Properties

Label 847.2.f.q.148.1
Level $847$
Weight $2$
Character 847.148
Analytic conductor $6.763$
Analytic rank $0$
Dimension $8$
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] = [847,2,Mod(148,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), degree \(4\), not 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: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.159390625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 148.1
Root \(1.43801 - 1.04478i\) of defining polynomial
Character \(\chi\) \(=\) 847.148
Dual form 847.2.f.q.372.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.549273 - 1.69049i) q^{2} +(-0.500000 - 0.363271i) q^{3} +(-0.938015 + 0.681508i) q^{4} +(-0.858290 + 2.64154i) q^{5} +(-0.339469 + 1.04478i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-1.20872 - 0.878189i) q^{8} +(-0.809017 - 2.48990i) q^{9} +O(q^{10})\) \(q+(-0.549273 - 1.69049i) q^{2} +(-0.500000 - 0.363271i) q^{3} +(-0.938015 + 0.681508i) q^{4} +(-0.858290 + 2.64154i) q^{5} +(-0.339469 + 1.04478i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-1.20872 - 0.878189i) q^{8} +(-0.809017 - 2.48990i) q^{9} +4.93693 q^{10} +0.716580 q^{12} +(1.32676 + 4.08334i) q^{13} +(1.43801 + 1.04478i) q^{14} +(1.38874 - 1.00898i) q^{15} +(-1.53723 + 4.73110i) q^{16} +(0.851514 - 2.62069i) q^{17} +(-3.76477 + 2.73527i) q^{18} +(1.56876 + 1.13977i) q^{19} +(-0.995144 - 3.06274i) q^{20} +0.618034 q^{21} +4.37009 q^{23} +(0.285341 + 0.878189i) q^{24} +(-2.19601 - 1.59550i) q^{25} +(6.17408 - 4.48573i) q^{26} +(-1.07295 + 3.30220i) q^{27} +(0.358290 - 1.10270i) q^{28} +(6.98027 - 5.07146i) q^{29} +(-2.46847 - 1.79345i) q^{30} +(-0.0619850 - 0.190770i) q^{31} +5.85410 q^{32} -4.89796 q^{34} +(-0.858290 - 2.64154i) q^{35} +(2.45576 + 1.78421i) q^{36} +(-0.837721 + 0.608640i) q^{37} +(1.06509 - 3.27802i) q^{38} +(0.819981 - 2.52364i) q^{39} +(3.35721 - 2.43916i) q^{40} +(7.77155 + 5.64636i) q^{41} +(-0.339469 - 1.04478i) q^{42} +4.70820 q^{43} +7.27155 q^{45} +(-2.40037 - 7.38759i) q^{46} +(10.5541 + 7.66797i) q^{47} +(2.48729 - 1.80712i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-1.49096 + 4.58869i) q^{50} +(-1.37778 + 1.00101i) q^{51} +(-4.02734 - 2.92604i) q^{52} +(-1.20520 - 3.70923i) q^{53} +6.17167 q^{54} +1.49406 q^{56} +(-0.370334 - 1.13977i) q^{57} +(-12.4073 - 9.01445i) q^{58} +(6.92286 - 5.02975i) q^{59} +(-0.615033 + 1.89288i) q^{60} +(0.305497 - 0.940223i) q^{61} +(-0.288448 + 0.209570i) q^{62} +(2.11803 + 1.53884i) q^{63} +(-0.141042 - 0.434084i) q^{64} -11.9251 q^{65} -5.41745 q^{67} +(0.987288 + 3.03856i) q^{68} +(-2.18505 - 1.58753i) q^{69} +(-3.99406 + 2.90186i) q^{70} +(-0.623302 + 1.91833i) q^{71} +(-1.20872 + 3.72007i) q^{72} +(-8.06677 + 5.86085i) q^{73} +(1.48904 + 1.08185i) q^{74} +(0.518408 + 1.59550i) q^{75} -2.24828 q^{76} -4.71658 q^{78} +(-1.94479 - 5.98545i) q^{79} +(-11.1780 - 8.12131i) q^{80} +(-4.61803 + 3.35520i) q^{81} +(5.27640 - 16.2391i) q^{82} +(0.531960 - 1.63720i) q^{83} +(-0.579725 + 0.421195i) q^{84} +(6.19182 + 4.49862i) q^{85} +(-2.58609 - 7.95916i) q^{86} -5.33245 q^{87} -15.3035 q^{89} +(-3.99406 - 12.2925i) q^{90} +(-3.47350 - 2.52364i) q^{91} +(-4.09921 + 2.97825i) q^{92} +(-0.0383089 + 0.117903i) q^{93} +(7.16556 - 22.0533i) q^{94} +(-4.35721 + 3.16570i) q^{95} +(-2.92705 - 2.12663i) q^{96} +(3.58961 + 11.0477i) q^{97} -1.77748 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} - 3 q^{8} - 2 q^{9} + 28 q^{10} - 14 q^{12} - 5 q^{13} + q^{14} + 6 q^{15} - 3 q^{16} + 11 q^{17} - 4 q^{18} + 9 q^{19} + 21 q^{20} - 4 q^{21} - 16 q^{23} - 21 q^{24} + 5 q^{25} + 21 q^{26} - 22 q^{27} - 7 q^{28} + 9 q^{29} - 14 q^{30} - 11 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} - 2 q^{36} + 6 q^{37} + 35 q^{38} + 5 q^{39} + 16 q^{40} + 22 q^{41} - 3 q^{42} - 16 q^{43} + 18 q^{45} - 29 q^{46} + 7 q^{47} + 4 q^{48} - 2 q^{49} + 34 q^{50} - 3 q^{51} - 21 q^{52} + 2 q^{53} - 4 q^{54} - 18 q^{56} + 3 q^{57} - 39 q^{58} + 25 q^{59} - 38 q^{60} - 7 q^{61} + 5 q^{62} + 8 q^{63} + q^{64} - 24 q^{65} - 30 q^{67} - 8 q^{68} + 8 q^{69} - 2 q^{70} - 14 q^{71} - 3 q^{72} - 3 q^{73} + 9 q^{74} + 5 q^{75} + 52 q^{76} - 18 q^{78} + 9 q^{79} - 33 q^{80} - 28 q^{81} + 31 q^{82} - 23 q^{83} - 4 q^{84} + 10 q^{85} - 17 q^{86} - 12 q^{87} - 34 q^{89} - 2 q^{90} + 5 q^{91} - 34 q^{92} + 8 q^{93} + 30 q^{94} - 24 q^{95} - 10 q^{96} + 30 q^{97} - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.549273 1.69049i −0.388395 1.19536i −0.933988 0.357305i \(-0.883696\pi\)
0.545593 0.838050i \(-0.316304\pi\)
\(3\) −0.500000 0.363271i −0.288675 0.209735i 0.434017 0.900905i \(-0.357096\pi\)
−0.722692 + 0.691170i \(0.757096\pi\)
\(4\) −0.938015 + 0.681508i −0.469007 + 0.340754i
\(5\) −0.858290 + 2.64154i −0.383839 + 1.18133i 0.553480 + 0.832862i \(0.313299\pi\)
−0.937319 + 0.348472i \(0.886701\pi\)
\(6\) −0.339469 + 1.04478i −0.138588 + 0.426529i
\(7\) −0.809017 + 0.587785i −0.305780 + 0.222162i
\(8\) −1.20872 0.878189i −0.427348 0.310487i
\(9\) −0.809017 2.48990i −0.269672 0.829966i
\(10\) 4.93693 1.56120
\(11\) 0 0
\(12\) 0.716580 0.206859
\(13\) 1.32676 + 4.08334i 0.367976 + 1.13251i 0.948096 + 0.317983i \(0.103006\pi\)
−0.580120 + 0.814531i \(0.696994\pi\)
\(14\) 1.43801 + 1.04478i 0.384326 + 0.279229i
\(15\) 1.38874 1.00898i 0.358572 0.260518i
\(16\) −1.53723 + 4.73110i −0.384307 + 1.18278i
\(17\) 0.851514 2.62069i 0.206522 0.635611i −0.793125 0.609059i \(-0.791547\pi\)
0.999647 0.0265518i \(-0.00845268\pi\)
\(18\) −3.76477 + 2.73527i −0.887365 + 0.644709i
\(19\) 1.56876 + 1.13977i 0.359898 + 0.261482i 0.753010 0.658009i \(-0.228601\pi\)
−0.393111 + 0.919491i \(0.628601\pi\)
\(20\) −0.995144 3.06274i −0.222521 0.684849i
\(21\) 0.618034 0.134866
\(22\) 0 0
\(23\) 4.37009 0.911228 0.455614 0.890178i \(-0.349420\pi\)
0.455614 + 0.890178i \(0.349420\pi\)
\(24\) 0.285341 + 0.878189i 0.0582450 + 0.179260i
\(25\) −2.19601 1.59550i −0.439202 0.319099i
\(26\) 6.17408 4.48573i 1.21084 0.879725i
\(27\) −1.07295 + 3.30220i −0.206489 + 0.635508i
\(28\) 0.358290 1.10270i 0.0677104 0.208391i
\(29\) 6.98027 5.07146i 1.29620 0.941747i 0.296293 0.955097i \(-0.404250\pi\)
0.999911 + 0.0133499i \(0.00424953\pi\)
\(30\) −2.46847 1.79345i −0.450678 0.327437i
\(31\) −0.0619850 0.190770i −0.0111328 0.0342634i 0.945336 0.326099i \(-0.105734\pi\)
−0.956469 + 0.291835i \(0.905734\pi\)
\(32\) 5.85410 1.03487
\(33\) 0 0
\(34\) −4.89796 −0.839993
\(35\) −0.858290 2.64154i −0.145077 0.446503i
\(36\) 2.45576 + 1.78421i 0.409293 + 0.297368i
\(37\) −0.837721 + 0.608640i −0.137720 + 0.100060i −0.654512 0.756051i \(-0.727126\pi\)
0.516792 + 0.856111i \(0.327126\pi\)
\(38\) 1.06509 3.27802i 0.172781 0.531765i
\(39\) 0.819981 2.52364i 0.131302 0.404106i
\(40\) 3.35721 2.43916i 0.530821 0.385664i
\(41\) 7.77155 + 5.64636i 1.21371 + 0.881813i 0.995563 0.0941021i \(-0.0299980\pi\)
0.218149 + 0.975915i \(0.429998\pi\)
\(42\) −0.339469 1.04478i −0.0523812 0.161213i
\(43\) 4.70820 0.717994 0.358997 0.933339i \(-0.383119\pi\)
0.358997 + 0.933339i \(0.383119\pi\)
\(44\) 0 0
\(45\) 7.27155 1.08398
\(46\) −2.40037 7.38759i −0.353916 1.08924i
\(47\) 10.5541 + 7.66797i 1.53947 + 1.11849i 0.950668 + 0.310210i \(0.100399\pi\)
0.588800 + 0.808279i \(0.299601\pi\)
\(48\) 2.48729 1.80712i 0.359009 0.260835i
\(49\) 0.309017 0.951057i 0.0441453 0.135865i
\(50\) −1.49096 + 4.58869i −0.210853 + 0.648939i
\(51\) −1.37778 + 1.00101i −0.192928 + 0.140170i
