Properties

Label 224.3.v.b.69.16
Level $224$
Weight $3$
Character 224.69
Analytic conductor $6.104$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [224,3,Mod(13,224)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(224, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("224.13");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.v (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(60\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 69.16
Character \(\chi\) \(=\) 224.69
Dual form 224.3.v.b.13.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41192 - 1.41651i) q^{2} +(2.79421 - 1.15740i) q^{3} +(-0.0129803 + 3.99998i) q^{4} +(1.86072 - 4.49217i) q^{5} +(-5.58465 - 2.32386i) q^{6} +(6.93602 + 0.944293i) q^{7} +(5.68432 - 5.62925i) q^{8} +(0.104065 - 0.104065i) q^{9} +O(q^{10})\) \(q+(-1.41192 - 1.41651i) q^{2} +(2.79421 - 1.15740i) q^{3} +(-0.0129803 + 3.99998i) q^{4} +(1.86072 - 4.49217i) q^{5} +(-5.58465 - 2.32386i) q^{6} +(6.93602 + 0.944293i) q^{7} +(5.68432 - 5.62925i) q^{8} +(0.104065 - 0.104065i) q^{9} +(-8.99036 + 3.70685i) q^{10} +(2.63807 - 6.36886i) q^{11} +(4.59330 + 11.1918i) q^{12} +(3.81272 + 9.20472i) q^{13} +(-8.45548 - 11.1582i) q^{14} -14.7056i q^{15} +(-15.9997 - 0.103842i) q^{16} +18.4549 q^{17} +(-0.294341 - 0.000477579i) q^{18} +(-6.94428 - 16.7650i) q^{19} +(17.9444 + 7.50114i) q^{20} +(20.4736 - 5.38918i) q^{21} +(-12.7463 + 5.25546i) q^{22} +(-1.72229 + 1.72229i) q^{23} +(9.36789 - 22.3083i) q^{24} +(0.960355 + 0.960355i) q^{25} +(7.65530 - 18.3970i) q^{26} +(-10.2463 + 24.7366i) q^{27} +(-3.86718 + 27.7317i) q^{28} +(-17.1745 - 41.4630i) q^{29} +(-20.8306 + 20.7632i) q^{30} +2.69268i q^{31} +(22.4431 + 22.8102i) q^{32} -20.8492i q^{33} +(-26.0568 - 26.1415i) q^{34} +(17.1479 - 29.4007i) q^{35} +(0.414908 + 0.417610i) q^{36} +(-63.1550 - 26.1596i) q^{37} +(-13.9429 + 33.5073i) q^{38} +(21.3071 + 21.3071i) q^{39} +(-14.7106 - 36.0094i) q^{40} +(-4.62617 - 4.62617i) q^{41} +(-36.5408 - 21.3919i) q^{42} +(1.15439 - 2.78695i) q^{43} +(25.4411 + 10.6349i) q^{44} +(-0.273843 - 0.661115i) q^{45} +(4.87136 + 0.00790397i) q^{46} +9.80819 q^{47} +(-44.8266 + 18.2278i) q^{48} +(47.2166 + 13.0993i) q^{49} +(0.00440728 - 2.71629i) q^{50} +(51.5668 - 21.3597i) q^{51} +(-36.8682 + 15.1313i) q^{52} +(10.8678 - 26.2371i) q^{53} +(49.5065 - 20.4122i) q^{54} +(-23.7013 - 23.7013i) q^{55} +(44.7422 - 33.6769i) q^{56} +(-38.8075 - 38.8075i) q^{57} +(-34.4835 + 82.8701i) q^{58} +(-30.6283 + 73.9432i) q^{59} +(58.8223 + 0.190883i) q^{60} +(-25.7376 + 10.6609i) q^{61} +(3.81420 - 3.80184i) q^{62} +(0.820067 - 0.623531i) q^{63} +(0.623044 - 63.9970i) q^{64} +48.4435 q^{65} +(-29.5331 + 29.4374i) q^{66} +(29.2049 + 70.5070i) q^{67} +(-0.239550 + 73.8192i) q^{68} +(-2.81906 + 6.80581i) q^{69} +(-65.8577 + 17.2212i) q^{70} +(33.8344 + 33.8344i) q^{71} +(0.00573093 - 1.17735i) q^{72} +(70.7687 + 70.7687i) q^{73} +(52.1143 + 126.395i) q^{74} +(3.79495 + 1.57192i) q^{75} +(67.1496 - 27.5593i) q^{76} +(24.3118 - 41.6834i) q^{77} +(0.0977829 - 60.2654i) q^{78} +89.2961i q^{79} +(-30.2373 + 71.6800i) q^{80} +82.3029i q^{81} +(-0.0212305 + 13.0848i) q^{82} +(54.0727 + 130.543i) q^{83} +(21.2909 + 81.9639i) q^{84} +(34.3394 - 82.9026i) q^{85} +(-5.57763 + 2.29973i) q^{86} +(-95.9784 - 95.9784i) q^{87} +(-20.8563 - 51.0530i) q^{88} +(-72.3174 + 72.3174i) q^{89} +(-0.549830 + 1.32134i) q^{90} +(17.7531 + 67.4444i) q^{91} +(-6.86676 - 6.91148i) q^{92} +(3.11650 + 7.52391i) q^{93} +(-13.8483 - 13.8934i) q^{94} -88.2324 q^{95} +(89.1113 + 37.7609i) q^{96} -108.153i q^{97} +(-48.1108 - 85.3777i) q^{98} +(-0.388246 - 0.937309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{11} + 12 q^{14} - 112 q^{16} - 176 q^{18} - 4 q^{21} - 192 q^{22} + 128 q^{23} - 8 q^{25} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 8 q^{32} + 92 q^{35} + 192 q^{36} - 8 q^{37} - 8 q^{39} - 424 q^{42} + 128 q^{43} - 16 q^{44} - 8 q^{46} - 320 q^{50} - 80 q^{51} - 192 q^{53} + 608 q^{56} - 8 q^{57} - 712 q^{58} + 264 q^{60} + 496 q^{63} - 272 q^{64} - 16 q^{65} + 304 q^{67} + 320 q^{70} + 504 q^{71} - 8 q^{72} + 232 q^{74} + 164 q^{77} + 560 q^{78} - 1000 q^{84} - 208 q^{85} - 8 q^{86} - 800 q^{88} + 188 q^{91} + 1560 q^{92} + 64 q^{93} - 16 q^{95} - 376 q^{98} + 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41192 1.41651i −0.705959 0.708253i
\(3\) 2.79421 1.15740i 0.931403 0.385800i 0.135192 0.990819i \(-0.456835\pi\)
0.796210 + 0.605020i \(0.206835\pi\)
\(4\) −0.0129803 + 3.99998i −0.00324507 + 0.999995i
\(5\) 1.86072 4.49217i 0.372143 0.898434i −0.621243 0.783618i \(-0.713372\pi\)
0.993387 0.114816i \(-0.0366279\pi\)
\(6\) −5.58465 2.32386i −0.930775 0.387310i
\(7\) 6.93602 + 0.944293i 0.990859 + 0.134899i
\(8\) 5.68432 5.62925i 0.710540 0.703656i
\(9\) 0.104065 0.104065i 0.0115628 0.0115628i
\(10\) −8.99036 + 3.70685i −0.899036 + 0.370685i
\(11\) 2.63807 6.36886i 0.239824 0.578988i −0.757440 0.652905i \(-0.773550\pi\)
0.997264 + 0.0739174i \(0.0235501\pi\)
\(12\) 4.59330 + 11.1918i 0.382775 + 0.932650i
\(13\) 3.81272 + 9.20472i 0.293286 + 0.708055i 1.00000 0.000555699i \(0.000176884\pi\)
−0.706714 + 0.707500i \(0.749823\pi\)
\(14\) −8.45548 11.1582i −0.603963 0.797012i
\(15\) 14.7056i 0.980376i
\(16\) −15.9997 0.103842i −0.999979 0.00649010i
\(17\) 18.4549 1.08558 0.542791 0.839868i \(-0.317367\pi\)
0.542791 + 0.839868i \(0.317367\pi\)
\(18\) −0.294341 0.000477579i −0.0163523 2.65322e-5i
\(19\) −6.94428 16.7650i −0.365488 0.882367i −0.994477 0.104952i \(-0.966531\pi\)
0.628989 0.777414i \(-0.283469\pi\)
\(20\) 17.9444 + 7.50114i 0.897221 + 0.375057i
\(21\) 20.4736 5.38918i 0.974933 0.256628i
\(22\) −12.7463 + 5.25546i −0.579376 + 0.238885i
\(23\) −1.72229 + 1.72229i −0.0748821 + 0.0748821i −0.743556 0.668674i \(-0.766862\pi\)
0.668674 + 0.743556i \(0.266862\pi\)
\(24\) 9.36789 22.3083i 0.390329 0.929514i
\(25\) 0.960355 + 0.960355i 0.0384142 + 0.0384142i
\(26\) 7.65530 18.3970i 0.294435 0.707579i
\(27\) −10.2463 + 24.7366i −0.379491 + 0.916172i
\(28\) −3.86718 + 27.7317i −0.138114 + 0.990416i
\(29\) −17.1745 41.4630i −0.592225 1.42976i −0.881349 0.472466i \(-0.843364\pi\)
0.289124 0.957292i \(-0.406636\pi\)
\(30\) −20.8306 + 20.7632i −0.694355 + 0.692105i
\(31\) 2.69268i 0.0868606i 0.999056 + 0.0434303i \(0.0138286\pi\)
−0.999056 + 0.0434303i \(0.986171\pi\)
\(32\) 22.4431 + 22.8102i 0.701347 + 0.712820i
\(33\) 20.8492i 0.631795i
\(34\) −26.0568 26.1415i −0.766376 0.768867i
\(35\) 17.1479 29.4007i 0.489940 0.840020i
\(36\) 0.414908 + 0.417610i 0.0115252 + 0.0116003i
\(37\) −63.1550 26.1596i −1.70689 0.707017i −0.706891 0.707323i \(-0.749903\pi\)
−1.00000 0.000305477i \(0.999903\pi\)
\(38\) −13.9429 + 33.5073i −0.366919 + 0.881772i
\(39\) 21.3071 + 21.3071i 0.546335 + 0.546335i
\(40\) −14.7106 36.0094i −0.367766 0.900235i
\(41\) −4.62617 4.62617i −0.112833 0.112833i 0.648436 0.761269i \(-0.275423\pi\)
−0.761269 + 0.648436i \(0.775423\pi\)
\(42\) −36.5408 21.3919i −0.870020 0.509331i
\(43\) 1.15439 2.78695i 0.0268463 0.0648127i −0.909888 0.414854i \(-0.863833\pi\)
0.936734 + 0.350042i \(0.113833\pi\)
\(44\) 25.4411 + 10.6349i 0.578206 + 0.241702i
\(45\) −0.273843 0.661115i −0.00608540 0.0146915i
\(46\) 4.87136 + 0.00790397i 0.105899 + 0.000171825i
\(47\) 9.80819 0.208685 0.104342 0.994541i \(-0.466726\pi\)
0.104342 + 0.994541i \(0.466726\pi\)
\(48\) −44.8266 + 18.2278i −0.933887 + 0.379747i
\(49\) 47.2166 + 13.0993i 0.963604 + 0.267332i
\(50\) 0.00440728 2.71629i 8.81457e−5 0.0543258i
\(51\) 51.5668 21.3597i 1.01111 0.418817i
\(52\) −36.8682 + 15.1313i −0.709003 + 0.290987i
\(53\) 10.8678 26.2371i 0.205052 0.495040i −0.787579 0.616213i \(-0.788666\pi\)
0.992631 + 0.121174i \(0.0386658\pi\)
\(54\) 49.5065 20.4122i 0.916787 0.378004i
\(55\) −23.7013 23.7013i −0.430933 0.430933i
\(56\) 44.7422 33.6769i 0.798968 0.601373i
