Properties

Label 441.2.z.a.142.15
Level $441$
Weight $2$
Character 441.142
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(4,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([14, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.z (of order \(21\), degree \(12\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 142.15
Character \(\chi\) \(=\) 441.142
Dual form 441.2.z.a.382.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.570548 + 1.45373i) q^{2} +(1.65353 + 0.515604i) q^{3} +(-0.321708 - 0.298502i) q^{4} +(2.55033 - 1.22817i) q^{5} +(-1.69297 + 2.10961i) q^{6} +(2.20166 - 1.46720i) q^{7} +(-2.19657 + 1.05781i) q^{8} +(2.46830 + 1.70513i) q^{9} +O(q^{10})\) \(q+(-0.570548 + 1.45373i) q^{2} +(1.65353 + 0.515604i) q^{3} +(-0.321708 - 0.298502i) q^{4} +(2.55033 - 1.22817i) q^{5} +(-1.69297 + 2.10961i) q^{6} +(2.20166 - 1.46720i) q^{7} +(-2.19657 + 1.05781i) q^{8} +(2.46830 + 1.70513i) q^{9} +(0.330351 + 4.40823i) q^{10} +(-2.88279 - 3.61490i) q^{11} +(-0.378045 - 0.659455i) q^{12} +(-1.70003 + 4.33160i) q^{13} +(0.876764 + 4.03774i) q^{14} +(4.85029 - 0.715859i) q^{15} +(-0.350120 - 4.67202i) q^{16} +(4.28838 - 3.97904i) q^{17} +(-3.88709 + 2.61540i) q^{18} +(-0.412459 + 0.714400i) q^{19} +(-1.18707 - 0.366164i) q^{20} +(4.39700 - 1.29087i) q^{21} +(6.89987 - 2.12833i) q^{22} +(-0.126064 + 0.552321i) q^{23} +(-4.17750 + 0.616561i) q^{24} +(1.87832 - 2.35534i) q^{25} +(-5.32704 - 4.94277i) q^{26} +(3.20224 + 4.09215i) q^{27} +(-1.14626 - 0.185189i) q^{28} +(-2.40287 - 0.741187i) q^{29} +(-1.72666 + 7.45945i) q^{30} +(-3.94519 + 6.83327i) q^{31} +(2.33224 + 0.719402i) q^{32} +(-2.90291 - 7.46372i) q^{33} +(3.33773 + 8.50439i) q^{34} +(3.81299 - 6.44587i) q^{35} +(-0.285090 - 1.28535i) q^{36} +(-1.13222 - 0.349242i) q^{37} +(-0.803219 - 1.00720i) q^{38} +(-5.04444 + 6.28588i) q^{39} +(-4.30280 + 5.39554i) q^{40} +(-10.1344 - 6.90954i) q^{41} +(-0.632120 + 7.12857i) q^{42} +(-0.809573 + 0.551957i) q^{43} +(-0.151638 + 2.02346i) q^{44} +(8.38919 + 1.31714i) q^{45} +(-0.731002 - 0.498388i) q^{46} +(-2.96723 + 7.56038i) q^{47} +(1.82998 - 7.90584i) q^{48} +(2.69464 - 6.46057i) q^{49} +(2.35236 + 4.07441i) q^{50} +(9.14256 - 4.36834i) q^{51} +(1.83991 - 0.886052i) q^{52} +(-5.50606 + 1.69839i) q^{53} +(-7.77592 + 2.32043i) q^{54} +(-11.7918 - 5.67863i) q^{55} +(-3.28408 + 5.55175i) q^{56} +(-1.05036 + 0.968615i) q^{57} +(2.44844 - 3.07024i) q^{58} +(-5.21727 + 3.55708i) q^{59} +(-1.77406 - 1.21752i) q^{60} +(3.86452 - 3.58575i) q^{61} +(-7.68283 - 9.63396i) q^{62} +(7.93615 + 0.132623i) q^{63} +(3.46578 - 4.34595i) q^{64} +(0.984328 + 13.1349i) q^{65} +(12.5065 + 0.0383530i) q^{66} +(-3.39113 + 5.87361i) q^{67} -2.56736 q^{68} +(-0.493229 + 0.848279i) q^{69} +(7.19508 + 9.22074i) q^{70} +(1.13414 - 4.96898i) q^{71} +(-7.22551 - 1.13444i) q^{72} +(2.74325 + 0.413479i) q^{73} +(1.15369 - 1.44668i) q^{74} +(4.32027 - 2.92615i) q^{75} +(0.345941 - 0.106709i) q^{76} +(-11.6507 - 3.72916i) q^{77} +(-6.25990 - 10.9197i) q^{78} +(3.90274 + 6.75974i) q^{79} +(-6.63098 - 11.4852i) q^{80} +(3.18506 + 8.41757i) q^{81} +(15.8268 - 10.7905i) q^{82} +(-3.49089 - 8.89464i) q^{83} +(-1.79988 - 0.897230i) q^{84} +(6.04984 - 15.4147i) q^{85} +(-0.340498 - 1.49182i) q^{86} +(-3.59105 - 2.46450i) q^{87} +(10.1561 + 4.89093i) q^{88} +(4.37271 + 11.1415i) q^{89} +(-6.70120 + 11.4441i) q^{90} +(2.61245 + 12.0310i) q^{91} +(0.205425 - 0.140056i) q^{92} +(-10.0467 + 9.26484i) q^{93} +(-9.29782 - 8.62712i) q^{94} +(-0.174499 + 2.32853i) q^{95} +(3.48550 + 2.39207i) q^{96} +(2.19157 - 3.79591i) q^{97} +(7.85451 + 7.60335i) q^{98} +(-0.951719 - 13.8382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9} - 22 q^{10} - 5 q^{11} + 2 q^{12} - 4 q^{13} + 52 q^{14} - 4 q^{15} + 38 q^{16} - 37 q^{17} - 16 q^{18} - 14 q^{19} - 11 q^{20} - 6 q^{21} - q^{22} - 20 q^{23} - 26 q^{24} - 97 q^{25} - 44 q^{26} + 14 q^{27} - 22 q^{28} - 53 q^{29} - 9 q^{30} + 10 q^{31} - 10 q^{32} + 2 q^{33} - 7 q^{34} - 32 q^{35} - 22 q^{36} - 39 q^{37} + 59 q^{38} - 26 q^{39} - 19 q^{40} - 17 q^{41} - 83 q^{42} - q^{43} - 31 q^{44} + 81 q^{45} + 56 q^{46} + 50 q^{47} - 23 q^{48} - 19 q^{49} - 21 q^{50} - 30 q^{51} - 9 q^{52} + 50 q^{53} + 48 q^{54} + 20 q^{55} - 239 q^{56} + 33 q^{57} + 17 q^{58} - 37 q^{59} - 152 q^{60} - 105 q^{61} - 30 q^{62} + 6 q^{63} - 88 q^{64} - 5 q^{65} - 99 q^{66} + 13 q^{67} - 290 q^{68} + 64 q^{69} + 17 q^{70} - 19 q^{71} + 11 q^{72} - 40 q^{73} - 57 q^{74} + 69 q^{75} - 41 q^{76} + 19 q^{77} + 81 q^{78} + 13 q^{79} + 163 q^{80} - 179 q^{81} - 28 q^{82} + 73 q^{83} - 341 q^{84} - 10 q^{85} + 15 q^{86} + 13 q^{87} - 13 q^{88} - 104 q^{89} + 171 q^{90} - 49 q^{91} - 91 q^{92} - 275 q^{93} - 4 q^{94} - 29 q^{95} + 231 q^{96} - 11 q^{97} - 33 q^{98} + 62 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.570548 + 1.45373i −0.403438 + 1.02794i 0.574399 + 0.818576i \(0.305236\pi\)
−0.977837 + 0.209368i \(0.932859\pi\)
\(3\) 1.65353 + 0.515604i 0.954664 + 0.297684i
\(4\) −0.321708 0.298502i −0.160854 0.149251i
\(5\) 2.55033 1.22817i 1.14054 0.549256i 0.234362 0.972149i \(-0.424700\pi\)
0.906180 + 0.422893i \(0.138985\pi\)
\(6\) −1.69297 + 2.10961i −0.691151 + 0.861244i
\(7\) 2.20166 1.46720i 0.832150 0.554550i
\(8\) −2.19657 + 1.05781i −0.776604 + 0.373993i
\(9\) 2.46830 + 1.70513i 0.822768 + 0.568377i
\(10\) 0.330351 + 4.40823i 0.104466 + 1.39400i
\(11\) −2.88279 3.61490i −0.869194 1.08993i −0.995196 0.0979042i \(-0.968786\pi\)
0.126002 0.992030i \(-0.459785\pi\)
\(12\) −0.378045 0.659455i −0.109132 0.190368i
\(13\) −1.70003 + 4.33160i −0.471503 + 1.20137i 0.475376 + 0.879783i \(0.342312\pi\)
−0.946880 + 0.321588i \(0.895783\pi\)
\(14\) 0.876764 + 4.03774i 0.234325 + 1.07913i
\(15\) 4.85029 0.715859i 1.25234 0.184834i
\(16\) −0.350120 4.67202i −0.0875299 1.16801i
\(17\) 4.28838 3.97904i 1.04009 0.965058i 0.0406675 0.999173i \(-0.487052\pi\)
0.999418 + 0.0341145i \(0.0108611\pi\)
\(18\) −3.88709 + 2.61540i −0.916196 + 0.616455i
\(19\) −0.412459 + 0.714400i −0.0946246 + 0.163895i −0.909452 0.415809i \(-0.863498\pi\)
0.814827 + 0.579704i \(0.196832\pi\)
\(20\) −1.18707 0.366164i −0.265438 0.0818768i
\(21\) 4.39700 1.29087i 0.959505 0.281691i
\(22\) 6.89987 2.12833i 1.47106 0.453761i
\(23\) −0.126064 + 0.552321i −0.0262861 + 0.115167i −0.986369 0.164549i \(-0.947383\pi\)
0.960083 + 0.279716i \(0.0902403\pi\)
\(24\) −4.17750 + 0.616561i −0.852728 + 0.125855i
\(25\) 1.87832 2.35534i 0.375664 0.471068i
\(26\) −5.32704 4.94277i −1.04472 0.969358i
\(27\) 3.20224 + 4.09215i 0.616271 + 0.787534i
\(28\) −1.14626 0.185189i −0.216622 0.0349975i
\(29\) −2.40287 0.741187i −0.446201 0.137635i 0.0635084 0.997981i \(-0.479771\pi\)
−0.509710 + 0.860346i \(0.670247\pi\)
\(30\) −1.72666 + 7.45945i −0.315243 + 1.36190i
\(31\) −3.94519 + 6.83327i −0.708577 + 1.22729i 0.256808 + 0.966463i \(0.417329\pi\)
−0.965385 + 0.260829i \(0.916004\pi\)
\(32\) 2.33224 + 0.719402i 0.412286 + 0.127174i
\(33\) −2.90291 7.46372i −0.505332 1.29927i
\(34\) 3.33773 + 8.50439i 0.572415 + 1.45849i
\(35\) 3.81299 6.44587i 0.644512 1.08955i
\(36\) −0.285090 1.28535i −0.0475150 0.214225i
\(37\) −1.13222 0.349242i −0.186135 0.0574151i 0.200286 0.979737i \(-0.435813\pi\)
−0.386421 + 0.922322i \(0.626289\pi\)
\(38\) −0.803219 1.00720i −0.130299 0.163390i
\(39\) −5.04444 + 6.28588i −0.807757 + 1.00655i
\(40\) −4.30280 + 5.39554i −0.680332 + 0.853109i
\(41\) −10.1344 6.90954i −1.58273 1.07909i −0.953296 0.302038i \(-0.902333\pi\)
−0.629437 0.777051i \(-0.716715\pi\)
\(42\) −0.632120 + 7.12857i −0.0975383 + 1.09996i
\(43\) −0.809573 + 0.551957i −0.123459 + 0.0841727i −0.623475 0.781843i \(-0.714280\pi\)
0.500016 + 0.866016i \(0.333327\pi\)
\(44\) −0.151638 + 2.02346i −0.0228602 + 0.305048i
\(45\) 8.38919 + 1.31714i 1.25059 + 0.196347i
\(46\) −0.731002 0.498388i −0.107780 0.0734834i
\(47\) −2.96723 + 7.56038i −0.432815 + 1.10279i 0.533584 + 0.845747i \(0.320845\pi\)
−0.966399 + 0.257047i \(0.917250\pi\)
\(48\) 1.82998 7.90584i 0.264135 1.14111i
\(49\) 2.69464 6.46057i 0.384948 0.922938i
\(50\) 2.35236 + 4.07441i 0.332674 + 0.576208i
