Properties

Label 1014.2.e.n.529.1
Level $1014$
Weight $2$
Character 1014.529
Analytic conductor $8.097$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.09683076496\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
Defining polynomial: \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 529.1
Root \(0.900969 + 1.56052i\) of defining polynomial
Character \(\chi\) \(=\) 1014.529
Dual form 1014.2.e.n.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.15883 q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.34601 + 4.06341i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.15883 q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.34601 + 4.06341i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.57942 + 2.73563i) q^{10} +(-0.0685317 + 0.118700i) q^{11} -1.00000 q^{12} +4.69202 q^{14} +(-1.57942 + 2.73563i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.80194 + 4.85310i) q^{17} -1.00000 q^{18} +(2.49396 + 4.31966i) q^{19} +(1.57942 + 2.73563i) q^{20} +4.69202 q^{21} +(0.0685317 + 0.118700i) q^{22} +(3.04892 - 5.28088i) q^{23} +(-0.500000 + 0.866025i) q^{24} +4.97823 q^{25} -1.00000 q^{27} +(2.34601 - 4.06341i) q^{28} +(0.425428 - 0.736862i) q^{29} +(1.57942 + 2.73563i) q^{30} +6.23490 q^{31} +(0.500000 + 0.866025i) q^{32} +(0.0685317 + 0.118700i) q^{33} +5.60388 q^{34} +(-7.41066 - 12.8356i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-5.85086 + 10.1340i) q^{37} +4.98792 q^{38} +3.15883 q^{40} +(2.13706 - 3.70150i) q^{41} +(2.34601 - 4.06341i) q^{42} +(1.04892 + 1.81678i) q^{43} +0.137063 q^{44} +(1.57942 + 2.73563i) q^{45} +(-3.04892 - 5.28088i) q^{46} +4.98792 q^{47} +(0.500000 + 0.866025i) q^{48} +(-7.50753 + 13.0034i) q^{49} +(2.48911 - 4.31127i) q^{50} +5.60388 q^{51} -1.82908 q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.216480 - 0.374955i) q^{55} +(-2.34601 - 4.06341i) q^{56} +4.98792 q^{57} +(-0.425428 - 0.736862i) q^{58} +(2.94989 + 5.10935i) q^{59} +3.15883 q^{60} +(-2.19806 - 3.80716i) q^{61} +(3.11745 - 5.39958i) q^{62} +(2.34601 - 4.06341i) q^{63} +1.00000 q^{64} +0.137063 q^{66} +(2.35690 - 4.08226i) q^{67} +(2.80194 - 4.85310i) q^{68} +(-3.04892 - 5.28088i) q^{69} -14.8213 q^{70} +(0.0489173 + 0.0847273i) q^{71} +(0.500000 + 0.866025i) q^{72} -2.32304 q^{73} +(5.85086 + 10.1340i) q^{74} +(2.48911 - 4.31127i) q^{75} +(2.49396 - 4.31966i) q^{76} -0.643104 q^{77} +14.5157 q^{79} +(1.57942 - 2.73563i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.13706 - 3.70150i) q^{82} -9.85623 q^{83} +(-2.34601 - 4.06341i) q^{84} +(-8.85086 - 15.3301i) q^{85} +2.09783 q^{86} +(-0.425428 - 0.736862i) q^{87} +(0.0685317 - 0.118700i) q^{88} +(-8.54288 + 14.7967i) q^{89} +3.15883 q^{90} -6.09783 q^{92} +(3.11745 - 5.39958i) q^{93} +(2.49396 - 4.31966i) q^{94} +(-7.87800 - 13.6451i) q^{95} +1.00000 q^{96} +(-1.06369 - 1.84236i) q^{97} +(7.50753 + 13.0034i) q^{98} +0.137063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9} - q^{10} + 5 q^{11} - 6 q^{12} + 18 q^{14} - q^{15} - 3 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + q^{20} + 18 q^{21} - 5 q^{22} - 3 q^{24} + 36 q^{25} - 6 q^{27} + 9 q^{28} - 11 q^{29} + q^{30} - 10 q^{31} + 3 q^{32} - 5 q^{33} + 16 q^{34} + 4 q^{35} - 3 q^{36} - 8 q^{37} - 8 q^{38} + 2 q^{40} + 2 q^{41} + 9 q^{42} - 12 q^{43} - 10 q^{44} + q^{45} - 8 q^{47} + 3 q^{48} - 20 q^{49} + 18 q^{50} + 16 q^{51} + 10 q^{53} - 3 q^{54} - 18 q^{55} - 9 q^{56} - 8 q^{57} + 11 q^{58} - 5 q^{59} + 2 q^{60} - 22 q^{61} - 5 q^{62} + 9 q^{63} + 6 q^{64} - 10 q^{66} + 6 q^{67} + 8 q^{68} + 8 q^{70} - 18 q^{71} + 3 q^{72} + 26 q^{73} + 8 q^{74} + 18 q^{75} - 4 q^{76} - 12 q^{77} + 62 q^{79} + q^{80} - 3 q^{81} - 2 q^{82} - 26 q^{83} - 9 q^{84} - 26 q^{85} - 24 q^{86} + 11 q^{87} - 5 q^{88} - 14 q^{89} + 2 q^{90} - 5 q^{93} - 4 q^{94} - 8 q^{95} + 6 q^{96} - 23 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −3.15883 −1.41267 −0.706337 0.707876i \(-0.749654\pi\)
−0.706337 + 0.707876i \(0.749654\pi\)
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 2.34601 + 4.06341i 0.886709 + 1.53582i 0.843743 + 0.536748i \(0.180347\pi\)
0.0429661 + 0.999077i \(0.486319\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.57942 + 2.73563i −0.499455 + 0.865082i
\(11\) −0.0685317 + 0.118700i −0.0206631 + 0.0357895i −0.876172 0.481998i \(-0.839911\pi\)
0.855509 + 0.517788i \(0.173244\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) 4.69202 1.25400
\(15\) −1.57942 + 2.73563i −0.407804 + 0.706337i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.80194 + 4.85310i 0.679570 + 1.17705i 0.975111 + 0.221719i \(0.0711668\pi\)
−0.295541 + 0.955330i \(0.595500\pi\)
\(18\) −1.00000 −0.235702
\(19\) 2.49396 + 4.31966i 0.572153 + 0.990999i 0.996345 + 0.0854262i \(0.0272252\pi\)
−0.424191 + 0.905573i \(0.639441\pi\)
\(20\) 1.57942 + 2.73563i 0.353168 + 0.611705i
\(21\) 4.69202 1.02388
\(22\) 0.0685317 + 0.118700i 0.0146110 + 0.0253070i
\(23\) 3.04892 5.28088i 0.635743 1.10114i −0.350614 0.936520i \(-0.614027\pi\)
0.986357 0.164619i \(-0.0526396\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 4.97823 0.995646
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 2.34601 4.06341i 0.443354 0.767912i
\(29\) 0.425428 0.736862i 0.0789999 0.136832i −0.823819 0.566853i \(-0.808161\pi\)
0.902819 + 0.430021i \(0.141494\pi\)
\(30\) 1.57942 + 2.73563i 0.288361 + 0.499455i
\(31\) 6.23490 1.11982 0.559910 0.828553i \(-0.310836\pi\)
