Properties

Label 380.2.u.a.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: \( x^{18} - 3 x^{17} + 3 x^{15} + 36 x^{14} + 72 x^{13} - 134 x^{12} - 741 x^{11} + 486 x^{10} + 5700 x^{9} + \cdots + 9 \) 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 \(-1.48541 - 0.540646i\) of defining polynomial
Character \(\chi\) \(=\) 380.321
Dual form 380.2.u.a.161.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.21092 + 1.01608i) q^{3} +(0.939693 - 0.342020i) q^{5} +(1.77958 + 3.08232i) q^{7} +(-0.0870410 - 0.493634i) q^{9} +O(q^{10})\) \(q+(1.21092 + 1.01608i) q^{3} +(0.939693 - 0.342020i) q^{5} +(1.77958 + 3.08232i) q^{7} +(-0.0870410 - 0.493634i) q^{9} +(1.71921 - 2.97776i) q^{11} +(-2.46113 + 2.06513i) q^{13} +(1.48541 + 0.540646i) q^{15} +(-0.843610 + 4.78435i) q^{17} +(4.05569 - 1.59731i) q^{19} +(-0.976964 + 5.54064i) q^{21} +(-6.41442 - 2.33466i) q^{23} +(0.766044 - 0.642788i) q^{25} +(2.76729 - 4.79308i) q^{27} +(0.331754 + 1.88147i) q^{29} +(1.52175 + 2.63575i) q^{31} +(5.10747 - 1.85897i) q^{33} +(2.72647 + 2.28778i) q^{35} +7.81318 q^{37} -5.07858 q^{39} +(-6.22608 - 5.22431i) q^{41} +(-10.6275 + 3.86808i) q^{43} +(-0.250624 - 0.434094i) q^{45} +(-0.899912 - 5.10365i) q^{47} +(-2.83380 + 4.90828i) q^{49} +(-5.88284 + 4.93629i) q^{51} +(6.97841 + 2.53993i) q^{53} +(0.597075 - 3.38618i) q^{55} +(6.53411 + 2.18670i) q^{57} +(1.53157 - 8.68599i) q^{59} +(-7.19444 - 2.61856i) q^{61} +(1.36664 - 1.14675i) q^{63} +(-1.60639 + 2.78235i) q^{65} +(1.15738 + 6.56383i) q^{67} +(-5.39514 - 9.34466i) q^{69} +(7.66249 - 2.78892i) q^{71} +(-5.87461 - 4.92939i) q^{73} +1.58074 q^{75} +12.2379 q^{77} +(-10.4195 - 8.74297i) q^{79} +(6.80808 - 2.47794i) q^{81} +(-8.21708 - 14.2324i) q^{83} +(0.843610 + 4.78435i) q^{85} +(-1.51000 + 2.61540i) q^{87} +(2.74230 - 2.30106i) q^{89} +(-10.7452 - 3.91092i) q^{91} +(-0.835422 + 4.73792i) q^{93} +(3.26479 - 2.88811i) q^{95} +(0.167924 - 0.952344i) q^{97} +(-1.61956 - 0.589473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) \) 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
\(3\) 1.21092 + 1.01608i 0.699125 + 0.586636i 0.921525 0.388320i \(-0.126944\pi\)
−0.222400 + 0.974956i \(0.571389\pi\)
\(4\) 0 0
\(5\) 0.939693 0.342020i 0.420243 0.152956i
\(6\) 0 0
\(7\) 1.77958 + 3.08232i 0.672617 + 1.16501i 0.977159 + 0.212508i \(0.0681633\pi\)
−0.304542 + 0.952499i \(0.598503\pi\)
\(8\) 0 0
\(9\) −0.0870410 0.493634i −0.0290137 0.164545i
\(10\) 0 0
\(11\) 1.71921 2.97776i 0.518361 0.897828i −0.481411 0.876495i \(-0.659876\pi\)
0.999772 0.0213331i \(-0.00679104\pi\)
\(12\) 0 0
\(13\) −2.46113 + 2.06513i −0.682595 + 0.572765i −0.916763 0.399431i \(-0.869208\pi\)
0.234169 + 0.972196i \(0.424763\pi\)
\(14\) 0 0
\(15\) 1.48541 + 0.540646i 0.383532 + 0.139594i
\(16\) 0 0
\(17\) −0.843610 + 4.78435i −0.204605 + 1.16038i 0.693454 + 0.720501i \(0.256088\pi\)
−0.898059 + 0.439874i \(0.855023\pi\)
\(18\) 0 0
\(19\) 4.05569 1.59731i 0.930439 0.366448i
\(20\) 0 0
\(21\) −0.976964 + 5.54064i −0.213191 + 1.20907i
\(22\) 0 0
\(23\) −6.41442 2.33466i −1.33750 0.486810i −0.428475 0.903554i \(-0.640949\pi\)
−0.909024 + 0.416744i \(0.863171\pi\)
\(24\) 0 0
\(25\) 0.766044 0.642788i 0.153209 0.128558i
\(26\) 0 0
\(27\) 2.76729 4.79308i 0.532565 0.922430i
\(28\) 0 0
\(29\) 0.331754 + 1.88147i 0.0616052 + 0.349380i 0.999993 + 0.00379579i \(0.00120824\pi\)
−0.938388 + 0.345585i \(0.887681\pi\)
\(30\) 0 0
\(31\) 1.52175 + 2.63575i 0.273315 + 0.473396i 0.969709 0.244265i \(-0.0785465\pi\)
−0.696394 + 0.717660i \(0.745213\pi\)
\(32\) 0 0
\(33\) 5.10747 1.85897i 0.889097 0.323605i
\(34\) 0 0
\(35\) 2.72647 + 2.28778i 0.460858 + 0.386706i
\(36\) 0 0
\(37\) 7.81318 1.28448 0.642240 0.766504i \(-0.278005\pi\)
0.642240 + 0.766504i \(0.278005\pi\)
\(38\) 0 0
\(39\) −5.07858 −0.813223
\(40\) 0 0
\(41\) −6.22608 5.22431i −0.972351 0.815899i 0.0105668 0.999944i \(-0.496636\pi\)
−0.982918 + 0.184045i \(0.941081\pi\)
\(42\) 0 0
\(43\) −10.6275 + 3.86808i −1.62067 + 0.589877i −0.983510 0.180851i \(-0.942115\pi\)
−0.637164 + 0.770728i \(0.719893\pi\)
\(44\) 0 0
\(45\) −0.250624 0.434094i −0.0373609 0.0647110i
\(46\) 0 0
\(47\) −0.899912 5.10365i −0.131266 0.744444i −0.977388 0.211455i \(-0.932180\pi\)
0.846122 0.532989i \(-0.178931\pi\)
\(48\) 0 0
\(49\) −2.83380 + 4.90828i −0.404828 + 0.701183i
\(50\) 0 0