\(51\) 9.14256 4.36834i 1.28022 0.611690i
\(52\) 1.83991 0.886052i 0.255149 0.122873i
\(53\) −5.50606 + 1.69839i −0.756315 + 0.233292i −0.648850 0.760917i \(-0.724750\pi\)
−0.107465 + 0.994209i \(0.534273\pi\)
\(54\) −7.77592 + 2.32043i −1.05817 + 0.315770i
\(55\) −11.7918 5.67863i −1.59000 0.765706i
\(56\) −3.28408 + 5.55175i −0.438854 + 0.741884i
\(57\) −1.05036 + 0.968615i −0.139124 + 0.128296i
\(58\) 2.44844 3.07024i 0.321496 0.403143i
\(59\) −5.21727 + 3.55708i −0.679231 + 0.463092i −0.853148 0.521668i \(-0.825310\pi\)
0.173917 + 0.984760i \(0.444357\pi\)
\(60\) −1.77406 1.21752i −0.229031 0.157182i
\(61\) 3.86452 3.58575i 0.494802 0.459109i −0.392865 0.919596i \(-0.628516\pi\)
0.887666 + 0.460488i \(0.152325\pi\)
\(62\) −7.68283 9.63396i −0.975720 1.22351i
\(63\) 7.93615 + 0.132623i 0.999860 + 0.0167089i
\(64\) 3.46578 4.34595i 0.433222 0.543244i
\(65\) 0.984328 + 13.1349i 0.122091 + 1.62919i
\(66\) 12.5065 + 0.0383530i 1.53944 + 0.00472093i
\(67\) −3.39113 + 5.87361i −0.414293 + 0.717576i −0.995354 0.0962838i \(-0.969304\pi\)
0.581061 + 0.813860i \(0.302638\pi\)
\(68\) −2.56736 −0.311338
\(69\) −0.493229 + 0.848279i −0.0593778 + 0.102121i
\(70\) 7.19508 + 9.22074i 0.859977 + 1.10209i
\(71\) 1.13414 4.96898i 0.134597 0.589709i −0.861973 0.506955i \(-0.830771\pi\)
0.996570 0.0827545i \(-0.0263717\pi\)
\(72\) −7.22551 1.13444i −0.851534 0.133694i
\(73\) 2.74325 + 0.413479i 0.321073 + 0.0483940i 0.307602 0.951515i \(-0.400474\pi\)
0.0134717 + 0.999909i \(0.495712\pi\)
\(74\) 1.15369 1.44668i 0.134113 0.168173i
\(75\) 4.32027 2.92615i 0.498862 0.337882i
\(76\) 0.345941 0.106709i 0.0396822 0.0122403i
\(77\) −11.6507 3.72916i −1.32772 0.424978i
\(78\) −6.25990 10.9197i −0.708794 1.23641i
\(79\) 3.90274 + 6.75974i 0.439092 + 0.760530i 0.997620 0.0689559i \(-0.0219668\pi\)
−0.558527 + 0.829486i \(0.688633\pi\)
\(80\) −6.63098 11.4852i −0.741366 1.28408i
\(81\) 3.18506 + 8.41757i 0.353895 + 0.935285i
\(82\) 15.8268 10.7905i 1.74778 1.19162i
\(83\) −3.49089 8.89464i −0.383175 0.976314i −0.984196 0.177081i \(-0.943335\pi\)
0.601021 0.799233i \(-0.294761\pi\)
\(84\) −1.79988 0.897230i −0.196383 0.0978958i
\(85\) 6.04984 15.4147i 0.656197 1.67196i
\(86\) −0.340498 1.49182i −0.0367169 0.160867i
\(87\) −3.59105 2.46450i −0.385001 0.264222i
\(88\) 10.1561 + 4.89093i 1.08265 + 0.521375i
\(89\) 4.37271 + 11.1415i 0.463506 + 1.18099i 0.951363 + 0.308071i \(0.0996833\pi\)
−0.487858 + 0.872923i \(0.662221\pi\)
\(90\) −6.70120 + 11.4441i −0.706368 + 1.20632i
\(91\) 2.61245 + 12.0310i 0.273859 + 1.26119i
\(92\) 0.205425 0.140056i 0.0214170 0.0146019i
\(93\) −10.0467 + 9.26484i −1.04180 + 0.960720i
\(94\) −9.29782 8.62712i −0.958997 0.889819i
\(95\) −0.174499 + 2.32853i −0.0179032 + 0.238902i
\(96\) 3.48550 + 2.39207i 0.355738 + 0.244139i
\(97\) 2.19157 3.79591i 0.222520 0.385416i −0.733052 0.680172i \(-0.761905\pi\)
0.955573 + 0.294756i \(0.0952383\pi\)
\(98\) 7.85451 + 7.60335i 0.793426 + 0.768054i
\(99\) −0.951719 13.8382i −0.0956513 1.39079i
\(100\) −1.30734 + 0.197050i −0.130734 + 0.0197050i
\(101\) 7.43571 3.58085i 0.739881 0.356308i −0.0256811 0.999670i \(-0.508175\pi\)
0.765562 + 0.643362i \(0.222461\pi\)
\(102\) 1.13412 + 15.7832i 0.112295 + 1.56277i
\(103\) 5.50078 2.64904i 0.542008 0.261017i −0.142786 0.989754i \(-0.545606\pi\)
0.684795 + 0.728736i \(0.259892\pi\)
\(104\) −0.847790 11.3130i −0.0831327 1.10933i
\(105\) 9.62840 8.69243i 0.939635 0.848295i
\(106\) 0.672459 8.97334i 0.0653150 0.871568i
\(107\) −7.17825 18.2899i −0.693948 1.76815i −0.638414 0.769693i \(-0.720409\pi\)
−0.0555337 0.998457i \(-0.517686\pi\)
\(108\) 0.191327 2.27235i 0.0184105 0.218657i
\(109\) 2.64583 6.74146i 0.253424 0.645715i −0.746379 0.665521i \(-0.768210\pi\)
0.999804 + 0.0198058i \(0.00630479\pi\)
\(110\) 14.9830 13.9022i 1.42857 1.32552i
\(111\) −1.69208 1.16126i −0.160605 0.110222i
\(112\) −7.62565 9.77252i −0.720556 0.923417i
\(113\) 13.3096 + 2.00611i 1.25207 + 0.188718i 0.741401 0.671062i \(-0.234162\pi\)
0.510664 + 0.859780i \(0.329400\pi\)
\(114\) −0.808826 2.07958i −0.0757535 0.194771i
\(115\) 0.356842 + 1.56343i 0.0332757 + 0.145790i
\(116\) 0.551777 + 0.955707i 0.0512313 + 0.0887351i
\(117\) −11.5821 + 7.79295i −1.07077 + 0.720458i
\(118\) −2.19433 9.61400i −0.202005 0.885040i
\(119\) 3.60352 15.0524i 0.330334 1.37985i
\(120\) −9.89675 + 6.70313i −0.903446 + 0.611909i
\(121\) −2.30932 + 10.1178i −0.209938 + 0.919799i
\(122\) 3.00783 + 7.66383i 0.272316 + 0.693850i
\(123\) −13.1950 16.6505i −1.18975 1.50132i
\(124\) 3.30895 1.02067i 0.297152 0.0916593i
\(125\) −1.25183 + 5.48462i −0.111967 + 0.490559i
\(126\) −4.72075 + 11.4614i −0.420558 + 1.02106i
\(127\) −2.98593 13.0822i −0.264958 1.16086i −0.915797 0.401642i \(-0.868440\pi\)
0.650839 0.759216i \(-0.274417\pi\)
\(128\) 6.78113 + 11.7453i 0.599373 + 1.03814i
\(129\) −1.62324 + 0.495257i −0.142918 + 0.0436050i
\(130\) −19.6563 6.06317i −1.72397 0.531775i
\(131\) 1.03410 + 0.497999i 0.0903501 + 0.0435103i 0.478513 0.878080i \(-0.341176\pi\)
−0.388163 + 0.921591i \(0.626890\pi\)
\(132\) −1.29404 + 3.26767i −0.112632 + 0.284414i
\(133\) 0.140073 + 2.17803i 0.0121459 + 0.188859i
\(134\) −6.60386 8.28098i −0.570486 0.715367i
\(135\) 13.1926 + 6.50342i 1.13544 + 0.559726i
\(136\) −5.21065 + 13.2765i −0.446810 + 1.13845i
\(137\) 16.6099 + 7.99889i 1.41908 + 0.683391i 0.976932 0.213552i \(-0.0685033\pi\)
0.442145 + 0.896944i \(0.354218\pi\)
\(138\) −0.951760 1.20101i −0.0810192 0.102236i
\(139\) −9.38935 6.40155i −0.796394 0.542972i 0.0953865 0.995440i \(-0.469591\pi\)
−0.891781 + 0.452468i \(0.850544\pi\)
\(140\) −3.15077 + 0.935508i −0.266289 + 0.0790649i
\(141\) −8.80456 + 10.9714i −0.741478 + 0.923957i
\(142\) 6.57648 + 4.48377i 0.551886 + 0.376270i
\(143\) 20.5592 6.34166i 1.71924 0.530316i
\(144\) 7.10221 12.1290i 0.591851 1.01075i
\(145\) −7.03841 + 1.06087i −0.584508 + 0.0881004i
\(146\) −2.16624 + 3.75204i −0.179280 + 0.310521i
\(147\) 7.78675 9.29336i 0.642241 0.766503i
\(148\) 0.259994 + 0.450323i 0.0213714 + 0.0370163i
\(149\) −1.41161 1.77010i −0.115643 0.145012i 0.720641 0.693309i \(-0.243848\pi\)
−0.836284 + 0.548297i \(0.815276\pi\)
\(150\) 1.78891 + 7.95003i 0.146064 + 0.649117i
\(151\) −2.83052 + 12.4013i −0.230344 + 1.00920i 0.719011 + 0.694999i \(0.244595\pi\)
−0.949355 + 0.314205i \(0.898262\pi\)
\(152\) 0.150294 2.00553i 0.0121904 0.162670i
\(153\) 17.3698 2.50922i 1.40427 0.202859i
\(154\) 12.0685 14.8094i 0.972507 1.19337i
\(155\) −1.66909 + 22.2725i −0.134065 + 1.78897i
\(156\) 3.49919 0.516448i 0.280159 0.0413489i
\(157\) 9.45913 6.44912i 0.754920 0.514696i −0.123640 0.992327i \(-0.539457\pi\)
0.878561 + 0.477631i \(0.158504\pi\)
\(158\) −12.0535 + 1.81678i −0.958929 + 0.144535i
\(159\) −9.98011 0.0306055i −0.791474 0.00242717i
\(160\) 6.83154 1.02969i 0.540081 0.0814041i
\(161\) 0.532817 + 1.40099i 0.0419918 + 0.110413i
\(162\) −14.0541 0.172404i −1.10420 0.0135453i
\(163\) −7.29398 + 4.97295i −0.571309 + 0.389512i −0.814237 0.580533i \(-0.802844\pi\)
0.242928 + 0.970044i \(0.421892\pi\)
\(164\) 1.19782 + 5.24801i 0.0935343 + 0.409800i
\(165\) −16.5701 15.4697i −1.28998 1.20431i
\(166\) 14.9221 1.15818
\(167\) 6.44290 5.97813i 0.498566 0.462602i −0.390353 0.920665i \(-0.627647\pi\)
0.888920 + 0.458063i \(0.151457\pi\)
\(168\) −8.29282 + 7.48669i −0.639805 + 0.577611i
\(169\) −6.34302 5.88546i −0.487925 0.452728i
\(170\) 18.9572 + 17.5897i 1.45395 + 1.34907i
\(171\) −2.23622 + 1.06006i −0.171008 + 0.0810649i
\(172\) 0.425207 + 0.0640896i 0.0324217 + 0.00488679i
\(173\) 11.5446 3.56105i 0.877722 0.270741i 0.177030 0.984205i \(-0.443351\pi\)
0.700692 + 0.713464i \(0.252875\pi\)
\(174\) 5.63159 3.81431i 0.426930 0.289162i
\(175\) 0.679670 7.94153i 0.0513783 0.600324i
\(176\) −15.8796 + 14.7341i −1.19697 + 1.11062i
\(177\) −10.4609 + 3.19167i −0.786293 + 0.239901i
\(178\) −18.6916 −1.40099
\(179\) −10.7228 + 9.94930i −0.801459 + 0.743646i −0.970276 0.242002i \(-0.922196\pi\)
0.168816 + 0.985648i \(0.446005\pi\)
\(180\) −2.30570 2.92792i −0.171857 0.218234i
