Properties

Label 539.2.q.c.471.1
Level $539$
Weight $2$
Character 539.471
Analytic conductor $4.304$
Analytic rank $0$
Dimension $16$
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] = [539,2,Mod(214,539)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(539, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("539.214");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.q (of order \(15\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{15})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} - 5 x^{14} + 16 x^{13} + 4 x^{12} - 29 x^{11} + 10 x^{10} - 156 x^{9} + 251 x^{8} + 240 x^{7} + 390 x^{6} - 1375 x^{5} - 300 x^{4} + 500 x^{3} + 375 x^{2} + 625 x + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 471.1
Root \(1.62381 - 0.722968i\) of defining polynomial
Character \(\chi\) \(=\) 539.471
Dual form 539.2.q.c.214.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.520239 - 0.577783i) q^{2} +(0.564602 + 0.251377i) q^{3} +(0.145871 - 1.38787i) q^{4} +(0.217653 + 0.0462636i) q^{5} +(-0.148486 - 0.456994i) q^{6} +(-2.13577 + 1.55173i) q^{8} +(-1.75181 - 1.94558i) q^{9} +O(q^{10})\) \(q+(-0.520239 - 0.577783i) q^{2} +(0.564602 + 0.251377i) q^{3} +(0.145871 - 1.38787i) q^{4} +(0.217653 + 0.0462636i) q^{5} +(-0.148486 - 0.456994i) q^{6} +(-2.13577 + 1.55173i) q^{8} +(-1.75181 - 1.94558i) q^{9} +(-0.0865012 - 0.149825i) q^{10} +(-3.14501 + 1.05306i) q^{11} +(0.431239 - 0.746928i) q^{12} +(2.01774 - 6.20997i) q^{13} +(0.111258 + 0.0808336i) q^{15} +(-0.722369 - 0.153544i) q^{16} +(-2.90042 + 3.22125i) q^{17} +(-0.212766 + 2.02433i) q^{18} +(-0.304701 - 2.89904i) q^{19} +(0.0959574 - 0.295327i) q^{20} +(2.24459 + 1.26929i) q^{22} +(1.94898 - 3.37573i) q^{23} +(-1.59593 + 0.339226i) q^{24} +(-4.52249 - 2.01354i) q^{25} +(-4.63772 + 2.06485i) q^{26} +(-1.07295 - 3.30220i) q^{27} +(3.05322 + 2.21829i) q^{29} +(-0.0111763 - 0.106336i) q^{30} +(6.73903 - 1.43242i) q^{31} +(2.92705 + 5.06980i) q^{32} +(-2.04039 - 0.196025i) q^{33} +3.37009 q^{34} +(-2.95576 + 2.14748i) q^{36} +(-5.16474 + 2.29949i) q^{37} +(-1.51650 + 1.68424i) q^{38} +(2.70026 - 2.99895i) q^{39} +(-0.536647 + 0.238931i) q^{40} +(-1.08255 + 0.786521i) q^{41} -4.70820 q^{43} +(1.00274 + 4.51848i) q^{44} +(-0.291277 - 0.504506i) q^{45} +(-2.96437 + 0.630097i) q^{46} +(-0.631931 - 6.01242i) q^{47} +(-0.369254 - 0.268279i) q^{48} +(1.18938 + 3.66055i) q^{50} +(-2.44733 + 1.08962i) q^{51} +(-8.32432 - 3.70622i) q^{52} +(1.68037 - 0.357175i) q^{53} +(-1.34977 + 2.33786i) q^{54} +(-0.733239 + 0.0837016i) q^{55} +(0.556717 - 1.71340i) q^{57} +(-0.306709 - 2.91814i) q^{58} +(0.996474 - 9.48082i) q^{59} +(0.128416 - 0.142621i) q^{60} +(9.41900 + 2.00207i) q^{61} +(-4.33353 - 3.14850i) q^{62} +(0.950059 - 2.92398i) q^{64} +(0.726463 - 1.25827i) q^{65} +(0.948230 + 1.28088i) q^{66} +(-0.635774 - 1.10119i) q^{67} +(4.04759 + 4.49531i) q^{68} +(1.94898 - 1.41602i) q^{69} +(-2.87670 - 8.85357i) q^{71} +(6.76048 + 1.43698i) q^{72} +(-0.584221 + 5.55850i) q^{73} +(4.01551 + 1.78782i) q^{74} +(-2.04725 - 2.27370i) q^{75} -4.06794 q^{76} -3.13752 q^{78} +(-3.03086 - 3.36611i) q^{79} +(-0.150123 - 0.0668389i) q^{80} +(-0.596670 + 5.67693i) q^{81} +(1.01763 + 0.216303i) q^{82} +(3.48688 + 10.7315i) q^{83} +(-0.780313 + 0.566931i) q^{85} +(2.44939 + 2.72032i) q^{86} +(1.16623 + 2.01996i) q^{87} +(5.08297 - 7.12929i) q^{88} +(-3.96078 + 6.86028i) q^{89} +(-0.139962 + 0.430759i) q^{90} +(-4.40079 - 3.19736i) q^{92} +(4.16495 + 0.885287i) q^{93} +(-3.14512 + 3.49301i) q^{94} +(0.0678008 - 0.645082i) q^{95} +(0.378188 + 3.59821i) q^{96} +(-2.79781 + 8.61078i) q^{97} +(7.55825 + 4.27411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + q^{2} + 4 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + q^{2} + 4 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 6 q^{8} + 2 q^{9} + 28 q^{10} - 5 q^{11} + 14 q^{12} + 10 q^{13} + 12 q^{15} + 3 q^{16} + 11 q^{17} - 4 q^{18} + 9 q^{19} + 42 q^{20} - 2 q^{22} + 16 q^{23} - 21 q^{24} - 5 q^{25} - 21 q^{26} - 44 q^{27} - 18 q^{29} - 14 q^{30} + 11 q^{31} + 20 q^{32} - 10 q^{33} - 48 q^{34} - 4 q^{36} - 6 q^{37} - 35 q^{38} + 5 q^{39} + 16 q^{40} - 44 q^{41} + 32 q^{43} - 29 q^{44} - 18 q^{45} - 29 q^{46} - 7 q^{47} + 8 q^{48} - 68 q^{50} - 3 q^{51} - 21 q^{52} - 2 q^{53} - 4 q^{54} + 52 q^{55} - 6 q^{57} + 39 q^{58} - 25 q^{59} + 38 q^{60} - 7 q^{61} - 10 q^{62} + 2 q^{64} - 24 q^{65} - 18 q^{66} + 30 q^{67} - 8 q^{68} + 16 q^{69} - 28 q^{71} - 3 q^{72} - 3 q^{73} + 9 q^{74} - 5 q^{75} - 104 q^{76} - 36 q^{78} + 9 q^{79} + 33 q^{80} + 28 q^{81} - 31 q^{82} + 46 q^{83} - 20 q^{85} + 17 q^{86} - 12 q^{87} + 7 q^{88} + 34 q^{89} + 4 q^{90} - 68 q^{92} - 8 q^{93} + 30 q^{94} - 24 q^{95} - 10 q^{96} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(442\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.520239 0.577783i −0.367864 0.408555i 0.530585 0.847632i \(-0.321972\pi\)
−0.898449 + 0.439077i \(0.855306\pi\)
\(3\) 0.564602 + 0.251377i 0.325973 + 0.145133i 0.563198 0.826322i \(-0.309571\pi\)
−0.237224 + 0.971455i \(0.576238\pi\)
\(4\) 0.145871 1.38787i 0.0729357 0.693937i
\(5\) 0.217653 + 0.0462636i 0.0973375 + 0.0206897i 0.256323 0.966591i \(-0.417489\pi\)
−0.158985 + 0.987281i \(0.550822\pi\)
\(6\) −0.148486 0.456994i −0.0606193 0.186567i
\(7\) 0 0
\(8\) −2.13577 + 1.55173i −0.755110 + 0.548620i
\(9\) −1.75181 1.94558i −0.583936 0.648526i
\(10\) −0.0865012 0.149825i −0.0273541 0.0473787i
\(11\) −3.14501 + 1.05306i −0.948255 + 0.317508i
\(12\) 0.431239 0.746928i 0.124488 0.215619i
\(13\) 2.01774 6.20997i 0.559620 1.72233i −0.123798 0.992307i \(-0.539507\pi\)
0.683418 0.730027i \(-0.260493\pi\)
\(14\) 0 0
\(15\) 0.111258 + 0.0808336i 0.0287267 + 0.0208711i
\(16\) −0.722369 0.153544i −0.180592 0.0383861i
\(17\) −2.90042 + 3.22125i −0.703456 + 0.781267i −0.983922 0.178597i \(-0.942844\pi\)
0.280466 + 0.959864i \(0.409511\pi\)
\(18\) −0.212766 + 2.02433i −0.0501493 + 0.477139i
\(19\) −0.304701 2.89904i −0.0699032 0.665085i −0.972229 0.234031i \(-0.924808\pi\)
0.902326 0.431054i \(-0.141858\pi\)
\(20\) 0.0959574 0.295327i 0.0214567 0.0660370i
\(21\) 0 0
\(22\) 2.24459 + 1.26929i 0.478549 + 0.270614i
\(23\) 1.94898 3.37573i 0.406390 0.703888i −0.588092 0.808794i \(-0.700121\pi\)
0.994482 + 0.104906i \(0.0334540\pi\)
\(24\) −1.59593 + 0.339226i −0.325768 + 0.0692442i
\(25\) −4.52249 2.01354i −0.904499 0.402709i
\(26\) −4.63772 + 2.06485i −0.909532 + 0.404950i
\(27\) −1.07295 3.30220i −0.206489 0.635508i
\(28\) 0 0
\(29\) 3.05322 + 2.21829i 0.566969 + 0.411927i 0.834003 0.551760i \(-0.186044\pi\)
−0.267034 + 0.963687i \(0.586044\pi\)
\(30\) −0.0111763 0.106336i −0.00204051 0.0194142i
\(31\) 6.73903 1.43242i 1.21037 0.257271i 0.441842 0.897093i \(-0.354325\pi\)
0.768523 + 0.639822i \(0.220992\pi\)
\(32\) 2.92705 + 5.06980i 0.517434 + 0.896223i
\(33\) −2.04039 0.196025i −0.355187 0.0341236i
\(34\) 3.37009 0.577966
\(35\) 0 0
\(36\) −2.95576 + 2.14748i −0.492626 + 0.357914i
\(37\) −5.16474 + 2.29949i −0.849078 + 0.378034i −0.784688 0.619891i \(-0.787177\pi\)
−0.0643903 + 0.997925i \(0.520510\pi\)
\(38\) −1.51650 + 1.68424i −0.246009 + 0.273220i
\(39\) 2.70026 2.99895i 0.432388 0.480216i
\(40\) −0.536647 + 0.238931i −0.0848513 + 0.0377782i
\(41\) −1.08255 + 0.786521i −0.169066 + 0.122834i −0.669101 0.743171i \(-0.733321\pi\)
0.500035 + 0.866005i \(0.333321\pi\)
\(42\) 0 0
\(43\) −4.70820 −0.717994 −0.358997 0.933339i \(-0.616881\pi\)
−0.358997 + 0.933339i \(0.616881\pi\)
\(44\) 1.00274 + 4.51848i 0.151169 + 0.681187i
\(45\) −0.291277 0.504506i −0.0434210 0.0752074i
\(46\) −2.96437 + 0.630097i −0.437073 + 0.0929028i
