Properties

Label 363.2.e.m.124.2
Level $363$
Weight $2$
Character 363.124
Analytic conductor $2.899$
Analytic rank $0$
Dimension $8$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [363,2,Mod(124,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.124");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.e (of order \(5\), degree \(4\), not 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: \(2.89856959337\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.324000000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 124.2
Root \(-0.535233 - 1.64728i\) of defining polynomial
Character \(\chi\) \(=\) 363.124
Dual form 363.2.e.m.202.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.40126 - 1.01807i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.42705 + 1.76336i) q^{5} +(-1.40126 - 1.01807i) q^{6} +(1.07047 - 3.29456i) q^{7} +(0.535233 + 1.64728i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(1.40126 - 1.01807i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.42705 + 1.76336i) q^{5} +(-1.40126 - 1.01807i) q^{6} +(1.07047 - 3.29456i) q^{7} +(0.535233 + 1.64728i) q^{8} +(-0.809017 + 0.587785i) q^{9} +5.19615 q^{10} -1.00000 q^{12} +(-1.40126 + 1.01807i) q^{13} +(-1.85410 - 5.70634i) q^{14} +(0.927051 - 2.85317i) q^{15} +(4.04508 + 2.93893i) q^{16} +(1.40126 + 1.01807i) q^{17} +(-0.535233 + 1.64728i) q^{18} +(-2.14093 - 6.58911i) q^{19} +(2.42705 - 1.76336i) q^{20} -3.46410 q^{21} -6.00000 q^{23} +(1.40126 - 1.01807i) q^{24} +(1.23607 + 3.80423i) q^{25} +(-0.927051 + 2.85317i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-2.80252 - 2.03615i) q^{28} +(0.535233 - 1.64728i) q^{29} +(-1.60570 - 4.94183i) q^{30} +(-3.23607 + 2.35114i) q^{31} +5.19615 q^{32} +3.00000 q^{34} +(8.40755 - 6.10844i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-3.39919 + 10.4616i) q^{37} +(-9.70820 - 7.05342i) q^{38} +(1.40126 + 1.01807i) q^{39} +(-1.60570 + 4.94183i) q^{40} +(0.535233 + 1.64728i) q^{41} +(-4.85410 + 3.52671i) q^{42} -3.46410 q^{43} -3.00000 q^{45} +(-8.40755 + 6.10844i) q^{46} +(1.54508 - 4.75528i) q^{48} +(-4.04508 - 2.93893i) q^{49} +(5.60503 + 4.07230i) q^{50} +(0.535233 - 1.64728i) q^{51} +(0.535233 + 1.64728i) q^{52} +(7.28115 - 5.29007i) q^{53} +1.73205 q^{54} +6.00000 q^{56} +(-5.60503 + 4.07230i) q^{57} +(-0.927051 - 2.85317i) q^{58} +(-1.85410 + 5.70634i) q^{59} +(-2.42705 - 1.76336i) q^{60} +(-2.14093 + 6.58911i) q^{62} +(1.07047 + 3.29456i) q^{63} +(-0.809017 + 0.587785i) q^{64} -5.19615 q^{65} -2.00000 q^{67} +(1.40126 - 1.01807i) q^{68} +(1.85410 + 5.70634i) q^{69} +(5.56231 - 17.1190i) q^{70} +(4.85410 + 3.52671i) q^{71} +(-1.40126 - 1.01807i) q^{72} +(-2.14093 + 6.58911i) q^{73} +(5.88756 + 18.1201i) q^{74} +(3.23607 - 2.35114i) q^{75} -6.92820 q^{76} +3.00000 q^{78} +(4.63525 + 14.2658i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.42705 + 1.76336i) q^{82} +(-1.07047 + 3.29456i) q^{84} +(1.60570 + 4.94183i) q^{85} +(-4.85410 + 3.52671i) q^{86} -1.73205 q^{87} +9.00000 q^{89} +(-4.20378 + 3.05422i) q^{90} +(1.85410 + 5.70634i) q^{91} +(-1.85410 + 5.70634i) q^{92} +(3.23607 + 2.35114i) q^{93} +(6.42280 - 19.7673i) q^{95} +(-1.60570 - 4.94183i) q^{96} +(5.66312 - 4.11450i) q^{97} -8.66025 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{9} - 8 q^{12} + 12 q^{14} - 6 q^{15} + 10 q^{16} + 6 q^{20} - 48 q^{23} - 8 q^{25} + 6 q^{26} + 2 q^{27} - 8 q^{31} + 24 q^{34} - 2 q^{36} + 22 q^{37} - 24 q^{38} - 12 q^{42} - 24 q^{45} - 10 q^{48} - 10 q^{49} + 18 q^{53} + 48 q^{56} + 6 q^{58} + 12 q^{59} - 6 q^{60} - 2 q^{64} - 16 q^{67} - 12 q^{69} - 36 q^{70} + 12 q^{71} + 8 q^{75} + 24 q^{78} - 30 q^{80} - 2 q^{81} + 6 q^{82} - 12 q^{86} + 72 q^{89} - 12 q^{91} + 12 q^{92} + 8 q^{93} + 14 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40126 1.01807i 0.990839 0.719887i 0.0307347 0.999528i \(-0.490215\pi\)
0.960105 + 0.279641i \(0.0902153\pi\)
\(3\) −0.309017 0.951057i −0.178411 0.549093i
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) 2.42705 + 1.76336i 1.08541 + 0.788597i 0.978618 0.205685i \(-0.0659421\pi\)
0.106792 + 0.994281i \(0.465942\pi\)
\(6\) −1.40126 1.01807i −0.572061 0.415627i
\(7\) 1.07047 3.29456i 0.404598 1.24523i −0.516632 0.856208i \(-0.672814\pi\)
0.921230 0.389018i \(-0.127186\pi\)
\(8\) 0.535233 + 1.64728i 0.189233 + 0.582401i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) 5.19615 1.64317
\(11\) 0 0
\(12\) −1.00000 −0.288675
\(13\) −1.40126 + 1.01807i −0.388639 + 0.282363i −0.764898 0.644152i \(-0.777210\pi\)
0.376258 + 0.926515i \(0.377210\pi\)
\(14\) −1.85410 5.70634i −0.495530 1.52508i
\(15\) 0.927051 2.85317i 0.239364 0.736685i
\(16\) 4.04508 + 2.93893i 1.01127 + 0.734732i
\(17\) 1.40126 + 1.01807i 0.339855 + 0.246919i 0.744601 0.667510i \(-0.232640\pi\)
−0.404746 + 0.914429i \(0.632640\pi\)
\(18\) −0.535233 + 1.64728i −0.126156 + 0.388267i
\(19\) −2.14093 6.58911i −0.491164 1.51165i −0.822851 0.568257i \(-0.807618\pi\)
0.331688 0.943389i \(-0.392382\pi\)
\(20\) 2.42705 1.76336i 0.542705 0.394298i
\(21\) −3.46410 −0.755929
\(22\) 0 0
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 1.40126 1.01807i 0.286031 0.207813i
\(25\) 1.23607 + 3.80423i 0.247214 + 0.760845i
\(26\) −0.927051 + 2.85317i −0.181810 + 0.559553i
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) −2.80252 2.03615i −0.529626 0.384796i
\(29\) 0.535233 1.64728i 0.0993903 0.305892i −0.888983 0.457941i \(-0.848587\pi\)
