Properties

Label 105.3.l.a.22.12
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 22.12
Character \(\chi\) \(=\) 105.22
Dual form 105.3.l.a.43.12

$q$-expansion

\(f(q)\) \(=\) \(q+(2.74240 + 2.74240i) q^{2} +(-1.22474 + 1.22474i) q^{3} +11.0415i q^{4} +(-0.683416 - 4.95307i) q^{5} -6.71747 q^{6} +(1.87083 + 1.87083i) q^{7} +(-19.3105 + 19.3105i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(2.74240 + 2.74240i) q^{2} +(-1.22474 + 1.22474i) q^{3} +11.0415i q^{4} +(-0.683416 - 4.95307i) q^{5} -6.71747 q^{6} +(1.87083 + 1.87083i) q^{7} +(-19.3105 + 19.3105i) q^{8} -3.00000i q^{9} +(11.7091 - 15.4575i) q^{10} +10.9331 q^{11} +(-13.5230 - 13.5230i) q^{12} +(8.10523 - 8.10523i) q^{13} +10.2611i q^{14} +(6.90326 + 5.22924i) q^{15} -61.7483 q^{16} +(-5.51018 - 5.51018i) q^{17} +(8.22719 - 8.22719i) q^{18} +12.1318i q^{19} +(54.6893 - 7.54592i) q^{20} -4.58258 q^{21} +(29.9829 + 29.9829i) q^{22} +(24.3210 - 24.3210i) q^{23} -47.3009i q^{24} +(-24.0659 + 6.77002i) q^{25} +44.4555 q^{26} +(3.67423 + 3.67423i) q^{27} +(-20.6567 + 20.6567i) q^{28} +14.8012i q^{29} +(4.59083 + 33.2721i) q^{30} -8.07276 q^{31} +(-92.0962 - 92.0962i) q^{32} +(-13.3902 + 13.3902i) q^{33} -30.2222i q^{34} +(7.98780 - 10.5449i) q^{35} +33.1244 q^{36} +(-34.6319 - 34.6319i) q^{37} +(-33.2701 + 33.2701i) q^{38} +19.8537i q^{39} +(108.844 + 82.4493i) q^{40} +32.0975 q^{41} +(-12.5672 - 12.5672i) q^{42} +(-13.0663 + 13.0663i) q^{43} +120.717i q^{44} +(-14.8592 + 2.05025i) q^{45} +133.395 q^{46} +(-54.1653 - 54.1653i) q^{47} +(75.6259 - 75.6259i) q^{48} +7.00000i q^{49} +(-84.5643 - 47.4321i) q^{50} +13.4971 q^{51} +(89.4937 + 89.4937i) q^{52} +(6.76541 - 6.76541i) q^{53} +20.1524i q^{54} +(-7.47185 - 54.1524i) q^{55} -72.2534 q^{56} +(-14.8583 - 14.8583i) q^{57} +(-40.5907 + 40.5907i) q^{58} -44.4162i q^{59} +(-57.7385 + 76.2222i) q^{60} -84.4444 q^{61} +(-22.1387 - 22.1387i) q^{62} +(5.61249 - 5.61249i) q^{63} -258.136i q^{64} +(-45.6850 - 34.6066i) q^{65} -73.4427 q^{66} +(0.661895 + 0.661895i) q^{67} +(60.8405 - 60.8405i) q^{68} +59.5739i q^{69} +(50.8240 - 7.01261i) q^{70} +103.429 q^{71} +(57.9316 + 57.9316i) q^{72} +(-55.1974 + 55.1974i) q^{73} -189.949i q^{74} +(21.1830 - 37.7661i) q^{75} -133.952 q^{76} +(20.4539 + 20.4539i) q^{77} +(-54.4467 + 54.4467i) q^{78} +68.8001i q^{79} +(42.1998 + 305.844i) q^{80} -9.00000 q^{81} +(88.0241 + 88.0241i) q^{82} +(-71.4410 + 71.4410i) q^{83} -50.5984i q^{84} +(-23.5266 + 