Properties

Label 1183.2.e.j.508.6
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.6
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.j.170.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0904119 - 0.156598i) q^{2} +(0.913006 - 1.58137i) q^{3} +(0.983651 - 1.70373i) q^{4} +(-1.34332 - 2.32670i) q^{5} -0.330186 q^{6} +(-1.64912 - 2.06892i) q^{7} -0.717383 q^{8} +(-0.167162 - 0.289532i) q^{9} +O(q^{10})\) \(q+(-0.0904119 - 0.156598i) q^{2} +(0.913006 - 1.58137i) q^{3} +(0.983651 - 1.70373i) q^{4} +(-1.34332 - 2.32670i) q^{5} -0.330186 q^{6} +(-1.64912 - 2.06892i) q^{7} -0.717383 q^{8} +(-0.167162 - 0.289532i) q^{9} +(-0.242904 + 0.420723i) q^{10} +(-1.34712 + 2.33328i) q^{11} +(-1.79616 - 3.11104i) q^{12} +(-0.174889 + 0.445303i) q^{14} -4.90584 q^{15} +(-1.90244 - 3.29513i) q^{16} +(-2.38247 + 4.12655i) q^{17} +(-0.0302268 + 0.0523543i) q^{18} +(-0.0942122 - 0.163180i) q^{19} -5.28544 q^{20} +(-4.77738 + 0.718933i) q^{21} +0.487183 q^{22} +(-2.19964 - 3.80989i) q^{23} +(-0.654975 + 1.13445i) q^{24} +(-1.10902 + 1.92088i) q^{25} +4.86756 q^{27} +(-5.14704 + 0.774561i) q^{28} +7.08560 q^{29} +(0.443546 + 0.768245i) q^{30} +(1.84965 - 3.20369i) q^{31} +(-1.06139 + 1.83838i) q^{32} +(2.45986 + 4.26060i) q^{33} +0.861613 q^{34} +(-2.59846 + 6.61622i) q^{35} -0.657715 q^{36} +(-3.97707 - 6.88848i) q^{37} +(-0.0170358 + 0.0295069i) q^{38} +(0.963675 + 1.66913i) q^{40} +5.42958 q^{41} +(0.544516 + 0.683129i) q^{42} -8.01065 q^{43} +(2.65020 + 4.59027i) q^{44} +(-0.449103 + 0.777869i) q^{45} +(-0.397748 + 0.688919i) q^{46} +(0.924445 + 1.60118i) q^{47} -6.94777 q^{48} +(-1.56084 + 6.82377i) q^{49} +0.401075 q^{50} +(4.35041 + 7.53514i) q^{51} +(3.53622 - 6.12491i) q^{53} +(-0.440085 - 0.762250i) q^{54} +7.23846 q^{55} +(1.18305 + 1.48421i) q^{56} -0.344066 q^{57} +(-0.640623 - 1.10959i) q^{58} +(-3.79444 + 6.57216i) q^{59} +(-4.82564 + 8.35825i) q^{60} +(0.205782 + 0.356425i) q^{61} -0.668922 q^{62} +(-0.323350 + 0.823315i) q^{63} -7.22592 q^{64} +(0.444801 - 0.770418i) q^{66} +(-5.70051 + 9.87358i) q^{67} +(4.68703 + 8.11818i) q^{68} -8.03315 q^{69} +(1.27102 - 0.191271i) q^{70} -3.34488 q^{71} +(0.119919 + 0.207705i) q^{72} +(7.10790 - 12.3112i) q^{73} +(-0.719148 + 1.24560i) q^{74} +(2.02509 + 3.50756i) q^{75} -0.370688 q^{76} +(7.04893 - 1.06077i) q^{77} +(-4.55529 - 7.89000i) q^{79} +(-5.11118 + 8.85283i) q^{80} +(4.94560 - 8.56603i) q^{81} +(-0.490899 - 0.850261i) q^{82} +16.5866 q^{83} +(-3.47441 + 8.84657i) q^{84} +12.8017 q^{85} +(0.724258 + 1.25445i) q^{86} +(6.46920 - 11.2050i) q^{87} +(0.966401 - 1.67386i) q^{88} +(2.94582 + 5.10232i) q^{89} +0.162417 q^{90} -8.65473 q^{92} +(-3.37749 - 5.84998i) q^{93} +(0.167162 - 0.289532i) q^{94} +(-0.253115 + 0.438407i) q^{95} +(1.93811 + 3.35691i) q^{96} -0.451094 q^{97} +(1.20971 - 0.372526i) q^{98} +0.900747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} + O(q^{10}) \) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} - 24q^{10} + 2q^{12} + 8q^{14} - 16q^{16} - 34q^{17} + 60q^{22} - 6q^{23} + 10q^{25} + 24q^{27} + 4q^{29} - 22q^{30} - 24q^{35} - 52q^{36} - 38q^{38} - 2q^{40} + 32q^{42} + 44q^{43} - 76q^{48} + 12q^{49} - 8q^{51} - 16q^{53} + 60q^{55} + 54q^{56} + 10q^{61} + 164q^{62} - 4q^{64} - 68q^{66} - 22q^{68} + 28q^{69} - 66q^{74} - 2q^{75} + 38q^{77} - 70q^{79} + 28q^{81} - 10q^{82} + 20q^{87} + 28q^{88} - 132q^{92} + 2q^{94} - 4q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0904119 0.156598i −0.0639308 0.110731i 0.832288 0.554343i \(-0.187030\pi\)
−0.896219 + 0.443611i \(0.853697\pi\)
\(3\) 0.913006 1.58137i 0.527125 0.913006i −0.472376 0.881397i \(-0.656603\pi\)
0.999500 0.0316092i \(-0.0100632\pi\)
\(4\) 0.983651 1.70373i 0.491826 0.851867i
\(5\) −1.34332 2.32670i −0.600751 1.04053i −0.992708 0.120548i \(-0.961535\pi\)
0.391956 0.919984i \(-0.371799\pi\)
\(6\) −0.330186 −0.134798
\(7\) −1.64912 2.06892i −0.623307 0.781977i
\(8\) −0.717383 −0.253633
\(9\) −0.167162 0.289532i −0.0557205 0.0965108i
\(10\) −0.242904 + 0.420723i −0.0768131 + 0.133044i
\(11\) −1.34712 + 2.33328i −0.406172 + 0.703511i −0.994457 0.105143i \(-0.966470\pi\)
0.588285 + 0.808654i \(0.299803\pi\)
\(12\) −1.79616 3.11104i −0.518507 0.898080i
\(13\) 0 0
\(14\) −0.174889 + 0.445303i −0.0467409 + 0.119012i
\(15\) −4.90584 −1.26668
\(16\) −1.90244 3.29513i −0.475611 0.823782i
\(17\) −2.38247 + 4.12655i −0.577833 + 1.00084i 0.417894 + 0.908496i \(0.362768\pi\)
−0.995727 + 0.0923405i \(0.970565\pi\)
\(18\) −0.0302268 + 0.0523543i −0.00712452 + 0.0123400i
\(19\) −0.0942122 0.163180i −0.0216138 0.0374361i 0.855016 0.518601i \(-0.173547\pi\)
−0.876630 + 0.481165i \(0.840214\pi\)
\(20\) −5.28544 −1.18186
\(21\) −4.77738 + 0.718933i −1.04251 + 0.156884i
\(22\) 0.487183 0.103868
\(23\) −2.19964 3.80989i −0.458657 0.794418i 0.540233 0.841516i \(-0.318336\pi\)
−0.998890 + 0.0470977i \(0.985003\pi\)
\(24\) −0.654975 + 1.13445i −0.133696 + 0.231569i
\(25\) −1.10902 + 1.92088i −0.221804 + 0.384177i
\(26\) 0 0
\(27\) 4.86756 0.936762
\(28\) −5.14704 + 0.774561i −0.972699 + 0.146378i
\(29\) 7.08560 1.31576 0.657882 0.753121i \(-0.271453\pi\)
0.657882 + 0.753121i \(0.271453\pi\)
\(30\) 0.443546 + 0.768245i 0.0809801 + 0.140262i
\(31\) 1.84965 3.20369i 0.332207 0.575400i −0.650737 0.759303i \(-0.725540\pi\)
0.982944 + 0.183903i \(0.0588732\pi\)
\(32\) −1.06139 + 1.83838i −0.187629 + 0.324983i
\(33\) 2.45986 + 4.26060i 0.428207 + 0.741676i
\(34\) 0.861613 0.147765
\(35\) −2.59846 + 6.61622i −0.439220 + 1.11834i
\(36\) −0.657715 −0.109619
\(37\) −3.97707 6.88848i −0.653826 1.13246i −0.982187 0.187907i \(-0.939830\pi\)
