Properties

Label 722.2.c.n.429.1
Level $722$
Weight $2$
Character 722.429
Analytic conductor $5.765$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.76519902594\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.324000000.2
Defining polynomial: \( x^{8} + 5x^{6} + 20x^{4} + 25x^{2} + 25 \) 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 429.1
Root \(-0.587785 + 1.01807i\) of defining polynomial
Character \(\chi\) \(=\) 722.429
Dual form 722.2.c.n.653.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.26007 + 2.18251i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22982 - 2.13012i) q^{5} +(1.26007 + 2.18251i) q^{6} -2.79360 q^{7} -1.00000 q^{8} +(-1.67557 - 2.90217i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.26007 + 2.18251i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22982 - 2.13012i) q^{5} +(1.26007 + 2.18251i) q^{6} -2.79360 q^{7} -1.00000 q^{8} +(-1.67557 - 2.90217i) q^{9} +(-1.22982 - 2.13012i) q^{10} -1.67853 q^{11} +2.52015 q^{12} +(3.17229 + 5.49456i) q^{13} +(-1.39680 + 2.41933i) q^{14} +(3.09934 + 5.36821i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.48459 + 4.30343i) q^{17} -3.35114 q^{18} -2.45965 q^{20} +(3.52015 - 6.09707i) q^{21} +(-0.839266 + 1.45365i) q^{22} +(1.24945 + 2.16411i) q^{23} +(1.26007 - 2.18251i) q^{24} +(-0.524938 - 0.909219i) q^{25} +6.34458 q^{26} +0.884927 q^{27} +(1.39680 + 2.41933i) q^{28} +(2.96589 + 5.13708i) q^{29} +6.19868 q^{30} -7.28408 q^{31} +(0.500000 + 0.866025i) q^{32} +(2.11507 - 3.66341i) q^{33} +(2.48459 + 4.30343i) q^{34} +(-3.43564 + 5.95071i) q^{35} +(-1.67557 + 2.90217i) q^{36} -0.550972 q^{37} -15.9893 q^{39} +(-1.22982 + 2.13012i) q^{40} +(-1.30371 + 2.25809i) q^{41} +(-3.52015 - 6.09707i) q^{42} +(-1.43564 + 2.48661i) q^{43} +(0.839266 + 1.45365i) q^{44} -8.24263 q^{45} +2.49890 q^{46} +(-0.372797 - 0.645703i) q^{47} +(-1.26007 - 2.18251i) q^{48} +0.804226 q^{49} -1.04988 q^{50} +(-6.26153 - 10.8453i) q^{51} +(3.17229 - 5.49456i) q^{52} +(-0.735136 - 1.27329i) q^{53} +(0.442463 - 0.766369i) q^{54} +(-2.06430 + 3.57547i) q^{55} +2.79360 q^{56} +5.93179 q^{58} +(-2.48131 + 4.29775i) q^{59} +(3.09934 - 5.36821i) q^{60} +(-4.66843 - 8.08596i) q^{61} +(-3.64204 + 6.30820i) q^{62} +(4.68088 + 8.10752i) q^{63} +1.00000 q^{64} +15.6054 q^{65} +(-2.11507 - 3.66341i) q^{66} +(5.78022 + 10.0116i) q^{67} +4.96917 q^{68} -6.29761 q^{69} +(3.43564 + 5.95071i) q^{70} +(-3.49849 + 6.05956i) q^{71} +(1.67557 + 2.90217i) q^{72} +(3.09310 - 5.35740i) q^{73} +(-0.275486 + 0.477156i) q^{74} +2.64584 q^{75} +4.68915 q^{77} +(-7.99463 + 13.8471i) q^{78} +(-2.95579 + 5.11958i) q^{79} +(1.22982 + 2.13012i) q^{80} +(3.91164 - 6.77516i) q^{81} +(1.30371 + 2.25809i) q^{82} +15.1773 q^{83} -7.04029 q^{84} +(6.11121 + 10.5849i) q^{85} +(1.43564 + 2.48661i) q^{86} -14.9490 q^{87} +1.67853 q^{88} +(3.45251 + 5.97992i) q^{89} +(-4.12132 + 7.13833i) q^{90} +(-8.86212 - 15.3496i) q^{91} +(1.24945 - 2.16411i) q^{92} +(9.17848 - 15.8976i) q^{93} -0.745593 q^{94} -2.52015 q^{96} +(7.19369 - 12.4598i) q^{97} +(0.402113 - 0.696480i) q^{98} +(2.81250 + 4.87139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{12} + 18 q^{13} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 6 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{21} + 2 q^{22} + 10 q^{23} - 2 q^{24} - 6 q^{25} + 36 q^{26} + 8 q^{27} + 2 q^{28} - 2 q^{29} + 8 q^{30} - 52 q^{31} + 4 q^{32} + 16 q^{33} + 6 q^{34} - 6 q^{35} - 4 q^{36} - 8 q^{37} - 12 q^{39} - 2 q^{40} - 12 q^{41} - 4 q^{42} + 10 q^{43} - 2 q^{44} - 44 q^{45} + 20 q^{46} + 12 q^{47} + 2 q^{48} - 24 q^{49} - 12 q^{50} - 2 q^{51} + 18 q^{52} + 8 q^{53} + 4 q^{54} + 26 q^{55} + 4 q^{56} - 4 q^{58} - 8 q^{59} + 4 q^{60} - 26 q^{62} + 22 q^{63} + 8 q^{64} + 8 q^{65} - 16 q^{66} + 10 q^{67} + 12 q^{68} + 40 q^{69} + 6 q^{70} + 4 q^{72} + 14 q^{73} - 4 q^{74} - 16 q^{75} + 8 q^{77} - 6 q^{78} + 22 q^{79} + 2 q^{80} + 4 q^{81} + 12 q^{82} - 24 q^{83} - 8 q^{84} + 18 q^{85} - 10 q^{86} - 52 q^{87} - 4 q^{88} - 16 q^{89} - 22 q^{90} - 4 q^{91} + 10 q^{92} - 8 q^{93} + 24 q^{94} + 4 q^{96} + 28 q^{97} - 12 q^{98} - 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −1.26007 + 2.18251i −0.727504 + 1.26007i 0.230431 + 0.973089i \(0.425986\pi\)
−0.957935 + 0.286985i \(0.907347\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.22982 2.13012i 0.549994 0.952618i −0.448280 0.893893i \(-0.647963\pi\)
0.998274 0.0587249i \(-0.0187035\pi\)
\(6\) 1.26007 + 2.18251i 0.514423 + 0.891007i
\(7\) −2.79360 −1.05588 −0.527942 0.849281i \(-0.677036\pi\)
−0.527942 + 0.849281i \(0.677036\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.67557 2.90217i −0.558524 0.967391i
\(10\) −1.22982 2.13012i −0.388905 0.673603i
\(11\) −1.67853 −0.506096 −0.253048 0.967454i \(-0.581433\pi\)
−0.253048 + 0.967454i \(0.581433\pi\)
\(12\) 2.52015 0.727504
\(13\) 3.17229 + 5.49456i 0.879834 + 1.52392i 0.851522 + 0.524319i \(0.175680\pi\)
0.0283125 + 0.999599i \(0.490987\pi\)
\(14\) −1.39680 + 2.41933i −0.373311 + 0.646594i
\(15\) 3.09934 + 5.36821i 0.800246 + 1.38607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.48459 + 4.30343i −0.602601 + 1.04374i 0.389825 + 0.920889i \(0.372536\pi\)
−0.992426 + 0.122846i \(0.960798\pi\)
\(18\) −3.35114 −0.789872
\(19\) 0 0
\(20\) −2.45965 −0.549994
\(21\) 3.52015 6.09707i 0.768159 1.33049i
\(22\) −0.839266 + 1.45365i −0.178932 + 0.309919i
\(23\) 1.24945 + 2.16411i 0.260529 + 0.451249i 0.966383 0.257109i \(-0.0827698\pi\)
−0.705854 + 0.708358i \(0.749436\pi\)
\(24\) 1.26007 2.18251i 0.257211 0.445503i
