Properties

Label 210.3.k.b.83.12
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 83.12
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.94039 + 2.28799i) q^{3} +2.00000i q^{4} +(-4.58449 + 1.99562i) q^{5} +(-0.347606 + 4.22838i) q^{6} +(5.57668 + 4.23091i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.46981 + 8.87917i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.94039 + 2.28799i) 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} +(-4.57598 + 3.88077i) q^{12} +(-3.48167 + 3.48167i) q^{13} +(1.34578 + 9.80759i) q^{14} +(-13.4616 - 6.61700i) q^{15} -4.00000 q^{16} +(-20.1653 + 20.1653i) q^{17} +(-10.3490 + 7.40936i) q^{18} +26.4132 q^{19} +(-3.99123 - 9.16897i) q^{20} +(1.14063 + 20.9690i) q^{21} +(14.6047 - 14.6047i) q^{22} +(2.68095 - 2.68095i) q^{23} +(-8.45675 - 0.695213i) q^{24} +(17.0350 - 18.2978i) q^{25} -6.96334 q^{26} +(-23.1675 + 13.8661i) q^{27} +(-8.46182 + 11.1534i) q^{28} +28.5159 q^{29} +(-6.84462 - 20.0786i) q^{30} -15.6511i q^{31} +(-4.00000 - 4.00000i) q^{32} +(33.4154 - 28.3387i) q^{33} -40.3306 q^{34} +(-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} +(-19.8284 + 22.1096i) q^{42} +(41.7817 + 41.7817i) q^{43} +29.2094 q^{44} +(-10.9811 - 43.6396i) q^{45} +5.36190 q^{46} +(21.0822 - 21.0822i) q^{47} +(-7.76154 - 9.15197i) q^{48} +(13.1988 + 47.1889i) q^{49} +(35.3328 - 1.26273i) q^{50} +(-85.2664 - 7.00958i) q^{51} +(-6.96334 - 6.96334i) q^{52} +(-47.4934 + 47.4934i) q^{53} +(-37.0336 - 9.30137i) q^{54} +(29.1453 + 66.9549i) q^{55} +(-19.6152 + 2.69155i) q^{56} +(51.2518 + 60.4332i) q^{57} +(28.5159 + 28.5159i) q^{58} -61.6589i q^{59} +(13.2340 - 26.9232i) q^{60} -54.1777i q^{61} +(15.6511 - 15.6511i) q^{62} +(-45.7636 + 43.2977i) 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} +(-14.8187 - 20.6980i) q^{72} +(6.51081 - 6.51081i) q^{73} +15.3969 q^{74} +(74.9196 + 3.47129i) q^{75} +52.8265i q^{76} +(61.7911 - 81.4457i) q^{77} +(-13.5116 - 15.9321i) q^{78} +42.7301i q^{79} +(18.3379 - 7.98247i) q^{80} +(-76.6793 - 26.1014i) q^{81} +(37.9832 + 37.9832i) q^{82} +(9.52614 + 9.52614i) q^{83} +(-41.9380 + 2.28126i) q^{84} +(52.2053 - 132.690i) q^{85} +83.5634i q^{86} +(55.3318 + 65.2441i) q^{87} +(29.2094 + 29.2094i) q^{88} +19.3830i q^{89} +(32.6585 - 54.6207i) q^{90} +(-34.1468 + 4.68555i) q^{91} +(5.36190 + 5.36190i) q^{92} +(35.8096 - 30.3692i) q^{93} +42.1644 q^{94} +(-121.091 + 52.7107i) q^{95} +(1.39043 - 16.9135i) q^{96} +(-84.6391 - 84.6391i) q^{97} +(-33.9901 + 60.3877i) q^{98} +(129.677 + 21.4661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} - 8q^{14} - 4q^{15} - 128q^{16} - 4q^{18} + 12q^{21} - 40q^{22} - 24q^{23} + 16q^{25} - 8q^{28} + 112q^{29} + 28q^{30} - 128q^{32} + 48q^{35} - 40q^{36} + 32q^{37} - 64q^{39} - 20q^{42} - 32q^{43} - 80q^{44} - 48q^{46} + 8q^{50} + 84q^{51} + 136q^{53} + 340q^{57} + 112q^{58} + 64q^{60} + 168q^{63} + 200q^{65} + 32q^{67} - 72q^{72} + 64q^{74} - 88q^{77} - 4q^{78} + 76q^{81} - 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} - 48q^{92} - 388q^{93} - 544q^{95} - 128q^{98} - 160q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) 1.94039 + 2.28799i 0.646795 + 0.762664i
\(4\) 2.00000i 0.500000i
\(5\) −4.58449 + 1.99562i −0.916897 + 0.399123i
\(6\) −0.347606 + 4.22838i −0.0579344 + 0.704729i
\(7\) 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 \(-0.231078\pi\)
\(12\) −4.57598 + 3.88077i −0.381332 + 0.323398i
\(13\) −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
\(15\) −13.4616 6.61700i −0.897442 0.441133i
\(16\) −4.00000 −0.250000
\(17\) −20.1653 + 20.1653i −1.18619 + 1.18619i −0.208081 + 0.978112i \(0.566722\pi\)
−0.978112 + 0.208081i \(0.933278\pi\)
\(18\) −10.3490 + 7.40936i −0.574943 + 0.411631i
\(19\) 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
\(21\) 1.14063 + 20.9690i 0.0543157 + 0.998524i
\(22\) 14.6047 14.6047i 0.663849 0.663849i
\(23\) 2.68095 2.68095i 0.116563 0.116563i −0.646419 0.762982i \(-0.723734\pi\)
0.762982 + 0.646419i \(0.223734\pi\)
\(24\) −8.45675 0.695213i −0.352365 0.0289672i
\(25\) 17.0350 18.2978i 0.681401 0.731910i
\(26\) −6.96334 −0.267821
\(27\) −23.1675 + 13.8661i −0.858054 + 0.513559i
\(28\) −8.46182 + 11.1534i −0.302208 + 0.398335i
\(29\) 28.5159 0.983306 0.491653 0.870791i \(-0.336393\pi\)
0.491653 + 0.870791i \(0.336393\pi\)
\(30\) −6.84462 20.0786i −0.228154 0.669287i
\(31\) 15.6511i 0.504875i −0.967613 0.252438i \(-0.918768\pi\)
0.967613 0.252438i \(-0.0812322\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 33.4154 28.3387i 1.01259 0.858748i
\(34\) −40.3306 −1.18619
\(35\) −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 \(-0.346698\pi\)
0.463209 + 0.886249i \(0.346698\pi\)
\(42\) −19.8284 + 22.1096i −0.472104 + 0.526420i
