Properties

Label 105.3.l.a.43.7
Level 105
Weight 3
Character 105.43
Analytic conductor 2.861
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.7
Character \(\chi\) \(=\) 105.43
Dual form 105.3.l.a.22.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.675544 - 0.675544i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.08728i q^{4} +(3.39488 - 3.67080i) q^{5} +1.65474 q^{6} +(-1.87083 + 1.87083i) q^{7} +(4.78777 + 4.78777i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(0.675544 - 0.675544i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.08728i q^{4} +(3.39488 - 3.67080i) q^{5} +1.65474 q^{6} +(-1.87083 + 1.87083i) q^{7} +(4.78777 + 4.78777i) q^{8} +3.00000i q^{9} +(-0.186396 - 4.77318i) q^{10} +7.59829 q^{11} +(-3.78113 + 3.78113i) q^{12} +(1.12200 + 1.12200i) q^{13} +2.52765i q^{14} +(8.65366 - 0.337932i) q^{15} -5.88043 q^{16} +(-3.43635 + 3.43635i) q^{17} +(2.02663 + 2.02663i) q^{18} -26.3120i q^{19} +(11.3328 + 10.4810i) q^{20} -4.58258 q^{21} +(5.13298 - 5.13298i) q^{22} +(-24.2663 - 24.2663i) q^{23} +11.7276i q^{24} +(-1.94957 - 24.9239i) q^{25} +1.51592 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-5.77577 - 5.77577i) q^{28} +22.3579i q^{29} +(5.61764 - 6.07421i) q^{30} -18.3927 q^{31} +(-23.1236 + 23.1236i) q^{32} +(9.30597 + 9.30597i) q^{33} +4.64281i q^{34} +(0.516200 + 13.2187i) q^{35} -9.26184 q^{36} +(-34.4244 + 34.4244i) q^{37} +(-17.7749 - 17.7749i) q^{38} +2.74832i q^{39} +(33.8289 - 1.32104i) q^{40} +37.4590 q^{41} +(-3.09573 + 3.09573i) q^{42} +(-55.1278 - 55.1278i) q^{43} +23.4581i q^{44} +(11.0124 + 10.1846i) q^{45} -32.7859 q^{46} +(40.8541 - 40.8541i) q^{47} +(-7.20203 - 7.20203i) q^{48} -7.00000i q^{49} +(-18.1542 - 15.5201i) q^{50} -8.41731 q^{51} +(-3.46392 + 3.46392i) q^{52} +(-9.39948 - 9.39948i) q^{53} +4.96421i q^{54} +(25.7953 - 27.8918i) q^{55} -17.9142 q^{56} +(32.2255 - 32.2255i) q^{57} +(15.1037 + 15.1037i) q^{58} +49.7795i q^{59} +(1.04329 + 26.7163i) q^{60} +88.3465 q^{61} +(-12.4251 + 12.4251i) q^{62} +(-5.61249 - 5.61249i) q^{63} +7.72024i q^{64} +(7.92767 - 0.309582i) q^{65} +12.5732 q^{66} +(-40.5887 + 40.5887i) q^{67} +(-10.6090 - 10.6090i) q^{68} -59.4401i q^{69} +(9.27851 + 8.58108i) q^{70} +136.425 q^{71} +(-14.3633 + 14.3633i) q^{72} +(5.85157 + 5.85157i) q^{73} +46.5103i q^{74} +(28.1377 - 32.9131i) q^{75} +81.2325 q^{76} +(-14.2151 + 14.2151i) q^{77} +(1.85661 + 1.85661i) q^{78} +66.4377i q^{79} +(-19.9634 + 21.5859i) q^{80} -9.00000 q^{81} +(25.3052 - 25.3052i) q^{82} +(-34.8615 - 34.8615i) q^{83} -14.1477i q^{84} +(0.948160 + 24.2802i) q^{85} -74.4824 q^{86} +(-27.3827 + 27.3827i) q^{87} +(36.3789 + 36.3789i) q^{88} -2.03390i q^{89} +(14.3195 - 0.559189i) q^{90} -4.19813 q^{91} +(74.9170 - 74.9170i) q^{92} +(-22.5264 - 22.5264i) q^{93} -55.1975i q^{94} +(-96.5860 - 89.3260i) q^{95} -56.6409 q^{96} +(-58.4649 + 58.4649i) q^{97} +(-4.72881 - 4.72881i) q^{98} +22.7949i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} - 40q^{10} - 48q^{12} + 64q^{13} - 184q^{16} + 24q^{17} + 24q^{18} + 72q^{20} + 8q^{22} + 8q^{23} - 136q^{25} - 80q^{26} + 96q^{30} + 96q^{31} + 56q^{32} - 72q^{33} + 168q^{36} + 8q^{37} + 56q^{38} + 232q^{40} + 320q^{41} - 112q^{43} - 72q^{45} + 320q^{46} + 64q^{47} + 192q^{48} - 256q^{50} - 192q^{51} + 96q^{52} - 72q^{53} - 80q^{55} - 336q^{56} + 48q^{57} - 512q^{58} - 192q^{60} - 496q^{61} - 776q^{62} + 312q^{65} - 192q^{66} - 192q^{67} + 568q^{68} + 112q^{70} - 144q^{71} + 144q^{72} + 224q^{73} + 144q^{75} + 416q^{76} + 112q^{77} - 216q^{78} - 528q^{80} - 216q^{81} + 352q^{82} - 32q^{83} + 24q^{85} + 240q^{86} + 384q^{87} + 216q^{88} - 24q^{90} + 1304q^{92} + 376q^{95} + 168q^{96} - 816q^{97} - 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.675544 0.675544i 0.337772 0.337772i −0.517756 0.855528i \(-0.673233\pi\)
0.855528 + 0.517756i \(0.173233\pi\)
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) 3.08728i 0.771820i
\(5\) 3.39488 3.67080i 0.678976 0.734160i
\(6\) 1.65474 0.275790
\(7\) −1.87083 + 1.87083i −0.267261 + 0.267261i
\(8\) 4.78777 + 4.78777i 0.598471 + 0.598471i
\(9\) 3.00000i 0.333333i
\(10\) −0.186396 4.77318i −0.0186396 0.477318i
\(11\) 7.59829 0.690754 0.345377 0.938464i \(-0.387751\pi\)
0.345377 + 0.938464i \(0.387751\pi\)
\(12\) −3.78113 + 3.78113i −0.315094 + 0.315094i
\(13\) 1.12200 + 1.12200i 0.0863074 + 0.0863074i 0.748942 0.662635i \(-0.230562\pi\)
−0.662635 + 0.748942i \(0.730562\pi\)
\(14\) 2.52765i 0.180547i
\(15\) 8.65366 0.337932i 0.576911 0.0225288i
\(16\) −5.88043 −0.367527
\(17\) −3.43635 + 3.43635i −0.202138 + 0.202138i −0.800916 0.598777i \(-0.795653\pi\)
0.598777 + 0.800916i \(0.295653\pi\)
\(18\) 2.02663 + 2.02663i 0.112591 + 0.112591i
\(19\) 26.3120i 1.38484i −0.721494 0.692420i \(-0.756544\pi\)
0.721494 0.692420i \(-0.243456\pi\)
\(20\) 11.3328 + 10.4810i 0.566640 + 0.524048i
\(21\) −4.58258 −0.218218
\(22\) 5.13298 5.13298i 0.233317 0.233317i
\(23\) −24.2663 24.2663i −1.05506 1.05506i −0.998393 0.0566642i \(-0.981954\pi\)
−0.0566642 0.998393i \(-0.518046\pi\)
\(24\) 11.7276i 0.488650i
\(25\) −1.94957 24.9239i −0.0779827 0.996955i
\(26\) 1.51592 0.0583044
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) −5.77577 5.77577i −0.206278 0.206278i
\(29\) 22.3579i 0.770962i 0.922716 + 0.385481i \(0.125965\pi\)
−0.922716 + 0.385481i \(0.874035\pi\)
\(30\) 5.61764 6.07421i 0.187255 0.202474i
\(31\) −18.3927 −0.593314 −0.296657 0.954984i \(-0.595872\pi\)
−0.296657 + 0.954984i \(0.595872\pi\)
\(32\) −23.1236 + 23.1236i −0.722611 + 0.722611i
