Properties

Label 552.2.bf.a.5.2
Level $552$
Weight $2$
Character 552.5
Analytic conductor $4.408$
Analytic rank $0$
Dimension $920$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [552,2,Mod(5,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 11, 11, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("552.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.bf (of order \(22\), degree \(10\), 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: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(920\)
Relative dimension: \(92\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.2
Character \(\chi\) \(=\) 552.5
Dual form 552.2.bf.a.221.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41317 + 0.0543574i) q^{2} +(0.873168 - 1.49585i) q^{3} +(1.99409 - 0.153632i) q^{4} +(-1.97986 - 0.284661i) q^{5} +(-1.15262 + 2.16136i) q^{6} +(2.90361 - 1.32603i) q^{7} +(-2.80963 + 0.325502i) q^{8} +(-1.47515 - 2.61226i) q^{9} +O(q^{10})\) \(q+(-1.41317 + 0.0543574i) q^{2} +(0.873168 - 1.49585i) q^{3} +(1.99409 - 0.153632i) q^{4} +(-1.97986 - 0.284661i) q^{5} +(-1.15262 + 2.16136i) q^{6} +(2.90361 - 1.32603i) q^{7} +(-2.80963 + 0.325502i) q^{8} +(-1.47515 - 2.61226i) q^{9} +(2.81335 + 0.294653i) q^{10} +(0.0155140 + 0.0528360i) q^{11} +(1.51137 - 3.11701i) q^{12} +(-6.52515 - 2.97994i) q^{13} +(-4.03121 + 2.03174i) q^{14} +(-2.15456 + 2.71302i) q^{15} +(3.95279 - 0.612714i) q^{16} +(0.218352 - 0.140326i) q^{17} +(2.22664 + 3.61138i) q^{18} +(4.96870 + 3.19319i) q^{19} +(-3.99175 - 0.263469i) q^{20} +(0.551788 - 5.50123i) q^{21} +(-0.0247960 - 0.0738228i) q^{22} +(-3.59799 - 3.17088i) q^{23} +(-1.96638 + 4.48702i) q^{24} +(-0.958658 - 0.281487i) q^{25} +(9.38313 + 3.85646i) q^{26} +(-5.19562 - 0.0743324i) q^{27} +(5.58634 - 3.09032i) q^{28} +(6.21239 - 3.99246i) q^{29} +(2.89728 - 3.95107i) q^{30} +(-4.18469 - 4.82939i) q^{31} +(-5.55266 + 1.08073i) q^{32} +(0.0925812 + 0.0229280i) q^{33} +(-0.300940 + 0.210173i) q^{34} +(-6.12621 + 1.79882i) q^{35} +(-3.34292 - 4.98246i) q^{36} +(0.947989 + 6.59341i) q^{37} +(-7.19518 - 4.24243i) q^{38} +(-10.1551 + 7.15869i) q^{39} +(5.65534 + 0.155344i) q^{40} +(0.898237 + 0.129147i) q^{41} +(-0.480737 + 7.80415i) q^{42} +(-0.831631 + 0.959753i) q^{43} +(0.0390537 + 0.102976i) q^{44} +(2.17699 + 5.59183i) q^{45} +(5.25693 + 4.28540i) q^{46} -0.188785i q^{47} +(2.53493 - 6.44780i) q^{48} +(2.08856 - 2.41033i) q^{49} +(1.37005 + 0.345679i) q^{50} +(-0.0192495 - 0.449150i) q^{51} +(-13.4696 - 4.93979i) q^{52} +(-8.20646 + 3.74777i) q^{53} +(7.34633 - 0.177376i) q^{54} +(-0.0156753 - 0.109024i) q^{55} +(-7.72646 + 4.67080i) q^{56} +(9.11505 - 4.64425i) q^{57} +(-8.56213 + 5.97971i) q^{58} +(4.21225 - 9.22355i) q^{59} +(-3.87958 + 5.74102i) q^{60} +(-8.61910 - 9.94698i) q^{61} +(6.17618 + 6.59727i) q^{62} +(-7.74722 - 5.62889i) q^{63} +(7.78810 - 1.82908i) q^{64} +(12.0706 + 7.75731i) q^{65} +(-0.132079 - 0.0273686i) q^{66} +(-4.09784 - 1.20324i) q^{67} +(0.413854 - 0.313369i) q^{68} +(-7.88482 + 2.61336i) q^{69} +(8.55959 - 2.87504i) q^{70} +(0.594995 - 2.02637i) q^{71} +(4.99494 + 6.85934i) q^{72} +(-2.56222 - 1.64664i) q^{73} +(-1.69807 - 9.26607i) q^{74} +(-1.25813 + 1.18823i) q^{75} +(10.3986 + 5.60415i) q^{76} +(0.115109 + 0.132843i) q^{77} +(13.9618 - 10.6684i) q^{78} +(-2.82384 - 1.28960i) q^{79} +(-8.00039 + 0.0878816i) q^{80} +(-4.64784 + 7.70698i) q^{81} +(-1.27638 - 0.133681i) q^{82} +(8.96634 - 1.28917i) q^{83} +(0.255149 - 11.0547i) q^{84} +(-0.472251 + 0.215670i) q^{85} +(1.12306 - 1.40150i) q^{86} +(-0.547672 - 12.7789i) q^{87} +(-0.0607870 - 0.143400i) q^{88} +(11.4022 - 13.1589i) q^{89} +(-3.38041 - 7.78386i) q^{90} -22.8980 q^{91} +(-7.66187 - 5.77024i) q^{92} +(-10.8780 + 2.04281i) q^{93} +(0.0102618 + 0.266784i) q^{94} +(-8.92834 - 7.73645i) q^{95} +(-3.23179 + 9.24962i) q^{96} +(5.29925 + 0.761917i) q^{97} +(-2.82047 + 3.51973i) q^{98} +(0.115136 - 0.118468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(e\left(\frac{1}{22}\right)\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41317 + 0.0543574i −0.999261 + 0.0384365i
\(3\) 0.873168 1.49585i 0.504124 0.863631i
\(4\) 1.99409 0.153632i 0.997045 0.0768162i
\(5\) −1.97986 0.284661i −0.885420 0.127304i −0.315423 0.948951i \(-0.602146\pi\)
−0.569997 + 0.821647i \(0.693055\pi\)
\(6\) −1.15262 + 2.16136i −0.470557 + 0.882370i
\(7\) 2.90361 1.32603i 1.09746 0.501194i 0.217414 0.976079i \(-0.430238\pi\)
0.880048 + 0.474885i \(0.157511\pi\)
\(8\) −2.80963 + 0.325502i −0.993356 + 0.115082i
\(9\) −1.47515 2.61226i −0.491718 0.870755i
\(10\) 2.81335 + 0.294653i 0.889658 + 0.0931776i
\(11\) 0.0155140 + 0.0528360i 0.00467766 + 0.0159306i 0.961799 0.273758i \(-0.0882666\pi\)
−0.957121 + 0.289688i \(0.906448\pi\)
\(12\) 1.51137 3.11701i 0.436294 0.899804i
\(13\) −6.52515 2.97994i −1.80975 0.826486i −0.947300 0.320348i \(-0.896200\pi\)
−0.862452 0.506138i \(-0.831073\pi\)
\(14\) −4.03121 + 2.03174i −1.07739 + 0.543006i
\(15\) −2.15456 + 2.71302i −0.556305 + 0.700499i
\(16\) 3.95279 0.612714i 0.988199 0.153178i
\(17\) 0.218352 0.140326i 0.0529580 0.0340341i −0.513894 0.857854i \(-0.671798\pi\)
0.566852 + 0.823820i \(0.308161\pi\)
\(18\) 2.22664 + 3.61138i 0.524823 + 0.851211i
\(19\) 4.96870 + 3.19319i 1.13990 + 0.732567i 0.967603 0.252478i \(-0.0812455\pi\)
0.172295 + 0.985045i \(0.444882\pi\)
\(20\) −3.99175 0.263469i −0.892582 0.0589134i
\(21\) 0.551788 5.50123i 0.120410 1.20047i
\(22\) −0.0247960 0.0738228i −0.00528652 0.0157391i
\(23\) −3.59799 3.17088i −0.750233 0.661173i
\(24\) −1.96638 + 4.48702i −0.401386 + 0.915909i
\(25\) −0.958658 0.281487i −0.191732 0.0562975i
\(26\) 9.38313 + 3.85646i 1.84018 + 0.756315i
\(27\) −5.19562 0.0743324i −0.999898 0.0143053i
\(28\) 5.58634 3.09032i 1.05572 0.584016i
\(29\) 6.21239 3.99246i 1.15361 0.741381i 0.183256 0.983065i \(-0.441336\pi\)
0.970355 + 0.241684i \(0.0776998\pi\)
\(30\) 2.89728 3.95107i 0.528969 0.721364i
\(31\) −4.18469 4.82939i −0.751592 0.867384i 0.243129 0.969994i \(-0.421826\pi\)
−0.994722 + 0.102610i \(0.967281\pi\)
\(32\) −5.55266 + 1.08073i −0.981581 + 0.191048i
\(33\) 0.0925812 + 0.0229280i 0.0161163 + 0.00399125i
\(34\) −0.300940 + 0.210173i −0.0516108 + 0.0360444i
\(35\) −6.12621 + 1.79882i −1.03552 + 0.304056i
\(36\) −3.34292 4.98246i −0.557153 0.830410i
\(37\) 0.947989 + 6.59341i 0.155848 + 1.08395i 0.906181 + 0.422889i \(0.138984\pi\)
−0.750333 + 0.661060i \(0.770107\pi\)
\(38\) −7.19518 4.24243i −1.16721 0.688212i
\(39\) −10.1551 + 7.15869i −1.62612 + 1.14631i
\(40\) 5.65534 + 0.155344i 0.894187 + 0.0245621i
\(41\) 0.898237 + 0.129147i 0.140281 + 0.0201694i 0.212098 0.977248i \(-0.431971\pi\)
−0.0718166 + 0.997418i \(0.522880\pi\)
\(42\) −0.480737 + 7.80415i −0.0741793 + 1.20421i
\(43\) −0.831631 + 0.959753i −0.126823 + 0.146361i −0.815609 0.578603i \(-0.803598\pi\)
0.688787 + 0.724964i \(0.258144\pi\)
\(44\) 0.0390537 + 0.102976i 0.00588757 + 0.0155243i
\(45\) 2.17699 + 5.59183i 0.324526 + 0.833581i
\(46\) 5.25693 + 4.28540i 0.775092 + 0.631848i
\(47\) 0.188785i 0.0275371i −0.999905 0.0137685i \(-0.995617\pi\)
0.999905 0.0137685i \(-0.00438280\pi\)
\(48\) 2.53493 6.44780i 0.365885 0.930660i
\(49\) 2.08856 2.41033i 0.298366 0.344333i
\(50\) 1.37005 + 0.345679i 0.193754 + 0.0488864i
\(51\) −0.0192495 0.449150i −0.00269546 0.0628936i
\(52\) −13.4696 4.93979i −1.86789 0.685026i
\(53\) −8.20646 + 3.74777i −1.12724 + 0.514795i −0.889684 0.456578i \(-0.849075\pi\)
−0.237561 + 0.971373i \(0.576348\pi\)
\(54\) 7.34633 0.177376i 0.999709 0.0241379i
\(55\) −0.0156753 0.109024i −0.00211365 0.0147008i
\(56\) −7.72646 + 4.67080i −1.03249 + 0.624163i
\(57\) 9.11505 4.64425i 1.20732 0.615146i
\(58\) −8.56213 + 5.97971i −1.12426 + 0.785174i
\(59\) 4.21225 9.22355i 0.548388 1.20080i −0.409142 0.912471i \(-0.634172\pi\)
0.957530 0.288333i \(-0.0931008\pi\)
\(60\) −3.87958 + 5.74102i −0.500852 + 0.741162i
\(61\) −8.61910 9.94698i −1.10356 1.27358i −0.958790 0.284115i \(-0.908300\pi\)
−0.144773 0.989465i \(-0.546245\pi\)
\(62\) 6.17618 + 6.59727i 0.784376 + 0.837854i
\(63\) −7.74722 5.62889i −0.976059 0.709174i