\(51\) −5.88284 + 4.93629i −0.823762 + 0.691219i
\(52\) 0 0
\(53\) 6.97841 + 2.53993i 0.958558 + 0.348887i 0.773468 0.633835i \(-0.218520\pi\)
0.185090 + 0.982722i \(0.440742\pi\)
\(54\) 0 0
\(55\) 0.597075 3.38618i 0.0805096 0.456593i
\(56\) 0 0
\(57\) 6.53411 + 2.18670i 0.865464 + 0.289636i
\(58\) 0 0
\(59\) 1.53157 8.68599i 0.199394 1.13082i −0.706627 0.707586i \(-0.749784\pi\)
0.906021 0.423233i \(-0.139105\pi\)
\(60\) 0 0
\(61\) −7.19444 2.61856i −0.921153 0.335272i −0.162456 0.986716i \(-0.551942\pi\)
−0.758697 + 0.651443i \(0.774164\pi\)
\(62\) 0 0
\(63\) 1.36664 1.14675i 0.172181 0.144477i
\(64\) 0 0
\(65\) −1.60639 + 2.78235i −0.199248 + 0.345108i
\(66\) 0 0
\(67\) 1.15738 + 6.56383i 0.141396 + 0.801899i 0.970190 + 0.242345i \(0.0779165\pi\)
−0.828794 + 0.559554i \(0.810972\pi\)
\(68\) 0 0
\(69\) −5.39514 9.34466i −0.649499 1.12496i
\(70\) 0 0
\(71\) 7.66249 2.78892i 0.909370 0.330984i 0.155369 0.987857i \(-0.450343\pi\)
0.754001 + 0.656873i \(0.228121\pi\)
\(72\) 0 0
\(73\) −5.87461 4.92939i −0.687572 0.576941i 0.230636 0.973040i \(-0.425919\pi\)
−0.918208 + 0.396099i \(0.870364\pi\)
\(74\) 0 0
\(75\) 1.58074 0.182529
\(76\) 0 0
\(77\) 12.2379 1.39463
\(78\) 0 0
\(79\) −10.4195 8.74297i −1.17228 0.983661i −0.172282 0.985048i \(-0.555114\pi\)
−0.999999 + 0.00138681i \(0.999559\pi\)
\(80\) 0 0
\(81\) 6.80808 2.47794i 0.756453 0.275326i
\(82\) 0 0
\(83\) −8.21708 14.2324i −0.901942 1.56221i −0.824971 0.565175i \(-0.808808\pi\)
−0.0769710 0.997033i \(-0.524525\pi\)
\(84\) 0 0
\(85\) 0.843610 + 4.78435i 0.0915024 + 0.518936i
\(86\) 0 0
\(87\) −1.51000 + 2.61540i −0.161889 + 0.280400i
\(88\) 0 0
\(89\) 2.74230 2.30106i 0.290683 0.243912i −0.485771 0.874086i \(-0.661461\pi\)
0.776454 + 0.630174i \(0.217017\pi\)
\(90\) 0 0
\(91\) −10.7452 3.91092i −1.12640 0.409976i
\(92\) 0 0
\(93\) −0.835422 + 4.73792i −0.0866293 + 0.491299i
\(94\) 0 0
\(95\) 3.26479 2.88811i 0.334960 0.296313i
\(96\) 0 0
\(97\) 0.167924 0.952344i 0.0170501 0.0966959i −0.975095 0.221787i \(-0.928811\pi\)
0.992145 + 0.125091i \(0.0399222\pi\)
\(98\) 0 0
\(99\) −1.61956 0.589473i −0.162772 0.0592443i
\(100\) 0 0
\(101\) −7.82623 + 6.56699i −0.778739 + 0.653440i −0.942931 0.332989i \(-0.891943\pi\)
0.164192 + 0.986428i \(0.447498\pi\)
\(102\) 0 0
\(103\) 0.292743 0.507046i 0.0288448 0.0499607i −0.851243 0.524772i \(-0.824150\pi\)
0.880087 + 0.474812i \(0.157484\pi\)
\(104\) 0 0
\(105\) 0.976964 + 5.54064i 0.0953420 + 0.540711i
\(106\) 0 0
\(107\) 0.376505 + 0.652125i 0.0363981 + 0.0630433i 0.883651 0.468147i \(-0.155078\pi\)
−0.847253 + 0.531190i \(0.821745\pi\)
\(108\) 0 0
\(109\) −16.4360 + 5.98221i −1.57428 + 0.572992i −0.973951 0.226760i \(-0.927187\pi\)
−0.600331 + 0.799752i \(0.704964\pi\)
\(110\) 0 0
\(111\) 9.46114 + 7.93884i 0.898012 + 0.753521i
\(112\) 0 0
\(113\) −1.03497 −0.0973620 −0.0486810 0.998814i \(-0.515502\pi\)
−0.0486810 + 0.998814i \(0.515502\pi\)
\(114\) 0 0
\(115\) −6.82608 −0.636535
\(116\) 0 0
\(117\) 1.23364 + 1.03515i 0.114050 + 0.0956993i
\(118\) 0 0
\(119\) −16.2482 + 5.91385i −1.48947 + 0.542122i
\(120\) 0 0
\(121\) −0.411363 0.712502i −0.0373967 0.0647729i
\(122\) 0 0
\(123\) −2.23097 12.6524i −0.201159 1.14083i
\(124\) 0 0
\(125\) 0.500000 0.866025i 0.0447214 0.0774597i
\(126\) 0 0
\(127\) 1.47363 1.23652i 0.130764 0.109724i −0.575060 0.818111i \(-0.695021\pi\)
0.705824 + 0.708387i \(0.250577\pi\)
\(128\) 0 0
\(129\) −16.7993 6.11445i −1.47910 0.538347i
\(130\) 0 0
\(131\) 2.35438 13.3523i 0.205703 1.16660i −0.690626 0.723212i \(-0.742665\pi\)
0.896330 0.443388i \(-0.146224\pi\)
\(132\) 0 0
\(133\) 12.1408 + 9.65839i 1.05274 + 0.837489i
\(134\) 0 0
\(135\) 0.961069 5.45049i 0.0827157 0.469104i
\(136\) 0 0
\(137\) 3.10060 + 1.12853i 0.264902 + 0.0964165i 0.471057 0.882103i \(-0.343873\pi\)
−0.206155 + 0.978519i \(0.566095\pi\)
\(138\) 0 0
\(139\) −2.96484 + 2.48780i −0.251475 + 0.211012i −0.759807 0.650149i \(-0.774707\pi\)
0.508332 + 0.861161i \(0.330262\pi\)
\(140\) 0 0
\(141\) 4.09601 7.09450i 0.344946 0.597465i
\(142\) 0 0
\(143\) 1.91827 + 10.8790i 0.160414 + 0.909752i
\(144\) 0 0
\(145\) 0.955248 + 1.65454i 0.0793290 + 0.137402i
\(146\) 0 0
\(147\) −8.41872 + 3.06416i −0.694364 + 0.252728i
\(148\) 0 0
\(149\) 16.6257 + 13.9506i 1.36203 + 1.14288i 0.975350 + 0.220664i \(0.0708224\pi\)
0.386679 + 0.922214i \(0.373622\pi\)
\(150\) 0 0
