Properties

Label 864.2.bu.a.13.6
Level $864$
Weight $2$
Character 864.13
Analytic conductor $6.899$
Analytic rank $0$
Dimension $3408$
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] = [864,2,Mod(13,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(72))
 
chi = DirichletCharacter(H, H._module([0, 63, 32]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.bu (of order \(72\), degree \(24\), 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: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(3408\)
Relative dimension: \(142\) over \(\Q(\zeta_{72})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{72}]$

Embedding invariants

Embedding label 13.6
Character \(\chi\) \(=\) 864.13
Dual form 864.2.bu.a.133.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.40602 + 0.152001i) q^{2} +(-0.406383 - 1.68370i) q^{3} +(1.95379 - 0.427432i) q^{4} +(2.49034 + 0.785202i) q^{5} +(0.827306 + 2.30555i) q^{6} +(-1.45250 + 0.677311i) q^{7} +(-2.68210 + 0.897956i) q^{8} +(-2.66971 + 1.36845i) q^{9} +O(q^{10})\) \(q+(-1.40602 + 0.152001i) q^{2} +(-0.406383 - 1.68370i) q^{3} +(1.95379 - 0.427432i) q^{4} +(2.49034 + 0.785202i) q^{5} +(0.827306 + 2.30555i) q^{6} +(-1.45250 + 0.677311i) q^{7} +(-2.68210 + 0.897956i) q^{8} +(-2.66971 + 1.36845i) q^{9} +(-3.62082 - 0.725477i) q^{10} +(0.290377 + 0.151161i) q^{11} +(-1.51366 - 3.11590i) q^{12} +(0.219810 - 0.345033i) q^{13} +(1.93929 - 1.17309i) q^{14} +(0.310015 - 4.51209i) q^{15} +(3.63460 - 1.67023i) q^{16} +(5.92910 + 3.42317i) q^{17} +(3.54566 - 2.32987i) q^{18} +(0.443392 + 3.36789i) q^{19} +(5.20123 + 0.469669i) q^{20} +(1.73066 + 2.17033i) q^{21} +(-0.431253 - 0.168398i) q^{22} +(-0.0888879 - 0.0414491i) q^{23} +(2.60185 + 4.15095i) q^{24} +(1.48950 + 1.04296i) q^{25} +(-0.256613 + 0.518535i) q^{26} +(3.38899 + 3.93887i) q^{27} +(-2.54837 + 1.94417i) q^{28} +(4.21899 + 0.935327i) q^{29} +(0.249953 + 6.39121i) q^{30} +(0.133305 - 0.0485189i) q^{31} +(-4.85645 + 2.90084i) q^{32} +(0.136505 - 0.550337i) q^{33} +(-8.85676 - 3.91182i) q^{34} +(-4.14904 + 0.546232i) q^{35} +(-4.63113 + 3.81479i) q^{36} +(-0.755966 + 5.74213i) q^{37} +(-1.13534 - 4.66793i) q^{38} +(-0.670260 - 0.229880i) q^{39} +(-7.38443 + 0.130226i) q^{40} +(8.72539 - 6.10958i) q^{41} +(-2.76324 - 2.78847i) q^{42} +(-3.79218 - 1.97408i) q^{43} +(0.631947 + 0.171220i) q^{44} +(-7.72299 + 1.31166i) q^{45} +(0.131279 + 0.0447673i) q^{46} +(1.85241 - 5.08945i) q^{47} +(-4.28920 - 5.44084i) q^{48} +(-2.84851 + 3.39472i) q^{49} +(-2.25280 - 1.24002i) q^{50} +(3.35411 - 11.3740i) q^{51} +(0.281985 - 0.768077i) q^{52} +(3.70734 + 8.95032i) q^{53} +(-5.36371 - 5.02301i) q^{54} +(0.604446 + 0.604446i) q^{55} +(3.28755 - 3.12090i) q^{56} +(5.49034 - 2.11519i) q^{57} +(-6.07416 - 0.673801i) q^{58} +(6.08293 + 1.91794i) q^{59} +(-1.32291 - 8.94819i) q^{60} +(1.01998 - 1.11311i) q^{61} +(-0.180054 + 0.0884810i) q^{62} +(2.95087 - 3.79590i) q^{63} +(6.38735 - 4.81682i) q^{64} +(0.818324 - 0.686655i) q^{65} +(-0.108278 + 0.794535i) q^{66} +(-8.92114 - 5.68339i) q^{67} +(13.0474 + 4.15387i) q^{68} +(-0.0336655 + 0.166505i) q^{69} +(5.75062 - 1.39867i) q^{70} +(3.05820 + 11.4134i) q^{71} +(5.93161 - 6.06761i) q^{72} +(-0.672816 + 2.51098i) q^{73} +(0.190097 - 8.18847i) q^{74} +(1.15073 - 2.93172i) q^{75} +(2.30584 + 6.39064i) q^{76} +(-0.524155 - 0.0228851i) q^{77} +(0.977342 + 0.221336i) q^{78} +(14.3943 - 2.53810i) q^{79} +(10.3629 - 1.30554i) q^{80} +(5.25467 - 7.30674i) q^{81} +(-11.3394 + 9.91647i) q^{82} +(2.32419 - 10.4838i) q^{83} +(4.30902 + 3.50063i) q^{84} +(12.0776 + 13.1804i) q^{85} +(5.63195 + 2.19919i) q^{86} +(-0.139711 - 7.48362i) q^{87} +(-0.914556 - 0.144683i) q^{88} +(1.94094 + 0.520073i) q^{89} +(10.6593 - 3.01812i) q^{90} +(-0.0855794 + 0.650040i) q^{91} +(-0.191385 - 0.0429894i) q^{92} +(-0.135864 - 0.204728i) q^{93} +(-1.83093 + 7.43744i) q^{94} +(-1.54028 + 8.73536i) q^{95} +(6.85772 + 6.99797i) q^{96} +(6.33507 - 5.31575i) q^{97} +(3.48907 - 5.20603i) q^{98} +(-0.982077 - 0.00618700i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3408 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 12 q^{8} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3408 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 12 q^{8} - 24 q^{9} - 12 q^{10} - 24 q^{11} - 24 q^{12} - 24 q^{13} - 24 q^{14} - 24 q^{16} - 24 q^{18} - 12 q^{19} - 24 q^{20} - 24 q^{21} - 24 q^{22} - 24 q^{23} + 36 q^{24} - 24 q^{25} - 48 q^{26} - 24 q^{27} - 48 q^{28} - 24 q^{29} - 24 q^{30} - 48 q^{31} - 24 q^{32} - 48 q^{33} - 48 q^{34} - 12 q^{35} - 24 q^{36} - 12 q^{37} - 24 q^{38} - 24 q^{39} - 24 q^{40} - 24 q^{41} - 144 q^{42} - 24 q^{43} - 12 q^{44} - 24 q^{45} - 12 q^{46} - 24 q^{48} + 288 q^{50} - 60 q^{51} - 24 q^{52} - 48 q^{53} - 24 q^{54} - 48 q^{55} - 24 q^{56} - 24 q^{57} + 84 q^{58} - 24 q^{59} - 24 q^{60} - 24 q^{61} - 12 q^{62} - 48 q^{63} - 12 q^{64} - 48 q^{65} + 168 q^{66} - 24 q^{67} - 72 q^{68} - 24 q^{69} - 24 q^{70} - 12 q^{71} - 24 q^{72} - 12 q^{73} - 24 q^{74} - 24 q^{75} - 24 q^{76} - 24 q^{77} - 24 q^{78} - 48 q^{80} - 48 q^{82} - 144 q^{83} - 252 q^{84} - 84 q^{85} - 24 q^{86} - 24 q^{87} - 24 q^{88} - 12 q^{89} - 24 q^{90} - 12 q^{91} + 204 q^{92} - 24 q^{93} - 24 q^{94} - 48 q^{95} - 24 q^{96} - 48 q^{97} - 12 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{4}{9}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40602 + 0.152001i −0.994207 + 0.107481i
\(3\) −0.406383 1.68370i −0.234625 0.972086i
\(4\) 1.95379 0.427432i 0.976896 0.213716i
\(5\) 2.49034 + 0.785202i 1.11371 + 0.351153i 0.800982 0.598688i \(-0.204311\pi\)
0.312733 + 0.949841i \(0.398756\pi\)
\(6\) 0.827306 + 2.30555i 0.337746 + 0.941237i
\(7\) −1.45250 + 0.677311i −0.548993 + 0.256000i −0.677265 0.735740i \(-0.736835\pi\)
0.128272 + 0.991739i \(0.459057\pi\)
\(8\) −2.68210 + 0.897956i −0.948267 + 0.317475i
\(9\) −2.66971 + 1.36845i −0.889902 + 0.456151i
\(10\) −3.62082 0.725477i −1.14501 0.229416i
\(11\) 0.290377 + 0.151161i 0.0875519 + 0.0455766i 0.504962 0.863142i \(-0.331507\pi\)
−0.417410 + 0.908718i \(0.637062\pi\)
\(12\) −1.51366 3.11590i −0.436955 0.899484i
\(13\) 0.219810 0.345033i 0.0609644 0.0956950i −0.811551 0.584282i \(-0.801376\pi\)
0.872515 + 0.488587i \(0.162487\pi\)
\(14\) 1.93929 1.17309i 0.518298 0.313523i
\(15\) 0.310015 4.51209i 0.0800454 1.16502i
\(16\) 3.63460 1.67023i 0.908651 0.417557i
\(17\) 5.92910 + 3.42317i 1.43802 + 0.830240i 0.997712 0.0676080i \(-0.0215367\pi\)
0.440306 + 0.897848i \(0.354870\pi\)
\(18\) 3.54566 2.32987i 0.835720 0.549156i
\(19\) 0.443392 + 3.36789i 0.101721 + 0.772648i 0.963941 + 0.266114i \(0.0857399\pi\)
−0.862220 + 0.506533i \(0.830927\pi\)
\(20\) 5.20123 + 0.469669i 1.16303 + 0.105021i
\(21\) 1.73066 + 2.17033i 0.377661 + 0.473604i
\(22\) −0.431253 0.168398i −0.0919433 0.0359025i
\(23\) −0.0888879 0.0414491i −0.0185344 0.00864274i 0.413329 0.910582i \(-0.364366\pi\)
−0.431863 + 0.901939i \(0.642144\pi\)
\(24\) 2.60185 + 4.15095i 0.531100 + 0.847309i
\(25\) 1.48950 + 1.04296i 0.297900 + 0.208592i
\(26\) −0.256613 + 0.518535i −0.0503259 + 0.101693i
\(27\) 3.38899 + 3.93887i 0.652212 + 0.758037i
\(28\) −2.54837 + 1.94417i −0.481598 + 0.367413i
\(29\) 4.21899 + 0.935327i 0.783446 + 0.173686i 0.589977 0.807420i \(-0.299137\pi\)
0.193470 + 0.981106i \(0.438026\pi\)
\(30\) 0.249953 + 6.39121i 0.0456349 + 1.16687i
\(31\) 0.133305 0.0485189i 0.0239422 0.00871425i −0.330021 0.943973i \(-0.607056\pi\)
0.353963 + 0.935259i \(0.384834\pi\)
\(32\) −4.85645 + 2.90084i −0.858508 + 0.512800i
\(33\) 0.136505 0.550337i 0.0237625 0.0958014i
\(34\) −8.85676 3.91182i −1.51892 0.670871i
\(35\) −4.14904 + 0.546232i −0.701316 + 0.0923300i
\(36\) −4.63113 + 3.81479i −0.771855 + 0.635799i
\(37\) −0.755966 + 5.74213i −0.124280 + 0.944001i 0.809742 + 0.586786i \(0.199607\pi\)
−0.934022 + 0.357215i \(0.883726\pi\)
\(38\) −1.13534 4.66793i −0.184176 0.757239i
\(39\) −0.670260 0.229880i −0.107328 0.0368102i
\(40\) −7.38443 + 0.130226i −1.16758 + 0.0205905i
\(41\) 8.72539 6.10958i 1.36268 0.954157i 0.362926 0.931818i \(-0.381778\pi\)
0.999750 0.0223389i \(-0.00711128\pi\)
\(42\) −2.76324 2.78847i −0.426377 0.430270i
\(43\) −3.79218 1.97408i −0.578302 0.301045i 0.147375 0.989081i \(-0.452918\pi\)
−0.725677 + 0.688036i \(0.758473\pi\)