\(47\) −0.631931 6.01242i −0.0921765 0.877001i −0.938720 0.344681i \(-0.887987\pi\)
0.846543 0.532320i \(-0.178680\pi\)
\(48\) −0.369254 0.268279i −0.0532972 0.0387227i
\(49\) 0 0
\(50\) 1.18938 + 3.66055i 0.168204 + 0.517679i
\(51\) −2.44733 + 1.08962i −0.342695 + 0.152578i
\(52\) −8.32432 3.70622i −1.15437 0.513961i
\(53\) 1.68037 0.357175i 0.230817 0.0490617i −0.0910509 0.995846i \(-0.529023\pi\)
0.321868 + 0.946785i \(0.395689\pi\)
\(54\) −1.34977 + 2.33786i −0.183680 + 0.318143i
\(55\) −0.733239 + 0.0837016i −0.0988700 + 0.0112863i
\(56\) 0 0
\(57\) 0.556717 1.71340i 0.0737389 0.226945i
\(58\) −0.306709 2.91814i −0.0402729 0.383171i
\(59\) 0.996474 9.48082i 0.129730 1.23430i −0.715008 0.699117i \(-0.753577\pi\)
0.844738 0.535181i \(-0.179756\pi\)
\(60\) 0.128416 0.142621i 0.0165784 0.0184122i
\(61\) 9.41900 + 2.00207i 1.20598 + 0.256339i 0.766696 0.642010i \(-0.221899\pi\)
0.439283 + 0.898349i \(0.355233\pi\)
\(62\) −4.33353 3.14850i −0.550359 0.399859i
\(63\) 0 0
\(64\) 0.950059 2.92398i 0.118757 0.365498i
\(65\) 0.726463 1.25827i 0.0901067 0.156069i
\(66\) 0.948230 + 1.28088i 0.116719 + 0.157666i
\(67\) −0.635774 1.10119i −0.0776722 0.134532i 0.824573 0.565756i \(-0.191415\pi\)
−0.902245 + 0.431223i \(0.858082\pi\)
\(68\) 4.04759 + 4.49531i 0.490843 + 0.545136i
\(69\) 1.94898 1.41602i 0.234629 0.170468i
\(70\) 0 0
\(71\) −2.87670 8.85357i −0.341401 1.05072i −0.963482 0.267772i \(-0.913713\pi\)
0.622081 0.782953i \(-0.286287\pi\)
\(72\) 6.76048 + 1.43698i 0.796730 + 0.169350i
\(73\) −0.584221 + 5.55850i −0.0683779 + 0.650573i 0.905632 + 0.424065i \(0.139397\pi\)
−0.974009 + 0.226507i \(0.927269\pi\)
\(74\) 4.01551 + 1.78782i 0.466793 + 0.207830i
\(75\) −2.04725 2.27370i −0.236396 0.262545i
\(76\) −4.06794 −0.466625
\(77\) 0 0
\(78\) −3.13752 −0.355254
\(79\) −3.03086 3.36611i −0.340998 0.378717i 0.548116 0.836402i \(-0.315345\pi\)
−0.889114 + 0.457686i \(0.848679\pi\)
\(80\) −0.150123 0.0668389i −0.0167842 0.00747281i
\(81\) −0.596670 + 5.67693i −0.0662966 + 0.630770i
\(82\) 1.01763 + 0.216303i 0.112378 + 0.0238867i
\(83\) 3.48688 + 10.7315i 0.382734 + 1.17793i 0.938111 + 0.346336i \(0.112574\pi\)
−0.555376 + 0.831599i \(0.687426\pi\)
\(84\) 0 0
\(85\) −0.780313 + 0.566931i −0.0846368 + 0.0614922i
\(86\) 2.44939 + 2.72032i 0.264124 + 0.293340i
\(87\) 1.16623 + 2.01996i 0.125033 + 0.216563i
\(88\) 5.08297 7.12929i 0.541846 0.759985i
\(89\) −3.96078 + 6.86028i −0.419842 + 0.727188i −0.995923 0.0902046i \(-0.971248\pi\)
0.576081 + 0.817393i \(0.304581\pi\)
\(90\) −0.139962 + 0.430759i −0.0147533 + 0.0454059i
\(91\) 0 0
\(92\) −4.40079 3.19736i −0.458814 0.333348i
\(93\) 4.16495 + 0.885287i 0.431885 + 0.0918000i
\(94\) −3.14512 + 3.49301i −0.324394 + 0.360277i
\(95\) 0.0678008 0.645082i 0.00695622 0.0661840i
\(96\) 0.378188 + 3.59821i 0.0385986 + 0.367241i
\(97\) −2.79781 + 8.61078i −0.284075 + 0.874292i 0.702600 + 0.711585i \(0.252023\pi\)
−0.986674 + 0.162707i \(0.947977\pi\)
\(98\) 0 0
\(99\) 7.55825 + 4.27411i 0.759633 + 0.429564i
\(100\) −3.45425 + 5.98293i −0.345425 + 0.598293i
\(101\) 18.7904 3.99402i 1.86971 0.397420i 0.873687 0.486489i \(-0.161723\pi\)
0.996025 + 0.0890694i \(0.0283893\pi\)
\(102\) 1.90276 + 0.847164i 0.188402 + 0.0838818i
\(103\) 14.8344 6.60471i 1.46168 0.650782i 0.486800 0.873513i \(-0.338164\pi\)
0.974880 + 0.222732i \(0.0714974\pi\)
\(104\) 5.32676 + 16.3941i 0.522332 + 1.60757i
\(105\) 0 0
\(106\) −1.08057 0.785077i −0.104954 0.0762534i
\(107\) 0.563759 + 5.36381i 0.0545007 + 0.518539i 0.987382 + 0.158356i \(0.0506193\pi\)
−0.932881 + 0.360184i \(0.882714\pi\)
\(108\) −4.73954 + 1.00742i −0.456063 + 0.0969392i
\(109\) −2.69951 4.67568i −0.258566 0.447849i 0.707292 0.706921i \(-0.249917\pi\)
−0.965858 + 0.259072i \(0.916583\pi\)
\(110\) 0.429821 + 0.380109i 0.0409818 + 0.0362419i
\(111\) −3.49406 −0.331642
\(112\) 0 0
\(113\) 13.3457 9.69624i 1.25546 0.912145i 0.256935 0.966429i \(-0.417287\pi\)
0.998526 + 0.0542834i \(0.0172875\pi\)
\(114\) −1.27960 + 0.569714i −0.119845 + 0.0533586i
\(115\) 0.580375 0.644572i 0.0541203 0.0601066i
\(116\) 3.52409 3.91390i 0.327203 0.363396i
\(117\) −15.6167 + 6.95299i −1.44376 + 0.642804i
\(118\) −5.99626 + 4.35654i −0.552001 + 0.401052i
\(119\) 0 0
\(120\) −0.363054 −0.0331421
\(121\) 8.78215 6.62374i 0.798377 0.602158i
\(122\) −3.74336 6.48370i −0.338908 0.587006i
\(123\) −0.808926 + 0.171942i −0.0729384 + 0.0155035i
\(124\) −1.00499 9.56187i −0.0902510 0.858681i
\(125\) −1.79128 1.30144i −0.160217 0.116404i
\(126\) 0 0
\(127\) 0.617194 + 1.89953i 0.0547671 + 0.168556i 0.974699 0.223523i \(-0.0717559\pi\)
−0.919931 + 0.392079i \(0.871756\pi\)
\(128\) 8.51229 3.78992i 0.752387 0.334984i
\(129\) −2.65826 1.18353i −0.234047 0.104204i
\(130\) −1.10494 + 0.234863i −0.0969099 + 0.0205988i
\(131\) −0.685047 + 1.18654i −0.0598528 + 0.103668i −0.894399 0.447270i \(-0.852396\pi\)
0.834546 + 0.550938i \(0.185730\pi\)
\(132\) −0.569693 + 2.80321i −0.0495854 + 0.243988i
\(133\) 0 0
\(134\) −0.305497 + 0.940223i −0.0263909 + 0.0812229i
\(135\) −0.0807592 0.768373i −0.00695065 0.0661310i
\(136\) 1.19614 11.3805i 0.102568 0.975872i
\(137\) 1.67232 1.85730i 0.142876 0.158680i −0.667460 0.744646i \(-0.732618\pi\)
0.810335 + 0.585966i \(0.199285\pi\)
\(138\) −1.83208 0.389422i −0.155957 0.0331498i
\(139\) 3.85302 + 2.79938i 0.326809 + 0.237441i 0.739075 0.673623i \(-0.235263\pi\)
−0.412266 + 0.911063i \(0.635263\pi\)
\(140\) 0 0
\(141\) 1.15459 3.55348i 0.0972344 0.299257i
\(142\) −3.61887 + 6.26807i −0.303689 + 0.526005i
\(143\) 0.193632 + 21.6552i 0.0161924 + 1.81090i
\(144\) 0.966719 + 1.67441i 0.0805599 + 0.139534i
\(145\) 0.561917 + 0.624072i 0.0466647 + 0.0518264i
\(146\) 3.51554 2.55419i 0.290948 0.211386i
\(147\) 0 0
\(148\) 2.43801 + 7.50344i 0.200404 + 0.616779i
\(149\) 7.07186 + 1.50317i 0.579350 + 0.123145i 0.488260 0.872698i \(-0.337632\pi\)
0.0910895 + 0.995843i \(0.470965\pi\)
\(150\) −0.248649 + 2.36574i −0.0203021 + 0.193162i
\(151\) 7.43597 + 3.31071i 0.605131 + 0.269422i 0.686346 0.727275i \(-0.259214\pi\)
−0.0812154 + 0.996697i \(0.525880\pi\)
\(152\) 5.14930 + 5.71888i 0.417663 + 0.463862i
\(153\) 11.3482 0.917445
\(154\) 0 0
\(155\) 1.53304 0.123137
\(156\) −3.76827 4.18508i −0.301703 0.335075i
\(157\) 18.4092 + 8.19632i 1.46922 + 0.654138i 0.976395 0.215993i \(-0.0692987\pi\)
0.492822 + 0.870130i \(0.335965\pi\)
\(158\) −0.368113 + 3.50236i −0.0292855 + 0.278633i
\(159\) 1.03853 + 0.220746i 0.0823607 + 0.0175063i
\(160\) 0.402535 + 1.23887i 0.0318232 + 0.0979416i
\(161\) 0 0
\(162\) 3.59045 2.60861i 0.282092 0.204952i
\(163\) 4.97465 + 5.52491i 0.389645 + 0.432744i 0.905770 0.423769i \(-0.139293\pi\)
−0.516126 + 0.856513i \(0.672626\pi\)
\(164\) 0.933679 + 1.61718i 0.0729080 + 0.126280i
\(165\) −0.435029 0.137061i −0.0338670 0.0106702i
\(166\) 4.38647 7.59760i 0.340456 0.589688i
\(167\) −0.683275 + 2.10290i −0.0528734 + 0.162728i −0.974006 0.226520i \(-0.927265\pi\)
0.921133 + 0.389248i \(0.127265\pi\)
\(168\) 0 0
\(169\) −23.9752 17.4190i −1.84424 1.33992i
\(170\) 0.733512 + 0.155913i 0.0562578 + 0.0119580i
\(171\) −5.10653 + 5.67137i −0.390506 + 0.433701i
\(172\) −0.686792 + 6.53439i −0.0523674 + 0.498243i
\(173\) 1.08314 + 10.3054i 0.0823500 + 0.783508i 0.955288 + 0.295677i \(0.0955451\pi\)
−0.872938 + 0.487831i \(0.837788\pi\)
\(174\) 0.560385 1.72469i 0.0424827 0.130748i
\(175\) 0 0
\(176\) 2.43355 0.277797i 0.183436 0.0209398i
\(177\) 2.94587 5.10240i 0.221425 0.383520i
\(178\) 6.02431 1.28051i 0.451541 0.0959780i
\(179\) −21.3856 9.52147i −1.59843 0.711668i −0.602196 0.798348i \(-0.705707\pi\)
−0.996236 + 0.0866804i \(0.972374\pi\)
\(180\) −0.742680 + 0.330662i −0.0553561 + 0.0246461i
