Properties

Label 189.2.e.d.109.1
Level $189$
Weight $2$
Character 189.109
Analytic conductor $1.509$
Analytic rank $0$
Dimension $4$
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] = [189,2,Mod(109,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 189.109
Dual form 189.2.e.d.163.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22474 - 2.12132i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(-0.500000 - 2.59808i) q^{7} +4.89898 q^{8} +O(q^{10})\) \(q+(-1.22474 - 2.12132i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-1.22474 - 2.12132i) q^{5} +(-0.500000 - 2.59808i) q^{7} +4.89898 q^{8} +(-3.00000 + 5.19615i) q^{10} +(-2.44949 + 4.24264i) q^{11} -4.00000 q^{13} +(-4.89898 + 4.24264i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(1.22474 - 2.12132i) q^{17} +(0.500000 + 0.866025i) q^{19} +9.79796 q^{20} +12.0000 q^{22} +(-1.22474 - 2.12132i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(4.89898 + 8.48528i) q^{26} +(10.0000 + 3.46410i) q^{28} -7.34847 q^{29} +(3.50000 - 6.06218i) q^{31} -6.00000 q^{34} +(-4.89898 + 4.24264i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(1.22474 - 2.12132i) q^{38} +(-6.00000 - 10.3923i) q^{40} +7.34847 q^{41} -1.00000 q^{43} +(-9.79796 - 16.9706i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-1.22474 - 2.12132i) q^{47} +(-6.50000 + 2.59808i) q^{49} +2.44949 q^{50} +(8.00000 - 13.8564i) q^{52} +(1.22474 - 2.12132i) q^{53} +12.0000 q^{55} +(-2.44949 - 12.7279i) q^{56} +(9.00000 + 15.5885i) q^{58} +(4.89898 - 8.48528i) q^{59} +(-2.50000 - 4.33013i) q^{61} -17.1464 q^{62} -8.00000 q^{64} +(4.89898 + 8.48528i) q^{65} +(-1.00000 + 1.73205i) q^{67} +(4.89898 + 8.48528i) q^{68} +(15.0000 + 5.19615i) q^{70} +(0.500000 - 0.866025i) q^{73} +(-9.79796 + 16.9706i) q^{74} -4.00000 q^{76} +(12.2474 + 4.24264i) q^{77} +(2.00000 + 3.46410i) q^{79} +(-4.89898 + 8.48528i) q^{80} +(-9.00000 - 15.5885i) q^{82} +14.6969 q^{83} -6.00000 q^{85} +(1.22474 + 2.12132i) q^{86} +(-12.0000 + 20.7846i) q^{88} +(-1.22474 - 2.12132i) q^{89} +(2.00000 + 10.3923i) q^{91} +9.79796 q^{92} +(-3.00000 + 5.19615i) q^{94} +(1.22474 - 2.12132i) q^{95} -1.00000 q^{97} +(13.4722 + 10.6066i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{4} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{4} - 2 q^{7} - 12 q^{10} - 16 q^{13} - 8 q^{16} + 2 q^{19} + 48 q^{22} - 2 q^{25} + 40 q^{28} + 14 q^{31} - 24 q^{34} - 16 q^{37} - 24 q^{40} - 4 q^{43} - 12 q^{46} - 26 q^{49} + 32 q^{52} + 48 q^{55} + 36 q^{58} - 10 q^{61} - 32 q^{64} - 4 q^{67} + 60 q^{70} + 2 q^{73} - 16 q^{76} + 8 q^{79} - 36 q^{82} - 24 q^{85} - 48 q^{88} + 8 q^{91} - 12 q^{94} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 2.12132i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −1.00000 + 1.73205i
\(5\) −1.22474 2.12132i −0.547723 0.948683i −0.998430 0.0560116i \(-0.982162\pi\)
0.450708 0.892672i \(-0.351172\pi\)
\(6\) 0 0
\(7\) −0.500000 2.59808i −0.188982 0.981981i
\(8\) 4.89898 1.73205
\(9\) 0 0
\(10\) −3.00000 + 5.19615i −0.948683 + 1.64317i
\(11\) −2.44949 + 4.24264i −0.738549 + 1.27920i 0.214600 + 0.976702i \(0.431155\pi\)
−0.953149 + 0.302502i \(0.902178\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −4.89898 + 4.24264i −1.30931 + 1.13389i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.500000 0.866025i
\(17\) 1.22474 2.12132i 0.297044 0.514496i −0.678414 0.734680i \(-0.737332\pi\)
0.975458 + 0.220184i \(0.0706658\pi\)
\(18\) 0 0
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 9.79796 2.19089
\(21\) 0 0
\(22\) 12.0000 2.55841
\(23\) −1.22474 2.12132i −0.255377 0.442326i 0.709621 0.704584i \(-0.248866\pi\)
−0.964998 + 0.262258i \(0.915533\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 4.89898 + 8.48528i 0.960769 + 1.66410i
\(27\) 0 0
\(28\) 10.0000 + 3.46410i 1.88982 + 0.654654i
\(29\) −7.34847 −1.36458 −0.682288 0.731083i \(-0.739015\pi\)
−0.682288 + 0.731083i \(0.739015\pi\)
\(30\) 0 0
\(31\) 3.50000 6.06218i 0.628619 1.08880i −0.359211 0.933257i \(-0.616954\pi\)
0.987829 0.155543i \(-0.0497126\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) −6.00000 −1.02899
\(35\) −4.89898 + 4.24264i −0.828079 + 0.717137i
\(36\) 0 0
\(37\) −4.00000 6.92820i −0.657596 1.13899i −0.981236 0.192809i \(-0.938240\pi\)
0.323640 0.946180i \(-0.395093\pi\)
\(38\) 1.22474 2.12132i 0.198680 0.344124i
\(39\) 0 0
\(40\) −6.00000 10.3923i −0.948683 1.64317i
\(41\) 7.34847 1.14764 0.573819 0.818982i \(-0.305461\pi\)
