Properties

Label 81.3.h.a.2.3
Level $81$
Weight $3$
Character 81.2
Analytic conductor $2.207$
Analytic rank $0$
Dimension $306$
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] = [81,3,Mod(2,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 81.h (of order \(54\), degree \(18\), 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: \(2.20709014132\)
Analytic rank: \(0\)
Dimension: \(306\)
Relative dimension: \(17\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 2.3
Character \(\chi\) \(=\) 81.2
Dual form 81.3.h.a.41.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.19159 - 0.185889i) q^{2} +(0.779433 - 2.89698i) q^{3} +(6.17872 + 0.722189i) q^{4} +(-1.14257 - 4.82088i) q^{5} +(-3.02614 + 9.10107i) q^{6} +(2.64358 + 3.55094i) q^{7} +(-6.99198 - 1.23288i) q^{8} +(-7.78497 - 4.51600i) q^{9} +O(q^{10})\) \(q+(-3.19159 - 0.185889i) q^{2} +(0.779433 - 2.89698i) q^{3} +(6.17872 + 0.722189i) q^{4} +(-1.14257 - 4.82088i) q^{5} +(-3.02614 + 9.10107i) q^{6} +(2.64358 + 3.55094i) q^{7} +(-6.99198 - 1.23288i) q^{8} +(-7.78497 - 4.51600i) q^{9} +(2.75046 + 15.5986i) q^{10} +(-7.62467 - 7.19350i) q^{11} +(6.90807 - 17.3367i) q^{12} +(-18.4878 - 9.28492i) q^{13} +(-7.77713 - 11.8246i) q^{14} +(-14.8565 - 0.447553i) q^{15} +(-2.12607 - 0.503887i) q^{16} +(-7.36388 + 20.2321i) q^{17} +(24.0069 + 15.8604i) q^{18} +(24.2736 - 8.83486i) q^{19} +(-3.57803 - 30.6120i) q^{20} +(12.3475 - 4.89067i) q^{21} +(22.9976 + 24.3760i) q^{22} +(-4.57221 - 3.40388i) q^{23} +(-9.02139 + 19.2947i) q^{24} +(0.405432 - 0.203616i) q^{25} +(57.2795 + 33.0703i) q^{26} +(-19.1506 + 19.0330i) q^{27} +(13.7695 + 23.8495i) q^{28} +(8.55301 - 13.0042i) q^{29} +(47.3327 + 4.19007i) q^{30} +(-4.91876 - 11.4030i) q^{31} +(33.8982 + 10.1484i) q^{32} +(-26.7823 + 16.4816i) q^{33} +(27.2634 - 63.2036i) q^{34} +(14.0982 - 16.8016i) q^{35} +(-44.8398 - 33.5253i) q^{36} +(-2.09116 + 1.75469i) q^{37} +(-79.1135 + 23.6850i) q^{38} +(-41.3082 + 46.3218i) q^{39} +(2.04528 + 35.1161i) q^{40} +(46.4366 - 2.70462i) q^{41} +(-40.3172 + 13.3137i) q^{42} +(-17.6743 - 59.0363i) q^{43} +(-41.9156 - 49.9531i) q^{44} +(-12.8762 + 42.6902i) q^{45} +(13.9599 + 11.7137i) q^{46} +(-20.6167 - 8.89317i) q^{47} +(-3.11688 + 5.76643i) q^{48} +(8.43268 - 28.1671i) q^{49} +(-1.33182 + 0.574492i) q^{50} +(52.8723 + 37.1025i) q^{51} +(-107.526 - 70.7207i) q^{52} +(80.0880 - 46.2388i) q^{53} +(64.6589 - 57.1855i) q^{54} +(-25.9673 + 44.9766i) q^{55} +(-14.1060 - 28.0873i) q^{56} +(-6.67477 - 77.2062i) q^{57} +(-29.7150 + 39.9142i) q^{58} +(-18.0204 + 17.0014i) q^{59} +(-91.4712 - 13.4945i) q^{60} +(114.228 - 13.3513i) q^{61} +(13.5790 + 37.3079i) q^{62} +(-4.54412 - 39.5824i) q^{63} +(-98.0897 - 35.7017i) q^{64} +(-23.6379 + 99.7361i) q^{65} +(88.5419 - 47.6241i) q^{66} +(-90.6215 + 59.6027i) q^{67} +(-60.1108 + 119.690i) q^{68} +(-13.4247 + 10.5925i) q^{69} +(-48.1188 + 51.0029i) q^{70} +(52.3835 - 9.23663i) q^{71} +(48.8647 + 41.1737i) q^{72} +(-13.3113 + 75.4922i) q^{73} +(7.00029 - 5.21152i) q^{74} +(-0.273863 - 1.33323i) q^{75} +(156.360 - 37.0580i) q^{76} +(5.38730 - 46.0913i) q^{77} +(140.450 - 140.161i) q^{78} +(1.48642 - 25.5209i) q^{79} +10.8252i q^{80} +(40.2115 + 70.3138i) q^{81} -148.709 q^{82} +(39.2142 + 2.28397i) q^{83} +(79.8237 - 21.3009i) q^{84} +(105.950 + 12.3838i) q^{85} +(45.4349 + 191.705i) q^{86} +(-31.0065 - 34.9138i) q^{87} +(44.4428 + 59.6971i) q^{88} +(-116.352 - 20.5161i) q^{89} +(49.0312 - 133.856i) q^{90} +(-15.9037 - 90.1945i) q^{91} +(-25.7922 - 24.3336i) q^{92} +(-36.8680 + 5.36169i) q^{93} +(64.1468 + 32.2158i) q^{94} +(-70.3260 - 106.925i) q^{95} +(55.8212 - 90.2922i) q^{96} +(128.810 + 30.5285i) q^{97} +(-32.1496 + 88.3302i) q^{98} +(26.8719 + 90.4342i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 306 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 306 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 90 q^{18} - 18 q^{19} - 234 q^{20} - 153 q^{21} - 18 q^{22} - 99 q^{23} - 126 q^{24} - 18 q^{25} - 27 q^{26} + 9 q^{27} - 9 q^{28} + 63 q^{29} + 198 q^{30} - 18 q^{31} + 306 q^{32} + 171 q^{33} - 18 q^{34} + 225 q^{35} + 342 q^{36} - 18 q^{37} + 90 q^{38} - 18 q^{39} - 18 q^{40} - 234 q^{41} - 513 q^{42} - 18 q^{43} - 666 q^{44} - 450 q^{45} - 18 q^{46} - 342 q^{47} - 513 q^{48} - 18 q^{49} - 369 q^{50} - 144 q^{51} - 54 q^{52} - 27 q^{53} + 108 q^{54} - 9 q^{55} + 396 q^{56} + 198 q^{57} - 18 q^{58} + 360 q^{59} + 801 q^{60} - 18 q^{61} + 873 q^{62} + 522 q^{63} - 18 q^{64} + 1170 q^{65} + 1926 q^{66} - 369 q^{67} + 2169 q^{68} + 1062 q^{69} - 558 q^{70} + 630 q^{71} + 1710 q^{72} - 18 q^{73} + 846 q^{74} + 432 q^{75} - 342 q^{76} + 414 q^{77} + 189 q^{78} - 72 q^{79} - 90 q^{81} - 36 q^{82} - 234 q^{83} - 945 q^{84} + 252 q^{85} - 882 q^{86} - 1026 q^{87} + 630 q^{88} - 1314 q^{89} - 2529 q^{90} - 18 q^{91} - 3960 q^{92} - 2214 q^{93} + 738 q^{94} - 2394 q^{95} - 3321 q^{96} + 441 q^{97} - 2853 q^{98} - 1566 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{54}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.19159 0.185889i −1.59579 0.0929444i −0.762952 0.646455i \(-0.776251\pi\)
−0.832842 + 0.553511i \(0.813288\pi\)
\(3\) 0.779433 2.89698i 0.259811 0.965659i
\(4\) 6.17872 + 0.722189i 1.54468 + 0.180547i
\(5\) −1.14257 4.82088i −0.228514 0.964175i −0.959483 0.281765i \(-0.909080\pi\)
0.730970 0.682410i \(-0.239068\pi\)
\(6\) −3.02614 + 9.10107i −0.504357 + 1.51685i
\(7\) 2.64358 + 3.55094i 0.377654 + 0.507277i 0.949793 0.312879i \(-0.101294\pi\)
−0.572139 + 0.820157i \(0.693886\pi\)
\(8\) −6.99198 1.23288i −0.873998 0.154109i
\(9\) −7.78497 4.51600i −0.864997 0.501778i
\(10\) 2.75046 + 15.5986i 0.275046 + 1.55986i
\(11\) −7.62467 7.19350i −0.693151 0.653955i 0.256760 0.966475i \(-0.417345\pi\)
−0.949911 + 0.312521i \(0.898827\pi\)
\(12\) 6.90807 17.3367i 0.575672 1.44473i
\(13\) −18.4878 9.28492i −1.42214 0.714225i −0.439240 0.898370i \(-0.644752\pi\)
−0.982899 + 0.184145i \(0.941048\pi\)
\(14\) −7.77713 11.8246i −0.555509 0.844611i
\(15\) −14.8565 0.447553i −0.990435 0.0298368i
\(16\) −2.12607 0.503887i −0.132879 0.0314930i
\(17\) −7.36388 + 20.2321i −0.433169 + 1.19012i 0.510687 + 0.859767i \(0.329391\pi\)
−0.943856 + 0.330356i \(0.892831\pi\)
\(18\) 24.0069 + 15.8604i 1.33372 + 0.881131i
\(19\) 24.2736 8.83486i 1.27756 0.464992i 0.387933 0.921688i \(-0.373189\pi\)
0.889623 + 0.456695i \(0.150967\pi\)
\(20\) −3.57803 30.6120i −0.178902 1.53060i
\(21\) 12.3475 4.89067i 0.587976 0.232889i
\(22\) 22.9976 + 24.3760i 1.04535 + 1.10800i
\(23\) −4.57221 3.40388i −0.198792 0.147995i 0.493160 0.869938i \(-0.335842\pi\)
−0.691952 + 0.721944i \(0.743249\pi\)
\(24\) −9.02139 + 19.2947i −0.375891 + 0.803945i
\(25\) 0.405432 0.203616i 0.0162173 0.00814463i
\(26\) 57.2795 + 33.0703i 2.20306 + 1.27194i
\(27\) −19.1506 + 19.0330i −0.709282 + 0.704925i
\(28\) 13.7695 + 23.8495i 0.491767 + 0.851766i
\(29\) 8.55301 13.0042i 0.294931 0.448421i −0.657376 0.753563i \(-0.728333\pi\)
0.952307 + 0.305142i \(0.0987038\pi\)
\(30\) 47.3327 + 4.19007i 1.57776 + 0.139669i
\(31\) −4.91876 11.4030i −0.158670 0.367837i 0.820273 0.571972i \(-0.193821\pi\)
−0.978943 + 0.204134i \(0.934562\pi\)
\(32\) 33.8982 + 10.1484i 1.05932 + 0.317139i
\(33\) −26.7823 + 16.4816i −0.811586 + 0.499444i
\(34\) 27.2634 63.2036i 0.801864 1.85893i
\(35\) 14.0982 16.8016i 0.402805 0.480044i
\(36\) −44.8398 33.5253i −1.24555 0.931259i
\(37\) −2.09116 + 1.75469i −0.0565178 + 0.0474240i −0.670609 0.741811i \(-0.733967\pi\)
0.614091 + 0.789235i \(0.289523\pi\)
\(38\) −79.1135 + 23.6850i −2.08193 + 0.623290i
\(39\) −41.3082 + 46.3218i −1.05919 + 1.18774i
\(40\) 2.04528 + 35.1161i 0.0511320 + 0.877903i
\(41\) 46.4366 2.70462i 1.13260 0.0659664i 0.518415 0.855129i \(-0.326522\pi\)
0.614184 + 0.789163i \(0.289485\pi\)
\(42\) −40.3172 + 13.3137i −0.959934 + 0.316994i
\(43\) −17.6743 59.0363i −0.411030 1.37294i −0.873726 0.486419i \(-0.838303\pi\)
0.462696 0.886517i \(-0.346882\pi\)
\(44\) −41.9156 49.9531i −0.952628 1.13530i
\(45\) −12.8762 + 42.6902i −0.286138 + 0.948671i
\(46\) 13.9599 + 11.7137i 0.303475 + 0.254646i
