Properties

Label 380.2.u.b.301.1
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 301.1
Root \(-0.838693 - 1.45266i\) of defining polynomial
Character \(\chi\) \(=\) 380.301
Dual form 380.2.u.b.101.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.57623 + 0.573700i) q^{3} +(0.173648 - 0.984808i) q^{5} +(0.230636 + 0.399473i) q^{7} +(-0.142773 + 0.119801i) q^{9} +O(q^{10})\) \(q+(-1.57623 + 0.573700i) q^{3} +(0.173648 - 0.984808i) q^{5} +(0.230636 + 0.399473i) q^{7} +(-0.142773 + 0.119801i) q^{9} +(-0.642179 + 1.11229i) q^{11} +(5.58829 + 2.03397i) q^{13} +(0.291275 + 1.65190i) q^{15} +(4.26171 + 3.57600i) q^{17} +(-3.93062 + 1.88419i) q^{19} +(-0.592712 - 0.497345i) q^{21} +(0.379967 + 2.15490i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(2.67239 - 4.62872i) q^{27} +(-7.31767 + 6.14026i) q^{29} +(4.61929 + 8.00084i) q^{31} +(0.374101 - 2.12163i) q^{33} +(0.433454 - 0.157764i) q^{35} +8.90443 q^{37} -9.97531 q^{39} +(4.53095 - 1.64913i) q^{41} +(-0.655751 + 3.71895i) q^{43} +(0.0931885 + 0.161407i) q^{45} +(-5.24811 + 4.40369i) q^{47} +(3.39361 - 5.87791i) q^{49} +(-8.76897 - 3.19164i) q^{51} +(-1.37327 - 7.78821i) q^{53} +(0.983875 + 0.825569i) q^{55} +(5.11460 - 5.22492i) q^{57} +(-4.10588 - 3.44524i) q^{59} +(-1.76051 - 9.98434i) q^{61} +(-0.0807859 - 0.0294036i) q^{63} +(2.97347 - 5.15020i) q^{65} +(5.05696 - 4.24330i) q^{67} +(-1.83518 - 3.17863i) q^{69} +(1.19711 - 6.78912i) q^{71} +(-12.3010 + 4.47721i) q^{73} +1.67739 q^{75} -0.592438 q^{77} +(-1.30465 + 0.474853i) q^{79} +(-1.45971 + 8.27842i) q^{81} +(-0.0660497 - 0.114402i) q^{83} +(4.26171 - 3.57600i) q^{85} +(8.01165 - 13.8766i) q^{87} +(2.89456 + 1.05353i) q^{89} +(0.476344 + 2.70148i) q^{91} +(-11.8711 - 9.96105i) q^{93} +(1.17302 + 4.19810i) q^{95} +(0.447812 + 0.375759i) q^{97} +(-0.0415670 - 0.235738i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) 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
\(3\) −1.57623 + 0.573700i −0.910035 + 0.331226i −0.754267 0.656568i \(-0.772008\pi\)
−0.155768 + 0.987794i \(0.549785\pi\)
\(4\) 0 0
\(5\) 0.173648 0.984808i 0.0776578 0.440419i
\(6\) 0 0
\(7\) 0.230636 + 0.399473i 0.0871722 + 0.150987i 0.906315 0.422603i \(-0.138884\pi\)
−0.819143 + 0.573590i \(0.805550\pi\)
\(8\) 0 0
\(9\) −0.142773 + 0.119801i −0.0475910 + 0.0399336i
\(10\) 0 0
\(11\) −0.642179 + 1.11229i −0.193624 + 0.335367i −0.946449 0.322854i \(-0.895358\pi\)
0.752824 + 0.658221i \(0.228691\pi\)
\(12\) 0 0
\(13\) 5.58829 + 2.03397i 1.54991 + 0.564122i 0.968397 0.249412i \(-0.0802375\pi\)
0.581516 + 0.813535i \(0.302460\pi\)
\(14\) 0 0
\(15\) 0.291275 + 1.65190i 0.0752069 + 0.426519i
\(16\) 0 0
\(17\) 4.26171 + 3.57600i 1.03362 + 0.867307i 0.991277 0.131796i \(-0.0420745\pi\)
0.0423393 + 0.999103i \(0.486519\pi\)
\(18\) 0 0
\(19\) −3.93062 + 1.88419i −0.901747 + 0.432264i
\(20\) 0 0
\(21\) −0.592712 0.497345i −0.129340 0.108530i
\(22\) 0 0
\(23\) 0.379967 + 2.15490i 0.0792287 + 0.449328i 0.998453 + 0.0555949i \(0.0177055\pi\)
−0.919225 + 0.393733i \(0.871183\pi\)
\(24\) 0 0
\(25\) −0.939693 0.342020i −0.187939 0.0684040i
\(26\) 0 0
\(27\) 2.67239 4.62872i 0.514302 0.890797i
\(28\) 0 0
\(29\) −7.31767 + 6.14026i −1.35886 + 1.14022i −0.382524 + 0.923945i \(0.624945\pi\)
−0.976333 + 0.216272i \(0.930610\pi\)
\(30\) 0 0
\(31\) 4.61929 + 8.00084i 0.829648 + 1.43699i 0.898314 + 0.439353i \(0.144792\pi\)
−0.0686661 + 0.997640i \(0.521874\pi\)
\(32\) 0 0
\(33\) 0.374101 2.12163i 0.0651227 0.369329i
\(34\) 0 0
\(35\) 0.433454 0.157764i 0.0732671 0.0266670i
\(36\) 0 0
\(37\) 8.90443 1.46388 0.731940 0.681369i \(-0.238615\pi\)
0.731940 + 0.681369i \(0.238615\pi\)
\(38\) 0 0
\(39\) −9.97531 −1.59733
\(40\) 0 0
\(41\) 4.53095 1.64913i 0.707615 0.257551i 0.0369563 0.999317i \(-0.488234\pi\)
0.670659 + 0.741766i \(0.266012\pi\)
\(42\) 0 0
\(43\) −0.655751 + 3.71895i −0.100001 + 0.567134i 0.893099 + 0.449861i \(0.148526\pi\)
−0.993100 + 0.117273i \(0.962585\pi\)
\(44\) 0 0
\(45\) 0.0931885 + 0.161407i 0.0138917 + 0.0240612i
\(46\) 0 0
\(47\) −5.24811 + 4.40369i −0.765516 + 0.642344i −0.939556 0.342395i \(-0.888762\pi\)
0.174041 + 0.984738i \(0.444318\pi\)
\(48\) 0 0
\(49\) 3.39361 5.87791i 0.484802 0.839702i
\(50\) 0 0
\(51\) −8.76897 3.19164i −1.22790 0.446919i
\(52\) 0 0
\(53\) −1.37327 7.78821i −0.188633 1.06979i −0.921198 0.389095i \(-0.872788\pi\)
