Properties

Label 462.2.w.a.365.1
Level $462$
Weight $2$
Character 462.365
Analytic conductor $3.689$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [462,2,Mod(29,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.w (of order \(10\), degree \(4\), 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: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 365.1
Character \(\chi\) \(=\) 462.365
Dual form 462.2.w.a.281.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 - 0.951057i) q^{2} +(-1.72172 + 0.188926i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.152745 - 0.0496298i) q^{5} +(-0.352360 + 1.69583i) q^{6} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.92861 - 0.650555i) q^{9} +O(q^{10})\) \(q+(0.309017 - 0.951057i) q^{2} +(-1.72172 + 0.188926i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.152745 - 0.0496298i) q^{5} +(-0.352360 + 1.69583i) q^{6} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.92861 - 0.650555i) q^{9} -0.160605i q^{10} +(3.12194 - 1.11961i) q^{11} +(1.50395 + 0.859155i) q^{12} +(-6.36388 - 2.06775i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(-0.253607 + 0.114306i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.841882 - 2.59105i) q^{17} +(0.286277 - 2.98631i) q^{18} +(-3.45842 - 4.76011i) q^{19} +(-0.152745 - 0.0496298i) q^{20} +(-0.859155 + 1.50395i) q^{21} +(-0.100078 - 3.31511i) q^{22} +2.94363i q^{23} +(1.28185 - 1.16484i) q^{24} +(-4.02422 + 2.92376i) q^{25} +(-3.93309 + 5.41344i) q^{26} +(-4.91934 + 1.67336i) q^{27} +(-0.951057 + 0.309017i) q^{28} +(-5.12098 - 3.72061i) q^{29} +(0.0303426 + 0.276517i) q^{30} +(2.60546 - 8.01878i) q^{31} +1.00000 q^{32} +(-5.16356 + 2.51746i) q^{33} -2.72439 q^{34} +(0.0496298 - 0.152745i) q^{35} +(-2.75168 - 1.19509i) q^{36} +(-0.501222 - 0.364159i) q^{37} +(-5.59585 + 1.81820i) q^{38} +(11.3474 + 2.35778i) q^{39} +(-0.0944015 + 0.129933i) q^{40} +(4.44808 - 3.23172i) q^{41} +(1.16484 + 1.28185i) q^{42} +2.41048i q^{43} +(-3.18379 - 0.929247i) q^{44} +(0.415044 - 0.244715i) q^{45} +(2.79955 + 0.909630i) q^{46} +(1.56714 + 2.15699i) q^{47} +(-0.711719 - 1.57907i) q^{48} +(-0.309017 - 0.951057i) q^{49} +(1.53711 + 4.73075i) q^{50} +(1.93900 + 4.30199i) q^{51} +(3.93309 + 5.41344i) q^{52} +(-2.46767 - 0.801796i) q^{53} +(0.0713040 + 5.19566i) q^{54} +(0.421294 - 0.325955i) q^{55} +1.00000i q^{56} +(6.85373 + 7.54218i) q^{57} +(-5.12098 + 3.72061i) q^{58} +(8.48442 - 11.6778i) q^{59} +(0.272360 + 0.0565910i) q^{60} +(-7.68134 + 2.49582i) q^{61} +(-6.82118 - 4.95588i) q^{62} +(1.19509 - 2.75168i) q^{63} +(0.309017 - 0.951057i) q^{64} -1.07467 q^{65} +(0.798618 + 5.68878i) q^{66} +9.38707 q^{67} +(-0.841882 + 2.59105i) q^{68} +(-0.556128 - 5.06809i) q^{69} +(-0.129933 - 0.0944015i) q^{70} +(10.0295 - 3.25877i) q^{71} +(-1.98691 + 2.24771i) q^{72} +(0.0597686 - 0.0822645i) q^{73} +(-0.501222 + 0.364159i) q^{74} +(6.37618 - 5.79417i) q^{75} +5.88382i q^{76} +(0.929247 - 3.18379i) q^{77} +(5.74893 - 10.0635i) q^{78} +(-8.72301 - 2.83428i) q^{79} +(0.0944015 + 0.129933i) q^{80} +(8.15356 - 3.81045i) q^{81} +(-1.69901 - 5.22903i) q^{82} +(4.39153 + 13.5157i) q^{83} +(1.57907 - 0.711719i) q^{84} +(-0.257186 - 0.353987i) q^{85} +(2.29250 + 0.744879i) q^{86} +(9.51979 + 5.43834i) q^{87} +(-1.86761 + 2.74081i) q^{88} +15.1000i q^{89} +(-0.104483 - 0.470351i) q^{90} +(-5.41344 + 3.93309i) q^{91} +(1.73022 - 2.38144i) q^{92} +(-2.97090 + 14.2983i) q^{93} +(2.53569 - 0.823897i) q^{94} +(-0.764500 - 0.555442i) q^{95} +(-1.72172 + 0.188926i) q^{96} +(-3.20306 + 9.85801i) q^{97} -1.00000 q^{98} +(8.41458 - 5.30988i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9} - 8 q^{11} + 6 q^{12} + 36 q^{15} - 12 q^{16} - 24 q^{17} + 30 q^{19} - 8 q^{22} - 4 q^{24} + 18 q^{25} - 20 q^{26} - 22 q^{27} + 8 q^{29} - 24 q^{30} - 32 q^{31} + 48 q^{32} - 14 q^{33} - 4 q^{34} + 6 q^{35} - 10 q^{36} - 20 q^{37} + 20 q^{38} - 6 q^{39} + 22 q^{44} + 12 q^{45} + 20 q^{46} + 20 q^{47} - 4 q^{48} + 12 q^{49} + 28 q^{50} + 8 q^{51} + 20 q^{52} + 20 q^{53} + 18 q^{54} + 16 q^{55} - 2 q^{57} + 8 q^{58} + 30 q^{59} - 4 q^{60} - 20 q^{61} + 8 q^{62} + 4 q^{63} - 12 q^{64} - 14 q^{66} + 36 q^{67} - 24 q^{68} - 70 q^{69} - 4 q^{70} + 10 q^{72} - 20 q^{73} - 20 q^{74} - 30 q^{75} - 16 q^{77} - 16 q^{78} - 20 q^{79} + 26 q^{81} - 10 q^{82} - 46 q^{83} - 10 q^{84} + 10 q^{85} - 30 q^{86} + 8 q^{87} - 8 q^{88} - 38 q^{90} - 36 q^{91} + 10 q^{92} - 36 q^{93} + 50 q^{95} - 4 q^{96} - 2 q^{97} - 48 q^{98} + 70 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 0.951057i 0.218508 0.672499i
\(3\) −1.72172 + 0.188926i −0.994033 + 0.109077i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0.152745 0.0496298i 0.0683096 0.0221951i −0.274663 0.961541i \(-0.588566\pi\)
0.342972 + 0.939345i \(0.388566\pi\)
\(6\) −0.352360 + 1.69583i −0.143850 + 0.692320i
\(7\) 0.587785 0.809017i 0.222162 0.305780i
\(8\) −0.809017 + 0.587785i −0.286031 + 0.207813i
\(9\) 2.92861 0.650555i 0.976205 0.216852i
\(10\) 0.160605i 0.0507879i
\(11\) 3.12194 1.11961i 0.941299 0.337574i
\(12\) 1.50395 + 0.859155i 0.434152 + 0.248017i
\(13\) −6.36388 2.06775i −1.76502 0.573491i −0.767322 0.641262i \(-0.778411\pi\)
−0.997701 + 0.0677714i \(0.978411\pi\)
\(14\) −0.587785 0.809017i −0.157092 0.216219i
\(15\) −0.253607 + 0.114306i −0.0654810 + 0.0295137i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −0.841882 2.59105i −0.204186 0.628421i −0.999746 0.0225456i \(-0.992823\pi\)
0.795559 0.605876i \(-0.207177\pi\)
\(18\) 0.286277 2.98631i 0.0674762 0.703880i
\(19\) −3.45842 4.76011i −0.793417 1.09204i −0.993674 0.112301i \(-0.964178\pi\)
0.200257 0.979743i \(-0.435822\pi\)
\(20\) −0.152745 0.0496298i −0.0341548 0.0110976i
\(21\) −0.859155 + 1.50395i −0.187483 + 0.328188i
\(22\) −0.100078 3.31511i −0.0213367 0.706785i
\(23\) 2.94363i 0.613788i 0.951744 + 0.306894i \(0.0992898\pi\)
−0.951744 + 0.306894i \(0.900710\pi\)
\(24\) 1.28185 1.16484i 0.261656 0.237773i
\(25\) −4.02422 + 2.92376i −0.804843 + 0.584753i
\(26\) −3.93309 + 5.41344i −0.771343 + 1.06166i
\(27\) −4.91934 + 1.67336i −0.946726 + 0.322039i
\(28\) −0.951057 + 0.309017i −0.179733 + 0.0583987i
\(29\) −5.12098 3.72061i −0.950942 0.690900i 8.76975e−5 1.00000i \(-0.499972\pi\)
−0.951029 + 0.309100i \(0.899972\pi\)
\(30\) 0.0303426 + 0.276517i 0.00553977 + 0.0504849i
\(31\) 2.60546 8.01878i 0.467954 1.44021i −0.387275 0.921964i \(-0.626584\pi\)
0.855229 0.518250i \(-0.173416\pi\)
\(32\) 1.00000 0.176777
\(33\) −5.16356 + 2.51746i −0.898861 + 0.438234i
\(34\) −2.72439 −0.467229
\(35\) 0.0496298 0.152745i 0.00838897 0.0258186i
\(36\) −2.75168 1.19509i −0.458614 0.199181i
\(37\) −0.501222 0.364159i −0.0824003 0.0598673i 0.545822 0.837901i \(-0.316217\pi\)
−0.628223 + 0.778034i \(0.716217\pi\)
\(38\) −5.59585 + 1.81820i −0.907766 + 0.294951i
\(39\) 11.3474 + 2.35778i 1.81705 + 0.377546i
\(40\) −0.0944015 + 0.129933i −0.0149262 + 0.0205441i
\(41\) 4.44808 3.23172i 0.694673 0.504709i −0.183520 0.983016i \(-0.558749\pi\)
0.878193 + 0.478307i \(0.158749\pi\)
\(42\) 1.16484 + 1.28185i 0.179739 + 0.197794i
\(43\) 2.41048i 0.367594i 0.982964 + 0.183797i \(0.0588390\pi\)
−0.982964 + 0.183797i \(0.941161\pi\)
\(44\) −3.18379 0.929247i −0.479974 0.140089i
\(45\) 0.415044 0.244715i 0.0618711 0.0364800i
\(46\) 2.79955 + 0.909630i 0.412772 + 0.134118i
\(47\) 1.56714 + 2.15699i 0.228592 + 0.314629i 0.907870 0.419251i \(-0.137707\pi\)
−0.679279 + 0.733880i \(0.737707\pi\)
\(48\) −0.711719 1.57907i −0.102728 0.227919i
\(49\) −0.309017 0.951057i −0.0441453 0.135865i
\(50\) 1.53711 + 4.73075i 0.217381 + 0.669029i
\(51\) 1.93900 + 4.30199i 0.271514 + 0.602400i
\(52\) 3.93309 + 5.41344i 0.545422 + 0.750709i
\(53\) −2.46767 0.801796i −0.338961 0.110135i 0.134590 0.990901i \(-0.457028\pi\)
−0.473551 + 0.880766i \(0.657028\pi\)
\(54\) 0.0713040 + 5.19566i 0.00970325 + 0.707040i
\(55\) 0.421294 0.325955i 0.0568072 0.0439518i
