Properties

Label 380.2.u.b.321.3
Level $380$
Weight $2$
Character 380.321
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 321.3
Root \(-1.14386 - 1.98122i\) of defining polynomial
Character \(\chi\) \(=\) 380.321
Dual form 380.2.u.b.161.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.75249 + 1.47051i) q^{3} +(-0.939693 + 0.342020i) q^{5} +(1.54340 + 2.67324i) q^{7} +(0.387867 + 2.19970i) q^{9} +O(q^{10})\) \(q+(1.75249 + 1.47051i) q^{3} +(-0.939693 + 0.342020i) q^{5} +(1.54340 + 2.67324i) q^{7} +(0.387867 + 2.19970i) q^{9} +(-0.285125 + 0.493851i) q^{11} +(-1.79996 + 1.51035i) q^{13} +(-2.14975 - 0.782445i) q^{15} +(0.907938 - 5.14917i) q^{17} +(-2.34334 + 3.67543i) q^{19} +(-1.22625 + 6.95443i) q^{21} +(8.47060 + 3.08305i) q^{23} +(0.766044 - 0.642788i) q^{25} +(0.876608 - 1.51833i) q^{27} +(-0.559736 - 3.17442i) q^{29} +(-1.68171 - 2.91280i) q^{31} +(-1.22589 + 0.446189i) q^{33} +(-2.36462 - 1.98416i) q^{35} -8.95901 q^{37} -5.37541 q^{39} +(3.75201 + 3.14831i) q^{41} +(2.26039 - 0.822715i) q^{43} +(-1.11682 - 1.93439i) q^{45} +(-0.782003 - 4.43496i) q^{47} +(-1.26416 + 2.18959i) q^{49} +(9.16309 - 7.68875i) q^{51} +(12.4799 + 4.54230i) q^{53} +(0.0990228 - 0.561586i) q^{55} +(-9.51145 + 2.99524i) q^{57} +(0.866435 - 4.91379i) q^{59} +(1.59516 + 0.580591i) q^{61} +(-5.28172 + 4.43189i) q^{63} +(1.17484 - 2.03489i) q^{65} +(-2.49900 - 14.1725i) q^{67} +(10.3110 + 17.8592i) q^{69} +(-2.26795 + 0.825465i) q^{71} +(-6.11131 - 5.12800i) q^{73} +2.28771 q^{75} -1.76024 q^{77} +(5.59819 + 4.69744i) q^{79} +(10.0658 - 3.66364i) q^{81} +(-4.06853 - 7.04691i) q^{83} +(0.907938 + 5.14917i) q^{85} +(3.68710 - 6.38624i) q^{87} +(3.72950 - 3.12942i) q^{89} +(-6.81559 - 2.48067i) q^{91} +(1.33614 - 7.57764i) q^{93} +(0.944948 - 4.25524i) q^{95} +(1.72255 - 9.76905i) q^{97} +(-1.19692 - 0.435642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(1\) \(1\)

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
\(3\) 1.75249 + 1.47051i 1.01180 + 0.849002i 0.988575 0.150728i \(-0.0481618\pi\)
0.0232260 + 0.999730i \(0.492606\pi\)
\(4\) 0 0
\(5\) −0.939693 + 0.342020i −0.420243 + 0.152956i
\(6\) 0 0
\(7\) 1.54340 + 2.67324i 0.583350 + 1.01039i 0.995079 + 0.0990853i \(0.0315917\pi\)
−0.411729 + 0.911306i \(0.635075\pi\)
\(8\) 0 0
\(9\) 0.387867 + 2.19970i 0.129289 + 0.733235i
\(10\) 0 0
\(11\) −0.285125 + 0.493851i −0.0859683 + 0.148902i −0.905803 0.423698i \(-0.860732\pi\)
0.819835 + 0.572600i \(0.194065\pi\)
\(12\) 0 0
\(13\) −1.79996 + 1.51035i −0.499220 + 0.418895i −0.857317 0.514789i \(-0.827870\pi\)
0.358097 + 0.933684i \(0.383426\pi\)
\(14\) 0 0
\(15\) −2.14975 0.782445i −0.555063 0.202026i
\(16\) 0 0
\(17\) 0.907938 5.14917i 0.220207 1.24886i −0.651431 0.758708i \(-0.725831\pi\)
0.871638 0.490150i \(-0.163058\pi\)
\(18\) 0 0
\(19\) −2.34334 + 3.67543i −0.537599 + 0.843201i
\(20\) 0 0
\(21\) −1.22625 + 6.95443i −0.267590 + 1.51758i
\(22\) 0 0
\(23\) 8.47060 + 3.08305i 1.76624 + 0.642860i 1.00000 0.000308691i \(9.82594e-5\pi\)
0.766243 + 0.642551i \(0.222124\pi\)
\(24\) 0 0
\(25\) 0.766044 0.642788i 0.153209 0.128558i
\(26\) 0 0
\(27\) 0.876608 1.51833i 0.168703 0.292203i
\(28\) 0 0
\(29\) −0.559736 3.17442i −0.103940 0.589475i −0.991638 0.129049i \(-0.958808\pi\)
0.887698 0.460426i \(-0.152303\pi\)
\(30\) 0 0
\(31\) −1.68171 2.91280i −0.302044 0.523155i 0.674555 0.738225i \(-0.264336\pi\)
−0.976599 + 0.215069i \(0.931002\pi\)
\(32\) 0 0
\(33\) −1.22589 + 0.446189i −0.213401 + 0.0776715i
\(34\) 0 0
\(35\) −2.36462 1.98416i −0.399694 0.335383i
\(36\) 0 0
\(37\) −8.95901 −1.47285 −0.736426 0.676518i \(-0.763488\pi\)
−0.736426 + 0.676518i \(0.763488\pi\)
\(38\) 0 0
\(39\) −5.37541 −0.860755
\(40\) 0 0
\(41\) 3.75201 + 3.14831i 0.585966 + 0.491684i 0.886900 0.461961i \(-0.152854\pi\)
−0.300934 + 0.953645i \(0.597298\pi\)
\(42\) 0 0
\(43\) 2.26039 0.822715i 0.344706 0.125463i −0.163865 0.986483i \(-0.552396\pi\)
0.508571 + 0.861020i \(0.330174\pi\)
\(44\) 0 0
\(45\) −1.11682 1.93439i −0.166486 0.288361i
\(46\) 0 0
\(47\) −0.782003 4.43496i −0.114067 0.646905i −0.987208 0.159438i \(-0.949032\pi\)
0.873141 0.487468i \(-0.162079\pi\)
\(48\) 0 0
\(49\) −1.26416 + 2.18959i −0.180594 + 0.312798i
\(50\) 0 0
\(51\) 9.16309 7.68875i 1.28309 1.07664i
\(52\) 0 0
\(53\) 12.4799 + 4.54230i 1.71424 + 0.623933i 0.997316 0.0732175i \(-0.0233267\pi\)
