Properties

Label 930.2.bg.g.691.1
Level $930$
Weight $2$
Character 930.691
Analytic conductor $7.426$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(121,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 0, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bg (of order \(15\), degree \(8\), 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: \(24\)
Relative dimension: \(3\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 691.1
Character \(\chi\) \(=\) 930.691
Dual form 930.2.bg.g.751.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 - 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.05288 + 0.914002i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\) \(q+(0.309017 - 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.05288 + 0.914002i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.978148 + 0.207912i) q^{10} +(-0.0978320 + 0.930809i) q^{11} +(0.669131 + 0.743145i) q^{12} +(-1.58460 + 1.75988i) q^{13} +(0.234892 + 2.23485i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.108095 - 1.02846i) q^{17} +(0.669131 - 0.743145i) q^{18} +(4.82120 + 5.35449i) q^{19} +(-0.104528 + 0.994522i) q^{20} +(2.19805 - 0.467211i) q^{21} +(0.855020 + 0.380680i) q^{22} +(2.80922 - 2.04102i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.18408 + 2.05088i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(2.19805 + 0.467211i) q^{28} +(-1.38557 + 4.26435i) q^{29} +1.00000 q^{30} +(5.38027 - 1.43273i) q^{31} +1.00000 q^{32} +(0.289220 - 0.890128i) q^{33} +(-1.01152 - 0.215006i) q^{34} +(1.81799 + 1.32085i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.47425 + 2.55347i) q^{37} +(6.58226 - 2.93061i) q^{38} +(1.91588 - 1.39197i) q^{39} +(0.913545 + 0.406737i) q^{40} +(-0.336978 + 0.0716269i) q^{41} +(0.234892 - 2.23485i) q^{42} +(0.815344 + 0.905531i) q^{43} +(0.626264 - 0.695536i) q^{44} +(-0.104528 - 0.994522i) q^{45} +(-1.07303 - 3.30244i) q^{46} +(0.920779 + 2.83387i) q^{47} +(-0.104528 - 0.994522i) q^{48} +(-1.30499 + 1.44934i) q^{49} +(0.669131 + 0.743145i) q^{50} +(-0.108095 + 1.02846i) q^{51} +(2.31640 - 0.492367i) q^{52} +(5.57251 + 2.48104i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(0.855020 - 0.380680i) q^{55} +(1.12358 - 1.94610i) q^{56} +(-3.60259 - 6.23986i) q^{57} +(3.62747 + 2.63551i) q^{58} +(11.2895 + 2.39966i) q^{59} +(0.309017 - 0.951057i) q^{60} -5.29557 q^{61} +(0.299987 - 5.55968i) q^{62} -2.24716 q^{63} +(0.309017 - 0.951057i) q^{64} +(2.31640 + 0.492367i) q^{65} +(-0.757188 - 0.550130i) q^{66} +(-1.21006 - 2.09589i) q^{67} +(-0.517061 + 0.895576i) q^{68} +(-3.17219 + 1.41235i) q^{69} +(1.81799 - 1.32085i) q^{70} +(5.31028 + 2.36429i) q^{71} +(-0.978148 + 0.207912i) q^{72} +(-1.06471 + 10.1301i) q^{73} +(1.97293 + 2.19116i) q^{74} +(0.669131 - 0.743145i) q^{75} +(-0.753146 - 7.16570i) q^{76} +(-0.649924 - 2.00026i) q^{77} +(-0.731800 - 2.25225i) q^{78} +(0.368162 + 3.50283i) q^{79} +(0.669131 - 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.0360107 + 0.342619i) q^{82} +(9.52394 - 2.02438i) q^{83} +(-2.05288 - 0.914002i) q^{84} +(-0.836622 + 0.607841i) q^{85} +(1.11317 - 0.495614i) q^{86} +(2.24190 - 3.88308i) q^{87} +(-0.467968 - 0.810545i) q^{88} +(-1.59021 - 1.15535i) q^{89} +(-0.978148 - 0.207912i) q^{90} +(1.64447 - 5.06116i) q^{91} -3.47239 q^{92} +(-5.56058 + 0.282801i) q^{93} +2.97970 q^{94} +(2.22652 - 6.85253i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-13.1974 - 9.58848i) q^{97} +(0.975137 + 1.68899i) q^{98} +(-0.467968 + 0.810545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 0.951057i 0.218508 0.672499i
\(3\) −0.978148 0.207912i −0.564734 0.120038i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −2.05288 + 0.914002i −0.775917 + 0.345460i −0.756196 0.654345i \(-0.772944\pi\)
−0.0197207 + 0.999806i \(0.506278\pi\)
\(8\) −0.809017 + 0.587785i −0.286031 + 0.207813i
\(9\) 0.913545 + 0.406737i 0.304515 + 0.135579i
\(10\) −0.978148 + 0.207912i −0.309317 + 0.0657474i
\(11\) −0.0978320 + 0.930809i −0.0294975 + 0.280650i 0.969824 + 0.243808i \(0.0783965\pi\)
−0.999321 + 0.0368420i \(0.988270\pi\)
\(12\) 0.669131 + 0.743145i 0.193161 + 0.214527i
\(13\) −1.58460 + 1.75988i −0.439490 + 0.488103i −0.921673 0.387967i \(-0.873177\pi\)
0.482183 + 0.876070i \(0.339844\pi\)
\(14\) 0.234892 + 2.23485i 0.0627776 + 0.597289i
\(15\) 0.309017 + 0.951057i 0.0797878 + 0.245562i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −0.108095 1.02846i −0.0262169 0.249437i −0.999779 0.0210154i \(-0.993310\pi\)
0.973562 0.228422i \(-0.0733566\pi\)
\(18\) 0.669131 0.743145i 0.157716 0.175161i
\(19\) 4.82120 + 5.35449i 1.10606 + 1.22840i 0.971384 + 0.237514i \(0.0763326\pi\)
0.134676 + 0.990890i \(0.457001\pi\)
\(20\) −0.104528 + 0.994522i −0.0233733 + 0.222382i
\(21\) 2.19805 0.467211i 0.479655 0.101954i
\(22\) 0.855020 + 0.380680i 0.182291 + 0.0811612i
\(23\) 2.80922 2.04102i 0.585764 0.425582i −0.255034 0.966932i \(-0.582087\pi\)
0.840797 + 0.541350i \(0.182087\pi\)
\(24\) 0.913545 0.406737i 0.186477 0.0830248i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 1.18408 + 2.05088i 0.232217 + 0.402211i
\(27\) −0.809017 0.587785i −0.155695 0.113119i
\(28\) 2.19805 + 0.467211i 0.415393 + 0.0882945i
\(29\) −1.38557 + 4.26435i −0.257294 + 0.791869i 0.736075 + 0.676900i \(0.236677\pi\)
−0.993369 + 0.114970i \(0.963323\pi\)
\(30\) 1.00000 0.182574
\(31\) 5.38027 1.43273i 0.966325 0.257326i
\(32\) 1.00000 0.176777
\(33\) 0.289220 0.890128i 0.0503468 0.154951i
\(34\) −1.01152 0.215006i −0.173475 0.0368732i
\(35\) 1.81799 + 1.32085i 0.307296 + 0.223264i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −1.47425 + 2.55347i −0.242365 + 0.419788i −0.961387 0.275199i \(-0.911256\pi\)
0.719023 + 0.694986i \(0.244590\pi\)
\(38\) 6.58226 2.93061i 1.06778 0.475408i
\(39\) 1.91588 1.39197i 0.306786 0.222893i
\(40\) 0.913545 + 0.406737i 0.144444 + 0.0643107i
\(41\) −0.336978 + 0.0716269i −0.0526271 + 0.0111862i −0.234150 0.972200i \(-0.575231\pi\)
0.181523 + 0.983387i \(0.441897\pi\)
\(42\) 0.234892 2.23485i 0.0362446 0.344845i
\(43\) 0.815344 + 0.905531i 0.124339 + 0.138092i 0.802100 0.597190i \(-0.203716\pi\)
−0.677761 + 0.735282i \(0.737050\pi\)
\(44\) 0.626264 0.695536i 0.0944128 0.104856i
\(45\) −0.104528 0.994522i −0.0155822 0.148255i
\(46\) −1.07303 3.30244i −0.158209 0.486918i
\(47\) 0.920779 + 2.83387i 0.134309 + 0.413362i 0.995482 0.0949509i \(-0.0302694\pi\)
−0.861173 + 0.508313i \(0.830269\pi\)
\(48\) −0.104528 0.994522i −0.0150874 0.143547i
\(49\) −1.30499 + 1.44934i −0.186427 + 0.207048i
\(50\) 0.669131 + 0.743145i 0.0946294 + 0.105097i
\(51\) −0.108095 + 1.02846i −0.0151363 + 0.144013i
\(52\) 2.31640 0.492367i 0.321227 0.0682790i
\(53\) 5.57251 + 2.48104i 0.765444 + 0.340797i 0.752044 0.659113i \(-0.229068\pi\)
0.0133995 + 0.999910i \(0.495735\pi\)
\(54\) −0.809017 + 0.587785i −0.110093 + 0.0799874i
\(55\) 0.855020 0.380680i 0.115291 0.0513308i
\(56\) 1.12358 1.94610i 0.150145 0.260058i
\(57\) −3.60259 6.23986i −0.477174 0.826490i
\(58\) 3.62747 + 2.63551i 0.476310 + 0.346060i
\(59\) 11.2895 + 2.39966i 1.46977 + 0.312409i 0.872098 0.489331i \(-0.162759\pi\)
0.597673 + 0.801740i \(0.296092\pi\)
\(60\) 0.309017 0.951057i 0.0398939 0.122781i
\(61\) −5.29557 −0.678028 −0.339014 0.940781i \(-0.610093\pi\)
−0.339014 + 0.940781i \(0.610093\pi\)
\(62\) 0.299987 5.55968i 0.0380983 0.706080i
\(63\) −2.24716 −0.283116
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) 2.31640 + 0.492367i 0.287315 + 0.0610706i
\(66\) −0.757188 0.550130i −0.0932035 0.0677163i
\(67\) −1.21006 2.09589i −0.147833 0.256054i 0.782593 0.622533i \(-0.213896\pi\)
−0.930426 + 0.366479i \(0.880563\pi\)
\(68\) −0.517061 + 0.895576i −0.0627028 + 0.108604i
\(69\) −3.17219 + 1.41235i −0.381887 + 0.170027i
\(70\) 1.81799 1.32085i 0.217291 0.157871i
\(71\) 5.31028 + 2.36429i 0.630215 + 0.280590i 0.696882 0.717186i \(-0.254570\pi\)
−0.0666676 + 0.997775i \(0.521237\pi\)