0.988373 + 0.152049i \(0.0485871\pi\)
\(30\) −1.60570 4.94183i −0.293159 0.902251i
\(31\) −3.23607 + 2.35114i −0.581215 + 0.422277i −0.839162 0.543882i \(-0.816954\pi\)
0.257947 + 0.966159i \(0.416954\pi\)
\(32\) 5.19615 0.918559
\(33\) 0 0
\(34\) 3.00000 0.514496
\(35\) 8.40755 6.10844i 1.42114 1.03252i
\(36\) 0.309017 + 0.951057i 0.0515028 + 0.158509i
\(37\) −3.39919 + 10.4616i −0.558823 + 1.71988i 0.126805 + 0.991928i \(0.459528\pi\)
−0.685628 + 0.727952i \(0.740472\pi\)
\(38\) −9.70820 7.05342i −1.57488 1.14422i
\(39\) 1.40126 + 1.01807i 0.224381 + 0.163022i
\(40\) −1.60570 + 4.94183i −0.253883 + 0.781373i
\(41\) 0.535233 + 1.64728i 0.0835894 + 0.257262i 0.984112 0.177547i \(-0.0568161\pi\)
−0.900523 + 0.434808i \(0.856816\pi\)
\(42\) −4.85410 + 3.52671i −0.749004 + 0.544183i
\(43\) −3.46410 −0.528271 −0.264135 0.964486i \(-0.585087\pi\)
−0.264135 + 0.964486i \(0.585087\pi\)
\(44\) 0 0
\(45\) −3.00000 −0.447214
\(46\) −8.40755 + 6.10844i −1.23963 + 0.900641i
\(47\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(48\) 1.54508 4.75528i 0.223014 0.686366i
\(49\) −4.04508 2.93893i −0.577869 0.419847i
\(50\) 5.60503 + 4.07230i 0.792672 + 0.575910i
\(51\) 0.535233 1.64728i 0.0749476 0.230665i
\(52\) 0.535233 + 1.64728i 0.0742235 + 0.228436i
\(53\) 7.28115 5.29007i 1.00014 0.726647i 0.0380244 0.999277i \(-0.487894\pi\)
0.962119 + 0.272630i \(0.0878935\pi\)
\(54\) 1.73205 0.235702
\(55\) 0 0
\(56\) 6.00000 0.801784
\(57\) −5.60503 + 4.07230i −0.742405 + 0.539389i
\(58\) −0.927051 2.85317i −0.121728 0.374640i
\(59\) −1.85410 + 5.70634i −0.241384 + 0.742902i 0.754827 + 0.655924i \(0.227721\pi\)
−0.996210 + 0.0869778i \(0.972279\pi\)
\(60\) −2.42705 1.76336i −0.313331 0.227648i
\(61\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(62\) −2.14093 + 6.58911i −0.271899 + 0.836818i
\(63\) 1.07047 + 3.29456i 0.134866 + 0.415075i
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) −5.19615 −0.644503
\(66\) 0 0
\(67\) −2.00000 −0.244339 −0.122169 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) 1.40126 1.01807i 0.169928 0.123460i
\(69\) 1.85410 + 5.70634i 0.223208 + 0.686963i
\(70\) 5.56231 17.1190i 0.664823 2.04611i
\(71\) 4.85410 + 3.52671i 0.576076 + 0.418544i 0.837307 0.546733i \(-0.184129\pi\)
−0.261231 + 0.965276i \(0.584129\pi\)
\(72\) −1.40126 1.01807i −0.165140 0.119981i
\(73\) −2.14093 + 6.58911i −0.250577 + 0.771197i 0.744092 + 0.668077i \(0.232883\pi\)
−0.994669 + 0.103120i \(0.967117\pi\)
\(74\) 5.88756 + 18.1201i 0.684415 + 2.10641i
\(75\) 3.23607 2.35114i 0.373669 0.271486i
\(76\) −6.92820 −0.794719
\(77\) 0 0
\(78\) 3.00000 0.339683
\(79\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(80\) 4.63525 + 14.2658i 0.518237 + 1.59497i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 2.42705 + 1.76336i 0.268023 + 0.194730i
\(83\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(84\) −1.07047 + 3.29456i −0.116797 + 0.359466i
\(85\) 1.60570 + 4.94183i 0.174163 + 0.536017i
\(86\) −4.85410 + 3.52671i −0.523431 + 0.380295i
\(87\) −1.73205 −0.185695
\(88\) 0 0
\(89\) 9.00000 0.953998 0.476999 0.878904i \(-0.341725\pi\)
0.476999 + 0.878904i \(0.341725\pi\)
\(90\) −4.20378 + 3.05422i −0.443117 + 0.321943i
\(91\) 1.85410 + 5.70634i 0.194363 + 0.598187i
\(92\) −1.85410 + 5.70634i −0.193303 + 0.594927i
\(93\) 3.23607 + 2.35114i 0.335565 + 0.243802i
\(94\) 0 0
\(95\) 6.42280 19.7673i 0.658965 2.02809i
\(96\) −1.60570 4.94183i −0.163881 0.504374i
\(97\) 5.66312 4.11450i 0.575003 0.417764i −0.261916 0.965091i \(-0.584354\pi\)
0.836919 + 0.547327i \(0.184354\pi\)
\(98\) −8.66025 −0.874818
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) −11.2101 + 8.14459i −1.11544 + 0.810417i −0.983512 0.180842i \(-0.942118\pi\)
−0.131931 + 0.991259i \(0.542118\pi\)
\(102\) −0.927051 2.85317i −0.0917917 0.282506i
\(103\) 4.32624 13.3148i 0.426277 1.31195i −0.475489 0.879721i \(-0.657729\pi\)
0.901766 0.432224i \(-0.142271\pi\)
\(104\) −2.42705 1.76336i −0.237992 0.172911i
\(105\) −8.40755 6.10844i −0.820493 0.596123i
\(106\) 4.81710 14.8255i 0.467878 1.43998i
\(107\) −1.07047 3.29456i −0.103486 0.318497i 0.885886 0.463903i \(-0.153551\pi\)
−0.989372 + 0.145406i \(0.953551\pi\)
\(108\) 0.809017 0.587785i 0.0778477 0.0565597i
\(109\) −15.5885 −1.49310 −0.746552 0.665327i \(-0.768292\pi\)
−0.746552 + 0.665327i \(0.768292\pi\)
\(110\) 0 0
\(111\) 11.0000 1.04407
\(112\) 14.0126 10.1807i 1.32406 0.961989i
\(113\) −6.48936 19.9722i −0.610467 1.87883i −0.453599 0.891206i \(-0.649860\pi\)
−0.156868 0.987620i \(-0.550140\pi\)
\(114\) −3.70820 + 11.4127i −0.347305 + 1.06890i
\(115\) −14.5623 10.5801i −1.35794 0.986603i
\(116\) −1.40126 1.01807i −0.130104 0.0945258i
\(117\) 0.535233 1.64728i 0.0494823 0.152291i
\(118\) 3.21140 + 9.88367i 0.295633 + 0.909866i
\(119\) 4.85410 3.52671i 0.444975 0.323293i
\(120\) 5.19615 0.474342
\(121\) 0 0
\(122\) 0 0
\(123\) 1.40126 1.01807i 0.126347 0.0917966i
\(124\) 1.23607 + 3.80423i 0.111002 + 0.341630i
\(125\) 0.927051 2.85317i 0.0829180 0.255195i
\(126\) 4.85410 + 3.52671i 0.432438 + 0.314184i
\(127\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(128\) −3.74663 + 11.5309i −0.331159 + 1.01920i
\(129\) 1.07047 + 3.29456i 0.0942493 + 0.290070i
\(130\) −7.28115 + 5.29007i −0.638599 + 0.463970i
\(131\) 17.3205 1.51330 0.756650 0.653820i \(-0.226835\pi\)
0.756650 + 0.653820i \(0.226835\pi\)
