Properties

Label 784.2.m.l.197.16
Level $784$
Weight $2$
Character 784.197
Analytic conductor $6.260$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 197.16
Character \(\chi\) \(=\) 784.197
Dual form 784.2.m.l.589.16

$q$-expansion

\(f(q)\) \(=\) \(q+(0.395893 + 1.35767i) q^{2} +(2.06976 - 2.06976i) q^{3} +(-1.68654 + 1.07498i) q^{4} +(2.64219 + 2.64219i) q^{5} +(3.62946 + 1.99065i) q^{6} +(-2.12716 - 1.86418i) q^{8} -5.56783i q^{9} +O(q^{10})\) \(q+(0.395893 + 1.35767i) q^{2} +(2.06976 - 2.06976i) q^{3} +(-1.68654 + 1.07498i) q^{4} +(2.64219 + 2.64219i) q^{5} +(3.62946 + 1.99065i) q^{6} +(-2.12716 - 1.86418i) q^{8} -5.56783i q^{9} +(-2.54120 + 4.63325i) q^{10} +(0.682946 + 0.682946i) q^{11} +(-1.26577 + 5.71569i) q^{12} +(4.19543 - 4.19543i) q^{13} +10.9374 q^{15} +(1.68882 - 3.62600i) q^{16} -1.45879 q^{17} +(7.55927 - 2.20426i) q^{18} +(-2.68222 + 2.68222i) q^{19} +(-7.29647 - 1.61584i) q^{20} +(-0.656842 + 1.19759i) q^{22} +1.79832i q^{23} +(-8.26113 + 0.544304i) q^{24} +8.96235i q^{25} +(7.35696 + 4.03507i) q^{26} +(-5.31479 - 5.31479i) q^{27} +(-0.295765 + 0.295765i) q^{29} +(4.33004 + 14.8494i) q^{30} -1.16351 q^{31} +(5.59151 + 0.857349i) q^{32} +2.82707 q^{33} +(-0.577524 - 1.98056i) q^{34} +(5.98533 + 9.39035i) q^{36} +(0.0493910 + 0.0493910i) q^{37} +(-4.70344 - 2.57970i) q^{38} -17.3671i q^{39} +(-0.694841 - 10.5459i) q^{40} +10.1128i q^{41} +(-4.55032 - 4.55032i) q^{43} +(-1.88597 - 0.417658i) q^{44} +(14.7113 - 14.7113i) q^{45} +(-2.44153 + 0.711944i) q^{46} -11.0875 q^{47} +(-4.00951 - 11.0004i) q^{48} +(-12.1679 + 3.54813i) q^{50} +(-3.01935 + 3.01935i) q^{51} +(-2.56573 + 11.5858i) q^{52} +(-0.417874 - 0.417874i) q^{53} +(5.11164 - 9.31982i) q^{54} +3.60895i q^{55} +11.1031i q^{57} +(-0.518643 - 0.284460i) q^{58} +(-3.74749 - 3.74749i) q^{59} +(-18.4464 + 11.7575i) q^{60} +(7.02257 - 7.02257i) q^{61} +(-0.460627 - 1.57967i) q^{62} +(1.04964 + 7.93084i) q^{64} +22.1703 q^{65} +(1.11922 + 3.83823i) q^{66} +(8.42467 - 8.42467i) q^{67} +(2.46030 - 1.56818i) q^{68} +(3.72210 + 3.72210i) q^{69} -2.89148i q^{71} +(-10.3795 + 11.8437i) q^{72} -0.640221i q^{73} +(-0.0475032 + 0.0866103i) q^{74} +(18.5499 + 18.5499i) q^{75} +(1.64032 - 7.40701i) q^{76} +(23.5788 - 6.87551i) q^{78} -0.749820 q^{79} +(14.0428 - 5.11841i) q^{80} -5.29721 q^{81} +(-13.7299 + 4.00359i) q^{82} +(-4.51473 + 4.51473i) q^{83} +(-3.85440 - 3.85440i) q^{85} +(4.37640 - 7.97928i) q^{86} +1.22433i q^{87} +(-0.179600 - 2.72587i) q^{88} +15.4712i q^{89} +(25.7971 + 14.1490i) q^{90} +(-1.93317 - 3.03294i) q^{92} +(-2.40820 + 2.40820i) q^{93} +(-4.38947 - 15.0532i) q^{94} -14.1739 q^{95} +(13.3476 - 9.79858i) q^{96} -13.7459 q^{97} +(3.80252 - 3.80252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 4q^{4} + O(q^{10}) \) \( 48q - 4q^{4} - 8q^{11} + 32q^{15} + 36q^{16} + 20q^{18} - 28q^{22} - 16q^{29} + 96q^{30} + 40q^{32} + 40q^{36} - 16q^{37} + 8q^{43} + 4q^{44} + 64q^{46} - 28q^{50} + 16q^{53} - 20q^{58} + 8q^{60} + 44q^{64} + 40q^{67} - 196q^{72} - 28q^{74} + 56q^{78} + 80q^{79} - 48q^{81} - 108q^{86} - 100q^{88} - 128q^{95} - 40q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.395893 + 1.35767i 0.279939 + 0.960018i
\(3\) 2.06976 2.06976i 1.19498 1.19498i 0.219326 0.975652i \(-0.429614\pi\)
0.975652 0.219326i \(-0.0703858\pi\)
\(4\) −1.68654 + 1.07498i −0.843269 + 0.537492i
\(5\) 2.64219 + 2.64219i 1.18162 + 1.18162i 0.979324 + 0.202300i \(0.0648417\pi\)
0.202300 + 0.979324i \(0.435158\pi\)
\(6\) 3.62946 + 1.99065i 1.48172 + 0.812679i
\(7\) 0 0
\(8\) −2.12716 1.86418i −0.752065 0.659088i
\(9\) 5.56783i 1.85594i
\(10\) −2.54120 + 4.63325i −0.803598 + 1.46516i
\(11\) 0.682946 + 0.682946i 0.205916 + 0.205916i 0.802529 0.596613i \(-0.203487\pi\)
−0.596613 + 0.802529i \(0.703487\pi\)
\(12\) −1.26577 + 5.71569i −0.365396 + 1.64998i
\(13\) 4.19543 4.19543i 1.16360 1.16360i 0.179924 0.983681i \(-0.442415\pi\)
0.983681 0.179924i \(-0.0575851\pi\)
\(14\) 0 0
\(15\) 10.9374 2.82403
\(16\) 1.68882 3.62600i 0.422205 0.906501i
\(17\) −1.45879 −0.353808 −0.176904 0.984228i \(-0.556608\pi\)
−0.176904 + 0.984228i \(0.556608\pi\)
\(18\) 7.55927 2.20426i 1.78174 0.519550i
\(19\) −2.68222 + 2.68222i −0.615343 + 0.615343i −0.944333 0.328990i \(-0.893292\pi\)
0.328990 + 0.944333i \(0.393292\pi\)
\(20\) −7.29647 1.61584i −1.63154 0.361313i
\(21\) 0 0
\(22\) −0.656842 + 1.19759i −0.140039 + 0.255327i
\(23\) 1.79832i 0.374977i 0.982267 + 0.187488i \(0.0600347\pi\)
−0.982267 + 0.187488i \(0.939965\pi\)
\(24\) −8.26113 + 0.544304i −1.68630 + 0.111106i
\(25\) 8.96235i 1.79247i
\(26\) 7.35696 + 4.03507i 1.44282 + 0.791343i
\(27\) −5.31479 5.31479i −1.02283 1.02283i
\(28\) 0 0
\(29\) −0.295765 + 0.295765i −0.0549222 + 0.0549222i −0.734034 0.679112i \(-0.762365\pi\)
0.679112 + 0.734034i \(0.262365\pi\)
\(30\) 4.33004 + 14.8494i 0.790554 + 2.71112i
\(31\) −1.16351 −0.208973 −0.104487 0.994526i \(-0.533320\pi\)
−0.104487 + 0.994526i \(0.533320\pi\)
\(32\) 5.59151 + 0.857349i 0.988448 + 0.151559i
\(33\) 2.82707 0.492130
\(34\) −0.577524 1.98056i −0.0990446 0.339662i
\(35\) 0 0
\(36\) 5.98533 + 9.39035i 0.997554 + 1.56506i
\(37\) 0.0493910 + 0.0493910i 0.00811983 + 0.00811983i 0.711155 0.703035i \(-0.248172\pi\)
−0.703035 + 0.711155i \(0.748172\pi\)
\(38\) −4.70344 2.57970i −0.762999 0.418482i
\(39\) 17.3671i 2.78096i
\(40\) −0.694841 10.5459i −0.109864 1.66745i