\(181\) −4.23851 13.0448i −0.315046 0.969611i −0.975736 0.218952i \(-0.929736\pi\)
0.660690 0.750659i \(-0.270264\pi\)
\(182\) 0 0
\(183\) 4.81471 + 3.49809i 0.355914 + 0.258587i
\(184\) 1.07565 + 10.2341i 0.0792977 + 0.754467i
\(185\) −1.23051 + 0.261552i −0.0904686 + 0.0192297i
\(186\) −1.65526 2.86700i −0.121370 0.210219i
\(187\) 5.72970 13.1851i 0.418997 0.964194i
\(188\) −8.43666 −0.615306
\(189\) 0 0
\(190\) −0.407990 + 0.296422i −0.0295987 + 0.0215047i
\(191\) −10.9853 + 4.89099i −0.794871 + 0.353899i −0.763664 0.645614i \(-0.776602\pi\)
−0.0312066 + 0.999513i \(0.509935\pi\)
\(192\) 1.27143 1.41206i 0.0917574 0.101907i
\(193\) 10.6284 11.8041i 0.765050 0.849675i −0.227210 0.973846i \(-0.572961\pi\)
0.992261 + 0.124171i \(0.0396272\pi\)
\(194\) 6.43070 2.86313i 0.461697 0.205561i
\(195\) 0.726463 0.527806i 0.0520231 0.0377970i
\(196\) 0 0
\(197\) 12.3035 0.876590 0.438295 0.898831i \(-0.355582\pi\)
0.438295 + 0.898831i \(0.355582\pi\)
\(198\) −1.46258 6.59059i −0.103941 0.468373i
\(199\) −7.63075 13.2168i −0.540929 0.936917i −0.998851 0.0479244i \(-0.984739\pi\)
0.457922 0.888993i \(-0.348594\pi\)
\(200\) 12.7835 2.71722i 0.903930 0.192136i
\(201\) −0.0821447 0.781555i −0.00579404 0.0551266i
\(202\) −12.0832 8.77892i −0.850168 0.617683i
\(203\) 0 0
\(204\) 1.15526 + 3.55553i 0.0808845 + 0.248937i
\(205\) −0.272009 + 0.121106i −0.0189979 + 0.00845841i
\(206\) −11.5335 5.13506i −0.803580 0.357777i
\(207\) −9.98198 + 2.12174i −0.693796 + 0.147471i
\(208\) −2.41106 + 4.17608i −0.167177 + 0.289559i
\(209\) 4.01114 + 8.79663i 0.277456 + 0.608476i
\(210\) 0 0
\(211\) 2.76058 8.49620i 0.190046 0.584903i −0.809952 0.586496i \(-0.800507\pi\)
0.999999 + 0.00159295i \(0.000507051\pi\)
\(212\) −0.250595 2.38425i −0.0172109 0.163751i
\(213\) 0.601394 5.72188i 0.0412068 0.392057i
\(214\) 2.80583 3.11619i 0.191803 0.213019i
\(215\) −1.02476 0.217819i −0.0698878 0.0148551i
\(216\) 7.41570 + 5.38782i 0.504574 + 0.366595i
\(217\) 0 0
\(218\) −1.29714 + 3.99220i −0.0878537 + 0.270386i
\(219\) −1.72713 + 2.99148i −0.116709 + 0.202145i
\(220\) 0.00920856 + 1.02985i 0.000620841 + 0.0694327i
\(221\) 14.1515 + 24.5112i 0.951935 + 1.64880i
\(222\) 1.81775 + 2.01881i 0.121999 + 0.135494i
\(223\) −0.578645 + 0.420410i −0.0387489 + 0.0281527i −0.606991 0.794709i \(-0.707624\pi\)
0.568242 + 0.822861i \(0.307624\pi\)
\(224\) 0 0
\(225\) 4.00503 + 12.3262i 0.267002 + 0.821747i
\(226\) −12.5453 2.66658i −0.834500 0.177378i
\(227\) 0.556261 5.29247i 0.0369203 0.351273i −0.960430 0.278522i \(-0.910155\pi\)
0.997350 0.0727512i \(-0.0231779\pi\)
\(228\) −2.29677 1.02259i −0.152107 0.0677225i
\(229\) −4.42183 4.91094i −0.292203 0.324524i 0.579113 0.815248i \(-0.303399\pi\)
−0.871315 + 0.490724i \(0.836733\pi\)
\(230\) −0.674356 −0.0444657
\(231\) 0 0
\(232\) −9.96318 −0.654115
\(233\) −6.39497 7.10233i −0.418948 0.465289i 0.496317 0.868142i \(-0.334685\pi\)
−0.915265 + 0.402852i \(0.868019\pi\)
\(234\) 12.1417 + 5.40584i 0.793729 + 0.353391i
\(235\) 0.140615 1.33786i 0.00917268 0.0872722i
\(236\) −13.0128 2.76596i −0.847062 0.180049i
\(237\) −0.865066 2.66240i −0.0561921 0.172941i
\(238\) 0 0
\(239\) −21.7194 + 15.7801i −1.40491 + 1.02073i −0.410872 + 0.911693i \(0.634776\pi\)
−0.994038 + 0.109034i \(0.965224\pi\)
\(240\) −0.0679578 0.0754747i −0.00438665 0.00487187i
\(241\) −9.43316 16.3387i −0.607643 1.05247i −0.991628 0.129129i \(-0.958782\pi\)
0.383985 0.923340i \(-0.374552\pi\)
\(242\) −8.39590 1.62826i −0.539709 0.104668i
\(243\) −6.97214 + 12.0761i −0.447263 + 0.774682i
\(244\) 4.15258 12.7803i 0.265842 0.818177i
\(245\) 0 0
\(246\) 0.520180 + 0.377933i 0.0331654 + 0.0240961i
\(247\) −18.6177 3.95732i −1.18462 0.251798i
\(248\) −12.1703 + 13.5165i −0.772815 + 0.858298i
\(249\) −0.728955 + 6.93555i −0.0461957 + 0.439522i
\(250\) 0.179941 + 1.71203i 0.0113805 + 0.108278i
\(251\) 9.07680 27.9355i 0.572923 1.76328i −0.0702229 0.997531i \(-0.522371\pi\)
0.643146 0.765744i \(-0.277629\pi\)
\(252\) 0 0
\(253\) −2.57472 + 12.6691i −0.161871 + 0.796498i
\(254\) 0.776427 1.34481i 0.0487174 0.0843810i
\(255\) −0.583080 + 0.123937i −0.0365139 + 0.00776126i
\(256\) −12.2355 5.44759i −0.764718 0.340474i
\(257\) −15.4539 + 6.88052i −0.963987 + 0.429195i −0.827512 0.561449i \(-0.810244\pi\)
−0.136476 + 0.990643i \(0.543578\pi\)
\(258\) 0.699104 + 2.15162i 0.0435243 + 0.133954i
\(259\) 0 0
\(260\) −1.64035 1.19178i −0.101730 0.0739114i
\(261\) −1.03279 9.82630i −0.0639278 0.608233i
\(262\) 1.04195 0.221473i 0.0643718 0.0136826i
\(263\) 4.09017 + 7.08438i 0.252211 + 0.436842i 0.964134 0.265415i \(-0.0855091\pi\)
−0.711923 + 0.702257i \(0.752176\pi\)
\(264\) 4.66200 2.74747i 0.286926 0.169095i
\(265\) 0.382263 0.0234822
\(266\) 0 0
\(267\) −3.96078 + 2.87768i −0.242396 + 0.176111i
\(268\) −1.62106 + 0.721741i −0.0990219 + 0.0440874i
\(269\) −4.18017 + 4.64255i −0.254869 + 0.283061i −0.856978 0.515353i \(-0.827661\pi\)
0.602109 + 0.798414i \(0.294327\pi\)
\(270\) −0.401939 + 0.446398i −0.0244612 + 0.0271669i
\(271\) 7.18675 3.19975i 0.436564 0.194371i −0.176673 0.984270i \(-0.556534\pi\)
0.613237 + 0.789899i \(0.289867\pi\)
\(272\) 2.58978 1.88159i 0.157029 0.114088i
\(273\) 0 0
\(274\) −1.94312 −0.117388
\(275\) 16.3437 + 1.57017i 0.985559 + 0.0946850i
\(276\) −1.68095 2.91149i −0.101181 0.175251i
\(277\) −11.7844 + 2.50485i −0.708055 + 0.150502i −0.547843 0.836581i \(-0.684551\pi\)
−0.160212 + 0.987083i \(0.551218\pi\)
\(278\) −0.387053 3.68256i −0.0232139 0.220865i
\(279\) −14.5924 10.6020i −0.873622 0.634724i
\(280\) 0 0
\(281\) 6.53723 + 20.1195i 0.389978 + 1.20023i 0.932804 + 0.360384i \(0.117354\pi\)
−0.542826 + 0.839846i \(0.682646\pi\)
\(282\) −2.65380 + 1.18155i −0.158032 + 0.0703603i
\(283\) −22.8417 10.1698i −1.35780 0.604531i −0.406741 0.913544i \(-0.633335\pi\)
−0.951058 + 0.309013i \(0.900001\pi\)
\(284\) −12.7073 + 2.70101i −0.754037 + 0.160275i
\(285\) 0.200439 0.347171i 0.0118730 0.0205646i
\(286\) 12.4113 11.3777i 0.733894 0.672780i
\(287\) 0 0
\(288\) 4.73607 14.5761i 0.279075 0.858906i
\(289\) −0.186988 1.77908i −0.0109993 0.104652i
\(290\) 0.0682476 0.649333i 0.00400764 0.0381301i
\(291\) −3.74420 + 4.15836i −0.219489 + 0.243767i
\(292\) 7.62927 + 1.62165i 0.446469 + 0.0948999i
\(293\) 0.368173 + 0.267494i 0.0215089 + 0.0156271i 0.598488 0.801132i \(-0.295769\pi\)
−0.576979 + 0.816759i \(0.695769\pi\)
\(294\) 0 0
\(295\) 0.655503 2.01743i 0.0381648 0.117459i
\(296\) 7.46253 12.9255i 0.433751 0.751278i
\(297\) 6.85183 + 9.25556i 0.397584 + 0.537062i
\(298\) −2.81055 4.86801i −0.162811 0.281996i
\(299\) −17.0306 18.9144i −0.984907 1.09385i
\(300\) −3.45425 + 2.50966i −0.199431 + 0.144895i
\(301\) 0 0
\(302\) −1.95561 6.01874i −0.112533 0.346339i
\(303\) 11.6131 + 2.46844i 0.667155 + 0.141808i
\(304\) −0.225024 + 2.14096i −0.0129060 + 0.122793i
\(305\) 1.95745 + 0.871514i 0.112083 + 0.0499028i
\(306\) −5.90375 6.55678i −0.337495 0.374826i
\(307\) −8.03578 −0.458626 −0.229313 0.973353i \(-0.573648\pi\)
−0.229313 + 0.973353i \(0.573648\pi\)
\(308\) 0 0
\(309\) 10.0358 0.570918
\(310\) −0.797547 0.885765i −0.0452976 0.0503081i
\(311\) 0.125124 + 0.0557086i 0.00709511 + 0.00315894i 0.410281 0.911959i \(-0.365431\pi\)
−0.403186 + 0.915118i \(0.632097\pi\)
\(312\) −1.11360 + 10.5952i −0.0630449 + 0.599832i
\(313\) 14.9558 + 3.17896i 0.845352 + 0.179685i 0.610174 0.792267i \(-0.291099\pi\)
0.235178 + 0.971952i \(0.424433\pi\)
\(314\) −4.84150 14.9006i −0.273221 0.840889i
\(315\) 0 0
\(316\) −5.11385 + 3.71543i −0.287676 + 0.209009i
\(317\) −22.0763 24.5182i −1.23993 1.37708i −0.899565 0.436787i \(-0.856116\pi\)
−0.340364 0.940294i \(-0.610550\pi\)
