Properties

Label 637.2.q.g.589.4
Level $637$
Weight $2$
Character 637.589
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \(x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 589.4
Root \(0.655911 - 1.25291i\) of defining polynomial
Character \(\chi\) \(=\) 637.589
Dual form 637.2.q.g.491.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.156598 + 0.0904119i) q^{2} +(0.913006 - 1.58137i) q^{3} +(-0.983651 - 1.70373i) q^{4} -2.68664i q^{5} +(0.285950 - 0.165093i) q^{6} -0.717383i q^{8} +(-0.167162 - 0.289532i) q^{9} +O(q^{10})\) \(q+(0.156598 + 0.0904119i) q^{2} +(0.913006 - 1.58137i) q^{3} +(-0.983651 - 1.70373i) q^{4} -2.68664i q^{5} +(0.285950 - 0.165093i) q^{6} -0.717383i q^{8} +(-0.167162 - 0.289532i) q^{9} +(0.242904 - 0.420723i) q^{10} +(-2.33328 - 1.34712i) q^{11} -3.59232 q^{12} +(1.92153 - 3.05086i) q^{13} +(-4.24858 - 2.45292i) q^{15} +(-1.90244 + 3.29513i) q^{16} +(2.38247 + 4.12655i) q^{17} -0.0604535i q^{18} +(-0.163180 + 0.0942122i) q^{19} +(-4.57732 + 2.64272i) q^{20} +(-0.243592 - 0.421913i) q^{22} +(2.19964 - 3.80989i) q^{23} +(-1.13445 - 0.654975i) q^{24} -2.21804 q^{25} +(0.576741 - 0.304029i) q^{26} +4.86756 q^{27} +(-3.54280 + 6.13631i) q^{29} +(-0.443546 - 0.768245i) q^{30} +3.69931i q^{31} +(-1.83838 + 1.06139i) q^{32} +(-4.26060 + 2.45986i) q^{33} +0.861613i q^{34} +(-0.328857 + 0.569598i) q^{36} +(-6.88848 - 3.97707i) q^{37} -0.0340716 q^{38} +(-3.07017 - 5.82411i) q^{39} -1.92735 q^{40} +(4.70215 + 2.71479i) q^{41} +(-4.00533 - 6.93743i) q^{43} +5.30039i q^{44} +(-0.777869 + 0.449103i) q^{45} +(0.688919 - 0.397748i) q^{46} -1.84889i q^{47} +(3.47389 + 6.01695i) q^{48} +(-0.347341 - 0.200538i) q^{50} +8.70083 q^{51} +(-7.08796 - 0.272800i) q^{52} -7.07244 q^{53} +(0.762250 + 0.440085i) q^{54} +(-3.61923 + 6.26869i) q^{55} +0.344066i q^{57} +(-1.10959 + 0.640623i) q^{58} +(6.57216 - 3.79444i) q^{59} +9.65128i q^{60} +(0.205782 + 0.356425i) q^{61} +(-0.334461 + 0.579304i) q^{62} +7.22592 q^{64} +(-8.19656 - 5.16247i) q^{65} -0.889602 q^{66} +(9.87358 + 5.70051i) q^{67} +(4.68703 - 8.11818i) q^{68} +(-4.01658 - 6.95692i) q^{69} +(2.89675 - 1.67244i) q^{71} +(-0.207705 + 0.119919i) q^{72} -14.2158i q^{73} +(-0.719148 - 1.24560i) q^{74} +(-2.02509 + 3.50756i) q^{75} +(0.321025 + 0.185344i) q^{76} +(0.0457859 - 1.18962i) q^{78} +9.11059 q^{79} +(8.85283 + 5.11118i) q^{80} +(4.94560 - 8.56603i) q^{81} +(0.490899 + 0.850261i) q^{82} -16.5866i q^{83} +(11.0866 - 6.40083i) q^{85} -1.44852i q^{86} +(6.46920 + 11.2050i) q^{87} +(-0.966401 + 1.67386i) q^{88} +(5.10232 + 2.94582i) q^{89} -0.162417 q^{90} -8.65473 q^{92} +(5.84998 + 3.37749i) q^{93} +(0.167162 - 0.289532i) q^{94} +(0.253115 + 0.438407i) q^{95} +3.87622i q^{96} +(0.390659 - 0.225547i) q^{97} +0.900747i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 3q^{3} + 4q^{4} - 9q^{6} - q^{9} + O(q^{10}) \) \( 12q - 3q^{3} + 4q^{4} - 9q^{6} - q^{9} + 12q^{10} - 12q^{11} + 2q^{12} - 2q^{13} - 12q^{15} - 8q^{16} + 17q^{17} - 9q^{19} - 3q^{20} - 15q^{22} + 3q^{23} - 15q^{24} + 10q^{25} + 15q^{26} + 12q^{27} - q^{29} + 11q^{30} - 18q^{32} + 6q^{33} - 13q^{36} - 15q^{37} - 38q^{38} + 5q^{39} + 2q^{40} - 6q^{41} + 11q^{43} + 9q^{45} + 30q^{46} + 19q^{48} + 18q^{50} - 8q^{51} - 40q^{52} + 16q^{53} - 6q^{54} - 15q^{55} + 24q^{58} - 27q^{59} + 5q^{61} + 41q^{62} + 2q^{64} - 18q^{65} + 68q^{66} - 15q^{67} - 11q^{68} + 7q^{69} + 30q^{71} - 57q^{72} - 33q^{74} + q^{75} - 45q^{76} + 44q^{78} + 70q^{79} + 63q^{80} + 14q^{81} + 5q^{82} - 21q^{85} + 10q^{87} - 14q^{88} - 48q^{89} - 66q^{92} + 81q^{93} + q^{94} + 2q^{95} - 3q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.156598 + 0.0904119i 0.110731 + 0.0639308i 0.554343 0.832288i \(-0.312970\pi\)
−0.443611 + 0.896219i \(0.646303\pi\)
\(3\) 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
\(5\) 2.68664i 1.20150i −0.799436 0.600751i \(-0.794868\pi\)
0.799436 0.600751i \(-0.205132\pi\)
\(6\) 0.285950 0.165093i 0.116739 0.0673990i
\(7\) 0 0
\(8\) 0.717383i 0.253633i
\(9\) −0.167162 0.289532i −0.0557205 0.0965108i
\(10\) 0.242904 0.420723i 0.0768131 0.133044i
\(11\) −2.33328 1.34712i −0.703511 0.406172i 0.105143 0.994457i \(-0.466470\pi\)
−0.808654 + 0.588285i \(0.799803\pi\)
\(12\) −3.59232 −1.03701
\(13\) 1.92153 3.05086i 0.532937 0.846155i
\(14\) 0 0
\(15\) −4.24858 2.45292i −1.09698 0.633342i
\(16\) −1.90244 + 3.29513i −0.475611 + 0.823782i
\(17\) 2.38247 + 4.12655i 0.577833 + 1.00084i 0.995727 + 0.0923405i \(0.0294348\pi\)
−0.417894 + 0.908496i \(0.637232\pi\)
\(18\) 0.0604535i 0.0142490i
\(19\) −0.163180 + 0.0942122i −0.0374361 + 0.0216138i −0.518601 0.855016i \(-0.673547\pi\)
0.481165 + 0.876630i \(0.340214\pi\)
\(20\) −4.57732 + 2.64272i −1.02352 + 0.590930i
\(21\) 0 0
\(22\) −0.243592 0.421913i −0.0519339 0.0899521i
\(23\) 2.19964 3.80989i 0.458657 0.794418i −0.540233 0.841516i \(-0.681664\pi\)
0.998890 + 0.0470977i \(0.0149972\pi\)
\(24\) −1.13445 0.654975i −0.231569 0.133696i
\(25\) −2.21804 −0.443609
\(26\) 0.576741 0.304029i 0.113108 0.0596249i
\(27\) 4.86756 0.936762
\(28\) 0 0
\(29\) −3.54280 + 6.13631i −0.657882 + 1.13948i 0.323281 + 0.946303i \(0.395214\pi\)
−0.981163 + 0.193182i \(0.938119\pi\)
\(30\) −0.443546 0.768245i −0.0809801 0.140262i
\(31\) 3.69931i 0.664415i 0.943206 + 0.332207i \(0.107793\pi\)
−0.943206 + 0.332207i \(0.892207\pi\)