\(47\) −20.6167 8.89317i −0.438653 0.189216i 0.165288 0.986245i \(-0.447145\pi\)
−0.603941 + 0.797029i \(0.706404\pi\)
\(48\) −3.11688 + 5.76643i −0.0649349 + 0.120134i
\(49\) 8.43268 28.1671i 0.172095 0.574839i
\(50\) −1.33182 + 0.574492i −0.0266365 + 0.0114898i
\(51\) 52.8723 + 37.1025i 1.03671 + 0.727501i
\(52\) −107.526 70.7207i −2.06780 1.36001i
\(53\) 80.0880 46.2388i 1.51109 0.872430i 0.511177 0.859475i \(-0.329210\pi\)
0.999916 0.0129550i \(-0.00412383\pi\)
\(54\) 64.6589 57.1855i 1.19739 1.05899i
\(55\) −25.9673 + 44.9766i −0.472132 + 0.817757i
\(56\) −14.1060 28.0873i −0.251893 0.501559i
\(57\) −6.67477 77.2062i −0.117101 1.35449i
\(58\) −29.7150 + 39.9142i −0.512328 + 0.688176i
\(59\) −18.0204 + 17.0014i −0.305431 + 0.288160i −0.823662 0.567081i \(-0.808072\pi\)
0.518230 + 0.855241i \(0.326591\pi\)
\(60\) −91.4712 13.4945i −1.52452 0.224909i
\(61\) 114.228 13.3513i 1.87259 0.218874i 0.897551 0.440910i \(-0.145344\pi\)
0.975039 + 0.222035i \(0.0712700\pi\)
\(62\) 13.5790 + 37.3079i 0.219016 + 0.601740i
\(63\) −4.54412 39.5824i −0.0721289 0.628292i
\(64\) −98.0897 35.7017i −1.53265 0.557840i
\(65\) −23.6379 + 99.7361i −0.363660 + 1.53440i
\(66\) 88.5419 47.6241i 1.34154 0.721577i
\(67\) −90.6215 + 59.6027i −1.35256 + 0.889592i −0.998951 0.0458013i \(-0.985416\pi\)
−0.353609 + 0.935393i \(0.615046\pi\)
\(68\) −60.1108 + 119.690i −0.883982 + 1.76015i
\(69\) −13.4247 + 10.5925i −0.194561 + 0.153514i
\(70\) −48.1188 + 51.0029i −0.687411 + 0.728614i
\(71\) 52.3835 9.23663i 0.737796 0.130093i 0.207893 0.978152i \(-0.433339\pi\)
0.529903 + 0.848058i \(0.322228\pi\)
\(72\) 48.8647 + 41.1737i 0.678676 + 0.571857i
\(73\) −13.3113 + 75.4922i −0.182347 + 1.03414i 0.746970 + 0.664857i \(0.231508\pi\)
−0.929317 + 0.369282i \(0.879603\pi\)
\(74\) 7.00029 5.21152i 0.0945985 0.0704260i
\(75\) −0.273863 1.33323i −0.00365151 0.0177764i
\(76\) 156.360 37.0580i 2.05737 0.487606i
\(77\) 5.38730 46.0913i 0.0699650 0.598589i
\(78\) 140.450 140.161i 1.80064 1.79694i
\(79\) 1.48642 25.5209i 0.0188155 0.323050i −0.975747 0.218903i \(-0.929752\pi\)
0.994562 0.104146i \(-0.0332109\pi\)
\(80\) 10.8252i 0.135315i
\(81\) 40.2115 + 70.3138i 0.496438 + 0.868072i
\(82\) −148.709 −1.81353
\(83\) 39.2142 + 2.28397i 0.472461 + 0.0275177i 0.292724 0.956197i \(-0.405438\pi\)
0.179737 + 0.983715i \(0.442475\pi\)
\(84\) 79.8237 21.3009i 0.950283 0.253582i
\(85\) 105.950 + 12.3838i 1.24647 + 0.145692i
\(86\) 45.4349 + 191.705i 0.528313 + 2.22913i
\(87\) −31.0065 34.9138i −0.356396 0.401308i
\(88\) 44.4428 + 59.6971i 0.505032 + 0.678376i
\(89\) −116.352 20.5161i −1.30733 0.230518i −0.523785 0.851851i \(-0.675480\pi\)
−0.783547 + 0.621333i \(0.786591\pi\)
\(90\) 49.0312 133.856i 0.544791 1.48729i
\(91\) −15.9037 90.1945i −0.174766 0.991149i
\(92\) −25.7922 24.3336i −0.280349 0.264496i
\(93\) −36.8680 + 5.36169i −0.396430 + 0.0576526i
\(94\) 64.1468 + 32.2158i 0.682413 + 0.342721i
\(95\) −70.3260 106.925i −0.740273 1.12553i
\(96\) 55.8212 90.2922i 0.581471 0.940544i
\(97\) 128.810 + 30.5285i 1.32794 + 0.314727i 0.832552 0.553947i \(-0.186879\pi\)
0.495385 + 0.868674i \(0.335027\pi\)
\(98\) −32.1496 + 88.3302i −0.328057 + 0.901329i
\(99\) 26.8719 + 90.4342i 0.271434 + 0.913476i
\(100\) 2.65210 0.965287i 0.0265210 0.00965287i
\(101\) −9.28869 79.4698i −0.0919672 0.786830i −0.957985 0.286817i \(-0.907403\pi\)
0.866018 0.500012i \(-0.166671\pi\)
\(102\) −161.850 128.244i −1.58676 1.25730i
\(103\) −36.0692 38.2311i −0.350186 0.371176i 0.528206 0.849116i \(-0.322865\pi\)
−0.878392 + 0.477940i \(0.841383\pi\)
\(104\) 117.819 + 87.7132i 1.13288 + 0.843396i
\(105\) −37.6852 53.9378i −0.358906 0.513693i
\(106\) −264.203 + 132.688i −2.49248 + 1.25177i
\(107\) −18.1741 10.4928i −0.169851 0.0980638i 0.412664 0.910883i \(-0.364598\pi\)
−0.582516 + 0.812819i \(0.697932\pi\)
\(108\) −132.072 + 103.769i −1.22289 + 0.960825i
\(109\) 44.6534 + 77.3420i 0.409665 + 0.709560i 0.994852 0.101338i \(-0.0323124\pi\)
−0.585188 + 0.810898i \(0.698979\pi\)
\(110\) 91.2375 138.720i 0.829432 1.26109i
\(111\) 3.45338 + 7.42570i 0.0311115 + 0.0668982i
\(112\) −3.83115 8.88161i −0.0342067 0.0793001i
\(113\) −3.39762 1.01718i −0.0300675 0.00900161i 0.271734 0.962372i \(-0.412403\pi\)
−0.301802 + 0.953371i \(0.597588\pi\)
\(114\) 6.95135 + 247.651i 0.0609768 + 2.17238i
\(115\) −11.1856 + 25.9312i −0.0972664 + 0.225489i
\(116\) 62.2382 74.1726i 0.536536 0.639419i
\(117\) 101.996 + 155.774i 0.871763 + 1.33140i
\(118\) 60.6742 50.9117i 0.514188 0.431455i
\(119\) −91.3099 + 27.3364i −0.767310 + 0.229718i
\(120\) 103.325 + 21.4455i 0.861040 + 0.178713i
\(121\) −0.646456 11.0992i −0.00534261 0.0917291i
\(122\) −367.051 + 21.3783i −3.00861 + 0.175232i
\(123\) 28.3590 136.634i 0.230561 1.11084i
\(124\) −22.1565 74.0080i −0.178682 0.596839i
\(125\) −81.0609 96.6046i −0.648487 0.772837i
\(126\) 7.14503 + 127.175i 0.0567066 + 1.00933i
\(127\) 7.37660 + 6.18970i 0.0580834 + 0.0487378i 0.671367 0.741125i \(-0.265707\pi\)
−0.613284 + 0.789863i \(0.710152\pi\)
\(128\) 176.462 + 76.1184i 1.37861 + 0.594675i
\(129\) −184.803 + 5.18725i −1.43258 + 0.0402113i
\(130\) 93.9822 313.922i 0.722940 2.41479i
\(131\) 99.9272 43.1044i 0.762803 0.329041i 0.0211071 0.999777i \(-0.493281\pi\)
0.741696 + 0.670736i \(0.234022\pi\)
\(132\) −177.383 + 82.4936i −1.34381 + 0.624951i
\(133\) 95.5411 + 62.8384i 0.718354 + 0.472469i
\(134\) 300.306 173.382i 2.24109 1.29389i
\(135\) 113.636 + 70.5763i 0.841752 + 0.522787i
\(136\) 76.4317 132.384i 0.561998 0.973409i
\(137\) 109.318 + 217.670i 0.797943 + 1.58884i 0.808215 + 0.588888i \(0.200434\pi\)
−0.0102718 + 0.999947i \(0.503270\pi\)
\(138\) 44.8151 31.3113i 0.324747 0.226894i
\(139\) 56.4795 75.8651i 0.406327 0.545792i −0.551110 0.834432i \(-0.685796\pi\)
0.957438 + 0.288640i \(0.0932031\pi\)
\(140\) 99.2427 93.6306i 0.708876 0.668790i
\(141\) −41.8327 + 52.7945i −0.296686 + 0.374429i
\(142\) −168.904 + 19.7420i −1.18946 + 0.139028i
\(143\) 74.1722 + 203.786i 0.518687 + 1.42508i
\(144\) 14.2758 + 13.5241i 0.0991376 + 0.0939171i
\(145\) −72.4641 26.3748i −0.499753 0.181895i
\(146\) 56.5174 238.466i 0.387105 1.63333i
\(147\) −75.0268 46.3837i −0.510386 0.315535i
\(148\) −14.1879 + 9.33153i −0.0958642 + 0.0630509i
\(149\) −53.4950 + 106.517i −0.359027 + 0.714881i −0.998547 0.0538935i \(-0.982837\pi\)
0.639520 + 0.768774i \(0.279133\pi\)
\(150\) 0.626225 + 4.30604i 0.00417484 + 0.0287069i
\(151\) −119.437 + 126.595i −0.790971 + 0.838380i −0.989920 0.141630i \(-0.954766\pi\)
0.198949 + 0.980010i \(0.436247\pi\)
\(152\) −180.613 + 31.8469i −1.18824 + 0.209519i
\(153\) 148.696 124.251i 0.971867 0.812097i
\(154\) −25.7619 + 146.103i −0.167285 + 0.948721i
\(155\) −49.3522 + 36.7414i −0.318402 + 0.237041i
\(156\) −288.685 + 256.377i −1.85055 + 1.64344i
\(157\) −146.265 + 34.6655i −0.931626 + 0.220799i −0.668287 0.743904i \(-0.732972\pi\)
−0.263339 + 0.964703i \(0.584824\pi\)
\(158\) −9.48811 + 81.1759i −0.0600513 + 0.513772i
\(159\) −71.5296 268.053i −0.449872 1.68587i
\(160\) 10.1934 175.014i 0.0637089 1.09384i
\(161\) 25.2341i 0.156733i
\(162\) −115.268 231.888i −0.711530 1.43141i
\(163\) 23.4367 0.143784 0.0718918 0.997412i \(-0.477096\pi\)
0.0718918 + 0.997412i \(0.477096\pi\)
\(164\) 288.872 + 16.8249i 1.76141 + 0.102591i
\(165\) 110.057 + 110.283i 0.667010 + 0.668381i
\(166\) −124.731 14.5790i −0.751392 0.0878252i
\(167\) −61.0756 257.698i −0.365722 1.54310i −0.775756 0.631033i \(-0.782631\pi\)
0.410034 0.912070i \(-0.365517\pi\)
\(168\) −92.3630 + 18.9726i −0.549780 + 0.112932i
\(169\) 154.669 + 207.757i 0.915203 + 1.22933i
\(170\) −335.847 59.2189i −1.97557 0.348346i
\(171\) −228.867 40.8404i −1.33840 0.238833i
\(172\) −66.5692 377.533i −0.387030 2.19496i
\(173\) −142.074 134.040i −0.821236 0.774796i 0.155819 0.987786i \(-0.450198\pi\)
−0.977054 + 0.212990i \(0.931680\pi\)
\(174\) 92.4697 + 117.194i 0.531435 + 0.673530i
\(175\) 1.79482 + 0.901392i 0.0102561 + 0.00515081i
\(176\) 12.5858 + 19.1358i 0.0715105 + 0.108726i
\(177\) 35.2070 + 65.4563i 0.198910 + 0.369810i
\(178\) 367.535 + 87.1075i 2.06481 + 0.489368i