\(56\) 1.00000i 0.133631i
\(57\) 6.85373 + 7.54218i 0.907799 + 0.998986i
\(58\) −5.12098 + 3.72061i −0.672417 + 0.488540i
\(59\) 8.48442 11.6778i 1.10458 1.52032i 0.275403 0.961329i \(-0.411189\pi\)
0.829174 0.558991i \(-0.188811\pi\)
\(60\) 0.272360 + 0.0565910i 0.0351615 + 0.00730586i
\(61\) −7.68134 + 2.49582i −0.983495 + 0.319557i −0.756251 0.654281i \(-0.772971\pi\)
−0.227243 + 0.973838i \(0.572971\pi\)
\(62\) −6.82118 4.95588i −0.866291 0.629397i
\(63\) 1.19509 2.75168i 0.150567 0.346680i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) −1.07467 −0.133297
\(66\) 0.798618 + 5.68878i 0.0983030 + 0.700240i
\(67\) 9.38707 1.14681 0.573407 0.819271i \(-0.305622\pi\)
0.573407 + 0.819271i \(0.305622\pi\)
\(68\) −0.841882 + 2.59105i −0.102093 + 0.314211i
\(69\) −0.556128 5.06809i −0.0669499 0.610126i
\(70\) −0.129933 0.0944015i −0.0155299 0.0112831i
\(71\) 10.0295 3.25877i 1.19028 0.386745i 0.354103 0.935207i \(-0.384786\pi\)
0.836176 + 0.548462i \(0.184786\pi\)
\(72\) −1.98691 + 2.24771i −0.234160 + 0.264895i
\(73\) 0.0597686 0.0822645i 0.00699539 0.00962833i −0.805505 0.592589i \(-0.798106\pi\)
0.812500 + 0.582961i \(0.198106\pi\)
\(74\) −0.501222 + 0.364159i −0.0582658 + 0.0423326i
\(75\) 6.37618 5.79417i 0.736258 0.669054i
\(76\) 5.88382i 0.674921i
\(77\) 0.929247 3.18379i 0.105898 0.362826i
\(78\) 5.74893 10.0635i 0.650938 1.13946i
\(79\) −8.72301 2.83428i −0.981415 0.318881i −0.226000 0.974127i \(-0.572565\pi\)
−0.755415 + 0.655246i \(0.772565\pi\)
\(80\) 0.0944015 + 0.129933i 0.0105544 + 0.0145269i
\(81\) 8.15356 3.81045i 0.905951 0.423383i
\(82\) −1.69901 5.22903i −0.187625 0.577450i
\(83\) 4.39153 + 13.5157i 0.482033 + 1.48355i 0.836232 + 0.548376i \(0.184754\pi\)
−0.354199 + 0.935170i \(0.615246\pi\)
\(84\) 1.57907 0.711719i 0.172290 0.0776549i
\(85\) −0.257186 0.353987i −0.0278958 0.0383953i
\(86\) 2.29250 + 0.744879i 0.247207 + 0.0803223i
\(87\) 9.51979 + 5.43834i 1.02063 + 0.583052i
\(88\) −1.86761 + 2.74081i −0.199088 + 0.292171i
\(89\) 15.1000i 1.60060i 0.599601 + 0.800299i \(0.295326\pi\)
−0.599601 + 0.800299i \(0.704674\pi\)
\(90\) −0.104483 0.470351i −0.0110134 0.0495794i
\(91\) −5.41344 + 3.93309i −0.567483 + 0.412300i
\(92\) 1.73022 2.38144i 0.180388 0.248283i
\(93\) −2.97090 + 14.2983i −0.308068 + 1.48266i
\(94\) 2.53569 0.823897i 0.261537 0.0849785i
\(95\) −0.764500 0.555442i −0.0784361 0.0569871i
\(96\) −1.72172 + 0.188926i −0.175722 + 0.0192822i
\(97\) −3.20306 + 9.85801i −0.325222 + 1.00093i 0.646119 + 0.763237i \(0.276391\pi\)
−0.971341 + 0.237692i \(0.923609\pi\)
\(98\) −1.00000 −0.101015
\(99\) 8.41458 5.30988i 0.845697 0.533663i
\(100\) 4.97421 0.497421
\(101\) 3.65609 11.2523i 0.363795 1.11964i −0.586938 0.809632i \(-0.699667\pi\)
0.950732 0.310013i \(-0.100333\pi\)
\(102\) 4.69062 0.514708i 0.464441 0.0509637i
\(103\) 0.881475 + 0.640429i 0.0868543 + 0.0631033i 0.630365 0.776299i \(-0.282905\pi\)
−0.543511 + 0.839402i \(0.682905\pi\)
\(104\) 6.36388 2.06775i 0.624030 0.202760i
\(105\) −0.0565910 + 0.272360i −0.00552271 + 0.0265796i
\(106\) −1.52511 + 2.09913i −0.148131 + 0.203885i
\(107\) 6.75237 4.90589i 0.652776 0.474270i −0.211439 0.977391i \(-0.567815\pi\)
0.864216 + 0.503121i \(0.167815\pi\)
\(108\) 4.96340 + 1.53773i 0.477604 + 0.147969i
\(109\) 0.765456i 0.0733174i 0.999328 + 0.0366587i \(0.0116714\pi\)
−0.999328 + 0.0366587i \(0.988329\pi\)
\(110\) −0.179815 0.501400i −0.0171447 0.0478066i
\(111\) 0.931761 + 0.532284i 0.0884388 + 0.0505222i
\(112\) 0.951057 + 0.309017i 0.0898664 + 0.0291994i
\(113\) −6.11535 8.41706i −0.575284 0.791810i 0.417885 0.908500i \(-0.362772\pi\)
−0.993168 + 0.116690i \(0.962772\pi\)
\(114\) 9.29096 4.18763i 0.870178 0.392207i
\(115\) 0.146092 + 0.449624i 0.0136231 + 0.0419276i
\(116\) 1.95604 + 6.02007i 0.181614 + 0.558950i
\(117\) −19.9825 1.91559i −1.84739 0.177096i
\(118\) −8.48442 11.6778i −0.781054 1.07503i
\(119\) −2.59105 0.841882i −0.237521 0.0771752i
\(120\) 0.137985 0.241542i 0.0125962 0.0220497i
\(121\) 8.49296 6.99068i 0.772088 0.635516i
\(122\) 8.07664i 0.731225i
\(123\) −7.04777 + 6.40446i −0.635476 + 0.577471i
\(124\) −6.82118 + 4.95588i −0.612560 + 0.445051i
\(125\) −0.941580 + 1.29597i −0.0842175 + 0.115915i
\(126\) −2.24771 1.98691i −0.200242 0.177008i
\(127\) 12.9700 4.21421i 1.15090 0.373951i 0.329419 0.944184i \(-0.393147\pi\)
0.821483 + 0.570233i \(0.193147\pi\)
\(128\) −0.809017 0.587785i −0.0715077 0.0519534i
\(129\) −0.455402 4.15016i −0.0400959 0.365401i
\(130\) −0.332092 + 1.02207i −0.0291264 + 0.0896418i
\(131\) 7.47224 0.652852 0.326426 0.945223i \(-0.394156\pi\)
0.326426 + 0.945223i \(0.394156\pi\)
\(132\) 5.65714 + 0.998399i 0.492391 + 0.0868995i
\(133\) −5.88382 −0.510192
\(134\) 2.90076 8.92763i 0.250588 0.771230i
\(135\) −0.668355 + 0.499743i −0.0575228 + 0.0430111i
\(136\) 2.20408 + 1.60136i 0.188998 + 0.137315i
\(137\) 4.15192 1.34904i 0.354722 0.115256i −0.126235 0.992000i \(-0.540289\pi\)
0.480957 + 0.876744i \(0.340289\pi\)
\(138\) −4.99189 1.03722i −0.424938 0.0882937i
\(139\) −12.1741 + 16.7562i −1.03260 + 1.42125i −0.129615 + 0.991564i \(0.541374\pi\)
−0.902981 + 0.429681i \(0.858626\pi\)
\(140\) −0.129933 + 0.0944015i −0.0109813 + 0.00797839i
\(141\) −3.10569 3.41765i −0.261546 0.287818i
\(142\) 10.5456i 0.884967i
\(143\) −22.1827 + 0.669659i −1.85501 + 0.0559997i
\(144\) 1.52371 + 2.58424i 0.126975 + 0.215354i
\(145\) −0.966856 0.314151i −0.0802930 0.0260888i
\(146\) −0.0597686 0.0822645i −0.00494649 0.00680826i
\(147\) 0.711719 + 1.57907i 0.0587016 + 0.130239i
\(148\) 0.191450 + 0.589221i 0.0157371 + 0.0484337i
\(149\) −0.923115 2.84105i −0.0756245 0.232748i 0.906097 0.423069i \(-0.139047\pi\)
−0.981722 + 0.190321i \(0.939047\pi\)
\(150\) −3.54024 7.85461i −0.289059 0.641326i
\(151\) 0.0890010 + 0.122499i 0.00724280 + 0.00996886i 0.812623 0.582790i \(-0.198039\pi\)
−0.805380 + 0.592759i \(0.798039\pi\)
\(152\) 5.59585 + 1.81820i 0.453883 + 0.147476i
\(153\) −4.15117 7.04049i −0.335602 0.569190i
\(154\) −2.74081 1.86761i −0.220861 0.150496i
\(155\) 1.35414i 0.108767i
\(156\) −7.79441 8.57734i −0.624052 0.686737i
\(157\) 1.43904 1.04552i 0.114848 0.0834417i −0.528879 0.848697i \(-0.677387\pi\)
0.643727 + 0.765256i \(0.277387\pi\)
\(158\) −5.39112 + 7.42024i −0.428894 + 0.590322i
\(159\) 4.40012 + 0.914257i 0.348952 + 0.0725053i
\(160\) 0.152745 0.0496298i 0.0120755 0.00392358i
\(161\) 2.38144 + 1.73022i 0.187684 + 0.136360i
\(162\) −1.10436 8.93199i −0.0867669 0.701763i
\(163\) 5.31247 16.3501i 0.416105 1.28064i −0.495154 0.868805i \(-0.664889\pi\)
0.911259 0.411833i \(-0.135111\pi\)
\(164\) −5.49813 −0.429331
\(165\) −0.663767 + 0.640796i −0.0516742 + 0.0498859i
\(166\) 14.2113 1.10301
\(167\) −6.43253 + 19.7973i −0.497764 + 1.53196i 0.314841 + 0.949145i \(0.398049\pi\)
−0.812605 + 0.582815i \(0.801951\pi\)
\(168\) −0.188926 1.72172i −0.0145760 0.132833i
\(169\) 25.7062 + 18.6766i 1.97740 + 1.43666i
\(170\) −0.416136 + 0.135211i −0.0319162 + 0.0103702i
\(171\) −13.2251 11.6906i −1.01135 0.894005i
\(172\) 1.41684 1.95012i 0.108033 0.148695i
\(173\) 14.9931 10.8931i 1.13990 0.828188i 0.152797 0.988258i \(-0.451172\pi\)
0.987106 + 0.160069i \(0.0511718\pi\)
\(174\) 8.11395 7.37332i 0.615117 0.558970i
\(175\) 4.97421i 0.376015i
\(176\) 2.02954 + 2.62316i 0.152982 + 0.197728i
\(177\) −12.4015 + 21.7088i −0.932155 + 1.63173i
\(178\) 14.3610 + 4.66616i 1.07640 + 0.349743i
\(179\) −10.7526 14.7997i −0.803686 1.10618i −0.992267 0.124121i \(-0.960389\pi\)
0.188581 0.982058i \(-0.439611\pi\)
\(180\) −0.479618 0.0459777i −0.0357486 0.00342697i
\(181\) 0.221317 + 0.681143i 0.0164503 + 0.0506289i 0.958945 0.283593i \(-0.0915265\pi\)
−0.942494 + 0.334222i \(0.891526\pi\)
\(182\) 2.06775 + 6.36388i 0.153272 + 0.471722i
\(183\) 12.7536 5.74830i 0.942770 0.424926i
\(184\) −1.73022 2.38144i −0.127553 0.175562i
\(185\) −0.0946322 0.0307479i −0.00695750 0.00226063i
