Properties

Label 43.3.f.a.8.1
Level $43$
Weight $3$
Character 43.8
Analytic conductor $1.172$
Analytic rank $0$
Dimension $42$
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] = [43,3,Mod(2,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([9]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 43.f (of order \(14\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.17166513675\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 8.1
Character \(\chi\) \(=\) 43.8
Dual form 43.3.f.a.27.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.53859 - 0.807660i) q^{2} +(1.86243 - 0.425087i) q^{3} +(8.26544 + 3.98042i) q^{4} +(-5.65332 - 4.50837i) q^{5} -6.93370 q^{6} -11.0869i q^{7} +(-14.6823 - 11.7087i) q^{8} +(-4.82078 + 2.32157i) q^{9} +O(q^{10})\) \(q+(-3.53859 - 0.807660i) q^{2} +(1.86243 - 0.425087i) q^{3} +(8.26544 + 3.98042i) q^{4} +(-5.65332 - 4.50837i) q^{5} -6.93370 q^{6} -11.0869i q^{7} +(-14.6823 - 11.7087i) q^{8} +(-4.82078 + 2.32157i) q^{9} +(16.3636 + 20.5192i) q^{10} +(8.18301 - 3.94073i) q^{11} +(17.0858 + 3.89972i) q^{12} +(3.48338 - 4.36802i) q^{13} +(-8.95445 + 39.2320i) q^{14} +(-12.4453 - 5.99336i) q^{15} +(19.6184 + 24.6007i) q^{16} +(7.68404 + 9.63548i) q^{17} +(18.9338 - 4.32152i) q^{18} +(-4.17143 + 8.66206i) q^{19} +(-28.7819 - 59.7663i) q^{20} +(-4.71290 - 20.6485i) q^{21} +(-32.1391 + 7.33554i) q^{22} +(23.3617 - 11.2504i) q^{23} +(-32.3218 - 15.5654i) q^{24} +(6.07158 + 26.6013i) q^{25} +(-15.8541 + 12.6432i) q^{26} +(-21.4334 + 17.0926i) q^{27} +(44.1306 - 91.6381i) q^{28} +(17.3222 + 3.95367i) q^{29} +(39.1984 + 31.2597i) q^{30} +(-4.39761 + 19.2672i) q^{31} +(-16.9603 - 35.2185i) q^{32} +(13.5651 - 10.8178i) q^{33} +(-19.4085 - 40.3021i) q^{34} +(-49.9839 + 62.6778i) q^{35} -49.0867 q^{36} -16.3680i q^{37} +(21.7570 - 27.2824i) q^{38} +(4.63075 - 9.61585i) q^{39} +(30.2163 + 132.386i) q^{40} +(10.5206 - 46.0940i) q^{41} +76.8732i q^{42} +(38.8262 - 18.4804i) q^{43} +83.3220 q^{44} +(37.7199 + 8.60932i) q^{45} +(-91.7542 + 20.9423i) q^{46} +(12.0673 + 5.81130i) q^{47} +(46.9953 + 37.4775i) q^{48} -73.9193 q^{49} -99.0350i q^{50} +(18.4069 + 14.6790i) q^{51} +(46.1782 - 22.2382i) q^{52} +(-48.3246 - 60.5972i) q^{53} +(89.6492 - 43.1728i) q^{54} +(-64.0275 - 14.6139i) q^{55} +(-129.813 + 162.781i) q^{56} +(-4.08685 + 17.9057i) q^{57} +(-58.1028 - 27.9809i) q^{58} +(33.9563 + 42.5798i) q^{59} +(-79.0101 - 99.0755i) q^{60} +(89.1648 - 20.3513i) q^{61} +(31.1227 - 64.6270i) q^{62} +(25.7390 + 53.4475i) q^{63} +(3.56420 + 15.6158i) q^{64} +(-39.3853 + 8.98943i) q^{65} +(-56.7385 + 27.3238i) q^{66} +(-53.0202 - 25.5332i) q^{67} +(25.1586 + 110.227i) q^{68} +(38.7271 - 30.8839i) q^{69} +(227.495 - 181.421i) q^{70} +(-47.5663 + 98.7724i) q^{71} +(97.9625 + 22.3593i) q^{72} +(54.6728 + 43.6001i) q^{73} +(-13.2198 + 57.9198i) q^{74} +(22.6157 + 46.9621i) q^{75} +(-68.9573 + 54.9916i) q^{76} +(-43.6905 - 90.7243i) q^{77} +(-24.1527 + 30.2865i) q^{78} -33.1652 q^{79} -227.522i q^{80} +(-2.62763 + 3.29495i) q^{81} +(-74.4565 + 154.611i) q^{82} +(3.02602 + 13.2578i) q^{83} +(43.2358 - 189.429i) q^{84} -89.1150i q^{85} +(-152.316 + 34.0363i) q^{86} +33.9419 q^{87} +(-166.286 - 37.9537i) q^{88} +(9.70773 - 2.21573i) q^{89} +(-126.522 - 60.9297i) q^{90} +(-48.4278 - 38.6198i) q^{91} +237.876 q^{92} +37.7531i q^{93} +(-38.0076 - 30.3101i) q^{94} +(62.6342 - 30.1630i) q^{95} +(-46.5583 - 58.3822i) q^{96} +(29.5117 - 14.2121i) q^{97} +(261.570 + 59.7017i) q^{98} +(-30.2999 + 37.9948i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42 q - 7 q^{2} - 7 q^{3} + 5 q^{4} - 7 q^{5} - 20 q^{6} + 21 q^{8} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 42 q - 7 q^{2} - 7 q^{3} + 5 q^{4} - 7 q^{5} - 20 q^{6} + 21 q^{8} - 36 q^{9} - 5 q^{10} - 24 q^{11} - 35 q^{12} - 34 q^{13} + 69 q^{14} + 7 q^{15} - 39 q^{16} + 22 q^{17} - 70 q^{18} - 49 q^{19} + 133 q^{20} + 77 q^{22} + 42 q^{23} - 349 q^{24} + 10 q^{25} + 49 q^{26} - 7 q^{27} + 105 q^{28} + 63 q^{29} - 252 q^{30} - 152 q^{31} + 343 q^{32} + 329 q^{33} + 161 q^{34} + 58 q^{35} + 576 q^{36} - 289 q^{38} + 77 q^{39} - 101 q^{40} + 133 q^{41} - 79 q^{43} + 148 q^{44} + 84 q^{45} - 504 q^{46} + 6 q^{47} - 595 q^{48} - 302 q^{49} + 161 q^{51} - 267 q^{52} - 394 q^{53} - 227 q^{54} - 637 q^{55} + 355 q^{56} - 7 q^{57} + 165 q^{58} - 46 q^{59} - 657 q^{60} - 175 q^{61} - 91 q^{62} + 511 q^{63} + 725 q^{64} + 161 q^{65} - 227 q^{66} - 756 q^{67} - 586 q^{68} + 441 q^{69} + 1526 q^{70} + 266 q^{71} + 1078 q^{72} - 252 q^{73} + 204 q^{74} + 112 q^{75} + 994 q^{76} + 791 q^{77} + 94 q^{78} - 178 q^{79} - 428 q^{81} + 245 q^{82} + 238 q^{83} + 66 q^{84} + 365 q^{86} + 426 q^{87} - 119 q^{88} + 252 q^{89} - 926 q^{90} - 224 q^{91} - 764 q^{92} + 133 q^{94} + 11 q^{95} - 2602 q^{96} - 491 q^{97} - 553 q^{98} + 431 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{13}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.53859 0.807660i −1.76930 0.403830i −0.791128 0.611650i \(-0.790506\pi\)
−0.978167 + 0.207820i \(0.933363\pi\)
\(3\) 1.86243 0.425087i 0.620809 0.141696i 0.0994635 0.995041i \(-0.468287\pi\)
0.521346 + 0.853346i \(0.325430\pi\)
\(4\) 8.26544 + 3.98042i 2.06636 + 0.995106i
\(5\) −5.65332 4.50837i −1.13066 0.901674i −0.134652 0.990893i \(-0.542992\pi\)
−0.996012 + 0.0892188i \(0.971563\pi\)
\(6\) −6.93370 −1.15562
\(7\) 11.0869i 1.58384i −0.610623 0.791921i \(-0.709081\pi\)
0.610623 0.791921i \(-0.290919\pi\)
\(8\) −14.6823 11.7087i −1.83528 1.46359i
\(9\) −4.82078 + 2.32157i −0.535643 + 0.257952i
\(10\) 16.3636 + 20.5192i 1.63636 + 2.05192i
\(11\) 8.18301 3.94073i 0.743910 0.358248i −0.0232278 0.999730i \(-0.507394\pi\)
0.767138 + 0.641482i \(0.221680\pi\)
\(12\) 17.0858 + 3.89972i 1.42382 + 0.324977i
\(13\) 3.48338 4.36802i 0.267952 0.336001i −0.629592 0.776926i \(-0.716778\pi\)
0.897544 + 0.440925i \(0.145349\pi\)
\(14\) −8.95445 + 39.2320i −0.639603 + 2.80229i
\(15\) −12.4453 5.99336i −0.829690 0.399557i
\(16\) 19.6184 + 24.6007i 1.22615 + 1.53754i
\(17\) 7.68404 + 9.63548i 0.452003 + 0.566793i 0.954662 0.297691i \(-0.0962166\pi\)
−0.502660 + 0.864484i \(0.667645\pi\)
\(18\) 18.9338 4.32152i 1.05188 0.240084i
\(19\) −4.17143 + 8.66206i −0.219549 + 0.455898i −0.981430 0.191819i \(-0.938561\pi\)
0.761882 + 0.647716i \(0.224276\pi\)
\(20\) −28.7819 59.7663i −1.43910 2.98831i
\(21\) −4.71290 20.6485i −0.224424 0.983264i
\(22\) −32.1391 + 7.33554i −1.46087 + 0.333434i
\(23\) 23.3617 11.2504i 1.01573 0.489149i 0.149481 0.988765i \(-0.452240\pi\)
0.866247 + 0.499616i \(0.166525\pi\)
\(24\) −32.3218 15.5654i −1.34674 0.648557i
\(25\) 6.07158 + 26.6013i 0.242863 + 1.06405i
\(26\) −15.8541 + 12.6432i −0.609774 + 0.486278i
\(27\) −21.4334 + 17.0926i −0.793831 + 0.633059i
\(28\) 44.1306 91.6381i 1.57609 3.27279i
\(29\) 17.3222 + 3.95367i 0.597316 + 0.136333i 0.510481 0.859889i \(-0.329467\pi\)
0.0868353 + 0.996223i \(0.472325\pi\)
\(30\) 39.1984 + 31.2597i 1.30661 + 1.04199i
\(31\) −4.39761 + 19.2672i −0.141858 + 0.621523i 0.853144 + 0.521675i \(0.174693\pi\)
−0.995003 + 0.0998476i \(0.968164\pi\)
\(32\) −16.9603 35.2185i −0.530010 1.10058i
\(33\) 13.5651 10.8178i 0.411064 0.327813i
\(34\) −19.4085 40.3021i −0.570838 1.18536i
\(35\) −49.9839 + 62.6778i −1.42811 + 1.79079i
\(36\) −49.0867 −1.36352
\(37\) 16.3680i 0.442380i −0.975231 0.221190i \(-0.929006\pi\)
0.975231 0.221190i \(-0.0709940\pi\)
\(38\) 21.7570 27.2824i 0.572552 0.717957i
\(39\) 4.63075 9.61585i 0.118737 0.246560i
\(40\) 30.2163 + 132.386i 0.755406 + 3.30965i
\(41\) 10.5206 46.0940i 0.256601 1.12424i −0.668257 0.743931i \(-0.732959\pi\)
0.924858 0.380313i \(-0.124184\pi\)
\(42\) 76.8732i 1.83031i
\(43\) 38.8262 18.4804i 0.902935 0.429777i
\(44\) 83.3220 1.89368
