Properties

Label 450.2.q.c.331.7
Level $450$
Weight $2$
Character 450.331
Analytic conductor $3.593$
Analytic rank $0$
Dimension $120$
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] = [450,2,Mod(31,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.q (of order \(15\), degree \(8\), 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: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(15\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 331.7
Character \(\chi\) \(=\) 450.331
Dual form 450.2.q.c.121.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.978148 + 0.207912i) q^{2} +(-0.236280 + 1.71586i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.20894 + 1.88108i) q^{5} +(-0.587864 + 1.62924i) q^{6} +(-0.359749 + 0.623104i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-2.88834 - 0.810846i) q^{9} +O(q^{10})\) \(q+(0.978148 + 0.207912i) q^{2} +(-0.236280 + 1.71586i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.20894 + 1.88108i) q^{5} +(-0.587864 + 1.62924i) q^{6} +(-0.359749 + 0.623104i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-2.88834 - 0.810846i) q^{9} +(0.791428 + 2.09133i) q^{10} +(1.83868 + 0.390823i) q^{11} +(-0.913755 + 1.47141i) q^{12} +(1.30552 - 0.277496i) q^{13} +(-0.481438 + 0.534691i) q^{14} +(-3.51331 + 1.62992i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-6.05141 - 4.39660i) q^{17} +(-2.65664 - 1.39365i) q^{18} +(2.56465 + 1.86332i) q^{19} +(0.339323 + 2.21017i) q^{20} +(-0.984156 - 0.764505i) q^{21} +(1.71724 + 0.764566i) q^{22} +(0.692061 - 0.768611i) q^{23} +(-1.19971 + 1.24928i) q^{24} +(-2.07691 + 4.54824i) q^{25} +1.33468 q^{26} +(2.07376 - 4.76440i) q^{27} +(-0.582086 + 0.422910i) q^{28} +(0.649741 + 6.18187i) q^{29} +(-3.77542 + 0.863841i) q^{30} +(0.233663 - 2.22315i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.10504 + 3.06257i) q^{33} +(-5.00506 - 5.55868i) q^{34} +(-1.60702 + 0.0765820i) q^{35} +(-2.30883 - 1.91554i) q^{36} +(3.26131 - 10.0373i) q^{37} +(2.12120 + 2.35583i) q^{38} +(0.167677 + 2.30565i) q^{39} +(-0.127613 + 2.23242i) q^{40} +(1.78485 - 0.379382i) q^{41} +(-0.803700 - 0.952417i) q^{42} +(2.58549 - 4.47821i) q^{43} +(1.52076 + 1.10489i) q^{44} +(-1.96658 - 6.41347i) q^{45} +(0.836741 - 0.607928i) q^{46} +(0.628177 + 5.97671i) q^{47} +(-1.43323 + 0.972543i) q^{48} +(3.24116 + 5.61386i) q^{49} +(-2.97715 + 4.01703i) q^{50} +(8.97378 - 9.34453i) q^{51} +(1.30552 + 0.277496i) q^{52} +(-7.70981 + 5.60151i) q^{53} +(3.01901 - 4.22913i) q^{54} +(1.48769 + 3.93118i) q^{55} +(-0.657294 + 0.292646i) q^{56} +(-3.80318 + 3.96030i) q^{57} +(-0.649741 + 6.18187i) q^{58} +(9.88782 - 2.10172i) q^{59} +(-3.87252 + 0.0600106i) q^{60} +(0.0745108 + 0.0158378i) q^{61} +(0.690776 - 2.12599i) q^{62} +(1.54432 - 1.50804i) q^{63} +(0.309017 + 0.951057i) q^{64} +(2.10029 + 2.12030i) q^{65} +(-1.71764 + 2.76590i) q^{66} +(1.34428 - 12.7899i) q^{67} +(-3.73997 - 6.47782i) q^{68} +(1.15531 + 1.36909i) q^{69} +(-1.58783 - 0.259210i) q^{70} +(1.99050 - 1.44618i) q^{71} +(-1.86012 - 2.35371i) q^{72} +(1.04369 + 3.21213i) q^{73} +(5.27691 - 9.13988i) q^{74} +(-7.31340 - 4.63833i) q^{75} +(1.58504 + 2.74537i) q^{76} +(-0.904987 + 1.00509i) q^{77} +(-0.315359 + 2.29013i) q^{78} +(-1.07795 - 10.2560i) q^{79} +(-0.588971 + 2.15711i) q^{80} +(7.68506 + 4.68401i) q^{81} +1.82473 q^{82} +(3.50329 - 1.55976i) q^{83} +(-0.588119 - 1.09870i) q^{84} +(0.954537 - 16.6984i) q^{85} +(3.46007 - 3.84279i) q^{86} +(-10.7607 - 0.345789i) q^{87} +(1.25780 + 1.39693i) q^{88} +(-1.59518 - 4.90946i) q^{89} +(-0.590174 - 6.68219i) q^{90} +(-0.296749 + 0.913300i) q^{91} +(0.944851 - 0.420675i) q^{92} +(3.75940 + 0.926218i) q^{93} +(-0.628177 + 5.97671i) q^{94} +(-0.404542 + 7.07695i) q^{95} +(-1.60412 + 0.653305i) q^{96} +(-1.26605 - 12.0456i) q^{97} +(2.00315 + 6.16506i) q^{98} +(-4.99384 - 2.61972i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q - 15 q^{2} + 2 q^{3} + 15 q^{4} + 4 q^{5} + 4 q^{6} + 16 q^{7} + 30 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 120 q - 15 q^{2} + 2 q^{3} + 15 q^{4} + 4 q^{5} + 4 q^{6} + 16 q^{7} + 30 q^{8} - 10 q^{9} - 2 q^{10} + 2 q^{11} - 3 q^{12} - 6 q^{13} + 4 q^{14} + 19 q^{15} + 15 q^{16} + 12 q^{17} + 2 q^{18} + 18 q^{19} - q^{20} - 8 q^{21} - 2 q^{22} - 2 q^{24} - 2 q^{25} + 48 q^{26} + 2 q^{27} + 8 q^{28} - 5 q^{30} + 60 q^{32} - q^{33} + 6 q^{34} + 10 q^{35} + 2 q^{36} + 32 q^{37} - 6 q^{38} - 46 q^{39} + q^{40} - 4 q^{41} - 16 q^{42} + 40 q^{43} - 4 q^{44} - 38 q^{45} + 13 q^{47} + 6 q^{48} - 48 q^{49} - 3 q^{50} - 106 q^{51} - 6 q^{52} - 72 q^{53} + 15 q^{54} - 12 q^{55} + 4 q^{56} - 10 q^{57} + 18 q^{59} - 9 q^{60} + 34 q^{61} - 53 q^{63} - 30 q^{64} - 22 q^{65} + 13 q^{66} + 24 q^{68} - 5 q^{69} - 25 q^{70} - 22 q^{71} - 5 q^{72} + 32 q^{73} - 64 q^{74} - 147 q^{75} + 6 q^{76} + 10 q^{77} - 9 q^{78} + 14 q^{79} + 2 q^{80} + 22 q^{81} - 88 q^{82} - 52 q^{83} + 12 q^{84} - 3 q^{85} + 10 q^{86} + 25 q^{87} - 2 q^{88} - 94 q^{89} - 82 q^{90} + 104 q^{91} + 22 q^{93} - 13 q^{94} + 4 q^{95} - 2 q^{96} - 14 q^{97} + 54 q^{98} - 86 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.978148 + 0.207912i 0.691655 + 0.147016i
\(3\) −0.236280 + 1.71586i −0.136416 + 0.990652i
\(4\) 0.913545 + 0.406737i 0.456773 + 0.203368i
\(5\) 1.20894 + 1.88108i 0.540657 + 0.841243i
\(6\) −0.587864 + 1.62924i −0.239994 + 0.665134i
\(7\) −0.359749 + 0.623104i −0.135972 + 0.235511i −0.925968 0.377601i \(-0.876749\pi\)
0.789996 + 0.613112i \(0.210082\pi\)
\(8\) 0.809017 + 0.587785i 0.286031 + 0.207813i
\(9\) −2.88834 0.810846i −0.962781 0.270282i
\(10\) 0.791428 + 2.09133i 0.250272 + 0.661335i
\(11\) 1.83868 + 0.390823i 0.554383 + 0.117838i 0.476580 0.879131i \(-0.341876\pi\)
0.0778027 + 0.996969i \(0.475210\pi\)
\(12\) −0.913755 + 1.47141i −0.263778 + 0.424760i
\(13\) 1.30552 0.277496i 0.362085 0.0769635i −0.0232769 0.999729i \(-0.507410\pi\)
0.385362 + 0.922766i \(0.374077\pi\)
\(14\) −0.481438 + 0.534691i −0.128670 + 0.142902i
\(15\) −3.51331 + 1.62992i −0.907134 + 0.420843i
\(16\) 0.669131 + 0.743145i 0.167283 + 0.185786i
\(17\) −6.05141 4.39660i −1.46768 1.06633i −0.981278 0.192599i \(-0.938308\pi\)
−0.486404 0.873734i \(-0.661692\pi\)
\(18\) −2.65664 1.39365i −0.626176 0.328486i
\(19\) 2.56465 + 1.86332i 0.588370 + 0.427476i 0.841732 0.539896i \(-0.181536\pi\)
−0.253362 + 0.967372i \(0.581536\pi\)
\(20\) 0.339323 + 2.21017i 0.0758749 + 0.494209i
\(21\) −0.984156 0.764505i −0.214760 0.166829i
\(22\) 1.71724 + 0.764566i 0.366118 + 0.163006i
\(23\) 0.692061 0.768611i 0.144305 0.160266i −0.666660 0.745362i \(-0.732276\pi\)
0.810964 + 0.585096i \(0.198943\pi\)
\(24\) −1.19971 + 1.24928i −0.244890 + 0.255008i
\(25\) −2.07691 + 4.54824i −0.415381 + 0.909647i
\(26\) 1.33468 0.261753
\(27\) 2.07376 4.76440i 0.399094 0.916910i
\(28\) −0.582086 + 0.422910i −0.110004 + 0.0799225i
\(29\) 0.649741 + 6.18187i 0.120654 + 1.14794i 0.872503 + 0.488609i \(0.162496\pi\)
−0.751849 + 0.659335i \(0.770838\pi\)
\(30\) −3.77542 + 0.863841i −0.689294 + 0.157715i
\(31\) 0.233663 2.22315i 0.0419671 0.399290i −0.953293 0.302046i \(-0.902331\pi\)
0.995261 0.0972443i \(-0.0310028\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −1.10504 + 3.06257i −0.192363 + 0.533125i
\(34\) −5.00506 5.55868i −0.858361 0.953307i
\(35\) −1.60702 + 0.0765820i −0.271636 + 0.0129447i
\(36\) −2.30883 1.91554i −0.384805 0.319257i
\(37\) 3.26131 10.0373i 0.536156 1.65012i −0.204981 0.978766i \(-0.565713\pi\)
0.741137 0.671353i \(-0.234287\pi\)
\(38\) 2.12120 + 2.35583i 0.344103 + 0.382165i
\(39\) 0.167677 + 2.30565i 0.0268497 + 0.369199i
\(40\) −0.127613 + 2.23242i −0.0201774 + 0.352977i
\(41\) 1.78485 0.379382i 0.278747 0.0592495i −0.0664168 0.997792i \(-0.521157\pi\)
0.345164 + 0.938542i \(0.387823\pi\)
\(42\) −0.803700 0.952417i −0.124014 0.146961i
\(43\) 2.58549 4.47821i 0.394284 0.682920i −0.598725 0.800954i \(-0.704326\pi\)
0.993010 + 0.118034i \(0.0376593\pi\)
\(44\) 1.52076 + 1.10489i 0.229263 + 0.166569i
\(45\) −1.96658 6.41347i −0.293161 0.956063i
\(46\) 0.836741 0.607928i 0.123371 0.0896340i
\(47\) 0.628177 + 5.97671i 0.0916291 + 0.871792i 0.939721 + 0.341943i \(0.111085\pi\)