\(72\) −0.978148 + 0.207912i −0.115276 + 0.0245026i
\(73\) −1.06471 + 10.1301i −0.124615 + 1.18564i 0.736217 + 0.676746i \(0.236610\pi\)
−0.860832 + 0.508889i \(0.830056\pi\)
\(74\) 1.97293 + 2.19116i 0.229348 + 0.254717i
\(75\) 0.669131 0.743145i 0.0772645 0.0858110i
\(76\) −0.753146 7.16570i −0.0863918 0.821963i
\(77\) −0.649924 2.00026i −0.0740657 0.227951i
\(78\) −0.731800 2.25225i −0.0828600 0.255017i
\(79\) 0.368162 + 3.50283i 0.0414215 + 0.394099i 0.995516 + 0.0945933i \(0.0301551\pi\)
−0.954095 + 0.299506i \(0.903178\pi\)
\(80\) 0.669131 0.743145i 0.0748111 0.0830861i
\(81\) 0.669131 + 0.743145i 0.0743478 + 0.0825716i
\(82\) −0.0360107 + 0.342619i −0.00397672 + 0.0378359i
\(83\) 9.52394 2.02438i 1.04539 0.222204i 0.346957 0.937881i \(-0.387215\pi\)
0.698431 + 0.715677i \(0.253882\pi\)
\(84\) −2.05288 0.914002i −0.223988 0.0997258i
\(85\) −0.836622 + 0.607841i −0.0907444 + 0.0659297i
\(86\) 1.11317 0.495614i 0.120036 0.0534434i
\(87\) 2.24190 3.88308i 0.240357 0.416310i
\(88\) −0.467968 0.810545i −0.0498856 0.0864044i
\(89\) −1.59021 1.15535i −0.168561 0.122467i 0.500306 0.865849i \(-0.333221\pi\)
−0.668868 + 0.743381i \(0.733221\pi\)
\(90\) −0.978148 0.207912i −0.103106 0.0219158i
\(91\) 1.64447 5.06116i 0.172387 0.530554i
\(92\) −3.47239 −0.362022
\(93\) −5.56058 + 0.282801i −0.576605 + 0.0293251i
\(94\) 2.97970 0.307333
\(95\) 2.22652 6.85253i 0.228436 0.703055i
\(96\) −0.978148 0.207912i −0.0998318 0.0212199i
\(97\) −13.1974 9.58848i −1.33999 0.973562i −0.999444 0.0333358i \(-0.989387\pi\)
−0.340550 0.940227i \(-0.610613\pi\)
\(98\) 0.975137 + 1.68899i 0.0985037 + 0.170613i
\(99\) −0.467968 + 0.810545i −0.0470326 + 0.0814628i
\(100\) 0.913545 0.406737i 0.0913545 0.0406737i
\(101\) −4.01975 + 2.92052i −0.399980 + 0.290603i −0.769533 0.638607i \(-0.779511\pi\)
0.369553 + 0.929210i \(0.379511\pi\)
\(102\) 0.944717 + 0.420615i 0.0935409 + 0.0416471i
\(103\) −17.5302 + 3.72616i −1.72730 + 0.367150i −0.961261 0.275639i \(-0.911110\pi\)
−0.766043 + 0.642789i \(0.777777\pi\)
\(104\) 0.247539 2.35518i 0.0242732 0.230944i
\(105\) −1.50364 1.66997i −0.146741 0.162972i
\(106\) 4.08161 4.53309i 0.396441 0.440293i
\(107\) −0.0604119 0.574781i −0.00584024 0.0555661i 0.991214 0.132271i \(-0.0422268\pi\)
−0.997054 + 0.0767046i \(0.975560\pi\)
\(108\) 0.309017 + 0.951057i 0.0297352 + 0.0915155i
\(109\) 5.56715 + 17.1339i 0.533237 + 1.64113i 0.747429 + 0.664342i \(0.231288\pi\)
−0.214192 + 0.976792i \(0.568712\pi\)
\(110\) −0.0978320 0.930809i −0.00932791 0.0887492i
\(111\) 1.97293 2.19116i 0.187262 0.207975i
\(112\) −1.50364 1.66997i −0.142081 0.157797i
\(113\) −0.944696 + 8.98818i −0.0888695 + 0.845537i 0.855754 + 0.517382i \(0.173093\pi\)
−0.944624 + 0.328155i \(0.893573\pi\)
\(114\) −7.04772 + 1.49804i −0.660080 + 0.140304i
\(115\) −3.17219 1.41235i −0.295808 0.131702i
\(116\) 3.62747 2.63551i 0.336802 0.244701i
\(117\) −2.16342 + 0.963215i −0.200008 + 0.0890492i
\(118\) 5.77087 9.99544i 0.531252 0.920155i
\(119\) 1.16192 + 2.01250i 0.106513 + 0.184486i
\(120\) −0.809017 0.587785i −0.0738528 0.0536572i
\(121\) 9.90279 + 2.10490i 0.900254 + 0.191355i
\(122\) −1.63642 + 5.03639i −0.148155 + 0.455973i
\(123\) 0.344506 0.0310631
\(124\) −5.19487 2.00334i −0.466513 0.179905i
\(125\) 1.00000 0.0894427
\(126\) −0.694411 + 2.13718i −0.0618630 + 0.190395i
\(127\) −1.28770 0.273709i −0.114265 0.0242878i 0.150424 0.988622i \(-0.451936\pi\)
−0.264689 + 0.964334i \(0.585269\pi\)
\(128\) −0.809017 0.587785i −0.0715077 0.0519534i
\(129\) −0.609256 1.05526i −0.0536420 0.0929107i
\(130\) 1.18408 2.05088i 0.103850 0.179874i
\(131\) 1.69248 0.753539i 0.147872 0.0658370i −0.331466 0.943467i \(-0.607543\pi\)
0.479339 + 0.877630i \(0.340877\pi\)
\(132\) −0.757188 + 0.550130i −0.0659048 + 0.0478826i
\(133\) −14.7914 6.58555i −1.28258 0.571039i
\(134\) −2.36724 + 0.503173i −0.204498 + 0.0434675i
\(135\) −0.104528 + 0.994522i −0.00899638 + 0.0855948i
\(136\) 0.691962 + 0.768502i 0.0593353 + 0.0658985i
\(137\) −3.75759 + 4.17323i −0.321033 + 0.356543i −0.881962 0.471321i \(-0.843777\pi\)
0.560929 + 0.827864i \(0.310444\pi\)
\(138\) 0.362964 + 3.45337i 0.0308975 + 0.293970i
\(139\) 2.82680 + 8.70001i 0.239766 + 0.737925i 0.996453 + 0.0841478i \(0.0268168\pi\)
−0.756687 + 0.653778i \(0.773183\pi\)
\(140\) −0.694411 2.13718i −0.0586884 0.180624i
\(141\) −0.311464 2.96338i −0.0262300 0.249562i
\(142\) 3.88954 4.31977i 0.326403 0.362507i
\(143\) −1.48309 1.64714i −0.124022 0.137740i
\(144\) −0.104528 + 0.994522i −0.00871071 + 0.0828768i
\(145\) 4.38582 0.932235i 0.364222 0.0774179i
\(146\) 9.30526 + 4.14297i 0.770108 + 0.342874i
\(147\) 1.57780 1.14634i 0.130135 0.0945487i
\(148\) 2.69358 1.19926i 0.221411 0.0985785i
\(149\) −3.95316 + 6.84707i −0.323855 + 0.560934i −0.981280 0.192586i \(-0.938312\pi\)
0.657425 + 0.753520i \(0.271646\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) −13.0260 9.46393i −1.06004 0.770164i −0.0859436 0.996300i \(-0.527390\pi\)
−0.974096 + 0.226136i \(0.927390\pi\)
\(152\) −7.04772 1.49804i −0.571646 0.121507i
\(153\) 0.319561 0.983508i 0.0258350 0.0795119i
\(154\) −2.10320 −0.169481
\(155\) −3.93091 3.94308i −0.315739 0.316716i
\(156\) −2.36815 −0.189604
\(157\) 0.477973 1.47105i 0.0381464 0.117403i −0.930170 0.367129i \(-0.880341\pi\)
0.968316 + 0.249726i \(0.0803407\pi\)
\(158\) 3.44516 + 0.732291i 0.274082 + 0.0582579i
\(159\) −4.93490 3.58542i −0.391363 0.284342i
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −3.90151 + 6.75761i −0.307482 + 0.532575i
\(162\) 0.913545 0.406737i 0.0717749 0.0319562i
\(163\) −9.62849 + 6.99551i −0.754162 + 0.547931i −0.897114 0.441799i \(-0.854340\pi\)
0.142952 + 0.989730i \(0.454340\pi\)
\(164\) 0.314722 + 0.140123i 0.0245757 + 0.0109418i
\(165\) −0.915484 + 0.194592i −0.0712703 + 0.0151490i
\(166\) 1.01776 9.68337i 0.0789938 0.751575i
\(167\) 0.846559 + 0.940199i 0.0655087 + 0.0727548i 0.775008 0.631951i \(-0.217746\pi\)
−0.709500 + 0.704706i \(0.751079\pi\)
\(168\) −1.50364 + 1.66997i −0.116009 + 0.128841i
\(169\) 0.772659 + 7.35136i 0.0594353 + 0.565489i
\(170\) 0.319561 + 0.983508i 0.0245092 + 0.0754316i
\(171\) 2.22652 + 6.85253i 0.170266 + 0.524026i
\(172\) −0.127369 1.21184i −0.00971182 0.0924018i
\(173\) −4.55119 + 5.05461i −0.346021 + 0.384295i −0.890885 0.454229i \(-0.849915\pi\)
0.544864 + 0.838524i \(0.316581\pi\)
\(174\) −3.00025 3.33211i −0.227448 0.252607i
\(175\) 0.234892 2.23485i 0.0177562 0.168939i
\(176\) −0.915484 + 0.194592i −0.0690072 + 0.0146679i
\(177\) −10.5439 4.69445i −0.792528 0.352856i
\(178\) −1.59021 + 1.15535i −0.119191 + 0.0865973i
\(179\) 13.8724 6.17639i 1.03687 0.461645i 0.183540 0.983012i \(-0.441244\pi\)
0.853333 + 0.521367i \(0.174578\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) −12.1888 21.1116i −0.905986 1.56921i −0.819589 0.572952i \(-0.805798\pi\)
−0.0863970 0.996261i \(-0.527535\pi\)
\(182\) −4.30528 3.12797i −0.319129 0.231860i
\(183\) 5.17985 + 1.10101i 0.382905 + 0.0813891i
\(184\) −1.07303 + 3.30244i −0.0791047 + 0.243459i
\(185\) 2.94849 0.216777
\(186\) −1.44935 + 5.37581i −0.106272 + 0.394174i
\(187\) 0.967872 0.0707778
\(188\) 0.920779 2.83387i 0.0671547 0.206681i
\(189\) 2.19805 + 0.467211i 0.159885 + 0.0339846i
\(190\) −5.82911 4.23510i −0.422888 0.307246i
\(191\) −2.68206 4.64547i −0.194067 0.336134i 0.752527 0.658561i \(-0.228835\pi\)
−0.946594 + 0.322427i \(0.895501\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −6.88889 + 3.06713i −0.495873 + 0.220777i −0.639407 0.768868i \(-0.720820\pi\)
0.143534 + 0.989645i \(0.454153\pi\)
\(194\) −13.1974 + 9.58848i −0.947519 + 0.688413i
\(195\) −2.16342 0.963215i −0.154925 0.0689772i
\(196\) 1.90766 0.405485i 0.136261 0.0289632i
\(197\) 2.59257 24.6666i 0.184713 1.75742i −0.373410 0.927666i \(-0.621812\pi\)
0.558123 0.829758i \(-0.311522\pi\)
\(198\) 0.626264 + 0.695536i 0.0445066 + 0.0494296i
