Properties

Label 1386.2.k.w.991.1
Level $1386$
Weight $2$
Character 1386.991
Analytic conductor $11.067$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1156923.1
Defining polynomial: \(x^{6} - 3 x^{5} + 12 x^{4} - 19 x^{3} + 27 x^{2} - 18 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 462)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.1
Root \(0.500000 + 2.43956i\) of defining polynomial
Character \(\chi\) \(=\) 1386.991
Dual form 1386.2.k.w.793.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.60074 - 2.77256i) q^{5} +(1.60074 + 2.10657i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.60074 - 2.77256i) q^{5} +(1.60074 + 2.10657i) q^{7} -1.00000 q^{8} +(1.60074 - 2.77256i) q^{10} +(0.500000 - 0.866025i) q^{11} -6.40294 q^{13} +(-1.02398 + 2.43956i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.576760 - 0.998977i) q^{19} +3.20147 q^{20} +1.00000 q^{22} +(0.976024 + 1.69052i) q^{23} +(-2.62471 + 4.54614i) q^{25} +(-3.20147 - 5.54511i) q^{26} +(-2.62471 + 0.332992i) q^{28} -7.24943 q^{29} +(-5.24943 + 9.09227i) q^{31} +(0.500000 - 0.866025i) q^{32} +1.00000 q^{34} +(3.27823 - 7.81020i) q^{35} +(-2.57676 - 4.46308i) q^{37} +(0.576760 - 0.998977i) q^{38} +(1.60074 + 2.77256i) q^{40} -8.24943 q^{41} +5.15352 q^{43} +(0.500000 + 0.866025i) q^{44} +(-0.976024 + 1.69052i) q^{46} +(-3.02398 - 5.23768i) q^{47} +(-1.87529 + 6.74413i) q^{49} -5.24943 q^{50} +(3.20147 - 5.54511i) q^{52} +(-3.20147 + 5.54511i) q^{53} -3.20147 q^{55} +(-1.60074 - 2.10657i) q^{56} +(-3.62471 - 6.27819i) q^{58} +(5.77823 - 10.0082i) q^{59} +(-4.85016 - 8.40073i) q^{61} -10.4989 q^{62} +1.00000 q^{64} +(10.2494 + 17.7525i) q^{65} +(-3.12471 + 5.41216i) q^{67} +(0.500000 + 0.866025i) q^{68} +(8.40294 - 1.06607i) q^{70} -5.24943 q^{71} +(1.04795 - 1.81511i) q^{73} +(2.57676 - 4.46308i) q^{74} +1.15352 q^{76} +(2.62471 - 0.332992i) q^{77} +(2.80221 + 4.85357i) q^{79} +(-1.60074 + 2.77256i) q^{80} +(-4.12471 - 7.14421i) q^{82} -6.55646 q^{83} -3.20147 q^{85} +(2.57676 + 4.46308i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-9.20147 - 15.9374i) q^{89} +(-10.2494 - 13.4883i) q^{91} -1.95205 q^{92} +(3.02398 - 5.23768i) q^{94} +(-1.84648 + 3.19820i) q^{95} -5.49885 q^{97} +(-6.77823 + 1.74802i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{2} - 3q^{4} - 6q^{8} + O(q^{10}) \) \( 6q + 3q^{2} - 3q^{4} - 6q^{8} + 3q^{11} - 3q^{14} - 3q^{16} + 3q^{17} + 3q^{19} + 6q^{22} + 9q^{23} - 3q^{25} - 3q^{28} - 18q^{29} - 6q^{31} + 3q^{32} + 6q^{34} - 6q^{35} - 9q^{37} - 3q^{38} - 24q^{41} + 18q^{43} + 3q^{44} - 9q^{46} - 15q^{47} - 24q^{49} - 6q^{50} - 9q^{58} + 9q^{59} + 6q^{61} - 12q^{62} + 6q^{64} + 36q^{65} - 6q^{67} + 3q^{68} + 12q^{70} - 6q^{71} + 9q^{74} - 6q^{76} + 3q^{77} - 12q^{79} - 12q^{82} + 12q^{83} + 9q^{86} - 3q^{88} - 36q^{89} - 36q^{91} - 18q^{92} + 15q^{94} - 24q^{95} + 18q^{97} - 15q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.60074 2.77256i −0.715871 1.23992i −0.962623 0.270846i \(-0.912697\pi\)
0.246752 0.969079i \(-0.420637\pi\)
\(6\) 0 0
\(7\) 1.60074 + 2.10657i 0.605021 + 0.796209i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.60074 2.77256i 0.506197 0.876759i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 0 0
\(13\) −6.40294 −1.77586 −0.887929 0.459981i \(-0.847856\pi\)
−0.887929 + 0.459981i \(0.847856\pi\)
\(14\) −1.02398 + 2.43956i −0.273669 + 0.652001i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.500000 0.866025i 0.121268 0.210042i −0.799000 0.601331i \(-0.794637\pi\)
0.920268 + 0.391289i \(0.127971\pi\)
\(18\) 0 0
\(19\) −0.576760 0.998977i −0.132318 0.229181i 0.792252 0.610194i \(-0.208909\pi\)
−0.924570 + 0.381013i \(0.875575\pi\)
\(20\) 3.20147 0.715871
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 0.976024 + 1.69052i 0.203515 + 0.352498i 0.949659 0.313287i \(-0.101430\pi\)
−0.746144 + 0.665785i \(0.768097\pi\)
\(24\) 0 0
\(25\) −2.62471 + 4.54614i −0.524943 + 0.909227i
\(26\) −3.20147 5.54511i −0.627860 1.08749i
\(27\) 0 0
\(28\) −2.62471 + 0.332992i −0.496024 + 0.0629297i
\(29\) −7.24943 −1.34618 −0.673092 0.739559i \(-0.735034\pi\)
−0.673092 + 0.739559i \(0.735034\pi\)
\(30\) 0 0
\(31\) −5.24943 + 9.09227i −0.942825 + 1.63302i −0.182775 + 0.983155i \(0.558508\pi\)
−0.760049 + 0.649865i \(0.774825\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 1.00000 0.171499
\(35\) 3.27823 7.81020i 0.554122 1.32016i
\(36\) 0 0
\(37\) −2.57676 4.46308i −0.423617 0.733726i 0.572673 0.819784i \(-0.305906\pi\)
−0.996290 + 0.0860579i \(0.972573\pi\)
\(38\) 0.576760 0.998977i 0.0935628 0.162056i
\(39\) 0 0
\(40\) 1.60074 + 2.77256i 0.253099 + 0.438380i
\(41\) −8.24943 −1.28834 −0.644172 0.764881i \(-0.722798\pi\)
−0.644172 + 0.764881i \(0.722798\pi\)