\(44\) 0.631947 + 0.171220i 0.0952696 + 0.0258124i
\(45\) −7.72299 + 1.31166i −1.15128 + 0.195531i
\(46\) 0.131279 + 0.0447673i 0.0193560 + 0.00660058i
\(47\) 1.85241 5.08945i 0.270202 0.742373i −0.728174 0.685393i \(-0.759631\pi\)
0.998375 0.0569802i \(-0.0181472\pi\)
\(48\) −4.28920 5.44084i −0.619093 0.785318i
\(49\) −2.84851 + 3.39472i −0.406930 + 0.484961i
\(50\) −2.25280 1.24002i −0.318594 0.175365i
\(51\) 3.35411 11.3740i 0.469670 1.59267i
\(52\) 0.281985 0.768077i 0.0391044 0.106513i
\(53\) 3.70734 + 8.95032i 0.509243 + 1.22942i 0.944320 + 0.329028i \(0.106721\pi\)
−0.435077 + 0.900393i \(0.643279\pi\)
\(54\) −5.36371 5.02301i −0.729908 0.683545i
\(55\) 0.604446 + 0.604446i 0.0815035 + 0.0815035i
\(56\) 3.28755 3.12090i 0.439318 0.417048i
\(57\) 5.49034 2.11519i 0.727214 0.280164i
\(58\) −6.07416 0.673801i −0.797576 0.0884744i
\(59\) 6.08293 + 1.91794i 0.791929 + 0.249694i 0.669529 0.742786i \(-0.266496\pi\)
0.122401 + 0.992481i \(0.460941\pi\)
\(60\) −1.32291 8.94819i −0.170787 1.15521i
\(61\) 1.01998 1.11311i 0.130595 0.142519i −0.668528 0.743687i \(-0.733075\pi\)
0.799123 + 0.601168i \(0.205298\pi\)
\(62\) −0.180054 + 0.0884810i −0.0228669 + 0.0112371i
\(63\) 2.95087 3.79590i 0.371775 0.478238i
\(64\) 6.38735 4.81682i 0.798419 0.602103i
\(65\) 0.818324 0.686655i 0.101501 0.0851691i
\(66\) −0.108278 + 0.794535i −0.0133281 + 0.0978005i
\(67\) −8.92114 5.68339i −1.08989 0.694337i −0.134866 0.990864i \(-0.543060\pi\)
−0.955025 + 0.296527i \(0.904172\pi\)
\(68\) 13.0474 + 4.15387i 1.58223 + 0.503730i
\(69\) −0.0336655 + 0.166505i −0.00405285 + 0.0200448i
\(70\) 5.75062 1.39867i 0.687330 0.167173i
\(71\) 3.05820 + 11.4134i 0.362942 + 1.35452i 0.870189 + 0.492717i \(0.163996\pi\)
−0.507247 + 0.861800i \(0.669337\pi\)
\(72\) 5.93161 6.06761i 0.699048 0.715075i
\(73\) −0.672816 + 2.51098i −0.0787471 + 0.293888i −0.994057 0.108862i \(-0.965279\pi\)
0.915310 + 0.402751i \(0.131946\pi\)
\(74\) 0.190097 8.18847i 0.0220983 0.951890i
\(75\) 1.15073 2.93172i 0.132874 0.338525i
\(76\) 2.30584 + 6.39064i 0.264498 + 0.733057i
\(77\) −0.524155 0.0228851i −0.0597330 0.00260800i
\(78\) 0.977342 + 0.221336i 0.110662 + 0.0250614i
\(79\) 14.3943 2.53810i 1.61948 0.285558i 0.710909 0.703284i \(-0.248284\pi\)
0.908573 + 0.417726i \(0.137173\pi\)
\(80\) 10.3629 1.30554i 1.15860 0.145964i
\(81\) 5.25467 7.30674i 0.583852 0.811860i
\(82\) −11.3394 + 9.91647i −1.25223 + 1.09509i
\(83\) 2.32419 10.4838i 0.255113 1.15074i −0.661178 0.750229i \(-0.729943\pi\)
0.916291 0.400512i \(-0.131168\pi\)
\(84\) 4.30902 + 3.50063i 0.470152 + 0.381950i
\(85\) 12.0776 + 13.1804i 1.31000 + 1.42961i
\(86\) 5.63195 + 2.19919i 0.607309 + 0.237145i
\(87\) −0.139711 7.48362i −0.0149786 0.802328i
\(88\) −0.914556 0.144683i −0.0974920 0.0154232i
\(89\) 1.94094 + 0.520073i 0.205739 + 0.0551277i 0.360217 0.932869i \(-0.382703\pi\)
−0.154477 + 0.987996i \(0.549369\pi\)
\(90\) 10.6593 3.01812i 1.12359 0.318138i
\(91\) −0.0855794 + 0.650040i −0.00897116 + 0.0681427i
\(92\) −0.191385 0.0429894i −0.0199533 0.00448195i
\(93\) −0.135864 0.204728i −0.0140884 0.0212293i
\(94\) −1.83093 + 7.43744i −0.188846 + 0.767114i
\(95\) −1.54028 + 8.73536i −0.158029 + 0.896229i
\(96\) 6.85772 + 6.99797i 0.699913 + 0.714228i
\(97\) 6.33507 5.31575i 0.643229 0.539733i −0.261779 0.965128i \(-0.584309\pi\)
0.905008 + 0.425395i \(0.139865\pi\)
\(98\) 3.48907 5.20603i 0.352449 0.525888i
\(99\) −0.982077 0.00618700i −0.0987025 0.000621817i
\(100\) 3.35597 + 1.40106i 0.335597 + 0.140106i
\(101\) 6.33808 0.276727i 0.630662 0.0275353i 0.273942 0.961746i \(-0.411673\pi\)
0.356721 + 0.934211i \(0.383895\pi\)
\(102\) −2.98710 + 16.5018i −0.295767 + 1.63393i
\(103\) −10.4452 + 0.913840i −1.02920 + 0.0900433i −0.589227 0.807968i \(-0.700568\pi\)
−0.439973 + 0.898011i \(0.645012\pi\)
\(104\) −0.279729 + 1.12279i −0.0274297 + 0.110099i
\(105\) 2.60579 + 6.76377i 0.254299 + 0.660077i
\(106\) −6.57306 12.0208i −0.638432 1.16757i
\(107\) 0.0989056 + 0.238779i 0.00956156 + 0.0230837i 0.928588 0.371112i \(-0.121023\pi\)
−0.919027 + 0.394195i \(0.871023\pi\)
\(108\) 8.30499 + 6.24718i 0.799148 + 0.601135i
\(109\) 4.39882 + 1.82205i 0.421330 + 0.174521i 0.583267 0.812280i \(-0.301774\pi\)
−0.161937 + 0.986801i \(0.551774\pi\)
\(110\) −0.941740 0.757988i −0.0897914 0.0722713i
\(111\) 9.97525 1.06068i 0.946809 0.100675i
\(112\) −4.14799 + 4.88776i −0.391948 + 0.461850i
\(113\) −2.13210 + 2.54093i −0.200571 + 0.239031i −0.856949 0.515401i \(-0.827643\pi\)
0.656378 + 0.754432i \(0.272087\pi\)
\(114\) −7.39803 + 3.80854i −0.692889 + 0.356703i
\(115\) −0.188815 0.173017i −0.0176071 0.0161340i
\(116\) 8.64281 + 0.0241034i 0.802465 + 0.00223795i
\(117\) −0.114667 + 1.22194i −0.0106010 + 0.112968i
\(118\) −8.84425 1.77205i −0.814179 0.163131i
\(119\) −10.9306 0.956300i −1.00200 0.0876639i
\(120\) 3.22016 + 12.3803i 0.293959 + 1.13016i
\(121\) −6.24787 8.92289i −0.567988 0.811171i
\(122\) −1.26492 + 1.72009i −0.114520 + 0.155730i
\(123\) −13.8326 12.2081i −1.24724 1.10077i
\(124\) 0.239711 0.151774i 0.0215267 0.0136297i
\(125\) −5.05755 6.59112i −0.452361 0.589528i
\(126\) −3.57201 + 5.78565i −0.318220 + 0.515427i
\(127\) −0.574267 0.994660i −0.0509580 0.0882618i 0.839421 0.543481i \(-0.182894\pi\)
−0.890379 + 0.455219i \(0.849561\pi\)
\(128\) −8.24859 + 7.74343i −0.729079 + 0.684429i
\(129\) −1.78269 + 7.18714i −0.156957 + 0.632792i
\(130\) −1.04621 + 1.08984i −0.0917586 + 0.0955851i
\(131\) 0.445189 10.1965i 0.0388963 0.890872i −0.874802 0.484480i \(-0.839009\pi\)
0.913699 0.406392i \(-0.133213\pi\)
\(132\) 0.0314713 1.13359i 0.00273923 0.0986664i
\(133\) −2.92514 4.59155i −0.253642 0.398137i
\(134\) 13.4072 + 6.63495i 1.15821 + 0.573173i
\(135\) 5.34694 + 12.4702i 0.460191 + 1.07326i
\(136\) −18.9763 3.85721i −1.62720 0.330753i
\(137\) 2.63563 3.76408i 0.225177 0.321587i −0.690627 0.723211i \(-0.742665\pi\)
0.915804 + 0.401624i \(0.131554\pi\)
\(138\) 0.0220255 0.239227i 0.00187494 0.0203643i
\(139\) 1.64341 + 1.79346i 0.139392 + 0.152120i 0.803040 0.595926i \(-0.203215\pi\)
−0.663648 + 0.748045i \(0.730993\pi\)
\(140\) −7.87289 + 2.84066i −0.665381 + 0.240079i
\(141\) −9.32191 1.05064i −0.785046 0.0884799i
\(142\) −6.03474 15.5826i −0.506424 1.30766i
\(143\) 0.115983 0.0669630i 0.00969901 0.00559973i
\(144\) −7.41770 + 9.43280i −0.618141 + 0.786067i
\(145\) 9.77230 + 5.64204i 0.811546 + 0.468546i
\(146\) 0.564323 3.63276i 0.0467037 0.300650i
\(147\) 6.87329 + 3.41649i 0.566899 + 0.281787i
\(148\) 0.977371 + 11.5421i 0.0803394 + 0.948751i
\(149\) 8.27779 1.83514i 0.678143 0.150341i 0.136105 0.990694i \(-0.456542\pi\)
0.542038 + 0.840354i \(0.317653\pi\)
\(150\) −1.17232 + 4.29697i −0.0957198 + 0.350846i
\(151\) 0.500013 + 0.0437455i 0.0406905 + 0.00355996i 0.107483 0.994207i \(-0.465721\pi\)
−0.0667923 + 0.997767i \(0.521276\pi\)
\(152\) −4.21344 8.63489i −0.341755 0.700382i
\(153\) −20.5134 1.02515i −1.65841 0.0828784i
\(154\) 0.740451 0.0474949i 0.0596673 0.00382725i
\(155\) 0.370071 0.0161577i 0.0297248 0.00129781i
\(156\) −1.40781 0.162646i −0.112715 0.0130221i
\(157\) 0.852048 0.443548i 0.0680009 0.0353990i −0.427409 0.904058i \(-0.640574\pi\)
0.495410 + 0.868659i \(0.335018\pi\)
\(158\) −19.8529 + 5.75656i −1.57941 + 0.457967i
\(159\) 13.5631 9.87932i 1.07562 0.783481i
\(160\) −14.3720 + 3.41078i −1.13620 + 0.269646i
\(161\) 0.157184 0.0123878
\(162\) −6.27754 + 11.0721i −0.493210 + 0.869910i
\(163\) −1.31141 + 3.16603i −0.102718 + 0.247983i −0.966880 0.255230i \(-0.917849\pi\)
0.864163 + 0.503213i \(0.167849\pi\)
\(164\) 14.4362 15.6664i 1.12727 1.22334i
\(165\) 0.772071 1.26334i 0.0601056 0.0983511i
\(166\) −1.67433 + 15.0937i −0.129953 + 1.17150i
\(167\) 14.9500 1.30796i 1.15687 0.101213i 0.507474 0.861667i \(-0.330579\pi\)
0.649392 + 0.760454i \(0.275024\pi\)
\(168\) −6.59067 4.26698i −0.508481 0.329205i
\(169\) 5.42331 + 11.6303i 0.417177 + 0.894640i
\(170\) −18.9848 16.6961i −1.45607 1.28053i
\(171\) −5.79253 8.38453i −0.442966 0.641181i
\(172\) −8.25292 2.23605i −0.629279 0.170497i
\(173\) −22.1801 + 6.99335i −1.68632 + 0.531695i −0.983692 0.179862i \(-0.942435\pi\)
−0.702629 + 0.711557i \(0.747990\pi\)
\(174\) 1.33395 + 10.5009i 0.101127 + 0.796071i
\(175\) −2.86990 0.506042i −0.216944 0.0382532i
\(176\) 1.30788 + 0.0644138i 0.0985850 + 0.00485537i