\(41\) 10.1128i 1.57935i 0.613522 + 0.789677i \(0.289752\pi\)
−0.613522 + 0.789677i \(0.710248\pi\)
\(42\) 0 0
\(43\) −4.55032 4.55032i −0.693918 0.693918i 0.269174 0.963092i \(-0.413249\pi\)
−0.963092 + 0.269174i \(0.913249\pi\)
\(44\) −1.88597 0.417658i −0.284321 0.0629643i
\(45\) 14.7113 14.7113i 2.19303 2.19303i
\(46\) −2.44153 + 0.711944i −0.359984 + 0.104970i
\(47\) −11.0875 −1.61728 −0.808641 0.588302i \(-0.799797\pi\)
−0.808641 + 0.588302i \(0.799797\pi\)
\(48\) −4.00951 11.0004i −0.578723 1.58777i
\(49\) 0 0
\(50\) −12.1679 + 3.54813i −1.72080 + 0.501781i
\(51\) −3.01935 + 3.01935i −0.422793 + 0.422793i
\(52\) −2.56573 + 11.5858i −0.355803 + 1.60666i
\(53\) −0.417874 0.417874i −0.0573994 0.0573994i 0.677824 0.735224i \(-0.262923\pi\)
−0.735224 + 0.677824i \(0.762923\pi\)
\(54\) 5.11164 9.31982i 0.695607 1.26827i
\(55\) 3.60895i 0.486630i
\(56\) 0 0
\(57\) 11.1031i 1.47064i
\(58\) −0.518643 0.284460i −0.0681012 0.0373515i
\(59\) −3.74749 3.74749i −0.487881 0.487881i 0.419756 0.907637i \(-0.362116\pi\)
−0.907637 + 0.419756i \(0.862116\pi\)
\(60\) −18.4464 + 11.7575i −2.38141 + 1.51789i
\(61\) 7.02257 7.02257i 0.899148 0.899148i −0.0962132 0.995361i \(-0.530673\pi\)
0.995361 + 0.0962132i \(0.0306731\pi\)
\(62\) −0.460627 1.57967i −0.0584997 0.200618i
\(63\) 0 0
\(64\) 1.04964 + 7.93084i 0.131205 + 0.991355i
\(65\) 22.1703 2.74988
\(66\) 1.11922 + 3.83823i 0.137766 + 0.472453i
\(67\) 8.42467 8.42467i 1.02924 1.02924i 0.0296779 0.999560i \(-0.490552\pi\)
0.999560 0.0296779i \(-0.00944816\pi\)
\(68\) 2.46030 1.56818i 0.298356 0.190169i
\(69\) 3.72210 + 3.72210i 0.448089 + 0.448089i
\(70\) 0 0
\(71\) 2.89148i 0.343156i −0.985171 0.171578i \(-0.945113\pi\)
0.985171 0.171578i \(-0.0548865\pi\)
\(72\) −10.3795 + 11.8437i −1.22323 + 1.39579i
\(73\) 0.640221i 0.0749322i −0.999298 0.0374661i \(-0.988071\pi\)
0.999298 0.0374661i \(-0.0119286\pi\)
\(74\) −0.0475032 + 0.0866103i −0.00552213 + 0.0100682i
\(75\) 18.5499 + 18.5499i 2.14196 + 2.14196i
\(76\) 1.64032 7.40701i 0.188158 0.849642i
\(77\) 0 0
\(78\) 23.5788 6.87551i 2.66977 0.778498i
\(79\) −0.749820 −0.0843613 −0.0421807 0.999110i \(-0.513431\pi\)
−0.0421807 + 0.999110i \(0.513431\pi\)
\(80\) 14.0428 5.11841i 1.57003 0.572256i
\(81\) −5.29721 −0.588579
\(82\) −13.7299 + 4.00359i −1.51621 + 0.442122i
\(83\) −4.51473 + 4.51473i −0.495556 + 0.495556i −0.910051 0.414495i \(-0.863958\pi\)
0.414495 + 0.910051i \(0.363958\pi\)
\(84\) 0 0
\(85\) −3.85440 3.85440i −0.418068 0.418068i
\(86\) 4.37640 7.97928i 0.471919 0.860428i
\(87\) 1.22433i 0.131262i
\(88\) −0.179600 2.72587i −0.0191455 0.290579i
\(89\) 15.4712i 1.63995i 0.572401 + 0.819974i \(0.306012\pi\)
−0.572401 + 0.819974i \(0.693988\pi\)
\(90\) 25.7971 + 14.1490i 2.71926 + 1.49143i
\(91\) 0 0
\(92\) −1.93317 3.03294i −0.201547 0.316206i
\(93\) −2.40820 + 2.40820i −0.249718 + 0.249718i
\(94\) −4.38947 15.0532i −0.452740 1.55262i
\(95\) −14.1739 −1.45421
\(96\) 13.3476 9.79858i 1.36228 1.00006i
\(97\) −13.7459 −1.39569 −0.697843 0.716250i \(-0.745857\pi\)
−0.697843 + 0.716250i \(0.745857\pi\)
\(98\) 0 0
\(99\) 3.80252 3.80252i 0.382168 0.382168i
\(100\) −9.63438 15.1153i −0.963438 1.51153i
\(101\) −3.27564 3.27564i −0.325938 0.325938i 0.525101 0.851040i \(-0.324027\pi\)
−0.851040 + 0.525101i \(0.824027\pi\)
\(102\) −5.29462 2.90394i −0.524245 0.287533i
\(103\) 8.74763i 0.861930i −0.902369 0.430965i \(-0.858173\pi\)
0.902369 0.430965i \(-0.141827\pi\)
\(104\) −16.7454 + 1.10331i −1.64202 + 0.108189i
\(105\) 0 0
\(106\) 0.401901 0.732768i 0.0390361 0.0711727i
\(107\) −3.17643 3.17643i −0.307078 0.307078i 0.536697 0.843775i \(-0.319672\pi\)
−0.843775 + 0.536697i \(0.819672\pi\)
\(108\) 14.6769 + 3.25028i 1.41229 + 0.312758i
\(109\) 4.35303 4.35303i 0.416945 0.416945i −0.467204 0.884149i \(-0.654739\pi\)
0.884149 + 0.467204i \(0.154739\pi\)
\(110\) −4.89976 + 1.42876i −0.467174 + 0.136227i
\(111\) 0.204455 0.0194060
\(112\) 0 0
\(113\) 0.0896489 0.00843346 0.00421673 0.999991i \(-0.498658\pi\)
0.00421673 + 0.999991i \(0.498658\pi\)
\(114\) −15.0744 + 4.39564i −1.41184 + 0.411690i
\(115\) −4.75152 + 4.75152i −0.443081 + 0.443081i
\(116\) 0.180876 0.816762i 0.0167939 0.0758345i
\(117\) −23.3595 23.3595i −2.15958 2.15958i
\(118\) 3.60425 6.57145i 0.331798 0.604951i
\(119\) 0 0
\(120\) −23.2657 20.3893i −2.12385 1.86128i
\(121\) 10.0672i 0.915197i
\(122\) 12.3145 + 6.75415i 1.11490 + 0.611492i
\(123\) 20.9311 + 20.9311i 1.88729 + 1.88729i
\(124\) 1.96231 1.25076i 0.176221 0.112321i
\(125\) −10.4693 + 10.4693i −0.936401 + 0.936401i
\(126\) 0 0
\(127\) −17.0084 −1.50925 −0.754624 0.656157i \(-0.772181\pi\)
−0.754624 + 0.656157i \(0.772181\pi\)
\(128\) −10.3519 + 4.56483i −0.914989 + 0.403478i
\(129\) −18.8362 −1.65843
\(130\) 8.77706 + 30.0999i 0.769799 + 2.63994i
\(131\) −14.0070 + 14.0070i −1.22379 + 1.22379i −0.257521 + 0.966273i \(0.582906\pi\)
−0.966273 + 0.257521i \(0.917094\pi\)
\(132\) −4.76796 + 3.03905i −0.414997 + 0.264516i
\(133\) 0 0
\(134\) 14.7732 + 8.10266i 1.27621 + 0.699963i
\(135\) 28.0854i 2.41720i
\(136\) 3.10308 + 2.71945i 0.266087 + 0.233191i
\(137\) 0.915437i 0.0782111i −0.999235 0.0391055i \(-0.987549\pi\)
0.999235 0.0391055i \(-0.0124509\pi\)
\(138\) −3.57983 + 6.52694i −0.304736 + 0.555610i
\(139\) −2.74533 2.74533i −0.232856 0.232856i 0.581028 0.813884i \(-0.302651\pi\)