\(25\) −0.524938 0.909219i −0.104988 0.181844i
\(26\) 6.34458 1.24427
\(27\) 0.884927 0.170304
\(28\) 1.39680 + 2.41933i 0.263971 + 0.457211i
\(29\) 2.96589 + 5.13708i 0.550752 + 0.953931i 0.998220 + 0.0596313i \(0.0189925\pi\)
−0.447468 + 0.894300i \(0.647674\pi\)
\(30\) 6.19868 1.13172
\(31\) −7.28408 −1.30826 −0.654130 0.756382i \(-0.726965\pi\)
−0.654130 + 0.756382i \(0.726965\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 2.11507 3.66341i 0.368187 0.637719i
\(34\) 2.48459 + 4.30343i 0.426103 + 0.738032i
\(35\) −3.43564 + 5.95071i −0.580730 + 1.00585i
\(36\) −1.67557 + 2.90217i −0.279262 + 0.483696i
\(37\) −0.550972 −0.0905792 −0.0452896 0.998974i \(-0.514421\pi\)
−0.0452896 + 0.998974i \(0.514421\pi\)
\(38\) 0 0
\(39\) −15.9893 −2.56033
\(40\) −1.22982 + 2.13012i −0.194452 + 0.336801i
\(41\) −1.30371 + 2.25809i −0.203605 + 0.352654i −0.949687 0.313200i \(-0.898599\pi\)
0.746083 + 0.665853i \(0.231932\pi\)
\(42\) −3.52015 6.09707i −0.543170 0.940799i
\(43\) −1.43564 + 2.48661i −0.218934 + 0.379204i −0.954482 0.298268i \(-0.903591\pi\)
0.735549 + 0.677472i \(0.236924\pi\)
\(44\) 0.839266 + 1.45365i 0.126524 + 0.219146i
\(45\) −8.24263 −1.22874
\(46\) 2.49890 0.368443
\(47\) −0.372797 0.645703i −0.0543780 0.0941854i 0.837555 0.546353i \(-0.183984\pi\)
−0.891933 + 0.452167i \(0.850651\pi\)
\(48\) −1.26007 2.18251i −0.181876 0.315018i
\(49\) 0.804226 0.114889
\(50\) −1.04988 −0.148475
\(51\) −6.26153 10.8453i −0.876789 1.51864i
\(52\) 3.17229 5.49456i 0.439917 0.761959i
\(53\) −0.735136 1.27329i −0.100979 0.174900i 0.811109 0.584894i \(-0.198864\pi\)
−0.912088 + 0.409994i \(0.865531\pi\)
\(54\) 0.442463 0.766369i 0.0602117 0.104290i
\(55\) −2.06430 + 3.57547i −0.278350 + 0.482117i
\(56\) 2.79360 0.373311
\(57\) 0 0
\(58\) 5.93179 0.778882
\(59\) −2.48131 + 4.29775i −0.323038 + 0.559519i −0.981113 0.193433i \(-0.938038\pi\)
0.658075 + 0.752952i \(0.271371\pi\)
\(60\) 3.09934 5.36821i 0.400123 0.693033i
\(61\) −4.66843 8.08596i −0.597731 1.03530i −0.993155 0.116802i \(-0.962736\pi\)
0.395424 0.918499i \(-0.370598\pi\)
\(62\) −3.64204 + 6.30820i −0.462539 + 0.801142i
\(63\) 4.68088 + 8.10752i 0.589736 + 1.02145i
\(64\) 1.00000 0.125000
\(65\) 15.6054 1.93562
\(66\) −2.11507 3.66341i −0.260347 0.450935i
\(67\) 5.78022 + 10.0116i 0.706166 + 1.22312i 0.966269 + 0.257535i \(0.0829103\pi\)
−0.260103 + 0.965581i \(0.583756\pi\)
\(68\) 4.96917 0.602601
\(69\) −6.29761 −0.758143
\(70\) 3.43564 + 5.95071i 0.410638 + 0.711246i
\(71\) −3.49849 + 6.05956i −0.415195 + 0.719138i −0.995449 0.0952973i \(-0.969620\pi\)
0.580254 + 0.814435i \(0.302953\pi\)
\(72\) 1.67557 + 2.90217i 0.197468 + 0.342024i
\(73\) 3.09310 5.35740i 0.362020 0.627036i −0.626274 0.779603i \(-0.715421\pi\)
0.988293 + 0.152567i \(0.0487540\pi\)
\(74\) −0.275486 + 0.477156i −0.0320246 + 0.0554682i
\(75\) 2.64584 0.305515
\(76\) 0 0
\(77\) 4.68915 0.534379
\(78\) −7.99463 + 13.8471i −0.905214 + 1.56788i
\(79\) −2.95579 + 5.11958i −0.332552 + 0.575998i −0.983012 0.183543i \(-0.941243\pi\)
0.650459 + 0.759541i \(0.274577\pi\)
\(80\) 1.22982 + 2.13012i 0.137499 + 0.238155i
\(81\) 3.91164 6.77516i 0.434626 0.752795i
\(82\) 1.30371 + 2.25809i 0.143970 + 0.249364i
\(83\) 15.1773 1.66593 0.832964 0.553328i \(-0.186642\pi\)
0.832964 + 0.553328i \(0.186642\pi\)
\(84\) −7.04029 −0.768159
\(85\) 6.11121 + 10.5849i 0.662854 + 1.14810i
\(86\) 1.43564 + 2.48661i 0.154809 + 0.268138i
\(87\) −14.9490 −1.60270
\(88\) 1.67853 0.178932
\(89\) 3.45251 + 5.97992i 0.365965 + 0.633870i 0.988931 0.148379i \(-0.0474056\pi\)
−0.622965 + 0.782249i \(0.714072\pi\)
\(90\) −4.12132 + 7.13833i −0.434425 + 0.752446i
\(91\) −8.86212 15.3496i −0.929002 1.60908i
\(92\) 1.24945 2.16411i 0.130264 0.225625i
\(93\) 9.17848 15.8976i 0.951764 1.64850i
\(94\) −0.745593 −0.0769021
\(95\) 0 0
\(96\) −2.52015 −0.257211
\(97\) 7.19369 12.4598i 0.730408 1.26510i −0.226300 0.974058i \(-0.572663\pi\)
0.956709 0.291047i \(-0.0940036\pi\)
\(98\) 0.402113 0.696480i 0.0406196 0.0703551i
\(99\) 2.81250 + 4.87139i 0.282667 + 0.489593i
\(100\) −0.524938 + 0.909219i −0.0524938 + 0.0909219i
\(101\) −5.64146 9.77130i −0.561347 0.972281i −0.997379 0.0723500i \(-0.976950\pi\)
0.436033 0.899931i \(-0.356383\pi\)
\(102\) −12.5231 −1.23997
\(103\) −14.8280 −1.46104 −0.730522 0.682889i \(-0.760723\pi\)
−0.730522 + 0.682889i \(0.760723\pi\)
\(104\) −3.17229 5.49456i −0.311068 0.538786i
\(105\) −8.65833 14.9967i −0.844966 1.46352i
\(106\) −1.47027 −0.142805
\(107\) 2.82849 0.273440 0.136720 0.990610i \(-0.456344\pi\)
0.136720 + 0.990610i \(0.456344\pi\)
\(108\) −0.442463 0.766369i −0.0425761 0.0737439i
\(109\) 0.862695 1.49423i 0.0826312 0.143121i −0.821748 0.569851i \(-0.807001\pi\)
0.904379 + 0.426729i \(0.140334\pi\)
\(110\) 2.06430 + 3.57547i 0.196823 + 0.340908i
\(111\) 0.694265 1.20250i 0.0658967 0.114137i
\(112\) 1.39680 2.41933i 0.131985 0.228605i
\(113\) 0.427785 0.0402426 0.0201213 0.999798i \(-0.493595\pi\)
0.0201213 + 0.999798i \(0.493595\pi\)
\(114\) 0 0
\(115\) 6.14643 0.573157
\(116\) 2.96589 5.13708i 0.275376 0.476966i
\(117\) 10.6308 18.4131i 0.982816 1.70229i
\(118\) 2.48131 + 4.29775i 0.228423 + 0.395640i
\(119\) 6.94095 12.0221i 0.636276 1.10206i
\(120\) −3.09934 5.36821i −0.282930 0.490049i
\(121\) −8.18253 −0.743867
\(122\) −9.33686 −0.845320
\(123\) −3.28553 5.69071i −0.296246 0.513114i
\(124\) 3.64204 + 6.30820i 0.327065 + 0.566493i
\(125\) 9.71592 0.869018
\(126\) 9.36176 0.834012
\(127\) −0.568158 0.984079i −0.0504159 0.0873229i 0.839716 0.543026i \(-0.182721\pi\)