−0.848092 + 0.529850i \(0.822248\pi\)
\(48\) −1.43323 + 0.972543i −0.206869 + 0.140375i
\(49\) 3.24116 + 5.61386i 0.463023 + 0.801979i
\(50\) −2.97715 + 4.01703i −0.421033 + 0.568094i
\(51\) 8.97378 9.34453i 1.25658 1.30850i
\(52\) 1.30552 + 0.277496i 0.181042 + 0.0384818i
\(53\) −7.70981 + 5.60151i −1.05902 + 0.769426i −0.973908 0.226945i \(-0.927126\pi\)
−0.0851168 + 0.996371i \(0.527126\pi\)
\(54\) 3.01901 4.22913i 0.410836 0.575512i
\(55\) 1.48769 + 3.93118i 0.200600 + 0.530081i
\(56\) −0.657294 + 0.292646i −0.0878346 + 0.0391065i
\(57\) −3.80318 + 3.96030i −0.503743 + 0.524555i
\(58\) −0.649741 + 6.18187i −0.0853151 + 0.811719i
\(59\) 9.88782 2.10172i 1.28728 0.273621i 0.487085 0.873355i \(-0.338060\pi\)
0.800200 + 0.599734i \(0.204727\pi\)
\(60\) −3.87252 + 0.0600106i −0.499940 + 0.00774733i
\(61\) 0.0745108 + 0.0158378i 0.00954014 + 0.00202782i 0.212679 0.977122i \(-0.431781\pi\)
−0.203139 + 0.979150i \(0.565114\pi\)
\(62\) 0.690776 2.12599i 0.0877286 0.270001i
\(63\) 1.54432 1.50804i 0.194566 0.189995i
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) 2.10029 + 2.12030i 0.260509 + 0.262991i
\(66\) −1.71764 + 2.76590i −0.211427 + 0.340458i
\(67\) 1.34428 12.7899i 0.164229 1.56254i −0.533265 0.845948i \(-0.679035\pi\)
0.697495 0.716590i \(-0.254298\pi\)
\(68\) −3.73997 6.47782i −0.453538 0.785552i
\(69\) 1.15531 + 1.36909i 0.139083 + 0.164819i
\(70\) −1.58783 0.259210i −0.189782 0.0309816i
\(71\) 1.99050 1.44618i 0.236228 0.171630i −0.463373 0.886163i \(-0.653361\pi\)
0.699601 + 0.714533i \(0.253361\pi\)
\(72\) −1.86012 2.35371i −0.219217 0.277388i
\(73\) 1.04369 + 3.21213i 0.122154 + 0.375952i 0.993372 0.114945i \(-0.0366692\pi\)
−0.871218 + 0.490897i \(0.836669\pi\)
\(74\) 5.27691 9.13988i 0.613429 1.06249i
\(75\) −7.31340 4.63833i −0.844479 0.535589i
\(76\) 1.58504 + 2.74537i 0.181816 + 0.314915i
\(77\) −0.904987 + 1.00509i −0.103133 + 0.114541i
\(78\) −0.315359 + 2.29013i −0.0357073 + 0.259306i
\(79\) −1.07795 10.2560i −0.121279 1.15389i −0.870706 0.491804i \(-0.836338\pi\)
0.749427 0.662087i \(-0.230329\pi\)
\(80\) −0.588971 + 2.15711i −0.0658490 + 0.241172i
\(81\) 7.68506 + 4.68401i 0.853895 + 0.520445i
\(82\) 1.82473 0.201507
\(83\) 3.50329 1.55976i 0.384536 0.171206i −0.205358 0.978687i \(-0.565836\pi\)
0.589894 + 0.807480i \(0.299169\pi\)
\(84\) −0.588119 1.09870i −0.0641691 0.119878i
\(85\) 0.954537 16.6984i 0.103534 1.81120i
\(86\) 3.46007 3.84279i 0.373109 0.414379i
\(87\) −10.7607 0.345789i −1.15367 0.0370725i
\(88\) 1.25780 + 1.39693i 0.134082 + 0.148913i
\(89\) −1.59518 4.90946i −0.169089 0.520401i 0.830226 0.557427i \(-0.188212\pi\)
−0.999314 + 0.0370261i \(0.988212\pi\)
\(90\) −0.590174 6.68219i −0.0622098 0.704365i
\(91\) −0.296749 + 0.913300i −0.0311078 + 0.0957399i
\(92\) 0.944851 0.420675i 0.0985075 0.0438584i
\(93\) 3.75940 + 0.926218i 0.389832 + 0.0960444i
\(94\) −0.628177 + 5.97671i −0.0647915 + 0.616450i
\(95\) −0.404542 + 7.07695i −0.0415052 + 0.726080i
\(96\) −1.60412 + 0.653305i −0.163720 + 0.0666777i
\(97\) −1.26605 12.0456i −0.128548 1.22305i −0.848564 0.529092i \(-0.822533\pi\)
0.720017 0.693957i \(-0.244134\pi\)
\(98\) 2.00315 + 6.16506i 0.202348 + 0.622765i
\(99\) −4.99384 2.61972i −0.501900 0.263292i
\(100\) −3.74728 + 3.31027i −0.374728 + 0.331027i
\(101\) 0.577106 0.999576i 0.0574242 0.0994616i −0.835884 0.548906i \(-0.815045\pi\)
0.893308 + 0.449444i \(0.148378\pi\)
\(102\) 10.7205 7.27457i 1.06149 0.720290i
\(103\) 14.8299 + 6.60270i 1.46123 + 0.650584i 0.974789 0.223127i \(-0.0716266\pi\)
0.486445 + 0.873711i \(0.338293\pi\)
\(104\) 1.21929 + 0.542864i 0.119561 + 0.0532322i
\(105\) 0.248303 2.77552i 0.0242319 0.270863i
\(106\) −8.70596 + 3.87614i −0.845597 + 0.376484i
\(107\) 0.112700 0.0108952 0.00544758 0.999985i \(-0.498266\pi\)
0.00544758 + 0.999985i \(0.498266\pi\)
\(108\) 3.83233 3.50903i 0.368766 0.337656i
\(109\) 0.949313 2.92168i 0.0909277 0.279847i −0.895243 0.445578i \(-0.852998\pi\)
0.986171 + 0.165731i \(0.0529983\pi\)
\(110\) 0.637844 + 4.15459i 0.0608161 + 0.396124i
\(111\) 16.4520 + 7.96756i 1.56155 + 0.756247i
\(112\) −0.703775 + 0.149592i −0.0665005 + 0.0141351i
\(113\) −16.5426 + 3.51624i −1.55620 + 0.330780i −0.904089 0.427344i \(-0.859449\pi\)
−0.652110 + 0.758124i \(0.726116\pi\)
\(114\) −4.54346 + 3.08304i −0.425534 + 0.288753i
\(115\) 2.28248 + 0.372611i 0.212842 + 0.0347462i
\(116\) −1.92083 + 5.91169i −0.178344 + 0.548887i
\(117\) −3.99579 0.257069i −0.369410 0.0237660i
\(118\) 10.1087 0.930583
\(119\) 4.91653 2.18898i 0.450697 0.200663i
\(120\) −3.80037 0.746443i −0.346925 0.0681406i
\(121\) −6.82100 3.03690i −0.620091 0.276082i
\(122\) 0.0695897 + 0.0309834i 0.00630036 + 0.00280510i
\(123\) 0.229241 + 3.15219i 0.0206700 + 0.284224i
\(124\) 1.11770 1.93591i 0.100372 0.173850i
\(125\) −11.0665 + 1.59175i −0.989813 + 0.142370i
\(126\) 1.82411 1.15400i 0.162505 0.102806i
\(127\) −3.41131 10.4989i −0.302705 0.931629i −0.980524 0.196400i \(-0.937075\pi\)
0.677819 0.735229i \(-0.262925\pi\)
\(128\) 0.104528 + 0.994522i 0.00923910 + 0.0879041i
\(129\) 7.07307 + 5.49445i 0.622749 + 0.483760i
\(130\) 1.61356 + 2.51064i 0.141518 + 0.220198i
\(131\) −1.60154 + 15.2376i −0.139927 + 1.33132i 0.668935 + 0.743321i \(0.266750\pi\)
−0.808863 + 0.587998i \(0.799916\pi\)
\(132\) −2.25517 + 2.34834i −0.196287 + 0.204397i
\(133\) −2.08367 + 0.927711i −0.180677 + 0.0804427i
\(134\) 3.97407 12.2309i 0.343308 1.05659i
\(135\) 11.4693 1.85900i 0.987117 0.159998i
\(136\) −2.31143 7.11385i −0.198204 0.610008i
\(137\) −13.7174 15.2347i −1.17196 1.30159i −0.944767 0.327743i \(-0.893712\pi\)
−0.227192 0.973850i \(-0.572955\pi\)
\(138\) 0.845413 + 1.57937i 0.0719663 + 0.134445i
\(139\) 5.22347 5.80126i 0.443049 0.492056i −0.479713 0.877425i \(-0.659259\pi\)
0.922762 + 0.385369i \(0.125926\pi\)
\(140\) −1.49924 0.583674i −0.126709 0.0493294i
\(141\) −10.4036 0.334313i −0.876142 0.0281542i
\(142\) 2.24768 1.00073i 0.188621 0.0839794i
\(143\) 2.50888 0.209803
\(144\) −1.33010 2.68902i −0.110842 0.224085i
\(145\) −10.8431 + 8.69575i −0.900468 + 0.722143i
\(146\) 0.353038 + 3.35893i 0.0292176 + 0.277987i
\(147\) −10.3984 + 4.23493i −0.857646 + 0.349291i
\(148\) 7.06189 7.84302i 0.580484 0.644692i
\(149\) 2.87961 + 4.98763i 0.235907 + 0.408603i 0.959536 0.281587i \(-0.0908606\pi\)
−0.723629 + 0.690189i \(0.757527\pi\)
\(150\) −6.18922 6.05752i −0.505348 0.494594i
\(151\) 0.160182 0.277444i 0.0130354 0.0225781i −0.859434 0.511247i \(-0.829184\pi\)
0.872470 + 0.488668i \(0.162517\pi\)
\(152\) 0.979608 + 3.01492i 0.0794567 + 0.244542i
\(153\) 13.9136 + 17.6057i 1.12485 + 1.42333i
\(154\) −1.09418 + 0.794969i −0.0881716 + 0.0640604i
\(155\) 4.46441 2.24813i 0.358590 0.180574i
\(156\) −0.784611 + 2.17451i −0.0628192 + 0.174100i
\(157\) 5.69272 + 9.86008i 0.454328 + 0.786920i 0.998649 0.0519572i \(-0.0165459\pi\)
−0.544321 + 0.838877i \(0.683213\pi\)
\(158\) 1.07795 10.2560i 0.0857571 0.815924i
\(159\) −7.78972 14.5525i −0.617765 1.15409i
\(160\) −1.02459 + 1.98752i −0.0810008 + 0.157127i
\(161\) 0.229956 + 0.707732i 0.0181231 + 0.0557771i
\(162\) 6.54326 + 6.17946i 0.514087 + 0.485504i
\(163\) −6.09769 + 18.7668i −0.477608 + 1.46993i 0.364801 + 0.931086i \(0.381137\pi\)
−0.842408 + 0.538840i \(0.818863\pi\)
\(164\) 1.78485 + 0.379382i 0.139373 + 0.0296247i
\(165\) −7.09687 + 1.62381i −0.552490 + 0.126414i
\(166\) 3.75103 0.797305i 0.291136 0.0618829i
\(167\) −2.41048 + 22.9341i −0.186528 + 1.77470i 0.355830 + 0.934551i \(0.384198\pi\)
−0.542359 + 0.840147i \(0.682469\pi\)
\(168\) −0.346834 1.19697i −0.0267588 0.0923483i
\(169\) −10.2487 + 4.56303i −0.788363 + 0.351002i
\(170\) 4.40547 16.1351i 0.337884 1.23750i
\(171\) −5.89671 7.46145i −0.450933 0.570592i
\(172\) 4.18342 3.03943i 0.318983 0.231754i
\(173\) −10.1768 2.16314i −0.773724 0.164460i −0.195903 0.980623i \(-0.562764\pi\)
−0.577821 + 0.816163i \(0.696097\pi\)
\(174\) −10.4537 2.57552i −0.792493 0.195249i
\(175\) −2.08686 2.93035i −0.157752 0.221514i
\(176\) 0.939879 + 1.62792i 0.0708460 + 0.122709i
\(177\) 1.26996 + 17.4627i 0.0954562 + 1.31258i
\(178\) −0.539587 5.13383i −0.0404438 0.384797i
\(179\) −6.70305 + 4.87005i −0.501010 + 0.364005i −0.809403 0.587254i \(-0.800209\pi\)
