Properties

Label 440.2.bi.b.181.1
Level $440$
Weight $2$
Character 440.181
Analytic conductor $3.513$
Analytic rank $0$
Dimension $8$
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] = [440,2,Mod(141,440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(440, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("440.141");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 440.bi (of order \(10\), degree \(4\), 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: \(3.51341768894\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 181.1
Root \(-0.587785 - 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 440.181
Dual form 440.2.bi.b.141.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.642040 + 1.26007i) q^{2} +(-0.363271 + 0.500000i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-0.951057 - 0.309017i) q^{5} +(-0.396802 - 0.778768i) q^{6} +(0.618034 - 0.449028i) q^{7} +(2.79360 - 0.442463i) q^{8} +(0.809017 + 2.48990i) q^{9} +O(q^{10})\) \(q+(-0.642040 + 1.26007i) q^{2} +(-0.363271 + 0.500000i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-0.951057 - 0.309017i) q^{5} +(-0.396802 - 0.778768i) q^{6} +(0.618034 - 0.449028i) q^{7} +(2.79360 - 0.442463i) q^{8} +(0.809017 + 2.48990i) q^{9} +(1.00000 - 1.00000i) q^{10} +(3.21644 + 0.809017i) q^{11} +1.23607 q^{12} +(-0.726543 + 0.236068i) q^{13} +(0.169006 + 1.06706i) q^{14} +(0.500000 - 0.363271i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-0.118034 + 0.363271i) q^{17} +(-3.65688 - 0.579192i) q^{18} +(-4.75528 + 6.54508i) q^{19} +(0.618034 + 1.90211i) q^{20} +0.472136i q^{21} +(-3.08450 + 3.53353i) q^{22} -3.23607 q^{23} +(-0.793604 + 1.55754i) q^{24} +(0.809017 + 0.587785i) q^{25} +(0.169006 - 1.06706i) q^{26} +(-3.30220 - 1.07295i) q^{27} +(-1.45309 - 0.472136i) q^{28} +(2.35114 + 3.23607i) q^{29} +(0.136729 + 0.863271i) q^{30} +(0.618034 + 1.90211i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-1.57295 + 1.31433i) q^{33} +(-0.381966 - 0.381966i) q^{34} +(-0.726543 + 0.236068i) q^{35} +(3.07768 - 4.23607i) q^{36} +(4.70228 + 6.47214i) q^{37} +(-5.19421 - 10.1942i) q^{38} +(0.145898 - 0.449028i) q^{39} +(-2.79360 - 0.442463i) q^{40} +(5.97214 + 4.33901i) q^{41} +(-0.594926 - 0.303130i) q^{42} -1.85410i q^{43} +(-2.47214 - 6.15537i) q^{44} -2.61803i q^{45} +(2.07768 - 4.07768i) q^{46} +(-8.85410 - 6.43288i) q^{47} +(-1.45309 - 2.00000i) q^{48} +(-1.98278 + 6.10237i) q^{49} +(-1.26007 + 0.642040i) q^{50} +(-0.138757 - 0.190983i) q^{51} +(1.23607 + 0.898056i) q^{52} +(2.62866 - 0.854102i) q^{53} +(3.47214 - 3.47214i) q^{54} +(-2.80902 - 1.76336i) q^{55} +(1.52786 - 1.52786i) q^{56} +(-1.54508 - 4.75528i) q^{57} +(-5.58721 + 0.884927i) q^{58} +(0.951057 + 1.30902i) q^{59} +(-1.17557 - 0.381966i) q^{60} +(4.25325 + 1.38197i) q^{61} +(-2.79360 - 0.442463i) q^{62} +(1.61803 + 1.17557i) q^{63} +(7.60845 - 2.47214i) q^{64} +0.763932 q^{65} +(-0.646254 - 2.82588i) q^{66} +13.3262i q^{67} +(0.726543 - 0.236068i) q^{68} +(1.17557 - 1.61803i) q^{69} +(0.169006 - 1.06706i) q^{70} +(3.38197 - 10.4086i) q^{71} +(3.36176 + 6.59783i) q^{72} +(6.35410 - 4.61653i) q^{73} +(-11.1744 + 1.76985i) q^{74} +(-0.587785 + 0.190983i) q^{75} +16.1803 q^{76} +(2.35114 - 0.944272i) q^{77} +(0.472136 + 0.472136i) q^{78} +(0.708204 + 2.17963i) q^{79} +(2.35114 - 3.23607i) q^{80} +(-4.61803 + 3.35520i) q^{81} +(-9.30182 + 4.73951i) q^{82} +(-4.39201 - 1.42705i) q^{83} +(0.763932 - 0.555029i) q^{84} +(0.224514 - 0.309017i) q^{85} +(2.33630 + 1.19041i) q^{86} -2.47214 q^{87} +(9.34342 + 0.836916i) q^{88} -5.56231 q^{89} +(3.29892 + 1.68088i) q^{90} +(-0.343027 + 0.472136i) q^{91} +(3.80423 + 5.23607i) q^{92} +(-1.17557 - 0.381966i) q^{93} +(13.7906 - 7.02666i) q^{94} +(6.54508 - 4.75528i) q^{95} +(3.45309 - 0.546915i) q^{96} +(-0.899187 - 2.76741i) q^{97} +(-6.41641 - 6.41641i) q^{98} +(0.587785 + 8.66312i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + 6 q^{6} - 4 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} + 6 q^{6} - 4 q^{7} + 4 q^{8} + 2 q^{9} + 8 q^{10} - 8 q^{12} - 4 q^{14} + 4 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} - 4 q^{20} - 22 q^{22} - 8 q^{23} + 12 q^{24} + 2 q^{25} - 4 q^{26} + 4 q^{30} - 4 q^{31} - 32 q^{32} - 26 q^{33} - 12 q^{34} + 20 q^{38} + 28 q^{39} - 4 q^{40} + 12 q^{41} - 28 q^{42} + 16 q^{44} - 8 q^{46} - 44 q^{47} - 74 q^{49} + 2 q^{50} - 8 q^{52} - 8 q^{54} - 18 q^{55} + 48 q^{56} + 10 q^{57} - 8 q^{58} - 4 q^{62} + 4 q^{63} + 24 q^{65} + 4 q^{66} - 4 q^{70} + 36 q^{71} - 4 q^{72} + 24 q^{73} - 16 q^{74} + 40 q^{76} - 32 q^{78} - 48 q^{79} - 28 q^{81} + 22 q^{82} + 24 q^{84} + 18 q^{86} + 16 q^{87} - 4 q^{88} + 36 q^{89} + 2 q^{90} + 36 q^{94} + 30 q^{95} + 16 q^{96} + 42 q^{97} + 56 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/440\mathbb{Z}\right)^\times\).

\(n\) \(111\) \(177\) \(221\) \(321\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.642040 + 1.26007i −0.453990 + 0.891007i
\(3\) −0.363271 + 0.500000i −0.209735 + 0.288675i −0.900905 0.434017i \(-0.857096\pi\)
0.691170 + 0.722692i \(0.257096\pi\)
\(4\) −1.17557 1.61803i −0.587785 0.809017i
\(5\) −0.951057 0.309017i −0.425325 0.138197i
\(6\) −0.396802 0.778768i −0.161994 0.317931i
\(7\) 0.618034 0.449028i 0.233595 0.169717i −0.464830 0.885400i \(-0.653885\pi\)
0.698425 + 0.715683i \(0.253885\pi\)
\(8\) 2.79360 0.442463i 0.987688 0.156434i
\(9\) 0.809017 + 2.48990i 0.269672 + 0.829966i
\(10\) 1.00000 1.00000i 0.316228 0.316228i
\(11\) 3.21644 + 0.809017i 0.969793 + 0.243928i
\(12\) 1.23607 0.356822
\(13\) −0.726543 + 0.236068i −0.201507 + 0.0654735i −0.408031 0.912968i \(-0.633785\pi\)
0.206525 + 0.978441i \(0.433785\pi\)
\(14\) 0.169006 + 1.06706i 0.0451688 + 0.285184i
\(15\) 0.500000 0.363271i 0.129099 0.0937962i
\(16\) −1.23607 + 3.80423i −0.309017 + 0.951057i
\(17\) −0.118034 + 0.363271i −0.0286274 + 0.0881062i −0.964349 0.264632i \(-0.914749\pi\)
0.935722 + 0.352738i \(0.114749\pi\)
\(18\) −3.65688 0.579192i −0.861934 0.136517i
\(19\) −4.75528 + 6.54508i −1.09094 + 1.50155i −0.244057 + 0.969761i \(0.578478\pi\)
−0.846880 + 0.531785i \(0.821522\pi\)
\(20\) 0.618034 + 1.90211i 0.138197 + 0.425325i
\(21\) 0.472136i 0.103029i
\(22\) −3.08450 + 3.53353i −0.657618 + 0.753351i
\(23\) −3.23607 −0.674767 −0.337383 0.941367i \(-0.609542\pi\)
−0.337383 + 0.941367i \(0.609542\pi\)
\(24\) −0.793604 + 1.55754i −0.161994 + 0.317931i
\(25\) 0.809017 + 0.587785i 0.161803 + 0.117557i
\(26\) 0.169006 1.06706i 0.0331448 0.209268i
\(27\) −3.30220 1.07295i −0.635508 0.206489i
\(28\) −1.45309 0.472136i −0.274607 0.0892253i
\(29\) 2.35114 + 3.23607i 0.436596 + 0.600923i 0.969451 0.245284i \(-0.0788811\pi\)
−0.532855 + 0.846206i \(0.678881\pi\)
\(30\) 0.136729 + 0.863271i 0.0249631 + 0.157611i
\(31\) 0.618034 + 1.90211i 0.111002 + 0.341630i 0.991092 0.133177i \(-0.0425179\pi\)
−0.880090 + 0.474807i \(0.842518\pi\)
\(32\) −4.00000 4.00000i −0.707107 0.707107i
\(33\) −1.57295 + 1.31433i −0.273815 + 0.228795i
\(34\) −0.381966 0.381966i −0.0655066 0.0655066i
\(35\) −0.726543 + 0.236068i −0.122808 + 0.0399028i
\(36\) 3.07768 4.23607i 0.512947 0.706011i
\(37\) 4.70228 + 6.47214i 0.773050 + 1.06401i 0.996015 + 0.0891861i \(0.0284266\pi\)
−0.222965 + 0.974827i \(0.571573\pi\)
\(38\) −5.19421 10.1942i −0.842612 1.65372i
\(39\) 0.145898 0.449028i 0.0233624 0.0719020i
\(40\) −2.79360 0.442463i −0.441708 0.0699596i
\(41\) 5.97214 + 4.33901i 0.932691 + 0.677640i 0.946650 0.322263i \(-0.104444\pi\)
−0.0139593 + 0.999903i \(0.504444\pi\)
\(42\) −0.594926 0.303130i −0.0917991 0.0467740i
\(43\) 1.85410i 0.282748i −0.989956 0.141374i \(-0.954848\pi\)
0.989956 0.141374i \(-0.0451520\pi\)
\(44\) −2.47214 6.15537i −0.372689 0.927957i
\(45\) 2.61803i 0.390273i
\(46\) 2.07768 4.07768i 0.306338 0.601222i
\(47\) −8.85410 6.43288i −1.29150 0.938332i −0.291669 0.956519i \(-0.594211\pi\)
−0.999835 + 0.0181871i \(0.994211\pi\)
