Properties

Label 201.3.h.a.172.6
Level $201$
Weight $3$
Character 201.172
Analytic conductor $5.477$
Analytic rank $0$
Dimension $22$
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] = [201,3,Mod(97,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.97");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.h (of order \(6\), degree \(2\), 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: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 172.6
Character \(\chi\) \(=\) 201.172
Dual form 201.3.h.a.97.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0720773 + 0.0416138i) q^{2} +1.73205i q^{3} +(-1.99654 - 3.45810i) q^{4} +1.32016i q^{5} +(-0.0720773 + 0.124841i) q^{6} +(1.88003 - 1.08543i) q^{7} -0.665245i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(0.0720773 + 0.0416138i) q^{2} +1.73205i q^{3} +(-1.99654 - 3.45810i) q^{4} +1.32016i q^{5} +(-0.0720773 + 0.124841i) q^{6} +(1.88003 - 1.08543i) q^{7} -0.665245i q^{8} -3.00000 q^{9} +(-0.0549368 + 0.0951533i) q^{10} +(18.4349 - 10.6434i) q^{11} +(5.98961 - 3.45810i) q^{12} +(6.76145 + 3.90372i) q^{13} +0.180676 q^{14} -2.28658 q^{15} +(-7.95846 + 13.7845i) q^{16} +(13.7876 - 23.8809i) q^{17} +(-0.216232 - 0.124841i) q^{18} +(3.95745 - 6.85451i) q^{19} +(4.56524 - 2.63574i) q^{20} +(1.88003 + 3.25630i) q^{21} +1.77165 q^{22} +(-11.7884 + 20.4181i) q^{23} +1.15224 q^{24} +23.2572 q^{25} +(0.324898 + 0.562739i) q^{26} -5.19615i q^{27} +(-7.50708 - 4.33422i) q^{28} +(-10.4969 - 18.1811i) q^{29} +(-0.164810 - 0.0951533i) q^{30} +(34.8799 - 20.1379i) q^{31} +(-3.45172 + 1.99285i) q^{32} +(18.4349 + 31.9302i) q^{33} +(1.98755 - 1.14751i) q^{34} +(1.43294 + 2.48193i) q^{35} +(5.98961 + 10.3743i) q^{36} +(-26.1129 + 45.2288i) q^{37} +(0.570485 - 0.329369i) q^{38} +(-6.76145 + 11.7112i) q^{39} +0.878227 q^{40} +(-8.87200 + 5.12225i) q^{41} +0.312940i q^{42} -3.99024i q^{43} +(-73.6120 - 42.4999i) q^{44} -3.96047i q^{45} +(-1.69935 + 0.981119i) q^{46} +(-27.2153 - 47.1383i) q^{47} +(-23.8754 - 13.7845i) q^{48} +(-22.1437 + 38.3540i) q^{49} +(1.67631 + 0.967820i) q^{50} +(41.3629 + 23.8809i) q^{51} -31.1757i q^{52} -18.5232i q^{53} +(0.216232 - 0.374524i) q^{54} +(14.0510 + 24.3370i) q^{55} +(-0.722079 - 1.25068i) q^{56} +(11.8724 + 6.85451i) q^{57} -1.74726i q^{58} +18.6108 q^{59} +(4.56524 + 7.90722i) q^{60} +(-41.8398 - 24.1562i) q^{61} +3.35207 q^{62} +(-5.64008 + 3.25630i) q^{63} +63.3360 q^{64} +(-5.15353 + 8.92617i) q^{65} +3.06859i q^{66} +(27.8247 + 60.9491i) q^{67} -110.110 q^{68} +(-35.3651 - 20.4181i) q^{69} +0.238521i q^{70} +(-43.8165 - 75.8924i) q^{71} +1.99573i q^{72} +(-22.6415 + 39.2163i) q^{73} +(-3.76429 + 2.17331i) q^{74} +40.2826i q^{75} -31.6048 q^{76} +(23.1054 - 40.0198i) q^{77} +(-0.974693 + 0.562739i) q^{78} +(-129.424 + 74.7227i) q^{79} +(-18.1977 - 10.5064i) q^{80} +9.00000 q^{81} -0.852626 q^{82} +(-72.7315 + 125.975i) q^{83} +(7.50708 - 13.0027i) q^{84} +(31.5265 + 18.2018i) q^{85} +(0.166049 - 0.287606i) q^{86} +(31.4906 - 18.1811i) q^{87} +(-7.08047 - 12.2637i) q^{88} +139.378 q^{89} +(0.164810 - 0.285460i) q^{90} +16.9489 q^{91} +94.1437 q^{92} +(34.8799 + 60.4138i) q^{93} -4.53013i q^{94} +(9.04903 + 5.22446i) q^{95} +(-3.45172 - 5.97856i) q^{96} +(25.9025 + 14.9548i) q^{97} +(-3.19211 + 1.84297i) q^{98} +(-55.3048 + 31.9302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9} + 6 q^{10} + 30 q^{11} - 78 q^{12} - 27 q^{13} + 6 q^{14} - 6 q^{15} - 58 q^{16} - 8 q^{17} + q^{19} - 12 q^{20} - 15 q^{21} + 14 q^{22} - q^{23} - 56 q^{25} + 71 q^{26} - 75 q^{28} + 42 q^{29} + 18 q^{30} + 120 q^{31} - 105 q^{32} + 30 q^{33} - 24 q^{34} + 3 q^{35} - 78 q^{36} + 13 q^{37} + 108 q^{38} + 27 q^{39} + 82 q^{40} - 159 q^{41} + 189 q^{44} + 372 q^{46} - 35 q^{47} - 174 q^{48} - 40 q^{49} + 285 q^{50} - 24 q^{51} - 212 q^{55} - 113 q^{56} + 3 q^{57} + 136 q^{59} - 12 q^{60} + 63 q^{61} - 150 q^{62} + 45 q^{63} - 284 q^{64} - 20 q^{65} + 94 q^{67} + 154 q^{68} - 3 q^{69} - 41 q^{71} - 16 q^{73} + 441 q^{74} - 390 q^{76} - 84 q^{77} - 213 q^{78} - 615 q^{79} + 267 q^{80} + 198 q^{81} - 302 q^{82} - 154 q^{83} + 75 q^{84} + 633 q^{85} + 221 q^{86} - 126 q^{87} + 410 q^{88} + 56 q^{89} - 18 q^{90} + 272 q^{91} + 636 q^{92} + 120 q^{93} + 588 q^{95} - 105 q^{96} - 441 q^{97} + 780 q^{98} - 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0720773 + 0.0416138i 0.0360386 + 0.0208069i 0.517911 0.855434i \(-0.326710\pi\)
−0.481872 + 0.876241i \(0.660043\pi\)
\(3\) 1.73205i 0.577350i
\(4\) −1.99654 3.45810i −0.499134 0.864526i
\(5\) 1.32016i 0.264031i 0.991248 + 0.132016i \(0.0421449\pi\)
−0.991248 + 0.132016i \(0.957855\pi\)
\(6\) −0.0720773 + 0.124841i −0.0120129 + 0.0208069i
\(7\) 1.88003 1.08543i 0.268575 0.155062i −0.359665 0.933082i \(-0.617109\pi\)
0.628240 + 0.778020i \(0.283776\pi\)
\(8\) 0.665245i 0.0831556i
\(9\) −3.00000 −0.333333
\(10\) −0.0549368 + 0.0951533i −0.00549368 + 0.00951533i
\(11\) 18.4349 10.6434i 1.67590 0.967582i 0.711673 0.702511i \(-0.247938\pi\)
0.964229 0.265071i \(-0.0853955\pi\)
\(12\) 5.98961 3.45810i 0.499134 0.288175i
\(13\) 6.76145 + 3.90372i 0.520111 + 0.300286i 0.736980 0.675914i \(-0.236251\pi\)
−0.216869 + 0.976201i \(0.569584\pi\)
\(14\) 0.180676 0.0129054
\(15\) −2.28658 −0.152439
\(16\) −7.95846 + 13.7845i −0.497404 + 0.861529i
\(17\) 13.7876 23.8809i 0.811038 1.40476i −0.101101 0.994876i \(-0.532237\pi\)
0.912139 0.409882i \(-0.134430\pi\)
\(18\) −0.216232 0.124841i −0.0120129 0.00693564i
\(19\) 3.95745 6.85451i 0.208287 0.360764i −0.742888 0.669416i \(-0.766545\pi\)
0.951175 + 0.308652i \(0.0998779\pi\)
\(20\) 4.56524 2.63574i 0.228262 0.131787i
\(21\) 1.88003 + 3.25630i 0.0895251 + 0.155062i
\(22\) 1.77165 0.0805296
\(23\) −11.7884 + 20.4181i −0.512538 + 0.887742i 0.487356 + 0.873203i \(0.337961\pi\)
−0.999894 + 0.0145390i \(0.995372\pi\)
\(24\) 1.15224 0.0480099
\(25\) 23.2572 0.930287
\(26\) 0.324898 + 0.562739i 0.0124961 + 0.0216438i
\(27\) 5.19615i 0.192450i
\(28\) −7.50708 4.33422i −0.268110 0.154793i
\(29\) −10.4969 18.1811i −0.361961 0.626935i 0.626322 0.779564i \(-0.284559\pi\)
−0.988284 + 0.152629i \(0.951226\pi\)
\(30\) −0.164810 0.0951533i −0.00549368 0.00317178i
\(31\) 34.8799 20.1379i 1.12516 0.649611i 0.182446 0.983216i \(-0.441599\pi\)
0.942713 + 0.333605i \(0.108265\pi\)
\(32\) −3.45172 + 1.99285i −0.107866 + 0.0622767i
\(33\) 18.4349 + 31.9302i 0.558634 + 0.967582i
\(34\) 1.98755 1.14751i 0.0584574 0.0337504i
\(35\) 1.43294 + 2.48193i 0.0409412 + 0.0709123i
\(36\) 5.98961 + 10.3743i 0.166378 + 0.288175i
\(37\) −26.1129 + 45.2288i −0.705754 + 1.22240i 0.260665 + 0.965429i \(0.416058\pi\)
−0.966419 + 0.256972i \(0.917275\pi\)
\(38\) 0.570485 0.329369i 0.0150128 0.00866762i
\(39\) −6.76145 + 11.7112i −0.173370 + 0.300286i
\(40\) 0.878227 0.0219557
\(41\) −8.87200 + 5.12225i −0.216390 + 0.124933i −0.604278 0.796774i \(-0.706538\pi\)
0.387888 + 0.921707i \(0.373205\pi\)
\(42\) 0.312940i 0.00745096i
\(43\) 3.99024i 0.0927963i −0.998923 0.0463982i \(-0.985226\pi\)
0.998923 0.0463982i \(-0.0147743\pi\)
\(44\) −73.6120 42.4999i −1.67300 0.965907i
\(45\) 3.96047i 0.0880105i
\(46\) −1.69935 + 0.981119i −0.0369424 + 0.0213287i
\(47\) −27.2153 47.1383i −0.579049 1.00294i −0.995589 0.0938247i \(-0.970091\pi\)
0.416540 0.909118i \(-0.363243\pi\)
\(48\) −23.8754 13.7845i −0.497404 0.287176i
