Properties

Label 380.2.i.c.201.1
Level $380$
Weight $2$
Character 380.201
Analytic conductor $3.034$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(121,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.i (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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 9x^{6} + 2x^{5} + 65x^{4} - 20x^{3} + 25x^{2} + 6x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.1
Root \(1.58253 - 2.74101i\) of defining polynomial
Character \(\chi\) \(=\) 380.201
Dual form 380.2.i.c.121.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.58253 + 2.74101i) q^{3} +(-0.500000 + 0.866025i) q^{5} -1.53315 q^{7} +(-3.50877 - 6.07738i) q^{9} +O(q^{10})\) \(q+(-1.58253 + 2.74101i) q^{3} +(-0.500000 + 0.866025i) q^{5} -1.53315 q^{7} +(-3.50877 - 6.07738i) q^{9} -3.79695 q^{11} +(3.34910 + 5.80081i) q^{13} +(-1.58253 - 2.74101i) q^{15} +(3.00877 - 5.21135i) q^{17} +(-3.93502 - 1.87499i) q^{19} +(2.42625 - 4.20239i) q^{21} +(-2.19282 - 3.79808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +12.7158 q^{27} +(0.549376 + 0.951547i) q^{29} -1.05555 q^{31} +(6.00877 - 10.4075i) q^{33} +(0.766575 - 1.32775i) q^{35} -10.7970 q^{37} -21.2002 q^{39} +(-1.76658 + 3.05980i) q^{41} +(-2.77535 + 4.80705i) q^{43} +7.01755 q^{45} +(5.61907 + 9.73252i) q^{47} -4.64945 q^{49} +(9.52293 + 16.4942i) q^{51} +(-0.788178 - 1.36516i) q^{53} +(1.89848 - 3.28826i) q^{55} +(11.3667 - 7.81874i) q^{57} +(-1.61568 + 2.79843i) q^{59} +(-0.0331500 - 0.0574175i) q^{61} +(5.37948 + 9.31753i) q^{63} -6.69820 q^{65} +(2.85250 + 4.94067i) q^{67} +13.8808 q^{69} +(3.23880 - 5.60977i) q^{71} +(-6.98978 + 12.1066i) q^{73} +3.16505 q^{75} +5.82130 q^{77} +(0.996602 - 1.72617i) q^{79} +(-9.59668 + 16.6219i) q^{81} -10.3477 q^{83} +(3.00877 + 5.21135i) q^{85} -3.47760 q^{87} +(-1.53655 - 2.66138i) q^{89} +(-5.13467 - 8.89352i) q^{91} +(1.67043 - 2.89327i) q^{93} +(3.59130 - 2.47034i) q^{95} +(-4.43502 + 7.68169i) q^{97} +(13.3227 + 23.0755i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{3} - 4 q^{5} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{3} - 4 q^{5} - 5 q^{9} + 4 q^{11} + 9 q^{13} - q^{15} + q^{17} + 3 q^{19} + 8 q^{21} - 4 q^{25} + 20 q^{27} + 5 q^{29} - 20 q^{31} + 25 q^{33} - 52 q^{37} - 54 q^{39} - 8 q^{41} + 7 q^{43} + 10 q^{45} + 16 q^{47} + 20 q^{49} + 12 q^{51} + 5 q^{53} - 2 q^{55} + 27 q^{57} + 11 q^{59} + 12 q^{61} - 3 q^{63} - 18 q^{65} + 6 q^{69} + 14 q^{71} - 4 q^{73} + 2 q^{75} - 44 q^{77} + 13 q^{79} - 24 q^{81} + 10 q^{83} + q^{85} - 4 q^{87} + 5 q^{89} - 46 q^{91} - 28 q^{93} - 6 q^{95} - q^{97} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.58253 + 2.74101i −0.913672 + 1.58253i −0.104837 + 0.994489i \(0.533432\pi\)
−0.808835 + 0.588036i \(0.799901\pi\)
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −1.53315 −0.579476 −0.289738 0.957106i \(-0.593568\pi\)
−0.289738 + 0.957106i \(0.593568\pi\)
\(8\) 0 0
\(9\) −3.50877 6.07738i −1.16959 2.02579i
\(10\) 0 0
\(11\) −3.79695 −1.14482 −0.572412 0.819966i \(-0.693992\pi\)
−0.572412 + 0.819966i \(0.693992\pi\)
\(12\) 0 0
\(13\) 3.34910 + 5.80081i 0.928873 + 1.60886i 0.785210 + 0.619229i \(0.212555\pi\)
0.143663 + 0.989627i \(0.454112\pi\)
\(14\) 0 0
\(15\) −1.58253 2.74101i −0.408606 0.707727i
\(16\) 0 0
\(17\) 3.00877 5.21135i 0.729735 1.26394i −0.227260 0.973834i \(-0.572977\pi\)
0.956995 0.290104i \(-0.0936899\pi\)
\(18\) 0 0
\(19\) −3.93502 1.87499i −0.902756 0.430152i
\(20\) 0 0
\(21\) 2.42625 4.20239i 0.529451 0.917036i
\(22\) 0 0
\(23\) −2.19282 3.79808i −0.457235 0.791955i 0.541578 0.840650i \(-0.317827\pi\)
−0.998814 + 0.0486953i \(0.984494\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 12.7158 2.44715
\(28\) 0 0
\(29\) 0.549376 + 0.951547i 0.102016 + 0.176698i 0.912515 0.409042i \(-0.134137\pi\)
−0.810499 + 0.585740i \(0.800804\pi\)
\(30\) 0 0
\(31\) −1.05555 −0.189582 −0.0947908 0.995497i \(-0.530218\pi\)
−0.0947908 + 0.995497i \(0.530218\pi\)
\(32\) 0 0
\(33\) 6.00877 10.4075i 1.04599 1.81171i
\(34\) 0 0
\(35\) 0.766575 1.32775i 0.129575 0.224430i
\(36\) 0 0
\(37\) −10.7970 −1.77501 −0.887504 0.460800i \(-0.847563\pi\)
−0.887504 + 0.460800i \(0.847563\pi\)