\(179\) 29.1486 80.0851i 0.162841 0.447403i −0.831257 0.555889i \(-0.812378\pi\)
0.994098 + 0.108486i \(0.0346002\pi\)
\(180\) −110.389 + 254.472i −0.613272 + 1.41373i
\(181\) −25.3144 + 9.21367i −0.139858 + 0.0509043i −0.411001 0.911635i \(-0.634821\pi\)
0.271143 + 0.962539i \(0.412598\pi\)
\(182\) 33.9920 + 290.820i 0.186769 + 1.59791i
\(183\) 50.3545 341.323i 0.275161 1.86515i
\(184\) 27.7722 + 29.4368i 0.150936 + 0.159983i
\(185\) 10.8484 + 8.07636i 0.0586402 + 0.0436560i
\(186\) 118.664 10.2590i 0.637979 0.0551557i
\(187\) 201.687 101.291i 1.07854 0.541662i
\(188\) −120.962 69.8376i −0.643417 0.371477i
\(189\) −118.211 17.6876i −0.625456 0.0935851i
\(190\) 204.575 + 354.335i 1.07671 + 1.86492i
\(191\) −46.6805 + 70.9743i −0.244401 + 0.371593i −0.936767 0.349953i \(-0.886198\pi\)
0.692367 + 0.721546i \(0.256568\pi\)
\(192\) −179.882 + 256.337i −0.936883 + 1.33509i
\(193\) 113.188 + 262.400i 0.586469 + 1.35959i 0.910487 + 0.413537i \(0.135707\pi\)
−0.324018 + 0.946051i \(0.605034\pi\)
\(194\) −405.433 121.379i −2.08986 0.625663i
\(195\) 270.509 + 146.216i 1.38723 + 0.749826i
\(196\) 72.4452 167.947i 0.369618 0.856871i
\(197\) 158.200 188.536i 0.803047 0.957034i −0.196678 0.980468i \(-0.563015\pi\)
0.999725 + 0.0234338i \(0.00745990\pi\)
\(198\) −68.9534 293.624i −0.348250 1.48295i
\(199\) 126.011 105.736i 0.633222 0.531336i −0.268707 0.963222i \(-0.586596\pi\)
0.901928 + 0.431886i \(0.142152\pi\)
\(200\) −3.08581 + 0.923831i −0.0154290 + 0.00461915i
\(201\) 102.034 + 308.985i 0.507633 + 1.53724i
\(202\) 14.8731 + 255.361i 0.0736293 + 1.26417i
\(203\) 68.7878 4.00643i 0.338856 0.0197361i
\(204\) 299.888 + 267.430i 1.47004 + 1.31093i
\(205\) −66.0956 220.775i −0.322418 1.07695i
\(206\) 108.011 + 128.723i 0.524326 + 0.624868i
\(207\) 20.2226 + 47.1472i 0.0976935 + 0.227764i
\(208\) 34.6278 + 29.0561i 0.166480 + 0.139693i
\(209\) −248.631 107.249i −1.18962 0.513154i
\(210\) 110.249 + 179.153i 0.524996 + 0.853107i
\(211\) −26.1196 + 87.2455i −0.123789 + 0.413486i −0.997310 0.0733021i \(-0.976646\pi\)
0.873520 + 0.486788i \(0.161831\pi\)
\(212\) 528.235 227.858i 2.49167 1.07480i
\(213\) 14.0711 158.953i 0.0660616 0.746260i
\(214\) 56.0537 + 36.8671i 0.261933 + 0.172276i
\(215\) −264.412 + 152.659i −1.22983 + 0.710040i
\(216\) 157.366 109.468i 0.728547 0.506796i
\(217\) 27.4881 47.6108i 0.126673 0.219405i
\(218\) −128.138 255.144i −0.587790 1.17039i
\(219\) 208.324 + 97.4037i 0.951251 + 0.444766i
\(220\) −192.926 + 259.145i −0.876937 + 1.17793i
\(221\) 323.995 305.674i 1.46604 1.38314i
\(222\) −9.64141 24.3417i −0.0434298 0.109647i
\(223\) −201.815 + 23.5888i −0.905002 + 0.105780i −0.555846 0.831285i \(-0.687606\pi\)
−0.349156 + 0.937065i \(0.613532\pi\)
\(224\) 53.5759 + 147.199i 0.239178 + 0.657137i
\(225\) −4.07581 0.245790i −0.0181147 0.00109240i
\(226\) 10.6547 + 3.87800i 0.0471448 + 0.0171593i
\(227\) −71.7190 + 302.606i −0.315943 + 1.33307i 0.550936 + 0.834547i \(0.314271\pi\)
−0.866879 + 0.498519i \(0.833877\pi\)
\(228\) 14.5159 481.856i 0.0636662 2.11340i
\(229\) −35.9040 + 23.6145i −0.156786 + 0.103120i −0.625478 0.780242i \(-0.715096\pi\)
0.468692 + 0.883362i \(0.344726\pi\)
\(230\) 40.5202 80.6824i 0.176175 0.350793i
\(231\) −129.327 51.5320i −0.559855 0.223082i
\(232\) −75.8351 + 80.3805i −0.326875 + 0.346468i
\(233\) −6.91457 + 1.21922i −0.0296763 + 0.00523272i −0.188467 0.982080i \(-0.560352\pi\)
0.158790 + 0.987312i \(0.449241\pi\)
\(234\) −296.573 516.126i −1.26741 2.20567i
\(235\) −19.3169 + 109.552i −0.0821996 + 0.466177i
\(236\) −123.622 + 92.0329i −0.523820 + 0.389970i
\(237\) −72.7750 24.1980i −0.307067 0.102101i
\(238\) 296.505 70.2730i 1.24582 0.295265i
\(239\) −11.6552 + 99.7168i −0.0487666 + 0.417225i 0.946700 + 0.322116i \(0.104394\pi\)
−0.995467 + 0.0951091i \(0.969680\pi\)
\(240\) 31.3605 + 8.43754i 0.130669 + 0.0351564i
\(241\) 0.460831 7.91217i 0.00191216 0.0328306i −0.997217 0.0745523i \(-0.976247\pi\)
0.999129 + 0.0417217i \(0.0132843\pi\)
\(242\) 35.5443i 0.146877i
\(243\) 235.040 61.6869i 0.967242 0.253855i
\(244\) 715.425 2.93207
\(245\) −145.425 8.47004i −0.593572 0.0345716i
\(246\) −115.909 + 430.807i −0.471174 + 1.75125i
\(247\) −530.796 62.0411i −2.14897 0.251179i
\(248\) 20.3334 + 85.7935i 0.0819897 + 0.345942i
\(249\) 37.1815 111.823i 0.149323 0.449087i
\(250\) 240.755 + 323.390i 0.963021 + 1.29356i
\(251\) −133.576 23.5530i −0.532174 0.0938367i −0.0988976 0.995098i \(-0.531532\pi\)
−0.433277 + 0.901261i \(0.642643\pi\)
\(252\) 0.509108 247.850i 0.00202027 0.983533i
\(253\) 10.3757 + 58.8436i 0.0410107 + 0.232583i
\(254\) −22.3925 21.1262i −0.0881593 0.0831740i
\(255\) 118.457 297.283i 0.464536 1.16582i
\(256\) −175.918 88.3493i −0.687180 0.345115i
\(257\) 152.893 + 232.463i 0.594914 + 0.904523i 0.999952 0.00977649i \(-0.00311200\pi\)
−0.405038 + 0.914300i \(0.632742\pi\)
\(258\) 590.778 + 17.7972i 2.28984 + 0.0689813i
\(259\) −11.7589 2.78692i −0.0454013 0.0107603i
\(260\) −218.080 + 599.171i −0.838770 + 2.30450i
\(261\) −125.312 + 62.6121i −0.480123 + 0.239893i
\(262\) −326.939 + 118.996i −1.24786 + 0.454184i
\(263\) 15.6938 + 134.269i 0.0596721 + 0.510527i 0.989713 + 0.143070i \(0.0456974\pi\)
−0.930040 + 0.367457i \(0.880228\pi\)
\(264\) 207.581 82.2201i 0.786293 0.311440i
\(265\) −314.418 333.263i −1.18648 1.25760i
\(266\) −293.247 218.314i −1.10243 0.820730i
\(267\) −150.124 + 321.080i −0.562261 + 1.20255i
\(268\) −602.969 + 302.823i −2.24989 + 1.12994i
\(269\) 227.979 + 131.624i 0.847506 + 0.489308i 0.859808 0.510617i \(-0.170583\pi\)
−0.0123028 + 0.999924i \(0.503916\pi\)
\(270\) −349.561 246.374i −1.29467 0.912497i
\(271\) −195.961 339.415i −0.723104 1.25245i −0.959749 0.280857i \(-0.909381\pi\)
0.236645 0.971596i \(-0.423952\pi\)
\(272\) 25.8508 39.3042i 0.0950397 0.144501i
\(273\) −273.688 24.2278i −1.00252 0.0887466i
\(274\) −308.436 715.035i −1.12568 2.60962i
\(275\) −4.55600 1.36398i −0.0165673 0.00495991i
\(276\) −90.5973 + 55.7529i −0.328251 + 0.202003i
\(277\) 71.3736 165.463i 0.257666 0.597338i −0.739451 0.673210i \(-0.764915\pi\)
0.997118 + 0.0758725i \(0.0241742\pi\)
\(278\) −194.362 + 231.631i −0.699143 + 0.833206i
\(279\) −13.2034 + 110.985i −0.0473240 + 0.397795i
\(280\) −119.288 + 100.095i −0.426030 + 0.357482i
\(281\) 90.4215 27.0704i 0.321785 0.0963361i −0.121837 0.992550i \(-0.538879\pi\)
0.443622 + 0.896214i \(0.353693\pi\)
\(282\) 143.327 160.722i 0.508250 0.569936i
\(283\) 10.6972 + 183.664i 0.0377994 + 0.648991i 0.962998 + 0.269508i \(0.0868611\pi\)
−0.925199 + 0.379483i \(0.876102\pi\)
\(284\) 330.334 19.2398i 1.16315 0.0677456i
\(285\) −364.575 + 120.392i −1.27921 + 0.422427i
\(286\) −198.845 664.190i −0.695264 2.32234i
\(287\) 132.363 + 157.744i 0.461194 + 0.549630i
\(288\) −218.066 232.090i −0.757173 0.805866i
\(289\) −133.724 112.208i −0.462712 0.388261i
\(290\) 226.373 + 97.6477i 0.780596 + 0.336716i
\(291\) 188.839 349.364i 0.648931 1.20056i
\(292\) −136.767 + 456.832i −0.468379 + 1.56449i
\(293\) −215.913 + 93.1358i −0.736905 + 0.317870i −0.731246 0.682114i \(-0.761061\pi\)
−0.00565910 + 0.999984i \(0.501801\pi\)
\(294\) 230.832 + 161.984i 0.785144 + 0.550966i
\(295\) 102.551 + 67.4491i 0.347632 + 0.228641i
\(296\) 16.7846 9.69062i 0.0567049 0.0327386i
\(297\) 282.931 7.36003i 0.952629 0.0247813i
\(298\) 190.534 330.015i 0.639377 1.10743i
\(299\) 52.9253 + 105.383i 0.177008 + 0.352451i
\(300\) −0.729278 8.43546i −0.00243093 0.0281182i
\(301\) 162.911 218.827i 0.541232 0.727001i
\(302\) 404.725 381.838i 1.34015 1.26437i
\(303\) −237.462 35.0322i −0.783703 0.115618i
\(304\) −56.0590 + 6.55236i −0.184405 + 0.0215538i
\(305\) −194.878 535.424i −0.638946 1.75549i
\(306\) −497.672 + 368.917i −1.62638 + 1.20561i
\(307\) −123.161 44.8269i −0.401175 0.146016i 0.133549 0.991042i \(-0.457363\pi\)
−0.534725 + 0.845026i \(0.679585\pi\)
\(308\) 66.5733 280.895i 0.216147 0.911996i
\(309\) −138.868 + 74.6931i −0.449412 + 0.241725i
\(310\) 164.342 108.089i 0.530135 0.348675i
\(311\) 0.0923505 0.183885i 0.000296947 0.000591270i −0.893484 0.449095i \(-0.851747\pi\)
0.893781 + 0.448504i \(0.148043\pi\)
\(312\) 345.935 272.953i 1.10877 0.874850i