\(151\) 20.6330 1.67909 0.839547 0.543288i \(-0.182821\pi\)
0.839547 + 0.543288i \(0.182821\pi\)
\(152\) 0 0
\(153\) 2.43515 0.196870
\(154\) 0 0
\(155\) 2.33146 + 1.95633i 0.187268 + 0.157136i
\(156\) 0 0
\(157\) −9.27210 + 3.37477i −0.739994 + 0.269336i −0.684389 0.729117i \(-0.739931\pi\)
−0.0556052 + 0.998453i \(0.517709\pi\)
\(158\) 0 0
\(159\) 5.86951 + 10.1663i 0.465483 + 0.806239i
\(160\) 0 0
\(161\) −4.21880 23.9260i −0.332488 1.88563i
\(162\) 0 0
\(163\) 4.08509 7.07559i 0.319969 0.554203i −0.660512 0.750815i \(-0.729661\pi\)
0.980481 + 0.196613i \(0.0629941\pi\)
\(164\) 0 0
\(165\) 4.16365 3.49372i 0.324140 0.271986i
\(166\) 0 0
\(167\) 10.2165 + 3.71851i 0.790579 + 0.287747i 0.705577 0.708634i \(-0.250688\pi\)
0.0850022 + 0.996381i \(0.472910\pi\)
\(168\) 0 0
\(169\) −0.465041 + 2.63738i −0.0357724 + 0.202875i
\(170\) 0 0
\(171\) −1.14150 1.86299i −0.0872924 0.142467i
\(172\) 0 0
\(173\) −0.722899 + 4.09976i −0.0549610 + 0.311699i −0.999878 0.0156103i \(-0.995031\pi\)
0.944917 + 0.327310i \(0.106142\pi\)
\(174\) 0 0
\(175\) 3.34451 + 1.21730i 0.252821 + 0.0920195i
\(176\) 0 0
\(177\) 10.6803 8.96183i 0.802780 0.673612i
\(178\) 0 0
\(179\) −6.14600 + 10.6452i −0.459374 + 0.795658i −0.998928 0.0462925i \(-0.985259\pi\)
0.539554 + 0.841951i \(0.318593\pi\)
\(180\) 0 0
\(181\) 4.38678 + 24.8787i 0.326067 + 1.84922i 0.502071 + 0.864826i \(0.332572\pi\)
−0.176004 + 0.984389i \(0.556317\pi\)
\(182\) 0 0
\(183\) −6.05122 10.4810i −0.447319 0.774779i
\(184\) 0 0
\(185\) 7.34199 2.67227i 0.539794 0.196469i
\(186\) 0 0
\(187\) 12.7963 + 10.7374i 0.935758 + 0.785194i
\(188\) 0 0
\(189\) 19.6984 1.43285
\(190\) 0 0
\(191\) 5.98781 0.433263 0.216631 0.976253i \(-0.430493\pi\)
0.216631 + 0.976253i \(0.430493\pi\)
\(192\) 0 0
\(193\) 12.1442 + 10.1902i 0.874157 + 0.733505i 0.964969 0.262363i \(-0.0845019\pi\)
−0.0908123 + 0.995868i \(0.528946\pi\)
\(194\) 0 0
\(195\) −4.77230 + 1.73698i −0.341752 + 0.124387i
\(196\) 0 0
\(197\) 0.0256952 + 0.0445054i 0.00183071 + 0.00317088i 0.866939 0.498414i \(-0.166084\pi\)
−0.865109 + 0.501585i \(0.832751\pi\)
\(198\) 0 0
\(199\) −0.877053 4.97401i −0.0621726 0.352598i −0.999985 0.00545618i \(-0.998263\pi\)
0.937813 0.347142i \(-0.112848\pi\)
\(200\) 0 0
\(201\) −5.26789 + 9.12426i −0.371569 + 0.643576i
\(202\) 0 0
\(203\) −5.20891 + 4.37080i −0.365594 + 0.306770i
\(204\) 0 0
\(205\) −7.63742 2.77979i −0.533421 0.194149i
\(206\) 0 0
\(207\) −0.594149 + 3.36958i −0.0412962 + 0.234202i
\(208\) 0 0
\(209\) 2.21618 14.8230i 0.153296 1.02533i
\(210\) 0 0
\(211\) −4.17249 + 23.6634i −0.287246 + 1.62906i 0.409903 + 0.912129i \(0.365563\pi\)
−0.697149 + 0.716926i \(0.745549\pi\)
\(212\) 0 0
\(213\) 12.1124 + 4.40856i 0.829930 + 0.302070i
\(214\) 0 0
\(215\) −8.66359 + 7.26962i −0.590852 + 0.495784i
\(216\) 0 0
\(217\) −5.41616 + 9.38106i −0.367673 + 0.636828i
\(218\) 0 0
\(219\) −2.10502 11.9382i −0.142244 0.806708i
\(220\) 0 0
\(221\) −7.80409 13.5171i −0.524960 0.909257i
\(222\) 0 0
\(223\) 16.0031 5.82465i 1.07165 0.390047i 0.254854 0.966979i \(-0.417973\pi\)
0.816792 + 0.576932i \(0.195750\pi\)
\(224\) 0 0
\(225\) −0.383979 0.322197i −0.0255986 0.0214798i
\(226\) 0 0
\(227\) 7.89987 0.524333 0.262166 0.965023i \(-0.415563\pi\)
0.262166 + 0.965023i \(0.415563\pi\)
\(228\) 0 0
\(229\) −5.63673 −0.372485 −0.186243 0.982504i \(-0.559631\pi\)
−0.186243 + 0.982504i \(0.559631\pi\)
\(230\) 0 0
\(231\) 14.8191 + 12.4347i 0.975024 + 0.818142i
\(232\) 0 0
\(233\) 0.388467 0.141390i 0.0254493 0.00926279i −0.329264 0.944238i \(-0.606801\pi\)
0.354713 + 0.934975i \(0.384578\pi\)
\(234\) 0 0
\(235\) −2.59119 4.48808i −0.169031 0.292770i
\(236\) 0 0
\(237\) −3.73356 21.1741i −0.242521 1.37540i
\(238\) 0 0
\(239\) −0.391298 + 0.677747i −0.0253109 + 0.0438398i −0.878403 0.477920i \(-0.841391\pi\)
0.853092 + 0.521760i \(0.174724\pi\)
\(240\) 0 0
\(241\) −7.81257 + 6.55553i −0.503252 + 0.422279i −0.858747 0.512400i \(-0.828757\pi\)
0.355495 + 0.934678i \(0.384312\pi\)
\(242\) 0 0
\(243\) −4.84058 1.76183i −0.310523 0.113021i
\(244\) 0 0
\(245\) −0.984167 + 5.58149i −0.0628761 + 0.356588i
\(246\) 0 0
\(247\) −6.68292 + 12.3067i −0.425224 + 0.783058i
\(248\) 0 0
\(249\) 4.51107 25.5835i 0.285877 1.62129i
\(250\) 0 0
\(251\) 17.1166 + 6.22993i 1.08039 + 0.393230i 0.820052 0.572288i \(-0.193944\pi\)
0.260337 + 0.965518i \(0.416166\pi\)
