Properties

Label 690.3.k.a.277.8
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.8
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-1.94861 - 4.60466i) q^{5} -2.44949 q^{6} +(-2.18869 - 2.18869i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-1.94861 - 4.60466i) q^{5} -2.44949 q^{6} +(-2.18869 - 2.18869i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(2.65606 - 6.55327i) q^{10} +0.598986 q^{11} +(-2.44949 - 2.44949i) q^{12} +(2.44971 - 2.44971i) q^{13} -4.37738i q^{14} +(8.02608 + 3.25299i) q^{15} -4.00000 q^{16} +(17.9496 + 17.9496i) q^{17} +(3.00000 - 3.00000i) q^{18} +17.4222i q^{19} +(9.20933 - 3.89721i) q^{20} +5.36117 q^{21} +(0.598986 + 0.598986i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-17.4059 + 17.9454i) q^{25} +4.89943 q^{26} +(3.67423 + 3.67423i) q^{27} +(4.37738 - 4.37738i) q^{28} +25.3649i q^{29} +(4.77309 + 11.2791i) q^{30} +49.7350 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.733605 + 0.733605i) q^{33} +35.8993i q^{34} +(-5.81329 + 14.3431i) q^{35} +6.00000 q^{36} +(42.3579 + 42.3579i) q^{37} +(-17.4222 + 17.4222i) q^{38} +6.00055i q^{39} +(13.1065 + 5.31212i) q^{40} -59.6411 q^{41} +(5.36117 + 5.36117i) q^{42} +(-37.2918 + 37.2918i) q^{43} +1.19797i q^{44} +(-13.8140 + 5.84582i) q^{45} -6.78233 q^{46} +(3.72350 + 3.72350i) q^{47} +(4.89898 - 4.89898i) q^{48} -39.4193i q^{49} +(-35.3512 + 0.539488i) q^{50} -43.9674 q^{51} +(4.89943 + 4.89943i) q^{52} +(66.2177 - 66.2177i) q^{53} +7.34847i q^{54} +(-1.16719 - 2.75813i) q^{55} +8.75476 q^{56} +(-21.3378 - 21.3378i) q^{57} +(-25.3649 + 25.3649i) q^{58} +106.735i q^{59} +(-6.50599 + 16.0522i) q^{60} +56.8619 q^{61} +(49.7350 + 49.7350i) q^{62} +(-6.56607 + 6.56607i) q^{63} -8.00000i q^{64} +(-16.0536 - 6.50658i) q^{65} -1.46721 q^{66} +(-5.50781 - 5.50781i) q^{67} +(-35.8993 + 35.8993i) q^{68} -8.30662i q^{69} +(-20.1564 + 8.52979i) q^{70} -18.4588 q^{71} +(6.00000 + 6.00000i) q^{72} +(1.41110 - 1.41110i) q^{73} +84.7158i q^{74} +(-0.660735 - 43.2962i) q^{75} -34.8444 q^{76} +(-1.31099 - 1.31099i) q^{77} +(-6.00055 + 6.00055i) q^{78} +123.331i q^{79} +(7.79442 + 18.4187i) q^{80} -9.00000 q^{81} +(-59.6411 - 59.6411i) q^{82} +(34.1108 - 34.1108i) q^{83} +10.7223i q^{84} +(47.6753 - 117.629i) q^{85} -74.5836 q^{86} +(-31.0655 - 31.0655i) q^{87} +(-1.19797 + 1.19797i) q^{88} -55.0628i q^{89} +(-19.6598 - 7.96817i) q^{90} -10.7233 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-60.9127 + 60.9127i) q^{93} +7.44701i q^{94} +(80.2234 - 33.9490i) q^{95} +9.79796 q^{96} +(55.4956 + 55.4956i) q^{97} +(39.4193 - 39.4193i) q^{98} -1.79696i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −1.94861 4.60466i −0.389721 0.920933i
\(6\) −2.44949 −0.408248
\(7\) −2.18869 2.18869i −0.312670 0.312670i 0.533273 0.845943i \(-0.320962\pi\)
−0.845943 + 0.533273i \(0.820962\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 2.65606 6.55327i 0.265606 0.655327i
\(11\) 0.598986 0.0544533 0.0272266 0.999629i \(-0.491332\pi\)
0.0272266 + 0.999629i \(0.491332\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) 2.44971 2.44971i 0.188440 0.188440i −0.606582 0.795021i \(-0.707460\pi\)
0.795021 + 0.606582i \(0.207460\pi\)
\(14\) 4.37738i 0.312670i
\(15\) 8.02608 + 3.25299i 0.535072 + 0.216866i
\(16\) −4.00000 −0.250000
\(17\) 17.9496 + 17.9496i 1.05586 + 1.05586i 0.998345 + 0.0575162i \(0.0183181\pi\)
0.0575162 + 0.998345i \(0.481682\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 17.4222i 0.916958i 0.888705 + 0.458479i \(0.151606\pi\)
−0.888705 + 0.458479i \(0.848394\pi\)
\(20\) 9.20933 3.89721i 0.460466 0.194861i
\(21\) 5.36117 0.255294
\(22\) 0.598986 + 0.598986i 0.0272266 + 0.0272266i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −17.4059 + 17.9454i −0.696235 + 0.717814i
\(26\) 4.89943 0.188440
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 4.37738 4.37738i 0.156335 0.156335i
\(29\) 25.3649i 0.874651i 0.899303 + 0.437326i \(0.144074\pi\)
−0.899303 + 0.437326i \(0.855926\pi\)
\(30\) 4.77309 + 11.2791i 0.159103 + 0.375969i
\(31\) 49.7350 1.60436 0.802178 0.597085i \(-0.203675\pi\)
0.802178 + 0.597085i \(0.203675\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −0.733605 + 0.733605i −0.0222305 + 0.0222305i
\(34\) 35.8993i 1.05586i
\(35\) −5.81329 + 14.3431i −0.166094 + 0.409802i
\(36\) 6.00000 0.166667
\(37\) 42.3579 + 42.3579i 1.14481 + 1.14481i 0.987559 + 0.157249i \(0.0502625\pi\)
0.157249 + 0.987559i \(0.449737\pi\)
\(38\) −17.4222 + 17.4222i −0.458479 + 0.458479i
\(39\) 6.00055i 0.153860i
\(40\) 13.1065 + 5.31212i 0.327664 + 0.132803i
\(41\) −59.6411 −1.45466 −0.727331 0.686287i \(-0.759239\pi\)
−0.727331 + 0.686287i \(0.759239\pi\)
\(42\) 5.36117 + 5.36117i 0.127647 + 0.127647i
\(43\) −37.2918 + 37.2918i −0.867251 + 0.867251i −0.992167 0.124916i \(-0.960134\pi\)
0.124916 + 0.992167i \(0.460134\pi\)
\(44\) 1.19797i 0.0272266i
\(45\) −13.8140 + 5.84582i −0.306978 + 0.129907i
\(46\) −6.78233 −0.147442
\(47\) 3.72350 + 3.72350i 0.0792235 + 0.0792235i 0.745608 0.666385i \(-0.232159\pi\)
−0.666385 + 0.745608i \(0.732159\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 39.4193i 0.804475i
\(50\) −35.3512 + 0.539488i −0.707024 + 0.0107898i
\(51\) −43.9674 −0.862107
\(52\) 4.89943 + 4.89943i 0.0942198 + 0.0942198i
\(53\) 66.2177 66.2177i 1.24939 1.24939i 0.293402 0.955989i \(-0.405213\pi\)
