Properties

Label 1638.2.bj.f.127.1
Level $1638$
Weight $2$
Character 1638.127
Analytic conductor $13.079$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.195105024.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 4 x^{5} - 20 x^{4} + 12 x^{3} + 45 x^{2} - 108 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 127.1
Root \(1.72124 - 0.193255i\) of defining polynomial
Character \(\chi\) \(=\) 1638.127
Dual form 1638.2.bj.f.1135.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.05596i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.05596i q^{5} +(0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(1.52798 + 2.64654i) q^{10} +(2.98127 - 1.72124i) q^{11} +(3.25253 - 1.55596i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.41449 - 2.44997i) q^{17} +(1.49425 + 0.862708i) q^{19} +(-2.64654 - 1.52798i) q^{20} +(-1.72124 + 2.98127i) q^{22} +(-1.53130 - 2.65229i) q^{23} -4.33891 q^{25} +(-2.03880 + 2.97377i) q^{26} +(0.866025 - 0.500000i) q^{28} +(1.92531 + 3.33473i) q^{29} +0.978370i q^{31} +(0.866025 + 0.500000i) q^{32} +2.82898i q^{34} +(1.52798 - 2.64654i) q^{35} +(4.58394 - 2.64654i) q^{37} -1.72542 q^{38} +3.05596 q^{40} +(-8.62781 + 4.98127i) q^{41} +(-1.51082 + 2.61681i) q^{43} -3.44247i q^{44} +(2.65229 + 1.53130i) q^{46} +8.04447i q^{47} +(0.500000 + 0.866025i) q^{49} +(3.75760 - 2.16945i) q^{50} +(0.278764 - 3.59476i) q^{52} +8.33405 q^{53} +(-5.26003 - 9.11064i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-3.33473 - 1.92531i) q^{58} +(-8.64080 - 4.98877i) q^{59} +(5.77260 - 9.99843i) q^{61} +(-0.489185 - 0.847293i) q^{62} -1.00000 q^{64} +(-4.75496 - 9.93962i) q^{65} +(4.11410 - 2.37527i) q^{67} +(-1.41449 - 2.44997i) q^{68} +3.05596i q^{70} +(3.17784 + 1.83473i) q^{71} -10.1119i q^{73} +(-2.64654 + 4.58394i) q^{74} +(1.49425 - 0.862708i) q^{76} +3.44247 q^{77} -4.49843 q^{79} +(-2.64654 + 1.52798i) q^{80} +(4.98127 - 8.62781i) q^{82} +7.15869i q^{83} +(-7.48701 - 4.32263i) q^{85} -3.02163i q^{86} +(1.72124 + 2.98127i) q^{88} +(6.84426 - 3.95154i) q^{89} +(3.59476 + 0.278764i) q^{91} -3.06260 q^{92} +(-4.02224 - 6.96672i) q^{94} +(2.63640 - 4.56638i) q^{95} +(-7.88016 - 4.54961i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + O(q^{10}) \) \( 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 3.05596i 1.36667i −0.730106 0.683334i \(-0.760529\pi\)
0.730106 0.683334i \(-0.239471\pi\)
\(6\) 0 0
\(7\) 0.866025 + 0.500000i 0.327327 + 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.52798 + 2.64654i 0.483190 + 0.836910i
\(11\) 2.98127 1.72124i 0.898886 0.518972i 0.0220475 0.999757i \(-0.492982\pi\)
0.876839 + 0.480785i \(0.159648\pi\)
\(12\) 0 0
\(13\) 3.25253 1.55596i 0.902091 0.431546i
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.41449 2.44997i 0.343064 0.594205i −0.641936 0.766758i \(-0.721868\pi\)
0.985000 + 0.172554i \(0.0552018\pi\)
\(18\) 0 0
\(19\) 1.49425 + 0.862708i 0.342805 + 0.197919i 0.661512 0.749935i \(-0.269915\pi\)
−0.318707 + 0.947853i \(0.603248\pi\)
\(20\) −2.64654 1.52798i −0.591785 0.341667i
\(21\) 0 0
\(22\) −1.72124 + 2.98127i −0.366969 + 0.635608i
\(23\) −1.53130 2.65229i −0.319298 0.553040i 0.661044 0.750347i \(-0.270114\pi\)
−0.980342 + 0.197307i \(0.936780\pi\)
\(24\) 0 0
\(25\) −4.33891 −0.867781
\(26\) −2.03880 + 2.97377i −0.399841 + 0.583204i
\(27\) 0 0
\(28\) 0.866025 0.500000i 0.163663 0.0944911i
\(29\) 1.92531 + 3.33473i 0.357520 + 0.619243i 0.987546 0.157331i \(-0.0502890\pi\)
−0.630026 + 0.776574i \(0.716956\pi\)
\(30\) 0 0
\(31\) 0.978370i 0.175720i 0.996133 + 0.0878602i \(0.0280029\pi\)
−0.996133 + 0.0878602i \(0.971997\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 2.82898i 0.485166i
\(35\) 1.52798 2.64654i 0.258276 0.447347i
\(36\) 0 0
\(37\) 4.58394 2.64654i 0.753596 0.435089i −0.0733959 0.997303i \(-0.523384\pi\)
0.826992 + 0.562214i \(0.190050\pi\)
\(38\) −1.72542 −0.279899
\(39\) 0 0
\(40\) 3.05596 0.483190
\(41\) −8.62781 + 4.98127i −1.34744 + 0.777943i −0.987886 0.155182i \(-0.950404\pi\)
−0.359551 + 0.933125i \(0.617070\pi\)
\(42\) 0 0
\(43\) −1.51082 + 2.61681i −0.230397 + 0.399060i −0.957925 0.287019i \(-0.907336\pi\)
0.727528 + 0.686078i \(0.240669\pi\)
\(44\) 3.44247i 0.518972i
\(45\) 0 0
\(46\) 2.65229 + 1.53130i 0.391058 + 0.225778i
\(47\) 8.04447i 1.17341i 0.809802 + 0.586703i \(0.199575\pi\)
−0.809802 + 0.586703i \(0.800425\pi\)
\(48\) 0 0
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) 3.75760 2.16945i 0.531405 0.306807i
\(51\) 0 0
\(52\) 0.278764 3.59476i 0.0386576 0.498503i
\(53\) 8.33405 1.14477 0.572385 0.819985i \(-0.306018\pi\)
0.572385 + 0.819985i \(0.306018\pi\)
