Properties

Label 363.2.e.m.202.1
Level $363$
Weight $2$
Character 363.202
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 202.1
Root \(0.535233 - 1.64728i\) of defining polynomial
Character \(\chi\) \(=\) 363.202
Dual form 363.2.e.m.124.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.40126 - 1.01807i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.42705 - 1.76336i) q^{5} +(1.40126 - 1.01807i) q^{6} +(-1.07047 - 3.29456i) q^{7} +(-0.535233 + 1.64728i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40126 1.01807i −0.990839 0.719887i −0.0307347 0.999528i \(-0.509785\pi\)
−0.960105 + 0.279641i \(0.909785\pi\)
\(3\) −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 0.106792 0.994281i \(-0.465942\pi\)
0.978618 + 0.205685i \(0.0659421\pi\)
\(6\) 1.40126 1.01807i 0.572061 0.415627i
\(7\) −1.07047 3.29456i −0.404598 1.24523i −0.921230 0.389018i \(-0.872814\pi\)
0.516632 0.856208i \(-0.327186\pi\)
\(8\) −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 \(-0.222790\pi\)
−0.376258 + 0.926515i \(0.622790\pi\)
\(14\) −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 \(-0.767360\pi\)
0.404746 + 0.914429i \(0.367360\pi\)
\(18\) 0.535233 + 1.64728i 0.126156 + 0.388267i
\(19\) 2.14093 6.58911i 0.491164 1.51165i −0.331688 0.943389i \(-0.607618\pi\)
0.822851 0.568257i \(-0.192382\pi\)
\(20\) 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 \(-0.151413\pi\)
−0.988373 + 0.152049i \(0.951413\pi\)
\(30\) 1.60570 4.94183i 0.293159 0.902251i
\(31\) −3.23607 2.35114i −0.581215 0.422277i 0.257947 0.966159i \(-0.416954\pi\)
−0.839162 + 0.543882i \(0.816954\pi\)
\(32\) −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 −0.685628 0.727952i \(-0.740472\pi\)
0.126805 0.991928i \(-0.459528\pi\)
\(38\) −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 \(-0.943184\pi\)
0.900523 + 0.434808i \(0.143184\pi\)
\(42\) −4.85410 3.52671i −0.749004 0.544183i
\(43\) 3.46410 0.528271 0.264135 0.964486i \(-0.414913\pi\)
0.264135 + 0.964486i \(0.414913\pi\)
\(44\) 0 0
\(45\) −3.00000 −0.447214
\(46\) 8.40755 + 6.10844i 1.23963 + 0.900641i
\(47\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(48\) 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 0.962119 0.272630i \(-0.0878935\pi\)
0.0380244 + 0.999277i \(0.487894\pi\)
\(54\) −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 −0.996210 0.0869778i \(-0.972279\pi\)
0.754827 0.655924i \(-0.227721\pi\)
\(60\) −2.42705 + 1.76336i −0.313331 + 0.227648i
\(61\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(62\) 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 −0.261231 0.965276i \(-0.584129\pi\)
0.837307 + 0.546733i \(0.184129\pi\)
\(72\) 1.40126 1.01807i 0.165140 0.119981i
\(73\) 2.14093 + 6.58911i 0.250577 + 0.771197i 0.994669 + 0.103120i \(0.0328825\pi\)
−0.744092 + 0.668077i \(0.767117\pi\)
\(74\) −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 \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(80\) 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 \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(84\) 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 0.836919 0.547327i \(-0.184354\pi\)
−0.261916 + 0.965091i \(0.584354\pi\)
\(98\) 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 \(-0.0578822\pi\)
0.131931 + 0.991259i \(0.457882\pi\)
\(102\) −0.927051 + 2.85317i −0.0917917 + 0.282506i
\(103\) 4.32624 + 13.3148i 0.426277 + 1.31195i 0.901766 + 0.432224i \(0.142271\pi\)