\(57\) −38.8075 38.8075i −0.680833 0.680833i
\(58\) −34.4835 + 82.8701i −0.594544 + 1.42879i
\(59\) −30.6283 + 73.9432i −0.519124 + 1.25328i 0.419319 + 0.907839i \(0.362269\pi\)
−0.938442 + 0.345436i \(0.887731\pi\)
\(60\) 58.8223 + 0.190883i 0.980371 + 0.00318139i
\(61\) −25.7376 + 10.6609i −0.421928 + 0.174768i −0.583537 0.812087i \(-0.698332\pi\)
0.161609 + 0.986855i \(0.448332\pi\)
\(62\) 3.81420 3.80184i 0.0615193 0.0613200i
\(63\) 0.820067 0.623531i 0.0130169 0.00989731i
\(64\) 0.623044 63.9970i 0.00973506 0.999953i
\(65\) 48.4435 0.745285
\(66\) −29.5331 + 29.4374i −0.447471 + 0.446021i
\(67\) 29.2049 + 70.5070i 0.435895 + 1.05234i 0.977353 + 0.211615i \(0.0678724\pi\)
−0.541458 + 0.840728i \(0.682128\pi\)
\(68\) −0.239550 + 73.8192i −0.00352279 + 1.08558i
\(69\) −2.81906 + 6.80581i −0.0408559 + 0.0986349i
\(70\) −65.8577 + 17.2212i −0.940824 + 0.246018i
\(71\) 33.8344 + 33.8344i 0.476541 + 0.476541i 0.904024 0.427483i \(-0.140599\pi\)
−0.427483 + 0.904024i \(0.640599\pi\)
\(72\) 0.00573093 1.17735i 7.95962e−5 0.0163521i
\(73\) 70.7687 + 70.7687i 0.969434 + 0.969434i 0.999547 0.0301127i \(-0.00958661\pi\)
−0.0301127 + 0.999547i \(0.509587\pi\)
\(74\) 52.1143 + 126.395i 0.704247 + 1.70804i
\(75\) 3.79495 + 1.57192i 0.0505993 + 0.0209589i
\(76\) 67.1496 27.5593i 0.883548 0.362623i
\(77\) 24.3118 41.6834i 0.315737 0.541343i
\(78\) 0.0977829 60.2654i 0.00125363 0.772633i
\(79\) 89.2961i 1.13033i 0.824978 + 0.565165i \(0.191188\pi\)
−0.824978 + 0.565165i \(0.808812\pi\)
\(80\) −30.2373 + 71.6800i −0.377967 + 0.896000i
\(81\) 82.3029i 1.01608i
\(82\) −0.0212305 + 13.0848i −0.000258909 + 0.159570i
\(83\) 54.0727 + 130.543i 0.651479 + 1.57281i 0.810633 + 0.585555i \(0.199123\pi\)
−0.159154 + 0.987254i \(0.550877\pi\)
\(84\) 21.2909 + 81.9639i 0.253463 + 0.975761i
\(85\) 34.3394 82.9026i 0.403993 0.975324i
\(86\) −5.57763 + 2.29973i −0.0648562 + 0.0267411i
\(87\) −95.9784 95.9784i −1.10320 1.10320i
\(88\) −20.8563 51.0530i −0.237003 0.580148i
\(89\) −72.3174 + 72.3174i −0.812555 + 0.812555i −0.985016 0.172461i \(-0.944828\pi\)
0.172461 + 0.985016i \(0.444828\pi\)
\(90\) −0.549830 + 1.32134i −0.00610923 + 0.0146816i
\(91\) 17.7531 + 67.4444i 0.195089 + 0.741147i
\(92\) −6.86676 6.91148i −0.0746387 0.0751247i
\(93\) 3.11650 + 7.52391i 0.0335108 + 0.0809022i
\(94\) −13.8483 13.8934i −0.147323 0.147802i
\(95\) −88.2324 −0.928762
\(96\) 89.1113 + 37.7609i 0.928242 + 0.393343i
\(97\) 108.153i 1.11498i −0.830185 0.557489i \(-0.811765\pi\)
0.830185 0.557489i \(-0.188235\pi\)
\(98\) −48.1108 85.3777i −0.490926 0.871201i
\(99\) −0.388246 0.937309i −0.00392168 0.00946777i
\(100\) −3.85387 + 3.82893i −0.0385387 + 0.0382893i
\(101\) 67.0471 161.866i 0.663832 1.60263i −0.127915 0.991785i \(-0.540829\pi\)
0.791748 0.610848i \(-0.209171\pi\)
\(102\) −103.064 42.8867i −1.01043 0.420457i
\(103\) 33.5902 33.5902i 0.326119 0.326119i −0.524990 0.851109i \(-0.675931\pi\)
0.851109 + 0.524990i \(0.175931\pi\)
\(104\) 73.4884 + 30.8598i 0.706619 + 0.296729i
\(105\) 13.8864 101.999i 0.132252 0.971415i
\(106\) −52.5094 + 21.6504i −0.495372 + 0.204249i
\(107\) −28.1712 + 68.0112i −0.263282 + 0.635619i −0.999138 0.0415197i \(-0.986780\pi\)
0.735856 + 0.677138i \(0.236780\pi\)
\(108\) −98.8131 41.3059i −0.914936 0.382462i
\(109\) −127.290 + 52.7253i −1.16780 + 0.483718i −0.880464 0.474113i \(-0.842769\pi\)
−0.287334 + 0.957830i \(0.592769\pi\)
\(110\) −0.108771 + 67.0373i −0.000988823 + 0.609430i
\(111\) −206.745 −1.86257
\(112\) −110.876 15.8286i −0.989963 0.141327i
\(113\) 16.9678i 0.150157i −0.997178 0.0750786i \(-0.976079\pi\)
0.997178 0.0750786i \(-0.0239208\pi\)
\(114\) −0.178096 + 109.764i −0.00156225 + 0.962842i
\(115\) 4.53212 + 10.9415i 0.0394097 + 0.0951435i
\(116\) 166.074 68.1595i 1.43167 0.587582i
\(117\) 1.35466 + 0.561120i 0.0115783 + 0.00479590i
\(118\) 147.986 61.0165i 1.25412 0.517089i
\(119\) 128.004 + 17.4268i 1.07566 + 0.146444i
\(120\) −82.7818 83.5916i −0.689848 0.696597i
\(121\) 51.9569 + 51.9569i 0.429396 + 0.429396i
\(122\) 51.4405 + 21.4052i 0.421644 + 0.175453i
\(123\) −18.2808 7.57216i −0.148624 0.0615623i
\(124\) −10.7707 0.0349517i −0.0868602 0.000281868i
\(125\) 118.405 49.0451i 0.947242 0.392361i
\(126\) −2.04110 0.281257i −0.0161992 0.00223220i
\(127\) −178.949 −1.40904 −0.704522 0.709682i \(-0.748839\pi\)
−0.704522 + 0.709682i \(0.748839\pi\)
\(128\) −91.5318 + 89.4759i −0.715092 + 0.699030i
\(129\) 9.12340i 0.0707240i
\(130\) −68.3983 68.6206i −0.526141 0.527851i
\(131\) 56.9742 23.5995i 0.434918 0.180149i −0.154473 0.987997i \(-0.549368\pi\)
0.589391 + 0.807848i \(0.299368\pi\)
\(132\) 83.3965 + 0.270628i 0.631791 + 0.00205022i
\(133\) −32.3346 122.839i −0.243117 0.923605i
\(134\) 58.6386 140.919i 0.437602 1.05163i
\(135\) 92.0558 + 92.0558i 0.681895 + 0.681895i
\(136\) 104.904 103.887i 0.771350 0.763877i
\(137\) −77.2919 + 77.2919i −0.564175 + 0.564175i −0.930491 0.366316i \(-0.880619\pi\)
0.366316 + 0.930491i \(0.380619\pi\)
\(138\) 13.6207 5.61602i 0.0987011 0.0406958i
\(139\) −103.517 42.8781i −0.744725 0.308475i −0.0221379 0.999755i \(-0.507047\pi\)
−0.722587 + 0.691280i \(0.757047\pi\)
\(140\) 117.380 + 68.9728i 0.838425 + 0.492663i
\(141\) 27.4061 11.3520i 0.194370 0.0805105i
\(142\) 0.155274 95.6981i 0.00109348 0.673930i
\(143\) 68.6818 0.480292
\(144\) −1.67582 + 1.65420i −0.0116376 + 0.0114875i
\(145\) −218.216 −1.50493
\(146\) 0.324773 200.164i 0.00222447 1.37098i
\(147\) 147.094 18.0464i 1.00064 0.122765i
\(148\) 105.458 252.279i 0.712553 1.70459i
\(149\) 29.7091 71.7241i 0.199390 0.481370i −0.792283 0.610154i \(-0.791107\pi\)
0.991673 + 0.128784i \(0.0411075\pi\)
\(150\) −3.13152 7.59498i −0.0208768 0.0506332i
\(151\) −90.0549 + 90.0549i −0.596390 + 0.596390i −0.939350 0.342960i \(-0.888571\pi\)
0.342960 + 0.939350i \(0.388571\pi\)
\(152\) −133.848 56.2064i −0.880577 0.369779i
\(153\) 1.92052 1.92052i 0.0125524 0.0125524i
\(154\) −93.3710 + 24.4158i −0.606305 + 0.158544i
\(155\) 12.0960 + 5.01031i 0.0780385 + 0.0323246i
\(156\) −85.5044 + 84.9512i −0.548105 + 0.544559i
\(157\) 177.979 73.7215i 1.13363 0.469563i 0.264614 0.964354i \(-0.414755\pi\)
0.869012 + 0.494791i \(0.164755\pi\)
\(158\) 126.489 126.079i 0.800560 0.797967i
\(159\) 85.8903i 0.540190i
\(160\) 144.228 58.3748i 0.901423 0.364843i
\(161\) −13.5722 + 10.3195i −0.0842992 + 0.0640961i
\(162\) 116.583 116.205i 0.719645 0.717314i
\(163\) −21.6782 52.3359i −0.132995 0.321079i 0.843327 0.537401i \(-0.180594\pi\)
−0.976322 + 0.216322i \(0.930594\pi\)
\(164\) 18.5646 18.4445i 0.113199 0.112467i
\(165\) −93.6583 38.7945i −0.567626 0.235118i
\(166\) 108.569 260.910i 0.654030 1.57175i
\(167\) −168.495 + 168.495i −1.00895 + 1.00895i −0.00899546 + 0.999960i \(0.502863\pi\)
−0.999960 + 0.00899546i \(0.997137\pi\)
\(168\) 86.0414 145.885i 0.512151 0.868362i
\(169\) 49.3110 49.3110i 0.291781 0.291781i
\(170\) −165.916 + 68.4096i −0.975978 + 0.402410i
\(171\) −2.46731 1.02199i −0.0144287 0.00597657i
\(172\) 11.1327 + 4.65371i 0.0647252 + 0.0270565i
\(173\) 50.4636 + 121.830i 0.291697 + 0.704220i 0.999999 0.00169064i \(-0.000538147\pi\)
−0.708301 + 0.705910i \(0.750538\pi\)
\(174\) −0.440466 + 271.467i −0.00253141 + 1.56016i
\(175\) 5.75418 + 7.56790i 0.0328810 + 0.0432451i
\(176\) −42.8696 + 101.626i −0.243577 + 0.577419i
\(177\) 242.062i 1.36758i
\(178\) 204.544 + 0.331881i 1.14912 + 0.00186450i
\(179\) −22.2421 + 9.21300i −0.124258 + 0.0514693i −0.443946 0.896054i \(-0.646422\pi\)
0.319688 + 0.947523i \(0.396422\pi\)
\(180\) 2.64800 1.08678i 0.0147111 0.00603769i
\(181\) −50.6351 20.9738i −0.279752 0.115877i 0.238396 0.971168i \(-0.423378\pi\)
−0.518148 + 0.855291i \(0.673378\pi\)
\(182\) 70.4695 120.373i 0.387195 0.661392i
\(183\) −59.5773 + 59.5773i −0.325559 + 0.325559i
\(184\) −0.0948473 + 19.4852i −0.000515474 + 0.105898i
\(185\) −235.027 + 235.027i −1.27042 + 1.27042i