0.716925 + 0.697150i \(0.245549\pi\)
\(54\) 0 0
\(55\) 0.0990228 0.561586i 0.0133522 0.0757243i
\(56\) 0 0
\(57\) −9.51145 + 2.99524i −1.25982 + 0.396729i
\(58\) 0 0
\(59\) 0.866435 4.91379i 0.112800 0.639722i −0.875016 0.484095i \(-0.839149\pi\)
0.987816 0.155627i \(-0.0497398\pi\)
\(60\) 0 0
\(61\) 1.59516 + 0.580591i 0.204239 + 0.0743371i 0.442114 0.896959i \(-0.354229\pi\)
−0.237875 + 0.971296i \(0.576451\pi\)
\(62\) 0 0
\(63\) −5.28172 + 4.43189i −0.665434 + 0.558365i
\(64\) 0 0
\(65\) 1.17484 2.03489i 0.145721 0.252397i
\(66\) 0 0
\(67\) −2.49900 14.1725i −0.305302 1.73145i −0.622082 0.782952i \(-0.713713\pi\)
0.316780 0.948499i \(-0.397398\pi\)
\(68\) 0 0
\(69\) 10.3110 + 17.8592i 1.24130 + 2.14999i
\(70\) 0 0
\(71\) −2.26795 + 0.825465i −0.269156 + 0.0979647i −0.473072 0.881024i \(-0.656855\pi\)
0.203917 + 0.978988i \(0.434633\pi\)
\(72\) 0 0
\(73\) −6.11131 5.12800i −0.715275 0.600187i 0.210799 0.977529i \(-0.432393\pi\)
−0.926074 + 0.377343i \(0.876838\pi\)
\(74\) 0 0
\(75\) 2.28771 0.264163
\(76\) 0 0
\(77\) −1.76024 −0.200598
\(78\) 0 0
\(79\) 5.59819 + 4.69744i 0.629846 + 0.528503i 0.900881 0.434066i \(-0.142922\pi\)
−0.271035 + 0.962569i \(0.587366\pi\)
\(80\) 0 0
\(81\) 10.0658 3.66364i 1.11842 0.407071i
\(82\) 0 0
\(83\) −4.06853 7.04691i −0.446580 0.773499i 0.551581 0.834121i \(-0.314025\pi\)
−0.998161 + 0.0606227i \(0.980691\pi\)
\(84\) 0 0
\(85\) 0.907938 + 5.14917i 0.0984797 + 0.558506i
\(86\) 0 0
\(87\) 3.68710 6.38624i 0.395298 0.684677i
\(88\) 0 0
\(89\) 3.72950 3.12942i 0.395326 0.331718i −0.423358 0.905963i \(-0.639149\pi\)
0.818684 + 0.574245i \(0.194704\pi\)
\(90\) 0 0
\(91\) −6.81559 2.48067i −0.714468 0.260045i
\(92\) 0 0
\(93\) 1.33614 7.57764i 0.138552 0.785765i
\(94\) 0 0
\(95\) 0.944948 4.25524i 0.0969496 0.436578i
\(96\) 0 0
\(97\) 1.72255 9.76905i 0.174898 0.991897i −0.763363 0.645970i \(-0.776453\pi\)
0.938261 0.345927i \(-0.112436\pi\)
\(98\) 0 0
\(99\) −1.19692 0.435642i −0.120295 0.0437836i
\(100\) 0 0
\(101\) −12.4977 + 10.4868i −1.24357 + 1.04348i −0.246331 + 0.969186i \(0.579225\pi\)
−0.997237 + 0.0742916i \(0.976330\pi\)
\(102\) 0 0
\(103\) −0.967982 + 1.67659i −0.0953781 + 0.165200i −0.909766 0.415121i \(-0.863739\pi\)
0.814388 + 0.580320i \(0.197073\pi\)
\(104\) 0 0
\(105\) −1.22625 6.95443i −0.119670 0.678683i
\(106\) 0 0
\(107\) −4.08835 7.08123i −0.395236 0.684569i 0.597895 0.801574i \(-0.296004\pi\)
−0.993131 + 0.117005i \(0.962670\pi\)
\(108\) 0 0
\(109\) −5.86767 + 2.13566i −0.562021 + 0.204559i −0.607379 0.794412i \(-0.707779\pi\)
0.0453585 + 0.998971i \(0.485557\pi\)
\(110\) 0 0
\(111\) −15.7006 13.1744i −1.49023 1.25045i
\(112\) 0 0
\(113\) −11.0563 −1.04009 −0.520043 0.854140i \(-0.674084\pi\)
−0.520043 + 0.854140i \(0.674084\pi\)
\(114\) 0 0
\(115\) −9.01423 −0.840581
\(116\) 0 0
\(117\) −4.02047 3.37357i −0.371692 0.311887i
\(118\) 0 0
\(119\) 15.1663 5.52009i 1.39029 0.506026i
\(120\) 0 0
\(121\) 5.33741 + 9.24466i 0.485219 + 0.840424i
\(122\) 0 0
\(123\) 1.94573 + 11.0348i 0.175441 + 0.994973i
\(124\) 0 0
\(125\) −0.500000 + 0.866025i −0.0447214 + 0.0774597i
\(126\) 0 0
\(127\) −1.38569 + 1.16273i −0.122960 + 0.103176i −0.702194 0.711986i \(-0.747796\pi\)
0.579234 + 0.815161i \(0.303352\pi\)
\(128\) 0 0
\(129\) 5.17113 + 1.88214i 0.455293 + 0.165713i
\(130\) 0 0
\(131\) 1.78473 10.1217i 0.155933 0.884340i −0.801995 0.597331i \(-0.796228\pi\)
0.957928 0.287009i \(-0.0926610\pi\)
\(132\) 0 0
\(133\) −13.4420 0.591670i −1.16557 0.0513043i
\(134\) 0 0
\(135\) −0.304443 + 1.72658i −0.0262023 + 0.148600i
\(136\) 0 0
\(137\) 1.34202 + 0.488457i 0.114657 + 0.0417317i 0.398711 0.917076i \(-0.369457\pi\)
−0.284055 + 0.958808i \(0.591680\pi\)
\(138\) 0 0
\(139\) 14.5734 12.2285i 1.23610 1.03721i 0.238278 0.971197i \(-0.423417\pi\)
0.997819 0.0660114i \(-0.0210274\pi\)
\(140\) 0 0
\(141\) 5.15122 8.92217i 0.433811 0.751383i
\(142\) 0 0
\(143\) −0.232672 1.31955i −0.0194570 0.110346i
\(144\) 0 0
\(145\) 1.61169 + 2.79154i 0.133844 + 0.231825i
\(146\) 0 0
\(147\) −5.43525 + 1.97827i −0.448292 + 0.163165i
\(148\) 0 0
\(149\) 1.41523 + 1.18752i 0.115940 + 0.0972852i 0.698914 0.715205i \(-0.253667\pi\)
−0.582974 + 0.812490i \(0.698111\pi\)
\(150\) 0 0
\(151\) −11.2163 −0.912774 −0.456387 0.889781i \(-0.650857\pi\)
