Properties

Label 210.3.k.a.167.4
Level 210
Weight 3
Character 210.167
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 167.4
Character \(\chi\) \(=\) 210.167
Dual form 210.3.k.a.83.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(-2.28799 + 1.94039i) q^{3} -2.00000i q^{4} +(4.58449 + 1.99562i) q^{5} +(0.347606 - 4.22838i) q^{6} +(5.57668 - 4.23091i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.46981 - 8.87917i) q^{9} +O(q^{10})\) \(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} +(5.57668 - 4.23091i) 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} +(-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} +(13.8661 + 23.1675i) q^{27} +(-8.46182 - 11.1534i) 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} +(34.0095 - 8.26762i) 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} +(-15.9514 - 25.0510i) 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} +(-29.3703 - 55.7350i) 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} +(-25.7419 + 42.2771i) 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} +(-61.7911 - 81.4457i) 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} +(41.0024 + 9.09963i) 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} +(33.9901 + 60.3877i) 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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

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

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
\(7\) 5.57668 4.23091i 0.796669 0.604416i
\(8\) 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 \(-0.231078\pi\)
\(12\) 3.88077 + 4.57598i 0.323398 + 0.381332i
\(13\) −3.48167 3.48167i −0.267821 0.267821i 0.560401 0.828222i \(-0.310647\pi\)
−0.828222 + 0.560401i \(0.810647\pi\)
\(14\) −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 0.978112 + 0.208081i \(0.0667219\pi\)
0.208081 + 0.978112i \(0.433278\pi\)
\(18\) 7.40936 + 10.3490i 0.411631 + 0.574943i
\(19\) 26.4132 1.39017 0.695085 0.718928i \(-0.255367\pi\)
0.695085 + 0.718928i \(0.255367\pi\)
\(20\) 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 \(-0.276266\pi\)
−0.762982 + 0.646419i \(0.776266\pi\)
\(24\) −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
\(28\) −8.46182 11.1534i −0.302208 0.398335i
\(29\) −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
\(35\) 34.0095 8.26762i 0.971700 0.236218i
\(36\) −17.7583 2.93962i −0.493287 0.0816562i
\(37\) 7.69844 + 7.69844i 0.208066 + 0.208066i 0.803445 0.595379i \(-0.202998\pi\)
−0.595379 + 0.803445i \(0.702998\pi\)
\(38\) −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 \(0.653302\pi\)
\(42\) −15.9514 25.0510i −0.379795 0.596453i
\(43\) 41.7817 41.7817i 0.971667 0.971667i −0.0279426 0.999610i \(-0.508896\pi\)
0.999610 + 0.0279426i \(0.00889555\pi\)
\(44\) −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 \(-0.352735\pi\)
−0.894875 + 0.446317i \(0.852735\pi\)
\(48\) 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 0.995089 0.0989866i \(-0.0315601\pi\)
−0.0989866 + 0.995089i \(0.531560\pi\)
\(54\) −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
\(63\) −29.3703 55.7350i −0.466195 0.884682i
\(64\) 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 0.999546 + 0.0301280i \(0.00959148\pi\)
0.0301280 + 0.999546i \(0.490409\pi\)
\(68\) 40.3306 40.3306i 0.593096 0.593096i
\(69\) 11.3361 + 0.931915i 0.164291 + 0.0135060i
\(70\) −25.7419 + 42.2771i −0.367741 + 0.603959i
\(71\) 65.9594i 0.929006i −0.885572 0.464503i \(-0.846233\pi\)
0.885572 0.464503i \(-0.153767\pi\)
\(72\) 20.6980 14.8187i 0.287472 0.205816i
\(73\) 6.51081 + 6.51081i 0.0891892 + 0.0891892i 0.750294 0.661105i \(-0.229912\pi\)