\(177\) 0.757244 11.0213i 0.0569179 0.828408i
\(178\) −2.80806 0.436210i −0.210473 0.0326953i
\(179\) −16.7947 + 12.8871i −1.25530 + 0.963224i −0.999993 0.00363629i \(-0.998843\pi\)
−0.255305 + 0.966861i \(0.582176\pi\)
\(180\) −14.5285 + 5.86377i −1.08289 + 0.437059i
\(181\) 11.7910 15.3663i 0.876419 1.14217i −0.112491 0.993653i \(-0.535883\pi\)
0.988910 0.148518i \(-0.0474504\pi\)
\(182\) 0.0215200 0.926979i 0.00159517 0.0687122i
\(183\) −2.28864 1.26499i −0.169181 0.0935106i
\(184\) 0.275626 + 0.0313533i 0.0203194 + 0.00231140i
\(185\) −6.39135 + 13.7063i −0.469901 + 1.00771i
\(186\) 0.222146 + 0.267200i 0.0162886 + 0.0195921i
\(187\) 1.20423 + 1.89025i 0.0880617 + 0.138229i
\(188\) 1.44383 10.7355i 0.105302 0.782967i
\(189\) −7.59035 3.42581i −0.552117 0.249191i
\(190\) 0.837886 12.5162i 0.0607866 0.908022i
\(191\) 4.69155 + 26.6071i 0.339468 + 1.92522i 0.377646 + 0.925950i \(0.376734\pi\)
−0.0381777 + 0.999271i \(0.512155\pi\)
\(192\) −10.7058 8.79692i −0.772625 0.634863i
\(193\) −22.8646 + 8.32202i −1.64583 + 0.599032i −0.988044 0.154174i \(-0.950728\pi\)
−0.657784 + 0.753207i \(0.728506\pi\)
\(194\) −8.09924 + 8.43700i −0.581492 + 0.605741i
\(195\) −1.48868 1.09877i −0.106606 0.0786845i
\(196\) −4.11438 + 7.85013i −0.293885 + 0.560724i
\(197\) −20.4404 15.6845i −1.45632 1.11747i −0.969829 0.243787i \(-0.921610\pi\)
−0.486490 0.873686i \(-0.661723\pi\)
\(198\) 1.38176 0.140577i 0.0981976 0.00999039i
\(199\) −0.771571 2.87954i −0.0546952 0.204125i 0.933171 0.359433i \(-0.117030\pi\)
−0.987866 + 0.155308i \(0.950363\pi\)
\(200\) −4.93152 1.45982i −0.348711 0.103225i
\(201\) −5.94375 + 17.3302i −0.419240 + 1.22238i
\(202\) −8.86941 + 1.35248i −0.624050 + 0.0951598i
\(203\) −6.76158 + 1.49901i −0.474570 + 0.105210i
\(204\) 1.69164 23.6560i 0.118439 1.65625i
\(205\) 26.5265 8.36376i 1.85269 0.584150i
\(206\) 14.5473 2.87256i 1.01356 0.200141i
\(207\) 0.294026 0.0109821i 0.0204362 0.000763308i
\(208\) 0.222640 1.62119i 0.0154373 0.112409i
\(209\) −0.380342 + 1.04498i −0.0263088 + 0.0722829i
\(210\) −4.69189 9.11393i −0.323772 0.628921i
\(211\) 1.34628 + 2.58618i 0.0926817 + 0.178040i 0.928873 0.370397i \(-0.120778\pi\)
−0.836192 + 0.548437i \(0.815223\pi\)
\(212\) 11.0690 + 15.9024i 0.760224 + 1.09218i
\(213\) 17.9739 9.78730i 1.23155 0.670615i
\(214\) −0.175358 0.320695i −0.0119872 0.0219223i
\(215\) −7.89377 7.89377i −0.538351 0.538351i
\(216\) −12.6266 7.52130i −0.859129 0.511760i
\(217\) −0.160762 + 0.160762i −0.0109133 + 0.0109133i
\(218\) −6.46178 1.89322i −0.437647 0.128225i
\(219\) 4.50117 + 0.112402i 0.304161 + 0.00759542i
\(220\) 1.43932 + 0.922602i 0.0970390 + 0.0622018i
\(221\) 2.48438 1.29329i 0.167118 0.0869960i
\(222\) −13.8642 + 3.00758i −0.930504 + 0.201856i
\(223\) 17.9461 + 6.53184i 1.20176 + 0.437404i 0.863837 0.503771i \(-0.168054\pi\)
0.337920 + 0.941175i \(0.390277\pi\)
\(224\) 5.08922 7.50279i 0.340038 0.501301i
\(225\) −5.40377 0.746082i −0.360251 0.0497388i
\(226\) 2.61155 3.89669i 0.173718 0.259204i
\(227\) −5.49098 17.4152i −0.364449 1.15588i −0.940880 0.338739i \(-0.890000\pi\)
0.576431 0.817145i \(-0.304445\pi\)
\(228\) 9.82288 6.47939i 0.650536 0.429108i
\(229\) 1.44531 + 6.51937i 0.0955088 + 0.430812i 0.999991 + 0.00430044i \(0.00136888\pi\)
−0.904482 + 0.426512i \(0.859742\pi\)
\(230\) 0.291777 + 0.214566i 0.0192392 + 0.0141481i
\(231\) 0.174476 + 0.891820i 0.0114797 + 0.0586775i
\(232\) −12.1556 + 1.27982i −0.798057 + 0.0840245i
\(233\) 9.55193 2.55943i 0.625768 0.167674i 0.0680194 0.997684i \(-0.478332\pi\)
0.557749 + 0.830010i \(0.311665\pi\)
\(234\) −0.0245110 1.73550i −0.00160233 0.113453i
\(235\) 8.60938 11.2200i 0.561614 0.731909i
\(236\) 12.7046 + 1.14722i 0.826996 + 0.0746774i
\(237\) −10.1230 23.2042i −0.657558 1.50728i
\(238\) 15.5140 0.316873i 1.00562 0.0205398i
\(239\) 6.85804 + 18.8423i 0.443609 + 1.21881i 0.937102 + 0.349057i \(0.113498\pi\)
−0.493492 + 0.869750i \(0.664280\pi\)
\(240\) −6.40943 16.9174i −0.413727 1.09202i
\(241\) −20.6248 + 3.63672i −1.32856 + 0.234262i −0.792477 0.609902i \(-0.791209\pi\)
−0.536086 + 0.844163i \(0.680098\pi\)
\(242\) 10.1409 + 11.5961i 0.651883 + 0.745425i
\(243\) −14.4378 5.87796i −0.926184 0.377071i
\(244\) 1.51704 2.61075i 0.0971187 0.167136i
\(245\) −9.75931 + 6.21737i −0.623500 + 0.397213i
\(246\) 21.3045 + 15.0623i 1.35833 + 0.960339i
\(247\) 1.25950 + 0.587313i 0.0801399 + 0.0373698i
\(248\) −0.313969 + 0.249834i −0.0199370 + 0.0158645i
\(249\) −18.5960 + 0.347167i −1.17848 + 0.0220008i
\(250\) 8.11287 + 8.49851i 0.513103 + 0.537493i
\(251\) −9.81873 7.53418i −0.619753 0.475553i 0.250528 0.968109i \(-0.419396\pi\)
−0.870281 + 0.492556i \(0.836063\pi\)
\(252\) 4.14291 8.67770i 0.260979 0.546643i
\(253\) −0.0195455 0.0254722i −0.00122882 0.00160142i
\(254\) 0.958621 + 1.31122i 0.0601492 + 0.0822736i
\(255\) 17.2837 25.6914i 1.08235 1.60886i
\(256\) 10.4207 12.1412i 0.651293 0.758826i
\(257\) −3.64721 + 20.6844i −0.227507 + 1.29025i 0.630328 + 0.776329i \(0.282920\pi\)
−0.857835 + 0.513926i \(0.828191\pi\)
\(258\) 1.41406 10.3762i 0.0880354 0.645996i
\(259\) −2.79117 8.85246i −0.173435 0.550065i
\(260\) 1.30534 1.69136i 0.0809535 0.104894i
\(261\) −12.5434 + 3.27644i −0.776418 + 0.202807i
\(262\) 0.923928 + 14.4042i 0.0570805 + 0.889892i
\(263\) −11.1507 + 5.19966i −0.687582 + 0.320625i −0.734823 0.678259i \(-0.762735\pi\)
0.0472411 + 0.998884i \(0.484957\pi\)
\(264\) 0.128057 + 1.59864i 0.00788137 + 0.0983893i
\(265\) 2.20475 + 25.2004i 0.135436 + 1.54805i
\(266\) 4.81072 + 6.01119i 0.294964 + 0.368570i
\(267\) 0.0868845 3.47931i 0.00531724 0.212931i
\(268\) −19.8593 7.29098i −1.21310 0.445368i
\(269\) −24.6788 10.2223i −1.50469 0.623265i −0.530240 0.847848i \(-0.677898\pi\)
−0.974455 + 0.224583i \(0.927898\pi\)
\(270\) −9.41338 16.7206i −0.572880 1.01758i
\(271\) 16.5408i 1.00478i −0.864640 0.502391i \(-0.832454\pi\)
0.864640 0.502391i \(-0.167546\pi\)
\(272\) 27.2674 + 2.53892i 1.65333 + 0.153944i
\(273\) 1.12925 0.120075i 0.0683455 0.00726725i
\(274\) −3.13362 + 5.69299i −0.189309 + 0.343926i
\(275\) 0.274862 + 0.528005i 0.0165748 + 0.0318399i
\(276\) 0.00539426 + 0.339706i 0.000324696 + 0.0204479i
\(277\) 0.162966 + 3.73253i 0.00979166 + 0.224266i 0.997631 + 0.0687891i \(0.0219136\pi\)
−0.987840 + 0.155477i \(0.950309\pi\)
\(278\) −2.58327 2.27185i −0.154934 0.136257i
\(279\) −0.289488 + 0.311952i −0.0173312 + 0.0186761i
\(280\) 10.6377 5.19071i 0.635722 0.310204i
\(281\) −1.06066 + 12.1233i −0.0632734 + 0.723218i 0.896610 + 0.442820i \(0.146022\pi\)
−0.959884 + 0.280398i \(0.909534\pi\)
\(282\) 13.2665 + 0.0602878i 0.790009 + 0.00359008i
\(283\) −4.11371 18.5557i −0.244535 1.10302i −0.927865 0.372915i \(-0.878358\pi\)
0.683331 0.730109i \(-0.260531\pi\)
\(284\) 10.8535 + 20.9922i 0.644039 + 1.24566i
\(285\) 15.3337 0.956525i 0.908289 0.0566597i
\(286\) −0.152897 + 0.111781i −0.00904096 + 0.00660974i
\(287\) −8.53553 + 14.7840i −0.503836 + 0.872670i
\(288\) 8.99565 14.3902i 0.530074 0.847952i
\(289\) 14.9361 + 25.8702i 0.878597 + 1.52177i
\(290\) −14.5977 6.44743i −0.857204 0.378606i
\(291\) −11.5246 8.50614i −0.675585 0.498639i
\(292\) −0.241267 + 5.19352i −0.0141191 + 0.303928i
\(293\) 4.16279 3.81450i 0.243193 0.222845i −0.544742 0.838604i \(-0.683372\pi\)
0.787935 + 0.615758i \(0.211150\pi\)
\(294\) −10.1833 3.75891i −0.593902 0.219224i
\(295\) 13.6426 + 9.55265i 0.794303 + 0.556177i
\(296\) −3.12860 16.0798i −0.181846 0.934620i
\(297\) 0.388682 + 1.65604i 0.0225536 + 0.0960932i
\(298\) −11.3598 + 3.83848i −0.658056 + 0.222357i
\(299\) −0.0338398 + 0.0215583i −0.00195701 + 0.00124675i
\(300\) 0.995170 6.21982i 0.0574561 0.359101i
\(301\) 6.84521 + 0.298868i 0.394551 + 0.0172265i
\(302\) −0.709678 + 0.0144952i −0.0408374 + 0.000834106i
\(303\) −3.04161 10.5590i −0.174736 0.606598i
\(304\) 7.23670 + 11.5004i 0.415053 + 0.659593i
\(305\) 3.41411 1.97113i 0.195491 0.112867i
\(306\) 28.9981 1.67667i 1.65771 0.0958487i
\(307\) −8.01151 + 6.14745i −0.457241 + 0.350853i −0.811558 0.584272i \(-0.801380\pi\)
0.354317 + 0.935125i \(0.384713\pi\)
\(308\) −1.03387 + 0.179328i −0.0589103 + 0.0102182i
\(309\) 5.78340 + 17.2153i 0.329006 + 0.979344i
\(310\) −0.517872 + 0.0789690i −0.0294131 + 0.00448514i
\(311\) −21.5804 + 15.1107i −1.22371 + 0.856851i −0.993223 0.116225i \(-0.962921\pi\)
