Properties

Label 588.2.x.a.559.2
Level $588$
Weight $2$
Character 588.559
Analytic conductor $4.695$
Analytic rank $0$
Dimension $168$
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] = [588,2,Mod(55,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 0, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.55");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 588.x (of order \(14\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.69520363885\)
Analytic rank: \(0\)
Dimension: \(168\)
Relative dimension: \(28\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 559.2
Character \(\chi\) \(=\) 588.559
Dual form 588.2.x.a.223.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41331 + 0.0505560i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(1.99489 - 0.142903i) q^{4} +(2.57339 - 0.587359i) q^{5} +(0.363779 + 1.36663i) q^{6} +(-2.51025 + 0.835852i) q^{7} +(-2.81217 + 0.302819i) q^{8} +(-0.900969 + 0.433884i) q^{9} +O(q^{10})\) \(q+(-1.41331 + 0.0505560i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(1.99489 - 0.142903i) q^{4} +(2.57339 - 0.587359i) q^{5} +(0.363779 + 1.36663i) q^{6} +(-2.51025 + 0.835852i) q^{7} +(-2.81217 + 0.302819i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(-3.60730 + 0.960221i) q^{10} +(1.03750 - 2.15439i) q^{11} +(-0.583224 - 1.91307i) q^{12} +(1.89781 - 3.94084i) q^{13} +(3.50550 - 1.30823i) q^{14} +(-1.14527 - 2.37817i) q^{15} +(3.95916 - 0.570149i) q^{16} +(-0.584700 - 0.466282i) q^{17} +(1.25141 - 0.658761i) q^{18} -5.65127 q^{19} +(5.04969 - 1.53946i) q^{20} +(1.37348 + 2.26132i) q^{21} +(-1.35739 + 3.09728i) q^{22} +(6.32994 - 5.04796i) q^{23} +(0.920994 + 2.67428i) q^{24} +(1.77249 - 0.853588i) q^{25} +(-2.48296 + 5.66558i) q^{26} +(0.623490 + 0.781831i) q^{27} +(-4.88822 + 2.02615i) q^{28} +(1.27868 - 1.60341i) q^{29} +(1.73885 + 3.30319i) q^{30} +0.240610 q^{31} +(-5.56669 + 1.00596i) q^{32} +(-2.33124 - 0.532091i) q^{33} +(0.849935 + 0.629441i) q^{34} +(-5.96890 + 3.62539i) q^{35} +(-1.73533 + 0.994300i) q^{36} +(-1.99964 + 2.50747i) q^{37} +(7.98699 - 0.285705i) q^{38} +(-4.26434 - 0.973308i) q^{39} +(-7.05894 + 2.43102i) q^{40} +(11.4238 - 2.60740i) q^{41} +(-2.05547 - 3.12650i) q^{42} +(-9.66372 - 2.20568i) q^{43} +(1.76183 - 4.44603i) q^{44} +(-2.06370 + 1.64574i) q^{45} +(-8.69097 + 7.45435i) q^{46} +(2.94725 + 1.41932i) q^{47} +(-1.43685 - 3.73302i) q^{48} +(5.60270 - 4.19639i) q^{49} +(-2.46193 + 1.29599i) q^{50} +(-0.324484 + 0.673798i) q^{51} +(3.22276 - 8.13274i) q^{52} +(-7.68409 - 9.63554i) q^{53} +(-0.920710 - 1.07345i) q^{54} +(1.40449 - 6.15347i) q^{55} +(6.80614 - 3.11071i) q^{56} +(1.25753 + 5.50958i) q^{57} +(-1.72610 + 2.33076i) q^{58} +(0.367809 - 1.61148i) q^{59} +(-2.62452 - 4.58052i) q^{60} +(-1.02870 - 0.820364i) q^{61} +(-0.340056 + 0.0121643i) q^{62} +(1.89899 - 1.84223i) q^{63} +(7.81660 - 1.70316i) q^{64} +(2.56911 - 11.2560i) q^{65} +(3.32167 + 0.634151i) q^{66} -9.89182i q^{67} +(-1.23304 - 0.846626i) q^{68} +(-6.32994 - 5.04796i) q^{69} +(8.25262 - 5.42556i) q^{70} +(2.19839 - 1.75316i) q^{71} +(2.40229 - 1.49299i) q^{72} +(-4.78064 - 9.92710i) q^{73} +(2.69934 - 3.64493i) q^{74} +(-1.22660 - 1.53811i) q^{75} +(-11.2736 + 0.807580i) q^{76} +(-0.803632 + 6.27526i) q^{77} +(6.07604 + 1.16000i) q^{78} +6.28692i q^{79} +(9.85357 - 3.79266i) q^{80} +(0.623490 - 0.781831i) q^{81} +(-16.0135 + 4.26260i) q^{82} +(5.85990 - 2.82198i) q^{83} +(3.06308 + 4.31480i) q^{84} +(-1.77853 - 0.856497i) q^{85} +(13.7693 + 2.62875i) q^{86} +(-1.84774 - 0.889825i) q^{87} +(-2.26524 + 6.37269i) q^{88} +(6.43770 + 13.3680i) q^{89} +(2.83344 - 2.43028i) q^{90} +(-1.47001 + 11.4788i) q^{91} +(11.9062 - 10.9747i) q^{92} +(-0.0535407 - 0.234577i) q^{93} +(-4.23713 - 1.85694i) q^{94} +(-14.5429 + 3.31932i) q^{95} +(2.21944 + 5.20328i) q^{96} +11.5887i q^{97} +(-7.70620 + 6.21405i) q^{98} +2.39120i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31} + 25 q^{32} - 68 q^{34} - 12 q^{35} - 10 q^{37} + 35 q^{38} + 14 q^{39} + 16 q^{40} + 9 q^{42} + 20 q^{44} - 28 q^{46} - 8 q^{47} + 8 q^{48} - 8 q^{49} + 114 q^{50} + 20 q^{52} - 8 q^{53} - q^{56} + 12 q^{57} - 6 q^{58} + 20 q^{59} + 10 q^{60} - 14 q^{61} - 16 q^{62} - 12 q^{63} + 42 q^{64} - 8 q^{65} - 6 q^{66} - 16 q^{68} + 59 q^{70} + 28 q^{71} - 15 q^{72} + 22 q^{74} + 18 q^{75} + 7 q^{76} + 8 q^{77} + 6 q^{78} + 26 q^{80} - 28 q^{81} + 12 q^{82} + 10 q^{83} + 11 q^{84} - 24 q^{85} - 6 q^{86} - 242 q^{88} + 20 q^{90} - 16 q^{91} + 7 q^{92} - 4 q^{93} - 53 q^{94} - 10 q^{96} - 118 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{13}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41331 + 0.0505560i −0.999361 + 0.0357485i
\(3\) −0.222521 0.974928i −0.128473 0.562875i
\(4\) 1.99489 0.142903i 0.997444 0.0714513i
\(5\) 2.57339 0.587359i 1.15085 0.262675i 0.395800 0.918337i \(-0.370467\pi\)
0.755055 + 0.655662i \(0.227610\pi\)
\(6\) 0.363779 + 1.36663i 0.148512 + 0.557922i
\(7\) −2.51025 + 0.835852i −0.948785 + 0.315922i
\(8\) −2.81217 + 0.302819i −0.994252 + 0.107063i
\(9\) −0.900969 + 0.433884i −0.300323 + 0.144628i
\(10\) −3.60730 + 0.960221i −1.14073 + 0.303648i
\(11\) 1.03750 2.15439i 0.312818 0.649574i −0.683983 0.729498i \(-0.739754\pi\)
0.996801 + 0.0799245i \(0.0254679\pi\)
\(12\) −0.583224 1.91307i −0.168362 0.552257i
\(13\) 1.89781 3.94084i 0.526358 1.09299i −0.453122 0.891449i \(-0.649690\pi\)
0.979479 0.201544i \(-0.0645960\pi\)
\(14\) 3.50550 1.30823i 0.936885 0.349638i
\(15\) −1.14527 2.37817i −0.295706 0.614040i
\(16\) 3.95916 0.570149i 0.989789 0.142537i
\(17\) −0.584700 0.466282i −0.141810 0.113090i 0.550015 0.835155i \(-0.314622\pi\)
−0.691826 + 0.722065i \(0.743193\pi\)
\(18\) 1.25141 0.658761i 0.294961 0.155272i
\(19\) −5.65127 −1.29649 −0.648245 0.761432i \(-0.724497\pi\)
−0.648245 + 0.761432i \(0.724497\pi\)
\(20\) 5.04969 1.53946i 1.12914 0.344234i
\(21\) 1.37348 + 2.26132i 0.299718 + 0.493460i
\(22\) −1.35739 + 3.09728i −0.289397 + 0.660341i
\(23\) 6.32994 5.04796i 1.31988 1.05257i 0.325634 0.945496i \(-0.394422\pi\)
0.994251 0.107077i \(-0.0341491\pi\)
\(24\) 0.920994 + 2.67428i 0.187997 + 0.545885i
\(25\) 1.77249 0.853588i 0.354499 0.170718i
\(26\) −2.48296 + 5.66558i −0.486948 + 1.11111i
\(27\) 0.623490 + 0.781831i 0.119991 + 0.150464i
\(28\) −4.88822 + 2.02615i −0.923787 + 0.382907i
\(29\) 1.27868 1.60341i 0.237444 0.297745i −0.648805 0.760955i \(-0.724731\pi\)
0.886249 + 0.463209i \(0.153302\pi\)
\(30\) 1.73885 + 3.30319i 0.317468 + 0.603077i
\(31\) 0.240610 0.0432148 0.0216074 0.999767i \(-0.493122\pi\)
0.0216074 + 0.999767i \(0.493122\pi\)
\(32\) −5.56669 + 1.00596i −0.984061 + 0.177830i
\(33\) −2.33124 0.532091i −0.405817 0.0926252i
\(34\) 0.849935 + 0.629441i 0.145763 + 0.107948i
\(35\) −5.96890 + 3.62539i −1.00893 + 0.612803i
\(36\) −1.73533 + 0.994300i −0.289222 + 0.165717i
\(37\) −1.99964 + 2.50747i −0.328739 + 0.412226i −0.918543 0.395321i \(-0.870633\pi\)
0.589804 + 0.807546i \(0.299205\pi\)
\(38\) 7.98699 0.285705i 1.29566 0.0463475i
\(39\) −4.26434 0.973308i −0.682841 0.155854i
\(40\) −7.05894 + 2.43102i −1.11612 + 0.384379i
\(41\) 11.4238 2.60740i 1.78409 0.407208i 0.802263 0.596971i \(-0.203629\pi\)
0.981830 + 0.189763i \(0.0607721\pi\)
\(42\) −2.05547 3.12650i −0.317166 0.482430i
\(43\) −9.66372 2.20568i −1.47370 0.336363i −0.591145 0.806565i \(-0.701324\pi\)
−0.882559 + 0.470202i \(0.844181\pi\)
\(44\) 1.76183 4.44603i 0.265606 0.670265i
\(45\) −2.06370 + 1.64574i −0.307638 + 0.245333i
\(46\) −8.69097 + 7.45435i −1.28141 + 1.09908i
\(47\) 2.94725 + 1.41932i 0.429900 + 0.207029i 0.636305 0.771438i \(-0.280462\pi\)
−0.206405 + 0.978467i \(0.566176\pi\)
\(48\) −1.43685 3.73302i −0.207391 0.538815i
\(49\) 5.60270 4.19639i 0.800386 0.599485i
\(50\) −2.46193 + 1.29599i −0.348169 + 0.183281i
\(51\) −0.324484 + 0.673798i −0.0454368 + 0.0943505i
\(52\) 3.22276 8.13274i 0.446917 1.12781i
\(53\) −7.68409 9.63554i −1.05549 1.32354i −0.944061 0.329771i \(-0.893028\pi\)
−0.111430 0.993772i \(-0.535543\pi\)
