Properties

Label 105.3.v.a.88.14
Level $105$
Weight $3$
Character 105.88
Analytic conductor $2.861$
Analytic rank $0$
Dimension $64$
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] = [105,3,Mod(37,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.37");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.v (of order \(12\), 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: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 88.14
Character \(\chi\) \(=\) 105.88
Dual form 105.3.v.a.37.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.88660 + 0.773463i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(4.27013 + 2.46536i) q^{4} +(0.160937 + 4.99741i) q^{5} -5.17611 q^{6} +(5.19830 + 4.68804i) q^{7} +(1.96674 + 1.96674i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(2.88660 + 0.773463i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(4.27013 + 2.46536i) q^{4} +(0.160937 + 4.99741i) q^{5} -5.17611 q^{6} +(5.19830 + 4.68804i) q^{7} +(1.96674 + 1.96674i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-3.40075 + 14.5500i) q^{10} +(6.71313 - 11.6275i) q^{11} +(-8.24925 - 2.21038i) q^{12} +(-3.94411 - 3.94411i) q^{13} +(11.3794 + 17.5532i) q^{14} +(-2.50953 - 8.28868i) q^{15} +(-5.70544 - 9.88212i) q^{16} +(-2.53643 - 9.46609i) q^{17} +(8.65981 - 2.32039i) q^{18} +(-4.57992 + 2.64422i) q^{19} +(-11.6332 + 21.7363i) q^{20} +(-10.7985 - 5.51290i) q^{21} +(28.3716 - 28.3716i) q^{22} +(-1.98091 + 7.39285i) q^{23} +(-4.17208 - 2.40875i) q^{24} +(-24.9482 + 1.60854i) q^{25} +(-8.33445 - 14.4357i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(10.6397 + 32.8342i) q^{28} -36.7188i q^{29} +(-0.833028 - 25.8672i) q^{30} +(-9.71723 + 16.8307i) q^{31} +(-11.7054 - 43.6852i) q^{32} +(-6.01883 + 22.4626i) q^{33} -29.2867i q^{34} +(-22.5914 + 26.7325i) q^{35} +14.7922 q^{36} +(43.7832 + 11.7317i) q^{37} +(-15.2656 + 4.09041i) q^{38} +(8.36672 + 4.83053i) q^{39} +(-9.51208 + 10.1451i) q^{40} +57.9301 q^{41} +(-26.9070 - 24.2658i) q^{42} +(46.3359 + 46.3359i) q^{43} +(57.3319 - 33.1006i) q^{44} +(7.91424 + 12.7422i) q^{45} +(-11.4362 + 19.8080i) q^{46} +(-61.3721 - 16.4446i) q^{47} +(13.9754 + 13.9754i) q^{48} +(5.04463 + 48.7396i) q^{49} +(-73.2597 - 14.6533i) q^{50} +(8.48707 + 14.7000i) q^{51} +(-7.11820 - 26.5655i) q^{52} +(-38.8830 + 10.4187i) q^{53} +(-13.4479 + 7.76417i) q^{54} +(59.1877 + 31.6770i) q^{55} +(1.00355 + 19.4438i) q^{56} +(6.47699 - 6.47699i) q^{57} +(28.4006 - 105.992i) q^{58} +(-60.4517 - 34.9018i) q^{59} +(9.71857 - 41.5806i) q^{60} +(-39.4523 - 68.3334i) q^{61} +(-41.0677 + 41.0677i) q^{62} +(20.5376 + 4.38243i) q^{63} -89.5118i q^{64} +(19.0756 - 20.3451i) q^{65} +(-34.7479 + 60.1852i) q^{66} +(28.7353 + 107.241i) q^{67} +(12.5064 - 46.6746i) q^{68} -13.2565i q^{69} +(-85.8891 + 59.6925i) q^{70} -121.479 q^{71} +(8.05985 + 2.15963i) q^{72} +(4.70119 - 1.25968i) q^{73} +(117.311 + 67.7293i) q^{74} +(41.0181 - 13.8751i) q^{75} -26.0758 q^{76} +(89.4070 - 28.9718i) q^{77} +(20.4152 + 20.4152i) q^{78} +(-116.005 + 66.9753i) q^{79} +(48.4668 - 30.1028i) q^{80} +(4.50000 - 7.79423i) q^{81} +(167.221 + 44.8068i) q^{82} +(99.6896 + 99.6896i) q^{83} +(-32.5197 - 50.1630i) q^{84} +(46.8977 - 14.1990i) q^{85} +(97.9142 + 169.592i) q^{86} +(16.4606 + 61.4317i) q^{87} +(36.0712 - 9.66526i) q^{88} +(-20.5641 + 11.8727i) q^{89} +(12.9896 + 42.9032i) q^{90} +(-2.01253 - 38.9928i) q^{91} +(-26.6847 + 26.6847i) q^{92} +(8.71223 - 32.5145i) q^{93} +(-164.438 - 94.9381i) q^{94} +(-13.9513 - 22.4622i) q^{95} +(39.1670 + 67.8393i) q^{96} +(-40.9086 + 40.9086i) q^{97} +(-23.1364 + 144.594i) q^{98} -40.2788i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 4 q^{5} - 4 q^{7} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 4 q^{5} - 4 q^{7} + 24 q^{8} - 16 q^{10} + 16 q^{11} - 48 q^{15} + 80 q^{16} + 56 q^{17} + 24 q^{21} - 96 q^{22} + 72 q^{23} - 4 q^{25} - 288 q^{26} - 380 q^{28} - 48 q^{30} - 136 q^{31} - 48 q^{32} - 72 q^{33} + 76 q^{35} + 384 q^{36} - 28 q^{37} - 68 q^{38} + 164 q^{40} + 128 q^{41} - 12 q^{42} + 344 q^{43} + 240 q^{46} + 412 q^{47} - 288 q^{48} - 72 q^{50} - 24 q^{51} + 388 q^{52} - 40 q^{53} - 8 q^{55} - 864 q^{56} - 192 q^{57} + 56 q^{58} - 180 q^{60} - 216 q^{61} - 912 q^{62} - 84 q^{63} + 20 q^{65} - 72 q^{66} - 368 q^{67} - 492 q^{68} + 416 q^{70} + 784 q^{71} + 36 q^{72} - 316 q^{73} + 96 q^{75} - 32 q^{76} + 844 q^{77} + 624 q^{78} + 908 q^{80} + 288 q^{81} + 556 q^{82} + 1408 q^{83} - 536 q^{85} + 1024 q^{86} + 108 q^{87} + 372 q^{88} + 216 q^{90} - 1064 q^{91} - 1704 q^{92} + 144 q^{93} + 260 q^{95} + 352 q^{97} + 272 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.88660 + 0.773463i 1.44330 + 0.386731i 0.893688 0.448688i \(-0.148109\pi\)
0.549613 + 0.835419i \(0.314775\pi\)
\(3\) −1.67303 + 0.448288i −0.557678 + 0.149429i
\(4\) 4.27013 + 2.46536i 1.06753 + 0.616340i
\(5\) 0.160937 + 4.99741i 0.0321874 + 0.999482i
\(6\) −5.17611 −0.862686
\(7\) 5.19830 + 4.68804i 0.742614 + 0.669719i
\(8\) 1.96674 + 1.96674i 0.245842 + 0.245842i
\(9\) 2.59808 1.50000i 0.288675 0.166667i
\(10\) −3.40075 + 14.5500i −0.340075 + 1.45500i
\(11\) 6.71313 11.6275i 0.610285 1.05704i −0.380907 0.924613i \(-0.624388\pi\)
0.991192 0.132431i \(-0.0422784\pi\)
\(12\) −8.24925 2.21038i −0.687438 0.184198i
\(13\) −3.94411 3.94411i −0.303393 0.303393i 0.538947 0.842340i \(-0.318822\pi\)
−0.842340 + 0.538947i \(0.818822\pi\)
\(14\) 11.3794 + 17.5532i 0.812814 + 1.25380i
\(15\) −2.50953 8.28868i −0.167302 0.552579i
\(16\) −5.70544 9.88212i −0.356590 0.617632i
\(17\) −2.53643 9.46609i −0.149202 0.556829i −0.999532 0.0305799i \(-0.990265\pi\)
0.850330 0.526249i \(-0.176402\pi\)
\(18\) 8.65981 2.32039i 0.481100 0.128910i
\(19\) −4.57992 + 2.64422i −0.241049 + 0.139169i −0.615659 0.788013i \(-0.711110\pi\)
0.374610 + 0.927182i \(0.377777\pi\)
\(20\) −11.6332 + 21.7363i −0.581659 + 1.08682i
\(21\) −10.7985 5.51290i −0.514215 0.262519i
\(22\) 28.3716 28.3716i 1.28962 1.28962i
\(23\) −1.98091 + 7.39285i −0.0861264 + 0.321428i −0.995525 0.0944974i \(-0.969876\pi\)
0.909399 + 0.415925i \(0.136542\pi\)
\(24\) −4.17208 2.40875i −0.173837 0.100365i
\(25\) −24.9482 + 1.60854i −0.997928 + 0.0643415i
\(26\) −8.33445 14.4357i −0.320556 0.555219i
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 10.6397 + 32.8342i 0.379990 + 1.17265i
\(29\) 36.7188i 1.26616i −0.774085 0.633082i \(-0.781789\pi\)
0.774085 0.633082i \(-0.218211\pi\)
\(30\) −0.833028 25.8672i −0.0277676 0.862239i
\(31\) −9.71723 + 16.8307i −0.313459 + 0.542927i −0.979109 0.203337i \(-0.934821\pi\)
0.665650 + 0.746264i \(0.268155\pi\)
\(32\) −11.7054 43.6852i −0.365794 1.36516i
\(33\) −6.01883 + 22.4626i −0.182389 + 0.680684i
\(34\) 29.2867i 0.861373i
\(35\) −22.5914 + 26.7325i −0.645470 + 0.763786i
\(36\) 14.7922 0.410893
\(37\) 43.7832 + 11.7317i 1.18333 + 0.317072i 0.796246 0.604973i \(-0.206816\pi\)
0.387083 + 0.922045i \(0.373483\pi\)
\(38\) −15.2656 + 4.09041i −0.401727 + 0.107642i
\(39\) 8.36672 + 4.83053i 0.214531 + 0.123860i
\(40\) −9.51208 + 10.1451i −0.237802 + 0.253628i
\(41\) 57.9301 1.41293 0.706464 0.707749i \(-0.250289\pi\)
0.706464 + 0.707749i \(0.250289\pi\)
\(42\) −26.9070 24.2658i −0.640643 0.577757i
\(43\) 46.3359 + 46.3359i 1.07758 + 1.07758i 0.996726 + 0.0808525i \(0.0257643\pi\)
0.0808525 + 0.996726i \(0.474236\pi\)
\(44\) 57.3319 33.1006i 1.30300 0.752286i
\(45\) 7.91424 + 12.7422i 0.175872 + 0.283161i
\(46\) −11.4362 + 19.8080i −0.248613 + 0.430610i
\(47\) −61.3721 16.4446i −1.30579 0.349885i −0.462153 0.886800i \(-0.652923\pi\)
−0.843636 + 0.536915i \(0.819590\pi\)
\(48\) 13.9754 + 13.9754i 0.291155 + 0.291155i
\(49\) 5.04463 + 48.7396i 0.102952 + 0.994686i
\(50\) −73.2597 14.6533i −1.46519 0.293066i
\(51\) 8.48707 + 14.7000i 0.166413 + 0.288236i
\(52\) −7.11820 26.5655i −0.136889 0.510875i
