Properties

Label 105.3.l.a.22.7
Level 105
Weight 3
Character 105.22
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 22.7
Character \(\chi\) \(=\) 105.22
Dual form 105.3.l.a.43.7

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.675544 + 0.675544i 0.337772 + 0.337772i 0.855528 0.517756i \(-0.173233\pi\)
−0.517756 + 0.855528i \(0.673233\pi\)
\(3\) 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 −0.662635 0.748942i \(-0.730562\pi\)
0.748942 + 0.662635i \(0.230562\pi\)
\(14\) 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 0.598777 0.800916i \(-0.295653\pi\)
−0.800916 + 0.598777i \(0.795653\pi\)
\(18\) 2.02663 2.02663i 0.112591 0.112591i
\(19\) 26.3120i 1.38484i 0.721494 + 0.692420i \(0.243456\pi\)
−0.721494 + 0.692420i \(0.756544\pi\)
\(20\) 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 −0.0566642 + 0.998393i \(0.518046\pi\)
−0.998393 + 0.0566642i \(0.981954\pi\)
\(24\) 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 \(-0.874035\pi\)
0.922716 0.385481i \(-0.125965\pi\)
\(30\) 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 0.0673418 0.997730i \(-0.478548\pi\)
−0.997730 + 0.0673418i \(0.978548\pi\)
\(38\) −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 −0.342537 + 0.939504i \(0.611286\pi\)
−0.939504 + 0.342537i \(0.888714\pi\)
\(44\) 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 0.992388 0.123151i \(-0.0393001\pi\)
−0.123151 + 0.992388i \(0.539300\pi\)
\(48\) −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 −0.790199 0.612850i \(-0.790023\pi\)
0.612850 + 0.790199i \(0.290023\pi\)
\(54\) 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 \(-0.861377\pi\)
0.906661 0.421860i \(-0.138623\pi\)
\(60\) 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 0.336044 0.941846i \(-0.390911\pi\)
−0.941846 + 0.336044i \(0.890911\pi\)
\(68\) −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 −0.665891 0.746049i \(-0.731948\pi\)
0.746049 + 0.665891i \(0.231948\pi\)
\(74\) 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 \(-0.861857\pi\)
0.907296 0.420492i \(-0.138143\pi\)
\(80\) −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 −0.885210 0.465192i \(-0.845985\pi\)
0.465192 + 0.885210i \(0.345985\pi\)
\(84\) 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 \(0.00363721\pi\)
−0.999935 + 0.0114264i \(0.996363\pi\)
\(90\) 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 0.338305 0.941036i \(-0.390146\pi\)
−0.941036 + 0.338305i \(0.890146\pi\)
\(98\) −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 −0.0587421 0.998273i \(-0.518709\pi\)
0.998273 + 0.0587421i \(0.0187090\pi\)
\(104\) 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 0.763017 0.646379i \(-0.223717\pi\)
−0.646379 + 0.763017i \(0.723717\pi\)
\(108\) −11.3434 + 11.3434i −0.105031 + 0.105031i
\(109\) 87.3675i 0.801537i −0.916179 0.400769i \(-0.868743\pi\)
0.916179 0.400769i \(-0.131257\pi\)
\(110\) −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 −0.604466 0.796631i \(-0.706613\pi\)
0.796631 + 0.604466i \(0.206613\pi\)
\(114\) 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 0.301709 0.953400i \(-0.402443\pi\)
−0.953400 + 0.301709i \(0.902443\pi\)
\(128\) −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 0.994974 0.100133i \(-0.0319268\pi\)
−0.100133 + 0.994974i \(0.531927\pi\)
\(138\) −40.1544 + 40.1544i −0.290974 + 0.290974i
\(139\) 149.073i 1.07247i 0.844070 + 0.536233i \(0.180153\pi\)
−0.844070 + 0.536233i \(0.819847\pi\)
\(140\) −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 \(-0.822571\pi\)
0.848628 0.528990i \(-0.177429\pi\)
\(150\) −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 0.425779 0.904827i \(-0.360000\pi\)
−0.904827 + 0.425779i \(0.860000\pi\)
\(158\) 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 −0.212918 0.977070i \(-0.568297\pi\)
0.977070 + 0.212918i \(0.0682966\pi\)
\(164\) 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 0.168814 0.985648i \(-0.446006\pi\)
−0.985648 + 0.168814i \(0.946006\pi\)
\(168\) −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 −0.264773 0.964311i \(-0.585297\pi\)
0.964311 + 0.264773i \(0.0852969\pi\)
\(174\) 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 \(0.0510904\pi\)
−0.987147 + 0.159817i \(0.948910\pi\)
\(180\) −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 −0.396268 0.918135i \(-0.629695\pi\)
0.918135 + 0.396268i \(0.129695\pi\)
\(194\) 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 0.668033 0.744132i \(-0.267137\pi\)
−0.744132 + 0.668033i \(0.767137\pi\)
