Properties

Label 637.2.u.g.30.3
Level $637$
Weight $2$
Character 637.30
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.u (of order \(6\), degree \(2\), not 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 30.3
Root \(0.655911 + 1.25291i\) of defining polynomial
Character \(\chi\) \(=\) 637.30
Dual form 637.2.u.g.361.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.156598 + 0.0904119i) q^{2} +1.82601 q^{3} +(-0.983651 + 1.70373i) q^{4} +(-2.32670 - 1.34332i) q^{5} +(-0.285950 + 0.165093i) q^{6} -0.717383i q^{8} +0.334323 q^{9} +O(q^{10})\) \(q+(-0.156598 + 0.0904119i) q^{2} +1.82601 q^{3} +(-0.983651 + 1.70373i) q^{4} +(-2.32670 - 1.34332i) q^{5} +(-0.285950 + 0.165093i) q^{6} -0.717383i q^{8} +0.334323 q^{9} +0.485809 q^{10} +2.69424i q^{11} +(-1.79616 + 3.11104i) 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} +(-0.0523543 + 0.0302268i) q^{18} +0.188424i q^{19} +(4.57732 - 2.64272i) q^{20} +(-0.243592 - 0.421913i) q^{22} +(2.19964 + 3.80989i) q^{23} -1.30995i q^{24} +(1.10902 + 1.92088i) q^{25} +(0.0250743 - 0.651487i) q^{26} -4.86756 q^{27} +(-3.54280 + 6.13631i) q^{29} +0.887093 q^{30} +(-3.20369 + 1.84965i) q^{31} +(1.83838 + 1.06139i) q^{32} +4.91972i q^{33} -0.861613i q^{34} +(-0.328857 + 0.569598i) q^{36} +(6.88848 - 3.97707i) q^{37} +(-0.0170358 - 0.0295069i) q^{38} +(-3.50874 + 5.57090i) q^{39} +(-0.963675 + 1.66913i) q^{40} +(-4.70215 - 2.71479i) q^{41} +(-4.00533 - 6.93743i) q^{43} +(-4.59027 - 2.65020i) q^{44} +(-0.777869 - 0.449103i) q^{45} +(-0.688919 - 0.397748i) q^{46} +(-1.60118 - 0.924445i) q^{47} +(-3.47389 - 6.01695i) q^{48} +(-0.347341 - 0.200538i) q^{50} +(-4.35041 + 7.53514i) q^{51} +(-3.30773 - 6.27476i) q^{52} +(3.53622 + 6.12491i) q^{53} +(0.762250 - 0.440085i) q^{54} +(3.61923 - 6.26869i) q^{55} +0.344066i q^{57} -1.28125i q^{58} +(6.57216 + 3.79444i) q^{59} +(8.35825 - 4.82564i) q^{60} +0.411564 q^{61} +(0.334461 - 0.579304i) q^{62} +7.22592 q^{64} +(8.56910 - 4.51719i) q^{65} +(-0.444801 - 0.770418i) q^{66} -11.4010i q^{67} +(-4.68703 - 8.11818i) q^{68} +(4.01658 + 6.95692i) q^{69} +(2.89675 - 1.67244i) q^{71} -0.239838i q^{72} +(12.3112 - 7.10790i) 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} +(-4.55529 + 7.89000i) q^{79} +10.2224i q^{80} -9.89120 q^{81} +0.981797 q^{82} +16.5866i q^{83} +(11.0866 - 6.40083i) q^{85} +(1.25445 + 0.724258i) q^{86} +(-6.46920 + 11.2050i) q^{87} +1.93280 q^{88} +(5.10232 - 2.94582i) q^{89} +0.162417 q^{90} -8.65473 q^{92} +(-5.84998 + 3.37749i) q^{93} +0.334323 q^{94} +(0.253115 - 0.438407i) q^{95} +(3.35691 + 1.93811i) q^{96} +(-0.390659 + 0.225547i) q^{97} +0.900747i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + O(q^{10}) \) \( 12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + 24q^{10} + q^{12} + 2q^{13} - 12q^{15} - 8q^{16} - 17q^{17} - 3q^{18} + 3q^{20} - 15q^{22} + 3q^{23} - 5q^{25} + 9q^{26} - 12q^{27} - q^{29} - 22q^{30} + 18q^{31} + 18q^{32} - 13q^{36} + 15q^{37} - 19q^{38} - q^{39} + q^{40} + 6q^{41} + 11q^{43} + 33q^{44} + 9q^{45} - 30q^{46} - 15q^{47} - 19q^{48} + 18q^{50} + 4q^{51} - 47q^{52} - 8q^{53} - 6q^{54} + 15q^{55} - 27q^{59} + 30q^{60} + 10q^{61} - 41q^{62} + 2q^{64} - 3q^{65} + 34q^{66} + 11q^{68} - 7q^{69} + 30q^{71} + 42q^{73} - 33q^{74} - q^{75} + 45q^{76} + 44q^{78} - 35q^{79} - 28q^{81} + 10q^{82} - 21q^{85} + 57q^{86} - 10q^{87} + 28q^{88} - 48q^{89} - 66q^{92} - 81q^{93} + 2q^{94} + 2q^{95} + 21q^{96} + 3q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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 \(-0.687030\pi\)
0.443611 + 0.896219i \(0.353697\pi\)
\(3\) 1.82601 1.05425 0.527125 0.849788i \(-0.323270\pi\)
0.527125 + 0.849788i \(0.323270\pi\)
\(4\) −0.983651 + 1.70373i −0.491826 + 0.851867i
\(5\) −2.32670 1.34332i −1.04053 0.600751i −0.120548 0.992708i \(-0.538465\pi\)
−0.919984 + 0.391956i \(0.871799\pi\)
\(6\) −0.285950 + 0.165093i −0.116739 + 0.0673990i
\(7\) 0 0
\(8\) 0.717383i 0.253633i
\(9\) 0.334323 0.111441
\(10\) 0.485809 0.153626
\(11\) 2.69424i 0.812345i 0.913796 + 0.406172i \(0.133137\pi\)
−0.913796 + 0.406172i \(0.866863\pi\)
\(12\) −1.79616 + 3.11104i −0.518507 + 0.898080i
\(13\) −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 0.417894 + 0.908496i \(0.362768\pi\)
−0.995727 + 0.0923405i \(0.970565\pi\)
\(18\) −0.0523543 + 0.0302268i −0.0123400 + 0.00712452i
\(19\) 0.188424i 0.0432275i 0.999766 + 0.0216138i \(0.00688041\pi\)
−0.999766 + 0.0216138i \(0.993120\pi\)
\(20\) 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 0.998890 0.0470977i \(-0.0149972\pi\)