0.732564 0.680698i \(-0.238323\pi\)
\(54\) 0 0
\(55\) 0.983875 + 0.825569i 0.132666 + 0.111320i
\(56\) 0 0
\(57\) 5.11460 5.22492i 0.677445 0.692057i
\(58\) 0 0
\(59\) −4.10588 3.44524i −0.534540 0.448532i 0.335126 0.942173i \(-0.391221\pi\)
−0.869666 + 0.493641i \(0.835666\pi\)
\(60\) 0 0
\(61\) −1.76051 9.98434i −0.225410 1.27836i −0.861900 0.507079i \(-0.830725\pi\)
0.636490 0.771285i \(-0.280386\pi\)
\(62\) 0 0
\(63\) −0.0807859 0.0294036i −0.0101781 0.00370451i
\(64\) 0 0
\(65\) 2.97347 5.15020i 0.368813 0.638804i
\(66\) 0 0
\(67\) 5.05696 4.24330i 0.617807 0.518401i −0.279307 0.960202i \(-0.590105\pi\)
0.897113 + 0.441801i \(0.145660\pi\)
\(68\) 0 0
\(69\) −1.83518 3.17863i −0.220930 0.382662i
\(70\) 0 0
\(71\) 1.19711 6.78912i 0.142070 0.805721i −0.827603 0.561314i \(-0.810296\pi\)
0.969673 0.244406i \(-0.0785931\pi\)
\(72\) 0 0
\(73\) −12.3010 + 4.47721i −1.43973 + 0.524017i −0.939702 0.341994i \(-0.888898\pi\)
−0.500024 + 0.866012i \(0.666675\pi\)
\(74\) 0 0
\(75\) 1.67739 0.193688
\(76\) 0 0
\(77\) −0.592438 −0.0675146
\(78\) 0 0
\(79\) −1.30465 + 0.474853i −0.146784 + 0.0534251i −0.414368 0.910110i \(-0.635997\pi\)
0.267583 + 0.963535i \(0.413775\pi\)
\(80\) 0 0
\(81\) −1.45971 + 8.27842i −0.162190 + 0.919825i
\(82\) 0 0
\(83\) −0.0660497 0.114402i −0.00724990 0.0125572i 0.862378 0.506265i \(-0.168974\pi\)
−0.869628 + 0.493708i \(0.835641\pi\)
\(84\) 0 0
\(85\) 4.26171 3.57600i 0.462247 0.387871i
\(86\) 0 0
\(87\) 8.01165 13.8766i 0.858939 1.48773i
\(88\) 0 0
\(89\) 2.89456 + 1.05353i 0.306823 + 0.111674i 0.490843 0.871248i \(-0.336689\pi\)
−0.184020 + 0.982922i \(0.558911\pi\)
\(90\) 0 0
\(91\) 0.476344 + 2.70148i 0.0499344 + 0.283192i
\(92\) 0 0
\(93\) −11.8711 9.96105i −1.23098 1.03291i
\(94\) 0 0
\(95\) 1.17302 + 4.19810i 0.120350 + 0.430716i
\(96\) 0 0
\(97\) 0.447812 + 0.375759i 0.0454684 + 0.0381525i 0.665239 0.746631i \(-0.268330\pi\)
−0.619770 + 0.784783i \(0.712774\pi\)
\(98\) 0 0
\(99\) −0.0415670 0.235738i −0.00417764 0.0236926i
\(100\) 0 0
\(101\) −5.06052 1.84188i −0.503541 0.183274i 0.0777450 0.996973i \(-0.475228\pi\)
−0.581286 + 0.813699i \(0.697450\pi\)
\(102\) 0 0
\(103\) −1.26492 + 2.19090i −0.124636 + 0.215876i −0.921591 0.388163i \(-0.873110\pi\)
0.796955 + 0.604039i \(0.206443\pi\)
\(104\) 0 0
\(105\) −0.592712 + 0.497345i −0.0578428 + 0.0485359i
\(106\) 0 0
\(107\) −3.63551 6.29689i −0.351458 0.608743i 0.635047 0.772473i \(-0.280981\pi\)
−0.986505 + 0.163730i \(0.947647\pi\)
\(108\) 0 0
\(109\) −1.19744 + 6.79102i −0.114694 + 0.650462i 0.872207 + 0.489136i \(0.162688\pi\)
−0.986901 + 0.161325i \(0.948423\pi\)
\(110\) 0 0
\(111\) −14.0354 + 5.10847i −1.33218 + 0.484875i
\(112\) 0 0
\(113\) 9.85398 0.926984 0.463492 0.886101i \(-0.346596\pi\)
0.463492 + 0.886101i \(0.346596\pi\)
\(114\) 0 0
\(115\) 2.18815 0.204046
\(116\) 0 0
\(117\) −1.04153 + 0.379086i −0.0962894 + 0.0350465i
\(118\) 0 0
\(119\) −0.445612 + 2.52719i −0.0408492 + 0.231667i
\(120\) 0 0
\(121\) 4.67521 + 8.09771i 0.425019 + 0.736155i
\(122\) 0 0
\(123\) −6.19569 + 5.19881i −0.558647 + 0.468760i
\(124\) 0 0
\(125\) −0.500000 + 0.866025i −0.0447214 + 0.0774597i
\(126\) 0 0
\(127\) 18.1523 + 6.60689i 1.61075 + 0.586267i 0.981589 0.191005i \(-0.0611746\pi\)
0.629165 + 0.777271i \(0.283397\pi\)
\(128\) 0 0
\(129\) −1.09995 6.23811i −0.0968449 0.549235i
\(130\) 0 0
\(131\) −7.55776 6.34171i −0.660324 0.554078i 0.249860 0.968282i \(-0.419615\pi\)
−0.910184 + 0.414204i \(0.864060\pi\)
\(132\) 0 0
\(133\) −1.65923 1.13562i −0.143873 0.0984705i
\(134\) 0 0
\(135\) −4.09434 3.43556i −0.352385 0.295686i
\(136\) 0 0
\(137\) 1.85178 + 10.5020i 0.158208 + 0.897242i 0.955794 + 0.294037i \(0.0949989\pi\)
−0.797586 + 0.603205i \(0.793890\pi\)
\(138\) 0 0
\(139\) −1.23752 0.450422i −0.104965 0.0382043i 0.289004 0.957328i \(-0.406676\pi\)
−0.393969 + 0.919124i \(0.628898\pi\)
\(140\) 0 0
\(141\) 5.74582 9.95205i 0.483885 0.838114i
\(142\) 0 0
\(143\) −5.85104 + 4.90961i −0.489289 + 0.410562i
\(144\) 0 0
\(145\) 4.77627 + 8.27274i 0.396648 + 0.687014i
\(146\) 0 0
\(147\) −1.97695 + 11.2118i −0.163056 + 0.924737i
\(148\) 0 0
\(149\) −15.8692 + 5.77592i −1.30006 + 0.473181i −0.897015 0.442001i \(-0.854269\pi\)
−0.403041 + 0.915182i \(0.632047\pi\)
\(150\) 0 0
\(151\) 21.5094 1.75041 0.875206 0.483751i \(-0.160726\pi\)
0.875206 + 0.483751i \(0.160726\pi\)
