Properties

Label 210.3.k.b.83.5
Level 210
Weight 3
Character 210.83
Analytic conductor 5.722
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 83.5
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.94039 - 2.28799i) q^{3} +2.00000i q^{4} +(4.58449 - 1.99562i) q^{5} +(0.347606 - 4.22838i) q^{6} +(-4.23091 - 5.57668i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.46981 + 8.87917i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.94039 - 2.28799i) q^{3} +2.00000i q^{4} +(4.58449 - 1.99562i) q^{5} +(0.347606 - 4.22838i) q^{6} +(-4.23091 - 5.57668i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.46981 + 8.87917i) q^{9} +(6.58010 + 2.58887i) q^{10} -14.6047i q^{11} +(4.57598 - 3.88077i) q^{12} +(3.48167 - 3.48167i) q^{13} +(1.34578 - 9.80759i) q^{14} +(-13.4616 - 6.61700i) q^{15} -4.00000 q^{16} +(20.1653 - 20.1653i) q^{17} +(-10.3490 + 7.40936i) q^{18} -26.4132 q^{19} +(3.99123 + 9.16897i) q^{20} +(-4.54981 + 20.5012i) q^{21} +(14.6047 - 14.6047i) q^{22} +(2.68095 - 2.68095i) q^{23} +(8.45675 + 0.695213i) q^{24} +(17.0350 - 18.2978i) q^{25} +6.96334 q^{26} +(23.1675 - 13.8661i) q^{27} +(11.1534 - 8.46182i) q^{28} +28.5159 q^{29} +(-6.84462 - 20.0786i) q^{30} +15.6511i q^{31} +(-4.00000 - 4.00000i) q^{32} +(-33.4154 + 28.3387i) q^{33} +40.3306 q^{34} +(-30.5255 - 17.1230i) q^{35} +(-17.7583 - 2.93962i) q^{36} +(7.69844 - 7.69844i) q^{37} +(-26.4132 - 26.4132i) q^{38} +(-14.7218 - 1.21025i) q^{39} +(-5.17774 + 13.1602i) q^{40} -37.9832 q^{41} +(-25.0510 + 15.9514i) q^{42} +(41.7817 + 41.7817i) q^{43} +29.2094 q^{44} +(10.9811 + 43.6396i) q^{45} +5.36190 q^{46} +(-21.0822 + 21.0822i) q^{47} +(7.76154 + 9.15197i) q^{48} +(-13.1988 + 47.1889i) q^{49} +(35.3328 - 1.26273i) q^{50} +(-85.2664 - 7.00958i) q^{51} +(6.96334 + 6.96334i) q^{52} +(-47.4934 + 47.4934i) q^{53} +(37.0336 + 9.30137i) q^{54} +(-29.1453 - 66.9549i) q^{55} +(19.6152 + 2.69155i) q^{56} +(51.2518 + 60.4332i) q^{57} +(28.5159 + 28.5159i) q^{58} +61.6589i q^{59} +(13.2340 - 26.9232i) q^{60} +54.1777i q^{61} +(-15.6511 + 15.6511i) q^{62} +(55.7350 - 29.3703i) q^{63} -8.00000i q^{64} +(9.01359 - 22.9098i) q^{65} +(-61.7541 - 5.07668i) q^{66} +(68.9882 - 68.9882i) q^{67} +(40.3306 + 40.3306i) q^{68} +(-11.3361 - 0.931915i) q^{69} +(-13.4025 - 47.6484i) q^{70} -65.9594i q^{71} +(-14.8187 - 20.6980i) q^{72} +(-6.51081 + 6.51081i) q^{73} +15.3969 q^{74} +(-74.9196 - 3.47129i) q^{75} -52.8265i q^{76} +(-81.4457 + 61.7911i) q^{77} +(-13.5116 - 15.9321i) q^{78} +42.7301i q^{79} +(-18.3379 + 7.98247i) q^{80} +(-76.6793 - 26.1014i) q^{81} +(-37.9832 - 37.9832i) q^{82} +(-9.52614 - 9.52614i) q^{83} +(-41.0024 - 9.09963i) q^{84} +(52.2053 - 132.690i) q^{85} +83.5634i q^{86} +(-55.3318 - 65.2441i) q^{87} +(29.2094 + 29.2094i) q^{88} -19.3830i q^{89} +(-32.6585 + 54.6207i) q^{90} +(-34.1468 - 4.68555i) q^{91} +(5.36190 + 5.36190i) q^{92} +(35.8096 - 30.3692i) q^{93} -42.1644 q^{94} +(-121.091 + 52.7107i) q^{95} +(-1.39043 + 16.9135i) q^{96} +(84.6391 + 84.6391i) q^{97} +(-60.3877 + 33.9901i) q^{98} +(129.677 + 21.4661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} - 8q^{14} - 4q^{15} - 128q^{16} - 4q^{18} + 12q^{21} - 40q^{22} - 24q^{23} + 16q^{25} - 8q^{28} + 112q^{29} + 28q^{30} - 128q^{32} + 48q^{35} - 40q^{36} + 32q^{37} - 64q^{39} - 20q^{42} - 32q^{43} - 80q^{44} - 48q^{46} + 8q^{50} + 84q^{51} + 136q^{53} + 340q^{57} + 112q^{58} + 64q^{60} + 168q^{63} + 200q^{65} + 32q^{67} - 72q^{72} + 64q^{74} - 88q^{77} - 4q^{78} + 76q^{81} - 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} - 48q^{92} - 388q^{93} - 544q^{95} - 128q^{98} - 160q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) −1.94039 2.28799i −0.646795 0.762664i
\(4\) 2.00000i 0.500000i
\(5\) 4.58449 1.99562i 0.916897 0.399123i
\(6\) 0.347606 4.22838i 0.0579344 0.704729i
\(7\) −4.23091 5.57668i −0.604416 0.796669i
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) −1.46981 + 8.87917i −0.163312 + 0.986574i
\(10\) 6.58010 + 2.58887i 0.658010 + 0.258887i
\(11\) 14.6047i 1.32770i −0.747867 0.663849i \(-0.768922\pi\)
0.747867 0.663849i \(-0.231078\pi\)
\(12\) 4.57598 3.88077i 0.381332 0.323398i
\(13\) 3.48167 3.48167i 0.267821 0.267821i −0.560401 0.828222i \(-0.689353\pi\)
0.828222 + 0.560401i \(0.189353\pi\)
\(14\) 1.34578 9.80759i 0.0961268 0.700542i
\(15\) −13.4616 6.61700i −0.897442 0.441133i
\(16\) −4.00000 −0.250000
\(17\) 20.1653 20.1653i 1.18619 1.18619i 0.208081 0.978112i \(-0.433278\pi\)
0.978112 0.208081i \(-0.0667219\pi\)
\(18\) −10.3490 + 7.40936i −0.574943 + 0.411631i
\(19\) −26.4132 −1.39017 −0.695085 0.718928i \(-0.744633\pi\)
−0.695085 + 0.718928i \(0.744633\pi\)
\(20\) 3.99123 + 9.16897i 0.199562 + 0.458449i
\(21\) −4.54981 + 20.5012i −0.216658 + 0.976248i
\(22\) 14.6047 14.6047i 0.663849 0.663849i
\(23\) 2.68095 2.68095i 0.116563 0.116563i −0.646419 0.762982i \(-0.723734\pi\)
0.762982 + 0.646419i \(0.223734\pi\)
\(24\) 8.45675 + 0.695213i 0.352365 + 0.0289672i
\(25\) 17.0350 18.2978i 0.681401 0.731910i
\(26\) 6.96334 0.267821
\(27\) 23.1675 13.8661i 0.858054 0.513559i
\(28\) 11.1534 8.46182i 0.398335 0.302208i
\(29\) 28.5159 0.983306 0.491653 0.870791i \(-0.336393\pi\)
0.491653 + 0.870791i \(0.336393\pi\)
\(30\) −6.84462 20.0786i −0.228154 0.669287i
\(31\) 15.6511i 0.504875i 0.967613 + 0.252438i \(0.0812322\pi\)
−0.967613 + 0.252438i \(0.918768\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −33.4154 + 28.3387i −1.01259 + 0.858748i
\(34\) 40.3306 1.18619
\(35\) −30.5255 17.1230i −0.872156 0.489227i
\(36\) −17.7583 2.93962i −0.493287 0.0816562i
\(37\) 7.69844 7.69844i 0.208066 0.208066i −0.595379 0.803445i \(-0.702998\pi\)
0.803445 + 0.595379i \(0.202998\pi\)
\(38\) −26.4132 26.4132i −0.695085 0.695085i
\(39\) −14.7218 1.21025i −0.377483 0.0310321i
