Properties

Label 225.2.h.a.91.1
Level $225$
Weight $2$
Character 225.91
Analytic conductor $1.797$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,2,Mod(46,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.46");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), 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: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 225.91
Dual form 225.2.h.a.136.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-0.690983 + 2.12663i) q^{5} +4.47214 q^{7} +(0.927051 - 2.85317i) q^{8} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-0.690983 + 2.12663i) q^{5} +4.47214 q^{7} +(0.927051 - 2.85317i) q^{8} +(-1.80902 + 1.31433i) q^{10} +(2.61803 + 1.90211i) q^{11} +(-2.73607 + 1.98787i) q^{13} +(3.61803 + 2.62866i) q^{14} +(0.809017 - 0.587785i) q^{16} +(0.881966 - 2.71441i) q^{17} +(-1.00000 + 3.07768i) q^{19} +2.23607 q^{20} +(1.00000 + 3.07768i) q^{22} +(-3.61803 - 2.62866i) q^{23} +(-4.04508 - 2.93893i) q^{25} -3.38197 q^{26} +(-1.38197 - 4.25325i) q^{28} +(-1.35410 - 4.16750i) q^{29} +(2.23607 - 6.88191i) q^{31} -5.00000 q^{32} +(2.30902 - 1.67760i) q^{34} +(-3.09017 + 9.51057i) q^{35} +(-6.54508 + 4.75528i) q^{37} +(-2.61803 + 1.90211i) q^{38} +(5.42705 + 3.94298i) q^{40} +(-1.11803 + 0.812299i) q^{41} -5.70820 q^{43} +(1.00000 - 3.07768i) q^{44} +(-1.38197 - 4.25325i) q^{46} +(1.61803 + 4.97980i) q^{47} +13.0000 q^{49} +(-1.54508 - 4.75528i) q^{50} +(2.73607 + 1.98787i) q^{52} +(-0.427051 - 1.31433i) q^{53} +(-5.85410 + 4.25325i) q^{55} +(4.14590 - 12.7598i) q^{56} +(1.35410 - 4.16750i) q^{58} +(-3.23607 + 2.35114i) q^{59} +(0.500000 + 0.363271i) q^{61} +(5.85410 - 4.25325i) q^{62} +(-5.66312 - 4.11450i) q^{64} +(-2.33688 - 7.19218i) q^{65} +(1.61803 - 4.97980i) q^{67} -2.85410 q^{68} +(-8.09017 + 5.87785i) q^{70} +(0.236068 + 0.726543i) q^{71} +(-2.50000 - 1.81636i) q^{73} -8.09017 q^{74} +3.23607 q^{76} +(11.7082 + 8.50651i) q^{77} +(0.690983 + 2.12663i) q^{80} -1.38197 q^{82} +(-1.09017 + 3.35520i) q^{83} +(5.16312 + 3.75123i) q^{85} +(-4.61803 - 3.35520i) q^{86} +(7.85410 - 5.70634i) q^{88} +(6.16312 + 4.47777i) q^{89} +(-12.2361 + 8.89002i) q^{91} +(-1.38197 + 4.25325i) q^{92} +(-1.61803 + 4.97980i) q^{94} +(-5.85410 - 4.25325i) q^{95} +(2.73607 + 8.42075i) q^{97} +(10.5172 + 7.64121i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} + q^{4} - 5 q^{5} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} + q^{4} - 5 q^{5} - 3 q^{8} - 5 q^{10} + 6 q^{11} - 2 q^{13} + 10 q^{14} + q^{16} + 8 q^{17} - 4 q^{19} + 4 q^{22} - 10 q^{23} - 5 q^{25} - 18 q^{26} - 10 q^{28} + 8 q^{29} - 20 q^{32} + 7 q^{34} + 10 q^{35} - 15 q^{37} - 6 q^{38} + 15 q^{40} + 4 q^{43} + 4 q^{44} - 10 q^{46} + 2 q^{47} + 52 q^{49} + 5 q^{50} + 2 q^{52} + 5 q^{53} - 10 q^{55} + 30 q^{56} - 8 q^{58} - 4 q^{59} + 2 q^{61} + 10 q^{62} - 7 q^{64} - 25 q^{65} + 2 q^{67} + 2 q^{68} - 10 q^{70} - 8 q^{71} - 10 q^{73} - 10 q^{74} + 4 q^{76} + 20 q^{77} + 5 q^{80} - 10 q^{82} + 18 q^{83} + 5 q^{85} - 14 q^{86} + 18 q^{88} + 9 q^{89} - 40 q^{91} - 10 q^{92} - 2 q^{94} - 10 q^{95} + 2 q^{97} + 13 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.572061 + 0.415627i 0.835853 0.548953i \(-0.184973\pi\)
−0.263792 + 0.964580i \(0.584973\pi\)
\(3\) 0 0
\(4\) −0.309017 0.951057i −0.154508 0.475528i
\(5\) −0.690983 + 2.12663i −0.309017 + 0.951057i
\(6\) 0 0
\(7\) 4.47214 1.69031 0.845154 0.534522i \(-0.179509\pi\)
0.845154 + 0.534522i \(0.179509\pi\)
\(8\) 0.927051 2.85317i 0.327762 1.00875i
\(9\) 0 0
\(10\) −1.80902 + 1.31433i −0.572061 + 0.415627i
\(11\) 2.61803 + 1.90211i 0.789367 + 0.573509i 0.907776 0.419456i \(-0.137779\pi\)
−0.118409 + 0.992965i \(0.537779\pi\)
\(12\) 0 0
\(13\) −2.73607 + 1.98787i −0.758849 + 0.551336i −0.898557 0.438857i \(-0.855384\pi\)
0.139708 + 0.990193i \(0.455384\pi\)
\(14\) 3.61803 + 2.62866i 0.966960 + 0.702538i
\(15\) 0 0
\(16\) 0.809017 0.587785i 0.202254 0.146946i
\(17\) 0.881966 2.71441i 0.213908 0.658342i −0.785321 0.619089i \(-0.787502\pi\)
0.999229 0.0392530i \(-0.0124978\pi\)
\(18\) 0 0
\(19\) −1.00000 + 3.07768i −0.229416 + 0.706069i 0.768398 + 0.639973i \(0.221054\pi\)
−0.997813 + 0.0660962i \(0.978946\pi\)
\(20\) 2.23607 0.500000
\(21\) 0 0
\(22\) 1.00000 + 3.07768i 0.213201 + 0.656164i
\(23\) −3.61803 2.62866i −0.754412 0.548113i 0.142779 0.989755i \(-0.454396\pi\)
−0.897191 + 0.441642i \(0.854396\pi\)
\(24\) 0 0
\(25\) −4.04508 2.93893i −0.809017 0.587785i
\(26\) −3.38197 −0.663258
\(27\) 0 0
\(28\) −1.38197 4.25325i −0.261167 0.803789i
\(29\) −1.35410 4.16750i −0.251450 0.773885i −0.994508 0.104658i \(-0.966625\pi\)
0.743058 0.669227i \(-0.233375\pi\)
\(30\) 0 0
\(31\) 2.23607 6.88191i 0.401610 1.23603i −0.522083 0.852894i \(-0.674845\pi\)
0.923693 0.383133i \(-0.125155\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) 2.30902 1.67760i 0.395993 0.287706i