\(32\) −1.83838 + 1.06139i −0.324983 + 0.187629i
\(33\) −4.26060 + 2.45986i −0.741676 + 0.428207i
\(34\) 0.861613i 0.147765i
\(35\) 0 0
\(36\) −0.328857 + 0.569598i −0.0548096 + 0.0949329i
\(37\) −6.88848 3.97707i −1.13246 0.653826i −0.187907 0.982187i \(-0.560170\pi\)
−0.944552 + 0.328361i \(0.893504\pi\)
\(38\) −0.0340716 −0.00552715
\(39\) −3.07017 5.82411i −0.491621 0.932604i
\(40\) −1.92735 −0.304741
\(41\) 4.70215 + 2.71479i 0.734353 + 0.423979i 0.820013 0.572345i \(-0.193966\pi\)
−0.0856594 + 0.996324i \(0.527300\pi\)
\(42\) 0 0
\(43\) −4.00533 6.93743i −0.610807 1.05795i −0.991105 0.133084i \(-0.957512\pi\)
0.380298 0.924864i \(-0.375821\pi\)
\(44\) 5.30039i 0.799064i
\(45\) −0.777869 + 0.449103i −0.115958 + 0.0669483i
\(46\) 0.688919 0.397748i 0.101576 0.0586447i
\(47\) 1.84889i 0.269688i −0.990867 0.134844i \(-0.956947\pi\)
0.990867 0.134844i \(-0.0430534\pi\)
\(48\) 3.47389 + 6.01695i 0.501412 + 0.868471i
\(49\) 0 0
\(50\) −0.347341 0.200538i −0.0491215 0.0283603i
\(51\) 8.70083 1.21836
\(52\) −7.08796 0.272800i −0.982924 0.0378305i
\(53\) −7.07244 −0.971474 −0.485737 0.874105i \(-0.661449\pi\)
−0.485737 + 0.874105i \(0.661449\pi\)
\(54\) 0.762250 + 0.440085i 0.103729 + 0.0598880i
\(55\) −3.61923 + 6.26869i −0.488017 + 0.845271i
\(56\) 0 0
\(57\) 0.344066i 0.0455726i
\(58\) −1.10959 + 0.640623i −0.145696 + 0.0841179i
\(59\) 6.57216 3.79444i 0.855623 0.493994i −0.00692130 0.999976i \(-0.502203\pi\)
0.862544 + 0.505982i \(0.168870\pi\)
\(60\) 9.65128i 1.24597i
\(61\) 0.205782 + 0.356425i 0.0263477 + 0.0456355i 0.878899 0.477009i \(-0.158279\pi\)
−0.852551 + 0.522644i \(0.824946\pi\)
\(62\) −0.334461 + 0.579304i −0.0424766 + 0.0735716i
\(63\) 0 0
\(64\) 7.22592 0.903240
\(65\) −8.19656 5.16247i −1.01666 0.640325i
\(66\) −0.889602 −0.109502
\(67\) 9.87358 + 5.70051i 1.20625 + 0.696429i 0.961938 0.273268i \(-0.0881046\pi\)
0.244312 + 0.969697i \(0.421438\pi\)
\(68\) 4.68703 8.11818i 0.568386 0.984474i
\(69\) −4.01658 6.95692i −0.483539 0.837514i
\(70\) 0 0
\(71\) 2.89675 1.67244i 0.343781 0.198482i −0.318162 0.948037i \(-0.603065\pi\)
0.661943 + 0.749554i \(0.269732\pi\)
\(72\) −0.207705 + 0.119919i −0.0244783 + 0.0141326i
\(73\) 14.2158i 1.66383i −0.554900 0.831917i \(-0.687244\pi\)
0.554900 0.831917i \(-0.312756\pi\)
\(74\) −0.719148 1.24560i −0.0835993 0.144798i
\(75\) −2.02509 + 3.50756i −0.233837 + 0.405018i
\(76\) 0.321025 + 0.185344i 0.0368241 + 0.0212604i
\(77\) 0 0
\(78\) 0.0457859 1.18962i 0.00518423 0.134698i
\(79\) 9.11059 1.02502 0.512511 0.858681i \(-0.328715\pi\)
0.512511 + 0.858681i \(0.328715\pi\)
\(80\) 8.85283 + 5.11118i 0.989776 + 0.571448i
\(81\) 4.94560 8.56603i 0.549511 0.951781i
\(82\) 0.490899 + 0.850261i 0.0542107 + 0.0938956i
\(83\) 16.5866i 1.82061i −0.413934 0.910307i \(-0.635845\pi\)
0.413934 0.910307i \(-0.364155\pi\)
\(84\) 0 0
\(85\) 11.0866 6.40083i 1.20251 0.694268i
\(86\) 1.44852i 0.156198i
\(87\) 6.46920 + 11.2050i 0.693571 + 1.20130i
\(88\) −0.966401 + 1.67386i −0.103019 + 0.178434i
\(89\) 5.10232 + 2.94582i 0.540844 + 0.312257i 0.745421 0.666594i \(-0.232248\pi\)
−0.204577 + 0.978851i \(0.565582\pi\)
\(90\) −0.162417 −0.0171203
\(91\) 0 0
\(92\) −8.65473 −0.902318
\(93\) 5.84998 + 3.37749i 0.606615 + 0.350229i
\(94\) 0.167162 0.289532i 0.0172414 0.0298630i
\(95\) 0.253115 + 0.438407i 0.0259690 + 0.0449796i
\(96\) 3.87622i 0.395615i
\(97\) 0.390659 0.225547i 0.0396654 0.0229008i −0.480036 0.877249i \(-0.659376\pi\)
0.519702 + 0.854348i \(0.326043\pi\)
\(98\) 0 0
\(99\) 0.900747i 0.0905285i
\(100\) 2.18178 + 3.77896i 0.218178 + 0.377896i
\(101\) −3.82840 + 6.63098i −0.380940 + 0.659807i −0.991197 0.132396i \(-0.957733\pi\)
0.610257 + 0.792204i \(0.291066\pi\)
\(102\) 1.36253 + 0.786658i 0.134911 + 0.0778908i
\(103\) −5.15740 −0.508173 −0.254087 0.967181i \(-0.581775\pi\)
−0.254087 + 0.967181i \(0.581775\pi\)
\(104\) −2.18863 1.37847i −0.214613 0.135170i
\(105\) 0 0
\(106\) −1.10753 0.639433i −0.107573 0.0621072i
\(107\) −4.01644 + 6.95669i −0.388284 + 0.672528i −0.992219 0.124506i \(-0.960265\pi\)
0.603935 + 0.797034i \(0.293599\pi\)
\(108\) −4.78798 8.29303i −0.460724 0.797997i
\(109\) 1.33356i 0.127732i −0.997958 0.0638660i \(-0.979657\pi\)
0.997958 0.0638660i \(-0.0203430\pi\)
\(110\) −1.13353 + 0.654443i −0.108078 + 0.0623987i
\(111\) −12.5785 + 7.26217i −1.19389 + 0.689295i
\(112\) 0 0
\(113\) 9.96917 + 17.2671i 0.937821 + 1.62435i 0.769525 + 0.638617i \(0.220493\pi\)
0.168296 + 0.985736i \(0.446173\pi\)
\(114\) −0.0311076 + 0.0538800i −0.00291349 + 0.00504632i
\(115\) −10.2358 5.90965i −0.954495 0.551078i
\(116\) 13.9395 1.29425
\(117\) −1.20453 0.0463595i −0.111359 0.00428594i
\(118\) 1.37225 0.126326
\(119\) 0 0
\(120\) −1.75968 + 3.04786i −0.160636 + 0.278230i
\(121\) −1.87053 3.23985i −0.170048 0.294532i
\(122\) 0.0744205i 0.00673772i
\(123\) 8.58619 4.95724i 0.774191 0.446979i
\(124\) 6.30263 3.63883i 0.565993 0.326776i
\(125\) 7.47412i 0.668505i
\(126\) 0 0
\(127\) −3.98361 + 6.89981i −0.353488 + 0.612259i −0.986858 0.161590i \(-0.948338\pi\)
0.633370 + 0.773849i \(0.281671\pi\)
\(128\) 4.80833 + 2.77609i 0.425000 + 0.245374i
\(129\) −14.6276 −1.28788
\(130\) −0.816816 1.54950i −0.0716395 0.135900i
\(131\) 10.0179 0.875271 0.437636 0.899152i \(-0.355816\pi\)
0.437636 + 0.899152i \(0.355816\pi\)