\(54\) −0.920710 1.07345i −0.125293 0.146078i
\(55\) 1.40449 6.15347i 0.189381 0.829734i
\(56\) 6.80614 3.11071i 0.909508 0.415686i
\(57\) 1.25753 + 5.50958i 0.166563 + 0.729761i
\(58\) −1.72610 + 2.33076i −0.226648 + 0.306043i
\(59\) 0.367809 1.61148i 0.0478847 0.209797i −0.945326 0.326127i \(-0.894256\pi\)
0.993211 + 0.116331i \(0.0371133\pi\)
\(60\) −2.62452 4.58052i −0.338824 0.591342i
\(61\) −1.02870 0.820364i −0.131712 0.105037i 0.555418 0.831571i \(-0.312558\pi\)
−0.687130 + 0.726535i \(0.741130\pi\)
\(62\) −0.340056 + 0.0121643i −0.0431872 + 0.00154486i
\(63\) 1.89899 1.84223i 0.239251 0.232100i
\(64\) 7.81660 1.70316i 0.977075 0.212895i
\(65\) 2.56911 11.2560i 0.318659 1.39614i
\(66\) 3.32167 + 0.634151i 0.408869 + 0.0780586i
\(67\) 9.89182i 1.20848i −0.796803 0.604239i \(-0.793477\pi\)
0.796803 0.604239i \(-0.206523\pi\)
\(68\) −1.23304 0.846626i −0.149528 0.102668i
\(69\) −6.32994 5.04796i −0.762036 0.607703i
\(70\) 8.25262 5.42556i 0.986377 0.648479i
\(71\) 2.19839 1.75316i 0.260901 0.208062i −0.484299 0.874902i \(-0.660925\pi\)
0.745200 + 0.666841i \(0.232354\pi\)
\(72\) 2.40229 1.49299i 0.283113 0.175950i
\(73\) −4.78064 9.92710i −0.559532 1.16188i −0.968427 0.249298i \(-0.919800\pi\)
0.408895 0.912581i \(-0.365914\pi\)
\(74\) 2.69934 3.64493i 0.313792 0.423714i
\(75\) −1.22660 1.53811i −0.141636 0.177606i
\(76\) −11.2736 + 0.807580i −1.29318 + 0.0926358i
\(77\) −0.803632 + 6.27526i −0.0915823 + 0.715132i
\(78\) 6.07604 + 1.16000i 0.687976 + 0.131344i
\(79\) 6.28692i 0.707334i 0.935371 + 0.353667i \(0.115065\pi\)
−0.935371 + 0.353667i \(0.884935\pi\)
\(80\) 9.85357 3.79266i 1.10166 0.424033i
\(81\) 0.623490 0.781831i 0.0692766 0.0868702i
\(82\) −16.0135 + 4.26260i −1.76840 + 0.470726i
\(83\) 5.85990 2.82198i 0.643208 0.309752i −0.0836967 0.996491i \(-0.526673\pi\)
0.726904 + 0.686739i \(0.240958\pi\)
\(84\) 3.06308 + 4.31480i 0.334210 + 0.470783i
\(85\) −1.77853 0.856497i −0.192909 0.0929001i
\(86\) 13.7693 + 2.62875i 1.48479 + 0.283466i
\(87\) −1.84774 0.889825i −0.198098 0.0953992i
\(88\) −2.26524 + 6.37269i −0.241475 + 0.679331i
\(89\) 6.43770 + 13.3680i 0.682395 + 1.41701i 0.897765 + 0.440476i \(0.145190\pi\)
−0.215369 + 0.976533i \(0.569096\pi\)
\(90\) 2.83344 2.43028i 0.298671 0.256174i
\(91\) −1.47001 + 11.4788i −0.154099 + 1.20330i
\(92\) 11.9062 10.9747i 1.24130 1.14419i
\(93\) −0.0535407 0.234577i −0.00555191 0.0243245i
\(94\) −4.23713 1.85694i −0.437026 0.191528i
\(95\) −14.5429 + 3.31932i −1.49207 + 0.340555i
\(96\) 2.21944 + 5.20328i 0.226521 + 0.531057i
\(97\) 11.5887i 1.17665i 0.808623 + 0.588326i \(0.200213\pi\)
−0.808623 + 0.588326i \(0.799787\pi\)
\(98\) −7.70620 + 6.21405i −0.778444 + 0.627714i
\(99\) 2.39120i 0.240324i
\(100\) 3.41394 1.95611i 0.341394 0.195611i
\(101\) −17.2863 + 3.94548i −1.72005 + 0.392590i −0.964828 0.262881i \(-0.915327\pi\)
−0.755220 + 0.655471i \(0.772470\pi\)
\(102\) 0.424532 0.968689i 0.0420349 0.0959145i
\(103\) 0.783993 + 3.43490i 0.0772491 + 0.338451i 0.998753 0.0499178i \(-0.0158959\pi\)
−0.921504 + 0.388368i \(0.873039\pi\)
\(104\) −4.14360 + 11.6570i −0.406314 + 1.14306i
\(105\) 4.86270 + 5.01252i 0.474551 + 0.489172i
\(106\) 11.3471 + 13.2295i 1.10213 + 1.28497i
\(107\) 0.779414 + 1.61847i 0.0753488 + 0.156463i 0.935240 0.354013i \(-0.115183\pi\)
−0.859892 + 0.510477i \(0.829469\pi\)
\(108\) 1.35552 + 1.47057i 0.130435 + 0.141505i
\(109\) 11.5268 + 5.55099i 1.10406 + 0.531689i 0.894934 0.446199i \(-0.147223\pi\)
0.209129 + 0.977888i \(0.432937\pi\)
\(110\) −1.67388 + 8.76777i −0.159599 + 0.835974i
\(111\) 2.88956 + 1.39154i 0.274265 + 0.132079i
\(112\) −9.46191 + 4.74049i −0.894067 + 0.447934i
\(113\) −6.74224 + 3.24689i −0.634257 + 0.305442i −0.723246 0.690591i \(-0.757351\pi\)
0.0889891 + 0.996033i \(0.471636\pi\)
\(114\) −2.05581 7.72316i −0.192545 0.723341i
\(115\) 13.3244 16.7083i 1.24251 1.55806i
\(116\) 2.32168 3.38135i 0.215563 0.313950i
\(117\) 4.37401i 0.404377i
\(118\) −0.438359 + 2.29611i −0.0403542 + 0.211374i
\(119\) 1.85748 + 0.681763i 0.170275 + 0.0624971i
\(120\) 3.94084 + 6.34101i 0.359748 + 0.578852i
\(121\) 3.29339 + 4.12978i 0.299399 + 0.375434i
\(122\) 1.49535 + 1.10742i 0.135383 + 0.100261i
\(123\) −5.08405 10.5571i −0.458414 0.951906i
\(124\) 0.479989 0.0343837i 0.0431043 0.00308775i
\(125\) −6.25854 + 4.99102i −0.559781 + 0.446410i
\(126\) −2.59073 + 2.69965i −0.230801 + 0.240504i
\(127\) 1.33618 + 1.06557i 0.118567 + 0.0945541i 0.680978 0.732304i \(-0.261555\pi\)
−0.562411 + 0.826858i \(0.690126\pi\)
\(128\) −10.9612 + 2.80227i −0.968840 + 0.247688i
\(129\) 9.91224i 0.872724i
\(130\) −3.06189 + 16.0381i −0.268546 + 1.40664i
\(131\) 1.25085 5.48033i 0.109287 0.478819i −0.890432 0.455117i \(-0.849598\pi\)
0.999719 0.0237021i \(-0.00754532\pi\)
\(132\) −4.72661 0.728321i −0.411398 0.0633922i
\(133\) 14.1861 4.72362i 1.23009 0.409590i
\(134\) 0.500091 + 13.9802i 0.0432013 + 1.20771i
\(135\) 2.06370 + 1.64574i 0.177615 + 0.141643i
\(136\) 1.78547 + 1.13421i 0.153103 + 0.0972575i
\(137\) 3.58829 15.7213i 0.306568 1.34316i −0.553443 0.832887i \(-0.686686\pi\)
0.860011 0.510275i \(-0.170457\pi\)
\(138\) 9.20138 + 6.81432i 0.783273 + 0.580073i
\(139\) 3.44631 + 15.0993i 0.292312 + 1.28070i 0.881299 + 0.472559i \(0.156670\pi\)
−0.588987 + 0.808142i \(0.700473\pi\)
\(140\) −11.3892 + 8.08522i −0.962564 + 0.683326i
\(141\) 0.727910 3.18918i 0.0613011 0.268578i
\(142\) −3.01837 + 2.58890i −0.253296 + 0.217255i
\(143\) −6.52114 8.17725i −0.545325 0.683816i
\(144\) −3.31970 + 2.23150i −0.276642 + 0.185958i
\(145\) 2.34875 4.87723i 0.195053 0.405032i
\(146\) 7.25840 + 13.7884i 0.600709 + 1.14113i
\(147\) −5.33790 4.52845i −0.440263 0.373500i
\(148\) −3.63074 + 5.28788i −0.298445 + 0.434661i
\(149\) 4.58673 + 2.20885i 0.375760 + 0.180956i 0.612225 0.790684i \(-0.290275\pi\)
−0.236465 + 0.971640i \(0.575989\pi\)
\(150\) 1.81133 + 2.11182i 0.147895 + 0.172429i
\(151\) 10.2339 8.16124i 0.832821 0.664153i −0.111287 0.993788i \(-0.535497\pi\)
0.944108 + 0.329636i \(0.106926\pi\)
\(152\) 15.8923 1.71131i 1.28904 0.138806i
\(153\) 0.729108 + 0.166414i 0.0589449 + 0.0134538i
\(154\) 0.818529 8.90951i 0.0659589 0.717949i
\(155\) 0.619182 0.141324i 0.0497339 0.0113514i
\(156\) −8.64597 1.33225i −0.692232 0.106666i
\(157\) −3.05369 0.696985i −0.243711 0.0556254i 0.0989205 0.995095i \(-0.468461\pi\)
−0.342631 + 0.939470i \(0.611318\pi\)
\(158\) −0.317842 8.88537i −0.0252861 0.706882i
\(159\) −7.68409 + 9.63554i −0.609388 + 0.764148i
\(160\) −13.7344 + 5.85836i −1.08580 + 0.463144i
\(161\) −11.6704 + 17.9625i −0.919755 + 1.41565i
\(162\) −0.841658 + 1.13649i −0.0661269 + 0.0892912i
\(163\) 22.9100 + 5.22906i 1.79445 + 0.409572i 0.984279 0.176619i \(-0.0565161\pi\)
0.810173 + 0.586191i \(0.199373\pi\)
\(164\) 22.4165 6.83396i 1.75044 0.533642i
\(165\) −6.31172 −0.491367
\(166\) −8.13919 + 4.28458i −0.631723 + 0.332548i
\(167\) −8.69453 + 10.9026i −0.672803 + 0.843668i −0.994669 0.103117i \(-0.967118\pi\)
0.321866 + 0.946785i \(0.395690\pi\)
\(168\) −4.54723 5.94329i −0.350826 0.458535i
\(169\) −3.82319 4.79413i −0.294092 0.368779i
\(170\) 2.55692 + 1.12058i 0.196107 + 0.0859445i
\(171\) 5.09162 2.45199i 0.389366 0.187509i
\(172\) −19.5932 3.01912i −1.49397 0.230206i
\(173\) −9.60754 + 7.66176i −0.730448 + 0.582513i −0.916504 0.400026i \(-0.869001\pi\)
0.186056 + 0.982539i \(0.440430\pi\)
\(174\) 2.65641 + 1.16418i 0.201382 + 0.0882565i
\(175\) −3.73593 + 3.62426i −0.282409 + 0.273968i
\(176\) 2.87930 9.12111i 0.217036 0.687530i
\(177\) −1.65292 −0.124241
\(178\) −9.77430 18.5677i −0.732615 1.39171i
\(179\) 11.1372 + 8.88166i 0.832437 + 0.663846i 0.944013 0.329910i \(-0.107018\pi\)
−0.111576 + 0.993756i \(0.535590\pi\)
\(180\) −3.88166 + 3.57798i −0.289322 + 0.266687i
\(181\) 0.495218 + 1.02833i 0.0368093 + 0.0764353i 0.918563 0.395276i \(-0.129351\pi\)
−0.881753 + 0.471711i \(0.843637\pi\)
\(182\) 1.49726 16.2974i 0.110985 1.20804i
\(183\) −0.570887 + 1.18546i −0.0422012 + 0.0876317i