−0.890132 + 0.455703i \(0.849388\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −3.61803 6.26662i −0.318550 0.551745i
\(130\) 7.80272 13.5147i 0.684344 1.18532i
\(131\) 8.92075 15.4512i 0.779410 1.34998i −0.152873 0.988246i \(-0.548852\pi\)
0.932282 0.361731i \(-0.117814\pi\)
\(132\) −4.23015 −0.368187
\(133\) 0 0
\(134\) 11.5604 0.998670
\(135\) 1.08831 1.88500i 0.0936664 0.162235i
\(136\) 2.48459 4.30343i 0.213052 0.369016i
\(137\) 7.95782 + 13.7833i 0.679882 + 1.17759i 0.975016 + 0.222135i \(0.0713025\pi\)
−0.295134 + 0.955456i \(0.595364\pi\)
\(138\) −3.14880 + 5.45389i −0.268044 + 0.464266i
\(139\) −5.06008 8.76432i −0.429191 0.743380i 0.567611 0.823297i \(-0.307868\pi\)
−0.996802 + 0.0799168i \(0.974535\pi\)
\(140\) 6.87129 0.580730
\(141\) 1.87901 0.158241
\(142\) 3.49849 + 6.05956i 0.293587 + 0.508507i
\(143\) −5.32479 9.22280i −0.445281 0.771249i
\(144\) 3.35114 0.279262
\(145\) 14.5901 1.21164
\(146\) −3.09310 5.35740i −0.255986 0.443382i
\(147\) −1.01338 + 1.75523i −0.0835825 + 0.144769i
\(148\) 0.275486 + 0.477156i 0.0226448 + 0.0392220i
\(149\) −4.69925 + 8.13935i −0.384978 + 0.666801i −0.991766 0.128062i \(-0.959124\pi\)
0.606788 + 0.794864i \(0.292458\pi\)
\(150\) 1.32292 2.29137i 0.108016 0.187089i
\(151\) 10.2632 0.835210 0.417605 0.908629i \(-0.362870\pi\)
0.417605 + 0.908629i \(0.362870\pi\)
\(152\) 0 0
\(153\) 16.6524 1.34627
\(154\) 2.34458 4.06093i 0.188931 0.327239i
\(155\) −8.95814 + 15.5160i −0.719535 + 1.24627i
\(156\) 7.99463 + 13.8471i 0.640083 + 1.10866i
\(157\) −1.48694 + 2.57545i −0.118671 + 0.205543i −0.919241 0.393695i \(-0.871197\pi\)
0.800571 + 0.599239i \(0.204530\pi\)
\(158\) 2.95579 + 5.11958i 0.235150 + 0.407292i
\(159\) 3.70530 0.293849
\(160\) 2.45965 0.194452
\(161\) −3.49047 6.04568i −0.275088 0.476466i
\(162\) −3.91164 6.77516i −0.307327 0.532307i
\(163\) 5.59191 0.437992 0.218996 0.975726i \(-0.429722\pi\)
0.218996 + 0.975726i \(0.429722\pi\)
\(164\) 2.60741 0.203605
\(165\) −5.20234 9.01071i −0.405001 0.701483i
\(166\) 7.58866 13.1439i 0.588994 1.02017i
\(167\) −3.54180 6.13458i −0.274073 0.474708i 0.695828 0.718209i \(-0.255038\pi\)
−0.969901 + 0.243500i \(0.921704\pi\)
\(168\) −3.52015 + 6.09707i −0.271585 + 0.470399i
\(169\) −13.6268 + 23.6024i −1.04822 + 1.81557i
\(170\) 12.2224 0.937418
\(171\) 0 0
\(172\) 2.87129 0.218934
\(173\) −11.5104 + 19.9366i −0.875120 + 1.51575i −0.0184843 + 0.999829i \(0.505884\pi\)
−0.856635 + 0.515922i \(0.827449\pi\)
\(174\) −7.47449 + 12.9462i −0.566639 + 0.981448i
\(175\) 1.46647 + 2.54000i 0.110855 + 0.192006i
\(176\) 0.839266 1.45365i 0.0632620 0.109573i
\(177\) −6.25325 10.8310i −0.470023 0.814104i
\(178\) 6.90502 0.517553
\(179\) −8.21471 −0.613996 −0.306998 0.951710i \(-0.599325\pi\)
−0.306998 + 0.951710i \(0.599325\pi\)
\(180\) 4.12132 + 7.13833i 0.307185 + 0.532060i
\(181\) −6.49994 11.2582i −0.483137 0.836818i 0.516676 0.856181i \(-0.327169\pi\)
−0.999813 + 0.0193635i \(0.993836\pi\)
\(182\) −17.7242 −1.31381
\(183\) 23.5303 1.73941
\(184\) −1.24945 2.16411i −0.0921108 0.159541i
\(185\) −0.677599 + 1.17364i −0.0498181 + 0.0862874i
\(186\) −9.17848 15.8976i −0.672998 1.16567i
\(187\) 4.17046 7.22345i 0.304974 0.528231i
\(188\) −0.372797 + 0.645703i −0.0271890 + 0.0470927i
\(189\) −2.47214 −0.179821
\(190\) 0 0
\(191\) 6.57479 0.475735 0.237868 0.971298i \(-0.423552\pi\)
0.237868 + 0.971298i \(0.423552\pi\)
\(192\) −1.26007 + 2.18251i −0.0909380 + 0.157509i
\(193\) 13.4413 23.2810i 0.967527 1.67581i 0.264859 0.964287i \(-0.414675\pi\)
0.702667 0.711518i \(-0.251992\pi\)
\(194\) −7.19369 12.4598i −0.516477 0.894564i
\(195\) −19.6640 + 34.0590i −1.40817 + 2.43902i
\(196\) −0.402113 0.696480i −0.0287224 0.0497486i
\(197\) −9.84940 −0.701741 −0.350870 0.936424i \(-0.614114\pi\)
−0.350870 + 0.936424i \(0.614114\pi\)
\(198\) 5.62500 0.399751
\(199\) 10.2331 + 17.7242i 0.725402 + 1.25643i 0.958808 + 0.284053i \(0.0916793\pi\)
−0.233407 + 0.972379i \(0.574987\pi\)
\(200\) 0.524938 + 0.909219i 0.0371187 + 0.0642915i
\(201\) −29.1340 −2.05495
\(202\) −11.2829 −0.793864
\(203\) −8.28553 14.3510i −0.581530 1.00724i
\(204\) −6.26153 + 10.8453i −0.438394 + 0.759322i
\(205\) 3.20666 + 5.55410i 0.223963 + 0.387915i
\(206\) −7.41399 + 12.8414i −0.516557 + 0.894703i
\(207\) 4.18709 7.25225i 0.291023 0.504066i
\(208\) −6.34458 −0.439917
\(209\) 0 0
\(210\) −17.3167 −1.19496
\(211\) 4.05815 7.02892i 0.279374 0.483891i −0.691855 0.722036i \(-0.743206\pi\)
0.971229 + 0.238146i \(0.0765396\pi\)
\(212\) −0.735136 + 1.27329i −0.0504893 + 0.0874501i
\(213\) −8.81671 15.2710i −0.604111 1.04635i
\(214\) 1.41424 2.44954i 0.0966757 0.167447i
\(215\) 3.53118 + 6.11619i 0.240825 + 0.417120i
\(216\) −0.884927 −0.0602117
\(217\) 20.3488 1.38137
\(218\) −0.862695 1.49423i −0.0584291 0.101202i
\(219\) 7.79506 + 13.5014i 0.526741 + 0.912342i
\(220\) 4.12860 0.278350
\(221\) −31.5273 −2.12076
\(222\) −0.694265 1.20250i −0.0465960 0.0807067i
\(223\) 5.37701 9.31326i 0.360071 0.623662i −0.627901 0.778293i \(-0.716086\pi\)
0.987972 + 0.154631i \(0.0494190\pi\)
\(224\) −1.39680 2.41933i −0.0933278 0.161648i
\(225\) −1.75914 + 3.04692i −0.117276 + 0.203128i
\(226\) 0.213892 0.370473i 0.0142279 0.0246435i
\(227\) −27.0936 −1.79827 −0.899133 0.437676i \(-0.855802\pi\)
−0.899133 + 0.437676i \(0.855802\pi\)
\(228\) 0 0
\(229\) 9.46557 0.625503 0.312751 0.949835i \(-0.398749\pi\)
0.312751 + 0.949835i \(0.398749\pi\)
\(230\) 3.07321 5.32296i 0.202642 0.350986i
\(231\) −5.90868 + 10.2341i −0.388762 + 0.673356i
\(232\) −2.96589 5.13708i −0.194720 0.337266i