\(132\) 0 0
\(133\) −24.0000 −2.08106
\(134\) −2.80252 + 2.03615i −0.242101 + 0.175896i
\(135\) 0.927051 + 2.85317i 0.0797878 + 0.245562i
\(136\) −0.927051 + 2.85317i −0.0794940 + 0.244657i
\(137\) 4.85410 + 3.52671i 0.414714 + 0.301307i 0.775507 0.631338i \(-0.217494\pi\)
−0.360794 + 0.932646i \(0.617494\pi\)
\(138\) 8.40755 + 6.10844i 0.715698 + 0.519985i
\(139\) −3.21140 + 9.88367i −0.272387 + 0.838322i 0.717512 + 0.696547i \(0.245281\pi\)
−0.989899 + 0.141775i \(0.954719\pi\)
\(140\) −3.21140 9.88367i −0.271413 0.835323i
\(141\) 0 0
\(142\) 10.3923 0.872103
\(143\) 0 0
\(144\) −5.00000 −0.416667
\(145\) 4.20378 3.05422i 0.349105 0.253639i
\(146\) 3.70820 + 11.4127i 0.306893 + 0.944520i
\(147\) −1.54508 + 4.75528i −0.127436 + 0.392209i
\(148\) 8.89919 + 6.46564i 0.731509 + 0.531472i
\(149\) −9.80881 7.12652i −0.803569 0.583827i 0.108390 0.994108i \(-0.465430\pi\)
−0.911959 + 0.410281i \(0.865430\pi\)
\(150\) 2.14093 6.58911i 0.174806 0.537999i
\(151\) −4.28187 13.1782i −0.348453 1.07243i −0.959709 0.280996i \(-0.909335\pi\)
0.611256 0.791433i \(-0.290665\pi\)
\(152\) 9.70820 7.05342i 0.787439 0.572108i
\(153\) −1.73205 −0.140028
\(154\) 0 0
\(155\) −12.0000 −0.963863
\(156\) 1.40126 1.01807i 0.112190 0.0815111i
\(157\) −4.32624 13.3148i −0.345271 1.06264i −0.961438 0.275020i \(-0.911315\pi\)
0.616167 0.787616i \(-0.288685\pi\)
\(158\) 0 0
\(159\) −7.28115 5.29007i −0.577433 0.419530i
\(160\) 12.6113 + 9.16267i 0.997013 + 0.724372i
\(161\) −6.42280 + 19.7673i −0.506187 + 1.55788i
\(162\) −0.535233 1.64728i −0.0420519 0.129422i
\(163\) −1.61803 + 1.17557i −0.126734 + 0.0920778i −0.649347 0.760493i \(-0.724958\pi\)
0.522612 + 0.852570i \(0.324958\pi\)
\(164\) 1.73205 0.135250
\(165\) 0 0
\(166\) 0 0
\(167\) −2.80252 + 2.03615i −0.216865 + 0.157562i −0.690914 0.722937i \(-0.742792\pi\)
0.474049 + 0.880498i \(0.342792\pi\)
\(168\) −1.85410 5.70634i −0.143047 0.440254i
\(169\) −3.09017 + 9.51057i −0.237705 + 0.731582i
\(170\) 7.28115 + 5.29007i 0.558439 + 0.405730i
\(171\) 5.60503 + 4.07230i 0.428628 + 0.311416i
\(172\) −1.07047 + 3.29456i −0.0816223 + 0.251208i
\(173\) −6.42280 19.7673i −0.488316 1.50288i −0.827120 0.562026i \(-0.810022\pi\)
0.338803 0.940857i \(-0.389978\pi\)
\(174\) −2.42705 + 1.76336i −0.183994 + 0.133680i
\(175\) 13.8564 1.04745
\(176\) 0 0
\(177\) 6.00000 0.450988
\(178\) 12.6113 9.16267i 0.945259 0.686771i
\(179\) 3.70820 + 11.4127i 0.277164 + 0.853024i 0.988639 + 0.150312i \(0.0480277\pi\)
−0.711474 + 0.702712i \(0.751972\pi\)
\(180\) −0.927051 + 2.85317i −0.0690983 + 0.212663i
\(181\) 5.66312 + 4.11450i 0.420936 + 0.305828i 0.778014 0.628246i \(-0.216227\pi\)
−0.357078 + 0.934075i \(0.616227\pi\)
\(182\) 8.40755 + 6.10844i 0.623209 + 0.452788i
\(183\) 0 0
\(184\) −3.21140 9.88367i −0.236747 0.728634i
\(185\) −26.6976 + 19.3969i −1.96284 + 1.42609i
\(186\) 6.92820 0.508001
\(187\) 0 0
\(188\) 0 0
\(189\) 2.80252 2.03615i 0.203853 0.148108i
\(190\) −11.1246 34.2380i −0.807064 2.48389i
\(191\) 3.70820 11.4127i 0.268316 0.825792i −0.722595 0.691272i \(-0.757051\pi\)
0.990911 0.134520i \(-0.0429494\pi\)
\(192\) 0.809017 + 0.587785i 0.0583858 + 0.0424197i
\(193\) −4.20378 3.05422i −0.302594 0.219848i 0.426118 0.904668i \(-0.359881\pi\)
−0.728712 + 0.684820i \(0.759881\pi\)
\(194\) 3.74663 11.5309i 0.268992 0.827874i
\(195\) 1.60570 + 4.94183i 0.114987 + 0.353892i
\(196\) −4.04508 + 2.93893i −0.288935 + 0.209923i
\(197\) 19.0526 1.35744 0.678719 0.734398i \(-0.262535\pi\)
0.678719 + 0.734398i \(0.262535\pi\)
\(198\) 0 0
\(199\) 10.0000 0.708881 0.354441 0.935079i \(-0.384671\pi\)
0.354441 + 0.935079i \(0.384671\pi\)
\(200\) −5.60503 + 4.07230i −0.396336 + 0.287955i
\(201\) 0.618034 + 1.90211i 0.0435928 + 0.134165i
\(202\) −7.41641 + 22.8254i −0.521817 + 1.60599i
\(203\) −4.85410 3.52671i −0.340691 0.247527i
\(204\) −1.40126 1.01807i −0.0981077 0.0712794i
\(205\) −1.60570 + 4.94183i −0.112147 + 0.345153i
\(206\) −7.49326 23.0619i −0.522080 1.60680i
\(207\) 4.85410 3.52671i 0.337383 0.245123i
\(208\) −8.66025 −0.600481
\(209\) 0 0
\(210\) −18.0000 −1.24212
\(211\) −14.0126 + 10.1807i −0.964666 + 0.700871i −0.954230 0.299075i \(-0.903322\pi\)
−0.0104364 + 0.999946i \(0.503322\pi\)
\(212\) −2.78115 8.55951i −0.191010 0.587869i
\(213\) 1.85410 5.70634i 0.127041 0.390992i
\(214\) −4.85410 3.52671i −0.331820 0.241081i
\(215\) −8.40755 6.10844i −0.573390 0.416592i
\(216\) −0.535233 + 1.64728i −0.0364180 + 0.112083i
\(217\) 4.28187 + 13.1782i 0.290672 + 0.894596i
\(218\) −21.8435 + 15.8702i −1.47943 + 1.07487i
\(219\) 6.92820 0.468165
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 15.4138 11.1988i 1.03451 0.751615i
\(223\) 6.18034 + 19.0211i 0.413866 + 1.27375i 0.913261 + 0.407375i \(0.133556\pi\)
−0.499395 + 0.866374i \(0.666444\pi\)
\(224\) 5.56231 17.1190i 0.371647 1.14381i
\(225\) −3.23607 2.35114i −0.215738 0.156743i
\(226\) −29.4264 21.3796i −1.95742 1.42215i
\(227\) 7.49326 23.0619i 0.497345 1.53067i −0.315924 0.948784i \(-0.602314\pi\)
0.813269 0.581887i \(-0.197686\pi\)
\(228\) 2.14093 + 6.58911i 0.141787 + 0.436375i
\(229\) 18.6074 13.5191i 1.22961 0.893365i 0.232750 0.972537i \(-0.425228\pi\)
0.996861 + 0.0791719i \(0.0252276\pi\)
\(230\) −31.1769 −2.05574
\(231\) 0 0
\(232\) 3.00000 0.196960
\(233\) 23.8214 17.3073i 1.56059 1.13384i 0.625069 0.780570i \(-0.285071\pi\)
0.935523 0.353266i \(-0.114929\pi\)