−0.813884 + 0.581028i \(0.802651\pi\)
\(140\) 0 0
\(141\) −22.9485 + 22.9485i −1.93262 + 1.93262i
\(142\) 3.92568 1.14472i 0.329436 0.0960625i
\(143\) 5.73051 0.479209
\(144\) −20.1890 9.40305i −1.68241 0.783587i
\(145\) −1.56294 −0.129795
\(146\) 0.869209 0.253459i 0.0719362 0.0209764i
\(147\) 0 0
\(148\) −0.136394 0.0302052i −0.0112115 0.00248286i
\(149\) −5.96683 5.96683i −0.488822 0.488822i 0.419112 0.907934i \(-0.362341\pi\)
−0.907934 + 0.419112i \(0.862341\pi\)
\(150\) −17.8409 + 32.5285i −1.45670 + 2.65594i
\(151\) 5.07755i 0.413206i −0.978425 0.206603i \(-0.933759\pi\)
0.978425 0.206603i \(-0.0662408\pi\)
\(152\) 10.7057 0.705367i 0.868344 0.0572129i
\(153\) 8.12229i 0.656648i
\(154\) 0 0
\(155\) −3.07423 3.07423i −0.246928 0.246928i
\(156\) 18.6694 + 29.2903i 1.49474 + 2.34510i
\(157\) 3.69391 3.69391i 0.294806 0.294806i −0.544169 0.838976i \(-0.683155\pi\)
0.838976 + 0.544169i \(0.183155\pi\)
\(158\) −0.296848 1.01801i −0.0236160 0.0809884i
\(159\) −1.72980 −0.137182
\(160\) 12.5085 + 17.0391i 0.988888 + 1.34706i
\(161\) 0 0
\(162\) −2.09713 7.19187i −0.164766 0.565047i
\(163\) 8.19576 8.19576i 0.641941 0.641941i −0.309091 0.951032i \(-0.600025\pi\)
0.951032 + 0.309091i \(0.100025\pi\)
\(164\) −10.8711 17.0556i −0.848891 1.33182i
\(165\) 7.46966 + 7.46966i 0.581512 + 0.581512i
\(166\) −7.91686 4.34216i −0.614468 0.337017i
\(167\) 13.7471i 1.06378i −0.846813 0.531891i \(-0.821482\pi\)
0.846813 0.531891i \(-0.178518\pi\)
\(168\) 0 0
\(169\) 22.2033i 1.70795i
\(170\) 3.70708 6.75894i 0.284320 0.518387i
\(171\) 14.9341 + 14.9341i 1.14204 + 1.14204i
\(172\) 12.5658 + 2.78277i 0.958135 + 0.212184i
\(173\) −5.58305 + 5.58305i −0.424472 + 0.424472i −0.886740 0.462268i \(-0.847036\pi\)
0.462268 + 0.886740i \(0.347036\pi\)
\(174\) −1.66223 + 0.484703i −0.126014 + 0.0367452i
\(175\) 0 0
\(176\) 3.62973 1.32299i 0.273601 0.0997242i
\(177\) −15.5128 −1.16601
\(178\) −21.0048 + 6.12495i −1.57438 + 0.459085i
\(179\) 6.82530 6.82530i 0.510147 0.510147i −0.404424 0.914571i \(-0.632528\pi\)
0.914571 + 0.404424i \(0.132528\pi\)
\(180\) −8.99672 + 40.6255i −0.670576 + 3.02804i
\(181\) 15.1263 + 15.1263i 1.12433 + 1.12433i 0.991083 + 0.133250i \(0.0425412\pi\)
0.133250 + 0.991083i \(0.457459\pi\)
\(182\) 0 0
\(183\) 29.0701i 2.14892i
\(184\) 3.35241 3.82533i 0.247143 0.282007i
\(185\) 0.261001i 0.0191892i
\(186\) −4.22292 2.31615i −0.309640 0.169828i
\(187\) −0.996274 0.996274i −0.0728548 0.0728548i
\(188\) 18.6995 11.9189i 1.36380 0.869277i
\(189\) 0 0
\(190\) −5.61134 19.2434i −0.407089 1.39607i
\(191\) 19.8728 1.43794 0.718971 0.695040i \(-0.244613\pi\)
0.718971 + 0.695040i \(0.244613\pi\)
\(192\) 18.5875 + 14.2424i 1.34143 + 1.02786i
\(193\) −11.8829 −0.855352 −0.427676 0.903932i \(-0.640668\pi\)
−0.427676 + 0.903932i \(0.640668\pi\)
\(194\) −5.44191 18.6624i −0.390707 1.33988i
\(195\) 45.8872 45.8872i 3.28605 3.28605i
\(196\) 0 0
\(197\) 6.61994 + 6.61994i 0.471651 + 0.471651i 0.902449 0.430797i \(-0.141768\pi\)
−0.430797 + 0.902449i \(0.641768\pi\)
\(198\) 6.66796 + 3.65718i 0.473872 + 0.259904i
\(199\) 24.0632i 1.70579i 0.522079 + 0.852897i \(0.325157\pi\)
−0.522079 + 0.852897i \(0.674843\pi\)
\(200\) 16.7075 19.0644i 1.18140 1.34805i
\(201\) 34.8741i 2.45983i
\(202\) 3.15044 5.74404i 0.221664 0.404149i
\(203\) 0 0
\(204\) 1.84649 8.33799i 0.129280 0.583776i
\(205\) −26.7200 + 26.7200i −1.86620 + 1.86620i
\(206\) 11.8764 3.46313i 0.827468 0.241287i
\(207\) 10.0128 0.695935
\(208\) −8.12733 22.2980i −0.563529 1.54609i
\(209\) −3.66362 −0.253418
\(210\) 0 0
\(211\) −18.2158 + 18.2158i −1.25403 + 1.25403i −0.300133 + 0.953897i \(0.597031\pi\)
−0.953897 + 0.300133i \(0.902969\pi\)
\(212\) 1.15397 + 0.255552i 0.0792548 + 0.0175514i
\(213\) −5.98468 5.98468i −0.410063 0.410063i
\(214\) 3.05502 5.57008i 0.208837 0.380763i
\(215\) 24.0457i 1.63990i
\(216\) 1.39768 + 21.2132i 0.0950999 + 1.44337i
\(217\) 0 0
\(218\) 7.63332 + 4.18665i 0.516994 + 0.283556i
\(219\) −1.32510 1.32510i −0.0895423 0.0895423i
\(220\) −3.87956 6.08662i −0.261560 0.410360i
\(221\) −6.12026 + 6.12026i −0.411693 + 0.411693i
\(222\) 0.0809424 + 0.277583i 0.00543250 + 0.0186301i
\(223\) −8.33457 −0.558124 −0.279062 0.960273i \(-0.590024\pi\)
−0.279062 + 0.960273i \(0.590024\pi\)
\(224\) 0 0
\(225\) 49.9008 3.32672
\(226\) 0.0354914 + 0.121714i 0.00236085 + 0.00809627i
\(227\) 7.87294 7.87294i 0.522545 0.522545i −0.395794 0.918339i \(-0.629531\pi\)
0.918339 + 0.395794i \(0.129531\pi\)
\(228\) −11.9357 18.7258i −0.790459 1.24015i
\(229\) 8.97014 + 8.97014i 0.592763 + 0.592763i 0.938377 0.345614i \(-0.112329\pi\)
−0.345614 + 0.938377i \(0.612329\pi\)
\(230\) −8.33209 4.56990i −0.549401 0.301330i
\(231\) 0 0
\(232\) 1.18050 0.0777801i 0.0775037 0.00510651i
\(233\) 22.5390i 1.47658i 0.674483 + 0.738291i \(0.264367\pi\)
−0.674483 + 0.738291i \(0.735633\pi\)
\(234\) 22.4666 40.9623i 1.46869 2.67779i
\(235\) −29.2954 29.2954i −1.91102 1.91102i
\(236\) 10.3488 + 2.29179i 0.673647 + 0.149183i
\(237\) −1.55195 + 1.55195i −0.100810 + 0.100810i
\(238\) 0 0
\(239\) 13.3677 0.864687 0.432344 0.901709i \(-0.357687\pi\)
0.432344 + 0.901709i \(0.357687\pi\)
\(240\) 18.4713 39.6591i 1.19232 2.55998i
\(241\) 19.3942 1.24929 0.624645 0.780909i \(-0.285244\pi\)
0.624645 + 0.780909i \(0.285244\pi\)
\(242\) 13.6679 3.98552i 0.878606 0.256199i
\(243\) 4.98040 4.98040i 0.319493 0.319493i