\(48\) −1.45309 2.00000i −0.209735 0.288675i
\(49\) −1.98278 + 6.10237i −0.283254 + 0.871767i
\(50\) −1.26007 + 0.642040i −0.178201 + 0.0907981i
\(51\) −0.138757 0.190983i −0.0194299 0.0267430i
\(52\) 1.23607 + 0.898056i 0.171412 + 0.124538i
\(53\) 2.62866 0.854102i 0.361074 0.117320i −0.122861 0.992424i \(-0.539207\pi\)
0.483935 + 0.875104i \(0.339207\pi\)
\(54\) 3.47214 3.47214i 0.472498 0.472498i
\(55\) −2.80902 1.76336i −0.378768 0.237771i
\(56\) 1.52786 1.52786i 0.204169 0.204169i
\(57\) −1.54508 4.75528i −0.204652 0.629853i
\(58\) −5.58721 + 0.884927i −0.733636 + 0.116197i
\(59\) 0.951057 + 1.30902i 0.123817 + 0.170419i 0.866426 0.499306i \(-0.166412\pi\)
−0.742609 + 0.669726i \(0.766412\pi\)
\(60\) −1.17557 0.381966i −0.151765 0.0493116i
\(61\) 4.25325 + 1.38197i 0.544573 + 0.176943i 0.568368 0.822774i \(-0.307575\pi\)
−0.0237949 + 0.999717i \(0.507575\pi\)
\(62\) −2.79360 0.442463i −0.354788 0.0561929i
\(63\) 1.61803 + 1.17557i 0.203853 + 0.148108i
\(64\) 7.60845 2.47214i 0.951057 0.309017i
\(65\) 0.763932 0.0947541
\(66\) −0.646254 2.82588i −0.0795484 0.347842i
\(67\) 13.3262i 1.62806i 0.580823 + 0.814030i \(0.302731\pi\)
−0.580823 + 0.814030i \(0.697269\pi\)
\(68\) 0.726543 0.236068i 0.0881062 0.0286274i
\(69\) 1.17557 1.61803i 0.141522 0.194788i
\(70\) 0.169006 1.06706i 0.0202001 0.127538i
\(71\) 3.38197 10.4086i 0.401366 1.23528i −0.522527 0.852623i \(-0.675010\pi\)
0.923892 0.382653i \(-0.124990\pi\)
\(72\) 3.36176 + 6.59783i 0.396188 + 0.777562i
\(73\) 6.35410 4.61653i 0.743691 0.540323i −0.150174 0.988660i \(-0.547983\pi\)
0.893865 + 0.448336i \(0.147983\pi\)
\(74\) −11.1744 + 1.76985i −1.29900 + 0.205741i
\(75\) −0.587785 + 0.190983i −0.0678716 + 0.0220528i
\(76\) 16.1803 1.85601
\(77\) 2.35114 0.944272i 0.267937 0.107610i
\(78\) 0.472136 + 0.472136i 0.0534589 + 0.0534589i
\(79\) 0.708204 + 2.17963i 0.0796792 + 0.245227i 0.982959 0.183824i \(-0.0588478\pi\)
−0.903280 + 0.429052i \(0.858848\pi\)
\(80\) 2.35114 3.23607i 0.262866 0.361803i
\(81\) −4.61803 + 3.35520i −0.513115 + 0.372800i
\(82\) −9.30182 + 4.73951i −1.02721 + 0.523392i
\(83\) −4.39201 1.42705i −0.482086 0.156639i 0.0578844 0.998323i \(-0.481565\pi\)
−0.539970 + 0.841684i \(0.681565\pi\)
\(84\) 0.763932 0.555029i 0.0833518 0.0605586i
\(85\) 0.224514 0.309017i 0.0243520 0.0335176i
\(86\) 2.33630 + 1.19041i 0.251930 + 0.128365i
\(87\) −2.47214 −0.265041
\(88\) 9.34342 + 0.836916i 0.996012 + 0.0892155i
\(89\) −5.56231 −0.589603 −0.294802 0.955558i \(-0.595254\pi\)
−0.294802 + 0.955558i \(0.595254\pi\)
\(90\) 3.29892 + 1.68088i 0.347736 + 0.177180i
\(91\) −0.343027 + 0.472136i −0.0359590 + 0.0494933i
\(92\) 3.80423 + 5.23607i 0.396618 + 0.545898i
\(93\) −1.17557 0.381966i −0.121901 0.0396080i
\(94\) 13.7906 7.02666i 1.42239 0.724744i
\(95\) 6.54508 4.75528i 0.671512 0.487882i
\(96\) 3.45309 0.546915i 0.352429 0.0558193i
\(97\) −0.899187 2.76741i −0.0912986 0.280988i 0.894973 0.446121i \(-0.147195\pi\)
−0.986271 + 0.165133i \(0.947195\pi\)
\(98\) −6.41641 6.41641i −0.648155 0.648155i
\(99\) 0.587785 + 8.66312i 0.0590746 + 0.870676i
\(100\) 2.00000i 0.200000i
\(101\) 13.4863 4.38197i 1.34194 0.436022i 0.451965 0.892036i \(-0.350723\pi\)
0.889973 + 0.456014i \(0.150723\pi\)
\(102\) 0.329740 0.0522257i 0.0326492 0.00517112i
\(103\) −9.47214 + 6.88191i −0.933317 + 0.678095i −0.946803 0.321814i \(-0.895707\pi\)
0.0134855 + 0.999909i \(0.495707\pi\)
\(104\) −1.92522 + 0.980949i −0.188783 + 0.0961900i
\(105\) 0.145898 0.449028i 0.0142382 0.0438206i
\(106\) −0.611469 + 3.86067i −0.0593912 + 0.374981i
\(107\) 1.26133 1.73607i 0.121937 0.167832i −0.743685 0.668531i \(-0.766924\pi\)
0.865622 + 0.500699i \(0.166924\pi\)
\(108\) 2.14590 + 6.60440i 0.206489 + 0.635508i
\(109\) 16.4721i 1.57774i −0.614557 0.788872i \(-0.710665\pi\)
0.614557 0.788872i \(-0.289335\pi\)
\(110\) 4.02546 2.40742i 0.383812 0.229539i
\(111\) −4.94427 −0.469290
\(112\) 0.944272 + 2.90617i 0.0892253 + 0.274607i
\(113\) 13.3992 + 9.73508i 1.26049 + 0.915799i 0.998782 0.0493479i \(-0.0157143\pi\)
0.261708 + 0.965147i \(0.415714\pi\)
\(114\) 6.98401 + 1.10616i 0.654113 + 0.103601i
\(115\) 3.07768 + 1.00000i 0.286995 + 0.0932505i
\(116\) 2.47214 7.60845i 0.229532 0.706427i
\(117\) −1.17557 1.61803i −0.108682 0.149587i
\(118\) −2.26007 + 0.357960i −0.208057 + 0.0329529i
\(119\) 0.0901699 + 0.277515i 0.00826587 + 0.0254397i
\(120\) 1.23607 1.23607i 0.112837 0.112837i
\(121\) 9.69098 + 5.20431i 0.880998 + 0.473119i
\(122\) −4.47214 + 4.47214i −0.404888 + 0.404888i
\(123\) −4.33901 + 1.40983i −0.391235 + 0.127120i
\(124\) 2.35114 3.23607i 0.211139 0.290607i
\(125\) −0.587785 0.809017i −0.0525731 0.0723607i
\(126\) −2.52015 + 1.28408i −0.224513 + 0.114395i
\(127\) 5.47214 16.8415i 0.485574 1.49444i −0.345575 0.938391i \(-0.612316\pi\)
0.831148 0.556051i \(-0.187684\pi\)
\(128\) −1.76985 + 11.1744i −0.156434 + 0.987688i
\(129\) 0.927051 + 0.673542i 0.0816223 + 0.0593021i
\(130\) −0.490475 + 0.962611i −0.0430175 + 0.0844265i
\(131\) 15.3262i 1.33906i −0.742785 0.669530i \(-0.766496\pi\)
0.742785 0.669530i \(-0.233504\pi\)
\(132\) 3.97574 + 1.00000i 0.346044 + 0.0870388i
\(133\) 6.18034i 0.535903i
\(134\) −16.7920 8.55597i −1.45061 0.739123i
\(135\) 2.80902 + 2.04087i 0.241762 + 0.175650i
\(136\) −0.169006 + 1.06706i −0.0144921 + 0.0914998i
\(137\) 4.89919 15.0781i 0.418566 1.28821i −0.490457 0.871466i \(-0.663170\pi\)
0.909022 0.416747i \(-0.136830\pi\)
\(138\) 1.28408 + 2.52015i 0.109308 + 0.214529i
\(139\) 0.898056 + 1.23607i 0.0761721 + 0.104842i 0.845403 0.534129i \(-0.179360\pi\)
−0.769231 + 0.638971i \(0.779360\pi\)
\(140\) 1.23607 + 0.898056i 0.104467 + 0.0758996i
\(141\) 6.43288 2.09017i 0.541746 0.176024i
\(142\) 10.9443 + 10.9443i 0.918423 + 0.918423i
\(143\) −2.52786 + 0.171513i −0.211391 + 0.0143427i
\(144\) −10.4721 −0.872678
\(145\) −1.23607 3.80423i −0.102650 0.315924i
\(146\) 1.73758 + 10.9706i 0.143803 + 0.907936i
\(147\) −2.33090 3.20820i −0.192249 0.264608i
\(148\) 4.94427 15.2169i 0.406417 1.25082i
\(149\) −6.43288 2.09017i −0.527002 0.171233i 0.0334186 0.999441i \(-0.489361\pi\)
−0.560421 + 0.828208i \(0.689361\pi\)
\(150\) 0.136729 0.863271i 0.0111639 0.0704858i
\(151\) 11.2361 + 8.16348i 0.914378 + 0.664335i 0.942118 0.335280i \(-0.108831\pi\)
−0.0277401 + 0.999615i \(0.508831\pi\)
\(152\) −10.3884 + 20.3884i −0.842612 + 1.65372i
\(153\) −1.00000 −0.0808452
\(154\) −0.319673 + 3.56887i −0.0257600 + 0.287588i
\(155\) 2.00000i 0.160644i
\(156\) −0.898056 + 0.291796i −0.0719020 + 0.0233624i
\(157\) −5.70634 + 7.85410i −0.455415 + 0.626826i −0.973550 0.228473i \(-0.926627\pi\)
0.518135 + 0.855299i \(0.326627\pi\)
\(158\) −3.20119 0.507018i −0.254673 0.0403362i
\(159\) −0.527864 + 1.62460i −0.0418623 + 0.128839i
\(160\) 2.56816 + 5.04029i 0.203031 + 0.398470i
\(161\) −2.00000 + 1.45309i −0.157622 + 0.114519i
\(162\) −1.26284 7.97323i −0.0992178 0.626436i
\(163\) 4.16750 1.35410i 0.326424 0.106061i −0.141221 0.989978i \(-0.545103\pi\)
0.467644 + 0.883917i \(0.345103\pi\)
\(164\) 14.7639i 1.15287i
\(165\) 1.90211 0.763932i 0.148079 0.0594720i
\(166\) 4.61803 4.61803i 0.358429 0.358429i
\(167\) −1.70820 5.25731i −0.132185 0.406823i 0.862957 0.505278i \(-0.168610\pi\)
−0.995142 + 0.0984549i \(0.968610\pi\)
\(168\) 0.208903 + 1.31896i 0.0161172 + 0.101760i
\(169\) −10.0451 + 7.29818i −0.772699 + 0.561399i
\(170\) 0.245237 + 0.481305i 0.0188088 + 0.0369144i
\(171\) −20.1437 6.54508i −1.54043 0.500515i
\(172\) −3.00000 + 2.17963i −0.228748 + 0.166195i
\(173\) 5.42882 7.47214i 0.412746 0.568096i −0.551140 0.834413i \(-0.685807\pi\)
0.963885 + 0.266317i \(0.0858068\pi\)
\(174\) 1.58721 3.11507i 0.120326 0.236153i
\(175\) 0.763932 0.0577478
\(176\) −7.05342 + 11.2361i −0.531672 + 0.846950i
\(177\) −1.00000 −0.0751646
\(178\) 3.57122 7.00891i 0.267674 0.525340i
\(179\) 4.20025 5.78115i 0.313942 0.432104i −0.622664 0.782490i \(-0.713950\pi\)
0.936605 + 0.350386i \(0.113950\pi\)