0.573819 + 0.818982i \(0.305461\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) −9.79796 16.9706i −1.47710 2.55841i
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) −1.22474 2.12132i −0.178647 0.309426i 0.762770 0.646670i \(-0.223839\pi\)
−0.941417 + 0.337243i \(0.890505\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 2.44949 0.346410
\(51\) 0 0
\(52\) 8.00000 13.8564i 1.10940 1.92154i
\(53\) 1.22474 2.12132i 0.168232 0.291386i −0.769567 0.638567i \(-0.779528\pi\)
0.937798 + 0.347181i \(0.112861\pi\)
\(54\) 0 0
\(55\) 12.0000 1.61808
\(56\) −2.44949 12.7279i −0.327327 1.70084i
\(57\) 0 0
\(58\) 9.00000 + 15.5885i 1.18176 + 2.04686i
\(59\) 4.89898 8.48528i 0.637793 1.10469i −0.348123 0.937449i \(-0.613181\pi\)
0.985916 0.167241i \(-0.0534857\pi\)
\(60\) 0 0
\(61\) −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i \(-0.270381\pi\)
−0.980507 + 0.196485i \(0.937047\pi\)
\(62\) −17.1464 −2.17760
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 4.89898 + 8.48528i 0.607644 + 1.05247i
\(66\) 0 0
\(67\) −1.00000 + 1.73205i −0.122169 + 0.211604i −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) 4.89898 + 8.48528i 0.594089 + 1.02899i
\(69\) 0 0
\(70\) 15.0000 + 5.19615i 1.79284 + 0.621059i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0.500000 0.866025i 0.0585206 0.101361i −0.835281 0.549823i \(-0.814695\pi\)
0.893801 + 0.448463i \(0.148028\pi\)
\(74\) −9.79796 + 16.9706i −1.13899 + 1.97279i
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) 12.2474 + 4.24264i 1.39573 + 0.483494i
\(78\) 0 0
\(79\) 2.00000 + 3.46410i 0.225018 + 0.389742i 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) −4.89898 + 8.48528i −0.547723 + 0.948683i
\(81\) 0 0
\(82\) −9.00000 15.5885i −0.993884 1.72146i
\(83\) 14.6969 1.61320 0.806599 0.591099i \(-0.201306\pi\)
0.806599 + 0.591099i \(0.201306\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) 1.22474 + 2.12132i 0.132068 + 0.228748i
\(87\) 0 0
\(88\) −12.0000 + 20.7846i −1.27920 + 2.21565i
\(89\) −1.22474 2.12132i −0.129823 0.224860i 0.793785 0.608198i \(-0.208107\pi\)
−0.923608 + 0.383339i \(0.874774\pi\)
\(90\) 0 0
\(91\) 2.00000 + 10.3923i 0.209657 + 1.08941i
\(92\) 9.79796 1.02151
\(93\) 0 0
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) 1.22474 2.12132i 0.125656 0.217643i
\(96\) 0 0
\(97\) −1.00000 −0.101535 −0.0507673 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) 13.4722 + 10.6066i 1.36090 + 1.07143i
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) −2.44949 + 4.24264i −0.243733 + 0.422159i −0.961775 0.273842i \(-0.911706\pi\)
0.718041 + 0.696000i \(0.245039\pi\)
\(102\) 0 0
\(103\) −1.00000 1.73205i −0.0985329 0.170664i 0.812545 0.582899i \(-0.198082\pi\)
−0.911078 + 0.412235i \(0.864748\pi\)
\(104\) −19.5959 −1.92154
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 9.79796 + 16.9706i 0.947204 + 1.64061i 0.751276 + 0.659988i \(0.229439\pi\)
0.195928 + 0.980618i \(0.437228\pi\)
\(108\) 0 0
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) −14.6969 25.4558i −1.40130 2.42712i
\(111\) 0 0
\(112\) −8.00000 + 6.92820i −0.755929 + 0.654654i
\(113\) −14.6969 −1.38257 −0.691286 0.722581i \(-0.742955\pi\)
−0.691286 + 0.722581i \(0.742955\pi\)
\(114\) 0 0
\(115\) −3.00000 + 5.19615i −0.279751 + 0.484544i
\(116\) 14.6969 25.4558i 1.36458 2.36352i
\(117\) 0 0
\(118\) −24.0000 −2.20938
\(119\) −6.12372 2.12132i −0.561361 0.194461i
\(120\) 0 0
\(121\) −6.50000 11.2583i −0.590909 1.02348i
\(122\) −6.12372 + 10.6066i −0.554416 + 0.960277i
\(123\) 0 0
\(124\) 14.0000 + 24.2487i 1.25724 + 2.17760i
\(125\) −9.79796 −0.876356
\(126\) 0 0
\(127\) 11.0000 0.976092 0.488046 0.872818i \(-0.337710\pi\)
0.488046 + 0.872818i \(0.337710\pi\)
\(128\) 9.79796 + 16.9706i 0.866025 + 1.50000i
\(129\) 0 0
\(130\) 12.0000 20.7846i 1.05247 1.82293i
\(131\) −1.22474 2.12132i −0.107006 0.185341i 0.807550 0.589799i \(-0.200793\pi\)
−0.914556 + 0.404459i \(0.867460\pi\)
\(132\) 0 0
\(133\) 2.00000 1.73205i 0.173422 0.150188i
\(134\) 4.89898 0.423207
\(135\) 0 0
\(136\) 6.00000 10.3923i 0.514496 0.891133i
\(137\) 8.57321 14.8492i 0.732459 1.26866i −0.223370 0.974734i \(-0.571706\pi\)
0.955829 0.293923i \(-0.0949608\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) −4.89898 25.4558i −0.414039 2.15141i
\(141\) 0 0
\(142\) 0 0
\(143\) 9.79796 16.9706i 0.819346 1.41915i
\(144\) 0 0
\(145\) 9.00000 + 15.5885i 0.747409 + 1.29455i
\(146\) −2.44949 −0.202721
\(147\) 0 0
\(148\) 32.0000 2.63038
\(149\) −1.22474 2.12132i −0.100335 0.173785i 0.811488 0.584370i \(-0.198658\pi\)