−0.456387 + 0.889781i \(0.650857\pi\)
\(152\) 0 0
\(153\) 11.6788 0.944177
\(154\) 0 0
\(155\) 2.57653 + 2.16196i 0.206952 + 0.173653i
\(156\) 0 0
\(157\) −8.66378 + 3.15336i −0.691445 + 0.251665i −0.663754 0.747951i \(-0.731038\pi\)
−0.0276912 + 0.999617i \(0.508815\pi\)
\(158\) 0 0
\(159\) 15.1913 + 26.3122i 1.20475 + 2.08669i
\(160\) 0 0
\(161\) 4.83178 + 27.4024i 0.380797 + 2.15961i
\(162\) 0 0
\(163\) −7.41466 + 12.8426i −0.580761 + 1.00591i 0.414628 + 0.909991i \(0.363912\pi\)
−0.995389 + 0.0959170i \(0.969422\pi\)
\(164\) 0 0
\(165\) 0.999357 0.838560i 0.0777999 0.0652818i
\(166\) 0 0
\(167\) 14.1961 + 5.16695i 1.09852 + 0.399830i 0.826772 0.562537i \(-0.190175\pi\)
0.271753 + 0.962367i \(0.412397\pi\)
\(168\) 0 0
\(169\) −1.29871 + 7.36535i −0.0999008 + 0.566566i
\(170\) 0 0
\(171\) −8.99376 3.72908i −0.687770 0.285170i
\(172\) 0 0
\(173\) −0.191331 + 1.08509i −0.0145466 + 0.0824981i −0.991217 0.132247i \(-0.957781\pi\)
0.976670 + 0.214745i \(0.0688920\pi\)
\(174\) 0 0
\(175\) 2.90064 + 1.05575i 0.219268 + 0.0798070i
\(176\) 0 0
\(177\) 8.74423 7.33728i 0.657256 0.551503i
\(178\) 0 0
\(179\) −5.77224 + 9.99781i −0.431437 + 0.747271i −0.996997 0.0774357i \(-0.975327\pi\)
0.565560 + 0.824707i \(0.308660\pi\)
\(180\) 0 0
\(181\) 1.82662 + 10.3593i 0.135772 + 0.769999i 0.974319 + 0.225171i \(0.0722940\pi\)
−0.838548 + 0.544828i \(0.816595\pi\)
\(182\) 0 0
\(183\) 1.94174 + 3.36319i 0.143537 + 0.248614i
\(184\) 0 0
\(185\) 8.41871 3.06416i 0.618956 0.225282i
\(186\) 0 0
\(187\) 2.28405 + 1.91654i 0.167026 + 0.140151i
\(188\) 0 0
\(189\) 5.41182 0.393652
\(190\) 0 0
\(191\) −4.44309 −0.321491 −0.160746 0.986996i \(-0.551390\pi\)
−0.160746 + 0.986996i \(0.551390\pi\)
\(192\) 0 0
\(193\) −3.40457 2.85678i −0.245067 0.205635i 0.511978 0.858999i \(-0.328913\pi\)
−0.757044 + 0.653363i \(0.773357\pi\)
\(194\) 0 0
\(195\) 5.05123 1.83850i 0.361726 0.131658i
\(196\) 0 0
\(197\) 6.56722 + 11.3748i 0.467895 + 0.810419i 0.999327 0.0366826i \(-0.0116791\pi\)
−0.531432 + 0.847101i \(0.678346\pi\)
\(198\) 0 0
\(199\) 4.13668 + 23.4603i 0.293242 + 1.66306i 0.674264 + 0.738490i \(0.264461\pi\)
−0.381022 + 0.924566i \(0.624428\pi\)
\(200\) 0 0
\(201\) 16.4615 28.5121i 1.16110 2.01109i
\(202\) 0 0
\(203\) 7.62210 6.39570i 0.534967 0.448890i
\(204\) 0 0
\(205\) −4.60253 1.67518i −0.321454 0.117000i
\(206\) 0 0
\(207\) −3.49632 + 19.8286i −0.243011 + 1.37819i
\(208\) 0 0
\(209\) −1.14697 2.20521i −0.0793374 0.152538i
\(210\) 0 0
\(211\) −3.22833 + 18.3088i −0.222247 + 1.26043i 0.645631 + 0.763650i \(0.276595\pi\)
−0.867878 + 0.496777i \(0.834517\pi\)
\(212\) 0 0
\(213\) −5.18842 1.88843i −0.355504 0.129393i
\(214\) 0 0
\(215\) −1.84269 + 1.54620i −0.125670 + 0.105450i
\(216\) 0 0
\(217\) 5.19109 8.99124i 0.352394 0.610365i
\(218\) 0 0
\(219\) −3.16922 17.9735i −0.214156 1.21454i
\(220\) 0 0
\(221\) 6.14279 + 10.6396i 0.413209 + 0.715699i
\(222\) 0 0
\(223\) 7.11744 2.59054i 0.476619 0.173475i −0.0925293 0.995710i \(-0.529495\pi\)
0.569148 + 0.822235i \(0.307273\pi\)
\(224\) 0 0
\(225\) 1.71107 + 1.43576i 0.114071 + 0.0957170i
\(226\) 0 0
\(227\) −24.1858 −1.60527 −0.802633 0.596473i \(-0.796568\pi\)
−0.802633 + 0.596473i \(0.796568\pi\)
\(228\) 0 0
\(229\) −18.3373 −1.21176 −0.605880 0.795556i \(-0.707179\pi\)
−0.605880 + 0.795556i \(0.707179\pi\)
\(230\) 0 0
\(231\) −3.08481 2.58847i −0.202966 0.170309i
\(232\) 0 0
\(233\) 10.6418 3.87330i 0.697167 0.253748i 0.0309662 0.999520i \(-0.490142\pi\)
0.666201 + 0.745772i \(0.267919\pi\)
\(234\) 0 0
\(235\) 2.25169 + 3.90004i 0.146884 + 0.254410i
\(236\) 0 0
\(237\) 2.90313 + 16.4644i 0.188578 + 1.06948i
\(238\) 0 0
\(239\) −5.03088 + 8.71375i −0.325421 + 0.563645i −0.981597 0.190962i \(-0.938839\pi\)
0.656177 + 0.754607i \(0.272173\pi\)
\(240\) 0 0
\(241\) −19.1783 + 16.0925i −1.23538 + 1.03661i −0.237514 + 0.971384i \(0.576332\pi\)
−0.997871 + 0.0652262i \(0.979223\pi\)
\(242\) 0 0
\(243\) 18.0852 + 6.58246i 1.16016 + 0.422265i
\(244\) 0 0
\(245\) 0.439038 2.48991i 0.0280491 0.159074i
\(246\) 0 0
\(247\) −1.33325 10.1549i −0.0848328 0.646140i
\(248\) 0 0
\(249\) 3.23251 18.3325i 0.204852 1.16177i
\(250\) 0 0
\(251\) 13.4284 + 4.88755i 0.847595 + 0.308499i 0.729059 0.684451i \(-0.239958\pi\)
0.118536 + 0.992950i \(0.462180\pi\)
\(252\) 0 0
\(253\) −3.93774 + 3.30416i −0.247564 + 0.207731i