−0.230487 + 0.973076i \(0.574032\pi\)
\(312\) 2.00413 + 0.0146969i 0.113461 + 0.000832046i
\(313\) 0.951509 10.8758i 0.0537825 0.614737i −0.920700 0.390272i \(-0.872381\pi\)
0.974482 0.224465i \(-0.0720634\pi\)
\(314\) −1.13058 + 0.753150i −0.0638022 + 0.0425027i
\(315\) 10.3292 7.13606i 0.581986 0.402071i
\(316\) 27.0385 11.1115i 1.52104 0.625070i
\(317\) −4.25483 + 4.64333i −0.238975 + 0.260796i −0.845142 0.534542i \(-0.820484\pi\)
0.606167 + 0.795338i \(0.292706\pi\)
\(318\) −17.5683 + 15.9521i −0.985182 + 0.894551i
\(319\) 1.08371 + 0.909342i 0.0606762 + 0.0509134i
\(320\) 19.6889 6.98017i 1.10064 0.390203i
\(321\) 0.361840 0.263563i 0.0201959 0.0147107i
\(322\) −0.221003 + 0.0238920i −0.0123160 + 0.00133145i
\(323\) −8.89995 + 21.4864i −0.495206 + 1.19553i
\(324\) 7.14338 16.5219i 0.396855 0.917881i
\(325\) 0.687263 0.284674i 0.0381225 0.0157909i
\(326\) 1.36264 4.65084i 0.0754695 0.257586i
\(327\) 1.28019 8.14674i 0.0707945 0.450516i
\(328\) −17.9163 + 24.2215i −0.989260 + 1.33741i
\(329\) 0.756521 + 8.64708i 0.0417084 + 0.476729i
\(330\) −0.893519 + 1.89364i −0.0491866 + 0.104242i
\(331\) 0.179686 + 4.11548i 0.00987643 + 0.226207i 0.997563 + 0.0697647i \(0.0222249\pi\)
−0.987687 + 0.156443i \(0.949997\pi\)
\(332\) 0.0598945 21.4765i 0.00328714 1.17868i
\(333\) −5.83964 16.3643i −0.320010 0.896759i
\(334\) −20.8212 + 4.11142i −1.13929 + 0.224967i
\(335\) −17.7541 21.1585i −0.970009 1.15601i
\(336\) 9.91520 + 4.99769i 0.540919 + 0.272646i
\(337\) −19.5844 3.45326i −1.06683 0.188111i −0.387445 0.921893i \(-0.626642\pi\)
−0.679385 + 0.733782i \(0.737754\pi\)
\(338\) −9.39310 15.5281i −0.510917 0.844619i
\(339\) 5.14462 + 2.55722i 0.279417 + 0.138889i
\(340\) 29.2308 + 20.5894i 1.58527 + 1.11662i
\(341\) 0.0460427 + 0.00606164i 0.00249335 + 0.000328256i
\(342\) 9.41888 + 10.9084i 0.509315 + 0.589856i
\(343\) 4.74176 17.6965i 0.256031 0.955520i
\(344\) 11.9437 + 1.88949i 0.643959 + 0.101874i
\(345\) −0.214579 + 0.388220i −0.0115525 + 0.0209011i
\(346\) 30.1227 13.2042i 1.61941 0.709862i
\(347\) 0.166803 0.152847i 0.00895447 0.00820526i −0.671101 0.741366i \(-0.734178\pi\)
0.680055 + 0.733161i \(0.261956\pi\)
\(348\) −3.47171 14.5617i −0.186103 0.780590i
\(349\) 8.95037 + 1.98425i 0.479103 + 0.106214i 0.449374 0.893344i \(-0.351647\pi\)
0.0297282 + 0.999558i \(0.490536\pi\)
\(350\) 4.11207 + 0.275278i 0.219799 + 0.0147142i
\(351\) 2.10398 0.303509i 0.112302 0.0162001i
\(352\) −1.84869 + 0.108231i −0.0985357 + 0.00576873i
\(353\) −0.349838 1.98403i −0.0186200 0.105599i 0.974081 0.226198i \(-0.0726297\pi\)
−0.992701 + 0.120599i \(0.961519\pi\)
\(354\) 0.610536 + 15.6112i 0.0324496 + 0.829727i
\(355\) −1.34583 + 30.8245i −0.0714291 + 1.63599i
\(356\) 4.01449 + 0.186495i 0.212768 + 0.00988421i
\(357\) 2.83186 + 18.7924i 0.149878 + 0.994601i
\(358\) 21.6549 20.6723i 1.14450 1.09256i
\(359\) 10.3974 + 2.78597i 0.548754 + 0.147038i 0.522534 0.852618i \(-0.324987\pi\)
0.0262191 + 0.999656i \(0.491653\pi\)
\(360\) 19.5360 10.4529i 1.02964 0.550917i
\(361\) 7.20648 1.93097i 0.379289 0.101630i
\(362\) −14.2427 + 23.3976i −0.748580 + 1.22975i
\(363\) −12.4845 + 14.1457i −0.655264 + 0.742455i
\(364\) 0.110644 + 1.30662i 0.00579931 + 0.0684856i
\(365\) −3.64717 + 5.72491i −0.190902 + 0.299655i
\(366\) 3.41016 + 1.43073i 0.178252 + 0.0747852i
\(367\) −16.1765 19.2784i −0.844405 1.00632i −0.999829 0.0184745i \(-0.994119\pi\)
0.155425 0.987848i \(-0.450325\pi\)
\(368\) −0.392302 0.00218815i −0.0204501 0.000114065i
\(369\) −14.9335 + 28.2511i −0.777409 + 1.47069i
\(370\) 6.90300 20.2428i 0.358870 1.05237i
\(371\) −11.4471 10.4893i −0.594302 0.544577i
\(372\) −0.352957 0.341923i −0.0183000 0.0177279i
\(373\) −3.06102 + 9.70833i −0.158494 + 0.502678i −0.999249 0.0387367i \(-0.987667\pi\)
0.840756 + 0.541415i \(0.182111\pi\)
\(374\) −1.98049 2.47470i −0.102408 0.127963i
\(375\) −9.04219 + 11.1939i −0.466937 + 0.578051i
\(376\) −0.398247 + 15.3138i −0.0205380 + 0.789750i
\(377\) 1.25010 1.25010i 0.0643833 0.0643833i
\(378\) 11.1929 + 3.66302i 0.575702 + 0.188405i
\(379\) −26.8964 + 11.1409i −1.38158 + 0.572268i −0.944902 0.327352i \(-0.893844\pi\)
−0.436674 + 0.899620i \(0.643844\pi\)
\(380\) 0.724388 + 17.7254i 0.0371603 + 0.909295i
\(381\) −1.44134 + 1.37111i −0.0738421 + 0.0702440i
\(382\) −10.6407 36.6970i −0.544426 1.87758i
\(383\) 26.1437 + 21.9372i 1.33588 + 1.12094i 0.982664 + 0.185398i \(0.0593573\pi\)
0.353219 + 0.935541i \(0.385087\pi\)
\(384\) 16.3897 + 10.7414i 0.836384 + 0.548143i
\(385\) −1.28735 0.468559i −0.0656097 0.0238800i
\(386\) 30.8831 15.1764i 1.57191 0.772457i
\(387\) 12.8255 + 0.0807993i 0.651955 + 0.00410726i
\(388\) 10.1053 13.0937i 0.513018 0.664731i
\(389\) −5.00736 + 9.61905i −0.253883 + 0.487705i −0.979775 0.200104i \(-0.935872\pi\)
0.725891 + 0.687809i \(0.241428\pi\)
\(390\) 2.26012 + 1.31861i 0.114446 + 0.0667706i
\(391\) −0.385138 0.550034i −0.0194773 0.0278164i
\(392\) 4.59169 11.6628i 0.231915 0.589062i
\(393\) −17.3488 + 3.39411i −0.875130 + 0.171210i
\(394\) 31.1237 + 18.9458i 1.56799 + 0.954473i
\(395\) 37.8396 + 4.98167i 1.90391 + 0.250655i
\(396\) −1.92142 + 0.407683i −0.0965549 + 0.0204869i
\(397\) 2.67436 + 20.3138i 0.134222 + 1.01952i 0.917469 + 0.397808i \(0.130229\pi\)
−0.783247 + 0.621711i \(0.786438\pi\)
\(398\) 1.52254 + 3.93142i 0.0763179 + 0.197064i
\(399\) −6.54207 + 6.79098i −0.327513 + 0.339974i
\(400\) 7.15572 + 1.30294i 0.357786 + 0.0651470i
\(401\) −5.44565 14.9618i −0.271943 0.747157i −0.998214 0.0597478i \(-0.980970\pi\)
0.726271 0.687409i \(-0.241252\pi\)
\(402\) 5.72284 25.2700i 0.285429 1.26036i
\(403\) 0.0125611 0.0566595i 0.000625713 0.00282241i
\(404\) 12.2650 3.24976i 0.610207 0.161682i
\(405\) 18.8232 14.0703i 0.935331 0.699160i
\(406\) 9.27908 3.13540i 0.460513 0.155607i
\(407\) −1.08750 + 1.55311i −0.0539053 + 0.0769848i
\(408\) 1.21724 + 33.5180i 0.0602623 + 1.65939i
\(409\) 12.5114 26.8308i 0.618648 1.32670i −0.308222 0.951314i \(-0.599734\pi\)
0.926871 0.375381i \(-0.122488\pi\)
\(410\) −36.0255 + 15.7917i −1.77917 + 0.779895i
\(411\) −7.40866 2.90797i −0.365442 0.143439i
\(412\) −20.0172 + 6.25008i −0.986177 + 0.307920i
\(413\) −10.1345 + 1.33423i −0.498685 + 0.0656532i
\(414\) −0.411737 + 0.0601332i −0.0202358 + 0.00295538i
\(415\) 14.0199 24.2832i 0.688210 1.19201i
\(416\) −0.0666145 + 2.31327i −0.00326604 + 0.113418i
\(417\) 2.35181 3.49584i 0.115169 0.171192i
\(418\) 0.375931 1.52708i 0.0183874 0.0746919i
\(419\) −17.9925 11.4625i −0.878991 0.559979i 0.0190854 0.999818i \(-0.493925\pi\)
−0.898077 + 0.439839i \(0.855036\pi\)
\(420\) 7.98223 + 12.1012i 0.389493 + 0.590478i
\(421\) 7.03062 13.5057i 0.342651 0.658227i −0.652369 0.757902i \(-0.726225\pi\)
0.995020 + 0.0996745i \(0.0317801\pi\)
\(422\) −2.28600 3.43159i −0.111281 0.167047i
\(423\) 2.01929 + 16.1223i 0.0981815 + 0.783892i
\(424\) −17.9805 20.6766i −0.873209 1.00415i
\(425\) 5.26117 + 11.2826i 0.255204 + 0.547287i
\(426\) −23.7840 + 16.4932i −1.15234 + 0.799098i
\(427\) −0.727593 + 2.30763i −0.0352107 + 0.111674i
\(428\) 0.295303 + 0.424249i 0.0142740 + 0.0205069i
\(429\) −0.159879 0.168069i −0.00771905 0.00811444i
\(430\) 12.2987 + 9.89895i 0.593095 + 0.477370i
\(431\) 5.67004i 0.273116i 0.990632 + 0.136558i \(0.0436040\pi\)
−0.990632 + 0.136558i \(0.956396\pi\)
\(432\) 18.8965 + 8.65586i 0.909156 + 0.416455i
\(433\) 21.9434i 1.05453i 0.849700 + 0.527266i \(0.176783\pi\)
−0.849700 + 0.527266i \(0.823217\pi\)
\(434\) 0.201599 0.250471i 0.00967707 0.0120230i
\(435\) 5.52822 18.7465i 0.265058 0.898825i
\(436\) 9.37317 + 1.67971i 0.448893 + 0.0804435i
\(437\) 0.100184 0.317743i 0.00479245 0.0151997i
\(438\) −6.34582 + 0.526141i −0.303215 + 0.0251400i
\(439\) 6.56183 + 14.0719i 0.313179 + 0.671615i 0.998390 0.0567303i \(-0.0180675\pi\)
−0.685210 + 0.728345i \(0.740290\pi\)
\(440\) −2.16395 1.07842i −0.103162 0.0514117i
\(441\) 2.95917 12.9610i 0.140913 0.617189i
\(442\) −3.29652 + 2.19602i −0.156799 + 0.104454i
\(443\) 13.6272 26.1776i 0.647447 1.24373i −0.308787 0.951131i \(-0.599923\pi\)
0.956234 0.292603i \(-0.0945215\pi\)
\(444\) 19.0362 6.33609i 0.903418 0.300698i
\(445\) 4.42524 + 2.81919i 0.209777 + 0.133642i
\(446\) −26.2254 6.45609i −1.24181 0.305705i
\(447\) −6.45378 13.1916i −0.305253 0.623940i