0.559910 + 0.828553i \(0.310836\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0.0685317 + 0.118700i 0.0119298 + 0.0206631i
\(34\) 5.60388 0.961057
\(35\) −7.41066 12.8356i −1.25263 2.16962i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −5.85086 + 10.1340i −0.961875 + 1.66602i −0.244087 + 0.969753i \(0.578488\pi\)
−0.717787 + 0.696263i \(0.754845\pi\)
\(38\) 4.98792 0.809147
\(39\) 0 0
\(40\) 3.15883 0.499455
\(41\) 2.13706 3.70150i 0.333753 0.578078i −0.649491 0.760369i \(-0.725018\pi\)
0.983245 + 0.182291i \(0.0583514\pi\)
\(42\) 2.34601 4.06341i 0.361997 0.626998i
\(43\) 1.04892 + 1.81678i 0.159958 + 0.277056i 0.934853 0.355034i \(-0.115531\pi\)
−0.774895 + 0.632090i \(0.782197\pi\)
\(44\) 0.137063 0.0206631
\(45\) 1.57942 + 2.73563i 0.235446 + 0.407804i
\(46\) −3.04892 5.28088i −0.449538 0.778623i
\(47\) 4.98792 0.727563 0.363781 0.931484i \(-0.381486\pi\)
0.363781 + 0.931484i \(0.381486\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −7.50753 + 13.0034i −1.07250 + 1.85763i
\(50\) 2.48911 4.31127i 0.352014 0.609706i
\(51\) 5.60388 0.784700
\(52\) 0 0
\(53\) −1.82908 −0.251244 −0.125622 0.992078i \(-0.540093\pi\)
−0.125622 + 0.992078i \(0.540093\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0.216480 0.374955i 0.0291902 0.0505589i
\(56\) −2.34601 4.06341i −0.313499 0.542996i
\(57\) 4.98792 0.660666
\(58\) −0.425428 0.736862i −0.0558614 0.0967547i
\(59\) 2.94989 + 5.10935i 0.384042 + 0.665181i 0.991636 0.129067i \(-0.0411983\pi\)
−0.607593 + 0.794248i \(0.707865\pi\)
\(60\) 3.15883 0.407804
\(61\) −2.19806 3.80716i −0.281433 0.487456i 0.690305 0.723519i \(-0.257476\pi\)
−0.971738 + 0.236062i \(0.924143\pi\)
\(62\) 3.11745 5.39958i 0.395916 0.685747i
\(63\) 2.34601 4.06341i 0.295570 0.511942i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0.137063 0.0168713
\(67\) 2.35690 4.08226i 0.287941 0.498728i −0.685377 0.728188i \(-0.740363\pi\)
0.973318 + 0.229460i \(0.0736961\pi\)
\(68\) 2.80194 4.85310i 0.339785 0.588525i
\(69\) −3.04892 5.28088i −0.367047 0.635743i
\(70\) −14.8213 −1.77149
\(71\) 0.0489173 + 0.0847273i 0.00580542 + 0.0100553i 0.868914 0.494964i \(-0.164819\pi\)
−0.863108 + 0.505019i \(0.831485\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −2.32304 −0.271892 −0.135946 0.990716i \(-0.543407\pi\)
−0.135946 + 0.990716i \(0.543407\pi\)
\(74\) 5.85086 + 10.1340i 0.680148 + 1.17805i
\(75\) 2.48911 4.31127i 0.287418 0.497823i
\(76\) 2.49396 4.31966i 0.286077 0.495499i
\(77\) −0.643104 −0.0732885
\(78\) 0 0
\(79\) 14.5157 1.63315 0.816574 0.577241i \(-0.195871\pi\)
0.816574 + 0.577241i \(0.195871\pi\)
\(80\) 1.57942 2.73563i 0.176584 0.305853i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −2.13706 3.70150i −0.235999 0.408763i
\(83\) −9.85623 −1.08186 −0.540931 0.841067i \(-0.681928\pi\)
−0.540931 + 0.841067i \(0.681928\pi\)
\(84\) −2.34601 4.06341i −0.255971 0.443354i
\(85\) −8.85086 15.3301i −0.960010 1.66279i
\(86\) 2.09783 0.226215
\(87\) −0.425428 0.736862i −0.0456106 0.0789999i
\(88\) 0.0685317 0.118700i 0.00730550 0.0126535i
\(89\) −8.54288 + 14.7967i −0.905543 + 1.56845i −0.0853566 + 0.996350i \(0.527203\pi\)
−0.820187 + 0.572096i \(0.806130\pi\)
\(90\) 3.15883 0.332970
\(91\) 0 0
\(92\) −6.09783 −0.635743
\(93\) 3.11745 5.39958i 0.323264 0.559910i
\(94\) 2.49396 4.31966i 0.257232 0.445539i
\(95\) −7.87800 13.6451i −0.808266 1.39996i
\(96\) 1.00000 0.102062
\(97\) −1.06369 1.84236i −0.108001 0.187063i 0.806959 0.590607i \(-0.201112\pi\)
−0.914960 + 0.403544i \(0.867778\pi\)
\(98\) 7.50753 + 13.0034i 0.758375 + 1.31354i
\(99\) 0.137063 0.0137754
\(100\) −2.48911 4.31127i −0.248911 0.431127i
\(101\) 4.59299 7.95529i 0.457020 0.791581i −0.541782 0.840519i \(-0.682250\pi\)
0.998802 + 0.0489377i \(0.0155836\pi\)
\(102\) 2.80194 4.85310i 0.277433 0.480528i
\(103\) 0.225209 0.0221905 0.0110953 0.999938i \(-0.496468\pi\)
0.0110953 + 0.999938i \(0.496468\pi\)
\(104\) 0 0
\(105\) −14.8213 −1.44641
\(106\) −0.914542 + 1.58403i −0.0888282 + 0.153855i
\(107\) −5.64191 + 9.77207i −0.545424 + 0.944702i 0.453156 + 0.891431i \(0.350298\pi\)
−0.998580 + 0.0532707i \(0.983035\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −0.195669 −0.0187417 −0.00937086 0.999956i \(-0.502983\pi\)
−0.00937086 + 0.999956i \(0.502983\pi\)
\(110\) −0.216480 0.374955i −0.0206406 0.0357505i
\(111\) 5.85086 + 10.1340i 0.555339 + 0.961875i
\(112\) −4.69202 −0.443354
\(113\) 0.219833 + 0.380761i 0.0206801 + 0.0358190i 0.876180 0.481984i \(-0.160084\pi\)
−0.855500 + 0.517803i \(0.826750\pi\)
\(114\) 2.49396 4.31966i 0.233581 0.404574i
\(115\) −9.63102 + 16.6814i −0.898097 + 1.55555i
\(116\) −0.850855 −0.0789999
\(117\) 0 0
\(118\) 5.89977 0.543118
\(119\) −13.1468 + 22.7708i −1.20516 + 2.08740i
\(120\) 1.57942 2.73563i 0.144180 0.249728i
\(121\) 5.49061 + 9.51001i 0.499146 + 0.864546i
\(122\) −4.39612 −0.398006
\(123\) −2.13706 3.70150i −0.192693 0.333753i
\(124\) −3.11745 5.39958i −0.279955 0.484897i
\(125\) 0.0687686 0.00615085
\(126\) −2.34601 4.06341i −0.208999 0.361997i
\(127\) 3.93631 6.81789i 0.349291 0.604990i −0.636832 0.771002i \(-0.719756\pi\)
0.986124 + 0.166012i \(0.0530890\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 2.09783 0.184704
\(130\) 0 0
\(131\) −0.621334 −0.0542862 −0.0271431 0.999632i \(-0.508641\pi\)
−0.0271431 + 0.999632i \(0.508641\pi\)
\(132\) 0.0685317 0.118700i 0.00596492 0.0103315i
\(133\) −11.7017 + 20.2680i −1.01467 + 1.75745i
\(134\) −2.35690 4.08226i −0.203605 0.352654i
\(135\) 3.15883 0.271869