\(35\) −3.09017 + 9.51057i −0.522334 + 1.60758i
\(36\) 0 0
\(37\) −6.54508 + 4.75528i −1.07601 + 0.781764i −0.976982 0.213321i \(-0.931572\pi\)
−0.0990233 + 0.995085i \(0.531572\pi\)
\(38\) −2.61803 + 1.90211i −0.424701 + 0.308563i
\(39\) 0 0
\(40\) 5.42705 + 3.94298i 0.858092 + 0.623440i
\(41\) −1.11803 + 0.812299i −0.174608 + 0.126860i −0.671657 0.740863i \(-0.734417\pi\)
0.497049 + 0.867722i \(0.334417\pi\)
\(42\) 0 0
\(43\) −5.70820 −0.870493 −0.435246 0.900311i \(-0.643339\pi\)
−0.435246 + 0.900311i \(0.643339\pi\)
\(44\) 1.00000 3.07768i 0.150756 0.463978i
\(45\) 0 0
\(46\) −1.38197 4.25325i −0.203760 0.627108i
\(47\) 1.61803 + 4.97980i 0.236015 + 0.726378i 0.996985 + 0.0775917i \(0.0247231\pi\)
−0.760971 + 0.648786i \(0.775277\pi\)
\(48\) 0 0
\(49\) 13.0000 1.85714
\(50\) −1.54508 4.75528i −0.218508 0.672499i
\(51\) 0 0
\(52\) 2.73607 + 1.98787i 0.379424 + 0.275668i
\(53\) −0.427051 1.31433i −0.0586600 0.180537i 0.917433 0.397890i \(-0.130258\pi\)
−0.976093 + 0.217354i \(0.930258\pi\)
\(54\) 0 0
\(55\) −5.85410 + 4.25325i −0.789367 + 0.573509i
\(56\) 4.14590 12.7598i 0.554019 1.70509i
\(57\) 0 0
\(58\) 1.35410 4.16750i 0.177802 0.547219i
\(59\) −3.23607 + 2.35114i −0.421300 + 0.306092i −0.778161 0.628065i \(-0.783847\pi\)
0.356861 + 0.934158i \(0.383847\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.363271i 0.0640184 + 0.0465121i 0.619334 0.785127i \(-0.287403\pi\)
−0.555316 + 0.831640i \(0.687403\pi\)
\(62\) 5.85410 4.25325i 0.743472 0.540164i
\(63\) 0 0
\(64\) −5.66312 4.11450i −0.707890 0.514312i
\(65\) −2.33688 7.19218i −0.289854 0.892080i
\(66\) 0 0
\(67\) 1.61803 4.97980i 0.197674 0.608379i −0.802261 0.596974i \(-0.796370\pi\)
0.999935 0.0114051i \(-0.00363042\pi\)
\(68\) −2.85410 −0.346111
\(69\) 0 0
\(70\) −8.09017 + 5.87785i −0.966960 + 0.702538i
\(71\) 0.236068 + 0.726543i 0.0280161 + 0.0862247i 0.964087 0.265587i \(-0.0855657\pi\)
−0.936071 + 0.351812i \(0.885566\pi\)
\(72\) 0 0
\(73\) −2.50000 1.81636i −0.292603 0.212588i 0.431793 0.901973i \(-0.357881\pi\)
−0.724396 + 0.689384i \(0.757881\pi\)
\(74\) −8.09017 −0.940463
\(75\) 0 0
\(76\) 3.23607 0.371202
\(77\) 11.7082 + 8.50651i 1.33427 + 0.969407i
\(78\) 0 0
\(79\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(80\) 0.690983 + 2.12663i 0.0772542 + 0.237764i
\(81\) 0 0
\(82\) −1.38197 −0.152613
\(83\) −1.09017 + 3.35520i −0.119662 + 0.368281i −0.992891 0.119029i \(-0.962022\pi\)
0.873229 + 0.487310i \(0.162022\pi\)
\(84\) 0 0
\(85\) 5.16312 + 3.75123i 0.560019 + 0.406878i
\(86\) −4.61803 3.35520i −0.497975 0.361800i
\(87\) 0 0
\(88\) 7.85410 5.70634i 0.837250 0.608298i
\(89\) 6.16312 + 4.47777i 0.653289 + 0.474642i 0.864390 0.502822i \(-0.167705\pi\)
−0.211101 + 0.977464i \(0.567705\pi\)
\(90\) 0 0
\(91\) −12.2361 + 8.89002i −1.28269 + 0.931928i
\(92\) −1.38197 + 4.25325i −0.144080 + 0.443432i
\(93\) 0 0
\(94\) −1.61803 + 4.97980i −0.166887 + 0.513627i
\(95\) −5.85410 4.25325i −0.600618 0.436375i
\(96\) 0 0
\(97\) 2.73607 + 8.42075i 0.277806 + 0.854998i 0.988463 + 0.151460i \(0.0483974\pi\)
−0.710658 + 0.703538i \(0.751603\pi\)
\(98\) 10.5172 + 7.64121i 1.06240 + 0.771879i
\(99\) 0 0
\(100\) −1.54508 + 4.75528i −0.154508 + 0.475528i
\(101\) 16.5623 1.64801 0.824006 0.566582i \(-0.191734\pi\)
0.824006 + 0.566582i \(0.191734\pi\)
\(102\) 0 0
\(103\) −0.381966 1.17557i −0.0376362 0.115832i 0.930473 0.366360i \(-0.119396\pi\)
−0.968110 + 0.250527i \(0.919396\pi\)
\(104\) 3.13525 + 9.64932i 0.307437 + 0.946194i
\(105\) 0 0
\(106\) 0.427051 1.31433i 0.0414789 0.127659i
\(107\) −16.4721 −1.59242 −0.796211 0.605019i \(-0.793165\pi\)
−0.796211 + 0.605019i \(0.793165\pi\)
\(108\) 0 0
\(109\) 15.4443 11.2209i 1.47929 1.07477i 0.501509 0.865152i \(-0.332778\pi\)
0.977784 0.209617i \(-0.0672217\pi\)
\(110\) −7.23607 −0.689932
\(111\) 0 0
\(112\) 3.61803 2.62866i 0.341872 0.248385i
\(113\) 2.16312 1.57160i 0.203489 0.147843i −0.481374 0.876515i \(-0.659862\pi\)
0.684863 + 0.728672i \(0.259862\pi\)
\(114\) 0 0
\(115\) 8.09017 5.87785i 0.754412 0.548113i
\(116\) −3.54508 + 2.57565i −0.329153 + 0.239144i
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) 3.94427 12.1392i 0.361571 1.11280i
\(120\) 0 0
\(121\) −0.163119 0.502029i −0.0148290 0.0456390i
\(122\) 0.190983 + 0.587785i 0.0172908 + 0.0532156i
\(123\) 0 0
\(124\) −7.23607 −0.649818
\(125\) 9.04508 6.57164i 0.809017 0.587785i
\(126\) 0 0
\(127\) −7.85410 5.70634i −0.696939 0.506356i 0.181995 0.983299i \(-0.441745\pi\)
−0.878934 + 0.476944i \(0.841745\pi\)
\(128\) 0.927051 + 2.85317i 0.0819405 + 0.252187i
\(129\) 0 0
\(130\) 2.33688 7.19218i 0.204958 0.630796i
\(131\) −4.38197 + 13.4863i −0.382854 + 1.17830i 0.555171 + 0.831736i \(0.312653\pi\)
−0.938025 + 0.346568i \(0.887347\pi\)
\(132\) 0 0
\(133\) −4.47214 + 13.7638i −0.387783 + 1.19347i
\(134\) 4.23607 3.07768i 0.365941 0.265871i
