Properties

Label 546.2.s.d.43.2
Level $546$
Weight $2$
Character 546.43
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(43,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.s (of order \(6\), degree \(2\), 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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 546.43
Dual form 546.2.s.d.127.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.36603 + 2.36603i) q^{10} +(0.232051 + 0.133975i) q^{11} +1.00000 q^{12} +(0.866025 + 3.50000i) q^{13} -1.00000 q^{14} +(2.36603 + 1.36603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.86603 + 3.23205i) q^{17} -1.00000i q^{18} +(2.13397 - 1.23205i) q^{19} +(-2.36603 + 1.36603i) q^{20} +1.00000i q^{21} +(0.133975 + 0.232051i) q^{22} +(-1.73205 + 3.00000i) q^{23} +(0.866025 + 0.500000i) q^{24} -2.46410 q^{25} +(-1.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(-0.866025 - 0.500000i) q^{28} +(1.50000 - 2.59808i) q^{29} +(1.36603 + 2.36603i) q^{30} -9.66025i q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.232051 - 0.133975i) q^{33} +3.73205i q^{34} +(-1.36603 - 2.36603i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-4.09808 - 2.36603i) q^{37} +2.46410 q^{38} +(3.46410 + 1.00000i) q^{39} -2.73205 q^{40} +(6.06218 + 3.50000i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-1.36603 - 2.36603i) q^{43} +0.267949i q^{44} +(2.36603 - 1.36603i) q^{45} +(-3.00000 + 1.73205i) q^{46} +2.46410i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-2.13397 - 1.23205i) q^{50} +3.73205 q^{51} +(-2.59808 + 2.50000i) q^{52} -3.53590 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.366025 + 0.633975i) q^{55} +(-0.500000 - 0.866025i) q^{56} -2.46410i q^{57} +(2.59808 - 1.50000i) q^{58} +(11.1962 - 6.46410i) q^{59} +2.73205i q^{60} +(4.13397 + 7.16025i) q^{61} +(4.83013 - 8.36603i) q^{62} +(0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(-9.56218 + 2.36603i) q^{65} +0.267949 q^{66} +(-0.803848 - 0.464102i) q^{67} +(-1.86603 + 3.23205i) q^{68} +(1.73205 + 3.00000i) q^{69} -2.73205i q^{70} +(7.09808 - 4.09808i) q^{71} +(0.866025 - 0.500000i) q^{72} -13.4641i q^{73} +(-2.36603 - 4.09808i) q^{74} +(-1.23205 + 2.13397i) q^{75} +(2.13397 + 1.23205i) q^{76} -0.267949 q^{77} +(2.50000 + 2.59808i) q^{78} -16.8564 q^{79} +(-2.36603 - 1.36603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.50000 + 6.06218i) q^{82} -11.6603i q^{83} +(-0.866025 + 0.500000i) q^{84} +(-8.83013 + 5.09808i) q^{85} -2.73205i q^{86} +(-1.50000 - 2.59808i) q^{87} +(-0.133975 + 0.232051i) q^{88} +(0.401924 + 0.232051i) q^{89} +2.73205 q^{90} +(-2.50000 - 2.59808i) q^{91} -3.46410 q^{92} +(-8.36603 - 4.83013i) q^{93} +(-1.23205 + 2.13397i) q^{94} +(3.36603 + 5.83013i) q^{95} +1.00000i q^{96} +(2.36603 - 1.36603i) q^{97} +(0.866025 - 0.500000i) q^{98} -0.267949i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{14} + 6 q^{15} - 2 q^{16} + 4 q^{17} + 12 q^{19} - 6 q^{20} + 4 q^{22} + 4 q^{25} - 4 q^{26} - 4 q^{27} + 6 q^{29} + 2 q^{30} - 6 q^{33} - 2 q^{35} + 2 q^{36} - 6 q^{37} - 4 q^{38} - 4 q^{40} - 2 q^{42} - 2 q^{43} + 6 q^{45} - 12 q^{46} + 2 q^{48} + 2 q^{49} - 12 q^{50} + 8 q^{51} - 28 q^{53} + 2 q^{55} - 2 q^{56} + 24 q^{59} + 20 q^{61} + 2 q^{62} - 4 q^{64} - 14 q^{65} + 8 q^{66} - 24 q^{67} - 4 q^{68} + 18 q^{71} - 6 q^{74} + 2 q^{75} + 12 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 6 q^{80} - 2 q^{81} + 14 q^{82} - 18 q^{85} - 6 q^{87} - 4 q^{88} + 12 q^{89} + 4 q^{90} - 10 q^{91} - 30 q^{93} + 2 q^{94} + 10 q^{95} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 2.73205i 1.22181i 0.791704 + 0.610905i \(0.209194\pi\)
−0.791704 + 0.610905i \(0.790806\pi\)
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.36603 + 2.36603i −0.431975 + 0.748203i
\(11\) 0.232051 + 0.133975i 0.0699660 + 0.0403949i 0.534575 0.845121i \(-0.320472\pi\)
−0.464609 + 0.885516i \(0.653805\pi\)
\(12\) 1.00000 0.288675
\(13\) 0.866025 + 3.50000i 0.240192 + 0.970725i
\(14\) −1.00000 −0.267261
\(15\) 2.36603 + 1.36603i 0.610905 + 0.352706i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.86603 + 3.23205i 0.452578 + 0.783887i 0.998545 0.0539188i \(-0.0171712\pi\)
−0.545968 + 0.837806i \(0.683838\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 2.13397 1.23205i 0.489567 0.282652i −0.234828 0.972037i \(-0.575453\pi\)
0.724395 + 0.689385i \(0.242119\pi\)
\(20\) −2.36603 + 1.36603i −0.529059 + 0.305453i
\(21\) 1.00000i 0.218218i
\(22\) 0.133975 + 0.232051i 0.0285635 + 0.0494734i
\(23\) −1.73205 + 3.00000i −0.361158 + 0.625543i −0.988152 0.153481i \(-0.950952\pi\)
0.626994 + 0.779024i \(0.284285\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) −2.46410 −0.492820
\(26\) −1.00000 + 3.46410i −0.196116 + 0.679366i
\(27\) −1.00000 −0.192450
\(28\) −0.866025 0.500000i −0.163663 0.0944911i
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) 1.36603 + 2.36603i 0.249401 + 0.431975i
\(31\) 9.66025i 1.73503i −0.497409 0.867516i \(-0.665715\pi\)
0.497409 0.867516i \(-0.334285\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0.232051 0.133975i 0.0403949 0.0233220i
\(34\) 3.73205i 0.640041i
\(35\) −1.36603 2.36603i −0.230900 0.399931i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −4.09808 2.36603i −0.673720 0.388972i 0.123765 0.992312i \(-0.460503\pi\)
−0.797485 + 0.603339i \(0.793836\pi\)
\(38\) 2.46410 0.399730
\(39\) 3.46410 + 1.00000i 0.554700 + 0.160128i
\(40\) −2.73205 −0.431975
\(41\) 6.06218 + 3.50000i 0.946753 + 0.546608i 0.892071 0.451896i \(-0.149252\pi\)
0.0546823 + 0.998504i \(0.482585\pi\)
\(42\) −0.500000 + 0.866025i −0.0771517 + 0.133631i