\(186\) 6.25741 15.0377i 0.0336420 0.0808477i
\(187\) 48.6853 117.537i 0.260349 0.628539i
\(188\) −0.127313 + 39.2325i −0.000677196 + 0.208684i
\(189\) −94.4268 + 161.898i −0.499613 + 0.856605i
\(190\) 124.577 + 124.982i 0.655667 + 0.657799i
\(191\) −240.133 −1.25724 −0.628621 0.777711i \(-0.716380\pi\)
−0.628621 + 0.777711i \(0.716380\pi\)
\(192\) −72.3291 179.542i −0.376714 0.935114i
\(193\) −237.252 −1.22928 −0.614642 0.788806i \(-0.710700\pi\)
−0.614642 + 0.788806i \(0.710700\pi\)
\(194\) −153.199 + 152.703i −0.789686 + 0.787128i
\(195\) 135.361 56.0685i 0.694161 0.287531i
\(196\) −53.0097 + 188.695i −0.270458 + 0.962732i
\(197\) −142.584 59.0603i −0.723777 0.299798i −0.00978503 0.999952i \(-0.503115\pi\)
−0.713992 + 0.700154i \(0.753115\pi\)
\(198\) −0.779533 + 1.87336i −0.00393704 + 0.00946140i
\(199\) −7.17452 + 7.17452i −0.0360529 + 0.0360529i −0.724903 0.688851i \(-0.758116\pi\)
0.688851 + 0.724903i \(0.258116\pi\)
\(200\) 10.8650 + 0.0528872i 0.0543252 + 0.000264436i
\(201\) 163.209 + 163.209i 0.811987 + 0.811987i
\(202\) −323.949 + 133.569i −1.60371 + 0.661231i
\(203\) −79.9695 303.806i −0.393939 1.49658i
\(204\) 84.7690 + 206.544i 0.415534 + 1.01247i
\(205\) −29.3895 + 12.1735i −0.143364 + 0.0593832i
\(206\) −95.0074 0.154153i −0.461201 0.000748316i
\(207\) 0.358461i 0.00173170i
\(208\) −60.0464 147.668i −0.288685 0.709944i
\(209\) −125.093 −0.598532
\(210\) −164.088 + 124.343i −0.781372 + 0.592111i
\(211\) 246.417 102.069i 1.16785 0.483740i 0.287370 0.957820i \(-0.407219\pi\)
0.880482 + 0.474079i \(0.157219\pi\)
\(212\) 104.807 + 43.8114i 0.494372 + 0.206657i
\(213\) 133.700 + 55.3805i 0.627701 + 0.260002i
\(214\) 136.114 56.1215i 0.636045 0.262250i
\(215\) −10.3714 10.3714i −0.0482392 0.0482392i
\(216\) 81.0058 + 198.290i 0.375027 + 0.918008i
\(217\) −2.54268 + 18.6765i −0.0117174 + 0.0860667i
\(218\) 254.409 + 105.863i 1.16701 + 0.485612i
\(219\) 279.650 + 115.835i 1.27694 + 0.528926i
\(220\) 95.1124 94.4971i 0.432329 0.429532i
\(221\) 70.3634 + 169.872i 0.318386 + 0.768653i
\(222\) 291.907 + 292.856i 1.31490 + 1.31917i
\(223\) 90.6780i 0.406628i −0.979114 0.203314i \(-0.934829\pi\)
0.979114 0.203314i \(-0.0651712\pi\)
\(224\) 134.126 + 179.405i 0.598778 + 0.800915i
\(225\) 0.199879 0.000888353
\(226\) −24.0349 + 23.9571i −0.106349 + 0.106005i
\(227\) 273.601 113.329i 1.20529 0.499248i 0.312586 0.949889i \(-0.398805\pi\)
0.892705 + 0.450641i \(0.148805\pi\)
\(228\) 155.733 154.725i 0.683039 0.678620i
\(229\) −101.693 + 245.509i −0.444075 + 1.07209i 0.530431 + 0.847728i \(0.322030\pi\)
−0.974506 + 0.224363i \(0.927970\pi\)
\(230\) 9.09973 21.8683i 0.0395641 0.0950795i
\(231\) 19.6878 144.611i 0.0852285 0.626020i
\(232\) −331.031 139.009i −1.42686 0.599177i
\(233\) 298.793 298.793i 1.28237 1.28237i 0.343062 0.939313i \(-0.388536\pi\)
0.939313 0.343062i \(-0.111464\pi\)
\(234\) −1.11784 2.71115i −0.00477711 0.0115861i
\(235\) 18.2503 44.0600i 0.0776607 0.187490i
\(236\) −295.374 123.472i −1.25158 0.523188i
\(237\) 103.351 + 249.512i 0.436081 + 1.05279i
\(238\) −156.045 205.923i −0.655652 0.865223i
\(239\) 277.379i 1.16058i 0.814410 + 0.580290i \(0.197061\pi\)
−0.814410 + 0.580290i \(0.802939\pi\)
\(240\) −1.52706 + 235.285i −0.00636274 + 0.980356i
\(241\) −298.909 −1.24028 −0.620142 0.784489i \(-0.712925\pi\)
−0.620142 + 0.784489i \(0.712925\pi\)
\(242\) 0.238442 146.956i 0.000985297 0.607257i
\(243\) 3.04096 + 7.34154i 0.0125143 + 0.0302121i
\(244\) −42.3091 103.088i −0.173398 0.422493i
\(245\) 146.701 187.731i 0.598779 0.766249i
\(246\) 15.0850 + 36.5861i 0.0613210 + 0.148724i
\(247\) 127.840 127.840i 0.517572 0.517572i
\(248\) 15.1578 + 15.3061i 0.0611200 + 0.0617180i
\(249\) 302.181 + 302.181i 1.21358 + 1.21358i
\(250\) −236.651 98.4742i −0.946604 0.393897i
\(251\) 141.027 340.469i 0.561861 1.35645i −0.346416 0.938081i \(-0.612601\pi\)
0.908277 0.418370i \(-0.137399\pi\)
\(252\) 2.48346 + 3.28834i 0.00985502 + 0.0130490i
\(253\) 6.42550 + 15.5125i 0.0253973 + 0.0613144i
\(254\) 252.661 + 253.482i 0.994727 + 0.997960i
\(255\) 271.391i 1.06428i
\(256\) 255.978 + 3.32286i 0.999916 + 0.0129799i
\(257\) 56.8547i 0.221225i −0.993864 0.110612i \(-0.964719\pi\)
0.993864 0.110612i \(-0.0352812\pi\)
\(258\) −12.9233 + 12.8815i −0.0500905 + 0.0499282i
\(259\) −413.341 241.080i −1.59591 0.930813i
\(260\) −0.628810 + 193.773i −0.00241850 + 0.745281i
\(261\) −6.10213 2.52758i −0.0233798 0.00968423i
\(262\) −113.872 47.3838i −0.434625 0.180854i
\(263\) −183.481 183.481i −0.697648 0.697648i 0.266255 0.963903i \(-0.414214\pi\)
−0.963903 + 0.266255i \(0.914214\pi\)
\(264\) −117.366 118.514i −0.444566 0.448916i
\(265\) −97.6397 97.6397i −0.368452 0.368452i
\(266\) −128.349 + 219.241i −0.482516 + 0.824215i
\(267\) −118.370 + 285.770i −0.443333 + 1.07030i
\(268\) −282.405 + 115.904i −1.05375 + 0.432477i
\(269\) −106.389 256.846i −0.395498 0.954817i −0.988720 0.149777i \(-0.952144\pi\)
0.593222 0.805039i \(-0.297856\pi\)
\(270\) 0.422465 260.373i 0.00156468 0.964344i
\(271\) 481.642 1.77728 0.888638 0.458610i \(-0.151653\pi\)
0.888638 + 0.458610i \(0.151653\pi\)
\(272\) −295.272 1.91639i −1.08556 0.00704554i
\(273\) 127.666 + 167.906i 0.467641 + 0.615041i
\(274\) 218.614 + 0.354710i 0.797862 + 0.00129456i
\(275\) 8.64985 3.58289i 0.0314540 0.0130287i
\(276\) −27.1865 11.3645i −0.0985018 0.0411758i
\(277\) −105.701 + 255.184i −0.381591 + 0.921242i 0.610068 + 0.792349i \(0.291142\pi\)
−0.991659 + 0.128893i \(0.958858\pi\)
\(278\) 85.4201 + 207.172i 0.307267 + 0.745225i
\(279\) 0.280215 + 0.280215i 0.00100435 + 0.00100435i
\(280\) −68.0298 263.653i −0.242963 0.941617i
\(281\) 106.402 + 106.402i 0.378653 + 0.378653i 0.870616 0.491963i \(-0.163720\pi\)
−0.491963 + 0.870616i \(0.663720\pi\)
\(282\) −54.7753 22.7929i −0.194239 0.0808258i
\(283\) −129.222 + 311.970i −0.456616 + 1.10237i 0.513142 + 0.858303i \(0.328481\pi\)
−0.969759 + 0.244066i \(0.921519\pi\)
\(284\) −135.776 + 134.898i −0.478085 + 0.474992i
\(285\) −246.540 + 102.120i −0.865051 + 0.358316i
\(286\) −96.9730 97.2882i −0.339067 0.340169i
\(287\) −27.7187 36.4557i −0.0965810 0.127023i
\(288\) 4.70930 + 0.0382059i 0.0163518 + 0.000132659i
\(289\) 51.5836 0.178490
\(290\) 308.102 + 309.104i 1.06242 + 1.06587i
\(291\) −125.176 302.201i −0.430158 1.03849i
\(292\) −283.992 + 282.155i −0.972575 + 0.966283i
\(293\) 188.644 455.427i 0.643837 1.55436i −0.177626 0.984098i \(-0.556842\pi\)
0.821463 0.570262i \(-0.193158\pi\)
\(294\) −233.248 182.880i −0.793359 0.622040i
\(295\) 275.175 + 275.175i 0.932796 + 0.932796i
\(296\) −506.252 + 206.815i −1.71031 + 0.698700i
\(297\) 130.514 + 130.514i 0.439441 + 0.439441i
\(298\) −143.544 + 59.1854i −0.481693 + 0.198609i
\(299\) −22.4198 9.28658i −0.0749826 0.0310588i
\(300\) −6.33690 + 15.1593i −0.0211230 + 0.0505310i
\(301\) 10.6386 18.2402i 0.0353441 0.0605987i
\(302\) 254.713 + 0.413282i 0.843422 + 0.00136848i
\(303\) 529.887i 1.74880i
\(304\) 109.365 + 268.955i 0.359754 + 0.884720i
\(305\) 135.454i 0.444113i
\(306\) −5.43203 0.00881368i −0.0177517 2.88029e-5i
\(307\) 206.101 + 497.572i 0.671338 + 1.62075i 0.779338 + 0.626603i \(0.215555\pi\)
−0.108000 + 0.994151i \(0.534445\pi\)
\(308\) 166.417 + 97.7876i 0.540316 + 0.317492i
\(309\) 54.9808 132.735i 0.177931 0.429564i
\(310\) −9.98136 24.2082i −0.0321979 0.0780909i
\(311\) 72.8833 + 72.8833i 0.234351 + 0.234351i 0.814506 0.580155i \(-0.197008\pi\)
−0.580155 + 0.814506i \(0.697008\pi\)
\(312\) 241.059 + 1.17339i 0.772625 + 0.00376087i
\(313\) 410.097 410.097i 1.31021 1.31021i 0.388960 0.921255i \(-0.372834\pi\)
0.921255 0.388960i \(-0.127166\pi\)
\(314\) −355.719 148.020i −1.13286 0.471402i
\(315\) −1.27509 4.84409i −0.00404791 0.0153781i
\(316\) −357.183 1.15909i −1.13032 0.00366800i
\(317\) 35.1735 + 84.9163i 0.110957 + 0.267875i 0.969598 0.244703i \(-0.0786905\pi\)
−0.858641 + 0.512578i \(0.828691\pi\)