\(152\) 0 0
\(153\) −1.03686 −0.0838256
\(154\) 0 0
\(155\) 8.68142 3.15978i 0.697308 0.253799i
\(156\) 0 0
\(157\) −0.0930096 + 0.527484i −0.00742297 + 0.0420978i −0.988294 0.152560i \(-0.951248\pi\)
0.980871 + 0.194657i \(0.0623595\pi\)
\(158\) 0 0
\(159\) 6.63268 + 11.4881i 0.526006 + 0.911069i
\(160\) 0 0
\(161\) −0.773192 + 0.648785i −0.0609360 + 0.0511314i
\(162\) 0 0
\(163\) 2.35598 4.08068i 0.184535 0.319624i −0.758885 0.651225i \(-0.774255\pi\)
0.943420 + 0.331601i \(0.107589\pi\)
\(164\) 0 0
\(165\) −2.02444 0.736836i −0.157602 0.0573626i
\(166\) 0 0
\(167\) −2.67217 15.1546i −0.206779 1.17270i −0.894616 0.446835i \(-0.852551\pi\)
0.687837 0.725865i \(-0.258560\pi\)
\(168\) 0 0
\(169\) 17.1334 + 14.3766i 1.31795 + 1.10589i
\(170\) 0 0
\(171\) 0.335459 0.739904i 0.0256532 0.0565819i
\(172\) 0 0
\(173\) −15.3406 12.8722i −1.16632 0.978659i −0.166348 0.986067i \(-0.553197\pi\)
−0.999973 + 0.00740809i \(0.997642\pi\)
\(174\) 0 0
\(175\) −0.0800990 0.454264i −0.00605492 0.0343392i
\(176\) 0 0
\(177\) 8.44833 + 3.07494i 0.635015 + 0.231127i
\(178\) 0 0
\(179\) 6.47084 11.2078i 0.483653 0.837712i −0.516170 0.856486i \(-0.672643\pi\)
0.999824 + 0.0187736i \(0.00597617\pi\)
\(180\) 0 0
\(181\) 5.41021 4.53971i 0.402138 0.337434i −0.419181 0.907903i \(-0.637683\pi\)
0.821319 + 0.570469i \(0.193238\pi\)
\(182\) 0 0
\(183\) 8.50298 + 14.7276i 0.628558 + 1.08869i
\(184\) 0 0
\(185\) 1.54624 8.76915i 0.113682 0.644721i
\(186\) 0 0
\(187\) −6.71431 + 2.44381i −0.490999 + 0.178709i
\(188\) 0 0
\(189\) 2.46540 0.179331
\(190\) 0 0
\(191\) −23.1066 −1.67194 −0.835968 0.548778i \(-0.815093\pi\)
−0.835968 + 0.548778i \(0.815093\pi\)
\(192\) 0 0
\(193\) 7.11202 2.58856i 0.511934 0.186329i −0.0731197 0.997323i \(-0.523296\pi\)
0.585054 + 0.810994i \(0.301073\pi\)
\(194\) 0 0
\(195\) −1.73219 + 9.82376i −0.124045 + 0.703494i
\(196\) 0 0
\(197\) 1.04381 + 1.80794i 0.0743687 + 0.128810i 0.900812 0.434210i \(-0.142972\pi\)
−0.826443 + 0.563021i \(0.809639\pi\)
\(198\) 0 0
\(199\) −8.17751 + 6.86174i −0.579688 + 0.486416i −0.884845 0.465886i \(-0.845736\pi\)
0.305157 + 0.952302i \(0.401291\pi\)
\(200\) 0 0
\(201\) −5.53655 + 9.58958i −0.390518 + 0.676397i
\(202\) 0 0
\(203\) −4.14059 1.50705i −0.290612 0.105774i
\(204\) 0 0
\(205\) −0.837285 4.74848i −0.0584785 0.331648i
\(206\) 0 0
\(207\) −0.312408 0.262142i −0.0217139 0.0182201i
\(208\) 0 0
\(209\) 0.428401 5.58197i 0.0296331 0.386113i
\(210\) 0 0
\(211\) −1.92530 1.61552i −0.132543 0.111217i 0.574106 0.818781i \(-0.305350\pi\)
−0.706649 + 0.707564i \(0.749794\pi\)
\(212\) 0 0
\(213\) 2.00801 + 11.3880i 0.137586 + 0.780292i
\(214\) 0 0
\(215\) 3.54858 + 1.29158i 0.242011 + 0.0880848i
\(216\) 0 0
\(217\) −2.13075 + 3.69056i −0.144645 + 0.250532i
\(218\) 0 0
\(219\) 16.8206 14.1142i 1.13663 0.953748i
\(220\) 0 0
\(221\) 16.5422 + 28.6519i 1.11275 + 1.92734i
\(222\) 0 0
\(223\) −0.994453 + 5.63982i −0.0665935 + 0.377671i 0.933237 + 0.359261i \(0.116971\pi\)
−0.999831 + 0.0184093i \(0.994140\pi\)
\(224\) 0 0
\(225\) 0.175137 0.0637447i 0.0116758 0.00424965i
\(226\) 0 0
\(227\) 10.9014 0.723551 0.361775 0.932265i \(-0.382171\pi\)
0.361775 + 0.932265i \(0.382171\pi\)
\(228\) 0 0
\(229\) 0.764616 0.0505272 0.0252636 0.999681i \(-0.491957\pi\)
0.0252636 + 0.999681i \(0.491957\pi\)
\(230\) 0 0
\(231\) 0.933817 0.339882i 0.0614407 0.0223626i
\(232\) 0 0
\(233\) −2.23090 + 12.6520i −0.146151 + 0.828863i 0.820285 + 0.571955i \(0.193815\pi\)
−0.966436 + 0.256908i \(0.917296\pi\)
\(234\) 0 0
\(235\) 3.42546 + 5.93307i 0.223452 + 0.387031i
\(236\) 0 0
\(237\) 1.78400 1.49695i 0.115883 0.0972375i
\(238\) 0 0
\(239\) 4.87692 8.44707i 0.315462 0.546396i −0.664074 0.747667i \(-0.731174\pi\)
0.979536 + 0.201271i \(0.0645073\pi\)
\(240\) 0 0
\(241\) −9.11167 3.31638i −0.586934 0.213626i 0.0314464 0.999505i \(-0.489989\pi\)
−0.618380 + 0.785879i \(0.712211\pi\)
\(242\) 0 0
\(243\) 0.335840 + 1.90464i 0.0215441 + 0.122183i
\(244\) 0 0
\(245\) −5.19932 4.36275i −0.332172 0.278726i
\(246\) 0 0
\(247\) −25.7979 + 2.53465i −1.64148 + 0.161276i
\(248\) 0 0
\(249\) 0.169741 + 0.142430i 0.0107569 + 0.00902614i
\(250\) 0 0
\(251\) 2.48507 + 14.0935i 0.156856 + 0.889576i 0.957069 + 0.289860i \(0.0936087\pi\)
−0.800213 + 0.599716i \(0.795280\pi\)
\(252\) 0 0
\(253\) −2.64088 0.961200i −0.166030 0.0604301i
\(254\) 0 0
