Properties

Label 690.3.k.b.277.9
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.9
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.00430 + 2.99426i) q^{5} +2.44949 q^{6} +(-4.65996 - 4.65996i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.00430 + 2.99426i) q^{5} +2.44949 q^{6} +(-4.65996 - 4.65996i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-1.01004 - 6.99856i) q^{10} -0.959032 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-7.15802 + 7.15802i) q^{13} +9.31993i q^{14} +(-8.57145 + 1.23704i) q^{15} -4.00000 q^{16} +(17.8295 + 17.8295i) q^{17} +(-3.00000 + 3.00000i) q^{18} -11.9544i q^{19} +(-5.98852 + 8.00860i) q^{20} +11.4145 q^{21} +(0.959032 + 0.959032i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(7.06884 + 23.9798i) q^{25} +14.3160 q^{26} +(3.67423 + 3.67423i) q^{27} +(9.31993 - 9.31993i) q^{28} -10.1798i q^{29} +(9.80849 + 7.33440i) q^{30} -17.8199 q^{31} +(4.00000 + 4.00000i) q^{32} +(1.17457 - 1.17457i) q^{33} -35.6590i q^{34} +(-4.70676 - 32.6130i) q^{35} +6.00000 q^{36} +(35.6436 + 35.6436i) q^{37} +(-11.9544 + 11.9544i) q^{38} -17.5335i q^{39} +(13.9971 - 2.02008i) q^{40} -70.4086 q^{41} +(-11.4145 - 11.4145i) q^{42} +(-32.3834 + 32.3834i) q^{43} -1.91806i q^{44} +(8.98277 - 12.0129i) q^{45} +6.78233 q^{46} +(-36.1043 - 36.1043i) q^{47} +(4.89898 - 4.89898i) q^{48} -5.56950i q^{49} +(16.9110 - 31.0487i) q^{50} -43.6732 q^{51} +(-14.3160 - 14.3160i) q^{52} +(-22.0370 + 22.0370i) q^{53} -7.34847i q^{54} +(-3.84025 - 2.87159i) q^{55} -18.6399 q^{56} +(14.6411 + 14.6411i) q^{57} +(-10.1798 + 10.1798i) q^{58} +7.49744i q^{59} +(-2.47409 - 17.1429i) q^{60} -83.1331 q^{61} +(17.8199 + 17.8199i) q^{62} +(-13.9799 + 13.9799i) q^{63} -8.00000i q^{64} +(-50.0958 + 7.22990i) q^{65} -2.34914 q^{66} +(36.1206 + 36.1206i) q^{67} +(-35.6590 + 35.6590i) q^{68} -8.30662i q^{69} +(-27.9063 + 37.3198i) q^{70} -19.9996 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-39.5875 + 39.5875i) q^{73} -71.2871i q^{74} +(-38.0267 - 20.7116i) q^{75} +23.9088 q^{76} +(4.46905 + 4.46905i) q^{77} +(-17.5335 + 17.5335i) q^{78} +26.1612i q^{79} +(-16.0172 - 11.9770i) q^{80} -9.00000 q^{81} +(70.4086 + 70.4086i) q^{82} +(-38.2400 + 38.2400i) q^{83} +22.8291i q^{84} +(18.0085 + 124.781i) q^{85} +64.7668 q^{86} +(12.4677 + 12.4677i) q^{87} +(-1.91806 + 1.91806i) q^{88} +67.4462i q^{89} +(-20.9957 + 3.03013i) q^{90} +66.7122 q^{91} +(-6.78233 - 6.78233i) q^{92} +(21.8248 - 21.8248i) q^{93} +72.2086i q^{94} +(35.7946 - 47.8690i) q^{95} -9.79796 q^{96} +(90.5751 + 90.5751i) q^{97} +(-5.56950 + 5.56950i) q^{98} +2.87709i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 4.00430 + 2.99426i 0.800860 + 0.598852i
\(6\) 2.44949 0.408248
\(7\) −4.65996 4.65996i −0.665709 0.665709i 0.291011 0.956720i \(-0.406008\pi\)
−0.956720 + 0.291011i \(0.906008\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −1.01004 6.99856i −0.101004 0.699856i
\(11\) −0.959032 −0.0871847 −0.0435923 0.999049i \(-0.513880\pi\)
−0.0435923 + 0.999049i \(0.513880\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −7.15802 + 7.15802i −0.550617 + 0.550617i −0.926619 0.376002i \(-0.877299\pi\)
0.376002 + 0.926619i \(0.377299\pi\)
\(14\) 9.31993i 0.665709i
\(15\) −8.57145 + 1.23704i −0.571430 + 0.0824696i
\(16\) −4.00000 −0.250000
\(17\) 17.8295 + 17.8295i 1.04879 + 1.04879i 0.998747 + 0.0500472i \(0.0159372\pi\)
0.0500472 + 0.998747i \(0.484063\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 11.9544i 0.629180i −0.949228 0.314590i \(-0.898133\pi\)
0.949228 0.314590i \(-0.101867\pi\)
\(20\) −5.98852 + 8.00860i −0.299426 + 0.400430i
\(21\) 11.4145 0.543549
\(22\) 0.959032 + 0.959032i 0.0435923 + 0.0435923i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 7.06884 + 23.9798i 0.282754 + 0.959193i
\(26\) 14.3160 0.550617
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 9.31993 9.31993i 0.332854 0.332854i
\(29\) 10.1798i 0.351028i −0.984477 0.175514i \(-0.943841\pi\)
0.984477 0.175514i \(-0.0561587\pi\)
\(30\) 9.80849 + 7.33440i 0.326950 + 0.244480i
\(31\) −17.8199 −0.574835 −0.287417 0.957805i \(-0.592797\pi\)
−0.287417 + 0.957805i \(0.592797\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 1.17457 1.17457i 0.0355930 0.0355930i
\(34\) 35.6590i 1.04879i
\(35\) −4.70676 32.6130i −0.134479 0.931801i
\(36\) 6.00000 0.166667
\(37\) 35.6436 + 35.6436i 0.963340 + 0.963340i 0.999351 0.0360119i \(-0.0114654\pi\)
−0.0360119 + 0.999351i \(0.511465\pi\)
\(38\) −11.9544 + 11.9544i −0.314590 + 0.314590i
\(39\) 17.5335i 0.449577i
\(40\) 13.9971 2.02008i 0.349928 0.0505021i
\(41\) −70.4086 −1.71728 −0.858642 0.512576i \(-0.828691\pi\)
−0.858642 + 0.512576i \(0.828691\pi\)
\(42\) −11.4145 11.4145i −0.271775 0.271775i
\(43\) −32.3834 + 32.3834i −0.753103 + 0.753103i −0.975057 0.221954i \(-0.928756\pi\)
0.221954 + 0.975057i \(0.428756\pi\)
\(44\) 1.91806i 0.0435923i
\(45\) 8.98277 12.0129i 0.199617 0.266953i
\(46\) 6.78233 0.147442
\(47\) −36.1043 36.1043i −0.768176 0.768176i 0.209609 0.977785i \(-0.432781\pi\)
−0.977785 + 0.209609i \(0.932781\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 5.56950i 0.113663i
\(50\) 16.9110 31.0487i 0.338220 0.620973i
\(51\) −43.6732 −0.856337
\(52\) −14.3160 14.3160i −0.275309 0.275309i
\(53\) −22.0370 + 22.0370i −0.415793 + 0.415793i −0.883751 0.467958i \(-0.844990\pi\)