\(233\) −11.4311 + 19.7992i −0.748873 + 1.29709i 0.199490 + 0.979900i \(0.436071\pi\)
−0.948363 + 0.317186i \(0.897262\pi\)
\(234\) −10.6308 18.4131i −0.694956 1.20370i
\(235\) −1.83390 −0.119630
\(236\) 4.96261 0.323038
\(237\) −7.44903 12.9021i −0.483866 0.838081i
\(238\) −6.94095 12.0221i −0.449915 0.779276i
\(239\) 8.66611 0.560564 0.280282 0.959918i \(-0.409572\pi\)
0.280282 + 0.959918i \(0.409572\pi\)
\(240\) −6.19868 −0.400123
\(241\) 2.82913 + 4.90020i 0.182240 + 0.315649i 0.942643 0.333802i \(-0.108332\pi\)
−0.760403 + 0.649452i \(0.774998\pi\)
\(242\) −4.09127 + 7.08628i −0.262997 + 0.455523i
\(243\) 11.1853 + 19.3735i 0.717537 + 1.24281i
\(244\) −4.66843 + 8.08596i −0.298866 + 0.517650i
\(245\) 0.989057 1.71310i 0.0631885 0.109446i
\(246\) −6.57106 −0.418956
\(247\) 0 0
\(248\) 7.28408 0.462539
\(249\) −19.1245 + 33.1247i −1.21197 + 2.09919i
\(250\) 4.85796 8.41423i 0.307244 0.532163i
\(251\) 6.77762 + 11.7392i 0.427799 + 0.740970i 0.996677 0.0814518i \(-0.0259557\pi\)
−0.568878 + 0.822422i \(0.692622\pi\)
\(252\) 4.68088 8.10752i 0.294868 0.510726i
\(253\) −2.09724 3.63253i −0.131853 0.228375i
\(254\) −1.13632 −0.0712988
\(255\) −30.8023 −1.92892
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 5.01963 + 8.69425i 0.313116 + 0.542332i 0.979035 0.203691i \(-0.0652939\pi\)
−0.665919 + 0.746024i \(0.731961\pi\)
\(258\) −7.23607 −0.450498
\(259\) 1.53920 0.0956411
\(260\) −7.80272 13.5147i −0.483904 0.838146i
\(261\) 9.93912 17.2151i 0.615216 1.06559i
\(262\) −8.92075 15.4512i −0.551126 0.954578i
\(263\) 9.41309 16.3040i 0.580436 1.00534i −0.414992 0.909825i \(-0.636215\pi\)
0.995428 0.0955194i \(-0.0304512\pi\)
\(264\) −2.11507 + 3.66341i −0.130174 + 0.225468i
\(265\) −3.61635 −0.222151
\(266\) 0 0
\(267\) −17.4017 −1.06496
\(268\) 5.78022 10.0116i 0.353083 0.611558i
\(269\) −8.19134 + 14.1878i −0.499435 + 0.865046i −1.00000 0.000652557i \(-0.999792\pi\)
0.500565 + 0.865699i \(0.333126\pi\)
\(270\) −1.08831 1.88500i −0.0662321 0.114717i
\(271\) 1.38342 2.39615i 0.0840367 0.145556i −0.820944 0.571009i \(-0.806552\pi\)
0.904980 + 0.425453i \(0.139885\pi\)
\(272\) −2.48459 4.30343i −0.150650 0.260934i
\(273\) 44.6677 2.70341
\(274\) 15.9156 0.961499
\(275\) 0.881125 + 1.52615i 0.0531338 + 0.0920305i
\(276\) 3.14880 + 5.45389i 0.189536 + 0.328285i
\(277\) 24.5321 1.47399 0.736996 0.675897i \(-0.236244\pi\)
0.736996 + 0.675897i \(0.236244\pi\)
\(278\) −10.1202 −0.606967
\(279\) 12.2050 + 21.1397i 0.730694 + 1.26560i
\(280\) 3.43564 5.95071i 0.205319 0.355623i
\(281\) 5.08518 + 8.80779i 0.303356 + 0.525429i 0.976894 0.213724i \(-0.0685594\pi\)
−0.673538 + 0.739153i \(0.735226\pi\)
\(282\) 0.939503 1.62727i 0.0559466 0.0969023i
\(283\) −13.8339 + 23.9610i −0.822340 + 1.42433i 0.0815955 + 0.996666i \(0.473998\pi\)
−0.903935 + 0.427669i \(0.859335\pi\)
\(284\) 6.99698 0.415195
\(285\) 0 0
\(286\) −10.6496 −0.629722
\(287\) 3.64204 6.30820i 0.214983 0.372361i
\(288\) 1.67557 2.90217i 0.0987339 0.171012i
\(289\) −3.84635 6.66207i −0.226256 0.391887i
\(290\) 7.29506 12.6354i 0.428380 0.741977i
\(291\) 18.1292 + 31.4006i 1.06275 + 1.84074i
\(292\) −6.18619 −0.362020
\(293\) −23.8386 −1.39267 −0.696333 0.717719i \(-0.745186\pi\)
−0.696333 + 0.717719i \(0.745186\pi\)
\(294\) 1.01338 + 1.75523i 0.0591018 + 0.102367i
\(295\) 6.10314 + 10.5710i 0.355339 + 0.615465i
\(296\) 0.550972 0.0320246
\(297\) −1.48538 −0.0861904
\(298\) 4.69925 + 8.13935i 0.272221 + 0.471500i
\(299\) −7.92724 + 13.7304i −0.458444 + 0.794049i
\(300\) −1.32292 2.29137i −0.0763789 0.132292i
\(301\) 4.01062 6.94660i 0.231168 0.400395i
\(302\) 5.13162 8.88822i 0.295291 0.511460i
\(303\) 28.4346 1.63353
\(304\) 0 0
\(305\) −22.9654 −1.31500
\(306\) 8.32620 14.4214i 0.475977 0.824417i
\(307\) 12.9942 22.5066i 0.741619 1.28452i −0.210138 0.977672i \(-0.567391\pi\)
0.951758 0.306851i \(-0.0992752\pi\)
\(308\) −2.34458 4.06093i −0.133595 0.231393i
\(309\) 18.6843 32.3622i 1.06291 1.84102i
\(310\) 8.95814 + 15.5160i 0.508788 + 0.881247i
\(311\) −23.1043 −1.31013 −0.655063 0.755574i \(-0.727358\pi\)
−0.655063 + 0.755574i \(0.727358\pi\)
\(312\) 15.9893 0.905214
\(313\) −6.13235 10.6215i −0.346621 0.600365i 0.639026 0.769185i \(-0.279338\pi\)
−0.985647 + 0.168820i \(0.946004\pi\)
\(314\) 1.48694 + 2.57545i 0.0839127 + 0.145341i
\(315\) 23.0267 1.29741
\(316\) 5.91158 0.332552
\(317\) −0.136152 0.235823i −0.00764708 0.0132451i 0.862177 0.506608i \(-0.169101\pi\)
−0.869824 + 0.493363i \(0.835767\pi\)
\(318\) 1.85265 3.20888i 0.103891 0.179945i
\(319\) −4.97834 8.62275i −0.278734 0.482781i
\(320\) 1.22982 2.13012i 0.0687493 0.119077i
\(321\) −3.56410 + 6.17320i −0.198929 + 0.344555i
\(322\) −6.98095 −0.389033
\(323\) 0 0
\(324\) −7.82328 −0.434626
\(325\) 3.33051 5.76861i 0.184743 0.319985i
\(326\) 2.79595 4.84273i 0.154854 0.268214i
\(327\) 2.17412 + 3.76568i 0.120229 + 0.208243i
\(328\) 1.30371 2.25809i 0.0719851 0.124682i
\(329\) 1.04145 + 1.80384i 0.0574168 + 0.0994488i
\(330\) −10.4047 −0.572759
\(331\) 19.9930 1.09891 0.549457 0.835522i \(-0.314835\pi\)
0.549457 + 0.835522i \(0.314835\pi\)
\(332\) −7.58866 13.1439i −0.416482 0.721368i
\(333\) 0.923192 + 1.59902i 0.0505906 + 0.0876256i
\(334\) −7.08361 −0.387598
\(335\) 28.4346 1.55355
\(336\) 3.52015 + 6.09707i 0.192040 + 0.332623i
\(337\) −8.64121 + 14.9670i −0.470717 + 0.815305i −0.999439 0.0334897i \(-0.989338\pi\)
0.528722 + 0.848795i \(0.322671\pi\)
\(338\) 13.6268 + 23.6024i 0.741202 + 1.28380i
\(339\) −0.539040 + 0.933645i −0.0292767 + 0.0507086i
\(340\) 6.11121 10.5849i 0.331427 0.574049i
