Properties

Label 210.3.k.a.83.13
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 83.13
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.13

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(2.28799 + 1.94039i) q^{3} +2.00000i q^{4} +(-4.58449 + 1.99562i) q^{5} +(-0.347606 - 4.22838i) q^{6} +(-4.23091 - 5.57668i) q^{7} +(2.00000 - 2.00000i) q^{8} +(1.46981 + 8.87917i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(2.28799 + 1.94039i) 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} +(-3.88077 + 4.57598i) q^{12} +(3.48167 - 3.48167i) q^{13} +(-1.34578 + 9.80759i) q^{14} +(-14.3615 - 4.32971i) q^{15} -4.00000 q^{16} +(-20.1653 + 20.1653i) q^{17} +(7.40936 - 10.3490i) q^{18} -26.4132 q^{19} +(-3.99123 - 9.16897i) q^{20} +(1.14063 - 20.9690i) 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} +(-13.8661 + 23.1675i) q^{27} +(11.1534 - 8.46182i) q^{28} -28.5159 q^{29} +(10.0318 + 18.6912i) q^{30} +15.6511i q^{31} +(4.00000 + 4.00000i) q^{32} +(-28.3387 + 33.4154i) 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} +(-22.1096 + 19.8284i) q^{42} +(41.7817 + 41.7817i) q^{43} -29.2094 q^{44} +(-24.4578 - 37.7732i) q^{45} +5.36190 q^{46} +(21.0822 - 21.0822i) q^{47} +(-9.15197 - 7.76154i) 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} +(-60.4332 - 51.2518i) q^{57} +(28.5159 + 28.5159i) q^{58} -61.6589i q^{59} +(8.65943 - 28.7231i) q^{60} +54.1777i q^{61} +(15.6511 - 15.6511i) q^{62} +(43.2977 - 45.7636i) 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} +(20.6980 + 14.8187i) q^{72} +(-6.51081 + 6.51081i) q^{73} -15.3969 q^{74} +(74.4807 - 8.81061i) q^{75} -52.8265i q^{76} +(81.4457 - 61.7911i) q^{77} +(-15.9321 - 13.5116i) 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} +(41.9380 + 2.28126i) q^{84} +(52.2053 - 132.690i) q^{85} -83.5634i q^{86} +(-65.2441 - 55.3318i) q^{87} +(29.2094 + 29.2094i) q^{88} +19.3830i q^{89} +(-13.3155 + 62.2310i) q^{90} +(-34.1468 - 4.68555i) q^{91} +(-5.36190 - 5.36190i) q^{92} +(-30.3692 + 35.8096i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + O(q^{10}) \) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + 8q^{14} - 20q^{15} - 128q^{16} + 36q^{18} + 12q^{21} - 40q^{22} + 24q^{23} + 16q^{25} - 8q^{28} - 112q^{29} + 68q^{30} + 128q^{32} - 48q^{35} - 40q^{36} + 32q^{37} + 64q^{39} - 44q^{42} - 32q^{43} + 80q^{44} - 48q^{46} - 8q^{50} + 84q^{51} - 136q^{53} + 244q^{57} + 112q^{58} - 96q^{60} + 72q^{63} - 200q^{65} + 32q^{67} + 8q^{72} - 64q^{74} + 88q^{77} - 124q^{78} + 76q^{81} + 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} + 48q^{92} - 452q^{93} + 544q^{95} + 128q^{98} + 160q^{99} + O(q^{100}) \)

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
\(3\) 2.28799 + 1.94039i 0.762664 + 0.646795i
\(4\) 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 \(0.231078\pi\)
−0.747867 + 0.663849i \(0.768922\pi\)
\(12\) −3.88077 + 4.57598i −0.323398 + 0.381332i
\(13\) 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
\(15\) −14.3615 4.32971i −0.957435 0.288648i
\(16\) −4.00000 −0.250000
\(17\) −20.1653 + 20.1653i −1.18619 + 1.18619i −0.208081 + 0.978112i \(0.566722\pi\)
−0.978112 + 0.208081i \(0.933278\pi\)
\(18\) 7.40936 10.3490i 0.411631 0.574943i
\(19\) −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
\(21\) 1.14063 20.9690i 0.0543157 0.998524i
\(22\) 14.6047 14.6047i 0.663849 0.663849i
\(23\) −2.68095 + 2.68095i −0.116563 + 0.116563i −0.762982 0.646419i \(-0.776266\pi\)
0.646419 + 0.762982i \(0.276266\pi\)
\(24\) 8.45675 0.695213i 0.352365 0.0289672i
\(25\) 17.0350 18.2978i 0.681401 0.731910i
