Properties

Label 380.2.u.b.301.3
Level $380$
Weight $2$
Character 380.301
Analytic conductor $3.034$
Analytic rank $0$
Dimension $18$
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(61,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(18))
 
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("380.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.u (of order \(9\), degree \(6\), 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: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 21 x^{16} - 30 x^{15} + 192 x^{14} - 207 x^{13} + 1178 x^{12} - 705 x^{11} + \cdots + 5329 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 301.3
Root \(1.55777 + 2.69813i\) of defining polynomial
Character \(\chi\) \(=\) 380.301
Dual form 380.2.u.b.101.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.92764 - 1.06558i) q^{3} +(0.173648 - 0.984808i) q^{5} +(0.643760 + 1.11502i) q^{7} +(5.13752 - 4.31089i) q^{9} +O(q^{10})\) \(q+(2.92764 - 1.06558i) q^{3} +(0.173648 - 0.984808i) q^{5} +(0.643760 + 1.11502i) q^{7} +(5.13752 - 4.31089i) q^{9} +(-2.25088 + 3.89864i) q^{11} +(-0.115094 - 0.0418907i) q^{13} +(-0.541007 - 3.06820i) q^{15} +(-0.730551 - 0.613005i) q^{17} +(-1.18925 - 4.19353i) q^{19} +(3.07284 + 2.57842i) q^{21} +(0.507981 + 2.88091i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(5.77395 - 10.0008i) q^{27} +(-5.12896 + 4.30371i) q^{29} +(-2.91189 - 5.04355i) q^{31} +(-2.43548 + 13.8123i) q^{33} +(1.20987 - 0.440358i) q^{35} -8.95982 q^{37} -0.381591 q^{39} +(7.45930 - 2.71496i) q^{41} +(-1.65520 + 9.38710i) q^{43} +(-3.35328 - 5.80804i) q^{45} +(-0.709210 + 0.595097i) q^{47} +(2.67115 - 4.62656i) q^{49} +(-2.79200 - 1.01620i) q^{51} +(-0.00414149 - 0.0234876i) q^{53} +(3.44855 + 2.89368i) q^{55} +(-7.95023 - 11.0099i) q^{57} +(8.19663 + 6.87779i) q^{59} +(1.02491 + 5.81255i) q^{61} +(8.11408 + 2.95328i) q^{63} +(-0.0612401 + 0.106071i) q^{65} +(12.0876 - 10.1427i) q^{67} +(4.55701 + 7.89297i) q^{69} +(-2.62142 + 14.8668i) q^{71} +(3.61254 - 1.31486i) q^{73} -3.11553 q^{75} -5.79610 q^{77} +(-2.80162 + 1.01971i) q^{79} +(2.75375 - 15.6173i) q^{81} +(-4.36455 - 7.55962i) q^{83} +(-0.730551 + 0.613005i) q^{85} +(-10.4299 + 18.0650i) q^{87} +(-14.0616 - 5.11801i) q^{89} +(-0.0273836 - 0.155300i) q^{91} +(-13.8993 - 11.6629i) q^{93} +(-4.33633 + 0.442988i) q^{95} +(-13.3023 - 11.1620i) q^{97} +(5.24266 + 29.7326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(1\) \(1\)

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
\(3\) 2.92764 1.06558i 1.69028 0.615210i 0.695616 0.718414i \(-0.255132\pi\)
0.994660 + 0.103204i \(0.0329093\pi\)
\(4\) 0 0
\(5\) 0.173648 0.984808i 0.0776578 0.440419i
\(6\) 0 0
\(7\) 0.643760 + 1.11502i 0.243318 + 0.421440i 0.961657 0.274253i \(-0.0884307\pi\)
−0.718339 + 0.695693i \(0.755097\pi\)
\(8\) 0 0
\(9\) 5.13752 4.31089i 1.71251 1.43696i
\(10\) 0 0
\(11\) −2.25088 + 3.89864i −0.678666 + 1.17548i 0.296717 + 0.954965i \(0.404108\pi\)
−0.975383 + 0.220518i \(0.929225\pi\)
\(12\) 0 0
\(13\) −0.115094 0.0418907i −0.0319213 0.0116184i 0.326010 0.945366i \(-0.394296\pi\)
−0.357931 + 0.933748i \(0.616518\pi\)
\(14\) 0 0
\(15\) −0.541007 3.06820i −0.139687 0.792206i
\(16\) 0 0
\(17\) −0.730551 0.613005i −0.177185 0.148676i 0.549882 0.835242i \(-0.314673\pi\)
−0.727067 + 0.686567i \(0.759117\pi\)
\(18\) 0 0
\(19\) −1.18925 4.19353i −0.272834 0.962061i
\(20\) 0 0
\(21\) 3.07284 + 2.57842i 0.670549 + 0.562658i
\(22\) 0 0
\(23\) 0.507981 + 2.88091i 0.105921 + 0.600710i 0.990848 + 0.134980i \(0.0430971\pi\)
−0.884927 + 0.465730i \(0.845792\pi\)
\(24\) 0 0
\(25\) −0.939693 0.342020i −0.187939 0.0684040i
\(26\) 0 0
\(27\) 5.77395 10.0008i 1.11120 1.92465i
\(28\) 0 0
\(29\) −5.12896 + 4.30371i −0.952425 + 0.799179i −0.979704 0.200449i \(-0.935760\pi\)
0.0272796 + 0.999628i \(0.491316\pi\)
\(30\) 0 0
\(31\) −2.91189 5.04355i −0.522991 0.905847i −0.999642 0.0267547i \(-0.991483\pi\)
0.476651 0.879093i \(-0.341851\pi\)
\(32\) 0 0
\(33\) −2.43548 + 13.8123i −0.423963 + 2.40441i
\(34\) 0 0
\(35\) 1.20987 0.440358i 0.204506 0.0744340i
\(36\) 0 0
\(37\) −8.95982 −1.47299 −0.736493 0.676445i \(-0.763520\pi\)
−0.736493 + 0.676445i \(0.763520\pi\)
\(38\) 0 0
\(39\) −0.381591 −0.0611035
\(40\) 0 0
\(41\) 7.45930 2.71496i 1.16495 0.424006i 0.314085 0.949395i \(-0.398302\pi\)
0.850862 + 0.525389i \(0.176080\pi\)
\(42\) 0 0