\(318\) −0.412739 0.714885i −0.0231453 0.0400888i
\(319\) −11.9384 3.76134i −0.668421 0.210595i
\(320\) 0.342058 0.592461i 0.0191216 0.0331196i
\(321\) −1.03004 + 3.17014i −0.0574912 + 0.176940i
\(322\) 0 0
\(323\) 10.2223 + 7.42692i 0.568783 + 0.413245i
\(324\) 7.79183 + 1.65620i 0.432879 + 0.0920113i
\(325\) −21.6293 + 24.0217i −1.19978 + 1.33249i
\(326\) 0.604196 5.74854i 0.0334633 0.318382i
\(327\) −0.348788 3.31850i −0.0192880 0.183513i
\(328\) 1.09162 3.35966i 0.0602747 0.185506i
\(329\) 0 0
\(330\) 0.147127 + 0.322657i 0.00809908 + 0.0177617i
\(331\) −14.7667 + 25.5767i −0.811653 + 1.40582i 0.100054 + 0.994982i \(0.468099\pi\)
−0.911707 + 0.410842i \(0.865235\pi\)
\(332\) 15.4026 3.27392i 0.845327 0.179680i
\(333\) 13.5215 + 6.02015i 0.740972 + 0.329902i
\(334\) 1.57049 0.699227i 0.0859333 0.0382600i
\(335\) −0.0874331 0.269091i −0.00477698 0.0147020i
\(336\) 0 0
\(337\) −4.55497 3.30938i −0.248125 0.180273i 0.456770 0.889585i \(-0.349006\pi\)
−0.704895 + 0.709311i \(0.749006\pi\)
\(338\) 2.40841 + 22.9145i 0.131000 + 1.24638i
\(339\) 9.97244 2.11971i 0.541628 0.115127i
\(340\) 0.673002 + 1.16567i 0.0364987 + 0.0632176i
\(341\) −19.6859 + 11.6016i −1.06605 + 0.628260i
\(342\) 5.93344 0.320844
\(343\) 0 0
\(344\) 10.0557 7.30586i 0.542165 0.393906i
\(345\) 0.489712 0.218034i 0.0263652 0.0117385i
\(346\) 5.39081 5.98711i 0.289812 0.321869i
\(347\) 5.84192 6.48811i 0.313611 0.348300i −0.565646 0.824648i \(-0.691373\pi\)
0.879257 + 0.476348i \(0.158040\pi\)
\(348\) 2.97357 1.32392i 0.159400 0.0709695i
\(349\) −14.9401 + 10.8546i −0.799724 + 0.581034i −0.910833 0.412774i \(-0.864560\pi\)
0.111109 + 0.993808i \(0.464560\pi\)
\(350\) 0 0
\(351\) −22.6715 −1.21011
\(352\) −14.5444 12.8622i −0.775218 0.685558i
\(353\) 11.7428 + 20.3392i 0.625009 + 1.08255i 0.988539 + 0.150964i \(0.0482379\pi\)
−0.363531 + 0.931582i \(0.618429\pi\)
\(354\) −4.48064 + 0.952389i −0.238143 + 0.0506189i
\(355\) −0.216525 2.06009i −0.0114919 0.109338i
\(356\) 8.94343 + 6.49778i 0.474001 + 0.344382i
\(357\) 0 0
\(358\) 5.62425 + 17.3097i 0.297251 + 0.914844i
\(359\) 13.5947 6.05273i 0.717499 0.319451i −0.0153128 0.999883i \(-0.504874\pi\)
0.732811 + 0.680432i \(0.238208\pi\)
\(360\) 1.40496 + 0.625528i 0.0740479 + 0.0329682i
\(361\) 10.2732 2.18364i 0.540696 0.114929i
\(362\) −5.33203 + 9.23534i −0.280245 + 0.485399i
\(363\) 6.62347 1.53215i 0.347642 0.0804168i
\(364\) 0 0
\(365\) −0.384314 + 1.18280i −0.0201159 + 0.0619104i
\(366\) −0.483659 4.60170i −0.0252812 0.240535i
\(367\) 3.57758 34.0384i 0.186748 1.77679i −0.353646 0.935379i \(-0.615058\pi\)
0.540394 0.841412i \(-0.318275\pi\)
\(368\) −1.92621 + 2.13927i −0.100410 + 0.111517i
\(369\) 3.42666 + 0.728360i 0.178385 + 0.0379169i
\(370\) 0.791277 + 0.574896i 0.0411365 + 0.0298874i
\(371\) 0 0
\(372\) 1.83621 5.65128i 0.0952032 0.293005i
\(373\) −1.50870 + 2.61314i −0.0781173 + 0.135303i −0.902438 0.430820i \(-0.858224\pi\)
0.824320 + 0.566124i \(0.191558\pi\)
\(374\) −10.5990 + 3.54890i −0.548060 + 0.183509i
\(375\) −0.684207 1.18508i −0.0353323 0.0611973i
\(376\) 10.6793 + 11.8606i 0.550744 + 0.611663i
\(377\) 19.9361 14.4845i 1.02676 0.745987i
\(378\) 0 0
\(379\) −1.89252 5.82457i −0.0972121 0.299188i 0.890612 0.454764i \(-0.150277\pi\)
−0.987824 + 0.155576i \(0.950277\pi\)
\(380\) −0.885401 0.188198i −0.0454201 0.00965435i
\(381\) −0.129029 + 1.22763i −0.00661034 + 0.0628932i
\(382\) 8.54092 + 3.80266i 0.436992 + 0.194561i
\(383\) 2.93814 + 3.26314i 0.150132 + 0.166738i 0.813520 0.581537i \(-0.197549\pi\)
−0.663388 + 0.748276i \(0.730882\pi\)
\(384\) 5.75876 0.293875
\(385\) 0 0
\(386\) −12.3495 −0.628573
\(387\) 8.24786 + 9.16018i 0.419262 + 0.465638i
\(388\) 11.5426 + 5.13908i 0.585984 + 0.260897i
\(389\) −1.09713 + 10.4385i −0.0556268 + 0.529253i 0.930856 + 0.365387i \(0.119063\pi\)
−0.986483 + 0.163866i \(0.947603\pi\)
\(390\) −0.682892 0.145153i −0.0345796 0.00735012i
\(391\) 5.22119 + 16.0692i 0.264047 + 0.812654i
\(392\) 0 0
\(393\) −0.685047 + 0.497716i −0.0345560 + 0.0251064i
\(394\) −6.40077 7.10878i −0.322466 0.358135i
\(395\) −0.503947 0.872863i −0.0253563 0.0439185i
\(396\) 7.03445 9.86642i 0.353495 0.495806i
\(397\) −5.69441 + 9.86301i −0.285794 + 0.495010i −0.972801 0.231640i \(-0.925591\pi\)
0.687007 + 0.726651i \(0.258924\pi\)
\(398\) −3.66666 + 11.2848i −0.183793 + 0.565657i
\(399\) 0 0
\(400\) 2.95774 + 2.14893i 0.147887 + 0.107446i
\(401\) 4.62170 + 0.982373i 0.230797 + 0.0490574i 0.321858 0.946788i \(-0.395693\pi\)
−0.0910613 + 0.995845i \(0.529026\pi\)
\(402\) −0.408835 + 0.454057i −0.0203908 + 0.0226463i
\(403\) 4.70230 44.7394i 0.234238 2.22863i
\(404\) −2.80221 26.6613i −0.139415 1.32645i
\(405\) −0.392503 + 1.20800i −0.0195036 + 0.0600260i
\(406\) 0 0
\(407\) 13.8217 12.6707i 0.685114 0.628062i
\(408\) 3.53615 6.12479i 0.175065 0.303222i
\(409\) −2.41156 + 0.512594i −0.119244 + 0.0253461i −0.267147 0.963656i \(-0.586081\pi\)
0.147903 + 0.989002i \(0.452748\pi\)
\(410\) 0.211482 + 0.0941581i 0.0104444 + 0.00465014i
\(411\) 1.41108 0.628252i 0.0696033 0.0309894i
\(412\) −7.00259 21.5518i −0.344993 1.06178i
\(413\) 0 0
\(414\) 6.41892 + 4.66362i 0.315472 + 0.229204i
\(415\) 0.262452 + 2.49706i 0.0128832 + 0.122576i
\(416\) 37.3893 7.94734i 1.83316 0.389651i
\(417\) 1.47172 + 2.54910i 0.0720706 + 0.124830i
\(418\) 2.99580 6.89391i 0.146529 0.337192i
\(419\) −14.3399 −0.700548 −0.350274 0.936647i \(-0.613912\pi\)
−0.350274 + 0.936647i \(0.613912\pi\)
\(420\) 0 0
\(421\) 14.0087 10.1779i 0.682744 0.496043i −0.191523 0.981488i \(-0.561343\pi\)
0.874267 + 0.485446i \(0.161343\pi\)
\(422\) −6.34513 + 2.82503i −0.308876 + 0.137520i
\(423\) −10.5906 + 11.7621i −0.514933 + 0.571891i
\(424\) −3.03466 + 3.37033i −0.147376 + 0.163678i
\(425\) 19.6033 8.72794i 0.950898 0.423367i
\(426\) −3.61887 + 2.62927i −0.175335 + 0.127388i
\(427\) 0 0
\(428\) 7.52653 0.363808
\(429\) −5.33429 + 12.2752i −0.257542 + 0.592654i
\(430\) 0.407266 + 0.705405i 0.0196401 + 0.0340176i
\(431\) −27.2828 + 5.79914i −1.31417 + 0.279335i −0.811097 0.584912i \(-0.801129\pi\)
−0.503069 + 0.864246i \(0.667796\pi\)
\(432\) 0.268032 + 2.55015i 0.0128957 + 0.122694i
\(433\) 23.9040 + 17.3673i 1.14875 + 0.834619i 0.988315 0.152426i \(-0.0487087\pi\)
0.160440 + 0.987046i \(0.448709\pi\)
\(434\) 0 0
\(435\) 0.160382 + 0.493605i 0.00768973 + 0.0236666i
\(436\) −6.88304 + 3.06453i −0.329638 + 0.146764i
\(437\) −10.3802 4.62157i −0.496554 0.221080i
\(438\) 2.62695 0.558375i 0.125520 0.0266802i
\(439\) 16.8328 29.1552i 0.803384 1.39150i −0.113992 0.993482i \(-0.536364\pi\)
0.917376 0.398021i \(-0.130303\pi\)
\(440\) 1.43615 1.31656i 0.0684658 0.0627644i
\(441\) 0 0
\(442\) 6.79997 20.9282i 0.323442 0.995451i
\(443\) −1.07944 10.2701i −0.0512856 0.487949i −0.989775 0.142640i \(-0.954441\pi\)
0.938489 0.345309i \(-0.112226\pi\)
\(444\) −0.509684 + 4.84932i −0.0241885 + 0.230138i
\(445\) −1.17946 + 1.30992i −0.0559117 + 0.0620962i
\(446\) 0.543939 + 0.115618i 0.0257563 + 0.00547466i
\(447\) 3.61493 + 2.62640i 0.170980 + 0.124224i
\(448\) 0 0
\(449\) −0.852224 + 2.62287i −0.0402189 + 0.123781i −0.969150 0.246471i \(-0.920729\pi\)
0.928931 + 0.370253i \(0.120729\pi\)
\(450\) 5.03831 8.72661i 0.237508 0.411376i
\(451\) 2.57639 3.61361i 0.121317 0.170158i
\(452\) −11.5104 19.9366i −0.541403 0.937738i
\(453\) 3.36613 + 3.73847i 0.158155 + 0.175648i
\(454\) −3.34729 + 2.43195i −0.157096 + 0.114137i
\(455\) 0 0
\(456\) 1.46971 + 4.52331i 0.0688255 + 0.211823i
\(457\) 39.4492 + 8.38518i 1.84535 + 0.392242i 0.991697 0.128593i \(-0.0410460\pi\)
0.853657 + 0.520835i \(0.174379\pi\)
\(458\) −0.537053 + 5.10972i −0.0250949 + 0.238762i