\(313\) 1.78261 1.88946i 0.00569525 0.00603661i −0.724520 0.689254i \(-0.757938\pi\)
0.730215 + 0.683217i \(0.239420\pi\)
\(314\) 473.262 83.4489i 1.50720 0.265761i
\(315\) −185.630 + 67.1322i −0.589301 + 0.213118i
\(316\) 27.6151 156.613i 0.0873897 0.495611i
\(317\) 316.531 235.649i 0.998521 0.743371i 0.0318761 0.999492i \(-0.489852\pi\)
0.966645 + 0.256121i \(0.0824444\pi\)
\(318\) 178.465 + 868.812i 0.561211 + 2.73211i
\(319\) −158.760 + 37.6267i −0.497679 + 0.117952i
\(320\) −60.0394 + 513.670i −0.187623 + 1.60522i
\(321\) −44.5630 + 44.4715i −0.138825 + 0.138541i
\(322\) −4.69073 + 80.5367i −0.0145675 + 0.250114i
\(323\) 556.164i 1.72187i
\(324\) 197.676 + 463.490i 0.610110 + 1.43053i
\(325\) −9.38611 −0.0288803
\(326\) −74.8003 4.35662i −0.229449 0.0133639i
\(327\) 258.863 69.0771i 0.791628 0.211245i
\(328\) −328.018 38.3398i −1.00006 0.116890i
\(329\) −22.9227 96.7185i −0.0696739 0.293977i
\(330\) −330.755 372.436i −1.00229 1.12859i
\(331\) 130.209 + 174.901i 0.393381 + 0.528402i 0.954054 0.299635i \(-0.0968650\pi\)
−0.560673 + 0.828037i \(0.689458\pi\)
\(332\) 240.645 + 42.4321i 0.724833 + 0.127808i
\(333\) 24.2038 4.21653i 0.0726840 0.0126623i
\(334\) 147.025 + 833.820i 0.440194 + 2.49647i
\(335\) 390.878 + 368.775i 1.16680 + 1.10082i
\(336\) −28.7159 + 4.17615i −0.0854641 + 0.0124290i
\(337\) 140.220 + 70.4212i 0.416084 + 0.208965i 0.644510 0.764596i \(-0.277062\pi\)
−0.228426 + 0.973561i \(0.573358\pi\)
\(338\) −455.021 691.826i −1.34622 2.04682i
\(339\) −5.59497 + 9.05002i −0.0165043 + 0.0266962i
\(340\) 645.693 + 153.032i 1.89910 + 0.450094i
\(341\) −44.5233 + 122.327i −0.130567 + 0.358730i
\(342\) 722.858 + 172.889i 2.11362 + 0.505525i
\(343\) 326.150 118.709i 0.950874 0.346090i
\(344\) 50.7940 + 434.571i 0.147657 + 1.26329i
\(345\) 66.4037 + 52.6162i 0.192475 + 0.152511i
\(346\) 428.524 + 454.209i 1.23851 + 1.31274i
\(347\) 227.682 + 169.503i 0.656144 + 0.488481i 0.872999 0.487723i \(-0.162172\pi\)
−0.216854 + 0.976204i \(0.569580\pi\)
\(348\) −166.366 238.115i −0.478063 0.684239i
\(349\) −148.380 + 74.5193i −0.425158 + 0.213522i −0.648495 0.761219i \(-0.724601\pi\)
0.223337 + 0.974741i \(0.428305\pi\)
\(350\) −5.56077 3.21051i −0.0158879 0.00917289i
\(351\) 530.773 174.066i 1.51217 0.495914i
\(352\) −185.459 321.225i −0.526873 0.912571i
\(353\) 146.479 222.710i 0.414954 0.630907i −0.566170 0.824289i \(-0.691575\pi\)
0.981124 + 0.193382i \(0.0619456\pi\)
\(354\) −100.199 215.454i −0.283047 0.608627i
\(355\) −104.380 241.981i −0.294029 0.681637i
\(356\) −704.093 210.792i −1.97779 0.592112i
\(357\) 8.02300 + 285.830i 0.0224734 + 0.800644i
\(358\) −107.917 + 250.180i −0.301445 + 0.698828i
\(359\) 157.361 187.536i 0.438333 0.522385i −0.500974 0.865462i \(-0.667025\pi\)
0.939307 + 0.343078i \(0.111469\pi\)
\(360\) 142.662 282.614i 0.396283 0.785040i
\(361\) 234.609 196.861i 0.649887 0.545320i
\(362\) 82.5057 24.7006i 0.227916 0.0682337i
\(363\) −32.6581 6.77833i −0.0899671 0.0186731i
\(364\) −33.1272 568.773i −0.0910089 1.56256i
\(365\) 379.148 22.0828i 1.03876 0.0605009i
\(366\) −224.159 + 1080.00i −0.612456 + 2.95082i
\(367\) −176.540 589.683i −0.481034 1.60677i −0.762359 0.647154i \(-0.775959\pi\)
0.281325 0.959612i \(-0.409226\pi\)
\(368\) 8.00565 + 9.54076i 0.0217545 + 0.0259260i
\(369\) −373.721 188.652i −1.01280 0.511253i
\(370\) −33.1224 27.7930i −0.0895200 0.0751162i
\(371\) 375.910 + 162.152i 1.01323 + 0.437067i
\(372\) −231.669 + 6.50276i −0.622767 + 0.0174805i
\(373\) −125.193 + 418.174i −0.335638 + 1.12111i 0.609048 + 0.793133i \(0.291552\pi\)
−0.944686 + 0.327976i \(0.893634\pi\)
\(374\) −662.529 + 285.787i −1.77147 + 0.764137i
\(375\) −343.043 + 159.535i −0.914781 + 0.425426i
\(376\) 133.187 + 87.5987i 0.354222 + 0.232975i
\(377\) −278.870 + 161.005i −0.739707 + 0.427070i
\(378\) 373.993 + 78.4256i 0.989400 + 0.207475i
\(379\) −221.611 + 383.841i −0.584725 + 1.01277i 0.410185 + 0.912002i \(0.365464\pi\)
−0.994910 + 0.100771i \(0.967869\pi\)
\(380\) −357.304 711.451i −0.940274 1.87224i
\(381\) 23.6810 16.5454i 0.0621548 0.0434262i
\(382\) 162.178 217.843i 0.424550 0.570270i
\(383\) −65.9798 + 62.2488i −0.172271 + 0.162529i −0.767549 0.640991i \(-0.778524\pi\)
0.595277 + 0.803520i \(0.297042\pi\)
\(384\) 358.054 451.878i 0.932432 1.17677i
\(385\) −228.356 + 26.6910i −0.593132 + 0.0693272i
\(386\) −312.474 858.514i −0.809517 2.22413i
\(387\) −129.014 + 539.413i −0.333369 + 1.39383i
\(388\) 773.833 + 281.652i 1.99441 + 0.725908i
\(389\) −63.5582 + 268.173i −0.163389 + 0.689391i 0.828252 + 0.560357i \(0.189336\pi\)
−0.991640 + 0.129034i \(0.958812\pi\)
\(390\) −836.174 516.946i −2.14404 1.32550i
\(391\) 102.537 67.4395i 0.262242 0.172480i
\(392\) −93.6877 + 186.547i −0.238999 + 0.475886i
\(393\) −46.9859 323.084i −0.119557 0.822097i
\(394\) −539.957 + 572.321i −1.37045 + 1.45259i
\(395\) −124.732 + 21.9935i −0.315776 + 0.0556798i
\(396\) 100.724 + 578.174i 0.254353 + 1.46004i
\(397\) 70.2814 398.586i 0.177031 1.00399i −0.758742 0.651392i \(-0.774186\pi\)
0.935773 0.352603i \(-0.114703\pi\)
\(398\) −421.831 + 314.041i −1.05988 + 0.789048i
\(399\) 256.509 227.802i 0.642881 0.570933i
\(400\) −0.964576 + 0.228609i −0.00241144 + 0.000571522i
\(401\) −1.22554 + 10.4852i −0.00305621 + 0.0261475i −0.994680 0.103009i \(-0.967153\pi\)
0.991624 + 0.129157i \(0.0412270\pi\)
\(402\) −268.215 1005.12i −0.667201 2.50030i
\(403\) −14.9386 + 256.486i −0.0370685 + 0.636442i
\(404\) 497.730i 1.23200i
\(405\) 293.030 274.193i 0.723531 0.677020i
\(406\) −220.287 −0.542579
\(407\) 28.5667 + 1.66382i 0.0701885 + 0.00408802i
\(408\) −323.939 324.605i −0.793969 0.795601i
\(409\) 397.987 + 46.5180i 0.973073 + 0.113736i 0.587747 0.809045i \(-0.300015\pi\)
0.385326 + 0.922781i \(0.374089\pi\)
\(410\) 169.910 + 716.908i 0.414416 + 1.74856i
\(411\) 715.793 147.033i 1.74159 0.357744i
\(412\) −195.251 262.268i −0.473911 0.636573i
\(413\) −108.009 19.0450i −0.261524 0.0461138i
\(414\) −55.7779 154.234i −0.134729 0.372545i
\(415\) −33.7942 191.657i −0.0814319 0.461823i
\(416\) −532.475 502.365i −1.27999 1.20761i
\(417\) −175.758 222.752i −0.421481 0.534177i
\(418\) 773.592 + 388.513i 1.85070 + 0.929456i
\(419\) 265.129 + 403.110i 0.632767 + 0.962076i 0.999496 + 0.0317477i \(0.0101073\pi\)
−0.366729 + 0.930328i \(0.619522\pi\)
\(420\) −193.893 360.483i −0.461650 0.858292i
\(421\) 31.4876 + 7.46269i 0.0747924 + 0.0177261i 0.267842 0.963463i \(-0.413690\pi\)
−0.193049 + 0.981189i \(0.561838\pi\)
\(422\) 99.5809 273.596i 0.235974 0.648332i
\(423\) 120.339 + 162.338i 0.284489 + 0.383778i
\(424\) −616.980 + 224.562i −1.45514 + 0.529628i
\(425\) 1.13402 + 9.70214i 0.00266828 + 0.0228286i
\(426\) −74.4569 + 504.698i −0.174781 + 1.18474i
\(427\) 349.380 + 370.322i 0.818221 + 0.867264i
\(428\) −104.715 77.9574i −0.244661 0.182143i
\(429\) 648.177 56.0374i 1.51090 0.130623i
\(430\) 872.273 438.072i 2.02854 1.01877i
\(431\) −32.1074 18.5372i −0.0744952 0.0430098i 0.462290 0.886729i \(-0.347028\pi\)
−0.536785 + 0.843719i \(0.680361\pi\)
\(432\) 50.3060 30.8156i 0.116449 0.0713325i
\(433\) −20.1115 34.8341i −0.0464469 0.0804483i 0.841867 0.539685i \(-0.181456\pi\)
−0.888314 + 0.459236i \(0.848123\pi\)
\(434\) −96.5811 + 146.844i −0.222537 + 0.338351i
\(435\) −132.888 + 189.370i −0.305490 + 0.435333i
\(436\) 220.046 + 510.123i 0.504692 + 1.17001i
\(437\) −141.057 42.2296i −0.322784 0.0966351i
\(438\) −646.778 349.598i −1.47666 0.798168i
\(439\) −117.258 + 271.834i −0.267102 + 0.619212i −0.997996 0.0632792i \(-0.979844\pi\)
0.730894 + 0.682491i \(0.239103\pi\)
\(440\) 237.013 282.461i 0.538667 0.641958i
\(441\) −192.851 + 181.198i −0.437303 + 0.410880i
\(442\) −1090.88 + 915.358i −2.46806 + 2.07094i
\(443\) −47.7176 + 14.2857i −0.107715 + 0.0322476i −0.340207 0.940351i \(-0.610497\pi\)
0.232492 + 0.972598i \(0.425312\pi\)
\(444\) 15.9747 + 48.3753i 0.0359791 + 0.108953i
\(445\) 34.0352 + 584.362i 0.0764836 + 1.31317i
\(446\) 648.496 37.7706i 1.45403 0.0846875i
\(447\) 266.882 + 237.997i 0.597052 + 0.532431i
\(448\) −132.533 442.691i −0.295833 0.988150i