\(42\) 0 0
\(43\) 5.15352 0.785904 0.392952 0.919559i \(-0.371454\pi\)
0.392952 + 0.919559i \(0.371454\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −0.976024 + 1.69052i −0.143907 + 0.249254i
\(47\) −3.02398 5.23768i −0.441092 0.763994i 0.556679 0.830728i \(-0.312076\pi\)
−0.997771 + 0.0667337i \(0.978742\pi\)
\(48\) 0 0
\(49\) −1.87529 + 6.74413i −0.267898 + 0.963447i
\(50\) −5.24943 −0.742381
\(51\) 0 0
\(52\) 3.20147 5.54511i 0.443964 0.768969i
\(53\) −3.20147 + 5.54511i −0.439756 + 0.761680i −0.997670 0.0682187i \(-0.978268\pi\)
0.557914 + 0.829899i \(0.311602\pi\)
\(54\) 0 0
\(55\) −3.20147 −0.431686
\(56\) −1.60074 2.10657i −0.213907 0.281502i
\(57\) 0 0
\(58\) −3.62471 6.27819i −0.475948 0.824366i
\(59\) 5.77823 10.0082i 0.752262 1.30296i −0.194462 0.980910i \(-0.562296\pi\)
0.946724 0.322046i \(-0.104370\pi\)
\(60\) 0 0
\(61\) −4.85016 8.40073i −0.621000 1.07560i −0.989300 0.145896i \(-0.953394\pi\)
0.368300 0.929707i \(-0.379940\pi\)
\(62\) −10.4989 −1.33336
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 10.2494 + 17.7525i 1.27128 + 2.20193i
\(66\) 0 0
\(67\) −3.12471 + 5.41216i −0.381744 + 0.661201i −0.991312 0.131534i \(-0.958010\pi\)
0.609567 + 0.792734i \(0.291343\pi\)
\(68\) 0.500000 + 0.866025i 0.0606339 + 0.105021i
\(69\) 0 0
\(70\) 8.40294 1.06607i 1.00434 0.127419i
\(71\) −5.24943 −0.622992 −0.311496 0.950247i \(-0.600830\pi\)
−0.311496 + 0.950247i \(0.600830\pi\)
\(72\) 0 0
\(73\) 1.04795 1.81511i 0.122654 0.212442i −0.798160 0.602446i \(-0.794193\pi\)
0.920813 + 0.390004i \(0.127526\pi\)
\(74\) 2.57676 4.46308i 0.299542 0.518822i
\(75\) 0 0
\(76\) 1.15352 0.132318
\(77\) 2.62471 0.332992i 0.299114 0.0379480i
\(78\) 0 0
\(79\) 2.80221 + 4.85357i 0.315273 + 0.546069i 0.979496 0.201466i \(-0.0645706\pi\)
−0.664222 + 0.747535i \(0.731237\pi\)
\(80\) −1.60074 + 2.77256i −0.178968 + 0.309981i
\(81\) 0 0
\(82\) −4.12471 7.14421i −0.455498 0.788946i
\(83\) −6.55646 −0.719665 −0.359833 0.933017i \(-0.617166\pi\)
−0.359833 + 0.933017i \(0.617166\pi\)
\(84\) 0 0
\(85\) −3.20147 −0.347248
\(86\) 2.57676 + 4.46308i 0.277859 + 0.481266i
\(87\) 0 0
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) −9.20147 15.9374i −0.975354 1.68936i −0.678761 0.734359i \(-0.737483\pi\)
−0.296593 0.955004i \(-0.595850\pi\)
\(90\) 0 0
\(91\) −10.2494 13.4883i −1.07443 1.41395i
\(92\) −1.95205 −0.203515
\(93\) 0 0
\(94\) 3.02398 5.23768i 0.311899 0.540226i
\(95\) −1.84648 + 3.19820i −0.189445 + 0.328128i
\(96\) 0 0
\(97\) −5.49885 −0.558324 −0.279162 0.960244i \(-0.590057\pi\)
−0.279162 + 0.960244i \(0.590057\pi\)
\(98\) −6.77823 + 1.74802i −0.684705 + 0.176577i
\(99\) 0 0
\(100\) −2.62471 4.54614i −0.262471 0.454614i
\(101\) −9.97970 + 17.2854i −0.993018 + 1.71996i −0.394348 + 0.918961i \(0.629029\pi\)
−0.598670 + 0.800996i \(0.704304\pi\)
\(102\) 0 0
\(103\) −0.153520 0.265904i −0.0151267 0.0262003i 0.858363 0.513043i \(-0.171482\pi\)
−0.873490 + 0.486843i \(0.838149\pi\)
\(104\) 6.40294 0.627860
\(105\) 0 0
\(106\) −6.40294 −0.621909
\(107\) −4.52766 7.84213i −0.437705 0.758128i 0.559807 0.828623i \(-0.310875\pi\)
−0.997512 + 0.0704955i \(0.977542\pi\)
\(108\) 0 0
\(109\) 4.85016 8.40073i 0.464561 0.804644i −0.534620 0.845092i \(-0.679545\pi\)
0.999182 + 0.0404487i \(0.0128787\pi\)
\(110\) −1.60074 2.77256i −0.152624 0.264353i
\(111\) 0 0
\(112\) 1.02398 2.43956i 0.0967567 0.230517i
\(113\) 12.4989 1.17579 0.587896 0.808936i \(-0.299956\pi\)
0.587896 + 0.808936i \(0.299956\pi\)
\(114\) 0 0
\(115\) 3.12471 5.41216i 0.291381 0.504687i
\(116\) 3.62471 6.27819i 0.336546 0.582915i
\(117\) 0 0
\(118\) 11.5565 1.06386
\(119\) 2.62471 0.332992i 0.240607 0.0305254i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 4.85016 8.40073i 0.439113 0.760566i
\(123\) 0 0
\(124\) −5.24943 9.09227i −0.471412 0.816510i
\(125\) 0.798528 0.0714225
\(126\) 0 0
\(127\) 8.35499 0.741386 0.370693 0.928756i \(-0.379120\pi\)
0.370693 + 0.928756i \(0.379120\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −10.2494 + 17.7525i −0.898934 + 1.55700i
\(131\) 7.65237 + 13.2543i 0.668591 + 1.15803i 0.978298 + 0.207201i \(0.0664355\pi\)
−0.309708 + 0.950832i \(0.600231\pi\)
\(132\) 0 0
\(133\) 1.18118 2.81408i 0.102421 0.244012i
\(134\) −6.24943 −0.539868
\(135\) 0 0
\(136\) −0.500000 + 0.866025i −0.0428746 + 0.0742611i
\(137\) −3.20147 + 5.54511i −0.273520 + 0.473751i −0.969761 0.244058i \(-0.921521\pi\)
0.696240 + 0.717809i \(0.254855\pi\)
\(138\) 0 0
\(139\) 21.7483 1.84466 0.922332 0.386398i \(-0.126281\pi\)
0.922332 + 0.386398i \(0.126281\pi\)
\(140\) 5.12471 + 6.74413i 0.433117 + 0.569983i
\(141\) 0 0
\(142\) −2.62471 4.54614i −0.220261 0.381503i
\(143\) −3.20147 + 5.54511i −0.267721 + 0.463706i