−0.661105 + 0.750294i \(0.729912\pi\)
\(74\) −15.3969 −0.208066
\(75\) −74.4807 8.81061i −0.993076 0.117475i
\(76\) 52.8265i 0.695085i
\(77\) −61.7911 81.4457i −0.802481 1.05774i
\(78\) −15.9321 + 13.5116i −0.204257 + 0.173225i
\(79\) 42.7301i 0.540887i −0.962736 0.270443i \(-0.912830\pi\)
0.962736 0.270443i \(-0.0871703\pi\)
\(80\) −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 \(-0.775861\pi\)
0.647388 + 0.762161i \(0.275861\pi\)
\(84\) 41.0024 + 9.09963i 0.488124 + 0.108329i
\(85\) 52.2053 + 132.690i 0.614180 + 1.56105i
\(86\) 83.5634i 0.971667i
\(87\) 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 \(-0.961652\pi\)
0.120184 + 0.992752i \(0.461652\pi\)
\(98\) 33.9901 + 60.3877i 0.346837 + 0.616201i
\(99\) −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 \(0.311298\pi\)
\(102\) 92.2760 78.2568i 0.904666 0.767224i
\(103\) −82.5883 82.5883i −0.801828 0.801828i 0.181553 0.983381i \(-0.441888\pi\)
−0.983381 + 0.181553i \(0.941888\pi\)
\(104\) 13.9267i 0.133910i
\(105\) −61.7711 + 84.9078i −0.588296 + 0.808646i
\(106\) −94.9868 −0.896102
\(107\) −125.554 + 125.554i −1.17340 + 1.17340i −0.192011 + 0.981393i \(0.561501\pi\)
−0.981393 + 0.192011i \(0.938499\pi\)
\(108\) 46.3349 27.7322i 0.429027 0.256780i
\(109\) 1.60754i 0.0147481i 0.999973 + 0.00737405i \(0.00234725\pi\)
−0.999973 + 0.00737405i \(0.997653\pi\)
\(110\) 37.8096 + 96.1003i 0.343724 + 0.873639i
\(111\) −32.5519 2.67603i −0.293261 0.0241084i
\(112\) −22.3067 + 16.9236i −0.199167 + 0.151104i
\(113\) −141.505 141.505i −1.25226 1.25226i −0.954704 0.297556i \(-0.903828\pi\)
−0.297556 0.954704i \(-0.596172\pi\)
\(114\) 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
\(126\) 85.1053 + 26.3647i 0.675439 + 0.209243i
\(127\) −39.5166 39.5166i −0.311154 0.311154i 0.534202 0.845357i \(-0.320612\pi\)
−0.845357 + 0.534202i \(0.820612\pi\)
\(128\) −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 \(0.345757\pi\)
\(132\) 66.8308 56.6774i 0.506294 0.429374i
\(133\) 147.298 111.752i 1.10751 0.840240i
\(134\) −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 0.0368001 0.999323i \(-0.488284\pi\)
0.999323 0.0368001i \(-0.0117165\pi\)
\(138\) −12.2680 + 10.4041i −0.0888984 + 0.0753924i
\(139\) 41.4554 0.298240 0.149120 0.988819i \(-0.452356\pi\)
0.149120 + 0.988819i \(0.452356\pi\)
\(140\) −16.5352 68.0190i −0.118109 0.485850i
\(141\) 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
\(147\) 61.3658 + 133.579i 0.417455 + 0.908698i
\(148\) 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 \(-0.937759\pi\)
0.194293 + 0.980944i \(0.437759\pi\)
\(158\) 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 −0.0669121 + 0.997759i \(0.521315\pi\)
−0.997759 + 0.0669121i \(0.978685\pi\)
\(164\) 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 \(-0.205919\pi\)
−0.602726 + 0.797948i \(0.705919\pi\)
\(168\) −50.1020 + 31.9028i −0.298226 + 0.189897i
\(169\) 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 \(-0.916317\pi\)
0.259880 + 0.965641i \(0.416317\pi\)
\(174\) −9.91231 + 120.576i −0.0569673 + 0.692965i
\(175\) 172.415 + 29.9672i 0.985229 + 0.171241i
\(176\) 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 \(0.933968\pi\)
\(182\) 38.8324 29.4613i 0.213365 0.161875i
\(183\) −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
\(189\) 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 \(-0.0183427\pi\)
\(192\) −15.5231 18.3039i −0.0808494 0.0953330i
\(193\) −73.7660 + 73.7660i −0.382207 + 0.382207i −0.871897 0.489690i \(-0.837110\pi\)
0.489690 + 0.871897i \(0.337110\pi\)