\(184\) −16.2723 + 16.1126i −1.19961 + 1.18783i
\(185\) −3.67307 + 7.62720i −0.270049 + 0.560763i
\(186\) 0.0875289 + 0.328823i 0.00641793 + 0.0241105i
\(187\) −1.61118 + 0.775904i −0.117821 + 0.0567397i
\(188\) 6.08225 + 2.41021i 0.443594 + 0.175783i
\(189\) −2.21861 1.44145i −0.161380 0.104850i
\(190\) 20.3858 5.42646i 1.47894 0.393677i
\(191\) 19.4936 4.44930i 1.41051 0.321940i 0.551618 0.834097i \(-0.314010\pi\)
0.858892 + 0.512157i \(0.171153\pi\)
\(192\) −3.39981 7.24163i −0.245360 0.522620i
\(193\) −2.19666 9.62418i −0.158119 0.692764i −0.990379 0.138379i \(-0.955811\pi\)
0.832260 0.554385i \(-0.187046\pi\)
\(194\) −0.585878 16.3784i −0.0420636 1.17590i
\(195\) −11.5455 −0.826789
\(196\) 10.5771 9.17198i 0.755506 0.655141i
\(197\) 0.917043 0.0653366 0.0326683 0.999466i \(-0.489600\pi\)
0.0326683 + 0.999466i \(0.489600\pi\)
\(198\) −0.120889 3.37950i −0.00859123 0.240171i
\(199\) −0.119882 0.525237i −0.00849821 0.0372331i 0.970501 0.241097i \(-0.0775072\pi\)
−0.978999 + 0.203864i \(0.934650\pi\)
\(200\) −4.72607 + 2.93718i −0.334183 + 0.207690i
\(201\) −9.64381 + 2.20114i −0.680222 + 0.155256i
\(202\) 24.2314 6.45011i 1.70491 0.453828i
\(203\) −1.86958 + 5.09374i −0.131219 + 0.357510i
\(204\) −0.551021 + 1.39052i −0.0385792 + 0.0973559i
\(205\) 27.8663 13.4197i 1.94627 0.937273i
\(206\) −1.28168 4.81494i −0.0892989 0.335473i
\(207\) −3.51285 + 7.29452i −0.244160 + 0.507004i
\(208\) 5.26686 16.6845i 0.365191 1.15686i
\(209\) −5.86319 + 12.1750i −0.405566 + 0.842166i
\(210\) −7.12591 6.83841i −0.491735 0.471895i
\(211\) 9.04895 + 18.7903i 0.622955 + 1.29358i 0.938700 + 0.344736i \(0.112032\pi\)
−0.315744 + 0.948844i \(0.602254\pi\)
\(212\) −16.7058 18.1238i −1.14736 1.24474i
\(213\) −2.19839 1.75316i −0.150631 0.120124i
\(214\) −1.18338 2.24799i −0.0808939 0.153670i
\(215\) −26.1640 −1.78437
\(216\) −1.99011 2.00984i −0.135410 0.136752i
\(217\) −0.603990 + 0.201114i −0.0410015 + 0.0136525i
\(218\) −16.5715 7.26252i −1.12236 0.491880i
\(219\) −8.61442 + 6.86977i −0.582108 + 0.464216i
\(220\) 1.92245 12.4762i 0.129612 0.841145i
\(221\) −2.94719 + 1.41929i −0.198250 + 0.0954720i
\(222\) −4.15420 1.82059i −0.278812 0.122190i
\(223\) 8.22903 + 10.3189i 0.551057 + 0.691003i 0.976876 0.213805i \(-0.0685856\pi\)
−0.425820 + 0.904808i \(0.640014\pi\)
\(224\) 13.1330 7.17813i 0.877482 0.479609i
\(225\) −1.22660 + 1.53811i −0.0817735 + 0.102541i
\(226\) 9.36472 4.92972i 0.622932 0.327920i
\(227\) 20.4246 1.35563 0.677814 0.735233i \(-0.262927\pi\)
0.677814 + 0.735233i \(0.262927\pi\)
\(228\) 3.29595 + 10.8113i 0.218280 + 0.715995i
\(229\) 0.219924 + 0.0501962i 0.0145330 + 0.00331706i 0.229781 0.973242i \(-0.426199\pi\)
−0.215248 + 0.976559i \(0.569056\pi\)
\(230\) −17.9869 + 24.2877i −1.18602 + 1.60148i
\(231\) 6.29675 0.612894i 0.414296 0.0403254i
\(232\) −3.11031 + 4.89626i −0.204202 + 0.321456i
\(233\) −0.802049 + 1.00574i −0.0525440 + 0.0658881i −0.807409 0.589992i \(-0.799131\pi\)
0.754865 + 0.655880i \(0.227702\pi\)
\(234\) −0.221132 6.18182i −0.0144559 0.404118i
\(235\) 8.41806 + 1.92137i 0.549134 + 0.125336i
\(236\) 0.503454 3.26728i 0.0327721 0.212682i
\(237\) 6.12929 1.39897i 0.398140 0.0908730i
\(238\) −2.65967 0.869635i −0.172401 0.0563700i
\(239\) 10.2200 + 2.33264i 0.661075 + 0.150886i 0.539879 0.841743i \(-0.318470\pi\)
0.121196 + 0.992629i \(0.461327\pi\)
\(240\) −5.89020 8.76257i −0.380211 0.565622i
\(241\) −10.4940 + 8.36870i −0.675979 + 0.539076i −0.900208 0.435461i \(-0.856585\pi\)
0.224228 + 0.974537i \(0.428014\pi\)
\(242\) −4.86336 5.67015i −0.312629 0.364491i
\(243\) −0.900969 0.433884i −0.0577972 0.0278337i
\(244\) −2.16938 1.48953i −0.138880 0.0953574i
\(245\) 11.9531 14.0898i 0.763658 0.900161i
\(246\) 7.71907 + 14.6635i 0.492150 + 0.934910i
\(247\) −10.7250 + 22.2708i −0.682417 + 1.41705i
\(248\) −0.676635 + 0.0728612i −0.0429664 + 0.00462669i
\(249\) −4.05518 5.08503i −0.256986 0.322251i
\(250\) 8.59292 7.37026i 0.543464 0.466136i
\(251\) 1.82478 7.99488i 0.115179 0.504632i −0.884122 0.467256i \(-0.845243\pi\)
0.999301 0.0373765i \(-0.0119001\pi\)
\(252\) 3.52502 3.94642i 0.222055 0.248601i
\(253\) −4.30797 18.8744i −0.270840 1.18663i
\(254\) −1.94231 1.43843i −0.121871 0.0902550i
\(255\) −0.439262 + 1.92453i −0.0275076 + 0.120519i
\(256\) 15.3499 4.51462i 0.959366 0.282164i
\(257\) 21.3595 + 17.0336i 1.33237 + 1.06253i 0.992525 + 0.122045i \(0.0389451\pi\)
0.339842 + 0.940482i \(0.389626\pi\)
\(258\) −0.501123 14.0091i −0.0311986 0.872166i
\(259\) 2.92372 7.96578i 0.181671 0.494969i
\(260\) 3.51658 22.8216i 0.218089 1.41534i
\(261\) −0.456354 + 1.99942i −0.0282476 + 0.123761i
\(262\) −1.49077 + 7.80864i −0.0921004 + 0.482420i
\(263\) 10.8080i 0.666449i 0.942848 + 0.333224i \(0.108137\pi\)
−0.942848 + 0.333224i \(0.891863\pi\)
\(264\) 6.71698 + 0.790385i 0.413402 + 0.0486449i
\(265\) −25.4337 20.2827i −1.56238 1.24595i
\(266\) −19.8105 + 7.39313i −1.21466 + 0.453302i
\(267\) 11.6003 9.25096i 0.709929 0.566150i
\(268\) −1.41357 19.7331i −0.0863473 1.20539i
\(269\) −2.63026 5.46178i −0.160369 0.333011i 0.805265 0.592915i \(-0.202023\pi\)
−0.965634 + 0.259905i \(0.916309\pi\)
\(270\) −2.99985 2.22161i −0.182565 0.135203i
\(271\) 4.14757 + 5.20089i 0.251947 + 0.315932i 0.891681 0.452665i \(-0.149527\pi\)
−0.639733 + 0.768597i \(0.720955\pi\)
\(272\) −2.58077 1.51272i −0.156482 0.0917221i
\(273\) 11.5181 1.12111i 0.697107 0.0678528i
\(274\) −4.27655 + 22.4005i −0.258356 + 1.35326i
\(275\) 4.70424i 0.283677i
\(276\) −13.3489 9.16555i −0.803509 0.551702i
\(277\) −17.5646 + 22.0253i −1.05536 + 1.32337i −0.111227 + 0.993795i \(0.535478\pi\)
−0.944128 + 0.329579i \(0.893093\pi\)
\(278\) −5.63405 21.1657i −0.337908 1.26943i
\(279\) −0.216782 + 0.104397i −0.0129784 + 0.00625006i
\(280\) 15.6877 12.0027i 0.937521 0.717299i
\(281\) −3.15435 1.51906i −0.188173 0.0906192i 0.337425 0.941352i \(-0.390444\pi\)
−0.525598 + 0.850733i \(0.676158\pi\)
\(282\) −0.867530 + 4.54410i −0.0516606 + 0.270597i
\(283\) −17.1181 8.24363i −1.01756 0.490033i −0.150701 0.988579i \(-0.548153\pi\)
−0.866863 + 0.498547i \(0.833867\pi\)
\(284\) 4.13501 3.81151i 0.245368 0.226172i
\(285\) 6.47220 + 13.4397i 0.383380 + 0.796097i
\(286\) 9.62980 + 11.2273i 0.569422 + 0.663885i
\(287\) −26.4971 + 16.0938i −1.56407 + 0.949987i
\(288\) 4.57895 3.32163i 0.269817 0.195729i
\(289\) −3.65840 16.0285i −0.215200 0.942853i
\(290\) −3.07294 + 7.01179i −0.180449 + 0.411746i
\(291\) 11.2981 2.57873i 0.662308 0.151168i
\(292\) −10.9555 19.1203i −0.641119 1.11893i
\(293\) 17.5315i 1.02420i −0.858925 0.512101i \(-0.828867\pi\)
0.858925 0.512101i \(-0.171133\pi\)
\(294\) 7.77305 + 6.13023i 0.453333 + 0.357522i
\(295\) 4.36299i 0.254023i
\(296\) 4.86402 7.65696i 0.282715 0.445052i
\(297\) 2.33124 0.532091i 0.135272 0.0308751i
\(298\) −6.59414 2.88991i −0.381988 0.167408i
\(299\) −7.88019 34.5254i −0.455723 1.99665i
\(300\) −2.66674 2.89308i −0.153964 0.167032i
\(301\) 26.1020 2.54063i 1.50449 0.146440i
\(302\) −14.0510 + 12.0517i −0.808546 + 0.693500i
\(303\) 7.69312 + 15.9749i 0.441958 + 0.917735i
\(304\) −22.3743 + 3.22207i −1.28325 + 0.184798i
\(305\) −3.12910 1.50690i −0.179172 0.0862846i
\(306\) −1.03887 0.198334i −0.0593882 0.0113380i
\(307\) 19.0864 + 9.19152i 1.08932 + 0.524588i 0.890284 0.455405i \(-0.150506\pi\)
0.199033 + 0.979993i \(0.436220\pi\)
\(308\) −0.706405 + 12.6333i −0.0402512 + 0.719848i
\(309\) 3.17432 1.52867i 0.180581 0.0869632i
\(310\) −0.867951 + 0.231038i −0.0492963 + 0.0131221i
\(311\) −13.1192 + 16.4510i −0.743922 + 0.932848i −0.999423 0.0339604i \(-0.989188\pi\)
0.255502 + 0.966809i \(0.417759\pi\)
\(312\) 12.2868 + 1.44578i 0.695602 + 0.0818513i
\(313\) 17.9475i 1.01445i 0.861812 + 0.507227i \(0.169330\pi\)
−0.861812 + 0.507227i \(0.830670\pi\)
\(314\) 4.35105 + 0.830673i 0.245544 + 0.0468776i
\(315\) 3.80480 5.85617i 0.214376 0.329958i
\(316\) 0.898417 + 12.5417i 0.0505399 + 0.705526i
\(317\) 9.83533 + 12.3331i 0.552407 + 0.692697i 0.977134 0.212625i \(-0.0682012\pi\)