\(144\) 0 0
\(145\) 11.6044 + 20.0994i 0.963694 + 1.66917i
\(146\) 2.09591 0.173458
\(147\) 0 0
\(148\) 5.15352 0.423617
\(149\) 3.42324 + 5.92923i 0.280443 + 0.485741i 0.971494 0.237065i \(-0.0761854\pi\)
−0.691051 + 0.722806i \(0.742852\pi\)
\(150\) 0 0
\(151\) −7.42692 + 12.8638i −0.604394 + 1.04684i 0.387753 + 0.921763i \(0.373251\pi\)
−0.992147 + 0.125078i \(0.960082\pi\)
\(152\) 0.576760 + 0.998977i 0.0467814 + 0.0810278i
\(153\) 0 0
\(154\) 1.60074 + 2.10657i 0.128991 + 0.169752i
\(155\) 33.6118 2.69976
\(156\) 0 0
\(157\) 4.73028 8.19308i 0.377517 0.653879i −0.613183 0.789941i \(-0.710111\pi\)
0.990700 + 0.136062i \(0.0434445\pi\)
\(158\) −2.80221 + 4.85357i −0.222932 + 0.386129i
\(159\) 0 0
\(160\) −3.20147 −0.253099
\(161\) −1.99885 + 4.76214i −0.157531 + 0.375310i
\(162\) 0 0
\(163\) −6.52766 11.3062i −0.511286 0.885573i −0.999914 0.0130809i \(-0.995836\pi\)
0.488629 0.872492i \(-0.337497\pi\)
\(164\) 4.12471 7.14421i 0.322086 0.557869i
\(165\) 0 0
\(166\) −3.27823 5.67806i −0.254440 0.440703i
\(167\) 6.70998 0.519234 0.259617 0.965712i \(-0.416404\pi\)
0.259617 + 0.965712i \(0.416404\pi\)
\(168\) 0 0
\(169\) 27.9977 2.15367
\(170\) −1.60074 2.77256i −0.122771 0.212645i
\(171\) 0 0
\(172\) −2.57676 + 4.46308i −0.196476 + 0.340307i
\(173\) −2.75057 4.76414i −0.209122 0.362211i 0.742316 0.670050i \(-0.233727\pi\)
−0.951438 + 0.307839i \(0.900394\pi\)
\(174\) 0 0
\(175\) −13.7782 + 1.74802i −1.04154 + 0.132138i
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) 9.20147 15.9374i 0.689680 1.19456i
\(179\) 0.826185 1.43099i 0.0617520 0.106958i −0.833497 0.552525i \(-0.813665\pi\)
0.895249 + 0.445567i \(0.146998\pi\)
\(180\) 0 0
\(181\) 24.9018 1.85094 0.925468 0.378826i \(-0.123672\pi\)
0.925468 + 0.378826i \(0.123672\pi\)
\(182\) 6.55646 15.6204i 0.485997 1.15786i
\(183\) 0 0
\(184\) −0.976024 1.69052i −0.0719534 0.124627i
\(185\) −8.24943 + 14.2884i −0.606510 + 1.05051i
\(186\) 0 0
\(187\) −0.500000 0.866025i −0.0365636 0.0633300i
\(188\) 6.04795 0.441092
\(189\) 0 0
\(190\) −3.69296 −0.267916
\(191\) −2.40294 4.16202i −0.173871 0.301153i 0.765899 0.642961i \(-0.222294\pi\)
−0.939770 + 0.341808i \(0.888961\pi\)
\(192\) 0 0
\(193\) −4.35499 + 7.54307i −0.313479 + 0.542962i −0.979113 0.203317i \(-0.934828\pi\)
0.665634 + 0.746278i \(0.268161\pi\)
\(194\) −2.74943 4.76214i −0.197397 0.341902i
\(195\) 0 0
\(196\) −4.90294 4.99611i −0.350210 0.356865i
\(197\) −0.654669 −0.0466433 −0.0233216 0.999728i \(-0.507424\pi\)
−0.0233216 + 0.999728i \(0.507424\pi\)
\(198\) 0 0
\(199\) 3.84648 6.66230i 0.272670 0.472278i −0.696875 0.717193i \(-0.745427\pi\)
0.969545 + 0.244915i \(0.0787600\pi\)
\(200\) 2.62471 4.54614i 0.185595 0.321460i
\(201\) 0 0
\(202\) −19.9594 −1.40434
\(203\) −11.6044 15.2714i −0.814470 1.07184i
\(204\) 0 0
\(205\) 13.2052 + 22.8720i 0.922288 + 1.59745i
\(206\) 0.153520 0.265904i 0.0106962 0.0185264i
\(207\) 0 0
\(208\) 3.20147 + 5.54511i 0.221982 + 0.384484i
\(209\) −1.15352 −0.0797906
\(210\) 0 0
\(211\) 14.5948 1.00474 0.502372 0.864651i \(-0.332461\pi\)
0.502372 + 0.864651i \(0.332461\pi\)
\(212\) −3.20147 5.54511i −0.219878 0.380840i
\(213\) 0 0
\(214\) 4.52766 7.84213i 0.309504 0.536077i
\(215\) −8.24943 14.2884i −0.562606 0.974462i
\(216\) 0 0
\(217\) −27.5565 + 3.49604i −1.87065 + 0.237326i
\(218\) 9.70032 0.656989
\(219\) 0 0
\(220\) 1.60074 2.77256i 0.107922 0.186926i
\(221\) −3.20147 + 5.54511i −0.215354 + 0.373005i
\(222\) 0 0
\(223\) −14.9018 −0.997898 −0.498949 0.866631i \(-0.666281\pi\)
−0.498949 + 0.866631i \(0.666281\pi\)
\(224\) 2.62471 0.332992i 0.175371 0.0222490i
\(225\) 0 0
\(226\) 6.24943 + 10.8243i 0.415706 + 0.720023i
\(227\) −0.124713 + 0.216009i −0.00827746 + 0.0143370i −0.870134 0.492814i \(-0.835968\pi\)
0.861857 + 0.507151i \(0.169301\pi\)
\(228\) 0 0
\(229\) 2.04795 + 3.54716i 0.135333 + 0.234403i 0.925724 0.378199i \(-0.123456\pi\)
−0.790392 + 0.612602i \(0.790123\pi\)
\(230\) 6.24943 0.412075
\(231\) 0 0
\(232\) 7.24943 0.475948
\(233\) 5.65352 + 9.79218i 0.370374 + 0.641507i 0.989623 0.143688i \(-0.0458961\pi\)
−0.619249 + 0.785195i \(0.712563\pi\)
\(234\) 0 0
\(235\) −9.68118 + 16.7683i −0.631530 + 1.09384i
\(236\) 5.77823 + 10.0082i 0.376131 + 0.651478i
\(237\) 0 0
\(238\) 1.60074 + 2.10657i 0.103760 + 0.136549i
\(239\) −6.59476 −0.426579 −0.213290 0.976989i \(-0.568418\pi\)
−0.213290 + 0.976989i \(0.568418\pi\)
\(240\) 0 0
\(241\) −8.55646 + 14.8202i −0.551170 + 0.954655i 0.447020 + 0.894524i \(0.352485\pi\)
−0.998190 + 0.0601311i \(0.980848\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) 0 0
\(244\) 9.70032 0.621000
\(245\) 21.7003 5.59623i 1.38638 0.357530i
\(246\) 0 0
\(247\) 3.69296 + 6.39640i 0.234977 + 0.406993i