\(318\) −121.664 + 121.270i −0.382591 + 0.381352i
\(319\) −309.380 −0.969842
\(320\) −286.326 121.879i −0.894768 0.380872i
\(321\) 222.643i 0.693591i
\(322\) 33.7804 + 4.65482i 0.104908 + 0.0144560i
\(323\) −128.156 309.396i −0.396768 0.957882i
\(324\) −329.210 1.06831i −1.01608 0.00329726i
\(325\) −5.17823 + 12.5014i −0.0159330 + 0.0384657i
\(326\) −43.5263 + 104.601i −0.133516 + 0.320863i
\(327\) −294.651 + 294.651i −0.901072 + 0.901072i
\(328\) −52.3385 0.254765i −0.159569 0.000776724i
\(329\) 68.0297 + 9.26181i 0.206777 + 0.0281514i
\(330\) 77.2850 + 187.442i 0.234197 + 0.568007i
\(331\) −125.459 + 302.885i −0.379030 + 0.915060i 0.613118 + 0.789991i \(0.289915\pi\)
−0.992148 + 0.125068i \(0.960085\pi\)
\(332\) −522.871 + 214.595i −1.57491 + 0.646371i
\(333\) −9.29455 + 3.84993i −0.0279116 + 0.0115614i
\(334\) 476.577 + 0.773263i 1.42688 + 0.00231516i
\(335\) 371.071 1.10768
\(336\) −328.130 + 84.0991i −0.976578 + 0.250295i
\(337\) 151.596i 0.449839i −0.974377 0.224919i \(-0.927788\pi\)
0.974377 0.224919i \(-0.0722119\pi\)
\(338\) −139.472 0.226299i −0.412640 0.000669524i
\(339\) −19.6385 47.4114i −0.0579306 0.139857i
\(340\) 331.163 + 138.433i 0.974008 + 0.407155i
\(341\) 17.1493 + 7.10347i 0.0502912 + 0.0208313i
\(342\) 2.03598 + 4.93793i 0.00595315 + 0.0144384i
\(343\) 315.126 + 135.443i 0.918734 + 0.394878i
\(344\) −9.12649 22.3403i −0.0265305 0.0649426i
\(345\) 25.3274 + 25.3274i 0.0734127 + 0.0734127i
\(346\) 101.322 243.496i 0.292840 0.703745i
\(347\) −242.136 100.296i −0.697798 0.289037i 0.00544685 0.999985i \(-0.498266\pi\)
−0.703245 + 0.710948i \(0.748266\pi\)
\(348\) 385.157 382.666i 1.10677 1.09961i
\(349\) −265.623 + 110.025i −0.761098 + 0.315257i −0.729261 0.684236i \(-0.760136\pi\)
−0.0318374 + 0.999493i \(0.510136\pi\)
\(350\) 2.59554 18.8361i 0.00741584 0.0538174i
\(351\) −266.760 −0.760000
\(352\) 204.482 82.7621i 0.580914 0.235120i
\(353\) 218.450i 0.618838i 0.950926 + 0.309419i \(0.100135\pi\)
−0.950926 + 0.309419i \(0.899865\pi\)
\(354\) 342.882 341.771i 0.968594 0.965456i
\(355\) 214.946 89.0336i 0.605482 0.250799i
\(356\) −288.329 290.207i −0.809914 0.815188i
\(357\) 377.838 99.4569i 1.05837 0.278591i
\(358\) 44.4543 + 18.4982i 0.124174 + 0.0516708i
\(359\) −172.506 172.506i −0.480517 0.480517i 0.424780 0.905297i \(-0.360352\pi\)
−0.905297 + 0.424780i \(0.860352\pi\)
\(360\) −5.27820 2.21646i −0.0146617 0.00615684i
\(361\) 22.4245 22.4245i 0.0621177 0.0621177i
\(362\) 41.7831 + 101.338i 0.115423 + 0.279940i
\(363\) 205.313 + 85.0436i 0.565601 + 0.234280i
\(364\) −270.007 + 70.1367i −0.741776 + 0.192683i
\(365\) 449.585 186.224i 1.23174 0.510204i
\(366\) 168.510 + 0.273414i 0.460410 + 0.000747032i
\(367\) −440.096 −1.19917 −0.599586 0.800310i \(-0.704668\pi\)
−0.599586 + 0.800310i \(0.704668\pi\)
\(368\) 27.7349 27.3772i 0.0753665 0.0743946i
\(369\) −0.962848 −0.00260934
\(370\) 664.756 + 1.07859i 1.79664 + 0.00291511i
\(371\) 100.154 171.719i 0.269958 0.462853i
\(372\) −30.1359 + 12.3683i −0.0810105 + 0.0332481i
\(373\) 156.000 376.618i 0.418232 1.00970i −0.564628 0.825346i \(-0.690980\pi\)
0.982860 0.184355i \(-0.0590197\pi\)
\(374\) −235.231 + 96.9891i −0.628960 + 0.259329i
\(375\) 274.084 274.084i 0.730891 0.730891i
\(376\) 55.7529 55.2128i 0.148279 0.146842i
\(377\) 316.173 316.173i 0.838656 0.838656i
\(378\) 362.653 94.8308i 0.959399 0.250875i
\(379\) 15.6501 + 6.48247i 0.0412931 + 0.0171042i 0.403234 0.915097i \(-0.367886\pi\)
−0.361941 + 0.932201i \(0.617886\pi\)
\(380\) 1.14528 352.928i 0.00301389 0.928757i
\(381\) −500.020 + 207.115i −1.31239 + 0.543609i
\(382\) 339.048 + 340.150i 0.887561 + 0.890446i
\(383\) 494.019i 1.28987i −0.764239 0.644933i \(-0.776885\pi\)
0.764239 0.644933i \(-0.223115\pi\)
\(384\) −152.200 + 355.953i −0.396353 + 0.926961i
\(385\) −142.012 186.774i −0.368861 0.485126i
\(386\) 334.980 + 336.069i 0.867824 + 0.870644i
\(387\) −0.169892 0.410156i −0.000438998 0.00105984i
\(388\) 432.609 + 1.40385i 1.11497 + 0.00361818i
\(389\) −676.486 280.209i −1.73904 0.720333i −0.998851 0.0479314i \(-0.984737\pi\)
−0.740187 0.672401i \(-0.765263\pi\)
\(390\) −270.540 112.576i −0.693693 0.288657i
\(391\) −31.7847 + 31.7847i −0.0812907 + 0.0812907i
\(392\) 342.134 191.334i 0.872790 0.488096i
\(393\) 131.884 131.884i 0.335582 0.335582i
\(394\) 117.658 + 285.359i 0.298624 + 0.724263i
\(395\) 401.133 + 166.155i 1.01553 + 0.420645i
\(396\) 3.75426 1.54081i 0.00948045 0.00389094i
\(397\) −55.2516 133.389i −0.139173 0.335993i 0.838891 0.544300i \(-0.183205\pi\)
−0.978064 + 0.208307i \(0.933205\pi\)
\(398\) 20.2926 + 0.0329255i 0.0509864 + 8.27274e-5i
\(399\) −232.524 305.815i −0.582766 0.766454i
\(400\) −15.2656 15.4651i −0.0381641 0.0386627i
\(401\) 249.583i 0.622400i −0.950344 0.311200i \(-0.899269\pi\)
0.950344 0.311200i \(-0.100731\pi\)
\(402\) 0.749004 461.625i 0.00186319 1.14832i
\(403\) −24.7854 + 10.2664i −0.0615021 + 0.0254750i
\(404\) 646.590 + 270.288i 1.60047 + 0.669030i
\(405\) 369.718 + 153.142i 0.912885 + 0.378129i
\(406\) −317.432 + 542.226i −0.781852 + 1.33553i
\(407\) −333.214 + 333.214i −0.818708 + 0.818708i
\(408\) 172.884 411.698i 0.423734 1.00906i
\(409\) −416.788 + 416.788i −1.01904 + 1.01904i −0.0192276 + 0.999815i \(0.506121\pi\)
−0.999815 + 0.0192276i \(0.993879\pi\)
\(410\) 58.7395 + 24.4424i 0.143267 + 0.0596157i
\(411\) −126.512 + 305.427i −0.307815 + 0.743132i
\(412\) 133.924 + 134.796i 0.325059 + 0.327175i
\(413\) −282.262 + 483.949i −0.683444 + 1.17179i
\(414\) 0.507762 0.506117i 0.00122648 0.00122251i
\(415\) 687.036 1.65551
\(416\) −124.393 + 293.552i −0.299021 + 0.705653i
\(417\) −338.875 −0.812649
\(418\) 176.621 + 177.195i 0.422539 + 0.423912i
\(419\) 122.245 50.6356i 0.291755 0.120849i −0.232006 0.972714i \(-0.574529\pi\)
0.523760 + 0.851866i \(0.324529\pi\)
\(420\) 407.812 + 56.8695i 0.970981 + 0.135403i
\(421\) 187.554 + 77.6873i 0.445496 + 0.184530i 0.594142 0.804360i \(-0.297492\pi\)
−0.148647 + 0.988890i \(0.547492\pi\)
\(422\) −492.502 204.938i −1.16707 0.485635i
\(423\) 1.02069 1.02069i 0.00241298 0.00241298i
\(424\) −85.9194 210.318i −0.202640 0.496032i
\(425\) 17.7233 + 17.7233i 0.0417018 + 0.0417018i
\(426\) −110.327 267.580i −0.258983 0.628122i
\(427\) −188.583 + 49.6401i −0.441647 + 0.116253i
\(428\) −271.678 113.567i −0.634761 0.265343i
\(429\) 191.911 79.4923i 0.447346 0.185297i
\(430\) −0.0475968 + 29.3348i −0.000110690 + 0.0682205i
\(431\) 372.076i 0.863285i −0.902045 0.431642i \(-0.857934\pi\)
0.902045 0.431642i \(-0.142066\pi\)
\(432\) 166.505 394.714i 0.385429 0.913690i
\(433\) 3.47840 0.00803326 0.00401663 0.999992i \(-0.498721\pi\)
0.00401663 + 0.999992i \(0.498721\pi\)
\(434\) 30.0454 22.7679i 0.0692290 0.0524606i
\(435\) −609.740 + 252.562i −1.40170 + 0.580603i
\(436\) −209.248 509.842i −0.479926 1.16936i
\(437\) 40.8342 + 16.9141i 0.0934420 + 0.0387049i
\(438\) −230.762 559.675i −0.526853 1.27780i
\(439\) 61.4292 + 61.4292i 0.139930 + 0.139930i 0.773602 0.633672i \(-0.218453\pi\)
−0.633672 + 0.773602i \(0.718453\pi\)
\(440\) −268.147 1.30524i −0.609424 0.00296646i
\(441\) 6.27679 3.55043i 0.0142331 0.00805087i
\(442\) 141.278 339.516i 0.319633 0.768135i
\(443\) −296.808 122.942i −0.669995 0.277521i 0.0216428 0.999766i \(-0.493110\pi\)
−0.691637 + 0.722245i \(0.743110\pi\)
\(444\) 2.68361 826.977i 0.00604416 1.86256i
\(445\) 190.300 + 459.424i 0.427640 + 1.03241i
\(446\) −128.446 + 128.030i −0.287995 + 0.287062i
\(447\) 234.797i 0.525274i
\(448\) 64.7534 443.296i 0.144539 0.989499i
\(449\) −648.742 −1.44486 −0.722430 0.691444i \(-0.756975\pi\)
−0.722430 + 0.691444i \(0.756975\pi\)
\(450\) −0.282213 0.283130i −0.000627140 0.000629179i
\(451\) −41.6676 + 17.2593i −0.0923894 + 0.0382689i
\(452\) 67.8707 + 0.220246i 0.150156 + 0.000487270i
\(453\) −147.403 + 355.862i −0.325392 + 0.785567i
\(454\) −546.834 227.546i −1.20448 0.501203i