0.328361 0.944552i \(-0.393504\pi\)
\(38\) −0.0170358 + 0.0295069i −0.00276357 + 0.00478665i
\(39\) 0 0
\(40\) 0.963675 + 1.66913i 0.152370 + 0.263913i
\(41\) 5.42958 0.847958 0.423979 0.905672i \(-0.360633\pi\)
0.423979 + 0.905672i \(0.360633\pi\)
\(42\) 0.544516 + 0.683129i 0.0840206 + 0.105409i
\(43\) −8.01065 −1.22161 −0.610807 0.791780i \(-0.709155\pi\)
−0.610807 + 0.791780i \(0.709155\pi\)
\(44\) 2.65020 + 4.59027i 0.399532 + 0.692010i
\(45\) −0.449103 + 0.777869i −0.0669483 + 0.115958i
\(46\) −0.397748 + 0.688919i −0.0586447 + 0.101576i
\(47\) 0.924445 + 1.60118i 0.134844 + 0.233557i 0.925538 0.378655i \(-0.123613\pi\)
−0.790694 + 0.612212i \(0.790280\pi\)
\(48\) −6.94777 −1.00282
\(49\) −1.56084 + 6.82377i −0.222977 + 0.974824i
\(50\) 0.401075 0.0567206
\(51\) 4.35041 + 7.53514i 0.609180 + 1.05513i
\(52\) 0 0
\(53\) 3.53622 6.12491i 0.485737 0.841321i −0.514128 0.857713i \(-0.671885\pi\)
0.999866 + 0.0163917i \(0.00521788\pi\)
\(54\) −0.440085 0.762250i −0.0598880 0.103729i
\(55\) 7.23846 0.976034
\(56\) 1.18305 + 1.48421i 0.158091 + 0.198335i
\(57\) −0.344066 −0.0455726
\(58\) −0.640623 1.10959i −0.0841179 0.145696i
\(59\) −3.79444 + 6.57216i −0.493994 + 0.855623i −0.999976 0.00692130i \(-0.997797\pi\)
0.505982 + 0.862544i \(0.331130\pi\)
\(60\) −4.82564 + 8.35825i −0.622987 + 1.07905i
\(61\) 0.205782 + 0.356425i 0.0263477 + 0.0456355i 0.878899 0.477009i \(-0.158279\pi\)
−0.852551 + 0.522644i \(0.824946\pi\)
\(62\) −0.668922 −0.0849532
\(63\) −0.323350 + 0.823315i −0.0407382 + 0.103728i
\(64\) −7.22592 −0.903240
\(65\) 0 0
\(66\) 0.444801 0.770418i 0.0547512 0.0948319i
\(67\) −5.70051 + 9.87358i −0.696429 + 1.20625i 0.273268 + 0.961938i \(0.411895\pi\)
−0.969697 + 0.244312i \(0.921438\pi\)
\(68\) 4.68703 + 8.11818i 0.568386 + 0.984474i
\(69\) −8.03315 −0.967078
\(70\) 1.27102 0.191271i 0.151916 0.0228613i
\(71\) −3.34488 −0.396965 −0.198482 0.980104i \(-0.563601\pi\)
−0.198482 + 0.980104i \(0.563601\pi\)
\(72\) 0.119919 + 0.207705i 0.0141326 + 0.0244783i
\(73\) 7.10790 12.3112i 0.831917 1.44092i −0.0645994 0.997911i \(-0.520577\pi\)
0.896516 0.443011i \(-0.146090\pi\)
\(74\) −0.719148 + 1.24560i −0.0835993 + 0.144798i
\(75\) 2.02509 + 3.50756i 0.233837 + 0.405018i
\(76\) −0.370688 −0.0425208
\(77\) 7.04893 1.06077i 0.803300 0.120886i
\(78\) 0 0
\(79\) −4.55529 7.89000i −0.512511 0.887695i −0.999895 0.0145069i \(-0.995382\pi\)
0.487384 0.873188i \(-0.337951\pi\)
\(80\) −5.11118 + 8.85283i −0.571448 + 0.989776i
\(81\) 4.94560 8.56603i 0.549511 0.951781i
\(82\) −0.490899 0.850261i −0.0542107 0.0938956i
\(83\) 16.5866 1.82061 0.910307 0.413934i \(-0.135845\pi\)
0.910307 + 0.413934i \(0.135845\pi\)
\(84\) −3.47441 + 8.84657i −0.379089 + 0.965240i
\(85\) 12.8017 1.38854
\(86\) 0.724258 + 1.25445i 0.0780988 + 0.135271i
\(87\) 6.46920 11.2050i 0.693571 1.20130i
\(88\) 0.966401 1.67386i 0.103019 0.178434i
\(89\) 2.94582 + 5.10232i 0.312257 + 0.540844i 0.978851 0.204577i \(-0.0655818\pi\)
−0.666594 + 0.745421i \(0.732248\pi\)
\(90\) 0.162417 0.0171203
\(91\) 0 0
\(92\) −8.65473 −0.902318
\(93\) −3.37749 5.84998i −0.350229 0.606615i
\(94\) 0.167162 0.289532i 0.0172414 0.0298630i
\(95\) −0.253115 + 0.438407i −0.0259690 + 0.0449796i
\(96\) 1.93811 + 3.35691i 0.197808 + 0.342613i
\(97\) −0.451094 −0.0458016 −0.0229008 0.999738i \(-0.507290\pi\)
−0.0229008 + 0.999738i \(0.507290\pi\)
\(98\) 1.20971 0.372526i 0.122199 0.0376308i
\(99\) 0.900747 0.0905285
\(100\) 2.18178 + 3.77896i 0.218178 + 0.377896i
\(101\) 3.82840 6.63098i 0.380940 0.659807i −0.610257 0.792204i \(-0.708934\pi\)
0.991197 + 0.132396i \(0.0422671\pi\)
\(102\) 0.786658 1.36253i 0.0778908 0.134911i
\(103\) −2.57870 4.46644i −0.254087 0.440091i 0.710560 0.703636i \(-0.248442\pi\)
−0.964647 + 0.263545i \(0.915108\pi\)
\(104\) 0 0
\(105\) 8.09030 + 10.1498i 0.789532 + 0.990517i
\(106\) −1.27887 −0.124214
\(107\) −4.01644 6.95669i −0.388284 0.672528i 0.603935 0.797034i \(-0.293599\pi\)
−0.992219 + 0.124506i \(0.960265\pi\)
\(108\) 4.78798 8.29303i 0.460724 0.797997i
\(109\) −0.666781 + 1.15490i −0.0638660 + 0.110619i −0.896190 0.443670i \(-0.853676\pi\)
0.832324 + 0.554289i \(0.187010\pi\)
\(110\) −0.654443 1.13353i −0.0623987 0.108078i
\(111\) −14.5243 −1.37859
\(112\) −3.68000 + 9.37004i −0.347727 + 0.885386i
\(113\) −19.9383 −1.87564 −0.937821 0.347119i \(-0.887160\pi\)
−0.937821 + 0.347119i \(0.887160\pi\)
\(114\) 0.0311076 + 0.0538800i 0.00291349 + 0.00504632i
\(115\) −5.90965 + 10.2358i −0.551078 + 0.954495i
\(116\) 6.96976 12.0720i 0.647126 1.12086i
\(117\) 0 0
\(118\) 1.37225 0.126326
\(119\) 12.4665 1.87604i 1.14280 0.171976i
\(120\) 3.51937 0.321273
\(121\) 1.87053 + 3.23985i 0.170048 + 0.294532i
\(122\) 0.0372103 0.0644501i 0.00336886 0.00583503i
\(123\) 4.95724 8.58619i 0.446979 0.774191i
\(124\) −3.63883 6.30263i −0.326776 0.565993i
\(125\) −7.47412 −0.668505
\(126\) 0.158164 0.0238016i 0.0140904 0.00212042i
\(127\) −7.96722 −0.706976 −0.353488 0.935439i \(-0.615005\pi\)
−0.353488 + 0.935439i \(0.615005\pi\)
\(128\) 2.77609 + 4.80833i 0.245374 + 0.425000i
\(129\) −7.31378 + 12.6678i −0.643942 + 1.11534i
\(130\) 0 0
\(131\) −5.00897 8.67579i −0.437636 0.758007i 0.559871 0.828580i \(-0.310851\pi\)
−0.997507 + 0.0705727i \(0.977517\pi\)
\(132\) 9.67858 0.842412
\(133\) −0.182240 + 0.464021i −0.0158022 + 0.0402357i
\(134\) 2.06158 0.178093
\(135\) −6.53870 11.3254i −0.562761 0.974731i
\(136\) 1.70914 2.96032i 0.146558 0.253845i
\(137\) 2.53348 4.38811i 0.216450 0.374902i −0.737270 0.675598i \(-0.763886\pi\)
0.953720 + 0.300696i \(0.0972189\pi\)