0.467958 + 0.883751i \(0.344990\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −3.84025 2.87159i −0.0698227 0.0522107i
\(56\) −18.6399 −0.332854
\(57\) 14.6411 + 14.6411i 0.256861 + 0.256861i
\(58\) −10.1798 + 10.1798i −0.175514 + 0.175514i
\(59\) 7.49744i 0.127075i 0.997979 + 0.0635376i \(0.0202383\pi\)
−0.997979 + 0.0635376i \(0.979762\pi\)
\(60\) −2.47409 17.1429i −0.0412348 0.285715i
\(61\) −83.1331 −1.36284 −0.681419 0.731893i \(-0.738637\pi\)
−0.681419 + 0.731893i \(0.738637\pi\)
\(62\) 17.8199 + 17.8199i 0.287417 + 0.287417i
\(63\) −13.9799 + 13.9799i −0.221903 + 0.221903i
\(64\) 8.00000i 0.125000i
\(65\) −50.0958 + 7.22990i −0.770705 + 0.111229i
\(66\) −2.34914 −0.0355930
\(67\) 36.1206 + 36.1206i 0.539114 + 0.539114i 0.923269 0.384155i \(-0.125507\pi\)
−0.384155 + 0.923269i \(0.625507\pi\)
\(68\) −35.6590 + 35.6590i −0.524397 + 0.524397i
\(69\) 8.30662i 0.120386i
\(70\) −27.9063 + 37.3198i −0.398661 + 0.533140i
\(71\) −19.9996 −0.281684 −0.140842 0.990032i \(-0.544981\pi\)
−0.140842 + 0.990032i \(0.544981\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) −39.5875 + 39.5875i −0.542295 + 0.542295i −0.924201 0.381906i \(-0.875268\pi\)
0.381906 + 0.924201i \(0.375268\pi\)
\(74\) 71.2871i 0.963340i
\(75\) −38.0267 20.7116i −0.507022 0.276155i
\(76\) 23.9088 0.314590
\(77\) 4.46905 + 4.46905i 0.0580396 + 0.0580396i
\(78\) −17.5335 + 17.5335i −0.224788 + 0.224788i
\(79\) 26.1612i 0.331154i 0.986197 + 0.165577i \(0.0529487\pi\)
−0.986197 + 0.165577i \(0.947051\pi\)
\(80\) −16.0172 11.9770i −0.200215 0.149713i
\(81\) −9.00000 −0.111111
\(82\) 70.4086 + 70.4086i 0.858642 + 0.858642i
\(83\) −38.2400 + 38.2400i −0.460723 + 0.460723i −0.898892 0.438170i \(-0.855627\pi\)
0.438170 + 0.898892i \(0.355627\pi\)
\(84\) 22.8291i 0.271775i
\(85\) 18.0085 + 124.781i 0.211865 + 1.46801i
\(86\) 64.7668 0.753103
\(87\) 12.4677 + 12.4677i 0.143306 + 0.143306i
\(88\) −1.91806 + 1.91806i −0.0217962 + 0.0217962i
\(89\) 67.4462i 0.757822i 0.925433 + 0.378911i \(0.123701\pi\)
−0.925433 + 0.378911i \(0.876299\pi\)
\(90\) −20.9957 + 3.03013i −0.233285 + 0.0336681i
\(91\) 66.7122 0.733101
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 21.8248 21.8248i 0.234675 0.234675i
\(94\) 72.2086i 0.768176i
\(95\) 35.7946 47.8690i 0.376785 0.503885i
\(96\) −9.79796 −0.102062
\(97\) 90.5751 + 90.5751i 0.933764 + 0.933764i 0.997939 0.0641750i \(-0.0204416\pi\)
−0.0641750 + 0.997939i \(0.520442\pi\)
\(98\) −5.56950 + 5.56950i −0.0568316 + 0.0568316i
\(99\) 2.87709i 0.0290616i
\(100\) −47.9596 + 14.1377i −0.479596 + 0.141377i
\(101\) −8.25159 −0.0816989 −0.0408495 0.999165i \(-0.513006\pi\)
−0.0408495 + 0.999165i \(0.513006\pi\)
\(102\) 43.6732 + 43.6732i 0.428168 + 0.428168i
\(103\) −82.0811 + 82.0811i −0.796904 + 0.796904i −0.982606 0.185702i \(-0.940544\pi\)
0.185702 + 0.982606i \(0.440544\pi\)
\(104\) 28.6321i 0.275309i
\(105\) 45.7072 + 34.1780i 0.435307 + 0.325505i
\(106\) 44.0740 0.415793
\(107\) −92.7956 92.7956i −0.867249 0.867249i 0.124918 0.992167i \(-0.460133\pi\)
−0.992167 + 0.124918i \(0.960133\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 11.0337i 0.101227i −0.998718 0.0506134i \(-0.983882\pi\)
0.998718 0.0506134i \(-0.0161176\pi\)
\(110\) 0.968662 + 6.71184i 0.00880602 + 0.0610167i
\(111\) −87.3085 −0.786563
\(112\) 18.6399 + 18.6399i 0.166427 + 0.166427i
\(113\) −63.3403 + 63.3403i −0.560534 + 0.560534i −0.929459 0.368925i \(-0.879726\pi\)
0.368925 + 0.929459i \(0.379726\pi\)
\(114\) 29.2822i 0.256861i
\(115\) −23.7333 + 3.42522i −0.206376 + 0.0297845i
\(116\) 20.3596 0.175514
\(117\) 21.4741 + 21.4741i 0.183539 + 0.183539i
\(118\) 7.49744 7.49744i 0.0635376 0.0635376i
\(119\) 166.170i 1.39638i
\(120\) −14.6688 + 19.6170i −0.122240 + 0.163475i
\(121\) −120.080 −0.992399
\(122\) 83.1331 + 83.1331i 0.681419 + 0.681419i
\(123\) 86.2326 86.2326i 0.701078 0.701078i
\(124\) 35.6398i 0.287417i
\(125\) −43.4960 + 117.188i −0.347968 + 0.937506i
\(126\) 27.9598 0.221903
\(127\) 115.171 + 115.171i 0.906861 + 0.906861i 0.996018 0.0891566i \(-0.0284172\pi\)
−0.0891566 + 0.996018i \(0.528417\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 79.3229i 0.614906i
\(130\) 57.3257 + 42.8659i 0.440967 + 0.329738i
\(131\) −59.8637 −0.456974 −0.228487 0.973547i \(-0.573378\pi\)
−0.228487 + 0.973547i \(0.573378\pi\)
\(132\) 2.34914 + 2.34914i 0.0177965 + 0.0177965i
\(133\) −55.7071 + 55.7071i −0.418850 + 0.418850i
\(134\) 72.2412i 0.539114i
\(135\) 3.71113 + 25.7143i 0.0274899 + 0.190477i
\(136\) 71.3180 0.524397
\(137\) −184.443 184.443i −1.34630 1.34630i −0.889642 0.456660i \(-0.849046\pi\)
−0.456660 0.889642i \(-0.650954\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 18.2325i 0.131169i 0.997847 + 0.0655844i \(0.0208912\pi\)
−0.997847 + 0.0655844i \(0.979109\pi\)
\(140\) 65.2260 9.41352i 0.465900 0.0672394i
\(141\) 88.4371 0.627213
\(142\) 19.9996 + 19.9996i 0.140842 + 0.140842i
\(143\) 6.86477 6.86477i 0.0480054 0.0480054i
\(144\) 12.0000i 0.0833333i
\(145\) 30.4810 40.7630i 0.210213 0.281124i
\(146\) 79.1751 0.542295
\(147\) 6.82121 + 6.82121i 0.0464028 + 0.0464028i
\(148\) −71.2871 + 71.2871i −0.481670 + 0.481670i
\(149\) 43.1692i 0.289726i 0.989452 + 0.144863i \(0.0462742\pi\)
−0.989452 + 0.144863i \(0.953726\pi\)
\(150\) 17.3150 + 58.7383i 0.115434 + 0.391589i
\(151\) 182.218 1.20674 0.603372 0.797460i \(-0.293824\pi\)
0.603372 + 0.797460i \(0.293824\pi\)
\(152\) −23.9088 23.9088i −0.157295 0.157295i