\(244\) −4.29467 + 19.3930i −0.274938 + 1.24151i
\(245\) 0 0
\(246\) −20.1311 + 36.7040i −1.28351 + 2.34016i
\(247\) 22.5062i 1.43203i
\(248\) 2.47498 + 2.16900i 0.157162 + 0.137732i
\(249\) 18.6888i 1.18436i
\(250\) −18.3585 10.0691i −1.16110 0.636827i
\(251\) 8.09990 + 8.09990i 0.511261 + 0.511261i 0.914913 0.403652i \(-0.132259\pi\)
−0.403652 + 0.914913i \(0.632259\pi\)
\(252\) 0 0
\(253\) −1.22816 + 1.22816i −0.0772136 + 0.0772136i
\(254\) −6.73349 23.0918i −0.422497 1.44891i
\(255\) −15.9554 −0.999165
\(256\) −10.2958 12.2473i −0.643487 0.765457i
\(257\) 16.9823 1.05932 0.529662 0.848209i \(-0.322319\pi\)
0.529662 + 0.848209i \(0.322319\pi\)
\(258\) −7.45711 25.5733i −0.464259 1.59212i
\(259\) 0 0
\(260\) −37.3910 + 23.8327i −2.31889 + 1.47804i
\(261\) 1.64677 + 1.64677i 0.101933 + 0.101933i
\(262\) −24.5621 13.4716i −1.51745 0.832277i
\(263\) 4.39734i 0.271152i −0.990767 0.135576i \(-0.956712\pi\)
0.990767 0.135576i \(-0.0432884\pi\)
\(264\) −6.01363 5.27018i −0.370114 0.324357i
\(265\) 2.20820i 0.135649i
\(266\) 0 0
\(267\) 32.0218 + 32.0218i 1.95970 + 1.95970i
\(268\) −5.15214 + 23.2649i −0.314717 + 1.42113i
\(269\) −7.71509 + 7.71509i −0.470397 + 0.470397i −0.902043 0.431646i \(-0.857933\pi\)
0.431646 + 0.902043i \(0.357933\pi\)
\(270\) 38.1307 11.1188i 2.32056 0.676669i
\(271\) 16.7376 1.01674 0.508369 0.861139i \(-0.330248\pi\)
0.508369 + 0.861139i \(0.330248\pi\)
\(272\) −2.46363 + 5.28957i −0.149380 + 0.320728i
\(273\) 0 0
\(274\) 1.24286 0.362415i 0.0750840 0.0218943i
\(275\) −6.12080 + 6.12080i −0.369098 + 0.369098i
\(276\) −10.2787 2.27626i −0.618703 0.137015i
\(277\) −13.6141 13.6141i −0.817989 0.817989i 0.167827 0.985816i \(-0.446325\pi\)
−0.985816 + 0.167827i \(0.946325\pi\)
\(278\) 2.64040 4.81411i 0.158360 0.288731i
\(279\) 6.47824i 0.387842i
\(280\) 0 0
\(281\) 14.9711i 0.893100i −0.894759 0.446550i \(-0.852652\pi\)
0.894759 0.446550i \(-0.147348\pi\)
\(282\) −40.2417 22.0714i −2.39636 1.31433i
\(283\) −6.66191 6.66191i −0.396010 0.396010i 0.480813 0.876823i \(-0.340341\pi\)
−0.876823 + 0.480813i \(0.840341\pi\)
\(284\) 3.10830 + 4.87659i 0.184444 + 0.289373i
\(285\) −29.3365 + 29.3365i −1.73775 + 1.73775i
\(286\) 2.26867 + 7.78014i 0.134149 + 0.460049i
\(287\) 0 0
\(288\) 4.77357 31.1325i 0.281285 1.83450i
\(289\) −14.8719 −0.874820
\(290\) −0.618756 2.12195i −0.0363346 0.124605i
\(291\) −28.4508 + 28.4508i −1.66781 + 1.66781i
\(292\) 0.688227 + 1.07976i 0.0402754 + 0.0631880i
\(293\) −1.24795 1.24795i −0.0729060 0.0729060i 0.669714 0.742620i \(-0.266417\pi\)
−0.742620 + 0.669714i \(0.766417\pi\)
\(294\) 0 0
\(295\) 19.8031i 1.15298i
\(296\) −0.0129888 0.197137i −0.000754959 0.0114583i
\(297\) 7.25942i 0.421234i
\(298\) 5.73876 10.4632i 0.332438 0.606118i
\(299\) 7.54475 + 7.54475i 0.436324 + 0.436324i
\(300\) −51.2260 11.3443i −2.95754 0.654962i
\(301\) 0 0
\(302\) 6.89365 2.01017i 0.396685 0.115672i
\(303\) −13.5596 −0.778978
\(304\) 5.19595 + 14.2555i 0.298008 + 0.817610i
\(305\) 37.1099 2.12491
\(306\) −11.0274 + 3.21556i −0.630394 + 0.183821i
\(307\) −17.4736 + 17.4736i −0.997273 + 0.997273i −0.999996 0.00272350i \(-0.999133\pi\)
0.00272350 + 0.999996i \(0.499133\pi\)
\(308\) 0 0
\(309\) −18.1055 18.1055i −1.02999 1.02999i
\(310\) 2.95672 5.39085i 0.167930 0.306180i
\(311\) 28.4805i 1.61498i −0.589880 0.807491i \(-0.700825\pi\)
0.589880 0.807491i \(-0.299175\pi\)
\(312\) −32.3755 + 36.9426i −1.83290 + 2.09147i
\(313\) 15.6876i 0.886714i 0.896345 + 0.443357i \(0.146213\pi\)
−0.896345 + 0.443357i \(0.853787\pi\)
\(314\) 6.47751 + 3.55272i 0.365547 + 0.200492i
\(315\) 0 0
\(316\) 1.26460 0.806044i 0.0711393 0.0453435i
\(317\) 11.9478 11.9478i 0.671054 0.671054i −0.286905 0.957959i \(-0.592626\pi\)
0.957959 + 0.286905i \(0.0926263\pi\)
\(318\) −0.684815 2.34849i −0.0384025 0.131697i
\(319\) −0.403983 −0.0226187
\(320\) −18.1815 + 23.7282i −1.01637 + 1.32644i
\(321\) −13.1489 −0.733901
\(322\) 0 0
\(323\) 3.91279 3.91279i 0.217714 0.217714i
\(324\) 8.93395 5.69442i 0.496331 0.316357i
\(325\) 37.6009 + 37.6009i 2.08573 + 2.08573i
\(326\) 14.3718 + 7.88250i 0.795979 + 0.436571i
\(327\) 18.0195i 0.996480i
\(328\) 18.8521 21.5116i 1.04093 1.18778i
\(329\) 0 0
\(330\) −7.18415 + 13.0985i −0.395474 + 0.721050i
\(331\) 21.0571 + 21.0571i 1.15741 + 1.15741i 0.985032 + 0.172374i \(0.0551437\pi\)
0.172374 + 0.985032i \(0.444856\pi\)
\(332\) 2.76100 12.4675i 0.151529 0.684244i
\(333\) 0.275001 0.275001i 0.0150699 0.0150699i
\(334\) 18.6640 5.44237i 1.02125 0.297793i
\(335\) 44.5192 2.43234
\(336\) 0 0
\(337\) −1.90123 −0.103567 −0.0517833 0.998658i \(-0.516491\pi\)
−0.0517833 + 0.998658i \(0.516491\pi\)
\(338\) 30.1448 8.79015i 1.63966 0.478121i
\(339\) 0.185552 0.185552i 0.0100778 0.0100778i
\(340\) 10.6440 + 2.35717i 0.577253 + 0.127836i
\(341\) −0.794617 0.794617i −0.0430309 0.0430309i
\(342\) −14.3633 + 26.1879i −0.776679 + 1.41608i
\(343\) 0 0
\(344\) 1.19664 + 18.1619i 0.0645185 + 0.979225i
\(345\) 19.6690i 1.05894i
\(346\) −9.79024 5.36965i −0.526326 0.288674i
\(347\) −20.2774 20.2774i −1.08855 1.08855i −0.995678 0.0928678i \(-0.970397\pi\)
−0.0928678 0.995678i \(-0.529603\pi\)
\(348\) −1.31613 2.06487i −0.0705521 0.110689i
\(349\) 5.48808 5.48808i 0.293770 0.293770i −0.544797 0.838568i \(-0.683393\pi\)
0.838568 + 0.544797i \(0.183393\pi\)
\(350\) 0 0
\(351\) −44.5957 −2.38034