\(40\) −5.17774 + 13.1602i −0.129443 + 0.329005i
\(41\) −37.9832 −0.926419 −0.463209 0.886249i \(-0.653302\pi\)
−0.463209 + 0.886249i \(0.653302\pi\)
\(42\) −25.0510 + 15.9514i −0.596453 + 0.379795i
\(43\) 41.7817 + 41.7817i 0.971667 + 0.971667i 0.999610 0.0279426i \(-0.00889555\pi\)
−0.0279426 + 0.999610i \(0.508896\pi\)
\(44\) 29.2094 0.663849
\(45\) 10.9811 + 43.6396i 0.244024 + 0.969769i
\(46\) 5.36190 0.116563
\(47\) −21.0822 + 21.0822i −0.448558 + 0.448558i −0.894875 0.446317i \(-0.852735\pi\)
0.446317 + 0.894875i \(0.352735\pi\)
\(48\) 7.76154 + 9.15197i 0.161699 + 0.190666i
\(49\) −13.1988 + 47.1889i −0.269364 + 0.963039i
\(50\) 35.3328 1.26273i 0.706656 0.0252547i
\(51\) −85.2664 7.00958i −1.67189 0.137443i
\(52\) 6.96334 + 6.96334i 0.133910 + 0.133910i
\(53\) −47.4934 + 47.4934i −0.896102 + 0.896102i −0.995089 0.0989866i \(-0.968440\pi\)
0.0989866 + 0.995089i \(0.468440\pi\)
\(54\) 37.0336 + 9.30137i 0.685807 + 0.172248i
\(55\) −29.1453 66.9549i −0.529915 1.21736i
\(56\) 19.6152 + 2.69155i 0.350271 + 0.0480634i
\(57\) 51.2518 + 60.4332i 0.899155 + 1.06023i
\(58\) 28.5159 + 28.5159i 0.491653 + 0.491653i
\(59\) 61.6589i 1.04507i 0.852619 + 0.522533i \(0.175013\pi\)
−0.852619 + 0.522533i \(0.824987\pi\)
\(60\) 13.2340 26.9232i 0.220567 0.448721i
\(61\) 54.1777i 0.888159i 0.895987 + 0.444080i \(0.146469\pi\)
−0.895987 + 0.444080i \(0.853531\pi\)
\(62\) −15.6511 + 15.6511i −0.252438 + 0.252438i
\(63\) 55.7350 29.3703i 0.884682 0.466195i
\(64\) 8.00000i 0.125000i
\(65\) 9.01359 22.9098i 0.138671 0.352458i
\(66\) −61.7541 5.07668i −0.935668 0.0769194i
\(67\) 68.9882 68.9882i 1.02967 1.02967i 0.0301280 0.999546i \(-0.490409\pi\)
0.999546 0.0301280i \(-0.00959148\pi\)
\(68\) 40.3306 + 40.3306i 0.593096 + 0.593096i
\(69\) −11.3361 0.931915i −0.164291 0.0135060i
\(70\) −13.4025 47.6484i −0.191465 0.680692i
\(71\) 65.9594i 0.929006i −0.885572 0.464503i \(-0.846233\pi\)
0.885572 0.464503i \(-0.153767\pi\)
\(72\) −14.8187 20.6980i −0.205816 0.287472i
\(73\) −6.51081 + 6.51081i −0.0891892 + 0.0891892i −0.750294 0.661105i \(-0.770088\pi\)
0.661105 + 0.750294i \(0.270088\pi\)
\(74\) 15.3969 0.208066
\(75\) −74.9196 3.47129i −0.998928 0.0462839i
\(76\) 52.8265i 0.695085i
\(77\) −81.4457 + 61.7911i −1.05774 + 0.802481i
\(78\) −13.5116 15.9321i −0.173225 0.204257i
\(79\) 42.7301i 0.540887i 0.962736 + 0.270443i \(0.0871703\pi\)
−0.962736 + 0.270443i \(0.912830\pi\)
\(80\) −18.3379 + 7.98247i −0.229224 + 0.0997809i
\(81\) −76.6793 26.1014i −0.946658 0.322240i
\(82\) −37.9832 37.9832i −0.463209 0.463209i
\(83\) −9.52614 9.52614i −0.114773 0.114773i 0.647388 0.762161i \(-0.275861\pi\)
−0.762161 + 0.647388i \(0.775861\pi\)
\(84\) −41.0024 9.09963i −0.488124 0.108329i
\(85\) 52.2053 132.690i 0.614180 1.56105i
\(86\) 83.5634i 0.971667i
\(87\) −55.3318 65.2441i −0.635998 0.749932i
\(88\) 29.2094 + 29.2094i 0.331924 + 0.331924i
\(89\) 19.3830i 0.217786i −0.994053 0.108893i \(-0.965269\pi\)
0.994053 0.108893i \(-0.0347306\pi\)
\(90\) −32.6585 + 54.6207i −0.362872 + 0.606897i
\(91\) −34.1468 4.68555i −0.375240 0.0514895i
\(92\) 5.36190 + 5.36190i 0.0582815 + 0.0582815i
\(93\) 35.8096 30.3692i 0.385050 0.326551i
\(94\) −42.1644 −0.448558
\(95\) −121.091 + 52.7107i −1.27464 + 0.554849i
\(96\) −1.39043 + 16.9135i −0.0144836 + 0.176182i
\(97\) 84.6391 + 84.6391i 0.872568 + 0.872568i 0.992752 0.120184i \(-0.0383484\pi\)
−0.120184 + 0.992752i \(0.538348\pi\)
\(98\) −60.3877 + 33.9901i −0.616201 + 0.346837i
\(99\) 129.677 + 21.4661i 1.30987 + 0.216829i
\(100\) 36.5955 + 34.0700i 0.365955 + 0.340700i
\(101\) 112.859 1.11741 0.558707 0.829365i \(-0.311298\pi\)
0.558707 + 0.829365i \(0.311298\pi\)
\(102\) −78.2568 92.2760i −0.767224 0.904666i
\(103\) 82.5883 82.5883i 0.801828 0.801828i −0.181553 0.983381i \(-0.558112\pi\)
0.983381 + 0.181553i \(0.0581123\pi\)
\(104\) 13.9267i 0.133910i
\(105\) 20.0540 + 103.067i 0.190990 + 0.981592i
\(106\) −94.9868 −0.896102
\(107\) 125.554 + 125.554i 1.17340 + 1.17340i 0.981393 + 0.192011i \(0.0615011\pi\)
0.192011 + 0.981393i \(0.438499\pi\)
\(108\) 27.7322 + 46.3349i 0.256780 + 0.429027i
\(109\) 1.60754i 0.0147481i −0.999973 0.00737405i \(-0.997653\pi\)
0.999973 0.00737405i \(-0.00234725\pi\)
\(110\) 37.8096 96.1003i 0.343724 0.873639i
\(111\) −32.5519 2.67603i −0.293261 0.0241084i
\(112\) 16.9236 + 22.3067i 0.151104 + 0.199167i
\(113\) 141.505 141.505i 1.25226 1.25226i 0.297556 0.954704i \(-0.403828\pi\)
0.954704 0.297556i \(-0.0961715\pi\)
\(114\) −9.18141 + 111.685i −0.0805387 + 0.979694i
\(115\) 6.94062 17.6409i 0.0603532 0.153399i
\(116\) 57.0318i 0.491653i
\(117\) 25.7970 + 36.0318i 0.220487 + 0.307964i
\(118\) −61.6589 + 61.6589i −0.522533 + 0.522533i
\(119\) −197.773 27.1379i −1.66196 0.228050i
\(120\) 40.1572 13.6892i 0.334644 0.114077i
\(121\) −92.2966 −0.762782
\(122\) −54.1777 + 54.1777i −0.444080 + 0.444080i
\(123\) 73.7020 + 86.9052i 0.599203 + 0.706546i
\(124\) −31.3023 −0.252438
\(125\) 41.5815 117.881i 0.332652 0.943050i
\(126\) 85.1053 + 26.3647i 0.675439 + 0.209243i
\(127\) −39.5166 + 39.5166i −0.311154 + 0.311154i −0.845357 0.534202i \(-0.820612\pi\)
0.534202 + 0.845357i \(0.320612\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 14.5236 176.669i 0.112586 1.36952i
\(130\) 31.9234 13.8962i 0.245564 0.106894i
\(131\) 122.046 0.931652 0.465826 0.884876i \(-0.345757\pi\)
0.465826 + 0.884876i \(0.345757\pi\)
\(132\) −56.6774 66.8308i −0.429374 0.506294i
\(133\) 111.752 + 147.298i 0.840240 + 1.10751i
\(134\) 137.976 1.02967
\(135\) 78.5395 109.802i 0.581774 0.813350i
\(136\) 80.6611i 0.593096i
\(137\) −141.949 141.949i −1.03612 1.03612i −0.999323 0.0368001i \(-0.988284\pi\)
−0.0368001 0.999323i \(-0.511716\pi\)
\(138\) −10.4041 12.2680i −0.0753924 0.0888984i