\(64\) 7.78810 1.82908i 0.973512 0.228636i
\(65\) 12.0706 + 7.75731i 1.49717 + 0.962176i
\(66\) −0.132079 0.0273686i −0.0162578 0.00336884i
\(67\) −4.09784 1.20324i −0.500631 0.146999i 0.0216607 0.999765i \(-0.493105\pi\)
−0.522292 + 0.852767i \(0.674923\pi\)
\(68\) 0.413854 0.313369i 0.0501872 0.0380015i
\(69\) −7.88482 + 2.61336i −0.949221 + 0.314612i
\(70\) 8.55959 2.87504i 1.02307 0.343633i
\(71\) 0.594995 2.02637i 0.0706129 0.240485i −0.916622 0.399754i \(-0.869095\pi\)
0.987235 + 0.159269i \(0.0509137\pi\)
\(72\) 4.99494 + 6.85934i 0.588659 + 0.808381i
\(73\) −2.56222 1.64664i −0.299885 0.192725i 0.382041 0.924145i \(-0.375221\pi\)
−0.681927 + 0.731421i \(0.738858\pi\)
\(74\) −1.69807 9.26607i −0.197396 1.07716i
\(75\) −1.25813 + 1.18823i −0.145277 + 0.137204i
\(76\) 10.3986 + 5.60415i 1.19280 + 0.642840i
\(77\) 0.115109 + 0.132843i 0.0131179 + 0.0151389i
\(78\) 13.9618 10.6684i 1.58086 1.20796i
\(79\) −2.82384 1.28960i −0.317706 0.145092i 0.250178 0.968200i \(-0.419511\pi\)
−0.567885 + 0.823108i \(0.692238\pi\)
\(80\) −8.00039 + 0.0878816i −0.894471 + 0.00982546i
\(81\) −4.64784 + 7.70698i −0.516427 + 0.856331i
\(82\) −1.27638 0.133681i −0.140953 0.0147625i
\(83\) 8.96634 1.28917i 0.984184 0.141504i 0.368611 0.929584i \(-0.379834\pi\)
0.615573 + 0.788080i \(0.288924\pi\)
\(84\) 0.255149 11.0547i 0.0278390 1.20617i
\(85\) −0.472251 + 0.215670i −0.0512228 + 0.0233927i
\(86\) 1.12306 1.40150i 0.121103 0.151127i
\(87\) −0.547672 12.7789i −0.0587166 1.37004i
\(88\) −0.0607870 0.143400i −0.00647992 0.0152865i
\(89\) 11.4022 13.1589i 1.20863 1.39484i 0.313175 0.949696i \(-0.398607\pi\)
0.895460 0.445143i \(-0.146847\pi\)
\(90\) −3.38041 7.78386i −0.356326 0.820491i
\(91\) −22.8980 −2.40036
\(92\) −7.66187 5.77024i −0.798805 0.601590i
\(93\) −10.8780 + 2.04281i −1.12800 + 0.211830i
\(94\) 0.0102618 + 0.266784i 0.00105843 + 0.0275167i
\(95\) −8.92834 7.73645i −0.916028 0.793743i
\(96\) −3.23179 + 9.24962i −0.329843 + 0.944036i
\(97\) 5.29925 + 0.761917i 0.538057 + 0.0773609i 0.405986 0.913879i \(-0.366928\pi\)
0.132071 + 0.991240i \(0.457837\pi\)
\(98\) −2.82047 + 3.51973i −0.284911 + 0.355547i
\(99\) 0.115136 0.118468i 0.0115716 0.0119065i
\(100\) −1.95490 0.414030i −0.195490 0.0414030i
\(101\) 2.25826 + 15.7065i 0.224705 + 1.56286i 0.719902 + 0.694076i \(0.244187\pi\)
−0.495197 + 0.868781i \(0.664904\pi\)
\(102\) 0.0516174 + 0.633679i 0.00511088 + 0.0627435i
\(103\) 2.05661 + 7.00418i 0.202644 + 0.690142i 0.996617 + 0.0821887i \(0.0261910\pi\)
−0.793973 + 0.607953i \(0.791991\pi\)
\(104\) 19.3033 + 6.24859i 1.89284 + 0.612724i
\(105\) −2.65845 + 10.7346i −0.259438 + 1.04759i
\(106\) 11.3934 5.74231i 1.10662 0.557742i
\(107\) −2.28968 + 1.98402i −0.221352 + 0.191802i −0.758476 0.651700i \(-0.774056\pi\)
0.537125 + 0.843503i \(0.319510\pi\)
\(108\) −10.3720 + 0.649990i −0.998042 + 0.0625453i
\(109\) 14.4636 9.29518i 1.38536 0.890317i 0.385880 0.922549i \(-0.373898\pi\)
0.999480 + 0.0322317i \(0.0102614\pi\)
\(110\) 0.0280781 + 0.153217i 0.00267714 + 0.0146087i
\(111\) 10.6905 + 4.33910i 1.01470 + 0.411849i
\(112\) 10.6649 7.02062i 1.00774 0.663387i
\(113\) 8.05933 + 2.36643i 0.758158 + 0.222615i 0.637891 0.770126i \(-0.279807\pi\)
0.120267 + 0.992742i \(0.461625\pi\)
\(114\) −12.6287 + 7.05858i −1.18278 + 0.661097i
\(115\) 6.22089 + 7.30209i 0.580101 + 0.680924i
\(116\) 11.7747 8.91575i 1.09325 0.827807i
\(117\) 1.84122 + 21.4413i 0.170221 + 1.98225i
\(118\) −5.45125 + 13.2634i −0.501829 + 1.22099i
\(119\) 0.447931 0.696994i 0.0410618 0.0638933i
\(120\) 5.17043 8.32391i 0.471994 0.759866i
\(121\) 9.25124 5.94541i 0.841022 0.540492i
\(122\) 12.7209 + 13.5882i 1.15170 + 1.23022i
\(123\) 0.977497 1.23086i 0.0881379 0.110983i
\(124\) −9.08660 8.98734i −0.816001 0.807087i
\(125\) 10.9152 + 4.98480i 0.976284 + 0.445854i
\(126\) 11.2541 + 7.53345i 1.00260 + 0.671133i
\(127\) 11.0253 3.23733i 0.978341 0.287267i 0.246802 0.969066i \(-0.420620\pi\)
0.731539 + 0.681799i \(0.238802\pi\)
\(128\) −10.9065 + 3.00814i −0.964005 + 0.265885i
\(129\) 0.709496 + 2.08202i 0.0624676 + 0.183312i
\(130\) −17.4795 10.3063i −1.53305 0.903919i
\(131\) 4.83007 + 10.5764i 0.422006 + 0.924063i 0.994557 + 0.104194i \(0.0332264\pi\)
−0.572551 + 0.819869i \(0.694046\pi\)
\(132\) 0.188138 + 0.0314970i 0.0163753 + 0.00274146i
\(133\) 18.6614 + 2.68311i 1.61815 + 0.232655i
\(134\) 5.85635 + 1.47763i 0.505911 + 0.127647i
\(135\) 10.2654 + 1.62616i 0.883508 + 0.139957i
\(136\) −0.567812 + 0.465339i −0.0486895 + 0.0399025i
\(137\) −2.12677 −0.181702 −0.0908512 0.995864i \(-0.528959\pi\)
−0.0908512 + 0.995864i \(0.528959\pi\)
\(138\) 11.0005 4.12172i 0.936427 0.350864i
\(139\) 5.52420i 0.468556i −0.972170 0.234278i \(-0.924727\pi\)
0.972170 0.234278i \(-0.0752727\pi\)
\(140\) −11.9399 + 4.52819i −1.00910 + 0.382702i
\(141\) −0.282394 0.164841i −0.0237819 0.0138821i
\(142\) −0.730680 + 2.89594i −0.0613173 + 0.243022i
\(143\) 0.0562164 0.390994i 0.00470105 0.0326965i
\(144\) −7.43155 9.42189i −0.619296 0.785158i
\(145\) −13.4361 + 6.13608i −1.11581 + 0.509574i
\(146\) 3.71036 + 2.18770i 0.307071 + 0.181056i
\(147\) −1.78183 5.22881i −0.146963 0.431265i
\(148\) 2.90334 + 13.0022i 0.238653 + 1.06878i
\(149\) 0.375378 + 1.27842i 0.0307522 + 0.104732i 0.973439 0.228946i \(-0.0735281\pi\)
−0.942687 + 0.333679i \(0.891710\pi\)
\(150\) 1.71337 1.74755i 0.139896 0.142687i
\(151\) −2.97813 + 6.52120i −0.242357 + 0.530688i −0.991249 0.132004i \(-0.957859\pi\)
0.748892 + 0.662692i \(0.230586\pi\)
\(152\) −14.9996 7.35437i −1.21663 0.596518i
\(153\) −0.688671 0.363389i −0.0556757 0.0293783i
\(154\) −0.169889 0.181472i −0.0136901 0.0146235i
\(155\) 6.91036 + 10.7527i 0.555053 + 0.863679i
\(156\) −19.1504 + 15.8352i −1.53326 + 1.26783i
\(157\) 4.35713 + 2.80016i 0.347737 + 0.223477i 0.702836 0.711352i \(-0.251917\pi\)
−0.355099 + 0.934829i \(0.615553\pi\)
\(158\) 4.06066 + 1.66893i 0.323048 + 0.132773i
\(159\) −1.55952 + 15.5481i −0.123678 + 1.23304i
\(160\) 11.3011 0.559072i 0.893432 0.0441985i
\(161\) −14.6519 4.43593i −1.15473 0.349600i
\(162\) 6.14925 11.1439i 0.483131 0.875548i
\(163\) 3.85714 13.1362i 0.302115 1.02891i −0.658859 0.752267i \(-0.728960\pi\)
0.960973 0.276641i \(-0.0892213\pi\)
\(164\) 1.81101 + 0.119532i 0.141416 + 0.00933391i
\(165\) −0.176771 0.0717484i −0.0137616 0.00558560i
\(166\) −12.6009 + 2.30920i −0.978018 + 0.179228i
\(167\) −5.91488 9.20373i −0.457707 0.712206i 0.533313 0.845918i \(-0.320947\pi\)
−0.991020 + 0.133712i \(0.957310\pi\)
\(168\) 0.240338 + 15.6360i 0.0185425 + 1.20635i
\(169\) 25.1844 + 29.0644i 1.93726 + 2.23572i
\(170\) 0.655646 0.330448i 0.0502858 0.0253442i
\(171\) 1.01186 17.6900i 0.0773785 1.35279i
\(172\) −1.51090 + 2.04160i −0.115205 + 0.155671i
\(173\) 4.60226 1.35135i 0.349903 0.102741i −0.102058 0.994778i \(-0.532543\pi\)
0.451961 + 0.892038i \(0.350725\pi\)
\(174\) 1.46858 + 18.0290i 0.111333 + 1.36677i
\(175\) −3.15683 + 0.453884i −0.238634 + 0.0343104i
\(176\) 0.0936971 + 0.199344i 0.00706269 + 0.0150261i
\(177\) −10.1191 14.3546i −0.760595 1.07896i
\(178\) −15.3980 + 19.2155i −1.15413 + 1.44026i
\(179\) −0.276056 + 1.92001i −0.0206334 + 0.143508i −0.997534 0.0701862i \(-0.977641\pi\)
0.976901 + 0.213695i \(0.0685498\pi\)
\(180\) 5.20020 + 10.8162i 0.387600 + 0.806189i
\(181\) 7.63190 8.80768i 0.567275 0.654670i −0.397545 0.917583i \(-0.630138\pi\)
0.964820 + 0.262913i \(0.0846832\pi\)
\(182\) 32.3587 1.24468i 2.39859 0.0922616i
\(183\) −22.4051 + 4.20753i −1.65624 + 0.311030i
\(184\) 11.1412 + 7.73785i 0.821338 + 0.570442i
\(185\) 13.3239i 0.979590i
\(186\) 15.2614 3.47814i 1.11902 0.255029i
\(187\) 0.0108018 + 0.00935979i 0.000789904 + 0.000684456i
\(188\) −0.0290034 0.376454i −0.00211529 0.0274557i
\(189\) −15.1846 + 6.67374i −1.10452 + 0.485443i
\(190\) 13.0378 + 10.4476i 0.945860 + 0.757948i
\(191\) 5.48466 + 12.0097i 0.396856 + 0.868993i 0.997579 + 0.0695361i \(0.0221519\pi\)
−0.600724 + 0.799457i \(0.705121\pi\)
\(192\) 4.06428 13.2469i 0.293314 0.956016i
\(193\) 2.00407 + 13.9386i 0.144256 + 1.00332i 0.925406 + 0.378978i \(0.123724\pi\)