\(186\) 12.6804 + 7.24391i 0.929774 + 0.531150i
\(187\) −5.52926 7.14651i −0.404339 0.522604i
\(188\) 2.66619i 0.194452i
\(189\) −1.53773 + 4.96340i −0.111854 + 0.361034i
\(190\) −0.764500 + 0.555442i −0.0554627 + 0.0402960i
\(191\) −15.3041 + 21.0643i −1.10737 + 1.52416i −0.282126 + 0.959377i \(0.591040\pi\)
−0.825240 + 0.564782i \(0.808960\pi\)
\(192\) −0.352360 + 1.69583i −0.0254294 + 0.122386i
\(193\) −2.38681 + 0.775523i −0.171807 + 0.0558234i −0.393657 0.919257i \(-0.628790\pi\)
0.221851 + 0.975081i \(0.428790\pi\)
\(194\) 8.38572 + 6.09258i 0.602060 + 0.437422i
\(195\) 1.85028 0.203034i 0.132501 0.0145395i
\(196\) −0.309017 + 0.951057i −0.0220726 + 0.0679326i
\(197\) −7.14552 −0.509097 −0.254549 0.967060i \(-0.581927\pi\)
−0.254549 + 0.967060i \(0.581927\pi\)
\(198\) −2.44975 9.64358i −0.174096 0.685340i
\(199\) 12.9631 0.918927 0.459464 0.888197i \(-0.348042\pi\)
0.459464 + 0.888197i \(0.348042\pi\)
\(200\) 1.53711 4.73075i 0.108690 0.334515i
\(201\) −16.1619 + 1.77346i −1.13997 + 0.125090i
\(202\) −9.57177 6.95430i −0.673467 0.489303i
\(203\) −6.02007 + 1.95604i −0.422526 + 0.137287i
\(204\) 0.959966 4.62010i 0.0672110 0.323472i
\(205\) 0.519031 0.714386i 0.0362507 0.0498948i
\(206\) 0.881475 0.640429i 0.0614153 0.0446208i
\(207\) 1.91499 + 8.62074i 0.133101 + 0.599183i
\(208\) 6.69138i 0.463964i
\(209\) −16.1264 10.9887i −1.11549 0.760104i
\(210\) 0.241542 + 0.137985i 0.0166680 + 0.00952187i
\(211\) −21.9899 7.14496i −1.51385 0.491879i −0.569828 0.821764i \(-0.692990\pi\)
−0.944021 + 0.329885i \(0.892990\pi\)
\(212\) 1.52511 + 2.09913i 0.104745 + 0.144169i
\(213\) −16.6522 + 7.50551i −1.14099 + 0.514269i
\(214\) −2.57918 7.93789i −0.176309 0.542623i
\(215\) 0.119632 + 0.368188i 0.00815881 + 0.0251102i
\(216\) 2.99625 4.24529i 0.203869 0.288855i
\(217\) −4.95588 6.82118i −0.336427 0.463052i
\(218\) 0.727992 + 0.236539i 0.0493058 + 0.0160204i
\(219\) −0.0873627 + 0.152928i −0.00590342 + 0.0103339i
\(220\) −0.532426 + 0.0160731i −0.0358961 + 0.00108364i
\(221\) 18.2299i 1.22628i
\(222\) 0.794162 0.721672i 0.0533007 0.0484355i
\(223\) 6.15373 4.47095i 0.412084 0.299397i −0.362361 0.932038i \(-0.618029\pi\)
0.774445 + 0.632641i \(0.218029\pi\)
\(224\) 0.587785 0.809017i 0.0392731 0.0540547i
\(225\) −9.88331 + 11.1806i −0.658887 + 0.745370i
\(226\) −9.89485 + 3.21503i −0.658195 + 0.213861i
\(227\) 19.2651 + 13.9969i 1.27867 + 0.929009i 0.999512 0.0312354i \(-0.00994417\pi\)
0.279160 + 0.960245i \(0.409944\pi\)
\(228\) −1.11161 10.1303i −0.0736181 0.670894i
\(229\) −4.25896 + 13.1077i −0.281440 + 0.866184i 0.706003 + 0.708209i \(0.250496\pi\)
−0.987443 + 0.157975i \(0.949504\pi\)
\(230\) 0.472762 0.0311730
\(231\) −0.998399 + 5.65714i −0.0656898 + 0.372212i
\(232\) 6.32988 0.415577
\(233\) −0.322037 + 0.991129i −0.0210974 + 0.0649310i −0.961051 0.276371i \(-0.910868\pi\)
0.939954 + 0.341302i \(0.110868\pi\)
\(234\) −7.99678 + 18.4126i −0.522766 + 1.20367i
\(235\) 0.346424 + 0.251692i 0.0225982 + 0.0164186i
\(236\) −13.7281 + 4.46052i −0.893621 + 0.290355i
\(237\) 15.5540 + 3.23182i 1.01034 + 0.209929i
\(238\) −1.60136 + 2.20408i −0.103800 + 0.142869i
\(239\) 17.2577 12.5384i 1.11630 0.811043i 0.132660 0.991162i \(-0.457648\pi\)
0.983645 + 0.180119i \(0.0576481\pi\)
\(240\) −0.187080 0.205872i −0.0120760 0.0132890i
\(241\) 12.2281i 0.787678i −0.919179 0.393839i \(-0.871147\pi\)
0.919179 0.393839i \(-0.128853\pi\)
\(242\) −4.02406 10.2375i −0.258676 0.658093i
\(243\) −13.3182 + 8.10093i −0.854364 + 0.519675i
\(244\) 7.68134 + 2.49582i 0.491747 + 0.159778i
\(245\) −0.0944015 0.129933i −0.00603109 0.00830109i
\(246\) 3.91312 + 8.68191i 0.249491 + 0.553539i
\(247\) 12.1663 + 37.4439i 0.774121 + 2.38250i
\(248\) 2.60546 + 8.01878i 0.165447 + 0.509193i
\(249\) −10.1145 22.4406i −0.640977 1.42212i
\(250\) 0.941580 + 1.29597i 0.0595508 + 0.0819646i
\(251\) 0.705970 + 0.229384i 0.0445604 + 0.0144786i 0.331212 0.943556i \(-0.392542\pi\)
−0.286652 + 0.958035i \(0.592542\pi\)
\(252\) −2.58424 + 1.52371i −0.162792 + 0.0959844i
\(253\) 3.29570 + 9.18981i 0.207199 + 0.577758i
\(254\) 13.6375i 0.855691i
\(255\) 0.509679 + 0.560875i 0.0319174 + 0.0351234i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 1.74642 2.40375i 0.108939 0.149942i −0.751066 0.660227i \(-0.770460\pi\)
0.860005 + 0.510285i \(0.170460\pi\)
\(258\) −4.08776 0.849356i −0.254493 0.0528786i
\(259\) −0.589221 + 0.191450i −0.0366124 + 0.0118961i
\(260\) 0.869428 + 0.631676i 0.0539196 + 0.0391749i
\(261\) −17.4178 7.56475i −1.07814 0.468246i
\(262\) 2.30905 7.10652i 0.142653 0.439042i
\(263\) −2.16498 −0.133499 −0.0667493 0.997770i \(-0.521263\pi\)
−0.0667493 + 0.997770i \(0.521263\pi\)
\(264\) 2.69769 5.07173i 0.166031 0.312144i
\(265\) −0.416718 −0.0255988
\(266\) −1.81820 + 5.59585i −0.111481 + 0.343103i
\(267\) −2.85279 25.9979i −0.174588 1.59105i
\(268\) −7.59430 5.51758i −0.463896 0.337040i
\(269\) −1.35856 + 0.441423i −0.0828328 + 0.0269140i −0.350140 0.936697i \(-0.613866\pi\)
0.267307 + 0.963611i \(0.413866\pi\)
\(270\) 0.268751 + 0.790072i 0.0163557 + 0.0480823i
\(271\) 8.04765 11.0766i 0.488860 0.672858i −0.491317 0.870981i \(-0.663484\pi\)
0.980177 + 0.198123i \(0.0634844\pi\)
\(272\) 2.20408 1.60136i 0.133642 0.0970964i
\(273\) 8.57734 7.79441i 0.519124 0.471739i
\(274\) 4.36559i 0.263735i
\(275\) −9.28988 + 13.6333i −0.560201 + 0.822122i
\(276\) −2.52903 + 4.42705i −0.152230 + 0.266477i
\(277\) −8.82592 2.86771i −0.530298 0.172304i 0.0316157 0.999500i \(-0.489935\pi\)
−0.561914 + 0.827196i \(0.689935\pi\)
\(278\) 12.1741 + 16.7562i 0.730155 + 1.00497i
\(279\) 2.41373 25.1789i 0.144506 1.50742i
\(280\) 0.0496298 + 0.152745i 0.00296595 + 0.00912825i
\(281\) 4.04096 + 12.4368i 0.241064 + 0.741918i 0.996259 + 0.0864177i \(0.0275420\pi\)
−0.755195 + 0.655500i \(0.772458\pi\)
\(282\) −4.21009 + 1.89758i −0.250707 + 0.112999i
\(283\) −8.51009 11.7131i −0.505873 0.696274i 0.477344 0.878717i \(-0.341600\pi\)
−0.983216 + 0.182443i \(0.941600\pi\)
\(284\) −10.0295 3.25877i −0.595139 0.193372i
\(285\) 1.42119 + 0.811879i 0.0841840 + 0.0480916i
\(286\) −6.21794 + 21.3039i −0.367675 + 1.25973i
\(287\) 5.49813i 0.324544i
\(288\) 2.92861 0.650555i 0.172570 0.0383343i
\(289\) 7.74853 5.62964i 0.455796 0.331155i
\(290\) −0.597550 + 0.822457i −0.0350893 + 0.0482963i
\(291\) 3.65233 17.5778i 0.214103 1.03043i
\(292\) −0.0967077 + 0.0314222i −0.00565939 + 0.00183885i
\(293\) 6.56633 + 4.77072i 0.383609 + 0.278708i 0.762832 0.646597i \(-0.223809\pi\)
−0.379223 + 0.925305i \(0.623809\pi\)
\(294\) 1.72172 0.188926i 0.100413 0.0110184i
\(295\) 0.716384 2.20480i 0.0417095 0.128369i
\(296\) 0.619544 0.0360103
\(297\) −13.4843 + 10.7318i −0.782441 + 0.622725i
\(298\) −2.98726 −0.173047
\(299\) 6.08668 18.7329i 0.352002 1.08335i
\(300\) −8.56417 + 0.939758i −0.494453 + 0.0542569i
\(301\) 1.95012 + 1.41684i 0.112403 + 0.0816655i
\(302\) 0.144007 0.0467906i 0.00828665 0.00269250i
\(303\) −4.16890 + 20.0640i −0.239497 + 1.15265i
\(304\) 3.45842 4.76011i 0.198354 0.273011i
\(305\) −1.04942 + 0.762447i −0.0600895 + 0.0436576i
\(306\) −7.97868 + 1.77236i −0.456111 + 0.101319i
\(307\) 20.9851i 1.19769i −0.800867 0.598843i \(-0.795627\pi\)
0.800867 0.598843i \(-0.204373\pi\)
\(308\) −2.62316 + 2.02954i −0.149468 + 0.115644i
\(309\) −1.63864 0.936103i −0.0932192 0.0532531i
\(310\) −1.28786 0.418451i −0.0731455 0.0237664i
\(311\) −4.45601 6.13317i −0.252677 0.347780i 0.663770 0.747937i \(-0.268956\pi\)
−0.916447 + 0.400157i \(0.868956\pi\)
\(312\) −10.5661 + 4.76238i −0.598190 + 0.269617i
\(313\) −0.203328 0.625778i −0.0114928 0.0353710i 0.945146 0.326649i \(-0.105920\pi\)
−0.956638 + 0.291278i \(0.905920\pi\)
\(314\) −0.549663 1.69169i −0.0310193 0.0954676i
\(315\) 0.0459777 0.479618i 0.00259055 0.0270234i
\(316\) 5.39112 + 7.42024i 0.303274 + 0.417421i
\(317\) −16.2965 5.29505i −0.915302 0.297400i −0.186764 0.982405i \(-0.559800\pi\)