\(136\) −2.80194 4.85310i −0.240264 0.416150i
\(137\) −2.00000 3.46410i −0.170872 0.295958i 0.767853 0.640626i \(-0.221325\pi\)
−0.938725 + 0.344668i \(0.887992\pi\)
\(138\) −6.09783 −0.519082
\(139\) 6.82908 + 11.8283i 0.579235 + 1.00327i 0.995567 + 0.0940524i \(0.0299821\pi\)
−0.416332 + 0.909213i \(0.636685\pi\)
\(140\) −7.41066 + 12.8356i −0.626315 + 1.08481i
\(141\) 2.49396 4.31966i 0.210029 0.363781i
\(142\) 0.0978347 0.00821010
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −1.34385 + 2.32762i −0.111601 + 0.193299i
\(146\) −1.16152 + 2.01182i −0.0961282 + 0.166499i
\(147\) 7.50753 + 13.0034i 0.619211 + 1.07250i
\(148\) 11.7017 0.961875
\(149\) −8.02930 13.9072i −0.657786 1.13932i −0.981188 0.193057i \(-0.938160\pi\)
0.323401 0.946262i \(-0.395174\pi\)
\(150\) −2.48911 4.31127i −0.203235 0.352014i
\(151\) −21.8823 −1.78076 −0.890379 0.455221i \(-0.849560\pi\)
−0.890379 + 0.455221i \(0.849560\pi\)
\(152\) −2.49396 4.31966i −0.202287 0.350371i
\(153\) 2.80194 4.85310i 0.226523 0.392350i
\(154\) −0.321552 + 0.556945i −0.0259114 + 0.0448799i
\(155\) −19.6950 −1.58194
\(156\) 0 0
\(157\) −7.90217 −0.630661 −0.315331 0.948982i \(-0.602115\pi\)
−0.315331 + 0.948982i \(0.602115\pi\)
\(158\) 7.25786 12.5710i 0.577405 1.00009i
\(159\) −0.914542 + 1.58403i −0.0725279 + 0.125622i
\(160\) −1.57942 2.73563i −0.124864 0.216271i
\(161\) 28.6112 2.25488
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −4.00969 6.94498i −0.314063 0.543973i 0.665175 0.746688i \(-0.268357\pi\)
−0.979238 + 0.202714i \(0.935024\pi\)
\(164\) −4.27413 −0.333753
\(165\) −0.216480 0.374955i −0.0168530 0.0291902i
\(166\) −4.92812 + 8.53575i −0.382496 + 0.662502i
\(167\) 8.54288 14.7967i 0.661068 1.14500i −0.319268 0.947665i \(-0.603437\pi\)
0.980335 0.197338i \(-0.0632297\pi\)
\(168\) −4.69202 −0.361997
\(169\) 0 0
\(170\) −17.7017 −1.35766
\(171\) 2.49396 4.31966i 0.190718 0.330333i
\(172\) 1.04892 1.81678i 0.0799792 0.138528i
\(173\) 7.67241 + 13.2890i 0.583322 + 1.01034i 0.995082 + 0.0990516i \(0.0315809\pi\)
−0.411760 + 0.911292i \(0.635086\pi\)
\(174\) −0.850855 −0.0645032
\(175\) 11.6790 + 20.2286i 0.882848 + 1.52914i
\(176\) −0.0685317 0.118700i −0.00516577 0.00894737i
\(177\) 5.89977 0.443454
\(178\) 8.54288 + 14.7967i 0.640316 + 1.10906i
\(179\) −0.261750 + 0.453364i −0.0195641 + 0.0338860i −0.875642 0.482961i \(-0.839561\pi\)
0.856078 + 0.516847i \(0.172895\pi\)
\(180\) 1.57942 2.73563i 0.117723 0.203902i
\(181\) 8.89008 0.660795 0.330397 0.943842i \(-0.392817\pi\)
0.330397 + 0.943842i \(0.392817\pi\)
\(182\) 0 0
\(183\) −4.39612 −0.324971
\(184\) −3.04892 + 5.28088i −0.224769 + 0.389312i
\(185\) 18.4819 32.0116i 1.35881 2.35354i
\(186\) −3.11745 5.39958i −0.228582 0.395916i
\(187\) −0.768086 −0.0561680
\(188\) −2.49396 4.31966i −0.181891 0.315044i
\(189\) −2.34601 4.06341i −0.170647 0.295570i
\(190\) −15.7560 −1.14306
\(191\) 3.51573 + 6.08942i 0.254389 + 0.440615i 0.964729 0.263243i \(-0.0847922\pi\)
−0.710340 + 0.703859i \(0.751459\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 8.87800 15.3772i 0.639053 1.10687i −0.346588 0.938017i \(-0.612660\pi\)
0.985641 0.168854i \(-0.0540067\pi\)
\(194\) −2.12737 −0.152737
\(195\) 0 0
\(196\) 15.0151 1.07250
\(197\) −9.32855 + 16.1575i −0.664632 + 1.15118i 0.314753 + 0.949174i \(0.398078\pi\)
−0.979385 + 0.202003i \(0.935255\pi\)
\(198\) 0.0685317 0.118700i 0.00487033 0.00843567i
\(199\) −3.83124 6.63590i −0.271589 0.470407i 0.697680 0.716410i \(-0.254216\pi\)
−0.969269 + 0.246003i \(0.920883\pi\)
\(200\) −4.97823 −0.352014
\(201\) −2.35690 4.08226i −0.166243 0.287941i
\(202\) −4.59299 7.95529i −0.323162 0.559732i
\(203\) 3.99223 0.280200
\(204\) −2.80194 4.85310i −0.196175 0.339785i
\(205\) −6.75063 + 11.6924i −0.471484 + 0.816635i
\(206\) 0.112605 0.195037i 0.00784554 0.0135889i
\(207\) −6.09783 −0.423829
\(208\) 0 0
\(209\) −0.683661 −0.0472898
\(210\) −7.41066 + 12.8356i −0.511384 + 0.885743i
\(211\) −5.58211 + 9.66849i −0.384288 + 0.665606i −0.991670 0.128803i \(-0.958886\pi\)
0.607382 + 0.794410i \(0.292220\pi\)
\(212\) 0.914542 + 1.58403i 0.0628110 + 0.108792i
\(213\) 0.0978347 0.00670352
\(214\) 5.64191 + 9.77207i 0.385673 + 0.668005i
\(215\) −3.31336 5.73890i −0.225969 0.391390i
\(216\) 1.00000 0.0680414
\(217\) 14.6271 + 25.3349i 0.992955 + 1.71985i
\(218\) −0.0978347 + 0.169455i −0.00662620 + 0.0114769i
\(219\) −1.16152 + 2.01182i −0.0784884 + 0.135946i
\(220\) −0.432960 −0.0291902
\(221\) 0 0
\(222\) 11.7017 0.785367
\(223\) 12.3177 21.3348i 0.824852 1.42869i −0.0771803 0.997017i \(-0.524592\pi\)
0.902032 0.431668i \(-0.142075\pi\)
\(224\) −2.34601 + 4.06341i −0.156749 + 0.271498i
\(225\) −2.48911 4.31127i −0.165941 0.287418i
\(226\) 0.439665 0.0292461
\(227\) −3.73825 6.47484i −0.248116 0.429750i 0.714887 0.699240i \(-0.246478\pi\)
−0.963003 + 0.269490i \(0.913145\pi\)
\(228\) −2.49396 4.31966i −0.165166 0.286077i
\(229\) 19.2271 1.27056 0.635282 0.772280i \(-0.280884\pi\)
0.635282 + 0.772280i \(0.280884\pi\)
\(230\) 9.63102 + 16.6814i 0.635051 + 1.09994i
\(231\) −0.321552 + 0.556945i −0.0211566 + 0.0366443i
\(232\) −0.425428 + 0.736862i −0.0279307 + 0.0483774i
\(233\) 3.70171 0.242507 0.121254 0.992622i \(-0.461309\pi\)
0.121254 + 0.992622i \(0.461309\pi\)
\(234\) 0 0
\(235\) −15.7560 −1.02781
\(236\) 2.94989 5.10935i 0.192021 0.332591i
\(237\) 7.25786 12.5710i 0.471449 0.816574i
\(238\) 13.1468 + 22.7708i 0.852177 + 1.47601i
\(239\) −8.51334 −0.550682 −0.275341 0.961347i \(-0.588791\pi\)
