Properties

Label 175.2.q.a.11.6
Level $175$
Weight $2$
Character 175.11
Analytic conductor $1.397$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [175,2,Mod(11,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([24, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.q (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(18\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 11.6
Character \(\chi\) \(=\) 175.11
Dual form 175.2.q.a.16.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.26136 - 0.561596i) q^{2} +(-0.564524 - 0.626968i) q^{3} +(-0.0626100 - 0.0695354i) q^{4} +(2.11758 + 0.718244i) q^{5} +(0.359969 + 1.10787i) q^{6} +(2.36555 + 1.18498i) q^{7} +(0.893265 + 2.74919i) q^{8} +(0.239184 - 2.27569i) q^{9} +O(q^{10})\) \(q+(-1.26136 - 0.561596i) q^{2} +(-0.564524 - 0.626968i) q^{3} +(-0.0626100 - 0.0695354i) q^{4} +(2.11758 + 0.718244i) q^{5} +(0.359969 + 1.10787i) q^{6} +(2.36555 + 1.18498i) q^{7} +(0.893265 + 2.74919i) q^{8} +(0.239184 - 2.27569i) q^{9} +(-2.26767 - 2.09519i) q^{10} +(-0.468722 - 4.45959i) q^{11} +(-0.00825162 + 0.0785089i) q^{12} +(-4.68752 - 3.40568i) q^{13} +(-2.31835 - 2.82317i) q^{14} +(-0.745107 - 1.73312i) q^{15} +(0.397637 - 3.78327i) q^{16} +(5.96728 + 1.26838i) q^{17} +(-1.57972 + 2.73615i) q^{18} +(0.220156 - 0.244509i) q^{19} +(-0.0826380 - 0.192216i) q^{20} +(-0.592470 - 2.15207i) q^{21} +(-1.91326 + 5.88840i) q^{22} +(0.656738 + 0.292399i) q^{23} +(1.21938 - 2.11203i) q^{24} +(3.96825 + 3.04187i) q^{25} +(4.00005 + 6.92830i) q^{26} +(-3.60944 + 2.62241i) q^{27} +(-0.0657094 - 0.238681i) q^{28} +(1.29917 - 3.99844i) q^{29} +(-0.0334595 + 2.60454i) q^{30} +(-1.97937 - 0.420729i) q^{31} +(0.264433 - 0.458011i) q^{32} +(-2.53141 + 2.81142i) q^{33} +(-6.81459 - 4.95109i) q^{34} +(4.15813 + 4.20832i) q^{35} +(-0.173216 + 0.125849i) q^{36} +(-0.384014 + 3.65365i) q^{37} +(-0.415013 + 0.184775i) q^{38} +(0.510966 + 4.86151i) q^{39} +(-0.0830300 + 6.46319i) q^{40} +(6.35005 + 4.61358i) q^{41} +(-0.461274 + 3.04728i) q^{42} -10.1001 q^{43} +(-0.280753 + 0.311808i) q^{44} +(2.14099 - 4.64715i) q^{45} +(-0.664177 - 0.737643i) q^{46} +(4.25203 - 0.903798i) q^{47} +(-2.59646 + 1.88644i) q^{48} +(4.19167 + 5.60624i) q^{49} +(-3.29711 - 6.06546i) q^{50} +(-2.57344 - 4.45733i) q^{51} +(0.0566699 + 0.539178i) q^{52} +(3.70396 + 4.11366i) q^{53} +(6.02555 - 1.28077i) q^{54} +(2.21052 - 9.78018i) q^{55} +(-1.14465 + 7.56184i) q^{56} -0.277583 q^{57} +(-3.88424 + 4.31388i) q^{58} +(-3.62670 + 1.61471i) q^{59} +(-0.0738620 + 0.160322i) q^{60} +(8.22500 + 3.66201i) q^{61} +(2.26043 + 1.64230i) q^{62} +(3.26244 - 5.09983i) q^{63} +(-6.74594 + 4.90121i) q^{64} +(-7.48006 - 10.5786i) q^{65} +(4.77192 - 2.12460i) q^{66} +(-9.58007 - 2.03631i) q^{67} +(-0.285414 - 0.494351i) q^{68} +(-0.187420 - 0.576820i) q^{69} +(-2.88155 - 7.64341i) q^{70} +(-3.25059 + 10.0043i) q^{71} +(6.46995 - 1.37523i) q^{72} +(-0.399784 - 3.80369i) q^{73} +(2.53626 - 4.39293i) q^{74} +(-0.333020 - 4.20518i) q^{75} -0.0307860 q^{76} +(4.17572 - 11.1048i) q^{77} +(2.08569 - 6.41910i) q^{78} +(-8.81200 + 1.87305i) q^{79} +(3.55933 - 7.72575i) q^{80} +(-3.03288 - 0.644659i) q^{81} +(-5.41876 - 9.38558i) q^{82} +(4.16541 + 12.8198i) q^{83} +(-0.112551 + 0.175939i) q^{84} +(11.7252 + 6.97186i) q^{85} +(12.7399 + 5.67219i) q^{86} +(-3.24031 + 1.44268i) q^{87} +(11.8416 - 5.27220i) q^{88} +(2.36630 + 1.05354i) q^{89} +(-5.31039 + 4.65938i) q^{90} +(-7.05291 - 13.6109i) q^{91} +(-0.0207863 - 0.0639737i) q^{92} +(0.853622 + 1.47852i) q^{93} +(-5.87094 - 1.24791i) q^{94} +(0.641815 - 0.359639i) q^{95} +(-0.436437 + 0.0927676i) q^{96} +(-3.36132 + 10.3451i) q^{97} +(-2.13878 - 9.42554i) q^{98} -10.2607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 3 q^{2} - 3 q^{3} + 13 q^{4} - 3 q^{5} - 12 q^{6} - 22 q^{7} - 2 q^{8} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 3 q^{2} - 3 q^{3} + 13 q^{4} - 3 q^{5} - 12 q^{6} - 22 q^{7} - 2 q^{8} + 11 q^{9} - 3 q^{10} - 6 q^{11} - 11 q^{12} - 12 q^{13} - 6 q^{14} - 64 q^{15} + 13 q^{16} + 9 q^{17} - 18 q^{18} - 11 q^{19} - 24 q^{20} - 3 q^{21} - 52 q^{22} - 17 q^{23} + 46 q^{24} - 3 q^{25} + 44 q^{26} - 84 q^{27} + 62 q^{28} - 24 q^{29} - 27 q^{30} - 21 q^{31} - 16 q^{32} - 18 q^{33} - 36 q^{34} + 24 q^{35} - 104 q^{36} - 5 q^{37} - 12 q^{38} + 25 q^{39} + q^{40} + 38 q^{41} - 58 q^{42} + 20 q^{43} - 7 q^{44} - 45 q^{45} + 21 q^{46} - q^{47} - 12 q^{48} - 38 q^{49} + 66 q^{50} - 8 q^{51} + 50 q^{52} + 37 q^{53} + 15 q^{54} - 28 q^{55} - 60 q^{56} + 136 q^{57} + 53 q^{58} - 39 q^{59} + 9 q^{60} - 13 q^{61} + 124 q^{62} + 75 q^{63} + 42 q^{64} - 9 q^{65} + 7 q^{66} - 13 q^{67} - 110 q^{68} + 50 q^{69} - 5 q^{70} + 22 q^{71} - 18 q^{72} - 41 q^{73} - 10 q^{74} + 27 q^{75} - 276 q^{76} + 37 q^{77} + 2 q^{78} + 9 q^{79} - 94 q^{80} + 57 q^{81} - 108 q^{82} + 86 q^{83} - 29 q^{84} - 58 q^{85} - 17 q^{86} - 7 q^{87} - 26 q^{88} - 42 q^{89} + 376 q^{90} - 34 q^{91} - 62 q^{92} + 98 q^{93} - 11 q^{94} + 45 q^{95} + 13 q^{96} + 96 q^{97} - 86 q^{98} - 68 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26136 0.561596i −0.891920 0.397108i −0.0909795 0.995853i \(-0.529000\pi\)
−0.800940 + 0.598745i \(0.795666\pi\)
\(3\) −0.564524 0.626968i −0.325928 0.361980i 0.557804 0.829973i \(-0.311644\pi\)
−0.883732 + 0.467993i \(0.844977\pi\)
\(4\) −0.0626100 0.0695354i −0.0313050 0.0347677i
\(5\) 2.11758 + 0.718244i 0.947009 + 0.321208i
\(6\) 0.359969 + 1.10787i 0.146957 + 0.452286i
\(7\) 2.36555 + 1.18498i 0.894094 + 0.447879i
\(8\) 0.893265 + 2.74919i 0.315817 + 0.971984i
\(9\) 0.239184 2.27569i 0.0797282 0.758563i
\(10\) −2.26767 2.09519i −0.717101 0.662557i
\(11\) −0.468722 4.45959i −0.141325 1.34462i −0.803517 0.595282i \(-0.797040\pi\)
0.662192 0.749335i \(-0.269626\pi\)
\(12\) −0.00825162 + 0.0785089i −0.00238204 + 0.0226636i
\(13\) −4.68752 3.40568i −1.30008 0.944566i −0.300127 0.953899i \(-0.597029\pi\)
−0.999956 + 0.00933331i \(0.997029\pi\)
\(14\) −2.31835 2.82317i −0.619604 0.754524i
\(15\) −0.745107 1.73312i −0.192386 0.447489i
\(16\) 0.397637 3.78327i 0.0994094 0.945817i
\(17\) 5.96728 + 1.26838i 1.44728 + 0.307628i 0.863526 0.504304i \(-0.168251\pi\)
0.583751 + 0.811932i \(0.301584\pi\)
\(18\) −1.57972 + 2.73615i −0.372343 + 0.644916i
\(19\) 0.220156 0.244509i 0.0505074 0.0560941i −0.717362 0.696701i \(-0.754650\pi\)
0.767869 + 0.640607i \(0.221317\pi\)
\(20\) −0.0826380 0.192216i −0.0184784 0.0429808i
\(21\) −0.592470 2.15207i −0.129288 0.469621i
\(22\) −1.91326 + 5.88840i −0.407908 + 1.25541i
\(23\) 0.656738 + 0.292399i 0.136939 + 0.0609693i 0.474062 0.880491i \(-0.342787\pi\)
−0.337123 + 0.941461i \(0.609454\pi\)
\(24\) 1.21938 2.11203i 0.248905 0.431117i
\(25\) 3.96825 + 3.04187i 0.793650 + 0.608374i
\(26\) 4.00005 + 6.92830i 0.784475 + 1.35875i
\(27\) −3.60944 + 2.62241i −0.694636 + 0.504683i
\(28\) −0.0657094 0.238681i −0.0124179 0.0451065i
\(29\) 1.29917 3.99844i 0.241250 0.742491i −0.754981 0.655747i \(-0.772354\pi\)
0.996231 0.0867442i \(-0.0276463\pi\)
\(30\) −0.0334595 + 2.60454i −0.00610885 + 0.475522i
\(31\) −1.97937 0.420729i −0.355506 0.0755652i 0.0266968 0.999644i \(-0.491501\pi\)
−0.382203 + 0.924078i \(0.624834\pi\)
\(32\) 0.264433 0.458011i 0.0467456 0.0809657i
\(33\) −2.53141 + 2.81142i −0.440663 + 0.489406i
\(34\) −6.81459 4.95109i −1.16869 0.849105i
\(35\) 4.15813 + 4.20832i 0.702853 + 0.711335i
\(36\) −0.173216 + 0.125849i −0.0288694 + 0.0209748i
\(37\) −0.384014 + 3.65365i −0.0631316 + 0.600657i 0.916525 + 0.399977i \(0.130982\pi\)
−0.979657 + 0.200680i \(0.935685\pi\)
\(38\) −0.415013 + 0.184775i −0.0673239 + 0.0299745i
\(39\) 0.510966 + 4.86151i 0.0818200 + 0.778465i
\(40\) −0.0830300 + 6.46319i −0.0131282 + 1.02192i
\(41\) 6.35005 + 4.61358i 0.991712 + 0.720521i 0.960295 0.278986i \(-0.0899982\pi\)
0.0314165 + 0.999506i \(0.489998\pi\)
\(42\) −0.461274 + 3.04728i −0.0711761 + 0.470205i
\(43\) −10.1001 −1.54025 −0.770127 0.637890i \(-0.779807\pi\)
−0.770127 + 0.637890i \(0.779807\pi\)
\(44\) −0.280753 + 0.311808i −0.0423251 + 0.0470068i
\(45\) 2.14099 4.64715i 0.319160 0.692756i
\(46\) −0.664177 0.737643i −0.0979275 0.108760i
\(47\) 4.25203 0.903798i 0.620223 0.131832i 0.112925 0.993603i \(-0.463978\pi\)
0.507297 + 0.861771i \(0.330645\pi\)