\(459\) 13.7492 + 6.12154i 0.641757 + 0.285729i
\(460\) −0.809924 0.899512i −0.0377629 0.0419400i
\(461\) −34.2251 −1.59402 −0.797011 0.603965i \(-0.793587\pi\)
−0.797011 + 0.603965i \(0.793587\pi\)
\(462\) 0 0
\(463\) 0.707349 0.0328733 0.0164367 0.999865i \(-0.494768\pi\)
0.0164367 + 0.999865i \(0.494768\pi\)
\(464\) −1.86495 2.07123i −0.0865780 0.0961546i
\(465\) 0.865558 + 0.385371i 0.0401393 + 0.0178712i
\(466\) −0.776701 + 7.38981i −0.0359800 + 0.342326i
\(467\) 27.9676 + 5.94470i 1.29419 + 0.275088i 0.803007 0.595970i \(-0.203232\pi\)
0.491180 + 0.871058i \(0.336566\pi\)
\(468\) 7.37184 + 22.6882i 0.340764 + 1.04876i
\(469\) 0 0
\(470\) −0.846145 + 0.614760i −0.0390298 + 0.0283568i
\(471\) 8.33353 + 9.25532i 0.383989 + 0.426463i
\(472\) 12.5834 + 21.7951i 0.579199 + 1.00320i
\(473\) 14.8073 4.95800i 0.680842 0.227969i
\(474\) −1.08825 + 1.88490i −0.0499850 + 0.0865765i
\(475\) −4.45933 + 13.7244i −0.204608 + 0.629719i
\(476\) 0 0
\(477\) −3.63860 2.64360i −0.166600 0.121042i
\(478\) 20.4167 + 4.33971i 0.933839 + 0.198494i
\(479\) −3.41067 + 3.78793i −0.155837 + 0.173075i −0.816008 0.578041i \(-0.803817\pi\)
0.660170 + 0.751116i \(0.270484\pi\)
\(480\) −0.0841527 + 0.800659i −0.00384103 + 0.0365449i
\(481\) 3.85865 + 36.7126i 0.175940 + 1.67395i
\(482\) −4.53274 + 13.9503i −0.206461 + 0.635421i
\(483\) 0 0
\(484\) −7.91185 13.1547i −0.359629 0.597942i
\(485\) −1.00732 + 1.74473i −0.0457400 + 0.0792240i
\(486\) 10.6045 2.25406i 0.481032 0.102246i
\(487\) 26.6648 + 11.8719i 1.20830 + 0.537969i 0.909243 0.416266i \(-0.136662\pi\)
0.299056 + 0.954236i \(0.403328\pi\)
\(488\) −23.2235 + 10.3398i −1.05128 + 0.468060i
\(489\) 1.41986 + 4.36989i 0.0642084 + 0.197613i
\(490\) 0 0
\(491\) −24.3870 17.7182i −1.10057 0.799610i −0.119416 0.992844i \(-0.538102\pi\)
−0.981153 + 0.193235i \(0.938102\pi\)
\(492\) 0.120635 + 1.14777i 0.00543866 + 0.0517454i
\(493\) −16.0013 + 3.40118i −0.720662 + 0.153182i
\(494\) 7.39919 + 12.8158i 0.332905 + 0.576609i
\(495\) 1.44734 + 1.27995i 0.0650532 + 0.0575293i
\(496\) −5.08801 −0.228458
\(497\) 0 0
\(498\) 4.38647 3.18696i 0.196563 0.142811i
\(499\) 5.43655 2.42051i 0.243373 0.108357i −0.281425 0.959583i \(-0.590807\pi\)
0.524799 + 0.851226i \(0.324141\pi\)
\(500\) −2.06753 + 2.29622i −0.0924627 + 0.102690i
\(501\) −0.914400 + 1.01554i −0.0408524 + 0.0453712i
\(502\) −20.8628 + 9.28871i −0.931152 + 0.414576i
\(503\) 4.02773 2.92632i 0.179588 0.130478i −0.494360 0.869257i \(-0.664597\pi\)
0.673947 + 0.738779i \(0.264597\pi\)
\(504\) 0 0
\(505\) 4.27456 0.190216
\(506\) 8.65945 5.10331i 0.384960 0.226870i
\(507\) −9.15770 15.8616i −0.406708 0.704439i
\(508\) 2.72633 0.579500i 0.120962 0.0257112i
\(509\) 2.22944 + 21.2117i 0.0988181 + 0.940191i 0.925813 + 0.377982i \(0.123382\pi\)
−0.826995 + 0.562209i \(0.809951\pi\)
\(510\) 0.374949 + 0.272417i 0.0166030 + 0.0120628i
\(511\) 0 0
\(512\) −2.54091 7.82012i −0.112293 0.345604i
\(513\) −9.24627 + 4.11670i −0.408233 + 0.181757i
\(514\) 12.0152 + 5.34949i 0.529966 + 0.235956i
\(515\) 3.53432 0.751243i 0.155741 0.0331037i
\(516\) −2.03036 + 3.51669i −0.0893816 + 0.154814i
\(517\) 8.31884 + 18.2436i 0.365862 + 0.802354i
\(518\) 0 0
\(519\) −1.97900 + 6.09075i −0.0868686 + 0.267354i
\(520\) 0.400937 + 3.81466i 0.0175822 + 0.167284i
\(521\) 2.31409 22.0171i 0.101382 0.964585i −0.819060 0.573707i \(-0.805505\pi\)
0.920442 0.390878i \(-0.127829\pi\)
\(522\) −5.14018 + 5.70875i −0.224980 + 0.249865i
\(523\) −4.80414 1.02115i −0.210070 0.0446518i 0.101674 0.994818i \(-0.467580\pi\)
−0.311745 + 0.950166i \(0.600913\pi\)
\(524\) 1.54683 + 1.12384i 0.0675737 + 0.0490952i
\(525\) 0 0
\(526\) 1.96537 6.04880i 0.0856944 0.263740i
\(527\) −14.9318 + 25.8627i −0.650441 + 1.12660i
\(528\) 1.44382 + 0.454893i 0.0628341 + 0.0197967i
\(529\) 3.90296 + 6.76013i 0.169694 + 0.293919i
\(530\) −0.198868 0.220865i −0.00863828 0.00959378i
\(531\) −20.1913 + 14.6698i −0.876228 + 0.636617i
\(532\) 0 0
\(533\) 2.69996 + 8.30962i 0.116948 + 0.359929i
\(534\) 3.72323 + 0.791396i 0.161120 + 0.0342471i
\(535\) −0.125445 + 1.19353i −0.00542347 + 0.0516009i
\(536\) 3.06662 + 1.36535i 0.132458 + 0.0589741i
\(537\) −9.68086 10.7517i −0.417760 0.463969i
\(538\) 4.85707 0.209403
\(539\) 0 0
\(540\) −1.07818 −0.0463977
\(541\) 12.9707 + 14.4055i 0.557656 + 0.619340i 0.954379 0.298599i \(-0.0965193\pi\)
−0.396723 + 0.917938i \(0.629853\pi\)
\(542\) −5.58758 2.48775i −0.240007 0.106858i
\(543\) 0.886089 8.43058i 0.0380257 0.361791i
\(544\) −24.8208 5.27582i −1.06418 0.226199i
\(545\) −0.371242 1.14257i −0.0159023 0.0489422i
\(546\) 0 0
\(547\) −11.6904 + 8.49354i −0.499843 + 0.363158i −0.808957 0.587868i \(-0.799968\pi\)
0.309114 + 0.951025i \(0.399968\pi\)
\(548\) −2.33375 2.59189i −0.0996929 0.110720i
\(549\) −12.6051 21.8326i −0.537972 0.931794i
\(550\) −7.59538 10.2600i −0.323868 0.437486i
\(551\) 5.50060 9.52732i 0.234333 0.405877i
\(552\) −1.96530 + 6.04858i −0.0836489 + 0.257445i
\(553\) 0 0
\(554\) 7.57795 + 5.50570i 0.321956 + 0.233915i
\(555\) −0.760494 0.161648i −0.0322812 0.00686158i
\(556\) 4.44724 4.93916i 0.188605 0.209467i
\(557\) −1.93073 + 18.3696i −0.0818075 + 0.778347i 0.874311 + 0.485366i \(0.161314\pi\)
−0.956118 + 0.292980i \(0.905353\pi\)
\(558\) 1.46587 + 13.9468i 0.0620551 + 0.590414i
\(559\) −9.49993 + 29.2378i −0.401804 + 1.23663i
\(560\) 0 0
\(561\) 6.54945 6.00405i 0.276518 0.253491i
\(562\) 8.22381 14.2441i 0.346900 0.600849i
\(563\) −30.6002 + 6.50428i −1.28965 + 0.274123i −0.801160 0.598450i \(-0.795784\pi\)
−0.488485 + 0.872572i \(0.662450\pi\)
\(564\) −4.76335 2.12078i −0.200573 0.0893010i
\(565\) 3.35332 1.49300i 0.141075 0.0628108i
\(566\) 6.00720 + 18.4883i 0.252502 + 0.777120i
\(567\) 0 0
\(568\) 19.8823 + 14.4454i 0.834244 + 0.606114i
\(569\) −0.181467 1.72654i −0.00760748 0.0723803i 0.990059 0.140649i \(-0.0449190\pi\)
−0.997667 + 0.0682691i \(0.978252\pi\)
\(570\) −0.304866 + 0.0648012i −0.0127694 + 0.00271422i
\(571\) −6.26546 10.8521i −0.262201 0.454146i 0.704625 0.709580i \(-0.251115\pi\)
−0.966827 + 0.255433i \(0.917782\pi\)
\(572\) 30.0829 + 2.89013i 1.25783 + 0.120843i
\(573\) −7.43182 −0.310469
\(574\) 0 0
\(575\) −15.6114 + 11.3424i −0.651042 + 0.473009i
\(576\) −7.35316 + 3.27384i −0.306382 + 0.136410i
\(577\) 13.5095 15.0038i 0.562407 0.624617i −0.393131 0.919482i \(-0.628608\pi\)
0.955539 + 0.294866i \(0.0952749\pi\)
\(578\) −0.930642 + 1.03358i −0.0387096 + 0.0429914i
\(579\) 8.96810 3.99285i 0.372701 0.165937i
\(580\) 0.948101 0.688835i 0.0393677 0.0286023i
\(581\) 0 0
\(582\) 4.35051 0.180334
\(583\) −4.90867 + 2.89285i −0.203296 + 0.119809i
\(584\) −7.37752 12.7782i −0.305284 0.528768i
\(585\) −3.72069 + 0.790857i −0.153832 + 0.0326979i
\(586\) −0.0369846 0.351885i −0.00152782 0.0145362i
\(587\) 0.00677611 + 0.00492314i 0.000279680 + 0.000203200i 0.587925 0.808915i \(-0.299945\pi\)
−0.587645 + 0.809119i \(0.699945\pi\)
\(588\) 0 0
\(589\) −6.20604 19.1002i −0.255716 0.787012i
\(590\) −1.50666 + 0.670806i −0.0620280 + 0.0276167i
\(591\) 6.94660 + 3.09283i 0.285745 + 0.127222i
\(592\) 4.08393 0.868065i 0.167848 0.0356773i
\(593\) 0.219649 0.380443i 0.00901989 0.0156229i −0.861480 0.507791i \(-0.830462\pi\)
0.870500 + 0.492168i \(0.163796\pi\)
\(594\) 1.78312 8.77397i 0.0731624 0.360001i
\(595\) 0 0
\(596\) 3.11779 9.59558i 0.127710 0.393050i
\(597\) −0.985925 9.38045i −0.0403512 0.383916i
\(598\) −2.06846 + 19.6800i −0.0845854 + 0.804777i
\(599\) 30.2222 33.5651i 1.23485 1.37143i 0.330968 0.943642i \(-0.392625\pi\)
0.903877 0.427793i \(-0.140709\pi\)
\(600\) 7.90064 + 1.67933i 0.322542 + 0.0685585i
\(601\) −9.01541 6.55008i −0.367746 0.267183i 0.388529 0.921436i \(-0.372983\pi\)