\(54\) 0 0
\(55\) −5.26003 9.11064i −0.709263 1.22848i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 0 0
\(58\) −3.33473 1.92531i −0.437871 0.252805i
\(59\) −8.64080 4.98877i −1.12494 0.649482i −0.182279 0.983247i \(-0.558348\pi\)
−0.942656 + 0.333765i \(0.891681\pi\)
\(60\) 0 0
\(61\) 5.77260 9.99843i 0.739106 1.28017i −0.213793 0.976879i \(-0.568582\pi\)
0.952899 0.303289i \(-0.0980849\pi\)
\(62\) −0.489185 0.847293i −0.0621266 0.107606i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −4.75496 9.93962i −0.589781 1.23286i
\(66\) 0 0
\(67\) 4.11410 2.37527i 0.502617 0.290186i −0.227177 0.973854i \(-0.572950\pi\)
0.729794 + 0.683668i \(0.239616\pi\)
\(68\) −1.41449 2.44997i −0.171532 0.297102i
\(69\) 0 0
\(70\) 3.05596i 0.365257i
\(71\) 3.17784 + 1.83473i 0.377140 + 0.217742i 0.676573 0.736375i \(-0.263464\pi\)
−0.299433 + 0.954117i \(0.596798\pi\)
\(72\) 0 0
\(73\) 10.1119i 1.18351i −0.806117 0.591756i \(-0.798435\pi\)
0.806117 0.591756i \(-0.201565\pi\)
\(74\) −2.64654 + 4.58394i −0.307654 + 0.532873i
\(75\) 0 0
\(76\) 1.49425 0.862708i 0.171403 0.0989594i
\(77\) 3.44247 0.392306
\(78\) 0 0
\(79\) −4.49843 −0.506113 −0.253057 0.967451i \(-0.581436\pi\)
−0.253057 + 0.967451i \(0.581436\pi\)
\(80\) −2.64654 + 1.52798i −0.295892 + 0.170833i
\(81\) 0 0
\(82\) 4.98127 8.62781i 0.550089 0.952782i
\(83\) 7.15869i 0.785768i 0.919588 + 0.392884i \(0.128523\pi\)
−0.919588 + 0.392884i \(0.871477\pi\)
\(84\) 0 0
\(85\) −7.48701 4.32263i −0.812081 0.468855i
\(86\) 3.02163i 0.325831i
\(87\) 0 0
\(88\) 1.72124 + 2.98127i 0.183484 + 0.317804i
\(89\) 6.84426 3.95154i 0.725490 0.418862i −0.0912800 0.995825i \(-0.529096\pi\)
0.816770 + 0.576963i \(0.195762\pi\)
\(90\) 0 0
\(91\) 3.59476 + 0.278764i 0.376833 + 0.0292224i
\(92\) −3.06260 −0.319298
\(93\) 0 0
\(94\) −4.02224 6.96672i −0.414862 0.718562i
\(95\) 2.63640 4.56638i 0.270489 0.468501i
\(96\) 0 0
\(97\) −7.88016 4.54961i −0.800109 0.461943i 0.0434004 0.999058i \(-0.486181\pi\)
−0.843509 + 0.537115i \(0.819514\pi\)
\(98\) −0.866025 0.500000i −0.0874818 0.0505076i
\(99\) 0 0
\(100\) −2.16945 + 3.75760i −0.216945 + 0.375760i
\(101\) −9.42664 16.3274i −0.937985 1.62464i −0.769222 0.638982i \(-0.779356\pi\)
−0.168764 0.985657i \(-0.553977\pi\)
\(102\) 0 0
\(103\) −13.7079 −1.35068 −0.675338 0.737509i \(-0.736002\pi\)
−0.675338 + 0.737509i \(0.736002\pi\)
\(104\) 1.55596 + 3.25253i 0.152575 + 0.318937i
\(105\) 0 0
\(106\) −7.21750 + 4.16702i −0.701025 + 0.404737i
\(107\) −1.65736 2.87063i −0.160223 0.277514i 0.774726 0.632297i \(-0.217888\pi\)
−0.934948 + 0.354784i \(0.884555\pi\)
\(108\) 0 0
\(109\) 8.67525i 0.830938i −0.909607 0.415469i \(-0.863617\pi\)
0.909607 0.415469i \(-0.136383\pi\)
\(110\) 9.11064 + 5.26003i 0.868666 + 0.501524i
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) −5.60557 + 9.70914i −0.527328 + 0.913359i 0.472165 + 0.881510i \(0.343473\pi\)
−0.999493 + 0.0318486i \(0.989861\pi\)
\(114\) 0 0
\(115\) −8.10529 + 4.67959i −0.755822 + 0.436374i
\(116\) 3.85061 0.357520
\(117\) 0 0
\(118\) 9.97753 0.918506
\(119\) 2.44997 1.41449i 0.224588 0.129666i
\(120\) 0 0
\(121\) 0.425305 0.736650i 0.0386641 0.0669682i
\(122\) 11.5452i 1.04525i
\(123\) 0 0
\(124\) 0.847293 + 0.489185i 0.0760892 + 0.0439301i
\(125\) 2.02028i 0.180699i
\(126\) 0 0
\(127\) 2.55753 + 4.42977i 0.226944 + 0.393078i 0.956901 0.290415i \(-0.0937932\pi\)
−0.729957 + 0.683493i \(0.760460\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 9.08773 + 6.23048i 0.797047 + 0.546450i
\(131\) 18.7757 1.64044 0.820219 0.572049i \(-0.193851\pi\)
0.820219 + 0.572049i \(0.193851\pi\)
\(132\) 0 0
\(133\) 0.862708 + 1.49425i 0.0748063 + 0.129568i
\(134\) −2.37527 + 4.11410i −0.205192 + 0.355404i
\(135\) 0 0
\(136\) 2.44997 + 1.41449i 0.210083 + 0.121292i
\(137\) −2.30457 1.33055i −0.196893 0.113676i 0.398312 0.917250i \(-0.369596\pi\)
−0.595205 + 0.803574i \(0.702929\pi\)
\(138\) 0 0
\(139\) 8.35322 14.4682i 0.708511 1.22718i −0.256898 0.966439i \(-0.582700\pi\)
0.965409 0.260739i \(-0.0839662\pi\)
\(140\) −1.52798 2.64654i −0.129138 0.223674i
\(141\) 0 0
\(142\) −3.66945 −0.307934
\(143\) 7.01850 10.2371i 0.586916 0.856071i
\(144\) 0 0
\(145\) 10.1908 5.88366i 0.846300 0.488611i
\(146\) 5.05596 + 8.75718i 0.418434 + 0.724750i
\(147\) 0 0
\(148\) 5.29308i 0.435089i
\(149\) −2.16642 1.25078i −0.177480 0.102468i 0.408628 0.912701i \(-0.366007\pi\)
−0.586108 + 0.810233i \(0.699341\pi\)
\(150\) 0 0
\(151\) 12.6465i 1.02916i 0.857444 + 0.514578i \(0.172051\pi\)
−0.857444 + 0.514578i \(0.827949\pi\)
\(152\) −0.862708 + 1.49425i −0.0699749 + 0.121200i
\(153\) 0 0