\(43\) −1.65520 + 9.38710i −0.252415 + 1.43152i 0.550205 + 0.835030i \(0.314550\pi\)
−0.802621 + 0.596490i \(0.796562\pi\)
\(44\) 0 0
\(45\) −3.35328 5.80804i −0.499877 0.865812i
\(46\) 0 0
\(47\) −0.709210 + 0.595097i −0.103449 + 0.0868039i −0.693045 0.720894i \(-0.743731\pi\)
0.589596 + 0.807698i \(0.299287\pi\)
\(48\) 0 0
\(49\) 2.67115 4.62656i 0.381592 0.660937i
\(50\) 0 0
\(51\) −2.79200 1.01620i −0.390958 0.142297i
\(52\) 0 0
\(53\) −0.00414149 0.0234876i −0.000568878 0.00322627i 0.984522 0.175261i \(-0.0560770\pi\)
−0.985091 + 0.172035i \(0.944966\pi\)
\(54\) 0 0
\(55\) 3.44855 + 2.89368i 0.465002 + 0.390183i
\(56\) 0 0
\(57\) −7.95023 11.0099i −1.05303 1.45830i
\(58\) 0 0
\(59\) 8.19663 + 6.87779i 1.06711 + 0.895411i 0.994787 0.101970i \(-0.0325145\pi\)
0.0723223 + 0.997381i \(0.476959\pi\)
\(60\) 0 0
\(61\) 1.02491 + 5.81255i 0.131226 + 0.744221i 0.977414 + 0.211335i \(0.0677813\pi\)
−0.846187 + 0.532886i \(0.821108\pi\)
\(62\) 0 0
\(63\) 8.11408 + 2.95328i 1.02228 + 0.372079i
\(64\) 0 0
\(65\) −0.0612401 + 0.106071i −0.00759590 + 0.0131565i
\(66\) 0 0
\(67\) 12.0876 10.1427i 1.47673 1.23913i 0.567145 0.823618i \(-0.308048\pi\)
0.909589 0.415509i \(-0.136397\pi\)
\(68\) 0 0
\(69\) 4.55701 + 7.89297i 0.548600 + 0.950202i
\(70\) 0 0
\(71\) −2.62142 + 14.8668i −0.311106 + 1.76437i 0.282165 + 0.959366i \(0.408947\pi\)
−0.593271 + 0.805003i \(0.702164\pi\)
\(72\) 0 0
\(73\) 3.61254 1.31486i 0.422816 0.153892i −0.121844 0.992549i \(-0.538881\pi\)
0.544660 + 0.838657i \(0.316659\pi\)
\(74\) 0 0
\(75\) −3.11553 −0.359751
\(76\) 0 0
\(77\) −5.79610 −0.660527
\(78\) 0 0
\(79\) −2.80162 + 1.01971i −0.315207 + 0.114726i −0.494779 0.869019i \(-0.664751\pi\)
0.179572 + 0.983745i \(0.442529\pi\)
\(80\) 0 0
\(81\) 2.75375 15.6173i 0.305972 1.73525i
\(82\) 0 0
\(83\) −4.36455 7.55962i −0.479071 0.829776i 0.520641 0.853776i \(-0.325693\pi\)
−0.999712 + 0.0240000i \(0.992360\pi\)
\(84\) 0 0
\(85\) −0.730551 + 0.613005i −0.0792394 + 0.0664897i
\(86\) 0 0
\(87\) −10.4299 + 18.0650i −1.11820 + 1.93677i
\(88\) 0 0
\(89\) −14.0616 5.11801i −1.49053 0.542508i −0.536939 0.843621i \(-0.680420\pi\)
−0.953588 + 0.301113i \(0.902642\pi\)
\(90\) 0 0
\(91\) −0.0273836 0.155300i −0.00287058 0.0162799i
\(92\) 0 0
\(93\) −13.8993 11.6629i −1.44129 1.20938i
\(94\) 0 0
\(95\) −4.33633 + 0.442988i −0.444898 + 0.0454496i
\(96\) 0 0
\(97\) −13.3023 11.1620i −1.35064 1.13332i −0.978752 0.205048i \(-0.934265\pi\)
−0.371891 0.928276i \(-0.621291\pi\)
\(98\) 0 0
\(99\) 5.24266 + 29.7326i 0.526907 + 2.98824i
\(100\) 0 0
\(101\) 6.82879 + 2.48548i 0.679490 + 0.247314i 0.658629 0.752468i \(-0.271137\pi\)
0.0208616 + 0.999782i \(0.493359\pi\)
\(102\) 0 0
\(103\) −0.425234 + 0.736527i −0.0418996 + 0.0725722i −0.886215 0.463275i \(-0.846674\pi\)
0.844315 + 0.535847i \(0.180008\pi\)
\(104\) 0 0
\(105\) 3.07284 2.57842i 0.299879 0.251628i
\(106\) 0 0
\(107\) 5.04809 + 8.74355i 0.488017 + 0.845271i 0.999905 0.0137816i \(-0.00438695\pi\)
−0.511888 + 0.859052i \(0.671054\pi\)
\(108\) 0 0
\(109\) −0.521529 + 2.95774i −0.0499534 + 0.283300i −0.999544 0.0301927i \(-0.990388\pi\)
0.949591 + 0.313492i \(0.101499\pi\)
\(110\) 0 0
\(111\) −26.2312 + 9.54737i −2.48975 + 0.906196i
\(112\) 0 0
\(113\) −6.06424 −0.570475 −0.285238 0.958457i \(-0.592073\pi\)
−0.285238 + 0.958457i \(0.592073\pi\)
\(114\) 0 0
\(115\) 2.92535 0.272790
\(116\) 0 0
\(117\) −0.771882 + 0.280942i −0.0713605 + 0.0259731i
\(118\) 0 0
\(119\) 0.213216 1.20921i 0.0195455 0.110848i
\(120\) 0 0
\(121\) −4.63292 8.02445i −0.421174 0.729496i
\(122\) 0 0
\(123\) 18.9452 15.8969i 1.70823 1.43337i
\(124\) 0 0
\(125\) −0.500000 + 0.866025i −0.0447214 + 0.0774597i
\(126\) 0 0
\(127\) −6.24161 2.27176i −0.553854 0.201586i 0.0499042 0.998754i \(-0.484108\pi\)
−0.603758 + 0.797168i \(0.706331\pi\)
\(128\) 0 0
\(129\) 5.15683 + 29.2458i 0.454033 + 2.57495i
\(130\) 0 0
\(131\) 7.06862 + 5.93127i 0.617588 + 0.518218i 0.897044 0.441941i \(-0.145710\pi\)
−0.279456 + 0.960158i \(0.590154\pi\)
\(132\) 0 0
\(133\) 3.91029 4.02567i 0.339065 0.349070i
\(134\) 0 0
\(135\) −8.84620 7.42284i −0.761359 0.638856i
\(136\) 0 0
\(137\) −0.634270 3.59712i −0.0541893 0.307323i 0.945651 0.325183i \(-0.105426\pi\)
−0.999840 + 0.0178599i \(0.994315\pi\)
\(138\) 0 0
\(139\) 17.6900 + 6.43863i 1.50044 + 0.546117i 0.956176 0.292794i \(-0.0945849\pi\)
0.544269 + 0.838911i \(0.316807\pi\)
\(140\) 0 0
\(141\) −1.44219 + 2.49795i −0.121454 + 0.210365i