\(194\) 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 −0.948539 0.316661i \(-0.897438\pi\)
0.316661 + 0.948539i \(0.397438\pi\)
\(198\) 151.144 108.211i 0.763351 0.546522i
\(199\) −324.188 −1.62908 −0.814542 0.580104i \(-0.803012\pi\)
−0.814542 + 0.580104i \(0.803012\pi\)
\(200\) −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
\(203\) −159.024 + 120.648i −0.783370 + 0.594326i
\(204\) −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
\(210\) −23.1367 146.679i −0.110175 0.698471i
\(211\) 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
\(217\) 66.2185 + 87.2814i 0.305154 + 0.402218i
\(218\) −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 \(-0.473325\pi\)
−0.996491 + 0.0837032i \(0.973325\pi\)
\(224\) 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 \(-0.407241\pi\)
−0.957839 + 0.287305i \(0.907241\pi\)
\(228\) 102.504 + 120.866i 0.449577 + 0.530116i
\(229\) 219.445 0.958275 0.479138 0.877740i \(-0.340949\pi\)
0.479138 + 0.877740i \(0.340949\pi\)
\(230\) 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 \(-0.478718\pi\)
−0.997766 + 0.0668091i \(0.978718\pi\)
\(234\) 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
\(238\) −224.911 + 170.635i −0.945003 + 0.716953i
\(239\) −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
\(245\) 154.681 189.997i 0.631350 0.775498i
\(246\) −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 \(0.800139\pi\)
\(252\) −111.470 + 58.7406i −0.442341 + 0.233098i
\(253\) −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 \(-0.200984\pi\)
−0.590284 + 0.807196i \(0.700984\pi\)
\(258\) −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 0.866452 0.499260i \(-0.166395\pi\)
−0.499260 + 0.866452i \(0.666395\pi\)
\(264\) −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
\(273\) 87.2194 55.5375i 0.319485 0.203434i
\(274\) 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 −0.991599 0.129348i \(-0.958712\pi\)
−0.129348 0.991599i \(-0.541288\pi\)
\(278\) −41.4554 + 41.4554i −0.149120 + 0.149120i
\(279\) 138.969 + 23.0042i 0.498097 + 0.0824523i
\(280\) 84.5542 + 51.4838i 0.301979 + 0.183871i
\(281\) 229.692i 0.817409i −0.912667 0.408704i \(-0.865981\pi\)
0.912667 0.408704i \(-0.134019\pi\)
\(282\) −96.4718 + 81.8152i −0.342099 + 0.290125i
\(283\) 170.587 + 170.587i 0.602781 + 0.602781i 0.941049 0.338269i \(-0.109841\pi\)
−0.338269 + 0.941049i \(0.609841\pi\)
\(284\) −131.919 −0.464503
\(285\) −379.334 + 114.362i −1.33100 + 0.401269i
\(286\) 101.697i 0.355585i
\(287\) −211.820 + 160.703i −0.738049 + 0.559942i
\(288\) −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 \(-0.898537\pi\)
0.313384 + 0.949627i \(0.398537\pi\)
\(294\) −194.944 72.2127i −0.663076 0.245622i
\(295\) 123.047 282.674i 0.417110 0.958218i
\(296\) 30.7938i 0.104033i
\(297\) 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 \(-0.757165\pi\)
0.691013 + 0.722842i \(0.257165\pi\)
\(308\) −162.891 + 123.582i −0.528868 + 0.401241i
\(309\) 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 \(0.424774\pi\)
\(312\) 27.0231 + 31.8641i 0.0866126 + 0.102129i
\(313\) 354.096 + 354.096i 1.13130 + 1.13130i 0.989962 + 0.141335i \(0.0451395\pi\)
0.141335 + 0.989962i \(0.454861\pi\)
\(314\) 247.008i 0.786651i
\(315\) −23.4220 314.128i −0.0743556 0.997232i
\(316\) −85.4601 −0.270443
\(317\) −136.486 + 136.486i −0.430556 + 0.430556i −0.888817 0.458262i \(-0.848472\pi\)
0.458262 + 0.888817i \(0.348472\pi\)
\(318\) 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
\(322\) 29.9016 22.6857i 0.0928621 0.0704525i
\(323\) 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
\(336\) 18.1993 82.0048i 0.0541644 0.244062i