\(449\) −302.186 360.131i −0.673020 0.802074i 0.316172 0.948702i \(-0.397602\pi\)
−0.989192 + 0.146628i \(0.953158\pi\)
\(450\) 12.9626 + 1.54211i 0.0288058 + 0.00342691i
\(451\) −373.519 313.420i −0.828202 0.694944i
\(452\) −20.2584 8.73861i −0.0448194 0.0193332i
\(453\) 273.651 + 444.678i 0.604087 + 0.981629i
\(454\) 285.148 952.462i 0.628080 2.09793i
\(455\) −416.646 + 179.723i −0.915705 + 0.394996i
\(456\) −48.5157 + 548.053i −0.106394 + 1.20187i
\(457\) 684.178 + 449.991i 1.49711 + 0.984663i 0.992623 + 0.121243i \(0.0386880\pi\)
0.504485 + 0.863420i \(0.331682\pi\)
\(458\) 118.981 68.6935i 0.259783 0.149986i
\(459\) −244.054 527.613i −0.531708 1.14948i
\(460\) −87.8402 + 152.144i −0.190957 + 0.330747i
\(461\) −101.335 201.774i −0.219815 0.437687i 0.756514 0.653977i \(-0.226901\pi\)
−0.976329 + 0.216290i \(0.930604\pi\)
\(462\) 403.178 + 188.509i 0.872679 + 0.408029i
\(463\) 342.497 460.054i 0.739735 0.993636i −0.259873 0.965643i \(-0.583681\pi\)
0.999608 0.0279935i \(-0.00891178\pi\)
\(464\) −24.7369 + 23.3381i −0.0533124 + 0.0502976i
\(465\) 67.9722 + 171.610i 0.146177 + 0.369053i
\(466\) 22.2951 2.60592i 0.0478435 0.00559211i
\(467\) −215.780 592.850i −0.462055 1.26949i −0.923937 0.382544i \(-0.875048\pi\)
0.461882 0.886941i \(-0.347174\pi\)
\(468\) 517.709 + 1036.14i 1.10621 + 2.21398i
\(469\) −451.211 164.227i −0.962069 0.350165i
\(470\) 82.0160 346.053i 0.174502 0.736282i
\(471\) −13.5787 + 450.747i −0.0288296 + 0.956999i
\(472\) 146.959 96.6566i 0.311354 0.204781i
\(473\) −289.917 + 577.272i −0.612932 + 1.22045i
\(474\) 227.770 + 90.7580i 0.480527 + 0.191473i
\(475\) 8.04237 8.52442i 0.0169313 0.0179461i
\(476\) −583.921 + 102.961i −1.22672 + 0.216305i
\(477\) −832.297 1.70962i −1.74486 0.00358410i
\(478\) 55.7349 316.088i 0.116600 0.661272i
\(479\) 496.933 369.953i 1.03744 0.772345i 0.0632314 0.997999i \(-0.479859\pi\)
0.974207 + 0.225654i \(0.0724520\pi\)
\(480\) −499.067 165.942i −1.03972 0.345712i
\(481\) 54.9531 13.0241i 0.114248 0.0270772i
\(482\) −2.94157 + 25.1667i −0.00610284 + 0.0522131i
\(483\) −73.1025 19.6683i −0.151351 0.0407210i
\(484\) 4.02146 69.0459i 0.00830881 0.142657i
\(485\) 655.857i 1.35228i
\(486\) −761.617 + 153.188i −1.56711 + 0.315201i
\(487\) 129.604 0.266128 0.133064 0.991107i \(-0.457518\pi\)
0.133064 + 0.991107i \(0.457518\pi\)
\(488\) −815.141 47.4765i −1.67037 0.0972880i
\(489\) 18.2673 67.8957i 0.0373565 0.138846i
\(490\) 462.562 + 54.0658i 0.944005 + 0.110338i
\(491\) 82.4199 + 347.757i 0.167861 + 0.708263i 0.990246 + 0.139331i \(0.0444951\pi\)
−0.822384 + 0.568932i \(0.807357\pi\)
\(492\) 273.898 823.742i 0.556703 1.67427i
\(493\) 200.119 + 268.807i 0.405921 + 0.545247i
\(494\) 1682.55 + 296.679i 3.40597 + 0.600564i
\(495\) 405.269 232.873i 0.818725 0.470451i
\(496\) 4.71180 + 26.7220i 0.00949960 + 0.0538749i
\(497\) 171.279 + 161.593i 0.344625 + 0.325137i
\(498\) −139.455 + 349.980i −0.280029 + 0.702771i
\(499\) −397.752 199.759i −0.797098 0.400318i 0.00314360 0.999995i \(-0.498999\pi\)
−0.800242 + 0.599677i \(0.795296\pi\)
\(500\) −431.086 655.434i −0.862172 1.31087i
\(501\) −794.151 23.9238i −1.58513 0.0477520i
\(502\) 421.941 + 100.002i 0.840519 + 0.199207i
\(503\) 281.148 772.447i 0.558942 1.53568i −0.262233 0.965004i \(-0.584459\pi\)
0.821175 0.570676i \(-0.193319\pi\)
\(504\) −17.0277 + 282.362i −0.0337852 + 0.560241i
\(505\) −372.501 + 135.579i −0.737626 + 0.268474i
\(506\) −22.1766 189.733i −0.0438274 0.374967i
\(507\) 722.422 286.141i 1.42489 0.564381i
\(508\) 41.1078 + 43.5717i 0.0809209 + 0.0857711i
\(509\) −5.24825 3.90718i −0.0103109 0.00767619i 0.591991 0.805945i \(-0.298342\pi\)
−0.602302 + 0.798269i \(0.705750\pi\)
\(510\) −433.326 + 926.785i −0.849659 + 1.81722i
\(511\) −303.258 + 152.302i −0.593460 + 0.298047i
\(512\) −120.694 69.6829i −0.235731 0.136100i
\(513\) −296.700 + 631.191i −0.578363 + 1.23039i
\(514\) −444.759 770.346i −0.865290 1.49873i
\(515\) −143.096 + 217.567i −0.277856 + 0.422460i
\(516\) −1145.59 101.412i −2.22014 0.196535i
\(517\) 93.2223 + 216.114i 0.180314 + 0.418015i
\(518\) 37.0116 + 11.0805i 0.0714510 + 0.0213910i
\(519\) −499.047 + 307.110i −0.961555 + 0.591734i
\(520\) 288.238 668.210i 0.554304 1.28502i
\(521\) −388.456 + 462.944i −0.745597 + 0.888568i −0.996846 0.0793541i \(-0.974714\pi\)
0.251249 + 0.967922i \(0.419159\pi\)
\(522\) 411.583 176.538i 0.788473 0.338195i
\(523\) 798.621 670.122i 1.52700 1.28130i 0.711148 0.703042i \(-0.248175\pi\)
0.815851 0.578263i \(-0.196269\pi\)
\(524\) 648.552 194.164i 1.23770 0.370542i
\(525\) 4.01026 4.49698i 0.00763858 0.00856568i
\(526\) −25.1290 431.447i −0.0477737 0.820242i
\(527\) 266.927 15.5467i 0.506502 0.0295004i
\(528\) 65.2459 21.5458i 0.123572 0.0408064i
\(529\) −142.400 475.650i −0.269188 0.899149i
\(530\) 941.541 + 1122.09i 1.77649 + 2.11714i
\(531\) 217.067 50.9751i 0.408789 0.0959984i
\(532\) 544.941 + 457.260i 1.02433 + 0.859511i
\(533\) −883.623 381.158i −1.65783 0.715117i
\(534\) 538.818 996.848i 1.00902 1.86676i
\(535\) −29.8194 + 99.6039i −0.0557373 + 0.186175i
\(536\) 707.106 305.016i 1.31923 0.569060i
\(537\) −209.286 146.864i −0.389731 0.273490i
\(538\) −703.148 462.467i −1.30697 0.859605i
\(539\) −266.916 + 154.104i −0.495207 + 0.285908i
\(540\) 651.159 + 518.138i 1.20585 + 0.959515i
\(541\) −214.268 + 371.123i −0.396059 + 0.685995i −0.993236 0.116115i \(-0.962956\pi\)
0.597177 + 0.802110i \(0.296289\pi\)
\(542\) 562.334 + 1119.70i 1.03752 + 2.06587i
\(543\) 6.96097 + 80.5166i 0.0128195 + 0.148281i
\(544\) −454.946 + 611.099i −0.836298 + 1.12334i
\(545\) 321.837 303.637i 0.590526 0.557133i
\(546\) 868.994 + 128.201i 1.59156 + 0.234800i
\(547\) −567.783 + 66.3643i −1.03799 + 0.121324i −0.617980 0.786194i \(-0.712049\pi\)
−0.420014 + 0.907518i \(0.637975\pi\)
\(548\) 518.248 + 1423.87i 0.945707 + 2.59831i
\(549\) −949.556 411.914i −1.72961 0.750299i
\(550\) 14.2873 + 5.20016i 0.0259769 + 0.00945483i
\(551\) 92.7217 391.223i 0.168279 0.710024i
\(552\) 106.924 57.5115i 0.193704 0.104188i
\(553\) 94.5528 62.1883i 0.170981 0.112456i
\(554\) −258.553 + 514.821i −0.466702 + 0.929279i
\(555\) 31.8526 25.1327i 0.0573922 0.0452841i
\(556\) 403.760 427.961i 0.726187 0.769713i
\(557\) −138.926 + 24.4964i −0.249419 + 0.0439792i −0.296960 0.954890i \(-0.595973\pi\)
0.0475410 + 0.998869i \(0.484862\pi\)
\(558\) 62.7707 351.763i 0.112492 0.630400i
\(559\) −221.388 + 1255.56i −0.396043 + 2.24607i
\(560\) −38.4398 + 28.6174i −0.0686425 + 0.0511024i
\(561\) −136.236 663.231i −0.242845 1.18223i
\(562\) −293.620 + 69.5893i −0.522456 + 0.123824i
\(563\) −14.0991 + 120.626i −0.0250428 + 0.214255i −0.999966 0.00828807i \(-0.997362\pi\)
0.974923 + 0.222543i \(0.0714359\pi\)
\(564\) −296.600 + 295.991i −0.525887 + 0.524808i
\(565\) −1.02169 + 17.5417i −0.00180830 + 0.0310473i
\(566\) 588.170i 1.03917i
\(567\) −143.378 + 328.669i −0.252872 + 0.579663i
\(568\) −377.652 −0.664881
\(569\) −138.870 8.08823i −0.244059 0.0142148i −0.0643207 0.997929i \(-0.520488\pi\)
−0.179738 + 0.983714i \(0.557525\pi\)
\(570\) 1185.95 316.470i 2.08062 0.555210i
\(571\) 707.946 + 82.7470i 1.23984 + 0.144916i 0.710623 0.703573i \(-0.248413\pi\)
0.529213 + 0.848489i \(0.322487\pi\)
\(572\) 311.117 + 1312.71i 0.543911 + 2.29494i
\(573\) 169.227 + 190.552i 0.295334 + 0.332552i
\(574\) −393.124 528.058i −0.684886 0.919961i
\(575\) −2.54680 0.449070i −0.00442922 0.000780992i
\(576\) 602.396 + 720.910i 1.04583 + 1.25158i
\(577\) −141.476 802.348i −0.245192 1.39055i −0.820047 0.572296i \(-0.806053\pi\)
0.574855 0.818255i \(-0.305058\pi\)
\(578\) 405.933 + 382.978i 0.702306 + 0.662592i
\(579\) 848.391 123.381i 1.46527 0.213093i
\(580\) −428.688 215.295i −0.739118 0.371199i
\(581\) 95.5557 + 145.285i 0.164468 + 0.250061i
\(582\) −667.639 + 1079.92i −1.14715 + 1.85554i
\(583\) −943.263 223.557i −1.61795 0.383460i
\(584\) 186.145 511.429i 0.318741 0.875735i
\(585\) 634.428 669.694i 1.08449 1.14478i
\(586\) 706.418 257.115i 1.20549 0.438763i
\(587\) −79.5174 680.315i −0.135464 1.15897i −0.874404 0.485198i \(-0.838747\pi\)
0.738940 0.673771i \(-0.235327\pi\)
\(588\) −430.072 340.775i −0.731415 0.579550i
