Properties

Label 432.2.bj.a.11.39
Level $432$
Weight $2$
Character 432.11
Analytic conductor $3.450$
Analytic rank $0$
Dimension $840$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,2,Mod(11,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([18, 9, 26]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.bj (of order \(36\), 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: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(840\)
Relative dimension: \(70\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 11.39
Character \(\chi\) \(=\) 432.11
Dual form 432.2.bj.a.275.39

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.146980 + 1.40655i) q^{2} +(0.0621762 - 1.73093i) q^{3} +(-1.95679 + 0.413472i) q^{4} +(3.40408 - 1.58735i) q^{5} +(2.44379 - 0.166959i) q^{6} +(-0.786764 + 4.46196i) q^{7} +(-0.869180 - 2.69157i) q^{8} +(-2.99227 - 0.215246i) q^{9} +O(q^{10})\) \(q+(0.146980 + 1.40655i) q^{2} +(0.0621762 - 1.73093i) q^{3} +(-1.95679 + 0.413472i) q^{4} +(3.40408 - 1.58735i) q^{5} +(2.44379 - 0.166959i) q^{6} +(-0.786764 + 4.46196i) q^{7} +(-0.869180 - 2.69157i) q^{8} +(-2.99227 - 0.215246i) q^{9} +(2.73302 + 4.55472i) q^{10} +(3.07254 + 1.43275i) q^{11} +(0.594026 + 3.41279i) q^{12} +(0.0327201 - 0.373992i) q^{13} +(-6.39164 - 0.450807i) q^{14} +(-2.53594 - 5.99093i) q^{15} +(3.65808 - 1.61816i) q^{16} +(2.48663 - 1.43566i) q^{17} +(-0.137049 - 4.24043i) q^{18} +(6.54437 - 1.75356i) q^{19} +(-6.00476 + 4.51360i) q^{20} +(7.67445 + 1.63927i) q^{21} +(-1.56364 + 4.53229i) q^{22} +(2.58417 - 0.455659i) q^{23} +(-4.71297 + 1.33714i) q^{24} +(5.85414 - 6.97670i) q^{25} +(0.530850 - 0.00894687i) q^{26} +(-0.558624 + 5.16604i) q^{27} +(-0.305359 - 9.05645i) q^{28} +(-0.395982 - 4.52609i) q^{29} +(8.05384 - 4.44749i) q^{30} +(-9.47680 + 1.67102i) q^{31} +(2.81369 + 4.90746i) q^{32} +(2.67104 - 5.22929i) q^{33} +(2.38482 + 3.28657i) q^{34} +(4.40448 + 16.4377i) q^{35} +(5.94425 - 0.816026i) q^{36} +(-0.275855 + 1.02951i) q^{37} +(3.42837 + 8.94728i) q^{38} +(-0.645322 - 0.0798898i) q^{39} +(-7.23121 - 7.78261i) q^{40} +(-3.38639 + 2.84152i) q^{41} +(-1.17773 + 11.0355i) q^{42} +(2.10910 - 4.52298i) q^{43} +(-6.60474 - 1.53319i) q^{44} +(-10.5276 + 4.01706i) q^{45} +(1.02073 + 3.56781i) q^{46} +(-1.03821 + 5.88800i) q^{47} +(-2.57348 - 6.43251i) q^{48} +(-12.7123 - 4.62689i) q^{49} +(10.6736 + 7.20874i) q^{50} +(-2.33042 - 4.39346i) q^{51} +(0.0906087 + 0.745355i) q^{52} +(-4.41531 + 4.41531i) q^{53} +(-7.34842 - 0.0264305i) q^{54} +12.7335 q^{55} +(12.6935 - 1.76062i) q^{56} +(-2.62839 - 11.4369i) q^{57} +(6.30800 - 1.22222i) q^{58} +(1.21763 + 2.61122i) q^{59} +(7.43940 + 10.6745i) q^{60} +(-5.01881 - 7.16760i) q^{61} +(-3.74328 - 13.0840i) q^{62} +(3.31463 - 13.1820i) q^{63} +(-6.48905 + 4.67891i) q^{64} +(-0.482274 - 1.32504i) q^{65} +(7.74787 + 2.98836i) q^{66} +(-1.09532 - 0.0958278i) q^{67} +(-4.27222 + 3.83744i) q^{68} +(-0.628042 - 4.50136i) q^{69} +(-22.4732 + 8.61117i) q^{70} +(-2.28401 + 1.31867i) q^{71} +(2.02147 + 8.24097i) q^{72} +(-0.225294 - 0.130074i) q^{73} +(-1.48860 - 0.236689i) q^{74} +(-11.7122 - 10.5669i) q^{75} +(-12.0809 + 6.13727i) q^{76} +(-8.81025 + 12.5823i) q^{77} +(0.0175198 - 0.919423i) q^{78} +(-7.98520 + 9.51639i) q^{79} +(9.88383 - 11.3150i) q^{80} +(8.90734 + 1.28815i) q^{81} +(-4.49449 - 4.34550i) q^{82} +(-9.12138 + 0.798018i) q^{83} +(-15.6951 - 0.0345391i) q^{84} +(6.18580 - 8.83424i) q^{85} +(6.67182 + 2.30178i) q^{86} +(-7.85899 + 0.404003i) q^{87} +(1.18575 - 9.51527i) q^{88} +(1.56222 - 2.70584i) q^{89} +(-7.19756 - 14.2172i) q^{90} +(1.64300 + 0.440240i) q^{91} +(-4.86829 + 1.96011i) q^{92} +(2.30319 + 16.5076i) q^{93} +(-8.43439 - 0.594884i) q^{94} +(19.4941 - 16.3575i) q^{95} +(8.66943 - 4.56519i) q^{96} +(0.783030 - 0.285000i) q^{97} +(4.63952 - 18.5606i) q^{98} +(-8.88548 - 4.94853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 24 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 24 q^{7} - 18 q^{8} - 6 q^{10} - 12 q^{11} + 6 q^{12} - 12 q^{13} - 12 q^{14} - 12 q^{16} - 36 q^{17} - 12 q^{18} - 6 q^{19} + 30 q^{20} - 12 q^{21} - 12 q^{22} - 24 q^{23} - 42 q^{24} - 12 q^{27} - 24 q^{28} - 12 q^{29} - 12 q^{30} - 12 q^{32} - 24 q^{33} - 24 q^{34} - 18 q^{35} - 12 q^{36} - 6 q^{37} - 12 q^{38} - 24 q^{39} - 12 q^{40} + 48 q^{42} - 12 q^{43} - 18 q^{44} - 12 q^{45} - 6 q^{46} - 12 q^{48} - 24 q^{49} + 144 q^{50} - 30 q^{51} - 12 q^{52} - 180 q^{54} - 48 q^{55} - 54 q^{56} - 66 q^{58} + 24 q^{59} - 72 q^{60} - 12 q^{61} - 216 q^{62} - 6 q^{64} - 24 q^{65} - 6 q^{66} - 12 q^{67} - 114 q^{68} - 12 q^{69} + 30 q^{70} - 36 q^{71} - 48 q^{72} - 96 q^{74} + 72 q^{75} - 12 q^{76} - 12 q^{77} - 90 q^{78} - 24 q^{81} - 24 q^{82} - 72 q^{83} - 192 q^{84} - 42 q^{85} - 72 q^{86} - 24 q^{87} - 12 q^{88} - 66 q^{90} - 6 q^{91} - 126 q^{92} - 12 q^{93} - 12 q^{94} + 96 q^{96} - 24 q^{97} - 18 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.146980 + 1.40655i 0.103931 + 0.994585i
\(3\) 0.0621762 1.73093i 0.0358974 0.999355i
\(4\) −1.95679 + 0.413472i −0.978397 + 0.206736i
\(5\) 3.40408 1.58735i 1.52235 0.709884i 0.531779 0.846883i \(-0.321524\pi\)
0.990571 + 0.136999i \(0.0437458\pi\)
\(6\) 2.44379 0.166959i 0.997674 0.0681607i
\(7\) −0.786764 + 4.46196i −0.297369 + 1.68646i 0.360046 + 0.932935i \(0.382761\pi\)
−0.657415 + 0.753529i \(0.728350\pi\)
\(8\) −0.869180 2.69157i −0.307302 0.951612i
\(9\) −2.99227 0.215246i −0.997423 0.0717486i
\(10\) 2.73302 + 4.55472i 0.864258 + 1.44033i
\(11\) 3.07254 + 1.43275i 0.926407 + 0.431991i 0.826456 0.563002i \(-0.190354\pi\)
0.0999513 + 0.994992i \(0.468131\pi\)
\(12\) 0.594026 + 3.41279i 0.171481 + 0.985188i
\(13\) 0.0327201 0.373992i 0.00907492 0.103727i −0.990306 0.138901i \(-0.955643\pi\)
0.999381 + 0.0351741i \(0.0111986\pi\)
\(14\) −6.39164 0.450807i −1.70824 0.120483i
\(15\) −2.53594 5.99093i −0.654778 1.54685i
\(16\) 3.65808 1.61816i 0.914521 0.404539i
\(17\) 2.48663 1.43566i 0.603097 0.348198i −0.167162 0.985929i \(-0.553460\pi\)
0.770259 + 0.637731i \(0.220127\pi\)
\(18\) −0.137049 4.24043i −0.0323028 0.999478i
\(19\) 6.54437 1.75356i 1.50138 0.402294i 0.587820 0.808992i \(-0.299986\pi\)
0.913563 + 0.406698i \(0.133320\pi\)
\(20\) −6.00476 + 4.51360i −1.34270 + 1.00927i
\(21\) 7.67445 + 1.63927i 1.67470 + 0.357717i
\(22\) −1.56364 + 4.53229i −0.333369 + 0.966287i
\(23\) 2.58417 0.455659i 0.538837 0.0950115i 0.102395 0.994744i \(-0.467349\pi\)
0.436442 + 0.899732i \(0.356238\pi\)
\(24\) −4.71297 + 1.33714i −0.962030 + 0.272943i
\(25\) 5.85414 6.97670i 1.17083 1.39534i
\(26\) 0.530850 0.00894687i 0.104108 0.00175463i
\(27\) −0.558624 + 5.16604i −0.107507 + 0.994204i
\(28\) −0.305359 9.05645i −0.0577074 1.71151i
\(29\) −0.395982 4.52609i −0.0735320 0.840474i −0.939985 0.341216i \(-0.889161\pi\)
0.866453 0.499259i \(-0.166394\pi\)
\(30\) 8.05384 4.44749i 1.47042 0.811997i
\(31\) −9.47680 + 1.67102i −1.70208 + 0.300123i −0.938422 0.345492i \(-0.887712\pi\)
−0.763662 + 0.645616i \(0.776601\pi\)
\(32\) 2.81369 + 4.90746i 0.497395 + 0.867524i
\(33\) 2.67104 5.22929i 0.464968 0.910303i
\(34\) 2.38482 + 3.28657i 0.408993 + 0.563642i
\(35\) 4.40448 + 16.4377i 0.744493 + 2.77849i
\(36\) 5.94425 0.816026i 0.990708 0.136004i
\(37\) −0.275855 + 1.02951i −0.0453503 + 0.169250i −0.984887 0.173199i \(-0.944590\pi\)
0.939537 + 0.342449i \(0.111256\pi\)
\(38\) 3.42837 + 8.94728i 0.556155 + 1.45144i
\(39\) −0.645322 0.0798898i −0.103334 0.0127926i
\(40\) −7.23121 7.78261i −1.14335 1.23054i
\(41\) −3.38639 + 2.84152i −0.528865 + 0.443771i −0.867709 0.497072i \(-0.834409\pi\)
0.338844 + 0.940843i \(0.389964\pi\)
\(42\) −1.17773 + 11.0355i −0.181727 + 1.70281i
\(43\) 2.10910 4.52298i 0.321635 0.689748i −0.677309 0.735699i \(-0.736854\pi\)
0.998944 + 0.0459505i \(0.0146316\pi\)
\(44\) −6.60474 1.53319i −0.995702 0.231137i
\(45\) −10.5276 + 4.01706i −1.56936 + 0.598828i
\(46\) 1.02073 + 3.56781i 0.150499 + 0.526044i
\(47\) −1.03821 + 5.88800i −0.151439 + 0.858853i 0.810531 + 0.585696i \(0.199179\pi\)
−0.961970 + 0.273157i \(0.911932\pi\)
\(48\) −2.57348 6.43251i −0.371450 0.928453i
\(49\) −12.7123 4.62689i −1.81604 0.660984i