\(26\) −6.96334 −0.267821
\(27\) −13.8661 + 23.1675i −0.513559 + 0.858054i
\(28\) 11.1534 8.46182i 0.398335 0.302208i
\(29\) −28.5159 −0.983306 −0.491653 0.870791i \(-0.663607\pi\)
−0.491653 + 0.870791i \(0.663607\pi\)
\(30\) 10.0318 + 18.6912i 0.334394 + 0.623041i
\(31\) 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
\(33\) −28.3387 + 33.4154i −0.858748 + 1.01259i
\(34\) 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 \(-0.346698\pi\)
0.463209 + 0.886249i \(0.346698\pi\)
\(42\) −22.1096 + 19.8284i −0.526420 + 0.472104i
\(43\) 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
\(45\) −24.4578 37.7732i −0.543506 0.839406i
\(46\) 5.36190 0.116563
\(47\) 21.0822 21.0822i 0.448558 0.448558i −0.446317 0.894875i \(-0.647265\pi\)
0.894875 + 0.446317i \(0.147265\pi\)
\(48\) −9.15197 7.76154i −0.190666 0.161699i
\(49\) −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 −0.0989866 0.995089i \(-0.531560\pi\)
0.995089 + 0.0989866i \(0.0315601\pi\)
\(54\) 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
\(57\) −60.4332 51.2518i −1.06023 0.899155i
\(58\) 28.5159 + 28.5159i 0.491653 + 0.491653i
\(59\) 61.6589i 1.04507i −0.852619 0.522533i \(-0.824987\pi\)
0.852619 0.522533i \(-0.175013\pi\)
\(60\) 8.65943 28.7231i 0.144324 0.478718i
\(61\) 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
\(63\) 43.2977 45.7636i 0.687265 0.726407i
\(64\) 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 \(0.153767\pi\)
−0.885572 + 0.464503i \(0.846233\pi\)
\(72\) 20.6980 + 14.8187i 0.287472 + 0.205816i
\(73\) −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
\(75\) 74.4807 8.81061i 0.993076 0.117475i
\(76\) 52.8265i 0.695085i
\(77\) 81.4457 61.7911i 1.05774 0.802481i
\(78\) −15.9321 13.5116i −0.204257 0.173225i
\(79\) 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 0.762161 0.647388i \(-0.224139\pi\)
−0.647388 + 0.762161i \(0.724139\pi\)
\(84\) 41.9380 + 2.28126i 0.499262 + 0.0271579i
\(85\) 52.2053 132.690i 0.614180 1.56105i
\(86\) 83.5634i 0.971667i
\(87\) −65.2441 55.3318i −0.749932 0.635998i
\(88\) 29.2094 + 29.2094i 0.331924 + 0.331924i
\(89\) 19.3830i 0.217786i 0.994053 + 0.108893i \(0.0347306\pi\)
−0.994053 + 0.108893i \(0.965269\pi\)
\(90\) −13.3155 + 62.2310i −0.147950 + 0.691456i
\(91\) −34.1468 4.68555i −0.375240 0.0514895i
\(92\) −5.36190 5.36190i −0.0582815 0.0582815i
\(93\) −30.3692 + 35.8096i −0.326551 + 0.385050i
\(94\) −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 \(-0.688702\pi\)
−0.558707 + 0.829365i \(0.688702\pi\)
\(102\) 92.2760 + 78.2568i 0.904666 + 0.767224i
\(103\) 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
\(105\) 36.6169 + 98.4083i 0.348732 + 0.937222i
\(106\) −94.9868 −0.896102
\(107\) −125.554 125.554i −1.17340 1.17340i −0.981393 0.192011i \(-0.938499\pi\)
−0.192011 0.981393i \(-0.561501\pi\)
\(108\) −46.3349 27.7322i −0.429027 0.256780i
\(109\) 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 \(0.596172\pi\)
−0.954704 + 0.297556i \(0.903828\pi\)
\(114\) 9.18141 + 111.685i 0.0805387 + 0.979694i
\(115\) 6.94062 17.6409i 0.0603532 0.153399i
\(116\) 57.0318i 0.491653i
\(117\) 36.0318 + 25.7970i 0.307964 + 0.220487i
\(118\) −61.6589 + 61.6589i −0.522533 + 0.522533i
\(119\) 197.773 + 27.1379i 1.66196 + 0.228050i
\(120\) −37.3825 + 20.0636i −0.311521 + 0.167197i
\(121\) −92.2966 −0.762782
\(122\) 54.1777 54.1777i 0.444080 0.444080i
\(123\) 86.9052 + 73.7020i 0.706546 + 0.599203i
\(124\) −31.3023 −0.252438
\(125\) −41.5815 + 117.881i −0.332652 + 0.943050i
\(126\) −89.0613 + 2.46594i −0.706836 + 0.0195710i