−0.540233 + 0.841516i \(0.681664\pi\)
\(24\) 1.30995i 0.267392i
\(25\) 1.10902 + 1.92088i 0.221804 + 0.384177i
\(26\) 0.0250743 0.651487i 0.00491747 0.127767i
\(27\) −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 \(0.938119\pi\)
\(30\) 0.887093 0.161960
\(31\) −3.20369 + 1.84965i −0.575400 + 0.332207i −0.759303 0.650737i \(-0.774460\pi\)
0.183903 + 0.982944i \(0.441127\pi\)
\(32\) 1.83838 + 1.06139i 0.324983 + 0.187629i
\(33\) 4.91972i 0.856414i
\(34\) 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 \(-0.439830\pi\)
0.944552 + 0.328361i \(0.106496\pi\)
\(38\) −0.0170358 0.0295069i −0.00276357 0.00478665i
\(39\) −3.50874 + 5.57090i −0.561848 + 0.892058i
\(40\) −0.963675 + 1.66913i −0.152370 + 0.263913i
\(41\) −4.70215 2.71479i −0.734353 0.423979i 0.0856594 0.996324i \(-0.472700\pi\)
−0.820013 + 0.572345i \(0.806034\pi\)
\(42\) 0 0
\(43\) −4.00533 6.93743i −0.610807 1.05795i −0.991105 0.133084i \(-0.957512\pi\)
0.380298 0.924864i \(-0.375821\pi\)
\(44\) −4.59027 2.65020i −0.692010 0.399532i
\(45\) −0.777869 0.449103i −0.115958 0.0669483i
\(46\) −0.688919 0.397748i −0.101576 0.0586447i
\(47\) −1.60118 0.924445i −0.233557 0.134844i 0.378655 0.925538i \(-0.376387\pi\)
−0.612212 + 0.790694i \(0.709720\pi\)
\(48\) −3.47389 6.01695i −0.501412 0.868471i
\(49\) 0 0
\(50\) −0.347341 0.200538i −0.0491215 0.0283603i
\(51\) −4.35041 + 7.53514i −0.609180 + 1.05513i
\(52\) −3.30773 6.27476i −0.458700 0.870152i
\(53\) 3.53622 + 6.12491i 0.485737 + 0.841321i 0.999866 0.0163917i \(-0.00521788\pi\)
−0.514128 + 0.857713i \(0.671885\pi\)
\(54\) 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
\(58\) 1.28125i 0.168236i
\(59\) 6.57216 + 3.79444i 0.855623 + 0.493994i 0.862544 0.505982i \(-0.168870\pi\)
−0.00692130 + 0.999976i \(0.502203\pi\)
\(60\) 8.35825 4.82564i 1.07905 0.622987i
\(61\) 0.411564 0.0526954 0.0263477 0.999653i \(-0.491612\pi\)
0.0263477 + 0.999653i \(0.491612\pi\)
\(62\) 0.334461 0.579304i 0.0424766 0.0735716i
\(63\) 0 0
\(64\) 7.22592 0.903240
\(65\) 8.56910 4.51719i 1.06287 0.560289i
\(66\) −0.444801 0.770418i −0.0547512 0.0948319i
\(67\) 11.4010i 1.39286i −0.717626 0.696429i \(-0.754771\pi\)
0.717626 0.696429i \(-0.245229\pi\)
\(68\) −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 \(0.269732\pi\)
\(72\) 0.239838i 0.0282651i
\(73\) 12.3112 7.10790i 1.44092 0.831917i 0.443011 0.896516i \(-0.353910\pi\)
0.997911 + 0.0645994i \(0.0205769\pi\)
\(74\) −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
\(79\) −4.55529 + 7.89000i −0.512511 + 0.887695i 0.487384 + 0.873188i \(0.337951\pi\)
−0.999895 + 0.0145069i \(0.995382\pi\)
\(80\) 10.2224i 1.14290i
\(81\) −9.89120 −1.09902
\(82\) 0.981797 0.108421
\(83\) 16.5866i 1.82061i 0.413934 + 0.910307i \(0.364155\pi\)
−0.413934 + 0.910307i \(0.635845\pi\)
\(84\) 0 0
\(85\) 11.0866 6.40083i 1.20251 0.694268i
\(86\) 1.25445 + 0.724258i 0.135271 + 0.0780988i
\(87\) −6.46920 + 11.2050i −0.693571 + 1.20130i
\(88\) 1.93280 0.206037
\(89\) 5.10232 2.94582i 0.540844 0.312257i −0.204577 0.978851i \(-0.565582\pi\)
0.745421 + 0.666594i \(0.232248\pi\)
\(90\) 0.162417 0.0171203
\(91\) 0 0
\(92\) −8.65473 −0.902318
\(93\) −5.84998 + 3.37749i −0.606615 + 0.350229i
\(94\) 0.334323 0.0344828
\(95\) 0.253115 0.438407i 0.0259690 0.0449796i
\(96\) 3.35691 + 1.93811i 0.342613 + 0.197808i
\(97\) −0.390659 + 0.225547i −0.0396654 + 0.0229008i −0.519702 0.854348i \(-0.673957\pi\)
0.480036 + 0.877249i \(0.340624\pi\)
\(98\) 0 0
\(99\) 0.900747i 0.0905285i
\(100\) −4.36356 −0.436356
\(101\) −7.65680 −0.761880 −0.380940 0.924600i \(-0.624400\pi\)
−0.380940 + 0.924600i \(0.624400\pi\)
\(102\) 1.57332i 0.155782i
\(103\) −2.57870 + 4.46644i −0.254087 + 0.440091i −0.964647 0.263545i \(-0.915108\pi\)
0.710560 + 0.703636i \(0.248442\pi\)
\(104\) 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 0.603935 0.797034i \(-0.293599\pi\)
−0.992219 + 0.124506i \(0.960265\pi\)
\(108\) 4.78798 8.29303i 0.460724 0.797997i
\(109\) −1.15490 + 0.666781i −0.110619 + 0.0638660i −0.554289 0.832324i \(-0.687010\pi\)
0.443670 + 0.896190i \(0.353676\pi\)
\(110\) 1.30889i 0.124797i
\(111\) 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
\(115\) 11.8193i 1.10216i
\(116\) −6.96976 12.0720i −0.647126 1.12086i
\(117\) −0.642412 + 1.01997i −0.0593910 + 0.0942964i
\(118\) −1.37225 −0.126326
\(119\) 0 0
\(120\) −1.75968 + 3.04786i −0.160636 + 0.278230i
\(121\) 3.74106 0.340096
\(122\) −0.0644501 + 0.0372103i −0.00583503 + 0.00336886i
\(123\) −8.58619 4.95724i −0.774191 0.446979i
\(124\) 7.27765i 0.653553i
\(125\) 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