\(252\) 0 0
\(253\) −17.9798 + 15.0868i −1.13038 + 0.948500i
\(254\) 0 0
\(255\) −3.83975 + 6.65064i −0.240454 + 0.416479i
\(256\) 0 0
\(257\) −3.06253 17.3685i −0.191036 1.08342i −0.917952 0.396691i \(-0.870158\pi\)
0.726917 0.686726i \(-0.240953\pi\)
\(258\) 0 0
\(259\) 13.9042 + 24.0827i 0.863963 + 1.49643i
\(260\) 0 0
\(261\) 0.899881 0.327530i 0.0557013 0.0202736i
\(262\) 0 0
\(263\) 8.55858 + 7.18150i 0.527745 + 0.442830i 0.867322 0.497748i \(-0.165840\pi\)
−0.339577 + 0.940578i \(0.610284\pi\)
\(264\) 0 0
\(265\) 7.42627 0.456192
\(266\) 0 0
\(267\) 5.65877 0.346311
\(268\) 0 0
\(269\) 18.8693 + 15.8332i 1.15048 + 0.965370i 0.999731 0.0232012i \(-0.00738584\pi\)
0.150753 + 0.988572i \(0.451830\pi\)
\(270\) 0 0
\(271\) −16.9412 + 6.16610i −1.02911 + 0.374564i −0.800740 0.599012i \(-0.795560\pi\)
−0.228366 + 0.973575i \(0.573338\pi\)
\(272\) 0 0
\(273\) −9.03773 15.6538i −0.546988 0.947411i
\(274\) 0 0
\(275\) −0.597075 3.38618i −0.0360050 0.204194i
\(276\) 0 0
\(277\) −9.41987 + 16.3157i −0.565985 + 0.980315i 0.430972 + 0.902365i \(0.358171\pi\)
−0.996957 + 0.0779498i \(0.975163\pi\)
\(278\) 0 0
\(279\) 1.16864 0.980608i 0.0699648 0.0587074i
\(280\) 0 0
\(281\) −30.1565 10.9761i −1.79899 0.654778i −0.998460 0.0554820i \(-0.982330\pi\)
−0.800528 0.599296i \(-0.795447\pi\)
\(282\) 0 0
\(283\) 0.903537 5.12421i 0.0537097 0.304603i −0.946105 0.323860i \(-0.895019\pi\)
0.999815 + 0.0192577i \(0.00613028\pi\)
\(284\) 0 0
\(285\) 6.88795 0.179971i 0.408007 0.0106606i
\(286\) 0 0
\(287\) 5.02318 28.4878i 0.296509 1.68158i
\(288\) 0 0
\(289\) −6.20355 2.25791i −0.364915 0.132818i
\(290\) 0 0
\(291\) 1.17100 0.982588i 0.0686454 0.0576003i
\(292\) 0 0
\(293\) −4.72077 + 8.17662i −0.275790 + 0.477683i −0.970334 0.241767i \(-0.922273\pi\)
0.694544 + 0.719450i \(0.255606\pi\)
\(294\) 0 0
\(295\) −1.53157 8.68599i −0.0891717 0.505718i
\(296\) 0 0
\(297\) −9.51510 16.4806i −0.552122 0.956303i
\(298\) 0 0
\(299\) 20.6081 7.50073i 1.19180 0.433779i
\(300\) 0 0
\(301\) −30.8351 25.8737i −1.77730 1.49134i
\(302\) 0 0
\(303\) −16.1495 −0.927767
\(304\) 0 0
\(305\) −7.65616 −0.438391
\(306\) 0 0
\(307\) −0.260664 0.218723i −0.0148769 0.0124832i 0.635319 0.772250i \(-0.280869\pi\)
−0.650196 + 0.759767i \(0.725313\pi\)
\(308\) 0 0
\(309\) 0.869688 0.316541i 0.0494748 0.0180074i
\(310\) 0 0
\(311\) −1.14512 1.98340i −0.0649337 0.112468i 0.831731 0.555179i \(-0.187350\pi\)
−0.896665 + 0.442711i \(0.854017\pi\)
\(312\) 0 0
\(313\) −4.51557 25.6091i −0.255235 1.44751i −0.795468 0.605995i \(-0.792775\pi\)
0.540233 0.841515i \(-0.318336\pi\)
\(314\) 0 0
\(315\) 0.892012 1.54501i 0.0502592 0.0870514i
\(316\) 0 0
\(317\) −23.6442 + 19.8398i −1.32799 + 1.11432i −0.343449 + 0.939171i \(0.611595\pi\)
−0.984543 + 0.175145i \(0.943960\pi\)
\(318\) 0 0
\(319\) 6.17292 + 2.24676i 0.345617 + 0.125794i
\(320\) 0 0
\(321\) −0.206696 + 1.17223i −0.0115366 + 0.0654276i
\(322\) 0 0
\(323\) 4.22066 + 20.7513i 0.234844 + 1.15464i
\(324\) 0 0
\(325\) −0.557893 + 3.16397i −0.0309463 + 0.175505i
\(326\) 0 0
\(327\) −25.9811 9.45634i −1.43676 0.522937i
\(328\) 0 0
\(329\) 14.1296 11.8562i 0.778992 0.653652i
\(330\) 0 0
\(331\) 7.63635 13.2265i 0.419732 0.726996i −0.576181 0.817322i \(-0.695458\pi\)
0.995912 + 0.0903260i \(0.0287909\pi\)
\(332\) 0 0
\(333\) −0.680067 3.85685i −0.0372674 0.211354i
\(334\) 0 0
\(335\) 3.33254 + 5.77213i 0.182076 + 0.315365i
\(336\) 0 0
\(337\) 4.75785 1.73172i 0.259177 0.0943327i −0.209164 0.977881i \(-0.567074\pi\)
0.468341 + 0.883548i \(0.344852\pi\)
\(338\) 0 0
\(339\) −1.25327 1.05162i −0.0680682 0.0571160i
\(340\) 0 0
\(341\) 10.4649 0.566704
\(342\) 0 0
\(343\) 4.74225 0.256057
\(344\) 0 0
\(345\) −8.26584 6.93586i −0.445018 0.373414i
\(346\) 0 0
\(347\) −7.71229 + 2.80704i −0.414017 + 0.150690i −0.540627 0.841263i \(-0.681813\pi\)
0.126609 + 0.991953i \(0.459591\pi\)
\(348\) 0 0
\(349\) 8.00920 + 13.8723i 0.428723 + 0.742569i 0.996760 0.0804334i \(-0.0256304\pi\)
−0.568037 + 0.823003i \(0.692297\pi\)
\(350\) 0 0
\(351\) 3.08770 + 17.5112i 0.164809 + 0.934680i
\(352\) 0 0
\(353\) −15.2156 + 26.3543i −0.809847 + 1.40270i 0.103123 + 0.994669i \(0.467116\pi\)
−0.912970 + 0.408027i \(0.866217\pi\)
\(354\) 0 0
\(355\) 6.24652 5.24145i 0.331531 0.278187i
\(356\) 0 0
\(357\) −25.6842 9.34828i −1.35935 0.494763i
\(358\) 0 0