\(49\) −22.1437 + 38.3540i −0.451912 + 0.782734i
\(50\) 1.67631 + 0.967820i 0.0335263 + 0.0193564i
\(51\) 41.3629 + 23.8809i 0.811038 + 0.468253i
\(52\) 31.1757i 0.599533i
\(53\) 18.5232i 0.349494i −0.984613 0.174747i \(-0.944089\pi\)
0.984613 0.174747i \(-0.0559108\pi\)
\(54\) 0.216232 0.374524i 0.00400429 0.00693564i
\(55\) 14.0510 + 24.3370i 0.255472 + 0.442491i
\(56\) −0.722079 1.25068i −0.0128943 0.0223335i
\(57\) 11.8724 + 6.85451i 0.208287 + 0.120255i
\(58\) 1.74726i 0.0301252i
\(59\) 18.6108 0.315437 0.157719 0.987484i \(-0.449586\pi\)
0.157719 + 0.987484i \(0.449586\pi\)
\(60\) 4.56524 + 7.90722i 0.0760873 + 0.131787i
\(61\) −41.8398 24.1562i −0.685898 0.396003i 0.116175 0.993229i \(-0.462937\pi\)
−0.802074 + 0.597225i \(0.796270\pi\)
\(62\) 3.35207 0.0540656
\(63\) −5.64008 + 3.25630i −0.0895251 + 0.0516873i
\(64\) 63.3360 0.989625
\(65\) −5.15353 + 8.92617i −0.0792850 + 0.137326i
\(66\) 3.06859i 0.0464938i
\(67\) 27.8247 + 60.9491i 0.415294 + 0.909687i
\(68\) −110.110 −1.61927
\(69\) −35.3651 20.4181i −0.512538 0.295914i
\(70\) 0.238521i 0.00340744i
\(71\) −43.8165 75.8924i −0.617133 1.06891i −0.990006 0.141024i \(-0.954961\pi\)
0.372873 0.927882i \(-0.378373\pi\)
\(72\) 1.99573i 0.0277185i
\(73\) −22.6415 + 39.2163i −0.310158 + 0.537210i −0.978396 0.206738i \(-0.933715\pi\)
0.668238 + 0.743947i \(0.267049\pi\)
\(74\) −3.76429 + 2.17331i −0.0508688 + 0.0293691i
\(75\) 40.2826i 0.537102i
\(76\) −31.6048 −0.415853
\(77\) 23.1054 40.0198i 0.300071 0.519737i
\(78\) −0.974693 + 0.562739i −0.0124961 + 0.00721461i
\(79\) −129.424 + 74.7227i −1.63827 + 0.945857i −0.656844 + 0.754026i \(0.728109\pi\)
−0.981428 + 0.191831i \(0.938558\pi\)
\(80\) −18.1977 10.5064i −0.227471 0.131330i
\(81\) 9.00000 0.111111
\(82\) −0.852626 −0.0103979
\(83\) −72.7315 + 125.975i −0.876283 + 1.51777i −0.0208927 + 0.999782i \(0.506651\pi\)
−0.855390 + 0.517984i \(0.826682\pi\)
\(84\) 7.50708 13.0027i 0.0893701 0.154793i
\(85\) 31.5265 + 18.2018i 0.370900 + 0.214139i
\(86\) 0.166049 0.287606i 0.00193081 0.00334425i
\(87\) 31.4906 18.1811i 0.361961 0.208978i
\(88\) −7.08047 12.2637i −0.0804599 0.139361i
\(89\) 139.378 1.56604 0.783020 0.621997i \(-0.213678\pi\)
0.783020 + 0.621997i \(0.213678\pi\)
\(90\) 0.164810 0.285460i 0.00183123 0.00317178i
\(91\) 16.9489 0.186252
\(92\) 94.1437 1.02330
\(93\) 34.8799 + 60.4138i 0.375053 + 0.649611i
\(94\) 4.53013i 0.0481929i
\(95\) 9.04903 + 5.22446i 0.0952529 + 0.0549943i
\(96\) −3.45172 5.97856i −0.0359555 0.0622767i
\(97\) 25.9025 + 14.9548i 0.267036 + 0.154173i 0.627540 0.778584i \(-0.284062\pi\)
−0.360504 + 0.932758i \(0.617395\pi\)
\(98\) −3.19211 + 1.84297i −0.0325725 + 0.0188058i
\(99\) −55.3048 + 31.9302i −0.558634 + 0.322527i
\(100\) −46.4338 80.4257i −0.464338 0.804257i
\(101\) −14.6542 + 8.46060i −0.145091 + 0.0837683i −0.570788 0.821097i \(-0.693362\pi\)
0.425697 + 0.904866i \(0.360029\pi\)
\(102\) 1.98755 + 3.44254i 0.0194858 + 0.0337504i
\(103\) 53.1047 + 91.9800i 0.515579 + 0.893009i 0.999836 + 0.0180837i \(0.00575652\pi\)
−0.484257 + 0.874926i \(0.660910\pi\)
\(104\) 2.59693 4.49802i 0.0249705 0.0432502i
\(105\) −4.29883 + 2.48193i −0.0409412 + 0.0236374i
\(106\) 0.770821 1.33510i 0.00727190 0.0125953i
\(107\) 27.2236 0.254427 0.127213 0.991875i \(-0.459397\pi\)
0.127213 + 0.991875i \(0.459397\pi\)
\(108\) −17.9688 + 10.3743i −0.166378 + 0.0960584i
\(109\) 153.905i 1.41198i −0.708223 0.705988i \(-0.750503\pi\)
0.708223 0.705988i \(-0.249497\pi\)
\(110\) 2.33886i 0.0212623i
\(111\) −78.3386 45.2288i −0.705754 0.407467i
\(112\) 34.5535i 0.308514i
\(113\) 120.926 69.8168i 1.07014 0.617848i 0.141923 0.989878i \(-0.454672\pi\)
0.928221 + 0.372030i \(0.121338\pi\)
\(114\) 0.570485 + 0.988108i 0.00500425 + 0.00866762i
\(115\) −26.9551 15.5625i −0.234392 0.135326i
\(116\) −41.9148 + 72.5985i −0.361334 + 0.625849i
\(117\) −20.2843 11.7112i −0.173370 0.100095i
\(118\) 1.34142 + 0.774466i 0.0113679 + 0.00656327i
\(119\) 59.8623i 0.503044i
\(120\) 1.52113i 0.0126761i
\(121\) 166.064 287.632i 1.37243 2.37712i
\(122\) −2.01046 3.48223i −0.0164792 0.0285428i
\(123\) −8.87200 15.3667i −0.0721300 0.124933i
\(124\) −139.278 80.4122i −1.12321 0.648486i
\(125\) 63.7071i 0.509656i
\(126\) −0.542029 −0.00430182
\(127\) 89.6263 + 155.237i 0.705719 + 1.22234i 0.966432 + 0.256924i \(0.0827091\pi\)
−0.260713 + 0.965416i \(0.583958\pi\)
\(128\) 18.3720 + 10.6071i 0.143531 + 0.0828677i
\(129\) 6.91130 0.0535760
\(130\) −0.742904 + 0.428916i −0.00571465 + 0.00329935i
\(131\) −52.2049 −0.398511 −0.199255 0.979948i \(-0.563852\pi\)
−0.199255 + 0.979948i \(0.563852\pi\)
\(132\) 73.6120 127.500i 0.557667 0.965907i
\(133\) 17.1822i 0.129190i
\(134\) −0.530797 + 5.55093i −0.00396117 + 0.0414249i
\(135\) 6.85974 0.0508129
\(136\) −15.8866 9.17215i −0.116814 0.0674423i
\(137\) 133.362i 0.973443i −0.873557 0.486722i \(-0.838193\pi\)
0.873557 0.486722i \(-0.161807\pi\)
\(138\) −1.69935 2.94336i −0.0123141 0.0213287i
\(139\) 119.427i 0.859184i 0.903023 + 0.429592i \(0.141343\pi\)
−0.903023 + 0.429592i \(0.858657\pi\)
\(140\) 5.72185 9.91053i 0.0408703 0.0707895i
\(141\) 81.6459 47.1383i 0.579049 0.334314i
\(142\) 7.29348i 0.0513626i
\(143\) 166.196 1.16221
\(144\) 23.8754 41.3534i 0.165801 0.287176i
\(145\) 24.0019 13.8575i 0.165531 0.0955691i
\(146\) −3.26388 + 1.88440i −0.0223554 + 0.0129069i
\(147\) −66.4310 38.3540i −0.451912 0.260911i
\(148\) 208.541 1.40906
\(149\) 107.903 0.724183 0.362091 0.932143i \(-0.382063\pi\)
0.362091 + 0.932143i \(0.382063\pi\)
\(150\) −1.67631 + 2.90346i −0.0111754 + 0.0193564i
\(151\) 0.0602967 0.104437i 0.000399316 0.000691635i −0.865826 0.500346i \(-0.833206\pi\)
0.866225 + 0.499654i \(0.166540\pi\)
\(152\) −4.55993 2.63267i −0.0299995 0.0173202i
\(153\) −41.3629 + 71.6427i −0.270346 + 0.468253i
\(154\) 3.33075 1.92301i 0.0216283 0.0124871i
\(155\) 26.5852 + 46.0470i 0.171518 + 0.297077i
\(156\) 53.9979 0.346140
\(157\) −82.5294 + 142.945i −0.525665 + 0.910478i 0.473888 + 0.880585i \(0.342850\pi\)
−0.999553 + 0.0298931i \(0.990483\pi\)
\(158\) −12.4380 −0.0787215
\(159\) 32.0831 0.201781
\(160\) −2.63088 4.55682i −0.0164430 0.0284801i
\(161\) 51.1820i 0.317901i
\(162\) 0.648695 + 0.374524i 0.00400429 + 0.00231188i
\(163\) 63.5218 + 110.023i 0.389704 + 0.674988i 0.992410 0.122976i \(-0.0392439\pi\)
−0.602705 + 0.797964i \(0.705911\pi\)
\(164\) 35.4265 + 20.4535i 0.216015 + 0.124717i
\(165\) −42.1529 + 24.3370i −0.255472 + 0.147497i
\(166\) −10.4846 + 6.05327i −0.0631601 + 0.0364655i
\(167\) −94.2251 163.203i −0.564222 0.977261i −0.997122 0.0758191i \(-0.975843\pi\)
0.432900 0.901442i \(-0.357490\pi\)
\(168\) 2.16624 1.25068i 0.0128943 0.00744451i
\(169\) −54.0219 93.5686i −0.319656 0.553661i
\(170\) 1.51490 + 2.62388i 0.00891116 + 0.0154346i
\(171\) −11.8724 + 20.5635i −0.0694290 + 0.120255i
\(172\) −13.7987 + 7.96666i −0.0802248 + 0.0463178i
\(173\) −25.1820 + 43.6164i −0.145560 + 0.252118i −0.929582 0.368616i \(-0.879832\pi\)
0.784021 + 0.620734i \(0.213165\pi\)
\(174\) 3.02634 0.0173928
\(175\) 43.7241 25.2441i 0.249852 0.144252i
\(176\) 338.821i 1.92512i
\(177\) 32.2348i 0.182118i
\(178\) 10.0460 + 5.80003i 0.0564379 + 0.0325845i
\(179\) 252.236i 1.40914i 0.709634 + 0.704571i \(0.248860\pi\)
−0.709634 + 0.704571i \(0.751140\pi\)
\(180\) −13.6957 + 7.90722i −0.0760873 + 0.0439290i