\(135\) 0 0
\(136\) −6.92705 5.03280i −0.593990 0.431559i
\(137\) −4.35410 + 3.16344i −0.371996 + 0.270271i −0.758038 0.652210i \(-0.773842\pi\)
0.386042 + 0.922481i \(0.373842\pi\)
\(138\) 0 0
\(139\) 4.09017 + 2.97168i 0.346924 + 0.252055i 0.747577 0.664175i \(-0.231217\pi\)
−0.400654 + 0.916230i \(0.631217\pi\)
\(140\) 10.0000 0.845154
\(141\) 0 0
\(142\) −0.236068 + 0.726543i −0.0198104 + 0.0609701i
\(143\) −10.9443 −0.915206
\(144\) 0 0
\(145\) 9.79837 0.813711
\(146\) −0.954915 2.93893i −0.0790293 0.243227i
\(147\) 0 0
\(148\) 6.54508 + 4.75528i 0.538003 + 0.390882i
\(149\) 12.1459 0.995031 0.497515 0.867455i \(-0.334246\pi\)
0.497515 + 0.867455i \(0.334246\pi\)
\(150\) 0 0
\(151\) 16.4721 1.34048 0.670242 0.742143i \(-0.266190\pi\)
0.670242 + 0.742143i \(0.266190\pi\)
\(152\) 7.85410 + 5.70634i 0.637052 + 0.462845i
\(153\) 0 0
\(154\) 4.47214 + 13.7638i 0.360375 + 1.10912i
\(155\) 13.0902 + 9.51057i 1.05143 + 0.763907i
\(156\) 0 0
\(157\) −13.7984 −1.10123 −0.550615 0.834759i \(-0.685607\pi\)
−0.550615 + 0.834759i \(0.685607\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 3.45492 10.6331i 0.273135 0.840623i
\(161\) −16.1803 11.7557i −1.27519 0.926479i
\(162\) 0 0
\(163\) −2.38197 + 1.73060i −0.186570 + 0.135551i −0.677150 0.735845i \(-0.736785\pi\)
0.490580 + 0.871396i \(0.336785\pi\)
\(164\) 1.11803 + 0.812299i 0.0873038 + 0.0634299i
\(165\) 0 0
\(166\) −2.85410 + 2.07363i −0.221521 + 0.160945i
\(167\) 7.23607 22.2703i 0.559944 1.72333i −0.122573 0.992460i \(-0.539114\pi\)
0.682517 0.730870i \(-0.260886\pi\)
\(168\) 0 0
\(169\) −0.482779 + 1.48584i −0.0371369 + 0.114295i
\(170\) 1.97214 + 6.06961i 0.151256 + 0.465518i
\(171\) 0 0
\(172\) 1.76393 + 5.42882i 0.134499 + 0.413944i
\(173\) 8.01722 + 5.82485i 0.609538 + 0.442855i 0.849252 0.527988i \(-0.177054\pi\)
−0.239714 + 0.970844i \(0.577054\pi\)
\(174\) 0 0
\(175\) −18.0902 13.1433i −1.36749 0.993538i
\(176\) 3.23607 0.243928
\(177\) 0 0
\(178\) 2.35410 + 7.24518i 0.176447 + 0.543049i
\(179\) −1.90983 5.87785i −0.142747 0.439331i 0.853967 0.520327i \(-0.174190\pi\)
−0.996714 + 0.0809958i \(0.974190\pi\)
\(180\) 0 0
\(181\) −3.02786 + 9.31881i −0.225059 + 0.692661i 0.773226 + 0.634130i \(0.218642\pi\)
−0.998286 + 0.0585312i \(0.981358\pi\)
\(182\) −15.1246 −1.12111
\(183\) 0 0
\(184\) −10.8541 + 7.88597i −0.800175 + 0.581361i
\(185\) −5.59017 17.2048i −0.410997 1.26492i
\(186\) 0 0
\(187\) 7.47214 5.42882i 0.546417 0.396995i
\(188\) 4.23607 3.07768i 0.308947 0.224463i
\(189\) 0 0
\(190\) −2.23607 6.88191i −0.162221 0.499266i
\(191\) −19.9443 + 14.4904i −1.44312 + 1.04849i −0.455737 + 0.890114i \(0.650624\pi\)
−0.987380 + 0.158371i \(0.949376\pi\)
\(192\) 0 0
\(193\) 7.67376 0.552369 0.276185 0.961105i \(-0.410930\pi\)
0.276185 + 0.961105i \(0.410930\pi\)
\(194\) −2.73607 + 8.42075i −0.196438 + 0.604575i
\(195\) 0 0
\(196\) −4.01722 12.3637i −0.286944 0.883124i
\(197\) −1.66312 5.11855i −0.118492 0.364682i 0.874167 0.485625i \(-0.161408\pi\)
−0.992659 + 0.120943i \(0.961408\pi\)
\(198\) 0 0
\(199\) −18.6525 −1.32224 −0.661119 0.750281i \(-0.729918\pi\)
−0.661119 + 0.750281i \(0.729918\pi\)
\(200\) −12.1353 + 8.81678i −0.858092 + 0.623440i
\(201\) 0 0
\(202\) 13.3992 + 9.73508i 0.942764 + 0.684958i
\(203\) −6.05573 18.6376i −0.425029 1.30810i
\(204\) 0 0
\(205\) −0.954915 2.93893i −0.0666942 0.205264i
\(206\) 0.381966 1.17557i 0.0266128 0.0819059i
\(207\) 0 0
\(208\) −1.04508 + 3.21644i −0.0724636 + 0.223020i
\(209\) −8.47214 + 6.15537i −0.586030 + 0.425776i
\(210\) 0 0
\(211\) 14.4721 + 10.5146i 0.996303 + 0.723856i 0.961292 0.275530i \(-0.0888535\pi\)
0.0350106 + 0.999387i \(0.488854\pi\)
\(212\) −1.11803 + 0.812299i −0.0767869 + 0.0557889i
\(213\) 0 0
\(214\) −13.3262 9.68208i −0.910963 0.661853i
\(215\) 3.94427 12.1392i 0.268997 0.827888i
\(216\) 0 0
\(217\) 10.0000 30.7768i 0.678844 2.08927i
\(218\) 19.0902 1.29295
\(219\) 0 0
\(220\) 5.85410 + 4.25325i 0.394683 + 0.286754i
\(221\) 2.98278 + 9.18005i 0.200643 + 0.617517i
\(222\) 0 0
\(223\) 11.4721 + 8.33499i 0.768231 + 0.558153i 0.901424 0.432938i \(-0.142523\pi\)
−0.133193 + 0.991090i \(0.542523\pi\)
\(224\) −22.3607 −1.49404
\(225\) 0 0
\(226\) 2.67376 0.177856
\(227\) −16.1803 11.7557i −1.07393 0.780254i −0.0973129 0.995254i \(-0.531025\pi\)
−0.976614 + 0.215000i \(0.931025\pi\)
\(228\) 0 0
\(229\) −7.71885 23.7562i −0.510076 1.56985i −0.792067 0.610435i \(-0.790995\pi\)
0.281991 0.959417i \(-0.409005\pi\)
\(230\) 10.0000 0.659380
\(231\) 0 0
\(232\) −13.1459 −0.863070
\(233\) −4.51722 + 13.9026i −0.295933 + 0.910788i 0.686973 + 0.726682i \(0.258939\pi\)
−0.982906 + 0.184106i \(0.941061\pi\)
\(234\) 0 0
\(235\) −11.7082 −0.763759
\(236\) 3.23607 + 2.35114i 0.210650 + 0.153046i
\(237\) 0 0
\(238\) 10.3262 7.50245i 0.669351 0.486312i
\(239\) −5.70820 4.14725i −0.369233 0.268263i 0.387660 0.921803i \(-0.373284\pi\)