\(142\) 0 0
\(143\) 0.422379 0.354418i 0.0353211 0.0296379i
\(144\) 0 0
\(145\) 3.34769 + 5.79837i 0.278011 + 0.481529i
\(146\) 0 0
\(147\) 2.89022 16.3912i 0.238381 1.35193i
\(148\) 0 0
\(149\) −11.0670 + 4.02805i −0.906641 + 0.329990i −0.752911 0.658122i \(-0.771351\pi\)
−0.153730 + 0.988113i \(0.549129\pi\)
\(150\) 0 0
\(151\) 6.94029 0.564793 0.282396 0.959298i \(-0.408871\pi\)
0.282396 + 0.959298i \(0.408871\pi\)
\(152\) 0 0
\(153\) −6.39581 −0.517071
\(154\) 0 0
\(155\) −5.47257 + 1.99185i −0.439567 + 0.159989i
\(156\) 0 0
\(157\) 3.03157 17.1929i 0.241946 1.37214i −0.585534 0.810648i \(-0.699115\pi\)
0.827480 0.561495i \(-0.189774\pi\)
\(158\) 0 0
\(159\) −0.0371526 0.0643502i −0.00294639 0.00510330i
\(160\) 0 0
\(161\) −2.88526 + 2.42102i −0.227391 + 0.190803i
\(162\) 0 0
\(163\) 6.12605 10.6106i 0.479829 0.831089i −0.519903 0.854225i \(-0.674032\pi\)
0.999732 + 0.0231364i \(0.00736520\pi\)
\(164\) 0 0
\(165\) 13.1796 + 4.79696i 1.02603 + 0.373443i
\(166\) 0 0
\(167\) −4.09639 23.2318i −0.316988 1.79773i −0.560848 0.827919i \(-0.689525\pi\)
0.243860 0.969811i \(-0.421586\pi\)
\(168\) 0 0
\(169\) −9.94709 8.34660i −0.765160 0.642046i
\(170\) 0 0
\(171\) −24.1876 16.4176i −1.84968 1.25548i
\(172\) 0 0
\(173\) −7.98365 6.69908i −0.606986 0.509321i 0.286697 0.958021i \(-0.407443\pi\)
−0.893683 + 0.448700i \(0.851887\pi\)
\(174\) 0 0
\(175\) −0.223575 1.26796i −0.0169007 0.0958487i
\(176\) 0 0
\(177\) 31.3256 + 11.4016i 2.35458 + 0.856996i
\(178\) 0 0
\(179\) −4.20212 + 7.27829i −0.314081 + 0.544005i −0.979242 0.202696i \(-0.935030\pi\)
0.665160 + 0.746701i \(0.268363\pi\)
\(180\) 0 0
\(181\) 17.2650 14.4870i 1.28329 1.07681i 0.290513 0.956871i \(-0.406174\pi\)
0.992781 0.119940i \(-0.0382703\pi\)
\(182\) 0 0
\(183\) 9.19428 + 15.9250i 0.679661 + 1.17721i
\(184\) 0 0
\(185\) −1.55586 + 8.82370i −0.114389 + 0.648732i
\(186\) 0 0
\(187\) 4.03427 1.46835i 0.295015 0.107377i
\(188\) 0 0
\(189\) 14.8681 1.08150
\(190\) 0 0
\(191\) 24.2967 1.75805 0.879025 0.476775i \(-0.158194\pi\)
0.879025 + 0.476775i \(0.158194\pi\)
\(192\) 0 0
\(193\) 4.36570 1.58898i 0.314250 0.114378i −0.180080 0.983652i \(-0.557636\pi\)
0.494330 + 0.869274i \(0.335413\pi\)
\(194\) 0 0
\(195\) −0.0662626 + 0.375794i −0.00474516 + 0.0269112i
\(196\) 0 0
\(197\) 6.00361 + 10.3986i 0.427740 + 0.740867i 0.996672 0.0815174i \(-0.0259766\pi\)
−0.568932 + 0.822384i \(0.692643\pi\)
\(198\) 0 0
\(199\) 8.96006 7.51838i 0.635162 0.532964i −0.267366 0.963595i \(-0.586153\pi\)
0.902528 + 0.430631i \(0.141709\pi\)
\(200\) 0 0
\(201\) 24.5804 42.5744i 1.73376 3.00297i
\(202\) 0 0
\(203\) −8.10057 2.94836i −0.568548 0.206935i
\(204\) 0 0
\(205\) −1.37842 7.81742i −0.0962732 0.545993i
\(206\) 0 0
\(207\) 15.0290 + 12.6108i 1.04459 + 0.876515i
\(208\) 0 0
\(209\) 19.0259 + 4.80266i 1.31605 + 0.332207i
\(210\) 0 0
\(211\) 9.63682 + 8.08626i 0.663426 + 0.556681i 0.911112 0.412160i \(-0.135225\pi\)
−0.247685 + 0.968841i \(0.579670\pi\)
\(212\) 0 0
\(213\) 8.16713 + 46.3181i 0.559603 + 3.17367i
\(214\) 0 0
\(215\) 8.95707 + 3.26011i 0.610867 + 0.222337i
\(216\) 0 0
\(217\) 3.74912 6.49366i 0.254507 0.440819i
\(218\) 0 0
\(219\) 9.17515 7.69887i 0.619999 0.520241i
\(220\) 0 0
\(221\) 0.0584026 + 0.101156i 0.00392858 + 0.00680451i
\(222\) 0 0
\(223\) 2.34163 13.2801i 0.156807 0.889299i −0.800307 0.599590i \(-0.795330\pi\)
0.957115 0.289709i \(-0.0935586\pi\)
\(224\) 0 0
\(225\) −6.30210 + 2.29378i −0.420140 + 0.152918i
\(226\) 0 0
\(227\) −21.1090 −1.40105 −0.700526 0.713627i \(-0.747051\pi\)
−0.700526 + 0.713627i \(0.747051\pi\)
\(228\) 0 0
\(229\) −19.3629 −1.27954 −0.639770 0.768567i \(-0.720970\pi\)
−0.639770 + 0.768567i \(0.720970\pi\)
\(230\) 0 0
\(231\) −16.9689 + 6.17619i −1.11647 + 0.406363i
\(232\) 0 0
\(233\) −0.321621 + 1.82400i −0.0210701 + 0.119494i −0.993529 0.113581i \(-0.963768\pi\)
0.972459 + 0.233075i \(0.0748789\pi\)
\(234\) 0 0
\(235\) 0.462904 + 0.801773i 0.0301965 + 0.0523019i
\(236\) 0 0
\(237\) −7.11558 + 5.97068i −0.462207 + 0.387837i
\(238\) 0 0
\(239\) 10.6784 18.4956i 0.690730 1.19638i −0.280869 0.959746i \(-0.590623\pi\)
0.971599 0.236633i \(-0.0760441\pi\)
\(240\) 0 0
\(241\) 5.67933 + 2.06711i 0.365838 + 0.133154i 0.518397 0.855140i \(-0.326529\pi\)
−0.152559 + 0.988294i \(0.548751\pi\)
\(242\) 0 0
\(243\) −2.56358 14.5388i −0.164454 0.932663i
\(244\) 0 0
\(245\) −4.09243 3.43396i −0.261456 0.219388i