\(254\) 0 0
\(255\) −5.98078 + 10.3590i −0.374531 + 0.648707i
\(256\) 0 0
\(257\) −3.05760 17.3405i −0.190728 1.08167i −0.918372 0.395717i \(-0.870496\pi\)
0.727645 0.685954i \(-0.240615\pi\)
\(258\) 0 0
\(259\) −13.8273 23.9496i −0.859188 1.48816i
\(260\) 0 0
\(261\) 6.76568 2.46251i 0.418785 0.152425i
\(262\) 0 0
\(263\) −1.01134 0.848619i −0.0623622 0.0523281i 0.611074 0.791574i \(-0.290738\pi\)
−0.673436 + 0.739246i \(0.735182\pi\)
\(264\) 0 0
\(265\) −13.2808 −0.815833
\(266\) 0 0
\(267\) 11.1378 0.681621
\(268\) 0 0
\(269\) −21.4196 17.9732i −1.30598 1.09585i −0.989079 0.147386i \(-0.952914\pi\)
−0.316898 0.948460i \(-0.602641\pi\)
\(270\) 0 0
\(271\) 28.1436 10.2434i 1.70960 0.622243i 0.712739 0.701429i \(-0.247454\pi\)
0.996860 + 0.0791858i \(0.0252320\pi\)
\(272\) 0 0
\(273\) −8.29640 14.3698i −0.502121 0.869699i
\(274\) 0 0
\(275\) 0.0990228 + 0.561586i 0.00597130 + 0.0338649i
\(276\) 0 0
\(277\) −9.05979 + 15.6920i −0.544350 + 0.942842i 0.454298 + 0.890850i \(0.349890\pi\)
−0.998648 + 0.0519916i \(0.983443\pi\)
\(278\) 0 0
\(279\) 5.75503 4.82904i 0.344545 0.289107i
\(280\) 0 0
\(281\) −9.37092 3.41073i −0.559022 0.203467i 0.0470285 0.998894i \(-0.485025\pi\)
−0.606050 + 0.795426i \(0.707247\pi\)
\(282\) 0 0
\(283\) −5.42712 + 30.7787i −0.322609 + 1.82960i 0.203365 + 0.979103i \(0.434812\pi\)
−0.525973 + 0.850501i \(0.676299\pi\)
\(284\) 0 0
\(285\) 7.91341 6.06771i 0.468750 0.359420i
\(286\) 0 0
\(287\) −2.62536 + 14.8892i −0.154970 + 0.878879i
\(288\) 0 0
\(289\) −9.71487 3.53592i −0.571463 0.207995i
\(290\) 0 0
\(291\) 17.3843 14.5871i 1.01908 0.855114i
\(292\) 0 0
\(293\) 10.2875 17.8184i 0.601001 1.04096i −0.391669 0.920106i \(-0.628102\pi\)
0.992670 0.120858i \(-0.0385645\pi\)
\(294\) 0 0
\(295\) 0.866435 + 4.91379i 0.0504458 + 0.286092i
\(296\) 0 0
\(297\) 0.499885 + 0.865827i 0.0290063 + 0.0502404i
\(298\) 0 0
\(299\) −19.9033 + 7.24419i −1.15103 + 0.418942i
\(300\) 0 0
\(301\) 5.68800 + 4.77280i 0.327851 + 0.275100i
\(302\) 0 0
\(303\) −37.3231 −2.14416
\(304\) 0 0
\(305\) −1.69753 −0.0972006
\(306\) 0 0
\(307\) 21.7222 + 18.2271i 1.23975 + 1.04027i 0.997544 + 0.0700496i \(0.0223158\pi\)
0.242207 + 0.970225i \(0.422129\pi\)
\(308\) 0 0
\(309\) −4.16184 + 1.51478i −0.236759 + 0.0861731i
\(310\) 0 0
\(311\) −16.3551 28.3278i −0.927412 1.60632i −0.787636 0.616141i \(-0.788695\pi\)
−0.139776 0.990183i \(-0.544638\pi\)
\(312\) 0 0
\(313\) −2.16822 12.2966i −0.122555 0.695046i −0.982730 0.185046i \(-0.940757\pi\)
0.860175 0.510000i \(-0.170355\pi\)
\(314\) 0 0
\(315\) 3.44739 5.97106i 0.194239 0.336431i
\(316\) 0 0
\(317\) 15.1328 12.6980i 0.849944 0.713188i −0.109833 0.993950i \(-0.535032\pi\)
0.959777 + 0.280762i \(0.0905872\pi\)
\(318\) 0 0
\(319\) 1.72728 + 0.628680i 0.0967093 + 0.0351993i
\(320\) 0 0
\(321\) 3.24826 18.4218i 0.181300 1.02820i
\(322\) 0 0
\(323\) 16.7978 + 15.4033i 0.934655 + 0.857064i
\(324\) 0 0
\(325\) −0.408019 + 2.31399i −0.0226328 + 0.128357i
\(326\) 0 0
\(327\) −13.4236 4.88577i −0.742324 0.270184i
\(328\) 0 0
\(329\) 10.6488 8.93540i 0.587087 0.492624i
\(330\) 0 0
\(331\) −8.89182 + 15.4011i −0.488738 + 0.846520i −0.999916 0.0129553i \(-0.995876\pi\)
0.511178 + 0.859475i \(0.329209\pi\)
\(332\) 0 0
\(333\) −3.47491 19.7072i −0.190424 1.07995i
\(334\) 0 0
\(335\) 7.19559 + 12.4631i 0.393137 + 0.680933i
\(336\) 0 0
\(337\) −23.9186 + 8.70567i −1.30293 + 0.474228i −0.897950 0.440098i \(-0.854944\pi\)
−0.404980 + 0.914325i \(0.632722\pi\)
\(338\) 0 0
\(339\) −19.3760 16.2584i −1.05236 0.883035i
\(340\) 0 0
\(341\) 1.91799 0.103865
\(342\) 0 0
\(343\) 13.8032 0.745302
\(344\) 0 0
\(345\) −15.7974 13.2556i −0.850501 0.713655i
\(346\) 0 0
\(347\) 5.83350 2.12322i 0.313159 0.113980i −0.180659 0.983546i \(-0.557823\pi\)
0.493818 + 0.869565i \(0.335601\pi\)
\(348\) 0 0
\(349\) −15.9635 27.6495i −0.854505 1.48005i −0.877104 0.480301i \(-0.840527\pi\)
0.0225985 0.999745i \(-0.492806\pi\)
\(350\) 0 0
\(351\) 0.715345 + 4.05692i 0.0381823 + 0.216543i
\(352\) 0 0
\(353\) 11.0062 19.0633i 0.585800 1.01464i −0.408975 0.912545i \(-0.634114\pi\)
0.994775 0.102090i \(-0.0325528\pi\)
\(354\) 0 0
\(355\) 1.84885 1.55137i 0.0981266 0.0823380i
\(356\) 0 0
\(357\) 34.6962 + 12.6284i 1.83632 + 0.668365i
\(358\) 0 0
\(359\) 0.856397 4.85687i 0.0451989 0.256336i −0.953832 0.300339i \(-0.902900\pi\)