\(43\) −1.36603 2.36603i −0.208317 0.360815i 0.742868 0.669438i \(-0.233465\pi\)
−0.951184 + 0.308623i \(0.900132\pi\)
\(44\) 0.267949i 0.0403949i
\(45\) 2.36603 1.36603i 0.352706 0.203635i
\(46\) −3.00000 + 1.73205i −0.442326 + 0.255377i
\(47\) 2.46410i 0.359426i 0.983719 + 0.179713i \(0.0575169\pi\)
−0.983719 + 0.179713i \(0.942483\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −2.13397 1.23205i −0.301790 0.174238i
\(51\) 3.73205 0.522592
\(52\) −2.59808 + 2.50000i −0.360288 + 0.346688i
\(53\) −3.53590 −0.485693 −0.242846 0.970065i \(-0.578081\pi\)
−0.242846 + 0.970065i \(0.578081\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) −0.366025 + 0.633975i −0.0493549 + 0.0854851i
\(56\) −0.500000 0.866025i −0.0668153 0.115728i
\(57\) 2.46410i 0.326378i
\(58\) 2.59808 1.50000i 0.341144 0.196960i
\(59\) 11.1962 6.46410i 1.45761 0.841554i 0.458721 0.888580i \(-0.348308\pi\)
0.998894 + 0.0470259i \(0.0149743\pi\)
\(60\) 2.73205i 0.352706i
\(61\) 4.13397 + 7.16025i 0.529301 + 0.916777i 0.999416 + 0.0341713i \(0.0108792\pi\)
−0.470115 + 0.882605i \(0.655787\pi\)
\(62\) 4.83013 8.36603i 0.613427 1.06249i
\(63\) 0.866025 + 0.500000i 0.109109 + 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) −9.56218 + 2.36603i −1.18604 + 0.293469i
\(66\) 0.267949 0.0329823
\(67\) −0.803848 0.464102i −0.0982056 0.0566990i 0.450093 0.892982i \(-0.351391\pi\)
−0.548298 + 0.836283i \(0.684724\pi\)
\(68\) −1.86603 + 3.23205i −0.226289 + 0.391944i
\(69\) 1.73205 + 3.00000i 0.208514 + 0.361158i
\(70\) 2.73205i 0.326543i
\(71\) 7.09808 4.09808i 0.842387 0.486352i −0.0156881 0.999877i \(-0.504994\pi\)
0.858075 + 0.513525i \(0.171661\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 13.4641i 1.57585i −0.615769 0.787927i \(-0.711154\pi\)
0.615769 0.787927i \(-0.288846\pi\)
\(74\) −2.36603 4.09808i −0.275045 0.476392i
\(75\) −1.23205 + 2.13397i −0.142265 + 0.246410i
\(76\) 2.13397 + 1.23205i 0.244784 + 0.141326i
\(77\) −0.267949 −0.0305356
\(78\) 2.50000 + 2.59808i 0.283069 + 0.294174i
\(79\) −16.8564 −1.89649 −0.948247 0.317534i \(-0.897145\pi\)
−0.948247 + 0.317534i \(0.897145\pi\)
\(80\) −2.36603 1.36603i −0.264530 0.152726i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 3.50000 + 6.06218i 0.386510 + 0.669456i
\(83\) 11.6603i 1.27988i −0.768425 0.639940i \(-0.778959\pi\)
0.768425 0.639940i \(-0.221041\pi\)
\(84\) −0.866025 + 0.500000i −0.0944911 + 0.0545545i
\(85\) −8.83013 + 5.09808i −0.957762 + 0.552964i
\(86\) 2.73205i 0.294605i
\(87\) −1.50000 2.59808i −0.160817 0.278543i
\(88\) −0.133975 + 0.232051i −0.0142817 + 0.0247367i
\(89\) 0.401924 + 0.232051i 0.0426038 + 0.0245973i 0.521151 0.853465i \(-0.325503\pi\)
−0.478547 + 0.878062i \(0.658836\pi\)
\(90\) 2.73205 0.287983
\(91\) −2.50000 2.59808i −0.262071 0.272352i
\(92\) −3.46410 −0.361158
\(93\) −8.36603 4.83013i −0.867516 0.500861i
\(94\) −1.23205 + 2.13397i −0.127076 + 0.220103i
\(95\) 3.36603 + 5.83013i 0.345347 + 0.598158i
\(96\) 1.00000i 0.102062i
\(97\) 2.36603 1.36603i 0.240233 0.138699i −0.375051 0.927004i \(-0.622375\pi\)
0.615284 + 0.788305i \(0.289041\pi\)
\(98\) 0.866025 0.500000i 0.0874818 0.0505076i
\(99\) 0.267949i 0.0269299i
\(100\) −1.23205 2.13397i −0.123205 0.213397i
\(101\) −5.00000 + 8.66025i −0.497519 + 0.861727i −0.999996 0.00286291i \(-0.999089\pi\)
0.502477 + 0.864590i \(0.332422\pi\)
\(102\) 3.23205 + 1.86603i 0.320021 + 0.184764i
\(103\) 1.80385 0.177738 0.0888692 0.996043i \(-0.471675\pi\)
0.0888692 + 0.996043i \(0.471675\pi\)
\(104\) −3.50000 + 0.866025i −0.343203 + 0.0849208i
\(105\) −2.73205 −0.266621
\(106\) −3.06218 1.76795i −0.297425 0.171718i
\(107\) 4.23205 7.33013i 0.409128 0.708630i −0.585664 0.810554i \(-0.699166\pi\)
0.994792 + 0.101923i \(0.0324997\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 13.6603i 1.30842i −0.756315 0.654208i \(-0.773002\pi\)
0.756315 0.654208i \(-0.226998\pi\)
\(110\) −0.633975 + 0.366025i −0.0604471 + 0.0348992i
\(111\) −4.09808 + 2.36603i −0.388972 + 0.224573i
\(112\) 1.00000i 0.0944911i
\(113\) −0.0980762 0.169873i −0.00922623 0.0159803i 0.861375 0.507969i \(-0.169604\pi\)
−0.870602 + 0.491989i \(0.836270\pi\)
\(114\) 1.23205 2.13397i 0.115392 0.199865i
\(115\) −8.19615 4.73205i −0.764295 0.441266i
\(116\) 3.00000 0.278543
\(117\) 2.59808 2.50000i 0.240192 0.231125i
\(118\) 12.9282 1.19014
\(119\) −3.23205 1.86603i −0.296282 0.171058i
\(120\) −1.36603 + 2.36603i −0.124700 + 0.215988i
\(121\) −5.46410 9.46410i −0.496737 0.860373i
\(122\) 8.26795i 0.748545i
\(123\) 6.06218 3.50000i 0.546608 0.315584i
\(124\) 8.36603 4.83013i 0.751291 0.433758i
\(125\) 6.92820i 0.619677i
\(126\) 0.500000 + 0.866025i 0.0445435 + 0.0771517i
\(127\) −9.73205 + 16.8564i −0.863580 + 1.49576i 0.00487054 + 0.999988i \(0.498450\pi\)
−0.868450 + 0.495776i \(0.834884\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −2.73205 −0.240544
\(130\) −9.46410 2.73205i −0.830057 0.239617i
\(131\) 5.07180 0.443125 0.221562 0.975146i \(-0.428884\pi\)
0.221562 + 0.975146i \(0.428884\pi\)
\(132\) 0.232051 + 0.133975i 0.0201974 + 0.0116610i
\(133\) −1.23205 + 2.13397i −0.106832 + 0.185039i
\(134\) −0.464102 0.803848i −0.0400923 0.0694419i
\(135\) 2.73205i 0.235137i
\(136\) −3.23205 + 1.86603i −0.277146 + 0.160010i
\(137\) −7.39230 + 4.26795i −0.631567 + 0.364636i −0.781359 0.624082i \(-0.785473\pi\)
0.149792 + 0.988718i \(0.452140\pi\)
\(138\) 3.46410i 0.294884i
\(139\) −3.06218 5.30385i −0.259731 0.449866i 0.706439 0.707774i \(-0.250300\pi\)
−0.966170 + 0.257907i \(0.916967\pi\)
\(140\) 1.36603 2.36603i 0.115450 0.199966i
\(141\) 2.13397 + 1.23205i 0.179713 + 0.103757i
\(142\) 8.19615 0.687806
