Properties

Label 690.2.m.d.361.2
Level $690$
Weight $2$
Character 690.361
Analytic conductor $5.510$
Analytic rank $0$
Dimension $20$
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] = [690,2,Mod(31,690)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(690, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("690.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.m (of order \(11\), 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: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 5 x^{19} + 8 x^{18} - 32 x^{17} + 277 x^{16} - 1138 x^{15} + 2950 x^{14} - 6404 x^{13} + 24088 x^{12} - 93423 x^{11} + 318055 x^{10} - 798006 x^{9} + 1869818 x^{8} + \cdots + 7921 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 361.2
Root \(-0.764548 + 1.67413i\) of defining polynomial
Character \(\chi\) \(=\) 690.361
Dual form 690.2.m.d.151.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(4.58950 - 1.34760i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\) \(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(4.58950 - 1.34760i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.959493 + 0.281733i) q^{10} +(-0.612128 - 0.706433i) q^{11} +(0.654861 + 0.755750i) q^{12} +(-6.39358 - 1.87733i) q^{13} +(-1.98704 + 4.35100i) q^{14} +(0.841254 + 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.0823460 + 0.572729i) q^{17} +(0.415415 + 0.909632i) q^{18} +(-1.08920 - 7.57554i) q^{19} +(-0.841254 + 0.540641i) q^{20} +(-3.13237 + 3.61494i) q^{21} +0.934745 q^{22} +(-3.66179 + 3.09698i) q^{23} -1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(5.60569 - 3.60256i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-1.98704 - 4.35100i) q^{28} +(-0.183105 + 1.27353i) q^{29} +(-0.959493 + 0.281733i) q^{30} +(-2.87363 - 1.84677i) q^{31} +(0.415415 - 0.909632i) q^{32} +(0.896881 + 0.263348i) q^{33} +(-0.378915 - 0.437291i) q^{34} +(-3.13237 - 3.61494i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(1.16563 - 2.55238i) q^{37} +(6.43848 + 4.13776i) q^{38} +(6.39358 - 1.87733i) q^{39} +(0.142315 - 0.989821i) q^{40} +(-3.53174 - 7.73343i) q^{41} +(-0.680728 - 4.73457i) q^{42} +(7.18103 - 4.61497i) q^{43} +(-0.612128 + 0.706433i) q^{44} -1.00000 q^{45} +(0.0574180 - 4.79549i) q^{46} +1.94160 q^{47} +(0.654861 - 0.755750i) q^{48} +(13.3587 - 8.58512i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(-0.240367 - 0.526330i) q^{51} +(-0.948315 + 6.59568i) q^{52} +(9.10767 - 2.67425i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(-0.388307 + 0.850274i) q^{55} +(4.58950 + 1.34760i) q^{56} +(5.01194 + 5.78408i) q^{57} +(-0.842558 - 0.972364i) q^{58} +(-10.8918 - 3.19813i) q^{59} +(0.415415 - 0.909632i) q^{60} +(-3.05825 - 1.96542i) q^{61} +(3.27753 - 0.962369i) q^{62} +(0.680728 - 4.73457i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.948315 + 6.59568i) q^{65} +(-0.786357 + 0.505361i) q^{66} +(6.31204 - 7.28449i) q^{67} +0.578619 q^{68} +(1.40614 - 4.58506i) q^{69} +4.78325 q^{70} +(-6.65447 + 7.67967i) q^{71} +(0.841254 - 0.540641i) q^{72} +(1.83935 + 12.7930i) q^{73} +(1.16563 + 2.55238i) q^{74} +(0.142315 - 0.989821i) q^{75} +(-7.34342 + 2.15622i) q^{76} +(-3.76135 - 2.41727i) q^{77} +(-2.76812 + 6.06133i) q^{78} +(4.08923 + 1.20071i) q^{79} +(0.654861 + 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(8.15734 + 2.39521i) q^{82} +(-1.13386 + 2.48281i) q^{83} +(4.02393 + 2.58602i) q^{84} +(0.555181 - 0.163016i) q^{85} +(-1.21481 + 8.44922i) q^{86} +(-0.534482 - 1.17035i) q^{87} +(-0.133028 - 0.925231i) q^{88} +(2.33801 - 1.50255i) q^{89} +(0.654861 - 0.755750i) q^{90} -31.8732 q^{91} +(3.58659 + 3.18377i) q^{92} +3.41590 q^{93} +(-1.27148 + 1.46736i) q^{94} +(-6.43848 + 4.13776i) q^{95} +(0.142315 + 0.989821i) q^{96} +(-2.27350 - 4.97827i) q^{97} +(-2.25989 + 15.7179i) q^{98} +(-0.896881 + 0.263348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{11}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.654861 + 0.755750i −0.463056 + 0.534396i
\(3\) −0.841254 + 0.540641i −0.485698 + 0.312139i
\(4\) −0.142315 0.989821i −0.0711574 0.494911i
\(5\) −0.415415 0.909632i −0.185779 0.406800i
\(6\) 0.142315 0.989821i 0.0580998 0.404093i
\(7\) 4.58950 1.34760i 1.73467 0.509344i 0.746854 0.664988i \(-0.231563\pi\)
0.987813 + 0.155643i \(0.0497451\pi\)
\(8\) 0.841254 + 0.540641i 0.297428 + 0.191145i
\(9\) 0.415415 0.909632i 0.138472 0.303211i
\(10\) 0.959493 + 0.281733i 0.303418 + 0.0890917i
\(11\) −0.612128 0.706433i −0.184563 0.212998i 0.655926 0.754825i \(-0.272278\pi\)
−0.840490 + 0.541827i \(0.817733\pi\)
\(12\) 0.654861 + 0.755750i 0.189042 + 0.218166i
\(13\) −6.39358 1.87733i −1.77326 0.520676i −0.778940 0.627098i \(-0.784242\pi\)
−0.994321 + 0.106422i \(0.966061\pi\)
\(14\) −1.98704 + 4.35100i −0.531058 + 1.16285i
\(15\) 0.841254 + 0.540641i 0.217211 + 0.139593i
\(16\) −0.959493 + 0.281733i −0.239873 + 0.0704331i
\(17\) −0.0823460 + 0.572729i −0.0199718 + 0.138907i −0.997368 0.0725104i \(-0.976899\pi\)
0.977396 + 0.211418i \(0.0678080\pi\)
\(18\) 0.415415 + 0.909632i 0.0979143 + 0.214402i
\(19\) −1.08920 7.57554i −0.249879 1.73795i −0.598892 0.800829i \(-0.704392\pi\)
0.349013 0.937118i \(-0.386517\pi\)
\(20\) −0.841254 + 0.540641i −0.188110 + 0.120891i
\(21\) −3.13237 + 3.61494i −0.683538 + 0.788845i
\(22\) 0.934745 0.199288
\(23\) −3.66179 + 3.09698i −0.763536 + 0.645766i
\(24\) −1.00000 −0.204124
\(25\) −0.654861 + 0.755750i −0.130972 + 0.151150i
\(26\) 5.60569 3.60256i 1.09937 0.706520i
\(27\) 0.142315 + 0.989821i 0.0273885 + 0.190491i
\(28\) −1.98704 4.35100i −0.375514 0.822262i
\(29\) −0.183105 + 1.27353i −0.0340018 + 0.236488i −0.999734 0.0230518i \(-0.992662\pi\)
0.965732 + 0.259540i \(0.0835708\pi\)
\(30\) −0.959493 + 0.281733i −0.175179 + 0.0514371i
\(31\) −2.87363 1.84677i −0.516120 0.331690i 0.256516 0.966540i \(-0.417426\pi\)
−0.772635 + 0.634850i \(0.781062\pi\)
\(32\) 0.415415 0.909632i 0.0734357 0.160802i
\(33\) 0.896881 + 0.263348i 0.156127 + 0.0458430i
\(34\) −0.378915 0.437291i −0.0649833 0.0749948i
\(35\) −3.13237 3.61494i −0.529466 0.611037i
\(36\) −0.959493 0.281733i −0.159915 0.0469554i
\(37\) 1.16563 2.55238i 0.191629 0.419609i −0.789291 0.614019i \(-0.789552\pi\)
0.980920 + 0.194410i \(0.0622792\pi\)
\(38\) 6.43848 + 4.13776i 1.04446 + 0.671233i
\(39\) 6.39358 1.87733i 1.02379 0.300613i
\(40\) 0.142315 0.989821i 0.0225020 0.156505i
\(41\) −3.53174 7.73343i −0.551565 1.20776i −0.956047 0.293213i \(-0.905275\pi\)
0.404482 0.914546i \(-0.367452\pi\)
\(42\) −0.680728 4.73457i −0.105039 0.730560i
\(43\) 7.18103 4.61497i 1.09510 0.703776i 0.137100 0.990557i \(-0.456222\pi\)
0.957996 + 0.286781i \(0.0925853\pi\)
\(44\) −0.612128 + 0.706433i −0.0922817 + 0.106499i
\(45\) −1.00000 −0.149071
\(46\) 0.0574180 4.79549i 0.00846583 0.707056i
\(47\) 1.94160 0.283211 0.141605 0.989923i \(-0.454774\pi\)
0.141605 + 0.989923i \(0.454774\pi\)
\(48\) 0.654861 0.755750i 0.0945210 0.109083i
\(49\) 13.3587 8.58512i 1.90839 1.22645i
\(50\) −0.142315 0.989821i −0.0201264 0.139982i
\(51\) −0.240367 0.526330i −0.0336581 0.0737010i
\(52\) −0.948315 + 6.59568i −0.131508 + 0.914656i
\(53\) 9.10767 2.67425i 1.25103 0.367337i 0.411884 0.911236i \(-0.364871\pi\)
0.839151 + 0.543899i \(0.183053\pi\)
\(54\) −0.841254 0.540641i −0.114480 0.0735719i
\(55\) −0.388307 + 0.850274i −0.0523593 + 0.114651i
\(56\) 4.58950 + 1.34760i 0.613298 + 0.180080i
\(57\) 5.01194 + 5.78408i 0.663847 + 0.766120i
\(58\) −0.842558 0.972364i −0.110633 0.127678i
\(59\) −10.8918 3.19813i −1.41799 0.416361i −0.519171 0.854670i \(-0.673759\pi\)
−0.898824 + 0.438310i \(0.855577\pi\)
\(60\) 0.415415 0.909632i 0.0536298 0.117433i
\(61\) −3.05825 1.96542i −0.391569 0.251646i 0.330011 0.943977i \(-0.392947\pi\)
−0.721580 + 0.692331i \(0.756584\pi\)
\(62\) 3.27753 0.962369i 0.416246 0.122221i
\(63\) 0.680728 4.73457i 0.0857637 0.596499i
\(64\) 0.415415 + 0.909632i 0.0519269 + 0.113704i