\(448\) −6.01513 + 11.3226i −0.284188 + 0.534945i
\(449\) −0.434796 + 0.753089i −0.0205193 + 0.0355405i −0.876103 0.482124i \(-0.839865\pi\)
0.855583 + 0.517665i \(0.173199\pi\)
\(450\) 7.71122 + 0.227631i 0.363510 + 0.0107306i
\(451\) 3.45718 0.455146i 0.162792 0.0214320i
\(452\) −3.07959 + 5.87578i −0.144852 + 0.276373i
\(453\) −0.129542 0.859651i −0.00608643 0.0403899i
\(454\) 10.3675 + 23.6514i 0.486573 + 1.11002i
\(455\) −0.723535 + 1.55163i −0.0339198 + 0.0727413i
\(456\) −12.8263 + 10.6032i −0.600647 + 0.496543i
\(457\) 10.1404 14.4819i 0.474346 0.677437i −0.508669 0.860962i \(-0.669862\pi\)
0.983015 + 0.183526i \(0.0587511\pi\)
\(458\) −3.02309 8.94669i −0.141260 0.418051i
\(459\) 6.61024 + 34.9551i 0.308540 + 1.63156i
\(460\) −0.442859 0.257334i −0.0206484 0.0119983i
\(461\) 7.53668 33.9957i 0.351018 1.58334i −0.395816 0.918330i \(-0.629538\pi\)
0.746834 0.665010i \(-0.231573\pi\)
\(462\) −0.380874 1.22740i −0.0177198 0.0571037i
\(463\) −11.1030 30.5052i −0.516000 1.41770i −0.874892 0.484319i \(-0.839067\pi\)
0.358892 0.933379i \(-0.383155\pi\)
\(464\) 16.8966 3.64712i 0.784403 0.169313i
\(465\) −0.177595 0.616523i −0.00823578 0.0285906i
\(466\) −13.0412 + 5.05052i −0.604121 + 0.233961i
\(467\) 4.61023 + 35.0182i 0.213336 + 1.62045i 0.678070 + 0.734997i \(0.262816\pi\)
−0.464734 + 0.885450i \(0.653850\pi\)
\(468\) 0.298260 + 2.43642i 0.0137871 + 0.112624i
\(469\) 16.8074 + 2.21273i 0.776092 + 0.102174i
\(470\) −10.3995 + 17.0841i −0.479694 + 0.788032i
\(471\) −1.09306 1.25435i −0.0503656 0.0577972i
\(472\) −18.0373 + 0.318091i −0.830232 + 0.0146413i
\(473\) −0.802758 1.14646i −0.0369108 0.0527141i
\(474\) 17.7602 + 31.0869i 0.815752 + 1.42787i
\(475\) −2.85214 + 5.47892i −0.130865 + 0.251390i
\(476\) −21.7648 + 2.80366i −0.997587 + 0.128506i
\(477\) −22.1456 18.8214i −1.01398 0.861772i
\(478\) −12.5066 25.4502i −0.572038 1.16407i
\(479\) 27.1348 + 9.87625i 1.23982 + 0.451258i 0.876950 0.480582i \(-0.159575\pi\)
0.362870 + 0.931840i \(0.381797\pi\)
\(480\) 11.5833 + 22.8120i 0.528701 + 1.04122i
\(481\) 1.81506 + 1.52301i 0.0827595 + 0.0694435i
\(482\) 28.4462 8.24829i 1.29569 0.375699i
\(483\) −0.0638766 0.264650i −0.00290649 0.0120420i
\(484\) −16.0210 14.7629i −0.728226 0.671042i
\(485\) 19.9504 8.26374i 0.905902 0.375237i
\(486\) 21.1933 + 6.06998i 0.961347 + 0.275340i
\(487\) −8.64027 + 8.64027i −0.391528 + 0.391528i −0.875232 0.483704i \(-0.839291\pi\)
0.483704 + 0.875232i \(0.339291\pi\)
\(488\) −1.73616 + 3.90137i −0.0785922 + 0.176607i
\(489\) 5.86359 + 0.921410i 0.265161 + 0.0416676i
\(490\) 12.7768 10.2252i 0.577195 0.461926i
\(491\) 2.51230 7.96801i 0.113379 0.359591i −0.879927 0.475109i \(-0.842408\pi\)
0.993305 + 0.115518i \(0.0368529\pi\)
\(492\) −32.2441 17.9397i −1.45368 0.808782i
\(493\) 21.8130 + 19.9879i 0.982409 + 0.900212i
\(494\) −1.86015 0.634331i −0.0836922 0.0285399i
\(495\) −2.44085 0.786537i −0.109708 0.0353522i
\(496\) 0.403472 0.398996i 0.0181164 0.0179154i
\(497\) −12.1724 14.5065i −0.546008 0.650708i
\(498\) 26.0936 3.31473i 1.16928 0.148537i
\(499\) 5.76476 9.04886i 0.258066 0.405083i −0.689677 0.724117i \(-0.742247\pi\)
0.947743 + 0.319035i \(0.103359\pi\)
\(500\) −12.6986 10.7159i −0.567901 0.479231i
\(501\) −8.27763 24.6398i −0.369817 1.10083i
\(502\) 14.9505 + 9.10076i 0.667275 + 0.406187i
\(503\) 28.2829 7.57839i 1.26107 0.337904i 0.434469 0.900687i \(-0.356936\pi\)
0.826605 + 0.562783i \(0.190269\pi\)
\(504\) −4.50600 + 12.8307i −0.200713 + 0.571527i
\(505\) 16.0013 + 4.28753i 0.712047 + 0.190792i
\(506\) 0.0313532 + 0.0328435i 0.00139382 + 0.00146007i
\(507\) 17.3781 13.8576i 0.771786 0.615437i
\(508\) −1.54715 1.69790i −0.0686436 0.0753321i
\(509\) 1.39301 31.9053i 0.0617443 1.41418i −0.674906 0.737903i \(-0.735816\pi\)
0.736651 0.676273i \(-0.236406\pi\)
\(510\) −20.3962 + 38.7498i −0.903158 + 1.71587i
\(511\) −0.723453 4.10290i −0.0320037 0.181502i
\(512\) −12.8062 + 18.6548i −0.565961 + 0.824432i
\(513\) −11.7631 + 13.1602i −0.519352 + 0.581038i
\(514\) 1.98402 29.6370i 0.0875114 1.30723i
\(515\) −26.7298 5.92585i −1.17785 0.261124i
\(516\) −0.411000 + 14.8041i −0.0180933 + 0.651716i
\(517\) 1.30722 1.19785i 0.0574915 0.0526813i
\(518\) 5.27002 + 12.0225i 0.231552 + 0.528238i
\(519\) 20.7883 + 34.5027i 0.912506 + 1.51450i
\(520\) −1.57824 + 2.57650i −0.0692105 + 0.112987i
\(521\) 8.54333 31.8841i 0.374290 1.39687i −0.480089 0.877220i \(-0.659396\pi\)
0.854379 0.519650i \(-0.173938\pi\)
\(522\) 17.1383 6.51336i 0.750122 0.285082i
\(523\) −34.6922 4.56731i −1.51698 0.199714i −0.674434 0.738335i \(-0.735612\pi\)
−0.842548 + 0.538621i \(0.818945\pi\)
\(524\) −3.48850 20.1121i −0.152396 0.878602i
\(525\) 0.314256 + 5.03771i 0.0137152 + 0.219864i
\(526\) 14.8878 9.00575i 0.649138 0.392669i
\(527\) 0.956464 + 0.168650i 0.0416642 + 0.00734653i
\(528\) −0.423045 2.22825i −0.0184107 0.0969722i
\(529\) −14.7779 17.6117i −0.642519 0.765724i
\(530\) −6.93039 35.0971i −0.301037 1.52452i
\(531\) −18.8642 + 3.20387i −0.818638 + 0.139036i
\(532\) −7.67768 7.72063i −0.332870 0.334732i
\(533\) −0.190078 4.35350i −0.00823319 0.188571i
\(534\) 0.406696 + 4.90520i 0.0175995 + 0.212269i
\(535\) 0.0588189 + 0.672303i 0.00254296 + 0.0290662i
\(536\) 29.0309 + 7.23265i 1.25394 + 0.312403i
\(537\) 28.5231 + 23.0403i 1.23086 + 0.994261i
\(538\) 36.2528 + 10.6216i 1.56297 + 0.457929i
\(539\) −1.34029 + 0.555167i −0.0577304 + 0.0239127i
\(540\) 15.7770 + 22.0787i 0.678932 + 0.950116i
\(541\) 5.42561 13.0986i 0.233265 0.563152i −0.763293 0.646053i \(-0.776418\pi\)
0.996558 + 0.0829009i \(0.0264185\pi\)
\(542\) 2.51421 + 23.2567i 0.107995 + 0.998962i
\(543\) −30.6640 13.6079i −1.31592 0.583972i
\(544\) −38.7244 + 0.574889i −1.66030 + 0.0246482i
\(545\) 9.52388 + 7.99148i 0.407958 + 0.342317i
\(546\) −1.56950 + 0.340475i −0.0671685 + 0.0145710i
\(547\) 8.03207 8.76546i 0.343426 0.374784i −0.541352 0.840796i \(-0.682087\pi\)
0.884778 + 0.466012i \(0.154310\pi\)
\(548\) 3.54059 8.48077i 0.151247 0.362281i
\(549\) −1.19980 + 4.36747i −0.0512062 + 0.186399i
\(550\) −0.466719 0.700607i −0.0199010 0.0298740i
\(551\) −1.27942 + 14.6238i −0.0545051 + 0.622996i
\(552\) −0.0592199 0.476814i −0.00252057 0.0202945i
\(553\) −19.1886 + 13.4360i −0.815981 + 0.571356i
\(554\) −0.796479 5.22324i −0.0338392 0.221914i
\(555\) 25.6746 + 5.19113i 1.08983 + 0.220351i
\(556\) 3.97746 + 2.80161i 0.168682 + 0.118815i
\(557\) 26.8147 20.5757i 1.13618 0.871819i 0.143149 0.989701i \(-0.454277\pi\)
0.993028 + 0.117883i \(0.0376106\pi\)
\(558\) 0.359610 0.482614i 0.0152235 0.0204307i
\(559\) −1.51469 + 0.874504i −0.0640644 + 0.0369876i
\(560\) −14.1678 + 8.91518i −0.598699 + 0.376735i
\(561\) 2.69325 2.79572i 0.113709 0.118036i
\(562\) −0.351452 17.2069i −0.0148251 0.725829i
\(563\) 11.9507 + 0.521780i 0.503663 + 0.0219904i 0.294043 0.955792i \(-0.404999\pi\)
0.209621 + 0.977783i \(0.432777\pi\)
\(564\) −18.6621 + 1.93175i −0.785818 + 0.0813413i
\(565\) −7.30479 + 4.65367i −0.307315 + 0.195781i
\(566\) 8.60444 + 25.4645i 0.361672 + 1.07035i
\(567\) −2.68345 + 14.1721i −0.112694 + 0.595171i
\(568\) −18.4511 27.8657i −0.774192 1.16922i
\(569\) −37.0156 25.9186i −1.55178 1.08657i −0.959828 0.280590i \(-0.909470\pi\)
−0.591948 0.805976i \(-0.701641\pi\)
\(570\) −21.4141 + 3.67562i −0.896938 + 0.153955i
\(571\) −21.0571 + 19.2953i −0.881214 + 0.807484i −0.982285 0.187396i \(-0.939995\pi\)
0.101071 + 0.994879i \(0.467773\pi\)
\(572\) 0.197985 0.180407i 0.00827817 0.00754318i
\(573\) 42.8918 18.7118i 1.79183 0.781698i
\(574\) 9.75396 22.0840i 0.407122 0.921767i
\(575\) −0.0891688 0.154445i −0.00371860 0.00644080i
\(576\) −10.4607 + 21.6003i −0.435865 + 0.900012i
\(577\) −18.6958 + 32.3821i −0.778318 + 1.34809i 0.154593 + 0.987978i \(0.450593\pi\)
−0.932911 + 0.360107i \(0.882740\pi\)
\(578\) −24.9328 34.1037i −1.03707 1.41853i
\(579\) 23.3036 + 35.1152i 0.968463 + 1.45934i
\(580\) 21.5046 + 6.84638i 0.892931 + 0.284280i
\(581\) 3.72488 + 16.8018i 0.154534 + 0.697058i
\(582\) 17.4968 + 10.2081i 0.725265 + 0.423138i
\(583\) −0.276409 + 3.15937i −0.0114477 + 0.130848i
\(584\) −0.450191 7.33887i −0.0186290 0.303685i
\(585\) −1.24503 + 2.95301i −0.0514756 + 0.122092i
\(586\) −5.27317 + 5.99601i −0.217833 + 0.247693i
\(587\) 1.06360 + 24.3605i 0.0438996 + 1.00547i 0.885290 + 0.465039i \(0.153960\pi\)
