Properties

Label 637.2.e.k.79.3
Level $637$
Weight $2$
Character 637.79
Analytic conductor $5.086$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(79,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.e (of order \(3\), degree \(2\), 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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.4406832.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.3
Root \(-0.827721 - 1.43366i\) of defining polynomial
Character \(\chi\) \(=\) 637.79
Dual form 637.2.e.k.508.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.32772 - 2.29968i) q^{2} +(-1.19797 - 2.07494i) q^{3} +(-2.52569 - 4.37462i) q^{4} +(-1.82772 + 3.16571i) q^{5} -6.36226 q^{6} -8.10275 q^{8} +(-1.37024 + 2.37333i) q^{9} +O(q^{10})\) \(q+(1.32772 - 2.29968i) q^{2} +(-1.19797 - 2.07494i) q^{3} +(-2.52569 - 4.37462i) q^{4} +(-1.82772 + 3.16571i) q^{5} -6.36226 q^{6} -8.10275 q^{8} +(-1.37024 + 2.37333i) q^{9} +(4.85341 + 8.40635i) q^{10} +(-0.327721 - 0.567630i) q^{11} +(-6.05137 + 10.4813i) q^{12} -1.00000 q^{13} +8.75819 q^{15} +(-5.70682 + 9.88450i) q^{16} +(-1.19797 - 2.07494i) q^{17} +(3.63861 + 6.30225i) q^{18} +(1.35341 - 2.34417i) q^{19} +18.4650 q^{20} -1.74049 q^{22} +(-3.68113 + 6.37590i) q^{23} +(9.70682 + 16.8127i) q^{24} +(-4.18113 - 7.24193i) q^{25} +(-1.32772 + 2.29968i) q^{26} -0.621770 q^{27} -0.208136 q^{29} +(11.6284 - 20.1410i) q^{30} +(0.568211 + 0.984170i) q^{31} +(7.05137 + 12.2133i) q^{32} +(-0.785198 + 1.36000i) q^{33} -6.36226 q^{34} +13.8432 q^{36} +(3.72365 - 6.44956i) q^{37} +(-3.59390 - 6.22481i) q^{38} +(1.19797 + 2.07494i) q^{39} +(14.8096 - 25.6509i) q^{40} -10.2055 q^{41} -3.10275 q^{43} +(-1.65544 + 2.86731i) q^{44} +(-5.00885 - 8.67558i) q^{45} +(9.77503 + 16.9308i) q^{46} +(-2.30203 + 3.98724i) q^{47} +27.3463 q^{48} -22.2055 q^{50} +(-2.87024 + 4.97141i) q^{51} +(2.52569 + 4.37462i) q^{52} +(-2.62976 - 4.55487i) q^{53} +(-0.825537 + 1.42987i) q^{54} +2.39593 q^{55} -6.48535 q^{57} +(-0.276347 + 0.478647i) q^{58} +(-4.12976 - 7.15295i) q^{59} +(-22.1204 - 38.3137i) q^{60} +(0.948626 - 1.64307i) q^{61} +3.01770 q^{62} +14.6218 q^{64} +(1.82772 - 3.16571i) q^{65} +(2.08505 + 3.61141i) q^{66} +(6.44731 + 11.1671i) q^{67} +(-6.05137 + 10.4813i) q^{68} +17.6395 q^{69} -6.75819 q^{71} +(11.1027 - 19.2305i) q^{72} +(-6.26836 - 10.8571i) q^{73} +(-9.88795 - 17.1264i) q^{74} +(-10.0177 + 17.3512i) q^{75} -13.6731 q^{76} +6.36226 q^{78} +(0.759511 - 1.31551i) q^{79} +(-20.8609 - 36.1322i) q^{80} +(4.85559 + 8.41013i) q^{81} +(-13.5501 + 23.4694i) q^{82} +15.7582 q^{83} +8.75819 q^{85} +(-4.11958 + 7.13533i) q^{86} +(0.249340 + 0.431870i) q^{87} +(2.65544 + 4.59936i) q^{88} +(7.40478 - 12.8255i) q^{89} -26.6014 q^{90} +37.1895 q^{92} +(1.36139 - 2.35800i) q^{93} +(6.11292 + 10.5879i) q^{94} +(4.94731 + 8.56899i) q^{95} +(16.8946 - 29.2623i) q^{96} -10.0177 q^{97} +1.79623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 5 q^{5} + 4 q^{6} - 12 q^{8} - 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 5 q^{5} + 4 q^{6} - 12 q^{8} - 11 q^{9} + 14 q^{10} + 4 q^{11} - 18 q^{12} - 6 q^{13} + 4 q^{15} - 4 q^{16} - 4 q^{17} - 8 q^{18} - 7 q^{19} + 32 q^{20} - 16 q^{22} - q^{23} + 28 q^{24} - 4 q^{25} - 2 q^{26} + 44 q^{27} - 14 q^{29} + 24 q^{30} + 3 q^{31} + 24 q^{32} + 10 q^{33} + 4 q^{34} + 52 q^{36} + 10 q^{37} - 12 q^{38} + 4 q^{39} + 22 q^{40} + 12 q^{41} + 18 q^{43} + 2 q^{44} - 3 q^{45} + 28 q^{46} - 17 q^{47} + 32 q^{48} - 60 q^{50} - 20 q^{51} + 6 q^{52} - 13 q^{53} - 28 q^{54} + 8 q^{55} + 8 q^{57} - 14 q^{58} - 22 q^{59} - 42 q^{60} + 24 q^{61} - 36 q^{62} + 40 q^{64} + 5 q^{65} + 30 q^{66} + 14 q^{67} - 18 q^{68} + 4 q^{69} + 8 q^{71} + 30 q^{72} - 5 q^{73} - 8 q^{74} - 6 q^{75} - 16 q^{76} - 4 q^{78} - q^{79} - 40 q^{80} - 15 q^{81} - 20 q^{82} + 46 q^{83} + 4 q^{85} - 6 q^{86} - 20 q^{87} + 4 q^{88} + 11 q^{89} - 80 q^{90} + 60 q^{92} + 38 q^{93} + 16 q^{94} + 5 q^{95} + 52 q^{96} - 6 q^{97} - 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.32772 2.29968i 0.938841 1.62612i 0.171203 0.985236i \(-0.445235\pi\)
0.767638 0.640884i \(-0.221432\pi\)
\(3\) −1.19797 2.07494i −0.691646 1.19797i −0.971298 0.237865i \(-0.923553\pi\)
0.279652 0.960101i \(-0.409781\pi\)
\(4\) −2.52569 4.37462i −1.26284 2.18731i
\(5\) −1.82772 + 3.16571i −0.817382 + 1.41575i 0.0902232 + 0.995922i \(0.471242\pi\)
−0.907605 + 0.419825i \(0.862091\pi\)
\(6\) −6.36226 −2.59738
\(7\) 0 0
\(8\) −8.10275 −2.86475
\(9\) −1.37024 + 2.37333i −0.456748 + 0.791111i
\(10\) 4.85341 + 8.40635i 1.53478 + 2.65832i
\(11\) −0.327721 0.567630i −0.0988117 0.171147i 0.812381 0.583126i \(-0.198171\pi\)
−0.911193 + 0.411980i \(0.864837\pi\)
\(12\) −6.05137 + 10.4813i −1.74688 + 3.02569i
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 8.75819 2.26136
\(16\) −5.70682 + 9.88450i −1.42670 + 2.47112i
\(17\) −1.19797 2.07494i −0.290549 0.503246i 0.683390 0.730053i \(-0.260505\pi\)
−0.973940 + 0.226807i \(0.927171\pi\)
\(18\) 3.63861 + 6.30225i 0.857628 + 1.48545i
\(19\) 1.35341 2.34417i 0.310493 0.537790i −0.667976 0.744183i \(-0.732839\pi\)
0.978469 + 0.206393i \(0.0661725\pi\)
\(20\) 18.4650 4.12890
\(21\) 0 0
\(22\) −1.74049 −0.371074
\(23\) −3.68113 + 6.37590i −0.767569 + 1.32947i 0.171309 + 0.985217i \(0.445200\pi\)