\(65\) 0.948315 + 6.59568i 0.117624 + 0.818093i
\(66\) −0.786357 + 0.505361i −0.0967939 + 0.0622057i
\(67\) 6.31204 7.28449i 0.771139 0.889942i −0.225297 0.974290i \(-0.572335\pi\)
0.996436 + 0.0843483i \(0.0268808\pi\)
\(68\) 0.578619 0.0701678
\(69\) 1.40614 4.58506i 0.169279 0.551976i
\(70\) 4.78325 0.571708
\(71\) −6.65447 + 7.67967i −0.789740 + 0.911409i −0.997772 0.0667133i \(-0.978749\pi\)
0.208032 + 0.978122i \(0.433294\pi\)
\(72\) 0.841254 0.540641i 0.0991427 0.0637151i
\(73\) 1.83935 + 12.7930i 0.215280 + 1.49731i 0.755147 + 0.655556i \(0.227566\pi\)
−0.539867 + 0.841751i \(0.681525\pi\)
\(74\) 1.16563 + 2.55238i 0.135502 + 0.296708i
\(75\) 0.142315 0.989821i 0.0164331 0.114295i
\(76\) −7.34342 + 2.15622i −0.842348 + 0.247336i
\(77\) −3.76135 2.41727i −0.428645 0.275474i
\(78\) −2.76812 + 6.06133i −0.313428 + 0.686311i
\(79\) 4.08923 + 1.20071i 0.460075 + 0.135090i 0.503553 0.863964i \(-0.332026\pi\)
−0.0434784 + 0.999054i \(0.513844\pi\)
\(80\) 0.654861 + 0.755750i 0.0732157 + 0.0844954i
\(81\) −0.654861 0.755750i −0.0727623 0.0839722i
\(82\) 8.15734 + 2.39521i 0.900827 + 0.264507i
\(83\) −1.13386 + 2.48281i −0.124457 + 0.272524i −0.961597 0.274466i \(-0.911499\pi\)
0.837139 + 0.546990i \(0.184226\pi\)
\(84\) 4.02393 + 2.58602i 0.439047 + 0.282158i
\(85\) 0.555181 0.163016i 0.0602178 0.0176815i
\(86\) −1.21481 + 8.44922i −0.130997 + 0.911103i
\(87\) −0.534482 1.17035i −0.0573025 0.125475i
\(88\) −0.133028 0.925231i −0.0141808 0.0986299i
\(89\) 2.33801 1.50255i 0.247828 0.159270i −0.410830 0.911712i \(-0.634761\pi\)
0.658658 + 0.752443i \(0.271125\pi\)
\(90\) 0.654861 0.755750i 0.0690284 0.0796630i
\(91\) −31.8732 −3.34122
\(92\) 3.58659 + 3.18377i 0.373928 + 0.331931i
\(93\) 3.41590 0.354212
\(94\) −1.27148 + 1.46736i −0.131143 + 0.151347i
\(95\) −6.43848 + 4.13776i −0.660574 + 0.424525i
\(96\) 0.142315 + 0.989821i 0.0145249 + 0.101023i
\(97\) −2.27350 4.97827i −0.230839 0.505466i 0.758398 0.651792i \(-0.225982\pi\)
−0.989236 + 0.146326i \(0.953255\pi\)
\(98\) −2.25989 + 15.7179i −0.228284 + 1.58775i
\(99\) −0.896881 + 0.263348i −0.0901399 + 0.0264675i
\(100\) 0.841254 + 0.540641i 0.0841254 + 0.0540641i
\(101\) 7.36636 16.1301i 0.732980 1.60500i −0.0617886 0.998089i \(-0.519680\pi\)
0.794768 0.606913i \(-0.207592\pi\)
\(102\) 0.555181 + 0.163016i 0.0549711 + 0.0161410i
\(103\) 9.44461 + 10.8997i 0.930606 + 1.07398i 0.997093 + 0.0761888i \(0.0242752\pi\)
−0.0664879 + 0.997787i \(0.521179\pi\)
\(104\) −4.36367 5.03594i −0.427893 0.493814i
\(105\) 4.58950 + 1.34760i 0.447889 + 0.131512i
\(106\) −3.94319 + 8.63438i −0.382997 + 0.838645i
\(107\) 2.57469 + 1.65465i 0.248905 + 0.159961i 0.659144 0.752016i \(-0.270919\pi\)
−0.410240 + 0.911978i \(0.634555\pi\)
\(108\) 0.959493 0.281733i 0.0923273 0.0271097i
\(109\) −0.000794403 0.00552520i −7.60900e−5 0.000529218i −0.989859 0.142050i \(-0.954631\pi\)
0.989783 + 0.142579i \(0.0455396\pi\)
\(110\) −0.388307 0.850274i −0.0370236 0.0810704i
\(111\) 0.399328 + 2.77739i 0.0379025 + 0.263618i
\(112\) −4.02393 + 2.58602i −0.380226 + 0.244356i
\(113\) 2.74614 3.16921i 0.258335 0.298134i −0.611735 0.791063i \(-0.709528\pi\)
0.870070 + 0.492929i \(0.164074\pi\)
\(114\) −7.65344 −0.716810
\(115\) 4.33828 + 2.04435i 0.404546 + 0.190636i
\(116\) 1.28662 0.119460
\(117\) −4.36367 + 5.03594i −0.403421 + 0.465573i
\(118\) 9.54961 6.13716i 0.879113 0.564972i
\(119\) 0.393882 + 2.73951i 0.0361071 + 0.251130i
\(120\) 0.415415 + 0.909632i 0.0379220 + 0.0830377i
\(121\) 1.44112 10.0232i 0.131011 0.911198i
\(122\) 3.48809 1.02420i 0.315797 0.0927263i
\(123\) 7.15210 + 4.59637i 0.644883 + 0.414441i
\(124\) −1.41901 + 3.10721i −0.127431 + 0.279035i
\(125\) 0.959493 + 0.281733i 0.0858197 + 0.0251989i
\(126\) 3.13237 + 3.61494i 0.279053 + 0.322045i
\(127\) −10.0424 11.5896i −0.891123 1.02841i −0.999412 0.0342909i \(-0.989083\pi\)
0.108289 0.994119i \(-0.465463\pi\)
\(128\) −0.959493 0.281733i −0.0848080 0.0249019i
\(129\) −3.54603 + 7.76471i −0.312210 + 0.683645i
\(130\) −5.60569 3.60256i −0.491652 0.315966i
\(131\) −16.3944 + 4.81382i −1.43238 + 0.420586i −0.903675 0.428218i \(-0.859141\pi\)
−0.528708 + 0.848804i \(0.677323\pi\)
\(132\) 0.133028 0.925231i 0.0115786 0.0805310i
\(133\) −15.2077 33.3001i −1.31867 2.88749i
\(134\) 1.37174 + 9.54065i 0.118500 + 0.824187i
\(135\) 0.841254 0.540641i 0.0724036 0.0465310i
\(136\) −0.378915 + 0.437291i −0.0324917 + 0.0374974i
\(137\) 13.1523 1.12368 0.561839 0.827246i \(-0.310094\pi\)
0.561839 + 0.827246i \(0.310094\pi\)
\(138\) 2.54433 + 4.06526i 0.216588 + 0.346058i
\(139\) −9.29892 −0.788724 −0.394362 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(140\) −3.13237 + 3.61494i −0.264733 + 0.305518i
\(141\) −1.63337 + 1.04971i −0.137555 + 0.0884012i
\(142\) −1.44615 10.0582i −0.121359 0.844067i
\(143\) 2.58748 + 5.66580i 0.216376 + 0.473798i
\(144\) −0.142315 + 0.989821i −0.0118596 + 0.0824851i
\(145\) 1.23450 0.362483i 0.102520 0.0301026i
\(146\) −10.8728 6.98754i −0.899841 0.578293i
\(147\) −6.59659 + 14.4445i −0.544078 + 1.19136i
\(148\) −2.69229 0.790527i −0.221305 0.0649809i
\(149\) 3.01872 + 3.48379i 0.247303 + 0.285403i 0.865806 0.500379i \(-0.166806\pi\)
−0.618503 + 0.785782i \(0.712261\pi\)
\(150\) 0.654861 + 0.755750i 0.0534692 + 0.0617067i
\(151\) −5.36177 1.57436i −0.436334 0.128119i 0.0561859 0.998420i \(-0.482106\pi\)
−0.492520 + 0.870301i \(0.663924\pi\)
\(152\) 3.17935 6.96181i 0.257880 0.564677i
\(153\) 0.486765 + 0.312825i 0.0393526 + 0.0252904i
\(154\) 4.29001 1.25966i 0.345699 0.101506i
\(155\) −0.486133 + 3.38113i −0.0390471 + 0.271579i
\(156\) −2.76812 6.06133i −0.221627 0.485295i
\(157\) 1.30394 + 9.06908i 0.104065 + 0.723791i 0.973324 + 0.229434i \(0.0736875\pi\)
−0.869259 + 0.494357i \(0.835403\pi\)
\(158\) −3.58531 + 2.30414i −0.285232 + 0.183308i
\(159\) −6.21605 + 7.17370i −0.492965 + 0.568912i
\(160\) −1.00000 −0.0790569
\(161\) −12.6323 + 19.1482i −0.995564 + 1.50909i
\(162\) 1.00000 0.0785674
\(163\) −8.94025 + 10.3176i −0.700254 + 0.808137i −0.988787 0.149334i \(-0.952287\pi\)
0.288533 + 0.957470i \(0.406833\pi\)
\(164\) −7.15210 + 4.59637i −0.558485 + 0.358917i
\(165\) −0.133028 0.925231i −0.0103562 0.0720291i
\(166\) −1.13386 2.48281i −0.0880047 0.192703i
\(167\) −2.67094 + 18.5768i −0.206683 + 1.43751i 0.577198 + 0.816604i \(0.304146\pi\)
−0.783882 + 0.620910i \(0.786763\pi\)
\(168\) −4.58950 + 1.34760i −0.354088 + 0.103969i
\(169\) 26.4173 + 16.9773i 2.03210 + 1.30595i
\(170\) −0.240367 + 0.526330i −0.0184353 + 0.0403677i
\(171\) −7.34342 2.15622i −0.561565 0.164890i
\(172\) −5.58996 6.45116i −0.426230 0.491896i
\(173\) −2.86818 3.31006i −0.218064 0.251659i 0.636169 0.771550i \(-0.280518\pi\)
−0.854233 + 0.519891i \(0.825973\pi\)
\(174\) 1.23450 + 0.362483i 0.0935876 + 0.0274798i
\(175\) −1.98704 + 4.35100i −0.150206 + 0.328905i
\(176\) 0.786357 + 0.505361i 0.0592739 + 0.0380930i
\(177\) 10.8918 3.19813i 0.818680 0.240386i
\(178\) −0.395521 + 2.75091i −0.0296455 + 0.206189i
\(179\) −0.193368 0.423416i −0.0144530 0.0316476i 0.902268 0.431176i \(-0.141901\pi\)
−0.916721 + 0.399528i \(0.869174\pi\)
\(180\) 0.142315 + 0.989821i 0.0106075 + 0.0737769i
\(181\) 9.50365 6.10762i 0.706401 0.453976i −0.137482 0.990504i \(-0.543901\pi\)
0.843882 + 0.536528i \(0.180265\pi\)
\(182\) 20.8725 24.0882i 1.54717 1.78553i
\(183\) 3.63535 0.268733
\(184\) −4.75485 + 0.625635i −0.350532 + 0.0461225i
\(185\) −2.80595 −0.206297
\(186\) −2.23694 + 2.58156i −0.164020 + 0.189289i
\(187\) 0.455001 0.292411i 0.0332730 0.0213832i
\(188\) −0.276318 1.92183i −0.0201526 0.140164i
\(189\) 1.98704 + 4.35100i 0.144536 + 0.316489i
\(190\) 1.08920 7.57554i 0.0790187 0.549587i
\(191\) 20.6288 6.05717i 1.49265 0.438281i 0.569264 0.822155i \(-0.307228\pi\)
0.923386 + 0.383874i \(0.125410\pi\)
\(192\) −0.841254 0.540641i −0.0607122 0.0390174i
