106\) −1.63003 0.346473i −0.158322 0.0336524i
\(107\) −0.752149 + 0.288723i −0.0727130 + 0.0279119i −0.394453 0.918916i \(-0.629066\pi\)
0.321740 + 0.946828i \(0.395732\pi\)
\(108\) 5.12905 + 0.832388i 0.493543 + 0.0800966i
\(109\) −16.0685 + 5.22096i −1.53908 + 0.500078i −0.951123 0.308814i \(-0.900068\pi\)
−0.587958 + 0.808891i \(0.700068\pi\)
\(110\) −2.01359 4.15247i −0.191989 0.395922i
\(111\) 2.20550 3.02752i 0.209336 0.287359i
\(112\) −0.500292 0.324894i −0.0472732 0.0306996i
\(113\) 0.917913 + 0.352354i 0.0863500 + 0.0331467i 0.401160 0.916008i \(-0.368607\pi\)
−0.314810 + 0.949155i \(0.601941\pi\)
\(114\) 0.570015 0.184410i 0.0533868 0.0172716i
\(115\) 4.95151 7.30496i 0.461731 0.681191i
\(116\) −4.02699 5.54268i −0.373897 0.514625i
\(117\) 4.55521 + 0.733329i 0.421129 + 0.0677963i
\(118\) −3.23595 0.867071i −0.297894 0.0798204i
\(119\) 0.459355 0.795626i 0.0421090 0.0729349i
\(120\) 3.18042 2.21018i 0.290332 0.201761i
\(121\) 4.51027 5.00916i 0.410025 0.455378i
\(122\) 3.65667 + 7.17663i 0.331060 + 0.649741i
\(123\) 8.09492 3.09557i 0.729895 0.279118i
\(124\) −1.82593 5.25985i −0.163973 0.472348i
\(125\) 10.8189 2.81980i 0.967672 0.252211i
\(126\) −0.723740 1.63671i −0.0644759 0.145810i
\(127\) 0.861785 0.0451642i 0.0764710 0.00400768i −0.0140621 0.999901i \(-0.504476\pi\)
0.0905331 + 0.995893i \(0.471143\pi\)
\(128\) −0.156434 0.987688i −0.0138270 0.0873001i
\(129\) −7.13269 + 5.16839i −0.627999 + 0.455051i
\(130\) 2.82152 1.96609i 0.247464 0.172437i
\(131\) −1.11327 0.117009i −0.0972666 0.0102231i 0.0557701 0.998444i \(-0.482239\pi\)
−0.153037 + 0.988221i \(0.548905\pi\)
\(132\) −2.99553 1.95073i −0.260727 0.169789i
\(133\) −0.160352 0.129851i −0.0139043 0.0112595i
\(134\) 4.47839 + 4.97376i 0.386874 + 0.429667i
\(135\) 11.6141 0.334829i 0.999585 0.0288175i
\(136\) 1.50644 0.320203i 0.129176 0.0274572i
\(137\) −6.50230 + 4.22264i −0.555529 + 0.360765i −0.791665 0.610955i \(-0.790786\pi\)
0.236136 + 0.971720i \(0.424119\pi\)
\(138\) 0.366419 6.82596i 0.0311917 0.581064i
\(139\) −4.39906 + 1.42934i −0.373123 + 0.121235i −0.489575 0.871961i \(-0.662848\pi\)
0.116452 + 0.993196i \(0.462848\pi\)
\(140\) −1.23561 0.502497i −0.104428 0.0424688i
\(141\) 4.99478 + 5.56144i 0.420636 + 0.468357i
\(142\) 6.15032 + 9.47066i 0.516123 + 0.794760i
\(143\) −2.66204 1.72875i −0.222611 0.144565i
\(144\) 1.22716 2.73753i 0.102263 0.228128i
\(145\) −11.1802 10.4734i −0.928465 0.869771i
\(146\) 0.331436 0.0348353i 0.0274298 0.00288299i
\(147\) 6.27995 9.64347i 0.517962 0.795380i
\(148\) −1.36095 1.68063i −0.111869 0.138147i
\(149\) −0.975371 1.68939i −0.0799055 0.138400i 0.823303 0.567601i \(-0.192129\pi\)
−0.903209 + 0.429201i \(0.858795\pi\)
\(150\) 6.05211 6.19451i 0.494152 0.505780i
\(151\) 4.80404 + 3.49034i 0.390947 + 0.284040i 0.765844 0.643027i \(-0.222322\pi\)
−0.374896 + 0.927067i \(0.622322\pi\)
\(152\) −0.0181026 0.345418i −0.00146831 0.0280171i
\(153\) 4.30918 + 1.66670i 0.348376 + 0.134745i
\(154\) 1.23115i 0.0992091i
\(155\) −6.22752 10.7804i −0.500206 0.865906i
\(156\) 1.08656 2.43214i 0.0869942 0.194727i
\(157\) −19.9204 + 10.1500i −1.58982 + 0.810054i −0.589824 + 0.807532i \(0.700803\pi\)
−0.999997 + 0.00252279i \(0.999197\pi\)
\(158\) 15.1567 0.794327i 1.20580 0.0631933i
\(159\) −2.50149 + 1.44001i −0.198381 + 0.114200i
\(160\) −0.759991 2.10295i −0.0600826 0.166253i
\(161\) −2.03887 + 1.17714i −0.160686 + 0.0927720i
\(162\) 7.57282 4.86338i 0.594977 0.382103i
\(163\) −0.298628 + 1.88546i −0.0233903 + 0.147681i −0.996619 0.0821563i \(-0.973819\pi\)
0.973229 + 0.229837i \(0.0738193\pi\)
\(164\) −0.523027 4.97627i −0.0408415 0.388581i
\(165\) −7.40058 3.02061i −0.576134 0.235154i
\(166\) −7.83186 + 3.48697i −0.607870 + 0.270641i
\(167\) 0.0788804 0.121465i 0.00610395 0.00939926i −0.835605 0.549330i \(-0.814883\pi\)
0.841709 + 0.539931i \(0.181550\pi\)
\(168\) −1.02070 + 0.160336i −0.0787490 + 0.0123702i
\(169\) −4.32552 + 9.71529i −0.332733 + 0.747330i
\(170\) 3.17304 1.33835i 0.243361 0.102647i
\(171\) 0.521117 0.897334i 0.0398508 0.0686209i
\(172\) 1.82249 + 4.74774i 0.138963 + 0.362012i
\(173\) −11.9718 18.4350i −0.910201 1.40159i −0.915814 0.401603i \(-0.868453\pi\)
0.00561265 0.999984i \(-0.498213\pi\)
\(174\) −11.6040 2.48191i −0.879700 0.188153i
\(175\) −2.92523 0.582452i −0.221126 0.0440292i
\(176\) −1.53374 + 1.38099i −0.115610 + 0.104096i
\(177\) −5.17345 + 2.62774i −0.388861 + 0.197513i
\(178\) 1.15331 7.28170i 0.0864441 0.545787i
\(179\) 0.429168 4.08326i 0.0320775 0.305197i −0.966706 0.255889i \(-0.917632\pi\)
0.998784 0.0493079i \(-0.0157016\pi\)
\(180\) 1.54048 6.52893i 0.114821 0.486638i
\(181\) 5.53677 9.58997i 0.411545 0.712817i −0.583514 0.812103i \(-0.698323\pi\)
0.995059 + 0.0992861i \(0.0316559\pi\)
\(182\) −0.906139 + 0.143518i −0.0671675 + 0.0106383i
\(183\) 13.0179 + 5.01605i 0.962309 + 0.370797i
\(184\) −3.75348 1.21958i −0.276710 0.0899086i
\(185\) −3.69723 3.11672i −0.271826 0.229146i
\(186\) −8.44035 4.66481i −0.618877 0.342040i
\(187\) −2.24756 2.24756i −0.164358 0.164358i
\(188\) 3.84537 1.95931i 0.280452 0.142898i
\(189\) −2.82686 1.27152i −0.205624 0.0924892i
\(190\) −0.185401 0.750888i −0.0134504 0.0544751i
\(191\) 12.1969 + 7.04191i 0.882540 + 0.509535i 0.871495 0.490404i \(-0.163151\pi\)
0.0110451 + 0.999939i \(0.496484\pi\)
\(192\) −1.34467 1.09172i −0.0970433 0.0787883i
\(193\) −0.0178341 0.0220232i −0.00128372 0.00158527i 0.776504 0.630113i \(-0.216991\pi\)
−0.777787 + 0.628527i \(0.783658\pi\)
\(194\) 8.22183 5.97351i 0.590293 0.428873i
\(195\) 1.36049 5.79901i 0.0974268 0.415276i
\(196\) −4.44581 4.93757i −0.317558 0.352683i
\(197\) 2.42576 6.31931i 0.172828 0.450232i −0.819619 0.572909i \(-0.805815\pi\)
0.992447 + 0.122677i \(0.0391480\pi\)
\(198\) −6.11778 + 0.953052i −0.434772 + 0.0677305i
\(199\) 3.74644 17.6256i 0.265578 1.24945i −0.619868 0.784706i \(-0.712814\pi\)
0.885446 0.464741i \(-0.153853\pi\)
\(200\) −2.55563 4.29753i −0.180711 0.303881i
\(201\) 11.5273 + 1.22636i 0.813074 + 0.0865008i
\(202\) −6.04474 + 11.8635i −0.425306 + 0.834710i
\(203\) 1.46461 + 3.81545i 0.102796 + 0.267792i
\(204\) 1.57066 2.15607i 0.109968 0.150955i
\(205\) −3.24683 10.7071i −0.226769 0.747816i
\(206\) 3.16686 + 7.11289i 0.220646 + 0.495579i
\(207\) −7.42773 9.22023i −0.516263 0.640850i
\(208\) −1.19521 0.967865i −0.0828731 0.0671093i
\(209\) −0.577534 + 0.419603i −0.0399489 + 0.0290246i
\(210\) −2.17381 + 0.782480i −0.150007 + 0.0539963i
\(211\) −10.8276 18.7540i −0.745404 1.29108i −0.950006 0.312232i \(-0.898923\pi\)
0.204602 0.978845i \(-0.434410\pi\)
\(212\) 0.431307 + 1.60966i 0.0296223 + 0.110552i
\(213\) 18.8862 + 5.08624i 1.29406 + 0.348504i
\(214\) 0.598722 + 0.539092i 0.0409278 + 0.0368516i
\(215\) 6.00403 + 9.65734i 0.409471 + 0.658625i
\(216\) −1.58688 4.94791i −0.107973 0.336663i