\(234\) −0.927051 2.85317i −0.0606032 0.186518i
\(235\) 0 0
\(236\) 4.85410 + 3.52671i 0.315975 + 0.229569i
\(237\) 0 0
\(238\) 3.21140 9.88367i 0.208164 0.640663i
\(239\) 2.14093 + 6.58911i 0.138485 + 0.426214i 0.996116 0.0880522i \(-0.0280642\pi\)
−0.857630 + 0.514266i \(0.828064\pi\)
\(240\) 12.1353 8.81678i 0.783327 0.569121i
\(241\) 20.7846 1.33885 0.669427 0.742878i \(-0.266540\pi\)
0.669427 + 0.742878i \(0.266540\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −4.63525 14.2658i −0.296136 0.911412i
\(246\) 0.927051 2.85317i 0.0591066 0.181911i
\(247\) 9.70820 + 7.05342i 0.617718 + 0.448799i
\(248\) −5.60503 4.07230i −0.355920 0.258591i
\(249\) 0 0
\(250\) −1.60570 4.94183i −0.101553 0.312549i
\(251\) 4.85410 3.52671i 0.306388 0.222604i −0.423957 0.905682i \(-0.639359\pi\)
0.730345 + 0.683078i \(0.239359\pi\)
\(252\) 3.46410 0.218218
\(253\) 0 0
\(254\) 0 0
\(255\) 4.20378 3.05422i 0.263251 0.191263i
\(256\) 5.87132 + 18.0701i 0.366958 + 1.12938i
\(257\) 2.78115 8.55951i 0.173484 0.533927i −0.826077 0.563557i \(-0.809433\pi\)
0.999561 + 0.0296292i \(0.00943265\pi\)
\(258\) 4.85410 + 3.52671i 0.302203 + 0.219563i
\(259\) 30.8277 + 22.3976i 1.91554 + 1.39172i
\(260\) −1.60570 + 4.94183i −0.0995812 + 0.306480i
\(261\) 0.535233 + 1.64728i 0.0331301 + 0.101964i
\(262\) 24.2705 17.6336i 1.49944 1.08940i
\(263\) −13.8564 −0.854423 −0.427211 0.904152i \(-0.640504\pi\)
−0.427211 + 0.904152i \(0.640504\pi\)
\(264\) 0 0
\(265\) 27.0000 1.65860
\(266\) −33.6302 + 24.4338i −2.06200 + 1.49813i
\(267\) −2.78115 8.55951i −0.170204 0.523833i
\(268\) −0.618034 + 1.90211i −0.0377524 + 0.116190i
\(269\) 16.9894 + 12.3435i 1.03586 + 0.752596i 0.969473 0.245198i \(-0.0788530\pi\)
0.0663864 + 0.997794i \(0.478853\pi\)
\(270\) 4.20378 + 3.05422i 0.255834 + 0.185874i
\(271\) 1.07047 3.29456i 0.0650262 0.200130i −0.913265 0.407367i \(-0.866447\pi\)
0.978291 + 0.207237i \(0.0664471\pi\)
\(272\) 2.67617 + 8.23639i 0.162266 + 0.499405i
\(273\) 4.85410 3.52671i 0.293784 0.213446i
\(274\) 10.3923 0.627822
\(275\) 0 0
\(276\) 6.00000 0.361158
\(277\) −4.20378 + 3.05422i −0.252580 + 0.183510i −0.706870 0.707344i \(-0.749893\pi\)
0.454289 + 0.890854i \(0.349893\pi\)
\(278\) 5.56231 + 17.1190i 0.333605 + 1.02673i
\(279\) 1.23607 3.80423i 0.0740015 0.227753i
\(280\) 14.5623 + 10.5801i 0.870264 + 0.632284i
\(281\) −5.60503 4.07230i −0.334368 0.242933i 0.407914 0.913021i \(-0.366256\pi\)
−0.742282 + 0.670088i \(0.766256\pi\)
\(282\) 0 0
\(283\) 9.63420 + 29.6510i 0.572694 + 1.76257i 0.643902 + 0.765108i \(0.277314\pi\)
−0.0712084 + 0.997461i \(0.522686\pi\)
\(284\) 4.85410 3.52671i 0.288038 0.209272i
\(285\) −20.7846 −1.23117
\(286\) 0 0
\(287\) 6.00000 0.354169
\(288\) −4.20378 + 3.05422i −0.247710 + 0.179972i
\(289\) −4.32624 13.3148i −0.254485 0.783223i
\(290\) 2.78115 8.55951i 0.163315 0.502632i
\(291\) −5.66312 4.11450i −0.331978 0.241196i
\(292\) 5.60503 + 4.07230i 0.328010 + 0.238313i
\(293\) −5.88756 + 18.1201i −0.343955 + 1.05859i 0.618186 + 0.786032i \(0.287868\pi\)
−0.962141 + 0.272553i \(0.912132\pi\)
\(294\) 2.67617 + 8.23639i 0.156077 + 0.480356i
\(295\) −14.5623 + 10.5801i −0.847850 + 0.615999i
\(296\) −19.0526 −1.10741
\(297\) 0 0
\(298\) −21.0000 −1.21650
\(299\) 8.40755 6.10844i 0.486221 0.353260i
\(300\) −1.23607 3.80423i −0.0713644 0.219637i
\(301\) −3.70820 + 11.4127i −0.213737 + 0.657816i
\(302\) −19.4164 14.1068i −1.11729 0.811758i
\(303\) 11.2101 + 8.14459i 0.644002 + 0.467895i
\(304\) 10.7047 32.9456i 0.613955 1.88956i
\(305\) 0 0
\(306\) −2.42705 + 1.76336i −0.138745 + 0.100804i
\(307\) −3.46410 −0.197707 −0.0988534 0.995102i \(-0.531517\pi\)
−0.0988534 + 0.995102i \(0.531517\pi\)
\(308\) 0 0
\(309\) −14.0000 −0.796432
\(310\) −16.8151 + 12.2169i −0.955034 + 0.693873i
\(311\) 3.70820 + 11.4127i 0.210273 + 0.647154i 0.999456 + 0.0329949i \(0.0105045\pi\)
−0.789183 + 0.614159i \(0.789495\pi\)
\(312\) −0.927051 + 2.85317i −0.0524839 + 0.161529i
\(313\) −5.66312 4.11450i −0.320098 0.232565i 0.416119 0.909310i \(-0.363390\pi\)
−0.736217 + 0.676745i \(0.763390\pi\)
\(314\) −19.6176 14.2530i −1.10709 0.804345i
\(315\) −3.21140 + 9.88367i −0.180942 + 0.556882i
\(316\) 0 0
\(317\) −4.85410 + 3.52671i −0.272634 + 0.198080i −0.715698 0.698410i \(-0.753891\pi\)
0.443064 + 0.896490i \(0.353891\pi\)
\(318\) −15.5885 −0.874157
\(319\) 0 0
\(320\) −3.00000 −0.167705
\(321\) −2.80252 + 2.03615i −0.156421 + 0.113647i
\(322\) 11.1246 + 34.2380i 0.619950 + 1.90801i
\(323\) 3.70820 11.4127i 0.206330 0.635018i
\(324\) −0.809017 0.587785i −0.0449454 0.0326547i
\(325\) −5.60503 4.07230i −0.310911 0.225890i
\(326\) −1.07047 + 3.29456i −0.0592876 + 0.182469i
\(327\) 4.81710 + 14.8255i 0.266386 + 0.819852i
\(328\) −2.42705 + 1.76336i −0.134011 + 0.0973650i
\(329\) 0 0
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 0 0
\(333\) −3.39919 10.4616i −0.186274 0.573293i
\(334\) −1.85410 + 5.70634i −0.101452 + 0.312237i
\(335\) −4.85410 3.52671i −0.265208 0.192685i
\(336\) −14.0126 10.1807i −0.764449 0.555405i
\(337\) 3.74663 11.5309i 0.204092 0.628131i −0.795657 0.605747i \(-0.792874\pi\)
0.999749 0.0223838i \(-0.00712559\pi\)
\(338\) 5.35233 + 16.4728i 0.291128 + 0.896001i
\(339\) −16.9894 + 12.3435i −0.922735 + 0.670406i
\(340\) 5.19615 0.281801
\(341\) 0 0
\(342\) 12.0000 0.648886
\(343\) 5.60503 4.07230i 0.302643 0.219883i
\(344\) −1.85410 5.70634i −0.0999665 0.307665i