\(154\) −2.98127 + 1.72124i −0.240237 + 0.138701i
\(155\) 2.98986 0.240151
\(156\) 0 0
\(157\) 17.8131 1.42164 0.710822 0.703372i \(-0.248323\pi\)
0.710822 + 0.703372i \(0.248323\pi\)
\(158\) 3.89576 2.24922i 0.309930 0.178938i
\(159\) 0 0
\(160\) 1.52798 2.64654i 0.120798 0.209227i
\(161\) 3.06260i 0.241366i
\(162\) 0 0
\(163\) −7.68884 4.43915i −0.602236 0.347701i 0.167684 0.985841i \(-0.446371\pi\)
−0.769921 + 0.638139i \(0.779704\pi\)
\(164\) 9.96254i 0.777943i
\(165\) 0 0
\(166\) −3.57934 6.19961i −0.277811 0.481183i
\(167\) 8.46097 4.88494i 0.654730 0.378008i −0.135536 0.990772i \(-0.543276\pi\)
0.790266 + 0.612764i \(0.209942\pi\)
\(168\) 0 0
\(169\) 8.15796 10.1216i 0.627535 0.778588i
\(170\) 8.64526 0.663061
\(171\) 0 0
\(172\) 1.51082 + 2.61681i 0.115199 + 0.199530i
\(173\) −4.33762 + 7.51299i −0.329783 + 0.571202i −0.982469 0.186427i \(-0.940309\pi\)
0.652685 + 0.757629i \(0.273642\pi\)
\(174\) 0 0
\(175\) −3.75760 2.16945i −0.284048 0.163995i
\(176\) −2.98127 1.72124i −0.224722 0.129743i
\(177\) 0 0
\(178\) −3.95154 + 6.84426i −0.296180 + 0.512999i
\(179\) 11.7139 + 20.2891i 0.875540 + 1.51648i 0.856187 + 0.516667i \(0.172827\pi\)
0.0193531 + 0.999813i \(0.493839\pi\)
\(180\) 0 0
\(181\) 7.66632 0.569833 0.284917 0.958552i \(-0.408034\pi\)
0.284917 + 0.958552i \(0.408034\pi\)
\(182\) −3.25253 + 1.55596i −0.241094 + 0.115336i
\(183\) 0 0
\(184\) 2.65229 1.53130i 0.195529 0.112889i
\(185\) −8.08773 14.0084i −0.594622 1.02992i
\(186\) 0 0
\(187\) 9.73869i 0.712163i
\(188\) 6.96672 + 4.02224i 0.508100 + 0.293352i
\(189\) 0 0
\(190\) 5.27281i 0.382530i
\(191\) 12.7472 22.0789i 0.922357 1.59757i 0.126600 0.991954i \(-0.459593\pi\)
0.795757 0.605616i \(-0.207073\pi\)
\(192\) 0 0
\(193\) −7.38361 + 4.26293i −0.531484 + 0.306852i −0.741621 0.670820i \(-0.765942\pi\)
0.210137 + 0.977672i \(0.432609\pi\)
\(194\) 9.09922 0.653286
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −20.5094 + 11.8411i −1.46124 + 0.843645i −0.999069 0.0431470i \(-0.986262\pi\)
−0.462168 + 0.886792i \(0.652928\pi\)
\(198\) 0 0
\(199\) −12.4233 + 21.5178i −0.880666 + 1.52536i −0.0300637 + 0.999548i \(0.509571\pi\)
−0.850602 + 0.525810i \(0.823762\pi\)
\(200\) 4.33891i 0.306807i
\(201\) 0 0
\(202\) 16.3274 + 9.42664i 1.14879 + 0.663256i
\(203\) 3.85061i 0.270260i
\(204\) 0 0
\(205\) 15.2226 + 26.3663i 1.06319 + 1.84150i
\(206\) 11.8714 6.85393i 0.827116 0.477536i
\(207\) 0 0
\(208\) −2.97377 2.03880i −0.206194 0.141365i
\(209\) 5.93970 0.410857
\(210\) 0 0
\(211\) −0.386509 0.669453i −0.0266084 0.0460871i 0.852415 0.522867i \(-0.175137\pi\)
−0.879023 + 0.476779i \(0.841804\pi\)
\(212\) 4.16702 7.21750i 0.286192 0.495700i
\(213\) 0 0
\(214\) 2.87063 + 1.65736i 0.196232 + 0.113295i
\(215\) 7.99687 + 4.61699i 0.545382 + 0.314876i
\(216\) 0 0
\(217\) −0.489185 + 0.847293i −0.0332080 + 0.0575180i
\(218\) 4.33762 + 7.51299i 0.293781 + 0.508844i
\(219\) 0 0
\(220\) −10.5201 −0.709263
\(221\) 0.788619 10.1695i 0.0530482 0.684075i
\(222\) 0 0
\(223\) −18.6502 + 10.7677i −1.24891 + 0.721060i −0.970892 0.239516i \(-0.923011\pi\)
−0.278019 + 0.960575i \(0.589678\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) 11.2111i 0.745754i
\(227\) −15.1939 8.77218i −1.00845 0.582230i −0.0977139 0.995215i \(-0.531153\pi\)
−0.910738 + 0.412985i \(0.864486\pi\)
\(228\) 0 0
\(229\) 10.3222i 0.682109i −0.940043 0.341055i \(-0.889216\pi\)
0.940043 0.341055i \(-0.110784\pi\)
\(230\) 4.67959 8.10529i 0.308563 0.534447i
\(231\) 0 0
\(232\) −3.33473 + 1.92531i −0.218936 + 0.126402i
\(233\) 17.8290 1.16802 0.584008 0.811748i \(-0.301484\pi\)
0.584008 + 0.811748i \(0.301484\pi\)
\(234\) 0 0
\(235\) 24.5836 1.60366
\(236\) −8.64080 + 4.98877i −0.562468 + 0.324741i
\(237\) 0 0
\(238\) −1.41449 + 2.44997i −0.0916878 + 0.158808i
\(239\) 5.71271i 0.369525i 0.982783 + 0.184762i \(0.0591515\pi\)
−0.982783 + 0.184762i \(0.940848\pi\)
\(240\) 0 0
\(241\) 0.868738 + 0.501566i 0.0559603 + 0.0323087i 0.527719 0.849419i \(-0.323047\pi\)
−0.471759 + 0.881728i \(0.656381\pi\)
\(242\) 0.850611i 0.0546793i
\(243\) 0 0
\(244\) −5.77260 9.99843i −0.369553 0.640084i
\(245\) 2.64654 1.52798i 0.169081 0.0976191i
\(246\) 0 0
\(247\) 6.20245 + 0.480984i 0.394653 + 0.0306043i
\(248\) −0.978370 −0.0621266
\(249\) 0 0
\(250\) 1.01014 + 1.74961i 0.0638867 + 0.110655i
\(251\) 0.336293 0.582476i 0.0212266 0.0367656i −0.855217 0.518270i \(-0.826576\pi\)
0.876444 + 0.481505i \(0.159910\pi\)
\(252\) 0 0
\(253\) −9.13042 5.27145i −0.574025 0.331413i
\(254\) −4.42977 2.55753i −0.277948 0.160474i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −12.1717 21.0820i −0.759248 1.31506i −0.943234 0.332128i \(-0.892234\pi\)