\(180\) −4.23607 + 3.07768i −0.315738 + 0.229397i
\(181\) −19.0211 6.18034i −1.41383 0.459381i −0.500193 0.865914i \(-0.666738\pi\)
−0.913636 + 0.406533i \(0.866738\pi\)
\(182\) −0.374689 0.735369i −0.0277738 0.0545092i
\(183\) −2.23607 + 1.62460i −0.165295 + 0.120094i
\(184\) −9.04029 + 1.43184i −0.666459 + 0.105557i
\(185\) −2.47214 7.60845i −0.181755 0.559385i
\(186\) 1.23607 1.23607i 0.0906329 0.0906329i
\(187\) −0.673542 + 1.07295i −0.0492543 + 0.0784618i
\(188\) 21.8885i 1.59639i
\(189\) −2.52265 + 0.819660i −0.183496 + 0.0596215i
\(190\) 1.78980 + 11.3004i 0.129846 + 0.819815i
\(191\) −9.85410 + 7.15942i −0.713018 + 0.518038i −0.884146 0.467211i \(-0.845259\pi\)
0.171128 + 0.985249i \(0.445259\pi\)
\(192\) −1.52786 + 4.70228i −0.110264 + 0.339358i
\(193\) −1.85410 + 5.70634i −0.133461 + 0.410751i −0.995347 0.0963503i \(-0.969283\pi\)
0.861886 + 0.507102i \(0.169283\pi\)
\(194\) 4.06446 + 0.643747i 0.291811 + 0.0462183i
\(195\) −0.277515 + 0.381966i −0.0198732 + 0.0273532i
\(196\) 12.2047 3.96556i 0.871767 0.283254i
\(197\) 14.9443i 1.06474i −0.846513 0.532368i \(-0.821302\pi\)
0.846513 0.532368i \(-0.178698\pi\)
\(198\) −11.2935 4.82141i −0.802598 0.342643i
\(199\) 8.65248 0.613358 0.306679 0.951813i \(-0.400782\pi\)
0.306679 + 0.951813i \(0.400782\pi\)
\(200\) 2.52015 + 1.28408i 0.178201 + 0.0907981i
\(201\) −6.66312 4.84104i −0.469980 0.341461i
\(202\) −3.13714 + 19.8071i −0.220728 + 1.39362i
\(203\) 2.90617 + 0.944272i 0.203973 + 0.0662749i
\(204\) −0.145898 + 0.449028i −0.0102149 + 0.0314382i
\(205\) −4.33901 5.97214i −0.303050 0.417112i
\(206\) −2.59023 16.3540i −0.180470 1.13944i
\(207\) −2.61803 8.05748i −0.181966 0.560034i
\(208\) 3.05573i 0.211877i
\(209\) −20.5902 + 17.2048i −1.42425 + 1.19008i
\(210\) 0.472136 + 0.472136i 0.0325805 + 0.0325805i
\(211\) −7.74721 + 2.51722i −0.533340 + 0.173293i −0.563291 0.826259i \(-0.690465\pi\)
0.0299509 + 0.999551i \(0.490465\pi\)
\(212\) −4.47214 3.24920i −0.307148 0.223156i
\(213\) 3.97574 + 5.47214i 0.272413 + 0.374945i
\(214\) 1.37775 + 2.70399i 0.0941811 + 0.184841i
\(215\) −0.572949 + 1.76336i −0.0390748 + 0.120260i
\(216\) −9.69977 1.53629i −0.659986 0.104532i
\(217\) 1.23607 + 0.898056i 0.0839098 + 0.0609640i
\(218\) 20.7561 + 10.5758i 1.40578 + 0.716281i
\(219\) 4.85410i 0.328010i
\(220\) 0.449028 + 6.61803i 0.0302735 + 0.446188i
\(221\) 0.291796i 0.0196283i
\(222\) 3.17442 6.23015i 0.213053 0.418140i
\(223\) 2.00000 + 1.45309i 0.133930 + 0.0973058i 0.652733 0.757588i \(-0.273622\pi\)
−0.518803 + 0.854894i \(0.673622\pi\)
\(224\) −4.26825 0.676024i −0.285184 0.0451688i
\(225\) −0.809017 + 2.48990i −0.0539345 + 0.165993i
\(226\) −20.8697 + 10.6337i −1.38823 + 0.707340i
\(227\) −12.1922 16.7812i −0.809226 1.11380i −0.991442 0.130546i \(-0.958327\pi\)
0.182216 0.983259i \(-0.441673\pi\)
\(228\) −5.87785 + 8.09017i −0.389270 + 0.535785i
\(229\) −4.42477 + 1.43769i −0.292397 + 0.0950055i −0.451542 0.892250i \(-0.649126\pi\)
0.159146 + 0.987255i \(0.449126\pi\)
\(230\) −3.23607 + 3.23607i −0.213380 + 0.213380i
\(231\) −0.381966 + 1.51860i −0.0251315 + 0.0999164i
\(232\) 8.00000 + 8.00000i 0.525226 + 0.525226i
\(233\) 0.0450850 + 0.138757i 0.00295361 + 0.00909029i 0.952522 0.304468i \(-0.0984788\pi\)
−0.949569 + 0.313559i \(0.898479\pi\)
\(234\) 2.79360 0.442463i 0.182624 0.0289247i
\(235\) 6.43288 + 8.85410i 0.419635 + 0.577578i
\(236\) 1.00000 3.07768i 0.0650945 0.200340i
\(237\) −1.34708 0.437694i −0.0875025 0.0284313i
\(238\) −0.407581 0.0645546i −0.0264196 0.00418445i
\(239\) 21.5623 + 15.6659i 1.39475 + 1.01334i 0.995325 + 0.0965787i \(0.0307900\pi\)
0.399424 + 0.916766i \(0.369210\pi\)
\(240\) 0.763932 + 2.35114i 0.0493116 + 0.151765i
\(241\) 21.9787 1.41577 0.707887 0.706326i \(-0.249649\pi\)
0.707887 + 0.706326i \(0.249649\pi\)
\(242\) −12.7798 + 8.86998i −0.821517 + 0.570184i
\(243\) 13.9443i 0.894525i
\(244\) −2.76393 8.50651i −0.176943 0.544573i
\(245\) 3.77147 5.19098i 0.240950 0.331640i
\(246\) 1.00933 6.37264i 0.0643523 0.406305i
\(247\) 1.90983 5.87785i 0.121520 0.373999i
\(248\) 2.56816 + 5.04029i 0.163078 + 0.320059i
\(249\) 2.30902 1.67760i 0.146328 0.106314i
\(250\) 1.39680 0.221232i 0.0883415 0.0139919i
\(251\) 11.4127 3.70820i 0.720362 0.234060i 0.0741818 0.997245i \(-0.476365\pi\)
0.646180 + 0.763185i \(0.276365\pi\)
\(252\) 4.00000i 0.251976i
\(253\) −10.4086 2.61803i −0.654384 0.164594i
\(254\) 17.7082 + 17.7082i 1.11111 + 1.11111i
\(255\) 0.0729490 + 0.224514i 0.00456824 + 0.0140596i
\(256\) −12.9443 9.40456i −0.809017 0.587785i
\(257\) −13.5902 + 9.87384i −0.847732 + 0.615913i −0.924520 0.381134i \(-0.875533\pi\)
0.0767881 + 0.997047i \(0.475533\pi\)
\(258\) −1.44392 + 0.735712i −0.0898943 + 0.0458034i
\(259\) 5.81234 + 1.88854i 0.361161 + 0.117348i
\(260\) −0.898056 1.23607i −0.0556951 0.0766577i
\(261\) −6.15537 + 8.47214i −0.381008 + 0.524412i
\(262\) 19.3122 + 9.84005i 1.19311 + 0.607920i
\(263\) −24.7639 −1.52701 −0.763505 0.645802i \(-0.776523\pi\)
−0.763505 + 0.645802i \(0.776523\pi\)
\(264\) −3.81266 + 4.36768i −0.234653 + 0.268812i
\(265\) −2.76393 −0.169787
\(266\) −7.78768 3.96802i −0.477493 0.243295i
\(267\) 2.02063 2.78115i 0.123660 0.170204i
\(268\) 21.5623 15.6659i 1.31713 0.956949i
\(269\) −13.2088 4.29180i −0.805354 0.261675i −0.122725 0.992441i \(-0.539163\pi\)
−0.682629 + 0.730765i \(0.739163\pi\)
\(270\) −4.37515 + 2.22925i −0.266263 + 0.135668i
\(271\) −12.7082 + 9.23305i −0.771968 + 0.560868i −0.902558 0.430569i \(-0.858313\pi\)
0.130589 + 0.991437i \(0.458313\pi\)
\(272\) −1.23607 0.898056i −0.0749476 0.0544526i
\(273\) −0.111456 0.343027i −0.00674563 0.0207609i
\(274\) 15.8541 + 15.8541i 0.957781 + 0.957781i
\(275\) 2.12663 + 2.54508i 0.128240 + 0.153474i
\(276\) −4.00000 −0.240772
\(277\) −12.7598 + 4.14590i −0.766660 + 0.249103i −0.666135 0.745832i \(-0.732052\pi\)
−0.100525 + 0.994935i \(0.532052\pi\)
\(278\) −2.13412 + 0.338012i −0.127996 + 0.0202726i
\(279\) −4.23607 + 3.07768i −0.253607 + 0.184256i
\(280\) −1.92522 + 0.980949i −0.115054 + 0.0586229i
\(281\) 3.04508 9.37181i 0.181655 0.559075i −0.818220 0.574905i \(-0.805039\pi\)
0.999875 + 0.0158298i \(0.00503900\pi\)
\(282\) −1.49640 + 9.44788i −0.0891091 + 0.562613i
\(283\) 6.15537 8.47214i 0.365899 0.503616i −0.585882 0.810397i \(-0.699252\pi\)
0.951780 + 0.306780i \(0.0992517\pi\)
\(284\) −20.8172 + 6.76393i −1.23528 + 0.401366i
\(285\) 5.00000i 0.296174i
\(286\) 1.40687 3.29541i 0.0831899 0.194862i
\(287\) 5.63932 0.332879
\(288\) 6.72353 13.1957i 0.396188 0.777562i
\(289\) 13.6353 + 9.90659i 0.802074 + 0.582741i
\(290\) 5.58721 + 0.884927i 0.328092 + 0.0519647i
\(291\) 1.71036 + 0.555728i 0.100263 + 0.0325774i
\(292\) −14.9394 4.85410i −0.874262 0.284065i
\(293\) 18.0171 + 24.7984i 1.05257 + 1.44874i 0.886561 + 0.462612i \(0.153088\pi\)
0.166008 + 0.986124i \(0.446912\pi\)
\(294\) 5.53910 0.877307i 0.323047 0.0511656i
\(295\) −0.500000 1.53884i −0.0291111 0.0895948i
\(296\) 16.0000 + 16.0000i 0.929981 + 0.929981i
\(297\) −9.75329 6.12261i −0.565943 0.355270i
\(298\) 6.76393 6.76393i 0.391824 0.391824i
\(299\) 2.35114 0.763932i 0.135970 0.0441793i
\(300\) 1.00000 + 0.726543i 0.0577350 + 0.0419470i
\(301\) −0.832544 1.14590i −0.0479870 0.0660485i
\(302\) −17.5006 + 8.91699i −1.00705 + 0.513115i
\(303\) −2.70820 + 8.33499i −0.155582 + 0.478833i
\(304\) −19.0211 26.1803i −1.09094 1.50155i
\(305\) −3.61803 2.62866i −0.207168 0.150516i
\(306\) 0.642040 1.26007i 0.0367030 0.0720336i
\(307\) 5.56231i 0.317458i −0.987322 0.158729i \(-0.949260\pi\)
0.987322 0.158729i \(-0.0507395\pi\)
\(308\) −4.29180 2.69417i −0.244548 0.153514i
\(309\) 7.23607i 0.411646i
\(310\) 2.52015 + 1.28408i 0.143135 + 0.0729308i
\(311\) 1.09017 + 0.792055i 0.0618179 + 0.0449133i 0.618265 0.785970i \(-0.287836\pi\)
−0.556447 + 0.830883i \(0.687836\pi\)
\(312\) 0.208903 1.31896i 0.0118268 0.0746715i
\(313\) 8.88197 27.3359i 0.502038 1.54512i −0.303655 0.952782i \(-0.598207\pi\)