31.0581i) q^{85} -71.6660 q^{86} +(-18.1277 - 18.1277i) q^{87} +(-211.124 + 211.124i) q^{88} +41.6575i q^{89} +(-46.3725 - 35.1273i) q^{90} +30.3270 q^{91} +(268.539 + 268.539i) q^{92} +(9.88708 - 9.88708i) q^{93} -297.086i q^{94} +(60.0895 - 8.29103i) q^{95} +225.589 q^{96} +(25.2508 + 25.2508i) q^{97} +(-19.1968 + 19.1968i) q^{98} -32.7993i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.74240 + 2.74240i 1.37120 + 1.37120i 0.858671 + 0.512527i \(0.171291\pi\)
0.512527 + 0.858671i \(0.328709\pi\)
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 11.0415i 2.76037i
\(5\) −0.683416 4.95307i −0.136683 0.990615i
\(6\) −6.71747 −1.11958
\(7\) 1.87083 + 1.87083i 0.267261 + 0.267261i
\(8\) −19.3105 + 19.3105i −2.41382 + 2.41382i
\(9\) 3.00000i 0.333333i
\(10\) 11.7091 15.4575i 1.17091 1.54575i
\(11\) 10.9331 0.993917 0.496958 0.867774i \(-0.334450\pi\)
0.496958 + 0.867774i \(0.334450\pi\)
\(12\) −13.5230 13.5230i −1.12692 1.12692i
\(13\) 8.10523 8.10523i 0.623479 0.623479i −0.322940 0.946419i \(-0.604671\pi\)
0.946419 + 0.322940i \(0.104671\pi\)
\(14\) 10.2611i 0.732936i
\(15\) 6.90326 + 5.22924i 0.460217 + 0.348616i
\(16\) −61.7483 −3.85927
\(17\) −5.51018 5.51018i −0.324128 0.324128i 0.526220 0.850348i \(-0.323609\pi\)
−0.850348 + 0.526220i \(0.823609\pi\)
\(18\) 8.22719 8.22719i 0.457066 0.457066i
\(19\) 12.1318i 0.638513i 0.947668 + 0.319257i \(0.103433\pi\)
−0.947668 + 0.319257i \(0.896567\pi\)
\(20\) 54.6893 7.54592i 2.73446 0.377296i
\(21\) −4.58258 −0.218218
\(22\) 29.9829 + 29.9829i 1.36286 + 1.36286i
\(23\) 24.3210 24.3210i 1.05743 1.05743i 0.0591858 0.998247i \(-0.481150\pi\)
0.998247 0.0591858i \(-0.0188504\pi\)
\(24\) 47.3009i 1.97087i
\(25\) −24.0659 + 6.77002i −0.962635 + 0.270801i
\(26\) 44.4555 1.70983
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −20.6567 + 20.6567i −0.737740 + 0.737740i
\(29\) 14.8012i 0.510385i 0.966890 + 0.255193i \(0.0821389\pi\)
−0.966890 + 0.255193i \(0.917861\pi\)
\(30\) 4.59083 + 33.2721i 0.153028 + 1.10907i
\(31\) −8.07276 −0.260412 −0.130206 0.991487i \(-0.541564\pi\)
−0.130206 + 0.991487i \(0.541564\pi\)
\(32\) −92.0962 92.0962i −2.87801 2.87801i
\(33\) −13.3902 + 13.3902i −0.405765 + 0.405765i
\(34\) 30.2222i 0.888888i
\(35\) 7.98780 10.5449i 0.228223 0.301283i
\(36\) 33.1244 0.920123
\(37\) −34.6319 34.6319i −0.935998 0.935998i 0.0620735 0.998072i \(-0.480229\pi\)
−0.998072 + 0.0620735i \(0.980229\pi\)
\(38\) −33.2701 + 33.2701i −0.875528 + 0.875528i