\(139\) −41.4554 −0.298240 −0.149120 0.988819i \(-0.547644\pi\)
−0.149120 + 0.988819i \(0.547644\pi\)
\(140\) 34.2459 61.0509i 0.244614 0.436078i
\(141\) 89.1435 + 7.32831i 0.632224 + 0.0519739i
\(142\) 65.9594 65.9594i 0.464503 0.464503i
\(143\) −50.8487 50.8487i −0.355585 0.355585i
\(144\) 5.87924 35.5167i 0.0408281 0.246644i
\(145\) 130.731 56.9068i 0.901591 0.392461i
\(146\) −13.0216 −0.0891892
\(147\) 133.579 61.3658i 0.908698 0.417455i
\(148\) 15.3969 + 15.3969i 0.104033 + 0.104033i
\(149\) −189.375 −1.27097 −0.635485 0.772113i \(-0.719200\pi\)
−0.635485 + 0.772113i \(0.719200\pi\)
\(150\) −71.4483 78.3909i −0.476322 0.522606i
\(151\) −117.328 −0.777007 −0.388503 0.921447i \(-0.627008\pi\)
−0.388503 + 0.921447i \(0.627008\pi\)
\(152\) 52.8265 52.8265i 0.347542 0.347542i
\(153\) 149.412 + 208.690i 0.976548 + 1.36399i
\(154\) −143.237 19.6546i −0.930109 0.127627i
\(155\) 31.2337 + 71.7524i 0.201507 + 0.462919i
\(156\) 2.42050 29.4436i 0.0155160 0.188741i
\(157\) 123.504 + 123.504i 0.786651 + 0.786651i 0.980944 0.194293i \(-0.0622411\pi\)
−0.194293 + 0.980944i \(0.562241\pi\)
\(158\) −42.7301 + 42.7301i −0.270443 + 0.270443i
\(159\) 200.820 + 16.5090i 1.26302 + 0.103830i
\(160\) −26.3204 10.3555i −0.164503 0.0647217i
\(161\) −26.2937 3.60795i −0.163315 0.0224096i
\(162\) −50.5779 102.781i −0.312209 0.634449i
\(163\) −173.541 173.541i −1.06467 1.06467i −0.997759 0.0669121i \(-0.978685\pi\)
−0.0669121 0.997759i \(-0.521315\pi\)
\(164\) 75.9663i 0.463209i
\(165\) −96.6391 + 196.603i −0.585692 + 1.19153i
\(166\) 19.0523i 0.114773i
\(167\) 32.6021 32.6021i 0.195222 0.195222i −0.602726 0.797948i \(-0.705919\pi\)
0.797948 + 0.602726i \(0.205919\pi\)
\(168\) −31.9028 50.1020i −0.189897 0.298226i
\(169\) 144.756i 0.856544i
\(170\) 184.895 80.4844i 1.08762 0.473437i
\(171\) 38.8225 234.528i 0.227032 1.37151i
\(172\) −83.5634 + 83.5634i −0.485833 + 0.485833i
\(173\) −122.097 122.097i −0.705761 0.705761i 0.259880 0.965641i \(-0.416317\pi\)
−0.965641 + 0.259880i \(0.916317\pi\)
\(174\) 9.91231 120.576i 0.0569673 0.692965i
\(175\) −174.114 17.5828i −0.994940 0.100473i
\(176\) 58.4187i 0.331924i
\(177\) 141.075 119.642i 0.797034 0.675943i
\(178\) 19.3830 19.3830i 0.108893 0.108893i
\(179\) 48.8414 0.272857 0.136429 0.990650i \(-0.456438\pi\)
0.136429 + 0.990650i \(0.456438\pi\)
\(180\) −87.2792 + 21.9622i −0.484885 + 0.122012i
\(181\) 74.5578i 0.411921i 0.978560 + 0.205961i \(0.0660319\pi\)
−0.978560 + 0.205961i \(0.933968\pi\)
\(182\) −29.4613 38.8324i −0.161875 0.213365i
\(183\) 123.958 105.126i 0.677367 0.574457i
\(184\) 10.7238i 0.0582815i
\(185\) 19.9303 50.6565i 0.107731 0.273819i
\(186\) 66.1789 + 5.44043i 0.355800 + 0.0292496i
\(187\) −294.507 294.507i −1.57491 1.57491i
\(188\) −42.1644 42.1644i −0.224279 0.224279i
\(189\) −175.346 70.5315i −0.927758 0.373182i
\(190\) −173.802 68.3804i −0.914746 0.359897i
\(191\) 22.0006i 0.115187i −0.998340 0.0575933i \(-0.981657\pi\)
0.998340 0.0575933i \(-0.0183427\pi\)
\(192\) −18.3039 + 15.5231i −0.0953330 + 0.0808494i
\(193\) −73.7660 73.7660i −0.382207 0.382207i 0.489690 0.871897i \(-0.337110\pi\)
−0.871897 + 0.489690i \(0.837110\pi\)
\(194\) 169.278i 0.872568i
\(195\) −69.9072 + 23.8307i −0.358498 + 0.122209i
\(196\) −94.3778 26.3976i −0.481519 0.134682i
\(197\) 124.480 + 124.480i 0.631878 + 0.631878i 0.948539 0.316661i \(-0.102562\pi\)
−0.316661 + 0.948539i \(0.602562\pi\)
\(198\) 108.211 + 151.144i 0.546522 + 0.763351i
\(199\) 324.188 1.62908 0.814542 0.580104i \(-0.196988\pi\)
0.814542 + 0.580104i \(0.196988\pi\)
\(200\) 2.52547 + 70.6656i 0.0126273 + 0.353328i
\(201\) −291.708 23.9807i −1.45128 0.119307i
\(202\) 112.859 + 112.859i 0.558707 + 0.558707i
\(203\) −120.648 159.024i −0.594326 0.783370i
\(204\) 14.0192 170.533i 0.0687214 0.835945i
\(205\) −174.133 + 75.7999i −0.849431 + 0.369755i
\(206\) 165.177 0.801828
\(207\) 19.8641 + 27.7451i 0.0959619 + 0.134034i
\(208\) −13.9267 + 13.9267i −0.0669552 + 0.0669552i
\(209\) 385.757i 1.84573i
\(210\) −83.0132 + 123.121i −0.395301 + 0.586291i
\(211\) 29.3640 0.139166 0.0695828 0.997576i \(-0.477833\pi\)
0.0695828 + 0.997576i \(0.477833\pi\)
\(212\) −94.9868 94.9868i −0.448051 0.448051i
\(213\) −150.915 + 127.987i −0.708519 + 0.600876i
\(214\) 251.108i 1.17340i
\(215\) 274.928 + 108.167i 1.27873 + 0.503104i
\(216\) −18.6027 + 74.0671i −0.0861238 + 0.342903i
\(217\) 87.2814 66.2185i 0.402218 0.305154i
\(218\) 1.60754 1.60754i 0.00737405 0.00737405i
\(219\) 27.5302 + 2.26320i 0.125709 + 0.0103342i
\(220\) 133.910 58.2907i 0.608681 0.264958i
\(221\) 140.418i 0.635375i
\(222\) −29.8759 35.2279i −0.134576 0.158684i
\(223\) 203.552 203.552i 0.912788 0.912788i −0.0837032 0.996491i \(-0.526675\pi\)
0.996491 + 0.0837032i \(0.0266748\pi\)
\(224\) −5.38310 + 39.2304i −0.0240317 + 0.175136i
\(225\) 137.431 + 178.151i 0.610803 + 0.791783i
\(226\) 283.011 1.25226
\(227\) −152.211 + 152.211i −0.670535 + 0.670535i −0.957839 0.287305i \(-0.907241\pi\)
0.287305 + 0.957839i \(0.407241\pi\)
\(228\) −120.866 + 102.504i −0.530116 + 0.449577i
\(229\) −219.445 −0.958275 −0.479138 0.877740i \(-0.659051\pi\)
−0.479138 + 0.877740i \(0.659051\pi\)
\(230\) 24.5815 10.7003i 0.106876 0.0465230i
\(231\) 299.413 + 66.4486i 1.29616 + 0.287656i
\(232\) −57.0318 + 57.0318i −0.245827 + 0.245827i
\(233\) 216.913 216.913i 0.930957 0.930957i −0.0668091 0.997766i \(-0.521282\pi\)
0.997766 + 0.0668091i \(0.0212819\pi\)
\(234\) −10.2348 + 61.8287i −0.0437385 + 0.264225i
\(235\) −54.5791 + 138.723i −0.232251 + 0.590311i
\(236\) −123.318 −0.522533
\(237\) 97.7660 82.9128i 0.412515 0.349843i
\(238\) −170.635 224.911i −0.716953 0.945003i
\(239\) 261.894 1.09579 0.547896 0.836547i \(-0.315429\pi\)
0.547896 + 0.836547i \(0.315429\pi\)
\(240\) 53.8465 + 26.4680i 0.224360 + 0.110283i