\(341\) 12.2266 0.662105
\(342\) 0 0
\(343\) 17.3085 0.934573
\(344\) 1.43564 2.48661i 0.0774047 0.134069i
\(345\) −7.74495 + 13.4146i −0.416974 + 0.722220i
\(346\) 11.5104 + 19.9366i 0.618803 + 1.07180i
\(347\) 9.27279 16.0609i 0.497789 0.862197i −0.502207 0.864747i \(-0.667479\pi\)
0.999997 + 0.00255065i \(0.000811898\pi\)
\(348\) 7.47449 + 12.9462i 0.400674 + 0.693989i
\(349\) −20.1210 −1.07705 −0.538527 0.842609i \(-0.681019\pi\)
−0.538527 + 0.842609i \(0.681019\pi\)
\(350\) 2.93294 0.156772
\(351\) 2.80724 + 4.86229i 0.149840 + 0.259530i
\(352\) −0.839266 1.45365i −0.0447330 0.0774799i
\(353\) 24.0557 1.28035 0.640177 0.768227i \(-0.278861\pi\)
0.640177 + 0.768227i \(0.278861\pi\)
\(354\) −12.5065 −0.664713
\(355\) 8.60506 + 14.9044i 0.456709 + 0.791044i
\(356\) 3.45251 5.97992i 0.182983 0.316935i
\(357\) 17.4922 + 30.2974i 0.925787 + 1.60351i
\(358\) −4.10736 + 7.11415i −0.217081 + 0.375994i
\(359\) 5.42673 9.39937i 0.286412 0.496080i −0.686539 0.727093i \(-0.740871\pi\)
0.972951 + 0.231013i \(0.0742041\pi\)
\(360\) 8.24263 0.434425
\(361\) 0 0
\(362\) −12.9999 −0.683259
\(363\) 10.3106 17.8585i 0.541166 0.937327i
\(364\) −8.86212 + 15.3496i −0.464501 + 0.804540i
\(365\) −7.60793 13.1773i −0.398217 0.689733i
\(366\) 11.7651 20.3778i 0.614973 1.06516i
\(367\) 16.3060 + 28.2429i 0.851168 + 1.47427i 0.880155 + 0.474687i \(0.157439\pi\)
−0.0289868 + 0.999580i \(0.509228\pi\)
\(368\) −2.49890 −0.130264
\(369\) 8.73781 0.454872
\(370\) 0.677599 + 1.17364i 0.0352267 + 0.0610144i
\(371\) 2.05368 + 3.55707i 0.106622 + 0.184674i
\(372\) −18.3570 −0.951764
\(373\) 5.30198 0.274526 0.137263 0.990535i \(-0.456169\pi\)
0.137263 + 0.990535i \(0.456169\pi\)
\(374\) −4.17046 7.22345i −0.215649 0.373515i
\(375\) −12.2428 + 21.2051i −0.632214 + 1.09503i
\(376\) 0.372797 + 0.645703i 0.0192255 + 0.0332996i
\(377\) −18.8173 + 32.5926i −0.969142 + 1.67860i
\(378\) −1.23607 + 2.14093i −0.0635765 + 0.110118i
\(379\) −24.6656 −1.26699 −0.633494 0.773748i \(-0.718380\pi\)
−0.633494 + 0.773748i \(0.718380\pi\)
\(380\) 0 0
\(381\) 2.86368 0.146711
\(382\) 3.28740 5.69394i 0.168198 0.291327i
\(383\) 1.82208 3.15593i 0.0931039 0.161261i −0.815712 0.578459i \(-0.803654\pi\)
0.908816 + 0.417198i \(0.136988\pi\)
\(384\) 1.26007 + 2.18251i 0.0643029 + 0.111376i
\(385\) 5.76684 9.98845i 0.293905 0.509059i
\(386\) −13.4413 23.2810i −0.684145 1.18497i
\(387\) 9.62209 0.489118
\(388\) −14.3874 −0.730408
\(389\) −1.39677 2.41927i −0.0708189 0.122662i 0.828442 0.560076i \(-0.189228\pi\)
−0.899260 + 0.437414i \(0.855895\pi\)
\(390\) 19.6640 + 34.0590i 0.995725 + 1.72465i
\(391\) −12.4175 −0.627979
\(392\) −0.804226 −0.0406196
\(393\) 22.4816 + 38.9393i 1.13405 + 1.96423i
\(394\) −4.92470 + 8.52983i −0.248103 + 0.429727i
\(395\) 7.27021 + 12.5924i 0.365804 + 0.633591i
\(396\) 2.81250 4.87139i 0.141333 0.244797i
\(397\) 19.7551 34.2168i 0.991478 1.71729i 0.382919 0.923782i \(-0.374919\pi\)
0.608559 0.793509i \(-0.291748\pi\)
\(398\) 20.4661 1.02587
\(399\) 0 0
\(400\) 1.04988 0.0524938
\(401\) −9.31073 + 16.1267i −0.464956 + 0.805327i −0.999200 0.0400033i \(-0.987263\pi\)
0.534244 + 0.845331i \(0.320596\pi\)
\(402\) −14.5670 + 25.2308i −0.726536 + 1.25840i
\(403\) −23.1072 40.0228i −1.15105 1.99368i
\(404\) −5.64146 + 9.77130i −0.280673 + 0.486140i
\(405\) −9.62126 16.6645i −0.478084 0.828066i
\(406\) −16.5711 −0.822408
\(407\) 0.924824 0.0458418
\(408\) 6.26153 + 10.8453i 0.309992 + 0.536921i
\(409\) −8.57164 14.8465i −0.423840 0.734113i 0.572471 0.819925i \(-0.305985\pi\)
−0.996311 + 0.0858120i \(0.972652\pi\)
\(410\) 6.41332 0.316731
\(411\) −40.1098 −1.97847
\(412\) 7.41399 + 12.8414i 0.365261 + 0.632651i
\(413\) 6.93179 12.0062i 0.341091 0.590787i
\(414\) −4.18709 7.25225i −0.205784 0.356429i
\(415\) 18.6654 32.3295i 0.916251 1.58699i
\(416\) −3.17229 + 5.49456i −0.155534 + 0.269393i
\(417\) 25.5043 1.24895
\(418\) 0 0
\(419\) −18.5042 −0.903989 −0.451995 0.892021i \(-0.649287\pi\)
−0.451995 + 0.892021i \(0.649287\pi\)
\(420\) −8.65833 + 14.9967i −0.422483 + 0.731762i
\(421\) −8.09980 + 14.0293i −0.394760 + 0.683745i −0.993071 0.117520i \(-0.962506\pi\)
0.598310 + 0.801264i \(0.295839\pi\)
\(422\) −4.05815 7.02892i −0.197548 0.342162i
\(423\) −1.24929 + 2.16384i −0.0607428 + 0.105210i
\(424\) 0.735136 + 1.27329i 0.0357013 + 0.0618365i
\(425\) 5.21702 0.253062
\(426\) −17.6334 −0.854342
\(427\) 13.0417 + 22.5890i 0.631134 + 1.09316i
\(428\) −1.41424 2.44954i −0.0683600 0.118403i
\(429\) 26.8385 1.29577
\(430\) 7.06236 0.340577
\(431\) 6.34983 + 10.9982i 0.305861 + 0.529766i 0.977453 0.211155i \(-0.0677225\pi\)
−0.671592 + 0.740921i \(0.734389\pi\)
\(432\) −0.442463 + 0.766369i −0.0212880 + 0.0368720i
\(433\) 7.11751 + 12.3279i 0.342046 + 0.592441i 0.984813 0.173621i \(-0.0555468\pi\)
−0.642767 + 0.766062i \(0.722213\pi\)
\(434\) 10.1744 17.6226i 0.488388 0.845912i
\(435\) −18.3846 + 31.8431i −0.881475 + 1.52676i
\(436\) −1.72539 −0.0826312
\(437\) 0 0
\(438\) 15.5901 0.744924
\(439\) 14.0950 24.4133i 0.672718 1.16518i −0.304412 0.952540i \(-0.598460\pi\)
0.977130 0.212642i \(-0.0682067\pi\)
\(440\) 2.06430 3.57547i 0.0984116 0.170454i
\(441\) −1.34754 2.33400i −0.0641685 0.111143i
\(442\) −15.7637 + 27.3035i −0.749801 + 1.29869i
\(443\) 16.4972 + 28.5740i 0.783805 + 1.35759i 0.929711 + 0.368291i \(0.120057\pi\)
−0.145906 + 0.989298i \(0.546610\pi\)
\(444\) −1.38853 −0.0658967
\(445\) 16.9839 0.805115
\(446\) −5.37701 9.31326i −0.254609 0.440995i
\(447\) −11.8428 20.5124i −0.560146 0.970201i
\(448\) −2.79360 −0.131985