\(138\) 0.726293 + 1.25798i 0.0618261 + 0.107086i
\(139\) 7.72578 0.655292 0.327646 0.944800i \(-0.393745\pi\)
0.327646 + 0.944800i \(0.393745\pi\)
\(140\) 8.71630 + 10.9351i 0.736662 + 0.924187i
\(141\) 3.37610 0.284319
\(142\) 0.302417 + 0.523802i 0.0253783 + 0.0439565i
\(143\) 0 0
\(144\) −0.636031 + 1.10164i −0.0530025 + 0.0918031i
\(145\) −9.51824 16.4861i −0.790447 1.36909i
\(146\) −2.57055 −0.212741
\(147\) 9.36587 + 8.69841i 0.772484 + 0.717433i
\(148\) −15.6482 −1.28627
\(149\) −7.15924 12.4002i −0.586507 1.01586i −0.994686 0.102958i \(-0.967169\pi\)
0.408178 0.912902i \(-0.366164\pi\)
\(150\) 0.366184 0.634250i 0.0298988 0.0517863i
\(151\) 3.23624 5.60534i 0.263362 0.456156i −0.703771 0.710427i \(-0.748502\pi\)
0.967133 + 0.254271i \(0.0818354\pi\)
\(152\) 0.0675862 + 0.117063i 0.00548197 + 0.00949504i
\(153\) 1.59303 0.128789
\(154\) −0.803421 1.00794i −0.0647415 0.0812222i
\(155\) −9.93871 −0.798296
\(156\) 0 0
\(157\) −7.95937 + 13.7860i −0.635227 + 1.10025i 0.351240 + 0.936285i \(0.385760\pi\)
−0.986467 + 0.163960i \(0.947573\pi\)
\(158\) −0.823705 + 1.42670i −0.0655305 + 0.113502i
\(159\) −6.45718 11.1842i −0.512088 0.886962i
\(160\) 5.70315 0.450873
\(161\) −4.25489 + 10.8338i −0.335332 + 0.853826i
\(162\) −1.78856 −0.140523
\(163\) −2.39081 4.14100i −0.187263 0.324348i 0.757074 0.653329i \(-0.226628\pi\)
−0.944337 + 0.328981i \(0.893295\pi\)
\(164\) 5.34081 9.25056i 0.417048 0.722348i
\(165\) 6.60876 11.4467i 0.514492 0.891126i
\(166\) −1.49962 2.59743i −0.116393 0.201599i
\(167\) 2.71042 0.209739 0.104869 0.994486i \(-0.466558\pi\)
0.104869 + 0.994486i \(0.466558\pi\)
\(168\) 3.42721 0.515750i 0.264415 0.0397910i
\(169\) 0 0
\(170\) −1.15742 2.00472i −0.0887703 0.153755i
\(171\) −0.0314973 + 0.0545550i −0.00240866 + 0.00417192i
\(172\) −7.87969 + 13.6480i −0.600821 + 1.04065i
\(173\) 0.449908 + 0.779264i 0.0342059 + 0.0592463i 0.882622 0.470084i \(-0.155776\pi\)
−0.848416 + 0.529331i \(0.822443\pi\)
\(174\) −2.33957 −0.177362
\(175\) 5.80305 0.873282i 0.438670 0.0660139i
\(176\) 10.2513 0.772720
\(177\) 6.92870 + 12.0009i 0.520793 + 0.902039i
\(178\) 0.532675 0.922620i 0.0399257 0.0691533i
\(179\) 5.52791 9.57462i 0.413175 0.715641i −0.582060 0.813146i \(-0.697753\pi\)
0.995235 + 0.0975054i \(0.0310863\pi\)
\(180\) 0.883522 + 1.53030i 0.0658538 + 0.114062i
\(181\) 3.52898 0.262307 0.131153 0.991362i \(-0.458132\pi\)
0.131153 + 0.991362i \(0.458132\pi\)
\(182\) 0 0
\(183\) 0.751521 0.0555540
\(184\) 1.57799 + 2.73315i 0.116331 + 0.201491i
\(185\) −10.6850 + 18.5069i −0.785573 + 1.36065i
\(186\) −0.610730 + 1.05782i −0.0447809 + 0.0775628i
\(187\) −6.41894 11.1179i −0.469400 0.813024i
\(188\) 3.63732 0.265279
\(189\) −8.02717 10.0706i −0.583891 0.732527i
\(190\) 0.0915382 0.00664088
\(191\) 10.2002 + 17.6672i 0.738059 + 1.27836i 0.953368 + 0.301810i \(0.0975909\pi\)
−0.215309 + 0.976546i \(0.569076\pi\)
\(192\) −6.59731 + 11.4269i −0.476120 + 0.824664i
\(193\) 8.63228 14.9515i 0.621365 1.07624i −0.367867 0.929878i \(-0.619912\pi\)
0.989232 0.146357i \(-0.0467549\pi\)
\(194\) 0.0407842 + 0.0706403i 0.00292814 + 0.00507168i
\(195\) 0 0
\(196\) 10.0906 + 9.37146i 0.720755 + 0.669390i
\(197\) −4.95672 −0.353152 −0.176576 0.984287i \(-0.556502\pi\)
−0.176576 + 0.984287i \(0.556502\pi\)
\(198\) −0.0814383 0.141055i −0.00578757 0.0100244i
\(199\) −3.59097 + 6.21975i −0.254557 + 0.440906i −0.964775 0.263076i \(-0.915263\pi\)
0.710218 + 0.703982i \(0.248596\pi\)
\(200\) 0.795593 1.37801i 0.0562569 0.0974399i
\(201\) 10.4092 + 18.0293i 0.734209 + 1.27169i
\(202\) −1.38453 −0.0974153
\(203\) −11.6850 14.6595i −0.820125 1.02890i
\(204\) 17.1172 1.19844
\(205\) −7.29367 12.6330i −0.509412 0.882327i
\(206\) −0.466290 + 0.807638i −0.0324880 + 0.0562708i
\(207\) −0.735392 + 1.27374i −0.0511132 + 0.0885307i
\(208\) 0 0
\(209\) 0.507661 0.0351157
\(210\) 0.857976 2.18459i 0.0592060 0.150751i
\(211\) −17.5927 −1.21113 −0.605566 0.795795i \(-0.707053\pi\)
−0.605566 + 0.795795i \(0.707053\pi\)
\(212\) −6.95682 12.0496i −0.477796 0.827567i
\(213\) −3.05390 + 5.28951i −0.209250 + 0.362431i
\(214\) −0.726269 + 1.25793i −0.0496467 + 0.0859906i
\(215\) 10.7609 + 18.6384i 0.733886 + 1.27113i
\(216\) −3.49190 −0.237594
\(217\) −9.67847 + 1.45648i −0.657017 + 0.0988723i
\(218\) 0.241140 0.0163320
\(219\) −12.9791 22.4805i −0.877048 1.51909i
\(220\) 7.12013 12.3324i 0.480039 0.831452i
\(221\) 0 0
\(222\) 1.31317 + 2.27448i 0.0881344 + 0.152653i
\(223\) 14.1054 0.944569 0.472284 0.881446i \(-0.343430\pi\)
0.472284 + 0.881446i \(0.343430\pi\)
\(224\) 5.55381 0.835775i 0.371080 0.0558425i
\(225\) 0.741543 0.0494362
\(226\) 1.80266 + 3.12230i 0.119911 + 0.207693i
\(227\) −1.43439 + 2.48443i −0.0952035 + 0.164897i −0.909694 0.415280i \(-0.863684\pi\)
0.814490 + 0.580178i \(0.197017\pi\)
\(228\) −0.338441 + 0.586196i −0.0224138 + 0.0388218i
\(229\) −4.38706 7.59860i −0.289905 0.502130i 0.683882 0.729593i \(-0.260290\pi\)
−0.973787 + 0.227463i \(0.926957\pi\)
\(230\) 2.13721 0.140924
\(231\) 4.75824 12.1155i 0.313069 0.797140i
\(232\) −5.08309 −0.333721
\(233\) −2.55371 4.42316i −0.167299 0.289771i 0.770170 0.637839i \(-0.220171\pi\)
−0.937469 + 0.348068i \(0.886838\pi\)
\(234\) 0 0
\(235\) 2.48365 4.30181i 0.162016 0.280619i
\(236\) 7.46481 + 12.9294i 0.485918 + 0.841634i
\(237\) −16.6361 −1.08063
\(238\) −1.42090 1.78261i −0.0921032 0.115549i
\(239\) 2.49797 0.161580 0.0807901 0.996731i \(-0.474256\pi\)
0.0807901 + 0.996731i \(0.474256\pi\)
\(240\) 9.33309 + 16.1654i 0.602448 + 1.04347i