\(193\) −4.74279 + 10.3853i −0.341393 + 0.747547i −0.999988 0.00495092i \(-0.998424\pi\)
0.658594 + 0.752498i \(0.271151\pi\)
\(194\) 5.25115 + 1.54188i 0.377010 + 0.110700i
\(195\) −4.36367 5.03594i −0.312489 0.360631i
\(196\) −10.3989 12.0009i −0.742777 0.857210i
\(197\) 6.99875 + 2.05502i 0.498640 + 0.146414i 0.521375 0.853328i \(-0.325419\pi\)
−0.0227351 + 0.999742i \(0.507237\pi\)
\(198\) 0.388307 0.850274i 0.0275958 0.0604263i
\(199\) 1.16826 + 0.750792i 0.0828154 + 0.0532222i 0.581393 0.813623i \(-0.302508\pi\)
−0.498578 + 0.866845i \(0.666144\pi\)
\(200\) −0.959493 + 0.281733i −0.0678464 + 0.0199215i
\(201\) −1.37174 + 9.54065i −0.0967550 + 0.672946i
\(202\) 7.36636 + 16.1301i 0.518295 + 1.13491i
\(203\) 0.875840 + 6.09160i 0.0614719 + 0.427547i
\(204\) −0.486765 + 0.312825i −0.0340804 + 0.0219021i
\(205\) −5.56744 + 6.42517i −0.388847 + 0.448753i
\(206\) −14.4223 −1.00485
\(207\) 1.29595 + 4.61741i 0.0900749 + 0.320932i
\(208\) 6.66350 0.462031
\(209\) −4.68488 + 5.40664i −0.324060 + 0.373985i
\(210\) −4.02393 + 2.58602i −0.277678 + 0.178453i
\(211\) 2.13906 + 14.8775i 0.147259 + 1.02421i 0.920681 + 0.390316i \(0.127634\pi\)
−0.773422 + 0.633891i \(0.781457\pi\)
\(212\) −3.94319 8.63438i −0.270819 0.593012i
\(213\) 1.44615 10.0582i 0.0990889 0.689178i
\(214\) −2.93657 + 0.862255i −0.200740 + 0.0589425i
\(215\) −7.18103 4.61497i −0.489742 0.314738i
\(216\) −0.415415 + 0.909632i −0.0282654 + 0.0618926i
\(217\) −15.6772 4.60326i −1.06424 0.312489i
\(218\) −0.00365544 0.00421860i −0.000247578 0.000285720i
\(219\) −8.46378 9.76772i −0.571929 0.660041i
\(220\) 0.896881 + 0.263348i 0.0604677 + 0.0177549i
\(221\) 1.60169 3.50720i 0.107741 0.235920i
\(222\) −2.36051 1.51701i −0.158427 0.101815i
\(223\) 8.69590 2.55335i 0.582320 0.170985i 0.0227123 0.999742i \(-0.492770\pi\)
0.559608 + 0.828757i \(0.310952\pi\)
\(224\) 0.680728 4.73457i 0.0454831 0.316342i
\(225\) 0.415415 + 0.909632i 0.0276943 + 0.0606421i
\(226\) 0.596792 + 4.15078i 0.0396980 + 0.276106i
\(227\) −3.38194 + 2.17344i −0.224467 + 0.144256i −0.648042 0.761605i \(-0.724412\pi\)
0.423574 + 0.905861i \(0.360775\pi\)
\(228\) 5.01194 5.78408i 0.331924 0.383060i
\(229\) 8.93990 0.590765 0.295383 0.955379i \(-0.404553\pi\)
0.295383 + 0.955379i \(0.404553\pi\)
\(230\) −4.38598 + 1.93989i −0.289203 + 0.127912i
\(231\) 4.47112 0.294178
\(232\) −0.842558 + 0.972364i −0.0553167 + 0.0638388i
\(233\) −17.9378 + 11.5279i −1.17514 + 0.755220i −0.974487 0.224442i \(-0.927944\pi\)
−0.200657 + 0.979662i \(0.564308\pi\)
\(234\) −0.948315 6.59568i −0.0619933 0.431173i
\(235\) −0.806568 1.76614i −0.0526147 0.115210i
\(236\) −1.61551 + 11.2361i −0.105161 + 0.731408i
\(237\) −4.08923 + 1.20071i −0.265624 + 0.0779943i
\(238\) −2.32832 1.49632i −0.150923 0.0969921i
\(239\) 11.3623 24.8800i 0.734969 1.60936i −0.0566894 0.998392i \(-0.518054\pi\)
0.791658 0.610965i \(-0.209218\pi\)
\(240\) −0.959493 0.281733i −0.0619350 0.0181858i
\(241\) 5.17393 + 5.97103i 0.333282 + 0.384628i 0.897512 0.440990i \(-0.145372\pi\)
−0.564230 + 0.825618i \(0.690827\pi\)
\(242\) 6.63128 + 7.65291i 0.426275 + 0.491948i
\(243\) 0.959493 + 0.281733i 0.0615515 + 0.0180732i
\(244\) −1.51018 + 3.30683i −0.0966792 + 0.211698i
\(245\) −13.3587 8.58512i −0.853456 0.548483i
\(246\) −8.15734 + 2.39521i −0.520093 + 0.152713i
\(247\) −7.25787 + 50.4796i −0.461807 + 3.21194i
\(248\) −1.41901 3.10721i −0.0901075 0.197308i
\(249\) −0.388443 2.70168i −0.0246166 0.171212i
\(250\) −0.841254 + 0.540641i −0.0532055 + 0.0341931i
\(251\) 12.3996 14.3098i 0.782653 0.903229i −0.214645 0.976692i \(-0.568860\pi\)
0.997298 + 0.0734627i \(0.0234050\pi\)
\(252\) −4.78325 −0.301317
\(253\) 4.42929 + 0.691059i 0.278467 + 0.0434465i
\(254\) 15.3352 0.962218
\(255\) −0.378915 + 0.437291i −0.0237286 + 0.0273842i
\(256\) 0.841254 0.540641i 0.0525783 0.0337901i
\(257\) −0.447910 3.11528i −0.0279399 0.194326i 0.971071 0.238791i \(-0.0767509\pi\)
−0.999011 + 0.0444645i \(0.985842\pi\)
\(258\) −3.54603 7.76471i −0.220766 0.483410i
\(259\) 1.91009 13.2850i 0.118687 0.825487i
\(260\) 6.39358 1.87733i 0.396513 0.116427i
\(261\) 1.08238 + 0.695600i 0.0669974 + 0.0430566i
\(262\) 7.09799 15.5424i 0.438515 0.960214i
\(263\) −22.8073 6.69684i −1.40636 0.412945i −0.511497 0.859285i \(-0.670909\pi\)
−0.894863 + 0.446340i \(0.852727\pi\)
\(264\) 0.612128 + 0.706433i 0.0376739 + 0.0434779i
\(265\) −6.21605 7.17370i −0.381849 0.440677i
\(266\) 35.1254 + 10.3138i 2.15368 + 0.632377i
\(267\) −1.15452 + 2.52804i −0.0706554 + 0.154714i
\(268\) −8.10864 5.21111i −0.495314 0.318319i
\(269\) 25.9521 7.62022i 1.58233 0.464613i 0.631768 0.775158i \(-0.282330\pi\)
0.950559 + 0.310545i \(0.100512\pi\)
\(270\) −0.142315 + 0.989821i −0.00866101 + 0.0602386i
\(271\) 9.84464 + 21.5568i 0.598020 + 1.30948i 0.930473 + 0.366360i \(0.119396\pi\)
−0.332454 + 0.943120i \(0.607876\pi\)
\(272\) −0.0823460 0.572729i −0.00499296 0.0347268i
\(273\) 26.8135 17.2320i 1.62282 1.04293i
\(274\) −8.61294 + 9.93986i −0.520327 + 0.600489i
\(275\) 0.934745 0.0563672
\(276\) −4.73851 0.739303i −0.285224 0.0445008i
\(277\) 6.73723 0.404801 0.202400 0.979303i \(-0.435126\pi\)
0.202400 + 0.979303i \(0.435126\pi\)
\(278\) 6.08950 7.02766i 0.365224 0.421491i
\(279\) −2.87363 + 1.84677i −0.172040 + 0.110563i
\(280\) −0.680728 4.73457i −0.0406813 0.282945i
\(281\) 5.05038 + 11.0588i 0.301281 + 0.659713i 0.998358 0.0572834i \(-0.0182439\pi\)
−0.697077 + 0.716996i \(0.745517\pi\)
\(282\) 0.276318 1.92183i 0.0164545 0.114444i
\(283\) −11.1687 + 3.27942i −0.663909 + 0.194941i −0.596289 0.802770i \(-0.703359\pi\)
−0.0676202 + 0.997711i \(0.521541\pi\)
\(284\) 8.54853 + 5.49381i 0.507262 + 0.325997i
\(285\) 3.17935 6.96181i 0.188329 0.412382i
\(286\) −5.97637 1.75482i −0.353390 0.103765i
\(287\) −26.6305 30.7332i −1.57195 1.81412i
\(288\) −0.654861 0.755750i −0.0385880 0.0445330i
\(289\) 15.9901 + 4.69513i 0.940597 + 0.276184i
\(290\) −0.534482 + 1.17035i −0.0313859 + 0.0687255i
\(291\) 4.60404 + 2.95884i 0.269894 + 0.173450i
\(292\) 12.4010 3.64126i 0.725714 0.213089i
\(293\) 0.337676 2.34859i 0.0197272 0.137206i −0.977578 0.210576i \(-0.932466\pi\)
0.997305 + 0.0733697i \(0.0233753\pi\)
\(294\) −6.59659 14.4445i −0.384721 0.842422i
\(295\) 1.61551 + 11.2361i 0.0940585 + 0.654191i
\(296\) 2.36051 1.51701i 0.137202 0.0881744i
\(297\) 0.612128 0.706433i 0.0355193 0.0409914i
\(298\) −4.60971 −0.267033
\(299\) 29.2260 12.9265i 1.69018 0.747556i
\(300\) −1.00000 −0.0577350
\(301\) 26.7382 30.8575i 1.54116 1.77860i
\(302\) 4.70103 3.02117i 0.270514 0.173849i
\(303\) 2.52360 + 17.5520i 0.144977 + 1.00834i
\(304\) 3.17935 + 6.96181i 0.182348 + 0.399287i
\(305\) −0.517364 + 3.59835i −0.0296242 + 0.206041i
\(306\) −0.555181 + 0.163016i −0.0317376 + 0.00931899i
\(307\) 3.06637 + 1.97064i 0.175007 + 0.112470i 0.625212 0.780455i \(-0.285013\pi\)
−0.450205 + 0.892925i \(0.648649\pi\)
\(308\) −1.85737 + 4.06708i −0.105834 + 0.231743i
\(309\) −13.8381 4.06324i −0.787223 0.231150i
\(310\) −2.23694 2.58156i −0.127049 0.146623i
\(311\) −19.5570 22.5700i −1.10898 1.27983i −0.956568 0.291509i \(-0.905843\pi\)
−0.152408 0.988318i \(-0.548703\pi\)
\(312\) 6.39358 + 1.87733i 0.361965 + 0.106283i
\(313\) 0.939940 2.05818i 0.0531286 0.116335i −0.881206 0.472732i \(-0.843268\pi\)
0.934335 + 0.356397i \(0.115995\pi\)
\(314\) −7.70785 4.95353i −0.434979 0.279544i
\(315\) −4.58950 + 1.34760i −0.258589 + 0.0759286i
\(316\) 0.606527 4.21849i 0.0341198 0.237309i
\(317\) −0.986163 2.15940i −0.0553884 0.121284i 0.879914 0.475133i \(-0.157600\pi\)
−0.935303 + 0.353849i \(0.884873\pi\)
\(318\) −1.35088 9.39555i −0.0757534 0.526877i
\(319\) 1.01174 0.650209i 0.0566468 0.0364047i
\(320\) 0.654861 0.755750i 0.0366078 0.0422477i
\(321\) −3.06054 −0.170823
\(322\) −6.19887 22.0863i −0.345450 1.23082i
\(323\) 4.42842 0.246404
\(324\) −0.654861 + 0.755750i −0.0363812 + 0.0419861i