\(449\) 17.1975 0.811601 0.405801 0.913962i \(-0.366993\pi\)
0.405801 + 0.913962i \(0.366993\pi\)
\(450\) 1.75914 + 3.04692i 0.0829267 + 0.143633i
\(451\) 2.18831 3.79027i 0.103044 0.178477i
\(452\) −0.213892 0.370473i −0.0100607 0.0174256i
\(453\) −12.9324 + 22.3996i −0.607618 + 1.05243i
\(454\) −13.5468 + 23.4637i −0.635783 + 1.10121i
\(455\) −43.5954 −2.04378
\(456\) 0 0
\(457\) −31.1517 −1.45722 −0.728608 0.684931i \(-0.759832\pi\)
−0.728608 + 0.684931i \(0.759832\pi\)
\(458\) 4.73279 8.19743i 0.221149 0.383041i
\(459\) −2.19868 + 3.80822i −0.102626 + 0.177753i
\(460\) −3.07321 5.32296i −0.143289 0.248184i
\(461\) −7.77050 + 13.4589i −0.361908 + 0.626843i −0.988275 0.152685i \(-0.951208\pi\)
0.626367 + 0.779528i \(0.284541\pi\)
\(462\) 5.90868 + 10.2341i 0.274897 + 0.476135i
\(463\) 20.6648 0.960374 0.480187 0.877166i \(-0.340569\pi\)
0.480187 + 0.877166i \(0.340569\pi\)
\(464\) −5.93179 −0.275376
\(465\) −22.5758 39.1025i −1.04693 1.81333i
\(466\) 11.4311 + 19.7992i 0.529533 + 0.917178i
\(467\) −28.4830 −1.31803 −0.659017 0.752128i \(-0.729028\pi\)
−0.659017 + 0.752128i \(0.729028\pi\)
\(468\) −21.2616 −0.982816
\(469\) −16.1477 27.9686i −0.745629 1.29147i
\(470\) −0.916949 + 1.58820i −0.0422957 + 0.0732583i
\(471\) −3.74730 6.49052i −0.172667 0.299067i
\(472\) 2.48131 4.29775i 0.114211 0.197820i
\(473\) 2.40977 4.17385i 0.110802 0.191914i
\(474\) −14.8981 −0.684290
\(475\) 0 0
\(476\) −13.8819 −0.636276
\(477\) −2.46354 + 4.26698i −0.112798 + 0.195372i
\(478\) 4.33306 7.50508i 0.198189 0.343274i
\(479\) 5.23632 + 9.06958i 0.239254 + 0.414400i 0.960500 0.278279i \(-0.0897639\pi\)
−0.721247 + 0.692678i \(0.756431\pi\)
\(480\) −3.09934 + 5.36821i −0.141465 + 0.245024i
\(481\) −1.74784 3.02735i −0.0796947 0.138035i
\(482\) 5.65826 0.257727
\(483\) 17.5930 0.800510
\(484\) 4.09127 + 7.08628i 0.185967 + 0.322104i
\(485\) −17.6940 30.6468i −0.803441 1.39160i
\(486\) 22.3706 1.01475
\(487\) −2.29894 −0.104175 −0.0520875 0.998643i \(-0.516587\pi\)
−0.0520875 + 0.998643i \(0.516587\pi\)
\(488\) 4.66843 + 8.08596i 0.211330 + 0.366034i
\(489\) −7.04622 + 12.2044i −0.318641 + 0.551902i
\(490\) −0.989057 1.71310i −0.0446810 0.0773898i
\(491\) −6.08059 + 10.5319i −0.274413 + 0.475297i −0.969987 0.243157i \(-0.921817\pi\)
0.695574 + 0.718455i \(0.255150\pi\)
\(492\) −3.28553 + 5.69071i −0.148123 + 0.256557i
\(493\) −29.4761 −1.32754
\(494\) 0 0
\(495\) 13.8355 0.621860
\(496\) 3.64204 6.30820i 0.163532 0.283246i
\(497\) 9.77340 16.9280i 0.438397 0.759326i
\(498\) 19.1245 + 33.1247i 0.856991 + 1.48435i
\(499\) −7.56742 + 13.1072i −0.338764 + 0.586757i −0.984201 0.177057i \(-0.943342\pi\)
0.645436 + 0.763814i \(0.276676\pi\)
\(500\) −4.85796 8.41423i −0.217255 0.376296i
\(501\) 17.8517 0.797556
\(502\) 13.5552 0.605000
\(503\) 0.286841 + 0.496824i 0.0127896 + 0.0221523i 0.872349 0.488883i \(-0.162595\pi\)
−0.859560 + 0.511035i \(0.829262\pi\)
\(504\) −4.68088 8.10752i −0.208503 0.361138i
\(505\) −27.7520 −1.23495
\(506\) −4.19449 −0.186468
\(507\) −34.3416 59.4814i −1.52516 2.64166i
\(508\) −0.568158 + 0.984079i −0.0252079 + 0.0436614i
\(509\) −13.1081 22.7039i −0.581008 1.00633i −0.995360 0.0962184i \(-0.969325\pi\)
0.414353 0.910116i \(-0.364008\pi\)
\(510\) −15.4012 + 26.6756i −0.681975 + 1.18121i
\(511\) −8.64089 + 14.9665i −0.382250 + 0.662077i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 10.0393 0.442813
\(515\) −18.2358 + 31.5854i −0.803566 + 1.39182i
\(516\) −3.61803 + 6.26662i −0.159275 + 0.275873i
\(517\) 0.625751 + 1.08383i 0.0275205 + 0.0476669i
\(518\) 0.769599 1.33298i 0.0338142 0.0585680i
\(519\) −29.0079 50.2432i −1.27331 2.20543i
\(520\) −15.6054 −0.684344
\(521\) 12.9637 0.567948 0.283974 0.958832i \(-0.408347\pi\)
0.283974 + 0.958832i \(0.408347\pi\)
\(522\) −9.93912 17.2151i −0.435024 0.753483i
\(523\) 8.88963 + 15.3973i 0.388716 + 0.673276i 0.992277 0.124041i \(-0.0395853\pi\)
−0.603561 + 0.797317i \(0.706252\pi\)
\(524\) −17.8415 −0.779410
\(525\) −7.39144 −0.322589
\(526\) −9.41309 16.3040i −0.410430 0.710886i
\(527\) 18.0979 31.3465i 0.788358 1.36548i
\(528\) 2.11507 + 3.66341i 0.0920467 + 0.159430i
\(529\) 8.37774 14.5107i 0.364250 0.630899i
\(530\) −1.80818 + 3.13185i −0.0785421 + 0.136039i
\(531\) 16.6304 0.721698
\(532\) 0 0
\(533\) −16.5429 −0.716554
\(534\) −8.70083 + 15.0703i −0.376522 + 0.652155i
\(535\) 3.47854 6.02501i 0.150391 0.260484i
\(536\) −5.78022 10.0116i −0.249668 0.432437i
\(537\) 10.3511 17.9287i 0.446685 0.773681i
\(538\) 8.19134 + 14.1878i 0.353154 + 0.611680i
\(539\) −1.34992 −0.0581451
\(540\) −2.17661 −0.0936664
\(541\) 2.67209 + 4.62820i 0.114882 + 0.198982i 0.917733 0.397199i \(-0.130018\pi\)
−0.802851 + 0.596180i \(0.796684\pi\)
\(542\) −1.38342 2.39615i −0.0594229 0.102923i
\(543\) 32.7616 1.40594
\(544\) −4.96917 −0.213052
\(545\) −2.12193 3.67529i −0.0908934 0.157432i
\(546\) 22.3338 38.6833i 0.955800 1.65549i
\(547\) 2.55056 + 4.41770i 0.109054 + 0.188887i 0.915387 0.402574i \(-0.131885\pi\)
−0.806333 + 0.591461i \(0.798551\pi\)
\(548\) 7.95782 13.7833i 0.339941 0.588795i
\(549\) −15.6446 + 27.0972i −0.667694 + 1.15648i
\(550\) 1.76225 0.0751426
\(551\) 0 0
\(552\) 6.29761 0.268044
\(553\) 8.25731 14.3021i 0.351137 0.608186i
\(554\) 12.2661 21.2454i 0.521135 0.902632i
\(555\) −1.70765 2.95774i −0.0724857 0.125549i
\(556\) −5.06008 + 8.76432i −0.214595 + 0.371690i
\(557\) 5.36176 + 9.28685i 0.227185 + 0.393496i 0.956973 0.290178i \(-0.0937144\pi\)
−0.729788 + 0.683674i \(0.760381\pi\)
\(558\) 24.4100 1.03336
\(559\) −18.2171 −0.770502
\(560\) −3.43564 5.95071i −0.145182 0.251463i