−0.728538 + 0.685005i \(0.759800\pi\)
\(318\) 2.22922 3.90224i 0.125008 0.218827i
\(319\) −20.1530 5.88202i −1.12835 0.329330i
\(320\) 0.160605i 0.00897812i
\(321\) −10.6988 + 9.72224i −0.597150 + 0.542643i
\(322\) 2.38144 1.73022i 0.132713 0.0964214i
\(323\) −9.42209 + 12.9684i −0.524259 + 0.721581i
\(324\) −8.83609 1.70982i −0.490894 0.0949903i
\(325\) 31.6552 10.2854i 1.75592 0.570532i
\(326\) −13.9082 10.1049i −0.770305 0.559660i
\(327\) −0.144615 1.31790i −0.00799721 0.0728799i
\(328\) −1.69901 + 5.22903i −0.0938124 + 0.288725i
\(329\) 2.66619 0.146992
\(330\) 0.404318 + 0.829297i 0.0222570 + 0.0456513i
\(331\) 11.6127 0.638293 0.319147 0.947705i \(-0.396604\pi\)
0.319147 + 0.947705i \(0.396604\pi\)
\(332\) 4.39153 13.5157i 0.241017 0.741773i
\(333\) −1.70479 0.740409i −0.0934219 0.0405741i
\(334\) 16.8406 + 12.2354i 0.921475 + 0.669491i
\(335\) 1.43383 0.465879i 0.0783383 0.0254537i
\(336\) −1.69583 0.352360i −0.0925152 0.0192228i
\(337\) 10.2525 14.1114i 0.558492 0.768698i −0.432642 0.901566i \(-0.642419\pi\)
0.991134 + 0.132868i \(0.0424186\pi\)
\(338\) 25.7062 18.6766i 1.39823 1.01587i
\(339\) 12.1191 + 13.3364i 0.658219 + 0.724336i
\(340\) 0.437552i 0.0237296i
\(341\) −0.843801 27.9512i −0.0456944 1.51364i
\(342\) −15.2052 + 8.96521i −0.822205 + 0.484783i
\(343\) −0.951057 0.309017i −0.0513522 0.0166853i
\(344\) −1.41684 1.95012i −0.0763911 0.105143i
\(345\) −0.336474 0.746524i −0.0181152 0.0401915i
\(346\) −5.72685 17.6254i −0.307877 0.947549i
\(347\) −3.71644 11.4380i −0.199509 0.614025i −0.999894 0.0145394i \(-0.995372\pi\)
0.800385 0.599486i \(-0.204628\pi\)
\(348\) −4.50509 9.99531i −0.241498 0.535805i
\(349\) 5.97931 + 8.22981i 0.320065 + 0.440532i 0.938487 0.345315i \(-0.112228\pi\)
−0.618422 + 0.785846i \(0.712228\pi\)
\(350\) 4.73075 + 1.53711i 0.252869 + 0.0821622i
\(351\) 34.7662 0.477122i 1.85568 0.0254669i
\(352\) 3.12194 1.11961i 0.166400 0.0596752i
\(353\) 9.39359i 0.499970i −0.968250 0.249985i \(-0.919574\pi\)
0.968250 0.249985i \(-0.0804257\pi\)
\(354\) 16.8140 + 18.5029i 0.893654 + 0.983419i
\(355\) 1.37022 0.995521i 0.0727236 0.0528368i
\(356\) 8.87556 12.2162i 0.470404 0.647455i
\(357\) 4.62010 + 0.959966i 0.244522 + 0.0508068i
\(358\) −17.3980 + 5.65297i −0.919515 + 0.298769i
\(359\) −17.8080 12.9382i −0.939869 0.682855i 0.00852040 0.999964i \(-0.497288\pi\)
−0.948389 + 0.317109i \(0.897288\pi\)
\(360\) −0.191937 + 0.441936i −0.0101160 + 0.0232921i
\(361\) −4.82665 + 14.8549i −0.254034 + 0.781837i
\(362\) 0.716196 0.0376424
\(363\) −13.3017 + 13.6405i −0.698161 + 0.715941i
\(364\) 6.69138 0.350724
\(365\) 0.00504658 0.0155318i 0.000264150 0.000812971i
\(366\) −1.52589 13.9057i −0.0797595 0.726862i
\(367\) 13.6048 + 9.88448i 0.710166 + 0.515966i 0.883227 0.468945i \(-0.155366\pi\)
−0.173061 + 0.984911i \(0.555366\pi\)
\(368\) −2.79955 + 0.909630i −0.145937 + 0.0474178i
\(369\) 10.9243 12.3582i 0.568696 0.643341i
\(370\) −0.0584859 + 0.0804989i −0.00304054 + 0.00418494i
\(371\) −2.09913 + 1.52511i −0.108981 + 0.0791796i
\(372\) 10.8078 9.82131i 0.560360 0.509211i
\(373\) 11.6100i 0.601145i −0.953759 0.300572i \(-0.902822\pi\)
0.953759 0.300572i \(-0.0971777\pi\)
\(374\) −8.50536 + 3.05024i −0.439802 + 0.157724i
\(375\) 1.37629 2.40919i 0.0710713 0.124410i
\(376\) −2.53569 0.823897i −0.130768 0.0424892i
\(377\) 24.8960 + 34.2664i 1.28221 + 1.76481i
\(378\) 4.24529 + 2.99625i 0.218354 + 0.154110i
\(379\) 5.02873 + 15.4768i 0.258308 + 0.794992i 0.993160 + 0.116763i \(0.0372519\pi\)
−0.734851 + 0.678228i \(0.762748\pi\)
\(380\) 0.292013 + 0.898724i 0.0149800 + 0.0461036i
\(381\) −21.5345 + 9.70605i −1.10325 + 0.497256i
\(382\) 15.3041 + 21.0643i 0.783026 + 1.07774i
\(383\) −14.2826 4.64070i −0.729807 0.237129i −0.0795372 0.996832i \(-0.525344\pi\)
−0.650270 + 0.759703i \(0.725344\pi\)
\(384\) 1.50395 + 0.859155i 0.0767479 + 0.0438436i
\(385\) −0.0160731 0.532426i −0.000819159 0.0271349i
\(386\) 2.50964i 0.127738i
\(387\) 1.56815 + 7.05936i 0.0797134 + 0.358847i
\(388\) 8.38572 6.09258i 0.425720 0.309304i
\(389\) 1.76075 2.42346i 0.0892736 0.122875i −0.762044 0.647525i \(-0.775804\pi\)
0.851318 + 0.524651i \(0.175804\pi\)
\(390\) 0.378672 1.82246i 0.0191748 0.0922840i
\(391\) 7.62707 2.47819i 0.385718 0.125327i
\(392\) 0.809017 + 0.587785i 0.0408615 + 0.0296876i
\(393\) −12.8651 + 1.41170i −0.648957 + 0.0712109i
\(394\) −2.20809 + 6.79580i −0.111242 + 0.342367i
\(395\) −1.47306 −0.0741177
\(396\) −9.92861 0.650178i −0.498931 0.0326727i
\(397\) 8.11214 0.407137 0.203568 0.979061i \(-0.434746\pi\)
0.203568 + 0.979061i \(0.434746\pi\)
\(398\) 4.00581 12.3286i 0.200793 0.617977i
\(399\) 10.1303 1.11161i 0.507148 0.0556500i
\(400\) −4.02422 2.92376i −0.201211 0.146188i
\(401\) 30.8478 10.0231i 1.54047 0.500528i 0.588962 0.808161i \(-0.299537\pi\)
0.951505 + 0.307633i \(0.0995368\pi\)
\(402\) −3.30763 + 15.9189i −0.164970 + 0.793962i
\(403\) −33.1617 + 45.6431i −1.65190 + 2.27364i
\(404\) −9.57177 + 6.95430i −0.476213 + 0.345989i
\(405\) 1.05630 0.986686i 0.0524881 0.0490288i
\(406\) 6.32988i 0.314147i
\(407\) −1.97250 0.575709i −0.0977730 0.0285369i
\(408\) −4.09733 2.34067i −0.202848 0.115881i
\(409\) 24.0621 + 7.81825i 1.18979 + 0.386587i 0.835997 0.548735i \(-0.184890\pi\)
0.353797 + 0.935322i \(0.384890\pi\)
\(410\) −0.519031 0.714386i −0.0256331 0.0352810i
\(411\) −6.89356 + 3.10707i −0.340034 + 0.153261i
\(412\) −0.336693 1.03624i −0.0165877 0.0510517i
\(413\) −4.46052 13.7281i −0.219488 0.675514i
\(414\) 8.79058 + 0.842693i 0.432033 + 0.0414161i
\(415\) 1.34157 + 1.84651i 0.0658550 + 0.0906416i
\(416\) −6.36388 2.06775i −0.312015 0.101380i
\(417\) 17.7947 31.1495i 0.871410 1.52540i
\(418\) −15.4342 + 11.9415i −0.754912 + 0.584076i
\(419\) 3.94839i 0.192892i 0.995338 + 0.0964458i \(0.0307475\pi\)
−0.995338 + 0.0964458i \(0.969253\pi\)
\(420\) 0.205872 0.187080i 0.0100455 0.00912858i
\(421\) −21.4274 + 15.5679i −1.04431 + 0.758733i −0.971121 0.238586i \(-0.923316\pi\)
−0.0731846 + 0.997318i \(0.523316\pi\)
\(422\) −13.5905 + 18.7057i −0.661576 + 0.910582i
\(423\) 5.99280 + 5.29748i 0.291380 + 0.257572i
\(424\) 2.46767 0.801796i 0.119841 0.0389387i
\(425\) 10.9635 + 7.96547i 0.531809 + 0.386382i
\(426\) 1.99234 + 18.1565i 0.0965292 + 0.879687i
\(427\) −2.49582 + 7.68134i −0.120781 + 0.371726i
\(428\) −8.34639 −0.403438
\(429\) 38.0658 5.34385i 1.83783 0.258004i
\(430\) 0.387136 0.0186694
\(431\) 11.3955 35.0716i 0.548900 1.68934i −0.162631 0.986687i \(-0.551998\pi\)
0.711531 0.702655i \(-0.248002\pi\)
\(432\) −3.11162 4.16147i −0.149708 0.200219i
\(433\) −17.7907 12.9257i −0.854966 0.621169i 0.0715448 0.997437i \(-0.477207\pi\)
−0.926511 + 0.376268i \(0.877207\pi\)
\(434\) −8.01878 + 2.60546i −0.384914 + 0.125066i
\(435\) 1.72400 + 0.358214i 0.0826596 + 0.0171750i
\(436\) 0.449924 0.619267i 0.0215474 0.0296575i
\(437\) 14.0120 10.1803i 0.670284 0.486990i
\(438\) 0.118447 + 0.130344i 0.00565959 + 0.00622809i
\(439\) 0.987382i 0.0471252i −0.999722 0.0235626i \(-0.992499\pi\)
0.999722 0.0235626i \(-0.00750090\pi\)
\(440\) −0.149242 + 0.511334i −0.00711484 + 0.0243769i
\(441\) −1.52371 2.58424i −0.0725574 0.123059i
\(442\) 17.3377 + 5.63335i 0.824669 + 0.267951i
\(443\) 5.42049 + 7.46066i 0.257535 + 0.354467i 0.918132 0.396274i \(-0.129697\pi\)
−0.660597 + 0.750740i \(0.729697\pi\)
\(444\) −0.440941 0.978302i −0.0209261 0.0464282i
\(445\) 0.749411 + 2.30645i 0.0355255 + 0.109336i
\(446\) −2.35051 7.23414i −0.111300 0.342547i
\(447\) 2.12609 + 4.71709i 0.100561 + 0.223111i
\(448\) −0.587785 0.809017i −0.0277702 0.0382225i
\(449\) 28.6076 + 9.29517i 1.35008 + 0.438666i 0.892718 0.450617i \(-0.148796\pi\)
0.457358 + 0.889283i \(0.348796\pi\)
\(450\) 7.57923 + 12.8546i 0.357288 + 0.605970i
\(451\) 10.2684 15.0693i 0.483518 0.709586i
\(452\) 10.4041i 0.489366i
\(453\) −0.176378 0.194095i −0.00828695 0.00911936i