\(181\) 14.7192 18.4572i 1.09407 1.37192i 0.171904 0.985114i \(-0.445008\pi\)
0.922162 0.386803i \(-0.126421\pi\)
\(182\) −18.9804 3.06648i −1.40692 0.227302i
\(183\) 8.23892 3.93658i 0.609039 0.291000i
\(184\) −0.307344 1.34656i −0.0226577 0.0992699i
\(185\) −3.31645 + 0.499875i −0.243830 + 0.0367515i
\(186\) −7.73645 19.8913i −0.567264 1.45850i
\(187\) −26.7463 4.03136i −1.95589 0.294802i
\(188\) 3.21137 1.54651i 0.234213 0.112791i
\(189\) 13.0543 + 4.31120i 0.949557 + 0.313594i
\(190\) −3.28550 1.58221i −0.238355 0.114786i
\(191\) 1.90622 + 1.29964i 0.137929 + 0.0940386i 0.630319 0.776336i \(-0.282924\pi\)
−0.492390 + 0.870375i \(0.663876\pi\)
\(192\) 7.97155 5.39918i 0.575297 0.389652i
\(193\) −1.55817 + 20.7923i −0.112160 + 1.49667i 0.603021 + 0.797726i \(0.293964\pi\)
−0.715180 + 0.698940i \(0.753655\pi\)
\(194\) 4.26784 + 5.35171i 0.306413 + 0.384230i
\(195\) −5.14482 + 22.2265i −0.368428 + 1.59167i
\(196\) −2.79538 + 1.27406i −0.199670 + 0.0910046i
\(197\) −2.21127 −0.157547 −0.0787733 0.996893i \(-0.525100\pi\)
−0.0787733 + 0.996893i \(0.525100\pi\)
\(198\) 20.6601 + 6.51182i 1.46825 + 0.462775i
\(199\) −21.2176 14.4659i −1.50408 1.02546i −0.985355 0.170518i \(-0.945456\pi\)
−0.518721 0.854943i \(-0.673592\pi\)
\(200\) −1.63435 + 7.16057i −0.115566 + 0.506329i
\(201\) −8.63579 + 7.96370i −0.609122 + 0.561716i
\(202\) 0.963167 + 12.8526i 0.0677682 + 0.904304i
\(203\) −6.37778 + 1.89365i −0.447632 + 0.132908i
\(204\) −4.24520 1.32374i −0.297223 0.0926804i
\(205\) −34.3323 5.17476i −2.39787 0.361421i
\(206\) 0.712531 + 9.50807i 0.0496444 + 0.662458i
\(207\) −1.25294 + 1.14834i −0.0870856 + 0.0798153i
\(208\) 20.8326 + 6.42600i 1.44448 + 0.445563i
\(209\) 3.77152 0.568465i 0.260882 0.0393216i
\(210\) 7.14301 + 18.9566i 0.492914 + 1.30813i
\(211\) −0.655196 0.0987549i −0.0451056 0.00679857i 0.126451 0.991973i \(-0.459641\pi\)
−0.171556 + 0.985174i \(0.554880\pi\)
\(212\) 2.27832 + 1.09718i 0.156476 + 0.0753547i
\(213\) 4.43735 7.63158i 0.304042 0.522907i
\(214\) 30.6841 2.09752
\(215\) −1.38678 + 2.40197i −0.0945774 + 0.163813i
\(216\) −11.3627 5.60132i −0.773131 0.381122i
\(217\) 1.33981 + 20.8330i 0.0909520 + 1.41423i
\(218\) 8.29071 + 7.69265i 0.561518 + 0.521012i
\(219\) 4.32285 + 2.09813i 0.292111 + 0.141779i
\(220\) 2.09844 + 5.34673i 0.141477 + 0.360477i
\(221\) 9.94524 + 25.3401i 0.668989 + 1.70456i
\(222\) 2.65357 1.79728i 0.178096 0.120625i
\(223\) −2.51255 2.33131i −0.168253 0.156116i 0.591552 0.806267i \(-0.298515\pi\)
−0.759805 + 0.650151i \(0.774706\pi\)
\(224\) 6.19032 1.83799i 0.413608 0.122806i
\(225\) 8.65242 2.61091i 0.576828 0.174061i
\(226\) −10.5101 + 18.2041i −0.699123 + 1.21092i
\(227\) 6.05998 0.402215 0.201107 0.979569i \(-0.435546\pi\)
0.201107 + 0.979569i \(0.435546\pi\)
\(228\) 0.627043 + 0.00192292i 0.0415269 + 0.000127348i
\(229\) 22.6760 + 10.9202i 1.49847 + 0.721625i 0.990211 0.139580i \(-0.0445751\pi\)
0.508259 + 0.861204i \(0.330289\pi\)
\(230\) −2.47640 0.373258i −0.163289 0.0246119i
\(231\) −17.3420 12.1734i −1.14102 0.800953i
\(232\) 6.06210 0.913715i 0.397996 0.0599883i
\(233\) −3.74370 1.15478i −0.245258 0.0756520i 0.169689 0.985498i \(-0.445724\pi\)
−0.414947 + 0.909846i \(0.636200\pi\)
\(234\) −4.72069 21.2836i −0.308601 1.39135i
\(235\) 1.71805 + 22.9257i 0.112073 + 1.49551i
\(236\) 2.74023 + 0.413024i 0.178374 + 0.0268856i
\(237\) 2.96793 + 13.1897i 0.192788 + 0.856762i
\(238\) 19.8262 + 13.8267i 1.28514 + 0.896251i
\(239\) 2.00981 + 26.8190i 0.130004 + 1.73478i 0.556988 + 0.830520i \(0.311957\pi\)
−0.426985 + 0.904259i \(0.640424\pi\)
\(240\) −5.04269 22.4100i −0.325504 1.44656i
\(241\) −2.42319 + 10.6167i −0.156092 + 0.683882i 0.834950 + 0.550326i \(0.185497\pi\)
−0.991041 + 0.133556i \(0.957361\pi\)
\(242\) −13.3910 9.12982i −0.860805 0.586887i
\(243\) 0.926447 + 15.5609i 0.0594316 + 0.998232i
\(244\) −2.31360 −0.148113
\(245\) −1.06248 19.7861i −0.0678795 1.26408i
\(246\) 31.7337 9.68207i 2.02327 0.617307i
\(247\) −2.39331 3.00111i −0.152282 0.190956i
\(248\) 1.43757 19.1830i 0.0912857 1.21812i
\(249\) −1.18617 16.5075i −0.0751703 1.04612i
\(250\) −7.25894 4.94906i −0.459095 0.313006i
\(251\) 18.1228 + 8.72748i 1.14390 + 0.550874i 0.907196 0.420708i \(-0.138218\pi\)
0.236705 + 0.971582i \(0.423932\pi\)
\(252\) −2.51354 2.41162i −0.158338 0.151918i
\(253\) 2.36000 1.13652i 0.148372 0.0714522i
\(254\) 20.7216 + 3.12328i 1.30019 + 0.195972i
\(255\) 17.9515 22.3694i 1.12416 1.40082i
\(256\) −9.95024 + 1.49976i −0.621890 + 0.0937348i
\(257\) −1.69558 7.42881i −0.105767 0.463397i −0.999879 0.0155528i \(-0.995049\pi\)
0.894112 0.447844i \(-0.147808\pi\)
\(258\) 0.206165 2.64233i 0.0128353 0.164504i
\(259\) −3.00517 + 0.892275i −0.186732 + 0.0554433i
\(260\) 3.60414 4.51945i 0.223519 0.280284i
\(261\) −4.66719 5.92668i −0.288892 0.366852i
\(262\) −1.31396 + 1.21918i −0.0811769 + 0.0753211i
\(263\) 17.7822 1.09650 0.548249 0.836315i \(-0.315295\pi\)
0.548249 + 0.836315i \(0.315295\pi\)
\(264\) 14.2716 + 13.3238i 0.878359 + 0.820025i
\(265\) −11.9563 + 11.0939i −0.734472 + 0.681490i
\(266\) −3.24619 1.03904i −0.199037 0.0637077i
\(267\) 1.48580 + 20.6773i 0.0909294 + 1.26543i
\(268\) 2.84424 0.877332i 0.173740 0.0535916i
\(269\) −23.2252 3.50064i −1.41607 0.213438i −0.603991 0.796991i \(-0.706424\pi\)
−0.812075 + 0.583553i \(0.801662\pi\)
\(270\) −16.9813 + 15.4680i −1.03345 + 0.941355i
\(271\) 12.5209 + 11.6177i 0.760588 + 0.705723i 0.961778 0.273829i \(-0.0882904\pi\)
−0.201190 + 0.979552i \(0.564481\pi\)
\(272\) −20.0916 18.6423i −1.21823 1.13035i
\(273\) −1.88349 + 21.2406i −0.113994 + 1.28554i
\(274\) −21.1050 + 19.5825i −1.27500 + 1.18303i
\(275\) −13.9291 −0.839957
\(276\) 0.411889 0.125669i 0.0247928 0.00756438i
\(277\) −0.739197 3.23863i −0.0444140 0.194591i 0.947854 0.318705i \(-0.103248\pi\)
−0.992268 + 0.124115i \(0.960391\pi\)
\(278\) 14.6632 9.99721i 0.879441 0.599593i
\(279\) −21.3896 + 10.1395i −1.28056 + 0.607038i
\(280\) −1.55697 + 18.1922i −0.0930466 + 1.08719i
\(281\) −22.6583 + 3.41519i −1.35168 + 0.203733i −0.784637 0.619956i \(-0.787151\pi\)
−0.567043 + 0.823688i \(0.691913\pi\)
\(282\) −10.9260 19.0592i −0.650635 1.13496i
\(283\) 4.16669 0.628028i 0.247684 0.0373324i −0.0240267 0.999711i \(-0.507649\pi\)
0.271711 + 0.962379i \(0.412411\pi\)
\(284\) −1.84811 + 1.26002i −0.109665 + 0.0747685i
\(285\) −1.48914 + 3.76031i −0.0882089 + 0.222742i
\(286\) −2.51091 + 33.5057i −0.148473 + 1.98123i
\(287\) −32.4503 0.343220i −1.91548 0.0202597i
\(288\) 4.53001 + 5.75249i 0.266934 + 0.338968i
\(289\) 1.28707 17.1748i 0.0757102 1.01028i
\(290\) 2.47353 10.8372i 0.145251 0.636385i
\(291\) 5.58101 5.14666i 0.327165 0.301703i
\(292\) −0.759103 0.951885i −0.0444232 0.0557049i
\(293\) 1.49489 + 2.58922i 0.0873323 + 0.151264i 0.906383 0.422458i \(-0.138832\pi\)
−0.819050 + 0.573722i \(0.805499\pi\)
\(294\) 9.06733 + 16.6222i 0.528818 + 0.969424i
\(295\) −8.93705 + 15.4794i −0.520335 + 0.901247i
\(296\) 2.85642 0.430536i 0.166026 0.0250244i
\(297\) 5.56135 23.3726i 0.322702 1.35621i
\(298\) 3.37864 1.04217i 0.195719 0.0603714i
\(299\) −2.17812 1.48502i −0.125964 0.0858809i
\(300\) −2.26333 0.348244i −0.130673 0.0201059i
\(301\) −0.972573 + 2.40303i −0.0560582 + 0.138508i
\(302\) −16.4132 11.1903i −0.944475 0.643932i
\(303\) 14.1414 2.08715i 0.812405 0.119904i
\(304\) 3.48211 + 1.67689i 0.199712 + 0.0961764i
\(305\) 5.45188 13.8912i 0.312174 0.795406i
\(306\) −6.26257 + 26.6827i −0.358007 + 1.52535i
\(307\) −19.5704 24.5405i −1.11694 1.40060i −0.906091 0.423084i \(-0.860948\pi\)
−0.210852 0.977518i \(-0.567624\pi\)
\(308\) 2.63497 + 4.67747i 0.150142 + 0.266523i
\(309\) 10.4615 1.54403i 0.595137 0.0878368i
\(310\) −31.4259 15.1339i −1.78487 0.859549i
\(311\) −1.48207 0.457160i −0.0840407 0.0259231i 0.252450 0.967610i \(-0.418764\pi\)
−0.336490 + 0.941687i \(0.609240\pi\)
\(312\) 4.43117 19.1434i 0.250866 1.08378i
\(313\) −13.3779 23.1711i −0.756161 1.30971i −0.944795 0.327662i \(-0.893739\pi\)
0.188634 0.982047i \(-0.439594\pi\)
\(314\) 3.97841 + 17.4306i 0.224515 + 0.983664i
\(315\) 20.4027 9.40874i 1.14956 0.530122i