\(129\) −7.31378 12.6678i −0.643942 1.11534i
\(130\) −0.933496 + 1.48213i −0.0818730 + 0.129992i
\(131\) 5.00897 8.67579i 0.437636 0.758007i −0.559871 0.828580i \(-0.689149\pi\)
0.997507 + 0.0705727i \(0.0224827\pi\)
\(132\) −8.38190 4.83929i −0.729551 0.421206i
\(133\) 0 0
\(134\) 1.03079 + 1.78538i 0.0890465 + 0.154233i
\(135\) 11.3254 + 6.53870i 0.974731 + 0.562761i
\(136\) 2.96032 + 1.70914i 0.253845 + 0.146558i
\(137\) 4.38811 + 2.53348i 0.374902 + 0.216450i 0.675598 0.737270i \(-0.263886\pi\)
−0.300696 + 0.953720i \(0.597219\pi\)
\(138\) −1.25798 0.726293i −0.107086 0.0618261i
\(139\) 3.86289 + 6.69073i 0.327646 + 0.567500i 0.982044 0.188650i \(-0.0604113\pi\)
−0.654398 + 0.756150i \(0.727078\pi\)
\(140\) 0 0
\(141\) −2.92378 1.68805i −0.246227 0.142159i
\(142\) −0.302417 + 0.523802i −0.0253783 + 0.0439565i
\(143\) −8.21974 5.17707i −0.687370 0.432928i
\(144\) −0.636031 1.10164i −0.0530025 0.0918031i
\(145\) 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
\(149\) 14.3185i 1.17301i −0.809944 0.586507i \(-0.800502\pi\)
0.809944 0.586507i \(-0.199498\pi\)
\(150\) −0.634250 0.366184i −0.0517863 0.0298988i
\(151\) −5.60534 + 3.23624i −0.456156 + 0.263362i −0.710427 0.703771i \(-0.751498\pi\)
0.254271 + 0.967133i \(0.418165\pi\)
\(152\) 0.135172 0.0109639
\(153\) −0.796513 + 1.37960i −0.0643943 + 0.111534i
\(154\) 0 0
\(155\) 9.93871 0.798296
\(156\) −6.03996 11.4578i −0.483584 0.917357i
\(157\) 7.95937 + 13.7860i 0.635227 + 1.10025i 0.986467 + 0.163960i \(0.0524267\pi\)
−0.351240 + 0.936285i \(0.614240\pi\)
\(158\) 1.64741i 0.131061i
\(159\) 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
\(163\) 4.78162i 0.374525i 0.982310 + 0.187263i \(0.0599616\pi\)
−0.982310 + 0.187263i \(0.940038\pi\)
\(164\) 9.25056 5.34081i 0.722348 0.417048i
\(165\) 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 0.588062 0.808816i \(-0.299891\pi\)
−0.406424 + 0.913685i \(0.633224\pi\)
\(168\) 0 0
\(169\) −5.61544 11.7246i −0.431957 0.901894i
\(170\) −1.15742 + 2.00472i −0.0887703 + 0.153755i
\(171\) 0.0629946i 0.00481732i
\(172\) 15.7594 1.20164
\(173\) −0.899816 −0.0684118 −0.0342059 0.999415i \(-0.510890\pi\)
−0.0342059 + 0.999415i \(0.510890\pi\)
\(174\) 2.33957i 0.177362i
\(175\) 0 0
\(176\) 8.87787 5.12564i 0.669195 0.386360i
\(177\) 12.0009 + 6.92870i 0.902039 + 0.520793i
\(178\) −0.532675 + 0.922620i −0.0399257 + 0.0691533i
\(179\) 11.0558 0.826351 0.413175 0.910651i \(-0.364420\pi\)
0.413175 + 0.910651i \(0.364420\pi\)
\(180\) 1.53030 0.883522i 0.114062 0.0658538i
\(181\) 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
\(184\) 2.73315 1.57799i 0.201491 0.116331i
\(185\) −21.3699 −1.57115
\(186\) 0.610730 1.05782i 0.0447809 0.0775628i
\(187\) −11.1179 6.41894i −0.813024 0.469400i
\(188\) 3.15002 1.81866i 0.229738 0.132640i
\(189\) 0 0
\(190\) 0.0915382i 0.00664088i
\(191\) −20.4004 −1.47612 −0.738059 0.674736i \(-0.764258\pi\)
−0.738059 + 0.674736i \(0.764258\pi\)
\(192\) 13.1946 0.952240
\(193\) 17.2646i 1.24273i −0.783521 0.621365i \(-0.786578\pi\)
0.783521 0.621365i \(-0.213422\pi\)
\(194\) 0.0407842 0.0706403i 0.00292814 0.00507168i
\(195\) 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 \(-0.915263\pi\)
0.710218 + 0.703982i \(0.248596\pi\)
\(200\) 1.37801 0.795593i 0.0974399 0.0562569i
\(201\) 20.8184i 1.46842i
\(202\) 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
\(206\) 0.932580i 0.0649759i
\(207\) 0.735392 + 1.27374i 0.0511132 + 0.0885307i
\(208\) 13.7086 + 0.527611i 0.950518 + 0.0365833i
\(209\) −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 \(-0.0403868\pi\)
\(212\) −13.9136 −0.955592
\(213\) 5.28951 3.05390i 0.362431 0.209250i
\(214\) 1.25793 + 0.726269i 0.0859906 + 0.0496467i
\(215\) 21.5218i 1.46777i
\(216\) 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
\(220\) 7.12013 + 12.3324i 0.480039 + 0.831452i
\(221\) −8.01153 15.1979i −0.538914 1.02232i
\(222\) −1.31317 + 2.27448i −0.0881344 + 0.152653i
\(223\) −12.2157 7.05271i −0.818020 0.472284i 0.0317129 0.999497i \(-0.489904\pi\)
−0.849733 + 0.527213i \(0.823237\pi\)
\(224\) 0 0
\(225\) 0.370772 + 0.642195i 0.0247181 + 0.0428130i
\(226\) −3.12230 1.80266i −0.207693 0.119911i
\(227\) −2.48443 1.43439i −0.164897 0.0952035i 0.415280 0.909694i \(-0.363684\pi\)
−0.580178 + 0.814490i \(0.697017\pi\)
\(228\) −0.586196 0.338441i −0.0388218 0.0224138i
\(229\) 7.59860 + 4.38706i 0.502130 + 0.289905i 0.729593 0.683882i \(-0.239710\pi\)
−0.227463 + 0.973787i \(0.573043\pi\)
\(230\) 1.06861 + 1.85088i 0.0704618 + 0.122043i