\(53\) −38.8830 + 10.4187i −0.733641 + 0.196578i −0.606250 0.795274i \(-0.707327\pi\)
−0.127391 + 0.991853i \(0.540660\pi\)
\(54\) −13.4479 + 7.76417i −0.249036 + 0.143781i
\(55\) 59.1877 + 31.6770i 1.07614 + 0.575945i
\(56\) 1.00355 + 19.4438i 0.0179206 + 0.347212i
\(57\) 6.47699 6.47699i 0.113631 0.113631i
\(58\) 28.4006 105.992i 0.489666 1.82746i
\(59\) −60.4517 34.9018i −1.02461 0.591556i −0.109171 0.994023i \(-0.534819\pi\)
−0.915434 + 0.402467i \(0.868153\pi\)
\(60\) 9.71857 41.5806i 0.161976 0.693010i
\(61\) −39.4523 68.3334i −0.646759 1.12022i −0.983892 0.178763i \(-0.942790\pi\)
0.337133 0.941457i \(-0.390543\pi\)
\(62\) −41.0677 + 41.0677i −0.662383 + 0.662383i
\(63\) 20.5376 + 4.38243i 0.325994 + 0.0695623i
\(64\) 89.5118i 1.39862i
\(65\) 19.0756 20.3451i 0.293470 0.313001i
\(66\) −34.7479 + 60.1852i −0.526484 + 0.911897i
\(67\) 28.7353 + 107.241i 0.428885 + 1.60062i 0.755291 + 0.655389i \(0.227495\pi\)
−0.326407 + 0.945229i \(0.605838\pi\)
\(68\) 12.5064 46.6746i 0.183918 0.686392i
\(69\) 13.2565i 0.192123i
\(70\) −85.8891 + 59.6925i −1.22699 + 0.852750i
\(71\) −121.479 −1.71097 −0.855486 0.517826i \(-0.826741\pi\)
−0.855486 + 0.517826i \(0.826741\pi\)
\(72\) 8.05985 + 2.15963i 0.111942 + 0.0299949i
\(73\) 4.70119 1.25968i 0.0643998 0.0172559i −0.226475 0.974017i \(-0.572720\pi\)
0.290875 + 0.956761i \(0.406054\pi\)
\(74\) 117.311 + 67.7293i 1.58528 + 0.915261i
\(75\) 41.0181 13.8751i 0.546907 0.185001i
\(76\) −26.0758 −0.343103
\(77\) 89.4070 28.9718i 1.16113 0.376257i
\(78\) 20.4152 + 20.4152i 0.261733 + 0.261733i
\(79\) −116.005 + 66.9753i −1.46841 + 0.847788i −0.999374 0.0353889i \(-0.988733\pi\)
−0.469039 + 0.883177i \(0.655400\pi\)
\(80\) 48.4668 30.1028i 0.605835 0.376285i
\(81\) 4.50000 7.79423i 0.0555556 0.0962250i
\(82\) 167.221 + 44.8068i 2.03928 + 0.546424i
\(83\) 99.6896 + 99.6896i 1.20108 + 1.20108i 0.973838 + 0.227242i \(0.0729707\pi\)
0.227242 + 0.973838i \(0.427029\pi\)
\(84\) −32.5197 50.1630i −0.387140 0.597179i
\(85\) 46.8977 14.1990i 0.551738 0.167047i
\(86\) 97.9142 + 169.592i 1.13854 + 1.97200i
\(87\) 16.4606 + 61.4317i 0.189202 + 0.706112i
\(88\) 36.0712 9.66526i 0.409900 0.109832i
\(89\) −20.5641 + 11.8727i −0.231058 + 0.133401i −0.611060 0.791584i \(-0.709257\pi\)
0.380002 + 0.924986i \(0.375923\pi\)
\(90\) 12.9896 + 42.9032i 0.144329 + 0.476702i
\(91\) −2.01253 38.9928i −0.0221158 0.428492i
\(92\) −26.6847 + 26.6847i −0.290052 + 0.290052i
\(93\) 8.71223 32.5145i 0.0936799 0.349618i
\(94\) −164.438 94.9381i −1.74934 1.00998i
\(95\) −13.9513 22.4622i −0.146856 0.236444i
\(96\) 39.1670 + 67.8393i 0.407990 + 0.706659i
\(97\) −40.9086 + 40.9086i −0.421738 + 0.421738i −0.885802 0.464064i \(-0.846391\pi\)
0.464064 + 0.885802i \(0.346391\pi\)
\(98\) −23.1364 + 144.594i −0.236086 + 1.47545i
\(99\) 40.2788i 0.406857i
\(100\) −110.498 54.6376i −1.10498 0.546376i
\(101\) 34.1609 59.1683i 0.338226 0.585825i −0.645873 0.763445i \(-0.723506\pi\)
0.984099 + 0.177620i \(0.0568397\pi\)
\(102\) 13.1289 + 48.9976i 0.128714 + 0.480368i
\(103\) 32.8404 122.562i 0.318839 1.18992i −0.601524 0.798855i \(-0.705439\pi\)
0.920362 0.391067i \(-0.127894\pi\)
\(104\) 15.5141i 0.149174i
\(105\) 25.8124 54.8518i 0.245832 0.522398i
\(106\) −120.298 −1.13489
\(107\) 58.6252 + 15.7086i 0.547899 + 0.146809i 0.522141 0.852859i \(-0.325133\pi\)
0.0257581 + 0.999668i \(0.491800\pi\)
\(108\) −24.7478 + 6.63114i −0.229146 + 0.0613995i
\(109\) 18.6575 + 10.7719i 0.171170 + 0.0988251i 0.583137 0.812374i \(-0.301825\pi\)
−0.411967 + 0.911199i \(0.635158\pi\)
\(110\) 146.350 + 137.218i 1.33046 + 1.24744i
\(111\) −78.5098 −0.707296
\(112\) 16.6691 78.1175i 0.148831 0.697478i
\(113\) 12.3946 + 12.3946i 0.109686 + 0.109686i 0.759820 0.650134i \(-0.225287\pi\)
−0.650134 + 0.759820i \(0.725287\pi\)
\(114\) 23.7062 13.6868i 0.207949 0.120060i
\(115\) −37.2639 8.70962i −0.324034 0.0757358i
\(116\) 90.5250 156.794i 0.780388 1.35167i
\(117\) −16.1633 4.33093i −0.138148 0.0370165i
\(118\) −147.505 147.505i −1.25004 1.25004i
\(119\) 31.1923 61.0985i 0.262120 0.513432i
\(120\) 11.3661 21.2373i 0.0947174 0.176977i
\(121\) −29.6323 51.3247i −0.244895 0.424171i
\(122\) −61.0298 227.766i −0.500244 1.86694i
\(123\) −96.9189 + 25.9693i −0.787959 + 0.211133i
\(124\) −82.9877 + 47.9129i −0.669255 + 0.386395i
\(125\) −12.0536 124.417i −0.0964288 0.995340i
\(126\) 55.8943 + 28.5354i 0.443606 + 0.226472i
\(127\) −21.0785 + 21.0785i −0.165973 + 0.165973i −0.785207 0.619234i \(-0.787443\pi\)
0.619234 + 0.785207i \(0.287443\pi\)
\(128\) 22.4125 83.6445i 0.175097 0.653472i
\(129\) −98.2932 56.7496i −0.761963 0.439920i
\(130\) 70.7998 43.9739i 0.544614 0.338261i
\(131\) −62.6091 108.442i −0.477932 0.827803i 0.521748 0.853100i \(-0.325280\pi\)
−0.999680 + 0.0252971i \(0.991947\pi\)
\(132\) −81.0795 + 81.0795i −0.614239 + 0.614239i
\(133\) −36.2040 7.72540i −0.272211 0.0580857i
\(134\) 331.789i 2.47604i
\(135\) −18.9530 17.7703i −0.140392 0.131632i
\(136\) 13.6288 23.6058i 0.100212 0.173572i
\(137\) −9.48345 35.3927i −0.0692222 0.258341i 0.922639 0.385665i \(-0.126028\pi\)
−0.991861 + 0.127324i \(0.959361\pi\)
\(138\) 10.2534 38.2662i 0.0743000 0.277291i
\(139\) 84.6491i 0.608986i 0.952515 + 0.304493i \(0.0984870\pi\)
−0.952515 + 0.304493i \(0.901513\pi\)
\(140\) −162.374 + 58.4552i −1.15981 + 0.417537i
\(141\) 110.049 0.780493
\(142\) −350.662 93.9595i −2.46945 0.661687i
\(143\) −72.3374 + 19.3828i −0.505856 + 0.135544i
\(144\) −29.6464 17.1163i −0.205877 0.118863i
\(145\) 183.499 5.90941i 1.26551 0.0407546i
\(146\) 14.5448 0.0996217
\(147\) −30.2892 79.2815i −0.206049 0.539330i
\(148\) 158.037 + 158.037i 1.06782 + 1.06782i
\(149\) 28.2589 16.3153i 0.189657 0.109499i −0.402165 0.915567i \(-0.631742\pi\)
0.591822 + 0.806069i \(0.298409\pi\)
\(150\) 129.135 8.32597i 0.860898 0.0555065i
\(151\) 78.0454 135.179i 0.516857 0.895223i −0.482951 0.875647i \(-0.660435\pi\)
0.999808 0.0195756i \(-0.00623149\pi\)
\(152\) −14.2080 3.80702i −0.0934737 0.0250462i
\(153\) −20.7890 20.7890i −0.135876 0.135876i
\(154\) 280.491 14.4770i 1.82137 0.0940063i
\(155\) −85.6740 45.8523i −0.552735 0.295821i
\(156\) 23.8180 + 41.2539i 0.152679 + 0.264448i
\(157\) 17.2166 + 64.2534i 0.109660 + 0.409257i 0.998832 0.0483159i \(-0.0153854\pi\)
−0.889172 + 0.457573i \(0.848719\pi\)
\(158\) −386.662 + 103.606i −2.44723 + 0.655733i
\(159\) 60.3819 34.8615i 0.379760 0.219255i
\(160\) 216.429 65.5272i 1.35268 0.409545i
\(161\) −44.9553 + 29.1437i −0.279225 + 0.181017i
\(162\) 19.0183 19.0183i 0.117397 0.117397i
\(163\) −15.1289 + 56.4617i −0.0928152 + 0.346391i −0.996679 0.0814289i \(-0.974052\pi\)
0.903864 + 0.427820i \(0.140718\pi\)
\(164\) 247.369 + 142.818i 1.50835 + 0.870844i
\(165\) −113.223 26.4635i −0.686202 0.160385i
\(166\) 210.658 + 364.871i 1.26902 + 2.19802i
\(167\) −93.0212 + 93.0212i −0.557013 + 0.557013i −0.928456 0.371443i \(-0.878863\pi\)
0.371443 + 0.928456i \(0.378863\pi\)
\(168\) −10.3954 32.0803i −0.0618775 0.190954i
\(169\) 137.888i 0.815905i
\(170\) 146.358 4.71331i 0.860927 0.0277254i
\(171\) −7.93266 + 13.7398i −0.0463898 + 0.0803495i
\(172\) 83.6255 + 312.095i 0.486195 + 1.81450i
\(173\) 62.6748 233.906i 0.362282 1.35206i −0.508786 0.860893i \(-0.669906\pi\)
0.871068 0.491162i \(-0.163428\pi\)
\(174\) 190.061i 1.09230i
\(175\) −137.229 108.596i −0.784166 0.620551i
\(176\) −153.206 −0.870486
\(177\) 116.784 + 31.2921i 0.659795 + 0.176792i
\(178\) −68.5435 + 18.3662i −0.385076 + 0.103181i
\(179\) 228.989 + 132.207i 1.27927 + 0.738585i 0.976713 0.214548i \(-0.0688279\pi\)
0.302553 + 0.953133i \(0.402161\pi\)
\(180\) 2.38061 + 73.9225i 0.0132256 + 0.410680i
\(181\) 286.020 1.58022 0.790110 0.612965i \(-0.210023\pi\)
0.790110 + 0.612965i \(0.210023\pi\)
\(182\) 24.3501 114.113i 0.133792 0.626996i
\(183\) 96.6381 + 96.6381i 0.528077 + 0.528077i
