Properties

Label 380.2.u.b.101.1
Level $380$
Weight $2$
Character 380.101
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 101.1
Root \(-0.838693 + 1.45266i\) of defining polynomial
Character \(\chi\) \(=\) 380.101
Dual form 380.2.u.b.301.1

$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(1\) \(1\)

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 −0.155768 0.987794i \(-0.549785\pi\)
−0.754267 + 0.656568i \(0.772008\pi\)
\(4\) 0 0
\(5\) 0.173648 + 0.984808i 0.0776578 + 0.440419i
\(6\) 0 0
\(7\) 0.230636 0.399473i 0.0871722 0.150987i −0.819143 0.573590i \(-0.805550\pi\)
0.906315 + 0.422603i \(0.138884\pi\)
\(8\) 0 0
\(9\) −0.142773 0.119801i −0.0475910 0.0399336i
\(10\) 0 0
\(11\) −0.642179 1.11229i −0.193624 0.335367i 0.752824 0.658221i \(-0.228691\pi\)
−0.946449 + 0.322854i \(0.895358\pi\)
\(12\) 0 0
\(13\) 5.58829 2.03397i 1.54991 0.564122i 0.581516 0.813535i \(-0.302460\pi\)
0.968397 + 0.249412i \(0.0802375\pi\)
\(14\) 0 0
\(15\) 0.291275 1.65190i 0.0752069 0.426519i
\(16\) 0 0
\(17\) 4.26171 3.57600i 1.03362 0.867307i 0.0423393 0.999103i \(-0.486519\pi\)
0.991277 + 0.131796i \(0.0420745\pi\)
\(18\) 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 −0.919225 0.393733i \(-0.871183\pi\)
0.998453 0.0555949i \(-0.0177055\pi\)
\(24\) 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 −0.976333 0.216272i \(-0.930610\pi\)
−0.382524 0.923945i \(-0.624945\pi\)
\(30\) 0 0
\(31\) 4.61929 8.00084i 0.829648 1.43699i −0.0686661 0.997640i \(-0.521874\pi\)
0.898314 0.439353i \(-0.144792\pi\)
\(32\) 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 0.670659 0.741766i \(-0.266012\pi\)
0.0369563 + 0.999317i \(0.488234\pi\)
\(42\) 0 0
\(43\) −0.655751 3.71895i −0.100001 0.567134i −0.993100 0.117273i \(-0.962585\pi\)
0.893099 0.449861i \(-0.148526\pi\)
\(44\) 0 0
\(45\) 0.0931885 0.161407i 0.0138917 0.0240612i
\(46\) 0 0
\(47\) −5.24811 4.40369i −0.765516 0.642344i 0.174041 0.984738i \(-0.444318\pi\)
−0.939556 + 0.342395i \(0.888762\pi\)
\(48\) 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 0.732564 + 0.680698i \(0.238323\pi\)
−0.921198 + 0.389095i \(0.872788\pi\)
\(54\) 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 −0.869666 0.493641i \(-0.835666\pi\)
0.335126 + 0.942173i \(0.391221\pi\)
\(60\) 0 0
\(61\) −1.76051 + 9.98434i −0.225410 + 1.27836i 0.636490 + 0.771285i \(0.280386\pi\)
−0.861900 + 0.507079i \(0.830725\pi\)
\(62\) 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 0.897113 0.441801i \(-0.145660\pi\)
−0.279307 + 0.960202i \(0.590105\pi\)
\(68\) 0 0
\(69\) −1.83518 + 3.17863i −0.220930 + 0.382662i
\(70\) 0 0
\(71\) 1.19711 + 6.78912i 0.142070 + 0.805721i 0.969673 + 0.244406i \(0.0785931\pi\)
−0.827603 + 0.561314i \(0.810296\pi\)
\(72\) 0 0
\(73\) −12.3010 4.47721i −1.43973 0.524017i −0.500024 0.866012i \(-0.666675\pi\)
−0.939702 + 0.341994i \(0.888898\pi\)
\(74\) 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 0.267583 0.963535i \(-0.413775\pi\)
−0.414368 + 0.910110i \(0.635997\pi\)