−0.756276 + 0.654253i \(0.772983\pi\)
\(602\) 0 0
\(603\) −1.02870 + 3.16603i −0.0418921 + 0.128931i
\(604\) 5.67954 9.83725i 0.231097 0.400272i
\(605\) 2.21790 1.03538i 0.0901705 0.0420943i
\(606\) −4.61535 7.99403i −0.187486 0.324735i
\(607\) −23.8878 26.5301i −0.969576 1.07682i −0.997016 0.0772000i \(-0.975402\pi\)
0.0274394 0.999623i \(-0.491265\pi\)
\(608\) 13.8057 10.0304i 0.559894 0.406787i
\(609\) 0 0
\(610\) −0.514796 1.58438i −0.0208435 0.0641496i
\(611\) −38.6120 8.20723i −1.56207 0.332029i
\(612\) 1.65537 15.7498i 0.0669145 0.636649i
\(613\) 15.7111 + 6.99505i 0.634567 + 0.282528i 0.698701 0.715414i \(-0.253762\pi\)
−0.0641337 + 0.997941i \(0.520428\pi\)
\(614\) 4.18052 + 4.64294i 0.168712 + 0.187374i
\(615\) −0.184020 −0.00742040
\(616\) 0 0
\(617\) −16.8852 −0.679774 −0.339887 0.940466i \(-0.610389\pi\)
−0.339887 + 0.940466i \(0.610389\pi\)
\(618\) −5.22102 5.79853i −0.210020 0.233251i
\(619\) 28.3831 + 12.6370i 1.14081 + 0.507924i 0.888115 0.459621i \(-0.152015\pi\)
0.252700 + 0.967545i \(0.418681\pi\)
\(620\) 0.223627 2.12767i 0.00898107 0.0854491i
\(621\) −13.2385 2.81393i −0.531242 0.112919i
\(622\) −0.0329066 0.101276i −0.00131943 0.00406080i
\(623\) 0 0
\(624\) −2.41106 + 1.75174i −0.0965196 + 0.0701256i
\(625\) 16.2329 + 18.0285i 0.649318 + 0.721140i
\(626\) −5.94384 10.2950i −0.237564 0.411472i
\(627\) 0.0534253 + 5.97490i 0.00213360 + 0.238615i
\(628\) 14.0608 24.3541i 0.561088 0.971834i
\(629\) 7.57271 23.3064i 0.301944 0.929287i
\(630\) 0 0
\(631\) −5.86832 4.26359i −0.233614 0.169731i 0.464819 0.885406i \(-0.346119\pi\)
−0.698434 + 0.715675i \(0.746119\pi\)
\(632\) 11.6965 + 2.48617i 0.465262 + 0.0988946i
\(633\) 3.69438 4.10303i 0.146839 0.163081i
\(634\) −2.68128 + 25.5106i −0.106487 + 1.01316i
\(635\) 0.0464552 + 0.441992i 0.00184352 + 0.0175399i
\(636\) 0.457859 1.40915i 0.0181553 0.0558763i
\(637\) 0 0
\(638\) 4.03757 + 8.85460i 0.159849 + 0.350557i
\(639\) −12.1859 + 21.1066i −0.482066 + 0.834963i
\(640\) 2.02806 0.431078i 0.0801662 0.0170399i
\(641\) −18.9560 8.43974i −0.748716 0.333350i −0.00334027 0.999994i \(-0.501063\pi\)
−0.745376 + 0.666645i \(0.767730\pi\)
\(642\) 2.36752 1.05409i 0.0934385 0.0416015i
\(643\) 2.19750 + 6.76322i 0.0866611 + 0.266715i 0.984991 0.172606i \(-0.0552188\pi\)
−0.898330 + 0.439322i \(0.855219\pi\)
\(644\) 0 0
\(645\) −0.523825 0.380581i −0.0206256 0.0149854i
\(646\) −1.02687 9.77003i −0.0404017 0.384397i
\(647\) −26.9762 + 5.73397i −1.06054 + 0.225426i −0.704981 0.709226i \(-0.749044\pi\)
−0.355564 + 0.934652i \(0.615711\pi\)
\(648\) −7.53472 13.0505i −0.295992 0.512673i
\(649\) 6.84991 + 30.8666i 0.268883 + 1.21162i
\(650\) 25.1317 0.985748
\(651\) 0 0
\(652\) 8.39353 6.09826i 0.328716 0.238826i
\(653\) 14.7575 6.57048i 0.577507 0.257123i −0.0971307 0.995272i \(-0.530966\pi\)
0.674638 + 0.738149i \(0.264300\pi\)
\(654\) −1.73592 + 1.92793i −0.0678798 + 0.0753881i
\(655\) −0.203996 + 0.226561i −0.00797079 + 0.00885246i
\(656\) 0.902770 0.401939i 0.0352472 0.0156931i
\(657\) 11.8379 8.60076i 0.461842 0.335548i
\(658\) 0 0
\(659\) −13.2085 −0.514531 −0.257266 0.966341i \(-0.582822\pi\)
−0.257266 + 0.966341i \(0.582822\pi\)
\(660\) −0.253682 + 0.583772i −0.00987457 + 0.0227233i
\(661\) 2.45330 + 4.24924i 0.0954223 + 0.165276i 0.909785 0.415080i \(-0.136247\pi\)
−0.814362 + 0.580357i \(0.802913\pi\)
\(662\) 22.4600 4.77403i 0.872934 0.185548i
\(663\) 1.82844 + 17.3964i 0.0710106 + 0.675621i
\(664\) −24.0996 17.5094i −0.935245 0.679495i
\(665\) 0 0
\(666\) −3.55605 10.9444i −0.137794 0.424087i
\(667\) 13.4390 5.98344i 0.520361 0.231680i
\(668\) 2.81889 + 1.25505i 0.109066 + 0.0485595i
\(669\) −0.432385 + 0.0919064i −0.0167170 + 0.00355331i
\(670\) −0.109991 + 0.190509i −0.00424930 + 0.00736001i
\(671\) −31.7311 + 3.62221i −1.22497 + 0.139834i
\(672\) 0 0
\(673\) −9.26654 + 28.5195i −0.357199 + 1.09935i 0.597524 + 0.801851i \(0.296151\pi\)
−0.954723 + 0.297495i \(0.903849\pi\)
\(674\) 0.457566 + 4.35345i 0.0176248 + 0.167689i
\(675\) −1.79671 + 17.0946i −0.0691556 + 0.657972i
\(676\) −27.6726 + 30.7336i −1.06433 + 1.18206i
\(677\) −12.3138 2.61739i −0.473259 0.100594i −0.0348934 0.999391i \(-0.511109\pi\)
−0.438366 + 0.898797i \(0.644442\pi\)
\(678\) −6.41278 4.65916i −0.246281 0.178934i
\(679\) 0 0
\(680\) 0.786849 2.42167i 0.0301743 0.0928668i
\(681\) 1.64447 2.84831i 0.0630163 0.109147i
\(682\) 16.9445 + 5.33859i 0.648840 + 0.204425i
\(683\) 14.2671 + 24.7114i 0.545916 + 0.945554i 0.998549 + 0.0538567i \(0.0171514\pi\)
−0.452633 + 0.891697i \(0.649515\pi\)
\(684\) 7.12625 + 7.91451i 0.272479 + 0.302619i
\(685\) 0.449911 0.326879i 0.0171902 0.0124894i
\(686\) 0 0
\(687\) −1.26208 3.88427i −0.0481513 0.148194i
\(688\) 3.40106 + 0.722918i 0.129664 + 0.0275610i
\(689\) 1.17252 11.1558i 0.0446693 0.425000i
\(690\) −0.380743 0.169518i −0.0144946 0.00645343i
\(691\) 16.9787 + 18.8567i 0.645899 + 0.717344i 0.973810 0.227365i \(-0.0730111\pi\)
−0.327910 + 0.944709i \(0.606344\pi\)
\(692\) 14.4606 0.549711
\(693\) 0 0
\(694\) −6.78791 −0.257666
\(695\) 0.709113 + 0.787550i 0.0268982 + 0.0298735i
\(696\) −5.62524 2.50452i −0.213224 0.0949334i
\(697\) 0.606285 5.76842i 0.0229647 0.218494i
\(698\) 14.0440 + 2.98515i 0.531574 + 0.112990i
\(699\) −1.82525 5.61754i −0.0690373 0.212475i
\(700\) 0 0
\(701\) 36.9738 26.8630i 1.39648 1.01460i 0.401363 0.915919i \(-0.368537\pi\)
0.995119 0.0986843i \(-0.0314634\pi\)
\(702\) 11.7946 + 13.0992i 0.445157 + 0.494397i
\(703\) 8.24002 + 14.2721i 0.310778 + 0.538283i
\(704\) 0.0911725 + 10.1964i 0.00343619 + 0.384292i
\(705\) 0.415698 0.720010i 0.0156561 0.0271171i
\(706\) 5.64257 17.3661i 0.212361 0.653580i
\(707\) 0 0
\(708\) −6.65177 4.83279i −0.249989 0.181627i
\(709\) −37.6884 8.01092i −1.41542 0.300856i −0.564187 0.825647i \(-0.690810\pi\)
−0.851231 + 0.524791i \(0.824144\pi\)
\(710\) −1.07764 + 1.19684i −0.0404432 + 0.0449168i
\(711\) −1.23955 + 11.7935i −0.0464868 + 0.442292i
\(712\) −2.18597 20.7981i −0.0819225 0.779441i
\(713\) 8.29874 25.5409i 0.310790 0.956515i
\(714\) 0 0
\(715\) −0.959703 + 4.72228i −0.0358908 + 0.176603i
\(716\) −16.3341 + 28.2915i −0.610435 + 1.05730i
\(717\) −16.2296 + 3.44970i −0.606104 + 0.128831i
\(718\) −10.5696 4.70590i −0.394455 0.175623i
\(719\) 5.20915 2.31926i 0.194269 0.0864939i −0.307297 0.951614i \(-0.599424\pi\)
0.501565 + 0.865120i \(0.332758\pi\)
\(720\) 0.132945 + 0.409164i 0.00495458 + 0.0152486i
\(721\) 0 0
\(722\) −6.60620 4.79969i −0.245857 0.178626i
\(723\) −1.21880 11.5962i −0.0453278 0.431266i
\(724\) −18.7228 + 3.97965i −0.695827 + 0.147903i
\(725\) −9.34154 16.1800i −0.346936 0.600911i
\(726\) −4.33104 3.02985i −0.160740 0.112448i
\(727\) 11.8221 0.438458 0.219229 0.975673i \(-0.429646\pi\)
0.219229 + 0.975673i \(0.429646\pi\)
\(728\) 0 0
\(729\) 6.88197 5.00004i 0.254888 0.185187i
\(730\) 0.883335 0.393286i 0.0326937 0.0145562i
\(731\) 13.6558 15.1663i 0.505077 0.560945i
\(732\) 5.55724 6.17194i 0.205401 0.228121i
\(733\) 8.05010 3.58413i 0.297337 0.132383i −0.252646 0.967559i \(-0.581301\pi\)
0.549983 + 0.835176i \(0.314634\pi\)
\(734\) −21.5280 + 15.6410i −0.794614 + 0.577321i
\(735\) 0 0
\(736\) 22.8190 0.841121
\(737\) 3.15913 + 2.79375i 0.116368 + 0.102909i
\(738\) −1.36185 2.35879i −0.0501303 0.0868283i
\(739\) −0.470302 + 0.0999658i −0.0173003 + 0.00367730i −0.216554 0.976271i \(-0.569482\pi\)
0.199253 + 0.979948i \(0.436148\pi\)
\(740\) 0.183506 + 1.74594i 0.00674580 + 0.0641820i
\(741\) −9.51683 6.91438i −0.349610 0.254006i
\(742\) 0 0
\(743\) 10.2730 + 31.6172i 0.376881 + 1.15992i 0.942201 + 0.335049i \(0.108753\pi\)
−0.565319 + 0.824872i \(0.691247\pi\)