\(50\) 10.6736 + 7.20874i 1.50947 + 1.01947i
\(51\) −2.33042 4.39346i −0.326324 0.615207i
\(52\) 0.0906087 + 0.745355i 0.0125652 + 0.103362i
\(53\) −4.41531 + 4.41531i −0.606489 + 0.606489i −0.942027 0.335538i \(-0.891082\pi\)
0.335538 + 0.942027i \(0.391082\pi\)
\(54\) −7.34842 0.0264305i −0.999994 0.00359673i
\(55\) 12.7335 1.71698
\(56\) 12.6935 1.76062i 1.69624 0.235273i
\(57\) −2.62839 11.4369i −0.348139 1.51486i
\(58\) 6.30800 1.22222i 0.828280 0.160485i
\(59\) 1.21763 + 2.61122i 0.158522 + 0.339952i 0.969487 0.245143i \(-0.0788349\pi\)
−0.810965 + 0.585095i \(0.801057\pi\)
\(60\) 7.43940 + 10.6745i 0.960422 + 1.37807i
\(61\) −5.01881 7.16760i −0.642592 0.917717i 0.357275 0.933999i \(-0.383706\pi\)
−0.999867 + 0.0162823i \(0.994817\pi\)
\(62\) −3.74328 13.0840i −0.475397 1.66167i
\(63\) 3.31463 13.1820i 0.417604 1.66078i
\(64\) −6.48905 + 4.67891i −0.811131 + 0.584864i
\(65\) −0.482274 1.32504i −0.0598188 0.164351i
\(66\) 7.74787 + 2.98836i 0.953697 + 0.367842i
\(67\) −1.09532 0.0958278i −0.133814 0.0117072i 0.0200518 0.999799i \(-0.493617\pi\)
−0.153866 + 0.988092i \(0.549172\pi\)
\(68\) −4.27222 + 3.83744i −0.518083 + 0.465357i
\(69\) −0.628042 4.50136i −0.0756074 0.541900i
\(70\) −22.4732 + 8.61117i −2.68606 + 1.02923i
\(71\) −2.28401 + 1.31867i −0.271062 + 0.156498i −0.629370 0.777106i \(-0.716687\pi\)
0.358308 + 0.933603i \(0.383354\pi\)
\(72\) 2.02147 + 8.24097i 0.238233 + 0.971208i
\(73\) −0.225294 0.130074i −0.0263687 0.0152240i 0.486758 0.873537i \(-0.338179\pi\)
−0.513126 + 0.858313i \(0.671513\pi\)
\(74\) −1.48860 0.236689i −0.173046 0.0275145i
\(75\) −11.7122 10.5669i −1.35241 1.22016i
\(76\) −12.0809 + 6.13727i −1.38578 + 0.703993i
\(77\) −8.81025 + 12.5823i −1.00402 + 1.43389i
\(78\) 0.0175198 0.919423i 0.00198373 0.104104i
\(79\) −7.98520 + 9.51639i −0.898405 + 1.07068i 0.0987363 + 0.995114i \(0.468520\pi\)
−0.997141 + 0.0755634i \(0.975924\pi\)
\(80\) 9.88383 11.3150i 1.10505 1.26505i
\(81\) 8.90734 + 1.28815i 0.989704 + 0.143127i
\(82\) −4.49449 4.34550i −0.496333 0.479880i
\(83\) −9.12138 + 0.798018i −1.00120 + 0.0875938i −0.575953 0.817483i \(-0.695369\pi\)
−0.425249 + 0.905076i \(0.639813\pi\)
\(84\) −15.6951 0.0345391i −1.71248 0.00376853i
\(85\) 6.18580 8.83424i 0.670944 0.958208i
\(86\) 6.67182 + 2.30178i 0.719441 + 0.248207i
\(87\) −7.85899 + 0.404003i −0.842572 + 0.0433137i
\(88\) 1.18575 9.51527i 0.126401 1.01433i
\(89\) 1.56222 2.70584i 0.165595 0.286818i −0.771272 0.636506i \(-0.780379\pi\)
0.936866 + 0.349688i \(0.113712\pi\)
\(90\) −7.19756 14.2172i −0.758689 1.49862i
\(91\) 1.64300 + 0.440240i 0.172233 + 0.0461497i
\(92\) −4.86829 + 1.96011i −0.507554 + 0.204356i
\(93\) 2.30319 + 16.5076i 0.238829 + 1.71176i
\(94\) −8.43439 0.594884i −0.869941 0.0613576i
\(95\) 19.4941 16.3575i 2.00005 1.67824i
\(96\) 8.66943 4.56519i 0.884820 0.465933i
\(97\) 0.783030 0.285000i 0.0795047 0.0289373i −0.301962 0.953320i \(-0.597641\pi\)
0.381466 + 0.924383i \(0.375419\pi\)
\(98\) 4.63952 18.5606i 0.468662 1.87490i
\(99\) −8.88548 4.94853i −0.893025 0.497346i
\(100\) −8.57069 + 16.0725i −0.857069 + 1.60725i
\(101\) 0.576425 + 0.823220i 0.0573564 + 0.0819134i 0.846806 0.531902i \(-0.178523\pi\)
−0.789449 + 0.613816i \(0.789634\pi\)
\(102\) 5.83712 3.92361i 0.577961 0.388496i
\(103\) 3.97219 + 1.44576i 0.391392 + 0.142455i 0.530217 0.847862i \(-0.322110\pi\)
−0.138825 + 0.990317i \(0.544333\pi\)
\(104\) −1.03506 + 0.236999i −0.101496 + 0.0232396i
\(105\) 28.7265 6.60183i 2.80342 0.644273i
\(106\) −6.85933 5.56141i −0.666237 0.540172i
\(107\) −5.50294 5.50294i −0.531989 0.531989i 0.389175 0.921164i \(-0.372760\pi\)
−0.921164 + 0.389175i \(0.872760\pi\)
\(108\) −1.04290 10.3398i −0.100353 0.994952i
\(109\) 9.38021 9.38021i 0.898462 0.898462i −0.0968385 0.995300i \(-0.530873\pi\)
0.995300 + 0.0968385i \(0.0308730\pi\)
\(110\) 1.87157 + 17.9103i 0.178447 + 1.70768i
\(111\) 1.76486 + 0.541498i 0.167513 + 0.0513967i
\(112\) 4.34211 + 17.5953i 0.410291 + 1.66260i
\(113\) −0.737378 + 2.02593i −0.0693667 + 0.190583i −0.969532 0.244965i \(-0.921223\pi\)
0.900165 + 0.435549i \(0.143446\pi\)
\(114\) 15.7003 5.37798i 1.47047 0.503694i
\(115\) 8.07344 5.65308i 0.752852 0.527153i
\(116\) 2.64626 + 8.69290i 0.245700 + 0.807116i
\(117\) −0.178408 + 1.11204i −0.0164938 + 0.102808i
\(118\) −3.49386 + 2.09647i −0.321636 + 0.192995i
\(119\) 4.44946 + 12.2248i 0.407881 + 1.12064i
\(120\) −13.9208 + 12.0329i −1.27079 + 1.09844i
\(121\) 0.317092 + 0.377895i 0.0288265 + 0.0343541i
\(122\) 9.34396 8.11272i 0.845962 0.734491i
\(123\) 4.70793 + 6.03830i 0.424500 + 0.544455i
\(124\) 17.8532 7.18822i 1.60327 0.645521i
\(125\) 3.99292 14.9018i 0.357138 1.33286i
\(126\) 19.0285 + 2.72471i 1.69519 + 0.242736i
\(127\) 7.07816 + 4.08658i 0.628085 + 0.362625i 0.780010 0.625767i \(-0.215214\pi\)
−0.151925 + 0.988392i \(0.548547\pi\)
\(128\) −7.53491 8.43950i −0.665998 0.745953i
\(129\) −7.69785 3.93194i −0.677758 0.346188i
\(130\) 1.79285 0.873100i 0.157244 0.0765759i
\(131\) −15.7496 11.0280i −1.37605 0.963522i −0.999308 0.0372045i \(-0.988155\pi\)
−0.376744 0.926317i \(-0.622956\pi\)
\(132\) −3.06451 + 11.3370i −0.266731 + 0.986763i
\(133\) 2.67544 + 30.5804i 0.231990 + 2.65166i
\(134\) −0.0262028 1.55471i −0.00226358 0.134306i
\(135\) 6.29870 + 18.4723i 0.542106 + 1.58985i
\(136\) −6.02550 5.44509i −0.516682 0.466912i
\(137\) 1.85512 + 1.55663i 0.158493 + 0.132992i 0.718586 0.695439i \(-0.244790\pi\)
−0.560092 + 0.828430i \(0.689234\pi\)
\(138\) 6.23911 1.54499i 0.531108 0.131518i
\(139\) −14.7157 10.3041i −1.24817 0.873979i −0.252562 0.967581i \(-0.581273\pi\)
−0.995610 + 0.0936015i \(0.970162\pi\)
\(140\) −15.4152 30.3442i −1.30282 2.56455i
\(141\) 10.1272 + 2.16317i 0.852863 + 0.182172i
\(142\) −2.19049 3.01876i −0.183822 0.253329i
\(143\) 0.636372 1.10223i 0.0532161 0.0921730i
\(144\) −11.2943 + 4.05457i −0.941189 + 0.337881i
\(145\) −8.53244 14.7786i −0.708580 1.22730i
\(146\) 0.149842 0.336007i 0.0124010 0.0278082i
\(147\) −8.79924 + 21.7164i −0.725749 + 1.79114i
\(148\) 0.114121 2.12859i 0.00938065 0.174969i
\(149\) −0.873604 + 9.98534i −0.0715684 + 0.818031i 0.872572 + 0.488486i \(0.162451\pi\)
−0.944140 + 0.329545i \(0.893105\pi\)
\(150\) 13.1415 18.0270i 1.07300 1.47190i
\(151\) −11.0324 + 4.01546i −0.897803 + 0.326773i −0.749372 0.662149i \(-0.769644\pi\)
−0.148431 + 0.988923i \(0.547422\pi\)
\(152\) −10.4081 16.0905i −0.844205 1.30511i
\(153\) −7.74969 + 3.76063i −0.626525 + 0.304029i
\(154\) −18.9927 10.5427i −1.53047 0.849559i
\(155\) −29.6073 + 20.7313i −2.37812 + 1.66517i
\(156\) 1.29579 0.110494i 0.103747 0.00884664i
\(157\) 10.8158 5.04351i 0.863198 0.402516i 0.0599789 0.998200i \(-0.480897\pi\)
0.803219 + 0.595684i \(0.203119\pi\)
\(158\) −14.5590 9.83290i −1.15825 0.782263i
\(159\) 7.36808 + 7.91713i 0.584327 + 0.627869i
\(160\) 17.3679 + 12.2391i 1.37305 + 0.967583i
\(161\) 11.8890i 0.936983i
\(162\) −0.502646 + 12.7180i −0.0394916 + 0.999220i
\(163\) −14.1257 14.1257i −1.10641 1.10641i −0.993619 0.112788i \(-0.964022\pi\)
−0.112788 0.993619i \(-0.535978\pi\)
\(164\) 5.45158 6.96044i 0.425697 0.543519i
\(165\) 0.791718 22.0408i 0.0616352 1.71587i
\(166\) −2.46312 12.7124i −0.191175 0.986676i
\(167\) 1.73289 4.76108i 0.134095 0.368423i −0.854412 0.519596i \(-0.826083\pi\)
0.988507 + 0.151172i \(0.0483049\pi\)
\(168\) −2.25829 22.0811i −0.174231 1.70359i
\(169\) 12.6637 + 2.23295i 0.974131 + 0.171766i
\(170\) 13.3350 + 7.40221i 1.02275 + 0.567724i
\(171\) −19.9600 + 3.83847i −1.52638 + 0.293535i
\(172\) −2.25695 + 9.72260i −0.172091 + 0.741341i
\(173\) −10.1636 4.73937i −0.772725 0.360328i −0.00407057 0.999992i \(-0.501296\pi\)
−0.768655 + 0.639664i \(0.779073\pi\)
\(174\) −1.72337 10.9947i −0.130648 0.833508i
\(175\) 26.5239 + 31.6100i 2.00502 + 2.38949i
\(176\) 13.5580 + 0.269263i 1.02198 + 0.0202965i
\(177\) 4.59556 1.94529i 0.345424 0.146217i
\(178\) 4.03552 + 1.79964i 0.302475 + 0.134889i
\(179\) 10.8156 + 2.89804i 0.808398 + 0.216610i 0.639268 0.768984i \(-0.279238\pi\)
0.169130 + 0.985594i \(0.445904\pi\)
\(180\) 18.9394 12.2134i 1.41166 0.910334i