\(38\) 0 0
\(39\) −21.2002 −3.39474
\(40\) 0 0
\(41\) −1.76658 + 3.05980i −0.275893 + 0.477860i −0.970360 0.241664i \(-0.922307\pi\)
0.694467 + 0.719524i \(0.255640\pi\)
\(42\) 0 0
\(43\) −2.77535 + 4.80705i −0.423237 + 0.733068i −0.996254 0.0864756i \(-0.972440\pi\)
0.573017 + 0.819543i \(0.305773\pi\)
\(44\) 0 0
\(45\) 7.01755 1.04611
\(46\) 0 0
\(47\) 5.61907 + 9.73252i 0.819626 + 1.41963i 0.905958 + 0.423368i \(0.139152\pi\)
−0.0863319 + 0.996266i \(0.527515\pi\)
\(48\) 0 0
\(49\) −4.64945 −0.664207
\(50\) 0 0
\(51\) 9.52293 + 16.4942i 1.33348 + 2.30965i
\(52\) 0 0
\(53\) −0.788178 1.36516i −0.108265 0.187520i 0.806803 0.590821i \(-0.201196\pi\)
−0.915067 + 0.403301i \(0.867863\pi\)
\(54\) 0 0
\(55\) 1.89848 3.28826i 0.255990 0.443389i
\(56\) 0 0
\(57\) 11.3667 7.81874i 1.50555 1.03562i
\(58\) 0 0
\(59\) −1.61568 + 2.79843i −0.210343 + 0.364325i −0.951822 0.306651i \(-0.900791\pi\)
0.741479 + 0.670976i \(0.234125\pi\)
\(60\) 0 0
\(61\) −0.0331500 0.0574175i −0.00424442 0.00735156i 0.863895 0.503671i \(-0.168018\pi\)
−0.868140 + 0.496320i \(0.834684\pi\)
\(62\) 0 0
\(63\) 5.37948 + 9.31753i 0.677751 + 1.17390i
\(64\) 0 0
\(65\) −6.69820 −0.830810
\(66\) 0 0
\(67\) 2.85250 + 4.94067i 0.348488 + 0.603599i 0.985981 0.166857i \(-0.0533618\pi\)
−0.637493 + 0.770456i \(0.720028\pi\)
\(68\) 0 0
\(69\) 13.8808 1.67105
\(70\) 0 0
\(71\) 3.23880 5.60977i 0.384375 0.665757i −0.607307 0.794467i \(-0.707750\pi\)
0.991682 + 0.128710i \(0.0410836\pi\)
\(72\) 0 0
\(73\) −6.98978 + 12.1066i −0.818091 + 1.41698i 0.0889951 + 0.996032i \(0.471634\pi\)
−0.907087 + 0.420944i \(0.861699\pi\)
\(74\) 0 0
\(75\) 3.16505 0.365469
\(76\) 0 0
\(77\) 5.82130 0.663398
\(78\) 0 0
\(79\) 0.996602 1.72617i 0.112127 0.194209i −0.804501 0.593951i \(-0.797567\pi\)
0.916627 + 0.399743i \(0.130900\pi\)
\(80\) 0 0
\(81\) −9.59668 + 16.6219i −1.06630 + 1.84688i
\(82\) 0 0
\(83\) −10.3477 −1.13580 −0.567901 0.823097i \(-0.692244\pi\)
−0.567901 + 0.823097i \(0.692244\pi\)
\(84\) 0 0
\(85\) 3.00877 + 5.21135i 0.326347 + 0.565250i
\(86\) 0 0
\(87\) −3.47760 −0.372838
\(88\) 0 0
\(89\) −1.53655 2.66138i −0.162874 0.282106i 0.773024 0.634376i \(-0.218743\pi\)
−0.935898 + 0.352271i \(0.885410\pi\)
\(90\) 0 0
\(91\) −5.13467 8.89352i −0.538260 0.932294i
\(92\) 0 0
\(93\) 1.67043 2.89327i 0.173215 0.300018i
\(94\) 0 0
\(95\) 3.59130 2.47034i 0.368460 0.253451i
\(96\) 0 0
\(97\) −4.43502 + 7.68169i −0.450308 + 0.779957i −0.998405 0.0564579i \(-0.982019\pi\)
0.548097 + 0.836415i \(0.315353\pi\)
\(98\) 0 0
\(99\) 13.3227 + 23.0755i 1.33898 + 2.31918i
\(100\) 0 0
\(101\) −3.10413 5.37651i −0.308872 0.534983i 0.669244 0.743043i \(-0.266618\pi\)
−0.978116 + 0.208060i \(0.933285\pi\)
\(102\) 0 0
\(103\) −0.253048 −0.0249336 −0.0124668 0.999922i \(-0.503968\pi\)
−0.0124668 + 0.999922i \(0.503968\pi\)
\(104\) 0 0
\(105\) 2.42625 + 4.20239i 0.236778 + 0.410111i
\(106\) 0 0
\(107\) −6.05555 −0.585412 −0.292706 0.956203i \(-0.594556\pi\)
−0.292706 + 0.956203i \(0.594556\pi\)
\(108\) 0 0
\(109\) −2.62445 + 4.54568i −0.251377 + 0.435397i −0.963905 0.266246i \(-0.914217\pi\)
0.712528 + 0.701643i \(0.247550\pi\)
\(110\) 0 0
\(111\) 17.0865 29.5946i 1.62177 2.80900i
\(112\) 0 0
\(113\) 2.42885 0.228487 0.114244 0.993453i \(-0.463556\pi\)
0.114244 + 0.993453i \(0.463556\pi\)
\(114\) 0 0
\(115\) 4.38565 0.408964
\(116\) 0 0
\(117\) 23.5025 40.7075i 2.17281 3.76341i
\(118\) 0 0
\(119\) −4.61290 + 7.98978i −0.422864 + 0.732422i
\(120\) 0 0
\(121\) 3.41685 0.310623
\(122\) 0 0
\(123\) −5.59130 9.68442i −0.504151 0.873214i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 9.64945 + 16.7133i 0.856250 + 1.48307i 0.875480 + 0.483254i \(0.160545\pi\)
−0.0192299 + 0.999815i \(0.506121\pi\)
\(128\) 0 0
\(129\) −8.78412 15.2146i −0.773399 1.33957i
\(130\) 0 0
\(131\) 6.62983 11.4832i 0.579251 1.00329i −0.416315 0.909221i \(-0.636679\pi\)
0.995565 0.0940711i \(-0.0299881\pi\)
\(132\) 0 0
\(133\) 6.03298 + 2.87464i 0.523126 + 0.249263i
\(134\) 0 0
\(135\) −6.35788 + 11.0122i −0.547199 + 0.947776i
\(136\) 0 0
\(137\) 7.77535 + 13.4673i 0.664293 + 1.15059i 0.979476 + 0.201558i \(0.0646006\pi\)
−0.315184 + 0.949031i \(0.602066\pi\)