\(241\) 187.969i 0.779955i 0.920824 + 0.389978i \(0.127517\pi\)
−0.920824 + 0.389978i \(0.872483\pi\)
\(242\) −92.2966 92.2966i −0.381391 0.381391i
\(243\) 89.0676 + 226.088i 0.366533 + 0.930405i
\(244\) −108.355 −0.444080
\(245\) 33.6612 + 242.677i 0.137393 + 0.990517i
\(246\) −13.2032 + 160.607i −0.0536715 + 0.652875i
\(247\) −91.9622 + 91.9622i −0.372317 + 0.372317i
\(248\) −31.3023 31.3023i −0.126219 0.126219i
\(249\) −3.31135 + 40.2801i −0.0132986 + 0.161768i
\(250\) 159.463 76.2997i 0.637851 0.305199i
\(251\) −406.255 −1.61855 −0.809273 0.587433i \(-0.800139\pi\)
−0.809273 + 0.587433i \(0.800139\pi\)
\(252\) 58.7406 + 111.470i 0.233098 + 0.442341i
\(253\) −39.1544 39.1544i −0.154760 0.154760i
\(254\) −79.0332 −0.311154
\(255\) −404.891 + 138.024i −1.58781 + 0.541270i
\(256\) 16.0000 0.0625000
\(257\) 55.7465 55.7465i 0.216912 0.216912i −0.590284 0.807196i \(-0.700984\pi\)
0.807196 + 0.590284i \(0.200984\pi\)
\(258\) 191.192 162.145i 0.741055 0.628469i
\(259\) −75.5032 10.3604i −0.291518 0.0400014i
\(260\) 45.8195 + 18.0272i 0.176229 + 0.0693353i
\(261\) −41.9130 + 253.197i −0.160586 + 0.970105i
\(262\) 122.046 + 122.046i 0.465826 + 0.465826i
\(263\) −96.5716 + 96.5716i −0.367192 + 0.367192i −0.866452 0.499260i \(-0.833605\pi\)
0.499260 + 0.866452i \(0.333605\pi\)
\(264\) 10.1534 123.508i 0.0384597 0.467834i
\(265\) −122.954 + 312.512i −0.463978 + 1.17929i
\(266\) −35.5463 + 259.050i −0.133633 + 0.973873i
\(267\) −44.3481 + 37.6105i −0.166098 + 0.140863i
\(268\) 137.976 + 137.976i 0.514837 + 0.514837i
\(269\) 100.672i 0.374246i 0.982336 + 0.187123i \(0.0599163\pi\)
−0.982336 + 0.187123i \(0.940084\pi\)
\(270\) 188.342 31.2628i 0.697562 0.115788i
\(271\) 299.070i 1.10358i 0.833983 + 0.551790i \(0.186055\pi\)
−0.833983 + 0.551790i \(0.813945\pi\)
\(272\) −80.6611 + 80.6611i −0.296548 + 0.296548i
\(273\) 55.5375 + 87.2194i 0.203434 + 0.319485i
\(274\) 283.898i 1.03612i
\(275\) −267.233 248.791i −0.971756 0.904695i
\(276\) 1.86383 22.6721i 0.00675301 0.0821454i
\(277\) −310.502 + 310.502i −1.12095 + 1.12095i −0.129348 + 0.991599i \(0.541288\pi\)
−0.991599 + 0.129348i \(0.958712\pi\)
\(278\) −41.4554 41.4554i −0.149120 0.149120i
\(279\) −138.969 23.0042i −0.498097 0.0824523i
\(280\) 95.2969 26.8050i 0.340346 0.0957323i
\(281\) 229.692i 0.817409i −0.912667 0.408704i \(-0.865981\pi\)
0.912667 0.408704i \(-0.134019\pi\)
\(282\) 81.8152 + 96.4718i 0.290125 + 0.342099i
\(283\) −170.587 + 170.587i −0.602781 + 0.602781i −0.941049 0.338269i \(-0.890159\pi\)
0.338269 + 0.941049i \(0.390159\pi\)
\(284\) 131.919 0.464503
\(285\) 355.565 + 174.776i 1.24760 + 0.613250i
\(286\) 101.697i 0.355585i
\(287\) 160.703 + 211.820i 0.559942 + 0.738049i
\(288\) 41.3959 29.6374i 0.143736 0.102908i
\(289\) 524.277i 1.81411i
\(290\) 187.637 + 73.8239i 0.647026 + 0.254565i
\(291\) 29.4211 357.886i 0.101103 1.22985i
\(292\) −13.0216 13.0216i −0.0445946 0.0445946i
\(293\) −186.419 186.419i −0.636243 0.636243i 0.313384 0.949627i \(-0.398537\pi\)
−0.949627 + 0.313384i \(0.898537\pi\)
\(294\) 194.944 + 72.2127i 0.663076 + 0.245622i
\(295\) 123.047 + 282.674i 0.417110 + 0.958218i
\(296\) 30.7938i 0.104033i
\(297\) −202.510 338.353i −0.681851 1.13924i
\(298\) −189.375 189.375i −0.635485 0.635485i
\(299\) 18.6684i 0.0624360i
\(300\) 6.94259 149.839i 0.0231420 0.499464i
\(301\) 56.2287 409.778i 0.186806 1.36139i
\(302\) −117.328 117.328i −0.388503 0.388503i
\(303\) −218.990 258.220i −0.722738 0.852211i
\(304\) 105.653 0.347542
\(305\) 108.118 + 248.377i 0.354485 + 0.814351i
\(306\) −59.2783 + 358.102i −0.193720 + 1.17027i
\(307\) 9.77168 + 9.77168i 0.0318296 + 0.0318296i 0.722842 0.691013i \(-0.242835\pi\)
−0.691013 + 0.722842i \(0.742835\pi\)
\(308\) −123.582 162.891i −0.401241 0.528868i
\(309\) −349.215 28.7082i −1.13014 0.0929069i
\(310\) −40.5187 + 102.986i −0.130706 + 0.332213i
\(311\) 145.632 0.468271 0.234136 0.972204i \(-0.424774\pi\)
0.234136 + 0.972204i \(0.424774\pi\)
\(312\) 31.8641 27.0231i 0.102129 0.0866126i
\(313\) −354.096 + 354.096i −1.13130 + 1.13130i −0.141335 + 0.989962i \(0.545139\pi\)
−0.989962 + 0.141335i \(0.954861\pi\)
\(314\) 247.008i 0.786651i
\(315\) 196.904 245.873i 0.625093 0.780550i
\(316\) −85.4601 −0.270443
\(317\) 136.486 + 136.486i 0.430556 + 0.430556i 0.888817 0.458262i \(-0.151528\pi\)
−0.458262 + 0.888817i \(0.651528\pi\)
\(318\) 184.311 + 217.329i 0.579594 + 0.683425i
\(319\) 416.465i 1.30553i
\(320\) −15.9649 36.6759i −0.0498904 0.114612i
\(321\) 43.6435 530.891i 0.135961 1.65386i
\(322\) −22.6857 29.9016i −0.0704525 0.0928621i
\(323\) −532.630 + 532.630i −1.64901 + 1.64901i
\(324\) 52.2028 153.359i 0.161120 0.473329i
\(325\) −4.39643 123.017i −0.0135275 0.378514i
\(326\) 347.083i 1.06467i
\(327\) −3.67804 + 3.11925i −0.0112478 + 0.00953899i
\(328\) 75.9663 75.9663i 0.231605 0.231605i
\(329\) 206.766 + 28.3719i 0.628467 + 0.0862368i
\(330\) −293.242 + 99.9635i −0.888612 + 0.302920i
\(331\) 317.945 0.960559 0.480279 0.877116i \(-0.340535\pi\)
0.480279 + 0.877116i \(0.340535\pi\)
\(332\) 19.0523 19.0523i 0.0573864 0.0573864i
\(333\) 57.0405 + 79.6710i 0.171293 + 0.239252i
\(334\) 65.2042 0.195222
\(335\) 178.601 453.949i 0.533138 1.35507i
\(336\) 18.1993 82.0048i 0.0541644 0.244062i
\(337\) 95.8647 95.8647i 0.284465 0.284465i −0.550422 0.834887i \(-0.685533\pi\)
0.834887 + 0.550422i \(0.185533\pi\)
\(338\) −144.756 + 144.756i −0.428272 + 0.428272i
\(339\) −598.338 49.1882i −1.76501 0.145098i
\(340\) 265.379 + 104.411i 0.780527 + 0.307090i
\(341\) 228.580 0.670322
\(342\) 273.350 195.705i 0.799269 0.572237i
\(343\) 319.001 126.046i 0.930031 0.367482i
\(344\) −167.127 −0.485833
\(345\) −53.8298 + 18.3501i −0.156028 + 0.0531886i
\(346\) 244.193i 0.705761i
\(347\) 76.3053 + 76.3053i 0.219900 + 0.219900i 0.808456 0.588556i \(-0.200303\pi\)