\(33\) 9.30597 + 9.30597i 0.281999 + 0.281999i
\(34\) 4.64281i 0.136553i
\(35\) 0.516200 + 13.2187i 0.0147486 + 0.377677i
\(36\) −9.26184 −0.257273
\(37\) −34.4244 + 34.4244i −0.930388 + 0.930388i −0.997730 0.0673418i \(-0.978548\pi\)
0.0673418 + 0.997730i \(0.478548\pi\)
\(38\) −17.7749 17.7749i −0.467760 0.467760i
\(39\) 2.74832i 0.0704697i
\(40\) 33.8289 1.32104i 0.845721 0.0330261i
\(41\) 37.4590 0.913633 0.456817 0.889561i \(-0.348990\pi\)
0.456817 + 0.889561i \(0.348990\pi\)
\(42\) −3.09573 + 3.09573i −0.0737079 + 0.0737079i
\(43\) −55.1278 55.1278i −1.28204 1.28204i −0.939504 0.342537i \(-0.888714\pi\)
−0.342537 0.939504i \(-0.611286\pi\)
\(44\) 23.4581i 0.533138i
\(45\) 11.0124 + 10.1846i 0.244720 + 0.226325i
\(46\) −32.7859 −0.712738
\(47\) 40.8541 40.8541i 0.869236 0.869236i −0.123151 0.992388i \(-0.539300\pi\)
0.992388 + 0.123151i \(0.0393001\pi\)
\(48\) −7.20203 7.20203i −0.150042 0.150042i
\(49\) 7.00000i 0.142857i
\(50\) −18.1542 15.5201i −0.363084 0.310403i
\(51\) −8.41731 −0.165045
\(52\) −3.46392 + 3.46392i −0.0666138 + 0.0666138i
\(53\) −9.39948 9.39948i −0.177349 0.177349i 0.612850 0.790199i \(-0.290023\pi\)
−0.790199 + 0.612850i \(0.790023\pi\)
\(54\) 4.96421i 0.0919299i
\(55\) 25.7953 27.8918i 0.469005 0.507124i
\(56\) −17.9142 −0.319896
\(57\) 32.2255 32.2255i 0.565359 0.565359i
\(58\) 15.1037 + 15.1037i 0.260409 + 0.260409i
\(59\) 49.7795i 0.843720i 0.906661 + 0.421860i \(0.138623\pi\)
−0.906661 + 0.421860i \(0.861377\pi\)
\(60\) 1.04329 + 26.7163i 0.0173882 + 0.445271i
\(61\) 88.3465 1.44830 0.724152 0.689641i \(-0.242232\pi\)
0.724152 + 0.689641i \(0.242232\pi\)
\(62\) −12.4251 + 12.4251i −0.200405 + 0.200405i
\(63\) −5.61249 5.61249i −0.0890871 0.0890871i
\(64\) 7.72024i 0.120629i
\(65\) 7.92767 0.309582i 0.121964 0.00476280i
\(66\) 12.5732 0.190503
\(67\) −40.5887 + 40.5887i −0.605802 + 0.605802i −0.941846 0.336044i \(-0.890911\pi\)
0.336044 + 0.941846i \(0.390911\pi\)
\(68\) −10.6090 10.6090i −0.156014 0.156014i
\(69\) 59.4401i 0.861451i
\(70\) 9.27851 + 8.58108i 0.132550 + 0.122587i
\(71\) 136.425 1.92148 0.960740 0.277451i \(-0.0894897\pi\)
0.960740 + 0.277451i \(0.0894897\pi\)
\(72\) −14.3633 + 14.3633i −0.199490 + 0.199490i
\(73\) 5.85157 + 5.85157i 0.0801585 + 0.0801585i 0.746049 0.665891i \(-0.231948\pi\)
−0.665891 + 0.746049i \(0.731948\pi\)
\(74\) 46.5103i 0.628518i
\(75\) 28.1377 32.9131i 0.375169 0.438841i
\(76\) 81.2325 1.06885
\(77\) −14.2151 + 14.2151i −0.184612 + 0.184612i
\(78\) 1.85661 + 1.85661i 0.0238027 + 0.0238027i
\(79\) 66.4377i 0.840984i 0.907296 + 0.420492i \(0.138143\pi\)
−0.907296 + 0.420492i \(0.861857\pi\)
\(80\) −19.9634 + 21.5859i −0.249542 + 0.269824i
\(81\) −9.00000 −0.111111
\(82\) 25.3052 25.3052i 0.308600 0.308600i
\(83\) −34.8615 34.8615i −0.420018 0.420018i 0.465192 0.885210i \(-0.345985\pi\)
−0.885210 + 0.465192i \(0.845985\pi\)
\(84\) 14.1477i 0.168425i
\(85\) 0.948160 + 24.2802i 0.0111548 + 0.285649i
\(86\) −74.4824 −0.866075
\(87\) −27.3827 + 27.3827i −0.314744 + 0.314744i
\(88\) 36.3789 + 36.3789i 0.413396 + 0.413396i
\(89\) 2.03390i 0.0228528i −0.999935 0.0114264i \(-0.996363\pi\)
0.999935 0.0114264i \(-0.00363721\pi\)
\(90\) 14.3195 0.559189i 0.159106 0.00621321i
\(91\) −4.19813 −0.0461332
\(92\) 74.9170 74.9170i 0.814315 0.814315i
\(93\) −22.5264 22.5264i −0.242220 0.242220i
\(94\) 55.1975i 0.587207i
\(95\) −96.5860 89.3260i −1.01670 0.940274i
\(96\) −56.6409 −0.590010
\(97\) −58.4649 + 58.4649i −0.602731 + 0.602731i −0.941036 0.338305i \(-0.890146\pi\)
0.338305 + 0.941036i \(0.390146\pi\)
\(98\) −4.72881 4.72881i −0.0482531 0.0482531i
\(99\) 22.7949i 0.230251i
\(100\) 76.9470 6.01886i 0.769470 0.0601886i
\(101\) 72.4773 0.717597 0.358798 0.933415i \(-0.383187\pi\)
0.358798 + 0.933415i \(0.383187\pi\)
\(102\) −5.68626 + 5.68626i −0.0557476 + 0.0557476i
\(103\) 96.7717 + 96.7717i 0.939531 + 0.939531i 0.998273 0.0587421i \(-0.0187090\pi\)
−0.0587421 + 0.998273i \(0.518709\pi\)
\(104\) 10.7437i 0.103305i
\(105\) −15.5573 + 16.8217i −0.148165 + 0.160207i
\(106\) −12.6995 −0.119807
\(107\) 12.4803 12.4803i 0.116638 0.116638i −0.646379 0.763017i \(-0.723717\pi\)
0.763017 + 0.646379i \(0.223717\pi\)
\(108\) −11.3434 11.3434i −0.105031 0.105031i
\(109\) 87.3675i 0.801537i 0.916179 + 0.400769i \(0.131257\pi\)
−0.916179 + 0.400769i \(0.868743\pi\)
\(110\) −1.41629 36.2680i −0.0128754 0.329709i
\(111\) −84.3221 −0.759659
\(112\) 11.0013 11.0013i 0.0982257 0.0982257i
\(113\) 21.7147 + 21.7147i 0.192165 + 0.192165i 0.796631 0.604466i \(-0.206613\pi\)
−0.604466 + 0.796631i \(0.706613\pi\)
\(114\) 43.5394i 0.381925i
\(115\) −171.458 + 6.69558i −1.49094 + 0.0582224i
\(116\) −69.0251 −0.595044
\(117\) −3.36599 + 3.36599i −0.0287691 + 0.0287691i
\(118\) 33.6282 + 33.6282i 0.284985 + 0.284985i
\(119\) 12.8576i 0.108047i
\(120\) 43.0497 + 39.8138i 0.358747 + 0.331781i
\(121\) −63.2659 −0.522859
\(122\) 59.6819 59.6819i 0.489196 0.489196i
\(123\) 45.8777 + 45.8777i 0.372989 + 0.372989i
\(124\) 56.7836i 0.457932i
\(125\) −98.1091 77.4571i −0.784873 0.619657i
\(126\) −7.58296 −0.0601822
\(127\) −82.7648 + 82.7648i −0.651692 + 0.651692i −0.953400 0.301709i \(-0.902443\pi\)
0.301709 + 0.953400i \(0.402443\pi\)
\(128\) −87.2789 87.2789i −0.681866 0.681866i
\(129\) 135.035i 1.04678i
\(130\) 5.14635 5.56462i 0.0395873 0.0428048i
\(131\) −190.287 −1.45257 −0.726285 0.687394i \(-0.758755\pi\)
−0.726285 + 0.687394i \(0.758755\pi\)
\(132\) −28.7301 + 28.7301i −0.217653 + 0.217653i
\(133\) 49.2252 + 49.2252i 0.370114 + 0.370114i