\(325\) 5.60569 3.60256i 0.310948 0.199834i
\(326\) −1.94290 13.5132i −0.107607 0.748426i
\(327\) −0.00231885 0.00507758i −0.000128233 0.000280791i
\(328\) 1.20992 8.41518i 0.0668067 0.464651i
\(329\) 8.91096 2.61649i 0.491277 0.144252i
\(330\) 0.786357 + 0.505361i 0.0432876 + 0.0278192i
\(331\) −12.6798 + 27.7648i −0.696942 + 1.52609i 0.146697 + 0.989181i \(0.453136\pi\)
−0.843640 + 0.536910i \(0.819592\pi\)
\(332\) 2.61890 + 0.768979i 0.143731 + 0.0422032i
\(333\) −1.83751 2.12059i −0.100695 0.116208i
\(334\) −12.2903 14.1838i −0.672495 0.776101i
\(335\) −9.24832 2.71555i −0.505290 0.148366i
\(336\) 1.98704 4.35100i 0.108402 0.237367i
\(337\) 16.8407 + 10.8229i 0.917372 + 0.589559i 0.911894 0.410426i \(-0.134620\pi\)
0.00547776 + 0.999985i \(0.498256\pi\)
\(338\) −30.1303 + 8.84704i −1.63887 + 0.481216i
\(339\) −0.596792 + 4.15078i −0.0324133 + 0.225440i
\(340\) −0.240367 0.526330i −0.0130357 0.0285443i
\(341\) 0.454410 + 3.16049i 0.0246077 + 0.171150i
\(342\) 6.43848 4.13776i 0.348153 0.223744i
\(343\) 27.8139 32.0990i 1.50181 1.73318i
\(344\) 8.53610 0.460236
\(345\) −4.75485 + 0.625635i −0.255992 + 0.0336831i
\(346\) 4.37983 0.235461
\(347\) 6.27030 7.23632i 0.336607 0.388466i −0.562060 0.827097i \(-0.689991\pi\)
0.898667 + 0.438631i \(0.144536\pi\)
\(348\) −1.08238 + 0.695600i −0.0580214 + 0.0372881i
\(349\) 0.696797 + 4.84633i 0.0372987 + 0.259418i 0.999935 0.0113786i \(-0.00362201\pi\)
−0.962637 + 0.270797i \(0.912713\pi\)
\(350\) −1.98704 4.35100i −0.106212 0.232571i
\(351\) 0.948315 6.59568i 0.0506173 0.352051i
\(352\) −0.896881 + 0.263348i −0.0478039 + 0.0140365i
\(353\) −5.90875 3.79732i −0.314491 0.202111i 0.373867 0.927482i \(-0.378032\pi\)
−0.688358 + 0.725371i \(0.741668\pi\)
\(354\) −4.71564 + 10.3258i −0.250634 + 0.548811i
\(355\) 9.75004 + 2.86287i 0.517478 + 0.151945i
\(356\) −1.81999 2.10037i −0.0964590 0.111320i
\(357\) −1.81245 2.09167i −0.0959248 0.110703i
\(358\) 0.446626 + 0.131141i 0.0236049 + 0.00693103i
\(359\) −12.7164 + 27.8451i −0.671148 + 1.46961i 0.200610 + 0.979671i \(0.435708\pi\)
−0.871758 + 0.489937i \(0.837020\pi\)
\(360\) −0.841254 0.540641i −0.0443380 0.0284943i
\(361\) −37.9720 + 11.1496i −1.99853 + 0.586821i
\(362\) −1.60773 + 11.1820i −0.0845005 + 0.587714i
\(363\) 4.20660 + 9.21116i 0.220789 + 0.483461i
\(364\) 4.53603 + 31.5488i 0.237753 + 1.65361i
\(365\) 10.8728 6.98754i 0.569109 0.365744i
\(366\) −2.38065 + 2.74741i −0.124438 + 0.143610i
\(367\) 21.4469 1.11952 0.559760 0.828655i \(-0.310893\pi\)
0.559760 + 0.828655i \(0.310893\pi\)
\(368\) 2.64094 4.00318i 0.137668 0.208680i
\(369\) −8.50172 −0.442582
\(370\) 1.83751 2.12059i 0.0955273 0.110244i
\(371\) 38.1958 24.5470i 1.98303 1.27442i
\(372\) −0.486133 3.38113i −0.0252048 0.175303i
\(373\) −3.67528 8.04774i −0.190299 0.416696i 0.790300 0.612719i \(-0.209924\pi\)
−0.980599 + 0.196023i \(0.937197\pi\)
\(374\) −0.0769725 + 0.535356i −0.00398015 + 0.0276826i
\(375\) −0.959493 + 0.281733i −0.0495480 + 0.0145486i
\(376\) 1.63337 + 1.04971i 0.0842349 + 0.0541345i
\(377\) 3.56152 7.79865i 0.183428 0.401651i
\(378\) −4.58950 1.34760i −0.236058 0.0693130i
\(379\) −12.9317 14.9240i −0.664257 0.766593i 0.319210 0.947684i \(-0.396583\pi\)
−0.983466 + 0.181091i \(0.942037\pi\)
\(380\) 5.01194 + 5.78408i 0.257107 + 0.296717i
\(381\) 14.7140 + 4.32043i 0.753824 + 0.221343i
\(382\) −8.93130 + 19.5568i −0.456965 + 1.00061i
\(383\) 0.534117 + 0.343256i 0.0272921 + 0.0175396i 0.554216 0.832373i \(-0.313018\pi\)
−0.526924 + 0.849913i \(0.676655\pi\)
\(384\) 0.959493 0.281733i 0.0489639 0.0143771i
\(385\) −0.636307 + 4.42561i −0.0324292 + 0.225550i
\(386\) −4.74279 10.3853i −0.241402 0.528596i
\(387\) −1.21481 8.44922i −0.0617525 0.429498i
\(388\) −4.60404 + 2.95884i −0.233735 + 0.150212i
\(389\) −18.6400 + 21.5117i −0.945085 + 1.09069i 0.0506769 + 0.998715i \(0.483862\pi\)
−0.995762 + 0.0919709i \(0.970683\pi\)
\(390\) 6.66350 0.337420
\(391\) −1.47220 2.35224i −0.0744523 0.118958i
\(392\) 15.8795 0.802037
\(393\) 11.1893 12.9131i 0.564424 0.651380i
\(394\) −6.13628 + 3.94355i −0.309141 + 0.198673i
\(395\) −0.606527 4.21849i −0.0305177 0.212255i
\(396\) 0.388307 + 0.850274i 0.0195132 + 0.0427279i
\(397\) −1.76486 + 12.2749i −0.0885757 + 0.616058i 0.896385 + 0.443277i \(0.146184\pi\)
−0.984960 + 0.172781i \(0.944725\pi\)
\(398\) −1.33246 + 0.391244i −0.0667900 + 0.0196113i
\(399\) 30.7969 + 19.7920i 1.54177 + 0.990837i
\(400\) 0.415415 0.909632i 0.0207708 0.0454816i
\(401\) −6.19434 1.81882i −0.309330 0.0908276i 0.123383 0.992359i \(-0.460626\pi\)
−0.432713 + 0.901532i \(0.642444\pi\)
\(402\) −6.31204 7.28449i −0.314816 0.363317i
\(403\) 14.9058 + 17.2022i 0.742512 + 0.856905i
\(404\) −17.0142 4.99583i −0.846490 0.248552i
\(405\) −0.415415 + 0.909632i −0.0206421 + 0.0452000i
\(406\) −5.17728 3.32723i −0.256944 0.165128i
\(407\) −2.51660 + 0.738941i −0.124743 + 0.0366279i
\(408\) 0.0823460 0.572729i 0.00407674 0.0283543i
\(409\) 4.56170 + 9.98872i 0.225561 + 0.493910i 0.988248 0.152857i \(-0.0488475\pi\)
−0.762687 + 0.646768i \(0.776120\pi\)
\(410\) −1.20992 8.41518i −0.0597537 0.415596i
\(411\) −11.0644 + 7.11068i −0.545768 + 0.350744i
\(412\) 9.44461 10.8997i 0.465303 0.536988i
\(413\) −54.2978 −2.67182
\(414\) −4.33828 2.04435i −0.213215 0.100474i
\(415\) 2.72947 0.133984
\(416\) −4.36367 + 5.03594i −0.213946 + 0.246907i
\(417\) 7.82275 5.02738i 0.383082 0.246192i
\(418\) −1.01812 7.08119i −0.0497980 0.346353i
\(419\) −1.97979 4.33513i −0.0967190 0.211785i 0.855088 0.518483i \(-0.173503\pi\)
−0.951807 + 0.306698i \(0.900776\pi\)
\(420\) 0.680728 4.73457i 0.0332161 0.231023i
\(421\) −19.8677 + 5.83368i −0.968293 + 0.284316i −0.727383 0.686231i \(-0.759264\pi\)
−0.240909 + 0.970548i \(0.577446\pi\)
\(422\) −12.6444 8.12608i −0.615521 0.395571i
\(423\) 0.806568 1.76614i 0.0392167 0.0858726i
\(424\) 9.10767 + 2.67425i 0.442308 + 0.129873i
\(425\) −0.378915 0.437291i −0.0183801 0.0212117i
\(426\) 6.65447 + 7.67967i 0.322410 + 0.372081i
\(427\) −16.6844 4.89899i −0.807416 0.237079i
\(428\) 1.27140 2.78397i 0.0614552 0.134568i
\(429\) −5.23989 3.36748i −0.252984 0.162583i
\(430\) 8.19033 2.40490i 0.394973 0.115975i
\(431\) 2.30241 16.0136i 0.110903 0.771348i −0.856142 0.516741i \(-0.827145\pi\)
0.967045 0.254607i \(-0.0819460\pi\)
\(432\) −0.415415 0.909632i −0.0199867 0.0437647i
\(433\) −3.96136 27.5519i −0.190371 1.32406i −0.831028 0.556231i \(-0.812247\pi\)
0.640657 0.767827i \(-0.278662\pi\)
\(434\) 13.7453 8.83358i 0.659797 0.424025i
\(435\) −0.842558 + 0.972364i −0.0403976 + 0.0466213i
\(436\) 0.00558201 0.000267330
\(437\) 27.4497 + 24.3668i 1.31310 + 1.16562i
\(438\) 12.9245 0.617559
\(439\) −12.9902 + 14.9915i −0.619991 + 0.715507i −0.975705 0.219087i \(-0.929692\pi\)
0.355715 + 0.934595i \(0.384237\pi\)
\(440\) −0.786357 + 0.505361i −0.0374881 + 0.0240922i
\(441\) −2.25989 15.7179i −0.107614 0.748471i
\(442\) 1.60169 + 3.50720i 0.0761844 + 0.166821i
\(443\) −4.10340 + 28.5398i −0.194958 + 1.35597i 0.623691 + 0.781671i \(0.285633\pi\)
−0.818649 + 0.574294i \(0.805277\pi\)
\(444\) 2.69229 0.790527i 0.127770 0.0375167i
\(445\) −2.33801 1.50255i −0.110832 0.0712275i
\(446\) −3.76491 + 8.24401i −0.178274 + 0.390365i
\(447\) −4.42299 1.29871i −0.209200 0.0614267i
\(448\) 3.13237 + 3.61494i 0.147990 + 0.170790i
\(449\) −21.9732 25.3585i −1.03698 1.19674i −0.980130 0.198357i \(-0.936440\pi\)
−0.0568505 0.998383i \(-0.518106\pi\)
\(450\) −0.959493 0.281733i −0.0452309 0.0132810i
\(451\) −3.30128 + 7.22879i −0.155451 + 0.340390i
\(452\) −3.52777 2.26716i −0.165932 0.106638i
\(453\) 5.36177 1.57436i 0.251918 0.0739697i
\(454\) 0.572123 3.97920i 0.0268511 0.186753i
\(455\) 13.2406 + 28.9929i 0.620730 + 1.35921i
\(456\) 1.08920 + 7.57554i 0.0510064 + 0.354757i
\(457\) 22.7974 14.6510i 1.06642 0.685344i 0.115035 0.993361i \(-0.463302\pi\)
0.951381 + 0.308018i \(0.0996656\pi\)