\(744\) −10.2691 + 4.57211i −0.376484 + 0.167622i
\(745\) 1.46967 + 0.654340i 0.0538446 + 0.0239732i
\(746\) 2.29471 0.487756i 0.0840153 0.0178580i
\(747\) 14.7706 25.5835i 0.540429 0.936051i
\(748\) −17.4635 9.87543i −0.638530 0.361082i
\(749\) 0 0
\(750\) −0.328769 + 1.01185i −0.0120050 + 0.0369475i
\(751\) −2.92749 27.8532i −0.106826 1.01638i −0.908292 0.418338i \(-0.862613\pi\)
0.801466 0.598040i \(-0.204054\pi\)
\(752\) −0.466686 + 4.44022i −0.0170183 + 0.161918i
\(753\) 12.1471 13.4908i 0.442666 0.491631i
\(754\) −18.7404 3.98340i −0.682486 0.145067i
\(755\) 1.46530 + 1.06460i 0.0533276 + 0.0387448i
\(756\) 0 0
\(757\) −6.87465 + 21.1580i −0.249863 + 0.769001i 0.744935 + 0.667137i \(0.232481\pi\)
−0.994798 + 0.101864i \(0.967519\pi\)
\(758\) −2.38078 + 4.12363i −0.0864738 + 0.149777i
\(759\) −4.63841 + 6.50577i −0.168364 + 0.236144i
\(760\) 0.856186 + 1.48296i 0.0310571 + 0.0537925i
\(761\) −32.2691 35.8385i −1.16975 1.29914i −0.945877 0.324525i \(-0.894795\pi\)
−0.223877 0.974618i \(-0.571871\pi\)
\(762\) 0.776427 0.564108i 0.0281270 0.0204355i
\(763\) 0 0
\(764\) 5.18562 + 15.9597i 0.187609 + 0.577402i
\(765\) 2.46997 + 0.525007i 0.0893018 + 0.0189817i
\(766\) 0.356852 3.39522i 0.0128936 0.122674i
\(767\) −56.8649 25.3179i −2.05327 0.914176i
\(768\) −5.53878 6.15144i −0.199864 0.221971i
\(769\) 43.6883 1.57544 0.787721 0.616032i \(-0.211261\pi\)
0.787721 + 0.616032i \(0.211261\pi\)
\(770\) 0 0
\(771\) −10.4549 −0.376524
\(772\) −14.8322 16.4728i −0.533821 0.592868i
\(773\) −0.534944 0.238173i −0.0192406 0.00856647i 0.397094 0.917778i \(-0.370019\pi\)
−0.416334 + 0.909212i \(0.636685\pi\)
\(774\) 1.00174 9.53096i 0.0360069 0.342583i
\(775\) −33.3615 7.09120i −1.19838 0.254723i
\(776\) −7.38612 22.7321i −0.265146 0.816036i
\(777\) 0 0
\(778\) 6.60197 4.79661i 0.236692 0.171967i
\(779\) 2.61001 + 2.89871i 0.0935133 + 0.103857i
\(780\) −0.626558 1.08523i −0.0224344 0.0388575i
\(781\) 18.3705 + 24.8152i 0.657349 + 0.887958i
\(782\) 6.56824 11.3765i 0.234880 0.406824i
\(783\) 4.04930 12.4625i 0.144710 0.445372i
\(784\) 0 0
\(785\) 3.62764 + 2.63563i 0.129476 + 0.0940698i
\(786\) 0.643960 + 0.136878i 0.0229693 + 0.00488227i
\(787\) 20.5534 22.8269i 0.732650 0.813690i −0.255561 0.966793i \(-0.582260\pi\)
0.988210 + 0.153103i \(0.0489267\pi\)
\(788\) 1.79473 17.0757i 0.0639347 0.608298i
\(789\) 0.528467 + 5.02803i 0.0188139 + 0.179003i
\(790\) −0.242153 + 0.745269i −0.00861540 + 0.0265155i
\(791\) 0 0
\(792\) −22.7750 + 2.59984i −0.809274 + 0.0923811i
\(793\) 31.4379 54.4520i 1.11639 1.93365i
\(794\) 8.66114 1.84098i 0.307372 0.0653340i
\(795\) 0.215827 + 0.0960922i 0.00765458 + 0.00340804i
\(796\) −19.4564 + 8.66255i −0.689614 + 0.307036i
\(797\) −3.34767 10.3031i −0.118581 0.364953i 0.874096 0.485752i \(-0.161454\pi\)
−0.992677 + 0.120799i \(0.961454\pi\)
\(798\) 0 0
\(799\) 21.2003 + 15.4029i 0.750014 + 0.544917i
\(800\) −3.02930 28.8219i −0.107102 1.01901i
\(801\) 20.2857 4.31187i 0.716761 0.152352i
\(802\) −1.83679 3.18141i −0.0648593 0.112340i
\(803\) −4.01603 18.0967i −0.141722 0.638620i
\(804\) −1.09668 −0.0386770
\(805\) 0 0
\(806\) −28.2960 + 20.5582i −0.996684 + 0.724133i
\(807\) −3.52716 + 1.57039i −0.124162 + 0.0552805i
\(808\) −33.9344 + 37.6879i −1.19381 + 1.32586i
\(809\) −25.8218 + 28.6780i −0.907846 + 1.00826i 0.0920761 + 0.995752i \(0.470650\pi\)
−0.999922 + 0.0125127i \(0.996017\pi\)
\(810\) 0.902157 0.401666i 0.0316986 0.0141131i
\(811\) 41.1737 29.9144i 1.44580 1.05044i 0.459015 0.888428i \(-0.348202\pi\)
0.986789 0.162010i \(-0.0517977\pi\)
\(812\) 0 0
\(813\) 4.86200 0.170518
\(814\) −14.5115 1.39415i −0.508627 0.0488650i
\(815\) 0.827146 + 1.43266i 0.0289737 + 0.0501839i
\(816\) 1.93518 0.411336i 0.0677450 0.0143996i
\(817\) 1.43460 + 13.6493i 0.0501901 + 0.477527i
\(818\) 1.55076 + 1.12669i 0.0542209 + 0.0393938i
\(819\) 0 0
\(820\) 0.128402 + 0.395180i 0.00448398 + 0.0138003i
\(821\) −36.8245 + 16.3953i −1.28518 + 0.572201i −0.931696 0.363239i \(-0.881671\pi\)
−0.353488 + 0.935439i \(0.615004\pi\)
\(822\) −1.09709 0.488456i −0.0382654 0.0170369i
\(823\) −25.1205 + 5.33953i −0.875647 + 0.186124i −0.623745 0.781628i \(-0.714389\pi\)
−0.251902 + 0.967753i \(0.581056\pi\)
\(824\) −21.4343 + 37.1252i −0.746698 + 1.29332i
\(825\) 8.83296 + 4.99494i 0.307524 + 0.173902i
\(826\) 0 0
\(827\) −9.87486 + 30.3917i −0.343382 + 1.05682i 0.619062 + 0.785342i \(0.287513\pi\)
−0.962444 + 0.271480i \(0.912487\pi\)
\(828\) 1.48862 + 14.1632i 0.0517330 + 0.492206i
\(829\) −5.05920 + 48.1351i −0.175713 + 1.67180i 0.450980 + 0.892534i \(0.351075\pi\)
−0.626693 + 0.779266i \(0.715592\pi\)
\(830\) 1.30622 1.45071i 0.0453397 0.0503548i
\(831\) −7.28315 1.54808i −0.252650 0.0537023i
\(832\) −16.2409 11.7997i −0.563050 0.409080i
\(833\) 0 0
\(834\) 0.707180 2.17648i 0.0244876 0.0753652i
\(835\) −0.246005 + 0.426093i −0.00851335 + 0.0147456i
\(836\) 12.7937 4.28377i 0.442480 0.148157i
\(837\) −11.9608 20.7167i −0.413425 0.716073i
\(838\) 7.46015 + 8.28534i 0.257707 + 0.286212i
\(839\) 30.5133 22.1692i 1.05344 0.765366i 0.0805734 0.996749i \(-0.474325\pi\)
0.972863 + 0.231382i \(0.0743249\pi\)
\(840\) 0 0
\(841\) −4.56017 14.0348i −0.157247 0.483957i
\(842\) −13.1685 2.79906i −0.453817 0.0964619i
\(843\) −1.36665 + 13.0028i −0.0470700 + 0.447841i
\(844\) −11.3890 5.07069i −0.392024 0.174541i
\(845\) −4.41241 4.90048i −0.151791 0.168582i
\(846\) 12.3056 0.423074
\(847\) 0 0
\(848\) −1.26869 −0.0435671
\(849\) −10.3400 11.4838i −0.354869 0.394122i
\(850\) −15.2412 6.78583i −0.522770 0.232752i
\(851\) −2.30351 + 21.9164i −0.0789633 + 0.751286i
\(852\) −7.85352 1.66932i −0.269057 0.0571898i
\(853\) 2.87035 + 8.83403i 0.0982789 + 0.302471i 0.988094 0.153849i \(-0.0491670\pi\)
−0.889815 + 0.456321i \(0.849167\pi\)
\(854\) 0 0
\(855\) −1.37383 + 0.998146i −0.0469840 + 0.0341359i
\(856\) −9.52725 10.5811i −0.325635 0.361654i
\(857\) 14.8822 + 25.7767i 0.508365 + 0.880515i 0.999953 + 0.00968670i \(0.00308342\pi\)
−0.491588 + 0.870828i \(0.663583\pi\)
\(858\) 9.86753 3.30399i 0.336872 0.112796i
\(859\) −16.6305 + 28.8050i −0.567427 + 0.982812i 0.429392 + 0.903118i \(0.358728\pi\)
−0.996819 + 0.0796943i \(0.974606\pi\)
\(860\) −0.451787 + 1.39046i −0.0154058 + 0.0474142i
\(861\) 0 0
\(862\) 17.5442 + 12.7466i 0.597558 + 0.434151i
\(863\) 18.1619 + 3.86043i 0.618239 + 0.131411i 0.506376 0.862313i \(-0.330985\pi\)
0.111863 + 0.993724i \(0.464318\pi\)
\(864\) 13.6009 15.1053i 0.462712 0.513894i
\(865\) −0.241017 + 2.29312i −0.00819482 + 0.0779685i
\(866\) −2.40126 22.8465i −0.0815982 0.776355i
\(867\) 0.341645 1.05147i 0.0116029 0.0357100i
\(868\) 0 0
\(869\) 13.0768 + 7.39477i 0.443599 + 0.250850i
\(870\) 0.201760 0.349459i 0.00684031 0.0118478i
\(871\) −8.12120 + 1.72621i −0.275176 + 0.0584905i
\(872\) 13.0209 + 5.79730i 0.440945 + 0.196321i
\(873\) 21.6542 9.64106i 0.732883 0.326300i
\(874\) 2.72992 + 8.40184i 0.0923411 + 0.284197i
\(875\) 0 0
\(876\) 3.89985 + 2.83341i 0.131764 + 0.0957321i
\(877\) 2.35107 + 22.3689i 0.0793899 + 0.755344i 0.959715 + 0.280974i \(0.0906575\pi\)
−0.880326 + 0.474370i \(0.842676\pi\)
\(878\) −25.6025 + 5.44197i −0.864041 + 0.183658i
\(879\) 0.140630 + 0.243578i 0.00474332 + 0.00821568i
\(880\) 0.542522 + 0.0521213i 0.0182884 + 0.00175701i
\(881\) 7.06565 0.238048 0.119024 0.992891i \(-0.462023\pi\)
0.119024 + 0.992891i \(0.462023\pi\)
\(882\) 0 0
\(883\) 16.1304 11.7194i 0.542830 0.394389i −0.282305 0.959325i \(-0.591099\pi\)
0.825135 + 0.564936i \(0.191099\pi\)
\(884\) 36.0827 16.0650i 1.21359 0.540326i
\(885\) 0.877234 0.974267i 0.0294879 0.0327496i
\(886\) −5.37236 + 5.96661i −0.180488 + 0.200452i