\(248\) 5.24943 9.09227i 0.333339 0.577360i
\(249\) 0 0
\(250\) 0.399264 + 0.691545i 0.0252517 + 0.0437372i
\(251\) −7.95941 −0.502393 −0.251197 0.967936i \(-0.580824\pi\)
−0.251197 + 0.967936i \(0.580824\pi\)
\(252\) 0 0
\(253\) 1.95205 0.122724
\(254\) 4.17750 + 7.23564i 0.262119 + 0.454004i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −11.2015 19.4015i −0.698729 1.21023i −0.968907 0.247423i \(-0.920416\pi\)
0.270179 0.962810i \(-0.412917\pi\)
\(258\) 0 0
\(259\) 5.27708 12.5723i 0.327902 0.781207i
\(260\) −20.4989 −1.27128
\(261\) 0 0
\(262\) −7.65237 + 13.2543i −0.472765 + 0.818853i
\(263\) −12.5085 + 21.6654i −0.771308 + 1.33594i 0.165539 + 0.986203i \(0.447064\pi\)
−0.936846 + 0.349741i \(0.886270\pi\)
\(264\) 0 0
\(265\) 20.4989 1.25923
\(266\) 3.02766 0.384113i 0.185638 0.0235515i
\(267\) 0 0
\(268\) −3.12471 5.41216i −0.190872 0.330600i
\(269\) 4.05163 7.01764i 0.247032 0.427873i −0.715669 0.698440i \(-0.753878\pi\)
0.962701 + 0.270567i \(0.0872112\pi\)
\(270\) 0 0
\(271\) 2.40294 + 4.16202i 0.145968 + 0.252825i 0.929734 0.368232i \(-0.120037\pi\)
−0.783765 + 0.621057i \(0.786704\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 0 0
\(274\) −6.40294 −0.386816
\(275\) 2.62471 + 4.54614i 0.158276 + 0.274142i
\(276\) 0 0
\(277\) 5.60442 9.70714i 0.336737 0.583245i −0.647080 0.762422i \(-0.724010\pi\)
0.983817 + 0.179177i \(0.0573434\pi\)
\(278\) 10.8741 + 18.8346i 0.652187 + 1.12962i
\(279\) 0 0
\(280\) −3.27823 + 7.81020i −0.195912 + 0.466749i
\(281\) 17.4989 1.04389 0.521947 0.852978i \(-0.325206\pi\)
0.521947 + 0.852978i \(0.325206\pi\)
\(282\) 0 0
\(283\) −13.7003 + 23.7297i −0.814400 + 1.41058i 0.0953585 + 0.995443i \(0.469600\pi\)
−0.909758 + 0.415139i \(0.863733\pi\)
\(284\) 2.62471 4.54614i 0.155748 0.269764i
\(285\) 0 0
\(286\) −6.40294 −0.378614
\(287\) −13.2052 17.3780i −0.779476 1.02579i
\(288\) 0 0
\(289\) 8.00000 + 13.8564i 0.470588 + 0.815083i
\(290\) −11.6044 + 20.0994i −0.681435 + 1.18028i
\(291\) 0 0
\(292\) 1.04795 + 1.81511i 0.0613268 + 0.106221i
\(293\) 19.7483 1.15371 0.576853 0.816848i \(-0.304280\pi\)
0.576853 + 0.816848i \(0.304280\pi\)
\(294\) 0 0
\(295\) −36.9977 −2.15409
\(296\) 2.57676 + 4.46308i 0.149771 + 0.259411i
\(297\) 0 0
\(298\) −3.42324 + 5.92923i −0.198303 + 0.343471i
\(299\) −6.24943 10.8243i −0.361414 0.625987i
\(300\) 0 0
\(301\) 8.24943 + 10.8563i 0.475489 + 0.625744i
\(302\) −14.8538 −0.854743
\(303\) 0 0
\(304\) −0.576760 + 0.998977i −0.0330794 + 0.0572953i
\(305\) −15.5277 + 26.8947i −0.889111 + 1.53999i
\(306\) 0 0
\(307\) 4.30704 0.245816 0.122908 0.992418i \(-0.460778\pi\)
0.122908 + 0.992418i \(0.460778\pi\)
\(308\) −1.02398 + 2.43956i −0.0583465 + 0.139007i
\(309\) 0 0
\(310\) 16.8059 + 29.1087i 0.954510 + 1.65326i
\(311\) −7.37897 + 12.7807i −0.418423 + 0.724730i −0.995781 0.0917613i \(-0.970750\pi\)
0.577358 + 0.816491i \(0.304084\pi\)
\(312\) 0 0
\(313\) −10.3753 17.9705i −0.586446 1.01575i −0.994693 0.102883i \(-0.967193\pi\)
0.408248 0.912871i \(-0.366140\pi\)
\(314\) 9.46056 0.533890
\(315\) 0 0
\(316\) −5.60442 −0.315273
\(317\) 8.09959 + 14.0289i 0.454918 + 0.787941i 0.998683 0.0512960i \(-0.0163352\pi\)
−0.543765 + 0.839237i \(0.683002\pi\)
\(318\) 0 0
\(319\) −3.62471 + 6.27819i −0.202945 + 0.351511i
\(320\) −1.60074 2.77256i −0.0894839 0.154991i
\(321\) 0 0
\(322\) −5.12356 + 0.650017i −0.285525 + 0.0362240i
\(323\) −1.15352 −0.0641835
\(324\) 0 0
\(325\) 16.8059 29.1087i 0.932223 1.61466i
\(326\) 6.52766 11.3062i 0.361533 0.626194i
\(327\) 0 0
\(328\) 8.24943 0.455498
\(329\) 6.19296 14.7544i 0.341429 0.813435i
\(330\) 0 0
\(331\) −10.6236 18.4006i −0.583924 1.01139i −0.995009 0.0997886i \(-0.968183\pi\)
0.411085 0.911597i \(-0.365150\pi\)
\(332\) 3.27823 5.67806i 0.179916 0.311624i
\(333\) 0 0
\(334\) 3.35499 + 5.81102i 0.183577 + 0.317965i
\(335\) 20.0074 1.09312
\(336\) 0 0
\(337\) −25.5159 −1.38994 −0.694969 0.719040i \(-0.744582\pi\)
−0.694969 + 0.719040i \(0.744582\pi\)
\(338\) 13.9989 + 24.2467i 0.761437 + 1.31885i
\(339\) 0 0
\(340\) 1.60074 2.77256i 0.0868121 0.150363i
\(341\) 5.24943 + 9.09227i 0.284272 + 0.492374i
\(342\) 0 0
\(343\) −17.2088 + 6.84515i −0.929190 + 0.369603i
\(344\) −5.15352 −0.277859
\(345\) 0 0
\(346\) 2.75057 4.76414i 0.147872 0.256122i
\(347\) 1.52766 2.64598i 0.0820089 0.142044i −0.822104 0.569338i \(-0.807200\pi\)
0.904113 + 0.427294i \(0.140533\pi\)
\(348\) 0 0
\(349\) −4.00736 −0.214509 −0.107255 0.994232i \(-0.534206\pi\)
−0.107255 + 0.994232i \(0.534206\pi\)
\(350\) −8.40294 11.0583i −0.449156 0.591090i
\(351\) 0 0
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −0.549103 + 0.951073i −0.0292258 + 0.0506205i −0.880268 0.474476i \(-0.842638\pi\)