\(134\) 54.8390i 0.409246i
\(135\) 1.01380 + 25.9610i 0.00750961 + 0.192304i
\(136\) −32.9049 −0.241948
\(137\) 122.593 122.593i 0.894841 0.894841i −0.100133 0.994974i \(-0.531927\pi\)
0.994974 + 0.100133i \(0.0319268\pi\)
\(138\) −40.1544 40.1544i −0.290974 0.290974i
\(139\) 149.073i 1.07247i −0.844070 0.536233i \(-0.819847\pi\)
0.844070 0.536233i \(-0.180153\pi\)
\(140\) −40.8098 + 1.59366i −0.291498 + 0.0113833i
\(141\) 100.072 0.709729
\(142\) 92.1611 92.1611i 0.649022 0.649022i
\(143\) 8.52526 + 8.52526i 0.0596172 + 0.0596172i
\(144\) 17.6413i 0.122509i
\(145\) 82.0714 + 75.9024i 0.566010 + 0.523465i
\(146\) 7.90599 0.0541506
\(147\) 8.57321 8.57321i 0.0583212 0.0583212i
\(148\) −106.278 106.278i −0.718093 0.718093i
\(149\) 157.639i 1.05798i 0.848628 + 0.528990i \(0.177429\pi\)
−0.848628 + 0.528990i \(0.822571\pi\)
\(150\) −3.22602 41.2425i −0.0215068 0.274950i
\(151\) −234.309 −1.55172 −0.775858 0.630908i \(-0.782682\pi\)
−0.775858 + 0.630908i \(0.782682\pi\)
\(152\) 125.976 125.976i 0.828787 0.828787i
\(153\) −10.3091 10.3091i −0.0673794 0.0673794i
\(154\) 19.2059i 0.124713i
\(155\) −62.4412 + 67.5161i −0.402846 + 0.435588i
\(156\) −8.48483 −0.0543899
\(157\) −75.2106 + 75.2106i −0.479048 + 0.479048i −0.904827 0.425779i \(-0.860000\pi\)
0.425779 + 0.904827i \(0.360000\pi\)
\(158\) 44.8816 + 44.8816i 0.284061 + 0.284061i
\(159\) 23.0239i 0.144805i
\(160\) 6.38027 + 163.384i 0.0398767 + 1.02115i
\(161\) 90.7963 0.563952
\(162\) −6.07989 + 6.07989i −0.0375302 + 0.0375302i
\(163\) 124.557 + 124.557i 0.764153 + 0.764153i 0.977070 0.212918i \(-0.0682966\pi\)
−0.212918 + 0.977070i \(0.568297\pi\)
\(164\) 115.646i 0.705161i
\(165\) 65.7530 2.56771i 0.398503 0.0155619i
\(166\) −47.1010 −0.283741
\(167\) −136.411 + 136.411i −0.816834 + 0.816834i −0.985648 0.168814i \(-0.946006\pi\)
0.168814 + 0.985648i \(0.446006\pi\)
\(168\) −21.9403 21.9403i −0.130597 0.130597i
\(169\) 166.482i 0.985102i
\(170\) 17.0428 + 15.7618i 0.100252 + 0.0927164i
\(171\) 78.9359 0.461614
\(172\) 170.195 170.195i 0.989505 0.989505i
\(173\) 121.020 + 121.020i 0.699538 + 0.699538i 0.964311 0.264773i \(-0.0852969\pi\)
−0.264773 + 0.964311i \(0.585297\pi\)
\(174\) 36.9965i 0.212623i
\(175\) 50.2756 + 42.9810i 0.287289 + 0.245606i
\(176\) −44.6812 −0.253871
\(177\) −60.9672 + 60.9672i −0.344447 + 0.344447i
\(178\) −1.37399 1.37399i −0.00771902 0.00771902i
\(179\) 57.2144i 0.319634i −0.987147 0.159817i \(-0.948910\pi\)
0.987147 0.159817i \(-0.0510904\pi\)
\(180\) −31.4429 + 33.9984i −0.174683 + 0.188880i
\(181\) 294.230 1.62558 0.812791 0.582555i \(-0.197947\pi\)
0.812791 + 0.582555i \(0.197947\pi\)
\(182\) −2.83602 + 2.83602i −0.0155825 + 0.0155825i
\(183\) 108.202 + 108.202i 0.591267 + 0.591267i
\(184\) 232.363i 1.26284i
\(185\) 9.49839 + 243.232i 0.0513427 + 1.31477i
\(186\) −30.4352 −0.163630
\(187\) −26.1104 + 26.1104i −0.139628 + 0.139628i
\(188\) 126.128 + 126.128i 0.670894 + 0.670894i
\(189\) 13.7477i 0.0727393i
\(190\) −125.592 + 4.90446i −0.661009 + 0.0258129i
\(191\) 246.643 1.29133 0.645663 0.763622i \(-0.276581\pi\)
0.645663 + 0.763622i \(0.276581\pi\)
\(192\) −9.45532 + 9.45532i −0.0492465 + 0.0492465i
\(193\) 100.720 + 100.720i 0.521867 + 0.521867i 0.918135 0.396268i \(-0.129695\pi\)
−0.396268 + 0.918135i \(0.629695\pi\)
\(194\) 78.9913i 0.407171i
\(195\) 10.0885 + 9.33021i 0.0517361 + 0.0478472i
\(196\) 21.6110 0.110260
\(197\) −14.9915 + 14.9915i −0.0760991 + 0.0760991i −0.744132 0.668033i \(-0.767137\pi\)
0.668033 + 0.744132i \(0.267137\pi\)
\(198\) 15.3989 + 15.3989i 0.0777724 + 0.0777724i
\(199\) 287.332i 1.44388i −0.691957 0.721939i \(-0.743251\pi\)
0.691957 0.721939i \(-0.256749\pi\)
\(200\) 109.996 128.664i 0.549978 0.643319i
\(201\) −99.4217 −0.494635
\(202\) 48.9616 48.9616i 0.242384 0.242384i
\(203\) −41.8278 41.8278i −0.206048 0.206048i
\(204\) 25.9866i 0.127385i
\(205\) 127.169 137.504i 0.620335 0.670753i
\(206\) 130.747 0.634694
\(207\) 72.7990 72.7990i 0.351686 0.351686i
\(208\) −6.59782 6.59782i −0.0317203 0.0317203i
\(209\) 199.926i 0.956584i
\(210\) 0.854176 + 21.8734i 0.00406750 + 0.104159i
\(211\) −399.559 −1.89365 −0.946823 0.321755i \(-0.895727\pi\)
−0.946823 + 0.321755i \(0.895727\pi\)
\(212\) 29.0188 29.0188i 0.136881 0.136881i
\(213\) 167.086 + 167.086i 0.784441 + 0.784441i
\(214\) 16.8619i 0.0787940i
\(215\) −389.515 + 15.2109i −1.81170 + 0.0707483i
\(216\) −35.1828 −0.162883
\(217\) 34.4097 34.4097i 0.158570 0.158570i
\(218\) 59.0206 + 59.0206i 0.270737 + 0.270737i
\(219\) 14.3334i 0.0654492i
\(220\) 86.1099 + 79.6373i 0.391409 + 0.361988i
\(221\) −7.71115 −0.0348921
\(222\) −56.9633 + 56.9633i −0.256591 + 0.256591i
\(223\) −210.325 210.325i −0.943162 0.943162i 0.0553078 0.998469i \(-0.482386\pi\)
−0.998469 + 0.0553078i \(0.982386\pi\)
\(224\) 86.5204i 0.386252i
\(225\) 74.7716 5.84870i 0.332318 0.0259942i
\(226\) 29.3384 0.129816
\(227\) 130.724 130.724i 0.575877 0.575877i −0.357888 0.933765i \(-0.616503\pi\)
0.933765 + 0.357888i \(0.116503\pi\)
\(228\) 99.4891 + 99.4891i 0.436356 + 0.436356i
\(229\) 256.942i 1.12202i 0.827809 + 0.561010i \(0.189587\pi\)
−0.827809 + 0.561010i \(0.810413\pi\)
\(230\) −111.304 + 120.351i −0.483932 + 0.523264i
\(231\) −34.8198 −0.150735
\(232\) −107.044 + 107.044i −0.461399 + 0.461399i
\(233\) −60.6918 60.6918i −0.260480 0.260480i 0.564769 0.825249i \(-0.308965\pi\)
−0.825249 + 0.564769i \(0.808965\pi\)
\(234\) 4.54775i 0.0194348i
\(235\) −11.2725 288.662i −0.0479680 1.22835i
\(236\) −153.683 −0.651200