−0.756893 + 0.653539i \(0.773284\pi\)
\(240\) 0 0
\(241\) 0.836881 0.608030i 0.0539082 0.0391666i −0.560505 0.828151i \(-0.689393\pi\)
0.614413 + 0.788985i \(0.289393\pi\)
\(242\) 0.163119 0.502029i 0.0104857 0.0322716i
\(243\) 0 0
\(244\) 0.190983 0.587785i 0.0122264 0.0376291i
\(245\) −8.98278 + 27.6462i −0.573889 + 1.76625i
\(246\) 0 0
\(247\) −3.38197 10.4086i −0.215189 0.662285i
\(248\) −17.5623 12.7598i −1.11521 0.810246i
\(249\) 0 0
\(250\) 11.1803 0.707107
\(251\) 26.9443 1.70071 0.850354 0.526212i \(-0.176388\pi\)
0.850354 + 0.526212i \(0.176388\pi\)
\(252\) 0 0
\(253\) −4.47214 13.7638i −0.281161 0.865324i
\(254\) −3.00000 9.23305i −0.188237 0.579333i
\(255\) 0 0
\(256\) −5.25329 + 16.1680i −0.328331 + 1.01050i
\(257\) 12.7984 0.798341 0.399170 0.916877i \(-0.369298\pi\)
0.399170 + 0.916877i \(0.369298\pi\)
\(258\) 0 0
\(259\) −29.2705 + 21.2663i −1.81878 + 1.32142i
\(260\) −6.11803 + 4.44501i −0.379424 + 0.275668i
\(261\) 0 0
\(262\) −11.4721 + 8.33499i −0.708751 + 0.514938i
\(263\) 9.61803 6.98791i 0.593073 0.430893i −0.250340 0.968158i \(-0.580542\pi\)
0.843414 + 0.537265i \(0.180542\pi\)
\(264\) 0 0
\(265\) 3.09017 0.189828
\(266\) −11.7082 + 8.50651i −0.717876 + 0.521567i
\(267\) 0 0
\(268\) −5.23607 −0.319844
\(269\) 0.0450850 0.138757i 0.00274888 0.00846018i −0.949673 0.313244i \(-0.898584\pi\)
0.952422 + 0.304784i \(0.0985842\pi\)
\(270\) 0 0
\(271\) 6.85410 + 21.0948i 0.416357 + 1.28142i 0.911031 + 0.412337i \(0.135287\pi\)
−0.494674 + 0.869078i \(0.664713\pi\)
\(272\) −0.881966 2.71441i −0.0534770 0.164585i
\(273\) 0 0
\(274\) −5.38197 −0.325136
\(275\) −5.00000 15.3884i −0.301511 0.927957i
\(276\) 0 0
\(277\) 4.69098 + 3.40820i 0.281854 + 0.204779i 0.719726 0.694259i \(-0.244268\pi\)
−0.437872 + 0.899037i \(0.644268\pi\)
\(278\) 1.56231 + 4.80828i 0.0937009 + 0.288382i
\(279\) 0 0
\(280\) 24.2705 + 17.6336i 1.45044 + 1.05381i
\(281\) 5.37132 16.5312i 0.320426 0.986171i −0.653037 0.757326i \(-0.726505\pi\)
0.973463 0.228844i \(-0.0734947\pi\)
\(282\) 0 0
\(283\) 0.0901699 0.277515i 0.00536005 0.0164965i −0.948341 0.317254i \(-0.897239\pi\)
0.953701 + 0.300757i \(0.0972393\pi\)
\(284\) 0.618034 0.449028i 0.0366736 0.0266449i
\(285\) 0 0
\(286\) −8.85410 6.43288i −0.523554 0.380384i
\(287\) −5.00000 + 3.63271i −0.295141 + 0.214432i
\(288\) 0 0
\(289\) 7.16312 + 5.20431i 0.421360 + 0.306136i
\(290\) 7.92705 + 5.75934i 0.465492 + 0.338200i
\(291\) 0 0
\(292\) −0.954915 + 2.93893i −0.0558822 + 0.171988i
\(293\) −3.79837 −0.221903 −0.110952 0.993826i \(-0.535390\pi\)
−0.110952 + 0.993826i \(0.535390\pi\)
\(294\) 0 0
\(295\) −2.76393 8.50651i −0.160922 0.495268i
\(296\) 7.50000 + 23.0826i 0.435929 + 1.34165i
\(297\) 0 0
\(298\) 9.82624 + 7.13918i 0.569219 + 0.413562i
\(299\) 15.1246 0.874679
\(300\) 0 0
\(301\) −25.5279 −1.47140
\(302\) 13.3262 + 9.68208i 0.766839 + 0.557141i
\(303\) 0 0
\(304\) 1.00000 + 3.07768i 0.0573539 + 0.176517i
\(305\) −1.11803 + 0.812299i −0.0640184 + 0.0465121i
\(306\) 0 0
\(307\) 1.34752 0.0769073 0.0384536 0.999260i \(-0.487757\pi\)
0.0384536 + 0.999260i \(0.487757\pi\)
\(308\) 4.47214 13.7638i 0.254824 0.784266i
\(309\) 0 0
\(310\) 5.00000 + 15.3884i 0.283981 + 0.874003i
\(311\) 3.47214 + 2.52265i 0.196887 + 0.143047i 0.681861 0.731482i \(-0.261171\pi\)
−0.484974 + 0.874529i \(0.661171\pi\)
\(312\) 0 0
\(313\) −6.85410 + 4.97980i −0.387417 + 0.281475i −0.764396 0.644747i \(-0.776963\pi\)
0.376979 + 0.926222i \(0.376963\pi\)
\(314\) −11.1631 8.11048i −0.629971 0.457701i
\(315\) 0 0
\(316\) 0 0
\(317\) 7.67376 23.6174i 0.431001 1.32649i −0.466128 0.884717i \(-0.654351\pi\)
0.897129 0.441768i \(-0.145649\pi\)
\(318\) 0 0
\(319\) 4.38197 13.4863i 0.245343 0.755088i
\(320\) 12.6631 9.20029i 0.707890 0.514312i
\(321\) 0 0
\(322\) −6.18034 19.0211i −0.344417 1.06001i
\(323\) 7.47214 + 5.42882i 0.415761 + 0.302068i
\(324\) 0 0
\(325\) 16.9098 0.937989
\(326\) −2.94427 −0.163068
\(327\) 0 0
\(328\) 1.28115 + 3.94298i 0.0707398 + 0.217715i
\(329\) 7.23607 + 22.2703i 0.398937 + 1.22780i
\(330\) 0 0
\(331\) 3.38197 10.4086i 0.185890 0.572110i −0.814073 0.580763i \(-0.802754\pi\)
0.999963 + 0.00865315i \(0.00275442\pi\)
\(332\) 3.52786 0.193617
\(333\) 0 0
\(334\) 18.9443 13.7638i 1.03658 0.753123i
\(335\) 9.47214 + 6.88191i 0.517518 + 0.375999i
\(336\) 0 0
\(337\) 12.0902 8.78402i 0.658594 0.478496i −0.207594 0.978215i \(-0.566563\pi\)
0.866188 + 0.499719i \(0.166563\pi\)
\(338\) −1.26393 + 0.918300i −0.0687488 + 0.0499490i
\(339\) 0 0
\(340\) 1.97214 6.06961i 0.106954 0.329171i
\(341\) 18.9443 13.7638i 1.02589 0.745353i
\(342\) 0 0
\(343\) 26.8328 1.44884
\(344\) −5.29180 + 16.2865i −0.285315 + 0.878108i
\(345\) 0 0
\(346\) 3.06231 + 9.42481i 0.164631 + 0.506681i
\(347\) 10.4164 + 32.0584i 0.559182 + 1.72099i 0.684635 + 0.728886i \(0.259962\pi\)