0.851043 + 0.525097i \(0.175971\pi\)
\(354\) 0 0
\(355\) 8.40294 + 14.5543i 0.445982 + 0.772463i
\(356\) 18.4029 0.975354
\(357\) 0 0
\(358\) 1.65237 0.0873305
\(359\) 7.80589 + 13.5202i 0.411979 + 0.713569i 0.995106 0.0988123i \(-0.0315043\pi\)
−0.583127 + 0.812381i \(0.698171\pi\)
\(360\) 0 0
\(361\) 8.83470 15.3021i 0.464984 0.805376i
\(362\) 12.4509 + 21.5656i 0.654405 + 1.13346i
\(363\) 0 0
\(364\) 16.8059 2.13213i 0.880868 0.111754i
\(365\) −6.70998 −0.351217
\(366\) 0 0
\(367\) −0.395583 + 0.685170i −0.0206493 + 0.0357656i −0.876165 0.482011i \(-0.839907\pi\)
0.855516 + 0.517776i \(0.173240\pi\)
\(368\) 0.976024 1.69052i 0.0508787 0.0881246i
\(369\) 0 0
\(370\) −16.4989 −0.857734
\(371\) −16.8059 + 2.13213i −0.872518 + 0.110695i
\(372\) 0 0
\(373\) −7.95573 13.7797i −0.411932 0.713487i 0.583169 0.812351i \(-0.301813\pi\)
−0.995101 + 0.0988637i \(0.968479\pi\)
\(374\) 0.500000 0.866025i 0.0258544 0.0447811i
\(375\) 0 0
\(376\) 3.02398 + 5.23768i 0.155950 + 0.270113i
\(377\) 46.4177 2.39063
\(378\) 0 0
\(379\) −17.0553 −0.876073 −0.438036 0.898957i \(-0.644326\pi\)
−0.438036 + 0.898957i \(0.644326\pi\)
\(380\) −1.84648 3.19820i −0.0947224 0.164064i
\(381\) 0 0
\(382\) 2.40294 4.16202i 0.122945 0.212948i
\(383\) 6.72062 + 11.6405i 0.343408 + 0.594799i 0.985063 0.172194i \(-0.0550855\pi\)
−0.641656 + 0.766993i \(0.721752\pi\)
\(384\) 0 0
\(385\) −5.12471 6.74413i −0.261180 0.343713i
\(386\) −8.70998 −0.443327
\(387\) 0 0
\(388\) 2.74943 4.76214i 0.139581 0.241761i
\(389\) −3.60074 + 6.23666i −0.182565 + 0.316211i −0.942753 0.333491i \(-0.891773\pi\)
0.760189 + 0.649702i \(0.225107\pi\)
\(390\) 0 0
\(391\) 1.95205 0.0987193
\(392\) 1.87529 6.74413i 0.0947163 0.340630i
\(393\) 0 0
\(394\) −0.327335 0.566960i −0.0164909 0.0285630i
\(395\) 8.97119 15.5386i 0.451390 0.781830i
\(396\) 0 0
\(397\) −6.47119 11.2084i −0.324780 0.562535i 0.656688 0.754162i \(-0.271957\pi\)
−0.981468 + 0.191627i \(0.938624\pi\)
\(398\) 7.69296 0.385613
\(399\) 0 0
\(400\) 5.24943 0.262471
\(401\) −8.45090 14.6374i −0.422018 0.730956i 0.574119 0.818772i \(-0.305345\pi\)
−0.996137 + 0.0878158i \(0.972011\pi\)
\(402\) 0 0
\(403\) 33.6118 58.2173i 1.67432 2.90001i
\(404\) −9.97970 17.2854i −0.496509 0.859979i
\(405\) 0 0
\(406\) 7.42324 17.6854i 0.368409 0.877713i
\(407\) −5.15352 −0.255450
\(408\) 0 0
\(409\) 18.5468 32.1240i 0.917080 1.58843i 0.113254 0.993566i \(-0.463873\pi\)
0.803827 0.594864i \(-0.202794\pi\)
\(410\) −13.2052 + 22.8720i −0.652156 + 1.12957i
\(411\) 0 0
\(412\) 0.307039 0.0151267
\(413\) 30.3324 3.84821i 1.49256 0.189358i
\(414\) 0 0
\(415\) 10.4952 + 18.1782i 0.515188 + 0.892331i
\(416\) −3.20147 + 5.54511i −0.156965 + 0.271872i
\(417\) 0 0
\(418\) −0.576760 0.998977i −0.0282102 0.0488616i
\(419\) −22.4583 −1.09716 −0.548579 0.836099i \(-0.684831\pi\)
−0.548579 + 0.836099i \(0.684831\pi\)
\(420\) 0 0
\(421\) −23.3453 −1.13778 −0.568891 0.822413i \(-0.692627\pi\)
−0.568891 + 0.822413i \(0.692627\pi\)
\(422\) 7.29738 + 12.6394i 0.355231 + 0.615278i
\(423\) 0 0
\(424\) 3.20147 5.54511i 0.155477 0.269294i
\(425\) 2.62471 + 4.54614i 0.127317 + 0.220520i
\(426\) 0 0
\(427\) 9.93290 23.6646i 0.480687 1.14521i
\(428\) 9.05531 0.437705
\(429\) 0 0
\(430\) 8.24943 14.2884i 0.397823 0.689049i
\(431\) 15.9115 27.5595i 0.766428 1.32749i −0.173060 0.984911i \(-0.555366\pi\)
0.939488 0.342581i \(-0.111301\pi\)
\(432\) 0 0
\(433\) 30.3047 1.45635 0.728176 0.685390i \(-0.240368\pi\)
0.728176 + 0.685390i \(0.240368\pi\)
\(434\) −16.8059 22.1166i −0.806709 1.06163i
\(435\) 0 0
\(436\) 4.85016 + 8.40073i 0.232281 + 0.402322i
\(437\) 1.12586 1.95005i 0.0538573 0.0932836i
\(438\) 0 0
\(439\) 5.33102 + 9.23359i 0.254435 + 0.440695i 0.964742 0.263197i \(-0.0847770\pi\)
−0.710307 + 0.703892i \(0.751444\pi\)
\(440\) 3.20147 0.152624
\(441\) 0 0
\(442\) −6.40294 −0.304557
\(443\) −18.0277 31.2248i −0.856520 1.48354i −0.875228 0.483711i \(-0.839289\pi\)
0.0187080 0.999825i \(-0.494045\pi\)
\(444\) 0 0
\(445\) −29.4583 + 51.0232i −1.39646 + 2.41873i
\(446\) −7.45090 12.9053i −0.352810 0.611085i
\(447\) 0 0
\(448\) 1.60074 + 2.10657i 0.0756277 + 0.0995262i
\(449\) −23.4006 −1.10434 −0.552172 0.833730i \(-0.686201\pi\)
−0.552172 + 0.833730i \(0.686201\pi\)
\(450\) 0 0
\(451\) −4.12471 + 7.14421i −0.194225 + 0.336408i
\(452\) −6.24943 + 10.8243i −0.293948 + 0.509133i
\(453\) 0 0
\(454\) −0.249425 −0.0117061
\(455\) −20.9903 + 50.0083i −0.984042 + 2.34442i
\(456\) 0 0
\(457\) 9.30704 + 16.1203i 0.435365 + 0.754074i 0.997325 0.0730899i \(-0.0232860\pi\)
−0.561960 + 0.827164i \(0.689953\pi\)
\(458\) −2.04795 + 3.54716i −0.0956945 + 0.165748i
\(459\) 0 0
\(460\) 3.12471 + 5.41216i 0.145690 + 0.252343i
\(461\) 31.4412 1.46436 0.732182 0.681109i \(-0.238502\pi\)