0.955989 0.293402i \(-0.0947874\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −1.16719 2.75813i −0.0212216 0.0501478i
\(56\) 8.75476 0.156335
\(57\) −21.3378 21.3378i −0.374347 0.374347i
\(58\) −25.3649 + 25.3649i −0.437326 + 0.437326i
\(59\) 106.735i 1.80907i 0.426399 + 0.904535i \(0.359782\pi\)
−0.426399 + 0.904535i \(0.640218\pi\)
\(60\) −6.50599 + 16.0522i −0.108433 + 0.267536i
\(61\) 56.8619 0.932163 0.466081 0.884742i \(-0.345665\pi\)
0.466081 + 0.884742i \(0.345665\pi\)
\(62\) 49.7350 + 49.7350i 0.802178 + 0.802178i
\(63\) −6.56607 + 6.56607i −0.104223 + 0.104223i
\(64\) 8.00000i 0.125000i
\(65\) −16.0536 6.50658i −0.246979 0.100101i
\(66\) −1.46721 −0.0222305
\(67\) −5.50781 5.50781i −0.0822061 0.0822061i 0.664808 0.747014i \(-0.268513\pi\)
−0.747014 + 0.664808i \(0.768513\pi\)
\(68\) −35.8993 + 35.8993i −0.527930 + 0.527930i
\(69\) 8.30662i 0.120386i
\(70\) −20.1564 + 8.52979i −0.287948 + 0.121854i
\(71\) −18.4588 −0.259983 −0.129992 0.991515i \(-0.541495\pi\)
−0.129992 + 0.991515i \(0.541495\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 1.41110 1.41110i 0.0193302 0.0193302i −0.697376 0.716706i \(-0.745649\pi\)
0.716706 + 0.697376i \(0.245649\pi\)
\(74\) 84.7158i 1.14481i
\(75\) −0.660735 43.2962i −0.00880980 0.577283i
\(76\) −34.8444 −0.458479
\(77\) −1.31099 1.31099i −0.0170259 0.0170259i
\(78\) −6.00055 + 6.00055i −0.0769301 + 0.0769301i
\(79\) 123.331i 1.56116i 0.625058 + 0.780578i \(0.285075\pi\)
−0.625058 + 0.780578i \(0.714925\pi\)
\(80\) 7.79442 + 18.4187i 0.0974303 + 0.230233i
\(81\) −9.00000 −0.111111
\(82\) −59.6411 59.6411i −0.727331 0.727331i
\(83\) 34.1108 34.1108i 0.410974 0.410974i −0.471104 0.882078i \(-0.656144\pi\)
0.882078 + 0.471104i \(0.156144\pi\)
\(84\) 10.7223i 0.127647i
\(85\) 47.6753 117.629i 0.560886 1.38387i
\(86\) −74.5836 −0.867251
\(87\) −31.0655 31.0655i −0.357075 0.357075i
\(88\) −1.19797 + 1.19797i −0.0136133 + 0.0136133i
\(89\) 55.0628i 0.618683i −0.950951 0.309342i \(-0.899891\pi\)
0.950951 0.309342i \(-0.100109\pi\)
\(90\) −19.6598 7.96817i −0.218442 0.0885353i
\(91\) −10.7233 −0.117839
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) −60.9127 + 60.9127i −0.654975 + 0.654975i
\(94\) 7.44701i 0.0792235i
\(95\) 80.2234 33.9490i 0.844457 0.357358i
\(96\) 9.79796 0.102062
\(97\) 55.4956 + 55.4956i 0.572120 + 0.572120i 0.932720 0.360600i \(-0.117428\pi\)
−0.360600 + 0.932720i \(0.617428\pi\)
\(98\) 39.4193 39.4193i 0.402238 0.402238i
\(99\) 1.79696i 0.0181511i
\(100\) −35.8907 34.8117i −0.358907 0.348117i
\(101\) −76.1500 −0.753961 −0.376980 0.926221i \(-0.623038\pi\)
−0.376980 + 0.926221i \(0.623038\pi\)
\(102\) −43.9674 43.9674i −0.431053 0.431053i
\(103\) −75.4678 + 75.4678i −0.732697 + 0.732697i −0.971153 0.238456i \(-0.923359\pi\)
0.238456 + 0.971153i \(0.423359\pi\)
\(104\) 9.79885i 0.0942198i
\(105\) −10.4468 24.6864i −0.0994934 0.235109i
\(106\) 132.435 1.24939
\(107\) −106.837 106.837i −0.998472 0.998472i 0.00152681 0.999999i \(-0.499514\pi\)
−0.999999 + 0.00152681i \(0.999514\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 105.073i 0.963970i 0.876179 + 0.481985i \(0.160084\pi\)
−0.876179 + 0.481985i \(0.839916\pi\)
\(110\) 1.59094 3.92532i 0.0144631 0.0356847i
\(111\) −103.755 −0.934732
\(112\) 8.75476 + 8.75476i 0.0781675 + 0.0781675i
\(113\) 40.8621 40.8621i 0.361612 0.361612i −0.502794 0.864406i \(-0.667695\pi\)
0.864406 + 0.502794i \(0.167695\pi\)
\(114\) 42.6755i 0.374347i
\(115\) 22.2232 + 9.00713i 0.193245 + 0.0783229i
\(116\) −50.7298 −0.437326
\(117\) −7.34914 7.34914i −0.0628132 0.0628132i
\(118\) −106.735 + 106.735i −0.904535 + 0.904535i
\(119\) 78.5723i 0.660272i
\(120\) −22.5582 + 9.54618i −0.187985 + 0.0795515i
\(121\) −120.641 −0.997035
\(122\) 56.8619 + 56.8619i 0.466081 + 0.466081i
\(123\) 73.0452 73.0452i 0.593863 0.593863i
\(124\) 99.4700i 0.802178i
\(125\) 116.550 + 45.1797i 0.932396 + 0.361438i
\(126\) −13.1321 −0.104223
\(127\) 119.382 + 119.382i 0.940018 + 0.940018i 0.998300 0.0582822i \(-0.0185623\pi\)
−0.0582822 + 0.998300i \(0.518562\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 91.3459i 0.708108i
\(130\) −9.54705 22.5602i −0.0734389 0.173540i
\(131\) 167.857 1.28135 0.640675 0.767813i \(-0.278655\pi\)
0.640675 + 0.767813i \(0.278655\pi\)
\(132\) −1.46721 1.46721i −0.0111152 0.0111152i
\(133\) 38.1318 38.1318i 0.286705 0.286705i
\(134\) 11.0156i 0.0822061i
\(135\) 9.75898 24.0783i 0.0722887 0.178357i
\(136\) −71.7985 −0.527930
\(137\) 129.149 + 129.149i 0.942694 + 0.942694i 0.998445 0.0557511i \(-0.0177553\pi\)
−0.0557511 + 0.998445i \(0.517755\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 40.2260i 0.289396i −0.989476 0.144698i \(-0.953779\pi\)
0.989476 0.144698i \(-0.0462211\pi\)
\(140\) −28.6861 11.6266i −0.204901 0.0830469i
\(141\) −9.12068 −0.0646857
\(142\) −18.4588 18.4588i −0.129992 0.129992i
\(143\) 1.46734 1.46734i 0.0102612 0.0102612i
\(144\) 12.0000i 0.0833333i
\(145\) 116.797 49.4262i 0.805495 0.340870i
\(146\) 2.82221 0.0193302
\(147\) 48.2786 + 48.2786i 0.328426 + 0.328426i
\(148\) −84.7158 + 84.7158i −0.572404 + 0.572404i
\(149\) 252.884i 1.69721i −0.529028 0.848604i \(-0.677443\pi\)
0.529028 0.848604i \(-0.322557\pi\)
\(150\) 42.6355 43.9570i 0.284237 0.293046i
\(151\) −24.4657 −0.162024 −0.0810122 0.996713i \(-0.525815\pi\)
−0.0810122 + 0.996713i \(0.525815\pi\)
\(152\) −34.8444 34.8444i −0.229240 0.229240i
\(153\) 53.8489 53.8489i 0.351954 0.351954i