\(454\) 19.2651 13.9969i 0.904157 0.656909i
\(455\) −0.631676 + 0.869428i −0.0296134 + 0.0407594i
\(456\) −9.97797 2.07322i −0.467261 0.0970876i
\(457\) −13.0274 + 4.23287i −0.609398 + 0.198005i −0.597427 0.801923i \(-0.703810\pi\)
−0.0119705 + 0.999928i \(0.503810\pi\)
\(458\) 11.1501 + 8.10103i 0.521010 + 0.378536i
\(459\) 8.47726 + 11.3375i 0.395685 + 0.529187i
\(460\) 0.146092 0.449624i 0.00681156 0.0209638i
\(461\) 2.00605 0.0934310 0.0467155 0.998908i \(-0.485125\pi\)
0.0467155 + 0.998908i \(0.485125\pi\)
\(462\) 5.07173 + 2.69769i 0.235958 + 0.125508i
\(463\) −22.4838 −1.04491 −0.522456 0.852666i \(-0.674984\pi\)
−0.522456 + 0.852666i \(0.674984\pi\)
\(464\) 1.95604 6.02007i 0.0908069 0.279475i
\(465\) 0.255832 + 2.33144i 0.0118639 + 0.108118i
\(466\) 0.843104 + 0.612551i 0.0390561 + 0.0283759i
\(467\) −14.7956 + 4.80739i −0.684659 + 0.222459i −0.630634 0.776080i \(-0.717205\pi\)
−0.0540251 + 0.998540i \(0.517205\pi\)
\(468\) 15.0403 + 13.2952i 0.695236 + 0.614570i
\(469\) 5.51758 7.59430i 0.254778 0.350672i
\(470\) 0.346424 0.251692i 0.0159794 0.0116097i
\(471\) −2.28009 + 2.07196i −0.105061 + 0.0954711i
\(472\) 14.4345i 0.664404i
\(473\) 2.69879 + 7.52536i 0.124090 + 0.346016i
\(474\) 7.88010 13.7941i 0.361945 0.633582i
\(475\) 27.8349 + 9.04411i 1.27715 + 0.414972i
\(476\) 1.60136 + 2.20408i 0.0733980 + 0.101024i
\(477\) −7.74848 0.742794i −0.354778 0.0340102i
\(478\) −6.59184 20.2876i −0.301504 0.927933i
\(479\) 7.65871 + 23.5711i 0.349935 + 1.07699i 0.958888 + 0.283784i \(0.0915898\pi\)
−0.608953 + 0.793206i \(0.708410\pi\)
\(480\) −0.253607 + 0.114306i −0.0115755 + 0.00521733i
\(481\) 2.43673 + 3.35386i 0.111105 + 0.152923i
\(482\) −11.6296 3.77868i −0.529712 0.172114i
\(483\) −4.42705 2.52903i −0.201438 0.115075i
\(484\) −10.9800 + 0.663539i −0.499089 + 0.0301609i
\(485\) 1.66473i 0.0755914i
\(486\) 3.58888 + 15.1697i 0.162795 + 0.688112i
\(487\) 18.9050 13.7353i 0.856667 0.622405i −0.0703088 0.997525i \(-0.522398\pi\)
0.926976 + 0.375120i \(0.122398\pi\)
\(488\) 4.74733 6.53414i 0.214901 0.295787i
\(489\) −6.05760 + 29.1539i −0.273934 + 1.31838i
\(490\) −0.152745 + 0.0496298i −0.00690031 + 0.00224205i
\(491\) 11.4997 + 8.35505i 0.518976 + 0.377058i 0.816218 0.577744i \(-0.196067\pi\)
−0.297242 + 0.954802i \(0.596067\pi\)
\(492\) 9.46621 1.03874i 0.426770 0.0468300i
\(493\) −5.32901 + 16.4010i −0.240007 + 0.738664i
\(494\) 39.3709 1.77138
\(495\) 1.02176 1.22867i 0.0459245 0.0552247i
\(496\) 8.43144 0.378583
\(497\) 3.25877 10.0295i 0.146176 0.449883i
\(498\) −24.4678 + 2.68489i −1.09643 + 0.120313i
\(499\) 31.5546 + 22.9258i 1.41258 + 1.02630i 0.992941 + 0.118606i \(0.0378424\pi\)
0.419636 + 0.907692i \(0.362158\pi\)
\(500\) 1.52351 0.495018i 0.0681334 0.0221379i
\(501\) 7.33476 35.3006i 0.327693 1.57711i
\(502\) 0.436314 0.600534i 0.0194736 0.0268031i
\(503\) 11.0554 8.03224i 0.492937 0.358140i −0.313376 0.949629i \(-0.601460\pi\)
0.806313 + 0.591489i \(0.201460\pi\)
\(504\) 0.650555 + 2.92861i 0.0289780 + 0.130451i
\(505\) 1.90018i 0.0845569i
\(506\) 9.75846 0.294592i 0.433816 0.0130962i
\(507\) −47.7872 27.2993i −2.12230 1.21240i
\(508\) −12.9700 4.21421i −0.575451 0.186975i
\(509\) 0.328071 + 0.451551i 0.0145415 + 0.0200146i 0.816226 0.577733i \(-0.196062\pi\)
−0.801684 + 0.597748i \(0.796062\pi\)
\(510\) 0.690924 0.311414i 0.0305946 0.0137896i
\(511\) −0.0314222 0.0967077i −0.00139004 0.00427810i
\(512\) 0.309017 + 0.951057i 0.0136568 + 0.0420312i
\(513\) 24.9785 + 17.6294i 1.10283 + 0.778357i
\(514\) −1.74642 2.40375i −0.0770314 0.106025i
\(515\) 0.166425 + 0.0540748i 0.00733357 + 0.00238282i
\(516\) −2.07097 + 3.62523i −0.0911695 + 0.159592i
\(517\) 7.30750 + 4.97940i 0.321384 + 0.218994i
\(518\) 0.619544i 0.0272212i
\(519\) −23.7558 + 21.5874i −1.04277 + 0.947583i
\(520\) 0.869428 0.631676i 0.0381269 0.0277008i
\(521\) −10.1785 + 14.0094i −0.445926 + 0.613765i −0.971516 0.236973i \(-0.923845\pi\)
0.525590 + 0.850738i \(0.323845\pi\)
\(522\) −12.5769 + 14.2277i −0.550476 + 0.622730i
\(523\) 3.75620 1.22046i 0.164247 0.0533672i −0.225739 0.974188i \(-0.572480\pi\)
0.389986 + 0.920821i \(0.372480\pi\)
\(524\) −6.04517 4.39207i −0.264084 0.191868i
\(525\) −0.939758 8.56417i −0.0410144 0.373771i
\(526\) −0.669016 + 2.05902i −0.0291705 + 0.0897776i
\(527\) −22.9705 −1.00061
\(528\) −3.98988 4.13290i −0.173637 0.179862i
\(529\) 14.3351 0.623264
\(530\) −0.128773 + 0.396322i −0.00559353 + 0.0172151i
\(531\) 17.2505 39.7193i 0.748609 1.72367i
\(532\) 4.76011 + 3.45842i 0.206377 + 0.149942i
\(533\) −34.9894 + 11.3687i −1.51556 + 0.492435i
\(534\) −25.6071 5.32064i −1.10813 0.230247i
\(535\) 0.787912 1.08447i 0.0340644 0.0468856i
\(536\) −7.59430 + 5.51758i −0.328024 + 0.238323i
\(537\) 21.3089 + 23.4494i 0.919549 + 1.01192i
\(538\) 1.42847i 0.0615859i
\(539\) −2.02954 2.62316i −0.0874185 0.112987i
\(540\) 0.834452 0.0114518i 0.0359091 0.000492808i
\(541\) −2.19061 0.711774i −0.0941819 0.0306015i 0.261547 0.965191i \(-0.415767\pi\)
−0.355729 + 0.934589i \(0.615767\pi\)
\(542\) −8.04765 11.0766i −0.345676 0.475783i
\(543\) −0.509730 1.13092i −0.0218746 0.0485325i
\(544\) −0.841882 2.59105i −0.0360954 0.111090i
\(545\) 0.0379894 + 0.116919i 0.00162729 + 0.00500828i
\(546\) −4.76238 10.5661i −0.203811 0.452189i
\(547\) −10.3976 14.3110i −0.444568 0.611895i 0.526652 0.850081i \(-0.323447\pi\)
−0.971219 + 0.238186i \(0.923447\pi\)
\(548\) −4.15192 1.34904i −0.177361 0.0576281i
\(549\) −20.8720 + 12.3064i −0.890796 + 0.525225i
\(550\) 10.0954 + 13.0481i 0.430467 + 0.556374i
\(551\) 37.2439i 1.58664i
\(552\) 3.42886 + 3.77329i 0.145942 + 0.160602i
\(553\) −7.42024 + 5.39112i −0.315541 + 0.229254i
\(554\) −5.45472 + 7.50777i −0.231749 + 0.318975i
\(555\) 0.168739 + 0.0350606i 0.00716257 + 0.00148824i
\(556\) 19.6981 6.40031i 0.835387 0.271434i
\(557\) −19.5079 14.1733i −0.826575 0.600542i 0.0920130 0.995758i \(-0.470670\pi\)
−0.918588 + 0.395216i \(0.870670\pi\)
\(558\) −23.2007 10.0763i −0.982163 0.426564i
\(559\) 4.98427 15.3400i 0.210812 0.648813i
\(560\) 0.160605 0.00678682
\(561\) 10.8700 + 11.2596i 0.458931 + 0.475382i
\(562\) 13.0768 0.551613
\(563\) −3.90298 + 12.0121i −0.164491 + 0.506251i −0.998998 0.0447455i \(-0.985752\pi\)
0.834507 + 0.550997i \(0.185752\pi\)
\(564\) 0.503712 + 4.59042i 0.0212101 + 0.193291i
\(565\) −1.35183 0.982159i −0.0568717 0.0413197i
\(566\) −13.7696 + 4.47402i −0.578780 + 0.188057i
\(567\) 1.70982 8.83609i 0.0718059 0.371081i
\(568\) −6.19855 + 8.53157i −0.260085 + 0.357977i
\(569\) 5.85782 4.25595i 0.245572 0.178419i −0.458190 0.888854i \(-0.651502\pi\)
0.703762 + 0.710436i \(0.251502\pi\)
\(570\) 1.21131 1.10075i 0.0507364 0.0461052i
\(571\) 23.6249i 0.988672i −0.869271 0.494336i \(-0.835411\pi\)
0.869271 0.494336i \(-0.164589\pi\)
\(572\) 18.3398 + 12.4969i 0.766825 + 0.522521i
\(573\) 22.3697 39.1581i 0.934509 1.63585i
\(574\) −5.22903 1.69901i −0.218255 0.0709155i
\(575\) −8.60647 11.8458i −0.358915 0.494004i
\(576\) 0.286277 2.98631i 0.0119282 0.124430i
\(577\) −7.52191 23.1501i −0.313141 0.963749i −0.976513 0.215459i \(-0.930875\pi\)
0.663372 0.748290i \(-0.269125\pi\)
\(578\) −2.95967 9.10894i −0.123106 0.378882i
\(579\) 3.96290 1.78616i 0.164692 0.0742304i
\(580\) 0.597550 + 0.822457i 0.0248119 + 0.0341507i
\(581\) 13.5157 + 4.39153i 0.560728 + 0.182191i
\(582\) −15.5889 8.90542i −0.646180 0.369141i
\(583\) −8.60162 + 0.259669i −0.356243 + 0.0107544i
\(584\) 0.101684i 0.00420773i
\(585\) −3.14730 + 0.699133i −0.130125 + 0.0289056i
\(586\) 6.56633 4.77072i 0.271253 0.197077i
\(587\) −10.3759 + 14.2812i −0.428259 + 0.589447i −0.967552 0.252670i \(-0.918691\pi\)
0.539294 + 0.842118i \(0.318691\pi\)
\(588\) 0.352360 1.69583i 0.0145311 0.0699349i
\(589\) −47.1811 + 15.3301i −1.94406 + 0.631664i
\(590\) −1.87552 1.36264i −0.0772138 0.0560991i
\(591\) 12.3026 1.34998i 0.506060 0.0555306i