−0.781150 + 0.624343i \(0.785367\pi\)
\(194\) −7.53015 0.788664i −0.540633 0.0566227i
\(195\) 22.1435 11.2824i 1.58573 0.807951i
\(196\) 3.79448 5.12729i 0.271034 0.366235i
\(197\) 7.78755 17.0524i 0.554840 1.21493i −0.399644 0.916670i \(-0.630866\pi\)
0.954485 0.298260i \(-0.0964063\pi\)
\(198\) −0.156267 + 0.173674i −0.0111054 + 0.0123424i
\(199\) 11.6411 10.0871i 0.825214 0.715052i −0.136044 0.990703i \(-0.543439\pi\)
0.961258 + 0.275651i \(0.0888933\pi\)
\(200\) 2.78510 + 0.478831i 0.196937 + 0.0338585i
\(201\) −5.37797 + 5.07914i −0.379333 + 0.358255i
\(202\) −4.04506 22.0732i −0.284610 1.55306i
\(203\) 12.7442 19.8304i 0.894469 1.39182i
\(204\) −0.107389 0.892689i −0.00751875 0.0625007i
\(205\) −1.74162 0.511385i −0.121640 0.0357167i
\(206\) −3.28707 9.78629i −0.229021 0.681843i
\(207\) −2.97557 + 14.0764i −0.206816 + 0.978380i
\(208\) −27.6184 7.78103i −1.91499 0.539517i
\(209\) −0.0916306 + 0.312065i −0.00633822 + 0.0215860i
\(210\) 3.17333 15.3143i 0.218980 1.05679i
\(211\) −10.0471 + 15.6336i −0.691669 + 1.07626i 0.300791 + 0.953690i \(0.402749\pi\)
−0.992460 + 0.122568i \(0.960887\pi\)
\(212\) −15.7886 + 8.73416i −1.08437 + 0.599865i
\(213\) −2.51162 2.65938i −0.172093 0.182218i
\(214\) 3.12786 2.92822i 0.213816 0.200169i
\(215\) 1.91972 1.66344i 0.130923 0.113446i
\(216\) 14.6220 1.48234i 0.994901 0.100860i
\(217\) −18.5546 8.47362i −1.25957 0.575227i
\(218\) −19.9342 + 13.9219i −1.35012 + 0.942908i
\(219\) −4.70038 + 2.39491i −0.317622 + 0.161833i
\(220\) −0.0480075 0.214995i −0.00323667 0.0144950i
\(221\) −1.84294 + 0.264975i −0.123970 + 0.0178241i
\(222\) −15.3434 5.55077i −1.02978 0.372544i
\(223\) 2.50053 + 5.47540i 0.167448 + 0.366660i 0.974690 0.223561i \(-0.0717680\pi\)
−0.807242 + 0.590221i \(0.799041\pi\)
\(224\) −14.6897 + 10.5010i −0.981495 + 0.701630i
\(225\) 0.678849 + 2.91950i 0.0452566 + 0.194634i
\(226\) −11.5178 2.90608i −0.766154 0.193310i
\(227\) −12.6652 10.9745i −0.840620 0.728402i 0.123933 0.992291i \(-0.460449\pi\)
−0.964553 + 0.263889i \(0.914995\pi\)
\(228\) 17.4627 10.6614i 1.15650 0.706070i
\(229\) 8.28742 0.547648 0.273824 0.961780i \(-0.411711\pi\)
0.273824 + 0.961780i \(0.411711\pi\)
\(230\) −9.18809 9.98093i −0.605845 0.658123i
\(231\) 0.299223 0.0561920i 0.0196874 0.00369716i
\(232\) −16.1550 + 13.2395i −1.06063 + 0.869216i
\(233\) 4.88566 + 4.23345i 0.320070 + 0.277342i 0.800045 0.599940i \(-0.204809\pi\)
−0.479975 + 0.877282i \(0.659354\pi\)
\(234\) −3.76745 30.2001i −0.246286 1.97424i
\(235\) −0.0537395 + 0.373767i −0.00350558 + 0.0243819i
\(236\) 6.98258 19.0397i 0.454527 1.23938i
\(237\) −4.39474 + 3.09800i −0.285469 + 0.201237i
\(238\) −0.595115 + 1.00932i −0.0385756 + 0.0654244i
\(239\) −13.2711 + 1.90810i −0.858437 + 0.123425i −0.557457 0.830206i \(-0.688223\pi\)
−0.300980 + 0.953631i \(0.597314\pi\)
\(240\) −6.85423 + 12.0441i −0.442439 + 0.777446i
\(241\) −6.06198 20.6452i −0.390486 1.32987i −0.886970 0.461828i \(-0.847194\pi\)
0.496483 0.868046i \(-0.334624\pi\)
\(242\) −12.7504 + 8.90474i −0.819626 + 0.572418i
\(243\) 7.47016 + 13.6820i 0.479211 + 0.877700i
\(244\) −18.7155 18.5110i −1.19813 1.18505i
\(245\) −4.82118 + 4.17758i −0.308014 + 0.266896i
\(246\) −1.31446 + 1.79255i −0.0838070 + 0.114289i
\(247\) −22.9060 35.6425i −1.45747 2.26787i
\(248\) 13.3294 + 12.2067i 0.846419 + 0.775126i
\(249\) 5.90072 14.5380i 0.373943 0.921308i
\(250\) −15.6960 6.45104i −0.992700 0.408000i
\(251\) 3.97193 13.5271i 0.250706 0.853825i −0.733933 0.679222i \(-0.762317\pi\)
0.984639 0.174604i \(-0.0558644\pi\)
\(252\) −16.3134 10.0343i −1.02765 0.632101i
\(253\) 0.111717 0.239296i 0.00702358 0.0150444i
\(254\) −15.4047 + 5.17421i −0.966577 + 0.324659i
\(255\) −0.0897442 + 0.894733i −0.00562000 + 0.0560304i
\(256\) 15.2492 4.84386i 0.953073 0.302741i
\(257\) 8.63035 13.4291i 0.538346 0.837683i −0.460401 0.887711i \(-0.652295\pi\)
0.998748 + 0.0500274i \(0.0159309\pi\)
\(258\) −1.11581 2.90368i −0.0694674 0.180775i
\(259\) 11.4957 + 17.8876i 0.714307 + 1.11148i
\(260\) 25.2617 + 13.6143i 1.56666 + 0.844326i
\(261\) −19.5936 10.3389i −1.21281 0.639962i
\(262\) −7.40061 14.6837i −0.457211 0.907160i
\(263\) 4.95594 10.8520i 0.305597 0.669163i −0.693065 0.720875i \(-0.743740\pi\)
0.998662 + 0.0517114i \(0.0164676\pi\)
\(264\) −0.267583 0.0342838i −0.0164686 0.00211002i
\(265\) 17.3145 5.08399i 1.06362 0.312307i
\(266\) −26.5176 2.77730i −1.62590 0.170287i
\(267\) −9.72768 28.5460i −0.595324 1.74699i
\(268\) −8.35633 1.76980i −0.510444 0.108108i
\(269\) 3.38101 + 7.40338i 0.206144 + 0.451392i 0.984260 0.176729i \(-0.0565516\pi\)
−0.778116 + 0.628121i \(0.783824\pi\)
\(270\) −14.5952 1.74003i −0.888234 0.105895i
\(271\) 0.0765703 0.532558i 0.00465131 0.0323506i −0.987364 0.158471i \(-0.949344\pi\)
0.992015 + 0.126121i \(0.0402526\pi\)
\(272\) 0.777119 0.688467i 0.0471198 0.0417445i
\(273\) −19.9938 + 34.2521i −1.21008 + 2.07303i
\(274\) 3.00549 0.115606i 0.181568 0.00698400i
\(275\) 0.0550186i 0.00331775i
\(276\) −15.3215 + 6.42264i −0.922249 + 0.386597i
\(277\) 16.3196i 0.980550i −0.871568 0.490275i \(-0.836896\pi\)
0.871568 0.490275i \(-0.163104\pi\)
\(278\) 0.300281 + 7.80662i 0.0180097 + 0.468210i
\(279\) −6.44258 + 18.0556i −0.385707 + 1.08096i
\(280\) 16.6269 7.04811i 0.993647 0.421205i
\(281\) 2.91601 20.2813i 0.173955 1.20988i −0.696472 0.717584i \(-0.745248\pi\)
0.870427 0.492298i \(-0.163843\pi\)
\(282\) 0.408031 + 0.217598i 0.0242979 + 0.0129577i
\(283\) 2.82248 + 6.18038i 0.167779 + 0.367385i 0.974781 0.223164i \(-0.0716385\pi\)
−0.807002 + 0.590549i \(0.798911\pi\)
\(284\) 0.875158 4.13217i 0.0519311 0.245199i
\(285\) −19.3685 + 6.60026i −1.14729 + 0.390966i
\(286\) −0.0581898 + 0.555596i −0.00344084 + 0.0328531i
\(287\) 2.77938 0.816100i 0.164062 0.0481729i
\(288\) 11.0142 + 12.9108i 0.649017 + 0.760774i
\(289\) −7.03407 + 15.4025i −0.413769 + 0.906027i
\(290\) 18.6540 9.40167i 1.09540 0.552085i
\(291\) 5.76685 7.26162i 0.338059 0.425684i
\(292\) −5.36228 2.88991i −0.313804 0.169119i
\(293\) −2.26890 3.53049i −0.132551 0.206253i 0.768633 0.639690i \(-0.220937\pi\)
−0.901184 + 0.433437i \(0.857301\pi\)
\(294\) 2.80225 + 7.29233i 0.163431 + 0.425297i
\(295\) −10.9652 + 17.0623i −0.638421 + 0.993403i
\(296\) −4.80967 18.2165i −0.279556 1.05881i
\(297\) −0.0766776 0.275669i −0.00444929 0.0159959i
\(298\) −0.599965 1.78622i −0.0347550 0.103473i
\(299\) 14.0284 + 31.4122i 0.811286 + 1.81662i
\(300\) −2.32628 + 2.56272i −0.134308 + 0.147959i
\(301\) −1.14207 + 3.88952i −0.0658276 + 0.224188i
\(302\) 3.85413 9.37744i 0.221780 0.539611i
\(303\) 25.4665 + 10.3364i 1.46301 + 0.593811i
\(304\) 21.5967 + 9.57762i 1.23866 + 0.549314i
\(305\) 14.2331 + 22.1471i 0.814984 + 1.26814i
\(306\) 0.992961 + 0.476096i 0.0567638 + 0.0272166i
\(307\) −9.03845 + 7.83186i −0.515852 + 0.446988i −0.873469 0.486880i \(-0.838135\pi\)
0.357617 + 0.933868i \(0.383589\pi\)
\(308\) 0.249947 + 0.247216i 0.0142420 + 0.0140865i
\(309\) 12.2730 + 3.03944i 0.698186 + 0.172907i
\(310\) −10.3500 14.8198i −0.587840 0.841707i
\(311\) 4.40419 + 14.9993i 0.249739 + 0.850531i 0.984972 + 0.172717i \(0.0552546\pi\)
−0.735233 + 0.677815i \(0.762927\pi\)
\(312\) 26.2020 23.4188i 1.48340 1.32583i
\(313\) −17.7415 + 2.55084i −1.00281 + 0.144182i −0.624108 0.781338i \(-0.714538\pi\)
−0.378699 + 0.925520i \(0.623628\pi\)
\(314\) −6.30957 3.72025i −0.356070 0.209946i
\(315\) 13.7361 + 13.3497i 0.773941 + 0.752173i
\(316\) −5.82911 2.13775i −0.327913 0.120258i
\(317\) 0.000574710 0.00399720i 3.22789e−5 0.000224505i −0.989805 0.142427i \(-0.954509\pi\)
0.989838 + 0.142203i \(0.0454184\pi\)
\(318\) 1.35870 22.0568i 0.0761924 1.23689i
\(319\) 0.307325 + 0.266298i 0.0172069 + 0.0149098i
\(320\) −15.9400 + 1.40436i −0.891073 + 0.0785063i
\(321\) 0.968526 + 5.15741i 0.0540578 + 0.287859i
\(322\) 20.9467 + 5.47227i 1.16731 + 0.304958i
\(323\) 1.53301 0.0852990
\(324\) −8.08418 + 16.0825i −0.449121 + 0.893471i
\(325\) 5.41657 + 4.69349i 0.300458 + 0.260348i
\(326\) −4.73674 + 18.7734i −0.262344 + 1.03976i
\(327\) −1.27508 29.7517i −0.0705122 1.64527i