\(359\) −0.324004 + 1.83752i −0.0171003 + 0.0969806i −0.992163 0.124947i \(-0.960124\pi\)
0.975063 + 0.221928i \(0.0712349\pi\)
\(360\) 0 0
\(361\) 13.8972 12.9564i 0.731432 0.681914i
\(362\) 0 0
\(363\) 0.225833 1.28076i 0.0118532 0.0672226i
\(364\) 0 0
\(365\) −7.20628 2.62287i −0.377194 0.137287i
\(366\) 0 0
\(367\) −24.3882 + 20.4641i −1.27305 + 1.06822i −0.278891 + 0.960323i \(0.589967\pi\)
−0.994162 + 0.107896i \(0.965589\pi\)
\(368\) 0 0
\(369\) −2.03697 + 3.52813i −0.106040 + 0.183667i
\(370\) 0 0
\(371\) 4.58974 + 26.0297i 0.238287 + 1.35139i
\(372\) 0 0
\(373\) −1.59251 2.75831i −0.0824572 0.142820i 0.821848 0.569707i \(-0.192943\pi\)
−0.904305 + 0.426887i \(0.859610\pi\)
\(374\) 0 0
\(375\) 1.48541 0.540646i 0.0767064 0.0279189i
\(376\) 0 0
\(377\) −4.70198 3.94543i −0.242164 0.203200i
\(378\) 0 0
\(379\) 37.5855 1.93064 0.965320 0.261070i \(-0.0840753\pi\)
0.965320 + 0.261070i \(0.0840753\pi\)
\(380\) 0 0
\(381\) 3.04086 0.155788
\(382\) 0 0
\(383\) −11.5073 9.65579i −0.587997 0.493388i 0.299566 0.954076i \(-0.403158\pi\)
−0.887562 + 0.460688i \(0.847603\pi\)
\(384\) 0 0
\(385\) 11.4998 4.18560i 0.586086 0.213318i
\(386\) 0 0
\(387\) 2.83444 + 4.90940i 0.144083 + 0.249559i
\(388\) 0 0
\(389\) −3.79034 21.4961i −0.192178 1.08990i −0.916381 0.400308i \(-0.868903\pi\)
0.724203 0.689587i \(-0.242208\pi\)
\(390\) 0 0
\(391\) 16.5811 28.7193i 0.838541 1.45240i
\(392\) 0 0
\(393\) 16.4181 13.7764i 0.828181 0.694927i
\(394\) 0 0
\(395\) −12.7814 4.65204i −0.643100 0.234069i
\(396\) 0 0
\(397\) 4.20882 23.8694i 0.211235 1.19797i −0.676088 0.736821i \(-0.736326\pi\)
0.887322 0.461150i \(-0.152563\pi\)
\(398\) 0 0
\(399\) 4.88785 + 24.0316i 0.244699 + 1.20309i
\(400\) 0 0
\(401\) 3.79091 21.4993i 0.189309 1.07363i −0.730983 0.682395i \(-0.760938\pi\)
0.920293 0.391231i \(-0.127951\pi\)
\(402\) 0 0
\(403\) −9.18842 3.34431i −0.457708 0.166592i
\(404\) 0 0
\(405\) 5.54999 4.65700i 0.275781 0.231408i
\(406\) 0 0
\(407\) 13.4325 23.2658i 0.665824 1.15324i
\(408\) 0 0
\(409\) 1.53859 + 8.72579i 0.0760785 + 0.431463i 0.998928 + 0.0463008i \(0.0147433\pi\)
−0.922849 + 0.385162i \(0.874146\pi\)
\(410\) 0 0
\(411\) 2.60790 + 4.51702i 0.128638 + 0.222808i
\(412\) 0 0
\(413\) 29.4985 10.7366i 1.45153 0.528313i
\(414\) 0 0
\(415\) −12.5893 10.5637i −0.617984 0.518550i
\(416\) 0 0
\(417\) −6.11800 −0.299600
\(418\) 0 0
\(419\) −13.0697 −0.638496 −0.319248 0.947671i \(-0.603430\pi\)
−0.319248 + 0.947671i \(0.603430\pi\)
\(420\) 0 0
\(421\) 11.9984 + 10.0678i 0.584764 + 0.490675i 0.886508 0.462714i \(-0.153124\pi\)
−0.301744 + 0.953389i \(0.597569\pi\)
\(422\) 0 0
\(423\) −2.44101 + 0.888454i −0.118686 + 0.0431981i
\(424\) 0 0
\(425\) 2.42908 + 4.20729i 0.117828 + 0.204083i
\(426\) 0 0
\(427\) −4.73182 26.8355i −0.228989 1.29866i
\(428\) 0 0
\(429\) −8.73114 + 15.1228i −0.421543 + 0.730135i
\(430\) 0 0
\(431\) −11.3818 + 9.55043i −0.548240 + 0.460028i −0.874344 0.485306i \(-0.838708\pi\)
0.326105 + 0.945334i \(0.394264\pi\)
\(432\) 0 0
\(433\) 22.3940 + 8.15074i 1.07619 + 0.391700i 0.818487 0.574526i \(-0.194813\pi\)
0.257699 + 0.966225i \(0.417036\pi\)
\(434\) 0 0
\(435\) −0.524418 + 2.97412i −0.0251439 + 0.142598i
\(436\) 0 0
\(437\) −29.7440 + 0.777164i −1.42285 + 0.0371768i
\(438\) 0 0
\(439\) 3.72592 21.1307i 0.177828 1.00852i −0.757000 0.653415i \(-0.773336\pi\)
0.934828 0.355100i \(-0.115553\pi\)
\(440\) 0 0
\(441\) 2.66955 + 0.971636i 0.127121 + 0.0462684i
\(442\) 0 0
\(443\) −29.3056 + 24.5903i −1.39235 + 1.16832i −0.427973 + 0.903791i \(0.640772\pi\)
−0.964378 + 0.264530i \(0.914783\pi\)
\(444\) 0 0
\(445\) 1.78991 3.10021i 0.0848497 0.146964i
\(446\) 0 0
\(447\) 5.95741 + 33.7861i 0.281776 + 1.59803i
\(448\) 0 0
\(449\) −9.36701 16.2241i −0.442056 0.765664i 0.555786 0.831326i \(-0.312418\pi\)
−0.997842 + 0.0656615i \(0.979084\pi\)
\(450\) 0 0
\(451\) −26.2607 + 9.55810i −1.23657 + 0.450073i
\(452\) 0 0
\(453\) 24.9850 + 20.9649i 1.17390 + 0.985016i
\(454\) 0 0
\(455\) −11.4348 −0.536071
\(456\) 0 0
\(457\) −23.4274 −1.09589 −0.547943 0.836516i \(-0.684589\pi\)
−0.547943 + 0.836516i \(0.684589\pi\)
\(458\) 0 0
\(459\) 20.5973 + 17.2832i 0.961399 + 0.806709i
\(460\) 0 0
\(461\) 27.2784 9.92851i 1.27048 0.462417i 0.383207 0.923662i \(-0.374819\pi\)
0.887273 + 0.461245i \(0.152597\pi\)
\(462\) 0 0
\(463\) −4.54270 7.86818i −0.211117 0.365665i 0.740947 0.671563i \(-0.234377\pi\)