\(592\) 0.191450 0.589221i 0.00786853 0.0242169i
\(593\) −22.6256 −0.929122 −0.464561 0.885541i \(-0.653788\pi\)
−0.464561 + 0.885541i \(0.653788\pi\)
\(594\) 6.03970 + 16.1407i 0.247812 + 0.662261i
\(595\) −0.437552 −0.0179379
\(596\) −0.923115 + 2.84105i −0.0378123 + 0.116374i
\(597\) −22.3187 + 2.44906i −0.913445 + 0.100233i
\(598\) −15.9351 11.5776i −0.651636 0.473442i
\(599\) 26.5826 8.63722i 1.08614 0.352907i 0.289384 0.957213i \(-0.406549\pi\)
0.796753 + 0.604306i \(0.206549\pi\)
\(600\) −1.75271 + 8.43541i −0.0715542 + 0.344374i
\(601\) −14.4751 + 19.9233i −0.590453 + 0.812688i −0.994793 0.101921i \(-0.967501\pi\)
0.404340 + 0.914609i \(0.367501\pi\)
\(602\) 1.95012 1.41684i 0.0794809 0.0577462i
\(603\) 27.4911 6.10680i 1.11952 0.248688i
\(604\) 0.151418i 0.00616109i
\(605\) 0.950310 1.48929i 0.0386356 0.0605484i
\(606\) 17.7937 + 10.1650i 0.722820 + 0.412924i
\(607\) 9.71031 + 3.15507i 0.394129 + 0.128060i 0.499375 0.866386i \(-0.333563\pi\)
−0.105246 + 0.994446i \(0.533563\pi\)
\(608\) −3.45842 4.76011i −0.140258 0.193048i
\(609\) 9.99531 4.50509i 0.405030 0.182556i
\(610\) 0.400842 + 1.23367i 0.0162296 + 0.0499496i
\(611\) −5.51301 16.9673i −0.223032 0.686423i
\(612\) −0.779930 + 8.13587i −0.0315268 + 0.328873i
\(613\) −19.0272 26.1887i −0.768501 1.05775i −0.996459 0.0840800i \(-0.973205\pi\)
0.227958 0.973671i \(-0.426795\pi\)
\(614\) −19.9581 6.48477i −0.805442 0.261704i
\(615\) −0.758659 + 1.32803i −0.0305921 + 0.0535513i
\(616\) 1.11961 + 3.12194i 0.0451102 + 0.125786i
\(617\) 1.78277i 0.0717717i 0.999356 + 0.0358859i \(0.0114253\pi\)
−0.999356 + 0.0358859i \(0.988575\pi\)
\(618\) −1.39666 + 1.26917i −0.0561817 + 0.0510535i
\(619\) −8.02668 + 5.83173i −0.322620 + 0.234397i −0.737292 0.675574i \(-0.763896\pi\)
0.414673 + 0.909971i \(0.363896\pi\)
\(620\) −0.795941 + 1.09552i −0.0319658 + 0.0439971i
\(621\) −4.92575 14.4807i −0.197664 0.581090i
\(622\) −7.20997 + 2.34266i −0.289094 + 0.0939322i
\(623\) 12.2162 + 8.87556i 0.489430 + 0.355592i
\(624\) 1.26418 + 11.5207i 0.0506076 + 0.461195i
\(625\) 7.60607 23.4091i 0.304243 0.936363i
\(626\) −0.657982 −0.0262982
\(627\) 29.8412 + 15.8727i 1.19174 + 0.633895i
\(628\) −1.77875 −0.0709798
\(629\) −0.521583 + 1.60527i −0.0207969 + 0.0640062i
\(630\) −0.441936 0.191937i −0.0176071 0.00764697i
\(631\) −37.9689 27.5860i −1.51152 1.09818i −0.965498 0.260411i \(-0.916142\pi\)
−0.546021 0.837771i \(-0.683858\pi\)
\(632\) 8.72301 2.83428i 0.346983 0.112742i
\(633\) 39.2103 + 8.14712i 1.55847 + 0.323819i
\(634\) −10.0718 + 13.8626i −0.400002 + 0.550555i
\(635\) 1.77195 1.28740i 0.0703177 0.0510888i
\(636\) −3.02238 3.32597i −0.119845 0.131883i
\(637\) 6.69138i 0.265122i
\(638\) −11.8217 + 17.3490i −0.468027 + 0.686853i
\(639\) 27.2524 16.0684i 1.07809 0.635656i
\(640\) −0.152745 0.0496298i −0.00603777 0.00196179i
\(641\) 24.6324 + 33.9036i 0.972920 + 1.33911i 0.940558 + 0.339634i \(0.110303\pi\)
0.0323623 + 0.999476i \(0.489697\pi\)
\(642\) 5.94029 + 13.1795i 0.234444 + 0.520154i
\(643\) −3.48769 10.7340i −0.137541 0.423308i 0.858435 0.512922i \(-0.171437\pi\)
−0.995977 + 0.0896133i \(0.971437\pi\)
\(644\) −0.909630 2.79955i −0.0358445 0.110318i
\(645\) −0.275532 0.611314i −0.0108491 0.0240705i
\(646\) 9.42209 + 12.9684i 0.370707 + 0.510235i
\(647\) −28.7627 9.34555i −1.13078 0.367412i −0.316905 0.948457i \(-0.602644\pi\)
−0.813871 + 0.581046i \(0.802644\pi\)
\(648\) −4.35664 + 7.87526i −0.171145 + 0.309369i
\(649\) 13.4133 45.9565i 0.526517 1.80395i
\(650\) 33.2843i 1.30552i
\(651\) 9.82131 + 10.8078i 0.384928 + 0.423593i
\(652\) −13.9082 + 10.1049i −0.544688 + 0.395739i
\(653\) −5.11472 + 7.03980i −0.200154 + 0.275489i −0.897282 0.441459i \(-0.854461\pi\)
0.697127 + 0.716947i \(0.254461\pi\)
\(654\) −1.29808 0.269716i −0.0507591 0.0105467i
\(655\) 1.14135 0.370846i 0.0445961 0.0144901i
\(656\) 4.44808 + 3.23172i 0.173668 + 0.126177i
\(657\) 0.121522 0.279804i 0.00474101 0.0109162i
\(658\) 0.823897 2.53569i 0.0321188 0.0988516i
\(659\) 1.04851 0.0408442 0.0204221 0.999791i \(-0.493499\pi\)
0.0204221 + 0.999791i \(0.493499\pi\)
\(660\) 0.913649 0.128262i 0.0355637 0.00499261i
\(661\) −37.7527 −1.46841 −0.734206 0.678927i \(-0.762445\pi\)
−0.734206 + 0.678927i \(0.762445\pi\)
\(662\) 3.58853 11.0444i 0.139472 0.429251i
\(663\) −3.44411 31.3867i −0.133758 1.21896i
\(664\) −11.4972 8.35319i −0.446177 0.324167i
\(665\) −0.898724 + 0.292013i −0.0348510 + 0.0113238i
\(666\) −1.23098 + 1.39255i −0.0476995 + 0.0539603i
\(667\) 10.9521 15.0742i 0.424066 0.583677i
\(668\) 16.8406 12.2354i 0.651581 0.473402i
\(669\) −9.75029 + 8.86030i −0.376968 + 0.342559i
\(670\) 1.50761i 0.0582442i
\(671\) −21.1863 + 16.3919i −0.817889 + 0.632801i
\(672\) −0.859155 + 1.50395i −0.0331426 + 0.0580160i
\(673\) −34.2404 11.1254i −1.31987 0.428851i −0.437419 0.899258i \(-0.644107\pi\)
−0.882450 + 0.470407i \(0.844107\pi\)
\(674\) −10.2525 14.1114i −0.394913 0.543552i
\(675\) 14.9040 21.1170i 0.573653 0.812792i
\(676\) −9.81888 30.2194i −0.377649 1.16228i
\(677\) −8.43360 25.9559i −0.324129 0.997568i −0.971832 0.235675i \(-0.924270\pi\)
0.647703 0.761893i \(-0.275730\pi\)
\(678\) 16.4287 7.40477i 0.630941 0.284378i
\(679\) 6.09258 + 8.38572i 0.233812 + 0.321814i
\(680\) 0.416136 + 0.135211i 0.0159581 + 0.00518510i
\(681\) −35.8135 20.4591i −1.37238 0.783993i
\(682\) −26.8439 7.83489i −1.02791 0.300013i
\(683\) 45.1710i 1.72842i 0.503131 + 0.864210i \(0.332181\pi\)
−0.503131 + 0.864210i \(0.667819\pi\)
\(684\) 3.82775 + 17.2314i 0.146358 + 0.658861i
\(685\) 0.567232 0.412118i 0.0216728 0.0157462i
\(686\) −0.587785 + 0.809017i −0.0224417 + 0.0308884i
\(687\) 4.85633 23.3724i 0.185281 0.891714i
\(688\) −2.29250 + 0.744879i −0.0874008 + 0.0283982i
\(689\) 14.0461 + 10.2051i 0.535113 + 0.388782i
\(690\) −0.813963 + 0.0893172i −0.0309870 + 0.00340025i
\(691\) 3.47116 10.6831i 0.132049 0.406406i −0.863070 0.505084i \(-0.831462\pi\)
0.995119 + 0.0986784i \(0.0314615\pi\)
\(692\) −18.5325 −0.704499
\(693\) 0.650178 9.92861i 0.0246982 0.377157i
\(694\) −12.0266 −0.456525
\(695\) −1.02793 + 3.16363i −0.0389914 + 0.120003i
\(696\) −10.8983 + 1.19588i −0.413097 + 0.0453297i
\(697\) −12.1183 8.80445i −0.459013 0.333492i
\(698\) 9.67472 3.14351i 0.366194 0.118983i
\(699\) 0.367207 1.76728i 0.0138890 0.0668448i
\(700\) 2.92376 4.02422i 0.110508 0.152101i
\(701\) −24.7251 + 17.9638i −0.933852 + 0.678483i −0.946933 0.321431i \(-0.895836\pi\)
0.0130806 + 0.999914i \(0.495836\pi\)
\(702\) 10.2896 33.2120i 0.388355 1.25351i
\(703\) 3.64529i 0.137485i
\(704\) −0.100078 3.31511i −0.00377183 0.124943i
\(705\) −0.643996 0.367894i −0.0242543 0.0138557i
\(706\) −8.93383 2.90278i −0.336229 0.109247i
\(707\) −6.95430 9.57177i −0.261543 0.359983i
\(708\) 22.7931 10.2733i 0.856618 0.386096i
\(709\) −3.50974 10.8019i −0.131811 0.405673i 0.863269 0.504744i \(-0.168413\pi\)
−0.995080 + 0.0990706i \(0.968413\pi\)
\(710\) −0.523376 1.61079i −0.0196420 0.0604517i
\(711\) −27.3902 2.62571i −1.02721 0.0984718i
\(712\) −8.87556 12.2162i −0.332626 0.457820i
\(713\) 23.6043 + 7.66949i 0.883987 + 0.287225i
\(714\) 2.34067 4.09733i 0.0875974 0.153339i
\(715\) −3.35506 + 1.20321i −0.125472 + 0.0449975i
\(716\) 18.2934i 0.683656i
\(717\) −27.3440 + 24.8480i −1.02118 + 0.927967i
\(718\) −17.8080 + 12.9382i −0.664587 + 0.482851i
\(719\) −9.17659 + 12.6305i −0.342229 + 0.471038i −0.945091 0.326808i \(-0.894027\pi\)
0.602862 + 0.797846i \(0.294027\pi\)
\(720\) 0.360994 + 0.319109i 0.0134534 + 0.0118925i
\(721\) 1.03624 0.336693i 0.0385914 0.0125391i
\(722\) 12.6363 + 9.18083i 0.470276 + 0.341675i
\(723\) 2.31020 + 21.0532i 0.0859173 + 0.782978i
\(724\) 0.221317 0.681143i 0.00822517 0.0253145i
\(725\) 31.4861 1.16936
\(726\) 8.86243 + 16.8659i 0.328916 + 0.625951i
\(727\) −43.2823 −1.60525 −0.802626 0.596483i \(-0.796564\pi\)
−0.802626 + 0.596483i \(0.796564\pi\)
\(728\) 2.06775 6.36388i 0.0766359 0.235861i