\(181\) −50.0517 86.6921i −0.276529 0.478962i 0.693991 0.719984i \(-0.255851\pi\)
−0.970520 + 0.241022i \(0.922517\pi\)
\(182\) 1.22163 + 0.705310i 0.00671227 + 0.00387533i
\(183\) 41.8398 72.4686i 0.228633 0.396003i
\(184\) 13.5830 + 7.84216i 0.0738207 + 0.0426204i
\(185\) −59.7092 34.4731i −0.322752 0.186341i
\(186\) 5.80595i 0.0312148i
\(187\) 586.990i 3.13898i
\(188\) −108.673 + 188.227i −0.578046 + 1.00121i
\(189\) −5.64008 9.76891i −0.0298417 0.0516873i
\(190\) 0.434819 + 0.753129i 0.00228852 + 0.00396384i
\(191\) 123.690 + 71.4122i 0.647590 + 0.373886i 0.787532 0.616274i \(-0.211358\pi\)
−0.139942 + 0.990160i \(0.544692\pi\)
\(192\) 109.701i 0.571360i
\(193\) −29.9393 −0.155126 −0.0775629 0.996987i \(-0.524714\pi\)
−0.0775629 + 0.996987i \(0.524714\pi\)
\(194\) 1.24465 + 2.15580i 0.00641574 + 0.0111124i
\(195\) −15.4606 8.92617i −0.0792850 0.0457752i
\(196\) 176.843 0.902258
\(197\) −113.500 + 65.5295i −0.576144 + 0.332637i −0.759600 0.650391i \(-0.774605\pi\)
0.183455 + 0.983028i \(0.441272\pi\)
\(198\) −5.31495 −0.0268432
\(199\) −127.781 + 221.323i −0.642115 + 1.11218i 0.342844 + 0.939392i \(0.388610\pi\)
−0.984960 + 0.172784i \(0.944724\pi\)
\(200\) 15.4717i 0.0773586i
\(201\) −105.567 + 48.1938i −0.525208 + 0.239770i
\(202\) −1.40831 −0.00697184
\(203\) −39.4688 22.7873i −0.194428 0.112253i
\(204\) 190.716i 0.934884i
\(205\) −6.76217 11.7124i −0.0329862 0.0571338i
\(206\) 8.83955i 0.0429104i
\(207\) 35.3651 61.2542i 0.170846 0.295914i
\(208\) −107.621 + 62.1353i −0.517411 + 0.298727i
\(209\) 168.483i 0.806139i
\(210\) −0.413130 −0.00196729
\(211\) −32.0595 + 55.5286i −0.151941 + 0.263169i −0.931941 0.362610i \(-0.881886\pi\)
0.780000 + 0.625779i \(0.215219\pi\)
\(212\) −64.0551 + 36.9823i −0.302147 + 0.174445i
\(213\) 131.449 75.8924i 0.617133 0.356302i
\(214\) 1.96221 + 1.13288i 0.00916919 + 0.00529383i
\(215\) 5.26775 0.0245011
\(216\) −3.45671 −0.0160033
\(217\) 43.7168 75.7197i 0.201460 0.348939i
\(218\) 6.40460 11.0931i 0.0293789 0.0508857i
\(219\) −67.9246 39.2163i −0.310158 0.179070i
\(220\) 56.1065 97.1794i 0.255030 0.441724i
\(221\) 186.449 107.646i 0.843660 0.487087i
\(222\) −3.76429 6.51994i −0.0169563 0.0293691i
\(223\) −421.085 −1.88827 −0.944137 0.329554i \(-0.893102\pi\)
−0.944137 + 0.329554i \(0.893102\pi\)
\(224\) −4.32622 + 7.49324i −0.0193135 + 0.0334519i
\(225\) −69.7716 −0.310096
\(226\) 11.6214 0.0514220
\(227\) 135.759 + 235.142i 0.598058 + 1.03587i 0.993107 + 0.117207i \(0.0373942\pi\)
−0.395049 + 0.918660i \(0.629272\pi\)
\(228\) 54.7411i 0.240093i
\(229\) −125.753 72.6038i −0.549142 0.317047i 0.199634 0.979871i \(-0.436025\pi\)
−0.748776 + 0.662823i \(0.769358\pi\)
\(230\) −1.29523 2.24341i −0.00563144 0.00975394i
\(231\) 69.3163 + 40.0198i 0.300071 + 0.173246i
\(232\) −12.0949 + 6.98299i −0.0521331 + 0.0300991i
\(233\) −111.144 + 64.1693i −0.477015 + 0.275405i −0.719172 0.694832i \(-0.755479\pi\)
0.242157 + 0.970237i \(0.422145\pi\)
\(234\) −0.974693 1.68822i −0.00416536 0.00721461i
\(235\) 62.2299 35.9285i 0.264808 0.152887i
\(236\) −37.1571 64.3580i −0.157445 0.272704i
\(237\) −129.424 224.168i −0.546091 0.945857i
\(238\) 2.49110 4.31471i 0.0104668 0.0181290i
\(239\) −100.961 + 58.2896i −0.422429 + 0.243890i −0.696116 0.717929i \(-0.745090\pi\)
0.273687 + 0.961819i \(0.411757\pi\)
\(240\) 18.1977 31.5193i 0.0758236 0.131330i
\(241\) −391.536 −1.62463 −0.812316 0.583218i \(-0.801793\pi\)
−0.812316 + 0.583218i \(0.801793\pi\)
\(242\) 23.9389 13.8211i 0.0989211 0.0571121i
\(243\) 15.5885i 0.0641500i
\(244\) 192.915i 0.790635i
\(245\) −50.6332 29.2331i −0.206666 0.119319i
\(246\) 1.47679i 0.00600321i
\(247\) 53.5162 30.8976i 0.216665 0.125091i
\(248\) −13.3967 23.2037i −0.0540188 0.0935633i
\(249\) −218.194 125.975i −0.876283 0.505922i
\(250\) −2.65109 + 4.59183i −0.0106044 + 0.0183673i
\(251\) −311.684 179.951i −1.24177 0.716935i −0.272314 0.962208i \(-0.587789\pi\)
−0.969454 + 0.245273i \(0.921122\pi\)
\(252\) 22.5213 + 13.0027i 0.0893701 + 0.0515978i
\(253\) 501.874i 1.98369i
\(254\) 14.9188i 0.0587353i
\(255\) −31.5265 + 54.6055i −0.123633 + 0.214139i
\(256\) −125.789 217.873i −0.491364 0.851067i
\(257\) 133.193 + 230.697i 0.518260 + 0.897652i 0.999775 + 0.0212144i \(0.00675326\pi\)
−0.481515 + 0.876438i \(0.659913\pi\)
\(258\) 0.498148 + 0.287606i 0.00193081 + 0.00111475i
\(259\) 113.375i 0.437742i
\(260\) 41.1568 0.158295
\(261\) 31.4906 + 54.5433i 0.120654 + 0.208978i
\(262\) −3.76279 2.17245i −0.0143618 0.00829178i
\(263\) 23.9607 0.0911055 0.0455527 0.998962i \(-0.485495\pi\)
0.0455527 + 0.998962i \(0.485495\pi\)
\(264\) 21.2414 12.2637i 0.0804599 0.0464535i
\(265\) 24.4535 0.0922775
\(266\) 0.715018 1.23845i 0.00268804 0.00465582i
\(267\) 241.409i 0.904154i
\(268\) 155.215 217.908i 0.579161 0.813088i
\(269\) 260.612 0.968818 0.484409 0.874842i \(-0.339035\pi\)
0.484409 + 0.874842i \(0.339035\pi\)
\(270\) 0.494431 + 0.285460i 0.00183123 + 0.00105726i
\(271\) 433.854i 1.60094i 0.599375 + 0.800469i \(0.295416\pi\)
−0.599375 + 0.800469i \(0.704584\pi\)
\(272\) 219.457 + 380.110i 0.806827 + 1.39746i
\(273\) 29.3564i 0.107533i
\(274\) 5.54969 9.61235i 0.0202544 0.0350816i
\(275\) 428.744 247.536i 1.55907 0.900130i
\(276\) 163.062i 0.590803i
\(277\) 244.786 0.883703 0.441852 0.897088i \(-0.354322\pi\)
0.441852 + 0.897088i \(0.354322\pi\)
\(278\) −4.96980 + 8.60794i −0.0178770 + 0.0309638i
\(279\) −104.640 + 60.4138i −0.375053 + 0.216537i
\(280\) 1.65109 0.953258i 0.00589675 0.00340449i
\(281\) −279.252 161.226i −0.993778 0.573758i −0.0873763 0.996175i \(-0.527848\pi\)
−0.906401 + 0.422418i \(0.861182\pi\)
\(282\) 7.84642 0.0278242
\(283\) −273.577 −0.966702 −0.483351 0.875427i \(-0.660581\pi\)
−0.483351 + 0.875427i \(0.660581\pi\)
\(284\) −174.962 + 303.044i −0.616065 + 1.06706i
\(285\) −9.04903 + 15.6734i −0.0317510 + 0.0549943i
\(286\) 11.9789 + 6.91604i 0.0418844 + 0.0241819i
\(287\) −11.1197 + 19.2599i −0.0387447 + 0.0671078i
\(288\) 10.3552 5.97856i 0.0359555 0.0207589i
\(289\) −235.698 408.241i −0.815564 1.41260i
\(290\) 2.30666 0.00795399
\(291\) −25.9025 + 44.8644i −0.0890119 + 0.154173i
\(292\) 180.819 0.619242
\(293\) −19.6953 −0.0672193 −0.0336096 0.999435i \(-0.510700\pi\)
−0.0336096 + 0.999435i \(0.510700\pi\)
\(294\) −3.19211 5.52890i −0.0108575 0.0188058i
\(295\) 24.5692i 0.0832853i
\(296\) 30.0882 + 17.3715i 0.101649 + 0.0586874i
\(297\) −55.3048 95.7907i −0.186211 0.322527i
\(298\) 7.77737 + 4.49027i 0.0260986 + 0.0150680i
\(299\) −159.413 + 92.0372i −0.533154 + 0.307817i
\(300\) 139.301 80.4257i 0.464338 0.268086i
\(301\) −4.33114 7.50176i −0.0143892 0.0249228i
\(302\) 0.00869204 0.00501835i 2.87816e−5 1.66171e-5i
\(303\) −14.6542 25.3818i −0.0483637 0.0837683i
\(304\) 62.9905 + 109.103i 0.207206 + 0.358890i
\(305\) 31.8900 55.2351i 0.104557 0.181099i
\(306\) −5.96265 + 3.44254i −0.0194858 + 0.0112501i
\(307\) 210.303 364.255i 0.685025 1.18650i −0.288405 0.957509i \(-0.593125\pi\)
0.973429 0.228989i \(-0.0735419\pi\)
\(308\) −184.523 −0.599102
\(309\) −159.314 + 91.9800i −0.515579 + 0.297670i
\(310\) 4.42525i 0.0142750i
\(311\) 289.143i 0.929719i 0.885385 + 0.464859i \(0.153895\pi\)
−0.885385 + 0.464859i \(0.846105\pi\)
\(312\) 7.79079 + 4.49802i 0.0249705 + 0.0144167i
\(313\) 388.890i 1.24246i −0.783628 0.621231i \(-0.786633\pi\)