0.805693 0.592333i \(-0.201793\pi\)
\(314\) −6.23305 12.2331i −0.351751 0.690351i
\(315\) −1.17557 1.61803i −0.0662359 0.0911659i
\(316\) 2.69417 3.70820i 0.151559 0.208603i
\(317\) 5.60034 1.81966i 0.314546 0.102202i −0.147489 0.989064i \(-0.547119\pi\)
0.462036 + 0.886861i \(0.347119\pi\)
\(318\) −1.70820 1.70820i −0.0957913 0.0957913i
\(319\) 4.94427 + 12.3107i 0.276826 + 0.689269i
\(320\) −8.00000 −0.447214
\(321\) 0.409830 + 1.26133i 0.0228745 + 0.0704004i
\(322\) −0.546915 3.45309i −0.0304784 0.192433i
\(323\) −1.81636 2.50000i −0.101065 0.139104i
\(324\) 10.8576 + 3.52786i 0.603203 + 0.195992i
\(325\) −0.726543 0.236068i −0.0403013 0.0130947i
\(326\) −0.969430 + 6.12074i −0.0536918 + 0.338996i
\(327\) 8.23607 + 5.98385i 0.455456 + 0.330908i
\(328\) 18.6036 + 9.47903i 1.02721 + 0.523392i
\(329\) −8.36068 −0.460939
\(330\) −0.258621 + 2.88728i −0.0142366 + 0.158939i
\(331\) 10.0344i 0.551543i −0.961223 0.275771i \(-0.911067\pi\)
0.961223 0.275771i \(-0.0889333\pi\)
\(332\) 2.85410 + 8.78402i 0.156639 + 0.482086i
\(333\) −12.3107 + 16.9443i −0.674624 + 0.928540i
\(334\) 7.72133 + 1.22294i 0.422493 + 0.0669162i
\(335\) 4.11803 12.6740i 0.224992 0.692455i
\(336\) −1.79611 0.583592i −0.0979859 0.0318376i
\(337\) 27.5795 20.0377i 1.50235 1.09152i 0.532920 0.846166i \(-0.321095\pi\)
0.969433 0.245357i \(-0.0789053\pi\)
\(338\) −2.74690 17.3433i −0.149412 0.943349i
\(339\) −9.73508 + 3.16312i −0.528737 + 0.171797i
\(340\) −0.763932 −0.0414300
\(341\) 0.449028 + 6.61803i 0.0243162 + 0.358387i
\(342\) 21.1803 21.1803i 1.14530 1.14530i
\(343\) 3.16718 + 9.74759i 0.171012 + 0.526320i
\(344\) −0.820372 5.17963i −0.0442315 0.279267i
\(345\) −1.61803 + 1.17557i −0.0871120 + 0.0632906i
\(346\) 5.92992 + 11.6381i 0.318795 + 0.625669i
\(347\) 20.4540 + 6.64590i 1.09803 + 0.356770i 0.801343 0.598205i \(-0.204119\pi\)
0.296684 + 0.954976i \(0.404119\pi\)
\(348\) 2.90617 + 4.00000i 0.155787 + 0.214423i
\(349\) 9.95959 13.7082i 0.533125 0.733783i −0.454478 0.890758i \(-0.650174\pi\)
0.987603 + 0.156975i \(0.0501741\pi\)
\(350\) −0.490475 + 0.962611i −0.0262170 + 0.0514537i
\(351\) 2.65248 0.141579
\(352\) −9.62970 16.1018i −0.513264 0.858230i
\(353\) 10.8541 0.577706 0.288853 0.957374i \(-0.406726\pi\)
0.288853 + 0.957374i \(0.406726\pi\)
\(354\) 0.642040 1.26007i 0.0341240 0.0669722i
\(355\) −6.43288 + 8.85410i −0.341422 + 0.469927i
\(356\) 6.53888 + 9.00000i 0.346560 + 0.476999i
\(357\) −0.171513 0.0557281i −0.00907745 0.00294944i
\(358\) 4.58795 + 9.00436i 0.242481 + 0.475895i
\(359\) 16.9443 12.3107i 0.894284 0.649736i −0.0427071 0.999088i \(-0.513598\pi\)
0.936992 + 0.349352i \(0.113598\pi\)
\(360\) −1.15838 7.31375i −0.0610522 0.385469i
\(361\) −14.3541 44.1774i −0.755479 2.32513i
\(362\) 20.0000 20.0000i 1.05118 1.05118i
\(363\) −6.12261 + 2.95492i −0.321354 + 0.155093i
\(364\) 1.16718 0.0611771
\(365\) −7.46969 + 2.42705i −0.390982 + 0.127038i
\(366\) −0.611469 3.86067i −0.0319620 0.201800i
\(367\) −6.23607 + 4.53077i −0.325520 + 0.236504i −0.738527 0.674224i \(-0.764478\pi\)
0.413007 + 0.910728i \(0.364478\pi\)
\(368\) 4.00000 12.3107i 0.208514 0.641741i
\(369\) −5.97214 + 18.3803i −0.310897 + 0.956843i
\(370\) 11.1744 + 1.76985i 0.580930 + 0.0920103i
\(371\) 1.24108 1.70820i 0.0644338 0.0886855i
\(372\) 0.763932 + 2.35114i 0.0396080 + 0.121901i
\(373\) 16.4721i 0.852895i 0.904512 + 0.426447i \(0.140235\pi\)
−0.904512 + 0.426447i \(0.859765\pi\)
\(374\) −0.919554 1.53759i −0.0475490 0.0795068i
\(375\) 0.618034 0.0319151
\(376\) −27.5812 14.0533i −1.42239 0.724744i
\(377\) −2.47214 1.79611i −0.127321 0.0925045i
\(378\) 0.586812 3.70498i 0.0301823 0.190564i
\(379\) 29.7400 + 9.66312i 1.52764 + 0.496361i 0.947935 0.318464i \(-0.103167\pi\)
0.579707 + 0.814825i \(0.303167\pi\)
\(380\) −15.3884 5.00000i −0.789409 0.256495i
\(381\) 6.43288 + 8.85410i 0.329567 + 0.453609i
\(382\) −2.69468 17.0135i −0.137872 0.870488i
\(383\) 7.94427 + 24.4500i 0.405933 + 1.24933i 0.920113 + 0.391652i \(0.128096\pi\)
−0.514180 + 0.857682i \(0.671904\pi\)
\(384\) −4.94427 4.94427i −0.252311 0.252311i
\(385\) −2.52786 + 0.171513i −0.128832 + 0.00874113i
\(386\) −6.00000 6.00000i −0.305392 0.305392i
\(387\) 4.61653 1.50000i 0.234671 0.0762493i
\(388\) −3.42071 + 4.70820i −0.173660 + 0.239023i
\(389\) −5.15131 7.09017i −0.261182 0.359486i 0.658206 0.752838i \(-0.271315\pi\)
−0.919388 + 0.393352i \(0.871315\pi\)
\(390\) −0.303130 0.594926i −0.0153496 0.0301252i
\(391\) 0.381966 1.17557i 0.0193169 0.0594512i
\(392\) −2.83903 + 17.9249i −0.143392 + 0.905344i
\(393\) 7.66312 + 5.56758i 0.386553 + 0.280847i
\(394\) 18.8309 + 9.59481i 0.948686 + 0.483380i
\(395\) 2.29180i 0.115313i
\(396\) 13.3262 11.1352i 0.669669 0.559563i
\(397\) 31.4164i 1.57674i 0.615199 + 0.788372i \(0.289076\pi\)
−0.615199 + 0.788372i \(0.710924\pi\)
\(398\) −5.55523 + 10.9028i −0.278459 + 0.546506i
\(399\) −3.09017 2.24514i −0.154702 0.112398i
\(400\) −3.23607 + 2.35114i −0.161803 + 0.117557i
\(401\) −10.9549 + 33.7158i −0.547062 + 1.68368i 0.168973 + 0.985621i \(0.445955\pi\)
−0.716035 + 0.698064i \(0.754045\pi\)
\(402\) 10.3781 5.28788i 0.517610 0.263736i
\(403\) −0.898056 1.23607i −0.0447354 0.0615729i
\(404\) −22.9443 16.6700i −1.14152 0.829363i
\(405\) 5.42882 1.76393i 0.269760 0.0876505i
\(406\) −3.05573 + 3.05573i −0.151653 + 0.151653i
\(407\) 9.88854 + 24.6215i 0.490157 + 1.22044i
\(408\) −0.472136 0.472136i −0.0233742 0.0233742i
\(409\) −6.79837 20.9232i −0.336158 1.03459i −0.966149 0.257985i \(-0.916941\pi\)
0.629991 0.776603i \(-0.283059\pi\)
\(410\) 10.3111 1.63313i 0.509231 0.0806543i
\(411\) 5.75934 + 7.92705i 0.284087 + 0.391013i
\(412\) 22.2703 + 7.23607i 1.09718 + 0.356495i
\(413\) 1.17557 + 0.381966i 0.0578460 + 0.0187953i
\(414\) 11.8339 + 1.87431i 0.581604 + 0.0921171i
\(415\) 3.73607 + 2.71441i 0.183396 + 0.133245i
\(416\) 3.85044 + 1.96190i 0.188783 + 0.0961900i
\(417\) −0.944272 −0.0462412
\(418\) −8.45958 36.9913i −0.413771 1.80930i
\(419\) 6.90983i 0.337567i 0.985653 + 0.168784i \(0.0539839\pi\)
−0.985653 + 0.168784i \(0.946016\pi\)
\(420\) −0.898056 + 0.291796i −0.0438206 + 0.0142382i
\(421\) −13.8293 + 19.0344i −0.674000 + 0.927682i −0.999843 0.0177422i \(-0.994352\pi\)
0.325842 + 0.945424i \(0.394352\pi\)
\(422\) 1.80213 11.3782i 0.0877264 0.553883i
\(423\) 8.85410 27.2501i 0.430501 1.32495i
\(424\) 6.96552 3.54911i 0.338275 0.172360i
\(425\) −0.309017 + 0.224514i −0.0149895 + 0.0108905i
\(426\) −9.44788 + 1.49640i −0.457751 + 0.0725006i
\(427\) 3.24920 1.05573i 0.157240 0.0510903i
\(428\) −4.29180 −0.207452
\(429\) 0.832544 1.32624i 0.0401956 0.0640314i
\(430\) −1.85410 1.85410i −0.0894127 0.0894127i
\(431\) −3.70820 11.4127i −0.178618 0.549729i 0.821162 0.570695i \(-0.193326\pi\)
−0.999780 + 0.0209654i \(0.993326\pi\)
\(432\) 8.16348 11.2361i 0.392766 0.540596i
\(433\) −15.3992 + 11.1882i −0.740038 + 0.537669i −0.892723 0.450606i \(-0.851208\pi\)
0.152685 + 0.988275i \(0.451208\pi\)
\(434\) −1.92522 + 0.980949i −0.0924136 + 0.0470871i
\(435\) 2.35114 + 0.763932i 0.112729 + 0.0366277i
\(436\) −26.6525 + 19.3642i −1.27642 + 0.927375i
\(437\) 15.3884 21.1803i 0.736128 1.01319i
\(438\) −6.11653 3.11653i −0.292259 0.148913i
\(439\) 6.65248 0.317505 0.158753 0.987318i \(-0.449253\pi\)
0.158753 + 0.987318i \(0.449253\pi\)
\(440\) −8.62750 3.68323i −0.411300 0.175591i
\(441\) −16.7984 −0.799923
\(442\) 0.367684 + 0.187345i 0.0174890 + 0.00891107i
\(443\) 20.6255 28.3885i 0.979946 1.34878i 0.0430880 0.999071i \(-0.486280\pi\)
0.936858 0.349709i \(-0.113720\pi\)
\(444\) 5.81234 + 8.00000i 0.275841 + 0.379663i
\(445\) 5.29007 + 1.71885i 0.250773 + 0.0814812i
\(446\) −3.11507 + 1.58721i −0.147503 + 0.0751565i
\(447\) 3.38197 2.45714i 0.159962 0.116219i
\(448\) 3.59222 4.94427i 0.169717 0.233595i
\(449\) −5.20820 16.0292i −0.245790 0.756465i −0.995505 0.0947042i \(-0.969809\pi\)