\(154\) 2.62199i 0.0170259i
\(155\) −96.9140 229.013i −0.625251 1.47750i
\(156\) −12.0011 −0.0769301
\(157\) 45.8667 + 45.8667i 0.292144 + 0.292144i 0.837927 0.545783i \(-0.183768\pi\)
−0.545783 + 0.837927i \(0.683768\pi\)
\(158\) −123.331 + 123.331i −0.780578 + 0.780578i
\(159\) 162.200i 1.02012i
\(160\) −10.6242 + 26.2131i −0.0664015 + 0.163832i
\(161\) 14.8444 0.0922013
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) 154.258 154.258i 0.946368 0.946368i −0.0522652 0.998633i \(-0.516644\pi\)
0.998633 + 0.0522652i \(0.0166441\pi\)
\(164\) 119.282i 0.727331i
\(165\) 4.80751 + 1.94850i 0.0291364 + 0.0118091i
\(166\) 68.2216 0.410974
\(167\) 107.910 + 107.910i 0.646169 + 0.646169i 0.952065 0.305896i \(-0.0989559\pi\)
−0.305896 + 0.952065i \(0.598956\pi\)
\(168\) −10.7223 + 10.7223i −0.0638235 + 0.0638235i
\(169\) 156.998i 0.928981i
\(170\) 165.304 69.9535i 0.972377 0.411491i
\(171\) 52.2666 0.305653
\(172\) −74.5836 74.5836i −0.433626 0.433626i
\(173\) 167.076 167.076i 0.965756 0.965756i −0.0336770 0.999433i \(-0.510722\pi\)
0.999433 + 0.0336770i \(0.0107218\pi\)
\(174\) 62.1310i 0.357075i
\(175\) 77.3728 1.18077i 0.442130 0.00674726i
\(176\) −2.39594 −0.0136133
\(177\) −130.723 130.723i −0.738550 0.738550i
\(178\) 55.0628 55.0628i 0.309342 0.309342i
\(179\) 182.846i 1.02149i 0.859733 + 0.510744i \(0.170630\pi\)
−0.859733 + 0.510744i \(0.829370\pi\)
\(180\) −11.6916 27.6280i −0.0649535 0.153489i
\(181\) −283.532 −1.56648 −0.783238 0.621722i \(-0.786433\pi\)
−0.783238 + 0.621722i \(0.786433\pi\)
\(182\) −10.7233 10.7233i −0.0589194 0.0589194i
\(183\) −69.6413 + 69.6413i −0.380554 + 0.380554i
\(184\) 13.5647i 0.0737210i
\(185\) 112.505 277.583i 0.608135 1.50045i
\(186\) −121.825 −0.654975
\(187\) 10.7516 + 10.7516i 0.0574951 + 0.0574951i
\(188\) −7.44701 + 7.44701i −0.0396117 + 0.0396117i
\(189\) 16.0835i 0.0850980i
\(190\) 114.172 + 46.2744i 0.600908 + 0.243549i
\(191\) −222.465 −1.16474 −0.582369 0.812924i \(-0.697874\pi\)
−0.582369 + 0.812924i \(0.697874\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 155.059 155.059i 0.803415 0.803415i −0.180213 0.983628i \(-0.557679\pi\)
0.983628 + 0.180213i \(0.0576786\pi\)
\(194\) 110.991i 0.572120i
\(195\) 27.6305 11.6927i 0.141695 0.0599626i
\(196\) 78.8386 0.402238
\(197\) −195.127 195.127i −0.990491 0.990491i 0.00946412 0.999955i \(-0.496987\pi\)
−0.999955 + 0.00946412i \(0.996987\pi\)
\(198\) 1.79696 1.79696i 0.00907555 0.00907555i
\(199\) 161.566i 0.811887i 0.913898 + 0.405944i \(0.133057\pi\)
−0.913898 + 0.405944i \(0.866943\pi\)
\(200\) −1.07898 70.7024i −0.00539488 0.353512i
\(201\) 13.4913 0.0671210
\(202\) −76.1500 76.1500i −0.376980 0.376980i
\(203\) 55.5158 55.5158i 0.273477 0.273477i
\(204\) 87.9349i 0.431053i
\(205\) 116.217 + 274.627i 0.566913 + 1.33965i
\(206\) −150.936 −0.732697
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) −9.79885 + 9.79885i −0.0471099 + 0.0471099i
\(209\) 10.4357i 0.0499314i
\(210\) 14.2396 35.1332i 0.0678075 0.167301i
\(211\) 253.473 1.20130 0.600648 0.799514i \(-0.294909\pi\)
0.600648 + 0.799514i \(0.294909\pi\)
\(212\) 132.435 + 132.435i 0.624695 + 0.624695i
\(213\) 22.6073 22.6073i 0.106138 0.106138i
\(214\) 213.673i 0.998472i
\(215\) 244.383 + 99.0492i 1.13667 + 0.460694i
\(216\) −14.6969 −0.0680414
\(217\) −108.854 108.854i −0.501634 0.501634i
\(218\) −105.073 + 105.073i −0.481985 + 0.481985i
\(219\) 3.45648i 0.0157830i
\(220\) 5.51626 2.33438i 0.0250739 0.0106108i
\(221\) 87.9429 0.397932
\(222\) −103.755 103.755i −0.467366 0.467366i
\(223\) −148.276 + 148.276i −0.664913 + 0.664913i −0.956534 0.291621i \(-0.905805\pi\)
0.291621 + 0.956534i \(0.405805\pi\)
\(224\) 17.5095i 0.0781675i
\(225\) 53.8361 + 52.2176i 0.239271 + 0.232078i
\(226\) 81.7243 0.361612
\(227\) −125.826 125.826i −0.554298 0.554298i 0.373380 0.927678i \(-0.378199\pi\)
−0.927678 + 0.373380i \(0.878199\pi\)
\(228\) 42.6755 42.6755i 0.187173 0.187173i
\(229\) 8.02492i 0.0350433i 0.999846 + 0.0175217i \(0.00557760\pi\)
−0.999846 + 0.0175217i \(0.994422\pi\)
\(230\) 13.2161 + 31.2304i 0.0574613 + 0.135784i
\(231\) 3.21127 0.0139016
\(232\) −50.7298 50.7298i −0.218663 0.218663i
\(233\) 301.851 301.851i 1.29550 1.29550i 0.364165 0.931334i \(-0.381354\pi\)
0.931334 0.364165i \(-0.118646\pi\)
\(234\) 14.6983i 0.0628132i
\(235\) 9.88984 24.4011i 0.0420844 0.103835i
\(236\) −213.470 −0.904535
\(237\) −151.049 151.049i −0.637339 0.637339i
\(238\) 78.5723 78.5723i 0.330136 0.330136i
\(239\) 74.3262i 0.310988i −0.987837 0.155494i \(-0.950303\pi\)
0.987837 0.155494i \(-0.0496970\pi\)
\(240\) −32.1043 13.0120i −0.133768 0.0542166i
\(241\) −259.415 −1.07641 −0.538206 0.842813i \(-0.680898\pi\)
−0.538206 + 0.842813i \(0.680898\pi\)
\(242\) −120.641 120.641i −0.498517 0.498517i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 113.724i 0.466081i
\(245\) −181.513 + 76.8127i −0.740868 + 0.313521i
\(246\) 146.090 0.593863
\(247\) 42.6794 + 42.6794i 0.172791 + 0.172791i
\(248\) −99.4700 + 99.4700i −0.401089 + 0.401089i
\(249\) 83.5541i 0.335559i
\(250\) 71.3698 + 161.729i 0.285479 + 0.646917i
\(251\) −461.482 −1.83857 −0.919287 0.393587i \(-0.871234\pi\)
−0.919287 + 0.393587i \(0.871234\pi\)
\(252\) −13.1321 13.1321i −0.0521116 0.0521116i
\(253\) −2.03126 + 2.03126i −0.00802870 + 0.00802870i
\(254\) 238.765i 0.940018i
\(255\) 85.6752 + 202.455i 0.335981 + 0.793942i
\(256\) 16.0000 0.0625000
