Properties

Label 456.2.bu.c.131.65
Level $456$
Weight $2$
Character 456.131
Analytic conductor $3.641$
Analytic rank $0$
Dimension $432$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [456,2,Mod(35,456)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(456, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("456.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.bu (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.64117833217\)
Analytic rank: \(0\)
Dimension: \(432\)
Relative dimension: \(72\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 131.65
Character \(\chi\) \(=\) 456.131
Dual form 456.2.bu.c.275.65

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.32022 - 0.506983i) q^{2} +(-0.675866 + 1.59474i) q^{3} +(1.48594 - 1.33865i) q^{4} +(-1.38328 + 0.503472i) q^{5} +(-0.0837809 + 2.44806i) q^{6} +(3.92214 - 2.26445i) q^{7} +(1.28308 - 2.52066i) q^{8} +(-2.08641 - 2.15567i) q^{9} +O(q^{10})\) \(q+(1.32022 - 0.506983i) q^{2} +(-0.675866 + 1.59474i) q^{3} +(1.48594 - 1.33865i) q^{4} +(-1.38328 + 0.503472i) q^{5} +(-0.0837809 + 2.44806i) q^{6} +(3.92214 - 2.26445i) q^{7} +(1.28308 - 2.52066i) q^{8} +(-2.08641 - 2.15567i) q^{9} +(-1.57097 + 1.36599i) q^{10} +(0.674933 + 0.389673i) q^{11} +(1.13051 + 3.27444i) q^{12} +(1.93582 + 2.30702i) q^{13} +(4.03003 - 4.97802i) q^{14} +(0.132002 - 2.54625i) q^{15} +(0.416012 - 3.97831i) q^{16} +(6.89185 + 1.21522i) q^{17} +(-3.84740 - 1.78817i) q^{18} +(-1.66915 + 4.02665i) q^{19} +(-1.38149 + 2.59986i) q^{20} +(0.960373 + 7.78528i) q^{21} +(1.08861 + 0.172272i) q^{22} +(-2.25555 - 0.820955i) q^{23} +(3.15261 + 3.74981i) q^{24} +(-2.17025 + 1.82106i) q^{25} +(3.72532 + 2.06434i) q^{26} +(4.84787 - 1.87035i) q^{27} +(2.79674 - 8.61522i) q^{28} +(-0.354954 - 2.01304i) q^{29} +(-1.11663 - 3.42852i) q^{30} +(-5.63852 + 3.25540i) q^{31} +(-1.46771 - 5.46313i) q^{32} +(-1.07759 + 0.812978i) q^{33} +(9.71482 - 1.88970i) q^{34} +(-4.28532 + 5.10705i) q^{35} +(-5.98596 - 0.410201i) q^{36} -5.12134i q^{37} +(-0.162188 + 6.16228i) q^{38} +(-4.98746 + 1.52790i) q^{39} +(-0.505777 + 4.13276i) q^{40} +(1.68681 - 2.01026i) q^{41} +(5.21490 + 9.79135i) q^{42} +(-0.343217 + 0.124921i) q^{43} +(1.52454 - 0.324473i) q^{44} +(3.97140 + 1.93143i) q^{45} +(-3.39403 + 0.0596913i) q^{46} +(-0.490410 - 2.78126i) q^{47} +(6.06321 + 3.35224i) q^{48} +(6.75547 - 11.7008i) q^{49} +(-1.94195 + 3.50447i) q^{50} +(-6.59593 + 10.1694i) q^{51} +(5.96481 + 0.836693i) q^{52} +(-6.24605 - 2.27338i) q^{53} +(5.45199 - 4.92705i) q^{54} +(-1.12981 - 0.199216i) q^{55} +(-0.675474 - 12.7918i) q^{56} +(-5.29336 - 5.38334i) q^{57} +(-1.48919 - 2.47769i) q^{58} +(-14.3723 - 2.53423i) q^{59} +(-3.21240 - 3.96027i) q^{60} +(2.28545 - 6.27923i) q^{61} +(-5.79363 + 7.15646i) q^{62} +(-13.0646 - 3.73026i) q^{63} +(-4.70741 - 6.46841i) q^{64} +(-3.83930 - 2.21662i) q^{65} +(-1.01049 + 1.61963i) q^{66} +(1.30535 + 7.40302i) q^{67} +(11.8676 - 7.42006i) q^{68} +(2.83366 - 3.04217i) q^{69} +(-3.06836 + 8.91499i) q^{70} +(-5.55190 + 2.02073i) q^{71} +(-8.11072 + 2.49323i) q^{72} +(1.02524 + 0.860276i) q^{73} +(-2.59643 - 6.76127i) q^{74} +(-1.43732 - 4.69178i) q^{75} +(2.91005 + 8.21776i) q^{76} +3.52958 q^{77} +(-5.80991 + 4.54572i) q^{78} +(-10.0657 + 11.9958i) q^{79} +(1.42750 + 5.71255i) q^{80} +(-0.293787 + 8.99520i) q^{81} +(1.20778 - 3.50917i) q^{82} +(2.94697 - 1.70143i) q^{83} +(11.8488 + 10.2828i) q^{84} +(-10.1452 + 1.78887i) q^{85} +(-0.389787 + 0.338927i) q^{86} +(3.45019 + 0.794487i) q^{87} +(1.84822 - 1.20129i) q^{88} +(10.1930 + 12.1475i) q^{89} +(6.22231 + 0.536476i) q^{90} +(12.8167 + 4.66490i) q^{91} +(-4.45058 + 1.79952i) q^{92} +(-1.38064 - 11.1922i) q^{93} +(-2.05750 - 3.42323i) q^{94} +(0.281587 - 6.41035i) q^{95} +(9.70427 + 1.35173i) q^{96} +(0.436566 - 2.47589i) q^{97} +(2.98656 - 18.8725i) q^{98} +(-0.568183 - 2.26795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 432 q - 18 q^{3} - 6 q^{4} + 6 q^{6} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 432 q - 18 q^{3} - 6 q^{4} + 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 6 q^{16} - 12 q^{18} - 24 q^{19} + 24 q^{22} - 18 q^{24} - 24 q^{25} - 36 q^{27} - 36 q^{28} - 48 q^{30} - 54 q^{34} + 66 q^{36} + 18 q^{40} - 51 q^{42} - 24 q^{43} - 6 q^{46} + 117 q^{48} + 228 q^{49} + 66 q^{51} + 12 q^{52} + 21 q^{54} - 12 q^{57} - 96 q^{58} + 48 q^{60} - 144 q^{64} - 78 q^{66} + 60 q^{67} - 162 q^{70} - 84 q^{72} - 72 q^{73} - 192 q^{75} - 132 q^{76} + 3 q^{78} - 42 q^{81} - 252 q^{82} - 45 q^{84} - 126 q^{88} + 24 q^{90} - 108 q^{91} - 48 q^{94} + 138 q^{96} - 84 q^{97} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(343\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.32022 0.506983i 0.933533 0.358491i
\(3\) −0.675866 + 1.59474i −0.390211 + 0.920725i
\(4\) 1.48594 1.33865i 0.742968 0.669327i
\(5\) −1.38328 + 0.503472i −0.618620 + 0.225159i −0.632271 0.774747i \(-0.717877\pi\)
0.0136505 + 0.999907i \(0.495655\pi\)
\(6\) −0.0837809 + 2.44806i −0.0342034 + 0.999415i
\(7\) 3.92214 2.26445i 1.48243 0.855882i 0.482630 0.875825i \(-0.339682\pi\)
0.999801 + 0.0199427i \(0.00634838\pi\)
\(8\) 1.28308 2.52066i 0.453637 0.891186i
\(9\) −2.08641 2.15567i −0.695470 0.718555i
\(10\) −1.57097 + 1.36599i −0.496785 + 0.431964i
\(11\) 0.674933 + 0.389673i 0.203500 + 0.117491i 0.598287 0.801282i \(-0.295848\pi\)
−0.394787 + 0.918773i \(0.629182\pi\)
\(12\) 1.13051 + 3.27444i 0.326351 + 0.945248i
\(13\) 1.93582 + 2.30702i 0.536900 + 0.639853i 0.964490 0.264120i \(-0.0850815\pi\)
−0.427589 + 0.903973i \(0.640637\pi\)
\(14\) 4.03003 4.97802i 1.07707 1.33043i
\(15\) 0.132002 2.54625i 0.0340828 0.657439i
\(16\) 0.416012 3.97831i 0.104003 0.994577i
\(17\) 6.89185 + 1.21522i 1.67152 + 0.294734i 0.927611 0.373549i \(-0.121859\pi\)
0.743908 + 0.668282i \(0.232970\pi\)
\(18\) −3.84740 1.78817i −0.906840 0.421475i
\(19\) −1.66915 + 4.02665i −0.382929 + 0.923778i
\(20\) −1.38149 + 2.59986i −0.308910 + 0.581345i
\(21\) 0.960373 + 7.78528i 0.209570 + 1.69889i
\(22\) 1.08861 + 0.172272i 0.232093 + 0.0367285i
\(23\) −2.25555 0.820955i −0.470316 0.171181i 0.0959797 0.995383i \(-0.469402\pi\)
−0.566295 + 0.824202i \(0.691624\pi\)
\(24\) 3.15261 + 3.74981i 0.643523 + 0.765427i
\(25\) −2.17025 + 1.82106i −0.434050 + 0.364211i
\(26\) 3.72532 + 2.06434i 0.730596 + 0.404850i
\(27\) 4.84787 1.87035i 0.932972 0.359948i
\(28\) 2.79674 8.61522i 0.528534 1.62812i
\(29\) −0.354954 2.01304i −0.0659132 0.373812i −0.999865 0.0164141i \(-0.994775\pi\)
0.933952 0.357398i \(-0.116336\pi\)
\(30\) −1.11663 3.42852i −0.203869 0.625960i
\(31\) −5.63852 + 3.25540i −1.01271 + 0.584687i −0.911983 0.410227i \(-0.865449\pi\)
−0.100725 + 0.994914i \(0.532116\pi\)
\(32\) −1.46771 5.46313i −0.259457 0.965755i
\(33\) −1.07759 + 0.812978i −0.187585 + 0.141521i
\(34\) 9.71482 1.88970i 1.66608 0.324081i
\(35\) −4.28532 + 5.10705i −0.724352 + 0.863249i
\(36\) −5.98596 0.410201i −0.997660 0.0683668i
\(37\) 5.12134i 0.841943i −0.907074 0.420972i \(-0.861689\pi\)
0.907074 0.420972i \(-0.138311\pi\)
\(38\) −0.162188 + 6.16228i −0.0263103 + 0.999654i
\(39\) −4.98746 + 1.52790i −0.798634 + 0.244660i
\(40\) −0.505777 + 4.13276i −0.0799704 + 0.653447i
\(41\) 1.68681 2.01026i 0.263436 0.313951i −0.618071 0.786123i \(-0.712085\pi\)
0.881506 + 0.472172i \(0.156530\pi\)
\(42\) 5.21490 + 9.79135i 0.804677 + 1.51084i
\(43\) −0.343217 + 0.124921i −0.0523401 + 0.0190502i −0.368058 0.929803i \(-0.619977\pi\)
0.315717 + 0.948853i \(0.397755\pi\)
\(44\) 1.52454 0.324473i 0.229834 0.0489161i
\(45\) 3.97140 + 1.93143i 0.592021 + 0.287921i
\(46\) −3.39403 + 0.0596913i −0.500422 + 0.00880101i
\(47\) −0.490410 2.78126i −0.0715337 0.405688i −0.999458 0.0329192i \(-0.989520\pi\)
0.927924 0.372769i \(-0.121592\pi\)
\(48\) 6.06321 + 3.35224i 0.875149 + 0.483854i
\(49\) 6.75547 11.7008i 0.965067 1.67155i
\(50\) −1.94195 + 3.50447i −0.274634 + 0.495606i
\(51\) −6.59593 + 10.1694i −0.923614 + 1.42400i
\(52\) 5.96481 + 0.836693i 0.827171 + 0.116028i
\(53\) −6.24605 2.27338i −0.857962 0.312272i −0.124680 0.992197i \(-0.539790\pi\)
−0.733282 + 0.679925i \(0.762013\pi\)