−0.588556 + 0.808456i \(0.700303\pi\)
\(348\) 130.488 110.664i 0.374966 0.317999i
\(349\) 27.7850 0.0796133 0.0398067 0.999207i \(-0.487326\pi\)
0.0398067 + 0.999207i \(0.487326\pi\)
\(350\) −156.532 191.697i −0.447233 0.547706i
\(351\) 32.3843 128.939i 0.0922630 0.367347i
\(352\) −58.4187 + 58.4187i −0.165962 + 0.165962i
\(353\) −188.774 188.774i −0.534769 0.534769i 0.387218 0.921988i \(-0.373436\pi\)
−0.921988 + 0.387218i \(0.873436\pi\)
\(354\) 260.717 + 21.4330i 0.736488 + 0.0605452i
\(355\) −131.630 302.390i −0.370788 0.851803i
\(356\) 38.7660 0.108893
\(357\) 321.664 + 505.161i 0.901020 + 1.41502i
\(358\) 48.8414 + 48.8414i 0.136429 + 0.136429i
\(359\) −171.974 −0.479037 −0.239519 0.970892i \(-0.576990\pi\)
−0.239519 + 0.970892i \(0.576990\pi\)
\(360\) −109.241 65.3170i −0.303448 0.181436i
\(361\) 336.659 0.932572
\(362\) −74.5578 + 74.5578i −0.205961 + 0.205961i
\(363\) 179.091 + 211.174i 0.493364 + 0.581746i
\(364\) 9.37109 68.2936i 0.0257448 0.187620i
\(365\) −16.8556 + 42.8418i −0.0461798 + 0.117375i
\(366\) 229.084 + 18.8325i 0.625912 + 0.0514550i
\(367\) 181.555 + 181.555i 0.494700 + 0.494700i 0.909784 0.415083i \(-0.136247\pi\)
−0.415083 + 0.909784i \(0.636247\pi\)
\(368\) −10.7238 + 10.7238i −0.0291407 + 0.0291407i
\(369\) 55.8281 337.259i 0.151296 0.913981i
\(370\) 70.5868 30.7263i 0.190775 0.0830440i
\(371\) 465.796 + 63.9154i 1.25552 + 0.172279i
\(372\) 60.7384 + 71.6193i 0.163275 + 0.192525i
\(373\) −104.153 104.153i −0.279231 0.279231i 0.553571 0.832802i \(-0.313265\pi\)
−0.832802 + 0.553571i \(0.813265\pi\)
\(374\) 589.015i 1.57491i
\(375\) −350.395 + 133.597i −0.934388 + 0.356258i
\(376\) 84.3288i 0.224279i
\(377\) 99.2830 99.2830i 0.263350 0.263350i
\(378\) −104.815 245.878i −0.277288 0.650470i
\(379\) 339.431i 0.895596i 0.894135 + 0.447798i \(0.147792\pi\)
−0.894135 + 0.447798i \(0.852208\pi\)
\(380\) −105.421 242.182i −0.277425 0.637321i
\(381\) 167.091 + 13.7362i 0.438559 + 0.0360531i
\(382\) 22.0006 22.0006i 0.0575933 0.0575933i
\(383\) 187.161 + 187.161i 0.488670 + 0.488670i 0.907886 0.419217i \(-0.137695\pi\)
−0.419217 + 0.907886i \(0.637695\pi\)
\(384\) −33.8270 2.78085i −0.0880912 0.00724180i
\(385\) −250.075 + 445.815i −0.649546 + 1.15796i
\(386\) 147.532i 0.382207i
\(387\) −432.398 + 309.575i −1.11731 + 0.799937i
\(388\) −169.278 + 169.278i −0.436284 + 0.436284i
\(389\) 511.312 1.31443 0.657214 0.753704i \(-0.271735\pi\)
0.657214 + 0.753704i \(0.271735\pi\)
\(390\) −93.7379 46.0764i −0.240354 0.118145i
\(391\) 108.124i 0.276532i
\(392\) −67.9801 120.775i −0.173419 0.308101i
\(393\) −236.817 279.241i −0.602588 0.710537i
\(394\) 248.960i 0.631878i
\(395\) 85.2729 + 195.895i 0.215881 + 0.495938i
\(396\) −42.9322 + 259.355i −0.108415 + 0.654936i
\(397\) −448.583 448.583i −1.12993 1.12993i −0.990188 0.139744i \(-0.955372\pi\)
−0.139744 0.990188i \(-0.544628\pi\)
\(398\) 324.188 + 324.188i 0.814542 + 0.814542i
\(399\) 120.175 541.503i 0.301191 1.35715i
\(400\) −68.1401 + 73.1910i −0.170350 + 0.182978i
\(401\) 44.3430i 0.110581i 0.998470 + 0.0552905i \(0.0176085\pi\)
−0.998470 + 0.0552905i \(0.982391\pi\)
\(402\) −267.727 315.689i −0.665988 0.785295i
\(403\) 54.4921 + 54.4921i 0.135216 + 0.135216i
\(404\) 225.718i 0.558707i
\(405\) −403.624 + 33.3610i −0.996602 + 0.0823729i
\(406\) 38.3760 279.672i 0.0945221 0.688848i
\(407\) −112.433 112.433i −0.276249 0.276249i
\(408\) 184.552 156.514i 0.452333 0.383612i
\(409\) 392.358 0.959311 0.479656 0.877457i \(-0.340762\pi\)
0.479656 + 0.877457i \(0.340762\pi\)
\(410\) −249.933 98.3335i −0.609593 0.239838i
\(411\) −49.3423 + 600.213i −0.120054 + 1.46037i
\(412\) 165.177 + 165.177i 0.400914 + 0.400914i
\(413\) 343.852 260.873i 0.832571 0.631654i
\(414\) −7.88097 + 47.6092i −0.0190362 + 0.114998i
\(415\) −62.6830 24.6619i −0.151043 0.0594263i
\(416\) −27.8534 −0.0669552
\(417\) 80.4394 + 94.8495i 0.192900 + 0.227457i
\(418\) −385.757 + 385.757i −0.922863 + 0.922863i
\(419\) 383.324i 0.914855i −0.889247 0.457427i \(-0.848771\pi\)
0.889247 0.457427i \(-0.151229\pi\)
\(420\) −206.134 + 40.1080i −0.490796 + 0.0954952i
\(421\) 809.373 1.92250 0.961250 0.275678i \(-0.0889023\pi\)
0.961250 + 0.275678i \(0.0889023\pi\)
\(422\) 29.3640 + 29.3640i 0.0695828 + 0.0695828i
\(423\) −156.206 218.179i −0.369281 0.515791i
\(424\) 189.974i 0.448051i
\(425\) −25.4634 712.495i −0.0599139 1.67646i
\(426\) −278.901 22.9279i −0.654698 0.0538214i
\(427\) 302.132 229.221i 0.707569 0.536817i
\(428\) −251.108 + 251.108i −0.586702 + 0.586702i
\(429\) −17.6753 + 215.007i −0.0412012 + 0.501183i
\(430\) 166.760 + 383.095i 0.387815 + 0.890919i
\(431\) 432.674i 1.00388i 0.864902 + 0.501942i \(0.167381\pi\)
−0.864902 + 0.501942i \(0.832619\pi\)
\(432\) −92.6699 + 55.4644i −0.214514 + 0.128390i
\(433\) 288.449 288.449i 0.666163 0.666163i −0.290662 0.956826i \(-0.593876\pi\)
0.956826 + 0.290662i \(0.0938756\pi\)
\(434\) 153.500 + 21.0629i 0.353686 + 0.0485320i
\(435\) −383.870 188.690i −0.882460 0.433769i
\(436\) 3.21508 0.00737405
\(437\) −70.8125 + 70.8125i −0.162042 + 0.162042i
\(438\) 25.2670 + 29.7934i 0.0576871 + 0.0680214i
\(439\) 652.665 1.48671 0.743354 0.668898i \(-0.233234\pi\)
0.743354 + 0.668898i \(0.233234\pi\)
\(440\) 192.201 + 75.6192i 0.436819 + 0.171862i
\(441\) −399.598 186.553i −0.906119 0.423023i
\(442\) 140.418 140.418i 0.317687 0.317687i
\(443\) −429.708 + 429.708i −0.969996 + 0.969996i −0.999563 0.0295673i \(-0.990587\pi\)
0.0295673 + 0.999563i \(0.490587\pi\)
\(444\) 5.35206 65.1038i 0.0120542 0.146630i
\(445\) −38.6810 88.8610i −0.0869236 0.199688i
\(446\) 407.103 0.912788
\(447\) 367.460 + 433.287i 0.822057 + 0.969323i
\(448\) −44.6135 + 33.8473i −0.0995836 + 0.0755519i
\(449\) −544.342 −1.21234 −0.606171 0.795334i \(-0.707295\pi\)