\(127\) −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 \(-0.654243\pi\)
−0.465826 + 0.884876i \(0.654243\pi\)
\(132\) −66.8308 56.6774i −0.506294 0.429374i
\(133\) 111.752 + 147.298i 0.840240 + 1.10751i
\(134\) −137.976 −1.02967
\(135\) 17.3355 133.882i 0.128411 0.991721i
\(136\) 80.6611i 0.593096i
\(137\) 141.949 + 141.949i 1.03612 + 1.03612i 0.999323 + 0.0368001i \(0.0117165\pi\)
0.0368001 + 0.999323i \(0.488284\pi\)
\(138\) 12.2680 + 10.4041i 0.0888984 + 0.0753924i
\(139\) −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
\(147\) −121.763 + 82.3570i −0.828322 + 0.560252i
\(148\) 15.3969 + 15.3969i 0.104033 + 0.104033i
\(149\) 189.375 1.27097 0.635485 0.772113i \(-0.280800\pi\)
0.635485 + 0.772113i \(0.280800\pi\)
\(150\) −83.2913 65.6701i −0.555275 0.437801i
\(151\) −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
\(153\) −208.690 149.412i −1.36399 0.976548i
\(154\) −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
\(162\) 102.781 + 50.5779i 0.634449 + 0.312209i
\(163\) −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
\(165\) 63.2341 209.746i 0.383237 1.27119i
\(166\) 19.0523i 0.114773i
\(167\) −32.6021 + 32.6021i −0.195222 + 0.195222i −0.797948 0.602726i \(-0.794081\pi\)
0.602726 + 0.797948i \(0.294081\pi\)
\(168\) −39.6567 44.2193i −0.236052 0.263210i
\(169\) 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 0.965641 0.259880i \(-0.0836830\pi\)
−0.259880 + 0.965641i \(0.583683\pi\)
\(174\) 9.91231 + 120.576i 0.0569673 + 0.692965i
\(175\) −174.114 17.5828i −0.994940 0.100473i
\(176\) 58.4187i 0.331924i
\(177\) 119.642 141.075i 0.675943 0.797034i
\(178\) 19.3830 19.3830i 0.108893 0.108893i
\(179\) −48.8414 −0.272857 −0.136429 0.990650i \(-0.543562\pi\)
−0.136429 + 0.990650i \(0.543562\pi\)
\(180\) 75.5465 48.9155i 0.419703 0.271753i
\(181\) 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
\(183\) −105.126 + 123.958i −0.574457 + 0.677367i
\(184\) 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
\(189\) 187.864 20.6926i 0.993988 0.109485i
\(190\) −173.802 68.3804i −0.914746 0.359897i
\(191\) 22.0006i 0.115187i 0.998340 + 0.0575933i \(0.0183427\pi\)
−0.998340 + 0.0575933i \(0.981657\pi\)
\(192\) 15.5231 18.3039i 0.0808494 0.0953330i
\(193\) −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
\(195\) −65.0768 + 34.9275i −0.333727 + 0.179115i
\(196\) −94.3778 26.3976i −0.481519 0.134682i
\(197\) −124.480 124.480i −0.631878 0.631878i 0.316661 0.948539i \(-0.397438\pi\)
−0.948539 + 0.316661i \(0.897438\pi\)
\(198\) 151.144 + 108.211i 0.763351 + 0.546522i
\(199\) 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
\(207\) −27.7451 19.8641i −0.134034 0.0959619i
\(208\) −13.9267 + 13.9267i −0.0669552 + 0.0669552i
\(209\) 385.757i 1.84573i
\(210\) 61.7915 135.025i 0.294245 0.642977i
\(211\) 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
\(213\) −127.987 + 150.915i −0.600876 + 0.708519i
\(214\) 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
\(222\) −35.2279 29.8759i −0.158684 0.134576i
\(223\) 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
\(225\) 187.507 + 124.363i 0.833365 + 0.552723i
\(226\) 283.011 1.25226
\(227\) 152.211 152.211i 0.670535 0.670535i −0.287305 0.957839i \(-0.592759\pi\)
0.957839 + 0.287305i \(0.0927592\pi\)
\(228\) 102.504 120.866i 0.449577 0.530116i
\(229\) −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
\(231\) 306.245 + 16.6585i 1.32574 + 0.0721149i
\(232\) −57.0318 + 57.0318i −0.245827 + 0.245827i
\(233\) −216.913 + 216.913i −0.930957 + 0.930957i −0.997766 0.0668091i \(-0.978718\pi\)
0.0668091 + 0.997766i \(0.478718\pi\)