\(52\) −4.02734 2.92604i −0.558492 0.405768i
\(53\) −1.20520 3.70923i −0.165547 0.509502i 0.833529 0.552476i \(-0.186317\pi\)
−0.999076 + 0.0429735i \(0.986317\pi\)
\(54\) 6.17167 0.839857
\(55\) 0 0
\(56\) 1.49406 0.199653
\(57\) −0.370334 1.13977i −0.0490520 0.150966i
\(58\) −12.4073 9.01445i −1.62916 1.18365i
\(59\) 6.92286 5.02975i 0.901280 0.654818i −0.0375144 0.999296i \(-0.511944\pi\)
0.938794 + 0.344478i \(0.111944\pi\)
\(60\) −0.615033 + 1.89288i −0.0794004 + 0.244369i
\(61\) 0.305497 0.940223i 0.0391149 0.120383i −0.929592 0.368589i \(-0.879841\pi\)
0.968707 + 0.248206i \(0.0798410\pi\)
\(62\) −0.288448 + 0.209570i −0.0366330 + 0.0266154i
\(63\) 2.11803 + 1.53884i 0.266847 + 0.193876i
\(64\) −0.141042 0.434084i −0.0176303 0.0542605i
\(65\) −11.9251 −1.47912
\(66\) 0 0
\(67\) −5.41745 −0.661846 −0.330923 0.943658i \(-0.607360\pi\)
−0.330923 + 0.943658i \(0.607360\pi\)
\(68\) 0.987288 + 3.03856i 0.119726 + 0.368479i
\(69\) −2.18505 1.58753i −0.263049 0.191116i
\(70\) −3.99406 + 2.90186i −0.477382 + 0.346838i
\(71\) −0.623302 + 1.91833i −0.0739724 + 0.227664i −0.981206 0.192964i \(-0.938190\pi\)
0.907234 + 0.420627i \(0.138190\pi\)
\(72\) −1.20872 + 3.72007i −0.142449 + 0.438414i
\(73\) −8.06677 + 5.86085i −0.944144 + 0.685961i −0.949415 0.314025i \(-0.898322\pi\)
0.00527037 + 0.999986i \(0.498322\pi\)
\(74\) 1.48904 + 1.08185i 0.173097 + 0.125762i
\(75\) 0.518408 + 1.59550i 0.0598606 + 0.184232i
\(76\) −2.24828 −0.257896
\(77\) 0 0
\(78\) −4.71658 −0.534047
\(79\) −1.94479 5.98545i −0.218806 0.673416i −0.998861 0.0477054i \(-0.984809\pi\)
0.780055 0.625711i \(-0.215191\pi\)
\(80\) −11.1780 8.12131i −1.24974 0.907991i
\(81\) −4.61803 + 3.35520i −0.513115 + 0.372800i
\(82\) 5.27640 16.2391i 0.582681 1.79331i
\(83\) 0.531960 1.63720i 0.0583902 0.179707i −0.917607 0.397488i \(-0.869882\pi\)
0.975998 + 0.217781i \(0.0698820\pi\)
\(84\) −0.579725 + 0.421195i −0.0632532 + 0.0459561i
\(85\) 6.19182 + 4.49862i 0.671598 + 0.487944i
\(86\) −2.58609 7.95916i −0.278865 0.858259i
\(87\) −5.33245 −0.571699
\(88\) 0 0
\(89\) −15.3035 −1.62217 −0.811086 0.584928i \(-0.801123\pi\)
−0.811086 + 0.584928i \(0.801123\pi\)
\(90\) −3.99406 12.2925i −0.421011 1.29574i
\(91\) −3.47350 2.52364i −0.364121 0.264550i
\(92\) −4.09921 + 2.97825i −0.427373 + 0.310504i
\(93\) −0.0383089 + 0.117903i −0.00397244 + 0.0122259i
\(94\) 7.16556 22.0533i 0.739071 2.27463i
\(95\) −4.35721 + 3.16570i −0.447040 + 0.324794i
\(96\) −2.92705 2.12663i −0.298741 0.217048i
\(97\) 3.58961 + 11.0477i 0.364470 + 1.12172i 0.950313 + 0.311297i \(0.100764\pi\)
−0.585843 + 0.810425i \(0.699236\pi\)
\(98\) −1.77748 −0.179553
\(99\) 0 0
\(100\) 3.14723 0.314723
\(101\) −1.05430 3.24480i −0.104907 0.322870i 0.884802 0.465968i \(-0.154294\pi\)
−0.989709 + 0.143098i \(0.954294\pi\)
\(102\) 2.44898 + 1.77929i 0.242485 + 0.176176i
\(103\) 14.7100 10.6875i 1.44942 1.05307i 0.463455 0.886121i \(-0.346610\pi\)
0.985966 0.166945i \(-0.0533903\pi\)
\(104\) 1.98226 6.10077i 0.194377 0.598230i
\(105\) −0.530452 + 1.63256i −0.0517668 + 0.159322i
\(106\) −5.60843 + 4.07476i −0.544739 + 0.395776i
\(107\) 2.62725 + 1.90881i 0.253986 + 0.184532i 0.707491 0.706722i \(-0.249827\pi\)
−0.453506 + 0.891253i \(0.649827\pi\)
\(108\) −1.24403 3.82873i −0.119707 0.368420i
\(109\) −12.6912 −1.21559 −0.607796 0.794093i \(-0.707946\pi\)
−0.607796 + 0.794093i \(0.707946\pi\)
\(110\) 0 0
\(111\) 0.639962 0.0607425
\(112\) −1.53723 4.73110i −0.145254 0.447047i
\(113\) 14.9248 + 10.8435i 1.40401 + 1.02007i 0.994160 + 0.107915i \(0.0344173\pi\)
0.409845 + 0.912155i \(0.365583\pi\)
\(114\) −1.72336 + 1.25209i −0.161407 + 0.117269i
\(115\) −3.75081 + 11.5438i −0.349765 + 1.07646i
\(116\) −3.09136 + 9.51422i −0.287025 + 0.883373i
\(117\) 9.09373 6.60698i 0.840715 0.610816i
\(118\) −12.3053 8.94031i −1.13279 0.823022i
\(119\) 0.851514 + 2.62069i 0.0780581 + 0.240238i
\(120\) −2.56468 −0.234122
\(121\) 0 0
\(122\) −1.75724 −0.159093
\(123\) −1.83461 5.64636i −0.165422 0.509115i
\(124\) 0.188154 + 0.136702i 0.0168968 + 0.0122762i
\(125\) −5.13577 + 3.73136i −0.459358 + 0.333743i
\(126\) 1.43801 4.42575i 0.128109 0.394278i
\(127\) −6.02870 + 18.5544i −0.534961 + 1.64644i 0.208772 + 0.977964i \(0.433053\pi\)
−0.743733 + 0.668476i \(0.766947\pi\)
\(128\) 8.81579 6.40505i 0.779213 0.566132i
\(129\) −2.35410 1.71036i −0.207267 0.150588i
\(130\) 6.55011 + 20.1592i 0.574483 + 1.76808i
\(131\) 6.89796 0.602677 0.301339 0.953517i \(-0.402567\pi\)
0.301339 + 0.953517i \(0.402567\pi\)
\(132\) 0 0
\(133\) −1.93910 −0.168141
\(134\) 2.97566 + 9.15813i 0.257058 + 0.791142i
\(135\) −7.80200 5.66849i −0.671489 0.487866i
\(136\) −3.33070 + 2.41990i −0.285606 + 0.207505i
\(137\) −0.806750 + 2.48292i −0.0689253 + 0.212130i −0.979586 0.201024i \(-0.935573\pi\)
0.910661 + 0.413154i \(0.135573\pi\)
\(138\) −1.48351 + 4.56578i −0.126285 + 0.388665i
\(139\) −0.810097 + 0.588570i −0.0687116 + 0.0499219i −0.621611 0.783326i \(-0.713521\pi\)
0.552899 + 0.833248i \(0.313521\pi\)
\(140\) 2.60532 + 1.89288i 0.220190 + 0.159977i
\(141\) −2.49148 7.66797i −0.209820 0.645760i
\(142\) 3.58527 0.300869
\(143\) 0 0
\(144\) 13.0236 1.08530
\(145\) 7.40540 + 22.7915i 0.614985 + 1.89273i
\(146\) 14.3386 + 10.4176i 1.18667 + 0.862165i
\(147\) −0.500000 + 0.363271i −0.0412393 + 0.0299621i
\(148\) 0.371002 1.14183i 0.0304962 0.0938576i
\(149\) 4.60273 14.1658i 0.377071 1.16050i −0.565000 0.825091i \(-0.691124\pi\)
0.942071 0.335413i \(-0.108876\pi\)
\(150\) 2.41242 1.75272i 0.196973 0.143109i
\(151\) 12.7862 + 9.28970i 1.04052 + 0.755985i 0.970388 0.241552i \(-0.0776564\pi\)
0.0701368 + 0.997537i \(0.477656\pi\)
\(152\) −0.895263 2.75534i −0.0726154 0.223487i
\(153\) −7.21414 −0.583229
\(154\) 0 0
\(155\) 0.557129 0.0447497
\(156\) 0.950727 + 2.92604i 0.0761191 + 0.234270i
\(157\) −3.71438 2.69866i −0.296440 0.215376i 0.429616 0.903011i \(-0.358649\pi\)
−0.726056 + 0.687635i \(0.758649\pi\)
\(158\) −9.05011 + 6.57529i −0.719988 + 0.523102i
\(159\) −0.744856 + 2.29243i −0.0590710 + 0.181802i
\(160\) −5.02452 + 15.4639i −0.397223 + 1.22253i
\(161\) −3.53548 + 2.56868i −0.278635 + 0.202440i
\(162\) 8.20848 + 5.96381i 0.644919 + 0.468561i
\(163\) 2.48377 + 7.64425i 0.194544 + 0.598744i 0.999982 + 0.00606379i \(0.00193018\pi\)
−0.805438 + 0.592680i \(0.798070\pi\)
\(164\) −11.1379 −0.869721
\(165\) 0 0
\(166\) −3.05987 −0.237492
\(167\) 4.14296 + 12.7507i 0.320592 + 0.986681i 0.973391 + 0.229150i \(0.0735946\pi\)
−0.652799 + 0.757531i \(0.726405\pi\)
\(168\) −0.747032 0.542750i −0.0576348 0.0418741i
\(169\) −4.39615 + 3.19399i −0.338165 + 0.245691i
\(170\) 4.20387 12.9382i 0.322422 0.992313i
\(171\) 1.56876 4.82815i 0.119966 0.369218i
\(172\) −4.41637 + 3.20868i −0.336745 + 0.244659i
\(173\) −16.6512 12.0978i −1.26597 0.919782i −0.266936 0.963714i \(-0.586011\pi\)
−0.999035 + 0.0439325i \(0.986011\pi\)
\(174\) 2.92897 + 9.01445i 0.222045 + 0.683383i
\(175\) 2.71442 0.205191
\(176\) 0 0
\(177\) −5.28860 −0.397515
\(178\) 8.40581 + 25.8704i 0.630042 + 1.93907i
\(179\) 3.00566 + 2.18374i 0.224653 + 0.163220i 0.694419 0.719571i \(-0.255662\pi\)
−0.469765 + 0.882791i \(0.655662\pi\)
\(180\) −6.82082 + 4.95562i −0.508394 + 0.369370i
\(181\) 1.47458 4.53828i 0.109604 0.337327i −0.881179 0.472783i \(-0.843250\pi\)
0.990783 + 0.135455i \(0.0432496\pi\)
\(182\) −2.35829 + 7.25807i −0.174808 + 0.538004i
\(183\) −0.494304 + 0.359133i −0.0365400 + 0.0265479i