0.999031 + 0.0440034i \(0.0140112\pi\)
\(360\) 0 0
\(361\) −8.01753 17.2255i −0.421975 0.906607i
\(362\) 0 0
\(363\) −4.24065 + 24.0499i −0.222576 + 1.26229i
\(364\) 0 0
\(365\) 7.49663 + 2.72855i 0.392392 + 0.142819i
\(366\) 0 0
\(367\) 24.2096 20.3143i 1.26373 1.06040i 0.268459 0.963291i \(-0.413485\pi\)
0.995274 0.0971072i \(-0.0309590\pi\)
\(368\) 0 0
\(369\) −5.47008 + 9.47445i −0.284761 + 0.493220i
\(370\) 0 0
\(371\) 7.11873 + 40.3723i 0.369586 + 2.09603i
\(372\) 0 0
\(373\) 10.0856 + 17.4688i 0.522214 + 0.904500i 0.999666 + 0.0258429i \(0.00822696\pi\)
−0.477452 + 0.878658i \(0.658440\pi\)
\(374\) 0 0
\(375\) −2.14975 + 0.782445i −0.111013 + 0.0404053i
\(376\) 0 0
\(377\) 5.80198 + 4.86844i 0.298817 + 0.250738i
\(378\) 0 0
\(379\) −11.8801 −0.610239 −0.305119 0.952314i \(-0.598696\pi\)
−0.305119 + 0.952314i \(0.598696\pi\)
\(380\) 0 0
\(381\) −4.13822 −0.212007
\(382\) 0 0
\(383\) −21.0413 17.6558i −1.07516 0.902168i −0.0796521 0.996823i \(-0.525381\pi\)
−0.995510 + 0.0946544i \(0.969825\pi\)
\(384\) 0 0
\(385\) 1.65409 0.602039i 0.0843002 0.0306828i
\(386\) 0 0
\(387\) 2.68646 + 4.65309i 0.136561 + 0.236530i
\(388\) 0 0
\(389\) 0.0727819 + 0.412767i 0.00369019 + 0.0209281i 0.986597 0.163174i \(-0.0521733\pi\)
−0.982907 + 0.184102i \(0.941062\pi\)
\(390\) 0 0
\(391\) 23.5659 40.8174i 1.19178 2.06422i
\(392\) 0 0
\(393\) 18.0119 15.1138i 0.908580 0.762389i
\(394\) 0 0
\(395\) −6.86720 2.49946i −0.345526 0.125761i
\(396\) 0 0
\(397\) −2.70976 + 15.3678i −0.135999 + 0.771289i 0.838160 + 0.545425i \(0.183632\pi\)
−0.974159 + 0.225864i \(0.927480\pi\)
\(398\) 0 0
\(399\) −22.6870 20.8036i −1.13577 1.04148i
\(400\) 0 0
\(401\) −4.10254 + 23.2667i −0.204871 + 1.16188i 0.692771 + 0.721157i \(0.256389\pi\)
−0.897643 + 0.440724i \(0.854722\pi\)
\(402\) 0 0
\(403\) 7.42637 + 2.70298i 0.369934 + 0.134645i
\(404\) 0 0
\(405\) −8.20570 + 6.88540i −0.407744 + 0.342138i
\(406\) 0 0
\(407\) 2.55443 4.42441i 0.126619 0.219310i
\(408\) 0 0
\(409\) −0.785457 4.45455i −0.0388384 0.220263i 0.959211 0.282691i \(-0.0912270\pi\)
−0.998050 + 0.0624273i \(0.980116\pi\)
\(410\) 0 0
\(411\) 1.63360 + 2.82948i 0.0805796 + 0.139568i
\(412\) 0 0
\(413\) 14.4730 5.26775i 0.712171 0.259209i
\(414\) 0 0
\(415\) 6.23336 + 5.23041i 0.305983 + 0.256751i
\(416\) 0 0
\(417\) 43.5219 2.13128
\(418\) 0 0
\(419\) 23.2692 1.13677 0.568386 0.822762i \(-0.307568\pi\)
0.568386 + 0.822762i \(0.307568\pi\)
\(420\) 0 0
\(421\) −16.2997 13.6771i −0.794401 0.666582i 0.152429 0.988314i \(-0.451290\pi\)
−0.946831 + 0.321733i \(0.895735\pi\)
\(422\) 0 0
\(423\) 9.45229 3.44035i 0.459586 0.167276i
\(424\) 0 0
\(425\) −2.61430 4.52811i −0.126812 0.219645i
\(426\) 0 0
\(427\) 0.909907 + 5.16034i 0.0440335 + 0.249726i
\(428\) 0 0
\(429\) 1.53266 2.65465i 0.0739976 0.128168i
\(430\) 0 0
\(431\) −29.2038 + 24.5049i −1.40670 + 1.18036i −0.448663 + 0.893701i \(0.648100\pi\)
−0.958033 + 0.286657i \(0.907456\pi\)
\(432\) 0 0
\(433\) −10.4460 3.80204i −0.502003 0.182714i 0.0785916 0.996907i \(-0.474958\pi\)
−0.580595 + 0.814193i \(0.697180\pi\)
\(434\) 0 0
\(435\) −1.28052 + 7.26216i −0.0613960 + 0.348194i
\(436\) 0 0
\(437\) −31.1810 + 23.9085i −1.49159 + 1.14370i
\(438\) 0 0
\(439\) 1.10226 6.25125i 0.0526082 0.298356i −0.947139 0.320822i \(-0.896041\pi\)
0.999748 + 0.0224664i \(0.00715189\pi\)
\(440\) 0 0
\(441\) −5.30677 1.93151i −0.252703 0.0919765i
\(442\) 0 0
\(443\) 27.6358 23.1892i 1.31302 1.10175i 0.325279 0.945618i \(-0.394542\pi\)
0.987736 0.156133i \(-0.0499028\pi\)
\(444\) 0 0
\(445\) −2.43426 + 4.21626i −0.115395 + 0.199870i
\(446\) 0 0
\(447\) 0.733913 + 4.16223i 0.0347129 + 0.196867i
\(448\) 0 0
\(449\) 3.55923 + 6.16477i 0.167971 + 0.290933i 0.937706 0.347429i \(-0.112945\pi\)
−0.769736 + 0.638363i \(0.779612\pi\)
\(450\) 0 0
\(451\) −2.62459 + 0.955272i −0.123587 + 0.0449820i
\(452\) 0 0
\(453\) −19.6566 16.4938i −0.923545 0.774947i
\(454\) 0 0
\(455\) 7.25300 0.340026
\(456\) 0 0
\(457\) 35.9355 1.68099 0.840496 0.541817i \(-0.182263\pi\)
0.840496 + 0.541817i \(0.182263\pi\)
\(458\) 0 0
\(459\) −7.02224 5.89236i −0.327770 0.275032i
\(460\) 0 0
\(461\) −25.1560 + 9.15604i −1.17163 + 0.426439i −0.853239 0.521519i \(-0.825365\pi\)
−0.318393 + 0.947959i \(0.603143\pi\)
\(462\) 0 0
\(463\) −11.6850 20.2390i −0.543048 0.940587i −0.998727 0.0504426i \(-0.983937\pi\)