0.308393 + 0.951259i \(0.400209\pi\)
\(180\) 0.812029 6.65887i 0.0605251 0.496323i
\(181\) 0.775526 + 0.563453i 0.0576444 + 0.0418811i 0.616234 0.787563i \(-0.288657\pi\)
−0.558590 + 0.829444i \(0.688657\pi\)
\(182\) −0.480150 + 0.831645i −0.0355911 + 0.0616456i
\(183\) −0.0447808 + 0.124108i −0.00331029 + 0.00917432i
\(184\) 1.01167 0.215036i 0.0745811 0.0158527i
\(185\) 22.8237 5.99974i 1.67803 0.441110i
\(186\) 3.48468 + 1.68760i 0.255509 + 0.123741i
\(187\) −9.40830 10.4490i −0.688003 0.764105i
\(188\) −1.85708 + 5.71550i −0.135441 + 0.416845i
\(189\) 2.22268 + 3.00615i 0.161677 + 0.218665i
\(190\) −1.86708 + 6.83820i −0.135452 + 0.496095i
\(191\) −8.87924 9.86140i −0.642479 0.713546i 0.330663 0.943749i \(-0.392728\pi\)
−0.973143 + 0.230203i \(0.926061\pi\)
\(192\) −1.70489 + 0.305514i −0.123040 + 0.0220486i
\(193\) −3.85974 6.68526i −0.277830 0.481215i 0.693015 0.720923i \(-0.256282\pi\)
−0.970845 + 0.239707i \(0.922948\pi\)
\(194\) 1.26605 12.0456i 0.0908969 0.864826i
\(195\) −4.13439 + 3.10281i −0.296070 + 0.222197i
\(196\) 0.677587 + 6.44681i 0.0483991 + 0.460487i
\(197\) −11.7828 + 8.56067i −0.839486 + 0.609922i −0.922227 0.386649i \(-0.873633\pi\)
0.0827409 + 0.996571i \(0.473633\pi\)
\(198\) −4.34004 3.60075i −0.308433 0.255894i
\(199\) 8.43837 0.598180 0.299090 0.954225i \(-0.403317\pi\)
0.299090 + 0.954225i \(0.403317\pi\)
\(200\) −4.35364 + 2.45883i −0.307849 + 0.173865i
\(201\) 21.6281 + 5.32859i 1.52553 + 0.375850i
\(202\) 0.772318 0.857746i 0.0543401 0.0603508i
\(203\) −4.08569 1.81907i −0.286759 0.127673i
\(204\) 11.9987 4.88669i 0.840078 0.342137i
\(205\) 2.87143 + 2.89879i 0.200550 + 0.202460i
\(206\) 13.1331 + 9.54173i 0.915024 + 0.664804i
\(207\) −2.62213 + 1.65886i −0.182251 + 0.115299i
\(208\) 1.07978 + 0.784506i 0.0748693 + 0.0543957i
\(209\) 3.98733 + 4.42838i 0.275810 + 0.306318i
\(210\) 0.819940 2.66324i 0.0565813 0.183781i
\(211\) 7.82806 8.69395i 0.538906 0.598516i −0.410774 0.911737i \(-0.634741\pi\)
0.949680 + 0.313221i \(0.101408\pi\)
\(212\) −9.32160 + 1.98137i −0.640210 + 0.136081i
\(213\) 2.01113 + 3.75711i 0.137800 + 0.257433i
\(214\) 0.110238 + 0.0234317i 0.00753569 + 0.00160176i
\(215\) 11.5496 0.550390i 0.787674 0.0375363i
\(216\) 4.47815 2.63556i 0.304699 0.179327i
\(217\) 1.30119 + 0.945373i 0.0883308 + 0.0641761i
\(218\) 1.53602 2.66047i 0.104032 0.180189i
\(219\) −5.75817 + 1.03185i −0.389101 + 0.0697262i
\(220\) −0.239881 + 4.19641i −0.0161728 + 0.282922i
\(221\) −9.12025 4.06059i −0.613494 0.273145i
\(222\) 14.4359 + 11.2140i 0.968875 + 0.752635i
\(223\) −10.7902 2.29352i −0.722564 0.153586i −0.168072 0.985775i \(-0.553754\pi\)
−0.554492 + 0.832189i \(0.687087\pi\)
\(224\) −0.719498 −0.0480735
\(225\) 9.68674 11.4528i 0.645783 0.763521i
\(226\) −16.9122 −1.12498
\(227\) −2.76541 0.587806i −0.183547 0.0390141i 0.115221 0.993340i \(-0.463242\pi\)
−0.298768 + 0.954326i \(0.596576\pi\)
\(228\) −5.08518 + 2.07103i −0.336774 + 0.137157i
\(229\) 3.54388 + 1.57784i 0.234186 + 0.104266i 0.520475 0.853877i \(-0.325755\pi\)
−0.286289 + 0.958143i \(0.592422\pi\)
\(230\) 2.15513 + 0.839023i 0.142105 + 0.0553235i
\(231\) −1.51076 1.79031i −0.0994008 0.117794i
\(232\) −3.10796 + 5.38315i −0.204048 + 0.353421i
\(233\) 6.63336 + 4.81942i 0.434566 + 0.315731i 0.783472 0.621427i \(-0.213447\pi\)
−0.348906 + 0.937158i \(0.613447\pi\)
\(234\) −3.85502 1.08222i −0.252011 0.0707471i
\(235\) −10.4832 + 8.40716i −0.683850 + 0.548423i
\(236\) 9.88782 + 2.10172i 0.643642 + 0.136810i
\(237\) 17.8526 + 0.573680i 1.15965 + 0.0372645i
\(238\) 5.26420 1.11894i 0.341228 0.0725301i
\(239\) 19.0368 21.1426i 1.23139 1.36760i 0.324692 0.945820i \(-0.394740\pi\)
0.906699 0.421778i \(-0.138594\pi\)
\(240\) −3.56213 1.52027i −0.229935 0.0981332i
\(241\) −3.16369 3.51364i −0.203791 0.226333i 0.632582 0.774493i \(-0.281995\pi\)
−0.836373 + 0.548160i \(0.815328\pi\)
\(242\) −6.04054 4.38871i −0.388300 0.282117i
\(243\) −9.85292 + 12.0797i −0.632065 + 0.774915i
\(244\) 0.0616272 + 0.0447748i 0.00394528 + 0.00286641i
\(245\) −6.64171 + 12.8837i −0.424324 + 0.823111i
\(246\) −0.431146 + 3.13097i −0.0274889 + 0.199624i
\(247\) 3.86525 + 1.72092i 0.245940 + 0.109500i
\(248\) 1.49577 1.66122i 0.0949817 0.105488i
\(249\) 1.84858 + 6.37969i 0.117149 + 0.404297i
\(250\) −11.1556 0.743881i −0.705540 0.0470471i
\(251\) 3.89570 0.245894 0.122947 0.992413i \(-0.460765\pi\)
0.122947 + 0.992413i \(0.460765\pi\)
\(252\) 2.02418 0.749528i 0.127511 0.0472158i
\(253\) 1.57287 1.14276i 0.0988854 0.0718445i
\(254\) −1.15391 10.9787i −0.0724029 0.688868i
\(255\) 28.4266 + 5.58335i 1.78014 + 0.349643i
\(256\) −0.104528 + 0.994522i −0.00653303 + 0.0621576i
\(257\) 13.9129 + 24.0978i 0.867861 + 1.50318i 0.864178 + 0.503186i \(0.167839\pi\)
0.00368262 + 0.999993i \(0.498828\pi\)
\(258\) 5.77615 + 6.84496i 0.359607 + 0.426149i
\(259\) 5.08101 + 5.64304i 0.315719 + 0.350641i
\(260\) 1.05631 + 2.79125i 0.0655093 + 0.173106i
\(261\) 3.13587 18.3822i 0.194106 1.13783i
\(262\) −4.73463 + 14.5717i −0.292506 + 0.900241i
\(263\) −11.8168 13.1239i −0.728655 0.809253i 0.259004 0.965876i \(-0.416606\pi\)
−0.987658 + 0.156623i \(0.949939\pi\)
\(264\) −2.69413 + 1.82815i −0.165812 + 0.112515i
\(265\) −19.8576 7.73085i −1.21984 0.474902i
\(266\) −2.23102 + 0.474218i −0.136793 + 0.0290762i
\(267\) 8.80084 1.57710i 0.538603 0.0965167i
\(268\) 6.43019 11.1374i 0.392786 0.680326i
\(269\) −9.26699 6.73286i −0.565018 0.410510i 0.268274 0.963343i \(-0.413547\pi\)
−0.833292 + 0.552833i \(0.813547\pi\)
\(270\) 11.6051 + 0.566214i 0.706267 + 0.0344587i
\(271\) −18.9129 + 13.7410i −1.14888 + 0.834707i −0.988331 0.152322i \(-0.951325\pi\)
−0.160544 + 0.987029i \(0.551325\pi\)
\(272\) −0.781867 7.43897i −0.0474077 0.451054i
\(273\) −1.49698 0.724975i −0.0906013 0.0438775i
\(274\) −10.2502 17.7538i −0.619237 1.07255i
\(275\) −5.59632 + 7.55105i −0.337471 + 0.455345i
\(276\) 0.498569 + 1.72063i 0.0300103 + 0.103570i
\(277\) −13.2017 2.80610i −0.793212 0.168602i −0.206552 0.978436i \(-0.566224\pi\)
−0.586660 + 0.809833i \(0.699558\pi\)
\(278\) 6.31548 4.58846i 0.378777 0.275198i
\(279\) −2.47753 + 6.23176i −0.148326 + 0.373086i
\(280\) −1.34512 0.882628i −0.0803864 0.0527471i
\(281\) −23.9117 + 10.6462i −1.42645 + 0.635098i −0.967387 0.253304i \(-0.918483\pi\)
−0.459067 + 0.888402i \(0.651816\pi\)
\(282\) −10.1068 2.49004i −0.601849 0.148280i
\(283\) −2.36194 + 22.4724i −0.140403 + 1.33584i 0.666652 + 0.745369i \(0.267727\pi\)
−0.807055 + 0.590476i \(0.798940\pi\)
\(284\) 2.40662 0.511543i 0.142807 0.0303545i
\(285\) −12.0475 2.36628i −0.713631 0.140166i
\(286\) 2.45405 + 0.521625i 0.145111 + 0.0308443i
\(287\) −0.405704 + 1.24863i −0.0239480 + 0.0737043i
\(288\) −0.741958 2.90680i −0.0437203 0.171285i
\(289\) 12.0361 + 37.0433i 0.708006 + 2.17902i
\(290\) −12.4141 + 6.25133i −0.728980 + 0.367090i
\(291\) 20.9677 + 0.673784i 1.22915 + 0.0394979i
\(292\) −0.353038 + 3.35893i −0.0206600 + 0.196567i
\(293\) −15.2515 26.4164i −0.891003 1.54326i −0.838675 0.544632i \(-0.816669\pi\)
−0.0523280 0.998630i \(-0.516664\pi\)
\(294\) −11.0517 + 1.98044i −0.644546 + 0.115502i
\(295\) 15.9073 + 16.0589i 0.926160 + 0.934985i
\(296\) 8.53822 6.20338i 0.496274 0.360564i
\(297\) 5.67501 7.94974i 0.329298 0.461291i
\(298\) 1.77970 + 5.47734i 0.103095 + 0.317294i
\(299\) 0.690210 1.19548i 0.0399159 0.0691363i
\(300\) −4.79455 7.21196i −0.276813 0.416383i
\(301\) 1.86026 + 3.22206i 0.107223 + 0.185716i
\(302\) 0.214366 0.238077i 0.0123354 0.0136998i
\(303\) 1.57877 + 1.22641i 0.0906982 + 0.0704555i
\(304\) 0.331363 + 3.15271i 0.0190050 + 0.180820i
\(305\) 0.0602874 + 0.159308i 0.00345205 + 0.00912193i
\(306\) 9.94910 + 20.1137i 0.568752 + 1.14983i
\(307\) −21.3008 −1.21570 −0.607850 0.794052i \(-0.707968\pi\)
−0.607850 + 0.794052i \(0.707968\pi\)
\(308\) −1.23555 + 0.550104i −0.0704022 + 0.0313451i
\(309\) −14.8333 + 23.8859i −0.843838 + 1.35882i
\(310\) 4.83426 1.27080i 0.274568 0.0721766i
\(311\) 8.32625 9.24724i 0.472138 0.524363i −0.459291 0.888286i \(-0.651896\pi\)
0.931429 + 0.363923i \(0.118563\pi\)
\(312\) −1.21957 + 1.96387i −0.0690447 + 0.111182i