\(345\) −5.56231 + 17.1190i −0.299464 + 0.921657i
\(346\) −29.1246 21.1603i −1.56575 1.13758i
\(347\) 22.4201 + 16.2892i 1.20358 + 0.874449i 0.994632 0.103478i \(-0.0329973\pi\)
0.208944 + 0.977928i \(0.432997\pi\)
\(348\) −0.535233 + 1.64728i −0.0286915 + 0.0883034i
\(349\) 0.535233 + 1.64728i 0.0286504 + 0.0881768i 0.964359 0.264596i \(-0.0852387\pi\)
−0.935709 + 0.352773i \(0.885239\pi\)
\(350\) 19.4164 14.1068i 1.03785 0.754043i
\(351\) −1.73205 −0.0924500
\(352\) 0 0
\(353\) 21.0000 1.11772 0.558859 0.829263i \(-0.311239\pi\)
0.558859 + 0.829263i \(0.311239\pi\)
\(354\) 8.40755 6.10844i 0.446856 0.324660i
\(355\) 5.56231 + 17.1190i 0.295217 + 0.908583i
\(356\) 2.78115 8.55951i 0.147401 0.453653i
\(357\) −4.85410 3.52671i −0.256906 0.186653i
\(358\) 16.8151 + 12.2169i 0.888706 + 0.645683i
\(359\) −9.63420 + 29.6510i −0.508473 + 1.56492i 0.286378 + 0.958117i \(0.407549\pi\)
−0.794852 + 0.606804i \(0.792451\pi\)
\(360\) −1.60570 4.94183i −0.0846278 0.260458i
\(361\) −23.4615 + 17.0458i −1.23482 + 0.897146i
\(362\) 12.1244 0.637242
\(363\) 0 0
\(364\) 6.00000 0.314485
\(365\) −16.8151 + 12.2169i −0.880143 + 0.639461i
\(366\) 0 0
\(367\) 8.03444 24.7275i 0.419394 1.29076i −0.488866 0.872359i \(-0.662589\pi\)
0.908261 0.418405i \(-0.137411\pi\)
\(368\) −24.2705 17.6336i −1.26519 0.919213i
\(369\) −1.40126 1.01807i −0.0729466 0.0529988i
\(370\) −17.6627 + 54.3602i −0.918240 + 2.82605i
\(371\) −9.63420 29.6510i −0.500183 1.53940i
\(372\) 3.23607 2.35114i 0.167782 0.121901i
\(373\) −20.7846 −1.07619 −0.538093 0.842885i \(-0.680855\pi\)
−0.538093 + 0.842885i \(0.680855\pi\)
\(374\) 0 0
\(375\) −3.00000 −0.154919
\(376\) 0 0
\(377\) 0.927051 + 2.85317i 0.0477456 + 0.146946i
\(378\) 1.85410 5.70634i 0.0953647 0.293502i
\(379\) −11.3262 8.22899i −0.581790 0.422695i 0.257579 0.966257i \(-0.417075\pi\)
−0.839369 + 0.543562i \(0.817075\pi\)
\(380\) −16.8151 12.2169i −0.862597 0.626713i
\(381\) 0 0
\(382\) −6.42280 19.7673i −0.328619 1.01139i
\(383\) −4.85410 + 3.52671i −0.248033 + 0.180207i −0.704855 0.709352i \(-0.748988\pi\)
0.456822 + 0.889558i \(0.348988\pi\)
\(384\) 12.1244 0.618718
\(385\) 0 0
\(386\) −9.00000 −0.458088
\(387\) 2.80252 2.03615i 0.142460 0.103503i
\(388\) −2.16312 6.65740i −0.109816 0.337978i
\(389\) −8.34346 + 25.6785i −0.423030 + 1.30195i 0.481838 + 0.876260i \(0.339969\pi\)
−0.904868 + 0.425692i \(0.860031\pi\)
\(390\) 7.28115 + 5.29007i 0.368696 + 0.267873i
\(391\) −8.40755 6.10844i −0.425188 0.308917i
\(392\) 2.67617 8.23639i 0.135167 0.416001i
\(393\) −5.35233 16.4728i −0.269989 0.830942i
\(394\) 26.6976 19.3969i 1.34500 0.977202i
\(395\) 0 0
\(396\) 0 0
\(397\) 11.0000 0.552074 0.276037 0.961147i \(-0.410979\pi\)
0.276037 + 0.961147i \(0.410979\pi\)
\(398\) 14.0126 10.1807i 0.702387 0.510314i
\(399\) 7.41641 + 22.8254i 0.371285 + 1.14270i
\(400\) −6.18034 + 19.0211i −0.309017 + 0.951057i
\(401\) −2.42705 1.76336i −0.121201 0.0880578i 0.525533 0.850773i \(-0.323866\pi\)
−0.646734 + 0.762715i \(0.723866\pi\)
\(402\) 2.80252 + 2.03615i 0.139777 + 0.101554i
\(403\) 2.14093 6.58911i 0.106647 0.328227i
\(404\) 4.28187 + 13.1782i 0.213031 + 0.655641i
\(405\) 2.42705 1.76336i 0.120601 0.0876219i
\(406\) −10.3923 −0.515761
\(407\) 0 0
\(408\) 3.00000 0.148522
\(409\) 1.40126 1.01807i 0.0692878 0.0503405i −0.552602 0.833445i \(-0.686365\pi\)
0.621890 + 0.783105i \(0.286365\pi\)
\(410\) 2.78115 + 8.55951i 0.137351 + 0.422724i
\(411\) 1.85410 5.70634i 0.0914561 0.281473i
\(412\) −11.3262 8.22899i −0.558004 0.405413i
\(413\) 16.8151 + 12.2169i 0.827417 + 0.601154i
\(414\) 3.21140 9.88367i 0.157832 0.485756i
\(415\) 0 0
\(416\) −7.28115 + 5.29007i −0.356988 + 0.259367i
\(417\) 10.3923 0.508913
\(418\) 0 0
\(419\) −30.0000 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) −8.40755 + 6.10844i −0.410246 + 0.298062i
\(421\) 2.16312 + 6.65740i 0.105424 + 0.324462i 0.989830 0.142257i \(-0.0454360\pi\)
−0.884406 + 0.466719i \(0.845436\pi\)
\(422\) −9.27051 + 28.5317i −0.451281 + 1.38890i
\(423\) 0 0
\(424\) 12.6113 + 9.16267i 0.612460 + 0.444978i
\(425\) −2.14093 + 6.58911i −0.103850 + 0.319619i
\(426\) −3.21140 9.88367i −0.155593 0.478865i
\(427\) 0 0
\(428\) −3.46410 −0.167444
\(429\) 0 0
\(430\) −18.0000 −0.868037
\(431\) −14.0126 + 10.1807i −0.674962 + 0.490389i −0.871683 0.490071i \(-0.836971\pi\)
0.196720 + 0.980460i \(0.436971\pi\)
\(432\) 1.54508 + 4.75528i 0.0743379 + 0.228789i
\(433\) −5.87132 + 18.0701i −0.282158 + 0.868392i 0.705078 + 0.709129i \(0.250912\pi\)
−0.987236 + 0.159263i \(0.949088\pi\)
\(434\) 19.4164 + 14.1068i 0.932017 + 0.677150i
\(435\) −4.20378 3.05422i −0.201556 0.146439i
\(436\) −4.81710 + 14.8255i −0.230697 + 0.710013i
\(437\) 12.8456 + 39.5347i 0.614488 + 1.89120i
\(438\) 9.70820 7.05342i 0.463876 0.337026i
\(439\) 6.92820 0.330665 0.165333 0.986238i \(-0.447130\pi\)
0.165333 + 0.986238i \(0.447130\pi\)
\(440\) 0 0
\(441\) 5.00000 0.238095
\(442\) −4.20378 + 3.05422i −0.199953 + 0.145275i
\(443\) −5.56231 17.1190i −0.264273 0.813349i −0.991860 0.127333i \(-0.959358\pi\)
0.727587 0.686016i \(-0.240642\pi\)
\(444\) 3.39919 10.4616i 0.161318 0.496487i
\(445\) 21.8435 + 15.8702i 1.03548 + 0.752320i
\(446\) 28.0252 + 20.3615i 1.32703 + 0.964144i
\(447\) −3.74663 + 11.5309i −0.177210 + 0.545395i
\(448\) 1.07047 + 3.29456i 0.0505748 + 0.155653i
\(449\) −16.9894 + 12.3435i −0.801777 + 0.582525i −0.911435 0.411444i \(-0.865025\pi\)
