Properties

Label 462.2.bc.b.107.6
Level $462$
Weight $2$
Character 462.107
Analytic conductor $3.689$
Analytic rank $0$
Dimension $128$
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] = [462,2,Mod(95,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([15, 20, 21]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.95");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.bc (of order \(30\), 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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(16\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 107.6
Character \(\chi\) \(=\) 462.107
Dual form 462.2.bc.b.95.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.104528 - 0.994522i) q^{2} +(-0.840980 + 1.51418i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.12093 + 2.51765i) q^{5} +(1.59380 + 0.678098i) q^{6} +(2.40939 + 1.09308i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.58551 - 2.54680i) q^{9} +O(q^{10})\) \(q+(-0.104528 - 0.994522i) q^{2} +(-0.840980 + 1.51418i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.12093 + 2.51765i) q^{5} +(1.59380 + 0.678098i) q^{6} +(2.40939 + 1.09308i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.58551 - 2.54680i) q^{9} +(2.38669 - 1.37795i) q^{10} +(-3.22424 - 0.777358i) q^{11} +(0.507786 - 1.65594i) q^{12} +(0.533779 + 0.734683i) q^{13} +(0.835242 - 2.51045i) q^{14} +(-4.75486 - 0.419999i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-0.233441 + 2.22105i) q^{17} +(-2.36711 + 1.84303i) q^{18} +(-1.38320 + 6.50747i) q^{19} +(-1.61988 - 2.22958i) q^{20} +(-3.68138 + 2.72901i) q^{21} +(-0.436075 + 3.28783i) q^{22} +(-4.85329 - 2.80205i) q^{23} +(-1.69995 - 0.331911i) q^{24} +(-1.73642 + 1.92849i) q^{25} +(0.674863 - 0.607650i) q^{26} +(5.18970 - 0.258941i) q^{27} +(-2.58401 - 0.568253i) q^{28} +(-1.35518 + 4.17081i) q^{29} +(0.0793202 + 4.77271i) q^{30} +(-0.217640 - 0.0968995i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.88858 - 4.22835i) q^{33} +2.23328 q^{34} +(-0.0512330 + 7.29127i) q^{35} +(2.08037 + 2.16150i) q^{36} +(7.25637 + 8.05901i) q^{37} +(6.61640 + 0.695412i) q^{38} +(-1.56134 + 0.190385i) q^{39} +(-2.04804 + 1.84406i) q^{40} +(-1.32308 - 4.07202i) q^{41} +(3.09886 + 3.37595i) q^{42} -8.42414i q^{43} +(3.31540 + 0.0900140i) q^{44} +(4.63470 - 6.84652i) q^{45} +(-2.27939 + 5.11959i) q^{46} +(-2.18126 + 10.2620i) q^{47} +(-0.152399 + 1.72533i) q^{48} +(4.61035 + 5.26732i) q^{49} +(2.09943 + 1.52532i) q^{50} +(-3.16675 - 2.22133i) q^{51} +(-0.674863 - 0.607650i) q^{52} +(1.15816 - 2.60126i) q^{53} +(-0.799994 - 5.13420i) q^{54} +(-1.65703 - 8.98886i) q^{55} +(-0.295038 + 2.62925i) q^{56} +(-8.69025 - 7.56707i) q^{57} +(4.28962 + 0.911786i) q^{58} +(-1.31314 - 6.17786i) q^{59} +(4.73828 - 0.577770i) q^{60} +(1.19589 + 2.68601i) q^{61} +(-0.0736192 + 0.226576i) q^{62} +(-1.03625 - 7.86932i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.25135 + 2.16739i) q^{65} +(-4.61165 - 3.42530i) q^{66} +(2.80878 + 4.86495i) q^{67} +(-0.233441 - 2.22105i) q^{68} +(8.32433 - 4.99230i) q^{69} +(7.25668 - 0.711193i) q^{70} +(-2.57763 + 3.54780i) q^{71} +(1.93220 - 2.29491i) q^{72} +(-2.21647 - 10.4277i) q^{73} +(7.25637 - 8.05901i) q^{74} +(-1.45979 - 4.25107i) q^{75} -6.65285i q^{76} +(-6.91874 - 5.39731i) q^{77} +(0.352547 + 1.53289i) q^{78} +(4.75825 - 0.500112i) q^{79} +(2.04804 + 1.84406i) q^{80} +(-3.97235 + 8.07592i) q^{81} +(-3.91141 + 1.74147i) q^{82} +(3.07387 + 2.23330i) q^{83} +(3.03354 - 3.43477i) q^{84} +(-5.85348 + 1.90191i) q^{85} +(-8.37800 + 0.880563i) q^{86} +(-5.17569 - 5.55956i) q^{87} +(-0.257033 - 3.30665i) q^{88} +(-3.00107 - 1.73267i) q^{89} +(-7.29347 - 3.89365i) q^{90} +(0.483015 + 2.35360i) q^{91} +(5.32981 + 1.73176i) q^{92} +(0.329755 - 0.248056i) q^{93} +(10.4338 + 1.09664i) q^{94} +(-17.9340 + 3.81199i) q^{95} +(1.73181 - 0.0287819i) q^{96} +(14.4550 - 10.5022i) q^{97} +(4.75655 - 5.13568i) q^{98} +(3.13227 + 9.44399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{10}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.104528 0.994522i −0.0739128 0.703233i
\(3\) −0.840980 + 1.51418i −0.485540 + 0.874214i
\(4\) −0.978148 + 0.207912i −0.489074 + 0.103956i
\(5\) 1.12093 + 2.51765i 0.501295 + 1.12593i 0.970118 + 0.242634i \(0.0780115\pi\)
−0.468823 + 0.883292i \(0.655322\pi\)
\(6\) 1.59380 + 0.678098i 0.650664 + 0.276832i
\(7\) 2.40939 + 1.09308i 0.910665 + 0.413146i
\(8\) 0.309017 + 0.951057i 0.109254 + 0.336249i
\(9\) −1.58551 2.54680i −0.528502 0.848932i
\(10\) 2.38669 1.37795i 0.754737 0.435747i
\(11\) −3.22424 0.777358i −0.972145 0.234382i
\(12\) 0.507786 1.65594i 0.146585 0.478030i
\(13\) 0.533779 + 0.734683i 0.148044 + 0.203764i 0.876598 0.481224i \(-0.159807\pi\)
−0.728554 + 0.684988i \(0.759807\pi\)
\(14\) 0.835242 2.51045i 0.223228 0.670947i
\(15\) −4.75486 0.419999i −1.22770 0.108443i
\(16\) 0.913545 0.406737i 0.228386 0.101684i
\(17\) −0.233441 + 2.22105i −0.0566178 + 0.538683i 0.929046 + 0.369963i \(0.120630\pi\)
−0.985664 + 0.168719i \(0.946037\pi\)
\(18\) −2.36711 + 1.84303i −0.557934 + 0.434407i
\(19\) −1.38320 + 6.50747i −0.317329 + 1.49291i 0.473454 + 0.880818i \(0.343007\pi\)
−0.790783 + 0.612097i \(0.790326\pi\)
\(20\) −1.61988 2.22958i −0.362217 0.498549i
\(21\) −3.68138 + 2.72901i −0.803342 + 0.595518i
\(22\) −0.436075 + 3.28783i −0.0929715 + 0.700968i
\(23\) −4.85329 2.80205i −1.01198 0.584267i −0.100209 0.994966i \(-0.531951\pi\)
−0.911771 + 0.410699i \(0.865285\pi\)
\(24\) −1.69995 0.331911i −0.347001 0.0677510i
\(25\) −1.73642 + 1.92849i −0.347283 + 0.385697i
\(26\) 0.674863 0.607650i 0.132352 0.119170i
\(27\) 5.18970 0.258941i 0.998758 0.0498333i
\(28\) −2.58401 0.568253i −0.488331 0.107390i
\(29\) −1.35518 + 4.17081i −0.251650 + 0.774500i 0.742821 + 0.669490i \(0.233487\pi\)
−0.994471 + 0.105010i \(0.966513\pi\)
\(30\) 0.0793202 + 4.77271i 0.0144818 + 0.871375i
\(31\) −0.217640 0.0968995i −0.0390893 0.0174037i 0.387099 0.922038i \(-0.373477\pi\)
−0.426188 + 0.904635i \(0.640144\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 3.88858 4.22835i 0.676915 0.736061i
\(34\) 2.23328 0.383004
\(35\) −0.0512330 + 7.29127i −0.00865996 + 1.23245i
\(36\) 2.08037 + 2.16150i 0.346728 + 0.360250i
\(37\) 7.25637 + 8.05901i 1.19294 + 1.32489i 0.933261 + 0.359199i \(0.116950\pi\)
0.259678 + 0.965695i \(0.416383\pi\)
\(38\) 6.61640 + 0.695412i 1.07332 + 0.112811i
\(39\) −1.56134 + 0.190385i −0.250015 + 0.0304860i
\(40\) −2.04804 + 1.84406i −0.323823 + 0.291572i
\(41\) −1.32308 4.07202i −0.206630 0.635942i −0.999643 0.0267365i \(-0.991488\pi\)
0.793012 0.609205i \(-0.208512\pi\)
\(42\) 3.09886 + 3.37595i 0.478165 + 0.520920i
\(43\) 8.42414i 1.28467i −0.766424 0.642335i \(-0.777966\pi\)
0.766424 0.642335i \(-0.222034\pi\)
\(44\) 3.31540 + 0.0900140i 0.499816 + 0.0135701i
\(45\) 4.63470 6.84652i 0.690900 1.02062i
\(46\) −2.27939 + 5.11959i −0.336078 + 0.754843i
\(47\) −2.18126 + 10.2620i −0.318169 + 1.49687i 0.470692 + 0.882297i \(0.344004\pi\)
−0.788862 + 0.614571i \(0.789329\pi\)
\(48\) −0.152399 + 1.72533i −0.0219970 + 0.249030i
\(49\) 4.61035 + 5.26732i 0.658621 + 0.752474i
\(50\) 2.09943 + 1.52532i 0.296904 + 0.215713i
\(51\) −3.16675 2.22133i −0.443434 0.311048i
\(52\) −0.674863 0.607650i −0.0935867 0.0842659i
\(53\) 1.15816 2.60126i 0.159085 0.357311i −0.816364 0.577538i \(-0.804013\pi\)
0.975448 + 0.220228i \(0.0706801\pi\)
\(54\) −0.799994 5.13420i −0.108865 0.698676i
\(55\) −1.65703 8.98886i −0.223434 1.21206i
\(56\) −0.295038 + 2.62925i −0.0394261 + 0.351348i
\(57\) −8.69025 7.56707i −1.15105 1.00228i
\(58\) 4.28962 + 0.911786i 0.563254 + 0.119723i
\(59\) −1.31314 6.17786i −0.170957 0.804288i −0.977136 0.212617i \(-0.931801\pi\)
0.806179 0.591672i \(-0.201532\pi\)
\(60\) 4.73828 0.577770i 0.611709 0.0745898i
\(61\) 1.19589 + 2.68601i 0.153118 + 0.343909i 0.973775 0.227512i \(-0.0730591\pi\)
−0.820657 + 0.571421i \(0.806392\pi\)
\(62\) −0.0736192 + 0.226576i −0.00934964 + 0.0287752i
\(63\) −1.03625 7.86932i −0.130555 0.991441i