\(153\) 53.4885 53.4885i 0.349598 0.349598i
\(154\) 8.93810i 0.0580396i
\(155\) −71.3561 53.3573i −0.460362 0.344241i
\(156\) 35.0670 0.224788
\(157\) 24.5503 + 24.5503i 0.156371 + 0.156371i 0.780957 0.624585i \(-0.214732\pi\)
−0.624585 + 0.780957i \(0.714732\pi\)
\(158\) 26.1612 26.1612i 0.165577 0.165577i
\(159\) 53.9794i 0.339493i
\(160\) 4.04017 + 27.9942i 0.0252511 + 0.174964i
\(161\) 31.6054 0.196307
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) −55.8359 + 55.8359i −0.342552 + 0.342552i −0.857326 0.514774i \(-0.827876\pi\)
0.514774 + 0.857326i \(0.327876\pi\)
\(164\) 140.817i 0.858642i
\(165\) 8.22029 1.18636i 0.0498199 0.00719009i
\(166\) 76.4800 0.460723
\(167\) −157.546 157.546i −0.943389 0.943389i 0.0550920 0.998481i \(-0.482455\pi\)
−0.998481 + 0.0550920i \(0.982455\pi\)
\(168\) 22.8291 22.8291i 0.135887 0.135887i
\(169\) 66.5254i 0.393642i
\(170\) 106.772 142.789i 0.628072 0.839937i
\(171\) −35.8632 −0.209727
\(172\) −64.7668 64.7668i −0.376551 0.376551i
\(173\) 167.938 167.938i 0.970741 0.970741i −0.0288432 0.999584i \(-0.509182\pi\)
0.999584 + 0.0288432i \(0.00918235\pi\)
\(174\) 24.9353i 0.143306i
\(175\) 78.8045 144.686i 0.450312 0.826775i
\(176\) 3.83613 0.0217962
\(177\) −9.18245 9.18245i −0.0518783 0.0518783i
\(178\) 67.4462 67.4462i 0.378911 0.378911i
\(179\) 237.552i 1.32711i −0.748128 0.663554i \(-0.769047\pi\)
0.748128 0.663554i \(-0.230953\pi\)
\(180\) 24.0258 + 17.9655i 0.133477 + 0.0998086i
\(181\) 74.4891 0.411542 0.205771 0.978600i \(-0.434030\pi\)
0.205771 + 0.978600i \(0.434030\pi\)
\(182\) −66.7122 66.7122i −0.366551 0.366551i
\(183\) 101.817 101.817i 0.556376 0.556376i
\(184\) 13.5647i 0.0737210i
\(185\) 36.0015 + 249.454i 0.194603 + 1.34840i
\(186\) −43.6496 −0.234675
\(187\) −17.0991 17.0991i −0.0914388 0.0914388i
\(188\) 72.2086 72.2086i 0.384088 0.384088i
\(189\) 34.2436i 0.181183i
\(190\) −83.6636 + 12.0745i −0.440335 + 0.0635498i
\(191\) 241.019 1.26188 0.630940 0.775832i \(-0.282670\pi\)
0.630940 + 0.775832i \(0.282670\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) −157.235 + 157.235i −0.814687 + 0.814687i −0.985332 0.170646i \(-0.945415\pi\)
0.170646 + 0.985332i \(0.445415\pi\)
\(194\) 181.150i 0.933764i
\(195\) 52.4998 70.2094i 0.269230 0.360048i
\(196\) 11.1390 0.0568316
\(197\) 155.381 + 155.381i 0.788736 + 0.788736i 0.981287 0.192551i \(-0.0616760\pi\)
−0.192551 + 0.981287i \(0.561676\pi\)
\(198\) 2.87709 2.87709i 0.0145308 0.0145308i
\(199\) 168.224i 0.845344i −0.906283 0.422672i \(-0.861092\pi\)
0.906283 0.422672i \(-0.138908\pi\)
\(200\) 62.0973 + 33.8220i 0.310487 + 0.169110i
\(201\) −88.4771 −0.440185
\(202\) 8.25159 + 8.25159i 0.0408495 + 0.0408495i
\(203\) −47.4375 + 47.4375i −0.233682 + 0.233682i
\(204\) 87.3463i 0.428168i
\(205\) −281.937 210.822i −1.37530 1.02840i
\(206\) 164.162 0.796904
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) 28.6321 28.6321i 0.137654 0.137654i
\(209\) 11.4647i 0.0548548i
\(210\) −11.5292 79.8853i −0.0549008 0.380406i
\(211\) −389.389 −1.84545 −0.922723 0.385463i \(-0.874042\pi\)
−0.922723 + 0.385463i \(0.874042\pi\)
\(212\) −44.0740 44.0740i −0.207896 0.207896i
\(213\) 24.4944 24.4944i 0.114997 0.114997i
\(214\) 185.591i 0.867249i
\(215\) −226.637 + 32.7086i −1.05413 + 0.152133i
\(216\) 14.6969 0.0680414
\(217\) 83.0400 + 83.0400i 0.382673 + 0.382673i
\(218\) −11.0337 + 11.0337i −0.0506134 + 0.0506134i
\(219\) 96.9693i 0.442782i
\(220\) 5.74318 7.68050i 0.0261053 0.0349114i
\(221\) −255.248 −1.15497
\(222\) 87.3085 + 87.3085i 0.393282 + 0.393282i
\(223\) 54.1820 54.1820i 0.242969 0.242969i −0.575109 0.818077i \(-0.695040\pi\)
0.818077 + 0.575109i \(0.195040\pi\)
\(224\) 37.2797i 0.166427i
\(225\) 71.9394 21.2065i 0.319731 0.0942512i
\(226\) 126.681 0.560534
\(227\) 180.088 + 180.088i 0.793339 + 0.793339i 0.982035 0.188697i \(-0.0604263\pi\)
−0.188697 + 0.982035i \(0.560426\pi\)
\(228\) −29.2822 + 29.2822i −0.128431 + 0.128431i
\(229\) 23.3678i 0.102043i −0.998698 0.0510213i \(-0.983752\pi\)
0.998698 0.0510213i \(-0.0162477\pi\)
\(230\) 27.1585 + 20.3080i 0.118080 + 0.0882958i
\(231\) −10.9469 −0.0473892
\(232\) −20.3596 20.3596i −0.0877569 0.0877569i
\(233\) 97.9581 97.9581i 0.420421 0.420421i −0.464928 0.885349i \(-0.653920\pi\)
0.885349 + 0.464928i \(0.153920\pi\)
\(234\) 42.9481i 0.183539i
\(235\) −36.4669 252.678i −0.155178 1.07523i
\(236\) −14.9949 −0.0635376
\(237\) −32.0408 32.0408i −0.135193 0.135193i
\(238\) −166.170 + 166.170i −0.698192 + 0.698192i
\(239\) 138.405i 0.579100i 0.957163 + 0.289550i \(0.0935056\pi\)
−0.957163 + 0.289550i \(0.906494\pi\)
\(240\) 34.2858 4.94818i 0.142857 0.0206174i
\(241\) 179.237 0.743723 0.371861 0.928288i \(-0.378720\pi\)
0.371861 + 0.928288i \(0.378720\pi\)
\(242\) 120.080 + 120.080i 0.496199 + 0.496199i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 166.266i 0.681419i
\(245\) 16.6765 22.3019i 0.0680674 0.0910283i
\(246\) −172.465 −0.701078
\(247\) 85.5699 + 85.5699i 0.346437 + 0.346437i
\(248\) −35.6398 + 35.6398i −0.143709 + 0.143709i
\(249\) 93.6685i 0.376179i
\(250\) 160.684 73.6923i 0.642737 0.294769i
\(251\) 310.376 1.23656 0.618279 0.785958i \(-0.287830\pi\)
0.618279 + 0.785958i \(0.287830\pi\)
\(252\) −27.9598 27.9598i −0.110951 0.110951i
\(253\) 3.25223 3.25223i 0.0128547 0.0128547i
\(254\) 230.343i 0.906861i
\(255\) −174.880 130.769i −0.685806 0.512819i