\(729\) 21.3997 16.4637i 0.792582 0.609765i
\(730\) −0.0132121 0.00959917i −0.000489003 0.000355281i
\(731\) 6.24566 2.02934i 0.231004 0.0750578i
\(732\) −13.6966 2.84589i −0.506241 0.105187i
\(733\) −7.76379 + 10.6859i −0.286762 + 0.394694i −0.927959 0.372682i \(-0.878438\pi\)
0.641197 + 0.767376i \(0.278438\pi\)
\(734\) 13.6048 9.88448i 0.502163 0.364843i
\(735\) 0.187080 + 0.205872i 0.00690056 + 0.00759371i
\(736\) 2.94363i 0.108503i
\(737\) 29.3058 10.5098i 1.07949 0.387134i
\(738\) −8.37753 14.2085i −0.308381 0.523022i
\(739\) −16.8990 5.49083i −0.621641 0.201983i −0.0187721 0.999824i \(-0.505976\pi\)
−0.602869 + 0.797840i \(0.705976\pi\)
\(740\) 0.0584859 + 0.0804989i 0.00214998 + 0.00295920i
\(741\) −28.0210 62.1693i −1.02938 2.28385i
\(742\) 0.801796 + 2.46767i 0.0294349 + 0.0905912i
\(743\) −6.86362 21.1240i −0.251802 0.774966i −0.994443 0.105277i \(-0.966427\pi\)
0.742641 0.669689i \(-0.233573\pi\)
\(744\) −6.00082 13.3138i −0.220001 0.488108i
\(745\) −0.282002 0.388143i −0.0103318 0.0142204i
\(746\) −11.0418 3.58770i −0.404269 0.131355i
\(747\) 21.6538 + 36.7255i 0.792272 + 1.34371i
\(748\) 0.272651 + 9.03166i 0.00996911 + 0.330230i
\(749\) 8.34639i 0.304970i
\(750\) −1.86598 2.05341i −0.0681359 0.0749799i
\(751\) −5.60877 + 4.07501i −0.204667 + 0.148699i −0.685397 0.728169i \(-0.740371\pi\)
0.480731 + 0.876868i \(0.340371\pi\)
\(752\) −1.56714 + 2.15699i −0.0571479 + 0.0786573i
\(753\) −1.25882 0.261557i −0.0458738 0.00953167i
\(754\) 40.2826 13.0886i 1.46700 0.476659i
\(755\) 0.0196741 + 0.0142941i 0.000716013 + 0.000520214i
\(756\) 4.16147 3.11162i 0.151351 0.113169i
\(757\) −10.4463 + 32.1505i −0.379678 + 1.16853i 0.560590 + 0.828094i \(0.310575\pi\)
−0.940268 + 0.340436i \(0.889425\pi\)
\(758\) 16.2733 0.591073
\(759\) −7.41046 15.1996i −0.268983 0.551711i
\(760\) 0.944974 0.0342778
\(761\) 5.92539 18.2365i 0.214795 0.661072i −0.784373 0.620290i \(-0.787015\pi\)
0.999168 0.0407823i \(-0.0129850\pi\)
\(762\) 2.57647 + 23.4798i 0.0933358 + 0.850585i
\(763\) 0.619267 + 0.449924i 0.0224190 + 0.0162883i
\(764\) 24.7626 8.04585i 0.895878 0.291088i
\(765\) −0.983487 0.869377i −0.0355581 0.0314324i
\(766\) −8.82714 + 12.1495i −0.318937 + 0.438980i
\(767\) −78.1406 + 56.7724i −2.82149 + 2.04993i
\(768\) 1.28185 1.16484i 0.0462548 0.0420327i
\(769\) 4.54196i 0.163787i −0.996641 0.0818936i \(-0.973903\pi\)
0.996641 0.0818936i \(-0.0260968\pi\)
\(770\) −0.511334 0.149242i −0.0184272 0.00537831i
\(771\) −2.55272 + 4.46851i −0.0919338 + 0.160930i
\(772\) 2.38681 + 0.775523i 0.0859033 + 0.0279117i
\(773\) 9.80576 + 13.4965i 0.352689 + 0.485434i 0.948094 0.317992i \(-0.103008\pi\)
−0.595405 + 0.803426i \(0.703008\pi\)
\(774\) 7.19843 + 0.690065i 0.258742 + 0.0248039i
\(775\) 12.9601 + 39.8870i 0.465540 + 1.43278i
\(776\) −3.20306 9.85801i −0.114983 0.353882i
\(777\) 0.978302 0.440941i 0.0350964 0.0158187i
\(778\) −1.76075 2.42346i −0.0631259 0.0868854i
\(779\) −30.7667 9.99670i −1.10233 0.358169i
\(780\) −1.61625 0.923310i −0.0578710 0.0330598i
\(781\) 27.6628 21.4027i 0.989853 0.765850i
\(782\) 8.01958i 0.286780i
\(783\) 31.4177 + 9.73367i 1.12278 + 0.347853i
\(784\) 0.809017 0.587785i 0.0288935 0.0209923i
\(785\) 0.167917 0.231117i 0.00599320 0.00824893i
\(786\) −2.63292 + 12.6716i −0.0939131 + 0.451983i
\(787\) 20.5616 6.68088i 0.732944 0.238148i 0.0813176 0.996688i \(-0.474087\pi\)
0.651626 + 0.758540i \(0.274087\pi\)
\(788\) 5.78085 + 4.20003i 0.205934 + 0.149620i
\(789\) 3.72749 0.409022i 0.132702 0.0145616i
\(790\) −0.455201 + 1.40096i −0.0161953 + 0.0498440i
\(791\) −10.4041 −0.369926
\(792\) −3.68647 + 9.24175i −0.130993 + 0.328391i
\(793\) 54.0439 1.91915
\(794\) 2.50679 7.71510i 0.0889626 0.273799i
\(795\) 0.717470 0.0787289i 0.0254460 0.00279223i
\(796\) −10.4873 7.61950i −0.371714 0.270066i
\(797\) 12.1477 3.94703i 0.430294 0.139811i −0.0858590 0.996307i \(-0.527363\pi\)
0.516153 + 0.856496i \(0.327363\pi\)
\(798\) 2.07322 9.97797i 0.0733913 0.353216i
\(799\) 4.26951 5.87648i 0.151044 0.207895i
\(800\) −4.02422 + 2.92376i −0.142278 + 0.103371i
\(801\) 9.82338 + 44.2221i 0.347092 + 1.56251i
\(802\) 32.4353i 1.14533i
\(803\) 0.0944900 0.323742i 0.00333448 0.0114246i
\(804\) 14.1176 + 8.06495i 0.497891 + 0.284429i
\(805\) 0.449624 + 0.146092i 0.0158472 + 0.00514905i
\(806\) 33.1617 + 45.6431i 1.16807 + 1.60771i
\(807\) 2.25566 1.01667i 0.0794029 0.0357886i
\(808\) 3.65609 + 11.2523i 0.128621 + 0.395854i
\(809\) 9.22491 + 28.3913i 0.324330 + 0.998187i 0.971742 + 0.236046i \(0.0758516\pi\)
−0.647411 + 0.762141i \(0.724148\pi\)
\(810\) −0.611979 1.30951i −0.0215027 0.0460113i
\(811\) 20.0631 + 27.6144i 0.704509 + 0.969674i 0.999898 + 0.0142968i \(0.00455097\pi\)
−0.295388 + 0.955377i \(0.595449\pi\)
\(812\) 6.02007 + 1.95604i 0.211263 + 0.0686435i
\(813\) −11.7631 + 20.5912i −0.412550 + 0.722167i
\(814\) −1.15707 + 1.69805i −0.0405552 + 0.0595167i
\(815\) 2.76105i 0.0967154i
\(816\) −3.49226 + 3.17349i −0.122253 + 0.111094i
\(817\) 11.4741 8.33645i 0.401430 0.291656i
\(818\) 14.8712 20.4684i 0.519959 0.715662i
\(819\) −13.2952 + 15.0403i −0.464571 + 0.525549i
\(820\) −0.839811 + 0.272871i −0.0293275 + 0.00952907i
\(821\) 21.7460 + 15.7994i 0.758939 + 0.551402i 0.898585 0.438800i \(-0.144596\pi\)
−0.139645 + 0.990202i \(0.544596\pi\)
\(822\) 0.824774 + 7.51630i 0.0287673 + 0.262161i
\(823\) −15.5036 + 47.7152i −0.540422 + 1.66325i 0.191211 + 0.981549i \(0.438758\pi\)
−0.731633 + 0.681699i \(0.761242\pi\)
\(824\) −1.08956 −0.0379567
\(825\) 13.4188 25.2279i 0.467184 0.878321i
\(826\) −14.4345 −0.502242
\(827\) 6.73474 20.7274i 0.234190 0.720762i −0.763038 0.646354i \(-0.776293\pi\)
0.997228 0.0744087i \(-0.0237069\pi\)
\(828\) 3.51789 8.09993i 0.122255 0.281492i
\(829\) −18.6834 13.5743i −0.648900 0.471453i 0.213996 0.976834i \(-0.431352\pi\)
−0.862896 + 0.505381i \(0.831352\pi\)
\(830\) 2.17070 0.705304i 0.0753462 0.0244815i
\(831\) 15.7375 + 3.26994i 0.545928 + 0.113433i
\(832\) −3.93309 + 5.41344i −0.136356 + 0.187677i
\(833\) −2.20408 + 1.60136i −0.0763667 + 0.0554837i
\(834\) −24.1261 26.5495i −0.835417 0.919333i
\(835\) 3.34318i 0.115695i
\(836\) 6.58757 + 18.3689i 0.227836 + 0.635302i
\(837\) 0.601195 + 43.8069i 0.0207804 + 1.51419i
\(838\) 3.75515 + 1.22012i 0.129719 + 0.0421484i
\(839\) −5.16175 7.10453i −0.178203 0.245276i 0.710566 0.703630i \(-0.248439\pi\)
−0.888769 + 0.458355i \(0.848439\pi\)
\(840\) −0.114306 0.253607i −0.00394393 0.00875027i
\(841\) 3.42000 + 10.5257i 0.117931 + 0.362954i
\(842\) 8.18453 + 25.1894i 0.282057 + 0.868083i
\(843\) −9.30703 20.6492i −0.320551 0.711196i
\(844\) 13.5905 + 18.7057i 0.467805 + 0.643878i
\(845\) 4.85340 + 1.57697i 0.166962 + 0.0542493i
\(846\) 6.89008 4.06248i 0.236886 0.139671i
\(847\) −0.663539 10.9800i −0.0227995 0.377276i
\(848\) 2.59467i 0.0891012i
\(849\) 16.8649 + 18.5589i 0.578801 + 0.636941i
\(850\) 10.9635 7.96547i 0.376046 0.273213i
\(851\) 1.07195 1.47541i 0.0367459 0.0505764i
\(852\) 17.8836 + 3.71585i 0.612681 + 0.127303i
\(853\) −1.26560 + 0.411219i −0.0433334 + 0.0140799i −0.330603 0.943770i \(-0.607252\pi\)
0.287270 + 0.957850i \(0.407252\pi\)
\(854\) 6.53414 + 4.74733i 0.223594 + 0.162450i
\(855\) −2.60027 1.12933i −0.0889274 0.0386221i
\(856\) −2.57918 + 7.93789i −0.0881544 + 0.271311i
\(857\) −8.79463 −0.300419 −0.150209 0.988654i \(-0.547995\pi\)
−0.150209 + 0.988654i \(0.547995\pi\)
\(858\) 6.68067 37.8541i 0.228074 1.29232i
\(859\) −19.7514 −0.673911 −0.336955 0.941521i \(-0.609397\pi\)
−0.336955 + 0.941521i \(0.609397\pi\)
\(860\) 0.119632 0.368188i 0.00407940 0.0125551i
\(861\) 1.03874 + 9.46621i 0.0354002 + 0.322608i
\(862\) −29.8337 21.6755i −1.01614 0.738269i
\(863\) 22.2608 7.23297i 0.757766 0.246213i 0.0954465 0.995435i \(-0.469572\pi\)
0.662320 + 0.749221i \(0.269572\pi\)
\(864\) −4.91934 + 1.67336i −0.167359 + 0.0569289i
\(865\) 1.74949 2.40797i 0.0594846 0.0818735i