\(43\) 41.7817 + 41.7817i 0.971667 + 0.971667i 0.999610 0.0279426i \(-0.00889555\pi\)
−0.0279426 + 0.999610i \(0.508896\pi\)
\(44\) 29.2094 0.663849
\(45\) −10.9811 43.6396i −0.244024 0.969769i
\(46\) 5.36190 0.116563
\(47\) 21.0822 21.0822i 0.448558 0.448558i −0.446317 0.894875i \(-0.647265\pi\)
0.894875 + 0.446317i \(0.147265\pi\)
\(48\) −7.76154 9.15197i −0.161699 0.190666i
\(49\) 13.1988 + 47.1889i 0.269364 + 0.963039i
\(50\) 35.3328 1.26273i 0.706656 0.0252547i
\(51\) −85.2664 7.00958i −1.67189 0.137443i
\(52\) −6.96334 6.96334i −0.133910 0.133910i
\(53\) −47.4934 + 47.4934i −0.896102 + 0.896102i −0.995089 0.0989866i \(-0.968440\pi\)
0.0989866 + 0.995089i \(0.468440\pi\)
\(54\) −37.0336 9.30137i −0.685807 0.172248i
\(55\) 29.1453 + 66.9549i 0.529915 + 1.21736i
\(56\) −19.6152 + 2.69155i −0.350271 + 0.0480634i
\(57\) 51.2518 + 60.4332i 0.899155 + 1.06023i
\(58\) 28.5159 + 28.5159i 0.491653 + 0.491653i
\(59\) 61.6589i 1.04507i −0.852619 0.522533i \(-0.824987\pi\)
0.852619 0.522533i \(-0.175013\pi\)
\(60\) 13.2340 26.9232i 0.220567 0.448721i
\(61\) 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
\(63\) −45.7636 + 43.2977i −0.726407 + 0.687265i
\(64\) 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 \(-0.846233\pi\)
0.885572 0.464503i \(-0.153767\pi\)
\(72\) −14.8187 20.6980i −0.205816 0.287472i
\(73\) 6.51081 6.51081i 0.0891892 0.0891892i −0.661105 0.750294i \(-0.729912\pi\)
0.750294 + 0.661105i \(0.229912\pi\)
\(74\) 15.3969 0.208066
\(75\) 74.9196 + 3.47129i 0.998928 + 0.0462839i
\(76\) 52.8265i 0.695085i
\(77\) 61.7911 81.4457i 0.802481 1.05774i
\(78\) −13.5116 15.9321i −0.173225 0.204257i
\(79\) 42.7301i 0.540887i 0.962736 + 0.270443i \(0.0871703\pi\)
−0.962736 + 0.270443i \(0.912830\pi\)
\(80\) 18.3379 7.98247i 0.229224 0.0997809i
\(81\) −76.6793 26.1014i −0.946658 0.322240i
\(82\) 37.9832 + 37.9832i 0.463209 + 0.463209i
\(83\) 9.52614 + 9.52614i 0.114773 + 0.114773i 0.762161 0.647388i \(-0.224139\pi\)
−0.647388 + 0.762161i \(0.724139\pi\)
\(84\) −41.9380 + 2.28126i −0.499262 + 0.0271579i
\(85\) 52.2053 132.690i 0.614180 1.56105i
\(86\) 83.5634i 0.971667i
\(87\) 55.3318 + 65.2441i 0.635998 + 0.749932i
\(88\) 29.2094 + 29.2094i 0.331924 + 0.331924i
\(89\) 19.3830i 0.217786i 0.994053 + 0.108893i \(0.0347306\pi\)
−0.994053 + 0.108893i \(0.965269\pi\)
\(90\) 32.6585 54.6207i 0.362872 0.606897i
\(91\) −34.1468 + 4.68555i −0.375240 + 0.0514895i
\(92\) 5.36190 + 5.36190i 0.0582815 + 0.0582815i
\(93\) 35.8096 30.3692i 0.385050 0.326551i
\(94\) 42.1644 0.448558
\(95\) −121.091 + 52.7107i −1.27464 + 0.554849i
\(96\) 1.39043 16.9135i 0.0144836 0.176182i
\(97\) −84.6391 84.6391i −0.872568 0.872568i 0.120184 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 \(-0.688702\pi\)
−0.558707 + 0.829365i \(0.688702\pi\)
\(102\) −78.2568 92.2760i −0.767224 0.904666i
\(103\) −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
\(105\) −47.0753 93.8558i −0.448336 0.893865i
\(106\) −94.9868 −0.896102
\(107\) 125.554 + 125.554i 1.17340 + 1.17340i 0.981393 + 0.192011i \(0.0615011\pi\)
0.192011 + 0.981393i \(0.438499\pi\)
\(108\) −27.7322 46.3349i −0.256780 0.429027i
\(109\) 1.60754i 0.0147481i −0.999973 0.00737405i \(-0.997653\pi\)
0.999973 0.00737405i \(-0.00234725\pi\)
\(110\) −37.8096 + 96.1003i −0.343724 + 0.873639i
\(111\) 32.5519 + 2.67603i 0.293261 + 0.0241084i
\(112\) −22.3067 16.9236i −0.199167 0.151104i
\(113\) 141.505 141.505i 1.25226 1.25226i 0.297556 0.954704i \(-0.403828\pi\)
0.954704 0.297556i \(-0.0961715\pi\)
\(114\) −9.18141 + 111.685i −0.0805387 + 0.979694i
\(115\) −6.94062 + 17.6409i −0.0603532 + 0.153399i
\(116\) 57.0318i 0.491653i
\(117\) −25.7970 36.0318i −0.220487 0.307964i
\(118\) 61.6589 61.6589i 0.522533 0.522533i
\(119\) −197.773 + 27.1379i −1.66196 + 0.228050i
\(120\) 40.1572 13.6892i 0.334644 0.114077i
\(121\) −92.2966 −0.762782
\(122\) 54.1777 54.1777i 0.444080 0.444080i
\(123\) 73.7020 + 86.9052i 0.599203 + 0.706546i
\(124\) 31.3023 0.252438
\(125\) −41.5815 + 117.881i −0.332652 + 0.943050i
\(126\) −89.0613 2.46594i −0.706836 0.0195710i
\(127\) −39.5166 + 39.5166i −0.311154 + 0.311154i −0.845357 0.534202i \(-0.820612\pi\)
0.534202 + 0.845357i \(0.320612\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) −14.5236 + 176.669i −0.112586 + 1.36952i
\(130\) 31.9234 13.8962i 0.245564 0.106894i
\(131\) −122.046 −0.931652 −0.465826 0.884876i \(-0.654243\pi\)
−0.465826 + 0.884876i \(0.654243\pi\)
\(132\) 56.6774 + 66.8308i 0.429374 + 0.506294i
\(133\) 147.298 + 111.752i 1.10751 + 0.840240i
\(134\) 137.976 1.02967
\(135\) 78.5395 109.802i 0.581774 0.813350i
\(136\) 80.6611i 0.593096i
\(137\) −141.949 141.949i −1.03612 1.03612i −0.999323 0.0368001i \(-0.988284\pi\)
−0.0368001 0.999323i \(-0.511716\pi\)