−0.125453 + 0.992100i \(0.540038\pi\)
\(348\) 0 0
\(349\) 25.0344 1.34006 0.670031 0.742333i \(-0.266281\pi\)
0.670031 + 0.742333i \(0.266281\pi\)
\(350\) −6.90983 21.2663i −0.369346 1.13673i
\(351\) 0 0
\(352\) −13.0902 9.51057i −0.697708 0.506915i
\(353\) 9.38197 + 28.8747i 0.499352 + 1.53685i 0.810063 + 0.586342i \(0.199433\pi\)
−0.310712 + 0.950504i \(0.600567\pi\)
\(354\) 0 0
\(355\) −1.70820 −0.0906621
\(356\) 2.35410 7.24518i 0.124767 0.383994i
\(357\) 0 0
\(358\) 1.90983 5.87785i 0.100938 0.310654i
\(359\) −8.56231 + 6.22088i −0.451901 + 0.328325i −0.790346 0.612661i \(-0.790099\pi\)
0.338445 + 0.940986i \(0.390099\pi\)
\(360\) 0 0
\(361\) 6.89919 + 5.01255i 0.363115 + 0.263819i
\(362\) −7.92705 + 5.75934i −0.416637 + 0.302704i
\(363\) 0 0
\(364\) 12.2361 + 8.89002i 0.641344 + 0.465964i
\(365\) 5.59017 4.06150i 0.292603 0.212588i
\(366\) 0 0
\(367\) −1.85410 + 5.70634i −0.0967833 + 0.297868i −0.987714 0.156270i \(-0.950053\pi\)
0.890931 + 0.454139i \(0.150053\pi\)
\(368\) −4.47214 −0.233126
\(369\) 0 0
\(370\) 5.59017 17.2048i 0.290619 0.894434i
\(371\) −1.90983 5.87785i −0.0991534 0.305163i
\(372\) 0 0
\(373\) −23.7984 17.2905i −1.23223 0.895270i −0.235178 0.971952i \(-0.575567\pi\)
−0.997056 + 0.0766827i \(0.975567\pi\)
\(374\) 9.23607 0.477586
\(375\) 0 0
\(376\) 15.7082 0.810089
\(377\) 11.9894 + 8.71078i 0.617483 + 0.448628i
\(378\) 0 0
\(379\) 7.23607 + 22.2703i 0.371692 + 1.14395i 0.945684 + 0.325089i \(0.105394\pi\)
−0.573992 + 0.818861i \(0.694606\pi\)
\(380\) −2.23607 + 6.88191i −0.114708 + 0.353035i
\(381\) 0 0
\(382\) −24.6525 −1.26133
\(383\) −6.43769 + 19.8132i −0.328951 + 1.01241i 0.640675 + 0.767812i \(0.278655\pi\)
−0.969626 + 0.244594i \(0.921345\pi\)
\(384\) 0 0
\(385\) −26.1803 + 19.0211i −1.33427 + 0.969407i
\(386\) 6.20820 + 4.51052i 0.315989 + 0.229580i
\(387\) 0 0
\(388\) 7.16312 5.20431i 0.363652 0.264209i
\(389\) −30.0066 21.8011i −1.52139 1.10536i −0.960791 0.277272i \(-0.910570\pi\)
−0.560603 0.828085i \(-0.689430\pi\)
\(390\) 0 0
\(391\) −10.3262 + 7.50245i −0.522220 + 0.379415i
\(392\) 12.0517 37.0912i 0.608701 1.87339i
\(393\) 0 0
\(394\) 1.66312 5.11855i 0.0837867 0.257869i
\(395\) 0 0
\(396\) 0 0
\(397\) 3.38197 + 10.4086i 0.169736 + 0.522394i 0.999354 0.0359377i \(-0.0114418\pi\)
−0.829618 + 0.558331i \(0.811442\pi\)
\(398\) −15.0902 10.9637i −0.756402 0.549558i
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) −33.4508 −1.67046 −0.835228 0.549904i \(-0.814664\pi\)
−0.835228 + 0.549904i \(0.814664\pi\)
\(402\) 0 0
\(403\) 7.56231 + 23.2744i 0.376705 + 1.15938i
\(404\) −5.11803 15.7517i −0.254632 0.783676i
\(405\) 0 0
\(406\) 6.05573 18.6376i 0.300541 0.924969i
\(407\) −26.1803 −1.29771
\(408\) 0 0
\(409\) −20.8713 + 15.1639i −1.03202 + 0.749807i −0.968712 0.248187i \(-0.920165\pi\)
−0.0633084 + 0.997994i \(0.520165\pi\)
\(410\) 0.954915 2.93893i 0.0471599 0.145143i
\(411\) 0 0
\(412\) −1.00000 + 0.726543i −0.0492665 + 0.0357942i
\(413\) −14.4721 + 10.5146i −0.712127 + 0.517391i
\(414\) 0 0
\(415\) −6.38197 4.63677i −0.313278 0.227610i
\(416\) 13.6803 9.93935i 0.670734 0.487317i
\(417\) 0 0
\(418\) −10.4721 −0.512209
\(419\) −10.1803 + 31.3319i −0.497342 + 1.53066i 0.315932 + 0.948782i \(0.397683\pi\)
−0.813275 + 0.581880i \(0.802317\pi\)
\(420\) 0 0
\(421\) 7.15248 + 22.0131i 0.348590 + 1.07285i 0.959634 + 0.281253i \(0.0907502\pi\)
−0.611043 + 0.791597i \(0.709250\pi\)
\(422\) 5.52786 + 17.0130i 0.269092 + 0.828181i
\(423\) 0 0
\(424\) −4.14590 −0.201343
\(425\) −11.5451 + 8.38800i −0.560019 + 0.406878i
\(426\) 0 0
\(427\) 2.23607 + 1.62460i 0.108211 + 0.0786198i
\(428\) 5.09017 + 15.6659i 0.246043 + 0.757241i
\(429\) 0 0
\(430\) 10.3262 7.50245i 0.497975 0.361800i
\(431\) 3.29180 10.1311i 0.158560 0.487998i −0.839944 0.542673i \(-0.817412\pi\)
0.998504 + 0.0546749i \(0.0174122\pi\)
\(432\) 0 0
\(433\) 7.71885 23.7562i 0.370944 1.14165i −0.575230 0.817991i \(-0.695088\pi\)
0.946174 0.323657i \(-0.104912\pi\)
\(434\) 26.1803 19.0211i 1.25670 0.913043i
\(435\) 0 0
\(436\) −15.4443 11.2209i −0.739646 0.537385i
\(437\) 11.7082 8.50651i 0.560079 0.406921i
\(438\) 0 0
\(439\) 5.00000 + 3.63271i 0.238637 + 0.173380i 0.700676 0.713480i \(-0.252882\pi\)
−0.462039 + 0.886860i \(0.652882\pi\)
\(440\) 6.70820 + 20.6457i 0.319801 + 0.984247i
\(441\) 0 0
\(442\) −2.98278 + 9.18005i −0.141876 + 0.436650i
\(443\) 30.7639 1.46164 0.730819 0.682571i \(-0.239138\pi\)
0.730819 + 0.682571i \(0.239138\pi\)
\(444\) 0 0
\(445\) −13.7812 + 10.0126i −0.653289 + 0.474642i
\(446\) 4.38197 + 13.4863i 0.207492 + 0.638595i
\(447\) 0 0
\(448\) −25.3262 18.4006i −1.19655 0.869346i
\(449\) 7.79837 0.368028 0.184014 0.982924i \(-0.441091\pi\)
0.184014 + 0.982924i \(0.441091\pi\)
\(450\) 0 0
\(451\) −4.47214 −0.210585
\(452\) −2.16312 1.57160i −0.101745 0.0739217i
\(453\) 0 0
\(454\) −6.18034 19.0211i −0.290058 0.892706i