\(138\) 0 0
\(139\) 9.31110 + 16.1273i 0.789758 + 1.36790i 0.926115 + 0.377241i \(0.123127\pi\)
−0.136358 + 0.990660i \(0.543540\pi\)
\(140\) 0 0
\(141\) −35.5693 −2.99548
\(142\) 0 0
\(143\) −12.7164 22.0254i −1.06340 1.84186i
\(144\) 0 0
\(145\) −1.09875 −0.0912463
\(146\) 0 0
\(147\) 7.35788 12.7442i 0.606867 1.05113i
\(148\) 0 0
\(149\) 2.34372 4.05945i 0.192005 0.332563i −0.753909 0.656978i \(-0.771834\pi\)
0.945915 + 0.324415i \(0.105168\pi\)
\(150\) 0 0
\(151\) −5.93370 −0.482878 −0.241439 0.970416i \(-0.577619\pi\)
−0.241439 + 0.970416i \(0.577619\pi\)
\(152\) 0 0
\(153\) −42.2285 −3.41397
\(154\) 0 0
\(155\) 0.527773 0.914130i 0.0423917 0.0734247i
\(156\) 0 0
\(157\) 4.64685 8.04857i 0.370859 0.642346i −0.618839 0.785518i \(-0.712397\pi\)
0.989698 + 0.143172i \(0.0457301\pi\)
\(158\) 0 0
\(159\) 4.98925 0.395673
\(160\) 0 0
\(161\) 3.36193 + 5.82303i 0.264957 + 0.458919i
\(162\) 0 0
\(163\) 5.88495 0.460945 0.230472 0.973079i \(-0.425973\pi\)
0.230472 + 0.973079i \(0.425973\pi\)
\(164\) 0 0
\(165\) 6.00877 + 10.4075i 0.467782 + 0.810223i
\(166\) 0 0
\(167\) −6.39848 11.0825i −0.495129 0.857589i 0.504855 0.863204i \(-0.331546\pi\)
−0.999984 + 0.00561549i \(0.998213\pi\)
\(168\) 0 0
\(169\) −15.9330 + 27.5967i −1.22561 + 2.12282i
\(170\) 0 0
\(171\) 2.41210 + 30.4935i 0.184458 + 2.33190i
\(172\) 0 0
\(173\) 7.52032 13.0256i 0.571760 0.990317i −0.424626 0.905369i \(-0.639594\pi\)
0.996385 0.0849476i \(-0.0270723\pi\)
\(174\) 0 0
\(175\) 0.766575 + 1.32775i 0.0579476 + 0.100368i
\(176\) 0 0
\(177\) −5.11370 8.85718i −0.384369 0.665747i
\(178\) 0 0
\(179\) 21.5452 1.61036 0.805180 0.593030i \(-0.202069\pi\)
0.805180 + 0.593030i \(0.202069\pi\)
\(180\) 0 0
\(181\) −2.13530 3.69845i −0.158716 0.274903i 0.775690 0.631114i \(-0.217402\pi\)
−0.934406 + 0.356210i \(0.884069\pi\)
\(182\) 0 0
\(183\) 0.209843 0.0155120
\(184\) 0 0
\(185\) 5.39848 9.35044i 0.396904 0.687458i
\(186\) 0 0
\(187\) −11.4242 + 19.7873i −0.835418 + 1.44699i
\(188\) 0 0
\(189\) −19.4952 −1.41806
\(190\) 0 0
\(191\) −6.30180 −0.455982 −0.227991 0.973663i \(-0.573216\pi\)
−0.227991 + 0.973663i \(0.573216\pi\)
\(192\) 0 0
\(193\) 7.68943 13.3185i 0.553497 0.958685i −0.444522 0.895768i \(-0.646626\pi\)
0.998019 0.0629169i \(-0.0200403\pi\)
\(194\) 0 0
\(195\) 10.6001 18.3599i 0.759087 1.31478i
\(196\) 0 0
\(197\) −12.7210 −0.906331 −0.453165 0.891426i \(-0.649705\pi\)
−0.453165 + 0.891426i \(0.649705\pi\)
\(198\) 0 0
\(199\) −5.10885 8.84879i −0.362157 0.627274i 0.626159 0.779696i \(-0.284626\pi\)
−0.988316 + 0.152422i \(0.951293\pi\)
\(200\) 0 0
\(201\) −18.0566 −1.27361
\(202\) 0 0
\(203\) −0.842275 1.45886i −0.0591161 0.102392i
\(204\) 0 0
\(205\) −1.76658 3.05980i −0.123383 0.213706i
\(206\) 0 0
\(207\) −15.3883 + 26.6532i −1.06956 + 1.85253i
\(208\) 0 0
\(209\) 14.9411 + 7.11925i 1.03350 + 0.492449i
\(210\) 0 0
\(211\) −2.53655 + 4.39343i −0.174623 + 0.302456i −0.940031 0.341090i \(-0.889204\pi\)
0.765408 + 0.643546i \(0.222537\pi\)
\(212\) 0 0
\(213\) 10.2510 + 17.7552i 0.702385 + 1.21657i
\(214\) 0 0
\(215\) −2.77535 4.80705i −0.189277 0.327838i
\(216\) 0 0
\(217\) 1.61831 0.109858
\(218\) 0 0
\(219\) −22.1230 38.3182i −1.49493 2.58930i
\(220\) 0 0
\(221\) 40.3068 2.71133
\(222\) 0 0
\(223\) 4.26318 7.38404i 0.285483 0.494472i −0.687243 0.726428i \(-0.741179\pi\)
0.972726 + 0.231956i \(0.0745125\pi\)
\(224\) 0 0
\(225\) −3.50877 + 6.07738i −0.233918 + 0.405158i
\(226\) 0 0
\(227\) −20.0566 −1.33120 −0.665602 0.746307i \(-0.731825\pi\)
−0.665602 + 0.746307i \(0.731825\pi\)
\(228\) 0 0
\(229\) 7.92955 0.524000 0.262000 0.965068i \(-0.415618\pi\)
0.262000 + 0.965068i \(0.415618\pi\)
\(230\) 0 0
\(231\) −9.21235 + 15.9563i −0.606128 + 1.04985i
\(232\) 0 0
\(233\) −5.28950 + 9.16169i −0.346527 + 0.600202i −0.985630 0.168919i \(-0.945972\pi\)
0.639103 + 0.769121i \(0.279306\pi\)
\(234\) 0 0
\(235\) −11.2381 −0.733096
\(236\) 0 0
\(237\) 3.15430 + 5.46340i 0.204894 + 0.354886i
\(238\) 0 0
\(239\) −5.68065 −0.367451 −0.183725 0.982978i \(-0.558816\pi\)
−0.183725 + 0.982978i \(0.558816\pi\)
\(240\) 0 0
\(241\) −4.75714 8.23962i −0.306435 0.530760i 0.671145 0.741326i \(-0.265803\pi\)