0.455679 0.890144i \(-0.349397\pi\)
\(464\) 0 0
\(465\) 1.33614 + 7.57764i 0.0619621 + 0.351405i
\(466\) 0 0
\(467\) −8.10209 + 14.0332i −0.374920 + 0.649380i −0.990315 0.138838i \(-0.955663\pi\)
0.615395 + 0.788219i \(0.288996\pi\)
\(468\) 0 0
\(469\) 34.0297 28.5543i 1.57135 1.31852i
\(470\) 0 0
\(471\) −19.8203 7.21398i −0.913269 0.332403i
\(472\) 0 0
\(473\) −0.238195 + 1.35087i −0.0109522 + 0.0621131i
\(474\) 0 0
\(475\) 0.567417 + 4.32181i 0.0260349 + 0.198298i
\(476\) 0 0
\(477\) −5.15118 + 29.2138i −0.235857 + 1.33761i
\(478\) 0 0
\(479\) −8.62752 3.14016i −0.394202 0.143478i 0.137311 0.990528i \(-0.456154\pi\)
−0.531513 + 0.847050i \(0.678376\pi\)
\(480\) 0 0
\(481\) 16.1259 13.5312i 0.735277 0.616971i
\(482\) 0 0
\(483\) −31.8279 + 55.1276i −1.44822 + 2.50839i
\(484\) 0 0
\(485\) 1.72255 + 9.76905i 0.0782169 + 0.443590i
\(486\) 0 0
\(487\) −18.5252 32.0866i −0.839458 1.45398i −0.890349 0.455279i \(-0.849540\pi\)
0.0508914 0.998704i \(-0.483794\pi\)
\(488\) 0 0
\(489\) −31.8793 + 11.6031i −1.44163 + 0.524711i
\(490\) 0 0
\(491\) −23.3003 19.5513i −1.05153 0.882337i −0.0582746 0.998301i \(-0.518560\pi\)
−0.993253 + 0.115964i \(0.963004\pi\)
\(492\) 0 0
\(493\) −16.8538 −0.759059
\(494\) 0 0
\(495\) 1.27373 0.0572500
\(496\) 0 0
\(497\) −5.70702 4.78876i −0.255995 0.214805i
\(498\) 0 0
\(499\) −14.9454 + 5.43969i −0.669049 + 0.243514i −0.654138 0.756375i \(-0.726969\pi\)
−0.0149107 + 0.999889i \(0.504746\pi\)
\(500\) 0 0
\(501\) 17.2804 + 29.9306i 0.772032 + 1.33720i
\(502\) 0 0
\(503\) −1.21681 6.90088i −0.0542550 0.307695i 0.945589 0.325364i \(-0.105487\pi\)
−0.999844 + 0.0176685i \(0.994376\pi\)
\(504\) 0 0
\(505\) 8.15730 14.1289i 0.362995 0.628726i
\(506\) 0 0
\(507\) −13.1068 + 10.9979i −0.582095 + 0.488436i
\(508\) 0 0
\(509\) 13.7407 + 5.00121i 0.609046 + 0.221675i 0.628086 0.778144i \(-0.283839\pi\)
−0.0190398 + 0.999819i \(0.506061\pi\)
\(510\) 0 0
\(511\) 4.27621 24.2516i 0.189168 1.07283i
\(512\) 0 0
\(513\) 3.52632 + 6.77987i 0.155691 + 0.299339i
\(514\) 0 0
\(515\) 0.336177 1.90655i 0.0148137 0.0840128i
\(516\) 0 0
\(517\) 2.41318 + 0.878324i 0.106131 + 0.0386286i
\(518\) 0 0
\(519\) −1.93095 + 1.62026i −0.0847594 + 0.0711216i
\(520\) 0 0
\(521\) 8.58227 14.8649i 0.375996 0.651244i −0.614479 0.788933i \(-0.710634\pi\)
0.990476 + 0.137688i \(0.0439673\pi\)
\(522\) 0 0
\(523\) −5.28473 29.9712i −0.231085 1.31055i −0.850703 0.525646i \(-0.823824\pi\)
0.619618 0.784903i \(-0.287287\pi\)
\(524\) 0 0
\(525\) 3.53086 + 6.11562i 0.154099 + 0.266908i
\(526\) 0 0
\(527\) −16.5254 + 6.01476i −0.719859 + 0.262007i
\(528\) 0 0
\(529\) 44.6269 + 37.4464i 1.94030 + 1.62811i
\(530\) 0 0
\(531\) 11.1450 0.483650
\(532\) 0 0
\(533\) −11.5085 −0.498490
\(534\) 0 0
\(535\) 6.26372 + 5.25588i 0.270804 + 0.227232i
\(536\) 0 0
\(537\) −24.8177 + 9.03291i −1.07096 + 0.389799i
\(538\) 0 0
\(539\) −0.720886 1.24861i −0.0310508 0.0537815i
\(540\) 0 0
\(541\) 2.72643 + 15.4624i 0.117219 + 0.664779i 0.985628 + 0.168931i \(0.0540316\pi\)
−0.868409 + 0.495848i \(0.834857\pi\)
\(542\) 0 0
\(543\) −12.0323 + 20.8406i −0.516357 + 0.894356i
\(544\) 0 0
\(545\) 4.78337 4.01372i 0.204897 0.171929i
\(546\) 0 0
\(547\) 12.1733 + 4.43071i 0.520491 + 0.189443i 0.588888 0.808215i \(-0.299566\pi\)
−0.0683963 + 0.997658i \(0.521788\pi\)
\(548\) 0 0
\(549\) −0.658418 + 3.73407i −0.0281006 + 0.159366i
\(550\) 0 0
\(551\) 12.9790 + 5.38147i 0.552924 + 0.229258i
\(552\) 0 0
\(553\) −3.91717 + 22.2154i −0.166575 + 0.944693i
\(554\) 0 0
\(555\) 19.2596 + 7.00993i 0.817525 + 0.297555i
\(556\) 0 0
\(557\) 32.0401 26.8849i 1.35758 1.13915i 0.380863 0.924632i \(-0.375627\pi\)
0.976720 0.214516i \(-0.0688175\pi\)
\(558\) 0 0
\(559\) −2.82603 + 4.89484i −0.119529 + 0.207029i
\(560\) 0 0
\(561\) 1.18447 + 6.71745i 0.0500083 + 0.283611i
\(562\) 0 0
\(563\) −4.72970 8.19209i −0.199333 0.345255i 0.748979 0.662594i \(-0.230544\pi\)
−0.948312 + 0.317338i \(0.897211\pi\)
\(564\) 0 0
\(565\) 10.3895 3.78146i 0.437089 0.159087i
\(566\) 0 0
\(567\) 25.3293 + 21.2538i 1.06373 + 0.892577i
\(568\) 0 0
\(569\) 1.30763 0.0548186 0.0274093 0.999624i \(-0.491274\pi\)
0.0274093 + 0.999624i \(0.491274\pi\)
\(570\) 0 0
\(571\) 11.7704 0.492576 0.246288 0.969197i \(-0.420789\pi\)
0.246288 + 0.969197i \(0.420789\pi\)
\(572\) 0 0