0.783628 0.621231i \(-0.213367\pi\)
\(314\) −11.8970 + 6.86873i −0.0378885 + 0.0218749i
\(315\) −4.29883 7.44579i −0.0136471 0.0236374i
\(316\) 516.798 + 298.373i 1.63544 + 0.944219i
\(317\) 127.371 220.613i 0.401801 0.695939i −0.592143 0.805833i \(-0.701718\pi\)
0.993943 + 0.109894i \(0.0350511\pi\)
\(318\) 2.31246 + 1.33510i 0.00727190 + 0.00419843i
\(319\) −387.018 223.445i −1.21322 0.700454i
\(320\) 83.6134i 0.261292i
\(321\) 47.1527i 0.146893i
\(322\) −2.12988 + 3.68906i −0.00661454 + 0.0114567i
\(323\) −109.128 189.015i −0.337857 0.585186i
\(324\) −17.9688 31.1229i −0.0554593 0.0960584i
\(325\) 157.252 + 90.7896i 0.483853 + 0.279353i
\(326\) 10.5735i 0.0324342i
\(327\) 266.572 0.815205
\(328\) 3.40755 + 5.90205i 0.0103889 + 0.0179941i
\(329\) −102.331 59.0808i −0.311036 0.179577i
\(330\) −4.05102 −0.0122758
\(331\) −55.9600 + 32.3085i −0.169063 + 0.0976088i −0.582144 0.813086i \(-0.697786\pi\)
0.413081 + 0.910694i \(0.364453\pi\)
\(332\) 580.844 1.74953
\(333\) 78.3386 135.687i 0.235251 0.407467i
\(334\) 15.6843i 0.0469589i
\(335\) −80.4623 + 36.7329i −0.240186 + 0.109651i
\(336\) −59.8485 −0.178121
\(337\) 323.719 + 186.900i 0.960592 + 0.554598i 0.896355 0.443337i \(-0.146205\pi\)
0.0642367 + 0.997935i \(0.479539\pi\)
\(338\) 8.99223i 0.0266042i
\(339\) 120.926 + 209.450i 0.356714 + 0.617848i
\(340\) 145.363i 0.427537i
\(341\) 428.672 742.482i 1.25710 2.17737i
\(342\) −1.71145 + 0.988108i −0.00500425 + 0.00288921i
\(343\) 202.514i 0.590421i
\(344\) −2.65449 −0.00771653
\(345\) 26.9551 46.6875i 0.0781306 0.135326i
\(346\) −3.63009 + 2.09584i −0.0104916 + 0.00605733i
\(347\) 410.827 237.191i 1.18394 0.683547i 0.227016 0.973891i \(-0.427103\pi\)
0.956922 + 0.290344i \(0.0937696\pi\)
\(348\) −125.744 72.5985i −0.361334 0.208616i
\(349\) −19.6065 −0.0561789 −0.0280895 0.999605i \(-0.508942\pi\)
−0.0280895 + 0.999605i \(0.508942\pi\)
\(350\) 4.20202 0.0120058
\(351\) 20.2843 35.1335i 0.0577902 0.100095i
\(352\) −42.4215 + 73.4762i −0.120516 + 0.208739i
\(353\) −274.593 158.536i −0.777884 0.449111i 0.0577960 0.998328i \(-0.481593\pi\)
−0.835680 + 0.549217i \(0.814926\pi\)
\(354\) −1.34142 + 2.32340i −0.00378931 + 0.00656327i
\(355\) 100.190 57.8446i 0.282225 0.162943i
\(356\) −278.272 481.982i −0.781664 1.35388i
\(357\) 103.685 0.290433
\(358\) −10.4965 + 18.1805i −0.0293199 + 0.0507835i
\(359\) −372.386 −1.03729 −0.518643 0.854991i \(-0.673563\pi\)
−0.518643 + 0.854991i \(0.673563\pi\)
\(360\) −2.63468 −0.00731856
\(361\) 149.177 + 258.382i 0.413233 + 0.715741i
\(362\) 8.33138i 0.0230148i
\(363\) 498.193 + 287.632i 1.37243 + 0.792373i
\(364\) −33.8392 58.6112i −0.0929648 0.161020i
\(365\) −51.7717 29.8904i −0.141840 0.0818915i
\(366\) 6.03139 3.48223i 0.0164792 0.00951428i
\(367\) 187.457 108.228i 0.510781 0.294900i −0.222374 0.974962i \(-0.571380\pi\)
0.733155 + 0.680062i \(0.238047\pi\)
\(368\) −187.635 324.993i −0.509877 0.883133i
\(369\) 26.6160 15.3667i 0.0721300 0.0416443i
\(370\) −2.86912 4.96945i −0.00775437 0.0134310i
\(371\) −20.1057 34.8241i −0.0541933 0.0938656i
\(372\) 139.278 241.237i 0.374403 0.648486i
\(373\) −161.356 + 93.1588i −0.432589 + 0.249756i −0.700449 0.713702i \(-0.747017\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(374\) 24.4269 42.3086i 0.0653125 0.113125i
\(375\) −110.344 −0.294250
\(376\) −31.3585 + 18.1048i −0.0834003 + 0.0481512i
\(377\) 163.908i 0.434768i
\(378\) 0.938821i 0.00248365i
\(379\) 207.017 + 119.521i 0.546219 + 0.315360i 0.747596 0.664154i \(-0.231208\pi\)
−0.201376 + 0.979514i \(0.564541\pi\)
\(380\) 41.7233i 0.109798i
\(381\) −268.879 + 155.237i −0.705719 + 0.407447i
\(382\) 5.94347 + 10.2944i 0.0155588 + 0.0269487i
\(383\) −307.739 177.673i −0.803497 0.463899i 0.0411955 0.999151i \(-0.486883\pi\)
−0.844693 + 0.535252i \(0.820217\pi\)
\(384\) −18.3720 + 31.8212i −0.0478437 + 0.0828677i
\(385\) 52.8324 + 30.5028i 0.137227 + 0.0792280i
\(386\) −2.15794 1.24589i −0.00559052 0.00322769i
\(387\) 11.9707i 0.0309321i
\(388\) 119.431i 0.307812i
\(389\) 36.5081 63.2339i 0.0938512 0.162555i −0.815277 0.579071i \(-0.803416\pi\)
0.909129 + 0.416516i \(0.136749\pi\)
\(390\) −0.742904 1.28675i −0.00190488 0.00329935i
\(391\) 325.068 + 563.034i 0.831376 + 1.43998i
\(392\) 25.5148 + 14.7310i 0.0650887 + 0.0375790i
\(393\) 90.4216i 0.230080i
\(394\) −10.9077 −0.0276846
\(395\) −98.6457 170.859i −0.249736 0.432555i
\(396\) 220.836 + 127.500i 0.557667 + 0.321969i
\(397\) 104.627 0.263544 0.131772 0.991280i \(-0.457933\pi\)
0.131772 + 0.991280i \(0.457933\pi\)
\(398\) −18.4202 + 10.6349i −0.0462819 + 0.0267209i
\(399\) 29.7605 0.0745876
\(400\) −185.091 + 320.588i −0.462729 + 0.801469i
\(401\) 164.349i 0.409848i 0.978778 + 0.204924i \(0.0656947\pi\)
−0.978778 + 0.204924i \(0.934305\pi\)
\(402\) −9.61450 0.919367i −0.0239167 0.00228698i
\(403\) 314.452 0.780277
\(404\) 58.5153 + 33.7838i 0.144840 + 0.0836233i
\(405\) 11.8814i 0.0293368i
\(406\) −1.89654 3.28490i −0.00467127 0.00809088i
\(407\) 1111.72i 2.73150i
\(408\) 15.8866 27.5165i 0.0389378 0.0674423i
\(409\) −148.651 + 85.8238i −0.363450 + 0.209838i −0.670593 0.741825i \(-0.733960\pi\)
0.307143 + 0.951663i \(0.400627\pi\)
\(410\) 1.12560i 0.00274536i
\(411\) 230.989 0.562018
\(412\) 212.051 367.283i 0.514686 0.891463i
\(413\) 34.9888 20.2008i 0.0847186 0.0489123i
\(414\) 5.09805 2.94336i 0.0123141 0.00710956i
\(415\) −166.306 96.0169i −0.400738 0.231366i
\(416\) −31.1182 −0.0748034
\(417\) −206.853 −0.496050
\(418\) 7.01123 12.1438i 0.0167733 0.0290522i
\(419\) −327.986 + 568.088i −0.782782 + 1.35582i 0.147534 + 0.989057i \(0.452867\pi\)
−0.930315 + 0.366761i \(0.880467\pi\)
\(420\) 17.1655 + 9.91053i 0.0408703 + 0.0235965i
\(421\) 306.271 530.478i 0.727485 1.26004i −0.230457 0.973082i \(-0.574022\pi\)
0.957943 0.286959i \(-0.0926445\pi\)
\(422\) −4.62152 + 2.66823i −0.0109515 + 0.00632283i
\(423\) 81.6459 + 141.415i 0.193016 + 0.334314i
\(424\) −12.3225 −0.0290624
\(425\) 320.662 555.402i 0.754498 1.30683i
\(426\) 12.6327 0.0296542
\(427\) −104.880 −0.245620
\(428\) −54.3530 94.1422i −0.126993 0.219958i
\(429\) 287.859i 0.671001i
\(430\) 0.379685 + 0.219211i 0.000882988 + 0.000509793i
\(431\) −327.147 566.635i −0.759041 1.31470i −0.943340 0.331828i \(-0.892335\pi\)
0.184299 0.982870i \(-0.440999\pi\)
\(432\) 71.6262 + 41.3534i 0.165801 + 0.0957254i
\(433\) 241.700 139.546i 0.558200 0.322277i −0.194223 0.980957i \(-0.562219\pi\)
0.752423 + 0.658681i \(0.228885\pi\)
\(434\) 6.30197 3.63845i 0.0145207 0.00838352i
\(435\) 24.0019 + 41.5726i 0.0551768 + 0.0955691i
\(436\) −532.221 + 307.278i −1.22069 + 0.704766i
\(437\) 93.3039 + 161.607i 0.213510 + 0.369810i
\(438\) −3.26388 5.65321i −0.00745178 0.0129069i
\(439\) −76.1249 + 131.852i −0.173405 + 0.300347i −0.939608 0.342252i \(-0.888810\pi\)
0.766203 + 0.642599i \(0.222144\pi\)
\(440\) 16.1901 9.34733i 0.0367956 0.0212439i
\(441\) 66.4310 115.062i 0.150637 0.260911i
\(442\) 17.9183 0.0405391
\(443\) 293.736 169.588i 0.663061 0.382818i −0.130381 0.991464i \(-0.541620\pi\)
0.793442 + 0.608646i \(0.208287\pi\)
\(444\) 361.204i 0.813523i
\(445\) 184.000i 0.413484i
\(446\) −30.3507 17.5230i −0.0680508 0.0392891i
\(447\) 186.894i 0.418107i
\(448\) 119.073 68.7470i 0.265789 0.153453i
\(449\) 64.4246 + 111.587i 0.143485 + 0.248523i 0.928807 0.370565i \(-0.120836\pi\)