\(48\) −2.59646 + 1.88644i −0.374767 + 0.272284i
\(49\) 4.19167 + 5.60624i 0.598809 + 0.800892i
\(50\) −3.29711 6.06546i −0.466282 0.857786i
\(51\) −2.57344 4.45733i −0.360353 0.624150i
\(52\) 0.0566699 + 0.539178i 0.00785870 + 0.0747706i
\(53\) 3.70396 + 4.11366i 0.508778 + 0.565055i 0.941733 0.336360i \(-0.109196\pi\)
−0.432955 + 0.901415i \(0.642529\pi\)
\(54\) 6.02555 1.28077i 0.819973 0.174291i
\(55\) 2.21052 9.78018i 0.298066 1.31876i
\(56\) −1.14465 + 7.56184i −0.152961 + 1.01049i
\(57\) −0.277583 −0.0367667
\(58\) −3.88424 + 4.31388i −0.510025 + 0.566440i
\(59\) −3.62670 + 1.61471i −0.472157 + 0.210218i −0.628999 0.777406i \(-0.716535\pi\)
0.156843 + 0.987624i \(0.449868\pi\)
\(60\) −0.0738620 + 0.160322i −0.00953554 + 0.0206975i
\(61\) 8.22500 + 3.66201i 1.05310 + 0.468872i 0.858929 0.512095i \(-0.171130\pi\)
0.194175 + 0.980967i \(0.437797\pi\)
\(62\) 2.26043 + 1.64230i 0.287075 + 0.208572i
\(63\) 3.26244 5.09983i 0.411029 0.642518i
\(64\) −6.74594 + 4.90121i −0.843242 + 0.612651i
\(65\) −7.48006 10.5786i −0.927788 1.31211i
\(66\) 4.77192 2.12460i 0.587383 0.261520i
\(67\) −9.58007 2.03631i −1.17039 0.248774i −0.418597 0.908172i \(-0.637478\pi\)
−0.751795 + 0.659397i \(0.770811\pi\)
\(68\) −0.285414 0.494351i −0.0346115 0.0599488i
\(69\) −0.187420 0.576820i −0.0225627 0.0694410i
\(70\) −2.88155 7.64341i −0.344411 0.913563i
\(71\) −3.25059 + 10.0043i −0.385774 + 1.18729i 0.550144 + 0.835070i \(0.314573\pi\)
−0.935917 + 0.352219i \(0.885427\pi\)
\(72\) 6.46995 1.37523i 0.762490 0.162072i
\(73\) −0.399784 3.80369i −0.0467912 0.445188i −0.992687 0.120717i \(-0.961480\pi\)
0.945896 0.324471i \(-0.105186\pi\)
\(74\) 2.53626 4.39293i 0.294834 0.510667i
\(75\) −0.333020 4.20518i −0.0384539 0.485572i
\(76\) −0.0307860 −0.00353140
\(77\) 4.17572 11.1048i 0.475867 1.26551i
\(78\) 2.08569 6.41910i 0.236158 0.726820i
\(79\) −8.81200 + 1.87305i −0.991428 + 0.210734i −0.674948 0.737865i \(-0.735834\pi\)
−0.316479 + 0.948599i \(0.602501\pi\)
\(80\) 3.55933 7.72575i 0.397946 0.863765i
\(81\) −3.03288 0.644659i −0.336987 0.0716287i
\(82\) −5.41876 9.38558i −0.598402 1.03646i
\(83\) 4.16541 + 12.8198i 0.457214 + 1.40716i 0.868517 + 0.495660i \(0.165074\pi\)
−0.411303 + 0.911499i \(0.634926\pi\)
\(84\) −0.112551 + 0.175939i −0.0122803 + 0.0191965i
\(85\) 11.7252 + 6.97186i 1.27177 + 0.756204i
\(86\) 12.7399 + 5.67219i 1.37378 + 0.611648i
\(87\) −3.24031 + 1.44268i −0.347397 + 0.154671i
\(88\) 11.8416 5.27220i 1.26231 0.562018i
\(89\) 2.36630 + 1.05354i 0.250827 + 0.111676i 0.528299 0.849058i \(-0.322830\pi\)
−0.277472 + 0.960734i \(0.589497\pi\)
\(90\) −5.31039 + 4.65938i −0.559764 + 0.491142i
\(91\) −7.05291 13.6109i −0.739346 1.42681i
\(92\) −0.0207863 0.0639737i −0.00216712 0.00666972i
\(93\) 0.853622 + 1.47852i 0.0885164 + 0.153315i
\(94\) −5.87094 1.24791i −0.605541 0.128712i
\(95\) 0.641815 0.359639i 0.0658488 0.0368982i
\(96\) −0.436437 + 0.0927676i −0.0445437 + 0.00946805i
\(97\) −3.36132 + 10.3451i −0.341290 + 1.05038i 0.622250 + 0.782819i \(0.286219\pi\)
−0.963540 + 0.267565i \(0.913781\pi\)
\(98\) −2.13878 9.42554i −0.216049 0.952123i
\(99\) −10.2607 −1.03124
\(100\) −0.0369344 0.466386i −0.00369344 0.0466386i
\(101\) 4.98802 8.63951i 0.496327 0.859663i −0.503664 0.863899i \(-0.668015\pi\)
0.999991 + 0.00423641i \(0.00134849\pi\)
\(102\) 0.742829 + 7.06754i 0.0735510 + 0.699791i
\(103\) 5.50550 1.17023i 0.542473 0.115306i 0.0714781 0.997442i \(-0.477228\pi\)
0.470995 + 0.882136i \(0.343895\pi\)
\(104\) 5.17566 15.9290i 0.507515 1.56197i
\(105\) 0.291113 4.98271i 0.0284097 0.486263i
\(106\) −2.36183 7.26896i −0.229401 0.706024i
\(107\) 0.255632 + 0.442768i 0.0247129 + 0.0428040i 0.878117 0.478445i \(-0.158800\pi\)
−0.853404 + 0.521249i \(0.825466\pi\)
\(108\) 0.408337 + 0.0867947i 0.0392923 + 0.00835183i
\(109\) −3.42433 + 1.52461i −0.327991 + 0.146031i −0.564125 0.825690i \(-0.690786\pi\)
0.236134 + 0.971721i \(0.424120\pi\)
\(110\) −8.28078 + 11.0950i −0.789541 + 1.05786i
\(111\) 2.50751 1.82181i 0.238002 0.172919i
\(112\) 5.42371 8.47832i 0.512493 0.801126i
\(113\) −6.40255 4.65173i −0.602302 0.437598i 0.244394 0.969676i \(-0.421411\pi\)
−0.846695 + 0.532078i \(0.821411\pi\)
\(114\) 0.350133 + 0.155889i 0.0327930 + 0.0146004i
\(115\) 1.18068 + 1.09087i 0.110099 + 0.101725i
\(116\) −0.359374 + 0.160004i −0.0333671 + 0.0148560i
\(117\) −8.87145 + 9.85274i −0.820166 + 0.910886i
\(118\) 5.48141 0.504605
\(119\) 12.6129 + 10.0715i 1.15622 + 0.923253i
\(120\) 4.09909 3.59657i 0.374194 0.328321i
\(121\) −8.90862 + 1.89359i −0.809875 + 0.172144i
\(122\) −8.31816 9.23825i −0.753091 0.836392i
\(123\) −0.692191 6.58576i −0.0624128 0.593818i
\(124\) 0.0946730 + 0.163978i 0.00850189 + 0.0147257i
\(125\) 6.21827 + 9.29156i 0.556179 + 0.831063i
\(126\) −6.97917 + 4.60057i −0.621754 + 0.409852i
\(127\) 7.64828 5.55680i 0.678676 0.493087i −0.194243 0.980954i \(-0.562225\pi\)
0.872918 + 0.487867i \(0.162225\pi\)
\(128\) 10.2270 2.17381i 0.903945 0.192139i
\(129\) 5.70177 + 6.33245i 0.502013 + 0.557542i
\(130\) 3.49421 + 17.5442i 0.306463 + 1.53873i
\(131\) −4.90415 + 5.44661i −0.428477 + 0.475872i −0.918263 0.395970i \(-0.870408\pi\)
0.489786 + 0.871843i \(0.337075\pi\)
\(132\) 0.353985 0.0308105
\(133\) 0.810528 0.317517i 0.0702817 0.0275323i
\(134\) 10.9404 + 7.94865i 0.945105 + 0.686659i
\(135\) −9.52678 + 2.96069i −0.819935 + 0.254816i
\(136\) 1.84333 + 17.5382i 0.158065 + 1.50388i
\(137\) −19.9385 + 8.87721i −1.70346 + 0.758431i −0.704660 + 0.709546i \(0.748900\pi\)
−0.998804 + 0.0488855i \(0.984433\pi\)
\(138\) −0.0875345 + 0.832835i −0.00745143 + 0.0708956i
\(139\) 6.92545 5.03163i 0.587409 0.426778i −0.253979 0.967210i \(-0.581739\pi\)
0.841388 + 0.540432i \(0.181739\pi\)
\(140\) 0.0322866 0.552620i 0.00272871 0.0467049i
\(141\) −2.96703 2.15567i −0.249869 0.181540i
\(142\) 9.71854 10.7935i 0.815561 0.905773i
\(143\) −12.9908 + 22.5007i −1.08635 + 1.88161i
\(144\) −8.51443 1.80980i −0.709536 0.150816i
\(145\) 5.62295 7.53387i 0.466960 0.625654i
\(146\) −1.63186 + 5.02236i −0.135054 + 0.415653i
\(147\) 1.14864 5.79290i 0.0947378 0.477790i
\(148\) 0.278101 0.202053i 0.0228598 0.0166086i
\(149\) 3.59235 + 6.22213i 0.294297 + 0.509737i 0.974821 0.222988i \(-0.0715812\pi\)
−0.680524 + 0.732726i \(0.738248\pi\)
\(150\) −1.94155 + 5.49128i −0.158527 + 0.448361i
\(151\) −0.184852 + 0.320173i −0.0150430 + 0.0260553i −0.873449 0.486916i \(-0.838122\pi\)
0.858406 + 0.512971i \(0.171455\pi\)
\(152\) 0.868857 + 0.386840i 0.0704736 + 0.0313769i
\(153\) 4.31373 13.2763i 0.348744 1.07332i
\(154\) −11.5035 + 11.6622i −0.926980 + 0.939763i
\(155\) −3.88929 2.31260i −0.312395 0.185752i
\(156\) 0.306056 0.339910i 0.0245041 0.0272145i
\(157\) 1.59621 2.76471i 0.127391 0.220648i −0.795274 0.606250i \(-0.792673\pi\)
0.922665 + 0.385602i \(0.126006\pi\)
\(158\) 12.1670 + 2.58618i 0.967958 + 0.205746i
\(159\) 0.488160 4.64453i 0.0387136 0.368335i
\(160\) 0.888920 0.779946i 0.0702753 0.0616601i
\(161\) 1.20706 + 1.46990i 0.0951299 + 0.115845i
\(162\) 3.46353 + 2.51640i 0.272121 + 0.197707i
\(163\) −2.29145 + 21.8016i −0.179480 + 1.70764i 0.420229 + 0.907418i \(0.361950\pi\)
−0.599709 + 0.800218i \(0.704717\pi\)
\(164\) −0.0767692 0.730410i −0.00599467 0.0570355i
\(165\) −7.37975 + 4.13522i −0.574513 + 0.321927i
\(166\) 1.94545 18.5098i 0.150997 1.43664i
\(167\) −3.32597 10.2363i −0.257371 0.792108i −0.993353 0.115106i \(-0.963279\pi\)
0.735982 0.677001i \(-0.236721\pi\)
\(168\) 5.38722 3.55118i 0.415633 0.273980i
\(169\) 6.35694 + 19.5646i 0.488995 + 1.50497i
\(170\) −10.8743 15.3789i −0.834023 1.17950i
\(171\) −0.503767 0.559490i −0.0385240 0.0427853i
\(172\) 0.632369 + 0.702317i 0.0482177 + 0.0535511i
\(173\) −7.04333 3.13589i −0.535494 0.238417i 0.121128 0.992637i \(-0.461349\pi\)
−0.656622 + 0.754220i \(0.728015\pi\)
\(174\) 4.89741 0.371272
\(175\) 5.78256 + 11.8980i 0.437121 + 0.899403i
\(176\) −17.0582 −1.28581
\(177\) 3.05974 + 1.36228i 0.229984 + 0.102395i
\(178\) −2.39310 2.65781i −0.179371 0.199211i
\(179\) −2.00200 2.22345i −0.149637 0.166188i 0.663666 0.748029i \(-0.269000\pi\)
−0.813303 + 0.581840i \(0.802333\pi\)
\(180\) −0.457189 + 0.142083i −0.0340769 + 0.0105903i
\(181\) 3.40661 + 10.4845i 0.253211 + 0.779303i 0.994177 + 0.107761i \(0.0343680\pi\)