\(132\) 8.38190 + 4.83929i 0.729551 + 0.421206i
\(133\) 0 0
\(134\) 1.03079 + 1.78538i 0.0890465 + 0.154233i
\(135\) 13.0774i 1.12552i
\(136\) 2.96032 1.70914i 0.253845 0.146558i
\(137\) −4.38811 + 2.53348i −0.374902 + 0.216450i −0.675598 0.737270i \(-0.736114\pi\)
0.300696 + 0.953720i \(0.402781\pi\)
\(138\) 1.45259i 0.123652i
\(139\) −3.86289 6.69073i −0.327646 0.567500i 0.654398 0.756150i \(-0.272922\pi\)
−0.982044 + 0.188650i \(0.939589\pi\)
\(140\) 0 0
\(141\) −2.92378 1.68805i −0.246227 0.142159i
\(142\) 0.604834 0.0507566
\(143\) −8.59335 + 4.52997i −0.718612 + 0.378815i
\(144\) 1.27206 0.106005
\(145\) 16.4861 + 9.51824i 1.36909 + 0.790447i
\(146\) 1.28528 2.22617i 0.106370 0.184239i
\(147\) 0 0
\(148\) 15.6482i 1.28627i
\(149\) −12.4002 + 7.15924i −1.01586 + 0.586507i −0.912902 0.408178i \(-0.866164\pi\)
−0.102958 + 0.994686i \(0.532831\pi\)
\(150\) −0.634250 + 0.366184i −0.0517863 + 0.0298988i
\(151\) 6.47249i 0.526724i −0.964697 0.263362i \(-0.915169\pi\)
0.964697 0.263362i \(-0.0848313\pi\)
\(152\) 0.0675862 + 0.117063i 0.00548197 + 0.00949504i
\(153\) 0.796513 1.37960i 0.0643943 0.111534i
\(154\) 0 0
\(155\) 9.93871 0.798296
\(156\) −6.90275 + 10.9596i −0.552663 + 0.877474i
\(157\) 15.9187 1.27045 0.635227 0.772326i \(-0.280907\pi\)
0.635227 + 0.772326i \(0.280907\pi\)
\(158\) 1.42670 + 0.823705i 0.113502 + 0.0655305i
\(159\) −6.45718 + 11.1842i −0.512088 + 0.886962i
\(160\) 2.85157 + 4.93907i 0.225437 + 0.390468i
\(161\) 0 0
\(162\) 1.54894 0.894282i 0.121696 0.0702614i
\(163\) 4.14100 2.39081i 0.324348 0.187263i −0.328981 0.944337i \(-0.606705\pi\)
0.653329 + 0.757074i \(0.273372\pi\)
\(164\) 10.6816i 0.834095i
\(165\) 6.60876 + 11.4467i 0.514492 + 0.891126i
\(166\) 1.49962 2.59743i 0.116393 0.201599i
\(167\) −2.34729 1.35521i −0.181639 0.104869i 0.406424 0.913685i \(-0.366776\pi\)
−0.588062 + 0.808816i \(0.700109\pi\)
\(168\) 0 0
\(169\) −5.61544 11.7246i −0.431957 0.901894i
\(170\) 2.31485 0.177541
\(171\) 0.0545550 + 0.0314973i 0.00417192 + 0.00240866i
\(172\) −7.87969 + 13.6480i −0.600821 + 1.04065i
\(173\) −0.449908 0.779264i −0.0342059 0.0592463i 0.848416 0.529331i \(-0.177557\pi\)
−0.882622 + 0.470084i \(0.844224\pi\)
\(174\) 2.33957i 0.177362i
\(175\) 0 0
\(176\) 8.87787 5.12564i 0.669195 0.386360i
\(177\) 13.8574i 1.04159i
\(178\) 0.532675 + 0.922620i 0.0399257 + 0.0691533i
\(179\) −5.52791 + 9.57462i −0.413175 + 0.715641i −0.995235 0.0975054i \(-0.968914\pi\)
0.582060 + 0.813146i \(0.302247\pi\)
\(180\) 1.53030 + 0.883522i 0.114062 + 0.0658538i
\(181\) −3.52898 −0.262307 −0.131153 0.991362i \(-0.541868\pi\)
−0.131153 + 0.991362i \(0.541868\pi\)
\(182\) 0 0
\(183\) 0.751521 0.0555540
\(184\) −2.73315 1.57799i −0.201491 0.116331i
\(185\) −10.6850 + 18.5069i −0.785573 + 1.36065i
\(186\) 0.610730 + 1.05782i 0.0447809 + 0.0775628i
\(187\) 12.8379i 0.938799i
\(188\) −3.15002 + 1.81866i −0.229738 + 0.132640i
\(189\) 0 0
\(190\) 0.0915382i 0.00664088i
\(191\) 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
\(193\) 14.9515 + 8.63228i 1.07624 + 0.621365i 0.929878 0.367867i \(-0.119912\pi\)
0.146357 + 0.989232i \(0.453245\pi\)
\(194\) 0.0815684 0.00585627
\(195\) −15.6473 + 8.24845i −1.12053 + 0.590684i
\(196\) 0 0
\(197\) −4.29264 2.47836i −0.305838 0.176576i 0.339224 0.940705i \(-0.389835\pi\)
−0.645063 + 0.764130i \(0.723169\pi\)
\(198\) −0.0814383 + 0.141055i −0.00578757 + 0.0100244i
\(199\) 3.59097 + 6.21975i 0.254557 + 0.440906i 0.964775 0.263076i \(-0.0847369\pi\)
−0.710218 + 0.703982i \(0.751404\pi\)
\(200\) 1.59119i 0.112514i
\(201\) 18.0293 10.4092i 1.27169 0.734209i
\(202\) −1.19904 + 0.692265i −0.0843641 + 0.0487076i
\(203\) 0 0
\(204\) −8.55858 14.8239i −0.599221 1.03788i
\(205\) 7.29367 12.6330i 0.509412 0.882327i
\(206\) −0.807638 0.466290i −0.0562708 0.0324880i
\(207\) −1.47078 −0.102226
\(208\) 6.39736 + 12.1358i 0.443577 + 0.841464i
\(209\) 0.507661 0.0351157
\(210\) 0 0
\(211\) 8.79636 15.2357i 0.605566 1.04887i −0.386395 0.922333i \(-0.626280\pi\)
0.991962 0.126539i \(-0.0403868\pi\)
\(212\) 6.95682 + 12.0496i 0.477796 + 0.827567i
\(213\) 6.10780i 0.418499i
\(214\) −1.25793 + 0.726269i −0.0859906 + 0.0496467i
\(215\) −18.6384 + 10.7609i −1.27113 + 0.733886i
\(216\) 3.49190i 0.237594i
\(217\) 0 0
\(218\) 0.120570 0.208833i 0.00816602 0.0141440i
\(219\) −22.4805 12.9791i −1.51909 0.877048i
\(220\) 14.2403 0.960078
\(221\) 17.1675 + 0.660738i 1.15481 + 0.0444461i
\(222\) −2.62635 −0.176269
\(223\) 12.2157 + 7.05271i 0.818020 + 0.472284i 0.849733 0.527213i \(-0.176763\pi\)
−0.0317129 + 0.999497i \(0.510096\pi\)
\(224\) 0 0
\(225\) 0.370772 + 0.642195i 0.0247181 + 0.0428130i
\(226\) 3.60533i 0.239823i
\(227\) −2.48443 + 1.43439i −0.164897 + 0.0952035i −0.580178 0.814490i \(-0.697017\pi\)
0.415280 + 0.909694i \(0.363684\pi\)
\(228\) 0.586196 0.338441i 0.0388218 0.0224138i
\(229\) 8.77411i 0.579810i 0.957055 + 0.289905i \(0.0936237\pi\)
−0.957055 + 0.289905i \(0.906376\pi\)
\(230\) −1.06861 1.85088i −0.0704618 0.122043i
\(231\) 0 0
\(232\) 4.40208 + 2.54154i 0.289011 + 0.166861i
\(233\) −5.10743 −0.334599 −0.167299 0.985906i \(-0.553505\pi\)
−0.167299 + 0.985906i \(0.553505\pi\)
\(234\) −0.184435 0.116163i −0.0120569 0.00759384i
\(235\) −4.96730 −0.324031
\(236\) −12.9294 7.46481i −0.841634 0.485918i
\(237\) 8.31803 14.4072i 0.540314 0.935851i
\(238\) 0 0