\(328\) −2.56575 0.0704778i −0.141670 0.00389149i
\(329\) −0.250335 0.548157i −0.0138014 0.0302209i
\(330\) 0.253707 + 0.0917837i 0.0139661 + 0.00505253i
\(331\) 10.3915 1.49407i 0.571167 0.0821215i 0.149321 0.988789i \(-0.452291\pi\)
0.421846 + 0.906667i \(0.361382\pi\)
\(332\) 17.6816 3.94823i 0.970406 0.216687i
\(333\) 15.8253 12.2027i 0.867220 0.668703i
\(334\) 8.85901 + 12.6849i 0.484744 + 0.694087i
\(335\) 7.77063 + 3.54873i 0.424555 + 0.193888i
\(336\) −1.18957 22.0833i −0.0648965 1.20474i
\(337\) −1.56676 + 1.35760i −0.0853468 + 0.0739534i −0.696489 0.717567i \(-0.745256\pi\)
0.611143 + 0.791521i \(0.290710\pi\)
\(338\) −37.1697 39.7039i −2.02177 2.15961i
\(339\) 10.5770 9.98928i 0.574463 0.542543i
\(340\) −0.908577 + 0.502618i −0.0492745 + 0.0272583i
\(341\) 0.190244 0.296025i 0.0103023 0.0160307i
\(342\) −0.468340 + 25.0539i −0.0253249 + 1.35476i
\(343\) −3.42698 + 11.6712i −0.185040 + 0.630187i
\(344\) 2.02418 2.96725i 0.109136 0.159984i
\(345\) 16.3547 2.92958i 0.880510 0.157724i
\(346\) −6.43031 + 2.15985i −0.345696 + 0.116114i
\(347\) −31.7336 9.31783i −1.70355 0.500208i −0.722078 0.691811i \(-0.756813\pi\)
−0.981472 + 0.191604i \(0.938631\pi\)
\(348\) −3.05536 25.3982i −0.163785 1.36148i
\(349\) 8.04540 12.5189i 0.430660 0.670121i −0.556319 0.830969i \(-0.687787\pi\)
0.986979 + 0.160848i \(0.0514230\pi\)
\(350\) 4.43646 0.813011i 0.237139 0.0434573i
\(351\) 33.6807 + 15.9677i 1.79774 + 0.852291i
\(352\) −0.143246 0.276614i −0.00763502 0.0147436i
\(353\) −0.584494 + 0.506467i −0.0311095 + 0.0269565i −0.670277 0.742111i \(-0.733825\pi\)
0.639167 + 0.769068i \(0.279279\pi\)
\(354\) 15.0802 + 19.7354i 0.801505 + 1.04893i
\(355\) −1.75483 + 3.84255i −0.0931368 + 0.203941i
\(356\) 20.7155 27.9917i 1.09792 1.48356i
\(357\) −0.651482 1.27863i −0.0344801 0.0676724i
\(358\) 0.285747 2.72831i 0.0151022 0.144196i
\(359\) 1.57852 + 10.9788i 0.0833110 + 0.579441i 0.988127 + 0.153638i \(0.0490990\pi\)
−0.904816 + 0.425802i \(0.859992\pi\)
\(360\) −7.93669 15.0024i −0.418300 0.790695i
\(361\) 6.59862 + 14.4490i 0.347296 + 0.760471i
\(362\) −10.3064 + 12.8616i −0.541692 + 0.675990i
\(363\) −0.815572 19.0298i −0.0428064 0.998807i
\(364\) −45.6607 + 3.51788i −2.39327 + 0.184387i
\(365\) 4.60410 + 3.98948i 0.240990 + 0.208819i
\(366\) 31.4335 7.16383i 1.64306 0.374460i
\(367\) 27.3870i 1.42959i 0.699333 + 0.714796i \(0.253480\pi\)
−0.699333 + 0.714796i \(0.746520\pi\)
\(368\) −16.1650 10.3293i −0.842657 0.538451i
\(369\) −0.987671 2.53694i −0.0514161 0.132068i
\(370\) 0.724251 + 18.8289i 0.0376520 + 0.978866i
\(371\) −18.8587 + 21.7641i −0.979095 + 1.12994i
\(372\) −21.3779 + 5.74476i −1.10839 + 0.297852i
\(373\) 3.85672 26.8241i 0.199693 1.38890i −0.605481 0.795860i \(-0.707019\pi\)
0.805174 0.593039i \(-0.202072\pi\)
\(374\) −0.0157735 0.0126398i −0.000815629 0.000653589i
\(375\) 16.9873 11.9749i 0.877222 0.618384i
\(376\) 0.0614498 + 0.530416i 0.00316903 + 0.0273541i
\(377\) −52.4341 + 7.53888i −2.70049 + 0.388272i
\(378\) 21.0957 10.2565i 1.08504 0.527538i
\(379\) −4.81820 + 1.41475i −0.247494 + 0.0726708i −0.403127 0.915144i \(-0.632077\pi\)
0.155633 + 0.987815i \(0.450258\pi\)
\(380\) −18.9925 14.0555i −0.974294 0.721032i
\(381\) 4.78441 19.3190i 0.245113 0.989744i
\(382\) −8.40356 16.6736i −0.429964 0.853097i
\(383\) −13.6411 15.7427i −0.697027 0.804412i 0.291321 0.956625i \(-0.405905\pi\)
−0.988348 + 0.152213i \(0.951360\pi\)
\(384\) −5.02344 + 18.9411i −0.256351 + 0.966584i
\(385\) −0.190084 0.295777i −0.00968760 0.0150742i
\(386\) −3.58975 19.5886i −0.182713 0.997035i
\(387\) 3.73391 + 0.756655i 0.189805 + 0.0384630i
\(388\) 10.6842 + 0.705195i 0.542410 + 0.0358009i
\(389\) −7.99687 + 27.2348i −0.405457 + 1.38086i 0.463554 + 0.886069i \(0.346574\pi\)
−0.869011 + 0.494792i \(0.835244\pi\)
\(390\) −30.6792 + 17.1476i −1.55350 + 0.868304i
\(391\) −1.23058 0.187474i −0.0622333 0.00948095i
\(392\) −5.08353 + 7.45198i −0.256757 + 0.376382i
\(393\) 20.0382 + 2.00989i 1.01079 + 0.101385i
\(394\) −10.0782 + 24.5212i −0.507733 + 1.23536i
\(395\) 5.22370 + 3.35707i 0.262833 + 0.168912i
\(396\) 0.211391 0.253924i 0.0106228 0.0127602i
\(397\) 10.4403 + 16.2455i 0.523986 + 0.815337i 0.997869 0.0652502i \(-0.0207845\pi\)
−0.473883 + 0.880588i \(0.657148\pi\)
\(398\) −15.9025 + 14.8875i −0.797120 + 0.746242i
\(399\) 20.3081 25.5720i 1.01668 1.28020i
\(400\) −3.96185 0.525279i −0.198092 0.0262639i
\(401\) −13.4396 + 29.4286i −0.671142 + 1.46960i 0.200622 + 0.979669i \(0.435704\pi\)
−0.871764 + 0.489927i \(0.837024\pi\)
\(402\) 7.32389 7.47002i 0.365282 0.372571i
\(403\) 12.9145 + 43.9826i 0.643315 + 2.19093i
\(404\) 6.91620 + 30.9733i 0.344094 + 1.54098i
\(405\) 11.3959 13.9357i 0.566269 0.692469i
\(406\) −16.9318 + 28.7164i −0.840311 + 1.42517i
\(407\) −0.333662 + 0.152378i −0.0165390 + 0.00755311i
\(408\) 0.200283 + 1.25568i 0.00991550 + 0.0621655i
\(409\) −0.117692 + 0.818568i −0.00581951 + 0.0404756i −0.992524 0.122047i \(-0.961054\pi\)
0.986705 + 0.162523i \(0.0519631\pi\)
\(410\) 2.48900 + 0.628004i 0.122923 + 0.0310149i
\(411\) −1.85703 + 3.18134i −0.0916005 + 0.156924i
\(412\) 5.17714 + 13.6510i 0.255059 + 0.672536i
\(413\) 32.3672i 1.59268i
\(414\) 3.43982 20.0541i 0.169058 0.985606i
\(415\) −18.1191 −0.889430
\(416\) 39.4525 + 9.49464i 1.93432 + 0.465513i
\(417\) −8.26339 4.82356i −0.404660 0.236211i
\(418\) 0.112526 0.445981i 0.00550385 0.0218137i
\(419\) −4.26622 0.613390i −0.208419 0.0299661i 0.0373146 0.999304i \(-0.488120\pi\)
−0.245733 + 0.969337i \(0.579029\pi\)
\(420\) −3.65200 + 21.8141i −0.178199 + 1.06442i
\(421\) −3.95796 8.66672i −0.192899 0.422390i 0.788326 0.615258i \(-0.210948\pi\)
−0.981225 + 0.192868i \(0.938221\pi\)
\(422\) 13.3484 22.6390i 0.649790 1.10205i
\(423\) −0.493155 + 0.278486i −0.0239780 + 0.0135405i
\(424\) 21.8373 13.2011i 1.06051 0.641101i
\(425\) −0.248824 + 0.0730615i −0.0120698 + 0.00354400i
\(426\) 3.69389 + 3.62163i 0.178970 + 0.175469i
\(427\) −38.2166 17.4529i −1.84943 0.844606i
\(428\) −4.26102 + 4.30809i −0.205964 + 0.208239i
\(429\) −0.535783 0.425495i −0.0258678 0.0205431i
\(430\) −2.62246 + 2.45508i −0.126466 + 0.118394i
\(431\) 12.0562 7.74805i 0.580727 0.373211i −0.217052 0.976160i \(-0.569644\pi\)
0.797779 + 0.602949i \(0.206008\pi\)
\(432\) −20.5828 + 2.88961i −0.990289 + 0.139026i
\(433\) 2.06454 3.21248i 0.0992154 0.154382i −0.788097 0.615551i \(-0.788933\pi\)
0.887312 + 0.461169i \(0.152570\pi\)
\(434\) 26.6814 + 10.9661i 1.28075 + 0.526388i
\(435\) −2.55334 + 25.4563i −0.122423 + 1.22054i
\(436\) 27.4137 20.7575i 1.31288 0.994105i
\(437\) −7.75213 27.2442i −0.370835 1.30327i
\(438\) 6.51225 3.63992i 0.311167 0.173922i
\(439\) −10.4357 3.06419i −0.498068 0.146246i 0.0230439 0.999734i \(-0.492664\pi\)
−0.521112 + 0.853489i \(0.674482\pi\)
\(440\) 0.0795293 + 0.301215i 0.00379141 + 0.0143599i
\(441\) −9.37737 1.90027i −0.446541 0.0904890i
\(442\) 2.58998 0.474632i 0.123193 0.0225759i
\(443\) −27.0293 + 17.3707i −1.28420 + 0.825307i −0.991400 0.130866i \(-0.958224\pi\)
−0.292803 + 0.956173i \(0.594588\pi\)
\(444\) 21.9845 + 7.01015i 1.04334 + 0.332687i
\(445\) −26.3206 + 22.8069i −1.24772 + 1.08115i
\(446\) −3.83130 7.60174i −0.181417 0.359953i
\(447\) 2.24010 + 0.554766i 0.105953 + 0.0262395i
\(448\) 20.1882 15.6382i 0.953802 0.738837i
\(449\) −1.63100 5.55467i −0.0769715 0.262141i 0.912013 0.410162i \(-0.134528\pi\)
−0.988984 + 0.148021i \(0.952710\pi\)
\(450\) −1.11802 4.08885i −0.0527042 0.192750i
\(451\) 0.00711168 + 0.0494628i 0.000334876 + 0.00232911i
\(452\) 16.4346 + 3.48071i 0.773018 + 0.163719i
\(453\) 7.15435 + 10.1490i 0.336141 + 0.476840i
\(454\) 18.4946 + 14.8203i 0.867996 + 0.695553i
\(455\) 45.3348 + 6.51816i 2.12533 + 0.305576i
\(456\) −24.0982 + 16.0156i −1.12850 + 0.750000i
\(457\) −15.5557 13.4791i −0.727665 0.630526i 0.210146 0.977670i \(-0.432606\pi\)
−0.937812 + 0.347144i \(0.887151\pi\)
\(458\) −11.7115 + 0.450483i −0.547243 + 0.0210497i
\(459\) −1.14490 + 0.712850i −0.0534395 + 0.0332730i
\(460\) 13.5269 + 13.6053i 0.630693 + 0.634350i
\(461\) −2.99612 −0.139543 −0.0697717 0.997563i \(-0.522227\pi\)