\(455\) −10.4508 32.1644i −0.489943 1.50789i
\(456\) 0 0
\(457\) 22.3607 1.04599 0.522994 0.852336i \(-0.324815\pi\)
0.522994 + 0.852336i \(0.324815\pi\)
\(458\) 7.71885 23.7562i 0.360678 1.11005i
\(459\) 0 0
\(460\) −8.09017 5.87785i −0.377206 0.274056i
\(461\) −6.63525 4.82079i −0.309035 0.224527i 0.422448 0.906387i \(-0.361171\pi\)
−0.731482 + 0.681861i \(0.761171\pi\)
\(462\) 0 0
\(463\) −18.7984 + 13.6578i −0.873635 + 0.634733i −0.931560 0.363588i \(-0.881552\pi\)
0.0579252 + 0.998321i \(0.481552\pi\)
\(464\) −3.54508 2.57565i −0.164576 0.119572i
\(465\) 0 0
\(466\) −11.8262 + 8.59226i −0.547840 + 0.398029i
\(467\) −1.79837 + 5.53483i −0.0832188 + 0.256121i −0.984005 0.178142i \(-0.942991\pi\)
0.900786 + 0.434263i \(0.142991\pi\)
\(468\) 0 0
\(469\) 7.23607 22.2703i 0.334131 1.02835i
\(470\) −9.47214 6.88191i −0.436917 0.317439i
\(471\) 0 0
\(472\) 3.70820 + 11.4127i 0.170684 + 0.525311i
\(473\) −14.9443 10.8576i −0.687138 0.499235i
\(474\) 0 0
\(475\) 13.0902 9.51057i 0.600618 0.436375i
\(476\) −12.7639 −0.585034
\(477\) 0 0
\(478\) −2.18034 6.71040i −0.0997264 0.306926i
\(479\) −0.326238 1.00406i −0.0149062 0.0458765i 0.943327 0.331865i \(-0.107678\pi\)
−0.958233 + 0.285989i \(0.907678\pi\)
\(480\) 0 0
\(481\) 8.45492 26.0216i 0.385511 1.18648i
\(482\) 1.03444 0.0471175
\(483\) 0 0
\(484\) −0.427051 + 0.310271i −0.0194114 + 0.0141032i
\(485\) −19.7984 −0.898998
\(486\) 0 0
\(487\) 3.00000 2.17963i 0.135943 0.0987684i −0.517736 0.855541i \(-0.673225\pi\)
0.653679 + 0.756772i \(0.273225\pi\)
\(488\) 1.50000 1.08981i 0.0679018 0.0493336i
\(489\) 0 0
\(490\) −23.5172 + 17.0863i −1.06240 + 0.771879i
\(491\) −24.1803 + 17.5680i −1.09124 + 0.792835i −0.979609 0.200915i \(-0.935609\pi\)
−0.111635 + 0.993749i \(0.535609\pi\)
\(492\) 0 0
\(493\) −12.5066 −0.563268
\(494\) 3.38197 10.4086i 0.152162 0.468306i
\(495\) 0 0
\(496\) −2.23607 6.88191i −0.100402 0.309007i
\(497\) 1.05573 + 3.24920i 0.0473559 + 0.145746i
\(498\) 0 0
\(499\) −6.00000 −0.268597 −0.134298 0.990941i \(-0.542878\pi\)
−0.134298 + 0.990941i \(0.542878\pi\)
\(500\) −9.04508 6.57164i −0.404508 0.293893i
\(501\) 0 0
\(502\) 21.7984 + 15.8374i 0.972909 + 0.706860i
\(503\) −10.9443 33.6830i −0.487981 1.50185i −0.827617 0.561294i \(-0.810304\pi\)
0.339636 0.940557i \(-0.389696\pi\)
\(504\) 0 0
\(505\) −11.4443 + 35.2218i −0.509263 + 1.56735i
\(506\) 4.47214 13.7638i 0.198811 0.611876i
\(507\) 0 0
\(508\) −3.00000 + 9.23305i −0.133103 + 0.409650i
\(509\) 21.7254 15.7844i 0.962963 0.699633i 0.00912564 0.999958i \(-0.497095\pi\)
0.953837 + 0.300325i \(0.0970952\pi\)
\(510\) 0 0
\(511\) −11.1803 8.12299i −0.494589 0.359340i
\(512\) −8.89919 + 6.46564i −0.393292 + 0.285744i
\(513\) 0 0
\(514\) 10.3541 + 7.52270i 0.456700 + 0.331812i
\(515\) 2.76393 0.121793
\(516\) 0 0
\(517\) −5.23607 + 16.1150i −0.230282 + 0.708735i
\(518\) −36.1803 −1.58967
\(519\) 0 0
\(520\) −22.6869 −0.994887
\(521\) −0.628677 1.93487i −0.0275428 0.0847682i 0.936340 0.351094i \(-0.114190\pi\)
−0.963883 + 0.266326i \(0.914190\pi\)
\(522\) 0 0
\(523\) 9.94427 + 7.22494i 0.434833 + 0.315924i 0.783578 0.621293i \(-0.213392\pi\)
−0.348746 + 0.937217i \(0.613392\pi\)
\(524\) 14.1803 0.619471
\(525\) 0 0
\(526\) 11.8885 0.518365
\(527\) −16.7082 12.1392i −0.727821 0.528793i
\(528\) 0 0
\(529\) −0.927051 2.85317i −0.0403066 0.124051i
\(530\) 2.50000 + 1.81636i 0.108593 + 0.0788975i
\(531\) 0 0
\(532\) 14.4721 0.627447
\(533\) 1.44427 4.44501i 0.0625584 0.192535i
\(534\) 0 0
\(535\) 11.3820 35.0301i 0.492085 1.51448i
\(536\) −12.7082 9.23305i −0.548911 0.398807i
\(537\) 0 0
\(538\) 0.118034 0.0857567i 0.00508881 0.00369723i
\(539\) 34.0344 + 24.7275i 1.46597 + 1.06509i
\(540\) 0 0
\(541\) 28.5795 20.7642i 1.22873 0.892724i 0.231936 0.972731i \(-0.425494\pi\)
0.996794 + 0.0800067i \(0.0254942\pi\)
\(542\) −6.85410 + 21.0948i −0.294409 + 0.906097i
\(543\) 0 0
\(544\) −4.40983 + 13.5721i −0.189070 + 0.581897i
\(545\) 13.1910 + 40.5977i 0.565040 + 1.73901i
\(546\) 0 0
\(547\) −0.729490 2.24514i −0.0311907 0.0959952i 0.934249 0.356621i \(-0.116071\pi\)
−0.965440 + 0.260626i \(0.916071\pi\)
\(548\) 4.35410 + 3.16344i 0.185998 + 0.135135i
\(549\) 0 0
\(550\) 5.00000 15.3884i 0.213201 0.656164i
\(551\) 14.1803 0.604103
\(552\) 0 0
\(553\) 0 0
\(554\) 1.79180 + 5.51458i 0.0761261 + 0.234292i
\(555\) 0 0
\(556\) 1.56231 4.80828i 0.0662565 0.203917i
\(557\) −22.2705 −0.943632 −0.471816 0.881697i \(-0.656401\pi\)
−0.471816 + 0.881697i \(0.656401\pi\)
\(558\) 0 0
\(559\) 15.6180 11.3472i 0.660572 0.479934i
\(560\) 3.09017 + 9.51057i 0.130584 + 0.401895i
\(561\) 0 0
\(562\) 14.0623 10.2169i 0.593183 0.430972i
\(563\) −14.1803 + 10.3026i −0.597630 + 0.434204i −0.845037 0.534708i \(-0.820422\pi\)
0.247407 + 0.968912i \(0.420422\pi\)
\(564\) 0 0
\(565\) 1.84752 + 5.68609i 0.0777259 + 0.239216i