\(255\) −4.66587 + 8.08153i −0.292188 + 0.506085i
\(256\) 0 0
\(257\) −12.5560 + 10.5357i −0.783221 + 0.657201i −0.944058 0.329780i \(-0.893025\pi\)
0.160836 + 0.986981i \(0.448581\pi\)
\(258\) 0 0
\(259\) 2.05368 + 3.55708i 0.127610 + 0.221026i
\(260\) 0 0
\(261\) 0.309159 1.75333i 0.0191365 0.108528i
\(262\) 0 0
\(263\) 28.3445 10.3166i 1.74780 0.636146i 0.748171 0.663506i \(-0.230932\pi\)
0.999626 + 0.0273600i \(0.00871003\pi\)
\(264\) 0 0
\(265\) −7.90836 −0.485807
\(266\) 0 0
\(267\) −5.16689 −0.316209
\(268\) 0 0
\(269\) −10.0213 + 3.64747i −0.611012 + 0.222390i −0.628946 0.777449i \(-0.716513\pi\)
0.0179339 + 0.999839i \(0.494291\pi\)
\(270\) 0 0
\(271\) 5.03825 28.5733i 0.306052 1.73571i −0.312460 0.949931i \(-0.601153\pi\)
0.618511 0.785776i \(-0.287736\pi\)
\(272\) 0 0
\(273\) −2.30067 3.98487i −0.139243 0.241175i
\(274\) 0 0
\(275\) 0.983875 0.825569i 0.0593299 0.0497837i
\(276\) 0 0
\(277\) 8.11556 14.0566i 0.487617 0.844577i −0.512282 0.858817i \(-0.671200\pi\)
0.999899 + 0.0142406i \(0.00453307\pi\)
\(278\) 0 0
\(279\) −1.61802 0.588910i −0.0968681 0.0352571i
\(280\) 0 0
\(281\) 0.339000 + 1.92256i 0.0202230 + 0.114690i 0.993248 0.116008i \(-0.0370099\pi\)
−0.973025 + 0.230699i \(0.925899\pi\)
\(282\) 0 0
\(283\) 15.3905 + 12.9142i 0.914873 + 0.767670i 0.973040 0.230637i \(-0.0740810\pi\)
−0.0581666 + 0.998307i \(0.518525\pi\)
\(284\) 0 0
\(285\) −4.25740 5.94419i −0.252186 0.352103i
\(286\) 0 0
\(287\) 1.70378 + 1.42964i 0.100571 + 0.0843892i
\(288\) 0 0
\(289\) 2.42238 + 13.7380i 0.142493 + 0.808117i
\(290\) 0 0
\(291\) −0.921426 0.335371i −0.0540149 0.0196598i
\(292\) 0 0
\(293\) 9.65324 16.7199i 0.563948 0.976787i −0.433199 0.901298i \(-0.642615\pi\)
0.997147 0.0754882i \(-0.0240515\pi\)
\(294\) 0 0
\(295\) −4.10588 + 3.44524i −0.239053 + 0.200590i
\(296\) 0 0
\(297\) 3.43231 + 5.94493i 0.199163 + 0.344960i
\(298\) 0 0
\(299\) −2.25964 + 12.8151i −0.130678 + 0.741115i
\(300\) 0 0
\(301\) −1.63686 + 0.595768i −0.0943471 + 0.0343395i
\(302\) 0 0
\(303\) 9.03322 0.518945
\(304\) 0 0
\(305\) −10.1384 −0.580521
\(306\) 0 0
\(307\) −10.2195 + 3.71959i −0.583257 + 0.212288i −0.616761 0.787150i \(-0.711556\pi\)
0.0335038 + 0.999439i \(0.489333\pi\)
\(308\) 0 0
\(309\) 0.736878 4.17904i 0.0419195 0.237737i
\(310\) 0 0
\(311\) 8.62121 + 14.9324i 0.488864 + 0.846737i 0.999918 0.0128113i \(-0.00407807\pi\)
−0.511054 + 0.859549i \(0.670745\pi\)
\(312\) 0 0
\(313\) 6.00211 5.03637i 0.339259 0.284672i −0.457201 0.889364i \(-0.651148\pi\)
0.796460 + 0.604691i \(0.206703\pi\)
\(314\) 0 0
\(315\) −0.0429853 + 0.0744527i −0.00242194 + 0.00419493i
\(316\) 0 0
\(317\) −9.67697 3.52213i −0.543513 0.197822i 0.0556491 0.998450i \(-0.482277\pi\)
−0.599162 + 0.800628i \(0.704499\pi\)
\(318\) 0 0
\(319\) −2.13047 12.0825i −0.119283 0.676490i
\(320\) 0 0
\(321\) 9.34291 + 7.83963i 0.521470 + 0.437566i
\(322\) 0 0
\(323\) −23.4891 6.02602i −1.30697 0.335297i
\(324\) 0 0
\(325\) −4.55562 3.82262i −0.252700 0.212041i
\(326\) 0 0
\(327\) −2.00857 11.3912i −0.111074 0.629933i
\(328\) 0 0
\(329\) −2.96956 1.08083i −0.163717 0.0595881i
\(330\) 0 0
\(331\) 16.7428 28.9993i 0.920266 1.59395i 0.121262 0.992621i \(-0.461306\pi\)
0.799004 0.601326i \(-0.205361\pi\)
\(332\) 0 0
\(333\) −1.27131 + 1.06676i −0.0696675 + 0.0584580i
\(334\) 0 0
\(335\) −3.30070 5.71698i −0.180336 0.312352i
\(336\) 0 0
\(337\) −4.32250 + 24.5141i −0.235462 + 1.33537i 0.606177 + 0.795330i \(0.292702\pi\)
−0.841639 + 0.540041i \(0.818409\pi\)
\(338\) 0 0
\(339\) −15.5321 + 5.65322i −0.843588 + 0.307041i
\(340\) 0 0
\(341\) −11.8656 −0.642560
\(342\) 0 0
\(343\) 6.35966 0.343389
\(344\) 0 0
\(345\) −3.44901 + 1.25534i −0.185689 + 0.0675851i
\(346\) 0 0
\(347\) 4.38162 24.8494i 0.235218 1.33399i −0.606937 0.794750i \(-0.707602\pi\)
0.842155 0.539236i \(-0.181287\pi\)
\(348\) 0 0
\(349\) −14.2024 24.5992i −0.760236 1.31677i −0.942729 0.333560i \(-0.891750\pi\)
0.182493 0.983207i \(-0.441583\pi\)
\(350\) 0 0
\(351\) 24.3488 20.4311i 1.29964 1.09053i
\(352\) 0 0
\(353\) 15.0606 26.0858i 0.801596 1.38841i −0.116969 0.993136i \(-0.537318\pi\)
0.918565 0.395270i \(-0.129349\pi\)
\(354\) 0 0
\(355\) −6.47811 2.35784i −0.343822 0.125141i
\(356\) 0 0
\(357\) −0.747464 4.23908i −0.0395600 0.224356i
\(358\) 0 0
\(359\) −26.1437 21.9372i −1.37981 1.15780i −0.969282 0.245952i \(-0.920899\pi\)