−0.740966 + 0.671543i \(0.765632\pi\)
\(182\) 1.25247 + 21.1292i 0.0928393 + 1.56620i
\(183\) −2.34725 7.22410i −0.173514 0.534021i
\(184\) −0.217217 + 2.06669i −0.0160135 + 0.152358i
\(185\) −3.43739 + 7.46107i −0.252722 + 0.548549i
\(186\) −0.246400 2.34434i −0.0180669 0.171895i
\(187\) 2.85948 27.2061i 0.209106 1.98951i
\(188\) −0.329066 0.239080i −0.0239996 0.0174367i
\(189\) −11.6458 + 1.92635i −0.847107 + 0.140121i
\(190\) −1.01153 + 0.0931959i −0.0733844 + 0.00676114i
\(191\) 2.13693 20.3316i 0.154623 1.47114i −0.592024 0.805921i \(-0.701671\pi\)
0.746647 0.665221i \(-0.231663\pi\)
\(192\) 6.88115 + 1.46263i 0.496604 + 0.105556i
\(193\) 10.7249 18.5760i 0.771994 1.33713i −0.164475 0.986381i \(-0.552593\pi\)
0.936469 0.350751i \(-0.114074\pi\)
\(194\) 10.0496 11.1612i 0.721519 0.801328i
\(195\) −2.40974 + 10.6616i −0.172565 + 0.763494i
\(196\) 0.127392 0.642476i 0.00909945 0.0458911i
\(197\) 2.10869 6.48989i 0.150238 0.462386i −0.847409 0.530940i \(-0.821839\pi\)
0.997647 + 0.0685548i \(0.0218388\pi\)
\(198\) 12.9425 + 5.76239i 0.919787 + 0.409515i
\(199\) 3.30428 5.72318i 0.234234 0.405705i −0.724816 0.688943i \(-0.758075\pi\)
0.959050 + 0.283237i \(0.0914085\pi\)
\(200\) −4.81797 + 13.6267i −0.340682 + 0.963550i
\(201\) 4.13148 + 7.15594i 0.291412 + 0.504741i
\(202\) −11.1436 + 8.09632i −0.784063 + 0.569655i
\(203\) 7.81131 7.91903i 0.548246 0.555807i
\(204\) −0.148819 + 0.458018i −0.0104194 + 0.0320677i
\(205\) 10.1330 + 14.3305i 0.707722 + 1.00089i
\(206\) −7.60164 1.61578i −0.529631 0.112577i
\(207\) 0.822490 1.42459i 0.0571670 0.0990162i
\(208\) −14.7485 + 16.3799i −1.02263 + 1.13574i
\(209\) −1.19360 0.867201i −0.0825630 0.0599856i
\(210\) −3.16547 + 6.12153i −0.218438 + 0.422426i
\(211\) 8.12908 5.90613i 0.559629 0.406594i −0.271694 0.962384i \(-0.587584\pi\)
0.831323 + 0.555789i \(0.187584\pi\)
\(212\) 0.0541406 0.515113i 0.00371839 0.0353781i
\(213\) 8.10740 3.60965i 0.555510 0.247329i
\(214\) −0.0737888 0.702053i −0.00504410 0.0479914i
\(215\) −21.3878 7.25435i −1.45863 0.494743i
\(216\) −10.4337 7.58051i −0.709921 0.515788i
\(217\) −4.18376 3.34077i −0.284012 0.226786i
\(218\) 5.17554 0.350532
\(219\) −2.15910 + 2.39793i −0.145899 + 0.162037i
\(220\) −0.818469 + 0.458627i −0.0551812 + 0.0309206i
\(221\) −23.6520 26.2682i −1.59101 1.76699i
\(222\) −4.18600 + 0.889763i −0.280946 + 0.0597170i
\(223\) −1.54979 + 1.12599i −0.103781 + 0.0754016i −0.638466 0.769650i \(-0.720431\pi\)
0.534684 + 0.845052i \(0.320431\pi\)
\(224\) 1.16826 0.770102i 0.0780578 0.0514546i
\(225\) 7.87149 8.30294i 0.524766 0.553529i
\(226\) 5.46356 + 9.46317i 0.363431 + 0.629481i
\(227\) 0.934471 + 8.89089i 0.0620230 + 0.590109i 0.980757 + 0.195232i \(0.0625461\pi\)
−0.918734 + 0.394877i \(0.870787\pi\)
\(228\) 0.0173795 + 0.0193018i 0.00115098 + 0.00127830i
\(229\) 12.9293 2.74820i 0.854390 0.181606i 0.240160 0.970733i \(-0.422800\pi\)
0.614230 + 0.789127i \(0.289467\pi\)
\(230\) −0.876637 2.03906i −0.0578037 0.134451i
\(231\) −9.31966 + 3.65090i −0.613188 + 0.240211i
\(232\) 12.1530 0.797881
\(233\) −7.75905 + 8.61729i −0.508312 + 0.564538i −0.941607 0.336715i \(-0.890684\pi\)
0.433295 + 0.901252i \(0.357351\pi\)
\(234\) 16.7234 7.44573i 1.09324 0.486743i
\(235\) 9.65315 + 1.14014i 0.629702 + 0.0743743i
\(236\) 0.339348 + 0.151087i 0.0220897 + 0.00983495i
\(237\) 6.14893 + 4.46746i 0.399416 + 0.290193i
\(238\) −10.2533 19.7872i −0.664626 1.28261i
\(239\) 5.13719 3.73239i 0.332297 0.241428i −0.409108 0.912486i \(-0.634160\pi\)
0.741405 + 0.671058i \(0.234160\pi\)
\(240\) −6.85313 + 2.12979i −0.442368 + 0.137477i
\(241\) −4.49380 + 2.00077i −0.289471 + 0.128881i −0.546335 0.837567i \(-0.683977\pi\)
0.256864 + 0.966448i \(0.417311\pi\)
\(242\) 12.3004 + 2.61454i 0.790703 + 0.168069i
\(243\) 8.00022 + 13.8568i 0.513214 + 0.888913i
\(244\) −0.260328 0.801207i −0.0166658 0.0512920i
\(245\) 4.84952 + 14.8823i 0.309825 + 0.950794i
\(246\) −2.82543 + 8.69578i −0.180143 + 0.554423i
\(247\) −1.86471 + 0.396355i −0.118648 + 0.0252195i
\(248\) −0.611443 5.81749i −0.0388267 0.369411i
\(249\) 5.68614 9.84869i 0.360345 0.624135i
\(250\) −2.62540 15.2122i −0.166045 0.962104i
\(251\) −1.51682 −0.0957407 −0.0478704 0.998854i \(-0.515243\pi\)
−0.0478704 + 0.998854i \(0.515243\pi\)
\(252\) −0.558880 + 0.0924452i −0.0352061 + 0.00582350i
\(253\) 0.996151 3.06584i 0.0626275 0.192748i
\(254\) −12.7680 + 2.71391i −0.801133 + 0.170286i
\(255\) −2.24800 11.2871i −0.140775 0.706824i
\(256\) 2.19170 + 0.465861i 0.136982 + 0.0291163i
\(257\) −6.40701 11.0973i −0.399658 0.692229i 0.594025 0.804446i \(-0.297538\pi\)
−0.993684 + 0.112218i \(0.964205\pi\)
\(258\) −3.63573 11.1896i −0.226351 0.696636i
\(259\) −5.23789 + 8.18785i −0.325467 + 0.508769i
\(260\) −0.267259 + 1.18245i −0.0165747 + 0.0733327i
\(261\) −8.78846 3.91287i −0.543992 0.242201i
\(262\) 9.24471 4.11601i 0.571140 0.254288i
\(263\) 1.29030 0.574481i 0.0795636 0.0354240i −0.366569 0.930391i \(-0.619468\pi\)
0.446133 + 0.894967i \(0.352801\pi\)
\(264\) −9.99034 4.44799i −0.614863 0.273755i
\(265\) 4.88880 + 11.3713i 0.300317 + 0.698536i
\(266\) −1.20069 0.0546838i −0.0736189 0.00335288i
\(267\) −0.675296 2.07835i −0.0413274 0.127193i
\(268\) 0.458213 + 0.793648i 0.0279898 + 0.0484797i
\(269\) 5.27072 + 1.12033i 0.321361 + 0.0683075i 0.365768 0.930706i \(-0.380806\pi\)
−0.0444065 + 0.999014i \(0.514140\pi\)
\(270\) 13.6795 + 1.61569i 0.832505 + 0.0983275i
\(271\) 5.04837 1.07306i 0.306666 0.0651840i −0.0520081 0.998647i \(-0.516562\pi\)
0.358674 + 0.933463i \(0.383229\pi\)
\(272\) 7.17145 22.0714i 0.434833 1.33828i
\(273\) −4.55206 + 12.1056i −0.275503 + 0.732667i
\(274\) 30.1352 1.82053
\(275\) 11.7055 19.1226i 0.705868 1.15313i
\(276\) −0.0283751 + 0.0491470i −0.00170798 + 0.00295830i
\(277\) −1.92029 18.2703i −0.115379 1.09776i −0.887030 0.461712i \(-0.847235\pi\)
0.771651 0.636046i \(-0.219431\pi\)
\(278\) −11.5613 + 2.45742i −0.693398 + 0.147386i
\(279\) −1.43088 + 4.40381i −0.0856648 + 0.263649i
\(280\) −7.85514 + 15.1906i −0.469434 + 0.907813i
\(281\) 3.25667 + 10.0230i 0.194277 + 0.597923i 0.999984 + 0.00560894i \(0.00178539\pi\)
−0.805707 + 0.592314i \(0.798215\pi\)
\(282\) 2.53189 + 4.38536i 0.150772 + 0.261144i
\(283\) −20.3202 4.31920i −1.20791 0.256750i −0.440411 0.897797i \(-0.645167\pi\)
−0.767502 + 0.641047i \(0.778500\pi\)
\(284\) 0.899171 0.400337i 0.0533560 0.0237556i
\(285\) −0.587802 0.199372i −0.0348184 0.0118098i
\(286\) 29.0224 21.0860i 1.71613 1.24684i
\(287\) 9.55439 + 18.4383i 0.563978 + 1.08838i
\(288\) −0.979042 0.711316i −0.0576906 0.0419147i
\(289\) 18.4693 + 8.22308i 1.08643 + 0.483710i
\(290\) −11.3236 + 6.34514i −0.664943 + 0.372599i
\(291\) 8.38358 3.73261i 0.491454 0.218809i
\(292\) −0.239461 + 0.265948i −0.0140134 + 0.0155634i
\(293\) 5.57062 0.325439 0.162719 0.986672i \(-0.447973\pi\)
0.162719 + 0.986672i \(0.447973\pi\)
\(294\) −4.70212 + 6.66189i −0.274233 + 0.388529i
\(295\) −8.83958 + 0.814419i −0.514660 + 0.0474173i
\(296\) −10.3876 + 2.20795i −0.603767 + 0.128335i
\(297\) 13.3867 + 14.8674i 0.776774 + 0.862695i
\(298\) −1.03694 9.86583i −0.0600684 0.571512i
\(299\) −2.08266 3.60727i −0.120443 0.208614i
\(300\) −0.271558 + 0.286443i −0.0156784 + 0.0165378i
\(301\) −23.8924 11.9684i −1.37713 0.689847i
\(302\) 0.412974 0.300043i 0.0237640 0.0172655i
\(303\) −8.23255 + 1.74988i −0.472948 + 0.100528i
\(304\) −0.837499 0.930136i −0.0480338 0.0533470i
\(305\) 14.7868 + 13.6621i 0.846692 + 0.782291i
\(306\) −12.8971 + 14.3237i −0.737278 + 0.818830i
\(307\) −18.4102 −1.05073 −0.525363 0.850878i \(-0.676070\pi\)
−0.525363 + 0.850878i \(0.676070\pi\)
\(308\) −1.03362 + 0.404912i −0.0588960 + 0.0230720i
\(309\) −3.84169 2.79115i −0.218546 0.158783i
\(310\) 3.60707 + 5.10124i 0.204868 + 0.289731i
\(311\) 3.26600 + 31.0739i 0.185198 + 1.76204i 0.553987 + 0.832526i \(0.313106\pi\)
−0.368789 + 0.929513i \(0.620227\pi\)
\(312\) −12.9088 + 5.74736i −0.730816 + 0.325380i
\(313\) 0.750370 7.13929i 0.0424134 0.403537i −0.952633 0.304123i \(-0.901637\pi\)
0.995046 0.0994137i \(-0.0316967\pi\)
\(314\) −3.56605 + 2.59089i −0.201244 + 0.146212i
\(315\) 10.5714 8.45605i 0.595630 0.476444i
\(316\) 0.681963 + 0.495475i 0.0383634 + 0.0278726i
\(317\) 7.01588 7.79192i 0.394051 0.437638i −0.513173 0.858285i \(-0.671530\pi\)