\(54\) 5.45199 4.92705i 0.741922 0.670486i
\(55\) −1.12981 0.199216i −0.152343 0.0268622i
\(56\) −0.675474 12.7918i −0.0902640 1.70938i
\(57\) −5.29336 5.38334i −0.701123 0.713041i
\(58\) −1.48919 2.47769i −0.195541 0.325337i
\(59\) −14.3723 2.53423i −1.87112 0.329928i −0.881332 0.472497i \(-0.843353\pi\)
−0.989785 + 0.142569i \(0.954464\pi\)
\(60\) −3.21240 3.96027i −0.414719 0.511269i
\(61\) 2.28545 6.27923i 0.292622 0.803973i −0.703059 0.711132i \(-0.748183\pi\)
0.995681 0.0928409i \(-0.0295948\pi\)
\(62\) −5.79363 + 7.15646i −0.735791 + 0.908872i
\(63\) −13.0646 3.73026i −1.64598 0.469968i
\(64\) −4.70741 6.46841i −0.588426 0.808551i
\(65\) −3.83930 2.21662i −0.476206 0.274938i
\(66\) −1.01049 + 1.61963i −0.124382 + 0.199362i
\(67\) 1.30535 + 7.40302i 0.159474 + 0.904423i 0.954581 + 0.297953i \(0.0963039\pi\)
−0.795106 + 0.606470i \(0.792585\pi\)
\(68\) 11.8676 7.42006i 1.43916 0.899814i
\(69\) 2.83366 3.04217i 0.341133 0.366235i
\(70\) −3.06836 + 8.91499i −0.366739 + 1.06555i
\(71\) −5.55190 + 2.02073i −0.658889 + 0.239816i −0.649757 0.760142i \(-0.725129\pi\)
−0.00913244 + 0.999958i \(0.502907\pi\)
\(72\) −8.11072 + 2.49323i −0.955858 + 0.293830i
\(73\) 1.02524 + 0.860276i 0.119995 + 0.100688i 0.700811 0.713347i \(-0.252822\pi\)
−0.580816 + 0.814035i \(0.697266\pi\)
\(74\) −2.59643 6.76127i −0.301829 0.785982i
\(75\) −1.43732 4.69178i −0.165967 0.541760i
\(76\) 2.91005 + 8.21776i 0.333806 + 0.942642i
\(77\) 3.52958 0.402233
\(78\) −5.80991 + 4.54572i −0.657842 + 0.514701i
\(79\) −10.0657 + 11.9958i −1.13248 + 1.34964i −0.203686 + 0.979036i \(0.565292\pi\)
−0.928793 + 0.370600i \(0.879152\pi\)
\(80\) 1.42750 + 5.71255i 0.159600 + 0.638683i
\(81\) −0.293787 + 8.99520i −0.0326430 + 0.999467i
\(82\) 1.20778 3.50917i 0.133377 0.387523i
\(83\) 2.94697 1.70143i 0.323472 0.186757i −0.329467 0.944167i \(-0.606869\pi\)
0.652939 + 0.757410i \(0.273536\pi\)
\(84\) 11.8488 + 10.2828i 1.29281 + 1.12195i
\(85\) −10.1452 + 1.78887i −1.10040 + 0.194030i
\(86\) −0.389787 + 0.338927i −0.0420319 + 0.0365475i
\(87\) 3.45019 + 0.794487i 0.369899 + 0.0851779i
\(88\) 1.84822 1.20129i 0.197021 0.128058i
\(89\) 10.1930 + 12.1475i 1.08046 + 1.28764i 0.955344 + 0.295495i \(0.0954846\pi\)
0.125112 + 0.992143i \(0.460071\pi\)
\(90\) 6.22231 + 0.536476i 0.655889 + 0.0565495i
\(91\) 12.8167 + 4.66490i 1.34356 + 0.489015i
\(92\) −4.45058 + 1.79952i −0.464005 + 0.187613i
\(93\) −1.38064 11.1922i −0.143166 1.16058i
\(94\) −2.05750 3.42323i −0.212215 0.353079i
\(95\) 0.281587 6.41035i 0.0288902 0.657688i
\(96\) 9.70427 + 1.35173i 0.990438 + 0.137960i
\(97\) 0.436566 2.47589i 0.0443266 0.251388i −0.954590 0.297922i \(-0.903706\pi\)
0.998917 + 0.0465338i \(0.0148175\pi\)
\(98\) 2.98656 18.8725i 0.301688 1.90641i
\(99\) −0.568183 2.26795i −0.0571045 0.227937i
\(100\) −0.787090 + 5.61119i −0.0787090 + 0.561119i
\(101\) −7.68054 + 6.44474i −0.764242 + 0.641276i −0.939227 0.343296i \(-0.888457\pi\)
0.174985 + 0.984571i \(0.444012\pi\)
\(102\) −3.55233 + 16.7698i −0.351733 + 1.66046i
\(103\) −14.9501 8.63142i −1.47307 0.850479i −0.473532 0.880777i \(-0.657021\pi\)
−0.999541 + 0.0302978i \(0.990354\pi\)
\(104\) 8.29903 1.91944i 0.813786 0.188217i
\(105\) −5.24813 10.2857i −0.512165 1.00378i
\(106\) −9.39870 + 0.165296i −0.912882 + 0.0160550i
\(107\) 10.3723 5.98847i 1.00273 0.578927i 0.0936759 0.995603i \(-0.470138\pi\)
0.909055 + 0.416676i \(0.136805\pi\)
\(108\) 4.69987 9.26883i 0.452246 0.891893i
\(109\) 3.39045 + 9.31520i 0.324747 + 0.892234i 0.989417 + 0.145098i \(0.0463496\pi\)
−0.664671 + 0.747136i \(0.731428\pi\)
\(110\) −1.59259 + 0.309786i −0.151847 + 0.0295370i
\(111\) 8.16722 + 3.46134i 0.775198 + 0.328536i
\(112\) −7.37702 16.5455i −0.697063 1.56341i
\(113\) 7.14511i 0.672155i 0.941834 + 0.336078i \(0.109100\pi\)
−0.941834 + 0.336078i \(0.890900\pi\)
\(114\) −9.71764 4.42352i −0.910140 0.414301i
\(115\) 3.53338 0.329490
\(116\) −3.22220 2.51609i −0.299174 0.233613i
\(117\) 0.934251 8.98638i 0.0863715 0.830791i
\(118\) −20.2594 + 3.94080i −1.86503 + 0.362780i
\(119\) 29.7826 10.8400i 2.73017 0.993700i
\(120\) −6.24885 3.59978i −0.570439 0.328613i
\(121\) −5.19631 9.00027i −0.472392 0.818207i
\(122\) −0.166174 9.44862i −0.0150447 0.855437i
\(123\) 2.06580 + 4.04870i 0.186267 + 0.365059i
\(124\) −4.02063 + 12.3853i −0.361063 + 1.11224i
\(125\) 5.76534 9.98586i 0.515668 0.893162i
\(126\) −19.1393 + 1.69879i −1.70506 + 0.151340i
\(127\) 8.25889 + 9.84257i 0.732858 + 0.873386i 0.995812 0.0914219i \(-0.0291412\pi\)
−0.262954 + 0.964808i \(0.584697\pi\)
\(128\) −9.49417 6.15311i −0.839174 0.543864i
\(129\) 0.0327522 0.631772i 0.00288367 0.0556245i
\(130\) −6.19249 0.979956i −0.543117 0.0859478i
\(131\) −6.38338 1.12556i −0.557719 0.0983409i −0.112318 0.993672i \(-0.535828\pi\)
−0.445401 + 0.895331i \(0.646939\pi\)
\(132\) −0.512937 + 2.65056i −0.0446454 + 0.230701i
\(133\) 2.57152 + 19.5728i 0.222979 + 1.69718i
\(134\) 5.47655 + 9.11179i 0.473102 + 0.787139i
\(135\) −5.76428 + 5.02797i −0.496110 + 0.432739i
\(136\) 11.9059 15.8127i 1.02093 1.35593i
\(137\) 2.01091 5.52493i 0.171804 0.472027i −0.823669 0.567070i \(-0.808077\pi\)
0.995473 + 0.0950435i \(0.0302990\pi\)
\(138\) 2.19872 5.45294i 0.187167 0.464185i
\(139\) −12.3615 + 10.3725i −1.04849 + 0.879783i −0.992933 0.118672i \(-0.962136\pi\)
−0.0555516 + 0.998456i \(0.517692\pi\)
\(140\) 0.468854 + 13.3253i 0.0396254 + 1.12619i
\(141\) 4.76684 + 1.09768i 0.401440 + 0.0924412i
\(142\) −6.30523 + 5.48251i −0.529123 + 0.460082i
\(143\) 0.407566 + 2.31142i 0.0340824 + 0.193291i
\(144\) −9.44387 + 7.40360i −0.786989 + 0.616966i
\(145\) 1.50451 + 2.60589i 0.124943 + 0.216407i
\(146\) 1.78968 + 0.615972i 0.148115 + 0.0509782i
\(147\) 14.0940 + 18.6814i 1.16245 + 1.54082i
\(148\) −6.85570 7.60998i −0.563535 0.625537i
\(149\) 8.14449 + 6.83404i 0.667222 + 0.559866i 0.912242 0.409652i \(-0.134350\pi\)
−0.245019 + 0.969518i \(0.578794\pi\)
\(150\) −4.27622 5.46547i −0.349152 0.446253i
\(151\) 0.110330i 0.00897852i −0.999990 0.00448926i \(-0.998571\pi\)
0.999990 0.00448926i \(-0.00142898\pi\)
\(152\) 8.00816 + 9.37387i 0.649547 + 0.760321i
\(153\) −11.7596 17.3920i −0.950708 1.40606i
\(154\) 4.65980 1.78944i 0.375498 0.144197i
\(155\) 6.16063 7.34196i 0.494834 0.589720i
\(156\) −5.36573 + 8.94685i −0.429602 + 0.716321i
\(157\) 4.26475 + 11.7173i 0.340364 + 0.935142i 0.985289 + 0.170896i \(0.0546662\pi\)
−0.644925 + 0.764246i \(0.723112\pi\)
\(158\) −7.20720 + 20.9402i −0.573374 + 1.66591i
\(159\) 7.84695 8.42435i 0.622304 0.668095i
\(160\) 4.78078 + 6.81808i 0.377954 + 0.539016i
\(161\) −10.7056 + 1.88769i −0.843721 + 0.148771i
\(162\) 4.17256 + 12.0245i 0.327827 + 0.944738i
\(163\) −1.39649 + 2.41879i −0.109381 + 0.189454i −0.915520 0.402273i \(-0.868220\pi\)
0.806138 + 0.591727i \(0.201554\pi\)
\(164\) −0.184553 5.24518i −0.0144112 0.409580i
\(165\) 1.08130 1.66711i 0.0841788 0.129784i
\(166\) 3.02803 3.74032i 0.235021 0.290305i
\(167\) −12.3186 4.48361i −0.953244 0.346952i −0.181861 0.983324i \(-0.558212\pi\)
−0.771382 + 0.636372i \(0.780434\pi\)
\(168\) 20.8562 + 7.56837i 1.60909 + 0.583912i
\(169\) 0.682479 3.87053i 0.0524984 0.297733i
\(170\) −12.4869 + 7.50511i −0.957699 + 0.575616i
\(171\) 12.1626 4.80313i 0.930101 0.367304i
\(172\) −0.342773 + 0.645073i −0.0261362 + 0.0491863i
\(173\) −2.85482 + 16.1905i −0.217048 + 1.23094i 0.660268 + 0.751030i \(0.270443\pi\)
−0.877317 + 0.479912i \(0.840669\pi\)
\(174\) 4.95778 0.700292i 0.375848 0.0530890i
\(175\) −4.38834 + 12.0569i −0.331727 + 0.911414i
\(176\) 1.83102 2.52298i 0.138018 0.190177i
\(177\) 13.7552 21.2074i 1.03390 1.59404i
\(178\) 19.6156 + 10.8697i 1.47025 + 0.814718i
\(179\) −10.6108 6.12613i −0.793086 0.457888i 0.0479621 0.998849i \(-0.484727\pi\)
−0.841048 + 0.540961i \(0.818061\pi\)
\(180\) 8.48677 2.44634i 0.632566 0.182339i
\(181\) 2.48360 0.437926i 0.184605 0.0325508i −0.0805815 0.996748i \(-0.525678\pi\)
0.265186 + 0.964197i \(0.414567\pi\)
\(182\) 19.2858 0.339183i 1.42956 0.0251419i
\(183\) 8.46909 + 7.88862i 0.626053 + 0.583144i
\(184\) −4.96340 + 4.63213i −0.365907 + 0.341485i