−0.275341 + 0.961347i \(0.588791\pi\)
\(240\) −1.57942 2.73563i −0.101951 0.176584i
\(241\) 8.71648 + 15.0974i 0.561478 + 0.972508i 0.997368 + 0.0725082i \(0.0231003\pi\)
−0.435890 + 0.900000i \(0.643566\pi\)
\(242\) 10.9812 0.705899
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −2.19806 + 3.80716i −0.140717 + 0.243728i
\(245\) 23.7150 41.0757i 1.51510 2.62423i
\(246\) −4.27413 −0.272508
\(247\) 0 0
\(248\) −6.23490 −0.395916
\(249\) −4.92812 + 8.53575i −0.312307 + 0.540931i
\(250\) 0.0343843 0.0595554i 0.00217466 0.00376661i
\(251\) 1.74214 + 3.01747i 0.109963 + 0.190461i 0.915755 0.401737i \(-0.131594\pi\)
−0.805792 + 0.592198i \(0.798260\pi\)
\(252\) −4.69202 −0.295570
\(253\) 0.417895 + 0.723815i 0.0262728 + 0.0455059i
\(254\) −3.93631 6.81789i −0.246986 0.427793i
\(255\) −17.7017 −1.10852
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.80194 11.7813i 0.424293 0.734897i −0.572061 0.820211i \(-0.693856\pi\)
0.996354 + 0.0853137i \(0.0271893\pi\)
\(258\) 1.04892 1.81678i 0.0653027 0.113108i
\(259\) −54.9047 −3.41161
\(260\) 0 0
\(261\) −0.850855 −0.0526666
\(262\) −0.310667 + 0.538091i −0.0191931 + 0.0332434i
\(263\) −5.72886 + 9.92267i −0.353256 + 0.611858i −0.986818 0.161834i \(-0.948259\pi\)
0.633561 + 0.773692i \(0.281592\pi\)
\(264\) −0.0685317 0.118700i −0.00421783 0.00730550i
\(265\) 5.77777 0.354926
\(266\) 11.7017 + 20.2680i 0.717478 + 1.24271i
\(267\) 8.54288 + 14.7967i 0.522816 + 0.905543i
\(268\) −4.71379 −0.287941
\(269\) −11.1833 19.3700i −0.681857 1.18101i −0.974413 0.224763i \(-0.927839\pi\)
0.292556 0.956248i \(-0.405494\pi\)
\(270\) 1.57942 2.73563i 0.0961202 0.166485i
\(271\) −1.93631 + 3.35379i −0.117623 + 0.203728i −0.918825 0.394665i \(-0.870861\pi\)
0.801202 + 0.598393i \(0.204194\pi\)
\(272\) −5.60388 −0.339785
\(273\) 0 0
\(274\) −4.00000 −0.241649
\(275\) −0.341166 + 0.590918i −0.0205731 + 0.0356337i
\(276\) −3.04892 + 5.28088i −0.183523 + 0.317872i
\(277\) −14.3545 24.8627i −0.862478 1.49386i −0.869529 0.493881i \(-0.835578\pi\)
0.00705077 0.999975i \(-0.497756\pi\)
\(278\) 13.6582 0.819163
\(279\) −3.11745 5.39958i −0.186637 0.323264i
\(280\) 7.41066 + 12.8356i 0.442871 + 0.767076i
\(281\) −29.0858 −1.73511 −0.867555 0.497341i \(-0.834310\pi\)
−0.867555 + 0.497341i \(0.834310\pi\)
\(282\) −2.49396 4.31966i −0.148513 0.257232i
\(283\) −6.87800 + 11.9130i −0.408855 + 0.708157i −0.994762 0.102221i \(-0.967405\pi\)
0.585907 + 0.810378i \(0.300738\pi\)
\(284\) 0.0489173 0.0847273i 0.00290271 0.00502764i
\(285\) −15.7560 −0.933305
\(286\) 0 0
\(287\) 20.0543 1.18377
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) −7.20171 + 12.4737i −0.423630 + 0.733749i
\(290\) 1.34385 + 2.32762i 0.0789139 + 0.136683i
\(291\) −2.12737 −0.124709
\(292\) 1.16152 + 2.01182i 0.0679729 + 0.117733i
\(293\) −13.8681 24.0202i −0.810182 1.40328i −0.912737 0.408548i \(-0.866035\pi\)
0.102555 0.994727i \(-0.467298\pi\)
\(294\) 15.0151 0.875696
\(295\) −9.31820 16.1396i −0.542527 0.939684i
\(296\) 5.85086 10.1340i 0.340074 0.589026i
\(297\) 0.0685317 0.118700i 0.00397661 0.00688769i
\(298\) −16.0586 −0.930250
\(299\) 0 0
\(300\) −4.97823 −0.287418
\(301\) −4.92154 + 8.52436i −0.283673 + 0.491336i
\(302\) −10.9412 + 18.9506i −0.629593 + 1.09049i
\(303\) −4.59299 7.95529i −0.263860 0.457020i
\(304\) −4.98792 −0.286077
\(305\) 6.94331 + 12.0262i 0.397573 + 0.688617i
\(306\) −2.80194 4.85310i −0.160176 0.277433i
\(307\) −12.4590 −0.711075 −0.355538 0.934662i \(-0.615702\pi\)
−0.355538 + 0.934662i \(0.615702\pi\)
\(308\) 0.321552 + 0.556945i 0.0183221 + 0.0317349i
\(309\) 0.112605 0.195037i 0.00640586 0.0110953i
\(310\) −9.84750 + 17.0564i −0.559301 + 0.968737i
\(311\) −6.09783 −0.345776 −0.172888 0.984941i \(-0.555310\pi\)
−0.172888 + 0.984941i \(0.555310\pi\)
\(312\) 0 0
\(313\) −12.7385 −0.720025 −0.360013 0.932947i \(-0.617228\pi\)
−0.360013 + 0.932947i \(0.617228\pi\)
\(314\) −3.95108 + 6.84348i −0.222972 + 0.386200i
\(315\) −7.41066 + 12.8356i −0.417543 + 0.723206i
\(316\) −7.25786 12.5710i −0.408287 0.707173i
\(317\) 14.8140 0.832038 0.416019 0.909356i \(-0.363425\pi\)
0.416019 + 0.909356i \(0.363425\pi\)
\(318\) 0.914542 + 1.58403i 0.0512850 + 0.0888282i
\(319\) 0.0583105 + 0.100997i 0.00326476 + 0.00565473i
\(320\) −3.15883 −0.176584
\(321\) 5.64191 + 9.77207i 0.314901 + 0.545424i
\(322\) 14.3056 24.7780i 0.797219 1.38082i
\(323\) −13.9758 + 24.2069i −0.777636 + 1.34691i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −8.01938 −0.444152
\(327\) −0.0978347 + 0.169455i −0.00541027 + 0.00937086i
\(328\) −2.13706 + 3.70150i −0.118000 + 0.204381i
\(329\) 11.7017 + 20.2680i 0.645136 + 1.11741i
\(330\) −0.432960 −0.0238337
\(331\) −3.85086 6.66988i −0.211662 0.366610i 0.740573 0.671976i \(-0.234554\pi\)
−0.952235 + 0.305367i \(0.901221\pi\)
\(332\) 4.92812 + 8.53575i 0.270465 + 0.468460i
\(333\) 11.7017 0.641250
\(334\) −8.54288 14.7967i −0.467445 0.809639i
\(335\) −7.44504 + 12.8952i −0.406766 + 0.704540i
\(336\) −2.34601 + 4.06341i −0.127985 + 0.221677i
\(337\) 26.5961 1.44878 0.724391 0.689389i \(-0.242121\pi\)
0.724391 + 0.689389i \(0.242121\pi\)
\(338\) 0 0
\(339\) 0.439665 0.0238793
\(340\) −8.85086 + 15.3301i −0.480005 + 0.831393i
\(341\) −0.427288 + 0.740084i −0.0231389 + 0.0400778i
\(342\) −2.49396 4.31966i −0.134858 0.233581i
\(343\) −37.6069 −2.03058
\(344\) −1.04892 1.81678i −0.0565538 0.0979541i
\(345\) 9.63102 + 16.6814i 0.518517 + 0.898097i
\(346\) 15.3448 0.824942