\(455\) 336.005 + 45.7449i 0.738473 + 0.100538i
\(456\) −439.052 2.13715i −0.962832 0.00468673i
\(457\) 83.0513 83.0513i 0.181731 0.181731i −0.610378 0.792110i \(-0.708983\pi\)
0.792110 + 0.610378i \(0.208983\pi\)
\(458\) 491.347 202.589i 1.07281 0.442335i
\(459\) −189.094 + 456.513i −0.411969 + 0.994581i
\(460\) −43.8246 + 17.9864i −0.0952709 + 0.0391008i
\(461\) 114.561 + 276.576i 0.248506 + 0.599947i 0.998078 0.0619765i \(-0.0197404\pi\)
−0.749571 + 0.661923i \(0.769740\pi\)
\(462\) −232.639 + 176.290i −0.503548 + 0.381581i
\(463\) 312.147i 0.674184i 0.941472 + 0.337092i \(0.109443\pi\)
−0.941472 + 0.337092i \(0.890557\pi\)
\(464\) 270.481 + 665.177i 0.582933 + 1.43357i
\(465\) 39.5976 0.0851561
\(466\) −845.114 1.37123i −1.81355 0.00294255i
\(467\) −301.498 727.881i −0.645606 1.55863i −0.819009 0.573781i \(-0.805476\pi\)
0.173403 0.984851i \(-0.444524\pi\)
\(468\) −2.26205 + 5.41134i −0.00483345 + 0.0115627i
\(469\) 135.987 + 516.615i 0.289950 + 1.10153i
\(470\) −88.1792 + 36.3575i −0.187615 + 0.0773564i
\(471\) 411.986 411.986i 0.874705 0.874705i
\(472\) 242.144 + 592.731i 0.513017 + 1.25579i
\(473\) −14.7043 14.7043i −0.0310873 0.0310873i
\(474\) 207.512 498.688i 0.437789 1.05208i
\(475\) 9.43135 22.7693i 0.0198555 0.0479353i
\(476\) −71.3685 + 511.785i −0.149934 + 1.07518i
\(477\) −1.59942 3.86133i −0.00335307 0.00809503i
\(478\) 392.908 391.635i 0.821984 0.819321i
\(479\) 519.705i 1.08498i −0.840063 0.542489i \(-0.817482\pi\)
0.840063 0.542489i \(-0.182518\pi\)
\(480\) 335.439 330.040i 0.698832 0.687584i
\(481\) 681.063i 1.41593i
\(482\) 422.034 + 423.406i 0.875590 + 0.878436i
\(483\) −25.9797 + 44.5432i −0.0537882 + 0.0922219i
\(484\) −208.501 + 207.152i −0.430787 + 0.428000i
\(485\) −485.841 201.242i −1.00173 0.414932i
\(486\) 6.10574 14.6732i 0.0125633 0.0301917i
\(487\) 576.480 + 576.480i 1.18374 + 1.18374i 0.978769 + 0.204968i \(0.0657089\pi\)
0.204968 + 0.978769i \(0.434291\pi\)
\(488\) −86.2881 + 205.483i −0.176820 + 0.421072i
\(489\) −121.147 121.147i −0.247745 0.247745i
\(490\) −473.052 + 57.2579i −0.965412 + 0.116853i
\(491\) −166.968 + 403.095i −0.340056 + 0.820968i 0.657653 + 0.753321i \(0.271549\pi\)
−0.997709 + 0.0676473i \(0.978451\pi\)
\(492\) 30.5258 73.0246i 0.0620442 0.148424i
\(493\) −316.954 765.195i −0.642909 1.55212i
\(494\) −361.586 0.586687i −0.731956 0.00118763i
\(495\) −4.93297 −0.00996559
\(496\) 0.279612 43.0820i 0.000563734 0.0868588i
\(497\) 202.726 + 266.626i 0.407900 + 0.536470i
\(498\) 1.38678 854.695i 0.00278469 1.71626i
\(499\) 342.105 141.704i 0.685581 0.283977i −0.0125767 0.999921i \(-0.504003\pi\)
0.698158 + 0.715944i \(0.254003\pi\)
\(500\) 194.642 + 474.255i 0.389285 + 0.948510i
\(501\) −275.795 + 665.828i −0.550489 + 1.32900i
\(502\) −681.395 + 280.949i −1.35736 + 0.559659i
\(503\) −46.8393 46.8393i −0.0931198 0.0931198i 0.659012 0.752132i \(-0.270974\pi\)
−0.752132 + 0.659012i \(0.770974\pi\)
\(504\) 1.15151 8.16071i 0.00228475 0.0161919i
\(505\) −602.374 602.374i −1.19282 1.19282i
\(506\) 12.9013 31.0042i 0.0254967 0.0612731i
\(507\) 80.7127 194.858i 0.159197 0.384335i
\(508\) 2.32280 715.791i 0.00457244 1.40904i
\(509\) 505.608 209.430i 0.993335 0.411453i 0.173986 0.984748i \(-0.444335\pi\)
0.819349 + 0.573295i \(0.194335\pi\)
\(510\) −384.428 + 383.182i −0.753780 + 0.751337i
\(511\) 424.026 + 557.679i 0.829797 + 1.09135i
\(512\) −356.713 367.287i −0.696706 0.717357i
\(513\) 485.862 0.947099
\(514\) −80.5351 + 80.2741i −0.156683 + 0.156175i
\(515\) −88.3911 213.395i −0.171633 0.414359i
\(516\) 36.4934 + 0.118424i 0.0707236 + 0.000229504i
\(517\) 25.8747 62.4670i 0.0500477 0.120826i
\(518\) 242.112 + 925.886i 0.467397 + 1.78743i
\(519\) 282.012 + 282.012i 0.543375 + 0.543375i
\(520\) 275.369 272.701i 0.529555 0.524425i
\(521\) 275.780 + 275.780i 0.529328 + 0.529328i 0.920372 0.391044i \(-0.127886\pi\)
−0.391044 + 0.920372i \(0.627886\pi\)
\(522\) 5.03536 + 12.2124i 0.00964629 + 0.0233955i
\(523\) −580.923 240.626i −1.11075 0.460089i −0.249556 0.968360i \(-0.580285\pi\)
−0.861197 + 0.508272i \(0.830285\pi\)
\(524\) 93.6580 + 228.202i 0.178737 + 0.435500i
\(525\) 24.8375 + 14.4864i 0.0473094 + 0.0275931i
\(526\) −0.842037 + 518.963i −0.00160083 + 0.986622i
\(527\) 49.6931i 0.0942944i
\(528\) −2.16502 + 333.581i −0.00410041 + 0.631781i
\(529\) 523.067i 0.988785i
\(530\) −0.448090 + 276.166i −0.000845453 + 0.521069i
\(531\) 4.50758 + 10.8823i 0.00848886 + 0.0204939i
\(532\) 491.775 127.743i 0.924389 0.240119i
\(533\) 24.9443 60.2209i 0.0467998 0.112985i
\(534\) 571.923 235.812i 1.07102 0.441595i
\(535\) 253.099 + 253.099i 0.473083 + 0.473083i
\(536\) 562.912 + 236.382i 1.05021 + 0.441012i
\(537\) −51.4861 + 51.4861i −0.0958772 + 0.0958772i
\(538\) −213.611 + 513.345i −0.397047 + 0.954174i
\(539\) 207.988 266.159i 0.385878 0.493802i
\(540\) −369.416 + 367.026i −0.684104 + 0.679679i
\(541\) −217.598 525.327i −0.402214 0.971030i −0.987128 0.159935i \(-0.948872\pi\)
0.584914 0.811096i \(-0.301128\pi\)
\(542\) −680.038 682.248i −1.25468 1.25876i
\(543\) −165.760 −0.305267
\(544\) 414.185 + 420.961i 0.761370 + 0.773825i
\(545\) 669.915i 1.22920i
\(546\) 57.5864 417.909i 0.105470 0.765402i
\(547\) 320.292 + 773.253i 0.585543 + 1.41362i 0.887725 + 0.460375i \(0.152285\pi\)
−0.302182 + 0.953250i \(0.597715\pi\)
\(548\) −308.163 310.169i −0.562341 0.566002i
\(549\) −1.56897 + 3.78782i −0.00285786 + 0.00689949i
\(550\) −17.2881 7.19383i −0.0314328 0.0130797i
\(551\) −575.860 + 575.860i −1.04512 + 1.04512i
\(552\) 22.2872 + 54.5556i 0.0403753 + 0.0988326i
\(553\) −84.3218 + 619.359i −0.152481 + 1.12000i
\(554\) 510.710 210.573i 0.921860 0.380096i
\(555\) −384.694 + 928.735i −0.693143 + 1.67340i
\(556\) 172.855 413.509i 0.310890 0.743720i
\(557\) 190.205 78.7854i 0.341481 0.141446i −0.205351 0.978688i \(-0.565834\pi\)
0.546832 + 0.837242i \(0.315834\pi\)
\(558\) 0.00128597 0.792565i 2.30460e−6 0.00142037i
\(559\) 30.0544 0.0537646
\(560\) −277.413 + 468.620i −0.495381 + 0.836822i
\(561\) 384.771i 0.685865i
\(562\) 0.488300 300.949i 0.000868862 0.535496i
\(563\) 125.324 + 302.558i 0.222600 + 0.537403i 0.995241 0.0974391i \(-0.0310651\pi\)
−0.772642 + 0.634842i \(0.781065\pi\)
\(564\) 45.0520 + 109.771i 0.0798794 + 0.194630i
\(565\) −76.2220 31.5722i −0.134906 0.0558800i
\(566\) 624.359 257.432i 1.10311 0.454827i
\(567\) −77.7181 + 570.854i −0.137069 + 1.00680i
\(568\) 382.788 + 1.86328i 0.673923 + 0.00328042i
\(569\) 49.0645 + 49.0645i 0.0862293 + 0.0862293i 0.748906 0.662676i \(-0.230580\pi\)
−0.662676 + 0.748906i \(0.730580\pi\)
\(570\) 492.747 + 205.040i 0.864469 + 0.359719i
\(571\) 435.785 + 180.508i 0.763196 + 0.316126i 0.730113 0.683326i \(-0.239467\pi\)
0.0330833 + 0.999453i \(0.489467\pi\)
\(572\) −0.891508 + 274.726i −0.00155858 + 0.480290i
\(573\) −670.983 + 277.930i −1.17100 + 0.485044i
\(574\) −12.5031 + 90.7361i −0.0217824 + 0.158077i
\(575\) −3.30802 −0.00575307
\(576\) −6.59503 6.72470i −0.0114497 0.0116748i
\(577\) 906.026i 1.57024i −0.619346 0.785118i \(-0.712602\pi\)
0.619346 0.785118i \(-0.287398\pi\)
\(578\) −72.8317 73.0685i −0.126006 0.126416i
\(579\) −662.931 + 274.595i −1.14496 + 0.474257i
\(580\) 2.83250 872.858i 0.00488361 1.50493i
\(581\) 251.778 + 956.509i 0.433353 + 1.64632i
\(582\) −251.332 + 603.996i −0.431842 + 1.03779i
\(583\) −138.431 138.431i −0.237445 0.237445i
\(584\) 800.647 + 3.89726i 1.37097 + 0.00667340i
\(585\) 5.04129 5.04129i 0.00861760 0.00861760i
\(586\) −911.466 + 375.810i −1.55540 + 0.641314i
\(587\) −1062.40 440.061i −1.80988 0.749678i −0.982027 0.188738i \(-0.939560\pi\)
−0.827856 0.560940i \(-0.810440\pi\)
\(588\) 70.2758 + 588.608i 0.119517 + 1.00103i
\(589\) 45.1427 18.6987i 0.0766429 0.0317465i
\(590\) 1.26284 778.311i 0.00214040 1.31917i
\(591\) −466.766 −0.789790
\(592\) 1007.74 + 425.104i 1.70227 + 0.718080i