\(138\) 10.4041 + 12.2680i 0.0753924 + 0.0888984i
\(139\) 41.4554 0.298240 0.149120 0.988819i \(-0.452356\pi\)
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
\(147\) −82.3570 + 121.763i −0.560252 + 0.828322i
\(148\) 15.3969 + 15.3969i 0.104033 + 0.104033i
\(149\) −189.375 −1.27097 −0.635485 0.772113i \(-0.719200\pi\)
−0.635485 + 0.772113i \(0.719200\pi\)
\(150\) 71.4483 + 78.3909i 0.476322 + 0.522606i
\(151\) −117.328 −0.777007 −0.388503 0.921447i \(-0.627008\pi\)
−0.388503 + 0.921447i \(0.627008\pi\)
\(152\) −52.8265 + 52.8265i −0.347542 + 0.347542i
\(153\) −149.412 208.690i −0.976548 1.36399i
\(154\) 143.237 19.6546i 0.930109 0.127627i
\(155\) 31.2337 + 71.7524i 0.201507 + 0.462919i
\(156\) 2.42050 29.4436i 0.0155160 0.188741i
\(157\) −123.504 123.504i −0.786651 0.786651i 0.194293 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
\(162\) −50.5779 102.781i −0.312209 0.634449i
\(163\) −173.541 173.541i −1.06467 1.06467i −0.997759 0.0669121i \(-0.978685\pi\)
−0.0669121 0.997759i \(-0.521315\pi\)
\(164\) 75.9663i 0.463209i
\(165\) −96.6391 + 196.603i −0.585692 + 1.19153i
\(166\) 19.0523i 0.114773i
\(167\) −32.6021 + 32.6021i −0.195222 + 0.195222i −0.797948 0.602726i \(-0.794081\pi\)
0.602726 + 0.797948i \(0.294081\pi\)
\(168\) −44.2193 39.6567i −0.263210 0.236052i
\(169\) 144.756i 0.856544i
\(170\) 184.895 80.4844i 1.08762 0.473437i
\(171\) −38.8225 + 234.528i −0.227032 + 1.37151i
\(172\) −83.5634 + 83.5634i −0.485833 + 0.485833i
\(173\) 122.097 + 122.097i 0.705761 + 0.705761i 0.965641 0.259880i \(-0.0836830\pi\)
−0.259880 + 0.965641i \(0.583683\pi\)
\(174\) −9.91231 + 120.576i −0.0569673 + 0.692965i
\(175\) 172.415 29.9672i 0.985229 0.171241i
\(176\) 58.4187i 0.331924i
\(177\) 141.075 119.642i 0.797034 0.675943i
\(178\) −19.3830 + 19.3830i −0.108893 + 0.108893i
\(179\) 48.8414 0.272857 0.136429 0.990650i \(-0.456438\pi\)
0.136429 + 0.990650i \(0.456438\pi\)
\(180\) 87.2792 21.9622i 0.484885 0.122012i
\(181\) 74.5578i 0.411921i −0.978560 0.205961i \(-0.933968\pi\)
0.978560 0.205961i \(-0.0660319\pi\)
\(182\) −38.8324 29.4613i −0.213365 0.161875i
\(183\) 123.958 105.126i 0.677367 0.574457i
\(184\) 10.7238i 0.0582815i
\(185\) −19.9303 + 50.6565i −0.107731 + 0.273819i
\(186\) 66.1789 + 5.44043i 0.355800 + 0.0292496i
\(187\) 294.507 + 294.507i 1.57491 + 1.57491i
\(188\) 42.1644 + 42.1644i 0.224279 + 0.224279i
\(189\) −187.864 20.6926i −0.993988 0.109485i
\(190\) −173.802 68.3804i −0.914746 0.359897i
\(191\) 22.0006i 0.115187i −0.998340 0.0575933i \(-0.981657\pi\)
0.998340 0.0575933i \(-0.0183427\pi\)
\(192\) 18.3039 15.5231i 0.0953330 0.0808494i
\(193\) −73.7660 73.7660i −0.382207 0.382207i 0.489690 0.871897i \(-0.337110\pi\)
−0.871897 + 0.489690i \(0.837110\pi\)
\(194\) 169.278i 0.872568i
\(195\) 69.9072 23.8307i 0.358498 0.122209i
\(196\) −94.3778 + 26.3976i −0.481519 + 0.134682i
\(197\) 124.480 + 124.480i 0.631878 + 0.631878i 0.948539 0.316661i \(-0.102562\pi\)
−0.316661 + 0.948539i \(0.602562\pi\)
\(198\) 108.211 + 151.144i 0.546522 + 0.763351i
\(199\) −324.188 −1.62908 −0.814542 0.580104i \(-0.803012\pi\)
−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
\(207\) 19.8641 + 27.7451i 0.0959619 + 0.134034i
\(208\) 13.9267 13.9267i 0.0669552 0.0669552i
\(209\) 385.757i 1.84573i
\(210\) 46.7805 140.931i 0.222764 0.671101i
\(211\) 29.3640 0.139166 0.0695828 0.997576i \(-0.477833\pi\)
0.0695828 + 0.997576i \(0.477833\pi\)
\(212\) −94.9868 94.9868i −0.448051 0.448051i
\(213\) 150.915 127.987i 0.708519 0.600876i
\(214\) 251.108i 1.17340i
\(215\) −274.928 108.167i −1.27873 0.503104i
\(216\) 18.6027 74.0671i 0.0861238 0.342903i
\(217\) 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
\(222\) 29.8759 + 35.2279i 0.134576 + 0.158684i
\(223\) −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
\(225\) 137.431 + 178.151i 0.610803 + 0.791783i
\(226\) 283.011 1.25226
\(227\) 152.211 152.211i 0.670535 0.670535i −0.287305 0.957839i \(-0.592759\pi\)
0.957839 + 0.287305i \(0.0927592\pi\)
\(228\) −120.866 + 102.504i −0.530116 + 0.449577i
\(229\) 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
\(231\) 306.245 16.6585i 1.32574 0.0721149i
\(232\) −57.0318 + 57.0318i −0.245827 + 0.245827i
\(233\) 216.913 216.913i 0.930957 0.930957i −0.0668091 0.997766i \(-0.521282\pi\)
0.997766 + 0.0668091i \(0.0212819\pi\)
\(234\) 10.2348 61.8287i 0.0437385 0.264225i
\(235\) −54.5791 + 138.723i −0.232251 + 0.590311i
\(236\) 123.318 0.522533
\(237\) −97.7660 + 82.9128i −0.412515 + 0.349843i
\(238\) −224.911 170.635i −0.945003 0.716953i
\(239\) 261.894 1.09579 0.547896 0.836547i \(-0.315429\pi\)
0.547896 + 0.836547i \(0.315429\pi\)
\(240\) 53.8465 + 26.4680i 0.224360 + 0.110283i
\(241\) 187.969i 0.779955i −0.920824 0.389978i \(-0.872483\pi\)