\(185\) 2.57845 + 7.08423i 0.189571 + 0.520843i
\(186\) −7.49701 14.0762i −0.549707 1.03211i
\(187\) 4.17800 + 3.50575i 0.305525 + 0.256366i
\(188\) −4.45186 3.47628i −0.324685 0.253534i
\(189\) 14.7787 18.3135i 1.07499 1.33211i
\(190\) −2.87818 8.60580i −0.208805 0.624330i
\(191\) 3.53097 0.255492 0.127746 0.991807i \(-0.459226\pi\)
0.127746 + 0.991807i \(0.459226\pi\)
\(192\) 13.4970 3.13533i 0.974064 0.226273i
\(193\) −2.83709 2.38060i −0.204218 0.171360i 0.534942 0.844888i \(-0.320333\pi\)
−0.739161 + 0.673529i \(0.764778\pi\)
\(194\) −0.678873 3.49004i −0.0487402 0.250570i
\(195\) 6.12979 4.62456i 0.438963 0.331171i
\(196\) −5.62515 26.4299i −0.401796 1.88785i
\(197\) −3.59817 6.23221i −0.256359 0.444026i 0.708905 0.705304i \(-0.249190\pi\)
−0.965264 + 0.261278i \(0.915856\pi\)
\(198\) −1.89993 2.70612i −0.135022 0.192315i
\(199\) 20.3950 3.59618i 1.44576 0.254927i 0.604954 0.796261i \(-0.293192\pi\)
0.840808 + 0.541334i \(0.182081\pi\)
\(200\) 1.80565 + 7.80702i 0.127679 + 0.552039i
\(201\) −12.6882 2.92175i −0.894954 0.206084i
\(202\) −6.87259 + 12.4023i −0.483554 + 0.872626i
\(203\) −5.95061 7.09166i −0.417651 0.497737i
\(204\) 3.81218 + 23.9407i 0.266906 + 1.67619i
\(205\) −1.32122 + 3.63001i −0.0922778 + 0.253531i
\(206\) −24.1133 3.81590i −1.68005 0.265867i
\(207\) 2.93631 + 6.57507i 0.204088 + 0.456999i
\(208\) 9.98337 6.74155i 0.692222 0.467442i
\(209\) −2.69564 + 2.06730i −0.186461 + 0.142998i
\(210\) −12.1433 10.9186i −0.837969 0.753454i
\(211\) 3.42858 19.4445i 0.236033 1.33861i −0.604393 0.796686i \(-0.706584\pi\)
0.840426 0.541926i \(-0.182305\pi\)
\(212\) −12.3245 + 4.98321i −0.846450 + 0.342248i
\(213\) 0.529802 10.2196i 0.0363014 0.700235i
\(214\) 10.6577 13.1647i 0.728542 0.899918i
\(215\) 0.411870 0.345600i 0.0280893 0.0235697i
\(216\) 1.50570 14.6196i 0.102450 0.994738i
\(217\) −14.7434 + 25.5363i −1.00085 + 1.73352i
\(218\) 9.19878 + 10.5792i 0.623020 + 0.716511i
\(219\) −2.06484 + 1.05356i −0.139529 + 0.0711929i
\(220\) −1.94550 + 1.21640i −0.131166 + 0.0820097i
\(221\) 10.5379 + 18.2521i 0.708853 + 1.22777i
\(222\) 12.5373 + 0.429070i 0.841450 + 0.0287973i
\(223\) 3.08611 + 8.47903i 0.206662 + 0.567798i 0.999112 0.0421387i \(-0.0134171\pi\)
−0.792450 + 0.609937i \(0.791195\pi\)
\(224\) −18.1276 18.1036i −1.21120 1.20960i
\(225\) 8.45362 + 0.878864i 0.563575 + 0.0585909i
\(226\) 3.62245 + 9.43308i 0.240962 + 0.627479i
\(227\) 5.08237i 0.337329i 0.985674 + 0.168664i \(0.0539454\pi\)
−0.985674 + 0.168664i \(0.946055\pi\)
\(228\) −15.0720 0.913325i −0.998169 0.0604865i
\(229\) 26.2190i 1.73260i −0.499524 0.866300i \(-0.666492\pi\)
0.499524 0.866300i \(-0.333508\pi\)
\(230\) 4.66483 1.79137i 0.307590 0.118119i
\(231\) −2.38552 + 5.62877i −0.156956 + 0.370346i
\(232\) −5.52962 1.68818i −0.363037 0.110834i
\(233\) −2.18872 6.01346i −0.143388 0.393955i 0.847122 0.531399i \(-0.178333\pi\)
−0.990510 + 0.137444i \(0.956111\pi\)
\(234\) −3.32253 12.3376i −0.217201 0.806534i
\(235\) 2.07866 + 3.60034i 0.135597 + 0.234860i
\(236\) −24.7488 + 15.4739i −1.61101 + 1.00726i
\(237\) −12.3272 24.1598i −0.800738 1.56935i
\(238\) 33.8238 29.4104i 2.19247 1.90639i
\(239\) 1.28049 2.21787i 0.0828281 0.143462i −0.821636 0.570013i \(-0.806938\pi\)
0.904464 + 0.426551i \(0.140271\pi\)
\(240\) −10.0749 1.58442i −0.650329 0.102274i
\(241\) 7.18930 6.03254i 0.463104 0.388590i −0.381168 0.924506i \(-0.624478\pi\)
0.844271 + 0.535916i \(0.180034\pi\)
\(242\) −11.4232 9.24786i −0.734313 0.594475i
\(243\) −14.1465 6.54807i −0.907497 0.420059i
\(244\) −5.00967 12.3900i −0.320712 0.793186i
\(245\) −3.45366 + 19.5867i −0.220646 + 1.25135i
\(246\) 4.77992 + 4.29783i 0.304756 + 0.274020i
\(247\) −12.5208 + 3.94413i −0.796677 + 0.250959i
\(248\) 0.971069 + 18.3897i 0.0616630 + 1.16775i
\(249\) 0.721592 + 5.84960i 0.0457290 + 0.370703i
\(250\) 2.54883 16.1064i 0.161202 1.01866i
\(251\) 6.57104 18.0538i 0.414760 1.13954i −0.539870 0.841749i \(-0.681526\pi\)
0.954630 0.297795i \(-0.0962513\pi\)
\(252\) −24.4067 + 11.9460i −1.53748 + 0.752530i
\(253\) −1.20244 1.43302i −0.0755970 0.0900930i
\(254\) 15.8935 + 8.80718i 0.997249 + 0.552612i
\(255\) 4.00399 17.3880i 0.250740 1.08888i
\(256\) −15.6539 3.31005i −0.978367 0.206878i
\(257\) 26.8702 4.73795i 1.67612 0.295545i 0.746862 0.664979i \(-0.231559\pi\)
0.929257 + 0.369434i \(0.120448\pi\)
\(258\) −0.277058 0.850680i −0.0172489 0.0529610i
\(259\) −11.5970 20.0866i −0.720604 1.24812i
\(260\) −8.67224 + 1.84574i −0.537829 + 0.114468i
\(261\) −3.59887 + 4.96519i −0.222764 + 0.307338i
\(262\) −8.99808 + 1.75028i −0.555903 + 0.108133i
\(263\) −6.72819 5.64563i −0.414878 0.348124i 0.411332 0.911485i \(-0.365064\pi\)
−0.826211 + 0.563361i \(0.809508\pi\)
\(264\) 0.666600 + 3.75935i 0.0410264 + 0.231372i
\(265\) 9.78461 0.601064
\(266\) 13.3181 + 24.5366i 0.816582 + 1.50444i
\(267\) −26.2613 + 8.04510i −1.60717 + 0.492352i
\(268\) 11.8498 + 9.25300i 0.723839 + 0.565217i
\(269\) 0.784327 + 0.658129i 0.0478213 + 0.0401268i 0.666385 0.745608i \(-0.267841\pi\)
−0.618564 + 0.785735i \(0.712285\pi\)
\(270\) −5.06099 + 9.56039i −0.308002 + 0.581827i
\(271\) −5.71464 15.7008i −0.347140 0.953759i −0.983266 0.182174i \(-0.941687\pi\)
0.636127 0.771585i \(-0.280536\pi\)
\(272\) 7.70161 26.9123i 0.466979 1.63180i
\(273\) −16.1017 + 17.2865i −0.974519 + 1.04623i
\(274\) −0.146213 8.31360i −0.00883303 0.502243i
\(275\) −2.17439 + 0.383404i −0.131121 + 0.0231201i
\(276\) 0.138227 8.31377i 0.00832028 0.500430i
\(277\) 8.62052 + 4.97706i 0.517957 + 0.299043i 0.736098 0.676875i \(-0.236666\pi\)
−0.218141 + 0.975917i \(0.569999\pi\)
\(278\) −11.0611 + 19.9610i −0.663401 + 1.19718i
\(279\) 18.7818 + 5.36266i 1.12444 + 0.321054i
\(280\) 7.37470 + 17.3546i 0.440723 + 1.03713i
\(281\) 2.58049 7.08984i 0.153939 0.422945i −0.838619 0.544719i \(-0.816636\pi\)
0.992558 + 0.121775i \(0.0388585\pi\)
\(282\) 6.84976 0.967536i 0.407897 0.0576160i
\(283\) −0.781735 + 4.43344i −0.0464693 + 0.263540i −0.999187 0.0403165i \(-0.987163\pi\)
0.952718 + 0.303857i \(0.0982745\pi\)
\(284\) −5.54471 + 10.4347i −0.329018 + 0.619188i
\(285\) 10.0325 + 4.78159i 0.594276 + 0.283237i
\(286\) 1.70993 + 2.84495i 0.101110 + 0.168225i
\(287\) 2.06377 11.7042i 0.121821 0.690880i
\(288\) −8.71445 + 14.5622i −0.513504 + 0.858087i
\(289\) 30.0460 + 10.9359i 1.76741 + 0.643286i
\(290\) 3.30741 + 2.67757i 0.194218 + 0.157232i
\(291\) 3.65335 + 2.36958i 0.214163 + 0.138907i
\(292\) 2.67505 0.0941222i 0.156545 0.00550808i
\(293\) 10.7771 18.6665i 0.629606 1.09051i −0.358025 0.933712i \(-0.616550\pi\)
0.987631 0.156797i \(-0.0501169\pi\)
\(294\) 28.0783 + 17.5181i 1.63756 + 1.02168i
\(295\) 21.1568 3.73052i 1.23180 0.217199i
\(296\) −12.9091 6.57109i −0.750328 0.381937i
\(297\) 4.00081 + 0.626723i 0.232150 + 0.0363661i
\(298\) 14.2172 + 4.89328i 0.823581 + 0.283460i
\(299\) −2.47239 6.79284i −0.142982 0.392840i
\(300\) −8.41643 5.04762i −0.485923 0.291424i
\(301\) −1.06327 + 1.26715i −0.0612858 + 0.0730376i
\(302\) −0.0559354 0.145659i −0.00321872 0.00838175i
\(303\) −5.08668 16.6043i −0.292222 0.953890i
\(304\) 15.3249 + 8.31552i 0.878942 + 0.476928i
\(305\) 9.83657i 0.563240i
\(306\) −24.3426 16.9992i −1.39158 0.971780i
\(307\) 9.91892 + 8.32296i 0.566103 + 0.475017i 0.880350 0.474325i \(-0.157308\pi\)
−0.314247 + 0.949341i \(0.601752\pi\)
\(308\) 5.24473 4.72488i 0.298846 0.269225i
\(309\) 23.8691 18.0078i 1.35787 1.02443i
\(310\) 4.41111 12.8163i 0.250534 0.727917i
\(311\) 15.7772 + 27.3270i 0.894644 + 1.54957i 0.834244 + 0.551395i \(0.185904\pi\)
0.0604003 + 0.998174i \(0.480762\pi\)
\(312\) −2.54801 + 14.5321i −0.144253 + 0.822718i
\(313\) 3.25294 + 18.4484i 0.183867 + 1.04276i 0.927402 + 0.374066i \(0.122037\pi\)
−0.743535 + 0.668697i \(0.766852\pi\)
\(314\) 11.5709 + 13.3072i 0.652981 + 0.750968i
\(315\) 19.9500 1.41768i 1.12406 0.0798770i
\(316\) 1.10128 + 31.2995i 0.0619518 + 1.76074i
\(317\) 3.02944 2.54200i 0.170150 0.142773i −0.553736 0.832692i \(-0.686798\pi\)
0.723886 + 0.689919i \(0.242354\pi\)
\(318\) 6.08866 15.1002i 0.341435 0.846779i
\(319\) 0.544857 1.49698i 0.0305062 0.0838150i