\(184\) −5.28223 3.83777i −0.389411 0.282924i
\(185\) −0.888742 2.73527i −0.0653416 0.201101i
\(186\) 0.220355 0.0161572
\(187\) 0 0
\(188\) −15.1257 −1.10315
\(189\) −1.07295 3.30220i −0.0780456 0.240200i
\(190\) 7.74487 + 5.62698i 0.561872 + 0.408224i
\(191\) 0.670803 0.487367i 0.0485376 0.0352646i −0.563252 0.826285i \(-0.690450\pi\)
0.611790 + 0.791021i \(0.290450\pi\)
\(192\) −0.0871690 + 0.268279i −0.00629088 + 0.0193613i
\(193\) 2.08216 6.40824i 0.149878 0.461276i −0.847728 0.530430i \(-0.822030\pi\)
0.997606 + 0.0691550i \(0.0220303\pi\)
\(194\) 16.7043 12.1364i 1.19930 0.871341i
\(195\) 5.96253 + 4.33203i 0.426986 + 0.310223i
\(196\) 0.358290 + 1.10270i 0.0255921 + 0.0787645i
\(197\) 10.9216 0.778129 0.389065 0.921210i \(-0.372798\pi\)
0.389065 + 0.921210i \(0.372798\pi\)
\(198\) 0 0
\(199\) 20.9746 1.48685 0.743424 0.668820i \(-0.233200\pi\)
0.743424 + 0.668820i \(0.233200\pi\)
\(200\) 1.25322 + 3.85702i 0.0886163 + 0.272733i
\(201\) 2.70872 + 1.96800i 0.191059 + 0.138812i
\(202\) −4.90620 + 3.56457i −0.345199 + 0.250802i
\(203\) −2.66623 + 8.20580i −0.187132 + 0.575934i
\(204\) 0.610177 1.87793i 0.0427210 0.131482i
\(205\) −21.5854 + 15.6827i −1.50759 + 1.09533i
\(206\) −26.1468 18.9968i −1.82174 1.32357i
\(207\) −3.53548 10.8811i −0.245733 0.756288i
\(208\) −21.3582 −1.48093
\(209\) 0 0
\(210\) 3.05119 0.210552
\(211\) 1.86140 + 5.72879i 0.128144 + 0.394386i 0.994461 0.105109i \(-0.0335190\pi\)
−0.866317 + 0.499495i \(0.833519\pi\)
\(212\) 3.65837 + 2.65796i 0.251258 + 0.182550i
\(213\) 1.00852 0.732736i 0.0691029 0.0502062i
\(214\) 1.78374 5.48979i 0.121934 0.375274i
\(215\) −4.04100 + 12.4369i −0.275594 + 0.848192i
\(216\) 4.19685 3.04919i 0.285560 0.207471i
\(217\) 0.162279 + 0.117903i 0.0110162 + 0.00800375i
\(218\) 6.97091 + 21.4542i 0.472129 + 1.45306i
\(219\) 6.16247 0.416421
\(220\) 0 0
\(221\) 11.8309 0.795833
\(222\) −0.351514 1.08185i −0.0235921 0.0726089i
\(223\) 3.74176 + 2.71855i 0.250567 + 0.182048i 0.705978 0.708234i \(-0.250508\pi\)
−0.455411 + 0.890281i \(0.650508\pi\)
\(224\) −4.73607 + 3.44095i −0.316442 + 0.229908i
\(225\) −2.19601 + 6.75863i −0.146401 + 0.450575i
\(226\) 10.1330 31.1862i 0.674038 2.07448i
\(227\) 13.9963 10.1689i 0.928965 0.674932i −0.0167745 0.999859i \(-0.505340\pi\)
0.945739 + 0.324927i \(0.105340\pi\)
\(228\) 1.12414 + 0.816737i 0.0744481 + 0.0540897i
\(229\) −1.36775 4.20949i −0.0903832 0.278171i 0.895640 0.444780i \(-0.146718\pi\)
−0.986023 + 0.166609i \(0.946718\pi\)
\(230\) 21.5749 1.42260
\(231\) 0 0
\(232\) −12.8909 −0.846330
\(233\) 3.25489 + 10.0175i 0.213235 + 0.656269i 0.999274 + 0.0380929i \(0.0121283\pi\)
−0.786039 + 0.618176i \(0.787872\pi\)
\(234\) −16.1640 11.7438i −1.05667 0.767716i
\(235\) −29.3137 + 21.2977i −1.91222 + 1.38931i
\(236\) −3.06593 + 9.43597i −0.199575 + 0.614229i
\(237\) −1.20195 + 3.69921i −0.0780748 + 0.240290i
\(238\) 3.96253 2.87895i 0.256853 0.186614i
\(239\) −7.89314 5.73470i −0.510565 0.370947i 0.302473 0.953158i \(-0.402188\pi\)
−0.813038 + 0.582211i \(0.802188\pi\)
\(240\) 2.63878 + 8.12131i 0.170332 + 0.524229i
\(241\) −12.5501 −0.808422 −0.404211 0.914666i \(-0.632454\pi\)
−0.404211 + 0.914666i \(0.632454\pi\)
\(242\) 0 0
\(243\) 13.9443 0.894525
\(244\) 0.354208 + 1.09014i 0.0226759 + 0.0697892i
\(245\) 2.24703 + 1.63256i 0.143558 + 0.104301i
\(246\) −8.53740 + 6.20278i −0.544325 + 0.395475i
\(247\) −2.57271 + 7.91798i −0.163698 + 0.503809i
\(248\) −0.0926096 + 0.285023i −0.00588072 + 0.0180990i
\(249\) −0.860729 + 0.625357i −0.0545465 + 0.0396304i
\(250\) 9.12876 + 6.63243i 0.577353 + 0.419472i
\(251\) −3.39646 10.4532i −0.214383 0.659803i −0.999197 0.0400713i \(-0.987241\pi\)
0.784814 0.619732i \(-0.212759\pi\)
\(252\) −3.03548 −0.191217
\(253\) 0 0
\(254\) 34.6775 2.17586
\(255\) −1.46169 4.49862i −0.0915346 0.281715i
\(256\) −16.4084 11.9214i −1.02553 0.745089i
\(257\) −4.31432 + 3.13454i −0.269120 + 0.195527i −0.714158 0.699985i \(-0.753190\pi\)
0.445038 + 0.895512i \(0.353190\pi\)
\(258\) −1.59829 + 4.91903i −0.0995052 + 0.306246i
\(259\) 0.319981 0.984800i 0.0198827 0.0611925i
\(260\) 11.1859 8.12702i 0.693719 0.504017i
\(261\) −18.2746 13.2773i −1.13117 0.821842i
\(262\) −3.78886 11.6609i −0.234077 0.720414i
\(263\) 8.18034 0.504421 0.252211 0.967672i \(-0.418842\pi\)
0.252211 + 0.967672i \(0.418842\pi\)
\(264\) 0 0
\(265\) 10.8325 0.665436
\(266\) 1.06509 + 3.27802i 0.0653050 + 0.200988i
\(267\) 7.65177 + 5.55933i 0.468280 + 0.340226i
\(268\) 5.08165 3.69203i 0.310411 0.225527i
\(269\) 3.96899 12.2153i 0.241993 0.744779i −0.754123 0.656733i \(-0.771938\pi\)
0.996116 0.0880459i \(-0.0280622\pi\)
\(270\) −5.29708 + 16.3027i −0.322370 + 0.992153i
\(271\) −17.8366 + 12.9590i −1.08349 + 0.787205i −0.978289 0.207246i \(-0.933550\pi\)
−0.105206 + 0.994450i \(0.533550\pi\)
\(272\) 11.0898 + 8.05720i 0.672417 + 0.488539i
\(273\) 0.819981 + 2.52364i 0.0496275 + 0.152738i
\(274\) 4.64047 0.280341
\(275\) 0 0
\(276\) 3.13152 0.188495
\(277\) −7.44019 22.8986i −0.447038 1.37584i −0.880234 0.474541i \(-0.842614\pi\)
0.433196 0.901300i \(-0.357386\pi\)
\(278\) 1.43994 + 1.04617i 0.0863616 + 0.0627454i
\(279\) −0.424852 + 0.308673i −0.0254352 + 0.0184798i
\(280\) −1.28234 + 3.94664i −0.0766345 + 0.235857i
\(281\) −4.77179 + 14.6861i −0.284661 + 0.876097i 0.701839 + 0.712336i \(0.252363\pi\)
−0.986500 + 0.163761i \(0.947637\pi\)
\(282\) −11.5941 + 8.42362i −0.690420 + 0.501619i
\(283\) −2.71613 1.97338i −0.161457 0.117305i 0.504123 0.863632i \(-0.331816\pi\)
−0.665580 + 0.746326i \(0.731816\pi\)
\(284\) −0.722688 2.22421i −0.0428836 0.131982i
\(285\) 3.32861 0.197170
\(286\) 0 0
\(287\) −9.60616 −0.567034
\(288\) −4.73607 14.5761i −0.279075 0.858906i
\(289\) 7.61035 + 5.52924i 0.447668 + 0.325250i
\(290\) 34.4611 25.0375i 2.02363 1.47025i
\(291\) 2.21850 6.82784i 0.130051 0.400255i
\(292\) 3.57254 10.9951i 0.209067 0.643442i
\(293\) 5.53129 4.01872i 0.323142 0.234776i −0.414373 0.910107i \(-0.635999\pi\)
0.737515 + 0.675331i \(0.235999\pi\)
\(294\) 0.888742 + 0.645709i 0.0518325 + 0.0376585i
\(295\) 7.34450 + 22.6040i 0.427613 + 1.31606i
\(296\) 1.54707 0.0899218
\(297\) 0 0
\(298\) −26.4752 −1.53367
\(299\) 5.79805 + 17.8446i 0.335310 + 1.03198i
\(300\) −1.57362 1.14330i −0.0908528 0.0660084i
\(301\) −3.80902 + 2.76741i −0.219548 + 0.159511i
\(302\) 8.68103 26.7175i 0.499537 1.53742i
\(303\) −0.651594 + 2.00540i −0.0374331 + 0.115207i
\(304\) −7.80392 + 5.66988i −0.447586 + 0.325190i
\(305\) 2.22144 + 1.61397i 0.127199 + 0.0924155i
\(306\) 3.96253 + 12.1954i 0.226523 + 0.697166i
\(307\) 11.7970 0.673293 0.336646 0.941631i \(-0.390707\pi\)
0.336646 + 0.941631i \(0.390707\pi\)
\(308\) 0 0
\(309\) −11.2375 −0.639276
\(310\) −0.306016 0.941821i −0.0173805 0.0534918i
\(311\) −20.4794 14.8791i −1.16128 0.843718i −0.171339 0.985212i \(-0.554809\pi\)
−0.989939 + 0.141494i \(0.954809\pi\)
\(312\) −3.20736 + 2.33029i −0.181581 + 0.131926i
\(313\) −6.07352 + 18.6924i −0.343296 + 1.05656i 0.619194 + 0.785238i \(0.287460\pi\)
−0.962490 + 0.271318i \(0.912540\pi\)
\(314\) −2.52184 + 7.76141i −0.142315 + 0.438002i
\(315\) −5.88281 + 4.27411i −0.331459 + 0.240819i
\(316\) 5.90337 + 4.28905i 0.332091 + 0.241278i
\(317\) 1.11572 + 3.43385i 0.0626653 + 0.192864i 0.977488 0.210992i \(-0.0676695\pi\)
−0.914822 + 0.403856i \(0.867670\pi\)
\(318\) 4.28446 0.240261
\(319\) 0 0
\(320\) 1.26771 0.0708670