\(239\) 2.49797i 0.161580i −0.996731 0.0807901i \(-0.974256\pi\)
0.996731 0.0807901i \(-0.0257443\pi\)
\(240\) 16.1654 9.33309i 1.04347 0.602448i
\(241\) −6.91532 + 3.99256i −0.445455 + 0.257183i −0.705909 0.708303i \(-0.749461\pi\)
0.260454 + 0.965486i \(0.416128\pi\)
\(242\) 0.676472i 0.0434853i
\(243\) −1.72939 2.99538i −0.110940 0.192154i
\(244\) 0.404835 0.701195i 0.0259169 0.0448894i
\(245\) 0 0
\(246\) 1.79277 0.114303
\(247\) −0.0261282 + 0.678871i −0.00166250 + 0.0431956i
\(248\) 2.65382 0.168518
\(249\) −26.2296 15.1437i −1.66223 0.959690i
\(250\) 0.675749 1.17043i 0.0427381 0.0740246i
\(251\) 12.6285 + 21.8732i 0.797105 + 1.38063i 0.921494 + 0.388393i \(0.126970\pi\)
−0.124389 + 0.992234i \(0.539697\pi\)
\(252\) 0 0
\(253\) −10.2648 + 5.92637i −0.645341 + 0.372588i
\(254\) −1.24765 + 0.720331i −0.0782845 + 0.0451976i
\(255\) 23.3760i 1.46386i
\(256\) −6.72394 11.6462i −0.420246 0.727888i
\(257\) −1.68682 + 2.92165i −0.105221 + 0.182248i −0.913828 0.406101i \(-0.866888\pi\)
0.808608 + 0.588348i \(0.200222\pi\)
\(258\) −2.29065 1.32250i −0.142609 0.0823355i
\(259\) 0 0
\(260\) −0.732915 + 19.0428i −0.0454535 + 1.18099i
\(261\) 2.36888 0.146630
\(262\) 1.56879 + 0.905740i 0.0969201 + 0.0559568i
\(263\) 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
\(265\) 19.0011i 1.16723i
\(266\) 0 0
\(267\) 9.31689 5.37911i 0.570185 0.329196i
\(268\) 22.4293i 1.37009i
\(269\) 11.6633 + 20.2014i 0.711124 + 1.23170i 0.964435 + 0.264318i \(0.0851470\pi\)
−0.253311 + 0.967385i \(0.581520\pi\)
\(270\) 1.18235 2.04789i 0.0719556 0.124631i
\(271\) −10.2373 5.91049i −0.621870 0.359037i 0.155727 0.987800i \(-0.450228\pi\)
−0.777597 + 0.628763i \(0.783561\pi\)
\(272\) −18.1300 −1.09929
\(273\) 0 0
\(274\) −0.916226 −0.0553513
\(275\) 5.17532 + 2.98797i 0.312084 + 0.180182i
\(276\) −7.90182 + 13.6864i −0.475634 + 0.823822i
\(277\) −13.6827 23.6991i −0.822111 1.42394i −0.904107 0.427306i \(-0.859463\pi\)
0.0819961 0.996633i \(-0.473870\pi\)
\(278\) 1.39701i 0.0837868i
\(279\) 1.07107 0.618382i 0.0641232 0.0370215i
\(280\) 0 0
\(281\) 28.5383i 1.70245i 0.524801 + 0.851225i \(0.324140\pi\)
−0.524801 + 0.851225i \(0.675860\pi\)
\(282\) −0.305239 0.528690i −0.0181767 0.0314830i
\(283\) 8.98604 15.5643i 0.534165 0.925201i −0.465038 0.885290i \(-0.653960\pi\)
0.999203 0.0399101i \(-0.0127072\pi\)
\(284\) −5.69879 3.29020i −0.338161 0.195237i
\(285\) 0.924381 0.0547556
\(286\) −1.75526 0.0675561i −0.103791 0.00399468i
\(287\) 0 0
\(288\) 0.614613 + 0.354847i 0.0362164 + 0.0209096i
\(289\) −2.85229 + 4.94032i −0.167782 + 0.290607i
\(290\) 1.72112 + 2.98107i 0.101068 + 0.175055i
\(291\) 0.823703i 0.0482863i
\(292\) −24.2199 + 13.9834i −1.41737 + 0.818316i
\(293\) 12.8943 7.44453i 0.753293 0.434914i −0.0735896 0.997289i \(-0.523446\pi\)
0.826882 + 0.562375i \(0.190112\pi\)
\(294\) 0 0
\(295\) −10.1943 17.6570i −0.593535 1.02803i
\(296\) −2.85308 + 4.94168i −0.165832 + 0.287229i
\(297\) −11.3574 6.55719i −0.659023 0.380487i
\(298\) −2.58912 −0.149984
\(299\) −7.39675 14.0316i −0.427765 0.811470i
\(300\) 7.96793 0.460028
\(301\) 0 0
\(302\) 0.585190 1.01358i 0.0336739 0.0583249i
\(303\) 6.99071 + 12.1083i 0.401606 + 0.695601i
\(304\) 0.716934i 0.0411190i
\(305\) 0.957586 0.552862i 0.0548312 0.0316568i
\(306\) 0.249465 0.144029i 0.0142610 0.00823356i
\(307\) 23.5161i 1.34214i −0.741396 0.671068i \(-0.765836\pi\)
0.741396 0.671068i \(-0.234164\pi\)
\(308\) 0 0
\(309\) −4.70874 + 8.15577i −0.267871 + 0.463966i
\(310\) 1.55638 + 0.898577i 0.0883965 + 0.0510358i
\(311\) −1.63090 −0.0924799 −0.0462399 0.998930i \(-0.514724\pi\)
−0.0462399 + 0.998930i \(0.514724\pi\)
\(312\) −4.17811 + 2.20249i −0.236539 + 0.124691i
\(313\) −0.696734 −0.0393817 −0.0196909 0.999806i \(-0.506268\pi\)
−0.0196909 + 0.999806i \(0.506268\pi\)
\(314\) 2.49284 + 1.43924i 0.140679 + 0.0812212i
\(315\) 0 0
\(316\) −8.96164 15.5220i −0.504132 0.873182i
\(317\) 21.4288i 1.20356i 0.798662 + 0.601780i \(0.205542\pi\)
−0.798662 + 0.601780i \(0.794458\pi\)
\(318\) −2.02236 + 1.16761i −0.113409 + 0.0654764i
\(319\) 16.5327 9.54517i 0.925654 0.534427i
\(320\) 19.4135i 1.08525i
\(321\) 7.33408 + 12.7030i 0.409348 + 0.709012i
\(322\) 0 0
\(323\) −0.777544 0.448915i −0.0432637 0.0249783i
\(324\) −19.4590 −1.08105
\(325\) −4.26204 + 6.76693i −0.236415 + 0.375362i
\(326\) 0.864630 0.0478874
\(327\) −2.10886 1.21755i −0.116620 0.0673307i
\(328\) 1.94754 3.37324i 0.107535 0.186256i
\(329\) 0 0
\(330\) 2.39004i 0.131568i
\(331\) 1.31676 0.760232i 0.0723757 0.0417861i −0.463375 0.886162i \(-0.653362\pi\)
0.535751 + 0.844376i \(0.320029\pi\)
\(332\) −28.2591 + 16.3154i −1.55092 + 0.895425i
\(333\) 2.65925i 0.145726i
\(334\) −0.245054 0.424446i −0.0134088 0.0232247i
\(335\) 15.3152 26.5268i 0.836761 1.44931i
\(336\) 0 0
\(337\) −32.2304 −1.75570 −0.877850 0.478936i \(-0.841023\pi\)
−0.877850 + 0.478936i \(0.841023\pi\)
\(338\) 0.180679 2.34375i 0.00982766 0.127483i
\(339\) 36.4077 1.97739
\(340\) −21.8106 12.5924i −1.18285 0.682918i
\(341\) 4.98341 8.63153i 0.269867 0.467423i
\(342\) 0.00569546 + 0.00986483i 0.000307975 + 0.000533429i
\(343\) 0 0
\(344\) −4.97679 + 2.87335i −0.268331 + 0.154921i
\(345\) −18.6907 + 10.7911i −1.00628 + 0.580974i
\(346\) 0.162708i 0.00874724i
\(347\) −4.09215 7.08782i −0.219678 0.380494i 0.735031 0.678033i \(-0.237167\pi\)