\(80\) 0 0
\(81\) −1.45971 8.27842i −0.162190 0.919825i
\(82\) 0 0
\(83\) −0.0660497 + 0.114402i −0.00724990 + 0.0125572i −0.869628 0.493708i \(-0.835641\pi\)
0.862378 + 0.506265i \(0.168974\pi\)
\(84\) 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 −0.184020 0.982922i \(-0.558911\pi\)
0.490843 + 0.871248i \(0.336689\pi\)
\(90\) 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 −0.619770 0.784783i \(-0.712774\pi\)
0.665239 + 0.746631i \(0.268330\pi\)
\(98\) 0 0
\(99\) −0.0415670 + 0.235738i −0.00417764 + 0.0236926i
\(100\) 0 0
\(101\) −5.06052 + 1.84188i −0.503541 + 0.183274i −0.581286 0.813699i \(-0.697450\pi\)
0.0777450 + 0.996973i \(0.475228\pi\)
\(102\) 0 0
\(103\) −1.26492 2.19090i −0.124636 0.215876i 0.796955 0.604039i \(-0.206443\pi\)
−0.921591 + 0.388163i \(0.873110\pi\)
\(104\) 0 0
\(105\) −0.592712 0.497345i −0.0578428 0.0485359i
\(106\) 0 0
\(107\) −3.63551 + 6.29689i −0.351458 + 0.608743i −0.986505 0.163730i \(-0.947647\pi\)
0.635047 + 0.772473i \(0.280981\pi\)
\(108\) 0 0
\(109\) −1.19744 6.79102i −0.114694 0.650462i −0.986901 0.161325i \(-0.948423\pi\)
0.872207 0.489136i \(-0.162688\pi\)
\(110\) 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 0.629165 0.777271i \(-0.283397\pi\)
0.981589 + 0.191005i \(0.0611746\pi\)
\(128\) 0 0
\(129\) −1.09995 + 6.23811i −0.0968449 + 0.549235i
\(130\) 0 0
\(131\) −7.55776 + 6.34171i −0.660324 + 0.554078i −0.910184 0.414204i \(-0.864060\pi\)
0.249860 + 0.968282i \(0.419615\pi\)
\(132\) 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 −0.797586 0.603205i \(-0.793890\pi\)
0.955794 0.294037i \(-0.0949989\pi\)
\(138\) 0 0
\(139\) −1.23752 + 0.450422i −0.104965 + 0.0382043i −0.393969 0.919124i \(-0.628898\pi\)
0.289004 + 0.957328i \(0.406676\pi\)
\(140\) 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 −0.403041 0.915182i \(-0.632047\pi\)
−0.897015 + 0.442001i \(0.854269\pi\)
\(150\) 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 0.980871 0.194657i \(-0.0623595\pi\)
−0.988294 + 0.152560i \(0.951248\pi\)
\(158\) 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 0.943420 0.331601i \(-0.107589\pi\)
−0.758885 + 0.651225i \(0.774255\pi\)
\(164\) 0 0
\(165\) −2.02444 + 0.736836i −0.157602 + 0.0573626i
\(166\) 0 0
\(167\) −2.67217 + 15.1546i −0.206779 + 1.17270i 0.687837 + 0.725865i \(0.258560\pi\)
−0.894616 + 0.446835i \(0.852551\pi\)
\(168\) 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 −0.999973 0.00740809i \(-0.997642\pi\)
−0.166348 + 0.986067i \(0.553197\pi\)
\(174\) 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 0.999824 0.0187736i \(-0.00597617\pi\)
−0.516170 + 0.856486i \(0.672643\pi\)
\(180\) 0 0
\(181\) 5.41021 + 4.53971i 0.402138 + 0.337434i 0.821319 0.570469i \(-0.193238\pi\)
−0.419181 + 0.907903i \(0.637683\pi\)
\(182\) 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 0.585054 0.810994i \(-0.301073\pi\)
−0.0731197 + 0.997323i \(0.523296\pi\)
\(194\) 0 0
\(195\) −1.73219 9.82376i −0.124045 0.703494i
\(196\) 0 0
