Properties

Label 210.3.k.a.83.4
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 83.4
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.4

$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

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

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
\(7\) 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 \(0.231078\pi\)
−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 −0.828222 0.560401i \(-0.810647\pi\)
0.560401 + 0.828222i \(0.310647\pi\)
\(14\) −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 \(-0.433278\pi\)
0.978112 0.208081i \(-0.0667219\pi\)
\(18\) 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 −0.762982 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
\(28\) −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 \(-0.918768\pi\)
0.967613 0.252438i \(-0.0812322\pi\)
\(32\) 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 −0.595379 0.803445i \(-0.702998\pi\)
0.803445 + 0.595379i \(0.202998\pi\)
\(38\) −26.4132 26.4132i −0.695085 0.695085i
\(39\) 14.7218 1.21025i 0.377483 0.0310321i
\(40\) 5.17774 13.1602i 0.129443 0.329005i
\(41\) −37.9832 −0.926419 −0.463209 0.886249i \(-0.653302\pi\)
−0.463209 + 0.886249i \(0.653302\pi\)
\(42\) −15.9514 + 25.0510i −0.379795 + 0.596453i
\(43\) 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 −0.894875 0.446317i \(-0.852735\pi\)
0.446317 + 0.894875i \(0.352735\pi\)
\(48\) 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 \(0.175013\pi\)
−0.852619 + 0.522533i \(0.824987\pi\)
\(60\) 8.65943 28.7231i 0.144324 0.478718i
\(61\) 54.1777i 0.888159i −0.895987 0.444080i \(-0.853531\pi\)
0.895987 0.444080i \(-0.146469\pi\)
\(62\) −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 0.0301280 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
\(70\) −25.7419 42.2771i −0.367741 0.603959i
\(71\) 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 −0.661105 0.750294i \(-0.729912\pi\)
0.750294 + 0.661105i \(0.229912\pi\)
\(74\) −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 \(0.0871703\pi\)
−0.962736 + 0.270443i \(0.912830\pi\)
\(80\) −18.3379 + 7.98247i −0.229224 + 0.0997809i
\(81\) −76.6793 + 26.1014i −0.946658 + 0.322240i
\(82\) 37.9832 + 37.9832i 0.463209 + 0.463209i
\(83\) −9.52614 9.52614i −0.114773 0.114773i 0.647388 0.762161i \(-0.275861\pi\)
−0.762161 + 0.647388i \(0.775861\pi\)
\(84\) 41.0024 9.09963i 0.488124 0.108329i
\(85\) 52.2053 132.690i 0.614180 1.56105i
\(86\) 83.5634i 0.971667i
\(87\) 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 \(-0.965269\pi\)
0.994053 0.108893i \(-0.0347306\pi\)
\(90\) 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 0.120184 0.992752i \(-0.461652\pi\)
−0.992752 + 0.120184i \(0.961652\pi\)
\(98\) 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 −0.983381 0.181553i \(-0.941888\pi\)
0.181553 + 0.983381i \(0.441888\pi\)
\(104\) 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 −0.981393 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
\(112\) −22.3067 16.9236i −0.199167 0.151104i
\(113\) −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
\(126\) 85.1053 26.3647i 0.675439 0.209243i
\(127\) −39.5166 + 39.5166i −0.311154 + 0.311154i −0.845357 0.534202i \(-0.820612\pi\)
0.534202 + 0.845357i \(0.320612\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) −14.5236 176.669i −0.112586 1.36952i
\(130\) 31.9234 13.8962i 0.245564 0.106894i
\(131\) 122.046 0.931652 0.465826 0.884876i \(-0.345757\pi\)
0.465826 + 0.884876i \(0.345757\pi\)
\(132\) 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 0.999323 + 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 \(-0.452356\pi\)
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 0.194293 0.980944i \(-0.437759\pi\)
−0.980944 + 0.194293i \(0.937759\pi\)
\(158\) 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 −0.602726 0.797948i \(-0.705919\pi\)
0.797948 + 0.602726i \(0.205919\pi\)
\(168\) −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 0.259880 0.965641i \(-0.416317\pi\)
−0.965641 + 0.259880i \(0.916317\pi\)
\(174\) −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 \(-0.933968\pi\)
0.978560 0.205961i \(-0.0660319\pi\)
\(182\) 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 \(0.0183427\pi\)
−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 \(-0.803012\pi\)
−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 −0.996491 0.0837032i \(-0.973325\pi\)
0.0837032 + 0.996491i \(0.473325\pi\)
\(224\) 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 −0.957839 0.287305i \(-0.907241\pi\)
