Properties

Label 930.2.bt.b.13.1
Level $930$
Weight $2$
Character 930.13
Analytic conductor $7.426$
Analytic rank $0$
Dimension $256$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(13,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([0, 45, 22]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bt (of order \(60\), degree \(16\), 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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(256\)
Relative dimension: \(16\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 13.1
Character \(\chi\) \(=\) 930.13
Dual form 930.2.bt.b.787.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.156434 + 0.987688i) q^{2} +(-0.358368 + 0.933580i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-2.21414 + 0.312392i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-3.70934 - 0.194398i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.743145 - 0.669131i) q^{9} +O(q^{10})\) \(q+(-0.156434 + 0.987688i) q^{2} +(-0.358368 + 0.933580i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-2.21414 + 0.312392i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-3.70934 - 0.194398i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-0.743145 - 0.669131i) q^{9} +(0.0378215 - 2.23575i) q^{10} +(0.167614 + 0.788560i) q^{11} +(0.629320 - 0.777146i) q^{12} +(0.615859 + 0.760522i) q^{13} +(0.772273 - 3.63326i) q^{14} +(0.501833 - 2.17903i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-0.729159 - 1.12281i) q^{17} +(0.777146 - 0.629320i) q^{18} +(-1.08224 + 0.113748i) q^{19} +(2.20231 + 0.387104i) q^{20} +(1.51079 - 3.39330i) q^{21} +(-0.805072 + 0.0421920i) q^{22} +(2.71169 + 1.38168i) q^{23} +(0.669131 + 0.743145i) q^{24} +(4.80482 - 1.38336i) q^{25} +(-0.847500 + 0.489305i) q^{26} +(0.891007 - 0.453990i) q^{27} +(3.46772 + 1.33113i) q^{28} +(7.08179 - 5.14523i) q^{29} +(2.07370 + 0.836530i) q^{30} +(-3.55575 - 4.28446i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.796251 - 0.126114i) q^{33} +(1.22305 - 0.544536i) q^{34} +(8.27371 - 0.728343i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-1.46045 + 0.391327i) q^{37} +(0.0569521 - 1.08671i) q^{38} +(-0.930713 + 0.302407i) q^{39} +(-0.726855 + 2.11464i) q^{40} +(3.04759 + 1.35688i) q^{41} +(3.11518 + 2.02302i) q^{42} +(2.99016 + 2.42138i) q^{43} +(0.0842684 - 0.801760i) q^{44} +(1.85446 + 1.24940i) q^{45} +(-1.78887 + 2.46217i) q^{46} +(6.36725 - 1.00847i) q^{47} +(-0.838671 + 0.544639i) q^{48} +(6.75973 + 0.710477i) q^{49} +(0.614688 + 4.96207i) q^{50} +(1.30954 - 0.278351i) q^{51} +(-0.350702 - 0.913610i) q^{52} +(-0.300775 - 5.73913i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-0.617460 - 1.69362i) q^{55} +(-1.85721 + 3.21679i) q^{56} +(0.281647 - 1.05112i) q^{57} +(3.97404 + 7.79950i) q^{58} +(-1.52791 - 3.43175i) q^{59} +(-1.15063 + 1.91730i) q^{60} -8.22925i q^{61} +(4.78796 - 2.84174i) q^{62} +(2.62650 + 2.62650i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-1.60118 - 1.49151i) q^{65} +(0.249122 - 0.766719i) q^{66} +(-11.8008 - 3.16203i) q^{67} +(0.346505 + 1.29317i) q^{68} +(-2.26169 + 2.03644i) q^{69} +(-0.574918 + 8.28579i) q^{70} +(4.80349 - 5.33482i) q^{71} +(-0.933580 + 0.358368i) q^{72} +(-8.66916 + 13.3493i) q^{73} +(-0.158044 - 1.50369i) q^{74} +(-0.430417 + 4.98144i) q^{75} +(1.06442 + 0.226250i) q^{76} +(-0.468441 - 2.95762i) q^{77} +(-0.153088 - 0.966561i) q^{78} +(1.12832 + 0.239832i) q^{79} +(-1.97490 - 1.04871i) q^{80} +(0.104528 + 0.994522i) q^{81} +(-1.81692 + 2.79781i) q^{82} +(-5.89056 + 2.26117i) q^{83} +(-2.48544 + 2.76036i) q^{84} +(1.96521 + 2.25826i) q^{85} +(-2.85933 + 2.57455i) q^{86} +(2.26559 + 8.45531i) q^{87} +(0.778707 + 0.208654i) q^{88} +(2.98215 - 9.17810i) q^{89} +(-1.52411 + 1.63618i) q^{90} +(-2.13658 - 2.94075i) q^{91} +(-2.15201 - 2.15201i) q^{92} +(5.27416 - 1.78417i) q^{93} +6.44662i q^{94} +(2.36070 - 0.589937i) q^{95} +(-0.406737 - 0.913545i) q^{96} +(2.25175 + 4.41931i) q^{97} +(-1.75918 + 6.56537i) q^{98} +(0.403088 - 0.698169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 256 q + 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 256 q + 16 q^{7} + 4 q^{10} + 24 q^{14} + 8 q^{15} + 64 q^{16} - 36 q^{17} + 40 q^{19} - 12 q^{20} - 16 q^{21} + 44 q^{22} + 32 q^{24} - 28 q^{25} - 8 q^{28} + 16 q^{29} - 8 q^{31} - 4 q^{33} - 24 q^{35} + 128 q^{36} - 76 q^{37} + 28 q^{38} + 48 q^{41} - 4 q^{42} + 120 q^{43} - 4 q^{44} + 12 q^{45} - 20 q^{46} + 72 q^{47} + 40 q^{49} + 48 q^{50} - 16 q^{53} - 64 q^{54} + 36 q^{55} - 4 q^{57} - 68 q^{58} + 24 q^{59} - 20 q^{62} + 4 q^{63} + 156 q^{65} + 12 q^{66} + 44 q^{67} + 4 q^{68} - 12 q^{69} + 104 q^{70} - 48 q^{71} - 84 q^{73} - 68 q^{74} - 48 q^{75} + 48 q^{76} - 124 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 112 q^{83} + 132 q^{85} + 24 q^{86} + 32 q^{87} + 52 q^{88} + 224 q^{89} + 40 q^{91} + 64 q^{93} - 204 q^{95} + 8 q^{97} - 32 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(e\left(\frac{11}{30}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.156434 + 0.987688i −0.110616 + 0.698401i
\(3\) −0.358368 + 0.933580i −0.206904 + 0.539003i
\(4\) −0.951057 0.309017i −0.475528 0.154508i
\(5\) −2.21414 + 0.312392i −0.990193 + 0.139706i
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) −3.70934 0.194398i −1.40200 0.0734756i −0.663724 0.747977i \(-0.731025\pi\)
−0.738273 + 0.674502i \(0.764358\pi\)
\(8\) 0.453990 0.891007i 0.160510 0.315018i
\(9\) −0.743145 0.669131i −0.247715 0.223044i
\(10\) 0.0378215 2.23575i 0.0119602 0.707006i
\(11\) 0.167614 + 0.788560i 0.0505374 + 0.237760i 0.996165 0.0874906i \(-0.0278848\pi\)
−0.945628 + 0.325250i \(0.894551\pi\)
\(12\) 0.629320 0.777146i 0.181669 0.224343i
\(13\) 0.615859 + 0.760522i 0.170808 + 0.210931i 0.855361 0.518033i \(-0.173336\pi\)
−0.684552 + 0.728964i \(0.740002\pi\)
\(14\) 0.772273 3.63326i 0.206399 0.971029i
\(15\) 0.501833 2.17903i 0.129573 0.562623i
\(16\) 0.809017 + 0.587785i 0.202254 + 0.146946i
\(17\) −0.729159 1.12281i −0.176847 0.272320i 0.739120 0.673573i \(-0.235241\pi\)
−0.915967 + 0.401253i \(0.868575\pi\)
\(18\) 0.777146 0.629320i 0.183175 0.148332i
\(19\) −1.08224 + 0.113748i −0.248283 + 0.0260956i −0.227852 0.973696i \(-0.573170\pi\)
−0.0204305 + 0.999791i \(0.506504\pi\)
\(20\) 2.20231 + 0.387104i 0.492451 + 0.0865591i
\(21\) 1.51079 3.39330i 0.329682 0.740478i
\(22\) −0.805072 + 0.0421920i −0.171642 + 0.00899537i
\(23\) 2.71169 + 1.38168i 0.565427 + 0.288100i 0.713245 0.700915i \(-0.247225\pi\)
−0.147817 + 0.989015i \(0.547225\pi\)
\(24\) 0.669131 + 0.743145i 0.136586 + 0.151694i
\(25\) 4.80482 1.38336i 0.960964 0.276672i
\(26\) −0.847500 + 0.489305i −0.166209 + 0.0959605i
\(27\) 0.891007 0.453990i 0.171474 0.0873705i
\(28\) 3.46772 + 1.33113i 0.655337 + 0.251560i
\(29\) 7.08179 5.14523i 1.31506 0.955444i 0.315077 0.949066i \(-0.397970\pi\)
0.999980 0.00637809i \(-0.00203022\pi\)
\(30\) 2.07370 + 0.836530i 0.378603 + 0.152729i
\(31\) −3.55575 4.28446i −0.638632 0.769512i
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −0.796251 0.126114i −0.138610 0.0219536i
\(34\) 1.22305 0.544536i 0.209751 0.0933871i
\(35\) 8.27371 0.728343i 1.39851 0.123113i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −1.46045 + 0.391327i −0.240097 + 0.0643337i −0.376861 0.926270i \(-0.622996\pi\)
0.136764 + 0.990604i \(0.456330\pi\)
\(38\) 0.0569521 1.08671i 0.00923884 0.176288i
\(39\) −0.930713 + 0.302407i −0.149033 + 0.0484239i
\(40\) −0.726855 + 2.11464i −0.114926 + 0.334353i
\(41\) 3.04759 + 1.35688i 0.475954 + 0.211908i 0.630671 0.776051i \(-0.282780\pi\)
−0.154717 + 0.987959i \(0.549447\pi\)
\(42\) 3.11518 + 2.02302i 0.480683 + 0.312159i
\(43\) 2.99016 + 2.42138i 0.455994 + 0.369257i 0.829625 0.558320i \(-0.188554\pi\)
−0.373631 + 0.927577i \(0.621887\pi\)
\(44\) 0.0842684 0.801760i 0.0127039 0.120870i
\(45\) 1.85446 + 1.24940i 0.276446 + 0.186249i
\(46\) −1.78887 + 2.46217i −0.263754 + 0.363027i
\(47\) 6.36725 1.00847i 0.928759 0.147101i 0.326314 0.945261i \(-0.394193\pi\)
0.602445 + 0.798160i \(0.294193\pi\)
\(48\) −0.838671 + 0.544639i −0.121052 + 0.0786119i
\(49\) 6.75973 + 0.710477i 0.965676 + 0.101497i
\(50\) 0.614688 + 4.96207i 0.0869300 + 0.701743i