−0.424727 + 0.905322i \(0.639630\pi\)
\(318\) 10.3729 14.0065i 0.581681 0.785444i
\(319\) −2.12774 4.41831i −0.119131 0.247378i
\(320\) 19.1148 8.97404i 1.06855 0.501664i
\(321\) 1.40446 1.12002i 0.0783890 0.0625132i
\(322\) 15.5858 25.9766i 0.868560 1.44762i
\(323\) 3.30429 + 2.63509i 0.183856 + 0.146620i
\(324\) 1.13207 1.64876i 0.0628926 0.0915980i
\(325\) 8.60506i 0.477323i
\(326\) −32.6433 6.23205i −1.80795 0.345161i
\(327\) 2.84687 12.4730i 0.157432 0.689757i
\(328\) −31.3360 + 10.7918i −1.73024 + 0.595877i
\(329\) −8.58467 1.09938i −0.473288 0.0606109i
\(330\) 8.92042 0.319095i 0.491053 0.0175656i
\(331\) −21.4744 17.1252i −1.18034 0.941288i −0.181227 0.983441i \(-0.558007\pi\)
−0.999111 + 0.0421528i \(0.986578\pi\)
\(332\) 11.2866 6.46693i 0.619431 0.354919i
\(333\) 0.713664 3.12676i 0.0391085 0.171346i
\(334\) 11.7369 15.8483i 0.642213 0.867181i
\(335\) −5.81005 25.4555i −0.317437 1.39078i
\(336\) 6.72711 + 8.16982i 0.366994 + 0.445700i
\(337\) 4.97482 21.7961i 0.270996 1.18731i −0.637845 0.770165i \(-0.720174\pi\)
0.908840 0.417144i \(-0.136969\pi\)
\(338\) 5.64572 + 6.58230i 0.307087 + 0.358030i
\(339\) 4.66578 + 5.85070i 0.253410 + 0.317766i
\(340\) −3.67037 1.45446i −0.199054 0.0788791i
\(341\) 0.249633 0.518368i 0.0135184 0.0280712i
\(342\) −7.07207 + 3.72284i −0.382414 + 0.201308i
\(343\) −10.5566 + 15.2170i −0.570004 + 0.821642i
\(344\) 27.8440 + 3.27639i 1.50125 + 0.176651i
\(345\) −19.2544 9.27242i −1.03662 0.499210i
\(346\) 13.1911 11.3142i 0.709157 0.608253i
\(347\) −7.49948 + 5.98063i −0.402593 + 0.321057i −0.803766 0.594945i \(-0.797174\pi\)
0.401174 + 0.916002i \(0.368602\pi\)
\(348\) −3.81319 1.51105i −0.204409 0.0810010i
\(349\) −14.1748 3.23530i −0.758758 0.173182i −0.174397 0.984675i \(-0.555798\pi\)
−0.584361 + 0.811494i \(0.698655\pi\)
\(350\) 5.09679 5.31107i 0.272435 0.283889i
\(351\) 4.26434 0.973308i 0.227614 0.0519513i
\(352\) −3.60822 + 13.0365i −0.192319 + 0.694849i
\(353\) 26.2175 + 5.98397i 1.39542 + 0.318494i 0.853129 0.521700i \(-0.174702\pi\)
0.542286 + 0.840194i \(0.317559\pi\)
\(354\) 2.33609 0.0835650i 0.124162 0.00444143i
\(355\) 4.62758 5.80280i 0.245607 0.307981i
\(356\) 14.7528 + 25.7478i 0.781898 + 1.36463i
\(357\) 0.251340 1.96262i 0.0133023 0.103873i
\(358\) −16.1894 11.9895i −0.855636 0.633664i
\(359\) −6.70228 1.52975i −0.353733 0.0807372i 0.0419622 0.999119i \(-0.486639\pi\)
−0.395695 + 0.918382i \(0.629496\pi\)
\(360\) 5.30510 5.25304i 0.279604 0.276859i
\(361\) 12.9368 0.680885
\(362\) −0.751885 1.42831i −0.0395182 0.0750705i
\(363\) 3.29339 4.12978i 0.172858 0.216757i
\(364\) −1.29216 + 23.1090i −0.0677278 + 1.21124i
\(365\) −18.1332 22.7383i −0.949136 1.19018i
\(366\) 0.746909 1.70428i 0.0390415 0.0890843i
\(367\) −20.4900 + 9.86746i −1.06957 + 0.515077i −0.883968 0.467548i \(-0.845138\pi\)
−0.185602 + 0.982625i \(0.559423\pi\)
\(368\) 22.1832 23.5947i 1.15638 1.22996i
\(369\) −9.16115 + 7.30577i −0.476910 + 0.380323i
\(370\) 4.80558 10.9653i 0.249830 0.570058i
\(371\) 27.3429 + 17.7648i 1.41957 + 0.922305i
\(372\) −0.140329 0.460304i −0.00727574 0.0238657i
\(373\) 18.8643 0.976754 0.488377 0.872633i \(-0.337589\pi\)
0.488377 + 0.872633i \(0.337589\pi\)
\(374\) 2.23787 1.17805i 0.115718 0.0609154i
\(375\) 6.25854 + 4.99102i 0.323189 + 0.257735i
\(376\) −8.71796 3.09888i −0.449594 0.159813i
\(377\) −3.89210 8.08202i −0.200453 0.416245i
\(378\) 3.20846 + 1.92505i 0.165025 + 0.0990137i
\(379\) 12.1250 25.1779i 0.622822 1.29330i −0.315954 0.948774i \(-0.602325\pi\)
0.938776 0.344528i \(-0.111961\pi\)
\(380\) −28.5371 + 8.69990i −1.46392 + 0.446295i
\(381\) 0.741525 1.53979i 0.0379895 0.0788860i
\(382\) −27.3256 + 7.27375i −1.39810 + 0.372158i
\(383\) −2.49312 + 1.20062i −0.127392 + 0.0613490i −0.496494 0.868040i \(-0.665380\pi\)
0.369102 + 0.929389i \(0.379665\pi\)
\(384\) 5.17110 + 10.0628i 0.263886 + 0.513515i
\(385\) 1.61777 + 16.6207i 0.0824494 + 0.847069i
\(386\) 3.59112 + 13.4909i 0.182783 + 0.686669i
\(387\) 9.66372 2.20568i 0.491235 0.112121i
\(388\) 1.65605 + 23.1181i 0.0840734 + 1.17365i
\(389\) −5.62109 24.6276i −0.285001 1.24867i −0.891293 0.453428i \(-0.850201\pi\)
0.606292 0.795242i \(-0.292656\pi\)
\(390\) 16.3173 0.583693i 0.826261 0.0295565i
\(391\) −6.05489 −0.306209
\(392\) −14.4850 + 13.4976i −0.731603 + 0.681731i
\(393\) −5.62127 −0.283555
\(394\) −1.29607 + 0.0463621i −0.0652949 + 0.00233569i
\(395\) 3.69268 + 16.1787i 0.185799 + 0.814038i
\(396\) 0.341708 + 4.77017i 0.0171715 + 0.239710i
\(397\) −19.6796 + 4.49173i −0.987689 + 0.225434i −0.685705 0.727879i \(-0.740506\pi\)
−0.301984 + 0.953313i \(0.597649\pi\)
\(398\) 0.195984 + 0.736262i 0.00982380 + 0.0369055i
\(399\) −7.76189 12.7793i −0.388581 0.639766i
\(400\) 6.53091 4.39007i 0.326545 0.219504i
\(401\) 14.8375 7.14538i 0.740951 0.356823i −0.0250300 0.999687i \(-0.507968\pi\)
0.765981 + 0.642864i \(0.222254\pi\)
\(402\) 13.5184 3.59844i 0.674237 0.179474i
\(403\) 0.456631 0.948205i 0.0227464 0.0472335i
\(404\) −33.9204 + 10.3410i −1.68760 + 0.514486i
\(405\) 1.14527 2.37817i 0.0569087 0.118172i
\(406\) 2.38478 7.29355i 0.118355 0.361973i
\(407\) 3.32745 + 6.90951i 0.164935 + 0.342492i
\(408\) 0.708465 1.99309i 0.0350742 0.0986728i
\(409\) 10.5952 + 8.44939i 0.523899 + 0.417795i 0.849403 0.527745i \(-0.176962\pi\)
−0.325504 + 0.945541i \(0.605534\pi\)
\(410\) −38.7053 + 20.3750i −1.91152 + 1.00625i
\(411\) −16.1256 −0.795418
\(412\) 2.05483 + 6.74020i 0.101234 + 0.332066i
\(413\) 0.423664 + 4.35265i 0.0208472 + 0.214180i
\(414\) 4.59597 10.4870i 0.225880 0.515408i
\(415\) 13.4223 10.7039i 0.658874 0.525434i
\(416\) −6.60020 + 23.8466i −0.323602 + 1.16917i
\(417\) 13.9538 6.71980i 0.683321 0.329070i
\(418\) 7.67099 17.5035i 0.375200 0.856126i
\(419\) −20.1801 25.3051i −0.985863 1.23623i −0.971672 0.236334i \(-0.924054\pi\)
−0.0141917 0.999899i \(-0.504518\pi\)
\(420\) 10.4168 + 9.30453i 0.508290 + 0.454015i
\(421\) −23.6613 + 29.6704i −1.15318 + 1.44604i −0.279103 + 0.960261i \(0.590037\pi\)
−0.874079 + 0.485783i \(0.838534\pi\)
\(422\) −13.7389 26.0991i −0.668801 1.27048i
\(423\) −3.27120 −0.159051
\(424\) 24.5268 + 24.7699i 1.19113 + 1.20293i
\(425\) −1.43439 0.327390i −0.0695781 0.0158807i
\(426\) 3.19564 + 2.36661i 0.154829 + 0.114663i
\(427\) 3.26801 + 1.19947i 0.158150 + 0.0580466i
\(428\) 1.78613 + 3.11729i 0.0863357 + 0.150680i
\(429\) −6.52114 + 8.17725i −0.314844 + 0.394802i
\(430\) 36.9779 1.32275i 1.78323 0.0637886i
\(431\) 3.22583 + 0.736274i 0.155383 + 0.0354651i 0.299505 0.954095i \(-0.403179\pi\)
−0.144122 + 0.989560i \(0.546036\pi\)
\(432\) 2.91426 + 2.73991i 0.140212 + 0.131824i
\(433\) −9.73502 + 2.22196i −0.467835 + 0.106780i −0.449939 0.893059i \(-0.648554\pi\)
−0.0178968 + 0.999840i \(0.505697\pi\)
\(434\) 0.843458 0.314772i 0.0404873 0.0151095i
\(435\) −5.27760 1.20458i −0.253041 0.0577551i
\(436\) 23.7878 + 9.42640i 1.13923 + 0.451443i
\(437\) −35.7722 + 28.5274i −1.71122 + 1.36465i
\(438\) 11.8275 10.1446i 0.565141 0.484729i
\(439\) 1.78933 + 0.861694i 0.0853999 + 0.0411264i 0.476096 0.879393i \(-0.342051\pi\)
−0.390696 + 0.920520i \(0.627766\pi\)
\(440\) −2.08628 + 17.7299i −0.0994593 + 0.845241i
\(441\) −3.22711 + 6.21174i −0.153672 + 0.295797i
\(442\) 4.09354 2.15490i 0.194710 0.102498i
\(443\) −0.971121 + 2.01655i −0.0461394 + 0.0958094i −0.922764 0.385365i \(-0.874075\pi\)
0.876625 + 0.481175i \(0.159790\pi\)
\(444\) 5.96321 + 2.36304i 0.283002 + 0.112145i
\(445\) 24.4185 + 30.6199i 1.15755 + 1.45152i
\(446\) −12.1519 14.1677i −0.575407 0.670862i
\(447\) 1.13283 4.96325i 0.0535810 0.234754i
\(448\) −18.1980 + 10.8089i −0.859776 + 0.510671i
\(449\) 5.83434 + 25.5619i 0.275340 + 1.20634i 0.903613 + 0.428349i \(0.140905\pi\)
−0.628274 + 0.777992i \(0.716238\pi\)
\(450\) 1.65581 2.23584i 0.0780556 0.105399i
\(451\) 6.23480 27.3165i 0.293585 1.28628i
\(452\) −12.9860 + 7.44067i −0.610811 + 0.349980i
\(453\) −10.2339 8.16124i −0.480829 0.383449i
\(454\) −28.8663 + 1.03259i −1.35476 + 0.0484617i