\(181\) −9.77541 + 2.61931i −0.726601 + 0.194692i −0.603115 0.797654i \(-0.706074\pi\)
−0.123486 + 0.992346i \(0.539407\pi\)
\(182\) −0.377733 + 2.37567i −0.0279995 + 0.176097i
\(183\) −12.7187 + 8.24157i −0.940193 + 0.609234i
\(184\) −3.47255 6.55942i −0.256000 0.483567i
\(185\) 0.695151 + 3.94240i 0.0511085 + 0.289851i
\(186\) −22.8804 + 5.66585i −1.67767 + 0.415441i
\(187\) 9.69722 0.848397i 0.709131 0.0620409i
\(188\) −0.402951 11.9509i −0.0293882 0.871607i
\(189\) −22.6112 6.55702i −1.64472 0.476953i
\(190\) 25.8729 + 25.0152i 1.87702 + 1.81480i
\(191\) −7.50351 6.29620i −0.542935 0.455577i 0.329605 0.944119i \(-0.393084\pi\)
−0.872540 + 0.488542i \(0.837529\pi\)
\(192\) 7.69543 + 11.5230i 0.555369 + 0.831604i
\(193\) −1.86274 10.5641i −0.134083 0.760423i −0.975494 0.220027i \(-0.929386\pi\)
0.841411 0.540396i \(-0.181726\pi\)
\(194\) 0.515958 + 1.05949i 0.0370436 + 0.0760667i
\(195\) −2.32354 + 0.752400i −0.166392 + 0.0538805i
\(196\) 26.7884 + 3.79770i 1.91346 + 0.271265i
\(197\) 6.22100 + 23.2171i 0.443228 + 1.65415i 0.720574 + 0.693378i \(0.243879\pi\)
−0.277346 + 0.960770i \(0.589455\pi\)
\(198\) 5.65439 13.2253i 0.401840 0.939878i
\(199\) −2.02223 3.50260i −0.143352 0.248293i 0.785405 0.618982i \(-0.212455\pi\)
−0.928757 + 0.370689i \(0.879121\pi\)
\(200\) −23.8665 9.69281i −1.68762 0.685385i
\(201\) −0.233974 + 1.88996i −0.0165033 + 0.133308i
\(202\) −1.07318 + 0.931770i −0.0755088 + 0.0655591i
\(203\) 20.5068 + 1.79411i 1.43930 + 0.125922i
\(204\) 6.37672 + 7.63353i 0.446460 + 0.534454i
\(205\) −7.01706 + 15.0481i −0.490093 + 1.05101i
\(206\) −1.44971 + 5.79960i −0.101006 + 0.404078i
\(207\) −7.83061 + 0.807222i −0.544265 + 0.0561058i
\(208\) −0.485486 1.42104i −0.0336624 0.0985315i
\(209\) 22.6203 + 3.98857i 1.56468 + 0.275895i
\(210\) 13.5081 + 39.4351i 0.932145 + 2.72128i
\(211\) 9.30837 + 19.9619i 0.640814 + 1.37423i 0.911395 + 0.411533i \(0.135007\pi\)
−0.270580 + 0.962697i \(0.587216\pi\)
\(212\) 6.81424 10.4654i 0.468004 0.718770i
\(213\) 2.14052 + 4.03545i 0.146666 + 0.276505i
\(214\) 6.93136 8.54901i 0.473818 0.584398i
\(215\) 18.7445i 1.27836i
\(216\) 14.3903 2.98664i 0.979134 0.203215i
\(217\) 43.5998i 2.95975i
\(218\) 14.5725 + 11.8151i 0.986974 + 0.800218i
\(219\) −0.239157 + 0.381882i −0.0161607 + 0.0258052i
\(220\) −24.9168 + 5.26492i −1.67989 + 0.354961i
\(221\) −0.455562 0.976956i −0.0306444 0.0657172i
\(222\) −0.502248 + 2.56196i −0.0337087 + 0.171947i
\(223\) −20.6400 3.63938i −1.38215 0.243711i −0.567364 0.823467i \(-0.692037\pi\)
−0.814790 + 0.579756i \(0.803148\pi\)
\(224\) −24.1106 + 8.69358i −1.61096 + 0.580864i
\(225\) −19.0189 + 19.6161i −1.26793 + 1.30774i
\(226\) −2.95796 0.739391i −0.196761 0.0491836i
\(227\) 8.10446 17.3801i 0.537912 1.15356i −0.430130 0.902767i \(-0.641532\pi\)
0.968042 0.250789i \(-0.0806901\pi\)
\(228\) 9.87206 + 21.2929i 0.653793 + 1.41016i
\(229\) 2.43686 + 0.213198i 0.161032 + 0.0140885i 0.167387 0.985891i \(-0.446467\pi\)
−0.00635440 + 0.999980i \(0.502023\pi\)
\(230\) 9.13800 + 10.5248i 0.602542 + 0.693987i
\(231\) 21.2314 + 16.0323i 1.39693 + 1.05485i
\(232\) −11.8381 + 4.99980i −0.777209 + 0.328253i
\(233\) 5.69954 + 9.87189i 0.373389 + 0.646729i 0.990085 0.140473i \(-0.0448623\pi\)
−0.616695 + 0.787202i \(0.711529\pi\)
\(234\) −1.59037 0.0874918i −0.103966 0.00571952i
\(235\) 5.81215 + 21.6912i 0.379143 + 1.41498i
\(236\) −3.46232 4.60617i −0.225378 0.299836i
\(237\) 15.9758 + 14.4135i 1.03774 + 0.936260i
\(238\) −16.5408 + 8.05520i −1.07218 + 0.522141i
\(239\) −1.07867 6.11744i −0.0697734 0.395704i −0.999615 0.0277445i \(-0.991168\pi\)
0.929842 0.367960i \(-0.119944\pi\)
\(240\) −18.9710 17.8118i −1.22457 1.14975i
\(241\) −12.5705 10.5479i −0.809734 0.679448i 0.140810 0.990037i \(-0.455029\pi\)
−0.950544 + 0.310589i \(0.899474\pi\)
\(242\) −0.484924 + 0.501550i −0.0311721 + 0.0322408i
\(243\) 2.78352 15.3379i 0.178563 0.983928i
\(244\) 12.7844 + 11.9504i 0.818435 + 0.765044i
\(245\) −50.6181 + 4.42851i −3.23387 + 0.282927i
\(246\) −7.80122 + 7.50947i −0.497388 + 0.478787i
\(247\) −0.441686 2.50492i −0.0281038 0.159384i
\(248\) 12.7347 + 24.0550i 0.808654 + 1.52750i
\(249\) 0.814183 + 15.8381i 0.0515968 + 1.00370i
\(250\) 21.5471 + 3.42599i 1.36276 + 0.216679i
\(251\) 17.4605 4.67853i 1.10210 0.295306i 0.338480 0.940974i \(-0.390087\pi\)
0.763619 + 0.645667i \(0.223421\pi\)
\(252\) −1.03565 + 27.1650i −0.0652396 + 1.71124i
\(253\) 8.59283 + 2.30244i 0.540227 + 0.144753i
\(254\) −4.70765 + 10.5565i −0.295384 + 0.662372i
\(255\) −14.9069 11.2565i −0.933505 0.704909i
\(256\) 10.7631 11.8387i 0.672696 0.739919i
\(257\) 9.02664 + 10.7575i 0.563066 + 0.671036i 0.970192 0.242336i \(-0.0779135\pi\)
−0.407126 + 0.913372i \(0.633469\pi\)
\(258\) 4.39906 11.4054i 0.273873 0.710067i
\(259\) −4.37659 2.04084i −0.271948 0.126811i
\(260\) 1.49158 + 2.39342i 0.0925037 + 0.148434i
\(261\) 0.210661 + 13.6285i 0.0130396 + 0.843584i
\(262\) 13.1966 23.7736i 0.815290 1.46874i
\(263\) 30.3415 + 5.35003i 1.87094 + 0.329897i 0.989744 0.142855i \(-0.0456283\pi\)
0.881195 + 0.472752i \(0.156739\pi\)
\(264\) −16.3966 2.64408i −1.00914 0.162732i
\(265\) −8.02142 + 22.0387i −0.492752 + 1.35383i
\(266\) −42.6198 + 8.25786i −2.61319 + 0.506322i
\(267\) −4.58649 2.87233i −0.280689 0.175784i
\(268\) 2.18293 0.265367i 0.133344 0.0162099i
\(269\) 17.1768 + 17.1768i 1.04729 + 1.04729i 0.998825 + 0.0484660i \(0.0154332\pi\)
0.0484660 + 0.998825i \(0.484567\pi\)
\(270\) −25.0566 + 11.5745i −1.52489 + 0.704404i
\(271\) 4.57756i 0.278067i −0.990288 0.139033i \(-0.955600\pi\)
0.990288 0.139033i \(-0.0443996\pi\)
\(272\) 6.77318 9.27551i 0.410685 0.562410i
\(273\) 0.864182 2.81655i 0.0523027 0.170465i
\(274\) −1.91682 + 2.83812i −0.115799 + 0.171457i
\(275\) 27.9830 13.0487i 1.68744 0.786865i
\(276\) 3.09013 + 8.54856i 0.186004 + 0.514563i
\(277\) 23.4228 16.4008i 1.40734 0.985429i 0.410032 0.912071i \(-0.365517\pi\)
0.997306 0.0733575i \(-0.0233714\pi\)
\(278\) 12.3303 22.2130i 0.739523 1.33225i
\(279\) 28.7168 2.96029i 1.71923 0.177228i
\(280\) 40.4150 26.1423i 2.41526 1.56230i
\(281\) −0.321536 + 0.117030i −0.0191812 + 0.00698140i −0.351593 0.936153i \(-0.614360\pi\)
0.332412 + 0.943134i \(0.392138\pi\)
\(282\) −1.55412 + 14.5624i −0.0925467 + 0.867178i
\(283\) −1.72433 + 19.7092i −0.102501 + 1.17159i 0.754509 + 0.656290i \(0.227875\pi\)
−0.857009 + 0.515301i \(0.827680\pi\)
\(284\) 3.92410 3.52474i 0.232852 0.209155i
\(285\) −27.1016 34.7600i −1.60536 2.05900i
\(286\) 1.64388 + 0.733087i 0.0972046 + 0.0433483i
\(287\) −10.0145 17.3456i −0.591135 1.02388i
\(288\) −7.36301 15.2901i −0.433870 0.900976i
\(289\) −4.37778 + 7.58253i −0.257516 + 0.446031i
\(290\) 19.5328 14.1735i 1.14701 0.832297i
\(291\) −0.444630 1.37309i −0.0260647 0.0804922i
\(292\) 0.494636 + 0.161375i 0.0289464 + 0.00944374i
\(293\) 2.86567 + 2.00657i 0.167414 + 0.117225i 0.654281 0.756252i \(-0.272971\pi\)
−0.486867 + 0.873476i \(0.661860\pi\)
\(294\) −31.8387 9.18473i −1.85687 0.535664i
\(295\) 8.28984 + 6.95600i 0.482653 + 0.404994i
\(296\) 3.01075 0.152344i 0.174996 0.00885480i
\(297\) −9.11804 + 15.0725i −0.529083 + 0.874596i
\(298\) −14.1733 + 0.238875i −0.821039 + 0.0138377i
\(299\) −0.0858588 0.981370i −0.00496534 0.0567541i
\(300\) 27.2875 + 15.8346i 1.57545 + 0.914212i
\(301\) 18.5220 + 12.9693i 1.06759 + 0.747536i
\(302\) −7.26951 14.9275i −0.418313 0.858979i
\(303\) 1.46078 0.946569i 0.0839196 0.0543790i
\(304\) 21.1023 17.0045i 1.21030 0.975274i
\(305\) −28.4619 16.4325i −1.62972 0.940921i
\(306\) −6.42859 10.3476i −0.367498 0.591534i
\(307\) −0.435684 + 1.62599i −0.0248658 + 0.0928003i −0.977244 0.212120i \(-0.931963\pi\)
0.952378 + 0.304920i \(0.0986299\pi\)
\(308\) 12.0374 28.2638i 0.685895 1.61048i
\(309\) 2.74949 6.78571i 0.156413 0.386026i
\(310\) −33.5113 38.5972i −1.90332 2.19217i
\(311\) 8.18907 + 9.75935i 0.464359 + 0.553402i 0.946505 0.322689i \(-0.104587\pi\)
−0.482146 + 0.876091i \(0.660142\pi\)
\(312\) 0.345873 + 1.80637i 0.0195812 + 0.102265i
\(313\) 0.833465 + 2.28993i 0.0471102 + 0.129434i 0.961017 0.276491i \(-0.0891716\pi\)
−0.913906 + 0.405925i \(0.866949\pi\)