\(199\) −14.9707 + 16.6267i −1.06125 + 1.17863i −0.0778859 + 0.996962i \(0.524817\pi\)
−0.983360 + 0.181670i \(0.941850\pi\)
\(200\) −0.104528 0.994522i −0.00739128 0.0703233i
\(201\) 0.747860 + 2.30168i 0.0527500 + 0.162348i
\(202\) 1.53541 + 4.72550i 0.108031 + 0.332485i
\(203\) −1.05321 10.0206i −0.0739208 0.703310i
\(204\) 0.691962 0.768502i 0.0484471 0.0538059i
\(205\) 0.230520 + 0.256018i 0.0161002 + 0.0178811i
\(206\) −1.87334 + 17.8237i −0.130522 + 1.24183i
\(207\) 3.39651 0.721951i 0.236074 0.0501791i
\(208\) −2.16342 0.963215i −0.150006 0.0667869i
\(209\) −5.45568 + 3.96378i −0.377377 + 0.274180i
\(210\) −2.05288 + 0.914002i −0.141662 + 0.0630721i
\(211\) 4.85234 8.40450i 0.334049 0.578589i −0.649253 0.760573i \(-0.724918\pi\)
0.983302 + 0.181983i \(0.0582517\pi\)
\(212\) −3.04994 5.28265i −0.209471 0.362814i
\(213\) −4.70268 3.41669i −0.322222 0.234108i
\(214\) −0.565317 0.120162i −0.0386443 0.00821410i
\(215\) 0.376541 1.15887i 0.0256799 0.0790346i
\(216\) 1.00000 0.0680414
\(217\) −9.73554 + 7.85880i −0.660891 + 0.533490i
\(218\) 18.0157 1.22018
\(219\) 3.14761 9.68734i 0.212696 0.654610i
\(220\) −0.915484 0.194592i −0.0617219 0.0131194i
\(221\) 1.98125 + 1.43946i 0.133273 + 0.0968287i
\(222\) −1.47425 2.55347i −0.0989449 0.171378i
\(223\) −1.57698 + 2.73141i −0.105603 + 0.182909i −0.913984 0.405750i \(-0.867010\pi\)
0.808382 + 0.588659i \(0.200344\pi\)
\(224\) −2.05288 + 0.914002i −0.137164 + 0.0610693i
\(225\) −0.809017 + 0.587785i −0.0539345 + 0.0391857i
\(226\) 8.25634 + 3.67596i 0.549204 + 0.244521i
\(227\) −3.57553 + 0.760003i −0.237316 + 0.0504432i −0.325034 0.945702i \(-0.605376\pi\)
0.0877180 + 0.996145i \(0.472043\pi\)
\(228\) −0.753146 + 7.16570i −0.0498783 + 0.474560i
\(229\) −0.970612 1.07797i −0.0641398 0.0712345i 0.710221 0.703979i \(-0.248595\pi\)
−0.774361 + 0.632744i \(0.781928\pi\)
\(230\) −2.32348 + 2.58049i −0.153206 + 0.170153i
\(231\) 0.219844 + 2.09168i 0.0144647 + 0.137622i
\(232\) −1.38557 4.26435i −0.0909672 0.279968i
\(233\) −1.48627 4.57428i −0.0973690 0.299671i 0.890495 0.454993i \(-0.150358\pi\)
−0.987864 + 0.155322i \(0.950358\pi\)
\(234\) 0.247539 + 2.35518i 0.0161822 + 0.153963i
\(235\) 1.99381 2.21435i 0.130062 0.144448i
\(236\) −7.72293 8.57718i −0.502720 0.558327i
\(237\) 0.368162 3.50283i 0.0239147 0.227533i
\(238\) 2.27305 0.483153i 0.147340 0.0313181i
\(239\) 19.5418 + 8.70058i 1.26406 + 0.562794i 0.925712 0.378228i \(-0.123467\pi\)
0.338344 + 0.941023i \(0.390133\pi\)
\(240\) −0.809017 + 0.587785i −0.0522218 + 0.0379414i
\(241\) 9.50861 4.23351i 0.612503 0.272704i −0.0769490 0.997035i \(-0.524518\pi\)
0.689452 + 0.724331i \(0.257851\pi\)
\(242\) 5.06201 8.76766i 0.325398 0.563607i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 4.28421 + 3.11266i 0.274268 + 0.199268i
\(245\) 1.90766 + 0.405485i 0.121876 + 0.0259055i
\(246\) 0.106458 0.327645i 0.00678753 0.0208899i
\(247\) −17.0630 −1.08569
\(248\) −3.51059 + 4.32155i −0.222923 + 0.274418i
\(249\) −9.73671 −0.617039
\(250\) 0.309017 0.951057i 0.0195440 0.0601501i
\(251\) 10.6834 + 2.27083i 0.674330 + 0.143333i 0.532334 0.846534i \(-0.321315\pi\)
0.141995 + 0.989867i \(0.454648\pi\)
\(252\) 1.81799 + 1.32085i 0.114523 + 0.0832056i
\(253\) 1.62497 + 2.81453i 0.102161 + 0.176948i
\(254\) −0.658235 + 1.14010i −0.0413013 + 0.0715360i
\(255\) 0.944717 0.420615i 0.0591605 0.0263399i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 10.8912 + 4.84907i 0.679373 + 0.302476i 0.717260 0.696806i \(-0.245396\pi\)
−0.0378868 + 0.999282i \(0.512063\pi\)
\(258\) −1.19189 + 0.253343i −0.0742035 + 0.0157724i
\(259\) 0.692578 6.58944i 0.0430347 0.409448i
\(260\) −1.58460 1.75988i −0.0982730 0.109143i
\(261\) −3.00025 + 3.33211i −0.185711 + 0.206253i
\(262\) −0.193654 1.84250i −0.0119640 0.113830i
\(263\) 1.77835 + 5.47320i 0.109658 + 0.337492i 0.990795 0.135368i \(-0.0432217\pi\)
−0.881138 + 0.472860i \(0.843222\pi\)
\(264\) 0.289220 + 0.890128i 0.0178003 + 0.0547836i
\(265\) −0.637611 6.06646i −0.0391681 0.372660i
\(266\) −10.8340 + 12.0324i −0.664276 + 0.737753i
\(267\) 1.31524 + 1.46073i 0.0804917 + 0.0893951i
\(268\) −0.252972 + 2.40687i −0.0154527 + 0.147023i
\(269\) −16.4185 + 3.48985i −1.00105 + 0.212780i −0.679155 0.733995i \(-0.737654\pi\)
−0.321897 + 0.946775i \(0.604320\pi\)
\(270\) 0.913545 + 0.406737i 0.0555966 + 0.0247532i
\(271\) −15.7544 + 11.4463i −0.957013 + 0.695311i −0.952455 0.304679i \(-0.901451\pi\)
−0.00455800 + 0.999990i \(0.501451\pi\)
\(272\) 0.944717 0.420615i 0.0572819 0.0255035i
\(273\) −2.66081 + 4.60866i −0.161040 + 0.278929i
\(274\) 2.80782 + 4.86328i 0.169626 + 0.293801i
\(275\) −0.757188 0.550130i −0.0456602 0.0331741i
\(276\) 3.39651 + 0.721951i 0.204446 + 0.0434563i
\(277\) 2.92426 8.99994i 0.175702 0.540754i −0.823963 0.566643i \(-0.808242\pi\)
0.999665 + 0.0258895i \(0.00824179\pi\)
\(278\) 9.14773 0.548645
\(279\) 5.49786 + 0.879488i 0.329148 + 0.0526536i
\(280\) −2.24716 −0.134293
\(281\) −5.27860 + 16.2459i −0.314895 + 0.969148i 0.660902 + 0.750472i \(0.270174\pi\)
−0.975798 + 0.218676i \(0.929826\pi\)
\(282\) −2.91459 0.619515i −0.173561 0.0368916i
\(283\) 0.359892 + 0.261477i 0.0213934 + 0.0155432i 0.598431 0.801175i \(-0.295791\pi\)
−0.577037 + 0.816718i \(0.695791\pi\)
\(284\) −2.90641 5.03406i −0.172464 0.298716i
\(285\) −3.60259 + 6.23986i −0.213399 + 0.369618i
\(286\) −2.02482 + 0.901508i −0.119730 + 0.0533073i
\(287\) 0.626309 0.455040i 0.0369699 0.0268602i
\(288\) 0.913545 + 0.406737i 0.0538312 + 0.0239672i
\(289\) 15.5825 3.31216i 0.916616 0.194833i
\(290\) 0.468685 4.45924i 0.0275221 0.261855i
\(291\) 10.9155 + 12.1228i 0.639875 + 0.710654i
\(292\) 6.81568 7.56958i 0.398857 0.442976i
\(293\) 2.45647 + 23.3718i 0.143509 + 1.36539i 0.794941 + 0.606687i \(0.207502\pi\)
−0.651432 + 0.758707i \(0.725832\pi\)
\(294\) −0.602668 1.85482i −0.0351483 0.108175i
\(295\) −3.56659 10.9768i −0.207655 0.639097i
\(296\) −0.308201 2.93234i −0.0179138 0.170439i
\(297\) 0.626264 0.695536i 0.0363395 0.0403591i
\(298\) 5.29036 + 5.87554i 0.306462 + 0.340361i
\(299\) −0.859554 + 8.17811i −0.0497093 + 0.472952i
\(300\) −0.978148 + 0.207912i −0.0564734 + 0.0120038i
\(301\) −2.50146 1.11372i −0.144182 0.0641939i
\(302\) −13.0260 + 9.46393i −0.749561 + 0.544588i
\(303\) 4.53912 2.02095i 0.260766 0.116100i
\(304\) −3.60259 + 6.23986i −0.206623 + 0.357881i
\(305\) 2.64778 + 4.58610i 0.151612 + 0.262599i
\(306\) −0.836622 0.607841i −0.0478265 0.0347480i
\(307\) 14.2764 + 3.03454i 0.814797 + 0.173190i 0.596418 0.802674i \(-0.296590\pi\)
0.218379 + 0.975864i \(0.429923\pi\)
\(308\) −0.649924 + 2.00026i −0.0370329 + 0.113975i
\(309\) 17.9219 1.01954
\(310\) −4.96481 + 2.52004i −0.281983 + 0.143129i
\(311\) −12.4384 −0.705319 −0.352660 0.935752i \(-0.614723\pi\)
−0.352660 + 0.935752i \(0.614723\pi\)
\(312\) −0.731800 + 2.25225i −0.0414300 + 0.127508i
\(313\) −8.93812 1.89986i −0.505212 0.107386i −0.0517472 0.998660i \(-0.516479\pi\)
−0.453465 + 0.891274i \(0.649812\pi\)
\(314\) −1.25135 0.909159i −0.0706178 0.0513068i
\(315\) 1.12358 + 1.94610i 0.0633066 + 0.109650i
\(316\) 1.76106 3.05025i 0.0990674 0.171590i
\(317\) 4.57544 2.03712i 0.256982 0.114416i −0.274202 0.961672i \(-0.588414\pi\)
0.531184 + 0.847256i \(0.321747\pi\)
\(318\) −4.93490 + 3.58542i −0.276736 + 0.201060i
\(319\) −3.83374 1.70689i −0.214648 0.0955676i
\(320\) −0.978148 + 0.207912i −0.0546801 + 0.0116226i
\(321\) −0.0604119 + 0.574781i −0.00337186 + 0.0320811i
\(322\) 5.22124 + 5.79877i 0.290968 + 0.323153i
\(323\) 4.98571 5.53719i 0.277412 0.308098i
\(324\) −0.104528 0.994522i −0.00580714 0.0552512i
\(325\) −0.731800 2.25225i −0.0405929 0.124932i
\(326\) 3.67776 + 11.3190i 0.203692 + 0.626900i
\(327\) −1.88315 17.9170i −0.104139 0.990812i
\(328\) 0.230520 0.256018i 0.0127283 0.0141362i
\(329\) −4.48041 4.97600i −0.247013 0.274336i
\(330\) −0.0978320 + 0.930809i −0.00538547 + 0.0512394i
\(331\) 16.6242 3.53357i 0.913746 0.194223i 0.273034 0.962004i \(-0.411973\pi\)