0.749715 0.661761i \(-0.230191\pi\)
\(450\) −2.61803 2.61803i −0.123415 0.123415i
\(451\) 15.6987 + 18.7877i 0.739222 + 0.884680i
\(452\) 33.1246i 1.55805i
\(453\) −8.16348 + 2.65248i −0.383554 + 0.124624i
\(454\) 28.9734 4.58893i 1.35979 0.215369i
\(455\) 0.472136 0.343027i 0.0221341 0.0160813i
\(456\) −6.42040 12.6007i −0.300663 0.590083i
\(457\) 9.01064 27.7319i 0.421500 1.29724i −0.484806 0.874622i \(-0.661110\pi\)
0.906306 0.422622i \(-0.138890\pi\)
\(458\) 1.02928 6.49859i 0.0480949 0.303659i
\(459\) 0.779543 1.07295i 0.0363860 0.0500810i
\(460\) −2.00000 6.15537i −0.0932505 0.286995i
\(461\) 39.5967i 1.84420i 0.386946 + 0.922102i \(0.373530\pi\)
−0.386946 + 0.922102i \(0.626470\pi\)
\(462\) −1.66831 1.45630i −0.0776167 0.0677534i
\(463\) −31.8885 −1.48199 −0.740993 0.671513i \(-0.765645\pi\)
−0.740993 + 0.671513i \(0.765645\pi\)
\(464\) −15.2169 + 4.94427i −0.706427 + 0.229532i
\(465\) 1.00000 + 0.726543i 0.0463739 + 0.0336926i
\(466\) −0.203791 0.0322773i −0.00944042 0.00149522i
\(467\) 16.6700 + 5.41641i 0.771395 + 0.250641i 0.668162 0.744016i \(-0.267081\pi\)
0.103233 + 0.994657i \(0.467081\pi\)
\(468\) −1.23607 + 3.80423i −0.0571373 + 0.175850i
\(469\) 5.98385 + 8.23607i 0.276309 + 0.380306i
\(470\) −15.2870 + 2.42122i −0.705136 + 0.111683i
\(471\) −1.85410 5.70634i −0.0854325 0.262934i
\(472\) 3.23607 + 3.23607i 0.148952 + 0.148952i
\(473\) 1.50000 5.96361i 0.0689701 0.274207i
\(474\) 1.41641 1.41641i 0.0650578 0.0650578i
\(475\) −7.69421 + 2.50000i −0.353035 + 0.114708i
\(476\) 0.343027 0.472136i 0.0157226 0.0216403i
\(477\) 4.25325 + 5.85410i 0.194743 + 0.268041i
\(478\) −33.5841 + 17.1119i −1.53610 + 0.782682i
\(479\) 5.05573 15.5599i 0.231002 0.710951i −0.766625 0.642096i \(-0.778065\pi\)
0.997627 0.0688557i \(-0.0219348\pi\)
\(480\) −3.45309 0.546915i −0.157611 0.0249631i
\(481\) −4.94427 3.59222i −0.225439 0.163791i
\(482\) −14.1112 + 27.6948i −0.642748 + 1.26146i
\(483\) 1.52786i 0.0695202i
\(484\) −2.97168 21.7984i −0.135076 0.990835i
\(485\) 2.90983i 0.132129i
\(486\) 17.5708 + 8.95277i 0.797028 + 0.406106i
\(487\) −8.85410 6.43288i −0.401218 0.291502i 0.368819 0.929501i \(-0.379762\pi\)
−0.770037 + 0.637999i \(0.779762\pi\)
\(488\) 12.4934 + 1.97876i 0.565549 + 0.0895741i
\(489\) −0.836881 + 2.57565i −0.0378451 + 0.116475i
\(490\) 4.11959 + 8.08515i 0.186104 + 0.365250i
\(491\) −1.15533 1.59017i −0.0521391 0.0717634i 0.782151 0.623089i \(-0.214122\pi\)
−0.834290 + 0.551325i \(0.814122\pi\)
\(492\) 7.38197 + 5.36331i 0.332805 + 0.241797i
\(493\) −1.45309 + 0.472136i −0.0654437 + 0.0212639i
\(494\) 6.18034 + 6.18034i 0.278067 + 0.278067i
\(495\) 2.11803 8.42075i 0.0951985 0.378485i
\(496\) −8.00000 −0.359211
\(497\) −2.58359 7.95148i −0.115890 0.356673i
\(498\) 0.631418 + 3.98662i 0.0282945 + 0.178645i
\(499\) 13.2945 + 18.2984i 0.595146 + 0.819148i 0.995253 0.0973205i \(-0.0310272\pi\)
−0.400107 + 0.916468i \(0.631027\pi\)
\(500\) −0.618034 + 1.90211i −0.0276393 + 0.0850651i
\(501\) 3.24920 + 1.05573i 0.145163 + 0.0471665i
\(502\) −2.65478 + 16.7616i −0.118489 + 0.748108i
\(503\) 26.5066 + 19.2582i 1.18187 + 0.858679i 0.992381 0.123204i \(-0.0393170\pi\)
0.189489 + 0.981883i \(0.439317\pi\)
\(504\) 5.04029 + 2.56816i 0.224513 + 0.114395i
\(505\) −14.1803 −0.631017
\(506\) 9.98166 11.4347i 0.443739 0.508336i
\(507\) 7.67376i 0.340804i
\(508\) −33.6830 + 10.9443i −1.49444 + 0.485574i
\(509\) 19.0866 26.2705i 0.846001 1.16442i −0.138729 0.990330i \(-0.544302\pi\)
0.984730 0.174090i \(-0.0556982\pi\)
\(510\) −0.329740 0.0522257i −0.0146011 0.00231259i
\(511\) 1.85410 5.70634i 0.0820206 0.252434i
\(512\) 20.1612 10.2726i 0.891007 0.453990i
\(513\) 22.7254 16.5110i 1.00335 0.728978i
\(514\) −3.71633 23.4640i −0.163920 1.03495i
\(515\) 11.1352 3.61803i 0.490674 0.159430i
\(516\) 2.29180i 0.100891i
\(517\) −23.2744 27.8541i −1.02361 1.22502i
\(518\) −6.11146 + 6.11146i −0.268522 + 0.268522i
\(519\) 1.76393 + 5.42882i 0.0774280 + 0.238299i
\(520\) 2.13412 0.338012i 0.0935875 0.0148228i
\(521\) −8.69098 + 6.31437i −0.380759 + 0.276638i −0.761658 0.647979i \(-0.775614\pi\)
0.380899 + 0.924617i \(0.375614\pi\)
\(522\) −6.72353 13.1957i −0.294281 0.577558i
\(523\) −4.51052 1.46556i −0.197231 0.0640844i 0.208736 0.977972i \(-0.433065\pi\)
−0.405967 + 0.913888i \(0.633065\pi\)
\(524\) −24.7984 + 18.0171i −1.08332 + 0.787079i
\(525\) −0.277515 + 0.381966i −0.0121117 + 0.0166704i
\(526\) 15.8994 31.2044i 0.693248 1.36058i
\(527\) −0.763932 −0.0332774
\(528\) −3.05573 7.60845i −0.132983 0.331115i
\(529\) −12.5279 −0.544690
\(530\) 1.77455 3.48276i 0.0770817 0.151281i
\(531\) −2.48990 + 3.42705i −0.108052 + 0.148721i
\(532\) 10.0000 7.26543i 0.433555 0.314996i
\(533\) −5.36331 1.74265i −0.232311 0.0754824i
\(534\) 2.20714 + 4.33175i 0.0955121 + 0.187453i
\(535\) −1.73607 + 1.26133i −0.0750568 + 0.0545319i
\(536\) 5.89637 + 37.2282i 0.254685 + 1.60801i
\(537\) 1.36475 + 4.20025i 0.0588931 + 0.181254i
\(538\) 13.8885 13.8885i 0.598778 0.598778i
\(539\) −11.3144 + 18.0238i −0.487346 + 0.776340i
\(540\) 6.94427i 0.298834i
\(541\) −13.9353 + 4.52786i −0.599127 + 0.194668i −0.592851 0.805312i \(-0.701998\pi\)
−0.00627582 + 0.999980i \(0.501998\pi\)
\(542\) −3.47515 21.9413i −0.149271 0.942458i
\(543\) 10.0000 7.26543i 0.429141 0.311789i
\(544\) 1.92522 0.980949i 0.0825432 0.0420578i
\(545\) −5.09017 + 15.6659i −0.218039 + 0.671055i
\(546\) 0.503798 + 0.0797938i 0.0215606 + 0.00341486i
\(547\) −14.8864 + 20.4894i −0.636496 + 0.876062i −0.998423 0.0561450i \(-0.982119\pi\)
0.361927 + 0.932207i \(0.382119\pi\)
\(548\) −30.1563 + 9.79837i −1.28821 + 0.418566i
\(549\) 11.7082i 0.499694i
\(550\) −4.57237 + 1.04566i −0.194967 + 0.0445871i
\(551\) −32.3607 −1.37861
\(552\) 2.56816 5.04029i 0.109308 0.214529i
\(553\) 1.41641 + 1.02908i 0.0602318 + 0.0437610i
\(554\) 2.96814 18.7401i 0.126104 0.796189i
\(555\) 4.70228 + 1.52786i 0.199601 + 0.0648542i
\(556\) 0.944272 2.90617i 0.0400460 0.123249i
\(557\) 9.23305 + 12.7082i 0.391217 + 0.538464i 0.958513 0.285050i \(-0.0920103\pi\)
−0.567296 + 0.823514i \(0.692010\pi\)
\(558\) −1.15838 7.31375i −0.0490383 0.309616i
\(559\) 0.437694 + 1.34708i 0.0185125 + 0.0569756i
\(560\) 3.05573i 0.129128i
\(561\) −0.291796 0.726543i −0.0123196 0.0306746i
\(562\) 9.85410 + 9.85410i 0.415670 + 0.415670i
\(563\) −7.36369 + 2.39261i −0.310343 + 0.100836i −0.460048 0.887894i \(-0.652168\pi\)
0.149705 + 0.988731i \(0.452168\pi\)
\(564\) −10.9443 7.95148i −0.460837 0.334818i
\(565\) −9.73508 13.3992i −0.409558 0.563708i
\(566\) 6.72353 + 13.1957i 0.282611 + 0.554655i
\(567\) −1.34752 + 4.14725i −0.0565907 + 0.174168i
\(568\) 4.84244 30.5740i 0.203184 1.28286i
\(569\) −7.16312 5.20431i −0.300294 0.218176i 0.427427 0.904050i \(-0.359420\pi\)
−0.727720 + 0.685874i \(0.759420\pi\)
\(570\) −6.30037 3.21020i −0.263893 0.134460i
\(571\) 16.3607i 0.684673i 0.939577 + 0.342337i \(0.111218\pi\)
−0.939577 + 0.342337i \(0.888782\pi\)
\(572\) 3.24920 + 3.88854i 0.135856 + 0.162588i
\(573\) 7.52786i 0.314481i
\(574\) −3.62067 + 7.10596i −0.151124 + 0.296597i
\(575\) −2.61803 1.90211i −0.109180 0.0793236i
\(576\) 12.3107 + 16.9443i 0.512947 + 0.706011i
\(577\) −13.7016 + 42.1693i −0.570406 + 1.75553i 0.0809081 + 0.996722i \(0.474218\pi\)
−0.651314 + 0.758808i \(0.725782\pi\)
\(578\) −21.2374 + 10.8210i −0.883360 + 0.450094i
\(579\) −2.17963 3.00000i −0.0905822 0.124676i
\(580\) −4.70228 + 6.47214i −0.195252 + 0.268741i
\(581\) −3.35520 + 1.09017i −0.139197 + 0.0452279i
\(582\) −1.79837 + 1.79837i −0.0745450 + 0.0745450i
\(583\) 9.14590 0.620541i 0.378784 0.0257002i
\(584\) 15.7082 15.7082i 0.650010 0.650010i
\(585\) 0.618034 + 1.90211i 0.0255526 + 0.0786427i
\(586\) −42.8154 + 6.78130i −1.76869 + 0.280133i
\(587\) −6.82891 9.39919i −0.281859 0.387946i 0.644489 0.764613i \(-0.277070\pi\)
−0.926349 + 0.376667i \(0.877070\pi\)
\(588\) −2.45085 + 7.54294i −0.101071 + 0.311066i