\(337\) 95.8647 + 95.8647i 0.284465 + 0.284465i 0.834887 0.550422i \(-0.185533\pi\)
−0.550422 + 0.834887i \(0.685533\pi\)
\(338\) 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
\(343\) −126.046 319.001i −0.367482 0.930031i
\(344\) 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 −0.808456 0.588556i \(-0.799697\pi\)
0.588556 + 0.808456i \(0.299697\pi\)
\(348\) −110.664 130.488i −0.317999 0.374966i
\(349\) −27.7850 −0.0796133 −0.0398067 0.999207i \(-0.512674\pi\)
−0.0398067 + 0.999207i \(0.512674\pi\)
\(350\) −202.382 + 142.448i −0.578235 + 0.406994i
\(351\) 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 \(-0.873436\pi\)
0.387218 + 0.921988i \(0.373436\pi\)
\(354\) −260.717 21.4330i −0.736488 0.0605452i
\(355\) 131.630 302.390i 0.370788 0.851803i
\(356\) 38.7660 0.108893
\(357\) −505.161 + 321.664i −1.41502 + 0.901020i
\(358\) 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 \(-0.863753\pi\)
0.415083 + 0.909784i \(0.363753\pi\)
\(368\) 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 −0.832802 0.553571i \(-0.813265\pi\)
0.553571 + 0.832802i \(0.313265\pi\)
\(374\) 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
\(378\) −245.878 + 104.815i −0.650470 + 0.277288i
\(379\) 339.431i 0.895596i −0.894135 0.447798i \(-0.852208\pi\)
0.894135 0.447798i \(-0.147792\pi\)
\(380\) 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 \(-0.637695\pi\)
0.907886 + 0.419217i \(0.137695\pi\)
\(384\) 33.8270 + 2.78085i 0.0880912 + 0.00724180i
\(385\) −120.746 496.698i −0.313626 1.29012i
\(386\) 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
\(392\) 120.775 67.9801i 0.308101 0.173419i
\(393\) −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 0.139744 0.990188i \(-0.455372\pi\)
0.990188 0.139744i \(-0.0446280\pi\)
\(398\) 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 \(0.982391\pi\)
\(402\) 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 \(-0.659238\pi\)
−0.479656 + 0.877457i \(0.659238\pi\)
\(410\) 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
\(413\) −260.873 343.852i −0.631654 0.832571i
\(414\) 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 \(0.848771\pi\)
\(420\) 169.816 + 123.542i 0.404323 + 0.294148i
\(421\) 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
\(427\) 229.221 + 302.132i 0.536817 + 0.707569i
\(428\) 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 \(0.832619\pi\)
\(432\) −55.4644 92.6699i −0.128390 0.214514i
\(433\) −288.449 288.449i −0.666163 0.666163i 0.290662 0.956826i \(-0.406124\pi\)
−0.956826 + 0.290662i \(0.906124\pi\)
\(434\) −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 \(-0.766766\pi\)
−0.743354 + 0.668898i \(0.766766\pi\)
\(440\) 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 \(-0.00941292\pi\)
−0.0295673 + 0.999563i \(0.509413\pi\)
\(444\) −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
\(448\) 33.8473 + 44.6135i 0.0755519 + 0.0995836i
\(449\) 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
\(455\) −147.195 89.6248i −0.323506 0.196978i
\(456\) −223.370 18.3628i −0.489847 0.0402693i
\(457\) −100.300 100.300i −0.219475 0.219475i 0.588802 0.808277i \(-0.299600\pi\)
−0.808277 + 0.588802i \(0.799600\pi\)
\(458\) −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 \(0.494369\pi\)
\(462\) −365.862 + 232.965i −0.791909 + 0.504253i
\(463\) −401.469 + 401.469i −0.867104 + 0.867104i −0.992151 0.125047i \(-0.960092\pi\)
0.125047 + 0.992151i \(0.460092\pi\)
\(464\) 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 \(-0.440151\pi\)
−0.982376 + 0.186914i \(0.940151\pi\)