\(246\) 0 0
\(247\) −0.0387941 + 0.532467i −0.00246841 + 0.0338801i
\(248\) 0 0
\(249\) −20.8332 17.4811i −1.32025 1.10782i
\(250\) 0 0
\(251\) −0.425210 2.41149i −0.0268390 0.152212i 0.968443 0.249235i \(-0.0801791\pi\)
−0.995282 + 0.0970230i \(0.969068\pi\)
\(252\) 0 0
\(253\) −12.3750 4.50414i −0.778010 0.283173i
\(254\) 0 0
\(255\) −1.48559 + 2.57312i −0.0930313 + 0.161135i
\(256\) 0 0
\(257\) 7.75878 6.51039i 0.483979 0.406107i −0.367884 0.929872i \(-0.619917\pi\)
0.851863 + 0.523765i \(0.175473\pi\)
\(258\) 0 0
\(259\) −5.76798 9.99043i −0.358405 0.620775i
\(260\) 0 0
\(261\) −7.79732 + 44.2208i −0.482642 + 2.73720i
\(262\) 0 0
\(263\) −10.3651 + 3.77260i −0.639141 + 0.232628i −0.641205 0.767370i \(-0.721565\pi\)
0.00206405 + 0.999998i \(0.499343\pi\)
\(264\) 0 0
\(265\) −0.0238499 −0.00146509
\(266\) 0 0
\(267\) −46.6210 −2.85316
\(268\) 0 0
\(269\) 18.7568 6.82690i 1.14362 0.416243i 0.300400 0.953813i \(-0.402880\pi\)
0.843219 + 0.537570i \(0.180658\pi\)
\(270\) 0 0
\(271\) −0.988320 + 5.60504i −0.0600362 + 0.340482i −1.00000 0.000792933i \(-0.999748\pi\)
0.939964 + 0.341275i \(0.110859\pi\)
\(272\) 0 0
\(273\) −0.245653 0.425484i −0.0148676 0.0257514i
\(274\) 0 0
\(275\) 3.44855 2.89368i 0.207955 0.174495i
\(276\) 0 0
\(277\) −16.0854 + 27.8607i −0.966477 + 1.67399i −0.260883 + 0.965370i \(0.584014\pi\)
−0.705594 + 0.708616i \(0.749320\pi\)
\(278\) 0 0
\(279\) −36.7021 13.3585i −2.19729 0.799750i
\(280\) 0 0
\(281\) 2.33744 + 13.2563i 0.139440 + 0.790805i 0.971664 + 0.236365i \(0.0759563\pi\)
−0.832224 + 0.554440i \(0.812933\pi\)
\(282\) 0 0
\(283\) 5.76933 + 4.84104i 0.342951 + 0.287770i 0.797952 0.602721i \(-0.205917\pi\)
−0.455001 + 0.890491i \(0.650361\pi\)
\(284\) 0 0
\(285\) −12.2232 + 5.91760i −0.724040 + 0.350528i
\(286\) 0 0
\(287\) 7.82925 + 6.56952i 0.462146 + 0.387787i
\(288\) 0 0
\(289\) −2.79409 15.8461i −0.164358 0.932122i
\(290\) 0 0
\(291\) −50.8383 18.5036i −2.98019 1.08470i
\(292\) 0 0
\(293\) 12.3915 21.4627i 0.723919 1.25386i −0.235499 0.971875i \(-0.575672\pi\)
0.959418 0.281989i \(-0.0909942\pi\)
\(294\) 0 0
\(295\) 8.19663 6.87779i 0.477226 0.400440i
\(296\) 0 0
\(297\) 25.9929 + 45.0210i 1.50826 + 2.61239i
\(298\) 0 0
\(299\) 0.0622176 0.352854i 0.00359814 0.0204061i
\(300\) 0 0
\(301\) −11.5324 + 4.19745i −0.664717 + 0.241937i
\(302\) 0 0
\(303\) 22.6407 1.30068
\(304\) 0 0
\(305\) 5.90222 0.337960
\(306\) 0 0
\(307\) 16.1933 5.89388i 0.924200 0.336381i 0.164292 0.986412i \(-0.447466\pi\)
0.759908 + 0.650031i \(0.225244\pi\)
\(308\) 0 0
\(309\) −0.460109 + 2.60941i −0.0261747 + 0.148444i
\(310\) 0 0
\(311\) 4.22506 + 7.31802i 0.239581 + 0.414967i 0.960594 0.277955i \(-0.0896565\pi\)
−0.721013 + 0.692922i \(0.756323\pi\)
\(312\) 0 0
\(313\) 1.13129 0.949265i 0.0639443 0.0536556i −0.610255 0.792205i \(-0.708933\pi\)
0.674200 + 0.738549i \(0.264489\pi\)
\(314\) 0 0
\(315\) 4.31741 7.47797i 0.243258 0.421336i
\(316\) 0 0
\(317\) −2.10586 0.766472i −0.118277 0.0430494i 0.282204 0.959355i \(-0.408935\pi\)
−0.400481 + 0.916305i \(0.631157\pi\)
\(318\) 0 0
\(319\) −5.23393 29.6831i −0.293044 1.66193i
\(320\) 0 0
\(321\) 24.0959 + 20.2189i 1.34490 + 1.12851i
\(322\) 0 0
\(323\) −1.70184 + 3.79260i −0.0946931 + 0.211026i
\(324\) 0 0
\(325\) 0.0938253 + 0.0787287i 0.00520449 + 0.00436708i
\(326\) 0 0
\(327\) 1.62484 + 9.21493i 0.0898539 + 0.509587i
\(328\) 0 0
\(329\) −1.12011 0.407686i −0.0617536 0.0224765i
\(330\) 0 0
\(331\) −1.35657 + 2.34964i −0.0745637 + 0.129148i −0.900896 0.434034i \(-0.857090\pi\)
0.826333 + 0.563182i \(0.190423\pi\)
\(332\) 0 0
\(333\) −46.0313 + 38.6248i −2.52250 + 2.11663i
\(334\) 0 0
\(335\) −7.88961 13.6652i −0.431056 0.746610i
\(336\) 0 0
\(337\) 2.01515 11.4285i 0.109772 0.622549i −0.879434 0.476020i \(-0.842079\pi\)
0.989206 0.146529i \(-0.0468101\pi\)
\(338\) 0 0
\(339\) −17.7539 + 6.46190i −0.964261 + 0.350962i
\(340\) 0 0
\(341\) 26.2173 1.41975
\(342\) 0 0
\(343\) 15.8909 0.858030
\(344\) 0 0
\(345\) 8.56438 3.11718i 0.461091 0.167823i
\(346\) 0 0
\(347\) −5.33836 + 30.2754i −0.286578 + 1.62527i 0.413014 + 0.910725i \(0.364476\pi\)
−0.699593 + 0.714542i \(0.746635\pi\)
\(348\) 0 0
\(349\) 9.56699 + 16.5705i 0.512109 + 0.886999i 0.999901 + 0.0140393i \(0.00446900\pi\)
−0.487792 + 0.872960i \(0.662198\pi\)
\(350\) 0 0
\(351\) −1.08348 + 0.909151i −0.0578321 + 0.0485269i
\(352\) 0 0