0.640712 + 0.767782i \(0.278639\pi\)
\(332\) −8.89493 3.96028i −0.488173 0.217348i
\(333\) −2.38538 + 1.73308i −0.130718 + 0.0949722i
\(334\) 1.15578 0.514588i 0.0632417 0.0281570i
\(335\) −1.21006 + 2.09589i −0.0661128 + 0.114511i
\(336\) 1.12358 + 1.94610i 0.0612963 + 0.106168i
\(337\) 10.9061 + 7.92377i 0.594095 + 0.431635i 0.843778 0.536693i \(-0.180326\pi\)
−0.249683 + 0.968328i \(0.580326\pi\)
\(338\) 7.23032 + 1.53685i 0.393278 + 0.0835937i
\(339\) 2.79280 8.59535i 0.151684 0.466836i
\(340\) 1.03412 0.0560831
\(341\) 0.807236 + 5.14817i 0.0437143 + 0.278789i
\(342\) 7.20518 0.389611
\(343\) 6.21516 19.1283i 0.335587 1.03283i
\(344\) −1.19189 0.253343i −0.0642621 0.0136593i
\(345\) 2.80922 + 2.04102i 0.151244 + 0.109885i
\(346\) 3.40083 + 5.89040i 0.182830 + 0.316670i
\(347\) 12.1934 21.1196i 0.654577 1.13376i −0.327423 0.944878i \(-0.606180\pi\)
0.982000 0.188883i \(-0.0604865\pi\)
\(348\) −4.09616 + 1.82373i −0.219577 + 0.0977620i
\(349\) 4.00680 2.91111i 0.214479 0.155828i −0.475359 0.879792i \(-0.657682\pi\)
0.689838 + 0.723964i \(0.257682\pi\)
\(350\) −2.05288 0.914002i −0.109731 0.0488555i
\(351\) 2.31640 0.492367i 0.123640 0.0262806i
\(352\) −0.0978320 + 0.930809i −0.00521446 + 0.0496123i
\(353\) −23.3727 25.9580i −1.24400 1.38160i −0.895966 0.444123i \(-0.853515\pi\)
−0.348037 0.937481i \(-0.613152\pi\)
\(354\) −7.72293 + 8.57718i −0.410469 + 0.455872i
\(355\) −0.607606 5.78098i −0.0322484 0.306823i
\(356\) 0.607405 + 1.86940i 0.0321924 + 0.0990779i
\(357\) −0.718105 2.21010i −0.0380061 0.116971i
\(358\) −1.58729 15.1021i −0.0838909 0.798168i
\(359\) 14.7651 16.3982i 0.779270 0.865467i −0.214523 0.976719i \(-0.568820\pi\)
0.993792 + 0.111253i \(0.0354862\pi\)
\(360\) 0.669131 + 0.743145i 0.0352663 + 0.0391672i
\(361\) −3.44051 + 32.7342i −0.181079 + 1.72285i
\(362\) −23.8449 + 5.06838i −1.25326 + 0.266388i
\(363\) −9.24876 4.11781i −0.485434 0.216129i
\(364\) −4.30528 + 3.12797i −0.225658 + 0.163950i
\(365\) 9.30526 4.14297i 0.487059 0.216853i
\(366\) 2.64778 4.58610i 0.138402 0.239719i
\(367\) −1.38471 2.39840i −0.0722815 0.125195i 0.827619 0.561290i \(-0.189695\pi\)
−0.899901 + 0.436095i \(0.856361\pi\)
\(368\) 2.80922 + 2.04102i 0.146441 + 0.106396i
\(369\) −0.336978 0.0716269i −0.0175424 0.00372875i
\(370\) 0.911134 2.80418i 0.0473676 0.145783i
\(371\) −13.7074 −0.711652
\(372\) 4.66483 + 3.03963i 0.241860 + 0.157598i
\(373\) 26.1604 1.35453 0.677266 0.735738i \(-0.263164\pi\)
0.677266 + 0.735738i \(0.263164\pi\)
\(374\) 0.299089 0.920501i 0.0154655 0.0475980i
\(375\) −0.978148 0.207912i −0.0505113 0.0107365i
\(376\) −2.41063 1.75143i −0.124319 0.0903229i
\(377\) −5.30916 9.19574i −0.273436 0.473605i
\(378\) 1.12358 1.94610i 0.0577907 0.100096i
\(379\) 13.0085 5.79178i 0.668204 0.297504i −0.0444578 0.999011i \(-0.514156\pi\)
0.712662 + 0.701508i \(0.247489\pi\)
\(380\) −5.82911 + 4.23510i −0.299027 + 0.217256i
\(381\) 1.20265 + 0.535456i 0.0616138 + 0.0274323i
\(382\) −5.24690 + 1.11526i −0.268455 + 0.0570618i
\(383\) 0.629391 5.98825i 0.0321604 0.305985i −0.966603 0.256277i \(-0.917504\pi\)
0.998764 0.0497085i \(-0.0158292\pi\)
\(384\) 0.669131 + 0.743145i 0.0341464 + 0.0379235i
\(385\) −1.40731 + 1.56298i −0.0717234 + 0.0796569i
\(386\) 0.788232 + 7.49952i 0.0401199 + 0.381716i
\(387\) 0.376541 + 1.15887i 0.0191407 + 0.0589089i
\(388\) 5.04096 + 15.5145i 0.255916 + 0.787629i
\(389\) −2.34401 22.3018i −0.118846 1.13075i −0.877608 0.479378i \(-0.840862\pi\)
0.758762 0.651368i \(-0.225804\pi\)
\(390\) −1.58460 + 1.75988i −0.0802395 + 0.0891150i
\(391\) −2.40277 2.66854i −0.121513 0.134954i
\(392\) 0.203859 1.93959i 0.0102964 0.0979641i
\(393\) −1.81216 + 0.385187i −0.0914114 + 0.0194301i
\(394\) −22.6582 10.0881i −1.14150 0.508230i
\(395\) 2.84946 2.07025i 0.143372 0.104166i
\(396\) 0.855020 0.380680i 0.0429664 0.0191299i
\(397\) 2.68504 4.65063i 0.134758 0.233408i −0.790747 0.612143i \(-0.790308\pi\)
0.925505 + 0.378735i \(0.123641\pi\)
\(398\) 11.1867 + 19.3759i 0.560738 + 0.971227i
\(399\) 13.0989 + 9.51694i 0.655767 + 0.476443i
\(400\) −0.978148 0.207912i −0.0489074 0.0103956i
\(401\) −4.40779 + 13.5658i −0.220115 + 0.677443i 0.778636 + 0.627476i \(0.215912\pi\)
−0.998751 + 0.0499674i \(0.984088\pi\)
\(402\) 2.42013 0.120705
\(403\) −6.00416 + 11.7389i −0.299088 + 0.584758i
\(404\) 4.96868 0.247201
\(405\) 0.309017 0.951057i 0.0153552 0.0472584i
\(406\) −9.85563 2.09488i −0.489127 0.103967i
\(407\) −2.23256 1.62205i −0.110664 0.0804022i
\(408\) −0.517061 0.895576i −0.0255983 0.0443376i
\(409\) 9.81332 16.9972i 0.485237 0.840456i −0.514619 0.857419i \(-0.672066\pi\)
0.999856 + 0.0169632i \(0.00539981\pi\)
\(410\) 0.314722 0.140123i 0.0155430 0.00692020i
\(411\) 4.54314 3.30079i 0.224097 0.162816i
\(412\) 16.3724 + 7.28948i 0.806612 + 0.359127i
\(413\) −25.3694 + 5.39242i −1.24834 + 0.265344i
\(414\) 0.362964 3.45337i 0.0178387 0.169724i
\(415\) −6.51513 7.23579i −0.319815 0.355191i
\(416\) −1.58460 + 1.75988i −0.0776916 + 0.0862853i
\(417\) −0.956198 9.09762i −0.0468252 0.445512i
\(418\) 2.08388 + 6.41353i 0.101926 + 0.313696i
\(419\) 4.30977 + 13.2641i 0.210546 + 0.647994i 0.999440 + 0.0334645i \(0.0106541\pi\)
−0.788894 + 0.614529i \(0.789346\pi\)
\(420\) 0.234892 + 2.23485i 0.0114616 + 0.109049i
\(421\) 14.4927 16.0958i 0.706330 0.784459i −0.278040 0.960569i \(-0.589685\pi\)
0.984370 + 0.176110i \(0.0563516\pi\)
\(422\) −6.49370 7.21198i −0.316108 0.351074i
\(423\) −0.311464 + 2.96338i −0.0151439 + 0.144084i
\(424\) −5.96658 + 1.26824i −0.289763 + 0.0615910i
\(425\) 0.944717 + 0.420615i 0.0458255 + 0.0204028i
\(426\) −4.70268 + 3.41669i −0.227845 + 0.165539i
\(427\) 10.8712 4.84016i 0.526093 0.234232i
\(428\) −0.288973 + 0.500516i −0.0139681 + 0.0241934i
\(429\) 1.10822 + 1.91949i 0.0535054 + 0.0926741i
\(430\) −0.985798 0.716224i −0.0475394 0.0345394i
\(431\) 22.3931 + 4.75981i 1.07864 + 0.229272i 0.712772 0.701396i \(-0.247439\pi\)
0.365867 + 0.930667i \(0.380773\pi\)
\(432\) 0.309017 0.951057i 0.0148676 0.0457577i
\(433\) −0.348812 −0.0167628 −0.00838142 0.999965i \(-0.502668\pi\)
−0.00838142 + 0.999965i \(0.502668\pi\)
\(434\) 4.46572 + 11.6876i 0.214361 + 0.561020i
\(435\) −4.48380 −0.214982
\(436\) 5.56715 17.1339i 0.266618 0.820567i
\(437\) 24.4725 + 5.20178i 1.17068 + 0.248835i
\(438\) −8.24054 5.98710i −0.393748 0.286075i
\(439\) −4.71032 8.15851i −0.224811 0.389384i 0.731452 0.681893i \(-0.238843\pi\)
−0.956263 + 0.292509i \(0.905510\pi\)
\(440\) −0.467968 + 0.810545i −0.0223095 + 0.0386412i
\(441\) −1.78166 + 0.793248i −0.0848411 + 0.0377737i
\(442\) 1.98125 1.43946i 0.0942384 0.0684682i
\(443\) 14.4447 + 6.43118i 0.686287 + 0.305555i 0.720097 0.693874i \(-0.244097\pi\)
−0.0338097 + 0.999428i \(0.510764\pi\)
\(444\) −2.88406 + 0.613026i −0.136871 + 0.0290929i
\(445\) −0.205461 + 1.95483i −0.00973980 + 0.0926680i
\(446\) 2.11041 + 2.34385i 0.0999310 + 0.110985i
\(447\) 5.29036 5.87554i 0.250225 0.277904i
\(448\) 0.234892 + 2.23485i 0.0110976 + 0.105587i
\(449\) −3.09746 9.53300i −0.146178 0.449890i 0.850982 0.525194i \(-0.176007\pi\)
−0.997161 + 0.0753040i \(0.976007\pi\)
\(450\) 0.309017 + 0.951057i 0.0145672 + 0.0448332i
\(451\) −0.0337037 0.320670i −0.00158705 0.0150997i
\(452\) 6.04739 6.71631i 0.284446 0.315909i
\(453\) 10.7737 + 11.9654i 0.506191 + 0.562182i
\(454\) −0.382095 + 3.63539i −0.0179326 + 0.170617i
\(455\) −5.20533 + 1.10643i −0.244030 + 0.0518701i
\(456\) 6.58226 + 2.93061i 0.308242 + 0.137238i
\(457\) −24.1090 + 17.5162i −1.12777 + 0.819375i −0.985369 0.170434i \(-0.945483\pi\)
−0.142404 + 0.989809i \(0.545483\pi\)
\(458\) −1.32515 + 0.589995i −0.0619202 + 0.0275686i
\(459\) −0.517061 + 0.895576i −0.0241343 + 0.0418019i
\(460\) 1.73620 + 3.00718i 0.0809506 + 0.140210i
\(461\) −17.8241 12.9500i −0.830151 0.603140i 0.0894509 0.995991i \(-0.471489\pi\)
−0.919602 + 0.392851i \(0.871489\pi\)
\(462\) 2.05724 + 0.437280i 0.0957114 + 0.0203441i