−0.785322 + 0.619088i \(0.787503\pi\)
\(450\) −5.02894 2.90346i −0.0111754 0.00645214i
\(451\) −109.036 + 188.857i −0.241766 + 0.418751i
\(452\) −482.867 278.784i −1.06829 0.616778i
\(453\) 0.180890 + 0.104437i 0.000399316 + 0.000230545i
\(454\) 22.5978i 0.0497750i
\(455\) 22.3753i 0.0491764i
\(456\) 4.55993 7.89802i 0.00999984 0.0173202i
\(457\) −125.105 216.688i −0.273752 0.474152i 0.696067 0.717976i \(-0.254931\pi\)
−0.969820 + 0.243824i \(0.921598\pi\)
\(458\) −6.04264 10.4662i −0.0131935 0.0228519i
\(459\) −124.089 71.6427i −0.270346 0.156084i
\(460\) 124.284i 0.270184i
\(461\) −248.045 −0.538059 −0.269029 0.963132i \(-0.586703\pi\)
−0.269029 + 0.963132i \(0.586703\pi\)
\(462\) 3.33075 + 5.76903i 0.00720942 + 0.0124871i
\(463\) −67.4470 38.9406i −0.145674 0.0841049i 0.425391 0.905009i \(-0.360136\pi\)
−0.571065 + 0.820905i \(0.693470\pi\)
\(464\) 334.156 0.720163
\(465\) −79.7557 + 46.0470i −0.171518 + 0.0990258i
\(466\) −10.6813 −0.0229213
\(467\) −36.2876 + 62.8520i −0.0777037 + 0.134587i −0.902259 0.431195i \(-0.858092\pi\)
0.824555 + 0.565782i \(0.191425\pi\)
\(468\) 93.5271i 0.199844i
\(469\) 118.467 + 84.3840i 0.252596 + 0.179923i
\(470\) 5.98048 0.0127244
\(471\) −247.588 142.945i −0.525665 0.303493i
\(472\) 12.3807i 0.0262304i
\(473\) −42.4698 73.5598i −0.0897881 0.155518i
\(474\) 21.5432i 0.0454499i
\(475\) 92.0392 159.417i 0.193767 0.335614i
\(476\) −207.010 + 119.517i −0.434895 + 0.251087i
\(477\) 55.5696i 0.116498i
\(478\) −9.70262 −0.0202984
\(479\) 398.024 689.398i 0.830949 1.43925i −0.0663382 0.997797i \(-0.521132\pi\)
0.897287 0.441448i \(-0.145535\pi\)
\(480\) 7.89264 4.55682i 0.0164430 0.00949337i
\(481\) −353.122 + 203.875i −0.734141 + 0.423856i
\(482\) −28.2209 16.2933i −0.0585495 0.0338036i
\(483\) −88.6499 −0.183540
\(484\) −1326.21 −2.74011
\(485\) −19.7427 + 34.1953i −0.0407066 + 0.0705058i
\(486\) −0.648695 + 1.12357i −0.00133476 + 0.00231188i
\(487\) 402.257 + 232.243i 0.825990 + 0.476885i 0.852478 0.522764i \(-0.175099\pi\)
−0.0264879 + 0.999649i \(0.508432\pi\)
\(488\) −16.0698 + 27.8337i −0.0329299 + 0.0570363i
\(489\) −190.565 + 110.023i −0.389704 + 0.224996i
\(490\) −2.43300 4.21409i −0.00496531 0.00860017i
\(491\) −35.1415 −0.0715713 −0.0357857 0.999359i \(-0.511393\pi\)
−0.0357857 + 0.999359i \(0.511393\pi\)
\(492\) −35.4265 + 61.3605i −0.0720051 + 0.124717i
\(493\) −578.908 −1.17426
\(494\) 5.14307 0.0104111
\(495\) −42.1529 73.0110i −0.0851574 0.147497i
\(496\) 641.068i 1.29248i
\(497\) −164.752 95.1198i −0.331494 0.191388i
\(498\) −10.4846 18.1598i −0.0210534 0.0364655i
\(499\) 841.000 + 485.552i 1.68537 + 0.973049i 0.957984 + 0.286822i \(0.0925989\pi\)
0.727387 + 0.686227i \(0.240734\pi\)
\(500\) 220.306 127.193i 0.440611 0.254387i
\(501\) 282.675 163.203i 0.564222 0.325754i
\(502\) −14.9769 25.9407i −0.0298344 0.0516747i
\(503\) −235.153 + 135.766i −0.467501 + 0.269912i −0.715193 0.698927i \(-0.753661\pi\)
0.247692 + 0.968839i \(0.420328\pi\)
\(504\) 2.16624 + 3.75203i 0.00429809 + 0.00744451i
\(505\) −11.1693 19.3458i −0.0221175 0.0383086i
\(506\) −20.8849 + 36.1737i −0.0412745 + 0.0714895i
\(507\) 162.066 93.5686i 0.319656 0.184554i
\(508\) 357.884 619.874i 0.704497 1.22022i
\(509\) −12.6359 −0.0248250 −0.0124125 0.999923i \(-0.503951\pi\)
−0.0124125 + 0.999923i \(0.503951\pi\)
\(510\) −4.54469 + 2.62388i −0.00891116 + 0.00514486i
\(511\) 98.3036i 0.192375i
\(512\) 105.795i 0.206630i
\(513\) −35.6171 20.5635i −0.0694290 0.0400848i
\(514\) 22.1706i 0.0431335i
\(515\) −121.428 + 70.1065i −0.235782 + 0.136129i
\(516\) −13.7987 23.9000i −0.0267416 0.0463178i
\(517\) −1003.42 579.327i −1.94086 1.12056i
\(518\) −4.71798 + 8.17178i −0.00910806 + 0.0157756i
\(519\) −75.5459 43.6164i −0.145560 0.0840394i
\(520\) 5.93809 + 3.42836i 0.0114194 + 0.00659299i
\(521\) 474.496i 0.910741i 0.890302 + 0.455370i \(0.150493\pi\)
−0.890302 + 0.455370i \(0.849507\pi\)
\(522\) 5.24178i 0.0100417i
\(523\) 29.1150 50.4287i 0.0556692 0.0964219i −0.836848 0.547436i \(-0.815604\pi\)
0.892517 + 0.451014i \(0.148937\pi\)
\(524\) 104.229 + 180.530i 0.198910 + 0.344523i
\(525\) 43.7241 + 75.7324i 0.0832841 + 0.144252i
\(526\) 1.72702 + 0.997098i 0.00328332 + 0.00189562i
\(527\) 1110.62i 2.10744i
\(528\) −586.854 −1.11147
\(529\) −13.4318 23.2646i −0.0253910 0.0439785i
\(530\) 1.76254 + 1.01761i 0.00332555 + 0.00192001i
\(531\) −55.8324 −0.105146
\(532\) −59.4179 + 34.3049i −0.111688 + 0.0644829i
\(533\) −79.9834 −0.150063
\(534\) −10.0460 + 17.4001i −0.0188126 + 0.0325845i
\(535\) 35.9395i 0.0671766i
\(536\) 40.5460 18.5102i 0.0756456 0.0345340i
\(537\) −436.886 −0.813568
\(538\) 18.7842 + 10.8451i 0.0349149 + 0.0201581i
\(539\) 942.736i 1.74905i
\(540\) −13.6957 23.7217i −0.0253624 0.0439290i
\(541\) 747.280i 1.38129i 0.723192 + 0.690647i \(0.242674\pi\)
−0.723192 + 0.690647i \(0.757326\pi\)
\(542\) −18.0543 + 31.2710i −0.0333106 + 0.0576956i
\(543\) 150.155 86.6921i 0.276529 0.159654i
\(544\) 109.907i 0.202035i
\(545\) 203.179 0.372806
\(546\) −1.22163 + 2.11593i −0.00223742 + 0.00387533i
\(547\) 430.040 248.284i 0.786179 0.453901i −0.0524366 0.998624i \(-0.516699\pi\)
0.838616 + 0.544724i \(0.183365\pi\)
\(548\) −461.179 + 266.262i −0.841567 + 0.485879i
\(549\) 125.519 + 72.4686i 0.228633 + 0.132001i
\(550\) 41.2036 0.0749157
\(551\) −166.163 −0.301567
\(552\) −13.5830 + 23.5265i −0.0246069 + 0.0426204i
\(553\) −162.213 + 280.961i −0.293333 + 0.508068i
\(554\) 17.6435 + 10.1865i 0.0318474 + 0.0183871i
\(555\) 59.7092 103.419i 0.107584 0.186341i
\(556\) 412.989 238.439i 0.742786 0.428848i
\(557\) 348.722 + 604.004i 0.626071 + 1.08439i 0.988333 + 0.152310i \(0.0486714\pi\)
−0.362262 + 0.932076i \(0.617995\pi\)
\(558\) −10.0562 −0.0180219
\(559\) 15.5768 26.9798i 0.0278655 0.0482644i
\(560\) −45.6161 −0.0814573
\(561\) 1016.70 1.81229
\(562\) −13.4185 23.2414i −0.0238763 0.0413549i
\(563\) 155.660i 0.276484i −0.990398 0.138242i \(-0.955855\pi\)
0.990398 0.138242i \(-0.0441451\pi\)
\(564\) −326.018 188.227i −0.578046 0.333735i
\(565\) 92.1691 + 159.642i 0.163131 + 0.282551i
\(566\) −19.7187 11.3846i −0.0348386 0.0201141i
\(567\) 16.9202 9.76891i 0.0298417 0.0172291i
\(568\) −50.4870 + 29.1487i −0.0888855 + 0.0513181i
\(569\) −114.037 197.518i −0.200416 0.347131i 0.748246 0.663421i \(-0.230896\pi\)
−0.948663 + 0.316290i \(0.897563\pi\)
\(570\) −1.30446 + 0.753129i −0.00228852 + 0.00132128i
\(571\) −85.4343 147.977i −0.149622 0.259153i 0.781466 0.623948i \(-0.214472\pi\)
−0.931088 + 0.364795i \(0.881139\pi\)
\(572\) −331.816 574.722i −0.580097 1.00476i
\(573\) −123.690 + 214.237i −0.215863 + 0.373886i
\(574\) −1.60296 + 0.925469i −0.00279261 + 0.00161231i
\(575\) −274.165 + 474.867i −0.476808 + 0.825856i
\(576\) −190.008 −0.329875
\(577\) −653.841 + 377.495i −1.13317 + 0.654238i −0.944731 0.327846i \(-0.893677\pi\)
−0.188442 + 0.982084i \(0.560344\pi\)
\(578\) 39.2332i 0.0678775i
\(579\) 51.8564i 0.0895619i
\(580\) −95.8414 55.3341i −0.165244 0.0954036i
\(581\) 315.781i 0.543513i
\(582\) −3.73396 + 2.15580i −0.00641574 + 0.00370413i
\(583\) −197.150 341.474i −0.338165 0.585718i
\(584\) 26.0884 + 15.0622i 0.0446720 + 0.0257914i
\(585\) 15.4606 26.7785i 0.0264283 0.0457752i
\(586\) −1.41958 0.819595i −0.00242249 0.00139863i
\(587\) 661.144 + 381.712i 1.12631 + 0.650276i 0.943004 0.332780i \(-0.107987\pi\)