−0.410530 0.911847i \(-0.634656\pi\)
\(360\) 0 0
\(361\) 11.8996 14.8121i 0.626296 0.779585i
\(362\) 0 0
\(363\) −12.0148 10.0817i −0.630616 0.529150i
\(364\) 0 0
\(365\) 2.27314 + 12.8916i 0.118981 + 0.674777i
\(366\) 0 0
\(367\) −21.2362 7.72935i −1.10852 0.403469i −0.278071 0.960561i \(-0.589695\pi\)
−0.830451 + 0.557092i \(0.811917\pi\)
\(368\) 0 0
\(369\) −0.449330 + 0.778263i −0.0233912 + 0.0405147i
\(370\) 0 0
\(371\) 2.79446 2.34483i 0.145081 0.121737i
\(372\) 0 0
\(373\) −6.05955 10.4955i −0.313752 0.543434i 0.665420 0.746469i \(-0.268253\pi\)
−0.979171 + 0.203036i \(0.934919\pi\)
\(374\) 0 0
\(375\) 0.291275 1.65190i 0.0150414 0.0853039i
\(376\) 0 0
\(377\) −53.3824 + 19.4296i −2.74933 + 1.00068i
\(378\) 0 0
\(379\) 34.8034 1.78773 0.893866 0.448335i \(-0.147983\pi\)
0.893866 + 0.448335i \(0.147983\pi\)
\(380\) 0 0
\(381\) −32.4025 −1.66003
\(382\) 0 0
\(383\) 25.9413 9.44187i 1.32554 0.482457i 0.420310 0.907381i \(-0.361921\pi\)
0.905229 + 0.424924i \(0.139699\pi\)
\(384\) 0 0
\(385\) −0.102876 + 0.583438i −0.00524304 + 0.0297347i
\(386\) 0 0
\(387\) −0.351910 0.609525i −0.0178886 0.0309839i
\(388\) 0 0
\(389\) 16.6736 13.9908i 0.845384 0.709362i −0.113384 0.993551i \(-0.536169\pi\)
0.958768 + 0.284190i \(0.0917246\pi\)
\(390\) 0 0
\(391\) −6.08662 + 10.5423i −0.307813 + 0.533148i
\(392\) 0 0
\(393\) 15.5510 + 5.66009i 0.784443 + 0.285514i
\(394\) 0 0
\(395\) 0.241089 + 1.36728i 0.0121305 + 0.0687956i
\(396\) 0 0
\(397\) 0.534594 + 0.448577i 0.0268305 + 0.0225134i 0.656104 0.754670i \(-0.272203\pi\)
−0.629274 + 0.777184i \(0.716648\pi\)
\(398\) 0 0
\(399\) 3.26682 + 0.838091i 0.163546 + 0.0419570i
\(400\) 0 0
\(401\) 8.08896 + 6.78745i 0.403944 + 0.338949i 0.822016 0.569465i \(-0.192850\pi\)
−0.418072 + 0.908414i \(0.637294\pi\)
\(402\) 0 0
\(403\) 9.54044 + 54.1065i 0.475243 + 2.69524i
\(404\) 0 0
\(405\) 7.89918 + 2.87507i 0.392513 + 0.142863i
\(406\) 0 0
\(407\) −5.71824 + 9.90428i −0.283443 + 0.490937i
\(408\) 0 0
\(409\) 9.35982 7.85383i 0.462814 0.388347i −0.381351 0.924430i \(-0.624541\pi\)
0.844165 + 0.536083i \(0.180097\pi\)
\(410\) 0 0
\(411\) −8.94379 15.4911i −0.441165 0.764119i
\(412\) 0 0
\(413\) 0.429318 2.43478i 0.0211254 0.119808i
\(414\) 0 0
\(415\) −0.124133 + 0.0451807i −0.00609344 + 0.00221783i
\(416\) 0 0
\(417\) 2.20902 0.108176
\(418\) 0 0
\(419\) 26.6471 1.30180 0.650899 0.759165i \(-0.274392\pi\)
0.650899 + 0.759165i \(0.274392\pi\)
\(420\) 0 0
\(421\) −14.4385 + 5.25519i −0.703690 + 0.256122i −0.668985 0.743276i \(-0.733271\pi\)
−0.0347043 + 0.999398i \(0.511049\pi\)
\(422\) 0 0
\(423\) 0.221723 1.25746i 0.0107806 0.0611396i
\(424\) 0 0
\(425\) −2.78163 4.81793i −0.134929 0.233704i
\(426\) 0 0
\(427\) 3.58244 3.00603i 0.173366 0.145472i
\(428\) 0 0
\(429\) 6.40593 11.0954i 0.309281 0.535691i
\(430\) 0 0
\(431\) −36.0199 13.1102i −1.73502 0.631494i −0.736049 0.676928i \(-0.763311\pi\)
−0.998967 + 0.0454340i \(0.985533\pi\)
\(432\) 0 0
\(433\) −5.71443 32.4082i −0.274618 1.55744i −0.740172 0.672417i \(-0.765256\pi\)
0.465554 0.885019i \(-0.345855\pi\)
\(434\) 0 0
\(435\) −12.2746 10.2996i −0.588520 0.493827i
\(436\) 0 0
\(437\) −5.55376 7.75418i −0.265673 0.370933i
\(438\) 0 0
\(439\) −18.1190 15.2037i −0.864775 0.725632i 0.0982162 0.995165i \(-0.468686\pi\)
−0.962991 + 0.269533i \(0.913131\pi\)
\(440\) 0 0
\(441\) 0.219662 + 1.24577i 0.0104601 + 0.0593222i
\(442\) 0 0
\(443\) 15.5447 + 5.65781i 0.738551 + 0.268811i 0.683780 0.729688i \(-0.260335\pi\)
0.0547713 + 0.998499i \(0.482557\pi\)
\(444\) 0 0
\(445\) 1.54016 2.66764i 0.0730107 0.126458i
\(446\) 0 0
\(447\) 21.6998 18.2083i 1.02637 0.861224i
\(448\) 0 0
\(449\) 14.6752 + 25.4181i 0.692563 + 1.19955i 0.970995 + 0.239099i \(0.0768520\pi\)
−0.278432 + 0.960456i \(0.589815\pi\)
\(450\) 0 0
\(451\) −1.07537 + 6.09875i −0.0506374 + 0.287179i
\(452\) 0 0
\(453\) −33.9037 + 12.3399i −1.59294 + 0.579781i
\(454\) 0 0
\(455\) 2.74316 0.128601
\(456\) 0 0
\(457\) −5.48753 −0.256696 −0.128348 0.991729i \(-0.540967\pi\)
−0.128348 + 0.991729i \(0.540967\pi\)
\(458\) 0 0
\(459\) 27.9412 10.1698i 1.30419 0.474685i
\(460\) 0 0
\(461\) −5.76350 + 32.6864i −0.268433 + 1.52236i 0.490646 + 0.871359i \(0.336761\pi\)
−0.759079 + 0.650999i \(0.774350\pi\)
\(462\) 0 0
\(463\) 6.07020 + 10.5139i 0.282106 + 0.488622i 0.971903 0.235381i \(-0.0756336\pi\)
