Properties

Label 637.2.u.g.361.3
Level $637$
Weight $2$
Character 637.361
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 361.3
Root \(0.655911 - 1.25291i\) of defining polynomial
Character \(\chi\) \(=\) 637.361
Dual form 637.2.u.g.30.3

$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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 0.443611 0.896219i \(-0.353697\pi\)
−0.554343 + 0.832288i \(0.687030\pi\)
\(3\) 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 −0.919984 0.391956i \(-0.871799\pi\)
−0.120548 + 0.992708i \(0.538465\pi\)
\(6\) −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 \(-0.866863\pi\)
0.913796 0.406172i \(-0.133137\pi\)
\(12\) −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 −0.995727 0.0923405i \(-0.970565\pi\)
0.417894 0.908496i \(-0.362768\pi\)
\(18\) −0.0523543 0.0302268i −0.0123400 0.00712452i
\(19\) 0.188424i 0.0432275i −0.999766 0.0216138i \(-0.993120\pi\)
0.999766 0.0216138i \(-0.00688041\pi\)
\(20\) 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 \(0.0149972\pi\)
\(24\) 1.30995i 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 −0.981163 0.193182i \(-0.938119\pi\)
0.323281 0.946303i \(-0.395214\pi\)
\(30\) 0.887093 0.161960
\(31\) −3.20369 1.84965i −0.575400 0.332207i 0.183903 0.982944i \(-0.441127\pi\)
−0.759303 + 0.650737i \(0.774460\pi\)
\(32\) 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 0.944552 0.328361i \(-0.106496\pi\)
0.187907 + 0.982187i \(0.439830\pi\)
\(38\) −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 −0.820013 0.572345i \(-0.806034\pi\)
0.0856594 + 0.996324i \(0.472700\pi\)
\(42\) 0 0
\(43\) −4.00533 + 6.93743i −0.610807 + 1.05795i 0.380298 + 0.924864i \(0.375821\pi\)
−0.991105 + 0.133084i \(0.957512\pi\)
\(44\) −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 −0.612212 0.790694i \(-0.709720\pi\)
0.378655 + 0.925538i \(0.376387\pi\)
\(48\) −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 −0.514128 0.857713i \(-0.671885\pi\)
0.999866 + 0.0163917i \(0.00521788\pi\)
\(54\) 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 −0.00692130 0.999976i \(-0.502203\pi\)
0.862544 + 0.505982i \(0.168870\pi\)
\(60\) 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 \(0.245229\pi\)
−0.717626 + 0.696429i \(0.754771\pi\)
\(68\) −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 0.661943 0.749554i \(-0.269732\pi\)
−0.318162 + 0.948037i \(0.603065\pi\)
\(72\) 0.239838i 0.0282651i
\(73\) 12.3112 + 7.10790i 1.44092 + 0.831917i 0.997911 0.0645994i \(-0.0205769\pi\)
0.443011 + 0.896516i \(0.353910\pi\)
\(74\) −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 −0.999895 0.0145069i \(-0.995382\pi\)
0.487384 0.873188i \(-0.337951\pi\)
\(80\) 10.2224i 1.14290i
\(81\) −9.89120 −1.09902
\(82\) 0.981797 0.108421
\(83\) 16.5866i 1.82061i −0.413934 0.910307i \(-0.635845\pi\)
0.413934 0.910307i \(-0.364155\pi\)
\(84\) 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 0.745421 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
\(94\) 0.334323 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 0.480036 0.877249i \(-0.340624\pi\)
−0.519702 + 0.854348i \(0.673957\pi\)
\(98\) 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 0.710560 0.703636i \(-0.248442\pi\)
−0.964647 + 0.263545i \(0.915108\pi\)
\(104\) 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
\(109\) −1.15490 0.666781i −0.110619 0.0638660i 0.443670 0.896190i \(-0.353676\pi\)
−0.554289 + 0.832324i \(0.687010\pi\)
\(110\) 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 0.168296 0.985736i \(-0.446173\pi\)
0.769525 0.638617i \(-0.220493\pi\)
\(114\) −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 0.633370 0.773849i \(-0.281671\pi\)
−0.986858 + 0.161590i \(0.948338\pi\)
\(128\) −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 0.997507 0.0705727i \(-0.0224827\pi\)
−0.559871 + 0.828580i \(0.689149\pi\)
\(132\) −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 −0.300696 0.953720i \(-0.597219\pi\)
0.675598 + 0.737270i \(0.263886\pi\)
\(138\) −1.25798 + 0.726293i −0.107086 + 0.0618261i