\(143\) −0.267949 + 0.928203i −0.0224070 + 0.0776203i
\(144\) 1.00000 0.0833333
\(145\) 7.09808 + 4.09808i 0.589463 + 0.340327i
\(146\) 6.73205 11.6603i 0.557148 0.965009i
\(147\) −0.500000 0.866025i −0.0412393 0.0714286i
\(148\) 4.73205i 0.388972i
\(149\) 4.39230 2.53590i 0.359832 0.207749i −0.309175 0.951005i \(-0.600053\pi\)
0.669007 + 0.743256i \(0.266720\pi\)
\(150\) −2.13397 + 1.23205i −0.174238 + 0.100597i
\(151\) 2.80385i 0.228174i −0.993471 0.114087i \(-0.963606\pi\)
0.993471 0.114087i \(-0.0363942\pi\)
\(152\) 1.23205 + 2.13397i 0.0999325 + 0.173088i
\(153\) 1.86603 3.23205i 0.150859 0.261296i
\(154\) −0.232051 0.133975i −0.0186992 0.0107960i
\(155\) 26.3923 2.11988
\(156\) 0.866025 + 3.50000i 0.0693375 + 0.280224i
\(157\) −8.53590 −0.681239 −0.340619 0.940201i \(-0.610637\pi\)
−0.340619 + 0.940201i \(0.610637\pi\)
\(158\) −14.5981 8.42820i −1.16136 0.670512i
\(159\) −1.76795 + 3.06218i −0.140207 + 0.242846i
\(160\) −1.36603 2.36603i −0.107994 0.187051i
\(161\) 3.46410i 0.273009i
\(162\) −0.866025 + 0.500000i −0.0680414 + 0.0392837i
\(163\) 15.7583 9.09808i 1.23429 0.712616i 0.266367 0.963872i \(-0.414177\pi\)
0.967921 + 0.251255i \(0.0808434\pi\)
\(164\) 7.00000i 0.546608i
\(165\) 0.366025 + 0.633975i 0.0284950 + 0.0493549i
\(166\) 5.83013 10.0981i 0.452506 0.783763i
\(167\) 18.9282 + 10.9282i 1.46471 + 0.845650i 0.999223 0.0394060i \(-0.0125466\pi\)
0.465485 + 0.885056i \(0.345880\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −11.5000 + 6.06218i −0.884615 + 0.466321i
\(170\) −10.1962 −0.782009
\(171\) −2.13397 1.23205i −0.163189 0.0942173i
\(172\) 1.36603 2.36603i 0.104158 0.180408i
\(173\) 8.63397 + 14.9545i 0.656429 + 1.13697i 0.981534 + 0.191290i \(0.0612672\pi\)
−0.325105 + 0.945678i \(0.605400\pi\)
\(174\) 3.00000i 0.227429i
\(175\) 2.13397 1.23205i 0.161313 0.0931343i
\(176\) −0.232051 + 0.133975i −0.0174915 + 0.0100987i
\(177\) 12.9282i 0.971743i
\(178\) 0.232051 + 0.401924i 0.0173929 + 0.0301255i
\(179\) 0.803848 1.39230i 0.0600824 0.104066i −0.834420 0.551130i \(-0.814197\pi\)
0.894502 + 0.447064i \(0.147530\pi\)
\(180\) 2.36603 + 1.36603i 0.176353 + 0.101818i
\(181\) 9.19615 0.683545 0.341772 0.939783i \(-0.388973\pi\)
0.341772 + 0.939783i \(0.388973\pi\)
\(182\) −0.866025 3.50000i −0.0641941 0.259437i
\(183\) 8.26795 0.611184
\(184\) −3.00000 1.73205i −0.221163 0.127688i
\(185\) 6.46410 11.1962i 0.475250 0.823157i
\(186\) −4.83013 8.36603i −0.354162 0.613427i
\(187\) 1.00000i 0.0731272i
\(188\) −2.13397 + 1.23205i −0.155636 + 0.0898565i
\(189\) 0.866025 0.500000i 0.0629941 0.0363696i
\(190\) 6.73205i 0.488394i
\(191\) −3.09808 5.36603i −0.224169 0.388272i 0.731901 0.681411i \(-0.238633\pi\)
−0.956070 + 0.293139i \(0.905300\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 5.89230 + 3.40192i 0.424137 + 0.244876i 0.696846 0.717221i \(-0.254586\pi\)
−0.272709 + 0.962097i \(0.587919\pi\)
\(194\) 2.73205 0.196150
\(195\) −2.73205 + 9.46410i −0.195646 + 0.677738i
\(196\) 1.00000 0.0714286
\(197\) −4.96410 2.86603i −0.353678 0.204196i 0.312626 0.949876i \(-0.398791\pi\)
−0.666304 + 0.745680i \(0.732125\pi\)
\(198\) 0.133975 0.232051i 0.00952116 0.0164911i
\(199\) 3.09808 + 5.36603i 0.219617 + 0.380387i 0.954691 0.297599i \(-0.0961860\pi\)
−0.735074 + 0.677987i \(0.762853\pi\)
\(200\) 2.46410i 0.174238i
\(201\) −0.803848 + 0.464102i −0.0566990 + 0.0327352i
\(202\) −8.66025 + 5.00000i −0.609333 + 0.351799i
\(203\) 3.00000i 0.210559i
\(204\) 1.86603 + 3.23205i 0.130648 + 0.226289i
\(205\) −9.56218 + 16.5622i −0.667851 + 1.15675i
\(206\) 1.56218 + 0.901924i 0.108842 + 0.0628400i
\(207\) 3.46410 0.240772
\(208\) −3.46410 1.00000i −0.240192 0.0693375i
\(209\) 0.660254 0.0456707
\(210\) −2.36603 1.36603i −0.163271 0.0942647i
\(211\) −5.92820 + 10.2679i −0.408114 + 0.706875i −0.994678 0.103028i \(-0.967147\pi\)
0.586564 + 0.809903i \(0.300480\pi\)
\(212\) −1.76795 3.06218i −0.121423 0.210311i
\(213\) 8.19615i 0.561591i
\(214\) 7.33013 4.23205i 0.501077 0.289297i
\(215\) 6.46410 3.73205i 0.440848 0.254524i
\(216\) 1.00000i 0.0680414i
\(217\) 4.83013 + 8.36603i 0.327890 + 0.567923i
\(218\) 6.83013 11.8301i 0.462595 0.801237i
\(219\) −11.6603 6.73205i −0.787927 0.454910i
\(220\) −0.732051 −0.0493549
\(221\) −9.69615 + 9.33013i −0.652234 + 0.627612i
\(222\) −4.73205 −0.317594
\(223\) 10.7321 + 6.19615i 0.718671 + 0.414925i 0.814263 0.580496i \(-0.197141\pi\)
−0.0955922 + 0.995421i \(0.530474\pi\)
\(224\) 0.500000 0.866025i 0.0334077 0.0578638i
\(225\) 1.23205 + 2.13397i 0.0821367 + 0.142265i
\(226\) 0.196152i 0.0130479i
\(227\) −13.3923 + 7.73205i −0.888878 + 0.513194i −0.873575 0.486689i \(-0.838205\pi\)
−0.0153030 + 0.999883i \(0.504871\pi\)
\(228\) 2.13397 1.23205i 0.141326 0.0815946i
\(229\) 24.3205i 1.60714i −0.595207 0.803572i \(-0.702930\pi\)
0.595207 0.803572i \(-0.297070\pi\)
\(230\) −4.73205 8.19615i −0.312022 0.540438i
\(231\) −0.133975 + 0.232051i −0.00881488 + 0.0152678i
\(232\) 2.59808 + 1.50000i 0.170572 + 0.0984798i
\(233\) 8.19615 0.536948 0.268474 0.963287i \(-0.413481\pi\)
0.268474 + 0.963287i \(0.413481\pi\)
\(234\) 3.50000 0.866025i 0.228802 0.0566139i
\(235\) −6.73205 −0.439151
\(236\) 11.1962 + 6.46410i 0.728807 + 0.420777i
\(237\) −8.42820 + 14.5981i −0.547471 + 0.948247i
\(238\) −1.86603 3.23205i −0.120956 0.209503i
\(239\) 24.1962i 1.56512i 0.622576 + 0.782559i \(0.286086\pi\)
−0.622576 + 0.782559i \(0.713914\pi\)
\(240\) −2.36603 + 1.36603i −0.152726 + 0.0881766i
\(241\) −24.9282 + 14.3923i −1.60577 + 0.927090i −0.615464 + 0.788165i \(0.711031\pi\)
−0.990303 + 0.138925i \(0.955635\pi\)