−0.954710 + 0.297539i \(0.903834\pi\)
\(348\) 12.7269 22.0436i 0.682232 1.18166i
\(349\) −18.9220 10.9246i −1.01287 0.584782i −0.100841 0.994903i \(-0.532153\pi\)
−0.912031 + 0.410120i \(0.865487\pi\)
\(350\) 0 0
\(351\) 9.35317 14.8502i 0.499235 0.792646i
\(352\) 5.71928 0.304839
\(353\) 0.491192 + 0.283590i 0.0261435 + 0.0150940i 0.513015 0.858380i \(-0.328529\pi\)
−0.486871 + 0.873474i \(0.661862\pi\)
\(354\) 1.25287 2.17004i 0.0665894 0.115336i
\(355\) −4.49325 7.78254i −0.238477 0.413054i
\(356\) 11.5907i 0.614303i
\(357\) 0 0
\(358\) −1.73132 + 0.999577i −0.0915030 + 0.0528293i
\(359\) 32.4043i 1.71024i −0.518434 0.855118i \(-0.673485\pi\)
0.518434 0.855118i \(-0.326515\pi\)
\(360\) 0.322179 + 0.558030i 0.0169803 + 0.0294108i
\(361\) −9.48225 + 16.4237i −0.499066 + 0.864407i
\(362\) −0.552631 0.319061i −0.0290456 0.0167695i
\(363\) −6.83122 −0.358546
\(364\) 0 0
\(365\) −38.1928 −1.99910
\(366\) 0.117687 + 0.0679464i 0.00615158 + 0.00355162i
\(367\) 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
\(369\) 1.81523i 0.0944973i
\(370\) −3.34648 + 1.93209i −0.173975 + 0.100445i
\(371\) 0 0
\(372\) 13.2891i 0.689007i
\(373\) 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
\(375\) −11.8194 6.82392i −0.610350 0.352386i
\(376\) −1.32636 −0.0684018
\(377\) 11.9134 + 22.5997i 0.613571 + 1.16394i
\(378\) 0 0
\(379\) 12.3983 + 7.15817i 0.636859 + 0.367691i 0.783404 0.621513i \(-0.213482\pi\)
−0.146545 + 0.989204i \(0.546815\pi\)
\(380\) 0.497953 0.862480i 0.0255444 0.0442443i
\(381\) 7.27412 + 12.5991i 0.372665 + 0.645474i
\(382\) 3.68887i 0.188739i
\(383\) −21.8129 + 12.5937i −1.11459 + 0.643507i −0.940013 0.341138i \(-0.889188\pi\)
−0.174573 + 0.984644i \(0.555854\pi\)
\(384\) 8.78006 5.06917i 0.448056 0.258685i
\(385\) 0 0
\(386\) 1.56092 + 2.70359i 0.0794488 + 0.137609i
\(387\) −1.33907 + 2.31934i −0.0680689 + 0.117899i
\(388\) −0.768544 0.443719i −0.0390169 0.0225264i
\(389\) −28.1023 −1.42484 −0.712422 0.701752i \(-0.752402\pi\)
−0.712422 + 0.701752i \(0.752402\pi\)
\(390\) −3.19609 0.123010i −0.161840 0.00622887i
\(391\) 20.9623 1.06011
\(392\) 0 0
\(393\) 9.14644 15.8421i 0.461377 0.799128i
\(394\) −0.448146 0.776212i −0.0225773 0.0391050i
\(395\) 24.4769i 1.23157i
\(396\) 1.53463 0.886021i 0.0771183 0.0445243i
\(397\) 18.8590 10.8882i 0.946504 0.546465i 0.0545111 0.998513i \(-0.482640\pi\)
0.891993 + 0.452049i \(0.149307\pi\)
\(398\) 1.29867i 0.0650963i
\(399\) 0 0
\(400\) 4.21970 7.30874i 0.210985 0.365437i
\(401\) 17.7786 + 10.2645i 0.887821 + 0.512584i 0.873229 0.487310i \(-0.162022\pi\)
0.0145918 + 0.999894i \(0.495355\pi\)
\(402\) 3.76447 0.187754
\(403\) 11.2860 + 7.10833i 0.562198 + 0.354091i
\(404\) 15.0632 0.749424
\(405\) −23.0138 13.2871i −1.14357 0.660239i
\(406\) 0 0
\(407\) 10.7152 + 18.5592i 0.531132 + 0.919947i
\(408\) 6.24182i 0.309016i
\(409\) −5.42879 + 3.13431i −0.268436 + 0.154982i −0.628177 0.778071i \(-0.716199\pi\)
0.359741 + 0.933052i \(0.382865\pi\)
\(410\) 2.28435 1.31887i 0.112816 0.0651343i
\(411\) 9.25233i 0.456384i
\(412\) 5.07308 + 8.78683i 0.249933 + 0.432896i
\(413\) 0 0
\(414\) −0.230322 0.132976i −0.0113197 0.00653543i
\(415\) −44.5622 −2.18747
\(416\) −0.294359 + 7.64813i −0.0144321 + 0.374980i
\(417\) −14.1074 −0.690841
\(418\) 0.0794987 + 0.0458986i 0.00388841 + 0.00224497i
\(419\) −17.0817 + 29.5864i −0.834497 + 1.44539i 0.0599424 + 0.998202i \(0.480908\pi\)
−0.894439 + 0.447189i \(0.852425\pi\)
\(420\) 0 0
\(421\) 11.5233i 0.561613i −0.959764 0.280806i \(-0.909398\pi\)
0.959764 0.280806i \(-0.0906019\pi\)
\(422\) 2.75498 1.59059i 0.134111 0.0774288i
\(423\) −0.535313 + 0.309063i −0.0260278 + 0.0150272i
\(424\) 5.07364i 0.246398i
\(425\) −5.28442 9.15288i −0.256332 0.443980i
\(426\) 0.552218 0.956469i 0.0267550 0.0463411i
\(427\) 0 0
\(428\) 15.8031 0.763873
\(429\) −0.682202 + 17.7252i −0.0329370 + 0.855780i
\(430\) −3.89164 −0.187672
\(431\) 7.59505 + 4.38500i 0.365841 + 0.211218i 0.671640 0.740878i \(-0.265590\pi\)
−0.305799 + 0.952096i \(0.598924\pi\)
\(432\) −9.26026 + 16.0392i −0.445534 + 0.771688i
\(433\) 11.0535 + 19.1452i 0.531196 + 0.920058i 0.999337 + 0.0364046i \(0.0115905\pi\)
−0.468141 + 0.883654i \(0.655076\pi\)
\(434\) 0 0
\(435\) 30.1038 17.3804i 1.44337 0.833328i
\(436\) −2.27203 + 1.31176i −0.108811 + 0.0628219i
\(437\) 0.828933i 0.0396533i
\(438\) −2.34693 4.06501i −0.112141 0.194234i
\(439\) −5.18547 + 8.98150i −0.247489 + 0.428664i −0.962828 0.270114i \(-0.912939\pi\)
0.715339 + 0.698777i \(0.246272\pi\)
\(440\) 4.49705 + 2.59637i 0.214389 + 0.123777i
\(441\) 0 0
\(442\) 2.62866 + 1.65562i 0.125032 + 0.0787496i
\(443\) 35.8137 1.70156 0.850780 0.525522i \(-0.176130\pi\)
0.850780 + 0.525522i \(0.176130\pi\)
\(444\) 24.7456 + 14.2869i 1.17438 + 0.678026i
\(445\) 7.91437 13.7081i 0.375177 0.649826i
\(446\) 1.27530 + 2.20888i 0.0603871 + 0.104593i
\(447\) 26.1457i 1.23665i
\(448\) 0 0
\(449\) −19.7023 + 11.3751i −0.929809 + 0.536825i −0.886751 0.462247i \(-0.847043\pi\)
−0.0430575 + 0.999073i \(0.513710\pi\)
\(450\) 0.134089i 0.00632100i
\(451\) −7.31430 12.6687i −0.344417 0.596548i
\(452\) 19.6124 33.9696i 0.922489 1.59780i
\(453\) −10.2354 5.90942i −0.480902 0.277649i
\(454\) −0.518742 −0.0243458
\(455\) 0 0
\(456\) 0.246827 0.0115587
\(457\) 27.1215 + 15.6586i 1.26869 + 0.732478i 0.974740 0.223344i \(-0.0716972\pi\)