\(589\) −15.3884 5.00000i −0.634069 0.206021i
\(590\) 2.26007 + 0.357960i 0.0930458 + 0.0147370i
\(591\) 7.47214 + 5.42882i 0.307363 + 0.223312i
\(592\) −30.4338 + 9.88854i −1.25082 + 0.406417i
\(593\) −12.5623 −0.515872 −0.257936 0.966162i \(-0.583042\pi\)
−0.257936 + 0.966162i \(0.583042\pi\)
\(594\) 13.9769 8.35890i 0.573481 0.342970i
\(595\) 0.291796i 0.0119625i
\(596\) 4.18034 + 12.8658i 0.171233 + 0.527002i
\(597\) −3.14320 + 4.32624i −0.128642 + 0.177061i
\(598\) −0.546915 + 3.45309i −0.0223650 + 0.141207i
\(599\) 2.03444 6.26137i 0.0831250 0.255833i −0.900852 0.434125i \(-0.857057\pi\)
0.983977 + 0.178293i \(0.0570575\pi\)
\(600\) −1.55754 + 0.793604i −0.0635862 + 0.0323988i
\(601\) 27.9164 20.2825i 1.13873 0.827339i 0.151792 0.988413i \(-0.451496\pi\)
0.986942 + 0.161074i \(0.0514957\pi\)
\(602\) 1.97844 0.313354i 0.0806353 0.0127714i
\(603\) −33.1810 + 10.7812i −1.35123 + 0.439042i
\(604\) 27.7771i 1.13023i
\(605\) −7.60845 7.94427i −0.309328 0.322981i
\(606\) −8.76393 8.76393i −0.356010 0.356010i
\(607\) 10.9443 + 33.6830i 0.444214 + 1.36715i 0.883343 + 0.468727i \(0.155287\pi\)
−0.439129 + 0.898424i \(0.644713\pi\)
\(608\) 45.2015 7.15921i 1.83316 0.290344i
\(609\) −1.52786 + 1.11006i −0.0619122 + 0.0449818i
\(610\) 5.63522 2.87129i 0.228163 0.116255i
\(611\) 7.95148 + 2.58359i 0.321682 + 0.104521i
\(612\) 1.17557 + 1.61803i 0.0475196 + 0.0654051i
\(613\) 4.35926 6.00000i 0.176069 0.242338i −0.711857 0.702324i \(-0.752146\pi\)
0.887926 + 0.459986i \(0.152146\pi\)
\(614\) 7.00891 + 3.57122i 0.282857 + 0.144123i
\(615\) 4.56231 0.183970
\(616\) 6.15035 3.67822i 0.247805 0.148200i
\(617\) 23.6180 0.950826 0.475413 0.879763i \(-0.342299\pi\)
0.475413 + 0.879763i \(0.342299\pi\)
\(618\) 9.11798 + 4.64584i 0.366779 + 0.186883i
\(619\) 1.29408 1.78115i 0.0520136 0.0715906i −0.782218 0.623005i \(-0.785912\pi\)
0.834232 + 0.551414i \(0.185912\pi\)
\(620\) −3.23607 + 2.35114i −0.129964 + 0.0944241i
\(621\) 10.6861 + 3.47214i 0.428820 + 0.139332i
\(622\) −1.69798 + 0.865164i −0.0680828 + 0.0346899i
\(623\) −3.43769 + 2.49763i −0.137728 + 0.100065i
\(624\) 1.52786 + 1.11006i 0.0611635 + 0.0444379i
\(625\) 0.309017 + 0.951057i 0.0123607 + 0.0380423i
\(626\) 28.7426 + 28.7426i 1.14879 + 1.14879i
\(627\) −1.12257 16.5451i −0.0448311 0.660747i
\(628\) 19.4164 0.774799
\(629\) −2.90617 + 0.944272i −0.115877 + 0.0376506i
\(630\) 2.79360 0.442463i 0.111300 0.0176282i
\(631\) −26.6525 + 19.3642i −1.06102 + 0.770875i −0.974277 0.225356i \(-0.927646\pi\)
−0.0867418 + 0.996231i \(0.527646\pi\)
\(632\) 2.94285 + 5.77566i 0.117060 + 0.229744i
\(633\) 1.55573 4.78804i 0.0618346 0.190307i
\(634\) −1.30273 + 8.22513i −0.0517381 + 0.326662i
\(635\) −10.4086 + 14.3262i −0.413054 + 0.568519i
\(636\) 3.24920 1.05573i 0.128839 0.0418623i
\(637\) 4.90170i 0.194212i
\(638\) −18.6868 1.67383i −0.739819 0.0662676i
\(639\) 28.6525 1.13347
\(640\) 5.13632 10.0806i 0.203031 0.398470i
\(641\) 15.4443 + 11.2209i 0.610012 + 0.443200i 0.849419 0.527720i \(-0.176953\pi\)
−0.239407 + 0.970919i \(0.576953\pi\)
\(642\) −1.85249 0.293406i −0.0731120 0.0115798i
\(643\) −19.3314 6.28115i −0.762356 0.247704i −0.0980665 0.995180i \(-0.531266\pi\)
−0.664290 + 0.747475i \(0.731266\pi\)
\(644\) 4.70228 + 1.52786i 0.185296 + 0.0602063i
\(645\) −0.673542 0.927051i −0.0265207 0.0365026i
\(646\) 4.31636 0.683644i 0.169825 0.0268976i
\(647\) 1.52786 + 4.70228i 0.0600665 + 0.184866i 0.976587 0.215121i \(-0.0690146\pi\)
−0.916521 + 0.399987i \(0.869015\pi\)
\(648\) −11.4164 + 11.4164i −0.448479 + 0.448479i
\(649\) 2.00000 + 4.97980i 0.0785069 + 0.195474i
\(650\) 0.763932 0.763932i 0.0299639 0.0299639i
\(651\) −0.898056 + 0.291796i −0.0351976 + 0.0114364i
\(652\) −7.09017 5.15131i −0.277672 0.201741i
\(653\) 13.6578 + 18.7984i 0.534472 + 0.735637i 0.987804 0.155705i \(-0.0497648\pi\)
−0.453332 + 0.891342i \(0.649765\pi\)
\(654\) −12.8280 + 6.53618i −0.501614 + 0.255585i
\(655\) −4.73607 + 14.5761i −0.185053 + 0.569536i
\(656\) −23.8885 + 17.3560i −0.932691 + 0.677640i
\(657\) 16.6353 + 12.0862i 0.649003 + 0.471528i
\(658\) 5.36789 10.5351i 0.209262 0.410700i
\(659\) 3.14590i 0.122547i −0.998121 0.0612734i \(-0.980484\pi\)
0.998121 0.0612734i \(-0.0195162\pi\)
\(660\) −3.47214 2.17963i −0.135153 0.0848419i
\(661\) 31.7082i 1.23331i −0.787235 0.616653i \(-0.788488\pi\)
0.787235 0.616653i \(-0.211512\pi\)
\(662\) 12.6441 + 6.44251i 0.491428 + 0.250395i
\(663\) 0.145898 + 0.106001i 0.00566621 + 0.00411674i
\(664\) −12.9010 2.04331i −0.500654 0.0792959i
\(665\) 1.90983 5.87785i 0.0740600 0.227933i
\(666\) −13.4471 26.3913i −0.521063 1.02264i
\(667\) −7.60845 10.4721i −0.294600 0.405483i
\(668\) −6.49839 + 8.94427i −0.251430 + 0.346064i
\(669\) −1.45309 + 0.472136i −0.0561795 + 0.0182538i
\(670\) 13.3262 + 13.3262i 0.514837 + 0.514837i
\(671\) 12.5623 + 7.88597i 0.484962 + 0.304434i
\(672\) 1.88854 1.88854i 0.0728522 0.0728522i
\(673\) 8.06231 + 24.8132i 0.310779 + 0.956480i 0.977457 + 0.211134i \(0.0677156\pi\)
−0.666678 + 0.745346i \(0.732284\pi\)
\(674\) 7.54183 + 47.6172i 0.290500 + 1.83415i
\(675\) −2.04087 2.80902i −0.0785531 0.108119i
\(676\) 23.6174 + 7.67376i 0.908362 + 0.295145i
\(677\) 36.3117 + 11.7984i 1.39557 + 0.453448i 0.907756 0.419499i \(-0.137794\pi\)
0.487815 + 0.872947i \(0.337794\pi\)
\(678\) 2.26454 14.2978i 0.0869693 0.549102i
\(679\) −1.79837 1.30660i −0.0690153 0.0501425i
\(680\) 0.490475 0.962611i 0.0188088 0.0369144i
\(681\) 12.8197 0.491250
\(682\) −8.62750 3.68323i −0.330364 0.141038i
\(683\) 27.7771i 1.06286i −0.847102 0.531430i \(-0.821655\pi\)
0.847102 0.531430i \(-0.178345\pi\)
\(684\) 13.0902 + 40.2874i 0.500515 + 1.54043i
\(685\) −9.31881 + 12.8262i −0.356053 + 0.490065i
\(686\) −14.3161 2.26745i −0.546593 0.0865718i
\(687\) 0.888544 2.73466i 0.0339001 0.104334i
\(688\) 7.05342 + 2.29180i 0.268909 + 0.0873739i
\(689\) −1.70820 + 1.24108i −0.0650774 + 0.0472815i
\(690\) −0.442463 2.79360i −0.0168443 0.106351i
\(691\) 9.14729 2.97214i 0.347979 0.113065i −0.129812 0.991539i \(-0.541437\pi\)
0.477792 + 0.878473i \(0.341437\pi\)
\(692\) −18.4721 −0.702205
\(693\) 4.25325 + 5.09017i 0.161568 + 0.193360i
\(694\) −21.5066 + 21.5066i −0.816379 + 0.816379i
\(695\) −0.472136 1.45309i −0.0179091 0.0551187i
\(696\) −6.90617 + 1.09383i −0.261778 + 0.0414615i
\(697\) −2.28115 + 1.65735i −0.0864048 + 0.0627768i
\(698\) 10.8789 + 21.3510i 0.411772 + 0.808148i
\(699\) −0.0857567 0.0278640i −0.00324362 0.00105391i
\(700\) −0.898056 1.23607i −0.0339433 0.0467190i
\(701\) 6.08985 8.38197i 0.230011 0.316582i −0.678375 0.734716i \(-0.737316\pi\)
0.908386 + 0.418133i \(0.137316\pi\)
\(702\) −1.70299 + 3.34231i −0.0642754 + 0.126148i
\(703\) −64.7214 −2.44101
\(704\) 26.4721 1.79611i 0.997706 0.0676935i
\(705\) −6.76393 −0.254744
\(706\) −6.96876 + 13.6770i −0.262273 + 0.514739i
\(707\) 6.36737 8.76393i 0.239470 0.329602i
\(708\) 1.17557 + 1.61803i 0.0441806 + 0.0608094i
\(709\) −25.6255 8.32624i −0.962387 0.312698i −0.214648 0.976691i \(-0.568860\pi\)
−0.747739 + 0.663993i \(0.768860\pi\)
\(710\) −7.02666 13.7906i −0.263706 0.517552i
\(711\) −4.85410 + 3.52671i −0.182043 + 0.132262i
\(712\) −15.5389 + 2.46112i −0.582344 + 0.0922343i
\(713\) −2.00000 6.15537i −0.0749006 0.230520i
\(714\) 0.180340 0.180340i 0.00674905 0.00674905i
\(715\) 2.45714 + 0.618034i 0.0918919 + 0.0231132i
\(716\) −14.2918 −0.534109
\(717\) −15.6659 + 5.09017i −0.585055 + 0.190096i
\(718\) 4.63354 + 29.2550i 0.172922 + 1.09179i
\(719\) 17.8541 12.9718i 0.665846 0.483765i −0.202786 0.979223i \(-0.565000\pi\)
0.868632 + 0.495458i \(0.165000\pi\)
\(720\) 9.95959 + 3.23607i 0.371172 + 0.120601i
\(721\) −2.76393 + 8.50651i −0.102934 + 0.316799i
\(722\) 64.8827 + 10.2764i 2.41468 + 0.382448i
\(723\) −7.98424 + 10.9894i −0.296937 + 0.408699i
\(724\) 12.3607 + 38.0423i 0.459381 + 1.41383i
\(725\) 4.00000i 0.148556i
\(726\) 0.207548 9.61211i 0.00770283 0.356739i