−0.977580 + 0.210566i \(0.932469\pi\)
\(242\) 0 0
\(243\) −11.3004 19.5728i −0.724918 1.25559i
\(244\) 0 0
\(245\) 2.32473 4.02654i 0.148521 0.257246i
\(246\) 0 0
\(247\) −2.30233 29.1059i −0.146494 1.85196i
\(248\) 0 0
\(249\) 16.3754 28.3631i 1.03775 1.79744i
\(250\) 0 0
\(251\) −6.26658 10.8540i −0.395543 0.685100i 0.597628 0.801774i \(-0.296110\pi\)
−0.993170 + 0.116674i \(0.962777\pi\)
\(252\) 0 0
\(253\) 8.32605 + 14.4211i 0.523454 + 0.906649i
\(254\) 0 0
\(255\) −19.0459 −1.19270
\(256\) 0 0
\(257\) 8.54453 + 14.7996i 0.532993 + 0.923171i 0.999258 + 0.0385258i \(0.0122662\pi\)
−0.466264 + 0.884645i \(0.654400\pi\)
\(258\) 0 0
\(259\) 16.5533 1.02857
\(260\) 0 0
\(261\) 3.85527 6.67753i 0.238635 0.413328i
\(262\) 0 0
\(263\) −0.460054 + 0.796838i −0.0283682 + 0.0491351i −0.879861 0.475231i \(-0.842364\pi\)
0.851493 + 0.524366i \(0.175698\pi\)
\(264\) 0 0
\(265\) 1.57636 0.0968347
\(266\) 0 0
\(267\) 9.72651 0.595252
\(268\) 0 0
\(269\) −12.6826 + 21.9669i −0.773272 + 1.33935i 0.162489 + 0.986710i \(0.448048\pi\)
−0.935761 + 0.352636i \(0.885285\pi\)
\(270\) 0 0
\(271\) 5.61828 9.73115i 0.341286 0.591125i −0.643386 0.765542i \(-0.722471\pi\)
0.984672 + 0.174417i \(0.0558041\pi\)
\(272\) 0 0
\(273\) 32.5030 1.96717
\(274\) 0 0
\(275\) 1.89848 + 3.28826i 0.114482 + 0.198289i
\(276\) 0 0
\(277\) 16.5491 0.994340 0.497170 0.867653i \(-0.334373\pi\)
0.497170 + 0.867653i \(0.334373\pi\)
\(278\) 0 0
\(279\) 3.70367 + 6.41495i 0.221733 + 0.384053i
\(280\) 0 0
\(281\) 5.28950 + 9.16169i 0.315545 + 0.546540i 0.979553 0.201185i \(-0.0644793\pi\)
−0.664008 + 0.747725i \(0.731146\pi\)
\(282\) 0 0
\(283\) −10.3707 + 17.9626i −0.616474 + 1.06776i 0.373650 + 0.927570i \(0.378106\pi\)
−0.990124 + 0.140195i \(0.955227\pi\)
\(284\) 0 0
\(285\) 1.08790 + 13.7532i 0.0644418 + 0.814668i
\(286\) 0 0
\(287\) 2.70842 4.69113i 0.159873 0.276909i
\(288\) 0 0
\(289\) −9.60545 16.6371i −0.565027 0.978655i
\(290\) 0 0
\(291\) −14.0371 24.3129i −0.822868 1.42525i
\(292\) 0 0
\(293\) 13.6846 0.799460 0.399730 0.916633i \(-0.369104\pi\)
0.399730 + 0.916633i \(0.369104\pi\)
\(294\) 0 0
\(295\) −1.61568 2.79843i −0.0940683 0.162931i
\(296\) 0 0
\(297\) −48.2811 −2.80155
\(298\) 0 0
\(299\) 14.6880 25.4403i 0.849428 1.47125i
\(300\) 0 0
\(301\) 4.25503 7.36992i 0.245256 0.424795i
\(302\) 0 0
\(303\) 19.6495 1.12883
\(304\) 0 0
\(305\) 0.0663000 0.00379633
\(306\) 0 0
\(307\) 4.31872 7.48025i 0.246483 0.426920i −0.716065 0.698034i \(-0.754059\pi\)
0.962547 + 0.271113i \(0.0873919\pi\)
\(308\) 0 0
\(309\) 0.400456 0.693609i 0.0227811 0.0394581i
\(310\) 0 0
\(311\) 29.7658 1.68786 0.843930 0.536453i \(-0.180236\pi\)
0.843930 + 0.536453i \(0.180236\pi\)
\(312\) 0 0
\(313\) −5.60413 9.70664i −0.316764 0.548651i 0.663047 0.748578i \(-0.269263\pi\)
−0.979811 + 0.199926i \(0.935930\pi\)
\(314\) 0 0
\(315\) −10.7590 −0.606199
\(316\) 0 0
\(317\) 2.34650 + 4.06425i 0.131792 + 0.228271i 0.924368 0.381503i \(-0.124593\pi\)
−0.792575 + 0.609774i \(0.791260\pi\)
\(318\) 0 0
\(319\) −2.08595 3.61298i −0.116791 0.202288i
\(320\) 0 0
\(321\) 9.58306 16.5983i 0.534874 0.926429i
\(322\) 0 0
\(323\) −21.6108 + 14.8654i −1.20246 + 0.827131i
\(324\) 0 0
\(325\) 3.34910 5.80081i 0.185775 0.321771i
\(326\) 0 0
\(327\) −8.30652 14.3873i −0.459352 0.795620i
\(328\) 0 0
\(329\) −8.61488 14.9214i −0.474954 0.822644i
\(330\) 0 0
\(331\) 29.1137 1.60024 0.800118 0.599843i \(-0.204770\pi\)
0.800118 + 0.599843i \(0.204770\pi\)
\(332\) 0 0
\(333\) 37.8841 + 65.6171i 2.07603 + 3.59580i
\(334\) 0 0
\(335\) −5.70500 −0.311697
\(336\) 0 0
\(337\) −11.5790 + 20.0554i −0.630749 + 1.09249i 0.356650 + 0.934238i \(0.383919\pi\)
−0.987399 + 0.158251i \(0.949415\pi\)
\(338\) 0 0
\(339\) −3.84372 + 6.65752i −0.208762 + 0.361587i
\(340\) 0 0
\(341\) 4.00786 0.217038
\(342\) 0 0
\(343\) 17.8604 0.964369
\(344\) 0 0
\(345\) −6.94040 + 12.0211i −0.373659 + 0.647196i
\(346\) 0 0
\(347\) −7.83090 + 13.5635i −0.420385 + 0.728127i −0.995977 0.0896094i \(-0.971438\pi\)
0.575592 + 0.817737i \(0.304771\pi\)
\(348\) 0 0
\(349\) −9.72130 −0.520369 −0.260185 0.965559i \(-0.583783\pi\)
−0.260185 + 0.965559i \(0.583783\pi\)
\(350\) 0 0
\(351\) 42.5863 + 73.7617i 2.27309 + 3.93711i