−0.0697717 + 0.997563i \(0.522227\pi\)
\(462\) −0.419798 + 0.0956738i −0.0195308 + 0.00445115i
\(463\) 9.21742 10.6375i 0.428370 0.494365i −0.499999 0.866026i \(-0.666666\pi\)
0.928368 + 0.371661i \(0.121212\pi\)
\(464\) 22.1101 19.5878i 1.02643 0.909340i
\(465\) 22.1184 0.947940i 1.02572 0.0439596i
\(466\) −7.13438 5.71700i −0.330494 0.264835i
\(467\) 23.5846 10.7707i 1.09137 0.498411i 0.213319 0.976983i \(-0.431573\pi\)
0.878048 + 0.478572i \(0.158845\pi\)
\(468\) 6.96564 + 42.4730i 0.321987 + 1.96332i
\(469\) −13.4941 + 1.94015i −0.623098 + 0.0895880i
\(470\) 0.0556260 0.531117i 0.00256584 0.0244986i
\(471\) 7.99314 4.07262i 0.368304 0.187656i
\(472\) −8.83261 + 27.2859i −0.406554 + 1.25593i
\(473\) −0.0636114 0.0290504i −0.00292486 0.00133574i
\(474\) 6.04211 4.61689i 0.277523 0.212061i
\(475\) −3.86444 4.45980i −0.177313 0.204630i
\(476\) 0.786134 1.45869i 0.0360324 0.0668588i
\(477\) 21.8959 + 15.9089i 1.00255 + 0.728419i
\(478\) 18.6506 3.41785i 0.853058 0.156329i
\(479\) 16.0401 + 10.3083i 0.732890 + 0.471000i 0.853099 0.521749i \(-0.174720\pi\)
−0.120209 + 0.992749i \(0.538356\pi\)
\(480\) 9.03149 17.3930i 0.412229 0.793877i
\(481\) 13.4622 45.8480i 0.613822 2.09049i
\(482\) 9.68881 + 28.8456i 0.441313 + 1.31388i
\(483\) −19.4290 + 18.0437i −0.884052 + 0.821018i
\(484\) 17.5344 13.2770i 0.797018 0.603499i
\(485\) −10.2749 3.01698i −0.466558 0.136994i
\(486\) −11.3003 18.9289i −0.512593 0.858632i
\(487\) −3.96837 2.55032i −0.179824 0.115566i 0.447632 0.894218i \(-0.352267\pi\)
−0.627456 + 0.778652i \(0.715904\pi\)
\(488\) 27.4543 + 25.1418i 1.24280 + 1.13812i
\(489\) −16.2819 17.2398i −0.736294 0.779613i
\(490\) 6.58606 6.16569i 0.297528 0.278538i
\(491\) 7.75644 + 8.95141i 0.350043 + 0.403971i 0.903279 0.429053i \(-0.141153\pi\)
−0.553236 + 0.833025i \(0.686607\pi\)
\(492\) 1.76012 2.60463i 0.0793522 0.117426i
\(493\) 0.796239 1.74352i 0.0358608 0.0785242i
\(494\) 34.3075 + 49.1237i 1.54357 + 2.21018i
\(495\) −0.261676 + 0.201775i −0.0117615 + 0.00906911i
\(496\) −19.5003 16.5256i −0.875587 0.742020i
\(497\) −0.959398 6.67276i −0.0430349 0.299314i
\(498\) −7.54847 + 20.8654i −0.338255 + 0.935000i
\(499\) −35.2232 + 16.0859i −1.57681 + 0.720105i −0.995605 0.0936531i \(-0.970146\pi\)
−0.581204 + 0.813758i \(0.697418\pi\)
\(500\) 22.5317 + 8.26321i 1.00765 + 0.369542i
\(501\) −18.9321 + 0.811384i −0.845825 + 0.0362499i
\(502\) −4.87770 + 19.3320i −0.217702 + 0.862831i
\(503\) −26.8470 + 30.9831i −1.19705 + 1.38147i −0.291862 + 0.956460i \(0.594275\pi\)
−0.905189 + 0.425010i \(0.860271\pi\)
\(504\) 23.5991 + 13.2934i 1.05119 + 0.592135i
\(505\) 31.7395i 1.41239i
\(506\) −0.144867 + 0.344239i −0.00644013 + 0.0153033i
\(507\) 65.4663 12.2941i 2.90746 0.546000i
\(508\) 21.4882 8.14939i 0.953384 0.361571i
\(509\) 3.49008 4.02776i 0.154695 0.178528i −0.673112 0.739541i \(-0.735043\pi\)
0.827807 + 0.561013i \(0.189588\pi\)
\(510\) 0.0781883 1.26929i 0.00346223 0.0562050i
\(511\) −9.62320 1.38361i −0.425705 0.0612072i
\(512\) −21.2863 + 7.67410i −0.940732 + 0.339151i
\(513\) −25.5781 16.9599i −1.12930 0.748799i
\(514\) −11.4662 + 19.4467i −0.505751 + 0.857757i
\(515\) −2.07799 14.4527i −0.0915670 0.636863i
\(516\) 1.73467 + 4.04274i 0.0763644 + 0.177972i
\(517\) 0.00997462 0.00292881i 0.000438683 0.000128809i
\(518\) −17.2177 24.6533i −0.756500 1.08321i
\(519\) 1.99713 8.06426i 0.0876644 0.353982i
\(520\) −36.4390 17.8662i −1.59796 0.783485i
\(521\) −23.3345 26.9294i −1.02230 1.17980i −0.983566 0.180549i \(-0.942212\pi\)
−0.0387356 0.999249i \(-0.512333\pi\)
\(522\) 28.2510 + 13.5456i 1.23651 + 0.592873i
\(523\) 21.1877 13.6165i 0.926471 0.595407i 0.0119430 0.999929i \(-0.496198\pi\)
0.914528 + 0.404522i \(0.132562\pi\)
\(524\) 11.2565 + 20.3482i 0.491742 + 0.888916i
\(525\) −2.07750 + 5.11847i −0.0906696 + 0.223388i
\(526\) −6.41370 + 15.6051i −0.279651 + 0.680415i
\(527\) −1.59142 0.467284i −0.0693235 0.0203552i
\(528\) 0.380003 + 0.0339038i 0.0165375 + 0.00147547i
\(529\) 2.89110 + 22.8176i 0.125700 + 0.992068i
\(530\) −24.1919 + 8.12570i −1.05083 + 0.352958i
\(531\) −30.3081 + 2.60264i −1.31526 + 0.112945i
\(532\) 37.6248 + 2.48336i 1.63124 + 0.107667i
\(533\) −5.47628 3.51939i −0.237204 0.152442i
\(534\) 15.2985 + 39.8115i 0.662033 + 1.72281i
\(535\) 5.09802 3.27630i 0.220407 0.141647i
\(536\) 11.9051 + 2.04680i 0.514222 + 0.0884081i
\(537\) 2.63101 + 2.08943i 0.113537 + 0.0901657i
\(538\) −5.18037 10.2784i −0.223341 0.443135i
\(539\) 0.159754 + 0.0729573i 0.00688110 + 0.00314249i
\(540\) 20.7200 + 1.66560i 0.891648 + 0.0716760i
\(541\) 7.42659 + 25.2926i 0.319294 + 1.08742i 0.950222 + 0.311574i \(0.100856\pi\)
−0.630928 + 0.775841i \(0.717326\pi\)
\(542\) −0.0792582 + 0.756756i −0.00340443 + 0.0325055i
\(543\) −6.51106 19.1068i −0.279417 0.819951i
\(544\) −1.06078 + 1.01516i −0.0454804 + 0.0435247i
\(545\) −31.2818 + 14.2859i −1.33997 + 0.611942i
\(546\) 26.3928 49.4908i 1.12951 2.11801i
\(547\) 31.5039 + 4.52958i 1.34701 + 0.193671i 0.777795 0.628518i \(-0.216338\pi\)
0.569215 + 0.822189i \(0.307247\pi\)
\(548\) −4.24098 + 0.326741i −0.181166 + 0.0139577i
\(549\) −13.2696 + 37.1887i −0.566334 + 1.58717i
\(550\) 0.00299067 + 0.0777506i 0.000127523 + 0.00331530i
\(551\) 43.6161 1.85811
\(552\) 21.3028 9.90911i 0.906708 0.421760i
\(553\) −9.90938 −0.421390
\(554\) 0.887091 + 23.0623i 0.0376889 + 0.979825i
\(555\) −19.9305 11.6340i −0.846005 0.493835i
\(556\) −0.848696 11.0158i −0.0359927 0.467172i
\(557\) −11.2631 1.61939i −0.477233 0.0686157i −0.100499 0.994937i \(-0.532044\pi\)
−0.376734 + 0.926321i \(0.622953\pi\)
\(558\) 8.12299 25.8658i 0.343874 1.09499i
\(559\) 8.28652 3.78433i 0.350483 0.160060i
\(560\) −23.1135 + 10.8640i −0.976723 + 0.459086i
\(561\) 0.0234326 0.00798520i 0.000989327 0.000337135i
\(562\) −3.01838 + 28.8194i −0.127323 + 1.21567i
\(563\) −4.88057 16.6217i −0.205692 0.700521i −0.996123 0.0879707i \(-0.971962\pi\)
0.790431 0.612550i \(-0.209856\pi\)
\(564\) −0.588444 0.285322i −0.0247780 0.0120142i
\(565\) −15.2827 6.97938i −0.642948 0.293625i
\(566\) −4.32459 8.58049i −0.181776 0.360665i
\(567\) −3.27580 + 28.5413i −0.137571 + 1.19862i
\(568\) −1.01213 + 5.88702i −0.0424681 + 0.247014i
\(569\) −0.347448 + 0.223291i −0.0145658 + 0.00936086i −0.547903 0.836542i \(-0.684574\pi\)
0.533338 + 0.845902i \(0.320938\pi\)
\(570\) 27.0122 10.3801i 1.13142 0.434775i
\(571\) −25.4115 16.3310i −1.06344 0.683430i −0.112764 0.993622i \(-0.535970\pi\)
−0.950674 + 0.310192i \(0.899607\pi\)
\(572\) 0.0520313 0.788314i 0.00217554 0.0329610i
\(573\) 22.7538 + 2.28227i 0.950554 + 0.0953431i
\(574\) −3.88338 + 1.30437i −0.162089 + 0.0544433i
\(575\) 2.55668 + 4.05257i 0.106621 + 0.169004i
\(576\) −16.2667 17.6464i −0.677779 0.735266i
\(577\) 24.5892 + 7.22005i 1.02366 + 0.300575i 0.750132 0.661289i \(-0.229990\pi\)
0.273531 + 0.961863i \(0.411808\pi\)
\(578\) 9.10309 22.1486i 0.378639 0.921262i
\(579\) 22.6000 + 9.17294i 0.939222 + 0.381214i
\(580\) −25.8502 + 14.3001i −1.07337 + 0.593781i
\(581\) 24.3253 15.6329i 1.00918 0.648563i
\(582\) −7.75481 + 10.5754i −0.321447 + 0.438363i
\(583\) −0.325332 0.375453i −0.0134739 0.0155497i
\(584\) 7.73489 + 3.79245i 0.320072 + 0.156933i
\(585\) 2.45813 42.9748i 0.101631 1.77679i
\(586\) 3.39825 + 4.86584i 0.140381 + 0.201006i
\(587\) 26.9524 7.91395i 1.11245 0.326644i 0.326660 0.945142i \(-0.394077\pi\)
0.785786 + 0.618498i \(0.212259\pi\)
\(588\) −4.35645 10.1530i −0.179657 0.418701i
\(589\) −5.37131 37.3583i −0.221321 1.53932i
\(590\) 14.5683 24.7079i 0.599766 1.01721i
\(591\) −18.7080 26.5386i −0.769544 1.09165i
\(592\) 7.78708 + 25.4815i 0.320047 + 1.04728i
\(593\) −9.38536 1.34941i −0.385410 0.0554137i −0.0531135 0.998588i \(-0.516915\pi\)
−0.332297 + 0.943175i \(0.607824\pi\)
\(594\) 0.123343 + 0.385398i 0.00506083 + 0.0158131i
\(595\) −1.08525 + 1.25244i −0.0444908 + 0.0513451i
\(596\) 0.944946 + 2.49162i 0.0387065 + 0.102061i
\(597\) −4.92413 26.2210i −0.201531 1.07316i
\(598\) −21.5320 43.6283i −0.880511 1.78409i
\(599\) 13.9967i 0.571889i 0.958246 + 0.285944i \(0.0923072\pi\)
−0.958246 + 0.285944i \(0.907693\pi\)