\(184\) −18.4357 + 10.6439i −0.100194 + 0.0578471i
\(185\) −51.5816 + 220.690i −0.278819 + 1.19292i
\(186\) 50.2975 87.1178i 0.270417 0.468375i
\(187\) −127.094 34.0548i −0.679649 0.182111i
\(188\) −221.525 221.525i −1.17832 1.17832i
\(189\) −36.3247 + 1.87483i −0.192194 + 0.00991972i
\(190\) −22.8983 75.6303i −0.120517 0.398054i
\(191\) 38.1037 + 65.9976i 0.199496 + 0.345537i 0.948365 0.317181i \(-0.102736\pi\)
−0.748869 + 0.662718i \(0.769403\pi\)
\(192\) 40.1271 + 149.756i 0.208995 + 0.779980i
\(193\) −236.585 + 63.3927i −1.22583 + 0.328459i −0.812953 0.582329i \(-0.802142\pi\)
−0.412874 + 0.910788i \(0.635475\pi\)
\(194\) −149.728 + 86.4456i −0.771795 + 0.445596i
\(195\) −22.7936 + 42.5893i −0.116890 + 0.218407i
\(196\) −98.6195 + 220.561i −0.503161 + 1.12531i
\(197\) 136.078 136.078i 0.690750 0.690750i −0.271647 0.962397i \(-0.587568\pi\)
0.962397 + 0.271647i \(0.0875684\pi\)
\(198\) 31.1542 116.269i 0.157344 0.587217i
\(199\) 107.888 + 62.2892i 0.542151 + 0.313011i 0.745950 0.666002i \(-0.231996\pi\)
−0.203799 + 0.979013i \(0.565329\pi\)
\(200\) −52.2302 45.9030i −0.261151 0.229515i
\(201\) −96.1501 166.537i −0.478359 0.828541i
\(202\) 144.373 144.373i 0.714720 0.714720i
\(203\) 172.139 190.875i 0.847975 0.940272i
\(204\) 83.6947i 0.410268i
\(205\) 9.32309 + 289.500i 0.0454785 + 1.41220i
\(206\) 189.594 328.387i 0.920360 1.59411i
\(207\) 5.94272 + 22.1785i 0.0287088 + 0.107143i
\(208\) −16.4733 + 61.4790i −0.0791984 + 0.295572i
\(209\) 71.0040i 0.339732i
\(210\) 116.936 138.371i 0.556837 0.658907i
\(211\) −25.5567 −0.121122 −0.0605610 0.998164i \(-0.519289\pi\)
−0.0605610 + 0.998164i \(0.519289\pi\)
\(212\) −191.721 51.3715i −0.904344 0.242318i
\(213\) 203.238 54.4576i 0.954171 0.255669i
\(214\) 157.078 + 90.6889i 0.734008 + 0.423780i
\(215\) −224.102 + 239.017i −1.04234 + 1.11170i
\(216\) −14.4525 −0.0669098
\(217\) −129.416 + 41.9365i −0.596388 + 0.193256i
\(218\) 45.5252 + 45.5252i 0.208831 + 0.208831i
\(219\) −7.30054 + 4.21497i −0.0333358 + 0.0192464i
\(220\) 174.644 + 281.184i 0.793836 + 1.27811i
\(221\) −27.3313 + 47.3393i −0.123671 + 0.214205i
\(222\) −226.627 60.7244i −1.02084 0.273533i
\(223\) −58.9789 58.9789i −0.264479 0.264479i 0.562392 0.826871i \(-0.309881\pi\)
−0.826871 + 0.562392i \(0.809881\pi\)
\(224\) 143.949 281.964i 0.642631 1.25877i
\(225\) −62.4045 + 41.6014i −0.277353 + 0.184895i
\(226\) 26.1914 + 45.3649i 0.115891 + 0.200730i
\(227\) 106.629 + 397.945i 0.469732 + 1.75306i 0.640704 + 0.767788i \(0.278642\pi\)
−0.170972 + 0.985276i \(0.554691\pi\)
\(228\) 43.6257 11.6895i 0.191341 0.0512696i
\(229\) −325.569 + 187.967i −1.42170 + 0.820818i −0.996444 0.0842553i \(-0.973149\pi\)
−0.425255 + 0.905074i \(0.639816\pi\)
\(230\) −100.829 53.9634i −0.438389 0.234624i
\(231\) −136.593 + 88.5507i −0.591312 + 0.383337i
\(232\) 72.2163 72.2163i 0.311277 0.311277i
\(233\) 6.28523 23.4568i 0.0269752 0.100673i −0.951126 0.308804i \(-0.900071\pi\)
0.978101 + 0.208131i \(0.0667380\pi\)
\(234\) −43.3071 25.0034i −0.185073 0.106852i
\(235\) 72.3034 309.348i 0.307674 1.31638i
\(236\) −172.091 298.070i −0.729199 1.26301i
\(237\) 164.055 164.055i 0.692216 0.692216i
\(238\) 137.297 152.241i 0.576878 0.639668i
\(239\) 50.6675i 0.211998i −0.994366 0.105999i \(-0.966196\pi\)
0.994366 0.105999i \(-0.0338040\pi\)
\(240\) −67.5917 + 72.0901i −0.281632 + 0.300375i
\(241\) 58.3080 100.992i 0.241942 0.419055i −0.719326 0.694673i \(-0.755549\pi\)
0.961267 + 0.275618i \(0.0888824\pi\)
\(242\) −45.8390 171.074i −0.189417 0.706916i
\(243\) −4.03459 + 15.0573i −0.0166032 + 0.0619642i
\(244\) 389.057i 1.59449i
\(245\) −242.760 + 33.0541i −0.990857 + 0.134915i
\(246\) −299.853 −1.21891
\(247\) 28.4928 + 7.63463i 0.115356 + 0.0309094i
\(248\) −52.2129 + 13.9904i −0.210536 + 0.0564130i
\(249\) −211.474 122.094i −0.849292 0.490339i
\(250\) 61.4383 368.467i 0.245753 1.47387i
\(251\) 320.629 1.27741 0.638704 0.769452i \(-0.279471\pi\)
0.638704 + 0.769452i \(0.279471\pi\)
\(252\) 76.8941 + 69.3462i 0.305135 + 0.275183i
\(253\) 72.6621 + 72.6621i 0.287202 + 0.287202i
\(254\) −77.1488 + 44.5419i −0.303736 + 0.175362i
\(255\) −72.0962 + 44.7791i −0.282730 + 0.175604i
\(256\) −49.6319 + 85.9650i −0.193875 + 0.335801i
\(257\) −191.876 51.4131i −0.746600 0.200051i −0.134591 0.990901i \(-0.542972\pi\)
−0.612009 + 0.790850i \(0.709639\pi\)
\(258\) −239.840 239.840i −0.929612 0.929612i
\(259\) 172.600 + 266.242i 0.666407 + 1.02796i
\(260\) 131.613 39.8480i 0.506204 0.153261i
\(261\) −55.0782 95.3982i −0.211027 0.365510i
\(262\) −96.8516 361.455i −0.369663 1.37960i
\(263\) −15.3255 + 4.10646i −0.0582720 + 0.0156139i −0.287837 0.957679i \(-0.592936\pi\)
0.229565 + 0.973293i \(0.426270\pi\)
\(264\) −56.0155 + 32.3406i −0.212180 + 0.122502i
\(265\) −58.3240 192.637i −0.220091 0.726933i
\(266\) −98.5313 50.3026i −0.370418 0.189108i
\(267\) 29.0821 29.0821i 0.108922 0.108922i
\(268\) −141.686 + 528.778i −0.528677 + 1.97305i
\(269\) −89.8942 51.9004i −0.334179 0.192938i 0.323516 0.946223i \(-0.395135\pi\)
−0.657695 + 0.753284i \(0.728468\pi\)
\(270\) −40.9650 65.9553i −0.151722 0.244279i
\(271\) 78.5571 + 136.065i 0.289878 + 0.502084i 0.973781 0.227490i \(-0.0730518\pi\)
−0.683902 + 0.729574i \(0.739718\pi\)
\(272\) −79.0736 + 79.0736i −0.290712 + 0.290712i
\(273\) 20.8470 + 64.3340i 0.0763627 + 0.235656i
\(274\) 109.500i 0.399634i
\(275\) −148.777 + 300.883i −0.541009 + 1.09412i
\(276\) 32.6820 56.6069i 0.118413 0.205097i
\(277\) 54.1211 + 201.983i 0.195383 + 0.729179i 0.992167 + 0.124916i \(0.0398660\pi\)
−0.796784 + 0.604264i \(0.793467\pi\)
\(278\) −65.4729 + 244.348i −0.235514 + 0.878950i
\(279\) 58.3034i 0.208973i
\(280\) −97.0073 + 8.14441i −0.346455 + 0.0290872i
\(281\) 454.909 1.61889 0.809446 0.587194i \(-0.199768\pi\)
0.809446 + 0.587194i \(0.199768\pi\)
\(282\) 317.669 + 85.1192i 1.12649 + 0.301841i
\(283\) 99.1636 26.5708i 0.350401 0.0938898i −0.0793253 0.996849i \(-0.525277\pi\)
0.429727 + 0.902959i \(0.358610\pi\)
\(284\) −518.731 299.489i −1.82652 1.05454i
\(285\) 33.4106 + 31.3258i 0.117230 + 0.109915i
\(286\) −223.801 −0.782522
\(287\) 301.138 + 271.578i 1.04926 + 0.946266i
\(288\) −95.9393 95.9393i −0.333122 0.333122i
\(289\) 167.108 96.4798i 0.578228 0.333840i
\(290\) 534.259 + 124.871i 1.84227 + 0.430591i
\(291\) 50.1026 86.7803i 0.172174 0.298214i
\(292\) 23.1802 + 6.21112i 0.0793843 + 0.0212710i
\(293\) 102.346 + 102.346i 0.349302 + 0.349302i 0.859850 0.510547i \(-0.170557\pi\)
−0.510547 + 0.859850i \(0.670557\pi\)
\(294\) −26.1116 252.282i −0.0888150 0.858102i
\(295\) 164.690 307.719i 0.558270 1.04311i
\(296\) 63.0369 + 109.183i 0.212963 + 0.368862i
\(297\) 18.0565 + 67.3878i 0.0607963 + 0.226895i
\(298\) 94.1914 25.2385i 0.316079 0.0846930i
\(299\) 36.9711 21.3453i 0.123649 0.0713889i
\(300\) 209.359 + 41.8758i 0.697865 + 0.139586i
\(301\) 23.6435 + 458.092i 0.0785498 + 1.52190i
\(302\) 329.842 329.842i 1.09219 1.09219i
\(303\) −30.6278 + 114.304i −0.101082 + 0.377242i
\(304\) 52.2610 + 30.1729i 0.171911 + 0.0992529i
\(305\) 335.141 208.157i 1.09882 0.682481i
\(306\) −43.9300 76.0890i −0.143562 0.248657i
\(307\) 29.1999 29.1999i 0.0951137 0.0951137i −0.657949 0.753063i \(-0.728576\pi\)
0.753063 + 0.657949i \(0.228576\pi\)
\(308\) 453.205 + 96.7072i 1.47144 + 0.313985i
\(309\) 219.772i 0.711236i
\(310\) −211.842 198.623i −0.683360 0.640719i
\(311\) −201.089 + 348.297i −0.646589 + 1.11992i 0.337343 + 0.941382i \(0.390472\pi\)
−0.983932 + 0.178543i \(0.942862\pi\)
\(312\) 6.95477 + 25.9555i 0.0222909 + 0.0831909i
\(313\) 74.2751 277.198i 0.237301 0.885618i −0.739798 0.672829i \(-0.765079\pi\)
0.977098 0.212788i \(-0.0682545\pi\)
\(314\) 198.790i 0.633091i
\(315\) −18.5955 + 103.340i −0.0590334 + 0.328064i
\(316\) −660.473 −2.09010
\(317\) −335.924 90.0106i −1.05970 0.283945i −0.313444 0.949607i \(-0.601483\pi\)