\(256\) 16.0000 0.0625000
\(257\) 219.443 + 219.443i 0.853863 + 0.853863i 0.990606 0.136744i \(-0.0436636\pi\)
−0.136744 + 0.990606i \(0.543664\pi\)
\(258\) −79.3229 + 79.3229i −0.307453 + 0.307453i
\(259\) 332.195i 1.28261i
\(260\) −14.4598 100.192i −0.0556146 0.385353i
\(261\) −30.5394 −0.117009
\(262\) 59.8637 + 59.8637i 0.228487 + 0.228487i
\(263\) −303.730 + 303.730i −1.15487 + 1.15487i −0.169303 + 0.985564i \(0.554152\pi\)
−0.985564 + 0.169303i \(0.945848\pi\)
\(264\) 4.69828i 0.0177965i
\(265\) −154.227 + 22.2583i −0.581990 + 0.0839936i
\(266\) 111.414 0.418850
\(267\) −82.6044 82.6044i −0.309380 0.309380i
\(268\) −72.2412 + 72.2412i −0.269557 + 0.269557i
\(269\) 472.776i 1.75753i −0.477254 0.878765i \(-0.658368\pi\)
0.477254 0.878765i \(-0.341632\pi\)
\(270\) 22.0032 29.4255i 0.0814934 0.108983i
\(271\) 64.8046 0.239131 0.119566 0.992826i \(-0.461850\pi\)
0.119566 + 0.992826i \(0.461850\pi\)
\(272\) −71.3180 71.3180i −0.262199 0.262199i
\(273\) −81.7055 + 81.7055i −0.299287 + 0.299287i
\(274\) 368.887i 1.34630i
\(275\) −6.77924 22.9974i −0.0246518 0.0836269i
\(276\) 16.6132 0.0601929
\(277\) 160.806 + 160.806i 0.580526 + 0.580526i 0.935048 0.354522i \(-0.115356\pi\)
−0.354522 + 0.935048i \(0.615356\pi\)
\(278\) 18.2325 18.2325i 0.0655844 0.0655844i
\(279\) 53.4596i 0.191612i
\(280\) −74.6396 55.8125i −0.266570 0.199330i
\(281\) −163.698 −0.582554 −0.291277 0.956639i \(-0.594080\pi\)
−0.291277 + 0.956639i \(0.594080\pi\)
\(282\) −88.4371 88.4371i −0.313607 0.313607i
\(283\) 353.193 353.193i 1.24803 1.24803i 0.291445 0.956588i \(-0.405864\pi\)
0.956588 0.291445i \(-0.0941360\pi\)
\(284\) 39.9992i 0.140842i
\(285\) 14.7881 + 102.467i 0.0518882 + 0.359532i
\(286\) −13.7295 −0.0480054
\(287\) 328.102 + 328.102i 1.14321 + 1.14321i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 346.782i 1.19994i
\(290\) −71.2439 + 10.2820i −0.245669 + 0.0354553i
\(291\) −221.863 −0.762415
\(292\) −79.1751 79.1751i −0.271148 0.271148i
\(293\) −93.8150 + 93.8150i −0.320188 + 0.320188i −0.848839 0.528651i \(-0.822698\pi\)
0.528651 + 0.848839i \(0.322698\pi\)
\(294\) 13.6424i 0.0464028i
\(295\) −22.4493 + 30.0220i −0.0760992 + 0.101770i
\(296\) 142.574 0.481670
\(297\) −3.52371 3.52371i −0.0118643 0.0118643i
\(298\) 43.1692 43.1692i 0.144863 0.144863i
\(299\) 48.5481i 0.162368i
\(300\) 41.4233 76.0534i 0.138078 0.253511i
\(301\) 301.811 1.00269
\(302\) −182.218 182.218i −0.603372 0.603372i
\(303\) 10.1061 10.1061i 0.0333535 0.0333535i
\(304\) 47.8176i 0.157295i
\(305\) −332.890 248.922i −1.09144 0.816138i
\(306\) −106.977 −0.349598
\(307\) 20.7338 + 20.7338i 0.0675367 + 0.0675367i 0.740068 0.672532i \(-0.234793\pi\)
−0.672532 + 0.740068i \(0.734793\pi\)
\(308\) −8.93810 + 8.93810i −0.0290198 + 0.0290198i
\(309\) 201.057i 0.650670i
\(310\) 17.9988 + 124.713i 0.0580607 + 0.402301i
\(311\) 530.664 1.70632 0.853158 0.521652i \(-0.174684\pi\)
0.853158 + 0.521652i \(0.174684\pi\)
\(312\) −35.0670 35.0670i −0.112394 0.112394i
\(313\) 264.744 264.744i 0.845826 0.845826i −0.143783 0.989609i \(-0.545927\pi\)
0.989609 + 0.143783i \(0.0459267\pi\)
\(314\) 49.1005i 0.156371i
\(315\) −97.8391 + 14.1203i −0.310600 + 0.0448263i
\(316\) −52.3224 −0.165577
\(317\) −74.8843 74.8843i −0.236228 0.236228i 0.579058 0.815286i \(-0.303420\pi\)
−0.815286 + 0.579058i \(0.803420\pi\)
\(318\) −53.9794 + 53.9794i −0.169747 + 0.169747i
\(319\) 9.76275i 0.0306042i
\(320\) 23.9541 32.0344i 0.0748564 0.100108i
\(321\) 227.302 0.708106
\(322\) −31.6054 31.6054i −0.0981534 0.0981534i
\(323\) 213.141 213.141i 0.659880 0.659880i
\(324\) 18.0000i 0.0555556i
\(325\) −222.247 121.049i −0.683837 0.372459i
\(326\) 111.672 0.342552
\(327\) 13.5135 + 13.5135i 0.0413256 + 0.0413256i
\(328\) −140.817 + 140.817i −0.429321 + 0.429321i
\(329\) 336.489i 1.02276i
\(330\) −9.40665 7.03392i −0.0285050 0.0213149i
\(331\) 512.969 1.54975 0.774877 0.632112i \(-0.217812\pi\)
0.774877 + 0.632112i \(0.217812\pi\)
\(332\) −76.4800 76.4800i −0.230361 0.230361i
\(333\) 106.931 106.931i 0.321113 0.321113i
\(334\) 315.092i 0.943389i
\(335\) 36.4834 + 252.792i 0.108906 + 0.754604i
\(336\) −45.6581 −0.135887
\(337\) 50.5137 + 50.5137i 0.149892 + 0.149892i 0.778070 0.628178i \(-0.216199\pi\)
−0.628178 + 0.778070i \(0.716199\pi\)
\(338\) 66.5254 66.5254i 0.196821 0.196821i
\(339\) 155.152i 0.457674i
\(340\) −249.562 + 36.0171i −0.734005 + 0.105933i
\(341\) 17.0898 0.0501168
\(342\) 35.8632 + 35.8632i 0.104863 + 0.104863i
\(343\) −254.292 + 254.292i −0.741376 + 0.741376i
\(344\) 129.534i 0.376551i
\(345\) 24.8722 33.2622i 0.0720933 0.0964122i
\(346\) −335.876 −0.970741
\(347\) 74.2970 + 74.2970i 0.214112 + 0.214112i 0.806012 0.591899i \(-0.201622\pi\)
−0.591899 + 0.806012i \(0.701622\pi\)
\(348\) −24.9353 + 24.9353i −0.0716532 + 0.0716532i
\(349\) 597.945i 1.71331i −0.515891 0.856654i \(-0.672539\pi\)
0.515891 0.856654i \(-0.327461\pi\)
\(350\) −223.490 + 65.8810i −0.638543 + 0.188232i
\(351\) −52.6005 −0.149859
\(352\) −3.83613 3.83613i −0.0108981 0.0108981i
\(353\) −5.18580 + 5.18580i −0.0146907 + 0.0146907i −0.714414 0.699723i \(-0.753307\pi\)
0.699723 + 0.714414i \(0.253307\pi\)
\(354\) 18.3649i 0.0518783i
\(355\) −80.0844 59.8839i −0.225590 0.168687i
\(356\) −134.892 −0.378911
\(357\) 203.515 + 203.515i 0.570071 + 0.570071i
\(358\) −237.552 + 237.552i −0.663554 + 0.663554i
\(359\) 173.219i 0.482503i −0.970463 0.241251i \(-0.922442\pi\)