−0.475489 + 0.879721i \(0.657729\pi\)
\(104\) −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 \(-0.846449\pi\)
0.989372 + 0.145406i \(0.0464488\pi\)
\(108\) 0.809017 + 0.587785i 0.0778477 + 0.0565597i
\(109\) 15.5885 1.49310 0.746552 0.665327i \(-0.231708\pi\)
0.746552 + 0.665327i \(0.231708\pi\)
\(110\) 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 −0.156868 + 0.987620i \(0.550140\pi\)
−0.453599 + 0.891206i \(0.649860\pi\)
\(114\) −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 \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(128\) 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 \(-0.773165\pi\)
−0.756650 + 0.653820i \(0.773165\pi\)
\(132\) 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 −0.360794 0.932646i \(-0.617494\pi\)
0.775507 + 0.631338i \(0.217494\pi\)
\(138\) −8.40755 + 6.10844i −0.715698 + 0.519985i
\(139\) 3.21140 + 9.88367i 0.272387 + 0.838322i 0.989899 + 0.141775i \(0.0452810\pi\)
−0.717512 + 0.696547i \(0.754719\pi\)
\(140\) 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 \(-0.534570\pi\)
0.911959 + 0.410281i \(0.134570\pi\)
\(150\) −2.14093 6.58911i −0.174806 0.537999i
\(151\) 4.28187 13.1782i 0.348453 1.07243i −0.611256 0.791433i \(-0.709335\pi\)
0.959709 0.280996i \(-0.0906647\pi\)
\(152\) 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 0.616167 + 0.787616i \(0.288685\pi\)
−0.961438 + 0.275020i \(0.911315\pi\)
\(158\) 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 0.522612 0.852570i \(-0.324958\pi\)
−0.649347 + 0.760493i \(0.724958\pi\)
\(164\) −1.73205 −0.135250
\(165\) 0 0
\(166\) 0 0
\(167\) 2.80252 + 2.03615i 0.216865 + 0.157562i 0.690914 0.722937i \(-0.257208\pi\)
−0.474049 + 0.880498i \(0.657208\pi\)
\(168\) −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 −0.338803 0.940857i \(-0.610022\pi\)
0.827120 0.562026i \(-0.189978\pi\)
\(174\) −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 −0.711474 0.702712i \(-0.751972\pi\)
0.988639 0.150312i \(-0.0480277\pi\)
\(180\) −0.927051 2.85317i −0.0690983 0.212663i
\(181\) 5.66312 4.11450i 0.420936 0.305828i −0.357078 0.934075i \(-0.616227\pi\)
0.778014 + 0.628246i \(0.216227\pi\)
\(182\) −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 0.990911 + 0.134520i \(0.0429494\pi\)
−0.722595 + 0.691272i \(0.757051\pi\)
\(192\) 0.809017 0.587785i 0.0583858 0.0424197i
\(193\) 4.20378 3.05422i 0.302594 0.219848i −0.426118 0.904668i \(-0.640119\pi\)
0.728712 + 0.684820i \(0.240119\pi\)
\(194\) −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 \(-0.737465\pi\)
−0.678719 + 0.734398i \(0.737465\pi\)
\(198\) 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 \(-0.0966779\pi\)
0.0104364 + 0.999946i \(0.496678\pi\)
\(212\) −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 −0.499395 0.866374i \(-0.666444\pi\)
0.913261 0.407375i \(-0.133556\pi\)
\(224\) 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 −0.813269 0.581887i \(-0.802314\pi\)
0.315924 0.948784i \(-0.397686\pi\)
\(228\) −2.14093 + 6.58911i −0.141787 + 0.436375i
\(229\) 18.6074 + 13.5191i 1.22961 + 0.893365i 0.996861 0.0791719i \(-0.0252276\pi\)
0.232750 + 0.972537i \(0.425228\pi\)
\(230\) 31.1769 2.05574
\(231\) 0 0
\(232\) 3.00000 0.196960
\(233\) −23.8214 17.3073i −1.56059 1.13384i −0.935523 0.353266i \(-0.885071\pi\)
−0.625069 0.780570i \(-0.714929\pi\)
\(234\) −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 \(-0.971936\pi\)
0.857630 + 0.514266i \(0.171936\pi\)