\(257\) 35.4321 + 35.4321i 0.137868 + 0.137868i 0.772673 0.634805i \(-0.218919\pi\)
−0.634805 + 0.772673i \(0.718919\pi\)
\(258\) 91.3459 91.3459i 0.354054 0.354054i
\(259\) 185.417i 0.715894i
\(260\) 13.0132 32.1073i 0.0500506 0.123490i
\(261\) 76.0947 0.291550
\(262\) 167.857 + 167.857i 0.640675 + 0.640675i
\(263\) 27.5897 27.5897i 0.104904 0.104904i −0.652707 0.757611i \(-0.726367\pi\)
0.757611 + 0.652707i \(0.226367\pi\)
\(264\) 2.93442i 0.0111152i
\(265\) −433.943 175.878i −1.63752 0.663691i
\(266\) 76.2636 0.286705
\(267\) 67.4379 + 67.4379i 0.252576 + 0.252576i
\(268\) 11.0156 11.0156i 0.0411031 0.0411031i
\(269\) 208.728i 0.775939i −0.921672 0.387970i \(-0.873177\pi\)
0.921672 0.387970i \(-0.126823\pi\)
\(270\) 33.8372 14.3193i 0.125323 0.0530343i
\(271\) 210.239 0.775789 0.387895 0.921704i \(-0.373202\pi\)
0.387895 + 0.921704i \(0.373202\pi\)
\(272\) −71.7985 71.7985i −0.263965 0.263965i
\(273\) 13.1333 13.1333i 0.0481075 0.0481075i
\(274\) 258.298i 0.942694i
\(275\) −10.4259 + 10.7490i −0.0379123 + 0.0390873i
\(276\) 16.6132 0.0601929
\(277\) 30.9260 + 30.9260i 0.111646 + 0.111646i 0.760723 0.649077i \(-0.224845\pi\)
−0.649077 + 0.760723i \(0.724845\pi\)
\(278\) 40.2260 40.2260i 0.144698 0.144698i
\(279\) 149.205i 0.534785i
\(280\) −17.0596 40.3127i −0.0609270 0.143974i
\(281\) −438.208 −1.55946 −0.779729 0.626117i \(-0.784643\pi\)
−0.779729 + 0.626117i \(0.784643\pi\)
\(282\) −9.12068 9.12068i −0.0323428 0.0323428i
\(283\) 118.312 118.312i 0.418064 0.418064i −0.466472 0.884536i \(-0.654475\pi\)
0.884536 + 0.466472i \(0.154475\pi\)
\(284\) 36.9176i 0.129992i
\(285\) −56.6743 + 139.832i −0.198857 + 0.490639i
\(286\) 2.93469 0.0102612
\(287\) 130.536 + 130.536i 0.454829 + 0.454829i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 355.379i 1.22968i
\(290\) 166.223 + 67.3706i 0.573183 + 0.232312i
\(291\) −135.936 −0.467134
\(292\) 2.82221 + 2.82221i 0.00966509 + 0.00966509i
\(293\) −24.6895 + 24.6895i −0.0842646 + 0.0842646i −0.747983 0.663718i \(-0.768977\pi\)
0.663718 + 0.747983i \(0.268977\pi\)
\(294\) 96.5571i 0.328426i
\(295\) 491.480 207.985i 1.66603 0.705033i
\(296\) −169.432 −0.572404
\(297\) 2.20082 + 2.20082i 0.00741015 + 0.00741015i
\(298\) 252.884 252.884i 0.848604 0.848604i
\(299\) 16.6148i 0.0555678i
\(300\) 86.5925 1.32147i 0.288642 0.00440490i
\(301\) 163.240 0.542327
\(302\) −24.4657 24.4657i −0.0810122 0.0810122i
\(303\) 93.2643 93.2643i 0.307803 0.307803i
\(304\) 69.6888i 0.229240i
\(305\) −110.801 261.830i −0.363284 0.858459i
\(306\) 107.698 0.351954
\(307\) 243.804 + 243.804i 0.794148 + 0.794148i 0.982166 0.188017i \(-0.0602061\pi\)
−0.188017 + 0.982166i \(0.560206\pi\)
\(308\) 2.62199 2.62199i 0.00851295 0.00851295i
\(309\) 184.858i 0.598245i
\(310\) 132.099 325.927i 0.426126 1.05138i
\(311\) −481.852 −1.54936 −0.774682 0.632350i \(-0.782090\pi\)
−0.774682 + 0.632350i \(0.782090\pi\)
\(312\) −12.0011 12.0011i −0.0384651 0.0384651i
\(313\) 60.0172 60.0172i 0.191748 0.191748i −0.604703 0.796451i \(-0.706708\pi\)
0.796451 + 0.604703i \(0.206708\pi\)
\(314\) 91.7333i 0.292144i
\(315\) 43.0292 + 17.4399i 0.136601 + 0.0553646i
\(316\) −246.663 −0.780578
\(317\) −13.7241 13.7241i −0.0432936 0.0432936i 0.685129 0.728422i \(-0.259746\pi\)
−0.728422 + 0.685129i \(0.759746\pi\)
\(318\) −162.200 + 162.200i −0.510062 + 0.510062i
\(319\) 15.1932i 0.0476276i
\(320\) −36.8373 + 15.5888i −0.115117 + 0.0487152i
\(321\) 261.695 0.815249
\(322\) 14.8444 + 14.8444i 0.0461007 + 0.0461007i
\(323\) −312.722 + 312.722i −0.968180 + 0.968180i
\(324\) 18.0000i 0.0555556i
\(325\) 1.32159 + 86.6004i 0.00406643 + 0.266463i
\(326\) 308.516 0.946368
\(327\) −128.687 128.687i −0.393539 0.393539i
\(328\) 119.282 119.282i 0.363665 0.363665i
\(329\) 16.2992i 0.0495416i
\(330\) 2.85902 + 6.75601i 0.00866368 + 0.0204728i
\(331\) 521.875 1.57666 0.788331 0.615251i \(-0.210945\pi\)
0.788331 + 0.615251i \(0.210945\pi\)
\(332\) 68.2216 + 68.2216i 0.205487 + 0.205487i
\(333\) 127.074 127.074i 0.381603 0.381603i
\(334\) 215.820i 0.646169i
\(335\) −14.6291 + 36.0942i −0.0436688 + 0.107744i
\(336\) −21.4447 −0.0638235
\(337\) −280.503 280.503i −0.832354 0.832354i 0.155484 0.987838i \(-0.450306\pi\)
−0.987838 + 0.155484i \(0.950306\pi\)
\(338\) −156.998 + 156.998i −0.464491 + 0.464491i
\(339\) 100.091i 0.295255i
\(340\) 235.258 + 95.3505i 0.691934 + 0.280443i
\(341\) 29.7906 0.0873624
\(342\) 52.2666 + 52.2666i 0.152826 + 0.152826i
\(343\) −193.522 + 193.522i −0.564205 + 0.564205i
\(344\) 149.167i 0.433626i
\(345\) −38.2492 + 16.1863i −0.110867 + 0.0469169i
\(346\) 334.151 0.965756
\(347\) −64.7394 64.7394i −0.186569 0.186569i 0.607642 0.794211i \(-0.292116\pi\)
−0.794211 + 0.607642i \(0.792116\pi\)
\(348\) 62.1310 62.1310i 0.178537 0.178537i
\(349\) 534.997i 1.53294i 0.642278 + 0.766472i \(0.277989\pi\)
−0.642278 + 0.766472i \(0.722011\pi\)
\(350\) 78.5536 + 76.1921i 0.224439 + 0.217692i
\(351\) 18.0016 0.0512867
\(352\) −2.39594 2.39594i −0.00680666 0.00680666i
\(353\) −8.45263 + 8.45263i −0.0239451 + 0.0239451i −0.718978 0.695033i \(-0.755390\pi\)
0.695033 + 0.718978i \(0.255390\pi\)
\(354\) 261.447i 0.738550i
\(355\) 35.9689 + 84.9966i 0.101321 + 0.239427i
\(356\) 110.126 0.309342
\(357\) 96.2311 + 96.2311i 0.269555 + 0.269555i
\(358\) −182.846 + 182.846i −0.510744 + 0.510744i
\(359\) 29.7289i 0.0828104i −0.999142 0.0414052i \(-0.986817\pi\)