0.970463 0.241251i \(-0.0775578\pi\)
\(360\) −6.06025 41.9913i −0.0168340 0.116643i
\(361\) 218.092 0.604133
\(362\) −74.4891 74.4891i −0.205771 0.205771i
\(363\) 147.068 147.068i 0.405145 0.405145i
\(364\) 133.424i 0.366551i
\(365\) −277.056 + 39.9851i −0.759057 + 0.109548i
\(366\) −203.634 −0.556376
\(367\) 134.667 + 134.667i 0.366941 + 0.366941i 0.866360 0.499419i \(-0.166453\pi\)
−0.499419 + 0.866360i \(0.666453\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 211.226i 0.572428i
\(370\) 213.452 285.455i 0.576897 0.771500i
\(371\) 205.383 0.553594
\(372\) 43.6496 + 43.6496i 0.117338 + 0.117338i
\(373\) −119.301 + 119.301i −0.319841 + 0.319841i −0.848706 0.528865i \(-0.822618\pi\)
0.528865 + 0.848706i \(0.322618\pi\)
\(374\) 34.1981i 0.0914388i
\(375\) −90.2543 196.797i −0.240678 0.524793i
\(376\) −144.417 −0.384088
\(377\) 72.8673 + 72.8673i 0.193282 + 0.193282i
\(378\) −34.2436 + 34.2436i −0.0905915 + 0.0905915i
\(379\) 180.139i 0.475301i −0.971351 0.237650i \(-0.923623\pi\)
0.971351 0.237650i \(-0.0763773\pi\)
\(380\) 95.7381 + 71.5892i 0.251942 + 0.188393i
\(381\) −282.111 −0.740449
\(382\) −241.019 241.019i −0.630940 0.630940i
\(383\) 203.565 203.565i 0.531502 0.531502i −0.389517 0.921019i \(-0.627358\pi\)
0.921019 + 0.389517i \(0.127358\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 4.51393 + 31.2769i 0.0117245 + 0.0812387i
\(386\) 314.469 0.814687
\(387\) 97.1503 + 97.1503i 0.251034 + 0.251034i
\(388\) −181.150 + 181.150i −0.466882 + 0.466882i
\(389\) 155.622i 0.400056i 0.979790 + 0.200028i \(0.0641032\pi\)
−0.979790 + 0.200028i \(0.935897\pi\)
\(390\) −122.709 + 17.7096i −0.314639 + 0.0454092i
\(391\) −120.926 −0.309272
\(392\) −11.1390 11.1390i −0.0284158 0.0284158i
\(393\) 73.3177 73.3177i 0.186559 0.186559i
\(394\) 310.762i 0.788736i
\(395\) −78.3334 + 104.757i −0.198312 + 0.265208i
\(396\) −5.75419 −0.0145308
\(397\) 253.869 + 253.869i 0.639469 + 0.639469i 0.950425 0.310955i \(-0.100649\pi\)
−0.310955 + 0.950425i \(0.600649\pi\)
\(398\) −168.224 + 168.224i −0.422672 + 0.422672i
\(399\) 136.454i 0.341990i
\(400\) −28.2754 95.9193i −0.0706884 0.239798i
\(401\) −85.8020 −0.213970 −0.106985 0.994261i \(-0.534120\pi\)
−0.106985 + 0.994261i \(0.534120\pi\)
\(402\) 88.4771 + 88.4771i 0.220092 + 0.220092i
\(403\) 127.555 127.555i 0.316514 0.316514i
\(404\) 16.5032i 0.0408495i
\(405\) −36.0387 26.9483i −0.0889844 0.0665391i
\(406\) 94.8750 0.233682
\(407\) −34.1833 34.1833i −0.0839885 0.0839885i
\(408\) −87.3463 + 87.3463i −0.214084 + 0.214084i
\(409\) 483.568i 1.18232i 0.806555 + 0.591158i \(0.201329\pi\)
−0.806555 + 0.591158i \(0.798671\pi\)
\(410\) 71.1157 + 492.759i 0.173453 + 1.20185i
\(411\) 451.792 1.09925
\(412\) −164.162 164.162i −0.398452 0.398452i
\(413\) 34.9378 34.9378i 0.0845952 0.0845952i
\(414\) 20.3470i 0.0491473i
\(415\) −267.625 + 38.6240i −0.644879 + 0.0930699i
\(416\) −57.2642 −0.137654
\(417\) −22.3301 22.3301i −0.0535494 0.0535494i
\(418\) 11.4647 11.4647i 0.0274274 0.0274274i
\(419\) 519.575i 1.24004i 0.784588 + 0.620018i \(0.212875\pi\)
−0.784588 + 0.620018i \(0.787125\pi\)
\(420\) −68.3561 + 91.4144i −0.162753 + 0.217653i
\(421\) −137.505 −0.326616 −0.163308 0.986575i \(-0.552216\pi\)
−0.163308 + 0.986575i \(0.552216\pi\)
\(422\) 389.389 + 389.389i 0.922723 + 0.922723i
\(423\) −108.313 + 108.313i −0.256059 + 0.256059i
\(424\) 88.1480i 0.207896i
\(425\) −301.514 + 553.582i −0.709445 + 1.30255i
\(426\) −48.9888 −0.114997
\(427\) 387.397 + 387.397i 0.907254 + 0.907254i
\(428\) 185.591 185.591i 0.433624 0.433624i
\(429\) 16.8152i 0.0391962i
\(430\) 259.346 + 193.929i 0.603130 + 0.450997i
\(431\) −555.836 −1.28964 −0.644822 0.764333i \(-0.723068\pi\)
−0.644822 + 0.764333i \(0.723068\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) −153.478 + 153.478i −0.354452 + 0.354452i −0.861763 0.507311i \(-0.830639\pi\)
0.507311 + 0.861763i \(0.330639\pi\)
\(434\) 166.080i 0.382673i
\(435\) 12.5929 + 87.2557i 0.0289491 + 0.200588i
\(436\) 22.0674 0.0506134
\(437\) 40.5394 + 40.5394i 0.0927675 + 0.0927675i
\(438\) −96.9693 + 96.9693i −0.221391 + 0.221391i
\(439\) 399.370i 0.909727i 0.890561 + 0.454864i \(0.150312\pi\)
−0.890561 + 0.454864i \(0.849688\pi\)
\(440\) −13.4237 + 1.93732i −0.0305084 + 0.00440301i
\(441\) −16.7085 −0.0378877
\(442\) 255.248 + 255.248i 0.577484 + 0.577484i
\(443\) 99.1260 99.1260i 0.223761 0.223761i −0.586319 0.810080i \(-0.699424\pi\)
0.810080 + 0.586319i \(0.199424\pi\)
\(444\) 174.617i 0.393282i
\(445\) −201.951 + 270.075i −0.453823 + 0.606909i
\(446\) −108.364 −0.242969
\(447\) −52.8713 52.8713i −0.118280 0.118280i
\(448\) −37.2797 + 37.2797i −0.0832136 + 0.0832136i
\(449\) 88.4775i 0.197055i 0.995134 + 0.0985273i \(0.0314132\pi\)
−0.995134 + 0.0985273i \(0.968587\pi\)
\(450\) −93.1460 50.7329i −0.206991 0.112740i
\(451\) 67.5241 0.149721
\(452\) −126.681 126.681i −0.280267 0.280267i
\(453\) −223.171 + 223.171i −0.492651 + 0.492651i
\(454\) 360.176i 0.793339i
\(455\) 267.136 + 199.754i 0.587112 + 0.439019i
\(456\) 58.5644 0.128431
\(457\) 349.592 + 349.592i 0.764972 + 0.764972i 0.977217 0.212245i \(-0.0680774\pi\)
−0.212245 + 0.977217i \(0.568077\pi\)
\(458\) −23.3678 + 23.3678i −0.0510213 + 0.0510213i
\(459\) 131.020i 0.285446i
\(460\) −6.85044 47.4665i −0.0148923 0.103188i
\(461\) −353.666 −0.767171 −0.383585 0.923505i \(-0.625311\pi\)
−0.383585 + 0.923505i \(0.625311\pi\)