−0.911823 + 0.410584i \(0.865325\pi\)
\(150\) 0 0
\(151\) −2.50000 + 4.33013i −0.203447 + 0.352381i −0.949637 0.313353i \(-0.898548\pi\)
0.746190 + 0.665733i \(0.231881\pi\)
\(152\) 2.44949 + 4.24264i 0.198680 + 0.344124i
\(153\) 0 0
\(154\) −6.00000 31.1769i −0.483494 2.51231i
\(155\) −17.1464 −1.37723
\(156\) 0 0
\(157\) −10.0000 + 17.3205i −0.798087 + 1.38233i 0.122774 + 0.992435i \(0.460821\pi\)
−0.920860 + 0.389892i \(0.872512\pi\)
\(158\) 4.89898 8.48528i 0.389742 0.675053i
\(159\) 0 0
\(160\) 0 0
\(161\) −4.89898 + 4.24264i −0.386094 + 0.334367i
\(162\) 0 0
\(163\) 0.500000 + 0.866025i 0.0391630 + 0.0678323i 0.884943 0.465700i \(-0.154198\pi\)
−0.845780 + 0.533533i \(0.820864\pi\)
\(164\) −14.6969 + 25.4558i −1.14764 + 1.98777i
\(165\) 0 0
\(166\) −18.0000 31.1769i −1.39707 2.41980i
\(167\) −14.6969 −1.13728 −0.568642 0.822585i \(-0.692531\pi\)
−0.568642 + 0.822585i \(0.692531\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 7.34847 + 12.7279i 0.563602 + 0.976187i
\(171\) 0 0
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) −1.22474 2.12132i −0.0931156 0.161281i 0.815705 0.578468i \(-0.196349\pi\)
−0.908821 + 0.417187i \(0.863016\pi\)
\(174\) 0 0
\(175\) 2.50000 + 0.866025i 0.188982 + 0.0654654i
\(176\) 19.5959 1.47710
\(177\) 0 0
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) 1.22474 2.12132i 0.0915417 0.158555i −0.816618 0.577178i \(-0.804154\pi\)
0.908160 + 0.418623i \(0.137487\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 19.5959 16.9706i 1.45255 1.25794i
\(183\) 0 0
\(184\) −6.00000 10.3923i −0.442326 0.766131i
\(185\) −9.79796 + 16.9706i −0.720360 + 1.24770i
\(186\) 0 0
\(187\) 6.00000 + 10.3923i 0.438763 + 0.759961i
\(188\) 9.79796 0.714590
\(189\) 0 0
\(190\) −6.00000 −0.435286
\(191\) −1.22474 2.12132i −0.0886194 0.153493i 0.818308 0.574779i \(-0.194912\pi\)
−0.906928 + 0.421286i \(0.861579\pi\)
\(192\) 0 0
\(193\) −10.0000 + 17.3205i −0.719816 + 1.24676i 0.241257 + 0.970461i \(0.422440\pi\)
−0.961073 + 0.276296i \(0.910893\pi\)
\(194\) 1.22474 + 2.12132i 0.0879316 + 0.152302i
\(195\) 0 0
\(196\) 4.00000 27.7128i 0.285714 1.97949i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 9.50000 16.4545i 0.673437 1.16643i −0.303486 0.952836i \(-0.598151\pi\)
0.976923 0.213591i \(-0.0685161\pi\)
\(200\) −2.44949 + 4.24264i −0.173205 + 0.300000i
\(201\) 0 0
\(202\) 12.0000 0.844317
\(203\) 3.67423 + 19.0919i 0.257881 + 1.33999i
\(204\) 0 0
\(205\) −9.00000 15.5885i −0.628587 1.08875i
\(206\) −2.44949 + 4.24264i −0.170664 + 0.295599i
\(207\) 0 0
\(208\) 8.00000 + 13.8564i 0.554700 + 0.960769i
\(209\) −4.89898 −0.338869
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) 4.89898 + 8.48528i 0.336463 + 0.582772i
\(213\) 0 0
\(214\) 24.0000 41.5692i 1.64061 2.84161i
\(215\) 1.22474 + 2.12132i 0.0835269 + 0.144673i
\(216\) 0 0
\(217\) −17.5000 6.06218i −1.18798 0.411527i
\(218\) −2.44949 −0.165900
\(219\) 0 0
\(220\) −24.0000 + 41.5692i −1.61808 + 2.80260i
\(221\) −4.89898 + 8.48528i −0.329541 + 0.570782i
\(222\) 0 0
\(223\) 26.0000 1.74109 0.870544 0.492090i \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 18.0000 + 31.1769i 1.19734 + 2.07386i
\(227\) 8.57321 14.8492i 0.569024 0.985579i −0.427639 0.903950i \(-0.640654\pi\)
0.996663 0.0816290i \(-0.0260123\pi\)
\(228\) 0 0
\(229\) 3.50000 + 6.06218i 0.231287 + 0.400600i 0.958187 0.286143i \(-0.0923732\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 14.6969 0.969087
\(231\) 0 0
\(232\) −36.0000 −2.36352
\(233\) −1.22474 2.12132i −0.0802357 0.138972i 0.823115 0.567874i \(-0.192234\pi\)
−0.903351 + 0.428902i \(0.858901\pi\)
\(234\) 0 0
\(235\) −3.00000 + 5.19615i −0.195698 + 0.338960i
\(236\) 19.5959 + 33.9411i 1.27559 + 2.20938i
\(237\) 0 0
\(238\) 3.00000 + 15.5885i 0.194461 + 1.01045i
\(239\) 7.34847 0.475333 0.237666 0.971347i \(-0.423617\pi\)
0.237666 + 0.971347i \(0.423617\pi\)
\(240\) 0 0
\(241\) 6.50000 11.2583i 0.418702 0.725213i −0.577107 0.816668i \(-0.695819\pi\)
0.995809 + 0.0914555i \(0.0291519\pi\)
\(242\) −15.9217 + 27.5772i −1.02348 + 1.77273i
\(243\) 0 0
\(244\) 20.0000 1.28037
\(245\) 13.4722 + 10.6066i 0.860707 + 0.677631i
\(246\) 0 0
\(247\) −2.00000 3.46410i −0.127257 0.220416i
\(248\) 17.1464 29.6985i 1.08880 1.88586i
\(249\) 0 0
\(250\) 12.0000 + 20.7846i 0.758947 + 1.31453i
\(251\) −22.0454 −1.39149 −0.695747 0.718287i \(-0.744926\pi\)
−0.695747 + 0.718287i \(0.744926\pi\)
\(252\) 0 0
\(253\) 12.0000 0.754434
\(254\) −13.4722 23.3345i −0.845321 1.46414i