\(234\) −10.2348 61.8287i −0.0437385 0.264225i
\(235\) −54.5791 + 138.723i −0.232251 + 0.590311i
\(236\) 123.318 0.522533
\(237\) −82.9128 + 97.7660i −0.349843 + 0.412515i
\(238\) −170.635 224.911i −0.716953 0.945003i
\(239\) −261.894 −1.09579 −0.547896 0.836547i \(-0.684571\pi\)
−0.547896 + 0.836547i \(0.684571\pi\)
\(240\) 57.4461 + 17.3189i 0.239359 + 0.0721619i
\(241\) 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
\(243\) −226.088 89.0676i −0.930405 0.366533i
\(244\) −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 \(-0.199861\pi\)
0.809273 + 0.587433i \(0.199861\pi\)
\(252\) 91.5273 + 86.5954i 0.363203 + 0.343632i
\(253\) −39.1544 39.1544i −0.154760 0.154760i
\(254\) 79.0332 0.311154
\(255\) 376.914 202.294i 1.47809 0.793311i
\(256\) 16.0000 0.0625000
\(257\) −55.7465 + 55.7465i −0.216912 + 0.216912i −0.807196 0.590284i \(-0.799016\pi\)
0.590284 + 0.807196i \(0.299016\pi\)
\(258\) 162.145 191.192i 0.628469 0.741055i
\(259\) −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 −0.499260 0.866452i \(-0.666395\pi\)
0.866452 + 0.499260i \(0.166395\pi\)
\(264\) 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
\(267\) −37.6105 + 44.3481i −0.140863 + 0.166098i
\(268\) 137.976 + 137.976i 0.514837 + 0.514837i
\(269\) 100.672i 0.374246i −0.982336 0.187123i \(-0.940084\pi\)
0.982336 0.187123i \(-0.0599163\pi\)
\(270\) −151.218 + 116.547i −0.560066 + 0.431655i
\(271\) 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
\(273\) −69.0359 76.9785i −0.252879 0.281972i
\(274\) 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 \(0.134019\pi\)
−0.912667 + 0.408704i \(0.865981\pi\)
\(282\) −96.4718 81.8152i −0.342099 0.290125i
\(283\) −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
\(285\) 379.334 + 114.362i 1.33100 + 0.401269i
\(286\) 101.697i 0.355585i
\(287\) −160.703 211.820i −0.559942 0.738049i
\(288\) −29.6374 + 41.3959i −0.102908 + 0.143736i
\(289\) 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 0.949627 0.313384i \(-0.101463\pi\)
−0.313384 + 0.949627i \(0.601463\pi\)
\(294\) 204.120 + 39.4064i 0.694287 + 0.134035i
\(295\) 123.047 + 282.674i 0.417110 + 0.958218i
\(296\) 30.7938i 0.104033i
\(297\) −338.353 202.510i −1.13924 0.681851i
\(298\) −189.375 189.375i −0.635485 0.635485i
\(299\) 18.6684i 0.0624360i
\(300\) 17.6212 + 148.961i 0.0587374 + 0.496538i
\(301\) 56.2287 409.778i 0.186806 1.36139i
\(302\) 117.328 + 117.328i 0.388503 + 0.388503i
\(303\) −258.220 218.990i −0.852211 0.722738i
\(304\) 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 \(-0.575226\pi\)
−0.234136 + 0.972204i \(0.575226\pi\)
\(312\) 27.0231 31.8641i 0.0866126 0.102129i
\(313\) −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
\(315\) −107.171 + 296.208i −0.340225 + 0.940344i
\(316\) −85.4601 −0.270443
\(317\) −136.486 136.486i −0.430556 0.430556i 0.458262 0.888817i \(-0.348472\pi\)
−0.888817 + 0.458262i \(0.848472\pi\)
\(318\) −217.329 184.311i −0.683425 0.579594i
\(319\) 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
\(327\) 3.11925 3.67804i 0.00953899 0.0112478i
\(328\) 75.9663 75.9663i 0.231605 0.231605i
\(329\) −206.766 28.3719i −0.628467 0.0862368i
\(330\) −272.980 + 146.511i −0.827211 + 0.443974i
\(331\) 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
\(333\) 79.6710 + 57.0405i 0.239252 + 0.171293i
\(334\) 65.2042 0.195222
\(335\) −178.601 + 453.949i −0.533138 + 1.35507i
\(336\) −4.56252 + 83.8760i −0.0135789 + 0.249631i
\(337\) 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
\(342\) −195.705 + 273.350i −0.572237 + 0.799269i
\(343\) 319.001 126.046i 0.930031 0.367482i