−0.952064 + 0.305898i \(0.901043\pi\)
\(464\) 0 0
\(465\) 0.835422 + 4.73792i 0.0387418 + 0.219716i
\(466\) 0 0
\(467\) −5.74457 + 9.94989i −0.265827 + 0.460426i −0.967780 0.251797i \(-0.918978\pi\)
0.701953 + 0.712223i \(0.252312\pi\)
\(468\) 0 0
\(469\) −18.1722 + 15.2483i −0.839112 + 0.704099i
\(470\) 0 0
\(471\) −14.6568 5.33465i −0.675351 0.245808i
\(472\) 0 0
\(473\) −6.75263 + 38.2961i −0.310486 + 1.76086i
\(474\) 0 0
\(475\) 2.08011 3.83056i 0.0954419 0.175758i
\(476\) 0 0
\(477\) 0.646389 3.66586i 0.0295961 0.167848i
\(478\) 0 0
\(479\) −21.3314 7.76399i −0.974656 0.354746i −0.194896 0.980824i \(-0.562437\pi\)
−0.779760 + 0.626078i \(0.784659\pi\)
\(480\) 0 0
\(481\) −19.2293 + 16.1353i −0.876779 + 0.735705i
\(482\) 0 0
\(483\) 19.2022 33.2591i 0.873728 1.51334i
\(484\) 0 0
\(485\) −0.167924 0.952344i −0.00762504 0.0432437i
\(486\) 0 0
\(487\) −10.0120 17.3412i −0.453685 0.785806i 0.544926 0.838484i \(-0.316558\pi\)
−0.998612 + 0.0526778i \(0.983224\pi\)
\(488\) 0 0
\(489\) 12.1361 4.41718i 0.548813 0.199752i
\(490\) 0 0
\(491\) −3.83634 3.21907i −0.173132 0.145275i 0.552104 0.833775i \(-0.313825\pi\)
−0.725236 + 0.688500i \(0.758269\pi\)
\(492\) 0 0
\(493\) −9.28149 −0.418017
\(494\) 0 0
\(495\) −1.72350 −0.0774657
\(496\) 0 0
\(497\) 22.2323 + 18.6551i 0.997257 + 0.836798i
\(498\) 0 0
\(499\) 23.3303 8.49153i 1.04441 0.380133i 0.237858 0.971300i \(-0.423555\pi\)
0.806549 + 0.591167i \(0.201332\pi\)
\(500\) 0 0
\(501\) 8.59309 + 14.8837i 0.383911 + 0.664953i
\(502\) 0 0
\(503\) 0.109422 + 0.620563i 0.00487888 + 0.0276695i 0.987150 0.159796i \(-0.0510837\pi\)
−0.982271 + 0.187466i \(0.939973\pi\)
\(504\) 0 0
\(505\) −5.10821 + 8.84768i −0.227312 + 0.393716i
\(506\) 0 0
\(507\) −3.24292 + 2.72113i −0.144023 + 0.120850i
\(508\) 0 0
\(509\) 2.83497 + 1.03185i 0.125658 + 0.0457357i 0.404084 0.914722i \(-0.367590\pi\)
−0.278426 + 0.960458i \(0.589813\pi\)
\(510\) 0 0
\(511\) 4.73961 26.8797i 0.209668 1.18909i
\(512\) 0 0
\(513\) 3.56722 23.8595i 0.157497 1.05342i
\(514\) 0 0
\(515\) 0.101669 0.576591i 0.00448005 0.0254076i
\(516\) 0 0
\(517\) −16.7446 6.09453i −0.736426 0.268037i
\(518\) 0 0
\(519\) −5.04107 + 4.22996i −0.221279 + 0.185675i
\(520\) 0 0
\(521\) 7.60555 13.1732i 0.333205 0.577129i −0.649933 0.759991i \(-0.725203\pi\)
0.983138 + 0.182863i \(0.0585364\pi\)
\(522\) 0 0
\(523\) −2.48329 14.0834i −0.108587 0.615825i −0.989727 0.142970i \(-0.954335\pi\)
0.881141 0.472855i \(-0.156776\pi\)
\(524\) 0 0
\(525\) 2.81306 + 4.87236i 0.122772 + 0.212647i
\(526\) 0 0
\(527\) −13.8941 + 5.05705i −0.605238 + 0.220289i
\(528\) 0 0
\(529\) 18.0751 + 15.1668i 0.785874 + 0.659427i
\(530\) 0 0
\(531\) −4.42101 −0.191855
\(532\) 0 0
\(533\) 26.1121 1.13104
\(534\) 0 0
\(535\) 0.576839 + 0.484025i 0.0249389 + 0.0209262i
\(536\) 0 0
\(537\) −18.2587 + 6.64562i −0.787921 + 0.286780i
\(538\) 0 0
\(539\) 9.74378 + 16.8767i 0.419694 + 0.726932i
\(540\) 0 0
\(541\) 7.94419 + 45.0537i 0.341547 + 1.93701i 0.349222 + 0.937040i \(0.386446\pi\)
−0.00767520 + 0.999971i \(0.502443\pi\)
\(542\) 0 0
\(543\) −19.9667 + 34.5834i −0.856854 + 1.48412i
\(544\) 0 0
\(545\) −13.3987 + 11.2429i −0.573939 + 0.481592i
\(546\) 0 0
\(547\) 31.6845 + 11.5322i 1.35473 + 0.493081i 0.914421 0.404765i \(-0.132647\pi\)
0.440309 + 0.897846i \(0.354869\pi\)
\(548\) 0 0
\(549\) −0.666400 + 3.77934i −0.0284412 + 0.161298i
\(550\) 0 0
\(551\) 4.35078 + 7.10074i 0.185349 + 0.302502i
\(552\) 0 0
\(553\) 8.40637 47.6749i 0.357475 2.02734i
\(554\) 0 0
\(555\) 11.6058 + 4.22417i 0.492639 + 0.179306i
\(556\) 0 0
\(557\) 21.8724 18.3531i 0.926762 0.777646i −0.0484714 0.998825i \(-0.515435\pi\)
0.975233 + 0.221179i \(0.0709905\pi\)
\(558\) 0 0
\(559\) 18.1675 31.4670i 0.768403 1.33091i
\(560\) 0 0
\(561\) 4.58524 + 26.0042i 0.193589 + 1.09790i
\(562\) 0 0
\(563\) 14.6828 + 25.4313i 0.618806 + 1.07180i 0.989704 + 0.143129i \(0.0457164\pi\)
−0.370898 + 0.928673i \(0.620950\pi\)
\(564\) 0 0
\(565\) −0.972556 + 0.353981i −0.0409157 + 0.0148921i
\(566\) 0 0
\(567\) 19.7533 + 16.5750i 0.829560 + 0.696084i
\(568\) 0 0
\(569\) −18.9129 −0.792868 −0.396434 0.918063i \(-0.629752\pi\)
−0.396434 + 0.918063i \(0.629752\pi\)
\(570\) 0 0
\(571\) −4.56984 −0.191242 −0.0956210 0.995418i \(-0.530484\pi\)
−0.0956210 + 0.995418i \(0.530484\pi\)
\(572\) 0 0