\(320\) 9.76831 + 6.57755i 0.546065 + 0.367696i
\(321\) 2.53976 + 20.5886i 0.141756 + 1.14914i
\(322\) −13.1767 + 7.91973i −0.734308 + 0.441349i
\(323\) −16.3968 + 25.7227i −0.912341 + 1.43125i
\(324\) 11.6049 + 13.7596i 0.644717 + 0.764421i
\(325\) −8.40244 1.48158i −0.466083 0.0821831i
\(326\) −0.617380 + 3.90132i −0.0341935 + 0.216074i
\(327\) −17.1468 0.888923i −0.948222 0.0491575i
\(328\) −2.90287 6.83120i −0.160284 0.377190i
\(329\) −8.22148 9.79797i −0.453265 0.540180i
\(330\) 0.582348 2.74914i 0.0320572 0.151335i
\(331\) 10.7723 18.6581i 0.592098 1.02554i −0.401851 0.915705i \(-0.631633\pi\)
0.993949 0.109839i \(-0.0350336\pi\)
\(332\) 2.10138 6.47319i 0.115328 0.355262i
\(333\) −11.0399 + 10.6852i −0.604983 + 0.585546i
\(334\) −18.5363 + 0.326002i −1.01426 + 0.0178380i
\(335\) −5.53288 9.58322i −0.302293 0.523587i
\(336\) 31.3717 0.581887i 1.71147 0.0317445i
\(337\) −27.7675 + 10.1066i −1.51259 + 0.550539i −0.959286 0.282437i \(-0.908857\pi\)
−0.553308 + 0.832977i \(0.686635\pi\)
\(338\) −1.06127 5.45594i −0.0577257 0.296764i
\(339\) −11.3946 4.82914i −0.618870 0.262283i
\(340\) −12.6804 + 16.2390i −0.687691 + 0.880683i
\(341\) −5.07416 −0.274781
\(342\) 13.6222 12.5074i 0.736604 0.676324i
\(343\) 29.4874i 1.59217i
\(344\) −0.125493 + 1.02542i −0.00676612 + 0.0552867i
\(345\) −2.38809 + 5.63484i −0.128571 + 0.303370i
\(346\) 4.43933 + 22.8223i 0.238660 + 1.22693i
\(347\) −1.35785 3.73066i −0.0728932 0.200272i 0.897895 0.440209i \(-0.145096\pi\)
−0.970789 + 0.239936i \(0.922873\pi\)
\(348\) 6.19030 3.43805i 0.331835 0.184299i
\(349\) 9.78332 5.64840i 0.523689 0.302352i −0.214754 0.976668i \(-0.568895\pi\)
0.738443 + 0.674316i \(0.235562\pi\)
\(350\) 0.319075 + 18.1425i 0.0170553 + 0.969756i
\(351\) 13.6995 + 7.56348i 0.731227 + 0.403709i
\(352\) 1.13823 4.25917i 0.0606678 0.227015i
\(353\) 15.3609 + 8.86865i 0.817581 + 0.472030i 0.849581 0.527457i \(-0.176855\pi\)
−0.0320008 + 0.999488i \(0.510188\pi\)
\(354\) 7.40806 34.9719i 0.393734 1.85874i
\(355\) 6.66243 5.59045i 0.353605 0.296710i
\(356\) 31.4075 + 4.40558i 1.66459 + 0.233495i
\(357\) −2.84207 + 54.8220i −0.150418 + 2.90149i
\(358\) −17.1143 2.70833i −0.904521 0.143140i
\(359\) −4.54098 + 25.7532i −0.239664 + 1.35920i 0.592902 + 0.805274i \(0.297982\pi\)
−0.832566 + 0.553926i \(0.813129\pi\)
\(360\) 9.96411 7.53234i 0.525154 0.396989i
\(361\) −13.4279 13.4422i −0.706731 0.707482i
\(362\) 3.05686 1.83730i 0.160665 0.0965663i
\(363\) 17.8651 2.20380i 0.937676 0.115669i
\(364\) 25.2895 10.2254i 1.32553 0.535956i
\(365\) −1.85131 0.673823i −0.0969021 0.0352695i
\(366\) 15.1804 + 6.12099i 0.793493 + 0.319949i
\(367\) 1.06048 + 1.26384i 0.0553568 + 0.0659717i 0.793012 0.609206i \(-0.208512\pi\)
−0.737656 + 0.675177i \(0.764067\pi\)
\(368\) −4.20435 + 8.63176i −0.219167 + 0.449962i
\(369\) −7.85284 + 0.558033i −0.408802 + 0.0290500i
\(370\) 6.99569 + 8.04548i 0.363689 + 0.418265i
\(371\) −29.6459 + 5.22737i −1.53914 + 0.271391i
\(372\) −17.0340 14.7827i −0.883173 0.766447i
\(373\) −29.8409 + 17.2287i −1.54510 + 0.892066i −0.546599 + 0.837394i \(0.684078\pi\)
−0.998504 + 0.0546719i \(0.982589\pi\)
\(374\) 7.29321 + 2.51018i 0.377123 + 0.129798i
\(375\) 12.0283 + 15.9433i 0.621138 + 0.823310i
\(376\) −7.63982 2.33242i −0.393994 0.120285i
\(377\) 3.95701 4.71578i 0.203796 0.242875i
\(378\) 10.2264 31.6703i 0.525991 1.62895i
\(379\) 1.76237 0.0905271 0.0452636 0.998975i \(-0.485587\pi\)
0.0452636 + 0.998975i \(0.485587\pi\)
\(380\) −8.16282 9.90231i −0.418744 0.507978i
\(381\) −21.2783 + 6.51856i −1.09012 + 0.333956i
\(382\) 4.66164 1.79014i 0.238510 0.0915916i
\(383\) 12.3911 + 10.3974i 0.633156 + 0.531281i 0.901908 0.431928i \(-0.142167\pi\)
−0.268752 + 0.963210i \(0.586611\pi\)
\(384\) 16.2294 10.9821i 0.828204 0.560427i
\(385\) −4.88238 + 1.77704i −0.248829 + 0.0905665i
\(386\) −4.95250 1.70455i −0.252076 0.0867594i
\(387\) 0.985379 + 0.479225i 0.0500896 + 0.0243604i
\(388\) −2.66565 4.26342i −0.135328 0.216443i
\(389\) −4.78738 27.1506i −0.242730 1.37659i −0.825706 0.564101i \(-0.809223\pi\)
0.582976 0.812489i \(-0.301888\pi\)
\(390\) 5.74807 9.21311i 0.291065 0.466524i
\(391\) −14.5473 8.39889i −0.735688 0.424750i
\(392\) −20.8259 32.0413i −1.05187 1.61833i
\(393\) 6.10929 9.41912i 0.308173 0.475132i
\(394\) −7.90998 6.40365i −0.398499 0.322611i
\(395\) 7.88408 21.6613i 0.396691 1.08990i
\(396\) −3.88028 2.60942i −0.194991 0.131128i
\(397\) −35.2581 6.21695i −1.76955 0.312020i −0.808522 0.588466i \(-0.799732\pi\)
−0.961029 + 0.276446i \(0.910843\pi\)
\(398\) 25.1025 15.0876i 1.25828 0.756275i
\(399\) −32.9516 9.12768i −1.64964 0.456956i
\(400\) 6.34187 + 9.39151i 0.317094 + 0.469575i
\(401\) 16.0877 + 2.83669i 0.803379 + 0.141657i 0.560236 0.828333i \(-0.310710\pi\)
0.243143 + 0.969990i \(0.421822\pi\)
\(402\) −18.2324 + 2.57535i −0.909349 + 0.128447i
\(403\) −18.4255 6.70632i −0.917837 0.334065i
\(404\) −2.78552 + 19.8581i −0.138585 + 0.987975i
\(405\) −4.12244 12.5908i −0.204846 0.625640i
\(406\) −11.4514 6.34566i −0.568326 0.314930i
\(407\) 1.99565 3.45656i 0.0989205 0.171335i
\(408\) 17.1704 + 29.6742i 0.850064 + 1.46909i
\(409\) 2.50225 + 14.1909i 0.123728 + 0.701697i 0.982055 + 0.188594i \(0.0603930\pi\)
−0.858327 + 0.513103i \(0.828496\pi\)
\(410\) 0.0960652 + 5.46223i 0.00474432 + 0.269761i
\(411\) 7.45174 + 6.94100i 0.367567 + 0.342374i
\(412\) −33.7693 + 7.18721i −1.66369 + 0.354088i
\(413\) −62.1089 + 22.6058i −3.05618 + 1.11236i
\(414\) 7.21001 + 7.19185i 0.354353 + 0.353460i
\(415\) −3.21985 + 3.83727i −0.158056 + 0.188364i
\(416\) 9.76235 13.9617i 0.478639 0.684528i
\(417\) −8.18677 26.7238i −0.400908 1.30867i
\(418\) −2.51074 + 4.09593i −0.122804 + 0.200338i
\(419\) 33.5961i 1.64128i 0.571447 + 0.820639i \(0.306382\pi\)
−0.571447 + 0.820639i \(0.693618\pi\)
\(420\) −21.5673 8.25843i −1.05238 0.402970i
\(421\) 17.1058 20.3858i 0.833684 0.993545i −0.166289 0.986077i \(-0.553178\pi\)
0.999972 0.00746828i \(-0.00237725\pi\)
\(422\) −5.33155 27.4091i −0.259536 1.33425i
\(423\) −4.97226 + 6.86000i −0.241760 + 0.333545i
\(424\) −13.7446 + 12.8272i −0.667496 + 0.622945i
\(425\) −17.1700 + 9.91311i −0.832868 + 0.480857i
\(426\) −4.48171 13.7607i −0.217139 0.666706i
\(427\) −5.25513 29.8033i −0.254314 1.44228i
\(428\) 7.39614 22.7834i 0.357506 1.10128i
\(429\) −3.96158 0.912249i −0.191267 0.0440438i
\(430\) 0.368544 0.665077i 0.0177728 0.0320729i
\(431\) −19.5027 + 16.3647i −0.939410 + 0.788259i −0.977483 0.211016i \(-0.932323\pi\)
0.0380726 + 0.999275i \(0.487878\pi\)
\(432\) −5.42404 20.0644i −0.260964 0.965348i
\(433\) 6.48946 + 2.36197i 0.311863 + 0.113509i 0.493210 0.869910i \(-0.335823\pi\)
−0.181347 + 0.983419i \(0.558046\pi\)
\(434\) −6.51797 + 41.1881i −0.312873 + 1.97709i
\(435\) −5.17256 + 0.638075i −0.248005 + 0.0305933i
\(436\) 17.5078 + 9.30314i 0.838473 + 0.445540i
\(437\) 7.07055 7.71204i 0.338230 0.368917i
\(438\) −2.19190 + 2.43776i −0.104733 + 0.116481i
\(439\) 30.5507 + 5.38691i 1.45810 + 0.257103i 0.845792 0.533513i \(-0.179128\pi\)
0.612312 + 0.790616i \(0.290240\pi\)
\(440\) −1.95179 + 2.59225i −0.0930479 + 0.123581i
\(441\) −39.3177 + 9.85017i −1.87227 + 0.469056i
\(442\) 23.1657 + 18.7542i 1.10188 + 0.892045i
\(443\) 16.4763 + 19.6356i 0.782810 + 0.932917i 0.999057 0.0434217i \(-0.0138259\pi\)
−0.216246 + 0.976339i \(0.569381\pi\)
\(444\) 16.7695 5.78975i 0.795845 0.274769i
\(445\) −20.2157 11.6715i −0.958316 0.553284i
\(446\) 8.37306 + 9.62954i 0.396476 + 0.455972i
\(447\) −16.4031 + 8.36947i −0.775841 + 0.395862i
\(448\) −33.1105 14.7103i −1.56433 0.694998i
\(449\) −3.93240 + 2.27037i −0.185581 + 0.107145i −0.589912 0.807467i \(-0.700838\pi\)
0.404331 + 0.914613i \(0.367504\pi\)
\(450\) 11.6062 3.12555i 0.547120 0.147340i
\(451\) 1.92183 0.699489i 0.0904954 0.0329376i
\(452\) 9.56483 + 10.6172i 0.449892 + 0.499390i
\(453\) 0.175948 + 0.0745683i 0.00826675 + 0.00350352i
\(454\) 2.57668 + 6.70982i 0.120929 + 0.314908i
\(455\) −20.0777 −0.941257
\(456\) −20.3614 + 6.43548i −0.953508 + 0.301369i
\(457\) 11.4634 0.536234 0.268117 0.963386i \(-0.413599\pi\)