0.999142 0.0414052i \(-0.0131834\pi\)
\(360\) 15.9363 39.3196i 0.0442676 0.109221i
\(361\) 57.4667 0.159187
\(362\) −283.532 283.532i −0.783238 0.783238i
\(363\) 147.755 147.755i 0.407038 0.407038i
\(364\) 21.4466i 0.0589194i
\(365\) −9.24734 3.74797i −0.0253352 0.0102684i
\(366\) −139.283 −0.380554
\(367\) −287.976 287.976i −0.784674 0.784674i 0.195941 0.980616i \(-0.437224\pi\)
−0.980616 + 0.195941i \(0.937224\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 178.923i 0.484887i
\(370\) 390.088 165.078i 1.05429 0.446156i
\(371\) −289.860 −0.781294
\(372\) −121.825 121.825i −0.327488 0.327488i
\(373\) −198.584 + 198.584i −0.532395 + 0.532395i −0.921285 0.388889i \(-0.872859\pi\)
0.388889 + 0.921285i \(0.372859\pi\)
\(374\) 21.5032i 0.0574951i
\(375\) −198.077 + 87.4098i −0.528206 + 0.233093i
\(376\) −14.8940 −0.0396117
\(377\) 62.1367 + 62.1367i 0.164819 + 0.164819i
\(378\) 16.0835 16.0835i 0.0425490 0.0425490i
\(379\) 533.203i 1.40687i 0.710761 + 0.703434i \(0.248351\pi\)
−0.710761 + 0.703434i \(0.751649\pi\)
\(380\) 67.8980 + 160.447i 0.178679 + 0.422229i
\(381\) −292.426 −0.767521
\(382\) −222.465 222.465i −0.582369 0.582369i
\(383\) 120.598 120.598i 0.314877 0.314877i −0.531919 0.846795i \(-0.678529\pi\)
0.846795 + 0.531919i \(0.178529\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −3.48208 + 8.59130i −0.00904436 + 0.0223151i
\(386\) 310.118 0.803415
\(387\) 111.875 + 111.875i 0.289084 + 0.289084i
\(388\) −110.991 + 110.991i −0.286060 + 0.286060i
\(389\) 292.831i 0.752778i −0.926462 0.376389i \(-0.877166\pi\)
0.926462 0.376389i \(-0.122834\pi\)
\(390\) 39.3232 + 15.9378i 0.100829 + 0.0408662i
\(391\) −121.740 −0.311356
\(392\) 78.8386 + 78.8386i 0.201119 + 0.201119i
\(393\) −205.582 + 205.582i −0.523109 + 0.523109i
\(394\) 390.253i 0.990491i
\(395\) 567.899 240.324i 1.43772 0.608416i
\(396\) 3.59392 0.00907555
\(397\) −221.984 221.984i −0.559153 0.559153i 0.369913 0.929066i \(-0.379387\pi\)
−0.929066 + 0.369913i \(0.879387\pi\)
\(398\) −161.566 + 161.566i −0.405944 + 0.405944i
\(399\) 93.4034i 0.234094i
\(400\) 69.6235 71.7814i 0.174059 0.179454i
\(401\) −453.324 −1.13048 −0.565242 0.824925i \(-0.691217\pi\)
−0.565242 + 0.824925i \(0.691217\pi\)
\(402\) 13.4913 + 13.4913i 0.0335605 + 0.0335605i
\(403\) 121.837 121.837i 0.302324 0.302324i
\(404\) 152.300i 0.376980i
\(405\) 17.5375 + 41.4420i 0.0433024 + 0.102326i
\(406\) 111.032 0.273477
\(407\) 25.3718 + 25.3718i 0.0623386 + 0.0623386i
\(408\) 87.9349 87.9349i 0.215527 0.215527i
\(409\) 685.562i 1.67619i −0.545523 0.838096i \(-0.683669\pi\)
0.545523 0.838096i \(-0.316331\pi\)
\(410\) −158.410 + 390.844i −0.386367 + 0.953279i
\(411\) −316.349 −0.769706
\(412\) −150.936 150.936i −0.366349 0.366349i
\(413\) 233.610 233.610i 0.565642 0.565642i
\(414\) 20.3470i 0.0491473i
\(415\) −223.537 90.6003i −0.538644 0.218314i
\(416\) −19.5977 −0.0471099
\(417\) 49.2666 + 49.2666i 0.118145 + 0.118145i
\(418\) −10.4357 + 10.4357i −0.0249657 + 0.0249657i
\(419\) 526.496i 1.25655i 0.777990 + 0.628277i \(0.216239\pi\)
−0.777990 + 0.628277i \(0.783761\pi\)
\(420\) 49.3728 20.8936i 0.117554 0.0497467i
\(421\) −23.9389 −0.0568620 −0.0284310 0.999596i \(-0.509051\pi\)
−0.0284310 + 0.999596i \(0.509051\pi\)
\(422\) 253.473 + 253.473i 0.600648 + 0.600648i
\(423\) 11.1705 11.1705i 0.0264078 0.0264078i
\(424\) 264.871i 0.624695i
\(425\) −634.541 + 9.68361i −1.49304 + 0.0227850i
\(426\) 45.2146 0.106138
\(427\) −124.453 124.453i −0.291459 0.291459i
\(428\) 213.673 213.673i 0.499236 0.499236i
\(429\) 3.59425i 0.00837819i
\(430\) 145.334 + 343.433i 0.337986 + 0.798680i
\(431\) 118.968 0.276027 0.138013 0.990430i \(-0.455928\pi\)
0.138013 + 0.990430i \(0.455928\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) −402.728 + 402.728i −0.930089 + 0.930089i −0.997711 0.0676224i \(-0.978459\pi\)
0.0676224 + 0.997711i \(0.478459\pi\)
\(434\) 217.709i 0.501634i
\(435\) −82.5118 + 203.581i −0.189682 + 0.468002i
\(436\) −210.146 −0.481985
\(437\) −59.0816 59.0816i −0.135198 0.135198i
\(438\) −3.45648 + 3.45648i −0.00789151 + 0.00789151i
\(439\) 517.562i 1.17896i 0.807784 + 0.589479i \(0.200667\pi\)
−0.807784 + 0.589479i \(0.799333\pi\)
\(440\) 7.85064 + 3.18188i 0.0178424 + 0.00723155i
\(441\) −118.258 −0.268158
\(442\) 87.9429 + 87.9429i 0.198966 + 0.198966i
\(443\) 256.263 256.263i 0.578472 0.578472i −0.356010 0.934482i \(-0.615863\pi\)
0.934482 + 0.356010i \(0.115863\pi\)
\(444\) 207.510i 0.467366i
\(445\) −253.546 + 107.296i −0.569766 + 0.241114i
\(446\) −296.551 −0.664913
\(447\) 309.718 + 309.718i 0.692882 + 0.692882i
\(448\) −17.5095 + 17.5095i −0.0390837 + 0.0390837i
\(449\) 347.606i 0.774178i 0.922042 + 0.387089i \(0.126519\pi\)
−0.922042 + 0.387089i \(0.873481\pi\)
\(450\) 1.61846 + 106.054i 0.00359658 + 0.235675i
\(451\) −35.7242 −0.0792111
\(452\) 81.7243 + 81.7243i 0.180806 + 0.180806i
\(453\) 29.9642 29.9642i 0.0661462 0.0661462i
\(454\) 251.651i 0.554298i
\(455\) 20.8955 + 49.3773i 0.0459242 + 0.108522i
\(456\) 85.3510 0.187173
\(457\) −112.362 112.362i −0.245868 0.245868i 0.573405 0.819272i \(-0.305622\pi\)
−0.819272 + 0.573405i \(0.805622\pi\)
\(458\) −8.02492 + 8.02492i −0.0175217 + 0.0175217i
\(459\) 131.902i 0.287369i
\(460\) −18.0143 + 44.4464i −0.0391614 + 0.0966227i
\(461\) 131.722 0.285730 0.142865 0.989742i \(-0.454369\pi\)
0.142865 + 0.989742i \(0.454369\pi\)
\(462\) 3.21127 + 3.21127i 0.00695079 + 0.00695079i