0.920824 0.389978i \(-0.127517\pi\)
\(242\) −92.2966 92.2966i −0.381391 0.381391i
\(243\) −89.0676 226.088i −0.366533 0.930405i
\(244\) 108.355 0.444080
\(245\) −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 \(-0.199861\pi\)
0.809273 + 0.587433i \(0.199861\pi\)
\(252\) −86.5954 91.5273i −0.343632 0.363203i
\(253\) −39.1544 39.1544i −0.154760 0.154760i
\(254\) −79.0332 −0.311154
\(255\) 404.891 138.024i 1.58781 0.541270i
\(256\) 16.0000 0.0625000
\(257\) −55.7465 + 55.7465i −0.216912 + 0.216912i −0.807196 0.590284i \(-0.799016\pi\)
0.590284 + 0.807196i \(0.299016\pi\)
\(258\) −191.192 + 162.145i −0.741055 + 0.628469i
\(259\) 75.5032 10.3604i 0.291518 0.0400014i
\(260\) 45.8195 + 18.0272i 0.176229 + 0.0693353i
\(261\) −41.9130 + 253.197i −0.160586 + 0.970105i
\(262\) −122.046 122.046i −0.465826 0.465826i
\(263\) −96.5716 + 96.5716i −0.367192 + 0.367192i −0.866452 0.499260i \(-0.833605\pi\)
0.499260 + 0.866452i \(0.333605\pi\)
\(264\) −10.1534 + 123.508i −0.0384597 + 0.467834i
\(265\) 122.954 312.512i 0.463978 1.17929i
\(266\) 35.5463 + 259.050i 0.133633 + 0.973873i
\(267\) −44.3481 + 37.6105i −0.166098 + 0.140863i
\(268\) 137.976 + 137.976i 0.514837 + 0.514837i
\(269\) 100.672i 0.374246i −0.982336 0.187123i \(-0.940084\pi\)
0.982336 0.187123i \(-0.0599163\pi\)
\(270\) 188.342 31.2628i 0.697562 0.115788i
\(271\) 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
\(273\) −76.9785 69.0359i −0.281972 0.252879i
\(274\) 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 \(-0.865981\pi\)
0.912667 0.408704i \(-0.134019\pi\)
\(282\) 81.8152 + 96.4718i 0.290125 + 0.342099i
\(283\) 170.587 170.587i 0.602781 0.602781i −0.338269 0.941049i \(-0.609841\pi\)
0.941049 + 0.338269i \(0.109841\pi\)
\(284\) 131.919 0.464503
\(285\) −355.565 174.776i −1.24760 0.613250i
\(286\) 101.697i 0.355585i
\(287\) 211.820 + 160.703i 0.738049 + 0.559942i
\(288\) 41.3959 29.6374i 0.143736 0.102908i
\(289\) 524.277i 1.81411i
\(290\) −187.637 73.8239i −0.647026 0.254565i
\(291\) 29.4211 357.886i 0.101103 1.22985i
\(292\) 13.0216 + 13.0216i 0.0445946 + 0.0445946i
\(293\) 186.419 + 186.419i 0.636243 + 0.636243i 0.949627 0.313384i \(-0.101463\pi\)
−0.313384 + 0.949627i \(0.601463\pi\)
\(294\) −204.120 + 39.4064i −0.694287 + 0.134035i
\(295\) 123.047 + 282.674i 0.417110 + 0.958218i
\(296\) 30.7938i 0.104033i
\(297\) 202.510 + 338.353i 0.681851 + 1.13924i
\(298\) −189.375 189.375i −0.635485 0.635485i
\(299\) 18.6684i 0.0624360i
\(300\) −6.94259 + 149.839i −0.0231420 + 0.499464i
\(301\) 56.2287 + 409.778i 0.186806 + 1.36139i
\(302\) −117.328 117.328i −0.388503 0.388503i
\(303\) −218.990 258.220i −0.722738 0.852211i
\(304\) −105.653 −0.347542
\(305\) 108.118 + 248.377i 0.354485 + 0.814351i
\(306\) 59.2783 358.102i 0.193720 1.17027i
\(307\) −9.77168 9.77168i −0.0318296 0.0318296i 0.691013 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 \(-0.575226\pi\)
−0.234136 + 0.972204i \(0.575226\pi\)
\(312\) 31.8641 27.0231i 0.102129 0.0866126i
\(313\) 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
\(315\) 123.397 289.824i 0.391737 0.920077i
\(316\) −85.4601 −0.270443
\(317\) 136.486 + 136.486i 0.430556 + 0.430556i 0.888817 0.458262i \(-0.151528\pi\)
−0.458262 + 0.888817i \(0.651528\pi\)
\(318\) −184.311 217.329i −0.579594 0.683425i
\(319\) 416.465i 1.30553i
\(320\) 15.9649 + 36.6759i 0.0498904 + 0.114612i
\(321\) −43.6435 + 530.891i −0.135961 + 1.65386i
\(322\) 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
\(327\) 3.67804 3.11925i 0.0112478 0.00953899i
\(328\) −75.9663 + 75.9663i −0.231605 + 0.231605i
\(329\) 206.766 28.3719i 0.628467 0.0862368i
\(330\) −293.242 + 99.9635i −0.888612 + 0.302920i
\(331\) 317.945 0.960559 0.480279 0.877116i \(-0.340535\pi\)
0.480279 + 0.877116i \(0.340535\pi\)
\(332\) −19.0523 + 19.0523i −0.0573864 + 0.0573864i
\(333\) 57.0405 + 79.6710i 0.171293 + 0.239252i
\(334\) −65.2042 −0.195222
\(335\) −178.601 + 453.949i −0.533138 + 1.35507i
\(336\) −4.56252 83.8760i −0.0135789 0.249631i
\(337\) 95.8647 95.8647i 0.284465 0.284465i −0.550422 0.834887i \(-0.685533\pi\)
0.834887 + 0.550422i \(0.185533\pi\)
\(338\) −144.756 + 144.756i −0.428272 + 0.428272i
\(339\) 598.338 + 49.1882i 1.76501 + 0.145098i
\(340\) 265.379 + 104.411i 0.780527 + 0.307090i
\(341\) −228.580 −0.670322
\(342\) −273.350 + 195.705i −0.799269 + 0.572237i
\(343\) −126.046 + 319.001i −0.367482 + 0.930031i
\(344\) −167.127 −0.485833
\(345\) −53.8298 + 18.3501i −0.156028 + 0.0531886i
\(346\) 244.193i 0.705761i
\(347\) 76.3053 + 76.3053i 0.219900 + 0.219900i 0.808456 0.588556i \(-0.200303\pi\)
−0.588556 + 0.808456i \(0.700303\pi\)
\(348\) −130.488 + 110.664i −0.374966 + 0.317999i
\(349\) −27.7850 −0.0796133 −0.0398067 0.999207i \(-0.512674\pi\)