\(463\) 5.24705 16.1488i 0.243851 0.750497i −0.751972 0.659195i \(-0.770897\pi\)
0.995823 0.0913018i \(-0.0291028\pi\)
\(464\) −4.48380 −0.208155
\(465\) 3.02520 + 4.67420i 0.140290 + 0.216761i
\(466\) −4.80968 −0.222804
\(467\) 12.9386 39.8211i 0.598729 1.84270i 0.0635171 0.997981i \(-0.479768\pi\)
0.535212 0.844718i \(-0.320232\pi\)
\(468\) 2.31640 + 0.492367i 0.107076 + 0.0227597i
\(469\) 4.39977 + 3.19662i 0.203162 + 0.147606i
\(470\) −1.48985 2.58050i −0.0687217 0.119029i
\(471\) −0.773377 + 1.33953i −0.0356353 + 0.0617222i
\(472\) −10.5439 + 4.69445i −0.485322 + 0.216079i
\(473\) −0.922644 + 0.670340i −0.0424232 + 0.0308223i
\(474\) −3.21762 1.43258i −0.147790 0.0658004i
\(475\) −7.04772 + 1.49804i −0.323372 + 0.0687348i
\(476\) 0.242907 2.31111i 0.0111336 0.105929i
\(477\) 4.08161 + 4.53309i 0.186884 + 0.207556i
\(478\) 14.3135 15.8968i 0.654685 0.727101i
\(479\) 1.47402 + 14.0244i 0.0673498 + 0.640791i 0.975174 + 0.221440i \(0.0710756\pi\)
−0.907824 + 0.419351i \(0.862258\pi\)
\(480\) 0.309017 + 0.951057i 0.0141046 + 0.0434096i
\(481\) −2.15771 6.64073i −0.0983829 0.302791i
\(482\) −1.08798 10.3515i −0.0495562 0.471496i
\(483\) 5.22124 5.79877i 0.237575 0.263853i
\(484\) −6.77429 7.52362i −0.307922 0.341983i
\(485\) −1.70516 + 16.2235i −0.0774274 + 0.736673i
\(486\) −0.978148 + 0.207912i −0.0443697 + 0.00943107i
\(487\) 23.8982 + 10.6401i 1.08293 + 0.482151i 0.869058 0.494711i \(-0.164726\pi\)
0.213872 + 0.976862i \(0.431393\pi\)
\(488\) 4.28421 3.11266i 0.193937 0.140903i
\(489\) 10.8725 4.84076i 0.491673 0.218907i
\(490\) 0.975137 1.68899i 0.0440522 0.0763006i
\(491\) −15.3256 26.5448i −0.691636 1.19795i −0.971302 0.237851i \(-0.923557\pi\)
0.279666 0.960097i \(-0.409776\pi\)
\(492\) −0.278711 0.202496i −0.0125653 0.00912921i
\(493\) 4.53547 + 0.964044i 0.204267 + 0.0434184i
\(494\) −5.27274 + 16.2278i −0.237232 + 0.730125i
\(495\) 0.935936 0.0420672
\(496\) 3.02520 + 4.67420i 0.135836 + 0.209878i
\(497\) −13.0624 −0.585927
\(498\) −3.00881 + 9.26016i −0.134828 + 0.414958i
\(499\) 36.3195 + 7.71995i 1.62588 + 0.345592i 0.928565 0.371169i \(-0.121043\pi\)
0.697319 + 0.716761i \(0.254376\pi\)
\(500\) −0.809017 0.587785i −0.0361803 0.0262866i
\(501\) −0.632581 1.09566i −0.0282616 0.0489506i
\(502\) 5.46103 9.45879i 0.243738 0.422166i
\(503\) 23.0708 10.2718i 1.02868 0.457997i 0.178192 0.983996i \(-0.442975\pi\)
0.850485 + 0.525999i \(0.176308\pi\)
\(504\) 1.81799 1.32085i 0.0809797 0.0588352i
\(505\) 4.53912 + 2.02095i 0.201988 + 0.0899309i
\(506\) 3.17892 0.675700i 0.141320 0.0300385i
\(507\) 0.772659 7.35136i 0.0343150 0.326485i
\(508\) 0.880890 + 0.978327i 0.0390832 + 0.0434062i
\(509\) 3.97213 4.41150i 0.176062 0.195536i −0.648655 0.761083i \(-0.724668\pi\)
0.824716 + 0.565546i \(0.191335\pi\)
\(510\) −0.108095 1.02846i −0.00478653 0.0455408i
\(511\) −7.07318 21.7690i −0.312899 0.963004i
\(512\) 0.309017 + 0.951057i 0.0136568 + 0.0420312i
\(513\) −0.753146 7.16570i −0.0332522 0.316374i
\(514\) 7.97730 8.85969i 0.351863 0.390784i
\(515\) 11.9921 + 13.3185i 0.528434 + 0.586885i
\(516\) −0.127369 + 1.21184i −0.00560712 + 0.0533482i
\(517\) −2.72787 + 0.579827i −0.119972 + 0.0255007i
\(518\) −6.05291 2.69493i −0.265949 0.118408i
\(519\) 5.50265 3.99791i 0.241540 0.175489i
\(520\) −2.16342 + 0.963215i −0.0948721 + 0.0422398i
\(521\) −0.811222 + 1.40508i −0.0355403 + 0.0615576i −0.883248 0.468905i \(-0.844649\pi\)
0.847708 + 0.530463i \(0.177982\pi\)
\(522\) 2.24190 + 3.88308i 0.0981253 + 0.169958i
\(523\) 29.5622 + 21.4782i 1.29266 + 0.939176i 0.999856 0.0169951i \(-0.00540997\pi\)
0.292809 + 0.956171i \(0.405410\pi\)
\(524\) −1.81216 0.385187i −0.0791646 0.0168270i
\(525\) −0.694411 + 2.13718i −0.0303066 + 0.0932740i
\(526\) 5.75486 0.250924
\(527\) −2.05508 5.37850i −0.0895208 0.234291i
\(528\) 0.935936 0.0407314
\(529\) −3.38142 + 10.4069i −0.147018 + 0.452475i
\(530\) −5.96658 1.26824i −0.259172 0.0550886i
\(531\) 9.33746 + 6.78406i 0.405211 + 0.294403i
\(532\) 8.09559 + 14.0220i 0.350988 + 0.607930i
\(533\) 0.407922 0.706541i 0.0176691 0.0306037i
\(534\) 1.79567 0.799483i 0.0777061 0.0345970i
\(535\) −0.467569 + 0.339708i −0.0202148 + 0.0146869i
\(536\) 2.21090 + 0.984354i 0.0954961 + 0.0425176i
\(537\) −14.8534 + 3.15719i −0.640972 + 0.136243i
\(538\) −1.75454 + 16.6933i −0.0756435 + 0.719700i
\(539\) −1.22139 1.35649i −0.0526088 0.0584280i
\(540\) 0.669131 0.743145i 0.0287948 0.0319799i
\(541\) 0.359054 + 3.41617i 0.0154369 + 0.146872i 0.999525 0.0308069i \(-0.00980768\pi\)
−0.984088 + 0.177679i \(0.943141\pi\)
\(542\) 6.01765 + 18.5204i 0.258480 + 0.795521i
\(543\) 7.53309 + 23.1845i 0.323276 + 0.994940i
\(544\) −0.108095 1.02846i −0.00463454 0.0440947i
\(545\) 12.0548 13.3883i 0.516373 0.573490i
\(546\) 3.56086 + 3.95473i 0.152391 + 0.169247i
\(547\) −2.49565 + 23.7446i −0.106706 + 1.01524i 0.801862 + 0.597509i \(0.203843\pi\)
−0.908569 + 0.417735i \(0.862824\pi\)
\(548\) 5.49292 1.16756i 0.234646 0.0498755i
\(549\) −4.83774 2.15390i −0.206470 0.0919263i
\(550\) −0.757188 + 0.550130i −0.0322866 + 0.0234576i
\(551\) −29.5135 + 13.1403i −1.25732 + 0.559794i
\(552\) 1.73620 3.00718i 0.0738974 0.127994i
\(553\) −3.95739 6.85439i −0.168285 0.291478i
\(554\) −7.65580 5.56227i −0.325264 0.236318i
\(555\) −2.88406 0.613026i −0.122422 0.0260215i
\(556\) 2.82680 8.70001i 0.119883 0.368963i
\(557\) −9.86795 −0.418118 −0.209059 0.977903i \(-0.567040\pi\)
−0.209059 + 0.977903i \(0.567040\pi\)
\(558\) 2.53538 4.95700i 0.107331 0.209847i
\(559\) −2.88563 −0.122049
\(560\) −0.694411 + 2.13718i −0.0293442 + 0.0903122i
\(561\) −0.946722 0.201232i −0.0399706 0.00849602i
\(562\) 13.8196 + 10.0405i 0.582943 + 0.423533i
\(563\) 8.24091 + 14.2737i 0.347313 + 0.601564i 0.985771 0.168093i \(-0.0537609\pi\)
−0.638458 + 0.769656i \(0.720428\pi\)
\(564\) −1.48985 + 2.58050i −0.0627341 + 0.108659i
\(565\) 8.25634 3.67596i 0.347347 0.154649i
\(566\) 0.359892 0.261477i 0.0151274 0.0109907i
\(567\) −2.05288 0.914002i −0.0862130 0.0383845i
\(568\) −5.68580 + 1.20855i −0.238571 + 0.0507098i
\(569\) 4.81426 45.8046i 0.201824 1.92023i −0.158422 0.987372i \(-0.550641\pi\)
0.360246 0.932857i \(-0.382693\pi\)
\(570\) 4.82120 + 5.35449i 0.201938 + 0.224275i
\(571\) −7.59756 + 8.43795i −0.317948 + 0.353117i −0.880841 0.473413i \(-0.843022\pi\)
0.562893 + 0.826530i \(0.309688\pi\)
\(572\) 0.231681 + 2.20430i 0.00968708 + 0.0921664i
\(573\) 1.65760 + 5.10158i 0.0692474 + 0.213122i
\(574\) −0.239229 0.736271i −0.00998522 0.0307313i
\(575\) 0.362964 + 3.45337i 0.0151366 + 0.144015i
\(576\) 0.669131 0.743145i 0.0278804 0.0309644i
\(577\) 19.4368 + 21.5867i 0.809163 + 0.898667i 0.996497 0.0836297i \(-0.0266513\pi\)
−0.187334 + 0.982296i \(0.559985\pi\)
\(578\) 1.66520 15.8433i 0.0692632 0.658995i
\(579\) 7.37605 1.56783i 0.306538 0.0651567i
\(580\) −4.09616 1.82373i −0.170084 0.0757261i
\(581\) −17.7012 + 12.8607i −0.734371 + 0.533552i
\(582\) 14.9026 6.63505i 0.617731 0.275032i
\(583\) −2.85455 + 4.94422i −0.118223 + 0.204769i
\(584\) −5.09294 8.82122i −0.210747 0.365025i
\(585\) 1.91588 + 1.39197i 0.0792117 + 0.0575507i
\(586\) 22.9870 + 4.88603i 0.949583 + 0.201840i
\(587\) −4.07703 + 12.5478i −0.168277 + 0.517903i −0.999263 0.0383905i \(-0.987777\pi\)
0.830986 + 0.556293i \(0.187777\pi\)
\(588\) −1.95027 −0.0804279
\(589\) 33.6109 + 21.9011i 1.38491 + 0.902419i
\(590\) −11.5417 −0.475166
\(591\) −7.66439 + 23.5886i −0.315271 + 0.970304i
\(592\) −2.88406 0.613026i −0.118534 0.0251952i
\(593\) −23.1755 16.8380i −0.951705 0.691454i −0.000495829 1.00000i \(-0.500158\pi\)
−0.951210 + 0.308545i \(0.900158\pi\)
\(594\) −0.467968 0.810545i −0.0192010 0.0332571i
\(595\) 1.16192 2.01250i 0.0476340 0.0825045i
\(596\) 7.22278 3.21579i 0.295857 0.131724i
\(597\) 18.1004 13.1507i 0.740802 0.538224i
\(598\) 7.51223 + 3.34466i 0.307198 + 0.136773i
\(599\) −45.0506 + 9.57580i −1.84072 + 0.391257i −0.990764 0.135600i \(-0.956704\pi\)