0.907224 + 0.420647i \(0.138197\pi\)
\(318\) −3.22409 + 5.58430i −0.180798 + 0.313152i
\(319\) −18.4403 3.91962i −1.03246 0.219456i
\(320\) −17.8053 + 5.53346i −0.995346 + 0.309330i
\(321\) 0.133291 0.410226i 0.00743955 0.0228966i
\(322\) −0.697055 2.53197i −0.0388454 0.141101i
\(323\) 1.62387 1.17981i 0.0903543 0.0656462i
\(324\) 0.145062 + 0.251255i 0.00805900 + 0.0139586i
\(325\) −8.24161 27.7734i −0.457162 1.54059i
\(326\) 15.1341 26.2130i 0.838198 1.45180i
\(327\) 2.88900 + 1.28626i 0.159762 + 0.0711306i
\(328\) −7.01132 + 21.5786i −0.387136 + 1.19148i
\(329\) 11.1294 + 2.90058i 0.613583 + 0.159914i
\(330\) 11.6309 1.07159i 0.640259 0.0589891i
\(331\) 22.5410 25.0343i 1.23897 1.37601i 0.338568 0.940942i \(-0.390057\pi\)
0.900397 0.435069i \(-0.143276\pi\)
\(332\) 0.630636 1.09229i 0.0346106 0.0599474i
\(333\) 8.22272 + 1.74779i 0.450603 + 0.0957785i
\(334\) −1.55339 + 14.7795i −0.0849979 + 0.808701i
\(335\) −18.8240 11.1929i −1.02846 0.611531i
\(336\) −8.37745 + 1.38573i −0.457028 + 0.0755976i
\(337\) −0.633700 0.460410i −0.0345198 0.0250801i 0.570392 0.821373i \(-0.306791\pi\)
−0.604911 + 0.796293i \(0.706791\pi\)
\(338\) 2.96900 28.2482i 0.161493 1.53650i
\(339\) 0.697914 + 6.64021i 0.0379055 + 0.360647i
\(340\) −0.249320 1.25182i −0.0135213 0.0678896i
\(341\) −0.948503 + 9.02440i −0.0513643 + 0.488699i
\(342\) 0.321227 + 0.988635i 0.0173700 + 0.0534592i
\(343\) 3.27234 + 18.2289i 0.176690 + 0.984267i
\(344\) −9.02209 27.7671i −0.486438 1.49710i
\(345\) 0.0174209 1.35607i 0.000937912 0.0730085i
\(346\) 7.12310 + 7.91100i 0.382940 + 0.425298i
\(347\) 3.78971 + 4.20890i 0.203443 + 0.225946i 0.836229 0.548381i \(-0.184755\pi\)
−0.632786 + 0.774327i \(0.718089\pi\)
\(348\) 0.303193 + 0.134990i 0.0162528 + 0.00723623i
\(349\) −29.3627 −1.57175 −0.785875 0.618386i \(-0.787787\pi\)
−0.785875 + 0.618386i \(0.787787\pi\)
\(350\) −0.612063 18.2552i −0.0327161 0.975779i
\(351\) 25.8504 1.37979
\(352\) −2.16649 0.964582i −0.115474 0.0514124i
\(353\) 14.6013 + 16.2164i 0.777149 + 0.863111i 0.993574 0.113188i \(-0.0361063\pi\)
−0.216425 + 0.976299i \(0.569440\pi\)
\(354\) −3.09439 3.43667i −0.164465 0.182657i
\(355\) −14.0689 + 18.8501i −0.746698 + 1.00046i
\(356\) −0.0748954 0.230504i −0.00396945 0.0122167i
\(357\) −0.805778 13.5935i −0.0426463 0.719444i
\(358\) 1.27658 + 3.92890i 0.0674691 + 0.207649i
\(359\) 2.14812 20.4380i 0.113373 1.07867i −0.778891 0.627160i \(-0.784217\pi\)
0.892264 0.451514i \(-0.149116\pi\)
\(360\) 14.6883 + 1.73485i 0.774144 + 0.0914344i
\(361\) 1.97473 + 18.7883i 0.103933 + 0.988856i
\(362\) 1.59105 15.1379i 0.0836239 0.795628i
\(363\) 6.21635 + 4.51644i 0.326274 + 0.237052i
\(364\) −0.504857 + 1.34261i −0.0264617 + 0.0703717i
\(365\) 1.88540 8.34174i 0.0986865 0.436627i
\(366\) −1.09628 + 10.4304i −0.0573036 + 0.545208i
\(367\) −14.9660 3.18112i −0.781219 0.166053i −0.199995 0.979797i \(-0.564093\pi\)
−0.581224 + 0.813744i \(0.697426\pi\)
\(368\) 1.36737 2.36835i 0.0712789 0.123459i
\(369\) 12.0179 13.3472i 0.625628 0.694830i
\(370\) 8.52591 7.48070i 0.443241 0.388903i
\(371\) 3.88732 + 14.1202i 0.201819 + 0.733084i
\(372\) 0.0493640 0.151927i 0.00255940 0.00787704i
\(373\) −21.1964 9.43726i −1.09751 0.488643i −0.223575 0.974687i \(-0.571773\pi\)
−0.873934 + 0.486044i \(0.838439\pi\)
\(374\) −18.8857 + 32.7110i −0.976556 + 1.69144i
\(375\) 2.31515 9.14397i 0.119554 0.472193i
\(376\) 6.28290 + 10.8823i 0.324016 + 0.561212i
\(377\) −19.7073 + 14.3182i −1.01498 + 0.737424i
\(378\) 15.7714 + 4.11040i 0.811195 + 0.211416i
\(379\) −5.71998 + 17.6043i −0.293816 + 0.904271i 0.689801 + 0.723999i \(0.257698\pi\)
−0.983617 + 0.180272i \(0.942302\pi\)
\(380\) −0.0651917 0.0221119i −0.00334426 0.00113431i
\(381\) −7.80158 1.65828i −0.399687 0.0849561i
\(382\) −14.1136 + 24.4454i −0.722114 + 1.25074i
\(383\) 8.53279 9.47662i 0.436005 0.484233i −0.484595 0.874738i \(-0.661033\pi\)
0.920601 + 0.390506i \(0.127700\pi\)
\(384\) −7.13628 5.18481i −0.364172 0.264586i
\(385\) 16.8184 20.5161i 0.857143 1.04560i
\(386\) −23.9602 + 17.4081i −1.21954 + 0.886050i
\(387\) −2.41579 + 22.9847i −0.122802 + 1.16838i
\(388\) 0.929802 0.413974i 0.0472035 0.0210164i
\(389\) −2.06987 19.6935i −0.104947 0.998502i −0.912603 0.408848i \(-0.865931\pi\)
0.807656 0.589654i \(-0.200736\pi\)
\(390\) 9.02708 12.0949i 0.457104 0.612449i
\(391\) 3.54807 + 2.57782i 0.179433 + 0.130366i
\(392\) −11.6683 + 16.5315i −0.589340 + 0.834968i
\(393\) 6.18336 0.311909
\(394\) −6.30453 + 7.00189i −0.317617 + 0.352750i
\(395\) −20.0054 2.36284i −1.00658 0.118887i
\(396\) 0.642425 + 0.713486i 0.0322831 + 0.0358540i
\(397\) −25.8818 + 5.50135i −1.29897 + 0.276105i −0.804949 0.593344i \(-0.797807\pi\)
−0.494022 + 0.869449i \(0.664474\pi\)
\(398\) −7.38201 + 5.36335i −0.370027 + 0.268840i
\(399\) −0.656636 0.328929i −0.0328729 0.0164670i
\(400\) 13.0861 13.8034i 0.654307 0.690170i
\(401\) 17.2314 + 29.8457i 0.860497 + 1.49042i 0.871450 + 0.490484i \(0.163180\pi\)
−0.0109534 + 0.999940i \(0.503487\pi\)
\(402\) −1.19256 11.3465i −0.0594796 0.565911i
\(403\) 7.84548 + 8.71329i 0.390811 + 0.434040i
\(404\) −0.913052 + 0.194075i −0.0454260 + 0.00965560i
\(405\) −5.95933 3.54346i −0.296122 0.176076i
\(406\) −14.3002 + 5.60198i −0.709707 + 0.278022i
\(407\) 16.4738 0.816575
\(408\) 9.95526 11.0564i 0.492859 0.547375i
\(409\) 0.322933 0.143779i 0.0159680 0.00710941i −0.398737 0.917065i \(-0.630551\pi\)
0.414705 + 0.909956i \(0.363885\pi\)
\(410\) −4.73351 23.7667i −0.233772 1.17375i
\(411\) 16.8215 + 7.48942i 0.829744 + 0.369426i
\(412\) −0.426072 0.309559i −0.0209910 0.0152509i
\(413\) −10.4926 0.477870i −0.516305 0.0235144i
\(414\) −1.83751 + 1.33503i −0.0903085 + 0.0656130i
\(415\) −0.387180 + 30.1387i −0.0190059 + 1.47945i
\(416\) −2.79937 + 1.24636i −0.137251 + 0.0611079i
\(417\) −7.06426 1.50155i −0.345938 0.0735314i
\(418\) 1.01855 + 1.76418i 0.0498188 + 0.0862887i
\(419\) 4.03100 + 12.4061i 0.196927 + 0.606079i 0.999949 + 0.0101292i \(0.00322428\pi\)
−0.803022 + 0.595950i \(0.796776\pi\)
\(420\) −0.364702 + 0.291725i −0.0177956 + 0.0142347i
\(421\) 2.49426 7.67653i 0.121563 0.374131i −0.871697 0.490046i \(-0.836980\pi\)
0.993259 + 0.115915i \(0.0369800\pi\)
\(422\) −13.5706 + 2.88452i −0.660606 + 0.140416i
\(423\) −1.03974 9.89248i −0.0505540 0.480989i
\(424\) −8.00061 + 13.8575i −0.388544 + 0.672978i
\(425\) 19.8214 + 23.1850i 0.961479 + 1.12464i
\(426\) −12.2535 −0.593686
\(427\) 15.1173 + 18.4091i 0.731576 + 0.890878i
\(428\) 0.0147829 0.0454972i 0.000714560 0.00219919i
\(429\) 21.4409 4.55739i 1.03517 0.220033i
\(430\) 22.9038 + 21.1617i 1.10452 + 1.02051i
\(431\) 19.8254 + 4.21402i 0.954956 + 0.202982i 0.658935 0.752200i \(-0.271007\pi\)
0.296020 + 0.955182i \(0.404340\pi\)
\(432\) 8.48603 + 14.6982i 0.408284 + 0.707169i
\(433\) 3.13997 + 9.66384i 0.150897 + 0.464414i 0.997722 0.0674577i \(-0.0214888\pi\)
−0.846825 + 0.531872i \(0.821489\pi\)
\(434\) 3.40108 + 6.56350i 0.163257 + 0.315058i
\(435\) −7.89779 + 0.727649i −0.378670 + 0.0348881i
\(436\) 0.320411 + 0.142656i 0.0153449 + 0.00683200i
\(437\) 0.216079 0.0962046i 0.0103365 0.00460209i
\(438\) 4.07008 1.81212i 0.194476 0.0865863i
\(439\) 4.14303 + 1.84460i 0.197736 + 0.0880378i 0.503216 0.864161i \(-0.332150\pi\)
−0.305480 + 0.952199i \(0.598817\pi\)
\(440\) 28.8621 2.65916i 1.37595 0.126770i
\(441\) 13.7606 8.19800i 0.655268 0.390381i
\(442\) 15.0817 + 46.4167i 0.717363 + 2.20782i
\(443\) −0.813208 1.40852i −0.0386367 0.0669207i 0.846060 0.533087i \(-0.178968\pi\)
−0.884697 + 0.466166i \(0.845635\pi\)
\(444\) −0.283676 0.0602971i −0.0134626 0.00286157i
\(445\) 4.25412 + 3.93054i 0.201665 + 0.186326i
\(446\) 2.58719 0.549925i 0.122507 0.0260397i
\(447\) 1.87311 5.76484i 0.0885950 0.272667i
\(448\) −21.7657 + 3.60029i −1.02833 + 0.170098i
\(449\) −35.2525 −1.66367 −0.831834 0.555025i \(-0.812709\pi\)
−0.831834 + 0.555025i \(0.812709\pi\)
\(450\) −14.5917 + 6.05243i −0.687860 + 0.285314i
\(451\) 17.5983 30.4811i 0.828671 1.43530i
\(452\) 0.0774039 + 0.736449i 0.00364077 + 0.0346396i
\(453\) 0.305092 0.0648493i 0.0143345 0.00304688i
\(454\) 3.81438 11.7395i 0.179018 0.550960i
\(455\) −5.15913 33.8878i −0.241864 1.58869i
\(456\) −0.247955 0.763127i −0.0116115 0.0357367i