\(455\) 2.95925 + 30.4028i 0.138732 + 1.42531i
\(456\) −5.20478 15.1131i −0.243736 0.707734i
\(457\) 7.06795 30.9667i 0.330625 1.44856i −0.487299 0.873235i \(-0.662018\pi\)
0.817924 0.575326i \(-0.195125\pi\)
\(458\) −0.313359 0.0598243i −0.0146423 0.00279541i
\(459\) 0.747859i 0.0349071i
\(460\) 24.1931 35.2353i 1.12801 1.64286i
\(461\) −3.31009 2.63971i −0.154166 0.122944i 0.543369 0.839494i \(-0.317149\pi\)
−0.697535 + 0.716550i \(0.745720\pi\)
\(462\) −8.86827 + 1.18455i −0.412589 + 0.0551101i
\(463\) −14.6687 + 11.6979i −0.681712 + 0.543647i −0.901972 0.431794i \(-0.857881\pi\)
0.220261 + 0.975441i \(0.429309\pi\)
\(464\) 4.14830 7.07718i 0.192580 0.328550i
\(465\) −0.275562 0.572210i −0.0127789 0.0265356i
\(466\) 1.08270 1.46197i 0.0501550 0.0677243i
\(467\) 3.58845 + 4.49977i 0.166054 + 0.208225i 0.857895 0.513825i \(-0.171772\pi\)
−0.691842 + 0.722049i \(0.743200\pi\)
\(468\) 0.625057 + 8.72565i 0.0288933 + 0.403343i
\(469\) 8.26810 + 24.8309i 0.381785 + 1.14659i
\(470\) −11.9945 2.28990i −0.553263 0.105625i
\(471\) 3.13222i 0.144325i
\(472\) −0.546356 + 4.64313i −0.0251481 + 0.213717i
\(473\) −14.7780 + 18.5311i −0.679494 + 0.852059i
\(474\) −8.59186 + 2.28705i −0.394637 + 0.105048i
\(475\) −10.0168 + 4.82385i −0.459604 + 0.221333i
\(476\) 3.80290 + 1.09460i 0.174306 + 0.0501709i
\(477\) 11.1038 + 5.34732i 0.508409 + 0.244837i
\(478\) −14.5619 2.78006i −0.666046 0.127157i
\(479\) −16.9367 8.15627i −0.773856 0.372669i 0.00490686 0.999988i \(-0.498438\pi\)
−0.778763 + 0.627319i \(0.784152\pi\)
\(480\) 8.76767 + 12.0864i 0.400188 + 0.551668i
\(481\) 6.08661 + 12.6390i 0.277525 + 0.576287i
\(482\) 14.4082 12.3581i 0.656276 0.562896i
\(483\) 20.1091 + 7.38074i 0.914995 + 0.335836i
\(484\) 7.16010 + 7.76781i 0.325459 + 0.353082i
\(485\) 6.80672 + 29.8222i 0.309077 + 1.35416i
\(486\) 1.29528 + 0.567663i 0.0587552 + 0.0257497i
\(487\) 17.0498 3.89151i 0.772601 0.176341i 0.181993 0.983300i \(-0.441745\pi\)
0.590608 + 0.806959i \(0.298888\pi\)
\(488\) 3.14131 + 1.99549i 0.142200 + 0.0903316i
\(489\) 23.4992i 1.06267i
\(490\) −16.1812 + 20.5175i −0.730990 + 0.926885i
\(491\) 35.5537i 1.60451i −0.596979 0.802257i \(-0.703632\pi\)
0.596979 0.802257i \(-0.296368\pi\)
\(492\) −11.6508 20.3338i −0.525257 0.916719i
\(493\) −1.49528 + 0.341288i −0.0673441 + 0.0153709i
\(494\) 14.0319 32.0177i 0.631323 1.44054i
\(495\) 1.40449 + 6.15347i 0.0631271 + 0.276578i
\(496\) 0.952612 0.137183i 0.0427735 0.00615972i
\(497\) −4.05313 + 6.23840i −0.181808 + 0.279830i
\(498\) 5.98830 + 6.98171i 0.268342 + 0.312858i
\(499\) −10.2078 21.1968i −0.456965 0.948898i −0.994409 0.105599i \(-0.966324\pi\)
0.537443 0.843300i \(-0.319390\pi\)
\(500\) −11.7719 + 10.8509i −0.526453 + 0.485266i
\(501\) 12.5640 + 6.05048i 0.561316 + 0.270316i
\(502\) −2.17479 + 11.3915i −0.0970655 + 0.508427i
\(503\) 4.75069 + 2.28781i 0.211823 + 0.102008i 0.536787 0.843718i \(-0.319638\pi\)
−0.324964 + 0.945726i \(0.605352\pi\)
\(504\) −4.78243 + 5.75572i −0.213026 + 0.256380i
\(505\) −42.1669 + 20.3065i −1.87640 + 0.903627i
\(506\) 7.04271 + 26.4576i 0.313087 + 1.17619i
\(507\) −3.82319 + 4.79413i −0.169794 + 0.212915i
\(508\) 2.81781 + 1.93475i 0.125020 + 0.0858406i
\(509\) 4.10916i 0.182135i −0.995845 0.0910676i \(-0.970972\pi\)
0.995845 0.0910676i \(-0.0290279\pi\)
\(510\) 0.523516 2.74217i 0.0231817 0.121425i
\(511\) 20.2982 + 20.9236i 0.897939 + 0.925605i
\(512\) −21.4659 + 7.15659i −0.948666 + 0.316279i
\(513\) −3.52351 4.41834i −0.155567 0.195074i
\(514\) −31.0487 22.9939i −1.36950 1.01422i
\(515\) 4.03504 + 8.37884i 0.177805 + 0.369216i
\(516\) 1.41648 + 19.7738i 0.0623573 + 0.870494i
\(517\) 6.11554 4.87698i 0.268961 0.214489i
\(518\) −3.72941 + 11.4059i −0.163861 + 0.501148i
\(519\) 9.60754 + 7.66176i 0.421724 + 0.336314i
\(520\) −3.81624 + 32.4318i −0.167353 + 1.42223i
\(521\) 3.57020i 0.156413i −0.996937 0.0782067i \(-0.975081\pi\)
0.996937 0.0782067i \(-0.0249194\pi\)
\(522\) 0.543887 2.84887i 0.0238053 0.124692i
\(523\) 0.550000 2.40971i 0.0240498 0.105369i −0.961478 0.274880i \(-0.911362\pi\)
0.985528 + 0.169511i \(0.0542189\pi\)
\(524\) 1.71215 11.1114i 0.0747957 0.485404i
\(525\) 4.36471 + 2.83578i 0.190492 + 0.123764i
\(526\) −0.546408 15.2750i −0.0238245 0.666023i
\(527\) −0.140684 0.112192i −0.00612831 0.00488716i
\(528\) −9.53313 0.777476i −0.414876 0.0338353i
\(529\) 9.46829 41.4833i 0.411665 1.80362i
\(530\) 36.9711 + 27.3799i 1.60592 + 1.18931i
\(531\) 0.367809 + 1.61148i 0.0159616 + 0.0699322i
\(532\) 27.6246 11.4503i 1.19768 0.496435i
\(533\) 11.4048 49.9676i 0.493996 2.16434i
\(534\) −15.9272 + 13.6609i −0.689237 + 0.591167i
\(535\) 2.95636 + 3.70715i 0.127814 + 0.160274i
\(536\) 2.99543 + 27.8175i 0.129383 + 1.20153i
\(537\) 6.18071 12.8344i 0.266717 0.553844i
\(538\) 3.99349 + 7.58621i 0.172172 + 0.327065i
\(539\) −3.22787 16.4242i −0.139034 0.707440i
\(540\) 4.35203 + 2.98817i 0.187281 + 0.128590i
\(541\) 2.51848 + 1.21284i 0.108278 + 0.0521439i 0.487239 0.873269i \(-0.338004\pi\)
−0.378961 + 0.925413i \(0.623718\pi\)
\(542\) −6.12474 7.14079i −0.263080 0.306723i
\(543\) 0.892353 0.711627i 0.0382945 0.0305389i
\(544\) 3.72390 + 2.00747i 0.159661 + 0.0860695i
\(545\) 32.9232 + 7.51451i 1.41028 + 0.321886i
\(546\) −16.2220 + 2.16679i −0.694236 + 0.0927300i
\(547\) 13.4255 3.06428i 0.574032 0.131019i 0.0743567 0.997232i \(-0.476310\pi\)
0.499676 + 0.866213i \(0.333453\pi\)
\(548\) 4.91162 31.8750i 0.209814 1.36163i
\(549\) 1.28277 + 0.292784i 0.0547474 + 0.0124957i
\(550\) 0.237828 + 6.64855i 0.0101410 + 0.283495i
\(551\) −7.22614 + 9.06129i −0.307844 + 0.386024i
\(552\) 19.3295 + 12.2789i 0.822718 + 0.522625i
\(553\) −5.25494 15.7817i −0.223463 0.671108i
\(554\) 23.7107 32.0166i 1.00737 1.36026i
\(555\) 8.25331 + 1.88376i 0.350333 + 0.0799613i
\(556\) 9.03272 + 29.6288i 0.383072 + 1.25654i
\(557\) −12.1343 −0.514147 −0.257074 0.966392i \(-0.582758\pi\)
−0.257074 + 0.966392i \(0.582758\pi\)
\(558\) 0.301102 0.158504i 0.0127467 0.00671003i
\(559\) −27.0321 + 33.8972i −1.14334 + 1.43370i
\(560\) −21.5648 + 17.7567i −0.911279 + 0.750356i
\(561\) 1.11497 + 1.39813i 0.0470742 + 0.0590291i
\(562\) 4.53487 + 1.98742i 0.191292 + 0.0838344i
\(563\) −28.9502 + 13.9417i −1.22010 + 0.587571i −0.929340 0.369224i \(-0.879624\pi\)
−0.290763 + 0.956795i \(0.593909\pi\)
\(564\) 0.996357 6.46608i 0.0419542 0.272271i
\(565\) −15.4433 + 12.3156i −0.649705 + 0.518122i
\(566\) 24.6099 + 10.7854i 1.03443 + 0.453343i
\(567\) −0.911619 + 2.48374i −0.0382844 + 0.104307i
\(568\) −5.65136 + 5.59590i −0.237126 + 0.234799i
\(569\) 45.2933 1.89880 0.949398 0.314077i \(-0.101695\pi\)
0.949398 + 0.314077i \(0.101695\pi\)
\(570\) −9.82668 18.6672i −0.411594 0.781883i
\(571\) 11.3592 + 9.05862i 0.475366 + 0.379092i 0.831663 0.555281i \(-0.187389\pi\)
−0.356297 + 0.934373i \(0.615961\pi\)
\(572\) −14.1775 15.3808i −0.592791 0.643104i
\(573\) −8.67549 18.0148i −0.362424 0.752580i
\(574\) 36.6350 24.0851i 1.52911 1.00529i
\(575\) 6.91090 14.3506i 0.288205 0.598463i
\(576\) −6.30354 + 4.92599i −0.262648 + 0.205250i
\(577\) 9.47811 19.6815i 0.394579 0.819351i −0.605151 0.796111i \(-0.706887\pi\)
0.999730 0.0232407i \(-0.00739842\pi\)
\(578\) 5.98079 + 22.4683i 0.248768 + 0.934557i
\(579\) −8.89408 + 4.28317i −0.369626 + 0.178002i
\(580\) 3.98853 10.0652i 0.165615 0.417934i
\(581\) −12.3511 + 11.9819i −0.512408 + 0.497092i
\(582\) −15.8374 + 4.21573i −0.656481 + 0.174747i
\(583\) −28.7310 + 6.55766i −1.18992 + 0.271591i
\(584\) 16.4501 + 26.4690i 0.680710 + 1.09530i
\(585\) 2.56911 + 11.2560i 0.106220 + 0.465379i
\(586\) 0.886324 + 24.7775i 0.0366137 + 1.02355i
\(587\) 35.3839 1.46045 0.730225 0.683207i \(-0.239415\pi\)
0.730225 + 0.683207i \(0.239415\pi\)
\(588\) −11.2956 8.27094i −0.465824 0.341088i
\(589\) −1.35975 −0.0560275
\(590\) 0.220576 + 6.16626i 0.00908095 + 0.253861i
\(591\) −0.204061 0.894051i −0.00839396 0.0367764i
\(592\) −6.48726 + 11.0676i −0.266625 + 0.454874i
\(593\) 3.91211 0.892914i 0.160651 0.0366676i −0.141439 0.989947i \(-0.545173\pi\)