\(458\) −5.85439 + 6.75633i −0.273558 + 0.315702i
\(459\) −0.578619 −0.0270076
\(460\) 1.40614 4.58506i 0.0655615 0.213780i
\(461\) 34.7252 1.61731 0.808656 0.588282i \(-0.200195\pi\)
0.808656 + 0.588282i \(0.200195\pi\)
\(462\) −2.92796 + 3.37905i −0.136221 + 0.157208i
\(463\) 24.5438 15.7734i 1.14065 0.733050i 0.172892 0.984941i \(-0.444689\pi\)
0.967756 + 0.251891i \(0.0810523\pi\)
\(464\) −0.183105 1.27353i −0.00850046 0.0591220i
\(465\) −1.41901 3.10721i −0.0658052 0.144093i
\(466\) 3.03454 21.1057i 0.140572 0.977702i
\(467\) −8.67569 + 2.54741i −0.401463 + 0.117880i −0.476230 0.879321i \(-0.657997\pi\)
0.0747667 + 0.997201i \(0.476179\pi\)
\(468\) 5.60569 + 3.60256i 0.259123 + 0.166528i
\(469\) 19.1526 41.9382i 0.884383 1.93653i
\(470\) 1.86295 + 0.547011i 0.0859314 + 0.0252317i
\(471\) −6.00006 6.92443i −0.276468 0.319061i
\(472\) −7.43375 8.57900i −0.342166 0.394881i
\(473\) −7.65587 2.24797i −0.352017 0.103362i
\(474\) 1.77044 3.87673i 0.0813192 0.178064i
\(475\) 6.43848 + 4.13776i 0.295418 + 0.189853i
\(476\) 2.65557 0.779746i 0.121718 0.0357396i
\(477\) 1.35088 9.39555i 0.0618524 0.430193i
\(478\) 11.3623 + 24.8800i 0.519701 + 1.13799i
\(479\) −4.57667 31.8315i −0.209114 1.45442i −0.776058 0.630661i \(-0.782784\pi\)
0.566945 0.823756i \(-0.308125\pi\)
\(480\) 0.841254 0.540641i 0.0383978 0.0246768i
\(481\) −12.2442 + 14.1306i −0.558288 + 0.644299i
\(482\) −7.90081 −0.359872
\(483\) 0.274645 22.9380i 0.0124968 1.04372i
\(484\) −10.1263 −0.460284
\(485\) −3.58394 + 4.13609i −0.162739 + 0.187810i
\(486\) −0.841254 + 0.540641i −0.0381600 + 0.0245240i
\(487\) −1.36697 9.50745i −0.0619431 0.430824i −0.997069 0.0765081i \(-0.975623\pi\)
0.935126 0.354316i \(-0.115286\pi\)
\(488\) −1.51018 3.30683i −0.0683625 0.149693i
\(489\) 1.94290 13.5132i 0.0878611 0.611087i
\(490\) 15.2363 4.47378i 0.688305 0.202105i
\(491\) 19.8137 + 12.7335i 0.894179 + 0.574654i 0.905059 0.425287i \(-0.139827\pi\)
−0.0108798 + 0.999941i \(0.503463\pi\)
\(492\) 3.53174 7.73343i 0.159223 0.348650i
\(493\) −0.714308 0.209740i −0.0321708 0.00944620i
\(494\) −33.3970 38.5422i −1.50260 1.73410i
\(495\) 0.612128 + 0.706433i 0.0275131 + 0.0317518i
\(496\) 3.27753 + 0.962369i 0.147165 + 0.0432116i
\(497\) −20.1916 + 44.2134i −0.905716 + 1.98324i
\(498\) 2.29617 + 1.47566i 0.102894 + 0.0661259i
\(499\) −2.76768 + 0.812665i −0.123898 + 0.0363799i −0.343094 0.939301i \(-0.611475\pi\)
0.219195 + 0.975681i \(0.429657\pi\)
\(500\) 0.142315 0.989821i 0.00636451 0.0442662i
\(501\) −7.79643 17.0718i −0.348319 0.762712i
\(502\) 2.69468 + 18.7419i 0.120269 + 0.836492i
\(503\) 31.4778 20.2295i 1.40352 0.901990i 0.403607 0.914932i \(-0.367756\pi\)
0.999916 + 0.0129423i \(0.00411979\pi\)
\(504\) 3.13237 3.61494i 0.139527 0.161022i
\(505\) −17.7325 −0.789087
\(506\) −3.42284 + 2.89489i −0.152164 + 0.128694i
\(507\) −31.4023 −1.39462
\(508\) −10.0424 + 11.5896i −0.445561 + 0.514205i
\(509\) −4.50239 + 2.89351i −0.199565 + 0.128253i −0.636607 0.771189i \(-0.719663\pi\)
0.437042 + 0.899441i \(0.356026\pi\)
\(510\) −0.0823460 0.572729i −0.00364634 0.0253609i
\(511\) 25.6815 + 56.2347i 1.13608 + 2.48768i
\(512\) −0.142315 + 0.989821i −0.00628949 + 0.0437443i
\(513\) 7.34342 2.15622i 0.324220 0.0951995i
\(514\) 2.64769 + 1.70157i 0.116785 + 0.0750530i
\(515\) 5.99125 13.1190i 0.264006 0.578093i
\(516\) 8.19033 + 2.40490i 0.360559 + 0.105870i
\(517\) −1.18851 1.37161i −0.0522704 0.0603232i
\(518\) 8.78925 + 10.1433i 0.386178 + 0.445673i
\(519\) 4.20242 + 1.23394i 0.184466 + 0.0541640i
\(520\) −2.76812 + 6.06133i −0.121390 + 0.265807i
\(521\) −12.6519 8.13087i −0.554289 0.356220i 0.233315 0.972401i \(-0.425043\pi\)
−0.787604 + 0.616181i \(0.788679\pi\)
\(522\) −1.23450 + 0.362483i −0.0540328 + 0.0158655i
\(523\) −2.00655 + 13.9558i −0.0877402 + 0.610247i 0.897749 + 0.440508i \(0.145202\pi\)
−0.985489 + 0.169739i \(0.945708\pi\)
\(524\) 7.09799 + 15.5424i 0.310077 + 0.678974i
\(525\) −0.680728 4.73457i −0.0297094 0.206633i
\(526\) 19.9968 12.8511i 0.871900 0.560336i
\(527\) 1.29433 1.49374i 0.0563820 0.0650683i
\(528\) −0.934745 −0.0406795
\(529\) 3.81739 22.6810i 0.165974 0.986130i
\(530\) 9.49217 0.412314
\(531\) −7.43375 + 8.57900i −0.322597 + 0.372297i
\(532\) −30.7969 + 19.7920i −1.33521 + 0.858090i
\(533\) 8.06231 + 56.0746i 0.349217 + 2.42886i
\(534\) −1.15452 2.52804i −0.0499609 0.109399i
\(535\) 0.435561 3.02939i 0.0188309 0.130972i
\(536\) 9.24832 2.71555i 0.399467 0.117294i
\(537\) 0.391588 + 0.251658i 0.0168983 + 0.0108598i
\(538\) −11.2360 + 24.6035i −0.484419 + 1.06073i
\(539\) −14.2420 4.18184i −0.613448 0.180125i
\(540\) −0.654861 0.755750i −0.0281807 0.0325223i
\(541\) 28.1867 + 32.5292i 1.21184 + 1.39854i 0.892589 + 0.450872i \(0.148887\pi\)
0.319254 + 0.947669i \(0.396568\pi\)
\(542\) −22.7384 6.67659i −0.976697 0.286784i
\(543\) −4.69295 + 10.2761i −0.201394 + 0.440990i
\(544\) 0.486765 + 0.312825i 0.0208699 + 0.0134123i
\(545\) 0.00535590 0.00157264i 0.000229422 6.73643e-5i
\(546\) −4.53603 + 31.5488i −0.194124 + 1.35016i
\(547\) −14.5496 31.8592i −0.622096 1.36220i −0.913985 0.405748i \(-0.867011\pi\)
0.291889 0.956452i \(-0.405716\pi\)
\(548\) −1.87177 13.0184i −0.0799581 0.556121i
\(549\) −3.05825 + 1.96542i −0.130523 + 0.0838820i
\(550\) −0.612128 + 0.706433i −0.0261012 + 0.0301224i
\(551\) 9.84708 0.419500
\(552\) 3.66179 3.09698i 0.155856 0.131816i
\(553\) 20.3856 0.866884
\(554\) −4.41195 + 5.09166i −0.187446 + 0.216324i
\(555\) 2.36051 1.51701i 0.100198 0.0643935i
\(556\) 1.32337 + 9.20427i 0.0561236 + 0.390348i
\(557\) 4.79460 + 10.4987i 0.203154 + 0.444844i 0.983597 0.180383i \(-0.0577336\pi\)
−0.780443 + 0.625227i \(0.785006\pi\)
\(558\) 0.486133 3.38113i 0.0205796 0.143134i
\(559\) −54.5763 + 16.0250i −2.30833 + 0.677787i
\(560\) 4.02393 + 2.58602i 0.170042 + 0.109279i
\(561\) −0.224682 + 0.491984i −0.00948607 + 0.0207716i
\(562\) −11.6650 3.42515i −0.492057 0.144481i
\(563\) −8.94836 10.3270i −0.377128 0.435229i 0.535177 0.844740i \(-0.320245\pi\)
−0.912305 + 0.409511i \(0.865699\pi\)
\(564\) 1.27148 + 1.46736i 0.0535388 + 0.0617870i
\(565\) −4.02360 1.18144i −0.169274 0.0497034i
\(566\) 4.83551 10.5883i 0.203252 0.445059i
\(567\) −4.02393 2.58602i −0.168989 0.108603i
\(568\) −9.75004 + 2.86287i −0.409102 + 0.120123i
\(569\) −0.0829117 + 0.576663i −0.00347584 + 0.0241750i −0.991486 0.130217i \(-0.958433\pi\)
0.988010 + 0.154392i \(0.0493418\pi\)
\(570\) 3.17935 + 6.96181i 0.133168 + 0.291598i
\(571\) −3.56688 24.8082i −0.149269 1.03819i −0.917419 0.397922i \(-0.869732\pi\)
0.768150 0.640270i \(-0.221177\pi\)
\(572\) 5.23989 3.36748i 0.219091 0.140801i
\(573\) −14.0793 + 16.2484i −0.588172 + 0.678787i
\(574\) 40.6659 1.69736
\(575\) 0.0574180 4.79549i 0.00239450 0.199986i
\(576\) 1.00000 0.0416667
\(577\) 3.62857 4.18759i 0.151059 0.174332i −0.675176 0.737656i \(-0.735933\pi\)
0.826236 + 0.563325i \(0.190478\pi\)
\(578\) −14.0197 + 9.00989i −0.583141 + 0.374762i
\(579\) −1.62481 11.3008i −0.0675247 0.469644i
\(580\) −0.534482 1.17035i −0.0221932 0.0485963i
\(581\) −1.85802 + 12.9228i −0.0770838 + 0.536130i
\(582\) −5.25115 + 1.54188i −0.217667 + 0.0639128i
\(583\) −7.46424 4.79698i −0.309137 0.198670i
\(584\) −5.36905 + 11.7566i −0.222173 + 0.486491i
\(585\) 6.39358 + 1.87733i 0.264342 + 0.0776179i
\(586\) 1.55381 + 1.79320i 0.0641874 + 0.0740762i
\(587\) −4.04160 4.66426i −0.166815 0.192514i 0.666187 0.745785i \(-0.267925\pi\)
−0.833002 + 0.553270i \(0.813380\pi\)
\(588\) 15.2363 + 4.47378i 0.628334 + 0.184496i
\(589\) −10.8603 + 23.7808i −0.447492 + 0.979872i
\(590\) −9.54961 6.13716i −0.393151 0.252663i
\(591\) −6.99875 + 2.05502i −0.287890 + 0.0845321i
\(592\) −0.399328 + 2.77739i −0.0164123 + 0.114150i
\(593\) −12.4921 27.3538i −0.512988 1.12329i −0.972027 0.234871i \(-0.924533\pi\)
0.459039 0.888416i \(-0.348194\pi\)
\(594\) 0.133028 + 0.925231i 0.00545821 + 0.0379627i