0.183986 0.982929i \(-0.441100\pi\)
\(258\) 0 0
\(259\) 5.29308 0.328896
\(260\) −10.9854 0.851893i −0.681289 0.0528322i
\(261\) 0 0
\(262\) −16.2602 + 9.38784i −1.00456 + 0.579983i
\(263\) −8.54648 14.8029i −0.526999 0.912788i −0.999505 0.0314610i \(-0.989984\pi\)
0.472506 0.881327i \(-0.343349\pi\)
\(264\) 0 0
\(265\) 25.4685i 1.56452i
\(266\) −1.49425 0.862708i −0.0916186 0.0528960i
\(267\) 0 0
\(268\) 4.75055i 0.290186i
\(269\) −13.3297 + 23.0877i −0.812727 + 1.40768i 0.0982223 + 0.995165i \(0.468684\pi\)
−0.910949 + 0.412519i \(0.864649\pi\)
\(270\) 0 0
\(271\) 21.1739 12.2247i 1.28622 0.742600i 0.308243 0.951308i \(-0.400259\pi\)
0.977978 + 0.208708i \(0.0669257\pi\)
\(272\) −2.82898 −0.171532
\(273\) 0 0
\(274\) 2.66109 0.160763
\(275\) −12.9354 + 7.46828i −0.780037 + 0.450354i
\(276\) 0 0
\(277\) −14.2406 + 24.6655i −0.855636 + 1.48201i 0.0204175 + 0.999792i \(0.493500\pi\)
−0.876054 + 0.482214i \(0.839833\pi\)
\(278\) 16.7064i 1.00199i
\(279\) 0 0
\(280\) 2.64654 + 1.52798i 0.158161 + 0.0913143i
\(281\) 9.76032i 0.582252i 0.956685 + 0.291126i \(0.0940298\pi\)
−0.956685 + 0.291126i \(0.905970\pi\)
\(282\) 0 0
\(283\) 5.83562 + 10.1076i 0.346891 + 0.600833i 0.985696 0.168536i \(-0.0539039\pi\)
−0.638804 + 0.769369i \(0.720571\pi\)
\(284\) 3.17784 1.83473i 0.188570 0.108871i
\(285\) 0 0
\(286\) −0.959638 + 12.3749i −0.0567446 + 0.731741i
\(287\) −9.96254 −0.588070
\(288\) 0 0
\(289\) 4.49843 + 7.79152i 0.264614 + 0.458324i
\(290\) −5.88366 + 10.1908i −0.345500 + 0.598424i
\(291\) 0 0
\(292\) −8.75718 5.05596i −0.512475 0.295878i
\(293\) −18.8968 10.9101i −1.10396 0.637373i −0.166704 0.986007i \(-0.553312\pi\)
−0.937259 + 0.348634i \(0.886646\pi\)
\(294\) 0 0
\(295\) −15.2455 + 26.4059i −0.887626 + 1.53741i
\(296\) 2.64654 + 4.58394i 0.153827 + 0.266436i
\(297\) 0 0
\(298\) 2.50157 0.144912
\(299\) −9.10746 6.24401i −0.526698 0.361101i
\(300\) 0 0
\(301\) −2.61681 + 1.51082i −0.150830 + 0.0870819i
\(302\) −6.32323 10.9522i −0.363861 0.630226i
\(303\) 0 0
\(304\) 1.72542i 0.0989594i
\(305\) −30.5548 17.6408i −1.74957 1.01011i
\(306\) 0 0
\(307\) 4.87046i 0.277972i 0.990294 + 0.138986i \(0.0443843\pi\)
−0.990294 + 0.138986i \(0.955616\pi\)
\(308\) 1.72124 2.98127i 0.0980765 0.169874i
\(309\) 0 0
\(310\) −2.58930 + 1.49493i −0.147062 + 0.0849064i
\(311\) 3.90344 0.221344 0.110672 0.993857i \(-0.464700\pi\)
0.110672 + 0.993857i \(0.464700\pi\)
\(312\) 0 0
\(313\) 26.0528 1.47259 0.736297 0.676659i \(-0.236573\pi\)
0.736297 + 0.676659i \(0.236573\pi\)
\(314\) −15.4266 + 8.90657i −0.870576 + 0.502627i
\(315\) 0 0
\(316\) −2.24922 + 3.89576i −0.126528 + 0.219154i
\(317\) 11.1107i 0.624040i 0.950076 + 0.312020i \(0.101006\pi\)
−0.950076 + 0.312020i \(0.898994\pi\)
\(318\) 0 0
\(319\) 11.4797 + 6.62781i 0.642740 + 0.371086i
\(320\) 3.05596i 0.170833i
\(321\) 0 0
\(322\) 1.53130 + 2.65229i 0.0853359 + 0.147806i
\(323\) 4.22722 2.44058i 0.235209 0.135798i
\(324\) 0 0
\(325\) −14.1124 + 6.75118i −0.782818 + 0.374488i
\(326\) 8.87831 0.491724
\(327\) 0 0
\(328\) −4.98127 8.62781i −0.275045 0.476391i
\(329\) −4.02224 + 6.96672i −0.221753 + 0.384087i
\(330\) 0 0
\(331\) 12.6854 + 7.32391i 0.697252 + 0.402559i 0.806323 0.591475i \(-0.201454\pi\)
−0.109071 + 0.994034i \(0.534788\pi\)
\(332\) 6.19961 + 3.57934i 0.340248 + 0.196442i
\(333\) 0 0
\(334\) −4.88494 + 8.46097i −0.267292 + 0.462964i
\(335\) −7.25875 12.5725i −0.396588 0.686910i
\(336\) 0 0
\(337\) −27.5456 −1.50050 −0.750251 0.661153i \(-0.770068\pi\)
−0.750251 + 0.661153i \(0.770068\pi\)
\(338\) −2.00418 + 12.8446i −0.109013 + 0.698653i
\(339\) 0 0
\(340\) −7.48701 + 4.32263i −0.406040 + 0.234427i
\(341\) 1.68401 + 2.91678i 0.0911940 + 0.157953i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −2.61681 1.51082i −0.141089 0.0814577i
\(345\) 0 0
\(346\) 8.67525i 0.466384i
\(347\) 2.62073 4.53924i 0.140688 0.243679i −0.787068 0.616867i \(-0.788402\pi\)
0.927756 + 0.373187i \(0.121735\pi\)
\(348\) 0 0
\(349\) −4.52901 + 2.61482i −0.242432 + 0.139968i −0.616294 0.787516i \(-0.711367\pi\)
0.373862 + 0.927484i \(0.378033\pi\)
\(350\) 4.33891 0.231924
\(351\) 0 0
\(352\) 3.44247 0.183484
\(353\) −3.26227 + 1.88348i −0.173633 + 0.100247i −0.584298 0.811539i \(-0.698630\pi\)
0.410665 + 0.911786i \(0.365297\pi\)
\(354\) 0 0
\(355\) 5.60686 9.71136i 0.297581 0.515425i
\(356\) 7.90307i 0.418862i
\(357\) 0 0
\(358\) −20.2891 11.7139i −1.07231 0.619100i
\(359\) 20.6003i 1.08724i 0.839330 + 0.543622i \(0.182947\pi\)
−0.839330 + 0.543622i \(0.817053\pi\)
\(360\) 0 0
\(361\) −8.01147 13.8763i −0.421656 0.730330i