\(39\) 19.8537i 0.509069i
\(40\) 108.844 + 82.4493i 2.72109 + 2.06123i
\(41\) 32.0975 0.782866 0.391433 0.920207i \(-0.371979\pi\)
0.391433 + 0.920207i \(0.371979\pi\)
\(42\) −12.5672 12.5672i −0.299220 0.299220i
\(43\) −13.0663 + 13.0663i −0.303868 + 0.303868i −0.842525 0.538657i \(-0.818932\pi\)
0.538657 + 0.842525i \(0.318932\pi\)
\(44\) 120.717i 2.74358i
\(45\) −14.8592 + 2.05025i −0.330205 + 0.0455611i
\(46\) 133.395 2.89990
\(47\) −54.1653 54.1653i −1.15245 1.15245i −0.986059 0.166394i \(-0.946788\pi\)
−0.166394 0.986059i \(-0.553212\pi\)
\(48\) 75.6259 75.6259i 1.57554 1.57554i
\(49\) 7.00000i 0.142857i
\(50\) −84.5643 47.4321i −1.69129 0.948642i
\(51\) 13.4971 0.264649
\(52\) 89.4937 + 89.4937i 1.72103 + 1.72103i
\(53\) 6.76541 6.76541i 0.127649 0.127649i −0.640396 0.768045i \(-0.721230\pi\)
0.768045 + 0.640396i \(0.221230\pi\)
\(54\) 20.1524i 0.373193i
\(55\) −7.47185 54.1524i −0.135852 0.984589i
\(56\) −72.2534 −1.29024
\(57\) −14.8583 14.8583i −0.260672 0.260672i
\(58\) −40.5907 + 40.5907i −0.699839 + 0.699839i
\(59\) 44.4162i 0.752816i −0.926454 0.376408i \(-0.877159\pi\)
0.926454 0.376408i \(-0.122841\pi\)
\(60\) −57.7385 + 76.2222i −0.962309 + 1.27037i
\(61\) −84.4444 −1.38433 −0.692167 0.721737i \(-0.743344\pi\)
−0.692167 + 0.721737i \(0.743344\pi\)
\(62\) −22.1387 22.1387i −0.357076 0.357076i
\(63\) 5.61249 5.61249i 0.0890871 0.0890871i
\(64\) 258.136i 4.03337i
\(65\) −45.6850 34.6066i −0.702847 0.532409i
\(66\) −73.4427 −1.11277
\(67\) 0.661895 + 0.661895i 0.00987903 + 0.00987903i 0.712029 0.702150i \(-0.247776\pi\)
−0.702150 + 0.712029i \(0.747776\pi\)
\(68\) 60.8405 60.8405i 0.894713 0.894713i
\(69\) 59.5739i 0.863390i
\(70\) 50.8240 7.01261i 0.726058 0.100180i
\(71\) 103.429 1.45675 0.728373 0.685181i \(-0.240277\pi\)
0.728373 + 0.685181i \(0.240277\pi\)
\(72\) 57.9316 + 57.9316i 0.804605 + 0.804605i
\(73\) −55.1974 + 55.1974i −0.756129 + 0.756129i −0.975616 0.219486i \(-0.929562\pi\)
0.219486 + 0.975616i \(0.429562\pi\)
\(74\) 189.949i 2.56688i
\(75\) 21.1830 37.7661i 0.282440 0.503548i
\(76\) −133.952 −1.76253
\(77\) 20.4539 + 20.4539i 0.265635 + 0.265635i
\(78\) −54.4467 + 54.4467i −0.698034 + 0.698034i
\(79\) 68.8001i 0.870887i 0.900216 + 0.435444i \(0.143408\pi\)
−0.900216 + 0.435444i \(0.856592\pi\)
\(80\) 42.1998 + 305.844i 0.527497 + 3.82305i
\(81\) −9.00000 −0.111111
\(82\) 88.0241 + 88.0241i 1.07346 + 1.07346i
\(83\) −71.4410 + 71.4410i −0.860735 + 0.860735i −0.991423 0.130688i \(-0.958281\pi\)