0.732182 + 0.681109i \(0.238502\pi\)
\(462\) 0 0
\(463\) −22.0959 −1.02688 −0.513442 0.858124i \(-0.671630\pi\)
−0.513442 + 0.858124i \(0.671630\pi\)
\(464\) 3.62471 + 6.27819i 0.168273 + 0.291457i
\(465\) 0 0
\(466\) −5.65352 + 9.79218i −0.261894 + 0.453614i
\(467\) 10.5288 + 18.2364i 0.487215 + 0.843881i 0.999892 0.0147004i \(-0.00467944\pi\)
−0.512677 + 0.858582i \(0.671346\pi\)
\(468\) 0 0
\(469\) −16.4029 + 2.08101i −0.757418 + 0.0960922i
\(470\) −19.3624 −0.893119
\(471\) 0 0
\(472\) −5.77823 + 10.0082i −0.265965 + 0.460664i
\(473\) 2.57676 4.46308i 0.118480 0.205213i
\(474\) 0 0
\(475\) 6.05531 0.277837
\(476\) −1.02398 + 2.43956i −0.0469339 + 0.111817i
\(477\) 0 0
\(478\) −3.29738 5.71123i −0.150819 0.261225i
\(479\) −10.6044 + 18.3674i −0.484528 + 0.839227i −0.999842 0.0177741i \(-0.994342\pi\)
0.515314 + 0.857002i \(0.327675\pi\)
\(480\) 0 0
\(481\) 16.4989 + 28.5768i 0.752283 + 1.30299i
\(482\) −17.1129 −0.779473
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 8.80221 + 15.2459i 0.399688 + 0.692279i
\(486\) 0 0
\(487\) 19.3550 33.5238i 0.877058 1.51911i 0.0225047 0.999747i \(-0.492836\pi\)
0.854554 0.519363i \(-0.173831\pi\)
\(488\) 4.85016 + 8.40073i 0.219556 + 0.380283i
\(489\) 0 0
\(490\) 15.6966 + 15.9949i 0.709102 + 0.722577i
\(491\) −19.1705 −0.865154 −0.432577 0.901597i \(-0.642396\pi\)
−0.432577 + 0.901597i \(0.642396\pi\)
\(492\) 0 0
\(493\) −3.62471 + 6.27819i −0.163249 + 0.282755i
\(494\) −3.69296 + 6.39640i −0.166154 + 0.287787i
\(495\) 0 0
\(496\) 10.4989 0.471412
\(497\) −8.40294 11.0583i −0.376924 0.496032i
\(498\) 0 0
\(499\) 13.9594 + 24.1784i 0.624909 + 1.08237i 0.988558 + 0.150838i \(0.0481973\pi\)
−0.363649 + 0.931536i \(0.618469\pi\)
\(500\) −0.399264 + 0.691545i −0.0178556 + 0.0309268i
\(501\) 0 0
\(502\) −3.97970 6.89305i −0.177623 0.307652i
\(503\) 8.70998 0.388359 0.194179 0.980966i \(-0.437796\pi\)
0.194179 + 0.980966i \(0.437796\pi\)
\(504\) 0 0
\(505\) 63.8995 2.84349
\(506\) 0.976024 + 1.69052i 0.0433895 + 0.0751529i
\(507\) 0 0
\(508\) −4.17750 + 7.23564i −0.185346 + 0.321029i
\(509\) −0.894433 1.54920i −0.0396451 0.0686673i 0.845522 0.533941i \(-0.179289\pi\)
−0.885167 + 0.465273i \(0.845956\pi\)
\(510\) 0 0
\(511\) 5.50115 0.697921i 0.243357 0.0308742i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 11.2015 19.4015i 0.494076 0.855764i
\(515\) −0.491489 + 0.851283i −0.0216576 + 0.0375120i
\(516\) 0 0
\(517\) −6.04795 −0.265989
\(518\) 13.5265 1.71608i 0.594321 0.0754004i
\(519\) 0 0
\(520\) −10.2494 17.7525i −0.449467 0.778500i
\(521\) 11.8059 20.4484i 0.517225 0.895861i −0.482574 0.875855i \(-0.660298\pi\)
0.999800 0.0200057i \(-0.00636845\pi\)
\(522\) 0 0
\(523\) −21.7003 37.5861i −0.948889 1.64352i −0.747771 0.663957i \(-0.768876\pi\)
−0.201118 0.979567i \(-0.564457\pi\)
\(524\) −15.3047 −0.668591
\(525\) 0 0
\(526\) −25.0170 −1.09079
\(527\) 5.24943 + 9.09227i 0.228669 + 0.396066i
\(528\) 0 0
\(529\) 9.59476 16.6186i 0.417163 0.722548i
\(530\) 10.2494 + 17.7525i 0.445207 + 0.771120i
\(531\) 0 0
\(532\) 1.84648 + 2.42997i 0.0800551 + 0.105353i
\(533\) 52.8206 2.28791
\(534\) 0 0
\(535\) −14.4952 + 25.1064i −0.626681 + 1.08544i
\(536\) 3.12471 5.41216i 0.134967 0.233770i
\(537\) 0 0
\(538\) 8.10327 0.349357
\(539\) 4.90294 + 4.99611i 0.211185 + 0.215198i
\(540\) 0 0
\(541\) −8.49517 14.7141i −0.365236 0.632607i 0.623578 0.781761i \(-0.285678\pi\)
−0.988814 + 0.149154i \(0.952345\pi\)
\(542\) −2.40294 + 4.16202i −0.103215 + 0.178774i
\(543\) 0 0
\(544\) −0.500000 0.866025i −0.0214373 0.0371305i
\(545\) −31.0553 −1.33026
\(546\) 0 0
\(547\) −1.34533 −0.0575222 −0.0287611 0.999586i \(-0.509156\pi\)
−0.0287611 + 0.999586i \(0.509156\pi\)
\(548\) −3.20147 5.54511i −0.136760 0.236875i
\(549\) 0 0
\(550\) −2.62471 + 4.54614i −0.111918 + 0.193848i
\(551\) 4.18118 + 7.24201i 0.178124 + 0.308520i
\(552\) 0 0
\(553\) −5.73879 + 13.6723i −0.244038 + 0.581407i
\(554\) 11.2088 0.476218
\(555\) 0 0
\(556\) −10.8741 + 18.8346i −0.461166 + 0.798763i
\(557\) −8.32733 + 14.4234i −0.352840 + 0.611138i −0.986746 0.162273i \(-0.948118\pi\)
0.633905 + 0.773411i \(0.281451\pi\)
\(558\) 0 0
\(559\) −32.9977 −1.39565
\(560\) −8.40294 + 1.06607i −0.355089 + 0.0450495i
\(561\) 0 0
\(562\) 8.74943 + 15.1544i 0.369072 + 0.639252i
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 0 0
\(565\) −20.0074 34.6538i −0.841716 1.45789i
\(566\) −27.4006 −1.15174
\(567\) 0 0
\(568\) 5.24943 0.220261
\(569\) −5.27708 9.14017i −0.221227 0.383176i 0.733954 0.679199i \(-0.237673\pi\)
−0.955181 + 0.296023i \(0.904339\pi\)
\(570\) 0 0
\(571\) −2.37529 + 4.11412i −0.0994027 + 0.172171i −0.911438 0.411438i \(-0.865027\pi\)
0.812035 + 0.583609i \(0.198360\pi\)