\(589\) −220.139 233.334i −0.373751 0.396153i
\(590\) −314.763 234.333i −0.533497 0.397174i
\(591\) −422.878 605.254i −0.715529 1.02412i
\(592\) 5.33011 2.67688i 0.00900356 0.00452176i
\(593\) 190.691 + 110.096i 0.321571 + 0.185659i 0.652092 0.758139i \(-0.273891\pi\)
−0.330522 + 0.943798i \(0.607225\pi\)
\(594\) −904.366 29.1035i −1.52250 0.0489957i
\(595\) 236.113 + 408.960i 0.396829 + 0.687328i
\(596\) −407.456 + 619.507i −0.683651 + 1.03944i
\(597\) −208.097 447.466i −0.348572 0.749523i
\(598\) −149.326 346.177i −0.249709 0.578891i
\(599\) −730.782 218.782i −1.22000 0.365245i −0.388857 0.921298i \(-0.627130\pi\)
−0.831147 + 0.556053i \(0.812315\pi\)
\(600\) 0.271136 + 9.65959i 0.000451894 + 0.0160993i
\(601\) 214.133 496.416i 0.356294 0.825983i −0.641950 0.766747i \(-0.721874\pi\)
0.998244 0.0592364i \(-0.0188666\pi\)
\(602\) −560.622 + 668.123i −0.931266 + 1.10984i
\(603\) 974.651 54.7584i 1.61634 0.0908099i
\(604\) −829.391 + 695.942i −1.37316 + 1.15222i
\(605\) −52.7693 + 15.7981i −0.0872220 + 0.0261126i
\(606\) 751.369 + 155.950i 1.23988 + 0.257343i
\(607\) −40.1775 689.821i −0.0661903 1.13644i −0.853914 0.520415i \(-0.825777\pi\)
0.787723 0.616029i \(-0.211260\pi\)
\(608\) 912.490 53.1465i 1.50081 0.0874120i
\(609\) 42.0089 202.399i 0.0689802 0.332347i
\(610\) 522.442 + 1745.08i 0.856463 + 2.86079i
\(611\) 298.585 + 355.840i 0.488682 + 0.582389i
\(612\) 1008.48 660.325i 1.64785 1.07896i
\(613\) 766.185 + 642.906i 1.24989 + 1.04879i 0.996684 + 0.0813747i \(0.0259311\pi\)
0.253211 + 0.967411i \(0.418513\pi\)
\(614\) 384.746 + 165.963i 0.626622 + 0.270298i
\(615\) −691.097 + 19.3985i −1.12373 + 0.0315423i
\(616\) −94.4928 + 315.628i −0.153397 + 0.512383i
\(617\) 917.181 395.633i 1.48652 0.641221i 0.510689 0.859765i \(-0.329390\pi\)
0.975827 + 0.218545i \(0.0701310\pi\)
\(618\) 457.095 212.576i 0.739635 0.343973i
\(619\) 94.0903 + 61.8842i 0.152004 + 0.0999745i 0.623233 0.782037i \(-0.285819\pi\)
−0.471229 + 0.882011i \(0.656189\pi\)
\(620\) −331.468 + 191.373i −0.534626 + 0.308666i
\(621\) 152.347 21.8362i 0.245325 0.0351630i
\(622\) −0.328927 + 0.569718i −0.000528821 + 0.000915945i
\(623\) −234.735 467.397i −0.376782 0.750236i
\(624\) 111.165 77.6686i 0.178149 0.124469i
\(625\) −366.328 + 492.064i −0.586125 + 0.787302i
\(626\) −6.04060 + 5.69901i −0.00964951 + 0.00910385i
\(627\) −504.490 + 636.686i −0.804609 + 1.01545i
\(628\) −928.768 + 108.557i −1.47893 + 0.172862i
\(629\) −20.1020 55.2298i −0.0319587 0.0878057i
\(630\) 604.933 179.752i 0.960211 0.285320i
\(631\) 442.316 + 160.990i 0.700976 + 0.255134i 0.667828 0.744316i \(-0.267224\pi\)
0.0331486 + 0.999450i \(0.489447\pi\)
\(632\) −41.8572 + 176.609i −0.0662297 + 0.279445i
\(633\) 232.390 + 143.670i 0.367124 + 0.226967i
\(634\) −1054.04 + 693.254i −1.66253 + 1.09346i
\(635\) 21.4115 42.6338i 0.0337189 0.0671399i
\(636\) −248.377 1707.88i −0.390529 2.68535i
\(637\) −417.431 + 442.451i −0.655308 + 0.694586i
\(638\) 513.690 90.5774i 0.805157 0.141971i
\(639\) −449.517 164.657i −0.703469 0.257679i
\(640\) 165.337 937.673i 0.258339 1.46511i
\(641\) −550.603 + 409.909i −0.858975 + 0.639483i −0.933832 0.357711i \(-0.883557\pi\)
0.0748576 + 0.997194i \(0.476150\pi\)
\(642\) 150.493 133.651i 0.234413 0.208179i
\(643\) −564.351 + 133.754i −0.877685 + 0.208015i −0.644673 0.764459i \(-0.723006\pi\)
−0.233012 + 0.972474i \(0.574858\pi\)
\(644\) 18.2238 155.914i 0.0282978 0.242103i
\(645\) 236.157 + 884.984i 0.366135 + 1.37207i
\(646\) 103.385 1775.05i 0.160038 2.74775i
\(647\) 1255.74i 1.94087i 0.241371 + 0.970433i \(0.422403\pi\)
−0.241371 + 0.970433i \(0.577597\pi\)
\(648\) −194.470 541.209i −0.300108 0.835199i
\(649\) 259.700 0.400153
\(650\) 29.9566 + 1.74477i 0.0460871 + 0.00268427i
\(651\) −116.502 116.742i −0.178959 0.179327i
\(652\) 144.809 + 16.9257i 0.222100 + 0.0259597i
\(653\) −83.6949 353.136i −0.128170 0.540791i −0.998806 0.0488626i \(-0.984440\pi\)
0.870636 0.491928i \(-0.163708\pi\)
\(654\) −839.023 + 172.346i −1.28291 + 0.263526i
\(655\) −321.975 432.487i −0.491564 0.660286i
\(656\) −100.090 17.6486i −0.152576 0.0269033i
\(657\) 444.551 527.591i 0.676638 0.803030i
\(658\) 55.1809 + 312.947i 0.0838616 + 0.475603i
\(659\) −192.238 181.367i −0.291711 0.275216i 0.526448 0.850208i \(-0.323524\pi\)
−0.818159 + 0.574992i \(0.805005\pi\)
\(660\) 600.364 + 760.889i 0.909643 + 1.15286i
\(661\) 646.490 + 324.680i 0.978049 + 0.491194i 0.864661 0.502356i \(-0.167533\pi\)
0.113388 + 0.993551i \(0.463830\pi\)
\(662\) −383.061 582.416i −0.578642 0.879783i
\(663\) −632.998 1176.86i −0.954748 1.77505i
\(664\) −271.369 64.3157i −0.408689 0.0968611i
\(665\) 193.774 532.389i 0.291389 0.800585i
\(666\) −78.0322 + 8.95823i −0.117166 + 0.0134508i
\(667\) −83.3710 + 30.3445i −0.124994 + 0.0454941i
\(668\) −191.262 1636.35i −0.286321 2.44963i
\(669\) −88.9652 + 603.041i −0.132982 + 0.901406i
\(670\) −1178.97 1249.64i −1.75966 1.86513i
\(671\) −966.993 719.900i −1.44112 1.07288i
\(672\) 468.190 40.4768i 0.696712 0.0602334i
\(673\) 434.026 217.976i 0.644912 0.323887i −0.0961072 0.995371i \(-0.530639\pi\)
0.741019 + 0.671484i \(0.234343\pi\)
\(674\) −434.435 250.821i −0.644562 0.372138i
\(675\) −3.88887 + 11.6159i −0.00576128 + 0.0172088i
\(676\) 805.619 + 1395.37i 1.19174 + 2.06416i
\(677\) −0.897293 + 1.36427i −0.00132540 + 0.00201517i −0.836150 0.548501i \(-0.815199\pi\)
0.834825 + 0.550516i \(0.185569\pi\)
\(678\) 19.5391 27.8439i 0.0288188 0.0410677i
\(679\) 232.114 + 538.101i 0.341847 + 0.792490i
\(680\) −725.534 217.211i −1.06696 0.319427i
\(681\) 820.743 + 443.629i 1.20520 + 0.651438i
\(682\) 164.839 382.140i 0.241700 0.560323i
\(683\) −749.496 + 893.215i −1.09736 + 1.30778i −0.149617 + 0.988744i \(0.547804\pi\)
−0.947742 + 0.319038i \(0.896640\pi\)
\(684\) −1384.61 417.627i −2.02429 0.610565i
\(685\) 924.459 775.713i 1.34957 1.13243i
\(686\) −1063.00 + 318.242i −1.54957 + 0.463910i
\(687\) 40.4258 + 122.419i 0.0588440 + 0.178194i
\(688\) 7.82913 + 134.421i 0.0113795 + 0.195379i
\(689\) −1909.97 + 111.243i −2.77210 + 0.161456i
\(690\) −202.152 180.273i −0.292975 0.261265i
\(691\) 271.988 + 908.502i 0.393614 + 1.31476i 0.893652 + 0.448760i \(0.148134\pi\)
−0.500038 + 0.866004i \(0.666681\pi\)
\(692\) −781.033 930.798i −1.12866 1.34508i
\(693\) −250.088 + 334.490i −0.360878 + 0.482670i
\(694\) −695.158 583.307i −1.00167 0.840500i
\(695\) −430.268 185.599i −0.619091 0.267050i
\(696\) 173.752 + 282.344i 0.249644 + 0.405666i
\(697\) −287.233 + 959.425i −0.412099 + 1.37651i
\(698\) 487.420 210.253i 0.698310 0.301221i
\(699\) −1.85737 + 20.9817i −0.00265719 + 0.0300167i
\(700\) 10.4387 + 6.86565i 0.0149125 + 0.00980808i
\(701\) 419.261 242.061i 0.598090 0.345308i −0.170200 0.985410i \(-0.554441\pi\)
0.768290 + 0.640102i \(0.221108\pi\)
\(702\) −1726.36 + 456.881i −2.45921 + 0.650828i
\(703\) −35.2574 + 61.0676i −0.0501528 + 0.0868672i
\(704\) 491.081 + 977.822i 0.697558 + 1.38895i
\(705\) 302.312 + 141.349i 0.428812 + 0.200495i
\(706\) −508.899 + 683.570i −0.720820 + 0.968230i
\(707\) 257.637 243.068i 0.364409 0.343802i
\(708\) 170.262 + 429.863i 0.240484 + 0.607150i
\(709\) 1273.89 148.897i 1.79674 0.210009i 0.848858 0.528620i \(-0.177290\pi\)
0.947886 + 0.318611i \(0.103216\pi\)
\(710\) 288.158 + 791.707i 0.405856 + 1.11508i
\(711\) −126.824 + 191.967i −0.178374 + 0.269996i
\(712\) 788.241 + 286.896i 1.10708 + 0.402944i
\(713\) −16.3248 + 68.8796i −0.0228959 + 0.0966053i
\(714\) 27.5265 913.742i 0.0385525 1.27975i
\(715\) 897.683 590.415i 1.25550 0.825755i
\(716\) 237.938 473.773i 0.332315 0.661694i
\(717\) 279.793 + 111.487i 0.390227 + 0.155492i
\(718\) −537.094 + 569.286i −0.748041 + 0.792877i
\(719\) −472.826 + 83.3719i −0.657616 + 0.115955i −0.492491 0.870317i \(-0.663914\pi\)
−0.165124 + 0.986273i \(0.552803\pi\)
\(720\) 48.8868 84.2741i 0.0678983 0.117047i
\(721\) 40.4047 229.147i 0.0560398 0.317818i
\(722\) −785.370 + 584.687i −1.08777 + 0.809815i
\(723\) −22.5622 7.50202i −0.0312064 0.0103762i
\(724\) −163.064 + 38.6470i −0.225227 + 0.0533798i
\(725\) 0.819803 7.01386i 0.00113076 0.00967429i
\(726\) 102.971 + 27.7044i 0.141833 + 0.0381603i