−0.849954 + 0.526857i \(0.823371\pi\)
\(600\) −0.104528 + 0.994522i −0.00426736 + 0.0406012i
\(601\) −20.9630 23.2818i −0.855100 0.949685i 0.144104 0.989563i \(-0.453970\pi\)
−0.999205 + 0.0398773i \(0.987303\pi\)
\(602\) −1.83221 + 2.03487i −0.0746752 + 0.0829353i
\(603\) −0.252972 2.40687i −0.0103018 0.0980153i
\(604\) 4.97548 + 15.3130i 0.202449 + 0.623075i
\(605\) −3.12850 9.62852i −0.127191 0.391455i
\(606\) −0.519369 4.94146i −0.0210979 0.200733i
\(607\) −22.3324 + 24.8027i −0.906445 + 1.00671i 0.0934937 + 0.995620i \(0.470196\pi\)
−0.999939 + 0.0110891i \(0.996470\pi\)
\(608\) 4.82120 + 5.35449i 0.195526 + 0.217153i
\(609\) −1.05321 + 10.0206i −0.0426782 + 0.406056i
\(610\) 5.17985 1.10101i 0.209726 0.0445786i
\(611\) −6.44634 2.87009i −0.260791 0.116112i
\(612\) −0.836622 + 0.607841i −0.0338184 + 0.0245705i
\(613\) 6.05158 2.69434i 0.244421 0.108823i −0.280870 0.959746i \(-0.590623\pi\)
0.525291 + 0.850923i \(0.323956\pi\)
\(614\) 7.29767 12.6399i 0.294510 0.510106i
\(615\) −0.172253 0.298351i −0.00694592 0.0120307i
\(616\) 1.70152 + 1.23623i 0.0685563 + 0.0498091i
\(617\) −6.97886 1.48340i −0.280958 0.0597195i 0.0652772 0.997867i \(-0.479207\pi\)
−0.346235 + 0.938148i \(0.612540\pi\)
\(618\) 5.53816 17.0447i 0.222777 0.685638i
\(619\) −3.41943 −0.137439 −0.0687193 0.997636i \(-0.521891\pi\)
−0.0687193 + 0.997636i \(0.521891\pi\)
\(620\) 0.862491 + 5.50056i 0.0346385 + 0.220908i
\(621\) −3.47239 −0.139342
\(622\) −3.84369 + 11.8297i −0.154118 + 0.474326i
\(623\) 4.32050 + 0.918351i 0.173097 + 0.0367929i
\(624\) 1.91588 + 1.39197i 0.0766964 + 0.0557232i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −4.56890 + 7.91357i −0.182610 + 0.316290i
\(627\) 6.16057 2.74286i 0.246030 0.109539i
\(628\) −1.25135 + 0.909159i −0.0499343 + 0.0362794i
\(629\) 2.78549 + 1.24018i 0.111065 + 0.0494492i
\(630\) 2.19805 0.467211i 0.0875726 0.0186141i
\(631\) 1.15340 10.9739i 0.0459161 0.436863i −0.947280 0.320407i \(-0.896180\pi\)
0.993196 0.116455i \(-0.0371532\pi\)
\(632\) −2.35676 2.61745i −0.0937469 0.104116i
\(633\) −6.49370 + 7.21198i −0.258101 + 0.286650i
\(634\) −0.523524 4.98100i −0.0207918 0.197821i
\(635\) 0.406811 + 1.25204i 0.0161438 + 0.0496856i
\(636\) 1.88497 + 5.80133i 0.0747437 + 0.230038i
\(637\) −0.482770 4.59325i −0.0191280 0.181991i
\(638\) −2.80804 + 3.11865i −0.111171 + 0.123468i
\(639\) 3.88954 + 4.31977i 0.153868 + 0.170888i
\(640\) −0.104528 + 0.994522i −0.00413185 + 0.0393119i
\(641\) −6.59305 + 1.40140i −0.260410 + 0.0553518i −0.336266 0.941767i \(-0.609164\pi\)
0.0758565 + 0.997119i \(0.475831\pi\)
\(642\) 0.527981 + 0.235072i 0.0208377 + 0.00927755i
\(643\) −8.23323 + 5.98179i −0.324687 + 0.235899i −0.738173 0.674612i \(-0.764311\pi\)
0.413486 + 0.910510i \(0.364311\pi\)
\(644\) 7.12841 3.17377i 0.280899 0.125064i
\(645\) −0.609256 + 1.05526i −0.0239894 + 0.0415509i
\(646\) −3.72551 6.45278i −0.146578 0.253881i
\(647\) 11.0509 + 8.02892i 0.434454 + 0.315650i 0.783428 0.621483i \(-0.213470\pi\)
−0.348973 + 0.937133i \(0.613470\pi\)
\(648\) −0.978148 0.207912i −0.0384253 0.00816754i
\(649\) −3.33810 + 10.2736i −0.131032 + 0.403275i
\(650\) −2.36815 −0.0928866
\(651\) 11.1567 5.66294i 0.437267 0.221948i
\(652\) 11.9015 0.466098
\(653\) 3.26513 10.0490i 0.127774 0.393249i −0.866622 0.498965i \(-0.833713\pi\)
0.994396 + 0.105716i \(0.0337135\pi\)
\(654\) −17.6220 3.74567i −0.689075 0.146467i
\(655\) −1.49882 1.08896i −0.0585638 0.0425491i
\(656\) −0.172253 0.298351i −0.00672536 0.0116487i
\(657\) −5.09294 + 8.82122i −0.198694 + 0.344149i
\(658\) −6.11698 + 2.72345i −0.238465 + 0.106171i
\(659\) 4.33669 3.15079i 0.168933 0.122737i −0.500106 0.865964i \(-0.666706\pi\)
0.669040 + 0.743227i \(0.266706\pi\)
\(660\) 0.855020 + 0.380680i 0.0332816 + 0.0148179i
\(661\) −9.75906 + 2.07435i −0.379583 + 0.0806829i −0.393752 0.919217i \(-0.628823\pi\)
0.0141687 + 0.999900i \(0.495490\pi\)
\(662\) 1.77652 16.9024i 0.0690464 0.656932i
\(663\) −1.63867 1.81993i −0.0636408 0.0706803i
\(664\) −6.51513 + 7.23579i −0.252836 + 0.280803i
\(665\) 1.69244 + 16.1025i 0.0656300 + 0.624427i
\(666\) 0.911134 + 2.80418i 0.0353057 + 0.108660i
\(667\) 4.81124 + 14.8075i 0.186292 + 0.573348i
\(668\) −0.132245 1.25823i −0.00511673 0.0486824i
\(669\) 2.11041 2.34385i 0.0815933 0.0906186i
\(670\) 1.61938 + 1.79850i 0.0625621 + 0.0694823i
\(671\) 0.518076 4.92917i 0.0200001 0.190288i
\(672\) 2.19805 0.467211i 0.0847918 0.0180230i
\(673\) 11.2430 + 5.00570i 0.433386 + 0.192956i 0.611822 0.790996i \(-0.290437\pi\)
−0.178436 + 0.983952i \(0.557104\pi\)
\(674\) 10.9061 7.92377i 0.420088 0.305212i
\(675\) 0.913545 0.406737i 0.0351624 0.0156553i
\(676\) 3.69592 6.40153i 0.142151 0.246213i
\(677\) −0.332241 0.575459i −0.0127691 0.0221167i 0.859570 0.511018i \(-0.170731\pi\)
−0.872339 + 0.488901i \(0.837398\pi\)
\(678\) −7.31164 5.31222i −0.280802 0.204015i
\(679\) 35.8566 + 7.62156i 1.37605 + 0.292489i
\(680\) 0.319561 0.983508i 0.0122546 0.0377158i
\(681\) 3.65541 0.140076
\(682\) 5.14565 + 0.823145i 0.197037 + 0.0315198i
\(683\) 19.0961 0.730691 0.365346 0.930872i \(-0.380951\pi\)
0.365346 + 0.930872i \(0.380951\pi\)
\(684\) 2.22652 6.85253i 0.0851332 0.262013i
\(685\) 5.49292 + 1.16756i 0.209874 + 0.0446100i
\(686\) −16.2715 11.8219i −0.621249 0.451364i
\(687\) 0.725278 + 1.25622i 0.0276711 + 0.0479277i
\(688\) −0.609256 + 1.05526i −0.0232277 + 0.0402315i
\(689\) −13.1966 + 5.87549i −0.502749 + 0.223838i
\(690\) 2.80922 2.04102i 0.106945 0.0777003i
\(691\) −24.4616 10.8910i −0.930564 0.414314i −0.115253 0.993336i \(-0.536768\pi\)
−0.815312 + 0.579022i \(0.803434\pi\)
\(692\) 6.65302 1.41414i 0.252910 0.0537576i
\(693\) 0.219844 2.09168i 0.00835119 0.0794562i
\(694\) −16.3180 18.1229i −0.619422 0.687938i
\(695\) 6.12103 6.79809i 0.232184 0.257866i
\(696\) 0.468685 + 4.45924i 0.0177654 + 0.169027i
\(697\) 0.110091 + 0.338825i 0.00416999 + 0.0128339i
\(698\) −1.53046 4.71028i −0.0579289 0.178287i
\(699\) 0.502748 + 4.78333i 0.0190157 + 0.180922i
\(700\) −1.50364 + 1.66997i −0.0568324 + 0.0631187i
\(701\) 15.6639 + 17.3965i 0.591617 + 0.657057i 0.962392 0.271666i \(-0.0875745\pi\)
−0.370775 + 0.928723i \(0.620908\pi\)
\(702\) 0.247539 2.35518i 0.00934277 0.0888906i
\(703\) −20.7802 + 4.41696i −0.783739 + 0.166589i
\(704\) 0.855020 + 0.380680i 0.0322248 + 0.0143474i
\(705\) −2.41063 + 1.75143i −0.0907896 + 0.0659625i
\(706\) −31.9101 + 14.2073i −1.20095 + 0.534698i
\(707\) 5.58271 9.66954i 0.209960 0.363661i
\(708\) 5.77087 + 9.99544i 0.216883 + 0.375652i
\(709\) −22.9144 16.6483i −0.860568 0.625239i 0.0674716 0.997721i \(-0.478507\pi\)
−0.928039 + 0.372482i \(0.878507\pi\)
\(710\) −5.68580 1.20855i −0.213384 0.0453563i
\(711\) −1.08840 + 3.34974i −0.0408180 + 0.125625i
\(712\) 1.96560 0.0736641
\(713\) 12.1901 15.0061i 0.456525 0.561983i
\(714\) −2.32384 −0.0869674
\(715\) −0.684918 + 2.10796i −0.0256145 + 0.0788333i
\(716\) −14.8534 3.15719i −0.555098 0.117990i
\(717\) −17.3058 12.5734i −0.646299 0.469563i
\(718\) −11.0330 19.1097i −0.411748 0.713169i
\(719\) −1.48364 + 2.56974i −0.0553305 + 0.0958352i −0.892364 0.451316i \(-0.850955\pi\)
0.837033 + 0.547152i \(0.184288\pi\)
\(720\) 0.913545 0.406737i 0.0340458 0.0151582i
\(721\) 32.5818 23.6720i 1.21341 0.881593i
\(722\) 30.0689 + 13.3876i 1.11905 + 0.498233i
\(723\) −10.1810 + 2.16404i −0.378636 + 0.0804816i
\(724\) −2.54815 + 24.2440i −0.0947013 + 0.901023i
\(725\) −3.00025 3.33211i −0.111426 0.123752i
\(726\) −6.77429 + 7.52362i −0.251418 + 0.279228i
\(727\) −1.26353 12.0216i −0.0468616 0.445858i −0.992645 0.121060i \(-0.961371\pi\)
0.945784 0.324798i \(-0.105296\pi\)
\(728\) 1.64447 + 5.06116i 0.0609481 + 0.187579i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) −1.06471 10.1301i −0.0394068 0.374931i
\(731\) 0.843165 0.936430i 0.0311856 0.0346351i
\(732\) −3.54343 3.93538i −0.130969 0.145456i