−0.746254 + 0.665662i \(0.768149\pi\)
\(318\) 201.263 53.9282i 0.632901 0.169585i
\(319\) −426.947 246.498i −1.33839 0.772721i
\(320\) 447.327 14.4058i 1.39790 0.0450180i
\(321\) −105.124 −0.327489
\(322\) −152.310 + 49.3549i −0.473011 + 0.153276i
\(323\) 36.6471 + 36.6471i 0.113458 + 0.113458i
\(324\) 38.4312 22.1882i 0.118615 0.0684822i
\(325\) 104.743 + 92.0542i 0.322285 + 0.283244i
\(326\) −87.3421 + 151.281i −0.267921 + 0.464052i
\(327\) −36.0436 9.65785i −0.110225 0.0295347i
\(328\) 113.933 + 113.933i 0.347358 + 0.347358i
\(329\) −241.938 373.199i −0.735373 1.13434i
\(330\) −306.362 163.964i −0.928371 0.496860i
\(331\) −36.2176 62.7307i −0.109419 0.189519i 0.806116 0.591757i \(-0.201566\pi\)
−0.915535 + 0.402239i \(0.868232\pi\)
\(332\) 179.917 + 671.458i 0.541918 + 2.02246i
\(333\) 131.349 35.1950i 0.394443 0.105691i
\(334\) −340.464 + 196.567i −1.01935 + 0.588523i
\(335\) −531.305 + 160.861i −1.58598 + 0.480182i
\(336\) 7.13115 + 138.166i 0.0212236 + 0.411208i
\(337\) −255.737 + 255.737i −0.758865 + 0.758865i −0.976116 0.217251i \(-0.930291\pi\)
0.217251 + 0.976116i \(0.430291\pi\)
\(338\) 106.651 398.028i 0.315536 1.17760i
\(339\) −26.2928 15.1802i −0.0775600 0.0447793i
\(340\) 235.265 + 54.9881i 0.691956 + 0.161730i
\(341\) 130.466 + 225.974i 0.382599 + 0.662680i
\(342\) −33.5256 + 33.5256i −0.0980282 + 0.0980282i
\(343\) −202.270 + 277.013i −0.589707 + 0.807617i
\(344\) 182.261i 0.529829i
\(345\) 66.2481 2.13346i 0.192023 0.00618394i
\(346\) 361.835 626.716i 1.04576 1.81132i
\(347\) −74.6974 278.775i −0.215266 0.803385i −0.986073 0.166315i \(-0.946813\pi\)
0.770806 0.637070i \(-0.219854\pi\)
\(348\) −81.1625 + 302.902i −0.233225 + 0.870409i
\(349\) 480.492i 1.37677i −0.725347 0.688384i \(-0.758320\pi\)
0.725347 0.688384i \(-0.241680\pi\)
\(350\) −312.131 419.616i −0.891802 1.19890i
\(351\) 28.9832 0.0825731
\(352\) −586.529 157.160i −1.66627 0.446477i
\(353\) −93.2268 + 24.9800i −0.264098 + 0.0707650i −0.388438 0.921475i \(-0.626985\pi\)
0.124340 + 0.992240i \(0.460319\pi\)
\(354\) 312.905 + 180.656i 0.883912 + 0.510327i
\(355\) −19.5505 607.080i −0.0550718 1.71009i
\(356\) −117.082 −0.328882
\(357\) −24.7960 + 116.203i −0.0694565 + 0.325498i
\(358\) 558.742 + 558.742i 1.56073 + 1.56073i
\(359\) 280.865 162.157i 0.782353 0.451692i −0.0549104 0.998491i \(-0.517487\pi\)
0.837264 + 0.546799i \(0.184154\pi\)
\(360\) −9.49543 + 40.6259i −0.0263762 + 0.112850i
\(361\) −166.516 + 288.415i −0.461264 + 0.798932i
\(362\) 825.626 + 221.226i 2.28073 + 0.611121i
\(363\) 72.5841 + 72.5841i 0.199956 + 0.199956i
\(364\) 87.5375 171.466i 0.240488 0.471060i
\(365\) 7.05173 + 23.2910i 0.0193198 + 0.0638110i
\(366\) 204.210 + 353.702i 0.557950 + 0.966398i
\(367\) −66.7783 249.220i −0.181957 0.679074i −0.995261 0.0972351i \(-0.969000\pi\)
0.813304 0.581839i \(-0.197667\pi\)
\(368\) 84.3589 22.6039i 0.229236 0.0614237i
\(369\) 150.507 86.8951i 0.407877 0.235488i
\(370\) −319.591 + 597.149i −0.863760 + 1.61392i
\(371\) −250.968 128.125i −0.676464 0.345352i
\(372\) 117.362 117.362i 0.315490 0.315490i
\(373\) 127.015 474.026i 0.340523 1.27085i −0.557234 0.830356i \(-0.688137\pi\)
0.897756 0.440492i \(-0.145196\pi\)
\(374\) −340.531 196.605i −0.910510 0.525683i
\(375\) 75.9409 + 202.751i 0.202509 + 0.540669i
\(376\) −88.3607 153.045i −0.235002 0.407035i
\(377\) −144.823 + 144.823i −0.384145 + 0.384145i
\(378\) −106.305 22.6839i −0.281230 0.0600104i
\(379\) 177.802i 0.469134i 0.972100 + 0.234567i \(0.0753672\pi\)
−0.972100 + 0.234567i \(0.924633\pi\)
\(380\) −4.19656 130.312i −0.0110436 0.342925i
\(381\) 25.8158 44.7143i 0.0677581 0.117360i
\(382\) 58.9436 + 219.981i 0.154303 + 0.575866i
\(383\) −119.288 + 445.189i −0.311457 + 1.16237i 0.615786 + 0.787913i \(0.288838\pi\)
−0.927243 + 0.374460i \(0.877828\pi\)
\(384\) 149.987i 0.390592i
\(385\) 159.173 + 442.141i 0.413435 + 1.14842i
\(386\) −731.958 −1.89626
\(387\) 189.888 + 50.8803i 0.490667 + 0.131474i
\(388\) −275.540 + 73.8306i −0.710153 + 0.190285i
\(389\) 258.574 + 149.288i 0.664714 + 0.383773i 0.794071 0.607825i \(-0.207958\pi\)
−0.129357 + 0.991598i \(0.541291\pi\)
\(390\) −98.7374 + 105.308i −0.253173 + 0.270022i
\(391\) 75.0058 0.191831
\(392\) −85.9367 + 105.780i −0.219226 + 0.269846i
\(393\) 153.360 + 153.360i 0.390230 + 0.390230i
\(394\) 498.053 287.551i 1.26409 0.729825i
\(395\) −353.372 568.944i −0.894614 1.44036i
\(396\) 99.3017 171.996i 0.250762 0.434332i
\(397\) 86.8147 + 23.2619i 0.218677 + 0.0585943i 0.366494 0.930420i \(-0.380558\pi\)
−0.147817 + 0.989015i \(0.547225\pi\)
\(398\) 263.252 + 263.252i 0.661436 + 0.661436i
\(399\) 64.0337 3.30497i 0.160485 0.00828313i
\(400\) 158.236 + 237.364i 0.395591 + 0.593409i
\(401\) −48.6620 84.2851i −0.121352 0.210187i 0.798949 0.601398i \(-0.205390\pi\)
−0.920301 + 0.391211i \(0.872056\pi\)
\(402\) −148.737 555.094i −0.369993 1.38083i
\(403\) 104.708 28.0565i 0.259822 0.0696190i
\(404\) 291.743 168.438i 0.722135 0.416925i
\(405\) 39.6752 + 21.2340i 0.0979634 + 0.0524295i
\(406\) 644.532 417.838i 1.58752 1.02916i
\(407\) 430.332 430.332i 1.05733 1.05733i
\(408\) −12.2193 + 45.6030i −0.0299492 + 0.111772i
\(409\) 232.510 + 134.240i 0.568485 + 0.328215i 0.756544 0.653943i \(-0.226886\pi\)
−0.188059 + 0.982158i \(0.560220\pi\)
\(410\) −197.006 + 842.883i −0.480502 + 2.05581i
\(411\) 31.7322 + 54.9618i 0.0772074 + 0.133727i
\(412\) 442.392 442.392i 1.07377 1.07377i
\(413\) −150.625 464.830i −0.364710 1.12550i
\(414\) 68.6171i 0.165742i
\(415\) −482.146 + 514.234i −1.16180 + 1.23912i
\(416\) −126.132 + 218.466i −0.303201 + 0.525160i
\(417\) −37.9471 141.621i −0.0910003 0.339618i
\(418\) −54.9190 + 204.960i −0.131385 + 0.490336i
\(419\) 515.863i 1.23118i −0.788068 0.615588i \(-0.788919\pi\)
0.788068 0.615588i \(-0.211081\pi\)
\(420\) 245.452 170.588i 0.584408 0.406161i
\(421\) −470.236 −1.11695 −0.558475 0.829521i \(-0.688613\pi\)
−0.558475 + 0.829521i \(0.688613\pi\)
\(422\) −73.7721 19.7672i −0.174815 0.0468417i
\(423\) −184.116 + 49.3338i −0.435263 + 0.116628i
\(424\) −96.9634 55.9819i −0.228687 0.132033i
\(425\) 78.5060 + 232.082i 0.184720 + 0.546075i
\(426\) 628.789 1.47603
\(427\) 115.265 540.172i 0.269941 1.26504i
\(428\) 211.610 + 211.610i 0.494416 + 0.494416i
\(429\) 112.334 64.8560i 0.261850 0.151179i
\(430\) −831.764 + 516.611i −1.93434 + 1.20142i
\(431\) −135.577 + 234.827i −0.314564 + 0.544841i −0.979345 0.202198i \(-0.935192\pi\)
0.664781 + 0.747039i \(0.268525\pi\)
\(432\) 57.2724 + 15.3461i 0.132575 + 0.0355233i
\(433\) −135.694 135.694i −0.313381 0.313381i 0.532837 0.846218i \(-0.321126\pi\)
−0.846218 + 0.532837i \(0.821126\pi\)
\(434\) −406.009 + 20.9554i −0.935506 + 0.0482842i
\(435\) −304.350 + 92.1469i −0.699656 + 0.211832i
\(436\) 53.1134 + 91.9950i 0.121820 + 0.210998i
\(437\) −10.4759 39.0966i −0.0239723 0.0894660i
\(438\) −24.3339 + 6.52024i −0.0555568 + 0.0148864i
\(439\) 406.331 234.596i 0.925584 0.534386i 0.0401720 0.999193i \(-0.487209\pi\)
0.885412 + 0.464806i \(0.153876\pi\)
\(440\) 54.1064 + 178.707i 0.122969 + 0.406153i
\(441\) 86.2158 + 119.062i 0.195501 + 0.269983i
\(442\) −115.510 + 115.510i −0.261335 + 0.261335i
\(443\) 79.5993 297.069i 0.179682 0.670584i −0.816024 0.578018i \(-0.803826\pi\)
0.995707 0.0925661i \(-0.0295070\pi\)
\(444\) −335.247 193.555i −0.755061 0.435934i
\(445\) −62.6423 100.857i −0.140769 0.226644i
\(446\) −124.631 215.867i −0.279441 0.484006i
\(447\) −39.9641 + 39.9641i −0.0894052 + 0.0894052i
\(448\) 419.635 465.309i 0.936685 1.03864i
\(449\) 556.174i 1.23870i 0.785117 + 0.619348i \(0.212603\pi\)
−0.785117 + 0.619348i \(0.787397\pi\)
\(450\) −212.314 + 71.8191i −0.471809 + 0.159598i
\(451\) 388.892 673.581i 0.862289 1.49353i
\(452\) 22.3693 + 83.4834i 0.0494896 + 0.184698i
\(453\) −69.9736 + 261.145i −0.154467 + 0.576479i
\(454\) 1231.18i 2.71186i