\(51\) 1.30954 0.278351i 0.183372 0.0389769i
\(52\) −0.350702 0.913610i −0.0486336 0.126695i
\(53\) −0.300775 5.73913i −0.0413146 0.788330i −0.938206 0.346078i \(-0.887513\pi\)
0.896891 0.442252i \(-0.145820\pi\)
\(54\) 0.309017 + 0.951057i 0.0420519 + 0.129422i
\(55\) −0.617460 1.69362i −0.0832582 0.228368i
\(56\) −1.85721 + 3.21679i −0.248181 + 0.429861i
\(57\) 0.281647 1.05112i 0.0373051 0.139224i
\(58\) 3.97404 + 7.79950i 0.521817 + 1.02412i
\(59\) −1.52791 3.43175i −0.198917 0.446776i 0.786353 0.617777i \(-0.211967\pi\)
−0.985271 + 0.171001i \(0.945300\pi\)
\(60\) −1.15063 + 1.91730i −0.148545 + 0.247523i
\(61\) 8.22925i 1.05365i −0.849975 0.526824i \(-0.823383\pi\)
0.849975 0.526824i \(-0.176617\pi\)
\(62\) 4.78796 2.84174i 0.608071 0.360901i
\(63\) 2.62650 + 2.62650i 0.330907 + 0.330907i
\(64\) −0.587785 0.809017i −0.0734732 0.101127i
\(65\) −1.60118 1.49151i −0.198602 0.184999i
\(66\) 0.249122 0.766719i 0.0306648 0.0943766i
\(67\) −11.8008 3.16203i −1.44170 0.386303i −0.548573 0.836103i \(-0.684829\pi\)
−0.893129 + 0.449800i \(0.851495\pi\)
\(68\) 0.346505 + 1.29317i 0.0420199 + 0.156820i
\(69\) −2.26169 + 2.03644i −0.272276 + 0.245158i
\(70\) −0.574918 + 8.28579i −0.0687158 + 0.990341i
\(71\) 4.80349 5.33482i 0.570070 0.633127i −0.387313 0.921948i \(-0.626597\pi\)
0.957383 + 0.288822i \(0.0932634\pi\)
\(72\) −0.933580 + 0.358368i −0.110024 + 0.0422341i
\(73\) −8.66916 + 13.3493i −1.01465 + 1.56242i −0.202238 + 0.979336i \(0.564822\pi\)
−0.812411 + 0.583086i \(0.801845\pi\)
\(74\) −0.158044 1.50369i −0.0183722 0.174800i
\(75\) −0.430417 + 4.98144i −0.0497003 + 0.575207i
\(76\) 1.06442 + 0.226250i 0.122098 + 0.0259526i
\(77\) −0.468441 2.95762i −0.0533838 0.337052i
\(78\) −0.153088 0.966561i −0.0173338 0.109441i
\(79\) 1.12832 + 0.239832i 0.126946 + 0.0269832i 0.270946 0.962594i \(-0.412663\pi\)
−0.144001 + 0.989578i \(0.545997\pi\)
\(80\) −1.97490 1.04871i −0.220800 0.117249i
\(81\) 0.104528 + 0.994522i 0.0116143 + 0.110502i
\(82\) −1.81692 + 2.79781i −0.200645 + 0.308966i
\(83\) −5.89056 + 2.26117i −0.646573 + 0.248196i −0.659482 0.751721i \(-0.729224\pi\)
0.0129087 + 0.999917i \(0.495891\pi\)
\(84\) −2.48544 + 2.76036i −0.271183 + 0.301180i
\(85\) 1.96521 + 2.25826i 0.213157 + 0.244943i
\(86\) −2.85933 + 2.57455i −0.308330 + 0.277621i
\(87\) 2.26559 + 8.45531i 0.242897 + 0.906504i
\(88\) 0.778707 + 0.208654i 0.0830104 + 0.0222426i
\(89\) 2.98215 9.17810i 0.316107 0.972877i −0.659189 0.751977i \(-0.729100\pi\)
0.975296 0.220900i \(-0.0708995\pi\)
\(90\) −1.52411 + 1.63618i −0.160656 + 0.172468i
\(91\) −2.13658 2.94075i −0.223975 0.308275i
\(92\) −2.15201 2.15201i −0.224363 0.224363i
\(93\) 5.27416 1.78417i 0.546905 0.185010i
\(94\) 6.44662i 0.664918i
\(95\) 2.36070 0.589937i 0.242202 0.0605263i
\(96\) −0.406737 0.913545i −0.0415124 0.0932383i
\(97\) 2.25175 + 4.41931i 0.228631 + 0.448713i 0.976613 0.215006i \(-0.0689771\pi\)
−0.747982 + 0.663719i \(0.768977\pi\)
\(98\) −1.75918 + 6.56537i −0.177705 + 0.663202i
\(99\) 0.403088 0.698169i 0.0405119 0.0701687i
\(100\) −4.99714 0.169119i −0.499714 0.0169119i
\(101\) −3.91121 12.0375i −0.389180 1.19777i −0.933403 0.358831i \(-0.883175\pi\)
0.544223 0.838941i \(-0.316825\pi\)
\(102\) 0.0700670 + 1.33696i 0.00693767 + 0.132379i
\(103\) 1.73313 + 4.51497i 0.170771 + 0.444873i 0.992080 0.125611i \(-0.0400890\pi\)
−0.821309 + 0.570484i \(0.806756\pi\)
\(104\) 0.957224 0.203464i 0.0938636 0.0199513i
\(105\) −2.28507 + 7.98519i −0.223000 + 0.779275i
\(106\) 5.71552 + 0.600726i 0.555141 + 0.0583477i
\(107\) 4.77403 3.10029i 0.461523 0.299716i −0.292855 0.956157i \(-0.594605\pi\)
0.754378 + 0.656441i \(0.227939\pi\)
\(108\) −0.987688 + 0.156434i −0.0950404 + 0.0150529i
\(109\) 5.70283 7.84927i 0.546232 0.751824i −0.443263 0.896392i \(-0.646179\pi\)
0.989495 + 0.144568i \(0.0461792\pi\)
\(110\) 1.76936 0.344917i 0.168702 0.0328866i
\(111\) 0.158044 1.50369i 0.0150009 0.142724i
\(112\) −2.88665 2.33756i −0.272763 0.220879i
\(113\) −0.303957 0.197392i −0.0285938 0.0185690i 0.530263 0.847833i \(-0.322093\pi\)
−0.558857 + 0.829264i \(0.688760\pi\)
\(114\) 0.994121 + 0.442611i 0.0931080 + 0.0414544i
\(115\) −6.43569 2.21211i −0.600131 0.206281i
\(116\) −8.32515 + 2.70500i −0.772971 + 0.251153i
\(117\) 0.0512164 0.977268i 0.00473496 0.0903485i
\(118\) 3.62852 0.972259i 0.334032 0.0895037i
\(119\) 2.48642 + 4.30661i 0.227930 + 0.394786i
\(120\) −1.71370 1.43639i −0.156439 0.131124i
\(121\) 9.45527 4.20976i 0.859570 0.382705i
\(122\) 8.12793 + 1.28734i 0.735869 + 0.116550i
\(123\) −2.35891 + 2.35891i −0.212696 + 0.212696i
\(124\) 2.05775 + 5.17355i 0.184791 + 0.464599i
\(125\) −10.2064 + 4.56394i −0.912888 + 0.408211i
\(126\) −3.00503 + 2.18329i −0.267710 + 0.194503i
\(127\) −17.4657 6.70446i −1.54983 0.594925i −0.575056 0.818114i \(-0.695020\pi\)
−0.974775 + 0.223189i \(0.928353\pi\)
\(128\) 0.891007 0.453990i 0.0787546 0.0401275i
\(129\) −3.33213 + 1.92381i −0.293378 + 0.169382i
\(130\) 1.72363 1.34814i 0.151172 0.118240i
\(131\) 0.734123 + 0.815326i 0.0641406 + 0.0712353i 0.774361 0.632744i \(-0.218071\pi\)
−0.710220 + 0.703979i \(0.751405\pi\)
\(132\) 0.718309 + 0.365997i 0.0625207 + 0.0318559i
\(133\) 4.03651 0.211544i 0.350009 0.0183432i
\(134\) 4.96915 11.1609i 0.429270 0.964155i
\(135\) −1.83099 + 1.28354i −0.157586 + 0.110470i
\(136\) −1.33146 + 0.139942i −0.114172 + 0.0119999i
\(137\) 12.7259 10.3052i 1.08724 0.880433i 0.0938958 0.995582i \(-0.470068\pi\)
0.993348 + 0.115149i \(0.0367346\pi\)
\(138\) −1.65756 2.55241i −0.141101 0.217276i
\(139\) −2.00191 1.45447i −0.169800 0.123367i 0.499640 0.866233i \(-0.333466\pi\)
−0.669440 + 0.742866i \(0.733466\pi\)
\(140\) −8.09384 1.86402i −0.684054 0.157539i
\(141\) −1.34033 + 6.30575i −0.112876 + 0.531040i
\(142\) 4.51771 + 5.57890i 0.379118 + 0.468171i
\(143\) −0.496491 + 0.613115i −0.0415187 + 0.0512713i
\(144\) −0.207912 0.978148i −0.0173260 0.0815123i
\(145\) −14.0727 + 13.6045i −1.16868 + 1.12980i
\(146\) −11.8288 10.6507i −0.978961 0.881461i
\(147\) −3.08576 + 6.05614i −0.254509 + 0.499502i
\(148\) 1.50990 + 0.0791304i 0.124113 + 0.00650448i
\(149\) 12.8271 + 7.40575i 1.05084 + 0.606702i 0.922884 0.385077i \(-0.125825\pi\)
0.127955 + 0.991780i \(0.459159\pi\)
\(150\) −4.85278 1.20439i −0.396228 0.0983378i
\(151\) 1.81855 + 0.590882i 0.147991 + 0.0480853i 0.382076 0.924131i \(-0.375209\pi\)
−0.234085 + 0.972216i \(0.575209\pi\)
\(152\) −0.389976 + 1.01592i −0.0316313 + 0.0824023i
\(153\) −0.209433 + 1.32231i −0.0169317 + 0.106902i
\(154\) 2.99448 0.241302
\(155\) 9.21136 + 8.37561i 0.739875 + 0.672745i
\(156\) 0.978609 0.0783514
\(157\) 2.18552 13.7988i 0.174423 1.10127i −0.732747 0.680501i \(-0.761762\pi\)
0.907170 0.420764i \(-0.138238\pi\)
\(158\) −0.413387 + 1.07691i −0.0328873 + 0.0856743i
\(159\) 5.46573 + 1.77592i 0.433460 + 0.140840i
\(160\) 1.34474 1.78653i 0.106311 0.141237i
\(161\) −9.78999 5.65225i −0.771559 0.445460i
\(162\) −0.998630 0.0523360i −0.0784597 0.00411190i
\(163\) −8.94059 + 17.5469i −0.700281 + 1.37438i 0.217013 + 0.976169i \(0.430369\pi\)
−0.917294 + 0.398211i \(0.869631\pi\)
\(164\) −2.47913 2.23222i −0.193588 0.174307i
\(165\) 1.80241 + 0.0304908i 0.140317 + 0.00237371i
\(166\) −1.31185 6.17176i −0.101819 0.479022i
\(167\) 2.78501 3.43920i 0.215510 0.266133i −0.657914 0.753093i \(-0.728561\pi\)
0.873424 + 0.486960i \(0.161894\pi\)
\(168\) −2.33756 2.88665i −0.180347 0.222710i
\(169\) 2.50374 11.7792i 0.192595 0.906090i
\(170\) −2.53789 + 1.58775i −0.194647 + 0.121775i
\(171\) 0.880373 + 0.639629i 0.0673238 + 0.0489136i
\(172\) −2.09556 3.22688i −0.159785 0.246047i
\(173\) 6.70454 5.42923i 0.509736 0.412776i −0.339647 0.940553i \(-0.610308\pi\)
0.849383 + 0.527777i \(0.176974\pi\)
\(174\) −8.70563 + 0.914998i −0.659972 + 0.0693658i
\(175\) −18.0916 + 4.19730i −1.36760 + 0.317286i
\(176\) −0.327902 + 0.736479i −0.0247165 + 0.0555142i
\(177\) 3.75137 0.196601i 0.281970 0.0147774i
\(178\) 8.59860 + 4.38120i 0.644492 + 0.328385i
\(179\) −12.3065 13.6678i −0.919833 1.02158i −0.999693 0.0247725i \(-0.992114\pi\)
0.0798596 0.996806i \(-0.474553\pi\)
\(180\) −1.37761 1.76130i −0.102681 0.131280i
\(181\) −14.6946 + 8.48393i −1.09224 + 0.630606i −0.934172 0.356822i \(-0.883860\pi\)