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) −1.25135 + 2.16739i −0.155210 + 0.268832i
\(66\) −4.61165 3.42530i −0.567655 0.421625i
\(67\) 2.80878 + 4.86495i 0.343147 + 0.594348i 0.985015 0.172467i \(-0.0551737\pi\)
−0.641868 + 0.766815i \(0.721840\pi\)
\(68\) −0.233441 2.22105i −0.0283089 0.269341i
\(69\) 8.32433 4.99230i 1.00213 0.601003i
\(70\) 7.25668 0.711193i 0.867339 0.0850038i
\(71\) −2.57763 + 3.54780i −0.305909 + 0.421047i −0.934100 0.357012i \(-0.883796\pi\)
0.628191 + 0.778059i \(0.283796\pi\)
\(72\) 1.93220 2.29491i 0.227712 0.270458i
\(73\) −2.21647 10.4277i −0.259418 1.22047i −0.894162 0.447743i \(-0.852228\pi\)
0.634744 0.772722i \(-0.281105\pi\)
\(74\) 7.25637 8.05901i 0.843536 0.936841i
\(75\) −1.45979 4.25107i −0.168562 0.490871i
\(76\) 6.65285i 0.763134i
\(77\) −6.91874 5.39731i −0.788464 0.615081i
\(78\) 0.352547 + 1.53289i 0.0399181 + 0.173565i
\(79\) 4.75825 0.500112i 0.535345 0.0562670i 0.167001 0.985957i \(-0.446592\pi\)
0.368344 + 0.929690i \(0.379925\pi\)
\(80\) 2.04804 + 1.84406i 0.228978 + 0.206173i
\(81\) −3.97235 + 8.07592i −0.441372 + 0.897324i
\(82\) −3.91141 + 1.74147i −0.431943 + 0.192313i
\(83\) 3.07387 + 2.23330i 0.337402 + 0.245137i 0.743565 0.668664i \(-0.233134\pi\)
−0.406163 + 0.913801i \(0.633134\pi\)
\(84\) 3.03354 3.43477i 0.330986 0.374764i
\(85\) −5.85348 + 1.90191i −0.634899 + 0.206291i
\(86\) −8.37800 + 0.880563i −0.903423 + 0.0949535i
\(87\) −5.17569 5.55956i −0.554893 0.596047i
\(88\) −0.257033 3.30665i −0.0273998 0.352490i
\(89\) −3.00107 1.73267i −0.318112 0.183662i 0.332439 0.943125i \(-0.392129\pi\)
−0.650551 + 0.759463i \(0.725462\pi\)
\(90\) −7.29347 3.89365i −0.768800 0.410427i
\(91\) 0.483015 + 2.35360i 0.0506337 + 0.246725i
\(92\) 5.32981 + 1.73176i 0.555671 + 0.180548i
\(93\) 0.329755 0.248056i 0.0341940 0.0257222i
\(94\) 10.4338 + 1.09664i 1.07616 + 0.113109i
\(95\) −17.9340 + 3.81199i −1.83999 + 0.391101i
\(96\) 1.73181 0.0287819i 0.176752 0.00293754i
\(97\) 14.4550 10.5022i 1.46768 1.06633i 0.486407 0.873732i \(-0.338307\pi\)
0.981277 0.192603i \(-0.0616928\pi\)
\(98\) 4.75655 5.13568i 0.480484 0.518782i
\(99\) 3.13227 + 9.44399i 0.314805 + 0.949156i
\(100\) 1.29752 2.24736i 0.129752 0.224736i
\(101\) 13.8161 + 6.15131i 1.37475 + 0.612078i 0.955283 0.295692i \(-0.0955502\pi\)
0.419467 + 0.907770i \(0.362217\pi\)
\(102\) −1.87814 + 3.38160i −0.185964 + 0.334828i
\(103\) −0.929037 1.03180i −0.0915408 0.101666i 0.695634 0.718397i \(-0.255124\pi\)
−0.787175 + 0.616730i \(0.788457\pi\)
\(104\) −0.533779 + 0.734683i −0.0523413 + 0.0720416i
\(105\) −10.9972 6.20939i −1.07322 0.605974i
\(106\) −2.70807 0.879905i −0.263031 0.0854640i
\(107\) −3.96332 0.842430i −0.383149 0.0814408i 0.0123107 0.999924i \(-0.496081\pi\)
−0.395459 + 0.918483i \(0.629415\pi\)
\(108\) −5.02245 + 1.33228i −0.483286 + 0.128199i
\(109\) 0.347989 0.200911i 0.0333313 0.0192438i −0.483242 0.875487i \(-0.660541\pi\)
0.516573 + 0.856243i \(0.327207\pi\)
\(110\) −8.76641 + 2.58754i −0.835845 + 0.246713i
\(111\) −18.3053 + 4.21001i −1.73746 + 0.399596i
\(112\) 2.64569 + 0.0185902i 0.249994 + 0.00175661i
\(113\) 17.6802 5.74465i 1.66321 0.540411i 0.681672 0.731658i \(-0.261253\pi\)
0.981542 + 0.191247i \(0.0612533\pi\)
\(114\) −6.61724 + 9.43362i −0.619762 + 0.883539i
\(115\) 1.61438 15.3598i 0.150541 1.43231i
\(116\) 0.458404 4.36142i 0.0425618 0.404948i
\(117\) 1.02478 2.52427i 0.0947409 0.233369i
\(118\) −6.00675 + 1.95171i −0.552966 + 0.179670i
\(119\) −2.99023 + 5.09620i −0.274114 + 0.467168i
\(120\) −1.06989 4.65193i −0.0976672 0.424661i
\(121\) 9.79143 + 5.01278i 0.890130 + 0.455707i
\(122\) 2.54629 1.47010i 0.230531 0.133097i
\(123\) 7.27846 + 1.42110i 0.656277 + 0.128136i
\(124\) 0.233031 + 0.0495322i 0.0209268 + 0.00444812i
\(125\) 6.30348 + 2.04812i 0.563800 + 0.183190i
\(126\) −7.71789 + 1.85314i −0.687564 + 0.165091i
\(127\) −3.41705 + 4.70316i −0.303214 + 0.417338i −0.933250 0.359228i \(-0.883040\pi\)
0.630036 + 0.776566i \(0.283040\pi\)
\(128\) 0.669131 + 0.743145i 0.0591433 + 0.0656853i
\(129\) 12.7557 + 7.08454i 1.12308 + 0.623759i
\(130\) 2.28632 + 1.01794i 0.200524 + 0.0892789i
\(131\) 8.02200 13.8945i 0.700885 1.21397i −0.267271 0.963621i \(-0.586122\pi\)
0.968156 0.250347i \(-0.0805447\pi\)
\(132\) −2.92449 + 4.94443i −0.254544 + 0.430357i
\(133\) −10.4459 + 14.1671i −0.905771 + 1.22844i
\(134\) 4.54470 3.30192i 0.392602 0.285242i
\(135\) 6.46920 + 12.7756i 0.556780 + 1.09955i
\(136\) −2.18448 + 0.464325i −0.187317 + 0.0398155i
\(137\) 9.04595 + 0.950767i 0.772848 + 0.0812295i 0.482739 0.875764i \(-0.339642\pi\)
0.290108 + 0.956994i \(0.406309\pi\)
\(138\) −5.83508 7.75689i −0.496715 0.660310i
\(139\) −15.7296 5.11087i −1.33417 0.433498i −0.446832 0.894618i \(-0.647448\pi\)
−0.887338 + 0.461119i \(0.847448\pi\)
\(140\) −1.46583 7.14259i −0.123885 0.603659i
\(141\) −13.7042 11.9330i −1.15410 1.00494i
\(142\) 3.79781 + 2.19266i 0.318705 + 0.184004i
\(143\) −1.14992 2.78373i −0.0961609 0.232787i
\(144\) −2.48431 1.68173i −0.207026 0.140144i
\(145\) −12.0197 + 1.26332i −0.998181 + 0.104913i
\(146\) −10.1389 + 3.29431i −0.839097 + 0.272639i
\(147\) −11.8529 + 2.55121i −0.977611 + 0.210420i
\(148\) −8.77336 6.37422i −0.721166 0.523958i
\(149\) 13.6840 6.09250i 1.12104 0.499117i 0.239340 0.970936i \(-0.423069\pi\)
0.881696 + 0.471818i \(0.156402\pi\)
\(150\) −4.07519 + 1.89615i −0.332738 + 0.154820i
\(151\) −3.87172 3.48611i −0.315076 0.283696i 0.496385 0.868103i \(-0.334661\pi\)
−0.811461 + 0.584407i \(0.801327\pi\)
\(152\) −6.61640 + 0.695412i −0.536661 + 0.0564053i
\(153\) 6.02667 2.92695i 0.487228 0.236630i
\(154\) −4.64454 + 7.44501i −0.374268 + 0.599936i
\(155\) 0.656558i 0.0527360i
\(156\) 1.48764 0.510846i 0.119107 0.0409004i
\(157\) 0.797111 0.885281i 0.0636164 0.0706532i −0.710497 0.703701i \(-0.751530\pi\)
0.774113 + 0.633048i \(0.218196\pi\)
\(158\) −0.994745 4.67991i −0.0791377 0.372314i
\(159\) 2.96480 + 3.94127i 0.235124 + 0.312563i
\(160\) 1.61988 2.22958i 0.128063 0.176264i
\(161\) −8.63061 12.0563i −0.680188 0.950167i
\(162\) 8.44690 + 3.10642i 0.663651 + 0.244064i
\(163\) −1.19889 11.4067i −0.0939045 0.893441i −0.935499 0.353331i \(-0.885049\pi\)
0.841594 0.540111i \(-0.181618\pi\)
\(164\) 2.14079 + 3.70795i 0.167167 + 0.289542i
\(165\) 15.0043 + 5.05041i 1.16808 + 0.393174i
\(166\) 1.89976 3.29048i 0.147450 0.255391i
\(167\) −13.4155 + 9.74696i −1.03813 + 0.754243i −0.969919 0.243429i \(-0.921728\pi\)
−0.0682071 + 0.997671i \(0.521728\pi\)
\(168\) −3.73305 2.65789i −0.288011 0.205060i
\(169\) 3.76238 11.5794i 0.289414 0.890725i
\(170\) 2.50335 + 5.62261i 0.191998 + 0.431235i
\(171\) 18.7663 6.79488i 1.43509 0.519617i
\(172\) 1.75148 + 8.24006i 0.133549 + 0.628298i
\(173\) 11.1481 + 2.36959i 0.847572 + 0.180157i 0.611171 0.791499i \(-0.290699\pi\)
0.236401 + 0.971656i \(0.424032\pi\)
\(174\) −4.98809 + 5.72847i −0.378146 + 0.434274i
\(175\) −6.29170 + 2.74844i −0.475608 + 0.207762i
\(176\) −3.26167 + 0.601264i −0.245858 + 0.0453220i
\(177\) 10.4587 + 3.20711i 0.786127 + 0.241061i
\(178\) −1.40948 + 3.16574i −0.105645 + 0.237282i
\(179\) 7.34748 + 6.61570i 0.549176 + 0.494481i 0.896366 0.443314i \(-0.146197\pi\)
−0.347190 + 0.937795i \(0.612864\pi\)
\(180\) −3.10995 + 7.66052i −0.231802 + 0.570981i
\(181\) 12.4958 + 9.07875i 0.928807 + 0.674818i 0.945701 0.325039i \(-0.105378\pi\)
−0.0168932 + 0.999857i \(0.505378\pi\)
\(182\) 2.29022 0.726387i 0.169762 0.0538434i
\(183\) −5.07284 0.448086i −0.374995 0.0331235i
\(184\) 1.16516 5.48163i 0.0858965 0.404111i
\(185\) −12.1559 + 27.3026i −0.893718 + 2.00732i
\(186\) −0.281166 0.302019i −0.0206161 0.0221451i
\(187\) 2.47922 6.97971i 0.181298 0.510407i
\(188\) 10.4913i 0.765155i
\(189\) 12.7871 + 5.04886i 0.930122 + 0.367251i
\(190\) 5.66571 + 17.4373i 0.411034 + 1.26503i
\(191\) 15.2558 13.7364i 1.10387 0.993932i 0.103873 0.994591i \(-0.466876\pi\)
1.00000 0.000658696i \(0.000209669\pi\)
\(192\) −0.209648 1.71932i −0.0151300 0.124081i
\(193\) −23.7227 2.49336i −1.70760 0.179476i −0.800196 0.599738i \(-0.795271\pi\)