−0.689797 + 0.724003i \(0.742300\pi\)
\(464\) 0 0
\(465\) −11.8711 + 9.96105i −0.550510 + 0.461933i
\(466\) 0 0
\(467\) −10.2092 + 17.6828i −0.472425 + 0.818264i −0.999502 0.0315536i \(-0.989955\pi\)
0.527077 + 0.849817i \(0.323288\pi\)
\(468\) 0 0
\(469\) 2.86140 + 1.04147i 0.132127 + 0.0480904i
\(470\) 0 0
\(471\) −0.156013 0.884793i −0.00718870 0.0407691i
\(472\) 0 0
\(473\) −3.71543 3.11761i −0.170835 0.143348i
\(474\) 0 0
\(475\) 4.33801 0.426210i 0.199042 0.0195559i
\(476\) 0 0
\(477\) 1.12910 + 0.947428i 0.0516980 + 0.0433798i
\(478\) 0 0
\(479\) 1.98862 + 11.2780i 0.0908621 + 0.515305i 0.995937 + 0.0900526i \(0.0287035\pi\)
−0.905075 + 0.425252i \(0.860185\pi\)
\(480\) 0 0
\(481\) 49.7606 + 18.1114i 2.26889 + 0.825807i
\(482\) 0 0
\(483\) 0.846518 1.46621i 0.0385179 0.0667150i
\(484\) 0 0
\(485\) 0.447812 0.375759i 0.0203341 0.0170623i
\(486\) 0 0
\(487\) 6.46021 + 11.1894i 0.292740 + 0.507041i 0.974457 0.224575i \(-0.0720995\pi\)
−0.681716 + 0.731617i \(0.738766\pi\)
\(488\) 0 0
\(489\) −1.37248 + 7.78371i −0.0620656 + 0.351992i
\(490\) 0 0
\(491\) 30.1324 10.9673i 1.35986 0.494947i 0.443846 0.896103i \(-0.353614\pi\)
0.916010 + 0.401156i \(0.131391\pi\)
\(492\) 0 0
\(493\) −53.1433 −2.39346
\(494\) 0 0
\(495\) −0.239375 −0.0107591
\(496\) 0 0
\(497\) 2.98817 1.08760i 0.134038 0.0487857i
\(498\) 0 0
\(499\) −0.339187 + 1.92363i −0.0151841 + 0.0861133i −0.991458 0.130425i \(-0.958366\pi\)
0.976274 + 0.216539i \(0.0694768\pi\)
\(500\) 0 0
\(501\) 12.9062 + 22.3541i 0.576604 + 0.998708i
\(502\) 0 0
\(503\) 20.8314 17.4796i 0.928824 0.779376i −0.0467817 0.998905i \(-0.514897\pi\)
0.975606 + 0.219529i \(0.0704521\pi\)
\(504\) 0 0
\(505\) −2.69265 + 4.66380i −0.119821 + 0.207537i
\(506\) 0 0
\(507\) −35.2540 12.8314i −1.56568 0.569863i
\(508\) 0 0
\(509\) 4.27733 + 24.2580i 0.189589 + 1.07521i 0.919916 + 0.392116i \(0.128257\pi\)
−0.730326 + 0.683098i \(0.760632\pi\)
\(510\) 0 0
\(511\) −4.62558 3.88133i −0.204624 0.171700i
\(512\) 0 0
\(513\) −1.78277 + 23.2291i −0.0787110 + 1.02559i
\(514\) 0 0
\(515\) 1.93797 + 1.62615i 0.0853970 + 0.0716566i
\(516\) 0 0
\(517\) −1.52794 8.66536i −0.0671986 0.381102i
\(518\) 0 0
\(519\) 31.5650 + 11.4887i 1.38555 + 0.504299i
\(520\) 0 0
\(521\) 0.800476 1.38646i 0.0350695 0.0607421i −0.847958 0.530064i \(-0.822168\pi\)
0.883027 + 0.469321i \(0.155501\pi\)
\(522\) 0 0
\(523\) −4.61410 + 3.87169i −0.201760 + 0.169297i −0.738070 0.674724i \(-0.764262\pi\)
0.536309 + 0.844021i \(0.319818\pi\)
\(524\) 0 0
\(525\) 0.386866 + 0.670071i 0.0168842 + 0.0292443i
\(526\) 0 0
\(527\) −8.92493 + 50.6158i −0.388776 + 2.20486i
\(528\) 0 0
\(529\) 17.1137 6.22888i 0.744074 0.270821i
\(530\) 0 0
\(531\) 0.998952 0.0433508
\(532\) 0 0
\(533\) 28.6745 1.24203
\(534\) 0 0
\(535\) −6.83252 + 2.48684i −0.295396 + 0.107515i
\(536\) 0 0
\(537\) −3.76959 + 21.3784i −0.162670 + 0.922546i
\(538\) 0 0
\(539\) 4.35861 + 7.54934i 0.187739 + 0.325173i
\(540\) 0 0
\(541\) −17.7515 + 14.8952i −0.763194 + 0.640396i −0.938956 0.344037i \(-0.888206\pi\)
0.175762 + 0.984433i \(0.443761\pi\)
\(542\) 0 0
\(543\) −5.92330 + 10.2595i −0.254193 + 0.440275i
\(544\) 0 0
\(545\) 6.47992 + 2.35850i 0.277569 + 0.101027i
\(546\) 0 0
\(547\) 4.25083 + 24.1076i 0.181752 + 1.03077i 0.930058 + 0.367414i \(0.119757\pi\)
−0.748305 + 0.663355i \(0.769132\pi\)
\(548\) 0 0
\(549\) 1.44749 + 1.21459i 0.0617772 + 0.0518372i
\(550\) 0 0
\(551\) 17.1936 37.9230i 0.732472 1.61557i
\(552\) 0 0
\(553\) −0.490590 0.411654i −0.0208620 0.0175053i
\(554\) 0 0
\(555\) 2.59364 + 14.7093i 0.110094 + 0.624373i
\(556\) 0 0
\(557\) −20.8341 7.58301i −0.882771 0.321302i −0.139443 0.990230i \(-0.544531\pi\)
−0.743327 + 0.668928i \(0.766754\pi\)
\(558\) 0 0
\(559\) −11.2288 + 19.4488i −0.474926 + 0.822596i
\(560\) 0 0
\(561\) 9.18127 7.70400i 0.387633 0.325263i
\(562\) 0 0
\(563\) −0.331404 0.574008i −0.0139670 0.0241916i 0.858957 0.512047i \(-0.171113\pi\)
−0.872924 + 0.487855i \(0.837779\pi\)
\(564\) 0 0
\(565\) 1.71112 9.70427i 0.0719876 0.408262i
\(566\) 0 0
\(567\) −3.64367 + 1.32619i −0.153020 + 0.0556947i
\(568\) 0 0
\(569\) 2.63574 0.110496 0.0552480 0.998473i \(-0.482405\pi\)
0.0552480 + 0.998473i \(0.482405\pi\)
\(570\) 0 0
\(571\) −38.1084 −1.59479 −0.797393 0.603461i \(-0.793788\pi\)
−0.797393 + 0.603461i \(0.793788\pi\)
\(572\) 0 0