\(727\) −2.76393 −0.102509 −0.0512543 0.998686i \(-0.516322\pi\)
−0.0512543 + 0.998686i \(0.516322\pi\)
\(728\) −0.749378 + 1.47074i −0.0277738 + 0.0545092i
\(729\) −6.88197 5.00004i −0.254888 0.185187i
\(730\) 1.73758 10.9706i 0.0643106 0.406041i
\(731\) 0.673542 + 0.218847i 0.0249118 + 0.00809435i
\(732\) 5.25731 + 1.70820i 0.194316 + 0.0631370i
\(733\) −13.2493 18.2361i −0.489373 0.673565i 0.490899 0.871217i \(-0.336668\pi\)
−0.980272 + 0.197652i \(0.936668\pi\)
\(734\) −1.70530 10.7668i −0.0629437 0.397411i
\(735\) 1.22542 + 3.77147i 0.0452005 + 0.139113i
\(736\) 12.9443 + 12.9443i 0.477132 + 0.477132i
\(737\) −10.7812 + 42.8631i −0.397129 + 1.57888i
\(738\) −19.3262 19.3262i −0.711409 0.711409i
\(739\) 22.7396 7.38854i 0.836490 0.271792i 0.140713 0.990050i \(-0.455060\pi\)
0.695776 + 0.718258i \(0.255060\pi\)
\(740\) −9.40456 + 12.9443i −0.345719 + 0.475841i
\(741\) 2.24514 + 3.09017i 0.0824773 + 0.113520i
\(742\) 1.35564 + 2.66059i 0.0497670 + 0.0976733i
\(743\) 9.32624 28.7032i 0.342146 1.05302i −0.620947 0.783852i \(-0.713252\pi\)
0.963094 0.269166i \(-0.0867481\pi\)
\(744\) −3.45309 0.546915i −0.126596 0.0200509i
\(745\) 5.47214 + 3.97574i 0.200484 + 0.145660i
\(746\) −20.7561 10.5758i −0.759935 0.387206i
\(747\) 12.0902i 0.442356i
\(748\) 2.52786 0.171513i 0.0924279 0.00627115i
\(749\) 1.63932i 0.0598995i
\(750\) −0.396802 + 0.778768i −0.0144892 + 0.0284366i
\(751\) −3.09017 2.24514i −0.112762 0.0819263i 0.529975 0.848013i \(-0.322201\pi\)
−0.642737 + 0.766087i \(0.722201\pi\)
\(752\) 35.4164 25.7315i 1.29150 0.938332i
\(753\) −2.29180 + 7.05342i −0.0835177 + 0.257041i
\(754\) 3.85044 1.96190i 0.140225 0.0714481i
\(755\) −8.16348 11.2361i −0.297100 0.408922i
\(756\) 4.29180 + 3.11817i 0.156091 + 0.113407i
\(757\) 29.0462 9.43769i 1.05570 0.343019i 0.270799 0.962636i \(-0.412712\pi\)
0.784904 + 0.619617i \(0.212712\pi\)
\(758\) −31.2705 + 31.2705i −1.13580 + 1.13580i
\(759\) 5.09017 4.25325i 0.184761 0.154383i
\(760\) 16.1803 16.1803i 0.586923 0.586923i
\(761\) 2.73607 + 8.42075i 0.0991824 + 0.305252i 0.988321 0.152386i \(-0.0486956\pi\)
−0.889139 + 0.457638i \(0.848696\pi\)
\(762\) −15.2870 + 2.42122i −0.553789 + 0.0877116i
\(763\) −7.39645 10.1803i −0.267769 0.368553i
\(764\) 23.1684 + 7.52786i 0.838203 + 0.272349i
\(765\) 0.951057 + 0.309017i 0.0343855 + 0.0111725i
\(766\) −35.9093 5.68747i −1.29745 0.205497i
\(767\) −1.00000 0.726543i −0.0361079 0.0262339i
\(768\) 9.40456 3.05573i 0.339358 0.110264i
\(769\) −4.83282 −0.174276 −0.0871379 0.996196i \(-0.527772\pi\)
−0.0871379 + 0.996196i \(0.527772\pi\)
\(770\) 1.40687 3.29541i 0.0507000 0.118758i
\(771\) 10.3820i 0.373897i
\(772\) 11.4127 3.70820i 0.410751 0.133461i
\(773\) 4.18774 5.76393i 0.150623 0.207314i −0.727038 0.686598i \(-0.759103\pi\)
0.877660 + 0.479283i \(0.159103\pi\)
\(774\) −1.07388 + 6.78022i −0.0385999 + 0.243710i
\(775\) −0.618034 + 1.90211i −0.0222004 + 0.0683259i
\(776\) −3.73645 7.33320i −0.134131 0.263247i
\(777\) −3.05573 + 2.22012i −0.109624 + 0.0796462i
\(778\) 12.2415 1.93886i 0.438878 0.0695115i
\(779\) −56.7984 + 18.4549i −2.03501 + 0.661216i
\(780\) 0.944272 0.0338104
\(781\) 19.2986 30.7426i 0.690560 1.10006i
\(782\) 1.23607 + 1.23607i 0.0442017 + 0.0442017i
\(783\) −4.29180 13.2088i −0.153376 0.472044i
\(784\) −20.7639 15.0859i −0.741569 0.538781i
\(785\) 7.85410 5.70634i 0.280325 0.203668i
\(786\) −11.9356 + 6.08149i −0.425728 + 0.216919i
\(787\) 10.4944 + 3.40983i 0.374084 + 0.121547i 0.490024 0.871709i \(-0.336988\pi\)
−0.115940 + 0.993256i \(0.536988\pi\)
\(788\) −24.1803 + 17.5680i −0.861389 + 0.625836i
\(789\) 8.99602 12.3820i 0.320267 0.440810i
\(790\) 2.88783 + 1.47142i 0.102744 + 0.0523509i
\(791\) 12.6525 0.449870
\(792\) 5.47515 + 23.9413i 0.194551 + 0.850715i
\(793\) −3.41641 −0.121320
\(794\) −39.5870 20.1706i −1.40489 0.715827i
\(795\) 1.00406 1.38197i 0.0356102 0.0490133i
\(796\) −10.1716 14.0000i −0.360523 0.496217i
\(797\) −21.0948 6.85410i −0.747215 0.242785i −0.0894324 0.995993i \(-0.528505\pi\)
−0.657782 + 0.753208i \(0.728505\pi\)
\(798\) 4.81305 2.45237i 0.170380 0.0868131i
\(799\) 3.38197 2.45714i 0.119645 0.0869274i
\(800\) −0.884927 5.58721i −0.0312869 0.197538i
\(801\) −4.50000 13.8496i −0.159000 0.489351i
\(802\) −35.4508 35.4508i −1.25181 1.25181i
\(803\) 24.1724 9.70820i 0.853027 0.342595i
\(804\) 16.4721i 0.580927i
\(805\) 2.35114 0.763932i 0.0828668 0.0269251i
\(806\) 2.13412 0.338012i 0.0751713 0.0119060i
\(807\) 6.94427 5.04531i 0.244450 0.177603i
\(808\) 35.7365 18.2087i 1.25721 0.640579i
\(809\) 9.68034 29.7930i 0.340343 1.04747i −0.623687 0.781674i \(-0.714366\pi\)
0.964030 0.265793i \(-0.0856338\pi\)
\(810\) −1.26284 + 7.97323i −0.0443715 + 0.280151i
\(811\) −14.1926 + 19.5344i −0.498370 + 0.685947i −0.981904 0.189378i \(-0.939353\pi\)
0.483535 + 0.875325i \(0.339353\pi\)
\(812\) −1.88854 5.81234i −0.0662749 0.203973i
\(813\) 9.70820i 0.340482i
\(814\) −37.3737 3.34766i −1.30995 0.117336i
\(815\) −4.38197 −0.153494
\(816\) 0.898056 0.291796i 0.0314382 0.0102149i
\(817\) 12.1353 + 8.81678i 0.424559 + 0.308460i
\(818\) 30.7296 + 4.86710i 1.07444 + 0.170174i
\(819\) −1.45309 0.472136i −0.0507749 0.0164978i
\(820\) −4.56231 + 14.0413i −0.159323 + 0.490345i
\(821\) −2.41665 3.32624i −0.0843418 0.116087i 0.764761 0.644314i \(-0.222857\pi\)
−0.849103 + 0.528227i \(0.822857\pi\)
\(822\) −13.6864 + 2.16771i −0.477368 + 0.0756076i
\(823\) −4.65248 14.3188i −0.162175 0.499124i 0.836642 0.547750i \(-0.184516\pi\)
−0.998817 + 0.0486265i \(0.984516\pi\)
\(824\) −23.4164 + 23.4164i −0.815749 + 0.815749i
\(825\) −2.04508 + 0.138757i −0.0712007 + 0.00483091i
\(826\) −1.23607 + 1.23607i −0.0430083 + 0.0430083i
\(827\) −41.6547 + 13.5344i −1.44848 + 0.470639i −0.924529 0.381112i \(-0.875541\pi\)
−0.523948 + 0.851750i \(0.675541\pi\)
\(828\) −9.95959 + 13.7082i −0.346120 + 0.476393i
\(829\) −23.1684 31.8885i −0.804671 1.10753i −0.992124 0.125261i \(-0.960023\pi\)
0.187453 0.982274i \(-0.439977\pi\)
\(830\) −5.81906 + 2.96496i −0.201983 + 0.102915i
\(831\) 2.56231 7.88597i 0.0888854 0.273561i
\(832\) −4.94427 + 3.59222i −0.171412 + 0.124538i
\(833\) −1.98278 1.44057i −0.0686992 0.0499129i
\(834\) 0.606260 1.18985i 0.0209931 0.0412012i
\(835\) 5.52786i 0.191300i
\(836\) 52.0431 + 13.0902i 1.79995 + 0.452733i
\(837\) 6.94427i 0.240029i
\(838\) −8.70689 4.43638i −0.300775 0.153252i
\(839\) −39.7426 28.8747i −1.37207 0.996866i −0.997572 0.0696377i \(-0.977816\pi\)
−0.374496 0.927228i \(-0.622184\pi\)
\(840\) 0.208903 1.31896i 0.00720784 0.0455085i
\(841\) 4.01722 12.3637i 0.138525 0.426336i
\(842\) −15.1058 29.6468i −0.520581 1.02170i
\(843\) 3.57971 + 4.92705i 0.123292 + 0.169697i
\(844\) 13.1803 + 9.57608i 0.453686 + 0.329622i
\(845\) 11.8087 3.83688i 0.406232 0.131993i
\(846\) 28.6525 + 28.6525i 0.985092 + 0.985092i
\(847\) 8.32624 1.13508i 0.286093 0.0390019i
\(848\) 11.0557i 0.379655i
\(849\) 2.00000 + 6.15537i 0.0686398 + 0.211252i
\(850\) −0.0845030 0.533531i −0.00289843 0.0183000i
\(851\) −15.2169 20.9443i −0.521629 0.717960i
\(852\) 4.18034 12.8658i 0.143216 0.440774i
\(853\) −2.73466 0.888544i −0.0936329 0.0304232i 0.261826 0.965115i \(-0.415675\pi\)
−0.355459 + 0.934692i \(0.615675\pi\)
\(854\) −0.755818 + 4.77205i −0.0258636 + 0.163296i
\(855\) 17.1353 + 12.4495i 0.586013 + 0.425764i
\(856\) 2.75550 5.40798i 0.0941811 0.184841i
\(857\) 0.798374 0.0272719 0.0136360 0.999907i \(-0.495659\pi\)
0.0136360 + 0.999907i \(0.495659\pi\)
\(858\) 1.13663 + 1.90056i 0.0388040 + 0.0648842i
\(859\) 44.6312i 1.52280i −0.648284 0.761398i \(-0.724513\pi\)
0.648284 0.761398i \(-0.275487\pi\)
\(860\) 3.52671 1.14590i 0.120260 0.0390748i
\(861\) −2.04860 + 2.81966i −0.0698162 + 0.0960938i
\(862\) 16.7616 + 2.65478i 0.570903 + 0.0904222i
\(863\) 6.05573 18.6376i 0.206139 0.634432i −0.793525 0.608537i \(-0.791757\pi\)
0.999665 0.0258945i \(-0.00824340\pi\)
\(864\) 8.91699 + 17.5006i 0.303362 + 0.595382i