\(237\) −81.3693 + 81.3693i −0.343330 + 0.343330i
\(238\) −8.68591 8.68591i −0.0364954 0.0364954i
\(239\) 66.9426i 0.280095i 0.990145 + 0.140047i \(0.0447255\pi\)
−0.990145 + 0.140047i \(0.955275\pi\)
\(240\) −50.8872 + 1.98719i −0.212030 + 0.00827995i
\(241\) 82.5830 0.342668 0.171334 0.985213i \(-0.445192\pi\)
0.171334 + 0.985213i \(0.445192\pi\)
\(242\) −42.7389 + 42.7389i −0.176607 + 0.176607i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 272.750i 1.11783i
\(245\) −25.6956 23.7642i −0.104880 0.0969966i
\(246\) 61.9848 0.251971
\(247\) 29.5219 29.5219i 0.119522 0.119522i
\(248\) −88.0602 88.0602i −0.355081 0.355081i
\(249\) 85.3929i 0.342943i
\(250\) −118.603 + 13.9514i −0.474411 + 0.0558054i
\(251\) 197.943 0.788619 0.394309 0.918978i \(-0.370984\pi\)
0.394309 + 0.918978i \(0.370984\pi\)
\(252\) 17.3273 17.3273i 0.0687592 0.0687592i
\(253\) −184.383 184.383i −0.728785 0.728785i
\(254\) 111.823i 0.440246i
\(255\) −28.5758 + 30.8983i −0.112062 + 0.121170i
\(256\) −148.802 −0.581259
\(257\) −206.394 + 206.394i −0.803091 + 0.803091i −0.983577 0.180487i \(-0.942233\pi\)
0.180487 + 0.983577i \(0.442233\pi\)
\(258\) −91.2220 91.2220i −0.353574 0.353574i
\(259\) 128.804i 0.497313i
\(260\) 0.955766 + 24.4749i 0.00367602 + 0.0941344i
\(261\) −67.0737 −0.256987
\(262\) −128.547 + 128.547i −0.490637 + 0.490637i
\(263\) 235.719 + 235.719i 0.896270 + 0.896270i 0.995104 0.0988340i \(-0.0315113\pi\)
−0.0988340 + 0.995104i \(0.531511\pi\)
\(264\) 89.1097i 0.337537i
\(265\) −66.4137 + 2.59351i −0.250618 + 0.00978683i
\(266\) 66.5076 0.250028
\(267\) 2.49100 2.49100i 0.00932960 0.00932960i
\(268\) −125.309 125.309i −0.467570 0.467570i
\(269\) 379.956i 1.41248i −0.707974 0.706238i \(-0.750391\pi\)
0.707974 0.706238i \(-0.249609\pi\)
\(270\) 18.2226 + 16.8529i 0.0674913 + 0.0624182i
\(271\) −239.134 −0.882414 −0.441207 0.897405i \(-0.645450\pi\)
−0.441207 + 0.897405i \(0.645450\pi\)
\(272\) 20.2072 20.2072i 0.0742913 0.0742913i
\(273\) −5.14163 5.14163i −0.0188338 0.0188338i
\(274\) 165.634i 0.604504i
\(275\) −14.8134 189.379i −0.0538668 0.688650i
\(276\) 183.508 0.664885
\(277\) 118.114 118.114i 0.426403 0.426403i −0.460998 0.887401i \(-0.652509\pi\)
0.887401 + 0.460998i \(0.152509\pi\)
\(278\) −100.705 100.705i −0.362249 0.362249i
\(279\) 55.1782i 0.197771i
\(280\) −60.8165 + 65.7594i −0.217202 + 0.234855i
\(281\) 337.248 1.20017 0.600086 0.799936i \(-0.295133\pi\)
0.600086 + 0.799936i \(0.295133\pi\)
\(282\) 67.6028 67.6028i 0.239726 0.239726i
\(283\) −91.9392 91.9392i −0.324873 0.324873i 0.525760 0.850633i \(-0.323781\pi\)
−0.850633 + 0.525760i \(0.823781\pi\)
\(284\) 421.182i 1.48304i
\(285\) −8.89167 227.695i −0.0311988 0.798929i
\(286\) 11.5184 0.0402740
\(287\) −70.0793 + 70.0793i −0.244179 + 0.244179i
\(288\) −69.3707 69.3707i −0.240870 0.240870i
\(289\) 265.383i 0.918280i
\(290\) 106.718 4.16743i 0.367994 0.0143705i
\(291\) −143.209 −0.492128
\(292\) −18.0654 + 18.0654i −0.0618680 + 0.0618680i
\(293\) −348.854 348.854i −1.19063 1.19063i −0.976891 0.213736i \(-0.931437\pi\)
−0.213736 0.976891i \(-0.568563\pi\)
\(294\) 11.5832i 0.0393985i
\(295\) 182.731 + 168.995i 0.619426 + 0.572866i
\(296\) −329.632 −1.11362
\(297\) −27.9179 + 27.9179i −0.0939997 + 0.0939997i
\(298\) 106.492 + 106.492i 0.357356 + 0.357356i
\(299\) 54.4534i 0.182119i
\(300\) 101.612 + 86.8689i 0.338707 + 0.289563i
\(301\) 206.269 0.685280
\(302\) −158.286 + 158.286i −0.524126 + 0.524126i
\(303\) 88.7662 + 88.7662i 0.292958 + 0.292958i
\(304\) 154.726i 0.508966i
\(305\) 299.926 324.302i 0.983363 1.06329i
\(306\) −13.9284 −0.0455178
\(307\) 306.607 306.607i 0.998720 0.998720i −0.00127914 0.999999i \(-0.500407\pi\)
0.999999 + 0.00127914i \(0.000407163\pi\)
\(308\) −43.8860 43.8860i −0.142487 0.142487i
\(309\) 237.041i 0.767124i
\(310\) 3.42834 + 87.7918i 0.0110592 + 0.283199i
\(311\) −74.8228 −0.240588 −0.120294 0.992738i \(-0.538384\pi\)
−0.120294 + 0.992738i \(0.538384\pi\)
\(312\) −13.1583 + 13.1583i −0.0421741 + 0.0421741i
\(313\) 101.601 + 101.601i 0.324605 + 0.324605i 0.850531 0.525925i \(-0.176281\pi\)
−0.525925 + 0.850531i \(0.676281\pi\)
\(314\) 101.616i 0.323618i
\(315\) −39.6560 + 1.54860i −0.125892 + 0.00491619i
\(316\) −205.112 −0.649089
\(317\) 124.097 124.097i 0.391475 0.391475i −0.483738 0.875213i \(-0.660721\pi\)
0.875213 + 0.483738i \(0.160721\pi\)
\(318\) −15.5537 15.5537i −0.0489109 0.0489109i
\(319\) 169.882i 0.532545i
\(320\) 28.3395 + 26.2093i 0.0885608 + 0.0819040i
\(321\) 30.5703 0.0952345
\(322\) 61.3369 61.3369i 0.190487 0.190487i
\(323\) 90.4172 + 90.4172i 0.279929 + 0.279929i
\(324\) 27.7855i 0.0857578i
\(325\) 25.7771 30.1519i 0.0793141 0.0927751i
\(326\) 168.287 0.516219
\(327\) −107.003 + 107.003i −0.327226 + 0.327226i
\(328\) 179.345 + 179.345i 0.546783 + 0.546783i
\(329\) 152.862i 0.464626i
\(330\) 42.6844 46.1536i 0.129347 0.139860i
\(331\) 397.089 1.19966 0.599832 0.800126i \(-0.295234\pi\)
0.599832 + 0.800126i \(0.295234\pi\)
\(332\) 107.627 107.627i 0.324179 0.324179i
\(333\) −103.273 103.273i −0.310129 0.310129i
\(334\) 184.304i 0.551807i
\(335\) 11.1993 + 286.787i 0.0334307 + 0.856081i
\(336\) 26.9475 0.0802009
\(337\) −185.463 + 185.463i −0.550334 + 0.550334i −0.926537 0.376203i \(-0.877230\pi\)
0.376203 + 0.926537i \(0.377230\pi\)
\(338\) −112.466 112.466i −0.332740 0.332740i
\(339\) 53.1898i 0.156902i
\(340\) −74.9597 + 2.92724i −0.220470 + 0.00860952i
\(341\) −139.753 −0.409834
\(342\) 53.3247 53.3247i 0.155920 0.155920i
\(343\) 13.0958 + 13.0958i 0.0381802 + 0.0381802i