\(463\) 304.225 304.225i 0.657074 0.657074i −0.297613 0.954687i \(-0.596190\pi\)
0.954687 + 0.297613i \(0.0961904\pi\)
\(464\) 101.460i 0.218663i
\(465\) 399.177 + 161.788i 0.858446 + 0.347931i
\(466\) 603.703 1.29550
\(467\) −153.989 153.989i −0.329741 0.329741i 0.522747 0.852488i \(-0.324907\pi\)
−0.852488 + 0.522747i \(0.824907\pi\)
\(468\) 14.6983 14.6983i 0.0314066 0.0314066i
\(469\) 24.1098i 0.0514067i
\(470\) 34.2910 14.5113i 0.0729595 0.0308751i
\(471\) −112.350 −0.238535
\(472\) −213.470 213.470i −0.452268 0.452268i
\(473\) −22.3373 + 22.3373i −0.0472247 + 0.0472247i
\(474\) 302.099i 0.637339i
\(475\) −312.648 303.249i −0.658206 0.638418i
\(476\) 157.145 0.330136
\(477\) −198.653 198.653i −0.416464 0.416464i
\(478\) 74.3262 74.3262i 0.155494 0.155494i
\(479\) 644.063i 1.34460i 0.740280 + 0.672299i \(0.234693\pi\)
−0.740280 + 0.672299i \(0.765307\pi\)
\(480\) −19.0924 45.1163i −0.0397758 0.0939923i
\(481\) 207.529 0.431454
\(482\) −259.415 259.415i −0.538206 0.538206i
\(483\) −18.1806 + 18.1806i −0.0376410 + 0.0376410i
\(484\) 241.282i 0.498517i
\(485\) 147.400 363.678i 0.303917 0.749851i
\(486\) 22.0454 0.0453609
\(487\) −331.877 331.877i −0.681472 0.681472i 0.278860 0.960332i \(-0.410044\pi\)
−0.960332 + 0.278860i \(0.910044\pi\)
\(488\) −113.724 + 113.724i −0.233041 + 0.233041i
\(489\) 377.853i 0.772706i
\(490\) −258.325 104.700i −0.527194 0.213673i
\(491\) 584.577 1.19058 0.595292 0.803509i \(-0.297036\pi\)
0.595292 + 0.803509i \(0.297036\pi\)
\(492\) 146.090 + 146.090i 0.296932 + 0.296932i
\(493\) −455.290 + 455.290i −0.923510 + 0.923510i
\(494\) 85.3588i 0.172791i
\(495\) −8.27439 + 3.50156i −0.0167159 + 0.00707387i
\(496\) −198.940 −0.401089
\(497\) 40.4006 + 40.4006i 0.0812889 + 0.0812889i
\(498\) −83.5541 + 83.5541i −0.167779 + 0.167779i
\(499\) 366.222i 0.733911i 0.930238 + 0.366956i \(0.119600\pi\)
−0.930238 + 0.366956i \(0.880400\pi\)
\(500\) −90.3595 + 233.099i −0.180719 + 0.466198i
\(501\) −264.325 −0.527595
\(502\) −461.482 461.482i −0.919287 0.919287i
\(503\) −391.814 + 391.814i −0.778954 + 0.778954i −0.979653 0.200699i \(-0.935679\pi\)
0.200699 + 0.979653i \(0.435679\pi\)
\(504\) 26.2643i 0.0521116i
\(505\) 148.386 + 350.645i 0.293834 + 0.694347i
\(506\) −4.06252 −0.00802870
\(507\) −192.282 192.282i −0.379255 0.379255i
\(508\) −238.765 + 238.765i −0.470009 + 0.470009i
\(509\) 154.418i 0.303376i −0.988428 0.151688i \(-0.951529\pi\)
0.988428 0.151688i \(-0.0484709\pi\)
\(510\) −116.780 + 288.131i −0.228981 + 0.564962i
\(511\) −6.17693 −0.0120879
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −64.0133 + 64.0133i −0.124782 + 0.124782i
\(514\) 70.8643i 0.137868i
\(515\) 494.561 + 200.447i 0.960313 + 0.389217i
\(516\) 182.692 0.354054
\(517\) 2.23033 + 2.23033i 0.00431398 + 0.00431398i
\(518\) 185.417 185.417i 0.357947 0.357947i
\(519\) 409.250i 0.788536i
\(520\) 45.1204 19.0941i 0.0867701 0.0367194i
\(521\) −568.142 −1.09048 −0.545242 0.838279i \(-0.683562\pi\)
−0.545242 + 0.838279i \(0.683562\pi\)
\(522\) 76.0947 + 76.0947i 0.145775 + 0.145775i
\(523\) −179.943 + 179.943i −0.344059 + 0.344059i −0.857891 0.513832i \(-0.828225\pi\)
0.513832 + 0.857891i \(0.328225\pi\)
\(524\) 335.713i 0.640675i
\(525\) −93.3158 + 96.2081i −0.177744 + 0.183254i
\(526\) 55.1794 0.104904
\(527\) 892.725 + 892.725i 1.69398 + 1.69398i
\(528\) 2.93442 2.93442i 0.00555762 0.00555762i
\(529\) 23.0000i 0.0434783i
\(530\) −258.065 609.821i −0.486914 1.15061i
\(531\) 320.205 0.603023
\(532\) 76.2636 + 76.2636i 0.143353 + 0.143353i
\(533\) −146.104 + 146.104i −0.274116 + 0.274116i
\(534\) 134.876i 0.252576i
\(535\) −283.764 + 700.129i −0.530400 + 1.30865i
\(536\) 22.0312 0.0411031
\(537\) −223.940 223.940i −0.417021 0.417021i
\(538\) 208.728 208.728i 0.387970 0.387970i
\(539\) 23.6116i 0.0438063i
\(540\) 48.1565 + 19.5180i 0.0891787 + 0.0361444i
\(541\) 257.058 0.475153 0.237576 0.971369i \(-0.423647\pi\)
0.237576 + 0.971369i \(0.423647\pi\)
\(542\) 210.239 + 210.239i 0.387895 + 0.387895i
\(543\) 347.255 347.255i 0.639511 0.639511i
\(544\) 143.597i 0.263965i
\(545\) 483.825 204.745i 0.887752 0.375680i
\(546\) 26.2667 0.0481075
\(547\) 254.464 + 254.464i 0.465200 + 0.465200i 0.900355 0.435155i \(-0.143307\pi\)
−0.435155 + 0.900355i \(0.643307\pi\)
\(548\) −258.298 + 258.298i −0.471347 + 0.471347i
\(549\) 170.586i 0.310721i
\(550\) −21.1749 + 0.323146i −0.0384998 + 0.000587538i
\(551\) −441.912 −0.802019
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) 269.934 269.934i 0.488126 0.488126i
\(554\) 61.8520i 0.111646i
\(555\) 202.178 + 477.758i 0.364285 + 0.860825i
\(556\) 80.4521 0.144698
\(557\) 40.9023 + 40.9023i 0.0734333 + 0.0734333i 0.742870 0.669436i \(-0.233464\pi\)
−0.669436 + 0.742870i \(0.733464\pi\)
\(558\) 149.205 149.205i 0.267393 0.267393i
\(559\) 182.709i 0.326849i
\(560\) 23.2531 57.3723i 0.0415235 0.102451i
\(561\) −26.3359 −0.0469445
\(562\) −438.208 438.208i −0.779729 0.779729i
\(563\) −220.043 + 220.043i −0.390840 + 0.390840i −0.874987 0.484147i \(-0.839130\pi\)
0.484147 + 0.874987i \(0.339130\pi\)
\(564\) 18.2414i 0.0323428i
\(565\) −267.781 108.532i −0.473948 0.192092i
\(566\) 236.624 0.418064
\(567\) 19.6982 + 19.6982i 0.0347411 + 0.0347411i
\(568\) 36.9176 36.9176i 0.0649958 0.0649958i
\(569\) 187.836i 0.330116i −0.986284 0.165058i \(-0.947219\pi\)
0.986284 0.165058i \(-0.0527811\pi\)