\(462\) 10.9469 + 10.9469i 0.0236946 + 0.0236946i
\(463\) −466.196 + 466.196i −1.00690 + 1.00690i −0.00692730 + 0.999976i \(0.502205\pi\)
−0.999976 + 0.00692730i \(0.997795\pi\)
\(464\) 40.7192i 0.0877569i
\(465\) 152.742 22.0440i 0.328478 0.0474064i
\(466\) −195.916 −0.420421
\(467\) −259.814 259.814i −0.556346 0.556346i 0.371919 0.928265i \(-0.378700\pi\)
−0.928265 + 0.371919i \(0.878700\pi\)
\(468\) −42.9481 + 42.9481i −0.0917695 + 0.0917695i
\(469\) 336.641i 0.717786i
\(470\) −216.211 + 289.145i −0.460024 + 0.615202i
\(471\) −60.1356 −0.127677
\(472\) 14.9949 + 14.9949i 0.0317688 + 0.0317688i
\(473\) 31.0567 31.0567i 0.0656590 0.0656590i
\(474\) 64.0816i 0.135193i
\(475\) 286.665 84.5038i 0.603504 0.177903i
\(476\) 332.339 0.698192
\(477\) 66.1110 + 66.1110i 0.138598 + 0.138598i
\(478\) 138.405 138.405i 0.289550 0.289550i
\(479\) 397.780i 0.830439i 0.909721 + 0.415220i \(0.136295\pi\)
−0.909721 + 0.415220i \(0.863705\pi\)
\(480\) −39.2340 29.3376i −0.0817374 0.0611200i
\(481\) −510.275 −1.06086
\(482\) −179.237 179.237i −0.371861 0.371861i
\(483\) −38.7086 + 38.7086i −0.0801419 + 0.0801419i
\(484\) 240.161i 0.496199i
\(485\) 91.4847 + 633.895i 0.188628 + 1.30700i
\(486\) −22.0454 −0.0453609
\(487\) −297.105 297.105i −0.610073 0.610073i 0.332892 0.942965i \(-0.391975\pi\)
−0.942965 + 0.332892i \(0.891975\pi\)
\(488\) −166.266 + 166.266i −0.340710 + 0.340710i
\(489\) 136.770i 0.279692i
\(490\) −38.9785 + 5.62543i −0.0795479 + 0.0114805i
\(491\) −670.158 −1.36488 −0.682442 0.730940i \(-0.739082\pi\)
−0.682442 + 0.730940i \(0.739082\pi\)
\(492\) 172.465 + 172.465i 0.350539 + 0.350539i
\(493\) 181.501 181.501i 0.368156 0.368156i
\(494\) 171.140i 0.346437i
\(495\) −8.61476 + 11.5208i −0.0174036 + 0.0232742i
\(496\) 71.2795 0.143709
\(497\) 93.1973 + 93.1973i 0.187520 + 0.187520i
\(498\) −93.6685 + 93.6685i −0.188089 + 0.188089i
\(499\) 76.3365i 0.152979i −0.997070 0.0764895i \(-0.975629\pi\)
0.997070 0.0764895i \(-0.0243712\pi\)
\(500\) −234.377 86.9920i −0.468753 0.173984i
\(501\) 385.907 0.770274
\(502\) −310.376 310.376i −0.618279 0.618279i
\(503\) −0.276837 + 0.276837i −0.000550372 + 0.000550372i −0.707382 0.706832i \(-0.750124\pi\)
0.706832 + 0.707382i \(0.250124\pi\)
\(504\) 55.9196i 0.110951i
\(505\) −33.0419 24.7074i −0.0654294 0.0489255i
\(506\) −6.50447 −0.0128547
\(507\) −81.4767 81.4767i −0.160704 0.160704i
\(508\) −230.343 + 230.343i −0.453431 + 0.453431i
\(509\) 33.4655i 0.0657476i 0.999460 + 0.0328738i \(0.0104659\pi\)
−0.999460 + 0.0328738i \(0.989534\pi\)
\(510\) 44.1117 + 305.649i 0.0864936 + 0.599312i
\(511\) 368.953 0.722021
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 43.9233 43.9233i 0.0856205 0.0856205i
\(514\) 438.886i 0.853863i
\(515\) −574.450 + 82.9054i −1.11544 + 0.160981i
\(516\) 158.646 0.307453
\(517\) 34.6252 + 34.6252i 0.0669732 + 0.0669732i
\(518\) −332.195 + 332.195i −0.641304 + 0.641304i
\(519\) 411.363i 0.792606i
\(520\) −85.7319 + 114.651i −0.164869 + 0.220484i
\(521\) 355.266 0.681892 0.340946 0.940083i \(-0.389253\pi\)
0.340946 + 0.940083i \(0.389253\pi\)
\(522\) 30.5394 + 30.5394i 0.0585046 + 0.0585046i
\(523\) 313.483 313.483i 0.599394 0.599394i −0.340757 0.940151i \(-0.610684\pi\)
0.940151 + 0.340757i \(0.110684\pi\)
\(524\) 119.727i 0.228487i
\(525\) 80.6875 + 273.718i 0.153690 + 0.521368i
\(526\) 607.460 1.15487
\(527\) −317.719 317.719i −0.602883 0.602883i
\(528\) −4.69828 + 4.69828i −0.00889825 + 0.00889825i
\(529\) 23.0000i 0.0434783i
\(530\) 176.486 + 131.969i 0.332992 + 0.248998i
\(531\) 22.4923 0.0423584
\(532\) −111.414 111.414i −0.209425 0.209425i
\(533\) 503.987 503.987i 0.945566 0.945566i
\(534\) 165.209i 0.309380i
\(535\) −93.7275 649.436i −0.175192 1.21390i
\(536\) 144.482 0.269557
\(537\) 290.941 + 290.941i 0.541790 + 0.541790i
\(538\) −472.776 + 472.776i −0.878765 + 0.878765i
\(539\) 5.34132i 0.00990969i
\(540\) −51.4287 + 7.42226i −0.0952383 + 0.0137449i
\(541\) 112.026 0.207071 0.103536 0.994626i \(-0.466984\pi\)
0.103536 + 0.994626i \(0.466984\pi\)
\(542\) −64.8046 64.8046i −0.119566 0.119566i
\(543\) −91.2302 + 91.2302i −0.168011 + 0.168011i
\(544\) 142.636i 0.262199i
\(545\) 33.0378 44.1823i 0.0606198 0.0810684i
\(546\) 163.411 0.299287
\(547\) −479.090 479.090i −0.875850 0.875850i 0.117252 0.993102i \(-0.462591\pi\)
−0.993102 + 0.117252i \(0.962591\pi\)
\(548\) 368.887 368.887i 0.673151 0.673151i
\(549\) 249.399i 0.454279i
\(550\) −16.2182 + 29.7766i −0.0294876 + 0.0541393i
\(551\) −121.694 −0.220859
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) 121.910 121.910i 0.220452 0.220452i
\(554\) 321.611i 0.580526i
\(555\) −349.610 261.424i −0.629927 0.471035i
\(556\) −36.4649 −0.0655844
\(557\) 41.0617 + 41.0617i 0.0737195 + 0.0737195i 0.743005 0.669286i \(-0.233400\pi\)
−0.669286 + 0.743005i \(0.733400\pi\)
\(558\) 53.4596 53.4596i 0.0958058 0.0958058i
\(559\) 463.603i 0.829343i
\(560\) 18.8270 + 130.452i 0.0336197 + 0.232950i
\(561\) 41.8840 0.0746595
\(562\) 163.698 + 163.698i 0.291277 + 0.291277i
\(563\) 302.703 302.703i 0.537661 0.537661i −0.385180 0.922841i \(-0.625861\pi\)
0.922841 + 0.385180i \(0.125861\pi\)
\(564\) 176.874i 0.313607i
\(565\) −443.291 + 63.9764i −0.784586 + 0.113233i
\(566\) −706.386 −1.24803
\(567\) 41.9397 + 41.9397i 0.0739677 + 0.0739677i
\(568\) −39.9992 + 39.9992i −0.0704211 + 0.0704211i
\(569\) 126.060i 0.221547i −0.993846 0.110774i \(-0.964667\pi\)
