Properties

Label 1183.2.e.j.508.7
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 508.7
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.j.170.7

$q$-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 0.896219 0.443611i \(-0.146303\pi\)
−0.832288 + 0.554343i \(0.812970\pi\)
\(3\) 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 \(0.0384652\pi\)
−0.391956 + 0.919984i \(0.628201\pi\)
\(6\) 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 −0.588285 0.808654i \(-0.700197\pi\)
0.994457 + 0.105143i \(0.0335299\pi\)
\(12\) −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 0.876630 0.481165i \(-0.159786\pi\)
−0.855016 + 0.518601i \(0.826453\pi\)
\(20\) 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 −0.982944 0.183903i \(-0.941127\pi\)
0.650737 + 0.759303i \(0.274460\pi\)
\(32\) 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 \(0.0601703\pi\)
−0.328361 + 0.944552i \(0.606496\pi\)
\(38\) −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 \(-0.639367\pi\)
−0.423979 + 0.905672i \(0.639367\pi\)
\(42\) 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 0.790694 0.612212i \(-0.209720\pi\)
−0.925538 + 0.378655i \(0.876387\pi\)
\(48\) −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 −0.505982 0.862544i \(-0.668870\pi\)
0.999976 + 0.00692130i \(0.00220314\pi\)
\(60\) 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 \(-0.588105\pi\)
0.969697 0.244312i \(-0.0785621\pi\)
\(68\) 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 \(-0.436399\pi\)
0.198482 + 0.980104i \(0.436399\pi\)
\(72\) −0.119919 0.207705i −0.0141326 0.0244783i
\(73\) −7.10790 + 12.3112i −0.831917 + 1.44092i 0.0645994 + 0.997911i \(0.479423\pi\)
−0.896516 + 0.443011i \(0.853910\pi\)
\(74\) −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 \(-0.864155\pi\)
−0.910307 + 0.413934i \(0.864155\pi\)
\(84\) 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 0.666594 0.745421i \(-0.267752\pi\)
−0.978851 + 0.204577i \(0.934418\pi\)
\(90\) 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 \(-0.492710\pi\)
0.0229008 + 0.999738i \(0.492710\pi\)
\(98\) −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 −0.832324 0.554289i \(-0.812990\pi\)
0.896190 + 0.443670i \(0.146324\pi\)
\(110\) 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 −0.953720 0.300696i \(-0.902781\pi\)
0.737270 + 0.675598i \(0.236114\pi\)
\(138\) −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 \(0.0328309\pi\)
−0.408178 + 0.912902i \(0.633836\pi\)
\(150\) −0.366184 + 0.634250i −0.0298988 + 0.0517863i
\(151\) −3.23624 + 5.60534i −0.263362 + 0.456156i −0.967133 0.254271i \(-0.918165\pi\)
0.703771 + 0.710427i \(0.251498\pi\)
\(152\) 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 0.944337 0.328981i \(-0.106705\pi\)
−0.757074 + 0.653329i \(0.773372\pi\)
\(164\) −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 \(-0.533442\pi\)
−0.104869 + 0.994486i \(0.533442\pi\)
\(168\) 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 \(0.380088\pi\)
−0.989232 + 0.146357i \(0.953245\pi\)
\(194\) 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 \(-0.443498\pi\)
0.176576 + 0.984287i \(0.443498\pi\)
\(198\) −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 \(-0.656570\pi\)
−0.472284 + 0.881446i \(0.656570\pi\)
\(224\) 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 −0.814490 0.580178i \(-0.802983\pi\)
0.909694 + 0.415280i \(0.136316\pi\)
\(228\) 0.338441 0.586196i 0.0224138 0.0388218i
\(229\) 4.38706 + 7.59860i 0.289905 + 0.502130i 0.973787 0.227463i \(-0.0730430\pi\)
−0.683882 + 0.729593i \(0.739710\pi\)
\(230\) 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 \(-0.525744\pi\)
−0.0807901 + 0.996731i \(0.525744\pi\)
\(240\) −9.33309 16.1654i −0.602448 1.04347i
\(241\) −3.99256 + 6.91532i −0.257183 + 0.445455i −0.965486 0.260454i \(-0.916128\pi\)
0.708303 + 0.705909i \(0.249461\pi\)
\(242\) −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 0.987800 0.155727i \(-0.0497719\pi\)
−0.628763 + 0.777597i \(0.716439\pi\)
\(272\) 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 \(-0.824140\pi\)
−0.851225 + 0.524801i \(0.824140\pi\)
\(282\) −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 \(-0.643221\pi\)
−0.434914 + 0.900472i \(0.643221\pi\)
\(294\) −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 \(-0.265836\pi\)
0.671068 + 0.741396i \(0.265836\pi\)
\(308\) 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 \(-0.961125\pi\)
0.390771 0.920488i \(-0.372208\pi\)
\(318\) 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 0.844376 0.535751i \(-0.179971\pi\)
−0.886162 + 0.463375i \(0.846638\pi\)
\(332\) −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 \(-0.698820\pi\)
−0.584782 + 0.811190i \(0.698820\pi\)