\(241\) 3.99256 6.91532i 0.257183 0.445455i −0.708303 0.705909i \(-0.750539\pi\)
0.965486 + 0.260454i \(0.0838722\pi\)
\(242\) 0.338236 0.585842i 0.0217426 0.0376593i
\(243\) −1.72939 2.99538i −0.110940 0.192154i
\(244\) 0.809671 0.0518339
\(245\) 17.9736 5.53491i 1.14829 0.353612i
\(246\) −1.79277 −0.114303
\(247\) 0 0
\(248\) −1.32691 + 2.29827i −0.0842588 + 0.145941i
\(249\) 15.1437 26.2296i 0.959690 1.66223i
\(250\) 0.675749 + 1.17043i 0.0427381 + 0.0740246i
\(251\) 25.2570 1.59421 0.797105 0.603841i \(-0.206364\pi\)
0.797105 + 0.603841i \(0.206364\pi\)
\(252\) 1.08465 + 1.36076i 0.0683264 + 0.0857196i
\(253\) 11.8527 0.745176
\(254\) 0.720331 + 1.24765i 0.0451976 + 0.0782845i
\(255\) 11.6880 20.2442i 0.731931 1.26774i
\(256\) −6.72394 + 11.6462i −0.420246 + 0.727888i
\(257\) 1.68682 + 2.92165i 0.105221 + 0.182248i 0.913828 0.406101i \(-0.133112\pi\)
−0.808608 + 0.588348i \(0.799778\pi\)
\(258\) 2.64501 0.164671
\(259\) −7.69305 + 19.5881i −0.478023 + 1.21715i
\(260\) 0 0
\(261\) −1.18444 2.05151i −0.0733150 0.126985i
\(262\) −0.905740 + 1.56879i −0.0559568 + 0.0969201i
\(263\) 0.0794677 0.137642i 0.00490019 0.00848737i −0.863565 0.504238i \(-0.831774\pi\)
0.868465 + 0.495750i \(0.165107\pi\)
\(264\) −1.76466 3.05648i −0.108607 0.188114i
\(265\) −19.0011 −1.16723
\(266\) 0.0891413 0.0134146i 0.00546561 0.000822501i
\(267\) 10.7582 0.658392
\(268\) 11.2146 + 19.4243i 0.685043 + 1.18653i
\(269\) 11.6633 20.2014i 0.711124 1.23170i −0.253311 0.967385i \(-0.581520\pi\)
0.964435 0.264318i \(-0.0851470\pi\)
\(270\) −1.18235 + 2.04789i −0.0719556 + 0.124631i
\(271\) −5.91049 10.2373i −0.359037 0.621870i 0.628763 0.777597i \(-0.283561\pi\)
−0.987800 + 0.155727i \(0.950228\pi\)
\(272\) 18.1300 1.09929
\(273\) 0 0
\(274\) −0.916226 −0.0553513
\(275\) −2.98797 5.17532i −0.180182 0.312084i
\(276\) −7.90182 + 13.6864i −0.475634 + 0.823822i
\(277\) 13.6827 23.6991i 0.822111 1.42394i −0.0819961 0.996633i \(-0.526130\pi\)
0.904107 0.427306i \(-0.140537\pi\)
\(278\) −0.698503 1.20984i −0.0418934 0.0725615i
\(279\) −1.23676 −0.0740431
\(280\) 1.86409 4.74636i 0.111401 0.283649i
\(281\) 28.5383 1.70245 0.851225 0.524801i \(-0.175860\pi\)
0.851225 + 0.524801i \(0.175860\pi\)
\(282\) −0.305239 0.528690i −0.0181767 0.0314830i
\(283\) −8.98604 + 15.5643i −0.534165 + 0.925201i 0.465038 + 0.885290i \(0.346040\pi\)
−0.999203 + 0.0399101i \(0.987293\pi\)
\(284\) −3.29020 + 5.69879i −0.195237 + 0.338161i
\(285\) 0.462190 + 0.800537i 0.0273778 + 0.0474197i
\(286\) 0 0
\(287\) −8.95400 11.2334i −0.528538 0.663084i
\(288\) 0.709694 0.0418191
\(289\) −2.85229 4.94032i −0.167782 0.290607i
\(290\) −1.72112 + 2.98107i −0.101068 + 0.175055i
\(291\) −0.411851 + 0.713347i −0.0241432 + 0.0418172i
\(292\) −13.9834 24.2199i −0.818316 1.41737i
\(293\) 14.8891 0.869828 0.434914 0.900472i \(-0.356779\pi\)
0.434914 + 0.900472i \(0.356779\pi\)
\(294\) 0.515367 2.25312i 0.0300568 0.131404i
\(295\) 20.3886 1.18707
\(296\) 2.85308 + 4.94168i 0.165832 + 0.287229i
\(297\) −6.55719 + 11.3574i −0.380487 + 0.659023i
\(298\) −1.29456 + 2.24224i −0.0749918 + 0.129890i
\(299\) 0 0
\(300\) 7.96793 0.460028
\(301\) 13.2105 + 16.5734i 0.761440 + 0.955274i
\(302\) −1.17038 −0.0673478
\(303\) −6.99071 12.1083i −0.401606 0.695601i
\(304\) −0.358467 + 0.620883i −0.0205595 + 0.0356101i
\(305\) 0.552862 0.957586i 0.0316568 0.0548312i
\(306\) −0.144029 0.249465i −0.00823356 0.0142610i
\(307\) −23.5161 −1.34214 −0.671068 0.741396i \(-0.734164\pi\)
−0.671068 + 0.741396i \(0.734164\pi\)
\(308\) 5.12642 13.0529i 0.292105 0.743759i
\(309\) −9.41747 −0.535741
\(310\) 0.898577 + 1.55638i 0.0510358 + 0.0883965i
\(311\) −0.815450 + 1.41240i −0.0462399 + 0.0800899i −0.888219 0.459420i \(-0.848057\pi\)
0.841979 + 0.539510i \(0.181391\pi\)
\(312\) 0 0
\(313\) 0.348367 + 0.603389i 0.0196909 + 0.0341056i 0.875703 0.482850i \(-0.160398\pi\)
−0.856012 + 0.516956i \(0.827065\pi\)
\(314\) 2.87849 0.162442
\(315\) 2.34997 0.353639i 0.132406 0.0199253i
\(316\) −17.9233 −1.00826
\(317\) 10.7144 + 18.5579i 0.601780 + 1.04231i 0.992551 + 0.121826i \(0.0388751\pi\)
−0.390771 + 0.920488i \(0.627792\pi\)
\(318\) −1.16761 + 2.02236i −0.0654764 + 0.113409i
\(319\) −9.54517 + 16.5327i −0.534427 + 0.925654i
\(320\) 9.70673 + 16.8126i 0.542623 + 0.939850i
\(321\) −14.6682 −0.818697
\(322\) 2.08125 0.313200i 0.115983 0.0174540i
\(323\) 0.897830 0.0499566
\(324\) −9.72949 16.8520i −0.540527 0.936221i
\(325\) 0 0
\(326\) −0.432315 + 0.748792i −0.0239437 + 0.0414717i
\(327\) 1.21755 + 2.10886i 0.0673307 + 0.116620i
\(328\) −3.89509 −0.215070
\(329\) 1.78820 4.55314i 0.0985868 0.251023i
\(330\) −2.39004 −0.131568
\(331\) 0.760232 + 1.31676i 0.0417861 + 0.0723757i 0.886162 0.463375i \(-0.153362\pi\)
−0.844376 + 0.535751i \(0.820029\pi\)
\(332\) 16.3154 28.2591i 0.895425 1.55092i
\(333\) −1.32962 + 2.30298i −0.0728630 + 0.126202i
\(334\) −0.245054 0.424446i −0.0134088 0.0232247i
\(335\) 30.6305 1.67352
\(336\) 11.4577 + 14.3744i 0.625067 + 0.784186i
\(337\) 32.2304 1.75570 0.877850 0.478936i \(-0.158977\pi\)
0.877850 + 0.478936i \(0.158977\pi\)
\(338\) 0 0
\(339\) −18.2038 + 31.5300i −0.988697 + 1.71247i
\(340\) 12.5924 21.8106i 0.682918 1.18285i
\(341\) 4.98341 + 8.63153i 0.269867 + 0.467423i
\(342\) 0.0113909 0.000615951
\(343\) 16.6918 8.02394i 0.901273 0.433252i
\(344\) 5.74670 0.309841
\(345\) 10.7911 + 18.6907i 0.580974 + 1.00628i
\(346\) 0.0813541 0.140909i 0.00437362 0.00757534i
\(347\) −4.09215 + 7.08782i −0.219678 + 0.380494i −0.954710 0.297539i \(-0.903834\pi\)
0.735031 + 0.678033i \(0.237167\pi\)
\(348\) −12.7269 22.0436i −0.682232 1.18166i