\(455\) 194.539 16.3328i 0.427558 0.0358964i
\(456\) 25.4771 0.0558708
\(457\) 496.047 + 132.915i 1.08544 + 0.290843i 0.756823 0.653620i \(-0.226750\pi\)
0.328618 + 0.944463i \(0.393417\pi\)
\(458\) −1085.17 + 290.772i −2.36938 + 0.634872i
\(459\) 44.1001 + 25.4612i 0.0960786 + 0.0554710i
\(460\) −137.649 129.060i −0.299237 0.280565i
\(461\) −140.261 −0.304254 −0.152127 0.988361i \(-0.548612\pi\)
−0.152127 + 0.988361i \(0.548612\pi\)
\(462\) −462.781 + 149.961i −1.00169 + 0.324591i
\(463\) −440.572 440.572i −0.951560 0.951560i 0.0473198 0.998880i \(-0.484932\pi\)
−0.998880 + 0.0473198i \(0.984932\pi\)
\(464\) −362.859 + 209.497i −0.782024 + 0.451502i
\(465\) 163.890 + 38.3058i 0.352452 + 0.0823781i
\(466\) 36.2859 62.8490i 0.0778667 0.134869i
\(467\) −428.655 114.858i −0.917892 0.245948i −0.231208 0.972904i \(-0.574268\pi\)
−0.686684 + 0.726956i \(0.740934\pi\)
\(468\) −58.3419 58.3419i −0.124662 0.124662i
\(469\) −353.377 + 692.185i −0.753470 + 1.47587i
\(470\) 447.980 837.041i 0.953150 1.78094i
\(471\) −57.6080 99.7800i −0.122310 0.211847i
\(472\) −50.2500 187.535i −0.106462 0.397321i
\(473\) 849.829 227.711i 1.79668 0.481419i
\(474\) 600.453 346.672i 1.26678 0.731375i
\(475\) 110.008 73.3355i 0.231595 0.154391i
\(476\) 283.825 183.998i 0.596270 0.386551i
\(477\) −85.3929 + 85.3929i −0.179021 + 0.179021i
\(478\) 39.1894 146.257i 0.0819862 0.305977i
\(479\) −190.500 109.985i −0.397703 0.229614i 0.287789 0.957694i \(-0.407080\pi\)
−0.685492 + 0.728080i \(0.740413\pi\)
\(480\) −332.717 + 206.652i −0.693161 + 0.430524i
\(481\) −126.415 218.957i −0.262816 0.455211i
\(482\) 246.426 246.426i 0.511257 0.511257i
\(483\) 62.1469 68.9112i 0.128669 0.142673i
\(484\) 292.217i 0.603755i
\(485\) −211.021 197.853i −0.435095 0.407945i
\(486\) −23.2925 + 40.3438i −0.0479270 + 0.0830120i
\(487\) −100.187 373.904i −0.205723 0.767770i −0.989228 0.146384i \(-0.953237\pi\)
0.783504 0.621386i \(-0.213430\pi\)
\(488\) 56.8016 211.987i 0.116397 0.434399i
\(489\) 101.244i 0.207044i
\(490\) −726.318 92.3518i −1.48228 0.188473i
\(491\) 285.045 0.580539 0.290269 0.956945i \(-0.406255\pi\)
0.290269 + 0.956945i \(0.406255\pi\)
\(492\) −477.880 128.048i −0.971301 0.260259i
\(493\) −347.583 + 93.1347i −0.705037 + 0.188914i
\(494\) 76.3423 + 44.0763i 0.154539 + 0.0892232i
\(495\) 201.290 6.48235i 0.406646 0.0130957i
\(496\) 221.764 0.447106
\(497\) −631.484 569.498i −1.27059 1.14587i
\(498\) −516.005 516.005i −1.03615 1.03615i
\(499\) 439.080 253.503i 0.879920 0.508022i 0.00928793 0.999957i \(-0.497044\pi\)
0.870632 + 0.491935i \(0.163710\pi\)
\(500\) 255.263 560.995i 0.510527 1.12199i
\(501\) 113.927 197.328i 0.227400 0.393868i
\(502\) 925.530 + 247.995i 1.84368 + 0.494014i
\(503\) 261.451 + 261.451i 0.519784 + 0.519784i 0.917506 0.397722i \(-0.130199\pi\)
−0.397722 + 0.917506i \(0.630199\pi\)
\(504\) 31.7731 + 49.0113i 0.0630418 + 0.0972446i
\(505\) 301.186 + 161.193i 0.596408 + 0.319195i
\(506\) 153.545 + 265.948i 0.303449 + 0.525589i
\(507\) 61.8135 + 230.691i 0.121920 + 0.455012i
\(508\) −141.974 + 38.0419i −0.279477 + 0.0748856i
\(509\) 9.46947 5.46720i 0.0186041 0.0107411i −0.490669 0.871346i \(-0.663248\pi\)
0.509273 + 0.860605i \(0.329914\pi\)
\(510\) −242.748 + 73.4958i −0.475976 + 0.144109i
\(511\) 30.3436 + 15.4911i 0.0593808 + 0.0303153i
\(512\) −454.686 + 454.686i −0.888059 + 0.888059i
\(513\) 7.11223 26.5432i 0.0138640 0.0517411i
\(514\) −514.104 296.818i −1.00020 0.577467i
\(515\) 617.777 + 144.392i 1.19957 + 0.280373i
\(516\) −279.816 484.656i −0.542280 0.939256i
\(517\) −603.209 + 603.209i −1.16675 + 1.16675i
\(518\) 292.298 + 902.033i 0.564282 + 1.74138i
\(519\) 419.428i 0.808146i
\(520\) 77.5302 2.49679i 0.149096 0.00480152i
\(521\) 71.2494 123.408i 0.136755 0.236867i −0.789511 0.613736i \(-0.789666\pi\)
0.926267 + 0.376869i \(0.122999\pi\)
\(522\) −85.2018 317.977i −0.163222 0.609152i
\(523\) 8.25954 30.8250i 0.0157926 0.0589389i −0.957580 0.288168i \(-0.906954\pi\)
0.973372 + 0.229229i \(0.0736205\pi\)
\(524\) 617.416i 1.17827i
\(525\) 278.271 + 120.167i 0.530040 + 0.228890i
\(526\) −47.4149 −0.0901424
\(527\) 183.968 + 49.2942i 0.349086 + 0.0935374i
\(528\) 256.318 68.6802i 0.485451 0.130076i
\(529\) 407.397 + 235.211i 0.770127 + 0.444633i
\(530\) −19.3604 601.179i −0.0365291 1.13430i
\(531\) −209.411 −0.394371
\(532\) −135.550 122.244i −0.254793 0.229783i
\(533\) −228.483 228.483i −0.428673 0.428673i
\(534\) 106.442 61.4545i 0.199330 0.115083i
\(535\) −69.0672 + 295.502i −0.129098 + 0.552341i
\(536\) −154.401 + 267.431i −0.288062 + 0.498938i
\(537\) −442.372 118.533i −0.823784 0.220732i
\(538\) −219.346 219.346i −0.407706 0.407706i
\(539\) 600.585 + 268.539i 1.11426 + 0.498218i
\(540\) −37.1214 122.607i −0.0687433 0.227051i
\(541\) −86.8285 150.391i −0.160496 0.277988i 0.774551 0.632512i \(-0.217976\pi\)
−0.935047 + 0.354524i \(0.884643\pi\)
\(542\) 121.522 + 453.526i 0.224210 + 0.836764i
\(543\) −478.521 + 128.219i −0.881253 + 0.236131i
\(544\) −383.838 + 221.609i −0.705584 + 0.407369i
\(545\) −50.8291 + 94.9729i −0.0932643 + 0.174262i
\(546\) 10.4171 + 201.831i 0.0190789 + 0.369654i
\(547\) 95.8716 95.8716i 0.175268 0.175268i −0.614021 0.789289i \(-0.710449\pi\)
0.789289 + 0.614021i \(0.210449\pi\)
\(548\) 46.7602 174.511i 0.0853289 0.318452i
\(549\) −205.000 118.357i −0.373407 0.215586i
\(550\) −662.183 + 753.457i −1.20397 + 1.36992i
\(551\) 97.0925 + 168.169i 0.176211 + 0.305207i
\(552\) 26.0721 26.0721i 0.0472320 0.0472320i
\(553\) −917.009 195.676i −1.65824 0.353845i
\(554\) 624.904i 1.12799i
\(555\) −12.6351 392.346i −0.0227660 0.706929i
\(556\) −208.690 + 361.462i −0.375342 + 0.650112i
\(557\) 12.5270 + 46.7512i 0.0224900 + 0.0839340i 0.976259 0.216608i \(-0.0694992\pi\)
−0.953769 + 0.300542i \(0.902833\pi\)
\(558\) −45.0955 + 168.299i −0.0808163 + 0.301611i
\(559\) 365.508i 0.653860i
\(560\) 393.068 + 70.7304i 0.701907 + 0.126304i
\(561\) 227.899 0.406238
\(562\) 1313.14 + 351.855i 2.33655 + 0.626076i
\(563\) 272.294 72.9609i 0.483648 0.129593i −0.00875281 0.999962i \(-0.502786\pi\)
0.492401 + 0.870369i \(0.336119\pi\)
\(564\) 469.925 + 271.312i 0.833201 + 0.481049i
\(565\) −59.9460 + 63.9355i −0.106099 + 0.113160i
\(566\) 306.797 0.542045
\(567\) 59.9320 19.4206i 0.105700 0.0342514i
\(568\) −238.918 238.918i −0.420629 0.420629i
\(569\) −466.721 + 269.461i −0.820247 + 0.473570i −0.850502 0.525972i \(-0.823702\pi\)
0.0302544 + 0.999542i \(0.490368\pi\)
\(570\) 72.2137 + 116.267i 0.126691 + 0.203977i
\(571\) 150.339 260.394i 0.263290 0.456032i −0.703824 0.710374i \(-0.748526\pi\)
0.967114 + 0.254342i \(0.0818590\pi\)
\(572\) −356.676 95.5709i −0.623559 0.167082i
\(573\) −93.3347 93.3347i −0.162888 0.162888i
\(574\) 659.210 + 1016.86i 1.14845 + 1.77153i
\(575\) 37.5284 187.625i 0.0652668 0.326304i
\(576\) −134.268 232.559i −0.233104 0.403748i
\(577\) 72.3090 + 269.861i 0.125319 + 0.467697i 0.999851 0.0172714i \(-0.00549794\pi\)
−0.874532 + 0.484968i \(0.838831\pi\)
\(578\) 556.998 149.247i 0.963664 0.258213i
\(579\) 367.396 212.116i 0.634535 0.366349i
\(580\) 798.132 + 427.156i 1.37609 + 0.736477i
\(581\) 50.8680 + 985.565i 0.0875524 + 1.69633i
\(582\) 211.748 211.748i 0.363828 0.363828i
\(583\) −139.884 + 522.053i −0.239938 + 0.895460i
\(584\) 11.7235 + 6.76855i 0.0200744 + 0.0115900i
\(585\) 19.0422 81.4714i 0.0325507 0.139267i
\(586\) 216.271 + 374.592i 0.369062 + 0.639235i
\(587\) −210.055 + 210.055i −0.357845 + 0.357845i −0.863018 0.505173i \(-0.831429\pi\)
0.505173 + 0.863018i \(0.331429\pi\)
\(588\) 66.1187 413.216i 0.112447 0.702749i
\(589\) 102.778i 0.174496i
\(590\) 713.403 760.881i 1.20916 1.28963i
\(591\) −166.660 + 288.664i −0.281997 + 0.488434i
\(592\) −133.869 499.605i −0.226129 0.843927i
\(593\) −271.762 + 1014.23i −0.458284 + 1.71034i 0.219966 + 0.975508i \(0.429405\pi\)
−0.678250 + 0.734831i \(0.737261\pi\)