\(313\) 11.3039 + 12.5543i 0.638937 + 0.709611i 0.972444 0.233136i \(-0.0748989\pi\)
−0.333507 + 0.942748i \(0.608232\pi\)
\(314\) 3.51829 + 10.8282i 0.198549 + 0.611070i
\(315\) 4.70373 + 1.08185i 0.265025 + 0.0609555i
\(316\) 3.18674 9.80777i 0.179268 0.551730i
\(317\) 29.0148 12.9182i 1.62964 0.725560i 0.630901 0.775863i \(-0.282685\pi\)
0.998734 + 0.0503026i \(0.0160186\pi\)
\(318\) −4.59387 15.8540i −0.257611 0.889051i
\(319\) −1.22135 + 11.6204i −0.0683827 + 0.650618i
\(320\) −1.41543 + 1.73106i −0.0791248 + 0.0967692i
\(321\) −0.0266289 + 0.193378i −0.00148628 + 0.0107933i
\(322\) 0.0777853 + 0.740077i 0.00433480 + 0.0412429i
\(323\) −7.32741 22.5515i −0.407708 1.25480i
\(324\) 5.11549 + 7.40485i 0.284194 + 0.411380i
\(325\) −1.44932 + 6.51413i −0.0803936 + 0.361339i
\(326\) −9.86626 + 17.0889i −0.546442 + 0.946465i
\(327\) 4.78890 + 2.31922i 0.264827 + 0.128253i
\(328\) 1.66697 + 0.742183i 0.0920430 + 0.0409802i
\(329\) −3.95009 1.75869i −0.217776 0.0969600i
\(330\) −7.27939 + 0.112805i −0.400717 + 0.00620972i
\(331\) −20.7656 + 9.24545i −1.14138 + 0.508176i −0.888298 0.459268i \(-0.848112\pi\)
−0.253084 + 0.967444i \(0.581445\pi\)
\(332\) 3.83483 0.210463
\(333\) −17.5585 + 26.3467i −0.962199 + 1.44379i
\(334\) −7.12608 + 21.9318i −0.389922 + 1.20006i
\(335\) 25.6840 12.9336i 1.40327 0.706639i
\(336\) −0.0903908 1.24292i −0.00493122 0.0678071i
\(337\) 13.1111 2.78685i 0.714207 0.151809i 0.163543 0.986536i \(-0.447708\pi\)
0.550664 + 0.834727i \(0.314374\pi\)
\(338\) −10.9735 + 2.33248i −0.596878 + 0.126870i
\(339\) −2.12469 29.2156i −0.115397 1.58678i
\(340\) 7.66387 14.8665i 0.415632 0.806250i
\(341\) 1.29849 3.99634i 0.0703172 0.216414i
\(342\) −4.21653 8.52440i −0.228004 0.460947i
\(343\) −9.70050 −0.523778
\(344\) 4.72393 2.10323i 0.254697 0.113399i
\(345\) −1.17865 + 3.82837i −0.0634565 + 0.206113i
\(346\) −9.50462 4.23173i −0.510972 0.227499i
\(347\) −32.4394 14.4430i −1.74144 0.775339i −0.993793 0.111243i \(-0.964517\pi\)
−0.747647 0.664096i \(-0.768817\pi\)
\(348\) −9.68978 4.69268i −0.519427 0.251554i
\(349\) 13.0622 22.6243i 0.699202 1.21105i −0.269542 0.962989i \(-0.586872\pi\)
0.968744 0.248064i \(-0.0797944\pi\)
\(350\) −1.43200 3.30020i −0.0765437 0.176403i
\(351\) 1.38522 6.79546i 0.0739375 0.362715i
\(352\) 0.580877 + 1.78776i 0.0309608 + 0.0952877i
\(353\) −0.664683 6.32404i −0.0353775 0.336595i −0.997867 0.0652764i \(-0.979207\pi\)
0.962490 0.271318i \(-0.0874596\pi\)
\(354\) −2.38849 + 17.3451i −0.126947 + 0.921884i
\(355\) 5.12678 + 1.99593i 0.272101 + 0.105933i
\(356\) 0.539587 5.13383i 0.0285981 0.272092i
\(357\) 2.59430 + 8.95328i 0.137305 + 0.473858i
\(358\) −7.56912 + 3.36999i −0.400040 + 0.178109i
\(359\) 3.11491 9.58670i 0.164398 0.505967i −0.834593 0.550867i \(-0.814297\pi\)
0.998991 + 0.0449006i \(0.0142971\pi\)
\(360\) 2.17874 6.34453i 0.114830 0.334386i
\(361\) −2.76589 8.51254i −0.145573 0.448028i
\(362\) 0.641431 + 0.712381i 0.0337129 + 0.0374419i
\(363\) 6.82257 10.9863i 0.358092 0.576632i
\(364\) −0.642567 + 0.713643i −0.0336796 + 0.0374050i
\(365\) −4.78051 + 5.84654i −0.250223 + 0.306022i
\(366\) −0.0696057 + 0.112085i −0.00363835 + 0.00585880i
\(367\) 7.37642 3.28419i 0.385046 0.171433i −0.205079 0.978745i \(-0.565745\pi\)
0.590125 + 0.807312i \(0.299078\pi\)
\(368\) 1.03427 0.0539150
\(369\) −5.46288 0.351455i −0.284386 0.0182960i
\(370\) 23.5723 1.12333i 1.22547 0.0583991i
\(371\) −0.716721 6.81915i −0.0372103 0.354033i
\(372\) 3.05766 + 2.37523i 0.158532 + 0.123150i
\(373\) −3.18230 + 3.53431i −0.164773 + 0.182999i −0.819877 0.572540i \(-0.805958\pi\)
0.655104 + 0.755539i \(0.272625\pi\)
\(374\) −7.03024 12.1767i −0.363525 0.629644i
\(375\) −0.116433 19.3646i −0.00601256 0.999982i
\(376\) −3.00481 + 5.20449i −0.154961 + 0.268401i
\(377\) 2.56369 + 7.89023i 0.132037 + 0.406367i
\(378\) 1.54910 + 3.40258i 0.0796771 + 0.175010i
\(379\) −10.0812 + 7.32445i −0.517839 + 0.376232i −0.815789 0.578350i \(-0.803697\pi\)
0.297950 + 0.954581i \(0.403697\pi\)
\(380\) −3.24802 + 6.30058i −0.166620 + 0.323213i
\(381\) 18.8207 3.37264i 0.964213 0.172785i
\(382\) −6.63491 11.4920i −0.339471 0.587982i
\(383\) 2.52527 24.0263i 0.129035 1.22769i −0.717960 0.696085i \(-0.754924\pi\)
0.846995 0.531601i \(-0.178410\pi\)
\(384\) −1.73116 0.0556295i −0.0883427 0.00283883i
\(385\) −2.98473 0.487252i −0.152116 0.0248327i
\(386\) −2.38545 7.34165i −0.121416 0.373680i
\(387\) −11.0989 + 10.8382i −0.564190 + 0.550935i
\(388\) 3.74281 11.5192i 0.190012 0.584798i
\(389\) 4.60101 + 0.977976i 0.233281 + 0.0495853i 0.323069 0.946376i \(-0.395286\pi\)
−0.0897878 + 0.995961i \(0.528619\pi\)
\(390\) −4.68916 + 2.17542i −0.237445 + 0.110157i
\(391\) −7.56722 + 1.60846i −0.382691 + 0.0813434i
\(392\) −0.677587 + 6.44681i −0.0342233 + 0.325613i
\(393\) −25.7672 6.34837i −1.29978 0.320233i
\(394\) −13.3051 + 5.92383i −0.670303 + 0.298438i
\(395\) 17.9892 14.4267i 0.905133 0.725884i
\(396\) −3.49657 4.42441i −0.175709 0.222335i
\(397\) 20.1200 14.6180i 1.00979 0.733657i 0.0456266 0.998959i \(-0.485472\pi\)
0.964165 + 0.265302i \(0.0854716\pi\)
\(398\) 8.25397 + 1.75444i 0.413734 + 0.0879419i
\(399\) −1.09949 3.79449i −0.0550434 0.189962i
\(400\) −4.76972 + 1.49992i −0.238486 + 0.0749962i
\(401\) 4.95946 + 8.59003i 0.247663 + 0.428966i 0.962877 0.269940i \(-0.0870039\pi\)
−0.715214 + 0.698906i \(0.753671\pi\)
\(402\) 20.0476 + 9.70888i 0.999882 + 0.484235i
\(403\) −0.311865 2.96720i −0.0155351 0.147807i
\(404\) 0.933777 0.678429i 0.0464571 0.0337531i
\(405\) 0.479831 + 20.1189i 0.0238430 + 0.999716i
\(406\) −3.61820 2.62878i −0.179568 0.130464i
\(407\) 9.91931 17.1808i 0.491682 0.851618i
\(408\) 12.7525 2.28523i 0.631343 0.113136i
\(409\) −13.6221 + 2.89547i −0.673570 + 0.143172i −0.531984 0.846754i \(-0.678553\pi\)
−0.141586 + 0.989926i \(0.545220\pi\)
\(410\) 2.20599 + 3.43245i 0.108946 + 0.169517i
\(411\) 29.3818 19.9375i 1.44930 0.983445i
\(412\) 10.8622 + 12.0637i 0.535144 + 0.594338i
\(413\) −2.24754 + 6.91723i −0.110594 + 0.340375i
\(414\) −2.90973 + 1.07744i −0.143005 + 0.0529531i
\(415\) 7.16932 + 4.70429i 0.351928 + 0.230924i
\(416\) 0.893077 + 0.991862i 0.0437867 + 0.0486300i
\(417\) 8.71993 + 10.3335i 0.427017 + 0.506032i
\(418\) 2.97949 + 5.16062i 0.145731 + 0.252414i
\(419\) −0.659592 + 6.27560i −0.0322232 + 0.306583i 0.966525 + 0.256571i \(0.0825927\pi\)
−0.998749 + 0.0500122i \(0.984074\pi\)
\(420\) 1.35574 2.43457i 0.0661534 0.118795i
\(421\) −0.0737356 0.701548i −0.00359365 0.0341913i 0.992578 0.121609i \(-0.0388053\pi\)
−0.996172 + 0.0874173i \(0.972139\pi\)
\(422\) 9.46457 6.87642i 0.460728 0.334739i
\(423\) 3.03180 17.7721i 0.147411 0.864111i
\(424\) −9.52985 −0.462811
\(425\) 32.5650 18.3919i 1.57963 0.892138i
\(426\) 1.18603 + 4.09315i 0.0574634 + 0.198314i
\(427\) −0.0366738 + 0.0407303i −0.00177477 + 0.00197108i
\(428\) 0.102957 + 0.0458394i 0.00497661 + 0.00221573i
\(429\) −0.592798 + 4.30488i −0.0286205 + 0.207842i
\(430\) 11.4116 + 1.86293i 0.550317 + 0.0898384i
\(431\) 22.6776 + 16.4762i 1.09234 + 0.793632i 0.979793 0.200014i \(-0.0640988\pi\)
0.112548 + 0.993646i \(0.464099\pi\)
\(432\) 4.92825 1.64691i 0.237111 0.0792369i
\(433\) 3.35151 + 2.43502i 0.161063 + 0.117019i 0.665398 0.746489i \(-0.268262\pi\)
−0.504334 + 0.863509i \(0.668262\pi\)
\(434\) 1.07621 + 1.19525i 0.0516595 + 0.0573737i
\(435\) −12.3587 20.6598i −0.592553 0.990562i
\(436\) 2.05560 2.28297i 0.0984452 0.109335i
\(437\) 3.20706 0.681682i 0.153415 0.0326093i
\(438\) −5.84687 0.187885i −0.279374 0.00897750i
\(439\) 14.8520 + 3.15689i 0.708848 + 0.150670i 0.548207 0.836343i \(-0.315311\pi\)
0.160641 + 0.987013i \(0.448644\pi\)
\(440\) −1.10712 + 4.05484i −0.0527800 + 0.193307i
\(441\) −4.80961 18.8428i −0.229029 0.897278i
\(442\) −8.07670 5.86807i −0.384169 0.279115i
\(443\) −1.82132 + 3.15463i −0.0865337 + 0.149881i −0.906044 0.423184i \(-0.860912\pi\)
0.819510 + 0.573065i \(0.194246\pi\)
\(444\) 11.7889 + 13.9704i 0.559478 + 0.663003i
\(445\) 7.30659 8.93592i 0.346365 0.423603i
\(446\) −10.0775 4.48681i −0.477185 0.212457i
\(447\) −9.23847 + 3.76253i −0.436964 + 0.177961i
\(448\) −0.703775 0.149592i −0.0332503 0.00706756i