0.268117 + 0.963386i \(0.413599\pi\)
\(458\) −13.2926 34.6147i −0.621122 1.61744i
\(459\) 35.6836 6.99892i 1.66557 0.326682i
\(460\) 5.25038 4.72998i 0.244800 0.220536i
\(461\) −28.7645 + 10.4694i −1.33970 + 0.487610i −0.909717 0.415228i \(-0.863702\pi\)
−0.429981 + 0.902838i \(0.641480\pi\)
\(462\) −0.295711 + 8.64061i −0.0137577 + 0.401997i
\(463\) 26.6080 15.3622i 1.23658 0.713940i 0.268186 0.963367i \(-0.413576\pi\)
0.968394 + 0.249427i \(0.0802424\pi\)
\(464\) −8.15616 + 0.574664i −0.378640 + 0.0266781i
\(465\) 7.54477 + 14.7868i 0.349880 + 0.685722i
\(466\) −5.93830 6.82941i −0.275087 0.316367i
\(467\) −17.5349 10.1238i −0.811419 0.468473i 0.0360293 0.999351i \(-0.488529\pi\)
−0.847448 + 0.530878i \(0.821862\pi\)
\(468\) −10.6414 14.6038i −0.491900 0.675062i
\(469\) 21.8836 + 26.0798i 1.01049 + 1.20425i
\(470\) 4.56959 + 3.69938i 0.210779 + 0.170640i
\(471\) −21.5685 1.11815i −0.993822 0.0515215i
\(472\) −24.8288 + 32.9761i −1.14284 + 1.51785i
\(473\) −0.280327 0.0494291i −0.0128894 0.00227275i
\(474\) −28.5231 25.6464i −1.31011 1.17798i
\(475\) −3.71030 11.7785i −0.170240 0.540433i
\(476\) 29.7441 55.9761i 1.36332 2.56566i
\(477\) 8.13119 + 18.2076i 0.372302 + 0.833669i
\(478\) 0.566098 3.57726i 0.0258927 0.163620i
\(479\) 25.6004 + 9.31777i 1.16971 + 0.425740i 0.852557 0.522634i \(-0.175051\pi\)
0.317154 + 0.948374i \(0.397273\pi\)
\(480\) −14.1042 + 3.01601i −0.643768 + 0.137661i
\(481\) 11.8150 9.91400i 0.538720 0.452040i
\(482\) 6.43303 11.6091i 0.293017 0.528780i
\(483\) 4.22519 18.3485i 0.192253 0.834887i
\(484\) −19.7696 6.41777i −0.898620 0.291717i
\(485\) 0.642648 + 3.64464i 0.0291811 + 0.165495i
\(486\) −21.9962 1.47283i −0.997766 0.0668090i
\(487\) −8.82502 + 5.09513i −0.399900 + 0.230882i −0.686441 0.727186i \(-0.740828\pi\)
0.286541 + 0.958068i \(0.407495\pi\)
\(488\) −12.8953 13.8176i −0.583745 0.625493i
\(489\) −2.91351 3.86182i −0.131753 0.174637i
\(490\) 5.37054 + 27.6096i 0.242616 + 1.24727i
\(491\) 13.2079 15.7406i 0.596064 0.710361i −0.380695 0.924700i \(-0.624315\pi\)
0.976759 + 0.214339i \(0.0687598\pi\)
\(492\) 8.48945 + 3.25073i 0.382734 + 0.146554i
\(493\) 14.3049i 0.644261i
\(494\) −14.5305 + 11.5549i −0.653758 + 0.519880i
\(495\) 1.92780 + 2.85113i 0.0866482 + 0.128149i
\(496\) 10.6053 + 23.7861i 0.476192 + 1.06803i
\(497\) −17.1995 + 20.4976i −0.771503 + 0.919442i
\(498\) 3.91830 + 7.35689i 0.175583 + 0.329670i
\(499\) −16.4401 + 5.98371i −0.735960 + 0.267868i −0.682686 0.730712i \(-0.739188\pi\)
−0.0532747 + 0.998580i \(0.516966\pi\)
\(500\) −4.80068 22.5561i −0.214693 1.00874i
\(501\) 15.4759 16.6147i 0.691414 0.742291i
\(502\) −0.477778 27.1663i −0.0213243 1.21249i
\(503\) −7.31597 41.4909i −0.326203 1.84999i −0.501082 0.865400i \(-0.667064\pi\)
0.174879 0.984590i \(-0.444047\pi\)
\(504\) −26.1656 + 28.1451i −1.16551 + 1.25368i
\(505\) 7.37957 12.7818i 0.328387 0.568782i
\(506\) −2.31400 1.28227i −0.102870 0.0570039i
\(507\) 5.71124 + 3.70434i 0.253645 + 0.164515i
\(508\) 25.4480 + 3.56963i 1.12907 + 0.158377i
\(509\) 5.18539 + 1.88733i 0.229838 + 0.0836544i 0.454372 0.890812i \(-0.349864\pi\)
−0.224534 + 0.974466i \(0.572086\pi\)
\(510\) −3.52927 24.9858i −0.156279 1.10639i
\(511\) 5.96918 + 1.05253i 0.264061 + 0.0465611i
\(512\) −22.3446 + 3.56627i −0.987502 + 0.157608i
\(513\) −0.560564 + 22.6426i −0.0247495 + 0.999694i
\(514\) 33.0724 19.8779i 1.45876 0.876775i
\(515\) 25.0257 + 4.41271i 1.10277 + 0.194447i
\(516\) −0.797057 0.982617i −0.0350885 0.0432573i
\(517\) 0.752785 2.06826i 0.0331075 0.0909620i
\(518\) −25.4941 20.6392i −1.12015 0.906833i
\(519\) −23.8902 15.4953i −1.04866 0.680169i
\(520\) −10.5135 + 6.83345i −0.461046 + 0.299666i
\(521\) 31.8798 + 18.4058i 1.39668 + 0.806373i 0.994043 0.108988i \(-0.0347609\pi\)
0.402635 + 0.915360i \(0.368094\pi\)
\(522\) −2.23401 + 8.37969i −0.0977799 + 0.366769i
\(523\) −0.151153 0.857230i −0.00660945 0.0374840i 0.981325 0.192359i \(-0.0616137\pi\)
−0.987934 + 0.154875i \(0.950503\pi\)
\(524\) −10.9920 + 6.87262i −0.480189 + 0.300232i
\(525\) −16.2617 15.1471i −0.709718 0.661074i
\(526\) −11.7449 4.04236i −0.512102 0.176255i
\(527\) −42.8158 + 15.5837i −1.86509 + 0.678836i
\(528\) 2.78598 + 4.62520i 0.121244 + 0.201286i
\(529\) −13.2055 11.0807i −0.574151 0.481769i
\(530\) 12.9178 4.96063i 0.561113 0.215476i
\(531\) 24.5236 + 36.2694i 1.06423 + 1.57396i
\(532\) 30.0223 + 25.6416i 1.30163 + 1.11170i
\(533\) 7.90309 0.342321
\(534\) −30.5919 + 23.9353i −1.32384 + 1.03578i
\(535\) −11.3328 + 13.5059i −0.489959 + 0.583910i
\(536\) 20.3353 + 6.20833i 0.878353 + 0.268159i
\(537\) 16.9411 12.7810i 0.731060 0.551541i
\(538\) 1.36914 + 0.471231i 0.0590279 + 0.0203162i
\(539\) 9.11898 5.26485i 0.392782 0.226773i
\(540\) −1.83463 + 15.1876i −0.0789501 + 0.653571i
\(541\) 10.2859 1.81368i 0.442225 0.0779763i 0.0518980 0.998652i \(-0.483473\pi\)
0.390327 + 0.920676i \(0.372362\pi\)
\(542\) −15.5046 17.8313i −0.665981 0.765919i
\(543\) −0.980202 + 4.25668i −0.0420645 + 0.182672i
\(544\) −3.47633 39.4347i −0.149046 1.69075i
\(545\) −9.37987 11.1785i −0.401790 0.478834i
\(546\) −12.4937 + 30.9852i −0.534683 + 1.32604i
\(547\) −6.24777 2.27400i −0.267135 0.0972293i 0.204980 0.978766i \(-0.434287\pi\)
−0.472115 + 0.881537i \(0.656509\pi\)
\(548\) −4.40789 10.9016i −0.188296 0.465694i
\(549\) −18.3043 + 8.17437i −0.781208 + 0.348874i
\(550\) −2.67628 + 1.60855i −0.114117 + 0.0685890i
\(551\) 8.69829 + 1.93079i 0.370560 + 0.0822543i
\(552\) −4.03245 11.0460i −0.171633 0.470151i
\(553\) −12.3151 + 69.8426i −0.523693 + 2.97001i
\(554\) 13.9042 + 2.20033i 0.590734 + 0.0934831i
\(555\) −13.0402 0.676028i −0.553526 0.0286958i
\(556\) −4.48316 + 31.9606i −0.190128 + 1.35543i
\(557\) 5.48953 4.60626i 0.232599 0.195173i −0.519037 0.854752i \(-0.673709\pi\)
0.751636 + 0.659578i \(0.229265\pi\)
\(558\) 27.5148 2.44220i 1.16480 0.103387i
\(559\) −0.952602 0.549985i −0.0402908 0.0232619i
\(560\) 18.5347 + 19.1729i 0.783233 + 0.810204i
\(561\) −8.41454 + 4.29341i −0.355262 + 0.181268i
\(562\) −0.187627 10.6684i −0.00791455 0.450019i
\(563\) 17.6840 10.2099i 0.745292 0.430294i −0.0786984 0.996898i \(-0.525076\pi\)
0.823990 + 0.566604i \(0.191743\pi\)
\(564\) 8.55263 4.75007i 0.360131 0.200014i
\(565\) −3.59736 9.88366i −0.151342 0.415809i
\(566\) 1.21562 + 6.24942i 0.0510963 + 0.262683i
\(567\) 19.2169 + 35.9457i 0.807035 + 1.50958i
\(568\) −2.02998 + 16.5872i −0.0851760 + 0.695982i
\(569\) 21.4277i 0.898297i −0.893457 0.449148i \(-0.851727\pi\)
0.893457 0.449148i \(-0.148273\pi\)
\(570\) 15.6693 + 1.22640i 0.656315 + 0.0513684i
\(571\) 17.1460 0.717539 0.358769 0.933426i \(-0.383196\pi\)
0.358769 + 0.933426i \(0.383196\pi\)
\(572\) 3.69981 + 2.88904i 0.154697 + 0.120797i
\(573\) −2.38646 + 5.63099i −0.0996959 + 0.235238i
\(574\) −3.20923 16.4984i −0.133951 0.688631i
\(575\) 6.39012 2.32581i 0.266487 0.0969932i
\(576\) −4.12214 + 23.6433i −0.171756 + 0.985140i
\(577\) −12.7105 22.0152i −0.529143 0.916503i −0.999422 0.0339852i \(-0.989180\pi\)
0.470279 0.882518i \(-0.344153\pi\)
\(578\) 45.2115 0.795142i 1.88055 0.0330735i
\(579\) 5.71395 2.91546i 0.237464 0.121163i
\(580\) 5.72398 + 1.85816i 0.237675 + 0.0771560i
\(581\) 7.70562 13.3465i 0.319683 0.553707i
\(582\) 6.02454 + 1.27617i 0.249725 + 0.0528990i
\(583\) −3.32979 3.96829i −0.137906 0.164350i
\(584\) 3.48392 1.48047i 0.144166 0.0612621i
\(585\) 3.23206 + 12.9010i 0.133629 + 0.533392i
\(586\) 4.76450 30.1076i 0.196820 1.24373i
\(587\) −2.07858 0.366509i −0.0857920 0.0151274i 0.130587 0.991437i \(-0.458314\pi\)
−0.216379 + 0.976309i \(0.569425\pi\)
\(588\) 45.9508 + 8.89242i 1.89498 + 0.366717i
\(589\) −3.69685 28.1381i −0.152326 1.15941i
\(590\) 26.0402 15.6512i 1.07206 0.644351i
\(591\) 12.3706 1.52601i 0.508860 0.0627718i
\(592\) −20.3743 2.13054i −0.837377 0.0875647i
\(593\) −11.0522 + 30.3658i −0.453861 + 1.24697i 0.476125 + 0.879378i \(0.342041\pi\)
−0.929986 + 0.367595i \(0.880181\pi\)
\(594\) 5.59966 1.20093i 0.229757 0.0492749i
\(595\) −35.7400 + 29.9894i −1.46520 + 1.22945i
\(596\) 21.2506 0.747707i 0.870458 0.0306273i
\(597\) −8.04928 + 34.9553i −0.329435 + 1.43062i