−0.158069 + 0.987428i \(0.550527\pi\)
\(182\) 3.23878 1.65024i 0.240075 0.122324i
\(183\) 7.68267 + 2.94910i 0.567919 + 0.218004i
\(184\) 2.46217 1.78887i 0.181513 0.131877i
\(185\) 3.11139 1.32269i 0.228754 0.0972458i
\(186\) 0.937141 + 5.48833i 0.0687145 + 0.402424i
\(187\) 0.763183 0.763183i 0.0558094 0.0558094i
\(188\) −6.36725 1.00847i −0.464380 0.0735505i
\(189\) −3.39330 + 1.51079i −0.246826 + 0.109894i
\(190\) 0.213380 + 2.42392i 0.0154802 + 0.175850i
\(191\) 9.15756 + 15.8614i 0.662618 + 1.14769i 0.979925 + 0.199365i \(0.0638878\pi\)
−0.317308 + 0.948323i \(0.602779\pi\)
\(192\) 0.965926 0.258819i 0.0697097 0.0186787i
\(193\) 0.0909916 1.73622i 0.00654972 0.124976i −0.993398 0.114721i \(-0.963402\pi\)
0.999947 0.0102546i \(-0.00326421\pi\)
\(194\) −4.71715 + 1.53270i −0.338672 + 0.110041i
\(195\) 1.96626 0.960318i 0.140807 0.0687698i
\(196\) −6.20934 2.76458i −0.443524 0.197470i
\(197\) −7.06624 4.58887i −0.503448 0.326943i 0.267803 0.963474i \(-0.413702\pi\)
−0.771252 + 0.636530i \(0.780369\pi\)
\(198\) 0.626517 + 0.507343i 0.0445246 + 0.0360553i
\(199\) 2.46057 23.4108i 0.174425 1.65955i −0.461011 0.887394i \(-0.652513\pi\)
0.635437 0.772153i \(-0.280820\pi\)
\(200\) 0.948761 4.90916i 0.0670876 0.347130i
\(201\) 7.18105 9.88386i 0.506512 0.697154i
\(202\) 12.5011 1.97998i 0.879575 0.139311i
\(203\) −27.2690 + 17.7087i −1.91391 + 1.24291i
\(204\) −1.33146 0.139942i −0.0932207 0.00979789i
\(205\) −7.17167 2.05227i −0.500891 0.143337i
\(206\) −4.73051 + 1.00550i −0.329590 + 0.0700565i
\(207\) −1.09066 2.84126i −0.0758060 0.197481i
\(208\) 0.0512164 + 0.977268i 0.00355122 + 0.0677613i
\(209\) −0.271095 0.834345i −0.0187520 0.0577129i
\(210\) −7.52942 3.50609i −0.519579 0.241943i
\(211\) 1.08498 1.87923i 0.0746928 0.129372i −0.826260 0.563289i \(-0.809536\pi\)
0.900953 + 0.433917i \(0.142869\pi\)
\(212\) −1.48743 + 5.55118i −0.102157 + 0.381257i
\(213\) 3.25907 + 6.39628i 0.223307 + 0.438266i
\(214\) 2.31530 + 5.20024i 0.158270 + 0.355481i
\(215\) −7.37704 4.42717i −0.503110 0.301931i
\(216\) 1.00000i 0.0680414i
\(217\) 12.3566 + 16.5837i 0.838820 + 1.12578i
\(218\) 6.86051 + 6.86051i 0.464653 + 0.464653i
\(219\) −9.35593 12.8773i −0.632215 0.870170i
\(220\) 0.0638817 + 1.80153i 0.00430690 + 0.121459i
\(221\) 0.404860 1.24603i 0.0272338 0.0838171i
\(222\) 1.46045 + 0.391327i 0.0980191 + 0.0262641i
\(223\) −3.24418 12.1074i −0.217246 0.810774i −0.985364 0.170465i \(-0.945473\pi\)
0.768117 0.640309i \(-0.221194\pi\)
\(224\) 2.76036 2.48544i 0.184434 0.166065i
\(225\) −4.49633 2.18702i −0.299755 0.145801i
\(226\) 0.242511 0.269335i 0.0161316 0.0179159i
\(227\) −6.41897 + 2.46401i −0.426042 + 0.163542i −0.561935 0.827181i \(-0.689943\pi\)
0.135893 + 0.990723i \(0.456610\pi\)
\(228\) −0.592677 + 0.912642i −0.0392510 + 0.0604412i
\(229\) −0.432150 4.11164i −0.0285573 0.271705i −0.999478 0.0323037i \(-0.989716\pi\)
0.970921 0.239401i \(-0.0769510\pi\)
\(230\) 3.19164 6.01041i 0.210451 0.396315i
\(231\) 2.92905 + 0.622588i 0.192717 + 0.0409633i
\(232\) −1.36936 8.64581i −0.0899030 0.567625i
\(233\) −3.06939 19.3793i −0.201082 1.26958i −0.857223 0.514945i \(-0.827812\pi\)
0.656141 0.754638i \(-0.272188\pi\)
\(234\) 0.957224 + 0.203464i 0.0625757 + 0.0133009i
\(235\) −13.7829 + 4.22198i −0.899100 + 0.275412i
\(236\) 0.392663 + 3.73594i 0.0255602 + 0.243189i
\(237\) −0.628255 + 0.967428i −0.0408096 + 0.0628412i
\(238\) −4.64255 + 1.78211i −0.300932 + 0.115517i
\(239\) −1.30282 + 1.44693i −0.0842725 + 0.0935941i −0.783806 0.621006i \(-0.786724\pi\)
0.699534 + 0.714600i \(0.253391\pi\)
\(240\) 1.68679 1.46790i 0.108882 0.0947526i
\(241\) −6.62302 + 5.96339i −0.426626 + 0.384136i −0.854285 0.519804i \(-0.826005\pi\)
0.427659 + 0.903940i \(0.359338\pi\)
\(242\) 2.67880 + 9.99741i 0.172200 + 0.642658i
\(243\) −0.965926 0.258819i −0.0619642 0.0166032i
\(244\) −2.54298 + 7.82648i −0.162798 + 0.501039i
\(245\) −15.1889 + 0.538594i −0.970386 + 0.0344095i
\(246\) −1.96085 2.69888i −0.125020 0.172075i
\(247\) −0.753015 0.753015i −0.0479132 0.0479132i
\(248\) −5.43176 + 1.22309i −0.344917 + 0.0776665i
\(249\) 6.30965i 0.399858i
\(250\) −2.91112 10.7947i −0.184115 0.682716i
\(251\) 4.43445 + 9.95993i 0.279900 + 0.628665i 0.997715 0.0675689i \(-0.0215242\pi\)
−0.717815 + 0.696234i \(0.754858\pi\)
\(252\) −1.68631 3.30958i −0.106228 0.208484i
\(253\) −0.635018 + 2.36992i −0.0399233 + 0.148996i
\(254\) 9.35416 16.2019i 0.586932 1.01660i
\(255\) −2.81254 + 1.02540i −0.176128 + 0.0642128i
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) −0.776734 14.8210i −0.0484514 0.924507i −0.909428 0.415862i \(-0.863480\pi\)
0.860976 0.508645i \(-0.169853\pi\)
\(258\) −1.37886 3.59205i −0.0858441 0.223632i
\(259\) 5.49338 1.16765i 0.341342 0.0725545i
\(260\) 1.06191 + 1.91330i 0.0658567 + 0.118658i
\(261\) −8.70563 0.914998i −0.538865 0.0566370i
\(262\) −0.920130 + 0.597539i −0.0568458 + 0.0369161i
\(263\) 12.4365 1.96974i 0.766865 0.121459i 0.239267 0.970954i \(-0.423093\pi\)
0.527598 + 0.849494i \(0.323093\pi\)
\(264\) −0.473859 + 0.652211i −0.0291640 + 0.0401408i
\(265\) 2.45882 + 12.6133i 0.151044 + 0.774827i
\(266\) −0.422509 + 4.01990i −0.0259057 + 0.246476i
\(267\) 7.49979 + 6.07321i 0.458980 + 0.371675i
\(268\) 10.2461 + 6.65393i 0.625883 + 0.406453i
\(269\) −19.0996 8.50370i −1.16453 0.518480i −0.268847 0.963183i \(-0.586643\pi\)
−0.895678 + 0.444703i \(0.853309\pi\)
\(270\) −0.981309 2.00924i −0.0597206 0.122278i
\(271\) −6.75389 + 2.19447i −0.410269 + 0.133305i −0.506878 0.862018i \(-0.669200\pi\)
0.0966086 + 0.995322i \(0.469200\pi\)
\(272\) 0.0700670 1.33696i 0.00424844 0.0810650i
\(273\) 3.51111 0.940800i 0.212502 0.0569398i
\(274\) 8.18756 + 14.1813i 0.494629 + 0.856722i
\(275\) 1.89621 + 3.55702i 0.114346 + 0.214496i
\(276\) 2.78029 1.23786i 0.167354 0.0745107i
\(277\) 20.3812 + 3.22806i 1.22459 + 0.193956i 0.735041 0.678022i \(-0.237163\pi\)
0.489546 + 0.871978i \(0.337163\pi\)
\(278\) 1.74974 1.74974i 0.104942 0.104942i
\(279\) −0.224425 + 5.56324i −0.0134360 + 0.333062i
\(280\) 3.10723 7.70260i 0.185692 0.460318i
\(281\) −15.4444 + 11.2210i −0.921338 + 0.669392i −0.943857 0.330355i \(-0.892832\pi\)
0.0225184 + 0.999746i \(0.492832\pi\)
\(282\) −6.01844 2.31026i −0.358393 0.137574i
\(283\) 13.3899 6.82250i 0.795948 0.405556i −0.00821402 0.999966i \(-0.502615\pi\)
0.804162 + 0.594411i \(0.202615\pi\)
\(284\) −6.21694 + 3.58935i −0.368908 + 0.212989i
\(285\) −0.295244 + 2.41531i −0.0174887 + 0.143071i
\(286\) −0.527898 0.586291i −0.0312153 0.0346681i
\(287\) −11.0408 5.62555i −0.651716 0.332066i
\(288\) 0.998630 0.0523360i 0.0588448 0.00308393i
\(289\) 6.18550 13.8929i 0.363853 0.817227i
\(290\) −11.2356 16.0277i −0.659776 0.941180i
\(291\) −4.93274 + 0.518452i −0.289162 + 0.0303922i
\(292\) 12.3700 10.0171i 0.723902 0.586204i
\(293\) −8.50404 13.0951i −0.496811 0.765022i 0.497955 0.867203i \(-0.334085\pi\)
−0.994766 + 0.102181i \(0.967418\pi\)
\(294\) −5.49886 3.99516i −0.320700 0.233002i
\(295\) 4.45507 + 7.12106i 0.259384 + 0.414604i
\(296\) −0.314356 + 1.47893i −0.0182716 + 0.0859611i
\(297\) 0.507343 + 0.626517i 0.0294390 + 0.0363542i
\(298\) −9.32118 + 11.5107i −0.539961 + 0.666797i
\(299\) 0.619224 + 2.91322i 0.0358107 + 0.168476i
\(300\) 1.94870 4.60462i 0.112508 0.265848i
\(301\) −10.6208 9.56299i −0.612172 0.551202i
\(302\) −0.868090 + 1.70372i −0.0499530 + 0.0980383i
\(303\) 12.6396 + 0.662413i 0.726125 + 0.0380546i
\(304\) −0.942410 0.544101i −0.0540509 0.0312063i
\(305\) 2.57075 + 18.2207i 0.147201 + 1.04331i
\(306\) −1.27327 0.413710i −0.0727878 0.0236502i
\(307\) −8.57053 + 22.3270i −0.489146 + 1.27427i 0.437799 + 0.899073i \(0.355758\pi\)
−0.926945 + 0.375197i \(0.877575\pi\)
\(308\) −0.468441 + 2.95762i −0.0266919 + 0.168526i
\(309\) −4.83619 −0.275121
\(310\) −9.71346 + 7.78772i −0.551688 + 0.442313i
\(311\) 9.12400 0.517374 0.258687 0.965961i \(-0.416710\pi\)
0.258687 + 0.965961i \(0.416710\pi\)
\(312\) −0.153088 + 0.966561i −0.00866691 + 0.0547207i
\(313\) −8.08091 + 21.0515i −0.456760 + 1.18990i 0.491069 + 0.871121i \(0.336606\pi\)
−0.947829 + 0.318780i \(0.896727\pi\)
\(314\) 13.2870 + 4.31722i 0.749831 + 0.243635i
\(315\) −6.63593 4.99493i −0.373892 0.281432i