\(217\) 0.240022 + 3.31265i 0.0162938 + 0.224878i
\(218\) 11.9468 + 11.9468i 0.809143 + 0.809143i
\(219\) 0.386784 0.428472i 0.0261364 0.0289535i
\(220\) −2.78572 + 3.67931i −0.187813 + 0.248059i
\(221\) 1.39222 1.91623i 0.0936508 0.128899i
\(222\) −3.69881 0.590647i −0.248248 0.0396416i
\(223\) 15.8176 + 4.23832i 1.05923 + 0.283819i 0.746059 0.665880i \(-0.231944\pi\)
0.313167 + 0.949698i \(0.398610\pi\)
\(224\) −0.0623544 + 0.593262i −0.00416623 + 0.0396390i
\(225\) 0.629831 14.9868i 0.0419887 0.999118i
\(226\) −0.102774 0.977832i −0.00683644 0.0650444i
\(227\) −14.4101 0.755200i −0.956430 0.0501244i −0.432270 0.901744i \(-0.642287\pi\)
−0.524160 + 0.851620i \(0.675621\pi\)
\(228\) −0.423092 0.424167i −0.0280199 0.0280911i
\(229\) −0.703625 3.31029i −0.0464968 0.218750i 0.948765 0.315983i \(-0.102334\pi\)
−0.995262 + 0.0972326i \(0.969001\pi\)
\(230\) −8.75670 1.09545i −0.577400 0.0722315i
\(231\) 1.42485 + 1.58651i 0.0937486 + 0.104384i
\(232\) −3.11035 + 6.10440i −0.204204 + 0.400773i
\(233\) −4.93377 + 9.68306i −0.323222 + 0.634358i −0.994251 0.107072i \(-0.965852\pi\)
0.671030 + 0.741431i \(0.265852\pi\)
\(234\) −1.41462 4.39164i −0.0924765 0.287091i
\(235\) 7.61808 5.92400i 0.496949 0.386439i
\(236\) 0.696526 + 3.27690i 0.0453400 + 0.213308i
\(237\) 18.6121 18.5649i 1.20899 1.20592i
\(238\) −0.917451 0.0480816i −0.0594695 0.00311667i
\(239\) 0.736252 + 7.00497i 0.0476242 + 0.453114i 0.992185 + 0.124777i \(0.0398215\pi\)
−0.944561 + 0.328337i \(0.893512\pi\)
\(240\) −3.41317 1.83037i −0.220319 0.118150i
\(241\) 1.10296 10.4940i 0.0710479 0.675976i −0.899804 0.436295i \(-0.856290\pi\)
0.970852 0.239681i \(-0.0770429\pi\)
\(242\) −6.51082 1.74457i −0.418531 0.112145i
\(243\) 4.13004 15.0314i 0.264942 0.964264i
\(244\) 4.73433 6.51624i 0.303084 0.417160i
\(245\) −11.8447 8.96804i −0.756733 0.572947i
\(246\) −6.43319 5.80727i −0.410165 0.370258i
\(247\) −0.376156 0.376156i −0.0239343 0.0239343i
\(248\) −3.85760 + 4.01484i −0.244958 + 0.254942i
\(249\) −6.05682 + 13.5575i −0.383835 + 0.859172i
\(250\) −7.42414 8.35955i −0.469544 0.528704i
\(251\) 20.0205 + 18.0265i 1.26368 + 1.13782i 0.984083 + 0.177708i \(0.0568681\pi\)
0.279599 + 0.960117i \(0.409799\pi\)
\(252\) −1.12975 + 1.38791i −0.0711677 + 0.0874301i
\(253\) 2.10816 + 7.86776i 0.132539 + 0.494642i
\(254\) −0.431484 0.747352i −0.0270737 0.0468930i
\(255\) 2.53997 5.39692i 0.159059 0.337968i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 13.6660 + 11.0665i 0.852461 + 0.690309i 0.952455 0.304679i \(-0.0985492\pi\)
−0.0999944 + 0.994988i \(0.531882\pi\)
\(258\) 7.84325 + 4.00888i 0.488299 + 0.249582i
\(259\) 0.524705 + 1.17851i 0.0326036 + 0.0732288i
\(260\) −3.03274 1.62141i −0.188083 0.100556i
\(261\) −17.8258 + 10.2315i −1.10339 + 0.633313i
\(262\) 0.401157 + 1.04505i 0.0247836 + 0.0645634i
\(263\) 12.2719 24.0850i 0.756720 1.48515i −0.114059 0.993474i \(-0.536385\pi\)
0.870780 0.491673i \(-0.163615\pi\)
\(264\) −0.378169 + 3.55465i −0.0232747 + 0.218773i
\(265\) 1.62586 + 3.35287i 0.0998758 + 0.205965i
\(266\) −0.0428995 + 0.201826i −0.00263033 + 0.0123747i
\(267\) −6.94117 10.7182i −0.424793 0.655944i
\(268\) 2.39850 6.24832i 0.146512 0.381677i
\(269\) 6.91199 + 7.67655i 0.421432 + 0.468047i 0.916051 0.401063i \(-0.131359\pi\)
−0.494619 + 0.869110i \(0.664692\pi\)
\(270\) −5.57104 10.1963i −0.339043 0.620524i
\(271\) 1.43275 1.04096i 0.0870336 0.0632336i −0.543418 0.839463i \(-0.682870\pi\)
0.630451 + 0.776229i \(0.282870\pi\)
\(272\) −0.969210 1.19688i −0.0587670 0.0725712i
\(273\) −1.00158 + 1.23365i −0.0606186 + 0.0746638i
\(274\) 6.71438 + 3.87655i 0.405631 + 0.234191i
\(275\) −4.56589 + 9.25420i −0.275334 + 0.558049i
\(276\) −6.24832 + 2.77244i −0.376105 + 0.166881i
\(277\) −20.3693 + 10.3787i −1.22387 + 0.623594i −0.941921 0.335834i \(-0.890982\pi\)
−0.281952 + 0.959429i \(0.590982\pi\)
\(278\) 3.27068 + 3.27068i 0.196163 + 0.196163i
\(279\) −16.2753 + 3.75708i −0.974375 + 0.224930i
\(280\) 0.113228 + 1.32907i 0.00676665 + 0.0794270i
\(281\) 23.8394 + 7.74589i 1.42214 + 0.462081i 0.916281 0.400535i \(-0.131176\pi\)
0.505858 + 0.862617i \(0.331176\pi\)
\(282\) 2.68769 6.97522i 0.160050 0.415368i
\(283\) 18.3767 2.91059i 1.09238 0.173017i 0.415853 0.909432i \(-0.363483\pi\)
0.676530 + 0.736415i \(0.263483\pi\)
\(284\) 5.64623 9.77956i 0.335042 0.580310i
\(285\) −1.10794 0.753049i −0.0656289 0.0446068i
\(286\) −0.331785 + 3.15673i −0.0196189 + 0.186661i
\(287\) −0.466932 + 2.94809i −0.0275621 + 0.174021i
\(288\) −2.99628 + 0.149404i −0.176557 + 0.00880373i
\(289\) −10.8708 + 9.78812i −0.639460 + 0.575772i
\(290\) −4.25619 + 14.7165i −0.249932 + 0.864181i
\(291\) 3.68159 17.2131i 0.215818 1.00905i
\(292\) −0.181507 0.279497i −0.0106219 0.0163563i
\(293\) −3.86978 10.0811i −0.226075 0.588945i 0.772885 0.634546i \(-0.218813\pi\)
−0.998960 + 0.0456010i \(0.985480\pi\)
\(294\) −11.4434 1.21744i −0.667394 0.0710023i
\(295\) 2.91127 + 6.90221i 0.169501 + 0.401862i
\(296\) −0.879595 + 1.97560i −0.0511254 + 0.114830i
\(297\) −6.78058 + 8.30845i −0.393449 + 0.482105i
\(298\) −1.06245 + 1.63603i −0.0615461 + 0.0947726i
\(299\) −5.54499 + 2.46879i −0.320675 + 0.142774i
\(300\) −8.26695 2.58022i −0.477293 0.148969i
\(301\) −0.317104 3.01705i −0.0182776 0.173900i
\(302\) 0.928927 5.86501i 0.0534537 0.337494i
\(303\) 5.94053 + 22.2834i 0.341275 + 1.28015i
\(304\) −0.299551 + 0.172946i −0.0171804 + 0.00991913i
\(305\) 7.64871 16.3056i 0.437964 0.933658i
\(306\) −0.471287 4.59617i −0.0269417 0.262746i
\(307\) 30.1981 1.58262i 1.72350 0.0903248i 0.835303 0.549790i \(-0.185292\pi\)
0.888196 + 0.459465i \(0.151959\pi\)
\(308\) 1.09697 0.558932i 0.0625054 0.0318481i
\(309\) 12.3129 + 5.50080i 0.700458 + 0.312929i
\(310\) −6.77821 + 10.4430i −0.384977 + 0.593121i
\(311\) 21.0947i 1.19617i 0.801433 + 0.598084i \(0.204071\pi\)
−0.801433 + 0.598084i \(0.795929\pi\)
\(312\) −2.66034 + 0.136037i −0.150612 + 0.00770160i
\(313\) 0.190164 + 3.62855i 0.0107487 + 0.205098i 0.998725 + 0.0504897i \(0.0160782\pi\)
−0.987976 + 0.154608i \(0.950588\pi\)
\(314\) 18.0873 + 13.1412i 1.02073 + 0.741602i
\(315\) −1.89565 + 3.52415i −0.106808 + 0.198564i
\(316\) −7.58873 13.1441i −0.426900 0.739412i
\(317\) 7.76089 + 9.58390i 0.435895 + 0.538285i 0.947000 0.321233i \(-0.104097\pi\)
−0.511105 + 0.859518i \(0.670764\pi\)
\(318\) 2.41871 + 1.57510i 0.135635 + 0.0883271i
\(319\) 14.0623 1.47801i 0.787337 0.0827524i
\(320\) −1.52872 + 1.63188i −0.0854579 + 0.0912248i
\(321\) 1.39544 + 0.00177072i 0.0778861 + 9.88318e-5i
\(322\) 1.97447 + 1.28224i 0.110033 + 0.0714563i
\(323\) −0.290132 0.446764i −0.0161434 0.0248586i
\(324\) −7.77129 4.53950i −0.431738 0.252195i
\(325\) −7.34343 2.28175i −0.407340 0.126569i
\(326\) 1.81553 0.589903i 0.100553 0.0326717i