0.130688 + 0.991423i \(0.458281\pi\)
\(84\) 50.5984i 0.602362i
\(85\) −23.5266 + 31.0581i −0.276783 + 0.365389i
\(86\) −71.6660 −0.833326
\(87\) −18.1277 18.1277i −0.208364 0.208364i
\(88\) −211.124 + 211.124i −2.39913 + 2.39913i
\(89\) 41.6575i 0.468062i 0.972229 + 0.234031i \(0.0751917\pi\)
−0.972229 + 0.234031i \(0.924808\pi\)
\(90\) −46.3725 35.1273i −0.515250 0.390303i
\(91\) 30.3270 0.333264
\(92\) 268.539 + 268.539i 2.91890 + 2.91890i
\(93\) 9.88708 9.88708i 0.106313 0.106313i
\(94\) 297.086i 3.16048i
\(95\) 60.0895 8.29103i 0.632521 0.0872740i
\(96\) 225.589 2.34988
\(97\) 25.2508 + 25.2508i 0.260318 + 0.260318i 0.825183 0.564865i \(-0.191072\pi\)
−0.564865 + 0.825183i \(0.691072\pi\)
\(98\) −19.1968 + 19.1968i −0.195885 + 0.195885i
\(99\) 32.7993i 0.331306i
\(100\) −74.7510 265.723i −0.747510 2.65723i
\(101\) 53.7274 0.531955 0.265977 0.963979i \(-0.414305\pi\)
0.265977 + 0.963979i \(0.414305\pi\)
\(102\) 37.0145 + 37.0145i 0.362887 + 0.362887i
\(103\) 39.6796 39.6796i 0.385239 0.385239i −0.487746 0.872985i \(-0.662181\pi\)
0.872985 + 0.487746i \(0.162181\pi\)
\(104\) 313.032i 3.00993i
\(105\) 3.13181 + 22.6978i 0.0298267 + 0.216170i
\(106\) 37.1069 0.350065
\(107\) −68.3716 68.3716i −0.638987 0.638987i 0.311318 0.950306i \(-0.399229\pi\)
−0.950306 + 0.311318i \(0.899229\pi\)
\(108\) −40.5690 + 40.5690i −0.375639 + 0.375639i
\(109\) 135.475i 1.24289i 0.783458 + 0.621445i \(0.213454\pi\)
−0.783458 + 0.621445i \(0.786546\pi\)
\(110\) 128.017 168.998i 1.16379 1.53635i
\(111\) 84.8306 0.764239
\(112\) −115.520 115.520i −1.03143 1.03143i
\(113\) 6.34998 6.34998i 0.0561945 0.0561945i −0.678451 0.734646i \(-0.737348\pi\)
0.734646 + 0.678451i \(0.237348\pi\)
\(114\) 81.4947i 0.714866i
\(115\) −137.085 103.842i −1.19204 0.902975i
\(116\) −163.427 −1.40885
\(117\) −24.3157 24.3157i −0.207826 0.207826i
\(118\) 121.807 121.807i 1.03226 1.03226i
\(119\) 20.6172i 0.173254i
\(120\) −234.285 + 32.3262i −1.95237 + 0.269385i
\(121\) −1.46766 −0.0121294
\(122\) −231.580 231.580i −1.89820 1.89820i
\(123\) −39.3113 + 39.3113i −0.319604 + 0.319604i
\(124\) 89.1352i 0.718833i
\(125\) 49.9794 + 114.573i 0.399835 + 0.916587i
\(126\) 30.7833 0.244312
\(127\) 20.2819 + 20.2819i 0.159700 + 0.159700i 0.782434 0.622734i \(-0.213978\pi\)
−0.622734 + 0.782434i \(0.713978\pi\)
\(128\) 339.525 339.525i 2.65254 2.65254i
\(129\) 32.0058i 0.248107i
\(130\) −30.3816 220.191i −0.233705 1.69378i