−0.907403 + 0.420263i \(0.861938\pi\)
\(194\) −11.9556 13.2780i −0.858363 0.953308i
\(195\) −2.22948 3.71750i −0.159656 0.266216i
\(196\) −5.60474 4.19367i −0.400339 0.299548i
\(197\) −16.7596 −1.19407 −0.597037 0.802214i \(-0.703656\pi\)
−0.597037 + 0.802214i \(0.703656\pi\)
\(198\) 9.06484 4.10228i 0.644210 0.291536i
\(199\) 11.4850 + 19.8927i 0.814152 + 1.41015i 0.909935 + 0.414751i \(0.136131\pi\)
−0.0957828 + 0.995402i \(0.530535\pi\)
\(200\) −2.37068 1.05550i −0.167632 0.0746348i
\(201\) −9.72855 + 0.161684i −0.686199 + 0.0114043i
\(202\) 4.67344 14.3834i 0.328822 1.01201i
\(203\) −7.82419 + 8.56780i −0.549150 + 0.601342i
\(204\) 3.55939 + 1.51438i 0.249207 + 0.106028i
\(205\) 8.76882 7.89548i 0.612441 0.551445i
\(206\) −0.929037 + 1.03180i −0.0647291 + 0.0718889i
\(207\) 0.558669 + 16.8030i 0.0388302 + 1.16789i
\(208\) 0.786453 + 0.454059i 0.0545307 + 0.0314833i
\(209\) 9.51841 19.9064i 0.658402 1.37695i
\(210\) −5.02585 + 11.5860i −0.346816 + 0.799513i
\(211\) 14.6884 + 20.2169i 1.01119 + 1.39179i 0.918198 + 0.396123i \(0.129644\pi\)
0.0929963 + 0.995666i \(0.470356\pi\)
\(212\) −0.592015 + 2.78521i −0.0406597 + 0.191289i
\(213\) −3.20429 6.88664i −0.219555 0.471865i
\(214\) −0.423535 + 4.02967i −0.0289523 + 0.275462i
\(215\) 21.2090 9.44287i 1.44644 0.643998i
\(216\) 1.84997 + 4.85568i 0.125875 + 0.330387i
\(217\) −0.418461 0.471367i −0.0284070 0.0319985i
\(218\) −0.236186 0.325082i −0.0159965 0.0220173i
\(219\) 17.6534 + 5.41331i 1.19291 + 0.365798i
\(220\) 3.48971 + 8.44792i 0.235276 + 0.569558i
\(221\) −1.75637 + 1.01404i −0.118146 + 0.0682118i
\(222\) 6.10037 + 17.7649i 0.409430 + 1.19231i
\(223\) −6.29557 19.3758i −0.421582 1.29750i −0.906229 0.422787i \(-0.861052\pi\)
0.484646 0.874710i \(-0.338948\pi\)
\(224\) −0.258061 2.63314i −0.0172424 0.175934i
\(225\) 7.66456 + 1.36467i 0.510970 + 0.0909783i
\(226\) −7.56126 16.9829i −0.502968 1.12968i
\(227\) 3.61620 0.768647i 0.240016 0.0510169i −0.0863331 0.996266i \(-0.527515\pi\)
0.326349 + 0.945249i \(0.394182\pi\)
\(228\) 10.0736 + 5.59491i 0.667143 + 0.370532i
\(229\) 1.37888 + 13.1192i 0.0911190 + 0.866940i 0.940645 + 0.339392i \(0.110221\pi\)
−0.849526 + 0.527547i \(0.823112\pi\)
\(230\) −15.4444 −1.01837
\(231\) 13.9910 5.93722i 0.920543 0.390640i
\(232\) −4.38545 −0.287919
\(233\) 1.32065 + 12.5652i 0.0865188 + 0.823171i 0.948616 + 0.316429i \(0.102484\pi\)
−0.862098 + 0.506742i \(0.830850\pi\)
\(234\) −2.61756 0.755308i −0.171115 0.0493760i
\(235\) −28.2812 + 6.01135i −1.84486 + 0.392137i
\(236\) 2.56890 + 5.76984i 0.167221 + 0.375584i
\(237\) −3.24433 + 7.62545i −0.210742 + 0.495326i
\(238\) 5.38085 + 2.44115i 0.348789 + 0.158237i
\(239\) 1.36443 + 4.19929i 0.0882578 + 0.271630i 0.985438 0.170035i \(-0.0543881\pi\)
−0.897180 + 0.441665i \(0.854388\pi\)
\(240\) −4.51461 + 1.55029i −0.291417 + 0.100071i
\(241\) −9.65705 + 5.57550i −0.622065 + 0.359150i −0.777673 0.628669i \(-0.783600\pi\)
0.155607 + 0.987819i \(0.450267\pi\)
\(242\) 3.96183 10.2618i 0.254676 0.659651i
\(243\) −8.88776 12.8065i −0.570150 0.821540i
\(244\) −1.72821 2.37868i −0.110637 0.152279i
\(245\) −8.09338 + 17.5115i −0.517067 + 1.11877i
\(246\) 0.652509 7.38713i 0.0416024 0.470987i
\(247\) −5.51925 + 2.45733i −0.351181 + 0.156356i
\(248\) 0.0249025 0.236932i 0.00158131 0.0150452i
\(249\) −5.96669 + 2.77625i −0.378124 + 0.175938i
\(250\) 1.37801 6.48303i 0.0871531 0.410023i
\(251\) 14.1993 + 19.5437i 0.896252 + 1.23359i 0.971648 + 0.236432i \(0.0759780\pi\)
−0.0753957 + 0.997154i \(0.524022\pi\)
\(252\) 2.64973 + 7.48191i 0.166917 + 0.471316i
\(253\) 13.4700 + 12.8072i 0.846849 + 0.805182i
\(254\) 5.03457 + 2.90671i 0.315897 + 0.182383i
\(255\) 2.04282 10.4627i 0.127926 0.655201i
\(256\) 0.669131 0.743145i 0.0418207 0.0464466i
\(257\) −3.99776 + 3.59960i −0.249373 + 0.224537i −0.784332 0.620342i \(-0.786994\pi\)
0.534958 + 0.844878i \(0.320327\pi\)
\(258\) 5.71239 13.4264i 0.355638 0.835889i
\(259\) 8.67429 + 27.3491i 0.538994 + 1.69939i
\(260\) 0.773374 2.38020i 0.0479626 0.147614i
\(261\) 12.7708 3.16148i 0.790495 0.195691i
\(262\) −14.6569 6.52568i −0.905507 0.403158i
\(263\) −6.87941 11.9155i −0.424203 0.734740i 0.572143 0.820154i \(-0.306112\pi\)
−0.996346 + 0.0854134i \(0.972779\pi\)
\(264\) 5.22304 + 2.39163i 0.321456 + 0.147195i
\(265\) 7.84727 0.482054
\(266\) 15.1814 + 8.90778i 0.930830 + 0.546171i
\(267\) 5.14741 3.08703i 0.315016 0.188923i
\(268\) −3.75888 4.17466i −0.229610 0.255008i
\(269\) 6.29328 + 0.661450i 0.383708 + 0.0403293i 0.294419 0.955676i \(-0.404874\pi\)
0.0892889 + 0.996006i \(0.471541\pi\)
\(270\) 12.0294 7.76918i 0.732084 0.472817i
\(271\) 1.69848 1.52932i 0.103175 0.0928996i −0.615929 0.787802i \(-0.711219\pi\)
0.719104 + 0.694902i \(0.244552\pi\)
\(272\) 0.690122 + 2.12398i 0.0418448 + 0.128785i
\(273\) −3.96999 1.24796i −0.240275 0.0755300i
\(274\) 9.09578i 0.549496i
\(275\) 7.09774 4.86808i 0.428010 0.293556i
\(276\) −7.10447 + 6.61393i −0.427639 + 0.398112i
\(277\) −3.73663 + 8.39261i −0.224512 + 0.504263i −0.990319 0.138807i \(-0.955673\pi\)
0.765807 + 0.643071i \(0.222340\pi\)
\(278\) −3.43868 + 16.1777i −0.206238 + 0.970274i
\(279\) 0.0982858 + 0.707919i 0.00588422 + 0.0423820i
\(280\) −6.95024 + 2.20440i −0.415356 + 0.131738i
\(281\) −5.24984 3.81423i −0.313179 0.227538i 0.420080 0.907487i \(-0.362002\pi\)
−0.733259 + 0.679949i \(0.762002\pi\)
\(282\) −10.4351 + 14.8764i −0.621403 + 0.885879i
\(283\) −4.90246 4.41420i −0.291421 0.262397i 0.510432 0.859918i \(-0.329486\pi\)
−0.801853 + 0.597521i \(0.796152\pi\)
\(284\) 1.78367 4.00620i 0.105842 0.237724i
\(285\) 9.31007 30.3611i 0.551481 1.79844i
\(286\) −2.64828 + 1.43460i −0.156596 + 0.0848295i
\(287\) 1.26323 11.2573i 0.0745658 0.664498i
\(288\) −1.41284 + 2.64649i −0.0832523 + 0.155946i
\(289\) 11.7500 + 2.49753i 0.691174 + 0.146914i
\(290\) 2.51280 + 11.8218i 0.147557 + 0.694199i
\(291\) 3.74586 + 30.7197i 0.219586 + 1.80082i
\(292\) 4.33606 + 9.73896i 0.253749 + 0.569929i
\(293\) 3.95822 12.1821i 0.231241 0.711688i −0.766356 0.642416i \(-0.777932\pi\)
0.997598 0.0692722i \(-0.0220677\pi\)
\(294\) 3.77620 + 11.5213i 0.220232 + 0.671936i
\(295\) 14.0817 10.2310i 0.819870 0.595670i
\(296\) −5.42224 + 9.39159i −0.315161 + 0.545875i
\(297\) −16.9341 3.19936i −0.982617 0.185646i
\(298\) −7.48949 12.9722i −0.433855 0.751459i
\(299\) −0.531964 5.06130i −0.0307643 0.292703i
\(300\) 2.31174 + 3.85467i 0.133468 + 0.222549i
\(301\) 9.20827 20.2971i 0.530756 1.16990i
\(302\) −3.06231 + 4.21491i −0.176216 + 0.242541i
\(303\) −20.9333 + 15.7469i −1.20258 + 0.904638i
\(304\) 1.38320 + 6.50747i 0.0793322 + 0.373229i
\(305\) −5.42193 + 6.02166i −0.310459 + 0.344799i
\(306\) −3.54088 5.68771i −0.202418 0.325145i
\(307\) 13.7899i 0.787032i 0.919318 + 0.393516i \(0.128741\pi\)
−0.919318 + 0.393516i \(0.871259\pi\)
\(308\) 7.88972 + 3.84088i 0.449558 + 0.218855i
\(309\) 2.34364 0.539010i 0.133325 0.0306632i
\(310\) −0.652962 + 0.0686290i −0.0370857 + 0.00389787i
\(311\) −22.7419 20.4769i −1.28957 1.16114i −0.977467 0.211089i \(-0.932299\pi\)
−0.312105 0.950048i \(-0.601034\pi\)
\(312\) −0.663548 1.42609i −0.0375660 0.0807366i
\(313\) −9.47181 + 4.21712i −0.535379 + 0.238366i −0.656572 0.754263i \(-0.727994\pi\)
0.121194 + 0.992629i \(0.461328\pi\)
\(314\) −0.963753 0.700207i −0.0543877 0.0395150i
\(315\) 18.6506 11.4299i 1.05084 0.644000i
\(316\) −4.55029 + 1.47848i −0.255974 + 0.0831710i
\(317\) −23.2914 + 2.44802i −1.30817 + 0.137495i −0.732827 0.680415i \(-0.761800\pi\)
−0.575347 + 0.817910i \(0.695133\pi\)
\(318\) 3.60977 3.36053i 0.202426 0.188449i
\(319\) 7.61163 12.3942i 0.426169 0.693943i
\(320\) −2.38669 1.37795i −0.133420 0.0770300i
\(321\) 4.60867 5.29273i 0.257231 0.295411i
\(322\) −11.0881 + 9.84356i −0.617914 + 0.548560i
\(323\) −14.1305 4.59127i −0.786241 0.255465i
\(324\) 2.20646 8.72534i 0.122581 0.484741i
\(325\) −2.34369 0.246331i −0.130004 0.0136640i
\(326\) −11.2189 + 2.38465i −0.621357 + 0.132073i
\(327\) 0.0115652 + 0.695882i 0.000639558 + 0.0384823i