\(316\) 0.762251 3.33964i 0.0428800 0.187869i
\(317\) 12.7427 3.93061i 0.715703 0.220765i 0.0845451 0.996420i \(-0.473056\pi\)
0.631158 + 0.775655i \(0.282580\pi\)
\(318\) 5.73862 14.4909i 0.321806 0.812612i
\(319\) 4.24764 + 10.8228i 0.237822 + 0.605962i
\(320\) 3.50130 15.3402i 0.195728 0.857542i
\(321\) −2.43909 33.9440i −0.136137 1.89457i
\(322\) −2.34066 0.0247566i −0.130440 0.00137963i
\(323\) 1.07384 + 4.70481i 0.0597502 + 0.261783i
\(324\) 1.48800 3.65875i 0.0826666 0.203264i
\(325\) 7.00919 + 12.1403i 0.388800 + 0.673422i
\(326\) −3.06778 13.4408i −0.169908 0.744417i
\(327\) 7.85087 9.78299i 0.434154 0.541001i
\(328\) 29.5700 + 4.45696i 1.63273 + 0.246094i
\(329\) 4.55976 + 20.9989i 0.251388 + 1.15771i
\(330\) 31.9428 15.2623i 1.75839 0.840164i
\(331\) 22.1031 20.5086i 1.21489 1.12726i 0.226714 0.973961i \(-0.427202\pi\)
0.988180 0.153296i \(-0.0489887\pi\)
\(332\) −1.53202 + 3.90352i −0.0840804 + 0.214233i
\(333\) −2.19915 2.79261i −0.120513 0.153034i
\(334\) 5.01462 + 12.7771i 0.274388 + 0.699129i
\(335\) −1.43469 + 19.1445i −0.0783852 + 1.04598i
\(336\) −7.57046 20.0909i −0.413002 1.09605i
\(337\) −1.88765 25.1890i −0.102827 1.37213i −0.775105 0.631832i \(-0.782303\pi\)
0.672278 0.740299i \(-0.265316\pi\)
\(338\) 12.1749 5.86312i 0.662226 0.318911i
\(339\) 20.9735 + 10.1797i 1.13912 + 0.552883i
\(340\) −6.54761 + 3.15316i −0.355094 + 0.171004i
\(341\) 36.0748 5.43740i 1.95356 0.294452i
\(342\) −0.265173 3.85568i −0.0143389 0.208491i
\(343\) −3.54627 18.1776i −0.191480 0.981496i
\(344\) 1.19441 2.06879i 0.0643985 0.111542i
\(345\) −0.216062 + 2.76916i −0.0116324 + 0.149087i
\(346\) −1.40996 + 18.8145i −0.0757997 + 1.01148i
\(347\) −10.2422 9.50334i −0.549828 0.510166i 0.355616 0.934632i \(-0.384271\pi\)
−0.905444 + 0.424466i \(0.860462\pi\)
\(348\) 0.419613 + 1.86479i 0.0224936 + 0.0999630i
\(349\) −4.71084 + 3.21180i −0.252166 + 0.171924i −0.682805 0.730600i \(-0.739240\pi\)
0.430640 + 0.902524i \(0.358288\pi\)
\(350\) 11.1571 + 5.51908i 0.596371 + 0.295007i
\(351\) −23.1695 + 6.91405i −1.23669 + 0.369045i
\(352\) −4.12280 10.5047i −0.219746 0.559903i
\(353\) −0.158768 0.0764587i −0.00845037 0.00406948i 0.429654 0.902994i \(-0.358636\pi\)
−0.438104 + 0.898924i \(0.644350\pi\)
\(354\) 1.32863 17.0284i 0.0706158 0.905050i
\(355\) −3.21035 14.0654i −0.170388 0.746516i
\(356\) 1.91901 4.88957i 0.101708 0.259147i
\(357\) 13.7196 23.0316i 0.726119 1.21896i
\(358\) −8.34575 21.2646i −0.441087 1.12387i
\(359\) −6.02615 + 4.10856i −0.318048 + 0.216841i −0.711812 0.702370i \(-0.752125\pi\)
0.393764 + 0.919212i \(0.371173\pi\)
\(360\) −19.8207 + 5.98100i −1.04464 + 0.315226i
\(361\) 9.15975 + 15.8652i 0.482092 + 0.835008i
\(362\) 18.4339 + 31.9285i 0.968865 + 1.67812i
\(363\) −9.03530 + 15.5394i −0.474230 + 0.815605i
\(364\) 2.75084 4.65030i 0.144183 0.243742i
\(365\) 7.50402 2.31468i 0.392778 0.121156i
\(366\) 1.02203 + 14.2232i 0.0534223 + 0.743458i
\(367\) 16.3008 20.4405i 0.850892 1.06699i −0.146083 0.989272i \(-0.546667\pi\)
0.996976 0.0777131i \(-0.0247618\pi\)
\(368\) 2.62459 + 0.395594i 0.136816 + 0.0206218i
\(369\) −13.2332 34.3354i −0.688893 1.78743i
\(370\) 1.16551 5.10644i 0.0605920 0.265471i
\(371\) −9.63059 + 11.8178i −0.499996 + 0.613549i
\(372\) 5.99770 + 0.0183928i 0.310966 + 0.000953622i
\(373\) −1.86918 −0.0967825 −0.0483913 0.998828i \(-0.515409\pi\)
−0.0483913 + 0.998828i \(0.515409\pi\)
\(374\) 21.1206 36.5819i 1.09212 1.89161i
\(375\) −4.89782 + 8.42352i −0.252923 + 0.434989i
\(376\) −1.47973 19.7457i −0.0763114 1.01830i
\(377\) 7.29547 9.14824i 0.375736 0.471158i
\(378\) −13.7154 + 16.5176i −0.705445 + 0.849576i
\(379\) 16.1405 + 20.2396i 0.829084 + 1.03964i 0.998536 + 0.0540995i \(0.0172288\pi\)
−0.169452 + 0.985538i \(0.554200\pi\)
\(380\) 0.751208 0.697019i 0.0385361 0.0357563i
\(381\) 1.80793 23.1713i 0.0926228 1.18710i
\(382\) −2.97692 + 2.02963i −0.152312 + 0.103845i
\(383\) −9.02080 + 11.3117i −0.460942 + 0.578002i −0.956927 0.290328i \(-0.906235\pi\)
0.495986 + 0.868331i \(0.334807\pi\)
\(384\) 5.15688 + 22.9175i 0.263161 + 1.16950i
\(385\) −34.2932 + 4.79851i −1.74775 + 0.244555i
\(386\) −29.3375 14.1282i −1.49324 0.719106i
\(387\) −2.93943 0.0180286i −0.149420 0.000916443i
\(388\) −1.83813 + 0.566989i −0.0933171 + 0.0287845i
\(389\) −18.4688 + 8.89410i −0.936405 + 0.450949i −0.838900 0.544286i \(-0.816801\pi\)
−0.0975052 + 0.995235i \(0.531086\pi\)
\(390\) −29.3760 20.1605i −1.48751 1.02087i
\(391\) 1.65710 + 2.87018i 0.0838030 + 0.145151i
\(392\) 0.915104 + 17.0415i 0.0462197 + 0.860726i
\(393\) 1.45315 + 1.35664i 0.0733017 + 0.0684336i
\(394\) 1.26164 3.21460i 0.0635603 0.161949i
\(395\) 18.2554 + 12.4463i 0.918529 + 0.626242i
\(396\) −3.82456 + 4.73596i −0.192191 + 0.237991i
\(397\) −1.47623 + 19.6989i −0.0740897 + 0.988659i 0.829012 + 0.559231i \(0.188904\pi\)
−0.903101 + 0.429427i \(0.858715\pi\)
\(398\) 33.1352 22.5912i 1.66092 1.13240i
\(399\) −0.891386 + 3.67365i −0.0446251 + 0.183913i
\(400\) −11.6618 7.95090i −0.583092 0.397545i
\(401\) 4.24438 5.32228i 0.211954 0.265782i −0.664478 0.747308i \(-0.731346\pi\)
0.876432 + 0.481526i \(0.159917\pi\)
\(402\) −6.64995 17.0978i −0.331670 0.852760i
\(403\) −22.8921 28.7058i −1.14034 1.42994i
\(404\) −3.46102 1.06758i −0.172192 0.0531143i
\(405\) 18.4612 + 17.5558i 0.917343 + 0.872353i
\(406\) 0.885968 10.3520i 0.0439699 0.513761i
\(407\) 2.00146 + 5.09964i 0.0992087 + 0.252780i
\(408\) −15.4614 + 19.2665i −0.765453 + 0.953832i
\(409\) −8.83444 2.72507i −0.436835 0.134746i 0.0685345 0.997649i \(-0.478168\pi\)
−0.505370 + 0.862903i \(0.668644\pi\)
\(410\) 27.1109 46.9575i 1.33891 2.31906i
\(411\) 23.3406 + 21.7905i 1.15131 + 1.07485i
\(412\) −2.56039 0.789776i −0.126141 0.0389095i
\(413\) −6.26773 + 15.4863i −0.308415 + 0.762030i
\(414\) −0.954517 2.47663i −0.0469120 0.121720i
\(415\) −19.8271 18.3968i −0.973273 0.903066i
\(416\) −7.08105 + 8.87935i −0.347177 + 0.435346i
\(417\) −12.2249 15.4263i −0.598655 0.755430i
\(418\) −1.32544 + 5.80712i −0.0648292 + 0.284035i
\(419\) −37.2060 + 11.4765i −1.81763 + 0.560665i −0.999889 0.0149164i \(-0.995252\pi\)
−0.817744 + 0.575582i \(0.804776\pi\)
\(420\) −5.69224 0.0776643i −0.277753 0.00378963i
\(421\) 30.0656 + 9.27401i 1.46531 + 0.451987i 0.921882 0.387470i \(-0.126651\pi\)
0.543425 + 0.839458i \(0.317127\pi\)
\(422\) 0.517384 0.896135i 0.0251859 0.0436232i
\(423\) −20.2155 + 13.6018i −0.982910 + 0.661342i
\(424\) 10.2978 9.55501i 0.500108 0.464032i
\(425\) −1.31703 17.5745i −0.0638852 0.852488i
\(426\) 8.56254 + 10.8049i 0.414857 + 0.523499i
\(427\) 3.24735 13.5647i 0.157150 0.656440i
\(428\) −3.15026 + 8.02673i −0.152274 + 0.387987i
\(429\) 37.2649 + 0.114278i 1.79917 + 0.00551740i
\(430\) −2.70060 3.38644i −0.130234 0.163309i
\(431\) −0.850707 11.3519i −0.0409771 0.546802i −0.979481 0.201534i \(-0.935407\pi\)
0.938504 0.345267i \(-0.112212\pi\)
\(432\) 17.9974 16.3937i 0.865903 0.788741i
\(433\) −11.8814 + 5.72176i −0.570981 + 0.274970i −0.697016 0.717056i \(-0.745489\pi\)
0.126034 + 0.992026i \(0.459775\pi\)
\(434\) −31.0500 9.93848i −1.49045 0.477062i
\(435\) −12.1852 1.87486i −0.584235 0.0898925i
\(436\) −2.86352 + 1.37900i −0.137138 + 0.0660421i
\(437\) −0.342582 0.317870i −0.0163879 0.0152058i
\(438\) −5.51651 + 5.08718i −0.263589 + 0.243075i
\(439\) −13.3582 + 34.0361i −0.637552 + 1.62445i 0.135991 + 0.990710i \(0.456578\pi\)
−0.773542 + 0.633745i \(0.781517\pi\)
\(440\) 31.9084 1.52117
\(441\) 17.6673 11.3519i 0.841300 0.540568i
\(442\) −42.5119 −2.02208
\(443\) −9.93495 + 25.3138i −0.472024 + 1.20270i 0.474556 + 0.880225i \(0.342609\pi\)
−0.946579 + 0.322471i \(0.895486\pi\)
\(444\) 0.197719 + 0.878675i 0.00938332 + 0.0417000i
\(445\) 24.8355 + 23.0440i 1.17732 + 1.09239i
\(446\) 4.82262 2.32245i 0.228358 0.109971i
\(447\) −1.42146 3.65473i −0.0672327 0.172863i
\(448\) 1.25409 14.6533i 0.0592503 0.692304i
\(449\) 32.3827 15.5947i 1.52823 0.735958i 0.534232 0.845338i \(-0.320601\pi\)
0.994000 + 0.109380i \(0.0348866\pi\)
\(450\) −1.14106 + 14.0680i −0.0537899 + 0.663170i
\(451\) 4.23812 + 56.5538i 0.199565 + 2.66301i