\(231\) 0 0
\(232\) 4.40208 + 2.54154i 0.289011 + 0.166861i
\(233\) 2.55371 4.42316i 0.167299 0.289771i −0.770170 0.637839i \(-0.779829\pi\)
0.937469 + 0.348068i \(0.113162\pi\)
\(234\) 0.00838290 0.217807i 0.000548007 0.0142385i
\(235\) 2.48365 + 4.30181i 0.162016 + 0.280619i
\(236\) −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 \(-0.0257443\pi\)
\(240\) 18.6662i 1.20490i
\(241\) −6.91532 3.99256i −0.445455 0.257183i 0.260454 0.965486i \(-0.416128\pi\)
−0.705909 + 0.708303i \(0.749461\pi\)
\(242\) −0.585842 + 0.338236i −0.0376593 + 0.0217426i
\(243\) −3.45877 −0.221880
\(244\) −0.404835 + 0.701195i −0.0259169 + 0.0448894i
\(245\) 0 0
\(246\) 1.79277 0.114303
\(247\) −0.574856 0.362063i −0.0365772 0.0230375i
\(248\) 1.32691 + 2.29827i 0.0842588 + 0.145941i
\(249\) 30.2873i 1.91938i
\(250\) −0.675749 1.17043i −0.0427381 0.0740246i
\(251\) −12.6285 21.8732i −0.797105 1.38063i −0.921494 0.388393i \(-0.873030\pi\)
0.124389 0.992234i \(-0.460303\pi\)
\(252\) 0 0
\(253\) −10.2648 + 5.92637i −0.645341 + 0.372588i
\(254\) 1.44066i 0.0903952i
\(255\) 20.2442 11.6880i 1.26774 0.731931i
\(256\) −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 \(0.799778\pi\)
\(258\) 2.29065 + 1.32250i 0.142609 + 0.0823355i
\(259\) 0 0
\(260\) −0.732915 + 19.0428i −0.0454535 + 1.18099i
\(261\) −1.18444 + 2.05151i −0.0733150 + 0.126985i
\(262\) 1.81148i 0.111914i
\(263\) −0.158935 −0.00980037 −0.00490019 0.999988i \(-0.501560\pi\)
−0.00490019 + 0.999988i \(0.501560\pi\)
\(264\) 3.52932 0.217215
\(265\) 19.0011i 1.16723i
\(266\) 0 0
\(267\) 9.31689 5.37911i 0.570185 0.329196i
\(268\) 19.4243 + 11.2146i 1.18653 + 0.685043i
\(269\) −11.6633 + 20.2014i −0.711124 + 1.23170i 0.253311 + 0.967385i \(0.418480\pi\)
−0.964435 + 0.264318i \(0.914853\pi\)
\(270\) −2.36470 −0.143911
\(271\) −10.2373 + 5.91049i −0.621870 + 0.359037i −0.777597 0.628763i \(-0.783561\pi\)
0.155727 + 0.987800i \(0.450228\pi\)
\(272\) 18.1300 1.09929
\(273\) 0 0
\(274\) −0.916226 −0.0553513
\(275\) −5.17532 + 2.98797i −0.312084 + 0.180182i
\(276\) −15.8036 −0.951268
\(277\) −13.6827 + 23.6991i −0.822111 + 1.42394i 0.0819961 + 0.996633i \(0.473870\pi\)
−0.904107 + 0.427306i \(0.859463\pi\)
\(278\) −1.20984 0.698503i −0.0725615 0.0418934i
\(279\) −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 \(0.675860\pi\)
\(282\) 0.610478 0.0363534
\(283\) 17.9721 1.06833 0.534165 0.845380i \(-0.320626\pi\)
0.534165 + 0.845380i \(0.320626\pi\)
\(284\) 6.58040i 0.390475i
\(285\) 0.462190 0.800537i 0.0273778 0.0474197i
\(286\) 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
\(291\) −0.713347 + 0.411851i −0.0418172 + 0.0241432i
\(292\) 27.9668i 1.63663i
\(293\) −12.8943 + 7.44453i −0.753293 + 0.434914i −0.826882 0.562375i \(-0.809888\pi\)
0.0735896 + 0.997289i \(0.476554\pi\)
\(294\) 0 0
\(295\) −10.1943 17.6570i −0.593535 1.02803i
\(296\) −2.85308 4.94168i −0.165832 0.287229i
\(297\) 13.1144i 0.760974i
\(298\) 1.29456 + 2.24224i 0.0749918 + 0.129890i
\(299\) −15.8501 0.610035i −0.916636 0.0352792i
\(300\) −7.96793 −0.460028
\(301\) 0 0
\(302\) 0.585190 1.01358i 0.0336739 0.0583249i
\(303\) −13.9814 −0.803211
\(304\) 0.620883 0.358467i 0.0356101 0.0205595i
\(305\) −0.957586 0.552862i −0.0548312 0.0316568i
\(306\) 0.288057i 0.0164671i
\(307\) 23.5161i 1.34214i 0.741396 + 0.671068i \(0.234164\pi\)
−0.741396 + 0.671068i \(0.765836\pi\)
\(308\) 0 0
\(309\) −4.70874 + 8.15577i −0.267871 + 0.463966i
\(310\) −1.55638 + 0.898577i −0.0883965 + 0.0510358i
\(311\) −0.815450 1.41240i −0.0462399 0.0800899i 0.841979 0.539510i \(-0.181391\pi\)
−0.888219 + 0.459420i \(0.848057\pi\)
\(312\) 3.99647 + 2.51711i 0.226255 + 0.142503i
\(313\) −0.348367 + 0.603389i −0.0196909 + 0.0341056i −0.875703 0.482850i \(-0.839602\pi\)
0.856012 + 0.516956i \(0.172935\pi\)
\(314\) −2.49284 1.43924i −0.140679 0.0812212i
\(315\) 0 0
\(316\) −8.96164 15.5220i −0.504132 0.873182i
\(317\) −18.5579 10.7144i −1.04231 0.601780i −0.121826 0.992551i \(-0.538875\pi\)
−0.920488 + 0.390771i \(0.872208\pi\)
\(318\) −2.02236 1.16761i −0.113409 0.0654764i
\(319\) −16.5327 9.54517i −0.925654 0.534427i
\(320\) −16.8126 9.70673i −0.939850 0.542623i
\(321\) −7.33408 12.7030i −0.409348 0.709012i
\(322\) 0 0
\(323\) −0.777544 0.448915i −0.0432637 0.0249783i
\(324\) 9.72949 16.8520i 0.540527 0.936221i
\(325\) −7.99136 0.307569i −0.443281 0.0170609i
\(326\) −0.432315 0.748792i −0.0239437 0.0414717i
\(327\) −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
\(331\) 1.52046i 0.0835722i 0.999127 + 0.0417861i \(0.0133048\pi\)
−0.999127 + 0.0417861i \(0.986695\pi\)