\(449\) −27.8605 −1.31482 −0.657408 0.753534i \(-0.728347\pi\)
−0.657408 + 0.753534i \(0.728347\pi\)
\(450\) 11.8562 9.18856i 0.558908 0.433153i
\(451\) 3.43004 0.161514
\(452\) −16.5426 3.51624i −0.778100 0.165390i
\(453\) 0.438206 + 0.340404i 0.0205887 + 0.0159936i
\(454\) −2.58277 1.14992i −0.121215 0.0539685i
\(455\) −2.07674 + 0.545921i −0.0973592 + 0.0255932i
\(456\) −5.40464 + 0.968503i −0.253096 + 0.0453543i
\(457\) 13.8941 24.0653i 0.649938 1.12573i −0.333199 0.942857i \(-0.608128\pi\)
0.983137 0.182870i \(-0.0585387\pi\)
\(458\) 3.13839 + 2.28017i 0.146647 + 0.106545i
\(459\) −33.4963 + 19.7139i −1.56347 + 0.920164i
\(460\) 1.93359 + 1.26877i 0.0901543 + 0.0591565i
\(461\) −34.8094 7.39897i −1.62124 0.344604i −0.694260 0.719724i \(-0.744268\pi\)
−0.926976 + 0.375120i \(0.877602\pi\)
\(462\) −1.10552 2.06529i −0.0514335 0.0960862i
\(463\) 5.10570 1.08525i 0.237282 0.0504359i −0.0877356 0.996144i \(-0.527963\pi\)
0.325018 + 0.945708i \(0.394630\pi\)
\(464\) −4.15926 + 4.61933i −0.193089 + 0.214447i
\(465\) 2.80262 + 8.19148i 0.129969 + 0.379871i
\(466\) 5.48640 + 6.09326i 0.254152 + 0.282265i
\(467\) 3.33870 + 2.42571i 0.154496 + 0.112248i 0.662348 0.749196i \(-0.269560\pi\)
−0.507851 + 0.861445i \(0.669560\pi\)
\(468\) −3.54577 1.86008i −0.163903 0.0859821i
\(469\) 7.48584 + 5.43878i 0.345664 + 0.251140i
\(470\) −12.0021 + 6.04386i −0.553615 + 0.278782i
\(471\) −18.2636 + 7.43816i −0.841541 + 0.342732i
\(472\) 9.23478 + 4.11159i 0.425065 + 0.189251i
\(473\) 6.50408 7.22352i 0.299058 0.332138i
\(474\) 17.3432 + 4.27290i 0.796598 + 0.196261i
\(475\) −13.8014 + 7.79467i −0.633250 + 0.357644i
\(476\) 5.38181 0.246675
\(477\) 26.8106 9.92760i 1.22757 0.454554i
\(478\) 23.0166 16.7226i 1.05276 0.764872i
\(479\) −1.19485 11.3682i −0.0545941 0.519428i −0.987309 0.158813i \(-0.949233\pi\)
0.932715 0.360615i \(-0.117433\pi\)
\(480\) −3.16821 2.22766i −0.144608 0.101678i
\(481\) 1.47239 14.0088i 0.0671351 0.638748i
\(482\) −2.36403 4.09463i −0.107679 0.186505i
\(483\) −1.26870 + 0.227349i −0.0577280 + 0.0103448i
\(484\) −4.99607 5.54870i −0.227094 0.252214i
\(485\) 21.1282 16.9440i 0.959381 0.769389i
\(486\) −12.1491 + 9.76723i −0.551096 + 0.443050i
\(487\) 4.35689 13.4091i 0.197430 0.607626i −0.802510 0.596639i \(-0.796503\pi\)
0.999940 0.0109872i \(-0.00349739\pi\)
\(488\) 0.0509713 + 0.0566094i 0.00230736 + 0.00256259i
\(489\) −30.7603 14.8970i −1.39103 0.673665i
\(490\) −9.17525 + 11.2213i −0.414496 + 0.506926i
\(491\) 17.4278 3.70439i 0.786505 0.167177i 0.202884 0.979203i \(-0.434969\pi\)
0.583621 + 0.812026i \(0.301635\pi\)
\(492\) −1.07269 + 2.97291i −0.0483606 + 0.134029i
\(493\) 23.2474 40.2656i 1.04701 1.81347i
\(494\) 3.42299 + 2.48695i 0.154007 + 0.111893i
\(495\) −1.10938 12.5609i −0.0498631 0.564570i
\(496\) 1.80847 1.31393i 0.0812029 0.0589974i
\(497\) 0.185041 + 1.76055i 0.00830022 + 0.0789713i
\(498\) 0.481771 + 6.62462i 0.0215887 + 0.296856i
\(499\) 7.72808 + 13.3854i 0.345956 + 0.599214i 0.985527 0.169518i \(-0.0542212\pi\)
−0.639571 + 0.768732i \(0.720888\pi\)
\(500\) −10.7571 3.04700i −0.481073 0.136266i
\(501\) −38.7822 9.55492i −1.73266 0.426882i
\(502\) 3.81057 + 0.809962i 0.170074 + 0.0361504i
\(503\) 32.1068 23.3269i 1.43157 1.04010i 0.441849 0.897089i \(-0.354323\pi\)
0.989722 0.143008i \(-0.0456774\pi\)
\(504\) 2.13578 0.312298i 0.0951353 0.0139109i
\(505\) 2.57797 0.122852i 0.114718 0.00546684i
\(506\) 1.77609 0.790766i 0.0789569 0.0351539i
\(507\) −5.40794 18.6635i −0.240175 0.828876i
\(508\) 1.15391 10.9787i 0.0511966 0.487103i
\(509\) 22.5833 4.80024i 1.00099 0.212767i 0.321861 0.946787i \(-0.395692\pi\)
0.679128 + 0.734020i \(0.262358\pi\)
\(510\) 26.6445 + 11.3716i 1.17984 + 0.503541i
\(511\) −2.37696 0.505238i −0.105150 0.0223504i
\(512\) −0.309017 + 0.951057i −0.0136568 + 0.0420312i
\(513\) 14.1961 8.35493i 0.626772 0.368879i
\(514\) 8.59863 + 26.4638i 0.379269 + 1.16727i
\(515\) 5.50835 + 35.8785i 0.242727 + 1.58100i
\(516\) 4.22678 + 7.89631i 0.186073 + 0.347616i
\(517\) −1.18082 + 11.2348i −0.0519324 + 0.494104i
\(518\) 3.79673 + 6.57612i 0.166819 + 0.288938i
\(519\) 6.11620 16.9508i 0.268471 0.744056i
\(520\) 0.452888 + 2.94988i 0.0198605 + 0.129361i
\(521\) −29.2107 + 21.2228i −1.27975 + 0.929790i −0.999545 0.0301516i \(-0.990401\pi\)
−0.280201 + 0.959941i \(0.590401\pi\)
\(522\) 6.88922 17.3285i 0.301533 0.758449i
\(523\) −12.3932 38.1422i −0.541915 1.66784i −0.728214 0.685350i \(-0.759649\pi\)
0.186299 0.982493i \(-0.440351\pi\)
\(524\) −7.66078 + 13.2689i −0.334663 + 0.579653i
\(525\) 5.52115 2.88837i 0.240963 0.126059i
\(526\) −8.82996 15.2939i −0.385005 0.666848i
\(527\) −11.1883 + 12.4259i −0.487370 + 0.541279i
\(528\) −3.01535 + 1.22805i −0.131226 + 0.0534442i
\(529\) 2.29234 + 21.8102i 0.0996669 + 0.948268i
\(530\) −17.8163 11.6905i −0.773892 0.507804i
\(531\) −30.2636 1.94701i −1.31333 0.0844930i
\(532\) −2.28086 −0.0988880
\(533\) 2.22487 0.990578i 0.0963700 0.0429067i
\(534\) 8.93642 + 0.287166i 0.386717 + 0.0124269i
\(535\) 0.136249 + 0.211998i 0.00589054 + 0.00916548i
\(536\) 8.60527 9.55712i 0.371691 0.412805i
\(537\) −6.77253 12.6522i −0.292256 0.545982i
\(538\) −7.66464 8.51245i −0.330446 0.366998i
\(539\) 3.76543 + 11.5888i 0.162189 + 0.499165i
\(540\) 11.2338 + 2.96669i 0.483427 + 0.127666i
\(541\) 7.77245 23.9211i 0.334164 1.02845i −0.632969 0.774177i \(-0.718164\pi\)
0.967132 0.254273i \(-0.0818362\pi\)
\(542\) −21.3565 + 9.50853i −0.917340 + 0.408426i
\(543\) −1.15005 + 1.19756i −0.0493532 + 0.0513923i
\(544\) 0.781867 7.43897i 0.0335223 0.318943i
\(545\) 6.64358 1.74642i 0.284580 0.0748086i
\(546\) −1.31354 1.02037i −0.0562141 0.0436679i
\(547\) 4.44152 + 42.2582i 0.189906 + 1.80683i 0.510782 + 0.859710i \(0.329356\pi\)
−0.320877 + 0.947121i \(0.603977\pi\)
\(548\) −6.33497 19.4970i −0.270616 0.832871i
\(549\) −0.202371 0.106162i −0.00863698 0.00453087i
\(550\) −7.04398 + 6.22250i −0.300356 + 0.265328i
\(551\) −9.85247 + 17.0650i −0.419729 + 0.726993i
\(552\) 0.129936 + 1.78669i 0.00553042 + 0.0760464i
\(553\) 6.77835 + 3.01791i 0.288245 + 0.128335i
\(554\) −12.3298 5.48957i −0.523842 0.233229i
\(555\) 4.90194 + 40.5798i 0.208076 + 1.72252i
\(556\) 7.13146 3.17513i 0.302441 0.134656i
\(557\) −10.1546 −0.430264 −0.215132 0.976585i \(-0.569018\pi\)
−0.215132 + 0.976585i \(0.569018\pi\)
\(558\) −3.71905 + 5.58047i −0.157440 + 0.236240i
\(559\) 2.13272 6.56383i 0.0902044 0.277621i
\(560\) −1.13222 1.14301i −0.0478450 0.0483009i
\(561\) 20.1520 13.6744i 0.850817 0.577335i
\(562\) −25.6027 + 5.44201i −1.07998 + 0.229557i
\(563\) −28.0175 + 5.95530i −1.18080 + 0.250986i −0.756165 0.654381i \(-0.772929\pi\)
−0.424631 + 0.905367i \(0.639596\pi\)
\(564\) −9.36820 4.53694i −0.394472 0.191040i
\(565\) −26.6134 26.8670i −1.11964 1.13030i
\(566\) −6.98260 + 21.4902i −0.293501 + 0.903302i
\(567\) −5.68331 + 3.10352i −0.238677 + 0.130336i
\(568\) 2.46039 0.103236
\(569\) 6.43720 2.86602i 0.269861 0.120150i −0.267345 0.963601i \(-0.586146\pi\)
0.537206 + 0.843451i \(0.319480\pi\)
\(570\) −11.2922 4.81938i −0.472979 0.201862i
\(571\) −40.2751 17.9316i −1.68546 0.750415i −0.999746 0.0225446i \(-0.992823\pi\)
−0.685714 0.727871i \(-0.740510\pi\)
\(572\) 2.29197 + 1.02045i 0.0958322 + 0.0426673i
\(573\) 19.0188 12.9055i 0.794520 0.539134i
\(574\) −0.656443 + 1.13699i −0.0273994 + 0.0474572i
\(575\) 2.05848 + 4.74399i 0.0858446 + 0.197838i
\(576\) −0.121387 2.99754i −0.00505777 0.124898i
\(577\) −8.55866 26.3408i −0.356302 1.09658i −0.955251 0.295796i \(-0.904415\pi\)
0.598949 0.800787i \(-0.295585\pi\)
\(578\) 4.07134 + 38.7363i 0.169346 + 1.61122i
\(579\) 12.3829 5.04317i 0.514617 0.209587i
\(580\) −13.4425 + 3.53369i −0.558170 + 0.146728i
\(581\) −0.288410 + 2.74404i −0.0119653 + 0.113842i
\(582\) 20.3695 + 5.01850i 0.844341 + 0.208023i
\(583\) −16.3651 + 7.28620i −0.677772 + 0.301764i
\(584\) −1.04369 + 3.21213i −0.0431880 + 0.132919i
\(585\) −4.34712 7.82716i −0.179731 0.323613i
\(586\) −9.42595 29.0101i −0.389383 1.19840i
\(587\) 28.0076 + 31.1056i 1.15600 + 1.28386i 0.952415 + 0.304806i \(0.0985915\pi\)
0.203581 + 0.979058i \(0.434742\pi\)
\(588\) −11.2219 0.360609i −0.462784 0.0148713i
\(589\) 4.74171 5.26621i 0.195379 0.216990i