−0.938878 + 0.344250i \(0.888133\pi\)
\(24\) 9.70682 + 16.8127i 1.98140 + 3.43188i
\(25\) −4.18113 7.24193i −0.836226 1.44839i
\(26\) −1.32772 + 2.29968i −0.260388 + 0.451004i
\(27\) −0.621770 −0.119660
\(28\) 0 0
\(29\) −0.208136 −0.0386499 −0.0193250 0.999813i \(-0.506152\pi\)
−0.0193250 + 0.999813i \(0.506152\pi\)
\(30\) 11.6284 20.1410i 2.12305 3.67723i
\(31\) 0.568211 + 0.984170i 0.102054 + 0.176762i 0.912531 0.409008i \(-0.134125\pi\)
−0.810477 + 0.585771i \(0.800792\pi\)
\(32\) 7.05137 + 12.2133i 1.24652 + 2.15903i
\(33\) −0.785198 + 1.36000i −0.136685 + 0.236746i
\(34\) −6.36226 −1.09112
\(35\) 0 0
\(36\) 13.8432 2.30721
\(37\) 3.72365 6.44956i 0.612165 1.06030i −0.378710 0.925515i \(-0.623632\pi\)
0.990875 0.134785i \(-0.0430344\pi\)
\(38\) −3.59390 6.22481i −0.583007 1.00980i
\(39\) 1.19797 + 2.07494i 0.191828 + 0.332256i
\(40\) 14.8096 25.6509i 2.34160 4.05577i
\(41\) −10.2055 −1.59383 −0.796915 0.604091i \(-0.793536\pi\)
−0.796915 + 0.604091i \(0.793536\pi\)
\(42\) 0 0
\(43\) −3.10275 −0.473165 −0.236582 0.971611i \(-0.576027\pi\)
−0.236582 + 0.971611i \(0.576027\pi\)
\(44\) −1.65544 + 2.86731i −0.249567 + 0.432263i
\(45\) −5.00885 8.67558i −0.746675 1.29328i
\(46\) 9.77503 + 16.9308i 1.44125 + 2.49632i
\(47\) −2.30203 + 3.98724i −0.335786 + 0.581599i −0.983636 0.180170i \(-0.942335\pi\)
0.647849 + 0.761768i \(0.275669\pi\)
\(48\) 27.3463 3.94710
\(49\) 0 0
\(50\) −22.2055 −3.14033
\(51\) −2.87024 + 4.97141i −0.401915 + 0.696137i
\(52\) 2.52569 + 4.37462i 0.350250 + 0.606650i
\(53\) −2.62976 4.55487i −0.361225 0.625659i 0.626938 0.779069i \(-0.284308\pi\)
−0.988163 + 0.153410i \(0.950975\pi\)
\(54\) −0.825537 + 1.42987i −0.112341 + 0.194581i
\(55\) 2.39593 0.323067
\(56\) 0 0
\(57\) −6.48535 −0.859005
\(58\) −0.276347 + 0.478647i −0.0362861 + 0.0628494i
\(59\) −4.12976 7.15295i −0.537648 0.931234i −0.999030 0.0440325i \(-0.985979\pi\)
0.461382 0.887202i \(-0.347354\pi\)
\(60\) −22.1204 38.3137i −2.85574 4.94628i
\(61\) 0.948626 1.64307i 0.121459 0.210373i −0.798884 0.601485i \(-0.794576\pi\)
0.920343 + 0.391112i \(0.127909\pi\)
\(62\) 3.01770 0.383248
\(63\) 0 0
\(64\) 14.6218 1.82772
\(65\) 1.82772 3.16571i 0.226701 0.392657i
\(66\) 2.08505 + 3.61141i 0.256652 + 0.444534i
\(67\) 6.44731 + 11.1671i 0.787664 + 1.36427i 0.927395 + 0.374084i \(0.122043\pi\)
−0.139731 + 0.990190i \(0.544624\pi\)
\(68\) −6.05137 + 10.4813i −0.733837 + 1.27104i
\(69\) 17.6395 2.12354
\(70\) 0 0
\(71\) −6.75819 −0.802050 −0.401025 0.916067i \(-0.631346\pi\)
−0.401025 + 0.916067i \(0.631346\pi\)
\(72\) 11.1027 19.2305i 1.30847 2.26634i
\(73\) −6.26836 10.8571i −0.733656 1.27073i −0.955310 0.295604i \(-0.904479\pi\)
0.221654 0.975125i \(-0.428854\pi\)
\(74\) −9.88795 17.1264i −1.14945 1.99091i
\(75\) −10.0177 + 17.3512i −1.15674 + 2.00354i
\(76\) −13.6731 −1.56842
\(77\) 0 0
\(78\) 6.36226 0.720384
\(79\) 0.759511 1.31551i 0.0854516 0.148007i −0.820132 0.572174i \(-0.806100\pi\)
0.905584 + 0.424168i \(0.139433\pi\)
\(80\) −20.8609 36.1322i −2.33232 4.03970i
\(81\) 4.85559 + 8.41013i 0.539510 + 0.934459i
\(82\) −13.5501 + 23.4694i −1.49635 + 2.59176i
\(83\) 15.7582 1.72969 0.864843 0.502042i \(-0.167418\pi\)
0.864843 + 0.502042i \(0.167418\pi\)
\(84\) 0 0
\(85\) 8.75819 0.949959
\(86\) −4.11958 + 7.13533i −0.444226 + 0.769422i
\(87\) 0.249340 + 0.431870i 0.0267321 + 0.0463013i
\(88\) 2.65544 + 4.59936i 0.283071 + 0.490294i
\(89\) 7.40478 12.8255i 0.784905 1.35950i −0.144150 0.989556i \(-0.546045\pi\)
0.929056 0.369940i \(-0.120622\pi\)
\(90\) −26.6014 −2.80404
\(91\) 0 0
\(92\) 37.1895 3.87728
\(93\) 1.36139 2.35800i 0.141170 0.244514i
\(94\) 6.11292 + 10.5879i 0.630499 + 1.09206i
\(95\) 4.94731 + 8.56899i 0.507583 + 0.879159i
\(96\) 16.8946 29.2623i 1.72430 2.98657i
\(97\) −10.0177 −1.01714 −0.508572 0.861020i \(-0.669826\pi\)
−0.508572 + 0.861020i \(0.669826\pi\)
\(98\) 0 0
\(99\) 1.79623 0.180528
\(100\) −21.1204 + 36.5817i −2.11204 + 3.65817i
\(101\) 1.50885 + 2.61341i 0.150136 + 0.260044i 0.931277 0.364311i \(-0.118695\pi\)
−0.781141 + 0.624354i \(0.785362\pi\)
\(102\) 7.62177 + 13.2013i 0.754668 + 1.30712i
\(103\) 2.51902 4.36307i 0.248207 0.429906i −0.714822 0.699307i \(-0.753492\pi\)
0.963028 + 0.269400i \(0.0868255\pi\)
\(104\) 8.10275 0.794540
\(105\) 0 0
\(106\) −13.9663 −1.35653
\(107\) −5.92162 + 10.2565i −0.572465 + 0.991538i 0.423848 + 0.905734i \(0.360679\pi\)
−0.996312 + 0.0858041i \(0.972654\pi\)
\(108\) 1.57040 + 2.72000i 0.151111 + 0.261733i
\(109\) −1.77503 3.07444i −0.170017 0.294478i 0.768409 0.639959i \(-0.221049\pi\)
−0.938425 + 0.345482i \(0.887716\pi\)
\(110\) 3.18113 5.50988i 0.303309 0.525346i
\(111\) −17.8432 −1.69361
\(112\) 0 0
\(113\) −9.46501 −0.890393 −0.445197 0.895433i \(-0.646866\pi\)
−0.445197 + 0.895433i \(0.646866\pi\)
\(114\) −8.61073 + 14.9142i −0.806469 + 1.39685i
\(115\) −13.4562 23.3067i −1.25479 2.17337i
\(116\) 0.525687 + 0.910517i 0.0488088 + 0.0845394i
\(117\) 1.37024 2.37333i 0.126679 0.219415i
\(118\) −21.9327 −2.01906
\(119\) 0 0
\(120\) −70.9654 −6.47823
\(121\) 5.28520 9.15423i 0.480473 0.832203i
\(122\) −2.51902 4.36307i −0.228061 0.395014i
\(123\) 12.2258 + 21.1758i 1.10237 + 1.90936i
\(124\) 2.87024 4.97141i 0.257756 0.446446i