\(593\) 78.5514 0.132464 0.0662322 0.997804i \(-0.478902\pi\)
0.0662322 + 0.997804i \(0.478902\pi\)
\(594\) 0.598958 369.149i 0.00100835 0.621463i
\(595\) 316.463 542.587i 0.531870 0.911911i
\(596\) 286.509 + 119.767i 0.480720 + 0.200951i
\(597\) −11.7433 + 28.3509i −0.0196706 + 0.0474889i
\(598\) 18.5004 + 44.8697i 0.0309371 + 0.0750329i
\(599\) 603.410 603.410i 1.00736 1.00736i 0.00738991 0.999973i \(-0.497648\pi\)
0.999973 0.00738991i \(-0.00235230\pi\)
\(600\) 30.4204 12.4274i 0.0507007 0.0207124i
\(601\) 114.383 114.383i 0.190322 0.190322i −0.605514 0.795835i \(-0.707032\pi\)
0.795835 + 0.605514i \(0.207032\pi\)
\(602\) −40.8581 + 10.6841i −0.0678707 + 0.0177476i
\(603\) 10.3766 + 4.29811i 0.0172082 + 0.00712788i
\(604\) −359.049 361.387i −0.594452 0.598322i
\(605\) 330.076 136.722i 0.545581 0.225987i
\(606\) −750.589 + 748.157i −1.23860 + 1.23458i
\(607\) 932.181i 1.53572i 0.640619 + 0.767859i \(0.278678\pi\)
−0.640619 + 0.767859i \(0.721322\pi\)
\(608\) 226.562 534.658i 0.372634 0.879372i
\(609\) −575.076 756.339i −0.944295 1.24194i
\(610\) 191.872 191.251i 0.314544 0.313525i
\(611\) 37.3959 + 90.2816i 0.0612044 + 0.147760i
\(612\) 7.65709 + 7.70695i 0.0125116 + 0.0125931i
\(613\) 531.042 + 219.965i 0.866300 + 0.358833i 0.771168 0.636632i \(-0.219673\pi\)
0.0951317 + 0.995465i \(0.469673\pi\)
\(614\) 413.816 994.473i 0.673967 1.61966i
\(615\) −68.0308 + 68.0308i −0.110619 + 0.110619i
\(616\) −96.4506 373.799i −0.156576 0.606817i
\(617\) 488.091 488.091i 0.791072 0.791072i −0.190597 0.981668i \(-0.561042\pi\)
0.981668 + 0.190597i \(0.0610422\pi\)
\(618\) −265.649 + 109.531i −0.429853 + 0.177234i
\(619\) 69.0349 + 28.5952i 0.111527 + 0.0461958i 0.437749 0.899097i \(-0.355776\pi\)
−0.326222 + 0.945293i \(0.605776\pi\)
\(620\) −20.1982 + 48.3186i −0.0325777 + 0.0779332i
\(621\) −24.9566 60.2507i −0.0401878 0.0970220i
\(622\) 0.334478 206.145i 0.000537745 0.331422i
\(623\) −569.883 + 433.306i −0.914741 + 0.695515i
\(624\) −338.693 343.118i −0.542778 0.549869i
\(625\) 589.202i 0.942723i
\(626\) −1159.93 1.88203i −1.85292 0.00300643i
\(627\) −349.537 + 144.783i −0.557475 + 0.230914i
\(628\) 292.574 + 712.871i 0.465882 + 1.13514i
\(629\) −1165.52 482.774i −1.85297 0.767526i
\(630\) −5.06137 + 8.64563i −0.00803391 + 0.0137232i
\(631\) −115.013 + 115.013i −0.182271 + 0.182271i −0.792345 0.610074i \(-0.791140\pi\)
0.610074 + 0.792345i \(0.291140\pi\)
\(632\) 502.671 + 507.588i 0.795365 + 0.803146i
\(633\) 570.405 570.405i 0.901114 0.901114i
\(634\) 70.6225 169.718i 0.111392 0.267694i
\(635\) −332.973 + 803.867i −0.524367 + 1.26593i
\(636\) 343.559 + 1.11488i 0.540187 + 0.00175295i
\(637\) 59.4487 + 484.560i 0.0933260 + 0.760690i
\(638\) 436.818 + 438.238i 0.684668 + 0.686893i
\(639\) 7.04198 0.0110203
\(640\) 231.626 + 577.666i 0.361916 + 0.902603i
\(641\) 7.26223 0.0113295 0.00566477 0.999984i \(-0.498197\pi\)
0.00566477 + 0.999984i \(0.498197\pi\)
\(642\) 315.375 314.353i 0.491238 0.489646i
\(643\) −666.011 + 275.871i −1.03579 + 0.429037i −0.834798 0.550557i \(-0.814415\pi\)
−0.200989 + 0.979594i \(0.564415\pi\)
\(644\) −41.1015 54.4223i −0.0638222 0.0845067i
\(645\) −40.9838 16.9761i −0.0635408 0.0263195i
\(646\) −257.316 + 618.375i −0.398321 + 0.957237i
\(647\) 280.132 280.132i 0.432971 0.432971i −0.456667 0.889638i \(-0.650957\pi\)
0.889638 + 0.456667i \(0.150957\pi\)
\(648\) 463.304 + 467.836i 0.714975 + 0.721969i
\(649\) 390.135 + 390.135i 0.601132 + 0.601132i
\(650\) 25.0195 10.3159i 0.0384915 0.0158706i
\(651\) 14.5113 + 55.1288i 0.0222909 + 0.0846833i
\(652\) 209.624 86.0332i 0.321509 0.131953i
\(653\) −1117.64 + 462.940i −1.71154 + 0.708944i −0.711561 + 0.702624i \(0.752012\pi\)
−0.999980 + 0.00631987i \(0.997988\pi\)
\(654\) 833.397 + 1.35222i 1.27431 + 0.00206761i
\(655\) 299.850i 0.457786i
\(656\) 73.5368 + 74.4976i 0.112099 + 0.113563i
\(657\) 14.7291 0.0224188
\(658\) −82.9329 109.441i −0.126038 0.166324i
\(659\) 80.8647 33.4953i 0.122708 0.0508274i −0.320485 0.947254i \(-0.603846\pi\)
0.443193 + 0.896426i \(0.353846\pi\)
\(660\) 156.393 374.127i 0.236959 0.566860i
\(661\) 584.186 + 241.978i 0.883791 + 0.366078i 0.777966 0.628307i \(-0.216252\pi\)
0.105825 + 0.994385i \(0.466252\pi\)
\(662\) 606.176 249.935i 0.915674 0.377545i
\(663\) 393.220 + 393.220i 0.593092 + 0.593092i
\(664\) 1042.23 + 437.660i 1.56962 + 0.659127i
\(665\) −611.981 83.3173i −0.920272 0.125289i
\(666\) 18.5766 + 7.73001i 0.0278928 + 0.0116066i
\(667\) 100.991 + 41.8317i 0.151410 + 0.0627162i
\(668\) −671.791 676.166i −1.00568 1.01222i
\(669\) −104.951 253.373i −0.156877 0.378734i
\(670\) −523.922 525.625i −0.781973 0.784515i
\(671\) 192.043i 0.286205i
\(672\) 582.420 + 346.058i 0.866696 + 0.514967i
\(673\) −514.767 −0.764884 −0.382442 0.923980i \(-0.624917\pi\)
−0.382442 + 0.923980i \(0.624917\pi\)
\(674\) −214.736 + 214.041i −0.318600 + 0.317568i
\(675\) −33.5960 + 13.9159i −0.0497719 + 0.0206162i
\(676\) 196.603 + 197.883i 0.290833 + 0.292727i
\(677\) 28.3586 68.4637i 0.0418886 0.101128i −0.901551 0.432674i \(-0.857570\pi\)
0.943439 + 0.331546i \(0.107570\pi\)
\(678\) −39.4307 + 94.7590i −0.0581574 + 0.139763i
\(679\) 102.128 750.149i 0.150409 1.10479i
\(680\) −271.483 664.550i −0.399240 0.977279i
\(681\) 633.331 633.331i 0.930002 0.930002i
\(682\) −14.1513 34.3216i −0.0207497 0.0503249i
\(683\) 505.795 1221.10i 0.740548 1.78784i 0.136911 0.990583i \(-0.456283\pi\)
0.603638 0.797259i \(-0.293717\pi\)
\(684\) 4.11998 9.85592i 0.00602336 0.0144092i
\(685\) 203.390 + 491.027i 0.296920 + 0.716827i
\(686\) −253.075 637.612i −0.368915 0.929463i
\(687\) 803.703i 1.16987i
\(688\) −18.7593 + 44.4703i −0.0272664 + 0.0646371i
\(689\) 282.941 0.410654
\(690\) 0.116233 71.6365i 0.000168454 0.103821i
\(691\) 70.8973 + 171.161i 0.102601 + 0.247701i 0.966841 0.255379i \(-0.0822002\pi\)
−0.864240 + 0.503080i \(0.832200\pi\)
\(692\) −487.972 + 200.272i −0.705163 + 0.289411i
\(693\) −1.80779 6.86781i −0.00260864 0.00991026i
\(694\) 199.806 + 484.597i 0.287905 + 0.698266i
\(695\) −385.231 + 385.231i −0.554289 + 0.554289i
\(696\) −1085.86 5.28557i −1.56014 0.00759422i
\(697\) −85.3756 85.3756i −0.122490 0.122490i
\(698\) 530.889 + 220.911i 0.760586 + 0.316492i
\(699\) 489.068 1180.71i 0.699668 1.68915i
\(700\) −30.3461 + 22.9184i −0.0433516 + 0.0327405i
\(701\) 186.955 + 451.349i 0.266697 + 0.643864i 0.999324 0.0367666i \(-0.0117058\pi\)
−0.732627 + 0.680631i \(0.761706\pi\)
\(702\) 376.643 + 377.867i 0.536528 + 0.538272i
\(703\) 1240.45i 1.76451i
\(704\) −405.944 172.797i −0.576625 0.245450i
\(705\) 144.236i 0.204590i
\(706\) 309.436 308.433i 0.438294 0.436874i
\(707\) 617.888 1059.39i 0.873958 1.49843i
\(708\) −968.243 3.14203i −1.36757 0.00443789i
\(709\) −172.457 71.4339i −0.243239 0.100753i 0.257734 0.966216i \(-0.417024\pi\)
−0.500973 + 0.865463i \(0.667024\pi\)
\(710\) −429.603 178.765i −0.605075 0.251781i
\(711\) 9.29263 + 9.29263i 0.0130698 + 0.0130698i
\(712\) −3.98255 + 818.168i −0.00559347 + 1.14911i
\(713\) −4.63757 4.63757i −0.00650431 0.00650431i
\(714\) −674.358 394.785i −0.944478 0.552921i
\(715\) 127.797 308.530i 0.178738 0.431511i
\(716\) −36.5631 89.0877i −0.0510658 0.124424i
\(717\) 321.038 + 775.053i 0.447751 + 1.08097i
\(718\) −0.791667 + 487.919i −0.00110260 + 0.679553i
\(719\) 1069.38 1.48732 0.743659 0.668559i \(-0.233089\pi\)
0.743659 + 0.668559i \(0.233089\pi\)
\(720\) 4.31274 + 10.6061i 0.00598992 + 0.0147306i
\(721\) 264.701 201.263i 0.367131 0.279145i
\(722\) −63.4259 0.102911i −0.0878476 0.000142536i
\(723\) −835.213 + 345.957i −1.15520 + 0.478501i
\(724\) 84.5518 202.267i 0.116784 0.279375i
\(725\) 23.3255 56.3128i 0.0321731 0.0776728i
\(726\) −169.421 410.902i −0.233362 0.565981i
\(727\) −315.123 315.123i −0.433456 0.433456i 0.456346 0.889802i \(-0.349158\pi\)
−0.889802 + 0.456346i \(0.849158\pi\)
\(728\) 480.576 + 283.439i 0.660132 + 0.389339i