0.293949 + 0.955821i \(0.405031\pi\)
\(458\) −0.793284 + 1.37401i −0.0370677 + 0.0642032i
\(459\) 11.5968 + 20.0862i 0.541292 + 0.937546i
\(460\) 23.2522i 1.08414i
\(461\) −7.28113 + 4.20376i −0.339116 + 0.195789i −0.659881 0.751370i \(-0.729393\pi\)
0.320765 + 0.947159i \(0.396060\pi\)
\(462\) 0 0
\(463\) 10.0392i 0.466563i 0.972409 + 0.233281i \(0.0749463\pi\)
−0.972409 + 0.233281i \(0.925054\pi\)
\(464\) −13.4800 23.3480i −0.625791 1.08390i
\(465\) 9.07411 15.7168i 0.420802 0.728850i
\(466\) −0.799813 0.461772i −0.0370506 0.0213912i
\(467\) 26.3513 1.21939 0.609696 0.792635i \(-0.291291\pi\)
0.609696 + 0.792635i \(0.291291\pi\)
\(468\) 1.10585 + 2.09780i 0.0511180 + 0.0969706i
\(469\) 0 0
\(470\) −0.777869 0.449103i −0.0358804 0.0207156i
\(471\) 14.5339 25.1735i 0.669687 1.15993i
\(472\) −2.72206 4.71475i −0.125293 0.217014i
\(473\) 21.5826i 0.992371i
\(474\) 2.60517 1.50410i 0.119660 0.0690855i
\(475\) 0.361941 0.208967i 0.0166070 0.00958806i
\(476\) 0 0
\(477\) 1.18224 + 2.04770i 0.0541310 + 0.0937577i
\(478\) 0.225846 0.391177i 0.0103300 0.0178920i
\(479\) 7.43409 + 4.29207i 0.339672 + 0.196110i 0.660127 0.751154i \(-0.270502\pi\)
−0.320455 + 0.947264i \(0.603836\pi\)
\(480\) 10.4140 0.475333
\(481\) −25.3699 + 13.3737i −1.15677 + 0.609788i
\(482\) −1.44390 −0.0657678
\(483\) 0 0
\(484\) −3.67990 + 6.37377i −0.167268 + 0.289717i
\(485\) −0.605963 1.04956i −0.0275154 0.0476580i
\(486\) 0.625428i 0.0283700i
\(487\) −18.4084 + 10.6281i −0.834166 + 0.481606i −0.855277 0.518171i \(-0.826613\pi\)
0.0211110 + 0.999777i \(0.493280\pi\)
\(488\) 0.255693 0.147624i 0.0115747 0.00668264i
\(489\) 8.73130i 0.394843i
\(490\) 0 0
\(491\) −11.2268 + 19.4453i −0.506657 + 0.877556i 0.493313 + 0.869852i \(0.335786\pi\)
−0.999970 + 0.00770409i \(0.997548\pi\)
\(492\) −16.8916 9.75240i −0.761534 0.439672i
\(493\) −33.7624 −1.52058
\(494\) −0.0654697 + 0.103948i −0.00294562 + 0.00467682i
\(495\) 2.41999 0.108770
\(496\) −12.1897 7.03772i −0.547333 0.316003i
\(497\) 0 0
\(498\) −2.73833 4.74293i −0.122708 0.212536i
\(499\) 38.8780i 1.74042i −0.492681 0.870210i \(-0.663983\pi\)
0.492681 0.870210i \(-0.336017\pi\)
\(500\) −12.7339 + 7.35193i −0.569478 + 0.328788i
\(501\) −4.28619 + 2.47463i −0.191493 + 0.110558i
\(502\) 4.56707i 0.203838i
\(503\) −2.72850 4.72591i −0.121658 0.210718i 0.798764 0.601645i \(-0.205488\pi\)
−0.920422 + 0.390927i \(0.872154\pi\)
\(504\) 0 0
\(505\) 17.8151 + 10.2855i 0.792760 + 0.457700i
\(506\) −2.14326 −0.0952794
\(507\) −23.6679 1.82455i −1.05113 0.0810313i
\(508\) 15.6739 0.695418
\(509\) −9.43315 5.44623i −0.418117 0.241400i 0.276154 0.961113i \(-0.410940\pi\)
−0.694271 + 0.719713i \(0.744273\pi\)
\(510\) 2.11347 3.66064i 0.0935860 0.162096i
\(511\) 0 0
\(512\) 13.5360i 0.598214i
\(513\) −0.794290 + 0.458584i −0.0350688 + 0.0202470i
\(514\) −0.528304 + 0.305017i −0.0233025 + 0.0134537i
\(515\) 13.8561i 0.610572i
\(516\) 14.3884 + 24.9215i 0.633415 + 1.09711i
\(517\) −2.49068 + 4.31398i −0.109540 + 0.189729i
\(518\) 0 0
\(519\) −1.64308 −0.0721230
\(520\) −3.70346 + 5.88007i −0.162408 + 0.257858i
\(521\) 27.8961 1.22215 0.611074 0.791573i \(-0.290738\pi\)
0.611074 + 0.791573i \(0.290738\pi\)
\(522\) 0.370962 + 0.214175i 0.0162366 + 0.00937418i
\(523\) −8.36180 + 14.4831i −0.365636 + 0.633300i −0.988878 0.148729i \(-0.952482\pi\)
0.623242 + 0.782029i \(0.285815\pi\)
\(524\) −9.85416 17.0679i −0.430481 0.745615i
\(525\) 0 0
\(526\) 0.0248890 0.0143696i 0.00108521 0.000626546i
\(527\) −15.2654 + 8.81347i −0.664970 + 0.383921i
\(528\) 18.7190i 0.814639i
\(529\) 1.82314 + 3.15777i 0.0792668 + 0.137294i
\(530\) −1.71793 + 2.97554i −0.0746219 + 0.129249i
\(531\) −2.19723 1.26857i −0.0953515 0.0550512i
\(532\) 0 0
\(533\) 17.3178 9.12904i 0.750116 0.395423i
\(534\) 1.94534 0.0841832
\(535\) 18.6901 + 10.7907i 0.808045 + 0.466525i
\(536\) 4.08945 7.08313i 0.176637 0.305945i
\(537\) 10.0940 + 17.4834i 0.435590 + 0.754464i
\(538\) 4.21800i 0.181851i
\(539\) 0 0
\(540\) −22.2804 + 12.8636i −0.958796 + 0.553561i
\(541\) 11.1605i 0.479828i 0.970794 + 0.239914i \(0.0771192\pi\)
−0.970794 + 0.239914i \(0.922881\pi\)
\(542\) −1.06876 1.85114i −0.0459070 0.0795133i
\(543\) −3.22198 + 5.58063i −0.138268 + 0.239488i
\(544\) −8.75976 5.05745i −0.375572 0.216836i
\(545\) −3.58280 −0.153470
\(546\) 0 0
\(547\) 36.6556 1.56728 0.783640 0.621215i \(-0.213361\pi\)
0.783640 + 0.621215i \(0.213361\pi\)
\(548\) 8.63275 + 4.98412i 0.368773 + 0.212911i
\(549\) 0.0687976 0.119161i 0.00293621 0.00508567i
\(550\) 0.540297 + 0.935821i 0.0230383 + 0.0399036i
\(551\) 1.33510i 0.0568772i
\(552\) −4.99077 + 2.88142i −0.212421 + 0.122641i
\(553\) 0 0
\(554\) 4.94830i 0.210233i
\(555\) 19.5109 + 33.7938i 0.828190 + 1.43447i
\(556\) −7.59948 + 13.1627i −0.322290 + 0.558222i
\(557\) 28.6461 + 16.5388i 1.21377 + 0.700772i 0.963579 0.267424i \(-0.0861725\pi\)
0.250193 + 0.968196i \(0.419506\pi\)
\(558\) 0.223636 0.00946727
\(559\) −28.8615 1.11081i −1.22071 0.0469823i
\(560\) 0 0
\(561\) −20.3015 11.7211i −0.857130 0.494864i
\(562\) −2.58020 + 4.46903i −0.108839 + 0.188515i
\(563\) 8.89836 + 15.4124i 0.375021 + 0.649556i 0.990330 0.138730i \(-0.0443021\pi\)
−0.615309 + 0.788286i \(0.710969\pi\)
\(564\) 6.64180i 0.279670i
\(565\) 46.3906 26.7836i 1.95167 1.12679i