−0.606171 + 0.795334i \(0.707295\pi\)
\(450\) −40.7205 + 315.582i −0.0904900 + 0.701293i
\(451\) 554.732i 1.23000i
\(452\) 283.011 + 283.011i 0.626130 + 0.626130i
\(453\) 227.662 + 268.446i 0.502564 + 0.592595i
\(454\) −304.423 −0.670535
\(455\) −165.896 + 46.6632i −0.364607 + 0.102556i
\(456\) −223.370 18.3628i −0.489847 0.0402693i
\(457\) −100.300 + 100.300i −0.219475 + 0.219475i −0.808277 0.588802i \(-0.799600\pi\)
0.588802 + 0.808277i \(0.299600\pi\)
\(458\) −219.445 219.445i −0.479138 0.479138i
\(459\) 187.565 746.792i 0.408638 1.62700i
\(460\) 35.2818 + 13.8812i 0.0766996 + 0.0301766i
\(461\) 16.3102 0.0353801 0.0176900 0.999844i \(-0.494369\pi\)
0.0176900 + 0.999844i \(0.494369\pi\)
\(462\) 232.965 + 365.862i 0.504253 + 0.791909i
\(463\) −401.469 401.469i −0.867104 0.867104i 0.125047 0.992151i \(-0.460092\pi\)
−0.992151 + 0.125047i \(0.960092\pi\)
\(464\) −114.064 −0.245827
\(465\) 103.564 210.690i 0.222717 0.453096i
\(466\) 433.826 0.930957
\(467\) −371.481 + 371.481i −0.795462 + 0.795462i −0.982376 0.186914i \(-0.940151\pi\)
0.186914 + 0.982376i \(0.440151\pi\)
\(468\) −72.0635 + 51.5939i −0.153982 + 0.110243i
\(469\) −676.608 92.8425i −1.44266 0.197959i
\(470\) −193.302 + 84.1441i −0.411281 + 0.179030i
\(471\) 42.9309 522.222i 0.0911483 1.10875i
\(472\) −123.318 123.318i −0.261266 0.261266i
\(473\) 610.208 610.208i 1.29008 1.29008i
\(474\) 180.679 + 14.8532i 0.381179 + 0.0313360i
\(475\) −449.950 + 483.303i −0.947263 + 1.01748i
\(476\) 54.2759 395.546i 0.114025 0.830978i
\(477\) −351.896 491.508i −0.737727 1.03042i
\(478\) 261.894 + 261.894i 0.547896 + 0.547896i
\(479\) 615.307i 1.28457i 0.766467 + 0.642283i \(0.222013\pi\)
−0.766467 + 0.642283i \(0.777987\pi\)
\(480\) 27.3785 + 80.3145i 0.0570385 + 0.167322i
\(481\) 53.6069i 0.111449i
\(482\) −187.969 + 187.969i −0.389978 + 0.389978i
\(483\) 42.7648 + 67.1605i 0.0885400 + 0.139049i
\(484\) 184.593i 0.381391i
\(485\) 556.934 + 219.119i 1.14832 + 0.451793i
\(486\) −137.021 + 315.156i −0.281936 + 0.648469i
\(487\) 597.102 597.102i 1.22608 1.22608i 0.260649 0.965434i \(-0.416064\pi\)
0.965434 0.260649i \(-0.0839364\pi\)
\(488\) −108.355 108.355i −0.222040 0.222040i
\(489\) −60.3241 + 733.798i −0.123362 + 1.50061i
\(490\) −209.015 + 276.338i −0.426562 + 0.563955i
\(491\) 11.7151i 0.0238597i 0.999929 + 0.0119298i \(0.00379747\pi\)
−0.999929 + 0.0119298i \(0.996203\pi\)
\(492\) −173.810 + 147.404i −0.353273 + 0.299602i
\(493\) 575.031 575.031i 1.16639 1.16639i
\(494\) −183.924 −0.372317
\(495\) 637.342 160.375i 1.28756 0.323991i
\(496\) 62.6045i 0.126219i
\(497\) −367.835 + 279.068i −0.740110 + 0.561506i
\(498\) −43.5915 + 36.9688i −0.0875330 + 0.0742345i
\(499\) 11.1783i 0.0224014i 0.999937 + 0.0112007i \(0.00356537\pi\)
−0.999937 + 0.0112007i \(0.996435\pi\)
\(500\) 235.762 + 83.1630i 0.471525 + 0.166326i
\(501\) −137.854 11.3327i −0.275157 0.0226201i
\(502\) −406.255 406.255i −0.809273 0.809273i
\(503\) −15.0212 15.0212i −0.0298632 0.0298632i 0.692017 0.721881i \(-0.256722\pi\)
−0.721881 + 0.692017i \(0.756722\pi\)
\(504\) −52.7293 + 170.211i −0.104622 + 0.337719i
\(505\) 517.400 225.223i 1.02455 0.445986i
\(506\) 78.3088i 0.154760i
\(507\) 331.200 280.882i 0.653255 0.554008i
\(508\) −79.0332 79.0332i −0.155577 0.155577i
\(509\) 62.6374i 0.123060i 0.998105 + 0.0615298i \(0.0195979\pi\)
−0.998105 + 0.0615298i \(0.980402\pi\)
\(510\) −542.915 266.867i −1.06454 0.523269i
\(511\) 63.8554 + 8.76209i 0.124962 + 0.0171469i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −611.928 + 366.248i −1.19284 + 0.713934i
\(514\) 111.493 0.216912
\(515\) 213.810 543.440i 0.415166 1.05522i
\(516\) 353.337 + 29.0472i 0.684762 + 0.0562930i
\(517\) 307.899 + 307.899i 0.595549 + 0.595549i
\(518\) −65.1428 85.8636i −0.125758 0.165760i
\(519\) −42.4416 + 516.271i −0.0817757 + 0.994741i
\(520\) 27.7923 + 63.8467i 0.0534468 + 0.122782i
\(521\) −2.86685 −0.00550258 −0.00275129 0.999996i \(-0.500876\pi\)
−0.00275129 + 0.999996i \(0.500876\pi\)
\(522\) −295.110 + 211.284i −0.565345 + 0.404759i
\(523\) −216.205 + 216.205i −0.413394 + 0.413394i −0.882919 0.469525i \(-0.844425\pi\)
0.469525 + 0.882919i \(0.344425\pi\)
\(524\) 244.093i 0.465826i
\(525\) 297.620 + 432.490i 0.566895 + 0.823790i
\(526\) −193.143 −0.367192
\(527\) 315.609 + 315.609i 0.598879 + 0.598879i
\(528\) 133.662 113.355i 0.253147 0.214687i
\(529\) 514.625i 0.972826i
\(530\) −435.466 + 189.557i −0.821634 + 0.357655i
\(531\) −547.479 90.6269i −1.03103 0.170672i
\(532\) −294.596 + 223.504i −0.553753 + 0.420120i
\(533\) −132.245 + 132.245i −0.248114 + 0.248114i
\(534\) −81.9586 6.73765i −0.153480 0.0126173i
\(535\) 826.160 + 325.043i 1.54422 + 0.607558i
\(536\) 275.953i 0.514837i
\(537\) −94.7712 111.749i −0.176483 0.208098i
\(538\) −100.672 + 100.672i −0.187123 + 0.187123i
\(539\) 689.179 + 192.764i 1.27862 + 0.357633i
\(540\) 219.605 + 157.079i 0.406675 + 0.290887i
\(541\) −544.738 −1.00691 −0.503454 0.864022i \(-0.667938\pi\)
−0.503454 + 0.864022i \(0.667938\pi\)
\(542\) −299.070 + 299.070i −0.551790 + 0.551790i
\(543\) 170.588 144.671i 0.314158 0.266429i
\(544\) −161.322 −0.296548
\(545\) −3.20804 7.36976i −0.00588631 0.0135225i
\(546\) −31.6819 + 142.757i −0.0580255 + 0.261460i
\(547\) −644.286 + 644.286i −1.17785 + 1.17785i −0.197564 + 0.980290i \(0.563303\pi\)
−0.980290 + 0.197564i \(0.936697\pi\)
\(548\) 283.898 283.898i 0.518061 0.518061i
\(549\) −481.053 79.6310i −0.876235 0.145047i
\(550\) −18.4418 516.024i −0.0335306 0.938225i
\(551\) −753.197 −1.36696
\(552\) 24.5359 20.8083i 0.0444492 0.0376962i
\(553\) 238.292 180.787i 0.430908 0.326921i
\(554\) −621.005 −1.12095
\(555\) −154.574 + 52.6929i −0.278512 + 0.0949423i
\(556\) 82.9107i 0.149120i
\(557\) −180.720 180.720i −0.324452 0.324452i 0.526020 0.850472i \(-0.323684\pi\)