\(729\) −506.778 506.778i −0.695169 0.695169i
\(730\) −898.565 373.907i −1.23091 0.512202i
\(731\) 21.3042 51.4328i 0.0291439 0.0703595i
\(732\) −237.535 239.081i −0.324501 0.326614i
\(733\) 786.082 325.606i 1.07242 0.444210i 0.224574 0.974457i \(-0.427901\pi\)
0.847843 + 0.530247i \(0.177901\pi\)
\(734\) 621.380 + 623.399i 0.846566 + 0.849318i
\(735\) 192.633 694.351i 0.262086 0.944695i
\(736\) −77.9393 0.632311i −0.105896 0.000859118i
\(737\) 526.094 0.713832
\(738\) 1.35946 + 1.36388i 0.00184209 + 0.00184808i
\(739\) 481.117 + 1161.52i 0.651037 + 1.57174i 0.811275 + 0.584665i \(0.198774\pi\)
−0.160238 + 0.987078i \(0.551226\pi\)
\(740\) −937.053 943.154i −1.26629 1.27453i
\(741\) 209.250 505.174i 0.282389 0.681747i
\(742\) −384.650 + 100.583i −0.518397 + 0.135557i
\(743\) 343.644 + 343.644i 0.462508 + 0.462508i 0.899477 0.436968i \(-0.143948\pi\)
−0.436968 + 0.899477i \(0.643948\pi\)
\(744\) 60.0692 + 25.2247i 0.0807381 + 0.0339042i
\(745\) −266.917 266.917i −0.358277 0.358277i
\(746\) −753.742 + 310.778i −1.01038 + 0.416593i
\(747\) 19.2121 + 7.95791i 0.0257190 + 0.0106532i
\(748\) 469.513 + 196.266i 0.627691 + 0.262388i
\(749\) −259.618 + 445.125i −0.346620 + 0.594292i
\(750\) −775.226 1.25783i −1.03363 0.00167711i
\(751\) 782.796i 1.04234i −0.853453 0.521169i \(-0.825496\pi\)
0.853453 0.521169i \(-0.174504\pi\)
\(752\) −156.928 1.01850i −0.208680 0.00135439i
\(753\) 1114.57i 1.48017i
\(754\) −894.272 1.45099i −1.18604 0.00192439i
\(755\) 236.975 + 572.109i 0.313874 + 0.757760i
\(756\) −646.364 379.807i −0.854979 0.502390i
\(757\) 431.979 1042.89i 0.570646 1.37766i −0.330359 0.943855i \(-0.607170\pi\)
0.901006 0.433807i \(-0.142830\pi\)
\(758\) −12.9141 31.3212i −0.0170371 0.0413208i
\(759\) 35.9084 + 35.9084i 0.0473101 + 0.0473101i
\(760\) −501.541 + 496.682i −0.659923 + 0.653529i
\(761\) 469.245 469.245i 0.616617 0.616617i −0.328045 0.944662i \(-0.606390\pi\)
0.944662 + 0.328045i \(0.106390\pi\)
\(762\) 999.366 + 415.852i 1.31150 + 0.545737i
\(763\) −932.674 + 245.504i −1.22238 + 0.321762i
\(764\) 3.11699 960.529i 0.00407984 1.25724i
\(765\) −5.05375 12.2008i −0.00660620 0.0159488i
\(766\) −699.780 + 697.513i −0.913551 + 0.910592i
\(767\) −797.404 −1.03964
\(768\) 719.103 286.984i 0.936332 0.373678i
\(769\) 763.899i 0.993366i 0.867932 + 0.496683i \(0.165449\pi\)
−0.867932 + 0.496683i \(0.834551\pi\)
\(770\) −64.0573 + 464.869i −0.0831914 + 0.603726i
\(771\) −65.8036 158.864i −0.0853483 0.206049i
\(772\) 3.07959 949.002i 0.00398911 1.22928i
\(773\) 221.966 535.873i 0.287148 0.693238i −0.712819 0.701348i \(-0.752582\pi\)
0.999967 + 0.00811074i \(0.00258176\pi\)
\(774\) −0.341115 + 0.819761i −0.000440717 + 0.00105912i
\(775\) −2.58593 + 2.58593i −0.00333668 + 0.00333668i
\(776\) −608.819 614.775i −0.784561 0.792236i
\(777\) −1433.99 195.228i −1.84554 0.251259i
\(778\) 558.223 + 1353.88i 0.717510 + 1.74020i
\(779\) −45.4322 + 109.683i −0.0583212 + 0.140800i
\(780\) 222.516 + 542.170i 0.285277 + 0.695090i
\(781\) 304.744 126.229i 0.390198 0.161625i
\(782\) 89.9005 + 0.145867i 0.114962 + 0.000186531i
\(783\) 1201.63 1.53465
\(784\) −754.090 214.487i −0.961849 0.273580i
\(785\) 936.688i 1.19323i
\(786\) −373.023 0.605244i −0.474584 0.000770031i
\(787\) −436.004 1052.61i −0.554007 1.33749i −0.914445 0.404709i \(-0.867373\pi\)
0.360438 0.932783i \(-0.382627\pi\)
\(788\) 238.091 569.567i 0.302145 0.722800i
\(789\) −725.047 300.324i −0.918944 0.380639i
\(790\) −331.008 802.805i −0.418997 1.01621i
\(791\) 16.0225 117.689i 0.0202561 0.148785i
\(792\) −7.48327 3.14243i −0.00944857 0.00396772i
\(793\) −196.260 196.260i −0.247491 0.247491i
\(794\) −110.936 + 266.599i −0.139718 + 0.335767i
\(795\) −385.834 159.817i −0.485325 0.201028i
\(796\) −28.6048 28.7911i −0.0359357 0.0361697i
\(797\) 1230.72 509.782i 1.54419 0.639626i 0.561939 0.827179i \(-0.310056\pi\)
0.982254 + 0.187553i \(0.0600557\pi\)
\(798\) −104.885 + 761.157i −0.131435 + 0.953831i
\(799\) 181.009 0.226545
\(800\) −0.352579 + 43.4593i −0.000440724 + 0.0543241i
\(801\) 15.0515i 0.0187908i
\(802\) −353.535 + 352.390i −0.440817 + 0.439389i
\(803\) 637.409 264.023i 0.793784 0.328796i
\(804\) −654.952 + 650.715i −0.814618 + 0.809348i
\(805\) 21.1029 + 80.1701i 0.0262147 + 0.0995902i
\(806\) 49.5373 + 20.6133i 0.0614607 + 0.0255748i
\(807\) −594.546 594.546i −0.736736 0.736736i
\(808\) −530.067 1297.52i −0.656024 1.60585i
\(809\) 116.122 116.122i 0.143538 0.143538i −0.631686 0.775224i \(-0.717637\pi\)
0.775224 + 0.631686i \(0.217637\pi\)
\(810\) −305.085 739.933i −0.376648 0.913497i
\(811\) −442.106 183.126i −0.545137 0.225803i 0.0930813 0.995659i \(-0.470328\pi\)
−0.638218 + 0.769855i \(0.720328\pi\)
\(812\) 1216.25 315.933i 1.49785 0.389080i
\(813\) 1345.81 557.451i 1.65536 0.685672i
\(814\) 942.471 + 1.52919i 1.15783 + 0.00187862i
\(815\) −275.439 −0.337962
\(816\) −827.270 + 336.393i −1.01381 + 0.412246i
\(817\) −54.7394 −0.0670005
\(818\) 1178.85 + 1.91274i 1.44114 + 0.00233831i
\(819\) 8.86611 + 5.17114i 0.0108255 + 0.00631397i
\(820\) −48.3124 117.716i −0.0589176 0.143556i
\(821\) 105.858 255.563i 0.128938 0.311283i −0.846206 0.532856i \(-0.821119\pi\)
0.975144 + 0.221572i \(0.0711189\pi\)
\(822\) 611.264 252.033i 0.743631 0.306609i
\(823\) 1009.32 1009.32i 1.22639 1.22639i 0.261074 0.965319i \(-0.415923\pi\)
0.965319 0.261074i \(-0.0840768\pi\)
\(824\) 1.84983 380.026i 0.00224494 0.461196i
\(825\) 20.0227 20.0227i 0.0242699 0.0242699i
\(826\) 1084.05 283.470i 1.31241 0.343184i
\(827\) 131.660 + 54.5353i 0.159202 + 0.0659436i 0.460861 0.887472i \(-0.347541\pi\)
−0.301659 + 0.953416i \(0.597541\pi\)
\(828\) −1.43384 0.00465292i −0.00173169 5.61947e-6i
\(829\) 215.638 89.3202i 0.260118 0.107745i −0.248813 0.968551i \(-0.580041\pi\)
0.508932 + 0.860807i \(0.330041\pi\)
\(830\) −970.037 973.190i −1.16872 1.17252i
\(831\) 835.375i 1.00526i
\(832\) 591.450 238.268i 0.710877 0.286379i
\(833\) 871.378 + 241.746i 1.04607 + 0.290211i
\(834\) 478.463 + 480.018i 0.573696 + 0.575561i
\(835\) 443.388 + 1070.43i 0.531003 + 1.28196i
\(836\) 1.62374 500.370i 0.00194228 0.598529i
\(837\) −66.6079 27.5899i −0.0795793 0.0329628i
\(838\) −244.326 101.668i −0.291558 0.121322i
\(839\) −298.113 + 298.113i −0.355319 + 0.355319i −0.862084 0.506765i \(-0.830841\pi\)
0.506765 + 0.862084i \(0.330841\pi\)
\(840\) −495.241 657.963i −0.589572 0.783290i
\(841\) −829.536 + 829.536i −0.986369 + 0.986369i
\(842\) −154.766 375.359i −0.183807 0.445794i
\(843\) 420.457 + 174.159i 0.498763 + 0.206594i
\(844\) 405.076 + 986.987i 0.479948 + 1.16942i
\(845\) −129.760 313.267i −0.153562 0.370731i
\(846\) −2.88695 0.00468418i −0.00341247 5.53686e-6i
\(847\) 311.311 + 409.437i 0.367546 + 0.483396i
\(848\) −176.605 + 418.656i −0.208261 + 0.493698i
\(849\) 1021.27i 1.20291i
\(850\) 0.0813360 50.1289i 9.56894e−5 0.0589752i
\(851\) 153.826 63.7166i 0.180759 0.0748726i
\(852\) −223.256 + 534.080i −0.262038 + 0.626854i
\(853\) −1031.22 427.145i −1.20893 0.500756i −0.315057 0.949073i \(-0.602024\pi\)
−0.893875 + 0.448317i \(0.852024\pi\)
\(854\) 336.579 + 197.042i 0.394121 + 0.230728i
\(855\) −9.18193 + 9.18193i −0.0107391 + 0.0107391i
\(856\) 222.718 + 545.180i 0.260185 + 0.636893i
\(857\) −432.255 + 432.255i −0.504381 + 0.504381i −0.912796 0.408415i \(-0.866082\pi\)
0.408415 + 0.912796i \(0.366082\pi\)
\(858\) −383.564 159.607i −0.447044 0.186022i
\(859\) 355.935 859.304i 0.414360 1.00035i −0.569593 0.821927i \(-0.692899\pi\)
0.983953 0.178427i \(-0.0571009\pi\)
\(860\) 41.6201 41.3509i 0.0483955 0.0480824i
\(861\) −119.646 69.7831i −0.138961 0.0810489i
\(862\) −527.048 + 525.340i −0.611424 + 0.609443i
\(863\) 804.494 0.932206 0.466103 0.884730i \(-0.345658\pi\)
0.466103 + 0.884730i \(0.345658\pi\)
\(864\) −794.207 + 321.448i −0.919221 + 0.372046i
\(865\) 641.180 0.741248
\(866\) −4.91121 4.92718i −0.00567115 0.00568958i