\(598\) −6.70794 7.71455i −0.274308 0.315471i
\(599\) −5.13441 29.1187i −0.209786 1.18976i −0.889728 0.456492i \(-0.849106\pi\)
0.679941 0.733267i \(-0.262005\pi\)
\(600\) −13.6706 2.39695i −0.558098 0.0978551i
\(601\) −6.55642 11.3561i −0.267442 0.463223i 0.700759 0.713398i \(-0.252845\pi\)
−0.968201 + 0.250176i \(0.919512\pi\)
\(602\) −0.761318 + 2.21198i −0.0310290 + 0.0901534i
\(603\) 13.2349 18.2596i 0.538968 0.743590i
\(604\) −0.147694 0.163943i −0.00600957 0.00667076i
\(605\) 11.7193 + 9.83368i 0.476458 + 0.399796i
\(606\) −15.1336 19.3423i −0.614761 0.785729i
\(607\) 8.94495i 0.363064i 0.983385 + 0.181532i \(0.0581057\pi\)
−0.983385 + 0.181532i \(0.941894\pi\)
\(608\) 24.4480 + 3.20882i 0.991496 + 0.130135i
\(609\) 15.3312 4.69668i 0.621251 0.190319i
\(610\) 4.98698 + 12.9864i 0.201917 + 0.525803i
\(611\) 5.46707 6.51540i 0.221174 0.263585i
\(612\) −40.7558 10.1013i −1.64746 0.408320i
\(613\) −7.25811 19.9415i −0.293152 0.805429i −0.995601 0.0936946i \(-0.970132\pi\)
0.702449 0.711734i \(-0.252090\pi\)
\(614\) 17.3147 + 5.95938i 0.698765 + 0.240501i
\(615\) −4.89597 4.56040i −0.197425 0.183893i
\(616\) 4.52873 8.89685i 0.182468 0.358464i
\(617\) −31.6906 + 5.58791i −1.27582 + 0.224961i −0.770203 0.637799i \(-0.779845\pi\)
−0.505614 + 0.862760i \(0.668734\pi\)
\(618\) 22.3827 35.8754i 0.900365 1.44312i
\(619\) −11.3746 + 19.7014i −0.457184 + 0.791866i −0.998811 0.0487529i \(-0.984475\pi\)
0.541627 + 0.840619i \(0.317809\pi\)
\(620\) −0.674030 19.1566i −0.0270697 0.769349i
\(621\) −12.4701 + 0.238790i −0.500408 + 0.00958231i
\(622\) 34.6836 + 28.0787i 1.39069 + 1.12585i
\(623\) 67.4859 + 24.5629i 2.70377 + 0.984091i
\(624\) 4.00361 + 20.4773i 0.160273 + 0.819748i
\(625\) −0.487684 + 2.76579i −0.0195074 + 0.110632i
\(626\) 13.6476 + 22.7066i 0.545468 + 0.907539i
\(627\) −1.47492 5.69607i −0.0589027 0.227479i
\(628\) 22.0225 + 11.7021i 0.878795 + 0.466966i
\(629\) 6.22355 35.2955i 0.248149 1.40732i
\(630\) 25.6196 11.9860i 1.02071 0.477532i
\(631\) −1.86340 + 5.11965i −0.0741808 + 0.203810i −0.971241 0.238098i \(-0.923476\pi\)
0.897060 + 0.441908i \(0.145698\pi\)
\(632\) 17.3223 + 40.7638i 0.689042 + 1.62150i
\(633\) 28.6917 + 18.6096i 1.14039 + 0.739664i
\(634\) 2.71076 4.89186i 0.107658 0.194281i
\(635\) −16.3798 9.45688i −0.650012 0.375285i
\(636\) 0.382776 23.0224i 0.0151781 0.912897i
\(637\) 40.0715 7.06568i 1.58769 0.279952i
\(638\) −0.0396164 2.25257i −0.00156843 0.0891803i
\(639\) 15.9395 + 7.75197i 0.630559 + 0.306663i
\(640\) 16.2310 + 3.73142i 0.641586 + 0.147497i
\(641\) 3.10143 + 8.52111i 0.122499 + 0.336564i 0.985751 0.168209i \(-0.0537984\pi\)
−0.863252 + 0.504773i \(0.831576\pi\)
\(642\) 13.7911 + 25.8938i 0.544292 + 1.02195i
\(643\) 0.680574 + 0.571069i 0.0268392 + 0.0225208i 0.656109 0.754667i \(-0.272201\pi\)
−0.629269 + 0.777187i \(0.716646\pi\)
\(644\) −13.3809 + 17.1361i −0.527282 + 0.675257i
\(645\) 0.272774 + 0.890406i 0.0107405 + 0.0350597i
\(646\) −8.60629 + 42.2724i −0.338610 + 1.66319i
\(647\) −24.7385 −0.972571 −0.486285 0.873800i \(-0.661648\pi\)
−0.486285 + 0.873800i \(0.661648\pi\)
\(648\) 22.2969 + 12.2821i 0.875903 + 0.482487i
\(649\) −8.71283 7.31094i −0.342009 0.286979i
\(650\) −11.8442 + 2.30389i −0.464566 + 0.0903662i
\(651\) −30.7593 40.7710i −1.20555 1.59794i
\(652\) 1.16283 + 5.46358i 0.0455398 + 0.213970i
\(653\) 1.58553 + 2.74622i 0.0620466 + 0.107468i 0.895380 0.445303i \(-0.146904\pi\)
−0.833334 + 0.552771i \(0.813571\pi\)
\(654\) −23.0882 + 7.51959i −0.902819 + 0.294039i
\(655\) 9.39667 1.65689i 0.367158 0.0647399i
\(656\) −7.29571 7.54695i −0.284850 0.294659i
\(657\) −0.284598 4.00496i −0.0111032 0.156248i
\(658\) −15.8215 8.76728i −0.616787 0.341784i
\(659\) 2.03309 + 2.42294i 0.0791980 + 0.0943845i 0.804188 0.594374i \(-0.202600\pi\)
−0.724990 + 0.688759i \(0.758156\pi\)
\(660\) −0.624946 3.92470i −0.0243260 0.152769i
\(661\) −0.186308 + 0.511876i −0.00724653 + 0.0199097i −0.943263 0.332046i \(-0.892261\pi\)
0.936017 + 0.351956i \(0.114483\pi\)
\(662\) 4.76237 30.0941i 0.185095 1.16964i
\(663\) −36.2296 + 4.46919i −1.40704 + 0.173569i
\(664\) −0.507529 9.61137i −0.0196959 0.372993i
\(665\) −13.4115 25.7799i −0.520075 0.999703i
\(666\) −9.15781 + 19.7038i −0.354858 + 0.763508i
\(667\) −0.851999 + 4.83193i −0.0329895 + 0.187093i
\(668\) −24.3067 + 9.82801i −0.940454 + 0.380257i
\(669\) −15.6077 0.809130i −0.603428 0.0312828i
\(670\) −12.1631 9.84684i −0.469902 0.380417i
\(671\) 3.98937 3.34748i 0.154008 0.129228i
\(672\) 41.1225 16.6732i 1.58633 0.643181i
\(673\) 14.9014 25.8101i 0.574408 0.994905i −0.421697 0.906737i \(-0.638565\pi\)
0.996106 0.0881678i \(-0.0281012\pi\)
\(674\) −31.5353 + 27.4205i −1.21469 + 1.05620i
\(675\) −7.11508 + 12.8874i −0.273859 + 0.496035i
\(676\) −4.16718 6.66496i −0.160276 0.256345i
\(677\) 17.9769 + 31.1369i 0.690907 + 1.19669i 0.971541 + 0.236872i \(0.0761222\pi\)
−0.280633 + 0.959815i \(0.590545\pi\)
\(678\) −17.4916 0.598623i −0.671762 0.0229900i
\(679\) −3.89425 10.6994i −0.149448 0.410604i
\(680\) −8.50794 + 27.8677i −0.326265 + 1.06868i
\(681\) −8.10508 3.43500i −0.310587 0.131630i
\(682\) −6.69899 + 2.57252i −0.256517 + 0.0985067i
\(683\) 18.4184i 0.704761i −0.935857 0.352380i \(-0.885372\pi\)
0.935857 0.352380i \(-0.114628\pi\)
\(684\) 11.6432 23.4187i 0.445188 0.895437i
\(685\) 8.65495i 0.330689i
\(686\) −14.9496 38.9297i −0.570779 1.48634i
\(687\) 41.8126 + 17.7205i 1.59525 + 0.676080i
\(688\) 0.354191 + 1.41739i 0.0135034 + 0.0540375i
\(689\) −6.84652 18.8106i −0.260831 0.716629i
\(690\) −0.296030 + 8.64992i −0.0112697 + 0.329297i
\(691\) 1.20204 + 2.08199i 0.0457276 + 0.0792025i 0.887983 0.459876i \(-0.152106\pi\)
−0.842256 + 0.539078i \(0.818773\pi\)
\(692\) 17.4314 + 27.8797i 0.662642 + 1.05983i
\(693\) −7.36415 7.60859i −0.279741 0.289026i
\(694\) −3.68404 4.23687i −0.139844 0.160829i
\(695\) 11.8771 20.5717i 0.450523 0.780328i
\(696\) 6.42949 7.67734i 0.243709 0.291009i
\(697\) 14.0682 11.8046i 0.532869 0.447131i
\(698\) 10.0524 12.4171i 0.380491 0.469994i
\(699\) 11.0692 + 0.573847i 0.418676 + 0.0217049i
\(700\) 9.61918 + 23.7902i 0.363571 + 0.899185i
\(701\) 0.496434 2.81541i 0.0187500 0.106337i −0.973996 0.226563i \(-0.927251\pi\)
0.992746 + 0.120227i \(0.0383621\pi\)
\(702\) 21.9209 + 3.03999i 0.827351 + 0.114737i
\(703\) 20.6219 + 8.54827i 0.777768 + 0.322404i
\(704\) −0.656623 6.20009i −0.0247474 0.233675i
\(705\) −7.14651 + 0.881576i −0.269153 + 0.0332021i
\(706\) 24.7760 + 3.92078i 0.932457 + 0.147561i
\(707\) −15.5304 + 42.6694i −0.584080 + 1.60475i
\(708\) −7.94995 49.9262i −0.298777 1.87634i
\(709\) 14.8741 + 17.7263i 0.558609 + 0.665724i 0.969252 0.246072i \(-0.0791400\pi\)
−0.410642 + 0.911796i \(0.634696\pi\)
\(710\) 5.96159 10.7583i 0.223734 0.403753i
\(711\) 46.8602 3.32994i 1.75739 0.124883i
\(712\) 43.6982 10.1068i 1.63766 0.378767i
\(713\) 15.3905 2.71376i 0.576380 0.101631i
\(714\) 24.0417 + 73.8177i 0.899737 + 2.76256i
\(715\) −1.72751 2.99214i −0.0646053 0.111900i
\(716\) −23.9677 + 5.10110i −0.895714 + 0.190637i
\(717\) 2.67150 + 3.54104i 0.0997690 + 0.132243i
\(718\) 7.06135 + 36.3019i 0.263527 + 1.35478i
\(719\) −31.3315 26.2902i −1.16847 0.980460i −0.168480 0.985705i \(-0.553886\pi\)
−0.999986 + 0.00524549i \(0.998330\pi\)
\(720\) 9.33599 14.9959i 0.347932 0.558866i
\(721\) −78.1817 −2.91164
\(722\) −24.5427 10.9388i −0.913383 0.407101i
\(723\) 4.76135 + 15.5423i 0.177076 + 0.578024i
\(724\) 3.10424 3.97541i 0.115368 0.147745i
\(725\) 4.43620 + 3.72241i 0.164756 + 0.138247i
\(726\) 22.4685 11.9668i 0.833885 0.444130i
\(727\) 0.992714 + 2.72746i 0.0368177 + 0.101156i 0.956739 0.290946i \(-0.0939701\pi\)
−0.919922 + 0.392102i \(0.871748\pi\)
\(728\) 28.2035 26.3211i 1.04529 0.975524i
\(729\) 20.0036 18.1344i 0.740874 0.671644i
\(730\) −2.78575 + 0.0489934i −0.103105 + 0.00181333i
\(731\) −2.51720 + 0.443851i −0.0931022 + 0.0164164i
\(732\) 23.1447 + 0.384809i 0.855451 + 0.0142230i
\(733\) 7.80127 + 4.50407i 0.288147 + 0.166362i 0.637106 0.770776i \(-0.280131\pi\)
−0.348959 + 0.937138i \(0.613465\pi\)