\(457\) −8.80051 15.2429i −0.411671 0.713035i 0.583402 0.812184i \(-0.301721\pi\)
−0.995073 + 0.0991491i \(0.968388\pi\)
\(458\) −17.8519 3.79454i −0.834165 0.177307i
\(459\) −24.8647 + 11.0705i −1.16059 + 0.516726i
\(460\) 0.00193211 0.150399i 9.00852e−5 0.00701238i
\(461\) 25.6978 18.6705i 1.19687 0.869574i 0.202893 0.979201i \(-0.434966\pi\)
0.993973 + 0.109627i \(0.0349656\pi\)
\(462\) 13.8058 + 0.628769i 0.642305 + 0.0292530i
\(463\) −1.10512 0.802914i −0.0513591 0.0373146i 0.561810 0.827267i \(-0.310105\pi\)
−0.613169 + 0.789952i \(0.710105\pi\)
\(464\) −14.6106 6.50504i −0.678278 0.301989i
\(465\) 0.745673 + 3.74398i 0.0345798 + 0.173623i
\(466\) 14.6264 6.51210i 0.677556 0.301667i
\(467\) 9.17571 10.1907i 0.424601 0.471567i −0.492448 0.870342i \(-0.663898\pi\)
0.917049 + 0.398775i \(0.130564\pi\)
\(468\) 1.24056 0.0573447
\(469\) −20.2492 16.1691i −0.935020 0.746621i
\(470\) −11.5358 6.85930i −0.532109 0.316396i
\(471\) −2.63448 + 0.559977i −0.121391 + 0.0258024i
\(472\) −7.67875 8.52812i −0.353443 0.392539i
\(473\) 4.73415 + 45.0424i 0.217676 + 2.07105i
\(474\) −5.24714 9.08831i −0.241009 0.417440i
\(475\) 1.61740 0.300584i 0.0742114 0.0137917i
\(476\) −0.0893668 1.50762i −0.00409612 0.0691017i
\(477\) 10.2473 7.44513i 0.469194 0.340889i
\(478\) −8.57596 + 1.82288i −0.392255 + 0.0833765i
\(479\) −16.0460 17.8209i −0.733161 0.814257i 0.255119 0.966910i \(-0.417885\pi\)
−0.988280 + 0.152652i \(0.951219\pi\)
\(480\) −0.990818 0.117026i −0.0452245 0.00534147i
\(481\) 14.2432 15.8187i 0.649436 0.721272i
\(482\) 6.79195 0.309365
\(483\) 0.240166 1.58659i 0.0109279 0.0721921i
\(484\) 0.689440 + 0.500907i 0.0313382 + 0.0227685i
\(485\) −14.5481 + 19.4922i −0.660597 + 0.885097i
\(486\) −2.30928 21.9713i −0.104751 0.996640i
\(487\) 20.3347 9.05357i 0.921451 0.410256i 0.109503 0.993986i \(-0.465074\pi\)
0.811948 + 0.583730i \(0.198407\pi\)
\(488\) −2.72043 + 25.8832i −0.123148 + 1.17168i
\(489\) 14.9625 10.8709i 0.676628 0.491599i
\(490\) 2.24081 21.4954i 0.101229 0.971065i
\(491\) −18.3293 13.3170i −0.827190 0.600988i 0.0915732 0.995798i \(-0.470810\pi\)
−0.918763 + 0.394810i \(0.870810\pi\)
\(492\) −0.414606 + 0.460466i −0.0186919 + 0.0207594i
\(493\) 12.8241 22.2119i 0.577567 1.00038i
\(494\) 2.57466 + 0.547262i 0.115840 + 0.0246225i
\(495\) −21.7279 7.36972i −0.976597 0.331244i
\(496\) −2.37880 + 7.32120i −0.106811 + 0.328732i
\(497\) −19.5443 + 19.8138i −0.876680 + 0.888769i
\(498\) −12.7033 + 9.22947i −0.569248 + 0.413583i
\(499\) −7.86655 13.6253i −0.352155 0.609951i 0.634472 0.772946i \(-0.281218\pi\)
−0.986627 + 0.162995i \(0.947884\pi\)
\(500\) 0.256767 1.01413i 0.0114830 0.0453535i
\(501\) −4.54023 + 7.86391i −0.202843 + 0.351334i
\(502\) 1.91326 + 0.851839i 0.0853930 + 0.0380194i
\(503\) −0.682974 + 2.10198i −0.0304523 + 0.0937226i −0.965127 0.261780i \(-0.915690\pi\)
0.934675 + 0.355503i \(0.115690\pi\)
\(504\) 16.9346 + 4.41355i 0.754327 + 0.196595i
\(505\) 16.7678 14.7122i 0.746157 0.654684i
\(506\) −2.97827 + 3.30770i −0.132400 + 0.147045i
\(507\) 8.67776 15.0303i 0.385393 0.667520i
\(508\) −0.865254 0.183915i −0.0383894 0.00815993i
\(509\) 1.98643 18.8996i 0.0880469 0.837710i −0.857993 0.513661i \(-0.828289\pi\)
0.946040 0.324049i \(-0.105044\pi\)
\(510\) −3.50322 + 15.4996i −0.155125 + 0.686333i
\(511\) 3.56157 9.47156i 0.157555 0.418997i
\(512\) −19.4202 14.1096i −0.858259 0.623561i
\(513\) −0.153439 + 1.45988i −0.00677451 + 0.0644552i
\(514\) 1.84940 + 17.5959i 0.0815735 + 0.776120i
\(515\) 12.4988 + 1.47624i 0.550764 + 0.0650509i
\(516\) 0.0833424 0.792950i 0.00366894 0.0349077i
\(517\) −6.02359 18.5387i −0.264917 0.815331i
\(518\) 11.2052 7.38629i 0.492326 0.324535i
\(519\) 2.01003 + 6.18623i 0.0882304 + 0.271545i
\(520\) 22.4008 30.0135i 0.982339 1.31618i
\(521\) 3.82307 + 4.24595i 0.167492 + 0.186018i 0.821047 0.570860i \(-0.193390\pi\)
−0.653556 + 0.756878i \(0.726723\pi\)
\(522\) 8.88800 + 9.87112i 0.389017 + 0.432047i
\(523\) −3.65009 1.62512i −0.159607 0.0710617i 0.325378 0.945584i \(-0.394508\pi\)
−0.484985 + 0.874522i \(0.661175\pi\)
\(524\) 0.685781 0.0299585
\(525\) 4.19526 10.3422i 0.183096 0.451370i
\(526\) −1.95017 −0.0850315
\(527\) −11.2778 5.02121i −0.491270 0.218727i
\(528\) 9.62977 + 10.6949i 0.419082 + 0.465438i
\(529\) −15.0442 16.7083i −0.654095 0.726447i
\(530\) 0.219535 17.0889i 0.00953598 0.742296i
\(531\) 2.80713 + 8.63946i 0.121819 + 0.374921i
\(532\) −0.0728259 0.0364807i −0.00315740 0.00158164i
\(533\) −14.0536 43.2525i −0.608729 1.87347i
\(534\) −0.315396 + 3.00080i −0.0136485 + 0.129857i
\(535\) 0.223305 + 1.12120i 0.00965432 + 0.0484737i
\(536\) −2.95935 28.1564i −0.127825 1.21617i
\(537\) −0.263852 + 2.51038i −0.0113860 + 0.108331i
\(538\) −6.01913 4.37315i −0.259503 0.188540i
\(539\) 23.0368 21.3209i 0.992266 0.918355i
\(540\) 0.802345 + 0.477080i 0.0345274 + 0.0205302i
\(541\) −4.13418 + 39.3340i −0.177742 + 1.69110i 0.434690 + 0.900580i \(0.356858\pi\)
−0.612432 + 0.790523i \(0.709809\pi\)
\(542\) −6.97046 1.48162i −0.299407 0.0636409i
\(543\) 4.65030 8.05456i 0.199564 0.345654i
\(544\) 2.15888 2.39768i 0.0925611 0.102800i
\(545\) −8.34631 + 0.768973i −0.357517 + 0.0329392i
\(546\) 12.5403 12.7132i 0.536675 0.544075i
\(547\) −4.12875 + 12.7070i −0.176533 + 0.543312i −0.999700 0.0244869i \(-0.992205\pi\)
0.823167 + 0.567799i \(0.192205\pi\)
\(548\) 1.86563 + 0.830633i 0.0796959 + 0.0354829i
\(549\) 10.3009 17.8416i 0.439631 0.761463i
\(550\) −25.5040 + 17.5468i −1.08750 + 0.748197i
\(551\) −0.691631 1.19794i −0.0294645 0.0510340i
\(552\) 1.41837 1.03051i 0.0603698 0.0438612i
\(553\) −23.0648 6.01121i −0.980813 0.255623i
\(554\) −7.83835 + 24.1240i −0.333020 + 1.02493i
\(555\) 6.61834 2.05682i 0.280933 0.0873072i
\(556\) −0.783479 0.166534i −0.0332269 0.00706260i
\(557\) −4.47486 + 7.75068i −0.189606 + 0.328407i −0.945119 0.326727i \(-0.894054\pi\)
0.755513 + 0.655134i \(0.227388\pi\)
\(558\) 4.27803 4.75123i 0.181103 0.201136i
\(559\) 47.3445 + 34.3978i 2.00246 + 1.45487i
\(560\) 17.5746 14.0579i 0.742663 0.594056i
\(561\) −18.6716 + 13.5657i −0.788316 + 0.572745i
\(562\) 1.52103 14.4716i 0.0641607 0.610448i
\(563\) 15.9800 7.11477i 0.673478 0.299852i −0.0413574 0.999144i \(-0.513168\pi\)
0.714836 + 0.699293i \(0.246502\pi\)
\(564\) 0.0358700 + 0.341280i 0.00151040 + 0.0143705i
\(565\) −10.2168 14.4490i −0.429825 0.607873i
\(566\) 23.2056 + 16.8598i 0.975403 + 0.708672i
\(567\) −6.41053 5.11886i −0.269217 0.214972i
\(568\) −30.4073 −1.27586
\(569\) 23.0921 25.6463i 0.968070 1.07515i −0.0290700 0.999577i \(-0.509255\pi\)
0.997140 0.0755735i \(-0.0240788\pi\)
\(570\) 0.629467 + 0.581588i 0.0263655 + 0.0243600i
\(571\) −9.04589 10.0465i −0.378559 0.420432i 0.523513 0.852017i \(-0.324621\pi\)
−0.902072 + 0.431586i \(0.857954\pi\)
\(572\) 2.37795 0.505449i 0.0994272 0.0211339i
\(573\) −13.9536 + 10.1379i −0.582920 + 0.423516i
\(574\) −1.69669 28.6232i −0.0708184 1.19471i
\(575\) 1.71666 + 3.15802i 0.0715898 + 0.131699i
\(576\) 9.54010 + 16.5239i 0.397504 + 0.688498i
\(577\) −0.627190 5.96732i −0.0261103 0.248423i −0.999790 0.0205013i \(-0.993474\pi\)
0.973680 0.227921i \(-0.0731929\pi\)
\(578\) −18.6785 20.7446i −0.776924 0.862862i
\(579\) −17.7010 + 3.76247i −0.735630 + 0.156363i
\(580\) −0.875924 + 0.0807017i −0.0363708 + 0.00335096i
\(581\) −5.33768 + 35.2619i −0.221444 + 1.46291i
\(582\) −12.6710 −0.525229
\(583\) 16.6091 18.4463i 0.687880 0.763968i
\(584\) 10.0999 4.49678i 0.417938 0.186078i
\(585\) −25.8626 + 14.4921i −1.06929 + 0.599173i
\(586\) −7.02658 3.12844i −0.290265 0.129234i
\(587\) 28.7281 + 20.8722i 1.18574 + 0.861488i 0.992807 0.119724i \(-0.0382010\pi\)
0.192930 + 0.981213i \(0.438201\pi\)
\(588\) −0.474728 + 0.282823i −0.0195774 + 0.0116634i
\(589\) −0.538644 + 0.391348i −0.0221944 + 0.0161252i
\(590\) 11.6073 + 3.93699i 0.477865 + 0.162083i
\(591\) −5.25936 + 2.34162i −0.216341 + 0.0963213i
\(592\) 13.6700 + 2.90566i 0.561835 + 0.119422i
\(593\) −1.01246 1.75364i −0.0415768 0.0720132i 0.844488 0.535574i \(-0.179905\pi\)
−0.886065 + 0.463561i \(0.846571\pi\)
\(594\) −8.53601 26.2712i −0.350237 1.07792i
\(595\) 19.4750 + 30.3863i 0.798396 + 1.24572i
\(596\) 0.207742 0.639364i 0.00850944 0.0261894i
\(597\) −5.45359 + 1.15920i −0.223201 + 0.0474428i
\(598\) 0.601163 + 5.71969i 0.0245834 + 0.233895i