\(600\) 3.14813 3.74800i 0.128522 0.153012i
\(601\) 5.37903 6.20774i 0.219415 0.253219i −0.635361 0.772215i \(-0.719149\pi\)
0.854776 + 0.518996i \(0.173694\pi\)
\(602\) 1.40251 5.55863i 0.0571620 0.226553i
\(603\) 2.90178 + 12.4796i 0.118170 + 0.508209i
\(604\) −4.93680 + 13.4614i −0.200876 + 0.547737i
\(605\) −20.0086 + 9.13761i −0.813464 + 0.371496i
\(606\) −36.5503 13.2228i −1.48475 0.537140i
\(607\) −3.92066 27.2688i −0.159135 1.10681i −0.900233 0.435409i \(-0.856604\pi\)
0.741098 0.671397i \(-0.234305\pi\)
\(608\) −31.0405 12.3609i −1.25886 0.501299i
\(609\) −18.5355 36.3787i −0.751097 1.47414i
\(610\) −21.3176 30.5239i −0.863125 1.23588i
\(611\) −0.562566 + 1.23185i −0.0227590 + 0.0498353i
\(612\) −1.42910 0.618829i −0.0577680 0.0250147i
\(613\) 15.3882 + 17.7589i 0.621523 + 0.717276i 0.975996 0.217790i \(-0.0698849\pi\)
−0.354472 + 0.935067i \(0.615339\pi\)
\(614\) 12.3471 11.5590i 0.498290 0.466485i
\(615\) −2.28568 + 2.15868i −0.0921676 + 0.0870464i
\(616\) −0.366655 0.335772i −0.0147730 0.0135286i
\(617\) 34.7823 + 22.3532i 1.40028 + 0.899908i 0.999865 0.0164249i \(-0.00522844\pi\)
0.400418 + 0.916332i \(0.368865\pi\)
\(618\) −17.5090 3.62811i −0.704316 0.145944i
\(619\) −11.9988 3.52317i −0.482273 0.141608i 0.0315538 0.999502i \(-0.489954\pi\)
−0.513827 + 0.857894i \(0.671773\pi\)
\(620\) 15.4318 + 20.3802i 0.619758 + 0.818490i
\(621\) 18.4581 + 16.7421i 0.740698 + 0.671838i
\(622\) −7.03918 20.9571i −0.282245 0.840304i
\(623\) 15.6585 53.3280i 0.627345 2.13654i
\(624\) −35.7548 + 34.5190i −1.43134 + 1.38187i
\(625\) −15.9889 10.2755i −0.639558 0.411019i
\(626\) 24.9330 4.56915i 0.996524 0.182620i
\(627\) 0.386795 + 0.409551i 0.0154471 + 0.0163559i
\(628\) 9.11871 + 4.91437i 0.363876 + 0.196105i
\(629\) 1.13222 + 1.30665i 0.0451446 + 0.0520997i
\(630\) −20.1371 18.1188i −0.802280 0.721869i
\(631\) 26.5893 + 12.1429i 1.05851 + 0.483403i 0.867113 0.498111i \(-0.165973\pi\)
0.191392 + 0.981514i \(0.438700\pi\)
\(632\) 8.35372 + 2.70415i 0.332293 + 0.107565i
\(633\) 14.6127 + 28.6797i 0.580803 + 1.13991i
\(634\) −0.000594885 0.00567995i −2.36259e−5 0.000225580i
\(635\) −22.7502 + 3.27098i −0.902813 + 0.129805i
\(636\) −0.721125 + 31.2439i −0.0285945 + 1.23890i
\(637\) −20.8108 + 9.50399i −0.824555 + 0.376562i
\(638\) −0.448777 0.359619i −0.0177672 0.0142375i
\(639\) −6.17111 + 1.43492i −0.244125 + 0.0567645i
\(640\) 22.4496 2.85106i 0.887397 0.112698i
\(641\) −5.25986 + 6.07020i −0.207752 + 0.239758i −0.850057 0.526690i \(-0.823433\pi\)
0.642305 + 0.766449i \(0.277978\pi\)
\(642\) −1.64903 7.23564i −0.0650822 0.285568i
\(643\) 30.1495 1.18898 0.594490 0.804103i \(-0.297354\pi\)
0.594490 + 0.804103i \(0.297354\pi\)
\(644\) −29.8986 6.59464i −1.17817 0.259865i
\(645\) −0.812031 4.32408i −0.0319737 0.170260i
\(646\) −2.16640 + 0.0833305i −0.0852359 + 0.00327859i
\(647\) −12.5040 10.8348i −0.491584 0.425960i 0.373467 0.927643i \(-0.378169\pi\)
−0.865051 + 0.501683i \(0.832714\pi\)
\(648\) 10.5501 23.1667i 0.414447 0.910073i
\(649\) 0.552684 + 0.0794640i 0.0216947 + 0.00311923i
\(650\) −7.90966 6.33826i −0.310242 0.248607i
\(651\) −28.8766 + 20.3561i −1.13176 + 0.797820i
\(652\) 5.67334 26.7874i 0.222185 1.04907i
\(653\) 4.52439 + 31.4678i 0.177053 + 1.23143i 0.863537 + 0.504286i \(0.168244\pi\)
−0.686483 + 0.727145i \(0.740847\pi\)
\(654\) 3.41913 + 41.9748i 0.133699 + 1.64135i
\(655\) −6.55218 22.3147i −0.256015 0.871907i
\(656\) 3.62967 0.0398708i 0.141715 0.00155669i
\(657\) −0.521786 + 9.12224i −0.0203568 + 0.355893i
\(658\) 0.383562 + 0.761031i 0.0149528 + 0.0296681i
\(659\) −14.1322 + 12.2456i −0.550514 + 0.477023i −0.885138 0.465329i \(-0.845936\pi\)
0.334624 + 0.942352i \(0.391391\pi\)
\(660\) −0.363520 0.115915i −0.0141500 0.00451198i
\(661\) −1.09180 + 0.701659i −0.0424662 + 0.0272914i −0.561702 0.827340i \(-0.689853\pi\)
0.519235 + 0.854631i \(0.326217\pi\)
\(662\) −14.6037 + 2.67623i −0.567589 + 0.104014i
\(663\) −1.21283 + 2.98814i −0.0471026 + 0.116050i
\(664\) −24.7725 + 6.54065i −0.961360 + 0.253826i
\(665\) −36.1832 10.6244i −1.40313 0.411995i
\(666\) −21.7005 + 18.1047i −0.840877 + 0.701542i
\(667\) −35.0117 5.33387i −1.35566 0.206528i
\(668\) −13.2088 17.4444i −0.511064 0.674943i
\(669\) 10.3738 + 1.04052i 0.401074 + 0.0402288i
\(670\) −11.1741 4.59256i −0.431694 0.177426i
\(671\) 0.391841 0.609716i 0.0151269 0.0235378i
\(672\) 2.88146 + 31.1428i 0.111155 + 1.20136i
\(673\) −6.29948 + 4.04843i −0.242827 + 0.156055i −0.656394 0.754418i \(-0.727919\pi\)
0.413567 + 0.910474i \(0.364283\pi\)
\(674\) 2.14030 2.00369i 0.0824412 0.0771792i
\(675\) 4.95990 + 1.53376i 0.190907 + 0.0590345i
\(676\) 54.6852 + 54.0878i 2.10328 + 2.08030i
\(677\) 12.8312 + 5.85982i 0.493144 + 0.225211i 0.646434 0.762970i \(-0.276260\pi\)
−0.153290 + 0.988181i \(0.548987\pi\)
\(678\) −14.4041 + 14.6915i −0.553185 + 0.564223i
\(679\) 16.3973 4.81468i 0.629270 0.184770i
\(680\) 1.25665 0.759671i 0.0481904 0.0291321i
\(681\) −27.4751 + 9.36275i −1.05285 + 0.358781i
\(682\) −0.252756 + 0.428675i −0.00967851 + 0.0164148i
\(683\) −6.31761 13.8336i −0.241736 0.529329i 0.749409 0.662107i \(-0.230338\pi\)
−0.991146 + 0.132778i \(0.957610\pi\)
\(684\) −0.700024 35.4309i −0.0267661 1.35473i
\(685\) 4.21071 + 0.605408i 0.160883 + 0.0231315i
\(686\) 4.20848 16.6797i 0.160681 0.636834i
\(687\) 7.23631 12.3968i 0.276083 0.472966i
\(688\) −2.69921 + 4.30326i −0.102906 + 0.164060i
\(689\) 64.7165 2.46550
\(690\) −22.9528 + 5.02900i −0.873797 + 0.191451i
\(691\) 12.6547i 0.481409i 0.970598 + 0.240704i \(0.0773785\pi\)
−0.970598 + 0.240704i \(0.922622\pi\)
\(692\) 8.96971 3.40176i 0.340977 0.129316i
\(693\) 0.177217 0.496659i 0.00673192 0.0188665i
\(694\) 45.3515 + 11.4427i 1.72152 + 0.434359i
\(695\) −1.57252 + 10.9371i −0.0596492 + 0.414869i
\(696\) 5.69832 + 35.7258i 0.215994 + 1.35418i
\(697\) 0.214254 0.0978466i 0.00811545 0.00370620i
\(698\) −10.6890 + 18.1286i −0.404585 + 0.686179i
\(699\) 10.5986 3.61172i 0.400877 0.136608i
\(700\) −6.22528 + 1.39008i −0.235293 + 0.0525400i
\(701\) −6.77345 23.0683i −0.255830 0.871276i −0.982810 0.184618i \(-0.940895\pi\)
0.726981 0.686658i \(-0.240923\pi\)
\(702\) −48.4645 20.7342i −1.82917 0.782562i
\(703\) −16.3437 + 35.7877i −0.616415 + 1.34976i
\(704\) 0.217466 + 0.383115i 0.00819607 + 0.0144392i
\(705\) 0.512177 + 0.406748i 0.0192897 + 0.0153190i
\(706\) 0.798459 0.747495i 0.0300504 0.0281324i
\(707\) 27.3845 + 42.6111i 1.02990 + 1.60255i
\(708\) −22.3837 27.0698i −0.841230 1.01735i
\(709\) −16.2304 10.4306i −0.609544 0.391730i 0.199142 0.979971i \(-0.436185\pi\)
−0.808686 + 0.588240i \(0.799821\pi\)
\(710\) 2.27100 5.52555i 0.0852292 0.207370i
\(711\) 0.796810 + 9.27897i 0.0298827 + 0.347988i
\(712\) −27.7529 + 40.6831i −1.04008 + 1.52466i
\(713\) −0.256912 + 30.6452i −0.00962143 + 1.14767i
\(714\) 0.990157 + 1.77151i 0.0370557 + 0.0662971i
\(715\) −0.222601 + 0.758110i −0.00832481 + 0.0283517i
\(716\) −0.255505 + 3.87109i −0.00954866 + 0.144669i
\(717\) −8.73368 + 21.5177i −0.326165 + 0.803594i
\(718\) −2.82749 15.4291i −0.105521 0.575810i
\(719\) −26.5692 41.3425i −0.990865 1.54182i −0.832194 0.554485i \(-0.812915\pi\)
−0.158672 0.987331i \(-0.550721\pi\)
\(720\) 12.0314 + 20.7695i 0.448383 + 0.774033i
\(721\) 15.2594 + 17.6103i 0.568289 + 0.655841i
\(722\) −10.1104 20.0601i −0.376269 0.746560i
\(723\) −36.1753 8.95891i −1.34537 0.333185i
\(724\) 13.8656 18.7358i 0.515309 0.696311i
\(725\) −7.07938 + 2.07869i −0.262922 + 0.0772007i
\(726\) 2.18695 + 26.8480i 0.0811654 + 0.996424i
\(727\) 39.9591 5.74525i 1.48200 0.213079i 0.646645 0.762791i \(-0.276171\pi\)
0.835355 + 0.549711i \(0.185262\pi\)
\(728\) 64.3351 7.45335i 2.38442 0.276240i
\(729\) 26.9889 + 0.772406i 0.999591 + 0.0286076i
\(730\) −6.72323 5.38754i −0.248838 0.199402i
\(731\) −0.0469096 + 0.326263i −0.00173501 + 0.0120673i
\(732\) −44.0315 + 11.8324i −1.62745 + 0.437336i
\(733\) −13.7800 + 15.9030i −0.508977 + 0.587390i −0.950836 0.309694i \(-0.899773\pi\)
0.441860 + 0.897084i \(0.354319\pi\)
\(734\) −1.48869 38.7025i −0.0549485 1.42854i