\(733\) −4.55868 + 43.3729i −0.168379 + 1.60202i 0.505268 + 0.862963i \(0.331394\pi\)
−0.673647 + 0.739054i \(0.735273\pi\)
\(734\) −2.70891 + 0.575797i −0.0999877 + 0.0212530i
\(735\) −1.78166 0.793248i −0.0657176 0.0292594i
\(736\) 2.80922 2.04102i 0.103549 0.0752330i
\(737\) 2.06926 0.921293i 0.0762221 0.0339363i
\(738\) −0.172253 + 0.298351i −0.00634073 + 0.0109825i
\(739\) 22.7672 + 39.4340i 0.837506 + 1.45060i 0.891974 + 0.452087i \(0.149320\pi\)
−0.0544682 + 0.998516i \(0.517346\pi\)
\(740\) −2.38538 1.73308i −0.0876883 0.0637093i
\(741\) 16.6901 + 3.54759i 0.613126 + 0.130324i
\(742\) −4.23582 + 13.0365i −0.155502 + 0.478585i
\(743\) −48.9563 −1.79603 −0.898015 0.439964i \(-0.854991\pi\)
−0.898015 + 0.439964i \(0.854991\pi\)
\(744\) 4.33238 3.49722i 0.158833 0.128214i
\(745\) 7.90632 0.289665
\(746\) 8.08400 24.8800i 0.295976 0.910921i
\(747\) 9.52394 + 2.02438i 0.348463 + 0.0740680i
\(748\) −0.783025 0.568901i −0.0286302 0.0208011i
\(749\) 0.649369 + 1.12474i 0.0237274 + 0.0410971i
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) 1.41768 0.631190i 0.0517317 0.0230324i −0.380708 0.924695i \(-0.624320\pi\)
0.432439 + 0.901663i \(0.357653\pi\)
\(752\) −2.41063 + 1.75143i −0.0879066 + 0.0638679i
\(753\) −9.97780 4.44240i −0.363611 0.161890i
\(754\) −10.3863 + 2.20767i −0.378246 + 0.0803988i
\(755\) −1.68301 + 16.0128i −0.0612511 + 0.582765i
\(756\) −1.50364 1.66997i −0.0546870 0.0607360i
\(757\) −26.6534 + 29.6016i −0.968735 + 1.07589i 0.0283504 + 0.999598i \(0.490975\pi\)
−0.997086 + 0.0762914i \(0.975692\pi\)
\(758\) −1.48845 14.1616i −0.0540628 0.514373i
\(759\) −1.00429 3.09088i −0.0364533 0.112192i
\(760\) 2.22652 + 6.85253i 0.0807644 + 0.248567i
\(761\) 0.644097 + 6.12818i 0.0233485 + 0.222146i 0.999974 + 0.00719863i \(0.00229141\pi\)
−0.976626 + 0.214948i \(0.931042\pi\)
\(762\) 0.880890 0.978327i 0.0319113 0.0354411i
\(763\) −27.0892 30.0856i −0.980694 1.08917i
\(764\) −0.560703 + 5.33474i −0.0202855 + 0.193004i
\(765\) −1.01152 + 0.215006i −0.0365717 + 0.00777356i
\(766\) −5.50067 2.44906i −0.198747 0.0884880i
\(767\) −22.1125 + 16.0657i −0.798438 + 0.580099i
\(768\) 0.913545 0.406737i 0.0329647 0.0146768i
\(769\) −1.97304 + 3.41740i −0.0711496 + 0.123235i −0.899405 0.437115i \(-0.856000\pi\)
0.828256 + 0.560350i \(0.189333\pi\)
\(770\) 1.05160 + 1.82142i 0.0378970 + 0.0656395i
\(771\) −9.64501 7.00751i −0.347356 0.252369i
\(772\) 7.37605 + 1.56783i 0.265470 + 0.0564273i
\(773\) 8.65248 26.6296i 0.311208 0.957800i −0.666079 0.745881i \(-0.732029\pi\)
0.977287 0.211919i \(-0.0679713\pi\)
\(774\) 1.21851 0.0437985
\(775\) −1.44935 + 5.37581i −0.0520623 + 0.193105i
\(776\) 16.3129 0.585599
\(777\) −2.04746 + 6.30145i −0.0734524 + 0.226063i
\(778\) −21.9346 4.66234i −0.786394 0.167153i
\(779\) −2.00816 1.45902i −0.0719500 0.0522747i
\(780\) 1.18408 + 2.05088i 0.0423967 + 0.0734333i
\(781\) −2.72022 + 4.71156i −0.0973371 + 0.168593i
\(782\) −3.28043 + 1.46054i −0.117308 + 0.0522288i
\(783\) 3.62747 2.63551i 0.129635 0.0941855i
\(784\) −1.78166 0.793248i −0.0636308 0.0283303i
\(785\) −1.51295 + 0.321588i −0.0539996 + 0.0114780i
\(786\) −0.193654 + 1.84250i −0.00690742 + 0.0657197i
\(787\) 18.0754 + 20.0747i 0.644317 + 0.715586i 0.973502 0.228679i \(-0.0734407\pi\)
−0.329185 + 0.944265i \(0.606774\pi\)
\(788\) −16.5961 + 18.4318i −0.591212 + 0.656607i
\(789\) −0.601547 5.72333i −0.0214156 0.203756i
\(790\) −1.08840 3.34974i −0.0387234 0.119178i
\(791\) −6.27587 19.3151i −0.223144 0.686767i
\(792\) −0.0978320 0.930809i −0.00347631 0.0330749i
\(793\) 8.39138 9.31957i 0.297987 0.330948i
\(794\) −3.59329 3.99075i −0.127521 0.141626i
\(795\) −0.637611 + 6.06646i −0.0226137 + 0.215155i
\(796\) 21.8845 4.65169i 0.775674 0.164875i
\(797\) 0.0415867 + 0.0185156i 0.00147308 + 0.000655857i 0.407473 0.913217i \(-0.366410\pi\)
−0.406000 + 0.913873i \(0.633077\pi\)
\(798\) 13.0989 9.51694i 0.463697 0.336896i
\(799\) 2.81498 1.25331i 0.0995867 0.0443388i
\(800\) −0.500000 + 0.866025i −0.0176777 + 0.0306186i
\(801\) −0.982801 1.70226i −0.0347256 0.0601465i
\(802\) 11.5397 + 8.38412i 0.407483 + 0.296053i
\(803\) −9.32500 1.98209i −0.329072 0.0699464i
\(804\) 0.747860 2.30168i 0.0263750 0.0811739i
\(805\) 7.80302 0.275020
\(806\) 9.30901 + 9.33783i 0.327896 + 0.328911i
\(807\) 16.7853 0.590870
\(808\) 1.53541 4.72550i 0.0540155 0.166242i
\(809\) −21.5286 4.57604i −0.756905 0.160885i −0.186733 0.982411i \(-0.559790\pi\)
−0.570172 + 0.821526i \(0.693123\pi\)
\(810\) −0.809017 0.587785i −0.0284260 0.0206527i
\(811\) −11.2240 19.4406i −0.394129 0.682651i 0.598861 0.800853i \(-0.295620\pi\)
−0.992990 + 0.118202i \(0.962287\pi\)
\(812\) −5.03791 + 8.72591i −0.176796 + 0.306219i
\(813\) 17.7900 7.92060i 0.623921 0.277788i
\(814\) −2.23256 + 1.62205i −0.0782513 + 0.0568529i
\(815\) 10.8725 + 4.84076i 0.380848 + 0.169565i
\(816\) −1.01152 + 0.215006i −0.0354104 + 0.00752671i
\(817\) −0.917718 + 8.73150i −0.0321069 + 0.305477i
\(818\) −13.1328 14.5854i −0.459177 0.509968i
\(819\) 3.56086 3.95473i 0.124426 0.138190i
\(820\) −0.0360107 0.342619i −0.00125755 0.0119648i
\(821\) 11.8821 + 36.5694i 0.414689 + 1.27628i 0.912529 + 0.409013i \(0.134127\pi\)
−0.497840 + 0.867269i \(0.665873\pi\)
\(822\) −1.73533 5.34078i −0.0605264 0.186281i
\(823\) 3.10023 + 29.4968i 0.108067 + 1.02819i 0.905373 + 0.424617i \(0.139591\pi\)
−0.797306 + 0.603575i \(0.793742\pi\)
\(824\) 11.9921 13.3185i 0.417763 0.463973i
\(825\) 0.626264 + 0.695536i 0.0218037 + 0.0242155i
\(826\) −2.71106 + 25.7940i −0.0943300 + 0.897490i
\(827\) −16.1008 + 3.42233i −0.559880 + 0.119006i −0.479155 0.877730i \(-0.659057\pi\)
−0.0807247 + 0.996736i \(0.525723\pi\)
\(828\) −3.17219 1.41235i −0.110241 0.0490825i
\(829\) −21.6206 + 15.7083i −0.750915 + 0.545571i −0.896110 0.443832i \(-0.853619\pi\)
0.145196 + 0.989403i \(0.453619\pi\)
\(830\) −8.89493 + 3.96028i −0.308747 + 0.137463i
\(831\) −4.73155 + 8.19528i −0.164136 + 0.284291i
\(832\) 1.18408 + 2.05088i 0.0410505 + 0.0711015i
\(833\) 1.63164 + 1.18546i 0.0565330 + 0.0410737i
\(834\) −8.94783 1.90192i −0.309838 0.0658581i
\(835\) 0.390957 1.20324i 0.0135296 0.0416399i
\(836\) 6.74359 0.233232
\(837\) −5.19487 2.00334i −0.179561 0.0692455i
\(838\) 13.9467 0.481781
\(839\) 14.0567 43.2619i 0.485290 1.49357i −0.346271 0.938134i \(-0.612552\pi\)
0.831561 0.555434i \(-0.187448\pi\)
\(840\) 2.19805 + 0.467211i 0.0758401 + 0.0161203i
\(841\) 7.19664 + 5.22866i 0.248160 + 0.180299i
\(842\) −10.8295 18.7572i −0.373209 0.646416i
\(843\) 8.54096 14.7934i 0.294166 0.509511i
\(844\) −8.86566 + 3.94725i −0.305169 + 0.135870i
\(845\) 5.98013 4.34482i 0.205723 0.149466i
\(846\) 2.72209 + 1.21195i 0.0935875 + 0.0416678i
\(847\) −22.2531 + 4.73005i −0.764627 + 0.162527i
\(848\) −0.637611 + 6.06646i −0.0218956 + 0.208323i
\(849\) −0.297664 0.330589i −0.0102158 0.0113458i
\(850\) 0.691962 0.768502i 0.0237341 0.0263594i
\(851\) 1.07020 + 10.1822i 0.0366858 + 0.349042i
\(852\) 1.79626 + 5.52833i 0.0615389 + 0.189397i
\(853\) −12.4658 38.3656i −0.426819 1.31361i −0.901241 0.433317i \(-0.857343\pi\)
0.474422 0.880297i \(-0.342657\pi\)
\(854\) −1.24389 11.8348i −0.0425650 0.404979i
\(855\) 4.82120 5.35449i 0.164882 0.183120i
\(856\) 0.386722 + 0.429498i 0.0132179 + 0.0146799i
\(857\) −0.0979126 + 0.931576i −0.00334463 + 0.0318220i −0.996067 0.0886041i \(-0.971759\pi\)
0.992722 + 0.120426i \(0.0384261\pi\)
\(858\) 2.16801 0.460824i 0.0740145 0.0157323i
\(859\) −41.0003 18.2545i −1.39891 0.622836i −0.437820 0.899063i \(-0.644249\pi\)
−0.961093 + 0.276227i \(0.910916\pi\)
\(860\) −0.985798 + 0.716224i −0.0336154 + 0.0244230i
\(861\) −0.707231 + 0.314879i −0.0241024 + 0.0107311i
\(862\) 11.4467 19.8263i 0.389876 0.675285i
\(863\) −26.2081 45.3938i −0.892134 1.54522i −0.837312 0.546725i \(-0.815874\pi\)
−0.0548222 0.998496i \(-0.517459\pi\)
\(864\) −0.809017 0.587785i −0.0275233 0.0199969i
\(865\) 6.65302 + 1.41414i 0.226209 + 0.0480823i