\(595\) 2.32832 1.49632i 0.0954519 0.0613432i
\(596\) 3.01872 3.48379i 0.123652 0.142702i
\(597\) −1.38871 −0.0568360
\(598\) −9.36980 + 30.5526i −0.383160 + 1.24939i
\(599\) 39.0335 1.59487 0.797434 0.603407i \(-0.206190\pi\)
0.797434 + 0.603407i \(0.206190\pi\)
\(600\) 0.654861 0.755750i 0.0267346 0.0308533i
\(601\) −17.8549 + 11.4747i −0.728317 + 0.468061i −0.851521 0.524321i \(-0.824319\pi\)
0.123204 + 0.992381i \(0.460683\pi\)
\(602\) 5.81077 + 40.4148i 0.236829 + 1.64718i
\(603\) −4.00408 8.76772i −0.163059 0.357049i
\(604\) −0.795273 + 5.53124i −0.0323592 + 0.225063i
\(605\) −9.71607 + 2.85289i −0.395014 + 0.115987i
\(606\) −14.9175 9.58693i −0.605984 0.389442i
\(607\) −10.2330 + 22.4072i −0.415346 + 0.909480i 0.580135 + 0.814520i \(0.303000\pi\)
−0.995481 + 0.0949603i \(0.969728\pi\)
\(608\) −7.34342 2.15622i −0.297815 0.0874464i
\(609\) −4.03017 4.65107i −0.163311 0.188471i
\(610\) −2.38065 2.74741i −0.0963896 0.111239i
\(611\) −12.4138 3.64501i −0.502207 0.147461i
\(612\) 0.240367 0.526330i 0.00971626 0.0212756i
\(613\) 7.25054 + 4.65964i 0.292847 + 0.188201i 0.678812 0.734312i \(-0.262495\pi\)
−0.385965 + 0.922513i \(0.626132\pi\)
\(614\) −3.49735 + 1.02691i −0.141142 + 0.0414429i
\(615\) 1.20992 8.41518i 0.0487887 0.339333i
\(616\) −1.85737 4.06708i −0.0748356 0.163867i
\(617\) 3.93950 + 27.3998i 0.158598 + 1.10308i 0.901219 + 0.433364i \(0.142673\pi\)
−0.742621 + 0.669712i \(0.766418\pi\)
\(618\) 12.1328 7.79730i 0.488054 0.313653i
\(619\) 2.53314 2.92340i 0.101815 0.117501i −0.702555 0.711630i \(-0.747957\pi\)
0.804370 + 0.594128i \(0.202503\pi\)
\(620\) 3.41590 0.137186
\(621\) −3.58659 3.18377i −0.143925 0.127760i
\(622\) 29.8644 1.19745
\(623\) 8.70545 10.0466i 0.348777 0.402510i
\(624\) −5.60569 + 3.60256i −0.224407 + 0.144218i
\(625\) −0.142315 0.989821i −0.00569259 0.0395929i
\(626\) 0.939940 + 2.05818i 0.0375676 + 0.0822615i
\(627\) 1.01812 7.08119i 0.0406599 0.282796i
\(628\) 8.79120 2.58133i 0.350807 0.103006i
\(629\) 1.36584 + 0.877770i 0.0544595 + 0.0349990i
\(630\) 1.98704 4.35100i 0.0791654 0.173348i
\(631\) −17.5707 5.15923i −0.699480 0.205386i −0.0873903 0.996174i \(-0.527853\pi\)
−0.612090 + 0.790788i \(0.709671\pi\)
\(632\) 2.79093 + 3.22091i 0.111017 + 0.128121i
\(633\) −9.84286 11.3593i −0.391218 0.451490i
\(634\) 2.27776 + 0.668811i 0.0904615 + 0.0265619i
\(635\) −6.37049 + 13.9494i −0.252805 + 0.553566i
\(636\) 7.98532 + 5.13186i 0.316639 + 0.203491i
\(637\) −101.527 + 29.8110i −4.02265 + 1.18116i
\(638\) −0.171157 + 1.19042i −0.00677616 + 0.0471293i
\(639\) 4.22130 + 9.24337i 0.166992 + 0.365662i
\(640\) 0.142315 + 0.989821i 0.00562549 + 0.0391261i
\(641\) 37.0696 23.8232i 1.46416 0.940960i 0.465733 0.884925i \(-0.345791\pi\)
0.998429 0.0560347i \(-0.0178458\pi\)
\(642\) 2.00423 2.31300i 0.0791006 0.0912870i
\(643\) −14.6599 −0.578132 −0.289066 0.957309i \(-0.593345\pi\)
−0.289066 + 0.957309i \(0.593345\pi\)
\(644\) 20.7511 + 9.77863i 0.817707 + 0.385332i
\(645\) 8.53610 0.336109
\(646\) −2.90000 + 3.34678i −0.114099 + 0.131677i
\(647\) −11.5633 + 7.43131i −0.454602 + 0.292155i −0.747833 0.663887i \(-0.768906\pi\)
0.293231 + 0.956041i \(0.405269\pi\)
\(648\) −0.142315 0.989821i −0.00559065 0.0388839i
\(649\) 4.40792 + 9.65201i 0.173026 + 0.378874i
\(650\) −0.948315 + 6.59568i −0.0371960 + 0.258704i
\(651\) 15.6772 4.60326i 0.614440 0.180416i
\(652\) 11.4849 + 7.38090i 0.449784 + 0.289058i
\(653\) −5.63336 + 12.3353i −0.220450 + 0.482719i −0.987252 0.159165i \(-0.949120\pi\)
0.766802 + 0.641884i \(0.221847\pi\)
\(654\) 0.00535590 + 0.00157264i 0.000209432 + 6.14949e-5i
\(655\) 11.1893 + 12.9131i 0.437201 + 0.504557i
\(656\) 5.56744 + 6.42517i 0.217372 + 0.250861i
\(657\) 12.4010 + 3.64126i 0.483809 + 0.142059i
\(658\) −3.85802 + 8.44789i −0.150401 + 0.329333i
\(659\) 7.01787 + 4.51011i 0.273377 + 0.175689i 0.670145 0.742230i \(-0.266232\pi\)
−0.396768 + 0.917919i \(0.629868\pi\)
\(660\) −0.896881 + 0.263348i −0.0349111 + 0.0102508i
\(661\) 0.589592 4.10070i 0.0229325 0.159499i −0.975137 0.221602i \(-0.928872\pi\)
0.998070 + 0.0621028i \(0.0197807\pi\)
\(662\) −12.6798 27.7648i −0.492813 1.07911i
\(663\) 0.548713 + 3.81638i 0.0213102 + 0.148216i
\(664\) −2.29617 + 1.47566i −0.0891088 + 0.0572667i
\(665\) −23.9734 + 27.6667i −0.929647 + 1.07287i
\(666\) 2.80595 0.108728
\(667\) −3.27360 5.23046i −0.126754 0.202524i
\(668\) 18.7678 0.726148
\(669\) −5.93501 + 6.84937i −0.229461 + 0.264812i
\(670\) 8.10864 5.21111i 0.313264 0.201323i
\(671\) 0.483603 + 3.36353i 0.0186693 + 0.129848i
\(672\) 1.98704 + 4.35100i 0.0766516 + 0.167844i
\(673\) 2.53714 17.6462i 0.0977995 0.680210i −0.880657 0.473755i \(-0.842898\pi\)
0.978456 0.206455i \(-0.0661928\pi\)
\(674\) −19.2077 + 5.63989i −0.739853 + 0.217240i
\(675\) −0.841254 0.540641i −0.0323799 0.0208093i
\(676\) 13.0450 28.5645i 0.501730 1.09863i
\(677\) 25.1399 + 7.38173i 0.966204 + 0.283703i 0.726518 0.687147i \(-0.241137\pi\)
0.239686 + 0.970851i \(0.422956\pi\)
\(678\) −2.74614 3.16921i −0.105465 0.121713i
\(679\) −17.1429 19.7840i −0.657885 0.759240i
\(680\) 0.555181 + 0.163016i 0.0212902 + 0.00625137i
\(681\) 1.67002 3.65683i 0.0639953 0.140130i
\(682\) −2.68611 1.72626i −0.102857 0.0661019i
\(683\) −17.7946 + 5.22496i −0.680891 + 0.199928i −0.603847 0.797100i \(-0.706366\pi\)
−0.0770437 + 0.997028i \(0.524548\pi\)
\(684\) −1.08920 + 7.57554i −0.0416465 + 0.289658i
\(685\) −5.46367 11.9638i −0.208756 0.457112i
\(686\) 6.04454 + 42.0407i 0.230782 + 1.60512i
\(687\) −7.52072 + 4.83328i −0.286934 + 0.184401i
\(688\) −5.58996 + 6.45116i −0.213115 + 0.245948i
\(689\) −63.2511 −2.40968
\(690\) 2.64094 4.00318i 0.100539 0.152398i
\(691\) −6.03026 −0.229402 −0.114701 0.993400i \(-0.536591\pi\)
−0.114701 + 0.993400i \(0.536591\pi\)
\(692\) −2.86818 + 3.31006i −0.109032 + 0.125830i
\(693\) −3.76135 + 2.41727i −0.142882 + 0.0918245i
\(694\) 1.36267 + 9.47756i 0.0517261 + 0.359763i
\(695\) 3.86291 + 8.45860i 0.146529 + 0.320853i
\(696\) 0.183105 1.27353i 0.00694059 0.0482729i
\(697\) 4.71999 1.38591i 0.178782 0.0524952i
\(698\) −4.11891 2.64707i −0.155903 0.100193i
\(699\) 8.85777 19.3958i 0.335032 0.733617i
\(700\) 4.58950 + 1.34760i 0.173467 + 0.0509344i
\(701\) −8.99626 10.3822i −0.339784 0.392132i 0.559982 0.828505i \(-0.310808\pi\)
−0.899766 + 0.436373i \(0.856263\pi\)
\(702\) 4.36367 + 5.03594i 0.164696 + 0.190069i
\(703\) −20.6053 6.05025i −0.777142 0.228189i
\(704\) 0.388307 0.850274i 0.0146349 0.0320459i
\(705\) 1.63337 + 1.04971i 0.0615165 + 0.0395342i
\(706\) 6.73924 1.97882i 0.253635 0.0744738i
\(707\) 12.0710 83.9558i 0.453978 3.15748i
\(708\) −4.71564 10.3258i −0.177225 0.388068i
\(709\) 3.82009 + 26.5693i 0.143467 + 0.997832i 0.926619 + 0.376002i \(0.122701\pi\)
−0.783152 + 0.621830i \(0.786389\pi\)
\(710\) −8.54853 + 5.49381i −0.320821 + 0.206179i
\(711\) 2.79093 3.22091i 0.104668 0.120793i
\(712\) 2.77919 0.104155
\(713\) 16.2421 2.13711i 0.608270 0.0800352i
\(714\) 2.76768 0.103578
\(715\) 4.07891 4.70732i 0.152543 0.176044i
\(716\) −0.391588 + 0.251658i −0.0146343 + 0.00940490i
\(717\) 3.89256 + 27.0734i 0.145370 + 1.01107i
\(718\) −12.7164 27.8451i −0.474573 1.03917i
\(719\) −2.25659 + 15.6949i −0.0841566 + 0.585322i 0.903488 + 0.428613i \(0.140998\pi\)
−0.987645 + 0.156709i \(0.949912\pi\)
\(720\) 0.959493 0.281733i 0.0357582 0.0104996i
\(721\) 58.0344 + 37.2965i 2.16131 + 1.38899i
\(722\) 16.4401 35.9988i 0.611837 1.33974i
\(723\) −7.58077 2.22591i −0.281932 0.0827827i
\(724\) −7.39797 8.53771i −0.274943 0.317301i
\(725\) −0.842558 0.972364i −0.0312918 0.0361127i
\(726\) −9.71607 2.85289i −0.360597 0.105881i
\(727\) −5.44771 + 11.9288i −0.202044 + 0.442416i −0.983347 0.181736i \(-0.941828\pi\)
0.781303 + 0.624152i \(0.214555\pi\)
\(728\) −26.8135 17.2320i −0.993773 0.638659i
\(729\) −0.959493 + 0.281733i −0.0355368 + 0.0104345i