\(240\) 12.1353 + 8.81678i 0.783327 + 0.569121i
\(241\) −20.7846 −1.33885 −0.669427 0.742878i \(-0.733460\pi\)
−0.669427 + 0.742878i \(0.733460\pi\)
\(242\) 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 0.730345 0.683078i \(-0.239359\pi\)
−0.423957 + 0.905682i \(0.639359\pi\)
\(252\) −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 0.999561 0.0296292i \(-0.00943265\pi\)
−0.826077 + 0.563557i \(0.809433\pi\)
\(258\) 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 \(-0.359496\pi\)
0.427211 + 0.904152i \(0.359496\pi\)
\(264\) 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 0.0663864 0.997794i \(-0.478853\pi\)
0.969473 + 0.245198i \(0.0788530\pi\)
\(270\) −4.20378 + 3.05422i −0.255834 + 0.185874i
\(271\) −1.07047 3.29456i −0.0650262 0.200130i 0.913265 0.407367i \(-0.133553\pi\)
−0.978291 + 0.207237i \(0.933553\pi\)
\(272\) −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 \(-0.250107\pi\)
−0.454289 + 0.890854i \(0.650107\pi\)
\(278\) 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 \(-0.633744\pi\)
0.742282 + 0.670088i \(0.233744\pi\)
\(282\) 0 0
\(283\) −9.63420 + 29.6510i −0.572694 + 1.76257i 0.0712084 + 0.997461i \(0.477314\pi\)
−0.643902 + 0.765108i \(0.722686\pi\)
\(284\) 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 0.962141 + 0.272553i \(0.0878680\pi\)
−0.618186 + 0.786032i \(0.712132\pi\)
\(294\) −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 \(-0.468483\pi\)
0.0988534 + 0.995102i \(0.468483\pi\)
\(308\) 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 −0.789183 0.614159i \(-0.789495\pi\)
0.999456 0.0329949i \(-0.0105045\pi\)
\(312\) −0.927051 2.85317i −0.0524839 0.161529i
\(313\) −5.66312 + 4.11450i −0.320098 + 0.232565i −0.736217 0.676745i \(-0.763390\pi\)
0.416119 + 0.909310i \(0.363390\pi\)
\(314\) 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 0.443064 0.896490i \(-0.353891\pi\)
−0.715698 + 0.698410i \(0.753891\pi\)
\(318\) 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 −0.999749 0.0223838i \(-0.992874\pi\)
0.795657 0.605747i \(-0.207126\pi\)
\(338\) −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 \(-0.967003\pi\)
−0.208944 + 0.977928i \(0.567003\pi\)
\(348\) 0.535233 + 1.64728i 0.0286915 + 0.0883034i
\(349\) −0.535233 + 1.64728i −0.0286504 + 0.0881768i −0.964359 0.264596i \(-0.914761\pi\)
0.935709 + 0.352773i \(0.114761\pi\)
\(350\) 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 0.794852 + 0.606804i \(0.207549\pi\)
−0.286378 + 0.958117i \(0.592451\pi\)
\(360\) 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 0.908261 + 0.418405i \(0.137411\pi\)
−0.488866 + 0.872359i \(0.662589\pi\)
\(368\) −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 \(-0.319145\pi\)
0.538093 + 0.842885i \(0.319145\pi\)
\(374\) 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 −0.839369 0.543562i \(-0.817075\pi\)
0.257579 + 0.966257i \(0.417075\pi\)
\(380\) 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 0.456822 0.889558i \(-0.348988\pi\)
−0.704855 + 0.709352i \(0.748988\pi\)
\(384\) −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 −0.904868 0.425692i \(-0.860031\pi\)
0.481838 0.876260i \(-0.339969\pi\)
\(390\) 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 −0.646734 0.762715i \(-0.723866\pi\)
0.525533 + 0.850773i \(0.323866\pi\)
\(402\) −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 \(-0.313635\pi\)
−0.621890 + 0.783105i \(0.713635\pi\)