\(734\) 2.04081 + 1.13089i 0.0753277 + 0.0417418i
\(735\) −28.9015 18.7457i −1.06605 0.691444i
\(736\) −1.17449 + 13.5273i −0.0432922 + 0.498624i
\(737\) −2.00373 + 5.50520i −0.0738084 + 0.202787i
\(738\) −10.0845 + 4.71798i −0.371216 + 0.173671i
\(739\) 7.66528 43.4719i 0.281972 1.59914i −0.433934 0.900945i \(-0.642875\pi\)
0.715906 0.698197i \(-0.246014\pi\)
\(740\) 13.3147 + 7.07506i 0.489460 + 0.260085i
\(741\) 2.17249 22.6331i 0.0798084 0.831447i
\(742\) −36.4887 + 21.9312i −1.33954 + 0.805120i
\(743\) 0.0629646 0.357090i 0.00230995 0.0131004i −0.983631 0.180195i \(-0.942327\pi\)
0.985941 + 0.167094i \(0.0534384\pi\)
\(744\) −29.9832 10.8804i −1.09924 0.398894i
\(745\) −14.7068 5.35285i −0.538816 0.196113i
\(746\) −30.6618 + 37.8744i −1.12261 + 1.38668i
\(747\) −9.81630 2.80279i −0.359160 0.102549i
\(748\) 10.9012 0.383562i 0.398588 0.0140244i
\(749\) 27.1212 46.9753i 0.990986 1.71644i
\(750\) 23.9629 + 14.9505i 0.875002 + 0.545915i
\(751\) 4.56350 0.804668i 0.166524 0.0293628i −0.0897642 0.995963i \(-0.528611\pi\)
0.256289 + 0.966600i \(0.417500\pi\)
\(752\) −11.2687 + 0.793967i −0.410928 + 0.0289530i
\(753\) 24.3500 + 22.6810i 0.887363 + 0.826543i
\(754\) 2.83328 8.23197i 0.103182 0.299791i
\(755\) 0.0555480 + 0.152617i 0.00202160 + 0.00555430i
\(756\) −2.55523 46.9963i −0.0929328 1.70924i
\(757\) −4.28010 + 5.10082i −0.155563 + 0.185393i −0.838197 0.545368i \(-0.816390\pi\)
0.682634 + 0.730760i \(0.260834\pi\)
\(758\) 2.32671 0.893494i 0.0845101 0.0324532i
\(759\) 3.09799 0.949062i 0.112450 0.0344488i
\(760\) −15.7970 8.93477i −0.573017 0.324098i
\(761\) 33.1635i 1.20217i 0.799184 + 0.601087i \(0.205266\pi\)
−0.799184 + 0.601087i \(0.794734\pi\)
\(762\) −24.7871 + 19.3936i −0.897942 + 0.702557i
\(763\) 34.3916 + 28.8580i 1.24506 + 1.04473i
\(764\) 5.24679 4.72674i 0.189822 0.171008i
\(765\) 25.0232 + 18.1373i 0.904714 + 0.655754i
\(766\) 21.6302 + 7.44469i 0.781532 + 0.268988i
\(767\) −21.9757 38.0631i −0.793498 1.37438i
\(768\) 15.8586 22.7267i 0.572248 0.820081i
\(769\) −0.936070 5.30871i −0.0337555 0.191437i 0.963267 0.268545i \(-0.0865427\pi\)
−0.997023 + 0.0771074i \(0.975432\pi\)
\(770\) −5.54487 + 4.82136i −0.199823 + 0.173750i
\(771\) −10.6049 + 46.0533i −0.381925 + 1.65857i
\(772\) −7.40254 + 0.260460i −0.266423 + 0.00937416i
\(773\) −7.89932 + 6.62832i −0.284119 + 0.238404i −0.773698 0.633555i \(-0.781595\pi\)
0.489579 + 0.871959i \(0.337151\pi\)
\(774\) 1.54387 + 0.133110i 0.0554933 + 0.00478453i
\(775\) 6.30873 17.3331i 0.226616 0.622623i
\(776\) −5.68071 4.27720i −0.203926 0.153542i
\(777\) 39.8710 4.91839i 1.43037 0.176446i
\(778\) −20.0853 33.4175i −0.720092 1.19808i
\(779\) 5.27910 + 10.1476i 0.189143 + 0.363577i
\(780\) 2.91780 15.0775i 0.104474 0.539860i
\(781\) −4.53458 0.799569i −0.162260 0.0286108i
\(782\) −23.4637 3.71310i −0.839059 0.132780i
\(783\) −5.48585 9.09507i −0.196048 0.325031i
\(784\) −43.7391 31.7430i −1.56211 1.13368i
\(785\) −11.7986 14.0611i −0.421112 0.501861i
\(786\) 3.29025 15.5326i 0.117359 0.554029i
\(787\) −15.3667 + 26.6159i −0.547764 + 0.948754i 0.450664 + 0.892694i \(0.351187\pi\)
−0.998427 + 0.0560605i \(0.982146\pi\)
\(788\) −13.6894 4.44396i −0.487665 0.158310i
\(789\) 13.5507 6.91405i 0.482417 0.246147i
\(790\) −0.573249 32.5947i −0.0203953 1.15967i
\(791\) 16.1797 + 28.0241i 0.575285 + 0.996424i
\(792\) −6.44574 1.47776i −0.229039 0.0525101i
\(793\) 18.9105 6.88288i 0.671533 0.244418i
\(794\) −49.7001 + 9.66754i −1.76379 + 0.343088i
\(795\) −6.61308 + 15.6039i −0.234542 + 0.553414i
\(796\) 25.4916 32.6455i 0.903525 1.15709i
\(797\) 33.0971 1.17236 0.586180 0.810181i \(-0.300631\pi\)
0.586180 + 0.810181i \(0.300631\pi\)
\(798\) −48.1308 + 4.65541i −1.70381 + 0.164800i
\(799\) 19.7639i 0.699198i
\(800\) 13.1340 + 9.18359i 0.464356 + 0.324689i
\(801\) 4.91927 47.3175i 0.173814 1.67188i
\(802\) 22.6773 4.41113i 0.800764 0.155762i
\(803\) 0.356740 + 0.980136i 0.0125891 + 0.0345882i
\(804\) −22.7650 + 12.6435i −0.802860 + 0.445903i
\(805\) 13.8584 8.00117i 0.488446 0.282004i
\(806\) −27.7256 + 0.487614i −0.976591 + 0.0171755i
\(807\) −1.57965 + 0.805994i −0.0556062 + 0.0283723i
\(808\) 6.39021 + 27.6291i 0.224807 + 0.971989i
\(809\) −24.4496 14.1160i −0.859600 0.496291i 0.00427805 0.999991i \(-0.498638\pi\)
−0.863878 + 0.503700i \(0.831972\pi\)
\(810\) −11.8258 14.5325i −0.415517 0.510621i
\(811\) −13.3614 + 11.2115i −0.469182 + 0.393690i −0.846496 0.532395i \(-0.821292\pi\)
0.377314 + 0.926085i \(0.376848\pi\)
\(812\) −18.3355 2.57195i −0.643450 0.0902577i
\(813\) 28.9011 + 1.49829i 1.01361 + 0.0525472i
\(814\) 0.882264 5.57516i 0.0309233 0.195409i
\(815\) 0.713938 4.04895i 0.0250082 0.141828i
\(816\) 37.7130 + 30.4712i 1.32022 + 1.06671i
\(817\) 0.0698669 1.59053i 0.00244433 0.0556455i
\(818\) 10.4981 + 17.4665i 0.367056 + 0.610702i
\(819\) −16.6849 37.3614i −0.583019 1.30551i
\(820\) 2.89609 + 7.16262i 0.101136 + 0.250130i
\(821\) 2.51028 + 0.913666i 0.0876093 + 0.0318872i 0.385453 0.922727i \(-0.374045\pi\)
−0.297844 + 0.954615i \(0.596267\pi\)
\(822\) 13.3569 + 5.38571i 0.465874 + 0.187848i
\(823\) −7.38961 8.80660i −0.257586 0.306979i 0.621717 0.783242i \(-0.286435\pi\)
−0.879303 + 0.476263i \(0.841991\pi\)
\(824\) −40.9390 + 26.6091i −1.42618 + 0.926973i
\(825\) 0.858166 3.72672i 0.0298775 0.129748i
\(826\) −70.5364 + 61.3327i −2.45428 + 2.13404i
\(827\) 33.9701 5.98985i 1.18126 0.208287i 0.451676 0.892182i \(-0.350826\pi\)
0.729581 + 0.683895i \(0.239715\pi\)
\(828\) 13.1649 + 5.83943i 0.457512 + 0.202934i
\(829\) 8.50873 4.91252i 0.295520 0.170619i −0.344908 0.938636i \(-0.612090\pi\)
0.640429 + 0.768018i \(0.278757\pi\)
\(830\) −2.30546 + 6.69843i −0.0800238 + 0.232506i
\(831\) −13.7635 + 10.3837i −0.477449 + 0.360206i
\(832\) 5.81006 23.3818i 0.201428 0.810618i
\(833\) 60.7767 72.4309i 2.10579 2.50958i
\(834\) −24.3568 31.1306i −0.843407 1.07796i
\(835\) 19.2974 0.667815
\(836\) −1.23815 + 6.68040i −0.0428223 + 0.231047i
\(837\) −21.2461 + 26.3277i −0.734371 + 0.910020i
\(838\) 17.0327 + 44.3541i 0.588384 + 1.53219i
\(839\) 26.9731 + 22.6331i 0.931214 + 0.781381i 0.976035 0.217614i \(-0.0698274\pi\)
−0.0448212 + 0.998995i \(0.514272\pi\)
\(840\) −32.6604 + 0.0313746i −1.12689 + 0.00108253i
\(841\) 23.3247 8.48951i 0.804301 0.292742i
\(842\) 12.2480 35.5860i 0.422094 1.22638i
\(843\) 9.56241 + 8.90700i 0.329347 + 0.306774i
\(844\) −20.9347 33.4829i −0.720604 1.15253i
\(845\) 1.00464 + 5.69762i 0.0345608 + 0.196004i
\(846\) −3.08655 + 11.5775i −0.106118 + 0.398044i
\(847\) −40.7613 23.5336i −1.40058 0.808623i
\(848\) −11.6426 + 23.9030i −0.399810 + 0.820832i
\(849\) −6.54184 4.24308i −0.224516 0.145622i
\(850\) −17.6423 + 21.7924i −0.605127 + 0.747471i
\(851\) −4.20439 + 11.5515i −0.144125 + 0.395979i
\(852\) −12.8932 15.8949i −0.441715 0.544550i
\(853\) 33.7848 + 5.95717i 1.15677 + 0.203969i 0.718929 0.695084i \(-0.244633\pi\)
0.437840 + 0.899053i \(0.355744\pi\)
\(854\) −22.0477 36.6825i −0.754456 1.25525i
\(855\) −14.4061 + 12.7676i −0.492677 + 0.436643i
\(856\) −1.78633 33.8288i −0.0610555 1.15624i
\(857\) 11.8672 + 2.09250i 0.405375 + 0.0714786i 0.372618 0.927985i \(-0.378460\pi\)
0.0327571 + 0.999463i \(0.489571\pi\)
\(858\) −5.69264 + 0.804092i −0.194343 + 0.0274512i
\(859\) 44.7691 + 16.2946i 1.52750 + 0.555966i 0.963008 0.269471i \(-0.0868489\pi\)
0.564494 + 0.825437i \(0.309071\pi\)
\(860\) 0.149374 1.06489i 0.00509361 0.0363125i
\(861\) 17.2704 + 11.2017i 0.588575 + 0.381753i
\(862\) −17.4511 + 31.4924i −0.594387 + 1.07264i
\(863\) −7.57109 + 13.1135i −0.257723 + 0.446389i −0.965632 0.259915i \(-0.916306\pi\)
0.707909 + 0.706304i \(0.249639\pi\)
\(864\) −17.3332 23.7394i −0.589688 0.807631i
\(865\) −4.20245 23.8333i −0.142888 0.810356i
\(866\) 9.76496 0.171738i 0.331827 0.00583589i
\(867\) −37.7470 + 40.5245i −1.28195 + 1.37628i
\(868\) 12.2765 + 57.6816i 0.416692 + 1.95784i
\(869\) −11.4681 + 4.17405i −0.389029 + 0.141595i
\(870\) −6.50540 + 3.46480i −0.220554 + 0.117468i
\(871\) −14.5520 + 17.3424i −0.493076 + 0.587625i
\(872\) 27.8306 + 3.40598i 0.942464 + 0.115341i
\(873\) −6.24804 + 4.22463i −0.211464 + 0.142982i