0.183306 + 0.983056i \(0.441320\pi\)
\(588\) 306.300i 0.520919i
\(589\) 318.780i 0.541222i
\(590\) −1.02242 + 1.77088i −0.00173291 + 0.00300149i
\(591\) −113.500 196.588i −0.192048 0.332637i
\(592\) −415.637 719.904i −0.702089 1.21605i
\(593\) 248.734 + 143.606i 0.419449 + 0.242169i 0.694842 0.719163i \(-0.255474\pi\)
−0.275392 + 0.961332i \(0.588808\pi\)
\(594\) 9.20577i 0.0154979i
\(595\) 79.0276 0.132820
\(596\) −215.433 373.140i −0.361464 0.626075i
\(597\) −383.343 221.323i −0.642115 0.370725i
\(598\) −15.3201 −0.0256189
\(599\) −793.555 + 458.159i −1.32480 + 0.764873i −0.984490 0.175441i \(-0.943865\pi\)
−0.340309 + 0.940314i \(0.610532\pi\)
\(600\) 26.7978 0.0446630
\(601\) 97.0535 168.102i 0.161487 0.279703i −0.773915 0.633289i \(-0.781704\pi\)
0.935402 + 0.353586i \(0.115038\pi\)
\(602\) 0.720942i 0.00119758i
\(603\) −83.4740 182.847i −0.138431 0.303229i
\(604\) −0.481538 −0.000797248
\(605\) 379.719 + 219.231i 0.627634 + 0.362365i
\(606\) 2.43927i 0.00402519i
\(607\) 52.7616 + 91.3858i 0.0869220 + 0.150553i 0.906209 0.422831i \(-0.138964\pi\)
−0.819287 + 0.573384i \(0.805630\pi\)
\(608\) 31.5465i 0.0518857i
\(609\) 39.4688 68.3620i 0.0648092 0.112253i
\(610\) 4.59709 2.65413i 0.00753621 0.00435103i
\(611\) 424.964i 0.695522i
\(612\) 330.330 0.539755
\(613\) 176.689 306.034i 0.288236 0.499240i −0.685153 0.728400i \(-0.740265\pi\)
0.973389 + 0.229160i \(0.0735979\pi\)
\(614\) 30.3161 17.5030i 0.0493747 0.0285065i
\(615\) 20.2865 11.7124i 0.0329862 0.0190446i
\(616\) −26.6229 15.3708i −0.0432191 0.0249525i
\(617\) 928.398 1.50470 0.752349 0.658765i \(-0.228921\pi\)
0.752349 + 0.658765i \(0.228921\pi\)
\(618\) −15.3106 −0.0247744
\(619\) 16.3011 28.2344i 0.0263346 0.0456129i −0.852558 0.522633i \(-0.824950\pi\)
0.878892 + 0.477020i \(0.158283\pi\)
\(620\) 106.157 183.869i 0.171221 0.296563i
\(621\) 106.095 + 61.2542i 0.170846 + 0.0986380i
\(622\) −12.0323 + 20.8406i −0.0193446 + 0.0335058i
\(623\) 262.034 151.285i 0.420600 0.242833i
\(624\) −107.621 186.406i −0.172470 0.298727i
\(625\) 497.326 0.795722
\(626\) 16.1832 28.0301i 0.0258518 0.0447766i
\(627\) 291.821 0.465425
\(628\) 659.092 1.04951
\(629\) 720.070 + 1247.20i 1.14479 + 1.98283i
\(630\) 0.715563i 0.00113581i
\(631\) 49.8363 + 28.7730i 0.0789799 + 0.0455991i 0.538970 0.842325i \(-0.318814\pi\)
−0.459990 + 0.887924i \(0.652147\pi\)
\(632\) 49.7089 + 86.0983i 0.0786533 + 0.136231i
\(633\) −96.1784 55.5286i −0.151941 0.0877230i
\(634\) 18.3611 10.6008i 0.0289607 0.0167205i
\(635\) −204.938 + 118.321i −0.322736 + 0.186332i
\(636\) −64.0551 110.947i −0.100716 0.174445i
\(637\) −299.446 + 172.886i −0.470089 + 0.271406i
\(638\) −18.5968 32.2106i −0.0291486 0.0504868i
\(639\) 131.449 + 227.677i 0.205711 + 0.356302i
\(640\) −14.0030 + 24.2539i −0.0218797 + 0.0378967i
\(641\) 534.834 308.787i 0.834375 0.481727i −0.0209732 0.999780i \(-0.506676\pi\)
0.855348 + 0.518053i \(0.173343\pi\)
\(642\) −1.96221 + 3.39864i −0.00305640 + 0.00529383i
\(643\) 127.673 0.198558 0.0992791 0.995060i \(-0.468346\pi\)
0.0992791 + 0.995060i \(0.468346\pi\)
\(644\) 176.993 102.187i 0.274833 0.158675i
\(645\) 9.12400i 0.0141457i
\(646\) 18.1649i 0.0281191i
\(647\) −485.276 280.174i −0.750041 0.433036i 0.0756679 0.997133i \(-0.475891\pi\)
−0.825709 + 0.564097i \(0.809224\pi\)
\(648\) 5.98720i 0.00923951i
\(649\) 343.089 198.082i 0.528642 0.305211i
\(650\) 7.55621 + 13.0877i 0.0116249 + 0.0201350i
\(651\) 131.150 + 75.7197i 0.201460 + 0.116313i
\(652\) 253.647 439.330i 0.389029 0.673819i
\(653\) 523.760 + 302.393i 0.802083 + 0.463083i 0.844199 0.536030i \(-0.180077\pi\)
−0.0421163 + 0.999113i \(0.513410\pi\)
\(654\) 19.2138 + 11.0931i 0.0293789 + 0.0169619i
\(655\) 68.9187i 0.105219i
\(656\) 163.061i 0.248568i
\(657\) 67.9246 117.649i 0.103386 0.179070i
\(658\) −4.91716 8.51677i −0.00747289 0.0129434i
\(659\) −144.030 249.468i −0.218559 0.378555i 0.735809 0.677189i \(-0.236802\pi\)
−0.954368 + 0.298634i \(0.903469\pi\)
\(660\) 168.320 + 97.1794i 0.255030 + 0.147241i
\(661\) 227.874i 0.344742i −0.985032 0.172371i \(-0.944857\pi\)
0.985032 0.172371i \(-0.0551428\pi\)
\(662\) −5.37792 −0.00812375
\(663\) 186.449 + 322.939i 0.281220 + 0.487087i
\(664\) 83.8039 + 48.3842i 0.126211 + 0.0728678i
\(665\) 22.6832 0.0341101
\(666\) 11.2929 6.51994i 0.0169563 0.00978970i
\(667\) 494.964 0.742076
\(668\) −376.248 + 651.680i −0.563245 + 0.975569i
\(669\) 729.341i 1.09020i
\(670\) −7.32810 0.700735i −0.0109375 0.00104587i
\(671\) −1028.42 −1.53266
\(672\) −12.9787 7.49324i −0.0193135 0.0111506i
\(673\) 1134.40i 1.68559i −0.538232 0.842797i \(-0.680908\pi\)
0.538232 0.842797i \(-0.319092\pi\)
\(674\) 15.5552 + 26.9424i 0.0230789 + 0.0399739i
\(675\) 120.848i 0.179034i
\(676\) −215.713 + 373.626i −0.319103 + 0.552702i
\(677\) −442.248 + 255.332i −0.653247 + 0.377153i −0.789699 0.613494i \(-0.789763\pi\)
0.136452 + 0.990647i \(0.456430\pi\)
\(678\) 20.1288i 0.0296885i
\(679\) 64.9298 0.0956256
\(680\) 12.1087 20.9729i 0.0178069 0.0308424i
\(681\) −407.278 + 235.142i −0.598058 + 0.345289i
\(682\) 61.7951 35.6774i 0.0906086 0.0523129i
\(683\) −397.948 229.756i −0.582648 0.336392i 0.179537 0.983751i \(-0.442540\pi\)
−0.762185 + 0.647359i \(0.775873\pi\)
\(684\) 94.8144 0.138618
\(685\) 176.058 0.257020
\(686\) −8.42740 + 14.5967i −0.0122848 + 0.0212780i
\(687\) 125.753 217.811i 0.183047 0.317047i
\(688\) 55.0033 + 31.7562i 0.0799467 + 0.0461573i
\(689\) 72.3095 125.244i 0.104948 0.181776i
\(690\) 3.88569 2.24341i 0.00563144 0.00325131i
\(691\) −37.8371 65.5358i −0.0547570 0.0948419i 0.837348 0.546671i \(-0.184105\pi\)
−0.892105 + 0.451829i \(0.850772\pi\)
\(692\) 201.107 0.290617
\(693\) −69.3163 + 120.059i −0.100024 + 0.173246i
\(694\) 39.4817 0.0568900
\(695\) −157.662 −0.226851
\(696\) −12.0949 20.9490i −0.0173777 0.0300991i
\(697\) 282.495i 0.405301i
\(698\) −1.41318 0.815899i −0.00202461 0.00116891i
\(699\) −111.144 192.508i −0.159005 0.275405i
\(700\) −174.594 100.802i −0.249420 0.144002i
\(701\) 635.047 366.645i 0.905916 0.523031i 0.0268011 0.999641i \(-0.491468\pi\)
0.879115 + 0.476610i \(0.158135\pi\)
\(702\) 2.92408 1.68822i 0.00416536 0.00240487i
\(703\) 206.681 + 357.982i 0.293999 + 0.509220i
\(704\) 1167.59 674.111i 1.65851 0.957543i
\(705\) 62.2299 + 107.785i 0.0882694 + 0.152887i
\(706\) −13.1946 22.8537i −0.0186892 0.0323707i
\(707\) −18.3669 + 31.8123i −0.0259786 + 0.0449962i
\(708\) 111.471 64.3580i 0.157445 0.0909012i
\(709\) −81.5736 + 141.290i −0.115054 + 0.199280i −0.917802 0.397040i \(-0.870038\pi\)
0.802747 + 0.596320i \(0.203371\pi\)
\(710\) 9.62854 0.0135613
\(711\) 388.271 224.168i 0.546091 0.315286i
\(712\) 92.7202i 0.130225i
\(713\) 949.575i 1.33180i
\(714\) 7.47330 + 4.31471i 0.0104668 + 0.00604301i
\(715\) 219.404i 0.306859i
\(716\) 872.259 503.599i 1.21824 0.703351i
\(717\) −100.961 174.869i −0.140810 0.243890i
\(718\) −26.8406 15.4964i −0.0373824 0.0215827i
\(719\) −339.980 + 588.863i −0.472851 + 0.819003i −0.999517 0.0310698i \(-0.990109\pi\)
0.526666 + 0.850072i \(0.323442\pi\)
\(720\) 54.5930 + 31.5193i 0.0758236 + 0.0437767i
\(721\) 199.676 + 115.283i 0.276944 + 0.159893i
\(722\) 24.8313i 0.0343924i
\(723\) 678.160i 0.937981i
\(724\) −199.860 + 346.168i −0.276050 + 0.478133i
\(725\) −244.128 422.842i −0.336728 0.583230i