\(350\) −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 −0.858380 0.513015i \(-0.828529\pi\)
0.873474 + 0.486871i \(0.161862\pi\)
\(354\) 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 \(-0.840152\pi\)
0.0214184 0.999771i \(-0.493182\pi\)
\(360\) 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 \(-0.619851\pi\)
−0.367691 + 0.929948i \(0.619851\pi\)
\(380\) 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 \(0.0558544\pi\)
−0.341138 + 0.940013i \(0.610812\pi\)
\(384\) −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 \(0.0173600\pi\)
−0.452049 + 0.891993i \(0.649307\pi\)
\(398\) −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 \(-0.995355\pi\)
0.487310 0.873229i \(-0.337978\pi\)
\(402\) 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 −0.778071 0.628177i \(-0.783801\pi\)
0.933052 + 0.359741i \(0.117135\pi\)
\(410\) 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 \(-0.590602\pi\)
−0.280806 + 0.959764i \(0.590602\pi\)
\(422\) −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 −0.740878 0.671640i \(-0.765590\pi\)
0.952096 + 0.305799i \(0.0989236\pi\)
\(432\) −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 \(-0.319623\pi\)
0.536825 + 0.843693i \(0.319623\pi\)
\(450\) 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 \(0.0949694\pi\)
−0.223344 + 0.974740i \(0.571697\pi\)
\(458\) −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 \(-0.562727\pi\)
−0.195789 + 0.980646i \(0.562727\pi\)
\(462\) 2.32746 0.350252i 0.108283 0.0162952i
\(463\) −10.0392 −0.466563 −0.233281 0.972409i \(-0.574946\pi\)
−0.233281 + 0.972409i \(0.574946\pi\)
\(464\) −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 −0.947264 0.320455i \(-0.896164\pi\)
0.751154 + 0.660127i \(0.229498\pi\)
\(480\) 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 −0.518171 0.855277i \(-0.673387\pi\)
0.999777 + 0.0211110i \(0.00672034\pi\)
\(488\) 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 \(0.169350\pi\)
0.00843082 + 0.999964i \(0.497316\pi\)
\(500\) 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 0.719713 0.694271i \(-0.244273\pi\)
−0.961113 + 0.276154i \(0.910940\pi\)
\(510\) −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 0.960689 0.277626i \(-0.0895475\pi\)
−0.720776 + 0.693169i \(0.756214\pi\)
\(542\) −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 \(0.413827\pi\)
−0.968196 + 0.250193i \(0.919506\pi\)
\(558\) 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 −0.873922 0.486066i \(-0.838431\pi\)
0.857907 + 0.513805i \(0.171765\pi\)
\(578\) 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 \(-0.419713\pi\)
0.249563 + 0.968358i \(0.419713\pi\)
\(588\) 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 0.654551 0.756018i \(-0.272858\pi\)
−0.982006 + 0.188848i \(0.939525\pi\)
\(594\) 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 −0.582450 0.812867i \(-0.697906\pi\)
0.995188 + 0.0979832i \(0.0312391\pi\)
\(614\) 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 \(-0.529504\pi\)
−0.0925567 + 0.995707i \(0.529504\pi\)
\(618\) −0.851451 1.47476i −0.0342504 0.0593234i
\(619\) 5.02641 8.70599i 0.202028 0.349923i −0.747154 0.664651i \(-0.768580\pi\)
0.949182 + 0.314728i \(0.101913\pi\)
\(620\) −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 \(-0.453752\pi\)
0.144781 + 0.989464i \(0.453752\pi\)
\(632\) −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 \(-0.481932\pi\)
0.0567307 + 0.998390i \(0.481932\pi\)
\(644\) −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 \(-0.462775\pi\)
0.801770 0.597633i \(-0.203892\pi\)
\(662\) 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 −0.999389 0.0349470i \(-0.988874\pi\)
0.529960 + 0.848023i \(0.322207\pi\)
\(684\) −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 0.939546 0.342423i \(-0.111247\pi\)
−0.766320 + 0.642459i \(0.777914\pi\)
\(692\) 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 0.637086 0.770793i \(-0.280140\pi\)
−0.986069 + 0.166336i \(0.946806\pi\)
\(710\) −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 0.759580 0.650413i \(-0.225404\pi\)
−0.943065 + 0.332609i \(0.892071\pi\)
\(734\) 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 −0.945690 0.325071i \(-0.894612\pi\)
0.754365 + 0.656455i \(0.227945\pi\)
\(740\) 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 \(-0.490022\pi\)
0.0313419 + 0.999509i \(0.490022\pi\)
\(744\) 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 \(-0.790359\pi\)
−0.134598 0.990900i \(-0.542974\pi\)
\(762\) −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 \(-0.495957\pi\)
0.0127014 + 0.999919i \(0.495957\pi\)
\(770\) −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 −0.877178 0.480166i \(-0.840577\pi\)
0.854425 + 0.519575i \(0.173910\pi\)
\(774\) −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
\(782\) 1.89524