\(599\) −9.60033 + 16.6283i −0.392259 + 0.679412i −0.992747 0.120221i \(-0.961640\pi\)
0.600488 + 0.799634i \(0.294973\pi\)
\(600\) 11.2633 4.67187i 0.459824 0.190728i
\(601\) −48.2192 −1.96690 −0.983452 0.181170i \(-0.942012\pi\)
−0.983452 + 0.181170i \(0.942012\pi\)
\(602\) 23.4156 + 28.5144i 0.954348 + 1.16216i
\(603\) −6.92540 + 21.3142i −0.282024 + 0.867981i
\(604\) 0.0338370 0.00719227i 0.00137681 0.000292649i
\(605\) −20.2247 2.38875i −0.822252 0.0971165i
\(606\) 11.3670 + 2.41613i 0.461752 + 0.0981484i
\(607\) 14.3402 + 24.8380i 0.582051 + 1.00814i 0.995236 + 0.0974954i \(0.0310831\pi\)
−0.413184 + 0.910647i \(0.635584\pi\)
\(608\) −0.0537710 0.165490i −0.00218070 0.00671151i
\(609\) −9.37465 0.426957i −0.379880 0.0173012i
\(610\) −10.9790 25.5372i −0.444527 1.03397i
\(611\) −23.0095 10.2445i −0.930866 0.414448i
\(612\) −1.19325 + 0.531271i −0.0482345 + 0.0214754i
\(613\) −16.5465 + 7.36699i −0.668308 + 0.297550i −0.712705 0.701464i \(-0.752530\pi\)
0.0443968 + 0.999014i \(0.485863\pi\)
\(614\) 23.2220 + 10.3391i 0.937163 + 0.417252i
\(615\) 3.26441 14.4430i 0.131634 0.582398i
\(616\) 34.2592 + 1.56029i 1.38034 + 0.0628660i
\(617\) 5.43643 + 16.7316i 0.218862 + 0.673589i 0.998857 + 0.0478027i \(0.0152219\pi\)
−0.779994 + 0.625787i \(0.784778\pi\)
\(618\) 3.27827 + 5.67813i 0.131871 + 0.228408i
\(619\) 13.6810 + 2.90800i 0.549888 + 0.116882i 0.474473 0.880270i \(-0.342639\pi\)
0.0754146 + 0.997152i \(0.475972\pi\)
\(620\) 0.0827008 + 0.415235i 0.00332134 + 0.0166762i
\(621\) −3.13724 + 0.666842i −0.125893 + 0.0267594i
\(622\) 13.3314 41.0297i 0.534539 1.64514i
\(623\) 4.34918 + 5.29622i 0.174246 + 0.212189i
\(624\) 18.5956 0.744419
\(625\) 6.49405 + 24.1418i 0.259762 + 0.965673i
\(626\) −4.95589 + 8.58385i −0.198077 + 0.343080i
\(627\) 0.130109 + 1.23791i 0.00519606 + 0.0494372i
\(628\) −0.292184 + 0.0621056i −0.0116594 + 0.00247828i
\(629\) −6.92576 + 21.3153i −0.276148 + 0.849896i
\(630\) −18.0832 + 4.72932i −0.720454 + 0.188421i
\(631\) −3.59361 11.0600i −0.143059 0.440291i 0.853697 0.520770i \(-0.174355\pi\)
−0.996756 + 0.0804789i \(0.974355\pi\)
\(632\) −13.0208 22.5527i −0.517940 0.897098i
\(633\) −8.29202 1.76252i −0.329578 0.0700540i
\(634\) −13.2255 + 5.88837i −0.525251 + 0.233857i
\(635\) 20.1870 6.27362i 0.801095 0.248961i
\(636\) −0.353523 + 0.256850i −0.0140181 + 0.0101847i
\(637\) −0.555440 40.5548i −0.0220073 1.60684i
\(638\) 21.0588 + 15.3001i 0.833725 + 0.605736i
\(639\) 21.9891 + 9.79019i 0.869876 + 0.387294i
\(640\) 23.2177 + 2.74225i 0.917760 + 0.108397i
\(641\) −35.5808 + 15.8416i −1.40536 + 0.625705i −0.962597 0.270936i \(-0.912667\pi\)
−0.442759 + 0.896641i \(0.646000\pi\)
\(642\) −0.398509 + 0.442589i −0.0157279 + 0.0174676i
\(643\) 37.0215 1.45999 0.729993 0.683455i \(-0.239523\pi\)
0.729993 + 0.683455i \(0.239523\pi\)
\(644\) 0.0266362 0.175964i 0.00104961 0.00693396i
\(645\) 7.52568 + 17.5047i 0.296323 + 0.689247i
\(646\) −2.71086 + 0.576211i −0.106657 + 0.0226707i
\(647\) 32.6067 + 36.2134i 1.28190 + 1.42369i 0.854346 + 0.519705i \(0.173958\pi\)
0.427555 + 0.903990i \(0.359375\pi\)
\(648\) −0.936879 8.91380i −0.0368041 0.350167i
\(649\) 8.90087 + 15.4168i 0.349390 + 0.605161i
\(650\) −5.20176 + 39.6609i −0.204030 + 1.55563i
\(651\) 0.267280 + 4.50903i 0.0104755 + 0.176723i
\(652\) 1.65945 1.20566i 0.0649893 0.0472175i
\(653\) −32.4251 + 6.89217i −1.26889 + 0.269711i −0.792690 0.609625i \(-0.791320\pi\)
−0.476202 + 0.879336i \(0.657987\pi\)
\(654\) −2.92172 3.24490i −0.114248 0.126885i
\(655\) −14.2969 + 8.01123i −0.558626 + 0.313025i
\(656\) 19.9794 22.1894i 0.780066 0.866351i
\(657\) −8.75163 −0.341434
\(658\) −12.4093 9.90890i −0.483763 0.386289i
\(659\) −12.6920 9.22127i −0.494409 0.359210i 0.312468 0.949928i \(-0.398844\pi\)
−0.806878 + 0.590719i \(0.798844\pi\)
\(660\) 0.749591 + 0.254248i 0.0291778 + 0.00989658i
\(661\) 1.19995 + 11.4168i 0.0466728 + 0.444062i 0.992757 + 0.120141i \(0.0383346\pi\)
−0.946084 + 0.323921i \(0.894999\pi\)
\(662\) −42.4916 + 18.9185i −1.65148 + 0.735287i
\(663\) −3.11719 + 29.6581i −0.121062 + 1.15183i
\(664\) −31.5233 + 22.9030i −1.22334 + 0.888809i
\(665\) 1.94441 0.0902105i 0.0754010 0.00349821i
\(666\) −9.39030 6.82245i −0.363867 0.264365i
\(667\) 2.02235 2.24605i 0.0783059 0.0869675i
\(668\) −0.503546 + 0.872167i −0.0194828 + 0.0337452i
\(669\) 1.58085 + 0.336020i 0.0611192 + 0.0129913i
\(670\) 17.4580 + 24.6897i 0.674462 + 0.953848i
\(671\) 12.4758 38.3966i 0.481623 1.48228i
\(672\) −1.14234 0.297721i −0.0440668 0.0114848i
\(673\) 14.5048 10.5383i 0.559117 0.406222i −0.272019 0.962292i \(-0.587691\pi\)
0.831136 + 0.556070i \(0.187691\pi\)
\(674\) 0.540763 + 0.936628i 0.0208294 + 0.0360776i
\(675\) −22.3002 0.573058i −0.858334 0.0220570i
\(676\) 0.962428 1.66697i 0.0370165 0.0641144i
\(677\) 5.52079 + 2.45801i 0.212181 + 0.0944692i 0.510075 0.860130i \(-0.329618\pi\)
−0.297894 + 0.954599i \(0.596284\pi\)
\(678\) 2.84879 8.76767i 0.109407 0.336720i
\(679\) −20.2100 + 20.4887i −0.775590 + 0.786285i
\(680\) −8.69327 + 38.4623i −0.333372 + 1.47496i
\(681\) 5.04677 5.60501i 0.193393 0.214784i
\(682\) 6.26447 10.8504i 0.239879 0.415483i
\(683\) 2.40969 + 0.512195i 0.0922042 + 0.0195986i 0.253783 0.967261i \(-0.418325\pi\)
−0.161579 + 0.986860i \(0.551659\pi\)
\(684\) −0.00736353 + 0.0700593i −0.000281552 + 0.00267879i
\(685\) −48.5974 + 4.47743i −1.85681 + 0.171074i
\(686\) 6.10964 24.8310i 0.233267 0.948052i
\(687\) −9.02192 6.55481i −0.344208 0.250082i
\(688\) −4.01619 + 38.2115i −0.153116 + 1.45680i
\(689\) −3.35255 31.8974i −0.127722 1.21519i
\(690\) −0.783539 + 1.70072i −0.0298288 + 0.0647453i
\(691\) −1.73108 + 16.4701i −0.0658535 + 0.626554i 0.910965 + 0.412484i \(0.135339\pi\)
−0.976818 + 0.214070i \(0.931328\pi\)
\(692\) 0.222927 + 0.686099i 0.00847441 + 0.0260816i
\(693\) −24.2723 12.1587i −0.922029 0.461872i
\(694\) −2.41651 7.43725i −0.0917295 0.282314i
\(695\) 18.2791 5.68070i 0.693366 0.215481i
\(696\) −6.86064 7.61951i −0.260052 0.288817i
\(697\) 32.0407 + 35.5848i 1.21363 + 1.34787i
\(698\) 37.0371 + 16.4900i 1.40187 + 0.624155i
\(699\) 9.78294 0.370025
\(700\) 0.465285 1.14703i 0.0175861 0.0433535i
\(701\) 30.3357 1.14576 0.572881 0.819639i \(-0.305826\pi\)
0.572881 + 0.819639i \(0.305826\pi\)
\(702\) −32.6068 14.5175i −1.23066 0.547926i
\(703\) 0.808806 + 0.898270i 0.0305047 + 0.0338789i
\(704\) 25.0194 + 27.7868i 0.942952 + 1.04725i
\(705\) −4.73461 6.69585i −0.178316 0.252180i
\(706\) −9.31051 28.6548i −0.350406 1.07844i
\(707\) 22.0370 14.5265i 0.828788 0.546326i
\(708\) −0.0968432 0.298053i −0.00363959 0.0112015i
\(709\) 0.103365 0.983449i 0.00388194 0.0369342i −0.992409 0.122978i \(-0.960756\pi\)
0.996291 + 0.0860433i \(0.0274224\pi\)
\(710\) 28.3321 15.8758i 1.06329 0.595809i
\(711\) 2.15478 + 20.5014i 0.0808106 + 0.768862i
\(712\) −0.782658 + 7.44650i −0.0293314 + 0.279069i
\(713\) −1.17691 0.855075i −0.0440756 0.0320228i
\(714\) −6.61767 + 17.5989i −0.247660 + 0.658621i
\(715\) −43.6700 + 38.3164i −1.63317 + 1.43295i
\(716\) −0.0292631 + 0.278420i −0.00109362 + 0.0104051i
\(717\) −5.24016 1.11383i −0.195697 0.0415967i
\(718\) −14.1874 + 24.5734i −0.529470 + 0.917069i
\(719\) −27.6836 + 30.7457i −1.03242 + 1.14662i −0.0433705 + 0.999059i \(0.513810\pi\)
−0.989053 + 0.147563i \(0.952857\pi\)
\(720\) −16.7301 9.94782i −0.623493 0.370733i
\(721\) 14.4102 + 3.75564i 0.536665 + 0.139867i
\(722\) 8.06056 24.8078i 0.299983 0.923252i
\(723\) 3.79128 + 1.68799i 0.140999 + 0.0627769i
\(724\) 0.515754 0.893311i 0.0191678 0.0331997i
\(725\) 17.3182 11.9149i 0.643181 0.442508i
\(726\) −5.30467 9.18796i −0.196875 0.340997i
\(727\) −7.43646 + 5.40290i −0.275803 + 0.200383i −0.717085 0.696986i \(-0.754524\pi\)
0.441282 + 0.897369i \(0.354524\pi\)
\(728\) 31.1188 31.5479i 1.15334 1.16924i
\(729\) 1.29699 3.99173i 0.0480367 0.147842i
\(730\) −7.06287 + 9.46314i −0.261408 + 0.350247i
\(731\) −60.2703 12.8108i −2.22918 0.473826i
\(732\) −0.355370 + 0.615518i −0.0131348 + 0.0227502i
\(733\) 10.2382 11.3707i 0.378157 0.419986i −0.523780 0.851854i \(-0.675479\pi\)
0.901937 + 0.431868i \(0.142145\pi\)
\(734\) 17.0911 + 12.4174i 0.630844 + 0.458335i
\(735\) 6.59304 11.4419i 0.243188 0.422041i
\(736\) 0.307585 0.223474i 0.0113377 0.00823735i