\(352\) 0 0
\(353\) 11.3789 0.605635 0.302818 0.953049i \(-0.402073\pi\)
0.302818 + 0.953049i \(0.402073\pi\)
\(354\) 0 0
\(355\) 3.23880 + 5.60977i 0.171898 + 0.297736i
\(356\) 0 0
\(357\) −14.6001 25.2881i −0.772718 1.33839i
\(358\) 0 0
\(359\) −14.3876 + 24.9201i −0.759350 + 1.31523i 0.183833 + 0.982958i \(0.441150\pi\)
−0.943183 + 0.332275i \(0.892184\pi\)
\(360\) 0 0
\(361\) 11.9688 + 14.7563i 0.629938 + 0.776645i
\(362\) 0 0
\(363\) −5.40725 + 9.36563i −0.283807 + 0.491568i
\(364\) 0 0
\(365\) −6.98978 12.1066i −0.365862 0.633691i
\(366\) 0 0
\(367\) 12.0649 + 20.8969i 0.629780 + 1.09081i 0.987596 + 0.157019i \(0.0501884\pi\)
−0.357815 + 0.933792i \(0.616478\pi\)
\(368\) 0 0
\(369\) 24.7941 1.29073
\(370\) 0 0
\(371\) 1.20839 + 2.09300i 0.0627367 + 0.108663i
\(372\) 0 0
\(373\) −26.7281 −1.38393 −0.691964 0.721932i \(-0.743254\pi\)
−0.691964 + 0.721932i \(0.743254\pi\)
\(374\) 0 0
\(375\) −1.58253 + 2.74101i −0.0817213 + 0.141545i
\(376\) 0 0
\(377\) −3.67983 + 6.37365i −0.189521 + 0.328260i
\(378\) 0 0
\(379\) 4.29369 0.220552 0.110276 0.993901i \(-0.464826\pi\)
0.110276 + 0.993901i \(0.464826\pi\)
\(380\) 0 0
\(381\) −61.0820 −3.12933
\(382\) 0 0
\(383\) −2.78610 + 4.82567i −0.142363 + 0.246580i −0.928386 0.371617i \(-0.878803\pi\)
0.786023 + 0.618197i \(0.212137\pi\)
\(384\) 0 0
\(385\) −2.91065 + 5.04139i −0.148340 + 0.256933i
\(386\) 0 0
\(387\) 38.9523 1.98006
\(388\) 0 0
\(389\) −14.0743 24.3774i −0.713594 1.23598i −0.963499 0.267711i \(-0.913733\pi\)
0.249905 0.968270i \(-0.419601\pi\)
\(390\) 0 0
\(391\) −26.3909 −1.33464
\(392\) 0 0
\(393\) 20.9837 + 36.3449i 1.05849 + 1.83336i
\(394\) 0 0
\(395\) 0.996602 + 1.72617i 0.0501445 + 0.0868528i
\(396\) 0 0
\(397\) −17.3712 + 30.0879i −0.871837 + 1.51007i −0.0117431 + 0.999931i \(0.503738\pi\)
−0.860094 + 0.510135i \(0.829595\pi\)
\(398\) 0 0
\(399\) −17.4268 + 11.9873i −0.872430 + 0.600116i
\(400\) 0 0
\(401\) 11.9370 20.6755i 0.596106 1.03249i −0.397284 0.917696i \(-0.630047\pi\)
0.993390 0.114789i \(-0.0366193\pi\)
\(402\) 0 0
\(403\) −3.53513 6.12302i −0.176097 0.305010i
\(404\) 0 0
\(405\) −9.59668 16.6219i −0.476863 0.825951i
\(406\) 0 0
\(407\) 40.9955 2.03207
\(408\) 0 0
\(409\) 18.7346 + 32.4492i 0.926365 + 1.60451i 0.789350 + 0.613943i \(0.210418\pi\)
0.137015 + 0.990569i \(0.456249\pi\)
\(410\) 0 0
\(411\) −49.2188 −2.42778
\(412\) 0 0
\(413\) 2.47707 4.29042i 0.121889 0.211118i
\(414\) 0 0
\(415\) 5.17383 8.96133i 0.253973 0.439894i
\(416\) 0 0
\(417\) −58.9402 −2.88632
\(418\) 0 0
\(419\) −0.360241 −0.0175989 −0.00879947 0.999961i \(-0.502801\pi\)
−0.00879947 + 0.999961i \(0.502801\pi\)
\(420\) 0 0
\(421\) −12.1243 + 20.9999i −0.590901 + 1.02347i 0.403210 + 0.915108i \(0.367894\pi\)
−0.994111 + 0.108364i \(0.965439\pi\)
\(422\) 0 0
\(423\) 39.4321 68.2984i 1.91726 3.32078i
\(424\) 0 0
\(425\) −6.01755 −0.291894
\(426\) 0 0
\(427\) 0.0508239 + 0.0880297i 0.00245954 + 0.00426005i
\(428\) 0 0
\(429\) 80.4960 3.88638
\(430\) 0 0
\(431\) 6.32067 + 10.9477i 0.304456 + 0.527333i 0.977140 0.212596i \(-0.0681920\pi\)
−0.672684 + 0.739930i \(0.734859\pi\)
\(432\) 0 0
\(433\) 12.2320 + 21.1864i 0.587831 + 1.01815i 0.994516 + 0.104585i \(0.0333514\pi\)
−0.406685 + 0.913569i \(0.633315\pi\)
\(434\) 0 0
\(435\) 1.73880 3.01169i 0.0833692 0.144400i
\(436\) 0 0
\(437\) 1.50745 + 19.0571i 0.0721111 + 0.911623i
\(438\) 0 0
\(439\) 12.4004 21.4782i 0.591840 1.02510i −0.402144 0.915576i \(-0.631735\pi\)
0.993985 0.109521i \(-0.0349316\pi\)
\(440\) 0 0
\(441\) 16.3139 + 28.2565i 0.776851 + 1.34555i
\(442\) 0 0
\(443\) −15.1318 26.2090i −0.718932 1.24523i −0.961423 0.275074i \(-0.911298\pi\)
0.242491 0.970154i \(-0.422036\pi\)
\(444\) 0 0
\(445\) 3.07310 0.145679
\(446\) 0 0
\(447\) 7.41801 + 12.8484i 0.350860 + 0.607707i
\(448\) 0 0
\(449\) −29.0742 −1.37209 −0.686047 0.727557i \(-0.740656\pi\)
−0.686047 + 0.727557i \(0.740656\pi\)
\(450\) 0 0
\(451\) 6.70760 11.6179i 0.315849 0.547066i
\(452\) 0 0
\(453\) 9.39023 16.2644i 0.441192 0.764166i
\(454\) 0 0
\(455\) 10.2693 0.481434
\(456\) 0 0
\(457\) −3.06234 −0.143250 −0.0716251 0.997432i \(-0.522819\pi\)
−0.0716251 + 0.997432i \(0.522819\pi\)