\(131\) 77.7144 0.593240 0.296620 0.954996i \(-0.404141\pi\)
0.296620 + 0.954996i \(0.404141\pi\)
\(132\) −147.848 147.848i −1.12006 1.12006i
\(133\) −22.6964 + 22.6964i −0.170650 + 0.170650i
\(134\) 3.63036i 0.0270922i
\(135\) 15.6877 20.7098i 0.116205 0.153406i
\(136\) 212.809 1.56477
\(137\) 146.870 + 146.870i 1.07205 + 1.07205i 0.997195 + 0.0748506i \(0.0238480\pi\)
0.0748506 + 0.997195i \(0.476152\pi\)
\(138\) −163.375 + 163.375i −1.18388 + 1.18388i
\(139\) 146.322i 1.05268i 0.850275 + 0.526339i \(0.176436\pi\)
−0.850275 + 0.526339i \(0.823564\pi\)
\(140\) 116.431 + 88.1971i 0.831653 + 0.629979i
\(141\) 132.677 0.940974
\(142\) 283.643 + 283.643i 1.99749 + 1.99749i
\(143\) 88.6152 88.6152i 0.619686 0.619686i
\(144\) 185.245i 1.28642i
\(145\) 73.3113 10.1154i 0.505595 0.0697611i
\(146\) −302.746 −2.07361
\(147\) −8.57321 8.57321i −0.0583212 0.0583212i
\(148\) 382.388 382.388i 2.58370 2.58370i
\(149\) 143.223i 0.961228i −0.876932 0.480614i \(-0.840414\pi\)
0.876932 0.480614i \(-0.159586\pi\)
\(150\) 161.662 45.4774i 1.07775 0.303183i
\(151\) 204.429 1.35384 0.676919 0.736058i \(-0.263315\pi\)
0.676919 + 0.736058i \(0.263315\pi\)
\(152\) −234.270 234.270i −1.54125 1.54125i
\(153\) −16.5305 + 16.5305i −0.108043 + 0.108043i
\(154\) 112.186i 0.728478i
\(155\) 5.51706 + 39.9850i 0.0355939 + 0.257968i
\(156\) −219.214 −1.40522
\(157\) −168.925 168.925i −1.07595 1.07595i −0.996868 0.0790870i \(-0.974800\pi\)
−0.0790870 0.996868i \(-0.525200\pi\)
\(158\) −188.677 + 188.677i −1.19416 + 1.19416i
\(159\) 16.5718i 0.104225i
\(160\) −393.219 + 519.100i −2.45762 + 3.24437i
\(161\) 91.0007 0.565222
\(162\) −24.6816 24.6816i −0.152355 0.152355i
\(163\) 167.373 167.373i 1.02683 1.02683i 0.0271997 0.999630i \(-0.491341\pi\)
0.999630 0.0271997i \(-0.00865900\pi\)
\(164\) 354.404i 2.16100i
\(165\) 75.4740 + 57.1717i 0.457418 + 0.346495i
\(166\) −391.839 −2.36048
\(167\) 80.3381 + 80.3381i 0.481066 + 0.481066i 0.905472 0.424406i \(-0.139517\pi\)
−0.424406 + 0.905472i \(0.639517\pi\)
\(168\) 88.4919 88.4919i 0.526738 0.526738i
\(169\) 37.6105i 0.222547i
\(170\) −149.693 + 20.6543i −0.880545 + 0.121496i
\(171\) 36.3953 0.212838
\(172\) −144.271 144.271i −0.838787 0.838787i
\(173\) −76.0306 + 76.0306i −0.439483 + 0.439483i −0.891838 0.452355i \(-0.850584\pi\)
0.452355 + 0.891838i \(0.350584\pi\)
\(174\) 99.4265i 0.571417i
\(175\) −57.6887 32.3576i −0.329650 0.184901i
\(176\) −675.099 −3.83579
\(177\) 54.3985 + 54.3985i 0.307336 + 0.307336i