\(125\) 12.2905 1.09930
\(126\) 0 0
\(127\) 5.46765 0.485175 0.242588 0.970130i \(-0.422004\pi\)
0.242588 + 0.970130i \(0.422004\pi\)
\(128\) 5.31088 9.19872i 0.469420 0.813060i
\(129\) 3.71699 + 6.43801i 0.327262 + 0.566835i
\(130\) −4.85341 8.40635i −0.425672 0.737286i
\(131\) −4.91495 + 8.51295i −0.429421 + 0.743780i −0.996822 0.0796622i \(-0.974616\pi\)
0.567400 + 0.823442i \(0.307949\pi\)
\(132\) 7.93265 0.690449
\(133\) 0 0
\(134\) 34.2409 2.95796
\(135\) 1.13642 1.96834i 0.0978076 0.169408i
\(136\) 9.70682 + 16.8127i 0.832353 + 1.44168i
\(137\) −8.77503 15.1988i −0.749701 1.29852i −0.947966 0.318372i \(-0.896864\pi\)
0.198265 0.980149i \(-0.436469\pi\)
\(138\) 23.4203 40.5651i 1.99367 3.45313i
\(139\) −4.91495 −0.416881 −0.208440 0.978035i \(-0.566839\pi\)
−0.208440 + 0.978035i \(0.566839\pi\)
\(140\) 0 0
\(141\) 11.0310 0.928981
\(142\) −8.97299 + 15.5417i −0.752997 + 1.30423i
\(143\) 0.327721 + 0.567630i 0.0274054 + 0.0474676i
\(144\) −15.6395 27.0884i −1.30329 2.25736i
\(145\) 0.380415 0.658898i 0.0315918 0.0547185i
\(146\) −33.2905 −2.75515
\(147\) 0 0
\(148\) −37.6191 −3.09227
\(149\) 5.17096 8.95636i 0.423621 0.733734i −0.572669 0.819787i \(-0.694092\pi\)
0.996291 + 0.0860527i \(0.0274253\pi\)
\(150\) 26.6014 + 46.0750i 2.17200 + 3.76201i
\(151\) −2.53586 4.39223i −0.206365 0.357435i 0.744202 0.667955i \(-0.232830\pi\)
−0.950567 + 0.310520i \(0.899497\pi\)
\(152\) −10.9663 + 18.9942i −0.889487 + 1.54064i
\(153\) 6.56603 0.530832
\(154\) 0 0
\(155\) −4.15412 −0.333667
\(156\) 6.05137 10.4813i 0.484498 0.839175i
\(157\) 6.30071 + 10.9132i 0.502852 + 0.870965i 0.999995 + 0.00329606i \(0.00104917\pi\)
−0.497143 + 0.867669i \(0.665617\pi\)
\(158\) −2.01684 3.49326i −0.160451 0.277909i
\(159\) −6.30071 + 10.9132i −0.499679 + 0.865470i
\(160\) −51.5518 −4.07553
\(161\) 0 0
\(162\) 25.7875 2.02606
\(163\) −1.60407 + 2.77833i −0.125640 + 0.217615i −0.921983 0.387230i \(-0.873432\pi\)
0.796343 + 0.604846i \(0.206765\pi\)
\(164\) 25.7759 + 44.6452i 2.01276 + 3.48620i
\(165\) −2.87024 4.97141i −0.223448 0.387024i
\(166\) 20.9225 36.2388i 1.62390 2.81268i
\(167\) 8.12045 0.628379 0.314190 0.949360i \(-0.398267\pi\)
0.314190 + 0.949360i \(0.398267\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 11.6284 20.1410i 0.891860 1.54475i
\(171\) 3.70900 + 6.42418i 0.283634 + 0.491269i
\(172\) 7.83657 + 13.5733i 0.597533 + 1.03496i
\(173\) 5.16429 8.94482i 0.392634 0.680062i −0.600162 0.799878i \(-0.704897\pi\)
0.992796 + 0.119816i \(0.0382306\pi\)
\(174\) 1.32422 0.100389
\(175\) 0 0
\(176\) 7.48098 0.563900
\(177\) −9.89461 + 17.1380i −0.743725 + 1.28817i
\(178\) −19.6630 34.0573i −1.47380 2.55270i
\(179\) 1.18912 + 2.05961i 0.0888786 + 0.153942i 0.907037 0.421050i \(-0.138338\pi\)
−0.818159 + 0.574992i \(0.805005\pi\)
\(180\) −25.3016 + 43.8236i −1.88587 + 3.26642i
\(181\) 21.8096 1.62109 0.810546 0.585675i \(-0.199170\pi\)
0.810546 + 0.585675i \(0.199170\pi\)
\(182\) 0 0
\(183\) −4.54569 −0.336027
\(184\) 29.8273 51.6623i 2.19890 3.80860i
\(185\) 13.6116 + 23.5760i 1.00074 + 1.73334i
\(186\) −3.61510 6.26154i −0.265072 0.459119i
\(187\) −0.785198 + 1.36000i −0.0574193 + 0.0994532i
\(188\) 23.2569 1.69618
\(189\) 0 0
\(190\) 26.2746 1.90616
\(191\) 12.5434 21.7258i 0.907608 1.57202i 0.0902297 0.995921i \(-0.471240\pi\)
0.817378 0.576102i \(-0.195427\pi\)
\(192\) −17.5164 30.3393i −1.26414 2.18955i
\(193\) −5.65544 9.79551i −0.407088 0.705096i 0.587474 0.809243i \(-0.300122\pi\)
−0.994562 + 0.104146i \(0.966789\pi\)
\(194\) −13.3007 + 23.0375i −0.954936 + 1.65400i
\(195\) −8.75819 −0.627187
\(196\) 0 0
\(197\) −16.7919 −1.19637 −0.598185 0.801358i \(-0.704111\pi\)
−0.598185 + 0.801358i \(0.704111\pi\)
\(198\) 2.38490 4.13076i 0.169487 0.293560i
\(199\) −10.2670 17.7830i −0.727811 1.26061i −0.957806 0.287414i \(-0.907204\pi\)
0.229995 0.973192i \(-0.426129\pi\)
\(200\) 33.8786 + 58.6795i 2.39558 + 4.14927i
\(201\) 15.4473 26.7555i 1.08957 1.88719i
\(202\) 8.01333 0.563816
\(203\) 0 0
\(204\) 28.9974 2.03022
\(205\) 18.6528 32.3076i 1.30277 2.25646i
\(206\) −6.68912 11.5859i −0.466053 0.807227i
\(207\) −10.0881 17.4731i −0.701171 1.21446i
\(208\) 5.70682 9.88450i 0.395697 0.685367i
\(209\) −1.77416 −0.122721
\(210\) 0 0
\(211\) −15.7785 −1.08624 −0.543119 0.839655i \(-0.682757\pi\)
−0.543119 + 0.839655i \(0.682757\pi\)
\(212\) −13.2839 + 23.0084i −0.912340 + 1.58022i
\(213\) 8.09608 + 14.0228i 0.554734 + 0.960828i
\(214\) 15.7245 + 27.2357i 1.07491 + 1.86179i
\(215\) 5.67096 9.82239i 0.386756 0.669881i
\(216\) 5.03804 0.342795
\(217\) 0 0
\(218\) −9.42697 −0.638475
\(219\) −15.0186 + 26.0129i −1.01486 + 1.75779i
\(220\) −6.05137 10.4813i −0.407984 0.706648i
\(221\) 1.19797 + 2.07494i 0.0805839 + 0.139575i
\(222\) −23.6908 + 41.0337i −1.59003 + 2.75400i
\(223\) −8.44731 −0.565673 −0.282837 0.959168i \(-0.591275\pi\)
−0.282837 + 0.959168i \(0.591275\pi\)
\(224\) 0 0
\(225\) 22.9167 1.52778
\(226\) −12.5669 + 21.7665i −0.835937 + 1.44789i
\(227\) −3.34456 5.79294i −0.221986 0.384491i 0.733425 0.679771i \(-0.237921\pi\)
−0.955411 + 0.295279i \(0.904587\pi\)
\(228\) 16.3800 + 28.3709i 1.08479 + 1.87891i
\(229\) −4.31755 + 7.47822i −0.285312 + 0.494175i −0.972685 0.232130i \(-0.925430\pi\)