\(198\) 15.3989 15.3989i 0.0777724 0.0777724i
\(199\) 287.332i 1.44388i 0.691957 + 0.721939i \(0.256749\pi\)
−0.691957 + 0.721939i \(0.743251\pi\)
\(200\) 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 −0.998469 0.0553078i \(-0.982386\pi\)
0.0553078 + 0.998469i \(0.482386\pi\)
\(224\) 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 0.933765 0.357888i \(-0.116503\pi\)
−0.357888 + 0.933765i \(0.616503\pi\)
\(228\) 99.4891 99.4891i 0.436356 0.436356i
\(229\) 256.942i 1.12202i −0.827809 0.561010i \(-0.810413\pi\)
0.827809 0.561010i \(-0.189587\pi\)
\(230\) −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 −0.825249 0.564769i \(-0.808965\pi\)
0.564769 + 0.825249i \(0.308965\pi\)
\(234\) 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 \(-0.955275\pi\)
0.990145 0.140047i \(-0.0447255\pi\)
\(240\) −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 0.180487 0.983577i \(-0.442233\pi\)
−0.983577 + 0.180487i \(0.942233\pi\)
\(258\) −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 −0.0988340 0.995104i \(-0.531511\pi\)
0.995104 + 0.0988340i \(0.0315113\pi\)
\(264\) 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 \(0.249609\pi\)
−0.707974 + 0.706238i \(0.750391\pi\)
\(270\) 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 0.887401 0.460998i \(-0.152509\pi\)
−0.460998 + 0.887401i \(0.652509\pi\)
\(278\) −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 −0.850633 0.525760i \(-0.823781\pi\)
0.525760 + 0.850633i \(0.323781\pi\)
\(284\) 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 −0.213736 + 0.976891i \(0.568563\pi\)
−0.976891 + 0.213736i \(0.931437\pi\)
\(294\) 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 0.999999 0.00127914i \(-0.000407163\pi\)
−0.00127914 + 0.999999i \(0.500407\pi\)
\(308\) −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 −0.525925 0.850531i \(-0.676281\pi\)
0.850531 + 0.525925i \(0.176281\pi\)
\(314\) 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 0.875213 0.483738i \(-0.160721\pi\)
−0.483738 + 0.875213i \(0.660721\pi\)
\(318\) −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 0.376203 0.926537i \(-0.377230\pi\)
−0.926537 + 0.376203i \(0.877230\pi\)
\(338\) −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 0.393984 0.919117i \(-0.371097\pi\)
−0.919117 + 0.393984i \(0.871097\pi\)
\(348\) −84.5382 + 84.5382i −0.242926 + 0.242926i
\(349\) 416.140i 1.19238i −0.802844 0.596189i \(-0.796681\pi\)
0.802844 0.596189i \(-0.203319\pi\)
\(350\) 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 −0.151921 + 0.988393i \(0.548546\pi\)
−0.988393 + 0.151921i \(0.951454\pi\)
\(354\) 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 \(-0.946471\pi\)
0.985894 0.167373i \(-0.0535285\pi\)
\(360\) 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 0.892785 0.450483i \(-0.148748\pi\)
−0.450483 + 0.892785i \(0.648748\pi\)
\(368\) 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 −0.164586 0.986363i \(-0.552629\pi\)
0.986363 + 0.164586i \(0.0526289\pi\)
\(374\) 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 \(-0.946781\pi\)
0.986056 0.166415i \(-0.0532192\pi\)
\(380\) 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 −0.0837685 0.996485i \(-0.526696\pi\)
0.996485 + 0.0837685i \(0.0266956\pi\)
\(384\) 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 \(-0.931830\pi\)
0.977155 0.212530i \(-0.0681704\pi\)
\(390\) 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 0.651171 0.758931i \(-0.274278\pi\)
−0.758931 + 0.651171i \(0.774278\pi\)
\(398\) −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 \(-0.972057\pi\)
0.996149 0.0876721i \(-0.0279428\pi\)
\(410\) −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 \(0.190460\pi\)
−0.826268 + 0.563277i \(0.809540\pi\)
\(420\) −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 −0.982328 0.187166i \(-0.940070\pi\)
0.187166 + 0.982328i \(0.440070\pi\)
\(434\) 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 \(-0.982170\pi\)
0.998432 0.0559848i \(-0.0178298\pi\)
\(440\) 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 −0.562224 0.826985i \(-0.690054\pi\)
0.826985 + 0.562224i \(0.190054\pi\)
\(444\) 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 \(0.107288\pi\)
−0.943733 + 0.330708i \(0.892712\pi\)
\(450\) 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 0.366948 0.930241i \(-0.380403\pi\)
−0.930241 + 0.366948i \(0.880403\pi\)
\(458\) 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 −0.616888 0.787051i \(-0.711607\pi\)
0.787051 + 0.616888i \(0.211607\pi\)