\(353\) −9.74328 + 16.8759i −0.518583 + 0.898211i 0.481184 + 0.876619i \(0.340207\pi\)
−0.999767 + 0.0215918i \(0.993127\pi\)
\(354\) 0 0
\(355\) 14.1858 + 5.16320i 0.752902 + 0.274034i
\(356\) 0 0
\(357\) −0.664283 3.76734i −0.0351576 0.199389i
\(358\) 0 0
\(359\) −25.7000 21.5649i −1.35639 1.13815i −0.977078 0.212884i \(-0.931714\pi\)
−0.379317 0.925267i \(-0.623841\pi\)
\(360\) 0 0
\(361\) −16.1714 + 9.97434i −0.851124 + 0.524965i
\(362\) 0 0
\(363\) −22.1142 18.5560i −1.16069 0.973938i
\(364\) 0 0
\(365\) −0.667571 3.78598i −0.0349422 0.198167i
\(366\) 0 0
\(367\) −10.1767 3.70401i −0.531219 0.193348i 0.0624636 0.998047i \(-0.480104\pi\)
−0.593683 + 0.804699i \(0.702327\pi\)
\(368\) 0 0
\(369\) 26.6184 46.1044i 1.38570 2.40010i
\(370\) 0 0
\(371\) 0.0235231 0.0197382i 0.00122126 0.00102476i
\(372\) 0 0
\(373\) −4.14975 7.18758i −0.214866 0.372159i 0.738365 0.674401i \(-0.235598\pi\)
−0.953231 + 0.302242i \(0.902265\pi\)
\(374\) 0 0
\(375\) −0.541007 + 3.06820i −0.0279375 + 0.158441i
\(376\) 0 0
\(377\) 0.770597 0.280474i 0.0396878 0.0144452i
\(378\) 0 0
\(379\) 2.75557 0.141544 0.0707720 0.997493i \(-0.477454\pi\)
0.0707720 + 0.997493i \(0.477454\pi\)
\(380\) 0 0
\(381\) −20.6940 −1.06018
\(382\) 0 0
\(383\) 2.15130 0.783010i 0.109926 0.0400100i −0.286471 0.958089i \(-0.592482\pi\)
0.396398 + 0.918079i \(0.370260\pi\)
\(384\) 0 0
\(385\) −1.00648 + 5.70805i −0.0512951 + 0.290909i
\(386\) 0 0
\(387\) 31.9631 + 55.3618i 1.62478 + 2.81420i
\(388\) 0 0
\(389\) −8.46044 + 7.09915i −0.428961 + 0.359941i −0.831560 0.555436i \(-0.812552\pi\)
0.402598 + 0.915377i \(0.368107\pi\)
\(390\) 0 0
\(391\) 1.39490 2.41604i 0.0705433 0.122185i
\(392\) 0 0
\(393\) 27.0146 + 9.83252i 1.36271 + 0.495985i
\(394\) 0 0
\(395\) 0.517719 + 2.93613i 0.0260493 + 0.147733i
\(396\) 0 0
\(397\) −14.4339 12.1114i −0.724415 0.607856i 0.204188 0.978932i \(-0.434545\pi\)
−0.928603 + 0.371076i \(0.878989\pi\)
\(398\) 0 0
\(399\) 7.15829 15.9525i 0.358363 0.798621i
\(400\) 0 0
\(401\) 1.34821 + 1.13128i 0.0673263 + 0.0564935i 0.675830 0.737058i \(-0.263785\pi\)
−0.608503 + 0.793551i \(0.708230\pi\)
\(402\) 0 0
\(403\) 0.123863 + 0.702462i 0.00617005 + 0.0349921i
\(404\) 0 0
\(405\) −14.9018 5.42382i −0.740478 0.269512i
\(406\) 0 0
\(407\) 20.1675 34.9311i 0.999665 1.73147i
\(408\) 0 0
\(409\) −9.30115 + 7.80459i −0.459912 + 0.385912i −0.843099 0.537759i \(-0.819271\pi\)
0.383187 + 0.923671i \(0.374827\pi\)
\(410\) 0 0
\(411\) −5.68992 9.85523i −0.280663 0.486123i
\(412\) 0 0
\(413\) −2.39224 + 13.5671i −0.117715 + 0.667593i
\(414\) 0 0
\(415\) −8.20267 + 2.98553i −0.402653 + 0.146554i
\(416\) 0 0
\(417\) 58.6508 2.87214
\(418\) 0 0
\(419\) −16.4679 −0.804509 −0.402255 0.915528i \(-0.631773\pi\)
−0.402255 + 0.915528i \(0.631773\pi\)
\(420\) 0 0
\(421\) 0.999150 0.363661i 0.0486956 0.0177237i −0.317558 0.948239i \(-0.602863\pi\)
0.366253 + 0.930515i \(0.380640\pi\)
\(422\) 0 0
\(423\) −1.07818 + 6.11465i −0.0524228 + 0.297304i
\(424\) 0 0
\(425\) 0.476833 + 0.825899i 0.0231298 + 0.0400620i
\(426\) 0 0
\(427\) −5.82134 + 4.88469i −0.281715 + 0.236387i
\(428\) 0 0
\(429\) 0.858916 1.48769i 0.0414688 0.0718261i
\(430\) 0 0
\(431\) 32.7978 + 11.9374i 1.57982 + 0.575006i 0.975164 0.221484i \(-0.0710902\pi\)
0.604651 + 0.796490i \(0.293312\pi\)
\(432\) 0 0
\(433\) −1.23492 7.00358i −0.0593465 0.336571i 0.940650 0.339379i \(-0.110217\pi\)
−0.999996 + 0.00280872i \(0.999106\pi\)
\(434\) 0 0
\(435\) 15.9795 + 13.4084i 0.766156 + 0.642882i
\(436\) 0 0
\(437\) 11.4770 5.55636i 0.549021 0.265797i
\(438\) 0 0
\(439\) −5.83392 4.89524i −0.278438 0.233637i 0.492864 0.870106i \(-0.335950\pi\)
−0.771302 + 0.636469i \(0.780394\pi\)
\(440\) 0 0
\(441\) −6.22153 35.2841i −0.296263 1.68019i
\(442\) 0 0
\(443\) −16.2738 5.92317i −0.773191 0.281419i −0.0748605 0.997194i \(-0.523851\pi\)
−0.698330 + 0.715776i \(0.746073\pi\)
\(444\) 0 0
\(445\) −7.48203 + 12.9592i −0.354682 + 0.614327i
\(446\) 0 0
\(447\) −28.1080 + 23.5854i −1.32946 + 1.11555i
\(448\) 0 0
\(449\) 0.462444 + 0.800976i 0.0218241 + 0.0378004i 0.876731 0.480981i \(-0.159719\pi\)
−0.854907 + 0.518781i \(0.826386\pi\)
\(450\) 0 0
\(451\) −6.20533 + 35.1922i −0.292197 + 1.65713i
\(452\) 0 0
\(453\) 20.3187 7.39540i 0.954656 0.347466i
\(454\) 0 0
\(455\) −0.157696 −0.00739289
\(456\) 0 0
\(457\) −20.6874 −0.967718 −0.483859 0.875146i \(-0.660765\pi\)
−0.483859 + 0.875146i \(0.660765\pi\)
\(458\) 0 0