−0.841390 + 0.540428i \(0.818262\pi\)
\(588\) 14.8893 + 3.73724i 0.614024 + 0.154121i
\(589\) 0.222513 + 0.427443i 0.00916847 + 0.0176125i
\(590\) −20.6338 11.3575i −0.849480 0.467583i
\(591\) −18.1014 + 40.7895i −0.744591 + 1.67785i
\(592\) 6.84302 + 22.1330i 0.281247 + 0.909661i
\(593\) 24.1333i 0.991038i −0.868597 0.495519i \(-0.834978\pi\)
0.868597 0.495519i \(-0.165022\pi\)
\(594\) −0.798214 2.26935i −0.0327511 0.0931125i
\(595\) −26.4699 10.9642i −1.08516 0.449489i
\(596\) 15.3887 7.12368i 0.630345 0.291797i
\(597\) −4.53474 + 2.46929i −0.185594 + 0.101061i
\(598\) 0.0443026 0.0354552i 0.00181167 0.00144987i
\(599\) −0.772775 8.83286i −0.0315747 0.360901i −0.995502 0.0947365i \(-0.969799\pi\)
0.963928 0.266164i \(-0.0857564\pi\)
\(600\) −0.453814 + 8.89646i −0.0185269 + 0.363197i
\(601\) 12.5472 5.85083i 0.511809 0.238660i −0.149517 0.988759i \(-0.547772\pi\)
0.661326 + 0.750099i \(0.269994\pi\)
\(602\) −9.66993 + 0.620260i −0.394117 + 0.0252799i
\(603\) 31.5943 + 2.96482i 1.28662 + 0.120737i
\(604\) 0.995620 0.128252i 0.0405112 0.00521850i
\(605\) −8.55307 27.1269i −0.347732 1.10286i
\(606\) 5.88154 + 14.3838i 0.238921 + 0.584303i
\(607\) −1.91745 + 10.8744i −0.0778268 + 0.441378i 0.920848 + 0.389921i \(0.127498\pi\)
−0.998675 + 0.0514569i \(0.983614\pi\)
\(608\) −11.9230 15.0698i −0.483542 0.611162i
\(609\) 5.27167 + 10.7753i 0.213619 + 0.436638i
\(610\) −4.50069 + 3.29040i −0.182228 + 0.133225i
\(611\) −1.34885 1.75786i −0.0545687 0.0711153i
\(612\) −40.5171 + 6.76516i −1.63781 + 0.273465i
\(613\) −6.17981 4.74193i −0.249600 0.191525i 0.476382 0.879238i \(-0.341948\pi\)
−0.725982 + 0.687713i \(0.758615\pi\)
\(614\) 10.3299 9.86120i 0.416882 0.397965i
\(615\) −24.8620 41.2638i −1.00253 1.66392i
\(616\) 1.42639 0.409288i 0.0574707 0.0164907i
\(617\) 16.8125 + 7.83978i 0.676845 + 0.315618i 0.730471 0.682943i \(-0.239300\pi\)
−0.0536269 + 0.998561i \(0.517078\pi\)
\(618\) −10.7483 23.3260i −0.432361 0.938309i
\(619\) 38.8747 24.7659i 1.56251 0.995426i 0.578837 0.815444i \(-0.303507\pi\)
0.983670 0.179983i \(-0.0576042\pi\)
\(620\) 0.716135 0.189749i 0.0287607 0.00762050i
\(621\) −0.137978 0.490589i −0.00553685 0.0196867i
\(622\) 28.0456 24.5262i 1.12453 0.983412i
\(623\) −3.17146 + 0.559215i −0.127062 + 0.0224045i
\(624\) −2.82008 + 0.283965i −0.112894 + 0.0113677i
\(625\) −10.5292 28.9288i −0.421168 1.15715i
\(626\) 0.315286 + 15.4362i 0.0126014 + 0.616956i
\(627\) 1.91400 + 0.215721i 0.0764379 + 0.00861506i
\(628\) 1.47514 1.23079i 0.0588644 0.0491140i
\(629\) −24.1385 + 31.4579i −0.962464 + 1.25431i
\(630\) −13.4384 + 11.6035i −0.535400 + 0.462294i
\(631\) 28.5626 7.65332i 1.13706 0.304674i 0.359290 0.933226i \(-0.383019\pi\)
0.777768 + 0.628552i \(0.216352\pi\)
\(632\) −36.3278 + 19.7329i −1.44504 + 0.784931i
\(633\) 3.80725 3.31771i 0.151325 0.131867i
\(634\) 5.27659 7.17536i 0.209560 0.284970i
\(635\) −0.649113 2.92796i −0.0257593 0.116193i
\(636\) 22.2767 25.0994i 0.883328 0.995257i
\(637\) 0.545160 + 1.72903i 0.0216000 + 0.0685066i
\(638\) −1.66194 1.11383i −0.0657969 0.0440969i
\(639\) −23.7832 26.2853i −0.940848 1.03983i
\(640\) −26.6220 + 12.8070i −1.05233 + 0.506241i
\(641\) −25.7436 9.36989i −1.01681 0.370088i −0.220765 0.975327i \(-0.570855\pi\)
−0.796044 + 0.605239i \(0.793078\pi\)
\(642\) −0.468692 + 0.425575i −0.0184978 + 0.0167961i
\(643\) 8.02344 4.17674i 0.316414 0.164715i −0.296138 0.955145i \(-0.595699\pi\)
0.612551 + 0.790431i \(0.290143\pi\)
\(644\) 0.307104 0.0671853i 0.0121016 0.00264747i
\(645\) −10.0829 + 16.4987i −0.397013 + 0.649634i
\(646\) 9.24757 31.5631i 0.363841 1.24183i
\(647\) −17.5454 + 17.5454i −0.689781 + 0.689781i −0.962183 0.272402i \(-0.912182\pi\)
0.272402 + 0.962183i \(0.412182\pi\)
\(648\) −7.53242 + 24.3159i −0.295901 + 0.955219i
\(649\) 1.47642 + 1.47642i 0.0579547 + 0.0579547i
\(650\) −0.923036 + 0.504722i −0.0362045 + 0.0197968i
\(651\) 0.336007 + 0.205345i 0.0131691 + 0.00804810i
\(652\) −1.20896 + 6.74631i −0.0473467 + 0.264206i
\(653\) −6.37177 12.2401i −0.249347 0.478991i 0.729393 0.684094i \(-0.239802\pi\)
−0.978740 + 0.205104i \(0.934247\pi\)
\(654\) −0.561659 + 11.6491i −0.0219626 + 0.455515i
\(655\) 9.11498 25.0432i 0.356152 0.978518i
\(656\) 21.5089 36.7793i 0.839783 1.43599i
\(657\) −1.63994 7.62431i −0.0639803 0.297452i
\(658\) −2.37805 12.0430i −0.0927059 0.469484i
\(659\) −31.7569 + 10.0129i −1.23707 + 0.390047i −0.847424 0.530917i \(-0.821848\pi\)
−0.389648 + 0.920964i \(0.627403\pi\)
\(660\) 0.968472 2.79832i 0.0376977 0.108924i
\(661\) 13.1318 2.91124i 0.510767 0.113234i 0.0464800 0.998919i \(-0.485200\pi\)
0.464287 + 0.885685i \(0.346311\pi\)
\(662\) −0.878198 5.75914i −0.0341321 0.223835i
\(663\) −3.18712 3.65739i −0.123778 0.142041i
\(664\) 3.18023 + 30.2055i 0.123417 + 1.17220i
\(665\) −3.67930 13.7313i −0.142677 0.532479i
\(666\) 10.6980 + 22.1209i 0.414541 + 0.857169i
\(667\) −0.336249 0.258013i −0.0130196 0.00999029i
\(668\) 28.6501 8.94558i 1.10851 0.346115i
\(669\) 3.70470 32.8703i 0.143232 1.27084i
\(670\) 28.1787 + 27.0507i 1.08864 + 1.04506i
\(671\) 0.464436 0.169041i 0.0179293 0.00652575i
\(672\) −14.7006 5.51973i −0.567089 0.212928i
\(673\) −4.02073 22.8027i −0.154988 0.878979i −0.958797 0.284092i \(-0.908308\pi\)
0.803809 0.594887i \(-0.202803\pi\)
\(674\) 28.0610 + 1.87852i 1.08087 + 0.0723577i
\(675\) 0.939818 + 9.40154i 0.0361736 + 0.361865i
\(676\) 15.5672 + 20.4051i 0.598738 + 0.784812i
\(677\) −9.85137 15.4635i −0.378619 0.594312i 0.599999 0.800001i \(-0.295168\pi\)
−0.978618 + 0.205689i \(0.934057\pi\)
\(678\) −7.62215 2.81353i −0.292727 0.108053i
\(679\) −5.60126 + 12.0119i −0.214957 + 0.460976i
\(680\) −44.2288 24.5060i −1.69610 0.939763i
\(681\) −27.0905 + 16.3224i −1.03811 + 0.625475i
\(682\) −0.0656584 0.00152427i −0.00251419 5.83674e-5i
\(683\) −11.6932 + 15.2388i −0.447427 + 0.583098i −0.961554 0.274616i \(-0.911449\pi\)
0.514127 + 0.857714i \(0.328116\pi\)
\(684\) −14.9012 13.9057i −0.569762 0.531698i
\(685\) 9.51919 7.30433i 0.363709 0.279084i
\(686\) −3.97714 + 25.6024i −0.151848 + 0.977503i
\(687\) 10.3893 5.08283i 0.396378 0.193922i
\(688\) −17.0802 0.841213i −0.651178 0.0320710i
\(689\) 3.90307 + 0.688217i 0.148695 + 0.0262190i
\(690\) 0.242692 0.578462i 0.00923914 0.0220217i
\(691\) −35.2589 + 11.1171i −1.34131 + 0.422914i −0.884455 0.466625i \(-0.845470\pi\)
−0.456858 + 0.889540i \(0.651025\pi\)
\(692\) −40.3461 + 23.1440i −1.53373 + 0.879804i
\(693\) 1.43066 0.656185i 0.0543461 0.0249264i
\(694\) −0.211296 + 0.240260i −0.00802069 + 0.00912016i
\(695\) 2.68442 + 5.75675i 0.101826 + 0.218366i
\(696\) 7.09468 + 19.9464i 0.268923 + 0.756066i
\(697\) 72.6478 6.35586i 2.75173 0.240745i
\(698\) −12.8860 1.42944i −0.487743 0.0541049i
\(699\) −8.19106 15.0425i −0.309814 0.568960i
\(700\) −5.82349 + 0.237989i −0.220107 + 0.00899516i
\(701\) 5.66519 13.6770i 0.213971 0.516572i −0.780055 0.625710i \(-0.784809\pi\)
0.994027 + 0.109138i \(0.0348092\pi\)
\(702\) −2.91210 + 0.746546i −0.109910 + 0.0281766i
\(703\) −19.6741 −0.742022
\(704\) 2.58285 0.433178i 0.0973449 0.0163260i
\(705\) −22.3898 9.93603i −0.843248 0.374213i
\(706\) 0.793454 + 2.73641i 0.0298620 + 0.102986i
\(707\) −9.01862 + 4.69480i −0.339180 + 0.176566i
\(708\) −3.23134 21.8569i −0.121441 0.821433i
\(709\) −17.9205 + 0.782427i −0.673019 + 0.0293846i −0.377580 0.925977i \(-0.623244\pi\)
−0.295439 + 0.955362i \(0.595466\pi\)
\(710\) −2.79308 43.5445i −0.104822 1.63419i
\(711\) −34.9552 + 26.4739i −1.31092 + 0.992848i
\(712\) −5.67281 + 0.347989i −0.212597 + 0.0130414i
\(713\) −0.0138602 0.00121261i −0.000519070 4.54127e-5i
\(714\) −6.83812 25.9921i −0.255910 0.972730i
\(715\) 0.341418 0.0756904i 0.0127683 0.00283066i
\(716\) −27.3051 + 32.3572i −1.02044 + 1.20925i
\(717\) 28.9378 19.2041i 1.08070 0.717189i
\(718\) −15.0424 2.33673i −0.561378 0.0872059i
\(719\) 17.1293 + 9.88960i 0.638815 + 0.368820i 0.784158 0.620562i \(-0.213095\pi\)
−0.145343 + 0.989381i \(0.546429\pi\)
\(720\) −25.8793 + 17.6665i −0.964463 + 0.658392i
\(721\) 14.5527 8.40203i 0.541972 0.312908i
\(722\) −9.83896 + 3.81038i −0.366168 + 0.141808i
\(723\) 14.5047 + 33.2482i 0.539437 + 1.23651i
\(724\) 16.4691 35.0625i 0.612069 1.30309i
\(725\) 5.30868 + 5.79340i 0.197159 + 0.215162i
\(726\) 15.4033 21.7867i 0.571669 0.808582i