\(45\) 37.7199 + 8.60932i 0.838220 + 0.191318i
\(46\) −91.7542 + 20.9423i −1.99466 + 0.455267i
\(47\) 12.0673 + 5.81130i 0.256751 + 0.123645i 0.557832 0.829954i \(-0.311633\pi\)
−0.301081 + 0.953598i \(0.597348\pi\)
\(48\) 46.9953 + 37.4775i 0.979068 + 0.780780i
\(49\) −73.9193 −1.50856
\(50\) 99.0350i 1.98070i
\(51\) 18.4069 + 14.6790i 0.360919 + 0.287824i
\(52\) 46.1782 22.2382i 0.888042 0.427659i
\(53\) −48.3246 60.5972i −0.911786 1.14334i −0.989233 0.146347i \(-0.953248\pi\)
0.0774476 0.996996i \(-0.475323\pi\)
\(54\) 89.6492 43.1728i 1.66017 0.799496i
\(55\) −64.0275 14.6139i −1.16414 0.265706i
\(56\) −129.813 + 162.781i −2.31809 + 2.90680i
\(57\) −4.08685 + 17.9057i −0.0716992 + 0.314135i
\(58\) −58.1028 27.9809i −1.00177 0.482429i
\(59\) 33.9563 + 42.5798i 0.575530 + 0.721692i 0.981343 0.192264i \(-0.0615831\pi\)
−0.405813 + 0.913956i \(0.633012\pi\)
\(60\) −79.0101 99.0755i −1.31683 1.65126i
\(61\) 89.1648 20.3513i 1.46172 0.333628i 0.583588 0.812050i \(-0.301648\pi\)
0.878130 + 0.478422i \(0.158791\pi\)
\(62\) 31.1227 64.6270i 0.501979 1.04237i
\(63\) 25.7390 + 53.4475i 0.408555 + 0.848374i
\(64\) 3.56420 + 15.6158i 0.0556906 + 0.243996i
\(65\) −39.3853 + 8.98943i −0.605927 + 0.138299i
\(66\) −56.7385 + 27.3238i −0.859675 + 0.413997i
\(67\) −53.0202 25.5332i −0.791347 0.381093i −0.00586940 0.999983i \(-0.501868\pi\)
−0.785478 + 0.618890i \(0.787583\pi\)
\(68\) 25.1586 + 110.227i 0.369980 + 1.62099i
\(69\) 38.7271 30.8839i 0.561263 0.447592i
\(70\) 227.495 181.421i 3.24993 2.59173i
\(71\) −47.5663 + 98.7724i −0.669948 + 1.39116i 0.237663 + 0.971348i \(0.423619\pi\)
−0.907611 + 0.419813i \(0.862096\pi\)
\(72\) 97.9625 + 22.3593i 1.36059 + 0.310546i
\(73\) 54.6728 + 43.6001i 0.748943 + 0.597262i 0.921791 0.387687i \(-0.126726\pi\)
−0.172849 + 0.984948i \(0.555297\pi\)
\(74\) −13.2198 + 57.9198i −0.178646 + 0.782700i
\(75\) 22.6157 + 46.9621i 0.301543 + 0.626161i
\(76\) −68.9573 + 54.9916i −0.907333 + 0.723574i
\(77\) −43.6905 90.7243i −0.567409 1.17824i
\(78\) −24.1527 + 30.2865i −0.309650 + 0.388288i
\(79\) −33.1652 −0.419813 −0.209906 0.977721i \(-0.567316\pi\)
−0.209906 + 0.977721i \(0.567316\pi\)
\(80\) 227.522i 2.84403i
\(81\) −2.62763 + 3.29495i −0.0324399 + 0.0406784i
\(82\) −74.4565 + 154.611i −0.908007 + 1.88550i
\(83\) 3.02602 + 13.2578i 0.0364580 + 0.159733i 0.989880 0.141906i \(-0.0453232\pi\)
−0.953422 + 0.301640i \(0.902466\pi\)
\(84\) 43.2358 189.429i 0.514712 2.25510i
\(85\) 89.1150i 1.04841i
\(86\) −152.316 + 34.0363i −1.77112 + 0.395771i
\(87\) 33.9419 0.390137
\(88\) −166.286 37.9537i −1.88961 0.431292i
\(89\) 9.70773 2.21573i 0.109076 0.0248958i −0.167635 0.985849i \(-0.553613\pi\)
0.276710 + 0.960953i \(0.410756\pi\)
\(90\) −126.522 60.9297i −1.40580 0.676997i
\(91\) −48.4278 38.6198i −0.532173 0.424394i
\(92\) 237.876 2.58561
\(93\) 37.7531i 0.405948i
\(94\) −38.0076 30.3101i −0.404336 0.322448i
\(95\) 62.6342 30.1630i 0.659307 0.317505i
\(96\) −46.5583 58.3822i −0.484982 0.608148i
\(97\) 29.5117 14.2121i 0.304245 0.146517i −0.275532 0.961292i \(-0.588854\pi\)
0.579777 + 0.814775i \(0.303140\pi\)
\(98\) 261.570 + 59.7017i 2.66908 + 0.609201i
\(99\) −30.2999 + 37.9948i −0.306059 + 0.383786i
\(100\) −55.7003 + 244.039i −0.557003 + 2.44039i
\(101\) 144.898 + 69.7792i 1.43463 + 0.690883i 0.979853 0.199721i \(-0.0640034\pi\)
0.454780 + 0.890604i \(0.349718\pi\)
\(102\) −53.2788 66.8095i −0.522341 0.654995i
\(103\) −46.8835 58.7901i −0.455180 0.570777i 0.500293 0.865856i \(-0.333226\pi\)
−0.955473 + 0.295079i \(0.904654\pi\)
\(104\) −102.288 + 23.3465i −0.983535 + 0.224485i
\(105\) −66.4478 + 137.980i −0.632836 + 1.31410i
\(106\) 122.059 + 253.459i 1.15150 + 2.39112i
\(107\) −13.7355 60.1791i −0.128369 0.562422i −0.997675 0.0681477i \(-0.978291\pi\)
0.869306 0.494274i \(-0.164566\pi\)
\(108\) −245.193 + 55.9636i −2.27030 + 0.518182i
\(109\) 58.1442 28.0008i 0.533433 0.256888i −0.147719 0.989029i \(-0.547193\pi\)
0.681153 + 0.732141i \(0.261479\pi\)
\(110\) 214.764 + 103.425i 1.95240 + 0.940226i
\(111\) −6.95784 30.4843i −0.0626833 0.274633i
\(112\) 272.745 217.507i 2.43523 1.94203i
\(113\) −42.7493 + 34.0914i −0.378312 + 0.301694i −0.794123 0.607757i \(-0.792069\pi\)
0.415811 + 0.909451i \(0.363498\pi\)
\(114\) 28.9234 60.0601i 0.253714 0.526843i
\(115\) −182.792 41.7212i −1.58950 0.362793i
\(116\) 127.438 + 101.628i 1.09860 + 0.876107i
\(117\) −6.65196 + 29.1441i −0.0568544 + 0.249095i
\(118\) −85.7673 178.098i −0.726841 1.50930i
\(119\) 106.828 85.1922i 0.897711 0.715901i
\(120\) 112.551 + 233.715i 0.937926 + 1.94762i
\(121\) −24.0099 + 30.1075i −0.198429 + 0.248822i
\(122\) −331.955 −2.72094
\(123\) 90.3189i 0.734300i
\(124\) −113.040 + 141.747i −0.911612 + 1.14312i
\(125\) 7.17018 14.8890i 0.0573615 0.119112i
\(126\) −47.9123 209.917i −0.380256 1.66601i
\(127\) −37.3496 + 163.639i −0.294091 + 1.28850i 0.584683 + 0.811262i \(0.301219\pi\)
−0.878775 + 0.477237i \(0.841638\pi\)
\(128\) 98.2218i 0.767357i
\(129\) 64.4552 50.9230i 0.499653 0.394752i
\(130\) 146.629 1.12791
\(131\) 70.1378 + 16.0085i 0.535403 + 0.122202i 0.481669 0.876353i \(-0.340031\pi\)
0.0537339 + 0.998555i \(0.482888\pi\)
\(132\) 155.181 35.4191i 1.17561 0.268326i
\(133\) 96.0353 + 46.2482i 0.722070 + 0.347731i
\(134\) 166.995 + 133.174i 1.24623 + 0.993835i
\(135\) 198.230 1.46837
\(136\) 231.441i 1.70177i
\(137\) −104.933 83.6816i −0.765937 0.610814i 0.160599 0.987020i \(-0.448657\pi\)
−0.926536 + 0.376205i \(0.877229\pi\)
\(138\) −161.983 + 78.0070i −1.17379 + 0.565268i
\(139\) 6.94309 + 8.70635i 0.0499503 + 0.0626356i 0.806179 0.591672i \(-0.201532\pi\)
−0.756229 + 0.654307i \(0.772960\pi\)
\(140\) −662.623 + 319.102i −4.73302 + 2.27930i
\(141\) 24.9447 + 5.69347i 0.176913 + 0.0403793i
\(142\) 248.092 311.098i 1.74713 2.19083i
\(143\) 11.2913 49.4706i 0.0789604 0.345948i
\(144\) −151.688 73.0491i −1.05339 0.507286i
\(145\) −80.1031 100.446i −0.552435 0.692732i
\(146\) −158.251 198.440i −1.08391 1.35918i
\(147\) −137.669 + 31.4221i −0.936527 + 0.213756i
\(148\) 65.1518 135.289i 0.440215 0.914115i
\(149\) −100.687 209.079i −0.675754 1.40322i −0.903112 0.429406i \(-0.858723\pi\)
0.227358 0.973811i \(-0.426991\pi\)
\(150\) −42.0985 184.445i −0.280656 1.22964i
\(151\) 101.814 23.2384i 0.674266 0.153897i 0.128340 0.991730i \(-0.459035\pi\)
0.545926 + 0.837833i \(0.316178\pi\)
\(152\) 162.667 78.3365i 1.07018 0.515372i
\(153\) −59.4125 28.6116i −0.388317 0.187004i
\(154\) 81.3284 + 356.323i 0.528107 + 2.31379i
\(155\) 111.725 89.0976i 0.720805 0.574823i
\(156\) 76.5503 61.0469i 0.490707 0.391326i
\(157\) −102.045 + 211.899i −0.649968 + 1.34967i 0.271958 + 0.962309i \(0.412329\pi\)
−0.921927 + 0.387364i \(0.873386\pi\)
\(158\) 117.358 + 26.7862i 0.742773 + 0.169533i
\(159\) −115.760 92.3157i −0.728052 0.580602i
\(160\) −62.8958 + 275.565i −0.393099 + 1.72228i
\(161\) −124.732 259.009i −0.774735 1.60875i
\(162\) 11.9593 9.53724i 0.0738229 0.0588718i
\(163\) −14.5755 30.2663i −0.0894201 0.185683i 0.851463 0.524415i \(-0.175716\pi\)
−0.940883 + 0.338733i \(0.890002\pi\)
\(164\) 270.431 339.110i 1.64897 2.06774i
\(165\) −125.459 −0.760356
\(166\) 49.3581i 0.297338i
\(167\) −153.423 + 192.386i −0.918700 + 1.15201i 0.0693052 + 0.997596i \(0.477922\pi\)
−0.988006 + 0.154418i \(0.950650\pi\)
\(168\) −172.572 + 358.349i −1.02721 + 2.13303i
\(169\) 30.6604 + 134.332i 0.181422 + 0.794863i
\(170\) −71.9746 + 315.341i −0.423380 + 1.85495i
\(171\) 51.4421i 0.300831i
\(172\) 394.475 + 1.79603i 2.29346 + 0.0104420i
\(173\) −60.3821 −0.349030 −0.174515 0.984655i \(-0.555836\pi\)
−0.174515 + 0.984655i \(0.555836\pi\)
\(174\) −120.107 27.4136i −0.690268 0.157549i
\(175\) 294.926 67.3150i 1.68529 0.384657i
\(176\) 257.482 + 123.997i 1.46297 + 0.704528i