\(464\) 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 0.793500 + 0.608570i \(0.208257\pi\)
0.608570 + 0.793500i \(0.291743\pi\)
\(468\) −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 \(-0.911579\pi\)
0.961666 0.274225i \(-0.0884212\pi\)
\(480\) −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 0.661705 0.749764i \(-0.269833\pi\)
−0.749764 + 0.661705i \(0.769833\pi\)
\(488\) 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 \(0.138634\pi\)
−0.906646 + 0.421892i \(0.861366\pi\)
\(500\) 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 −0.255718 0.966751i \(-0.582312\pi\)
0.966751 + 0.255718i \(0.0823118\pi\)
\(504\) 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 \(0.370502\pi\)
−0.395700 + 0.918380i \(0.629498\pi\)
\(510\) 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 −0.653945 0.756542i \(-0.726887\pi\)
0.756542 + 0.653945i \(0.226887\pi\)
\(524\) 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 0.994367 + 0.105994i \(0.0338026\pi\)
0.105994 + 0.994367i \(0.466197\pi\)
\(548\) 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 0.455558 0.890206i \(-0.349440\pi\)
−0.890206 + 0.455558i \(0.849440\pi\)
\(558\) −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 −0.636195 0.771529i \(-0.719492\pi\)
0.771529 + 0.636195i \(0.219492\pi\)
\(564\) 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 \(-0.909552\pi\)
0.959900 0.280341i \(-0.0904476\pi\)
\(570\) −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 0.918783 0.394764i \(-0.129174\pi\)
−0.394764 + 0.918783i \(0.629174\pi\)
\(578\) 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 0.721358 0.692562i \(-0.243518\pi\)
−0.692562 + 0.721358i \(0.743518\pi\)
\(588\) 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 −0.269535 0.962991i \(-0.586870\pi\)
0.962991 + 0.269535i \(0.0868699\pi\)
\(594\) 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 \(-0.821319\pi\)
0.846541 0.532324i \(-0.178681\pi\)
\(600\) 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 0.577555 0.816352i \(-0.304007\pi\)
−0.816352 + 0.577555i \(0.804007\pi\)
\(608\) 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 −0.0396852 0.999212i \(-0.512636\pi\)
0.999212 + 0.0396852i \(0.0126355\pi\)
\(614\) 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 0.992396 + 0.123088i \(0.0392798\pi\)
0.123088 + 0.992396i \(0.460720\pi\)
\(618\) 160.132 160.132i 0.259113 0.259113i
\(619\) 1033.56i 1.66972i 0.550459 + 0.834862i \(0.314453\pi\)
−0.550459 + 0.834862i \(0.685547\pi\)
\(620\) −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 −0.692762 0.721166i \(-0.743606\pi\)
0.721166 + 0.692762i \(0.243606\pi\)
\(644\) 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 0.890242 0.455488i \(-0.150535\pi\)
−0.455488 + 0.890242i \(0.650535\pi\)
\(648\) −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 −0.989988 0.141152i \(-0.954919\pi\)
0.141152 + 0.989988i \(0.454919\pi\)
\(654\) 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 \(0.0773941\pi\)
−0.970587 + 0.240752i \(0.922606\pi\)
\(660\) 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 −0.865139 0.501533i \(-0.832770\pi\)
0.501533 + 0.865139i \(0.332770\pi\)
\(674\) 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 0.368213 0.929742i \(-0.379970\pi\)
−0.929742 + 0.368213i \(0.879970\pi\)
\(678\) 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 −0.0869848 + 0.996210i \(0.527723\pi\)
−0.996210 + 0.0869848i \(0.972277\pi\)
\(684\) 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 \(0.0635407\pi\)
−0.980142 + 0.198296i \(0.936459\pi\)
\(710\) −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 \(0.285144\pi\)
−0.624890 + 0.780713i \(0.714856\pi\)
\(720\) −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 0.549328 0.835607i \(-0.314884\pi\)
−0.835607 + 0.549328i \(0.814884\pi\)
\(728\) −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 −0.0380787 + 0.999275i \(0.512124\pi\)
−0.999275 + 0.0380787i \(0.987876\pi\)
\(734\) 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 \(-0.906949\pi\)
0.957575 0.288183i \(-0.0930510\pi\)
\(740\) −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 −0.891277 0.453459i \(-0.850190\pi\)
0.453459 + 0.891277i \(0.350190\pi\)
\(744\) 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 0.966539 0.256521i \(-0.0825764\pi\)
−0.256521 + 0.966539i \(0.582576\pi\)
\(758\) 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 \(-0.925992\pi\)
0.973093 0.230413i \(-0.0740077\pi\)
\(770\) 70.5009 65.2016i 0.0915596 0.0846774i
\(771\) −505.561 −0.655721
\(772\) −310.952