−0.850472 + 0.526020i \(0.823684\pi\)
\(558\) −115.965 161.973i −0.207822 0.290275i
\(559\) 290.940 0.520465
\(560\) 122.102 + 68.4918i 0.218039 + 0.122307i
\(561\) −102.373 + 1245.29i −0.182482 + 2.21977i
\(562\) 229.692 229.692i 0.408704 0.408704i
\(563\) 16.4783 + 16.4783i 0.0292687 + 0.0292687i 0.721590 0.692321i \(-0.243412\pi\)
−0.692321 + 0.721590i \(0.743412\pi\)
\(564\) −14.6566 + 178.287i −0.0259869 + 0.316112i
\(565\) 366.339 931.120i 0.648388 1.64800i
\(566\) −341.174 −0.602781
\(567\) 178.864 + 538.049i 0.315457 + 0.948940i
\(568\) 131.919 + 131.919i 0.232251 + 0.232251i
\(569\) −354.571 −0.623147 −0.311574 0.950222i \(-0.600856\pi\)
−0.311574 + 0.950222i \(0.600856\pi\)
\(570\) 180.789 + 530.341i 0.317173 + 0.930423i
\(571\) −110.075 −0.192777 −0.0963883 0.995344i \(-0.530729\pi\)
−0.0963883 + 0.995344i \(0.530729\pi\)
\(572\) 101.697 101.697i 0.177793 0.177793i
\(573\) −50.3372 + 42.6897i −0.0878486 + 0.0745021i
\(574\) −51.1168 + 372.524i −0.0890537 + 0.648996i
\(575\) −3.38533 94.7254i −0.00588752 0.164740i
\(576\) 71.0334 + 11.7585i 0.123322 + 0.0204140i
\(577\) −212.392 212.392i −0.368097 0.368097i 0.498686 0.866783i \(-0.333816\pi\)
−0.866783 + 0.498686i \(0.833816\pi\)
\(578\) 524.277 524.277i 0.907054 0.907054i
\(579\) −25.6415 + 311.910i −0.0442859 + 0.538705i
\(580\) 113.814 + 261.461i 0.196230 + 0.450795i
\(581\) −12.8200 + 93.4285i −0.0220655 + 0.160806i
\(582\) 387.307 328.465i 0.665476 0.564372i
\(583\) 693.626 + 693.626i 1.18975 + 1.18975i
\(584\) 26.0432i 0.0445946i
\(585\) 190.171 + 113.706i 0.325079 + 0.194370i
\(586\) 372.838i 0.636243i
\(587\) 277.047 277.047i 0.471972 0.471972i −0.430580 0.902552i \(-0.641691\pi\)
0.902552 + 0.430580i \(0.141691\pi\)
\(588\) 122.732 + 267.157i 0.208727 + 0.454349i
\(589\) 413.397i 0.701862i
\(590\) −159.627 + 405.722i −0.270554 + 0.687664i
\(591\) 43.2700 526.348i 0.0732150 0.890606i
\(592\) −30.7938 + 30.7938i −0.0520165 + 0.0520165i
\(593\) −118.407 118.407i −0.199674 0.199674i 0.600186 0.799860i \(-0.295093\pi\)
−0.799860 + 0.600186i \(0.795093\pi\)
\(594\) 135.844 540.863i 0.228693 0.910544i
\(595\) −960.844 + 270.265i −1.61486 + 0.454228i
\(596\) 378.749i 0.635485i
\(597\) −629.049 741.739i −1.05368 1.24244i
\(598\) 18.6684 18.6684i 0.0312180 0.0312180i
\(599\) 254.409 0.424722 0.212361 0.977191i \(-0.431885\pi\)
0.212361 + 0.977191i \(0.431885\pi\)
\(600\) 156.782 142.897i 0.261303 0.238161i
\(601\) 335.032i 0.557458i −0.960370 0.278729i \(-0.910087\pi\)
0.960370 0.278729i \(-0.0899131\pi\)
\(602\) 466.006 353.549i 0.774097 0.587291i
\(603\) 511.158 + 713.957i 0.847692 + 1.18401i
\(604\) 234.656i 0.388503i
\(605\) −423.132 + 184.189i −0.699393 + 0.304444i
\(606\) 39.2304 477.210i 0.0647367 0.787474i
\(607\) −537.196 537.196i −0.885002 0.885002i 0.109036 0.994038i \(-0.465224\pi\)
−0.994038 + 0.109036i \(0.965224\pi\)
\(608\) 105.653 + 105.653i 0.173771 + 0.173771i
\(609\) −129.742 + 584.610i −0.213041 + 0.959950i
\(610\) −140.259 + 356.495i −0.229933 + 0.584418i
\(611\) 146.803i 0.240266i
\(612\) −417.380 + 298.824i −0.681994 + 0.488274i
\(613\) −155.599 155.599i −0.253832 0.253832i 0.568708 0.822540i \(-0.307444\pi\)
−0.822540 + 0.568708i \(0.807444\pi\)
\(614\) 19.5434i 0.0318296i
\(615\) 511.315 + 251.335i 0.831407 + 0.408674i
\(616\) 39.3092 286.473i 0.0638137 0.465054i
\(617\) −533.777 533.777i −0.865116 0.865116i 0.126811 0.991927i \(-0.459526\pi\)
−0.991927 + 0.126811i \(0.959526\pi\)
\(618\) −320.506 377.923i −0.518619 0.611526i
\(619\) 96.5213 0.155931 0.0779655 0.996956i \(-0.475158\pi\)
0.0779655 + 0.996956i \(0.475158\pi\)
\(620\) −143.505 + 62.4673i −0.231459 + 0.100754i
\(621\) 24.9365 99.2851i 0.0401554 0.159879i
\(622\) 145.632 + 145.632i 0.234136 + 0.234136i
\(623\) −108.093 + 82.0076i −0.173504 + 0.131633i
\(624\) 58.8873 + 4.84101i 0.0943706 + 0.00775802i
\(625\) −44.6159 623.406i −0.0713855 0.997449i
\(626\) −708.192 −1.13130
\(627\) 882.608 748.516i 1.40767 1.19381i
\(628\) −247.008 + 247.008i −0.393326 + 0.393326i
\(629\) 310.482i 0.493613i
\(630\) 442.778 48.9690i 0.702822 0.0777286i
\(631\) −797.287 −1.26353 −0.631765 0.775160i \(-0.717669\pi\)
−0.631765 + 0.775160i \(0.717669\pi\)
\(632\) −85.4601 85.4601i −0.135222 0.135222i
\(633\) −56.9774 67.1845i −0.0900117 0.106137i
\(634\) 272.972i 0.430556i
\(635\) −102.303 + 260.023i −0.161108 + 0.409485i
\(636\) −33.0180 + 401.640i −0.0519151 + 0.631510i
\(637\) 118.342 + 210.250i 0.185781 + 0.330063i
\(638\) 416.465 416.465i 0.652767 0.652767i
\(639\) 585.665 + 96.9479i 0.916533 + 0.151718i
\(640\) 20.7110 52.6408i 0.0323609 0.0822513i
\(641\) 816.250i 1.27340i 0.771111 + 0.636701i \(0.219701\pi\)
−0.771111 + 0.636701i \(0.780299\pi\)
\(642\) 574.534 487.247i 0.894913 0.758952i
\(643\) −397.740 + 397.740i −0.618569 + 0.618569i −0.945164 0.326595i \(-0.894099\pi\)
0.326595 + 0.945164i \(0.394099\pi\)
\(644\) 7.21591 52.5873i 0.0112048 0.0816573i
\(645\) −285.980 838.919i −0.443380 1.30065i
\(646\) −1065.26 −1.64901
\(647\) 593.146 593.146i 0.916763 0.916763i −0.0800295 0.996792i \(-0.525501\pi\)
0.996792 + 0.0800295i \(0.0255014\pi\)
\(648\) 205.561 101.156i 0.317224 0.156105i
\(649\) 900.508 1.38753
\(650\) 118.621 127.414i 0.182493 0.196021i
\(651\) −320.867 71.2097i −0.492883 0.109385i
\(652\) 347.083 347.083i 0.532335 0.532335i
\(653\) 525.550 525.550i 0.804824 0.804824i −0.179021 0.983845i \(-0.557293\pi\)
0.983845 + 0.179021i \(0.0572930\pi\)
\(654\) −6.79729 0.558792i −0.0103934 0.000854422i
\(655\) 559.520 243.558i 0.854229 0.371844i
\(656\) 151.933 0.231605
\(657\) −48.2409 67.3803i −0.0734261 0.102557i
\(658\) 178.394 + 235.138i 0.271115 + 0.357352i
\(659\) −415.401 −0.630350 −0.315175 0.949034i \(-0.602063\pi\)