\(349\) 21.8493 1.16956 0.584782 0.811190i \(-0.301180\pi\)
0.584782 + 0.811190i \(0.301180\pi\)
\(350\) −0.661419 0.829791i −0.0353543 0.0443542i
\(351\) 0 0
\(352\) −2.85964 4.95304i −0.152419 0.263998i
\(353\) −0.283590 + 0.491192i −0.0150940 + 0.0261435i −0.873474 0.486871i \(-0.838138\pi\)
0.858380 + 0.513015i \(0.171471\pi\)
\(354\) 1.25287 2.17004i 0.0665894 0.115336i
\(355\) 4.49325 + 7.78254i 0.238477 + 0.413054i
\(356\) 11.5907 0.614303
\(357\) 8.41524 21.4270i 0.445382 1.13404i
\(358\) −1.99915 −0.105659
\(359\) 16.2022 + 28.0630i 0.855118 + 1.48111i 0.876536 + 0.481336i \(0.159848\pi\)
−0.0214184 + 0.999771i \(0.506818\pi\)
\(360\) 0.322179 0.558030i 0.0169803 0.0294108i
\(361\) 9.48225 16.4237i 0.499066 0.864407i
\(362\) −0.319061 0.552631i −0.0167695 0.0290456i
\(363\) 6.83122 0.358546
\(364\) 0 0
\(365\) −38.1928 −1.99910
\(366\) −0.0679464 0.117687i −0.00355162 0.00615158i
\(367\) 3.93444 6.81465i 0.205376 0.355722i −0.744876 0.667202i \(-0.767492\pi\)
0.950252 + 0.311481i \(0.100825\pi\)
\(368\) −8.36939 + 14.4962i −0.436285 + 0.755667i
\(369\) −0.907617 1.57204i −0.0472487 0.0818371i
\(370\) 3.86419 0.200889
\(371\) −18.5036 + 2.78454i −0.960658 + 0.144566i
\(372\) −13.2891 −0.689007
\(373\) 1.04581 + 1.81140i 0.0541502 + 0.0937909i 0.891830 0.452371i \(-0.149422\pi\)
−0.837680 + 0.546162i \(0.816088\pi\)
\(374\) −1.16070 + 2.01039i −0.0600182 + 0.103955i
\(375\) −6.82392 + 11.8194i −0.352386 + 0.610350i
\(376\) −0.663180 1.14866i −0.0342009 0.0592377i
\(377\) 0 0
\(378\) −0.851281 + 2.16754i −0.0437852 + 0.111486i
\(379\) 14.3163 0.735381 0.367691 0.929948i \(-0.380149\pi\)
0.367691 + 0.929948i \(0.380149\pi\)
\(380\) 0.497953 + 0.862480i 0.0255444 + 0.0442443i
\(381\) −7.27412 + 12.5991i −0.372665 + 0.645474i
\(382\) 1.84444 3.19466i 0.0943695 0.163453i
\(383\) −12.5937 21.8129i −0.643507 1.11459i −0.984644 0.174573i \(-0.944146\pi\)
0.341138 0.940013i \(-0.389188\pi\)
\(384\) 10.1383 0.517370
\(385\) −11.9371 14.9758i −0.608369 0.763237i
\(386\) −3.12184 −0.158898
\(387\) 1.33907 + 2.31934i 0.0680689 + 0.117899i
\(388\) −0.443719 + 0.768544i −0.0225264 + 0.0390169i
\(389\) −14.0512 + 24.3373i −0.712422 + 1.23395i 0.251524 + 0.967851i \(0.419068\pi\)
−0.963946 + 0.266099i \(0.914265\pi\)
\(390\) 0 0
\(391\) 20.9623 1.06011
\(392\) 1.11972 4.89525i 0.0565543 0.247248i
\(393\) −18.2929 −0.922754
\(394\) 0.448146 + 0.776212i 0.0225773 + 0.0391050i
\(395\) −12.2384 + 21.1976i −0.615783 + 1.06657i
\(396\) 0.886021 1.53463i 0.0445243 0.0771183i
\(397\) −10.8882 18.8590i −0.546465 0.946504i −0.998513 0.0545111i \(-0.982640\pi\)
0.452049 0.891993i \(-0.350693\pi\)
\(398\) 1.29867 0.0650963
\(399\) 0.567404 + 0.711843i 0.0284057 + 0.0356367i
\(400\) 8.43941 0.421970
\(401\) 10.2645 + 17.7786i 0.512584 + 0.887821i 0.999894 + 0.0145918i \(0.00464489\pi\)
−0.487310 + 0.873229i \(0.662022\pi\)
\(402\) 1.88223 3.26012i 0.0938772 0.162600i
\(403\) 0 0
\(404\) −7.53162 13.0451i −0.374712 0.649020i
\(405\) −26.5741 −1.32048
\(406\) −1.23919 + 3.15524i −0.0615000 + 0.156592i
\(407\) 21.4304 1.06226
\(408\) −3.12091 5.40558i −0.154508 0.267616i
\(409\) −3.13431 + 5.42879i −0.154982 + 0.268436i −0.933052 0.359741i \(-0.882865\pi\)
0.778071 + 0.628177i \(0.216199\pi\)
\(410\) −1.31887 + 2.28435i −0.0651343 + 0.112816i
\(411\) −4.62616 8.01275i −0.228192 0.395240i
\(412\) −10.1462 −0.499865
\(413\) 19.8547 2.98787i 0.976987 0.147024i
\(414\) 0.265953 0.0130709
\(415\) −22.2811 38.5920i −1.09374 1.89441i
\(416\) 0 0
\(417\) 7.05369 12.2174i 0.345421 0.598286i
\(418\) −0.0458986 0.0794987i −0.00224497 0.00388841i
\(419\) 34.1635 1.66899 0.834497 0.551013i \(-0.185758\pi\)
0.834497 + 0.551013i \(0.185758\pi\)
\(420\) 25.2506 3.79987i 1.23210 0.185415i
\(421\) 11.5233 0.561613 0.280806 0.959764i \(-0.409398\pi\)
0.280806 + 0.959764i \(0.409398\pi\)
\(422\) 1.59059 + 2.75498i 0.0774288 + 0.134111i
\(423\) 0.309063 0.535313i 0.0150272 0.0260278i
\(424\) −2.53682 + 4.39391i −0.123199 + 0.213387i
\(425\) −5.28442 9.15288i −0.256332 0.443980i
\(426\) 1.10444 0.0535101
\(427\) 0.398055 1.01353i 0.0192632 0.0490482i
\(428\) −15.8031 −0.763873
\(429\) 0 0
\(430\) 1.94582 3.37026i 0.0938359 0.162529i
\(431\) −4.38500 + 7.59505i −0.211218 + 0.365841i −0.952096 0.305799i \(-0.901076\pi\)
0.740878 + 0.671640i \(0.234410\pi\)
\(432\) −9.26026 16.0392i −0.445534 0.771688i
\(433\) 22.1069 1.06239 0.531196 0.847249i \(-0.321743\pi\)
0.531196 + 0.847249i \(0.321743\pi\)
\(434\) 1.10313 + 1.38394i 0.0529519 + 0.0664315i
\(435\) −34.7609 −1.66666
\(436\) 1.31176 + 2.27203i 0.0628219 + 0.108811i
\(437\) −0.414467 + 0.717877i −0.0198266 + 0.0343407i
\(438\) −2.34693 + 4.06501i −0.112141 + 0.194234i
\(439\) 5.18547 + 8.98150i 0.247489 + 0.428664i 0.962828 0.270114i \(-0.0870612\pi\)
−0.715339 + 0.698777i \(0.753728\pi\)
\(440\) −5.19275 −0.247555
\(441\) 2.23661 0.688759i 0.106505 0.0327980i
\(442\) 0 0
\(443\) −17.9068 31.0156i −0.850780 1.47359i −0.880506 0.474036i \(-0.842797\pi\)
0.0297257 0.999558i \(-0.490537\pi\)
\(444\) −14.2869 + 24.7456i −0.678026 + 1.17438i
\(445\) 7.91437 13.7081i 0.375177 0.649826i
\(446\) −1.27530 2.20888i −0.0603871 0.104593i
\(447\) −26.1457 −1.23665
\(448\) 11.9164 + 14.9498i 0.562996 + 0.706313i
\(449\) −22.7502 −1.07365 −0.536825 0.843693i \(-0.680377\pi\)
−0.536825 + 0.843693i \(0.680377\pi\)
\(450\) −0.0670443 0.116124i −0.00316050 0.00547415i
\(451\) −7.31430 + 12.6687i −0.344417 + 0.596548i
\(452\) −19.6124 + 33.9696i −0.922489 + 1.59780i
\(453\) −5.90942 10.2354i −0.277649 0.480902i
\(454\) 0.518742 0.0243458