\(727\) 6.08699 8.69312i 0.225754 0.322410i −0.690256 0.723565i \(-0.742502\pi\)
0.916010 + 0.401155i \(0.131391\pi\)
\(728\) −0.354175 1.82032i −0.0131266 0.0674656i
\(729\) −4.02947 + 26.6976i −0.149240 + 0.988801i
\(730\) 4.25781 8.60372i 0.157589 0.318438i
\(731\) −15.7266 24.6858i −0.581669 0.913038i
\(732\) −5.01223 1.49328i −0.185257 0.0551934i
\(733\) −1.64703 + 37.7232i −0.0608344 + 1.39334i 0.685648 + 0.727933i \(0.259519\pi\)
−0.746483 + 0.665405i \(0.768259\pi\)
\(734\) 25.6748 + 24.6470i 0.947673 + 0.909736i
\(735\) 14.4342 + 13.9051i 0.532414 + 0.512899i
\(736\) 0.551917 0.0565535i 0.0203439 0.00208459i
\(737\) −1.73139 2.99885i −0.0637765 0.110464i
\(738\) 16.7027 41.9915i 0.614835 1.54573i
\(739\) −10.8997 14.2048i −0.400952 0.522530i 0.548624 0.836069i \(-0.315152\pi\)
−0.949575 + 0.313539i \(0.898485\pi\)
\(740\) −6.62885 + 29.5111i −0.243681 + 1.08485i
\(741\) 0.477023 2.35929i 0.0175239 0.0866708i
\(742\) 17.6892 + 13.0082i 0.649391 + 0.477547i
\(743\) −18.9884 27.1182i −0.696616 0.994871i −0.999129 0.0417254i \(-0.986715\pi\)
0.302513 0.953145i \(-0.402174\pi\)
\(744\) 0.548238 + 0.427101i 0.0200994 + 0.0156583i
\(745\) 22.0555 + 1.92961i 0.808051 + 0.0706953i
\(746\) 2.82819 14.1154i 0.103547 0.516801i
\(747\) 8.14163 + 31.1691i 0.297887 + 1.14042i
\(748\) 3.16076 + 3.17844i 0.115569 + 0.116215i
\(749\) −0.305388 0.279837i −0.0111586 0.0102250i
\(750\) 11.0120 17.1133i 0.402102 0.624890i
\(751\) −18.3912 + 21.9178i −0.671104 + 0.799791i −0.988934 0.148357i \(-0.952602\pi\)
0.317830 + 0.948148i \(0.397046\pi\)
\(752\) −1.76777 21.5921i −0.0644638 0.787382i
\(753\) −8.69515 + 19.5936i −0.316869 + 0.714030i
\(754\) −1.56765 + 1.94768i −0.0570903 + 0.0709302i
\(755\) 1.21085 + 0.501552i 0.0440675 + 0.0182534i
\(756\) −16.2943 3.44896i −0.592617 0.125437i
\(757\) −3.83392 9.25590i −0.139346 0.336411i 0.838765 0.544493i \(-0.183278\pi\)
−0.978111 + 0.208082i \(0.933278\pi\)
\(758\) 36.1235 19.7526i 1.31207 0.717445i
\(759\) −0.0349447 + 0.0432603i −0.00126841 + 0.00157025i
\(760\) −3.71278 24.8122i −0.134677 0.900034i
\(761\) 16.1801 1.41557i 0.586527 0.0513145i 0.209970 0.977708i \(-0.432663\pi\)
0.376557 + 0.926393i \(0.377108\pi\)
\(762\) 1.81815 2.14689i 0.0658644 0.0777737i
\(763\) −7.62337 + 0.332843i −0.275984 + 0.0120497i
\(764\) 20.5390 + 49.9794i 0.743076 + 1.80819i
\(765\) −50.2804 18.6601i −1.81789 0.674658i
\(766\) −40.0931 26.8703i −1.44862 0.970864i
\(767\) 1.99884 1.67723i 0.0721740 0.0605612i
\(768\) −24.6770 12.6114i −0.890454 0.455073i
\(769\) 4.60472 26.1147i 0.166051 0.941720i −0.781924 0.623374i \(-0.785762\pi\)
0.947975 0.318346i \(-0.103127\pi\)
\(770\) 1.88127 + 0.463125i 0.0677962 + 0.0166899i
\(771\) 36.3085 2.26495i 1.30762 0.0815700i
\(772\) −41.1155 + 26.0325i −1.47978 + 0.936932i
\(773\) 1.65826 12.5957i 0.0596435 0.453037i −0.935400 0.353592i \(-0.884960\pi\)
0.995043 0.0994449i \(-0.0317067\pi\)
\(774\) −18.0451 + 1.83587i −0.648619 + 0.0659890i
\(775\) 0.249160 + 0.0667623i 0.00895011 + 0.00239817i
\(776\) −12.2180 + 19.9460i −0.438600 + 0.716020i
\(777\) −13.7706 + 8.29699i −0.494018 + 0.297653i
\(778\) 5.57836 14.2857i 0.199994 0.512168i
\(779\) 24.4452 + 26.6772i 0.875840 + 0.955811i
\(780\) −3.37821 1.51046i −0.120959 0.0540831i
\(781\) −0.837221 + 3.77646i −0.0299581 + 0.135132i
\(782\) 0.625118 + 0.714818i 0.0223542 + 0.0255619i
\(783\) 10.6140 + 19.7879i 0.379313 + 0.707161i
\(784\) −4.68325 + 17.0961i −0.167259 + 0.610576i
\(785\) 2.47017 0.435557i 0.0881640 0.0155457i
\(786\) 23.8768 7.40922i 0.851659 0.264278i
\(787\) −20.6294 0.900697i −0.735357 0.0321064i −0.327121 0.944983i \(-0.606078\pi\)
−0.408236 + 0.912876i \(0.633856\pi\)
\(788\) −46.6404 21.9073i −1.66149 0.780416i
\(789\) 13.2861 + 16.6614i 0.472999 + 0.593162i
\(790\) −53.9604 1.25270i −1.91983 0.0445692i
\(791\) 1.37586 5.13479i 0.0489201 0.182572i
\(792\) 2.63959 0.865268i 0.0937937 0.0307460i
\(793\) −0.159858 0.596599i −0.00567673 0.0211858i
\(794\) −6.84791 28.1551i −0.243023 0.999187i
\(795\) 41.5339 13.9531i 1.47306 0.494866i
\(796\) −2.73830 5.29623i −0.0970563 0.187720i
\(797\) 34.5518 + 22.0119i 1.22389 + 0.779702i 0.981683 0.190523i \(-0.0610183\pi\)
0.242205 + 0.970225i \(0.422129\pi\)
\(798\) 8.16606 10.5427i 0.289075 0.373206i
\(799\) 28.4052 23.8348i 1.00490 0.843213i
\(800\) −10.2591 0.744289i −0.362716 0.0263146i
\(801\) −5.89344 + 1.26765i −0.208234 + 0.0447900i
\(802\) 9.93090 + 20.2089i 0.350672 + 0.713600i
\(803\) −0.574932 + 0.627428i −0.0202889 + 0.0221415i
\(804\) −4.20537 + 36.4001i −0.148312 + 1.28373i
\(805\) 0.391441 + 0.123421i 0.0137965 + 0.00435001i
\(806\) −0.00904890 + 0.0815737i −0.000318734 + 0.00287331i
\(807\) −7.18227 + 45.7060i −0.252828 + 1.60893i
\(808\) −16.7509 + 6.43353i −0.589294 + 0.226331i
\(809\) −19.6654 19.6654i −0.691399 0.691399i 0.271141 0.962540i \(-0.412599\pi\)
−0.962540 + 0.271141i \(0.912599\pi\)
\(810\) −24.3271 + 22.6443i −0.854767 + 0.795640i
\(811\) 9.38549 + 22.6586i 0.329569 + 0.795651i 0.998624 + 0.0524376i \(0.0166991\pi\)
−0.669055 + 0.743213i \(0.733301\pi\)
\(812\) −12.5700 + 5.81886i −0.441120 + 0.204202i
\(813\) −27.8498 + 6.72190i −0.976735 + 0.235747i
\(814\) 1.29297 2.34901i 0.0453187 0.0823326i
\(815\) −5.75184 + 6.85478i −0.201478 + 0.240112i
\(816\) −6.80621 46.9419i −0.238265 1.64330i
\(817\) 4.96708 13.6470i 0.173776 0.477446i
\(818\) −13.5130 + 39.6264i −0.472470 + 1.38550i
\(819\) −0.661079 1.85253i −0.0231000 0.0647326i
\(820\) 48.2522 27.6793i 1.68504 0.966603i
\(821\) −2.99824 1.56079i −0.104639 0.0544718i 0.408625 0.912702i \(-0.366008\pi\)
−0.513264 + 0.858231i \(0.671564\pi\)
\(822\) 10.8587 + 2.96254i 0.378742 + 0.103331i
\(823\) −11.7510 + 8.22816i −0.409615 + 0.286816i −0.760167 0.649728i \(-0.774883\pi\)
0.350552 + 0.936543i \(0.385994\pi\)
\(824\) 27.1946 11.8304i 0.947369 0.412131i
\(825\) 0.777304 0.677358i 0.0270623 0.0235826i
\(826\) 14.0465 3.41640i 0.488740 0.118872i
\(827\) −3.80742 + 28.9202i −0.132397 + 1.00566i 0.788276 + 0.615322i \(0.210974\pi\)
−0.920673 + 0.390334i \(0.872360\pi\)
\(828\) 0.569771 0.147133i 0.0198009 0.00511322i
\(829\) −52.5178 + 6.91410i −1.82402 + 0.240136i −0.963202 0.268780i \(-0.913380\pi\)
−0.860816 + 0.508916i \(0.830046\pi\)
\(830\) −16.0212 + 36.2737i −0.556104 + 1.25908i
\(831\) 6.21824 1.79122i 0.215708 0.0621367i
\(832\) −0.257957 3.26264i −0.00894306 0.113112i
\(833\) −28.5098 + 10.3767i −0.987807 + 0.359532i
\(834\) −2.77532 + 5.27270i −0.0961016 + 0.182579i
\(835\) 38.2576 + 8.48151i 1.32396 + 0.293515i
\(836\) −0.296451 + 2.20425i −0.0102530 + 0.0762355i
\(837\) 0.642878 + 0.360640i 0.0222211 + 0.0124655i
\(838\) 27.0402 + 13.3816i 0.934087 + 0.462261i
\(839\) 33.2959 + 23.3140i 1.14950 + 0.804889i 0.983441 0.181227i \(-0.0580068\pi\)
0.166059 + 0.986116i \(0.446896\pi\)
\(840\) −13.0626 15.8013i −0.450702 0.545195i
\(841\) −9.35790 4.36366i −0.322686 0.150471i
\(842\) −7.83233 + 20.0580i −0.269920 + 0.691243i
\(843\) 20.8431 3.14089i 0.717876 0.108178i
\(844\) 3.73577 + 4.47741i 0.128590 + 0.154119i
\(845\) 4.37374 + 33.2219i 0.150461 + 1.14287i
\(846\) −5.28977 22.3613i −0.181866 0.768799i
\(847\) 15.1186 + 8.72872i 0.519481 + 0.299923i
\(848\) 28.4238 + 26.3388i 0.976077 + 0.904477i
\(849\) −29.5706 + 14.4670i −1.01486 + 0.496506i
\(850\) −9.11228 15.0639i −0.312549 0.516687i
\(851\) 0.305203 0.479072i 0.0104622 0.0164224i
\(852\) 30.9339 26.8050i 1.05978 0.918323i
\(853\) −13.9428 7.25818i −0.477393 0.248515i 0.206019 0.978548i \(-0.433949\pi\)
−0.683412 + 0.730033i \(0.739505\pi\)
\(854\) 0.672250 3.35517i 0.0230039 0.114812i
\(855\) −7.84184 25.4286i −0.268185 0.869641i
\(856\) −0.479688 0.551617i −0.0163954 0.0188539i
\(857\) −22.8655 + 10.6623i −0.781070 + 0.364219i −0.771904 0.635739i \(-0.780695\pi\)
−0.00916585 + 0.999958i \(0.502918\pi\)
\(858\) 0.250340 + 0.212006i 0.00854648 + 0.00723778i
\(859\) −44.9123 14.1608i −1.53239 0.483161i −0.587133 0.809490i \(-0.699744\pi\)
−0.945256 + 0.326330i \(0.894188\pi\)
\(860\) −18.7968 12.0487i −0.640967 0.410858i
\(861\) 28.3605 + 8.36334i 0.966523 + 0.285022i
\(862\) −0.861849 7.97220i −0.0293547 0.271534i
\(863\) −24.1497 −0.822066 −0.411033 0.911621i \(-0.634832\pi\)
−0.411033 + 0.911621i \(0.634832\pi\)
\(864\) −27.8845 9.29806i −0.948650 0.316326i