\(314\) 8.68369 + 14.4718i 0.490049 + 0.816689i
\(315\) −9.64123 50.1342i −0.543222 2.82474i
\(316\) 11.6906 21.9233i 0.657649 1.23328i
\(317\) −12.2235 + 8.55900i −0.686541 + 0.480721i −0.864055 0.503397i \(-0.832083\pi\)
0.177514 + 0.984118i \(0.443194\pi\)
\(318\) −10.0529 + 11.5273i −0.563740 + 0.646417i
\(319\) 5.26809 14.4740i 0.294957 0.810386i
\(320\) −14.6622 + 26.2278i −0.819641 + 1.46618i
\(321\) −9.86738 + 9.18307i −0.550743 + 0.512549i
\(322\) −16.7225 + 1.74744i −0.931908 + 0.0973813i
\(323\) 13.7559 13.7559i 0.765401 0.765401i
\(324\) −17.9624 + 1.16229i −0.997913 + 0.0645719i
\(325\) −2.41768 2.41768i −0.134109 0.134109i
\(326\) 17.7923 21.9447i 0.985425 1.21540i
\(327\) −15.6533 16.8198i −0.865630 0.930135i
\(328\) 10.5915 + 6.64490i 0.584819 + 0.366903i
\(329\) −25.4552 9.26494i −1.40339 0.510793i
\(330\) 31.1179 2.12596i 1.71299 0.117031i
\(331\) −5.62987 8.04029i −0.309446 0.441934i 0.634063 0.773281i \(-0.281386\pi\)
−0.943509 + 0.331347i \(0.892497\pi\)
\(332\) 17.5187 5.33299i 0.961464 0.292686i
\(333\) 1.04703 3.02118i 0.0573769 0.165560i
\(334\) 6.95141 + 1.73762i 0.380364 + 0.0950784i
\(335\) −3.88066 + 1.41244i −0.212023 + 0.0771701i
\(336\) 30.7264 6.42189i 1.67626 0.350343i
\(337\) 18.5945 15.6026i 1.01291 0.849929i 0.0241862 0.999707i \(-0.492301\pi\)
0.988720 + 0.149779i \(0.0478561\pi\)
\(338\) −1.27946 + 18.1404i −0.0695933 + 0.986707i
\(339\) 3.46090 + 1.40232i 0.187971 + 0.0761635i
\(340\) −8.45163 + 19.8444i −0.458354 + 1.07622i
\(341\) −31.5121 8.44363i −1.70647 0.457248i
\(342\) −8.33274 27.5106i −0.450583 1.48760i
\(343\) 14.7888 25.6149i 0.798519 1.38308i
\(344\) −14.0071 1.74550i −0.755212 0.0941109i
\(345\) −9.28314 14.3261i −0.499787 0.771290i
\(346\) 5.17234 14.9923i 0.278066 0.805990i
\(347\) −6.63602 + 9.47722i −0.356240 + 0.508764i −0.956773 0.290836i \(-0.906066\pi\)
0.600532 + 0.799600i \(0.294955\pi\)
\(348\) 15.2114 4.04002i 0.815415 0.216568i
\(349\) −11.7754 + 1.03022i −0.630324 + 0.0551462i −0.397841 0.917454i \(-0.630240\pi\)
−0.232483 + 0.972601i \(0.574685\pi\)
\(350\) −40.5627 + 41.9534i −2.16817 + 2.24250i
\(351\) 1.91378 + 0.377955i 0.102150 + 0.0201737i
\(352\) 1.61403 + 19.1097i 0.0860281 + 1.01855i
\(353\) 6.58106 7.84300i 0.350274 0.417441i −0.561925 0.827188i \(-0.689939\pi\)
0.912199 + 0.409748i \(0.134383\pi\)
\(354\) 3.41161 + 6.17800i 0.181325 + 0.328357i
\(355\) −5.68175 + 8.11438i −0.301556 + 0.430666i
\(356\) −1.93815 + 5.94070i −0.102722 + 0.314856i
\(357\) 21.4369 6.94163i 1.13456 0.367390i
\(358\) −2.48657 + 15.6387i −0.131419 + 0.826532i
\(359\) −26.4539 15.2732i −1.39619 0.806088i −0.402195 0.915554i \(-0.631753\pi\)
−0.993991 + 0.109466i \(0.965086\pi\)
\(360\) 19.9625 + 24.8441i 1.05212 + 1.30940i
\(361\) 23.2994 13.4519i 1.22628 0.707995i
\(362\) −5.12100 13.3647i −0.269154 0.702431i
\(363\) 0.673827 0.525369i 0.0353668 0.0275747i
\(364\) −3.39703 0.182126i −0.178053 0.00954599i
\(365\) −0.973393 0.0851608i −0.0509497 0.00445752i
\(366\) −13.4616 16.6782i −0.703650 0.871783i
\(367\) 4.85781 + 13.3467i 0.253575 + 0.696693i 0.999529 + 0.0306947i \(0.00977196\pi\)
−0.745953 + 0.665998i \(0.768006\pi\)
\(368\) 8.71579 5.84843i 0.454342 0.304871i
\(369\) 10.7446 7.77368i 0.559342 0.404682i
\(370\) −5.44303 + 1.55722i −0.282970 + 0.0809562i
\(371\) −16.2271 23.1747i −0.842470 1.20317i
\(372\) −11.3323 31.3497i −0.587552 1.62541i
\(373\) 6.63264 + 14.2237i 0.343425 + 0.736477i 0.999839 0.0179232i \(-0.00570544\pi\)
−0.656414 + 0.754401i \(0.727928\pi\)
\(374\) 2.61862 + 13.5150i 0.135405 + 0.698843i
\(375\) −25.5457 7.83802i −1.31918 0.404754i
\(376\) 16.7503 2.32331i 0.863832 0.119816i
\(377\) −1.70568 −0.0878470
\(378\) 5.89941 32.7676i 0.303433 1.68538i
\(379\) −9.86219 + 9.86219i −0.506587 + 0.506587i −0.913477 0.406890i \(-0.866613\pi\)
0.406890 + 0.913477i \(0.366613\pi\)
\(380\) −31.3825 + 40.0684i −1.60989 + 2.05547i
\(381\) 7.51370 11.9978i 0.384938 0.614663i
\(382\) 7.75308 11.4795i 0.396682 0.587343i
\(383\) 12.5052 + 4.55151i 0.638984 + 0.232571i 0.641137 0.767426i \(-0.278463\pi\)
−0.00215284 + 0.999998i \(0.500685\pi\)
\(384\) −15.0767 + 12.5177i −0.769380 + 0.638791i
\(385\) −10.0182 + 56.8162i −0.510577 + 2.89562i
\(386\) 14.5852 4.17277i 0.742370 0.212388i
\(387\) −7.28455 + 13.0800i −0.370295 + 0.664894i
\(388\) −1.41439 + 0.881446i −0.0718047 + 0.0447487i
\(389\) −1.56614 + 3.35860i −0.0794065 + 0.170288i −0.942003 0.335605i \(-0.891059\pi\)
0.862596 + 0.505893i \(0.168837\pi\)
\(390\) −1.39981 3.15760i −0.0708819 0.159891i
\(391\) 5.77171 4.84304i 0.291888 0.244923i
\(392\) −1.40432 + 38.2375i −0.0709287 + 1.93129i
\(393\) −20.0680 + 26.5759i −1.01230 + 1.34058i
\(394\) −31.7417 + 12.1626i −1.59913 + 0.612744i
\(395\) −12.0764 + 45.0698i −0.607631 + 2.26771i
\(396\) 19.4331 + 6.00935i 0.976552 + 0.301981i
\(397\) 0.490833 + 1.83182i 0.0246342 + 0.0919362i 0.977149 0.212558i \(-0.0681793\pi\)
−0.952514 + 0.304494i \(0.901513\pi\)
\(398\) 4.62937 3.35919i 0.232050 0.168381i
\(399\) 53.0990 2.72964i 2.65828 0.136653i
\(400\) 10.1256 34.9943i 0.506278 1.74971i
\(401\) −1.48542 + 0.261920i −0.0741784 + 0.0130797i −0.210614 0.977569i \(-0.567546\pi\)
0.136436 + 0.990649i \(0.456435\pi\)
\(402\) −2.69273 0.0513105i −0.134301 0.00255913i
\(403\) 0.314865 + 3.59893i 0.0156846 + 0.179275i
\(404\) −1.46832 1.37254i −0.0730518 0.0682862i
\(405\) 32.3660 9.75410i 1.60828 0.484685i
\(406\) 0.490576 + 29.1076i 0.0243469 + 1.44459i
\(407\) −2.32260 + 2.76797i −0.115127 + 0.137203i
\(408\) −9.79973 + 10.0912i −0.485159 + 0.499588i
\(409\) −26.5057 + 4.67367i −1.31062 + 0.231098i −0.784934 0.619580i \(-0.787303\pi\)
−0.525688 + 0.850678i \(0.676192\pi\)
\(410\) −22.1974 7.65811i −1.09625 0.378207i
\(411\) 2.80977 3.11430i 0.138596 0.153617i
\(412\) −8.37054 1.18666i −0.412387 0.0584628i
\(413\) −12.6092 + 3.37862i −0.620457 + 0.166251i
\(414\) −2.28635 10.8955i −0.112368 0.535487i
\(415\) −29.7832 + 17.1953i −1.46200 + 0.844086i
\(416\) 1.92742 0.891727i 0.0944994 0.0437205i
\(417\) −18.7506 + 24.8313i −0.918222 + 1.21599i
\(418\) −2.28541 + 32.4029i −0.111783 + 1.58488i
\(419\) 2.71049 30.9810i 0.132416 1.51352i −0.581647 0.813441i \(-0.697591\pi\)
0.714063 0.700081i \(-0.246853\pi\)
\(420\) −53.4822 + 24.7960i −2.60966 + 1.20992i
\(421\) −25.8889 12.0722i −1.26175 0.588362i −0.327454 0.944867i \(-0.606191\pi\)
−0.934294 + 0.356505i \(0.883968\pi\)
\(422\) −26.7093 + 16.0267i −1.30019 + 0.780169i
\(423\) 4.37398 17.3950i 0.212670 0.845774i
\(424\) 15.7218 + 8.04639i 0.763517 + 0.390767i
\(425\) 4.54095 25.7530i 0.220269 1.24920i
\(426\) −5.36147 + 3.60390i −0.259764 + 0.174609i
\(427\) 35.9302 16.7545i 1.73878 0.810808i
\(428\) 13.0434 + 8.49280i 0.630478 + 0.410515i
\(429\) −1.86832 1.17005i −0.0902033 0.0564906i
\(430\) 26.3651 2.75507i 1.27144 0.132861i
\(431\) −25.4884 −1.22773 −0.613866 0.789410i \(-0.710386\pi\)
−0.613866 + 0.789410i \(0.710386\pi\)
\(432\) 6.31596 + 19.8017i 0.303877 + 0.952711i
\(433\) −5.41154 −0.260062 −0.130031 0.991510i \(-0.541508\pi\)
−0.130031 + 0.991510i \(0.541508\pi\)
\(434\) 61.3256 6.40831i 2.94372 0.307609i
\(435\) −26.1113 + 13.8502i −1.25194 + 0.664067i
\(436\) −14.4767 + 22.2336i −0.693308 + 1.06480i
\(437\) 16.1128 7.51351i 0.770778 0.359420i
\(438\) −0.572290 0.280259i −0.0273451 0.0133913i
\(439\) 1.88851 10.7102i 0.0901335 0.511172i −0.905997 0.423284i \(-0.860877\pi\)
0.996130 0.0878880i \(-0.0280118\pi\)
\(440\) −11.0677 34.2729i −0.527631 1.63390i
\(441\) 37.0426 + 16.5812i 1.76393 + 0.789579i
\(442\) 1.30718 0.784366i 0.0621764 0.0373085i
\(443\) 0.930036 + 0.433683i 0.0441873 + 0.0206049i 0.444586 0.895736i \(-0.353351\pi\)
−0.400399 + 0.916341i \(0.631128\pi\)
\(444\) −3.67735 0.329883i −0.174519 0.0156555i
\(445\) 1.02280 11.6907i 0.0484854 0.554191i
\(446\) 2.08532 29.5662i 0.0987430 1.40000i
\(447\) 17.2296 + 2.13300i 0.814934 + 0.100888i
\(448\) −15.7718 32.6351i −0.745146 1.54186i
\(449\) 27.3877 15.8123i 1.29251 0.746229i 0.313409 0.949618i \(-0.398529\pi\)
0.979098 + 0.203389i \(0.0651955\pi\)
\(450\) −30.3865 23.8679i −1.43243 1.12514i
\(451\) −14.4760 + 3.87884i −0.681650 + 0.182647i