\(332\) −28.2591 16.3154i −1.55092 0.895425i
\(333\) 2.30298 1.32962i 0.126202 0.0728630i
\(334\) −0.490108 −0.0268175
\(335\) −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 \(0.841023\pi\)
\(338\) 1.93941 + 1.32835i 0.105490 + 0.0722527i
\(339\) 18.2038 + 31.5300i 0.988697 + 1.71247i
\(340\) 25.1848i 1.36584i
\(341\) −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
\(345\) 21.5822i 1.16195i
\(346\) 0.140909 0.0813541i 0.00757534 0.00437362i
\(347\) −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
\(349\) 18.9220 + 10.9246i 1.01287 + 0.584782i 0.912031 0.410120i \(-0.134513\pi\)
0.100841 + 0.994903i \(0.467847\pi\)
\(350\) 0 0
\(351\) 9.35317 14.8502i 0.499235 0.792646i
\(352\) −2.85964 + 4.95304i −0.152419 + 0.263998i
\(353\) 0.567179i 0.0301879i 0.999886 + 0.0150940i \(0.00480474\pi\)
−0.999886 + 0.0150940i \(0.995195\pi\)
\(354\) −2.50575 −0.133179
\(355\) −8.98650 −0.476954
\(356\) 11.5907i 0.614303i
\(357\) 0 0
\(358\) −1.73132 + 0.999577i −0.0915030 + 0.0528293i
\(359\) 28.0630 + 16.2022i 1.48111 + 0.855118i 0.999771 0.0214184i \(-0.00681822\pi\)
0.481336 + 0.876536i \(0.340152\pi\)
\(360\) −0.322179 + 0.558030i −0.0169803 + 0.0294108i
\(361\) 18.9645 0.998131
\(362\) −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
\(367\) 7.86888 0.410752 0.205376 0.978683i \(-0.434158\pi\)
0.205376 + 0.978683i \(0.434158\pi\)
\(368\) 8.36939 14.4962i 0.436285 0.755667i
\(369\) −1.57204 0.907617i −0.0818371 0.0472487i
\(370\) 3.34648 1.93209i 0.173975 0.100445i
\(371\) 0 0
\(372\) 13.2891i 0.689007i
\(373\) −2.09163 −0.108300 −0.0541502 0.998533i \(-0.517245\pi\)
−0.0541502 + 0.998533i \(0.517245\pi\)
\(374\) 2.32139 0.120036
\(375\) 13.6478i 0.704771i
\(376\) −0.663180 + 1.14866i −0.0342009 + 0.0592377i
\(377\) −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
\(382\) 3.19466 1.84444i 0.163453 0.0943695i
\(383\) 25.1873i 1.28701i 0.765441 + 0.643507i \(0.222521\pi\)
−0.765441 + 0.643507i \(0.777479\pi\)
\(384\) −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
\(388\) 0.887438i 0.0450528i
\(389\) 14.0512 + 24.3373i 0.712422 + 1.23395i 0.963946 + 0.266099i \(0.0857350\pi\)
−0.251524 + 0.967851i \(0.580932\pi\)
\(390\) −1.70458 + 2.70639i −0.0863146 + 0.137043i
\(391\) −20.9623 −1.06011
\(392\) 0 0
\(393\) 9.14644 15.8421i 0.461377 0.799128i
\(394\) 0.896292 0.0451546
\(395\) 21.1976 12.2384i 1.06657 0.615783i
\(396\) −1.53463 0.886021i −0.0771183 0.0445243i
\(397\) 21.7765i 1.09293i −0.837482 0.546465i \(-0.815973\pi\)
0.837482 0.546465i \(-0.184027\pi\)
\(398\) 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 \(-0.837978\pi\)
−0.0145918 + 0.999894i \(0.504645\pi\)
\(402\) 1.88223 + 3.26012i 0.0938772 + 0.162600i
\(403\) 0.512971 13.3282i 0.0255529 0.663923i
\(404\) 7.53162 13.0451i 0.374712 0.649020i
\(405\) 23.0138 + 13.2871i 1.14357 + 0.660239i
\(406\) 0 0
\(407\) 10.7152 + 18.5592i 0.531132 + 0.919947i
\(408\) 5.40558 + 3.12091i 0.267616 + 0.154508i
\(409\) −5.42879 3.13431i −0.268436 0.154982i 0.359741 0.933052i \(-0.382865\pi\)
−0.628177 + 0.778071i \(0.716199\pi\)
\(410\) −2.28435 1.31887i −0.112816 0.0651343i
\(411\) 8.01275 + 4.62616i 0.395240 + 0.228192i
\(412\) −5.07308 8.78683i −0.249933 0.432896i
\(413\) 0 0
\(414\) −0.230322 0.132976i −0.0113197 0.00653543i
\(415\) 22.2811 38.5920i 1.09374 1.89441i
\(416\) −6.77065 + 3.56914i −0.331958 + 0.174991i
\(417\) 7.05369 + 12.2174i 0.345421 + 0.598286i
\(418\) 0.0794987 0.0458986i 0.00388841 0.00224497i
\(419\) 17.0817 29.5864i 0.834497 1.44539i −0.0599424 0.998202i \(-0.519092\pi\)
0.894439 0.447189i \(-0.147575\pi\)
\(420\) 0 0
\(421\) 11.5233i 0.561613i −0.959764 0.280806i \(-0.909398\pi\)
0.959764 0.280806i \(-0.0906019\pi\)
\(422\) 3.18118i 0.154858i
\(423\) −0.535313 0.309063i −0.0260278 0.0150272i
\(424\) 4.39391 2.53682i 0.213387 0.123199i
\(425\) −10.5688 −0.512664
\(426\) −0.552218 + 0.956469i −0.0267550 + 0.0463411i
\(427\) 0 0
\(428\) 15.8031 0.763873
\(429\) −15.0094 9.45340i −0.724659 0.456414i
\(430\) −1.94582 3.37026i −0.0938359 0.162529i
\(431\) 8.77001i 0.422436i −0.977439 0.211218i \(-0.932257\pi\)
0.977439 0.211218i \(-0.0677431\pi\)
\(432\) 9.26026 + 16.0392i 0.445534 + 0.771688i
\(433\) −11.0535 19.1452i −0.531196 0.920058i −0.999337 0.0364046i \(-0.988409\pi\)
0.468141 0.883654i \(-0.344924\pi\)
\(434\) 0 0
\(435\) 30.1038 17.3804i 1.44337 0.833328i
\(436\) 2.62352i 0.125644i
\(437\) −0.717877 + 0.414467i −0.0343407 + 0.0198266i
\(438\) −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 \(0.753728\pi\)