−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 \(-0.126564\pi\)
−0.387218 + 0.921988i \(0.626564\pi\)
\(354\) 260.717 + 21.4330i 0.736488 + 0.0605452i
\(355\) 131.630 + 302.390i 0.370788 + 0.851803i
\(356\) −38.7660 −0.108893
\(357\) −445.847 399.845i −1.24887 1.12001i
\(358\) 48.8414 + 48.8414i 0.136429 + 0.136429i
\(359\) −171.974 −0.479037 −0.239519 0.970892i \(-0.576990\pi\)
−0.239519 + 0.970892i \(0.576990\pi\)
\(360\) 109.241 + 65.3170i 0.303448 + 0.181436i
\(361\) 336.659 0.932572
\(362\) 74.5578 74.5578i 0.205961 0.205961i
\(363\) −179.091 211.174i −0.493364 0.581746i
\(364\) −9.37109 68.2936i −0.0257448 0.187620i
\(365\) −16.8556 + 42.8418i −0.0461798 + 0.117375i
\(366\) 229.084 + 18.8325i 0.625912 + 0.0514550i
\(367\) −181.555 181.555i −0.494700 0.494700i 0.415083 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
\(372\) 60.7384 + 71.6193i 0.163275 + 0.192525i
\(373\) −104.153 104.153i −0.279231 0.279231i 0.553571 0.832802i \(-0.313265\pi\)
−0.832802 + 0.553571i \(0.813265\pi\)
\(374\) 589.015i 1.57491i
\(375\) −350.395 + 133.597i −0.934388 + 0.356258i
\(376\) 84.3288i 0.224279i
\(377\) −99.2830 + 99.2830i −0.263350 + 0.263350i
\(378\) −167.171 208.556i −0.442252 0.551737i
\(379\) 339.431i 0.895596i 0.894135 + 0.447798i \(0.147792\pi\)
−0.894135 + 0.447798i \(0.852208\pi\)
\(380\) −105.421 242.182i −0.277425 0.637321i
\(381\) −167.091 13.7362i −0.438559 0.0360531i
\(382\) 22.0006 22.0006i 0.0575933 0.0575933i
\(383\) −187.161 187.161i −0.488670 0.488670i 0.419217 0.907886i \(-0.362305\pi\)
−0.907886 + 0.419217i \(0.862305\pi\)
\(384\) 33.8270 + 2.78085i 0.0880912 + 0.00724180i
\(385\) −120.746 + 496.698i −0.313626 + 1.29012i
\(386\) 147.532i 0.382207i
\(387\) −432.398 + 309.575i −1.11731 + 0.799937i
\(388\) 169.278 169.278i 0.436284 0.436284i
\(389\) 511.312 1.31443 0.657214 0.753704i \(-0.271735\pi\)
0.657214 + 0.753704i \(0.271735\pi\)
\(390\) 93.7379 + 46.0764i 0.240354 + 0.118145i
\(391\) 108.124i 0.276532i
\(392\) −120.775 67.9801i −0.308101 0.173419i
\(393\) −236.817 279.241i −0.602588 0.710537i
\(394\) 248.960i 0.631878i
\(395\) −85.2729 195.895i −0.215881 0.495938i
\(396\) −42.9322 + 259.355i −0.108415 + 0.654936i
\(397\) 448.583 + 448.583i 1.12993 + 1.12993i 0.990188 + 0.139744i \(0.0446280\pi\)
0.139744 + 0.990188i \(0.455372\pi\)
\(398\) −324.188 324.188i −0.814542 0.814542i
\(399\) 30.1277 + 553.859i 0.0755081 + 1.38812i
\(400\) −68.1401 + 73.1910i −0.170350 + 0.182978i
\(401\) 44.3430i 0.110581i 0.998470 + 0.0552905i \(0.0176085\pi\)
−0.998470 + 0.0552905i \(0.982391\pi\)
\(402\) 267.727 + 315.689i 0.665988 + 0.785295i
\(403\) 54.4921 + 54.4921i 0.135216 + 0.135216i
\(404\) 225.718i 0.558707i
\(405\) 403.624 33.3610i 0.996602 0.0823729i
\(406\) 38.3760 + 279.672i 0.0945221 + 0.688848i
\(407\) −112.433 112.433i −0.276249 0.276249i
\(408\) 184.552 156.514i 0.452333 0.383612i
\(409\) −392.358 −0.959311 −0.479656 0.877457i \(-0.659238\pi\)
−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
\(417\) 80.4394 + 94.8495i 0.192900 + 0.227457i
\(418\) 385.757 385.757i 0.922863 0.922863i
\(419\) 383.324i 0.914855i 0.889247 + 0.457427i \(0.151229\pi\)
−0.889247 + 0.457427i \(0.848771\pi\)
\(420\) 187.712 94.1506i 0.446933 0.224168i
\(421\) 809.373 1.92250 0.961250 0.275678i \(-0.0889023\pi\)
0.961250 + 0.275678i \(0.0889023\pi\)
\(422\) 29.3640 + 29.3640i 0.0695828 + 0.0695828i
\(423\) 156.206 + 218.179i 0.369281 + 0.515791i
\(424\) 189.974i 0.448051i
\(425\) 25.4634 + 712.495i 0.0599139 + 1.67646i
\(426\) 278.901 + 22.9279i 0.654698 + 0.0538214i
\(427\) 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 \(0.832619\pi\)
\(432\) 92.6699 55.4644i 0.214514 0.128390i
\(433\) −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
\(435\) −383.870 188.690i −0.882460 0.433769i
\(436\) 3.21508 0.00737405
\(437\) 70.8125 70.8125i 0.162042 0.162042i
\(438\) 25.2670 + 29.7934i 0.0576871 + 0.0680214i
\(439\) −652.665 −1.48671 −0.743354 0.668898i \(-0.766766\pi\)
−0.743354 + 0.668898i \(0.766766\pi\)
\(440\) −192.201 75.6192i −0.436819 0.171862i
\(441\) −438.398 + 47.8358i −0.994100 + 0.108471i
\(442\) 140.418 140.418i 0.317687 0.317687i
\(443\) −429.708 + 429.708i −0.969996 + 0.969996i −0.999563 0.0295673i \(-0.990587\pi\)
0.0295673 + 0.999563i \(0.490587\pi\)
\(444\) −5.35206 + 65.1038i −0.0120542 + 0.146630i
\(445\) −38.6810 88.8610i −0.0869236 0.199688i
\(446\) −407.103 −0.912788
\(447\) −367.460 433.287i −0.822057 0.969323i
\(448\) 33.8473 44.6135i 0.0755519 0.0995836i
\(449\) −544.342 −1.21234 −0.606171 0.795334i \(-0.707295\pi\)
−0.606171 + 0.795334i \(0.707295\pi\)
\(450\) −40.7205 + 315.582i −0.0904900 + 0.701293i
\(451\) 554.732i 1.23000i
\(452\) 283.011 + 283.011i 0.626130 + 0.626130i