\(452\) −3.68300 4.61833i −0.173234 0.217228i
\(453\) −11.0745 + 19.0465i −0.520325 + 0.894881i
\(454\) −3.45751 + 8.80958i −0.162269 + 0.413454i
\(455\) 21.4388 + 27.4745i 1.00507 + 1.28803i
\(456\) 1.28258 3.23871i 0.0600621 0.151667i
\(457\) 1.54261 + 20.5848i 0.0721604 + 0.962914i 0.909358 + 0.416014i \(0.136573\pi\)
−0.837198 + 0.546900i \(0.815808\pi\)
\(458\) −28.8127 + 26.7343i −1.34633 + 1.24921i
\(459\) 30.0152 + 4.80688i 1.40099 + 0.224366i
\(460\) 0.351887 0.609486i 0.0164068 0.0284175i
\(461\) 10.7916 + 3.32878i 0.502617 + 0.155037i 0.535688 0.844416i \(-0.320052\pi\)
−0.0330706 + 0.999453i \(0.510529\pi\)
\(462\) 27.5914 18.2651i 1.28367 0.849770i
\(463\) −4.53265 + 1.39814i −0.210650 + 0.0649770i −0.398284 0.917262i \(-0.630394\pi\)
0.187634 + 0.982239i \(0.439918\pi\)
\(464\) −2.62155 + 11.4858i −0.121702 + 0.533213i
\(465\) −14.2437 + 35.9676i −0.660534 + 1.66796i
\(466\) 3.81470 4.78348i 0.176712 0.221590i
\(467\) −27.8451 25.8365i −1.28852 1.19557i −0.968740 0.248079i \(-0.920201\pi\)
−0.319780 0.947492i \(-0.603609\pi\)
\(468\) 6.05228 + 0.950234i 0.279767 + 0.0439246i
\(469\) 1.15164 + 17.9072i 0.0531780 + 0.826877i
\(470\) −34.3081 10.5826i −1.58251 0.488141i
\(471\) 18.9661 5.78664i 0.873913 0.266634i
\(472\) 7.69738 13.3322i 0.354301 0.613667i
\(473\) 4.32910 + 1.33535i 0.199052 + 0.0613995i
\(474\) −20.8676 3.21076i −0.958481 0.147475i
\(475\) 0.907924 + 2.31335i 0.0416584 + 0.106144i
\(476\) −5.65246 + 3.76683i −0.259080 + 0.172653i
\(477\) −16.4866 5.19639i −0.754870 0.237927i
\(478\) −40.1344 12.3798i −1.83570 0.566240i
\(479\) 6.21114 + 7.78852i 0.283794 + 0.355867i 0.903212 0.429195i \(-0.141203\pi\)
−0.619418 + 0.785062i \(0.712631\pi\)
\(480\) 11.8271 + 1.81975i 0.539829 + 0.0830599i
\(481\) 3.43758 4.31059i 0.156740 0.196546i
\(482\) −14.0513 9.58001i −0.640019 0.436357i
\(483\) 0.158673 + 2.59129i 0.00721987 + 0.117908i
\(484\) 3.76311 2.56564i 0.171050 0.116620i
\(485\) 0.927187 12.3725i 0.0421014 0.561804i
\(486\) −23.1500 7.53143i −1.05010 0.341633i
\(487\) −11.4329 7.79481i −0.518073 0.353216i 0.275883 0.961191i \(-0.411030\pi\)
−0.793956 + 0.607975i \(0.791982\pi\)
\(488\) −4.69564 + 11.9643i −0.212562 + 0.541598i
\(489\) −14.6249 + 4.46211i −0.661360 + 0.201783i
\(490\) 29.3698 + 9.74433i 1.32679 + 0.440204i
\(491\) −0.245966 0.426025i −0.0111003 0.0192262i 0.860422 0.509582i \(-0.170200\pi\)
−0.871522 + 0.490356i \(0.836867\pi\)
\(492\) −0.725260 + 9.29533i −0.0326973 + 0.419066i
\(493\) −13.2536 + 6.38261i −0.596913 + 0.287458i
\(494\) 5.72831 1.76695i 0.257729 0.0794988i
\(495\) −19.4229 34.1231i −0.872996 1.53372i
\(496\) 33.3065 + 16.0396i 1.49551 + 0.720198i
\(497\) −4.79351 12.6040i −0.215018 0.565368i
\(498\) 24.6742 + 7.69392i 1.10568 + 0.344773i
\(499\) 3.82612 4.79780i 0.171281 0.214779i −0.688781 0.724970i \(-0.741854\pi\)
0.860061 + 0.510191i \(0.170425\pi\)
\(500\) 2.03989 1.39077i 0.0912268 0.0621973i
\(501\) 13.7359 6.56302i 0.613673 0.293214i
\(502\) −23.0274 + 21.3663i −1.02776 + 0.953623i
\(503\) −21.4000 26.8348i −0.954179 1.19650i −0.980434 0.196848i \(-0.936930\pi\)
0.0262550 0.999655i \(-0.491642\pi\)
\(504\) −17.5726 + 8.10363i −0.782745 + 0.360964i
\(505\) 14.5656 18.2647i 0.648161 0.812768i
\(506\) 0.305697 + 4.07925i 0.0135899 + 0.181345i
\(507\) −7.45379 13.0023i −0.331034 0.577451i
\(508\) −2.94446 + 5.09996i −0.130639 + 0.226274i
\(509\) −25.8652 −1.14645 −0.573227 0.819397i \(-0.694309\pi\)
−0.573227 + 0.819397i \(0.694309\pi\)
\(510\) 22.2769 + 38.8594i 0.986437 + 1.72072i
\(511\) 6.64637 3.11456i 0.294018 0.137780i
\(512\) −2.53893 + 11.1238i −0.112206 + 0.491607i
\(513\) −4.24422 + 0.599835i −0.187387 + 0.0264833i
\(514\) 11.7669 + 1.77358i 0.519016 + 0.0782291i
\(515\) 10.7753 13.5118i 0.474818 0.595403i
\(516\) 0.670046 + 0.325212i 0.0294971 + 0.0143167i
\(517\) 35.8839 11.0687i 1.57817 0.486802i
\(518\) 0.417462 4.87779i 0.0183422 0.214318i
\(519\) 20.9254 + 0.0641709i 0.918525 + 0.00281679i
\(520\) −16.0564 27.8106i −0.704122 1.21957i
\(521\) 18.5025 + 32.0473i 0.810611 + 1.40402i 0.912437 + 0.409217i \(0.134198\pi\)
−0.101826 + 0.994802i \(0.532468\pi\)
\(522\) 11.2787 3.40339i 0.493654 0.148962i
\(523\) −21.1121 + 14.3940i −0.923167 + 0.629405i −0.928801 0.370579i \(-0.879159\pi\)
0.00563357 + 0.999984i \(0.498207\pi\)
\(524\) −0.184027 0.468892i −0.00803925 0.0204837i
\(525\) 5.21854 12.7811i 0.227756 0.557813i
\(526\) −10.1456 + 25.8506i −0.442369 + 1.12714i
\(527\) 10.2714 + 45.0017i 0.447427 + 1.96031i
\(528\) −33.8543 + 16.1757i −1.47332 + 0.703955i
\(529\) 20.4331 + 9.84007i 0.888396 + 0.427829i
\(530\) −9.30584 23.7109i −0.404220 1.02993i
\(531\) −18.9431 0.116185i −0.822060 0.00504198i
\(532\) 0.605083 0.742503i 0.0262337 0.0321916i
\(533\) 47.1582 32.1519i 2.04265 1.39266i
\(534\) −30.9070 9.63744i −1.33748 0.417053i
\(535\) −40.7701 37.8291i −1.76264 1.63549i
\(536\) 1.23568 16.4890i 0.0533731 0.712215i
\(537\) −22.8603 + 10.9227i −0.986496 + 0.471350i
\(538\) 18.3401 31.7660i 0.790697 1.36953i
\(539\) −31.1224 + 8.88359i −1.34054 + 0.382643i
\(540\) −2.30290 6.03023i −0.0991009 0.259500i
\(541\) −3.67067 + 0.553264i −0.157814 + 0.0237867i −0.227474 0.973784i \(-0.573047\pi\)
0.0696598 + 0.997571i \(0.477809\pi\)
\(542\) −24.0327 + 11.5735i −1.03229 + 0.497126i
\(543\) 33.8552 22.9303i 1.45286 0.984033i
\(544\) 12.8641 6.19502i 0.551543 0.265609i
\(545\) −1.53195 20.4425i −0.0656216 0.875660i
\(546\) −29.8035 14.8569i −1.27547 0.635816i
\(547\) −0.588402 + 7.85168i −0.0251583 + 0.335714i 0.970396 + 0.241521i \(0.0776461\pi\)
−0.995554 + 0.0941930i \(0.969973\pi\)
\(548\) −2.95585 7.53139i −0.126268 0.321725i
\(549\) 15.6530 2.26121i 0.668054 0.0965063i
\(550\) 7.94723 20.2492i 0.338871 0.863429i
\(551\) 1.52059 1.41090i 0.0647793 0.0601064i
\(552\) 0.186091 2.38505i 0.00792057 0.101514i
\(553\) 18.5104 + 9.15656i 0.787143 + 0.389377i
\(554\) 5.12985 + 0.773201i 0.217946 + 0.0328501i
\(555\) −5.74158 0.883420i −0.243717 0.0374991i
\(556\) 1.10976 + 4.86217i 0.0470643 + 0.206202i
\(557\) 16.0539 + 27.8062i 0.680226 + 1.17819i 0.974912 + 0.222592i \(0.0714517\pi\)
−0.294686 + 0.955594i \(0.595215\pi\)
\(558\) −2.53639 36.8798i −0.107374 1.56125i
\(559\) −1.01456 4.44509i −0.0429114 0.188007i
\(560\) −31.4503 15.5575i −1.32902 0.657426i
\(561\) −42.1472 20.4565i −1.77946 0.863673i
\(562\) 7.96287 34.8876i 0.335893 1.47164i
\(563\) 10.0165 + 25.5216i 0.422145 + 1.07561i 0.970870 + 0.239605i \(0.0770180\pi\)
−0.548725 + 0.836003i \(0.684887\pi\)
\(564\) 6.10748 0.901408i 0.257171 0.0379561i
\(565\) 36.4078 11.2303i 1.53169 0.472463i
\(566\) −1.46431 + 6.41557i −0.0615497 + 0.269667i
\(567\) 19.3627 + 13.8595i 0.813156 + 0.582045i
\(568\) 2.76503 + 12.1144i 0.116018 + 0.508309i
\(569\) 1.53973 + 2.66689i 0.0645488 + 0.111802i 0.896494 0.443056i \(-0.146106\pi\)
−0.831945 + 0.554858i \(0.812773\pi\)
\(570\) −4.61686 4.31024i −0.193379 0.180536i
\(571\) 23.2230 + 7.16333i 0.971850 + 0.299776i 0.739725 0.672910i \(-0.234956\pi\)
0.232126 + 0.972686i \(0.425432\pi\)
\(572\) −8.50705 4.09678i −0.355698 0.171295i
\(573\) 2.48189 + 3.13184i 0.103682 + 0.130835i
\(574\) 19.0134 46.9782i 0.793604 1.96083i
\(575\) 1.06411 + 1.33436i 0.0443767 + 0.0556466i
\(576\) 15.9650 4.81752i 0.665209 0.200730i
\(577\) 1.46833 3.74125i 0.0611274 0.155750i −0.897047 0.441935i \(-0.854292\pi\)
0.958174 + 0.286185i \(0.0923873\pi\)
\(578\) 24.2332 + 11.6701i 1.00797 + 0.485412i
\(579\) −13.2971 + 33.5773i −0.552608 + 1.39543i
\(580\) 2.58099 + 1.75969i 0.107170 + 0.0730671i
\(581\) −20.7360 14.4612i −0.860274 0.599950i
\(582\) 4.29763 + 11.0497i 0.178143 + 0.458025i
\(583\) 22.0123 + 15.0077i 0.911657 + 0.621557i
\(584\) −6.46312 + 1.99361i −0.267446 + 0.0824961i
\(585\) −19.9672 + 34.0995i −0.825542 + 1.40984i
\(586\) −4.61694 + 0.695892i −0.190724 + 0.0287470i
\(587\) 10.1113 17.5133i 0.417340 0.722853i −0.578331 0.815802i \(-0.696296\pi\)
0.995671 + 0.0929487i \(0.0296293\pi\)
\(588\) −5.27915 + 0.665391i −0.217708 + 0.0274403i
\(589\) −3.25446 5.63689i −0.134098 0.232264i
\(590\) −17.4039 21.8238i −0.716508 0.898473i