\(362\) −6.63923 + 3.83316i −0.348950 + 0.201466i
\(363\) 0 0
\(364\) 2.03880 2.97377i 0.106862 0.155868i
\(365\) −30.9017 −1.61747
\(366\) 0 0
\(367\) 13.9579 + 24.1759i 0.728598 + 1.26197i 0.957476 + 0.288514i \(0.0931612\pi\)
−0.228877 + 0.973455i \(0.573505\pi\)
\(368\) −1.53130 + 2.65229i −0.0798245 + 0.138260i
\(369\) 0 0
\(370\) 14.0084 + 8.08773i 0.728260 + 0.420461i
\(371\) 7.21750 + 4.16702i 0.374714 + 0.216341i
\(372\) 0 0
\(373\) −15.7091 + 27.2090i −0.813388 + 1.40883i 0.0970910 + 0.995276i \(0.469046\pi\)
−0.910479 + 0.413554i \(0.864287\pi\)
\(374\) 4.86934 + 8.43395i 0.251788 + 0.436109i
\(375\) 0 0
\(376\) −8.04447 −0.414862
\(377\) 11.4508 + 7.85061i 0.589748 + 0.404327i
\(378\) 0 0
\(379\) −27.5747 + 15.9203i −1.41642 + 0.817770i −0.995982 0.0895514i \(-0.971457\pi\)
−0.420437 + 0.907322i \(0.638123\pi\)
\(380\) −2.63640 4.56638i −0.135245 0.234251i
\(381\) 0 0
\(382\) 25.4945i 1.30441i
\(383\) 4.08962 + 2.36114i 0.208970 + 0.120649i 0.600832 0.799375i \(-0.294836\pi\)
−0.391863 + 0.920024i \(0.628169\pi\)
\(384\) 0 0
\(385\) 10.5201i 0.536152i
\(386\) 4.26293 7.38361i 0.216977 0.375816i
\(387\) 0 0
\(388\) −7.88016 + 4.54961i −0.400054 + 0.230972i
\(389\) 30.5902 1.55099 0.775493 0.631356i \(-0.217501\pi\)
0.775493 + 0.631356i \(0.217501\pi\)
\(390\) 0 0
\(391\) −8.66403 −0.438159
\(392\) −0.866025 + 0.500000i −0.0437409 + 0.0252538i
\(393\) 0 0
\(394\) 11.8411 20.5094i 0.596547 1.03325i
\(395\) 13.7470i 0.691689i
\(396\) 0 0
\(397\) 10.1133 + 5.83891i 0.507571 + 0.293046i 0.731835 0.681482i \(-0.238664\pi\)
−0.224264 + 0.974529i \(0.571998\pi\)
\(398\) 24.8466i 1.24545i
\(399\) 0 0
\(400\) 2.16945 + 3.75760i 0.108473 + 0.187880i
\(401\) −8.01677 + 4.62849i −0.400339 + 0.231136i −0.686630 0.727007i \(-0.740911\pi\)
0.286292 + 0.958143i \(0.407577\pi\)
\(402\) 0 0
\(403\) 1.52231 + 3.18218i 0.0758315 + 0.158516i
\(404\) −18.8533 −0.937985
\(405\) 0 0
\(406\) −1.92531 3.33473i −0.0955513 0.165500i
\(407\) 9.11064 15.7801i 0.451598 0.782190i
\(408\) 0 0
\(409\) −22.1693 12.7994i −1.09620 0.632891i −0.160980 0.986958i \(-0.551465\pi\)
−0.935220 + 0.354066i \(0.884799\pi\)
\(410\) −26.3663 15.2226i −1.30214 0.751789i
\(411\) 0 0
\(412\) −6.85393 + 11.8714i −0.337669 + 0.584860i
\(413\) −4.98877 8.64080i −0.245481 0.425186i
\(414\) 0 0
\(415\) 21.8767 1.07388
\(416\) 3.59476 + 0.278764i 0.176248 + 0.0136675i
\(417\) 0 0
\(418\) −5.14393 + 2.96985i −0.251598 + 0.145260i
\(419\) 14.1018 + 24.4251i 0.688920 + 1.19324i 0.972188 + 0.234203i \(0.0752481\pi\)
−0.283268 + 0.959041i \(0.591419\pi\)
\(420\) 0 0
\(421\) 5.07012i 0.247102i −0.992338 0.123551i \(-0.960572\pi\)
0.992338 0.123551i \(-0.0394283\pi\)
\(422\) 0.669453 + 0.386509i 0.0325885 + 0.0188150i
\(423\) 0 0
\(424\) 8.33405i 0.404737i
\(425\) −6.13734 + 10.6302i −0.297705 + 0.515640i
\(426\) 0 0
\(427\) 9.99843 5.77260i 0.483858 0.279356i
\(428\) −3.31471 −0.160223
\(429\) 0 0
\(430\) −9.23399 −0.445302
\(431\) 13.9808 8.07185i 0.673434 0.388807i −0.123943 0.992289i \(-0.539554\pi\)
0.797376 + 0.603482i \(0.206221\pi\)
\(432\) 0 0
\(433\) −11.3014 + 19.5747i −0.543113 + 0.940699i 0.455610 + 0.890179i \(0.349421\pi\)
−0.998723 + 0.0505195i \(0.983912\pi\)
\(434\) 0.978370i 0.0469633i
\(435\) 0 0
\(436\) −7.51299 4.33762i −0.359807 0.207735i
\(437\) 5.28425i 0.252780i
\(438\) 0 0
\(439\) 14.1486 + 24.5060i 0.675273 + 1.16961i 0.976389 + 0.216020i \(0.0693077\pi\)
−0.301115 + 0.953588i \(0.597359\pi\)
\(440\) 9.11064 5.26003i 0.434333 0.250762i
\(441\) 0 0
\(442\) 4.40179 + 9.20136i 0.209372 + 0.437664i
\(443\) 1.38096 0.0656112 0.0328056 0.999462i \(-0.489556\pi\)
0.0328056 + 0.999462i \(0.489556\pi\)
\(444\) 0 0
\(445\) −12.0757 20.9158i −0.572445 0.991504i
\(446\) 10.7677 18.6502i 0.509866 0.883114i
\(447\) 0 0
\(448\) −0.866025 0.500000i −0.0409159 0.0236228i
\(449\) 32.0480 + 18.5029i 1.51244 + 0.873208i 0.999894 + 0.0145487i \(0.00463115\pi\)
0.512547 + 0.858659i \(0.328702\pi\)
\(450\) 0 0
\(451\) −17.1479 + 29.7010i −0.807462 + 1.39856i
\(452\) 5.60557 + 9.70914i 0.263664 + 0.456679i
\(453\) 0 0
\(454\) 17.5444 0.823398
\(455\) 0.851893 10.9854i 0.0399374 0.515006i
\(456\) 0 0
\(457\) 12.0530 6.95878i 0.563813 0.325518i −0.190861 0.981617i \(-0.561128\pi\)
0.754675 + 0.656099i \(0.227795\pi\)
\(458\) 5.16109 + 8.93928i 0.241162 + 0.417705i
\(459\) 0 0
\(460\) 9.35918i 0.436374i
\(461\) −4.19845 2.42397i −0.195541 0.112896i 0.399033 0.916937i \(-0.369346\pi\)
−0.594574 + 0.804041i \(0.702679\pi\)
\(462\) 0 0
\(463\) 24.4377i 1.13571i −0.823127 0.567857i \(-0.807773\pi\)