\(197\) 1.04381 1.80794i 0.0743687 0.128810i −0.826443 0.563021i \(-0.809639\pi\)
0.900812 + 0.434210i \(0.142972\pi\)
\(198\) 0 0
\(199\) −8.17751 6.86174i −0.579688 0.486416i 0.305157 0.952302i \(-0.401291\pi\)
−0.884845 + 0.465886i \(0.845736\pi\)
\(200\) 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 −0.706649 0.707564i \(-0.749794\pi\)
0.574106 + 0.818781i \(0.305350\pi\)
\(212\) 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 −0.999831 0.0184093i \(-0.994140\pi\)
0.933237 0.359261i \(-0.116971\pi\)
\(224\) 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 −0.966436 0.256908i \(-0.917296\pi\)
0.820285 0.571955i \(-0.193815\pi\)
\(234\) 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 0.979536 0.201271i \(-0.0645073\pi\)
−0.664074 + 0.747667i \(0.731174\pi\)
\(240\) 0 0
\(241\) −9.11167 + 3.31638i −0.586934 + 0.213626i −0.618380 0.785879i \(-0.712211\pi\)
0.0314464 + 0.999505i \(0.489989\pi\)
\(242\) 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 −0.800213 0.599716i \(-0.795280\pi\)
0.957069 0.289860i \(-0.0936087\pi\)
\(252\) 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 0.160836 0.986981i \(-0.448581\pi\)
−0.944058 + 0.329780i \(0.893025\pi\)
\(258\) 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 0.999626 0.0273600i \(-0.00871003\pi\)
0.748171 + 0.663506i \(0.230932\pi\)
\(264\) 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 0.0179339 0.999839i \(-0.494291\pi\)
−0.628946 + 0.777449i \(0.716513\pi\)
\(270\) 0 0
\(271\) 5.03825 + 28.5733i 0.306052 + 1.73571i 0.618511 + 0.785776i \(0.287736\pi\)
−0.312460 + 0.949931i \(0.601153\pi\)
\(272\) 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 0.999899 0.0142406i \(-0.00453307\pi\)
−0.512282 + 0.858817i \(0.671200\pi\)
\(278\) 0 0
\(279\) −1.61802 + 0.588910i −0.0968681 + 0.0352571i
\(280\) 0 0
\(281\) 0.339000 1.92256i 0.0202230 0.114690i −0.973025 0.230699i \(-0.925899\pi\)
0.993248 + 0.116008i \(0.0370099\pi\)
\(282\) 0 0
\(283\) 15.3905 12.9142i 0.914873 0.767670i −0.0581666 0.998307i \(-0.518525\pi\)
0.973040 + 0.230637i \(0.0740810\pi\)
\(284\) 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 0.997147 + 0.0754882i \(0.0240515\pi\)
−0.433199 + 0.901298i \(0.642615\pi\)
\(294\) 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 0.0335038 0.999439i \(-0.489333\pi\)
−0.616761 + 0.787150i \(0.711556\pi\)
\(308\) 0 0
\(309\) 0.736878 + 4.17904i 0.0419195 + 0.237737i
\(310\) 0 0
\(311\) 8.62121 14.9324i 0.488864 0.846737i −0.511054 0.859549i \(-0.670745\pi\)
0.999918 + 0.0128113i \(0.00407807\pi\)
\(312\) 0 0
\(313\) 6.00211 + 5.03637i 0.339259 + 0.284672i 0.796460 0.604691i \(-0.206703\pi\)
−0.457201 + 0.889364i \(0.651148\pi\)
\(314\) 0 0
\(315\) −0.0429853 0.0744527i −0.00242194 0.00419493i
\(316\) 0 0
\(317\) −9.67697 + 3.52213i −0.543513 + 0.197822i −0.599162 0.800628i \(-0.704499\pi\)
0.0556491 + 0.998450i \(0.482277\pi\)
\(318\) 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 0.799004 + 0.601326i \(0.205361\pi\)