0.287305 + 0.957839i \(0.407241\pi\)
\(228\) 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 −0.997766 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
\(238\) −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 \(-0.872483\pi\)
0.920824 0.389978i \(-0.127517\pi\)
\(242\) 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 −0.590284 0.807196i \(-0.700984\pi\)
0.807196 + 0.590284i \(0.200984\pi\)
\(258\) −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 \(0.0599163\pi\)
−0.982336 + 0.187123i \(0.940084\pi\)
\(270\) −151.218 + 116.547i −0.560066 + 0.431655i
\(271\) 299.070i 1.10358i −0.833983 0.551790i \(-0.813945\pi\)
0.833983 0.551790i \(-0.186055\pi\)
\(272\) −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 −0.129348 + 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
\(280\) 84.5542 51.4838i 0.301979 0.183871i
\(281\) 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 −0.338269 0.941049i \(-0.609841\pi\)
0.941049 + 0.338269i \(0.109841\pi\)
\(284\) −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 0.313384 0.949627i \(-0.398537\pi\)
−0.949627 + 0.313384i \(0.898537\pi\)
\(294\) −194.944 + 72.2127i −0.663076 + 0.245622i
\(295\) 123.047 + 282.674i 0.417110 + 0.958218i
\(296\) 30.7938i 0.104033i
\(297\) 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 0.691013 0.722842i \(-0.257165\pi\)
−0.722842 + 0.691013i \(0.757165\pi\)
\(308\) −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 0.141335 0.989962i \(-0.454861\pi\)
0.989962 0.141335i \(-0.0451395\pi\)
\(314\) 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 0.458262 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
\(322\) 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 −0.550422 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
\(343\) −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 0.588556 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 \(-0.512674\pi\)
−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 0.387218 0.921988i \(-0.373436\pi\)
−0.921988 + 0.387218i \(0.873436\pi\)
\(354\) −260.717 + 21.4330i −0.736488 + 0.0605452i
\(355\) 131.630 + 302.390i 0.370788 + 0.851803i
\(356\) 38.7660 0.108893
\(357\) −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 0.415083 0.909784i \(-0.363753\pi\)
−0.909784 + 0.415083i \(0.863753\pi\)
\(368\) 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
\(378\) −245.878 104.815i −0.650470 0.277288i
\(379\) 339.431i 0.895596i 0.894135 + 0.447798i \(0.147792\pi\)
−0.894135 + 0.447798i \(0.852208\pi\)
\(380\) 105.421 + 242.182i 0.277425 + 0.637321i
\(381\) 167.091 13.7362i 0.438559 0.0360531i
\(382\) 22.0006 22.0006i 0.0575933 0.0575933i
\(383\) 187.161 + 187.161i 0.488670 + 0.488670i 0.907886 0.419217i \(-0.137695\pi\)
−0.419217 + 0.907886i \(0.637695\pi\)
\(384\) 33.8270 2.78085i 0.0880912 0.00724180i
\(385\) −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 0.990188 + 0.139744i \(0.0446280\pi\)
0.139744 + 0.990188i \(0.455372\pi\)
\(398\) 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 \(-0.982391\pi\)
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 \(-0.659238\pi\)
−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 \(-0.848771\pi\)
0.889247 0.457427i \(-0.151229\pi\)
\(420\) 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 \(-0.832619\pi\)
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 −0.956826 0.290662i \(-0.906124\pi\)
0.290662 + 0.956826i \(0.406124\pi\)
\(434\) −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 −0.0295673 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
\(448\) 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 −0.808277 0.588802i \(-0.799600\pi\)
0.588802 + 0.808277i \(0.299600\pi\)
\(458\) −219.445 219.445i −0.479138 0.479138i
\(459\) −187.565 746.792i −0.408638 1.62700i
\(460\) −35.2818 13.8812i −0.0766996 0.0301766i
\(461\) 16.3102 0.0353801 0.0176900 0.999844i \(-0.494369\pi\)
0.0176900 + 0.999844i \(0.494369\pi\)
\(462\) −365.862 232.965i −0.791909 0.504253i
\(463\) −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 −0.982376 0.186914i \(-0.940151\pi\)
0.186914 + 0.982376i \(0.440151\pi\)
\(468\) 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 \(0.222013\pi\)
−0.766467 + 0.642283i \(0.777987\pi\)
\(480\) −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 0.260649 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
\(490\) 35.3163 344.678i 0.0720740 0.703424i
\(491\) 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
\(497\) −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 \(0.00356537\pi\)