0.687373 + 0.726305i \(0.258764\pi\)
\(230\) −71.4641 −4.71220
\(231\) 0 0
\(232\) 1.68648 0.110723
\(233\) 2.08373 3.60912i 0.136510 0.236441i −0.789664 0.613540i \(-0.789745\pi\)
0.926173 + 0.377099i \(0.123078\pi\)
\(234\) −3.63861 6.30225i −0.237863 0.411991i
\(235\) −8.41495 14.5751i −0.548931 0.950776i
\(236\) −20.8609 + 36.1322i −1.35793 + 2.35201i
\(237\) −3.63947 −0.236409
\(238\) 0 0
\(239\) −1.79450 −0.116077 −0.0580384 0.998314i \(-0.518485\pi\)
−0.0580384 + 0.998314i \(0.518485\pi\)
\(240\) −49.9814 + 86.5703i −3.22628 + 5.58809i
\(241\) −6.93047 12.0039i −0.446431 0.773241i 0.551720 0.834029i \(-0.313972\pi\)
−0.998151 + 0.0607887i \(0.980638\pi\)
\(242\) −14.0345 24.3085i −0.902174 1.56261i
\(243\) 10.7010 18.5347i 0.686470 1.18900i
\(244\) −9.58373 −0.613535
\(245\) 0 0
\(246\) 64.9300 4.13979
\(247\) −1.35341 + 2.34417i −0.0861153 + 0.149156i
\(248\) −4.60407 7.97448i −0.292359 0.506380i
\(249\) −18.8778 32.6973i −1.19633 2.07211i
\(250\) 16.3184 28.2643i 1.03207 1.78759i
\(251\) 14.7449 0.930687 0.465344 0.885130i \(-0.345931\pi\)
0.465344 + 0.885130i \(0.345931\pi\)
\(252\) 0 0
\(253\) 4.82554 0.303379
\(254\) 7.25951 12.5738i 0.455502 0.788953i
\(255\) −10.4920 18.1727i −0.657035 1.13802i
\(256\) 0.519021 + 0.898971i 0.0324388 + 0.0561857i
\(257\) −11.8534 + 20.5307i −0.739395 + 1.28067i 0.213373 + 0.976971i \(0.431555\pi\)
−0.952768 + 0.303699i \(0.901778\pi\)
\(258\) 19.7405 1.22899
\(259\) 0 0
\(260\) −18.4650 −1.14515
\(261\) 0.285198 0.493977i 0.0176533 0.0305764i
\(262\) 13.0514 + 22.6056i 0.806317 + 1.39658i
\(263\) −5.68780 9.85155i −0.350725 0.607473i 0.635652 0.771976i \(-0.280731\pi\)
−0.986377 + 0.164503i \(0.947398\pi\)
\(264\) 6.36226 11.0198i 0.391570 0.678219i
\(265\) 19.2258 1.18103
\(266\) 0 0
\(267\) −35.4827 −2.17151
\(268\) 32.5678 56.4090i 1.98939 3.44573i
\(269\) 5.55269 + 9.61755i 0.338554 + 0.586392i 0.984161 0.177277i \(-0.0567290\pi\)
−0.645607 + 0.763670i \(0.723396\pi\)
\(270\) −3.01770 5.22681i −0.183651 0.318094i
\(271\) 6.36226 11.0198i 0.386480 0.669402i −0.605494 0.795850i \(-0.707024\pi\)
0.991973 + 0.126448i \(0.0403576\pi\)
\(272\) 27.3463 1.65811
\(273\) 0 0
\(274\) −46.6032 −2.81540
\(275\) −2.74049 + 4.74667i −0.165258 + 0.286235i
\(276\) −44.5518 77.1660i −2.68170 4.64484i
\(277\) 1.50000 + 2.59808i 0.0901263 + 0.156103i 0.907564 0.419914i \(-0.137940\pi\)
−0.817438 + 0.576017i \(0.804606\pi\)
\(278\) −6.52569 + 11.3028i −0.391385 + 0.677898i
\(279\) −3.11435 −0.186451
\(280\) 0 0
\(281\) 3.44731 0.205649 0.102825 0.994700i \(-0.467212\pi\)
0.102825 + 0.994700i \(0.467212\pi\)
\(282\) 14.6461 25.3679i 0.872165 1.51063i
\(283\) 6.23917 + 10.8066i 0.370880 + 0.642383i 0.989701 0.143149i \(-0.0457227\pi\)
−0.618821 + 0.785532i \(0.712389\pi\)
\(284\) 17.0691 + 29.5645i 1.01286 + 1.75433i
\(285\) 11.8534 20.5307i 0.702135 1.21613i
\(286\) 1.74049 0.102917
\(287\) 0 0
\(288\) −38.6484 −2.27738
\(289\) 5.62976 9.75102i 0.331162 0.573590i
\(290\) −1.01017 1.74967i −0.0593192 0.102744i
\(291\) 12.0009 + 20.7861i 0.703503 + 1.21850i
\(292\) −31.6638 + 54.8434i −1.85299 + 3.20947i
\(293\) −13.5341 −0.790670 −0.395335 0.918537i \(-0.629371\pi\)
−0.395335 + 0.918537i \(0.629371\pi\)
\(294\) 0 0
\(295\) 30.1922 1.75786
\(296\) −30.1718 + 52.2591i −1.75370 + 3.03750i
\(297\) 0.203767 + 0.352935i 0.0118238 + 0.0204794i
\(298\) −13.7312 23.7831i −0.795426 1.37772i
\(299\) 3.68113 6.37590i 0.212885 0.368728i
\(300\) 101.206 5.84315
\(301\) 0 0
\(302\) −13.4676 −0.774976
\(303\) 3.61510 6.26154i 0.207682 0.359716i
\(304\) 15.4473 + 26.7555i 0.885964 + 1.53453i
\(305\) 3.46765 + 6.00614i 0.198557 + 0.343911i
\(306\) 8.71785 15.0998i 0.498366 0.863196i
\(307\) 28.2365 1.61154 0.805772 0.592226i \(-0.201751\pi\)
0.805772 + 0.592226i \(0.201751\pi\)
\(308\) 0 0
\(309\) −12.0708 −0.686684
\(310\) −5.51552 + 9.55316i −0.313260 + 0.542583i
\(311\) 12.3521 + 21.3944i 0.700423 + 1.21317i 0.968318 + 0.249720i \(0.0803385\pi\)
−0.267895 + 0.963448i \(0.586328\pi\)
\(312\) −9.70682 16.8127i −0.549540 0.951832i
\(313\) 10.4061 18.0239i 0.588188 1.01877i −0.406282 0.913748i \(-0.633175\pi\)
0.994470 0.105023i \(-0.0334917\pi\)
\(314\) 33.4624 1.88839
\(315\) 0 0
\(316\) −7.67314 −0.431648
\(317\) −13.0691 + 22.6363i −0.734032 + 1.27138i 0.221114 + 0.975248i \(0.429031\pi\)
−0.955147 + 0.296134i \(0.904303\pi\)
\(318\) 16.7312 + 28.9793i 0.938238 + 1.62508i
\(319\) 0.0682107 + 0.118144i 0.00381906 + 0.00661481i
\(320\) −26.7245 + 46.2882i −1.49395 + 2.58759i
\(321\) 28.3756 1.58377
\(322\) 0 0
\(323\) −6.48535 −0.360854
\(324\) 24.5274 42.4827i 1.36263 2.36015i
\(325\) 4.18113 + 7.24193i 0.231927 + 0.401710i
\(326\) 4.25951 + 7.37769i 0.235912 + 0.408612i
\(327\) −4.25284 + 7.36614i −0.235183 + 0.407349i
\(328\) 82.6926 4.56593
\(329\) 0 0
\(330\) −15.2435 −0.839129
\(331\) 12.0691 20.9043i 0.663376 1.14900i −0.316346 0.948644i \(-0.602456\pi\)
0.979723 0.200358i \(-0.0642105\pi\)
\(332\) −39.8003 68.9361i −2.18432 3.78336i
\(333\) 10.2046 + 17.6749i 0.559210 + 0.968581i
\(334\) 10.7817 18.6744i 0.589948 1.02182i
\(335\) −47.1355 −2.57529
\(336\) 0 0
\(337\) −30.5297 −1.66306 −0.831530 0.555480i \(-0.812534\pi\)
−0.831530 + 0.555480i \(0.812534\pi\)
\(338\) 1.32772 2.29968i 0.0722185 0.125086i