\(352\) 3.23317 + 4.40422i 0.172329 + 0.234746i
\(353\) −2.10289 −0.111925 −0.0559627 0.998433i \(-0.517823\pi\)
−0.0559627 + 0.998433i \(0.517823\pi\)
\(354\) −6.14141 21.0613i −0.326412 1.11939i
\(355\) 7.63985 7.63985i 0.405481 0.405481i
\(356\) −16.6313 26.0928i −0.881459 1.38292i
\(357\) 0 0
\(358\) 11.9686 + 6.56442i 0.632560 + 0.346941i
\(359\) 10.7107i 0.565288i −0.959225 0.282644i \(-0.908789\pi\)
0.959225 0.282644i \(-0.0912115\pi\)
\(360\) −58.7177 + 3.86875i −3.09470 + 0.203901i
\(361\) 4.61140i 0.242705i
\(362\) −14.5482 + 26.5250i −0.764635 + 1.39412i
\(363\) −20.8366 20.8366i −1.09364 1.09364i
\(364\) 0 0
\(365\) 1.69159 1.69159i 0.0885416 0.0885416i
\(366\) 39.4676 11.5086i 2.06300 0.601566i
\(367\) −18.1890 −0.949460 −0.474730 0.880131i \(-0.657454\pi\)
−0.474730 + 0.880131i \(0.657454\pi\)
\(368\) 6.52073 + 3.03704i 0.339916 + 0.158317i
\(369\) 56.3063 2.93119
\(370\) −0.354353 + 0.103328i −0.0184220 + 0.00537179i
\(371\) 0 0
\(372\) 1.47274 6.65029i 0.0763580 0.344801i
\(373\) −0.690889 0.690889i −0.0357729 0.0357729i 0.688994 0.724767i \(-0.258053\pi\)
−0.724767 + 0.688994i \(0.758053\pi\)
\(374\) 0.958194 1.74703i 0.0495470 0.0903367i
\(375\) 43.3378i 2.23796i
\(376\) 23.5850 + 20.6692i 1.21630 + 1.06593i
\(377\) 2.48173i 0.127816i
\(378\) 0 0
\(379\) 17.6845 + 17.6845i 0.908391 + 0.908391i 0.996142 0.0877516i \(-0.0279682\pi\)
−0.0877516 + 0.996142i \(0.527968\pi\)
\(380\) 23.9048 15.2367i 1.22629 0.781626i
\(381\) −35.2033 + 35.2033i −1.80352 + 1.80352i
\(382\) 7.86749 + 26.9807i 0.402536 + 1.38045i
\(383\) −11.2504 −0.574869 −0.287435 0.957800i \(-0.592802\pi\)
−0.287435 + 0.957800i \(0.592802\pi\)
\(384\) −11.9779 + 30.8741i −0.611245 + 1.57554i
\(385\) 0 0
\(386\) −4.70437 16.1331i −0.239446 0.821153i
\(387\) −25.3354 + 25.3354i −1.28787 + 1.28787i
\(388\) 23.1830 14.7766i 1.17694 0.750171i
\(389\) 25.1321 + 25.1321i 1.27425 + 1.27425i 0.943838 + 0.330408i \(0.107186\pi\)
0.330408 + 0.943838i \(0.392814\pi\)
\(390\) 80.4661 + 44.1333i 4.07456 + 2.23478i
\(391\) 2.62338i 0.132670i
\(392\) 0 0
\(393\) 57.9821i 2.92481i
\(394\) −6.36691 + 11.6085i −0.320760 + 0.584827i
\(395\) −1.98117 1.98117i −0.0996834 0.0996834i
\(396\) −2.32545 + 10.5007i −0.116858 + 0.527682i
\(397\) 2.16775 2.16775i 0.108796 0.108796i −0.650613 0.759409i \(-0.725488\pi\)
0.759409 + 0.650613i \(0.225488\pi\)
\(398\) −32.6699 + 9.52645i −1.63759 + 0.477518i
\(399\) 0 0
\(400\) 32.4975 + 15.1358i 1.62487 + 0.756789i
\(401\) 21.3633 1.06683 0.533416 0.845853i \(-0.320908\pi\)
0.533416 + 0.845853i \(0.320908\pi\)
\(402\) 47.3476 13.8064i 2.36148 0.688602i
\(403\) −4.88145 + 4.88145i −0.243162 + 0.243162i
\(404\) 9.04575 + 2.00323i 0.450043 + 0.0996643i
\(405\) −13.9963 13.9963i −0.695479 0.695479i
\(406\) 0 0
\(407\) 0.0674628i 0.00334400i
\(408\) 12.0513 0.794025i 0.596626 0.0393101i
\(409\) 10.1161i 0.500210i −0.968219 0.250105i \(-0.919535\pi\)
0.968219 0.250105i \(-0.0804652\pi\)
\(410\) −46.8551 25.6987i −2.31401 1.26917i
\(411\) −1.89474 1.89474i −0.0934605 0.0934605i
\(412\) 9.40357 + 14.7532i 0.463280 + 0.726839i
\(413\) 0 0
\(414\) 3.96398 + 13.5940i 0.194819 + 0.668110i
\(415\) −23.8576 −1.17112
\(416\) 27.0558 19.8618i 1.32652 0.973807i
\(417\) −11.3644 −0.556515
\(418\) −1.45040 4.97399i −0.0709414 0.243286i
\(419\) −17.7452 + 17.7452i −0.866909 + 0.866909i −0.992129 0.125220i \(-0.960036\pi\)
0.125220 + 0.992129i \(0.460036\pi\)
\(420\) 0 0
\(421\) −18.2787 18.2787i −0.890851 0.890851i 0.103752 0.994603i \(-0.466915\pi\)
−0.994603 + 0.103752i \(0.966915\pi\)
\(422\) −31.9426 17.5196i −1.55494 0.852840i
\(423\) 61.7334i 3.00158i
\(424\) 0.109892 + 1.66788i 0.00533683 + 0.0809993i
\(425\) 13.0742i 0.634191i
\(426\) 5.75593 10.4945i 0.278876 0.508461i
\(427\) 0 0
\(428\) 8.77179 + 1.94256i 0.424001 + 0.0938972i
\(429\) 11.8608 11.8608i 0.572644 0.572644i
\(430\) 32.6461 9.51950i 1.57433 0.459071i
\(431\) 22.3440 1.07627 0.538136 0.842858i \(-0.319128\pi\)
0.538136 + 0.842858i \(0.319128\pi\)
\(432\) −28.2472 + 10.2957i −1.35904 + 0.495353i
\(433\) 9.86560 0.474111 0.237055 0.971496i \(-0.423818\pi\)
0.237055 + 0.971496i \(0.423818\pi\)
\(434\) 0 0
\(435\) −3.23491 + 3.23491i −0.155102 + 0.155102i
\(436\) −2.66211 + 12.0210i −0.127492 + 0.575702i
\(437\) −4.82350 4.82350i −0.230739 0.230739i
\(438\) 1.27446 2.32365i 0.0608958 0.111028i
\(439\) 19.4362i 0.927640i 0.885929 + 0.463820i \(0.153522\pi\)
−0.885929 + 0.463820i \(0.846478\pi\)
\(440\) 6.72774 7.67681i 0.320732 0.365978i
\(441\) 0 0
\(442\) −10.7323 5.88632i −0.510481 0.279984i
\(443\) 17.8660 + 17.8660i 0.848841 + 0.848841i 0.989989 0.141148i \(-0.0450792\pi\)
−0.141148 + 0.989989i \(0.545079\pi\)
\(444\) −0.344822 + 0.219786i −0.0163645 + 0.0104306i
\(445\) −40.8780 + 40.8780i −1.93780 + 1.93780i
\(446\) −3.29960 11.3156i −0.156240 0.535809i
\(447\) −24.6998 −1.16826
\(448\) 0 0
\(449\) −18.8980 −0.891850 −0.445925 0.895070i \(-0.647125\pi\)
−0.445925 + 0.895070i \(0.647125\pi\)
\(450\) 19.7554 + 67.7488i 0.931277 + 3.19371i
\(451\) −6.90650 + 6.90650i −0.325214 + 0.325214i
\(452\) −0.151196 + 0.0963712i −0.00711167 + 0.00453292i
\(453\) −10.5093 10.5093i −0.493771 0.493771i
\(454\) 13.8057 + 7.57202i 0.647934 + 0.355372i
\(455\) 0 0
\(456\) 20.6982 23.6181i 0.969284 1.10602i
\(457\) 9.22546i 0.431549i 0.976443 + 0.215774i \(0.0692275\pi\)