\(327\) 29.2216 + 1.56862i 1.61596 + 0.0867451i
\(328\) −4.19644 + 2.72520i −0.231709 + 0.150474i
\(329\) −2.51822 + 0.535265i −0.138834 + 0.0295101i
\(330\) 0.668410 + 7.96529i 0.0367948 + 0.438475i
\(331\) −4.48942 4.98601i −0.246761 0.274056i 0.607022 0.794685i \(-0.292364\pi\)
−0.853783 + 0.520629i \(0.825697\pi\)
\(332\) 6.66250 + 5.39519i 0.365652 + 0.296099i
\(333\) −5.44999 + 3.51963i −0.298658 + 0.192875i
\(334\) −0.144037 0.0151389i −0.00788137 0.000828365i
\(335\) 2.63233 14.7324i 0.143820 0.804915i
\(336\) 0.606250 + 0.836663i 0.0330737 + 0.0456437i
\(337\) 2.49297 + 15.7400i 0.135801 + 0.857411i 0.957698 + 0.287775i \(0.0929156\pi\)
−0.821897 + 0.569635i \(0.807084\pi\)
\(338\) 10.6201 0.556577i 0.577659 0.0302738i
\(339\) −1.26412 1.14112i −0.0686574 0.0619773i
\(340\) −2.63301 2.21960i −0.142795 0.120375i
\(341\) 11.2854 + 2.16421i 0.611140 + 0.117198i
\(342\) −1.03611 0.0569375i −0.0560266 0.00307882i
\(343\) 3.69510 + 7.25203i 0.199516 + 0.391573i
\(344\) 3.40288 3.77928i 0.183471 0.203765i
\(345\) −12.5520 + 8.72280i −0.675776 + 0.469620i
\(346\) −10.9906 + 19.0363i −0.590859 + 1.02340i
\(347\) 1.00895 + 0.270348i 0.0541635 + 0.0145131i 0.285799 0.958290i \(-0.407741\pi\)
−0.231636 + 0.972803i \(0.574408\pi\)
\(348\) 3.05673 + 11.4660i 0.163858 + 0.614644i
\(349\) −11.3401 15.6083i −0.607022 0.835495i 0.389306 0.921108i \(-0.372715\pi\)
−0.996328 + 0.0856139i \(0.972715\pi\)
\(350\) 0.809057 + 2.87082i 0.0432459 + 0.153452i
\(351\) −6.90552 4.02203i −0.368590 0.214680i
\(352\) 1.92678 + 0.739620i 0.102698 + 0.0394219i
\(353\) −23.4199 15.2090i −1.24651 0.809496i −0.258825 0.965924i \(-0.583335\pi\)
−0.987689 + 0.156428i \(0.950002\pi\)
\(354\) 4.69003 + 3.41661i 0.249272 + 0.181591i
\(355\) 8.27520 23.8562i 0.439202 1.26616i
\(356\) −7.01164 + 2.27822i −0.371616 + 0.120745i
\(357\) −1.23791 + 0.999838i −0.0655169 + 0.0529170i
\(358\) −3.83305 + 1.47137i −0.202583 + 0.0777643i
\(359\) −13.2769 2.82210i −0.700730 0.148945i −0.156249 0.987718i \(-0.549940\pi\)
−0.544481 + 0.838773i \(0.683274\pi\)
\(360\) −6.51668 + 1.59149i −0.343459 + 0.0838791i
\(361\) 17.2481 7.67933i 0.907793 0.404175i
\(362\) −11.0584 0.579545i −0.581215 0.0304602i
\(363\) −10.4091 + 5.28708i −0.546337 + 0.277500i
\(364\) 0.539255 + 0.742220i 0.0282646 + 0.0389029i
\(365\) −0.516434 0.537227i −0.0270314 0.0281197i
\(366\) −1.44065 13.8762i −0.0753041 0.725323i
\(367\) −7.96123 + 2.13320i −0.415573 + 0.111352i −0.460546 0.887636i \(-0.652346\pi\)
0.0449733 + 0.998988i \(0.485680\pi\)
\(368\) 0.617391 + 3.89805i 0.0321837 + 0.203200i
\(369\) −15.0110 0.0380958i −0.781440 0.00198319i
\(370\) −1.09852 + 4.70922i −0.0571091 + 0.244821i
\(371\) 0.994084i 0.0516103i
\(372\) −0.324534 + 9.63819i −0.0168263 + 0.499717i
\(373\) −14.1090 + 14.1090i −0.730538 + 0.730538i −0.970726 0.240188i \(-0.922791\pi\)
0.240188 + 0.970726i \(0.422791\pi\)
\(374\) −0.982219 + 3.02296i −0.0507893 + 0.156313i
\(375\) −19.2418 2.18019i −0.993642 0.112584i
\(376\) −3.49152 2.53674i −0.180062 0.130822i
\(377\) 2.72710 + 10.1777i 0.140453 + 0.524177i
\(378\) 0.150439 + 3.09601i 0.00773775 + 0.159241i
\(379\) 22.6519 + 2.38081i 1.16355 + 0.122294i 0.666552 0.745459i \(-0.267769\pi\)
0.496997 + 0.867752i \(0.334436\pi\)
\(380\) −0.584876 + 0.506090i −0.0300035 + 0.0259619i
\(381\) −1.42096 0.463692i −0.0727980 0.0237557i
\(382\) 0.737090 14.0645i 0.0377128 0.719603i
\(383\) −13.7608 5.28229i −0.703146 0.269912i −0.0195873 0.999808i \(-0.506235\pi\)
−0.683558 + 0.729896i \(0.739569\pi\)
\(384\) −0.362263 + 1.69374i −0.0184867 + 0.0864335i
\(385\) 2.17320 1.68993i 0.110757 0.0861270i
\(386\) −0.0115264 + 0.0258886i −0.000586676 + 0.00131770i
\(387\) 14.7467 3.91128i 0.749616 0.198821i
\(388\) −9.05507 4.61379i −0.459702 0.234230i
\(389\) 28.0126 + 12.4720i 1.42029 + 0.632355i 0.966011 0.258502i \(-0.0832289\pi\)
0.454283 + 0.890858i \(0.349896\pi\)
\(390\) −5.78461 + 1.42049i −0.292915 + 0.0719292i
\(391\) −5.94536 + 1.26373i −0.300670 + 0.0639093i
\(392\) −2.38105 + 6.20285i −0.120261 + 0.313291i
\(393\) 1.72642 + 0.882414i 0.0870862 + 0.0445119i
\(394\) −6.73182 + 0.707542i −0.339144 + 0.0356455i
\(395\) −22.2068 25.6639i −1.11735 1.29129i
\(396\) 3.62659 + 5.01831i 0.182243 + 0.252179i
\(397\) −1.39074 + 5.19032i −0.0697993 + 0.260495i −0.992004 0.126208i \(-0.959719\pi\)
0.922204 + 0.386703i \(0.126386\pi\)
\(398\) −17.4054 + 4.66376i −0.872454 + 0.233773i
\(399\) 0.178298 + 0.309729i 0.00892609 + 0.0155058i
\(400\) −2.66889 + 4.22812i −0.133444 + 0.211406i
\(401\) 7.99284 + 2.59703i 0.399143 + 0.129690i 0.501709 0.865037i \(-0.332705\pi\)
−0.102565 + 0.994726i \(0.532705\pi\)
\(402\) −4.14060 10.8277i −0.206514 0.540035i
\(403\) −0.277306 + 8.55846i −0.0138136 + 0.426327i
\(404\) 13.3147 0.662430
\(405\) −18.9795 6.69169i −0.943099 0.332513i
\(406\) 2.73467 3.03716i 0.135719 0.150732i
\(407\) 4.40828 0.698203i 0.218510 0.0346086i
\(408\) −2.63414 0.420634i −0.130409 0.0208245i
\(409\) 3.60364 2.08056i 0.178188 0.102877i −0.408253 0.912869i \(-0.633862\pi\)
0.586441 + 0.809992i \(0.300528\pi\)
\(410\) −8.06606 + 7.75387i −0.398354 + 0.382936i
\(411\) 13.1389 2.77533i 0.648092 0.136897i
\(412\) 4.89991 6.05088i 0.241401 0.298106i
\(413\) 0.104590 1.99570i 0.00514655 0.0982020i
\(414\) −4.84317 + 10.8041i −0.238029 + 0.530990i
\(415\) 16.9055 + 9.03826i 0.829857 + 0.443671i
\(416\) −0.319758 + 1.50434i −0.0156774 + 0.0737565i
\(417\) 7.99999 + 0.429442i 0.391761 + 0.0210298i
\(418\) 0.636064 + 0.324091i 0.0311109 + 0.0158518i
\(419\) −0.209539 0.644894i −0.0102366 0.0315051i 0.945808 0.324727i \(-0.105272\pi\)
−0.956044 + 0.293222i \(0.905272\pi\)
\(420\) 1.68408 + 1.58164i 0.0821749 + 0.0771761i
\(421\) −1.32552 0.281747i −0.0646017 0.0137315i 0.175497 0.984480i \(-0.443847\pi\)
−0.240099 + 0.970748i \(0.577180\pi\)
\(422\) −11.7943 + 18.1616i −0.574137 + 0.884093i
\(423\) −4.60920 12.0991i −0.224107 0.588277i
\(424\) 1.23841 1.11507i 0.0601425 0.0541525i
\(425\) −6.71789 3.76390i −0.325865 0.182576i
\(426\) −4.04229 19.1369i −0.195850 0.927184i
\(427\) −3.73400 + 3.02373i −0.180701 + 0.146329i
\(428\) 0.208520 0.778208i 0.0100792 0.0376161i
\(429\) 3.22584 + 4.45185i 0.155745 + 0.214937i
\(430\) 5.87898 9.73397i 0.283510 0.469414i
\(431\) −7.87392 7.08971i −0.379274 0.341499i 0.457341 0.889291i \(-0.348802\pi\)
−0.836615 + 0.547792i \(0.815469\pi\)
\(432\) −3.68819 + 3.66022i −0.177448 + 0.176102i
\(433\) 28.4327 28.4327i 1.36639 1.36639i 0.500857 0.865530i \(-0.333018\pi\)
0.865530 0.500857i \(-0.166982\pi\)
\(434\) 2.84263 1.71777i 0.136451 0.0824558i
\(435\) 11.5472 + 23.8900i 0.553646 + 1.14544i
\(436\) 5.22096 16.0685i 0.250039 0.769540i
\(437\) 0.0714444 + 1.36324i 0.00341765 + 0.0652127i
\(438\) −0.557368 0.150105i −0.0266321 0.00717227i