\(328\) 3.46386 2.51664i 0.191260 0.138958i
\(329\) −16.4727 + 22.3409i −0.908170 + 1.23170i
\(330\) 3.45436 15.4500i 0.190156 0.850496i
\(331\) 5.45074 9.44095i 0.299600 0.518922i −0.676445 0.736493i \(-0.736480\pi\)
0.976044 + 0.217572i \(0.0698136\pi\)
\(332\) −3.47103 1.54540i −0.190498 0.0848150i
\(333\) 9.01966 31.2581i 0.494274 1.71293i
\(334\) 11.0959 + 12.3232i 0.607139 + 0.674296i
\(335\) −9.09979 + 12.5248i −0.497174 + 0.684302i
\(336\) −2.25312 + 3.99042i −0.122918 + 0.217695i
\(337\) −24.0108 7.80159i −1.30795 0.424979i −0.429611 0.903014i \(-0.641349\pi\)
−0.878341 + 0.478034i \(0.841349\pi\)
\(338\) −11.9093 2.53139i −0.647778 0.137690i
\(339\) −6.17025 + 31.6022i −0.335122 + 1.71640i
\(340\) 5.33014 3.07736i 0.289067 0.166893i
\(341\) 0.626397 + 0.481611i 0.0339213 + 0.0260807i
\(342\) −8.71927 17.9532i −0.471484 0.970798i
\(343\) 5.35054 + 17.7305i 0.288902 + 0.957359i
\(344\) 8.01184 2.60320i 0.431969 0.140355i
\(345\) 21.8998 + 15.3617i 1.17905 + 0.827047i
\(346\) 1.19132 11.3347i 0.0640459 0.609356i
\(347\) −0.936447 + 8.90970i −0.0502711 + 0.478298i 0.940205 + 0.340610i \(0.110634\pi\)
−0.990476 + 0.137688i \(0.956033\pi\)
\(348\) 6.21849 + 4.36198i 0.333346 + 0.233827i
\(349\) −3.82596 + 1.24313i −0.204799 + 0.0665433i −0.409620 0.912256i \(-0.634339\pi\)
0.204821 + 0.978799i \(0.434339\pi\)
\(350\) 3.39104 + 5.96994i 0.181259 + 0.319107i
\(351\) 2.96039 + 3.67456i 0.158014 + 0.196134i
\(352\) 0.938908 + 3.18095i 0.0500439 + 0.169545i
\(353\) −20.7273 + 11.9669i −1.10320 + 0.636935i −0.937061 0.349167i \(-0.886465\pi\)
−0.166143 + 0.986102i \(0.553131\pi\)
\(354\) 2.09631 10.7367i 0.111417 0.570648i
\(355\) −11.8215 2.51273i −0.627418 0.133362i
\(356\) 3.29573 + 1.07085i 0.174673 + 0.0567548i
\(357\) −5.20186 8.81357i −0.275312 0.466463i
\(358\) 5.81144 7.99876i 0.307144 0.422748i
\(359\) −17.7065 19.6650i −0.934512 1.03788i −0.999201 0.0399755i \(-0.987272\pi\)
0.0646884 0.997906i \(-0.479395\pi\)
\(360\) 7.94363 + 2.29217i 0.418666 + 0.120808i
\(361\) −23.0765 10.2743i −1.21455 0.540753i
\(362\) 7.72284 13.3764i 0.405904 0.703046i
\(363\) −15.8247 + 10.6104i −0.830579 + 0.556900i
\(364\) −0.961801 2.20175i −0.0504121 0.115403i
\(365\) 23.7687 17.2689i 1.24411 0.903898i
\(366\) 0.0846246 + 5.09188i 0.00442340 + 0.266157i
\(367\) −9.15707 + 1.94640i −0.477995 + 0.101601i −0.440608 0.897700i \(-0.645237\pi\)
−0.0373877 + 0.999301i \(0.511904\pi\)
\(368\) −5.57339 0.585787i −0.290533 0.0305363i
\(369\) −8.27285 + 9.82581i −0.430667 + 0.511511i
\(370\) 28.4236 + 9.23540i 1.47767 + 0.480126i
\(371\) 5.63384 5.00150i 0.292494 0.259665i
\(372\) −0.270975 + 0.311196i −0.0140494 + 0.0161347i
\(373\) −21.2488 12.2680i −1.10022 0.635214i −0.163943 0.986470i \(-0.552421\pi\)
−0.936279 + 0.351256i \(0.885755\pi\)
\(374\) −7.20063 1.73606i −0.372336 0.0897694i
\(375\) −8.40234 + 7.82219i −0.433895 + 0.403936i
\(376\) −10.4338 + 1.09664i −0.538082 + 0.0565547i
\(377\) −3.78759 + 1.23066i −0.195071 + 0.0633823i
\(378\) 3.68459 13.2448i 0.189515 0.681237i
\(379\) −19.2969 14.0200i −0.991217 0.720161i −0.0310297 0.999518i \(-0.509879\pi\)
−0.960187 + 0.279357i \(0.909879\pi\)
\(380\) 16.7495 7.45737i 0.859232 0.382555i
\(381\) −4.24778 9.12930i −0.217620 0.467708i
\(382\) −15.2558 13.7364i −0.780556 0.702816i
\(383\) 19.3608 2.03491i 0.989293 0.103979i 0.403964 0.914775i \(-0.367632\pi\)
0.585329 + 0.810796i \(0.300965\pi\)
\(384\) −1.68798 + 0.388217i −0.0861395 + 0.0198111i
\(385\) 5.83311 23.4690i 0.297283 1.19609i
\(386\) 23.8534i 1.21411i
\(387\) −21.4546 + 13.3565i −1.09060 + 0.678950i
\(388\) −11.9556 + 13.2780i −0.606954 + 0.674091i
\(389\) 3.11706 + 14.6646i 0.158041 + 0.743526i 0.983766 + 0.179454i \(0.0574330\pi\)
−0.825725 + 0.564073i \(0.809234\pi\)
\(390\) −3.46409 + 2.60585i −0.175411 + 0.131952i
\(391\) 7.35643 10.1253i 0.372031 0.512056i
\(392\) −3.58484 + 6.01240i −0.181062 + 0.303672i
\(393\) 14.2925 + 23.8318i 0.720961 + 1.20215i
\(394\) 1.75186 + 16.6678i 0.0882574 + 0.839713i
\(395\) 6.59277 + 11.4190i 0.331718 + 0.574553i
\(396\) −5.02734 8.58638i −0.252633 0.431482i
\(397\) 12.3184 21.3361i 0.618243 1.07083i −0.371563 0.928408i \(-0.621178\pi\)
0.989806 0.142421i \(-0.0454887\pi\)
\(398\) 18.5832 13.5015i 0.931490 0.676767i
\(399\) −12.6668 27.7312i −0.634134 1.38830i
\(400\) −0.801909 + 2.46802i −0.0400955 + 0.123401i
\(401\) 9.87635 + 22.1827i 0.493202 + 1.10775i 0.973091 + 0.230420i \(0.0740100\pi\)
−0.479890 + 0.877329i \(0.659323\pi\)
\(402\) 1.17771 + 9.65836i 0.0587388 + 0.481715i
\(403\) −0.0449811 0.211619i −0.00224067 0.0105415i
\(404\) −14.7931 3.14437i −0.735984 0.156438i
\(405\) −24.7850 0.948437i −1.23158 0.0471282i
\(406\) 9.33872 + 6.88575i 0.463473 + 0.341734i
\(407\) −17.1315 31.6250i −0.849178 1.56759i
\(408\) 1.13403 3.69819i 0.0561428 0.183088i
\(409\) 10.9353 24.5611i 0.540715 1.21447i −0.412162 0.911110i \(-0.635226\pi\)
0.952877 0.303356i \(-0.0981070\pi\)
\(410\) −8.76882 7.89548i −0.433061 0.389930i
\(411\) −9.04710 + 12.8977i −0.446260 + 0.636194i
\(412\) 1.12326 + 0.816095i 0.0553390 + 0.0402061i
\(413\) 3.58901 16.3203i 0.176604 0.803067i
\(414\) 16.6525 2.31200i 0.818428 0.113629i
\(415\) −2.17707 + 10.2423i −0.106868 + 0.502775i
\(416\) 0.369365 0.829607i 0.0181096 0.0406748i
\(417\) 20.9671 19.5194i 1.02676 0.955870i
\(418\) −20.7923 7.38549i −1.01698 0.361236i
\(419\) 9.11719i 0.445404i 0.974887 + 0.222702i \(0.0714877\pi\)
−0.974887 + 0.222702i \(0.928512\pi\)
\(420\) 12.0479 + 3.78724i 0.587879 + 0.184799i
\(421\) −5.30508 16.3274i −0.258554 0.795747i −0.993109 0.117198i \(-0.962609\pi\)
0.734555 0.678550i \(-0.237391\pi\)
\(422\) 18.5708 16.7212i 0.904012 0.813976i
\(423\) 29.5937 10.7153i 1.43889 0.520993i
\(424\) 2.83184 + 0.297638i 0.137526 + 0.0144546i
\(425\) −3.87790 4.30685i −0.188106 0.208913i
\(426\) −6.51397 + 3.90659i −0.315603 + 0.189275i
\(427\) −0.0546591 + 7.77886i −0.00264514 + 0.376446i
\(428\) 4.05186 0.195854
\(429\) 5.18214 + 0.599875i 0.250196 + 0.0289623i
\(430\) −11.6081 20.1058i −0.559792 0.969588i
\(431\) 35.8153 + 15.9460i 1.72516 + 0.768092i 0.996534 + 0.0831836i \(0.0265088\pi\)
0.728629 + 0.684909i \(0.240158\pi\)
\(432\) 4.63570 2.34739i 0.223035 0.112939i
\(433\) −2.30058 + 7.08046i −0.110559 + 0.340265i −0.990995 0.133900i \(-0.957250\pi\)
0.880436 + 0.474165i \(0.157250\pi\)
\(434\) −0.425044 + 0.465440i −0.0204028 + 0.0223418i
\(435\) 8.19542 19.2624i 0.392940 0.923564i
\(436\) −0.298613 + 0.268872i −0.0143010 + 0.0128766i
\(437\) 24.9473 27.7068i 1.19339 1.32540i
\(438\) 3.53838 18.1225i 0.169070 0.865928i
\(439\) 24.1794 + 13.9600i 1.15402 + 0.666273i 0.949863 0.312666i \(-0.101222\pi\)
0.204155 + 0.978939i \(0.434555\pi\)
\(440\) 8.03686 4.35364i 0.383142 0.207552i
\(441\) 6.10506 20.0930i 0.290717 0.956809i
\(442\) 1.19208 + 1.64075i 0.0567013 + 0.0780427i
\(443\) 1.21132 5.69881i 0.0575516 0.270759i −0.939958 0.341290i \(-0.889136\pi\)
0.997510 + 0.0705313i \(0.0224695\pi\)
\(444\) 17.0300 7.92389i 0.808206 0.376051i
\(445\) 0.998261 9.49782i 0.0473221 0.450240i
\(446\) −18.6116 + 8.28640i −0.881283 + 0.392372i
\(447\) −2.28279 + 25.8437i −0.107972 + 1.22237i
\(448\) −2.59174 + 0.531885i −0.122448 + 0.0251292i
\(449\) −6.92207 9.52742i −0.326673 0.449627i 0.613817 0.789448i \(-0.289633\pi\)
−0.940490 + 0.339822i \(0.889633\pi\)
\(450\) 0.556035 7.76522i 0.0262117 0.366056i
\(451\) 1.10051 + 14.1577i 0.0518208 + 0.666658i
\(452\) −16.0995 + 9.29503i −0.757255 + 0.437202i
\(453\) 8.53466 2.93075i 0.400993 0.137698i
\(454\) −1.14243 3.51604i −0.0536170 0.165016i
\(455\) −5.38412 + 3.85428i −0.252411 + 0.180692i
\(456\) 4.51128 10.6033i 0.211260 0.496544i
\(457\) −12.2727 27.5649i −0.574092 1.28943i −0.934276 0.356550i \(-0.883953\pi\)
0.360185 0.932881i \(-0.382714\pi\)
\(458\) 12.9032 2.74265i 0.602926 0.128156i
\(459\) −0.636369 + 11.5870i −0.0297032 + 0.540835i
\(460\) 1.61438 + 15.3598i 0.0752707 + 0.716153i
\(461\) −11.0690 −0.515533 −0.257767 0.966207i \(-0.582987\pi\)