\(726\) 23.9389 + 41.4634i 0.0329737 + 0.0571121i
\(727\) 696.345 + 402.035i 0.957833 + 0.553005i 0.895505 0.445051i \(-0.146814\pi\)
0.0623277 + 0.998056i \(0.480148\pi\)
\(728\) 11.2752i 0.0154879i
\(729\) −27.0000 −0.0370370
\(730\) −2.48771 4.30884i −0.00340782 0.00590251i
\(731\) −95.2905 55.0160i −0.130356 0.0752613i
\(732\) −334.139 −0.456474
\(733\) 1098.27 634.089i 1.49833 0.865060i 0.498329 0.866988i \(-0.333947\pi\)
0.999998 + 0.00192791i \(0.000613674\pi\)
\(734\) 18.0152 0.0245438
\(735\) 50.6332 87.6993i 0.0688888 0.119319i
\(736\) 93.9701i 0.127677i
\(737\) 1161.65 + 827.442i 1.57619 + 1.12272i
\(738\) 2.55788 0.00346596
\(739\) −310.358 179.185i −0.419970 0.242470i 0.275094 0.961417i \(-0.411291\pi\)
−0.695065 + 0.718947i \(0.744624\pi\)
\(740\) 275.307i 0.372037i
\(741\) 53.5162 + 92.6928i 0.0722216 + 0.125091i
\(742\) 3.34670i 0.00451038i
\(743\) −610.173 + 1056.85i −0.821229 + 1.42241i 0.0835379 + 0.996505i \(0.473378\pi\)
−0.904767 + 0.425906i \(0.859955\pi\)
\(744\) 40.1900 23.2037i 0.0540188 0.0311878i
\(745\) 142.449i 0.191207i
\(746\) −15.5068 −0.0207866
\(747\) 218.194 377.924i 0.292094 0.505922i
\(748\) −2029.87 + 1171.95i −2.71373 + 1.56677i
\(749\) 51.1812 29.5495i 0.0683327 0.0394519i
\(750\) −7.95328 4.59183i −0.0106044 0.00612244i
\(751\) −512.994 −0.683081 −0.341541 0.939867i \(-0.610949\pi\)
−0.341541 + 0.939867i \(0.610949\pi\)
\(752\) 866.368 1.15208
\(753\) 311.684 539.852i 0.413923 0.716935i
\(754\) 6.82082 11.8140i 0.00904618 0.0156684i
\(755\) 0.137873 + 0.0796011i 0.000182613 + 0.000105432i
\(756\) −22.5213 + 39.0080i −0.0297900 + 0.0515978i
\(757\) 937.541 541.290i 1.23850 0.715046i 0.269709 0.962942i \(-0.413072\pi\)
0.968787 + 0.247896i \(0.0797391\pi\)
\(758\) 9.94748 + 17.2295i 0.0131233 + 0.0227303i
\(759\) −869.271 −1.14529
\(760\) 3.47554 6.01982i 0.00457308 0.00792081i
\(761\) −689.803 −0.906443 −0.453221 0.891398i \(-0.649725\pi\)
−0.453221 + 0.891398i \(0.649725\pi\)
\(762\) −25.8401 −0.0339109
\(763\) −167.054 289.346i −0.218944 0.379222i
\(764\) 570.309i 0.746477i
\(765\) −94.5796 54.6055i −0.123633 0.0713798i
\(766\) −14.7873 25.6124i −0.0193046 0.0334366i
\(767\) 125.836 + 72.6514i 0.164062 + 0.0947215i
\(768\) 377.367 217.873i 0.491364 0.283689i
\(769\) −1062.06 + 613.178i −1.38109 + 0.797370i −0.992288 0.123953i \(-0.960443\pi\)
−0.388798 + 0.921323i \(0.627110\pi\)
\(770\) 2.53868 + 4.39712i 0.00329698 + 0.00571054i
\(771\) −399.578 + 230.697i −0.518260 + 0.299217i
\(772\) 59.7749 + 103.533i 0.0774286 + 0.134110i
\(773\) −412.476 714.429i −0.533604 0.924229i −0.999230 0.0392476i \(-0.987504\pi\)
0.465625 0.884982i \(-0.345829\pi\)
\(774\) −0.498148 + 0.862817i −0.000643602 + 0.00111475i
\(775\) 811.209 468.352i 1.04672 0.604325i
\(776\) 9.94860 17.2315i 0.0128204 0.0222055i
\(777\) −196.372 −0.252731
\(778\) 5.26281 3.03848i 0.00676454 0.00390551i
\(779\) 81.0842i 0.104088i
\(780\) 71.2857i 0.0913919i
\(781\) −1615.51 932.713i −2.06851 1.19425i
\(782\) 54.1093i 0.0691934i
\(783\) −94.4718 + 54.5433i −0.120654 + 0.0696594i
\(784\) −352.459 610.477i −0.449565 0.778670i
\(785\) −188.710 108.952i −0.240395 0.138792i
\(786\) 3.76279 6.51734i 0.00478726 0.00829178i
\(787\) 175.898 + 101.555i 0.223505 + 0.129041i 0.607572 0.794265i \(-0.292144\pi\)
−0.384067 + 0.923305i \(0.625477\pi\)
\(788\) 453.215 + 261.664i 0.575146 + 0.332061i
\(789\) 41.5012i 0.0525998i
\(790\) 16.4201i 0.0207849i
\(791\) 151.563 262.515i 0.191609 0.331877i
\(792\) 21.2414 + 36.7912i 0.0268200 + 0.0464535i
\(793\) −188.598 326.662i −0.237829 0.411932i
\(794\) 7.54122 + 4.35392i 0.00949776 + 0.00548353i
\(795\) 42.3548i 0.0532764i
\(796\) 1020.48 1.28201
\(797\) 522.435 + 904.883i 0.655501 + 1.13536i 0.981768 + 0.190084i \(0.0608760\pi\)
−0.326266 + 0.945278i \(0.605791\pi\)
\(798\) 2.14505 + 1.23845i 0.00268804 + 0.00155194i
\(799\) −1500.94 −1.87852
\(800\) −80.2774 + 46.3482i −0.100347 + 0.0579352i
\(801\) −418.133 −0.522013
\(802\) −6.83919 + 11.8458i −0.00852767 + 0.0147704i
\(803\) 963.933i 1.20041i
\(804\) 377.427 + 268.840i 0.469437 + 0.334379i
\(805\) −67.5683 −0.0839358
\(806\) 22.6648 + 13.0855i 0.0281201 + 0.0162352i
\(807\) 451.393i 0.559347i
\(808\) 5.62837 + 9.74862i 0.00696581 + 0.0120651i
\(809\) 829.138i 1.02489i −0.858719 0.512447i \(-0.828739\pi\)
0.858719 0.512447i \(-0.171261\pi\)
\(810\) −0.494431 + 0.856380i −0.000610409 + 0.00105726i
\(811\) 1073.72 619.912i 1.32394 0.764379i 0.339588 0.940574i \(-0.389712\pi\)
0.984355 + 0.176195i \(0.0563789\pi\)
\(812\) 181.983i 0.224117i
\(813\) −751.457 −0.924302
\(814\) −46.2629 + 80.1297i −0.0568341 + 0.0984395i
\(815\) −145.248 + 83.8587i −0.178218 + 0.102894i
\(816\) −658.370 + 380.110i −0.806827 + 0.465822i
\(817\) −27.3511 15.7912i −0.0334775 0.0193283i
\(818\) −14.2858 −0.0174643
\(819\) −50.8468 −0.0620840
\(820\) −27.0019 + 46.7686i −0.0329291 + 0.0570349i
\(821\) −498.817 + 863.976i −0.607572 + 1.05235i 0.384067 + 0.923305i \(0.374523\pi\)
−0.991639 + 0.129041i \(0.958810\pi\)
\(822\) 16.6491 + 9.61235i 0.0202544 + 0.0116939i
\(823\) 236.793 410.137i 0.287719 0.498343i −0.685546 0.728029i \(-0.740436\pi\)
0.973265 + 0.229686i \(0.0737698\pi\)
\(824\) 61.1892 35.3276i 0.0742587 0.0428733i
\(825\) 428.744 + 742.607i 0.519690 + 0.900130i
\(826\) 3.36253 0.00407086
\(827\) 334.190 578.834i 0.404099 0.699920i −0.590117 0.807318i \(-0.700919\pi\)
0.994216 + 0.107398i \(0.0342519\pi\)
\(828\) −282.431 −0.341100
\(829\) 611.395 0.737509 0.368754 0.929527i \(-0.379784\pi\)
0.368754 + 0.929527i \(0.379784\pi\)
\(830\) −7.99127 13.8413i −0.00962803 0.0166762i
\(831\) 423.981i 0.510206i
\(832\) 428.243 + 247.246i 0.514715 + 0.297171i
\(833\) 610.618 + 1057.62i 0.733034 + 1.26965i
\(834\) −14.9094 8.60794i −0.0178770 0.0103213i
\(835\) 215.453 124.392i 0.258028 0.148972i
\(836\) −582.632 + 336.383i −0.696928 + 0.402372i
\(837\) −104.640 181.241i −0.125018 0.216537i
\(838\) −47.2806 + 27.2975i −0.0564208 + 0.0325745i
\(839\) −41.7200 72.2612i −0.0497259 0.0861278i 0.840091 0.542445i \(-0.182501\pi\)
−0.889817 + 0.456318i \(0.849168\pi\)
\(840\) 1.65109 + 2.85977i 0.00196558 + 0.00340449i
\(841\) 200.131 346.638i 0.237968 0.412173i
\(842\) 44.1504 25.4902i 0.0524352 0.0302735i
\(843\) 279.252 483.678i 0.331259 0.573758i
\(844\) 256.032 0.303355
\(845\) 123.525 71.3174i 0.146184 0.0843992i
\(846\) 13.5904i 0.0160643i
\(847\) 721.007i 0.851248i
\(848\) 255.332 + 147.416i 0.301100 + 0.173840i
\(849\) 473.849i 0.558126i
\(850\) 46.2248 26.6879i 0.0543822 0.0313976i
\(851\) −615.657 1066.35i −0.723451 1.25305i
\(852\) −524.887 303.044i −0.616065 0.355685i
\(853\) −351.581 + 608.956i −0.412170 + 0.713899i −0.995127 0.0986038i \(-0.968562\pi\)
0.582957 + 0.812503i \(0.301896\pi\)
\(854\) −7.55946 4.36445i −0.00885182 0.00511060i
\(855\) −27.1471 15.6734i −0.0317510 0.0183314i
\(856\) 18.1104i 0.0211570i
\(857\) 728.725i 0.850321i −0.905118 0.425161i \(-0.860218\pi\)
0.905118 0.425161i \(-0.139782\pi\)
\(858\) −11.9789 + 20.7481i −0.0139615 + 0.0241819i
\(859\) −347.836 602.470i −0.404931 0.701362i 0.589382 0.807854i \(-0.299371\pi\)
−0.994313 + 0.106493i \(0.966038\pi\)
\(860\) −10.5172 18.2164i −0.0122294 0.0211819i
\(861\) −33.3592 19.2599i −0.0387447 0.0223693i
\(862\) 54.4553i 0.0631732i
\(863\) 1156.79 1.34043 0.670213 0.742169i \(-0.266203\pi\)