\(572\) −3.20147 5.54511i −0.133860 0.231853i
\(573\) 0 0
\(574\) 8.44722 20.1250i 0.352580 0.840001i
\(575\) −10.2471 −0.427335
\(576\) 0 0
\(577\) −18.7771 + 32.5229i −0.781700 + 1.35394i 0.149250 + 0.988799i \(0.452314\pi\)
−0.930951 + 0.365145i \(0.881019\pi\)
\(578\) −8.00000 + 13.8564i −0.332756 + 0.576351i
\(579\) 0 0
\(580\) −23.2088 −0.963694
\(581\) −10.4952 13.8117i −0.435413 0.573004i
\(582\) 0 0
\(583\) 3.20147 + 5.54511i 0.132591 + 0.229655i
\(584\) −1.04795 + 1.81511i −0.0433646 + 0.0751097i
\(585\) 0 0
\(586\) 9.87414 + 17.1025i 0.407897 + 0.706498i
\(587\) 17.0982 0.705718 0.352859 0.935676i \(-0.385209\pi\)
0.352859 + 0.935676i \(0.385209\pi\)
\(588\) 0 0
\(589\) 12.1106 0.499010
\(590\) −18.4989 32.0409i −0.761586 1.31910i
\(591\) 0 0
\(592\) −2.57676 + 4.46308i −0.105904 + 0.183431i
\(593\) −16.1236 27.9268i −0.662115 1.14682i −0.980059 0.198708i \(-0.936326\pi\)
0.317943 0.948110i \(-0.397008\pi\)
\(594\) 0 0
\(595\) −5.12471 6.74413i −0.210093 0.276482i
\(596\) −6.84648 −0.280443
\(597\) 0 0
\(598\) 6.24943 10.8243i 0.255558 0.442639i
\(599\) 1.69664 2.93867i 0.0693229 0.120071i −0.829281 0.558833i \(-0.811249\pi\)
0.898603 + 0.438762i \(0.144583\pi\)
\(600\) 0 0
\(601\) 30.4989 1.24407 0.622037 0.782988i \(-0.286305\pi\)
0.622037 + 0.782988i \(0.286305\pi\)
\(602\) −5.27708 + 12.5723i −0.215078 + 0.512410i
\(603\) 0 0
\(604\) −7.42692 12.8638i −0.302197 0.523421i
\(605\) −1.60074 + 2.77256i −0.0650792 + 0.112720i
\(606\) 0 0
\(607\) −6.49517 11.2500i −0.263631 0.456622i 0.703573 0.710623i \(-0.251587\pi\)
−0.967204 + 0.254001i \(0.918253\pi\)
\(608\) −1.15352 −0.0467814
\(609\) 0 0
\(610\) −31.0553 −1.25739
\(611\) 19.3624 + 33.5366i 0.783317 + 1.35674i
\(612\) 0 0
\(613\) −10.0996 + 17.4930i −0.407918 + 0.706535i −0.994656 0.103241i \(-0.967079\pi\)
0.586738 + 0.809777i \(0.300412\pi\)
\(614\) 2.15352 + 3.73001i 0.0869090 + 0.150531i
\(615\) 0 0
\(616\) −2.62471 + 0.332992i −0.105753 + 0.0134166i
\(617\) −17.0936 −0.688163 −0.344081 0.938940i \(-0.611810\pi\)
−0.344081 + 0.938940i \(0.611810\pi\)
\(618\) 0 0
\(619\) −20.8347 + 36.0868i −0.837417 + 1.45045i 0.0546300 + 0.998507i \(0.482602\pi\)
−0.892047 + 0.451942i \(0.850731\pi\)
\(620\) −16.8059 + 29.1087i −0.674941 + 1.16903i
\(621\) 0 0
\(622\) −14.7579 −0.591739
\(623\) 18.8442 44.8952i 0.754976 1.79869i
\(624\) 0 0
\(625\) 11.8453 + 20.5167i 0.473813 + 0.820669i
\(626\) 10.3753 17.9705i 0.414680 0.718247i
\(627\) 0 0
\(628\) 4.73028 + 8.19308i 0.188759 + 0.326940i
\(629\) −5.15352 −0.205484
\(630\) 0 0
\(631\) −23.8995 −0.951424 −0.475712 0.879601i \(-0.657810\pi\)
−0.475712 + 0.879601i \(0.657810\pi\)
\(632\) −2.80221 4.85357i −0.111466 0.193065i
\(633\) 0 0
\(634\) −8.09959 + 14.0289i −0.321676 + 0.557159i
\(635\) −13.3741 23.1647i −0.530736 0.919263i
\(636\) 0 0
\(637\) 12.0074 43.1823i 0.475749 1.71094i
\(638\) −7.24943 −0.287007
\(639\) 0 0
\(640\) 1.60074 2.77256i 0.0632747 0.109595i
\(641\) −7.15352 + 12.3903i −0.282547 + 0.489386i −0.972011 0.234934i \(-0.924513\pi\)
0.689464 + 0.724320i \(0.257846\pi\)
\(642\) 0 0
\(643\) −35.4966 −1.39985 −0.699924 0.714218i \(-0.746783\pi\)
−0.699924 + 0.714218i \(0.746783\pi\)
\(644\) −3.12471 4.11213i −0.123131 0.162041i
\(645\) 0 0
\(646\) −0.576760 0.998977i −0.0226923 0.0393042i
\(647\) 11.9078 20.6249i 0.468143 0.810847i −0.531194 0.847250i \(-0.678257\pi\)
0.999337 + 0.0364027i \(0.0115899\pi\)
\(648\) 0 0
\(649\) −5.77823 10.0082i −0.226815 0.392856i
\(650\) 33.6118 1.31836
\(651\) 0 0
\(652\) 13.0553 0.511286
\(653\) −6.89811 11.9479i −0.269944 0.467557i 0.698903 0.715216i \(-0.253672\pi\)
−0.968847 + 0.247660i \(0.920339\pi\)
\(654\) 0 0
\(655\) 24.4989 42.4333i 0.957249 1.65800i
\(656\) 4.12471 + 7.14421i 0.161043 + 0.278935i
\(657\) 0 0
\(658\) 15.8741 2.01392i 0.618838 0.0785109i
\(659\) −18.9447 −0.737980 −0.368990 0.929433i \(-0.620296\pi\)
−0.368990 + 0.929433i \(0.620296\pi\)
\(660\) 0 0
\(661\) −1.97970 + 3.42895i −0.0770016 + 0.133371i −0.901955 0.431830i \(-0.857868\pi\)
0.824953 + 0.565201i \(0.191201\pi\)
\(662\) 10.6236 18.4006i 0.412896 0.715158i
\(663\) 0 0
\(664\) 6.55646 0.254440
\(665\) −9.69296 + 1.22973i −0.375877 + 0.0476868i
\(666\) 0 0
\(667\) −7.07561 12.2553i −0.273969 0.474528i
\(668\) −3.35499 + 5.81102i −0.129809 + 0.224835i
\(669\) 0 0
\(670\) 10.0037 + 17.3269i 0.386476 + 0.669396i
\(671\) −9.70032 −0.374477
\(672\) 0 0
\(673\) −8.69066 −0.335000 −0.167500 0.985872i \(-0.553569\pi\)
−0.167500 + 0.985872i \(0.553569\pi\)
\(674\) −12.7579 22.0974i −0.491417 0.851160i
\(675\) 0 0
\(676\) −13.9989 + 24.2467i −0.538417 + 0.932566i
\(677\) −15.7303 27.2456i −0.604564 1.04714i −0.992120 0.125289i \(-0.960014\pi\)