\(139\) 3.86289 6.69073i 0.327646 0.567500i −0.654398 0.756150i \(-0.727078\pi\)
0.982044 + 0.188650i \(0.0604113\pi\)
\(140\) 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 \(0.199498\pi\)
−0.809944 + 0.586507i \(0.800502\pi\)
\(150\) −0.634250 + 0.366184i −0.0517863 + 0.0298988i
\(151\) −5.60534 3.23624i −0.456156 0.263362i 0.254271 0.967133i \(-0.418165\pi\)
−0.710427 + 0.703771i \(0.751498\pi\)
\(152\) 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 −0.351240 0.936285i \(-0.614240\pi\)
0.986467 0.163960i \(-0.0524267\pi\)
\(158\) 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 \(-0.940038\pi\)
0.982310 0.187263i \(-0.0599616\pi\)
\(164\) 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 −0.406424 0.913685i \(-0.633224\pi\)
0.588062 + 0.808816i \(0.299891\pi\)
\(168\) 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 \(0.213422\pi\)
−0.783521 + 0.621365i \(0.786578\pi\)
\(194\) 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 −0.645063 0.764130i \(-0.723169\pi\)
0.339224 + 0.940705i \(0.389835\pi\)
\(198\) −0.0814383 + 0.141055i −0.00578757 + 0.0100244i
\(199\) −3.59097 6.21975i −0.254557 0.440906i 0.710218 0.703982i \(-0.248596\pi\)
−0.964775 + 0.263076i \(0.915263\pi\)
\(200\) 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 0.991962 + 0.126539i \(0.0403868\pi\)
−0.386395 + 0.922333i \(0.626280\pi\)
\(212\) −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 −0.849733 0.527213i \(-0.823237\pi\)
0.0317129 + 0.999497i \(0.489904\pi\)
\(224\) 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 −0.580178 0.814490i \(-0.697017\pi\)
0.415280 + 0.909694i \(0.363684\pi\)
\(228\) −0.586196 + 0.338441i −0.0388218 + 0.0224138i
\(229\) 7.59860 4.38706i 0.502130 0.289905i −0.227463 0.973787i \(-0.573043\pi\)
0.729593 + 0.683882i \(0.239710\pi\)
\(230\) 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 0.937469 0.348068i \(-0.113162\pi\)
−0.770170 + 0.637839i \(0.779829\pi\)
\(234\) 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 \(0.0257443\pi\)
−0.996731 + 0.0807901i \(0.974256\pi\)
\(240\) 18.6662i 1.20490i
\(241\) −6.91532 + 3.99256i −0.445455 + 0.257183i −0.705909 0.708303i \(-0.749461\pi\)
0.260454 + 0.965486i \(0.416128\pi\)
\(242\) −0.585842 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 0.124389 + 0.992234i \(0.460303\pi\)
−0.921494 + 0.388393i \(0.873030\pi\)
\(252\) 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 −0.808608 0.588348i \(-0.799778\pi\)
0.913828 + 0.406101i \(0.133112\pi\)
\(258\) 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 −0.964435 0.264318i \(-0.914853\pi\)
0.253311 0.967385i \(-0.418480\pi\)
\(270\) −2.36470 −0.143911
\(271\) −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
\(276\) −15.8036 −0.951268
\(277\) −13.6827 23.6991i −0.822111 1.42394i −0.904107 0.427306i \(-0.859463\pi\)
0.0819961 0.996633i \(-0.473870\pi\)
\(278\) −1.20984 + 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 \(-0.675860\pi\)
0.524801 0.851225i \(-0.324140\pi\)
\(282\) 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 0.0735896 0.997289i \(-0.476554\pi\)
−0.826882 + 0.562375i \(0.809888\pi\)
\(294\) 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 \(-0.765836\pi\)
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
\(311\) −0.815450 + 1.41240i −0.0462399 + 0.0800899i −0.888219 0.459420i \(-0.848057\pi\)
0.841979 + 0.539510i \(0.181391\pi\)
\(312\) 3.99647 2.51711i 0.226255 0.142503i
\(313\) −0.348367 0.603389i −0.0196909 0.0341056i 0.856012 0.516956i \(-0.172935\pi\)
−0.875703 + 0.482850i \(0.839602\pi\)
\(314\) −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 −0.920488 0.390771i \(-0.872208\pi\)
−0.121826 + 0.992551i \(0.538875\pi\)
\(318\) −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 \(-0.986695\pi\)
0.999127 0.0417861i \(-0.0133048\pi\)
\(332\) −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 0.735031 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 \(-0.467847\pi\)
0.912031 + 0.410120i \(0.134513\pi\)
\(350\) 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 \(-0.995195\pi\)