\(440\) −4.49705 2.59637i −0.214389 0.123777i
\(441\) 0 0
\(442\) 2.62866 + 1.65562i 0.125032 + 0.0787496i
\(443\) −17.9068 + 31.0156i −0.850780 + 1.47359i 0.0297257 + 0.999558i \(0.490537\pi\)
−0.880506 + 0.474036i \(0.842797\pi\)
\(444\) 28.5738i 1.35605i
\(445\) −15.8287 −0.750354
\(446\) 2.55059 0.120774
\(447\) 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 \(0.513710\pi\)
\(450\) −0.116124 0.0670443i −0.00547415 0.00316050i
\(451\) 7.31430 12.6687i 0.344417 0.596548i
\(452\) −39.2248 −1.84498
\(453\) −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 \(-0.928303\pi\)
−0.293949 + 0.955821i \(0.594969\pi\)
\(458\) −1.58657 −0.0741354
\(459\) 11.5968 20.0862i 0.541292 0.937546i
\(460\) 20.1370 + 11.6261i 0.938891 + 0.542069i
\(461\) 7.28113 4.20376i 0.339116 0.195789i −0.320765 0.947159i \(-0.603940\pi\)
0.659881 + 0.751370i \(0.270607\pi\)
\(462\) 0 0
\(463\) 10.0392i 0.466563i 0.972409 + 0.233281i \(0.0749463\pi\)
−0.972409 + 0.233281i \(0.925054\pi\)
\(464\) 26.9599 1.25158
\(465\) 18.1482 0.841603
\(466\) 0.923545i 0.0427824i
\(467\) 13.1756 22.8209i 0.609696 1.05602i −0.381594 0.924330i \(-0.624625\pi\)
0.991290 0.131695i \(-0.0420418\pi\)
\(468\) −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
\(473\) 18.6911 10.7913i 0.859418 0.496185i
\(474\) 3.00819i 0.138171i
\(475\) −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
\(479\) 8.58414i 0.392220i 0.980582 + 0.196110i \(0.0628309\pi\)
−0.980582 + 0.196110i \(0.937169\pi\)
\(480\) −5.20701 9.01880i −0.237666 0.411650i
\(481\) −1.10297 + 28.6578i −0.0502913 + 1.30668i
\(482\) 1.44390 0.0657678
\(483\) 0 0
\(484\) −3.67990 + 6.37377i −0.167268 + 0.289717i
\(485\) 1.21193 0.0550308
\(486\) 0.541637 0.312714i 0.0245691 0.0141850i
\(487\) 18.4084 + 10.6281i 0.834166 + 0.481606i 0.855277 0.518171i \(-0.173387\pi\)
−0.0211110 + 0.999777i \(0.506720\pi\)
\(488\) 0.295249i 0.0133653i
\(489\) 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
\(493\) −16.8812 29.2391i −0.760292 1.31686i
\(494\) 0.122756 + 0.00472460i 0.00552306 + 0.000212570i
\(495\) 1.20999 2.09577i 0.0543851 0.0941978i
\(496\) 12.1897 + 7.03772i 0.547333 + 0.316003i
\(497\) 0 0
\(498\) −2.73833 4.74293i −0.122708 0.212536i
\(499\) 33.6694 + 19.4390i 1.50725 + 0.870210i 0.999964 + 0.00843082i \(0.00268365\pi\)
0.507284 + 0.861779i \(0.330650\pi\)
\(500\) −12.7339 7.35193i −0.569478 0.328788i
\(501\) 4.28619 + 2.47463i 0.191493 + 0.110558i
\(502\) 3.95520 + 2.28354i 0.176529 + 0.101919i
\(503\) 2.72850 + 4.72591i 0.121658 + 0.210718i 0.920422 0.390927i \(-0.127846\pi\)
−0.798764 + 0.601645i \(0.794512\pi\)
\(504\) 0 0
\(505\) 17.8151 + 10.2855i 0.792760 + 0.457700i
\(506\) 1.07163 1.85612i 0.0476397 0.0825144i
\(507\) −10.2539 21.4093i −0.455390 0.950821i
\(508\) −7.83697 13.5740i −0.347709 0.602250i
\(509\) −9.43315 + 5.44623i −0.418117 + 0.241400i −0.694271 0.719713i \(-0.744273\pi\)
0.276154 + 0.961113i \(0.410940\pi\)
\(510\) −2.11347 + 3.66064i −0.0935860 + 0.162096i
\(511\) 0 0
\(512\) 13.5360i 0.598214i
\(513\) 0.917168i 0.0404939i
\(514\) −0.528304 0.305017i −0.0233025 0.0134537i
\(515\) 11.9997 6.92804i 0.528771 0.305286i
\(516\) 28.7768 1.26683
\(517\) 2.49068 4.31398i 0.109540 0.189729i
\(518\) 0 0
\(519\) −1.64308 −0.0721230
\(520\) −3.24056 6.14733i −0.142108 0.269578i
\(521\) 13.9480 + 24.1587i 0.611074 + 1.05841i 0.991060 + 0.133419i \(0.0425957\pi\)
−0.379985 + 0.924993i \(0.624071\pi\)
\(522\) 0.428350i 0.0187484i
\(523\) 8.36180 + 14.4831i 0.365636 + 0.633300i 0.988878 0.148729i \(-0.0475182\pi\)
−0.623242 + 0.782029i \(0.714185\pi\)
\(524\) 9.85416 + 17.0679i 0.430481 + 0.745615i
\(525\) 0 0
\(526\) 0.0248890 0.0143696i 0.00108521 0.000626546i
\(527\) 17.6269i 0.767842i
\(528\) 16.2111 9.35949i 0.705498 0.407319i
\(529\) 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
\(534\) −0.972671 + 1.68472i −0.0420916 + 0.0729048i
\(535\) 21.5815i 0.933049i
\(536\) −8.17890 −0.353275
\(537\) 20.1881 0.871179
\(538\) 4.21800i 0.181851i
\(539\) 0 0
\(540\) −22.2804 + 12.8636i −0.958796 + 0.553561i
\(541\) −9.66528 5.58025i −0.415543 0.239914i 0.277626 0.960689i \(-0.410453\pi\)
−0.693169 + 0.720776i \(0.743786\pi\)
\(542\) 1.06876 1.85114i 0.0459070 0.0795133i
\(543\) 6.44396 0.276537
\(544\) −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
\(549\) 0.137595 0.00587242
\(550\) 0.540297 0.935821i 0.0230383 0.0399036i
\(551\) −1.15623 0.667551i −0.0492571 0.0284386i
\(552\) 4.99077 2.88142i 0.212421 0.122641i
\(553\) 0 0
\(554\) 4.94830i 0.210233i
\(555\) −39.0217 −1.65638
\(556\) −15.1990 −0.644579