0.993846 0.110774i \(-0.0353329\pi\)
\(570\) 87.6785 117.255i 0.153822 0.205710i
\(571\) −997.870 −1.74758 −0.873791 0.486301i \(-0.838346\pi\)
−0.873791 + 0.486301i \(0.838346\pi\)
\(572\) 13.7295 + 13.7295i 0.0240027 + 0.0240027i
\(573\) −295.187 + 295.187i −0.515160 + 0.515160i
\(574\) 656.203i 1.14321i
\(575\) −105.291 57.3479i −0.183115 0.0997355i
\(576\) −24.0000 −0.0416667
\(577\) −97.7737 97.7737i −0.169452 0.169452i 0.617287 0.786738i \(-0.288232\pi\)
−0.786738 + 0.617287i \(0.788232\pi\)
\(578\) 346.782 346.782i 0.599969 0.599969i
\(579\) 385.144i 0.665189i
\(580\) 81.5260 + 60.9619i 0.140562 + 0.105107i
\(581\) 356.394 0.613414
\(582\) 221.863 + 221.863i 0.381207 + 0.381207i
\(583\) 21.1342 21.1342i 0.0362507 0.0362507i
\(584\) 158.350i 0.271148i
\(585\) 21.6897 + 150.287i 0.0370764 + 0.256902i
\(586\) 187.630 0.320188
\(587\) −222.168 222.168i −0.378480 0.378480i 0.492074 0.870553i \(-0.336239\pi\)
−0.870553 + 0.492074i \(0.836239\pi\)
\(588\) −13.6424 + 13.6424i −0.0232014 + 0.0232014i
\(589\) 213.026i 0.361674i
\(590\) 52.4713 7.57273i 0.0889344 0.0128351i
\(591\) −380.604 −0.644000
\(592\) −142.574 142.574i −0.240835 0.240835i
\(593\) −724.293 + 724.293i −1.22141 + 1.22141i −0.254273 + 0.967133i \(0.581836\pi\)
−0.967133 + 0.254273i \(0.918164\pi\)
\(594\) 7.04741i 0.0118643i
\(595\) 497.555 665.393i 0.836226 1.11831i
\(596\) −86.3384 −0.144863
\(597\) 206.031 + 206.031i 0.345110 + 0.345110i
\(598\) −48.5481 + 48.5481i −0.0811841 + 0.0811841i
\(599\) 511.979i 0.854723i −0.904081 0.427361i \(-0.859443\pi\)
0.904081 0.427361i \(-0.140557\pi\)
\(600\) −117.477 + 34.6301i −0.195794 + 0.0577168i
\(601\) 1102.28 1.83408 0.917039 0.398797i \(-0.130572\pi\)
0.917039 + 0.398797i \(0.130572\pi\)
\(602\) −301.811 301.811i −0.501347 0.501347i
\(603\) 108.362 108.362i 0.179705 0.179705i
\(604\) 364.437i 0.603372i
\(605\) −480.837 359.551i −0.794773 0.594300i
\(606\) −20.2122 −0.0333535
\(607\) −616.238 616.238i −1.01522 1.01522i −0.999882 0.0153372i \(-0.995118\pi\)
−0.0153372 0.999882i \(-0.504882\pi\)
\(608\) 47.8176 47.8176i 0.0786474 0.0786474i
\(609\) 116.198i 0.190801i
\(610\) 83.9680 + 581.812i 0.137652 + 0.953790i
\(611\) 516.871 0.845942
\(612\) 106.977 + 106.977i 0.174799 + 0.174799i
\(613\) −373.603 + 373.603i −0.609467 + 0.609467i −0.942807 0.333340i \(-0.891824\pi\)
0.333340 + 0.942807i \(0.391824\pi\)
\(614\) 41.4675i 0.0675367i
\(615\) 603.504 87.0986i 0.981307 0.141624i
\(616\) 17.8762 0.0290198
\(617\) 460.974 + 460.974i 0.747121 + 0.747121i 0.973938 0.226816i \(-0.0728317\pi\)
−0.226816 + 0.973938i \(0.572832\pi\)
\(618\) −201.057 + 201.057i −0.325335 + 0.325335i
\(619\) 447.560i 0.723037i 0.932365 + 0.361518i \(0.117742\pi\)
−0.932365 + 0.361518i \(0.882258\pi\)
\(620\) 106.715 142.712i 0.172120 0.230181i
\(621\) −24.9199 −0.0401286
\(622\) −530.664 530.664i −0.853158 0.853158i
\(623\) 314.297 314.297i 0.504489 0.504489i
\(624\) 70.1340i 0.112394i
\(625\) −525.063 + 339.019i −0.840101 + 0.542430i
\(626\) −529.487 −0.845826
\(627\) −14.0413 14.0413i −0.0223944 0.0223944i
\(628\) −49.1005 + 49.1005i −0.0781856 + 0.0781856i
\(629\) 1271.01i 2.02069i
\(630\) 111.959 + 83.7188i 0.177713 + 0.132887i
\(631\) 382.818 0.606685 0.303342 0.952882i \(-0.401897\pi\)
0.303342 + 0.952882i \(0.401897\pi\)
\(632\) 52.3224 + 52.3224i 0.0827886 + 0.0827886i
\(633\) 476.902 476.902i 0.753400 0.753400i
\(634\) 149.769i 0.236228i
\(635\) 116.328 + 806.033i 0.183194 + 1.26934i
\(636\) 107.959 0.169747
\(637\) 39.8666 + 39.8666i 0.0625849 + 0.0625849i
\(638\) 9.76275 9.76275i 0.0153021 0.0153021i
\(639\) 59.9988i 0.0938948i
\(640\) −55.9885 + 8.08034i −0.0874820 + 0.0126255i
\(641\) 120.162 0.187460 0.0937302 0.995598i \(-0.470121\pi\)
0.0937302 + 0.995598i \(0.470121\pi\)
\(642\) −227.302 227.302i −0.354053 0.354053i
\(643\) 211.922 211.922i 0.329583 0.329583i −0.522845 0.852428i \(-0.675129\pi\)
0.852428 + 0.522845i \(0.175129\pi\)
\(644\) 63.2108i 0.0981534i
\(645\) 237.513 317.633i 0.368237 0.492454i
\(646\) −426.282 −0.659880
\(647\) −292.174 292.174i −0.451583 0.451583i 0.444297 0.895880i \(-0.353454\pi\)
−0.895880 + 0.444297i \(0.853454\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 7.19028i 0.0110790i
\(650\) 101.198 + 343.296i 0.155689 + 0.528148i
\(651\) −203.406 −0.312451
\(652\) −111.672 111.672i −0.171276 0.171276i
\(653\) 537.675 537.675i 0.823391 0.823391i −0.163201 0.986593i \(-0.552182\pi\)
0.986593 + 0.163201i \(0.0521820\pi\)
\(654\) 27.0270i 0.0413256i
\(655\) −239.712 179.247i −0.365973 0.273660i
\(656\) 281.635 0.429321
\(657\) 118.763 + 118.763i 0.180765 + 0.180765i
\(658\) 336.489 336.489i 0.511382 0.511382i
\(659\) 783.117i 1.18834i 0.804339 + 0.594170i \(0.202520\pi\)
−0.804339 + 0.594170i \(0.797480\pi\)
\(660\) 2.37273 + 16.4406i 0.00359504 + 0.0249100i
\(661\) 752.684 1.13870 0.569352 0.822094i \(-0.307194\pi\)
0.569352 + 0.822094i \(0.307194\pi\)
\(662\) −512.969 512.969i −0.774877 0.774877i
\(663\) 312.614 312.614i 0.471514 0.471514i
\(664\) 152.960i 0.230361i
\(665\) −389.869 + 56.2665i −0.586270 + 0.0846113i
\(666\) −213.861 −0.321113
\(667\) 34.5214 + 34.5214i 0.0517562 + 0.0517562i
\(668\) 315.092 315.092i 0.471695 0.471695i
\(669\) 132.718i 0.198383i
\(670\) 216.309 289.276i 0.322849 0.431755i
\(671\) 79.7273 0.118819
\(672\) 45.6581 + 45.6581i 0.0679436 + 0.0679436i