−0.976443 + 0.215774i \(0.930772\pi\)
\(458\) −8.62727 + 15.7297i −0.403126 + 0.735001i
\(459\) 7.75316 + 7.75316i 0.361886 + 0.361886i
\(460\) 2.90581 13.1214i 0.135484 0.611789i
\(461\) 10.6272 10.6272i 0.494960 0.494960i −0.414905 0.909865i \(-0.636185\pi\)
0.909865 + 0.414905i \(0.136185\pi\)
\(462\) 0 0
\(463\) 32.4877 1.50983 0.754916 0.655821i \(-0.227678\pi\)
0.754916 + 0.655821i \(0.227678\pi\)
\(464\) 0.572952 + 1.57194i 0.0265986 + 0.0729755i
\(465\) −12.7258 −0.590146
\(466\) −30.6006 + 8.92304i −1.41754 + 0.413352i
\(467\) −12.4328 + 12.4328i −0.575323 + 0.575323i −0.933611 0.358288i \(-0.883360\pi\)
0.358288 + 0.933611i \(0.383360\pi\)
\(468\) 64.5076 + 14.2856i 2.98187 + 0.660350i
\(469\) 0 0
\(470\) 28.1756 51.3713i 1.29964 2.36958i
\(471\) 15.2910i 0.704574i
\(472\) 0.985510 + 14.9575i 0.0453618 + 0.688475i
\(473\) 6.21525i 0.285777i
\(474\) −2.72144 1.49263i −0.125000 0.0685587i
\(475\) −24.0390 24.0390i −1.10298 1.10298i
\(476\) 0 0
\(477\) −2.32665 + 2.32665i −0.106530 + 0.106530i
\(478\) 5.29220 + 18.1490i 0.242059 + 0.830115i
\(479\) 36.2808 1.65771 0.828857 0.559461i \(-0.188992\pi\)
0.828857 + 0.559461i \(0.188992\pi\)
\(480\) 61.1566 + 9.37718i 2.79140 + 0.428008i
\(481\) 0.414434 0.0188965
\(482\) 7.67802 + 26.3309i 0.349724 + 1.19934i
\(483\) 0 0
\(484\) 10.8220 + 16.9787i 0.491911 + 0.771757i
\(485\) −36.3193 36.3193i −1.64918 1.64918i
\(486\) 8.73344 + 4.79003i 0.396157 + 0.217280i
\(487\) 7.29888i 0.330744i −0.986231 0.165372i \(-0.947118\pi\)
0.986231 0.165372i \(-0.0528824\pi\)
\(488\) −28.0295 + 1.84679i −1.26884 + 0.0836002i
\(489\) 33.9265i 1.53421i
\(490\) 0 0
\(491\) 11.4241 + 11.4241i 0.515561 + 0.515561i 0.916225 0.400664i \(-0.131221\pi\)
−0.400664 + 0.916225i \(0.631221\pi\)
\(492\) −57.8017 12.8005i −2.60590 0.577090i
\(493\) 0.431459 0.431459i 0.0194320 0.0194320i
\(494\) −30.5559 + 8.91003i −1.37478 + 0.400881i
\(495\) 20.0940 0.903157
\(496\) −1.96496 + 4.21890i −0.0882294 + 0.189434i
\(497\) 0 0
\(498\) −25.3733 + 7.39877i −1.13700 + 0.331547i
\(499\) 16.3221 16.3221i 0.730679 0.730679i −0.240076 0.970754i \(-0.577172\pi\)
0.970754 + 0.240076i \(0.0771722\pi\)
\(500\) 6.40253 28.9112i 0.286330 1.29295i
\(501\) −28.4532 28.4532i −1.27119 1.27119i
\(502\) −7.79030 + 14.2037i −0.347698 + 0.633941i
\(503\) 11.6303i 0.518568i 0.965801 + 0.259284i \(0.0834866\pi\)
−0.965801 + 0.259284i \(0.916513\pi\)
\(504\) 0 0
\(505\) 17.3097i 0.770273i
\(506\) −2.15365 1.18121i −0.0957415 0.0525114i
\(507\) −45.9556 45.9556i −2.04096 2.04096i
\(508\) 28.6853 18.2837i 1.27270 0.811209i
\(509\) −19.8640 + 19.8640i −0.880457 + 0.880457i −0.993581 0.113124i \(-0.963914\pi\)
0.113124 + 0.993581i \(0.463914\pi\)
\(510\) −6.31662 21.6621i −0.279705 0.959216i
\(511\) 0 0
\(512\) 12.5518 18.8269i 0.554716 0.832040i
\(513\) 28.5109 1.25879
\(514\) 6.72315 + 23.0563i 0.296546 + 1.01697i
\(515\) 23.1129 23.1129i 1.01848 1.01848i
\(516\) 31.7679 20.2486i 1.39850 0.891394i
\(517\) −7.57218 7.57218i −0.333024 0.333024i
\(518\) 0 0
\(519\) 23.1112i 1.01447i
\(520\) −47.1598 41.3295i −2.06809 1.81242i
\(521\) 6.68809i 0.293010i −0.989210 0.146505i \(-0.953197\pi\)
0.989210 0.146505i \(-0.0468025\pi\)
\(522\) −1.58383 + 2.88772i −0.0693222 + 0.126392i
\(523\) −9.25913 9.25913i −0.404874 0.404874i 0.475073 0.879946i \(-0.342422\pi\)
−0.879946 + 0.475073i \(0.842422\pi\)
\(524\) 8.56600 38.6805i 0.374208 1.68977i
\(525\) 0 0
\(526\) 5.97014 1.74088i 0.260310 0.0759058i
\(527\) 1.69732 0.0739365
\(528\) 4.77440 10.2510i 0.207779 0.446116i
\(529\) 19.7660 0.859393
\(530\) 2.99801 0.874212i 0.130225 0.0379734i
\(531\) −20.8654 + 20.8654i −0.905479 + 0.905479i
\(532\) 0 0
\(533\) 42.4276 + 42.4276i 1.83774 + 1.83774i
\(534\) −30.7978 + 56.1522i −1.33275 + 2.42994i
\(535\) 16.7855i 0.725700i
\(536\) −33.6258 + 2.21551i −1.45241 + 0.0956955i
\(537\) 28.2535i 1.21923i
\(538\) −13.5289 7.42020i −0.583272 0.319908i
\(539\) 0 0
\(540\) 30.1913 + 47.3670i 1.29923 + 2.03835i
\(541\) 13.4444 13.4444i 0.578019 0.578019i −0.356338 0.934357i \(-0.615975\pi\)
0.934357 + 0.356338i \(0.115975\pi\)
\(542\) 6.62631 + 22.7242i 0.284624 + 0.976088i
\(543\) 62.6158 2.68710
\(544\) −8.15683 1.25069i −0.349721 0.0536230i
\(545\) 23.0031 0.985345
\(546\) 0 0
\(547\) −12.0842 + 12.0842i −0.516683 + 0.516683i −0.916566 0.399883i \(-0.869051\pi\)
0.399883 + 0.916566i \(0.369051\pi\)
\(548\) 0.984080 + 1.54392i 0.0420378 + 0.0659530i
\(549\) −39.1004 39.1004i −1.66877 1.66877i
\(550\) −10.7332 5.88684i −0.457665 0.251016i
\(551\) 1.58662i 0.0675921i
\(552\) −0.978835 14.8562i −0.0416620 0.632322i
\(553\) 0 0
\(554\) 13.0937 23.8731i 0.556298 1.01427i
\(555\) 0.540210 + 0.540210i 0.0229306 + 0.0229306i
\(556\) 7.58129 + 1.67892i 0.321518 + 0.0712019i
\(557\) 23.8656 23.8656i 1.01122 1.01122i 0.0112795 0.999936i \(-0.496410\pi\)
0.999936 0.0112795i \(-0.00359046\pi\)
\(558\) −8.79532 + 2.56469i −0.372336 + 0.108572i
\(559\) −38.1812 −1.61489
\(560\) 0 0
\(561\) −4.12410 −0.174120
\(562\) 20.3258 5.92695i 0.857392 0.250013i
\(563\) −20.6614 + 20.6614i −0.870774 + 0.870774i −0.992557 0.121783i \(-0.961139\pi\)
0.121783 + 0.992557i \(0.461139\pi\)
\(564\) 14.0343 63.3729i 0.590949 2.66848i
\(565\) 0.236870 + 0.236870i 0.00996518 + 0.00996518i
\(566\) 6.40728 11.6821i 0.269318 0.491035i
\(567\) 0 0
\(568\) −5.39025 + 6.15065i −0.226170 + 0.258076i