\(566\) 2.81439 1.62489i 0.118298 0.0682992i
\(567\) 0 0
\(568\) −1.19978 2.07808i −0.0503417 0.0871943i
\(569\) −4.11047 + 7.11954i −0.172320 + 0.298467i −0.939231 0.343287i \(-0.888460\pi\)
0.766911 + 0.641754i \(0.221793\pi\)
\(570\) 0.144756 + 0.0835750i 0.00606317 + 0.00350057i
\(571\) 25.7553 1.07782 0.538912 0.842362i \(-0.318835\pi\)
0.538912 + 0.842362i \(0.318835\pi\)
\(572\) 16.1707 + 10.1849i 0.676132 + 0.425851i
\(573\) 37.2513 1.55620
\(574\) 0 0
\(575\) −4.87891 + 8.45051i −0.203464 + 0.352411i
\(576\) −1.20790 2.09214i −0.0503290 0.0871724i
\(577\) 0.769393i 0.0320302i 0.999872 + 0.0160151i \(0.00509799\pi\)
−0.999872 + 0.0160151i \(0.994902\pi\)
\(578\) −0.893326 + 0.515762i −0.0371575 + 0.0214529i
\(579\) 27.3017 15.7626i 1.13462 0.655073i
\(580\) 37.4505i 1.55505i
\(581\) 0 0
\(582\) 0.0744725 0.128990i 0.00308698 0.00534681i
\(583\) 16.5020 + 9.52743i 0.683443 + 0.394586i
\(584\) −10.1982 −0.422003
\(585\) −0.124551 + 3.23613i −0.00514957 + 0.133798i
\(586\) 2.69229 0.111218
\(587\) −10.4727 6.04644i −0.432256 0.249563i 0.268051 0.963405i \(-0.413620\pi\)
−0.700307 + 0.713841i \(0.746954\pi\)
\(588\) 0 0
\(589\) −0.348520 0.603654i −0.0143605 0.0248731i
\(590\) 3.68674i 0.151781i
\(591\) −7.83842 + 4.52552i −0.322430 + 0.186155i
\(592\) 26.2099 15.1323i 1.07722 0.621933i
\(593\) 15.9481i 0.654911i −0.944867 0.327456i \(-0.893809\pi\)
0.944867 0.327456i \(-0.106191\pi\)
\(594\) −1.18570 2.05369i −0.0486497 0.0842638i
\(595\) 0 0
\(596\) 24.3949 + 14.0844i 0.999253 + 0.576919i
\(597\) 13.1143 0.536734
\(598\) 0.110309 2.86608i 0.00451086 0.117203i
\(599\) −7.11022 −0.290516 −0.145258 0.989394i \(-0.546401\pi\)
−0.145258 + 0.989394i \(0.546401\pi\)
\(600\) 2.51626 + 1.45276i 0.102726 + 0.0593088i
\(601\) −10.3953 + 18.0051i −0.424032 + 0.734445i −0.996329 0.0856011i \(-0.972719\pi\)
0.572297 + 0.820046i \(0.306052\pi\)
\(602\) 0 0
\(603\) 3.81163i 0.155221i
\(604\) −11.0274 + 6.36667i −0.448698 + 0.259056i
\(605\) −8.70432 + 5.02544i −0.353881 + 0.204313i
\(606\) 2.52817i 0.102700i
\(607\) 3.85702 + 6.68056i 0.156552 + 0.271156i 0.933623 0.358257i \(-0.116629\pi\)
−0.777071 + 0.629413i \(0.783296\pi\)
\(608\) 0.199992 0.346396i 0.00811074 0.0140482i
\(609\) 0 0
\(610\) 0.199941 0.00809539
\(611\) −5.64069 3.55270i −0.228198 0.143727i
\(612\) −3.13397 −0.126683
\(613\) 17.6997 + 10.2189i 0.714883 + 0.412738i 0.812867 0.582450i \(-0.197906\pi\)
−0.0979832 + 0.995188i \(0.531239\pi\)
\(614\) 2.12614 3.68257i 0.0858038 0.148617i
\(615\) −13.3183 23.0680i −0.537047 0.930193i
\(616\) 0 0
\(617\) −3.98209 + 2.29906i −0.160313 + 0.0925567i −0.578010 0.816030i \(-0.696171\pi\)
0.417697 + 0.908586i \(0.362837\pi\)
\(618\) −1.47476 + 0.851451i −0.0593234 + 0.0342504i
\(619\) 10.0528i 0.404057i 0.979380 + 0.202028i \(0.0647533\pi\)
−0.979380 + 0.202028i \(0.935247\pi\)
\(620\) −9.77623 16.9329i −0.392623 0.680042i
\(621\) 10.7069 18.5449i 0.429653 0.744181i
\(622\) −0.255396 0.147453i −0.0102404 0.00591232i
\(623\) 0 0
\(624\) 25.0320 + 0.963425i 1.00208 + 0.0385679i
\(625\) −31.1705 −1.24682
\(626\) −0.109107 0.0629930i −0.00436080 0.00251771i
\(627\) 0.463498 0.802802i 0.0185103 0.0320608i
\(628\) −15.6585 27.1213i −0.624842 1.08226i
\(629\) 37.9009i 1.51121i
\(630\) 0 0
\(631\) −6.29923 + 3.63686i −0.250768 + 0.144781i −0.620116 0.784510i \(-0.712914\pi\)
0.369348 + 0.929291i \(0.379581\pi\)
\(632\) 6.53578i 0.259979i
\(633\) −16.0623 27.8207i −0.638418 1.10577i
\(634\) −1.93742 + 3.35570i −0.0769447 + 0.133272i
\(635\) 18.5373 + 10.7025i 0.735631 + 0.424717i
\(636\) 25.4065 1.00743
\(637\) 0 0
\(638\) 3.45199 0.136665
\(639\) −0.968451 0.559136i −0.0383113 0.0221191i
\(640\) 7.45835 12.9182i 0.294817 0.510639i
\(641\) 1.92516 + 3.33448i 0.0760394 + 0.131704i 0.901538 0.432700i \(-0.142439\pi\)
−0.825498 + 0.564404i \(0.809106\pi\)
\(642\) 2.65235i 0.104680i
\(643\) 2.49163 1.43855i 0.0982605 0.0567307i −0.450065 0.892996i \(-0.648599\pi\)
0.548325 + 0.836265i \(0.315266\pi\)
\(644\) 0 0
\(645\) 39.2990i 1.54740i
\(646\) −0.0811745 0.140598i −0.00319377 0.00553177i
\(647\) 18.5501 32.1296i 0.729278 1.26315i −0.227911 0.973682i \(-0.573190\pi\)
0.957189 0.289464i \(-0.0934771\pi\)
\(648\) −6.14512 3.54789i −0.241403 0.139374i
\(649\) −20.4463 −0.802587
\(650\) −1.27924 + 0.674349i −0.0501758 + 0.0264501i
\(651\) 0 0
\(652\) −8.14661 4.70345i −0.319046 0.184201i
\(653\) −10.0475 + 17.4028i −0.393189 + 0.681023i −0.992868 0.119218i \(-0.961961\pi\)
0.599679 + 0.800240i \(0.295295\pi\)
\(654\) −0.220162 0.381332i −0.00860902 0.0149113i
\(655\) 26.9146i 1.05164i
\(656\) −17.8912 + 10.3295i −0.698532 + 0.403298i
\(657\) −4.11593 + 2.37634i −0.160578 + 0.0927097i
\(658\) 0 0
\(659\) −4.95529 8.58281i −0.193031 0.334339i 0.753223 0.657766i \(-0.228498\pi\)
−0.946253 + 0.323427i \(0.895165\pi\)
\(660\) 13.0014 22.5192i 0.506080 0.876557i
\(661\) −40.8994 23.6133i −1.59080 0.918450i −0.993170 0.116680i \(-0.962775\pi\)
−0.597633 0.801770i \(-0.703892\pi\)
\(662\) 0.274936 0.0106857
\(663\) 16.7189 26.5450i 0.649309 1.03092i
\(664\) −11.8989 −0.461768
\(665\) 0 0
\(666\) −0.240428 + 0.416433i −0.00931639 + 0.0161365i
\(667\) 15.5858 + 26.9954i 0.603485 + 1.04527i
\(668\) 5.33222i 0.206310i
\(669\) 22.3059 12.8783i 0.862397 0.497905i
\(670\) 4.79667 2.76936i 0.185312 0.106990i
\(671\) 1.10885i 0.0428068i