\(177\) 81.3412 + 64.8674i 0.459555 + 0.366483i
\(178\) −36.1413 −0.203041
\(179\) 100.540i 0.561674i 0.959755 + 0.280837i \(0.0906121\pi\)
−0.959755 + 0.280837i \(0.909388\pi\)
\(180\) 277.503 + 221.301i 1.54168 + 1.22945i
\(181\) 193.035 92.9607i 1.06649 0.513595i 0.183517 0.983017i \(-0.441252\pi\)
0.882974 + 0.469422i \(0.155538\pi\)
\(182\) 140.174 + 175.773i 0.770188 + 0.965786i
\(183\) 157.412 75.8056i 0.860174 0.414238i
\(184\) −474.731 108.354i −2.58006 0.588882i
\(185\) −73.7932 + 92.5338i −0.398882 + 0.500183i
\(186\) 30.4917 133.593i 0.163934 0.718241i
\(187\) 100.849 + 48.5666i 0.539302 + 0.259714i
\(188\) 76.6099 + 96.0658i 0.407500 + 0.510988i
\(189\) 189.504 + 237.630i 1.00267 + 1.25730i
\(190\) −245.998 + 56.1475i −1.29473 + 0.295513i
\(191\) −76.2443 + 158.323i −0.399185 + 0.828916i 0.600389 + 0.799708i \(0.295013\pi\)
−0.999573 + 0.0292073i \(0.990702\pi\)
\(192\) 13.2761 + 27.5681i 0.0691464 + 0.143584i
\(193\) 51.6500 + 226.293i 0.267617 + 1.17250i 0.912777 + 0.408458i \(0.133933\pi\)
−0.645161 + 0.764047i \(0.723210\pi\)
\(194\) −115.909 + 26.4554i −0.597467 + 0.136368i
\(195\) −69.5309 + 33.4843i −0.356569 + 0.171715i
\(196\) −610.976 294.230i −3.11722 1.50118i
\(197\) −25.2236 110.512i −0.128039 0.560974i −0.997728 0.0673739i \(-0.978538\pi\)
0.869689 0.493600i \(-0.164319\pi\)
\(198\) 137.906 109.976i 0.696494 0.555435i
\(199\) 100.763 80.3556i 0.506345 0.403797i −0.336723 0.941604i \(-0.609319\pi\)
0.843068 + 0.537807i \(0.180747\pi\)
\(200\) 222.323 461.658i 1.11161 2.30829i
\(201\) −109.600 25.0155i −0.545275 0.124455i
\(202\) −456.377 363.948i −2.25929 1.80172i
\(203\) 43.8340 192.049i 0.215931 0.946055i
\(204\) 93.7123 + 194.596i 0.459374 + 0.953900i
\(205\) −267.285 + 213.153i −1.30383 + 1.03977i
\(206\) 118.419 + 245.900i 0.574851 + 1.19369i
\(207\) −86.5033 + 108.472i −0.417890 + 0.524018i
\(208\) 175.794 0.845165
\(209\) 87.3202i 0.417800i
\(210\) 346.573 434.589i 1.65035 2.06947i
\(211\) 6.17150 12.8152i 0.0292488 0.0607358i −0.885833 0.464005i \(-0.846412\pi\)
0.915081 + 0.403269i \(0.132126\pi\)
\(212\) −158.222 693.215i −0.746329 3.26988i
\(213\) −46.6019 + 204.176i −0.218788 + 0.958574i
\(214\) 224.043i 1.04693i
\(215\) −302.813 70.5672i −1.40843 0.328220i
\(216\) 514.824 2.38344
\(217\) 213.614 + 48.7559i 0.984394 + 0.224682i
\(218\) −228.364 + 52.1225i −1.04754 + 0.239094i
\(219\) 120.358 + 57.9613i 0.549580 + 0.264664i
\(220\) −471.046 375.646i −2.14112 1.70748i
\(221\) 68.8544 0.311558
\(222\) 113.491i 0.511221i
\(223\) 188.473 + 150.302i 0.845169 + 0.674000i 0.947152 0.320786i \(-0.103947\pi\)
−0.101982 + 0.994786i \(0.532518\pi\)
\(224\) −390.464 + 188.037i −1.74314 + 0.839453i
\(225\) −91.0265 114.144i −0.404562 0.507305i
\(226\) 178.806 86.1087i 0.791179 0.381012i
\(227\) 191.912 + 43.8027i 0.845427 + 0.192963i 0.623230 0.782039i \(-0.285820\pi\)
0.222197 + 0.975002i \(0.428677\pi\)
\(228\) −105.052 + 131.731i −0.460753 + 0.577766i
\(229\) 15.1913 66.5573i 0.0663375 0.290643i −0.930868 0.365357i \(-0.880947\pi\)
0.997205 + 0.0747133i \(0.0238042\pi\)
\(230\) 613.131 + 295.268i 2.66579 + 1.28378i
\(231\) −119.936 150.395i −0.519204 0.651061i
\(232\) −208.036 260.869i −0.896707 1.12443i
\(233\) −124.112 + 28.3278i −0.532670 + 0.121578i −0.480391 0.877054i \(-0.659505\pi\)
−0.0522782 + 0.998633i \(0.516648\pi\)
\(234\) 47.0771 97.7567i 0.201184 0.417764i
\(235\) −42.0207 87.2569i −0.178812 0.371306i
\(236\) 111.178 + 487.101i 0.471092 + 2.06399i
\(237\) −61.7678 + 14.0981i −0.260624 + 0.0594856i
\(238\) −446.826 + 215.180i −1.87742 + 0.904117i
\(239\) −238.606 114.907i −0.998353 0.480782i −0.137974 0.990436i \(-0.544059\pi\)
−0.860379 + 0.509654i \(0.829773\pi\)
\(240\) −96.7168 423.744i −0.402987 1.76560i
\(241\) −326.311 + 260.224i −1.35399 + 1.07977i −0.365121 + 0.930960i \(0.618972\pi\)
−0.988866 + 0.148808i \(0.952456\pi\)
\(242\) 109.278 87.1462i 0.451562 0.360108i
\(243\) 103.559 215.042i 0.426168 0.884947i
\(244\) 817.993 + 186.702i 3.35243 + 0.765170i
\(245\) 417.890 + 333.256i 1.70567 + 1.36023i
\(246\) −72.9470 + 319.602i −0.296532 + 1.29919i
\(247\) 23.3053 + 48.3941i 0.0943536 + 0.195927i
\(248\) 290.161 231.396i 1.17000 0.933047i
\(249\) 11.2715 + 23.4054i 0.0452669 + 0.0939978i
\(250\) −37.3976 + 46.8951i −0.149591 + 0.187581i
\(251\) 276.471 1.10148 0.550739 0.834678i \(-0.314346\pi\)
0.550739 + 0.834678i \(0.314346\pi\)
\(252\) 544.219i 2.15960i
\(253\) 146.835 184.125i 0.580374 0.727766i
\(254\) 264.330 548.887i 1.04067 2.16097i
\(255\) −37.8816 165.970i −0.148555 0.650863i
\(256\) 93.5866 410.030i 0.365573 1.60168i
\(257\) 121.871i 0.474206i 0.971485 + 0.237103i \(0.0761978\pi\)
−0.971485 + 0.237103i \(0.923802\pi\)
\(258\) −269.209 + 128.138i −1.04345 + 0.496657i
\(259\) −181.471 −0.700660
\(260\) −361.318 82.4685i −1.38969 0.317187i
\(261\) −92.6851 + 21.1548i −0.355115 + 0.0810528i
\(262\) −235.260 113.295i −0.897938 0.432424i
\(263\) −364.495 290.675i −1.38591 1.10523i −0.981672 0.190577i \(-0.938964\pi\)
−0.404241 0.914652i \(-0.632464\pi\)
\(264\) −325.829 −1.23420
\(265\) 560.441i 2.11487i
\(266\) −302.477 241.217i −1.13713 0.906832i
\(267\) 17.1381 8.25326i 0.0641875 0.0309111i
\(268\) −336.602 422.086i −1.25598 1.57495i
\(269\) 76.0369 36.6174i 0.282665 0.136124i −0.287180 0.957877i \(-0.592718\pi\)
0.569845 + 0.821752i \(0.307003\pi\)
\(270\) −701.455 160.102i −2.59798 0.592972i
\(271\) 15.2184 19.0832i 0.0561563 0.0704177i −0.752960 0.658066i \(-0.771375\pi\)
0.809116 + 0.587648i \(0.199946\pi\)
\(272\) −86.2909 + 378.065i −0.317246 + 1.38995i
\(273\) −106.610 51.3407i −0.390513 0.188061i
\(274\) 303.730 + 380.865i 1.10850 + 1.39002i
\(275\) 154.512 + 193.753i 0.561864 + 0.704555i
\(276\) 443.028 101.118i 1.60517 0.366370i
\(277\) 192.181 399.067i 0.693793 1.44068i −0.194267 0.980949i \(-0.562233\pi\)
0.888060 0.459727i \(-0.152053\pi\)
\(278\) −17.5370 36.4159i −0.0630826 0.130992i
\(279\) −23.5302 103.092i −0.0843375 0.369507i
\(280\) 1467.75 335.005i 5.24197 1.19644i
\(281\) 417.971 201.284i 1.48744 0.716315i 0.498816 0.866708i \(-0.333768\pi\)
0.988626 + 0.150393i \(0.0480540\pi\)
\(282\) −83.6708 40.2938i −0.296705 0.142886i
\(283\) 63.9676 + 280.260i 0.226034 + 0.990319i 0.952839 + 0.303475i \(0.0981470\pi\)
−0.726805 + 0.686843i \(0.758996\pi\)
\(284\) −786.312 + 627.063i −2.76870 + 2.20797i
\(285\) 103.830 82.8014i 0.364315 0.290531i
\(286\) −79.9109 + 165.937i −0.279409 + 0.580198i
\(287\) −511.039 116.641i −1.78062 0.406416i
\(288\) 163.524 + 130.406i 0.567792 + 0.452799i
\(289\) 30.5105 133.675i 0.105573 0.462544i
\(290\) 202.326 + 420.134i 0.697675 + 1.44874i
\(291\) 48.9221 39.0141i 0.168117 0.134069i
\(292\) 278.348 + 577.995i 0.953246 + 1.97943i
\(293\) 189.051 237.063i 0.645226 0.809088i −0.346420 0.938080i \(-0.612603\pi\)
0.991646 + 0.128992i \(0.0411741\pi\)
\(294\) 512.534 1.74331
\(295\) 393.805i 1.33493i
\(296\) −191.649 + 240.320i −0.647462 + 0.811891i
\(297\) −108.033 + 224.332i −0.363747 + 0.755328i
\(298\) 187.426 + 821.167i 0.628947 + 2.75559i
\(299\) 32.2357 141.234i 0.107812 0.472354i
\(300\) 478.182i 1.59394i
\(301\) −204.891 430.462i −0.680700 1.43011i
\(302\) −379.048 −1.25512
\(303\) 299.524 + 68.3644i 0.988529 + 0.225625i
\(304\) −294.929 + 67.3156i −0.970162 + 0.221433i
\(305\) −595.828 286.936i −1.95353 0.940773i
\(306\) 187.128 + 149.230i 0.611530 + 0.487679i
\(307\) −294.750 −0.960097 −0.480049 0.877242i \(-0.659381\pi\)
−0.480049 + 0.877242i \(0.659381\pi\)
\(308\) 923.782i 2.99929i
\(309\) −112.308 89.5627i −0.363456 0.289847i
\(310\) −467.309 + 225.044i −1.50745 + 0.725949i
\(311\) 146.441 + 183.631i 0.470870 + 0.590452i 0.959384 0.282104i \(-0.0910323\pi\)
−0.488514 + 0.872556i \(0.662461\pi\)