\(439\) 29.7222 + 17.1601i 1.41856 + 0.819008i 0.996173 0.0874057i \(-0.0278577\pi\)
0.422391 + 0.906414i \(0.361191\pi\)
\(440\) 4.54298 + 0.811726i 0.216578 + 0.0386975i
\(441\) −16.1554 + 11.6750i −0.769304 + 0.555954i
\(442\) −2.33942 0.370528i −0.111275 0.0176242i
\(443\) −14.1229 + 17.4404i −0.671001 + 0.828617i −0.992999 0.118123i \(-0.962312\pi\)
0.321998 + 0.946740i \(0.395645\pi\)
\(444\) 1.15296 + 3.56381i 0.0547169 + 0.169131i
\(445\) −14.4366 + 7.95939i −0.684360 + 0.377311i
\(446\) −3.40468 16.0178i −0.161216 0.758463i
\(447\) 0.524323 + 3.33785i 0.0247996 + 0.157875i
\(448\) 0.556909 0.213777i 0.0263115 0.0101000i
\(449\) 6.61531 + 20.3598i 0.312196 + 0.960839i 0.976893 + 0.213727i \(0.0685603\pi\)
−0.664698 + 0.747112i \(0.731440\pi\)
\(450\) −13.6392 + 6.24267i −0.642960 + 0.294282i
\(451\) 9.43407 + 4.20032i 0.444233 + 0.197785i
\(452\) −0.824596 + 0.535499i −0.0387857 + 0.0251878i
\(453\) −5.59073 8.63293i −0.262675 0.405611i
\(454\) 5.86915 + 13.1823i 0.275453 + 0.618677i
\(455\) 1.49714 + 1.40250i 0.0701871 + 0.0657501i
\(456\) −0.185856 + 0.569545i −0.00870349 + 0.0266714i
\(457\) 16.9253 + 2.68070i 0.791730 + 0.125398i 0.539185 0.842187i \(-0.318732\pi\)
0.252545 + 0.967585i \(0.418732\pi\)
\(458\) −2.63005 + 2.12978i −0.122894 + 0.0995179i
\(459\) −5.92662 5.37735i −0.276631 0.250993i
\(460\) 2.99941 + 8.29960i 0.139848 + 0.386971i
\(461\) −12.7024 + 17.4833i −0.591607 + 0.814278i −0.994908 0.100790i \(-0.967863\pi\)
0.403300 + 0.915068i \(0.367863\pi\)
\(462\) 0.766716 1.98981i 0.0356709 0.0925745i
\(463\) 6.94105 + 13.6226i 0.322578 + 0.633095i 0.994170 0.107827i \(-0.0343891\pi\)
−0.671592 + 0.740921i \(0.734389\pi\)
\(464\) 6.85112 0.318055
\(465\) 3.35138 + 21.3018i 0.155416 + 0.987849i
\(466\) 10.8676 0.503430
\(467\) −13.3151 26.1324i −0.616150 1.20926i −0.962532 0.271169i \(-0.912590\pi\)
0.346382 0.938094i \(-0.387410\pi\)
\(468\) −3.27076 + 3.25420i −0.151191 + 0.150425i
\(469\) −2.34673 + 3.22999i −0.108362 + 0.149147i
\(470\) −8.73686 4.09832i −0.403001 0.189042i
\(471\) 38.5168 3.99887i 1.77476 0.184258i
\(472\) 2.60352 2.10829i 0.119837 0.0970419i
\(473\) −10.3666 1.64190i −0.476655 0.0754948i
\(474\) −24.9912 8.15520i −1.14788 0.374581i
\(475\) −1.07096 + 1.35797i −0.0491391 + 0.0623078i
\(476\) 0.373673 + 0.839284i 0.0171273 + 0.0384685i
\(477\) 4.93975 0.769534i 0.226176 0.0352345i
\(478\) 5.90722 3.83619i 0.270190 0.175463i
\(479\) −24.7758 11.0309i −1.13203 0.504014i −0.246757 0.969077i \(-0.579365\pi\)
−0.885277 + 0.465063i \(0.846032\pi\)
\(480\) −0.0813287 + 3.87213i −0.00371213 + 0.176738i
\(481\) 1.02777 + 3.16314i 0.0468621 + 0.144227i
\(482\) −9.85093 + 3.78142i −0.448697 + 0.172239i
\(483\) 4.02835 0.632789i 0.183296 0.0287929i
\(484\) 1.40143 + 6.59320i 0.0637013 + 0.299691i
\(485\) −21.8299 6.31350i −0.991247 0.286681i
\(486\) −15.2681 + 3.14422i −0.692574 + 0.142625i
\(487\) −11.8293 + 14.6080i −0.536036 + 0.661950i −0.971162 0.238420i \(-0.923371\pi\)
0.435126 + 0.900370i \(0.356704\pi\)
\(488\) −7.95535 1.26000i −0.360122 0.0570377i
\(489\) 1.65684 2.86135i 0.0749251 0.129395i
\(490\) −2.61318 + 14.6252i −0.118051 + 0.660697i
\(491\) −9.38202 5.41671i −0.423405 0.244453i 0.273128 0.961978i \(-0.411942\pi\)
−0.696533 + 0.717525i \(0.745275\pi\)
\(492\) −2.25371 + 8.36846i −0.101605 + 0.377279i
\(493\) 0.552215 + 10.5369i 0.0248705 + 0.474558i
\(494\) −0.164386 + 0.505929i −0.00739609 + 0.0227628i
\(495\) 10.0798 + 9.49077i 0.453055 + 0.426578i
\(496\) 5.32856 + 1.61445i 0.239259 + 0.0724910i
\(497\) −4.76328 + 4.76328i −0.213662 + 0.213662i
\(498\) 14.8296 0.758317i 0.664529 0.0339810i
\(499\) −3.75964 3.38519i −0.168304 0.151542i 0.580674 0.814136i \(-0.302789\pi\)
−0.748979 + 0.662594i \(0.769456\pi\)
\(500\) −4.07792 + 10.4101i −0.182370 + 0.465555i
\(501\) −0.203132 + 0.147191i −0.00907527 + 0.00657599i
\(502\) 6.97264 26.0223i 0.311204 1.16143i
\(503\) −26.5030 + 21.4617i −1.18171 + 0.956931i −0.999653 0.0263568i \(-0.991609\pi\)
−0.182059 + 0.983288i \(0.558276\pi\)
\(504\) 1.74953 + 0.376518i 0.0779304 + 0.0167714i
\(505\) 29.2384 5.61426i 1.30109 0.249832i
\(506\) 6.05314 5.45027i 0.269095 0.242294i
\(507\) 13.0413 13.0083i 0.579185 0.577717i
\(508\) −0.470006 + 0.723745i −0.0208531 + 0.0321110i
\(509\) 32.2661 + 6.85837i 1.43017 + 0.303992i 0.856946 0.515407i \(-0.172359\pi\)
0.573224 + 0.819399i \(0.305692\pi\)
\(510\) −5.96181 + 0.187020i −0.263993 + 0.00828138i
\(511\) 0.0614328 + 0.189071i 0.00271763 + 0.00836399i
\(512\) 0.891007 + 0.453990i 0.0393773 + 0.0200637i
\(513\) −1.40107 + 1.12576i −0.0618586 + 0.0497034i
\(514\) 3.65609 17.2006i 0.161263 0.758684i
\(515\) 8.20854 15.3535i 0.361712 0.676558i
\(516\) 0.0111772 8.80837i 0.000492048 0.387767i
\(517\) −0.466162 + 8.89490i −0.0205018 + 0.391197i
\(518\) 0.811846 1.00255i 0.0356705 0.0440494i
\(519\) 7.86847 + 37.2506i 0.345388 + 1.63512i
\(520\) −0.0678519 + 3.43830i −0.00297550 + 0.150779i
\(521\) −19.1712 + 11.0685i −0.839907 + 0.484920i −0.857233 0.514929i \(-0.827818\pi\)
0.0173257 + 0.999850i \(0.494485\pi\)
\(522\) 17.2090 + 11.2379i 0.753219 + 0.491869i
\(523\) 3.80611 0.602829i 0.166430 0.0263599i −0.0726634 0.997357i \(-0.523150\pi\)
0.239093 + 0.970997i \(0.423150\pi\)
\(524\) 0.749024 0.831876i 0.0327213 0.0363407i
\(525\) 4.36508 + 2.76309i 0.190508 + 0.120591i
\(526\) −27.0313 −1.17862
\(527\) −2.05350 + 8.32534i −0.0894519 + 0.362658i
\(528\) 3.33890 1.27682i 0.145307 0.0555666i
\(529\) −7.06067 2.29415i −0.306985 0.0997456i
\(530\) 2.24931 2.97082i 0.0977036 0.129044i
\(531\) 9.99790 1.02517i 0.433872 0.0444888i
\(532\) 0.199304 0.0534034i 0.00864094 0.00231533i
\(533\) −1.99172 + 7.43320i −0.0862710 + 0.321968i
\(534\) −6.39878 + 11.0506i −0.276902 + 0.478206i
\(535\) 0.129761 1.79683i 0.00561006 0.0776838i
\(536\) −6.65619 + 0.699594i −0.287504 + 0.0302178i
\(537\) −3.23653 + 6.33217i −0.139667 + 0.273253i
\(538\) 3.70187 9.64371i 0.159599 0.415770i
\(539\) 13.4129 2.85101i 0.577736 0.122802i
\(540\) −6.55573 + 9.59283i −0.282114 + 0.412810i
\(541\) 17.2160 + 7.66506i 0.740174 + 0.329547i 0.741953 0.670452i \(-0.233900\pi\)
−0.00177941 + 0.999998i \(0.500566\pi\)
\(542\) −1.57796 0.804008i −0.0677790 0.0345351i
\(543\) −14.9209 + 12.0514i −0.640318 + 0.517175i
\(544\) −0.626411 + 1.40694i −0.0268572 + 0.0603222i
\(545\) 4.68955 37.4871i 0.200878 1.60577i
\(546\) 1.55390 + 0.332353i 0.0665007 + 0.0142234i
\(547\) 17.0649 + 6.55061i 0.729644 + 0.280084i 0.694694 0.719305i \(-0.255540\pi\)
0.0349495 + 0.999389i \(0.488873\pi\)
\(548\) 0.405766 7.74248i 0.0173335 0.330742i
\(549\) −17.9159 16.2141i −0.764633 0.692001i
\(550\) 10.3184 0.133081i 0.439979 0.00567458i
\(551\) 2.35677 + 0.247706i 0.100402 + 0.0105526i
\(552\) 5.30694 + 4.30864i 0.225878 + 0.183388i
\(553\) 2.34330 + 8.74531i 0.0996472 + 0.371888i