\(452\) 0.605233 4.26921i 0.0284678 0.200807i
\(453\) 6.26455 + 19.3460i 0.294334 + 0.908954i
\(454\) 25.6372 + 8.84485i 1.20321 + 0.415109i
\(455\) 6.29171 1.10940i 0.294960 0.0520094i
\(456\) −28.4987 + 17.0152i −1.33457 + 0.796811i
\(457\) 13.5837 16.1884i 0.635416 0.757260i −0.348222 0.937412i \(-0.613215\pi\)
0.983639 + 0.180152i \(0.0576590\pi\)
\(458\) 0.0582961 + 3.45892i 0.00272400 + 0.161625i
\(459\) 6.02757 + 13.6480i 0.281343 + 0.637035i
\(460\) −13.4607 + 14.4000i −0.627607 + 0.671406i
\(461\) 0.373067 + 4.26417i 0.0173754 + 0.198602i 0.999921 + 0.0125795i \(0.00400428\pi\)
−0.982545 + 0.186023i \(0.940440\pi\)
\(462\) −19.4297 + 32.2196i −0.903951 + 1.49899i
\(463\) 20.9817 3.69964i 0.975103 0.171937i 0.336677 0.941620i \(-0.390697\pi\)
0.638426 + 0.769683i \(0.279586\pi\)
\(464\) −8.77246 15.9161i −0.407251 0.738884i
\(465\) 34.0436 + 52.5373i 1.57873 + 2.43636i
\(466\) −13.0476 + 9.46769i −0.604420 + 0.438582i
\(467\) 5.13977 + 19.1819i 0.237840 + 0.887632i 0.976848 + 0.213935i \(0.0686281\pi\)
−0.739007 + 0.673697i \(0.764705\pi\)
\(468\) −0.110691 2.24980i −0.00511670 0.103997i
\(469\) 1.28934 4.81187i 0.0595360 0.222192i
\(470\) −29.6556 + 11.3633i −1.36791 + 0.524149i
\(471\) −8.05749 19.0351i −0.371270 0.877091i
\(472\) 5.96994 5.54696i 0.274789 0.255320i
\(473\) 12.9606 10.8752i 0.595930 0.500045i
\(474\) −17.9253 + 24.5893i −0.823337 + 1.12942i
\(475\) 26.0777 55.9237i 1.19652 2.56596i
\(476\) −13.7613 22.0816i −0.630747 1.01211i
\(477\) 14.1622 12.2614i 0.648441 0.561411i
\(478\) 8.44597 2.41635i 0.386310 0.110521i
\(479\) 0.0894240 0.507149i 0.00408589 0.0231722i −0.982697 0.185222i \(-0.940699\pi\)
0.986783 + 0.162050i \(0.0518106\pi\)
\(480\) 22.2649 29.3017i 1.01625 1.33743i
\(481\) 0.376002 + 0.136853i 0.0171442 + 0.00623998i
\(482\) 12.9885 19.2314i 0.591612 0.875965i
\(483\) 20.5790 + 0.739211i 0.936379 + 0.0336353i
\(484\) −0.776732 0.608354i −0.0353060 0.0276525i
\(485\) 2.21310 2.21310i 0.100492 0.100492i
\(486\) 21.9828 + 1.66080i 0.997158 + 0.0753356i
\(487\) −35.1405 −1.59237 −0.796184 0.605055i \(-0.793151\pi\)
−0.796184 + 0.605055i \(0.793151\pi\)
\(488\) −14.9298 + 19.7384i −0.675841 + 0.893515i
\(489\) −25.3289 + 23.5723i −1.14541 + 1.06598i
\(490\) −13.6688 70.5462i −0.617493 3.18695i
\(491\) 7.58555 + 16.2673i 0.342331 + 0.734131i 0.999813 0.0193391i \(-0.00615621\pi\)
−0.657482 + 0.753470i \(0.728378\pi\)
\(492\) −11.7091 9.86910i −0.527888 0.444934i
\(493\) −7.48258 10.6862i −0.336998 0.481283i
\(494\) 3.45839 0.989429i 0.155600 0.0445165i
\(495\) −38.1019 2.74082i −1.71255 0.123191i
\(496\) −31.9630 + 21.4477i −1.43518 + 0.963029i
\(497\) −4.08689 11.2286i −0.183322 0.503673i
\(498\) −22.1575 + 3.47309i −0.992903 + 0.155633i
\(499\) 12.4786 + 1.09174i 0.558619 + 0.0488729i 0.362970 0.931801i \(-0.381763\pi\)
0.195650 + 0.980674i \(0.437318\pi\)
\(500\) −1.65186 + 30.8107i −0.0738734 + 1.37789i
\(501\) −8.13337 3.29554i −0.363372 0.147234i
\(502\) 9.14697 + 23.8715i 0.408249 + 1.06544i
\(503\) 14.5390 8.39410i 0.648262 0.374274i −0.139528 0.990218i \(-0.544558\pi\)
0.787790 + 0.615944i \(0.211225\pi\)
\(504\) −38.3613 + 2.53603i −1.70875 + 0.112964i
\(505\) 3.26893 + 1.88732i 0.145466 + 0.0839846i
\(506\) −1.97554 + 12.4247i −0.0878232 + 0.552345i
\(507\) 4.65247 21.7812i 0.206624 0.967337i
\(508\) −15.5402 5.06997i −0.689484 0.224944i
\(509\) 2.11218 3.01651i 0.0936209 0.133705i −0.769609 0.638515i \(-0.779549\pi\)
0.863230 + 0.504811i \(0.168438\pi\)
\(510\) 13.6419 22.6218i 0.604072 1.00171i
\(511\) 0.757638 0.902918i 0.0335159 0.0399427i
\(512\) 18.2338 + 13.3989i 0.805826 + 0.592153i
\(513\) 5.40311 + 34.7881i 0.238553 + 1.53593i
\(514\) −13.8043 + 14.2776i −0.608882 + 0.629758i
\(515\) 15.8166 1.38377i 0.696962 0.0609763i
\(516\) 16.6889 + 4.51115i 0.734686 + 0.198592i
\(517\) −11.6260 + 16.6036i −0.511311 + 0.730227i
\(518\) 2.22728 6.45587i 0.0978609 0.283655i
\(519\) −8.83547 + 17.2979i −0.387834 + 0.759292i
\(520\) −3.14724 + 2.44977i −0.138016 + 0.107430i
\(521\) −10.6538 + 18.4529i −0.466752 + 0.808437i −0.999279 0.0379755i \(-0.987909\pi\)
0.532527 + 0.846413i \(0.321242\pi\)
\(522\) −19.1383 + 2.29943i −0.837660 + 0.100643i
\(523\) −20.9985 5.62654i −0.918202 0.246031i −0.231385 0.972862i \(-0.574326\pi\)
−0.686817 + 0.726831i \(0.740992\pi\)
\(524\) 35.3785 + 15.0675i 1.54552 + 0.658228i
\(525\) 56.3640 43.9458i 2.45993 1.91795i
\(526\) −3.06551 + 43.4634i −0.133662 + 1.89509i
\(527\) −21.1663 + 17.7606i −0.922019 + 0.773666i
\(528\) 1.30906 23.4513i 0.0569697 1.02059i
\(529\) −15.1426 + 5.51146i −0.658374 + 0.239629i
\(530\) −32.1776 8.04332i −1.39771 0.349380i
\(531\) −3.08143 8.07557i −0.133723 0.350450i
\(532\) −17.8794 58.7333i −0.775170 2.54641i
\(533\) 0.951904 + 1.35946i 0.0412315 + 0.0588847i
\(534\) 3.36597 6.87333i 0.145660 0.297438i
\(535\) −27.4675 9.99736i −1.18752 0.432223i
\(536\) 0.694101 + 3.03141i 0.0299806 + 0.130937i
\(537\) 5.68879 18.5409i 0.245489 0.800101i
\(538\) −21.6355 + 26.6848i −0.932774 + 1.15046i
\(539\) −32.4298 32.4298i −1.39685 1.39685i
\(540\) −19.9630 33.5422i −0.859072 1.44343i
\(541\) 20.2882 20.2882i 0.872260 0.872260i −0.120458 0.992718i \(-0.538436\pi\)
0.992718 + 0.120458i \(0.0384365\pi\)
\(542\) 6.43859 0.672811i 0.276561 0.0288997i
\(543\) 3.92606 + 17.0835i 0.168484 + 0.733121i
\(544\) 14.0420 + 8.16354i 0.602047 + 0.350009i
\(545\) 17.0413 46.8207i 0.729970 2.00558i
\(546\) 4.08865 + 0.801542i 0.174978 + 0.0343028i
\(547\) 8.73168 6.11399i 0.373340 0.261415i −0.371815 0.928307i \(-0.621264\pi\)
0.745155 + 0.666892i \(0.232376\pi\)
\(548\) −4.27370 2.27896i −0.182564 0.0973525i
\(549\) 13.4748 + 22.5277i 0.575091 + 0.961457i
\(550\) 22.4666 + 37.4417i 0.957981 + 1.59652i
\(551\) −10.5282 28.9261i −0.448518 1.23229i
\(552\) −11.5698 + 5.60291i −0.492445 + 0.238476i
\(553\) −36.1793 43.1168i −1.53850 1.83351i
\(554\) 26.5113 + 30.5348i 1.12636 + 1.29730i
\(555\) 6.86726 0.958138i 0.291499 0.0406707i
\(556\) 33.0561 + 14.0784i 1.40189 + 0.597057i
\(557\) −1.35347 + 5.05120i −0.0573482 + 0.214026i −0.988654 0.150213i \(-0.952004\pi\)
0.931306 + 0.364239i \(0.118671\pi\)
\(558\) 8.38461 + 39.9567i 0.354949 + 1.69150i
\(559\) −1.62255 0.936781i −0.0686266 0.0396216i
\(560\) 42.7108 + 53.0035i 1.80486 + 2.23981i
\(561\) −0.865583 16.8380i −0.0365450 0.710901i
\(562\) −0.211868 0.435057i −0.00893711 0.0183518i
\(563\) 29.7731 + 20.8473i 1.25479 + 0.878610i 0.996176 0.0873720i \(-0.0278469\pi\)
0.258609 + 0.965982i \(0.416736\pi\)
\(564\) −20.7112 0.0455778i −0.872100 0.00191917i
\(565\) 0.705763 + 8.06690i 0.0296917 + 0.339377i
\(566\) −27.9755 + 0.471496i −1.17590 + 0.0198184i
\(567\) −12.7556 + 38.7307i −0.535687 + 1.62654i
\(568\) 5.53450 + 5.00139i 0.232223 + 0.209854i
\(569\) −19.7591 16.5799i −0.828346 0.695065i 0.126565 0.991958i \(-0.459605\pi\)
−0.954911 + 0.296894i \(0.904049\pi\)
\(570\) 44.9084 43.2290i 1.88101 1.81066i
\(571\) 36.8960 + 25.8349i 1.54405 + 1.08116i 0.963768 + 0.266740i \(0.0859467\pi\)
0.580282 + 0.814415i \(0.302942\pi\)
\(572\) −0.789509 + 2.41996i −0.0330110 + 0.101183i
\(573\) −11.3648 + 12.5966i −0.474773 + 0.526231i
\(574\) 22.9256 16.6353i 0.956894 0.694346i
\(575\) 11.9491 20.6965i 0.498313 0.863103i
\(576\) 20.4241 12.6038i 0.851004 0.525159i
\(577\) 3.29626 + 5.70928i 0.137225 + 0.237680i 0.926445 0.376430i \(-0.122848\pi\)
−0.789220 + 0.614110i \(0.789515\pi\)
\(578\) −11.3087 5.04310i −0.470380 0.209765i
\(579\) −18.4016 + 2.56745i −0.764746 + 0.106699i
\(580\) 22.8068 + 25.3908i 0.946999 + 1.05429i
\(581\) 3.61566 41.3271i 0.150003 1.71454i
\(582\) 1.86598 0.827214i 0.0773474 0.0342891i
\(583\) −19.8923 + 7.24019i −0.823853 + 0.299858i
\(584\) −0.154281 + 0.719452i −0.00638418 + 0.0297711i
\(585\) 1.15789 + 4.06868i 0.0478727 + 0.168219i
\(586\) −2.40115 + 4.32565i −0.0991905 + 0.178691i
\(587\) 11.7319 8.21474i 0.484226 0.339058i −0.305838 0.952084i \(-0.598937\pi\)
0.790063 + 0.613025i \(0.210048\pi\)
\(588\) 8.23917 46.1328i 0.339778 1.90248i
\(589\) −59.0895 + 27.5539i −2.43474 + 1.13534i
\(590\) −8.56556 + 12.6825i −0.352638 + 0.522131i