\(867\) 144.135 59.7028i 0.166246 0.0688613i
\(868\) −74.6725 10.4131i −0.0860282 0.0119966i
\(869\) 568.715 + 235.569i 0.654448 + 0.271081i
\(870\) 1218.66 + 507.103i 1.40076 + 0.582877i
\(871\) −537.647 + 537.647i −0.617275 + 0.617275i
\(872\) −426.754 + 1016.25i −0.489397 + 1.16543i
\(873\) −11.2550 11.2550i −0.0128923 0.0128923i
\(874\) −33.6956 81.7231i −0.0385533 0.0935047i
\(875\) 867.574 228.368i 0.991513 0.260992i
\(876\) −466.967 + 1117.09i −0.533067 + 1.27522i
\(877\) −1400.91 + 580.275i −1.59739 + 0.661659i −0.991043 0.133545i \(-0.957364\pi\)
−0.606343 + 0.795203i \(0.707364\pi\)
\(878\) 0.281912 173.748i 0.000321085 0.197890i
\(879\) 1490.90i 1.69613i
\(880\) 376.752 + 381.674i 0.428127 + 0.433721i
\(881\) −628.518 −0.713415 −0.356707 0.934216i \(-0.616101\pi\)
−0.356707 + 0.934216i \(0.616101\pi\)
\(882\) −13.8915 3.87820i −0.0157500 0.00439705i
\(883\) −100.974 + 41.8249i −0.114354 + 0.0473668i −0.439127 0.898425i \(-0.644712\pi\)
0.324773 + 0.945792i \(0.394712\pi\)
\(884\) −680.399 + 279.247i −0.769682 + 0.315890i
\(885\) 1087.38 + 450.409i 1.22868 + 0.508936i
\(886\) 244.920 + 594.013i 0.276433 + 0.670444i
\(887\) −1043.47 1043.47i −1.17641 1.17641i −0.980653 0.195753i \(-0.937285\pi\)
−0.195753 0.980653i \(-0.562715\pi\)
\(888\) −1175.21 + 1163.82i −1.32343 + 1.31061i
\(889\) −1241.19 168.980i −1.39616 0.190079i
\(890\) 382.090 918.230i 0.429314 1.03172i
\(891\) 524.176 + 217.121i 0.588300 + 0.243682i
\(892\) 362.710 + 1.17702i 0.406626 + 0.00131953i
\(893\) −68.1108 164.434i −0.0762718 0.184137i
\(894\) −332.592 + 331.514i −0.372027 + 0.370822i
\(895\) 117.058i 0.130791i
\(896\) −719.357 + 534.173i −0.802854 + 0.596175i
\(897\) −73.3938 −0.0818214
\(898\) 915.970 + 918.947i 1.02001 + 1.02333i
\(899\) 111.646 46.2455i 0.124190 0.0514410i
\(900\) −0.00259449 + 0.799513i −2.88276e−6 + 0.000888348i
\(901\) 200.564 484.203i 0.222601 0.537407i
\(902\) 83.2791 + 34.6537i 0.0923272 + 0.0384188i
\(903\) 8.61516 63.2800i 0.00954060 0.0700775i
\(904\) −95.5158 96.4502i −0.105659 0.106693i
\(905\) −188.435 + 188.435i −0.208216 + 0.208216i
\(906\) 712.201 293.650i 0.786093 0.324117i
\(907\) 251.489 607.148i 0.277276 0.669403i −0.722483 0.691389i \(-0.756999\pi\)
0.999758 + 0.0219864i \(0.00699907\pi\)
\(908\) 449.763 + 1095.87i 0.495334 + 1.20691i
\(909\) −9.86736 23.8219i −0.0108552 0.0262067i
\(910\) −409.614 540.542i −0.450125 0.594002i
\(911\) 1559.69i 1.71207i 0.516921 + 0.856033i \(0.327078\pi\)
−0.516921 + 0.856033i \(0.672922\pi\)
\(912\) 616.877 + 624.937i 0.676400 + 0.685238i
\(913\) 974.059 1.06688
\(914\) −234.904 0.381141i −0.257007 0.000417003i
\(915\) 156.775 + 378.488i 0.171339 + 0.413648i
\(916\) −980.711 409.957i −1.07064 0.447551i
\(917\) 417.459 109.886i 0.455244 0.119832i
\(918\) 913.637 376.705i 0.995248 0.410355i
\(919\) 184.416 184.416i 0.200671 0.200671i −0.599617 0.800287i \(-0.704680\pi\)
0.800287 + 0.599617i \(0.204680\pi\)
\(920\) 87.3545 + 36.6826i 0.0949506 + 0.0398724i
\(921\) 1151.78 + 1151.78i 1.25057 + 1.25057i
\(922\) 230.020 552.779i 0.249479 0.599543i
\(923\) −182.435 + 440.437i −0.197655 + 0.477180i
\(924\) 578.184 + 80.6278i 0.625740 + 0.0872595i
\(925\) −35.5286 85.7737i −0.0384093 0.0927284i
\(926\) 442.158 440.726i 0.477493 0.475946i
\(927\) 6.99116i 0.00754170i
\(928\) 560.330 1322.31i 0.603804 1.42491i
\(929\) 675.607i 0.727242i 0.931547 + 0.363621i \(0.118460\pi\)
−0.931547 + 0.363621i \(0.881540\pi\)
\(930\) −55.9085 56.0902i −0.0601167 0.0603121i
\(931\) −108.276 882.550i −0.116301 0.947959i
\(932\) 1191.29 + 1199.05i 1.27821 + 1.28653i
\(933\) 288.006 + 119.296i 0.308688 + 0.127863i
\(934\) −605.358 + 1454.78i −0.648134 + 1.55758i
\(935\) −437.405 437.405i −0.467813 0.467813i
\(936\) 10.8590 4.43616i 0.0116015 0.00473948i
\(937\) −94.4110 94.4110i −0.100759 0.100759i 0.654930 0.755689i \(-0.272698\pi\)
−0.755689 + 0.654930i \(0.772698\pi\)
\(938\) 539.787 922.044i 0.575466 0.982989i
\(939\) 671.251 1620.54i 0.714857 1.72582i
\(940\) 176.002 + 73.5726i 0.187237 + 0.0782687i
\(941\) 221.846 + 535.585i 0.235756 + 0.569166i 0.996835 0.0794933i \(-0.0253302\pi\)
−0.761079 + 0.648659i \(0.775330\pi\)
\(942\) −1165.27 1.89070i −1.23702 0.00200711i
\(943\) 15.9352 0.0168984
\(944\) 497.721 1179.89i 0.527246 1.24988i
\(945\) 551.573 + 725.428i 0.583675 + 0.767649i
\(946\) −0.0674814 + 41.5900i −7.13334e−5 + 0.0439641i
\(947\) −1430.30 + 592.450i −1.51035 + 0.625607i −0.975630 0.219422i \(-0.929583\pi\)
−0.534720 + 0.845029i \(0.679583\pi\)
\(948\) −999.384 + 410.164i −1.05420 + 0.432663i
\(949\) −381.585 + 921.227i −0.402091 + 0.970734i
\(950\) −45.5691 + 18.7888i −0.0479675 + 0.0197777i
\(951\) 196.564 + 196.564i 0.206692 + 0.206692i
\(952\) 825.713 621.504i 0.867346 0.652841i
\(953\) 615.729 + 615.729i 0.646095 + 0.646095i 0.952047 0.305952i \(-0.0989747\pi\)
−0.305952 + 0.952047i \(0.598975\pi\)
\(954\) −3.21136 + 7.71746i −0.00336620 + 0.00808958i
\(955\) −446.820 + 1078.72i −0.467875 + 1.12955i
\(956\) −1109.51 3.60045i −1.16057 0.00376616i
\(957\) −864.471 + 358.075i −0.903313 + 0.374165i
\(958\) −736.165 + 733.780i −0.768439 + 0.765950i
\(959\) −609.084 + 463.112i −0.635124 + 0.482911i
\(960\) −941.117 9.16226i −0.980330 0.00954403i
\(961\) 953.749 0.992455
\(962\) −964.730 + 961.604i −1.00284 + 0.999589i
\(963\) 4.14597 + 10.0092i 0.00430526 + 0.0103938i
\(964\) 3.87991 1195.63i 0.00402481 1.24028i
\(965\) −441.459 + 1065.78i −0.457470 + 1.10443i
\(966\) 99.7769 26.0908i 0.103289 0.0270092i
\(967\) −346.586 346.586i −0.358413 0.358413i 0.504815 0.863228i \(-0.331561\pi\)
−0.863228 + 0.504815i \(0.831561\pi\)
\(968\) 587.818 + 2.86129i 0.607250 + 0.00295588i
\(969\) −716.189 716.189i −0.739101 0.739101i
\(970\) 400.906 + 972.333i 0.413306 + 1.00241i
\(971\) 788.658 + 326.673i 0.812212 + 0.336429i 0.749836 0.661624i \(-0.230132\pi\)
0.0623758 + 0.998053i \(0.480132\pi\)
\(972\) −29.4055 + 12.0685i −0.0302525 + 0.0124161i
\(973\) −677.505 395.153i −0.696305 0.406118i
\(974\) 2.64559 1630.53i 0.00271621 1.67405i
\(975\) 40.9247i 0.0419740i
\(976\) 412.900 167.898i 0.423053 0.172026i
\(977\) 382.984i 0.392000i −0.980604 0.196000i \(-0.937205\pi\)
0.980604 0.196000i \(-0.0627952\pi\)
\(978\) −0.555971 + 342.655i −0.000568477 + 0.350363i
\(979\) 269.801 + 651.358i 0.275589 + 0.665330i
\(980\) 749.016 + 589.237i 0.764302 + 0.601263i
\(981\) −7.75961 + 18.7333i −0.00790990 + 0.0190962i
\(982\) 806.732 332.627i 0.821519 0.338724i
\(983\) −711.598 711.598i −0.723904 0.723904i 0.245494 0.969398i \(-0.421050\pi\)
−0.969398 + 0.245494i \(0.921050\pi\)
\(984\) −146.540 + 59.8647i −0.148922 + 0.0608381i
\(985\) −530.617 + 530.617i −0.538698 + 0.538698i
\(986\) −636.391 + 1529.36i −0.645427 + 1.55107i
\(987\) 200.809 52.8581i 0.203454 0.0535543i
\(988\) 509.699 + 513.018i 0.515889 + 0.519249i
\(989\) 2.81173 + 6.78812i 0.00284300 + 0.00686362i
\(990\) 6.96494 + 6.98758i 0.00703530 + 0.00705816i
\(991\) 1183.70 1.19445 0.597227 0.802072i \(-0.296269\pi\)
0.597227 + 0.802072i \(0.296269\pi\)
\(992\) −61.4207 + 60.4321i −0.0619160 + 0.0609194i
\(993\) 991.529i 0.998519i
\(994\) 91.4440 663.617i 0.0919960 0.667622i
\(995\) 18.8794 + 45.5789i 0.0189743 + 0.0458080i
\(996\) −1212.64 + 1204.79i −1.21751 + 1.20963i
\(997\) −541.906 + 1308.28i −0.543537 + 1.31221i 0.378675 + 0.925530i \(0.376380\pi\)
−0.922212 + 0.386684i \(0.873620\pi\)
\(998\) −683.749 284.519i −0.685119 0.285089i
\(999\) 1294.20 1294.20i 1.29550 1.29550i
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 224.3.v.b.69.16 yes 240
7.6 odd 2 inner 224.3.v.b.69.15 yes 240
32.13 even 8 inner 224.3.v.b.13.15 240
224.13 odd 8 inner 224.3.v.b.13.16 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.3.v.b.13.15 240 32.13 even 8 inner
224.3.v.b.13.16 yes 240 224.13 odd 8 inner
224.3.v.b.69.15 yes 240 7.6 odd 2 inner
224.3.v.b.69.16 yes 240 1.1 even 1 trivial