\(554\) 18.4949 + 13.4374i 0.785775 + 0.570899i
\(555\) 4.03455 + 7.33981i 0.171257 + 0.311558i
\(556\) 1.42934 4.39906i 0.0606176 0.186562i
\(557\) −0.907582 + 0.907582i −0.0384555 + 0.0384555i −0.726073 0.687618i \(-0.758657\pi\)
0.687618 + 0.726073i \(0.258657\pi\)
\(558\) 10.7364 + 12.7957i 0.454508 + 0.541685i
\(559\) 7.82129i 0.330805i
\(560\) 1.13280 0.704271i 0.0478697 0.0297609i
\(561\) 2.23285 + 5.03224i 0.0942711 + 0.212461i
\(562\) −3.92122 24.7576i −0.165407 1.04434i
\(563\) −38.3317 + 10.2709i −1.61549 + 0.432869i −0.949672 0.313247i \(-0.898583\pi\)
−0.665816 + 0.746116i \(0.731917\pi\)
\(564\) −7.43515 + 0.771928i −0.313076 + 0.0325040i
\(565\) −1.58497 + 1.52363i −0.0666804 + 0.0640996i
\(566\) −10.9362 15.0524i −0.459683 0.632700i
\(567\) 3.77698 + 3.81551i 0.158618 + 0.160237i
\(568\) −11.2770 0.591002i −0.473172 0.0247979i
\(569\) 6.05889 2.69759i 0.254002 0.113089i −0.275786 0.961219i \(-0.588938\pi\)
0.529788 + 0.848130i \(0.322271\pi\)
\(570\) −0.167976 + 1.32906i −0.00703573 + 0.0556682i
\(571\) 16.4213 + 3.49045i 0.687208 + 0.146071i 0.538266 0.842775i \(-0.319080\pi\)
0.148943 + 0.988846i \(0.452413\pi\)
\(572\) 2.96329 1.13750i 0.123901 0.0475613i
\(573\) −15.3275 18.9771i −0.640316 0.792779i
\(574\) 2.83875 0.922367i 0.118487 0.0384989i
\(575\) 10.0862 + 16.9608i 0.420623 + 0.707314i
\(576\) 1.49340 + 2.60187i 0.0622251 + 0.108411i
\(577\) −17.9730 11.6718i −0.748227 0.485904i 0.113335 0.993557i \(-0.463847\pi\)
−0.861562 + 0.507653i \(0.830513\pi\)
\(578\) 13.6565 + 5.24225i 0.568037 + 0.218049i
\(579\) 0.0151085 + 0.0467008i 0.000627889 + 0.00194082i
\(580\) 15.0447 2.88884i 0.624699 0.119953i
\(581\) −3.00598 4.13737i −0.124709 0.171647i
\(582\) −17.0084 + 4.53425i −0.705020 + 0.187951i
\(583\) −3.32211 0.890157i −0.137588 0.0368665i
\(584\) −0.166631 + 0.288613i −0.00689523 + 0.0119429i
\(585\) −5.81026 + 8.52521i −0.240225 + 0.352474i
\(586\) −7.22550 + 8.02473i −0.298483 + 0.331499i
\(587\) 19.1525 + 37.5890i 0.790510 + 1.55146i 0.833585 + 0.552391i \(0.186285\pi\)
−0.0430751 + 0.999072i \(0.513715\pi\)
\(588\) 4.11047 + 10.7489i 0.169513 + 0.443276i
\(589\) 1.77464 + 0.748024i 0.0731227 + 0.0308218i
\(590\) 4.82823 5.72750i 0.198775 0.235798i
\(591\) −7.85599 + 8.70272i −0.323152 + 0.357982i
\(592\) 2.15960 0.113180i 0.0887591 0.00465167i
\(593\) −5.38415 33.9942i −0.221101 1.39597i −0.809365 0.587306i \(-0.800189\pi\)
0.588264 0.808669i \(-0.299811\pi\)
\(594\) 10.4812 + 2.26959i 0.430049 + 0.0931222i
\(595\) 1.17446 + 1.68546i 0.0481482 + 0.0690972i
\(596\) 1.94006 + 0.203908i 0.0794678 + 0.00835240i
\(597\) −17.0317 + 26.1537i −0.697059 + 1.07040i
\(598\) 4.71708 + 3.81981i 0.192896 + 0.156204i
\(599\) −22.7321 25.2466i −0.928809 1.03155i −0.999420 0.0340435i \(-0.989162\pi\)
0.0706109 0.997504i \(-0.477505\pi\)
\(600\) 1.45413 + 8.53730i 0.0593645 + 0.348534i
\(601\) 23.1130 4.91281i 0.942797 0.200398i 0.289224 0.957261i \(-0.406603\pi\)
0.653573 + 0.756864i \(0.273269\pi\)
\(602\) −2.54425 + 1.65225i −0.103696 + 0.0673408i
\(603\) −17.8669 9.16085i −0.727598 0.373059i
\(604\) −5.64749 + 1.83498i −0.229793 + 0.0746643i
\(605\) 5.85755 + 13.8874i 0.238143 + 0.564604i
\(606\) 17.1577 15.4095i 0.696986 0.625969i
\(607\) −18.2229 28.0609i −0.739647 1.13896i −0.985504 0.169650i \(-0.945736\pi\)
0.245858 0.969306i \(-0.420930\pi\)
\(608\) 0.290089 + 0.188386i 0.0117647 + 0.00764007i
\(609\) 0.00898238 7.07871i 0.000363984 0.286844i
\(610\) −18.0009 + 0.587546i −0.728834 + 0.0237890i
\(611\) −6.60107 + 0.693801i −0.267051 + 0.0280682i
\(612\) −3.88126 + 2.50654i −0.156891 + 0.101321i
\(613\) −3.23461 3.99441i −0.130645 0.161333i 0.707626 0.706587i \(-0.249766\pi\)
−0.838270 + 0.545255i \(0.816433\pi\)
\(614\) −15.1198 26.1882i −0.610185 1.05687i
\(615\) −1.42039 + 19.3270i −0.0572756 + 0.779341i
\(616\) −0.996023 0.723653i −0.0401309 0.0291568i
\(617\) −0.445657 8.50365i −0.0179415 0.342344i −0.992821 0.119611i \(-0.961835\pi\)
0.974879 0.222733i \(-0.0714979\pi\)
\(618\) −0.688703 13.4682i −0.0277037 0.541771i
\(619\) 28.2955i 1.13729i −0.822582 0.568647i \(-0.807467\pi\)
0.822582 0.568647i \(-0.192533\pi\)
\(620\) 12.3820 + 1.29842i 0.497273 + 0.0521458i
\(621\) 6.26283 + 19.5276i 0.251319 + 0.783617i
\(622\) 18.7955 9.57677i 0.753630 0.383994i
\(623\) 4.39187 0.230168i 0.175957 0.00922150i
\(624\) 1.32898 + 2.30862i 0.0532017 + 0.0924186i
\(625\) −4.56539 + 24.5796i −0.182616 + 0.983184i
\(626\) 3.14673 1.81677i 0.125769 0.0726126i
\(627\) 1.19474 0.318504i 0.0477131 0.0127198i
\(628\) 3.49744 22.0819i 0.139563 0.881165i
\(629\) 0.348137 + 3.31230i 0.0138811 + 0.132070i
\(630\) 4.00065 + 0.0891071i 0.159390 + 0.00355011i
\(631\) −37.2499 + 16.5847i −1.48290 + 0.660228i −0.979060 0.203572i \(-0.934745\pi\)
−0.503835 + 0.863800i \(0.668078\pi\)
\(632\) −8.26624 + 12.7289i −0.328813 + 0.506328i
\(633\) 5.82053 + 37.0536i 0.231345 + 1.47275i
\(634\) 5.01595 11.2660i 0.199209 0.447430i
\(635\) −0.726935 + 1.78749i −0.0288475 + 0.0709345i
\(636\) 0.305350 2.87017i 0.0121079 0.113810i
\(637\) 3.66194 + 9.53969i 0.145091 + 0.377976i
\(638\) −7.70105 11.8586i −0.304888 0.469486i
\(639\) −27.3568 19.9821i −1.08222 0.790481i
\(640\) 2.14804 + 0.621239i 0.0849086 + 0.0245566i
\(641\) 6.80948 6.13129i 0.268958 0.242171i −0.523604 0.851962i \(-0.675413\pi\)
0.792563 + 0.609790i \(0.208746\pi\)
\(642\) −0.631940 1.24415i −0.0249407 0.0491028i
\(643\) −4.84718 + 30.6039i −0.191154 + 1.20690i 0.686328 + 0.727292i \(0.259221\pi\)
−0.877483 + 0.479608i \(0.840779\pi\)
\(644\) 0.246090 2.34139i 0.00969732 0.0922638i
\(645\) −3.68959 19.3475i −0.145278 0.761806i
\(646\) −0.266352 + 0.461336i −0.0104795 + 0.0181510i
\(647\) −22.9516 + 3.63518i −0.902322 + 0.142914i −0.590322 0.807168i \(-0.700999\pi\)
−0.312001 + 0.950082i \(0.600999\pi\)
\(648\) −0.516636 + 8.98516i −0.0202954 + 0.352970i
\(649\) −6.57574 2.13659i −0.258120 0.0838684i
\(650\) 1.30079 + 7.57894i 0.0510213 + 0.297271i
\(651\) 1.67507 5.50345i 0.0656512 0.215697i
\(652\) −1.34984 1.34984i −0.0528639 0.0528639i
\(653\) 18.5541 9.45379i 0.726078 0.369955i −0.0515580 0.998670i \(-0.516419\pi\)
0.777636 + 0.628715i \(0.216419\pi\)
\(654\) −11.8687 26.7488i −0.464102 1.04596i
\(655\) 1.29405 2.14259i 0.0505628 0.0837180i
\(656\) 4.33331 + 2.50184i 0.169187 + 0.0976804i
\(657\) −0.891964 + 0.451631i −0.0347988 + 0.0176198i
\(658\) 1.62017 + 2.00075i 0.0631609 + 0.0779972i
\(659\) −8.37551 + 6.08516i −0.326263 + 0.237044i −0.738843 0.673877i \(-0.764628\pi\)
0.412580 + 0.910921i \(0.364628\pi\)
\(660\) 6.79367 4.21172i 0.264443 0.163941i
\(661\) −22.9474 25.4857i −0.892551 0.991278i 0.107445 0.994211i \(-0.465733\pi\)
−0.999996 + 0.00293299i \(0.999066\pi\)
\(662\) −2.40441 + 6.26370i −0.0934501 + 0.243446i
\(663\) −3.44349 + 2.23002i −0.133734 + 0.0866068i