−0.257767 + 0.966207i \(0.582987\pi\)
\(462\) −7.36715 13.2938i −0.342751 0.618483i
\(463\) 2.93172 0.136249 0.0681243 0.997677i \(-0.478299\pi\)
0.0681243 + 0.997677i \(0.478299\pi\)
\(464\) 0.458404 + 4.36142i 0.0212809 + 0.202474i
\(465\) 0.994150 + 0.552152i 0.0461026 + 0.0256055i
\(466\) 12.3583 2.62683i 0.572486 0.121686i
\(467\) 14.5556 + 32.6924i 0.673552 + 1.51282i 0.849033 + 0.528341i \(0.177186\pi\)
−0.175480 + 0.984483i \(0.556148\pi\)
\(468\) −0.477561 + 2.68217i −0.0220753 + 0.123983i
\(469\) 1.44967 + 14.7918i 0.0669397 + 0.683022i
\(470\) 8.93461 + 27.4979i 0.412123 + 1.26838i
\(471\) 0.670124 + 1.95148i 0.0308777 + 0.0899193i
\(472\) 5.46971 3.15794i 0.251764 0.145356i
\(473\) −6.54858 + 27.1615i −0.301104 + 1.24888i
\(474\) 7.92280 + 2.42948i 0.363906 + 0.111590i
\(475\) −10.1477 13.9672i −0.465610 0.640857i
\(476\) 1.86533 5.60654i 0.0854973 0.256975i
\(477\) −8.46114 + 1.17472i −0.387409 + 0.0537869i
\(478\) 4.03367 1.79590i 0.184496 0.0821427i
\(479\) 2.02764 19.2917i 0.0926454 0.881462i −0.845210 0.534435i \(-0.820525\pi\)
0.937855 0.347027i \(-0.112809\pi\)
\(480\) 2.01370 + 4.32783i 0.0919124 + 0.197537i
\(481\) −2.04753 + 9.63286i −0.0933592 + 0.439221i
\(482\) 6.55440 + 9.02135i 0.298545 + 0.410911i
\(483\) 25.5136 2.92926i 1.16091 0.133286i
\(484\) −10.6197 2.86748i −0.482713 0.130340i
\(485\) 42.6438 + 24.6204i 1.93636 + 1.11796i
\(486\) −11.8074 + 10.1777i −0.535593 + 0.461671i
\(487\) −5.39572 + 5.99255i −0.244503 + 0.271548i −0.852888 0.522094i \(-0.825151\pi\)
0.608385 + 0.793642i \(0.291818\pi\)
\(488\) −2.18500 + 1.96738i −0.0989103 + 0.0890592i
\(489\) 18.2801 + 7.77746i 0.826654 + 0.351709i
\(490\) 18.2616 + 6.21859i 0.824975 + 0.280927i
\(491\) 8.27669 25.4730i 0.373522 1.14958i −0.570948 0.820986i \(-0.693424\pi\)
0.944470 0.328597i \(-0.106576\pi\)
\(492\) −7.41487 + 0.123232i −0.334288 + 0.00555571i
\(493\) −8.94720 3.98355i −0.402962 0.179410i
\(494\) 3.02079 + 5.23215i 0.135912 + 0.235406i
\(495\) −20.2656 + 18.4720i −0.910870 + 0.830255i
\(496\) −0.238237 −0.0106971
\(497\) −10.0886 + 5.73050i −0.452534 + 0.257048i
\(498\) 3.38473 + 5.64381i 0.151673 + 0.252905i
\(499\) −6.22535 6.91395i −0.278685 0.309511i 0.587510 0.809217i \(-0.300108\pi\)
−0.866195 + 0.499706i \(0.833441\pi\)
\(500\) −6.59156 0.692801i −0.294784 0.0309830i
\(501\) −3.47649 28.5106i −0.155318 1.27376i
\(502\) 17.9524 16.1644i 0.801254 0.721452i
\(503\) −1.28741 3.96225i −0.0574029 0.176668i 0.918244 0.396015i \(-0.129607\pi\)
−0.975647 + 0.219347i \(0.929607\pi\)
\(504\) 7.16395 3.41729i 0.319108 0.152218i
\(505\) 41.6792i 1.85470i
\(506\) 11.3291 14.7349i 0.503638 0.655046i
\(507\) 14.3693 + 15.4350i 0.638162 + 0.685492i
\(508\) 2.36453 5.31083i 0.104909 0.235630i
\(509\) 3.84990 18.1123i 0.170644 0.802815i −0.806667 0.591006i \(-0.798731\pi\)
0.977311 0.211809i \(-0.0679356\pi\)
\(510\) −10.6189 0.937975i −0.470214 0.0415342i
\(511\) 6.05793 27.5471i 0.267987 1.21861i
\(512\) −0.809017 0.587785i −0.0357538 0.0259767i
\(513\) −5.49336 + 34.1299i −0.242538 + 1.50687i
\(514\) 3.99776 + 3.59960i 0.176334 + 0.158771i
\(515\) 1.55633 3.49556i 0.0685799 0.154033i
\(516\) −13.9499 4.27766i −0.614111 0.188314i
\(517\) 15.0102 31.3916i 0.660146 1.38060i
\(518\) 26.2926 11.4855i 1.15523 0.504646i
\(519\) −12.9633 + 14.8874i −0.569026 + 0.653486i
\(520\) −2.44800 0.520339i −0.107352 0.0228184i
\(521\) 2.41312 + 11.3528i 0.105721 + 0.497377i 0.998866 + 0.0476089i \(0.0151601\pi\)
−0.893145 + 0.449768i \(0.851507\pi\)
\(522\) −4.47908 12.3704i −0.196044 0.541439i
\(523\) −3.45369 7.75711i −0.151019 0.339195i 0.822155 0.569263i \(-0.192772\pi\)
−0.973174 + 0.230069i \(0.926105\pi\)
\(524\) −4.95787 + 15.2587i −0.216585 + 0.666581i
\(525\) 1.12955 11.8382i 0.0492978 0.516660i
\(526\) −11.1311 + 8.08723i −0.485340 + 0.352620i
\(527\) 0.266025 0.460768i 0.0115882 0.0200714i
\(528\) 1.83257 5.44442i 0.0797525 0.236938i
\(529\) 4.20293 + 7.27968i 0.182736 + 0.316508i
\(530\) −0.820263 7.80428i −0.0356299 0.338996i
\(531\) −13.6517 + 13.1393i −0.592435 + 0.570199i
\(532\) 7.27210 16.0293i 0.315285 0.694959i
\(533\) 2.28541 3.14560i 0.0989921 0.136251i
\(534\) −3.60817 4.79653i −0.156141 0.207566i
\(535\) −2.32166 10.9226i −0.100374 0.472223i
\(536\) −3.75888 + 4.17466i −0.162359 + 0.180318i
\(537\) −16.1965 + 5.56176i −0.698929 + 0.240008i
\(538\) 6.32794i 0.272817i
\(539\) −10.7703 20.5670i −0.463909 0.885883i
\(540\) −8.98403 11.1514i −0.386611 0.479879i
\(541\) −39.5292 + 4.15468i −1.69949 + 0.178624i −0.904056 0.427414i \(-0.859425\pi\)
−0.795436 + 0.606038i \(0.792758\pi\)
\(542\) −1.69848 1.52932i −0.0729560 0.0656899i
\(543\) −24.2556 + 11.2859i −1.04091 + 0.484326i
\(544\) 2.04020 0.908357i 0.0874730 0.0389455i
\(545\) 0.895895 + 0.650906i 0.0383759 + 0.0278818i
\(546\) −0.826147 + 4.07869i −0.0353558 + 0.174552i
\(547\) −8.50536 + 2.76356i −0.363663 + 0.118161i −0.485148 0.874432i \(-0.661234\pi\)
0.121485 + 0.992593i \(0.461234\pi\)
\(548\) −9.04595 + 0.950767i −0.386424 + 0.0406148i
\(549\) 4.94464 7.30437i 0.211032 0.311743i
\(550\) −5.58333 6.55001i −0.238074 0.279293i
\(551\) −25.2669 14.5879i −1.07641 0.621464i
\(552\) 7.32032 + 6.37420i 0.311574 + 0.271304i
\(553\) 12.0112 + 3.99618i 0.510766 + 0.169935i
\(554\) 8.73722 + 2.83890i 0.371209 + 0.120613i
\(555\) −31.1182 41.3672i −1.32090 1.75594i
\(556\) 16.4485 + 1.72881i 0.697572 + 0.0733178i
\(557\) 14.2055 3.01946i 0.601904 0.127939i 0.103126 0.994668i \(-0.467115\pi\)
0.498778 + 0.866730i \(0.333782\pi\)
\(558\) 0.693768 0.171745i 0.0293695 0.00727055i
\(559\) 6.18908 4.49663i 0.261770 0.190187i
\(560\) 2.91882 + 6.68174i 0.123343 + 0.282355i
\(561\) 8.48360 + 9.62379i 0.358178 + 0.406317i
\(562\) −3.24458 + 5.61977i −0.136864 + 0.237056i
\(563\) −31.7810 14.1498i −1.33941 0.596344i −0.393069 0.919509i \(-0.628587\pi\)
−0.946343 + 0.323165i \(0.895253\pi\)
\(564\) 15.8857 + 8.82295i 0.668909 + 0.371513i
\(565\) 34.2812 + 38.0732i 1.44222 + 1.60175i
\(566\) −3.87757 + 5.33702i −0.162986 + 0.224331i
\(567\) −18.3986 + 15.1160i −0.772667 + 0.634811i
\(568\) −4.17069 1.35514i −0.174998 0.0568604i
\(569\) −39.3585 8.36592i −1.65000 0.350717i −0.713299 0.700859i \(-0.752800\pi\)
−0.936697 + 0.350142i \(0.886133\pi\)
\(570\) −31.1680 6.08547i −1.30548 0.254892i
\(571\) 13.0787 7.55102i 0.547328 0.316000i −0.200715 0.979650i \(-0.564327\pi\)
0.748044 + 0.663649i \(0.230993\pi\)
\(572\) 1.70356 + 2.48382i 0.0712294 + 0.103854i
\(573\) 7.96960 + 34.6522i 0.332935 + 1.44762i
\(574\) −11.3277 0.0795954i −0.472809 0.00332225i
\(575\) 13.8310 4.49397i 0.576794 0.187412i
\(576\) 2.77967 + 1.12847i 0.115820 + 0.0470194i
\(577\) −1.60227 + 15.2446i −0.0667034 + 0.634640i 0.909188 + 0.416385i \(0.136703\pi\)
−0.975892 + 0.218255i \(0.929964\pi\)
\(578\) 1.25564 11.9467i 0.0522279 0.496915i
\(579\) 23.7257 33.8237i 0.986008 1.40566i
\(580\) 11.4944 3.73475i 0.477278 0.155077i
\(581\) 4.96499 + 8.74089i 0.205983 + 0.362633i
\(582\) 30.1598 6.93642i 1.25017 0.287524i
\(583\) −5.75628 + 7.48678i −0.238401 + 0.310071i
\(584\) 9.23237 5.33031i 0.382038 0.220570i
\(585\) 7.50393 0.249492i 0.310249 0.0103152i
\(586\) −12.5291 2.66315i −0.517574 0.110014i
\(587\) −5.75326 1.86935i −0.237462 0.0771562i 0.187868 0.982194i \(-0.439842\pi\)
−0.425331 + 0.905038i \(0.639842\pi\)
\(588\) 11.0635 4.95981i 0.456250 0.204539i
\(589\) 0.931611 1.28225i 0.0383864 0.0528343i
\(590\) −11.6469 12.9352i −0.479494 0.532532i
\(591\) 14.0945 25.3772i 0.579771 1.04388i
\(592\) 9.90692 + 4.41084i 0.407172 + 0.181285i
\(593\) −6.96755 + 12.0681i −0.286123 + 0.495579i −0.972881 0.231307i \(-0.925700\pi\)
0.686758 + 0.726886i \(0.259033\pi\)
\(594\) −1.41174 + 17.1758i −0.0579244 + 0.704730i
\(595\) −16.1823 1.81587i −0.663409 0.0744436i
\(596\) −12.1183 + 8.80443i −0.496383 + 0.360643i
\(597\) −39.7798 + 0.661121i −1.62808 + 0.0270579i
\(598\) −4.97797 + 1.05810i −0.203564 + 0.0432689i
\(599\) 24.6676 + 2.59267i 1.00789 + 0.105933i 0.594060 0.804421i \(-0.297524\pi\)