\(459\) −10.3487 + 3.76661i −0.483035 + 0.175810i
\(460\) 0 0
\(461\) 2.46202 13.9628i 0.114667 0.650312i −0.872247 0.489066i \(-0.837338\pi\)
0.986914 0.161246i \(-0.0515512\pi\)
\(462\) 0 0
\(463\) 18.7765 + 32.5218i 0.872616 + 1.51141i 0.859281 + 0.511504i \(0.170911\pi\)
0.0133346 + 0.999911i \(0.495755\pi\)
\(464\) 0 0
\(465\) −13.8993 + 11.6629i −0.644563 + 0.540852i
\(466\) 0 0
\(467\) 2.95532 5.11877i 0.136756 0.236868i −0.789511 0.613736i \(-0.789666\pi\)
0.926267 + 0.376868i \(0.122999\pi\)
\(468\) 0 0
\(469\) 19.0909 + 6.94850i 0.881534 + 0.320852i
\(470\) 0 0
\(471\) −9.44497 53.5651i −0.435201 2.46815i
\(472\) 0 0
\(473\) −32.8713 27.5823i −1.51142 1.26823i
\(474\) 0 0
\(475\) −0.316738 + 4.34738i −0.0145329 + 0.199471i
\(476\) 0 0
\(477\) −0.122529 0.102814i −0.00561023 0.00470755i
\(478\) 0 0
\(479\) 1.61205 + 9.14240i 0.0736565 + 0.417727i 0.999233 + 0.0391656i \(0.0124700\pi\)
−0.925576 + 0.378561i \(0.876419\pi\)
\(480\) 0 0
\(481\) 1.03122 + 0.375333i 0.0470196 + 0.0171137i
\(482\) 0 0
\(483\) −5.86724 + 10.1624i −0.266969 + 0.462403i
\(484\) 0 0
\(485\) −13.3023 + 11.1620i −0.604026 + 0.506838i
\(486\) 0 0
\(487\) 12.4983 + 21.6477i 0.566353 + 0.980951i 0.996922 + 0.0783942i \(0.0249793\pi\)
−0.430570 + 0.902557i \(0.641687\pi\)
\(488\) 0 0
\(489\) 6.62847 37.5919i 0.299750 1.69997i
\(490\) 0 0
\(491\) −21.1513 + 7.69846i −0.954547 + 0.347427i −0.771894 0.635751i \(-0.780691\pi\)
−0.182652 + 0.983178i \(0.558468\pi\)
\(492\) 0 0
\(493\) 6.38516 0.287573
\(494\) 0 0
\(495\) 30.1913 1.35700
\(496\) 0 0
\(497\) −18.2645 + 6.64772i −0.819273 + 0.298191i
\(498\) 0 0
\(499\) −4.60596 + 26.1217i −0.206191 + 1.16937i 0.689364 + 0.724415i \(0.257890\pi\)
−0.895555 + 0.444951i \(0.853221\pi\)
\(500\) 0 0
\(501\) −36.7480 63.6494i −1.64178 2.84364i
\(502\) 0 0
\(503\) −30.1792 + 25.3234i −1.34563 + 1.12911i −0.365484 + 0.930818i \(0.619096\pi\)
−0.980142 + 0.198296i \(0.936459\pi\)
\(504\) 0 0
\(505\) 3.63352 6.29345i 0.161690 0.280055i
\(506\) 0 0
\(507\) −38.0155 13.8365i −1.68833 0.614500i
\(508\) 0 0
\(509\) −3.40757 19.3253i −0.151038 0.856578i −0.962319 0.271922i \(-0.912341\pi\)
0.811281 0.584656i \(-0.198771\pi\)
\(510\) 0 0
\(511\) 3.79171 + 3.18162i 0.167735 + 0.140747i
\(512\) 0 0
\(513\) −48.8052 12.3198i −2.15480 0.543930i
\(514\) 0 0
\(515\) 0.651497 + 0.546671i 0.0287084 + 0.0240892i
\(516\) 0 0
\(517\) −0.723724 4.10444i −0.0318294 0.180513i
\(518\) 0 0
\(519\) −30.5117 11.1053i −1.33931 0.487470i
\(520\) 0 0
\(521\) −8.49964 + 14.7218i −0.372376 + 0.644974i −0.989931 0.141554i \(-0.954790\pi\)
0.617554 + 0.786528i \(0.288124\pi\)
\(522\) 0 0
\(523\) 25.3000 21.2293i 1.10629 0.928291i 0.108461 0.994101i \(-0.465408\pi\)
0.997832 + 0.0658102i \(0.0209632\pi\)
\(524\) 0 0
\(525\) −2.00566 3.47390i −0.0875340 0.151613i
\(526\) 0 0
\(527\) −0.964433 + 5.46957i −0.0420114 + 0.238258i
\(528\) 0 0
\(529\) 13.5714 4.93957i 0.590059 0.214764i
\(530\) 0 0
\(531\) 71.7597 3.11410
\(532\) 0 0
\(533\) −0.972250 −0.0421128
\(534\) 0 0
\(535\) 9.48731 3.45310i 0.410172 0.149290i
\(536\) 0 0
\(537\) −4.54675 + 25.7859i −0.196207 + 1.11274i
\(538\) 0 0
\(539\) 12.0249 + 20.8277i 0.517947 + 0.897111i
\(540\) 0 0
\(541\) −15.8252 + 13.2789i −0.680378 + 0.570905i −0.916117 0.400912i \(-0.868693\pi\)
0.235739 + 0.971816i \(0.424249\pi\)
\(542\) 0 0
\(543\) 35.1086 60.8099i 1.50666 2.60960i
\(544\) 0 0
\(545\) 2.82224 + 1.02721i 0.120891 + 0.0440009i
\(546\) 0 0
\(547\) 3.19901 + 18.1425i 0.136780 + 0.775717i 0.973604 + 0.228245i \(0.0732988\pi\)
−0.836824 + 0.547472i \(0.815590\pi\)
\(548\) 0 0
\(549\) 30.3228 + 25.4438i 1.29414 + 1.08592i
\(550\) 0 0
\(551\) 24.1474 + 16.3902i 1.02871 + 0.698248i
\(552\) 0 0
\(553\) −2.94057 2.46743i −0.125046 0.104926i
\(554\) 0 0
\(555\) 4.84733 + 27.4906i 0.205758 + 1.16691i
\(556\) 0 0
\(557\) 30.4882 + 11.0968i 1.29183 + 0.470186i 0.894326 0.447416i \(-0.147656\pi\)
0.397500 + 0.917602i \(0.369878\pi\)
\(558\) 0 0
\(559\) 0.583735 1.01106i 0.0246894 0.0427632i
\(560\) 0 0
\(561\) 10.2463 8.59763i 0.432597 0.362992i
\(562\) 0 0
\(563\) −4.29185 7.43371i −0.180880 0.313293i 0.761300 0.648399i \(-0.224561\pi\)
−0.942180 + 0.335106i \(0.891228\pi\)
\(564\) 0 0
\(565\) −1.05304 + 5.97211i −0.0443019 + 0.251248i
\(566\) 0 0
\(567\) 19.1864 6.98328i 0.805753 0.293270i
\(568\) 0 0
\(569\) 18.8173 0.788861 0.394431 0.918926i \(-0.370942\pi\)