\(312\) −180.579 + 86.9623i −0.578779 + 0.278725i
\(313\) −110.395 25.1969i −0.352699 0.0805012i 0.0425008 0.999096i \(-0.486467\pi\)
−0.395200 + 0.918595i \(0.629325\pi\)
\(314\) 532.238 667.405i 1.69502 2.12549i
\(315\) 95.4507 418.197i 0.303018 1.32761i
\(316\) −274.125 132.012i −0.867484 0.417758i
\(317\) 58.6493 + 73.5439i 0.185014 + 0.232000i 0.865685 0.500589i \(-0.166883\pi\)
−0.680671 + 0.732589i \(0.738312\pi\)
\(318\) 335.068 + 420.162i 1.05367 + 1.32127i
\(319\) 157.328 35.9091i 0.493191 0.112568i
\(320\) 50.2521 104.350i 0.157038 0.326093i
\(321\) −51.1627 106.240i −0.159385 0.330967i
\(322\) 232.185 + 1017.27i 0.721072 + 3.15922i
\(323\) −115.517 + 26.3659i −0.357636 + 0.0816281i
\(324\) −34.8338 + 16.7751i −0.107512 + 0.0517750i
\(325\) 137.345 + 66.1417i 0.422599 + 0.203513i
\(326\) 27.1318 + 118.872i 0.0832263 + 0.364638i
\(327\) 96.3867 76.8658i 0.294760 0.235064i
\(328\) −694.167 + 553.580i −2.11636 + 1.68774i
\(329\) 64.4293 133.789i 0.195834 0.406653i
\(330\) 443.947 + 101.328i 1.34529 + 0.307055i
\(331\) 320.751 + 255.791i 0.969037 + 0.772782i 0.973847 0.227207i \(-0.0729593\pi\)
−0.00480903 + 0.999988i \(0.501531\pi\)
\(332\) −27.7605 + 121.627i −0.0836160 + 0.366345i
\(333\) 37.9995 + 78.9068i 0.114113 + 0.236957i
\(334\) 698.284 556.863i 2.09067 1.66725i
\(335\) 184.627 + 383.382i 0.551126 + 1.14442i
\(336\) 415.509 521.032i 1.23663 1.55069i
\(337\) −318.775 −0.945921 −0.472960 0.881084i \(-0.656815\pi\)
−0.472960 + 0.881084i \(0.656815\pi\)
\(338\) 500.109i 1.47961i
\(339\) −65.1256 + 81.6649i −0.192111 + 0.240900i
\(340\) 354.715 736.574i 1.04328 2.16639i
\(341\) 39.9411 + 174.994i 0.117129 + 0.513178i
\(342\) −41.5478 + 182.033i −0.121485 + 0.532259i
\(343\) 276.278i 0.805476i
\(344\) −786.438 183.270i −2.28616 0.532763i
\(345\) −358.173 −1.03818
\(346\) 213.668 + 48.7683i 0.617537 + 0.140949i
\(347\) 91.8179 20.9568i 0.264605 0.0603943i −0.0881600 0.996106i \(-0.528099\pi\)
0.352765 + 0.935712i \(0.385242\pi\)
\(348\) 280.545 + 135.103i 0.806163 + 0.388228i
\(349\) −510.018 406.725i −1.46137 1.16540i −0.952492 0.304563i \(-0.901490\pi\)
−0.508876 0.860840i \(-0.669939\pi\)
\(350\) −1097.99 −3.13712
\(351\) 153.162i 0.436358i
\(352\) −277.573 221.357i −0.788560 0.628856i
\(353\) 275.129 132.495i 0.779401 0.375340i −0.00149626 0.999999i \(-0.500476\pi\)
0.780898 + 0.624659i \(0.214762\pi\)
\(354\) −235.442 295.235i −0.665091 0.833998i
\(355\) 714.210 343.945i 2.01186 0.968860i
\(356\) 89.0582 + 20.3269i 0.250163 + 0.0570982i
\(357\) 162.745 204.075i 0.455867 0.571640i
\(358\) 81.2020 355.769i 0.226821 0.993768i
\(359\) −106.443 51.2602i −0.296498 0.142786i 0.279721 0.960081i \(-0.409758\pi\)
−0.576219 + 0.817295i \(0.695472\pi\)
\(360\) −453.009 568.055i −1.25836 1.57793i
\(361\) 167.449 + 209.975i 0.463849 + 0.581648i
\(362\) −758.152 + 173.043i −2.09434 + 0.478020i
\(363\) −31.9184 + 66.2793i −0.0879296 + 0.182588i
\(364\) −246.553 511.973i −0.677344 1.40652i
\(365\) −112.517 492.971i −0.308267 1.35060i
\(366\) −618.242 + 141.110i −1.68918 + 0.385545i
\(367\) −313.419 + 150.934i −0.854002 + 0.411265i −0.809061 0.587724i \(-0.800024\pi\)
−0.0449402 + 0.998990i \(0.514310\pi\)
\(368\) 735.088 + 354.000i 1.99752 + 0.961955i
\(369\) 56.2925 + 246.633i 0.152554 + 0.668383i
\(370\) 335.860 267.839i 0.907730 0.723890i
\(371\) −671.835 + 535.770i −1.81088 + 1.44413i
\(372\) −150.274 + 312.046i −0.403961 + 0.838834i
\(373\) 613.063 + 139.928i 1.64360 + 0.375141i 0.941520 0.336957i \(-0.109398\pi\)
0.702080 + 0.712098i \(0.252255\pi\)
\(374\) −317.640 253.309i −0.849304 0.677298i
\(375\) 7.02481 30.7777i 0.0187328 0.0820739i
\(376\) −109.132 226.615i −0.290245 0.602700i
\(377\) 77.6093 61.8914i 0.205860 0.164168i
\(378\) −478.652 993.932i −1.26628 2.62945i
\(379\) −179.127 + 224.618i −0.472629 + 0.592659i −0.959813 0.280641i \(-0.909453\pi\)
0.487183 + 0.873300i \(0.338024\pi\)
\(380\) 637.760 1.67832
\(381\) 320.643i 0.841583i
\(382\) 397.669 498.661i 1.04102 1.30539i
\(383\) −94.6602 + 196.564i −0.247154 + 0.513222i −0.987230 0.159302i \(-0.949076\pi\)
0.740075 + 0.672524i \(0.234790\pi\)
\(384\) 41.7528 + 182.931i 0.108731 + 0.476383i
\(385\) −162.022 + 709.866i −0.420837 + 1.84381i
\(386\) 842.475i 2.18258i
\(387\) −144.269 + 179.228i −0.372789 + 0.463121i
\(388\) 300.498 0.774479
\(389\) 211.232 + 48.2124i 0.543013 + 0.123939i 0.485225 0.874390i \(-0.338738\pi\)
0.0577888 + 0.998329i \(0.481595\pi\)
\(390\) 273.085 62.3300i 0.700219 0.159820i
\(391\) 287.916 + 138.653i 0.736358 + 0.354611i
\(392\) 1085.30 + 865.500i 2.76863 + 2.20791i
\(393\) 137.432 0.349699
\(394\) 411.428i 1.04423i
\(395\) 187.494 + 149.521i 0.474667 + 0.378534i
\(396\) −401.677 + 193.438i −1.01434 + 0.488479i
\(397\) −6.48080 8.12667i −0.0163244 0.0204702i 0.773602 0.633671i \(-0.218453\pi\)
−0.789927 + 0.613201i \(0.789881\pi\)
\(398\) −421.458 + 202.964i −1.05894 + 0.509959i
\(399\) 198.518 + 45.3105i 0.497540 + 0.113560i
\(400\) −535.296 + 671.240i −1.33824 + 1.67810i
\(401\) −118.641 + 519.801i −0.295863 + 1.29626i 0.580361 + 0.814359i \(0.302911\pi\)
−0.876224 + 0.481903i \(0.839946\pi\)
\(402\) 367.626 + 177.039i 0.914493 + 0.440397i
\(403\) 68.8409 + 86.3238i 0.170821 + 0.214203i
\(404\) 919.894 + 1153.51i 2.27697 + 2.85522i
\(405\) 29.7097 6.78104i 0.0733573 0.0167433i
\(406\) −310.221 + 644.180i −0.764091 + 1.58665i
\(407\) −64.5021 133.940i −0.158482 0.329091i
\(408\) −98.3824 431.042i −0.241133 1.05647i
\(409\) −17.3967 + 3.97068i −0.0425347 + 0.00970827i −0.243735 0.969842i \(-0.578373\pi\)
0.201201 + 0.979550i \(0.435516\pi\)
\(410\) 1117.97 538.385i 2.72675 1.31313i
\(411\) −231.003 111.245i −0.562050 0.270669i
\(412\) −153.503 672.542i −0.372581 1.63238i
\(413\) 472.078 376.470i 1.14305 0.911549i
\(414\) 393.708 313.972i 0.950986 0.758386i
\(415\) 42.6642 88.5932i 0.102805 0.213478i
\(416\) −212.914 48.5962i −0.511813 0.116818i
\(417\) 16.6319 + 13.2635i 0.0398848 + 0.0318070i
\(418\) 70.5251 308.990i 0.168720 0.739212i
\(419\) 277.631 + 576.507i 0.662605 + 1.37591i 0.913076 + 0.407789i \(0.133700\pi\)
−0.250472 + 0.968124i \(0.580586\pi\)
\(420\) −1098.44 + 875.977i −2.61533 + 2.08566i
\(421\) −277.767 576.789i −0.659780 1.37005i −0.915115 0.403194i \(-0.867900\pi\)
0.255335 0.966853i \(-0.417814\pi\)
\(422\) −32.1888 + 40.3635i −0.0762767 + 0.0956480i
\(423\) −71.6651 −0.169421
\(424\) 1455.52i 3.43283i
\(425\) −209.662 + 262.908i −0.493323 + 0.618608i
\(426\) 329.810 684.858i 0.774202 1.60765i
\(427\) −225.633 988.561i −0.528414 2.31513i
\(428\) 126.009 552.080i 0.294413 1.28991i
\(429\) 96.9352i 0.225956i
\(430\) 1014.54 + 494.279i 2.35939 + 1.14949i
\(431\) 90.4497 0.209860 0.104930 0.994480i \(-0.466538\pi\)
0.104930 + 0.994480i \(0.466538\pi\)
\(432\) −840.979 191.948i −1.94671 0.444324i
\(433\) −388.048 + 88.5694i −0.896184 + 0.204548i −0.645717 0.763577i \(-0.723441\pi\)
−0.250467 + 0.968125i \(0.580584\pi\)
\(434\) −716.513 345.054i −1.65095 0.795056i
\(435\) −191.885 153.023i −0.441114 0.351777i
\(436\) 592.043 1.35790
\(437\) 249.291i 0.570460i
\(438\) −379.085 302.310i −0.865490 0.690205i
\(439\) −742.597 + 357.616i −1.69156 + 0.814615i −0.696263 + 0.717786i \(0.745155\pi\)
−0.995301 + 0.0968282i \(0.969130\pi\)
\(440\) 768.958 + 964.243i 1.74763 + 2.19146i
\(441\) 356.349 171.609i 0.808048 0.389135i
\(442\) −243.647 55.6109i −0.551239 0.125817i
\(443\) 270.689 339.433i 0.611035 0.766214i −0.376017 0.926613i \(-0.622707\pi\)
0.987052 + 0.160399i \(0.0512780\pi\)
\(444\) 63.8309 279.661i 0.143763 0.629868i
\(445\) −64.8702 31.2399i −0.145776 0.0702019i
\(446\) −545.535 684.079i −1.22317 1.53381i
\(447\) −276.400 346.594i −0.618344 0.775378i
\(448\) 173.130 39.5159i 0.386452 0.0882051i