\(566\) 0.236068 0.171513i 0.00992268 0.00720925i
\(567\) 0 0
\(568\) 2.29180 0.0961616
\(569\) 9.35410 28.7890i 0.392144 1.20690i −0.539019 0.842294i \(-0.681205\pi\)
0.931163 0.364603i \(-0.118795\pi\)
\(570\) 0 0
\(571\) −6.56231 20.1967i −0.274624 0.845206i −0.989319 0.145769i \(-0.953434\pi\)
0.714695 0.699437i \(-0.246566\pi\)
\(572\) 3.38197 + 10.4086i 0.141407 + 0.435206i
\(573\) 0 0
\(574\) −6.18034 −0.257962
\(575\) 6.90983 + 21.2663i 0.288160 + 0.886865i
\(576\) 0 0
\(577\) 25.0344 + 18.1886i 1.04220 + 0.757201i 0.970713 0.240241i \(-0.0772265\pi\)
0.0714842 + 0.997442i \(0.477226\pi\)
\(578\) 2.73607 + 8.42075i 0.113805 + 0.350257i
\(579\) 0 0
\(580\) −3.02786 9.31881i −0.125725 0.386942i
\(581\) −4.87539 + 15.0049i −0.202265 + 0.622508i
\(582\) 0 0
\(583\) 1.38197 4.25325i 0.0572352 0.176152i
\(584\) −7.50000 + 5.44907i −0.310352 + 0.225484i
\(585\) 0 0
\(586\) −3.07295 2.23263i −0.126942 0.0922290i
\(587\) −11.7984 + 8.57202i −0.486971 + 0.353805i −0.804018 0.594605i \(-0.797309\pi\)
0.317047 + 0.948410i \(0.397309\pi\)
\(588\) 0 0
\(589\) 18.9443 + 13.7638i 0.780585 + 0.567128i
\(590\) 2.76393 8.50651i 0.113789 0.350207i
\(591\) 0 0
\(592\) −2.50000 + 7.69421i −0.102749 + 0.316230i
\(593\) 32.7426 1.34458 0.672290 0.740288i \(-0.265311\pi\)
0.672290 + 0.740288i \(0.265311\pi\)
\(594\) 0 0
\(595\) 23.0902 + 16.7760i 0.946605 + 0.687749i
\(596\) −3.75329 11.5514i −0.153741 0.473165i
\(597\) 0 0
\(598\) 12.2361 + 8.89002i 0.500370 + 0.363540i
\(599\) 12.4721 0.509598 0.254799 0.966994i \(-0.417991\pi\)
0.254799 + 0.966994i \(0.417991\pi\)
\(600\) 0 0
\(601\) −24.3262 −0.992288 −0.496144 0.868240i \(-0.665251\pi\)
−0.496144 + 0.868240i \(0.665251\pi\)
\(602\) −20.6525 15.0049i −0.841732 0.611554i
\(603\) 0 0
\(604\) −5.09017 15.6659i −0.207116 0.637438i
\(605\) 1.18034 0.0479876
\(606\) 0 0
\(607\) −39.2361 −1.59254 −0.796271 0.604940i \(-0.793197\pi\)
−0.796271 + 0.604940i \(0.793197\pi\)
\(608\) 5.00000 15.3884i 0.202777 0.624083i
\(609\) 0 0
\(610\) −1.38197 −0.0559542
\(611\) −14.3262 10.4086i −0.579578 0.421088i
\(612\) 0 0
\(613\) −31.9615 + 23.2214i −1.29091 + 0.937903i −0.999823 0.0187931i \(-0.994018\pi\)
−0.291089 + 0.956696i \(0.594018\pi\)
\(614\) 1.09017 + 0.792055i 0.0439957 + 0.0319647i
\(615\) 0 0
\(616\) 35.1246 25.5195i 1.41521 1.02821i
\(617\) −8.33688 + 25.6583i −0.335630 + 1.03296i 0.630781 + 0.775961i \(0.282735\pi\)
−0.966411 + 0.257002i \(0.917265\pi\)
\(618\) 0 0
\(619\) 8.76393 26.9726i 0.352252 1.08412i −0.605333 0.795972i \(-0.706960\pi\)
0.957586 0.288149i \(-0.0930398\pi\)
\(620\) 5.00000 15.3884i 0.200805 0.618014i
\(621\) 0 0
\(622\) 1.32624 + 4.08174i 0.0531773 + 0.163663i
\(623\) 27.5623 + 20.0252i 1.10426 + 0.802292i
\(624\) 0 0
\(625\) 7.72542 + 23.7764i 0.309017 + 0.951057i
\(626\) −8.47214 −0.338615
\(627\) 0 0
\(628\) 4.26393 + 13.1230i 0.170149 + 0.523666i
\(629\) 7.13525 + 21.9601i 0.284501 + 0.875605i
\(630\) 0 0
\(631\) 3.18034 9.78808i 0.126607 0.389657i −0.867583 0.497292i \(-0.834328\pi\)
0.994190 + 0.107635i \(0.0343277\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 20.0902 14.5964i 0.797883 0.579696i
\(635\) 17.5623 12.7598i 0.696939 0.506356i
\(636\) 0 0
\(637\) −35.5689 + 25.8423i −1.40929 + 1.02391i
\(638\) 11.4721 8.33499i 0.454186 0.329986i
\(639\) 0 0
\(640\) −6.70820 −0.265165
\(641\) 31.5066 22.8909i 1.24444 0.904135i 0.246549 0.969130i \(-0.420703\pi\)
0.997886 + 0.0649953i \(0.0207032\pi\)
\(642\) 0 0
\(643\) 13.8885 0.547711 0.273855 0.961771i \(-0.411701\pi\)
0.273855 + 0.961771i \(0.411701\pi\)
\(644\) −6.18034 + 19.0211i −0.243540 + 0.749538i
\(645\) 0 0
\(646\) 2.85410 + 8.78402i 0.112293 + 0.345603i
\(647\) −3.20163 9.85359i −0.125869 0.387385i 0.868189 0.496233i \(-0.165284\pi\)
−0.994058 + 0.108848i \(0.965284\pi\)
\(648\) 0 0
\(649\) −12.9443 −0.508107
\(650\) 13.6803 + 9.93935i 0.536587 + 0.389853i
\(651\) 0 0
\(652\) 2.38197 + 1.73060i 0.0932850 + 0.0677755i
\(653\) −13.9377 42.8958i −0.545424 1.67864i −0.719979 0.693995i \(-0.755849\pi\)
0.174555 0.984647i \(-0.444151\pi\)
\(654\) 0 0
\(655\) −25.6525 18.6376i −1.00233 0.728232i
\(656\) −0.427051 + 1.31433i −0.0166735 + 0.0513159i
\(657\) 0 0
\(658\) −7.23607 + 22.2703i −0.282091 + 0.868188i
\(659\) −5.32624 + 3.86974i −0.207481 + 0.150744i −0.686673 0.726966i \(-0.740930\pi\)
0.479192 + 0.877710i \(0.340930\pi\)
\(660\) 0 0
\(661\) −20.5623 14.9394i −0.799781 0.581075i 0.111069 0.993813i \(-0.464573\pi\)
−0.910850 + 0.412738i \(0.864573\pi\)
\(662\) 8.85410 6.43288i 0.344124 0.250021i
\(663\) 0 0
\(664\) 8.56231 + 6.22088i 0.332282 + 0.241417i
\(665\) −26.1803 19.0211i −1.01523 0.737608i
\(666\) 0 0
\(667\) −6.05573 + 18.6376i −0.234479 + 0.721651i
\(668\) −23.4164 −0.906008
\(669\) 0 0
\(670\) 3.61803 + 11.1352i 0.139777 + 0.430189i
\(671\) 0.618034 + 1.90211i 0.0238589 + 0.0734303i