\(344\) 527.878i 1.53453i
\(345\) −218.193 201.792i −0.632443 0.584905i
\(346\) 163.509 0.472569
\(347\) −182.221 + 182.221i −0.525133 + 0.525133i −0.919117 0.393984i \(-0.871097\pi\)
0.393984 + 0.919117i \(0.371097\pi\)
\(348\) −84.5382 84.5382i −0.242926 0.242926i
\(349\) 416.140i 1.19238i 0.802844 + 0.596189i \(0.203319\pi\)
−0.802844 + 0.596189i \(0.796681\pi\)
\(350\) 62.9989 4.92783i 0.179997 0.0140795i
\(351\) −8.24495 −0.0234899
\(352\) −175.700 + 175.700i −0.499147 + 0.499147i
\(353\) −402.531 402.531i −1.14031 1.14031i −0.988393 0.151921i \(-0.951454\pi\)
−0.151921 0.988393i \(-0.548546\pi\)
\(354\) 82.3720i 0.232689i
\(355\) 463.147 500.789i 1.30464 1.41067i
\(356\) 6.27921 0.0176382
\(357\) 15.7473 15.7473i 0.0441102 0.0441102i
\(358\) −38.6508 38.6508i −0.107963 0.107963i
\(359\) 120.174i 0.334747i 0.985894 + 0.167373i \(0.0535285\pi\)
−0.985894 + 0.167373i \(0.946471\pi\)
\(360\) 3.96313 + 101.487i 0.0110087 + 0.281907i
\(361\) −331.320 −0.917785
\(362\) 198.766 198.766i 0.549076 0.549076i
\(363\) −77.4846 77.4846i −0.213456 0.213456i
\(364\) 12.9608i 0.0356066i
\(365\) 41.3453 1.61457i 0.113275 0.00442348i
\(366\) 146.190 0.399427
\(367\) 162.325 162.325i 0.442301 0.442301i −0.450483 0.892785i \(-0.648748\pi\)
0.892785 + 0.450483i \(0.148748\pi\)
\(368\) 142.696 + 142.696i 0.387762 + 0.387762i
\(369\) 112.377i 0.304544i
\(370\) 170.730 + 157.897i 0.461433 + 0.426749i
\(371\) 35.1696 0.0947968
\(372\) 69.5454 69.5454i 0.186950 0.186950i
\(373\) 306.523 + 306.523i 0.821776 + 0.821776i 0.986363 0.164586i \(-0.0526289\pi\)
−0.164586 + 0.986363i \(0.552629\pi\)
\(374\) 35.2774i 0.0943247i
\(375\) −25.2935 215.024i −0.0674493 0.573397i
\(376\) 391.200 1.04043
\(377\) −25.0855 + 25.0855i −0.0665398 + 0.0665398i
\(378\) −9.28719 9.28719i −0.0245693 0.0245693i
\(379\) 126.143i 0.332830i 0.986056 + 0.166415i \(0.0532192\pi\)
−0.986056 + 0.166415i \(0.946781\pi\)
\(380\) 275.775 298.188i 0.725723 0.784706i
\(381\) −202.732 −0.532104
\(382\) 166.618 166.618i 0.436174 0.436174i
\(383\) 349.571 + 349.571i 0.912717 + 0.912717i 0.996485 0.0837685i \(-0.0266956\pi\)
−0.0837685 + 0.996485i \(0.526696\pi\)
\(384\) 213.789i 0.556742i
\(385\) 3.92224 + 100.439i 0.0101876 + 0.260882i
\(386\) 136.082 0.352544
\(387\) 165.383 165.383i 0.427347 0.427347i
\(388\) −180.498 180.498i −0.465200 0.465200i
\(389\) 165.348i 0.425060i 0.977155 + 0.212530i \(0.0681704\pi\)
−0.977155 + 0.212530i \(0.931830\pi\)
\(390\) 13.1182 0.512277i 0.0336364 0.00131353i
\(391\) 166.775 0.426535
\(392\) 33.5144 33.5144i 0.0854959 0.0854959i
\(393\) −233.053 233.053i −0.593009 0.593009i
\(394\) 20.2549i 0.0514083i
\(395\) 243.880 + 225.548i 0.617417 + 0.571008i
\(396\) −70.3742 −0.177713
\(397\) −42.7811 + 42.7811i −0.107761 + 0.107761i −0.758931 0.651171i \(-0.774278\pi\)
0.651171 + 0.758931i \(0.274278\pi\)
\(398\) −194.105 194.105i −0.487701 0.487701i
\(399\) 120.577i 0.302197i
\(400\) 11.4643 + 146.563i 0.0286607 + 0.366408i
\(401\) 92.5492 0.230796 0.115398 0.993319i \(-0.463186\pi\)
0.115398 + 0.993319i \(0.463186\pi\)
\(402\) −67.1637 + 67.1637i −0.167074 + 0.167074i
\(403\) −20.6366 20.6366i −0.0512074 0.0512074i
\(404\) 223.758i 0.553856i
\(405\) −30.5539 + 33.0372i −0.0754418 + 0.0815734i
\(406\) −56.5130 −0.139195
\(407\) −261.566 + 261.566i −0.642669 + 0.642669i
\(408\) −40.3001 40.3001i −0.0987748 0.0987748i
\(409\) 71.7158i 0.175344i 0.996149 + 0.0876721i \(0.0279428\pi\)
−0.996149 + 0.0876721i \(0.972057\pi\)
\(410\) −6.98222 178.798i −0.0170298 0.436094i
\(411\) 300.291 0.730635
\(412\) −298.761 + 298.761i −0.725149 + 0.725149i
\(413\) −93.1289 93.1289i −0.225494 0.225494i
\(414\) 98.3578i 0.237579i
\(415\) −246.320 + 9.61901i −0.593543 + 0.0231783i
\(416\) −51.8891 −0.124733
\(417\) 182.576 182.576i 0.437832 0.437832i
\(418\) −135.059 135.059i −0.323107 0.323107i
\(419\) 472.026i 1.12655i −0.826268 0.563277i \(-0.809540\pi\)
0.826268 0.563277i \(-0.190460\pi\)
\(420\) −51.9334 48.0298i −0.123651 0.114357i
\(421\) 746.988 1.77432 0.887159 0.461464i \(-0.152676\pi\)
0.887159 + 0.461464i \(0.152676\pi\)
\(422\) −269.920 + 269.920i −0.639620 + 0.639620i
\(423\) 122.562 + 122.562i 0.289745 + 0.289745i
\(424\) 90.0051i 0.212276i
\(425\) 92.3466 + 78.9478i 0.217286 + 0.185759i
\(426\) 225.748 0.529924
\(427\) −165.281 + 165.281i −0.387075 + 0.387075i
\(428\) 38.5301 + 38.5301i 0.0900235 + 0.0900235i
\(429\) 20.8825i 0.0486772i
\(430\) −252.859 + 273.410i −0.588044 + 0.635838i
\(431\) −754.426 −1.75041 −0.875204 0.483754i \(-0.839273\pi\)
−0.875204 + 0.483754i \(0.839273\pi\)
\(432\) 21.6061 21.6061i 0.0500141 0.0500141i
\(433\) −344.305 344.305i −0.795162 0.795162i 0.187166 0.982328i \(-0.440070\pi\)
−0.982328 + 0.187166i \(0.940070\pi\)
\(434\) 46.4905i 0.107121i
\(435\) 7.55546 + 193.478i 0.0173689 + 0.444776i
\(436\) −269.728 −0.618643
\(437\) −638.495 + 638.495i −1.46109 + 1.46109i
\(438\) 9.68282 + 9.68282i 0.0221069 + 0.0221069i
\(439\) 49.1546i 0.111970i 0.998432 + 0.0559848i \(0.0178298\pi\)
−0.998432 + 0.0559848i \(0.982170\pi\)
\(440\) 257.042 10.0377i 0.584185 0.0228129i
\(441\) 21.0000 0.0476190
\(442\) −5.20922 + 5.20922i −0.0117856 + 0.0117856i
\(443\) 117.289 + 117.289i 0.264762 + 0.264762i 0.826985 0.562224i \(-0.190054\pi\)
−0.562224 + 0.826985i \(0.690054\pi\)
\(444\) 260.326i 0.586320i
\(445\) −7.46603 6.90484i −0.0167776 0.0155165i
\(446\) −284.168 −0.637147
\(447\) −193.068 + 193.068i −0.431918 + 0.431918i
\(448\) −14.4432 14.4432i −0.0322394 0.0322394i