\(664\) 1.78244 8.38570i 0.0691719 0.325428i
\(665\) 0.415144 0.201310i 0.0160986 0.00780646i
\(666\) 5.61026 + 3.25810i 0.217393 + 0.126249i
\(667\) 12.2754 24.0919i 0.475306 0.932841i
\(668\) 0.0519027 + 0.135211i 0.00200817 + 0.00523147i
\(669\) −22.9253 16.7007i −0.886342 0.645685i
\(670\) −14.3217 + 4.34292i −0.553295 + 0.167782i
\(671\) 6.76134 + 15.1862i 0.261018 + 0.586257i
\(672\) 0.470240 0.920010i 0.0181399 0.0354902i
\(673\) −6.08185 4.92499i −0.234438 0.189844i 0.504901 0.863177i \(-0.331529\pi\)
−0.739340 + 0.673333i \(0.764862\pi\)
\(674\) 12.8926 9.36704i 0.496606 0.360805i
\(675\) −10.3511 + 23.8297i −0.398416 + 0.917205i
\(676\) −5.31735 9.20992i −0.204514 0.354228i
\(677\) −9.64644 36.0010i −0.370743 1.38363i −0.859466 0.511192i \(-0.829204\pi\)
0.488724 0.872439i \(-0.337463\pi\)
\(678\) −0.442852 + 1.64440i −0.0170076 + 0.0631526i
\(679\) 4.50523 + 4.05653i 0.172895 + 0.155675i
\(680\) −0.782317 + 3.35371i −0.0300005 + 0.128609i
\(681\) 22.8195 + 10.1946i 0.874447 + 0.390659i
\(682\) −3.19516 11.0379i −0.122349 0.422664i
\(683\) 27.5893 + 27.5893i 1.05567 + 1.05567i 0.998356 + 0.0573177i \(0.0182548\pi\)
0.0573177 + 0.998356i \(0.481745\pi\)
\(684\) 0.419654 + 0.949032i 0.0160459 + 0.0362872i
\(685\) −2.37365 17.1732i −0.0906925 0.656154i
\(686\) 4.78407 6.58471i 0.182657 0.251405i
\(687\) −0.924316 + 5.78835i −0.0352649 + 0.220840i
\(688\) −4.91224 1.31623i −0.187277 0.0501808i
\(689\) 0.267897 2.54887i 0.0102061 0.0971042i
\(690\) 13.4706 + 7.22383i 0.512815 + 0.275007i
\(691\) −1.55915 14.8344i −0.0593130 0.564325i −0.983312 0.181930i \(-0.941766\pi\)
0.923999 0.382396i \(-0.124901\pi\)
\(692\) 21.9511 + 1.15041i 0.834455 + 0.0437320i
\(693\) −1.31486 3.45149i −0.0499475 0.131111i
\(694\) −0.217173 1.02172i −0.00824379 0.0387840i
\(695\) 1.28386 10.2628i 0.0486995 0.389291i
\(696\) 8.82859 7.92904i 0.334647 0.300549i
\(697\) −3.49850 + 6.86620i −0.132515 + 0.260076i
\(698\) −8.75882 + 17.1901i −0.331526 + 0.650657i
\(699\) 14.0043 12.5774i 0.529691 0.475720i
\(700\) 2.19062 2.02420i 0.0827976 0.0765076i
\(701\) 7.15334 + 33.6538i 0.270178 + 1.27109i 0.878633 + 0.477498i \(0.158456\pi\)
−0.608455 + 0.793588i \(0.708210\pi\)
\(702\) −0.448616 + 7.97883i −0.0169319 + 0.301142i
\(703\) 0.746989 + 0.0391481i 0.0281732 + 0.00147650i
\(704\) −0.215732 2.05255i −0.00813070 0.0773584i
\(705\) −16.0017 + 4.83022i −0.602660 + 0.181917i
\(706\) −2.91896 + 27.7720i −0.109856 + 1.04521i
\(707\) −7.67197 2.05570i −0.288534 0.0773124i
\(708\) 0.914991 5.72996i 0.0343875 0.215345i
\(709\) 8.00773 11.0217i 0.300737 0.413928i −0.631728 0.775190i \(-0.717654\pi\)
0.932464 + 0.361262i \(0.117654\pi\)
\(710\) −25.0129 + 3.45724i −0.938718 + 0.129748i
\(711\) −41.6428 + 18.4141i −1.56173 + 0.690582i
\(712\) 5.21313 + 5.21313i 0.195370 + 0.195370i
\(713\) 15.2246 15.8451i 0.570165 0.593404i
\(714\) 1.45286 + 0.649065i 0.0543719 + 0.0242906i
\(715\) 6.02760 3.74740i 0.225420 0.140145i
\(716\) 3.05117 + 2.74728i 0.114027 + 0.102671i
\(717\) 3.17249 11.7801i 0.118479 0.439935i
\(718\) 3.51310 + 13.1111i 0.131108 + 0.489300i
\(719\) −14.9722 25.9326i −0.558368 0.967122i −0.997633 0.0687643i \(-0.978094\pi\)
0.439265 0.898358i \(-0.355239\pi\)
\(720\) 4.37654 + 5.08388i 0.163104 + 0.189465i
\(721\) −3.75756 + 2.73003i −0.139939 + 0.101672i
\(722\) −14.6728 11.8818i −0.546065 0.442195i
\(723\) −8.31788 + 16.2737i −0.309345 + 0.605224i
\(724\) 4.50402 + 10.1162i 0.167391 + 0.375965i
\(725\) 31.8194 12.6875i 1.18174 0.471203i
\(726\) 9.43646 + 6.87430i 0.350220 + 0.255129i
\(727\) −12.2280 31.8551i −0.453513 1.18144i −0.949682 0.313215i \(-0.898594\pi\)
0.496170 0.868226i \(-0.334739\pi\)
\(728\) 0.416507 0.817440i 0.0154368 0.0302963i
\(729\) −16.0360 + 21.7220i −0.593928 + 0.804518i
\(730\) −0.244217 + 0.704042i −0.00903887 + 0.0260578i
\(731\) 1.62840 7.66101i 0.0602285 0.283353i
\(732\) −11.7098 + 7.58332i −0.432806 + 0.280287i
\(733\) 7.08226 18.4499i 0.261589 0.681463i −0.738386 0.674379i \(-0.764412\pi\)
0.999975 0.00708468i \(-0.00225514\pi\)
\(734\) 5.51502 + 6.12505i 0.203563 + 0.226080i
\(735\) 13.5588 + 21.8708i 0.500122 + 0.806716i
\(736\) 3.19290 2.31978i 0.117692 0.0855081i
\(737\) 8.69286 + 10.7348i 0.320206 + 0.395421i
\(738\) 6.78090 + 13.3922i 0.249608 + 0.492973i
\(739\) −2.28171 1.31734i −0.0839339 0.0484593i 0.457446 0.889238i \(-0.348764\pi\)
−0.541380 + 0.840778i \(0.682098\pi\)
\(740\) 4.69466 1.15916i 0.172579 0.0426114i
\(741\) 0.373695 + 0.842207i 0.0137280 + 0.0309393i
\(742\) −0.885735 + 0.451305i −0.0325164 + 0.0165679i
\(743\) 27.0117 + 27.0117i 0.990964 + 0.990964i 0.999960 0.00899564i \(-0.00286344\pi\)
−0.00899564 + 0.999960i \(0.502863\pi\)
\(744\) 8.73502 4.08648i 0.320242 0.149818i
\(745\) 4.34625 0.370271i 0.159234 0.0135657i
\(746\) 18.9766 + 6.16588i 0.694783 + 0.225749i
\(747\) 18.2323 18.1400i 0.667084 0.663706i
\(748\) 3.13939 0.497231i 0.114788 0.0181806i
\(749\) −0.240300 + 0.416212i −0.00878038 + 0.0152081i
\(750\) 6.79303 + 18.1344i 0.248046 + 0.662173i
\(751\) −3.01392 + 28.6755i −0.109979 + 1.04638i 0.790790 + 0.612087i \(0.209670\pi\)
−0.900770 + 0.434297i \(0.856997\pi\)
\(752\) −0.675134 + 4.26263i −0.0246196 + 0.155442i
\(753\) −21.1313 41.6029i −0.770066 1.51609i
\(754\) 7.83029 7.05043i 0.285163 0.256761i
\(755\) −11.6279 + 6.41085i −0.423182 + 0.233315i
\(756\) 2.69027 1.53960i 0.0978440 0.0559947i
\(757\) −10.2147 15.7292i −0.371259 0.571689i 0.602825 0.797873i \(-0.294042\pi\)
−0.974085 + 0.226184i \(0.927375\pi\)
\(758\) −8.16242 21.2638i −0.296472 0.772337i
\(759\) 1.49250 14.0289i 0.0541743 0.509217i
\(760\) 0.716457 + 0.291368i 0.0259886 + 0.0105690i
\(761\) −19.4906 + 43.7767i −0.706535 + 1.58690i 0.0995012 + 0.995037i \(0.468275\pi\)
−0.806036 + 0.591866i \(0.798391\pi\)
\(762\) 0.231950 + 1.47660i 0.00840265 + 0.0534914i
\(763\) −5.48920 + 8.45263i −0.198723 + 0.306006i
\(764\) −12.8662 + 5.72841i −0.465483 + 0.207246i
\(765\) −7.46615 + 7.14081i −0.269939 + 0.258176i
\(766\) 1.54073 + 14.6591i 0.0556690 + 0.529655i
\(767\) 0.805998 5.08887i 0.0291029 0.183748i
\(768\) 1.67360 0.446164i 0.0603908 0.0160996i
\(769\) 22.1589 12.7935i 0.799071 0.461344i −0.0440751 0.999028i \(-0.514034\pi\)
0.843146 + 0.537684i \(0.180701\pi\)
\(770\) −2.49235 1.16912i −0.0898182 0.0421323i
\(771\) −15.1954 26.3966i −0.547250 0.950649i
\(772\) 0.0282998 0.00148313i 0.00101853 5.33790e-5i
\(773\) 19.0319 9.69726i 0.684531 0.348786i −0.0768936 0.997039i \(-0.524500\pi\)
0.761425 + 0.648253i \(0.224500\pi\)
\(774\) −10.1798 11.3637i −0.365906 0.408460i
\(775\) 27.7378 2.36973i 0.996370 0.0851233i
\(776\) 10.1627i 0.364821i
\(777\) −0.114108 2.23149i −0.00409361 0.0800543i
\(778\) −1.60481 30.6215i −0.0575351 1.09784i
\(779\) 1.40019 + 1.01730i 0.0501671 + 0.0364485i