\(449\) −154.251 + 320.306i −0.343544 + 0.713376i −0.999128 0.0417461i \(-0.986708\pi\)
0.655585 + 0.755122i \(0.272422\pi\)
\(450\) 229.916 + 477.426i 0.510925 + 1.06095i
\(451\) −95.5534 418.647i −0.211870 0.928263i
\(452\) −489.040 + 111.620i −1.08195 + 0.246947i
\(453\) 179.743 86.5598i 0.396784 0.191081i
\(454\) −643.720 309.999i −1.41789 0.682818i
\(455\) 99.6649 + 436.661i 0.219044 + 0.959694i
\(456\) 269.656 215.044i 0.591352 0.471587i
\(457\) 404.830 322.841i 0.885842 0.706435i −0.0708657 0.997486i \(-0.522576\pi\)
0.956708 + 0.291050i \(0.0940047\pi\)
\(458\) −107.511 + 223.250i −0.234741 + 0.487445i
\(459\) −329.391 75.1814i −0.717628 0.163794i
\(460\) −1344.79 1072.44i −2.92346 2.33138i
\(461\) 75.1765 329.370i 0.163073 0.714468i −0.825585 0.564278i \(-0.809154\pi\)
0.988657 0.150190i \(-0.0479884\pi\)
\(462\) 302.937 + 629.054i 0.655707 + 1.36159i
\(463\) 163.105 130.072i 0.352278 0.280932i −0.431322 0.902198i \(-0.641953\pi\)
0.783600 + 0.621266i \(0.213381\pi\)
\(464\) 242.570 + 503.702i 0.522780 + 1.08556i
\(465\) 170.205 213.431i 0.366033 0.458990i
\(466\) 462.061 0.991547
\(467\) 127.080i 0.272121i −0.990701 0.136060i \(-0.956556\pi\)
0.990701 0.136060i \(-0.0434442\pi\)
\(468\) −170.987 + 214.411i −0.365358 + 0.458144i
\(469\) −283.084 + 587.830i −0.603591 + 1.25337i
\(470\) 78.2202 + 342.705i 0.166426 + 0.729159i
\(471\) −99.9761 + 438.024i −0.212263 + 0.929987i
\(472\) 1022.75i 2.16685i
\(473\) 244.889 304.229i 0.517736 0.643191i
\(474\) 229.957 0.485142
\(475\) −255.749 58.3731i −0.538419 0.122891i
\(476\) 1222.08 278.931i 2.56739 0.585990i
\(477\) 373.643 + 179.937i 0.783319 + 0.377226i
\(478\) 751.525 + 599.321i 1.57223 + 1.25381i
\(479\) 543.915 1.13552 0.567761 0.823194i \(-0.307810\pi\)
0.567761 + 0.823194i \(0.307810\pi\)
\(480\) 539.955i 1.12491i
\(481\) −71.4959 57.0161i −0.148640 0.118537i
\(482\) 1364.85 657.279i 2.83165 1.36365i
\(483\) −342.406 429.364i −0.708916 0.888952i
\(484\) −318.293 + 153.282i −0.657630 + 0.316698i
\(485\) −230.913 52.7043i −0.476109 0.108669i
\(486\) −540.134 + 677.306i −1.11139 + 1.39363i
\(487\) −56.0260 + 245.466i −0.115043 + 0.504037i 0.884270 + 0.466976i \(0.154657\pi\)
−0.999313 + 0.0370606i \(0.988201\pi\)
\(488\) −1547.43 745.202i −3.17096 1.52705i
\(489\) −40.0116 50.1729i −0.0818233 0.102603i
\(490\) −1209.58 1516.77i −2.46854 3.09545i
\(491\) −50.5810 + 11.5448i −0.103016 + 0.0235128i −0.273718 0.961810i \(-0.588254\pi\)
0.170702 + 0.985323i \(0.445396\pi\)
\(492\) 359.507 746.525i 0.730706 1.51733i
\(493\) 95.0087 + 197.288i 0.192715 + 0.400178i
\(494\) −43.3821 190.070i −0.0878181 0.384756i
\(495\) 342.590 78.1938i 0.692100 0.157967i
\(496\) −560.260 + 269.807i −1.12956 + 0.543966i
\(497\) 1095.08 + 527.363i 2.20338 + 1.06109i
\(498\) −20.9815 91.9258i −0.0421315 0.184590i
\(499\) −396.319 + 316.054i −0.794227 + 0.633375i −0.934188 0.356782i \(-0.883874\pi\)
0.139961 + 0.990157i \(0.455302\pi\)
\(500\) 118.529 94.5240i 0.237059 0.189048i
\(501\) −203.958 + 423.524i −0.407102 + 0.845357i
\(502\) −978.318 223.295i −1.94884 0.444810i
\(503\) 559.050 + 445.827i 1.11143 + 0.886336i 0.994283 0.106778i \(-0.0340535\pi\)
0.117148 + 0.993115i \(0.462625\pi\)
\(504\) 247.895 1086.10i 0.491856 2.15496i
\(505\) −504.564 1047.74i −0.999136 2.07473i
\(506\) −668.298 + 532.950i −1.32075 + 1.05326i
\(507\) 114.205 + 237.150i 0.225257 + 0.467752i
\(508\) −960.065 + 1203.88i −1.88989 + 2.36985i
\(509\) −426.880 −0.838664 −0.419332 0.907833i \(-0.637736\pi\)
−0.419332 + 0.907833i \(0.637736\pi\)
\(510\) 617.896i 1.21156i
\(511\) 483.390 606.152i 0.945969 1.18621i
\(512\) −491.862 + 1021.36i −0.960668 + 1.99485i
\(513\) −58.6490 256.958i −0.114326 0.500893i
\(514\) 98.4302 431.251i 0.191499 0.839010i
\(515\) 543.727i 1.05578i
\(516\) 735.445 164.341i 1.42528 0.318491i
\(517\) 121.647 0.235295
\(518\) 642.151 + 146.567i 1.23967 + 0.282948i
\(519\) −112.457 + 25.6677i −0.216681 + 0.0494560i
\(520\) 683.519 + 329.165i 1.31446 + 0.633010i
\(521\) −579.975 462.515i −1.11320 0.887744i −0.118743 0.992925i \(-0.537886\pi\)
−0.994453 + 0.105181i \(0.966458\pi\)
\(522\) 345.061 0.661036
\(523\) 486.520i 0.930248i 0.885245 + 0.465124i \(0.153990\pi\)
−0.885245 + 0.465124i \(0.846010\pi\)
\(524\) 515.999 + 411.496i 0.984731 + 0.785297i
\(525\) 520.664 250.738i 0.991741 0.477597i
\(526\) 1055.03 + 1322.97i 2.00577 + 2.51515i
\(527\) −219.440 + 105.677i −0.416395 + 0.200525i
\(528\) 532.251 + 121.483i 1.00805 + 0.230081i
\(529\) 89.3729 112.070i 0.168947 0.211853i
\(530\) 452.646 1983.17i 0.854048 3.74183i
\(531\) −262.548 126.436i −0.494440 0.238110i
\(532\) 609.687 + 764.523i 1.14603 + 1.43707i
\(533\) −164.692 206.517i −0.308990 0.387462i
\(534\) −67.3105 + 15.3632i −0.126050 + 0.0287700i
\(535\) −193.659 + 402.136i −0.361979 + 0.751657i
\(536\) 479.496 + 995.683i 0.894582 + 1.85762i
\(537\) 42.7381 + 187.248i 0.0795868 + 0.348693i
\(538\) −298.638 + 68.1622i −0.555089 + 0.126695i
\(539\) −604.883 + 291.296i −1.12223 + 0.540438i
\(540\) 1638.46 + 789.039i 3.03418 + 1.46118i
\(541\) −160.412 702.810i −0.296510 1.29909i −0.875285 0.483607i \(-0.839326\pi\)
0.578775 0.815487i \(-0.303531\pi\)
\(542\) −69.2643 + 55.2364i −0.127794 + 0.101912i
\(543\) 319.997 255.189i 0.589313 0.469961i
\(544\) 209.023 434.041i 0.384234 0.797870i
\(545\) −454.946 103.838i −0.834763 0.190529i
\(546\) 335.783 + 267.778i 0.614988 + 0.490436i
\(547\) 175.322 768.134i 0.320515 1.40427i −0.516125 0.856513i \(-0.672626\pi\)
0.836640 0.547754i \(-0.184517\pi\)
\(548\) −534.232 1109.34i −0.974876 2.02435i
\(549\) −382.597 + 305.111i −0.696898 + 0.555758i
\(550\) −390.270 810.405i −0.709582 1.47346i
\(551\) −106.505 + 133.553i −0.193294 + 0.242383i
\(552\) −930.212 −1.68517
\(553\) 367.699i 0.664918i
\(554\) −1002.36 + 1256.92i −1.80931 + 2.26881i
\(555\) −98.0997 + 203.706i −0.176756 + 0.367038i
\(556\) 22.7326 + 99.5982i 0.0408861 + 0.179134i
\(557\) 49.3092 216.038i 0.0885264 0.387859i −0.911182 0.412004i \(-0.864829\pi\)
0.999708 + 0.0241445i \(0.00768617\pi\)
\(558\) 383.806i 0.687824i
\(559\) 54.5235 233.968i 0.0975376 0.418547i
\(560\) −2522.52 −4.50450
\(561\) 208.470 + 47.5819i 0.371604 + 0.0848162i
\(562\) −1641.60 + 374.684i −2.92099 + 0.666698i
\(563\) 193.185 + 93.0328i 0.343134 + 0.165245i 0.597511 0.801860i \(-0.296156\pi\)
−0.254377 + 0.967105i \(0.581871\pi\)
\(564\) 183.517 + 146.350i 0.325384 + 0.259485i
\(565\) 395.372 0.699773
\(566\) 1043.39i 1.84345i
\(567\) 36.5307 + 29.1323i 0.0644281 + 0.0513797i
\(568\) 1854.88 893.262i 3.26563 1.57264i
\(569\) −592.360 742.796i −1.04106 1.30544i −0.950895 0.309514i \(-0.899833\pi\)
−0.0901603 0.995927i \(-0.528738\pi\)
\(570\) −434.286 + 209.141i −0.761906 + 0.366914i
\(571\) 996.896 + 227.535i 1.74588 + 0.398485i 0.972025 0.234879i \(-0.0754694\pi\)
0.773854 + 0.633364i \(0.218327\pi\)
\(572\) 290.242 363.952i 0.507416 0.636279i
\(573\) −74.6985 + 327.275i −0.130364 + 0.571161i
\(574\) 1714.15 + 825.492i 2.98633 + 1.43814i
\(575\) 441.119 + 553.145i 0.767163 + 0.961992i
\(576\) −53.4353 67.0057i −0.0927695 0.116329i
\(577\) 986.398 225.139i 1.70953 0.390189i 0.747743 0.663989i \(-0.231138\pi\)
0.961787 + 0.273800i \(0.0882806\pi\)
\(578\) −215.928 + 448.380i −0.373578 + 0.775744i
\(579\) 192.389 + 399.499i 0.332278 + 0.689982i
\(580\) −262.269 1149.08i −0.452188 1.98116i
\(581\) 146.988 33.5491i 0.252992 0.0577438i
\(582\) −204.625 + 98.5424i −0.351590 + 0.169317i
\(583\) −634.238 305.433i −1.08789 0.523899i
\(584\) −292.219 1280.30i −0.500375 2.19229i
\(585\) 168.998 134.772i 0.288886 0.230379i
\(586\) −860.441 + 686.179i −1.46833 + 1.17095i
\(587\) −368.008 + 764.177i −0.626930 + 1.30183i 0.309473 + 0.950908i \(0.399847\pi\)