\(557\) 33.0776i 1.40154i −0.713386 0.700772i \(-0.752839\pi\)
0.713386 0.700772i \(-0.247161\pi\)
\(558\) 0.111818 0.193675i 0.00473364 0.00819890i
\(559\) 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 \(-0.955698\pi\)
0.615309 + 0.788286i \(0.289031\pi\)
\(564\) 5.75197 3.32090i 0.242202 0.139835i
\(565\) 53.5672i 2.25359i
\(566\) −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 0.766911 0.641754i \(-0.221793\pi\)
−0.939231 + 0.343287i \(0.888460\pi\)
\(570\) 0.167150i 0.00700114i
\(571\) −12.8776 22.3047i −0.538912 0.933424i −0.998963 0.0455309i \(-0.985502\pi\)
0.460051 0.887893i \(-0.347831\pi\)
\(572\) 16.9057 8.91183i 0.706863 0.372622i
\(573\) −37.2513 −1.55620
\(574\) 0 0
\(575\) −4.87891 + 8.45051i −0.203464 + 0.352411i
\(576\) 2.41579 0.100658
\(577\) −0.666314 + 0.384697i −0.0277390 + 0.0160151i −0.513805 0.857907i \(-0.671765\pi\)
0.486066 + 0.873922i \(0.338431\pi\)
\(578\) 0.893326 + 0.515762i 0.0371575 + 0.0214529i
\(579\) 31.5253i 1.31015i
\(580\) 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
\(584\) −5.09908 8.83187i −0.211002 0.365465i
\(585\) 2.86485 1.51020i 0.118447 0.0624392i
\(586\) 1.34615 2.33159i 0.0556088 0.0963173i
\(587\) 10.4727 + 6.04644i 0.432256 + 0.249563i 0.700307 0.713841i \(-0.253046\pi\)
−0.268051 + 0.963405i \(0.586380\pi\)
\(588\) 0 0
\(589\) −0.348520 0.603654i −0.0143605 0.0248731i
\(590\) 3.19281 + 1.84337i 0.131446 + 0.0758904i
\(591\) −7.83842 4.52552i −0.322430 0.186155i
\(592\) −26.2099 15.1323i −1.07722 0.621933i
\(593\) −13.8115 7.97406i −0.567170 0.327456i 0.188848 0.982006i \(-0.439525\pi\)
−0.756018 + 0.654551i \(0.772858\pi\)
\(594\) 1.18570 + 2.05369i 0.0486497 + 0.0842638i
\(595\) 0 0
\(596\) 24.3949 + 14.0844i 0.999253 + 0.576919i
\(597\) −6.55717 + 11.3573i −0.268367 + 0.464825i
\(598\) 2.53725 1.33751i 0.103756 0.0546948i
\(599\) 3.55511 + 6.15763i 0.145258 + 0.251594i 0.929469 0.368900i \(-0.120266\pi\)
−0.784211 + 0.620494i \(0.786932\pi\)
\(600\) 2.51626 1.45276i 0.102726 0.0593088i
\(601\) 10.3953 18.0051i 0.424032 0.734445i −0.572297 0.820046i \(-0.693948\pi\)
0.996329 + 0.0856011i \(0.0272811\pi\)
\(602\) 0 0
\(603\) 3.81163i 0.155221i
\(604\) 12.7333i 0.518112i
\(605\) −8.70432 5.02544i −0.353881 0.204313i
\(606\) 2.18946 1.26409i 0.0889408 0.0513500i
\(607\) 7.71405 0.313104 0.156552 0.987670i \(-0.449962\pi\)
0.156552 + 0.987670i \(0.449962\pi\)
\(608\) −0.199992 + 0.346396i −0.00811074 + 0.0140482i
\(609\) 0 0
\(610\) 0.199941 0.00809539
\(611\) 5.89707 3.10864i 0.238570 0.125762i
\(612\) −1.56698 2.71409i −0.0633415 0.109711i
\(613\) 20.4378i 0.825476i −0.910850 0.412738i \(-0.864572\pi\)
0.910850 0.412738i \(-0.135428\pi\)
\(614\) −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 \(0.362837\pi\)
\(618\) 1.70290i 0.0685008i
\(619\) −8.70599 + 5.02641i −0.349923 + 0.202028i −0.664651 0.747154i \(-0.731420\pi\)
0.314728 + 0.949182i \(0.398087\pi\)
\(620\) −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
\(625\) 15.5853 26.9944i 0.623410 1.07978i
\(626\) 0.125986i 0.00503541i
\(627\) −0.926996 −0.0370207
\(628\) −31.3170 −1.24968
\(629\) 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 \(0.379581\pi\)
\(632\) 5.66015 + 3.26789i 0.225149 + 0.129990i
\(633\) 16.0623 27.8207i 0.638418 1.10577i
\(634\) 3.87483 0.153889
\(635\) 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
\(640\) 14.9167 0.589635
\(641\) 1.92516 3.33448i 0.0760394 0.131704i −0.825498 0.564404i \(-0.809106\pi\)
0.901538 + 0.432700i \(0.142439\pi\)
\(642\) 2.29700 + 1.32618i 0.0906555 + 0.0523400i
\(643\) −2.49163 + 1.43855i −0.0982605 + 0.0567307i −0.548325 0.836265i \(-0.684734\pi\)
0.450065 + 0.892996i \(0.351401\pi\)
\(644\) 0 0
\(645\) 39.2990i 1.54740i
\(646\) 0.162349 0.00638754
\(647\) 37.1001 1.45856 0.729278 0.684218i \(-0.239856\pi\)
0.729278 + 0.684218i \(0.239856\pi\)
\(648\) 7.09577i 0.278748i
\(649\) −10.2231 + 17.7070i −0.401293 + 0.695061i
\(650\) 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 0.599679 0.800240i \(-0.295295\pi\)
−0.992868 + 0.119218i \(0.961961\pi\)
\(654\) 0.220162 0.381332i 0.00860902 0.0149113i
\(655\) −23.3087 + 13.4573i −0.910748 + 0.525820i
\(656\) 20.6589i 0.806596i
\(657\) 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
\(661\) 47.2266i 1.83690i −0.395537 0.918450i \(-0.629442\pi\)
0.395537 0.918450i \(-0.370558\pi\)
\(662\) −0.137468 0.238102i −0.00534284 0.00925408i
\(663\) −14.6292 27.7515i −0.568150 1.07778i
\(664\) 11.8989 0.461768
\(665\) 0 0
\(666\) −0.240428 + 0.416433i −0.00931639 + 0.0161365i