\(255\) 0 0
\(256\) 16.0000 27.7128i 1.00000 1.73205i
\(257\) −12.2474 21.2132i −0.763975 1.32324i −0.940787 0.338999i \(-0.889912\pi\)
0.176812 0.984245i \(-0.443422\pi\)
\(258\) 0 0
\(259\) −16.0000 + 13.8564i −0.994192 + 0.860995i
\(260\) −39.1918 −2.43057
\(261\) 0 0
\(262\) −3.00000 + 5.19615i −0.185341 + 0.321019i
\(263\) −2.44949 + 4.24264i −0.151042 + 0.261612i −0.931611 0.363457i \(-0.881596\pi\)
0.780569 + 0.625070i \(0.214930\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) −6.12372 2.12132i −0.375470 0.130066i
\(267\) 0 0
\(268\) −4.00000 6.92820i −0.244339 0.423207i
\(269\) 12.2474 21.2132i 0.746740 1.29339i −0.202637 0.979254i \(-0.564951\pi\)
0.949377 0.314138i \(-0.101715\pi\)
\(270\) 0 0
\(271\) 0.500000 + 0.866025i 0.0303728 + 0.0526073i 0.880812 0.473466i \(-0.156997\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) −9.79796 −0.594089
\(273\) 0 0
\(274\) −42.0000 −2.53731
\(275\) −2.44949 4.24264i −0.147710 0.255841i
\(276\) 0 0
\(277\) −11.5000 + 19.9186i −0.690968 + 1.19679i 0.280553 + 0.959839i \(0.409482\pi\)
−0.971521 + 0.236953i \(0.923851\pi\)
\(278\) −17.1464 29.6985i −1.02837 1.78120i
\(279\) 0 0
\(280\) −24.0000 + 20.7846i −1.43427 + 1.24212i
\(281\) 14.6969 0.876746 0.438373 0.898793i \(-0.355555\pi\)
0.438373 + 0.898793i \(0.355555\pi\)
\(282\) 0 0
\(283\) 12.5000 21.6506i 0.743048 1.28700i −0.208053 0.978117i \(-0.566713\pi\)
0.951101 0.308879i \(-0.0999539\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −48.0000 −2.83830
\(287\) −3.67423 19.0919i −0.216883 1.12696i
\(288\) 0 0
\(289\) 5.50000 + 9.52628i 0.323529 + 0.560369i
\(290\) 22.0454 38.1838i 1.29455 2.24223i
\(291\) 0 0
\(292\) 2.00000 + 3.46410i 0.117041 + 0.202721i
\(293\) 29.3939 1.71721 0.858604 0.512639i \(-0.171332\pi\)
0.858604 + 0.512639i \(0.171332\pi\)
\(294\) 0 0
\(295\) −24.0000 −1.39733
\(296\) −19.5959 33.9411i −1.13899 1.97279i
\(297\) 0 0
\(298\) −3.00000 + 5.19615i −0.173785 + 0.301005i
\(299\) 4.89898 + 8.48528i 0.283315 + 0.490716i
\(300\) 0 0
\(301\) 0.500000 + 2.59808i 0.0288195 + 0.149751i
\(302\) 12.2474 0.704761
\(303\) 0 0
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) −6.12372 + 10.6066i −0.350643 + 0.607332i
\(306\) 0 0
\(307\) −25.0000 −1.42683 −0.713413 0.700744i \(-0.752851\pi\)
−0.713413 + 0.700744i \(0.752851\pi\)
\(308\) −39.1918 + 33.9411i −2.23316 + 1.93398i
\(309\) 0 0
\(310\) 21.0000 + 36.3731i 1.19272 + 2.06585i
\(311\) −17.1464 + 29.6985i −0.972285 + 1.68405i −0.283666 + 0.958923i \(0.591551\pi\)
−0.688619 + 0.725123i \(0.741783\pi\)
\(312\) 0 0
\(313\) −11.5000 19.9186i −0.650018 1.12586i −0.983118 0.182973i \(-0.941428\pi\)
0.333099 0.942892i \(-0.391906\pi\)
\(314\) 48.9898 2.76465
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) −12.2474 21.2132i −0.687885 1.19145i −0.972521 0.232816i \(-0.925206\pi\)
0.284635 0.958636i \(-0.408127\pi\)
\(318\) 0 0
\(319\) 18.0000 31.1769i 1.00781 1.74557i
\(320\) 9.79796 + 16.9706i 0.547723 + 0.948683i
\(321\) 0 0
\(322\) 15.0000 + 5.19615i 0.835917 + 0.289570i
\(323\) 2.44949 0.136293
\(324\) 0 0
\(325\) 2.00000 3.46410i 0.110940 0.192154i
\(326\) 1.22474 2.12132i 0.0678323 0.117489i
\(327\) 0 0
\(328\) 36.0000 1.98777
\(329\) −4.89898 + 4.24264i −0.270089 + 0.233904i
\(330\) 0 0
\(331\) 6.50000 + 11.2583i 0.357272 + 0.618814i 0.987504 0.157593i \(-0.0503735\pi\)
−0.630232 + 0.776407i \(0.717040\pi\)
\(332\) −29.3939 + 50.9117i −1.61320 + 2.79414i
\(333\) 0 0
\(334\) 18.0000 + 31.1769i 0.984916 + 1.70592i
\(335\) 4.89898 0.267660
\(336\) 0 0
\(337\) 5.00000 0.272367 0.136184 0.990684i \(-0.456516\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(338\) −3.67423 6.36396i −0.199852 0.346154i
\(339\) 0 0
\(340\) 12.0000 20.7846i 0.650791 1.12720i
\(341\) 17.1464 + 29.6985i 0.928531 + 1.60826i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −4.89898 −0.264135
\(345\) 0 0
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) 4.89898 8.48528i 0.262991 0.455514i −0.704044 0.710156i \(-0.748624\pi\)
0.967035 + 0.254642i \(0.0819577\pi\)
\(348\) 0 0
\(349\) 35.0000 1.87351 0.936754 0.349990i \(-0.113815\pi\)
0.936754 + 0.349990i \(0.113815\pi\)
\(350\) −1.22474 6.36396i −0.0654654 0.340168i
\(351\) 0 0
\(352\) 0 0
\(353\) −2.44949 + 4.24264i −0.130373 + 0.225813i −0.923820 0.382826i \(-0.874951\pi\)
0.793447 + 0.608639i \(0.208284\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 9.79796 0.519291
\(357\) 0 0
\(358\) −6.00000 −0.317110
\(359\) 9.79796 + 16.9706i 0.517116 + 0.895672i 0.999802 + 0.0198785i \(0.00632794\pi\)