\(573\) 7.25076 + 6.08411i 0.302905 + 0.254167i
\(574\) 0 0
\(575\) −6.41442 + 2.33466i −0.267500 + 0.0973619i
\(576\) 0 0
\(577\) 5.67068 + 9.82191i 0.236074 + 0.408892i 0.959584 0.281422i \(-0.0908060\pi\)
−0.723511 + 0.690313i \(0.757473\pi\)
\(578\) 0 0
\(579\) 4.35157 + 24.6790i 0.180845 + 1.02562i
\(580\) 0 0
\(581\) 29.2459 50.6553i 1.21332 2.10154i
\(582\) 0 0
\(583\) 19.5606 16.4133i 0.810119 0.679771i
\(584\) 0 0
\(585\) 1.51328 + 0.550790i 0.0625665 + 0.0227723i
\(586\) 0 0
\(587\) −0.221815 + 1.25798i −0.00915530 + 0.0519223i −0.989043 0.147627i \(-0.952837\pi\)
0.979888 + 0.199549i \(0.0639477\pi\)
\(588\) 0 0
\(589\) 10.3819 + 8.25909i 0.427778 + 0.340310i
\(590\) 0 0
\(591\) −0.0141063 + 0.0800009i −0.000580256 + 0.00329080i
\(592\) 0 0
\(593\) 37.0067 + 13.4693i 1.51968 + 0.553120i 0.961069 0.276308i \(-0.0891109\pi\)
0.558615 + 0.829427i \(0.311333\pi\)
\(594\) 0 0
\(595\) −13.2456 + 11.1144i −0.543018 + 0.455646i
\(596\) 0 0
\(597\) 3.99197 6.91429i 0.163380 0.282983i
\(598\) 0 0
\(599\) −1.75174 9.93461i −0.0715741 0.405917i −0.999454 0.0330380i \(-0.989482\pi\)
0.927880 0.372879i \(-0.121629\pi\)
\(600\) 0 0
\(601\) −7.99956 13.8556i −0.326309 0.565184i 0.655467 0.755223i \(-0.272472\pi\)
−0.981776 + 0.190040i \(0.939138\pi\)
\(602\) 0 0
\(603\) 3.13939 1.14264i 0.127846 0.0465320i
\(604\) 0 0
\(605\) −0.630245 0.528838i −0.0256231 0.0215003i
\(606\) 0 0
\(607\) 34.5238 1.40128 0.700639 0.713516i \(-0.252898\pi\)
0.700639 + 0.713516i \(0.252898\pi\)
\(608\) 0 0
\(609\) −10.7487 −0.435558
\(610\) 0 0
\(611\) 12.7545 + 10.7023i 0.515993 + 0.432969i
\(612\) 0 0
\(613\) 14.6354 5.32686i 0.591119 0.215150i −0.0291024 0.999576i \(-0.509265\pi\)
0.620222 + 0.784427i \(0.287043\pi\)
\(614\) 0 0
\(615\) −6.42381 11.1264i −0.259033 0.448658i
\(616\) 0 0
\(617\) 3.11076 + 17.6420i 0.125234 + 0.710240i 0.981168 + 0.193155i \(0.0618719\pi\)
−0.855934 + 0.517085i \(0.827017\pi\)
\(618\) 0 0
\(619\) −16.3044 + 28.2401i −0.655330 + 1.13507i 0.326480 + 0.945204i \(0.394137\pi\)
−0.981811 + 0.189862i \(0.939196\pi\)
\(620\) 0 0
\(621\) −28.9408 + 24.2842i −1.16135 + 0.974490i
\(622\) 0 0
\(623\) 11.9727 + 4.35772i 0.479677 + 0.174588i
\(624\) 0 0
\(625\) 0.173648 0.984808i 0.00694593 0.0393923i
\(626\) 0 0
\(627\) 17.7450 15.6976i 0.708666 0.626902i
\(628\) 0 0
\(629\) −6.59128 + 37.3810i −0.262812 + 1.49048i
\(630\) 0 0
\(631\) 11.8466 + 4.31180i 0.471604 + 0.171650i 0.566879 0.823801i \(-0.308151\pi\)
−0.0952746 + 0.995451i \(0.530373\pi\)
\(632\) 0 0
\(633\) −29.0965 + 24.4149i −1.15648 + 0.970404i
\(634\) 0 0
\(635\) 0.961845 1.66597i 0.0381697 0.0661118i
\(636\) 0 0
\(637\) −3.16191 17.9321i −0.125279 0.710495i
\(638\) 0 0
\(639\) −2.04365 3.53971i −0.0808457 0.140029i
\(640\) 0 0
\(641\) 21.4326 7.80083i 0.846537 0.308114i 0.117909 0.993024i \(-0.462381\pi\)
0.728627 + 0.684910i \(0.240159\pi\)
\(642\) 0 0
\(643\) −24.8012 20.8106i −0.978062 0.820692i 0.00573352 0.999984i \(-0.498175\pi\)
−0.983796 + 0.179292i \(0.942619\pi\)
\(644\) 0 0
\(645\) −17.8775 −0.703924
\(646\) 0 0
\(647\) −4.51050 −0.177326 −0.0886630 0.996062i \(-0.528259\pi\)
−0.0886630 + 0.996062i \(0.528259\pi\)
\(648\) 0 0
\(649\) −23.2317 19.4937i −0.911923 0.765194i
\(650\) 0 0
\(651\) −16.0905 + 5.85645i −0.630635 + 0.229532i
\(652\) 0 0
\(653\) 5.78138 + 10.0136i 0.226243 + 0.391864i 0.956692 0.291103i \(-0.0940223\pi\)
−0.730449 + 0.682968i \(0.760689\pi\)
\(654\) 0 0
\(655\) −2.35438 13.3523i −0.0919932 0.521719i
\(656\) 0 0
\(657\) −1.92198 + 3.32897i −0.0749836 + 0.129875i
\(658\) 0 0
\(659\) 13.4591 11.2935i 0.524291 0.439932i −0.341834 0.939760i \(-0.611048\pi\)
0.866125 + 0.499828i \(0.166603\pi\)
\(660\) 0 0
\(661\) −3.55033 1.29221i −0.138092 0.0502613i 0.272050 0.962283i \(-0.412298\pi\)
−0.410142 + 0.912022i \(0.634521\pi\)
\(662\) 0 0
\(663\) 4.28434 24.2977i 0.166390 0.943644i
\(664\) 0 0
\(665\) 14.7120 + 4.92351i 0.570507 + 0.190926i
\(666\) 0 0
\(667\) 2.26458 12.8431i 0.0876849 0.497286i
\(668\) 0 0
\(669\) 25.2968 + 9.20728i 0.978030 + 0.355974i
\(670\) 0 0
\(671\) −20.1662 + 16.9214i −0.778507 + 0.653245i
\(672\) 0 0
\(673\) −18.3166 + 31.7253i −0.706053 + 1.22292i 0.260257 + 0.965539i \(0.416193\pi\)
−0.966310 + 0.257380i \(0.917141\pi\)
\(674\) 0 0
\(675\) −0.961069 5.45049i −0.0369916 0.209790i
\(676\) 0 0