\(569\) 26.4857i 1.11034i −0.831738 0.555169i \(-0.812654\pi\)
0.831738 0.555169i \(-0.187346\pi\)
\(570\) −51.4435 28.2152i −2.15473 1.18181i
\(571\) 23.7561 + 23.7561i 0.994161 + 0.994161i 0.999983 0.00582227i \(-0.00185330\pi\)
−0.00582227 + 0.999983i \(0.501853\pi\)
\(572\) −9.66471 + 6.16020i −0.404102 + 0.257571i
\(573\) 41.1319 41.1319i 1.71831 1.71831i
\(574\) 0 0
\(575\) −16.1172 −0.672134
\(576\) 44.1576 5.84421i 1.83990 0.243509i
\(577\) −27.5648 −1.14754 −0.573770 0.819017i \(-0.694520\pi\)
−0.573770 + 0.819017i \(0.694520\pi\)
\(578\) −5.88769 20.1912i −0.244896 0.839842i
\(579\) −24.5948 + 24.5948i −1.02213 + 1.02213i
\(580\) 2.63595 1.68013i 0.109452 0.0697637i
\(581\) 0 0
\(582\) −49.8902 27.3633i −2.06802 1.13425i
\(583\) 0.570770i 0.0236389i
\(584\) −1.19349 + 1.36185i −0.0493869 + 0.0563539i
\(585\) 123.440i 5.10363i
\(586\) 1.20025 2.18836i 0.0495818 0.0904002i
\(587\) 23.6471 + 23.6471i 0.976018 + 0.976018i 0.999719 0.0237007i \(-0.00754488\pi\)
−0.0237007 + 0.999719i \(0.507545\pi\)
\(588\) 0 0
\(589\) 3.12080 3.12080i 0.128590 0.128590i
\(590\) 26.8861 7.83993i 1.10689 0.322765i
\(591\) 27.4034 1.12723
\(592\) 0.262504 0.0956795i 0.0107889 0.00393240i
\(593\) 41.8302 1.71776 0.858881 0.512175i \(-0.171160\pi\)
0.858881 + 0.512175i \(0.171160\pi\)
\(594\) 9.85590 2.87395i 0.404393 0.117920i
\(595\) 0 0
\(596\) 16.4775 + 3.64904i 0.674946 + 0.149470i
\(597\) 49.8051 + 49.8051i 2.03839 + 2.03839i
\(598\) −7.25637 + 13.2302i −0.296735 + 0.541023i
\(599\) 27.7720i 1.13473i 0.823465 + 0.567367i \(0.192038\pi\)
−0.823465 + 0.567367i \(0.807962\pi\)
\(600\) −4.87824 74.0392i −0.199153 3.02264i
\(601\) 26.3860i 1.07631i −0.842846 0.538154i \(-0.819122\pi\)
0.842846 0.538154i \(-0.180878\pi\)
\(602\) 0 0
\(603\) −46.9071 46.9071i −1.91021 1.91021i
\(604\) 5.45829 + 8.56349i 0.222095 + 0.348443i
\(605\) 26.5994 26.5994i 1.08142 1.08142i
\(606\) −5.36814 18.4094i −0.218066 0.747832i
\(607\) 18.9982 0.771113 0.385557 0.922684i \(-0.374009\pi\)
0.385557 + 0.922684i \(0.374009\pi\)
\(608\) −17.2972 + 12.6981i −0.701496 + 0.514974i
\(609\) 0 0
\(610\) 14.6916 + 50.3830i 0.594844 + 2.03995i
\(611\) −46.5170 + 46.5170i −1.88188 + 1.88188i
\(612\) −8.73133 13.6985i −0.352943 0.553731i
\(613\) −3.03271 3.03271i −0.122490 0.122490i 0.643204 0.765694i \(-0.277605\pi\)
−0.765694 + 0.643204i \(0.777605\pi\)
\(614\) −30.6411 16.8057i −1.23657 0.678225i
\(615\) 110.608i 4.46014i
\(616\) 0 0
\(617\) 1.11707i 0.0449717i −0.999747 0.0224859i \(-0.992842\pi\)
0.999747 0.0224859i \(-0.00715808\pi\)
\(618\) 17.4135 31.7492i 0.700473 1.27714i
\(619\) 5.95717 + 5.95717i 0.239439 + 0.239439i 0.816618 0.577179i \(-0.195846\pi\)
−0.577179 + 0.816618i \(0.695846\pi\)
\(620\) 8.48954 + 1.88005i 0.340948 + 0.0755048i
\(621\) 9.55772 9.55772i 0.383538 0.383538i
\(622\) 38.6672 11.2752i 1.55041 0.452096i
\(623\) 0 0
\(624\) −62.9731 29.3299i −2.52094 1.17413i
\(625\) −10.5119 −0.420478
\(626\) −21.2986 + 6.21060i −0.851261 + 0.248225i
\(627\) −7.58282 + 7.58282i −0.302829 + 0.302829i
\(628\) −2.25903 + 10.2008i −0.0901449 + 0.407057i
\(629\) −0.0720511 0.0720511i −0.00287287 0.00287287i
\(630\) 0 0
\(631\) 12.4799i 0.496819i −0.968655 0.248409i \(-0.920092\pi\)
0.968655 0.248409i \(-0.0799078\pi\)
\(632\) 1.59499 + 1.39780i 0.0634452 + 0.0556016i
\(633\) 75.4049i 2.99708i
\(634\) 20.9512 + 11.4911i 0.832078 + 0.456370i
\(635\) −44.9394 44.9394i −1.78336 1.78336i
\(636\) 2.91737 1.85951i 0.115681 0.0737342i
\(637\) 0 0
\(638\) −0.159934 0.548476i −0.00633185 0.0217144i
\(639\) −16.0993 −0.636877
\(640\) −39.4129 15.2906i −1.55793 0.604414i
\(641\) −10.1980 −0.402797 −0.201398 0.979509i \(-0.564549\pi\)
−0.201398 + 0.979509i \(0.564549\pi\)
\(642\) −5.20557 17.8519i −0.205447 0.704559i
\(643\) 10.9741 10.9741i 0.432777 0.432777i −0.456795 0.889572i \(-0.651003\pi\)
0.889572 + 0.456795i \(0.151003\pi\)
\(644\) 0 0
\(645\) −49.7688 49.7688i −1.95964 1.95964i
\(646\) 6.86133 + 3.76324i 0.269955 + 0.148063i
\(647\) 6.58567i 0.258909i −0.991585 0.129455i \(-0.958677\pi\)
0.991585 0.129455i \(-0.0413227\pi\)
\(648\) 11.2680 + 9.87498i 0.442650 + 0.387926i
\(649\) 5.11866i 0.200925i
\(650\) −36.1637 + 65.9356i −1.41846 + 2.58621i
\(651\) 0 0
\(652\) −5.01214 + 22.6328i −0.196291 + 0.886367i
\(653\) 3.62950 3.62950i 0.142033 0.142033i −0.632515 0.774548i \(-0.717977\pi\)
0.774548 + 0.632515i \(0.217977\pi\)
\(654\) 24.4645 7.13379i 0.956639 0.278953i
\(655\) −74.0181 −2.89213
\(656\) 36.6691 + 17.0787i 1.43169 + 0.666811i
\(657\) −3.56464 −0.139070
\(658\) 0 0
\(659\) −5.78706 + 5.78706i −0.225432 + 0.225432i −0.810781 0.585349i \(-0.800957\pi\)
0.585349 + 0.810781i \(0.300957\pi\)
\(660\) −20.6276 4.56809i −0.802929 0.177813i
\(661\) 19.4549 + 19.4549i 0.756709 + 0.756709i 0.975722 0.219013i \(-0.0702838\pi\)
−0.219013 + 0.975722i \(0.570284\pi\)
\(662\) −20.2523 + 36.9250i −0.787127 + 1.43513i
\(663\) 25.3349i 0.983928i
\(664\) 18.0198 1.18728i 0.699306 0.0460754i
\(665\) 0 0
\(666\) 0.482231 + 0.264489i 0.0186861 + 0.0102488i
\(667\) −0.531882 0.531882i −0.0205946 0.0205946i
\(668\) 14.7779 + 23.1850i 0.571774 + 0.897053i
\(669\) −17.2506 + 17.2506i −0.666946 + 0.666946i
\(670\) 17.6248 + 60.4424i 0.680907 + 2.33509i
\(671\) 9.59206 0.370297
\(672\) 0 0
\(673\) −37.3667 −1.44038 −0.720190 0.693776i \(-0.755946\pi\)