\(570\) −196.506 + 83.1578i −0.344748 + 0.145891i
\(571\) 72.3367 0.126684 0.0633421 0.997992i \(-0.479824\pi\)
0.0633421 + 0.997992i \(0.479824\pi\)
\(572\) 2.93469 + 2.93469i 0.00513058 + 0.00513058i
\(573\) 272.463 272.463i 0.475503 0.475503i
\(574\) 261.072i 0.454829i
\(575\) −1.82949 119.882i −0.00318172 0.208490i
\(576\) −24.0000 −0.0416667
\(577\) −229.527 229.527i −0.397794 0.397794i 0.479660 0.877454i \(-0.340760\pi\)
−0.877454 + 0.479660i \(0.840760\pi\)
\(578\) −355.379 + 355.379i −0.614842 + 0.614842i
\(579\) 379.816i 0.655986i
\(580\) 98.8523 + 233.594i 0.170435 + 0.402748i
\(581\) −149.316 −0.256998
\(582\) −135.936 135.936i −0.233567 0.233567i
\(583\) 39.6635 39.6635i 0.0680334 0.0680334i
\(584\) 5.64441i 0.00966509i
\(585\) −19.5197 + 48.1609i −0.0333671 + 0.0823263i
\(586\) −49.3790 −0.0842646
\(587\) −381.748 381.748i −0.650337 0.650337i 0.302737 0.953074i \(-0.402100\pi\)
−0.953074 + 0.302737i \(0.902100\pi\)
\(588\) −96.5571 + 96.5571i −0.164213 + 0.164213i
\(589\) 866.494i 1.47113i
\(590\) 699.464 + 283.495i 1.18553 + 0.480500i
\(591\) 477.961 0.808733
\(592\) −169.432 169.432i −0.286202 0.286202i
\(593\) −46.1542 + 46.1542i −0.0778317 + 0.0778317i −0.744951 0.667119i \(-0.767527\pi\)
0.667119 + 0.744951i \(0.267527\pi\)
\(594\) 4.40163i 0.00741015i
\(595\) −361.799 + 153.107i −0.608066 + 0.257322i
\(596\) 505.768 0.848604
\(597\) −197.877 197.877i −0.331451 0.331451i
\(598\) −16.6148 + 16.6148i −0.0277839 + 0.0277839i
\(599\) 109.193i 0.182292i 0.995838 + 0.0911461i \(0.0290530\pi\)
−0.995838 + 0.0911461i \(0.970947\pi\)
\(600\) 87.9139 + 85.2710i 0.146523 + 0.142118i
\(601\) −966.016 −1.60735 −0.803674 0.595070i \(-0.797124\pi\)
−0.803674 + 0.595070i \(0.797124\pi\)
\(602\) 163.240 + 163.240i 0.271163 + 0.271163i
\(603\) −16.5234 + 16.5234i −0.0274020 + 0.0274020i
\(604\) 48.9314i 0.0810122i
\(605\) 235.082 + 555.512i 0.388566 + 0.918202i
\(606\) 186.529 0.307803
\(607\) 399.940 + 399.940i 0.658880 + 0.658880i 0.955115 0.296235i \(-0.0957313\pi\)
−0.296235 + 0.955115i \(0.595731\pi\)
\(608\) 69.6888 69.6888i 0.114620 0.114620i
\(609\) 135.985i 0.223293i
\(610\) 151.029 372.632i 0.247588 0.610871i
\(611\) 18.2430 0.0298577
\(612\) 107.698 + 107.698i 0.175977 + 0.175977i
\(613\) −8.23463 + 8.23463i −0.0134333 + 0.0134333i −0.713792 0.700358i \(-0.753024\pi\)
0.700358 + 0.713792i \(0.253024\pi\)
\(614\) 487.607i 0.794148i
\(615\) −478.685 194.012i −0.778349 0.315467i
\(616\) 5.24398 0.00851295
\(617\) 456.432 + 456.432i 0.739761 + 0.739761i 0.972532 0.232771i \(-0.0747792\pi\)
−0.232771 + 0.972532i \(0.574779\pi\)
\(618\) 184.858 184.858i 0.299122 0.299122i
\(619\) 695.598i 1.12375i 0.827224 + 0.561873i \(0.189919\pi\)
−0.827224 + 0.561873i \(0.810081\pi\)
\(620\) 458.026 193.828i 0.738752 0.312626i
\(621\) −24.9199 −0.0401286
\(622\) −481.852 481.852i −0.774682 0.774682i
\(623\) −120.515 + 120.515i −0.193444 + 0.193444i
\(624\) 24.0022i 0.0384651i
\(625\) −19.0715 624.709i −0.0305145 0.999534i
\(626\) 120.034 0.191748
\(627\) −12.7810 12.7810i −0.0203844 0.0203844i
\(628\) −91.7333 + 91.7333i −0.146072 + 0.146072i
\(629\) 1520.62i 2.41752i
\(630\) 25.5894 + 60.4691i 0.0406180 + 0.0959826i
\(631\) 920.371 1.45859 0.729296 0.684199i \(-0.239848\pi\)
0.729296 + 0.684199i \(0.239848\pi\)
\(632\) −246.663 246.663i −0.390289 0.390289i
\(633\) −310.440 + 310.440i −0.490427 + 0.490427i
\(634\) 27.4482i 0.0432936i
\(635\) 317.086 782.344i 0.499348 1.23204i
\(636\) −324.399 −0.510062
\(637\) −96.5660 96.5660i −0.151595 0.151595i
\(638\) −15.1932 + 15.1932i −0.0238138 + 0.0238138i
\(639\) 55.3764i 0.0866610i
\(640\) −52.4262 21.2485i −0.0819159 0.0332007i
\(641\) 1166.08 1.81915 0.909576 0.415539i \(-0.136407\pi\)
0.909576 + 0.415539i \(0.136407\pi\)
\(642\) 261.695 + 261.695i 0.407624 + 0.407624i
\(643\) 804.965 804.965i 1.25189 1.25189i 0.297018 0.954872i \(-0.404008\pi\)
0.954872 0.297018i \(-0.0959921\pi\)
\(644\) 29.6888i 0.0461007i
\(645\) −420.617 + 177.997i −0.652120 + 0.275965i
\(646\) −625.444 −0.968180
\(647\) −202.286 202.286i −0.312652 0.312652i 0.533284 0.845936i \(-0.320958\pi\)
−0.845936 + 0.533284i \(0.820958\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 63.9329i 0.0985098i
\(650\) −85.2788 + 87.9220i −0.131198 + 0.135265i
\(651\) 266.638 0.409582
\(652\) 308.516 + 308.516i 0.473184 + 0.473184i
\(653\) 192.092 192.092i 0.294169 0.294169i −0.544556 0.838725i \(-0.683302\pi\)
0.838725 + 0.544556i \(0.183302\pi\)
\(654\) 257.375i 0.393539i
\(655\) −327.087 772.924i −0.499369 1.18004i
\(656\) 238.565 0.363665
\(657\) −4.23331 4.23331i −0.00644339 0.00644339i
\(658\) 16.2992 16.2992i 0.0247708 0.0247708i
\(659\) 955.049i 1.44924i −0.689149 0.724620i \(-0.742016\pi\)
0.689149 0.724620i \(-0.257984\pi\)
\(660\) −3.89700 + 9.61503i −0.00590454 + 0.0145682i
\(661\) 270.809 0.409696 0.204848 0.978794i \(-0.434330\pi\)
0.204848 + 0.978794i \(0.434330\pi\)
\(662\) 521.875 + 521.875i 0.788331 + 0.788331i
\(663\) −107.708 + 107.708i −0.162455 + 0.162455i
\(664\) 136.443i 0.205487i
\(665\) −249.888 101.280i −0.375771 0.152301i
\(666\) 254.147 0.381603
\(667\) −86.0165 86.0165i −0.128960 0.128960i
\(668\) −215.820 + 215.820i −0.323085 + 0.323085i
\(669\) 363.199i 0.542899i
\(670\) −50.7232 + 21.4651i −0.0757063 + 0.0320375i
\(671\) 34.0595 0.0507593
\(672\) −21.4447 21.4447i −0.0319117 0.0319117i