\(453\) −227.662 268.446i −0.502564 0.592595i
\(454\) 304.423 0.670535
\(455\) 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 \(-0.505631\pi\)
−0.0176900 + 0.999844i \(0.505631\pi\)
\(462\) 322.904 + 289.587i 0.698926 + 0.626812i
\(463\) −401.469 401.469i −0.867104 0.867104i 0.125047 0.992151i \(-0.460092\pi\)
−0.992151 + 0.125047i \(0.960092\pi\)
\(464\) −114.064 −0.245827
\(465\) −103.564 + 210.690i −0.222717 + 0.453096i
\(466\) 433.826 0.930957
\(467\) 371.481 371.481i 0.795462 0.795462i −0.186914 0.982376i \(-0.559849\pi\)
0.982376 + 0.186914i \(0.0598486\pi\)
\(468\) 72.0635 51.5939i 0.153982 0.110243i
\(469\) 676.608 92.8425i 1.44266 0.197959i
\(470\) −193.302 + 84.1441i −0.411281 + 0.179030i
\(471\) 42.9309 522.222i 0.0911483 1.10875i
\(472\) 123.318 + 123.318i 0.261266 + 0.261266i
\(473\) 610.208 610.208i 1.29008 1.29008i
\(474\) −180.679 14.8532i −0.381179 0.0313360i
\(475\) 449.950 483.303i 0.947263 1.01748i
\(476\) −54.2759 395.546i −0.114025 0.830978i
\(477\) −351.896 491.508i −0.737727 1.03042i
\(478\) 261.894 + 261.894i 0.547896 + 0.547896i
\(479\) 615.307i 1.28457i −0.766467 0.642283i \(-0.777987\pi\)
0.766467 0.642283i \(-0.222013\pi\)
\(480\) 27.3785 + 80.3145i 0.0570385 + 0.167322i
\(481\) 53.6069i 0.111449i
\(482\) 187.969 187.969i 0.389978 0.389978i
\(483\) 59.2748 + 53.1588i 0.122722 + 0.110060i
\(484\) 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 \(0.00379747\pi\)
−0.999929 + 0.0119298i \(0.996203\pi\)
\(492\) −173.810 + 147.404i −0.353273 + 0.299602i
\(493\) −575.031 + 575.031i −1.16639 + 1.16639i
\(494\) −183.924 −0.372317
\(495\) −637.342 + 160.375i −1.28756 + 0.323991i
\(496\) 62.6045i 0.126219i
\(497\) 279.068 367.835i 0.561506 0.740110i
\(498\) −43.5915 + 36.9688i −0.0875330 + 0.0742345i
\(499\) 11.1783i 0.0224014i 0.999937 + 0.0112007i \(0.00356537\pi\)
−0.999937 + 0.0112007i \(0.996435\pi\)
\(500\) −235.762 83.1630i −0.471525 0.166326i
\(501\) −137.854 11.3327i −0.275157 0.0226201i
\(502\) 406.255 + 406.255i 0.809273 + 0.809273i
\(503\) 15.0212 + 15.0212i 0.0298632 + 0.0298632i 0.721881 0.692017i \(-0.243278\pi\)
−0.692017 + 0.721881i \(0.743278\pi\)
\(504\) 4.93189 178.123i 0.00978549 0.353418i
\(505\) 517.400 225.223i 1.02455 0.445986i
\(506\) 78.3088i 0.154760i
\(507\) −331.200 + 280.882i −0.653255 + 0.554008i
\(508\) −79.0332 79.0332i −0.155577 0.155577i
\(509\) 62.6374i 0.123060i −0.998105 0.0615298i \(-0.980402\pi\)
0.998105 0.0615298i \(-0.0195979\pi\)
\(510\) 542.915 + 266.867i 1.06454 + 0.523269i
\(511\) 63.8554 8.76209i 0.124962 0.0171469i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −611.928 + 366.248i −1.19284 + 0.713934i
\(514\) −111.493 −0.216912
\(515\) 213.810 543.440i 0.415166 1.05522i
\(516\) −353.337 29.0472i −0.684762 0.0562930i
\(517\) −307.899 307.899i −0.595549 0.595549i
\(518\) 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 \(-0.499124\pi\)
0.00275129 + 0.999996i \(0.499124\pi\)
\(522\) −295.110 + 211.284i −0.565345 + 0.404759i
\(523\) 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
\(525\) 403.116 + 336.336i 0.767841 + 0.640641i
\(526\) −193.143 −0.367192
\(527\) 315.609 + 315.609i 0.598879 + 0.598879i
\(528\) −133.662 + 113.355i −0.253147 + 0.214687i
\(529\) 514.625i 0.972826i
\(530\) 435.466 189.557i 0.821634 0.357655i
\(531\) 547.479 + 90.6269i 1.03103 + 0.170672i
\(532\) −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
\(537\) 94.7712 + 111.749i 0.176483 + 0.208098i
\(538\) 100.672 100.672i 0.187123 0.187123i
\(539\) 689.179 192.764i 1.27862 0.357633i
\(540\) 219.605 + 157.079i 0.406675 + 0.290887i
\(541\) −544.738 −1.00691 −0.503454 0.864022i \(-0.667938\pi\)
−0.503454 + 0.864022i \(0.667938\pi\)
\(542\) 299.070 299.070i 0.551790 0.551790i
\(543\) 170.588 144.671i 0.314158 0.266429i
\(544\) 161.322 0.296548
\(545\) 3.20804 + 7.36976i 0.00588631 + 0.0135225i
\(546\) −7.94260 146.014i −0.0145469 0.267426i
\(547\) −644.286 + 644.286i −1.17785 + 1.17785i −0.197564 + 0.980290i \(0.563303\pi\)
−0.980290 + 0.197564i \(0.936697\pi\)
\(548\) 283.898 283.898i 0.518061 0.518061i
\(549\) 481.053 + 79.6310i 0.876235 + 0.145047i
\(550\) −18.4418 516.024i −0.0335306 0.938225i
\(551\) 753.197 1.36696
\(552\) −24.5359 + 20.8083i −0.0444492 + 0.0376962i
\(553\) −180.787 + 238.292i −0.326921 + 0.430908i
\(554\) −621.005 −1.12095
\(555\) −154.574 + 52.6929i −0.278512 + 0.0949423i
\(556\) 82.9107i 0.149120i
\(557\) −180.720 180.720i −0.324452 0.324452i 0.526020 0.850472i \(-0.323684\pi\)
−0.850472 + 0.526020i \(0.823684\pi\)
\(558\) 115.965 + 161.973i 0.207822 + 0.290275i
\(559\) −290.940 −0.520465
\(560\) 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 \(-0.256588\pi\)
−0.721590 + 0.692321i \(0.756588\pi\)