\(730\) −1.83935 + 12.7930i −0.0680776 + 0.473490i
\(731\) 2.05180 + 4.49281i 0.0758885 + 0.166173i
\(732\) −0.517364 3.59835i −0.0191223 0.132999i
\(733\) 30.4333 19.5583i 1.12408 0.722402i 0.159763 0.987155i \(-0.448927\pi\)
0.964316 + 0.264754i \(0.0852907\pi\)
\(734\) −14.0448 + 16.2085i −0.518401 + 0.598267i
\(735\) 15.8795 0.585725
\(736\) 1.29595 + 4.61741i 0.0477695 + 0.170200i
\(737\) −9.00978 −0.331879
\(738\) 5.56744 6.42517i 0.204940 0.236514i
\(739\) −4.09526 + 2.63186i −0.150646 + 0.0968146i −0.613793 0.789467i \(-0.710357\pi\)
0.463146 + 0.886282i \(0.346721\pi\)
\(740\) 0.399328 + 2.77739i 0.0146796 + 0.102099i
\(741\) −21.1856 46.3900i −0.778273 1.70418i
\(742\) −6.46159 + 44.9413i −0.237212 + 1.64985i
\(743\) −37.9060 + 11.1302i −1.39064 + 0.408327i −0.889458 0.457017i \(-0.848918\pi\)
−0.501177 + 0.865345i \(0.667100\pi\)
\(744\) 2.87363 + 1.84677i 0.105353 + 0.0677060i
\(745\) 1.91494 4.19314i 0.0701581 0.153625i
\(746\) 8.48887 + 2.49256i 0.310800 + 0.0912590i
\(747\) 1.78742 + 2.06279i 0.0653983 + 0.0754736i
\(748\) −0.354189 0.408755i −0.0129504 0.0149456i
\(749\) 14.0464 + 4.12438i 0.513243 + 0.150702i
\(750\) 0.415415 0.909632i 0.0151688 0.0332151i
\(751\) 30.5452 + 19.6302i 1.11461 + 0.716315i 0.962293 0.272016i \(-0.0876905\pi\)
0.152316 + 0.988332i \(0.451327\pi\)
\(752\) −1.86295 + 0.547011i −0.0679347 + 0.0199474i
\(753\) −2.69468 + 18.7419i −0.0981996 + 0.682993i
\(754\) 3.56152 + 7.79865i 0.129703 + 0.284010i
\(755\) 0.795273 + 5.53124i 0.0289429 + 0.201303i
\(756\) 4.02393 2.58602i 0.146349 0.0940527i
\(757\) 27.1611 31.3456i 0.987187 1.13927i −0.00306619 0.999995i \(-0.500976\pi\)
0.990253 0.139279i \(-0.0444785\pi\)
\(758\) 19.7472 0.717252
\(759\) −4.09977 + 1.81330i −0.148812 + 0.0658186i
\(760\) −7.65344 −0.277619
\(761\) 15.4767 17.8610i 0.561029 0.647462i −0.402388 0.915469i \(-0.631820\pi\)
0.963417 + 0.268007i \(0.0863650\pi\)
\(762\) −12.9008 + 8.29085i −0.467347 + 0.300346i
\(763\) 0.00379983 + 0.0264284i 0.000137563 + 0.000956773i
\(764\) −8.93130 19.5568i −0.323123 0.707541i
\(765\) 0.0823460 0.572729i 0.00297723 0.0207071i
\(766\) −0.609188 + 0.178874i −0.0220109 + 0.00646297i
\(767\) 63.6339 + 40.8950i 2.29769 + 1.47663i
\(768\) −0.415415 + 0.909632i −0.0149900 + 0.0328235i
\(769\) 28.4756 + 8.36120i 1.02686 + 0.301513i 0.751432 0.659810i \(-0.229363\pi\)
0.275425 + 0.961323i \(0.411181\pi\)
\(770\) −2.92796 3.37905i −0.105516 0.121772i
\(771\) 2.06106 + 2.37859i 0.0742271 + 0.0856627i
\(772\) 10.9545 + 3.21654i 0.394262 + 0.115766i
\(773\) −9.71312 + 21.2688i −0.349357 + 0.764984i 0.650628 + 0.759397i \(0.274506\pi\)
−0.999984 + 0.00558740i \(0.998221\pi\)
\(774\) 7.18103 + 4.61497i 0.258117 + 0.165882i
\(775\) 3.27753 0.962369i 0.117732 0.0345693i
\(776\) 0.778866 5.41713i 0.0279596 0.194464i
\(777\) 5.57552 + 12.2087i 0.200021 + 0.437984i
\(778\) −4.05086 28.1743i −0.145230 1.01010i
\(779\) −54.7381 + 35.1781i −1.96120 + 1.26039i
\(780\) −4.36367 + 5.03594i −0.156244 + 0.180316i
\(781\) 9.49855 0.339885
\(782\) 2.74179 + 0.427774i 0.0980461 + 0.0152972i
\(783\) −1.28662 −0.0459801
\(784\) −10.3989 + 12.0009i −0.371388 + 0.428605i
\(785\) 7.70785 4.95353i 0.275105 0.176799i
\(786\) 2.43166 + 16.9126i 0.0867345 + 0.603252i
\(787\) 6.21057 + 13.5993i 0.221383 + 0.484761i 0.987437 0.158015i \(-0.0505096\pi\)
−0.766054 + 0.642777i \(0.777782\pi\)
\(788\) 1.03807 7.21997i 0.0369799 0.257201i
\(789\) 22.8073 6.69684i 0.811963 0.238414i
\(790\) 3.58531 + 2.30414i 0.127560 + 0.0819777i
\(791\) 8.33257 18.2458i 0.296272 0.648745i
\(792\) −0.896881 0.263348i −0.0318693 0.00935767i
\(793\) 15.8634 + 18.3074i 0.563327 + 0.650114i
\(794\) −8.12099 9.37212i −0.288203 0.332604i
\(795\) 9.10767 + 2.67425i 0.323016 + 0.0948460i
\(796\) 0.576890 1.26321i 0.0204473 0.0447734i
\(797\) −2.10888 1.35529i −0.0747003 0.0480070i 0.502758 0.864427i \(-0.332319\pi\)
−0.577458 + 0.816420i \(0.695955\pi\)
\(798\) −35.1254 + 10.3138i −1.24343 + 0.365103i
\(799\) −0.159883 + 1.11201i −0.00565625 + 0.0393401i
\(800\) 0.415415 + 0.909632i 0.0146871 + 0.0321603i
\(801\) −0.395521 2.75091i −0.0139750 0.0971985i
\(802\) 5.43100 3.49029i 0.191775 0.123247i
\(803\) 7.91147 9.13032i 0.279190 0.322202i
\(804\) 9.63876 0.339933
\(805\) 22.6655 + 3.53627i 0.798853 + 0.124637i
\(806\) −22.7618 −0.801751
\(807\) −17.7125 + 20.4413i −0.623509 + 0.719567i
\(808\) 14.9175 9.58693i 0.524797 0.337267i
\(809\) −4.95382 34.4545i −0.174167 1.21136i −0.869963 0.493118i \(-0.835857\pi\)
0.695796 0.718240i \(-0.255052\pi\)
\(810\) −0.415415 0.909632i −0.0145962 0.0319612i
\(811\) 4.85432 33.7625i 0.170458 1.18556i −0.707461 0.706753i \(-0.750159\pi\)
0.877919 0.478810i \(-0.158932\pi\)
\(812\) 5.90495 1.73385i 0.207223 0.0608462i
\(813\) −19.9363 12.8123i −0.699197 0.449347i
\(814\) 1.08957 2.38582i 0.0381894 0.0836231i
\(815\) 13.0991 + 3.84625i 0.458843 + 0.134728i
\(816\) 0.378915 + 0.437291i 0.0132647 + 0.0153082i
\(817\) −42.7824 49.3735i −1.49677 1.72736i
\(818\) −10.5362 3.09372i −0.368391 0.108169i
\(819\) −13.2406 + 28.9929i −0.462665 + 1.01309i
\(820\) 7.15210 + 4.59637i 0.249762 + 0.160512i
\(821\) 24.5713 7.21479i 0.857545 0.251798i 0.176735 0.984258i \(-0.443446\pi\)
0.680810 + 0.732460i \(0.261628\pi\)
\(822\) 1.87177 13.0184i 0.0652855 0.454070i
\(823\) −7.53519 16.4998i −0.262660 0.575145i 0.731649 0.681682i \(-0.238751\pi\)
−0.994309 + 0.106536i \(0.966024\pi\)
\(824\) 2.05251 + 14.2755i 0.0715026 + 0.497312i
\(825\) −0.786357 + 0.505361i −0.0273775 + 0.0175944i
\(826\) 35.5575 41.0356i 1.23720 1.42781i
\(827\) −34.9870 −1.21662 −0.608309 0.793700i \(-0.708152\pi\)
−0.608309 + 0.793700i \(0.708152\pi\)
\(828\) 4.38598 1.93989i 0.152423 0.0674158i
\(829\) 24.6616 0.856533 0.428267 0.903652i \(-0.359124\pi\)
0.428267 + 0.903652i \(0.359124\pi\)
\(830\) −1.78742 + 2.06279i −0.0620422 + 0.0716006i
\(831\) −5.66772 + 3.64242i −0.196611 + 0.126354i
\(832\) −0.948315 6.59568i −0.0328769 0.228664i
\(833\) 3.81691 + 8.35787i 0.132248 + 0.289583i
\(834\) −1.32337 + 9.20427i −0.0458247 + 0.318718i
\(835\) 18.0076 5.28750i 0.623178 0.182982i
\(836\) 6.01834 + 3.86775i 0.208149 + 0.133769i
\(837\) 1.41901 3.10721i 0.0490483 0.107401i
\(838\) 4.57276 + 1.34268i 0.157963 + 0.0463822i
\(839\) 12.4615 + 14.3813i 0.430219 + 0.496499i 0.928923 0.370274i \(-0.120736\pi\)
−0.498704 + 0.866772i \(0.666191\pi\)
\(840\) 3.13237 + 3.61494i 0.108077 + 0.124727i
\(841\) 26.2370 + 7.70387i 0.904723 + 0.265651i
\(842\) 8.60177 18.8353i 0.296437 0.649106i
\(843\) −10.2275 6.57281i −0.352253 0.226380i
\(844\) 14.4216 4.23457i 0.496413 0.145760i
\(845\) 4.46901 31.0826i 0.153739 1.06928i
\(846\) 0.806568 + 1.76614i 0.0277304 + 0.0607211i
\(847\) −6.89322 47.9434i −0.236854 1.64736i
\(848\) −7.98532 + 5.13186i −0.274217 + 0.176229i
\(849\) 7.62271 8.79707i 0.261611 0.301915i
\(850\) 0.578619 0.0198465
\(851\) 3.63638 + 12.9562i 0.124653 + 0.444134i
\(852\) −10.1617 −0.348133
\(853\) −21.6539 + 24.9899i −0.741414 + 0.855637i −0.993707 0.112014i \(-0.964270\pi\)
0.252293 + 0.967651i \(0.418815\pi\)
\(854\) 14.6284 9.40109i 0.500573 0.321699i
\(855\) 1.08920 + 7.57554i 0.0372498 + 0.259078i
\(856\) 1.27140 + 2.78397i 0.0434554 + 0.0951541i
\(857\) 6.86165 47.7238i 0.234390 1.63022i −0.444362 0.895847i \(-0.646570\pi\)
0.678752 0.734368i \(-0.262521\pi\)
\(858\) 5.97637 1.75482i 0.204030 0.0599086i
\(859\) 7.52601 + 4.83668i 0.256784 + 0.165025i 0.662699 0.748886i \(-0.269411\pi\)
−0.405915 + 0.913911i \(0.633047\pi\)
\(860\) −3.54603 + 7.76471i −0.120918 + 0.264775i
\(861\) 39.0186 + 11.4569i 1.32975 + 0.390450i
\(862\) 10.5945 + 12.2267i 0.360850 + 0.416444i
\(863\) 35.8955 + 41.4256i 1.22190 + 1.41014i 0.883035 + 0.469307i \(0.155496\pi\)
0.338861 + 0.940837i \(0.389958\pi\)
\(864\) 0.959493 + 0.281733i 0.0326426 + 0.00958474i
\(865\) −1.81945 + 3.98404i −0.0618631 + 0.135461i