0.823127 0.567857i \(-0.192227\pi\)
\(464\) 1.92531 3.33473i 0.0893801 0.154811i
\(465\) 0 0
\(466\) −15.4404 + 8.91449i −0.715260 + 0.412956i
\(467\) 36.0027 1.66600 0.833002 0.553270i \(-0.186620\pi\)
0.833002 + 0.553270i \(0.186620\pi\)
\(468\) 0 0
\(469\) 4.75055 0.219360
\(470\) −21.2900 + 12.2918i −0.982035 + 0.566978i
\(471\) 0 0
\(472\) 4.98877 8.64080i 0.229627 0.397725i
\(473\) 10.4019i 0.478279i
\(474\) 0 0
\(475\) −6.48343 3.74321i −0.297480 0.171750i
\(476\) 2.82898i 0.129666i
\(477\) 0 0
\(478\) −2.85636 4.94735i −0.130647 0.226287i
\(479\) 8.22108 4.74644i 0.375631 0.216870i −0.300285 0.953850i \(-0.597082\pi\)
0.675915 + 0.736979i \(0.263748\pi\)
\(480\) 0 0
\(481\) 10.7915 15.7404i 0.492051 0.717701i
\(482\) −1.00313 −0.0456914
\(483\) 0 0
\(484\) −0.425305 0.736650i −0.0193321 0.0334841i
\(485\) −13.9034 + 24.0815i −0.631323 + 1.09348i
\(486\) 0 0
\(487\) −35.4383 20.4603i −1.60586 0.927144i −0.990283 0.139069i \(-0.955589\pi\)
−0.615578 0.788076i \(-0.711078\pi\)
\(488\) 9.99843 + 5.77260i 0.452608 + 0.261313i
\(489\) 0 0
\(490\) −1.52798 + 2.64654i −0.0690272 + 0.119559i
\(491\) 2.55753 + 4.42977i 0.115420 + 0.199913i 0.917947 0.396702i \(-0.129845\pi\)
−0.802528 + 0.596615i \(0.796512\pi\)
\(492\) 0 0
\(493\) 10.8933 0.490610
\(494\) −5.61197 + 2.68468i −0.252495 + 0.120790i
\(495\) 0 0
\(496\) 0.847293 0.489185i 0.0380446 0.0219651i
\(497\) 1.83473 + 3.17784i 0.0822987 + 0.142546i
\(498\) 0 0
\(499\) 19.5827i 0.876640i −0.898819 0.438320i \(-0.855574\pi\)
0.898819 0.438320i \(-0.144426\pi\)
\(500\) −1.74961 1.01014i −0.0782450 0.0451747i
\(501\) 0 0
\(502\) 0.672585i 0.0300189i
\(503\) −14.5429 + 25.1890i −0.648436 + 1.12312i 0.335060 + 0.942197i \(0.391243\pi\)
−0.983496 + 0.180928i \(0.942090\pi\)
\(504\) 0 0
\(505\) −49.8960 + 28.8075i −2.22034 + 1.28191i
\(506\) 10.5429 0.468689
\(507\) 0 0
\(508\) 5.11506 0.226944
\(509\) 4.52051 2.60992i 0.200368 0.115682i −0.396459 0.918052i \(-0.629761\pi\)
0.596827 + 0.802370i \(0.296428\pi\)
\(510\) 0 0
\(511\) 5.05596 8.75718i 0.223663 0.387395i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 21.0820 + 12.1717i 0.929885 + 0.536870i
\(515\) 41.8907i 1.84592i
\(516\) 0 0
\(517\) 13.8464 + 23.9827i 0.608965 + 1.05476i
\(518\) −4.58394 + 2.64654i −0.201407 + 0.116282i
\(519\) 0 0
\(520\) 9.93962 4.75496i 0.435881 0.208519i
\(521\) 14.5259 0.636389 0.318195 0.948025i \(-0.396923\pi\)
0.318195 + 0.948025i \(0.396923\pi\)
\(522\) 0 0
\(523\) −13.9367 24.1391i −0.609410 1.05553i −0.991338 0.131337i \(-0.958073\pi\)
0.381927 0.924192i \(-0.375260\pi\)
\(524\) 9.38784 16.2602i 0.410110 0.710331i
\(525\) 0 0
\(526\) 14.8029 + 8.54648i 0.645439 + 0.372644i
\(527\) 2.39698 + 1.38389i 0.104414 + 0.0602834i
\(528\) 0 0
\(529\) 6.81025 11.7957i 0.296098 0.512856i
\(530\) 12.7343 + 22.0564i 0.553141 + 0.958069i
\(531\) 0 0
\(532\) 1.72542 0.0748063
\(533\) −20.3116 + 29.6263i −0.879792 + 1.28326i
\(534\) 0 0
\(535\) −8.77252 + 5.06482i −0.379269 + 0.218971i
\(536\) 2.37527 + 4.11410i 0.102596 + 0.177702i
\(537\) 0 0
\(538\) 26.6594i 1.14937i
\(539\) 2.98127 + 1.72124i 0.128412 + 0.0741389i
\(540\) 0 0
\(541\) 1.42341i 0.0611970i 0.999532 + 0.0305985i \(0.00974133\pi\)
−0.999532 + 0.0305985i \(0.990259\pi\)
\(542\) −12.2247 + 21.1739i −0.525097 + 0.909496i
\(543\) 0 0
\(544\) 2.44997 1.41449i 0.105042 0.0606458i
\(545\) −26.5112 −1.13562
\(546\) 0 0
\(547\) −9.33008 −0.398925 −0.199463 0.979905i \(-0.563920\pi\)
−0.199463 + 0.979905i \(0.563920\pi\)
\(548\) −2.30457 + 1.33055i −0.0984465 + 0.0568381i
\(549\) 0 0
\(550\) 7.46828 12.9354i 0.318449 0.551569i
\(551\) 6.64390i 0.283040i
\(552\) 0 0
\(553\) −3.89576 2.24922i −0.165664 0.0956464i
\(554\) 28.4812i 1.21005i
\(555\) 0 0
\(556\) −8.35322 14.4682i −0.354256 0.613589i
\(557\) −9.34071 + 5.39286i −0.395779 + 0.228503i −0.684661 0.728862i \(-0.740050\pi\)
0.288882 + 0.957365i \(0.406716\pi\)
\(558\) 0 0
\(559\) −0.842322 + 10.8620i −0.0356264 + 0.459415i
\(560\) −3.05596 −0.129138
\(561\) 0 0
\(562\) −4.88016 8.45268i −0.205857 0.356555i
\(563\) −12.7541 + 22.0908i −0.537522 + 0.931016i 0.461514 + 0.887133i \(0.347306\pi\)
−0.999037 + 0.0438831i \(0.986027\pi\)
\(564\) 0 0
\(565\) 29.6708 + 17.1304i 1.24826 + 0.720682i
\(566\) −10.1076 5.83562i −0.424853 0.245289i
\(567\) 0 0
\(568\) −1.83473 + 3.17784i −0.0769834 + 0.133339i
\(569\) 4.10835 + 7.11587i 0.172231 + 0.298313i 0.939200 0.343372i \(-0.111569\pi\)
−0.766969 + 0.641685i \(0.778236\pi\)
\(570\) 0 0
\(571\) 2.70500 0.113201 0.0566003 0.998397i \(-0.481974\pi\)
0.0566003 + 0.998397i \(0.481974\pi\)
\(572\) −5.35636 11.1968i −0.223961 0.468160i