\(316\) −0.998983 0.576763i −0.0561972 0.0324454i
\(317\) 27.9261 + 1.46354i 1.56848 + 0.0822008i 0.816643 0.577143i \(-0.195833\pi\)
0.751842 + 0.659344i \(0.229166\pi\)
\(318\) −2.60909 + 5.12062i −0.146310 + 0.287150i
\(319\) 5.24432 + 4.72201i 0.293626 + 0.264382i
\(320\) 1.55417 + 1.60766i 0.0868807 + 0.0898707i
\(321\) 1.18351 + 5.56798i 0.0660572 + 0.310775i
\(322\) 7.11416 8.78525i 0.396457 0.489583i
\(323\) 0.916842 + 1.13221i 0.0510144 + 0.0629976i
\(324\) 0.207912 0.978148i 0.0115506 0.0543415i
\(325\) 4.01117 + 2.80222i 0.222500 + 0.155439i
\(326\) −15.9323 11.5755i −0.882406 0.641105i
\(327\) 5.28421 + 8.13697i 0.292218 + 0.449976i
\(328\) 2.59256 2.09942i 0.143150 0.115921i
\(329\) −23.8143 + 2.50299i −1.31293 + 0.137994i
\(330\) −0.312074 + 1.77545i −0.0171791 + 0.0977352i
\(331\) −5.95092 + 13.3660i −0.327092 + 0.734661i −0.999987 0.00507716i \(-0.998384\pi\)
0.672895 + 0.739738i \(0.265051\pi\)
\(332\) 6.30100 0.330221i 0.345812 0.0181232i
\(333\) 1.34718 + 0.686420i 0.0738248 + 0.0376156i
\(334\) 2.96118 + 3.28873i 0.162029 + 0.179951i
\(335\) 27.1165 + 3.31467i 1.48153 + 0.181100i
\(336\) 3.21679 1.85721i 0.175490 0.101319i
\(337\) −1.55128 + 0.790415i −0.0845034 + 0.0430567i −0.495731 0.868476i \(-0.665100\pi\)
0.411228 + 0.911532i \(0.365100\pi\)
\(338\) 11.2425 + 4.31558i 0.611510 + 0.234737i
\(339\) 0.293209 0.213029i 0.0159249 0.0115701i
\(340\) −1.17119 2.75502i −0.0635166 0.149412i
\(341\) 2.78256 3.52206i 0.150684 0.190730i
\(342\) −0.769475 + 0.769475i −0.0416084 + 0.0416084i
\(343\) 0.744860 + 0.117974i 0.0402187 + 0.00637001i
\(344\) 3.51497 1.56496i 0.189514 0.0843772i
\(345\) 4.37153 5.21549i 0.235355 0.280792i
\(346\) 4.31356 + 7.47131i 0.231899 + 0.401660i
\(347\) −15.2389 + 4.08325i −0.818066 + 0.219200i −0.643501 0.765445i \(-0.722519\pi\)
−0.174565 + 0.984646i \(0.555852\pi\)
\(348\) 0.458127 8.74158i 0.0245582 0.468598i
\(349\) 27.3508 8.88682i 1.46406 0.475700i 0.534749 0.845011i \(-0.320406\pi\)
0.929306 + 0.369311i \(0.120406\pi\)
\(350\) −1.31547 18.5255i −0.0703147 0.990229i
\(351\) 0.894004 + 0.398036i 0.0477184 + 0.0212456i
\(352\) −0.676117 0.439075i −0.0360371 0.0234028i
\(353\) 12.7884 + 10.3558i 0.680658 + 0.551186i 0.906096 0.423071i \(-0.139048\pi\)
−0.225438 + 0.974257i \(0.572381\pi\)
\(354\) −0.392663 + 3.73594i −0.0208698 + 0.198563i
\(355\) −8.96905 + 13.3126i −0.476028 + 0.706560i
\(356\) −5.67238 + 7.80736i −0.300636 + 0.413789i
\(357\) −4.91162 + 0.777925i −0.259951 + 0.0411721i
\(358\) 15.4247 10.0169i 0.815220 0.529410i
\(359\) 3.70915 + 0.389848i 0.195762 + 0.0205754i 0.201902 0.979406i \(-0.435288\pi\)
−0.00614014 + 0.999981i \(0.501954\pi\)
\(360\) 1.95513 1.08512i 0.103044 0.0571908i
\(361\) −17.4265 + 3.70412i −0.917184 + 0.194954i
\(362\) −6.08074 15.8409i −0.319597 0.832578i
\(363\) 0.541681 + 10.3359i 0.0284309 + 0.542494i
\(364\) 1.12327 + 3.45706i 0.0588753 + 0.181199i
\(365\) 15.0245 32.2655i 0.786418 1.68885i
\(366\) −4.11463 + 7.12674i −0.215075 + 0.372521i
\(367\) 5.60217 20.9076i 0.292431 1.09137i −0.650805 0.759245i \(-0.725568\pi\)
0.943236 0.332123i \(-0.107765\pi\)
\(368\) 1.38168 + 2.71169i 0.0720249 + 0.141357i
\(369\) −1.35688 3.04759i −0.0706361 0.158651i
\(370\) 0.819672 + 3.28000i 0.0426127 + 0.170519i
\(371\) 21.3468i 1.10827i
\(372\) −5.56736 + 0.0670395i −0.288654 + 0.00347584i
\(373\) −6.73507 6.73507i −0.348729 0.348729i 0.510907 0.859636i \(-0.329310\pi\)
−0.859636 + 0.510907i \(0.829310\pi\)
\(374\) 0.634398 + 0.873175i 0.0328040 + 0.0451508i
\(375\) −0.603160 11.1641i −0.0311470 0.576509i
\(376\) 1.99212 6.13110i 0.102736 0.316187i
\(377\) 8.27444 + 2.21713i 0.426155 + 0.114188i
\(378\) −0.961364 3.58786i −0.0494473 0.184540i
\(379\) −11.2494 + 10.1290i −0.577844 + 0.520293i −0.905412 0.424534i \(-0.860438\pi\)
0.327567 + 0.944828i \(0.393771\pi\)
\(380\) −2.42746 0.168431i −0.124526 0.00864035i
\(381\) 12.5183 13.9030i 0.641332 0.712272i
\(382\) −17.0986 + 6.56355i −0.874842 + 0.335820i
\(383\) −10.2003 + 15.7071i −0.521212 + 0.802595i −0.997035 0.0769452i \(-0.975483\pi\)
0.475824 + 0.879541i \(0.342150\pi\)
\(384\) 0.104528 + 0.994522i 0.00533420 + 0.0507515i
\(385\) 1.96113 + 6.40224i 0.0999484 + 0.326288i
\(386\) 1.70061 + 0.361476i 0.0865589 + 0.0183987i
\(387\) −0.601899 3.80024i −0.0305962 0.193177i
\(388\) −0.775901 4.89884i −0.0393904 0.248701i
\(389\) −13.7765 2.92828i −0.698495 0.148470i −0.155040 0.987908i \(-0.549551\pi\)
−0.543455 + 0.839439i \(0.682884\pi\)
\(390\) 0.640905 + 2.09228i 0.0324535 + 0.105947i
\(391\) −0.425900 4.05217i −0.0215387 0.204927i
\(392\) 3.70189 5.70042i 0.186974 0.287915i
\(393\) −1.02426 + 0.393176i −0.0516670 + 0.0198331i
\(394\) 5.63777 6.26138i 0.284027 0.315444i
\(395\) −2.57318 0.178542i −0.129471 0.00898344i
\(396\) −0.599106 + 0.539437i −0.0301062 + 0.0271078i
\(397\) 3.34340 + 12.4777i 0.167800 + 0.626240i 0.997666 + 0.0682769i \(0.0217501\pi\)
−0.829866 + 0.557963i \(0.811583\pi\)
\(398\) 22.7376 + 6.09253i 1.13974 + 0.305391i
\(399\) −1.24906 + 3.84421i −0.0625312 + 0.192451i
\(400\) 4.70030 + 1.70504i 0.235015 + 0.0852521i
\(401\) 11.6042 + 15.9718i 0.579487 + 0.797596i 0.993639 0.112612i \(-0.0359217\pi\)
−0.414152 + 0.910208i \(0.635922\pi\)
\(402\) 8.63881 + 8.63881i 0.430865 + 0.430865i
\(403\) 1.06859 5.34285i 0.0532301 0.266146i
\(404\) 12.6569i 0.629706i
\(405\) −0.542121 2.16936i −0.0269382 0.107796i
\(406\) −13.2249 29.7035i −0.656338 1.47416i
\(407\) −0.553376 1.08606i −0.0274298 0.0538341i
\(408\) 0.346505 1.29317i 0.0171546 0.0640217i
\(409\) 10.0362 17.3831i 0.496256 0.859541i −0.503734 0.863859i \(-0.668041\pi\)
0.999991 + 0.00431731i \(0.00137425\pi\)
\(410\) 3.14890 6.76233i 0.155513 0.333968i
\(411\) 5.06019 + 15.5737i 0.249601 + 0.768193i
\(412\) −0.253106 4.82956i −0.0124697 0.237935i
\(413\) 5.00042 + 13.0265i 0.246055 + 0.640994i
\(414\) 2.97690 0.632760i 0.146307 0.0310984i
\(415\) 12.3361 6.84672i 0.605558 0.336092i
\(416\) −0.973248 0.102293i −0.0477174 0.00501530i
\(417\) 2.07529 1.34771i 0.101627 0.0659976i
\(418\) 0.866482 0.137237i 0.0423810 0.00671249i
\(419\) −16.2115 + 22.3133i −0.791986 + 1.09007i 0.201872 + 0.979412i \(0.435297\pi\)
−0.993858 + 0.110663i \(0.964703\pi\)
\(420\) 4.64079 6.88825i 0.226447 0.336112i
\(421\) 3.31940 31.5820i 0.161778 1.53921i −0.549016 0.835812i \(-0.684997\pi\)
0.710793 0.703401i \(-0.248336\pi\)
\(422\) 1.68637 + 1.36559i 0.0820911 + 0.0664761i
\(423\) −5.40659 3.51108i −0.262878 0.170715i
\(424\) −5.25015 2.33752i −0.254970 0.113520i
\(425\) −5.05672 4.38619i −0.245287 0.212762i
\(426\) −6.82736 + 2.21834i −0.330787 + 0.107479i
\(427\) −1.59975 + 30.5251i −0.0774174 + 1.47721i
\(428\) −5.49841 + 1.47330i −0.265776 + 0.0712144i
\(429\) −0.394466 0.683235i −0.0190450 0.0329869i
\(430\) 5.52669 6.59365i 0.266521 0.317974i
\(431\) −1.45244 + 0.646669i −0.0699617 + 0.0311490i −0.441419 0.897301i \(-0.645525\pi\)
0.371457 + 0.928450i \(0.378858\pi\)
\(432\) 0.987688 + 0.156434i 0.0475202 + 0.00752646i
\(433\) 17.4370 17.4370i 0.837967 0.837967i −0.150624 0.988591i \(-0.548128\pi\)
0.988591 + 0.150624i \(0.0481284\pi\)
\(434\) −18.3126 + 9.61019i −0.879031 + 0.461304i
\(435\) −7.65771 18.0135i −0.367159 0.863680i
\(436\) −7.84927 + 5.70283i −0.375912 + 0.273116i
\(437\) −3.09187 1.18686i −0.147904 0.0567751i
\(438\) 14.1824 7.22629i 0.677661 0.345285i
\(439\) −15.2575 + 8.80894i −0.728202 + 0.420428i −0.817764 0.575554i \(-0.804787\pi\)
0.0895620 + 0.995981i \(0.471453\pi\)
\(440\) −1.78935 0.218727i −0.0853038 0.0104274i
\(441\) −4.54806 5.05113i −0.216574 0.240530i
\(442\) 1.16736 + 0.594798i 0.0555255 + 0.0282916i
\(443\) 33.1736 1.73855i 1.57613 0.0826012i 0.755917 0.654667i \(-0.227191\pi\)
0.820208 + 0.572066i \(0.193858\pi\)
\(444\) −0.614974 + 1.38125i −0.0291854 + 0.0655514i
\(445\) −3.73572 + 21.2532i −0.177090 + 1.00750i
\(446\) 12.4659 1.31022i 0.590277 0.0620406i
\(447\) −11.5107 + 9.32118i −0.544437 + 0.440876i
\(448\) 2.02302 + 3.11518i 0.0955788 + 0.147178i
\(449\) 23.5140 + 17.0839i 1.10969 + 0.806239i 0.982615 0.185654i \(-0.0594404\pi\)
0.127077 + 0.991893i \(0.459440\pi\)
\(450\) 2.86347 4.09884i 0.134985 0.193221i