\(591\) −3.65640 1.14014i −0.150404 0.0468991i
\(592\) −1.23526 + 5.41201i −0.0507687 + 0.222432i
\(593\) 1.07819 14.3874i 0.0442758 0.590820i −0.930305 0.366786i \(-0.880458\pi\)
0.974581 0.224034i \(-0.0719227\pi\)
\(594\) 30.8044 + 21.4199i 1.26392 + 0.878868i
\(595\) −9.29682 42.8144i −0.381132 1.75522i
\(596\) −0.0742519 + 0.990822i −0.00304148 + 0.0405857i
\(597\) −27.6252 34.8597i −1.13062 1.42671i
\(598\) 3.40155 2.31913i 0.139100 0.0948365i
\(599\) 21.2117 3.19715i 0.866687 0.130632i 0.299376 0.954135i \(-0.403222\pi\)
0.567311 + 0.823503i \(0.307984\pi\)
\(600\) −6.39447 + 10.9975i −0.261053 + 0.448972i
\(601\) 8.14096 1.22705i 0.332077 0.0500525i 0.0191122 0.999817i \(-0.493916\pi\)
0.312964 + 0.949765i \(0.398678\pi\)
\(602\) −2.93846 2.78490i −0.119763 0.113504i
\(603\) −18.3856 + 8.71554i −0.748721 + 0.354924i
\(604\) 4.61241 3.14469i 0.187676 0.127956i
\(605\) 6.53688 + 28.6400i 0.265762 + 1.16438i
\(606\) −5.03422 + 21.7487i −0.204501 + 0.883480i
\(607\) 26.6737 1.08265 0.541327 0.840812i \(-0.317922\pi\)
0.541327 + 0.840812i \(0.317922\pi\)
\(608\) −1.47590 + 1.36943i −0.0598555 + 0.0555378i
\(609\) −11.5222 0.157208i −0.466903 0.00637037i
\(610\) 17.0835 + 15.8511i 0.691689 + 0.641794i
\(611\) −27.7042 25.7057i −1.12079 1.03994i
\(612\) −6.33702 4.37768i −0.256159 0.176957i
\(613\) −9.58952 1.44539i −0.387317 0.0583786i −0.0475024 0.998871i \(-0.515126\pi\)
−0.339814 + 0.940492i \(0.610364\pi\)
\(614\) 46.8412 14.4486i 1.89036 0.583098i
\(615\) −54.1012 26.2585i −2.18157 1.05884i
\(616\) 29.5364 4.13290i 1.19005 0.166519i
\(617\) −26.4655 + 24.5564i −1.06546 + 0.988603i −0.999957 0.00924889i \(-0.997056\pi\)
−0.0655039 + 0.997852i \(0.520865\pi\)
\(618\) −3.72421 + 16.0892i −0.149810 + 0.647204i
\(619\) −23.2559 −0.934734 −0.467367 0.884063i \(-0.654797\pi\)
−0.467367 + 0.884063i \(0.654797\pi\)
\(620\) 7.18534 6.66702i 0.288570 0.267754i
\(621\) −2.66387 + 1.25279i −0.106897 + 0.0502728i
\(622\) 1.51018 1.89371i 0.0605528 0.0759308i
\(623\) 25.9740 + 18.1141i 1.04063 + 0.725727i
\(624\) 31.1340 + 21.3669i 1.24636 + 0.855361i
\(625\) 6.89531 + 30.2103i 0.275812 + 1.20841i
\(626\) 41.3173 6.22758i 1.65137 0.248904i
\(627\) 6.52942 + 1.00464i 0.260760 + 0.0401214i
\(628\) −4.96816 0.748829i −0.198251 0.0298815i
\(629\) −6.24502 + 3.00744i −0.249005 + 0.119915i
\(630\) 2.03708 + 35.0281i 0.0811593 + 1.39555i
\(631\) −10.6396 5.12376i −0.423556 0.203974i 0.209949 0.977712i \(-0.432670\pi\)
−0.633505 + 0.773739i \(0.718384\pi\)
\(632\) −15.7232 10.7199i −0.625434 0.426413i
\(633\) −1.03247 0.501116i −0.0410368 0.0199176i
\(634\) −1.55628 + 20.7671i −0.0618078 + 0.824767i
\(635\) −23.6823 29.6967i −0.939804 1.17848i
\(636\) 3.20155 + 2.98893i 0.126950 + 0.118519i
\(637\) 23.4037 + 22.6553i 0.927286 + 0.897634i
\(638\) −18.1570 −0.718841
\(639\) 11.2722 10.3311i 0.445920 0.408692i
\(640\) 31.7193 + 21.6259i 1.25382 + 0.854838i
\(641\) 1.65013 7.22971i 0.0651764 0.285556i −0.931828 0.362900i \(-0.881787\pi\)
0.997004 + 0.0773436i \(0.0246438\pi\)
\(642\) 50.7370 + 15.8209i 2.00243 + 0.624400i
\(643\) −2.03685 27.1798i −0.0803254 1.07187i −0.881109 0.472913i \(-0.843202\pi\)
0.800784 0.598954i \(-0.204417\pi\)
\(644\) 0.246785 0.609756i 0.00972470 0.0240277i
\(645\) −3.53154 + 3.25669i −0.139054 + 0.128232i
\(646\) −7.45222 1.12324i −0.293203 0.0441933i
\(647\) 1.65482 + 22.0820i 0.0650576 + 0.868133i 0.930305 + 0.366788i \(0.119542\pi\)
−0.865247 + 0.501346i \(0.832839\pi\)
\(648\) −15.9004 15.1206i −0.624626 0.593992i
\(649\) 27.8988 + 8.60563i 1.09512 + 0.337801i
\(650\) −21.6478 + 3.26288i −0.849096 + 0.127981i
\(651\) −8.52615 + 35.1387i −0.334166 + 1.37719i
\(652\) 3.83097 + 0.577426i 0.150032 + 0.0226137i
\(653\) 28.5245 + 13.7367i 1.11625 + 0.537557i 0.898731 0.438499i \(-0.144490\pi\)
0.217517 + 0.976056i \(0.430204\pi\)
\(654\) 9.74255 + 16.9947i 0.380964 + 0.664547i
\(655\) 3.24894 0.126946
\(656\) −28.7333 + 49.7675i −1.12185 + 1.94309i
\(657\) 6.06615 + 5.69820i 0.236663 + 0.222308i
\(658\) −33.1284 5.35222i −1.29148 0.208651i
\(659\) 9.80102 + 9.09402i 0.381794 + 0.354253i 0.847602 0.530633i \(-0.178046\pi\)
−0.465808 + 0.884886i \(0.654236\pi\)
\(660\) 0.713027 + 9.92293i 0.0277545 + 0.386250i
\(661\) −5.84587 14.8950i −0.227378 0.579349i 0.770966 0.636876i \(-0.219774\pi\)
−0.998344 + 0.0575268i \(0.981679\pi\)
\(662\) 17.2032 + 43.8331i 0.668622 + 1.70362i
\(663\) 3.37929 + 47.0283i 0.131241 + 1.82643i
\(664\) 17.0768 + 15.8450i 0.662710 + 0.614905i
\(665\) 3.03223 + 5.38266i 0.117585 + 0.208731i
\(666\) 5.31443 1.60366i 0.205930 0.0621404i
\(667\) 0.712287 1.23372i 0.0275799 0.0477698i
\(668\) −3.85722 −0.149240
\(669\) −2.95254 5.15036i −0.114152 0.199124i
\(670\) −27.0125 13.0085i −1.04358 0.502563i
\(671\) −24.1028 3.63291i −0.930477 0.140247i
\(672\) 11.1835 + 0.152587i 0.431415 + 0.00588617i
\(673\) −4.99836 + 0.753381i −0.192673 + 0.0290407i −0.244670 0.969607i \(-0.578679\pi\)
0.0519970 + 0.998647i \(0.483441\pi\)
\(674\) 37.6950 + 11.6274i 1.45196 + 0.447870i
\(675\) 15.6532 + 0.144012i 0.602493 + 0.00554303i
\(676\) 0.283782 + 3.78681i 0.0109147 + 0.145646i
\(677\) −29.2040 4.40179i −1.12240 0.169174i −0.438486 0.898738i \(-0.644485\pi\)
−0.683913 + 0.729563i \(0.739723\pi\)
\(678\) −26.7649 + 24.6819i −1.02790 + 0.947901i
\(679\) −0.744268 11.5728i −0.0285624 0.444123i
\(680\) 3.01700 + 40.2591i 0.115697 + 1.54387i
\(681\) 10.0203 + 3.12455i 0.383980 + 0.119733i
\(682\) −12.6779 + 55.5453i −0.485460 + 2.12694i
\(683\) 2.87986 + 1.96345i 0.110195 + 0.0751294i 0.617163 0.786835i \(-0.288282\pi\)
−0.506969 + 0.861964i \(0.669234\pi\)
\(684\) 1.03584 + 0.326486i 0.0396064 + 0.0124835i
\(685\) 52.1847 1.99387
\(686\) 28.4486 + 5.21585i 1.08617 + 0.199142i
\(687\) 31.8648 + 29.7486i 1.21572 + 1.13498i
\(688\) 2.86220 + 3.58909i 0.109121 + 0.136833i
\(689\) 2.00369 26.7374i 0.0763345 1.01861i
\(690\) −3.90235 1.89403i −0.148560 0.0721047i
\(691\) −16.5683 11.2961i −0.630288 0.429723i 0.205590 0.978638i \(-0.434089\pi\)
−0.835878 + 0.548915i \(0.815041\pi\)
\(692\) −4.77698 2.30047i −0.181594 0.0874509i
\(693\) −22.3988 29.0707i −0.850861 1.10431i
\(694\) 19.6589 9.46725i 0.746243 0.359372i
\(695\) −31.8081 4.79431i −1.20655 0.181858i
\(696\) 10.4950 + 1.61479i 0.397811 + 0.0612085i
\(697\) −70.9537 + 10.6945i −2.68756 + 0.405085i
\(698\) −1.98133 8.68079i −0.0749946 0.328573i
\(699\) −5.59490 3.83972i −0.211619 0.145232i
\(700\) −2.58922 + 2.35198i −0.0978633 + 0.0888963i
\(701\) −14.5925 + 18.2984i −0.551150 + 0.691120i −0.976894 0.213724i \(-0.931441\pi\)
0.425744 + 0.904843i \(0.360012\pi\)
\(702\) 3.16811 37.6270i 0.119573 1.42014i
\(703\) 0.716491 0.664807i 0.0270230 0.0250737i
\(704\) −25.7013 −0.968654
\(705\) −8.97977 + 38.7942i −0.338198 + 1.46107i
\(706\) 0.201735 0.187183i 0.00759240 0.00704472i
\(707\) 11.1171 18.7935i 0.418101 0.706802i
\(708\) 4.31810 + 2.09582i 0.162284 + 0.0787658i
\(709\) 22.8557 7.05004i 0.858362 0.264770i 0.165828 0.986155i \(-0.446970\pi\)
0.692534 + 0.721385i \(0.256494\pi\)
\(710\) 22.2790 + 3.35803i 0.836118 + 0.126024i
\(711\) −1.89310 + 23.3398i −0.0709966 + 0.875310i
\(712\) −21.3905 19.8475i −0.801644 0.743817i
\(713\) −3.27681 3.04044i −0.122718 0.113865i
\(714\) 25.6541 + 33.0853i 0.960080 + 1.23818i
\(715\) 44.6440 41.4235i 1.66959 1.54915i
\(716\) 6.41950 0.239908
\(717\) −10.5047 + 45.3823i −0.392306 + 1.69483i
\(718\) −2.53454 11.1045i −0.0945881 0.414418i
\(719\) 15.4706 10.5477i 0.576956 0.393362i −0.239392 0.970923i \(-0.576948\pi\)
0.816347 + 0.577561i \(0.195996\pi\)
\(720\) 3.21648 39.6556i 0.119871 1.47788i
\(721\) 8.22420 13.9030i 0.306285 0.517776i
\(722\) −28.2898 + 4.26400i −1.05284 + 0.158690i
\(723\) −9.48083 + 16.3056i −0.352596 + 0.606411i
\(724\) −10.2448 + 1.54416i −0.380745 + 0.0573881i
\(725\) −6.25910 + 4.26738i −0.232457 + 0.158487i
\(726\) −17.4350 22.0009i −0.647073 0.816528i
\(727\) 2.14526 28.6265i 0.0795632 1.06170i −0.804384 0.594110i \(-0.797504\pi\)
0.883947 0.467587i \(-0.154877\pi\)
\(728\) −18.4650 23.6635i −0.684357 0.877027i