\(866\) −17.7907 + 12.9257i −0.604552 + 0.439233i
\(867\) −12.2772 + 11.1565i −0.416955 + 0.378896i
\(868\) 8.43144i 0.286182i
\(869\) −30.4059 + 0.917906i −1.03145 + 0.0311378i
\(870\) 0.873428 1.52893i 0.0296120 0.0518356i
\(871\) −59.7382 19.4101i −2.02415 0.657687i
\(872\) −0.449924 0.619267i −0.0152363 0.0209710i
\(873\) −2.96736 + 30.9541i −0.100430 + 1.04764i
\(874\) −5.35210 16.4721i −0.181038 0.557176i
\(875\) 0.495018 + 1.52351i 0.0167347 + 0.0515040i
\(876\) 0.160567 0.0723708i 0.00542505 0.00244518i
\(877\) 16.8980 + 23.2581i 0.570606 + 0.785372i 0.992626 0.121215i \(-0.0386789\pi\)
−0.422020 + 0.906586i \(0.638679\pi\)
\(878\) −0.939056 0.305118i −0.0316916 0.0102972i
\(879\) −12.2067 6.97327i −0.411721 0.235203i
\(880\) 0.440189 + 0.299949i 0.0148388 + 0.0101113i
\(881\) 40.1934i 1.35415i −0.735915 0.677074i \(-0.763248\pi\)
0.735915 0.677074i \(-0.236752\pi\)
\(882\) −2.92861 + 0.650555i −0.0986116 + 0.0219053i
\(883\) 8.15600 5.92568i 0.274471 0.199415i −0.442031 0.897000i \(-0.645742\pi\)
0.716502 + 0.697585i \(0.245742\pi\)
\(884\) 10.7153 14.7483i 0.360394 0.496039i
\(885\) −0.816865 + 3.93139i −0.0274586 + 0.132152i
\(886\) 8.77053 2.84972i 0.294652 0.0957382i
\(887\) −43.7299 31.7717i −1.46831 1.06679i −0.981100 0.193501i \(-0.938016\pi\)
−0.487207 0.873286i \(-0.661984\pi\)
\(888\) −1.06668 + 0.117048i −0.0357954 + 0.00392788i
\(889\) 4.21421 12.9700i 0.141340 0.435000i
\(890\) 2.42514 0.0812910
\(891\) 21.1887 21.0247i 0.709847 0.704355i
\(892\) −7.60643 −0.254682
\(893\) 4.84766 14.9196i 0.162221 0.499264i
\(894\) 5.14322 0.564372i 0.172015 0.0188754i
\(895\) −2.37691 1.72692i −0.0794512 0.0577247i
\(896\) −0.951057 + 0.309017i −0.0317726 + 0.0103235i
\(897\) −6.94041 + 33.4026i −0.231733 + 1.11528i
\(898\) 17.6805 24.3351i 0.590005 0.812072i
\(899\) −43.1772 + 31.3701i −1.44004 + 1.04625i
\(900\) 14.5675 3.23599i 0.485584 0.107866i
\(901\) 7.06888i 0.235498i
\(902\) −11.1587 14.4225i −0.371543 0.480215i
\(903\) −3.62523 2.07097i −0.120640 0.0689177i
\(904\) 9.89485 + 3.21503i 0.329098 + 0.106930i
\(905\) 0.0676100 + 0.0930572i 0.00224743 + 0.00309332i
\(906\) −0.239099 + 0.107767i −0.00794352 + 0.00358031i
\(907\) −3.39484 10.4482i −0.112724 0.346928i 0.878742 0.477298i \(-0.158384\pi\)
−0.991465 + 0.130370i \(0.958384\pi\)
\(908\) −7.35862 22.6475i −0.244205 0.751584i
\(909\) 3.38705 35.3321i 0.112341 1.17189i
\(910\) 0.631676 + 0.869428i 0.0209399 + 0.0288213i
\(911\) 3.17983 + 1.03319i 0.105353 + 0.0342311i 0.361219 0.932481i \(-0.382361\pi\)
−0.255866 + 0.966712i \(0.582361\pi\)
\(912\) −5.05511 + 8.84895i −0.167392 + 0.293018i
\(913\) 28.8424 + 37.2785i 0.954544 + 1.23374i
\(914\) 13.6979i 0.453085i
\(915\) 1.66275 1.51098i 0.0549690 0.0499515i
\(916\) 11.1501 8.10103i 0.368410 0.267665i
\(917\) 4.39207 6.04517i 0.145039 0.199629i
\(918\) 13.4022 4.55889i 0.442338 0.150466i
\(919\) −31.5660 + 10.2564i −1.04127 + 0.338328i −0.779235 0.626732i \(-0.784392\pi\)
−0.262030 + 0.965060i \(0.584392\pi\)
\(920\) −0.382473 0.277883i −0.0126098 0.00916152i
\(921\) 3.96464 + 36.1305i 0.130639 + 1.19054i
\(922\) 0.619903 1.90787i 0.0204154 0.0628322i
\(923\) −70.5646 −2.32266
\(924\) 4.13290 3.98988i 0.135963 0.131257i
\(925\) 3.08174 0.101327
\(926\) −6.94788 + 21.3834i −0.228322 + 0.702702i
\(927\) 2.99813 + 1.30212i 0.0984716 + 0.0427673i
\(928\) −5.12098 3.72061i −0.168104 0.122135i
\(929\) 26.2935 8.54327i 0.862662 0.280296i 0.155922 0.987769i \(-0.450165\pi\)
0.706740 + 0.707474i \(0.250165\pi\)
\(930\) 2.29638 + 0.477143i 0.0753014 + 0.0156461i
\(931\) −3.45842 + 4.76011i −0.113345 + 0.156006i
\(932\) 0.843104 0.612551i 0.0276168 0.0200648i
\(933\) 8.83070 + 9.71772i 0.289104 + 0.318144i
\(934\) 15.5570i 0.509041i
\(935\) −1.19925 0.817176i −0.0392195 0.0267245i
\(936\) 17.2922 10.1957i 0.565212 0.333257i
\(937\) 18.3228 + 5.95344i 0.598580 + 0.194490i 0.592607 0.805492i \(-0.298099\pi\)
0.00597291 + 0.999982i \(0.498099\pi\)
\(938\) −5.51758 7.59430i −0.180155 0.247963i
\(939\) 0.468298 + 1.03900i 0.0152823 + 0.0339064i
\(940\) −0.132322 0.407246i −0.00431588 0.0132829i
\(941\) −12.7583 39.2661i −0.415910 1.28004i −0.911435 0.411445i \(-0.865024\pi\)
0.495525 0.868594i \(-0.334976\pi\)
\(942\) 1.26597 + 2.80876i 0.0412475 + 0.0915145i
\(943\) 9.51297 + 13.0935i 0.309785 + 0.426382i
\(944\) 13.7281 + 4.46052i 0.446811 + 0.145178i
\(945\) 0.0114518 + 0.834452i 0.000372527 + 0.0271447i
\(946\) 7.99101 0.241235i 0.259810 0.00784324i
\(947\) 8.56801i 0.278423i −0.990263 0.139211i \(-0.955543\pi\)
0.990263 0.139211i \(-0.0444568\pi\)
\(948\) −10.6838 11.7570i −0.346995 0.381850i
\(949\) −0.550463 + 0.399935i −0.0178688 + 0.0129824i
\(950\) 17.2029 23.6778i 0.558136 0.768209i
\(951\) 29.0583 + 6.03774i 0.942280 + 0.195787i
\(952\) 2.59105 0.841882i 0.0839763 0.0272856i
\(953\) 23.6082 + 17.1523i 0.764744 + 0.555619i 0.900362 0.435142i \(-0.143302\pi\)
−0.135618 + 0.990761i \(0.543302\pi\)
\(954\) −3.10085 + 7.13970i −0.100394 + 0.231156i
\(955\) −1.29221 + 3.97700i −0.0418148 + 0.128693i
\(956\) −21.3316 −0.689914
\(957\) 35.8090 + 6.31974i 1.15754 + 0.204288i
\(958\) 24.7841 0.800738
\(959\) 1.34904 4.15192i 0.0435628 0.134072i
\(960\) 0.0303426 + 0.276517i 0.000979303 + 0.00892455i
\(961\) −32.4328 23.5638i −1.04622 0.760124i
\(962\) 3.94270 1.28106i 0.127118 0.0413031i
\(963\) 16.5835 18.7602i 0.534397 0.604540i
\(964\) −7.18747 + 9.89270i −0.231493 + 0.318623i
\(965\) −0.326085 + 0.236914i −0.0104970 + 0.00762654i
\(966\) −3.77329 + 3.42886i −0.121403 + 0.110322i
\(967\) 32.6733i 1.05070i 0.850886 + 0.525351i \(0.176066\pi\)
−0.850886 + 0.525351i \(0.823934\pi\)
\(968\) −2.76193 + 10.6476i −0.0887719 + 0.342227i
\(969\) 13.7721 24.1080i 0.442423 0.774460i
\(970\) 1.58325 + 0.514429i 0.0508351 + 0.0165173i
\(971\) 16.0175 + 22.0462i 0.514027 + 0.707497i 0.984592 0.174868i \(-0.0559500\pi\)
−0.470565 + 0.882365i \(0.655950\pi\)
\(972\) 15.5363 + 1.27446i 0.498326 + 0.0408785i
\(973\) 6.40031 + 19.6981i 0.205185 + 0.631493i
\(974\) −7.22107 22.2242i −0.231378 0.712108i
\(975\) −52.5582 + 23.6891i −1.68321 + 0.758657i
\(976\) −4.74733 6.53414i −0.151958 0.209153i
\(977\) −34.2685 11.1345i −1.09635 0.356224i −0.295651 0.955296i \(-0.595536\pi\)
−0.800695 + 0.599072i \(0.795536\pi\)
\(978\) 25.8551 + 14.7702i 0.826755 + 0.472298i
\(979\) 16.9061 + 47.1413i 0.540320 + 1.50664i
\(980\) 0.160605i 0.00513035i
\(981\) 0.497971 + 2.24172i 0.0158990 + 0.0715727i
\(982\) 11.4997 8.35505i 0.366971 0.266620i
\(983\) 28.8851 39.7569i 0.921292 1.26805i −0.0418690 0.999123i \(-0.513331\pi\)
0.963161 0.268926i \(-0.0866688\pi\)
\(984\) 1.93732 9.32389i 0.0617595 0.297235i
\(985\) −1.09144 + 0.354631i −0.0347762 + 0.0112995i
\(986\) 13.9515 + 10.1364i 0.444307 + 0.322808i
\(987\) −4.59042 + 0.503712i −0.146115 + 0.0160333i
\(988\) 12.1663 37.4439i 0.387061 1.19125i
\(989\) −7.09554 −0.225625
\(990\) −0.852796 1.35143i −0.0271037 0.0429512i
\(991\) 14.6512 0.465409 0.232705 0.972547i \(-0.425242\pi\)
0.232705 + 0.972547i \(0.425242\pi\)
\(992\) 2.60546 8.01878i 0.0827234 0.254596i
\(993\) −19.9938 + 2.19395i −0.634485 + 0.0696229i
\(994\) −8.53157 6.19855i −0.270605 0.196606i
\(995\) 1.98004 0.643355i 0.0627716 0.0203957i
\(996\) −5.00749 + 24.1000i −0.158669 + 0.763636i
\(997\) 28.5607 39.3105i 0.904528 1.24498i −0.0644734 0.997919i \(-0.520537\pi\)
0.969001 0.247056i \(-0.0794632\pi\)
\(998\) 31.5546 22.9258i 0.998843 0.725702i
\(999\) 3.07505 + 0.952694i 0.0972902 + 0.0301419i
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.w.a.365.1 yes 48
3.2 odd 2 462.2.w.b.365.7 yes 48
11.6 odd 10 462.2.w.b.281.7 yes 48
33.17 even 10 inner 462.2.w.a.281.1 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.w.a.281.1 48 33.17 even 10 inner
462.2.w.a.365.1 yes 48 1.1 even 1 trivial
462.2.w.b.281.7 yes 48 11.6 odd 10
462.2.w.b.365.7 yes 48 3.2 odd 2