\(321\) −0.620210 1.90881i −0.0346167 0.106539i
\(322\) 6.28426 + 4.56578i 0.350208 + 0.254441i
\(323\) 4.32281 3.14071i 0.240528 0.174754i
\(324\) 2.04519 6.29445i 0.113622 0.349692i
\(325\) 3.60137 11.0839i 0.199768 0.614824i
\(326\) 11.5582 8.39756i 0.640152 0.465098i
\(327\) 6.34558 + 4.61033i 0.350911 + 0.254952i
\(328\) −4.43508 13.6498i −0.244886 0.753683i
\(329\) −13.0455 −0.719224
\(330\) 0 0
\(331\) −26.5335 −1.45841 −0.729205 0.684295i \(-0.760110\pi\)
−0.729205 + 0.684295i \(0.760110\pi\)
\(332\) 0.616781 + 1.89826i 0.0338503 + 0.104180i
\(333\) 2.19318 + 1.59344i 0.120186 + 0.0873200i
\(334\) 19.2793 14.0073i 1.05492 0.766443i
\(335\) 4.64974 14.3104i 0.254042 0.781862i
\(336\) −0.950059 + 2.92398i −0.0518300 + 0.159516i
\(337\) −0.554969 + 0.403208i −0.0302311 + 0.0219642i −0.602798 0.797894i \(-0.705948\pi\)
0.572567 + 0.819858i \(0.305948\pi\)
\(338\) 7.81408 + 5.67726i 0.425030 + 0.308802i
\(339\) −3.52326 10.8435i −0.191357 0.588938i
\(340\) −8.87387 −0.481253
\(341\) 0 0
\(342\) −9.02361 −0.487941
\(343\) 0.309017 + 0.951057i 0.0166853 + 0.0513522i
\(344\) −5.69091 4.13469i −0.306834 0.222928i
\(345\) 6.06893 4.40934i 0.326740 0.237391i
\(346\) −11.3052 + 34.7937i −0.607770 + 1.87052i
\(347\) −6.64555 + 20.4529i −0.356752 + 1.09797i 0.598235 + 0.801321i \(0.295869\pi\)
−0.954987 + 0.296649i \(0.904131\pi\)
\(348\) 5.00192 3.63411i 0.268131 0.194809i
\(349\) 15.7296 + 11.4282i 0.841987 + 0.611739i 0.922925 0.384980i \(-0.125792\pi\)
−0.0809381 + 0.996719i \(0.525792\pi\)
\(350\) −1.49096 4.58869i −0.0796950 0.245276i
\(351\) −14.9075 −0.795705
\(352\) 0 0
\(353\) −20.9307 −1.11403 −0.557015 0.830502i \(-0.688053\pi\)
−0.557015 + 0.830502i \(0.688053\pi\)
\(354\) 2.90488 + 8.94031i 0.154393 + 0.475172i
\(355\) −4.53237 3.29296i −0.240553 0.174772i
\(356\) 14.3549 10.4295i 0.760810 0.552761i
\(357\) 0.526264 1.61968i 0.0278529 0.0857223i
\(358\) 2.04066 6.28050i 0.107852 0.331935i
\(359\) 7.90512 5.74341i 0.417216 0.303125i −0.359300 0.933222i \(-0.616985\pi\)
0.776517 + 0.630096i \(0.216985\pi\)
\(360\) −8.78929 6.38579i −0.463236 0.336561i
\(361\) −4.70939 14.4940i −0.247863 0.762843i
\(362\) −8.48185 −0.445796
\(363\) 0 0
\(364\) 4.97807 0.260922
\(365\) −8.55808 26.3390i −0.447950 1.37865i
\(366\) 0.878618 + 0.638353i 0.0459261 + 0.0333673i
\(367\) −8.00901 + 5.81889i −0.418067 + 0.303744i −0.776860 0.629674i \(-0.783189\pi\)
0.358793 + 0.933417i \(0.383189\pi\)
\(368\) −6.71783 + 20.6754i −0.350191 + 1.07778i
\(369\) 7.77155 23.9184i 0.404571 1.24514i
\(370\) −4.13577 + 3.00482i −0.215009 + 0.156213i
\(371\) 3.15526 + 2.29243i 0.163813 + 0.119017i
\(372\) −0.0444172 0.136702i −0.00230293 0.00708768i
\(373\) 4.27475 0.221338 0.110669 0.993857i \(-0.464701\pi\)
0.110669 + 0.993857i \(0.464701\pi\)
\(374\) 0 0
\(375\) 3.92338 0.202603
\(376\) −6.02301 18.5369i −0.310613 0.955968i
\(377\) 29.9696 + 21.7742i 1.54351 + 1.12143i
\(378\) −4.99298 + 3.62761i −0.256811 + 0.186584i
\(379\) 1.33679 4.11421i 0.0686662 0.211333i −0.910835 0.412770i \(-0.864561\pi\)
0.979501 + 0.201437i \(0.0645612\pi\)
\(380\) 1.92968 5.93894i 0.0989905 0.304661i
\(381\) 9.75465 7.08717i 0.499746 0.363087i
\(382\) −1.19234 0.866287i −0.0610055 0.0443231i
\(383\) −0.408551 1.25739i −0.0208760 0.0642497i 0.940076 0.340966i \(-0.110754\pi\)
−0.960952 + 0.276716i \(0.910754\pi\)
\(384\) −6.73467 −0.343677
\(385\) 0 0
\(386\) −11.9767 −0.609600
\(387\) −3.80902 11.7229i −0.193623 0.595911i
\(388\) −10.8962 7.91654i −0.553170 0.401902i
\(389\) 31.1546 22.6351i 1.57960 1.14765i 0.662447 0.749109i \(-0.269518\pi\)
0.917152 0.398537i \(-0.130482\pi\)
\(390\) 4.04819 12.4591i 0.204988 0.630889i
\(391\) 3.72119 11.4527i 0.188189 0.579186i
\(392\) −1.20872 + 0.878189i −0.0610497 + 0.0443552i
\(393\) −3.44898 2.50583i −0.173978 0.126402i
\(394\) −5.99892 18.4628i −0.302221 0.930141i
\(395\) 17.4800 0.879516
\(396\) 0 0
\(397\) −0.410109 −0.0205828 −0.0102914 0.999947i \(-0.503276\pi\)
−0.0102914 + 0.999947i \(0.503276\pi\)
\(398\) −11.5208 35.4573i −0.577484 1.77731i
\(399\) 0.969548 + 0.704418i 0.0485381 + 0.0352650i
\(400\) 10.9242 7.93691i 0.546211 0.396846i
\(401\) −0.484180 + 1.49015i −0.0241788 + 0.0744147i −0.962418 0.271573i \(-0.912456\pi\)
0.938239 + 0.345988i \(0.112456\pi\)
\(402\) 1.83906 5.66003i 0.0917238 0.282297i
\(403\) 0.696741 0.506212i 0.0347071 0.0252162i
\(404\) 3.20031 + 2.32516i 0.159221 + 0.115681i
\(405\) −4.89929 15.0785i −0.243448 0.749255i
\(406\) 15.3363 0.761127
\(407\) 0 0
\(408\) 2.54443 0.125968
\(409\) 2.09468 + 6.44676i 0.103575 + 0.318772i 0.989393 0.145261i \(-0.0464021\pi\)
−0.885818 + 0.464032i \(0.846402\pi\)
\(410\) 38.3676 + 27.8757i 1.89484 + 1.37668i
\(411\) 1.30535 0.948391i 0.0643881 0.0467807i
\(412\) −6.51463 + 20.0500i −0.320953 + 0.987792i
\(413\) −2.64430 + 8.13831i −0.130117 + 0.400460i
\(414\) −16.4524 + 11.9534i −0.808592 + 0.587476i
\(415\) 3.86817 + 2.81039i 0.189881 + 0.137957i
\(416\) 7.76697 + 23.9043i 0.380807 + 1.17200i
\(417\) 0.618859 0.0303057
\(418\) 0 0
\(419\) 28.7218 1.40315 0.701577 0.712594i \(-0.252480\pi\)
0.701577 + 0.712594i \(0.252480\pi\)
\(420\) −0.615033 1.89288i −0.0300105 0.0923629i
\(421\) −9.89070 7.18601i −0.482043 0.350225i 0.320073 0.947393i \(-0.396293\pi\)
−0.802116 + 0.597168i \(0.796293\pi\)
\(422\) 8.66204 6.29334i 0.421661 0.306355i
\(423\) 10.5541 32.4821i 0.513156 1.57933i
\(424\) −1.80065 + 5.54183i −0.0874473 + 0.269135i
\(425\) −6.05123 + 4.39648i −0.293528 + 0.213260i
\(426\) −1.79264 1.30243i −0.0868535 0.0631028i
\(427\) 0.305497 + 0.940223i 0.0147840 + 0.0455006i
\(428\) −3.76527 −0.182001
\(429\) 0 0
\(430\) 23.2441 1.12093
\(431\) −1.14067 3.51063i −0.0549442 0.169101i 0.919819 0.392344i \(-0.128336\pi\)
−0.974763 + 0.223243i \(0.928336\pi\)
\(432\) −13.9737 10.1525i −0.672308 0.488461i
\(433\) −23.5221 + 17.0898i −1.13040 + 0.821283i −0.985753 0.168201i \(-0.946204\pi\)
−0.144646 + 0.989483i \(0.546204\pi\)
\(434\) 0.110177 0.339091i 0.00528869 0.0162769i
\(435\) 4.57679 14.0859i 0.219440 0.675368i
\(436\) 11.9045 8.64912i 0.570122 0.414218i
\(437\) 6.85563 + 4.98091i 0.327949 + 0.238269i
\(438\) −3.38488 10.4176i −0.161736 0.497771i
\(439\) 14.2017 0.677811 0.338905 0.940820i \(-0.389943\pi\)
0.338905 + 0.940820i \(0.389943\pi\)
\(440\) 0 0
\(441\) −2.61803 −0.124668
\(442\) −6.49840 20.0000i −0.309097 0.951304i
\(443\) −22.0341 16.0087i −1.04687 0.760595i −0.0752548 0.997164i \(-0.523977\pi\)
−0.971615 + 0.236569i \(0.923977\pi\)
\(444\) −0.600294 + 0.436139i −0.0284887 + 0.0206982i
\(445\) 13.1349 40.4250i 0.622652 1.91633i
\(446\) 2.54043 7.81863i 0.120293 0.370223i
\(447\) −7.44738 + 5.41084i −0.352249 + 0.255924i
\(448\) 0.369254 + 0.268279i 0.0174456 + 0.0126750i
\(449\) −12.9527 39.8644i −0.611277 1.88132i −0.445888 0.895089i \(-0.647112\pi\)
−0.165389 0.986228i \(-0.552888\pi\)
\(450\) 12.6316 0.595459
\(451\) 0 0
\(452\) −21.3896 −1.00608
\(453\) −3.01841 9.28970i −0.141817 0.436468i
\(454\) −24.8781 18.0750i −1.16759 0.848303i
\(455\) 9.64758 7.00938i 0.452285 0.328605i
\(456\) −0.553303 + 1.70289i −0.0259108 + 0.0797452i
\(457\) −6.02512 + 18.5434i −0.281843 + 0.867424i 0.705484 + 0.708726i \(0.250730\pi\)
−0.987327 + 0.158698i \(0.949270\pi\)
\(458\) −6.36483 + 4.62432i −0.297409 + 0.216080i
\(459\) 7.74040 + 5.62373i 0.361291 + 0.262493i
\(460\) −4.34887 13.3845i −0.202767 0.624054i
\(461\) −12.2251 −0.569380 −0.284690 0.958620i \(-0.591891\pi\)