\(591\) 40.5740 9.32459i 1.66899 0.383562i
\(592\) 0.656801 + 4.21240i 0.0269943 + 0.173128i
\(593\) 17.4258i 0.715592i −0.933800 0.357796i \(-0.883528\pi\)
0.933800 0.357796i \(-0.116472\pi\)
\(594\) −22.5405 10.6097i −0.924847 0.435320i
\(595\) 34.5513 + 34.5513i 1.41646 + 1.41646i
\(596\) −2.41919 19.9005i −0.0990939 0.815154i
\(597\) −6.18851 + 3.28257i −0.253279 + 0.134346i
\(598\) 1.36773 0.265007i 0.0559307 0.0108369i
\(599\) 3.91365 10.7527i 0.159907 0.439342i −0.833702 0.552214i \(-0.813783\pi\)
0.993609 + 0.112873i \(0.0360052\pi\)
\(600\) −18.2615 + 40.7088i −0.745524 + 1.66193i
\(601\) −9.47924 1.67145i −0.386666 0.0681797i −0.0230640 0.999734i \(-0.507342\pi\)
−0.363602 + 0.931554i \(0.618453\pi\)
\(602\) −15.5196 + 27.9585i −0.632532 + 1.13950i
\(603\) 3.25686 + 0.522505i 0.132629 + 0.0212780i
\(604\) 19.9278 12.4190i 0.810852 0.505322i
\(605\) 1.67926 + 0.783050i 0.0682715 + 0.0318355i
\(606\) 1.54611 + 1.91554i 0.0628063 + 0.0778135i
\(607\) 14.3202 + 17.0662i 0.581240 + 0.692694i 0.973897 0.226990i \(-0.0728886\pi\)
−0.392657 + 0.919685i \(0.628444\pi\)
\(608\) 27.0194 + 27.1823i 1.09578 + 1.10239i
\(609\) 4.38053 35.3844i 0.177508 1.43385i
\(610\) 18.9299 42.4485i 0.766447 1.71869i
\(611\) 2.16810 + 0.580940i 0.0877118 + 0.0235023i
\(612\) 13.6096 10.5631i 0.550136 0.426986i
\(613\) 25.8790 6.93426i 1.04524 0.280072i 0.304958 0.952366i \(-0.401357\pi\)
0.740284 + 0.672294i \(0.234691\pi\)
\(614\) −2.35109 0.373824i −0.0948821 0.0150863i
\(615\) 25.6111 + 13.0817i 1.03274 + 0.527506i
\(616\) 41.5239 + 12.7770i 1.67305 + 0.514802i
\(617\) 0.890714 + 5.05149i 0.0358588 + 0.203365i 0.997474 0.0710374i \(-0.0226310\pi\)
−0.961615 + 0.274403i \(0.911520\pi\)
\(618\) 9.94860 + 2.86994i 0.400191 + 0.115446i
\(619\) −38.1435 + 3.33712i −1.53312 + 0.134130i −0.822221 0.569168i \(-0.807265\pi\)
−0.710895 + 0.703299i \(0.751710\pi\)
\(620\) 49.3636 52.8086i 1.98249 2.12084i
\(621\) 0.910371 + 13.6045i 0.0365319 + 0.545929i
\(622\) −12.5234 + 12.9528i −0.502144 + 0.519360i
\(623\) 10.8442 + 9.09941i 0.434466 + 0.364560i
\(624\) −2.48992 + 0.751989i −0.0996764 + 0.0301036i
\(625\) −2.15465 12.2196i −0.0861862 0.488786i
\(626\) −3.09840 + 1.50889i −0.123837 + 0.0603073i
\(627\) 8.31040 38.9063i 0.331885 1.55377i
\(628\) −19.0790 + 14.3411i −0.761336 + 0.572274i
\(629\) 0.792067 + 2.95604i 0.0315818 + 0.117865i
\(630\) 69.0994 20.9297i 2.75299 0.833858i
\(631\) −13.4648 23.3217i −0.536026 0.928424i −0.999113 0.0421111i \(-0.986592\pi\)
0.463087 0.886313i \(-0.346742\pi\)
\(632\) 32.5546 + 13.2212i 1.29495 + 0.525912i
\(633\) 35.1314 14.8710i 1.39635 0.591070i
\(634\) −13.8353 15.9350i −0.549471 0.632862i
\(635\) 30.5815 + 2.67553i 1.21359 + 0.106175i
\(636\) −17.6913 12.4457i −0.701506 0.493504i
\(637\) −2.14637 + 4.60290i −0.0850422 + 0.182374i
\(638\) 21.1327 + 5.28247i 0.836653 + 0.209135i
\(639\) 7.11820 3.45420i 0.281592 0.136646i
\(640\) −39.0459 16.7682i −1.54342 0.662821i
\(641\) 26.6970 + 4.70740i 1.05447 + 0.185931i 0.673900 0.738822i \(-0.264618\pi\)
0.380567 + 0.924753i \(0.375729\pi\)
\(642\) −14.3668 12.5293i −0.567013 0.494491i
\(643\) −3.06621 6.57551i −0.120920 0.259313i 0.836526 0.547928i \(-0.184583\pi\)
−0.957445 + 0.288615i \(0.906805\pi\)
\(644\) −4.91575 23.2643i −0.193708 0.916741i
\(645\) −32.4455 1.16546i −1.27754 0.0458899i
\(646\) 21.3703 + 17.3266i 0.840804 + 0.681707i
\(647\) 43.3886i 1.70578i 0.522089 + 0.852891i \(0.325153\pi\)
−0.522089 + 0.852891i \(0.674847\pi\)
\(648\) −4.27495 25.0943i −0.167936 0.985798i
\(649\) 9.76767i 0.383414i
\(650\) 3.04525 3.75596i 0.119445 0.147321i
\(651\) −75.4685 2.71087i −2.95784 0.106247i
\(652\) 33.4816 + 21.8004i 1.31124 + 0.853771i
\(653\) 8.26652 + 17.7276i 0.323494 + 0.693735i 0.999050 0.0435734i \(-0.0138742\pi\)
−0.675556 + 0.737308i \(0.736096\pi\)
\(654\) 21.3572 24.4894i 0.835132 0.957612i
\(655\) −71.1183 12.5401i −2.77882 0.489981i
\(656\) −7.78967 + 15.8742i −0.304136 + 0.619784i
\(657\) 0.646143 + 0.437709i 0.0252085 + 0.0170767i
\(658\) 9.29023 37.1659i 0.362171 1.44888i
\(659\) −19.0534 + 40.8601i −0.742214 + 1.59168i 0.0625175 + 0.998044i \(0.480087\pi\)
−0.804731 + 0.593639i \(0.797691\pi\)
\(660\) 7.56401 + 43.4566i 0.294429 + 1.69155i
\(661\) −38.6092 3.37787i −1.50172 0.131384i −0.693585 0.720375i \(-0.743970\pi\)
−0.808140 + 0.588991i \(0.799525\pi\)
\(662\) 10.4816 9.10049i 0.407380 0.353701i
\(663\) −1.71937 + 0.727805i −0.0667749 + 0.0282656i
\(664\) 10.0760 + 23.8572i 0.391026 + 0.925838i
\(665\) 57.6491 + 99.8513i 2.23554 + 3.87207i
\(666\) 4.40335 + 1.02865i 0.170626 + 0.0398594i
\(667\) −3.08564 11.5158i −0.119476 0.445892i
\(668\) −1.42234 + 10.0329i −0.0550319 + 0.388186i
\(669\) −7.58285 + 35.5001i −0.293170 + 1.37251i
\(670\) −2.55706 5.25076i −0.0987879 0.202854i
\(671\) −5.15112 29.2135i −0.198857 1.12777i
\(672\) 13.5489 + 42.2744i 0.522660 + 1.63077i
\(673\) 11.2740 + 9.46002i 0.434581 + 0.364657i 0.833677 0.552252i \(-0.186231\pi\)
−0.399096 + 0.916909i \(0.630676\pi\)
\(674\) 24.6790 + 23.8609i 0.950598 + 0.919087i
\(675\) 32.7716 + 34.1401i 1.26138 + 1.31405i
\(676\) −25.7035 + 0.866653i −0.988597 + 0.0333328i
\(677\) −13.7083 + 1.19932i −0.526854 + 0.0460938i −0.347480 0.937687i \(-0.612963\pi\)
−0.179374 + 0.983781i \(0.557407\pi\)
\(678\) −1.46375 + 5.07407i −0.0562151 + 0.194868i
\(679\) 0.655598 + 3.71808i 0.0251595 + 0.142687i
\(680\) −29.1545 8.97094i −1.11802 0.344020i
\(681\) −29.5799 15.1089i −1.13350 0.578975i
\(682\) 7.24478 45.5645i 0.277417 1.74475i
\(683\) 19.3369 5.18132i 0.739907 0.198258i 0.130870 0.991399i \(-0.458223\pi\)
0.609037 + 0.793142i \(0.291556\pi\)
\(684\) 37.4704 15.7640i 1.43272 0.602751i
\(685\) 8.78588 + 2.35417i 0.335691 + 0.0899482i
\(686\) 38.2024 + 17.0363i 1.45858 + 0.650451i
\(687\) 0.520546 4.20479i 0.0198601 0.160423i
\(688\) 0.396372 19.9583i 0.0151116 0.760903i
\(689\) 1.50682 + 1.79576i 0.0574053 + 0.0684130i
\(690\) 18.7860 15.1629i 0.715170 0.577241i
\(691\) −35.9683 16.7723i −1.36830 0.638047i −0.406966 0.913443i \(-0.633413\pi\)
−0.961331 + 0.275396i \(0.911191\pi\)
\(692\) 21.8477 + 5.07161i 0.830524 + 0.192794i
\(693\) 29.0709 35.7534i 1.10431 1.35816i
\(694\) −14.3056 7.94097i −0.543033 0.301435i
\(695\) −66.4496 11.7169i −2.52058 0.444446i
\(696\) 7.91828 + 20.8018i 0.300142 + 0.788492i
\(697\) −4.34126 + 11.9275i −0.164437 + 0.451787i
\(698\) −3.17981 16.4114i −0.120358 0.621179i
\(699\) 17.4420 9.25173i 0.659716 0.349933i
\(700\) −64.9717 50.8873i −2.45570 1.92336i
\(701\) 30.5858 + 30.5858i 1.15521 + 1.15521i 0.985493 + 0.169717i \(0.0542855\pi\)
0.169717 + 0.985493i \(0.445715\pi\)
\(702\) −0.250326 + 2.74739i −0.00944794 + 0.103694i
\(703\) 7.22120i 0.272353i
\(704\) −26.6416 + 5.07897i −1.00409 + 0.191421i
\(705\) 37.9075 8.71177i 1.42768 0.328104i
\(706\) 11.9989 + 8.10385i 0.451584 + 0.304992i
\(707\) −4.12669 + 1.92431i −0.155200 + 0.0723710i
\(708\) −8.18825 + 5.70666i −0.307733 + 0.214469i
\(709\) −37.2519 + 26.0841i −1.39903 + 0.979608i −0.401047 + 0.916057i \(0.631354\pi\)
−0.997979 + 0.0635512i \(0.979757\pi\)
\(710\) −12.2484 6.79904i −0.459675 0.255163i
\(711\) 25.9422 26.7568i 0.972909 1.00346i
\(712\) −8.64079 1.85295i −0.323827 0.0694421i
\(713\) −23.7283 + 8.63639i −0.888631 + 0.323435i
\(714\) 12.9146 + 29.1320i 0.483316 + 1.09024i
\(715\) 0.416640 4.76222i 0.0155815 0.178097i
\(716\) −22.3622 1.19891i −0.835715 0.0448054i
\(717\) −10.6560 + 1.48675i −0.397954 + 0.0555236i
\(718\) 17.5944 39.4538i 0.656616 1.47240i
\(719\) −11.0871 19.2033i −0.413477 0.716164i 0.581790 0.813339i \(-0.302353\pi\)
−0.995267 + 0.0971753i \(0.969019\pi\)
\(720\) −32.0106 + 31.7300i −1.19296 + 1.18251i
\(721\) −9.57611 + 16.5863i −0.356633 + 0.617706i
\(722\) 22.3454 + 30.7947i 0.831610 + 1.14606i
\(723\) −19.0392 + 21.1028i −0.708077 + 0.784822i
\(724\) 18.0455 9.16731i 0.670654 0.340701i
\(725\) −33.8953 23.7338i −1.25884 0.881449i
\(726\) 0.837999 + 0.870556i 0.0311011 + 0.0323094i
\(727\) 36.8865 + 30.9515i 1.36805 + 1.14793i 0.973405 + 0.229092i \(0.0735756\pi\)
0.394641 + 0.918835i \(0.370869\pi\)