\(874\) 5.42478 13.7662i 0.183496 0.465649i
\(875\) 52.2213i 1.76540i
\(876\) −1.65787 + 4.32963i −0.0560144 + 0.146285i
\(877\) −16.5145 + 19.6812i −0.557654 + 0.664586i −0.969048 0.246872i \(-0.920597\pi\)
0.411394 + 0.911457i \(0.365042\pi\)
\(878\) 43.0645 8.37680i 1.45336 0.282703i
\(879\) 22.4844 + 29.8028i 0.758380 + 1.00522i
\(880\) −1.26256 + 4.41185i −0.0425607 + 0.148723i
\(881\) −12.0939 + 6.98240i −0.407453 + 0.235243i −0.689695 0.724100i \(-0.742255\pi\)
0.282242 + 0.959343i \(0.408922\pi\)
\(882\) −46.9140 + 32.9378i −1.57968 + 1.10907i
\(883\) −9.54729 54.1454i −0.321292 1.82214i −0.534546 0.845140i \(-0.679517\pi\)
0.213254 0.976997i \(-0.431594\pi\)
\(884\) 40.0918 + 13.0149i 1.34843 + 0.437739i
\(885\) −8.34996 + 36.2610i −0.280681 + 1.21890i
\(886\) 31.7071 + 17.5701i 1.06522 + 0.590278i
\(887\) 20.7612 17.4207i 0.697092 0.584930i −0.223852 0.974623i \(-0.571863\pi\)
0.920945 + 0.389693i \(0.127419\pi\)
\(888\) 19.2040 16.1456i 0.644446 0.541810i
\(889\) 54.6806 + 19.9021i 1.83393 + 0.667495i
\(890\) −32.6063 5.15992i −1.09297 0.172961i
\(891\) −3.70347 + 5.95668i −0.124071 + 0.199556i
\(892\) 15.9363 + 8.46806i 0.533585 + 0.283532i
\(893\) 12.0177 + 2.66761i 0.402158 + 0.0892682i
\(894\) −17.4125 + 19.3656i −0.582360 + 0.647683i
\(895\) 17.7620 + 3.13191i 0.593717 + 0.104688i
\(896\) −51.1709 2.63432i −1.70950 0.0880066i
\(897\) 12.5038 + 0.648221i 0.417491 + 0.0216435i
\(898\) −4.04057 + 4.99104i −0.134836 + 0.166553i
\(899\) 8.55467 + 10.1951i 0.285314 + 0.340024i
\(900\) 13.7380 10.0105i 0.457935 0.333685i
\(901\) −40.2842 23.2581i −1.34206 0.774839i
\(902\) 2.18260 1.89781i 0.0726726 0.0631902i
\(903\) −1.30216 2.55207i −0.0433331 0.0849275i
\(904\) 18.0104 + 9.16775i 0.599016 + 0.304915i
\(905\) −3.21502 + 1.85619i −0.106871 + 0.0617020i
\(906\) 0.270094 + 0.00924354i 0.00897327 + 0.000307096i
\(907\) 6.93582 2.52443i 0.230300 0.0838224i −0.224292 0.974522i \(-0.572007\pi\)
0.454593 + 0.890699i \(0.349785\pi\)
\(908\) 6.80354 + 7.55208i 0.225783 + 0.250625i
\(909\) 29.9175 + 3.11031i 0.992299 + 0.103162i
\(910\) −26.5069 + 10.1791i −0.878695 + 0.337433i
\(911\) 7.56349 0.250590 0.125295 0.992120i \(-0.460012\pi\)
0.125295 + 0.992120i \(0.460012\pi\)
\(912\) −23.6187 + 18.8191i −0.782093 + 0.623162i
\(913\) 2.65201 0.0877686
\(914\) 15.1341 5.81174i 0.500593 0.192235i
\(915\) −15.6868 6.64820i −0.518590 0.219783i
\(916\) −35.0982 38.9598i −1.15968 1.28727i
\(917\) −27.5853 + 10.0402i −0.910948 + 0.331558i
\(918\) 43.5617 27.3311i 1.43775 0.902060i
\(919\) −10.5977 + 6.11856i −0.349584 + 0.201833i −0.664502 0.747286i \(-0.731356\pi\)
0.314918 + 0.949119i \(0.398023\pi\)
\(920\) 4.53362 8.90644i 0.149469 0.293637i
\(921\) −19.9768 + 10.1929i −0.658260 + 0.335868i
\(922\) −32.6676 + 28.4050i −1.07585 + 0.935470i
\(923\) −15.4093 8.89659i −0.507205 0.292835i
\(924\) 3.99024 + 11.5574i 0.131269 + 0.380210i
\(925\) 9.32625 + 11.1146i 0.306645 + 0.365445i
\(926\) 27.3400 33.7712i 0.898447 1.10979i
\(927\) 12.5855 + 50.2360i 0.413362 + 1.64997i
\(928\) −10.4765 + 4.89372i −0.343910 + 0.160644i
\(929\) 3.23037 + 0.569602i 0.105985 + 0.0186880i 0.226389 0.974037i \(-0.427308\pi\)
−0.120404 + 0.992725i \(0.538419\pi\)
\(930\) 17.4574 + 15.6967i 0.572450 + 0.514715i
\(931\) 35.8393 + 46.7323i 1.17459 + 1.53159i
\(932\) −11.3022 6.00568i −0.370217 0.196722i
\(933\) −54.2428 + 6.69126i −1.77583 + 0.219062i
\(934\) −28.2825 4.47567i −0.925430 0.146448i
\(935\) −7.54437 2.74593i −0.246727 0.0898014i
\(936\) −21.4528 13.8852i −0.701208 0.453851i
\(937\) 23.7387 19.9191i 0.775509 0.650729i −0.166605 0.986024i \(-0.553280\pi\)
0.942113 + 0.335295i \(0.108836\pi\)
\(938\) 42.1130 + 23.3364i 1.37504 + 0.761959i
\(939\) −31.6189 7.28101i −1.03185 0.237607i
\(940\) 7.90836 + 2.56727i 0.257942 + 0.0837352i
\(941\) 4.41289 + 25.0268i 0.143856 + 0.815849i 0.968278 + 0.249874i \(0.0803892\pi\)
−0.824422 + 0.565975i \(0.808500\pi\)
\(942\) −29.0419 + 9.45865i −0.946236 + 0.308180i
\(943\) −5.45503 + 3.14946i −0.177640 + 0.102561i
\(944\) −16.0610 + 56.1233i −0.522741 + 1.82666i
\(945\) −11.2227 + 32.7733i −0.365075 + 1.06612i
\(946\) −0.395151 + 0.0768638i −0.0128475 + 0.00249906i
\(947\) −24.4309 + 29.1156i −0.793898 + 0.946131i −0.999471 0.0325108i \(-0.989650\pi\)
0.205573 + 0.978642i \(0.434094\pi\)
\(948\) −50.6590 19.3980i −1.64533 0.630018i
\(949\) 4.03059i 0.130838i
\(950\) −10.8699 13.6690i −0.352665 0.443482i
\(951\) 2.00634 + 6.54923i 0.0650601 + 0.212373i
\(952\) 10.8896 88.9803i 0.352935 2.88387i
\(953\) 0.998729 1.19024i 0.0323520 0.0385556i −0.749626 0.661862i \(-0.769767\pi\)
0.781978 + 0.623306i \(0.214211\pi\)
\(954\) 19.9659 + 19.9156i 0.646419 + 0.644791i
\(955\) −4.88431 + 1.77774i −0.158053 + 0.0575264i
\(956\) −1.06624 5.00975i −0.0344846 0.162027i
\(957\) 2.01905 + 1.88067i 0.0652667 + 0.0607934i
\(958\) 38.5219 0.677492i 1.24459 0.0218888i
\(959\) −4.62385 26.2232i −0.149312 0.846791i
\(960\) −17.0916 + 11.1324i −0.551628 + 0.359297i
\(961\) 5.69527 9.86449i 0.183718 0.318209i
\(962\) 10.5722 19.0786i 0.340861 0.615120i
\(963\) −34.5501 9.86488i −1.11336 0.317891i
\(964\) 2.60736 18.5880i 0.0839775 0.598678i
\(965\) 5.12305 + 1.86464i 0.164917 + 0.0600248i
\(966\) −3.72424 26.3661i −0.119826 0.848316i
\(967\) −13.8409 2.44053i −0.445094 0.0784821i −0.0533909 0.998574i \(-0.517003\pi\)
−0.391703 + 0.920092i \(0.628114\pi\)
\(968\) −29.3539 + 1.55003i −0.943469 + 0.0498199i
\(969\) −29.9391 43.5337i −0.961782 1.39851i
\(970\) 2.69620 + 4.48590i 0.0865699 + 0.144033i
\(971\) −6.27762 1.10691i −0.201458 0.0355226i 0.0720082 0.997404i \(-0.477059\pi\)
−0.273467 + 0.961881i \(0.588170\pi\)
\(972\) −29.7864 + 9.20722i −0.955398 + 0.295322i
\(973\) −24.9954 + 68.6743i −0.801316 + 2.20160i
\(974\) −9.06778 + 11.2008i −0.290550 + 0.358897i
\(975\) 8.04166 12.3984i 0.257539 0.397066i
\(976\) −24.0299 11.7045i −0.769179 0.374651i
\(977\) −38.9574 22.4921i −1.24636 0.719585i −0.275977 0.961164i \(-0.589001\pi\)
−0.970381 + 0.241579i \(0.922335\pi\)
\(978\) −5.80433 3.62133i −0.185602 0.115797i
\(979\) 2.14603 + 12.1707i 0.0685873 + 0.388978i
\(980\) 21.0878 + 33.7278i 0.673627 + 1.07739i
\(981\) 13.0066 26.7440i 0.415268 0.853870i
\(982\) 9.45706 27.4771i 0.301787 0.876829i
\(983\) −48.5128 + 17.6572i −1.54732 + 0.563178i −0.967787 0.251772i \(-0.918987\pi\)
−0.579532 + 0.814950i \(0.696764\pi\)
\(984\) 12.8560 0.0123498i 0.409833 0.000393698i
\(985\) 8.11500 + 6.80929i 0.258565 + 0.216962i
\(986\) −7.25235 18.8856i −0.230962 0.601439i
\(987\) 21.1819 6.48902i 0.674226 0.206548i
\(988\) −13.3252 + 22.6217i −0.423932 + 0.719691i
\(989\) 0.876699 0.0278774
\(990\) 3.99059 + 2.78675i 0.126829 + 0.0885687i
\(991\) −22.3860 + 26.6785i −0.711113 + 0.847472i −0.993735 0.111759i \(-0.964351\pi\)
0.282622 + 0.959231i \(0.408796\pi\)
\(992\) 26.0604 + 26.0260i 0.827418 + 0.826326i
\(993\) 22.4743 + 29.7894i 0.713201 + 0.945339i
\(994\) −12.3151 + 35.7811i −0.390612 + 1.13491i
\(995\) −26.4013 + 15.2428i −0.836978 + 0.483230i
\(996\) 8.90283 + 7.72617i 0.282097 + 0.244813i
\(997\) 31.1768 5.49731i 0.987380 0.174102i 0.343437 0.939176i \(-0.388409\pi\)
0.643942 + 0.765074i \(0.277298\pi\)
\(998\) −18.6708 + 16.2346i −0.591015 + 0.513899i
\(999\) −9.57868 24.8276i −0.303056 0.785509i
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 456.2.bu.c.131.65 yes 432
3.2 odd 2 inner 456.2.bu.c.131.8 432
8.3 odd 2 inner 456.2.bu.c.131.58 yes 432
19.9 even 9 inner 456.2.bu.c.275.15 yes 432
24.11 even 2 inner 456.2.bu.c.131.15 yes 432
57.47 odd 18 inner 456.2.bu.c.275.58 yes 432
152.123 odd 18 inner 456.2.bu.c.275.8 yes 432
456.275 even 18 inner 456.2.bu.c.275.65 yes 432
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
456.2.bu.c.131.8 432 3.2 odd 2 inner
456.2.bu.c.131.15 yes 432 24.11 even 2 inner
456.2.bu.c.131.58 yes 432 8.3 odd 2 inner
456.2.bu.c.131.65 yes 432 1.1 even 1 trivial
456.2.bu.c.275.8 yes 432 152.123 odd 18 inner
456.2.bu.c.275.15 yes 432 19.9 even 9 inner
456.2.bu.c.275.58 yes 432 57.47 odd 18 inner
456.2.bu.c.275.65 yes 432 456.275 even 18 inner