\(729\) −6.49136 + 26.2081i −0.240421 + 0.970669i
\(730\) −0.916472 + 12.2295i −0.0339202 + 0.452633i
\(731\) −1.27550 + 5.58832i −0.0471760 + 0.206692i
\(732\) −3.82561 1.19290i −0.141399 0.0440910i
\(733\) −8.57713 10.7554i −0.316803 0.397259i 0.597777 0.801662i \(-0.296051\pi\)
−0.914581 + 0.404403i \(0.867479\pi\)
\(734\) 20.4147 + 35.3592i 0.753519 + 1.30513i
\(735\) 8.44493 33.2646i 0.311496 1.22698i
\(736\) −0.691352 + 1.19746i −0.0254836 + 0.0441389i
\(737\) 31.0085 4.67377i 1.14221 0.172161i
\(738\) 57.4647 + 0.352451i 2.11530 + 0.0129739i
\(739\) −8.78706 + 2.71045i −0.323237 + 0.0997055i −0.452127 0.891953i \(-0.649335\pi\)
0.128890 + 0.991659i \(0.458859\pi\)
\(740\) 1.21614 + 0.829153i 0.0447064 + 0.0304803i
\(741\) −2.41001 6.19642i −0.0885340 0.227631i
\(742\) −11.6852 20.7429i −0.428976 0.761496i
\(743\) 29.4583 + 20.0843i 1.08072 + 0.736823i 0.966509 0.256633i \(-0.0826132\pi\)
0.114212 + 0.993456i \(0.463566\pi\)
\(744\) 12.2679 30.9784i 0.449763 1.13572i
\(745\) −5.77405 2.78063i −0.211545 0.101875i
\(746\) 1.06646 2.71729i 0.0390458 0.0994870i
\(747\) 6.54995 27.9071i 0.239650 1.02107i
\(748\) 7.40115 + 9.28075i 0.270613 + 0.339338i
\(749\) −42.6390 29.7362i −1.55800 1.08654i
\(750\) −9.45109 11.9261i −0.345105 0.435481i
\(751\) 0.00488539 + 0.00235268i 0.000178271 + 8.58506e-5i 0.433973 0.900926i \(-0.357111\pi\)
−0.433795 + 0.901012i \(0.642826\pi\)
\(752\) 36.3612 + 11.2159i 1.32595 + 0.409003i
\(753\) 25.4666 + 23.7753i 0.928056 + 0.866421i
\(754\) 9.13667 + 15.8252i 0.332738 + 0.576319i
\(755\) 8.01221 + 35.1038i 0.291594 + 1.27756i
\(756\) −2.91276 5.28367i −0.105936 0.192165i
\(757\) 4.38546 19.2140i 0.159392 0.698343i −0.830559 0.556931i \(-0.811979\pi\)
0.989951 0.141412i \(-0.0451641\pi\)
\(758\) −38.6319 + 11.9164i −1.40317 + 0.432822i
\(759\) 4.48832 0.662435i 0.162916 0.0240449i
\(760\) −2.07984 5.29936i −0.0754439 0.192228i
\(761\) 0.0743968 0.325954i 0.00269688 0.0118158i −0.973562 0.228425i \(-0.926643\pi\)
0.976258 + 0.216609i \(0.0694997\pi\)
\(762\) 32.6534 + 15.8486i 1.18291 + 0.574134i
\(763\) −4.06586 18.7244i −0.147194 0.677868i
\(764\) −0.225303 0.987115i −0.00815116 0.0357126i
\(765\) 41.2170 27.7325i 1.49020 1.00267i
\(766\) −11.2974 19.5677i −0.408193 0.707010i
\(767\) −6.53833 28.6463i −0.236085 1.03436i
\(768\) −17.2263 2.65049i −0.621600 0.0956415i
\(769\) −24.1401 3.63854i −0.870515 0.131209i −0.301431 0.953488i \(-0.597464\pi\)
−0.569085 + 0.822279i \(0.692702\pi\)
\(770\) 12.5902 52.5910i 0.453719 1.89525i
\(771\) 1.02664 13.1580i 0.0369736 0.473874i
\(772\) 6.70783 6.22396i 0.241420 0.224005i
\(773\) 7.20675 18.3625i 0.259209 0.660453i −0.740727 0.671806i \(-0.765519\pi\)
0.999936 + 0.0113534i \(0.00361399\pi\)
\(774\) 1.70329 4.26286i 0.0612237 0.153225i
\(775\) 8.68434 + 22.1273i 0.311951 + 0.794837i
\(776\) −0.798575 + 10.6562i −0.0286672 + 0.382537i
\(777\) −5.42918 0.0740751i −0.194771 0.00265743i
\(778\) −2.39231 31.9232i −0.0857685 1.14450i
\(779\) 9.11622 4.39014i 0.326623 0.157293i
\(780\) 8.28979 5.61472i 0.296822 0.201039i
\(781\) −21.2318 + 10.2247i −0.759735 + 0.365869i
\(782\) −5.11792 + 0.771402i −0.183016 + 0.0275853i
\(783\) −4.66151 12.2063i −0.166589 0.436219i
\(784\) −31.1274 10.3274i −1.11169 0.368837i
\(785\) 16.2032 28.0648i 0.578319 1.00168i
\(786\) −2.80129 + 1.33846i −0.0999186 + 0.0477413i
\(787\) 1.19366 15.9283i 0.0425495 0.567783i −0.934665 0.355529i \(-0.884301\pi\)
0.977215 0.212254i \(-0.0680804\pi\)
\(788\) 0.711385 + 0.660069i 0.0253420 + 0.0235140i
\(789\) 29.4034 + 9.16858i 1.04679 + 0.326410i
\(790\) −28.5092 + 19.4372i −1.01431 + 0.691546i
\(791\) 32.2467 15.1112i 1.14656 0.537291i
\(792\) 16.7287 + 29.3898i 0.594430 + 1.04432i
\(793\) 8.96226 + 22.8355i 0.318259 + 0.810912i
\(794\) −27.7946 13.3852i −0.986395 0.475023i
\(795\) −25.4902 + 12.1793i −0.904043 + 0.431954i
\(796\) 2.50778 + 10.9873i 0.0888859 + 0.389435i
\(797\) 6.91503 17.6192i 0.244943 0.624104i −0.754540 0.656254i \(-0.772140\pi\)
0.999483 + 0.0321496i \(0.0102353\pi\)
\(798\) −4.83193 3.39183i −0.171048 0.120070i
\(799\) 17.3584 + 44.2285i 0.614097 + 1.56469i
\(800\) 6.07513 4.14196i 0.214788 0.146440i
\(801\) −8.20450 + 34.9566i −0.289892 + 1.23513i
\(802\) 5.31555 + 9.20680i 0.187699 + 0.325103i
\(803\) −6.41353 11.1086i −0.226329 0.392013i
\(804\) 5.15539 + 0.0158097i 0.181816 + 0.000557566i
\(805\) 3.07951 + 2.91858i 0.108539 + 0.102867i
\(806\) 54.7915 16.9009i 1.92995 0.595311i
\(807\) −36.5986 17.7634i −1.28833 0.625302i
\(808\) −12.5452 + 15.7312i −0.441338 + 0.553420i
\(809\) 18.8956 + 2.84806i 0.664335 + 0.100132i 0.472549 0.881304i \(-0.343334\pi\)
0.191786 + 0.981437i \(0.438572\pi\)
\(810\) −36.0544 + 16.8212i −1.26682 + 0.591037i
\(811\) −1.01264 + 4.43666i −0.0355586 + 0.155792i −0.989590 0.143913i \(-0.954031\pi\)
0.954032 + 0.299706i \(0.0968885\pi\)
\(812\) 2.61704 + 1.29458i 0.0918402 + 0.0454307i
\(813\) 14.7135 + 25.6659i 0.516024 + 0.900144i
\(814\) −8.55544 −0.299868
\(815\) −12.4944 + 21.6409i −0.437660 + 0.758049i
\(816\) −23.6100 41.1848i −0.826514 1.44176i
\(817\) −0.0604028 0.806019i −0.00211323 0.0281990i
\(818\) 9.00199 11.2881i 0.314747 0.394680i
\(819\) −14.0662 + 34.1508i −0.491511 + 1.19332i
\(820\) 9.50031 + 11.9130i 0.331765 + 0.416020i
\(821\) −15.0317 + 13.9474i −0.524611 + 0.486768i −0.897443 0.441131i \(-0.854577\pi\)
0.372831 + 0.927899i \(0.378387\pi\)
\(822\) −44.9945 + 21.4985i −1.56936 + 0.749845i
\(823\) 39.2832 26.7829i 1.36933 0.933592i 0.369337 0.929296i \(-0.379585\pi\)
0.999991 0.00429609i \(-0.00136749\pi\)
\(824\) −9.28066 + 11.6376i −0.323307 + 0.405414i
\(825\) −23.0322 7.18191i −0.801877 0.250042i
\(826\) −18.9369 17.9473i −0.658897 0.624465i
\(827\) −18.3914 8.85681i −0.639530 0.307981i 0.0858727 0.996306i \(-0.472632\pi\)
−0.725403 + 0.688325i \(0.758346\pi\)
\(828\) 0.745865 + 0.00457465i 0.0259206 + 0.000158980i
\(829\) 27.0372 8.33989i 0.939042 0.289656i 0.212801 0.977096i \(-0.431742\pi\)
0.726242 + 0.687439i \(0.241265\pi\)
\(830\) 38.0564 18.3270i 1.32096 0.636139i
\(831\) 0.447570 5.73630i 0.0155260 0.198990i
\(832\) 12.9330 + 22.4006i 0.448371 + 0.776602i
\(833\) −14.1512 38.4274i −0.490310 1.33143i
\(834\) 29.4006 8.97024i 1.01806 0.310614i
\(835\) 9.08932 23.1592i 0.314549 0.801457i
\(836\) −1.38302 0.942926i −0.0478327 0.0326118i
\(837\) −40.5962 + 5.73744i −1.40321 + 0.198315i
\(838\) 4.54400 60.6355i 0.156970 2.09462i
\(839\) −41.7265 + 28.4487i −1.44056 + 0.982157i −0.444288 + 0.895884i \(0.646543\pi\)
−0.996272 + 0.0862732i \(0.972504\pi\)
\(840\) −11.9545 + 29.2786i −0.412468 + 1.01021i
\(841\) −18.7365 12.7743i −0.646086 0.440494i
\(842\) −30.6358 + 38.4161i −1.05578 + 1.32390i
\(843\) −39.2270 6.03560i −1.35105 0.207877i
\(844\) 0.181304 + 0.227348i 0.00624073 + 0.00782562i
\(845\) −23.4052 7.21954i −0.805162 0.248360i
\(846\) −8.23949 37.1484i −0.283280 1.27719i
\(847\) 9.76050 + 25.6642i 0.335375 + 0.881833i
\(848\) 9.86271 + 25.1298i 0.338687 + 0.862960i
\(849\) 7.21355 + 1.10990i 0.247568 + 0.0380918i
\(850\) 26.3000 + 8.11248i 0.902084 + 0.278256i
\(851\) 0.335625 0.581320i 0.0115051 0.0199274i
\(852\) −3.70557 + 1.13058i −0.126951 + 0.0387332i
\(853\) 45.6581 + 14.0837i 1.56330 + 0.482215i 0.951203 0.308565i \(-0.0998487\pi\)
0.612100 + 0.790780i \(0.290325\pi\)
\(854\) 17.8666 + 12.4601i 0.611383 + 0.426375i
\(855\) −4.40116 + 5.44997i −0.150517 + 0.186385i
\(856\) 35.1148 + 32.5817i 1.20020 + 1.11362i
\(857\) −25.5700 + 32.0637i −0.873454 + 1.09528i 0.121263 + 0.992620i \(0.461306\pi\)
−0.994717 + 0.102656i \(0.967266\pi\)
\(858\) −21.4275 + 54.1080i −0.731524 + 1.84722i
\(859\) −4.63960 + 20.3274i −0.158301 + 0.693562i 0.832018 + 0.554749i \(0.187186\pi\)
−0.990319 + 0.138813i \(0.955671\pi\)
\(860\) 1.16313 0.358778i 0.0396624 0.0122342i
\(861\) −53.4805 17.2990i −1.82261 0.589550i
\(862\) 16.9880 + 5.24010i 0.578613 + 0.178479i
\(863\) −8.49577 + 14.7151i −0.289199 + 0.500908i −0.973619 0.228180i \(-0.926722\pi\)
0.684419 + 0.729089i \(0.260056\pi\)
\(864\) 4.52450 + 11.8476i 0.153927 + 0.403063i