\(344\) 167.127 0.485833
\(345\) 50.1103 26.8948i 0.145247 0.0779559i
\(346\) 244.193i 0.705761i
\(347\) −76.3053 76.3053i −0.219900 0.219900i 0.588556 0.808456i \(-0.299697\pi\)
−0.808456 + 0.588556i \(0.799697\pi\)
\(348\) 110.664 130.488i 0.317999 0.374966i
\(349\) 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 0.921988 0.387218i \(-0.126564\pi\)
−0.387218 + 0.921988i \(0.626564\pi\)
\(354\) −260.717 + 21.4330i −0.736488 + 0.0605452i
\(355\) −131.630 302.390i −0.370788 0.851803i
\(356\) −38.7660 −0.108893
\(357\) 399.845 + 445.847i 1.12001 + 1.24887i
\(358\) 48.8414 + 48.8414i 0.136429 + 0.136429i
\(359\) 171.974 0.479037 0.239519 0.970892i \(-0.423010\pi\)
0.239519 + 0.970892i \(0.423010\pi\)
\(360\) −124.462 26.6310i −0.345728 0.0739750i
\(361\) 336.659 0.932572
\(362\) 74.5578 74.5578i 0.205961 0.205961i
\(363\) −211.174 179.091i −0.581746 0.493364i
\(364\) 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
\(372\) −71.6193 60.7384i −0.192525 0.163275i
\(373\) −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
\(375\) −323.873 + 189.027i −0.863662 + 0.504072i
\(376\) 84.3288i 0.224279i
\(377\) −99.2830 + 99.2830i −0.263350 + 0.263350i
\(378\) −208.556 167.171i −0.551737 0.442252i
\(379\) 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 0.419217 0.907886i \(-0.362305\pi\)
−0.907886 + 0.419217i \(0.862305\pi\)
\(384\) −33.8270 + 2.78085i −0.0880912 + 0.00724180i
\(385\) −250.075 + 445.815i −0.649546 + 1.15796i
\(386\) 147.532i 0.382207i
\(387\) −309.575 + 432.398i −0.799937 + 1.11731i
\(388\) −169.278 + 169.278i −0.436284 + 0.436284i
\(389\) −511.312 −1.31443 −0.657214 0.753704i \(-0.728265\pi\)
−0.657214 + 0.753704i \(0.728265\pi\)
\(390\) 100.004 + 30.1493i 0.256421 + 0.0773059i
\(391\) 108.124i 0.276532i
\(392\) 67.9801 + 120.775i 0.173419 + 0.308101i
\(393\) −279.241 236.817i −0.710537 0.602588i
\(394\) 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
\(399\) −30.1277 + 553.859i −0.0755081 + 1.38812i
\(400\) −68.1401 + 73.1910i −0.170350 + 0.182978i
\(401\) 44.3430i 0.110581i −0.998470 0.0552905i \(-0.982391\pi\)
0.998470 0.0552905i \(-0.0176085\pi\)
\(402\) −315.689 267.727i −0.785295 0.665988i
\(403\) 54.4921 + 54.4921i 0.135216 + 0.135216i
\(404\) 225.718i 0.558707i
\(405\) 299.447 272.684i 0.739375 0.673294i
\(406\) 38.3760 279.672i 0.0945221 0.688848i
\(407\) 112.433 + 112.433i 0.276249 + 0.276249i
\(408\) −156.514 + 184.552i −0.383612 + 0.452333i
\(409\) 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
\(417\) −94.8495 80.4394i −0.227457 0.192900i
\(418\) −385.757 + 385.757i −0.922863 + 0.922863i
\(419\) 383.324i 0.914855i 0.889247 + 0.457427i \(0.151229\pi\)
−0.889247 + 0.457427i \(0.848771\pi\)
\(420\) −196.817 + 73.2338i −0.468611 + 0.174366i
\(421\) 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
\(423\) 218.179 + 156.206i 0.515791 + 0.369281i
\(424\) 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 \(-0.832619\pi\)
0.864902 0.501942i \(-0.167381\pi\)
\(432\) 55.4644 92.6699i 0.128390 0.214514i
\(433\) 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
\(435\) 409.532 + 123.466i 0.941452 + 0.283829i
\(436\) 3.21508 0.00737405
\(437\) 70.8125 70.8125i 0.162042 0.162042i
\(438\) 29.7934 + 25.2670i 0.0680214 + 0.0576871i
\(439\) 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
\(441\) −438.398 47.8358i −0.994100 0.108471i
\(442\) 140.418 140.418i 0.317687 0.317687i
\(443\) 429.708 429.708i 0.969996 0.969996i −0.0295673 0.999563i \(-0.509413\pi\)
0.999563 + 0.0295673i \(0.00941292\pi\)
\(444\) 5.35206 + 65.1038i 0.0120542 + 0.146630i