\(866\) 23.4165 + 15.0488i 0.795723 + 0.511380i
\(867\) −15.9901 + 4.69513i −0.543054 + 0.159455i
\(868\) −2.32530 + 16.1728i −0.0789257 + 0.548940i
\(869\) −1.65491 3.62376i −0.0561391 0.122928i
\(870\) −0.183105 1.27353i −0.00620786 0.0431766i
\(871\) −54.0319 + 34.7242i −1.83080 + 1.17659i
\(872\) −0.00365544 + 0.00421860i −0.000123789 + 0.000142860i
\(873\) −5.47283 −0.185227
\(874\) −36.3909 + 4.78826i −1.23094 + 0.161965i
\(875\) 4.78325 0.161704
\(876\) −8.46378 + 9.76772i −0.285964 + 0.330021i
\(877\) −8.36195 + 5.37390i −0.282363 + 0.181464i −0.674155 0.738590i \(-0.735492\pi\)
0.391791 + 0.920054i \(0.371855\pi\)
\(878\) −2.82305 19.6347i −0.0952733 0.662641i
\(879\) 0.985671 + 2.15832i 0.0332459 + 0.0727983i
\(880\) 0.133028 0.925231i 0.00448438 0.0311895i
\(881\) 19.7155 5.78899i 0.664232 0.195036i 0.0677991 0.997699i \(-0.478402\pi\)
0.596433 + 0.802663i \(0.296584\pi\)
\(882\) 13.3587 + 8.58512i 0.449811 + 0.289076i
\(883\) −6.63807 + 14.5354i −0.223389 + 0.489154i −0.987829 0.155541i \(-0.950288\pi\)
0.764441 + 0.644694i \(0.223015\pi\)
\(884\) −3.69945 1.08626i −0.124426 0.0365347i
\(885\) −7.43375 8.57900i −0.249883 0.288380i
\(886\) −18.8818 21.7907i −0.634345 0.732073i
\(887\) −17.4365 5.11982i −0.585460 0.171907i −0.0244295 0.999702i \(-0.507777\pi\)
−0.561031 + 0.827795i \(0.689595\pi\)
\(888\) −1.16563 + 2.55238i −0.0391161 + 0.0856523i
\(889\) −61.7079 39.6573i −2.06962 1.33006i
\(890\) 2.66662 0.782989i 0.0893852 0.0262459i
\(891\) −0.133028 + 0.925231i −0.00445661 + 0.0309964i
\(892\) −3.76491 8.24401i −0.126059 0.276030i
\(893\) −2.11478 14.7086i −0.0707685 0.492206i
\(894\) 3.87794 2.49220i 0.129698 0.0833516i
\(895\) −0.304825 + 0.351787i −0.0101892 + 0.0117589i
\(896\) −4.78325 −0.159797
\(897\) −17.5979 + 26.6752i −0.587577 + 0.890659i
\(898\) 33.5540 1.11971
\(899\) 2.87809 3.32149i 0.0959897 0.110778i
\(900\) 0.841254 0.540641i 0.0280418 0.0180214i
\(901\) 0.781643 + 5.43644i 0.0260403 + 0.181114i
\(902\) −3.30128 7.22879i −0.109920 0.240692i
\(903\) −5.81077 + 40.4148i −0.193370 + 1.34492i
\(904\) 4.02360 1.18144i 0.133823 0.0392940i
\(905\) −9.50365 6.10762i −0.315912 0.203024i
\(906\) −2.32139 + 5.08314i −0.0771230 + 0.168876i
\(907\) −5.90241 1.73310i −0.195986 0.0575468i 0.182266 0.983249i \(-0.441657\pi\)
−0.378253 + 0.925702i \(0.623475\pi\)
\(908\) 2.63262 + 3.03821i 0.0873666 + 0.100826i
\(909\) −11.6123 13.4013i −0.385157 0.444495i
\(910\) −30.5821 8.97973i −1.01379 0.297675i
\(911\) 22.9774 50.3135i 0.761275 1.66696i 0.0163012 0.999867i \(-0.494811\pi\)
0.744974 0.667093i \(-0.232462\pi\)
\(912\) −6.43848 4.13776i −0.213199 0.137015i
\(913\) 2.44801 0.718799i 0.0810172 0.0237888i
\(914\) −3.85663 + 26.8234i −0.127566 + 0.887241i
\(915\) −1.51018 3.30683i −0.0499249 0.109320i
\(916\) −1.27228 8.84891i −0.0420373 0.292376i
\(917\) −68.7549 + 44.1861i −2.27049 + 1.45915i
\(918\) 0.378915 0.437291i 0.0125060 0.0144327i
\(919\) 1.69063 0.0557688 0.0278844 0.999611i \(-0.491123\pi\)
0.0278844 + 0.999611i \(0.491123\pi\)
\(920\) 2.54433 + 4.06526i 0.0838842 + 0.134028i
\(921\) −3.64500 −0.120107
\(922\) −22.7401 + 26.2435i −0.748907 + 0.864285i
\(923\) 56.9631 36.6080i 1.87496 1.20497i
\(924\) −0.636307 4.42561i −0.0209330 0.145592i
\(925\) 1.16563 + 2.55238i 0.0383258 + 0.0839217i
\(926\) −4.15208 + 28.8783i −0.136446 + 0.949001i
\(927\) 13.8381 4.06324i 0.454503 0.133454i
\(928\) 1.08238 + 0.695600i 0.0355307 + 0.0228342i
\(929\) −16.9133 + 37.0349i −0.554906 + 1.21507i 0.399547 + 0.916713i \(0.369167\pi\)
−0.954453 + 0.298361i \(0.903560\pi\)
\(930\) 3.27753 + 0.962369i 0.107474 + 0.0315573i
\(931\) −79.5871 91.8485i −2.60836 3.01021i
\(932\) 13.9634 + 16.1146i 0.457387 + 0.527852i
\(933\) 28.6547 + 8.41377i 0.938111 + 0.275454i
\(934\) 3.75616 8.22485i 0.122905 0.269125i
\(935\) −0.455001 0.292411i −0.0148801 0.00956288i
\(936\) −6.39358 + 1.87733i −0.208981 + 0.0613623i
\(937\) 6.78194 47.1695i 0.221556 1.54096i −0.510598 0.859820i \(-0.670576\pi\)
0.732154 0.681139i \(-0.238515\pi\)
\(938\) 19.1526 + 41.9382i 0.625353 + 1.36933i
\(939\) 0.322009 + 2.23962i 0.0105084 + 0.0730874i
\(940\) −1.63337 + 1.04971i −0.0532748 + 0.0342376i
\(941\) −3.48469 + 4.02154i −0.113598 + 0.131099i −0.809700 0.586844i \(-0.800370\pi\)
0.696103 + 0.717942i \(0.254916\pi\)
\(942\) 9.16234 0.298525
\(943\) 36.8828 + 17.3805i 1.20107 + 0.565986i
\(944\) 11.3516 0.369465
\(945\) 3.13237 3.61494i 0.101896 0.117594i
\(946\) 6.71243 4.31382i 0.218240 0.140254i
\(947\) 1.29919 + 9.03609i 0.0422181 + 0.293633i 0.999982 + 0.00607611i \(0.00193410\pi\)
−0.957763 + 0.287557i \(0.907157\pi\)
\(948\) 1.77044 + 3.87673i 0.0575014 + 0.125910i
\(949\) 12.2565 85.2461i 0.397864 2.76721i
\(950\) −7.34342 + 2.15622i −0.238252 + 0.0699571i
\(951\) 1.99707 + 1.28344i 0.0647595 + 0.0416184i
\(952\) −1.14974 + 2.51757i −0.0372632 + 0.0815949i
\(953\) −26.0404 7.64614i −0.843530 0.247683i −0.168711 0.985666i \(-0.553960\pi\)
−0.674820 + 0.737983i \(0.735779\pi\)
\(954\) 6.21605 + 7.17370i 0.201252 + 0.232257i
\(955\) −14.0793 16.2484i −0.455596 0.525786i
\(956\) −26.2438 7.70589i −0.848786 0.249226i
\(957\) −0.499604 + 1.09398i −0.0161499 + 0.0353634i
\(958\) 27.0537 + 17.3864i 0.874065 + 0.561728i
\(959\) 60.3626 17.7240i 1.94921 0.572339i
\(960\) −0.142315 + 0.989821i −0.00459319 + 0.0319463i
\(961\) −8.03066 17.5847i −0.259054 0.567248i
\(962\) −2.66092 18.5071i −0.0857916 0.596694i
\(963\) 2.57469 1.65465i 0.0829683 0.0533205i
\(964\) 5.17393 5.97103i 0.166641 0.192314i
\(965\) 11.4170 0.367526
\(966\) 17.1556 + 15.2288i 0.551971 + 0.489978i
\(967\) 53.9128 1.73372 0.866859 0.498553i \(-0.166135\pi\)
0.866859 + 0.498553i \(0.166135\pi\)
\(968\) 6.63128 7.65291i 0.213138 0.245974i
\(969\) −3.72543 + 2.39419i −0.119678 + 0.0769123i
\(970\) −0.778866 5.41713i −0.0250079 0.173934i
\(971\) 6.49889 + 14.2306i 0.208559 + 0.456681i 0.984786 0.173773i \(-0.0555960\pi\)
−0.776226 + 0.630454i \(0.782869\pi\)
\(972\) 0.142315 0.989821i 0.00456475 0.0317485i
\(973\) −42.6774 + 12.5312i −1.36817 + 0.401732i
\(974\) 8.08043 + 5.19297i 0.258914 + 0.166394i
\(975\) −2.76812 + 6.06133i −0.0886508 + 0.194118i
\(976\) 3.48809 + 1.02420i 0.111651 + 0.0327837i
\(977\) 17.4473 + 20.1353i 0.558188 + 0.644184i 0.962771 0.270318i \(-0.0871287\pi\)
−0.404583 + 0.914501i \(0.632583\pi\)
\(978\) 8.94025 + 10.3176i 0.285878 + 0.329920i
\(979\) −2.49261 0.731895i −0.0796641 0.0233915i
\(980\) −6.59659 + 14.4445i −0.210720 + 0.461413i
\(981\) 0.00469589 + 0.00301786i 0.000149928 + 9.63530e-5i
\(982\) −22.5985 + 6.63552i −0.721148 + 0.211748i
\(983\) −2.83425 + 19.7127i −0.0903986 + 0.628736i 0.893374 + 0.449315i \(0.148332\pi\)
−0.983772 + 0.179422i \(0.942577\pi\)
\(984\) 3.53174 + 7.73343i 0.112588 + 0.246533i
\(985\) −1.03807 7.21997i −0.0330758 0.230047i
\(986\) 0.626283 0.402487i 0.0199449 0.0128178i
\(987\) −6.08179 + 7.01876i −0.193586 + 0.223410i
\(988\) 50.9987 1.62248
\(989\) −12.0029 + 39.1386i −0.381671 + 1.24453i
\(990\) −0.934745 −0.0297081
\(991\) 31.4108 36.2500i 0.997796 1.15152i 0.00934850 0.999956i \(-0.497024\pi\)
0.988448 0.151562i \(-0.0484303\pi\)
\(992\) −2.87363 + 1.84677i −0.0912380 + 0.0586351i
\(993\) −4.34389 30.2124i −0.137849 0.958762i
\(994\) −20.1916 44.2134i −0.640438 1.40236i
\(995\) 0.197634 1.37457i 0.00626541 0.0435769i
\(996\) −2.61890 + 0.768979i −0.0829831 + 0.0243660i
\(997\) 15.0055 + 9.64347i 0.475230 + 0.305412i 0.756241 0.654293i \(-0.227034\pi\)
−0.281012 + 0.959704i \(0.590670\pi\)
\(998\) 1.19828 2.62386i 0.0379307 0.0830567i
\(999\) 2.69229 + 0.790527i 0.0851802 + 0.0250112i
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 690.2.m.d.361.2 yes 20
23.13 even 11 inner 690.2.m.d.151.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.m.d.151.2 20 23.13 even 11 inner
690.2.m.d.361.2 yes 20 1.1 even 1 trivial