\(735\) 2.03934 + 10.8595i 0.0752222 + 0.400559i
\(736\) 23.4053 + 13.7183i 0.862730 + 0.505664i
\(737\) 0.235181i 0.00866299i
\(738\) 1.53365 + 3.53144i 0.0564544 + 0.129994i
\(739\) −8.49777 7.36336i −0.312595 0.270866i 0.484405 0.874844i \(-0.339036\pi\)
−0.797001 + 0.603978i \(0.793581\pi\)
\(740\) −2.04698 26.5690i −0.0752484 0.976696i
\(741\) −73.3167 + 3.14217i −2.69336 + 0.115431i
\(742\) 25.4675 31.7815i 0.934941 1.16673i
\(743\) −4.47602 9.80111i −0.164209 0.359568i 0.809584 0.587004i \(-0.199693\pi\)
−0.973793 + 0.227437i \(0.926966\pi\)
\(744\) 29.8983 9.28036i 1.09612 0.340235i
\(745\) −0.379280 2.63795i −0.0138957 0.0966470i
\(746\) −3.99211 + 38.1166i −0.146162 + 1.39555i
\(747\) −16.5944 21.5207i −0.607156 0.787402i
\(748\) 0.0229777 + 0.0170048i 0.000840148 + 0.000621756i
\(749\) −4.01746 + 8.79702i −0.146795 + 0.321436i
\(750\) −23.3550 + 17.8460i −0.852805 + 0.651644i
\(751\) −12.1309 + 10.5115i −0.442662 + 0.383569i −0.847479 0.530829i \(-0.821881\pi\)
0.404817 + 0.914398i \(0.367335\pi\)
\(752\) −0.115671 0.746227i −0.00421808 0.0272121i
\(753\) −16.7665 17.7529i −0.611003 0.646951i
\(754\) 73.6884 13.5039i 2.68357 0.491783i
\(755\) 7.75261 12.0633i 0.282146 0.439028i
\(756\) −29.2542 + 15.6409i −1.06397 + 0.568854i
\(757\) 33.3100 + 9.78071i 1.21067 + 0.355486i 0.823925 0.566699i \(-0.191780\pi\)
0.386749 + 0.922185i \(0.373598\pi\)
\(758\) 6.73202 2.26118i 0.244518 0.0821299i
\(759\) −0.260405 0.376058i −0.00945209 0.0136500i
\(760\) 27.6036 + 18.8304i 1.00129 + 0.683051i
\(761\) −7.30750 + 24.8871i −0.264897 + 0.902155i 0.714402 + 0.699735i \(0.246699\pi\)
−0.979299 + 0.202420i \(0.935119\pi\)
\(762\) −5.71104 + 27.5611i −0.206889 + 0.998434i
\(763\) 29.6709 46.1688i 1.07416 1.67142i
\(764\) 12.7820 + 23.1058i 0.462436 + 0.835940i
\(765\) 1.26003 + 0.915497i 0.0455564 + 0.0330999i
\(766\) 20.1329 + 21.5055i 0.727431 + 0.777026i
\(767\) −54.9712 + 47.6328i −1.98489 + 1.71992i
\(768\) 6.06938 27.0400i 0.219010 0.975723i
\(769\) −28.6177 13.0693i −1.03198 0.471290i −0.173878 0.984767i \(-0.555630\pi\)
−0.858103 + 0.513477i \(0.828357\pi\)
\(770\) 0.284699 + 0.407650i 0.0102598 + 0.0146907i
\(771\) −12.5522 24.6356i −0.452056 0.887229i
\(772\) 6.13771 + 27.4869i 0.220901 + 0.989275i
\(773\) 31.1136 4.47346i 1.11908 0.160899i 0.442145 0.896943i \(-0.354217\pi\)
0.676934 + 0.736044i \(0.263308\pi\)
\(774\) −5.31778 0.866316i −0.191144 0.0311391i
\(775\) 2.65227 + 5.80767i 0.0952725 + 0.208618i
\(776\) −15.1370 0.415792i −0.543385 0.0149261i
\(777\) 36.7949 1.57694i 1.32001 0.0565724i
\(778\) 9.82051 38.9221i 0.352082 1.39542i
\(779\) 4.05068 + 3.50993i 0.145130 + 0.125756i
\(780\) 42.4227 25.9001i 1.51898 0.927373i
\(781\) 0.116296 0.00416139
\(782\) 1.74921 + 0.198041i 0.0625517 + 0.00708192i
\(783\) −32.5740 + 20.2815i −1.16410 + 0.724802i
\(784\) 6.77882 10.8072i 0.242101 0.385972i
\(785\) −7.82941 6.78422i −0.279444 0.242139i
\(786\) −28.4266 1.75108i −1.01394 0.0624590i
\(787\) 3.30702 23.0009i 0.117883 0.819892i −0.841997 0.539482i \(-0.818620\pi\)
0.959880 0.280411i \(-0.0904707\pi\)
\(788\) 12.9093 35.2004i 0.459874 1.25396i
\(789\) −11.9056 16.8890i −0.423852 0.601264i
\(790\) −7.56444 4.46015i −0.269131 0.158685i
\(791\) 26.5391 3.81575i 0.943623 0.135673i
\(792\) −0.284928 + 0.370329i −0.0101245 + 0.0131591i
\(793\) 26.5996 + 90.5900i 0.944580 + 3.21694i
\(794\) −15.6370 22.3901i −0.554937 0.794595i
\(795\) 7.51355 30.3391i 0.266478 1.07602i
\(796\) 21.6637 21.9029i 0.767848 0.776329i
\(797\) −37.6837 + 32.6531i −1.33482 + 1.15663i −0.360176 + 0.932884i \(0.617284\pi\)
−0.974647 + 0.223747i \(0.928171\pi\)
\(798\) −27.3088 + 37.2414i −0.966720 + 1.31833i
\(799\) −0.0264914 0.0412214i −0.000937198 0.00145831i
\(800\) 5.62731 + 0.526951i 0.198955 + 0.0186305i
\(801\) −51.1945 10.3743i −1.80887 0.366557i
\(802\) 17.3928 42.3181i 0.614160 1.49431i
\(803\) 0.0472514 0.160923i 0.00166747 0.00567887i
\(804\) −9.94384 + 10.9545i −0.350692 + 0.386336i
\(805\) 27.7459 + 12.9533i 0.977914 + 0.456544i
\(806\) −20.6411 61.4529i −0.727052 2.16459i
\(807\) 14.0266 + 1.40690i 0.493758 + 0.0495253i
\(808\) −11.4574 43.3945i −0.403069 1.52661i
\(809\) −25.0021 + 38.9040i −0.879027 + 1.36779i 0.0503776 + 0.998730i \(0.483958\pi\)
−0.929405 + 0.369062i \(0.879679\pi\)
\(810\) −15.3469 + 20.3129i −0.539234 + 0.713723i
\(811\) −20.3146 31.6101i −0.713342 1.10998i −0.988883 0.148693i \(-0.952494\pi\)
0.275541 0.961289i \(-0.411143\pi\)
\(812\) 22.3665 41.5015i 0.784911 1.45642i
\(813\) −0.729770 0.579551i −0.0255941 0.0203257i
\(814\) 0.463238 0.233473i 0.0162365 0.00818323i
\(815\) −11.3760 + 24.9099i −0.398482 + 0.872555i
\(816\) −0.351290 1.76360i −0.0122976 0.0617385i
\(817\) −7.19679 + 2.11317i −0.251784 + 0.0739304i
\(818\) 0.121824 1.16317i 0.00425947 0.0406694i
\(819\) 33.7781 + 59.8156i 1.18030 + 2.09013i
\(820\) −3.55151 0.752180i −0.124024 0.0262672i
\(821\) −6.72843 14.7332i −0.234824 0.514193i 0.755131 0.655574i \(-0.227573\pi\)
−0.989955 + 0.141381i \(0.954846\pi\)
\(822\) 2.45137 4.59671i 0.0855012 0.160329i
\(823\) 4.58527 31.8913i 0.159833 1.11166i −0.739107 0.673588i \(-0.764752\pi\)
0.898940 0.438072i \(-0.144339\pi\)
\(824\) −8.05820 19.0097i −0.280721 0.662236i
\(825\) −0.0822998 0.0480405i −0.00286531 0.00167256i
\(826\) 1.75940 + 45.7403i 0.0612172 + 1.59151i
\(827\) 37.6484i 1.30916i −0.755991 0.654582i \(-0.772845\pi\)
0.755991 0.654582i \(-0.227155\pi\)
\(828\) −3.77096 + 28.5268i −0.131050 + 0.991376i
\(829\) 26.5649i 0.922637i −0.887235 0.461319i \(-0.847377\pi\)
0.887235 0.461319i \(-0.152623\pi\)
\(830\) 25.6053 0.984906i 0.888773 0.0341866i
\(831\) −24.4117 14.2498i −0.846833 0.494319i
\(832\) −56.2691 11.2730i −1.95078 0.390821i
\(833\) 0.117809 0.819379i 0.00408184 0.0283898i
\(834\) 11.9398 + 6.36732i 0.413440 + 0.220482i
\(835\) 9.09068 + 19.9058i 0.314596 + 0.688869i
\(836\) −0.134776 + 0.636364i −0.00466134 + 0.0220091i
\(837\) 21.3831 + 25.4027i 0.739107 + 0.878047i
\(838\) 6.06223 + 0.634923i 0.209416 + 0.0219330i
\(839\) 36.7802 10.7996i 1.26979 0.372845i 0.423662 0.905820i \(-0.360744\pi\)
0.846131 + 0.532976i \(0.178926\pi\)
\(840\) 3.97513 31.0256i 0.137155 1.07048i
\(841\) 10.6070 23.2261i 0.365758 0.800899i
\(842\) 6.06436 + 12.0324i 0.208992 + 0.414664i
\(843\) −27.7917 22.0709i −0.957197 0.760164i
\(844\) −17.6330 + 32.7183i −0.606951 + 1.12621i
\(845\) −41.5881 64.7124i −1.43067 2.22617i
\(846\) 0.681773 0.420355i 0.0234399 0.0144521i
\(847\) 18.9782 29.5306i 0.652098 1.01468i
\(848\) −30.1421 + 19.8424i −1.03509 + 0.681389i
\(849\) 11.7094 + 1.17449i 0.401867 + 0.0403083i
\(850\) 0.347659 0.116774i 0.0119246 0.00400530i
\(851\) 17.4960 26.7290i 0.599756 0.916258i
\(852\) −5.41696 4.91719i −0.185582 0.168460i
\(853\) 11.6489 39.6724i 0.398849 1.35836i −0.478325 0.878183i \(-0.658756\pi\)
0.877174 0.480173i \(-0.159426\pi\)
\(854\) 54.9551 + 22.5866i 1.88053 + 0.772896i
\(855\) −7.03897 + 34.7356i −0.240728 + 1.18793i
\(856\) 5.78737 6.31967i 0.197808 0.216002i
\(857\) −11.3135 17.6042i −0.386463 0.601348i 0.592455 0.805604i \(-0.298159\pi\)
−0.978918 + 0.204256i \(0.934523\pi\)
\(858\) 0.780280 + 0.572172i 0.0266383 + 0.0195336i
\(859\) −26.8976 + 23.3069i −0.917736 + 0.795223i −0.979202 0.202886i \(-0.934968\pi\)
0.0614664 + 0.998109i \(0.480422\pi\)
\(860\) 3.57253 3.61199i 0.121822 0.123168i
\(861\) 1.20610 4.87014i 0.0411039 0.165974i
\(862\) −16.6163 + 11.6046i −0.565953 + 0.395256i
\(863\) 6.94888 + 23.6657i 0.236543 + 0.805590i 0.989123 + 0.147090i \(0.0469906\pi\)
−0.752581 + 0.658500i \(0.771191\pi\)
\(864\) 28.9298 5.20233i 0.984213 0.176987i
\(865\) −9.49650 + 1.36539i −0.322891 + 0.0464247i
\(866\) −2.74292 + 4.65200i −0.0932081 + 0.158082i
\(867\) 16.8979 + 23.9709i 0.573883 + 0.814094i
\(868\) −38.3015 14.0466i −1.30004 0.476772i
\(869\) 0.0243283 0.169207i 0.000825281 0.00573996i
\(870\) 2.22456 36.1129i 0.0754196 1.22434i
\(871\) 23.1535 + 20.0626i 0.784526 + 0.679796i
\(872\) −37.6118 + 30.8240i −1.27370 + 1.04383i
\(873\) −5.82688 14.9670i −0.197210 0.506556i
\(874\) 12.4360 + 38.0792i 0.420654 + 1.28805i