\(445\) −38.6810 88.8610i −0.0869236 0.199688i
\(446\) −407.103 −0.912788
\(447\) 433.287 + 367.460i 0.969323 + 0.822057i
\(448\) −44.6135 + 33.8473i −0.0995836 + 0.0755519i
\(449\) 544.342 1.21234 0.606171 0.795334i \(-0.292705\pi\)
0.606171 + 0.795334i \(0.292705\pi\)
\(450\) −63.1445 311.870i −0.140321 0.693044i
\(451\) 554.732i 1.23000i
\(452\) −283.011 283.011i −0.626130 0.626130i
\(453\) −268.446 227.662i −0.592595 0.502564i
\(454\) −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 \(-0.505631\pi\)
−0.0176900 + 0.999844i \(0.505631\pi\)
\(462\) −289.587 322.904i −0.626812 0.698926i
\(463\) −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
\(465\) 67.7649 224.774i 0.145731 0.483385i
\(466\) 433.826 0.930957
\(467\) 371.481 371.481i 0.795462 0.795462i −0.186914 0.982376i \(-0.559849\pi\)
0.982376 + 0.186914i \(0.0598486\pi\)
\(468\) −51.5939 + 72.0635i −0.110243 + 0.153982i
\(469\) −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
\(477\) 491.508 + 351.896i 1.03042 + 0.737727i
\(478\) 261.894 + 261.894i 0.547896 + 0.547896i
\(479\) 615.307i 1.28457i −0.766467 0.642283i \(-0.777987\pi\)
0.766467 0.642283i \(-0.222013\pi\)
\(480\) −40.1273 74.7650i −0.0835985 0.155760i
\(481\) 53.6069i 0.111449i
\(482\) 187.969 187.969i 0.389978 0.389978i
\(483\) 53.1588 + 59.2748i 0.110060 + 0.122722i
\(484\) 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 \(-0.996203\pi\)
0.999929 0.0119298i \(-0.00379747\pi\)
\(492\) −147.404 + 173.810i −0.299602 + 0.353273i
\(493\) 575.031 575.031i 1.16639 1.16639i
\(494\) 183.924 0.372317
\(495\) 551.666 357.198i 1.11448 0.721611i
\(496\) 62.6045i 0.126219i
\(497\) 367.835 279.068i 0.740110 0.561506i
\(498\) 36.9688 43.5915i 0.0742345 0.0875330i
\(499\) 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 0.721881 0.692017i \(-0.243278\pi\)
−0.692017 + 0.721881i \(0.743278\pi\)
\(504\) −4.93189 178.123i −0.00978549 0.353418i
\(505\) 517.400 225.223i 1.02455 0.445986i
\(506\) 78.3088i 0.154760i
\(507\) −280.882 + 331.200i −0.554008 + 0.653255i
\(508\) −79.0332 79.0332i −0.155577 0.155577i
\(509\) 62.6374i 0.123060i −0.998105 0.0615298i \(-0.980402\pi\)
0.998105 0.0615298i \(-0.0195979\pi\)
\(510\) −579.209 174.620i −1.13570 0.342392i
\(511\) 63.8554 + 8.76209i 0.124962 + 0.0171469i
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 366.248 611.928i 0.713934 1.19284i
\(514\) 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 \(-0.499124\pi\)
0.00275129 + 0.999996i \(0.499124\pi\)
\(522\) −211.284 + 295.110i −0.404759 + 0.565345i
\(523\) −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
\(525\) −364.255 378.078i −0.693819 0.720149i
\(526\) −193.143 −0.367192
\(527\) −315.609 315.609i −0.598879 0.598879i
\(528\) 113.355 133.662i 0.214687 0.253147i
\(529\) 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
\(537\) −111.749 94.7712i −0.208098 0.176483i
\(538\) −100.672 + 100.672i −0.187123 + 0.187123i
\(539\) −689.179 192.764i −1.27862 0.357633i
\(540\) 267.765 + 34.6710i 0.495861 + 0.0642056i
\(541\) −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
\(543\) −144.671 + 170.588i −0.266429 + 0.314158i
\(544\) −161.322 −0.296548
\(545\) 3.20804 + 7.36976i 0.00588631 + 0.0135225i
\(546\) −7.94260 + 146.014i −0.0145469 + 0.267426i
\(547\) −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
\(552\) −20.8083 + 24.5359i −0.0376962 + 0.0444492i
\(553\) 238.292 180.787i 0.430908 0.326921i
\(554\) 621.005 1.12095
\(555\) −143.893 + 77.2294i −0.259268 + 0.139152i
\(556\) 82.9107i 0.149120i