\(347\) −0.455927 0.789689i −0.0244754 0.0423927i 0.853528 0.521047i \(-0.174458\pi\)
−0.878004 + 0.478654i \(0.841125\pi\)
\(348\) −0.425428 + 0.736862i −0.0228053 + 0.0395000i
\(349\) 8.86054 15.3469i 0.474294 0.821501i −0.525273 0.850934i \(-0.676037\pi\)
0.999567 + 0.0294326i \(0.00937003\pi\)
\(350\) 23.3580 1.24854
\(351\) 0 0
\(352\) −0.137063 −0.00730550
\(353\) 13.2174 22.8933i 0.703493 1.21849i −0.263739 0.964594i \(-0.584956\pi\)
0.967233 0.253892i \(-0.0817108\pi\)
\(354\) 2.94989 5.10935i 0.156785 0.271559i
\(355\) −0.154522 0.267639i −0.00820116 0.0142048i
\(356\) 17.0858 0.905543
\(357\) 13.1468 + 22.7708i 0.695800 + 1.20516i
\(358\) 0.261750 + 0.453364i 0.0138339 + 0.0239610i
\(359\) 7.76941 0.410054 0.205027 0.978756i \(-0.434272\pi\)
0.205027 + 0.978756i \(0.434272\pi\)
\(360\) −1.57942 2.73563i −0.0832426 0.144180i
\(361\) −2.93967 + 5.09165i −0.154719 + 0.267982i
\(362\) 4.44504 7.69904i 0.233626 0.404652i
\(363\) 10.9812 0.576364
\(364\) 0 0
\(365\) 7.33811 0.384094
\(366\) −2.19806 + 3.80716i −0.114895 + 0.199003i
\(367\) 6.66368 11.5418i 0.347841 0.602479i −0.638025 0.770016i \(-0.720248\pi\)
0.985866 + 0.167537i \(0.0535815\pi\)
\(368\) 3.04892 + 5.28088i 0.158936 + 0.275285i
\(369\) −4.27413 −0.222502
\(370\) −18.4819 32.0116i −0.960827 1.66420i
\(371\) −4.29105 7.43232i −0.222780 0.385867i
\(372\) −6.23490 −0.323264
\(373\) −3.35152 5.80500i −0.173535 0.300572i 0.766118 0.642700i \(-0.222186\pi\)
−0.939653 + 0.342128i \(0.888852\pi\)
\(374\) −0.384043 + 0.665182i −0.0198584 + 0.0343957i
\(375\) 0.0343843 0.0595554i 0.00177560 0.00307543i
\(376\) −4.98792 −0.257232
\(377\) 0 0
\(378\) −4.69202 −0.241332
\(379\) −1.20775 + 2.09189i −0.0620380 + 0.107453i −0.895376 0.445310i \(-0.853093\pi\)
0.833338 + 0.552763i \(0.186427\pi\)
\(380\) −7.87800 + 13.6451i −0.404133 + 0.699979i
\(381\) −3.93631 6.81789i −0.201663 0.349291i
\(382\) 7.03146 0.359761
\(383\) −5.04892 8.74498i −0.257988 0.446848i 0.707715 0.706498i \(-0.249726\pi\)
−0.965703 + 0.259650i \(0.916393\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 2.03146 0.103533
\(386\) −8.87800 15.3772i −0.451878 0.782676i
\(387\) 1.04892 1.81678i 0.0533195 0.0923520i
\(388\) −1.06369 + 1.84236i −0.0540005 + 0.0935317i
\(389\) 25.1336 1.27432 0.637162 0.770730i \(-0.280108\pi\)
0.637162 + 0.770730i \(0.280108\pi\)
\(390\) 0 0
\(391\) 34.1715 1.72813
\(392\) 7.50753 13.0034i 0.379188 0.656772i
\(393\) −0.310667 + 0.538091i −0.0156711 + 0.0271431i
\(394\) 9.32855 + 16.1575i 0.469966 + 0.814004i
\(395\) −45.8528 −2.30710
\(396\) −0.0685317 0.118700i −0.00344385 0.00596492i
\(397\) −10.4179 18.0443i −0.522859 0.905619i −0.999646 0.0265998i \(-0.991532\pi\)
0.476787 0.879019i \(-0.341801\pi\)
\(398\) −7.66248 −0.384085
\(399\) 11.7017 + 20.2680i 0.585818 + 1.01467i
\(400\) −2.48911 + 4.31127i −0.124456 + 0.215564i
\(401\) 2.97823 5.15845i 0.148726 0.257600i −0.782031 0.623239i \(-0.785816\pi\)
0.930757 + 0.365639i \(0.119150\pi\)
\(402\) −4.71379 −0.235103
\(403\) 0 0
\(404\) −9.18598 −0.457020
\(405\) 1.57942 2.73563i 0.0784819 0.135935i
\(406\) 1.99612 3.45737i 0.0990655 0.171587i
\(407\) −0.801938 1.38900i −0.0397506 0.0688500i
\(408\) −5.60388 −0.277433
\(409\) 0.900969 + 1.56052i 0.0445500 + 0.0771629i 0.887441 0.460922i \(-0.152481\pi\)
−0.842891 + 0.538085i \(0.819148\pi\)
\(410\) 6.75063 + 11.6924i 0.333390 + 0.577448i
\(411\) −4.00000 −0.197305
\(412\) −0.112605 0.195037i −0.00554763 0.00960878i
\(413\) −13.8409 + 23.9732i −0.681068 + 1.17964i
\(414\) −3.04892 + 5.28088i −0.149846 + 0.259541i
\(415\) 31.1342 1.52832
\(416\) 0 0
\(417\) 13.6582 0.668843
\(418\) −0.341830 + 0.592068i −0.0167195 + 0.0289590i
\(419\) 14.2250 24.6384i 0.694935 1.20366i −0.275267 0.961368i \(-0.588766\pi\)
0.970202 0.242296i \(-0.0779004\pi\)
\(420\) 7.41066 + 12.8356i 0.361603 + 0.626315i
\(421\) 13.9323 0.679019 0.339509 0.940603i \(-0.389739\pi\)
0.339509 + 0.940603i \(0.389739\pi\)
\(422\) 5.58211 + 9.66849i 0.271733 + 0.470655i
\(423\) −2.49396 4.31966i −0.121260 0.210029i
\(424\) 1.82908 0.0888282
\(425\) 13.9487 + 24.1598i 0.676611 + 1.17192i
\(426\) 0.0489173 0.0847273i 0.00237005 0.00410505i
\(427\) 10.3134 17.8633i 0.499098 0.864464i
\(428\) 11.2838 0.545424
\(429\) 0 0
\(430\) −6.62671 −0.319568
\(431\) 7.95108 13.7717i 0.382990 0.663358i −0.608498 0.793555i \(-0.708228\pi\)
0.991488 + 0.130197i \(0.0415610\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −2.38859 4.13716i −0.114788 0.198819i 0.802907 0.596105i \(-0.203286\pi\)
−0.917695 + 0.397285i \(0.869952\pi\)
\(434\) 29.2543 1.40425
\(435\) 1.34385 + 2.32762i 0.0644329 + 0.111601i
\(436\) 0.0978347 + 0.169455i 0.00468543 + 0.00811541i
\(437\) 30.4155 1.45497
\(438\) 1.16152 + 2.01182i 0.0554997 + 0.0961282i
\(439\) 16.8158 29.1258i 0.802575 1.39010i −0.115342 0.993326i \(-0.536796\pi\)
0.917916 0.396774i \(-0.129870\pi\)
\(440\) −0.216480 + 0.374955i −0.0103203 + 0.0178753i
\(441\) 15.0151 0.715003
\(442\) 0 0
\(443\) −35.3749 −1.68071 −0.840357 0.542033i \(-0.817655\pi\)
−0.840357 + 0.542033i \(0.817655\pi\)
\(444\) 5.85086 10.1340i 0.277669 0.480937i
\(445\) 26.9855 46.7403i 1.27924 2.21570i
\(446\) −12.3177 21.3348i −0.583258 1.01023i
\(447\) −16.0586 −0.759546
\(448\) 2.34601 + 4.06341i 0.110839 + 0.191978i
\(449\) −9.03146 15.6429i −0.426221 0.738236i 0.570313 0.821428i \(-0.306822\pi\)
−0.996534 + 0.0831914i \(0.973489\pi\)
\(450\) −4.97823 −0.234676
\(451\) 0.292913 + 0.507340i 0.0137927 + 0.0238897i