\(727\) −3.03147 + 52.0484i −0.00416984 + 0.0715934i −0.999751 0.0223107i \(-0.992898\pi\)
0.995581 + 0.0939041i \(0.0299347\pi\)
\(728\) 650.246i 0.893195i
\(729\) 4.49227 728.986i 0.00616224 0.999981i
\(730\) −1214.19 −1.66327
\(731\) 1324.58 + 77.1479i 1.81201 + 0.105537i
\(732\) 557.626 2072.57i 0.761784 2.83138i
\(733\) 557.332 + 65.1427i 0.760343 + 0.0888714i 0.487424 0.873166i \(-0.337937\pi\)
0.272919 + 0.962037i \(0.412011\pi\)
\(734\) 453.826 + 1914.84i 0.618292 + 2.60878i
\(735\) −137.887 + 414.691i −0.187601 + 0.564206i
\(736\) −120.445 161.786i −0.163649 0.219818i
\(737\) 1119.71 + 197.435i 1.51928 + 0.267890i
\(738\) 1157.70 + 671.571i 1.56869 + 0.909987i
\(739\) 175.676 + 996.309i 0.237721 + 1.34819i 0.836806 + 0.547500i \(0.184420\pi\)
−0.599084 + 0.800686i \(0.704469\pi\)
\(740\) 61.1968 + 57.7362i 0.0826984 + 0.0780219i
\(741\) −593.452 + 1489.35i −0.800879 + 2.00992i
\(742\) −1169.61 587.399i −1.57629 0.791643i
\(743\) 27.9386 + 42.4785i 0.0376024 + 0.0571716i 0.853800 0.520601i \(-0.174292\pi\)
−0.816197 + 0.577773i \(0.803922\pi\)
\(744\) 264.391 + 7.96476i 0.355364 + 0.0107053i
\(745\) 574.628 + 136.189i 0.771313 + 0.182805i
\(746\) 477.298 1311.37i 0.639810 1.75786i
\(747\) −294.967 194.872i −0.394869 0.260873i
\(748\) 1319.32 480.192i 1.76379 0.641968i
\(749\) −10.7853 92.2738i −0.0143995 0.123196i
\(750\) 1124.51 445.402i 1.49934 0.593869i
\(751\) −208.467 220.962i −0.277586 0.294224i 0.573549 0.819172i \(-0.305566\pi\)
−0.851135 + 0.524948i \(0.824085\pi\)
\(752\) 39.3513 + 29.2960i 0.0523289 + 0.0389574i
\(753\) −172.346 + 368.608i −0.228879 + 0.489519i
\(754\) 919.966 462.024i 1.22011 0.612764i
\(755\) 746.765 + 431.145i 0.989093 + 0.571053i
\(756\) −717.620 194.657i −0.949233 0.257483i
\(757\) −111.434 193.010i −0.147205 0.254967i 0.782988 0.622036i \(-0.213694\pi\)
−0.930193 + 0.367070i \(0.880361\pi\)
\(758\) 778.642 1183.87i 1.02723 1.56183i
\(759\) 178.556 + 15.8064i 0.235252 + 0.0208253i
\(760\) 359.892 + 834.324i 0.473542 + 1.09779i
\(761\) 888.457 + 265.986i 1.16749 + 0.349522i 0.811151 0.584836i \(-0.198841\pi\)
0.356334 + 0.934359i \(0.384026\pi\)
\(762\) −78.6555 + 48.4040i −0.103222 + 0.0635223i
\(763\) −156.592 + 363.021i −0.205232 + 0.475782i
\(764\) −339.683 + 404.818i −0.444611 + 0.529867i
\(765\) −768.893 574.878i −1.00509 0.751475i
\(766\) 222.152 186.407i 0.290015 0.243352i
\(767\) 491.015 147.000i 0.640176 0.191656i
\(768\) −393.062 + 440.768i −0.511800 + 0.573917i
\(769\) −5.13006 88.0797i −0.00667108 0.114538i 0.993329 0.115318i \(-0.0367887\pi\)
−1.00000 0.000780074i \(0.999752\pi\)
\(770\) 733.779 42.7378i 0.952960 0.0555036i
\(771\) 792.609 261.739i 1.02803 0.339480i
\(772\) 509.858 + 1703.04i 0.660437 + 2.20601i
\(773\) −362.045 431.468i −0.468363 0.558173i 0.479215 0.877698i \(-0.340921\pi\)
−0.947578 + 0.319524i \(0.896477\pi\)
\(774\) 512.030 1697.60i 0.661537 2.19328i
\(775\) −4.31605 3.62159i −0.00556909 0.00467302i
\(776\) −862.998 372.261i −1.11211 0.479718i
\(777\) −17.2389 + 31.8932i −0.0221865 + 0.0410465i
\(778\) 252.702 844.083i 0.324810 1.08494i
\(779\) 1103.29 475.911i 1.41629 0.610926i
\(780\) 1565.81 + 1098.79i 2.00744 + 1.40870i
\(781\) −465.851 306.395i −0.596480 0.392311i
\(782\) −339.791 + 196.179i −0.434516 + 0.250868i
\(783\) 83.7135 + 411.828i 0.106914 + 0.525962i
\(784\) −32.1215 + 55.6360i −0.0409713 + 0.0709643i
\(785\) 334.236 + 665.519i 0.425779 + 0.847795i
\(786\) 89.9021 + 1039.89i 0.114379 + 1.32301i
\(787\) 374.157 502.581i 0.475422 0.638603i −0.498120 0.867108i \(-0.665976\pi\)
0.973543 + 0.228505i \(0.0733836\pi\)
\(788\) 1113.63 1050.66i 1.41324 1.33332i
\(789\) 401.206 + 59.1889i 0.508499 + 0.0750177i
\(790\) 402.180 47.0081i 0.509088 0.0595039i
\(791\) −5.36993 14.7538i −0.00678879 0.0186520i
\(792\) −76.3940 665.444i −0.0964571 0.840207i
\(793\) −2235.79 813.761i −2.81941 1.02618i
\(794\) −298.402 + 1259.06i −0.375821 + 1.58571i
\(795\) −1210.52 + 651.105i −1.52267 + 0.818999i
\(796\) 854.949 562.309i 1.07406 0.706418i
\(797\) 244.328 486.498i 0.306560 0.610412i −0.686618 0.727018i \(-0.740905\pi\)
0.993178 + 0.116607i \(0.0372018\pi\)
\(798\) −861.018 + 679.369i −1.07897 + 0.851339i
\(799\) 331.746 351.631i 0.415202 0.440088i
\(800\) 15.8098 2.78769i 0.0197623 0.00348462i
\(801\) 813.150 + 685.165i 1.01517 + 0.855387i
\(802\) 5.86049 33.2365i 0.00730735 0.0414420i
\(803\) 644.547 479.848i 0.802674 0.597569i
\(804\) 407.296 + 1982.82i 0.506588 + 2.46619i
\(805\) −121.650 + 28.8316i −0.151118 + 0.0358157i
\(806\) 95.3558 815.821i 0.118307 1.01218i
\(807\) 559.005 557.858i 0.692696 0.691274i
\(808\) −33.0300 + 567.103i −0.0408787 + 0.701860i
\(809\) 372.469i 0.460407i −0.973143 0.230203i \(-0.926061\pi\)
0.973143 0.230203i \(-0.0739391\pi\)
\(810\) −986.200 + 820.640i −1.21753 + 1.01314i
\(811\) −182.339 −0.224832 −0.112416 0.993661i \(-0.535859\pi\)
−0.112416 + 0.993661i \(0.535859\pi\)
\(812\) 427.914 + 24.9232i 0.526988 + 0.0306935i
\(813\) −1136.02 + 303.145i −1.39731 + 0.372872i
\(814\) −90.8639 10.6205i −0.111626 0.0130473i
\(815\) −26.7781 112.986i −0.0328565 0.138633i
\(816\) −93.7145 105.524i −0.114846 0.129319i
\(817\) −950.595 1276.87i −1.16352 1.56288i
\(818\) −1261.56 222.447i −1.54225 0.271941i
\(819\) −283.509 + 773.983i −0.346164 + 0.945034i
\(820\) −248.945 1411.84i −0.303592 1.72176i
\(821\) 38.9026 + 36.7027i 0.0473844 + 0.0447049i 0.709570 0.704635i \(-0.248889\pi\)
−0.662185 + 0.749340i \(0.730371\pi\)
\(822\) −2311.85 + 336.211i −2.81247 + 0.409016i
\(823\) −1015.23 509.868i −1.23357 0.619523i −0.292027 0.956410i \(-0.594330\pi\)
−0.941545 + 0.336887i \(0.890626\pi\)
\(824\) 205.061 + 311.780i 0.248860 + 0.378374i
\(825\) −7.50250 + 12.1355i −0.00909394 + 0.0147097i
\(826\) 341.181 + 80.8615i 0.413053 + 0.0978953i
\(827\) −241.982 + 664.840i −0.292602 + 0.803918i 0.703082 + 0.711109i \(0.251807\pi\)
−0.995684 + 0.0928090i \(0.970415\pi\)
\(828\) 90.9004 + 305.914i 0.109783 + 0.369461i
\(829\) 744.260 270.889i 0.897781 0.326765i 0.148418 0.988925i \(-0.452582\pi\)
0.749363 + 0.662159i \(0.230360\pi\)
\(830\) 72.2304 + 617.971i 0.0870246 + 0.744543i
\(831\) −423.710 335.735i −0.509880 0.404013i
\(832\) 1481.98 + 1570.80i 1.78122 + 1.88798i
\(833\) 507.782 + 378.030i 0.609582 + 0.453817i
\(834\) 519.539 + 743.603i 0.622948 + 0.891610i
\(835\) −1172.55 + 588.876i −1.40425 + 0.705241i
\(836\) −1458.77 842.221i −1.74494 1.00744i
\(837\) 311.229 + 124.755i 0.371839 + 0.149050i
\(838\) −771.250 1335.84i −0.920346 1.59409i
\(839\) −824.466 + 1253.54i −0.982677 + 1.49409i −0.117219 + 0.993106i \(0.537398\pi\)
−0.865458 + 0.500981i \(0.832972\pi\)
\(840\) 196.995 + 423.593i 0.234518 + 0.504278i
\(841\) 237.147 + 549.769i 0.281983 + 0.653709i
\(842\) −99.1081 29.6710i −0.117706 0.0352388i
\(843\) −7.94494 283.049i −0.00942460 0.335764i
\(844\) −224.393 + 520.202i −0.265869 + 0.616353i
\(845\) 824.850 983.018i 0.976154 1.16334i
\(846\) −353.895 540.486i −0.418315 0.638872i
\(847\) 37.7037 31.6372i 0.0445144 0.0373520i
\(848\) −193.572 + 57.9515i −0.228268 + 0.0683390i
\(849\) 540.410 + 112.164i 0.636525 + 0.132114i
\(850\) −1.81580 31.1760i −0.00213623 0.0366777i
\(851\) 15.5340 0.904750i 0.0182538 0.00106316i
\(852\) 201.736 971.966i 0.236779 1.14081i
\(853\) 114.917 + 383.851i 0.134721 + 0.450001i 0.998553 0.0537803i \(-0.0171271\pi\)
−0.863831 + 0.503781i \(0.831942\pi\)
\(854\) −1046.24 1246.86i −1.22511 1.46002i
\(855\) 64.6101 + 1150.00i 0.0755674 + 1.34503i
\(856\) 114.137 + 95.7720i 0.133337 + 0.111883i
\(857\) −78.7212 33.9570i −0.0918567 0.0396231i 0.349656 0.936878i \(-0.386299\pi\)
−0.441512 + 0.897255i \(0.645558\pi\)
\(858\) −2079.13 + 58.3594i −2.42323 + 0.0680180i
\(859\) 413.936 1382.64i 0.481881 1.60959i −0.278718 0.960373i \(-0.589910\pi\)
0.760599 0.649222i \(-0.224905\pi\)
\(860\) −1743.98 + 752.279i −2.02788 + 0.874743i
\(861\) 560.148 260.501i 0.650578 0.302557i
\(862\) 99.0278 + 65.1316i 0.114881 + 0.0755587i
\(863\) 22.7298 13.1230i 0.0263381 0.0152063i −0.486773 0.873528i \(-0.661826\pi\)
0.513111 + 0.858322i \(0.328493\pi\)