−0.482686 + 0.875794i \(0.660339\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 8.57321 + 14.8492i 0.450598 + 0.780459i
\(363\) 0 0
\(364\) −40.0000 13.8564i −2.09657 0.726273i
\(365\) −2.44949 −0.128212
\(366\) 0 0
\(367\) 6.50000 11.2583i 0.339297 0.587680i −0.645003 0.764180i \(-0.723144\pi\)
0.984301 + 0.176500i \(0.0564774\pi\)
\(368\) −4.89898 + 8.48528i −0.255377 + 0.442326i
\(369\) 0 0
\(370\) 48.0000 2.49540
\(371\) −6.12372 2.12132i −0.317928 0.110133i
\(372\) 0 0
\(373\) −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i \(-0.258587\pi\)
−0.972556 + 0.232671i \(0.925254\pi\)
\(374\) 14.6969 25.4558i 0.759961 1.31629i
\(375\) 0 0
\(376\) −6.00000 10.3923i −0.309426 0.535942i
\(377\) 29.3939 1.51386
\(378\) 0 0
\(379\) −34.0000 −1.74646 −0.873231 0.487306i \(-0.837980\pi\)
−0.873231 + 0.487306i \(0.837980\pi\)
\(380\) 4.89898 + 8.48528i 0.251312 + 0.435286i
\(381\) 0 0
\(382\) −3.00000 + 5.19615i −0.153493 + 0.265858i
\(383\) 9.79796 + 16.9706i 0.500652 + 0.867155i 1.00000 0.000753393i \(0.000239813\pi\)
−0.499347 + 0.866402i \(0.666427\pi\)
\(384\) 0 0
\(385\) −6.00000 31.1769i −0.305788 1.58892i
\(386\) 48.9898 2.49351
\(387\) 0 0
\(388\) 2.00000 3.46410i 0.101535 0.175863i
\(389\) 8.57321 14.8492i 0.434679 0.752886i −0.562590 0.826736i \(-0.690195\pi\)
0.997269 + 0.0738494i \(0.0235284\pi\)
\(390\) 0 0
\(391\) −6.00000 −0.303433
\(392\) −31.8434 + 12.7279i −1.60833 + 0.642857i
\(393\) 0 0
\(394\) 0 0
\(395\) 4.89898 8.48528i 0.246494 0.426941i
\(396\) 0 0
\(397\) −8.50000 14.7224i −0.426603 0.738898i 0.569966 0.821668i \(-0.306956\pi\)
−0.996569 + 0.0827707i \(0.973623\pi\)
\(398\) −46.5403 −2.33285
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) −12.2474 21.2132i −0.611608 1.05934i −0.990969 0.134088i \(-0.957189\pi\)
0.379361 0.925249i \(-0.376144\pi\)
\(402\) 0 0
\(403\) −14.0000 + 24.2487i −0.697390 + 1.20791i
\(404\) −9.79796 16.9706i −0.487467 0.844317i
\(405\) 0 0
\(406\) 36.0000 31.1769i 1.78665 1.54728i
\(407\) 39.1918 1.94267
\(408\) 0 0
\(409\) −10.0000 + 17.3205i −0.494468 + 0.856444i −0.999980 0.00637586i \(-0.997970\pi\)
0.505511 + 0.862820i \(0.331304\pi\)
\(410\) −22.0454 + 38.1838i −1.08875 + 1.88576i
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) −24.4949 8.48528i −1.20532 0.417533i
\(414\) 0 0
\(415\) −18.0000 31.1769i −0.883585 1.53041i
\(416\) 0 0
\(417\) 0 0
\(418\) 6.00000 + 10.3923i 0.293470 + 0.508304i
\(419\) 7.34847 0.358996 0.179498 0.983758i \(-0.442553\pi\)
0.179498 + 0.983758i \(0.442553\pi\)
\(420\) 0 0
\(421\) 35.0000 1.70580 0.852898 0.522078i \(-0.174843\pi\)
0.852898 + 0.522078i \(0.174843\pi\)
\(422\) −6.12372 10.6066i −0.298098 0.516321i
\(423\) 0 0
\(424\) 6.00000 10.3923i 0.291386 0.504695i
\(425\) 1.22474 + 2.12132i 0.0594089 + 0.102899i
\(426\) 0 0
\(427\) −10.0000 + 8.66025i −0.483934 + 0.419099i
\(428\) −78.3837 −3.78882
\(429\) 0 0
\(430\) 3.00000 5.19615i 0.144673 0.250581i
\(431\) −9.79796 + 16.9706i −0.471951 + 0.817443i −0.999485 0.0320907i \(-0.989783\pi\)
0.527534 + 0.849534i \(0.323117\pi\)
\(432\) 0 0
\(433\) −7.00000 −0.336399 −0.168199 0.985753i \(-0.553795\pi\)
−0.168199 + 0.985753i \(0.553795\pi\)
\(434\) 8.57321 + 44.5477i 0.411527 + 2.13836i
\(435\) 0 0
\(436\) 2.00000 + 3.46410i 0.0957826 + 0.165900i
\(437\) 1.22474 2.12132i 0.0585875 0.101477i
\(438\) 0 0
\(439\) −7.00000 12.1244i −0.334092 0.578664i 0.649218 0.760602i \(-0.275096\pi\)
−0.983310 + 0.181938i \(0.941763\pi\)
\(440\) 58.7878 2.80260
\(441\) 0 0
\(442\) 24.0000 1.14156
\(443\) −1.22474 2.12132i −0.0581894 0.100787i 0.835463 0.549546i \(-0.185199\pi\)
−0.893653 + 0.448759i \(0.851866\pi\)
\(444\) 0 0
\(445\) −3.00000 + 5.19615i −0.142214 + 0.246321i
\(446\) −31.8434 55.1543i −1.50783 2.61163i
\(447\) 0 0
\(448\) 4.00000 + 20.7846i 0.188982 + 0.981981i
\(449\) 22.0454 1.04039 0.520194 0.854048i \(-0.325860\pi\)
0.520194 + 0.854048i \(0.325860\pi\)
\(450\) 0 0
\(451\) −18.0000 + 31.1769i −0.847587 + 1.46806i
\(452\) 29.3939 50.9117i 1.38257 2.39468i
\(453\) 0 0
\(454\) −42.0000 −1.97116
\(455\) 19.5959 16.9706i 0.918671 0.795592i
\(456\) 0 0
\(457\) −11.5000 19.9186i −0.537947 0.931752i −0.999014 0.0443868i \(-0.985867\pi\)
0.461067 0.887365i \(-0.347467\pi\)
\(458\) 8.57321 14.8492i 0.400600 0.693860i
\(459\) 0 0
\(460\) −12.0000 20.7846i −0.559503 0.969087i
\(461\) −29.3939 −1.36901 −0.684505 0.729008i \(-0.739981\pi\)
−0.684505 + 0.729008i \(0.739981\pi\)
\(462\) 0 0