\(573\) −7.78648 6.53363i −0.325285 0.272947i
\(574\) 0 0
\(575\) 8.47060 3.08305i 0.353249 0.128572i
\(576\) 0 0
\(577\) 1.75149 + 3.03367i 0.0729155 + 0.126293i 0.900178 0.435522i \(-0.143436\pi\)
−0.827262 + 0.561816i \(0.810103\pi\)
\(578\) 0 0
\(579\) −1.76555 10.0130i −0.0733739 0.416124i
\(580\) 0 0
\(581\) 12.5587 21.7524i 0.521024 0.902441i
\(582\) 0 0
\(583\) −5.80153 + 4.86807i −0.240275 + 0.201615i
\(584\) 0 0
\(585\) 4.93183 + 1.79504i 0.203906 + 0.0742158i
\(586\) 0 0
\(587\) −1.47722 + 8.37771i −0.0609713 + 0.345785i 0.939027 + 0.343844i \(0.111729\pi\)
−0.999998 + 0.00194144i \(0.999382\pi\)
\(588\) 0 0
\(589\) 14.6466 + 0.644691i 0.603503 + 0.0265641i
\(590\) 0 0
\(591\) −5.21776 + 29.5914i −0.214630 + 1.21723i
\(592\) 0 0
\(593\) −0.638258 0.232307i −0.0262101 0.00953971i 0.328882 0.944371i \(-0.393328\pi\)
−0.355092 + 0.934831i \(0.615550\pi\)
\(594\) 0 0
\(595\) −12.3637 + 10.3744i −0.506862 + 0.425308i
\(596\) 0 0
\(597\) −27.2492 + 47.1970i −1.11524 + 1.93164i
\(598\) 0 0
\(599\) −0.629002 3.56724i −0.0257003 0.145754i 0.969257 0.246049i \(-0.0791324\pi\)
−0.994958 + 0.100295i \(0.968021\pi\)
\(600\) 0 0
\(601\) 12.9137 + 22.3672i 0.526761 + 0.912376i 0.999514 + 0.0311814i \(0.00992697\pi\)
−0.472753 + 0.881195i \(0.656740\pi\)
\(602\) 0 0
\(603\) 30.2061 10.9941i 1.23009 0.447716i
\(604\) 0 0
\(605\) −8.17738 6.86164i −0.332458 0.278965i
\(606\) 0 0
\(607\) 2.64689 0.107434 0.0537169 0.998556i \(-0.482893\pi\)
0.0537169 + 0.998556i \(0.482893\pi\)
\(608\) 0 0
\(609\) 22.7626 0.922389
\(610\) 0 0
\(611\) 8.10591 + 6.80167i 0.327930 + 0.275166i
\(612\) 0 0
\(613\) −27.8737 + 10.1452i −1.12581 + 0.409760i −0.836768 0.547558i \(-0.815558\pi\)
−0.289038 + 0.957318i \(0.593335\pi\)
\(614\) 0 0
\(615\) −5.60251 9.70383i −0.225915 0.391296i
\(616\) 0 0
\(617\) 1.69384 + 9.60623i 0.0681913 + 0.386732i 0.999733 + 0.0230981i \(0.00735302\pi\)
−0.931542 + 0.363634i \(0.881536\pi\)
\(618\) 0 0
\(619\) 11.1539 19.3192i 0.448315 0.776504i −0.549962 0.835190i \(-0.685358\pi\)
0.998276 + 0.0586859i \(0.0186911\pi\)
\(620\) 0 0
\(621\) 12.1065 10.1585i 0.485816 0.407648i
\(622\) 0 0
\(623\) 14.1218 + 5.13992i 0.565779 + 0.205927i
\(624\) 0 0
\(625\) 0.173648 0.984808i 0.00694593 0.0393923i
\(626\) 0 0
\(627\) 1.23275 5.55125i 0.0492313 0.221696i
\(628\) 0 0
\(629\) −8.13423 + 46.1315i −0.324333 + 1.83938i
\(630\) 0 0
\(631\) 43.7131 + 15.9103i 1.74019 + 0.633377i 0.999270 0.0382155i \(-0.0121673\pi\)
0.740920 + 0.671593i \(0.234390\pi\)
\(632\) 0 0
\(633\) −32.5809 + 27.3386i −1.29498 + 1.08661i
\(634\) 0 0
\(635\) 0.904443 1.56654i 0.0358917 0.0621663i
\(636\) 0 0
\(637\) −1.03160 5.85050i −0.0408735 0.231805i
\(638\) 0 0
\(639\) −2.69544 4.66864i −0.106630 0.184689i
\(640\) 0 0
\(641\) −41.1061 + 14.9614i −1.62359 + 0.590939i −0.984062 0.177826i \(-0.943094\pi\)
−0.639531 + 0.768765i \(0.720871\pi\)
\(642\) 0 0
\(643\) 30.1438 + 25.2936i 1.18875 + 0.997483i 0.999880 + 0.0154814i \(0.00492809\pi\)
0.188874 + 0.982001i \(0.439516\pi\)
\(644\) 0 0
\(645\) −5.50300 −0.216680
\(646\) 0 0
\(647\) −9.53143 −0.374719 −0.187360 0.982291i \(-0.559993\pi\)
−0.187360 + 0.982291i \(0.559993\pi\)
\(648\) 0 0
\(649\) 2.17964 + 1.82893i 0.0855583 + 0.0717919i
\(650\) 0 0
\(651\) 22.3191 8.12348i 0.874754 0.318384i
\(652\) 0 0
\(653\) −20.8821 36.1689i −0.817180 1.41540i −0.907752 0.419508i \(-0.862203\pi\)
0.0905712 0.995890i \(-0.471131\pi\)
\(654\) 0 0
\(655\) 1.78473 + 10.1217i 0.0697354 + 0.395489i
\(656\) 0 0
\(657\) 8.90970 15.4321i 0.347601 0.602062i
\(658\) 0 0
\(659\) −9.64513 + 8.09322i −0.375721 + 0.315267i −0.811020 0.585019i \(-0.801087\pi\)
0.435299 + 0.900286i \(0.356643\pi\)
\(660\) 0 0
\(661\) −41.2288 15.0060i −1.60361 0.583667i −0.623450 0.781863i \(-0.714270\pi\)
−0.980162 + 0.198196i \(0.936492\pi\)
\(662\) 0 0
\(663\) −4.88054 + 27.6789i −0.189545 + 1.07496i
\(664\) 0 0
\(665\) 12.8337 4.04145i 0.497671 0.156721i
\(666\) 0 0
\(667\) 5.04558 28.6149i 0.195366 1.10797i
\(668\) 0 0
\(669\) 16.2827 + 5.92641i 0.629525 + 0.229128i
\(670\) 0 0
\(671\) −0.741545 + 0.622230i −0.0286270 + 0.0240209i
\(672\) 0 0
\(673\) 6.37316 11.0386i 0.245667 0.425508i −0.716652 0.697431i \(-0.754326\pi\)
0.962319 + 0.271923i \(0.0876596\pi\)
\(674\) 0 0
\(675\) −0.304443 1.72658i −0.0117180 0.0664561i