\(452\) 0.219833 0.380761i 0.0103401 0.0179095i
\(453\) −10.9412 + 18.9506i −0.514060 + 0.890379i
\(454\) −7.47650 −0.350890
\(455\) 0 0
\(456\) −4.98792 −0.233581
\(457\) −7.73341 + 13.3947i −0.361753 + 0.626575i −0.988250 0.152849i \(-0.951155\pi\)
0.626496 + 0.779425i \(0.284488\pi\)
\(458\) 9.61356 16.6512i 0.449212 0.778059i
\(459\) −2.80194 4.85310i −0.130783 0.226523i
\(460\) 19.2620 0.898097
\(461\) −9.40462 16.2893i −0.438017 0.758667i 0.559520 0.828817i \(-0.310986\pi\)
−0.997536 + 0.0701499i \(0.977652\pi\)
\(462\) 0.321552 + 0.556945i 0.0149600 + 0.0259114i
\(463\) 15.8431 0.736291 0.368145 0.929768i \(-0.379993\pi\)
0.368145 + 0.929768i \(0.379993\pi\)
\(464\) 0.425428 + 0.736862i 0.0197500 + 0.0342080i
\(465\) −9.84750 + 17.0564i −0.456667 + 0.790970i
\(466\) 1.85086 3.20578i 0.0857392 0.148505i
\(467\) 22.0006 1.01807 0.509033 0.860747i \(-0.330003\pi\)
0.509033 + 0.860747i \(0.330003\pi\)
\(468\) 0 0
\(469\) 22.1172 1.02128
\(470\) −7.87800 + 13.6451i −0.363385 + 0.629402i
\(471\) −3.95108 + 6.84348i −0.182056 + 0.315331i
\(472\) −2.94989 5.10935i −0.135780 0.235177i
\(473\) −0.287536 −0.0132209
\(474\) −7.25786 12.5710i −0.333365 0.577405i
\(475\) 12.4155 + 21.5043i 0.569662 + 0.986684i
\(476\) 26.2935 1.20516
\(477\) 0.914542 + 1.58403i 0.0418740 + 0.0725279i
\(478\) −4.25667 + 7.37277i −0.194695 + 0.337222i
\(479\) −10.6746 + 18.4889i −0.487733 + 0.844779i −0.999900 0.0141070i \(-0.995509\pi\)
0.512167 + 0.858886i \(0.328843\pi\)
\(480\) −3.15883 −0.144180
\(481\) 0 0
\(482\) 17.4330 0.794050
\(483\) 14.3056 24.7780i 0.650927 1.12744i
\(484\) 5.49061 9.51001i 0.249573 0.432273i
\(485\) 3.36001 + 5.81971i 0.152570 + 0.264259i
\(486\) 1.00000 0.0453609
\(487\) −15.8197 27.4005i −0.716859 1.24164i −0.962238 0.272209i \(-0.912246\pi\)
0.245380 0.969427i \(-0.421087\pi\)
\(488\) 2.19806 + 3.80716i 0.0995016 + 0.172342i
\(489\) −8.01938 −0.362649
\(490\) −23.7150 41.0757i −1.07134 1.85561i
\(491\) 0.699554 1.21166i 0.0315704 0.0546816i −0.849808 0.527092i \(-0.823282\pi\)
0.881379 + 0.472410i \(0.156616\pi\)
\(492\) −2.13706 + 3.70150i −0.0963463 + 0.166877i
\(493\) 4.76809 0.214744
\(494\) 0 0
\(495\) −0.432960 −0.0194601
\(496\) −3.11745 + 5.39958i −0.139978 + 0.242448i
\(497\) −0.229521 + 0.397542i −0.0102954 + 0.0178322i
\(498\) 4.92812 + 8.53575i 0.220834 + 0.382496i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) −0.0343843 0.0595554i −0.00153771 0.00266340i
\(501\) −8.54288 14.7967i −0.381668 0.661068i
\(502\) 3.48427 0.155511
\(503\) 9.19136 + 15.9199i 0.409822 + 0.709833i 0.994870 0.101166i \(-0.0322573\pi\)
−0.585047 + 0.810999i \(0.698924\pi\)
\(504\) −2.34601 + 4.06341i −0.104500 + 0.180999i
\(505\) −14.5085 + 25.1294i −0.645619 + 1.11825i
\(506\) 0.835790 0.0371554
\(507\) 0 0
\(508\) −7.87263 −0.349291
\(509\) 0.0663757 0.114966i 0.00294205 0.00509578i −0.864551 0.502546i \(-0.832397\pi\)
0.867493 + 0.497450i \(0.165730\pi\)
\(510\) −8.85086 + 15.3301i −0.391922 + 0.678830i
\(511\) −5.44989 9.43948i −0.241089 0.417578i
\(512\) −1.00000 −0.0441942
\(513\) −2.49396 4.31966i −0.110111 0.190718i
\(514\) −6.80194 11.7813i −0.300021 0.519651i
\(515\) −0.711399 −0.0313480
\(516\) −1.04892 1.81678i −0.0461760 0.0799792i
\(517\) −0.341830 + 0.592068i −0.0150337 + 0.0260391i
\(518\) −27.4523 + 47.5488i −1.20619 + 2.08918i
\(519\) 15.3448 0.673563
\(520\) 0 0
\(521\) 37.0508 1.62323 0.811613 0.584195i \(-0.198590\pi\)
0.811613 + 0.584195i \(0.198590\pi\)
\(522\) −0.425428 + 0.736862i −0.0186205 + 0.0322516i
\(523\) 1.57673 2.73097i 0.0689455 0.119417i −0.829492 0.558519i \(-0.811370\pi\)
0.898437 + 0.439102i \(0.144703\pi\)
\(524\) 0.310667 + 0.538091i 0.0135715 + 0.0235066i
\(525\) 23.3580 1.01942
\(526\) 5.72886 + 9.92267i 0.249790 + 0.432649i
\(527\) 17.4698 + 30.2586i 0.760996 + 1.31808i
\(528\) −0.137063 −0.00596492
\(529\) −7.09179 12.2833i −0.308339 0.534059i
\(530\) 2.88889 5.00370i 0.125485 0.217347i
\(531\) 2.94989 5.10935i 0.128014 0.221727i
\(532\) 23.4034 1.01467
\(533\) 0 0
\(534\) 17.0858 0.739373
\(535\) 17.8218 30.8683i 0.770506 1.33455i
\(536\) −2.35690 + 4.08226i −0.101802 + 0.176327i
\(537\) 0.261750 + 0.453364i 0.0112953 + 0.0195641i
\(538\) −22.3666 −0.964292
\(539\) −1.02901 1.78229i −0.0443225 0.0767688i
\(540\) −1.57942 2.73563i −0.0679673 0.117723i
\(541\) 4.07846 0.175347 0.0876733 0.996149i \(-0.472057\pi\)
0.0876733 + 0.996149i \(0.472057\pi\)
\(542\) 1.93631 + 3.35379i 0.0831718 + 0.144058i
\(543\) 4.44504 7.69904i 0.190755 0.330397i
\(544\) −2.80194 + 4.85310i −0.120132 + 0.208075i
\(545\) 0.618087 0.0264759
\(546\) 0 0
\(547\) −23.0508 −0.985583 −0.492791 0.870148i \(-0.664023\pi\)
−0.492791 + 0.870148i \(0.664023\pi\)
\(548\) −2.00000 + 3.46410i −0.0854358 + 0.147979i
\(549\) −2.19806 + 3.80716i −0.0938110 + 0.162485i
\(550\) 0.341166 + 0.590918i 0.0145474 + 0.0251968i
\(551\) 4.24400 0.180800
\(552\) 3.04892 + 5.28088i 0.129771 + 0.224769i
\(553\) 34.0541 + 58.9834i 1.44813 + 2.50823i
\(554\) −28.7090 −1.21973
\(555\) −18.4819 32.0116i −0.784512 1.35881i
\(556\) 6.82908 11.8283i 0.289618 0.501633i
\(557\) −10.2078 + 17.6803i −0.432516 + 0.749140i −0.997089 0.0762430i \(-0.975708\pi\)
0.564573 + 0.825383i \(0.309041\pi\)
\(558\) −6.23490 −0.263944
\(559\) 0 0
\(560\) 14.8213 0.626315
\(561\) −0.384043 + 0.665182i −0.0162143 + 0.0280840i
\(562\) −14.5429 + 25.1890i −0.613454 + 1.06253i
\(563\) −10.7805 18.6723i −0.454342 0.786944i 0.544308 0.838886i \(-0.316792\pi\)