\(451\) −0.559160 + 2.63064i −0.0263298 + 0.123872i
\(452\) 0.228082 + 0.281658i 0.0107281 + 0.0132481i
\(453\) −1.20334 + 1.48601i −0.0565381 + 0.0698187i
\(454\) −1.42953 6.72539i −0.0670910 0.315638i
\(455\) 5.64936 + 5.84379i 0.264846 + 0.273961i
\(456\) −0.808691 0.728149i −0.0378704 0.0340987i
\(457\) 18.0874 35.4986i 0.846095 1.66055i 0.0997330 0.995014i \(-0.468201\pi\)
0.746362 0.665540i \(-0.231799\pi\)
\(458\) 4.12862 + 0.216372i 0.192918 + 0.0101104i
\(459\) −1.15943 0.669396i −0.0541175 0.0312447i
\(460\) 5.43713 + 4.09258i 0.253507 + 0.190818i
\(461\) 27.0509 + 8.78939i 1.25989 + 0.409363i 0.861455 0.507835i \(-0.169554\pi\)
0.398434 + 0.917197i \(0.369554\pi\)
\(462\) −1.07313 + 2.79559i −0.0499264 + 0.130063i
\(463\) −1.37825 + 8.70191i −0.0640526 + 0.404412i 0.934742 + 0.355327i \(0.115630\pi\)
−0.998795 + 0.0490849i \(0.984370\pi\)
\(464\) 8.75358 0.406375
\(465\) −11.1204 + 5.59800i −0.515694 + 0.259601i
\(466\) 19.6209 0.908921
\(467\) −6.00285 + 37.9005i −0.277779 + 1.75383i 0.315589 + 0.948896i \(0.397798\pi\)
−0.593368 + 0.804931i \(0.702202\pi\)
\(468\) −0.350702 + 0.913610i −0.0162112 + 0.0422317i
\(469\) 43.1586 + 14.0231i 1.99288 + 0.647526i
\(470\) −2.01387 14.2737i −0.0928931 0.658397i
\(471\) 12.0991 + 6.98541i 0.557496 + 0.321871i
\(472\) −3.75137 0.196601i −0.172671 0.00904929i
\(473\) −1.40821 + 2.76377i −0.0647497 + 0.127078i
\(474\) −0.857237 0.771859i −0.0393742 0.0354527i
\(475\) −5.04262 + 2.04367i −0.231371 + 0.0937698i
\(476\) −1.03391 4.86418i −0.0473893 0.222949i
\(477\) −3.61671 + 4.46626i −0.165598 + 0.204496i
\(478\) −1.22531 1.51313i −0.0560443 0.0692090i
\(479\) −5.56110 + 26.1629i −0.254093 + 1.19541i 0.647239 + 0.762287i \(0.275923\pi\)
−0.901332 + 0.433128i \(0.857410\pi\)
\(480\) 1.18596 + 1.89566i 0.0541312 + 0.0865244i
\(481\) −1.19704 0.869704i −0.0545805 0.0396551i
\(482\) −4.85390 7.47436i −0.221089 0.340448i
\(483\) 8.78525 7.11416i 0.399743 0.323705i
\(484\) −10.2934 + 1.08188i −0.467881 + 0.0491763i
\(485\) −6.36625 9.08154i −0.289076 0.412371i
\(486\) 0.406737 0.913545i 0.0184499 0.0414393i
\(487\) 21.4438 1.12382i 0.971711 0.0509252i 0.440131 0.897933i \(-0.354932\pi\)
0.531580 + 0.847008i \(0.321599\pi\)
\(488\) −7.33232 3.73600i −0.331918 0.169121i
\(489\) −13.1774 14.6350i −0.595904 0.661818i
\(490\) 1.84411 15.0862i 0.0833084 0.681525i
\(491\) 15.5363 8.96991i 0.701145 0.404806i −0.106629 0.994299i \(-0.534006\pi\)
0.807774 + 0.589492i \(0.200672\pi\)
\(492\) 2.97240 1.51451i 0.134006 0.0682796i
\(493\) −10.9408 4.19980i −0.492751 0.189149i
\(494\) 0.861541 0.625947i 0.0387626 0.0281627i
\(495\) −0.674391 + 1.67177i −0.0303116 + 0.0751403i
\(496\) −0.358321 5.55622i −0.0160891 0.249482i
\(497\) −18.8549 + 18.8549i −0.845756 + 0.845756i
\(498\) 6.23196 + 0.987046i 0.279261 + 0.0442306i
\(499\) −17.3566 + 7.72764i −0.776987 + 0.345937i −0.756619 0.653856i \(-0.773150\pi\)
−0.0203675 + 0.999793i \(0.506484\pi\)
\(500\) 11.1172 1.18661i 0.497176 0.0530670i
\(501\) 2.21271 + 3.83253i 0.0988566 + 0.171225i
\(502\) −10.5310 + 2.82177i −0.470022 + 0.125942i
\(503\) 1.32904 25.3596i 0.0592589 1.13073i −0.793550 0.608505i \(-0.791770\pi\)
0.852809 0.522223i \(-0.174897\pi\)
\(504\) 3.53263 1.14782i 0.157356 0.0511280i
\(505\) 12.4204 + 25.4308i 0.552699 + 1.13165i
\(506\) −2.24140 0.997937i −0.0996426 0.0443637i
\(507\) 10.0995 + 6.55872i 0.448536 + 0.291283i
\(508\) 14.5391 + 11.7735i 0.645068 + 0.522366i
\(509\) 0.724587 6.89399i 0.0321168 0.305571i −0.966657 0.256073i \(-0.917571\pi\)
0.998774 0.0494977i \(-0.0157621\pi\)
\(510\) −0.572793 2.93832i −0.0253637 0.130111i
\(511\) 34.7519 47.8319i 1.53733 2.11596i
\(512\) −0.987688 + 0.156434i −0.0436501 + 0.00691349i
\(513\) −0.912642 + 0.592677i −0.0402941 + 0.0261673i
\(514\) 14.7600 + 1.55134i 0.651036 + 0.0684267i
\(515\) −5.24784 9.45535i −0.231248 0.416653i
\(516\) 3.76353 0.799963i 0.165680 0.0352164i
\(517\) 1.86248 + 4.85193i 0.0819118 + 0.213387i
\(518\) 0.293924 + 5.60841i 0.0129143 + 0.246419i
\(519\) 2.66593 + 8.20488i 0.117021 + 0.360154i
\(520\) −2.05587 + 0.749528i −0.0901557 + 0.0328690i
\(521\) −0.335722 + 0.581488i −0.0147083 + 0.0254755i −0.873286 0.487208i \(-0.838015\pi\)
0.858578 + 0.512684i \(0.171349\pi\)
\(522\) 2.26559 8.45531i 0.0991623 0.370079i
\(523\) −0.659012 1.29338i −0.0288166 0.0565557i 0.876149 0.482040i \(-0.160104\pi\)
−0.904966 + 0.425484i \(0.860104\pi\)
\(524\) −0.446243 1.00228i −0.0194942 0.0437847i
\(525\) 2.56494 18.3942i 0.111943 0.802787i
\(526\) 12.5915i 0.549014i
\(527\) −2.21791 + 7.11647i −0.0966137 + 0.309998i
\(528\) −0.570053 0.570053i −0.0248084 0.0248084i
\(529\) −8.07481 11.1140i −0.351079 0.483218i
\(530\) −12.8426 + 0.455395i −0.557848 + 0.0197811i
\(531\) −1.16083 + 3.57266i −0.0503756 + 0.155040i
\(532\) −3.90432 1.04616i −0.169274 0.0453567i
\(533\) 0.844952 + 3.15341i 0.0365989 + 0.136589i
\(534\) −7.17167 + 6.45740i −0.310348 + 0.279439i
\(535\) −9.60185 + 8.35584i −0.415124 + 0.361254i
\(536\) −8.17485 + 9.07910i −0.353100 + 0.392157i
\(537\) 17.1702 6.59104i 0.740951 0.284424i
\(538\) 11.3869 17.5342i 0.490922 0.755954i
\(539\) 0.572770 + 5.44954i 0.0246709 + 0.234728i
\(540\) 2.13801 0.654914i 0.0920053 0.0281830i
\(541\) 7.83120 + 1.66457i 0.336689 + 0.0715655i 0.373154 0.927769i \(-0.378276\pi\)
−0.0364646 + 0.999335i \(0.511610\pi\)
\(542\) −1.11091 7.01402i −0.0477178 0.301278i
\(543\) −2.65436 16.7590i −0.113909 0.719196i
\(544\) 1.30954 + 0.278351i 0.0561459 + 0.0119342i
\(545\) −10.1748 + 19.1609i −0.435841 + 0.820762i
\(546\) 0.379958 + 3.61506i 0.0162607 + 0.154710i
\(547\) 10.1171 15.5790i 0.432576 0.666109i −0.553415 0.832906i \(-0.686676\pi\)
0.985991 + 0.166797i \(0.0533424\pi\)
\(548\) −15.2875 + 5.86832i −0.653050 + 0.250682i
\(549\) −5.50644 + 6.11553i −0.235009 + 0.261004i
\(550\) −3.80986 + 1.31643i −0.162453 + 0.0561327i
\(551\) −7.07894 + 6.37391i −0.301573 + 0.271538i
\(552\) 0.787691 + 2.93970i 0.0335264 + 0.125122i
\(553\) −4.13869 1.10896i −0.175995 0.0471577i
\(554\) −6.37664 + 19.6253i −0.270918 + 0.833798i
\(555\) 0.119809 + 3.37875i 0.00508561 + 0.143420i
\(556\) 1.45447 + 2.00191i 0.0616835 + 0.0849000i
\(557\) −28.2645 28.2645i −1.19760 1.19760i −0.974882 0.222721i \(-0.928506\pi\)
−0.222721 0.974882i \(-0.571494\pi\)
\(558\) −5.45964 1.09194i −0.231125 0.0462257i
\(559\) 3.76531i 0.159256i
\(560\) 7.12169 + 4.27393i 0.300946 + 0.180606i
\(561\) 0.438992 + 0.985993i 0.0185343 + 0.0416286i
\(562\) −8.66685 17.0097i −0.365589 0.717509i
\(563\) 3.19150 11.9108i 0.134506 0.501982i −0.865494 0.500920i \(-0.832995\pi\)
0.999999 0.00106238i \(-0.000338167\pi\)
\(564\) 3.22331 5.58294i 0.135726 0.235084i
\(565\) 0.734666 + 0.342099i 0.0309076 + 0.0143922i
\(566\) 4.64386 + 14.2923i 0.195196 + 0.600752i
\(567\) −0.194398 3.70934i −0.00816395 0.155777i
\(568\) −2.57262 6.70190i −0.107945 0.281206i
\(569\) 30.7693 6.54022i 1.28992 0.274180i 0.488646 0.872482i \(-0.337491\pi\)
0.801271 + 0.598302i \(0.204158\pi\)
\(570\) −2.33939 0.669447i −0.0979863 0.0280401i
\(571\) 17.7403 + 1.86458i 0.742406 + 0.0780301i 0.468178 0.883634i \(-0.344911\pi\)
0.274229 + 0.961664i \(0.411577\pi\)
\(572\) 0.661654 0.429683i 0.0276651 0.0179660i
\(573\) −18.0896 + 2.86511i −0.755705 + 0.119692i
\(574\) 7.28345 10.0248i 0.304005 0.418428i
\(575\) 14.9406 + 2.88747i 0.623065 + 0.120416i
\(576\) −0.104528 + 0.994522i −0.00435535 + 0.0414384i
\(577\) −19.9097 16.1226i −0.828852 0.671191i 0.117946 0.993020i \(-0.462369\pi\)
−0.946798 + 0.321829i \(0.895702\pi\)
\(578\) 12.7542 + 8.28267i 0.530505 + 0.344514i
\(579\) 1.58830 + 0.707155i 0.0660073 + 0.0293883i
\(580\) 17.5880 8.58997i 0.730303 0.356679i
\(581\) 22.2896 7.24234i 0.924730 0.300463i
\(582\) 0.259582 4.95311i 0.0107600 0.205313i
\(583\) 4.47523 1.19914i 0.185345 0.0496631i
\(584\) 7.95863 + 13.7848i 0.329331 + 0.570417i
\(585\) 0.191891 + 2.17981i 0.00793370 + 0.0901239i
\(586\) 14.2642 6.35082i 0.589248 0.262350i
\(587\) 5.53445 + 0.876570i 0.228431 + 0.0361799i 0.269601 0.962972i \(-0.413108\pi\)
−0.0411695 + 0.999152i \(0.513108\pi\)
\(588\) 4.80618 4.80618i 0.198204 0.198204i
\(589\) 4.33553 + 4.23236i 0.178642 + 0.174391i