0.413830 + 0.910354i \(0.364191\pi\)
\(600\) 3.59191 2.70200i 0.146639 0.110309i
\(601\) 3.63278 + 1.18036i 0.148184 + 0.0481479i 0.382170 0.924092i \(-0.375177\pi\)
−0.233986 + 0.972240i \(0.575177\pi\)
\(602\) −21.1484 7.03620i −0.861945 0.286774i
\(603\) 7.93670 14.8668i 0.323207 0.605423i
\(604\) 4.51192 + 2.60496i 0.183587 + 0.105994i
\(605\) −1.64491 + 30.2703i −0.0668749 + 1.23066i
\(606\) 17.8488 + 19.1726i 0.725058 + 0.778833i
\(607\) 10.2443 1.07672i 0.415802 0.0437026i 0.105682 0.994400i \(-0.466297\pi\)
0.310120 + 0.950697i \(0.399631\pi\)
\(608\) 6.32723 2.05584i 0.256603 0.0833754i
\(609\) −6.39324 19.0526i −0.259067 0.772051i
\(610\) 6.55542 + 4.76279i 0.265421 + 0.192840i
\(611\) −8.70364 + 3.87511i −0.352111 + 0.156770i
\(612\) −5.28643 + 4.11601i −0.213691 + 0.166380i
\(613\) −19.8888 17.9080i −0.803302 0.723297i 0.161329 0.986901i \(-0.448422\pi\)
−0.964631 + 0.263604i \(0.915089\pi\)
\(614\) 13.7144 1.44144i 0.553467 0.0581717i
\(615\) 4.58081 + 19.9176i 0.184716 + 0.803153i
\(616\) 2.99514 8.24798i 0.120678 0.332320i
\(617\) 0.534245i 0.0215079i −0.999942 0.0107539i \(-0.996577\pi\)
0.999942 0.0107539i \(-0.00342315\pi\)
\(618\) −0.781034 2.27446i −0.0314178 0.0914921i
\(619\) 6.98455 7.75712i 0.280733 0.311785i −0.586243 0.810135i \(-0.699394\pi\)
0.866976 + 0.498350i \(0.166060\pi\)
\(620\) 0.136506 + 0.642211i 0.00548222 + 0.0257918i
\(621\) −25.9127 13.2851i −1.03984 0.533111i
\(622\) −17.9875 + 24.7577i −0.721234 + 0.992693i
\(623\) −5.33680 7.45508i −0.213815 0.298681i
\(624\) −1.34892 + 0.808980i −0.0540000 + 0.0323851i
\(625\) 3.26557 + 31.0698i 0.130623 + 1.24279i
\(626\) 5.18410 + 8.97912i 0.207198 + 0.358878i
\(627\) 22.1371 + 31.1535i 0.884071 + 1.24415i
\(628\) −0.595632 + 1.03166i −0.0237683 + 0.0411679i
\(629\) −19.5934 + 14.2354i −0.781239 + 0.567603i
\(630\) −13.3168 17.3537i −0.530553 0.691388i
\(631\) −9.40698 + 28.9517i −0.374486 + 1.15255i 0.569339 + 0.822103i \(0.307199\pi\)
−0.943825 + 0.330446i \(0.892801\pi\)
\(632\) 1.94602 + 4.37082i 0.0774083 + 0.173862i
\(633\) −42.9648 + 5.23899i −1.70770 + 0.208231i
\(634\) 4.86922 + 22.9079i 0.193382 + 0.909789i
\(635\) −15.6712 3.33101i −0.621891 0.132187i
\(636\) −3.71945 3.23873i −0.147486 0.128424i
\(637\) −1.40891 + 6.19873i −0.0558229 + 0.245603i
\(638\) −13.1220 6.27438i −0.519503 0.248405i
\(639\) 13.1224 + 0.939639i 0.519114 + 0.0371715i
\(640\) −1.12093 + 2.51765i −0.0443086 + 0.0995188i
\(641\) 2.88041 + 2.59353i 0.113769 + 0.102438i 0.724052 0.689745i \(-0.242277\pi\)
−0.610283 + 0.792184i \(0.708944\pi\)
\(642\) −5.74547 4.03018i −0.226756 0.159059i
\(643\) 36.1152 + 26.2392i 1.42425 + 1.03477i 0.991052 + 0.133473i \(0.0426131\pi\)
0.433193 + 0.901301i \(0.357387\pi\)
\(644\) 10.9487 + 9.99840i 0.431437 + 0.393992i
\(645\) −3.53813 + 40.0556i −0.139314 + 1.57719i
\(646\) −3.08908 + 14.5330i −0.121538 + 0.571793i
\(647\) 8.39624 18.8583i 0.330090 0.741395i −0.669909 0.742443i \(-0.733667\pi\)
0.999999 + 0.00104834i \(0.000333697\pi\)
\(648\) −8.90818 1.28233i −0.349946 0.0503747i
\(649\) −0.568517 + 20.9397i −0.0223162 + 0.821954i
\(650\) 2.35660i 0.0924333i
\(651\) 1.06565 0.237217i 0.0417663 0.00929726i
\(652\) 3.54428 + 10.9082i 0.138805 + 0.427197i
\(653\) 1.51251 1.36187i 0.0591891 0.0532941i −0.639005 0.769202i \(-0.720654\pi\)
0.698194 + 0.715908i \(0.253987\pi\)
\(654\) 0.690861 0.0842413i 0.0270148 0.00329410i
\(655\) 43.9736 + 4.62181i 1.71819 + 0.180589i
\(656\) −2.86493 3.18183i −0.111857 0.124229i
\(657\) −23.0429 + 22.1780i −0.898989 + 0.865246i
\(658\) 23.9404 + 14.0472i 0.933295 + 0.547617i
\(659\) −42.4842 −1.65495 −0.827475 0.561503i \(-0.810223\pi\)
−0.827475 + 0.561503i \(0.810223\pi\)
\(660\) −15.7265 1.82047i −0.612152 0.0708617i
\(661\) 3.30366 + 5.72211i 0.128498 + 0.222564i 0.923095 0.384573i \(-0.125651\pi\)
−0.794597 + 0.607137i \(0.792318\pi\)
\(662\) −9.95899 4.43403i −0.387067 0.172333i
\(663\) −0.0583720 3.51226i −0.00226698 0.136405i
\(664\) −1.17412 + 3.61356i −0.0455645 + 0.140233i
\(665\) −47.3768 10.4187i −1.83719 0.404020i
\(666\) −32.0297 5.70289i −1.24112 0.220982i
\(667\) 18.2639 16.4449i 0.707180 0.636748i
\(668\) 11.0959 12.3232i 0.429312 0.476800i
\(669\) 34.6329 + 6.76199i 1.33899 + 0.261433i
\(670\) 13.4074 + 7.74074i 0.517971 + 0.299051i
\(671\) −1.76784 9.58998i −0.0682467 0.370217i
\(672\) 4.20408 + 1.82366i 0.162176 + 0.0703493i
\(673\) −7.43753 10.2369i −0.286696 0.394603i 0.641242 0.767339i \(-0.278420\pi\)
−0.927937 + 0.372736i \(0.878420\pi\)
\(674\) −5.24903 + 24.6948i −0.202185 + 0.951207i
\(675\) −8.51211 + 10.4579i −0.327631 + 0.402524i
\(676\) −1.27267 + 12.1086i −0.0489488 + 0.465716i
\(677\) 35.4891 15.8007i 1.36396 0.607272i 0.411349 0.911478i \(-0.365058\pi\)
0.952606 + 0.304206i \(0.0983911\pi\)
\(678\) 32.0741 + 2.83312i 1.23180 + 0.108805i
\(679\) 46.3075 9.50339i 1.77712 0.364707i
\(680\) −3.61765 4.97927i −0.138731 0.190946i
\(681\) −1.87728 + 6.12201i −0.0719375 + 0.234596i
\(682\) 0.413497 0.673308i 0.0158336 0.0257823i
\(683\) 16.8137 9.70740i 0.643359 0.371443i −0.142549 0.989788i \(-0.545530\pi\)
0.785907 + 0.618345i \(0.212196\pi\)
\(684\) −16.9434 + 10.5481i −0.647849 + 0.403318i
\(685\) 7.74617 + 23.8403i 0.295966 + 0.910889i
\(686\) 17.0741 7.17457i 0.651893 0.273927i
\(687\) −21.0245 8.94509i −0.802133 0.341276i
\(688\) −3.42641 7.69584i −0.130631 0.293401i
\(689\) 2.52930 0.537619i 0.0963587 0.0204817i
\(690\) 12.9884 23.3856i 0.494460 0.890275i
\(691\) −0.0343623 0.326935i −0.00130720 0.0124372i 0.993849 0.110745i \(-0.0353237\pi\)
−0.995156 + 0.0983078i \(0.968657\pi\)
\(692\) −11.3971 −0.433253
\(693\) −2.77616 + 26.1781i −0.105457 + 0.994424i
\(694\) 8.95878 0.340071
\(695\) −4.76444 45.3306i −0.180725 1.71949i
\(696\) 3.68807 6.64038i 0.139796 0.251703i
\(697\) 9.35299 1.98804i 0.354270 0.0753024i
\(698\) 1.63624 + 3.67506i 0.0619327 + 0.139103i
\(699\) −20.1366 8.56734i −0.761636 0.324047i
\(700\) 5.58278 3.99649i 0.211009 0.151053i
\(701\) 9.58667 + 29.5047i 0.362084 + 1.11438i 0.951787 + 0.306759i \(0.0992446\pi\)
−0.589704 + 0.807620i \(0.700755\pi\)
\(702\) 3.34499 3.32827i 0.126249 0.125617i
\(703\) −62.4808 + 36.0733i −2.35651 + 1.36053i
\(704\) 3.06538 1.26626i 0.115531 0.0477241i
\(705\) 14.6816 47.8783i 0.552942 1.80320i
\(706\) 14.0680 + 19.3629i 0.529454 + 0.728732i
\(707\) 26.5645 + 29.9230i 0.999060 + 1.12537i
\(708\) −10.8970 0.962535i −0.409534 0.0361743i
\(709\) −38.1680 + 16.9935i −1.43343 + 0.638204i −0.968923 0.247364i \(-0.920436\pi\)
−0.464508 + 0.885569i \(0.653769\pi\)
\(710\) −1.26329 + 12.0194i −0.0474103 + 0.451078i
\(711\) −8.81792 11.3254i −0.330698 0.424734i
\(712\) 0.720483 3.38961i 0.0270012 0.127031i
\(713\) 0.784752 + 1.08012i 0.0293892 + 0.0404508i
\(714\) −8.22154 + 6.09463i −0.307684 + 0.228086i
\(715\) 5.71948 6.01545i 0.213896 0.224965i
\(716\) −8.56240 4.94350i −0.319992 0.184747i
\(717\) −7.50596 1.46552i −0.280315 0.0547308i
\(718\) −17.7065 + 19.6650i −0.660800 + 0.733893i
\(719\) −7.76133 + 6.98833i −0.289449 + 0.260621i −0.801044 0.598606i \(-0.795722\pi\)
0.511595 + 0.859227i \(0.329055\pi\)
\(720\) 1.44928 8.13971i 0.0540113 0.303349i
\(721\) −1.11057 3.50152i −0.0413600 0.130404i
\(722\) −7.80588 + 24.0240i −0.290505 + 0.894082i
\(723\) −0.320947 19.3114i −0.0119361 0.718200i
\(724\) −14.1103 6.28233i −0.524407 0.233481i
\(725\) −5.69019 9.85570i −0.211328 0.366032i
\(726\) 12.2064 + 14.6289i 0.453021 + 0.542929i
\(727\) 40.2565 1.49303 0.746515 0.665368i \(-0.231725\pi\)
0.746515 + 0.665368i \(0.231725\pi\)
\(728\) −2.08915 + 1.18668i −0.0774290 + 0.0439812i
\(729\) 26.8659 2.68765i 0.995033 0.0995427i
\(730\) −19.6589 21.8334i −0.727607 0.808089i
\(731\) 18.7104 + 1.96654i 0.692030 + 0.0727352i
\(732\) 5.05514 0.616408i 0.186844 0.0227831i
\(733\) −4.49741 + 4.04948i −0.166115 + 0.149571i −0.747996 0.663703i \(-0.768984\pi\)
0.581881 + 0.813274i \(0.302317\pi\)
\(734\) 2.89291 + 8.90345i 0.106779 + 0.328633i
\(735\) −19.7093 26.9817i −0.726989 0.995236i