\(677\) −16.8483 29.1822i −0.647534 1.12156i −0.983710 0.179763i \(-0.942467\pi\)
0.336176 0.941799i \(-0.390866\pi\)
\(678\) 0 0
\(679\) 3.23426 1.17718i 0.124120 0.0451759i
\(680\) 0 0
\(681\) 9.56611 + 8.02692i 0.366574 + 0.307592i
\(682\) 0 0
\(683\) 14.9190 0.570861 0.285430 0.958399i \(-0.407864\pi\)
0.285430 + 0.958399i \(0.407864\pi\)
\(684\) 0 0
\(685\) 3.29959 0.126071
\(686\) 0 0
\(687\) −6.82563 5.72738i −0.260414 0.218513i
\(688\) 0 0
\(689\) −22.4201 + 8.16024i −0.854137 + 0.310880i
\(690\) 0 0
\(691\) 21.8621 + 37.8663i 0.831675 + 1.44050i 0.896709 + 0.442621i \(0.145951\pi\)
−0.0650338 + 0.997883i \(0.520716\pi\)
\(692\) 0 0
\(693\) −1.06520 6.04103i −0.0404635 0.229480i
\(694\) 0 0
\(695\) −1.93516 + 3.35180i −0.0734050 + 0.127141i
\(696\) 0 0
\(697\) 30.2473 25.3805i 1.14570 0.961355i
\(698\) 0 0
\(699\) 0.614067 + 0.223502i 0.0232261 + 0.00845362i
\(700\) 0 0
\(701\) 3.52875 20.0125i 0.133279 0.755862i −0.842764 0.538283i \(-0.819073\pi\)
0.976043 0.217579i \(-0.0698159\pi\)
\(702\) 0 0
\(703\) 31.6878 12.4801i 1.19513 0.470695i
\(704\) 0 0
\(705\) 1.42253 8.06757i 0.0535756 0.303842i
\(706\) 0 0
\(707\) −34.1689 12.4365i −1.28506 0.467722i
\(708\) 0 0
\(709\) −1.81966 + 1.52687i −0.0683387 + 0.0573429i −0.676317 0.736611i \(-0.736425\pi\)
0.607979 + 0.793953i \(0.291981\pi\)
\(710\) 0 0
\(711\) −3.40890 + 5.90440i −0.127844 + 0.221432i
\(712\) 0 0
\(713\) −3.60758 20.4596i −0.135105 0.766218i
\(714\) 0 0
\(715\) 5.52344 + 9.56687i 0.206565 + 0.357781i
\(716\) 0 0
\(717\) −1.16248 + 0.423107i −0.0434135 + 0.0158012i
\(718\) 0 0
\(719\) −25.0761 21.0413i −0.935179 0.784708i 0.0415609 0.999136i \(-0.486767\pi\)
−0.976740 + 0.214428i \(0.931211\pi\)
\(720\) 0 0
\(721\) 2.08384 0.0776061
\(722\) 0 0
\(723\) −16.1214 −0.599560
\(724\) 0 0
\(725\) 1.46352 + 1.22804i 0.0543539 + 0.0456084i
\(726\) 0 0
\(727\) −3.43792 + 1.25130i −0.127506 + 0.0464082i −0.404985 0.914323i \(-0.632723\pi\)
0.277479 + 0.960732i \(0.410501\pi\)
\(728\) 0 0
\(729\) −14.9389 25.8749i −0.553293 0.958331i
\(730\) 0 0
\(731\) −9.54082 54.1087i −0.352880 2.00128i
\(732\) 0 0
\(733\) −13.5536 + 23.4755i −0.500614 + 0.867088i 0.499386 + 0.866379i \(0.333559\pi\)
−1.00000 0.000708563i \(0.999774\pi\)
\(734\) 0 0
\(735\) −6.86300 + 5.75874i −0.253146 + 0.212414i
\(736\) 0 0
\(737\) 21.5353 + 7.83820i 0.793262 + 0.288724i
\(738\) 0 0
\(739\) 1.34091 7.60465i 0.0493260 0.279742i −0.950161 0.311759i \(-0.899082\pi\)
0.999487 + 0.0320170i \(0.0101931\pi\)
\(740\) 0 0
\(741\) −20.5971 + 8.11206i −0.756654 + 0.298004i
\(742\) 0 0
\(743\) −1.88374 + 10.6832i −0.0691077 + 0.391929i 0.930560 + 0.366140i \(0.119321\pi\)
−0.999667 + 0.0257890i \(0.991790\pi\)
\(744\) 0 0
\(745\) 20.3944 + 7.42296i 0.747194 + 0.271956i
\(746\) 0 0
\(747\) −6.31037 + 5.29503i −0.230884 + 0.193735i
\(748\) 0 0
\(749\) −1.34004 + 2.32102i −0.0489639 + 0.0848080i
\(750\) 0 0
\(751\) 2.92223 + 16.5728i 0.106634 + 0.604750i 0.990555 + 0.137115i \(0.0437829\pi\)
−0.883921 + 0.467636i \(0.845106\pi\)
\(752\) 0 0
\(753\) 14.3967 + 24.9358i 0.524645 + 0.908711i
\(754\) 0 0
\(755\) 19.3887 7.05692i 0.705628 0.256827i
\(756\) 0 0
\(757\) 2.07783 + 1.74350i 0.0755199 + 0.0633687i 0.679766 0.733429i \(-0.262081\pi\)
−0.604246 + 0.796798i \(0.706526\pi\)
\(758\) 0 0
\(759\) −37.1015 −1.34670
\(760\) 0 0
\(761\) −15.0957 −0.547219 −0.273609 0.961841i \(-0.588218\pi\)
−0.273609 + 0.961841i \(0.588218\pi\)
\(762\) 0 0
\(763\) −47.6882 40.0151i −1.72643 1.44865i
\(764\) 0 0
\(765\) 2.28829 0.832869i 0.0827332 0.0301124i
\(766\) 0 0
\(767\) 14.1683 + 24.5402i 0.511588 + 0.886097i
\(768\) 0 0
\(769\) −5.01576 28.4458i −0.180873 1.02578i −0.931144 0.364652i \(-0.881188\pi\)
0.750271 0.661130i \(-0.229923\pi\)
\(770\) 0 0
\(771\) 13.9393 24.1436i 0.502013 0.869512i
\(772\) 0 0
\(773\) −30.6310 + 25.7025i −1.10172 + 0.924454i −0.997540 0.0701039i \(-0.977667\pi\)
−0.104182 + 0.994558i \(0.533222\pi\)
\(774\) 0 0
\(775\) 2.85996 + 1.04094i 0.102733 + 0.0373917i
\(776\) 0 0
\(777\) −7.63320 + 43.2900i −0.273840 + 1.55302i
\(778\) 0 0
\(779\) −33.5959 11.2432i −1.20370 0.402828i
\(780\) 0 0
\(781\) 4.86870 27.6118i 0.174216 0.988027i
\(782\) 0 0
\(783\) 9.93611 + 3.61645i 0.355088 + 0.129241i
\(784\) 0 0
\(785\) −7.55869 + 6.34249i −0.269781 + 0.226373i
\(786\) 0 0
\(787\) −3.36252 + 5.82405i −0.119861 + 0.207605i −0.919712 0.392593i