\(557\) 180.720 + 180.720i 0.324452 + 0.324452i 0.850472 0.526020i \(-0.176316\pi\)
−0.526020 + 0.850472i \(0.676316\pi\)
\(558\) 161.973 + 115.965i 0.290275 + 0.207822i
\(559\) 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 0.692321 0.721590i \(-0.256588\pi\)
−0.721590 + 0.692321i \(0.756588\pi\)
\(564\) 14.6566 + 178.287i 0.0259869 + 0.316112i
\(565\) 366.339 931.120i 0.648388 1.64800i
\(566\) 341.174 0.602781
\(567\) 469.982 + 317.184i 0.828893 + 0.559407i
\(568\) 131.919 + 131.919i 0.232251 + 0.232251i
\(569\) 354.571 0.623147 0.311574 0.950222i \(-0.399144\pi\)
0.311574 + 0.950222i \(0.399144\pi\)
\(570\) −264.973 493.696i −0.464864 0.866133i
\(571\) −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
\(573\) −42.6897 + 50.3372i −0.0745021 + 0.0878486i
\(574\) −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
\(582\) 328.465 387.307i 0.564372 0.665476i
\(583\) 693.626 + 693.626i 1.18975 + 1.18975i
\(584\) 26.0432i 0.0445946i
\(585\) −216.668 46.3602i −0.370373 0.0792482i
\(586\) 372.838i 0.636243i
\(587\) −277.047 + 277.047i −0.471972 + 0.471972i −0.902552 0.430580i \(-0.858309\pi\)
0.430580 + 0.902552i \(0.358309\pi\)
\(588\) −164.714 243.527i −0.280126 0.414161i
\(589\) 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 0.799860 0.600186i \(-0.204907\pi\)
−0.600186 + 0.799860i \(0.704907\pi\)
\(594\) 135.844 + 540.863i 0.228693 + 0.910544i
\(595\) −960.844 + 270.265i −1.61486 + 0.454228i
\(596\) 378.749i 0.635485i
\(597\) 741.739 + 629.049i 1.24244 + 1.05368i
\(598\) 18.6684 18.6684i 0.0312180 0.0312180i
\(599\) −254.409 −0.424722 −0.212361 0.977191i \(-0.568115\pi\)
−0.212361 + 0.977191i \(0.568115\pi\)
\(600\) 131.340 166.583i 0.218900 0.277638i
\(601\) 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
\(603\) 713.957 + 511.158i 1.18401 + 0.847692i
\(604\) 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
\(609\) −32.5261 + 597.950i −0.0534090 + 0.981855i
\(610\) −140.259 + 356.495i −0.229933 + 0.584418i
\(611\) 146.803i 0.240266i
\(612\) 298.824 417.380i 0.488274 0.681994i
\(613\) −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
\(615\) −545.497 164.456i −0.886986 0.267409i
\(616\) 39.3092 286.473i 0.0638137 0.465054i
\(617\) 533.777 + 533.777i 0.865116 + 0.865116i 0.991927 0.126811i \(-0.0404741\pi\)
−0.126811 + 0.991927i \(0.540474\pi\)
\(618\) −377.923 320.506i −0.611526 0.518619i
\(619\) 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
\(627\) 748.516 882.608i 1.19381 1.40767i
\(628\) −247.008 + 247.008i −0.393326 + 0.393326i
\(629\) 310.482i 0.493613i
\(630\) 403.379 189.037i 0.640285 0.300059i
\(631\) −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
\(633\) 67.1845 + 56.9774i 0.106137 + 0.0900117i
\(634\) 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 \(-0.780299\pi\)
0.771111 0.636701i \(-0.219701\pi\)
\(642\) −487.247 + 574.534i −0.758952 + 0.894913i
\(643\) −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
\(645\) −419.146 780.952i −0.649839 1.21078i
\(646\) −1065.26 −1.64901
\(647\) −593.146 + 593.146i −0.916763 + 0.916763i −0.996792 0.0800295i \(-0.974499\pi\)
0.0800295 + 0.996792i \(0.474499\pi\)
\(648\) −101.156 + 205.561i −0.156105 + 0.317224i
\(649\) 900.508 1.38753
\(650\) −118.621 + 127.414i −0.182493 + 0.196021i
\(651\) 328.189 + 17.8522i 0.504130 + 0.0274227i
\(652\) 347.083 347.083i 0.532335 0.532335i
\(653\) −525.550 + 525.550i −0.804824 + 0.804824i −0.983845 0.179021i \(-0.942707\pi\)
0.179021 + 0.983845i \(0.442707\pi\)
\(654\) −6.79729 + 0.558792i −0.0103934 + 0.000854422i
\(655\) 559.520 243.558i 0.854229 0.371844i
\(656\) −151.933 −0.231605