\(590\) 12.2209 + 19.0153i 0.503126 + 0.782847i
\(591\) −11.9049 22.2403i −0.489701 0.914842i
\(592\) 9.64140 4.29263i 0.396259 0.176426i
\(593\) 27.4194 1.12598 0.562990 0.826464i \(-0.309651\pi\)
0.562990 + 0.826464i \(0.309651\pi\)
\(594\) 7.20384 6.59612i 0.295577 0.270642i
\(595\) 10.0614 + 6.60201i 0.412479 + 0.270656i
\(596\) 0.602002 + 5.72767i 0.0246590 + 0.234615i
\(597\) −1.99382 + 14.4791i −0.0816015 + 0.592588i
\(598\) 0.923681 1.02585i 0.0377721 0.0419502i
\(599\) 18.2288 + 31.5733i 0.744810 + 1.29005i 0.950283 + 0.311387i \(0.100793\pi\)
−0.205473 + 0.978663i \(0.565873\pi\)
\(600\) −3.19032 8.05120i −0.130244 0.328689i
\(601\) −6.56748 + 11.3752i −0.267893 + 0.464004i −0.968318 0.249722i \(-0.919661\pi\)
0.700425 + 0.713726i \(0.252994\pi\)
\(602\) 1.14970 + 3.53842i 0.0468584 + 0.144215i
\(603\) −14.2534 + 35.8517i −0.580443 + 1.45999i
\(604\) 0.259180 0.188305i 0.0105459 0.00766204i
\(605\) −2.53356 16.5023i −0.103004 0.670913i
\(606\) 1.28929 + 1.52786i 0.0523738 + 0.0620650i
\(607\) 14.1686 + 24.5407i 0.575085 + 0.996077i 0.996032 + 0.0889920i \(0.0283645\pi\)
−0.420947 + 0.907085i \(0.638302\pi\)
\(608\) −0.331363 + 3.15271i −0.0134386 + 0.127859i
\(609\) 4.08663 6.58065i 0.165598 0.266662i
\(610\) 0.0258481 + 0.168361i 0.00104656 + 0.00681673i
\(611\) 2.47861 + 7.62837i 0.100274 + 0.308611i
\(612\) 5.54981 + 21.7427i 0.224338 + 0.878898i
\(613\) −3.52020 + 10.8341i −0.142180 + 0.437584i −0.996638 0.0819367i \(-0.973889\pi\)
0.854458 + 0.519521i \(0.173889\pi\)
\(614\) −20.8353 4.42868i −0.840845 0.178727i
\(615\) −5.65238 + 4.24205i −0.227926 + 0.171056i
\(616\) −1.32293 + 0.281197i −0.0533022 + 0.0113297i
\(617\) 0.174388 1.65919i 0.00702061 0.0667966i −0.990451 0.137868i \(-0.955975\pi\)
0.997471 + 0.0710712i \(0.0226417\pi\)
\(618\) −19.4753 + 20.2800i −0.783413 + 0.815780i
\(619\) −24.8400 + 11.0595i −0.998403 + 0.444518i −0.839842 0.542831i \(-0.817352\pi\)
−0.158561 + 0.987349i \(0.550686\pi\)
\(620\) 4.99283 0.237931i 0.200517 0.00955555i
\(621\) −2.22681 4.89117i −0.0893588 0.196276i
\(622\) 10.0669 7.31404i 0.403646 0.293266i
\(623\) 3.63296 + 0.772210i 0.145552 + 0.0309380i
\(624\) −1.60123 + 1.66739i −0.0641006 + 0.0667489i
\(625\) −16.3729 18.8925i −0.654917 0.755701i
\(626\) 8.44674 + 14.6302i 0.337600 + 0.584740i
\(627\) −8.54060 + 5.79536i −0.341079 + 0.231444i
\(628\) 1.19010 + 11.3231i 0.0474903 + 0.451840i
\(629\) −63.8655 + 46.4010i −2.54648 + 1.85013i
\(630\) 4.37601 + 2.03617i 0.174344 + 0.0811231i
\(631\) 19.0417 + 13.8346i 0.758036 + 0.550746i 0.898307 0.439367i \(-0.144797\pi\)
−0.140271 + 0.990113i \(0.544797\pi\)
\(632\) 5.15625 8.93089i 0.205105 0.355252i
\(633\) 13.0680 + 15.4861i 0.519405 + 0.615516i
\(634\) 31.0666 6.60342i 1.23381 0.262255i
\(635\) 15.6252 19.1096i 0.620067 0.758339i
\(636\) −1.19724 16.4627i −0.0474736 0.652789i
\(637\) 5.78921 + 6.42957i 0.229377 + 0.254749i
\(638\) −3.61068 + 11.1125i −0.142948 + 0.439950i
\(639\) −6.92187 + 2.56308i −0.273825 + 0.101394i
\(640\) −1.74440 + 1.39895i −0.0689536 + 0.0552983i
\(641\) 10.0023 + 11.1087i 0.395068 + 0.438768i 0.907559 0.419925i \(-0.137944\pi\)
−0.512491 + 0.858693i \(0.671277\pi\)
\(642\) −0.0662525 + 0.183616i −0.00261478 + 0.00724674i
\(643\) 6.32557 + 10.9562i 0.249456 + 0.432071i 0.963375 0.268158i \(-0.0864148\pi\)
−0.713919 + 0.700229i \(0.753081\pi\)
\(644\) −0.0777853 + 0.740077i −0.00306517 + 0.0291631i
\(645\) −1.78454 + 19.9475i −0.0702663 + 0.785431i
\(646\) −2.47858 23.5821i −0.0975184 0.927826i
\(647\) −32.7616 + 23.8027i −1.28799 + 0.935781i −0.999763 0.0217810i \(-0.993066\pi\)
−0.288229 + 0.957562i \(0.593066\pi\)
\(648\) 3.46415 + 8.30660i 0.136085 + 0.326314i
\(649\) 19.0019 0.745891
\(650\) −2.77201 + 6.07045i −0.108727 + 0.238103i
\(651\) −1.92957 + 2.00929i −0.0756259 + 0.0787504i
\(652\) −13.2036 + 14.6641i −0.517094 + 0.574292i
\(653\) 25.8587 + 11.5130i 1.01193 + 0.450540i 0.844621 0.535365i \(-0.179826\pi\)
0.167308 + 0.985905i \(0.446493\pi\)
\(654\) 4.20205 + 3.26421i 0.164313 + 0.127641i
\(655\) −30.5993 + 15.4088i −1.19562 + 0.602073i
\(656\) 1.47623 + 1.07255i 0.0576373 + 0.0418759i
\(657\) −0.409975 10.1240i −0.0159947 0.394975i
\(658\) −3.49812 2.54153i −0.136371 0.0990793i
\(659\) −4.35331 4.83484i −0.169581 0.188339i 0.652364 0.757906i \(-0.273777\pi\)
−0.821945 + 0.569567i \(0.807111\pi\)
\(660\) −7.14378 1.40313i −0.278071 0.0546168i
\(661\) 5.46763 6.07242i 0.212666 0.236190i −0.627368 0.778723i \(-0.715868\pi\)
0.840035 + 0.542533i \(0.182535\pi\)
\(662\) −22.2341 + 4.72600i −0.864152 + 0.183681i
\(663\) 9.12234 14.6896i 0.354282 0.570497i
\(664\) 3.75103 + 0.797305i 0.145568 + 0.0309415i
\(665\) −4.26414 2.79800i −0.165356 0.108502i
\(666\) −22.6526 + 22.1203i −0.877769 + 0.857146i
\(667\) 5.20111 + 3.77883i 0.201388 + 0.146317i
\(668\) −11.5302 + 19.9710i −0.446118 + 0.772700i
\(669\) 6.48487 17.9725i 0.250719 0.694858i
\(670\) 27.8118 7.31099i 1.07446 0.282448i
\(671\) 0.130812 + 0.0582412i 0.00504993 + 0.00224838i
\(672\) 0.170003 1.23456i 0.00655801 0.0476241i
\(673\) 17.6525 + 3.75215i 0.680453 + 0.144635i 0.535156 0.844753i \(-0.320253\pi\)
0.145297 + 0.989388i \(0.453586\pi\)
\(674\) 13.4040 0.516303
\(675\) 17.3626 + 19.3271i 0.668288 + 0.743902i
\(676\) −11.2186 −0.431486
\(677\) 11.6319 + 2.47244i 0.447051 + 0.0950237i 0.425936 0.904753i \(-0.359945\pi\)
0.0211155 + 0.999777i \(0.493278\pi\)
\(678\) 3.99601 29.0189i 0.153466 1.11447i
\(679\) 7.96113 + 3.54453i 0.305520 + 0.136026i
\(680\) 10.5873 12.9482i 0.406005 0.496542i
\(681\) 1.66200 4.60617i 0.0636881 0.176509i
\(682\) 2.10100 3.63904i 0.0804515 0.139346i
\(683\) −13.7406 9.98316i −0.525771 0.381995i 0.293003 0.956112i \(-0.405346\pi\)
−0.818773 + 0.574117i \(0.805346\pi\)
\(684\) −2.35206 9.21479i −0.0899334 0.352336i
\(685\) 12.0741 44.2215i 0.461329 1.68962i
\(686\) −9.48852 2.01685i −0.362274 0.0770036i
\(687\) −3.54469 + 5.70799i −0.135239 + 0.217773i
\(688\) 5.05799 1.07511i 0.192834 0.0409881i
\(689\) −8.51089 + 9.45230i −0.324239 + 0.360104i
\(690\) −1.94886 + 3.49966i −0.0741918 + 0.133230i
\(691\) 34.1926 + 37.9747i 1.30075 + 1.44463i 0.825097 + 0.564991i \(0.191121\pi\)
0.475650 + 0.879634i \(0.342213\pi\)
\(692\) −8.41710 6.11538i −0.319970 0.232472i
\(693\) 3.42889 2.16924i 0.130253 0.0824026i
\(694\) −28.7277 20.8719i −1.09049 0.792286i
\(695\) 17.2275 + 2.81236i 0.653476 + 0.106679i
\(696\) −8.50237 6.60475i −0.322281 0.250352i
\(697\) −12.4688 5.55149i −0.472291 0.210278i
\(698\) 17.4806 19.4142i 0.661650 0.734837i
\(699\) −9.83678 + 10.2432i −0.372061 + 0.387433i
\(700\) −0.714559 3.52581i −0.0270078 0.133263i
\(701\) 4.13453 0.156159 0.0780795 0.996947i \(-0.475121\pi\)
0.0780795 + 0.996947i \(0.475121\pi\)
\(702\) 2.76780 6.35896i 0.104464 0.240004i
\(703\) 27.0668 19.6652i 1.02084 0.741687i
\(704\) 0.196488 + 1.86946i 0.00740542 + 0.0704579i
\(705\) −11.9485 19.9742i −0.450007 0.752271i
\(706\) 0.664683 6.32404i 0.0250157 0.238008i
\(707\) 0.415226 + 0.719193i 0.0156162 + 0.0270480i
\(708\) −5.94255 + 16.4695i −0.223335 + 0.618962i
\(709\) 13.0310 + 14.4724i 0.489390 + 0.543523i 0.936367 0.351023i \(-0.114166\pi\)
−0.446977 + 0.894546i \(0.647499\pi\)
\(710\) 4.59977 + 3.01823i 0.172626 + 0.113272i
\(711\) −5.20256 + 30.4969i −0.195111 + 1.14372i
\(712\) 1.59518 4.90946i 0.0597819 0.183990i
\(713\) −1.54703 1.71815i −0.0579367 0.0643453i
\(714\) 0.676119 + 9.29701i 0.0253031 + 0.347932i
\(715\) 3.03309 + 4.71939i 0.113431 + 0.176495i
\(716\) −8.10437 + 1.72264i −0.302875 + 0.0643780i
\(717\) 31.7796 + 37.6601i 1.18683 + 1.40644i
\(718\) 5.04002 8.72958i 0.188092 0.325785i
\(719\) 28.6950 + 20.8482i 1.07014 + 0.777505i 0.975938 0.218047i \(-0.0699687\pi\)
0.0942062 + 0.995553i \(0.469969\pi\)
\(720\) 3.45023 5.75290i 0.128583 0.214398i
\(721\) −9.44921 + 6.86525i −0.351907 + 0.255675i
\(722\) −0.935594 8.90158i −0.0348192 0.331283i
\(723\) 6.77642 4.59825i 0.252018 0.171011i
\(724\) 0.479302 + 0.830175i 0.0178131 + 0.0308532i
\(725\) −29.4661 9.88398i −1.09434 0.367082i
\(726\) 8.95766 9.32774i 0.332450 0.346185i
\(727\) −9.79765 2.08256i −0.363375 0.0772377i 0.0226061 0.999744i \(-0.492804\pi\)