0.999886 0.0150940i \(-0.00480474\pi\)
\(354\) −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 0.481336 0.876536i \(-0.340152\pi\)
0.999771 + 0.0214184i \(0.00681822\pi\)
\(360\) −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 −0.146545 0.989204i \(-0.546815\pi\)
0.783404 + 0.621513i \(0.213482\pi\)
\(380\) 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 \(-0.777479\pi\)
0.765441 0.643507i \(-0.222521\pi\)
\(384\) −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 −0.251524 0.967851i \(-0.580932\pi\)
0.963946 0.266099i \(-0.0857350\pi\)
\(390\) −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 \(0.184027\pi\)
−0.837482 + 0.546465i \(0.815973\pi\)
\(398\) 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 −0.0145918 0.999894i \(-0.504645\pi\)
−0.873229 + 0.487310i \(0.837978\pi\)
\(402\) 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 −0.628177 0.778071i \(-0.716199\pi\)
0.359741 + 0.933052i \(0.382865\pi\)
\(410\) −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 0.894439 + 0.447189i \(0.147575\pi\)
−0.0599424 + 0.998202i \(0.519092\pi\)
\(420\) 0 0
\(421\) 11.5233i 0.561613i 0.959764 + 0.280806i \(0.0906019\pi\)
−0.959764 + 0.280806i \(0.909398\pi\)
\(422\) 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 \(0.0677431\pi\)
−0.977439 + 0.211218i \(0.932257\pi\)
\(432\) 9.26026 16.0392i 0.445534 0.771688i
\(433\) −11.0535 + 19.1452i −0.531196 + 0.920058i 0.468141 + 0.883654i \(0.344924\pi\)
−0.999337 + 0.0364046i \(0.988409\pi\)
\(434\) 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 −0.715339 0.698777i \(-0.753728\pi\)
0.962828 + 0.270114i \(0.0870612\pi\)
\(440\) −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 −0.880506 0.474036i \(-0.842797\pi\)
0.0297257 0.999558i \(-0.490537\pi\)
\(444\) 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 −0.0430575 0.999073i \(-0.513710\pi\)
−0.886751 + 0.462247i \(0.847043\pi\)
\(450\) −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 −0.293949 0.955821i \(-0.594969\pi\)
−0.974740 + 0.223344i \(0.928303\pi\)
\(458\) −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 0.659881 0.751370i \(-0.270607\pi\)
−0.320765 + 0.947159i \(0.603940\pi\)
\(462\) 0 0
\(463\) 10.0392i 0.466563i −0.972409 0.233281i \(-0.925054\pi\)
0.972409 0.233281i \(-0.0749463\pi\)
\(464\) 26.9599 1.25158
\(465\) 18.1482 0.841603
\(466\) 0.923545i 0.0427824i
\(467\) 13.1756 + 22.8209i 0.609696 + 1.05602i 0.991290 + 0.131695i \(0.0420418\pi\)
−0.381594 + 0.924330i \(0.624625\pi\)
\(468\) −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 \(-0.937169\pi\)
0.980582 0.196110i \(-0.0628309\pi\)
\(480\) −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 −0.0211110 0.999777i \(-0.506720\pi\)
0.855277 + 0.518171i \(0.173387\pi\)
\(488\) 0.295249i 0.0133653i
\(489\) 8.73130i 0.394843i
\(490\) 0 0
\(491\) −11.2268 19.4453i −0.506657 0.877556i −0.999970 0.00770409i \(-0.997548\pi\)
0.493313 0.869852i \(-0.335786\pi\)
\(492\) 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 0.507284 0.861779i \(-0.330650\pi\)
0.999964 0.00843082i \(-0.00268365\pi\)
\(500\) −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 −0.798764 0.601645i \(-0.794512\pi\)
0.920422 + 0.390927i \(0.127846\pi\)
\(504\) 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 0.276154 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
\(513\) 0.917168i 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 −0.379985 0.924993i \(-0.624071\pi\)
0.991060 0.133419i \(-0.0425957\pi\)
\(522\) 0.428350i 0.0187484i
\(523\) 8.36180 14.4831i 0.365636 0.633300i −0.623242 0.782029i \(-0.714185\pi\)
0.988878 + 0.148729i \(0.0475182\pi\)
\(524\) 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 −0.693169 0.720776i \(-0.743786\pi\)
0.277626 + 0.960689i \(0.410453\pi\)
\(542\) 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 \(0.247161\pi\)
−0.713386 + 0.700772i \(0.752839\pi\)
\(558\) 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 0.615309 0.788286i \(-0.289031\pi\)
−0.990330 + 0.138730i \(0.955698\pi\)