\(676\) 0 0
\(677\) 17.2366 + 29.8547i 0.662457 + 1.14741i 0.979968 + 0.199155i \(0.0638197\pi\)
−0.317511 + 0.948255i \(0.602847\pi\)
\(678\) 0 0
\(679\) 28.7737 10.4728i 1.10423 0.401907i
\(680\) 0 0
\(681\) −42.3854 35.5655i −1.62421 1.36287i
\(682\) 0 0
\(683\) 16.8008 0.642867 0.321433 0.946932i \(-0.395835\pi\)
0.321433 + 0.946932i \(0.395835\pi\)
\(684\) 0 0
\(685\) −1.42815 −0.0545669
\(686\) 0 0
\(687\) −32.1359 26.9652i −1.22606 1.02879i
\(688\) 0 0
\(689\) −29.3238 + 10.6730i −1.11715 + 0.406608i
\(690\) 0 0
\(691\) 8.29618 + 14.3694i 0.315602 + 0.546638i 0.979565 0.201127i \(-0.0644604\pi\)
−0.663964 + 0.747765i \(0.731127\pi\)
\(692\) 0 0
\(693\) −0.682741 3.87202i −0.0259352 0.147086i
\(694\) 0 0
\(695\) −9.51209 + 16.4754i −0.360814 + 0.624948i
\(696\) 0 0
\(697\) 19.6178 16.4613i 0.743078 0.623516i
\(698\) 0 0
\(699\) 24.3454 + 8.86100i 0.920827 + 0.335154i
\(700\) 0 0
\(701\) −2.49187 + 14.1321i −0.0941167 + 0.533762i 0.900898 + 0.434031i \(0.142909\pi\)
−0.995014 + 0.0997310i \(0.968202\pi\)
\(702\) 0 0
\(703\) 20.9940 32.9282i 0.791803 1.24191i
\(704\) 0 0
\(705\) −1.78900 + 10.1459i −0.0673776 + 0.382118i
\(706\) 0 0
\(707\) −47.3228 17.2241i −1.77976 0.647778i
\(708\) 0 0
\(709\) 20.3960 17.1143i 0.765987 0.642740i −0.173690 0.984800i \(-0.555569\pi\)
0.939678 + 0.342061i \(0.111125\pi\)
\(710\) 0 0
\(711\) −8.16162 + 14.1363i −0.306085 + 0.530154i
\(712\) 0 0
\(713\) −5.26477 29.8580i −0.197167 1.11819i
\(714\) 0 0
\(715\) 0.669954 + 1.16039i 0.0250548 + 0.0433963i
\(716\) 0 0
\(717\) −21.6303 + 7.87277i −0.807797 + 0.294014i
\(718\) 0 0
\(719\) 19.9847 + 16.7692i 0.745304 + 0.625385i 0.934256 0.356602i \(-0.116065\pi\)
−0.188952 + 0.981986i \(0.560509\pi\)
\(720\) 0 0
\(721\) −5.97593 −0.222555
\(722\) 0 0
\(723\) −57.2741 −2.13005
\(724\) 0 0
\(725\) −2.46926 2.07195i −0.0917060 0.0769505i
\(726\) 0 0
\(727\) 8.47243 3.08371i 0.314225 0.114369i −0.180093 0.983650i \(-0.557640\pi\)
0.494318 + 0.869281i \(0.335418\pi\)
\(728\) 0 0
\(729\) 5.94683 + 10.3002i 0.220253 + 0.381489i
\(730\) 0 0
\(731\) −2.18401 12.3861i −0.0807784 0.458117i
\(732\) 0 0
\(733\) −17.8405 + 30.9006i −0.658953 + 1.14134i 0.321934 + 0.946762i \(0.395667\pi\)
−0.980887 + 0.194578i \(0.937666\pi\)
\(734\) 0 0
\(735\) 4.43085 3.71793i 0.163434 0.137138i
\(736\) 0 0
\(737\) 7.71164 + 2.80681i 0.284062 + 0.103390i
\(738\) 0 0
\(739\) −2.85870 + 16.2125i −0.105159 + 0.596386i 0.885998 + 0.463689i \(0.153475\pi\)
−0.991157 + 0.132697i \(0.957636\pi\)
\(740\) 0 0
\(741\) 12.5964 19.7569i 0.462741 0.725789i
\(742\) 0 0
\(743\) 5.47679 31.0604i 0.200924 1.13950i −0.702802 0.711385i \(-0.748068\pi\)
0.903726 0.428111i \(-0.140821\pi\)
\(744\) 0 0
\(745\) −1.73603 0.631865i −0.0636034 0.0231497i
\(746\) 0 0
\(747\) 13.9231 11.6828i 0.509418 0.427453i
\(748\) 0 0
\(749\) 12.6199 21.8583i 0.461122 0.798686i
\(750\) 0 0
\(751\) 1.55178 + 8.80057i 0.0566252 + 0.321138i 0.999942 0.0107557i \(-0.00342373\pi\)
−0.943317 + 0.331893i \(0.892313\pi\)
\(752\) 0 0
\(753\) 16.3460 + 28.3121i 0.595681 + 1.03175i
\(754\) 0 0
\(755\) 10.5399 3.83622i 0.383587 0.139614i
\(756\) 0 0
\(757\) 5.34941 + 4.48869i 0.194428 + 0.163144i 0.734805 0.678279i \(-0.237274\pi\)
−0.540377 + 0.841423i \(0.681718\pi\)
\(758\) 0 0
\(759\) −11.7597 −0.426849
\(760\) 0 0
\(761\) −19.1207 −0.693124 −0.346562 0.938027i \(-0.612651\pi\)
−0.346562 + 0.938027i \(0.612651\pi\)
\(762\) 0 0
\(763\) −14.7653 12.3895i −0.534539 0.448532i
\(764\) 0 0
\(765\) −10.9745 + 3.99439i −0.396784 + 0.144418i
\(766\) 0 0
\(767\) 5.86199 + 10.1533i 0.211664 + 0.366613i
\(768\) 0 0
\(769\) −1.92416 10.9125i −0.0693870 0.393513i −0.999646 0.0266095i \(-0.991529\pi\)
0.930259 0.366904i \(-0.119582\pi\)
\(770\) 0 0
\(771\) 20.1411 34.8853i 0.725362 1.25636i
\(772\) 0 0
\(773\) 14.1680 11.8884i 0.509588 0.427595i −0.351396 0.936227i \(-0.614293\pi\)
0.860984 + 0.508632i \(0.169849\pi\)
\(774\) 0 0
\(775\) −3.16058 1.15036i −0.113531 0.0413220i
\(776\) 0 0
\(777\) 10.9860 62.3048i 0.394121 2.23517i
\(778\) 0 0
\(779\) −20.3636 + 6.41269i −0.729603 + 0.229758i
\(780\) 0 0
\(781\) 0.238991 1.35539i 0.00855178 0.0484996i
\(782\) 0 0
\(783\) −5.31048 1.93286i −0.189781 0.0690747i
\(784\) 0 0
\(785\) 7.06278 5.92637i 0.252081 0.211521i
\(786\) 0 0
\(787\) 15.4354 26.7349i 0.550214 0.952998i