\(667\) −31.1716 −1.20697
\(668\) −4.61783 + 2.66611i −0.178669 + 0.103155i
\(669\) −22.3059 12.8783i −0.862397 0.497905i
\(670\) 5.53872i 0.213979i
\(671\) 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
\(675\) −5.39823 9.35001i −0.207778 0.359882i
\(676\) 25.4993 + 1.96573i 0.980742 + 0.0756050i
\(677\) −6.16453 + 10.6773i −0.236922 + 0.410361i −0.959830 0.280584i \(-0.909472\pi\)
0.722908 + 0.690945i \(0.242805\pi\)
\(678\) −5.70137 3.29169i −0.218960 0.126416i
\(679\) 0 0
\(680\) −4.59185 7.95331i −0.176089 0.304996i
\(681\) −4.53660 2.61921i −0.173843 0.100368i
\(682\) 1.56078 + 0.901120i 0.0597655 + 0.0345057i
\(683\) 21.2491 + 12.2682i 0.813076 + 0.469430i 0.848023 0.529960i \(-0.177793\pi\)
−0.0349470 + 0.999389i \(0.511126\pi\)
\(684\) −0.107326 0.0619648i −0.00410372 0.00236928i
\(685\) −6.80655 11.7893i −0.260065 0.450446i
\(686\) 0 0
\(687\) 13.8751 + 8.01082i 0.529370 + 0.305632i
\(688\) −15.2398 + 26.3961i −0.581012 + 1.00634i
\(689\) −25.4812 0.980713i −0.970756 0.0373622i
\(690\) 1.95129 + 3.37973i 0.0742843 + 0.128664i
\(691\) 7.88703 4.55358i 0.300037 0.173226i −0.342423 0.939546i \(-0.611247\pi\)
0.642459 + 0.766320i \(0.277914\pi\)
\(692\) 0.885106 1.53305i 0.0336467 0.0582777i
\(693\) 0 0
\(694\) 1.47992i 0.0561769i
\(695\) 20.7564i 0.787336i
\(696\) 8.03826 + 4.64089i 0.304690 + 0.175913i
\(697\) 22.4055 12.9358i 0.848667 0.489978i
\(698\) −3.95087 −0.149542
\(699\) 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 \(0.498275\pi\)
\(702\) −0.122050 + 3.17115i −0.00460650 + 0.119687i
\(703\) 0.749377 + 1.29796i 0.0282633 + 0.0489534i
\(704\) 19.4684i 0.733742i
\(705\) 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
\(709\) 18.5848i 0.697967i −0.937129 0.348984i \(-0.886527\pi\)
0.937129 0.348984i \(-0.113473\pi\)
\(710\) 1.40727 0.812486i 0.0528138 0.0304921i
\(711\) −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
\(716\) −10.8751 + 18.8362i −0.406421 + 0.703941i
\(717\) 4.56132i 0.170346i
\(718\) −5.85947 −0.218674
\(719\) 41.6949 1.55496 0.777479 0.628909i \(-0.216498\pi\)
0.777479 + 0.628909i \(0.216498\pi\)
\(720\) 3.41757i 0.127365i
\(721\) 0 0
\(722\) −2.96980 + 1.71462i −0.110525 + 0.0638114i
\(723\) −12.6275 7.29046i −0.469620 0.271135i
\(724\) −3.47128 + 6.01244i −0.129009 + 0.223451i
\(725\) −15.7162 −0.583684
\(726\) −1.06975 + 0.617623i −0.0397023 + 0.0229221i
\(727\) −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
\(730\) 5.98091 3.45308i 0.221363 0.127804i
\(731\) 38.1702 1.41178
\(732\) −0.739235 + 1.28039i −0.0273229 + 0.0473246i
\(733\) 8.60423 + 4.96765i 0.317804 + 0.183484i 0.650413 0.759580i \(-0.274596\pi\)
−0.332609 + 0.943065i \(0.607929\pi\)
\(734\) −1.23225 + 0.711440i −0.0454832 + 0.0262597i
\(735\) 0 0
\(736\) 9.33871i 0.344230i
\(737\) 30.7171 1.13148
\(738\) 0.328237 0.0120826
\(739\) 10.4022i 0.382649i −0.981527 0.191325i \(-0.938722\pi\)
0.981527 0.191325i \(-0.0612784\pi\)
\(740\) 21.0205 36.4086i 0.772730 1.33841i
\(741\) −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
\(746\) 0.327545 0.189108i 0.0119923 0.00692374i
\(747\) 5.54528i 0.202891i
\(748\) 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 0.998477 + 0.0551673i \(0.0175692\pi\)
−0.451462 + 0.892290i \(0.649097\pi\)
\(752\) 7.03481i 0.256533i
\(753\) −23.0598 39.9408i −0.840347 1.45552i
\(754\) 3.90890 + 2.46195i 0.142354 + 0.0896590i
\(755\) 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 \(0.215475\pi\)
\(758\) −2.58874 −0.0940271
\(759\) −18.7436 + 10.8216i −0.680350 + 0.392800i
\(760\) −0.314506 0.181580i −0.0114083 0.00658660i
\(761\) 51.0590i 1.85089i 0.378885 + 0.925444i \(0.376308\pi\)
−0.378885 + 0.925444i \(0.623692\pi\)
\(762\) 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
\(766\) −2.27723 3.94429i −0.0822798 0.142513i
\(767\) −24.2049 + 12.7596i −0.873988 + 0.460722i
\(768\) −12.2780 + 21.2661i −0.443044 + 0.767375i
\(769\) 0.610062 + 0.352220i 0.0219994 + 0.0127014i 0.510959 0.859605i \(-0.329290\pi\)
−0.488960 + 0.872306i \(0.662624\pi\)
\(770\) 0 0
\(771\) 3.08015 + 5.33498i 0.110929 + 0.192134i
\(772\) 29.4142 + 16.9823i 1.05864 + 0.611206i
\(773\) 1.09571 + 0.632607i 0.0394099 + 0.0227533i 0.519575 0.854425i \(-0.326090\pi\)
−0.480166 + 0.877178i \(0.659423\pi\)
\(774\) 0.419392 + 0.242136i 0.0150747 + 0.00870341i
\(775\) −7.10593 4.10261i −0.255253 0.147370i
\(776\) 0.161803 + 0.280252i 0.00580840 + 0.0100604i
\(777\) 0 0
\(778\) −4.40076 2.54078i −0.157775 0.0910914i
\(779\) 0.511533 0.886001i 0.0183276 0.0317443i
\(780\) −1.33831 + 34.7724i −0.0479193 + 1.24505i