\(564\) 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 −0.939231 0.343287i \(-0.888460\pi\)
0.766911 + 0.641754i \(0.221793\pi\)
\(570\) 0.167150i 0.00700114i
\(571\) −12.8776 + 22.3047i −0.538912 + 0.933424i 0.460051 + 0.887893i \(0.347831\pi\)
−0.998963 + 0.0455309i \(0.985502\pi\)
\(572\) 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 0.486066 0.873922i \(-0.338431\pi\)
−0.513805 + 0.857907i \(0.671765\pi\)
\(578\) 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 −0.268051 0.963405i \(-0.586380\pi\)
0.700307 + 0.713841i \(0.253046\pi\)
\(588\) 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 −0.756018 0.654551i \(-0.772858\pi\)
0.188848 + 0.982006i \(0.439525\pi\)
\(594\) 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 −0.784211 0.620494i \(-0.786932\pi\)
0.929469 + 0.368900i \(0.120266\pi\)
\(600\) 2.51626 + 1.45276i 0.102726 + 0.0593088i
\(601\) 10.3953 + 18.0051i 0.424032 + 0.734445i 0.996329 0.0856011i \(-0.0272811\pi\)
−0.572297 + 0.820046i \(0.693948\pi\)
\(602\) 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 \(0.135428\pi\)
−0.910850 + 0.412738i \(0.864572\pi\)
\(614\) −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 0.417697 0.908586i \(-0.362837\pi\)
−0.578010 + 0.816030i \(0.696171\pi\)
\(618\) 1.70290i 0.0685008i
\(619\) −8.70599 5.02641i −0.349923 0.202028i 0.314728 0.949182i \(-0.398087\pi\)
−0.664651 + 0.747154i \(0.731420\pi\)
\(620\) −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 0.369348 0.929291i \(-0.379581\pi\)
−0.620116 + 0.784510i \(0.712914\pi\)
\(632\) 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 0.901538 0.432700i \(-0.142439\pi\)
−0.825498 + 0.564404i \(0.809106\pi\)
\(642\) 2.29700 1.32618i 0.0906555 0.0523400i
\(643\) −2.49163 1.43855i −0.0982605 0.0567307i 0.450065 0.892996i \(-0.351401\pi\)
−0.548325 + 0.836265i \(0.684734\pi\)
\(644\) 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 −0.992868 0.119218i \(-0.961961\pi\)
0.599679 + 0.800240i \(0.295295\pi\)
\(654\) 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 −0.946253 0.323427i \(-0.895165\pi\)
0.753223 + 0.657766i \(0.228498\pi\)
\(660\) 13.0014 22.5192i 0.506080 0.876557i
\(661\) 47.2266i 1.83690i 0.395537 + 0.918450i \(0.370558\pi\)
−0.395537 + 0.918450i \(0.629442\pi\)
\(662\) −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 0.924952 0.380084i \(-0.124105\pi\)
−0.791639 + 0.610990i \(0.790772\pi\)
\(674\) 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 0.722908 0.690945i \(-0.242805\pi\)
−0.959830 + 0.280584i \(0.909472\pi\)
\(678\) −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 −0.0349470 0.999389i \(-0.511126\pi\)
0.848023 + 0.529960i \(0.177793\pi\)
\(684\) −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 0.642459 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
\(695\) 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 \(0.113473\pi\)
−0.937129 + 0.348984i \(0.886527\pi\)
\(710\) 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 −0.332609 0.943065i \(-0.607929\pi\)
0.650413 + 0.759580i \(0.274596\pi\)
\(734\) −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 \(0.0612784\pi\)
−0.981527 + 0.191325i \(0.938722\pi\)
\(740\) 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 −0.526897 0.849929i \(-0.676645\pi\)
0.472612 + 0.881271i \(0.343311\pi\)
\(744\) 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 −0.451462 0.892290i \(-0.649097\pi\)
0.998477 0.0551673i \(-0.0175692\pi\)
\(752\) 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 0.779497 0.626406i \(-0.215475\pi\)
−0.932232 + 0.361861i \(0.882141\pi\)
\(758\) −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 \(-0.623692\pi\)
0.378885 0.925444i \(-0.376308\pi\)
\(762\) 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 −0.488960 0.872306i \(-0.662624\pi\)
0.510959 + 0.859605i \(0.329290\pi\)
\(770\) 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 −0.480166 0.877178i \(-0.659423\pi\)
0.519575 + 0.854425i \(0.326090\pi\)
\(774\) 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