\(561\) 10.5102 + 18.2041i 0.443740 + 0.768580i
\(562\) 10.1704 0.429011
\(563\) −9.76285 −0.411455 −0.205728 0.978609i \(-0.565956\pi\)
−0.205728 + 0.978609i \(0.565956\pi\)
\(564\) −0.939503 1.62727i −0.0395602 0.0685203i
\(565\) 0.526100 0.911233i 0.0221332 0.0383358i
\(566\) 13.8339 + 23.9610i 0.581482 + 1.00716i
\(567\) −10.9276 + 18.9271i −0.458915 + 0.794864i
\(568\) 3.49849 6.05956i 0.146793 0.254254i
\(569\) 8.84194 0.370674 0.185337 0.982675i \(-0.440662\pi\)
0.185337 + 0.982675i \(0.440662\pi\)
\(570\) 0 0
\(571\) 22.8411 0.955871 0.477935 0.878395i \(-0.341385\pi\)
0.477935 + 0.878395i \(0.341385\pi\)
\(572\) −5.32479 + 9.22280i −0.222640 + 0.385625i
\(573\) −8.28472 + 14.3496i −0.346099 + 0.599461i
\(574\) −3.64204 6.30820i −0.152016 0.263299i
\(575\) 1.31177 2.27205i 0.0547046 0.0947511i
\(576\) −1.67557 2.90217i −0.0698154 0.120924i
\(577\) −14.0176 −0.583560 −0.291780 0.956486i \(-0.594247\pi\)
−0.291780 + 0.956486i \(0.594247\pi\)
\(578\) −7.69270 −0.319974
\(579\) 33.8741 + 58.6716i 1.40776 + 2.43831i
\(580\) −7.29506 12.6354i −0.302911 0.524657i
\(581\) −42.3994 −1.75903
\(582\) 36.2583 1.50296
\(583\) 1.23395 + 2.13726i 0.0511049 + 0.0885163i
\(584\) −3.09310 + 5.35740i −0.127993 + 0.221691i
\(585\) −26.1480 45.2897i −1.08109 1.87250i
\(586\) −11.9193 + 20.6448i −0.492382 + 0.852830i
\(587\) −10.5178 + 18.2174i −0.434116 + 0.751911i −0.997223 0.0744731i \(-0.976273\pi\)
0.563107 + 0.826384i \(0.309606\pi\)
\(588\) 2.02677 0.0835825
\(589\) 0 0
\(590\) 12.2063 0.502525
\(591\) 12.4110 21.4964i 0.510519 0.884245i
\(592\) 0.275486 0.477156i 0.0113224 0.0196110i
\(593\) 17.4596 + 30.2410i 0.716981 + 1.24185i 0.962190 + 0.272377i \(0.0878099\pi\)
−0.245210 + 0.969470i \(0.578857\pi\)
\(594\) −0.742689 + 1.28637i −0.0304729 + 0.0527806i
\(595\) −17.0723 29.5701i −0.699897 1.21226i
\(596\) 9.39851 0.384978
\(597\) −51.5776 −2.11093
\(598\) 7.92724 + 13.7304i 0.324169 + 0.561477i
\(599\) 10.7553 + 18.6288i 0.439450 + 0.761150i 0.997647 0.0685583i \(-0.0218399\pi\)
−0.558197 + 0.829709i \(0.688507\pi\)
\(600\) −2.64584 −0.108016
\(601\) 14.3417 0.585012 0.292506 0.956264i \(-0.405511\pi\)
0.292506 + 0.956264i \(0.405511\pi\)
\(602\) −4.01062 6.94660i −0.163461 0.283122i
\(603\) 19.3703 33.5504i 0.788821 1.36628i
\(604\) −5.13162 8.88822i −0.208803 0.361657i
\(605\) −10.0631 + 17.4298i −0.409122 + 0.708621i
\(606\) 14.2173 24.6251i 0.577539 1.00033i
\(607\) 10.3488 0.420046 0.210023 0.977696i \(-0.432646\pi\)
0.210023 + 0.977696i \(0.432646\pi\)
\(608\) 0 0
\(609\) 41.7615 1.69226
\(610\) −11.4827 + 19.8886i −0.464921 + 0.805267i
\(611\) 2.36524 4.09671i 0.0956873 0.165735i
\(612\) −8.32620 14.4214i −0.336567 0.582951i
\(613\) −9.78370 + 16.9459i −0.395160 + 0.684437i −0.993122 0.117088i \(-0.962644\pi\)
0.597962 + 0.801525i \(0.295978\pi\)
\(614\) −12.9942 22.5066i −0.524404 0.908294i
\(615\) −16.1625 −0.651735
\(616\) −4.68915 −0.188931
\(617\) 2.96261 + 5.13139i 0.119270 + 0.206582i 0.919479 0.393140i \(-0.128611\pi\)
−0.800208 + 0.599722i \(0.795278\pi\)
\(618\) −18.6843 32.3622i −0.751594 1.30180i
\(619\) 8.03958 0.323138 0.161569 0.986861i \(-0.448345\pi\)
0.161569 + 0.986861i \(0.448345\pi\)
\(620\) 17.9163 0.719535
\(621\) 1.10567 + 1.91508i 0.0443692 + 0.0768496i
\(622\) −11.5522 + 20.0089i −0.463200 + 0.802286i
\(623\) −9.64494 16.7055i −0.386417 0.669293i
\(624\) 7.99463 13.8471i 0.320041 0.554328i
\(625\) 14.5736 25.2422i 0.582943 1.00969i
\(626\) −12.2647 −0.490196
\(627\) 0 0
\(628\) 2.97387 0.118671
\(629\) 1.36894 2.37107i 0.0545831 0.0945408i
\(630\) 11.5133 19.9417i 0.458702 0.794495i
\(631\) 6.45032 + 11.1723i 0.256783 + 0.444762i 0.965378 0.260854i \(-0.0840040\pi\)
−0.708595 + 0.705615i \(0.750671\pi\)
\(632\) 2.95579 5.11958i 0.117575 0.203646i
\(633\) 10.2271 + 17.7139i 0.406492 + 0.704065i
\(634\) −0.272305 −0.0108146
\(635\) −2.79494 −0.110914
\(636\) −1.85265 3.20888i −0.0734623 0.127241i
\(637\) 2.55124 + 4.41887i 0.101084 + 0.175082i
\(638\) −9.95669 −0.394189
\(639\) 23.4479 0.927584
\(640\) −1.22982 2.13012i −0.0486131 0.0842003i
\(641\) −14.4319 + 24.9969i −0.570028 + 0.987317i 0.426535 + 0.904471i \(0.359734\pi\)
−0.996562 + 0.0828458i \(0.973599\pi\)
\(642\) 3.56410 + 6.17320i 0.140664 + 0.243637i
\(643\) −13.1697 + 22.8106i −0.519363 + 0.899563i 0.480384 + 0.877058i \(0.340497\pi\)
−0.999747 + 0.0225047i \(0.992836\pi\)
\(644\) −3.49047 + 6.04568i −0.137544 + 0.238233i
\(645\) −17.7982 −0.700803
\(646\) 0 0
\(647\) −3.04601 −0.119751 −0.0598756 0.998206i \(-0.519070\pi\)
−0.0598756 + 0.998206i \(0.519070\pi\)
\(648\) −3.91164 + 6.77516i −0.153664 + 0.266153i
\(649\) 4.16495 7.21390i 0.163489 0.283170i
\(650\) −3.33051 5.76861i −0.130633 0.226264i
\(651\) −25.6410 + 44.4116i −1.00495 + 1.74063i
\(652\) −2.79595 4.84273i −0.109498 0.189656i
\(653\) −15.1973 −0.594717 −0.297359 0.954766i \(-0.596106\pi\)
−0.297359 + 0.954766i \(0.596106\pi\)
\(654\) 4.34824 0.170030
\(655\) −21.9419 38.0045i −0.857342 1.48496i
\(656\) −1.30371 2.25809i −0.0509012 0.0881634i
\(657\) −20.7308 −0.808786
\(658\) 2.08289 0.0811996
\(659\) 8.93704 + 15.4794i 0.348138 + 0.602992i 0.985919 0.167226i \(-0.0534808\pi\)
−0.637781 + 0.770218i \(0.720148\pi\)
\(660\) −5.20234 + 9.01071i −0.202501 + 0.350742i
\(661\) 18.9263 + 32.7812i 0.736146 + 1.27504i 0.954219 + 0.299110i \(0.0966898\pi\)
−0.218072 + 0.975933i \(0.569977\pi\)
\(662\) 9.99650 17.3144i 0.388525 0.672945i
\(663\) 39.7267 68.8087i 1.54286 2.67231i
\(664\) −15.1773 −0.588994
\(665\) 0 0
\(666\) 1.84638 0.0715460