−0.936403 + 0.350926i \(0.885867\pi\)
\(588\) −1262.97 288.265i −2.14791 0.490246i
\(589\) −148.549 118.464i −0.252206 0.201127i
\(590\) −318.060 + 1393.51i −0.539085 + 2.36189i
\(591\) −93.9542 195.098i −0.158975 0.330115i
\(592\) 402.665 321.115i 0.680178 0.542424i
\(593\) 172.295 + 357.775i 0.290549 + 0.603331i 0.994240 0.107175i \(-0.0341805\pi\)
−0.703691 + 0.710506i \(0.748466\pi\)
\(594\) 563.468 706.567i 0.948600 1.18951i
\(595\) −988.009 −1.66052
\(596\) 2128.91i 3.57200i
\(597\) 153.505 192.489i 0.257128 0.322428i
\(598\) −228.138 + 473.734i −0.381502 + 0.792197i
\(599\) −8.60496 37.7008i −0.0143655 0.0629395i 0.967237 0.253875i \(-0.0817051\pi\)
−0.981603 + 0.190935i \(0.938848\pi\)
\(600\) 217.815 954.310i 0.363025 1.59052i
\(601\) 561.024i 0.933485i −0.884393 0.466742i \(-0.845428\pi\)
0.884393 0.466742i \(-0.154572\pi\)
\(602\) 377.357 + 1688.71i 0.626838 + 2.80517i
\(603\) 314.876 0.522183
\(604\) 934.037 + 213.188i 1.54642 + 0.352960i
\(605\) 271.471 61.9616i 0.448713 0.102416i
\(606\) −1004.68 483.828i −1.65789 0.798395i
\(607\) 198.596 + 158.375i 0.327176 + 0.260914i 0.773277 0.634069i \(-0.218616\pi\)
−0.446101 + 0.894983i \(0.647188\pi\)
\(608\) 375.813 0.618114
\(609\) 376.311i 0.617916i
\(610\) 1876.65 + 1496.57i 3.07647 + 2.45340i
\(611\) 67.4187 32.4671i 0.110342 0.0531377i
\(612\) −377.184 472.974i −0.616314 0.772833i
\(613\) −770.564 + 371.084i −1.25704 + 0.605358i −0.939390 0.342851i \(-0.888607\pi\)
−0.317648 + 0.948209i \(0.602893\pi\)
\(614\) 1043.00 + 238.058i 1.69870 + 0.387716i
\(615\) −407.191 + 510.601i −0.662099 + 0.830246i
\(616\) −420.789 + 1843.60i −0.683098 + 2.99285i
\(617\) 678.741 + 326.865i 1.10007 + 0.529764i 0.893679 0.448706i \(-0.148115\pi\)
0.206388 + 0.978470i \(0.433829\pi\)
\(618\) 325.076 + 407.632i 0.526013 + 0.659600i
\(619\) 202.593 + 254.043i 0.327290 + 0.410409i 0.918066 0.396426i \(-0.129750\pi\)
−0.590776 + 0.806835i \(0.701178\pi\)
\(620\) 1278.10 291.718i 2.06145 0.470513i
\(621\) −308.424 + 640.448i −0.496657 + 1.03132i
\(622\) −369.882 768.068i −0.594666 1.23484i
\(623\) −24.5655 107.629i −0.0394310 0.172759i
\(624\) 327.404 74.7279i 0.524686 0.119756i
\(625\) 506.922 244.121i 0.811076 0.390593i
\(626\) 370.291 + 178.323i 0.591520 + 0.284861i
\(627\) 37.1187 + 162.628i 0.0592004 + 0.259374i
\(628\) −1686.89 + 1345.25i −2.68614 + 2.14212i
\(629\) 157.714 125.773i 0.250738 0.199957i
\(630\) −675.522 + 1402.74i −1.07226 + 2.22656i
\(631\) −490.091 111.860i −0.776689 0.177274i −0.184239 0.982881i \(-0.558982\pi\)
−0.592450 + 0.805607i \(0.701839\pi\)
\(632\) 486.940 + 388.322i 0.770475 + 0.614433i
\(633\) 6.04637 26.4909i 0.00955193 0.0418498i
\(634\) −148.137 307.611i −0.233655 0.485190i
\(635\) 948.896 756.720i 1.49432 1.19168i
\(636\) −589.353 1223.80i −0.926656 1.92422i
\(637\) −257.489 + 322.881i −0.404221 + 0.506877i
\(638\) −585.721 −0.918059
\(639\) 586.589i 0.917979i
\(640\) 442.820 555.279i 0.691906 0.867623i
\(641\) 16.8968 35.0865i 0.0263600 0.0547371i −0.887373 0.461052i \(-0.847472\pi\)
0.913733 + 0.406315i \(0.133186\pi\)
\(642\) 95.2377 + 417.264i 0.148345 + 0.649943i
\(643\) −12.4460 + 54.5296i −0.0193562 + 0.0848050i −0.983683 0.179908i \(-0.942420\pi\)
0.964327 + 0.264713i \(0.0852772\pi\)
\(644\) 2637.31i 4.09521i
\(645\) −593.965 2.70430i −0.920877 0.00419271i
\(646\) 430.060 0.665728
\(647\) −912.741 208.327i −1.41073 0.321989i −0.551753 0.834007i \(-0.686041\pi\)
−0.858975 + 0.512018i \(0.828898\pi\)
\(648\) 77.1591 17.6111i 0.119073 0.0271776i
\(649\) 445.660 + 214.619i 0.686687 + 0.330691i
\(650\) −432.586 344.976i −0.665517 0.530732i
\(651\) 418.565 0.642957
\(652\) 308.181i 0.472670i
\(653\) −769.287 613.486i −1.17808 0.939489i −0.179065 0.983837i \(-0.557307\pi\)
−0.999016 + 0.0443486i \(0.985879\pi\)
\(654\) −403.154 + 194.149i −0.616444 + 0.296864i
\(655\) −324.339 406.709i −0.495174 0.620929i
\(656\) 1340.34 645.474i 2.04320 0.983955i
\(657\) −364.786 83.2601i −0.555230 0.126728i
\(658\) −336.045 + 421.387i −0.510706 + 0.640405i
\(659\) −70.0648 + 306.974i −0.106320 + 0.465818i 0.893539 + 0.448987i \(0.148215\pi\)
−0.999858 + 0.0168311i \(0.994642\pi\)
\(660\) −1036.97 499.379i −1.57117 0.756634i
\(661\) −14.3813 18.0336i −0.0217569 0.0272823i 0.770834 0.637036i \(-0.219840\pi\)
−0.792591 + 0.609754i \(0.791268\pi\)
\(662\) −928.416 1164.20i −1.40244 1.75861i
\(663\) 128.236 29.2691i 0.193418 0.0441464i
\(664\) 110.803 230.086i 0.166873 0.346515i
\(665\) −334.414 694.419i −0.502879 1.04424i
\(666\) −70.7349 309.910i −0.106208 0.465330i
\(667\) 449.156 102.517i 0.673398 0.153699i
\(668\) −2033.89 + 979.468i −3.04474 + 1.46627i
\(669\) 414.908 + 199.809i 0.620192 + 0.298669i
\(670\) −343.677 1505.75i −0.512951 2.24739i
\(671\) 649.438 517.909i 0.967866 0.771847i
\(672\) −647.278 + 516.187i −0.963211 + 0.768135i
\(673\) 429.761 892.407i 0.638574 1.32601i −0.290768 0.956794i \(-0.593911\pi\)
0.929342 0.369220i \(-0.120375\pi\)
\(674\) 1128.02 + 257.462i 1.67361 + 0.381991i
\(675\) −584.821 466.379i −0.866401 0.690932i
\(676\) −281.277 + 1232.35i −0.416090 + 1.82301i
\(677\) 434.321 + 901.876i 0.641537 + 1.33217i 0.927463 + 0.373914i \(0.121985\pi\)
−0.285926 + 0.958252i \(0.592301\pi\)
\(678\) 296.410 236.379i 0.437184 0.348642i
\(679\) −157.568 327.194i −0.232059 0.481876i
\(680\) −1043.42 + 1308.41i −1.53444 + 1.92413i
\(681\) 376.042 0.552191
\(682\) 651.490i 0.955263i
\(683\) −719.357 + 902.045i −1.05323 + 1.32071i −0.108056 + 0.994145i \(0.534463\pi\)
−0.945175 + 0.326565i \(0.894109\pi\)
\(684\) 204.762 425.192i 0.299359 0.621625i
\(685\) 215.954 + 946.157i 0.315262 + 1.38125i
\(686\) 223.139 977.635i 0.325275 1.42512i
\(687\) 130.416i 0.189834i
\(688\) 1216.34 + 592.595i 1.76793 + 0.861330i
\(689\) −433.022 −0.628480
\(690\) 1267.43 + 289.282i 1.83685 + 0.419249i
\(691\) 225.043 51.3647i 0.325678 0.0743338i −0.0565562 0.998399i \(-0.518012\pi\)
0.382234 + 0.924066i \(0.375155\pi\)
\(692\) −499.085 240.347i −0.721221 0.347322i
\(693\) 421.245 + 335.932i 0.607857 + 0.484750i
\(694\) −341.832 −0.492553
\(695\) 80.5218i 0.115859i
\(696\) −498.344 397.416i −0.716011 0.571000i
\(697\) 524.979 252.817i 0.753198 0.362721i
\(698\) 1476.25 + 1851.16i 2.11497 + 2.65209i
\(699\) −219.108 + 105.517i −0.313459 + 0.150954i
\(700\) 2705.64 + 617.544i 3.86519 + 0.882205i
\(701\) −411.060 + 515.453i −0.586391 + 0.735311i −0.983188 0.182596i \(-0.941550\pi\)
0.396797 + 0.917906i \(0.370122\pi\)
\(702\) 123.703 541.976i 0.176214 0.772046i
\(703\) 141.781 + 68.2781i 0.201680 + 0.0971239i
\(704\) 90.7034 + 113.738i 0.128840 + 0.161560i
\(705\) −115.352 144.647i −0.163620 0.205173i
\(706\) −1080.58 + 246.635i −1.53057 + 0.349342i
\(707\) 773.635 1606.47i 1.09425 2.27223i
\(708\) 414.120 + 859.930i 0.584916 + 1.21459i
\(709\) −43.1041 188.851i −0.0607956 0.266363i 0.935391 0.353616i \(-0.115048\pi\)
−0.996186 + 0.0872534i \(0.972191\pi\)
\(710\) −2805.09 + 640.243i −3.95083 + 0.901751i
\(711\) 159.882 76.9953i 0.224870 0.108291i
\(712\) −168.475 81.1331i −0.236622 0.113951i
\(713\) 114.028 + 499.590i 0.159927 + 0.700688i
\(714\) −740.710 + 590.697i −1.03741 + 0.827306i
\(715\) −286.865 + 228.767i −0.401210 + 0.319954i
\(716\) −400.191 + 831.005i −0.558926 + 1.16062i
\(717\) −493.233 112.577i −0.687911 0.157011i
\(718\) 335.257 + 267.358i 0.466932 + 0.372366i
\(719\) 158.708 695.345i 0.220734 0.967100i −0.736193 0.676772i \(-0.763378\pi\)
0.956927 0.290328i \(-0.0937645\pi\)
\(720\) 528.209 + 1096.84i 0.733623 + 1.52338i
\(721\) −651.800 + 519.793i −0.904022 + 0.720933i
\(722\) −422.947 878.258i −0.585799 1.21642i
\(723\) −497.112 + 623.359i −0.687569 + 0.862184i
\(724\) 1965.54 2.71483
\(725\) 484.798i 0.668686i