\(242\) 10.9282i 0.702492i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −4.13397 + 7.16025i −0.264651 + 0.458388i
\(245\) 2.36603 + 1.36603i 0.151160 + 0.0872722i
\(246\) 7.00000 0.446304
\(247\) 6.16025 + 6.40192i 0.391968 + 0.407345i
\(248\) 9.66025 0.613427
\(249\) −10.0981 5.83013i −0.639940 0.369469i
\(250\) −3.46410 + 6.00000i −0.219089 + 0.379473i
\(251\) 3.90192 + 6.75833i 0.246287 + 0.426582i 0.962493 0.271307i \(-0.0874560\pi\)
−0.716205 + 0.697889i \(0.754123\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) −0.803848 + 0.464102i −0.0505375 + 0.0291778i
\(254\) −16.8564 + 9.73205i −1.05767 + 0.610643i
\(255\) 10.1962i 0.638508i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −13.5263 + 23.4282i −0.843746 + 1.46141i 0.0429595 + 0.999077i \(0.486321\pi\)
−0.886706 + 0.462334i \(0.847012\pi\)
\(258\) −2.36603 1.36603i −0.147302 0.0850450i
\(259\) 4.73205 0.294035
\(260\) −6.83013 7.09808i −0.423586 0.440204i
\(261\) −3.00000 −0.185695
\(262\) 4.39230 + 2.53590i 0.271357 + 0.156668i
\(263\) 7.63397 13.2224i 0.470731 0.815330i −0.528709 0.848803i \(-0.677324\pi\)
0.999440 + 0.0334733i \(0.0106569\pi\)
\(264\) 0.133975 + 0.232051i 0.00824557 + 0.0142817i
\(265\) 9.66025i 0.593425i
\(266\) −2.13397 + 1.23205i −0.130842 + 0.0755419i
\(267\) 0.401924 0.232051i 0.0245973 0.0142013i
\(268\) 0.928203i 0.0566990i
\(269\) −15.8564 27.4641i −0.966782 1.67452i −0.704749 0.709457i \(-0.748940\pi\)
−0.262033 0.965059i \(-0.584393\pi\)
\(270\) 1.36603 2.36603i 0.0831337 0.143992i
\(271\) 20.3660 + 11.7583i 1.23715 + 0.714268i 0.968510 0.248974i \(-0.0800932\pi\)
0.268638 + 0.963241i \(0.413427\pi\)
\(272\) −3.73205 −0.226289
\(273\) −3.50000 + 0.866025i −0.211830 + 0.0524142i
\(274\) −8.53590 −0.515672
\(275\) −0.571797 0.330127i −0.0344806 0.0199074i
\(276\) −1.73205 + 3.00000i −0.104257 + 0.180579i
\(277\) −2.80385 4.85641i −0.168467 0.291793i 0.769414 0.638750i \(-0.220548\pi\)
−0.937881 + 0.346957i \(0.887215\pi\)
\(278\) 6.12436i 0.367314i
\(279\) −8.36603 + 4.83013i −0.500861 + 0.289172i
\(280\) 2.36603 1.36603i 0.141397 0.0816356i
\(281\) 7.80385i 0.465539i −0.972532 0.232769i \(-0.925221\pi\)
0.972532 0.232769i \(-0.0747787\pi\)
\(282\) 1.23205 + 2.13397i 0.0733676 + 0.127076i
\(283\) −4.53590 + 7.85641i −0.269631 + 0.467015i −0.968767 0.247974i \(-0.920235\pi\)
0.699135 + 0.714989i \(0.253568\pi\)
\(284\) 7.09808 + 4.09808i 0.421193 + 0.243176i
\(285\) 6.73205 0.398772
\(286\) −0.696152 + 0.669873i −0.0411644 + 0.0396104i
\(287\) −7.00000 −0.413197
\(288\) 0.866025 + 0.500000i 0.0510310 + 0.0294628i
\(289\) 1.53590 2.66025i 0.0903470 0.156486i
\(290\) 4.09808 + 7.09808i 0.240647 + 0.416813i
\(291\) 2.73205i 0.160156i
\(292\) 11.6603 6.73205i 0.682365 0.393963i
\(293\) −24.9282 + 14.3923i −1.45632 + 0.840807i −0.998828 0.0484056i \(-0.984586\pi\)
−0.457493 + 0.889213i \(0.651253\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) 17.6603 + 30.5885i 1.02822 + 1.78093i
\(296\) 2.36603 4.09808i 0.137522 0.238196i
\(297\) −0.232051 0.133975i −0.0134650 0.00777399i
\(298\) 5.07180 0.293801
\(299\) −12.0000 3.46410i −0.693978 0.200334i
\(300\) −2.46410 −0.142265
\(301\) 2.36603 + 1.36603i 0.136375 + 0.0787364i
\(302\) 1.40192 2.42820i 0.0806716 0.139727i
\(303\) 5.00000 + 8.66025i 0.287242 + 0.497519i
\(304\) 2.46410i 0.141326i
\(305\) −19.5622 + 11.2942i −1.12013 + 0.646706i
\(306\) 3.23205 1.86603i 0.184764 0.106674i
\(307\) 7.78461i 0.444291i −0.975014 0.222146i \(-0.928694\pi\)
0.975014 0.222146i \(-0.0713060\pi\)
\(308\) −0.133975 0.232051i −0.00763391 0.0132223i
\(309\) 0.901924 1.56218i 0.0513087 0.0888692i
\(310\) 22.8564 + 13.1962i 1.29816 + 0.749491i
\(311\) 8.80385 0.499220 0.249610 0.968346i \(-0.419698\pi\)
0.249610 + 0.968346i \(0.419698\pi\)
\(312\) −1.00000 + 3.46410i −0.0566139 + 0.196116i
\(313\) 12.1962 0.689367 0.344684 0.938719i \(-0.387986\pi\)
0.344684 + 0.938719i \(0.387986\pi\)
\(314\) −7.39230 4.26795i −0.417172 0.240854i
\(315\) −1.36603 + 2.36603i −0.0769668 + 0.133310i
\(316\) −8.42820 14.5981i −0.474123 0.821206i
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) −3.06218 + 1.76795i −0.171718 + 0.0991417i
\(319\) 0.696152 0.401924i 0.0389771 0.0225034i
\(320\) 2.73205i 0.152726i
\(321\) −4.23205 7.33013i −0.236210 0.409128i
\(322\) 1.73205 3.00000i 0.0965234 0.167183i
\(323\) 7.96410 + 4.59808i 0.443134 + 0.255844i
\(324\) −1.00000 −0.0555556
\(325\) −2.13397 8.62436i −0.118372 0.478393i
\(326\) 18.1962 1.00779
\(327\) −11.8301 6.83013i −0.654208 0.377707i
\(328\) −3.50000 + 6.06218i −0.193255 + 0.334728i
\(329\) −1.23205 2.13397i −0.0679252 0.117650i
\(330\) 0.732051i 0.0402981i
\(331\) 2.66025 1.53590i 0.146221 0.0844206i −0.425105 0.905144i \(-0.639763\pi\)
0.571325 + 0.820724i \(0.306429\pi\)
\(332\) 10.0981 5.83013i 0.554204 0.319970i
\(333\) 4.73205i 0.259315i
\(334\) 10.9282 + 18.9282i 0.597965 + 1.03571i
\(335\) 1.26795 2.19615i 0.0692755 0.119989i
\(336\) −0.866025 0.500000i −0.0472456 0.0272772i
\(337\) 13.7846 0.750896 0.375448 0.926844i \(-0.377489\pi\)
0.375448 + 0.926844i \(0.377489\pi\)
\(338\) −12.9904 0.500000i −0.706584 0.0271964i
\(339\) −0.196152 −0.0106535
\(340\) −8.83013 5.09808i −0.478881 0.276482i
\(341\) 1.29423 2.24167i 0.0700864 0.121393i
\(342\) −1.23205 2.13397i −0.0666217 0.115392i
\(343\) 1.00000i 0.0539949i
\(344\) 2.36603 1.36603i 0.127568 0.0736512i
\(345\) −8.19615 + 4.73205i −0.441266 + 0.254765i
\(346\) 17.2679i 0.928331i
\(347\) 2.42820 + 4.20577i 0.130353 + 0.225778i 0.923813 0.382845i \(-0.125056\pi\)
−0.793460 + 0.608623i \(0.791722\pi\)
\(348\) 1.50000 2.59808i 0.0804084 0.139272i