\(573\) 0 0
\(574\) 8.62781 4.98127i 0.360118 0.207914i
\(575\) 6.64416 + 11.5080i 0.277081 + 0.479918i
\(576\) 0 0
\(577\) 21.4253i 0.891946i −0.895046 0.445973i \(-0.852858\pi\)
0.895046 0.445973i \(-0.147142\pi\)
\(578\) −7.79152 4.49843i −0.324084 0.187110i
\(579\) 0 0
\(580\) 11.7673i 0.488611i
\(581\) −3.57934 + 6.19961i −0.148496 + 0.257203i
\(582\) 0 0
\(583\) 24.8460 14.3449i 1.02902 0.594104i
\(584\) 10.1119 0.418434
\(585\) 0 0
\(586\) 21.8202 0.901382
\(587\) 4.96515 2.86663i 0.204934 0.118319i −0.394021 0.919101i \(-0.628916\pi\)
0.598955 + 0.800783i \(0.295583\pi\)
\(588\) 0 0
\(589\) −0.844048 + 1.46193i −0.0347784 + 0.0602379i
\(590\) 30.4910i 1.25529i
\(591\) 0 0
\(592\) −4.58394 2.64654i −0.188399 0.108772i
\(593\) 17.3442i 0.712240i −0.934440 0.356120i \(-0.884099\pi\)
0.934440 0.356120i \(-0.115901\pi\)
\(594\) 0 0
\(595\) −4.32263 7.48701i −0.177211 0.306938i
\(596\) −2.16642 + 1.25078i −0.0887400 + 0.0512341i
\(597\) 0 0
\(598\) 11.0093 + 0.853743i 0.450204 + 0.0349121i
\(599\) 31.5835 1.29047 0.645234 0.763985i \(-0.276760\pi\)
0.645234 + 0.763985i \(0.276760\pi\)
\(600\) 0 0
\(601\) −12.4478 21.5603i −0.507757 0.879462i −0.999960 0.00898069i \(-0.997141\pi\)
0.492202 0.870481i \(-0.336192\pi\)
\(602\) 1.51082 2.61681i 0.0615762 0.106653i
\(603\) 0 0
\(604\) 10.9522 + 6.32323i 0.445637 + 0.257289i
\(605\) −2.25118 1.29972i −0.0915233 0.0528410i
\(606\) 0 0
\(607\) −7.62951 + 13.2147i −0.309672 + 0.536368i −0.978291 0.207238i \(-0.933553\pi\)
0.668618 + 0.743606i \(0.266886\pi\)
\(608\) 0.862708 + 1.49425i 0.0349874 + 0.0606000i
\(609\) 0 0
\(610\) 35.2817 1.42851
\(611\) 12.5169 + 26.1649i 0.506379 + 1.05852i
\(612\) 0 0
\(613\) −39.6220 + 22.8757i −1.60032 + 0.923943i −0.608892 + 0.793253i \(0.708386\pi\)
−0.991423 + 0.130690i \(0.958281\pi\)
\(614\) −2.43523 4.21794i −0.0982779 0.170222i
\(615\) 0 0
\(616\) 3.44247i 0.138701i
\(617\) −36.6167 21.1406i −1.47413 0.851090i −0.474555 0.880226i \(-0.657391\pi\)
−0.999575 + 0.0291358i \(0.990724\pi\)
\(618\) 0 0
\(619\) 22.0261i 0.885303i −0.896694 0.442651i \(-0.854038\pi\)
0.896694 0.442651i \(-0.145962\pi\)
\(620\) 1.49493 2.58930i 0.0600379 0.103989i
\(621\) 0 0
\(622\) −3.38048 + 1.95172i −0.135545 + 0.0782569i
\(623\) 7.90307 0.316630
\(624\) 0 0
\(625\) −27.8684 −1.11474
\(626\) −22.5624 + 13.0264i −0.901775 + 0.520640i
\(627\) 0 0
\(628\) 8.90657 15.4266i 0.355411 0.615590i
\(629\) 14.9740i 0.597054i
\(630\) 0 0
\(631\) 18.0721 + 10.4339i 0.719440 + 0.415369i 0.814547 0.580098i \(-0.196986\pi\)
−0.0951064 + 0.995467i \(0.530319\pi\)
\(632\) 4.49843i 0.178938i
\(633\) 0 0
\(634\) −5.55536 9.62216i −0.220631 0.382145i
\(635\) 13.5372 7.81571i 0.537208 0.310157i
\(636\) 0 0
\(637\) 2.97377 + 2.03880i 0.117825 + 0.0807800i
\(638\) −13.2556 −0.524795
\(639\) 0 0
\(640\) −1.52798 2.64654i −0.0603988 0.104614i
\(641\) 10.4526 18.1045i 0.412853 0.715083i −0.582347 0.812940i \(-0.697866\pi\)
0.995200 + 0.0978574i \(0.0311989\pi\)
\(642\) 0 0
\(643\) 33.8703 + 19.5550i 1.33571 + 0.771174i 0.986168 0.165746i \(-0.0530032\pi\)
0.349544 + 0.936920i \(0.386337\pi\)
\(644\) −2.65229 1.53130i −0.104515 0.0603416i
\(645\) 0 0
\(646\) −2.44058 + 4.22722i −0.0960235 + 0.166318i
\(647\) 3.96755 + 6.87201i 0.155981 + 0.270166i 0.933416 0.358797i \(-0.116813\pi\)
−0.777435 + 0.628963i \(0.783480\pi\)
\(648\) 0 0
\(649\) −34.3474 −1.34825
\(650\) 8.84615 12.9029i 0.346974 0.506094i
\(651\) 0 0
\(652\) −7.68884 + 4.43915i −0.301118 + 0.173851i
\(653\) 21.3998 + 37.0655i 0.837439 + 1.45049i 0.892029 + 0.451978i \(0.149281\pi\)
−0.0545901 + 0.998509i \(0.517385\pi\)
\(654\) 0 0
\(655\) 57.3778i 2.24194i
\(656\) 8.62781 + 4.98127i 0.336859 + 0.194486i
\(657\) 0 0
\(658\) 8.04447i 0.313606i
\(659\) 0.364274 0.630941i 0.0141901 0.0245780i −0.858843 0.512239i \(-0.828816\pi\)
0.873033 + 0.487661i \(0.162150\pi\)
\(660\) 0 0
\(661\) −2.04352 + 1.17983i −0.0794836 + 0.0458899i −0.539215 0.842168i \(-0.681279\pi\)
0.459731 + 0.888058i \(0.347946\pi\)
\(662\) −14.6478 −0.569304
\(663\) 0 0
\(664\) −7.15869 −0.277811
\(665\) 4.56638 2.63640i 0.177077 0.102235i
\(666\) 0 0
\(667\) 5.89644 10.2129i 0.228311 0.395446i
\(668\) 9.76989i 0.378008i
\(669\) 0 0
\(670\) 12.5725 + 7.25875i 0.485719 + 0.280430i
\(671\) 39.7440i 1.53430i
\(672\) 0 0
\(673\) 15.6279 + 27.0682i 0.602410 + 1.04340i 0.992455 + 0.122609i \(0.0391260\pi\)
−0.390045 + 0.920796i \(0.627541\pi\)
\(674\) 23.8552 13.7728i 0.918867 0.530508i
\(675\) 0 0
\(676\) −4.68662 12.1258i −0.180255 0.466378i
\(677\) 41.7294 1.60379 0.801895 0.597464i \(-0.203825\pi\)