\(339\) 11.3388 + 19.6393i 0.615837 + 1.06666i
\(340\) −22.1204 38.3137i −1.19965 2.07785i
\(341\) 0.372429 0.645067i 0.0201682 0.0349323i
\(342\) 19.6981 1.06515
\(343\) 0 0
\(344\) 25.1408 1.35550
\(345\) −32.2400 + 55.8414i −1.73575 + 3.00640i
\(346\) −13.7135 23.7524i −0.737241 1.27694i
\(347\) 12.4987 + 21.6483i 0.670964 + 1.16214i 0.977631 + 0.210327i \(0.0674530\pi\)
−0.306667 + 0.951817i \(0.599214\pi\)
\(348\) 1.25951 2.18154i 0.0675169 0.116943i
\(349\) −1.83887 −0.0984324 −0.0492162 0.998788i \(-0.515672\pi\)
−0.0492162 + 0.998788i \(0.515672\pi\)
\(350\) 0 0
\(351\) 0.621770 0.0331876
\(352\) 4.62177 8.00514i 0.246341 0.426675i
\(353\) 11.6284 + 20.1410i 0.618919 + 1.07200i 0.989683 + 0.143272i \(0.0457625\pi\)
−0.370764 + 0.928727i \(0.620904\pi\)
\(354\) 26.2746 + 45.5089i 1.39648 + 2.41877i
\(355\) 12.3521 21.3944i 0.655581 1.13550i
\(356\) −74.8087 −3.96485
\(357\) 0 0
\(358\) 6.31525 0.333772
\(359\) 10.7237 18.5739i 0.565973 0.980294i −0.430986 0.902359i \(-0.641834\pi\)
0.996958 0.0779348i \(-0.0248326\pi\)
\(360\) 40.5855 + 70.2961i 2.13904 + 3.70493i
\(361\) 5.83657 + 10.1092i 0.307188 + 0.532065i
\(362\) 28.9570 50.1550i 1.52195 2.63609i
\(363\) −25.3259 −1.32927
\(364\) 0 0
\(365\) 45.8273 2.39871
\(366\) −6.03540 + 10.4536i −0.315476 + 0.546420i
\(367\) 0.560225 + 0.970338i 0.0292435 + 0.0506512i 0.880277 0.474461i \(-0.157357\pi\)
−0.851033 + 0.525112i \(0.824024\pi\)
\(368\) −42.0151 72.7722i −2.19019 3.79351i
\(369\) 13.9840 24.2210i 0.727979 1.26090i
\(370\) 72.2896 3.75816
\(371\) 0 0
\(372\) −13.7538 −0.713102
\(373\) −7.80290 + 13.5150i −0.404019 + 0.699781i −0.994207 0.107485i \(-0.965720\pi\)
0.590188 + 0.807266i \(0.299054\pi\)
\(374\) 2.08505 + 3.61141i 0.107815 + 0.186741i
\(375\) −14.7237 25.5021i −0.760326 1.31692i
\(376\) 18.6528 32.3076i 0.961945 1.66614i
\(377\) 0.208136 0.0107196
\(378\) 0 0
\(379\) 12.7849 0.656714 0.328357 0.944554i \(-0.393505\pi\)
0.328357 + 0.944554i \(0.393505\pi\)
\(380\) 24.9907 43.2852i 1.28200 2.22048i
\(381\) −6.55005 11.3450i −0.335569 0.581223i
\(382\) −33.3082 57.6916i −1.70420 2.95176i
\(383\) −17.0177 + 29.4755i −0.869564 + 1.50613i −0.00712095 + 0.999975i \(0.502267\pi\)
−0.862443 + 0.506154i \(0.831067\pi\)
\(384\) −25.4490 −1.29869
\(385\) 0 0
\(386\) −30.0354 −1.52876
\(387\) 4.25152 7.36386i 0.216117 0.374326i
\(388\) 25.3016 + 43.8236i 1.28449 + 2.22481i
\(389\) 12.3353 + 21.3653i 0.625422 + 1.08326i 0.988459 + 0.151488i \(0.0484065\pi\)
−0.363037 + 0.931775i \(0.618260\pi\)
\(390\) −11.6284 + 20.1410i −0.588829 + 1.01988i
\(391\) 17.6395 0.892066
\(392\) 0 0
\(393\) 23.5518 1.18803
\(394\) −22.2949 + 38.6159i −1.12320 + 1.94544i
\(395\) 2.77635 + 4.80877i 0.139693 + 0.241956i
\(396\) −4.53672 7.85783i −0.227979 0.394871i
\(397\) 2.48983 4.31251i 0.124961 0.216439i −0.796757 0.604300i \(-0.793453\pi\)
0.921718 + 0.387861i \(0.126786\pi\)
\(398\) −54.5271 −2.73320
\(399\) 0 0
\(400\) 95.4438 4.77219
\(401\) −0.344558 + 0.596791i −0.0172064 + 0.0298023i −0.874500 0.485025i \(-0.838811\pi\)
0.857294 + 0.514827i \(0.172144\pi\)
\(402\) −41.0194 71.0477i −2.04586 3.54354i
\(403\) −0.568211 0.984170i −0.0283046 0.0490250i
\(404\) 7.62177 13.2013i 0.379197 0.656789i
\(405\) −35.4987 −1.76394
\(406\) 0 0
\(407\) −4.88128 −0.241956
\(408\) 23.2569 40.2821i 1.15139 1.99426i
\(409\) −9.98851 17.3006i −0.493900 0.855460i 0.506075 0.862489i \(-0.331096\pi\)
−0.999975 + 0.00702937i \(0.997762\pi\)
\(410\) −49.5314 85.7910i −2.44618 4.23691i
\(411\) −21.0244 + 36.4153i −1.03706 + 1.79623i
\(412\) −25.4490 −1.25378
\(413\) 0 0
\(414\) −53.5767 −2.63315
\(415\) −28.8016 + 49.8858i −1.41381 + 2.44880i
\(416\) −7.05137 12.2133i −0.345722 0.598808i
\(417\) 5.88795 + 10.1982i 0.288334 + 0.499409i
\(418\) −2.35559 + 4.08001i −0.115216 + 0.199560i
\(419\) 19.6661 0.960754 0.480377 0.877062i \(-0.340500\pi\)
0.480377 + 0.877062i \(0.340500\pi\)
\(420\) 0 0
\(421\) 14.9283 0.727560 0.363780 0.931485i \(-0.381486\pi\)
0.363780 + 0.931485i \(0.381486\pi\)
\(422\) −20.9495 + 36.2856i −1.01981 + 1.76635i
\(423\) −6.30870 10.9270i −0.306739 0.531288i
\(424\) 21.3082 + 36.9070i 1.03482 + 1.79236i
\(425\) −10.0177 + 17.3512i −0.485930 + 0.841655i
\(426\) 42.9974 2.08323
\(427\) 0 0
\(428\) 59.8246 2.89173
\(429\) 0.785198 1.36000i 0.0379097 0.0656615i
\(430\) −15.0589 26.0828i −0.726205 1.25782i
\(431\) 16.3419 + 28.3050i 0.787163 + 1.36341i 0.927699 + 0.373330i \(0.121784\pi\)
−0.140536 + 0.990076i \(0.544883\pi\)
\(432\) 3.54832 6.14588i 0.170719 0.295694i
\(433\) −8.96196 −0.430684 −0.215342 0.976539i \(-0.569087\pi\)
−0.215342 + 0.976539i \(0.569087\pi\)
\(434\) 0 0
\(435\) −1.82290 −0.0874012
\(436\) −8.96633 + 15.5301i −0.429409 + 0.743759i
\(437\) 9.96414 + 17.2584i 0.476650 + 0.825581i
\(438\) 39.8809 + 69.0758i 1.90558 + 3.30057i
\(439\) 3.96633 6.86988i 0.189302 0.327881i −0.755715 0.654900i \(-0.772711\pi\)
0.945018 + 0.327019i \(0.106044\pi\)
\(440\) −19.4136 −0.925509
\(441\) 0 0
\(442\) 6.36226 0.302622
\(443\) 4.45529 7.71679i 0.211677 0.366636i −0.740562 0.671988i \(-0.765441\pi\)
0.952240 + 0.305352i \(0.0987741\pi\)
\(444\) 45.0664 + 78.0574i 2.13876 + 3.70444i
\(445\) 27.0678 + 46.8827i 1.28313 + 2.22245i