\(349\) 27.4641 + 15.8564i 1.47012 + 0.848774i 0.999438 0.0335290i \(-0.0106746\pi\)
0.470682 + 0.882303i \(0.344008\pi\)
\(350\) 2.46410 0.131712
\(351\) −0.866025 3.50000i −0.0462250 0.186816i
\(352\) −0.267949 −0.0142817
\(353\) −4.73205 2.73205i −0.251862 0.145412i 0.368755 0.929527i \(-0.379784\pi\)
−0.620616 + 0.784114i \(0.713118\pi\)
\(354\) 6.46410 11.1962i 0.343563 0.595069i
\(355\) 11.1962 + 19.3923i 0.594230 + 1.02924i
\(356\) 0.464102i 0.0245973i
\(357\) −3.23205 + 1.86603i −0.171058 + 0.0987605i
\(358\) 1.39230 0.803848i 0.0735856 0.0424847i
\(359\) 26.1962i 1.38258i −0.722577 0.691290i \(-0.757043\pi\)
0.722577 0.691290i \(-0.242957\pi\)
\(360\) 1.36603 + 2.36603i 0.0719959 + 0.124700i
\(361\) −6.46410 + 11.1962i −0.340216 + 0.589271i
\(362\) 7.96410 + 4.59808i 0.418584 + 0.241670i
\(363\) −10.9282 −0.573582
\(364\) 1.00000 3.46410i 0.0524142 0.181568i
\(365\) 36.7846 1.92539
\(366\) 7.16025 + 4.13397i 0.374272 + 0.216086i
\(367\) 16.1244 27.9282i 0.841685 1.45784i −0.0467851 0.998905i \(-0.514898\pi\)
0.888470 0.458935i \(-0.151769\pi\)
\(368\) −1.73205 3.00000i −0.0902894 0.156386i
\(369\) 7.00000i 0.364405i
\(370\) 11.1962 6.46410i 0.582060 0.336053i
\(371\) 3.06218 1.76795i 0.158980 0.0917873i
\(372\) 9.66025i 0.500861i
\(373\) −5.29423 9.16987i −0.274125 0.474798i 0.695789 0.718246i \(-0.255055\pi\)
−0.969914 + 0.243448i \(0.921721\pi\)
\(374\) −0.500000 + 0.866025i −0.0258544 + 0.0447811i
\(375\) 6.00000 + 3.46410i 0.309839 + 0.178885i
\(376\) −2.46410 −0.127076
\(377\) 10.3923 + 3.00000i 0.535231 + 0.154508i
\(378\) 1.00000 0.0514344
\(379\) −14.3660 8.29423i −0.737933 0.426046i 0.0833842 0.996517i \(-0.473427\pi\)
−0.821317 + 0.570472i \(0.806760\pi\)
\(380\) −3.36603 + 5.83013i −0.172673 + 0.299079i
\(381\) 9.73205 + 16.8564i 0.498588 + 0.863580i
\(382\) 6.19615i 0.317023i
\(383\) −30.6506 + 17.6962i −1.56617 + 0.904231i −0.569565 + 0.821946i \(0.692888\pi\)
−0.996609 + 0.0822852i \(0.973778\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 0.732051i 0.0373088i
\(386\) 3.40192 + 5.89230i 0.173153 + 0.299910i
\(387\) −1.36603 + 2.36603i −0.0694390 + 0.120272i
\(388\) 2.36603 + 1.36603i 0.120117 + 0.0693494i
\(389\) −29.1769 −1.47933 −0.739664 0.672976i \(-0.765016\pi\)
−0.739664 + 0.672976i \(0.765016\pi\)
\(390\) −7.09808 + 6.83013i −0.359425 + 0.345857i
\(391\) −12.9282 −0.653807
\(392\) 0.866025 + 0.500000i 0.0437409 + 0.0252538i
\(393\) 2.53590 4.39230i 0.127919 0.221562i
\(394\) −2.86603 4.96410i −0.144388 0.250088i
\(395\) 46.0526i 2.31716i
\(396\) 0.232051 0.133975i 0.0116610 0.00673248i
\(397\) 8.25833 4.76795i 0.414474 0.239297i −0.278236 0.960513i \(-0.589750\pi\)
0.692710 + 0.721216i \(0.256417\pi\)
\(398\) 6.19615i 0.310585i
\(399\) 1.23205 + 2.13397i 0.0616797 + 0.106832i
\(400\) 1.23205 2.13397i 0.0616025 0.106699i
\(401\) 8.66025 + 5.00000i 0.432472 + 0.249688i 0.700399 0.713751i \(-0.253005\pi\)
−0.267927 + 0.963439i \(0.586339\pi\)
\(402\) −0.928203 −0.0462946
\(403\) 33.8109 8.36603i 1.68424 0.416741i
\(404\) −10.0000 −0.497519
\(405\) −2.36603 1.36603i −0.117569 0.0678783i
\(406\) −1.50000 + 2.59808i −0.0744438 + 0.128940i
\(407\) −0.633975 1.09808i −0.0314250 0.0544296i
\(408\) 3.73205i 0.184764i
\(409\) −14.4904 + 8.36603i −0.716503 + 0.413673i −0.813464 0.581615i \(-0.802421\pi\)
0.0969611 + 0.995288i \(0.469088\pi\)
\(410\) −16.5622 + 9.56218i −0.817948 + 0.472242i
\(411\) 8.53590i 0.421045i
\(412\) 0.901924 + 1.56218i 0.0444346 + 0.0769630i
\(413\) −6.46410 + 11.1962i −0.318078 + 0.550927i
\(414\) 3.00000 + 1.73205i 0.147442 + 0.0851257i
\(415\) 31.8564 1.56377
\(416\) −2.50000 2.59808i −0.122573 0.127381i
\(417\) −6.12436 −0.299911
\(418\) 0.571797 + 0.330127i 0.0279675 + 0.0161470i
\(419\) −2.09808 + 3.63397i −0.102498 + 0.177531i −0.912713 0.408601i \(-0.866017\pi\)
0.810215 + 0.586132i \(0.199350\pi\)
\(420\) −1.36603 2.36603i −0.0666552 0.115450i
\(421\) 6.39230i 0.311542i −0.987793 0.155771i \(-0.950214\pi\)
0.987793 0.155771i \(-0.0497862\pi\)
\(422\) −10.2679 + 5.92820i −0.499836 + 0.288580i
\(423\) 2.13397 1.23205i 0.103757 0.0599044i
\(424\) 3.53590i 0.171718i
\(425\) −4.59808 7.96410i −0.223039 0.386316i
\(426\) 4.09808 7.09808i 0.198552 0.343903i
\(427\) −7.16025 4.13397i −0.346509 0.200057i
\(428\) 8.46410 0.409128
\(429\) 0.669873 + 0.696152i 0.0323418 + 0.0336106i
\(430\) 7.46410 0.359951
\(431\) 2.70577 + 1.56218i 0.130332 + 0.0752475i 0.563749 0.825946i \(-0.309359\pi\)
−0.433416 + 0.901194i \(0.642692\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −2.46410 4.26795i −0.118417 0.205105i 0.800723 0.599034i \(-0.204449\pi\)
−0.919141 + 0.393930i \(0.871115\pi\)
\(434\) 9.66025i 0.463707i
\(435\) 7.09808 4.09808i 0.340327 0.196488i
\(436\) 11.8301 6.83013i 0.566560 0.327104i
\(437\) 8.53590i 0.408327i
\(438\) −6.73205 11.6603i −0.321670 0.557148i
\(439\) 2.19615 3.80385i 0.104817 0.181548i −0.808847 0.588020i \(-0.799908\pi\)
0.913663 + 0.406472i \(0.133241\pi\)
\(440\) −0.633975 0.366025i −0.0302236 0.0174496i
\(441\) −1.00000 −0.0476190
\(442\) −13.0622 + 3.23205i −0.621304 + 0.153733i
\(443\) −10.6077 −0.503987 −0.251993 0.967729i \(-0.581086\pi\)
−0.251993 + 0.967729i \(0.581086\pi\)
\(444\) −4.09808 2.36603i −0.194486 0.112287i
\(445\) −0.633975 + 1.09808i −0.0300533 + 0.0520538i
\(446\) 6.19615 + 10.7321i 0.293396 + 0.508177i
\(447\) 5.07180i 0.239888i
\(448\) 0.866025 0.500000i 0.0409159 0.0236228i
\(449\) 6.29423 3.63397i 0.297043 0.171498i −0.344071 0.938944i \(-0.611806\pi\)
0.641114 + 0.767446i \(0.278473\pi\)
\(450\) 2.46410i 0.116159i
\(451\) 0.937822 + 1.62436i 0.0441603 + 0.0764879i