−0.720190 + 0.693776i \(0.755946\pi\)
\(674\) −0.752683 2.58124i −0.0289923 0.0994258i
\(675\) 47.6330 47.6330i 1.83339 1.83339i
\(676\) 23.8682 + 37.4468i 0.918009 + 1.44026i
\(677\) 16.1658 + 16.1658i 0.621303 + 0.621303i 0.945865 0.324561i \(-0.105217\pi\)
−0.324561 + 0.945865i \(0.605217\pi\)
\(678\) 0.325377 + 0.178460i 0.0124960 + 0.00685370i
\(679\) 0 0
\(680\) 1.01363 + 15.3842i 0.0388708 + 0.589959i
\(681\) 32.5902i 1.24886i
\(682\) 0.764244 1.39341i 0.0292644 0.0533564i
\(683\) 13.2551 + 13.2551i 0.507192 + 0.507192i 0.913663 0.406472i \(-0.133241\pi\)
−0.406472 + 0.913663i \(0.633241\pi\)
\(684\) −41.2409 9.13302i −1.57689 0.349210i
\(685\) 2.41876 2.41876i 0.0924161 0.0924161i
\(686\) 0 0
\(687\) 37.1321 1.41668
\(688\) −24.1842 + 8.81482i −0.922012 + 0.336062i
\(689\) −3.50632 −0.133580
\(690\) −26.7040 + 7.78682i −1.01661 + 0.296439i
\(691\) 6.24472 6.24472i 0.237560 0.237560i −0.578279 0.815839i \(-0.696275\pi\)
0.815839 + 0.578279i \(0.196275\pi\)
\(692\) 3.41433 15.4177i 0.129794 0.586094i
\(693\) 0 0
\(694\) 19.5023 35.5577i 0.740298 1.34975i
\(695\) 14.5074i 0.550296i
\(696\) 2.28237 2.60434i 0.0865130 0.0987174i
\(697\) 14.7525i 0.558789i
\(698\) 9.62370 + 5.27831i 0.364262 + 0.199787i
\(699\) 46.6504 + 46.6504i 1.76448 + 1.76448i
\(700\) 0 0
\(701\) 28.1681 28.1681i 1.06389 1.06389i 0.0660783 0.997814i \(-0.478951\pi\)
0.997814 0.0660783i \(-0.0210487\pi\)
\(702\) −17.6551 60.5463i −0.666350 2.28517i
\(703\) −0.264955 −0.00999297
\(704\) −4.69949 + 6.13318i −0.177119 + 0.231153i
\(705\) −121.269 −4.56725
\(706\) −0.832519 2.85503i −0.0313322 0.107450i
\(707\) 0 0
\(708\) 26.1629 16.6760i 0.983263 0.626723i
\(709\) 10.8738 + 10.8738i 0.408376 + 0.408376i 0.881172 0.472796i \(-0.156755\pi\)
−0.472796 + 0.881172i \(0.656755\pi\)
\(710\) 13.3970 + 7.34783i 0.502779 + 0.275759i
\(711\) 4.17487i 0.156570i
\(712\) 28.8412 32.9098i 1.08087 1.23335i
\(713\) 2.09238i 0.0783601i
\(714\) 0 0
\(715\) 15.1411 + 15.1411i 0.566245 + 0.566245i
\(716\) −4.17404 + 18.8482i −0.155991 + 0.704391i
\(717\) 27.6680 27.6680i 1.03328 1.03328i
\(718\) 14.5416 4.24028i 0.542686 0.158246i
\(719\) 21.4416 0.799638 0.399819 0.916594i \(-0.369073\pi\)
0.399819 + 0.916594i \(0.369073\pi\)
\(720\) −28.4984 78.1877i −1.06207 2.91388i
\(721\) 0 0
\(722\) −6.26076 + 1.82562i −0.233001 + 0.0679425i
\(723\) 40.1413 40.1413i 1.49287 1.49287i
\(724\) −41.7717 9.25056i −1.55243 0.343795i
\(725\) −2.65075 2.65075i −0.0984465 0.0984465i
\(726\) 20.0402 36.5384i 0.743762 1.35607i
\(727\) 30.4747i 1.13024i −0.825007 0.565122i \(-0.808829\pi\)
0.825007 0.565122i \(-0.191171\pi\)
\(728\) 0 0
\(729\) 36.5081i 1.35215i
\(730\) 2.96630 + 1.62693i 0.109788 + 0.0602153i
\(731\) 6.63796 + 6.63796i 0.245514 + 0.245514i
\(732\) 31.2499 + 49.0278i 1.15503 + 1.81212i
\(733\) −32.8283 + 32.8283i −1.21254 + 1.21254i −0.242351 + 0.970189i \(0.577919\pi\)
−0.970189 + 0.242351i \(0.922081\pi\)
\(734\) −7.20091 24.6947i −0.265791 0.911499i
\(735\) 0 0
\(736\) −1.54179 + 10.0553i −0.0568312 + 0.370645i
\(737\) 11.5072 0.423873
\(738\) 22.2913 + 76.4455i 0.820554 + 2.81400i
\(739\) −15.4736 + 15.4736i −0.569207 + 0.569207i −0.931906 0.362699i \(-0.881855\pi\)
0.362699 + 0.931906i \(0.381855\pi\)
\(740\) −0.280572 0.440188i −0.0103140 0.0161816i
\(741\) 46.5824 + 46.5824i 1.71125 + 1.71125i
\(742\) 0 0
\(743\) 19.2071i 0.704639i −0.935880 0.352320i \(-0.885393\pi\)
0.935880 0.352320i \(-0.114607\pi\)
\(744\) 9.61194 0.633305i 0.352391 0.0232181i
\(745\) 31.5310i 1.15521i
\(746\) 0.664482 1.21152i 0.0243284 0.0443568i
\(747\) 25.1372 + 25.1372i 0.919723 + 0.919723i
\(748\) 2.75123 + 0.609275i 0.100595 + 0.0222773i
\(749\) 0 0
\(750\) −58.8385 + 17.1571i −2.14848 + 0.626490i
\(751\) −35.8573 −1.30845 −0.654225 0.756300i \(-0.727005\pi\)
−0.654225 + 0.756300i \(0.727005\pi\)
\(752\) −18.7248 + 40.2034i −0.682824 + 1.46607i
\(753\) 33.5297 1.22189
\(754\) −3.36937 + 0.982499i −0.122705 + 0.0357805i
\(755\) 13.4159 13.4159i 0.488253 0.488253i
\(756\) 0 0
\(757\) 22.1772 + 22.1772i 0.806045 + 0.806045i 0.984033 0.177988i \(-0.0569587\pi\)
−0.177988 + 0.984033i \(0.556959\pi\)
\(758\) −17.0085 + 31.0109i −0.617778 + 1.12636i
\(759\) 5.08399i 0.184537i
\(760\) 30.1501 + 26.4227i 1.09366 + 0.958452i
\(761\) 29.5689i 1.07187i 0.844258 + 0.535936i \(0.180041\pi\)
−0.844258 + 0.535936i \(0.819959\pi\)
\(762\) −61.7312 33.8577i −2.23628 1.22654i
\(763\) 0 0
\(764\) −33.5162 + 21.3629i −1.21257 + 0.772883i
\(765\) −21.4606 + 21.4606i −0.775911 + 0.775911i
\(766\) −4.45396 15.2744i −0.160928 0.551885i
\(767\) −31.4447 −1.13540
\(768\) −46.6589 4.03920i −1.68366 0.145752i
\(769\) −30.8038 −1.11081 −0.555406 0.831579i \(-0.687437\pi\)
−0.555406 + 0.831579i \(0.687437\pi\)
\(770\) 0 0
\(771\) 35.1492 35.1492i 1.26587 1.26587i
\(772\) 20.0410 12.7740i 0.721292 0.459745i
\(773\) 36.3527 + 36.3527i 1.30752 + 1.30752i 0.923203 + 0.384313i \(0.125562\pi\)
0.384313 + 0.923203i \(0.374438\pi\)
\(774\) −44.4273 24.3670i −1.59690 0.875855i
\(775\) 10.4278i 0.374578i
\(776\) 29.2398 + 25.6249i 1.04965 + 0.919881i
\(777\) 0 0
\(778\) −24.1715 + 44.0707i −0.866589 + 1.58001i
\(779\) −27.1248 27.1248i −0.971845 0.971845i
\(780\) −28.0625 + 126.718i −1.00480 + 4.53725i
\(781\) 1.97472 1.97472i 0.0706612 0.0706612i
\(782\) 3.56168 1.03858i 0.127365 0.0371394i
\(783\) 3.14386