−0.385981 + 0.922507i \(0.626137\pi\)
\(728\) −0.776900 + 0.564451i −0.0287938 + 0.0209199i
\(729\) −18.3991 19.7604i −0.681447 0.731867i
\(730\) −5.89161 + 4.72486i −0.218058 + 0.174875i
\(731\) −35.3348 + 15.7321i −1.30690 + 0.581871i
\(732\) −0.0913885 + 0.0951643i −0.00337782 + 0.00351737i
\(733\) −3.45557 + 32.8775i −0.127634 + 1.21436i 0.723842 + 0.689966i \(0.242374\pi\)
−0.851476 + 0.524393i \(0.824292\pi\)
\(734\) 7.89805 1.67878i 0.291522 0.0619650i
\(735\) −20.5373 14.4404i −0.757531 0.532642i
\(736\) 1.01167 + 0.215036i 0.0372905 + 0.00792635i
\(737\) 7.47029 22.9912i 0.275172 0.846892i
\(738\) −5.27044 1.47957i −0.194007 0.0544638i
\(739\) −4.45748 13.7187i −0.163971 0.504651i 0.834988 0.550268i \(-0.185475\pi\)
−0.998959 + 0.0456173i \(0.985475\pi\)
\(740\) 23.2908 + 3.80218i 0.856185 + 0.139771i
\(741\) −3.86614 + 6.22561i −0.142026 + 0.228703i
\(742\) 0.716721 6.81915i 0.0263117 0.250339i
\(743\) 17.1644 + 29.7296i 0.629701 + 1.09067i 0.987611 + 0.156919i \(0.0501561\pi\)
−0.357910 + 0.933756i \(0.616511\pi\)
\(744\) 2.49700 + 2.95905i 0.0915446 + 0.108484i
\(745\) −5.90083 + 11.4465i −0.216190 + 0.419369i
\(746\) −3.84759 + 2.79544i −0.140870 + 0.102348i
\(747\) −11.3834 + 1.66451i −0.416498 + 0.0609011i
\(748\) −4.34493 13.3723i −0.158866 0.488940i
\(749\) −0.0405439 + 0.0702240i −0.00148144 + 0.00256593i
\(750\) 3.91223 18.9656i 0.142854 0.692526i
\(751\) 14.9442 + 25.8842i 0.545323 + 0.944528i 0.998586 + 0.0531511i \(0.0169265\pi\)
−0.453263 + 0.891377i \(0.649740\pi\)
\(752\) −4.02123 + 4.46602i −0.146639 + 0.162859i
\(753\) −0.920476 + 6.68447i −0.0335440 + 0.243596i
\(754\) 0.867197 + 8.25083i 0.0315815 + 0.300477i
\(755\) 0.715545 0.0340990i 0.0260413 0.00124099i
\(756\) 0.807811 + 3.65031i 0.0293798 + 0.132760i
\(757\) −20.5936 −0.748487 −0.374243 0.927331i \(-0.622098\pi\)
−0.374243 + 0.927331i \(0.622098\pi\)
\(758\) −11.3838 + 5.06839i −0.413478 + 0.184092i
\(759\) 1.58917 + 2.96883i 0.0576833 + 0.107762i
\(760\) −4.48701 + 5.48759i −0.162761 + 0.199056i
\(761\) 4.20743 4.67283i 0.152519 0.169390i −0.662043 0.749466i \(-0.730310\pi\)
0.814562 + 0.580076i \(0.196977\pi\)
\(762\) 19.1106 + 0.614107i 0.692305 + 0.0222467i
\(763\) 1.47900 + 1.64259i 0.0535433 + 0.0594659i
\(764\) −4.10060 12.6203i −0.148354 0.456588i
\(765\) −16.2969 + 47.4568i −0.589215 + 1.71580i
\(766\) 7.46543 22.9762i 0.269737 0.830165i
\(767\) 12.3255 5.48766i 0.445048 0.198148i
\(768\) −1.68176 0.414342i −0.0606853 0.0149513i
\(769\) −2.70249 + 25.7124i −0.0974541 + 0.927214i 0.831126 + 0.556083i \(0.187697\pi\)
−0.928581 + 0.371131i \(0.878970\pi\)
\(770\) −2.81820 1.09717i −0.101561 0.0395391i
\(771\) −44.6357 + 18.1787i −1.60752 + 0.654690i
\(772\) −0.806904 7.67718i −0.0290411 0.276308i
\(773\) 11.6961 + 35.9969i 0.420679 + 1.29472i 0.907071 + 0.420977i \(0.138313\pi\)
−0.486392 + 0.873741i \(0.661687\pi\)
\(774\) −13.1098 + 8.29372i −0.471221 + 0.298112i
\(775\) 9.62613 + 5.68003i 0.345781 + 0.204033i
\(776\) 6.05599 10.4893i 0.217397 0.376543i
\(777\) −10.8832 + 7.38496i −0.390433 + 0.264934i
\(778\) 4.29714 + 1.91321i 0.154060 + 0.0685919i
\(779\) 5.28442 + 2.35278i 0.189334 + 0.0842970i
\(780\) −5.03898 + 1.15295i −0.180424 + 0.0412823i
\(781\) 4.22509 1.88113i 0.151185 0.0673121i
\(782\) −7.73627 −0.276649
\(783\) 30.8003 + 9.72406i 1.10071 + 0.347510i
\(784\) −2.00315 + 6.16506i −0.0715410 + 0.220181i
\(785\) −11.6654 + 22.6287i −0.416356 + 0.807654i
\(786\) −23.8842 11.5669i −0.851923 0.412579i
\(787\) 38.2124 8.12230i 1.36213 0.289529i 0.531830 0.846851i \(-0.321505\pi\)
0.830296 + 0.557322i \(0.188171\pi\)
\(788\) −14.2460 + 3.02808i −0.507493 + 0.107871i
\(789\) 25.3108 17.1750i 0.901088 0.611448i
\(790\) 20.5955 10.3712i 0.732756 0.368992i
\(791\) 3.76021 11.5727i 0.133698 0.411479i
\(792\) −2.50027 5.05470i −0.0888432 0.179611i
\(793\) 0.101670 0.00361041
\(794\) 22.7195 10.1154i 0.806287 0.358982i
\(795\) 17.9570 32.2462i 0.636869 1.14366i
\(796\) 7.70883 + 3.43219i 0.273232 + 0.121651i
\(797\) 26.8341 + 11.9473i 0.950511 + 0.423195i 0.822619 0.568593i \(-0.192512\pi\)
0.127892 + 0.991788i \(0.459179\pi\)
\(798\) −0.286546 3.94017i −0.0101436 0.139480i
\(799\) 22.4759 38.9293i 0.795139 1.37722i
\(800\) −4.97734 + 0.475466i −0.175976 + 0.0168103i
\(801\) 0.626611 + 15.4736i 0.0221402 + 0.546734i
\(802\) 3.06511 + 9.43345i 0.108233 + 0.333107i
\(803\) 0.663626 + 6.31398i 0.0234189 + 0.222816i
\(804\) 17.5909 + 13.6648i 0.620383 + 0.481922i
\(805\) −1.05330 + 1.28817i −0.0371238 + 0.0454022i
\(806\) 0.311865 2.96720i 0.0109850 0.104515i
\(807\) 13.7422 14.3100i 0.483750 0.503736i
\(808\) 1.05442 0.469460i 0.0370945 0.0165155i
\(809\) −5.79238 + 17.8271i −0.203649 + 0.626768i 0.796117 + 0.605143i \(0.206884\pi\)
−0.999766 + 0.0216251i \(0.993116\pi\)
\(810\) −3.71361 + 19.7790i −0.130483 + 0.694963i
\(811\) 6.41141 + 19.7323i 0.225135 + 0.692895i 0.998278 + 0.0586626i \(0.0186836\pi\)
−0.773143 + 0.634232i \(0.781316\pi\)
\(812\) −2.99258 3.32360i −0.105019 0.116635i
\(813\) −19.1089 35.6985i −0.670178 1.25200i
\(814\) 13.2746 14.7430i 0.465276 0.516741i
\(815\) −42.6735 + 11.2177i −1.49479 + 0.392940i
\(816\) 12.9490 + 0.416106i 0.453304 + 0.0145666i
\(817\) 14.9752 6.66740i 0.523917 0.233263i
\(818\) −13.9264 −0.486926
\(819\) 1.59766 2.39731i 0.0558268 0.0837687i
\(820\) 1.44414 + 3.81610i 0.0504316 + 0.133264i
\(821\) −2.00483 19.0746i −0.0699689 0.665709i −0.972151 0.234354i \(-0.924702\pi\)
0.902182 0.431355i \(-0.141964\pi\)
\(822\) 32.8850 13.3930i 1.14700 0.467134i
\(823\) −12.9569 + 14.3900i −0.451647 + 0.501605i −0.925368 0.379070i \(-0.876244\pi\)
0.473721 + 0.880675i \(0.342911\pi\)
\(824\) 8.11668 + 14.0585i 0.282758 + 0.489751i
\(825\) −11.6342 11.3867i −0.405052 0.396433i
\(826\) −3.63660 + 6.29878i −0.126534 + 0.219163i
\(827\) 1.39912 + 4.30604i 0.0486520 + 0.149736i 0.972431 0.233190i \(-0.0749165\pi\)
−0.923779 + 0.382926i \(0.874916\pi\)
\(828\) −3.07016 + 0.448924i −0.106695 + 0.0156012i
\(829\) 29.3340 21.3124i 1.01881 0.740209i 0.0527718 0.998607i \(-0.483194\pi\)
0.966039 + 0.258397i \(0.0831944\pi\)
\(830\) 6.03458 + 6.09207i 0.209463 + 0.211459i
\(831\) 7.93417 21.9892i 0.275233 0.762797i
\(832\) 0.667341 + 1.15587i 0.0231359 + 0.0400725i
\(833\) 5.06832 48.2218i 0.175607 1.67079i
\(834\) 6.38093 + 11.9206i 0.220954 + 0.412778i
\(835\) −46.0550 + 23.1918i −1.59380 + 0.802586i
\(836\) 1.84142 + 5.66732i 0.0636870 + 0.196008i
\(837\) −10.1074 5.72354i −0.349364 0.197834i
\(838\) −1.94995 + 6.00133i −0.0673599 + 0.207312i
\(839\) −42.5798 9.05061i −1.47002 0.312462i −0.597826 0.801626i \(-0.703968\pi\)
−0.872192 + 0.489164i \(0.837302\pi\)
\(840\) 1.83229 2.09949i 0.0632200 0.0724394i
\(841\) −9.42706 + 2.00378i −0.325071 + 0.0690960i
\(842\) 0.0737356 0.701548i 0.00254110 0.0241769i
\(843\) −12.6175 43.5446i −0.434569 1.49976i
\(844\) 10.6874 4.75835i 0.367877 0.163789i
\(845\) −20.9735 13.7622i −0.721512 0.473434i
\(846\) 6.66058 16.7534i 0.228996 0.575995i
\(847\) 4.34615 3.15767i 0.149336 0.108499i
\(848\) −9.32160 1.98137i −0.320105 0.0680405i
\(849\) −38.0014 9.36254i −1.30420 0.321321i
\(850\) 35.6773 11.2193i 1.22372 0.384820i
\(851\) −5.45774 9.45309i −0.187089 0.324048i
\(852\) 0.309100 + 4.25029i 0.0105896 + 0.145613i
\(853\) −3.90572 37.1604i −0.133729 1.27235i −0.831296 0.555830i \(-0.812401\pi\)
0.697567 0.716520i \(-0.254266\pi\)
\(854\) −0.0443407 + 0.0322154i −0.00151731 + 0.00110239i
\(855\) 6.90678 20.1127i 0.236207 0.687838i
\(856\) 0.0911766 + 0.0662437i 0.00311635 + 0.00226416i
\(857\) 20.3383 35.2270i 0.694745 1.20333i −0.275522 0.961295i \(-0.588851\pi\)
0.970267 0.242038i \(-0.0778159\pi\)
\(858\) −1.47488 + 4.08756i −0.0503515 + 0.139547i
\(859\) −30.2389 + 6.42747i −1.03174 + 0.219303i −0.692515 0.721403i \(-0.743497\pi\)
−0.339223 + 0.940706i \(0.610164\pi\)
\(860\) 10.7749 + 4.19483i 0.367422 + 0.143042i
\(861\) −2.04661 0.991157i −0.0697483 0.0337786i
\(862\) 18.7564 + 20.8311i 0.638846 + 0.709511i
\(863\) 4.25655 13.1003i 0.144895 0.445940i −0.852103 0.523374i \(-0.824673\pi\)
0.996997 + 0.0774347i \(0.0246729\pi\)
\(864\) 5.16297 0.586276i 0.175648 0.0199455i