\(590\) −7.73032 + 3.28624i −0.318252 + 0.135292i
\(591\) 6.81639 4.95240i 0.280389 0.203714i
\(592\) −1.41155 0.541842i −0.0580142 0.0222696i
\(593\) 14.4876 7.38181i 0.594935 0.303135i −0.130475 0.991452i \(-0.541650\pi\)
0.725410 + 0.688317i \(0.241650\pi\)
\(594\) −0.698169 + 0.403088i −0.0286462 + 0.0165389i
\(595\) −6.85064 8.75870i −0.280849 0.359072i
\(596\) −9.91082 11.0071i −0.405963 0.450868i
\(597\) 20.9741 + 10.6868i 0.858411 + 0.437382i
\(598\) −2.97422 + 0.155872i −0.121625 + 0.00637410i
\(599\) −13.5888 + 30.5209i −0.555222 + 1.24705i 0.390058 + 0.920790i \(0.372455\pi\)
−0.945280 + 0.326259i \(0.894212\pi\)
\(600\) 4.24309 + 2.64503i 0.173223 + 0.107983i
\(601\) 31.4898 3.30971i 1.28449 0.135006i 0.562438 0.826839i \(-0.309863\pi\)
0.722057 + 0.691834i \(0.243197\pi\)
\(602\) 11.1067 8.99404i 0.452676 0.366570i
\(603\) 6.65393 + 10.2461i 0.270969 + 0.417255i
\(604\) −1.54695 1.12392i −0.0629444 0.0457318i
\(605\) −19.6202 + 12.2747i −0.797674 + 0.499039i
\(606\) −2.63152 + 12.3803i −0.106898 + 0.502917i
\(607\) −22.7713 28.1202i −0.924259 1.14136i −0.989650 0.143505i \(-0.954163\pi\)
0.0653904 0.997860i \(-0.479171\pi\)
\(608\) 0.684827 0.845691i 0.0277734 0.0342973i
\(609\) −6.76015 31.8040i −0.273935 1.28876i
\(610\) −18.3985 0.311243i −0.744935 0.0126018i
\(611\) 4.68830 + 4.22136i 0.189668 + 0.170778i
\(612\) 0.607799 1.19287i 0.0245688 0.0482190i
\(613\) −39.6861 2.07986i −1.60291 0.0840048i −0.770231 0.637765i \(-0.779859\pi\)
−0.832676 + 0.553760i \(0.813192\pi\)
\(614\) −20.7114 11.9577i −0.835844 0.482575i
\(615\) 4.48605 5.95986i 0.180895 0.240325i
\(616\) −2.84792 0.925346i −0.114746 0.0372833i
\(617\) −1.27917 + 3.33235i −0.0514975 + 0.134156i −0.956916 0.290364i \(-0.906224\pi\)
0.905419 + 0.424519i \(0.139557\pi\)
\(618\) 0.756546 4.77665i 0.0304328 0.192145i
\(619\) 1.32331 0.0531885 0.0265943 0.999646i \(-0.491534\pi\)
0.0265943 + 0.999646i \(0.491534\pi\)
\(620\) −6.17232 10.8121i −0.247886 0.434226i
\(621\) 3.04341 0.122128
\(622\) −1.42731 + 9.01166i −0.0572298 + 0.361335i
\(623\) −12.8460 + 33.4650i −0.514664 + 1.34075i
\(624\) −0.930713 0.302407i −0.0372583 0.0121060i
\(625\) 21.1726 13.2936i 0.846905 0.531744i
\(626\) −19.5282 11.2746i −0.780503 0.450624i
\(627\) 0.876080 + 0.0459134i 0.0349873 + 0.00183361i
\(628\) −6.34262 + 12.4481i −0.253098 + 0.496733i
\(629\) 1.50428 + 1.35446i 0.0599798 + 0.0540060i
\(630\) 5.97152 5.77285i 0.237911 0.229996i
\(631\) −2.36096 11.1075i −0.0939885 0.442181i −0.999828 0.0185596i \(-0.994092\pi\)
0.905839 0.423622i \(-0.139241\pi\)
\(632\) 0.725937 0.896458i 0.0288762 0.0356592i
\(633\) 1.36559 + 1.68637i 0.0542775 + 0.0670271i
\(634\) −5.81413 + 27.3533i −0.230908 + 1.08634i
\(635\) 40.7659 + 9.38845i 1.61775 + 0.372569i
\(636\) −4.64943 3.37801i −0.184362 0.133947i
\(637\) 3.62271 + 5.57848i 0.143537 + 0.221027i
\(638\) −5.48427 + 4.44107i −0.217124 + 0.175824i
\(639\) −7.13938 + 0.750379i −0.282430 + 0.0296845i
\(640\) −1.83099 + 1.28354i −0.0723762 + 0.0507364i
\(641\) −9.45700 + 21.2408i −0.373529 + 0.838960i 0.624778 + 0.780802i \(0.285189\pi\)
−0.998307 + 0.0581577i \(0.981477\pi\)
\(642\) −5.68457 + 0.297916i −0.224352 + 0.0117578i
\(643\) −26.7948 13.6526i −1.05668 0.538407i −0.162777 0.986663i \(-0.552045\pi\)
−0.893905 + 0.448256i \(0.852045\pi\)
\(644\) 7.56419 + 8.40089i 0.298071 + 0.331041i
\(645\) 6.77681 5.30050i 0.266837 0.208707i
\(646\) −1.26169 + 0.728438i −0.0496406 + 0.0286600i
\(647\) 15.6001 7.94864i 0.613302 0.312493i −0.119605 0.992822i \(-0.538163\pi\)
0.732907 + 0.680328i \(0.238163\pi\)
\(648\) 0.933580 + 0.358368i 0.0366745 + 0.0140780i
\(649\) 2.45004 1.78006i 0.0961725 0.0698734i
\(650\) −3.39520 + 3.52342i −0.133171 + 0.138200i
\(651\) −19.9105 + 5.59279i −0.780353 + 0.219199i
\(652\) 13.9253 13.9253i 0.545357 0.545357i
\(653\) −19.4965 3.08795i −0.762959 0.120841i −0.237184 0.971465i \(-0.576224\pi\)
−0.525775 + 0.850624i \(0.676224\pi\)
\(654\) −8.86343 + 3.94625i −0.346587 + 0.154311i
\(655\) −1.88015 1.57591i −0.0734636 0.0615759i
\(656\) 1.66800 + 2.88907i 0.0651246 + 0.112799i
\(657\) 15.3749 4.11969i 0.599832 0.160724i
\(658\) 1.25321 23.9127i 0.0488553 0.932214i
\(659\) −35.8513 + 11.6488i −1.39657 + 0.453773i −0.908080 0.418796i \(-0.862452\pi\)
−0.488490 + 0.872570i \(0.662452\pi\)
\(660\) −1.70477 0.585973i −0.0663581 0.0228090i
\(661\) −26.2351 11.6806i −1.02043 0.454323i −0.172822 0.984953i \(-0.555289\pi\)
−0.847603 + 0.530630i \(0.821955\pi\)
\(662\) −12.2705 7.96855i −0.476906 0.309707i
\(663\) 1.01818 + 0.824507i 0.0395429 + 0.0320212i
\(664\) −0.659538 + 6.27508i −0.0255950 + 0.243520i
\(665\) −8.87130 + 1.72936i −0.344014 + 0.0670617i
\(666\) −0.888714 + 1.22321i −0.0344370 + 0.0473984i
\(667\) 26.3127 4.16752i 1.01883 0.161367i
\(668\) −3.71147 + 2.41026i −0.143601 + 0.0932556i
\(669\) 12.4659 + 1.31022i 0.481959 + 0.0506559i
\(670\) −7.51582 + 26.2641i −0.290361 + 1.01467i
\(671\) 6.48926 1.37933i 0.250515 0.0532486i
\(672\) 1.33113 + 3.46772i 0.0513495 + 0.133770i
\(673\) 0.686912 + 13.1071i 0.0264785 + 0.505240i 0.979388 + 0.201986i \(0.0647396\pi\)
−0.952910 + 0.303254i \(0.901927\pi\)
\(674\) −0.538011 1.65583i −0.0207234 0.0637800i
\(675\) 3.65310 3.41393i 0.140608 0.131402i
\(676\) −6.02116 + 10.4290i −0.231583 + 0.401114i
\(677\) −8.67592 + 32.3790i −0.333443 + 1.24443i 0.572105 + 0.820181i \(0.306127\pi\)
−0.905547 + 0.424245i \(0.860540\pi\)
\(678\) 0.164538 + 0.322924i 0.00631905 + 0.0124018i
\(679\) −7.49340 16.8304i −0.287570 0.645893i
\(680\) 2.90432 0.725788i 0.111375 0.0278327i
\(681\) 6.87564i 0.263475i
\(682\) 3.04341 + 3.29928i 0.116538 + 0.126336i
\(683\) −31.9481 31.9481i −1.22246 1.22246i −0.966755 0.255704i \(-0.917693\pi\)
−0.255704 0.966755i \(-0.582307\pi\)
\(684\) −0.639629 0.880373i −0.0244568 0.0336619i
\(685\) −24.9576 + 26.7926i −0.953580 + 1.02369i
\(686\) −0.233044 + 0.717234i −0.00889764 + 0.0273841i
\(687\) 3.99341 + 1.07003i 0.152358 + 0.0408243i
\(688\) 0.995835 + 3.71651i 0.0379659 + 0.141690i
\(689\) 4.17950 3.76324i 0.159226 0.143368i
\(690\) 4.46742 + 5.13359i 0.170072 + 0.195433i
\(691\) 2.28947 2.54271i 0.0870954 0.0967293i −0.698022 0.716077i \(-0.745936\pi\)
0.785117 + 0.619347i \(0.212603\pi\)
\(692\) −8.05411 + 3.09168i −0.306171 + 0.117528i
\(693\) −1.63091 + 2.51139i −0.0619533 + 0.0953997i
\(694\) −1.64909 15.6900i −0.0625986 0.595586i
\(695\) 4.88688 + 2.59503i 0.185370 + 0.0984350i
\(696\) 8.56229 + 1.81997i 0.324553 + 0.0689858i
\(697\) −0.698671 4.41123i −0.0264640 0.167087i
\(698\) 4.49880 + 28.4043i 0.170282 + 1.07512i
\(699\) 19.1921 + 4.07942i 0.725914 + 0.154298i
\(700\) 18.5032 + 1.59875i 0.699355 + 0.0604272i
\(701\) 4.02369 + 38.2829i 0.151973 + 1.44592i 0.758921 + 0.651183i \(0.225727\pi\)
−0.606948 + 0.794742i \(0.707606\pi\)
\(702\) −0.532989 + 0.820731i −0.0201164 + 0.0309765i
\(703\) 1.53605 0.589633i 0.0579331 0.0222384i
\(704\) 0.539437 0.599106i 0.0203308 0.0225797i
\(705\) 0.997806 14.3805i 0.0375796 0.541601i
\(706\) −12.2289 + 11.0109i −0.460240 + 0.414402i
\(707\) 12.1679 + 45.4113i 0.457622 + 1.70787i
\(708\) −3.62852 0.972259i −0.136368 0.0365397i
\(709\) −3.68481 + 11.3407i −0.138386 + 0.425908i −0.996101 0.0882170i \(-0.971883\pi\)
0.857716 + 0.514125i \(0.171883\pi\)
\(710\) −11.7456 10.9412i −0.440806 0.410615i
\(711\) −0.678025 0.933222i −0.0254279 0.0349986i
\(712\) −6.82388 6.82388i −0.255736 0.255736i
\(713\) −3.72237 16.5311i −0.139404 0.619093i
\(714\) 4.97285i 0.186104i
\(715\) 0.907767 1.51262i 0.0339486 0.0565689i
\(716\) 7.48063 + 16.8018i 0.279564 + 0.627912i
\(717\) −0.883936 1.73482i −0.0330112 0.0647881i
\(718\) −0.965288 + 3.60250i −0.0360242 + 0.134444i
\(719\) 4.08050 7.06763i 0.152177 0.263578i −0.779851 0.625966i \(-0.784705\pi\)
0.932028 + 0.362388i \(0.118038\pi\)
\(720\) 0.765911 + 2.10080i 0.0285438 + 0.0782924i
\(721\) −5.55108 17.0845i −0.206733 0.636259i
\(722\) −0.932408 17.7914i −0.0347006 0.662127i
\(723\) −3.19383 8.32021i −0.118780 0.309432i
\(724\) 16.5971 3.52782i 0.616826 0.131110i
\(725\) 26.9091 34.5186i 0.999378 1.28199i
\(726\) −10.2934 1.08188i −0.382023 0.0401523i
\(727\) 21.0132 13.6461i 0.779337 0.506108i −0.0926128 0.995702i \(-0.529522\pi\)