0.121262 + 0.992621i \(0.461306\pi\)
\(332\) 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 −0.841639 0.540041i \(-0.818409\pi\)
0.606177 0.795330i \(-0.292702\pi\)
\(338\) 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 0.842155 + 0.539236i \(0.181287\pi\)
−0.606937 + 0.794750i \(0.707602\pi\)
\(348\) 0 0
\(349\) −14.2024 + 24.5992i −0.760236 + 1.31677i 0.182493 + 0.983207i \(0.441583\pi\)
−0.942729 + 0.333560i \(0.891750\pi\)
\(350\) 0 0
\(351\) 24.3488 + 20.4311i 1.29964 + 1.09053i
\(352\) 0 0
\(353\) 15.0606 + 26.0858i 0.801596 + 1.38841i 0.918565 + 0.395270i \(0.129349\pi\)
−0.116969 + 0.993136i \(0.537318\pi\)
\(354\) 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 −0.410530 + 0.911847i \(0.634656\pi\)
−0.969282 + 0.245952i \(0.920899\pi\)
\(360\) 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 −0.830451 0.557092i \(-0.811917\pi\)
−0.278071 + 0.960561i \(0.589695\pi\)
\(368\) 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 −0.979171 0.203036i \(-0.934919\pi\)
0.665420 + 0.746469i \(0.268253\pi\)
\(374\) 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 0.905229 0.424924i \(-0.139699\pi\)
0.420310 + 0.907381i \(0.361921\pi\)
\(384\) 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 0.958768 0.284190i \(-0.0917246\pi\)
−0.113384 + 0.993551i \(0.536169\pi\)
\(390\) 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 −0.629274 0.777184i \(-0.716648\pi\)
0.656104 + 0.754670i \(0.272203\pi\)
\(398\) 0 0
\(399\) 3.26682 0.838091i 0.163546 0.0419570i
\(400\) 0 0
\(401\) 8.08896 6.78745i 0.403944 0.338949i −0.418072 0.908414i \(-0.637294\pi\)
0.822016 + 0.569465i \(0.192850\pi\)
\(402\) 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 0.844165 0.536083i \(-0.180097\pi\)
−0.381351 + 0.924430i \(0.624541\pi\)
\(410\) 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 −0.0347043 0.999398i \(-0.511049\pi\)
−0.668985 + 0.743276i \(0.733271\pi\)
\(422\) 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 −0.998967 0.0454340i \(-0.985533\pi\)
−0.736049 + 0.676928i \(0.763311\pi\)
\(432\) 0 0
\(433\) −5.71443 + 32.4082i −0.274618 + 1.55744i 0.465554 + 0.885019i \(0.345855\pi\)
−0.740172 + 0.672417i \(0.765256\pi\)
\(434\) 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 −0.962991 0.269533i \(-0.913131\pi\)
0.0982162 + 0.995165i \(0.468686\pi\)
\(440\) 0 0
\(441\) 0.219662 1.24577i 0.0104601 0.0593222i
\(442\) 0 0
\(443\) 15.5447 5.65781i 0.738551 0.268811i 0.0547713 0.998499i \(-0.482557\pi\)
0.683780 + 0.729688i \(0.260335\pi\)
\(444\) 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 −0.278432 0.960456i \(-0.589815\pi\)
0.970995 0.239099i \(-0.0768520\pi\)
\(450\) 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 −0.759079 0.650999i \(-0.774350\pi\)
0.490646 0.871359i \(-0.336761\pi\)
\(462\) 0 0
\(463\) 6.07020 10.5139i 0.282106 0.488622i −0.689797 0.724003i \(-0.742300\pi\)
0.971903 + 0.235381i \(0.0756336\pi\)
\(464\) 0 0
\(465\) −11.8711 9.96105i −0.550510 0.461933i