\(458\) 0 0
\(459\) 38.2588 66.2662i 1.78577 3.09304i
\(460\) 0 0
\(461\) 13.2934 23.0249i 0.619137 1.07238i −0.370507 0.928830i \(-0.620816\pi\)
0.989644 0.143547i \(-0.0458507\pi\)
\(462\) 0 0
\(463\) 4.82684 0.224322 0.112161 0.993690i \(-0.464223\pi\)
0.112161 + 0.993690i \(0.464223\pi\)
\(464\) 0 0
\(465\) 1.67043 + 2.89327i 0.0774643 + 0.134172i
\(466\) 0 0
\(467\) −1.31539 −0.0608690 −0.0304345 0.999537i \(-0.509689\pi\)
−0.0304345 + 0.999537i \(0.509689\pi\)
\(468\) 0 0
\(469\) −4.37331 7.57479i −0.201941 0.349771i
\(470\) 0 0
\(471\) 14.7075 + 25.4741i 0.677686 + 1.17379i
\(472\) 0 0
\(473\) 10.5379 18.2521i 0.484532 0.839234i
\(474\) 0 0
\(475\) 0.343724 + 4.34533i 0.0157711 + 0.199377i
\(476\) 0 0
\(477\) −5.53108 + 9.58011i −0.253251 + 0.438643i
\(478\) 0 0
\(479\) −9.53915 16.5223i −0.435855 0.754923i 0.561510 0.827470i \(-0.310221\pi\)
−0.997365 + 0.0725469i \(0.976887\pi\)
\(480\) 0 0
\(481\) −36.1601 62.6311i −1.64876 2.85573i
\(482\) 0 0
\(483\) −21.2814 −0.968335
\(484\) 0 0
\(485\) −4.43502 7.68169i −0.201384 0.348807i
\(486\) 0 0
\(487\) −8.23656 −0.373234 −0.186617 0.982433i \(-0.559752\pi\)
−0.186617 + 0.982433i \(0.559752\pi\)
\(488\) 0 0
\(489\) −9.31308 + 16.1307i −0.421152 + 0.729457i
\(490\) 0 0
\(491\) −15.4776 + 26.8079i −0.698493 + 1.20983i 0.270496 + 0.962721i \(0.412812\pi\)
−0.968989 + 0.247104i \(0.920521\pi\)
\(492\) 0 0
\(493\) 6.61179 0.297780
\(494\) 0 0
\(495\) −26.6453 −1.19762
\(496\) 0 0
\(497\) −4.96557 + 8.60062i −0.222736 + 0.385790i
\(498\) 0 0
\(499\) −0.554753 + 0.960860i −0.0248341 + 0.0430140i −0.878175 0.478339i \(-0.841239\pi\)
0.853341 + 0.521353i \(0.174572\pi\)
\(500\) 0 0
\(501\) 40.5030 1.80954
\(502\) 0 0
\(503\) −4.32552 7.49202i −0.192865 0.334053i 0.753333 0.657639i \(-0.228445\pi\)
−0.946199 + 0.323586i \(0.895111\pi\)
\(504\) 0 0
\(505\) 6.20826 0.276264
\(506\) 0 0
\(507\) −50.4286 87.3449i −2.23961 3.87912i
\(508\) 0 0
\(509\) 10.3944 + 18.0037i 0.460725 + 0.797999i 0.998997 0.0447722i \(-0.0142562\pi\)
−0.538273 + 0.842771i \(0.680923\pi\)
\(510\) 0 0
\(511\) 10.7164 18.5613i 0.474065 0.821104i
\(512\) 0 0
\(513\) −50.0368 23.8419i −2.20918 1.05265i
\(514\) 0 0
\(515\) 0.126524 0.219146i 0.00557532 0.00965674i
\(516\) 0 0
\(517\) −21.3354 36.9539i −0.938328 1.62523i
\(518\) 0 0
\(519\) 23.8022 + 41.2266i 1.04480 + 1.80965i
\(520\) 0 0
\(521\) −24.5098 −1.07379 −0.536897 0.843648i \(-0.680404\pi\)
−0.536897 + 0.843648i \(0.680404\pi\)
\(522\) 0 0
\(523\) −9.03447 15.6482i −0.395050 0.684247i 0.598058 0.801453i \(-0.295939\pi\)
−0.993108 + 0.117207i \(0.962606\pi\)
\(524\) 0 0
\(525\) −4.85250 −0.211780
\(526\) 0 0
\(527\) −3.17590 + 5.50082i −0.138344 + 0.239619i
\(528\) 0 0
\(529\) 1.88304 3.26153i 0.0818715 0.141806i
\(530\) 0 0
\(531\) 22.6762 0.984062
\(532\) 0 0
\(533\) −23.6658 −1.02508
\(534\) 0 0
\(535\) 3.02777 5.24426i 0.130902 0.226729i
\(536\) 0 0
\(537\) −34.0958 + 59.0556i −1.47134 + 2.54844i
\(538\) 0 0
\(539\) 17.6537 0.760401
\(540\) 0 0
\(541\) 8.75440 + 15.1631i 0.376381 + 0.651911i 0.990533 0.137277i \(-0.0438350\pi\)
−0.614152 + 0.789188i \(0.710502\pi\)
\(542\) 0 0
\(543\) 13.5167 0.580055
\(544\) 0 0
\(545\) −2.62445 4.54568i −0.112419 0.194716i
\(546\) 0 0
\(547\) −13.4864 23.3591i −0.576636 0.998763i −0.995862 0.0908807i \(-0.971032\pi\)
0.419226 0.907882i \(-0.362302\pi\)
\(548\) 0 0
\(549\) −0.232632 + 0.402930i −0.00992849 + 0.0171966i
\(550\) 0 0
\(551\) −0.377667 4.77443i −0.0160891 0.203398i
\(552\) 0 0
\(553\) −1.52794 + 2.64647i −0.0649746 + 0.112539i
\(554\) 0 0
\(555\) 17.0865 + 29.5946i 0.725280 + 1.25622i
\(556\) 0 0
\(557\) 7.98361 + 13.8280i 0.338276 + 0.585912i 0.984109 0.177568i \(-0.0568228\pi\)
−0.645832 + 0.763479i \(0.723490\pi\)
\(558\) 0 0
\(559\) −37.1797 −1.57253
\(560\) 0 0
\(561\) −36.1581 62.6277i −1.52660 2.64414i
\(562\) 0 0
\(563\) −8.58711 −0.361904 −0.180952 0.983492i \(-0.557918\pi\)
−0.180952 + 0.983492i \(0.557918\pi\)
\(564\) 0 0
\(565\) −1.21443 + 2.10345i −0.0510913 + 0.0884928i
\(566\) 0 0
\(567\) 14.7131 25.4839i 0.617894 1.07022i
\(568\) 0 0
\(569\) 22.5910 0.947064 0.473532 0.880777i \(-0.342979\pi\)
0.473532 + 0.880777i \(0.342979\pi\)