\(463\) 23.0000 1.06890 0.534450 0.845200i \(-0.320519\pi\)
0.534450 + 0.845200i \(0.320519\pi\)
\(464\) 14.6969 + 25.4558i 0.682288 + 1.18176i
\(465\) 0 0
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) −12.2474 21.2132i −0.566744 0.981630i −0.996885 0.0788681i \(-0.974869\pi\)
0.430141 0.902762i \(-0.358464\pi\)
\(468\) 0 0
\(469\) 5.00000 + 1.73205i 0.230879 + 0.0799787i
\(470\) 14.6969 0.677919
\(471\) 0 0
\(472\) 24.0000 41.5692i 1.10469 1.91338i
\(473\) 2.44949 4.24264i 0.112628 0.195077i
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 19.5959 16.9706i 0.898177 0.777844i
\(477\) 0 0
\(478\) −9.00000 15.5885i −0.411650 0.712999i
\(479\) −13.4722 + 23.3345i −0.615560 + 1.06618i 0.374726 + 0.927136i \(0.377737\pi\)
−0.990286 + 0.139046i \(0.955596\pi\)
\(480\) 0 0
\(481\) 16.0000 + 27.7128i 0.729537 + 1.26360i
\(482\) −31.8434 −1.45043
\(483\) 0 0
\(484\) 52.0000 2.36364
\(485\) 1.22474 + 2.12132i 0.0556128 + 0.0963242i
\(486\) 0 0
\(487\) 9.50000 16.4545i 0.430486 0.745624i −0.566429 0.824110i \(-0.691675\pi\)
0.996915 + 0.0784867i \(0.0250088\pi\)
\(488\) −12.2474 21.2132i −0.554416 0.960277i
\(489\) 0 0
\(490\) 6.00000 41.5692i 0.271052 1.87791i
\(491\) −14.6969 −0.663264 −0.331632 0.943409i \(-0.607599\pi\)
−0.331632 + 0.943409i \(0.607599\pi\)
\(492\) 0 0
\(493\) −9.00000 + 15.5885i −0.405340 + 0.702069i
\(494\) −4.89898 + 8.48528i −0.220416 + 0.381771i
\(495\) 0 0
\(496\) −28.0000 −1.25724
\(497\) 0 0
\(498\) 0 0
\(499\) 3.50000 + 6.06218i 0.156682 + 0.271380i 0.933670 0.358134i \(-0.116587\pi\)
−0.776989 + 0.629515i \(0.783254\pi\)
\(500\) 19.5959 33.9411i 0.876356 1.51789i
\(501\) 0 0
\(502\) 27.0000 + 46.7654i 1.20507 + 2.08724i
\(503\) −22.0454 −0.982956 −0.491478 0.870890i \(-0.663543\pi\)
−0.491478 + 0.870890i \(0.663543\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) −14.6969 25.4558i −0.653359 1.13165i
\(507\) 0 0
\(508\) −22.0000 + 38.1051i −0.976092 + 1.69064i
\(509\) 9.79796 + 16.9706i 0.434287 + 0.752207i 0.997237 0.0742838i \(-0.0236671\pi\)
−0.562950 + 0.826491i \(0.690334\pi\)
\(510\) 0 0
\(511\) −2.50000 0.866025i −0.110593 0.0383107i
\(512\) −39.1918 −1.73205
\(513\) 0 0
\(514\) −30.0000 + 51.9615i −1.32324 + 2.29192i
\(515\) −2.44949 + 4.24264i −0.107937 + 0.186953i
\(516\) 0 0
\(517\) 12.0000 0.527759
\(518\) 48.9898 + 16.9706i 2.15249 + 0.745644i
\(519\) 0 0
\(520\) 24.0000 + 41.5692i 1.05247 + 1.82293i
\(521\) −9.79796 + 16.9706i −0.429256 + 0.743494i −0.996807 0.0798444i \(-0.974558\pi\)
0.567551 + 0.823338i \(0.307891\pi\)
\(522\) 0 0
\(523\) −4.00000 6.92820i −0.174908 0.302949i 0.765222 0.643767i \(-0.222629\pi\)
−0.940129 + 0.340818i \(0.889296\pi\)
\(524\) 9.79796 0.428026
\(525\) 0 0
\(526\) 12.0000 0.523225
\(527\) −8.57321 14.8492i −0.373455 0.646843i
\(528\) 0 0
\(529\) 8.50000 14.7224i 0.369565 0.640106i
\(530\) 7.34847 + 12.7279i 0.319197 + 0.552866i
\(531\) 0 0
\(532\) 2.00000 + 10.3923i 0.0867110 + 0.450564i
\(533\) −29.3939 −1.27319
\(534\) 0 0
\(535\) 24.0000 41.5692i 1.03761 1.79719i
\(536\) −4.89898 + 8.48528i −0.211604 + 0.366508i
\(537\) 0 0
\(538\) −60.0000 −2.58678
\(539\) 4.89898 33.9411i 0.211014 1.46195i
\(540\) 0 0
\(541\) −17.5000 30.3109i −0.752384 1.30317i −0.946664 0.322221i \(-0.895571\pi\)
0.194281 0.980946i \(-0.437763\pi\)
\(542\) 1.22474 2.12132i 0.0526073 0.0911185i
\(543\) 0 0
\(544\) 0 0
\(545\) −2.44949 −0.104925
\(546\) 0 0
\(547\) −37.0000 −1.58201 −0.791003 0.611812i \(-0.790441\pi\)
−0.791003 + 0.611812i \(0.790441\pi\)
\(548\) 34.2929 + 59.3970i 1.46492 + 2.53731i
\(549\) 0 0
\(550\) −6.00000 + 10.3923i −0.255841 + 0.443129i
\(551\) −3.67423 6.36396i −0.156528 0.271114i
\(552\) 0 0
\(553\) 8.00000 6.92820i 0.340195 0.294617i
\(554\) 56.3383 2.39358
\(555\) 0 0
\(556\) −28.0000 + 48.4974i −1.18746 + 2.05675i
\(557\) −20.8207 + 36.0624i −0.882200 + 1.52801i −0.0333100 + 0.999445i \(0.510605\pi\)
−0.848890 + 0.528570i \(0.822728\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) 24.4949 + 8.48528i 1.03510 + 0.358569i
\(561\) 0 0
\(562\) −18.0000 31.1769i −0.759284 1.31512i
\(563\) −6.12372 + 10.6066i −0.258084 + 0.447015i −0.965729 0.259554i \(-0.916425\pi\)
0.707644 + 0.706569i \(0.249758\pi\)
\(564\) 0 0
\(565\) 18.0000 + 31.1769i 0.757266 + 1.31162i
\(566\) −61.2372 −2.57399
\(567\) 0 0
\(568\) 0 0
\(569\) 9.79796 + 16.9706i 0.410752 + 0.711443i 0.994972 0.100152i \(-0.0319329\pi\)
−0.584220 + 0.811595i \(0.698600\pi\)
\(570\) 0 0
\(571\) −14.5000 + 25.1147i −0.606806 + 1.05102i 0.384957 + 0.922934i \(0.374216\pi\)