\(455\) 0 0
\(456\) 0.246827 0.0115587
\(457\) −15.6586 27.1215i −0.732478 1.26869i −0.955821 0.293949i \(-0.905031\pi\)
0.223344 0.974740i \(-0.428303\pi\)
\(458\) −0.793284 + 1.37401i −0.0370677 + 0.0642032i
\(459\) −11.5968 + 20.0862i −0.541292 + 0.937546i
\(460\) 11.6261 + 20.1370i 0.542069 + 0.938891i
\(461\) 8.40753 0.391578 0.195789 0.980646i \(-0.437273\pi\)
0.195789 + 0.980646i \(0.437273\pi\)
\(462\) −2.32746 + 0.350252i −0.108283 + 0.0162952i
\(463\) 10.0392 0.466563 0.233281 0.972409i \(-0.425054\pi\)
0.233281 + 0.972409i \(0.425054\pi\)
\(464\) −13.4800 23.3480i −0.625791 1.08390i
\(465\) −9.07411 + 15.7168i −0.420802 + 0.728850i
\(466\) −0.461772 + 0.799813i −0.0213912 + 0.0370506i
\(467\) 13.1756 + 22.8209i 0.609696 + 1.05602i 0.991290 + 0.131695i \(0.0420418\pi\)
−0.381594 + 0.924330i \(0.624625\pi\)
\(468\) 0 0
\(469\) 29.8284 4.48878i 1.37735 0.207273i
\(470\) −0.898206 −0.0414312
\(471\) 14.5339 + 25.1735i 0.669687 + 1.15993i
\(472\) 2.72206 4.71475i 0.125293 0.217014i
\(473\) 10.7913 18.6911i 0.496185 0.859418i
\(474\) 1.50410 + 2.60517i 0.0690855 + 0.119660i
\(475\) 0.417934 0.0191761
\(476\) 9.06638 23.0849i 0.415557 1.05809i
\(477\) −2.36448 −0.108262
\(478\) −0.225846 0.391177i −0.0103300 0.0178920i
\(479\) 4.29207 7.43409i 0.196110 0.339672i −0.751154 0.660127i \(-0.770502\pi\)
0.947264 + 0.320455i \(0.103836\pi\)
\(480\) 5.20701 9.01880i 0.237666 0.411650i
\(481\) 0 0
\(482\) −1.44390 −0.0657678
\(483\) 13.2476 + 16.6199i 0.602787 + 0.756233i
\(484\) 7.35979 0.334536
\(485\) 0.605963 + 1.04956i 0.0275154 + 0.0476580i
\(486\) −0.312714 + 0.541637i −0.0141850 + 0.0245691i
\(487\) −10.6281 + 18.4084i −0.481606 + 0.834166i −0.999777 0.0211110i \(-0.993280\pi\)
0.518171 + 0.855277i \(0.326613\pi\)
\(488\) −0.147624 0.255693i −0.00668264 0.0115747i
\(489\) −8.73130 −0.394843
\(490\) −2.49178 2.31420i −0.112567 0.104545i
\(491\) −22.4535 −1.01331 −0.506657 0.862148i \(-0.669119\pi\)
−0.506657 + 0.862148i \(0.669119\pi\)
\(492\) −9.75240 16.8916i −0.439672 0.761534i
\(493\) −16.8812 + 29.2391i −0.760292 + 1.31686i
\(494\) 0 0
\(495\) −1.20999 2.09577i −0.0543851 0.0941978i
\(496\) −14.0754 −0.632006
\(497\) 5.51610 + 6.92029i 0.247431 + 0.310417i
\(498\) −5.47667 −0.245415
\(499\) −19.4390 33.6694i −0.870210 1.50725i −0.861779 0.507284i \(-0.830650\pi\)
−0.00843082 0.999964i \(-0.502684\pi\)
\(500\) −7.35193 + 12.7339i −0.328788 + 0.569478i
\(501\) 2.47463 4.28619i 0.110558 0.191493i
\(502\) −2.28354 3.95520i −0.101919 0.176529i
\(503\) 5.45701 0.243316 0.121658 0.992572i \(-0.461179\pi\)
0.121658 + 0.992572i \(0.461179\pi\)
\(504\) 0.231965 0.590632i 0.0103326 0.0263088i
\(505\) −20.5711 −0.915401
\(506\) −1.07163 1.85612i −0.0476397 0.0825144i
\(507\) 0 0
\(508\) −7.83697 + 13.5740i −0.347709 + 0.602250i
\(509\) 5.44623 + 9.43315i 0.241400 + 0.418117i 0.961113 0.276154i \(-0.0890601\pi\)
−0.719713 + 0.694271i \(0.755727\pi\)
\(510\) −4.22694 −0.187172
\(511\) −37.1927 + 5.59701i −1.64531 + 0.247597i
\(512\) 13.5360 0.598214
\(513\) −0.458584 0.794290i −0.0202470 0.0350688i
\(514\) 0.305017 0.528304i 0.0134537 0.0233025i
\(515\) −6.92804 + 11.9997i −0.305286 + 0.528771i
\(516\) 14.3884 + 24.9215i 0.633415 + 1.09711i
\(517\) −4.98136 −0.219080
\(518\) 3.76300 0.566282i 0.165337 0.0248810i
\(519\) 1.64308 0.0721230
\(520\) 0 0
\(521\) −13.9480 + 24.1587i −0.611074 + 1.05841i 0.379985 + 0.924993i \(0.375929\pi\)
−0.991060 + 0.133419i \(0.957404\pi\)
\(522\) −0.214175 + 0.370962i −0.00937418 + 0.0162366i
\(523\) −8.36180 14.4831i −0.365636 0.633300i 0.623242 0.782029i \(-0.285815\pi\)
−0.988878 + 0.148729i \(0.952482\pi\)
\(524\) −19.7083 −0.860962
\(525\) 3.91724 9.97411i 0.170962 0.435306i
\(526\) −0.0287393 −0.00125309
\(527\) 8.81347 + 15.2654i 0.383921 + 0.664970i
\(528\) 9.35949 16.2111i 0.407319 0.705498i
\(529\) 1.82314 3.15777i 0.0792668 0.137294i
\(530\) 1.71793 + 2.97554i 0.0746219 + 0.129249i
\(531\) 2.53714 0.110102
\(532\) 0.611307 + 0.766923i 0.0265035 + 0.0332503i
\(533\) 0 0
\(534\) −0.972671 1.68472i −0.0420916 0.0729048i
\(535\) −10.7907 + 18.6901i −0.466525 + 0.808045i
\(536\) 4.08945 7.08313i 0.176637 0.305945i
\(537\) −10.0940 17.4834i −0.435590 0.754464i
\(538\) −4.21800 −0.181851
\(539\) −13.8191 12.8343i −0.595232 0.552813i
\(540\) −25.7272 −1.10712
\(541\) −5.58025 9.66528i −0.239914 0.415543i 0.720776 0.693169i \(-0.243786\pi\)
−0.960689 + 0.277626i \(0.910453\pi\)
\(542\) −1.06876 + 1.85114i −0.0459070 + 0.0795133i
\(543\) 3.22198 5.58063i 0.138268 0.239488i
\(544\) −5.05745 8.75976i −0.216836 0.375572i
\(545\) 3.58280 0.153470
\(546\) 0 0
\(547\) 36.6556 1.56728 0.783640 0.621215i \(-0.213361\pi\)
0.783640 + 0.621215i \(0.213361\pi\)
\(548\) −4.98412 8.63275i −0.212911 0.368773i
\(549\) 0.0687976 0.119161i 0.00293621 0.00508567i
\(550\) −0.540297 + 0.935821i −0.0230383 + 0.0399036i
\(551\) −0.667551 1.15623i −0.0284386 0.0492571i
\(552\) 5.76285 0.245283
\(553\) −8.81155 + 22.4361i −0.374705 + 0.954078i
\(554\) −4.94830 −0.210233
\(555\) 19.5109 + 33.7938i 0.828190 + 1.43447i
\(556\) 7.59948 13.1627i 0.322290 0.558222i
\(557\) 16.5388 28.6461i 0.700772 1.21377i −0.267424 0.963579i \(-0.586173\pi\)
0.968196 0.250193i \(-0.0804942\pi\)
\(558\) 0.111818 + 0.193675i 0.00473364 + 0.00819890i
\(559\) 0 0
\(560\) 26.7447 4.02472i 1.13017 0.170076i
\(561\) −23.4421 −0.989728
\(562\) −2.58020 4.46903i −0.108839 0.188515i
\(563\) −8.89836 + 15.4124i −0.375021 + 0.649556i −0.990330 0.138730i \(-0.955698\pi\)
0.615309 + 0.788286i \(0.289031\pi\)
\(564\) 3.32090 5.75197i 0.139835 0.242202i