\(672\) 0 0
\(673\) −24.1074 17.5150i −0.929272 0.675155i 0.0165428 0.999863i \(-0.494734\pi\)
−0.945814 + 0.324708i \(0.894734\pi\)
\(674\) 14.9443 0.575632
\(675\) 0 0
\(676\) 1.56231 0.0600887
\(677\) 30.2705 + 21.9928i 1.16339 + 0.845252i 0.990203 0.139636i \(-0.0445934\pi\)
0.173187 + 0.984889i \(0.444593\pi\)
\(678\) 0 0
\(679\) 12.2361 + 37.6587i 0.469577 + 1.44521i
\(680\) 15.4894 11.2537i 0.593990 0.431559i
\(681\) 0 0
\(682\) 23.4164 0.896661
\(683\) −2.29180 + 7.05342i −0.0876931 + 0.269892i −0.985281 0.170945i \(-0.945318\pi\)
0.897588 + 0.440836i \(0.145318\pi\)
\(684\) 0 0
\(685\) −3.71885 11.4454i −0.142090 0.437308i
\(686\) 21.7082 + 15.7719i 0.828823 + 0.602175i
\(687\) 0 0
\(688\) −4.61803 + 3.35520i −0.176061 + 0.127916i
\(689\) 3.78115 + 2.74717i 0.144050 + 0.104659i
\(690\) 0 0
\(691\) 17.1803 12.4822i 0.653571 0.474847i −0.210915 0.977504i \(-0.567644\pi\)
0.864486 + 0.502657i \(0.167644\pi\)
\(692\) 3.06231 9.42481i 0.116411 0.358277i
\(693\) 0 0
\(694\) −10.4164 + 32.0584i −0.395401 + 1.21692i
\(695\) −9.14590 + 6.64488i −0.346924 + 0.252055i
\(696\) 0 0
\(697\) 1.21885 + 3.75123i 0.0461671 + 0.142088i
\(698\) 20.2533 + 14.7149i 0.766598 + 0.556966i
\(699\) 0 0
\(700\) −6.90983 + 21.2663i −0.261167 + 0.803789i
\(701\) −0.437694 −0.0165315 −0.00826574 0.999966i \(-0.502631\pi\)
−0.00826574 + 0.999966i \(0.502631\pi\)
\(702\) 0 0
\(703\) −8.09017 24.8990i −0.305127 0.939083i
\(704\) −7.00000 21.5438i −0.263822 0.811962i
\(705\) 0 0
\(706\) −9.38197 + 28.8747i −0.353095 + 1.08671i
\(707\) 74.0689 2.78565
\(708\) 0 0
\(709\) 5.44427 3.95550i 0.204464 0.148552i −0.480841 0.876808i \(-0.659669\pi\)
0.685305 + 0.728256i \(0.259669\pi\)
\(710\) −1.38197 1.00406i −0.0518643 0.0376816i
\(711\) 0 0
\(712\) 18.4894 13.4333i 0.692918 0.503434i
\(713\) −26.1803 + 19.0211i −0.980461 + 0.712347i
\(714\) 0 0
\(715\) 7.56231 23.2744i 0.282814 0.870413i
\(716\) −5.00000 + 3.63271i −0.186859 + 0.135761i
\(717\) 0 0
\(718\) −10.5836 −0.394976
\(719\) 11.0902 34.1320i 0.413594 1.27291i −0.499909 0.866078i \(-0.666633\pi\)
0.913503 0.406832i \(-0.133367\pi\)
\(720\) 0 0
\(721\) −1.70820 5.25731i −0.0636168 0.195792i
\(722\) 2.63525 + 8.11048i 0.0980740 + 0.301841i
\(723\) 0 0
\(724\) 9.79837 0.364154
\(725\) −6.77051 + 20.8375i −0.251450 + 0.773885i
\(726\) 0 0
\(727\) −12.4164 9.02105i −0.460499 0.334572i 0.333228 0.942846i \(-0.391862\pi\)
−0.793727 + 0.608274i \(0.791862\pi\)
\(728\) 14.0213 + 43.1531i 0.519663 + 1.59936i
\(729\) 0 0
\(730\) 6.90983 0.255744
\(731\) −5.03444 + 15.4944i −0.186206 + 0.573082i
\(732\) 0 0
\(733\) 0.798374 2.45714i 0.0294886 0.0907566i −0.935229 0.354043i \(-0.884807\pi\)
0.964718 + 0.263287i \(0.0848065\pi\)
\(734\) −4.85410 + 3.52671i −0.179168 + 0.130173i
\(735\) 0 0
\(736\) 18.0902 + 13.1433i 0.666813 + 0.484468i
\(737\) 13.7082 9.95959i 0.504948 0.366866i
\(738\) 0 0
\(739\) −14.3262 10.4086i −0.526999 0.382887i 0.292235 0.956347i \(-0.405601\pi\)
−0.819234 + 0.573459i \(0.805601\pi\)
\(740\) −14.6353 + 10.6331i −0.538003 + 0.390882i
\(741\) 0 0
\(742\) 1.90983 5.87785i 0.0701121 0.215783i
\(743\) −0.875388 −0.0321149 −0.0160574 0.999871i \(-0.505111\pi\)
−0.0160574 + 0.999871i \(0.505111\pi\)
\(744\) 0 0
\(745\) −8.39261 + 25.8298i −0.307481 + 0.946330i
\(746\) −9.09017 27.9767i −0.332815 1.02430i
\(747\) 0 0
\(748\) −7.47214 5.42882i −0.273208 0.198497i
\(749\) −73.6656 −2.69168
\(750\) 0 0
\(751\) 5.34752 0.195134 0.0975670 0.995229i \(-0.468894\pi\)
0.0975670 + 0.995229i \(0.468894\pi\)
\(752\) 4.23607 + 3.07768i 0.154474 + 0.112232i
\(753\) 0 0
\(754\) 4.57953 + 14.0943i 0.166777 + 0.513285i
\(755\) −11.3820 + 35.0301i −0.414232 + 1.27488i
\(756\) 0 0
\(757\) 27.3820 0.995214 0.497607 0.867402i \(-0.334212\pi\)
0.497607 + 0.867402i \(0.334212\pi\)
\(758\) −7.23607 + 22.2703i −0.262826 + 0.808895i
\(759\) 0 0
\(760\) −17.5623 + 12.7598i −0.637052 + 0.462845i
\(761\) −7.88197 5.72658i −0.285721 0.207588i 0.435688 0.900098i \(-0.356505\pi\)
−0.721409 + 0.692509i \(0.756505\pi\)
\(762\) 0 0
\(763\) 69.0689 50.1815i 2.50046 1.81669i
\(764\) 19.9443 + 14.4904i 0.721558 + 0.524243i
\(765\) 0 0
\(766\) −16.8541 + 12.2452i −0.608963 + 0.442438i
\(767\) 4.18034 12.8658i 0.150943 0.464556i
\(768\) 0 0
\(769\) −1.74265 + 5.36331i −0.0628414 + 0.193406i −0.977548 0.210712i \(-0.932422\pi\)
0.914707 + 0.404118i \(0.132422\pi\)
\(770\) −32.3607 −1.16620
\(771\) 0 0
\(772\) −2.37132 7.29818i −0.0853458 0.262667i
\(773\) −29.0623 21.1150i −1.04530 0.759454i −0.0739857 0.997259i \(-0.523572\pi\)
−0.971313 + 0.237805i \(0.923572\pi\)
\(774\) 0 0
\(775\) −29.2705 + 21.2663i −1.05143 + 0.763907i
\(776\) 26.5623 0.953531
\(777\) 0 0
\(778\) −11.4615 35.2748i −0.410914 1.26466i
\(779\) −1.38197 4.25325i −0.0495141 0.152389i
\(780\) 0 0
\(781\) −0.763932 + 2.35114i −0.0273356