\(737\) −4.59071 + 43.6776i −0.169101 + 1.60889i
\(738\) −22.6547 + 10.0865i −0.833932 + 0.371290i
\(739\) −4.20983 40.0539i −0.154861 1.47341i −0.745519 0.666484i \(-0.767799\pi\)
0.590658 0.806922i \(-0.298868\pi\)
\(740\) 0.734024 0.228117i 0.0269833 0.00838574i
\(741\) 1.30117 + 0.945358i 0.0477998 + 0.0347286i
\(742\) 3.02651 19.9938i 0.111107 0.733996i
\(743\) 18.1378 0.665413 0.332706 0.943030i \(-0.392038\pi\)
0.332706 + 0.943030i \(0.392038\pi\)
\(744\) −3.30221 + 3.66747i −0.121065 + 0.134456i
\(745\) 3.13807 + 15.7560i 0.114970 + 0.577256i
\(746\) 21.4365 + 23.8076i 0.784846 + 0.871660i
\(747\) 30.1702 6.41288i 1.10387 0.234635i
\(748\) −2.07082 + 1.50454i −0.0757168 + 0.0550115i
\(749\) 0.0800418 + 1.35031i 0.00292466 + 0.0493392i
\(750\) −8.05546 + 10.2337i −0.294144 + 0.373682i
\(751\) −20.2543 35.0816i −0.739092 1.28014i −0.952905 0.303270i \(-0.901922\pi\)
0.213813 0.976875i \(-0.431412\pi\)
\(752\) −1.72854 16.4460i −0.0630334 0.599723i
\(753\) 0.856281 + 0.950996i 0.0312046 + 0.0346562i
\(754\) 32.8991 6.99292i 1.19812 0.254667i
\(755\) −0.621401 + 0.545222i −0.0226151 + 0.0198427i
\(756\) 0.863093 + 0.689187i 0.0313904 + 0.0250655i
\(757\) −24.9165 −0.905607 −0.452803 0.891610i \(-0.649576\pi\)
−0.452803 + 0.891610i \(0.649576\pi\)
\(758\) 17.1015 18.9931i 0.621153 0.689861i
\(759\) −2.48453 + 1.10619i −0.0901828 + 0.0401520i
\(760\) 1.56203 + 1.44321i 0.0566606 + 0.0523509i
\(761\) −36.2547 16.1416i −1.31423 0.585134i −0.374557 0.927204i \(-0.622205\pi\)
−0.939674 + 0.342070i \(0.888872\pi\)
\(762\) 8.90936 + 6.47303i 0.322752 + 0.234493i
\(763\) −9.90704 0.451204i −0.358659 0.0163347i
\(764\) −1.54756 + 1.12437i −0.0559887 + 0.0406782i
\(765\) 18.6703 25.0152i 0.675024 0.904428i
\(766\) −16.0850 + 7.16150i −0.581174 + 0.258755i
\(767\) 22.4994 + 4.78240i 0.812408 + 0.172683i
\(768\) −0.945191 1.63712i −0.0341066 0.0590744i
\(769\) −0.311588 0.958970i −0.0112362 0.0345813i 0.945281 0.326257i \(-0.105787\pi\)
−0.956517 + 0.291675i \(0.905787\pi\)
\(770\) −32.7358 + 16.4332i −1.17972 + 0.592210i
\(771\) −3.34072 + 10.2817i −0.120313 + 0.370285i
\(772\) −1.96318 + 0.417286i −0.0706563 + 0.0150185i
\(773\) −3.79249 36.0832i −0.136407 1.29782i −0.821853 0.569699i \(-0.807060\pi\)
0.685447 0.728123i \(-0.259607\pi\)
\(774\) 15.9553 27.6354i 0.573502 0.993335i
\(775\) −6.57485 7.69056i −0.236176 0.276253i
\(776\) −31.4431 −1.12874
\(777\) 8.09044 1.33825i 0.290243 0.0480095i
\(778\) −8.44894 + 26.0032i −0.302909 + 0.932259i
\(779\) 2.52607 0.536932i 0.0905057 0.0192376i
\(780\) 0.892234 0.499961i 0.0319471 0.0179015i
\(781\) 46.1386 + 9.80706i 1.65097 + 0.350924i
\(782\) −3.02771 5.24415i −0.108271 0.187530i
\(783\) 5.79626 + 17.8391i 0.207142 + 0.637516i
\(784\) 22.8767 13.6289i 0.817024 0.486748i
\(785\) 5.36583 4.70802i 0.191515 0.168036i
\(786\) −7.79947 3.47255i −0.278198 0.123862i
\(787\) −21.3276 + 9.49565i −0.760246 + 0.338484i −0.749977 0.661464i \(-0.769936\pi\)
−0.0102693 + 0.999947i \(0.503269\pi\)
\(788\) −0.583303 + 0.259703i −0.0207793 + 0.00925154i
\(789\) −1.08859 0.484671i −0.0387548 0.0172548i
\(790\) 23.9071 + 14.2153i 0.850577 + 0.505759i
\(791\) −9.63339 18.5908i −0.342524 0.661012i
\(792\) −9.16556 28.2087i −0.325684 1.00235i
\(793\) −26.0832 45.1775i −0.926242 1.60430i
\(794\) 35.7359 + 7.59591i 1.26822 + 0.269569i
\(795\) 4.36962 9.48452i 0.154974 0.336381i
\(796\) −0.604844 + 0.128564i −0.0214381 + 0.00455682i
\(797\) 6.64062 20.4377i 0.235223 0.723942i −0.761869 0.647731i \(-0.775718\pi\)
0.997092 0.0762104i \(-0.0242821\pi\)
\(798\) 0.643533 + 0.783663i 0.0227808 + 0.0277414i
\(799\) 26.5194 0.938190
\(800\) 2.44255 1.01313i 0.0863571 0.0358197i
\(801\) 2.96352 5.13297i 0.104711 0.181365i
\(802\) −4.97389 47.3234i −0.175634 1.67105i
\(803\) −16.7755 + 3.56574i −0.591995 + 0.125832i
\(804\) 0.238919 0.735318i 0.00842604 0.0259327i
\(805\) 1.50030 + 3.97960i 0.0528786 + 0.140262i
\(806\) −5.00267 15.3966i −0.176211 0.542323i
\(807\) −2.27304 3.93702i −0.0800149 0.138590i
\(808\) 28.2072 + 5.99563i 0.992327 + 0.210926i
\(809\) 18.3690 8.17841i 0.645820 0.287537i −0.0575704 0.998341i \(-0.518335\pi\)
0.703390 + 0.710804i \(0.251669\pi\)
\(810\) 5.52690 + 7.81633i 0.194195 + 0.274638i
\(811\) −24.3807 + 17.7136i −0.856123 + 0.622009i −0.926827 0.375488i \(-0.877475\pi\)
0.0707047 + 0.997497i \(0.477475\pi\)
\(812\) −1.03972 0.0473527i −0.0364870 0.00166175i
\(813\) −3.52270 2.55939i −0.123547 0.0897618i
\(814\) −20.7795 9.25161i −0.728320 0.324269i
\(815\) −20.5112 + 44.5208i −0.718476 + 1.55950i
\(816\) −17.8865 + 7.96360i −0.626154 + 0.278782i
\(817\) −2.22361 + 2.46957i −0.0777942 + 0.0863992i
\(818\) −0.488082 −0.0170654
\(819\) −32.6611 + 12.7947i −1.14127 + 0.447084i
\(820\) 0.362048 1.60184i 0.0126433 0.0559386i
\(821\) −7.58856 + 1.61300i −0.264843 + 0.0562940i −0.338419 0.940996i \(-0.609892\pi\)
0.0735763 + 0.997290i \(0.476559\pi\)
\(822\) −17.0120 18.8938i −0.593363 0.658996i
\(823\) −1.78564 16.9892i −0.0622434 0.592207i −0.980541 0.196315i \(-0.937102\pi\)
0.918297 0.395891i \(-0.129564\pi\)
\(824\) 8.13505 + 14.0903i 0.283398 + 0.490859i
\(825\) −18.5973 + 3.45619i −0.647474 + 0.120329i
\(826\) 12.9666 + 6.49534i 0.451164 + 0.226002i
\(827\) 12.9888 9.43693i 0.451666 0.328154i −0.338587 0.940935i \(-0.609949\pi\)
0.790253 + 0.612781i \(0.209949\pi\)
\(828\) −0.150556 + 0.0320016i −0.00523218 + 0.00111213i
\(829\) 9.53957 + 10.5948i 0.331323 + 0.367972i 0.885671 0.464314i \(-0.153699\pi\)
−0.554348 + 0.832285i \(0.687032\pi\)
\(830\) 17.4142 37.7985i 0.604454 1.31201i
\(831\) −10.3709 + 11.5180i −0.359761 + 0.399555i
\(832\) 48.3137 1.67497
\(833\) 17.9020 + 38.7706i 0.620266 + 1.34332i
\(834\) 8.06734 + 5.86126i 0.279349 + 0.202959i
\(835\) 0.309153 24.0650i 0.0106987 0.832803i
\(836\) 0.0144301 + 0.137293i 0.000499074 + 0.00474838i
\(837\) 8.24775 3.67213i 0.285084 0.126927i
\(838\) 1.88267 17.9124i 0.0650359 0.618775i
\(839\) −15.9924 + 11.6192i −0.552120 + 0.401138i −0.828566 0.559891i \(-0.810843\pi\)
0.276447 + 0.961029i \(0.410843\pi\)
\(840\) 13.9584 3.65056i 0.481612 0.125956i
\(841\) 9.16183 + 6.65646i 0.315925 + 0.229533i
\(842\) −7.45727 + 8.28214i −0.256995 + 0.285421i
\(843\) 4.44563 7.70006i 0.153116 0.265204i
\(844\) −0.919647 0.195477i −0.0316556 0.00672860i
\(845\) −0.590885 + 45.9954i −0.0203271 + 1.58229i
\(846\) −4.24408 + 13.0619i −0.145915 + 0.449079i
\(847\) −23.3177 6.07712i −0.801204 0.208812i
\(848\) 17.0359 12.3773i 0.585016 0.425039i
\(849\) 8.76327 + 15.1784i 0.300755 + 0.520922i
\(850\) −11.9814 40.3763i −0.410960 1.38490i
\(851\) −1.32052 + 2.28721i −0.0452669 + 0.0784045i
\(852\) −0.758602 0.337752i −0.0259893 0.0115712i
\(853\) 16.9930 52.2992i 0.581831 1.79069i −0.0298115 0.999556i \(-0.509491\pi\)
0.611642 0.791135i \(-0.290509\pi\)
\(854\) −8.72993 31.7104i −0.298732 1.08511i
\(855\) −0.664915 1.54659i −0.0227396 0.0528923i
\(856\) −0.988904 + 1.09829i −0.0338000 + 0.0375387i
\(857\) −0.765940 + 1.32665i −0.0261640 + 0.0453174i −0.878811 0.477170i \(-0.841663\pi\)
0.852647 + 0.522488i \(0.174996\pi\)
\(858\) −29.6042 6.29256i −1.01067 0.214824i
\(859\) 0.0477457 0.454270i 0.00162906 0.0154995i −0.993677 0.112275i \(-0.964186\pi\)
0.995306 + 0.0967755i \(0.0308529\pi\)
\(860\) 0.834654 + 1.94140i 0.0284615 + 0.0662013i
\(861\) 6.16655 16.3992i 0.210155 0.558883i
\(862\) −22.6405 16.4493i −0.771138 0.560264i
\(863\) 1.57515 14.9866i 0.0536188 0.510149i −0.934445 0.356107i \(-0.884104\pi\)
0.988064 0.154043i \(-0.0492293\pi\)
\(864\) 0.246639 + 2.34661i 0.00839083 + 0.0798334i
\(865\) −12.6624 11.6993i −0.430536 0.397788i
\(866\) 1.46652 13.9530i 0.0498344 0.474143i
\(867\) −5.27078 16.2218i −0.179005 0.550921i
\(868\) 0.0296434 + 0.500085i 0.00100616 + 0.0169740i
\(869\) 12.4834 + 38.4200i 0.423471 + 1.30331i
\(870\) 10.3706 + 3.51753i 0.351598 + 0.119256i
\(871\) 37.9717 + 42.1719i 1.28662 + 1.42894i
\(872\) −7.25026 8.05223i −0.245525 0.272683i
\(873\) 22.7382 + 10.1237i 0.769571 + 0.342635i
\(874\) −0.326583 −0.0110468
\(875\) 3.69936 + 29.3482i 0.125061 + 0.992149i
\(876\) 0.301922 0.0102010
\(877\) 19.6896 + 8.76639i 0.664871 + 0.296020i 0.711286 0.702902i \(-0.248113\pi\)
−0.0464148 + 0.998922i \(0.514780\pi\)
\(878\) −4.18995 4.65342i −0.141404 0.157045i