\(449\) 296.976i 0.661416i −0.943733 0.330708i \(-0.892712\pi\)
0.943733 0.330708i \(-0.107288\pi\)
\(450\) 46.5604 54.4625i 0.103468 0.121028i
\(451\) 284.624 0.631096
\(452\) −67.0393 + 67.0393i −0.148317 + 0.148317i
\(453\) −286.969 286.969i −0.633485 0.633485i
\(454\) 176.620i 0.389030i
\(455\) −14.2521 + 15.4105i −0.0313234 + 0.0338692i
\(456\) 308.576 0.676702
\(457\) −257.425 + 257.425i −0.563293 + 0.563293i −0.930241 0.366948i \(-0.880403\pi\)
0.366948 + 0.930241i \(0.380403\pi\)
\(458\) 173.576 + 173.576i 0.378987 + 0.378987i
\(459\) 25.2519i 0.0550151i
\(460\) −20.6711 529.339i −0.0449372 1.15074i
\(461\) −357.600 −0.775704 −0.387852 0.921722i \(-0.626783\pi\)
−0.387852 + 0.921722i \(0.626783\pi\)
\(462\) −23.5223 + 23.5223i −0.0509140 + 0.0509140i
\(463\) 78.7851 + 78.7851i 0.170162 + 0.170162i 0.787051 0.616888i \(-0.211607\pi\)
−0.616888 + 0.787051i \(0.711607\pi\)
\(464\) 131.474i 0.283349i
\(465\) −159.165 + 6.21550i −0.342289 + 0.0133667i
\(466\) −81.9999 −0.175965
\(467\) 654.767 654.767i 1.40207 1.40207i 0.608570 0.793500i \(-0.291743\pi\)
0.793500 0.608570i \(-0.208257\pi\)
\(468\) −10.3918 10.3918i −0.0222046 0.0222046i
\(469\) 151.869i 0.323815i
\(470\) −202.619 187.389i −0.431104 0.398700i
\(471\) −184.228 −0.391141
\(472\) −238.333 + 238.333i −0.504942 + 0.504942i
\(473\) −418.877 418.877i −0.885575 0.885575i
\(474\) 109.937i 0.231935i
\(475\) −655.796 + 51.2970i −1.38062 + 0.107994i
\(476\) 39.6952 0.0833932
\(477\) 28.1984 28.1984i 0.0591162 0.0591162i
\(478\) 45.2227 + 45.2227i 0.0946081 + 0.0946081i
\(479\) 262.707i 0.548449i 0.961666 + 0.274225i \(0.0884212\pi\)
−0.961666 + 0.274225i \(0.911579\pi\)
\(480\) −192.289 + 207.918i −0.400603 + 0.433162i
\(481\) −77.2480 −0.160599
\(482\) 55.7884 55.7884i 0.115744 0.115744i
\(483\) 111.202 + 111.202i 0.230232 + 0.230232i
\(484\) 195.320i 0.403553i
\(485\) 16.1317 + 413.095i 0.0332612 + 0.851742i
\(486\) −14.8926 −0.0306433
\(487\) −42.8848 + 42.8848i −0.0880591 + 0.0880591i −0.749764 0.661705i \(-0.769833\pi\)
0.661705 + 0.749764i \(0.269833\pi\)
\(488\) 422.983 + 422.983i 0.866768 + 0.866768i
\(489\) 305.101i 0.623928i
\(490\) −33.4122 + 1.30478i −0.0681883 + 0.00266281i
\(491\) −58.5988 −0.119346 −0.0596730 0.998218i \(-0.519006\pi\)
−0.0596730 + 0.998218i \(0.519006\pi\)
\(492\) −141.637 + 141.637i −0.287881 + 0.287881i
\(493\) −76.8296 76.8296i −0.155841 0.155841i
\(494\) 39.8867i 0.0807424i
\(495\) 83.6755 + 77.3859i 0.169041 + 0.156335i
\(496\) 108.157 0.218059
\(497\) −255.228 + 255.228i −0.513537 + 0.513537i
\(498\) −57.6867 57.6867i −0.115837 0.115837i
\(499\) 421.048i 0.843784i −0.906646 0.421892i \(-0.861366\pi\)
0.906646 0.421892i \(-0.138634\pi\)
\(500\) 239.132 302.890i 0.478264 0.605781i
\(501\) −334.138 −0.666942
\(502\) 133.719 133.719i 0.266373 0.266373i
\(503\) 357.650 + 357.650i 0.711034 + 0.711034i 0.966751 0.255718i \(-0.0823118\pi\)
−0.255718 + 0.966751i \(0.582312\pi\)
\(504\) 53.7426i 0.106632i
\(505\) 246.052 266.050i 0.487231 0.526831i
\(506\) −249.117 −0.492326
\(507\) 203.898 203.898i 0.402166 0.402166i
\(508\) −255.518 255.518i −0.502989 0.502989i
\(509\) 934.911i 1.83676i −0.395700 0.918380i \(-0.629498\pi\)
0.395700 0.918380i \(-0.370502\pi\)
\(510\) 1.56896 + 40.1773i 0.00307638 + 0.0787790i
\(511\) −21.8946 −0.0428465
\(512\) 248.593 248.593i 0.485533 0.485533i
\(513\) 96.6764 + 96.6764i 0.188453 + 0.188453i
\(514\) 278.857i 0.542523i
\(515\) 683.758 26.7013i 1.32769 0.0518472i
\(516\) 416.891 0.807928
\(517\) 310.421 310.421i 0.600428 0.600428i
\(518\) −87.0129 87.0129i −0.167978 0.167978i
\(519\) 296.438i 0.571171i
\(520\) 39.4381 + 36.4736i 0.0758424 + 0.0701416i
\(521\) −73.1865 −0.140473 −0.0702366 0.997530i \(-0.522375\pi\)
−0.0702366 + 0.997530i \(0.522375\pi\)
\(522\) −45.3112 + 45.3112i −0.0868031 + 0.0868031i
\(523\) 53.6581 + 53.6581i 0.102597 + 0.102597i 0.756542 0.653945i \(-0.226887\pi\)
−0.653945 + 0.756542i \(0.726887\pi\)
\(524\) 587.469i 1.12112i
\(525\) 8.93404 + 114.216i 0.0170172 + 0.217553i
\(526\) 318.477 0.605470
\(527\) 63.2039 63.2039i 0.119932 0.119932i
\(528\) −54.7231 54.7231i −0.103642 0.103642i
\(529\) 648.709i 1.22629i
\(530\) −43.1134 + 46.6174i −0.0813460 + 0.0879574i
\(531\) −149.338 −0.281240
\(532\) −151.972 + 151.972i −0.285662 + 0.285662i
\(533\) 42.0288 + 42.0288i 0.0788533 + 0.0788533i
\(534\) 3.36556i 0.00630256i
\(535\) −3.44356 88.1816i −0.00643656 0.164825i
\(536\) −388.659 −0.725110
\(537\) 70.0731 70.0731i 0.130490 0.130490i
\(538\) −256.677 256.677i −0.477095 0.477095i
\(539\) 53.1880i 0.0986791i
\(540\) −80.1488 + 3.12988i −0.148424 + 0.00579607i
\(541\) −1071.71 −1.98098 −0.990490 0.137581i \(-0.956067\pi\)
−0.990490 + 0.137581i \(0.956067\pi\)
\(542\) −161.546 + 161.546i −0.298055 + 0.298055i
\(543\) 360.357 + 360.357i 0.663641 + 0.663641i
\(544\) 158.921i 0.292135i
\(545\) 320.709 + 296.602i 0.588457 + 0.544225i
\(546\) −6.94680 −0.0127231
\(547\) 601.898 601.898i 1.10036 1.10036i 0.105994 0.994367i \(-0.466197\pi\)
0.994367 0.105994i \(-0.0338026\pi\)
\(548\) 378.480 + 378.480i 0.690656 + 0.690656i
\(549\) 265.039i 0.482768i
\(550\) −137.941 117.927i −0.250801 0.214412i
\(551\) 588.281 1.06766
\(552\) 284.586 284.586i 0.515553 0.515553i
\(553\) −124.294 124.294i −0.224762 0.224762i
\(554\) 159.582i 0.288054i
\(555\) −286.264 + 309.530i −0.515790 + 0.557711i
\(556\) 460.229 0.827751
\(557\) −242.099 + 242.099i −0.434648 + 0.434648i −0.890206 0.455558i \(-0.849440\pi\)
0.455558 + 0.890206i \(0.349440\pi\)
\(558\) −37.2753 37.2753i −0.0668016 0.0668016i