\(672\) 0 0
\(673\) 3.45845 5.99020i 0.133313 0.230905i −0.791639 0.610990i \(-0.790772\pi\)
0.924952 + 0.380084i \(0.124105\pi\)
\(674\) −5.04721 2.91401i −0.194411 0.112243i
\(675\) −10.7965 −0.415556
\(676\) −14.4520 + 21.1002i −0.555847 + 0.811545i
\(677\) −12.3291 −0.473844 −0.236922 0.971529i \(-0.576139\pi\)
−0.236922 + 0.971529i \(0.576139\pi\)
\(678\) 5.70137 + 3.29169i 0.218960 + 0.126416i
\(679\) 0 0
\(680\) −4.59185 7.95331i −0.176089 0.304996i
\(681\) 5.23841i 0.200736i
\(682\) 1.56078 0.901120i 0.0597655 0.0345057i
\(683\) −21.2491 + 12.2682i −0.813076 + 0.469430i −0.848023 0.529960i \(-0.822207\pi\)
0.0349470 + 0.999389i \(0.488874\pi\)
\(684\) 0.123930i 0.00473856i
\(685\) 6.80655 + 11.7893i 0.260065 + 0.450446i
\(686\) 0 0
\(687\) 13.8751 + 8.01082i 0.529370 + 0.305632i
\(688\) 30.4796 1.16202
\(689\) −13.5899 + 21.5770i −0.517734 + 0.822018i
\(690\) −3.90258 −0.148569
\(691\) 7.88703 + 4.55358i 0.300037 + 0.173226i 0.642459 0.766320i \(-0.277914\pi\)
−0.342423 + 0.939546i \(0.611247\pi\)
\(692\) −0.885106 + 1.53305i −0.0336467 + 0.0582777i
\(693\) 0 0
\(694\) 1.47992i 0.0561769i
\(695\) −17.9756 + 10.3782i −0.681853 + 0.393668i
\(696\) 8.03826 4.64089i 0.304690 0.175913i
\(697\) 25.8716i 0.979956i
\(698\) −1.97543 3.42155i −0.0747712 0.129508i
\(699\) −4.66312 + 8.07675i −0.176375 + 0.305491i
\(700\) 0 0
\(701\) 0.286950 0.0108380 0.00541898 0.999985i \(-0.498275\pi\)
0.00541898 + 0.999985i \(0.498275\pi\)
\(702\) 2.80732 1.47988i 0.105956 0.0558544i
\(703\) 1.49875 0.0565265
\(704\) −16.8601 9.73419i −0.635440 0.366871i
\(705\) −4.53518 + 7.85516i −0.170805 + 0.295842i
\(706\) 0.0512797 + 0.0888191i 0.00192994 + 0.00334275i
\(707\) 0 0
\(708\) −23.6093 + 13.6308i −0.887292 + 0.512278i
\(709\) −16.0949 + 9.29241i −0.604457 + 0.348984i −0.770793 0.637086i \(-0.780140\pi\)
0.166336 + 0.986069i \(0.446806\pi\)
\(710\) 1.62497i 0.0609841i
\(711\) −1.52294 2.63781i −0.0571147 0.0989256i
\(712\) 2.11328 3.66031i 0.0791986 0.137176i
\(713\) 14.0940 + 8.13715i 0.527823 + 0.304739i
\(714\) 0 0
\(715\) 12.1704 + 23.0872i 0.455148 + 0.863414i
\(716\) 21.7501 0.812841
\(717\) −3.95022 2.28066i −0.147524 0.0851729i
\(718\) 2.92974 5.07445i 0.109337 0.189377i
\(719\) 20.8475 + 36.1088i 0.777479 + 1.34663i 0.933391 + 0.358862i \(0.116835\pi\)
−0.155912 + 0.987771i \(0.549832\pi\)
\(720\) 3.41757i 0.127365i
\(721\) 0 0
\(722\) −2.96980 + 1.71462i −0.110525 + 0.0638114i
\(723\) 14.5809i 0.542271i
\(724\) 3.47128 + 6.01244i 0.129009 + 0.223451i
\(725\) 7.85809 13.6106i 0.291842 0.505486i
\(726\) −1.06975 0.617623i −0.0397023 0.0229221i
\(727\) 32.7039 1.21292 0.606461 0.795113i \(-0.292589\pi\)
0.606461 + 0.795113i \(0.292589\pi\)
\(728\) 0 0
\(729\) 23.3578 0.865105
\(730\) −5.98091 3.45308i −0.221363 0.127804i
\(731\) 19.0851 33.0564i 0.705888 1.22263i
\(732\) −0.739235 1.28039i −0.0273229 0.0473246i
\(733\) 9.93531i 0.366969i 0.983023 + 0.183484i \(0.0587377\pi\)
−0.983023 + 0.183484i \(0.941262\pi\)
\(734\) 1.23225 0.711440i 0.0454832 0.0262597i
\(735\) 0 0
\(736\) 9.33871i 0.344230i
\(737\) −15.3586 26.6018i −0.565740 0.979891i
\(738\) 0.164119 0.284262i 0.00604129 0.0104638i
\(739\) 9.00853 + 5.20108i 0.331384 + 0.191325i 0.656455 0.754365i \(-0.272055\pi\)
−0.325071 + 0.945690i \(0.605388\pi\)
\(740\) 42.0411 1.54546
\(741\) 1.04969 + 0.661133i 0.0385615 + 0.0242873i
\(742\) 0 0
\(743\) −1.47972 0.854317i −0.0542857 0.0313419i 0.472612 0.881271i \(-0.343311\pi\)
−0.526897 + 0.849929i \(0.676645\pi\)
\(744\) 2.42295 4.19668i 0.0888297 0.153858i
\(745\) 19.2343 + 33.3148i 0.704690 + 1.22056i
\(746\) 0.378216i 0.0138475i
\(747\) −4.80235 + 2.77264i −0.175709 + 0.101446i
\(748\) −21.8723 + 12.6280i −0.799732 + 0.461726i
\(749\) 0 0
\(750\) −1.23393 2.13722i −0.0450566 0.0780404i
\(751\) 14.9906 25.9645i 0.547015 0.947458i −0.451462 0.892290i \(-0.649097\pi\)
0.998477 0.0551673i \(-0.0175692\pi\)
\(752\) 6.09233 + 3.51741i 0.222164 + 0.128267i
\(753\) 46.1197 1.68069
\(754\) −0.177666 + 4.61618i −0.00647022 + 0.168111i
\(755\) −17.3893 −0.632860
\(756\) 0 0
\(757\) −4.20229 + 7.27858i −0.152735 + 0.264545i −0.932232 0.361861i \(-0.882141\pi\)
0.779497 + 0.626406i \(0.215475\pi\)
\(758\) 1.29437 + 2.24191i 0.0470136 + 0.0814299i
\(759\) 21.6433i 0.785601i
\(760\) 0.314506 0.181580i 0.0114083 0.00658660i
\(761\) −44.2184 + 25.5295i −1.60292 + 0.925444i −0.612015 + 0.790846i \(0.709641\pi\)
−0.990900 + 0.134598i \(0.957026\pi\)
\(762\) 2.63067i 0.0952990i
\(763\) 0 0
\(764\) 20.0668 34.7568i 0.725993 1.25746i
\(765\) −3.70650 2.13995i −0.134009 0.0773699i
\(766\) −4.55447 −0.164560
\(767\) 1.05233 27.3419i 0.0379973 0.987257i
\(768\) −24.5560 −0.886088
\(769\) −0.610062 0.352220i −0.0219994 0.0127014i 0.488960 0.872306i \(-0.337376\pi\)
−0.510959 + 0.859605i \(0.670710\pi\)
\(770\) 0 0
\(771\) 3.08015 + 5.33498i 0.110929 + 0.192134i
\(772\) 33.9646i 1.22241i
\(773\) 1.09571 0.632607i 0.0394099 0.0227533i −0.480166 0.877178i \(-0.659423\pi\)
0.519575 + 0.854425i \(0.326090\pi\)
\(774\) −0.419392 + 0.242136i −0.0150747 + 0.00870341i
\(775\) 8.20522i 0.294740i
\(776\) −0.161803 0.280252i −0.00580840 0.0100604i
\(777\) 0 0
\(778\) −4.40076 2.54078i −0.157775 0.0910914i
\(779\) −1.02307 −0.0366551
\(780\) 29.4447 + 18.5452i 1.05429 + 0.664026i
\(781\) −9.01193 −0.322472