\(410\) 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 −0.884406 0.466719i \(-0.845436\pi\)
0.989830 + 0.142257i \(0.0454360\pi\)
\(422\) −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 \(-0.163029\pi\)
−0.196720 + 0.980460i \(0.563029\pi\)
\(432\) 1.54508 4.75528i 0.0743379 0.228789i
\(433\) −5.87132 18.0701i −0.282158 0.868392i −0.987236 0.159263i \(-0.949088\pi\)
0.705078 0.709129i \(-0.250912\pi\)
\(434\) 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 \(-0.552870\pi\)
−0.165333 + 0.986238i \(0.552870\pi\)
\(440\) 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 0.727587 + 0.686016i \(0.240642\pi\)
−0.991860 + 0.127333i \(0.959358\pi\)
\(444\) 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 0.109658 0.993969i \(-0.465025\pi\)
−0.911435 + 0.411444i \(0.865025\pi\)
\(450\) 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 \(-0.458188\pi\)
0.983338 + 0.181786i \(0.0581877\pi\)
\(458\) −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 \(-0.618252\pi\)
−0.363013 + 0.931784i \(0.618252\pi\)
\(462\) 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 −0.197453 0.980312i \(-0.563267\pi\)
0.871316 + 0.490722i \(0.163267\pi\)
\(468\) 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 \(-0.886890\pi\)
0.0411745 + 0.999152i \(0.486890\pi\)
\(480\) −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 0.217702 + 0.976015i \(0.430144\pi\)
−0.749812 + 0.661651i \(0.769856\pi\)
\(488\) 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 −0.984901 0.173120i \(-0.944615\pi\)
0.695044 0.718967i \(-0.255385\pi\)
\(492\) 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 0.979924 + 0.199373i \(0.0638904\pi\)
−0.675587 + 0.737280i \(0.736110\pi\)
\(500\) −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 −0.468985 0.883206i \(-0.655380\pi\)
0.898552 0.438867i \(-0.144620\pi\)
\(504\) −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 −0.748834 0.662758i \(-0.769386\pi\)
0.995379 0.0960291i \(-0.0306142\pi\)
\(510\) 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 0.983421 0.181337i \(-0.0580424\pi\)
−0.902191 + 0.431336i \(0.858042\pi\)
\(522\) 2.42705 1.76336i 0.106229 0.0771800i
\(523\) 33.6302 24.4338i 1.47055 1.06841i 0.490091 0.871671i \(-0.336963\pi\)
0.980455 0.196743i \(-0.0630365\pi\)
\(524\) −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 \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(542\) −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 0.410240 + 0.911978i \(0.365445\pi\)
−0.867938 + 0.496673i \(0.834555\pi\)
\(548\) 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 \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(558\) 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 \(-0.418926\pi\)
−0.842516 + 0.538672i \(0.818926\pi\)
\(564\) 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 0.594637 + 0.803994i \(0.297296\pi\)
−0.953648 + 0.300926i \(0.902704\pi\)
\(570\) −29.1246 21.1603i −1.21990 0.886306i
\(571\) 3.46410 0.144968 0.0724841 0.997370i \(-0.476907\pi\)
0.0724841 + 0.997370i \(0.476907\pi\)
\(572\) 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 −0.784775 0.619781i \(-0.787222\pi\)
0.346938 + 0.937888i \(0.387222\pi\)
\(578\) 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 0.844905 0.534917i \(-0.179657\pi\)
−0.997959 + 0.0638654i \(0.979657\pi\)
\(588\) 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 \(-0.652984\pi\)
−0.462324 + 0.886711i \(0.652984\pi\)