0.801895 + 0.597464i \(0.203825\pi\)
\(678\) 0 0
\(679\) −4.54961 7.88016i −0.174598 0.302413i
\(680\) 4.32263 7.48701i 0.165765 0.287114i
\(681\) 0 0
\(682\) −2.91678 1.68401i −0.111689 0.0644839i
\(683\) 7.98473 + 4.60999i 0.305527 + 0.176396i 0.644923 0.764247i \(-0.276889\pi\)
−0.339396 + 0.940644i \(0.610223\pi\)
\(684\) 0 0
\(685\) −4.06610 + 7.04269i −0.155358 + 0.269087i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 0 0
\(688\) 3.02163 0.115199
\(689\) 27.1068 12.9675i 1.03269 0.494021i
\(690\) 0 0
\(691\) −7.97487 + 4.60429i −0.303378 + 0.175156i −0.643960 0.765060i \(-0.722709\pi\)
0.340581 + 0.940215i \(0.389376\pi\)
\(692\) 4.33762 + 7.51299i 0.164892 + 0.285601i
\(693\) 0 0
\(694\) 5.24146i 0.198963i
\(695\) −44.2143 25.5271i −1.67714 0.968300i
\(696\) 0 0
\(697\) 28.1838i 1.06754i
\(698\) 2.61482 4.52901i 0.0989725 0.171425i
\(699\) 0 0
\(700\) −3.75760 + 2.16945i −0.142024 + 0.0819976i
\(701\) −20.8683 −0.788184 −0.394092 0.919071i \(-0.628941\pi\)
−0.394092 + 0.919071i \(0.628941\pi\)
\(702\) 0 0
\(703\) 9.13277 0.344449
\(704\) −2.98127 + 1.72124i −0.112361 + 0.0648715i
\(705\) 0 0
\(706\) 1.88348 3.26227i 0.0708855 0.122777i
\(707\) 18.8533i 0.709050i
\(708\) 0 0
\(709\) −12.8731 7.43226i −0.483458 0.279124i 0.238399 0.971167i \(-0.423378\pi\)
−0.721856 + 0.692043i \(0.756711\pi\)
\(710\) 11.2137i 0.420843i
\(711\) 0 0
\(712\) 3.95154 + 6.84426i 0.148090 + 0.256499i
\(713\) 2.59492 1.49818i 0.0971804 0.0561072i
\(714\) 0 0
\(715\) −31.2843 21.4483i −1.16996 0.802120i
\(716\) 23.4278 0.875540
\(717\) 0 0
\(718\) −10.3002 17.8404i −0.384399 0.665798i
\(719\) 12.8265 22.2162i 0.478349 0.828524i −0.521343 0.853347i \(-0.674569\pi\)
0.999692 + 0.0248229i \(0.00790218\pi\)
\(720\) 0 0
\(721\) −11.8714 6.85393i −0.442112 0.255254i
\(722\) 13.8763 + 8.01147i 0.516421 + 0.298156i
\(723\) 0 0
\(724\) 3.83316 6.63923i 0.142458 0.246745i
\(725\) −8.35372 14.4691i −0.310249 0.537368i
\(726\) 0 0
\(727\) 41.6568 1.54497 0.772483 0.635036i \(-0.219015\pi\)
0.772483 + 0.635036i \(0.219015\pi\)
\(728\) −0.278764 + 3.59476i −0.0103317 + 0.133231i
\(729\) 0 0
\(730\) 26.7616 15.4508i 0.990492 0.571861i
\(731\) 4.27407 + 7.40290i 0.158082 + 0.273806i
\(732\) 0 0
\(733\) 26.4965i 0.978671i 0.872096 + 0.489336i \(0.162761\pi\)
−0.872096 + 0.489336i \(0.837239\pi\)
\(734\) −24.1759 13.9579i −0.892347 0.515197i
\(735\) 0 0
\(736\) 3.06260i 0.112889i
\(737\) 8.17682 14.1627i 0.301197 0.521688i
\(738\) 0 0
\(739\) 18.1009 10.4506i 0.665853 0.384431i −0.128650 0.991690i \(-0.541064\pi\)
0.794504 + 0.607259i \(0.207731\pi\)
\(740\) −16.1755 −0.594622
\(741\) 0 0
\(742\) −8.33405 −0.305953
\(743\) −4.88999 + 2.82323i −0.179396 + 0.103574i −0.587009 0.809580i \(-0.699695\pi\)
0.407613 + 0.913155i \(0.366361\pi\)
\(744\) 0 0
\(745\) −3.82235 + 6.62050i −0.140040 + 0.242556i
\(746\) 31.4183i 1.15030i
\(747\) 0 0
\(748\) −8.43395 4.86934i −0.308376 0.178041i
\(749\) 3.31471i 0.121117i
\(750\) 0 0
\(751\) 7.70439 + 13.3444i 0.281137 + 0.486944i 0.971665 0.236362i \(-0.0759551\pi\)
−0.690528 + 0.723306i \(0.742622\pi\)
\(752\) 6.96672 4.02224i 0.254050 0.146676i
\(753\) 0 0
\(754\) −13.8420 1.07341i −0.504097 0.0390914i
\(755\) 38.6471 1.40651
\(756\) 0 0
\(757\) 17.7686 + 30.7761i 0.645811 + 1.11858i 0.984114 + 0.177540i \(0.0568139\pi\)
−0.338303 + 0.941037i \(0.609853\pi\)
\(758\) 15.9203 27.5747i 0.578251 1.00156i
\(759\) 0 0
\(760\) 4.56638 + 2.63640i 0.165640 + 0.0956324i
\(761\) −36.2213 20.9124i −1.31302 0.758073i −0.330425 0.943832i \(-0.607192\pi\)
−0.982595 + 0.185759i \(0.940526\pi\)
\(762\) 0 0
\(763\) 4.33762 7.51299i 0.157033 0.271988i
\(764\) −12.7472 22.0789i −0.461179 0.798785i
\(765\) 0 0
\(766\) −4.72228 −0.170623
\(767\) −35.8668 2.78138i −1.29508 0.100430i
\(768\) 0 0
\(769\) 15.4609 8.92635i 0.557534 0.321893i −0.194621 0.980879i \(-0.562348\pi\)
0.752155 + 0.658986i \(0.229014\pi\)
\(770\) 5.26003 + 9.11064i 0.189558 + 0.328325i
\(771\) 0 0
\(772\) 8.52586i 0.306852i
\(773\) −10.4892 6.05596i −0.377272 0.217818i 0.299359 0.954141i \(-0.403227\pi\)
−0.676630 + 0.736323i \(0.736561\pi\)
\(774\) 0 0
\(775\) 4.24506i 0.152487i
\(776\) 4.54961 7.88016i 0.163322 0.282881i
\(777\) 0 0
\(778\) −26.4919 + 15.2951i −0.949781 + 0.548357i
\(779\) −17.1895 −0.615878
\(780\) 0 0
\(781\) 12.6320 0.452008
\(782\) 7.50327 4.33201i 0.268316 0.154913i
\(783\) 0 0
\(784\) 0.500000 0.866025i 0.0178571 0.0309295i
\(785\) 54.4363i 1.94292i
\(786\) 0 0
\(787\) 27.7604 + 16.0275i 0.989551 + 0.571317i 0.905140 0.425114i \(-0.139766\pi\)
0.0844108 + 0.996431i \(0.473099\pi\)
\(788\) 23.6823i 0.843645i
\(789\) 0