\(780\) 3.89182 + 4.50923i 0.139350 + 0.161456i
\(781\) 11.6530 + 20.1836i 0.416978 + 0.722227i
\(782\) 3.82513 + 4.72364i 0.136786 + 0.168917i
\(783\) 35.1821 5.43510i 1.25731 0.194234i
\(784\) 6.60775 0.694503i 0.235991 0.0248037i
\(785\) −1.63087 49.9656i −0.0582082 1.78335i
\(786\) 0.00246027 1.93886i 8.77548e−5 0.0691567i
\(787\) −27.9090 18.1243i −0.994848 0.646062i −0.0589235 0.998263i \(-0.518767\pi\)
−0.935925 + 0.352201i \(0.885433\pi\)
\(788\) 3.68661 + 5.67688i 0.131330 + 0.202230i
\(789\) −34.8334 + 31.2842i −1.24010 + 1.11375i
\(790\) −12.7850 + 31.4376i −0.454870 + 1.11850i
\(791\) 0.557813 0.181244i 0.0198335 0.00644431i
\(792\) 2.82491 5.50958i 0.100379 0.195774i
\(793\) −10.3890 + 6.74670i −0.368924 + 0.239582i
\(794\) 5.25599 1.11720i 0.186528 0.0396478i
\(795\) −0.539702 6.43150i −0.0191413 0.228102i
\(796\) 12.0573 + 13.3910i 0.427361 + 0.474632i
\(797\) 13.9758 + 11.3174i 0.495048 + 0.400882i 0.844070 0.536233i \(-0.180153\pi\)
−0.349023 + 0.937114i \(0.613486\pi\)
\(798\) 0.195025 0.299479i 0.00690380 0.0106014i
\(799\) −6.61025 0.694765i −0.233854 0.0245790i
\(800\) 4.97894 + 0.458471i 0.176032 + 0.0162094i
\(801\) 4.54355 + 21.6457i 0.160538 + 0.764813i
\(802\) −1.31470 8.30070i −0.0464237 0.293108i
\(803\) 0.686862 0.0359969i 0.0242388 0.00127030i
\(804\) −7.76773 + 8.60495i −0.273947 + 0.303473i
\(805\) −0.446869 5.24535i −0.0157501 0.184874i
\(806\) 7.75154 3.63838i 0.273036 0.128156i
\(807\) −6.39063 16.7115i −0.224961 0.588273i
\(808\) −6.04474 11.8635i −0.212653 0.417355i
\(809\) 35.6719 39.6176i 1.25416 1.39288i 0.367781 0.929912i \(-0.380117\pi\)
0.886374 0.462969i \(-0.153216\pi\)
\(810\) 2.65417 + 19.9488i 0.0932582 + 0.700930i
\(811\) 28.4716 49.3143i 0.999774 1.73166i 0.481490 0.876451i \(-0.340096\pi\)
0.518284 0.855209i \(-0.326571\pi\)
\(812\) −3.94764 1.05777i −0.138535 0.0371204i
\(813\) −2.96391 + 0.790149i −0.103949 + 0.0277117i
\(814\) −2.62342 3.61083i −0.0919508 0.126559i
\(815\) −3.53336 2.39501i −0.123768 0.0838937i
\(816\) 0.821088 + 2.53800i 0.0287438 + 0.0888478i
\(817\) −1.64221 0.630384i −0.0574535 0.0220543i
\(818\) −3.48981 2.26631i −0.122018 0.0792397i
\(819\) 2.38705 1.37010i 0.0834103 0.0478751i
\(820\) 10.5707 + 3.66673i 0.369144 + 0.128048i
\(821\) 42.5969 13.8406i 1.48664 0.483039i 0.550552 0.834801i \(-0.314417\pi\)
0.936090 + 0.351762i \(0.114417\pi\)
\(822\) −8.43775 10.4468i −0.294300 0.364375i
\(823\) −43.9594 + 16.8744i −1.53233 + 0.588206i −0.970935 0.239342i \(-0.923068\pi\)
−0.561394 + 0.827549i \(0.689735\pi\)
\(824\) −7.61589 1.61881i −0.265312 0.0563938i
\(825\) 13.1427 12.1134i 0.457569 0.421733i
\(826\) −1.82567 + 0.812838i −0.0635230 + 0.0282823i
\(827\) −25.1882 1.32006i −0.875881 0.0459030i −0.390906 0.920431i \(-0.627838\pi\)
−0.484975 + 0.874528i \(0.661171\pi\)
\(828\) 11.8252 0.589645i 0.410955 0.0204916i
\(829\) −13.0132 17.9111i −0.451966 0.622078i 0.520852 0.853647i \(-0.325614\pi\)
−0.972819 + 0.231569i \(0.925614\pi\)
\(830\) 0.378228 19.1662i 0.0131285 0.665268i
\(831\) 39.3847 4.08898i 1.36624 0.141845i
\(832\) 1.48555 0.398051i 0.0515021 0.0137999i
\(833\) 1.60073 + 10.1066i 0.0554620 + 0.350173i
\(834\) −3.24928 7.32300i −0.112513 0.253575i
\(835\) 0.170989 + 0.275032i 0.00591731 + 0.00951786i
\(836\) 0.713872i 0.0246898i
\(837\) 28.6442 + 4.06337i 0.990088 + 0.140451i
\(838\) −0.479476 + 0.479476i −0.0165632 + 0.0165632i
\(839\) −2.75095 + 8.46655i −0.0949734 + 0.292298i −0.987247 0.159198i \(-0.949109\pi\)
0.892273 + 0.451496i \(0.149109\pi\)
\(840\) 0.644693 2.21858i 0.0222440 0.0765482i
\(841\) −14.5121 10.5436i −0.500416 0.363574i
\(842\) 0.350733 + 1.30895i 0.0120871 + 0.0451095i
\(843\) −33.7059 27.3654i −1.16089 0.942513i
\(844\) 21.5366 + 2.26359i 0.741321 + 0.0779159i
\(845\) −15.5601 17.9824i −0.535284 0.618614i
\(846\) −8.68781 + 9.59969i −0.298693 + 0.330044i
\(847\) 0.210438 4.01540i 0.00723074 0.137971i
\(848\) −1.55576 0.597200i −0.0534250 0.0205079i
\(849\) −31.5134 6.74020i −1.08154 0.231323i
\(850\) −0.303806 + 7.69446i −0.0104204 + 0.263918i
\(851\) 3.47145 7.79700i 0.119000 0.267278i
\(852\) −15.2159 + 12.2897i −0.521288 + 0.421037i
\(853\) 14.3910 + 7.33260i 0.492740 + 0.251063i 0.682660 0.730736i \(-0.260823\pi\)
−0.189920 + 0.981800i \(0.560823\pi\)
\(854\) 4.38937 + 1.95427i 0.150201 + 0.0668738i
\(855\) 1.32171 + 1.90708i 0.0452015 + 0.0652207i
\(856\) −0.788055 + 0.167506i −0.0269352 + 0.00572524i
\(857\) −3.20692 + 8.35431i −0.109546 + 0.285378i −0.977385 0.211469i \(-0.932175\pi\)
0.867839 + 0.496846i \(0.165509\pi\)
\(858\) 2.50213 4.89534i 0.0854213 0.167124i
\(859\) −35.3261 + 3.71293i −1.20531 + 0.126683i −0.685807 0.727784i \(-0.740551\pi\)
−0.519506 + 0.854467i \(0.673884\pi\)
\(860\) −11.3420 0.819084i −0.386760 0.0279305i
\(861\) 2.59063 4.47398i 0.0882884 0.152473i
\(862\) −2.74229 + 10.2344i −0.0934029 + 0.348584i
\(863\) 32.1641 8.61835i 1.09488 0.293372i 0.334201 0.942502i \(-0.391533\pi\)
0.760678 + 0.649130i \(0.224867\pi\)
\(864\) 4.93569 + 1.62450i 0.167915 + 0.0552666i
\(865\) 48.6886 6.72966i 1.65546 0.228815i
\(866\) −38.2419 12.4255i −1.29951 0.422237i
\(867\) 23.6653 9.04982i 0.803716 0.307348i
\(868\) −2.82108 1.75295i −0.0957535 0.0594989i
\(869\) 31.3241 1.06260
\(870\) 16.0438 21.1344i 0.543936 0.716525i
\(871\) −6.88755 + 7.64940i −0.233376 + 0.259190i
\(872\) −16.6874 + 2.64302i −0.565106 + 0.0895040i
\(873\) −16.6699 + 25.5274i −0.564191 + 0.863970i
\(874\) 1.18222 0.682556i 0.0399892 0.0230878i
\(875\) 3.95697 5.36874i 0.133770 0.181497i
\(876\) 0.119296 + 0.564764i 0.00403062 + 0.0190816i
\(877\) 15.9604 19.7094i 0.538943 0.665539i −0.432825 0.901478i \(-0.642483\pi\)
0.971768 + 0.235939i \(0.0758165\pi\)
\(878\) 1.79618 34.2732i 0.0606182 1.15667i
\(879\) −0.0237331 + 18.7033i −0.000800497 + 0.630845i
\(880\) −1.33922 4.41634i −0.0451449 0.148875i
\(881\) 2.00586 9.43682i 0.0675791 0.317935i −0.931354 0.364115i \(-0.881372\pi\)
0.998933 + 0.0461803i \(0.0147049\pi\)
\(882\) 17.7369 + 9.09419i 0.597233 + 0.306217i
\(883\) −50.7112 25.8387i −1.70657 0.869540i −0.983984 0.178257i \(-0.942954\pi\)
−0.722584 0.691283i \(-0.757046\pi\)
\(884\) 0.731933 + 2.25266i 0.0246176 + 0.0757651i
\(885\) −0.406818 12.9685i −0.0136750 0.435932i
\(886\) 21.9512 + 4.66586i 0.737463 + 0.156753i
\(887\) 22.3600 34.4313i 0.750775 1.15609i −0.232257 0.972654i \(-0.574611\pi\)
0.983031 0.183437i \(-0.0587223\pi\)
\(888\) 2.65195 2.64523i 0.0889937 0.0887681i
\(889\) 0.382560 0.344459i 0.0128307 0.0115528i
\(890\) 13.6459 + 9.24960i 0.457413 + 0.310047i
\(891\) 16.1331 9.20559i 0.540479 0.308399i
\(892\) −12.7262 + 10.3055i −0.426106 + 0.345054i
\(893\) −0.386362 + 1.44192i −0.0129291 + 0.0482521i
\(894\) 2.73601 1.98253i 0.0915059 0.0663057i
\(895\) 7.85863 + 4.74635i 0.262685 + 0.158653i