\(446\) −11.2157 + 19.4261i −0.531077 + 0.919853i
\(447\) −24.7785 −1.17198
\(448\) 0 0
\(449\) −8.45168 −0.398859 −0.199430 0.979912i \(-0.563909\pi\)
−0.199430 + 0.979912i \(0.563909\pi\)
\(450\) 30.4270 52.7010i 1.43434 2.48435i
\(451\) 3.34456 + 5.79294i 0.157489 + 0.272779i
\(452\) 23.9056 + 41.4058i 1.12443 + 1.94756i
\(453\) −6.07574 + 10.5235i −0.285463 + 0.494437i
\(454\) −17.7626 −0.833638
\(455\) 0 0
\(456\) 52.5491 2.46084
\(457\) −11.5846 + 20.0651i −0.541904 + 0.938606i 0.456890 + 0.889523i \(0.348963\pi\)
−0.998795 + 0.0490829i \(0.984370\pi\)
\(458\) 11.4650 + 19.8580i 0.535725 + 0.927902i
\(459\) 0.744859 + 1.29013i 0.0347670 + 0.0602183i
\(460\) −67.9721 + 117.731i −3.16921 + 5.48924i
\(461\) 2.27284 0.105857 0.0529284 0.998598i \(-0.483144\pi\)
0.0529284 + 0.998598i \(0.483144\pi\)
\(462\) 0 0
\(463\) −4.10976 −0.190997 −0.0954983 0.995430i \(-0.530444\pi\)
−0.0954983 + 0.995430i \(0.530444\pi\)
\(464\) 1.18780 2.05732i 0.0551420 0.0955088i
\(465\) 4.97650 + 8.61955i 0.230780 + 0.399722i
\(466\) −5.53322 9.58381i −0.256321 0.443962i
\(467\) −16.4575 + 28.5052i −0.761561 + 1.31906i 0.180484 + 0.983578i \(0.442233\pi\)
−0.942046 + 0.335485i \(0.891100\pi\)
\(468\) −13.8432 −0.639904
\(469\) 0 0
\(470\) −44.6908 −2.06143
\(471\) 15.0961 26.1472i 0.695591 1.20480i
\(472\) 33.4624 + 57.9585i 1.54023 + 2.66776i
\(473\) 1.01684 + 1.76121i 0.0467542 + 0.0809806i
\(474\) −4.83220 + 8.36962i −0.221950 + 0.384429i
\(475\) −22.6351 −1.03857
\(476\) 0 0
\(477\) 14.4136 0.659955
\(478\) −2.38260 + 4.12678i −0.108978 + 0.188755i
\(479\) 4.65763 + 8.06725i 0.212812 + 0.368602i 0.952594 0.304246i \(-0.0984043\pi\)
−0.739781 + 0.672847i \(0.765071\pi\)
\(480\) 61.7573 + 106.967i 2.81882 + 4.88234i
\(481\) −3.72365 + 6.44956i −0.169784 + 0.294074i
\(482\) −36.8069 −1.67651
\(483\) 0 0
\(484\) −53.3950 −2.42705
\(485\) 18.3096 31.7131i 0.831395 1.44002i
\(486\) −28.4159 49.2178i −1.28897 2.23257i
\(487\) −10.1204 17.5291i −0.458601 0.794321i 0.540286 0.841481i \(-0.318316\pi\)
−0.998887 + 0.0471606i \(0.984983\pi\)
\(488\) −7.68648 + 13.3134i −0.347950 + 0.602668i
\(489\) 7.68648 0.347594
\(490\) 0 0
\(491\) −4.36226 −0.196866 −0.0984330 0.995144i \(-0.531383\pi\)
−0.0984330 + 0.995144i \(0.531383\pi\)
\(492\) 61.7573 106.967i 2.78423 4.82243i
\(493\) 0.249340 + 0.431870i 0.0112297 + 0.0194504i
\(494\) 3.59390 + 6.22481i 0.161697 + 0.280068i
\(495\) −3.28301 + 5.68635i −0.147560 + 0.255582i
\(496\) −12.9707 −0.582401
\(497\) 0 0
\(498\) −100.258 −4.49265
\(499\) −4.84674 + 8.39480i −0.216970 + 0.375803i −0.953880 0.300188i \(-0.902951\pi\)
0.736910 + 0.675991i \(0.236284\pi\)
\(500\) −31.0421 53.7664i −1.38824 2.40451i
\(501\) −9.72802 16.8494i −0.434616 0.752777i
\(502\) 19.5771 33.9085i 0.873767 1.51341i
\(503\) 2.64843 0.118088 0.0590439 0.998255i \(-0.481195\pi\)
0.0590439 + 0.998255i \(0.481195\pi\)
\(504\) 0 0
\(505\) −11.0310 −0.490875
\(506\) 6.40697 11.0972i 0.284824 0.493330i
\(507\) −1.19797 2.07494i −0.0532035 0.0921512i
\(508\) −13.8096 23.9189i −0.612700 1.06123i
\(509\) 6.97081 12.0738i 0.308976 0.535162i −0.669163 0.743116i \(-0.733347\pi\)
0.978139 + 0.207954i \(0.0666805\pi\)
\(510\) −55.7219 −2.46741
\(511\) 0 0
\(512\) 24.0000 1.06066
\(513\) −0.841508 + 1.45753i −0.0371535 + 0.0643517i
\(514\) 31.4760 + 54.5181i 1.38835 + 2.40469i
\(515\) 9.20814 + 15.9490i 0.405759 + 0.702795i
\(516\) 18.7759 32.5208i 0.826563 1.43165i
\(517\) 3.01770 0.132718
\(518\) 0 0
\(519\) −24.7466 −1.08625
\(520\) −14.8096 + 25.6509i −0.649442 + 1.12487i
\(521\) 7.31088 + 12.6628i 0.320296 + 0.554768i 0.980549 0.196275i \(-0.0628844\pi\)
−0.660253 + 0.751043i \(0.729551\pi\)
\(522\) −0.757326 1.31173i −0.0331473 0.0574127i
\(523\) −8.25951 + 14.3059i −0.361163 + 0.625553i −0.988153 0.153475i \(-0.950954\pi\)
0.626989 + 0.779028i \(0.284287\pi\)
\(524\) 49.6545 2.16917
\(525\) 0 0
\(526\) −30.2072 −1.31710
\(527\) 1.36139 2.35800i 0.0593033 0.102716i
\(528\) −8.96196 15.5226i −0.390019 0.675533i
\(529\) −15.6014 27.0225i −0.678323 1.17489i
\(530\) 25.5266 44.2133i 1.10880 1.92050i
\(531\) 22.6351 0.982280
\(532\) 0 0
\(533\) 10.2055 0.442049
\(534\) −47.1111 + 81.5989i −2.03870 + 3.53113i
\(535\) −21.6461 37.4922i −0.935844 1.62093i
\(536\) −52.2409 90.4839i −2.25646 3.90831i
\(537\) 2.84904 4.93468i 0.122945 0.212947i
\(538\) 29.4897 1.27139
\(539\) 0 0
\(540\) −11.4810 −0.494063
\(541\) 21.5509 37.3273i 0.926546 1.60483i 0.137491 0.990503i \(-0.456096\pi\)
0.789055 0.614322i \(-0.210571\pi\)
\(542\) −16.8946 29.2623i −0.725686 1.25692i
\(543\) −26.1271 45.2535i −1.12122 1.94201i
\(544\) 16.8946 29.2623i 0.724351 1.25461i
\(545\) 12.9770 0.555874
\(546\) 0 0
\(547\) −13.5057 −0.577462 −0.288731 0.957410i \(-0.593233\pi\)
−0.288731 + 0.957410i \(0.593233\pi\)
\(548\) −44.3259 + 76.7748i −1.89351 + 3.27966i
\(549\) 2.59970 + 4.50281i 0.110952 + 0.192175i
\(550\) 7.27721 + 12.6045i 0.310301 + 0.537458i
\(551\) −0.281693 + 0.487907i −0.0120005 + 0.0207855i
\(552\) −142.928 −6.08343
\(553\) 0 0
\(554\) 7.96633 0.338457
\(555\) 32.6125 56.4864i 1.38432 2.39772i
\(556\) 12.4136 + 21.5010i 0.526455 + 0.911847i
\(557\) −0.675783 1.17049i −0.0286338 0.0495953i 0.851353 0.524593i \(-0.175782\pi\)
−0.879987 + 0.474997i \(0.842449\pi\)