\(468\) 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
\(483\) 67.1605 42.7648i 0.139049 0.0885400i
\(484\) 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 0.965434 + 0.260649i \(0.0839364\pi\)
0.260649 + 0.965434i \(0.416064\pi\)
\(488\) −108.355 + 108.355i −0.222040 + 0.222040i
\(489\) 60.3241 733.798i 0.123362 1.50061i
\(490\) 35.3163 + 344.678i 0.0720740 + 0.703424i
\(491\) 11.7151i 0.0238597i 0.999929 + 0.0119298i \(0.00379747\pi\)
−0.999929 + 0.0119298i \(0.996203\pi\)
\(492\) −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
\(497\) −279.068 367.835i −0.561506 0.740110i
\(498\) 36.9688 + 43.5915i 0.0742345 + 0.0875330i
\(499\) 11.1783i 0.0224014i −0.999937 0.0112007i \(-0.996435\pi\)
0.999937 0.0112007i \(-0.00356537\pi\)
\(500\) 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 \(-0.756722\pi\)
0.692017 + 0.721881i \(0.256722\pi\)
\(504\) 52.7293 170.211i 0.104622 0.337719i
\(505\) 517.400 + 225.223i 1.02455 + 0.445986i
\(506\) 78.3088i 0.154760i
\(507\) 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
\(518\) −85.8636 + 65.1428i −0.165760 + 0.125758i
\(519\) 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 \(0.500876\pi\)
\(522\) −211.284 295.110i −0.404759 0.565345i
\(523\) 216.205 + 216.205i 0.413394 + 0.413394i 0.882919 0.469525i \(-0.155575\pi\)
−0.469525 + 0.882919i \(0.655575\pi\)
\(524\) 244.093i 0.465826i
\(525\) −452.632 + 265.987i −0.862157 + 0.506642i
\(526\) −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
\(532\) −223.504 294.596i −0.420120 0.553753i
\(533\) 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
\(546\) −31.6819 + 142.757i −0.0580255 + 0.261460i
\(547\) −644.286 644.286i −1.17785 1.17785i −0.980290 0.197564i \(-0.936697\pi\)
−0.197564 0.980290i \(-0.563303\pi\)
\(548\) −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
\(553\) −180.787 238.292i −0.326921 0.430908i
\(554\) 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 −0.526020 0.850472i \(-0.676316\pi\)
0.850472 + 0.526020i \(0.176316\pi\)
\(558\) −161.973 + 115.965i −0.290275 + 0.207822i
\(559\) −290.940 −0.520465
\(560\) −136.038 + 33.0705i −0.242925 + 0.0590544i
\(561\) −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 \(-0.743412\pi\)
0.721590 + 0.692321i \(0.243412\pi\)
\(564\) 14.6566 178.287i 0.0259869 0.316112i
\(565\) −366.339 931.120i −0.648388 1.64800i
\(566\) −341.174 −0.602781
\(567\) −538.049 + 178.864i −0.948940 + 0.315457i
\(568\) 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 \(-0.666184\pi\)
0.866783 + 0.498686i \(0.166184\pi\)
\(578\) −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 \(-0.141691\pi\)
−0.430580 + 0.902552i \(0.641691\pi\)
\(588\) 267.157 122.732i 0.454349 0.208727i
\(589\) 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 \(-0.795093\pi\)
0.600186 + 0.799860i \(0.295093\pi\)
\(594\) −135.844 + 540.863i −0.228693 + 0.910544i
\(595\) 852.530 + 519.092i 1.43282 + 0.872424i
\(596\) 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 \(-0.0899131\pi\)
\(602\) 353.549 + 466.006i 0.587291 + 0.774097i
\(603\) 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 \(-0.534776\pi\)
0.994038 + 0.109036i \(0.0347763\pi\)
\(608\) 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
\(612\) −298.824 417.380i −0.488274 0.681994i
\(613\) −155.599 + 155.599i −0.253832 + 0.253832i −0.822540 0.568708i \(-0.807444\pi\)
0.568708 + 0.822540i \(0.307444\pi\)
\(614\) 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 −0.126811 0.991927i \(-0.540474\pi\)
0.991927 + 0.126811i \(0.0404741\pi\)
\(618\) −377.923 + 320.506i −0.611526 + 0.518619i
\(619\) −96.5213 −0.155931 −0.0779655 0.996956i \(-0.524842\pi\)