−0.998650 + 0.0519416i \(0.983459\pi\)
\(564\) −4.98792 −0.210029
\(565\) −0.694414 1.20276i −0.0292142 0.0506005i
\(566\) 6.87800 + 11.9130i 0.289104 + 0.500743i
\(567\) −4.69202 −0.197046
\(568\) −0.0489173 0.0847273i −0.00205253 0.00355508i
\(569\) −4.49396 + 7.78377i −0.188397 + 0.326312i −0.944716 0.327890i \(-0.893662\pi\)
0.756319 + 0.654203i \(0.226996\pi\)
\(570\) −7.87800 + 13.6451i −0.329973 + 0.571530i
\(571\) 13.5603 0.567482 0.283741 0.958901i \(-0.408424\pi\)
0.283741 + 0.958901i \(0.408424\pi\)
\(572\) 0 0
\(573\) 7.03146 0.293743
\(574\) 10.0271 17.3675i 0.418525 0.724907i
\(575\) 15.1782 26.2894i 0.632975 1.09635i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 16.2825 0.677849 0.338924 0.940814i \(-0.389937\pi\)
0.338924 + 0.940814i \(0.389937\pi\)
\(578\) 7.20171 + 12.4737i 0.299552 + 0.518839i
\(579\) −8.87800 15.3772i −0.368957 0.639053i
\(580\) 2.68771 0.111601
\(581\) −23.1228 40.0499i −0.959296 1.66155i
\(582\) −1.06369 + 1.84236i −0.0440913 + 0.0763683i
\(583\) 0.125350 0.217113i 0.00519148 0.00899190i
\(584\) 2.32304 0.0961282
\(585\) 0 0
\(586\) −27.7362 −1.14577
\(587\) −23.7853 + 41.1974i −0.981725 + 1.70040i −0.326052 + 0.945352i \(0.605718\pi\)
−0.655673 + 0.755045i \(0.727615\pi\)
\(588\) 7.50753 13.0034i 0.309605 0.536252i
\(589\) 15.5496 + 26.9327i 0.640709 + 1.10974i
\(590\) −18.6364 −0.767248
\(591\) 9.32855 + 16.1575i 0.383725 + 0.664632i
\(592\) −5.85086 10.1340i −0.240469 0.416504i
\(593\) 31.0267 1.27411 0.637056 0.770817i \(-0.280152\pi\)
0.637056 + 0.770817i \(0.280152\pi\)
\(594\) −0.0685317 0.118700i −0.00281189 0.00487033i
\(595\) 41.5284 71.9293i 1.70250 2.94881i
\(596\) −8.02930 + 13.9072i −0.328893 + 0.569660i
\(597\) −7.66248 −0.313604
\(598\) 0 0
\(599\) 22.3263 0.912228 0.456114 0.889921i \(-0.349241\pi\)
0.456114 + 0.889921i \(0.349241\pi\)
\(600\) −2.48911 + 4.31127i −0.101618 + 0.176007i
\(601\) 4.09030 7.08461i 0.166847 0.288987i −0.770463 0.637485i \(-0.779975\pi\)
0.937310 + 0.348498i \(0.113308\pi\)
\(602\) 4.92154 + 8.52436i 0.200587 + 0.347427i
\(603\) −4.71379 −0.191960
\(604\) 10.9412 + 18.9506i 0.445189 + 0.771091i
\(605\) −17.3439 30.0405i −0.705130 1.22132i
\(606\) −9.18598 −0.373155
\(607\) −1.65399 2.86479i −0.0671334 0.116278i 0.830505 0.557011i \(-0.188052\pi\)
−0.897638 + 0.440733i \(0.854719\pi\)
\(608\) −2.49396 + 4.31966i −0.101143 + 0.175186i
\(609\) 1.99612 3.45737i 0.0808867 0.140100i
\(610\) 13.8866 0.562253
\(611\) 0 0
\(612\) −5.60388 −0.226523
\(613\) 5.44265 9.42694i 0.219827 0.380751i −0.734928 0.678145i \(-0.762784\pi\)
0.954755 + 0.297394i \(0.0961175\pi\)
\(614\) −6.22952 + 10.7898i −0.251403 + 0.435443i
\(615\) 6.75063 + 11.6924i 0.272212 + 0.471484i
\(616\) 0.643104 0.0259114
\(617\) 17.2838 + 29.9364i 0.695820 + 1.20520i 0.969903 + 0.243490i \(0.0782923\pi\)
−0.274083 + 0.961706i \(0.588374\pi\)
\(618\) −0.112605 0.195037i −0.00452962 0.00784554i
\(619\) 2.86592 0.115191 0.0575955 0.998340i \(-0.481657\pi\)
0.0575955 + 0.998340i \(0.481657\pi\)
\(620\) 9.84750 + 17.0564i 0.395485 + 0.685001i
\(621\) −3.04892 + 5.28088i −0.122349 + 0.211914i
\(622\) −3.04892 + 5.28088i −0.122250 + 0.211744i
\(623\) −80.1667 −3.21181
\(624\) 0 0
\(625\) −25.1084 −1.00434
\(626\) −6.36927 + 11.0319i −0.254567 + 0.440924i
\(627\) −0.341830 + 0.592068i −0.0136514 + 0.0236449i
\(628\) 3.95108 + 6.84348i 0.157665 + 0.273084i
\(629\) −65.5749 −2.61464
\(630\) 7.41066 + 12.8356i 0.295248 + 0.511384i
\(631\) 21.3315 + 36.9473i 0.849195 + 1.47085i 0.881928 + 0.471385i \(0.156246\pi\)
−0.0327326 + 0.999464i \(0.510421\pi\)
\(632\) −14.5157 −0.577405
\(633\) 5.58211 + 9.66849i 0.221869 + 0.384288i
\(634\) 7.40701 12.8293i 0.294170 0.509517i
\(635\) −12.4342 + 21.5366i −0.493434 + 0.854654i
\(636\) 1.82908 0.0725279
\(637\) 0 0
\(638\) 0.116621 0.00461707
\(639\) 0.0489173 0.0847273i 0.00193514 0.00335176i
\(640\) −1.57942 + 2.73563i −0.0624319 + 0.108135i
\(641\) −20.6963 35.8471i −0.817456 1.41588i −0.907551 0.419942i \(-0.862050\pi\)
0.0900948 0.995933i \(-0.471283\pi\)
\(642\) 11.2838 0.445337
\(643\) −6.85623 11.8753i −0.270383 0.468318i 0.698577 0.715535i \(-0.253817\pi\)
−0.968960 + 0.247217i \(0.920484\pi\)
\(644\) −14.3056 24.7780i −0.563719 0.976390i
\(645\) −6.62671 −0.260926
\(646\) 13.9758 + 24.2069i 0.549872 + 0.952406i
\(647\) −9.00431 + 15.5959i −0.353996 + 0.613139i −0.986946 0.161054i \(-0.948511\pi\)
0.632950 + 0.774193i \(0.281844\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) −0.808643 −0.0317420
\(650\) 0 0
\(651\) 29.2543 1.14657
\(652\) −4.00969 + 6.94498i −0.157032 + 0.271987i
\(653\) −23.2826 + 40.3267i −0.911119 + 1.57810i −0.0986335 + 0.995124i \(0.531447\pi\)
−0.812486 + 0.582981i \(0.801886\pi\)
\(654\) 0.0978347 + 0.169455i 0.00382564 + 0.00662620i
\(655\) 1.96269 0.0766887
\(656\) 2.13706 + 3.70150i 0.0834383 + 0.144519i
\(657\) 1.16152 + 2.01182i 0.0453153 + 0.0784884i
\(658\) 23.4034 0.912360
\(659\) −6.92812 11.9998i −0.269881 0.467448i 0.698950 0.715171i \(-0.253651\pi\)
−0.968831 + 0.247723i \(0.920318\pi\)
\(660\) −0.216480 + 0.374955i −0.00842648 + 0.0145951i
\(661\) 21.5526 37.3301i 0.838298 1.45197i −0.0530194 0.998593i \(-0.516885\pi\)
0.891317 0.453381i \(-0.149782\pi\)
\(662\) −7.70171 −0.299335
\(663\) 0 0
\(664\) 9.85623 0.382496
\(665\) 36.9638 64.0231i 1.43339 2.48271i
\(666\) 5.85086 10.1340i 0.226716 0.392684i
\(667\) −2.59419 4.49326i −0.100447 0.173980i
\(668\) −17.0858 −0.661068
\(669\) −12.3177 21.3348i −0.476229 0.824852i