\(736\) 5.60409i 0.206570i
\(737\) −5.27437 17.8692i −0.194284 0.658220i
\(738\) 10.6367 + 7.20045i 0.391544 + 0.265052i
\(739\) 7.30925 16.4169i 0.268875 0.603904i −0.727763 0.685828i \(-0.759440\pi\)
0.996639 + 0.0819247i \(0.0261067\pi\)
\(740\) 6.21373 29.2333i 0.228421 1.07464i
\(741\) 0.920732 10.4237i 0.0338239 0.382925i
\(742\) −5.56300 5.08018i −0.204224 0.186499i
\(743\) 27.5255 + 19.9984i 1.00981 + 0.733672i 0.964170 0.265286i \(-0.0854664\pi\)
0.0456429 + 0.998958i \(0.485466\pi\)
\(744\) 0.337815 + 0.236962i 0.0123849 + 0.00868743i
\(745\) 30.6776 + 27.6222i 1.12394 + 1.01200i
\(746\) −9.97970 + 22.4148i −0.365383 + 0.820663i
\(747\) 0.814118 11.3694i 0.0297870 0.415986i
\(748\) −0.973877 + 7.34265i −0.0356085 + 0.268474i
\(749\) −8.62835 6.36197i −0.315273 0.232461i
\(750\) 8.65763 + 7.53867i 0.316132 + 0.275273i
\(751\) 1.92014 + 0.408137i 0.0700667 + 0.0148931i 0.242812 0.970073i \(-0.421930\pi\)
−0.172745 + 0.984967i \(0.555264\pi\)
\(752\) 2.18126 + 10.2620i 0.0795423 + 0.374217i
\(753\) −41.5340 + 5.06453i −1.51358 + 0.184562i
\(754\) 1.61983 + 3.63820i 0.0589908 + 0.132495i
\(755\) 4.43688 13.6553i 0.161475 0.496968i
\(756\) −13.5574 2.27995i −0.493076 0.0829212i
\(757\) 14.6142 10.6179i 0.531163 0.385913i −0.289629 0.957139i \(-0.593532\pi\)
0.820793 + 0.571226i \(0.193532\pi\)
\(758\) −11.9262 + 20.6567i −0.433178 + 0.750286i
\(759\) −30.7204 + 9.62539i −1.11508 + 0.349380i
\(760\) −9.16732 15.8783i −0.332534 0.575965i
\(761\) −0.925539 8.80591i −0.0335507 0.319214i −0.998406 0.0564334i \(-0.982027\pi\)
0.964856 0.262781i \(-0.0846395\pi\)
\(762\) −8.63527 + 5.17878i −0.312823 + 0.187608i
\(763\) 1.05805 0.103695i 0.0383041 0.00375401i
\(764\) −12.0665 + 16.6081i −0.436550 + 0.600860i
\(765\) 14.1245 + 11.8921i 0.510673 + 0.429961i
\(766\) −4.04752 19.0421i −0.146243 0.688018i
\(767\) 3.83784 4.26235i 0.138576 0.153905i
\(768\) 0.562532 + 1.63816i 0.0202986 + 0.0591119i
\(769\) 5.92488i 0.213657i 0.994277 + 0.106828i \(0.0340695\pi\)
−0.994277 + 0.106828i \(0.965930\pi\)
\(770\) −23.9501 3.34798i −0.863103 0.120653i
\(771\) −2.08842 9.08053i −0.0752125 0.327027i
\(772\) 23.7227 2.49336i 0.853799 0.0897379i
\(773\) −24.0733 21.6757i −0.865855 0.779619i 0.110933 0.993828i \(-0.464616\pi\)
−0.976788 + 0.214209i \(0.931283\pi\)
\(774\) 15.5260 + 19.9409i 0.558070 + 0.716761i
\(775\) 0.564783 0.251458i 0.0202876 0.00903262i
\(776\) 14.4550 + 10.5022i 0.518905 + 0.377006i
\(777\) −48.7065 9.86559i −1.74734 0.353926i
\(778\) 14.2585 4.63286i 0.511191 0.166096i
\(779\) 28.3286 2.97745i 1.01498 0.106678i
\(780\) 2.95367 + 3.17273i 0.105758 + 0.113602i
\(781\) 11.0688 9.43523i 0.396073 0.337619i
\(782\) −10.8387 6.25775i −0.387593 0.223777i
\(783\) −5.95297 + 21.9961i −0.212742 + 0.786078i
\(784\) 6.35418 + 2.93674i 0.226935 + 0.104884i
\(785\) 3.12233 + 1.01451i 0.111441 + 0.0362093i
\(786\) 22.2073 16.7053i 0.792106 0.595858i
\(787\) 5.51325 + 0.579466i 0.196526 + 0.0206557i 0.202280 0.979328i \(-0.435165\pi\)
−0.00575389 + 0.999983i \(0.501832\pi\)
\(788\) 16.3934 3.48452i 0.583990 0.124131i
\(789\) 23.8277 0.396004i 0.848288 0.0140981i
\(790\) 10.6673 7.75026i 0.379526 0.275742i
\(791\) 48.8779 + 5.48477i 1.73790 + 0.195016i
\(792\) −8.01384 + 5.89732i −0.284759 + 0.209552i
\(793\) −1.33503 + 2.31234i −0.0474082 + 0.0821134i
\(794\) −22.5069 10.0207i −0.798739 0.355621i
\(795\) −6.59939 + 11.8822i −0.234056 + 0.421418i
\(796\) −15.3700 17.0701i −0.544774 0.605033i
\(797\) 12.1374 16.7057i 0.429929 0.591747i −0.538008 0.842940i \(-0.680823\pi\)
0.967937 + 0.251193i \(0.0808229\pi\)
\(798\) −26.2552 + 15.4961i −0.929426 + 0.548557i
\(799\) −22.2832 7.24025i −0.788323 0.256142i
\(800\) 2.53833 + 0.539538i 0.0897434 + 0.0190755i
\(801\) 0.345457 + 10.3903i 0.0122061 + 0.367122i
\(802\) 21.0288 12.1410i 0.742552 0.428712i
\(803\) −0.959605 + 35.3442i −0.0338637 + 1.24727i
\(804\) 9.48235 2.18083i 0.334417 0.0769120i
\(805\) 20.6791 35.2431i 0.728843 1.24215i
\(806\) −0.205758 + 0.0668549i −0.00724752 + 0.00235486i
\(807\) −6.29408 + 8.97291i −0.221562 + 0.315861i
\(808\) −1.58084 + 15.0407i −0.0556139 + 0.529131i
\(809\) −3.70144 + 35.2168i −0.130136 + 1.23816i 0.713273 + 0.700886i \(0.247212\pi\)
−0.843409 + 0.537272i \(0.819455\pi\)
\(810\) 1.64750 + 24.7484i 0.0578873 + 0.869570i
\(811\) 9.00660 2.92642i 0.316265 0.102761i −0.146583 0.989198i \(-0.546828\pi\)
0.462848 + 0.886438i \(0.346828\pi\)
\(812\) 5.87186 10.0073i 0.206062 0.351188i
\(813\) 0.887282 + 3.85794i 0.0311183 + 0.135304i
\(814\) −29.6610 + 20.3434i −1.03962 + 0.713035i
\(815\) 27.3742 15.8045i 0.958875 0.553607i
\(816\) −3.79647 0.741250i −0.132903 0.0259489i
\(817\) 54.8198 + 11.6523i 1.91790 + 0.407663i
\(818\) −25.5696 8.30805i −0.894019 0.290484i
\(819\) 5.22833 4.96179i 0.182693 0.173379i
\(820\) −6.93564 + 9.54609i −0.242203 + 0.333364i
\(821\) 14.3879 + 15.9794i 0.502141 + 0.557684i 0.939918 0.341399i \(-0.110901\pi\)
−0.437777 + 0.899083i \(0.644234\pi\)
\(822\) 13.7727 + 7.64937i 0.480377 + 0.266802i
\(823\) −5.99816 2.67055i −0.209083 0.0930896i 0.299523 0.954089i \(-0.403172\pi\)
−0.508606 + 0.860999i \(0.669839\pi\)
\(824\) 0.694212 1.20241i 0.0241840 0.0418880i
\(825\) 1.40211 + 14.8412i 0.0488151 + 0.516706i
\(826\) −16.6060 1.86342i −0.577797 0.0648367i
\(827\) 39.8068 28.9213i 1.38422 1.00569i 0.387745 0.921767i \(-0.373254\pi\)
0.996472 0.0839259i \(-0.0267459\pi\)
\(828\) −4.04000 16.3197i −0.140400 0.567147i
\(829\) −0.584827 + 0.124309i −0.0203119 + 0.00431743i −0.218056 0.975936i \(-0.569972\pi\)
0.197745 + 0.980254i \(0.436638\pi\)
\(830\) 10.4138 + 1.09453i 0.361467 + 0.0379917i
\(831\) −9.56553 12.7160i −0.331824 0.441112i
\(832\) −0.863672 0.280624i −0.0299424 0.00972889i
\(833\) −12.7752 + 9.01019i −0.442635 + 0.312185i
\(834\) −21.6042 18.8119i −0.748091 0.651403i
\(835\) −39.5773 22.8500i −1.36963 0.790756i
\(836\) −5.17164 + 21.4504i −0.178865 + 0.741876i
\(837\) −1.15458 0.446523i −0.0399080 0.0154341i
\(838\) 9.06724 0.953006i 0.313223 0.0329210i
\(839\) 35.2570 11.4557i 1.21721 0.395494i 0.371142 0.928576i \(-0.378966\pi\)
0.846063 + 0.533082i \(0.178966\pi\)
\(840\) 2.50715 12.3778i 0.0865048 0.427075i
\(841\) 7.90235 + 5.74139i 0.272495 + 0.197979i
\(842\) −15.6834 + 6.98270i −0.540485 + 0.240640i
\(843\) 10.1904 4.74153i 0.350978 0.163307i
\(844\) −18.5708 16.7212i −0.639233 0.575568i
\(845\) 33.3703 3.50736i 1.14797 0.120657i
\(846\) −13.7499 28.3115i −0.472732 0.973369i
\(847\) 18.1120 + 22.7806i 0.622337 + 0.782750i
\(848\) 2.84743i 0.0977813i
\(849\) 10.8068 3.71098i 0.370888 0.127360i
\(850\) −3.87790 + 4.30685i −0.133011 + 0.147724i
\(851\) −12.6355 59.4454i −0.433140 2.03776i
\(852\) 4.56608 + 6.06994i 0.156431 + 0.207953i
\(853\) −3.16081 + 4.35048i −0.108224 + 0.148958i −0.859693 0.510810i \(-0.829345\pi\)
0.751469 + 0.659768i \(0.229345\pi\)
\(854\) 7.74196 0.758753i 0.264925 0.0259640i
\(855\) 38.1428 + 39.6303i 1.30446 + 1.35533i
\(856\) −0.423535 4.02967i −0.0144761 0.137731i
\(857\) −10.1726 17.6194i −0.347488 0.601867i 0.638315 0.769776i \(-0.279632\pi\)
−0.985803 + 0.167909i \(0.946299\pi\)
\(858\) 0.0549083 5.21645i 0.00187454 0.178087i
\(859\) −17.2318 + 29.8464i −0.587941 + 1.01834i 0.406560 + 0.913624i \(0.366728\pi\)
−0.994502 + 0.104721i \(0.966605\pi\)
\(860\) −18.7823 + 13.6461i −0.640470 + 0.465329i
\(861\) 15.9833 + 11.3799i 0.544709 + 0.387827i
\(862\) 12.1149 37.2859i 0.412636 1.26996i
\(863\) −18.0794 40.6070i −0.615430 1.38228i −0.905119 0.425158i \(-0.860219\pi\)
0.289689 0.957121i \(-0.406448\pi\)
\(864\) −2.81910 4.36494i −0.0959077 0.148498i
\(865\) 6.53039 + 30.7230i 0.222040 + 1.04461i
\(866\) 7.28215 + 1.54787i 0.247458 + 0.0525987i
\(867\) −13.6632 + 15.6912i −0.464027 + 0.532902i
\(868\) 0.507320 + 0.374064i 0.0172195 + 0.0126965i
\(869\) −15.7305 2.08638i −0.533621 0.0707757i
\(870\) −20.0136 6.13705i −0.678524 0.208065i
\(871\) −2.07493 + 4.66037i −0.0703063 + 0.157911i
\(872\) 0.298613 + 0.268872i 0.0101123 + 0.00910516i