\(558\) −4.13499 + 7.16201i −0.175048 + 0.303192i
\(559\) 3.10275 0.131232
\(560\) 0 0
\(561\) 3.76256 0.158855
\(562\) 4.57706 7.92770i 0.193072 0.334410i
\(563\) −15.8813 27.5072i −0.669316 1.15929i −0.978096 0.208156i \(-0.933254\pi\)
0.308779 0.951134i \(-0.400079\pi\)
\(564\) −27.8609 48.2566i −1.17316 2.03197i
\(565\) 17.2994 29.9634i 0.727791 1.26057i
\(566\) 33.1355 1.39279
\(567\) 0 0
\(568\) 54.7599 2.29768
\(569\) −15.1865 + 26.3037i −0.636650 + 1.10271i 0.349513 + 0.936932i \(0.386347\pi\)
−0.986163 + 0.165779i \(0.946986\pi\)
\(570\) −31.4760 54.5181i −1.31839 2.28351i
\(571\) 0.216122 + 0.374334i 0.00904442 + 0.0156654i 0.870512 0.492147i \(-0.163788\pi\)
−0.861468 + 0.507812i \(0.830454\pi\)
\(572\) 1.65544 2.86731i 0.0692175 0.119888i
\(573\) −60.1062 −2.51097
\(574\) 0 0
\(575\) 61.5651 2.56744
\(576\) −20.0354 + 34.7023i −0.834808 + 1.44593i
\(577\) −9.06908 15.7081i −0.377551 0.653937i 0.613155 0.789963i \(-0.289900\pi\)
−0.990705 + 0.136026i \(0.956567\pi\)
\(578\) −14.9495 25.8933i −0.621817 1.07702i
\(579\) −13.5501 + 23.4694i −0.563121 + 0.975354i
\(580\) −3.84324 −0.159582
\(581\) 0 0
\(582\) 63.7352 2.64191
\(583\) −1.72365 + 2.98545i −0.0713864 + 0.123645i
\(584\) 50.7910 + 87.9725i 2.10174 + 3.64033i
\(585\) 5.00885 + 8.67558i 0.207090 + 0.358691i
\(586\) −17.9695 + 31.1241i −0.742313 + 1.28572i
\(587\) 19.3065 0.796865 0.398433 0.917198i \(-0.369554\pi\)
0.398433 + 0.917198i \(0.369554\pi\)
\(588\) 0 0
\(589\) 3.07608 0.126748
\(590\) 40.0868 69.4323i 1.65035 2.85848i
\(591\) 20.1161 + 34.8421i 0.827465 + 1.43321i
\(592\) 42.5004 + 73.6129i 1.74676 + 3.02547i
\(593\) −4.10056 + 7.10238i −0.168390 + 0.291660i −0.937854 0.347030i \(-0.887190\pi\)
0.769464 + 0.638690i \(0.220523\pi\)
\(594\) 1.08218 0.0444025
\(595\) 0 0
\(596\) −52.2409 −2.13987
\(597\) −24.5991 + 42.6069i −1.00678 + 1.74379i
\(598\) −9.77503 16.9308i −0.399731 0.692354i
\(599\) −11.7392 20.3328i −0.479649 0.830777i 0.520078 0.854119i \(-0.325903\pi\)
−0.999728 + 0.0233415i \(0.992570\pi\)
\(600\) 81.1709 140.592i 3.31379 5.73965i
\(601\) −8.96196 −0.365566 −0.182783 0.983153i \(-0.558511\pi\)
−0.182783 + 0.983153i \(0.558511\pi\)
\(602\) 0 0
\(603\) −35.3375 −1.43906
\(604\) −12.8096 + 22.1868i −0.521214 + 0.902769i
\(605\) 19.3197 + 33.4628i 0.785459 + 1.36045i
\(606\) −9.59970 16.6272i −0.389961 0.675432i
\(607\) −21.7320 + 37.6410i −0.882077 + 1.52780i −0.0330487 + 0.999454i \(0.510522\pi\)
−0.849028 + 0.528348i \(0.822812\pi\)
\(608\) 38.1736 1.54814
\(609\) 0 0
\(610\) 18.4163 0.745653
\(611\) 2.30203 3.98724i 0.0931303 0.161306i
\(612\) −16.5837 28.7239i −0.670357 1.16109i
\(613\) 10.7245 + 18.5754i 0.433159 + 0.750254i 0.997143 0.0755318i \(-0.0240655\pi\)
−0.563984 + 0.825786i \(0.690732\pi\)
\(614\) 37.4902 64.9350i 1.51298 2.62056i
\(615\) −89.3817 −3.60422
\(616\) 0 0
\(617\) −12.1294 −0.488312 −0.244156 0.969736i \(-0.578511\pi\)
−0.244156 + 0.969736i \(0.578511\pi\)
\(618\) −16.0267 + 27.7590i −0.644687 + 1.11663i
\(619\) −6.36226 11.0198i −0.255721 0.442921i 0.709370 0.704836i \(-0.248979\pi\)
−0.965091 + 0.261915i \(0.915646\pi\)
\(620\) 10.4920 + 18.1727i 0.421369 + 0.729833i
\(621\) 2.28881 3.96434i 0.0918469 0.159084i
\(622\) 65.6005 2.63034
\(623\) 0 0
\(624\) −27.3463 −1.09473
\(625\) −1.55804 + 2.69860i −0.0623216 + 0.107944i
\(626\) −27.6328 47.8614i −1.10443 1.91293i
\(627\) 2.12539 + 3.68128i 0.0848797 + 0.147016i
\(628\) 31.8273 55.1264i 1.27005 2.19978i
\(629\) −17.8432 −0.711456
\(630\) 0 0
\(631\) −11.7538 −0.467912 −0.233956 0.972247i \(-0.575167\pi\)
−0.233956 + 0.972247i \(0.575167\pi\)
\(632\) −6.15412 + 10.6593i −0.244798 + 0.424002i
\(633\) 18.9021 + 32.7395i 0.751293 + 1.30128i
\(634\) 34.7042 + 60.1094i 1.37828 + 2.38725i
\(635\) −9.99333 + 17.3090i −0.396573 + 0.686885i
\(636\) 63.6545 2.52407
\(637\) 0 0
\(638\) 0.362259 0.0143420
\(639\) 9.26038 16.0394i 0.366335 0.634510i
\(640\) 19.4136 + 33.6254i 0.767391 + 1.32916i
\(641\) −2.34324 4.05861i −0.0925523 0.160305i 0.816032 0.578007i \(-0.196169\pi\)
−0.908584 + 0.417701i \(0.862836\pi\)
\(642\) 37.6749 65.2548i 1.48691 2.57540i
\(643\) −0.751182 −0.0296237 −0.0148119 0.999890i \(-0.504715\pi\)
−0.0148119 + 0.999890i \(0.504715\pi\)
\(644\) 0 0
\(645\) −27.1745 −1.06999
\(646\) −8.61073 + 14.9142i −0.338785 + 0.586792i
\(647\) −20.4238 35.3751i −0.802943 1.39074i −0.917671 0.397340i \(-0.869933\pi\)
0.114729 0.993397i \(-0.463400\pi\)
\(648\) −39.3436 68.1452i −1.54556 2.67700i
\(649\) −2.70682 + 4.68834i −0.106252 + 0.184034i
\(650\) 22.2055 0.870971
\(651\) 0 0
\(652\) 16.2055 0.634656
\(653\) 23.2392 40.2514i 0.909419 1.57516i 0.0945459 0.995521i \(-0.469860\pi\)
0.814873 0.579639i \(-0.196807\pi\)
\(654\) 11.2932 + 19.5604i 0.441598 + 0.764871i
\(655\) −17.9663 31.1186i −0.702002 1.21590i
\(656\) 58.2409 100.876i 2.27393 3.93855i
\(657\) 34.3568 1.34038
\(658\) 0 0
\(659\) 30.3596 1.18264 0.591321 0.806436i \(-0.298606\pi\)
0.591321 + 0.806436i \(0.298606\pi\)
\(660\) −14.4987 + 25.1125i −0.564360 + 0.977501i
\(661\) 0.0535589 + 0.0927667i 0.00208320 + 0.00360820i 0.867065 0.498195i \(-0.166004\pi\)
−0.864982 + 0.501803i \(0.832670\pi\)
\(662\) −32.0487 55.5100i −1.24561 2.15746i
\(663\) 2.87024 4.97141i 0.111471 0.193074i