0.394431 + 0.918926i \(0.370942\pi\)
\(570\) 0 0
\(571\) −9.57993 −0.400907 −0.200454 0.979703i \(-0.564242\pi\)
−0.200454 + 0.979703i \(0.564242\pi\)
\(572\) 0 0
\(573\) 71.1322 25.8900i 2.97159 1.08157i
\(574\) 0 0
\(575\) 0.507981 2.88091i 0.0211843 0.120142i
\(576\) 0 0
\(577\) 6.41220 + 11.1063i 0.266943 + 0.462359i 0.968071 0.250676i \(-0.0806530\pi\)
−0.701128 + 0.713036i \(0.747320\pi\)
\(578\) 0 0
\(579\) 11.0880 9.30396i 0.460803 0.386660i
\(580\) 0 0
\(581\) 5.61944 9.73316i 0.233134 0.403799i
\(582\) 0 0
\(583\) 0.100892 + 0.0367215i 0.00417850 + 0.00152085i
\(584\) 0 0
\(585\) 0.142638 + 0.808941i 0.00589736 + 0.0334456i
\(586\) 0 0
\(587\) −20.7329 17.3970i −0.855739 0.718050i 0.105307 0.994440i \(-0.466417\pi\)
−0.961046 + 0.276390i \(0.910862\pi\)
\(588\) 0 0
\(589\) −17.6873 + 18.2092i −0.728791 + 0.750295i
\(590\) 0 0
\(591\) 28.6569 + 24.0460i 1.17879 + 0.989120i
\(592\) 0 0
\(593\) −5.90373 33.4817i −0.242437 1.37493i −0.826370 0.563127i \(-0.809598\pi\)
0.583933 0.811802i \(-0.301513\pi\)
\(594\) 0 0
\(595\) −1.15382 0.419954i −0.0473018 0.0172164i
\(596\) 0 0
\(597\) 18.2205 31.5588i 0.745714 1.29161i
\(598\) 0 0
\(599\) 0.383051 0.321418i 0.0156510 0.0131328i −0.634929 0.772571i \(-0.718970\pi\)
0.650580 + 0.759438i \(0.274526\pi\)
\(600\) 0 0
\(601\) −3.43562 5.95066i −0.140142 0.242733i 0.787408 0.616432i \(-0.211422\pi\)
−0.927550 + 0.373699i \(0.878089\pi\)
\(602\) 0 0
\(603\) 18.3762 104.217i 0.748336 4.24402i
\(604\) 0 0
\(605\) −8.70704 + 3.16910i −0.353991 + 0.128842i
\(606\) 0 0
\(607\) −7.65201 −0.310586 −0.155293 0.987868i \(-0.549632\pi\)
−0.155293 + 0.987868i \(0.549632\pi\)
\(608\) 0 0
\(609\) −26.8573 −1.08831
\(610\) 0 0
\(611\) 0.106555 0.0387827i 0.00431074 0.00156898i
\(612\) 0 0
\(613\) −5.77627 + 32.7589i −0.233302 + 1.32312i 0.612860 + 0.790192i \(0.290019\pi\)
−0.846161 + 0.532927i \(0.821092\pi\)
\(614\) 0 0
\(615\) −12.3656 21.4178i −0.498629 0.863650i
\(616\) 0 0
\(617\) 11.5490 9.69076i 0.464945 0.390135i −0.380002 0.924986i \(-0.624077\pi\)
0.844947 + 0.534851i \(0.179632\pi\)
\(618\) 0 0
\(619\) −15.4112 + 26.6930i −0.619428 + 1.07288i 0.370162 + 0.928967i \(0.379302\pi\)
−0.989590 + 0.143914i \(0.954031\pi\)
\(620\) 0 0
\(621\) 31.7443 + 11.5540i 1.27386 + 0.463645i
\(622\) 0 0
\(623\) −3.34560 18.9738i −0.134038 0.760170i
\(624\) 0 0
\(625\) 0.766044 + 0.642788i 0.0306418 + 0.0257115i
\(626\) 0 0
\(627\) 60.8187 6.21308i 2.42887 0.248126i
\(628\) 0 0
\(629\) 6.54561 + 5.49242i 0.260990 + 0.218997i
\(630\) 0 0
\(631\) −5.76052 32.6695i −0.229323 1.30055i −0.854247 0.519868i \(-0.825981\pi\)
0.624924 0.780685i \(-0.285130\pi\)
\(632\) 0 0
\(633\) 36.8297 + 13.4049i 1.46385 + 0.532798i
\(634\) 0 0
\(635\) −3.32109 + 5.75230i −0.131794 + 0.228273i
\(636\) 0 0
\(637\) −0.501242 + 0.420592i −0.0198599 + 0.0166645i
\(638\) 0 0
\(639\) 50.6217 + 87.6793i 2.00256 + 3.46854i
\(640\) 0 0
\(641\) −3.69073 + 20.9312i −0.145775 + 0.826732i 0.820966 + 0.570977i \(0.193435\pi\)
−0.966741 + 0.255756i \(0.917676\pi\)
\(642\) 0 0
\(643\) −43.7776 + 15.9338i −1.72642 + 0.628366i −0.998366 0.0571513i \(-0.981798\pi\)
−0.728056 + 0.685517i \(0.759576\pi\)
\(644\) 0 0
\(645\) 29.6970 1.16932
\(646\) 0 0
\(647\) 4.02896 0.158395 0.0791974 0.996859i \(-0.474764\pi\)
0.0791974 + 0.996859i \(0.474764\pi\)
\(648\) 0 0
\(649\) −45.2636 + 16.4746i −1.77675 + 0.646685i
\(650\) 0 0
\(651\) 4.05660 23.0061i 0.158991 0.901681i
\(652\) 0 0
\(653\) −6.38069 11.0517i −0.249696 0.432486i 0.713746 0.700405i \(-0.246997\pi\)
−0.963441 + 0.267919i \(0.913664\pi\)
\(654\) 0 0
\(655\) 7.06862 5.93127i 0.276194 0.231754i
\(656\) 0 0
\(657\) 12.8913 22.3284i 0.502937 0.871112i
\(658\) 0 0
\(659\) 17.6911 + 6.43902i 0.689146 + 0.250829i 0.662770 0.748823i \(-0.269381\pi\)
0.0263766 + 0.999652i \(0.491603\pi\)
\(660\) 0 0
\(661\) 2.07438 + 11.7644i 0.0806842 + 0.457583i 0.998205 + 0.0598944i \(0.0190764\pi\)
−0.917521 + 0.397688i \(0.869812\pi\)
\(662\) 0 0
\(663\) 0.278772 + 0.233917i 0.0108266 + 0.00908459i
\(664\) 0 0
\(665\) −3.28550 4.54994i −0.127406 0.176439i
\(666\) 0 0
\(667\) −15.0040 12.5899i −0.580957 0.487481i
\(668\) 0 0
\(669\) −7.29544 41.3745i −0.282058 1.59963i
\(670\) 0 0
\(671\) −24.9680 9.08760i −0.963878 0.350823i
\(672\) 0 0
\(673\) 11.9605 20.7161i 0.461042 0.798547i −0.537972 0.842963i \(-0.680809\pi\)
0.999013 + 0.0444155i \(0.0141426\pi\)
\(674\) 0 0