\(879\) −3.14475 3.49260i −0.106070 0.117802i
\(880\) −36.1220 12.2519i −1.21767 0.413013i
\(881\) −10.5178 32.3706i −0.354355 1.09059i −0.956382 0.292118i \(-0.905640\pi\)
0.602027 0.798476i \(-0.294360\pi\)
\(882\) −21.9611 + 2.61275i −0.739470 + 0.0879759i
\(883\) 2.83583 + 8.72780i 0.0954334 + 0.293714i 0.987366 0.158454i \(-0.0506509\pi\)
−0.891933 + 0.452168i \(0.850651\pi\)
\(884\) −0.345720 + 3.28931i −0.0116278 + 0.110631i
\(885\) 5.50077 + 5.08237i 0.184906 + 0.170842i
\(886\) 0.234734 + 2.23335i 0.00788606 + 0.0750308i
\(887\) 2.28043 21.6969i 0.0765695 0.728510i −0.887130 0.461520i \(-0.847304\pi\)
0.963699 0.266990i \(-0.0860291\pi\)
\(888\) 7.24837 + 5.26625i 0.243239 + 0.176724i
\(889\) 24.6771 4.08187i 0.827643 0.136902i
\(890\) −3.15862 7.34694i −0.105877 0.246270i
\(891\) −1.45334 + 13.8276i −0.0486886 + 0.463241i
\(892\) 0.175328 + 0.0372671i 0.00587042 + 0.00124780i
\(893\) 0.715127 1.23864i 0.0239308 0.0414494i
\(894\) −5.60018 + 6.21963i −0.187298 + 0.208016i
\(895\) −2.64241 6.14625i −0.0883261 0.205446i
\(896\) 26.7683 + 6.97645i 0.894267 + 0.233067i
\(897\) −1.08593 + 3.34215i −0.0362581 + 0.111591i
\(898\) 44.4662 + 19.7976i 1.48386 + 0.660656i
\(899\) −4.25381 + 7.36781i −0.141872 + 0.245730i
\(900\) −1.07018 0.0275010i −0.0356728 0.000916699i
\(901\) 16.8849 + 29.2454i 0.562516 + 0.974306i
\(902\) −39.3159 + 28.5647i −1.30908 + 0.951100i
\(903\) 5.98402 + 21.7362i 0.199136 + 0.723335i
\(904\) 7.06929 21.7570i 0.235121 0.723628i
\(905\) −0.316648 + 24.6484i −0.0105257 + 0.819340i
\(906\) −0.421251 0.0895397i −0.0139951 0.00297476i
\(907\) −2.58447 + 4.47644i −0.0858160 + 0.148638i −0.905739 0.423837i \(-0.860683\pi\)
0.819923 + 0.572474i \(0.194016\pi\)
\(908\) 0.559725 0.621638i 0.0185751 0.0206298i
\(909\) −18.4678 13.4176i −0.612537 0.445034i
\(910\) −12.5237 + 45.6423i −0.415157 + 1.51303i
\(911\) −21.5602 + 15.6644i −0.714320 + 0.518984i −0.884564 0.466418i \(-0.845544\pi\)
0.170245 + 0.985402i \(0.445544\pi\)
\(912\) −0.110377 + 1.05017i −0.00365496 + 0.0347746i
\(913\) 55.2188 24.5850i 1.82747 0.813644i
\(914\) 2.54029 + 24.1692i 0.0840253 + 0.799447i
\(915\) 0.218180 16.9835i 0.00721281 0.561457i
\(916\) −1.00060 0.726978i −0.0330607 0.0240200i
\(917\) −18.0551 + 7.07293i −0.596232 + 0.233569i
\(918\) 37.5806 1.24035
\(919\) −4.72890 + 5.25198i −0.155992 + 0.173247i −0.816075 0.577946i \(-0.803854\pi\)
0.660083 + 0.751193i \(0.270521\pi\)
\(920\) −1.94436 + 4.22035i −0.0641036 + 0.139141i
\(921\) 10.3930 + 11.5426i 0.342461 + 0.380342i
\(922\) −42.8996 + 9.11859i −1.41282 + 0.300305i
\(923\) 49.3086 35.8248i 1.62301 1.17919i
\(924\) 0.837370 + 0.419464i 0.0275475 + 0.0137993i
\(925\) −12.6378 + 13.3305i −0.415528 + 0.438304i
\(926\) 0.943041 + 1.63340i 0.0309903 + 0.0536767i
\(927\) −1.34625 12.8087i −0.0442166 0.420693i
\(928\) −1.48779 1.65235i −0.0488390 0.0542412i
\(929\) −44.9694 + 9.55854i −1.47540 + 0.313606i −0.874228 0.485516i \(-0.838632\pi\)
−0.601170 + 0.799121i \(0.705299\pi\)
\(930\) 1.16204 5.14129i 0.0381046 0.168589i
\(931\) 2.29360 + 0.209352i 0.0751696 + 0.00686124i
\(932\) 1.08500 0.0355404
\(933\) 17.6386 19.5896i 0.577462 0.641336i
\(934\) −17.2969 + 7.70110i −0.565973 + 0.251988i
\(935\) 25.5958 55.5572i 0.837072 1.81692i
\(936\) −35.0116 15.5882i −1.14439 0.509515i
\(937\) −11.8858 8.63554i −0.388292 0.282111i 0.376463 0.926432i \(-0.377140\pi\)
−0.764755 + 0.644321i \(0.777140\pi\)
\(938\) 16.4611 + 31.7670i 0.537473 + 1.03723i
\(939\) −4.89971 + 3.55985i −0.159896 + 0.116171i
\(940\) −0.525104 0.742620i −0.0171270 0.0242216i
\(941\) 24.9810 11.1222i 0.814356 0.362575i 0.0430771 0.999072i \(-0.486284\pi\)
0.771279 + 0.636497i \(0.219617\pi\)
\(942\) 3.63753 + 0.773180i 0.118517 + 0.0251916i
\(943\) 2.82132 + 4.88666i 0.0918747 + 0.159132i
\(944\) 4.66678 + 14.3629i 0.151891 + 0.467471i
\(945\) −26.0444 4.28533i −0.847226 0.139402i
\(946\) 19.3241 59.4736i 0.628282 1.93365i
\(947\) 35.0819 7.45688i 1.14001 0.242316i 0.401042 0.916060i \(-0.368648\pi\)
0.738965 + 0.673744i \(0.235315\pi\)
\(948\) −0.0743377 0.707276i −0.00241438 0.0229713i
\(949\) −11.0802 + 19.1914i −0.359677 + 0.622979i
\(950\) −2.20894 0.529179i −0.0716674 0.0171688i
\(951\) −8.84592 −0.286849
\(952\) −16.4218 + 43.6717i −0.532233 + 1.41541i
\(953\) −0.303846 + 0.935141i −0.00984253 + 0.0302922i −0.955857 0.293832i \(-0.905069\pi\)
0.946015 + 0.324124i \(0.105069\pi\)
\(954\) −17.1068 + 3.63616i −0.553853 + 0.117725i
\(955\) 19.1281 41.5188i 0.618972 1.34352i
\(956\) −0.581173 0.123532i −0.0187965 0.00399531i
\(957\) 7.95255 + 13.7742i 0.257070 + 0.445258i
\(958\) 10.2317 + 31.4900i 0.330572 + 1.01740i
\(959\) −57.6849 2.62719i −1.86274 0.0848363i
\(960\) 13.5208 + 8.03958i 0.436383 + 0.259476i
\(961\) −24.5790 10.9433i −0.792871 0.353009i
\(962\) −26.8497 + 11.9542i −0.865668 + 0.385420i
\(963\) 1.06874 0.475836i 0.0344398 0.0153336i
\(964\) 0.420481 + 0.187210i 0.0135428 + 0.00602964i
\(965\) 36.0529 31.6331i 1.16058 1.01831i
\(966\) −1.19396 + 1.86639i −0.0384149 + 0.0600500i
\(967\) −18.4039 56.6414i −0.591830 1.82147i −0.569911 0.821706i \(-0.693022\pi\)
−0.0219192 0.999760i \(-0.506978\pi\)
\(968\) −13.1636 22.8000i −0.423093 0.732819i
\(969\) −1.65641 0.352081i −0.0532117 0.0113105i
\(970\) 29.2973 16.4166i 0.940678 0.527107i
\(971\) 50.6814 10.7727i 1.62644 0.345711i 0.697687 0.716403i \(-0.254213\pi\)
0.928756 + 0.370691i \(0.120879\pi\)
\(972\) 0.462644 1.42387i 0.0148393 0.0456707i
\(973\) 22.3449 3.69610i 0.716344 0.118491i
\(974\) −30.7339 −0.984776
\(975\) −12.7605 + 20.8460i −0.408662 + 0.667606i
\(976\) 17.1249 29.6612i 0.548155 0.949433i
\(977\) −5.32241 50.6394i −0.170279 1.62010i −0.662110 0.749406i \(-0.730339\pi\)
0.491831 0.870690i \(-0.336328\pi\)
\(978\) −24.9782 + 5.30929i −0.798716 + 0.169772i
\(979\) 3.58924 11.0465i 0.114713 0.353049i
\(980\) 0.731217 1.26899i 0.0233579 0.0405365i
\(981\) 2.65049 + 8.15736i 0.0846236 + 0.260445i
\(982\) 15.6412 + 27.0913i 0.499129 + 0.864517i
\(983\) −25.7708 5.47776i −0.821962 0.174713i −0.222312 0.974976i \(-0.571360\pi\)
−0.599650 + 0.800262i \(0.704694\pi\)
\(984\) 17.4872 7.78579i 0.557471 0.248202i
\(985\) 9.12664 12.2283i 0.290799 0.389625i
\(986\) −28.6500 + 20.8154i −0.912401 + 0.662898i
\(987\) −4.46424 8.61521i −0.142098 0.274225i
\(988\) 0.144310 + 0.104847i 0.00459111 + 0.00333564i
\(989\) −6.63314 2.95326i −0.210922 0.0939083i
\(990\) 23.2680 + 21.4982i 0.739506 + 0.683258i
\(991\) −34.0823 + 15.1744i −1.08266 + 0.482031i −0.868967 0.494870i \(-0.835216\pi\)
−0.213693 + 0.976901i \(0.568549\pi\)
\(992\) −0.716110 + 0.795321i −0.0227365 + 0.0252515i
\(993\) −28.4207 −0.901902
\(994\) 35.7798 14.0164i 1.13487 0.444574i
\(995\) 11.1077 9.74598i 0.352138 0.308968i
\(996\) −1.04084 + 0.221238i −0.0329803 + 0.00701019i
\(997\) −34.7196 38.5600i −1.09958 1.22121i −0.973378 0.229205i \(-0.926388\pi\)
−0.126203 0.992004i \(-0.540279\pi\)
\(998\) 2.27070 + 21.6043i 0.0718777 + 0.683871i
\(999\) −8.19529 14.1947i −0.259288 0.449099i
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 175.2.q.a.11.6 144
5.2 odd 4 875.2.u.b.74.26 288
5.3 odd 4 875.2.u.b.74.11 288
5.4 even 2 875.2.q.a.676.13 144
7.2 even 3 inner 175.2.q.a.86.13 yes 144
25.9 even 10 875.2.q.a.326.6 144
25.12 odd 20 875.2.u.b.424.26 288
25.13 odd 20 875.2.u.b.424.11 288
25.16 even 5 inner 175.2.q.a.116.13 yes 144
35.2 odd 12 875.2.u.b.324.11 288
35.9 even 6 875.2.q.a.51.6 144
35.23 odd 12 875.2.u.b.324.26 288
175.9 even 30 875.2.q.a.576.13 144
175.16 even 15 inner 175.2.q.a.16.6 yes 144
175.37 odd 60 875.2.u.b.674.11 288
175.163 odd 60 875.2.u.b.674.26 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.q.a.11.6 144 1.1 even 1 trivial
175.2.q.a.16.6 yes 144 175.16 even 15 inner
175.2.q.a.86.13 yes 144 7.2 even 3 inner
175.2.q.a.116.13 yes 144 25.16 even 5 inner
875.2.q.a.51.6 144 35.9 even 6
875.2.q.a.326.6 144 25.9 even 10
875.2.q.a.576.13 144 175.9 even 30
875.2.q.a.676.13 144 5.4 even 2
875.2.u.b.74.11 288 5.3 odd 4
875.2.u.b.74.26 288 5.2 odd 4
875.2.u.b.324.11 288 35.2 odd 12
875.2.u.b.324.26 288 35.23 odd 12
875.2.u.b.424.11 288 25.13 odd 20
875.2.u.b.424.26 288 25.12 odd 20
875.2.u.b.674.11 288 175.37 odd 60
875.2.u.b.674.26 288 175.163 odd 60