0.109658 + 0.993969i \(0.465025\pi\)
\(450\) −6.92820 −0.326599
\(451\) 0 0
\(452\) −21.0000 −0.987757
\(453\) −11.2101 + 8.14459i −0.526695 + 0.382666i
\(454\) −12.9787 39.9444i −0.609121 1.87468i
\(455\) −5.56231 + 17.1190i −0.260765 + 0.802552i
\(456\) −9.70820 7.05342i −0.454628 0.330307i
\(457\) −23.8214 17.3073i −1.11432 0.809599i −0.130980 0.991385i \(-0.541812\pi\)
−0.983338 + 0.181786i \(0.941812\pi\)
\(458\) 12.3104 37.8874i 0.575225 1.77036i
\(459\) 0.535233 + 1.64728i 0.0249825 + 0.0768884i
\(460\) −14.5623 + 10.5801i −0.678971 + 0.493301i
\(461\) 15.5885 0.726027 0.363013 0.931784i \(-0.381748\pi\)
0.363013 + 0.931784i \(0.381748\pi\)
\(462\) 0 0
\(463\) −34.0000 −1.58011 −0.790057 0.613033i \(-0.789949\pi\)
−0.790057 + 0.613033i \(0.789949\pi\)
\(464\) 7.00629 5.09037i 0.325259 0.236314i
\(465\) 3.70820 + 11.4127i 0.171964 + 0.529250i
\(466\) 15.7599 48.5039i 0.730062 2.24690i
\(467\) 14.5623 + 10.5801i 0.673863 + 0.489590i 0.871316 0.490722i \(-0.163267\pi\)
−0.197453 + 0.980312i \(0.563267\pi\)
\(468\) −1.40126 1.01807i −0.0647732 0.0470605i
\(469\) −2.14093 + 6.58911i −0.0988591 + 0.304257i
\(470\) 0 0
\(471\) −11.3262 + 8.22899i −0.521885 + 0.379172i
\(472\) −10.3923 −0.478345
\(473\) 0 0
\(474\) 0 0
\(475\) 22.4201 16.2892i 1.02871 0.747399i
\(476\) −1.85410 5.70634i −0.0849826 0.261550i
\(477\) −2.78115 + 8.55951i −0.127340 + 0.391913i
\(478\) 9.70820 + 7.05342i 0.444043 + 0.322616i
\(479\) 19.6176 + 14.2530i 0.896352 + 0.651238i 0.937526 0.347914i \(-0.113110\pi\)
−0.0411745 + 0.999152i \(0.513110\pi\)
\(480\) 4.81710 14.8255i 0.219869 0.676689i
\(481\) −5.88756 18.1201i −0.268450 0.826204i
\(482\) 29.1246 21.1603i 1.32659 0.963824i
\(483\) 20.7846 0.945732
\(484\) 0 0
\(485\) 21.0000 0.953561
\(486\) −1.40126 + 1.01807i −0.0635624 + 0.0461808i
\(487\) −11.7426 36.1401i −0.532110 1.63767i −0.749812 0.661651i \(-0.769856\pi\)
0.217702 0.976015i \(-0.430144\pi\)
\(488\) 0 0
\(489\) 1.61803 + 1.17557i 0.0731700 + 0.0531611i
\(490\) −21.0189 15.2711i −0.949536 0.689878i
\(491\) 6.42280 19.7673i 0.289857 0.892087i −0.695044 0.718967i \(-0.744615\pi\)
0.984901 0.173120i \(-0.0553849\pi\)
\(492\) −0.535233 1.64728i −0.0241302 0.0742650i
\(493\) 2.42705 1.76336i 0.109309 0.0794175i
\(494\) 20.7846 0.935144
\(495\) 0 0
\(496\) −20.0000 −0.898027
\(497\) 16.8151 12.2169i 0.754260 0.548002i
\(498\) 0 0
\(499\) 6.79837 20.9232i 0.304337 0.936653i −0.675587 0.737280i \(-0.736110\pi\)
0.979924 0.199373i \(-0.0638904\pi\)
\(500\) −2.42705 1.76336i −0.108541 0.0788597i
\(501\) 2.80252 + 2.03615i 0.125207 + 0.0909684i
\(502\) 3.21140 9.88367i 0.143332 0.441130i
\(503\) −9.63420 29.6510i −0.429568 1.32207i −0.898552 0.438867i \(-0.855380\pi\)
0.468985 0.883206i \(-0.344620\pi\)
\(504\) −4.85410 + 3.52671i −0.216219 + 0.157092i
\(505\) −41.5692 −1.84981
\(506\) 0 0
\(507\) 10.0000 0.444116
\(508\) 0 0
\(509\) 5.56231 + 17.1190i 0.246545 + 0.758787i 0.995379 + 0.0960291i \(0.0306142\pi\)
−0.748834 + 0.662758i \(0.769386\pi\)
\(510\) 2.78115 8.55951i 0.123152 0.379021i
\(511\) 19.4164 + 14.1068i 0.858931 + 0.624050i
\(512\) 7.00629 + 5.09037i 0.309637 + 0.224965i
\(513\) 2.14093 6.58911i 0.0945245 0.290916i
\(514\) −4.81710 14.8255i −0.212473 0.653925i
\(515\) 33.9787 24.6870i 1.49728 1.08784i
\(516\) 3.46410 0.152499
\(517\) 0 0
\(518\) 66.0000 2.89987
\(519\) −16.8151 + 12.2169i −0.738101 + 0.536262i
\(520\) −2.78115 8.55951i −0.121962 0.375359i
\(521\) 1.85410 5.70634i 0.0812297 0.249999i −0.902191 0.431336i \(-0.858042\pi\)
0.983421 + 0.181337i \(0.0580424\pi\)
\(522\) 2.42705 + 1.76336i 0.106229 + 0.0771800i
\(523\) −33.6302 24.4338i −1.47055 1.06841i −0.980455 0.196743i \(-0.936963\pi\)
−0.490091 0.871671i \(-0.663037\pi\)
\(524\) 5.35233 16.4728i 0.233818 0.719617i
\(525\) −4.28187 13.1782i −0.186876 0.575145i
\(526\) −19.4164 + 14.1068i −0.846596 + 0.615088i
\(527\) −6.92820 −0.301797
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 37.8340 27.4880i 1.64340 1.19400i
\(531\) −1.85410 5.70634i −0.0804612 0.247634i
\(532\) −7.41641 + 22.8254i −0.321542 + 0.989605i
\(533\) −2.42705 1.76336i −0.105127 0.0763794i
\(534\) −12.6113 9.16267i −0.545745 0.396507i
\(535\) 3.21140 9.88367i 0.138841 0.427308i
\(536\) −1.07047 3.29456i −0.0462371 0.142303i
\(537\) 9.70820 7.05342i 0.418940 0.304378i
\(538\) 36.3731 1.56815
\(539\) 0 0
\(540\) 3.00000 0.129099
\(541\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(542\) −1.85410 5.70634i −0.0796405 0.245108i
\(543\) 2.16312 6.65740i 0.0928283 0.285696i
\(544\) 7.28115 + 5.29007i 0.312177 + 0.226810i
\(545\) −37.8340 27.4880i −1.62063 1.17746i
\(546\) 3.21140 9.88367i 0.137435 0.422982i
\(547\) 10.7047 + 32.9456i 0.457698 + 1.40865i 0.867938 + 0.496673i \(0.165445\pi\)
−0.410240 + 0.911978i \(0.634555\pi\)
\(548\) 4.85410 3.52671i 0.207357 0.150654i
\(549\) 0 0
\(550\) 0 0
\(551\) −12.0000 −0.511217
\(552\) −8.40755 + 6.10844i −0.357849 + 0.259993i
\(553\) 0 0
\(554\) −2.78115 + 8.55951i −0.118160 + 0.363659i
\(555\) 26.6976 + 19.3969i 1.13325 + 0.823353i
\(556\) 8.40755 + 6.10844i 0.356560 + 0.259056i
\(557\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(558\) −2.14093 6.58911i −0.0906329 0.278939i
\(559\) 4.85410 3.52671i 0.205307 0.149164i
\(560\) 51.9615 2.19578
\(561\) 0 0
\(562\) −12.0000 −0.506189
\(563\) 14.0126 10.1807i 0.590560 0.429067i −0.251956 0.967739i \(-0.581074\pi\)