0.302090 + 0.953279i \(0.402316\pi\)
\(594\) −3.26787 + 0.869868i −0.134082 + 0.0356911i
\(595\) 5.18047 + 0.663429i 0.212379 + 0.0271979i
\(596\) 9.46567 + 3.75096i 0.387729 + 0.153645i
\(597\) −0.485392 + 0.233753i −0.0198658 + 0.00956685i
\(598\) 12.8826 + 48.3967i 0.526809 + 1.97909i
\(599\) −0.793069 + 1.64683i −0.0324039 + 0.0672875i −0.916542 0.399937i \(-0.869032\pi\)
0.884139 + 0.467225i \(0.154746\pi\)
\(600\) 3.91519 + 3.95399i 0.159837 + 0.161421i
\(601\) −19.2202 + 39.9111i −0.784007 + 1.62801i −0.00581301 + 0.999983i \(0.501850\pi\)
−0.778194 + 0.628024i \(0.783864\pi\)
\(602\) −36.7617 + 4.91031i −1.49830 + 0.200129i
\(603\) 4.29190 + 8.91222i 0.174780 + 0.362934i
\(604\) 19.2492 17.7432i 0.783238 0.721961i
\(605\) 10.9008 + 8.69312i 0.443182 + 0.353426i
\(606\) −11.6804 22.1886i −0.474483 0.901349i
\(607\) 5.42979 0.220388 0.110194 0.993910i \(-0.464853\pi\)
0.110194 + 0.993910i \(0.464853\pi\)
\(608\) 31.4589 5.68493i 1.27583 0.230554i
\(609\) 5.38205 + 0.689244i 0.218092 + 0.0279296i
\(610\) 4.49857 + 1.97152i 0.182142 + 0.0798243i
\(611\) 11.1866 8.92104i 0.452562 0.360907i
\(612\) 1.47827 + 0.227786i 0.0597556 + 0.00920772i
\(613\) 42.0070 20.2295i 1.69665 0.817061i 0.702180 0.712000i \(-0.252210\pi\)
0.994466 0.105062i \(-0.0335040\pi\)
\(614\) −27.4396 12.0255i −1.10737 0.485311i
\(615\) −19.2841 24.1815i −0.777609 0.975091i
\(616\) 0.359681 17.8905i 0.0144919 0.720827i
\(617\) −3.14118 + 3.93891i −0.126459 + 0.158575i −0.841030 0.540988i \(-0.818050\pi\)
0.714571 + 0.699563i \(0.246622\pi\)
\(618\) −4.40902 + 2.32097i −0.177357 + 0.0933631i
\(619\) −13.9091 −0.559053 −0.279526 0.960138i \(-0.590177\pi\)
−0.279526 + 0.960138i \(0.590177\pi\)
\(620\) 1.21500 0.370409i 0.0487957 0.0148760i
\(621\) 7.89331 + 1.80160i 0.316748 + 0.0722956i
\(622\) 17.7098 23.9136i 0.710098 0.958846i
\(623\) −27.3339 28.1761i −1.09511 1.12885i
\(624\) −17.4381 1.42217i −0.698084 0.0569323i
\(625\) −19.3071 + 24.2104i −0.772286 + 0.968416i
\(626\) −0.907356 25.3654i −0.0362652 1.01381i
\(627\) 13.1745 + 3.00699i 0.526138 + 0.120088i
\(628\) −6.19137 0.954026i −0.247063 0.0380698i
\(629\) 2.33838 0.533720i 0.0932373 0.0212808i
\(630\) −5.08129 + 8.46894i −0.202443 + 0.337411i
\(631\) −37.5419 8.56869i −1.49452 0.341114i −0.604340 0.796727i \(-0.706563\pi\)
−0.890178 + 0.455613i \(0.849420\pi\)
\(632\) −1.90380 17.6799i −0.0757291 0.703268i
\(633\) 16.3056 13.0033i 0.648091 0.516835i
\(634\) −14.5239 16.9333i −0.576817 0.672506i
\(635\) 4.06439 + 1.95731i 0.161290 + 0.0776733i
\(636\) −13.9520 + 20.3199i −0.553231 + 0.805737i
\(637\) −5.90447 30.0433i −0.233943 1.19036i
\(638\) 3.23053 + 6.13686i 0.127898 + 0.242961i
\(639\) −1.22002 + 2.53339i −0.0482631 + 0.100219i
\(640\) −26.5614 + 13.6495i −1.04993 + 0.539542i
\(641\) −3.99746 5.01266i −0.157890 0.197988i 0.696594 0.717466i \(-0.254698\pi\)
−0.854484 + 0.519478i \(0.826127\pi\)
\(642\) −1.92831 + 1.65393i −0.0761042 + 0.0652755i
\(643\) 10.5471 46.2097i 0.415936 1.82233i −0.138818 0.990318i \(-0.544330\pi\)
0.554754 0.832015i \(-0.312813\pi\)
\(644\) −20.7142 + 37.5010i −0.816255 + 1.47775i
\(645\) 5.82205 + 25.5080i 0.229243 + 1.00438i
\(646\) −4.80321 3.55714i −0.188980 0.139954i
\(647\) 5.09918 22.3410i 0.200470 0.878315i −0.770182 0.637824i \(-0.779835\pi\)
0.970652 0.240490i \(-0.0773083\pi\)
\(648\) −1.51661 + 2.38745i −0.0595779 + 0.0937878i
\(649\) −3.09015 2.46432i −0.121299 0.0967328i
\(650\) 0.435038 + 12.1616i 0.0170636 + 0.477018i
\(651\) 0.330472 + 0.544095i 0.0129522 + 0.0213248i
\(652\) 46.4502 + 7.15750i 1.81913 + 0.280309i
\(653\) 2.71804 11.9085i 0.106365 0.466015i −0.893492 0.449080i \(-0.851752\pi\)
0.999857 0.0169355i \(-0.00539098\pi\)
\(654\) −3.39293 + 17.7721i −0.132674 + 0.694944i
\(655\) 14.8377i 0.579758i
\(656\) 43.7419 16.8364i 1.70783 0.657350i
\(657\) 8.61442 + 6.86977i 0.336080 + 0.268015i
\(658\) 12.1884 + 1.11976i 0.475152 + 0.0436528i
\(659\) −8.46957 + 6.75426i −0.329928 + 0.263108i −0.774417 0.632676i \(-0.781957\pi\)
0.444489 + 0.895784i \(0.353385\pi\)
\(660\) −12.5912 + 0.901961i −0.490111 + 0.0351088i
\(661\) 13.9357 + 28.9378i 0.542036 + 1.12555i 0.974601 + 0.223946i \(0.0718941\pi\)
−0.432566 + 0.901602i \(0.642392\pi\)
\(662\) 31.2157 + 23.1176i 1.21323 + 0.898491i
\(663\) 2.03952 + 2.55748i 0.0792084 + 0.0993243i
\(664\) −15.6245 + 9.71038i −0.606348 + 0.376836i
\(665\) 33.7318 20.4880i 1.30806 0.794492i
\(666\) −0.850551 + 4.45517i −0.0329582 + 0.172634i
\(667\) 16.6042i 0.642917i
\(668\) −15.7866 + 22.9919i −0.610802 + 0.889584i
\(669\) 8.22903 10.3189i 0.318153 0.398951i
\(670\) 9.49833 + 35.6828i 0.366952 + 1.37855i
\(671\) −2.83467 + 1.36510i −0.109431 + 0.0526992i
\(672\) −9.92052 11.2064i −0.382692 0.432296i
\(673\) −21.4151 10.3130i −0.825493 0.397536i −0.0270699 0.999634i \(-0.508618\pi\)
−0.798423 + 0.602097i \(0.794332\pi\)
\(674\) −5.92904 + 31.0562i −0.228378 + 1.19624i
\(675\) 1.77249 + 0.853588i 0.0682233 + 0.0328546i
\(676\) −8.31193 9.01741i −0.319690 0.346823i
\(677\) −15.7669 32.7403i −0.605970 1.25831i −0.947895 0.318583i \(-0.896793\pi\)
0.341924 0.939727i \(-0.388921\pi\)
\(678\) −6.88997 8.03296i −0.264608 0.308504i
\(679\) −9.68643 29.0905i −0.371731 1.11639i
\(680\) 5.26090 + 1.87004i 0.201746 + 0.0717128i
\(681\) −4.54490 19.9125i −0.174161 0.763049i
\(682\) −0.326602 + 0.745235i −0.0125062 + 0.0285365i
\(683\) 4.47652 1.02174i 0.171289 0.0390956i −0.136016 0.990707i \(-0.543430\pi\)
0.307305 + 0.951611i \(0.400573\pi\)
\(684\) 9.80681 5.61906i 0.374973 0.214850i
\(685\) 42.5647i 1.62631i
\(686\) 14.1505 22.0401i 0.540267 0.841494i
\(687\) 0.225580i 0.00860641i
\(688\) −39.5178 3.22288i −1.50660 0.122871i
\(689\) −52.5551 + 11.9954i −2.00219 + 0.456987i
\(690\) 27.6812 + 12.1314i 1.05380 + 0.461833i
\(691\) 9.72102 + 42.5906i 0.369805 + 1.62022i 0.727309 + 0.686310i \(0.240771\pi\)
−0.357504 + 0.933912i \(0.616372\pi\)
\(692\) −18.0711 + 16.6573i −0.686960 + 0.633215i
\(693\) −1.99869 6.00250i −0.0759238 0.228016i
\(694\) 10.2967 8.83163i 0.390858 0.335244i
\(695\) 17.7374 + 36.8320i 0.672817 + 1.39712i
\(696\) 5.46561 + 1.94281i 0.207174 + 0.0736419i
\(697\) −7.89526 3.80216i −0.299054 0.144017i
\(698\) 20.1969 + 3.85586i 0.764464 + 0.145946i
\(699\) 1.15899 + 0.558142i 0.0438372 + 0.0211109i
\(700\) −6.93484 + 7.76387i −0.262112 + 0.293447i
\(701\) 12.1120 5.83283i 0.457464 0.220303i −0.190937 0.981602i \(-0.561153\pi\)
0.648401 + 0.761299i \(0.275438\pi\)
\(702\) −5.97763 + 1.59117i −0.225611 + 0.0600550i
\(703\) 11.3005 14.1704i 0.426207 0.534446i
\(704\) 4.44046 18.6071i 0.167356 0.701280i
\(705\) 8.63455i 0.325196i
\(706\) −37.3559 7.13175i −1.40591 0.268407i
\(707\) 40.0950 24.3529i 1.50793 0.915885i
\(708\) −3.29739 + 0.236207i −0.123924 + 0.00887718i
\(709\) 2.42715 + 3.04355i 0.0911534 + 0.114303i 0.825317 0.564670i \(-0.190997\pi\)
−0.734163 + 0.678973i \(0.762425\pi\)
\(710\) −6.24684 + 8.43511i −0.234440 + 0.316564i
\(711\) −2.72779 5.66432i −0.102300 0.212429i
\(712\) −22.1520 35.6437i −0.830182 1.33580i
\(713\) 1.52305 1.21459i 0.0570385 0.0454867i
\(714\) −0.255999 + 2.78650i −0.00958052 + 0.104282i
\(715\) −21.5844 17.2130i −0.807211 0.643730i
\(716\) 23.4868 + 16.1264i 0.877742 + 0.602671i
\(717\) 10.4828i 0.391487i
\(718\) 9.54973 + 1.82317i 0.356393 + 0.0680402i
\(719\) 3.97257 17.4050i 0.148152 0.649096i −0.845246 0.534377i \(-0.820546\pi\)
0.993398 0.114719i \(-0.0365966\pi\)
\(720\) −7.23218 + 7.69237i −0.269528 + 0.286678i
\(721\) −4.83909 7.96715i −0.180217 0.296712i
\(722\) −18.2837 + 0.654033i −0.680450 + 0.0243406i
\(723\) 10.4940 + 8.36870i 0.390277 + 0.311235i
\(724\) 1.13486 + 1.98064i 0.0421766 + 0.0736098i
\(725\) 0.897794 3.93349i 0.0333432 0.146086i
\(726\) −4.44579 + 6.00316i −0.164999 + 0.222798i
\(727\) 3.13918 + 13.7536i 0.116426 + 0.510094i 0.999189 + 0.0402754i \(0.0128235\pi\)
−0.882763 + 0.469819i \(0.844319\pi\)
\(728\) 0.657932 32.7254i 0.0243846 1.21289i