\(466\) 0 0
\(467\) −10.2092 17.6828i −0.472425 0.818264i 0.527077 0.849817i \(-0.323288\pi\)
−0.999502 + 0.0315536i \(0.989955\pi\)
\(468\) 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 −0.905075 0.425252i \(-0.860185\pi\)
0.995937 0.0900526i \(-0.0287035\pi\)
\(480\) 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 −0.681716 0.731617i \(-0.738766\pi\)
0.974457 + 0.224575i \(0.0720995\pi\)
\(488\) 0 0
\(489\) −1.37248 7.78371i −0.0620656 0.351992i
\(490\) 0 0
\(491\) 30.1324 + 10.9673i 1.35986 + 0.494947i 0.916010 0.401156i \(-0.131391\pi\)
0.443846 + 0.896103i \(0.353614\pi\)
\(492\) 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 0.976274 0.216539i \(-0.0694768\pi\)
−0.991458 + 0.130425i \(0.958366\pi\)
\(500\) 0 0
\(501\) 12.9062 22.3541i 0.576604 0.998708i
\(502\) 0 0
\(503\) 20.8314 + 17.4796i 0.928824 + 0.779376i 0.975606 0.219529i \(-0.0704521\pi\)
−0.0467817 + 0.998905i \(0.514897\pi\)
\(504\) 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 −0.730326 0.683098i \(-0.760632\pi\)
0.919916 0.392116i \(-0.128257\pi\)
\(510\) 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 0.883027 0.469321i \(-0.155501\pi\)
−0.847958 + 0.530064i \(0.822168\pi\)
\(522\) 0 0
\(523\) −4.61410 3.87169i −0.201760 0.169297i 0.536309 0.844021i \(-0.319818\pi\)
−0.738070 + 0.674724i \(0.764262\pi\)
\(524\) 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 0.175762 0.984433i \(-0.443761\pi\)
−0.938956 + 0.344037i \(0.888206\pi\)
\(542\) 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 −0.748305 0.663355i \(-0.769132\pi\)
0.930058 0.367414i \(-0.119757\pi\)
\(548\) 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 −0.743327 0.668928i \(-0.766754\pi\)
−0.139443 + 0.990230i \(0.544531\pi\)
\(558\) 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 −0.872924 0.487855i \(-0.837779\pi\)
0.858957 + 0.512047i \(0.171113\pi\)
\(564\) 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 −0.0938036 + 0.995591i \(0.529903\pi\)
−0.815305 + 0.579032i \(0.803431\pi\)
\(578\) 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 0.161671 0.986845i \(-0.448312\pi\)
0.999926 + 0.0121486i \(0.00386711\pi\)
\(588\) 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 0.938948 + 0.344058i \(0.111802\pi\)
−0.999998 + 0.00216936i \(0.999309\pi\)
\(594\) 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 0.912396 0.409310i \(-0.134230\pi\)
−0.244655 + 0.969610i \(0.578675\pi\)
\(600\) 0 0
\(601\) 5.27120 9.12999i 0.215017 0.372420i −0.738261 0.674515i \(-0.764353\pi\)
0.953278 + 0.302095i \(0.0976860\pi\)
\(602\) 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 −0.965279 0.261223i \(-0.915874\pi\)
0.817722 0.575614i \(-0.195237\pi\)
\(614\) 0 0
\(615\) 4.04395 7.00433i 0.163068 0.282442i
\(616\) 0 0
\(617\) 6.98028 + 5.85715i 0.281015 + 0.235800i 0.772390 0.635148i \(-0.219061\pi\)
−0.491375 + 0.870948i \(0.663505\pi\)
\(618\) 0 0
\(619\) −5.64698 9.78086i −0.226971 0.393126i 0.729938 0.683514i \(-0.239549\pi\)