\(564\) −14.6566 + 178.287i −0.0259869 + 0.316112i
\(565\) −366.339 + 931.120i −0.648388 + 1.64800i
\(566\) 341.174 0.602781
\(567\) −317.184 469.982i −0.559407 0.828893i
\(568\) 131.919 + 131.919i 0.232251 + 0.232251i
\(569\) −354.571 −0.623147 −0.311574 0.950222i \(-0.600856\pi\)
−0.311574 + 0.950222i \(0.600856\pi\)
\(570\) −180.789 530.341i −0.317173 0.930423i
\(571\) −110.075 −0.192777 −0.0963883 0.995344i \(-0.530729\pi\)
−0.0963883 + 0.995344i \(0.530729\pi\)
\(572\) −101.697 + 101.697i −0.177793 + 0.177793i
\(573\) 50.3372 42.6897i 0.0878486 0.0745021i
\(574\) 51.1168 + 372.524i 0.0890537 + 0.648996i
\(575\) −3.38533 94.7254i −0.00588752 0.164740i
\(576\) 71.0334 + 11.7585i 0.123322 + 0.0204140i
\(577\) 212.392 + 212.392i 0.368097 + 0.368097i 0.866783 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
\(582\) 387.307 328.465i 0.665476 0.564372i
\(583\) 693.626 + 693.626i 1.18975 + 1.18975i
\(584\) 26.0432i 0.0445946i
\(585\) 190.171 + 113.706i 0.325079 + 0.194370i
\(586\) 372.838i 0.636243i
\(587\) −277.047 + 277.047i −0.471972 + 0.471972i −0.902552 0.430580i \(-0.858309\pi\)
0.430580 + 0.902552i \(0.358309\pi\)
\(588\) −243.527 164.714i −0.414161 0.280126i
\(589\) 413.397i 0.701862i
\(590\) −159.627 + 405.722i −0.270554 + 0.687664i
\(591\) −43.2700 + 526.348i −0.0732150 + 0.890606i
\(592\) −30.7938 + 30.7938i −0.0520165 + 0.0520165i
\(593\) 118.407 + 118.407i 0.199674 + 0.199674i 0.799860 0.600186i \(-0.204907\pi\)
−0.600186 + 0.799860i \(0.704907\pi\)
\(594\) −135.844 + 540.863i −0.228693 + 0.910544i
\(595\) 852.530 519.092i 1.43282 0.872424i
\(596\) 378.749i 0.635485i
\(597\) −629.049 741.739i −1.05368 1.24244i
\(598\) −18.6684 + 18.6684i −0.0312180 + 0.0312180i
\(599\) 254.409 0.424722 0.212361 0.977191i \(-0.431885\pi\)
0.212361 + 0.977191i \(0.431885\pi\)
\(600\) −156.782 + 142.897i −0.261303 + 0.238161i
\(601\) 335.032i 0.557458i 0.960370 + 0.278729i \(0.0899131\pi\)
−0.960370 + 0.278729i \(0.910087\pi\)
\(602\) −353.549 + 466.006i −0.587291 + 0.774097i
\(603\) 511.158 + 713.957i 0.847692 + 1.18401i
\(604\) 234.656i 0.388503i
\(605\) 423.132 184.189i 0.699393 0.304444i
\(606\) 39.2304 477.210i 0.0647367 0.787474i
\(607\) 537.196 + 537.196i 0.885002 + 0.885002i 0.994038 0.109036i \(-0.0347763\pi\)
−0.109036 + 0.994038i \(0.534776\pi\)
\(608\) −105.653 105.653i −0.173771 0.173771i
\(609\) 32.5261 + 597.950i 0.0534090 + 0.981855i
\(610\) −140.259 + 356.495i −0.229933 + 0.584418i
\(611\) 146.803i 0.240266i
\(612\) 417.380 298.824i 0.681994 0.488274i
\(613\) −155.599 155.599i −0.253832 0.253832i 0.568708 0.822540i \(-0.307444\pi\)
−0.822540 + 0.568708i \(0.807444\pi\)
\(614\) 19.5434i 0.0318296i
\(615\) −511.315 251.335i −0.831407 0.408674i
\(616\) 39.3092 + 286.473i 0.0638137 + 0.465054i
\(617\) −533.777 533.777i −0.865116 0.865116i 0.126811 0.991927i \(-0.459526\pi\)
−0.991927 + 0.126811i \(0.959526\pi\)
\(618\) −320.506 377.923i −0.518619 0.611526i
\(619\) −96.5213 −0.155931 −0.0779655 0.996956i \(-0.524842\pi\)
−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
\(627\) 882.608 748.516i 1.40767 1.19381i
\(628\) 247.008 247.008i 0.393326 0.393326i
\(629\) 310.482i 0.493613i
\(630\) 413.221 166.427i 0.655907 0.264170i
\(631\) −797.287 −1.26353 −0.631765 0.775160i \(-0.717669\pi\)
−0.631765 + 0.775160i \(0.717669\pi\)
\(632\) −85.4601 85.4601i −0.135222 0.135222i
\(633\) 56.9774 + 67.1845i 0.0900117 + 0.106137i
\(634\) 272.972i 0.430556i
\(635\) 102.303 260.023i 0.161108 0.409485i
\(636\) 33.0180 401.640i 0.0519151 0.631510i
\(637\) −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 \(0.780299\pi\)
\(642\) −574.534 + 487.247i −0.894913 + 0.758952i
\(643\) 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
\(645\) −285.980 838.919i −0.443380 1.30065i
\(646\) −1065.26 −1.64901
\(647\) −593.146 + 593.146i −0.916763 + 0.916763i −0.996792 0.0800295i \(-0.974499\pi\)
0.0800295 + 0.996792i \(0.474499\pi\)
\(648\) 205.561 101.156i 0.317224 0.156105i
\(649\) −900.508 −1.38753
\(650\) −118.621 + 127.414i −0.182493 + 0.196021i
\(651\) 328.189 17.8522i 0.504130 0.0274227i
\(652\) 347.083 347.083i 0.532335 0.532335i
\(653\) 525.550 525.550i 0.804824 0.804824i −0.179021 0.983845i \(-0.557293\pi\)
0.983845 + 0.179021i \(0.0572930\pi\)
\(654\) 6.79729 + 0.558792i 0.0103934 + 0.000854422i
\(655\) 559.520 243.558i 0.854229 0.371844i
\(656\) −151.933 −0.231605
\(657\) 48.2409 + 67.3803i 0.0734261 + 0.102557i
\(658\) 235.138 + 178.394i 0.357352 + 0.271115i
\(659\) −415.401 −0.630350 −0.315175 0.949034i \(-0.602063\pi\)
−0.315175 + 0.949034i \(0.602063\pi\)
\(660\) −393.205 193.278i −0.595766 0.292846i
\(661\) 723.547i 1.09462i −0.836929 0.547312i \(-0.815651\pi\)
0.836929 0.547312i \(-0.184349\pi\)