\(559\) 123.706i 0.221299i
\(560\) −3.03548 77.7315i −0.00542050 0.138806i
\(561\) −63.9572 −0.114006
\(562\) 227.826 227.826i 0.405384 0.405384i
\(563\) 76.1930 + 76.1930i 0.135334 + 0.135334i 0.771529 0.636195i \(-0.219492\pi\)
−0.636195 + 0.771529i \(0.719492\pi\)
\(564\) 308.950i 0.547783i
\(565\) 153.429 5.99152i 0.271556 0.0106045i
\(566\) −124.218 −0.219466
\(567\) 16.8375 16.8375i 0.0296957 0.0296957i
\(568\) 653.172 + 653.172i 1.14995 + 1.14995i
\(569\) 319.028i 0.560683i 0.959900 + 0.280341i \(0.0904476\pi\)
−0.959900 + 0.280341i \(0.909552\pi\)
\(570\) −159.825 147.811i −0.280394 0.259318i
\(571\) −26.8933 −0.0470987 −0.0235493 0.999723i \(-0.507497\pi\)
−0.0235493 + 0.999723i \(0.507497\pi\)
\(572\) −26.3199 + 26.3199i −0.0460137 + 0.0460137i
\(573\) 302.075 + 302.075i 0.527182 + 0.527182i
\(574\) 94.6833i 0.164953i
\(575\) −557.502 + 652.119i −0.969568 + 1.13412i
\(576\) −23.1607 −0.0402096
\(577\) 302.359 302.359i 0.524019 0.524019i −0.394764 0.918783i \(-0.629174\pi\)
0.918783 + 0.394764i \(0.129174\pi\)
\(578\) 179.278 + 179.278i 0.310169 + 0.310169i
\(579\) 246.713i 0.426102i
\(580\) −234.332 + 253.378i −0.404021 + 0.436858i
\(581\) 130.440 0.224509
\(582\) −96.7441 + 96.7441i −0.166227 + 0.166227i
\(583\) −71.4200 71.4200i −0.122504 0.122504i
\(584\) 56.0319i 0.0959451i
\(585\) 0.928746 + 23.7830i 0.00158760 + 0.0406547i
\(586\) −471.332 −0.804321
\(587\) 16.9036 16.9036i 0.0287966 0.0287966i −0.692562 0.721358i \(-0.743518\pi\)
0.721358 + 0.692562i \(0.243518\pi\)
\(588\) 26.4679 + 26.4679i 0.0450135 + 0.0450135i
\(589\) 483.949i 0.821646i
\(590\) 237.606 9.27872i 0.402723 0.0157266i
\(591\) −36.7216 −0.0621347
\(592\) 202.430 202.430i 0.341943 0.341943i
\(593\) 411.219 + 411.219i 0.693456 + 0.693456i 0.962991 0.269535i \(-0.0868699\pi\)
−0.269535 + 0.962991i \(0.586870\pi\)
\(594\) 37.7195i 0.0635009i
\(595\) −47.1979 43.6502i −0.0793242 0.0733617i
\(596\) −486.676 −0.816570
\(597\) 351.908 351.908i 0.589461 0.589461i
\(598\) −36.7857 36.7857i −0.0615145 0.0615145i
\(599\) 637.724i 1.06465i 0.846541 + 0.532324i \(0.178681\pi\)
−0.846541 + 0.532324i \(0.821319\pi\)
\(600\) 292.297 22.8637i 0.487162 0.0381062i
\(601\) 576.764 0.959674 0.479837 0.877358i \(-0.340696\pi\)
0.479837 + 0.877358i \(0.340696\pi\)
\(602\) 139.344 139.344i 0.231468 0.231468i
\(603\) −121.766 121.766i −0.201934 0.201934i
\(604\) 723.378i 1.19765i
\(605\) −214.780 + 232.237i −0.355009 + 0.383862i
\(606\) 119.931 0.197906
\(607\) −144.949 + 144.949i −0.238796 + 0.238796i −0.816352 0.577555i \(-0.804007\pi\)
0.577555 + 0.816352i \(0.304007\pi\)
\(608\) 608.427 + 608.427i 1.00070 + 1.00070i
\(609\) 102.457i 0.168238i
\(610\) −16.4675 421.694i −0.0269959 0.691301i
\(611\) 91.6763 0.150043
\(612\) 31.8269 31.8269i 0.0520048 0.0520048i
\(613\) 588.190 + 588.190i 0.959527 + 0.959527i 0.999212 0.0396852i \(-0.0126355\pi\)
−0.0396852 + 0.999212i \(0.512636\pi\)
\(614\) 414.253i 0.674679i
\(615\) 324.157 12.6586i 0.527085 0.0205831i
\(616\) −136.117 −0.220970
\(617\) 688.254 688.254i 1.11548 1.11548i 0.123088 0.992396i \(-0.460720\pi\)
0.992396 0.123088i \(-0.0392798\pi\)
\(618\) 160.132 + 160.132i 0.259113 + 0.259113i
\(619\) 1033.56i 1.66972i −0.550459 0.834862i \(-0.685547\pi\)
0.550459 0.834862i \(-0.314453\pi\)
\(620\) −208.441 192.773i −0.336195 0.310925i
\(621\) 178.320 0.287150
\(622\) −50.5461 + 50.5461i −0.0812638 + 0.0812638i
\(623\) 3.80507 + 3.80507i 0.00610766 + 0.00610766i
\(624\) 16.1613i 0.0258995i
\(625\) −617.398 + 97.1815i −0.987837 + 0.155490i
\(626\) 137.272 0.219285
\(627\) 244.858 244.858i 0.390524 0.390524i
\(628\) −232.196 232.196i −0.369739 0.369739i
\(629\) 236.588i 0.376134i
\(630\) −25.7432 + 27.8355i −0.0408623 + 0.0441834i
\(631\) −53.6569 −0.0850346 −0.0425173 0.999096i \(-0.513538\pi\)
−0.0425173 + 0.999096i \(0.513538\pi\)
\(632\) −318.089 + 318.089i −0.503305 + 0.503305i
\(633\) −489.358 489.358i −0.773078 0.773078i
\(634\) 167.666i 0.264458i
\(635\) 22.8365 + 584.790i 0.0359630 + 0.920929i
\(636\) 71.0813 0.111763
\(637\) 7.85397 7.85397i 0.0123296 0.0123296i
\(638\) 114.763 + 114.763i 0.179879 + 0.179879i
\(639\) 409.275i 0.640493i
\(640\) −616.685 + 24.0820i −0.963570 + 0.0376282i
\(641\) −120.207 −0.187531 −0.0937653 0.995594i \(-0.529890\pi\)
−0.0937653 + 0.995594i \(0.529890\pi\)
\(642\) 20.6516 20.6516i 0.0321675 0.0321675i
\(643\) 18.2639 + 18.2639i 0.0284042 + 0.0284042i 0.721166 0.692762i \(-0.243606\pi\)
−0.692762 + 0.721166i \(0.743606\pi\)
\(644\) 280.314i 0.435270i
\(645\) −495.686 458.427i −0.768506 0.710740i
\(646\) 122.162 0.189105
\(647\) 281.286 281.286i 0.434754 0.434754i −0.455488 0.890242i \(-0.650535\pi\)
0.890242 + 0.455488i \(0.150535\pi\)
\(648\) −43.0899 43.0899i −0.0664968 0.0664968i
\(649\) 378.239i 0.582803i
\(650\) −2.95538 37.7825i −0.00454674 0.0581269i
\(651\) 84.2861 0.129472
\(652\) −384.542 + 384.542i −0.589789 + 0.589789i
\(653\) −554.289 554.289i −0.848835 0.848835i 0.141152 0.989988i \(-0.454919\pi\)
−0.989988 + 0.141152i \(0.954919\pi\)
\(654\) 144.570i 0.221056i
\(655\) −646.001 + 698.505i −0.986261 + 1.06642i
\(656\) −220.275 −0.335785
\(657\) −17.5547 + 17.5547i −0.0267195 + 0.0267195i
\(658\) 103.265 + 103.265i 0.156938 + 0.156938i
\(659\) 317.311i 0.481504i −0.970587 0.240752i \(-0.922606\pi\)
0.970587 0.240752i \(-0.0773941\pi\)
\(660\) 7.92724 + 202.998i 0.0120110 + 0.307573i
\(661\) −533.264 −0.806753 −0.403377 0.915034i \(-0.632164\pi\)
−0.403377 + 0.915034i \(0.632164\pi\)