−0.956909 + 0.290388i \(0.906216\pi\)
\(620\) 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 −0.998717 0.0506469i \(-0.983872\pi\)
0.955809 + 0.293989i \(0.0949828\pi\)
\(632\) 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 −0.986325 0.164814i \(-0.947298\pi\)
0.870472 0.492218i \(-0.163814\pi\)
\(642\) 0 0
\(643\) −21.6034 7.86301i −0.851957 0.310087i −0.121119 0.992638i \(-0.538648\pi\)
−0.730838 + 0.682551i \(0.760870\pi\)
\(644\) 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 −0.949093 0.314995i \(-0.897997\pi\)
0.747340 + 0.664442i \(0.231331\pi\)
\(654\) 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 0.0273992 0.999625i \(-0.491277\pi\)
0.663535 + 0.748145i \(0.269055\pi\)
\(660\) 0 0
\(661\) −4.53848 + 25.7390i −0.176526 + 1.00113i 0.759841 + 0.650109i \(0.225277\pi\)
−0.936367 + 0.351022i \(0.885834\pi\)
\(662\) 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 0.909214 0.416328i \(-0.136683\pi\)
−0.815158 + 0.579239i \(0.803350\pi\)
\(674\) 0 0
\(675\) −4.09434 3.43556i −0.157591 0.132235i
\(676\) 0 0
\(677\) 5.91099 10.2381i 0.227178 0.393484i −0.729793 0.683668i \(-0.760383\pi\)
0.956971 + 0.290185i \(0.0937168\pi\)
\(678\) 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 −0.708866 0.705343i \(-0.750793\pi\)
0.965278 + 0.261225i \(0.0841264\pi\)
\(692\) 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 −0.208049 0.978118i \(-0.566711\pi\)
0.927131 + 0.374737i \(0.122267\pi\)
\(702\) 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 −0.374030 0.927417i \(-0.622024\pi\)
0.309609 + 0.950864i \(0.399802\pi\)
\(710\) 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 −0.301141 0.953580i \(-0.597367\pi\)
−0.843636 + 0.536915i \(0.819590\pi\)
\(720\) 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 0.992165 + 0.124932i \(0.0398713\pi\)
−0.889601 + 0.456738i \(0.849018\pi\)
\(728\) 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 0.729899 0.683555i \(-0.239567\pi\)
−0.956926 + 0.290333i \(0.906234\pi\)
\(734\) 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 −0.183222 0.983071i \(-0.558653\pi\)
0.936320 + 0.351147i \(0.114208\pi\)
\(740\) 0 0
\(741\) 39.2092 + 18.7954i 1.44039 + 0.690467i
\(742\) 0 0
\(743\) −10.9203 + 9.16320i −0.400626 + 0.336165i −0.820736 0.571308i \(-0.806436\pi\)
0.420109 + 0.907473i \(0.361992\pi\)
\(744\) 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 0.474305 0.880361i \(-0.342700\pi\)
−0.784624 + 0.619972i \(0.787144\pi\)
\(752\) 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 0.303862 0.952716i \(-0.401724\pi\)
−0.379622 + 0.925142i \(0.623946\pi\)
\(758\) 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 0.968348 0.249604i \(-0.0803006\pi\)
−0.0776605 + 0.996980i \(0.524745\pi\)
\(770\) 0 0
\(771\) 13.7468 + 23.8101i 0.495077 + 0.857499i
\(772\) 0 0
\(773\) 5.75551 2.09483i 0.207011 0.0753459i −0.236433 0.971648i \(-0.575979\pi\)
0.443445 + 0.896302i \(0.353756\pi\)
\(774\) 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