−0.315175 + 0.949034i \(0.602063\pi\)
\(660\) −393.205 193.278i −0.595766 0.292846i
\(661\) 723.547i 1.09462i 0.836929 + 0.547312i \(0.184349\pi\)
−0.836929 + 0.547312i \(0.815651\pi\)
\(662\) 317.945 + 317.945i 0.480279 + 0.480279i
\(663\) −321.275 + 272.465i −0.484577 + 0.410957i
\(664\) 38.1046 0.0573864
\(665\) 806.276 + 452.273i 1.21245 + 0.680109i
\(666\) −22.6305 + 136.712i −0.0339797 + 0.205273i
\(667\) 76.4496 76.4496i 0.114617 0.114617i
\(668\) 65.2042 + 65.2042i 0.0976110 + 0.0976110i
\(669\) −860.693 70.7559i −1.28654 0.105764i
\(670\) 632.550 275.348i 0.944105 0.410967i
\(671\) 791.248 1.17921
\(672\) 100.204 63.8055i 0.149113 0.0949487i
\(673\) 95.8909 + 95.8909i 0.142483 + 0.142483i 0.774750 0.632267i \(-0.217876\pi\)
−0.632267 + 0.774750i \(0.717876\pi\)
\(674\) 191.729 0.284465
\(675\) 140.940 660.122i 0.208800 0.977958i
\(676\) −289.512 −0.428272
\(677\) 90.8203 90.8203i 0.134151 0.134151i −0.636843 0.770994i \(-0.719760\pi\)
0.770994 + 0.636843i \(0.219760\pi\)
\(678\) −549.150 647.526i −0.809956 0.955054i
\(679\) 113.905 830.106i 0.167754 1.22254i
\(680\) 160.969 + 369.790i 0.236719 + 0.543808i
\(681\) 643.607 + 52.9096i 0.945091 + 0.0776940i
\(682\) 228.580 + 228.580i 0.335161 + 0.335161i
\(683\) −572.076 + 572.076i −0.837593 + 0.837593i −0.988542 0.150948i \(-0.951767\pi\)
0.150948 + 0.988542i \(0.451767\pi\)
\(684\) 469.055 + 77.6449i 0.685753 + 0.113516i
\(685\) −934.038 367.487i −1.36356 0.536477i
\(686\) 445.047 + 192.954i 0.648756 + 0.281274i
\(687\) 425.808 + 502.088i 0.619808 + 0.730842i
\(688\) −167.127 167.127i −0.242917 0.242917i
\(689\) 330.713i 0.479990i
\(690\) −72.1798 35.4797i −0.104608 0.0514198i
\(691\) 941.057i 1.36188i 0.732340 + 0.680939i \(0.238428\pi\)
−0.732340 + 0.680939i \(0.761572\pi\)
\(692\) 244.193 244.193i 0.352880 0.352880i
\(693\) −428.944 813.991i −0.618966 1.17459i
\(694\) 152.611i 0.219900i
\(695\) −190.052 + 82.7290i −0.273455 + 0.119035i
\(696\) 241.152 + 19.8246i 0.346482 + 0.0284836i
\(697\) −765.941 + 765.941i −1.09891 + 1.09891i
\(698\) 27.7850 + 27.7850i 0.0398067 + 0.0398067i
\(699\) −917.189 75.4003i −1.31215 0.107869i
\(700\) 35.1656 348.229i 0.0502366 0.497470i
\(701\) 305.599i 0.435947i −0.975955 0.217973i \(-0.930055\pi\)
0.975955 0.217973i \(-0.0699446\pi\)
\(702\) 161.323 96.5544i 0.229805 0.137542i
\(703\) −203.341 + 203.341i −0.289247 + 0.289247i
\(704\) −116.837 −0.165962
\(705\) 423.302 144.300i 0.600428 0.204681i
\(706\) 377.547i 0.534769i
\(707\) −477.495 629.378i −0.675382 0.890209i
\(708\) 239.284 + 282.150i 0.337972 + 0.398517i
\(709\) 976.020i 1.37661i 0.725419 + 0.688307i \(0.241646\pi\)
−0.725419 + 0.688307i \(0.758354\pi\)
\(710\) 170.760 434.020i 0.240507 0.611295i
\(711\) −379.408 62.8051i −0.533625 0.0883335i
\(712\) 38.7660 + 38.7660i 0.0544466 + 0.0544466i
\(713\) 41.9599 + 41.9599i 0.0588497 + 0.0588497i
\(714\) −183.497 + 826.825i −0.256998 + 1.15802i
\(715\) −334.590 131.641i −0.467958 0.184113i
\(716\) 97.6829i 0.136429i
\(717\) −508.176 599.212i −0.708753 0.835721i
\(718\) −171.974 171.974i −0.239519 0.239519i
\(719\) 792.968i 1.10288i −0.834216 0.551438i \(-0.814079\pi\)
0.834216 0.551438i \(-0.185921\pi\)
\(720\) −43.9244 174.558i −0.0610061 0.242442i
\(721\) −809.993 111.145i −1.12343 0.154154i
\(722\) 336.659 + 336.659i 0.466286 + 0.466286i
\(723\) 430.072 364.733i 0.594844 0.504471i
\(724\) −149.116 −0.205961
\(725\) 485.769 521.777i 0.670026 0.719692i
\(726\) −32.0829 + 390.265i −0.0441913 + 0.537555i
\(727\) 666.489 + 666.489i 0.916767 + 0.916767i 0.996793 0.0800261i \(-0.0255004\pi\)
−0.0800261 + 0.996793i \(0.525500\pi\)
\(728\) 77.6647 58.9226i 0.106682 0.0809376i
\(729\) 344.463 642.484i 0.472514 0.881323i
\(730\) −59.6975 + 25.9862i −0.0817773 + 0.0355975i
\(731\) 1685.08 2.30517
\(732\) 210.251 + 247.916i 0.287228 + 0.338683i
\(733\) −338.466 + 338.466i −0.461754 + 0.461754i −0.899230 0.437476i \(-0.855873\pi\)
0.437476 + 0.899230i \(0.355873\pi\)
\(734\) 363.110i 0.494700i
\(735\) 489.926 547.903i 0.666566 0.745446i
\(736\) −21.4476 −0.0291407
\(737\) −1007.55 1007.55i −1.36710 1.36710i
\(738\) 393.087 281.431i 0.532638 0.381343i
\(739\) 1021.49i 1.38226i 0.722730 + 0.691130i \(0.242887\pi\)
−0.722730 + 0.691130i \(0.757113\pi\)
\(740\) 101.313 + 39.8605i 0.136910 + 0.0538656i
\(741\) 388.851 + 31.9667i 0.524765 + 0.0431399i
\(742\) 401.881 + 529.712i 0.541618 + 0.713897i
\(743\) −262.382 + 262.382i −0.353138 + 0.353138i −0.861276 0.508138i \(-0.830334\pi\)
0.508138 + 0.861276i \(0.330334\pi\)
\(744\) −10.8809 + 132.358i −0.0146248 + 0.177900i
\(745\) −868.185 + 377.919i −1.16535 + 0.507274i
\(746\) 208.307i 0.279231i
\(747\) 98.5858 70.5826i 0.131976 0.0944881i
\(748\) 589.015 589.015i 0.787453 0.787453i
\(749\) 168.968 1231.38i 0.225591 1.64404i
\(750\) −483.992 216.799i −0.645323 0.289065i
\(751\) −429.513 −0.571922 −0.285961 0.958241i \(-0.592313\pi\)
−0.285961 + 0.958241i \(0.592313\pi\)
\(752\) 84.3288 84.3288i 0.112139 0.112139i
\(753\) 788.291 + 929.508i 1.04687 + 1.23441i
\(754\) 198.566 0.263350
\(755\) −537.889 + 234.142i −0.712436 + 0.310122i
\(756\) 141.063 350.693i 0.186591 0.463879i
\(757\) 439.564 439.564i 0.580666 0.580666i −0.354420 0.935086i \(-0.615322\pi\)
0.935086 + 0.354420i \(0.115322\pi\)
\(758\) −339.431 + 339.431i −0.447798 + 0.447798i
\(759\) −13.6103 + 165.559i −0.0179319 + 0.218128i
\(760\) 136.761 347.604i 0.179948 0.457373i
\(761\) −1005.16 −1.32084 −0.660420 0.750897i \(-0.729622\pi\)
−0.660420 + 0.750897i \(0.729622\pi\)
\(762\) 153.355 + 180.827i 0.201253 + 0.237306i
\(763\) −8.96476 + 6.80137i −0.0117494 + 0.00891398i
\(764\) 44.0013 0.0575933
\(765\) 1101.44 + 658.568i 1.43979 + 0.860873i
\(766\) 374.321i 0.488670i
\(767\) 214.676 + 214.676i 0.279890 + 0.279890i
\(768\) −31.0462