0.871950 + 0.489595i \(0.162855\pi\)
\(728\) −3.59022 + 0.568635i −0.133062 + 0.0210750i
\(729\) 0.587785 0.809017i 0.0217698 0.0299636i
\(730\) 29.5179 + 19.8870i 1.09251 + 0.736049i
\(731\) 0.538442 5.12293i 0.0199150 0.189479i
\(732\) −6.39533 5.17884i −0.236378 0.191415i
\(733\) −43.0340 27.9466i −1.58950 1.03223i −0.968691 0.248270i \(-0.920138\pi\)
−0.620808 0.783963i \(-0.713195\pi\)
\(734\) 19.7738 + 8.80387i 0.729865 + 0.324957i
\(735\) 4.94041 14.3731i 0.182230 0.530160i
\(736\) −2.89445 + 0.940464i −0.106691 + 0.0346660i
\(737\) 0.515465 9.83566i 0.0189874 0.362301i
\(738\) 3.22233 0.863422i 0.118616 0.0317830i
\(739\) 15.4010 + 26.6753i 0.566534 + 0.981265i 0.996905 + 0.0786133i \(0.0250492\pi\)
−0.430372 + 0.902652i \(0.641617\pi\)
\(740\) −3.36784 + 0.296475i −0.123804 + 0.0108986i
\(741\) 0.972856 0.433144i 0.0357388 0.0159119i
\(742\) −21.0840 3.33938i −0.774019 0.122593i
\(743\) 26.9904 26.9904i 0.990182 0.990182i −0.00976993 0.999952i \(-0.503110\pi\)
0.999952 + 0.00976993i \(0.00310991\pi\)
\(744\) 0.804713 5.50930i 0.0295022 0.201981i
\(745\) −30.7145 12.3903i −1.12529 0.453944i
\(746\) 7.70574 5.59855i 0.282127 0.204977i
\(747\) 5.89056 + 2.26117i 0.215524 + 0.0827321i
\(748\) −0.961666 + 0.489993i −0.0351620 + 0.0179159i
\(749\) −18.3112 + 10.5720i −0.669075 + 0.386291i
\(750\) 11.1210 + 1.15071i 0.406080 + 0.0420180i
\(751\) 12.4177 + 13.7913i 0.453130 + 0.503251i 0.925813 0.377981i \(-0.123381\pi\)
−0.472684 + 0.881232i \(0.656715\pi\)
\(752\) 5.74398 + 2.92671i 0.209461 + 0.106726i
\(753\) −10.8876 + 0.570593i −0.396765 + 0.0207936i
\(754\) −3.48424 + 7.82574i −0.126889 + 0.284996i
\(755\) −4.21110 0.740194i −0.153258 0.0269384i
\(756\) 3.69408 0.388263i 0.134352 0.0141210i
\(757\) −22.6312 + 18.3264i −0.822547 + 0.666085i −0.945246 0.326359i \(-0.894178\pi\)
0.122699 + 0.992444i \(0.460845\pi\)
\(758\) −8.24453 12.6955i −0.299455 0.461120i
\(759\) −1.98494 1.44214i −0.0720488 0.0523465i
\(760\) 0.546096 2.37122i 0.0198090 0.0860132i
\(761\) 4.32604 20.3524i 0.156819 0.737774i −0.827513 0.561447i \(-0.810245\pi\)
0.984332 0.176327i \(-0.0564217\pi\)
\(762\) 11.7735 + 14.5391i 0.426510 + 0.526696i
\(763\) −22.6796 + 28.0070i −0.821056 + 1.01392i
\(764\) −3.80793 17.9149i −0.137766 0.648138i
\(765\) 0.0506351 2.99320i 0.00183072 0.108219i
\(766\) −13.9180 12.5319i −0.502879 0.452795i
\(767\) 1.66894 3.27549i 0.0602621 0.118271i
\(768\) −0.998630 0.0523360i −0.0360349 0.00188851i
\(769\) −29.8533 17.2358i −1.07654 0.621539i −0.146577 0.989199i \(-0.546826\pi\)
−0.929960 + 0.367661i \(0.880159\pi\)
\(770\) −6.63020 + 0.935453i −0.238936 + 0.0337114i
\(771\) 14.1149 + 4.58622i 0.508337 + 0.165169i
\(772\) −0.623060 + 1.62313i −0.0224244 + 0.0584177i
\(773\) −1.02711 + 6.48489i −0.0369424 + 0.233245i −0.999250 0.0387175i \(-0.987673\pi\)
0.962308 + 0.271963i \(0.0876728\pi\)
\(774\) 3.84761 0.138300
\(775\) −23.0117 15.6672i −0.826605 0.562782i
\(776\) 4.95991 0.178050
\(777\) −0.878552 + 5.54696i −0.0315179 + 0.198996i
\(778\) 5.04734 13.1488i 0.180956 0.471406i
\(779\) −3.45257 1.12181i −0.123701 0.0401929i
\(780\) −2.16678 + 0.305710i −0.0775831 + 0.0109462i
\(781\) 5.01195 + 2.89365i 0.179342 + 0.103543i
\(782\) 4.06890 + 0.213242i 0.145504 + 0.00762553i
\(783\) 3.97404 7.79950i 0.142021 0.278731i
\(784\) 5.05113 + 4.54806i 0.180398 + 0.162431i
\(785\) −0.528397 + 31.2352i −0.0188593 + 1.11483i
\(786\) −0.228106 1.07315i −0.00813627 0.0382781i
\(787\) −26.9500 + 33.2805i −0.960665 + 1.18632i 0.0217788 + 0.999763i \(0.493067\pi\)
−0.982444 + 0.186560i \(0.940266\pi\)
\(788\) 5.30235 + 6.54786i 0.188888 + 0.233258i
\(789\) −2.61792 + 12.3163i −0.0932002 + 0.438473i
\(790\) 0.578878 2.51357i 0.0205955 0.0894286i
\(791\) 1.08910 + 0.791281i 0.0387241 + 0.0281347i
\(792\) −0.439075 0.676117i −0.0156019 0.0240248i
\(793\) 6.25853 5.06806i 0.222247 0.179972i
\(794\) −12.8471 + 1.35029i −0.455928 + 0.0479199i
\(795\) −12.6567 2.22469i −0.448886 0.0789016i
\(796\) −9.57448 + 21.5046i −0.339358 + 0.762211i
\(797\) −35.1098 + 1.84003i −1.24365 + 0.0651770i −0.662778 0.748816i \(-0.730623\pi\)
−0.580874 + 0.813993i \(0.697289\pi\)
\(798\) −3.60149 1.83505i −0.127491 0.0649601i
\(799\) −5.77506 6.41385i −0.204307 0.226906i
\(800\) −2.41934 + 4.37571i −0.0855366 + 0.154705i
\(801\) −8.35752 + 4.82522i −0.295298 + 0.170491i
\(802\) −17.5905 + 8.96281i −0.621142 + 0.316488i
\(803\) −11.9798 4.59862i −0.422759 0.162282i
\(804\) −9.88386 + 7.18105i −0.348577 + 0.253256i
\(805\) 23.4421 + 9.45656i 0.826226 + 0.333300i
\(806\) 5.10991 + 1.89124i 0.179989 + 0.0666160i
\(807\) 14.7836 14.7836i 0.520407 0.520407i
\(808\) −12.5011 1.97998i −0.439787 0.0696555i
\(809\) 30.9754 13.7911i 1.08904 0.484870i 0.217930 0.975964i \(-0.430070\pi\)
0.871106 + 0.491094i \(0.163403\pi\)
\(810\) 2.22745 0.196085i 0.0782648 0.00688972i
\(811\) 15.0390 + 26.0482i 0.528089 + 0.914677i 0.999464 + 0.0327443i \(0.0104247\pi\)
−0.471375 + 0.881933i \(0.656242\pi\)
\(812\) 31.4066 8.41538i 1.10216 0.295322i
\(813\) 0.371661 7.09172i 0.0130347 0.248718i
\(814\) 1.15926 0.376665i 0.0406319 0.0132021i
\(815\) 14.3142 41.6443i 0.501405 1.45873i
\(816\) 1.22305 + 0.544536i 0.0428152 + 0.0190626i
\(817\) −3.51149 2.28039i −0.122852 0.0797808i
\(818\) 15.5991 + 12.6319i 0.545411 + 0.441665i
\(819\) −0.379958 + 3.61506i −0.0132768 + 0.126320i
\(820\) 6.18648 + 4.16799i 0.216041 + 0.145553i
\(821\) 9.84634 13.5523i 0.343640 0.472979i −0.601860 0.798601i \(-0.705574\pi\)
0.945500 + 0.325622i \(0.105574\pi\)
\(822\) −16.1735 + 2.56163i −0.564116 + 0.0893473i
\(823\) −10.3447 + 6.71791i −0.360593 + 0.234172i −0.712201 0.701976i \(-0.752302\pi\)
0.351608 + 0.936147i \(0.385635\pi\)
\(824\) 4.80969 + 0.505519i 0.167554 + 0.0176106i
\(825\) −4.00031 + 0.495547i −0.139273 + 0.0172527i
\(826\) −13.6484 + 2.90106i −0.474889 + 0.100941i
\(827\) −11.7532 30.6181i −0.408698 1.06469i −0.971277 0.237951i \(-0.923524\pi\)
0.562579 0.826743i \(-0.309809\pi\)
\(828\) 0.159280 + 3.03923i 0.00553535 + 0.105621i
\(829\) −3.38291 10.4115i −0.117493 0.361607i 0.874966 0.484185i \(-0.160884\pi\)
−0.992459 + 0.122578i \(0.960884\pi\)
\(830\) 4.83263 + 13.2553i 0.167743 + 0.460099i
\(831\) −10.3176 + 17.8706i −0.357914 + 0.619926i
\(832\) 0.253283 0.945264i 0.00878100 0.0327711i
\(833\) −4.13119 8.10792i −0.143137 0.280923i
\(834\) 1.00647 + 2.26057i 0.0348512 + 0.0782771i
\(835\) −5.09201 + 8.48488i −0.176216 + 0.293631i
\(836\) 0.877282i 0.0303414i
\(837\) −5.11330 2.20321i −0.176742 0.0761539i
\(838\) −19.5025 19.5025i −0.673703 0.673703i
\(839\) −28.0572 38.6175i −0.968643 1.33322i −0.942729 0.333559i \(-0.891750\pi\)
−0.0259141 0.999664i \(-0.508250\pi\)
\(840\) 6.07746 + 5.66121i 0.209692 + 0.195330i
\(841\) 14.7170 45.2942i 0.507482 1.56187i
\(842\) 30.6739 + 8.21905i 1.05709 + 0.283247i
\(843\) −4.94096 18.4399i −0.170176 0.635104i
\(844\) −1.61259 + 1.45198i −0.0555076 + 0.0499792i
\(845\) −1.86391 + 26.8629i −0.0641204 + 0.924111i
\(846\) 4.31363 4.79077i 0.148306 0.164710i
\(847\) −35.8911 + 13.7773i −1.23323 + 0.473394i
\(848\) 3.13004 4.81985i 0.107486 0.165514i
\(849\) 1.57084 + 14.9455i 0.0539110 + 0.512929i
\(850\) 5.12324 4.30831i 0.175726 0.147774i
\(851\) −4.50098 0.956714i −0.154292 0.0327957i
\(852\) −1.12300 7.09033i −0.0384733 0.242911i
\(853\) 0.499587 + 3.15427i 0.0171055 + 0.108000i 0.994764 0.102200i \(-0.0325883\pi\)
−0.977658 + 0.210201i \(0.932588\pi\)
\(854\) −29.8990 6.35523i −1.02312 0.217471i
\(855\) −2.14908 1.14121i −0.0734971 0.0390284i
\(856\) −0.595015 5.66119i −0.0203372 0.193496i
\(857\) 7.89033 12.1500i 0.269528 0.415037i −0.677827 0.735222i \(-0.737078\pi\)
0.947355 + 0.320184i \(0.103745\pi\)
\(858\) 0.736531 0.282728i 0.0251448 0.00965217i
\(859\) 15.9198 17.6807i 0.543176 0.603259i −0.407591 0.913165i \(-0.633631\pi\)
0.950767 + 0.309906i \(0.100298\pi\)
\(860\) 5.64791 + 6.49012i 0.192592 + 0.221311i
\(861\) 9.20857 8.29143i 0.313827 0.282571i
\(862\) −0.411496 1.53572i −0.0140156 0.0523069i
\(863\) 4.70651 + 1.26111i 0.160212 + 0.0429286i 0.338033 0.941134i \(-0.390238\pi\)
−0.177822 + 0.984063i \(0.556905\pi\)
\(864\) −0.309017 + 0.951057i −0.0105130 + 0.0323556i