0.842516 + 0.538672i \(0.181074\pi\)
\(564\) 0 0
\(565\) 19.4681 59.9166i 0.819028 2.52071i
\(566\) 43.6869 + 31.7404i 1.83630 + 1.33415i
\(567\) −2.80252 2.03615i −0.117695 0.0855102i
\(568\) −3.21140 + 9.88367i −0.134747 + 0.414710i
\(569\) 8.56373 + 26.3565i 0.359010 + 1.10492i 0.953648 + 0.300926i \(0.0972957\pi\)
−0.594637 + 0.803994i \(0.702704\pi\)
\(570\) −29.1246 + 21.1603i −1.21990 + 0.886306i
\(571\) −3.46410 −0.144968 −0.0724841 0.997370i \(-0.523093\pi\)
−0.0724841 + 0.997370i \(0.523093\pi\)
\(572\) 0 0
\(573\) −12.0000 −0.501307
\(574\) 8.40755 6.10844i 0.350924 0.254962i
\(575\) −7.41641 22.8254i −0.309286 0.951883i
\(576\) 0.309017 0.951057i 0.0128757 0.0396274i
\(577\) −10.5172 7.64121i −0.437838 0.318108i 0.346938 0.937888i \(-0.387222\pi\)
−0.784775 + 0.619781i \(0.787222\pi\)
\(578\) −19.6176 14.2530i −0.815985 0.592848i
\(579\) −1.60570 + 4.94183i −0.0667306 + 0.205376i
\(580\) −1.60570 4.94183i −0.0666730 0.205199i
\(581\) 0 0
\(582\) −12.1244 −0.502571
\(583\) 0 0
\(584\) −12.0000 −0.496564
\(585\) 4.20378 3.05422i 0.173805 0.126277i
\(586\) 10.1976 + 31.3849i 0.421257 + 1.29650i
\(587\) −3.70820 + 11.4127i −0.153054 + 0.471052i −0.997959 0.0638654i \(-0.979657\pi\)
0.844905 + 0.534917i \(0.179657\pi\)
\(588\) 4.04508 + 2.93893i 0.166816 + 0.121199i
\(589\) 22.4201 + 16.2892i 0.923806 + 0.671184i
\(590\) −9.63420 + 29.6510i −0.396634 + 1.22071i
\(591\) −5.88756 18.1201i −0.242182 0.745360i
\(592\) −44.4959 + 32.3282i −1.82877 + 1.32868i
\(593\) 22.5167 0.924648 0.462324 0.886711i \(-0.347016\pi\)
0.462324 + 0.886711i \(0.347016\pi\)
\(594\) 0 0
\(595\) 18.0000 0.737928
\(596\) −9.80881 + 7.12652i −0.401785 + 0.291914i
\(597\) −3.09017 9.51057i −0.126472 0.389242i
\(598\) 5.56231 17.1190i 0.227460 0.700049i
\(599\) −19.4164 14.1068i −0.793333 0.576390i 0.115618 0.993294i \(-0.463115\pi\)
−0.908951 + 0.416904i \(0.863115\pi\)
\(600\) 5.60503 + 4.07230i 0.228825 + 0.166251i
\(601\) 6.95803 21.4146i 0.283824 0.873520i −0.702925 0.711264i \(-0.748123\pi\)
0.986749 0.162256i \(-0.0518771\pi\)
\(602\) 6.42280 + 19.7673i 0.261774 + 0.805657i
\(603\) 1.61803 1.17557i 0.0658914 0.0478729i
\(604\) −13.8564 −0.563809
\(605\) 0 0
\(606\) 24.0000 0.974933
\(607\) 16.8151 12.2169i 0.682504 0.495868i −0.191683 0.981457i \(-0.561395\pi\)
0.874187 + 0.485589i \(0.161395\pi\)
\(608\) −11.1246 34.2380i −0.451163 1.38854i
\(609\) −1.85410 + 5.70634i −0.0751320 + 0.231233i
\(610\) 0 0
\(611\) 0 0
\(612\) −0.535233 + 1.64728i −0.0216355 + 0.0665873i
\(613\) −5.88756 18.1201i −0.237796 0.731862i −0.996738 0.0807037i \(-0.974283\pi\)
0.758942 0.651159i \(-0.225717\pi\)
\(614\) −4.85410 + 3.52671i −0.195896 + 0.142326i
\(615\) 5.19615 0.209529
\(616\) 0 0
\(617\) −9.00000 −0.362326 −0.181163 0.983453i \(-0.557986\pi\)
−0.181163 + 0.983453i \(0.557986\pi\)
\(618\) −19.6176 + 14.2530i −0.789136 + 0.573341i
\(619\) −3.09017 9.51057i −0.124204 0.382262i 0.869551 0.493843i \(-0.164408\pi\)
−0.993755 + 0.111581i \(0.964408\pi\)
\(620\) −3.70820 + 11.4127i −0.148925 + 0.458344i
\(621\) −4.85410 3.52671i −0.194788 0.141522i
\(622\) 16.8151 + 12.2169i 0.674224 + 0.489853i
\(623\) 9.63420 29.6510i 0.385986 1.18794i
\(624\) 2.67617 + 8.23639i 0.107132 + 0.329720i
\(625\) 23.4615 17.0458i 0.938460 0.681831i
\(626\) −12.1244 −0.484587
\(627\) 0 0
\(628\) −14.0000 −0.558661
\(629\) −15.4138 + 11.1988i −0.614590 + 0.446526i
\(630\) 5.56231 + 17.1190i 0.221608 + 0.682038i
\(631\) −4.32624 + 13.3148i −0.172225 + 0.530053i −0.999496 0.0317495i \(-0.989892\pi\)
0.827271 + 0.561803i \(0.189892\pi\)
\(632\) 0 0
\(633\) 14.0126 + 10.1807i 0.556950 + 0.404648i
\(634\) −3.21140 + 9.88367i −0.127541 + 0.392531i
\(635\) 0 0
\(636\) −7.28115 + 5.29007i −0.288716 + 0.209765i
\(637\) 8.66025 0.343132
\(638\) 0 0
\(639\) −6.00000 −0.237356
\(640\) −29.4264 + 21.3796i −1.16318 + 0.845101i
\(641\) −4.63525 14.2658i −0.183082 0.563467i 0.816828 0.576881i \(-0.195730\pi\)
−0.999910 + 0.0134135i \(0.995730\pi\)
\(642\) −1.85410 + 5.70634i −0.0731756 + 0.225211i
\(643\) 12.9443 + 9.40456i 0.510472 + 0.370880i 0.813003 0.582260i \(-0.197831\pi\)
−0.302530 + 0.953140i \(0.597831\pi\)
\(644\) 16.8151 + 12.2169i 0.662608 + 0.481413i
\(645\) −3.21140 + 9.88367i −0.126449 + 0.389169i
\(646\) −6.42280 19.7673i −0.252702 0.777736i
\(647\) 9.70820 7.05342i 0.381669 0.277299i −0.380364 0.924837i \(-0.624201\pi\)
0.762033 + 0.647538i \(0.224201\pi\)
\(648\) 1.73205 0.0680414
\(649\) 0 0
\(650\) −12.0000 −0.470679
\(651\) 11.2101 8.14459i 0.439357 0.319212i
\(652\) 0.618034 + 1.90211i 0.0242041 + 0.0744925i
\(653\) −9.27051 + 28.5317i −0.362783 + 1.11653i 0.588575 + 0.808443i \(0.299689\pi\)
−0.951358 + 0.308089i \(0.900311\pi\)
\(654\) 21.8435 + 15.8702i 0.854147 + 0.620574i
\(655\) 42.0378 + 30.5422i 1.64255 + 1.19338i
\(656\) −2.67617 + 8.23639i −0.104487 + 0.321577i
\(657\) −2.14093 6.58911i −0.0835257 0.257066i
\(658\) 0 0
\(659\) −13.8564 −0.539769 −0.269884 0.962893i \(-0.586986\pi\)
−0.269884 + 0.962893i \(0.586986\pi\)
\(660\) 0 0
\(661\) −41.0000 −1.59472 −0.797358 0.603507i \(-0.793769\pi\)
−0.797358 + 0.603507i \(0.793769\pi\)
\(662\) 28.0252 20.3615i 1.08923 0.791371i
\(663\) 0.927051 + 2.85317i 0.0360037 + 0.110808i
\(664\) 0 0
\(665\) −58.2492 42.3205i −2.25881 1.64112i
\(666\) −15.4138 11.1988i −0.597274 0.433945i