\(866\) −0.107789 + 0.331740i −0.00366282 + 0.0112730i
\(867\) −15.9306 −0.541031
\(868\) 12.4955 0.635499i 0.424125 0.0215703i
\(869\) −3.29648 −0.111826
\(870\) −1.38557 + 4.26435i −0.0469752 + 0.144575i
\(871\) 5.60599 + 1.19159i 0.189952 + 0.0403755i
\(872\) −14.5750 10.5894i −0.493572 0.358601i
\(873\) −8.15645 14.1274i −0.276054 0.478139i
\(874\) 12.5096 21.6673i 0.423143 0.732906i
\(875\) −2.05288 + 0.914002i −0.0694001 + 0.0308989i
\(876\) −8.24054 + 5.98710i −0.278422 + 0.202286i
\(877\) −13.3550 5.94601i −0.450965 0.200783i 0.168670 0.985673i \(-0.446053\pi\)
−0.619635 + 0.784890i \(0.712719\pi\)
\(878\) −9.21477 + 1.95866i −0.310983 + 0.0661016i
\(879\) 2.45647 23.3718i 0.0828548 0.788310i
\(880\) 0.626264 + 0.695536i 0.0211113 + 0.0234465i
\(881\) 4.65323 5.16794i 0.156771 0.174112i −0.659642 0.751580i \(-0.729292\pi\)
0.816414 + 0.577467i \(0.195959\pi\)
\(882\) 0.203859 + 1.93959i 0.00686429 + 0.0653094i
\(883\) 5.35973 + 16.4955i 0.180369 + 0.555119i 0.999838 0.0180047i \(-0.00573137\pi\)
−0.819469 + 0.573124i \(0.805731\pi\)
\(884\) −0.756770 2.32910i −0.0254529 0.0783360i
\(885\) 1.20644 + 11.4785i 0.0405540 + 0.385846i
\(886\) 10.5801 11.7504i 0.355444 0.394761i
\(887\) 21.4038 + 23.7713i 0.718668 + 0.798161i 0.986230 0.165379i \(-0.0528848\pi\)
−0.267562 + 0.963541i \(0.586218\pi\)
\(888\) −0.308201 + 2.93234i −0.0103426 + 0.0984029i
\(889\) 2.89367 0.615069i 0.0970506 0.0206287i
\(890\) 1.79567 + 0.799483i 0.0601909 + 0.0267987i
\(891\) −0.757188 + 0.550130i −0.0253668 + 0.0184300i
\(892\) 2.88129 1.28283i 0.0964727 0.0429524i
\(893\) −10.7346 + 18.5929i −0.359221 + 0.622189i
\(894\) −3.95316 6.84707i −0.132213 0.229000i
\(895\) −12.2851 8.92566i −0.410646 0.298352i
\(896\) 2.19805 + 0.467211i 0.0734318 + 0.0156084i
\(897\) 2.54110 7.82069i 0.0848447 0.261125i
\(898\) −10.0236 −0.334492
\(899\) −1.34508 + 24.9285i −0.0448609 + 0.831411i
\(900\) 1.00000 0.0333333
\(901\) 1.94928 5.99928i 0.0649400 0.199865i
\(902\) −0.315390 0.0670382i −0.0105013 0.00223213i
\(903\) 2.21524 + 1.60947i 0.0737187 + 0.0535598i
\(904\) −4.51884 7.82687i −0.150295 0.260318i
\(905\) −12.1888 + 21.1116i −0.405169 + 0.701773i
\(906\) 14.7090 6.54887i 0.488674 0.217571i
\(907\) −31.8765 + 23.1596i −1.05844 + 0.769003i −0.973800 0.227408i \(-0.926975\pi\)
−0.0846428 + 0.996411i \(0.526975\pi\)
\(908\) 3.33939 + 1.48679i 0.110821 + 0.0493409i
\(909\) −4.86011 + 1.03305i −0.161200 + 0.0342640i
\(910\) −0.556261 + 5.29247i −0.0184399 + 0.175444i
\(911\) −28.4383 31.5839i −0.942202 1.04642i −0.998846 0.0480269i \(-0.984707\pi\)
0.0566441 0.998394i \(-0.481960\pi\)
\(912\) 4.82120 5.35449i 0.159646 0.177305i
\(913\) 0.952562 + 9.06302i 0.0315252 + 0.299942i
\(914\) 9.20883 + 28.3419i 0.304601 + 0.937466i
\(915\) −1.63642 5.03639i −0.0540984 0.166498i
\(916\) 0.151624 + 1.44261i 0.00500981 + 0.0476652i
\(917\) −2.78572 + 3.09385i −0.0919925 + 0.102168i
\(918\) 0.691962 + 0.768502i 0.0228382 + 0.0253643i
\(919\) 0.561318 5.34058i 0.0185162 0.176170i −0.981355 0.192202i \(-0.938437\pi\)
0.999871 + 0.0160329i \(0.00510364\pi\)
\(920\) 3.39651 0.721951i 0.111980 0.0238020i
\(921\) −13.3335 5.93646i −0.439354 0.195613i
\(922\) −17.8241 + 12.9500i −0.587006 + 0.426485i
\(923\) −12.5756 + 5.59900i −0.413930 + 0.184293i
\(924\) 1.05160 1.82142i 0.0345951 0.0599204i
\(925\) −1.47425 2.55347i −0.0484729 0.0839575i
\(926\) −13.7370 9.98049i −0.451425 0.327979i
\(927\) −17.5302 3.72616i −0.575768 0.122383i
\(928\) −1.38557 + 4.26435i −0.0454836 + 0.139984i
\(929\) −16.8351 −0.552342 −0.276171 0.961108i \(-0.589066\pi\)
−0.276171 + 0.961108i \(0.589066\pi\)
\(930\) 5.38027 1.43273i 0.176426 0.0469811i
\(931\) −14.0521 −0.460538
\(932\) −1.48627 + 4.57428i −0.0486845 + 0.149835i
\(933\) 12.1666 + 2.58610i 0.398317 + 0.0846650i
\(934\) −33.8738 24.6108i −1.10838 0.805289i
\(935\) −0.483936 0.838202i −0.0158264 0.0274121i
\(936\) 1.18408 2.05088i 0.0387028 0.0670351i
\(937\) 36.3098 16.1662i 1.18619 0.528125i 0.283731 0.958904i \(-0.408428\pi\)
0.902458 + 0.430778i \(0.141761\pi\)
\(938\) 4.39977 3.19662i 0.143657 0.104373i
\(939\) 8.34780 + 3.71668i 0.272420 + 0.121289i
\(940\) −2.91459 + 0.619515i −0.0950634 + 0.0202063i
\(941\) −3.32026 + 31.5901i −0.108237 + 1.02981i 0.796732 + 0.604332i \(0.206560\pi\)
−0.904970 + 0.425476i \(0.860107\pi\)
\(942\) 1.03498 + 1.14946i 0.0337215 + 0.0374515i
\(943\) −0.800455 + 0.888995i −0.0260664 + 0.0289497i
\(944\) 1.20644 + 11.4785i 0.0392663 + 0.373594i
\(945\) −0.694411 2.13718i −0.0225892 0.0695223i
\(946\) 0.352419 + 1.08463i 0.0114581 + 0.0352645i
\(947\) −0.0295815 0.281449i −0.000961269 0.00914586i 0.994031 0.109100i \(-0.0347970\pi\)
−0.994992 + 0.0999544i \(0.968130\pi\)
\(948\) −2.35676 + 2.61745i −0.0765440 + 0.0850107i
\(949\) −16.1406 17.9259i −0.523945 0.581900i
\(950\) −0.753146 + 7.16570i −0.0244353 + 0.232486i
\(951\) −4.89899 + 1.04131i −0.158861 + 0.0337669i
\(952\) −2.12293 0.945189i −0.0688046 0.0306338i
\(953\) 18.3920 13.3626i 0.595775 0.432856i −0.248602 0.968606i \(-0.579971\pi\)
0.844377 + 0.535750i \(0.179971\pi\)
\(954\) 5.57251 2.48104i 0.180417 0.0803267i
\(955\) −2.68206 + 4.64547i −0.0867894 + 0.150324i
\(956\) −10.6956 18.5253i −0.345920 0.599152i
\(957\) 3.39508 + 2.46667i 0.109747 + 0.0797362i
\(958\) 13.7935 + 2.93190i 0.445647 + 0.0947253i
\(959\) 3.89955 12.0016i 0.125923 0.387552i
\(960\) 1.00000 0.0322749
\(961\) 26.8946 15.4169i 0.867567 0.497321i
\(962\) −6.98248 −0.225124
\(963\) 0.178595 0.549660i 0.00575515 0.0177125i
\(964\) −10.1810 2.16404i −0.327909 0.0696991i
\(965\) 6.10066 + 4.43239i 0.196387 + 0.142684i
\(966\) −3.90151 6.75761i −0.125529 0.217423i
\(967\) −1.94747 + 3.37312i −0.0626264 + 0.108472i −0.895639 0.444782i \(-0.853281\pi\)
0.833012 + 0.553255i \(0.186614\pi\)
\(968\) −9.24876 + 4.11781i −0.297266 + 0.132351i
\(969\) −6.02801 + 4.37960i −0.193648 + 0.140693i
\(970\) 14.9026 + 6.63505i 0.478493 + 0.213039i
\(971\) −51.4461 + 10.9352i −1.65098 + 0.350928i −0.937026 0.349260i \(-0.886433\pi\)
−0.713959 + 0.700188i \(0.753100\pi\)
\(972\) −0.104528 + 0.994522i −0.00335275 + 0.0318993i
\(973\) −13.7549 15.2764i −0.440963 0.489739i
\(974\) 17.5043 19.4405i 0.560875 0.622914i
\(975\) 0.247539 + 2.35518i 0.00792761 + 0.0754261i
\(976\) −1.63642 5.03639i −0.0523806 0.161211i
\(977\) 1.93196 + 5.94595i 0.0618087 + 0.190228i 0.977193 0.212354i \(-0.0681130\pi\)
−0.915384 + 0.402582i \(0.868113\pi\)
\(978\) −1.24404 11.8363i −0.0397801 0.378482i
\(979\) 1.23099 1.36715i 0.0393425 0.0436942i
\(980\) −1.30499 1.44934i −0.0416863 0.0462973i
\(981\) −1.88315 + 17.9170i −0.0601244 + 0.572046i
\(982\) −29.9814 + 6.37275i −0.956746 + 0.203363i
\(983\) −18.2595 8.12966i −0.582388 0.259296i 0.0943265 0.995541i \(-0.469930\pi\)
−0.676715 + 0.736245i \(0.736597\pi\)
\(984\) −0.278711 + 0.202496i −0.00888500 + 0.00645533i
\(985\) −22.6582 + 10.0881i −0.721951 + 0.321433i
\(986\) 2.31840 4.01558i 0.0738328 0.127882i
\(987\) 3.34793 + 5.79879i 0.106566 + 0.184578i
\(988\) 13.8042 + 10.0294i 0.439171 + 0.319076i
\(989\) 4.13869 + 0.879706i 0.131603 + 0.0279730i
\(990\) 0.289220 0.890128i 0.00919202 0.0282901i
\(991\) −58.1464 −1.84708 −0.923540 0.383502i \(-0.874718\pi\)
−0.923540 + 0.383502i \(0.874718\pi\)
\(992\) 5.38027 1.43273i 0.170824 0.0454892i
\(993\) −16.9955 −0.539337
\(994\) −4.03649 + 12.4230i −0.128030 + 0.394035i
\(995\) 21.8845 + 4.65169i 0.693784 + 0.147468i
\(996\) 7.87716 + 5.72309i 0.249597 + 0.181343i
\(997\) 0.815359 + 1.41224i 0.0258227 + 0.0447262i 0.878648 0.477470i \(-0.158446\pi\)
−0.852825 + 0.522196i \(0.825113\pi\)
\(998\) 18.5654 32.1563i 0.587679 1.01789i
\(999\) 2.69358 1.19926i 0.0852211 0.0379429i
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.bg.g.691.1 24
31.7 even 15 inner 930.2.bg.g.751.1 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bg.g.691.1 24 1.1 even 1 trivial
930.2.bg.g.751.1 yes 24 31.7 even 15 inner