\(673\) 652.940 652.940i 0.970193 0.970193i −0.0293759 0.999568i \(-0.509352\pi\)
0.999568 + 0.0293759i \(0.00935199\pi\)
\(674\) 101.027i 0.149892i
\(675\) −62.1349 + 114.080i −0.0920517 + 0.169007i
\(676\) −133.051 −0.196821
\(677\) −824.188 824.188i −1.21741 1.21741i −0.968535 0.248876i \(-0.919939\pi\)
−0.248876 0.968535i \(-0.580061\pi\)
\(678\) −155.152 + 155.152i −0.228837 + 0.228837i
\(679\) 844.153i 1.24323i
\(680\) 285.579 + 213.544i 0.419969 + 0.314036i
\(681\) −441.123 −0.647758
\(682\) −17.0898 17.0898i −0.0250584 0.0250584i
\(683\) −335.080 + 335.080i −0.490601 + 0.490601i −0.908495 0.417895i \(-0.862768\pi\)
0.417895 + 0.908495i \(0.362768\pi\)
\(684\) 71.7265i 0.104863i
\(685\) −186.295 1290.84i −0.271964 1.88443i
\(686\) 508.584 0.741376
\(687\) 28.6196 + 28.6196i 0.0416588 + 0.0416588i
\(688\) 129.534 129.534i 0.188276 0.188276i
\(689\) 315.483i 0.457885i
\(690\) −58.1344 + 8.39004i −0.0842527 + 0.0121595i
\(691\) −1243.37 −1.79938 −0.899690 0.436528i \(-0.856208\pi\)
−0.899690 + 0.436528i \(0.856208\pi\)
\(692\) 335.876 + 335.876i 0.485370 + 0.485370i
\(693\) 13.4072 13.4072i 0.0193465 0.0193465i
\(694\) 148.594i 0.214112i
\(695\) −54.5927 + 73.0082i −0.0785506 + 0.105048i
\(696\) 49.8706 0.0716532
\(697\) −1255.35 1255.35i −1.80108 1.80108i
\(698\) −597.945 + 597.945i −0.856654 + 0.856654i
\(699\) 239.947i 0.343272i
\(700\) 289.371 + 157.609i 0.413387 + 0.225156i
\(701\) 1034.82 1.47621 0.738103 0.674688i \(-0.235722\pi\)
0.738103 + 0.674688i \(0.235722\pi\)
\(702\) 52.6005 + 52.6005i 0.0749295 + 0.0749295i
\(703\) 426.098 426.098i 0.606113 0.606113i
\(704\) 7.67225i 0.0108981i
\(705\) 354.129 + 264.803i 0.502310 + 0.375608i
\(706\) 10.3716 0.0146907
\(707\) 38.4521 + 38.4521i 0.0543877 + 0.0543877i
\(708\) 18.3649 18.3649i 0.0259391 0.0259391i
\(709\) 1255.04i 1.77015i 0.465444 + 0.885077i \(0.345895\pi\)
−0.465444 + 0.885077i \(0.654105\pi\)
\(710\) 20.2004 + 139.968i 0.0284513 + 0.197138i
\(711\) 78.4836 0.110385
\(712\) 134.892 + 134.892i 0.189456 + 0.189456i
\(713\) 60.4301 60.4301i 0.0847548 0.0847548i
\(714\) 407.031i 0.570071i
\(715\) 48.0435 6.93371i 0.0671937 0.00969749i
\(716\) 475.105 0.663554
\(717\) −169.511 169.511i −0.236417 0.236417i
\(718\) −173.219 + 173.219i −0.241251 + 0.241251i
\(719\) 621.764i 0.864762i −0.901691 0.432381i \(-0.857674\pi\)
0.901691 0.432381i \(-0.142326\pi\)
\(720\) −35.9311 + 48.0516i −0.0499043 + 0.0667383i
\(721\) 764.990 1.06101
\(722\) −218.092 218.092i −0.302067 0.302067i
\(723\) −219.520 + 219.520i −0.303624 + 0.303624i
\(724\) 148.978i 0.205771i
\(725\) 244.110 71.9594i 0.336703 0.0992543i
\(726\) −294.135 −0.405145
\(727\) 908.910 + 908.910i 1.25022 + 1.25022i 0.955621 + 0.294600i \(0.0951863\pi\)
0.294600 + 0.955621i \(0.404814\pi\)
\(728\) 133.424 133.424i 0.183275 0.183275i
\(729\) 27.0000i 0.0370370i
\(730\) 317.041 + 237.071i 0.434302 + 0.324754i
\(731\) −1154.76 −1.57970
\(732\) 203.634 + 203.634i 0.278188 + 0.278188i
\(733\) −425.796 + 425.796i −0.580895 + 0.580895i −0.935149 0.354254i \(-0.884735\pi\)
0.354254 + 0.935149i \(0.384735\pi\)
\(734\) 269.335i 0.366941i
\(735\) 6.88971 + 47.7387i 0.00937376 + 0.0649506i
\(736\) −27.1293 −0.0368605
\(737\) −34.6408 34.6408i −0.0470025 0.0470025i
\(738\) 211.226 211.226i 0.286214 0.286214i
\(739\) 390.351i 0.528215i −0.964493 0.264108i \(-0.914923\pi\)
0.964493 0.264108i \(-0.0850774\pi\)
\(740\) −498.907 + 72.0030i −0.674199 + 0.0973014i
\(741\) −209.603 −0.282865
\(742\) −205.383 205.383i −0.276797 0.276797i
\(743\) 935.528 935.528i 1.25912 1.25912i 0.307611 0.951512i \(-0.400471\pi\)
0.951512 0.307611i \(-0.0995294\pi\)
\(744\) 87.2992i 0.117338i
\(745\) −129.260 + 172.863i −0.173503 + 0.232030i
\(746\) 238.602 0.319841
\(747\) 114.720 + 114.720i 0.153574 + 0.153574i
\(748\) 34.1981 34.1981i 0.0457194 0.0457194i
\(749\) 864.848i 1.15467i
\(750\) −106.543 + 287.052i −0.142057 + 0.382735i
\(751\) 1021.05 1.35958 0.679791 0.733406i \(-0.262071\pi\)
0.679791 + 0.733406i \(0.262071\pi\)
\(752\) 144.417 + 144.417i 0.192044 + 0.192044i
\(753\) −380.132 + 380.132i −0.504823 + 0.504823i
\(754\) 145.735i 0.193282i
\(755\) 729.657 + 545.609i 0.966433 + 0.722660i
\(756\) 68.4872 0.0905915
\(757\) 262.137 + 262.137i 0.346284 + 0.346284i 0.858724 0.512439i \(-0.171258\pi\)
−0.512439 + 0.858724i \(0.671258\pi\)
\(758\) −180.139 + 180.139i −0.237650 + 0.237650i
\(759\) 7.96631i 0.0104958i
\(760\) −24.1489 167.327i −0.0317749 0.220167i
\(761\) 441.996 0.580809 0.290405 0.956904i \(-0.406210\pi\)
0.290405 + 0.956904i \(0.406210\pi\)
\(762\) 282.111 + 282.111i 0.370224 + 0.370224i
\(763\) −51.4167 + 51.4167i −0.0673875 + 0.0673875i
\(764\) 482.038i 0.630940i
\(765\) 374.342 54.0256i 0.489336 0.0706217i
\(766\) −407.130 −0.531502
\(767\) −53.6669 53.6669i −0.0699698 0.0699698i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 657.250i 0.854682i 0.904091 + 0.427341i \(0.140550\pi\)
−0.904091 + 0.427341i \(0.859450\pi\)
\(770\) 26.7630 35.7908i 0.0347571 0.0464816i
\(771\) −537.523 −0.697176
\(772\) −314.469 314.469i −0.407343 0.407343i
\(773\) 994.081 994.081i 1.28600 1.28600i 0.348810 0.937193i \(-0.386586\pi\)
0.937193 0.348810i \(-0.113414\pi\)
\(774\) 194.301i 0.251034i
\(775\) −125.966 427.317i −0.162537 0.551377i
\(776\) 362.300 0.466882
\(777\) 406.855 + 406.855i 0.523622 + 0.523622i
\(778\) 155.622 155.622i 0.200028 0.200028i
\(779\)