\(573\) 36.4213 13.2563i 1.52152 0.553788i
\(574\) 0 0
\(575\) 0.379967 2.15490i 0.0158457 0.0898656i
\(576\) 0 0
\(577\) −21.8375 37.8237i −0.909109 1.57462i −0.815305 0.579032i \(-0.803431\pi\)
−0.0938036 0.995591i \(-0.529903\pi\)
\(578\) 0 0
\(579\) −9.72510 + 8.16033i −0.404161 + 0.339132i
\(580\) 0 0
\(581\) 0.0304669 0.0527702i 0.00126398 0.00218928i
\(582\) 0 0
\(583\) 9.54461 + 3.47395i 0.395297 + 0.143876i
\(584\) 0 0
\(585\) 0.192467 + 1.09153i 0.00795753 + 0.0451294i
\(586\) 0 0
\(587\) 28.1433 + 23.6150i 1.16160 + 0.974696i 0.999926 0.0121486i \(-0.00386711\pi\)
0.161671 + 0.986845i \(0.448312\pi\)
\(588\) 0 0
\(589\) −33.2318 22.7447i −1.36929 0.937177i
\(590\) 0 0
\(591\) −2.68250 2.25089i −0.110343 0.0925892i
\(592\) 0 0
\(593\) −1.48665 8.43118i −0.0610492 0.346227i −0.999998 0.00216936i \(-0.999309\pi\)
0.938948 0.344058i \(-0.111802\pi\)
\(594\) 0 0
\(595\) 2.41142 + 0.877685i 0.0988585 + 0.0359816i
\(596\) 0 0
\(597\) 8.95303 15.5071i 0.366423 0.634663i
\(598\) 0 0
\(599\) 16.3426 13.7131i 0.667740 0.560301i −0.244655 0.969610i \(-0.578675\pi\)
0.912396 + 0.409310i \(0.134230\pi\)
\(600\) 0 0
\(601\) 5.27120 + 9.12999i 0.215017 + 0.372420i 0.953278 0.302095i \(-0.0976860\pi\)
−0.738261 + 0.674515i \(0.764353\pi\)
\(602\) 0 0
\(603\) −0.213648 + 1.21166i −0.00870041 + 0.0493425i
\(604\) 0 0
\(605\) 8.78653 3.19803i 0.357223 0.130019i
\(606\) 0 0
\(607\) −5.51930 −0.224022 −0.112011 0.993707i \(-0.535729\pi\)
−0.112011 + 0.993707i \(0.535729\pi\)
\(608\) 0 0
\(609\) 7.39110 0.299502
\(610\) 0 0
\(611\) −38.2850 + 13.9346i −1.54884 + 0.563733i
\(612\) 0 0
\(613\) −3.65334 + 20.7191i −0.147557 + 0.836837i 0.817722 + 0.575614i \(0.195237\pi\)
−0.965279 + 0.261223i \(0.915874\pi\)
\(614\) 0 0
\(615\) 4.04395 + 7.00433i 0.163068 + 0.282442i
\(616\) 0 0
\(617\) 6.98028 5.85715i 0.281015 0.235800i −0.491375 0.870948i \(-0.663505\pi\)
0.772390 + 0.635148i \(0.219061\pi\)
\(618\) 0 0
\(619\) −5.64698 + 9.78086i −0.226971 + 0.393126i −0.956909 0.290388i \(-0.906216\pi\)
0.729938 + 0.683514i \(0.239549\pi\)
\(620\) 0 0
\(621\) 10.9899 + 3.99998i 0.441008 + 0.160514i
\(622\) 0 0
\(623\) 0.246731 + 1.39928i 0.00988507 + 0.0560610i
\(624\) 0 0
\(625\) 0.766044 + 0.642788i 0.0306418 + 0.0257115i
\(626\) 0 0
\(627\) 2.52712 + 9.04423i 0.100923 + 0.361192i
\(628\) 0 0
\(629\) 37.9481 + 31.8422i 1.51309 + 1.26963i
\(630\) 0 0
\(631\) −1.07783 6.11268i −0.0429077 0.243342i 0.955809 0.293989i \(-0.0949828\pi\)
−0.998717 + 0.0506469i \(0.983872\pi\)
\(632\) 0 0
\(633\) 3.96153 + 1.44188i 0.157457 + 0.0573096i
\(634\) 0 0
\(635\) 9.65863 16.7292i 0.383291 0.663879i
\(636\) 0 0
\(637\) 30.9200 25.9450i 1.22510 1.02798i
\(638\) 0 0
\(639\) 0.642428 + 1.11272i 0.0254141 + 0.0440185i
\(640\) 0 0
\(641\) −2.93315 + 16.6347i −0.115852 + 0.657032i 0.870472 + 0.492218i \(0.163814\pi\)
−0.986325 + 0.164814i \(0.947298\pi\)
\(642\) 0 0
\(643\) −21.6034 + 7.86301i −0.851957 + 0.310087i −0.730838 0.682551i \(-0.760870\pi\)
−0.121119 + 0.992638i \(0.538648\pi\)
\(644\) 0 0
\(645\) −6.33434 −0.249415
\(646\) 0 0
\(647\) 12.9497 0.509105 0.254553 0.967059i \(-0.418072\pi\)
0.254553 + 0.967059i \(0.418072\pi\)
\(648\) 0 0
\(649\) 6.46880 2.35445i 0.253923 0.0924203i
\(650\) 0 0
\(651\) 1.24127 7.03957i 0.0486491 0.275903i
\(652\) 0 0
\(653\) −5.15557 8.92972i −0.201753 0.349447i 0.747340 0.664442i \(-0.231331\pi\)
−0.949093 + 0.314995i \(0.897997\pi\)
\(654\) 0 0
\(655\) −7.55776 + 6.34171i −0.295306 + 0.247791i
\(656\) 0 0
\(657\) 1.21988 2.11290i 0.0475921 0.0824320i
\(658\) 0 0
\(659\) 17.7370 + 6.45573i 0.690934 + 0.251480i 0.663535 0.748145i \(-0.269055\pi\)
0.0273992 + 0.999625i \(0.491277\pi\)
\(660\) 0 0
\(661\) −4.53848 25.7390i −0.176526 1.00113i −0.936367 0.351022i \(-0.885834\pi\)
0.759841 0.650109i \(-0.225277\pi\)
\(662\) 0 0
\(663\) −42.5119 35.6717i −1.65102 1.38537i
\(664\) 0 0
\(665\) −1.40649 + 1.43682i −0.0545412 + 0.0557176i
\(666\) 0 0
\(667\) −16.0121 13.4358i −0.619992 0.520235i
\(668\) 0 0
\(669\) −1.66808 9.46016i −0.0644918 0.365751i
\(670\) 0 0
\(671\) 12.2360 + 4.45354i 0.472366 + 0.171927i
\(672\) 0 0
\(673\) 2.44003 4.22625i 0.0940562 0.162910i −0.815158 0.579239i \(-0.803350\pi\)
0.909214 + 0.416328i \(0.136683\pi\)
\(674\) 0 0
\(675\) −4.09434 + 3.43556i −0.157591 + 0.132235i
\(676\) 0 0
\(677\) 5.91099 + 10.2381i 0.227178 + 0.393484i 0.956971 0.290185i \(-0.0937168\pi\)