\(594\) 208.488i 0.350989i
\(595\) 310.354 + 146.047i 0.521603 + 0.245458i
\(596\) 160.892 0.269953
\(597\) −208.424 55.8470i −0.349119 0.0935461i
\(598\) 123.231 33.0196i 0.206071 0.0552167i
\(599\) −516.500 298.201i −0.862270 0.497832i 0.00250190 0.999997i \(-0.499204\pi\)
−0.864772 + 0.502165i \(0.832537\pi\)
\(600\) 107.961 + 53.3831i 0.179934 + 0.0889719i
\(601\) −480.552 −0.799588 −0.399794 0.916605i \(-0.630918\pi\)
−0.399794 + 0.916605i \(0.630918\pi\)
\(602\) −286.068 + 1340.62i −0.475196 + 2.22694i
\(603\) 235.519 + 235.519i 0.390578 + 0.390578i
\(604\) 666.528 384.820i 1.10352 0.637119i
\(605\) 251.722 156.345i 0.416069 0.258421i
\(606\) −176.821 + 306.262i −0.291783 + 0.505383i
\(607\) 822.130 + 220.289i 1.35441 + 0.362914i 0.861762 0.507312i \(-0.169361\pi\)
0.492652 + 0.870226i \(0.336028\pi\)
\(608\) 169.123 + 169.123i 0.278163 + 0.278163i
\(609\) −202.427 + 396.508i −0.332393 + 0.651081i
\(610\) 1128.42 341.647i 1.84987 0.560077i
\(611\) 177.199 + 306.918i 0.290015 + 0.502320i
\(612\) −37.5193 140.024i −0.0613060 0.228797i
\(613\) 1030.27 276.060i 1.68070 0.450343i 0.712737 0.701431i \(-0.247455\pi\)
0.967964 + 0.251089i \(0.0807885\pi\)
\(614\) 106.874 61.7035i 0.174061 0.100494i
\(615\) −145.377 480.164i −0.236386 0.780754i
\(616\) 232.820 + 118.860i 0.377955 + 0.192955i
\(617\) −270.729 + 270.729i −0.438783 + 0.438783i −0.891602 0.452819i \(-0.850418\pi\)
0.452819 + 0.891602i \(0.350418\pi\)
\(618\) −169.986 + 634.395i −0.275057 + 1.02653i
\(619\) 136.247 + 78.6625i 0.220109 + 0.127080i 0.606001 0.795464i \(-0.292773\pi\)
−0.385892 + 0.922544i \(0.626106\pi\)
\(620\) −252.796 407.012i −0.407736 0.656471i
\(621\) −19.8847 34.4414i −0.0320205 0.0554611i
\(622\) −849.859 + 849.859i −1.36633 + 1.36633i
\(623\) −162.558 34.6875i −0.260928 0.0556782i
\(624\) 110.241i 0.176669i
\(625\) 619.825 80.2602i 0.991720 0.128416i
\(626\) 428.805 742.712i 0.684992 1.18644i
\(627\) −31.8302 118.792i −0.0507659 0.189461i
\(628\) −84.8905 + 316.816i −0.135176 + 0.504483i
\(629\) 444.212i 0.706219i
\(630\) −133.608 + 283.919i −0.212076 + 0.450666i
\(631\) −131.406 −0.208250 −0.104125 0.994564i \(-0.533204\pi\)
−0.104125 + 0.994564i \(0.533204\pi\)
\(632\) −359.874 96.4279i −0.569421 0.152576i
\(633\) 42.7572 11.4568i 0.0675470 0.0180992i
\(634\) −900.060 519.650i −1.41965 0.819637i
\(635\) −108.730 101.946i −0.171229 0.160545i
\(636\) 343.785 0.540542
\(637\) 172.338 212.131i 0.270546 0.333016i
\(638\) −1041.77 1041.77i −1.63287 1.63287i
\(639\) −315.612 + 182.219i −0.493915 + 0.285162i
\(640\) 421.613 + 98.5428i 0.658770 + 0.153973i
\(641\) −128.958 + 223.362i −0.201182 + 0.348458i −0.948910 0.315548i \(-0.897812\pi\)
0.747727 + 0.664006i \(0.231145\pi\)
\(642\) −303.451 81.3094i −0.472665 0.126650i
\(643\) 778.940 + 778.940i 1.21142 + 1.21142i 0.970561 + 0.240854i \(0.0774274\pi\)
0.240854 + 0.970561i \(0.422573\pi\)
\(644\) −263.814 + 13.6162i −0.409650 + 0.0211432i
\(645\) 267.782 500.345i 0.415166 0.775728i
\(646\) 77.4404 + 134.131i 0.119877 + 0.207633i
\(647\) 98.6974 + 368.344i 0.152546 + 0.569310i 0.999303 + 0.0373301i \(0.0118853\pi\)
−0.846757 + 0.531980i \(0.821448\pi\)
\(648\) 24.1795 6.47889i 0.0373141 0.00999829i
\(649\) −811.641 + 468.601i −1.25060 + 0.722035i
\(650\) 231.150 + 346.738i 0.355615 + 0.533444i
\(651\) 197.718 128.177i 0.303714 0.196892i
\(652\) −203.801 + 203.801i −0.312578 + 0.312578i
\(653\) 291.908 1089.41i 0.447026 1.66832i −0.263506 0.964658i \(-0.584879\pi\)
0.710532 0.703665i \(-0.248454\pi\)
\(654\) −96.5735 55.7567i −0.147666 0.0852550i
\(655\) 531.854 330.336i 0.811990 0.504329i
\(656\) −330.517 572.472i −0.503836 0.872670i
\(657\) 10.3245 10.3245i 0.0157146 0.0157146i
\(658\) −409.723 1264.41i −0.622679 1.92159i
\(659\) 737.560i 1.11921i −0.828759 0.559605i \(-0.810953\pi\)
0.828759 0.559605i \(-0.189047\pi\)
\(660\) −418.236 392.139i −0.633691 0.594150i
\(661\) −166.939 + 289.147i −0.252555 + 0.437439i −0.964229 0.265072i \(-0.914604\pi\)
0.711673 + 0.702511i \(0.247938\pi\)
\(662\) −56.0259 209.092i −0.0846313 0.315848i
\(663\) 24.5046 91.4524i 0.0369602 0.137937i
\(664\) 392.127i 0.590553i
\(665\) 32.7804 182.170i 0.0492939 0.273939i
\(666\) 406.376 0.610174
\(667\) 271.456 + 72.7365i 0.406981 + 0.109050i
\(668\) −626.543 + 167.882i −0.937939 + 0.251320i
\(669\) 125.113 + 72.2341i 0.187015 + 0.107973i
\(670\) −1658.09 + 53.3972i −2.47476 + 0.0796973i
\(671\) −1059.40 −1.57883
\(672\) −114.431 + 536.266i −0.170284 + 0.798014i
\(673\) −183.139 183.139i −0.272123 0.272123i 0.557831 0.829954i \(-0.311634\pi\)
−0.829954 + 0.557831i \(0.811634\pi\)
\(674\) −936.016 + 540.409i −1.38875 + 0.801794i
\(675\) 85.7554 97.5757i 0.127045 0.144557i
\(676\) 339.943 588.799i 0.502875 0.871005i
\(677\) −806.946 216.220i −1.19194 0.319380i −0.392290 0.919842i \(-0.628317\pi\)
−0.799654 + 0.600461i \(0.794984\pi\)
\(678\) −64.1557 64.1557i −0.0946249 0.0946249i
\(679\) −404.436 + 20.8742i −0.595635 + 0.0307425i
\(680\) 120.161 + 64.3098i 0.176708 + 0.0945733i
\(681\) −356.788 617.975i −0.523918 0.907452i
\(682\) 201.821 + 753.208i 0.295926 + 1.10441i
\(683\) −909.178 + 243.613i −1.33115 + 0.356681i −0.853145 0.521674i \(-0.825308\pi\)
−0.478008 + 0.878355i \(0.658641\pi\)
\(684\) −67.7469 + 39.1137i −0.0990452 + 0.0571838i
\(685\) 175.346 53.0887i 0.255979 0.0775017i
\(686\) −798.131 + 643.177i −1.16346 + 0.937576i
\(687\) 460.424 460.424i 0.670195 0.670195i
\(688\) 193.530 722.263i 0.281293 1.04980i
\(689\) 194.451 + 112.266i 0.282222 + 0.162941i
\(690\) 192.882 + 45.0820i 0.279539 + 0.0653362i
\(691\) −409.191 708.740i −0.592172 1.02567i −0.993939 0.109931i \(-0.964937\pi\)
0.401767 0.915742i \(-0.368396\pi\)
\(692\) 844.291 844.291i 1.22007 1.22007i
\(693\) 188.828 209.381i 0.272480 0.302137i
\(694\) 862.487i 1.24278i
\(695\) −423.026 + 13.6232i −0.608670 + 0.0196017i
\(696\) −88.4465 + 153.194i −0.127078 + 0.220106i
\(697\) −146.936 548.371i −0.210812 0.786760i
\(698\) 371.643 1386.99i 0.532439 1.98709i
\(699\) 42.0616i 0.0601739i
\(700\) −318.257 802.040i −0.454652 1.14577i
\(701\) 480.047 0.684803 0.342402 0.939554i \(-0.388760\pi\)
0.342402 + 0.939554i \(0.388760\pi\)
\(702\) 83.6629 + 22.4174i 0.119178 + 0.0319336i
\(703\) −231.545 + 62.0422i −0.329366 + 0.0882535i
\(704\) −1040.80 600.905i −1.47841 0.853558i
\(705\) 17.7110 + 549.962i 0.0251220 + 0.780088i
\(706\) −288.430 −0.408541
\(707\) 454.962 147.427i 0.643510 0.208525i
\(708\) 421.535 + 421.535i 0.595389 + 0.595389i
\(709\) −1211.17 + 699.271i −1.70828 + 0.986278i −0.771597 + 0.636112i \(0.780542\pi\)
−0.936688 + 0.350166i \(0.886125\pi\)
\(710\) 413.120 1767.52i 0.581859 2.48947i
\(711\) −200.926 + 348.014i −0.282596 + 0.489471i
\(712\) −63.7948 17.0938i −0.0895994 0.0240081i
\(713\) −105.178 105.178i −0.147515 0.147515i
\(714\) −161.455 + 316.253i −0.226127 + 0.442931i
\(715\) −108.505 358.380i −0.151756 0.501231i
\(716\) 651.874 + 1129.08i 0.910438 + 1.57693i
\(717\) 22.7136 + 84.7684i 0.0316787 + 0.118226i
\(718\) 936.168 250.845i 1.30385 0.349367i
\(719\) 742.957 428.946i 1.03332 0.596587i 0.115386 0.993321i \(-0.463190\pi\)
0.917934 + 0.396734i \(0.129856\pi\)
\(720\) 80.7661 150.910i 0.112175 0.209597i
\(721\) 745.289 483.157i 1.03369 0.670120i
\(722\) −703.744 + 703.744i −0.974715 + 0.974715i
\(723\) −52.2775 + 195.102i −0.0723063 + 0.269851i
\(724\) 1221.34 + 705.142i 1.68694 + 0.973953i
\(725\) 59.0635 + 916.067i 0.0814669 + 1.26354i
\(726\) 153.380 + 265.663i 0.211268 + 0.365926i
\(727\) 8.47406 8.47406i 0.0116562 0.0116562i −0.701255 0.712911i \(-0.747376\pi\)
0.712911 + 0.701255i \(0.247376\pi\)
\(728\) 72.7305 80.6468i 0.0999046 0.110779i
\(729\) 27.0000i 0.0370370i
\(730\) 2.34079 + 72.6862i 0.00320656 + 0.0995701i
\(731\) 321.092 556.147i 0.439250 0.760804i
\(732\) 174.409 + 650.905i 0.238264 + 0.889214i