−0.284690 + 0.958620i \(0.591891\pi\)
\(462\) 0 0
\(463\) 13.8550 0.643894 0.321947 0.946758i \(-0.395663\pi\)
0.321947 + 0.946758i \(0.395663\pi\)
\(464\) 13.2633 + 40.8204i 0.615735 + 1.89504i
\(465\) −0.278565 0.202389i −0.0129181 0.00938557i
\(466\) 15.1467 11.0047i 0.701656 0.509783i
\(467\) −5.07428 + 15.6170i −0.234810 + 0.722671i 0.762337 + 0.647181i \(0.224052\pi\)
−0.997147 + 0.0754899i \(0.975948\pi\)
\(468\) −4.02734 + 12.3949i −0.186164 + 0.572954i
\(469\) 4.38281 3.18429i 0.202379 0.147037i
\(470\) 52.1047 + 37.8563i 2.40341 + 1.74618i
\(471\) 0.876846 + 2.69866i 0.0404029 + 0.124347i
\(472\) −12.7849 −0.588473
\(473\) 0 0
\(474\) 6.91367 0.317555
\(475\) −1.62652 5.00590i −0.0746297 0.229687i
\(476\) −2.58475 1.87793i −0.118472 0.0860749i
\(477\) −8.26058 + 6.00167i −0.378226 + 0.274797i
\(478\) −5.35896 + 16.4932i −0.245113 + 0.754380i
\(479\) 7.66096 23.5780i 0.350038 1.07731i −0.608793 0.793329i \(-0.708346\pi\)
0.958831 0.283977i \(-0.0916540\pi\)
\(480\) 8.12984 5.90667i 0.371075 0.269602i
\(481\) −3.59674 2.61318i −0.163997 0.119151i
\(482\) 6.89342 + 21.2158i 0.313987 + 0.966352i
\(483\) 2.70087 0.122894
\(484\) 0 0
\(485\) −32.2639 −1.46503
\(486\) −7.65921 23.5726i −0.347429 1.06928i
\(487\) 11.5966 + 8.42542i 0.525492 + 0.381792i 0.818669 0.574266i \(-0.194712\pi\)
−0.293177 + 0.956058i \(0.594712\pi\)
\(488\) −1.19495 + 0.868185i −0.0540930 + 0.0393009i
\(489\) 1.53505 4.72441i 0.0694175 0.213645i
\(490\) 1.52560 4.69530i 0.0689194 0.212112i
\(491\) −17.8140 + 12.9426i −0.803935 + 0.584093i −0.912066 0.410044i \(-0.865514\pi\)
0.108131 + 0.994137i \(0.465514\pi\)
\(492\) 5.56893 + 4.04607i 0.251067 + 0.182411i
\(493\) −7.34694 22.6115i −0.330889 1.01837i
\(494\) 14.7984 0.665810
\(495\) 0 0
\(496\) 0.997839 0.0448043
\(497\) −0.623302 1.91833i −0.0279589 0.0860487i
\(498\) 1.52993 + 1.11156i 0.0685579 + 0.0498103i
\(499\) 20.4776 14.8779i 0.916704 0.666024i −0.0259975 0.999662i \(-0.508276\pi\)
0.942701 + 0.333638i \(0.108276\pi\)
\(500\) 2.27448 7.00014i 0.101718 0.313056i
\(501\) 2.56049 7.88038i 0.114394 0.352070i
\(502\) −15.8055 + 11.4834i −0.705434 + 0.512528i
\(503\) −21.0518 15.2950i −0.938653 0.681971i 0.00944301 0.999955i \(-0.496994\pi\)
−0.948096 + 0.317984i \(0.896994\pi\)
\(504\) −1.20872 3.72007i −0.0538408 0.165705i
\(505\) 9.47619 0.421685
\(506\) 0 0
\(507\) 3.35836 0.149150
\(508\) −6.98998 21.5130i −0.310130 0.954483i
\(509\) −30.8453 22.4104i −1.36719 0.993325i −0.997950 0.0639922i \(-0.979617\pi\)
−0.369244 0.929333i \(-0.620383\pi\)
\(510\) −6.80200 + 4.94194i −0.301198 + 0.218833i
\(511\) 3.08123 9.48306i 0.136306 0.419506i
\(512\) −4.40566 + 13.5592i −0.194704 + 0.599238i
\(513\) −5.44695 + 3.95744i −0.240489 + 0.174725i
\(514\) 7.66864 + 5.57159i 0.338249 + 0.245753i
\(515\) 15.6059 + 48.0301i 0.687679 + 2.11646i
\(516\) 3.37380 0.148523
\(517\) 0 0
\(518\) −1.84055 −0.0808691
\(519\) 3.93083 + 12.0978i 0.172544 + 0.531036i
\(520\) 14.4141 + 10.4725i 0.632100 + 0.459248i
\(521\) 21.0684 15.3071i 0.923024 0.670616i −0.0212509 0.999774i \(-0.506765\pi\)
0.944275 + 0.329158i \(0.106765\pi\)
\(522\) −12.4073 + 38.1858i −0.543054 + 1.67135i
\(523\) −5.90933 + 18.1870i −0.258397 + 0.795263i 0.734745 + 0.678344i \(0.237302\pi\)
−0.993141 + 0.116920i \(0.962698\pi\)
\(524\) −6.47039 + 4.70101i −0.282660 + 0.205365i
\(525\) −1.35721 0.986070i −0.0592335 0.0430356i
\(526\) −4.49324 13.8288i −0.195915 0.602963i
\(527\) −0.552731 −0.0240773
\(528\) 0 0
\(529\) −3.90228 −0.169664
\(530\) −5.95001 18.3122i −0.258452 0.795433i
\(531\) −18.1243 13.1681i −0.786527 0.571445i
\(532\) 1.81890 1.32151i 0.0788593 0.0572947i
\(533\) −12.7450 + 39.2252i −0.552049 + 1.69903i
\(534\) 5.19508 15.9888i 0.224813 0.691903i
\(535\) −7.29714 + 5.30169i −0.315483 + 0.229212i
\(536\) 6.54819 + 4.75754i 0.282839 + 0.205494i
\(537\) −0.709539 2.18374i −0.0306189 0.0942352i
\(538\) −22.8298 −0.984265
\(539\) 0 0
\(540\) 11.1815 0.481176
\(541\) −3.36397 10.3532i −0.144628 0.445120i 0.852335 0.522997i \(-0.175186\pi\)
−0.996963 + 0.0778764i \(0.975186\pi\)
\(542\) 31.7042 + 23.0345i 1.36181 + 0.989415i
\(543\) −2.38591 + 1.73347i −0.102389 + 0.0743902i
\(544\) 4.98485 15.3418i 0.213724 0.657774i
\(545\) 10.8927 33.5243i 0.466592 1.43602i
\(546\) 3.81579 2.77234i 0.163301 0.118645i
\(547\) −10.4436 7.58775i −0.446538 0.324429i 0.341689 0.939813i \(-0.389001\pi\)
−0.788227 + 0.615384i \(0.789001\pi\)
\(548\) −0.935386 2.87882i −0.0399577 0.122977i
\(549\) −2.58821 −0.110462
\(550\) 0 0
\(551\) 16.7307 0.712751
\(552\) 1.24697 + 3.83777i 0.0530744 + 0.163346i
\(553\) 5.09153 + 3.69921i 0.216514 + 0.157307i
\(554\) −34.6230 + 25.1551i −1.47099 + 1.06874i
\(555\) −0.549273 + 1.69049i −0.0233153 + 0.0717572i
\(556\) 0.358768 1.10418i 0.0152152 0.0468275i
\(557\) −0.616977 + 0.448260i −0.0261422 + 0.0189934i −0.600780 0.799415i \(-0.705143\pi\)
0.574637 + 0.818408i \(0.305143\pi\)
\(558\) 0.755167 + 0.548661i 0.0319688 + 0.0232267i
\(559\) 6.24664 + 19.2252i 0.264205 + 0.813139i
\(560\) 13.8168 0.583867
\(561\) 0 0
\(562\) 27.4476 1.15781
\(563\) 6.86886 + 21.1402i 0.289488 + 0.890953i 0.985017 + 0.172455i \(0.0551700\pi\)
−0.695529 + 0.718498i \(0.744830\pi\)
\(564\) 7.56283 + 5.49471i 0.318452 + 0.231369i
\(565\) −41.4534 + 30.1176i −1.74396 + 1.26706i
\(566\) −1.84408 + 5.67551i −0.0775127 + 0.238559i
\(567\) 1.76393 5.42882i 0.0740782 0.227989i
\(568\) 2.43805 1.77135i 0.102298 0.0743242i
\(569\) −16.5955 12.0573i −0.695719 0.505469i 0.182816 0.983147i \(-0.441479\pi\)
−0.878535 + 0.477678i \(0.841479\pi\)
\(570\) −1.82832 5.62698i −0.0765797 0.235688i
\(571\) 19.5654 0.818785 0.409393 0.912358i \(-0.365741\pi\)
0.409393 + 0.912358i \(0.365741\pi\)
\(572\) 0 0
\(573\) −0.512448 −0.0214078
\(574\) 5.27640 + 16.2391i 0.220233 + 0.677807i
\(575\) −9.59677 6.97246i −0.400213 0.290772i
\(576\) −0.966719 + 0.702362i −0.0402800 + 0.0292651i
\(577\) −6.04795 + 18.6137i −0.251780 + 0.774898i 0.742668 + 0.669660i \(0.233560\pi\)
−0.994447 + 0.105237i \(0.966440\pi\)
\(578\) 5.16696 15.9023i 0.214917 0.661447i
\(579\) −3.36901 + 2.44773i −0.140011 + 0.101724i
\(580\) −22.4790 16.3319i −0.933388 0.678146i
\(581\) 0.531960 + 1.63720i 0.0220694 + 0.0679227i
\(582\) −12.7609 −0.528958
\(583\) 0 0
\(584\) 14.8974 0.616460
\(585\) 9.64758 + 29.6922i 0.398878 + 1.22762i
\(586\) −9.83178 7.14321i −0.406147 0.295083i
\(587\) −1.27071 + 0.923224i −0.0524477 + 0.0381055i −0.613700 0.789539i \(-0.710320\pi\)
0.561253 + 0.827645i \(0.310320\pi\)
\(588\) 0.221435 0.681508i 0.00913184 0.0281049i
\(589\) 0.120195 0.369922i 0.00495254 0.0152424i
\(590\) 34.1777 24.8316i 1.40707 1.02230i
\(591\) −5.46078 3.96749i −0.224627 0.163201i
\(592\) −1.59177 4.89896i −0.0654213 0.201346i
\(593\) 30.1230 1.23700 0.618502 0.785783i \(-0.287740\pi\)
0.618502 + 0.785783i \(0.287740\pi\)
\(594\) 0 0
\(595\) −7.65351 −0.313763
\(596\) 5.33664 + 16.4245i 0.218597 + 0.672773i
\(597\) −10.4873 7.61946i −0.429216 0.311844i
\(598\) 26.9813 19.6031i 1.10335 0.801629i
\(599\) 1.78547 5.49513i 0.0729525 0.224525i −0.907931 0.419119i \(-0.862339\pi\)
0.980884 + 0.194594i \(0.0623390\pi\)
\(600\) 0.774534 2.38377i 0.0316202 0.0973171i
\(601\) 36.8625 26.7822i 1.50365 1.09247i 0.534754 0.845008i \(-0.320404\pi\)
0.968898 0.247460i \(-0.0795958\pi\)
\(602\) 6.77047 + 4.91903i 0.275944 + 0.200485i
\(603\) 4.38281 + 13.4889i 0.178482 + 0.549310i