\(728\) −0.243127 4.80488i −0.00901087 0.178081i
\(729\) −26.3759 5.77175i −0.976884 0.213768i
\(730\) −0.0232861 1.38165i −0.000861857 0.0511371i
\(731\) −1.24890 14.2749i −0.0461921 0.527978i
\(732\) 21.4802 21.3859i 0.793931 0.790444i
\(733\) 23.3789 + 16.3701i 0.863518 + 0.604642i 0.919193 0.393807i \(-0.128842\pi\)
−0.0556750 + 0.998449i \(0.517731\pi\)
\(734\) −18.0589 + 8.79448i −0.666566 + 0.324610i
\(735\) 4.51822 + 87.8919i 0.166657 + 3.24194i
\(736\) 9.50719 + 11.3996i 0.350440 + 0.420196i
\(737\) −3.22811 1.86375i −0.118909 0.0686522i
\(738\) 12.5134 + 13.9703i 0.460623 + 0.514254i
\(739\) −2.60066 + 9.70580i −0.0956669 + 0.357034i −0.997120 0.0758436i \(-0.975835\pi\)
0.901453 + 0.432877i \(0.142502\pi\)
\(740\) −2.99034 7.42704i −0.109927 0.273023i
\(741\) −4.36332 + 0.608782i −0.160291 + 0.0223642i
\(742\) 30.2115 26.2306i 1.10910 0.962955i
\(743\) 0.567275 + 0.676052i 0.0208113 + 0.0248019i 0.776350 0.630302i \(-0.217069\pi\)
−0.755538 + 0.655104i \(0.772625\pi\)
\(744\) 42.4295 20.5473i 1.55554 0.753300i
\(745\) 12.8764 + 35.3776i 0.471755 + 1.29613i
\(746\) −19.0316 + 11.4198i −0.696797 + 0.418108i
\(747\) 27.4654 0.424543i 1.00491 0.0155332i
\(748\) −18.6247 + 5.66966i −0.680986 + 0.207303i
\(749\) 28.8834 20.2244i 1.05538 0.738983i
\(750\) 7.26989 37.0835i 0.265459 1.35410i
\(751\) 5.67720 15.5980i 0.207164 0.569179i −0.791980 0.610547i \(-0.790950\pi\)
0.999144 + 0.0413686i \(0.0131718\pi\)
\(752\) 5.72984 + 23.2188i 0.208946 + 0.846702i
\(753\) −7.01261 30.5139i −0.255554 1.11199i
\(754\) −0.250701 2.39913i −0.00913000 0.0873713i
\(755\) −31.1812 + 31.1812i −1.13480 + 1.13480i
\(756\) 46.9565 + 3.48166i 1.70779 + 0.126627i
\(757\) 1.01715 + 1.01715i 0.0369689 + 0.0369689i 0.725350 0.688381i \(-0.241678\pi\)
−0.688381 + 0.725350i \(0.741678\pi\)
\(758\) −15.3213 12.4222i −0.556493 0.451193i
\(759\) 4.51965 14.7305i 0.164053 0.534682i
\(760\) −60.9710 38.2520i −2.21165 1.38754i
\(761\) 36.0640 + 13.1262i 1.30732 + 0.475825i 0.899373 0.437181i \(-0.144023\pi\)
0.407945 + 0.913006i \(0.366245\pi\)
\(762\) 17.9799 + 8.80499i 0.651342 + 0.318971i
\(763\) 34.4742 + 49.2342i 1.24805 + 1.78240i
\(764\) 17.2861 + 9.21787i 0.625390 + 0.333491i
\(765\) −20.4111 + 25.1029i −0.737965 + 0.907599i
\(766\) −4.56393 + 18.2582i −0.164902 + 0.659695i
\(767\) 1.01642 0.369946i 0.0367008 0.0133580i
\(768\) −19.8228 19.3664i −0.715294 0.698824i
\(769\) −8.27991 + 6.94767i −0.298581 + 0.250539i −0.779754 0.626087i \(-0.784656\pi\)
0.481172 + 0.876626i \(0.340211\pi\)
\(770\) −81.3876 5.74034i −2.93301 0.206867i
\(771\) 19.1818 14.9557i 0.690816 0.538615i
\(772\) 8.01297 + 19.9016i 0.288393 + 0.716276i
\(773\) 38.8377 + 10.4065i 1.39690 + 0.374297i 0.877229 0.480072i \(-0.159389\pi\)
0.519667 + 0.854369i \(0.326056\pi\)
\(774\) −19.4684 8.32362i −0.699778 0.299186i
\(775\) −43.8204 + 75.8992i −1.57408 + 2.72638i
\(776\) −1.44769 1.85986i −0.0519690 0.0667651i
\(777\) −3.80467 + 7.44869i −0.136492 + 0.267220i
\(778\) −4.95425 1.70922i −0.177618 0.0612784i
\(779\) −17.1790 + 24.5342i −0.615503 + 0.879029i
\(780\) 4.23559 2.43301i 0.151659 0.0871157i
\(781\) −8.90704 + 0.779265i −0.318719 + 0.0278843i
\(782\) 7.66033 + 7.40640i 0.273933 + 0.264852i
\(783\) 23.6032 + 0.482729i 0.843508 + 0.0172513i
\(784\) −53.9896 + 3.64491i −1.92820 + 0.130175i
\(785\) 28.8122 34.3370i 1.02835 1.22554i
\(786\) −40.3301 24.3206i −1.43853 0.867488i
\(787\) 16.2571 23.2175i 0.579502 0.827614i −0.417196 0.908817i \(-0.636987\pi\)
0.996698 + 0.0812023i \(0.0258760\pi\)
\(788\) −21.7728 42.8588i −0.775624 1.52678i
\(789\) 11.1471 52.1866i 0.396846 1.85789i
\(790\) −65.1682 10.3618i −2.31858 0.368656i
\(791\) −8.45948 4.88408i −0.300785 0.173658i
\(792\) −5.59620 + 28.2170i −0.198852 + 1.00265i
\(793\) −2.84484 + 1.64247i −0.101023 + 0.0583259i
\(794\) −2.50441 + 0.959625i −0.0888780 + 0.0340558i
\(795\) 37.6488 + 15.2548i 1.33526 + 0.541033i
\(796\) 5.40531 + 6.01773i 0.191586 + 0.213293i
\(797\) −43.9492 3.84506i −1.55676 0.136199i −0.723987 0.689813i \(-0.757693\pi\)
−0.832773 + 0.553614i \(0.813248\pi\)
\(798\) 11.6439 + 74.2855i 0.412189 + 2.62968i
\(799\) 5.87149 + 16.1318i 0.207719 + 0.570702i
\(800\) 50.7096 + 9.09868i 1.79286 + 0.321687i
\(801\) −5.25699 + 7.76033i −0.185747 + 0.274198i
\(802\) −0.586732 2.05083i −0.0207182 0.0724173i
\(803\) −0.505864 0.722448i −0.0178515 0.0254946i
\(804\) −0.323607 3.79501i −0.0114127 0.133840i
\(805\) 18.8719 + 40.4710i 0.665149 + 1.42642i
\(806\) −5.01581 + 0.971847i −0.176674 + 0.0342318i
\(807\) 30.8000 28.6640i 1.08421 1.00902i
\(808\) 1.71473 2.26701i 0.0603241 0.0797532i
\(809\) −28.3126 −0.995420 −0.497710 0.867344i \(-0.665826\pi\)
−0.497710 + 0.867344i \(0.665826\pi\)
\(810\) 18.4768 + 44.0909i 0.649210 + 1.54920i
\(811\) 31.9185 31.9185i 1.12081 1.12081i 0.129191 0.991620i \(-0.458762\pi\)
0.991620 0.129191i \(-0.0412381\pi\)
\(812\) −40.8694 + 4.96827i −1.43423 + 0.174352i
\(813\) −7.92346 0.284615i −0.277888 0.00998189i
\(814\) −4.23468 2.86003i −0.148425 0.100244i
\(815\) −70.5072 25.6625i −2.46976 0.898919i
\(816\) −15.6342 12.3007i −0.547305 0.430609i
\(817\) 5.87143 33.2985i 0.205415 1.16497i
\(818\) −10.4696 36.5948i −0.366060 1.27951i
\(819\) −4.82153 1.67096i −0.168478 0.0583882i
\(820\) 7.50897 32.3475i 0.262225 1.12962i
\(821\) 12.0908 25.9287i 0.421970 0.904918i −0.574301 0.818644i \(-0.694726\pi\)
0.996271 0.0862742i \(-0.0274961\pi\)
\(822\) 4.79342 + 3.49435i 0.167190 + 0.121879i
\(823\) −13.6967 + 11.4929i −0.477436 + 0.400617i −0.849498 0.527591i \(-0.823095\pi\)
0.372062 + 0.928208i \(0.378651\pi\)
\(824\) 0.438806 11.9480i 0.0152865 0.416230i
\(825\) −20.8465 49.2480i −0.725783 1.71460i
\(826\) −6.60551 17.2389i −0.229835 0.599818i
\(827\) −1.58874 + 5.92926i −0.0552460 + 0.206181i −0.988032 0.154250i \(-0.950704\pi\)
0.932786 + 0.360431i \(0.117370\pi\)
\(828\) 14.9891 4.81730i 0.520908 0.167413i
\(829\) 4.36652 + 16.2961i 0.151656 + 0.565986i 0.999369 + 0.0355312i \(0.0113123\pi\)
−0.847713 + 0.530455i \(0.822021\pi\)
\(830\) −28.5637 39.3643i −0.991461 1.36636i
\(831\) −26.9324 41.5630i −0.934274 1.44181i
\(832\) 1.53756 + 2.57995i 0.0533051 + 0.0894437i
\(833\) −38.2533 + 6.74510i −1.32540 + 0.233704i
\(834\) −37.6825 22.7241i −1.30484 0.786870i
\(835\) −1.65859 18.9578i −0.0573979 0.656061i
\(836\) −45.9124 + 1.54804i −1.58791 + 0.0535402i
\(837\) −3.33856 49.8910i −0.115397 1.72448i
\(838\) 43.9749 0.741147i 1.51909 0.0256025i
\(839\) 18.2327 21.7289i 0.629463 0.750165i −0.353204 0.935546i \(-0.614908\pi\)
0.982667 + 0.185382i \(0.0593522\pi\)
\(840\) −42.7378 71.5811i −1.47459 2.46978i
\(841\) 8.23072 1.45130i 0.283818 0.0500447i
\(842\) 13.1750 38.1885i 0.454042 1.31606i
\(843\) 0.182579 + 0.563835i 0.00628834 + 0.0194195i
\(844\) −26.4682 35.2125i −0.911073 1.21206i
\(845\) 46.6527 12.5006i 1.60490 0.430032i
\(846\) 25.1099 + 3.59552i 0.863297 + 0.123617i
\(847\) −1.93563 + 1.11754i −0.0665090 + 0.0383990i
\(848\) −9.00690 + 23.2962i −0.309298 + 0.799995i
\(849\) 34.0081 + 4.21015i 1.16716 + 0.144492i
\(850\) 36.8905 + 2.60191i 1.26533 + 0.0892449i
\(851\) −0.243754 + 2.78612i −0.00835577 + 0.0955069i
\(852\) −5.85711 7.01151i −0.200661 0.240210i
\(853\) −6.00566 2.80048i −0.205630 0.0958868i 0.317075 0.948400i \(-0.397299\pi\)
−0.522705 + 0.852514i \(0.675077\pi\)
\(854\) 28.8472 + 48.0752i 0.987130 + 1.64510i
\(855\) −61.8523 + 44.7499i −2.11531 + 1.53041i
\(856\) −10.0285 + 19.5946i −0.342766 + 0.669728i
\(857\) 7.78416 44.1461i 0.265902 1.50800i −0.500553 0.865706i \(-0.666870\pi\)
0.766455 0.642298i \(-0.222019\pi\)
\(858\) 1.37113 2.79987i 0.0468098 0.0955859i
\(859\) 26.9601 12.5717i 0.919868 0.428941i 0.0957793 0.995403i \(-0.469466\pi\)
0.824088 + 0.566461i \(0.191688\pi\)
\(860\) 7.75031 + 36.6791i 0.264283 + 1.25075i
\(861\) −30.6467 + 16.2559i −1.04444 + 0.554000i
\(862\) −3.74629 35.8508i −0.127599 1.22108i
\(863\) 47.3978 1.61344 0.806720 0.590934i \(-0.201241\pi\)
0.806720 + 0.590934i \(0.201241\pi\)
\(864\) −26.9239 + 11.7942i −0.915970 + 0.401247i
\(865\) −42.1208 −1.43215
\(866\) −0.795390 7.61163i −0.0270284 0.258654i