\(662\) 317.945 + 317.945i 0.480279 + 0.480279i
\(663\) 321.275 272.465i 0.484577 0.410957i
\(664\) −38.1046 −0.0573864
\(665\) −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
\(672\) 79.3135 88.4385i 0.118026 0.131605i
\(673\) 95.8909 + 95.8909i 0.142483 + 0.142483i 0.774750 0.632267i \(-0.217876\pi\)
−0.632267 + 0.774750i \(0.717876\pi\)
\(674\) 191.729 0.284465
\(675\) −140.940 + 660.122i −0.208800 + 0.977958i
\(676\) −289.512 −0.428272
\(677\) −90.8203 + 90.8203i −0.134151 + 0.134151i −0.770994 0.636843i \(-0.780240\pi\)
0.636843 + 0.770994i \(0.280240\pi\)
\(678\) 549.150 + 647.526i 0.809956 + 0.955054i
\(679\) −113.905 830.106i −0.167754 1.22254i
\(680\) 160.969 + 369.790i 0.236719 + 0.543808i
\(681\) 643.607 + 52.9096i 0.945091 + 0.0776940i
\(682\) −228.580 228.580i −0.335161 0.335161i
\(683\) −572.076 + 572.076i −0.837593 + 0.837593i −0.988542 0.150948i \(-0.951767\pi\)
0.150948 + 0.988542i \(0.451767\pi\)
\(684\) −469.055 77.6449i −0.685753 0.113516i
\(685\) 934.038 + 367.487i 1.36356 + 0.536477i
\(686\) −445.047 + 192.954i −0.648756 + 0.281274i
\(687\) 425.808 + 502.088i 0.619808 + 0.730842i
\(688\) −167.127 167.127i −0.242917 0.242917i
\(689\) 330.713i 0.479990i
\(690\) −72.1798 35.4797i −0.104608 0.0514198i
\(691\) 941.057i 1.36188i −0.732340 0.680939i \(-0.761572\pi\)
0.732340 0.680939i \(-0.238428\pi\)
\(692\) −244.193 + 244.193i −0.352880 + 0.352880i
\(693\) 632.349 + 668.363i 0.912480 + 0.964449i
\(694\) 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 \(-0.0699446\pi\)
\(702\) 161.323 96.5544i 0.229805 0.137542i
\(703\) 203.341 203.341i 0.289247 0.289247i
\(704\) −116.837 −0.165962
\(705\) −423.302 + 144.300i −0.600428 + 0.204681i
\(706\) 377.547i 0.534769i
\(707\) −629.378 477.495i −0.890209 0.675382i
\(708\) 239.284 + 282.150i 0.337972 + 0.398517i
\(709\) 976.020i 1.37661i 0.725419 + 0.688307i \(0.241646\pi\)
−0.725419 + 0.688307i \(0.758354\pi\)
\(710\) −170.760 + 434.020i −0.240507 + 0.611295i
\(711\) −379.408 62.8051i −0.533625 0.0883335i
\(712\) −38.7660 38.7660i −0.0544466 0.0544466i
\(713\) −41.9599 41.9599i −0.0588497 0.0588497i
\(714\) −46.0023 845.691i −0.0644289 1.18444i
\(715\) −334.590 131.641i −0.467958 0.184113i
\(716\) 97.6829i 0.136429i
\(717\) 508.176 + 599.212i 0.708753 + 0.835721i
\(718\) −171.974 171.974i −0.239519 0.239519i
\(719\) 792.968i 1.10288i 0.834216 + 0.551438i \(0.185921\pi\)
−0.834216 + 0.551438i \(0.814079\pi\)
\(720\) 43.9244 + 174.558i 0.0610061 + 0.242442i
\(721\) −809.993 + 111.145i −1.12343 + 0.154154i
\(722\) 336.659 + 336.659i 0.466286 + 0.466286i
\(723\) 430.072 364.733i 0.594844 0.504471i
\(724\) 149.116 0.205961
\(725\) 485.769 521.777i 0.670026 0.719692i
\(726\) 32.0829 390.265i 0.0441913 0.537555i
\(727\) −666.489 666.489i −0.916767 0.916767i 0.0800261 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
\(732\) 210.251 + 247.916i 0.287228 + 0.338683i
\(733\) 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
\(735\) 134.571 722.576i 0.183090 0.983096i
\(736\) −21.4476 −0.0291407
\(737\) −1007.55 1007.55i −1.36710 1.36710i
\(738\) −393.087 + 281.431i −0.532638 + 0.381343i
\(739\) 1021.49i 1.38226i 0.722730 + 0.691130i \(0.242887\pi\)
−0.722730 + 0.691130i \(0.757113\pi\)
\(740\) −101.313 39.8605i −0.136910 0.0538656i
\(741\) −388.851 31.9667i −0.524765 0.0431399i
\(742\) −529.712 401.881i −0.713897 0.541618i
\(743\) −262.382 + 262.382i −0.353138 + 0.353138i −0.861276 0.508138i \(-0.830334\pi\)
0.508138 + 0.861276i \(0.330334\pi\)
\(744\) −10.8809 + 132.358i −0.0146248 + 0.177900i
\(745\) 868.185 377.919i 1.16535 0.507274i
\(746\) 208.307i 0.279231i
\(747\) −98.5858 + 70.5826i −0.131976 + 0.0944881i
\(748\) −589.015 + 589.015i −0.787453 + 0.787453i
\(749\) 168.968 + 1231.38i 0.225591 + 1.64404i
\(750\) −483.992 216.799i −0.645323 0.289065i
\(751\) −429.513 −0.571922 −0.285961 0.958241i \(-0.592313\pi\)
−0.285961 + 0.958241i \(0.592313\pi\)
\(752\) −84.3288 + 84.3288i −0.112139 + 0.112139i
\(753\) 788.291 + 929.508i 1.04687 + 1.23441i
\(754\) −198.566 −0.263350
\(755\) 537.889 234.142i 0.712436 0.310122i
\(756\) 41.3852 375.728i 0.0547424 0.496994i
\(757\) 439.564 439.564i 0.580666 0.580666i −0.354420 0.935086i \(-0.615322\pi\)
0.935086 + 0.354420i \(0.115322\pi\)
\(758\) −339.431 + 339.431i −0.447798 + 0.447798i
\(759\) 13.6103 165.559i 0.0179319 0.218128i
\(760\) 136.761 347.604i 0.179948 0.457373i
\(761\) 1005.16 1.32084 0.660420 0.750897i \(-0.270378\pi\)
0.660420 + 0.750897i \(0.270378\pi\)
\(762\) −153.355 180.827i −0.201253 0.237306i
\(763\) 6.80137 8.96476i 0.00891398 0.0117494i
\(764\) 44.0013 0.0575933
\(765\) 1101.44 + 658.568i 1.43979 + 0.860873i
\(766\) 374.321i 0.488670i
\(767\) 214.676 + 214.676i 0.279890 + 0.279890i
\(768\)