\(887\) 6.35353 2.82878i 0.213331 0.0949810i −0.297289 0.954787i \(-0.596083\pi\)
0.510620 + 0.859806i \(0.329416\pi\)
\(888\) 7.46253 5.42185i 0.250426 0.181945i
\(889\) 0 0
\(890\) 1.37045 0.0459376
\(891\) −4.10160 18.4823i −0.137409 0.619181i
\(892\) 0.499068 + 0.864411i 0.0167100 + 0.0289426i
\(893\) −17.2377 + 3.66398i −0.576837 + 0.122610i
\(894\) −0.363135 3.45500i −0.0121450 0.115552i
\(895\) −4.21414 3.06175i −0.140863 0.102343i
\(896\) 0 0
\(897\) −4.86088 14.9602i −0.162300 0.499508i
\(898\) 1.95881 0.872120i 0.0653664 0.0291030i
\(899\) 23.7533 + 10.5756i 0.792216 + 0.352717i
\(900\) 17.6914 3.76043i 0.589715 0.125348i
\(901\) −3.72325 + 6.44886i −0.124039 + 0.214843i
\(902\) −3.42822 + 0.391342i −0.114147 + 0.0130303i
\(903\) 0 0
\(904\) −13.4575 + 41.4179i −0.447590 + 1.37754i
\(905\) −0.319026 3.03533i −0.0106048 0.100898i
\(906\) 0.408833 3.88979i 0.0135826 0.129230i
\(907\) −15.6845 + 17.4194i −0.520796 + 0.578402i −0.944961 0.327182i \(-0.893901\pi\)
0.424165 + 0.905585i \(0.360568\pi\)
\(908\) −7.26413 1.54404i −0.241069 0.0512407i
\(909\) −40.6878 29.5614i −1.34953 0.980490i
\(910\) 0 0
\(911\) 14.4650 44.5186i 0.479246 1.47497i −0.360899 0.932605i \(-0.617530\pi\)
0.840145 0.542362i \(-0.182470\pi\)
\(912\) −0.665238 + 1.15223i −0.0220282 + 0.0381540i
\(913\) −22.2671 30.0788i −0.736934 0.995462i
\(914\) −15.6782 27.1554i −0.518588 0.898220i
\(915\) 0.886103 + 0.984117i 0.0292937 + 0.0325339i
\(916\) −7.46078 + 5.42058i −0.246511 + 0.179101i
\(917\) 0 0
\(918\) −3.61594 11.1287i −0.119344 0.367302i
\(919\) −10.3951 2.20954i −0.342902 0.0728861i 0.0332419 0.999447i \(-0.489417\pi\)
−0.376144 + 0.926561i \(0.622750\pi\)
\(920\) −0.239348 + 2.27725i −0.00789108 + 0.0750786i
\(921\) −4.53702 2.02001i −0.149500 0.0665616i
\(922\) 17.8052 + 19.7747i 0.586383 + 0.651245i
\(923\) −60.7848 −2.00075
\(924\) 0 0
\(925\) 27.9876 0.920228
\(926\) −0.367990 0.408695i −0.0120929 0.0134305i
\(927\) −38.8370 17.2914i −1.27558 0.567923i
\(928\) −2.30938 + 21.9723i −0.0758091 + 0.721275i
\(929\) 35.8696 + 7.62432i 1.17684 + 0.250146i 0.754506 0.656293i \(-0.227876\pi\)
0.422337 + 0.906439i \(0.361210\pi\)
\(930\) −0.227635 0.700590i −0.00746446 0.0229733i
\(931\) 0 0
\(932\) −10.7900 + 7.83938i −0.353438 + 0.256787i
\(933\) 0.0566412 + 0.0629064i 0.00185435 + 0.00205946i
\(934\) −11.1151 19.2519i −0.363697 0.629941i
\(935\) 1.85708 2.60471i 0.0607330 0.0851833i
\(936\) 22.5645 39.0829i 0.737544 1.27746i
\(937\) −12.4278 + 38.2490i −0.406000 + 1.24954i 0.514057 + 0.857756i \(0.328142\pi\)
−0.920057 + 0.391784i \(0.871858\pi\)
\(938\) 0 0
\(939\) 7.64497 + 5.55439i 0.249484 + 0.181261i
\(940\) −1.83627 0.390310i −0.0598924 0.0127305i
\(941\) 16.6678 18.5115i 0.543355 0.603457i −0.407457 0.913224i \(-0.633584\pi\)
0.950812 + 0.309767i \(0.100251\pi\)
\(942\) 1.01215 9.62995i 0.0329776 0.313761i
\(943\) 0.545210 + 5.18732i 0.0177545 + 0.168922i
\(944\) −2.17555 + 6.69565i −0.0708081 + 0.217925i
\(945\) 0 0
\(946\) −10.5680 5.97609i −0.343595 0.194299i
\(947\) 16.1031 27.8913i 0.523279 0.906347i −0.476353 0.879254i \(-0.658042\pi\)
0.999633 0.0270927i \(-0.00862493\pi\)
\(948\) −3.82126 + 0.812234i −0.124109 + 0.0263801i
\(949\) 33.3393 + 14.8436i 1.08224 + 0.481843i
\(950\) 10.2497 4.56344i 0.332543 0.148058i
\(951\) −6.30101 19.3925i −0.204324 0.628846i
\(952\) 0 0
\(953\) −36.4552 26.4863i −1.18090 0.857975i −0.188628 0.982049i \(-0.560404\pi\)
−0.992273 + 0.124074i \(0.960404\pi\)
\(954\) 0.365513 + 3.47763i 0.0118339 + 0.112592i
\(955\) −2.61727 + 0.556317i −0.0846928 + 0.0180020i
\(956\) 18.7325 + 32.4456i 0.605852 + 1.04937i
\(957\) −5.79493 5.12470i −0.187323 0.165658i
\(958\) 3.96296 0.128038
\(959\) 0 0
\(960\) 0.342058 0.248519i 0.0110399 0.00802093i
\(961\) 15.0428 6.69746i 0.485250 0.216047i
\(962\) 19.2045 21.3288i 0.619179 0.687668i
\(963\) 9.44812 10.4932i 0.304461 0.338139i
\(964\) −24.0521 + 10.7087i −0.774666 + 0.344903i
\(965\) 2.85941 2.07748i 0.0920476 0.0668765i
\(966\) 0 0
\(967\) 1.81387 0.0583300 0.0291650 0.999575i \(-0.490715\pi\)
0.0291650 + 0.999575i \(0.490715\pi\)
\(968\) −8.47842 + 27.7743i −0.272507 + 0.892701i
\(969\) 3.90456 + 6.76290i 0.125433 + 0.217256i
\(970\) 1.53212 0.325662i 0.0491934 0.0104564i
\(971\) −2.40979 22.9276i −0.0773338 0.735782i −0.962642 0.270777i \(-0.912719\pi\)
0.885308 0.465005i \(-0.153947\pi\)
\(972\) 15.7431 + 11.4380i 0.504959 + 0.366874i
\(973\) 0 0
\(974\) −7.01266 21.5827i −0.224700 0.691555i
\(975\) −18.2504 + 8.12562i −0.584482 + 0.260228i
\(976\) −6.49659 2.89247i −0.207951 0.0925857i
\(977\) 6.93946 1.47503i 0.222013 0.0471903i −0.0955620 0.995423i \(-0.530465\pi\)
0.317575 + 0.948233i \(0.397131\pi\)
\(978\) 1.78618 3.09376i 0.0571158 0.0989274i
\(979\) 5.23244 25.7466i 0.167229 0.822863i
\(980\) 0 0
\(981\) −4.36789 + 13.4430i −0.139456 + 0.429202i
\(982\) 2.44978 + 23.3081i 0.0781755 + 0.743790i
\(983\) −4.00869 + 38.1402i −0.127857 + 1.21648i 0.722911 + 0.690941i \(0.242804\pi\)
−0.850768 + 0.525541i \(0.823863\pi\)
\(984\) 1.46087 1.62246i 0.0465710 0.0517223i
\(985\) 2.67790 + 0.569206i 0.0853251 + 0.0181364i
\(986\) 10.2896 + 7.47586i 0.327689 + 0.238080i
\(987\) 0 0
\(988\) −8.20806 + 25.2618i −0.261133 + 0.803685i
\(989\) −9.17619 + 15.8936i −0.291786 + 0.505388i
\(990\) −0.0134314 1.50213i −0.000426879 0.0477407i
\(991\) −10.1361 17.5562i −0.321984 0.557692i 0.658914 0.752219i \(-0.271016\pi\)
−0.980897 + 0.194527i \(0.937683\pi\)
\(992\) 26.9876 + 29.9728i 0.856857 + 0.951636i
\(993\) −14.7667 + 10.7287i −0.468608 + 0.340464i
\(994\) 0 0
\(995\) −1.04940 3.22971i −0.0332681 0.102389i
\(996\) 9.51933 + 2.02340i 0.301631 + 0.0641137i
\(997\) −1.61086 + 15.3263i −0.0510164 + 0.485389i 0.938947 + 0.344063i \(0.111803\pi\)
−0.989963 + 0.141326i \(0.954863\pi\)
\(998\) −4.22683 1.88191i −0.133798 0.0595707i
\(999\) 13.1349 + 14.5878i 0.415569 + 0.461536i
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 539.2.q.c.471.1 16
7.2 even 3 77.2.f.a.64.1 8
7.3 odd 6 539.2.q.b.361.2 16
7.4 even 3 inner 539.2.q.c.361.2 16
7.5 odd 6 539.2.f.d.295.1 8
7.6 odd 2 539.2.q.b.471.1 16
11.5 even 5 inner 539.2.q.c.324.2 16
21.2 odd 6 693.2.m.g.64.2 8
77.2 odd 30 847.2.f.s.729.1 8
77.5 odd 30 539.2.f.d.148.1 8
77.9 even 15 847.2.f.p.729.2 8
77.16 even 15 77.2.f.a.71.1 yes 8
77.26 odd 30 5929.2.a.bi.1.2 4
77.27 odd 10 539.2.q.b.324.2 16
77.30 odd 30 847.2.f.s.323.1 8
77.37 even 15 847.2.a.l.1.2 4
77.38 odd 30 539.2.q.b.214.1 16
77.40 even 30 5929.2.a.bb.1.3 4
77.51 odd 30 847.2.a.k.1.3 4
77.58 even 15 847.2.f.p.323.2 8
77.60 even 15 inner 539.2.q.c.214.1 16
77.65 odd 6 847.2.f.q.372.2 8
77.72 odd 30 847.2.f.q.148.2 8
231.128 even 30 7623.2.a.co.1.2 4
231.170 odd 30 693.2.m.g.379.2 8
231.191 odd 30 7623.2.a.ch.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.a.64.1 8 7.2 even 3
77.2.f.a.71.1 yes 8 77.16 even 15
539.2.f.d.148.1 8 77.5 odd 30
539.2.f.d.295.1 8 7.5 odd 6
539.2.q.b.214.1 16 77.38 odd 30
539.2.q.b.324.2 16 77.27 odd 10
539.2.q.b.361.2 16 7.3 odd 6
539.2.q.b.471.1 16 7.6 odd 2
539.2.q.c.214.1 16 77.60 even 15 inner
539.2.q.c.324.2 16 11.5 even 5 inner
539.2.q.c.361.2 16 7.4 even 3 inner
539.2.q.c.471.1 16 1.1 even 1 trivial
693.2.m.g.64.2 8 21.2 odd 6
693.2.m.g.379.2 8 231.170 odd 30
847.2.a.k.1.3 4 77.51 odd 30
847.2.a.l.1.2 4 77.37 even 15
847.2.f.p.323.2 8 77.58 even 15
847.2.f.p.729.2 8 77.9 even 15
847.2.f.q.148.2 8 77.72 odd 30
847.2.f.q.372.2 8 77.65 odd 6
847.2.f.s.323.1 8 77.30 odd 30
847.2.f.s.729.1 8 77.2 odd 30
5929.2.a.bb.1.3 4 77.40 even 30
5929.2.a.bi.1.2 4 77.26 odd 30
7623.2.a.ch.1.3 4 231.191 odd 30
7623.2.a.co.1.2 4 231.128 even 30