\(867\) 12.8527 + 8.04910i 0.436500 + 0.273362i
\(868\) 18.0273 + 85.3159i 0.611886 + 2.89581i
\(869\) −38.1695 + 17.7987i −1.29481 + 0.603780i
\(870\) −23.3189 34.6913i −0.790586 1.17615i
\(871\) −0.0716778 + 0.406505i −0.00242871 + 0.0137739i
\(872\) −33.4006 17.0944i −1.13109 0.578888i
\(873\) −2.40438 + 0.684252i −0.0813760 + 0.0231584i
\(874\) 12.9364 + 21.5592i 0.437581 + 0.729249i
\(875\) 63.3497 + 29.5405i 2.14161 + 0.998650i
\(876\) 0.310084 0.846150i 0.0104768 0.0285887i
\(877\) 4.27306 48.8413i 0.144291 1.64925i −0.486776 0.873527i \(-0.661827\pi\)
0.631068 0.775728i \(-0.282617\pi\)
\(878\) 15.3421 + 1.08209i 0.517772 + 0.0365189i
\(879\) 3.65141 4.83553i 0.123159 0.163098i
\(880\) 46.5801 20.6047i 1.57021 0.694586i
\(881\) −36.9760 + 21.3481i −1.24575 + 0.719236i −0.970260 0.242067i \(-0.922175\pi\)
−0.275494 + 0.961303i \(0.588841\pi\)
\(882\) −17.8778 + 54.5396i −0.601976 + 1.83644i
\(883\) 5.96743 1.59897i 0.200820 0.0538096i −0.157007 0.987598i \(-0.550184\pi\)
0.357827 + 0.933788i \(0.383518\pi\)
\(884\) 1.29538 + 1.72334i 0.0435685 + 0.0579622i
\(885\) 12.5558 13.9167i 0.422059 0.467804i
\(886\) −0.473302 + 1.37189i −0.0159009 + 0.0460895i
\(887\) −37.5007 + 6.61238i −1.25915 + 0.222022i −0.763105 0.646275i \(-0.776326\pi\)
−0.496045 + 0.868297i \(0.665215\pi\)
\(888\) −0.0765000 5.22089i −0.00256717 0.175201i
\(889\) −23.8030 + 28.3673i −0.798328 + 0.951410i
\(890\) 16.5939 0.279671i 0.556229 0.00937460i
\(891\) 25.5226 + 16.7199i 0.855039 + 0.560137i
\(892\) 41.8929 1.41252i 1.40268 0.0472945i
\(893\) 3.53050 + 40.3538i 0.118144 + 1.35039i
\(894\) −0.467766 + 24.5480i −0.0156444 + 0.821007i
\(895\) 41.4174 7.30301i 1.38443 0.244113i
\(896\) 43.5849 26.9806i 1.45607 0.901358i
\(897\) −1.70403 + 0.0875980i −0.0568958 + 0.00292481i
\(898\) 26.2664 + 36.1983i 0.876519 + 1.20795i
\(899\) 11.3158 + 42.2312i 0.377404 + 1.40849i
\(900\) 29.1053 46.2484i 0.970178 1.54161i
\(901\) −4.64037 + 17.3181i −0.154593 + 0.576950i
\(902\) −7.58349 19.7912i −0.252503 0.658975i
\(903\) 23.6006 31.2540i 0.785378 1.04007i
\(904\) 6.09384 + 0.223803i 0.202678 + 0.00744359i
\(905\) −29.1185 + 24.4333i −0.967932 + 0.812192i
\(906\) −26.2904 + 11.6549i −0.873442 + 0.387208i
\(907\) 2.96418 6.35670i 0.0984239 0.211071i −0.850930 0.525279i \(-0.823961\pi\)
0.949354 + 0.314208i \(0.101739\pi\)
\(908\) −8.67260 + 37.3602i −0.287810 + 1.23984i
\(909\) −1.54762 2.58737i −0.0513314 0.0858176i
\(910\) 2.48519 + 8.68657i 0.0823831 + 0.287957i
\(911\) −7.10211 + 40.2781i −0.235303 + 1.33447i 0.606670 + 0.794954i \(0.292505\pi\)
−0.841974 + 0.539519i \(0.818606\pi\)
\(912\) −28.1216 37.5840i −0.931199 1.24453i
\(913\) −29.1692 10.6167i −0.965360 0.351362i
\(914\) 24.7664 + 16.7268i 0.819198 + 0.553273i
\(915\) −30.2132 + 48.2440i −0.998817 + 1.59490i
\(916\) −4.85659 + 0.590389i −0.160466 + 0.0195070i
\(917\) 61.5978 61.5978i 2.03414 2.03414i
\(918\) −18.3108 + 10.4841i −0.604345 + 0.346027i
\(919\) −22.1295 −0.729985 −0.364992 0.931011i \(-0.618928\pi\)
−0.364992 + 0.931011i \(0.618928\pi\)
\(920\) −22.2329 16.8166i −0.732997 0.554428i
\(921\) 2.78740 + 0.855238i 0.0918479 + 0.0281810i
\(922\) −5.94296 + 1.15149i −0.195721 + 0.0379222i
\(923\) 0.418440 + 0.897348i 0.0137731 + 0.0295366i
\(924\) −48.1744 22.5933i −1.58482 0.743265i
\(925\) 5.56766 + 7.95144i 0.183063 + 0.261442i
\(926\) 8.28765 + 28.9682i 0.272349 + 0.951953i
\(927\) −11.5747 5.18110i −0.380162 0.170170i
\(928\) 21.0974 14.6783i 0.692557 0.481839i
\(929\) 0.359891 + 0.988793i 0.0118076 + 0.0324412i 0.945456 0.325749i \(-0.105616\pi\)
−0.933649 + 0.358190i \(0.883394\pi\)
\(930\) −68.8929 + 55.6061i −2.25909 + 1.82340i
\(931\) −91.3074 7.98836i −2.99248 0.261808i
\(932\) −15.2346 16.9607i −0.499025 0.555565i
\(933\) 17.4020 13.5679i 0.569714 0.444194i
\(934\) −26.2250 + 10.0487i −0.858107 + 0.328805i
\(935\) 31.6634 18.2809i 1.03550 0.597849i
\(936\) 3.14820 0.486370i 0.102902 0.0158975i
\(937\) 30.4793 + 17.5972i 0.995715 + 0.574876i 0.906978 0.421179i \(-0.138384\pi\)
0.0887372 + 0.996055i \(0.471717\pi\)
\(938\) 6.95767 + 1.10627i 0.227176 + 0.0361211i
\(939\) 4.01553 1.30029i 0.131042 0.0424335i
\(940\) −20.3419 40.0421i −0.663479 1.30603i
\(941\) −8.67754 + 12.3928i −0.282880 + 0.403994i −0.935296 0.353867i \(-0.884867\pi\)
0.652416 + 0.757861i \(0.273756\pi\)
\(942\) 25.5896 14.1311i 0.833755 0.460416i
\(943\) −7.45625 + 8.88602i −0.242809 + 0.289368i
\(944\) 8.67957 + 7.58175i 0.282496 + 0.246765i
\(945\) −87.3785 + 13.5712i −2.84242 + 0.441471i
\(946\) 17.2016 + 16.6314i 0.559272 + 0.540733i
\(947\) 31.2942 2.73788i 1.01692 0.0889693i 0.433513 0.901147i \(-0.357274\pi\)
0.583410 + 0.812178i \(0.301718\pi\)
\(948\) −37.2208 21.5988i −1.20888 0.701497i
\(949\) −0.0560183 + 0.0800024i −0.00181843 + 0.00259699i
\(950\) 82.4927 + 28.4600i 2.67642 + 0.923364i
\(951\) 14.0551 + 21.6903i 0.455766 + 0.703355i
\(952\) 29.0364 22.6015i 0.941076 0.732520i
\(953\) 16.2242 28.1011i 0.525552 0.910283i −0.474005 0.880522i \(-0.657192\pi\)
0.999557 0.0297606i \(-0.00947449\pi\)
\(954\) 19.3279 + 18.1177i 0.625764 + 0.586581i
\(955\) −35.5368 9.52206i −1.14994 0.308127i
\(956\) 4.64012 + 11.5246i 0.150072 + 0.372731i
\(957\) −24.7259 10.0187i −0.799276 0.323857i
\(958\) 0.726476 + 0.0512389i 0.0234714 + 0.00165545i
\(959\) −8.40516 + 7.05277i −0.271417 + 0.227746i
\(960\) 44.4869 + 27.0100i 1.43581 + 0.871745i
\(961\) 57.8870 21.0692i 1.86732 0.679650i
\(962\) −0.137227 + 0.548982i −0.00442438 + 0.0176999i
\(963\) 15.2818 + 17.6507i 0.492448 + 0.568787i
\(964\) 28.9590 + 15.4425i 0.932708 + 0.497368i
\(965\) −23.1099 33.0043i −0.743933 1.06245i
\(966\) 1.98497 + 29.0542i 0.0638654 + 0.934804i
\(967\) −9.66995 3.51958i −0.310965 0.113182i 0.181823 0.983331i \(-0.441800\pi\)
−0.492788 + 0.870149i \(0.664022\pi\)
\(968\) 0.741520 1.18193i 0.0238333 0.0379887i
\(969\) −22.9553 24.6659i −0.737431 0.792383i
\(970\) 3.43813 + 2.78757i 0.110392 + 0.0895035i
\(971\) −20.8585 20.8585i −0.669380 0.669380i 0.288192 0.957573i \(-0.406946\pi\)
−0.957573 + 0.288192i \(0.906946\pi\)
\(972\) 0.895018 + 31.1641i 0.0287077 + 0.999588i
\(973\) 57.5542 57.5542i 1.84510 1.84510i
\(974\) −5.16496 49.4270i −0.165496 1.58374i
\(975\) −4.33518 + 4.03453i −0.138837 + 0.129208i
\(976\) −29.9575 18.0985i −0.958916 0.579317i
\(977\) −17.8802 + 49.1254i −0.572038 + 1.57166i 0.229241 + 0.973370i \(0.426376\pi\)
−0.801279 + 0.598291i \(0.795847\pi\)
\(978\) −36.8786 32.1618i −1.17925 1.02842i
\(979\) 8.67677 6.07554i 0.277311 0.194175i
\(980\) 97.2180 29.5948i 3.10552 0.945371i
\(981\) −30.0872 + 26.0491i −0.960609 + 0.831683i
\(982\) −21.7659 + 13.0605i −0.694577 + 0.416776i
\(983\) 13.3293 + 36.6221i 0.425140 + 1.16806i 0.948729 + 0.316091i \(0.102371\pi\)
−0.523589 + 0.851971i \(0.675407\pi\)
\(984\) 12.1604 17.9201i 0.387660 0.571271i
\(985\) 58.0304 + 69.1579i 1.84900 + 2.20355i
\(986\) 13.9310 12.0953i 0.443653 0.385193i
\(987\) −17.6197 + 43.4852i −0.560841 + 1.38415i
\(988\) 1.90000 + 4.71899i 0.0604471 + 0.150131i
\(989\) 3.38934 12.6492i 0.107775 0.402221i
\(990\) −1.74511 53.9953i −0.0554632 1.71608i
\(991\) −6.33438 3.65716i −0.201218 0.116173i 0.396005 0.918248i \(-0.370396\pi\)
−0.597224 + 0.802075i \(0.703730\pi\)
\(992\) −34.8652 41.8053i −1.10697 1.32732i
\(993\) −14.2673 + 9.24503i −0.452758 + 0.293382i
\(994\) 15.1930 7.39882i 0.481893 0.234676i
\(995\) −12.4437 8.71315i −0.394491 0.276226i
\(996\) −8.14181 30.6553i −0.257983 0.971351i
\(997\) −4.16348 47.5888i −0.131859 1.50715i −0.717487 0.696572i \(-0.754708\pi\)
0.585628 0.810580i \(-0.300848\pi\)
\(998\) 0.298521 + 17.7123i 0.00944952 + 0.560674i
\(999\) −5.16437 2.00019i −0.163393 0.0632831i
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 432.2.bj.a.11.39 840
16.3 odd 4 inner 432.2.bj.a.227.1 yes 840
27.5 odd 18 inner 432.2.bj.a.59.1 yes 840
432.275 even 36 inner 432.2.bj.a.275.39 yes 840
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
432.2.bj.a.11.39 840 1.1 even 1 trivial
432.2.bj.a.59.1 yes 840 27.5 odd 18 inner
432.2.bj.a.227.1 yes 840 16.3 odd 4 inner
432.2.bj.a.275.39 yes 840 432.275 even 36 inner