\(570\) 0 0
\(571\) 17.1000 0.715613 0.357806 0.933796i \(-0.383525\pi\)
0.357806 + 0.933796i \(0.383525\pi\)
\(572\) 0 0
\(573\) 9.97276 17.2733i 0.416618 0.721603i
\(574\) 0 0
\(575\) −2.19282 + 3.79808i −0.0914471 + 0.158391i
\(576\) 0 0
\(577\) −0.677755 −0.0282153 −0.0141077 0.999900i \(-0.504491\pi\)
−0.0141077 + 0.999900i \(0.504491\pi\)
\(578\) 0 0
\(579\) 24.3374 + 42.1537i 1.01143 + 1.75185i
\(580\) 0 0
\(581\) 15.8645 0.658171
\(582\) 0 0
\(583\) 2.99267 + 5.18346i 0.123944 + 0.214677i
\(584\) 0 0
\(585\) 23.5025 + 40.7075i 0.971708 + 1.68305i
\(586\) 0 0
\(587\) −13.6859 + 23.7047i −0.564878 + 0.978397i 0.432183 + 0.901786i \(0.357743\pi\)
−0.997061 + 0.0766112i \(0.975590\pi\)
\(588\) 0 0
\(589\) 4.15360 + 1.97914i 0.171146 + 0.0815489i
\(590\) 0 0
\(591\) 20.1312 34.8683i 0.828089 1.43429i
\(592\) 0 0
\(593\) −4.18940 7.25625i −0.172038 0.297978i 0.767094 0.641534i \(-0.221702\pi\)
−0.939132 + 0.343556i \(0.888368\pi\)
\(594\) 0 0
\(595\) −4.61290 7.98978i −0.189111 0.327549i
\(596\) 0 0
\(597\) 32.3395 1.32357
\(598\) 0 0
\(599\) 16.9553 + 29.3675i 0.692777 + 1.19992i 0.970924 + 0.239386i \(0.0769462\pi\)
−0.278148 + 0.960538i \(0.589720\pi\)
\(600\) 0 0
\(601\) −5.74951 −0.234528 −0.117264 0.993101i \(-0.537412\pi\)
−0.117264 + 0.993101i \(0.537412\pi\)
\(602\) 0 0
\(603\) 20.0175 34.6714i 0.815178 1.41193i
\(604\) 0 0
\(605\) −1.70842 + 2.95908i −0.0694573 + 0.120304i
\(606\) 0 0
\(607\) −8.87815 −0.360353 −0.180177 0.983634i \(-0.557667\pi\)
−0.180177 + 0.983634i \(0.557667\pi\)
\(608\) 0 0
\(609\) 5.33169 0.216051
\(610\) 0 0
\(611\) −37.6377 + 65.1904i −1.52266 + 2.63732i
\(612\) 0 0
\(613\) 6.02098 10.4286i 0.243185 0.421209i −0.718435 0.695594i \(-0.755141\pi\)
0.961620 + 0.274386i \(0.0884745\pi\)
\(614\) 0 0
\(615\) 11.1826 0.450926
\(616\) 0 0
\(617\) −23.4362 40.5927i −0.943505 1.63420i −0.758717 0.651420i \(-0.774173\pi\)
−0.184788 0.982778i \(-0.559160\pi\)
\(618\) 0 0
\(619\) 14.8700 0.597678 0.298839 0.954304i \(-0.403401\pi\)
0.298839 + 0.954304i \(0.403401\pi\)
\(620\) 0 0
\(621\) −27.8834 48.2955i −1.11892 1.93803i
\(622\) 0 0
\(623\) 2.35576 + 4.08029i 0.0943815 + 0.163473i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −43.1586 + 29.6874i −1.72359 + 1.18560i
\(628\) 0 0
\(629\) −32.4856 + 56.2667i −1.29529 + 2.24350i
\(630\) 0 0
\(631\) −8.71235 15.0902i −0.346833 0.600733i 0.638852 0.769330i \(-0.279410\pi\)
−0.985685 + 0.168597i \(0.946076\pi\)
\(632\) 0 0
\(633\) −8.02830 13.9054i −0.319096 0.552691i
\(634\) 0 0
\(635\) −19.2989 −0.765854
\(636\) 0 0
\(637\) −15.5715 26.9706i −0.616964 1.06861i
\(638\) 0 0
\(639\) −45.4569 −1.79825
\(640\) 0 0
\(641\) −15.9973 + 27.7081i −0.631854 + 1.09440i 0.355318 + 0.934745i \(0.384373\pi\)
−0.987172 + 0.159658i \(0.948961\pi\)
\(642\) 0 0
\(643\) −17.5203 + 30.3461i −0.690934 + 1.19673i 0.280598 + 0.959825i \(0.409467\pi\)
−0.971532 + 0.236908i \(0.923866\pi\)
\(644\) 0 0
\(645\) 17.5682 0.691749
\(646\) 0 0
\(647\) 17.4260 0.685087 0.342544 0.939502i \(-0.388712\pi\)
0.342544 + 0.939502i \(0.388712\pi\)
\(648\) 0 0
\(649\) 6.13464 10.6255i 0.240806 0.417088i
\(650\) 0 0
\(651\) −2.56102 + 4.43581i −0.100374 + 0.173853i
\(652\) 0 0
\(653\) −49.1457 −1.92322 −0.961609 0.274422i \(-0.911513\pi\)
−0.961609 + 0.274422i \(0.911513\pi\)
\(654\) 0 0
\(655\) 6.62983 + 11.4832i 0.259049 + 0.448686i
\(656\) 0 0
\(657\) 98.1022 3.82733
\(658\) 0 0
\(659\) −0.862722 1.49428i −0.0336069 0.0582088i 0.848733 0.528822i \(-0.177366\pi\)
−0.882340 + 0.470613i \(0.844033\pi\)
\(660\) 0 0
\(661\) −10.9594 18.9822i −0.426270 0.738321i 0.570268 0.821459i \(-0.306839\pi\)
−0.996538 + 0.0831373i \(0.973506\pi\)
\(662\) 0 0
\(663\) −63.7865 + 110.481i −2.47726 + 4.29074i
\(664\) 0 0
\(665\) −5.50600 + 3.78740i −0.213514 + 0.146869i
\(666\) 0 0
\(667\) 2.40937 4.17315i 0.0932911 0.161585i
\(668\) 0 0
\(669\) 13.4932 + 23.3709i 0.521676 + 0.903570i
\(670\) 0 0
\(671\) 0.125869 + 0.218012i 0.00485912 + 0.00841624i
\(672\) 0 0
\(673\) 6.63165 0.255631 0.127816 0.991798i \(-0.459203\pi\)
0.127816 + 0.991798i \(0.459203\pi\)
\(674\) 0 0
\(675\) −6.35788 11.0122i −0.244715 0.423858i
\(676\) 0 0