\(594\) 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 −0.908951 0.416904i \(-0.863115\pi\)
0.115618 + 0.993294i \(0.463115\pi\)
\(600\) −5.60503 + 4.07230i −0.228825 + 0.166251i
\(601\) −6.95803 21.4146i −0.283824 0.873520i −0.986749 0.162256i \(-0.948123\pi\)
0.702925 0.711264i \(-0.251877\pi\)
\(602\) −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 \(-0.438605\pi\)
−0.874187 + 0.485589i \(0.838605\pi\)
\(608\) −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 −0.758942 0.651159i \(-0.774283\pi\)
0.996738 0.0807037i \(-0.0257168\pi\)
\(614\) −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 −0.993755 0.111581i \(-0.964408\pi\)
0.869551 + 0.493843i \(0.164408\pi\)
\(620\) −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 0.827271 0.561803i \(-0.189892\pi\)
−0.999496 + 0.0317495i \(0.989892\pi\)
\(632\) 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 −0.999910 0.0134135i \(-0.995730\pi\)
0.816828 + 0.576881i \(0.195730\pi\)
\(642\) −1.85410 5.70634i −0.0731756 0.225211i
\(643\) 12.9443 9.40456i 0.510472 0.370880i −0.302530 0.953140i \(-0.597831\pi\)
0.813003 + 0.582260i \(0.197831\pi\)
\(644\) −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 0.762033 0.647538i \(-0.224201\pi\)
−0.380364 + 0.924837i \(0.624201\pi\)
\(648\) −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 −0.951358 0.308089i \(-0.900311\pi\)
0.588575 0.808443i \(-0.299689\pi\)
\(654\) 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 \(-0.413014\pi\)
0.269884 + 0.962893i \(0.413014\pi\)
\(660\) 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 \(-0.168804\pi\)
−0.214474 + 0.976730i \(0.568804\pi\)
\(674\) −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 \(-0.917929\pi\)
−0.0562955 + 0.998414i \(0.517929\pi\)
\(678\) 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 0.730937 0.682445i \(-0.239083\pi\)
−0.423172 + 0.906049i \(0.639083\pi\)
\(692\) 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 0.394082 + 0.919075i \(0.371063\pi\)
−0.859038 + 0.511912i \(0.828937\pi\)
\(702\) −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 −0.869500 0.493933i \(-0.835559\pi\)
0.201068 + 0.979577i \(0.435559\pi\)
\(710\) −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 −0.961191 0.275884i \(-0.911029\pi\)
0.615459 0.788169i \(-0.288971\pi\)
\(720\) −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 \(-0.0488709\pi\)
−0.889391 + 0.457148i \(0.848871\pi\)
\(734\) 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 \(-0.129750\pi\)
−0.0933277 + 0.995635i \(0.529750\pi\)
\(740\) 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 0.593289 0.804990i \(-0.297829\pi\)
0.948927 0.315495i \(-0.102171\pi\)
\(744\) 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 −0.961699 0.274107i \(-0.911618\pi\)
0.939147 + 0.343516i \(0.111618\pi\)
\(752\) 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 0.808968 0.587853i \(-0.200027\pi\)
−0.309096 + 0.951031i \(0.600027\pi\)
\(758\) 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 \(-0.503432\pi\)
−0.954333 + 0.298744i \(0.903432\pi\)
\(762\) 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 \(-0.344814\pi\)
0.468445 + 0.883493i \(0.344814\pi\)
\(770\) 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 −0.799818 0.600243i \(-0.795071\pi\)
0.999880 0.0154855i \(-0.00492938\pi\)
\(774\) 1.85410 + 5.70634i 0.0666443 + 0.205110i
\(775\) −12.9443 + 9.40456i </