\(452\) 0.0980762 0.169873i 0.00461312 0.00799015i
\(453\) −2.42820 1.40192i −0.114087 0.0658681i
\(454\) −15.4641 −0.725766
\(455\) 7.09808 6.83013i 0.332763 0.320201i
\(456\) 2.46410 0.115392
\(457\) 30.1244 + 17.3923i 1.40916 + 0.813578i 0.995307 0.0967670i \(-0.0308502\pi\)
0.413851 + 0.910345i \(0.364183\pi\)
\(458\) 12.1603 21.0622i 0.568211 0.984171i
\(459\) −1.86603 3.23205i −0.0870986 0.150859i
\(460\) 9.46410i 0.441266i
\(461\) −24.0000 + 13.8564i −1.11779 + 0.645357i −0.940836 0.338862i \(-0.889958\pi\)
−0.176955 + 0.984219i \(0.556625\pi\)
\(462\) −0.232051 + 0.133975i −0.0107960 + 0.00623306i
\(463\) 9.19615i 0.427381i −0.976901 0.213691i \(-0.931452\pi\)
0.976901 0.213691i \(-0.0685485\pi\)
\(464\) 1.50000 + 2.59808i 0.0696358 + 0.120613i
\(465\) 13.1962 22.8564i 0.611957 1.05994i
\(466\) 7.09808 + 4.09808i 0.328812 + 0.189840i
\(467\) −17.8564 −0.826296 −0.413148 0.910664i \(-0.635571\pi\)
−0.413148 + 0.910664i \(0.635571\pi\)
\(468\) 3.46410 + 1.00000i 0.160128 + 0.0462250i
\(469\) 0.928203 0.0428604
\(470\) −5.83013 3.36603i −0.268924 0.155263i
\(471\) −4.26795 + 7.39230i −0.196657 + 0.340619i
\(472\) 6.46410 + 11.1962i 0.297534 + 0.515345i
\(473\) 0.732051i 0.0336597i
\(474\) −14.5981 + 8.42820i −0.670512 + 0.387120i
\(475\) −5.25833 + 3.03590i −0.241269 + 0.139297i
\(476\) 3.73205i 0.171058i
\(477\) 1.76795 + 3.06218i 0.0809488 + 0.140207i
\(478\) −12.0981 + 20.9545i −0.553353 + 0.958436i
\(479\) −9.18653 5.30385i −0.419743 0.242339i 0.275224 0.961380i \(-0.411248\pi\)
−0.694968 + 0.719041i \(0.744581\pi\)
\(480\) −2.73205 −0.124700
\(481\) 4.73205 16.3923i 0.215763 0.747425i
\(482\) −28.7846 −1.31110
\(483\) −3.00000 1.73205i −0.136505 0.0788110i
\(484\) 5.46410 9.46410i 0.248368 0.430186i
\(485\) 3.73205 + 6.46410i 0.169464 + 0.293520i
\(486\) 1.00000i 0.0453609i
\(487\) −9.35641 + 5.40192i −0.423979 + 0.244785i −0.696778 0.717286i \(-0.745384\pi\)
0.272799 + 0.962071i \(0.412051\pi\)
\(488\) −7.16025 + 4.13397i −0.324129 + 0.187136i
\(489\) 18.1962i 0.822858i
\(490\) 1.36603 + 2.36603i 0.0617107 + 0.106886i
\(491\) −6.12436 + 10.6077i −0.276388 + 0.478719i −0.970484 0.241164i \(-0.922471\pi\)
0.694096 + 0.719882i \(0.255804\pi\)
\(492\) 6.06218 + 3.50000i 0.273304 + 0.157792i
\(493\) 11.1962 0.504249
\(494\) 2.13397 + 8.62436i 0.0960121 + 0.388028i
\(495\) 0.732051 0.0329032
\(496\) 8.36603 + 4.83013i 0.375646 + 0.216879i
\(497\) −4.09808 + 7.09808i −0.183824 + 0.318392i
\(498\) −5.83013 10.0981i −0.261254 0.452506i
\(499\) 38.9808i 1.74502i −0.488598 0.872509i \(-0.662491\pi\)
0.488598 0.872509i \(-0.337509\pi\)
\(500\) −6.00000 + 3.46410i −0.268328 + 0.154919i
\(501\) 18.9282 10.9282i 0.845650 0.488236i
\(502\) 7.80385i 0.348303i
\(503\) −15.8564 27.4641i −0.707002 1.22456i −0.965964 0.258676i \(-0.916714\pi\)
0.258962 0.965888i \(-0.416620\pi\)
\(504\) −0.500000 + 0.866025i −0.0222718 + 0.0385758i
\(505\) −23.6603 13.6603i −1.05287 0.607873i
\(506\) −0.928203 −0.0412637
\(507\) −0.500000 + 12.9904i −0.0222058 + 0.576923i
\(508\) −19.4641 −0.863580
\(509\) −10.4378 6.02628i −0.462648 0.267110i 0.250509 0.968114i \(-0.419402\pi\)
−0.713157 + 0.701004i \(0.752735\pi\)
\(510\) −5.09808 + 8.83013i −0.225747 + 0.391005i
\(511\) 6.73205 + 11.6603i 0.297808 + 0.515819i
\(512\) 1.00000i 0.0441942i
\(513\) −2.13397 + 1.23205i −0.0942173 + 0.0543964i
\(514\) −23.4282 + 13.5263i −1.03337 + 0.596619i
\(515\) 4.92820i 0.217163i
\(516\) −1.36603 2.36603i −0.0601359 0.104158i
\(517\) −0.330127 + 0.571797i −0.0145190 + 0.0251476i
\(518\) 4.09808 + 2.36603i 0.180059 + 0.103957i
\(519\) 17.2679 0.757979
\(520\) −2.36603 9.56218i −0.103757 0.419329i
\(521\) −5.73205 −0.251126 −0.125563 0.992086i \(-0.540074\pi\)
−0.125563 + 0.992086i \(0.540074\pi\)
\(522\) −2.59808 1.50000i −0.113715 0.0656532i
\(523\) 14.5981 25.2846i 0.638329 1.10562i −0.347470 0.937691i \(-0.612959\pi\)
0.985799 0.167928i \(-0.0537075\pi\)
\(524\) 2.53590 + 4.39230i 0.110781 + 0.191879i
\(525\) 2.46410i 0.107542i
\(526\) 13.2224 7.63397i 0.576525 0.332857i
\(527\) 31.2224 18.0263i 1.36007 0.785237i
\(528\) 0.267949i 0.0116610i
\(529\) 5.50000 + 9.52628i 0.239130 + 0.414186i
\(530\) 4.83013 8.36603i 0.209807 0.363397i
\(531\) −11.1962 6.46410i −0.485872 0.280518i
\(532\) −2.46410 −0.106832
\(533\) −7.00000 + 24.2487i −0.303204 + 1.05033i
\(534\) 0.464102 0.0200836
\(535\) 20.0263 + 11.5622i 0.865812 + 0.499877i
\(536\) 0.464102 0.803848i 0.0200461 0.0347209i
\(537\) −0.803848 1.39230i −0.0346886 0.0600824i
\(538\) 31.7128i 1.36724i
\(539\) 0.232051 0.133975i 0.00999514 0.00577069i
\(540\) 2.36603 1.36603i 0.101818 0.0587844i
\(541\) 19.8038i 0.851434i −0.904856 0.425717i \(-0.860022\pi\)
0.904856 0.425717i \(-0.139978\pi\)
\(542\) 11.7583 + 20.3660i 0.505064 + 0.874796i
\(543\) 4.59808 7.96410i 0.197322 0.341772i
\(544\) −3.23205 1.86603i −0.138573 0.0800052i
\(545\) 37.3205 1.59863
\(546\) −3.46410 1.00000i −0.148250 0.0427960i
\(547\) −37.1244 −1.58732 −0.793661 0.608360i \(-0.791828\pi\)
−0.793661 + 0.608360i \(0.791828\pi\)
\(548\) −7.39230 4.26795i −0.315784 0.182318i
\(549\) 4.13397 7.16025i 0.176434 0.305592i
\(550\) −0.330127 0.571797i −0.0140767 0.0243815i
\(551\) 7.39230i 0.314923i
\(552\) −3.00000 + 1.73205i −0.127688 + 0.0737210i
\(553\) 14.5981 8.42820i 0.620773 0.358404i
\(554\) 5.60770i 0.238248i
\(555\) −6.46410 11.1962i −0.274386 0.475250i
\(556\) 3.06218 5.30385i 0.129865 0.224933i
\(557\) −16.7487 9.66987i −0.709666 0.409726i 0.101272 0.994859i \(-0.467709\pi\)
−0.810937 + 0.585133i \(0.801042\pi\)
\(558\) −9.66025 −0.408951
\(559\) 7.09808 6.83013i 0.300217 0.288884i
\(560\) 2.73205 0.115450