\(604\) −18.3246 −0.745619
\(605\) 0 0
\(606\) 3.74801 0.152252
\(607\) −10.7294 33.0217i −0.435493 1.34031i −0.892581 0.450887i \(-0.851108\pi\)
0.457088 0.889421i \(-0.348892\pi\)
\(608\) 9.18369 + 6.67234i 0.372448 + 0.270599i
\(609\) 4.31404 3.13434i 0.174814 0.127010i
\(610\) 1.50822 4.64182i 0.0610660 0.187942i
\(611\) −17.3083 + 53.2693i −0.700217 + 2.15505i
\(612\) 6.76697 4.91649i 0.273539 0.198737i
\(613\) −19.5315 14.1905i −0.788870 0.573148i 0.118758 0.992923i \(-0.462109\pi\)
−0.907628 + 0.419776i \(0.862109\pi\)
\(614\) −6.47979 19.9428i −0.261503 0.804824i
\(615\) 16.4897 0.664931
\(616\) 0 0
\(617\) −13.4967 −0.543358 −0.271679 0.962388i \(-0.587579\pi\)
−0.271679 + 0.962388i \(0.587579\pi\)
\(618\) 6.17243 + 18.9968i 0.248291 + 0.764162i
\(619\) 35.1806 + 25.5602i 1.41403 + 1.02735i 0.992721 + 0.120433i \(0.0384284\pi\)
0.421307 + 0.906918i \(0.361572\pi\)
\(620\) −0.522596 + 0.379688i −0.0209879 + 0.0152486i
\(621\) −4.68889 + 14.4309i −0.188159 + 0.579093i
\(622\) −13.9042 + 42.7928i −0.557509 + 1.71584i
\(623\) 12.3808 8.99519i 0.496027 0.360385i
\(624\) 10.6791 + 7.75883i 0.427507 + 0.310602i
\(625\) −9.64257 29.6768i −0.385703 1.18707i
\(626\) 34.9353 1.39629
\(627\) 0 0
\(628\) 5.32330 0.212423
\(629\) 0.881726 + 2.71367i 0.0351567 + 0.108201i
\(630\) 10.4566 + 7.59716i 0.416601 + 0.302678i
\(631\) −5.19398 + 3.77365i −0.206769 + 0.150227i −0.686351 0.727271i \(-0.740788\pi\)
0.479581 + 0.877497i \(0.340788\pi\)
\(632\) −2.90564 + 8.94265i −0.115580 + 0.355719i
\(633\) 1.15041 3.54059i 0.0457246 0.140726i
\(634\) 5.19204 3.77224i 0.206202 0.149815i
\(635\) −43.8380 31.8502i −1.73966 1.26394i
\(636\) −0.863624 2.65796i −0.0342449 0.105395i
\(637\) 4.29348 0.170114
\(638\) 0 0
\(639\) 5.28070 0.208901
\(640\) 9.35272 + 28.7847i 0.369699 + 1.13782i
\(641\) 5.17447 + 3.75947i 0.204379 + 0.148490i 0.685267 0.728292i \(-0.259686\pi\)
−0.480888 + 0.876782i \(0.659686\pi\)
\(642\) −2.88615 + 2.09691i −0.113907 + 0.0827586i
\(643\) 0.201683 0.620716i 0.00795360 0.0244787i −0.947001 0.321231i \(-0.895903\pi\)
0.954955 + 0.296752i \(0.0959035\pi\)
\(644\) 1.56576 4.81891i 0.0616996 0.189892i
\(645\) 6.53848 4.75048i 0.257452 0.187050i
\(646\) −7.68373 5.58255i −0.302312 0.219643i
\(647\) 5.55061 + 17.0830i 0.218217 + 0.671603i 0.998910 + 0.0466874i \(0.0148665\pi\)
−0.780693 + 0.624915i \(0.785134\pi\)
\(648\) 8.52842 0.335028
\(649\) 0 0
\(650\) −20.7153 −0.812522
\(651\) −0.0383089 0.117903i −0.00150144 0.00462096i
\(652\) −7.53943 5.47771i −0.295267 0.214524i
\(653\) 13.6870 9.94419i 0.535614 0.389146i −0.286840 0.957979i \(-0.592605\pi\)
0.822454 + 0.568832i \(0.192605\pi\)
\(654\) 4.30826 13.2595i 0.168466 0.518486i
\(655\) −5.92045 + 18.2213i −0.231331 + 0.711964i
\(656\) −38.6602 + 28.0882i −1.50943 + 1.09666i
\(657\) 21.1191 + 15.3439i 0.823934 + 0.598623i
\(658\) 7.16556 + 22.0533i 0.279343 + 0.859728i
\(659\) −23.6249 −0.920297 −0.460148 0.887842i \(-0.652204\pi\)
−0.460148 + 0.887842i \(0.652204\pi\)
\(660\) 0 0
\(661\) −20.9819 −0.816103 −0.408051 0.912959i \(-0.633792\pi\)
−0.408051 + 0.912959i \(0.633792\pi\)
\(662\) 14.5741 + 44.8545i 0.566439 + 1.74332i
\(663\) −5.91546 4.29783i −0.229737 0.166914i
\(664\) −2.08077 + 1.51177i −0.0807494 + 0.0586679i
\(665\) 1.66431 5.12221i 0.0645390 0.198631i
\(666\) 1.48904 4.58278i 0.0576990 0.177579i
\(667\) 30.5044 22.1628i 1.18114 0.858146i
\(668\) −12.5759 9.13691i −0.486575 0.353518i
\(669\) −0.883311 2.71855i −0.0341508 0.105105i
\(670\) −26.7456 −1.03327
\(671\) 0 0
\(672\) 3.61803 0.139569
\(673\) −3.73868 11.5065i −0.144116 0.443542i 0.852781 0.522269i \(-0.174914\pi\)
−0.996896 + 0.0787272i \(0.974914\pi\)
\(674\) 0.986448 + 0.716696i 0.0379965 + 0.0276061i
\(675\) 7.62485 5.53978i 0.293481 0.213226i
\(676\) 1.94692 5.99202i 0.0748817 0.230462i
\(677\) 2.91399 8.96834i 0.111994 0.344681i −0.879314 0.476242i \(-0.841999\pi\)
0.991308 + 0.131560i \(0.0419987\pi\)
\(678\) −16.3956 + 11.9121i −0.629668 + 0.457480i
\(679\) −9.39772 6.82784i −0.360651 0.262029i
\(680\) −3.53356 10.8752i −0.135506 0.417044i
\(681\) −10.6922 −0.409726
\(682\) 0 0
\(683\) −15.2986 −0.585385 −0.292692 0.956207i \(-0.594551\pi\)
−0.292692 + 0.956207i \(0.594551\pi\)
\(684\) 1.81890 + 5.59800i 0.0695474 + 0.214045i
\(685\) −5.86632 4.26213i −0.224141 0.162848i
\(686\) 1.43801 1.04478i 0.0549037 0.0398898i
\(687\) −0.845314 + 2.60161i −0.0322507 + 0.0992575i
\(688\) −7.23758 + 22.2750i −0.275930 + 0.849226i
\(689\) 13.5470 9.84250i 0.516101 0.374970i
\(690\) −10.7874 7.83753i −0.410671 0.298370i
\(691\) 7.05154 + 21.7024i 0.268253 + 0.825599i 0.990926 + 0.134408i \(0.0429134\pi\)
−0.722673 + 0.691190i \(0.757087\pi\)
\(692\) 23.8639 0.907169
\(693\) 0 0
\(694\) 38.2256 1.45102
\(695\) −0.859436 2.64507i −0.0326003 0.100333i
\(696\) 6.44546 + 4.68290i 0.244314 + 0.177505i
\(697\) 21.4149 15.5589i 0.811149 0.589334i
\(698\) 10.6794 32.8679i 0.404223 1.24407i
\(699\) 2.01163 6.19117i 0.0760869 0.234171i
\(700\) −2.54617 + 1.84990i −0.0962360 + 0.0699196i
\(701\) −26.1508 18.9997i −0.987702 0.717607i −0.0282853 0.999600i \(-0.509005\pi\)
−0.959417 + 0.281992i \(0.909005\pi\)
\(702\) 8.18830 + 25.2010i 0.309048 + 0.951151i
\(703\) −2.00789 −0.0757292
\(704\) 0 0
\(705\) 22.3937 0.843396
\(706\) 11.4967 + 35.3831i 0.432683 + 1.33166i
\(707\) 2.76020 + 2.00540i 0.103808 + 0.0754208i
\(708\) 4.96078 3.60422i 0.186438 0.135455i
\(709\) 4.49922 13.8472i 0.168972 0.520041i −0.830335 0.557264i \(-0.811851\pi\)
0.999307 + 0.0372228i \(0.0118511\pi\)
\(710\) −3.07720 + 9.47066i −0.115485 + 0.355427i
\(711\) −13.3298 + 9.68466i −0.499906 + 0.363203i
\(712\) 18.4977 + 13.4394i 0.693232 + 0.503662i
\(713\) −0.270880 0.833684i −0.0101446 0.0312217i
\(714\) −3.02710 −0.113287
\(715\) 0 0
\(716\) −4.30759 −0.160982
\(717\) 1.86332 + 5.73470i 0.0695869 + 0.214166i
\(718\) −14.0512 10.2088i −0.524387 0.380990i
\(719\) −36.2926 + 26.3682i −1.35349 + 0.983366i −0.354658 + 0.934996i \(0.615403\pi\)
−0.998829 + 0.0483700i \(0.984597\pi\)
\(720\) −11.1780 + 34.4024i −0.416581 + 1.28210i
\(721\) −5.61873 + 17.2927i −0.209252 + 0.644012i
\(722\) −21.9152 + 15.9223i −0.815600 + 0.592568i
\(723\) 6.27504 + 4.55909i 0.233371 + 0.169554i
\(724\) 1.70970 + 5.26191i 0.0635404 + 0.195557i
\(725\) −23.4202 −0.869806
\(726\) 0 0
\(727\) 28.3582 1.05175 0.525874 0.850562i \(-0.323738\pi\)
0.525874 + 0.850562i \(0.323738\pi\)
\(728\) 1.98226 + 6.10077i 0.0734674 + 0.226110i
\(729\) 6.88197 + 5.00004i 0.254888 + 0.185187i
\(730\) −39.8251 + 28.9346i −1.47399 + 1.07092i
\(731\) 4.00910 12.3387i 0.148282 0.456365i
\(732\) 0.218913 0.673744i 0.00809125 0.0249023i
\(733\) 5.06199 3.67775i 0.186969 0.135841i −0.490364 0.871518i \(-0.663136\pi\)
0.677332 + 0.735677i \(0.263136\pi\)
\(734\) 14.2359 + 10.3430i 0.525456 + 0.381766i
\(735\) −0.530452 1.63256i −0.0195660 0.0602180i
\(736\) 25.5830 0.943001
\(737\) 0 0
\(738\) −44.7024 −1.64552
\(739\) −2.88993 8.89429i −0.106308 0.327182i 0.883727 0.468002i \(-0.155026\pi\)
−0.990035 + 0.140820i \(0.955026\pi\)
\(740\) 2.69776 + 1.96004i 0.0991716 + 0.0720524i
\(741\) 4.16273 3.02440i 0.152922 0.111104i
\(742\) 2.14223 6.59310i 0.0786437 0.242040i
\(743\) −7.78926 + 23.9729i −0.285760 + 0.879480i 0.700409 + 0.713741i \(0.253001\pi\)
−0.986170 + 0.165739i \(0.946999\pi\)
\(744\) 0.149845 0.108869i 0.00549360 0.00399134i