\(896\) −0.443308 0.399156i −0.0148099 0.0133349i
\(897\) 10.4994 0.536891i 0.350564 0.0179263i
\(898\) 15.1374 15.1374i 0.505143 0.505143i
\(899\) −23.0331 30.4064i −0.768197 1.01411i
\(900\) 11.7543 + 9.31855i 0.391812 + 0.310618i
\(901\) 0.793084 2.44086i 0.0264215 0.0813169i
\(902\) −0.540467 10.3127i −0.0179956 0.343376i
\(903\) −1.36639 + 5.07369i −0.0454708 + 0.168842i
\(904\) 0.851492 + 0.491609i 0.0283202 + 0.0163507i
\(905\) 14.1562 + 20.3155i 0.470568 + 0.675310i
\(906\) −5.15386 + 8.90065i −0.171226 + 0.295704i
\(907\) 34.5933 + 5.47905i 1.14865 + 0.181929i 0.701595 0.712576i \(-0.252472\pi\)
0.447058 + 0.894505i \(0.352472\pi\)
\(908\) 9.08100 11.2141i 0.301364 0.372153i
\(909\) 4.27609 39.7145i 0.141829 1.31725i
\(910\) 0.569946 1.97068i 0.0188935 0.0653275i
\(911\) 5.93106 + 27.9035i 0.196505 + 0.924483i 0.960288 + 0.279010i \(0.0900063\pi\)
−0.763783 + 0.645473i \(0.776660\pi\)
\(912\) 0.591845 0.0929694i 0.0195979 0.00307852i
\(913\) −16.5183 + 6.34079i −0.546677 + 0.209850i
\(914\) −5.29539 16.2975i −0.175156 0.539074i
\(915\) −22.5165 + 21.5901i −0.744374 + 0.713748i
\(916\) 3.09166 + 1.37650i 0.102151 + 0.0454808i
\(917\) −0.560027 + 0.363686i −0.0184937 + 0.0120100i
\(918\) −2.10062 + 7.72192i −0.0693308 + 0.254861i
\(919\) 2.79861 + 6.28578i 0.0923176 + 0.207349i 0.953802 0.300435i \(-0.0971317\pi\)
−0.861485 + 0.507783i \(0.830465\pi\)
\(920\) 6.03330 6.44044i 0.198912 0.212335i
\(921\) −49.7924 16.2484i −1.64072 0.535404i
\(922\) 21.3445 + 3.38063i 0.702943 + 0.111335i
\(923\) −13.4969 + 10.9296i −0.444256 + 0.359751i
\(924\) −2.12102 + 0.220207i −0.0697764 + 0.00724429i
\(925\) 9.82048 4.52500i 0.322895 0.148781i
\(926\) 8.98663 12.3690i 0.295319 0.406472i
\(927\) −16.4747 16.5585i −0.541100 0.543853i
\(928\) −3.11035 6.10440i −0.102102 0.200387i
\(929\) 53.4603 1.75398 0.876988 0.480512i \(-0.159549\pi\)
0.876988 + 0.480512i \(0.159549\pi\)
\(930\) 17.4586 12.6569i 0.572489 0.415037i
\(931\) 2.29816 0.0753191
\(932\) −4.93377 9.68306i −0.161611 0.317179i
\(933\) 13.1370 34.0936i 0.430085 1.11617i
\(934\) −17.2392 + 23.7277i −0.564083 + 0.776394i
\(935\) 6.68429 2.41565i 0.218600 0.0790003i
\(936\) 4.38441 + 1.43689i 0.143309 + 0.0469663i
\(937\) −0.806074 + 0.652746i −0.0263333 + 0.0213243i −0.642397 0.766372i \(-0.722060\pi\)
0.616063 + 0.787697i \(0.288726\pi\)
\(938\) 3.94333 + 0.624563i 0.128754 + 0.0203927i
\(939\) 1.95238 5.98297i 0.0637135 0.195247i
\(940\) 0.314818 + 9.64520i 0.0102682 + 0.314592i
\(941\) −5.53661 12.4354i −0.180488 0.405384i 0.800532 0.599291i \(-0.204551\pi\)
−0.981020 + 0.193907i \(0.937884\pi\)
\(942\) −21.0493 32.5032i −0.685822 1.05901i
\(943\) 16.5618 10.7554i 0.539327 0.350243i
\(944\) −3.06047 1.36261i −0.0996100 0.0443492i
\(945\) 5.25850 4.51526i 0.171059 0.146882i
\(946\) 3.24338 + 9.98209i 0.105451 + 0.324546i
\(947\) −33.0425 + 12.6838i −1.07374 + 0.412169i −0.830052 0.557686i \(-0.811689\pi\)
−0.243684 + 0.969855i \(0.578356\pi\)
\(948\) 4.07942 + 25.9697i 0.132493 + 0.843456i
\(949\) 0.106563 + 0.501340i 0.00345919 + 0.0162742i
\(950\) 1.69616 + 0.337729i 0.0550308 + 0.0109574i
\(951\) −6.57481 20.3229i −0.213203 0.659015i
\(952\) 0.578163 0.713972i 0.0187384 0.0231400i
\(953\) −18.7548 2.97047i −0.607529 0.0962231i −0.154912 0.987928i \(-0.549509\pi\)
−0.452617 + 0.891705i \(0.649509\pi\)
\(954\) −2.92826 4.05199i −0.0948059 0.131188i
\(955\) −25.8381 + 18.0045i −0.836102 + 0.582611i
\(956\) −6.09990 3.52178i −0.197285 0.113902i
\(957\) −23.6482 6.36869i −0.764437 0.205870i
\(958\) 1.41938 + 27.0833i 0.0458579 + 0.875022i
\(959\) −1.42919 + 4.39860i −0.0461510 + 0.142038i
\(960\) 3.48701 1.68545i 0.112543 0.0543975i
\(961\) −10.7491 29.0767i −0.346745 0.937959i
\(962\) 2.35178 2.35178i 0.0758245 0.0758245i
\(963\) −2.25424 0.871892i −0.0726419 0.0280963i
\(964\) 7.84149 + 7.06051i 0.252557 + 0.227404i
\(965\) 0.0615196 0.0151898i 0.00198038 0.000488976i
\(966\) −2.39265 3.30201i −0.0769824 0.106240i
\(967\) −1.44665 + 5.39896i −0.0465210 + 0.173619i −0.985278 0.170962i \(-0.945312\pi\)
0.938757 + 0.344581i \(0.111979\pi\)
\(968\) 5.23835 4.24193i 0.168367 0.136341i
\(969\) 0.190689 + 0.902752i 0.00612581 + 0.0290006i
\(970\) 4.28522 + 22.3169i 0.137590 + 0.716552i
\(971\) −9.41681 + 8.47894i −0.302200 + 0.272102i −0.806253 0.591571i \(-0.798508\pi\)
0.504053 + 0.863672i \(0.331841\pi\)
\(972\) 9.73307 + 12.1765i 0.312189 + 0.390562i
\(973\) −1.50278 + 2.31407i −0.0481768 + 0.0741858i
\(974\) 18.3862 + 3.90810i 0.589131 + 0.125224i
\(975\) 10.4476 + 8.26103i 0.334591 + 0.264565i
\(976\) 2.48898 + 7.66030i 0.0796704 + 0.245200i
\(977\) 21.3243 + 10.8653i 0.682225 + 0.347611i 0.760516 0.649320i \(-0.224946\pi\)
−0.0782908 + 0.996931i \(0.524946\pi\)
\(978\) −3.30167 0.177235i −0.105576 0.00566734i
\(979\) 3.16353 14.8832i 0.101107 0.475670i
\(980\) 14.2175 4.31132i 0.454160 0.137720i
\(981\) −46.2517 20.7334i −1.47670 0.661966i
\(982\) −0.566978 + 10.8186i −0.0180930 + 0.345235i
\(983\) 4.17301 5.15324i 0.133098 0.164363i −0.706239 0.707973i \(-0.749610\pi\)
0.839338 + 0.543610i \(0.182943\pi\)
\(984\) 8.47951 1.79113i 0.270317 0.0570993i
\(985\) 10.4893 + 10.9116i 0.334217 + 0.347674i
\(986\) 9.13774 5.27568i 0.291005 0.168012i
\(987\) 4.40334 + 0.703150i 0.140160 + 0.0223815i
\(988\) 0.525416 0.0832177i 0.0167157 0.00264751i
\(989\) −13.4299 + 14.9155i −0.427047 + 0.474284i
\(990\) 3.88019 13.2899i 0.123320 0.422381i
\(991\) 31.9965 1.01640 0.508202 0.861238i \(-0.330310\pi\)
0.508202 + 0.861238i \(0.330310\pi\)
\(992\) −0.980628 5.48073i −0.0311350 0.174013i
\(993\) 4.15079 + 10.8543i 0.131721 + 0.344452i
\(994\) 6.40660 + 2.08163i 0.203205 + 0.0660253i
\(995\) 32.1238 + 24.3219i 1.01839 + 0.771057i
\(996\) −7.40815 12.8690i −0.234736 0.407769i
\(997\) 49.5168 13.2680i 1.56821 0.420201i 0.632960 0.774184i \(-0.281840\pi\)
0.935252 + 0.353983i \(0.115173\pi\)
\(998\) −1.30939 + 4.88671i −0.0414480 + 0.154686i
\(999\) 11.0003 2.29445i 0.348034 0.0725932i
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 930.2.bs.a.107.5 1024
3.2 odd 2 inner 930.2.bs.a.107.59 yes 1024
5.3 odd 4 inner 930.2.bs.a.293.19 yes 1024
15.8 even 4 inner 930.2.bs.a.293.53 yes 1024
31.20 even 15 inner 930.2.bs.a.857.53 yes 1024
93.20 odd 30 inner 930.2.bs.a.857.19 yes 1024
155.113 odd 60 inner 930.2.bs.a.113.59 yes 1024
465.113 even 60 inner 930.2.bs.a.113.5 yes 1024
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bs.a.107.5 1024 1.1 even 1 trivial
930.2.bs.a.107.59 yes 1024 3.2 odd 2 inner
930.2.bs.a.113.5 yes 1024 465.113 even 60 inner
930.2.bs.a.113.59 yes 1024 155.113 odd 60 inner
930.2.bs.a.293.19 yes 1024 5.3 odd 4 inner
930.2.bs.a.293.53 yes 1024 15.8 even 4 inner
930.2.bs.a.857.19 yes 1024 93.20 odd 30 inner
930.2.bs.a.857.53 yes 1024 31.20 even 15 inner