\(561\) 0.866025 + 0.500000i 0.0365636 + 0.0211100i
\(562\) 3.90192 6.75833i 0.164593 0.285083i
\(563\) −18.3660 31.8109i −0.774036 1.34067i −0.935335 0.353764i \(-0.884902\pi\)
0.161299 0.986906i \(-0.448432\pi\)
\(564\) 2.46410i 0.103757i
\(565\) 0.464102 0.267949i 0.0195249 0.0112727i
\(566\) −7.85641 + 4.53590i −0.330229 + 0.190658i
\(567\) 1.00000i 0.0419961i
\(568\) 4.09808 + 7.09808i 0.171951 + 0.297829i
\(569\) 9.63397 16.6865i 0.403877 0.699536i −0.590313 0.807175i \(-0.700996\pi\)
0.994190 + 0.107639i \(0.0343290\pi\)
\(570\) 5.83013 + 3.36603i 0.244197 + 0.140987i
\(571\) −30.1962 −1.26367 −0.631835 0.775103i \(-0.717698\pi\)
−0.631835 + 0.775103i \(0.717698\pi\)
\(572\) −0.937822 + 0.232051i −0.0392123 + 0.00970253i
\(573\) −6.19615 −0.258848
\(574\) −6.06218 3.50000i −0.253030 0.146087i
\(575\) 4.26795 7.39230i 0.177986 0.308280i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 16.7321i 0.696564i 0.937390 + 0.348282i \(0.113235\pi\)
−0.937390 + 0.348282i \(0.886765\pi\)
\(578\) 2.66025 1.53590i 0.110652 0.0638850i
\(579\) 5.89230 3.40192i 0.244876 0.141379i
\(580\) 8.19615i 0.340327i
\(581\) 5.83013 + 10.0981i 0.241874 + 0.418939i
\(582\) 1.36603 2.36603i 0.0566236 0.0980749i
\(583\) −0.820508 0.473721i −0.0339820 0.0196195i
\(584\) 13.4641 0.557148
\(585\) 6.83013 + 7.09808i 0.282391 + 0.293469i
\(586\) −28.7846 −1.18908
\(587\) −35.8301 20.6865i −1.47887 0.853825i −0.479153 0.877731i \(-0.659056\pi\)
−0.999714 + 0.0239066i \(0.992390\pi\)
\(588\) 0.500000 0.866025i 0.0206197 0.0357143i
\(589\) −11.9019 20.6147i −0.490410 0.849415i
\(590\) 35.3205i 1.45412i
\(591\) −4.96410 + 2.86603i −0.204196 + 0.117893i
\(592\) 4.09808 2.36603i 0.168430 0.0972430i
\(593\) 48.3205i 1.98429i −0.125111 0.992143i \(-0.539929\pi\)
0.125111 0.992143i \(-0.460071\pi\)
\(594\) −0.133975 0.232051i −0.00549704 0.00952116i
\(595\) 5.09808 8.83013i 0.209001 0.362000i
\(596\) 4.39230 + 2.53590i 0.179916 + 0.103874i
\(597\) 6.19615 0.253592
\(598\) −8.66025 9.00000i −0.354144 0.368037i
\(599\) 33.7128 1.37747 0.688734 0.725014i \(-0.258167\pi\)
0.688734 + 0.725014i \(0.258167\pi\)
\(600\) −2.13397 1.23205i −0.0871191 0.0502983i
\(601\) 18.5622 32.1506i 0.757167 1.31145i −0.187123 0.982337i \(-0.559916\pi\)
0.944290 0.329115i \(-0.106750\pi\)
\(602\) 1.36603 + 2.36603i 0.0556750 + 0.0964320i
\(603\) 0.928203i 0.0377994i
\(604\) 2.42820 1.40192i 0.0988022 0.0570435i
\(605\) 25.8564 14.9282i 1.05121 0.606918i
\(606\) 10.0000i 0.406222i
\(607\) 12.9545 + 22.4378i 0.525806 + 0.910723i 0.999548 + 0.0300594i \(0.00956963\pi\)
−0.473742 + 0.880664i \(0.657097\pi\)
\(608\) −1.23205 + 2.13397i −0.0499663 + 0.0865441i
\(609\) 2.59808 + 1.50000i 0.105279 + 0.0607831i
\(610\) −22.5885 −0.914580
\(611\) −8.62436 + 2.13397i −0.348904 + 0.0863314i
\(612\) 3.73205 0.150859
\(613\) −12.2487 7.07180i −0.494721 0.285627i 0.231810 0.972761i \(-0.425535\pi\)
−0.726531 + 0.687134i \(0.758869\pi\)
\(614\) 3.89230 6.74167i 0.157081 0.272072i
\(615\) 9.56218 + 16.5622i 0.385584 + 0.667851i
\(616\) 0.267949i 0.0107960i
\(617\) 3.04552 1.75833i 0.122608 0.0707877i −0.437442 0.899247i \(-0.644115\pi\)
0.560050 + 0.828459i \(0.310782\pi\)
\(618\) 1.56218 0.901924i 0.0628400 0.0362807i
\(619\) 32.3205i 1.29907i 0.760331 + 0.649535i \(0.225037\pi\)
−0.760331 + 0.649535i \(0.774963\pi\)
\(620\) 13.1962 + 22.8564i 0.529970 + 0.917935i
\(621\) 1.73205 3.00000i 0.0695048 0.120386i
\(622\) 7.62436 + 4.40192i 0.305709 + 0.176501i
\(623\) −0.464102 −0.0185938
\(624\) −2.59808 + 2.50000i −0.104006 + 0.100080i
\(625\) −31.2487 −1.24995
\(626\) 10.5622 + 6.09808i 0.422150 + 0.243728i
\(627\) 0.330127 0.571797i 0.0131840 0.0228354i
\(628\) −4.26795 7.39230i −0.170310 0.294985i
\(629\) 17.6603i 0.704160i
\(630\) −2.36603 + 1.36603i −0.0942647 + 0.0544238i
\(631\) −31.1603 + 17.9904i −1.24047 + 0.716186i −0.969190 0.246315i \(-0.920780\pi\)
−0.271280 + 0.962500i \(0.587447\pi\)
\(632\) 16.8564i 0.670512i
\(633\) 5.92820 + 10.2679i 0.235625 + 0.408114i
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) −46.0526 26.5885i −1.82754 1.05513i
\(636\) −3.53590 −0.140207
\(637\) 3.46410 + 1.00000i 0.137253 + 0.0396214i
\(638\) 0.803848 0.0318246
\(639\) −7.09808 4.09808i −0.280796 0.162117i
\(640\) 1.36603 2.36603i 0.0539969 0.0935254i
\(641\) 16.1244 + 27.9282i 0.636874 + 1.10310i 0.986115 + 0.166065i \(0.0531061\pi\)
−0.349241 + 0.937033i \(0.613561\pi\)
\(642\) 8.46410i 0.334051i
\(643\) −31.4545 + 18.1603i −1.24044 + 0.716171i −0.969185 0.246336i \(-0.920773\pi\)
−0.271259 + 0.962506i \(0.587440\pi\)
\(644\) 3.00000 1.73205i 0.118217 0.0682524i
\(645\) 7.46410i 0.293899i
\(646\) 4.59808 + 7.96410i 0.180909 + 0.313343i
\(647\) −0.866025 + 1.50000i −0.0340470 + 0.0589711i −0.882547 0.470225i \(-0.844173\pi\)
0.848500 + 0.529196i \(0.177506\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) 3.46410 0.135978
\(650\) 2.46410 8.53590i 0.0966500 0.334805i
\(651\) 9.66025 0.378615
\(652\) 15.7583 + 9.09808i 0.617144 + 0.356308i
\(653\) −23.1603 + 40.1147i −0.906331 + 1.56981i −0.0872099 + 0.996190i \(0.527795\pi\)
−0.819121 + 0.573621i \(0.805538\pi\)
\(654\) −6.83013 11.8301i −0.267079 0.462595i
\(655\) 13.8564i 0.541415i
\(656\) −6.06218 + 3.50000i −0.236688 + 0.136652i
\(657\) −11.6603 + 6.73205i −0.454910 + 0.262642i
\(658\) 2.46410i 0.0960607i
\(659\) −10.0359 17.3827i −0.390943 0.677133i 0.601631 0.798774i \(-0.294518\pi\)
−0.992574 + 0.121641i \(0.961184\pi\)
\(660\) −0.366025 + 0.633975i −0.0142475 + 0.0246774i
\(661\) −41.9090 24.1962i −1.63007 0.941121i −0.984070 0.177784i \(-0.943107\pi\)