\(675\) −8.84620 + 7.42284i −0.340490 + 0.285705i
\(676\) 0 0
\(677\) −5.45024 9.44010i −0.209470 0.362812i 0.742078 0.670314i \(-0.233840\pi\)
−0.951548 + 0.307501i \(0.900507\pi\)
\(678\) 0 0
\(679\) 3.88237 22.0180i 0.148992 0.844973i
\(680\) 0 0
\(681\) −61.7996 + 22.4932i −2.36816 + 0.861941i
\(682\) 0 0
\(683\) −0.353548 −0.0135282 −0.00676408 0.999977i \(-0.502153\pi\)
−0.00676408 + 0.999977i \(0.502153\pi\)
\(684\) 0 0
\(685\) −3.65261 −0.139559
\(686\) 0 0
\(687\) −56.6878 + 20.6327i −2.16278 + 0.787186i
\(688\) 0 0
\(689\) −0.000507251 0.00287676i −1.93247e−5 0.000109596i
\(690\) 0 0
\(691\) −1.06320 1.84152i −0.0404460 0.0700546i 0.845094 0.534618i \(-0.179545\pi\)
−0.885540 + 0.464564i \(0.846211\pi\)
\(692\) 0 0
\(693\) −29.7776 + 24.9864i −1.13116 + 0.949153i
\(694\) 0 0
\(695\) 9.41264 16.3032i 0.357042 0.618415i
\(696\) 0 0
\(697\) −7.11368 2.58917i −0.269450 0.0980718i
\(698\) 0 0
\(699\) 1.00202 + 5.68274i 0.0378999 + 0.214941i
\(700\) 0 0
\(701\) 16.4345 + 13.7902i 0.620722 + 0.520848i 0.898030 0.439933i \(-0.144998\pi\)
−0.277308 + 0.960781i \(0.589442\pi\)
\(702\) 0 0
\(703\) 10.6555 + 37.5733i 0.401880 + 1.41710i
\(704\) 0 0
\(705\) 2.20957 + 1.85405i 0.0832171 + 0.0698274i
\(706\) 0 0
\(707\) 1.62473 + 9.21432i 0.0611044 + 0.346540i
\(708\) 0 0
\(709\) 39.1314 + 14.2427i 1.46961 + 0.534895i 0.947995 0.318286i \(-0.103107\pi\)
0.521616 + 0.853180i \(0.325329\pi\)
\(710\) 0 0
\(711\) −9.99754 + 17.3162i −0.374937 + 0.649410i
\(712\) 0 0
\(713\) 13.0508 10.9509i 0.488756 0.410115i
\(714\) 0 0
\(715\) −0.275688 0.477506i −0.0103102 0.0178577i
\(716\) 0 0
\(717\) 11.5542 65.5272i 0.431500 2.44716i
\(718\) 0 0
\(719\) 11.1111 4.04411i 0.414374 0.150820i −0.126416 0.991977i \(-0.540347\pi\)
0.540790 + 0.841157i \(0.318125\pi\)
\(720\) 0 0
\(721\) −1.09499 −0.0407797
\(722\) 0 0
\(723\) 18.8297 0.700285
\(724\) 0 0
\(725\) 6.29160 2.28996i 0.233664 0.0850469i
\(726\) 0 0
\(727\) 1.05821 6.00138i 0.0392467 0.222579i −0.958876 0.283825i \(-0.908396\pi\)
0.998123 + 0.0612463i \(0.0195075\pi\)
\(728\) 0 0
\(729\) 0.789882 + 1.36812i 0.0292549 + 0.0506709i
\(730\) 0 0
\(731\) 6.96355 5.84311i 0.257556 0.216115i
\(732\) 0 0
\(733\) −26.7539 + 46.3391i −0.988177 + 1.71157i −0.361310 + 0.932446i \(0.617670\pi\)
−0.626867 + 0.779126i \(0.715663\pi\)
\(734\) 0 0
\(735\) −15.6403 5.69262i −0.576902 0.209975i
\(736\) 0 0
\(737\) 12.3350 + 69.9551i 0.454365 + 2.57683i
\(738\) 0 0
\(739\) 22.9031 + 19.2180i 0.842504 + 0.706945i 0.958126 0.286348i \(-0.0924415\pi\)
−0.115621 + 0.993293i \(0.536886\pi\)
\(740\) 0 0
\(741\) 0.453809 + 1.60021i 0.0166711 + 0.0587853i
\(742\) 0 0
\(743\) −36.6959 30.7915i −1.34624 1.12963i −0.979975 0.199122i \(-0.936191\pi\)
−0.366268 0.930510i \(-0.619365\pi\)
\(744\) 0 0
\(745\) 2.04509 + 11.5983i 0.0749264 + 0.424929i
\(746\) 0 0
\(747\) −55.0116 20.0226i −2.01277 0.732588i
\(748\) 0 0
\(749\) −6.49952 + 11.2575i −0.237487 + 0.411340i
\(750\) 0 0
\(751\) 19.4465 16.3175i 0.709611 0.595434i −0.214879 0.976641i \(-0.568936\pi\)
0.924490 + 0.381206i \(0.124491\pi\)
\(752\) 0 0
\(753\) −3.81448 6.60688i −0.139008 0.240768i
\(754\) 0 0
\(755\) 1.20517 6.83485i 0.0438606 0.248746i
\(756\) 0 0
\(757\) −24.9241 + 9.07161i −0.905880 + 0.329713i −0.752607 0.658470i \(-0.771204\pi\)
−0.153274 + 0.988184i \(0.548982\pi\)
\(758\) 0 0
\(759\) −41.0291 −1.48926
\(760\) 0 0
\(761\) 42.9695 1.55764 0.778822 0.627244i \(-0.215817\pi\)
0.778822 + 0.627244i \(0.215817\pi\)
\(762\) 0 0
\(763\) −3.63369 + 1.32255i −0.131548 + 0.0478797i
\(764\) 0 0
\(765\) −1.11062 + 6.29865i −0.0401546 + 0.227728i
\(766\) 0 0
\(767\) −0.655265 1.13495i −0.0236602 0.0409807i
\(768\) 0 0
\(769\) −36.0908 + 30.2838i −1.30147 + 1.09206i −0.311577 + 0.950221i \(0.600857\pi\)
−0.989890 + 0.141839i \(0.954698\pi\)
\(770\) 0 0
\(771\) 15.7776 27.3277i 0.568217 0.984182i
\(772\) 0 0
\(773\) −20.4768 7.45294i −0.736499 0.268064i −0.0535859 0.998563i \(-0.517065\pi\)
−0.682913 + 0.730499i \(0.739287\pi\)
\(774\) 0 0
\(775\) 1.01129 + 5.73531i 0.0363266 + 0.206018i
\(776\) 0 0
\(777\) −27.5321 23.1022i −0.987710 0.828787i
\(778\) 0 0
\(779\) −20.2563 28.0520i −0.725756 1.00507i
\(780\) 0 0
\(781\) −52.0599 43.6834i −1.86285 1.56312i
\(782\) 0 0
\(783\) 13.4261 + 76.1430i 0.479808 + 2.72113i
\(784\) 0 0
\(785\) −16.4053 5.97103i −0.585530 0.213115i
\(786\) 0 0
\(787\) −24.0963 + 41.7360i −0.858940