\(873\) −49.6654 20.1627i −1.68092 0.682404i
\(874\) −30.1627 21.9145i −1.02027 0.741269i
\(875\) 12.9488 + 11.8249i 0.437749 + 0.399756i
\(876\) −18.3931 1.62467i −0.621446 0.0548926i
\(877\) 3.80533 17.9027i 0.128497 0.604530i −0.866025 0.500001i \(-0.833333\pi\)
0.994522 0.104529i \(-0.0333336\pi\)
\(878\) 11.3561 25.5061i 0.383248 0.860790i
\(879\) 15.1172 + 16.2384i 0.509891 + 0.547708i
\(880\) −5.16987 7.53776i −0.174276 0.254098i
\(881\) 10.9054i 0.367412i −0.982981 0.183706i \(-0.941191\pi\)
0.982981 0.183706i \(-0.0588094\pi\)
\(882\) −20.6211 3.97133i −0.694348 0.133722i
\(883\) −1.16254 3.57794i −0.0391227 0.120407i 0.929588 0.368601i \(-0.120163\pi\)
−0.968710 + 0.248194i \(0.920163\pi\)
\(884\) 1.50716 1.35705i 0.0506912 0.0456426i
\(885\) 3.64912 + 29.9264i 0.122664 + 1.00596i
\(886\) −5.79421 0.608996i −0.194660 0.0204596i
\(887\) 30.2166 + 33.5589i 1.01457 + 1.12680i 0.991895 + 0.127056i \(0.0405529\pi\)
0.0226791 + 0.999743i \(0.492780\pi\)
\(888\) −9.66060 16.1084i −0.324188 0.540563i
\(889\) −13.3739 + 7.59665i −0.448547 + 0.254784i
\(890\) −9.55014 −0.320121
\(891\) 19.0857 22.9508i 0.639394 0.768879i
\(892\) 10.1864 + 17.6434i 0.341067 + 0.590746i
\(893\) −63.7626 28.3889i −2.13373 0.949999i
\(894\) 25.9408 0.431123i 0.867590 0.0144189i
\(895\) −8.42000 + 25.9141i −0.281450 + 0.866213i
\(896\) 0.799882 + 2.52194i 0.0267222 + 0.0842522i
\(897\) 8.11111 + 3.45096i 0.270822 + 0.115224i
\(898\) −8.75167 + 7.88004i −0.292047 + 0.262960i
\(899\) 0.699090 0.776419i 0.0233160 0.0258950i
\(900\) −7.78080 + 0.258698i −0.259360 + 0.00862325i
\(901\) 5.50716 + 3.17956i 0.183470 + 0.105926i
\(902\) 13.9651 2.57435i 0.464986 0.0857166i
\(903\) 22.9895 + 31.0124i 0.765044 + 1.03203i
\(904\) 10.9270 + 15.0397i 0.363425 + 0.500212i
\(905\) −8.85016 + 41.6367i −0.294189 + 1.38405i
\(906\) −3.80681 8.18156i −0.126473 0.271814i
\(907\) 5.58670 53.1539i 0.185503 1.76495i −0.365848 0.930675i \(-0.619221\pi\)
0.551352 0.834273i \(-0.314112\pi\)
\(908\) −3.37737 + 1.50370i −0.112082 + 0.0499021i
\(909\) −6.23932 44.9397i −0.206945 1.49055i
\(910\) 4.39596 + 4.95174i 0.145725 + 0.164149i
\(911\) −18.7287 25.7778i −0.620509 0.854057i 0.376881 0.926262i \(-0.376997\pi\)
−0.997390 + 0.0722044i \(0.976997\pi\)
\(912\) −11.0167 3.37822i −0.364801 0.111864i
\(913\) −8.17483 9.59019i −0.270547 0.317389i
\(914\) −26.1310 + 15.0868i −0.864338 + 0.499026i
\(915\) −4.55817 13.2739i −0.150688 0.438821i
\(916\) −4.07638 12.5458i −0.134687 0.414525i
\(917\) 34.5160 24.7086i 1.13982 0.815951i
\(918\) 11.5900 0.578289i 0.382529 0.0190864i
\(919\) 9.71005 + 21.8091i 0.320305 + 0.719417i 0.999900 0.0141710i \(-0.00451093\pi\)
−0.679595 + 0.733588i \(0.737844\pi\)
\(920\) 15.1069 3.21106i 0.498059 0.105866i
\(921\) −20.8805 11.5970i −0.688035 0.382136i
\(922\) 1.15702 + 11.0083i 0.0381045 + 0.362540i
\(923\) −3.98240 −0.131082
\(924\) −12.4509 + 8.71638i −0.409604 + 0.286748i
\(925\) −28.1418 −0.925296
\(926\) −0.306448 2.91566i −0.0100705 0.0958145i
\(927\) −1.15479 + 4.00199i −0.0379284 + 0.131443i
\(928\) 4.28962 0.911786i 0.140814 0.0299308i
\(929\) 18.7080 + 42.0189i 0.613790 + 1.37859i 0.906424 + 0.422370i \(0.138802\pi\)
−0.292634 + 0.956225i \(0.594532\pi\)
\(930\) 0.445211 1.04642i 0.0145990 0.0343134i
\(931\) −40.6540 + 22.7159i −1.33238 + 0.744484i
\(932\) −3.90424 12.0160i −0.127887 0.393597i
\(933\) 50.1312 17.2147i 1.64122 0.563585i
\(934\) 30.9918 17.8931i 1.01408 0.585481i
\(935\) 20.3515 1.58197i 0.665565 0.0517358i
\(936\) 2.71740 + 0.194581i 0.0888209 + 0.00636009i
\(937\) −1.10579 1.52199i −0.0361246 0.0497213i 0.790573 0.612368i \(-0.209783\pi\)
−0.826697 + 0.562647i \(0.809783\pi\)
\(938\) 14.5592 2.98790i 0.475376 0.0975583i
\(939\) 1.58011 17.8886i 0.0515648 0.583772i
\(940\) 26.4133 11.7600i 0.861508 0.383568i
\(941\) −3.01561 + 28.6916i −0.0983062 + 0.935321i 0.828553 + 0.559911i \(0.189165\pi\)
−0.926859 + 0.375410i \(0.877502\pi\)
\(942\) 1.87074 0.870438i 0.0609520 0.0283604i
\(943\) −4.98870 + 23.4700i −0.162454 + 0.764288i
\(944\) −3.71238 5.10965i −0.120828 0.166305i
\(945\) 1.62213 + 37.8527i 0.0527678 + 1.23135i
\(946\) 27.6972 + 3.67356i 0.900513 + 0.119438i
\(947\) −14.5984 8.42840i −0.474385 0.273886i 0.243689 0.969853i \(-0.421642\pi\)
−0.718073 + 0.695967i \(0.754976\pi\)
\(948\) 1.58802 8.13335i 0.0515763 0.264159i
\(949\) 6.47792 7.19446i 0.210282 0.233542i
\(950\) −12.8299 + 11.5521i −0.416257 + 0.374800i
\(951\) 15.8808 37.3262i 0.514971 1.21038i
\(952\) −5.77081 1.26907i −0.187033 0.0411307i
\(953\) −9.78823 + 30.1251i −0.317072 + 0.975847i 0.657821 + 0.753174i \(0.271478\pi\)
−0.974893 + 0.222673i \(0.928522\pi\)
\(954\) 2.05272 + 8.29200i 0.0664593 + 0.268463i
\(955\) 51.6842 + 23.0113i 1.67246 + 0.744627i
\(956\) −2.20770 3.82385i −0.0714021 0.123672i
\(957\) 12.3659 + 21.9487i 0.399733 + 0.709501i
\(958\) −19.3980 −0.626721
\(959\) 20.7560 + 12.1787i 0.670246 + 0.393271i
\(960\) 4.09363 2.45505i 0.132121 0.0792364i
\(961\) −20.7051 22.9953i −0.667906 0.741784i
\(962\) 9.79411 + 1.02940i 0.315775 + 0.0331893i
\(963\) 4.13837 + 11.4294i 0.133357 + 0.368309i
\(964\) 8.28681 7.46148i 0.266900 0.240318i
\(965\) −20.3141 62.5203i −0.653934 2.01260i
\(966\) −5.58011 25.0676i −0.179537 0.806537i
\(967\) 0.0899523i 0.00289267i −0.999999 0.00144634i \(-0.999540\pi\)
0.999999 0.00144634i \(-0.000460383\pi\)
\(968\) −1.74171 + 10.8612i −0.0559808 + 0.349093i
\(969\) 18.8355 17.5350i 0.605083 0.563305i
\(970\) 20.0281 44.9838i 0.643062 1.44434i
\(971\) 1.22134 5.74596i 0.0391947 0.184397i −0.954195 0.299184i \(-0.903285\pi\)
0.993390 + 0.114788i \(0.0366188\pi\)
\(972\) 11.3562 + 10.6788i 0.364249 + 0.342523i
\(973\) −32.3123 29.5079i −1.03588 0.945978i
\(974\) 6.52373 + 4.73977i 0.209034 + 0.151872i
\(975\) 2.34399 3.34161i 0.0750676 0.107017i
\(976\) 2.18500 + 1.96738i 0.0699401 + 0.0629744i
\(977\) 14.8825 33.4266i 0.476133 1.06941i −0.502646 0.864493i \(-0.667640\pi\)
0.978779 0.204920i \(-0.0656934\pi\)
\(978\) 5.82406 18.9929i 0.186233 0.607326i
\(979\) 8.32925 + 7.91943i 0.266204 + 0.253106i
\(980\) 4.27567 18.8116i 0.136581 0.600914i
\(981\) −1.06342 0.567711i −0.0339524 0.0181256i
\(982\) −26.1987 5.56870i −0.836033 0.177704i
\(983\) 8.19645 + 38.5613i 0.261426 + 1.22991i 0.891371 + 0.453274i \(0.149744\pi\)
−0.629945 + 0.776640i \(0.716923\pi\)
\(984\) 0.897622 + 7.36137i 0.0286151 + 0.234672i
\(985\) −18.7864 42.1949i −0.598583 1.34444i
\(986\) −3.02649 + 9.31459i −0.0963832 + 0.296637i
\(987\) −19.9751 43.7310i −0.635813 1.39197i
\(988\) 4.88773 3.55115i 0.155500 0.112977i
\(989\) −23.6048 + 40.8848i −0.750590 + 1.30006i
\(990\) 20.4891 + 18.2237i 0.651188 + 0.579187i
\(991\) 0.245349 + 0.424956i 0.00779376 + 0.0134992i 0.869896 0.493235i \(-0.164186\pi\)
−0.862102 + 0.506734i \(0.830852\pi\)
\(992\) 0.0249025 + 0.236932i 0.000790655 + 0.00752258i
\(993\) 9.71138 + 16.1931i 0.308181 + 0.513871i
\(994\) 6.75365 + 9.43430i 0.214213 + 0.299238i
\(995\) −37.2088 + 51.2135i −1.17960 + 1.62358i
\(996\) 5.25909 3.95613i 0.166641 0.125355i
\(997\) 4.98138 + 23.4356i 0.157762 + 0.742212i 0.983897 + 0.178739i \(0.0572018\pi\)
−0.826135 + 0.563473i \(0.809465\pi\)
\(998\) −6.22535 + 6.91395i −0.197060 + 0.218857i
\(999\) 39.7452 + 39.9449i 1.25748 + 1.26380i
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 462.2.bc.b.107.6 yes 128
3.2 odd 2 462.2.bc.a.107.4 yes 128
7.4 even 3 inner 462.2.bc.b.305.16 yes 128
11.7 odd 10 462.2.bc.a.359.15 yes 128
21.11 odd 6 462.2.bc.a.305.15 yes 128
33.29 even 10 inner 462.2.bc.b.359.16 yes 128
77.18 odd 30 462.2.bc.a.95.4 128
231.95 even 30 inner 462.2.bc.b.95.6 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.bc.a.95.4 128 77.18 odd 30
462.2.bc.a.107.4 yes 128 3.2 odd 2
462.2.bc.a.305.15 yes 128 21.11 odd 6
462.2.bc.a.359.15 yes 128 11.7 odd 10
462.2.bc.b.95.6 yes 128 231.95 even 30 inner
462.2.bc.b.107.6 yes 128 1.1 even 1 trivial
462.2.bc.b.305.16 yes 128 7.4 even 3 inner
462.2.bc.b.359.16 yes 128 33.29 even 10 inner