\(673\) 2.52466 2.52466i 0.00375136 0.00375136i −0.705229 0.708980i \(-0.749156\pi\)
0.708980 + 0.705229i \(0.249156\pi\)
\(674\) 561.007i 0.832354i
\(675\) −129.889 + 1.98220i −0.192428 + 0.00293660i
\(676\) −313.996 −0.464491
\(677\) 717.605 + 717.605i 1.05998 + 1.05998i 0.998083 + 0.0618948i \(0.0197143\pi\)
0.0618948 + 0.998083i \(0.480286\pi\)
\(678\) −100.091 + 100.091i −0.147627 + 0.147627i
\(679\) 242.925i 0.357769i
\(680\) 139.907 + 330.608i 0.205746 + 0.486188i
\(681\) 308.209 0.452582
\(682\) 29.7906 + 29.7906i 0.0436812 + 0.0436812i
\(683\) 872.239 872.239i 1.27707 1.27707i 0.334771 0.942300i \(-0.391341\pi\)
0.942300 0.334771i \(-0.108659\pi\)
\(684\) 104.533i 0.152826i
\(685\) 343.027 846.349i 0.500770 1.23555i
\(686\) −387.045 −0.564205
\(687\) −9.82848 9.82848i −0.0143064 0.0143064i
\(688\) 149.167 149.167i 0.216813 0.216813i
\(689\) 324.429i 0.470869i
\(690\) −54.4356 22.0629i −0.0788921 0.0319752i
\(691\) −596.416 −0.863120 −0.431560 0.902084i \(-0.642037\pi\)
−0.431560 + 0.902084i \(0.642037\pi\)
\(692\) 334.151 + 334.151i 0.482878 + 0.482878i
\(693\) −3.93298 + 3.93298i −0.00567530 + 0.00567530i
\(694\) 129.479i 0.186569i
\(695\) −185.227 + 78.3847i −0.266514 + 0.112784i
\(696\) 124.262 0.178537
\(697\) −1070.54 1070.54i −1.53592 1.53592i
\(698\) −534.997 + 534.997i −0.766472 + 0.766472i
\(699\) 739.382i 1.05777i
\(700\) 2.36154 + 154.746i 0.00337363 + 0.221065i
\(701\) 526.896 0.751635 0.375817 0.926694i \(-0.377362\pi\)
0.375817 + 0.926694i \(0.377362\pi\)
\(702\) 18.0016 + 18.0016i 0.0256434 + 0.0256434i
\(703\) −737.968 + 737.968i −1.04974 + 1.04974i
\(704\) 4.79189i 0.00680666i
\(705\) 17.7726 + 41.9977i 0.0252094 + 0.0595712i
\(706\) −16.9053 −0.0239451
\(707\) 166.669 + 166.669i 0.235741 + 0.235741i
\(708\) 261.447 261.447i 0.369275 0.369275i
\(709\) 934.208i 1.31764i −0.752300 0.658821i \(-0.771056\pi\)
0.752300 0.658821i \(-0.228944\pi\)
\(710\) −49.0276 + 120.965i −0.0690530 + 0.170374i
\(711\) 369.994 0.520385
\(712\) 110.126 + 110.126i 0.154671 + 0.154671i
\(713\) −168.660 + 168.660i −0.236549 + 0.236549i
\(714\) 192.462i 0.269555i
\(715\) −9.61591 3.89735i −0.0134488 0.00545084i
\(716\) −365.693 −0.510744
\(717\) 91.0306 + 91.0306i 0.126960 + 0.126960i
\(718\) 29.7289 29.7289i 0.0414052 0.0414052i
\(719\) 683.253i 0.950283i −0.879909 0.475142i \(-0.842397\pi\)
0.879909 0.475142i \(-0.157603\pi\)
\(720\) 55.2560 23.3833i 0.0767444 0.0324768i
\(721\) 330.351 0.458185
\(722\) 57.4667 + 57.4667i 0.0795937 + 0.0795937i
\(723\) 317.718 317.718i 0.439443 0.439443i
\(724\) 567.064i 0.783238i
\(725\) −455.182 441.498i −0.627837 0.608962i
\(726\) 295.509 0.407038
\(727\) 543.867 + 543.867i 0.748098 + 0.748098i 0.974122 0.226024i \(-0.0725726\pi\)
−0.226024 + 0.974122i \(0.572573\pi\)
\(728\) 21.4466 21.4466i 0.0294597 0.0294597i
\(729\) 27.0000i 0.0370370i
\(730\) −5.49937 12.9953i −0.00753338 0.0178018i
\(731\) −1338.75 −1.83139
\(732\) −139.283 139.283i −0.190277 0.190277i
\(733\) 808.113 808.113i 1.10247 1.10247i 0.108362 0.994111i \(-0.465439\pi\)
0.994111 0.108362i \(-0.0345607\pi\)
\(734\) 575.951i 0.784674i
\(735\) 128.231 316.382i 0.174463 0.430452i
\(736\) 27.1293 0.0368605
\(737\) −3.29910 3.29910i −0.00447639 0.00447639i
\(738\) −178.923 + 178.923i −0.242444 + 0.242444i
\(739\) 1188.76i 1.60860i −0.594223 0.804300i \(-0.702540\pi\)
0.594223 0.804300i \(-0.297460\pi\)
\(740\) 555.165 + 225.010i 0.750224 + 0.304068i
\(741\) −104.543 −0.141083
\(742\) −289.860 289.860i −0.390647 0.390647i
\(743\) −38.8612 + 38.8612i −0.0523031 + 0.0523031i −0.732775 0.680471i \(-0.761775\pi\)
0.680471 + 0.732775i \(0.261775\pi\)
\(744\) 243.651i 0.327488i
\(745\) −1164.45 + 492.771i −1.56301 + 0.661438i
\(746\) −397.167 −0.532395
\(747\) −102.332 102.332i −0.136991 0.136991i
\(748\) −21.5032 + 21.5032i −0.0287475 + 0.0287475i
\(749\) 467.664i 0.624384i
\(750\) −285.487 110.667i −0.380649 0.147556i
\(751\) −787.039 −1.04799 −0.523994 0.851722i \(-0.675559\pi\)
−0.523994 + 0.851722i \(0.675559\pi\)
\(752\) −14.8940 14.8940i −0.0198059 0.0198059i
\(753\) 565.198 565.198i 0.750595 0.750595i
\(754\) 124.273i 0.164819i
\(755\) 47.6740 + 112.656i 0.0631444 + 0.149214i
\(756\) 32.1670 0.0425490
\(757\) 582.426 + 582.426i 0.769387 + 0.769387i 0.977998 0.208612i \(-0.0668946\pi\)
−0.208612 + 0.977998i \(0.566895\pi\)
\(758\) −533.203 + 533.203i −0.703434 + 0.703434i
\(759\) 4.97555i 0.00655541i
\(760\) −92.5488 + 228.345i −0.121775 + 0.300454i
\(761\) −228.038 −0.299655 −0.149828 0.988712i \(-0.547872\pi\)
−0.149828 + 0.988712i \(0.547872\pi\)
\(762\) −292.426 292.426i −0.383761 0.383761i
\(763\) 229.972 229.972i 0.301404 0.301404i
\(764\) 444.930i 0.582369i
\(765\) −352.886 143.026i −0.461289 0.186962i
\(766\) 241.196 0.314877
\(767\) 261.471 + 261.471i 0.340900 + 0.340900i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 63.2584i 0.0822606i −0.999154 0.0411303i \(-0.986904\pi\)
0.999154 0.0411303i \(-0.0130959\pi\)
\(770\) −12.0734 + 5.10922i −0.0156797 + 0.00663536i
\(771\) −86.7907 −0.112569
\(772\) 310.118 + 310.118i 0.401708 + 0.401708i
\(773\) −268.204 + 268.204i −0.346965 + 0.346965i −0.858978 0.512013i \(-0.828900\pi\)
0.512013 + 0.858978i \(0.328900\pi\)
\(774\) 223.751i 0.289084i
\(775\) −865.681 + 892.513i −1.11701 + 1.15163i
\(776\) −221.983 −0.286060
\(777\) 227.088 + 227.088i 0.292262 + 0.292262i
\(778\) 292.831 292.831i 0.376389 0.376389i
\(779\) 1039.08i