\(733\) −288.580 + 1076.99i −0.393697 + 1.46930i 0.430292 + 0.902690i \(0.358411\pi\)
−0.823989 + 0.566606i \(0.808256\pi\)
\(734\) 771.050i 1.05048i
\(735\) 391.328 164.127i 0.532419 0.223302i
\(736\) 346.145 0.470306
\(737\) 1439.85 + 385.807i 1.95367 + 0.523483i
\(738\) 501.663 134.420i 0.679761 0.182141i
\(739\) −635.156 366.708i −0.859481 0.496221i 0.00435760 0.999991i \(-0.498613\pi\)
−0.863838 + 0.503769i \(0.831946\pi\)
\(740\) −764.341 + 815.209i −1.03289 + 1.10163i
\(741\) −51.0919 −0.0689500
\(742\) −625.345 563.962i −0.842784 0.760056i
\(743\) −342.256 342.256i −0.460641 0.460641i 0.438225 0.898865i \(-0.355607\pi\)
−0.898865 + 0.438225i \(0.855607\pi\)
\(744\) 81.0822 46.8128i 0.108981 0.0629205i
\(745\) 86.0820 + 138.595i 0.115546 + 0.186034i
\(746\) 733.284 1270.08i 0.982954 1.70253i
\(747\) 408.536 + 109.467i 0.546902 + 0.146542i
\(748\) −458.752 458.752i −0.613304 0.613304i
\(749\) 231.109 + 356.495i 0.308557 + 0.475961i
\(750\) 62.3908 + 643.999i 0.0831878 + 0.858665i
\(751\) −217.704 377.075i −0.289886 0.502097i 0.683897 0.729579i \(-0.260284\pi\)
−0.973782 + 0.227482i \(0.926951\pi\)
\(752\) 187.648 + 700.310i 0.249531 + 0.931264i
\(753\) −536.424 + 143.734i −0.712382 + 0.190882i
\(754\) −530.061 + 306.031i −0.702999 + 0.405877i
\(755\) 688.103 + 368.270i 0.911395 + 0.487774i
\(756\) −159.733 81.5477i −0.211287 0.107867i
\(757\) 136.675 136.675i 0.180548 0.180548i −0.611047 0.791595i \(-0.709251\pi\)
0.791595 + 0.611047i \(0.209251\pi\)
\(758\) −137.523 + 513.243i −0.181429 + 0.677101i
\(759\) −154.140 88.9926i −0.203083 0.117250i
\(760\) 16.7387 71.6159i 0.0220246 0.0942315i
\(761\) 191.516 + 331.716i 0.251664 + 0.435895i 0.963984 0.265960i \(-0.0856889\pi\)
−0.712320 + 0.701855i \(0.752356\pi\)
\(762\) 109.105 109.105i 0.143182 0.143182i
\(763\) 46.4882 + 143.463i 0.0609282 + 0.188025i
\(764\) 375.758i 0.491829i
\(765\) 100.545 107.237i 0.131432 0.140179i
\(766\) −688.674 + 1192.82i −0.899052 + 1.55720i
\(767\) 100.772 + 376.085i 0.131384 + 0.490332i
\(768\) 44.4987 166.072i 0.0579411 0.216239i
\(769\) 210.497i 0.273729i −0.990590 0.136864i \(-0.956298\pi\)
0.990590 0.136864i \(-0.0437024\pi\)
\(770\) 117.489 + 1399.40i 0.152583 + 1.81740i
\(771\) 344.063 0.446255
\(772\) −1166.53 312.571i −1.51105 0.404885i
\(773\) −415.715 + 111.390i −0.537794 + 0.144101i −0.517485 0.855692i \(-0.673132\pi\)
−0.0203089 + 0.999794i \(0.506465\pi\)
\(774\) 508.777 + 293.743i 0.657335 + 0.379512i
\(775\) 215.355 435.527i 0.277877 0.561971i
\(776\) −160.913 −0.207362
\(777\) −408.118 368.057i −0.525248 0.473690i
\(778\) 630.931 + 630.931i 0.810965 + 0.810965i
\(779\) −265.315 + 153.180i −0.340584 + 0.196637i
\(780\) −202.330 + 125.667i −0.259397 + 0.161112i
\(781\) −815.505 + 1412.50i −1.04418 + 1.80857i
\(782\) 216.512 + 58.0142i 0.276869 + 0.0741869i
\(783\) 134.913 + 134.913i 0.172303 + 0.172303i
\(784\) 452.869 327.933i 0.577639 0.418282i
\(785\) −318.330 + 96.3794i −0.405516 + 0.122776i
\(786\) 324.072 + 561.309i 0.412305 + 0.714133i
\(787\) −190.107 709.488i −0.241559 0.901510i −0.975082 0.221845i \(-0.928792\pi\)
0.733523 0.679665i \(-0.237875\pi\)
\(788\) 916.549 245.589i 1.16313 0.311661i
\(789\) 23.7992 13.7405i 0.0301638 0.0174151i
\(790\) −579.989 1915.63i −0.734163 2.42485i
\(791\) 6.32449 + 122.537i 0.00799556 + 0.154914i
\(792\) 79.2179 79.2179i 0.100023 0.100023i
\(793\) −113.910 + 425.119i −0.143645 + 0.536089i
\(794\) 232.607 + 134.296i 0.292956 + 0.169138i
\(795\) 183.935 + 296.143i 0.231365 + 0.372506i
\(796\) 307.131 + 531.966i 0.385843 + 0.668299i
\(797\) 657.078 657.078i 0.824439 0.824439i −0.162302 0.986741i \(-0.551892\pi\)
0.986741 + 0.162302i \(0.0518919\pi\)
\(798\) 187.396 + 39.9875i 0.234832 + 0.0501097i
\(799\) 622.665i 0.779305i
\(800\) 362.298 + 1071.04i 0.452872 + 1.33880i
\(801\) −35.6181 + 61.6924i −0.0444671 + 0.0770192i
\(802\) −75.2765 280.936i −0.0938610 0.350294i
\(803\) 16.9128 63.1194i 0.0210620 0.0786045i
\(804\) 948.178i 1.17933i
\(805\) −152.878 219.970i −0.189910 0.273254i
\(806\) 323.951 0.401925
\(807\) 173.662 + 46.5327i 0.215195 + 0.0576613i
\(808\) 183.554 49.1832i 0.227171 0.0608703i
\(809\) 366.207 + 211.430i 0.452666 + 0.261347i 0.708956 0.705253i \(-0.249167\pi\)
−0.256289 + 0.966600i \(0.582500\pi\)
\(810\) 98.1028 + 91.9813i 0.121115 + 0.113557i
\(811\) 549.264 0.677268 0.338634 0.940918i \(-0.390035\pi\)
0.338634 + 0.940918i \(0.390035\pi\)
\(812\) 1205.63 390.677i 1.48477 0.481129i
\(813\) −192.425 192.425i −0.236685 0.236685i
\(814\) 1575.04 909.352i 1.93494 1.11714i
\(815\) −284.597 66.5184i −0.349199 0.0816177i
\(816\) 96.8449 167.740i 0.118683 0.205564i
\(817\) −334.737 89.6925i −0.409715 0.109783i
\(818\) 567.335 + 567.335i 0.693564 + 0.693564i
\(819\) −63.7179 98.2874i −0.0777996 0.120009i
\(820\) −673.911 + 1259.19i −0.821843 + 1.53560i
\(821\) −97.9130 169.590i −0.119261 0.206566i 0.800214 0.599714i \(-0.204719\pi\)
−0.919475 + 0.393149i \(0.871386\pi\)
\(822\) 49.0874 + 183.197i 0.0597170 + 0.222867i
\(823\) −1419.82 + 380.440i −1.72518 + 0.462260i −0.979063 0.203559i \(-0.934749\pi\)
−0.746114 + 0.665818i \(0.768083\pi\)
\(824\) 305.636 176.459i 0.370917 0.214149i
\(825\) 114.027 570.083i 0.138215 0.691009i
\(826\) −75.2663 1458.28i −0.0911214 1.76547i
\(827\) −645.663 + 645.663i −0.780729 + 0.780729i −0.979954 0.199225i \(-0.936158\pi\)
0.199225 + 0.979954i \(0.436158\pi\)
\(828\) −29.3019 + 109.356i −0.0353888 + 0.132073i
\(829\) 946.305 + 546.349i 1.14150 + 0.659046i 0.946802 0.321816i \(-0.104293\pi\)
0.194700 + 0.980863i \(0.437627\pi\)
\(830\) −1789.51 + 1111.47i −2.15603 + 1.33912i
\(831\) −181.093 313.662i −0.217921 0.377451i
\(832\) −353.044 + 353.044i −0.424332 + 0.424332i
\(833\) 448.578 171.378i 0.538510 0.205736i
\(834\) 438.153i 0.525364i
\(835\) −479.835 449.894i −0.574653 0.538796i
\(836\) −175.050 + 303.196i −0.209390 + 0.362675i
\(837\) −26.1367 97.5435i −0.0312266 0.116539i
\(838\) 399.001 1489.09i 0.476134 1.77696i
\(839\) 682.503i 0.813472i 0.913546 + 0.406736i \(0.133333\pi\)
−0.913546 + 0.406736i \(0.866667\pi\)
\(840\) 158.645 57.1131i 0.188864 0.0679917i
\(841\) −507.268 −0.603173
\(842\) −1357.38 363.710i −1.61210 0.431960i
\(843\) −761.077 + 203.930i −0.902820 + 0.241910i
\(844\) −109.131 63.0065i −0.129302 0.0746523i
\(845\) 689.083 22.1913i 0.815483 0.0262619i
\(846\) −569.629 −0.673320
\(847\) 86.5744 405.719i 0.102213 0.479007i
\(848\) 324.803 + 324.803i 0.383022 + 0.383022i
\(849\) −153.993 + 88.9077i −0.181381 + 0.104720i
\(850\) 47.1087 + 730.650i 0.0554220 + 0.859588i
\(851\) −173.461 + 300.443i −0.203832 + 0.353047i
\(852\) 1002.11 + 268.515i 1.17619 + 0.315158i
\(853\) 201.182 + 201.182i 0.235852 + 0.235852i 0.815130 0.579278i \(-0.196665\pi\)
−0.579278 + 0.815130i \(0.696665\pi\)
\(854\) 750.526 1470.11i 0.878836 1.72144i
\(855\) −69.9399 37.4315i −0.0818011 0.0437795i
\(856\) 84.4059 + 146.195i 0.0986050 + 0.170789i
\(857\) −337.813 1260.74i −0.394181 1.47110i −0.823171 0.567794i \(-0.807797\pi\)
0.428990 0.903309i \(-0.358870\pi\)
\(858\) 374.427 100.327i 0.436395 0.116932i
\(859\) 1064.26 614.453i 1.23896 0.715313i 0.270076 0.962839i \(-0.412951\pi\)
0.968881 + 0.247526i \(0.0796177\pi\)
\(860\) −1546.21 + 468.139i −1.79791 + 0.544347i
\(861\) −625.559 319.363i −0.726549 0.370921i
\(862\) −572.987 + 572.987i −0.664718 + 0.664718i
\(863\) −259.341 + 967.875i −0.300511 + 1.12152i 0.636229 + 0.771500i \(0.280493\pi\)
−0.936741 + 0.350024i \(0.886173\pi\)
\(864\) 203.518 + 117.501i 0.235553 + 0.135997i
\(865\) 1179.01 + 275.568i 1.36302 + 0.318575i
\(866\) −286.740 496.649i −0.331109 0.573498i
\(867\) −236.326 + 236.326i −0.272579 + 0.272579i
\(868\) −656.012 139.983i −0.755775 0.161271i
\(869\) 1798.46i 2.06957i
\(870\) −949.810 + 30.5878i −1.09174 + 0.0351584i