\(677\) 32.7008 1.25679 0.628397 0.777893i \(-0.283711\pi\)
0.628397 + 0.777893i \(0.283711\pi\)
\(678\) 0 0
\(679\) 6.79956 11.7772i 0.260943 0.451967i
\(680\) 0 0
\(681\) 31.7401 54.9755i 1.21628 2.10666i
\(682\) 0 0
\(683\) −51.9872 −1.98923 −0.994617 0.103622i \(-0.966957\pi\)
−0.994617 + 0.103622i \(0.966957\pi\)
\(684\) 0 0
\(685\) −15.5507 −0.594162
\(686\) 0 0
\(687\) −12.5487 + 21.7350i −0.478764 + 0.829243i
\(688\) 0 0
\(689\) 5.27937 9.14414i 0.201128 0.348364i
\(690\) 0 0
\(691\) −8.93635 −0.339955 −0.169977 0.985448i \(-0.554369\pi\)
−0.169977 + 0.985448i \(0.554369\pi\)
\(692\) 0 0
\(693\) −20.4256 35.3782i −0.775905 1.34391i
\(694\) 0 0
\(695\) −18.6222 −0.706381
\(696\) 0 0
\(697\) 10.6305 + 18.4125i 0.402657 + 0.697423i
\(698\) 0 0
\(699\) −16.7415 28.9972i −0.633223 1.09678i
\(700\) 0 0
\(701\) −1.12927 + 1.95595i −0.0426518 + 0.0738751i −0.886563 0.462607i \(-0.846914\pi\)
0.843911 + 0.536483i \(0.180247\pi\)
\(702\) 0 0
\(703\) 42.4863 + 20.2442i 1.60240 + 0.763523i
\(704\) 0 0
\(705\) 17.7847 30.8039i 0.669809 1.16014i
\(706\) 0 0
\(707\) 4.75909 + 8.24299i 0.178984 + 0.310010i
\(708\) 0 0
\(709\) −23.4045 40.5378i −0.878975 1.52243i −0.852467 0.522781i \(-0.824894\pi\)
−0.0265084 0.999649i \(-0.508439\pi\)
\(710\) 0 0
\(711\) −13.9874 −0.524569
\(712\) 0 0
\(713\) 2.31463 + 4.00905i 0.0866834 + 0.150140i
\(714\) 0 0
\(715\) 25.4328 0.951131
\(716\) 0 0
\(717\) 8.98978 15.5708i 0.335729 0.581500i
\(718\) 0 0
\(719\) 11.7570 20.3637i 0.438462 0.759439i −0.559109 0.829094i \(-0.688857\pi\)
0.997571 + 0.0696552i \(0.0221899\pi\)
\(720\) 0 0
\(721\) 0.387961 0.0144484
\(722\) 0 0
\(723\) 30.1132 1.11992
\(724\) 0 0
\(725\) 0.549376 0.951547i 0.0204033 0.0353396i
\(726\) 0 0
\(727\) 12.7374 22.0617i 0.472402 0.818225i −0.527099 0.849804i \(-0.676720\pi\)
0.999501 + 0.0315791i \(0.0100536\pi\)
\(728\) 0 0
\(729\) 13.9523 0.516752
\(730\) 0 0
\(731\) 16.7008 + 28.9266i 0.617702 + 1.06989i
\(732\) 0 0
\(733\) −1.41916 −0.0524179 −0.0262090 0.999656i \(-0.508344\pi\)
−0.0262090 + 0.999656i \(0.508344\pi\)
\(734\) 0 0
\(735\) 7.35788 + 12.7442i 0.271399 + 0.470077i
\(736\) 0 0
\(737\) −10.8308 18.7595i −0.398958 0.691015i
\(738\) 0 0
\(739\) 10.7699 18.6540i 0.396176 0.686198i −0.597074 0.802186i \(-0.703670\pi\)
0.993251 + 0.115988i \(0.0370035\pi\)
\(740\) 0 0
\(741\) 83.4231 + 39.7501i 3.06462 + 1.46025i
\(742\) 0 0
\(743\) 21.2813 36.8602i 0.780734 1.35227i −0.150781 0.988567i \(-0.548179\pi\)
0.931515 0.363703i \(-0.118488\pi\)
\(744\) 0 0
\(745\) 2.34372 + 4.05945i 0.0858674 + 0.148727i
\(746\) 0 0
\(747\) 36.3076 + 62.8866i 1.32842 + 2.30090i
\(748\) 0 0
\(749\) 9.28406 0.339232
\(750\) 0 0
\(751\) −9.30708 16.1203i −0.339620 0.588239i 0.644741 0.764401i \(-0.276965\pi\)
−0.984361 + 0.176162i \(0.943632\pi\)
\(752\) 0 0
\(753\) 39.6681 1.44558
\(754\) 0 0
\(755\) 2.96685 5.13873i 0.107975 0.187018i
\(756\) 0 0
\(757\) 15.3842 26.6462i 0.559148 0.968473i −0.438420 0.898770i \(-0.644462\pi\)
0.997568 0.0697028i \(-0.0222051\pi\)
\(758\) 0 0
\(759\) −52.7047 −1.91306
\(760\) 0 0
\(761\) 13.9270 0.504853 0.252427 0.967616i \(-0.418771\pi\)
0.252427 + 0.967616i \(0.418771\pi\)
\(762\) 0 0
\(763\) 4.02368 6.96921i 0.145667 0.252302i
\(764\) 0 0
\(765\) 21.1142 36.5709i 0.763387 1.32222i
\(766\) 0 0
\(767\) −21.6442 −0.781528
\(768\) 0 0
\(769\) 24.3166 + 42.1176i 0.876880 + 1.51880i 0.854747 + 0.519045i \(0.173712\pi\)
0.0221329 + 0.999755i \(0.492954\pi\)
\(770\) 0 0
\(771\) −54.0877 −1.94792
\(772\) 0 0
\(773\) 9.79276 + 16.9616i 0.352221 + 0.610065i 0.986638 0.162926i \(-0.0520932\pi\)
−0.634417 + 0.772991i \(0.718760\pi\)
\(774\) 0 0
\(775\) 0.527773 + 0.914130i 0.0189582 + 0.0328365i
\(776\) 0 0
\(777\) −26.1961 + 45.3730i −0.939780 + 1.62775i
\(778\) 0 0
\(779\) 12.6886 8.72807i 0.454616 0.312715i
\(780\) 0 0
\(781\) −12.2976 + 21.3000i −0.440042 + 0.762175i
\(782\) 0 0
\(783\) 6.98572 + 12.0996i 0.249649 + 0.432405i
\(784\) 0 0
\(785\) 4.64685 + 8.04857i 0.165853 + 0.287266i
\(786\) 0 0
\(787\) 13.4029 0.477760 0.238880 0.971049i \(-0.423220\pi\)
0.238880 + 0.971049i \(0.423220\pi\)
\(788\) 0 0
\(789\) −1.45610 2.52203i −0.0518384 0.0897867i
\(790\)