\(875\) 38.3035 1.29489
\(876\) −9.00505 + 5.49781i −0.304252 + 0.185754i
\(877\) 9.90976 + 8.58686i 0.334629 + 0.289958i 0.805925 0.592017i \(-0.201668\pi\)
−0.471296 + 0.881975i \(0.656214\pi\)
\(878\) 14.9139 + 3.76296i 0.503321 + 0.126994i
\(879\) −7.26222 + 0.311241i −0.244949 + 0.0104979i
\(880\) −0.128762 0.421345i −0.00434055 0.0142035i
\(881\) −10.5992 23.2090i −0.357097 0.781933i −0.999874 0.0158795i \(-0.994945\pi\)
0.642777 0.766053i \(-0.277782\pi\)
\(882\) 13.3551 + 2.17567i 0.449689 + 0.0732586i
\(883\) 41.1951 5.92297i 1.38633 0.199324i 0.591571 0.806253i \(-0.298508\pi\)
0.794756 + 0.606929i \(0.207599\pi\)
\(884\) −3.63428 + 0.811519i −0.122234 + 0.0272944i
\(885\) 15.9481 + 31.3006i 0.536090 + 1.05216i
\(886\) 37.2528 26.0170i 1.25153 0.874058i
\(887\) −1.40912 0.643526i −0.0473138 0.0216075i 0.391618 0.920128i \(-0.371916\pi\)
−0.438931 + 0.898521i \(0.644643\pi\)
\(888\) −31.4489 8.71151i −1.05535 0.292339i
\(889\) 27.7205 24.0199i 0.929715 0.805603i
\(890\) 35.9557 33.6608i 1.20524 1.12831i
\(891\) −0.479313 0.126007i −0.0160576 0.00422139i
\(892\) 5.82749 + 10.5343i 0.195119 + 0.352714i
\(893\) 0.602825 0.938013i 0.0201728 0.0313894i
\(894\) −3.19579 0.662212i −0.106883 0.0221477i
\(895\) 1.09310 3.72277i 0.0365384 0.124439i
\(896\) −27.6792 + 23.1968i −0.924698 + 0.774952i
\(897\) 59.2373 + 6.44369i 1.97788 + 0.215149i
\(898\) 2.60681 + 7.76102i 0.0869904 + 0.258989i
\(899\) −45.2781 13.2948i −1.51011 0.443408i
\(900\) 1.80222 + 5.71746i 0.0600739 + 0.190582i
\(901\) −1.26599 + 1.96991i −0.0421761 + 0.0656273i
\(902\) −0.0127387 0.0695127i −0.000424151 0.00231452i
\(903\) 4.82094 + 5.10457i 0.160431 + 0.169869i
\(904\) −23.4141 4.02548i −0.778740 0.133886i
\(905\) −17.6173 + 15.2655i −0.585618 + 0.507441i
\(906\) −10.6620 13.9533i −0.354220 0.463567i
\(907\) −18.3070 + 40.0867i −0.607873 + 1.33106i 0.316147 + 0.948710i \(0.397611\pi\)
−0.924019 + 0.382345i \(0.875116\pi\)
\(908\) −26.9416 19.9383i −0.894089 0.661676i
\(909\) 37.6983 29.0687i 1.25037 0.964147i
\(910\) −64.4200 6.74698i −2.13550 0.223660i
\(911\) 6.63428 + 46.1424i 0.219803 + 1.52877i 0.738762 + 0.673967i \(0.235411\pi\)
−0.518959 + 0.854799i \(0.673680\pi\)
\(912\) 33.1843 23.9427i 1.09884 0.792821i
\(913\) 0.207218 + 0.453745i 0.00685793 + 0.0150168i
\(914\) 22.7155 + 18.2027i 0.751363 + 0.602091i
\(915\) 45.5567 1.95245i 1.50606 0.0645459i
\(916\) 16.5259 1.27322i 0.546030 0.0420682i
\(917\) 28.0493 + 24.3049i 0.926270 + 0.802617i
\(918\) 1.57919 1.06961i 0.0521211 0.0353024i
\(919\) 41.0957i 1.35562i 0.735236 + 0.677812i \(0.237072\pi\)
−0.735236 + 0.677812i \(0.762928\pi\)
\(920\) −19.8553 18.4913i −0.654609 0.609640i
\(921\) 3.82323 + 20.3587i 0.125980 + 0.670843i
\(922\) 4.23403 0.162862i 0.139440 0.00536356i
\(923\) −9.92088 + 11.4493i −0.326550 + 0.376858i
\(924\) 0.588045 0.158022i 0.0193453 0.00519855i
\(925\) 0.947164 6.58767i 0.0311425 0.216601i
\(926\) −12.4475 + 15.5336i −0.409052 + 0.510465i
\(927\) 15.2629 15.7046i 0.501301 0.515808i
\(928\) −30.1805 + 28.8827i −0.990723 + 0.948121i
\(929\) 29.1277 4.18794i 0.955650 0.137402i 0.353191 0.935551i \(-0.385097\pi\)
0.602459 + 0.798150i \(0.294188\pi\)
\(930\) −31.2055 + 2.54190i −1.02327 + 0.0833521i
\(931\) 18.0741 5.30703i 0.592354 0.173931i
\(932\) 10.3928 + 7.69128i 0.340429 + 0.251936i
\(933\) 26.2823 + 6.50888i 0.860445 + 0.213091i
\(934\) −32.7436 + 16.5029i −1.07140 + 0.539991i
\(935\) −0.0187216 0.0216059i −0.000612263 0.000706589i
\(936\) −12.1523 59.6429i −0.397212 1.94949i
\(937\) −7.25428 11.2879i −0.236987 0.368759i 0.702306 0.711875i \(-0.252154\pi\)
−0.939293 + 0.343116i \(0.888517\pi\)
\(938\) 18.9639 3.47527i 0.619194 0.113472i
\(939\) −11.6756 + 28.7660i −0.381019 + 0.938741i
\(940\) −0.0497388 + 0.753581i −0.00162230 + 0.0245791i
\(941\) −5.82395 + 19.8345i −0.189855 + 0.646588i 0.808459 + 0.588552i \(0.200302\pi\)
−0.998315 + 0.0580354i \(0.981516\pi\)
\(942\) −11.0743 + 6.18978i −0.360819 + 0.201674i
\(943\) −2.82234 3.31287i −0.0919080 0.107882i
\(944\) 10.9988 39.0397i 0.357980 1.27063i
\(945\) 31.9632 8.89059i 1.03976 0.289211i
\(946\) 0.0914728 + 0.0375953i 0.00297404 + 0.00122233i
\(947\) −14.6406 9.40895i −0.475756 0.305750i 0.280699 0.959796i \(-0.409434\pi\)
−0.756455 + 0.654046i \(0.773070\pi\)
\(948\) −8.28756 + 6.85288i −0.269167 + 0.222571i
\(949\) 11.8120 + 18.3798i 0.383434 + 0.596635i
\(950\) 5.70352 + 6.09239i 0.185047 + 0.197663i
\(951\) −0.00547740 0.00434991i −0.000177617 0.000141055i
\(952\) −1.03165 + 2.10410i −0.0334359 + 0.0681943i
\(953\) 3.41827 7.48496i 0.110729 0.242462i −0.846153 0.532940i \(-0.821087\pi\)
0.956882 + 0.290478i \(0.0938144\pi\)
\(954\) −31.8074 21.2918i −1.02980 0.689346i
\(955\) −7.44015 25.3388i −0.240757 0.819945i
\(956\) −26.1706 + 5.84379i −0.846419 + 0.189002i
\(957\) 0.666689 0.227189i 0.0215510 0.00734399i
\(958\) −23.2277 13.6955i −0.750452 0.442482i
\(959\) −6.17532 + 2.82017i −0.199411 + 0.0910681i
\(960\) −11.8176 + 25.0701i −0.381411 + 0.809135i
\(961\) −1.39961 + 9.73453i −0.0451488 + 0.314017i
\(962\) −16.5321 + 65.5226i −0.533018 + 2.11253i
\(963\) 8.56042 + 3.05452i 0.275856 + 0.0984304i
\(964\) −15.2599 40.2371i −0.491488 1.29595i
\(965\) 28.1669i 0.906725i
\(966\) 26.4757 26.5549i 0.851841 0.854391i
\(967\) −26.3208 −0.846420 −0.423210 0.906032i \(-0.639097\pi\)
−0.423210 + 0.906032i \(0.639097\pi\)
\(968\) −24.0574 + 19.7157i −0.773233 + 0.633687i
\(969\) 1.33858 2.29316i 0.0430013 0.0736669i
\(970\) 14.6841 + 3.70498i 0.471479 + 0.118960i
\(971\) −15.2635 2.19456i −0.489829 0.0704268i −0.107025 0.994256i \(-0.534133\pi\)
−0.382804 + 0.923829i \(0.625042\pi\)
\(972\) 16.9982 + 26.1355i 0.545217 + 0.838295i
\(973\) −7.32528 16.0401i −0.234838 0.514223i
\(974\) 5.74660 + 3.38831i 0.184133 + 0.108569i
\(975\) 11.7504 4.00419i 0.376312 0.128237i
\(976\) −40.1642 34.0373i −1.28562 1.08951i
\(977\) 31.3903 9.21703i 1.00427 0.294879i 0.262060 0.965051i \(-0.415598\pi\)
0.742205 + 0.670172i \(0.233780\pi\)
\(978\) 23.9462 + 23.4778i 0.765715 + 0.750736i
\(979\) 0.872157 + 0.398301i 0.0278742 + 0.0127297i
\(980\) −8.97207 + 9.07116i −0.286602 + 0.289768i
\(981\) −45.6175 24.0709i −1.45645 0.768524i
\(982\) −11.4477 12.2282i −0.365312 0.390218i
\(983\) −36.2739 + 23.3118i −1.15696 + 0.743532i −0.971013 0.239028i \(-0.923171\pi\)
−0.185946 + 0.982560i \(0.559535\pi\)
\(984\) −2.34576 + 3.77645i −0.0747801 + 0.120389i
\(985\) −20.2724 + 31.5445i −0.645932 + 1.00509i
\(986\) −1.03045 + 2.50717i −0.0328161 + 0.0798445i
\(987\) −1.03855 0.104169i −0.0330573 0.00331574i
\(988\) −51.1525 67.5552i −1.62738 2.14922i
\(989\) 6.03546 0.816186i 0.191916 0.0259532i
\(990\) 0.358824 0.299366i 0.0114042 0.00951448i
\(991\) −52.2985 15.3562i −1.66132 0.487806i −0.689646 0.724147i \(-0.742234\pi\)
−0.971670 + 0.236340i \(0.924052\pi\)
\(992\) 28.4554 + 22.2934i 0.903461 + 0.707817i
\(993\) 6.83860 16.8487i 0.217016 0.534677i
\(994\) 1.71851 + 9.37759i 0.0545077 + 0.297439i
\(995\) −25.9191 + 16.6572i −0.821690 + 0.528068i
\(996\) 9.53307 29.8966i 0.302067 0.947310i
\(997\) −22.2705 + 19.2975i −0.705313 + 0.611157i −0.931849 0.362845i \(-0.881805\pi\)
0.226536 + 0.974003i \(0.427260\pi\)
\(998\) 48.9020 24.6468i 1.54797 0.780180i
\(999\) −4.43529 34.3273i −0.140326 1.08607i
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 552.2.bf.a.5.2 920
3.2 odd 2 inner 552.2.bf.a.5.91 yes 920
8.5 even 2 inner 552.2.bf.a.5.75 yes 920
23.14 odd 22 inner 552.2.bf.a.221.18 yes 920
24.5 odd 2 inner 552.2.bf.a.5.18 yes 920
69.14 even 22 inner 552.2.bf.a.221.75 yes 920
184.37 odd 22 inner 552.2.bf.a.221.91 yes 920
552.221 even 22 inner 552.2.bf.a.221.2 yes 920
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.bf.a.5.2 920 1.1 even 1 trivial
552.2.bf.a.5.18 yes 920 24.5 odd 2 inner
552.2.bf.a.5.75 yes 920 8.5 even 2 inner
552.2.bf.a.5.91 yes 920 3.2 odd 2 inner
552.2.bf.a.221.2 yes 920 552.221 even 22 inner
552.2.bf.a.221.18 yes 920 23.14 odd 22 inner
552.2.bf.a.221.75 yes 920 69.14 even 22 inner
552.2.bf.a.221.91 yes 920 184.37 odd 22 inner