\(865\) −7.47214 + 5.42882i −0.254060 + 0.184586i
\(866\) −4.21102 26.5874i −0.143096 0.903475i
\(867\) −9.90659 + 3.21885i −0.336446 + 0.109318i
\(868\) 3.05573i 0.103718i
\(869\) 0.514540 + 7.58359i 0.0174546 + 0.257256i
\(870\) −2.47214 + 2.47214i −0.0838133 + 0.0838133i
\(871\) −3.14590 9.68208i −0.106595 0.328065i
\(872\) −7.28832 46.0166i −0.246814 1.55832i
\(873\) 6.16312 4.47777i 0.208590 0.151549i
\(874\) 16.8088 + 32.9892i 0.568567 + 1.11587i
\(875\) −0.726543 0.236068i −0.0245616 0.00798055i
\(876\) 7.85410 5.70634i 0.265366 0.192799i
\(877\) −9.78808 + 13.4721i −0.330520 + 0.454922i −0.941643 0.336614i \(-0.890718\pi\)
0.611123 + 0.791536i \(0.290718\pi\)
\(878\) −4.27115 + 8.38261i −0.144144 + 0.282899i
\(879\) −18.9443 −0.638974
\(880\) 10.1803 8.50651i 0.343179 0.286754i
\(881\) −6.43769 −0.216891 −0.108446 0.994102i \(-0.534587\pi\)
−0.108446 + 0.994102i \(0.534587\pi\)
\(882\) 10.7852 21.1672i 0.363157 0.712736i
\(883\) 9.42481 12.9721i 0.317170 0.436547i −0.620430 0.784261i \(-0.713042\pi\)
0.937601 + 0.347714i \(0.113042\pi\)
\(884\) −0.472136 + 0.343027i −0.0158797 + 0.0115372i
\(885\) 0.951057 + 0.309017i 0.0319694 + 0.0103875i
\(886\) 22.5293 + 44.2162i 0.756886 + 1.48547i
\(887\) −12.2361 + 8.89002i −0.410847 + 0.298498i −0.773945 0.633253i \(-0.781719\pi\)
0.363098 + 0.931751i \(0.381719\pi\)
\(888\) −13.8123 + 2.18766i −0.463512 + 0.0734131i
\(889\) −4.18034 12.8658i −0.140204 0.431504i
\(890\) −5.56231 + 5.56231i −0.186449 + 0.186449i
\(891\) −17.5680 + 7.05573i −0.588552 + 0.236376i
\(892\) 4.94427i 0.165546i
\(893\) 84.2075 27.3607i 2.81790 0.915590i
\(894\) 0.924824 + 5.83911i 0.0309307 + 0.195289i
\(895\) −5.78115 + 4.20025i −0.193243 + 0.140399i
\(896\) 3.92380 + 7.70088i 0.131085 + 0.257268i
\(897\) −0.472136 + 1.45309i −0.0157642 + 0.0485171i
\(898\) 23.5418 + 3.72866i 0.785602 + 0.124427i
\(899\) −4.70228 + 6.47214i −0.156830 + 0.215858i
\(900\) 4.97980 1.61803i 0.165993 0.0539345i
\(901\) 1.05573i 0.0351714i
\(902\) −33.7531 + 7.71904i −1.12386 + 0.257016i
\(903\) 0.875388 0.0291311
\(904\) 41.7394 + 21.2673i 1.38823 + 0.707340i
\(905\) 16.1803 + 11.7557i 0.537853 + 0.390773i
\(906\) 1.89896 11.9896i 0.0630888 0.398327i
\(907\) 42.8958 + 13.9377i 1.42433 + 0.462794i 0.916976 0.398943i \(-0.130623\pi\)
0.507356 + 0.861736i \(0.330623\pi\)
\(908\) −12.8197 + 39.4549i −0.425435 + 1.30936i
\(909\) 21.8213 + 30.0344i 0.723767 + 0.996180i
\(910\) 0.129109 + 0.815163i 0.00427993 + 0.0270224i
\(911\) −14.0689 43.2996i −0.466123 1.43458i −0.857565 0.514376i \(-0.828024\pi\)
0.391442 0.920203i \(-0.371976\pi\)
\(912\) 20.0000 0.662266
\(913\) −12.9721 8.14324i −0.429315 0.269502i
\(914\) 29.1591 + 29.1591i 0.964496 + 0.964496i
\(915\) 2.62866 0.854102i 0.0869007 0.0282357i
\(916\) 7.52786 + 5.46931i 0.248728 + 0.180711i
\(917\) −6.88191 9.47214i −0.227261 0.312797i
\(918\) 0.851497 + 1.67116i 0.0281036 + 0.0551564i
\(919\) −6.36068 + 19.5762i −0.209819 + 0.645758i 0.789661 + 0.613543i \(0.210256\pi\)
−0.999481 + 0.0322151i \(0.989744\pi\)
\(920\) 9.04029 + 1.43184i 0.298050 + 0.0472064i
\(921\) 2.78115 + 2.02063i 0.0916421 + 0.0665819i
\(922\) −49.8948 25.4227i −1.64320 0.837251i
\(923\) 8.36068i 0.275195i
\(924\) 2.90617 1.16718i 0.0956060 0.0383975i
\(925\) 8.00000i 0.263038i
\(926\) 20.4737 40.1819i 0.672808 1.32046i
\(927\) −24.7984 18.0171i −0.814485 0.591758i
\(928\) 3.53971 22.3488i 0.116197 0.733636i
\(929\) 0.319660 0.983813i 0.0104877 0.0322778i −0.945676 0.325111i \(-0.894598\pi\)
0.956163 + 0.292834i \(0.0945982\pi\)
\(930\) −1.55754 + 0.793604i −0.0510736 + 0.0260233i
\(931\) −30.5118 41.9959i −0.999985 1.37636i
\(932\) 0.171513 0.236068i 0.00561811 0.00773266i
\(933\) −0.792055 + 0.257354i −0.0259307 + 0.00842540i
\(934\) −17.5279 + 17.5279i −0.573529 + 0.573529i
\(935\) 0.972136 0.812299i 0.0317922 0.0265650i
\(936\) −4.00000 4.00000i −0.130744 0.130744i
\(937\) 4.93769 + 15.1967i 0.161307 + 0.496453i 0.998745 0.0500794i \(-0.0159474\pi\)
−0.837438 + 0.546533i \(0.815947\pi\)
\(938\) −14.2199 + 2.25221i −0.464297 + 0.0735374i
\(939\) 10.4414 + 14.3713i 0.340741 + 0.468990i
\(940\) 6.76393 20.8172i 0.220615 0.678984i
\(941\) −37.2752 12.1115i −1.21514 0.394822i −0.369829 0.929100i \(-0.620584\pi\)
−0.845309 + 0.534278i \(0.820584\pi\)
\(942\) 8.38081 + 1.32739i 0.273062 + 0.0432487i
\(943\) −19.3262 14.0413i −0.629349 0.457249i
\(944\) −6.15537 + 2.00000i −0.200340 + 0.0650945i
\(945\) 2.65248 0.0862850
\(946\) 6.55153 + 5.71898i 0.213009 + 0.185940i
\(947\) 52.3820i 1.70219i 0.525016 + 0.851093i \(0.324059\pi\)
−0.525016 + 0.851093i \(0.675941\pi\)
\(948\) 0.875388 + 2.69417i 0.0284313 + 0.0875025i
\(949\) −3.52671 + 4.85410i −0.114482 + 0.157571i
\(950\) 1.78980 11.3004i 0.0580689 0.366632i
\(951\) −1.12461 + 3.46120i −0.0364680 + 0.112237i
\(952\) 0.374689 + 0.735369i 0.0121437 + 0.0238334i
\(953\) 32.4787 23.5972i 1.05209 0.764387i 0.0794802 0.996836i \(-0.474674\pi\)
0.972609 + 0.232449i \(0.0746740\pi\)
\(954\) −10.1074 + 1.60085i −0.327238 + 0.0518294i
\(955\) 11.5842 3.76393i 0.374856 0.121798i
\(956\) 53.3050i 1.72401i
\(957\) −7.95148 2.00000i −0.257035 0.0646508i
\(958\) 16.3607 + 16.3607i 0.528590 + 0.528590i
\(959\) −3.74265 11.5187i −0.120856 0.371958i
\(960\) 2.90617 4.00000i 0.0937962 0.129099i
\(961\) 21.8435 15.8702i 0.704628 0.511942i
\(962\) 7.70088 3.92380i 0.248286 0.126508i
\(963\) 5.34307 + 1.73607i 0.172178 + 0.0559440i
\(964\) −25.8375 35.5623i −0.832171 1.14538i
\(965\) 3.52671 4.85410i 0.113529 0.156259i
\(966\) 1.92522 + 0.980949i 0.0619430 + 0.0315615i
\(967\) −58.7214 −1.88835 −0.944176 0.329442i \(-0.893139\pi\)
−0.944176 + 0.329442i \(0.893139\pi\)
\(968\) 29.3755 + 10.2509i 0.944164 + 0.329476i
\(969\) 1.90983 0.0613526
\(970\) −3.66660 1.86823i −0.117727 0.0599851i
\(971\) 26.4176 36.3607i 0.847780 1.16687i −0.136567 0.990631i \(-0.543607\pi\)
0.984347 0.176239i \(-0.0563931\pi\)
\(972\) −22.5623 + 16.3925i −0.723686 + 0.525789i
\(973\) 1.11006 + 0.360680i 0.0355868 + 0.0115629i
\(974\) 13.7906 7.02666i 0.441879 0.225149i
\(975\) 0.381966 0.277515i 0.0122327 0.00888758i
\(976\) −10.5146 + 14.4721i −0.336565 + 0.463242i
\(977\) 1.56231 + 4.80828i 0.0499826 + 0.153831i 0.972933 0.231089i \(-0.0742290\pi\)
−0.922950 + 0.384920i \(0.874229\pi\)
\(978\) −2.70820 2.70820i −0.0865988 0.0865988i
\(979\) −17.8908 4.50000i −0.571793 0.143821i
\(980\) −12.8328 −0.409929
\(981\) 41.0139 13.3262i 1.30947 0.425474i
\(982\) 2.74550 0.434844i 0.0876123 0.0138764i
\(983\) 22.9443 16.6700i 0.731809 0.531690i −0.158326 0.987387i \(-0.550610\pi\)
0.890135 + 0.455697i \(0.150610\pi\)
\(984\) −11.4977 + 5.85836i −0.366533 + 0.186758i
\(985\) −4.61803 + 14.2128i −0.147143 + 0.452859i
\(986\) 0.338012 2.13412i 0.0107645 0.0679644i
\(987\) 3.03719 4.18034i 0.0966750 0.133062i
\(988\) −11.7557 + 3.81966i −0.373999 + 0.121520i
\(989\) 6.00000i 0.190789i
\(990\) 9.25090 + 8.07533i 0.294013 + 0.256651i
\(991\) 32.0689 1.01870 0.509351 0.860559i \(-0.329886\pi\)
0.509351 + 0.860559i \(0.329886\pi\)
\(992\) 5.13632 10.0806i 0.163078 0.320059i
\(993\) 5.01722 + 3.64522i 0.159217 + 0.115678i
\(994\) 11.6782 + 1.84965i 0.370411 + 0.0586673i
\(995\) −8.22899 2.67376i −0.260877 0.0847640i
\(996\) −5.42882 1.76393i −0.172019 0.0558923i
\(997\) −27.5276 37.8885i −0.871809 1.19994i −0.978623 0.205663i \(-0.934065\pi\)
0.106814 0.994279i \(-0.465935\pi\)
\(998\) −31.5929 + 5.00383i −1.00006 + 0.158393i
\(999\) −8.58359 26.4176i −0.271573 0.835815i
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 440.2.bi.b.181.1 yes 8
8.5 even 2 inner 440.2.bi.b.181.2 yes 8
11.9 even 5 inner 440.2.bi.b.141.2 yes 8
88.53 even 10 inner 440.2.bi.b.141.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
440.2.bi.b.141.1 8 88.53 even 10 inner
440.2.bi.b.141.2 yes 8 11.9 even 5 inner
440.2.bi.b.181.1 yes 8 1.1 even 1 trivial
440.2.bi.b.181.2 yes 8 8.5 even 2 inner