\(565\) 26.7836 + 46.3906i 1.12679 + 1.95167i
\(566\) 3.24978 0.136598
\(567\) −25.8783 + 3.89433i −1.08679 + 0.163547i
\(568\) 2.39956 0.100683
\(569\) 4.11047 + 7.11954i 0.172320 + 0.298467i 0.939231 0.343287i \(-0.111540\pi\)
−0.766911 + 0.641754i \(0.778207\pi\)
\(570\) 0.0835750 0.144756i 0.00350057 0.00606317i
\(571\) 12.8776 22.3047i 0.538912 0.933424i −0.460051 0.887893i \(-0.652169\pi\)
0.998963 0.0455309i \(-0.0144980\pi\)
\(572\) 0 0
\(573\) 37.2513 1.55620
\(574\) −0.949572 + 2.41781i −0.0396344 + 0.100917i
\(575\) 9.75781 0.406929
\(576\) 1.20790 + 2.09214i 0.0503290 + 0.0871724i
\(577\) 0.384697 0.666314i 0.0160151 0.0277390i −0.857907 0.513805i \(-0.828235\pi\)
0.873922 + 0.486066i \(0.161569\pi\)
\(578\) −0.515762 + 0.893326i −0.0214529 + 0.0371575i
\(579\) −15.7626 27.3017i −0.655073 1.13462i
\(580\) −37.4505 −1.55505
\(581\) −27.3532 34.3163i −1.13480 1.42368i
\(582\) 0.148945 0.00617397
\(583\) 9.52743 + 16.5020i 0.394586 + 0.683443i
\(584\) −5.09908 + 8.83187i −0.211002 + 0.365465i
\(585\) 0 0
\(586\) −1.34615 2.33159i −0.0556088 0.0963173i
\(587\) −12.0929 −0.499127 −0.249563 0.968358i \(-0.580287\pi\)
−0.249563 + 0.968358i \(0.580287\pi\)
\(588\) 24.0325 7.40075i 0.991085 0.305202i
\(589\) −0.697040 −0.0287210
\(590\) −1.84337 3.19281i −0.0758904 0.131446i
\(591\) −4.52552 + 7.83842i −0.186155 + 0.322430i
\(592\) −15.1323 + 26.2099i −0.621933 + 1.07722i
\(593\) 7.97406 + 13.8115i 0.327456 + 0.567170i 0.982006 0.188848i \(-0.0604755\pi\)
−0.654551 + 0.756018i \(0.727142\pi\)
\(594\) 2.37139 0.0972994
\(595\) −21.1114 26.4856i −0.865484 1.08580i
\(596\) −28.1688 −1.15384
\(597\) 6.55717 + 11.3573i 0.268367 + 0.464825i
\(598\) 0 0
\(599\) 3.55511 6.15763i 0.145258 0.251594i −0.784211 0.620494i \(-0.786932\pi\)
0.929469 + 0.368900i \(0.120266\pi\)
\(600\) −1.45276 2.51626i −0.0593088 0.102726i
\(601\) 20.7905 0.848064 0.424032 0.905647i \(-0.360614\pi\)
0.424032 + 0.905647i \(0.360614\pi\)
\(602\) 1.40097 3.56717i 0.0570994 0.145387i
\(603\) 3.81163 0.155221
\(604\) −6.36667 11.0274i −0.259056 0.448698i
\(605\) 5.02544 8.70432i 0.204313 0.353881i
\(606\) −1.26409 + 2.18946i −0.0513500 + 0.0889408i
\(607\) 3.85702 + 6.68056i 0.156552 + 0.271156i 0.933623 0.358257i \(-0.116629\pi\)
−0.777071 + 0.629413i \(0.783296\pi\)
\(608\) 0.399983 0.0162215
\(609\) −33.8507 + 5.09407i −1.37170 + 0.206422i
\(610\) −0.199941 −0.00809539
\(611\) 0 0
\(612\) 1.56698 2.71409i 0.0633415 0.109711i
\(613\) −10.2189 + 17.6997i −0.412738 + 0.714883i −0.995188 0.0979832i \(-0.968761\pi\)
0.582450 + 0.812867i \(0.302094\pi\)
\(614\) 2.12614 + 3.68257i 0.0858038 + 0.148617i
\(615\) −26.6367 −1.07409
\(616\) −5.05678 + 0.760978i −0.203743 + 0.0306607i
\(617\) 4.59812 0.185113 0.0925567 0.995707i \(-0.470496\pi\)
0.0925567 + 0.995707i \(0.470496\pi\)
\(618\) 0.851451 + 1.47476i 0.0342504 + 0.0593234i
\(619\) −5.02641 + 8.70599i −0.202028 + 0.349923i −0.949182 0.314728i \(-0.898087\pi\)
0.747154 + 0.664651i \(0.231420\pi\)
\(620\) −9.77623 + 16.9329i −0.392623 + 0.680042i
\(621\) −10.7069 18.5449i −0.429653 0.744181i
\(622\) 0.294906 0.0118246
\(623\) 5.69827 14.5090i 0.228296 0.581290i
\(624\) 0 0
\(625\) 15.5853 + 26.9944i 0.623410 + 1.07978i
\(626\) 0.0629930 0.109107i 0.00251771 0.00436080i
\(627\) 0.463498 0.802802i 0.0185103 0.0320608i
\(628\) 15.6585 + 27.1213i 0.624842 + 1.08226i
\(629\) 37.9009 1.51121
\(630\) −0.267844 0.336027i −0.0106712 0.0133877i
\(631\) −7.27372 −0.289562 −0.144781 0.989464i \(-0.546248\pi\)
−0.144781 + 0.989464i \(0.546248\pi\)
\(632\) 3.26789 + 5.66015i 0.129990 + 0.225149i
\(633\) −16.0623 + 27.8207i −0.638418 + 1.10577i
\(634\) 1.93742 3.35570i 0.0769447 0.133272i
\(635\) 10.7025 + 18.5373i 0.424717 + 0.735631i
\(636\) −25.4065 −1.00743
\(637\) 0 0
\(638\) 3.45199 0.136665
\(639\) 0.559136 + 0.968451i 0.0221191 + 0.0383113i
\(640\) 7.45835 12.9182i 0.294817 0.510639i
\(641\) −1.92516 + 3.33448i −0.0760394 + 0.131704i −0.901538 0.432700i \(-0.857561\pi\)
0.825498 + 0.564404i \(0.190894\pi\)
\(642\) 1.32618 + 2.29700i 0.0523400 + 0.0906555i
\(643\) −2.87709 −0.113461 −0.0567307 0.998390i \(-0.518068\pi\)
−0.0567307 + 0.998390i \(0.518068\pi\)
\(644\) 14.2726 + 17.9059i 0.562421 + 0.705592i
\(645\) 39.2990 1.54740
\(646\) −0.0811745 0.140598i −0.00319377 0.00553177i
\(647\) −18.5501 + 32.1296i −0.729278 + 1.26315i 0.227911 + 0.973682i \(0.426810\pi\)
−0.957189 + 0.289464i \(0.906523\pi\)
\(648\) −3.54789 + 6.14512i −0.139374 + 0.241403i
\(649\) −10.2231 17.7070i −0.401293 0.695061i
\(650\) 0 0
\(651\) −6.53326 + 16.6350i −0.256059 + 0.651979i
\(652\) −9.40689 −0.368402
\(653\) −10.0475 17.4028i −0.393189 0.681023i 0.599679 0.800240i \(-0.295295\pi\)
−0.992868 + 0.119218i \(0.961961\pi\)
\(654\) 0.220162 0.381332i 0.00860902 0.0149113i
\(655\) −13.4573 + 23.3087i −0.525820 + 0.910748i
\(656\) −10.3295 17.8912i −0.403298 0.698532i
\(657\) −4.75267 −0.185419
\(658\) −0.874687 + 0.131629i −0.0340988 + 0.00513142i
\(659\) 9.91058 0.386061 0.193031 0.981193i \(-0.438168\pi\)
0.193031 + 0.981193i \(0.438168\pi\)
\(660\) −13.0014 22.5192i −0.506080 0.876557i
\(661\) −23.6133 + 40.8994i −0.918450 + 1.59080i −0.116680 + 0.993170i \(0.537225\pi\)
−0.801770 + 0.597633i \(0.796108\pi\)
\(662\) 0.137468 0.238102i 0.00534284 0.00925408i
\(663\) 0 0
\(664\) −11.8989 −0.461768
\(665\) 1.32444 0.199311i 0.0513597 0.00772895i
\(666\) 0.480855 0.0186328
\(667\) −15.5858 26.9954i −0.603485 1.04527i
\(668\) 2.66611 4.61783i 0.103155 0.178669i
\(669\) 12.8783 22.3059i 0.497905 0.862397i
\(670\) −2.76936 4.79667i −0.106990 0.185312i