−0.999937 + 0.0112007i \(0.996435\pi\)
\(500\) 235.762 + 83.1630i 0.471525 + 0.166326i
\(501\) −137.854 + 11.3327i −0.275157 + 0.0226201i
\(502\) 406.255 + 406.255i 0.809273 + 0.809273i
\(503\) −15.0212 15.0212i −0.0298632 0.0298632i 0.692017 0.721881i \(-0.256722\pi\)
−0.721881 + 0.692017i \(0.756722\pi\)
\(504\) 52.7293 + 170.211i 0.104622 + 0.337719i
\(505\) 517.400 225.223i 1.02455 0.445986i
\(506\) 78.3088i 0.154760i
\(507\) 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 \(0.0195979\pi\)
−0.998105 + 0.0615298i \(0.980402\pi\)
\(510\) 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 −0.469525 0.882919i \(-0.655575\pi\)
0.882919 + 0.469525i \(0.155575\pi\)
\(524\) 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 −0.197564 + 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
\(553\) −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 0.850472 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
\(560\) −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 0.721590 0.692321i \(-0.243412\pi\)
−0.692321 + 0.721590i \(0.743412\pi\)
\(564\) 14.6566 + 178.287i 0.0259869 + 0.316112i
\(565\) −366.339 + 931.120i −0.648388 + 1.64800i
\(566\) −341.174 −0.602781
\(567\) −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 0.866783 0.498686i \(-0.166184\pi\)
−0.498686 + 0.866783i \(0.666184\pi\)
\(578\) −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 −0.430580 0.902552i \(-0.641691\pi\)
0.902552 + 0.430580i \(0.141691\pi\)
\(588\) 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 0.600186 0.799860i \(-0.295093\pi\)
−0.799860 + 0.600186i \(0.795093\pi\)
\(594\) −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 \(0.0899131\pi\)
−0.960370 + 0.278729i \(0.910087\pi\)
\(602\) 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 0.994038 0.109036i \(-0.0347763\pi\)
−0.109036 + 0.994038i \(0.534776\pi\)
\(608\) 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 0.568708 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 \(-0.524842\pi\)
−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 \(-0.780299\pi\)
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 −0.326595 0.945164i \(-0.605901\pi\)
0.945164 + 0.326595i \(0.105901\pi\)
\(644\) −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 −0.0800295 0.996792i \(-0.525501\pi\)
0.996792 + 0.0800295i \(0.0255014\pi\)
\(648\) −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 −0.983845 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
\(658\) 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 \(-0.815651\pi\)
0.836929 0.547312i \(-0.184349\pi\)
\(662\) −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 0.774750 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 −0.636843 0.770994i \(-0.719760\pi\)
0.770994 + 0.636843i \(0.219760\pi\)
\(678\) −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 \(-0.761572\pi\)
0.732340 0.680939i \(-0.238428\pi\)
\(692\) 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 \(0.0699446\pi\)
−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
\(707\) 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 \(0.241646\pi\)
−0.725419 + 0.688307i \(0.758354\pi\)
\(710\) 170.760 434.020i 0.240507 0.611295i
\(711\) −379.408 + 62.8051i −0.533625 + 0.0883335i
\(712\) −38.7660 38.7660i −0.0544466 0.0544466i
\(713\) 41.9599 + 41.9599i 0.0588497 + 0.0588497i
\(714\) 183.497 + 826.825i 0.256998 + 1.15802i
\(715\) −334.590 131.641i −0.467958 0.184113i
\(716\) 97.6829i 0.136429i
\(717\) 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 \(-0.814079\pi\)
0.834216 0.551438i \(-0.185921\pi\)
\(720\) −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 0.0800261 0.996793i \(-0.474500\pi\)
−0.996793 + 0.0800261i \(0.974500\pi\)
\(728\) −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 −0.437476 0.899230i \(-0.644127\pi\)
0.899230 + 0.437476i \(0.144127\pi\)
\(734\) 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 \(0.242887\pi\)
−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
\(742\) −529.712 401.881i −0.713897 0.541618i
\(743\) 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
\(756\) 141.063 + 350.693i 0.186591 + 0.463879i
\(757\) 439.564 439.564i 0.580666 0.580666i −0.354420 0.935086i \(-0.615322\pi\)
0.935086 + 0.354420i \(0.115322\pi\)
\(758\) 339.431 339.431i 0.447798 0.447798i
\(759\) 13.6103 + 165.559i 0.0179319 + 0.218128i
\(760\) 136.761 347.604i 0.179948 0.457373i
\(761\) −1005.16 −1.32084 −0.660420 0.750897i \(-0.729622\pi\)
−0.660420 + 0.750897i \(0.729622\pi\)
\(762\) −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
\(767\)