\(662\) 268.251 268.251i 0.405213 0.405213i
\(663\) −9.44419 9.44419i −0.0142446 0.0142446i
\(664\) 333.818i 0.502738i
\(665\) 347.810 13.5822i 0.523022 0.0204244i
\(666\) −139.531 −0.209506
\(667\) 542.544 542.544i 0.813410 0.813410i
\(668\) −421.140 421.140i −0.630449 0.630449i
\(669\) 515.189i 0.770088i
\(670\) 201.303 + 186.172i 0.300452 + 0.277868i
\(671\) 671.282 1.00042
\(672\) 105.965 105.965i 0.157687 0.157687i
\(673\) −244.707 244.707i −0.363606 0.363606i 0.501533 0.865139i \(-0.332770\pi\)
−0.865139 + 0.501533i \(0.832770\pi\)
\(674\) 250.576i 0.371775i
\(675\) 98.7393 + 84.4130i 0.146280 + 0.125056i
\(676\) 513.978 0.760322
\(677\) −380.155 + 380.155i −0.561529 + 0.561529i −0.929742 0.368213i \(-0.879970\pi\)
0.368213 + 0.929742i \(0.379970\pi\)
\(678\) 35.9321 + 35.9321i 0.0529971 + 0.0529971i
\(679\) 218.756i 0.322173i
\(680\) −111.708 + 120.787i −0.164277 + 0.177629i
\(681\) 320.207 0.470202
\(682\) −94.4096 + 94.4096i −0.138430 + 0.138430i
\(683\) −739.822 739.822i −1.08319 1.08319i −0.996210 0.0869848i \(-0.972277\pi\)
−0.0869848 0.996210i \(-0.527723\pi\)
\(684\) 243.697i 0.356283i
\(685\) −33.8260 866.205i −0.0493810 1.26453i
\(686\) 17.6936 0.0257924
\(687\) −314.689 + 314.689i −0.458062 + 0.458062i
\(688\) 324.175 + 324.175i 0.471185 + 0.471185i
\(689\) 21.0924i 0.0306130i
\(690\) −283.718 + 11.0794i −0.411186 + 0.0160571i
\(691\) −909.333 −1.31597 −0.657984 0.753032i \(-0.728590\pi\)
−0.657984 + 0.753032i \(0.728590\pi\)
\(692\) −373.623 + 373.623i −0.539918 + 0.539918i
\(693\) −42.6453 42.6453i −0.0615372 0.0615372i
\(694\) 246.197i 0.354750i
\(695\) −547.216 506.084i −0.787362 0.728179i
\(696\) −262.204 −0.376730
\(697\) −128.722 + 128.722i −0.184680 + 0.184680i
\(698\) 281.121 + 281.121i 0.402752 + 0.402752i
\(699\) 148.664i 0.212681i
\(700\) −132.694 + 155.215i −0.189563 + 0.221736i
\(701\) −794.647 −1.13359 −0.566795 0.823859i \(-0.691817\pi\)
−0.566795 + 0.823859i \(0.691817\pi\)
\(702\) −5.56983 + 5.56983i −0.00793423 + 0.00793423i
\(703\) 905.773 + 905.773i 1.28844 + 1.28844i
\(704\) 58.6606i 0.0833248i
\(705\) 339.732 367.343i 0.481889 0.521055i
\(706\) −543.854 −0.770332
\(707\) −135.593 + 135.593i −0.191786 + 0.191786i
\(708\) −188.223 188.223i −0.265851 0.265851i
\(709\) 281.184i 0.396592i −0.980142 0.198296i \(-0.936459\pi\)
0.980142 0.198296i \(-0.0635407\pi\)
\(710\) −25.4291 651.181i −0.0358157 0.917156i
\(711\) −199.313 −0.280328
\(712\) 9.73783 9.73783i 0.0136767 0.0136767i
\(713\) 446.324 + 446.324i 0.625981 + 0.625981i
\(714\) 21.2760i 0.0297984i
\(715\) 60.2368 2.35229i 0.0842472 0.00328992i
\(716\) 176.637 0.246700
\(717\) −81.9877 + 81.9877i −0.114348 + 0.114348i
\(718\) 81.1829 + 81.1829i 0.113068 + 0.113068i
\(719\) 1122.66i 1.56143i −0.624890 0.780713i \(-0.714856\pi\)
0.624890 0.780713i \(-0.285144\pi\)
\(720\) −64.7577 59.8901i −0.0899412 0.0831807i
\(721\) −362.087 −0.502201
\(722\) −223.821 + 223.821i −0.310002 + 0.310002i
\(723\) 101.143 + 101.143i 0.139894 + 0.139894i
\(724\) 908.372i 1.25466i
\(725\) 557.245 43.5882i 0.768614 0.0601217i
\(726\) −104.689 −0.144199
\(727\) −208.125 + 208.125i −0.286279 + 0.286279i −0.835607 0.549328i \(-0.814884\pi\)
0.549328 + 0.835607i \(0.314884\pi\)
\(728\) −20.0997 20.0997i −0.0276094 0.0276094i
\(729\) 27.0000i 0.0370370i
\(730\) 26.8399 29.0213i 0.0367670 0.0397552i
\(731\) 378.877 0.518299
\(732\) −334.050 + 334.050i −0.456352 + 0.456352i
\(733\) −760.380 760.380i −1.03735 1.03735i −0.999275 0.0380787i \(-0.987876\pi\)
−0.0380787 0.999275i \(-0.512124\pi\)
\(734\) 219.315i 0.298794i
\(735\) −2.36553 60.5756i −0.00321840 0.0824158i
\(736\) 1122.25 1.52479
\(737\) −308.405 + 308.405i −0.418460 + 0.418460i
\(738\) 75.9155 + 75.9155i 0.102867 + 0.102867i
\(739\) 425.934i 0.576365i 0.957575 + 0.288183i \(0.0930510\pi\)
−0.957575 + 0.288183i \(0.906949\pi\)
\(740\) −750.924 + 29.3242i −1.01476 + 0.0396273i
\(741\) 72.3137 0.0975893
\(742\) 23.7586 23.7586i 0.0320197 0.0320197i
\(743\) −325.298 325.298i −0.437818 0.437818i 0.453459 0.891277i \(-0.350190\pi\)
−0.891277 + 0.453459i \(0.850190\pi\)
\(744\) 215.703i 0.289923i
\(745\) 578.661 + 535.166i 0.776727 + 0.718343i
\(746\) 414.139 0.555146
\(747\) 104.585 104.585i 0.140006 0.140006i
\(748\) −80.6102 80.6102i −0.107768 0.107768i
\(749\) 46.6969i 0.0623456i
\(750\) −162.345 128.171i −0.216460 0.170895i
\(751\) −107.270 −0.142836 −0.0714182 0.997446i \(-0.522752\pi\)
−0.0714182 + 0.997446i \(0.522752\pi\)
\(752\) −240.240 + 240.240i −0.319468 + 0.319468i
\(753\) 242.430 + 242.430i 0.321952 + 0.321952i
\(754\) 33.8927i 0.0449505i
\(755\) −795.451 + 860.102i −1.05358 + 1.13921i
\(756\) 42.4431 0.0561417
\(757\) 537.483 537.483i 0.710017 0.710017i −0.256521 0.966539i \(-0.582576\pi\)
0.966539 + 0.256521i \(0.0825764\pi\)
\(758\) 85.2149 + 85.2149i 0.112421 + 0.112421i
\(759\) 451.643i 0.595051i
\(760\) −34.7593 890.104i −0.0457359 1.17119i
\(761\) −547.917 −0.719996 −0.359998 0.932953i \(-0.617223\pi\)
−0.359998 + 0.932953i \(0.617223\pi\)
\(762\) −136.954 + 136.954i −0.179730 + 0.179730i
\(763\) −163.450 163.450i −0.214220 0.214220i
\(764\) 761.458i 0.996672i
\(765\) −72.8405 + 2.84448i −0.0952163 + 0.00371828i
\(766\) 472.300 0.616580
\(767\) −55.8524 + 55.8524i −0.0728193 + 0.0728193i
\(768\) −182.245 182.245i −0.237298 0.237298i
\(769\) 354.375i 0.460826i 0.973093 + 0.230413i \(0.0740077\pi\)
−0.973093 + 0.230413i \(0.925992\pi\)
\(770\) 70.5009 + 65.2016i 0.0915596 + 0.0846774i
\(771\) −505.561 −0.655721
\(772\) −310.952 + 310.952i