−0.729793 + 0.683668i \(0.760383\pi\)
\(678\) 0 0
\(679\) −0.0468240 + 0.265552i −0.00179694 + 0.0101910i
\(680\) 0 0
\(681\) −17.1831 + 6.25412i −0.658456 + 0.239659i
\(682\) 0 0
\(683\) −1.10522 −0.0422901 −0.0211450 0.999776i \(-0.506731\pi\)
−0.0211450 + 0.999776i \(0.506731\pi\)
\(684\) 0 0
\(685\) 10.6640 0.407449
\(686\) 0 0
\(687\) −1.20521 + 0.438660i −0.0459816 + 0.0167359i
\(688\) 0 0
\(689\) 8.16676 46.3160i 0.311129 1.76450i
\(690\) 0 0
\(691\) 6.74026 + 11.6745i 0.256412 + 0.444118i 0.965278 0.261225i \(-0.0841264\pi\)
−0.708866 + 0.705343i \(0.750793\pi\)
\(692\) 0 0
\(693\) 0.0845843 0.0709746i 0.00321309 0.00269610i
\(694\) 0 0
\(695\) −0.658472 + 1.14051i −0.0249773 + 0.0432619i
\(696\) 0 0
\(697\) 25.2069 + 9.17454i 0.954778 + 0.347511i
\(698\) 0 0
\(699\) −3.74207 21.2223i −0.141538 0.802703i
\(700\) 0 0
\(701\) 19.0387 + 15.9754i 0.719082 + 0.603381i 0.927131 0.374737i \(-0.122267\pi\)
−0.208049 + 0.978118i \(0.566711\pi\)
\(702\) 0 0
\(703\) −35.0000 + 16.7777i −1.32005 + 0.632782i
\(704\) 0 0
\(705\) −8.80311 7.38668i −0.331544 0.278199i
\(706\) 0 0
\(707\) −0.431357 2.44635i −0.0162229 0.0920044i
\(708\) 0 0
\(709\) −1.71534 0.624331i −0.0644208 0.0234473i 0.309609 0.950864i \(-0.399802\pi\)
−0.374030 + 0.927417i \(0.622024\pi\)
\(710\) 0 0
\(711\) 0.129381 0.224094i 0.00485216 0.00840419i
\(712\) 0 0
\(713\) −15.4858 + 12.9942i −0.579950 + 0.486635i
\(714\) 0 0
\(715\) 3.81900 + 6.61470i 0.142822 + 0.247376i
\(716\) 0 0
\(717\) −2.84105 + 16.1124i −0.106101 + 0.601728i
\(718\) 0 0
\(719\) −30.6963 + 11.1725i −1.14478 + 0.416665i −0.843636 0.536915i \(-0.819590\pi\)
−0.301141 + 0.953580i \(0.597367\pi\)
\(720\) 0 0
\(721\) −1.16694 −0.0434592
\(722\) 0 0
\(723\) 16.2647 0.604889
\(724\) 0 0
\(725\) 8.97645 3.26716i 0.333377 0.121339i
\(726\) 0 0
\(727\) 2.76543 15.6835i 0.102564 0.581670i −0.889601 0.456738i \(-0.849018\pi\)
0.992165 0.124932i \(-0.0398713\pi\)
\(728\) 0 0
\(729\) −14.2313 24.6492i −0.527083 0.912935i
\(730\) 0 0
\(731\) −16.0936 + 13.5041i −0.595242 + 0.499467i
\(732\) 0 0
\(733\) −6.14652 + 10.6461i −0.227027 + 0.393222i −0.956926 0.290333i \(-0.906234\pi\)
0.729899 + 0.683555i \(0.239567\pi\)
\(734\) 0 0
\(735\) 10.6982 + 3.89383i 0.394610 + 0.143626i
\(736\) 0 0
\(737\) 1.47229 + 8.34975i 0.0542324 + 0.307567i
\(738\) 0 0
\(739\) 20.4726 + 17.1786i 0.753098 + 0.631924i 0.936320 0.351147i \(-0.114208\pi\)
−0.183222 + 0.983071i \(0.558653\pi\)
\(740\) 0 0
\(741\) 39.2092 18.7954i 1.44039 0.690467i
\(742\) 0 0
\(743\) −10.9203 9.16320i −0.400626 0.336165i 0.420109 0.907473i \(-0.361992\pi\)
−0.820736 + 0.571308i \(0.806436\pi\)
\(744\) 0 0
\(745\) 2.93251 + 16.6311i 0.107439 + 0.609316i
\(746\) 0 0
\(747\) 0.0231355 + 0.00842064i 0.000846485 + 0.000308095i
\(748\) 0 0
\(749\) 1.67696 2.90458i 0.0612747 0.106131i
\(750\) 0 0
\(751\) −8.50411 + 7.13580i −0.310319 + 0.260389i −0.784624 0.619972i \(-0.787144\pi\)
0.474305 + 0.880361i \(0.342700\pi\)
\(752\) 0 0
\(753\) −12.0025 20.7889i −0.437395 0.757590i
\(754\) 0 0
\(755\) 3.73507 21.1826i 0.135933 0.770915i
\(756\) 0 0
\(757\) −2.08443 + 0.758670i −0.0757599 + 0.0275743i −0.379622 0.925142i \(-0.623946\pi\)
0.303862 + 0.952716i \(0.401724\pi\)
\(758\) 0 0
\(759\) 4.71406 0.171110
\(760\) 0 0
\(761\) −49.1007 −1.77990 −0.889950 0.456058i \(-0.849261\pi\)
−0.889950 + 0.456058i \(0.849261\pi\)
\(762\) 0 0
\(763\) −2.98900 + 1.08791i −0.108209 + 0.0393849i
\(764\) 0 0
\(765\) −0.180050 + 1.02111i −0.00650971 + 0.0369184i
\(766\) 0 0
\(767\) −15.9373 27.6043i −0.575463 0.996732i
\(768\) 0 0
\(769\) 24.6995 20.7254i 0.890687 0.747376i −0.0776605 0.996980i \(-0.524745\pi\)
0.968348 + 0.249604i \(0.0803006\pi\)
\(770\) 0 0
\(771\) 13.7468 23.8101i 0.495077 0.857499i
\(772\) 0 0
\(773\) 5.75551 + 2.09483i 0.207011 + 0.0753459i 0.443445 0.896302i \(-0.353756\pi\)
−0.236433 + 0.971648i \(0.575979\pi\)
\(774\) 0 0
\(775\) −1.60426 9.09822i −0.0576268 0.326818i
\(776\) 0 0
\(777\) −5.27777 4.42857i −0.189339 0.158874i
\(778\) 0 0
\(779\) −14.7022 + 15.0193i −0.526760 + 0.538122i
\(780\) 0 0
\(781\) 6.78270 + 5.69136i 0.242704 + 0.203653i
\(782\) 0 0
\(783\) 8.86583 + 50.2806i 0.316839 + 1.79688i
\(784\) 0 0
\(785\) 0.503319 + 0.183193i 0.0179642 + 0.00653844i
\(786\) 0 0
\(787\) −7.55427 + 13.0844i −0.269281 +