\(729\) −0.222521 + 0.974928i −0.00824152 + 0.0361084i
\(730\) 26.7774 + 31.2196i 0.991076 + 1.15549i
\(731\) 4.62190 + 5.79568i 0.170947 + 0.214361i
\(732\) −0.969451 + 2.44644i −0.0358320 + 0.0904231i
\(733\) −21.6721 + 45.0026i −0.800477 + 1.66221i −0.0523730 + 0.998628i \(0.516678\pi\)
−0.748104 + 0.663581i \(0.769036\pi\)
\(734\) 28.4599 14.9817i 1.05047 0.552984i
\(735\) −16.3963 8.51818i −0.604787 0.314198i
\(736\) −30.1588 + 34.4681i −1.11167 + 1.27051i
\(737\) −21.3109 10.2628i −0.784996 0.378034i
\(738\) 12.5782 10.7885i 0.463010 0.397129i
\(739\) 19.0718 15.2093i 0.701567 0.559481i −0.206428 0.978462i \(-0.566184\pi\)
0.907995 + 0.418980i \(0.137612\pi\)
\(740\) −6.23741 + 15.7403i −0.229292 + 0.578625i
\(741\) 24.0989 + 5.50042i 0.885296 + 0.202063i
\(742\) −39.5421 23.7249i −1.45163 0.870968i
\(743\) −15.9092 + 3.63118i −0.583654 + 0.133215i −0.504145 0.863619i \(-0.668192\pi\)
−0.0795086 + 0.996834i \(0.525335\pi\)
\(744\) 0.221600 + 0.643458i 0.00812425 + 0.0235903i
\(745\) 13.1008 + 2.99018i 0.479977 + 0.109552i
\(746\) −26.6610 + 0.953702i −0.976130 + 0.0349175i
\(747\) −4.05518 + 5.08503i −0.148371 + 0.186052i
\(748\) −3.10325 + 1.77808i −0.113466 + 0.0650132i
\(749\) −3.30932 3.41129i −0.120920 0.124646i
\(750\) −9.09758 6.73744i −0.332196 0.246017i
\(751\) −48.0662 10.9708i −1.75396 0.400330i −0.779772 0.626063i \(-0.784665\pi\)
−0.974189 + 0.225733i \(0.927522\pi\)
\(752\) 12.4778 + 3.93894i 0.455020 + 0.143638i
\(753\) −8.20048 −0.298842
\(754\) 5.90933 + 11.2256i 0.215205 + 0.408813i
\(755\) 21.5422 27.0130i 0.783999 0.983104i
\(756\) −4.63187 2.55848i −0.168459 0.0930510i
\(757\) 5.16090 + 6.47157i 0.187576 + 0.235213i 0.866724 0.498789i \(-0.166222\pi\)
−0.679147 + 0.734002i \(0.737650\pi\)
\(758\) −15.8635 + 36.1972i −0.576190 + 1.31474i
\(759\) −17.4426 + 8.39992i −0.633127 + 0.304898i
\(760\) 39.8920 13.7384i 1.44703 0.498343i
\(761\) 31.0552 24.7657i 1.12575 0.897754i 0.130152 0.991494i \(-0.458454\pi\)
0.995597 + 0.0937398i \(0.0298822\pi\)
\(762\) −0.970159 + 2.21369i −0.0351452 + 0.0801937i
\(763\) −33.5748 4.29971i −1.21549 0.155660i
\(764\) 38.2518 11.6615i 1.38390 0.421900i
\(765\) 1.97402 0.0713710
\(766\) 3.46285 1.82289i 0.125118 0.0658638i
\(767\) −5.65255 4.50776i −0.204102 0.162766i
\(768\) −7.81710 13.9604i −0.282075 0.503753i
\(769\) −7.63740 15.8592i −0.275412 0.571898i 0.716682 0.697400i \(-0.245660\pi\)
−0.992093 + 0.125502i \(0.959946\pi\)
\(770\) −3.12669 23.4084i −0.112678 0.843580i
\(771\) 11.8536 24.6143i 0.426897 0.886461i
\(772\) −5.75741 18.8853i −0.207214 0.679696i
\(773\) −13.7267 + 28.5037i −0.493714 + 1.02521i 0.494076 + 0.869418i \(0.335506\pi\)
−0.987790 + 0.155789i \(0.950208\pi\)
\(774\) −13.5463 + 3.60587i −0.486912 + 0.129610i
\(775\) 0.426479 0.205381i 0.0153196 0.00737752i
\(776\) −3.50928 32.5894i −0.125976 1.16989i
\(777\) −8.41665 1.07787i −0.301946 0.0386682i
\(778\) 9.18942 + 34.5223i 0.329457 + 1.23768i
\(779\) −64.5588 + 14.7351i −2.31306 + 0.527940i
\(780\) −23.0319 + 1.64988i −0.824676 + 0.0590752i
\(781\) −1.49616 6.55510i −0.0535368 0.234560i
\(782\) 8.55744 0.306111i 0.306013 0.0109465i
\(783\) 2.05084 0.0732909
\(784\) 19.7894 19.8086i 0.706765 0.707449i
\(785\) −8.26771 −0.295087
\(786\) 7.94459 0.284189i 0.283374 0.0101367i
\(787\) −3.67981 16.1223i −0.131171 0.574698i −0.997205 0.0747127i \(-0.976196\pi\)
0.866034 0.499985i \(-0.166661\pi\)
\(788\) 1.82940 0.131048i 0.0651696 0.00466839i
\(789\) 10.5370 2.40500i 0.375127 0.0856203i
\(790\) −6.03683 22.6788i −0.214781 0.806876i
\(791\) 14.2108 13.7860i 0.505277 0.490175i
\(792\) −0.724100 6.72445i −0.0257298 0.238943i
\(793\) −5.18521 + 2.49706i −0.184132 + 0.0886734i
\(794\) 27.5862 7.34313i 0.978999 0.260598i
\(795\) −14.1146 + 29.3093i −0.500594 + 1.03949i
\(796\) −0.314209 1.03066i −0.0111368 0.0365307i
\(797\) 6.44658 13.3865i 0.228350 0.474173i −0.755040 0.655678i \(-0.772383\pi\)
0.983390 + 0.181506i \(0.0580970\pi\)
\(798\) 11.6160 + 17.6687i 0.411203 + 0.625465i
\(799\) −1.06145 2.20412i −0.0375514 0.0779763i
\(800\) −9.00825 + 6.53471i −0.318490 + 0.231037i
\(801\) −11.6003 9.25096i −0.409878 0.326867i
\(802\) −20.6088 + 10.8488i −0.727721 + 0.383083i
\(803\) −26.3468 −0.929758
\(804\) −18.9238 + 5.76915i −0.667390 + 0.203462i
\(805\) −19.4820 + 53.0793i −0.686649 + 1.87080i
\(806\) −0.597424 + 1.36319i −0.0210434 + 0.0480164i
\(807\) −4.73956 + 3.77967i −0.166840 + 0.133051i
\(808\) 47.4172 16.3300i 1.66813 0.574486i
\(809\) 36.9283 17.7837i 1.29833 0.625242i 0.348294 0.937385i \(-0.386761\pi\)
0.950035 + 0.312143i \(0.101047\pi\)
\(810\) −1.49838 + 3.41899i −0.0526479 + 0.120131i
\(811\) −14.2306 17.8446i −0.499703 0.626607i 0.466460 0.884543i \(-0.345529\pi\)
−0.966162 + 0.257935i \(0.916958\pi\)
\(812\) −3.00170 + 10.4286i −0.105339 + 0.365972i
\(813\) 4.14757 5.20089i 0.145462 0.182403i
\(814\) −5.05203 9.59706i −0.177074 0.336377i
\(815\) 62.0277 2.17274
\(816\) −0.900517 + 2.85267i −0.0315244 + 0.0998636i
\(817\) 54.6123 + 12.4649i 1.91064 + 0.436091i
\(818\) −15.4015 11.4060i −0.538500 0.398800i
\(819\) −3.65602 10.9798i −0.127752 0.383667i
\(820\) 53.6725 30.7530i 1.87432 1.07394i
\(821\) −0.0238844 + 0.0299501i −0.000833572 + 0.00104527i −0.782248 0.622967i \(-0.785927\pi\)
0.781415 + 0.624012i \(0.214498\pi\)
\(822\) 22.7905 0.815247i 0.794910 0.0284350i
\(823\) 38.7006 + 8.83315i 1.34902 + 0.307904i 0.835177 0.549982i \(-0.185365\pi\)
0.513840 + 0.857886i \(0.328223\pi\)
\(824\) −3.24488 9.42211i −0.113041 0.328235i
\(825\) −4.58630 + 1.04679i −0.159674 + 0.0364446i
\(826\) −0.818821 6.13022i −0.0284904 0.213298i
\(827\) −32.7294 7.47027i −1.13811 0.259767i −0.388375 0.921501i \(-0.626963\pi\)
−0.749738 + 0.661735i \(0.769821\pi\)
\(828\) −5.96535 + 15.0537i −0.207310 + 0.523154i
\(829\) −12.8407 + 10.2401i −0.445976 + 0.355654i −0.820581 0.571531i \(-0.806350\pi\)
0.374605 + 0.927185i \(0.377778\pi\)
\(830\) −18.4287 + 15.8065i −0.639669 + 0.548652i
\(831\) 25.3816 + 12.2231i 0.880478 + 0.424016i
\(832\) 8.12254 34.0363i 0.281599 1.18000i
\(833\) −5.23260 0.158811i −0.181299 0.00550248i
\(834\) −19.3813 + 10.2026i −0.671120 + 0.353287i
\(835\) −15.9707 + 33.1634i −0.552688 + 1.14767i
\(836\) −9.95657 + 25.1257i −0.344355 + 0.868991i
\(837\) 0.150018 + 0.188116i 0.00518537 + 0.00650225i
\(838\) 29.8001 + 34.7437i 1.02943 + 1.20020i
\(839\) −2.94685 + 12.9110i −0.101737 + 0.445737i 0.898244 + 0.439497i \(0.144843\pi\)
−0.999981 + 0.00623994i \(0.998014\pi\)
\(840\) −15.1926 12.6235i −0.524195 0.435554i
\(841\) 5.51720 + 24.1724i 0.190248 + 0.833532i
\(842\) 31.9408 43.1296i 1.10075 1.48634i
\(843\) −0.779060 + 3.41329i −0.0268323 + 0.117560i
\(844\) 20.7368 + 36.1915i 0.713791 + 1.24576i
\(845\) −12.6544 10.0916i −0.435326 0.347161i
\(846\) 4.62321 0.165379i 0.158949 0.00568584i
\(847\) −11.7191 7.61399i −0.402673 0.261620i
\(848\) −35.9162 33.7676i −1.23337 1.15958i
\(849\) −4.22781 + 18.5233i −0.145098 + 0.635717i
\(850\) 2.04379 + 0.390186i 0.0701013 + 0.0133833i
\(851\) 25.9663i 0.890112i
\(852\) −4.63608 3.18320i −0.158829 0.109055i
\(853\) 17.7230 + 14.1337i 0.606825 + 0.483927i 0.878037 0.478593i \(-0.158853\pi\)
−0.271212 + 0.962520i \(0.587424\pi\)
\(854\) −4.67934 1.53001i −0.160124 0.0523559i
\(855\) 11.6625 9.30054i 0.398849 0.318072i
\(856\) −2.68195 4.31539i −0.0916671 0.147497i
\(857\) −2.03871 4.23342i −0.0696410 0.144611i 0.863242 0.504790i \(-0.168430\pi\)
−0.932883 + 0.360179i \(0.882716\pi\)
\(858\) 8.80298 11.8867i 0.300529 0.405804i
\(859\) 15.9026 + 19.9412i 0.542588 + 0.680384i 0.975233 0.221180i \(-0.0709909\pi\)
−0.432645 + 0.901565i \(0.642420\pi\)
\(860\) −52.1943 + 3.73891i −1.77981 + 0.127496i
\(861\) 21.5865 + 22.2516i 0.735665 + 0.758331i
\(862\) −4.59632 0.877498i −0.156551 0.0298877i
\(863\) 15.3968i 0.524115i 0.965052 + 0.262057i \(0.0844009\pi\)
−0.965052 + 0.262057i \(0.915599\pi\)
\(864\) −4.25726 3.72501i −0.144835 0.126727i
\(865\) −20.2237 + 25.3598i −0.687628 + 0.862258i