\(726\) 166.477 208.756i 0.229308 0.287543i
\(727\) 423.494 879.395i 0.582523 1.20962i −0.376533 0.926403i \(-0.622884\pi\)
0.959056 0.283218i \(-0.0914020\pi\)
\(728\) 258.840 + 1134.05i 0.355550 + 1.55776i
\(729\) 109.899 481.501i 0.150754 0.660495i
\(730\) 1835.30i 2.51411i
\(731\) 476.410 + 232.105i 0.651724 + 0.317517i
\(732\) 1602.82 2.18964
\(733\) −522.196 119.188i −0.712409 0.162603i −0.149068 0.988827i \(-0.547627\pi\)
−0.563341 + 0.826224i \(0.690484\pi\)
\(734\) 1230.96 280.959i 1.67706 0.382779i
\(735\) 919.952 + 443.025i 1.25163 + 0.602756i
\(736\) −792.445 631.954i −1.07669 0.858633i
\(737\) −534.485 −0.725217
\(738\) 918.200i 1.24417i
\(739\) −515.544 411.133i −0.697624 0.556336i 0.209186 0.977876i \(-0.432918\pi\)
−0.906810 + 0.421539i \(0.861490\pi\)
\(740\) −978.257 + 471.104i −1.32197 + 0.636627i
\(741\) 63.9762 + 80.2236i 0.0863377 + 0.108264i
\(742\) 2810.07 1353.26i 3.78716 1.82380i
\(743\) −53.3684 12.1810i −0.0718282 0.0163943i 0.186456 0.982463i \(-0.440300\pi\)
−0.258284 + 0.966069i \(0.583157\pi\)
\(744\) 442.040 554.301i 0.594140 0.745028i
\(745\) −373.390 + 1635.93i −0.501194 + 2.19588i
\(746\) −2056.36 990.293i −2.75652 1.32747i
\(747\) −45.3667 56.8881i −0.0607319 0.0761554i
\(748\) 640.250 + 802.848i 0.855949 + 1.07333i
\(749\) −667.200 + 152.284i −0.890788 + 0.203316i
\(750\) −49.7159 + 103.236i −0.0662878 + 0.137648i
\(751\) 78.2859 + 162.562i 0.104242 + 0.216461i 0.946566 0.322511i \(-0.104527\pi\)
−0.842323 + 0.538972i \(0.818813\pi\)
\(752\) 93.7788 + 410.872i 0.124706 + 0.546372i
\(753\) 514.907 117.524i 0.683808 0.156075i
\(754\) −324.615 + 156.326i −0.430524 + 0.207329i
\(755\) −680.355 327.642i −0.901133 0.433963i
\(756\) 620.463 + 2718.43i 0.820718 + 3.59580i
\(757\) 15.6363 12.4695i 0.0206556 0.0164723i −0.613108 0.789999i \(-0.710081\pi\)
0.633763 + 0.773527i \(0.281509\pi\)
\(758\) 815.270 650.156i 1.07555 0.857726i
\(759\) 195.200 405.336i 0.257180 0.534040i
\(760\) −1272.78 290.504i −1.67471 0.382242i
\(761\) 61.5912 + 49.1173i 0.0809346 + 0.0645432i 0.663121 0.748512i \(-0.269231\pi\)
−0.582187 + 0.813055i \(0.697803\pi\)
\(762\) 258.971 1134.63i 0.339857 1.48901i
\(763\) −310.442 644.639i −0.406870 0.844875i
\(764\) −1260.38 + 1005.12i −1.64972 + 1.31561i
\(765\) 206.886 + 429.604i 0.270440 + 0.561574i
\(766\) 493.720 619.106i 0.644544 0.808232i
\(767\) 304.272 0.396704
\(768\) 803.433i 1.04614i
\(769\) −516.616 + 647.816i −0.671802 + 0.842413i −0.994571 0.104065i \(-0.966815\pi\)
0.322768 + 0.946478i \(0.395386\pi\)
\(770\) 1146.66 2381.07i 1.48917 3.09229i
\(771\) 51.8057 + 226.976i 0.0671929 + 0.294391i
\(772\) −473.834 + 2076.00i −0.613775 + 2.68912i
\(773\) 748.866i 0.968779i 0.874852 + 0.484390i \(0.160958\pi\)
−0.874852 + 0.484390i \(0.839042\pi\)
\(774\) 655.265 517.693i 0.846595 0.668854i
\(775\) −539.233 −0.695785
\(776\) −599.704 136.879i −0.772815 0.176390i
\(777\) −337.976 + 77.1409i −0.434976 + 0.0992804i
\(778\) −708.525 341.208i −0.910701 0.438570i
\(779\) 355.382 + 283.408i 0.456203 + 0.363810i
\(780\) −707.985 −0.907674
\(781\) 995.702i 1.27491i
\(782\) −906.832 723.175i −1.15963 0.924776i
\(783\) −438.852 + 211.340i −0.560475 + 0.269911i
\(784\) −1450.18 1818.47i −1.84972 2.31947i
\(785\) 1532.21 737.874i 1.95186 0.939967i
\(786\) −486.314 110.998i −0.618721 0.141219i
\(787\) 199.457 250.112i 0.253440 0.317804i −0.638793 0.769378i \(-0.720566\pi\)
0.892233 + 0.451575i \(0.149138\pi\)
\(788\) 231.400 1013.83i 0.293655 1.28658i
\(789\) −802.408 386.419i −1.01699 0.489759i
\(790\) −542.701 680.525i −0.686963 0.861424i
\(791\) 377.968 + 473.957i 0.477836 + 0.599187i
\(792\) 889.740 203.077i 1.12341 0.256411i
\(793\) 221.700 460.364i 0.279571 0.580535i
\(794\) 16.3693 + 33.9912i 0.0206163 + 0.0428101i
\(795\) 238.236 + 1043.78i 0.299668 + 1.31293i
\(796\) 1152.70 263.096i 1.44811 0.330522i
\(797\) 415.766 200.222i 0.521663 0.251220i −0.154472 0.987997i \(-0.549368\pi\)
0.676135 + 0.736777i \(0.263653\pi\)
\(798\) −665.880 320.671i −0.834436 0.401843i
\(799\) 36.7308 + 160.928i 0.0459710 + 0.201412i
\(800\) 833.882 664.999i 1.04235 0.831248i
\(801\) −41.6549 + 33.2187i −0.0520036 + 0.0414715i
\(802\) 839.646 1743.54i 1.04694 2.17399i
\(803\) 619.205 + 141.329i 0.771114 + 0.176002i
\(804\) −806.321 643.020i −1.00289 0.799776i
\(805\) −462.559 + 2026.60i −0.574607 + 2.51752i
\(806\) −173.880 361.065i −0.215731 0.447971i
\(807\) 126.048 100.520i 0.156193 0.124560i
\(808\) −1310.40 2721.08i −1.62179 3.36768i
\(809\) −243.386 + 305.196i −0.300848 + 0.377251i −0.909160 0.416447i \(-0.863275\pi\)
0.608313 + 0.793698i \(0.291847\pi\)
\(810\) −110.607 −0.136552
\(811\) 101.122i 0.124688i −0.998055 0.0623439i \(-0.980142\pi\)
0.998055 0.0623439i \(-0.0198576\pi\)
\(812\) 1126.74 1412.89i 1.38762 1.74001i
\(813\) 20.2311 42.0102i 0.0248844 0.0516731i
\(814\) 120.069 + 526.055i 0.147504 + 0.646259i
\(815\) −54.0519 + 236.817i −0.0663213 + 0.290573i
\(816\) 740.800i 0.907844i
\(817\) −1.88221 + 413.404i −0.00230381 + 0.506003i
\(818\) 64.7667 0.0791769
\(819\) 323.118 + 73.7496i 0.394528 + 0.0900484i
\(820\) −3057.67 + 697.893i −3.72886 + 0.851089i
\(821\) −328.283 158.093i −0.399858 0.192561i 0.223137 0.974787i \(-0.428370\pi\)
−0.622995 + 0.782226i \(0.714084\pi\)
\(822\) 727.576 + 580.223i 0.885129 + 0.705867i
\(823\) −471.027 −0.572329 −0.286164 0.958181i \(-0.592380\pi\)
−0.286164 + 0.958181i \(0.592380\pi\)
\(824\) 1412.12i 1.71373i
\(825\) 370.130 + 295.169i 0.448642 + 0.357780i
\(826\) −1974.55 + 950.893i −2.39050 + 1.15120i
\(827\) 264.259 + 331.370i 0.319539 + 0.400689i 0.915496 0.402327i \(-0.131799\pi\)
−0.595957 + 0.803016i \(0.703227\pi\)
\(828\) −1146.75 + 552.246i −1.38496 + 0.666964i
\(829\) 328.286 + 74.9291i 0.396002 + 0.0903849i 0.415885 0.909417i \(-0.363472\pi\)
−0.0198824 + 0.999802i \(0.506329\pi\)
\(830\) −222.525 + 279.037i −0.268102 + 0.336189i
\(831\) 188.284 824.927i 0.226576 0.992692i
\(832\) 80.6253 + 38.8271i 0.0969055 + 0.0466672i
\(833\) −567.999 712.249i −0.681872 0.855040i
\(834\) −48.1412 60.3672i −0.0577233 0.0723827i
\(835\) 1734.70 395.933i 2.07748 0.474172i
\(836\) −347.571 + 721.740i −0.415755 + 0.863325i
\(837\) −235.071 488.129i −0.280849 0.583189i
\(838\) −516.802 2264.26i −0.616708 2.70198i
\(839\) −221.701 + 50.6018i −0.264244 + 0.0603120i −0.352590 0.935778i \(-0.614699\pi\)
0.0883459 + 0.996090i \(0.471842\pi\)
\(840\) 2591.17 1247.84i 3.08473 1.48553i
\(841\) −473.289 227.924i −0.562769 0.271015i
\(842\) 517.054 + 2265.36i 0.614079 + 2.69046i
\(843\) 692.878 552.552i 0.821919 0.655459i
\(844\) 102.020 81.3584i 0.120877 0.0963963i
\(845\) 432.285 897.650i 0.511580 1.06231i
\(846\) 253.593 + 57.8810i 0.299756 + 0.0684173i
\(847\) 333.799 + 266.196i 0.394095 + 0.314280i
\(848\) 542.680 2377.64i 0.639953 2.80382i
\(849\) 238.270 + 494.773i 0.280648 + 0.582771i
\(850\) 954.250 760.989i 1.12265 0.895281i
\(851\) −184.147 382.386i −0.216390 0.449337i
\(852\) −1197.89 + 1502.11i −1.40598 + 1.76304i
\(853\) −749.133 −0.878233 −0.439116 0.898430i \(-0.644708\pi\)
−0.439116 + 0.898430i \(0.644708\pi\)
\(854\) 3680.35i 4.30954i
\(855\) −231.920 + 290.819i −0.271252 + 0.340139i
\(856\) −502.952 + 1044.39i −0.587560 + 1.22008i
\(857\) 113.883 + 498.952i 0.132885 + 0.582208i 0.996896 + 0.0787339i \(0.0250877\pi\)
−0.864011 + 0.503474i \(0.832055\pi\)
\(858\) −78.2907 + 343.014i −0.0912479 + 0.399783i
\(859\) 663.778i 0.772733i −0.922345 0.386367i \(-0.873730\pi\)
0.922345 0.386367i \(-0.126270\pi\)
\(860\) −2222.00 1788.60i −2.58372 2.07976i
\(861\) −1001.36 −1.16302
\(862\) −320.065 73.0526i −0.371305 0.0847478i
\(863\) 1051.97 240.106i 1.21897 0.278222i 0.435809 0.900039i \(-0.356462\pi\)
0.783163 + 0.621817i \(0.213605\pi\)