\(865\) −13.1487 + 14.1155i −0.447070 + 0.479942i
\(866\) 14.4945 + 19.9500i 0.492545 + 0.677929i
\(867\) 10.7534 + 10.7534i 0.365205 + 0.365205i
\(868\) −6.62716 19.5905i −0.224940 0.664944i
\(869\) 0.929946i 0.0315462i
\(870\) 18.9896 4.74550i 0.643809 0.160888i
\(871\) −4.86286 10.9222i −0.164772 0.370083i
\(872\) −4.40472 8.64475i −0.149163 0.292748i
\(873\) 1.28372 4.79090i 0.0434473 0.162148i
\(874\) 1.65592 2.86814i 0.0560123 0.0970161i
\(875\) 38.7462 14.9451i 1.30986 0.505236i
\(876\) 4.91871 + 15.1382i 0.166188 + 0.511473i
\(877\) 1.84685 + 35.2400i 0.0623637 + 1.18997i 0.833213 + 0.552952i \(0.186499\pi\)
−0.770849 + 0.637017i \(0.780168\pi\)
\(878\) −6.31368 16.4477i −0.213076 0.555083i
\(879\) 15.2729 3.24635i 0.515141 0.109497i
\(880\) 0.495949 1.73310i 0.0167184 0.0584228i
\(881\) −27.1870 2.85747i −0.915953 0.0962706i −0.365191 0.930933i \(-0.618996\pi\)
−0.550762 + 0.834662i \(0.685663\pi\)
\(882\) 5.70042 3.70189i 0.191943 0.124649i
\(883\) 32.6251 5.16731i 1.09792 0.173894i 0.418915 0.908026i \(-0.362411\pi\)
0.679007 + 0.734132i \(0.262411\pi\)
\(884\) −0.770090 + 1.05994i −0.0259009 + 0.0356496i
\(885\) −8.24464 + 1.60720i −0.277140 + 0.0540255i
\(886\) −3.47234 + 33.0371i −0.116656 + 1.10990i
\(887\) 16.4309 + 13.3055i 0.551695 + 0.446754i 0.864190 0.503166i \(-0.167831\pi\)
−0.312495 + 0.949919i \(0.601165\pi\)
\(888\) −1.26805 0.823478i −0.0425528 0.0276341i
\(889\) 63.4829 + 28.2644i 2.12915 + 0.947957i
\(890\) −20.4071 7.01446i −0.684049 0.235125i
\(891\) −0.766719 + 0.249122i −0.0256861 + 0.00834591i
\(892\) −0.656007 + 12.5174i −0.0219648 + 0.419112i
\(893\) −6.77619 + 1.81567i −0.226756 + 0.0607592i
\(894\) −7.40575 12.8271i −0.247685 0.429003i
\(895\) 31.5181 + 26.4179i 1.05353 + 0.883054i
\(896\) −3.39330 + 1.51079i −0.113362 + 0.0504721i
\(897\) −2.94164 0.465910i −0.0982184 0.0155563i
\(898\) −20.5520 + 20.5520i −0.685828 + 0.685828i
\(899\) −47.2256 12.0465i −1.57506 0.401774i
\(900\) 3.60044 + 3.46942i 0.120015 + 0.115647i
\(901\) −6.22462 + 4.52245i −0.207372 + 0.150665i
\(902\) −2.51078 0.963798i −0.0835998 0.0320910i
\(903\) 12.7340 6.48828i 0.423760 0.215917i
\(904\) −0.313871 + 0.181213i −0.0104392 + 0.00602706i
\(905\) 29.8856 23.3751i 0.993430 0.777014i
\(906\) −1.27947 1.42099i −0.0425074 0.0472093i
\(907\) −51.9104 26.4497i −1.72366 0.878247i −0.977058 0.212972i \(-0.931686\pi\)
−0.746598 0.665275i \(-0.768314\pi\)
\(908\) 6.86622 0.359843i 0.227864 0.0119418i
\(909\) −5.14804 + 11.5627i −0.170750 + 0.383510i
\(910\) −6.65560 + 4.66564i −0.220631 + 0.154664i
\(911\) −12.8660 + 1.35228i −0.426271 + 0.0448029i −0.315235 0.949014i \(-0.602083\pi\)
−0.111036 + 0.993816i \(0.535417\pi\)
\(912\) 0.845691 0.684827i 0.0280036 0.0226769i
\(913\) −2.77041 4.26606i −0.0916872 0.141186i
\(914\) 32.2321 + 23.4180i 1.06614 + 0.774597i
\(915\) −17.9318 4.12971i −0.592806 0.136524i
\(916\) −0.859566 + 4.04394i −0.0284009 + 0.133616i
\(917\) −2.56461 3.16703i −0.0846909 0.104585i
\(918\) 0.842529 1.04044i 0.0278076 0.0343395i
\(919\) −9.65310 45.4143i −0.318426 1.49808i −0.788270 0.615329i \(-0.789023\pi\)
0.469844 0.882749i \(-0.344310\pi\)
\(920\) −4.89275 + 4.72997i −0.161309 + 0.155942i
\(921\) −17.7727 16.0026i −0.585629 0.527303i
\(922\) −12.9129 + 25.3429i −0.425263 + 0.834625i
\(923\) 7.01552 + 0.367668i 0.230919 + 0.0121019i
\(924\) −2.59330 1.49724i −0.0853133 0.0492556i
\(925\) −6.47586 + 3.90058i −0.212925 + 0.128250i
\(926\) −8.37917 2.72256i −0.275357 0.0894688i
\(927\) 1.73313 4.51497i 0.0569236 0.148291i
\(928\) −1.36936 + 8.64581i −0.0449515 + 0.283813i
\(929\) −54.2789 −1.78083 −0.890417 0.455146i \(-0.849587\pi\)
−0.890417 + 0.455146i \(0.849587\pi\)
\(930\) −3.78947 11.8592i −0.124262 0.388877i
\(931\) −7.39647 −0.242410
\(932\) −3.06939 + 19.3793i −0.100541 + 0.634792i
\(933\) −3.26975 + 8.51798i −0.107047 + 0.278866i
\(934\) −36.4949 11.8579i −1.19415 0.388002i
\(935\) −1.45138 + 1.92820i −0.0474652 + 0.0630590i
\(936\) −0.847500 0.489305i −0.0277014 0.0159934i
\(937\) −38.5106 2.01825i −1.25809 0.0659335i −0.588395 0.808573i \(-0.700240\pi\)
−0.669691 + 0.742640i \(0.733573\pi\)
\(938\) −20.6019 + 40.4335i −0.672677 + 1.32020i
\(939\) −16.7573 15.0884i −0.546854 0.492390i
\(940\) 14.4130 + 0.243821i 0.470101 + 0.00795256i
\(941\) −5.06863 23.8460i −0.165233 0.777359i −0.980225 0.197887i \(-0.936592\pi\)
0.814992 0.579472i \(-0.196741\pi\)
\(942\) −8.79212 + 10.8574i −0.286463 + 0.353752i
\(943\) 6.38937 + 7.89022i 0.208067 + 0.256941i
\(944\) 0.781024 3.67443i 0.0254202 0.119592i
\(945\) 7.04127 4.40515i 0.229053 0.143299i
\(946\) −2.50945 1.82322i −0.0815893 0.0592781i
\(947\) 6.74282 + 10.3830i 0.219112 + 0.337403i 0.931084 0.364805i \(-0.118864\pi\)
−0.711972 + 0.702208i \(0.752198\pi\)
\(948\) 0.896458 0.725937i 0.0291156 0.0235773i
\(949\) −15.4914 + 1.62822i −0.502874 + 0.0528542i
\(950\) −1.22967 5.30023i −0.0398956 0.171962i
\(951\) −11.3741 + 25.5467i −0.368832 + 0.828410i
\(952\) 4.96603 0.260259i 0.160950 0.00843503i
\(953\) 29.7938 + 15.1807i 0.965117 + 0.491751i 0.864203 0.503144i \(-0.167823\pi\)
0.100914 + 0.994895i \(0.467823\pi\)
\(954\) −3.84550 4.27086i −0.124503 0.138274i
\(955\) −25.2311 32.2585i −0.816458 1.04386i
\(956\) 1.68618 0.973518i 0.0545350 0.0314858i
\(957\) −6.28777 + 3.20378i −0.203255 + 0.103563i
\(958\) −24.9709 9.58542i −0.806772 0.309691i
\(959\) −49.2078 + 35.7516i −1.58900 + 1.15448i
\(960\) −2.05784 + 0.874809i −0.0664165 + 0.0282343i
\(961\) −5.71324 + 30.4690i −0.184298 + 0.982870i
\(962\) 1.04626 1.04626i 0.0337326 0.0337326i
\(963\) −5.62229 0.890484i −0.181176 0.0286954i
\(964\) 8.14165 3.62490i 0.262225 0.116750i
\(965\) 0.340914 + 3.87266i 0.0109744 + 0.124665i
\(966\) 5.65225 + 9.78999i 0.181858 + 0.314988i
\(967\) −11.6313 + 3.11659i −0.374037 + 0.100223i −0.440940 0.897537i \(-0.645355\pi\)
0.0669031 + 0.997759i \(0.478688\pi\)
\(968\) 0.541681 10.3359i 0.0174103 0.332208i
\(969\) −1.38557 + 0.450199i −0.0445110 + 0.0144625i
\(970\) 9.96563 4.86720i 0.319977 0.156276i
\(971\) −8.26559 3.68008i −0.265255 0.118099i 0.269800 0.962916i \(-0.413042\pi\)
−0.535055 + 0.844817i \(0.679709\pi\)
\(972\) 0.838671 + 0.544639i 0.0269004 + 0.0174693i
\(973\) 7.14302 + 5.78430i 0.228995 + 0.185436i
\(974\) −2.24456 + 21.3556i −0.0719204 + 0.684277i
\(975\) −4.05357 + 2.74052i −0.129818 + 0.0877669i
\(976\) 4.83703 6.65760i 0.154830 0.213105i
\(977\) −30.6405 + 4.85298i −0.980277 + 0.155261i −0.625952 0.779862i \(-0.715289\pi\)
−0.354325 + 0.935122i \(0.615289\pi\)
\(978\) 16.5162 10.7258i 0.528131 0.342972i
\(979\) 7.73733 + 0.813226i 0.247286 + 0.0259908i
\(980\) 14.6120 + 4.18141i 0.466762 + 0.133570i
\(981\) −9.49021 + 2.01721i −0.302999 + 0.0644045i
\(982\) 6.42906 + 16.7483i 0.205159 + 0.534459i
\(983\) −2.63349 50.2500i −0.0839953 1.60273i −0.637883 0.770134i \(-0.720190\pi\)
0.553887 0.832592i \(-0.313144\pi\)
\(984\) 1.03088 + 3.17273i 0.0328633 + 0.101143i
\(985\) 17.0792 + 7.95295i 0.544187 + 0.253402i
\(986\) 5.85961 10.1491i 0.186608 0.323215i
\(987\) 6.19755 23.1296i 0.197270 0.736223i
\(988\) 0.483465 + 0.948854i 0.0153811 + 0.0301871i
\(989\) 4.76282 + 10.6975i 0.151449 + 0.340160i
\(990\) −1.54569 0.927610i −0.0491251 0.0294814i
\(991\) 29.1390i 0.925629i −0.886455 0.462815i \(-0.846840\pi\)
0.886455 0.462815i \(-0.153160\pi\)
\(992\) 5.54387 + 0.515275i 0.176018 + 0.0163600i
\(993\) −10.3456 10.3456i −0.328308 0.328308i
\(994\) −15.6732 21.5723i −0.497123 0.684231i
\(995\) 1.86530 + 52.6034i 0.0591339 + 1.66764i
\(996\) −1.94979 + 6.00083i −0.0617814 + 0.190144i
\(997\) −18.9643 5.08146i −0.600605 0.160931i −0.0543093 0.998524i \(-0.517296\pi\)
−0.546295 + 0.837593i \(0.683962\pi\)
\(998\) −4.91734 18.3517i −0.155656 0.580914i
\(999\) −1.12361 + 1.01171i −0.0355495 + 0.0320090i
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 930.2.bt.b.13.1 yes 256
5.2 odd 4 930.2.bt.a.757.6 yes 256
31.12 odd 30 930.2.bt.a.43.6 256
155.12 even 60 inner 930.2.bt.b.787.1 yes 256
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bt.a.43.6 256 31.12 odd 30
930.2.bt.a.757.6 yes 256 5.2 odd 4
930.2.bt.b.13.1 yes 256 1.1 even 1 trivial
930.2.bt.b.787.1 yes 256 155.12 even 60 inner