0.387557 0.921846i \(-0.373319\pi\)
\(678\) 0 0
\(679\) −8.80221 11.5837i −0.337798 0.444542i
\(680\) 3.20147 0.122771
\(681\) 0 0
\(682\) −5.24943 + 9.09227i −0.201011 + 0.348161i
\(683\) 12.3730 21.4306i 0.473439 0.820021i −0.526098 0.850424i \(-0.676346\pi\)
0.999538 + 0.0304028i \(0.00967902\pi\)
\(684\) 0 0
\(685\) 20.4989 0.783221
\(686\) −14.5325 11.4807i −0.554853 0.438336i
\(687\) 0 0
\(688\) −2.57676 4.46308i −0.0982380 0.170153i
\(689\) 20.4989 35.5051i 0.780944 1.35263i
\(690\) 0 0
\(691\) −12.7771 22.1306i −0.486063 0.841886i 0.513809 0.857905i \(-0.328234\pi\)
−0.999872 + 0.0160188i \(0.994901\pi\)
\(692\) 5.50115 0.209122
\(693\) 0 0
\(694\) 3.05531 0.115978
\(695\) −34.8133 60.2983i −1.32054 2.28725i
\(696\) 0 0
\(697\) −4.12471 + 7.14421i −0.156235 + 0.270606i
\(698\) −2.00368 3.47048i −0.0758404 0.131359i
\(699\) 0 0
\(700\) 5.37529 12.8063i 0.203167 0.484033i
\(701\) 14.1512 0.534484 0.267242 0.963629i \(-0.413888\pi\)
0.267242 + 0.963629i \(0.413888\pi\)
\(702\) 0 0
\(703\) −2.97234 + 5.14825i −0.112104 + 0.194170i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) 0 0
\(706\) −1.09821 −0.0413315
\(707\) −52.3877 + 6.64633i −1.97024 + 0.249961i
\(708\) 0 0
\(709\) 5.37529 + 9.31027i 0.201873 + 0.349655i 0.949132 0.314879i \(-0.101964\pi\)
−0.747259 + 0.664533i \(0.768630\pi\)
\(710\) −8.40294 + 14.5543i −0.315357 + 0.546214i
\(711\) 0 0
\(712\) 9.20147 + 15.9374i 0.344840 + 0.597280i
\(713\) −20.4943 −0.767516
\(714\) 0 0
\(715\) 20.4989 0.766614
\(716\) 0.826185 + 1.43099i 0.0308760 + 0.0534788i
\(717\) 0 0
\(718\) −7.80589 + 13.5202i −0.291313 + 0.504569i
\(719\) 1.37897 + 2.38844i 0.0514268 + 0.0890739i 0.890593 0.454801i \(-0.150290\pi\)
−0.839166 + 0.543875i \(0.816956\pi\)
\(720\) 0 0
\(721\) 0.314401 0.749041i 0.0117089 0.0278958i
\(722\) 17.6694 0.657587
\(723\) 0 0
\(724\) −12.4509 + 21.5656i −0.462734 + 0.801479i
\(725\) 19.0277 32.9569i 0.706669 1.22399i
\(726\) 0 0
\(727\) 14.6141 0.542006 0.271003 0.962578i \(-0.412645\pi\)
0.271003 + 0.962578i \(0.412645\pi\)
\(728\) 10.2494 + 13.4883i 0.379869 + 0.499908i
\(729\) 0 0
\(730\) −3.35499 5.81102i −0.124174 0.215075i
\(731\) 2.57676 4.46308i 0.0953049 0.165073i
\(732\) 0 0
\(733\) −3.55278 6.15360i −0.131225 0.227288i 0.792924 0.609321i \(-0.208558\pi\)
−0.924149 + 0.382032i \(0.875224\pi\)
\(734\) −0.791166 −0.0292025
\(735\) 0 0
\(736\) 1.95205 0.0719534
\(737\) 3.12471 + 5.41216i 0.115100 + 0.199360i
\(738\) 0 0
\(739\) 20.7483 35.9371i 0.763238 1.32197i −0.177936 0.984042i \(-0.556942\pi\)
0.941173 0.337924i \(-0.109725\pi\)
\(740\) −8.24943 14.2884i −0.303255 0.525253i
\(741\) 0 0
\(742\) −10.2494 13.4883i −0.376268 0.495170i
\(743\) 31.9041 1.17045 0.585224 0.810872i \(-0.301007\pi\)
0.585224 + 0.810872i \(0.301007\pi\)
\(744\) 0 0
\(745\) 10.9594 18.9823i 0.401522 0.695456i
\(746\) 7.95573 13.7797i 0.291280 0.504512i
\(747\) 0 0
\(748\) 1.00000 0.0365636
\(749\) 9.27243 22.0910i 0.338807 0.807188i
\(750\) 0 0
\(751\) −6.75794 11.7051i −0.246601 0.427125i 0.715980 0.698121i \(-0.245980\pi\)
−0.962580 + 0.270996i \(0.912647\pi\)
\(752\) −3.02398 + 5.23768i −0.110273 + 0.190999i
\(753\) 0 0
\(754\) 23.2088 + 40.1989i 0.845216 + 1.46396i
\(755\) 47.5542 1.73067
\(756\) 0 0
\(757\) −18.5542 −0.674363 −0.337181 0.941440i \(-0.609474\pi\)
−0.337181 + 0.941440i \(0.609474\pi\)
\(758\) −8.52766 14.7703i −0.309738 0.536483i
\(759\) 0 0
\(760\) 1.84648 3.19820i 0.0669789 0.116011i
\(761\) 7.87529 + 13.6404i 0.285479 + 0.494464i 0.972725 0.231960i \(-0.0745140\pi\)
−0.687246 + 0.726425i \(0.741181\pi\)
\(762\) 0 0
\(763\) 25.4606 3.23013i 0.921734 0.116939i
\(764\) 4.80589 0.173871
\(765\) 0 0
\(766\) −6.72062 + 11.6405i −0.242826 + 0.420587i
\(767\) −36.9977 + 64.0819i −1.33591 + 2.31386i
\(768\) 0 0
\(769\) 41.2854 1.48879 0.744395 0.667739i \(-0.232738\pi\)
0.744395 + 0.667739i \(0.232738\pi\)
\(770\) 3.27823 7.81020i 0.118139 0.281460i
\(771\) 0 0
\(772\) −4.35499 7.54307i −0.156740 0.271481i
\(773\) 2.45458 4.25145i 0.0882850 0.152914i −0.818501 0.574505i \(-0.805195\pi\)
0.906786 + 0.421591i \(0.138528\pi\)
\(774\) 0 0
\(775\) −27.5565 47.7292i −0.989857 1.71448i
\(776\) 5.49885 0.197397
\(777\) 0 0
\(778\) −7.20147 −0.258185
\(779\) 4.75794 + 8.24099i 0.170471 + 0.295264i
\(780\) 0 0
\(781\) −2.62471 + 4.54614i −0.0939196 + 0.162674i
\(782\) 0.976024 + 1.69052i 0.0349025 + 0.0604530i
\(783\) 0 0
\(784\) 6.77823 1.74802i 0.242080 0.0624292i
\(785\) −30.2877 −1.08101
\(786\) 0 0
\(787\) −0.384949 + 0.666751i −0.0137219 + 0.0237671i −0.872805 0.488069i \(-0.837701\pi\)
0.859083 + 0.511836i \(0.171035\pi\)
\(788\) 0.327335 0.566960i 0.0116608 0.0201971i
\(789\) 0 0
\(790\) 17.9424 0.638361
\(791\) 20.0074 + 26.3297i