\(865\) 25.0690 23.2607i 0.852372 0.790886i
\(866\) −1.53902 20.5368i −0.0522981 0.697870i
\(867\) 10.9836 27.7354i 0.373023 0.941943i
\(868\) 5.78765 7.10207i 0.196446 0.241060i
\(869\) 13.1850 33.5949i 0.447272 1.13963i
\(870\) 9.67777 16.6443i 0.328107 0.564295i
\(871\) −19.6771 24.6744i −0.666735 0.836059i
\(872\) 1.31945 + 17.6069i 0.0446823 + 0.596244i
\(873\) 11.8820 5.63255i 0.402144 0.190633i
\(874\) 0.657557 0.316663i 0.0222422 0.0107113i
\(875\) 5.29094 + 13.9120i 0.178866 + 0.470310i
\(876\) −0.764402 1.96537i −0.0258267 0.0664035i
\(877\) 15.0569 7.25101i 0.508435 0.244849i −0.162037 0.986785i \(-0.551806\pi\)
0.670471 + 0.741936i \(0.266092\pi\)
\(878\) −41.8579 38.8385i −1.41264 1.31073i
\(879\) 1.13682 + 5.05212i 0.0383441 + 0.170404i
\(880\) −22.4021 + 57.0797i −0.755176 + 1.92416i
\(881\) −12.9194 −0.435267 −0.217634 0.976031i \(-0.569834\pi\)
−0.217634 + 0.976031i \(0.569834\pi\)
\(882\) 6.42263 + 32.1603i 0.216261 + 1.08290i
\(883\) −32.2583 −1.08558 −0.542789 0.839869i \(-0.682631\pi\)
−0.542789 + 0.839869i \(0.682631\pi\)
\(884\) 4.36459 11.1208i 0.146797 0.374032i
\(885\) −22.7589 + 20.9877i −0.765033 + 0.705493i
\(886\) −31.1312 28.8855i −1.04587 0.970428i
\(887\) −31.8509 + 15.3386i −1.06945 + 0.515019i −0.883928 0.467622i \(-0.845111\pi\)
−0.185519 + 0.982641i \(0.559396\pi\)
\(888\) 4.94516 + 0.760879i 0.165949 + 0.0255334i
\(889\) −25.7682 24.4216i −0.864239 0.819076i
\(890\) −47.6696 + 22.9565i −1.59789 + 0.769503i
\(891\) 21.2468 35.7797i 0.711796 1.19867i
\(892\) 0.112410 + 1.50000i 0.00376375 + 0.0502238i
\(893\) −4.17728 5.23814i −0.139787 0.175288i
\(894\) 6.12402 + 0.0187802i 0.204818 + 0.000628103i
\(895\) −15.1272 + 38.5434i −0.505646 + 1.28837i
\(896\) 32.1624 + 15.9098i 1.07447 + 0.531510i
\(897\) −2.83591 3.57857i −0.0946881 0.119485i
\(898\) 4.19461 + 55.9732i 0.139976 + 1.86785i
\(899\) 14.5445 13.4953i 0.485086 0.450094i
\(900\) −3.56292 1.74281i −0.118764 0.0580937i
\(901\) −16.8541 + 29.1922i −0.561492 + 0.972532i
\(902\) −84.6321 26.1055i −2.81794 0.869219i
\(903\) −2.84719 + 3.47201i −0.0947485 + 0.115541i
\(904\) −31.3576 + 9.67254i −1.04294 + 0.321704i
\(905\) 14.8700 65.1498i 0.494296 2.16565i
\(906\) −21.3699 26.9663i −0.709968 0.895894i
\(907\) 25.5867 32.0847i 0.849593 1.06536i −0.147493 0.989063i \(-0.547120\pi\)
0.997085 0.0762923i \(-0.0243082\pi\)
\(908\) −1.94955 1.80891i −0.0646980 0.0600309i
\(909\) 24.4594 + 3.84023i 0.811267 + 0.127372i
\(910\) −52.1724 + 15.4907i −1.72950 + 0.513512i
\(911\) 10.7168 + 3.30570i 0.355064 + 0.109523i 0.467155 0.884175i \(-0.345279\pi\)
−0.112092 + 0.993698i \(0.535755\pi\)
\(912\) 4.89314 + 4.56818i 0.162028 + 0.151267i
\(913\) −22.0898 + 38.2606i −0.731065 + 1.26624i
\(914\) −30.8049 9.50204i −1.01893 0.314300i
\(915\) 16.1772 20.1584i 0.534801 0.666416i
\(916\) −4.03536 10.2819i −0.133332 0.339724i
\(917\) 3.00741 0.420815i 0.0993136 0.0138965i
\(918\) −24.1130 + 40.8915i −0.795849 + 1.34962i
\(919\) 34.6106 + 10.6760i 1.14170 + 0.352167i 0.807228 0.590239i \(-0.200967\pi\)
0.334470 + 0.942407i \(0.391443\pi\)
\(920\) −2.43764 3.05671i −0.0803667 0.100777i
\(921\) −19.7070 50.6690i −0.649368 1.66960i
\(922\) −10.9963 + 13.7889i −0.362144 + 0.454114i
\(923\) 19.5956 + 13.3600i 0.644996 + 0.439751i
\(924\) 1.94528 + 9.09292i 0.0639950 + 0.299135i
\(925\) −2.94925 + 2.01076i −0.0969706 + 0.0661134i
\(926\) 0.553577 7.38697i 0.0181917 0.242751i
\(927\) 18.0946 + 2.84092i 0.594303 + 0.0933082i
\(928\) −5.07086 3.45726i −0.166459 0.113490i
\(929\) −4.44295 + 11.3204i −0.145768 + 0.371412i −0.985046 0.172291i \(-0.944883\pi\)
0.839278 + 0.543703i \(0.182978\pi\)
\(930\) −44.1605 41.2277i −1.44808 1.35191i
\(931\) 3.50400 + 4.58977i 0.114839 + 0.150424i
\(932\) 0.859676 + 1.48900i 0.0281596 + 0.0487739i
\(933\) −2.21494 1.52009i −0.0725138 0.0497655i
\(934\) 53.4464 25.7384i 1.74882 0.842186i
\(935\) −73.1632 + 22.5678i −2.39269 + 0.738048i
\(936\) 17.1975 29.3695i 0.562118 0.959971i
\(937\) 12.4586 + 5.99973i 0.407004 + 0.196003i 0.626173 0.779684i \(-0.284620\pi\)
−0.219169 + 0.975687i \(0.570335\pi\)
\(938\) −26.6893 8.54273i −0.871437 0.278930i
\(939\) −10.1735 45.2118i −0.332000 1.47543i
\(940\) 6.29066 7.88824i 0.205179 0.257286i
\(941\) 34.1726 23.2985i 1.11399 0.759508i 0.140924 0.990020i \(-0.454993\pi\)
0.973069 + 0.230513i \(0.0740403\pi\)
\(942\) −2.40886 + 30.8732i −0.0784848 + 1.00590i
\(943\) 5.09387 4.72642i 0.165879 0.153913i
\(944\) 18.4454 + 23.1298i 0.600347 + 0.752811i
\(945\) 38.5876 5.03790i 1.25525 0.163883i
\(946\) −4.41120 + 5.53147i −0.143420 + 0.179844i
\(947\) 0.858153 + 11.4513i 0.0278862 + 0.372116i 0.993636 + 0.112640i \(0.0359307\pi\)
−0.965750 + 0.259476i \(0.916450\pi\)
\(948\) 2.98233 5.12917i 0.0968617 0.166588i
\(949\) −6.45463 + 11.1798i −0.209526 + 0.362910i
\(950\) −3.88101 −0.125917
\(951\) 23.0971 + 0.0708305i 0.748974 + 0.00229684i
\(952\) 8.00724 + 36.8755i 0.259516 + 1.19514i
\(953\) 5.69150 24.9361i 0.184366 0.807760i −0.795153 0.606409i \(-0.792610\pi\)
0.979519 0.201351i \(-0.0645332\pi\)
\(954\) 16.9606 21.0023i 0.549118 0.679975i
\(955\) 6.45767 + 0.973338i 0.208965 + 0.0314965i
\(956\) 7.35896 9.22784i 0.238006 0.298450i
\(957\) 1.44330 + 20.0859i 0.0466554 + 0.649286i
\(958\) −14.8662 + 4.58561i −0.480304 + 0.148154i
\(959\) 48.3053 6.75916i 1.55986 0.218265i
\(960\) 13.6990 23.5601i 0.442132 0.760400i
\(961\) −15.6291 27.0703i −0.504164 0.873237i
\(962\) 4.30514 + 7.45671i 0.138803 + 0.240414i
\(963\) 13.4685 57.3849i 0.434018 1.84920i
\(964\) 3.94867 2.69215i 0.127178 0.0867085i
\(965\) 21.5628 + 54.9410i 0.694130 + 1.76861i
\(966\) −3.85757 1.24779i −0.124115 0.0401469i
\(967\) −1.75355 + 4.46798i −0.0563905 + 0.143681i −0.956293 0.292411i \(-0.905542\pi\)
0.899902 + 0.436092i \(0.143638\pi\)
\(968\) −5.63014 24.6673i −0.180960 0.792836i
\(969\) −0.650192 + 8.33321i −0.0208872 + 0.267701i
\(970\) 17.4572 + 8.40696i 0.560518 + 0.269931i
\(971\) −12.7372 32.4538i −0.408755 1.04149i −0.975967 0.217919i \(-0.930073\pi\)
0.567212 0.823572i \(-0.308022\pi\)
\(972\) 4.34691 5.28262i 0.139427 0.169440i
\(973\) −30.0645 0.317987i −0.963825 0.0101942i
\(974\) 17.8546 12.1730i 0.572097 0.390049i
\(975\) 5.33032 + 23.6883i 0.170707 + 0.758631i
\(976\) −18.1058 16.7997i −0.579552 0.537745i
\(977\) 3.24529 43.3054i 0.103826 1.38546i −0.665400 0.746487i \(-0.731739\pi\)
0.769226 0.638977i \(-0.220642\pi\)
\(978\) 1.85748 23.8065i 0.0593957 0.761248i
\(979\) 27.6698 47.9254i 0.884329 1.53170i
\(980\) −5.56437 + 6.68250i −0.177747 + 0.213464i
\(981\) 18.0258 12.1285i 0.575519 0.387233i
\(982\) 0.759662 0.114501i 0.0242418 0.00365386i
\(983\) 21.2916 10.2535i 0.679097 0.327036i −0.0623435 0.998055i \(-0.519857\pi\)
0.741440 + 0.671019i \(0.234143\pi\)
\(984\) 46.5967 + 22.6161i 1.48545 + 0.720975i
\(985\) −5.63947 + 2.71583i −0.179689 + 0.0865335i
\(986\) −1.71678 22.9088i −0.0546733 0.729565i
\(987\) −3.28745 + 37.0733i −0.104641 + 1.18006i
\(988\) −0.125890 + 1.67989i −0.00400510 + 0.0534444i
\(989\) −0.202800 0.516726i −0.00644866 0.0164309i
\(990\) 60.6876 8.76686i 1.92878 0.278629i
\(991\) −5.69725 + 14.5163i −0.180979 + 0.461127i −0.992358 0.123394i \(-0.960622\pi\)
0.811379 + 0.584521i \(0.198717\pi\)
\(992\) −14.1170 + 13.0987i −0.448216 + 0.415883i
\(993\) 47.1224 22.5152i 1.49538 0.714497i
\(994\) 21.0578 + 0.222724i 0.667913 + 0.00706438i
\(995\) −71.8785 10.8339i −2.27870 0.343459i
\(996\) −4.54590 + 5.66466i −0.144043 + 0.179492i
\(997\) −5.04058 22.0842i −0.159637 0.699415i −0.989867 0.141995i \(-0.954648\pi\)
0.830231 0.557420i \(-0.188209\pi\)
\(998\) 4.79174 + 8.29953i 0.151680 + 0.262717i
\(999\) −2.19647 5.75155i −0.0694933 0.181971i
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 441.2.z.a.142.15 yes 648
9.4 even 3 441.2.y.a.436.15 yes 648
49.39 even 21 441.2.y.a.88.15 648
441.382 even 21 inner 441.2.z.a.382.15 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.y.a.88.15 648 49.39 even 21
441.2.y.a.436.15 yes 648 9.4 even 3
441.2.z.a.142.15 yes 648 1.1 even 1 trivial
441.2.z.a.382.15 yes 648 441.382 even 21 inner