−0.991763 + 0.128085i \(0.959117\pi\)
\(572\) 39.1918 + 67.8823i 1.63869 + 2.83830i
\(573\) 0 0
\(574\) −36.0000 + 31.1769i −1.50261 + 1.30130i
\(575\) 2.44949 0.102151
\(576\) 0 0
\(577\) −4.00000 + 6.92820i −0.166522 + 0.288425i −0.937195 0.348806i \(-0.886587\pi\)
0.770673 + 0.637231i \(0.219920\pi\)
\(578\) 13.4722 23.3345i 0.560369 0.970588i
\(579\) 0 0
\(580\) −72.0000 −2.98964
\(581\) −7.34847 38.1838i −0.304866 1.58413i
\(582\) 0 0
\(583\) 6.00000 + 10.3923i 0.248495 + 0.430405i
\(584\) 2.44949 4.24264i 0.101361 0.175562i
\(585\) 0 0
\(586\) −36.0000 62.3538i −1.48715 2.57581i
\(587\) −7.34847 −0.303304 −0.151652 0.988434i \(-0.548459\pi\)
−0.151652 + 0.988434i \(0.548459\pi\)
\(588\) 0 0
\(589\) 7.00000 0.288430
\(590\) 29.3939 + 50.9117i 1.21013 + 2.09600i
\(591\) 0 0
\(592\) −16.0000 + 27.7128i −0.657596 + 1.13899i
\(593\) −12.2474 21.2132i −0.502942 0.871122i −0.999994 0.00340097i \(-0.998917\pi\)
0.497052 0.867721i \(-0.334416\pi\)
\(594\) 0 0
\(595\) 3.00000 + 15.5885i 0.122988 + 0.639064i
\(596\) 9.79796 0.401340
\(597\) 0 0
\(598\) 12.0000 20.7846i 0.490716 0.849946i
\(599\) 15.9217 27.5772i 0.650542 1.12677i −0.332449 0.943121i \(-0.607875\pi\)
0.982991 0.183651i \(-0.0587917\pi\)
\(600\) 0 0
\(601\) 17.0000 0.693444 0.346722 0.937968i \(-0.387295\pi\)
0.346722 + 0.937968i \(0.387295\pi\)
\(602\) 4.89898 4.24264i 0.199667 0.172917i
\(603\) 0 0
\(604\) −10.0000 17.3205i −0.406894 0.704761i
\(605\) −15.9217 + 27.5772i −0.647308 + 1.12117i
\(606\) 0 0
\(607\) −14.5000 25.1147i −0.588537 1.01938i −0.994424 0.105453i \(-0.966371\pi\)
0.405887 0.913923i \(-0.366962\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 30.0000 1.21466
\(611\) 4.89898 + 8.48528i 0.198191 + 0.343278i
\(612\) 0 0
\(613\) −8.50000 + 14.7224i −0.343312 + 0.594633i −0.985046 0.172294i \(-0.944882\pi\)
0.641734 + 0.766927i \(0.278215\pi\)
\(614\) 30.6186 + 53.0330i 1.23567 + 2.14024i
\(615\) 0 0
\(616\) 60.0000 + 20.7846i 2.41747 + 0.837436i
\(617\) 29.3939 1.18335 0.591676 0.806176i \(-0.298466\pi\)
0.591676 + 0.806176i \(0.298466\pi\)
\(618\) 0 0
\(619\) −7.00000 + 12.1244i −0.281354 + 0.487319i −0.971718 0.236143i \(-0.924117\pi\)
0.690365 + 0.723462i \(0.257450\pi\)
\(620\) 34.2929 59.3970i 1.37723 2.38544i
\(621\) 0 0
\(622\) 84.0000 3.36809
\(623\) −4.89898 + 4.24264i −0.196273 + 0.169978i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −28.1691 + 48.7904i −1.12586 + 1.95006i
\(627\) 0 0
\(628\) −40.0000 69.2820i −1.59617 2.76465i
\(629\) −19.5959 −0.781340
\(630\) 0 0
\(631\) −25.0000 −0.995234 −0.497617 0.867397i \(-0.665792\pi\)
−0.497617 + 0.867397i \(0.665792\pi\)
\(632\) 9.79796 + 16.9706i 0.389742 + 0.675053i
\(633\) 0 0
\(634\) −30.0000 + 51.9615i −1.19145 + 2.06366i
\(635\) −13.4722 23.3345i −0.534628 0.926002i
\(636\) 0 0
\(637\) 26.0000 10.3923i 1.03016 0.411758i
\(638\) −88.1816 −3.49114
\(639\) 0 0
\(640\) 24.0000 41.5692i 0.948683 1.64317i
\(641\) −13.4722 + 23.3345i −0.532120 + 0.921658i 0.467177 + 0.884164i \(0.345271\pi\)
−0.999297 + 0.0374946i \(0.988062\pi\)
\(642\) 0 0
\(643\) 5.00000 0.197181 0.0985904 0.995128i \(-0.468567\pi\)
0.0985904 + 0.995128i \(0.468567\pi\)
\(644\) −4.89898 25.4558i −0.193047 1.00310i
\(645\) 0 0
\(646\) −3.00000 5.19615i −0.118033 0.204440i
\(647\) −9.79796 + 16.9706i −0.385198 + 0.667182i −0.991797 0.127826i \(-0.959200\pi\)
0.606599 + 0.795008i \(0.292533\pi\)
\(648\) 0 0
\(649\) 24.0000 + 41.5692i 0.942082 + 1.63173i
\(650\) −9.79796 −0.384308
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) −1.22474 2.12132i −0.0479280 0.0830137i 0.841066 0.540932i \(-0.181928\pi\)
−0.888994 + 0.457919i \(0.848595\pi\)
\(654\) 0 0
\(655\) −3.00000 + 5.19615i −0.117220 + 0.203030i
\(656\) −14.6969 25.4558i −0.573819 0.993884i
\(657\) 0 0
\(658\) 15.0000 + 5.19615i 0.584761 + 0.202567i
\(659\) −7.34847 −0.286256 −0.143128 0.989704i \(-0.545716\pi\)
−0.143128 + 0.989704i \(0.545716\pi\)
\(660\) 0 0
\(661\) −5.50000 + 9.52628i −0.213925 + 0.370529i −0.952940 0.303160i \(-0.901958\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) 15.9217 27.5772i 0.618814 1.07182i
\(663\) 0 0
\(664\) 72.0000 2.79414
\(665\) −6.12372 2.12132i −0.237468 0.0822613i
\(666\) 0 0
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) 29.3939 50.9117i 1.13728 1.96983i
\(669\) 0 0
\(670\) −6.00000 10.3923i −0.231800 0.401490i
\(671\) 24.4949 0.945615
\(672\) 0 0
\(673\) 17.0000 0.655302 0.327651 0.944799i \(-0.393743\pi\)
0.327651 + 0.944799i \(0.393743\pi\)