\(866\) 13.6463 3.63248i 0.463719 0.123437i
\(867\) −14.8126 + 7.13336i −0.503061 + 0.242261i
\(868\) −1.17615 + 0.487512i −0.0399212 + 0.0165472i
\(869\) 13.5445 + 6.52268i 0.459466 + 0.221267i
\(870\) 7.51978 + 1.43563i 0.254944 + 0.0486723i
\(871\) −38.9821 18.7728i −1.32086 0.636092i
\(872\) −34.0961 12.1198i −1.15464 0.410429i
\(873\) −5.02814 10.4410i −0.170177 0.353376i
\(874\) 49.1150 42.1265i 1.66134 1.42495i
\(875\) 11.5387 17.7599i 0.390080 0.600394i
\(876\) −16.2031 + 14.9354i −0.547452 + 0.504622i
\(877\) −1.14958 5.03664i −0.0388186 0.170075i 0.951803 0.306711i \(-0.0992283\pi\)
−0.990621 + 0.136635i \(0.956371\pi\)
\(878\) −2.57244 1.12738i −0.0868155 0.0380472i
\(879\) −17.0920 + 3.90113i −0.576498 + 0.131582i
\(880\) 2.05220 25.1633i 0.0691796 0.848256i
\(881\) 32.0721i 1.08054i 0.841492 + 0.540269i \(0.181678\pi\)
−0.841492 + 0.540269i \(0.818322\pi\)
\(882\) 4.24687 8.94226i 0.143000 0.301102i
\(883\) 50.0789i 1.68529i 0.538471 + 0.842644i \(0.319002\pi\)
−0.538471 + 0.842644i \(0.680998\pi\)
\(884\) −5.67650 + 3.25249i −0.190921 + 0.109393i
\(885\) −4.25361 + 0.970858i −0.142983 + 0.0326350i
\(886\) 1.27055 2.89911i 0.0426848 0.0973976i
\(887\) 5.08745 + 22.2896i 0.170820 + 0.748410i 0.985663 + 0.168728i \(0.0539660\pi\)
−0.814843 + 0.579682i \(0.803177\pi\)
\(888\) −8.54733 3.03823i −0.286830 0.101956i
\(889\) −4.24481 1.55800i −0.142366 0.0522535i
\(890\) −36.0590 42.0409i −1.20870 1.40921i
\(891\) −1.03750 2.15439i −0.0347576 0.0721749i
\(892\) 17.8906 + 19.4091i 0.599021 + 0.649864i
\(893\) −16.6557 8.02095i −0.557361 0.268411i
\(894\) −1.35012 + 7.07188i −0.0451546 + 0.236519i
\(895\) 33.8772 + 16.3144i 1.13239 + 0.545330i
\(896\) 25.1730 16.1963i 0.840971 0.541081i
\(897\) −31.9063 + 15.3652i −1.06532 + 0.513030i
\(898\) −9.53804 35.8319i −0.318288 1.19573i
\(899\) 0.307662 0.385796i 0.0102611 0.0128670i
\(900\) −2.22714 + 3.24365i −0.0742379 + 0.108122i
\(901\) 9.21685i 0.307058i
\(902\) −7.43070 + 38.9218i −0.247415 + 1.29595i
\(903\) −8.28517 24.8822i −0.275713 0.828028i
\(904\) 17.9771 11.1725i 0.597910 0.371592i
\(905\) 1.87839 + 2.35543i 0.0624398 + 0.0782970i
\(906\) 14.8762 + 11.0170i 0.494230 + 0.366015i
\(907\) 0.00210864 + 0.00437864i 7.00163e−5 + 0.000145390i 0.901004 0.433811i \(-0.142831\pi\)
−0.900934 + 0.433956i \(0.857117\pi\)
\(908\) 40.7448 2.91873i 1.35216 0.0968614i
\(909\) 13.8625 11.0550i 0.459791 0.366671i
\(910\) −5.71938 42.8190i −0.189596 1.41943i
\(911\) 21.6568 + 17.2707i 0.717521 + 0.572204i 0.912733 0.408557i \(-0.133968\pi\)
−0.195212 + 0.980761i \(0.562539\pi\)
\(912\) 8.12002 + 21.0963i 0.268881 + 0.698569i
\(913\) 15.5523i 0.514707i
\(914\) −8.42365 + 44.1229i −0.278630 + 1.45946i
\(915\) −0.772824 + 3.38596i −0.0255488 + 0.111937i
\(916\) 0.445897 + 0.0687082i 0.0147329 + 0.00227018i
\(917\) 1.44080 + 14.8025i 0.0475795 + 0.488822i
\(918\) 0.0378088 + 1.05696i 0.00124787 + 0.0348847i
\(919\) −34.1168 27.2072i −1.12541 0.897483i −0.129841 0.991535i \(-0.541447\pi\)
−0.995567 + 0.0940514i \(0.970018\pi\)
\(920\) −32.4110 + 51.0215i −1.06856 + 1.68213i
\(921\) 4.71395 20.6531i 0.155330 0.680544i
\(922\) 4.81164 + 3.56338i 0.158463 + 0.117354i
\(923\) −2.73679 11.9907i −0.0900827 0.394678i
\(924\) 12.4737 2.12248i 0.410356 0.0698243i
\(925\) −1.40400 + 6.15134i −0.0461634 + 0.202255i
\(926\) 20.1400 17.2743i 0.661841 0.567670i
\(927\) −2.19670 2.75457i −0.0721491 0.0904721i
\(928\) −5.50503 + 10.2120i −0.180712 + 0.335224i
\(929\) 26.2768 54.5644i 0.862114 1.79020i 0.328383 0.944545i \(-0.393496\pi\)
0.533732 0.845654i \(-0.320789\pi\)
\(930\) 0.418383 + 0.794779i 0.0137193 + 0.0260618i
\(931\) −31.6624 + 23.7149i −1.03769 + 0.777226i
\(932\) −1.45628 + 2.12095i −0.0477019 + 0.0694740i
\(933\) 18.9578 + 9.12959i 0.620650 + 0.298889i
\(934\) −5.29908 6.17816i −0.173391 0.202155i
\(935\) −3.69046 + 2.94304i −0.120691 + 0.0962479i
\(936\) −1.32453 12.3004i −0.0432937 0.402053i
\(937\) −15.5567 3.55071i −0.508215 0.115997i −0.0392778 0.999228i \(-0.512506\pi\)
−0.468937 + 0.883232i \(0.655363\pi\)
\(938\) −12.9407 34.6758i −0.422530 1.13220i
\(939\) 17.4976 3.99370i 0.571011 0.130330i
\(940\) 17.0677 + 2.62995i 0.556686 + 0.0857795i
\(941\) 45.4140 + 10.3655i 1.48045 + 0.337904i 0.885040 0.465515i \(-0.154131\pi\)
0.595414 + 0.803419i \(0.296988\pi\)
\(942\) −0.158353 4.42680i −0.00515941 0.144233i
\(943\) 59.1498 74.1714i 1.92618 2.41535i
\(944\) 0.537432 6.58980i 0.0174919 0.214480i
\(945\) −6.55599 2.40628i −0.213266 0.0782763i
\(946\) 19.9491 26.9372i 0.648600 0.875805i
\(947\) 22.4986 + 5.13516i 0.731107 + 0.166870i 0.571840 0.820365i \(-0.306230\pi\)
0.159267 + 0.987236i \(0.449087\pi\)
\(948\) 12.0273 3.66668i 0.390630 0.119088i
\(949\) −48.1939 −1.56444
\(950\) 13.9130 7.32400i 0.451398 0.237622i
\(951\) 9.83533 12.3331i 0.318933 0.399929i
\(952\) −5.43001 1.35475i −0.175988 0.0439077i
\(953\) 15.2751 + 19.1543i 0.494808 + 0.620469i 0.965049 0.262069i \(-0.0844047\pi\)
−0.470242 + 0.882538i \(0.655833\pi\)
\(954\) −15.9635 6.99606i −0.516837 0.226506i
\(955\) 47.5514 22.8995i 1.53873 0.741012i
\(956\) 20.7210 + 3.19290i 0.670166 + 0.103266i
\(957\) −3.83406 + 3.05756i −0.123938 + 0.0988370i
\(958\) 24.3491 + 10.6711i 0.786684 + 0.344767i
\(959\) 4.13320 + 42.4637i 0.133468 + 1.37122i
\(960\) −13.0025 16.6386i −0.419653 0.537009i
\(961\) −30.9421 −0.998132
\(962\) −9.24124 17.5551i −0.297949 0.565998i
\(963\) −1.40446 1.12002i −0.0452579 0.0360920i
\(964\) −19.7385 + 18.1942i −0.635734 + 0.585997i
\(965\) −11.3057 23.4765i −0.363944 0.755737i
\(966\) −28.7935 9.41464i −0.926416 0.302911i
\(967\) −1.96545 + 4.08129i −0.0632045 + 0.131246i −0.930178 0.367109i \(-0.880348\pi\)
0.866974 + 0.498354i \(0.166062\pi\)
\(968\) −10.5121 10.6163i −0.337873 0.341222i
\(969\) 1.83374 3.80781i 0.0589084 0.122324i
\(970\) −11.1277 41.8039i −0.357289 1.34224i
\(971\) −18.3965 + 8.85927i −0.590370 + 0.284307i −0.705121 0.709087i \(-0.749107\pi\)
0.114751 + 0.993394i \(0.463393\pi\)
\(972\) −1.85934 0.736799i −0.0596382 0.0236328i
\(973\) −21.2718 35.0223i −0.681943 1.12276i
\(974\) −23.8999 + 6.36188i −0.765804 + 0.203848i
\(975\) −8.38931 + 1.91481i −0.268673 + 0.0613229i
\(976\) −4.54053 2.66143i −0.145339 0.0851904i
\(977\) −11.3043 49.5274i −0.361657 1.58452i −0.748990 0.662582i \(-0.769461\pi\)
0.387333 0.921940i \(-0.373396\pi\)
\(978\) 1.18803 + 33.2117i 0.0379889 + 1.06199i
\(979\) 35.4791 1.13392
\(980\) 21.8317 29.8156i 0.697389 0.952425i
\(981\) −12.7937 −0.408472
\(982\) 1.79745 + 50.2483i 0.0573590 + 1.60349i
\(983\) 8.78144 + 38.4740i 0.280085 + 1.22713i 0.897685 + 0.440638i \(0.145248\pi\)
−0.617600 + 0.786492i \(0.711895\pi\)
\(984\) 17.4941 + 28.1489i 0.557693 + 0.897356i
\(985\) 2.35991 0.538634i 0.0751930 0.0171623i
\(986\) 2.09604 0.557942i 0.0667516 0.0177685i
\(987\) 0.838449 + 8.61407i 0.0266881 + 0.274189i
\(988\) −18.2127 + 45.9603i −0.579423 + 1.46219i
\(989\) −72.3050 + 34.8203i −2.29917 + 1.10722i
\(990\) −2.29607 8.62576i −0.0729740 0.274145i
\(991\) 4.14620 8.60967i 0.131708 0.273495i −0.824677 0.565605i \(-0.808643\pi\)
0.956385 + 0.292109i \(0.0943572\pi\)
\(992\) −1.33940 + 0.242043i −0.0425260 + 0.00768487i
\(993\) −11.9174 + 24.7467i −0.378187 + 0.785313i
\(994\) 5.41294 9.02169i 0.171688 0.286151i
\(995\) −0.617006 1.28123i −0.0195604 0.0406176i
\(996\) −8.81629 9.56457i −0.279355 0.303065i
\(997\) −8.45075 6.73925i −0.267638 0.213434i 0.480470 0.877011i \(-0.340466\pi\)
−0.748108 + 0.663577i \(0.769038\pi\)
\(998\) 15.4985 + 29.4416i 0.490595 + 0.931956i
\(999\) −3.20717 −0.101471
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 588.2.x.a.559.2 yes 168
4.3 odd 2 588.2.x.b.559.10 yes 168
49.27 odd 14 588.2.x.b.223.10 yes 168
196.27 even 14 inner 588.2.x.a.223.2 168
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
588.2.x.a.223.2 168 196.27 even 14 inner
588.2.x.a.559.2 yes 168 1.1 even 1 trivial
588.2.x.b.223.10 yes 168 49.27 odd 14
588.2.x.b.559.10 yes 168 4.3 odd 2