\(745\) 33.4690 + 24.3167i 1.22621 + 0.890893i
\(746\) −2.34800 7.22641i −0.0859665 0.264578i
\(747\) −4.50684 −0.164897
\(748\) 0 0
\(749\) −3.24746 −0.118660
\(750\) −2.15501 6.63243i −0.0786897 0.242182i
\(751\) 28.1128 + 20.4251i 1.02585 + 0.745323i 0.967474 0.252972i \(-0.0814079\pi\)
0.0583755 + 0.998295i \(0.481408\pi\)
\(752\) −52.5020 + 38.1449i −1.91455 + 1.39100i
\(753\) −2.09913 + 6.46046i −0.0764966 + 0.235432i
\(754\) 20.3475 62.6233i 0.741014 2.28061i
\(755\) −35.5134 + 25.8020i −1.29247 + 0.939031i
\(756\) 3.25692 + 2.36629i 0.118453 + 0.0860610i
\(757\) 10.7526 + 33.0930i 0.390808 + 1.20278i 0.932178 + 0.362000i \(0.117906\pi\)
−0.541370 + 0.840784i \(0.682094\pi\)
\(758\) −7.68929 −0.279288
\(759\) 0 0
\(760\) 8.04674 0.291886
\(761\) 3.77787 + 11.6271i 0.136948 + 0.421482i 0.995888 0.0905941i \(-0.0288766\pi\)
−0.858940 + 0.512076i \(0.828877\pi\)
\(762\) −17.3387 12.5973i −0.628116 0.456353i
\(763\) 10.2674 7.45967i 0.371703 0.270058i
\(764\) −0.297079 + 0.914315i −0.0107479 + 0.0330788i
\(765\) 6.19182 19.0565i 0.223866 0.688988i
\(766\) −1.90120 + 1.38130i −0.0686931 + 0.0499085i
\(767\) 29.7231 + 21.5951i 1.07324 + 0.779755i
\(768\) 3.87351 + 11.9214i 0.139773 + 0.430178i
\(769\) 2.61946 0.0944603 0.0472301 0.998884i \(-0.484961\pi\)
0.0472301 + 0.998884i \(0.484961\pi\)
\(770\) 0 0
\(771\) 3.29585 0.118697
\(772\) 2.41417 + 7.43004i 0.0868878 + 0.267413i
\(773\) 0.172162 + 0.125083i 0.00619225 + 0.00449894i 0.590877 0.806762i \(-0.298782\pi\)
−0.584685 + 0.811261i \(0.698782\pi\)
\(774\) −17.7253 + 12.8782i −0.637123 + 0.462897i
\(775\) −0.168253 + 0.517831i −0.00604384 + 0.0186010i
\(776\) 5.36310 16.5059i 0.192524 0.592529i
\(777\) −0.517740 + 0.376160i −0.0185738 + 0.0134947i
\(778\) −55.3767 40.2336i −1.98535 1.44244i
\(779\) 5.75614 + 17.7156i 0.206235 + 0.634727i
\(780\) −8.54526 −0.305969
\(781\) 0 0
\(782\) −21.4045 −0.765425
\(783\) 9.25750 + 28.4917i 0.330836 + 1.01821i
\(784\) 4.02452 + 2.92398i 0.143733 + 0.104428i
\(785\) 10.3166 7.49547i 0.368216 0.267525i
\(786\) −2.34164 + 7.20684i −0.0835237 + 0.257060i
\(787\) −9.00399 + 27.7114i −0.320958 + 0.987806i 0.652275 + 0.757983i \(0.273815\pi\)
−0.973232 + 0.229823i \(0.926185\pi\)
\(788\) −10.2446 + 7.44313i −0.364948 + 0.265151i
\(789\) −4.09017 2.97168i −0.145614 0.105795i
\(790\) −9.60131 29.5498i −0.341599 1.05133i
\(791\) −18.4480 −0.655937
\(792\) 0 0
\(793\) 4.24457 0.150729
\(794\) 0.225262 + 0.693284i 0.00799424 + 0.0246037i
\(795\) −5.41626 3.93514i −0.192095 0.139565i
\(796\) −19.6745 + 14.2943i −0.697343 + 0.506649i
\(797\) 9.95913 30.6510i 0.352770 1.08572i −0.604521 0.796589i \(-0.706635\pi\)
0.957291 0.289126i \(-0.0933647\pi\)
\(798\) 0.658263 2.02593i 0.0233023 0.0717170i
\(799\) 29.0823 21.1295i 1.02886 0.747509i
\(800\) −12.8557 9.34019i −0.454517 0.330226i
\(801\) 12.3808 + 38.1042i 0.437455 + 1.34635i
\(802\) 2.78503 0.0983430
\(803\) 0 0
\(804\) −3.88203 −0.136909
\(805\) −3.75081 11.5438i −0.132199 0.406865i
\(806\) −1.23845 0.899783i −0.0436224 0.0316935i
\(807\) −6.42195 + 4.66582i −0.226064 + 0.164245i
\(808\) −1.57519 + 4.84794i −0.0554151 + 0.170550i
\(809\) 9.06844 27.9098i 0.318829 0.981256i −0.655320 0.755351i \(-0.727466\pi\)
0.974149 0.225905i \(-0.0725338\pi\)
\(810\) −22.7989 + 16.5644i −0.801073 + 0.582013i
\(811\) 0.840891 + 0.610943i 0.0295277 + 0.0214531i 0.602451 0.798156i \(-0.294191\pi\)
−0.572924 + 0.819609i \(0.694191\pi\)
\(812\) −3.09136 9.51422i −0.108485 0.333884i
\(813\) 13.6259 0.477882
\(814\) 0 0
\(815\) −22.3244 −0.781990
\(816\) −2.61794 8.05720i −0.0916463 0.282058i
\(817\) 7.38605 + 5.36628i 0.258405 + 0.187742i
\(818\) 9.74762 7.08206i 0.340817 0.247618i
\(819\) −3.47350 + 10.6903i −0.121374 + 0.373550i
\(820\) 9.55952 29.4212i 0.333833 1.02743i
\(821\) 23.0831 16.7709i 0.805607 0.585308i −0.106946 0.994265i \(-0.534107\pi\)
0.912554 + 0.408957i \(0.134107\pi\)
\(822\) −2.32024 1.68575i −0.0809275 0.0587973i
\(823\) 8.23767 + 25.3529i 0.287147 + 0.883748i 0.985747 + 0.168235i \(0.0538068\pi\)
−0.698600 + 0.715513i \(0.746193\pi\)
\(824\) −27.1659 −0.946370
\(825\) 0 0
\(826\) 15.2102 0.529229
\(827\) −0.531399 1.63548i −0.0184785 0.0568711i 0.941392 0.337314i \(-0.109519\pi\)
−0.959871 + 0.280443i \(0.909519\pi\)
\(828\) 10.7319 + 7.79717i 0.372959 + 0.270970i
\(829\) −22.6205 + 16.4347i −0.785642 + 0.570802i −0.906667 0.421847i \(-0.861382\pi\)
0.121025 + 0.992649i \(0.461382\pi\)
\(830\) 2.62625 8.08277i 0.0911585 0.280557i
\(831\) −4.59829 + 14.1521i −0.159513 + 0.490930i
\(832\) 1.58538 1.15185i 0.0549632 0.0399331i
\(833\) −2.22929 1.61968i −0.0772404 0.0561184i
\(834\) −0.339923 1.04617i −0.0117706 0.0362261i
\(835\) −37.2375 −1.28866
\(836\) 0 0
\(837\) 0.696468 0.0240735
\(838\) −15.7761 48.5539i −0.544977 1.67727i
\(839\) −29.0133 21.0794i −1.00165 0.727742i −0.0392091 0.999231i \(-0.512484\pi\)
−0.962441 + 0.271489i \(0.912484\pi\)
\(840\) 2.07487 1.50748i 0.0715898 0.0520130i
\(841\) 14.0429 43.2197i 0.484240 1.49034i
\(842\) −6.71518 + 20.6672i −0.231420 + 0.712239i
\(843\) 7.72092 5.60957i 0.265922 0.193204i
\(844\) −5.65023 4.10514i −0.194489 0.141305i
\(845\) −4.66389 14.3540i −0.160443 0.493792i
\(846\) −60.7076 −2.08717
\(847\) 0 0
\(848\) 19.4014 0.666248
\(849\) 0.641191 + 1.97338i 0.0220056 + 0.0677263i
\(850\) 10.7560 + 7.81467i 0.368927 + 0.268041i
\(851\) −3.66092 + 2.65981i −0.125495 + 0.0911772i
\(852\) −0.446646 + 1.37463i −0.0153018 + 0.0470942i
\(853\) 4.67937 14.4016i 0.160218 0.493102i −0.838434 0.545004i \(-0.816528\pi\)
0.998652 + 0.0519019i \(0.0165283\pi\)
\(854\) 1.42163 1.03288i 0.0486473 0.0353443i
\(855\) 11.4073 + 8.28790i 0.390122 + 0.283440i
\(856\) −1.49932 4.61444i −0.0512458 0.157718i
\(857\) −25.3267 −0.865142 −0.432571 0.901600i \(-0.642394\pi\)
−0.432571 + 0.901600i \(0.642394\pi\)
\(858\) 0 0
\(859\) 41.5291 1.41696 0.708478 0.705733i \(-0.249382\pi\)
0.708478 + 0.705733i \(0.249382\pi\)
\(860\) −4.68534 14.4200i −0.159769 0.491718i
\(861\) 4.80308 + 3.48964i 0.163689 + 0.118927i
\(862\) −5.30813 + 3.85658i −0.180796 + 0.131356i
\(863\) −7.43197 + 22.8733i −0.252987 + 0.778615i 0.741232 + 0.671249i \(0.234242\pi\)
−0.994220 + 0.107366i \(0.965758\pi\)
\(864\) −6.28115 + 19.3314i −0.213689 + 0.657668i
\(865\) 46.2486 33.6016i 1.57250 1.14249i
\(866\) 41.8101 + 30.3768i 1.42077 + 1.03225i
\(867\) −1.79656 5.52924i −0.0610144 0.187783i
\(868\) −0.232572 −0.00789399
\(869\) 0 0
\(870\) −26.3260 −0.892534
\(871\) −7.18764 22.1213i −0.243544 0.749551i
\(872\) 15.3401 + 11.1452i 0.519481 + 0.377425i
\(873\) 24.6035 17.8755i 0.832704 0.604995i
\(874\) 4.65455 14.3252i 0.157443 0.484559i
\(875\) 1.96169 6.03746i 0.0663173 0.204104i
\(876\) −5.78049 + 4.19977i −0.195304 + 0.141897i
\(877\) 27.3490 + 19.8702i 0.923509 + 0.670969i 0.944395 0.328813i \(-0.106649\pi\)
−0.0208857 + 0.999782i \(0.506649\pi\)
\(878\) −7.80061 24.0078i −0.263258 0.810225i
\(879\) −4.22553 −0.142524
\(880\) 0 0
\(881\) −36.8296 −1.24082 −0.620410 0.784278i \(-0.713034\pi\)
−0.620410 + 0.784278i \(0.713034\pi\)
\(882\) 1.43801 + 4.42575i 0.0484205 + 0.149023i
\(883\) −43.2099 31.3938i −1.45413 1.05649i −0.984845 0.173438i \(-0.944512\pi\)
−0.469283 0.883048i \(-0.655488\pi\)
\(884\) −11.0976 + 8.06286i −0.373252 + 0.271183i
\(885\) 4.53915 13.9701i 0.152582 0.469599i
\(886\) −14.9598 + 46.0414i −0.502583 + 1.54679i
\(887\) 9.27263 6.73696i 0.311344 0.226205i −0.421129 0.907001i \(-0.638366\pi\)