\(657\) −67.3803 48.2409i −0.102557 0.0734261i
\(658\) 178.394 + 235.138i 0.271115 + 0.357352i
\(659\) 415.401 0.630350 0.315175 0.949034i \(-0.397937\pi\)
0.315175 + 0.949034i \(0.397937\pi\)
\(660\) 419.491 + 126.468i 0.635593 + 0.191618i
\(661\) 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
\(663\) −272.465 + 321.275i −0.410957 + 0.484577i
\(664\) 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
\(672\) 88.4385 79.3135i 0.131605 0.118026i
\(673\) 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
\(675\) 187.703 + 648.377i 0.278079 + 0.960558i
\(676\) −289.512 −0.428272
\(677\) −90.8203 + 90.8203i −0.134151 + 0.134151i −0.770994 0.636843i \(-0.780240\pi\)
0.636843 + 0.770994i \(0.280240\pi\)
\(678\) 647.526 + 549.150i 0.955054 + 0.809956i
\(679\) 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 −0.150948 0.988542i \(-0.548233\pi\)
0.988542 + 0.150948i \(0.0482327\pi\)
\(684\) 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
\(687\) −502.088 425.808i −0.730842 0.619808i
\(688\) −167.127 167.127i −0.242917 0.242917i
\(689\) 330.713i 0.479990i
\(690\) −77.0050 23.2155i −0.111602 0.0336456i
\(691\) 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
\(693\) 668.363 + 632.349i 0.964449 + 0.912480i
\(694\) 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 \(0.0699446\pi\)
−0.975955 + 0.217973i \(0.930055\pi\)
\(702\) 96.5544 161.323i 0.137542 0.229805i
\(703\) −203.341 + 203.341i −0.289247 + 0.289247i
\(704\) 116.837 0.165962
\(705\) −394.053 + 211.493i −0.558940 + 0.299990i
\(706\) 377.547i 0.534769i
\(707\) 477.495 + 629.378i 0.675382 + 0.890209i
\(708\) 282.150 + 239.284i 0.398517 + 0.337972i
\(709\) 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
\(714\) 46.0023 845.691i 0.0644289 1.18444i
\(715\) −334.590 131.641i −0.467958 0.184113i
\(716\) 97.6829i 0.136429i
\(717\) −599.212 508.176i −0.835721 0.708753i
\(718\) −171.974 171.974i −0.239519 0.239519i
\(719\) 792.968i 1.10288i 0.834216 + 0.551438i \(0.185921\pi\)
−0.834216 + 0.551438i \(0.814079\pi\)
\(720\) 97.8310 + 151.093i 0.135876 + 0.209851i
\(721\) −809.993 111.145i −1.12343 0.154154i
\(722\) −336.659 336.659i −0.466286 0.466286i
\(723\) −364.733 + 430.072i −0.504471 + 0.594844i
\(724\) −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
\(732\) −247.916 210.251i −0.338683 0.287228i
\(733\) −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
\(735\) 393.870 620.558i 0.535877 0.844296i
\(736\) −21.4476 −0.0291407
\(737\) 1007.55 + 1007.55i 1.36710 + 1.36710i
\(738\) 281.431 393.087i 0.381343 0.532638i
\(739\) 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 −0.508138 0.861276i \(-0.669666\pi\)
0.861276 + 0.508138i \(0.169666\pi\)
\(744\) 10.8809 + 132.358i 0.0146248 + 0.177900i
\(745\) −868.185 + 377.919i −1.16535 + 0.507274i
\(746\) 208.307i 0.279231i
\(747\) −70.5826 + 98.5858i −0.0944881 + 0.131976i
\(748\) 589.015 589.015i 0.787453 0.787453i
\(749\) −168.968 + 1231.38i −0.225591 + 1.64404i
\(750\) 512.900 + 134.846i 0.683867 + 0.179795i
\(751\) −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
\(753\) 929.508 + 788.291i 1.23441 + 1.04687i
\(754\) 198.566 0.263350
\(755\) 537.889 234.142i 0.712436 0.310122i
\(756\) 41.3852 + 375.728i 0.0547424 + 0.496994i
\(757\) 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 \(-0.270378\pi\)
0.660420 + 0.750897i \(0.270378\pi\)
\(762\) 180.827 + 153.355i 0.237306 + 0.201253i
\(763\) −8.96476 + 6.80137i −0.0117494 + 0.00891398i
\(764\) −44.0013 −0.0575933
\(765\) 1254.91 + 268.511i 1.64040 + 0.350994i
\(766\) 374.321i 0.488670i
\(767