\(667\) −7.41148 + 12.8371i −0.286974 + 0.497053i
\(668\) −3.54180 + 6.13458i −0.137036 + 0.237354i
\(669\) 13.5509 + 23.4708i 0.523906 + 0.907433i
\(670\) 14.2173 24.6251i 0.549263 0.951351i
\(671\) 7.83611 + 13.5725i 0.302510 + 0.523962i
\(672\) 7.04029 0.271585
\(673\) 8.28461 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(674\) 8.64121 + 14.9670i 0.332847 + 0.576508i
\(675\) −0.464532 0.804593i −0.0178798 0.0309688i
\(676\) 27.2537 1.04822
\(677\) 18.3233 0.704223 0.352111 0.935958i \(-0.385464\pi\)
0.352111 + 0.935958i \(0.385464\pi\)
\(678\) 0.539040 + 0.933645i 0.0207017 + 0.0358564i
\(679\) −20.0963 + 34.8079i −0.771226 + 1.33580i
\(680\) −6.11121 10.5849i −0.234354 0.405914i
\(681\) 34.1399 59.1321i 1.30825 2.26595i
\(682\) 6.11328 10.5885i 0.234090 0.405455i
\(683\) 49.2217 1.88342 0.941709 0.336429i \(-0.109219\pi\)
0.941709 + 0.336429i \(0.109219\pi\)
\(684\) 0 0
\(685\) 39.1469 1.49573
\(686\) 8.65427 14.9896i 0.330422 0.572307i
\(687\) −11.9273 + 20.6587i −0.455055 + 0.788179i
\(688\) −1.43564 2.48661i −0.0547334 0.0948011i
\(689\) 4.66412 8.07850i 0.177689 0.307766i
\(690\) 7.74495 + 13.4146i 0.294845 + 0.510687i
\(691\) 16.6779 0.634458 0.317229 0.948349i \(-0.397248\pi\)
0.317229 + 0.948349i \(0.397248\pi\)
\(692\) 23.0208 0.875120
\(693\) −7.85701 13.6087i −0.298463 0.516953i
\(694\) −9.27279 16.0609i −0.351990 0.609665i
\(695\) −24.8921 −0.944210
\(696\) 14.9490 0.566639
\(697\) −6.47834 11.2208i −0.245385 0.425019i
\(698\) −10.0605 + 17.4253i −0.380796 + 0.659558i
\(699\) −28.8079 49.8968i −1.08962 1.88727i
\(700\) 1.46647 2.54000i 0.0554273 0.0960029i
\(701\) 15.4533 26.7659i 0.583663 1.01093i −0.411378 0.911465i \(-0.634952\pi\)
0.995041 0.0994688i \(-0.0317143\pi\)
\(702\) 5.61449 0.211905
\(703\) 0 0
\(704\) −1.67853 −0.0632620
\(705\) 2.31085 4.00250i 0.0870315 0.150743i
\(706\) 12.0278 20.8328i 0.452674 0.784054i
\(707\) 15.7600 + 27.2972i 0.592716 + 1.02661i
\(708\) −6.25325 + 10.8310i −0.235012 + 0.407052i
\(709\) −20.0528 34.7325i −0.753098 1.30440i −0.946314 0.323248i \(-0.895225\pi\)
0.193216 0.981156i \(-0.438108\pi\)
\(710\) 17.2101 0.645884
\(711\) 19.8105 0.742953
\(712\) −3.45251 5.97992i −0.129388 0.224107i
\(713\) −9.10111 15.7636i −0.340839 0.590351i
\(714\) 34.9845 1.30926
\(715\) −26.1942 −0.979608
\(716\) 4.10736 + 7.11415i 0.153499 + 0.265868i
\(717\) −10.9199 + 18.9139i −0.407813 + 0.706352i
\(718\) −5.42673 9.39937i −0.202524 0.350781i
\(719\) 22.8264 39.5365i 0.851282 1.47446i −0.0287690 0.999586i \(-0.509159\pi\)
0.880051 0.474878i \(-0.157508\pi\)
\(720\) 4.12132 7.13833i 0.153592 0.266030i
\(721\) 41.4235 1.54269
\(722\) 0 0
\(723\) −14.2596 −0.530322
\(724\) −6.49994 + 11.2582i −0.241569 + 0.418409i
\(725\) 3.11382 5.39329i 0.115644 0.200302i
\(726\) −10.3106 17.8585i −0.382662 0.662790i
\(727\) 7.59053 13.1472i 0.281517 0.487602i −0.690242 0.723579i \(-0.742496\pi\)
0.971759 + 0.235977i \(0.0758291\pi\)
\(728\) 8.86212 + 15.3496i 0.328452 + 0.568896i
\(729\) −32.9073 −1.21879
\(730\) −15.2159 −0.563164
\(731\) −7.13397 12.3564i −0.263859 0.457018i
\(732\) −11.7651 20.3778i −0.434852 0.753185i
\(733\) −26.9986 −0.997217 −0.498608 0.866827i \(-0.666155\pi\)
−0.498608 + 0.866827i \(0.666155\pi\)
\(734\) 32.6121 1.20373
\(735\) 2.49257 + 4.31726i 0.0919398 + 0.159244i
\(736\) −1.24945 + 2.16411i −0.0460554 + 0.0797703i
\(737\) −9.70228 16.8048i −0.357388 0.619014i
\(738\) 4.36890 7.56716i 0.160822 0.278551i
\(739\) 2.60391 4.51010i 0.0957864 0.165907i −0.814150 0.580654i \(-0.802797\pi\)
0.909937 + 0.414748i \(0.136130\pi\)
\(740\) 1.35520 0.0498181
\(741\) 0 0
\(742\) 4.10736 0.150786
\(743\) 11.0539 19.1460i 0.405529 0.702398i −0.588853 0.808240i \(-0.700420\pi\)
0.994383 + 0.105842i \(0.0337538\pi\)
\(744\) −9.17848 + 15.8976i −0.336499 + 0.582834i
\(745\) 11.5585 + 20.0199i 0.423471 + 0.733474i
\(746\) 2.65099 4.59165i 0.0970596 0.168112i
\(747\) −25.4307 44.0472i −0.930460 1.61160i
\(748\) −8.34092 −0.304974
\(749\) −7.90167 −0.288721
\(750\) 12.2428 + 21.2051i 0.447043 + 0.774301i
\(751\) −6.24798 10.8218i −0.227992 0.394894i 0.729221 0.684279i \(-0.239883\pi\)
−0.957213 + 0.289384i \(0.906549\pi\)
\(752\) 0.745593 0.0271890
\(753\) −34.1612 −1.24490
\(754\) 18.8173 + 32.5926i 0.685287 + 1.18695i
\(755\) 12.6220 21.8619i 0.459361 0.795636i
\(756\) 1.23607 + 2.14093i 0.0449554 + 0.0778650i
\(757\) 15.4994 26.8458i 0.563336 0.975727i −0.433866 0.900977i \(-0.642851\pi\)
0.997202 0.0747495i \(-0.0238157\pi\)
\(758\) −12.3328 + 21.3610i −0.447948 + 0.775868i
\(759\) 10.5707 0.383693
\(760\) 0 0
\(761\) 1.96398 0.0711941 0.0355971 0.999366i \(-0.488667\pi\)
0.0355971 + 0.999366i \(0.488667\pi\)
\(762\) 1.43184 2.48002i 0.0518702 0.0898418i
\(763\) −2.41003 + 4.17429i −0.0872489 + 0.151120i
\(764\) −3.28740 5.69394i −0.118934 0.205999i
\(765\) 20.4795 35.4716i 0.740439 1.28248i
\(766\) −1.82208 3.15593i −0.0658344 0.114029i
\(767\) −31.4857 −1.13688
\(768\) 2.52015 0.0909380
\(769\) 11.1661 + 19.3402i 0.402659 + 0.697426i 0.994046 0.108962i \(-0.0347527\pi\)
−0.591387 + 0.806388i \(0.701419\pi\)
\(770\) −5.76684 9.98845i −0.207822 0.359959i
\(771\) −25.3004 −0.911172
\(772\) −26.8826 −0.967527
\(773\) 13.6776 + 23.6904i 0.491951 + 0.852084i 0.999957 0.00926978i \(-0.00295070\pi\)
−0.508006 + 0.861353i \(0.669617\pi\)
\(774\) 4.81105 8.33298i 0.172929 0.299523i
\(775\) 3.82369 + 6.62282i 0.137351 + 0.237899i
\(776\) −7.19369 + 12.4598i −0.258238 + 0.447282i
\(777\) −1.93950 + 3.35932i −0.0695793 + 0.120515i
\(778\) −2.79353 −0.100153