\(865\) −8.23410 21.7584i −0.279968 0.739807i
\(866\) 2.77201 + 3.07863i 0.0941966 + 0.104616i
\(867\) −66.4049 + 11.8997i −2.25523 + 0.404133i
\(868\) 0.804182 + 1.39288i 0.0272957 + 0.0472776i
\(869\) 2.02628 19.2788i 0.0687370 0.653989i
\(870\) −7.79319 22.7779i −0.264214 0.772242i
\(871\) −1.79418 17.0705i −0.0607935 0.578411i
\(872\) 2.48533 1.80570i 0.0841640 0.0611487i
\(873\) −6.11038 + 35.8185i −0.206805 + 1.21227i
\(874\) 3.27871 0.110904
\(875\) 2.98932 7.46817i 0.101057 0.252470i
\(876\) −5.68004 1.39941i −0.191911 0.0472818i
\(877\) −21.0184 + 23.3434i −0.709743 + 0.788249i −0.984895 0.173152i \(-0.944605\pi\)
0.275153 + 0.961401i \(0.411272\pi\)
\(878\) 13.8711 + 6.17581i 0.468127 + 0.208424i
\(879\) 48.9304 19.9278i 1.65038 0.672147i
\(880\) −1.92598 + 3.73605i −0.0649247 + 0.125942i
\(881\) −7.76529 5.64181i −0.261619 0.190078i 0.449241 0.893410i \(-0.351694\pi\)
−0.710861 + 0.703333i \(0.751694\pi\)
\(882\) −0.786867 19.4310i −0.0264952 0.654277i
\(883\) −20.2132 14.6857i −0.680228 0.494215i 0.193205 0.981158i \(-0.438112\pi\)
−0.873433 + 0.486944i \(0.838112\pi\)
\(884\) −6.68017 7.41908i −0.224678 0.249531i
\(885\) −31.3134 + 23.5003i −1.05259 + 0.789955i
\(886\) −2.43741 + 2.70701i −0.0818863 + 0.0909439i
\(887\) 10.3475 2.19944i 0.347437 0.0738499i −0.0308881 0.999523i \(-0.509834\pi\)
0.378325 + 0.925673i \(0.376500\pi\)
\(888\) 8.62672 + 16.1161i 0.289494 + 0.540822i
\(889\) 7.76913 + 1.65138i 0.260568 + 0.0553855i
\(890\) 9.00480 7.22152i 0.301842 0.242066i
\(891\) 12.2997 + 11.6159i 0.412057 + 0.389147i
\(892\) −8.92446 6.48400i −0.298813 0.217100i
\(893\) −9.52549 + 16.4986i −0.318758 + 0.552106i
\(894\) −9.81886 + 1.75952i −0.328392 + 0.0588472i
\(895\) −17.2646 6.72134i −0.577091 0.224670i
\(896\) −0.657294 0.292646i −0.0219587 0.00977662i
\(897\) 1.88819 + 1.46677i 0.0630448 + 0.0489740i
\(898\) −27.2517 5.79252i −0.909399 0.193299i
\(899\) 13.8951 0.463426
\(900\) 13.5076 6.52272i 0.450252 0.217424i
\(901\) 71.2828 2.37477
\(902\) 3.35509 + 0.713146i 0.111712 + 0.0237452i
\(903\) −5.96814 + 2.43063i −0.198607 + 0.0808863i
\(904\) −15.4501 6.87881i −0.513861 0.228786i
\(905\) −0.122330 + 2.14001i −0.00406639 + 0.0711363i
\(906\) 0.357857 + 0.424074i 0.0118890 + 0.0140889i
\(907\) −9.91278 + 17.1694i −0.329148 + 0.570102i −0.982343 0.187088i \(-0.940095\pi\)
0.653195 + 0.757190i \(0.273428\pi\)
\(908\) −2.28725 1.66178i −0.0759049 0.0551481i
\(909\) −2.47738 + 2.41918i −0.0821696 + 0.0802390i
\(910\) −2.14486 + 0.102213i −0.0711016 + 0.00338831i
\(911\) −10.6329 2.26010i −0.352285 0.0748805i 0.0283704 0.999597i \(-0.490968\pi\)
−0.380655 + 0.924717i \(0.624302\pi\)
\(912\) −5.48790 0.176350i −0.181723 0.00583953i
\(913\) 7.05102 1.49874i 0.233355 0.0496011i
\(914\) 18.5939 20.6507i 0.615033 0.683063i
\(915\) −0.287594 + 0.0658035i −0.00950757 + 0.00217540i
\(916\) 2.59573 + 2.88285i 0.0857654 + 0.0952521i
\(917\) −8.91847 6.47965i −0.294514 0.213977i
\(918\) −36.8631 + 12.3188i −1.21666 + 0.406580i
\(919\) −25.7762 18.7275i −0.850280 0.617765i 0.0749433 0.997188i \(-0.476122\pi\)
−0.925223 + 0.379423i \(0.876122\pi\)
\(920\) 1.62755 + 1.64306i 0.0536587 + 0.0541700i
\(921\) 5.03295 36.5491i 0.165841 1.20434i
\(922\) −32.5104 14.4746i −1.07067 0.476695i
\(923\) 2.19731 2.44037i 0.0723255 0.0803256i
\(924\) −0.651964 2.25001i −0.0214480 0.0740200i
\(925\) 38.8785 + 35.6797i 1.27832 + 1.17314i
\(926\) 5.21977 0.171532
\(927\) −37.4801 31.0957i −1.23101 1.02132i
\(928\) −5.02879 + 3.65363i −0.165078 + 0.119936i
\(929\) −2.67698 25.4697i −0.0878288 0.835635i −0.946412 0.322961i \(-0.895322\pi\)
0.858583 0.512674i \(-0.171345\pi\)
\(930\) 1.03828 + 8.59517i 0.0340464 + 0.281847i
\(931\) −2.14800 + 20.4369i −0.0703980 + 0.669792i
\(932\) 4.09964 + 7.10079i 0.134288 + 0.232594i
\(933\) 13.8996 + 16.4716i 0.455053 + 0.539256i
\(934\) 2.76141 + 3.06685i 0.0903560 + 0.100350i
\(935\) 8.28122 30.3300i 0.270825 0.991896i
\(936\) −3.08156 2.55664i −0.100724 0.0835663i
\(937\) −11.8258 + 36.3961i −0.386332 + 1.18901i 0.549177 + 0.835706i \(0.314941\pi\)
−0.935509 + 0.353302i \(0.885059\pi\)
\(938\) 6.19147 + 6.87633i 0.202159 + 0.224520i
\(939\) −24.2123 + 16.4296i −0.790139 + 0.536161i
\(940\) −12.9964 + 3.41641i −0.423896 + 0.111431i
\(941\) 7.42016 1.57720i 0.241890 0.0514154i −0.0853711 0.996349i \(-0.527208\pi\)
0.327261 + 0.944934i \(0.393874\pi\)
\(942\) −19.4110 + 3.47841i −0.632443 + 0.113333i
\(943\) 0.943628 1.63441i 0.0307288 0.0532238i
\(944\) 8.17813 + 5.94176i 0.266175 + 0.193388i
\(945\) −2.96770 + 7.81532i −0.0965394 + 0.254232i
\(946\) 7.86381 5.71339i 0.255674 0.185758i
\(947\) 2.67354 + 25.4371i 0.0868785 + 0.826594i 0.948016 + 0.318222i \(0.103086\pi\)
−0.861138 + 0.508372i \(0.830248\pi\)
\(948\) 16.0758 + 7.78537i 0.522117 + 0.252857i
\(949\) 2.25390 + 3.90387i 0.0731647 + 0.126725i
\(950\) −15.1204 + 4.75487i −0.490570 + 0.154268i
\(951\) 15.3102 + 52.8377i 0.496469 + 1.71338i
\(952\) 5.26420 + 1.11894i 0.170614 + 0.0362651i
\(953\) 6.93928 5.04168i 0.224785 0.163316i −0.469693 0.882830i \(-0.655635\pi\)
0.694478 + 0.719514i \(0.255635\pi\)
\(954\) 28.2887 4.13644i 0.915882 0.133922i
\(955\) 7.81554 28.6244i 0.252905 0.926265i
\(956\) 25.9905 11.5717i 0.840592 0.374256i
\(957\) −19.6504 4.84134i −0.635207 0.156498i
\(958\) 1.19485 11.3682i 0.0386039 0.367291i
\(959\) 14.4277 3.06669i 0.465893 0.0990287i
\(960\) −2.63582 2.83769i −0.0850706 0.0915860i
\(961\) 25.4348 + 5.40633i 0.820476 + 0.174398i
\(962\) 4.35281 13.3966i 0.140340 0.431923i
\(963\) −0.325518 0.0913827i −0.0104897 0.00294477i
\(964\) −1.46105 4.49666i −0.0470573 0.144828i
\(965\) 7.90928 15.3426i 0.254609 0.493895i
\(966\) −1.28825 0.0413969i −0.0414487 0.00133192i
\(967\) 1.52627 14.5214i 0.0490814 0.466978i −0.942184 0.335096i \(-0.891231\pi\)
0.991265 0.131882i \(-0.0421021\pi\)
\(968\) −3.73326 6.46619i −0.119991 0.207831i
\(969\) 40.4264 7.24435i 1.29868 0.232722i
\(970\) 24.1893 12.1810i 0.776673 0.391107i
\(971\) 0.802141 0.582789i 0.0257419 0.0187026i −0.574840 0.818266i \(-0.694936\pi\)
0.600582 + 0.799563i \(0.294936\pi\)
\(972\) −13.9144 + 7.02785i −0.446303 + 0.225418i
\(973\) 1.73564 + 5.34176i 0.0556422 + 0.171249i
\(974\) 7.04960 12.2103i 0.225884 0.391242i
\(975\) −10.8349 4.02598i −0.346994 0.128935i
\(976\) 0.0380877 + 0.0659699i 0.00121916 + 0.00211164i
\(977\) 13.9210 15.4609i 0.445374 0.494638i −0.478097 0.878307i \(-0.658673\pi\)
0.923470 + 0.383670i \(0.125340\pi\)
\(978\) −26.9909 20.9669i −0.863074 0.670447i
\(979\) −1.01429 9.65035i −0.0324169 0.308427i
\(980\) −11.3078 + 9.06843i −0.361214 + 0.289680i
\(981\) −5.11098 + 7.66908i −0.163181 + 0.244855i
\(982\) 17.8171 0.568567
\(983\) 1.42941 0.636416i 0.0455912 0.0202985i −0.383814 0.923410i \(-0.625390\pi\)
0.429406 + 0.903112i \(0.358723\pi\)
\(984\) −1.66735 + 2.68492i −0.0531533 + 0.0855922i
\(985\) −30.3480 11.8149i −0.966967 0.376454i
\(986\) 31.1111 34.5523i 0.990778 1.10037i
\(987\) 3.95100 6.36226i 0.125762 0.202513i
\(988\) 2.83112 + 3.14428i 0.0900700 + 0.100033i
\(989\) −1.65268 5.08643i −0.0525522 0.161739i
\(990\) 1.52642 12.5171i 0.0485127 0.397818i
\(991\) −13.7377 + 42.2802i −0.436391 + 1.34307i 0.455263 + 0.890357i \(0.349545\pi\)
−0.891654 + 0.452717i \(0.850455\pi\)
\(992\) 2.04214 0.909218i 0.0648379 0.0288677i
\(993\) −10.9574 37.8154i −0.347722 1.20003i
\(994\) −0.185041 + 1.76055i −0.00586914 + 0.0558412i
\(995\) 10.2015 + 15.8732i 0.323410 + 0.503215i
\(996\) −0.906093 + 6.58002i −0.0287107 + 0.208496i
\(997\) −2.82392 26.8678i −0.0894346 0.850913i −0.943639 0.330976i \(-0.892622\pi\)
0.854205 0.519937i \(-0.174045\pi\)
\(998\) 4.77621 + 14.6997i 0.151188 + 0.465310i
\(999\) −41.0585 36.3531i −1.29903 1.15016i
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 450.2.q.c.331.7 yes 120
9.4 even 3 inner 450.2.q.c.31.1 120
25.21 even 5 inner 450.2.q.c.421.1 yes 120
225.121 even 15 inner 450.2.q.c.121.7 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.q.c.31.1 120 9.4 even 3 inner
450.2.q.c.121.7 yes 120 225.121 even 15 inner
450.2.q.c.331.7 yes 120 1.1 even 1 trivial
450.2.q.c.421.1 yes 120 25.21 even 5 inner