\(670\) 7.44504 + 12.8952i 0.287627 + 0.498185i
\(671\) 0.602548 0.0232611
\(672\) 2.34601 + 4.06341i 0.0904993 + 0.156749i
\(673\) −15.3708 + 26.6229i −0.592499 + 1.02624i 0.401395 + 0.915905i \(0.368525\pi\)
−0.993895 + 0.110334i \(0.964808\pi\)
\(674\) 13.2981 23.0329i 0.512222 0.887194i
\(675\) −4.97823 −0.191612
\(676\) 0 0
\(677\) 16.5894 0.637582 0.318791 0.947825i \(-0.396723\pi\)
0.318791 + 0.947825i \(0.396723\pi\)
\(678\) 0.219833 0.380761i 0.00844262 0.0146230i
\(679\) 4.99084 8.64440i 0.191531 0.331741i
\(680\) 8.85086 + 15.3301i 0.339415 + 0.587884i
\(681\) −7.47650 −0.286500
\(682\) 0.427288 + 0.740084i 0.0163617 + 0.0283393i
\(683\) 17.4943 + 30.3009i 0.669399 + 1.15943i 0.978072 + 0.208265i \(0.0667817\pi\)
−0.308673 + 0.951168i \(0.599885\pi\)
\(684\) −4.98792 −0.190718
\(685\) 6.31767 + 10.9425i 0.241386 + 0.418092i
\(686\) −18.8034 + 32.5685i −0.717918 + 1.24347i
\(687\) 9.61356 16.6512i 0.366780 0.635282i
\(688\) −2.09783 −0.0799792
\(689\) 0 0
\(690\) 19.2620 0.733294
\(691\) −7.04354 + 12.1998i −0.267949 + 0.464101i −0.968332 0.249666i \(-0.919679\pi\)
0.700383 + 0.713767i \(0.253013\pi\)
\(692\) 7.67241 13.2890i 0.291661 0.505172i
\(693\) 0.321552 + 0.556945i 0.0122148 + 0.0211566i
\(694\) −0.911854 −0.0346135
\(695\) −21.5719 37.3637i −0.818270 1.41729i
\(696\) 0.425428 + 0.736862i 0.0161258 + 0.0279307i
\(697\) 23.9517 0.907234
\(698\) −8.86054 15.3469i −0.335377 0.580889i
\(699\) 1.85086 3.20578i 0.0700058 0.121254i
\(700\) 11.6790 20.2286i 0.441424 0.764569i
\(701\) 48.6112 1.83602 0.918009 0.396559i \(-0.129796\pi\)
0.918009 + 0.396559i \(0.129796\pi\)
\(702\) 0 0
\(703\) −58.3672 −2.20136
\(704\) −0.0685317 + 0.118700i −0.00258288 + 0.00447369i
\(705\) −7.87800 + 13.6451i −0.296703 + 0.513904i
\(706\) −13.2174 22.8933i −0.497445 0.861600i
\(707\) 43.1008 1.62097
\(708\) −2.94989 5.10935i −0.110864 0.192021i
\(709\) −8.64310 14.9703i −0.324599 0.562221i 0.656832 0.754037i \(-0.271896\pi\)
−0.981431 + 0.191815i \(0.938563\pi\)
\(710\) −0.309043 −0.0115982
\(711\) −7.25786 12.5710i −0.272191 0.471449i
\(712\) 8.54288 14.7967i 0.320158 0.554530i
\(713\) 19.0097 32.9257i 0.711918 1.23308i
\(714\) 26.2935 0.984010
\(715\) 0 0
\(716\) 0.523499 0.0195641
\(717\) −4.25667 + 7.37277i −0.158968 + 0.275341i
\(718\) 3.88471 6.72851i 0.144976 0.251106i
\(719\) −14.5603 25.2192i −0.543009 0.940519i −0.998729 0.0503960i \(-0.983952\pi\)
0.455720 0.890123i \(-0.349382\pi\)
\(720\) −3.15883 −0.117723
\(721\) 0.528344 + 0.915118i 0.0196765 + 0.0340808i
\(722\) 2.93967 + 5.09165i 0.109403 + 0.189492i
\(723\) 17.4330 0.648339
\(724\) −4.44504 7.69904i −0.165199 0.286133i
\(725\) 2.11788 3.66827i 0.0786559 0.136236i
\(726\) 5.49061 9.51001i 0.203776 0.352950i
\(727\) 45.5666 1.68997 0.844985 0.534790i \(-0.179609\pi\)
0.844985 + 0.534790i \(0.179609\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 3.66905 6.35499i 0.135798 0.235209i
\(731\) −5.87800 + 10.1810i −0.217406 + 0.376558i
\(732\) 2.19806 + 3.80716i 0.0812427 + 0.140717i
\(733\) −21.7995 −0.805185 −0.402592 0.915379i \(-0.631891\pi\)
−0.402592 + 0.915379i \(0.631891\pi\)
\(734\) −6.66368 11.5418i −0.245961 0.426017i
\(735\) −23.7150 41.0757i −0.874743 1.51510i
\(736\) 6.09783 0.224769
\(737\) 0.323044 + 0.559529i 0.0118995 + 0.0206105i
\(738\) −2.13706 + 3.70150i −0.0786664 + 0.136254i
\(739\) 20.7832 35.9975i 0.764521 1.32419i −0.175979 0.984394i \(-0.556309\pi\)
0.940500 0.339795i \(-0.110358\pi\)
\(740\) −36.9638 −1.35881
\(741\) 0 0
\(742\) −8.58211 −0.315059
\(743\) −14.4112 + 24.9609i −0.528695 + 0.915727i 0.470745 + 0.882269i \(0.343985\pi\)
−0.999440 + 0.0334577i \(0.989348\pi\)
\(744\) −3.11745 + 5.39958i −0.114291 + 0.197958i
\(745\) 25.3632 + 43.9304i 0.929237 + 1.60949i
\(746\) −6.70304 −0.245416
\(747\) 4.92812 + 8.53575i 0.180310 + 0.312307i
\(748\) 0.384043 + 0.665182i 0.0140420 + 0.0243215i
\(749\) −52.9439 −1.93453
\(750\) −0.0343843 0.0595554i −0.00125554 0.00217466i
\(751\) −8.31013 + 14.3936i −0.303241 + 0.525229i −0.976868 0.213842i \(-0.931402\pi\)
0.673627 + 0.739071i \(0.264735\pi\)
\(752\) −2.49396 + 4.31966i −0.0909453 + 0.157522i
\(753\) 3.48427 0.126974
\(754\) 0 0
\(755\) 69.1226 2.51563
\(756\) −2.34601 + 4.06341i −0.0853236 + 0.147785i
\(757\) 20.1957 34.9799i 0.734024 1.27137i −0.221126 0.975245i \(-0.570973\pi\)
0.955150 0.296122i \(-0.0956934\pi\)
\(758\) 1.20775 + 2.09189i 0.0438675 + 0.0759807i
\(759\) 0.835790 0.0303372
\(760\) 7.87800 + 13.6451i 0.285765 + 0.494960i
\(761\) 1.64742 + 2.85341i 0.0597188 + 0.103436i 0.894339 0.447390i \(-0.147646\pi\)
−0.834620 + 0.550826i \(0.814313\pi\)
\(762\) −7.87263 −0.285195
\(763\) −0.459042 0.795085i −0.0166185 0.0287840i
\(764\) 3.51573 6.08942i 0.127195 0.220308i
\(765\) −8.85086 + 15.3301i −0.320003 + 0.554262i
\(766\) −10.0978 −0.364850
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) 1.17629 2.03740i 0.0424182 0.0734704i −0.844037 0.536285i \(-0.819827\pi\)
0.886455 + 0.462815i \(0.153160\pi\)
\(770\) 1.01573 1.75930i 0.0366043 0.0634006i
\(771\) −6.80194 11.7813i −0.244966 0.424293i
\(772\) −17.7560 −0.639053
\(773\) 10.1969 + 17.6615i 0.366756 + 0.635240i 0.989056 0.147539i \(-0.0471351\pi\)
−0.622300 + 0.782778i \(0.713802\pi\)
\(774\) −1.04892 1.81678i −0.0377026 0.0653027i
\(775\) 31.0388 1.11494
\(776\) 1.06369 + 1.84236i 0.0381841 + 0.0661369i
\(777\) −27.4523 + 47.5488i −0.984847 + 1.70581i
\(778\) 12.5668 21.7663i 0.450542 0.780361i