\(664\) −127.685 −4.95513
\(665\) 0 0
\(666\) 54.1956 2.10004
\(667\) 0.766177 1.32706i 0.0296665 0.0513838i
\(668\) −20.5097 35.5239i −0.793545 1.37446i
\(669\) 10.1196 + 17.5276i 0.391246 + 0.677658i
\(670\) −62.5828 + 108.397i −2.41779 + 4.18773i
\(671\) −1.24354 −0.0480063
\(672\) 0 0
\(673\) 38.5385 1.48555 0.742774 0.669542i \(-0.233510\pi\)
0.742774 + 0.669542i \(0.233510\pi\)
\(674\) −40.5349 + 70.2086i −1.56135 + 2.70433i
\(675\) 2.59970 + 4.50281i 0.100062 + 0.173313i
\(676\) −2.52569 4.37462i −0.0971418 0.168255i
\(677\) 10.3901 17.9962i 0.399325 0.691651i −0.594318 0.804230i \(-0.702578\pi\)
0.993643 + 0.112579i \(0.0359111\pi\)
\(678\) 60.2188 2.31269
\(679\) 0 0
\(680\) −70.9654 −2.72140
\(681\) −8.01333 + 13.8795i −0.307072 + 0.531864i
\(682\) −0.988965 1.71294i −0.0378694 0.0655918i
\(683\) −13.7919 23.8882i −0.527731 0.914057i −0.999477 0.0323227i \(-0.989710\pi\)
0.471746 0.881734i \(-0.343624\pi\)
\(684\) 18.7356 32.4509i 0.716372 1.24079i
\(685\) 64.1532 2.45117
\(686\) 0 0
\(687\) 20.6891 0.789339
\(688\) 17.7068 30.6691i 0.675066 1.16925i
\(689\) 2.62976 + 4.55487i 0.100186 + 0.173527i
\(690\) 85.6116 + 148.284i 3.25918 + 5.64506i
\(691\) −21.8388 + 37.8258i −0.830785 + 1.43896i 0.0666308 + 0.997778i \(0.478775\pi\)
−0.897416 + 0.441185i \(0.854558\pi\)
\(692\) −52.1736 −1.98334
\(693\) 0 0
\(694\) 66.3791 2.51971
\(695\) 8.98316 15.5593i 0.340751 0.590198i
\(696\) −2.02034 3.49933i −0.0765808 0.132642i
\(697\) 12.2258 + 21.1758i 0.463087 + 0.802090i
\(698\) −2.44150 + 4.22881i −0.0924123 + 0.160063i
\(699\) −9.98494 −0.377665
\(700\) 0 0
\(701\) −20.8973 −0.789278 −0.394639 0.918836i \(-0.629130\pi\)
−0.394639 + 0.918836i \(0.629130\pi\)
\(702\) 0.825537 1.42987i 0.0311579 0.0539670i
\(703\) −10.0792 17.4578i −0.380146 0.658432i
\(704\) −4.79186 8.29975i −0.180600 0.312809i
\(705\) −20.1617 + 34.9210i −0.759332 + 1.31520i
\(706\) 61.7573 2.32427
\(707\) 0 0
\(708\) 99.9628 3.75683
\(709\) −4.96983 + 8.60800i −0.186646 + 0.323280i −0.944130 0.329574i \(-0.893095\pi\)
0.757484 + 0.652854i \(0.226428\pi\)
\(710\) −32.8003 56.8117i −1.23097 2.13211i
\(711\) 2.08143 + 3.60514i 0.0780597 + 0.135203i
\(712\) −59.9991 + 103.921i −2.24856 + 3.89462i
\(713\) −8.36663 −0.313333
\(714\) 0 0
\(715\) −2.39593 −0.0896028
\(716\) 6.00667 10.4039i 0.224480 0.388810i
\(717\) 2.14975 + 3.72348i 0.0802840 + 0.139056i
\(718\) −28.4760 49.3220i −1.06272 1.84068i
\(719\) 5.98983 10.3747i 0.223383 0.386911i −0.732450 0.680821i \(-0.761623\pi\)
0.955833 + 0.293910i \(0.0949566\pi\)
\(720\) 114.338 4.26114
\(721\) 0 0
\(722\) 30.9974 1.15360
\(723\) −16.6049 + 28.7606i −0.617544 + 1.06962i
\(724\) −55.0841 95.4085i −2.04719 3.54583i
\(725\) 0.870245 + 1.50731i 0.0323201 + 0.0559800i
\(726\) −33.6258 + 58.2416i −1.24797 + 2.16155i
\(727\) 24.1736 0.896547 0.448274 0.893896i \(-0.352039\pi\)
0.448274 + 0.893896i \(0.352039\pi\)
\(728\) 0 0
\(729\) −22.1443 −0.820157
\(730\) 60.8458 105.388i 2.25201 3.90059i
\(731\) 3.71699 + 6.43801i 0.137478 + 0.238118i
\(732\) 11.4810 + 19.8856i 0.424349 + 0.734994i
\(733\) 18.2237 31.5643i 0.673106 1.16585i −0.303913 0.952700i \(-0.598293\pi\)
0.977019 0.213154i \(-0.0683736\pi\)
\(734\) 2.97529 0.109820
\(735\) 0 0
\(736\) −103.828 −3.82715
\(737\) 4.22584 7.31937i 0.155661 0.269612i
\(738\) −37.1338 64.3176i −1.36691 2.36756i
\(739\) −21.6386 37.4792i −0.795989 1.37869i −0.922209 0.386691i \(-0.873618\pi\)
0.126220 0.992002i \(-0.459715\pi\)
\(740\) 68.7573 119.091i 2.52757 4.37788i
\(741\) 6.48535 0.238245
\(742\) 0 0
\(743\) 22.6572 0.831211 0.415606 0.909545i \(-0.363570\pi\)
0.415606 + 0.909545i \(0.363570\pi\)
\(744\) −11.0310 + 19.1063i −0.404417 + 0.700471i
\(745\) 18.9021 + 32.7395i 0.692521 + 1.19948i
\(746\) 20.7201 + 35.8884i 0.758619 + 1.31397i
\(747\) −21.5926 + 37.3994i −0.790031 + 1.36837i
\(748\) 7.93265 0.290047
\(749\) 0 0
\(750\) −78.1956 −2.85530
\(751\) −14.9340 + 25.8664i −0.544948 + 0.943878i 0.453662 + 0.891174i \(0.350117\pi\)
−0.998610 + 0.0527044i \(0.983216\pi\)
\(752\) −26.2746 45.5089i −0.958135 1.65954i
\(753\) −17.6638 30.5947i −0.643706 1.11493i
\(754\) 0.276347 0.478647i 0.0100640 0.0174313i
\(755\) 18.5394 0.674716
\(756\) 0 0
\(757\) 2.55706 0.0929380 0.0464690 0.998920i \(-0.485203\pi\)
0.0464690 + 0.998920i \(0.485203\pi\)
\(758\) 16.9747 29.4011i 0.616550 1.06790i
\(759\) −5.78083 10.0127i −0.209831 0.363438i
\(760\) −40.0868 69.4323i −1.45410 2.51858i
\(761\) −7.36444 + 12.7556i −0.266961 + 0.462390i −0.968075 0.250659i \(-0.919353\pi\)
0.701115 + 0.713049i \(0.252686\pi\)
\(762\) −34.7866 −1.26019
\(763\) 0 0
\(764\) −126.723 −4.58467
\(765\) −12.0009 + 20.7861i −0.433892 + 0.751523i
\(766\) 45.1895 + 78.2706i 1.63276 + 2.82803i
\(767\) 4.12976 + 7.15295i 0.149117 + 0.258278i
\(768\) 1.24354 2.15387i 0.0448724 0.0777212i
\(769\) −36.1692 −1.30429 −0.652147 0.758092i \(-0.726132\pi\)
−0.652147 + 0.758092i \(0.726132\pi\)
\(770\) 0 0
\(771\) 56.7999 2.04560
\(772\) −28.5678 + 49.4808i −1.02818 + 1.78085i
\(773\) −19.4783 33.7375i −0.700587 1.21345i −0.968261 0.249943i \(-0.919588\pi\)
0.267673 0.963510i \(-0.413745\pi\)
\(774\) −11.2897 19.5543i −0.405799 0.702865i
\(775\) 4.75152 8.22988i 0.170680 0.295626i