\(864\) −842.326 + 450.834i −0.974914 + 0.521798i
\(865\) −483.860 + 838.070i −0.559375 + 0.968867i
\(866\) 57.7123 + 114.915i 0.0666424 + 0.132696i
\(867\) −429.292 + 299.937i −0.495146 + 0.345948i
\(868\) 204.226 274.323i 0.235283 0.316040i
\(869\) −194.918 + 183.896i −0.224302 + 0.211618i
\(870\) 459.326 579.688i 0.527961 0.666308i
\(871\) 2228.80 260.509i 2.55890 0.299092i
\(872\) −216.863 595.826i −0.248696 0.683287i
\(873\) −864.914 819.369i −0.990738 0.938567i
\(874\) 442.344 + 161.000i 0.506115 + 0.184211i
\(875\) 128.747 543.224i 0.147139 0.620828i
\(876\) 1216.83 + 752.280i 1.38908 + 0.858767i
\(877\) −604.040 + 397.284i −0.688758 + 0.453003i −0.845036 0.534710i \(-0.820421\pi\)
0.156278 + 0.987713i \(0.450050\pi\)
\(878\) 424.769 845.785i 0.483792 0.963309i
\(879\) 101.523 + 698.089i 0.115498 + 0.794185i
\(880\) 77.8713 82.5388i 0.0884901 0.0937941i
\(881\) 830.463 146.433i 0.942637 0.166212i 0.318849 0.947806i \(-0.396704\pi\)
0.623788 + 0.781593i \(0.285593\pi\)
\(882\) 649.183 542.461i 0.736035 0.615035i
\(883\) 188.153 1067.07i 0.213083 1.20846i −0.671119 0.741350i \(-0.734186\pi\)
0.884202 0.467105i \(-0.154703\pi\)
\(884\) 2222.63 1654.69i 2.51429 1.87182i
\(885\) 275.330 244.517i 0.311108 0.276290i
\(886\) 154.950 36.7239i 0.174887 0.0414491i
\(887\) 22.1789 189.753i 0.0250044 0.213926i −0.974960 0.222381i \(-0.928617\pi\)
0.999964 + 0.00845463i \(0.00269122\pi\)
\(888\) −14.9910 56.1779i −0.0168818 0.0632635i
\(889\) −2.47865 + 42.5568i −0.00278814 + 0.0478704i
\(890\) 1871.37i 2.10266i
\(891\) 199.204 825.381i 0.223573 0.926353i
\(892\) −1264.00 −1.41704
\(893\) −579.011 33.7235i −0.648388 0.0377643i
\(894\) −807.538 809.198i −0.903286 0.905143i
\(895\) −419.385 49.0191i −0.468586 0.0547699i
\(896\) 196.200 + 827.832i 0.218973 + 0.923920i
\(897\) 346.544 71.1845i 0.386336 0.0793584i
\(898\) 897.508 + 1205.56i 0.999453 + 1.34250i
\(899\) −190.357 33.5650i −0.211743 0.0373360i
\(900\) −25.0058 4.46217i −0.0277842 0.00495797i
\(901\) 345.750 + 1960.84i 0.383740 + 2.17630i
\(902\) 1133.86 + 1069.74i 1.25705 + 1.18596i
\(903\) −506.960 642.511i −0.561417 0.711529i
\(904\) 22.5021 + 11.3010i 0.0248917 + 0.0125011i
\(905\) 73.3414 + 111.510i 0.0810402 + 0.123216i
\(906\) −790.721 1470.10i −0.872761 1.62262i
\(907\) −1500.93 355.726i −1.65482 0.392201i −0.706052 0.708160i \(-0.749526\pi\)
−0.948773 + 0.315959i \(0.897674\pi\)
\(908\) −661.670 + 1817.92i −0.728712 + 2.00212i
\(909\) −286.573 + 660.617i −0.315262 + 0.726752i
\(910\) 1363.17 496.153i 1.49799 0.545223i
\(911\) −50.6099 432.995i −0.0555542 0.475296i −0.992166 0.124927i \(-0.960130\pi\)
0.936612 0.350369i \(-0.113944\pi\)
\(912\) −24.7122 + 167.509i −0.0270967 + 0.183672i
\(913\) −282.566 299.502i −0.309492 0.328042i
\(914\) −2099.97 1563.37i −2.29756 1.71047i
\(915\) −1703.01 + 147.232i −1.86121 + 0.160909i
\(916\) −238.895 + 119.978i −0.260803 + 0.130980i
\(917\) 417.227 + 240.886i 0.454991 + 0.262689i
\(918\) 680.842 + 1729.29i 0.741658 + 1.88376i
\(919\) 125.340 + 217.095i 0.136387 + 0.236230i 0.926127 0.377213i \(-0.123117\pi\)
−0.789739 + 0.613443i \(0.789784\pi\)
\(920\) 110.180 167.520i 0.119761 0.182087i
\(921\) −225.858 + 321.855i −0.245231 + 0.349462i
\(922\) 285.911 + 662.816i 0.310098 + 0.718889i
\(923\) −1054.22 315.612i −1.14216 0.341942i
\(924\) −761.857 411.800i −0.824521 0.445671i
\(925\) −0.490540 + 1.13720i −0.000530314 + 0.00122941i
\(926\) −1178.63 + 1404.63i −1.27282 + 1.51688i
\(927\) 108.146 + 460.517i 0.116662 + 0.496782i
\(928\) 421.904 354.020i 0.454638 0.381487i
\(929\) 248.912 74.5195i 0.267936 0.0802147i −0.150017 0.988683i \(-0.547933\pi\)
0.417953 + 0.908469i \(0.362748\pi\)
\(930\) −185.039 560.343i −0.198967 0.602519i
\(931\) −44.1611 758.218i −0.0474341 0.814412i
\(932\) −43.6037 + 2.53963i −0.0467851 + 0.00272492i
\(933\) −0.460730 0.410863i −0.000493815 0.000440368i
\(934\) 578.475 + 1932.24i 0.619353 + 2.06878i
\(935\) −718.751 856.574i −0.768718 0.916122i
\(936\) −521.106 1214.92i −0.556738 1.29799i
\(937\) −225.234 188.994i −0.240378 0.201701i 0.514638 0.857408i \(-0.327926\pi\)
−0.755016 + 0.655706i \(0.772371\pi\)
\(938\) 1409.55 + 608.021i 1.50272 + 0.648210i
\(939\) −4.08430 6.63690i −0.00434962 0.00706805i
\(940\) −198.471 + 662.939i −0.211139 + 0.705254i
\(941\) −1243.25 + 536.286i −1.32120 + 0.569911i −0.935700 0.352796i \(-0.885231\pi\)
−0.385502 + 0.922707i \(0.625972\pi\)
\(942\) 127.126 1436.07i 0.134954 1.52449i
\(943\) −221.524 145.699i −0.234914 0.154505i
\(944\) 46.8795 27.0659i 0.0496605 0.0286715i
\(945\) 49.7946 + 590.090i 0.0526927 + 0.624434i
\(946\) 1032.60 1788.52i 1.09155 1.89061i
\(947\) −701.295 1396.39i −0.740544 1.47454i −0.875256 0.483660i \(-0.839307\pi\)
0.134712 0.990885i \(-0.456989\pi\)
\(948\) −432.181 202.070i −0.455887 0.213154i
\(949\) 947.036 1272.09i 0.997931 1.34045i
\(950\) −27.2525 + 25.7114i −0.0286869 + 0.0270647i
\(951\) −435.954 1100.66i −0.458417 1.15737i
\(952\) 672.140 78.5619i 0.706029 0.0825230i
\(953\) 636.918 + 1749.92i 0.668329 + 1.83622i 0.534405 + 0.845228i \(0.320536\pi\)
0.133924 + 0.990992i \(0.457242\pi\)
\(954\) 2656.03 + 160.171i 2.78410 + 0.167894i
\(955\) 395.494 + 143.948i 0.414130 + 0.150731i
\(956\) −144.029 + 607.705i −0.150658 + 0.635675i
\(957\) −14.7387 + 489.251i −0.0154009 + 0.511234i
\(958\) −1654.78 + 1088.36i −1.72732 + 1.13608i
\(959\) −483.944 + 963.611i −0.504634 + 1.00481i
\(960\) 1441.29 + 574.304i 1.50135 + 0.598234i
\(961\) 553.645 586.829i 0.576113 0.610644i
\(962\) −177.809 + 31.3524i −0.184832 + 0.0325909i
\(963\) 94.0992 + 163.761i 0.0977147 + 0.170052i
\(964\) 8.56143 48.5543i 0.00888116 0.0503675i
\(965\) 1135.67 845.478i 1.17686 0.876143i
\(966\) 229.657 + 76.3619i 0.237740 + 0.0790496i
\(967\) 1344.53 318.660i 1.39041 0.329534i 0.533852 0.845578i \(-0.320744\pi\)
0.856562 + 0.516044i \(0.172596\pi\)
\(968\) −9.16394 + 78.4025i −0.00946688 + 0.0809944i
\(969\) 1611.19 + 433.492i 1.66274 + 0.447360i
\(970\) −121.917 + 2093.23i −0.125687 + 2.15796i
\(971\) 510.161i 0.525398i 0.964878 + 0.262699i \(0.0846125\pi\)
−0.964878 + 0.262699i \(0.915387\pi\)
\(972\) 1496.80 211.403i 1.53991 0.217493i
\(973\) 418.701 0.430319
\(974\) −413.643 24.0920i −0.424685 0.0247351i
\(975\) −7.31584 + 27.1914i −0.00750343 + 0.0278886i
\(976\) −249.584 29.1722i −0.255721 0.0298895i
\(977\) 177.519 + 749.011i 0.181698 + 0.766644i 0.985209 + 0.171355i \(0.0548144\pi\)
−0.803511 + 0.595289i \(0.797037\pi\)
\(978\) −70.9229 + 213.299i −0.0725183 + 0.218097i
\(979\) 739.566 + 993.410i 0.755430 + 1.01472i
\(980\) −892.424 157.358i −0.910637 0.160570i
\(981\) 1.65100 803.760i 0.00168298 0.819327i
\(982\) −198.406 1125.22i −0.202043 1.14584i
\(983\) 422.683 + 398.781i 0.429993 + 0.405677i 0.870576 0.492035i \(-0.163747\pi\)
−0.440583 + 0.897712i \(0.645228\pi\)
\(984\) −366.738 + 920.378i −0.372701 + 0.935344i
\(985\) −1089.66 547.249i −1.10626 0.555583i
\(986\) −588.730 895.120i −0.597089 0.907830i
\(987\) −298.058 8.97899i −0.301984 0.00909726i
\(988\) −3234.84 766.670i −3.27413 0.775982i
\(989\) −120.142 + 330.087i −0.121478 + 0.333758i
\(990\) −1336.74 + 667.901i −1.35024 + 0.674648i
\(991\) −537.716 + 195.712i −0.542599 + 0.197490i −0.598755 0.800932i \(-0.704338\pi\)
0.0561562 + 0.998422i \(0.482116\pi\)
\(992\) −51.0145 436.457i −0.0514260 0.439977i
\(993\) 608.173 240.889i 0.612461 0.242587i
\(994\) −516.613 547.577i −0.519731 0.550883i
\(995\) −653.716 486.673i −0.657001 0.489119i
\(996\) 310.491 664.069i 0.311738 0.666736i
\(997\) 235.252 118.148i 0.235960 0.118504i −0.326890 0.945062i \(-0.606001\pi\)
0.562851 + 0.826558i \(0.309705\pi\)
\(998\) 1232.33 + 711.485i 1.23480 + 0.712911i
\(999\) 6.65001 73.4043i 0.00665666 0.0734778i
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 81.3.h.a.2.3 306
3.2 odd 2 243.3.h.a.8.15 306
81.40 even 27 243.3.h.a.152.15 306
81.41 odd 54 inner 81.3.h.a.41.3 yes 306
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.3.h.a.2.3 306 1.1 even 1 trivial
81.3.h.a.41.3 yes 306 81.41 odd 54 inner
243.3.h.a.8.15 306 3.2 odd 2
243.3.h.a.152.15 306 81.40 even 27