0.732473 + 0.680796i \(0.238366\pi\)
\(888\) −0.773537 0.562007i −0.0259582 0.0188597i
\(889\) −6.02870 18.5544i −0.202196 0.622296i
\(890\) −75.5525 −2.53253
\(891\) 0 0
\(892\) −5.36254 −0.179551
\(893\) 7.81706 + 24.0584i 0.261588 + 0.805085i
\(894\) 13.2376 + 9.61768i 0.442732 + 0.321663i
\(895\) −8.34817 + 6.06530i −0.279048 + 0.202741i
\(896\) −3.36733 + 10.3636i −0.112495 + 0.346223i
\(897\) 3.58339 11.0286i 0.119646 0.368233i
\(898\) −60.2757 + 43.7929i −2.01143 + 1.46139i
\(899\) −1.40016 1.01727i −0.0466979 0.0339280i
\(900\) −2.54617 7.83629i −0.0848722 0.261210i
\(901\) −10.7470 −0.358034
\(902\) 0 0
\(903\) 2.90983 0.0968331
\(904\) −8.51730 26.2136i −0.283281 0.871850i
\(905\) 10.7224 + 7.79031i 0.356426 + 0.258959i
\(906\) −14.0462 + 10.2052i −0.466654 + 0.339044i
\(907\) 17.6319 54.2655i 0.585459 1.80186i −0.0119596 0.999928i \(-0.503807\pi\)
0.597419 0.801929i \(-0.296193\pi\)
\(908\) −6.19853 + 19.0771i −0.205706 + 0.633097i
\(909\) −7.22628 + 5.25020i −0.239681 + 0.174138i
\(910\) −17.1484 12.4591i −0.568465 0.413014i
\(911\) 2.06289 + 6.34893i 0.0683467 + 0.210350i 0.979396 0.201947i \(-0.0647268\pi\)
−0.911050 + 0.412296i \(0.864727\pi\)
\(912\) 5.96167 0.197410
\(913\) 0 0
\(914\) 34.6568 1.14635
\(915\) −0.524410 1.61397i −0.0173365 0.0533561i
\(916\) 4.15177 + 3.01643i 0.137178 + 0.0996658i
\(917\) −5.58057 + 4.05452i −0.184286 + 0.133892i
\(918\) 5.25526 16.1740i 0.173449 0.533822i
\(919\) 9.00287 27.7080i 0.296977 0.914002i −0.685573 0.728004i \(-0.740448\pi\)
0.982550 0.185998i \(-0.0595518\pi\)
\(920\) 14.6713 10.6593i 0.483699 0.351428i
\(921\) −5.89852 4.28553i −0.194363 0.141213i
\(922\) 6.71491 + 20.6664i 0.221144 + 0.680611i
\(923\) −8.66015 −0.285052
\(924\) 0 0
\(925\) 2.81073 0.0924161
\(926\) −7.61015 23.4216i −0.250085 0.769683i
\(927\) −38.5113 27.9801i −1.26488 0.918987i
\(928\) 40.8632 29.6889i 1.34140 0.974585i
\(929\) 0.724557 2.22996i 0.0237720 0.0731626i −0.938467 0.345370i \(-0.887754\pi\)
0.962239 + 0.272207i \(0.0877536\pi\)
\(930\) −0.189128 + 0.582077i −0.00620176 + 0.0190871i
\(931\) 1.56876 1.13977i 0.0514141 0.0373545i
\(932\) −9.88015 7.17835i −0.323635 0.235135i
\(933\) 4.83452 + 14.8791i 0.158275 + 0.487121i
\(934\) 29.1876 0.955047
\(935\) 0 0
\(936\) −16.7940 −0.548928
\(937\) −2.71558 8.35769i −0.0887141 0.273034i 0.896850 0.442334i \(-0.145849\pi\)
−0.985565 + 0.169300i \(0.945849\pi\)
\(938\) −7.79037 5.66003i −0.254365 0.184807i
\(939\) 9.82717 7.13986i 0.320698 0.233000i
\(940\) 12.9822 39.9551i 0.423432 1.30319i
\(941\) −2.74676 + 8.45366i −0.0895419 + 0.275582i −0.985793 0.167966i \(-0.946280\pi\)
0.896251 + 0.443547i \(0.146280\pi\)
\(942\) 4.08042 2.96460i 0.132947 0.0965918i
\(943\) 33.9624 + 24.6751i 1.10597 + 0.803533i
\(944\) 13.1543 + 40.4847i 0.428135 + 1.31766i
\(945\) 9.64380 0.313713
\(946\) 0 0
\(947\) −7.86275 −0.255505 −0.127752 0.991806i \(-0.540776\pi\)
−0.127752 + 0.991806i \(0.540776\pi\)
\(948\) −1.39360 4.28905i −0.0452620 0.139302i
\(949\) −34.6345 25.1634i −1.12428 0.816840i
\(950\) −7.56902 + 5.49921i −0.245571 + 0.178418i
\(951\) 0.689556 2.12223i 0.0223604 0.0688182i
\(952\) 1.27222 3.91548i 0.0412328 0.126901i
\(953\) −14.1290 + 10.2653i −0.457683 + 0.332526i −0.792622 0.609714i \(-0.791284\pi\)
0.334939 + 0.942240i \(0.391284\pi\)
\(954\) 14.6831 + 10.6679i 0.475382 + 0.345385i
\(955\) 0.711658 + 2.19026i 0.0230287 + 0.0708751i
\(956\) 11.3121 0.365860
\(957\) 0 0
\(958\) −44.0663 −1.42372
\(959\) −0.806750 2.48292i −0.0260513 0.0801777i
\(960\) −0.633854 0.460522i −0.0204575 0.0148633i
\(961\) 25.0470 18.1977i 0.807967 0.587022i
\(962\) −2.44196 + 7.51559i −0.0787320 + 0.242312i
\(963\) 2.62725 8.08584i 0.0846619 0.260563i
\(964\) 11.7722 8.55298i 0.379156 0.275473i
\(965\) 15.1406 + 11.0003i 0.487392 + 0.354111i
\(966\) −1.48351 4.56578i −0.0477312 0.146902i
\(967\) 45.6122 1.46679 0.733395 0.679802i \(-0.237934\pi\)
0.733395 + 0.679802i \(0.237934\pi\)
\(968\) 0 0
\(969\) −3.30233 −0.106086
\(970\) 17.7217 + 54.5417i 0.569008 + 1.75123i
\(971\) −1.92852 1.40115i −0.0618892 0.0449651i 0.556411 0.830908i \(-0.312178\pi\)
−0.618300 + 0.785942i \(0.712178\pi\)
\(972\) −13.0799 + 9.50313i −0.419539 + 0.304813i
\(973\) 0.309430 0.952327i 0.00991986 0.0305302i
\(974\) 7.87338 24.2318i 0.252279 0.776436i
\(975\) −5.82715 + 4.23367i −0.186618 + 0.135586i
\(976\) 3.97867 + 2.89067i 0.127354 + 0.0925282i
\(977\) −5.95358 18.3232i −0.190472 0.586212i 0.809528 0.587082i \(-0.199723\pi\)
−1.00000 0.000869450i \(0.999723\pi\)
\(978\) −8.82972 −0.282343
\(979\) 0 0
\(980\) −3.22035 −0.102870
\(981\) 10.2674 + 31.5997i 0.327812 + 1.00890i
\(982\) 31.6641 + 23.0053i 1.01044 + 0.734130i
\(983\) 13.1268 9.53718i 0.418680 0.304189i −0.358426 0.933558i \(-0.616687\pi\)
0.777107 + 0.629369i \(0.216687\pi\)
\(984\) −2.74103 + 8.43602i −0.0873808 + 0.268931i
\(985\) −9.37387 + 28.8498i −0.298676 + 0.919231i
\(986\) −34.1891 + 24.8398i −1.08880 + 0.791061i
\(987\) 6.52277 + 4.73907i 0.207622 + 0.150846i
\(988\) −2.98293 9.18051i −0.0948996 0.292071i
\(989\) 20.5753 0.654256
\(990\) 0 0
\(991\) −50.5214 −1.60487 −0.802433 0.596743i \(-0.796461\pi\)
−0.802433 + 0.596743i \(0.796461\pi\)
\(992\) −0.362867 1.11679i −0.0115210 0.0354581i
\(993\) 13.2667 + 9.63884i 0.421007 + 0.305879i
\(994\) −2.90055 + 2.10737i −0.0919997 + 0.0668417i
\(995\) −18.0023 + 55.4053i −0.570710 + 1.75647i
\(996\) 0.381192 1.17319i 0.0120785 0.0371739i
\(997\) −36.4224 + 26.4625i −1.15351 + 0.838074i −0.988944 0.148292i \(-0.952623\pi\)
−0.164567 + 0.986366i \(0.552623\pi\)
\(998\) −36.3986 26.4452i −1.15218 0.837107i
\(999\) −1.11102 3.41936i −0.0351510 0.108184i
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 847.2.f.q.148.1 8
11.2 odd 10 77.2.f.a.64.2 8
11.3 even 5 847.2.a.k.1.2 4
11.4 even 5 847.2.f.s.729.2 8
11.5 even 5 847.2.f.s.323.2 8
11.6 odd 10 847.2.f.p.323.1 8
11.7 odd 10 847.2.f.p.729.1 8
11.8 odd 10 847.2.a.l.1.3 4
11.9 even 5 inner 847.2.f.q.372.1 8
11.10 odd 2 77.2.f.a.71.2 yes 8
33.2 even 10 693.2.m.g.64.1 8
33.8 even 10 7623.2.a.ch.1.2 4
33.14 odd 10 7623.2.a.co.1.3 4
33.32 even 2 693.2.m.g.379.1 8
77.2 odd 30 539.2.q.c.361.1 16
77.10 even 6 539.2.q.b.324.1 16
77.13 even 10 539.2.f.d.295.2 8
77.24 even 30 539.2.q.b.471.2 16
77.32 odd 6 539.2.q.c.324.1 16
77.41 even 10 5929.2.a.bi.1.3 4
77.46 odd 30 539.2.q.c.471.2 16
77.54 even 6 539.2.q.b.214.2 16
77.65 odd 6 539.2.q.c.214.2 16
77.68 even 30 539.2.q.b.361.1 16
77.69 odd 10 5929.2.a.bb.1.2 4
77.76 even 2 539.2.f.d.148.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.a.64.2 8 11.2 odd 10
77.2.f.a.71.2 yes 8 11.10 odd 2
539.2.f.d.148.2 8 77.76 even 2
539.2.f.d.295.2 8 77.13 even 10
539.2.q.b.214.2 16 77.54 even 6
539.2.q.b.324.1 16 77.10 even 6
539.2.q.b.361.1 16 77.68 even 30
539.2.q.b.471.2 16 77.24 even 30
539.2.q.c.214.2 16 77.65 odd 6
539.2.q.c.324.1 16 77.32 odd 6
539.2.q.c.361.1 16 77.2 odd 30
539.2.q.c.471.2 16 77.46 odd 30
693.2.m.g.64.1 8 33.2 even 10
693.2.m.g.379.1 8 33.32 even 2
847.2.a.k.1.2 4 11.3 even 5
847.2.a.l.1.3 4 11.8 odd 10
847.2.f.p.323.1 8 11.6 odd 10
847.2.f.p.729.1 8 11.7 odd 10
847.2.f.q.148.1 8 1.1 even 1 trivial
847.2.f.q.372.1 8 11.9 even 5 inner
847.2.f.s.323.2 8 11.5 even 5
847.2.f.s.729.2 8 11.4 even 5
5929.2.a.bb.1.2 4 77.69 odd 10
5929.2.a.bi.1.3 4 77.41 even 10
7623.2.a.ch.1.2 4 33.8 even 10
7623.2.a.co.1.3 4 33.14 odd 10