−0.0779655 + 0.996956i \(0.524842\pi\)
\(620\) 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
\(623\) 82.0076 + 108.093i 0.131633 + 0.173504i
\(624\) −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
\(630\) 337.550 + 290.706i 0.535794 + 0.461438i
\(631\) −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
\(637\) −210.250 + 118.342i −0.330063 + 0.185781i
\(638\) −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 \(0.780299\pi\)
\(642\) 487.247 + 574.534i 0.758952 + 0.894913i
\(643\) 397.740 + 397.740i 0.618569 + 0.618569i 0.945164 0.326595i \(-0.105901\pi\)
−0.326595 + 0.945164i \(0.605901\pi\)
\(644\) −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 \(-0.0255014\pi\)
−0.0800295 + 0.996792i \(0.525501\pi\)
\(648\) −101.156 205.561i −0.156105 0.317224i
\(649\) −900.508 −1.38753
\(650\) 118.621 + 127.414i 0.182493 + 0.196021i
\(651\) −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 \(-0.442707\pi\)
−0.983845 + 0.179021i \(0.942707\pi\)
\(654\) 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
\(658\) 235.138 178.394i 0.357352 0.271115i
\(659\) 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
\(665\) 898.301 218.374i 1.35083 0.328383i
\(666\) −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
\(672\) 63.8055 + 100.204i 0.0949487 + 0.149113i
\(673\) 95.8909 95.8909i 0.142483 0.142483i −0.632267 0.774750i \(-0.717876\pi\)
0.774750 + 0.632267i \(0.217876\pi\)
\(674\) −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 \(-0.219760\pi\)
−0.636843 + 0.770994i \(0.719760\pi\)
\(678\) −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 0.988542 0.150948i \(-0.0482327\pi\)
−0.150948 + 0.988542i \(0.548233\pi\)
\(684\) −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
\(693\) −813.991 + 428.944i −1.17459 + 0.618966i
\(694\) 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
\(700\) 59.9344 344.830i 0.0856205 0.492615i
\(701\) 305.599i 0.435947i −0.975955 0.217973i \(-0.930055\pi\)
0.975955 0.217973i \(-0.0699446\pi\)
\(702\) 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
\(707\) 629.378 477.495i 0.890209 0.675382i
\(708\) 282.150 239.284i 0.398517 0.337972i
\(709\) 976.020i 1.37661i −0.725419 0.688307i \(-0.758354\pi\)
0.725419 0.688307i \(-0.241646\pi\)
\(710\) 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
\(717\) 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 \(-0.974500\pi\)
0.0800261 + 0.996793i \(0.474500\pi\)
\(728\) −58.9226 77.6647i −0.0809376 0.106682i
\(729\) −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 \(-0.144127\pi\)
−0.437476 + 0.899230i \(0.644127\pi\)
\(734\) 363.110i 0.494700i
\(735\) 14.7592 + 734.852i 0.0200805 + 0.999798i
\(736\) −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 \(-0.757113\pi\)
0.722730 0.691130i \(-0.242887\pi\)
\(740\) 101.313 39.8605i 0.136910 0.0538656i
\(741\) 388.851 + 31.9667i 0.524765 + 0.0431399i
\(742\) −529.712 + 401.881i −0.713897 + 0.541618i
\(743\) 262.382 + 262.382i 0.353138 + 0.353138i 0.861276 0.508138i \(-0.169666\pi\)
−0.508138 + 0.861276i \(0.669666\pi\)
\(744\) 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
\(756\) 141.063 350.693i 0.186591 0.463879i
\(757\) 439.564 + 439.564i 0.580666 + 0.580666i 0.935086 0.354420i \(-0.115322\pi\)
−0.354420 + 0.935086i \(0.615322\pi\)
\(758\) 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 \(0.729622\pi\)
\(762\) −180.827 + 153.355i −0.237306 + 0.201253i
\(763\) 6.80137 + 8.96476i 0.00891398 + 0.0117494i
\(764\) −44.0013 −0.0575933
\(765\) 1254.91 268.511i 1.64040 0.350994i
\(766\) 374.321i 0.488670i
\(767\)