\(865\) −60.7272 −2.06479
\(866\) −3.33541 30.8529i −0.113342 1.04842i
\(867\) 37.4879 35.6612i 1.27315 1.21112i
\(868\) −0.245381 + 0.382811i −0.00832878 + 0.0129935i
\(869\) 4.56342 + 1.43884i 0.154803 + 0.0488094i
\(870\) −4.92333 + 27.1982i −0.166916 + 0.922107i
\(871\) −3.92192 + 1.82882i −0.132889 + 0.0619672i
\(872\) −13.4342 0.936979i −0.454939 0.0317301i
\(873\) −9.63841 + 22.8608i −0.326211 + 0.773719i
\(874\) −0.0925638 + 0.461982i −0.00313102 + 0.0156268i
\(875\) 11.8103 + 6.14806i 0.399262 + 0.207842i
\(876\) 8.84239 1.70433i 0.298757 0.0575841i
\(877\) 5.10752 8.01720i 0.172469 0.270722i −0.746224 0.665695i \(-0.768135\pi\)
0.918693 + 0.394973i \(0.129246\pi\)
\(878\) −11.3650 18.7880i −0.383551 0.634064i
\(879\) −8.11417 5.45876i −0.273684 0.184119i
\(880\) 3.20648 + 1.18736i 0.108091 + 0.0400259i
\(881\) 46.6370 + 26.9259i 1.57124 + 0.907156i 0.996017 + 0.0891603i \(0.0284183\pi\)
0.575224 + 0.817996i \(0.304915\pi\)
\(882\) −2.19057 + 18.6732i −0.0737604 + 0.628759i
\(883\) −5.42514 41.2081i −0.182571 1.38676i −0.799936 0.600085i \(-0.795133\pi\)
0.617366 0.786676i \(-0.288200\pi\)
\(884\) 4.30118 3.58872i 0.144664 0.120702i
\(885\) 10.5397 26.8521i 0.354288 0.902623i
\(886\) −15.1811 + 38.8776i −0.510019 + 1.30612i
\(887\) −13.2544 6.18065i −0.445041 0.207526i 0.187162 0.982329i \(-0.440071\pi\)
−0.632202 + 0.774803i \(0.717849\pi\)
\(888\) −25.8022 + 11.8022i −0.865865 + 0.396056i
\(889\) 1.50782 + 1.05578i 0.0505706 + 0.0354099i
\(890\) −6.65050 3.29120i −0.222925 0.110321i
\(891\) 2.63032 1.32741i 0.0881192 0.0444699i
\(892\) 37.8548 + 5.09112i 1.26747 + 0.170463i
\(893\) 17.9621 + 3.98210i 0.601078 + 0.133256i
\(894\) 11.0793 + 17.5666i 0.370547 + 0.587517i
\(895\) −51.9436 + 18.9059i −1.73628 + 0.631955i
\(896\) 6.73635 16.8342i 0.225046 0.562391i
\(897\) 0.0500497 + 0.0482152i 0.00167111 + 0.00160986i
\(898\) 0.496863 1.12495i 0.0165805 0.0375400i
\(899\) 0.607791 0.0800173i 0.0202710 0.00266873i
\(900\) −10.8767 + 0.852056i −0.362558 + 0.0284019i
\(901\) −8.65723 + 65.7582i −0.288414 + 2.19072i
\(902\) −4.79169 + 1.16544i −0.159546 + 0.0388049i
\(903\) −2.27857 11.6467i −0.0758260 0.387579i
\(904\) 3.43685 8.72957i 0.114308 0.290341i
\(905\) 41.4293 29.0091i 1.37716 0.964296i
\(906\) 0.312807 + 1.18900i 0.0103923 + 0.0395018i
\(907\) 38.2219 + 19.8971i 1.26914 + 0.660672i 0.957199 0.289430i \(-0.0934658\pi\)
0.311940 + 0.950102i \(0.399021\pi\)
\(908\) −18.1720 31.6786i −0.603060 1.05129i
\(909\) −16.5421 + 9.41215i −0.548668 + 0.312181i
\(910\) 0.781457 2.29160i 0.0259051 0.0759657i
\(911\) 3.45665 9.49707i 0.114524 0.314652i −0.869167 0.494519i \(-0.835344\pi\)
0.983691 + 0.179867i \(0.0575666\pi\)
\(912\) 16.4224 16.8580i 0.543799 0.558224i
\(913\) 2.25962 2.69291i 0.0747826 0.0891224i
\(914\) −12.0563 + 21.9033i −0.398787 + 0.724495i
\(915\) −4.70624 4.94730i −0.155583 0.163553i
\(916\) 5.61042 + 12.1197i 0.185374 + 0.400447i
\(917\) 6.25956 + 15.1119i 0.206709 + 0.499040i
\(918\) −14.6073 48.1428i −0.482114 1.58895i
\(919\) 34.6917 + 34.6917i 1.14437 + 1.14437i 0.987641 + 0.156732i \(0.0500960\pi\)
0.156732 + 0.987641i \(0.449904\pi\)
\(920\) 0.661784 + 0.294503i 0.0218184 + 0.00970946i
\(921\) 13.6062 + 10.9908i 0.448340 + 0.362159i
\(922\) −5.42935 + 48.9443i −0.178806 + 1.61190i
\(923\) 4.61022 + 1.45360i 0.151747 + 0.0478457i
\(924\) 0.722082 + 1.66785i 0.0237547 + 0.0548684i
\(925\) −7.11482 + 7.76446i −0.233934 + 0.255294i
\(926\) 20.2479 + 41.2033i 0.665386 + 1.35403i
\(927\) 26.6352 16.7335i 0.874814 0.549601i
\(928\) −23.2026 + 7.69622i −0.761661 + 0.252641i
\(929\) 35.6447 29.9095i 1.16947 0.981298i 0.169475 0.985535i \(-0.445793\pi\)
0.999991 + 0.00423619i \(0.00134842\pi\)
\(930\) 0.343414 + 0.839850i 0.0112610 + 0.0275398i
\(931\) −12.6961 8.08829i −0.416097 0.265083i
\(932\) 17.5685 9.08340i 0.575475 0.297537i
\(933\) 34.2118 + 30.1942i 1.12005 + 0.988512i
\(934\) −11.8049 48.5355i −0.386267 1.58813i
\(935\) 1.51470 + 5.65294i 0.0495360 + 0.184871i
\(936\) −0.789698 3.38033i −0.0258121 0.110490i
\(937\) 10.1105 37.7328i 0.330295 1.23268i −0.578586 0.815622i \(-0.696395\pi\)
0.908881 0.417056i \(-0.136938\pi\)
\(938\) −23.9679 0.556419i −0.782578 0.0181677i
\(939\) −18.6983 + 2.81768i −0.610196 + 0.0919514i
\(940\) 12.0252 25.6014i 0.392217 0.835025i
\(941\) −18.7352 0.817998i −0.610751 0.0266660i −0.263844 0.964565i \(-0.584990\pi\)
−0.346907 + 0.937899i \(0.612768\pi\)
\(942\) 1.72753 + 1.59749i 0.0562859 + 0.0520490i
\(943\) −1.02882 + 0.181408i −0.0335029 + 0.00590747i
\(944\) 25.3124 3.18892i 0.823849 0.103790i
\(945\) −16.2126 14.4914i −0.527396 0.471405i
\(946\) 1.30296 + 1.48992i 0.0423628 + 0.0484416i
\(947\) 10.2381 46.1809i 0.332692 1.50068i −0.458270 0.888813i \(-0.651531\pi\)
0.790962 0.611865i \(-0.209580\pi\)
\(948\) −29.6964 41.0093i −0.964495 1.33192i
\(949\) 0.718481 + 0.784084i 0.0233229 + 0.0254524i
\(950\) 3.17738 8.13700i 0.103088 0.263999i
\(951\) 9.54708 + 5.27690i 0.309585 + 0.171115i
\(952\) 30.1756 7.25027i 0.977996 0.234982i
\(953\) 50.3838 + 13.5003i 1.63209 + 0.437317i 0.954522 0.298142i \(-0.0963669\pi\)
0.677569 + 0.735459i \(0.263034\pi\)
\(954\) 33.9981 + 23.0971i 1.10073 + 0.747797i
\(955\) −9.20837 + 69.9445i −0.297976 + 2.26335i
\(956\) 21.4530 + 33.8826i 0.693839 + 1.09584i
\(957\) 1.09066 2.19419i 0.0352560 0.0709281i
\(958\) −39.6533 9.76172i −1.28114 0.315387i
\(959\) −1.27880 + 7.25246i −0.0412947 + 0.234194i
\(960\) −19.7537 30.3136i −0.637549 0.978366i
\(961\) −23.7320 + 19.9135i −0.765547 + 0.642370i
\(962\) −2.78351 1.86550i −0.0897439 0.0601461i
\(963\) −0.590807 0.502123i −0.0190385 0.0161807i
\(964\) −38.7422 + 15.9211i −1.24780 + 0.512784i
\(965\) −63.4751 + 2.77138i −2.04333 + 0.0892139i
\(966\) 0.130039 + 0.362395i 0.00418393 + 0.0116599i
\(967\) 50.8382 4.44777i 1.63485 0.143031i 0.767607 0.640921i \(-0.221447\pi\)
0.867240 + 0.497890i \(0.165892\pi\)
\(968\) 24.7698 + 18.3218i 0.796131 + 0.588884i
\(969\) 39.7934 + 6.25317i 1.27835 + 0.200881i
\(970\) −26.7946 + 14.6515i −0.860324 + 0.470430i
\(971\) −18.3885 44.3937i −0.590114 1.42466i −0.883392 0.468635i \(-0.844746\pi\)
0.293278 0.956027i \(-0.405254\pi\)
\(972\) −30.7208 5.31313i −0.985372 0.170419i
\(973\) −3.60178 1.49191i −0.115468 0.0478283i
\(974\) 10.8351 13.4617i 0.347178 0.431342i
\(975\) −0.758598 1.04146i −0.0242946 0.0333534i
\(976\) 1.84807 5.74930i 0.0591551 0.184031i
\(977\) 26.8410 31.9878i 0.858718 1.02338i −0.140726 0.990049i \(-0.544944\pi\)
0.999444 0.0333322i \(-0.0106119\pi\)
\(978\) −8.38439 0.404252i −0.268103 0.0129266i
\(979\) 0.484990 + 0.444411i 0.0155003 + 0.0142034i
\(980\) −16.4102 + 16.3189i −0.524203 + 0.521288i
\(981\) −14.2369 + 1.15524i −0.454550 + 0.0368841i
\(982\) −2.32121 + 11.5851i −0.0740728 + 0.369694i
\(983\) 36.6338 + 3.20504i 1.16844 + 0.102225i 0.654814 0.755790i \(-0.272747\pi\)
0.513624 + 0.858015i \(0.328303\pi\)
\(984\) 48.0627 + 20.3224i 1.53218 + 0.647855i
\(985\) −38.5881 55.1096i −1.22952 1.75594i
\(986\) −33.7077 24.7879i −1.07347 0.789407i
\(987\) 14.2517 4.78778i 0.453636 0.152397i
\(988\) 2.71183 + 0.609138i 0.0862749 + 0.0193793i
\(989\) 0.255255 + 0.332655i 0.00811664 + 0.0105778i
\(990\) 3.55144 + 0.734877i 0.112872 + 0.0233559i
\(991\) 4.29793 + 7.44423i 0.136528 + 0.236474i 0.926180 0.377081i \(-0.123072\pi\)
−0.789652 + 0.613555i \(0.789739\pi\)
\(992\) −0.506642 + 0.622324i −0.0160859 + 0.0197588i
\(993\) 6.85622 1.97500i 0.217576 0.0626746i
\(994\) 19.3197 + 18.5463i 0.612784 + 0.588253i
\(995\) 0.339546 7.77688i 0.0107643 0.246544i
\(996\) −36.1844 + 8.62683i −1.14655 + 0.273352i
\(997\) 3.43478 + 5.39152i 0.108780 + 0.170751i 0.893449 0.449164i \(-0.148278\pi\)
−0.784669 + 0.619915i \(0.787167\pi\)
\(998\) −6.72994 + 13.5991i −0.213033 + 0.430473i
\(999\) −25.1795 + 16.4824i −0.796644 + 0.521480i
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 864.2.bu.a.13.6 3408
27.25 even 9 inner 864.2.bu.a.781.132 yes 3408
32.5 even 8 inner 864.2.bu.a.229.132 yes 3408
864.133 even 72 inner 864.2.bu.a.133.6 yes 3408
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
864.2.bu.a.13.6 3408 1.1 even 1 trivial
864.2.bu.a.133.6 yes 3408 864.133 even 72 inner
864.2.bu.a.229.132 yes 3408 32.5 even 8 inner
864.2.bu.a.781.132 yes 3408 27.25 even 9 inner