\(864\) 965.494 + 464.957i 1.11747 + 0.538145i
\(865\) 341.359 + 272.225i 0.394635 + 0.314711i
\(866\) 1444.68 1.66822
\(867\) 261.930i 0.302111i
\(868\) 1571.54 + 1253.26i 1.81053 + 1.44385i
\(869\) −271.391 + 130.695i −0.312303 + 0.150397i
\(870\) 555.411 + 696.463i 0.638403 + 0.800532i
\(871\) −296.219 + 142.652i −0.340091 + 0.163779i
\(872\) −1181.54 269.679i −1.35498 0.309265i
\(873\) −109.275 + 137.027i −0.125172 + 0.156961i
\(874\) 201.342 882.139i 0.230369 1.00931i
\(875\) −165.073 79.4951i −0.188655 0.0908515i
\(876\) 764.100 + 958.152i 0.872261 + 1.09378i
\(877\) 537.003 + 673.381i 0.612318 + 0.767823i 0.987241 0.159233i \(-0.0509021\pi\)
−0.374923 + 0.927056i \(0.622331\pi\)
\(878\) 2916.58 665.690i 3.32184 0.758189i
\(879\) 251.322 521.875i 0.285918 0.593715i
\(880\) −896.605 1861.82i −1.01887 2.11570i
\(881\) 3.66727 + 16.0674i 0.00416263 + 0.0182377i 0.976967 0.213392i \(-0.0684513\pi\)
−0.972804 + 0.231630i \(0.925594\pi\)
\(882\) −1399.58 + 319.444i −1.58682 + 0.362181i
\(883\) −1010.01 + 486.394i −1.14384 + 0.550842i −0.907176 0.420750i \(-0.861767\pi\)
−0.236659 + 0.971593i \(0.576053\pi\)
\(884\) 569.111 + 274.070i 0.643791 + 0.310033i
\(885\) −167.401 733.432i −0.189154 0.828737i
\(886\) −1232.00 + 982.489i −1.39052 + 1.10890i
\(887\) −1171.09 + 933.914i −1.32028 + 1.05289i −0.326083 + 0.945341i \(0.605729\pi\)
−0.994200 + 0.107550i \(0.965700\pi\)
\(888\) −254.775 + 529.046i −0.286909 + 0.595772i
\(889\) 1814.25 + 414.091i 2.04078 + 0.465795i
\(890\) 204.318 + 162.938i 0.229571 + 0.183077i
\(891\) −8.51745 + 37.3174i −0.00955943 + 0.0418826i
\(892\) 959.544 + 1992.51i 1.07572 + 2.23376i
\(893\) −100.676 + 80.2861i −0.112739 + 0.0899060i
\(894\) 698.135 + 1449.69i 0.780912 + 1.62158i
\(895\) 453.270 568.383i 0.506447 0.635065i
\(896\) 1088.97 1.21537
\(897\) 276.741i 0.308518i
\(898\) 804.530 1008.85i 0.895913 1.12344i
\(899\) −152.352 + 316.363i −0.169469 + 0.351905i
\(900\) −298.034 1305.77i −0.331149 1.45086i
\(901\) 212.555 931.263i 0.235910 1.03359i
\(902\) 1558.59i 1.72793i
\(903\) −564.578 714.608i −0.625224 0.791371i
\(904\) 1026.82 1.13586
\(905\) −1510.39 344.736i −1.66894 0.380924i
\(906\) −705.948 + 161.128i −0.779193 + 0.177846i
\(907\) −816.659 393.282i −0.900396 0.433608i −0.0743642 0.997231i \(-0.523693\pi\)
−0.826032 + 0.563623i \(0.809407\pi\)
\(908\) 1411.88 + 1125.94i 1.55494 + 1.24002i
\(909\) −860.519 −0.946665
\(910\) 1625.66i 1.78644i
\(911\) 773.335 + 616.714i 0.848886 + 0.676964i 0.948055 0.318107i \(-0.103047\pi\)
−0.0991693 + 0.995071i \(0.531619\pi\)
\(912\) −520.669 + 250.741i −0.570909 + 0.274935i
\(913\) 77.0075 + 96.5644i 0.0843456 + 0.105766i
\(914\) −1693.27 + 815.437i −1.85260 + 0.892163i
\(915\) −1231.66 281.118i −1.34608 0.307233i
\(916\) 390.489 489.658i 0.426298 0.534561i
\(917\) 177.485 777.611i 0.193549 0.847995i
\(918\) 1104.86 + 532.072i 1.20355 + 0.579599i
\(919\) 122.826 + 154.020i 0.133652 + 0.167595i 0.844154 0.536101i \(-0.180103\pi\)
−0.710502 + 0.703696i \(0.751532\pi\)
\(920\) 2195.30 + 2752.82i 2.38620 + 2.99220i
\(921\) −548.950 + 125.294i −0.596037 + 0.136042i
\(922\) −532.038 + 1104.79i −0.577048 + 1.19825i
\(923\) 265.748 + 551.832i 0.287918 + 0.597868i
\(924\) −392.688 1720.48i −0.424987 1.86199i
\(925\) 435.412 99.3799i 0.470715 0.107438i
\(926\) −682.215 + 328.537i −0.736733 + 0.354792i
\(927\) 362.500 + 174.571i 0.391047 + 0.188318i
\(928\) −154.547 677.116i −0.166538 0.729651i
\(929\) 79.3250 63.2596i 0.0853875 0.0680943i −0.579866 0.814712i \(-0.696895\pi\)
0.665253 + 0.746618i \(0.268324\pi\)
\(930\) −774.666 + 617.775i −0.832974 + 0.664275i
\(931\) 308.349 640.293i 0.331202 0.687748i
\(932\) −1138.60 259.877i −1.22167 0.278838i
\(933\) 350.794 + 279.749i 0.375985 + 0.299838i
\(934\) −102.638 + 449.686i −0.109891 + 0.481462i
\(935\) −351.178 729.229i −0.375592 0.779924i
\(936\) 438.906 350.016i 0.468917 0.373949i
\(937\) 329.508 + 684.231i 0.351663 + 0.730236i 0.999502 0.0315411i \(-0.0100415\pi\)
−0.647839 + 0.761777i \(0.724327\pi\)
\(938\) 1476.49 1851.45i 1.57408 1.97383i
\(939\) −216.313 −0.230365
\(940\) 888.477i 0.945188i
\(941\) −344.534 + 432.032i −0.366136 + 0.459120i −0.930439 0.366448i \(-0.880574\pi\)
0.564302 + 0.825568i \(0.309145\pi\)
\(942\) 707.549 1469.24i 0.751114 1.55970i
\(943\) −272.796 1195.20i −0.289285 1.26744i
\(944\) −381.325 + 1670.69i −0.403946 + 1.76980i
\(945\) 2197.76i 2.32567i
\(946\) −1112.28 + 878.756i −1.17577 + 0.928917i
\(947\) −374.964 −0.395949 −0.197975 0.980207i \(-0.563436\pi\)
−0.197975 + 0.980207i \(0.563436\pi\)
\(948\) −566.654 129.335i −0.597737 0.136429i
\(949\) 380.892 86.9361i 0.401361 0.0916081i
\(950\) 857.846 + 413.117i 0.902996 + 0.434860i
\(951\) 140.493 + 112.039i 0.147732 + 0.117812i
\(952\) −2565.96 −2.69534
\(953\) 1123.12i 1.17851i −0.807946 0.589256i \(-0.799421\pi\)
0.807946 0.589256i \(-0.200579\pi\)
\(954\) −1176.84 938.500i −1.23359 0.983753i
\(955\) 1144.81 551.312i 1.19876 0.577290i
\(956\) −1514.81 1899.51i −1.58453 1.98693i
\(957\) 277.747 133.756i 0.290227 0.139766i
\(958\) −1924.69 439.298i −2.00907 0.458558i
\(959\) −927.769 + 1163.39i −0.967434 + 1.21312i
\(960\) 49.2333 215.705i 0.0512847 0.224693i
\(961\) 513.945 + 247.503i 0.534802 + 0.257547i
\(962\) 206.945 + 259.501i 0.215120 + 0.269752i
\(963\) 205.926 + 258.223i 0.213838 + 0.268144i
\(964\) −3732.90 + 852.011i −3.87231 + 0.883829i
\(965\) 728.221 1512.17i 0.754633 1.56701i
\(966\) 864.856 + 1795.89i 0.895296 + 1.85910i
\(967\) 405.766 + 1777.78i 0.419613 + 1.83844i 0.534636 + 0.845082i \(0.320449\pi\)
−0.115023 + 0.993363i \(0.536694\pi\)
\(968\) 705.039 160.921i 0.728346 0.166240i
\(969\) −203.933 + 98.2091i −0.210458 + 0.101351i
\(970\) 774.539 + 372.998i 0.798494 + 0.384534i
\(971\) −386.164 1691.90i −0.397697 1.74243i −0.636424 0.771339i \(-0.719587\pi\)
0.238727 0.971087i \(-0.423270\pi\)
\(972\) 1711.92 1365.21i 1.76123 1.40454i
\(973\) 96.5265 76.9773i 0.0992050 0.0791133i
\(974\) 396.506 823.354i 0.407091 0.845332i
\(975\) 283.910 + 64.8007i 0.291190 + 0.0664622i
\(976\) 2249.93 + 1794.26i 2.30525 + 1.83838i
\(977\) 1.75913 7.70725i 0.00180054 0.00788869i −0.974020 0.226463i \(-0.927284\pi\)
0.975820 + 0.218575i \(0.0701408\pi\)
\(978\) 101.062 + 209.857i 0.103335 + 0.214578i
\(979\) 70.7069 56.3869i 0.0722236 0.0575964i
\(980\) 2127.54 + 4417.88i 2.17096 + 4.50804i
\(981\) −215.295 + 269.971i −0.219465 + 0.275200i
\(982\) 188.310 0.191761
\(983\) 1165.48i 1.18563i −0.805337 0.592817i \(-0.798016\pi\)
0.805337 0.592817i \(-0.201984\pi\)
\(984\) −1057.52 + 1326.08i −1.07471 + 1.34765i
\(985\) −355.631 + 738.476i −0.361047 + 0.749721i
\(986\) −176.856 774.855i −0.179367 0.785857i
\(987\) 63.1230 276.560i 0.0639544 0.280202i
\(988\) 492.763i 0.498748i
\(989\) 699.135 868.546i 0.706911 0.878206i
\(990\) −1275.44 −1.28832
\(991\) 1345.16 + 307.023i 1.35737 + 0.309811i 0.838435 0.545001i \(-0.183471\pi\)
0.518937 + 0.854813i \(0.326328\pi\)
\(992\) 753.146 171.901i 0.759220 0.173287i
\(993\) 706.110 + 340.044i 0.711087 + 0.342442i
\(994\) −3449.11 2750.57i −3.46993 2.76718i
\(995\) −931.917 −0.936600
\(996\) 238.321i 0.239279i
\(997\) −1492.00 1189.83i −1.49649 1.19341i −0.929027 0.370012i \(-0.879353\pi\)
−0.567463 0.823399i \(-0.692075\pi\)
\(998\) 1657.68 798.295i 1.66100 0.799894i
\(999\) 279.773 + 350.824i 0.280053 + 0.351175i
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 43.3.f.a.8.1 42
3.2 odd 2 387.3.w.b.352.7 42
43.27 odd 14 inner 43.3.f.a.27.1 yes 42
129.113 even 14 387.3.w.b.199.7 42
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.3.f.a.8.1 42 1.1 even 1 trivial
43.3.f.a.27.1 yes 42 43.27 odd 14 inner
387.3.w.b.199.7 42 129.113 even 14
387.3.w.b.352.7 42 3.2 odd 2