\(667\) −3.21140 + 9.88367i −0.124346 + 0.382697i
\(668\) 1.07047 + 3.29456i 0.0414176 + 0.127470i
\(669\) 16.1803 11.7557i 0.625568 0.454502i
\(670\) −10.3923 −0.401490
\(671\) 0 0
\(672\) −18.0000 −0.694365
\(673\) −16.8151 + 12.2169i −0.648175 + 0.470926i −0.862649 0.505803i \(-0.831196\pi\)
0.214474 + 0.976730i \(0.431196\pi\)
\(674\) −6.48936 19.9722i −0.249961 0.769300i
\(675\) −1.23607 + 3.80423i −0.0475763 + 0.146425i
\(676\) 8.09017 + 5.87785i 0.311160 + 0.226071i
\(677\) 26.6239 + 19.3434i 1.02324 + 0.743427i 0.966945 0.254987i \(-0.0820711\pi\)
0.0562955 + 0.998414i \(0.482071\pi\)
\(678\) −11.2399 + 34.5928i −0.431666 + 1.32853i
\(679\) −7.49326 23.0619i −0.287565 0.885034i
\(680\) −7.28115 + 5.29007i −0.279219 + 0.202865i
\(681\) −24.2487 −0.929213
\(682\) 0 0
\(683\) −6.00000 −0.229584 −0.114792 0.993390i \(-0.536620\pi\)
−0.114792 + 0.993390i \(0.536620\pi\)
\(684\) 5.60503 4.07230i 0.214314 0.155708i
\(685\) 5.56231 + 17.1190i 0.212525 + 0.654084i
\(686\) 3.70820 11.4127i 0.141580 0.435738i
\(687\) −18.6074 13.5191i −0.709916 0.515784i
\(688\) −14.0126 10.1807i −0.534225 0.388137i
\(689\) −4.81710 + 14.8255i −0.183517 + 0.564807i
\(690\) 9.63420 + 29.6510i 0.366768 + 1.12879i
\(691\) 8.09017 5.87785i 0.307765 0.223604i −0.423172 0.906049i \(-0.639083\pi\)
0.730937 + 0.682445i \(0.239083\pi\)
\(692\) −20.7846 −0.790112
\(693\) 0 0
\(694\) 48.0000 1.82206
\(695\) −25.2227 + 18.3253i −0.956750 + 0.695119i
\(696\) −0.927051 2.85317i −0.0351398 0.108149i
\(697\) −0.927051 + 2.85317i −0.0351146 + 0.108072i
\(698\) 2.42705 + 1.76336i 0.0918652 + 0.0667440i
\(699\) −23.8214 17.3073i −0.901008 0.654621i
\(700\) 4.28187 13.1782i 0.161839 0.498090i
\(701\) 12.3104 + 37.8874i 0.464956 + 1.43099i 0.859038 + 0.511912i \(0.171063\pi\)
−0.394082 + 0.919075i \(0.628937\pi\)
\(702\) −2.42705 + 1.76336i −0.0916031 + 0.0665536i
\(703\) 76.2102 2.87432
\(704\) 0 0
\(705\) 0 0
\(706\) 29.4264 21.3796i 1.10748 0.804630i
\(707\) 14.8328 + 45.6507i 0.557845 + 1.71687i
\(708\) 1.85410 5.70634i 0.0696814 0.214457i
\(709\) −17.7984 12.9313i −0.668432 0.485644i 0.201068 0.979577i \(-0.435559\pi\)
−0.869500 + 0.493933i \(0.835559\pi\)
\(710\) 25.2227 + 18.3253i 0.946589 + 0.687737i
\(711\) 0 0
\(712\) 4.81710 + 14.8255i 0.180528 + 0.555609i
\(713\) 19.4164 14.1068i 0.727150 0.528306i
\(714\) −10.3923 −0.388922
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 5.60503 4.07230i 0.209324 0.152083i
\(718\) 16.6869 + 51.3571i 0.622750 + 1.91663i
\(719\) −9.27051 + 28.5317i −0.345732 + 1.06405i 0.615459 + 0.788169i \(0.288971\pi\)
−0.961191 + 0.275884i \(0.911029\pi\)
\(720\) −12.1353 8.81678i −0.452254 0.328582i
\(721\) −39.2352 28.5061i −1.46120 1.06162i
\(722\) −15.5218 + 47.7711i −0.577660 + 1.77786i
\(723\) −6.42280 19.7673i −0.238866 0.735155i
\(724\) 5.66312 4.11450i 0.210468 0.152914i
\(725\) 6.92820 0.257307
\(726\) 0 0
\(727\) −2.00000 −0.0741759 −0.0370879 0.999312i \(-0.511808\pi\)
−0.0370879 + 0.999312i \(0.511808\pi\)
\(728\) −8.40755 + 6.10844i −0.311605 + 0.226394i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) −11.1246 + 34.2380i −0.411740 + 1.26721i
\(731\) −4.85410 3.52671i −0.179535 0.130440i
\(732\) 0 0
\(733\) −2.67617 + 8.23639i −0.0988464 + 0.304218i −0.988237 0.152930i \(-0.951129\pi\)
0.889391 + 0.457148i \(0.151129\pi\)
\(734\) −13.9161 42.8292i −0.513651 1.58086i
\(735\) −12.1353 + 8.81678i −0.447616 + 0.325212i
\(736\) −31.1769 −1.14920
\(737\) 0 0
\(738\) −3.00000 −0.110432
\(739\) −22.4201 + 16.2892i −0.824738 + 0.599207i −0.918066 0.396428i \(-0.870250\pi\)
0.0933277 + 0.995635i \(0.470250\pi\)
\(740\) 10.1976 + 31.3849i 0.374870 + 1.15373i
\(741\) 3.70820 11.4127i 0.136224 0.419255i
\(742\) −43.6869 31.7404i −1.60380 1.16523i
\(743\) −42.0378 30.5422i −1.54222 1.12049i −0.948927 0.315495i \(-0.897829\pi\)
−0.593289 0.804990i \(-0.702171\pi\)
\(744\) −2.14093 + 6.58911i −0.0784904 + 0.241569i
\(745\) −11.2399 34.5928i −0.411798 1.26738i
\(746\) −29.1246 + 21.1603i −1.06633 + 0.774732i
\(747\) 0 0
\(748\) 0 0
\(749\) −12.0000 −0.438470
\(750\) −4.20378 + 3.05422i −0.153500 + 0.111524i
\(751\) −0.618034 1.90211i −0.0225524 0.0694091i 0.939147 0.343516i \(-0.111618\pi\)
−0.961699 + 0.274107i \(0.911618\pi\)
\(752\) 0 0
\(753\) −4.85410 3.52671i −0.176893 0.128521i
\(754\) 4.20378 + 3.05422i 0.153092 + 0.111228i
\(755\) 12.8456 39.5347i 0.467499 1.43881i
\(756\) −1.07047 3.29456i −0.0389325 0.119822i
\(757\) 13.7533 9.99235i 0.499872 0.363178i −0.309096 0.951031i \(-0.600027\pi\)
0.808968 + 0.587853i \(0.200027\pi\)
\(758\) −24.2487 −0.880753
\(759\) 0 0
\(760\) 36.0000 1.30586
\(761\) 26.6239 19.3434i 0.965116 0.701198i 0.0107828 0.999942i \(-0.496568\pi\)
0.954333 + 0.298744i \(0.0965677\pi\)
\(762\) 0 0
\(763\) −16.6869 + 51.3571i −0.604107 + 1.85925i
\(764\) −9.70820 7.05342i −0.351230 0.255184i
\(765\) −4.20378 3.05422i −0.151988 0.110426i
\(766\) −3.21140 + 9.88367i −0.116033 + 0.357111i
\(767\) −3.21140 9.88367i −0.115957 0.356879i
\(768\) 15.3713 11.1679i 0.554665 0.402988i
\(769\) −25.9808 −0.936890 −0.468445 0.883493i \(-0.655186\pi\)
−0.468445 + 0.883493i \(0.655186\pi\)
\(770\) 0 0
\(771\) −9.00000 −0.324127
\(772\) −4.20378 + 3.05422i −0.151297 + 0.109924i
\(773\) 5.56231 + 17.1190i 0.200062 + 0.615728i 0.999880 + 0.0154855i \(0.00492938\pi\)
−0.799818 + 0.600243i \(0.795071\pi\)
\(774\) 1.85410 5.70634i 0.0666443 0.205110i
\(775\)