\(674\) −6.12372 10.6066i −0.235877 0.408551i
\(675\) 0 0
\(676\) −6.00000 + 10.3923i −0.230769 + 0.399704i
\(677\) 9.79796 + 16.9706i 0.376566 + 0.652232i 0.990560 0.137079i \(-0.0437714\pi\)
−0.613994 + 0.789311i \(0.710438\pi\)
\(678\) 0 0
\(679\) 0.500000 + 2.59808i 0.0191882 + 0.0997050i
\(680\) −29.3939 −1.12720
\(681\) 0 0
\(682\) 42.0000 72.7461i 1.60826 2.78559i
\(683\) 12.2474 21.2132i 0.468636 0.811701i −0.530722 0.847546i \(-0.678079\pi\)
0.999357 + 0.0358455i \(0.0114124\pi\)
\(684\) 0 0
\(685\) −42.0000 −1.60474
\(686\) 20.8207 40.3051i 0.794937 1.53886i
\(687\) 0 0
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) −4.89898 + 8.48528i −0.186636 + 0.323263i
\(690\) 0 0
\(691\) −20.5000 35.5070i −0.779857 1.35075i −0.932024 0.362397i \(-0.881959\pi\)
0.152167 0.988355i \(-0.451375\pi\)
\(692\) 9.79796 0.372463
\(693\) 0 0
\(694\) −24.0000 −0.911028
\(695\) −17.1464 29.6985i −0.650401 1.12653i
\(696\) 0 0
\(697\) 9.00000 15.5885i 0.340899 0.590455i
\(698\) −42.8661 74.2462i −1.62250 2.81026i
\(699\) 0 0
\(700\) −8.00000 + 6.92820i −0.302372 + 0.261861i
\(701\) 22.0454 0.832644 0.416322 0.909217i \(-0.363319\pi\)
0.416322 + 0.909217i \(0.363319\pi\)
\(702\) 0 0
\(703\) 4.00000 6.92820i 0.150863 0.261302i
\(704\) 19.5959 33.9411i 0.738549 1.27920i
\(705\) 0 0
\(706\) 12.0000 0.451626
\(707\) 12.2474 + 4.24264i 0.460613 + 0.159561i
\(708\) 0 0
\(709\) 24.5000 + 42.4352i 0.920117 + 1.59369i 0.799232 + 0.601023i \(0.205240\pi\)
0.120885 + 0.992667i \(0.461427\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −6.00000 10.3923i −0.224860 0.389468i
\(713\) −17.1464 −0.642139
\(714\) 0 0
\(715\) −48.0000 −1.79510
\(716\) 4.89898 + 8.48528i 0.183083 + 0.317110i
\(717\) 0 0
\(718\) 24.0000 41.5692i 0.895672 1.55135i
\(719\) 9.79796 + 16.9706i 0.365402 + 0.632895i 0.988841 0.148977i \(-0.0475981\pi\)
−0.623438 + 0.781872i \(0.714265\pi\)
\(720\) 0 0
\(721\) −4.00000 + 3.46410i −0.148968 + 0.129010i
\(722\) −44.0908 −1.64089
\(723\) 0 0
\(724\) 14.0000 24.2487i 0.520306 0.901196i
\(725\) 3.67423 6.36396i 0.136458 0.236352i
\(726\) 0 0
\(727\) −19.0000 −0.704671 −0.352335 0.935874i \(-0.614612\pi\)
−0.352335 + 0.935874i \(0.614612\pi\)
\(728\) 9.79796 + 50.9117i 0.363137 + 1.88691i
\(729\) 0 0
\(730\) 3.00000 + 5.19615i 0.111035 + 0.192318i
\(731\) −1.22474 + 2.12132i −0.0452988 + 0.0784599i
\(732\) 0 0
\(733\) −5.50000 9.52628i −0.203147 0.351861i 0.746394 0.665505i \(-0.231784\pi\)
−0.949541 + 0.313644i \(0.898450\pi\)
\(734\) −31.8434 −1.17536
\(735\) 0 0
\(736\) 0 0
\(737\) −4.89898 8.48528i −0.180456 0.312559i
\(738\) 0 0
\(739\) 9.50000 16.4545i 0.349463 0.605288i −0.636691 0.771119i \(-0.719697\pi\)
0.986154 + 0.165831i \(0.0530307\pi\)
\(740\) −39.1918 67.8823i −1.44072 2.49540i
\(741\) 0 0
\(742\) 3.00000 + 15.5885i 0.110133 + 0.572270i
\(743\) 7.34847 0.269589 0.134795 0.990874i \(-0.456963\pi\)
0.134795 + 0.990874i \(0.456963\pi\)
\(744\) 0 0
\(745\) −3.00000 + 5.19615i −0.109911 + 0.190372i
\(746\) −13.4722 + 23.3345i −0.493252 + 0.854338i
\(747\) 0 0
\(748\) −48.0000 −1.75505
\(749\) 39.1918 33.9411i 1.43204 1.24018i
\(750\) 0 0
\(751\) 21.5000 + 37.2391i 0.784546 + 1.35887i 0.929270 + 0.369402i \(0.120437\pi\)
−0.144724 + 0.989472i \(0.546229\pi\)
\(752\) −4.89898 + 8.48528i −0.178647 + 0.309426i
\(753\) 0 0
\(754\) −36.0000 62.3538i −1.31104 2.27079i
\(755\) 12.2474 0.445730
\(756\) 0 0
\(757\) 47.0000 1.70824 0.854122 0.520073i \(-0.174095\pi\)
0.854122 + 0.520073i \(0.174095\pi\)
\(758\) 41.6413 + 72.1249i 1.51248 + 2.61969i
\(759\) 0 0
\(760\) 6.00000 10.3923i 0.217643 0.376969i
\(761\) 9.79796 + 16.9706i 0.355176 + 0.615182i 0.987148 0.159809i \(-0.0510877\pi\)
−0.631972 + 0.774991i \(0.717754\pi\)
\(762\) 0 0
\(763\) −2.50000 0.866025i −0.0905061 0.0313522i
\(764\) 9.79796 0.354478
\(765\) 0 0
\(766\) 24.0000 41.5692i 0.867155 1.50196i
\(767\) −19.5959 + 33.9411i −0.707568 + 1.22554i
\(768\) 0 0
\(769\) 5.00000 0.180305 0.0901523 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) −58.7878 + 50.9117i −2.11856 + 1.83473i
\(771\) 0 0
\(772\) −40.0000 69.2820i −1.43963 2.49351i
\(773\) 23.2702 40.3051i 0.836969 1.44967i −0.0554478 0.998462i \(-0.517659\pi\)
0.892417 0.451212i \(-0.149008\pi\)
\(774\) 0 0
\(775\) 3.50000 + 6.06218i 0.125724 + 0.217760i
\(776\) −4.89898 −0.175863
\(777\) 0 0
\(778\) −42.0000 −1.50577
\(779\) 3.67423 + 6.36396i 0.131643 + 0.228013i
\(780\) 0 0
\(781\) 0 0
\(782\) 7.34847 + 12.7279i 0.262781 + 0.455150i
\(783\) 0 0
\(784\) 22.0000