−0.646000 0.763337i \(-0.723560\pi\)
\(662\) 3.07180 0.119389
\(663\) 3.23205 + 13.0622i 0.125522 + 0.507293i
\(664\) 11.6603 0.452506
\(665\) −5.83013 3.36603i −0.226083 0.130529i
\(666\) −2.36603 + 4.09808i −0.0916816 + 0.158797i
\(667\) 5.19615 + 9.00000i 0.201196 + 0.348481i
\(668\) 21.8564i 0.845650i
\(669\) 10.7321 6.19615i 0.414925 0.239557i
\(670\) 2.19615 1.26795i 0.0848448 0.0489852i
\(671\) 2.21539i 0.0855242i
\(672\) −0.500000 0.866025i −0.0192879 0.0334077i
\(673\) −17.0359 + 29.5070i −0.656686 + 1.13741i 0.324783 + 0.945789i \(0.394709\pi\)
−0.981468 + 0.191624i \(0.938625\pi\)
\(674\) 11.9378 + 6.89230i 0.459828 + 0.265482i
\(675\) 2.46410 0.0948433
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) 45.7654 1.75891 0.879453 0.475986i \(-0.157909\pi\)
0.879453 + 0.475986i \(0.157909\pi\)
\(678\) −0.169873 0.0980762i −0.00652393 0.00376659i
\(679\) −1.36603 + 2.36603i −0.0524232 + 0.0907997i
\(680\) −5.09808 8.83013i −0.195502 0.338620i
\(681\) 15.4641i 0.592586i
\(682\) 2.24167 1.29423i 0.0858380 0.0495586i
\(683\) 4.85641 2.80385i 0.185825 0.107286i −0.404201 0.914670i \(-0.632451\pi\)
0.590027 + 0.807384i \(0.299117\pi\)
\(684\) 2.46410i 0.0942173i
\(685\) −11.6603 20.1962i −0.445515 0.771655i
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) −21.0622 12.1603i −0.803572 0.463943i
\(688\) 2.73205 0.104158
\(689\) −3.06218 12.3756i −0.116660 0.471475i
\(690\) −9.46410 −0.360292
\(691\) 0.679492 + 0.392305i 0.0258491 + 0.0149240i 0.512869 0.858467i \(-0.328583\pi\)
−0.487020 + 0.873391i \(0.661916\pi\)
\(692\) −8.63397 + 14.9545i −0.328214 + 0.568484i
\(693\) 0.133975 + 0.232051i 0.00508927 + 0.00881488i
\(694\) 4.85641i 0.184347i
\(695\) 14.4904 8.36603i 0.549651 0.317341i
\(696\) 2.59808 1.50000i 0.0984798 0.0568574i
\(697\) 26.1244i 0.989531i
\(698\) 15.8564 + 27.4641i 0.600174 + 1.03953i
\(699\) 4.09808 7.09808i 0.155003 0.268474i
\(700\) 2.13397 + 1.23205i 0.0806567 + 0.0465671i
\(701\) 20.3205 0.767495 0.383747 0.923438i \(-0.374633\pi\)
0.383747 + 0.923438i \(0.374633\pi\)
\(702\) 1.00000 3.46410i 0.0377426 0.130744i
\(703\) −11.6603 −0.439775
\(704\) −0.232051 0.133975i −0.00874574 0.00504936i
\(705\) −3.36603 + 5.83013i −0.126772 + 0.219575i
\(706\) −2.73205 4.73205i −0.102822 0.178093i
\(707\) 10.0000i 0.376089i
\(708\) 11.1962 6.46410i 0.420777 0.242936i
\(709\) 12.1699 7.02628i 0.457049 0.263877i −0.253754 0.967269i \(-0.581665\pi\)
0.710803 + 0.703391i \(0.248332\pi\)
\(710\) 22.3923i 0.840368i
\(711\) 8.42820 + 14.5981i 0.316082 + 0.547471i
\(712\) −0.232051 + 0.401924i −0.00869647 + 0.0150627i
\(713\) 28.9808 + 16.7321i 1.08534 + 0.626620i
\(714\) −3.73205 −0.139668
\(715\) −2.53590 0.732051i −0.0948372 0.0273771i
\(716\) 1.60770 0.0600824
\(717\) 20.9545 + 12.0981i 0.782559 + 0.451811i
\(718\) 13.0981 22.6865i 0.488816 0.846654i
\(719\) −17.5263 30.3564i −0.653620 1.13210i −0.982238 0.187640i \(-0.939916\pi\)
0.328618 0.944463i \(-0.393417\pi\)
\(720\) 2.73205i 0.101818i
\(721\) −1.56218 + 0.901924i −0.0581785 + 0.0335894i
\(722\) −11.1962 + 6.46410i −0.416678 + 0.240569i
\(723\) 28.7846i 1.07051i
\(724\) 4.59808 + 7.96410i 0.170886 + 0.295984i
\(725\) −3.69615 + 6.40192i −0.137272 + 0.237761i
\(726\) −9.46410 5.46410i −0.351246 0.202792i
\(727\) 5.46410 0.202652 0.101326 0.994853i \(-0.467691\pi\)
0.101326 + 0.994853i \(0.467691\pi\)
\(728\) 2.59808 2.50000i 0.0962911 0.0926562i
\(729\) 1.00000 0.0370370
\(730\) 31.8564 + 18.3923i 1.17906 + 0.680730i
\(731\) 5.09808 8.83013i 0.188559 0.326594i
\(732\) 4.13397 + 7.16025i 0.152796 + 0.264651i
\(733\) 20.8564i 0.770349i −0.922844 0.385174i \(-0.874141\pi\)
0.922844 0.385174i \(-0.125859\pi\)
\(734\) 27.9282 16.1244i 1.03085 0.595161i
\(735\) 2.36603 1.36603i 0.0872722 0.0503866i
\(736\) 3.46410i 0.127688i
\(737\) −0.124356 0.215390i −0.00458070 0.00793400i
\(738\) 3.50000 6.06218i 0.128837 0.223152i
\(739\) 12.4641 + 7.19615i 0.458499 + 0.264715i 0.711413 0.702774i \(-0.248056\pi\)
−0.252914 + 0.967489i \(0.581389\pi\)
\(740\) 12.9282 0.475250
\(741\) 8.62436 2.13397i 0.316824 0.0783935i
\(742\) 3.53590 0.129807
\(743\) −22.0981 12.7583i −0.810700 0.468058i 0.0364990 0.999334i \(-0.488379\pi\)
−0.847199 + 0.531276i \(0.821713\pi\)
\(744\) 4.83013 8.36603i 0.177081 0.306713i
\(745\) 6.92820 + 12.0000i 0.253830 + 0.439646i
\(746\) 10.5885i 0.387671i
\(747\) −10.0981 + 5.83013i −0.369469 + 0.213313i
\(748\) −0.866025 + 0.500000i −0.0316650 + 0.0182818i
\(749\) 8.46410i 0.309272i
\(750\) 3.46410 + 6.00000i 0.126491 + 0.219089i
\(751\) 10.4282 18.0622i 0.380531 0.659098i −0.610608 0.791933i \(-0.709075\pi\)
0.991138 + 0.132835i \(0.0424081\pi\)
\(752\) −2.13397 1.23205i −0.0778180 0.0449283i
\(753\) 7.80385 0.284388
\(754\) 7.50000 + 7.79423i 0.273134 + 0.283849i
\(755\) 7.66025 0.278785
\(756\) 0.866025 + 0.500000i 0.0314970 + 0.0181848i
\(757\) −0.0262794 + 0.0455173i −0.000955143 + 0.00165436i −0.866503 0.499173i \(-0.833637\pi\)
0.865547 + 0.500827i \(0.166971\pi\)
\(758\) −8.29423 14.3660i −0.301260 0.521798i
\(759\) 0.928203i 0.0336916i
\(760\) −5.83013 + 3.36603i −0.211481 + 0.122099i
\(761\) 30.5885 17.6603i 1.10883 0.640184i 0.170304 0.985391i \(-0.445525\pi\)
0.938526 + 0.345208i \(0.112192\pi\)
\(762\) 19.4641i 0.705110i
\(763\) 6.83013 + 11.8301i 0.247267 + 0.428279i
\(764\) 3.09808 5.36603i 0.112084 0.194136i
\(765\) 8.83013 + 5.09808i 0.319254 + 0.184321i
\(766\) −35.3923 −1.27878
\(767\) 32.3205 + 33.5885i 1.16703 + 1.21281i
\(768\) −1.00000 −0.0360844
\(769\) 29.8301 + 17.2224i 1.07570 + 0.621057i 0.929734 0.368233i \(-0.120037\pi\)
0.145968 + 0.989289i \(0.453370\pi\)