\(871\) 309.637 536.307i 0.355496 0.615737i
\(872\) 15.5089 + 57.8801i 0.0177855 + 0.0663762i
\(873\) −44.9208 + 167.647i −0.0514557 + 0.192035i
\(874\) 120.959i 0.138397i
\(875\) 520.615 703.267i 0.594989 0.803734i
\(876\) −41.5656 −0.0474494
\(877\) −330.906 88.6659i −0.377315 0.101101i 0.0651767 0.997874i \(-0.479239\pi\)
−0.442492 + 0.896772i \(0.645906\pi\)
\(878\) 1354.37 362.902i 1.54256 0.413328i
\(879\) −217.108 125.347i −0.246994 0.142602i
\(880\) −24.6565 765.631i −0.0280187 0.870035i
\(881\) 291.629 0.331021 0.165510 0.986208i \(-0.447073\pi\)
0.165510 + 0.986208i \(0.447073\pi\)
\(882\) 156.780 + 410.370i 0.177756 + 0.465272i
\(883\) 993.613 + 993.613i 1.12527 + 1.12527i 0.990936 + 0.134333i \(0.0428892\pi\)
0.134333 + 0.990936i \(0.457111\pi\)
\(884\) −233.417 + 134.763i −0.264046 + 0.152447i
\(885\) −137.585 + 588.652i −0.155463 + 0.665144i
\(886\) 459.543 795.952i 0.518672 0.898366i
\(887\) −88.2058 23.6347i −0.0994428 0.0266456i 0.208755 0.977968i \(-0.433059\pi\)
−0.308197 + 0.951322i \(0.599726\pi\)
\(888\) −154.408 154.408i −0.173883 0.173883i
\(889\) −208.389 + 10.7556i −0.234409 + 0.0120985i
\(890\) −102.815 339.584i −0.115522 0.381555i
\(891\) −60.4182 104.647i −0.0678094 0.117449i
\(892\) −106.443 397.251i −0.119331 0.445349i
\(893\) 324.563 86.9663i 0.363452 0.0973867i
\(894\) −146.271 + 84.4497i −0.163614 + 0.0944628i
\(895\) −623.838 + 1165.63i −0.697026 + 1.30238i
\(896\) 508.635 329.739i 0.567673 0.368012i
\(897\) −52.2850 + 52.2850i −0.0582888 + 0.0582888i
\(898\) −430.180 + 1605.45i −0.479043 + 1.78781i
\(899\) 618.004 + 356.805i 0.687435 + 0.396891i
\(900\) −369.038 + 23.7937i −0.410042 + 0.0264375i
\(901\) 197.248 + 341.643i 0.218921 + 0.379183i
\(902\) 1643.57 1643.57i 1.82214 1.82214i
\(903\) −244.913 755.804i −0.271222 0.836992i
\(904\) 48.7538i 0.0539312i
\(905\) 46.0312 + 1429.36i 0.0508632 + 1.57940i
\(906\) −403.972 + 699.700i −0.445885 + 0.772296i
\(907\) 13.3362 + 49.7713i 0.0147036 + 0.0548746i 0.972888 0.231277i \(-0.0742905\pi\)
−0.958184 + 0.286152i \(0.907624\pi\)
\(908\) −525.758 + 1962.16i −0.579029 + 2.16097i
\(909\) 204.965i 0.225484i
\(910\) 574.190 + 103.322i 0.630978 + 0.113541i
\(911\) 30.4579 0.0334334 0.0167167 0.999860i \(-0.494679\pi\)
0.0167167 + 0.999860i \(0.494679\pi\)
\(912\) −100.960 27.0523i −0.110702 0.0296626i
\(913\) 1828.37 489.910i 2.00260 0.536594i
\(914\) 1329.08 + 767.347i 1.45414 + 0.839548i
\(915\) −467.387 + 498.493i −0.510806 + 0.544801i
\(916\) −1853.63 −2.02361
\(917\) 182.920 857.228i 0.199476 0.934818i
\(918\) 107.606 + 107.606i 0.117218 + 0.117218i
\(919\) 408.961 236.114i 0.445007 0.256925i −0.260712 0.965417i \(-0.583957\pi\)
0.705719 + 0.708492i \(0.250624\pi\)
\(920\) −56.1588 90.4179i −0.0610422 0.0982803i
\(921\) −35.7625 + 61.9424i −0.0388300 + 0.0672556i
\(922\) −404.879 108.487i −0.439131 0.117665i
\(923\) 479.127 + 479.127i 0.519097 + 0.519097i
\(924\) −801.579 + 41.3719i −0.867510 + 0.0447748i
\(925\) −1111.18 222.257i −1.20128 0.240278i
\(926\) −930.991 1612.52i −1.00539 1.74139i
\(927\) −98.5211 367.686i −0.106280 0.396641i
\(928\) −1604.07 + 429.808i −1.72852 + 0.463155i
\(929\) 747.921 431.812i 0.805081 0.464814i −0.0401635 0.999193i \(-0.512788\pi\)
0.845245 + 0.534379i \(0.179455\pi\)
\(930\) 443.458 + 237.337i 0.476837 + 0.255201i
\(931\) −151.982 209.885i −0.163246 0.225440i
\(932\) 84.6681 84.6681i 0.0908456 0.0908456i
\(933\) 180.292 672.857i 0.193239 0.721176i
\(934\) −1148.52 663.098i −1.22968 0.709955i
\(935\) 149.732 640.623i 0.160141 0.685158i
\(936\) −23.2711 40.3067i −0.0248623 0.0430628i
\(937\) −543.193 + 543.193i −0.579715 + 0.579715i −0.934825 0.355110i \(-0.884443\pi\)
0.355110 + 0.934825i \(0.384443\pi\)
\(938\) −1555.44 + 1724.74i −1.65825 + 1.83874i
\(939\) 497.058i 0.529349i
\(940\) 1071.40 1142.70i 1.13979 1.21564i
\(941\) 215.568 373.375i 0.229084 0.396785i −0.728453 0.685096i \(-0.759760\pi\)
0.957537 + 0.288311i \(0.0930937\pi\)
\(942\) −89.1153 332.583i −0.0946023 0.353060i
\(943\) −114.754 + 428.268i −0.121690 + 0.454155i
\(944\) 796.521i 0.843772i
\(945\) −15.2153 181.228i −0.0161008 0.191775i
\(946\) 2629.24 2.77933
\(947\) −671.694 179.980i −0.709287 0.190053i −0.113900 0.993492i \(-0.536334\pi\)
−0.595387 + 0.803439i \(0.703001\pi\)
\(948\) 1104.99 296.082i 1.16560 0.312323i
\(949\) −23.5103 13.5737i −0.0247738 0.0143031i
\(950\) 374.270 126.604i 0.393969 0.133267i
\(951\) 602.363 0.633399
\(952\) 181.512 58.8177i 0.190664 0.0617833i
\(953\) −936.706 936.706i −0.982902 0.982902i 0.0169540 0.999856i \(-0.494603\pi\)
−0.999856 + 0.0169540i \(0.994603\pi\)
\(954\) −312.544 + 180.447i −0.327614 + 0.189148i
\(955\) −323.685 + 201.041i −0.338937 + 0.210515i
\(956\) 124.914 216.357i 0.130663 0.226315i
\(957\) 824.799 + 221.004i 0.861858 + 0.230934i
\(958\) −464.828 464.828i −0.485207 0.485207i
\(959\) 116.624 228.441i 0.121611 0.238207i
\(960\) −741.935 + 224.633i −0.772849 + 0.233992i
\(961\) 291.651 + 505.154i 0.303487 + 0.525654i
\(962\) −195.554 729.817i −0.203279 0.758646i
\(963\) 175.876 47.1257i 0.182633 0.0489364i
\(964\) 497.965 287.500i 0.516561 0.298237i
\(965\) −354.874 1172.11i −0.367745 1.21462i
\(966\) 232.694 150.851i 0.240884 0.156160i
\(967\) −580.505 + 580.505i −0.600315 + 0.600315i −0.940396 0.340081i \(-0.889545\pi\)
0.340081 + 0.940396i \(0.389545\pi\)
\(968\) 42.6633 159.221i 0.0440736 0.164485i
\(969\) −77.7402 44.8833i −0.0802273 0.0463192i
\(970\) −456.101 734.341i −0.470207 0.757053i
\(971\) 460.985 + 798.449i 0.474753 + 0.822296i 0.999582 0.0289117i \(-0.00920417\pi\)
−0.524829 + 0.851208i \(0.675871\pi\)
\(972\) −54.3499 + 54.3499i −0.0559155 + 0.0559155i
\(973\) −396.838 + 440.031i −0.407850 + 0.452242i
\(974\) 1156.80i 1.18768i
\(975\) −216.505 107.055i −0.222056 0.109800i
\(976\) −450.186 + 779.745i −0.461256 + 0.798919i
\(977\) 23.7849 + 88.7663i 0.0243448 + 0.0908560i 0.977029 0.213105i \(-0.0683575\pi\)
−0.952685 + 0.303961i \(0.901691\pi\)
\(978\) 78.3088 292.252i 0.0800704 0.298827i
\(979\) 318.812i 0.325651i
\(980\) −1118.11 457.345i −1.14093 0.466679i
\(981\) 64.6316 0.0658834
\(982\) 822.810 + 220.471i 0.837892 + 0.224513i
\(983\) −558.417 + 149.627i −0.568074 + 0.152215i −0.531413 0.847113i \(-0.678339\pi\)
−0.0366611 + 0.999328i \(0.511672\pi\)
\(984\) −241.689 139.539i −0.245619 0.141808i
\(985\) 701.936 + 658.136i 0.712625 + 0.668158i
\(986\) −1075.37 −1.09064
\(987\) 572.070 + 515.916i 0.579605 + 0.522711i
\(988\) 102.846 + 102.846i 0.104095 + 0.104095i
\(989\) −434.341 + 250.767i −0.439172 + 0.253556i
\(990\) 586.057 + 136.978i 0.591977 + 0.138362i
\(991\) −823.906 + 1427.05i −0.831389 + 1.44001i 0.0655482 + 0.997849i \(0.479120\pi\)
−0.896937 + 0.442158i \(0.854213\pi\)
\(992\) 848.998 + 227.488i 0.855844 + 0.229323i
\(993\) 88.7146 + 88.7146i 0.0893400 + 0.0893400i
\(994\) −1382.36 2132.34i −1.39070 2.14522i
\(995\) −293.922 + 549.186i −0.295399 + 0.551945i
\(996\) −602.013 1042.72i −0.604431 1.04690i
\(997\) −466.765 1741.99i −0.468170 1.74723i −0.646161 0.763201i \(-0.723627\pi\)
0.177991 0.984032i \(-0.443040\pi\)
\(998\) 1463.52 392.150i 1.46646 0.392936i
\(999\) −203.974 + 117.765i −0.204179 + 0.117883i
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 105.3.v.a.88.14 yes 64
3.2 odd 2 315.3.ca.b.298.3 64
5.2 odd 4 inner 105.3.v.a.67.3 yes 64
7.2 even 3 inner 105.3.v.a.58.3 yes 64
15.2 even 4 315.3.ca.b.172.14 64
21.2 odd 6 315.3.ca.b.163.14 64
35.2 odd 12 inner 105.3.v.a.37.14 64
105.2 even 12 315.3.ca.b.37.3 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.v.a.37.14 64 35.2 odd 12 inner
105.3.v.a.58.3 yes 64 7.2 even 3 inner
105.3.v.a.67.3 yes 64 5.2 odd 4 inner
105.3.v.a.88.14 yes 64 1.1 even 1 trivial
315.3.ca.b.37.3 64 105.2 even 12
315.3.ca.b.163.14 64 21.2 odd 6
315.3.ca.b.172.14 64 15.2 even 4
315.3.ca.b.298.3 64 3.2 odd 2