\(671\) −1.10885 −0.0428068
\(672\) 3.74899 9.54572i 0.144621 0.368234i
\(673\) 6.91689 0.266627 0.133313 0.991074i \(-0.457438\pi\)
0.133313 + 0.991074i \(0.457438\pi\)
\(674\) −2.91401 5.04721i −0.112243 0.194411i
\(675\) −5.39823 + 9.35001i −0.207778 + 0.359882i
\(676\) 0 0
\(677\) 6.16453 + 10.6773i 0.236922 + 0.410361i 0.959830 0.280584i \(-0.0905281\pi\)
−0.722908 + 0.690945i \(0.757195\pi\)
\(678\) 6.58337 0.252833
\(679\) 0.743905 + 0.933275i 0.0285485 + 0.0358158i
\(680\) −9.18369 −0.352179
\(681\) 2.61921 + 4.53660i 0.100368 + 0.173843i
\(682\) 0.901120 1.56078i 0.0345057 0.0597655i
\(683\) 12.2682 21.2491i 0.469430 0.813076i −0.529960 0.848023i \(-0.677793\pi\)
0.999389 + 0.0349470i \(0.0111262\pi\)
\(684\) 0.0619648 + 0.107326i 0.00236928 + 0.00410372i
\(685\) −13.6131 −0.520130
\(686\) −2.76567 1.88844i −0.105594 0.0721011i
\(687\) −16.0216 −0.611264
\(688\) 15.2398 + 26.3961i 0.581012 + 1.00634i
\(689\) 0 0
\(690\) 1.95129 3.37973i 0.0742843 0.128664i
\(691\) −4.55358 7.88703i −0.173226 0.300037i 0.766320 0.642459i \(-0.222086\pi\)
−0.939546 + 0.342423i \(0.888753\pi\)
\(692\) 1.77021 0.0672933
\(693\) −1.48544 1.86357i −0.0564271 0.0707912i
\(694\) 1.47992 0.0561769
\(695\) −10.3782 17.9756i −0.393668 0.681853i
\(696\) −4.64089 + 8.03826i −0.175913 + 0.304690i
\(697\) −12.9358 + 22.4055i −0.489978 + 0.848667i
\(698\) −1.97543 3.42155i −0.0747712 0.129508i
\(699\) −9.32623 −0.352750
\(700\) 4.22034 10.7459i 0.159514 0.406156i
\(701\) −0.286950 −0.0108380 −0.00541898 0.999985i \(-0.501725\pi\)
−0.00541898 + 0.999985i \(0.501725\pi\)
\(702\) 0 0
\(703\) −0.749377 + 1.29796i −0.0282633 + 0.0489534i
\(704\) 9.73419 16.8601i 0.366871 0.635440i
\(705\) −4.53518 7.85516i −0.170805 0.295842i
\(706\) 0.102559 0.00385988
\(707\) −20.0324 + 3.01461i −0.753397 + 0.113376i
\(708\) 27.2617 1.02456
\(709\) 9.29241 + 16.0949i 0.348984 + 0.604457i 0.986069 0.166336i \(-0.0531936\pi\)
−0.637086 + 0.770793i \(0.719860\pi\)
\(710\) 0.812486 1.40727i 0.0304921 0.0528138i
\(711\) −1.52294 + 2.63781i −0.0571147 + 0.0989256i
\(712\) −2.11328 3.66031i −0.0791986 0.137176i
\(713\) −16.2743 −0.609478
\(714\) −4.11626 + 0.619442i −0.154047 + 0.0231820i
\(715\) 0 0
\(716\) −10.8751 18.8362i −0.406421 0.703941i
\(717\) 2.28066 3.95022i 0.0851729 0.147524i
\(718\) 2.92974 5.07445i 0.109337 0.189377i
\(719\) −20.8475 36.1088i −0.777479 1.34663i −0.933391 0.358862i \(-0.883165\pi\)
0.155912 0.987771i \(-0.450168\pi\)
\(720\) 3.41757 0.127365
\(721\) −4.98812 + 12.7008i −0.185767 + 0.473002i
\(722\) −3.42923 −0.127623
\(723\) −7.29046 12.6275i −0.271135 0.469620i
\(724\) 3.47128 6.01244i 0.129009 0.223451i
\(725\) −7.85809 + 13.6106i −0.291842 + 0.505486i
\(726\) −0.617623 1.06975i −0.0229221 0.0397023i
\(727\) −32.7039 −1.21292 −0.606461 0.795113i \(-0.707411\pi\)
−0.606461 + 0.795113i \(0.707411\pi\)
\(728\) 0 0
\(729\) 23.3578 0.865105
\(730\) 3.45308 + 5.98091i 0.127804 + 0.221363i
\(731\) 19.0851 33.0564i 0.705888 1.22263i
\(732\) 0.739235 1.28039i 0.0273229 0.0473246i
\(733\) 4.96765 + 8.60423i 0.183484 + 0.317804i 0.943065 0.332609i \(-0.107929\pi\)
−0.759580 + 0.650413i \(0.774596\pi\)
\(734\) −1.42288 −0.0525195
\(735\) 7.65722 33.4763i 0.282441 1.23479i
\(736\) 9.33871 0.344230
\(737\) −15.3586 26.6018i −0.565740 0.979891i
\(738\) −0.164119 + 0.284262i −0.00604129 + 0.0104638i
\(739\) 5.20108 9.00853i 0.191325 0.331384i −0.754365 0.656455i \(-0.772055\pi\)
0.945690 + 0.325071i \(0.105388\pi\)
\(740\) 21.0205 + 36.4086i 0.772730 + 1.33841i
\(741\) 0 0
\(742\) 2.10900 + 2.64587i 0.0774237 + 0.0971328i
\(743\) −1.70863 −0.0626837 −0.0313419 0.999509i \(-0.509978\pi\)
−0.0313419 + 0.999509i \(0.509978\pi\)
\(744\) 2.42295 + 4.19668i 0.0888297 + 0.153858i
\(745\) −19.2343 + 33.3148i −0.704690 + 1.22056i
\(746\) 0.189108 0.327545i 0.00692374 0.0119923i
\(747\) −2.77264 4.80235i −0.101446 0.175709i
\(748\) −25.2560 −0.923451
\(749\) −7.76923 + 19.7821i −0.283881 + 0.722821i
\(750\) 2.46785 0.0901132
\(751\) −14.9906 25.9645i −0.547015 0.947458i −0.998477 0.0551673i \(-0.982431\pi\)
0.451462 0.892290i \(-0.350903\pi\)
\(752\) 3.51741 6.09233i 0.128267 0.222164i
\(753\) 23.0598 39.9408i 0.840347 1.45552i
\(754\) 0 0
\(755\) −17.3893 −0.632860
\(756\) −25.0535 + 3.77022i −0.911188 + 0.137122i
\(757\) 8.40458 0.305470 0.152735 0.988267i \(-0.451192\pi\)
0.152735 + 0.988267i \(0.451192\pi\)
\(758\) −1.29437 2.24191i −0.0470136 0.0814299i
\(759\) 10.8216 18.7436i 0.392800 0.680350i
\(760\) 0.181580 0.314506i 0.00658660 0.0114083i
\(761\) 25.5295 + 44.2184i 0.925444 + 1.60292i 0.790846 + 0.612015i \(0.209641\pi\)
0.134598 + 0.990900i \(0.457026\pi\)
\(762\) 2.63067 0.0952990
\(763\) 3.48899 0.525046i 0.126310 0.0190079i
\(764\) 40.1337 1.45199
\(765\) −2.13995 3.70650i −0.0773699 0.134009i
\(766\) −2.27723 + 3.94429i −0.0822798 + 0.142513i
\(767\) 0 0
\(768\) 12.2780 + 21.2661i 0.443044 + 0.767375i
\(769\) −0.704439 −0.0254027 −0.0127014 0.999919i \(-0.504043\pi\)
−0.0127014 + 0.999919i \(0.504043\pi\)
\(770\) −1.26592 + 3.22331i −0.0456208 + 0.116160i
\(771\) 6.16030 0.221858
\(772\) −16.9823 29.4142i −0.611206 1.05864i
\(773\) 0.632607 1.09571i 0.0227533 0.0394099i −0.854425 0.519575i \(-0.826090\pi\)
0.877178 + 0.480166i \(0.159423\pi\)
\(774\) 0.242136 0.419392i 0.00870341 0.0150747i
\(775\) 4.10261 + 7.10593i 0.147370 + 0.255253i
\(776\) 0.323607 0.0116168
\(777\) 23.9523 + 30.0497i 0.859285 + 1.07803i
\(778\) 5.08156 0.182183
\(779\) −0.511533 0.886001i −0.0183276 0.0317443i
\(780\) 0 0
\(781\) 4.50596 7.80456i 0.161236 0.279269i