0.670213 + 0.742169i \(0.266203\pi\)
\(864\) 10.3552 + 17.9357i 0.0119852 + 0.0207589i
\(865\) −57.5805 33.2441i −0.0665671 0.0384325i
\(866\) 23.2281 0.0268223
\(867\) 707.094 408.241i 0.815564 0.470866i
\(868\) −349.129 −0.402222
\(869\) −1590.61 + 2755.01i −1.83039 + 3.17033i
\(870\) 3.99525i 0.00459224i
\(871\) −49.7932 + 520.724i −0.0571678 + 0.597846i
\(872\) −102.385 −0.117414
\(873\) −77.7074 44.8644i −0.0890119 0.0513911i
\(874\) 15.5309i 0.0177699i
\(875\) 69.1498 + 119.771i 0.0790284 + 0.136881i
\(876\) 313.187i 0.357520i
\(877\) 45.3347 78.5221i 0.0516930 0.0895349i −0.839021 0.544099i \(-0.816872\pi\)
0.890714 + 0.454564i \(0.150205\pi\)
\(878\) −10.9737 + 6.33569i −0.0124986 + 0.00721605i
\(879\) 34.1132i 0.0388091i
\(880\) −447.296 −0.508291
\(881\) 243.251 421.323i 0.276108 0.478233i −0.694306 0.719680i \(-0.744289\pi\)
0.970414 + 0.241447i \(0.0776219\pi\)
\(882\) 9.57633 5.52890i 0.0108575 0.00626859i
\(883\) −1351.19 + 780.108i −1.53022 + 0.883475i −0.530873 + 0.847452i \(0.678136\pi\)
−0.999351 + 0.0360235i \(0.988531\pi\)
\(884\) −744.504 429.839i −0.842199 0.486244i
\(885\) −42.5551 −0.0480848
\(886\) 28.2289 0.0318611
\(887\) −345.476 + 598.381i −0.389488 + 0.674613i −0.992381 0.123209i \(-0.960681\pi\)
0.602893 + 0.797822i \(0.294015\pi\)
\(888\) −30.0882 + 52.1144i −0.0338832 + 0.0586874i
\(889\) 337.000 + 194.567i 0.379077 + 0.218860i
\(890\) −7.65695 + 13.2622i −0.00860332 + 0.0149014i
\(891\) 165.914 95.7907i 0.186211 0.107509i
\(892\) 840.712 + 1456.16i 0.942502 + 1.63246i
\(893\) −430.813 −0.482433
\(894\) −7.77737 + 13.4708i −0.00869952 + 0.0150680i
\(895\) −332.992 −0.372058
\(896\) 46.0531 0.0513985
\(897\) −159.413 276.111i −0.177718 0.307817i
\(898\) 10.7238i 0.0119419i
\(899\) −732.260 422.771i −0.814527 0.470268i
\(900\) 139.301 + 241.277i 0.154779 + 0.268086i
\(901\) −442.351 255.391i −0.490955 0.283453i
\(902\) −15.7181 + 9.07484i −0.0174258 + 0.0100608i
\(903\) 12.9934 7.50176i 0.0143892 0.00830760i
\(904\) −46.4452 80.4455i −0.0513775 0.0889884i
\(905\) 114.447 66.0761i 0.126461 0.0730123i
\(906\) 0.00869204 + 0.0150550i 9.59386e−6 + 1.66171e-5i
\(907\) −647.886 1122.17i −0.714318 1.23723i −0.963222 0.268707i \(-0.913404\pi\)
0.248904 0.968528i \(-0.419930\pi\)
\(908\) 542.097 938.939i 0.597023 1.03407i
\(909\) 43.9626 25.3818i 0.0483637 0.0279228i
\(910\) −0.931120 + 1.61275i −0.00102321 + 0.00177225i
\(911\) 219.215 0.240631 0.120316 0.992736i \(-0.461609\pi\)
0.120316 + 0.992736i \(0.461609\pi\)
\(912\) −188.971 + 109.103i −0.207206 + 0.119630i
\(913\) 3096.44i 3.39150i
\(914\) 20.8243i 0.0227837i
\(915\) 95.6700 + 55.2351i 0.104557 + 0.0603662i
\(916\) 579.824i 0.632996i
\(917\) −98.1466 + 56.6650i −0.107030 + 0.0617939i
\(918\) −5.96265 10.3276i −0.00649526 0.0112501i
\(919\) −1105.73 638.393i −1.20319 0.694661i −0.241925 0.970295i \(-0.577779\pi\)
−0.961263 + 0.275634i \(0.911112\pi\)
\(920\) −10.3529 + 17.9317i −0.0112531 + 0.0194910i
\(921\) 630.908 + 364.255i 0.685025 + 0.395499i
\(922\) −17.8784 10.3221i −0.0193909 0.0111953i
\(923\) 684.190i 0.741267i
\(924\) 319.604i 0.345892i
\(925\) −607.312 + 1051.90i −0.656554 + 1.13718i
\(926\) −3.24093 5.61346i −0.00349993 0.00606205i
\(927\) −159.314 275.940i −0.171860 0.297670i
\(928\) 72.4646 + 41.8375i 0.0780869 + 0.0450835i
\(929\) 1104.12i 1.18850i −0.804280 0.594251i \(-0.797449\pi\)
0.804280 0.594251i \(-0.202551\pi\)
\(930\) −7.66476 −0.00824168
\(931\) 175.265 + 303.568i 0.188255 + 0.326066i
\(932\) 443.808 + 256.233i 0.476189 + 0.274928i
\(933\) −500.810 −0.536773
\(934\) −5.23103 + 3.02014i −0.00560067 + 0.00323355i
\(935\) 774.919 0.828790
\(936\) −7.79079 + 13.4941i −0.00832350 + 0.0144167i
\(937\) 1371.16i 1.46335i 0.681655 + 0.731674i \(0.261260\pi\)
−0.681655 + 0.731674i \(0.738740\pi\)
\(938\) 5.02726 + 11.0120i 0.00535955 + 0.0117399i
\(939\) 673.578 0.717335
\(940\) −248.489 143.465i −0.264350 0.152622i
\(941\) 1180.46i 1.25447i −0.778828 0.627237i \(-0.784186\pi\)
0.778828 0.627237i \(-0.215814\pi\)
\(942\) −11.8970 20.6062i −0.0126295 0.0218749i
\(943\) 241.532i 0.256132i
\(944\) −148.113 + 256.540i −0.156900 + 0.271758i
\(945\) 12.8965 7.44579i 0.0136471 0.00787914i
\(946\) 7.06932i 0.00747285i
\(947\) −1175.44 −1.24123 −0.620614 0.784116i \(-0.713117\pi\)
−0.620614 + 0.784116i \(0.713117\pi\)
\(948\) −516.798 + 895.120i −0.545145 + 0.944219i
\(949\) −306.179 + 176.773i −0.322634 + 0.186273i
\(950\) 13.2679 7.66021i 0.0139662 0.00806338i
\(951\) 382.112 + 220.613i 0.401801 + 0.231980i
\(952\) −39.8231 −0.0418310
\(953\) −1533.59 −1.60923 −0.804614 0.593798i \(-0.797628\pi\)
−0.804614 + 0.593798i \(0.797628\pi\)
\(954\) −2.31246 + 4.00531i −0.00242397 + 0.00419843i
\(955\) −94.2754 + 163.290i −0.0987177 + 0.170984i
\(956\) 403.143 + 232.755i 0.421698 + 0.243467i
\(957\) 387.018 670.335i 0.404407 0.700454i
\(958\) 57.3770 33.1266i 0.0598925 0.0345790i
\(959\) −144.755 250.724i −0.150944 0.261443i
\(960\) −144.823 −0.150857
\(961\) 330.573 572.569i 0.343988 0.595805i
\(962\) −33.9361 −0.0352766
\(963\) −81.6709 −0.0848089
\(964\) 781.716 + 1353.97i 0.810909 + 1.40454i
\(965\) 39.5246i 0.0409581i
\(966\) −6.38964 3.68906i −0.00661454 0.00381890i
\(967\) −460.837 798.194i −0.476564 0.825433i 0.523075 0.852286i \(-0.324785\pi\)
−0.999639 + 0.0268534i \(0.991451\pi\)
\(968\) −191.345 110.473i −0.197671 0.114125i
\(969\) 327.384 189.015i 0.337857 0.195062i
\(970\) −2.84600 + 1.64314i −0.00293402 + 0.00169396i
\(971\) −596.521 1033.20i −0.614337 1.06406i −0.990501 0.137509i \(-0.956090\pi\)
0.376164 0.926553i \(-0.377243\pi\)
\(972\) 53.9065 31.1229i 0.0554593 0.0320195i
\(973\) 129.630 + 224.525i 0.133227 + 0.230756i
\(974\) 19.3291 + 33.4789i 0.0198450 + 0.0343726i
\(975\) −157.252 + 272.369i −0.161284 + 0.279353i
\(976\) 665.961 384.493i 0.682337 0.393947i
\(977\) 164.558 285.022i 0.168432 0.291732i −0.769437 0.638723i \(-0.779463\pi\)
0.937869 + 0.346990i \(0.112796\pi\)
\(978\) −18.3139 −0.0187259
\(979\) 2569.41 1483.45i 2.62453 1.51527i
\(980\) 233.460i 0.238224i
\(981\) 461.716i 0.470659i
\(982\) −2.53291 1.46237i −0.00257933 0.00148918i
\(983\) 715.983i 0.728366i 0.931328 + 0.364183i \(0.118652\pi\)
−0.931328 + 0.364183i \(0.881348\pi\)
\(984\) −10.2226 + 5.90205i −0.0103889 + 0.00599802i
\(985\) −86.5092 149.838i −0.0878266 0.152120i
\(986\) −41.7261 24.0906i −0.0423186 0.0244326i
\(987\) 102.331 177.242i 0.103679 0.179577i
\(988\) −213.694 123.376i −0.216290 0.124875i
\(989\) 81.4731 + 47.0385i 0.0823792 + 0.0475617i
\(990\) 7.01657i 0.00708745i
\(991\) 246.871i 0.249113i −0.992213 0.124556i \(-0.960249\pi\)
0.992213 0.124556i \(-0.0397508\pi\)
\(992\) −80.2639 + 139.021i −0.0809112 + 0.140142i
\(993\) −55.9600 96.9256i −0.0563545 0.0976088i
\(994\) −7.91660 13.7119i −0.00796438 0.0137947i
\(995\) −292.181 168.691i −0.293649 0.169539i
\(996\) 1006.05i 1.01009i
\(997\) −1407.00 −1.41123 −0.705617 0.708593i \(-0.749330\pi\)
−0.705617 + 0.708593i \(0.749330\pi\)
\(998\) 40.4113 + 69.9945i 0.0404923 + 0.0701347i
\(999\) 235.016 + 135.687i 0.235251 + 0.135822i
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 201.3.h.a.172.6 yes 22
67.30 odd 6 inner 201.3.h.a.97.6 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.3.h.a.97.6 22 67.30 odd 6 inner
201.3.h.a.172.6 yes 22 1.1 even 1 trivial