\(178\) −114.241 + 114.241i −0.641806 + 0.641806i
\(179\) 72.8033i 0.406722i −0.979104 0.203361i \(-0.934813\pi\)
0.979104 0.203361i \(-0.0651865\pi\)
\(180\) −22.6378 164.068i −0.125765 0.911488i
\(181\) 116.021 0.641000 0.320500 0.947249i \(-0.396149\pi\)
0.320500 + 0.947249i \(0.396149\pi\)
\(182\) 83.1686 + 83.1686i 0.456971 + 0.456971i
\(183\) 103.423 103.423i 0.565152 0.565152i
\(184\) 939.301i 5.10489i
\(185\) −147.866 + 195.203i −0.799278 + 1.05515i
\(186\) 54.2286 0.291551
\(187\) −60.2432 60.2432i −0.322156 0.322156i
\(188\) 598.065 598.065i 3.18120 3.18120i
\(189\) 13.7477i 0.0727393i
\(190\) 187.526 + 142.052i 0.986981 + 0.747641i
\(191\) −134.337 −0.703336 −0.351668 0.936125i \(-0.614385\pi\)
−0.351668 + 0.936125i \(0.614385\pi\)
\(192\) 316.150 + 316.150i 1.64662 + 1.64662i
\(193\) −5.00682 + 5.00682i −0.0259421 + 0.0259421i −0.719959 0.694017i \(-0.755839\pi\)
0.694017 + 0.719959i \(0.255839\pi\)
\(194\) 138.495i 0.713894i
\(195\) 98.3367 13.5683i 0.504291 0.0695811i
\(196\) −77.2903 −0.394338
\(197\) −207.221 207.221i −1.05188 1.05188i −0.998578 0.0533056i \(-0.983024\pi\)
−0.0533056 0.998578i \(-0.516976\pi\)
\(198\) 89.9486 89.9486i 0.454286 0.454286i
\(199\) 115.701i 0.581414i 0.956812 + 0.290707i \(0.0938905\pi\)
−0.956812 + 0.290707i \(0.906109\pi\)
\(200\) 333.992 595.457i 1.66996 2.97729i
\(201\) −1.62130 −0.00806619
\(202\) 147.342 + 147.342i 0.729416 + 0.729416i
\(203\) −27.6905 + 27.6905i −0.136406 + 0.136406i
\(204\) 149.028i 0.730530i
\(205\) −21.9360 158.981i −0.107005 0.775519i
\(206\) 217.634 1.05648
\(207\) −72.9629 72.9629i −0.352478 0.352478i
\(208\) −500.484 + 500.484i −2.40617 + 2.40617i
\(209\) 132.637i 0.634629i
\(210\) −53.6578 + 70.8351i −0.255513 + 0.337310i
\(211\) 66.2124 0.313803 0.156901 0.987614i \(-0.449850\pi\)
0.156901 + 0.987614i \(0.449850\pi\)
\(212\) 74.7001 + 74.7001i 0.352359 + 0.352359i
\(213\) −126.674 + 126.674i −0.594714 + 0.594714i
\(214\) 375.004i 1.75236i
\(215\) 73.6482 + 55.7887i 0.342550 + 0.259482i
\(216\) −141.903 −0.656957
\(217\) −15.1028 15.1028i −0.0695980 0.0695980i
\(218\) −371.526 + 371.526i −1.70425 + 1.70425i
\(219\) 135.206i 0.617377i
\(220\) 597.922 82.5002i 2.71783 0.375001i
\(221\) −89.3225 −0.404174
\(222\) 232.639 + 232.639i 1.04792 + 1.04792i
\(223\) −51.3641 + 51.3641i −0.230332 + 0.230332i −0.812831 0.582499i \(-0.802075\pi\)
0.582499 + 0.812831i \(0.302075\pi\)
\(224\) 344.593i 1.53836i
\(225\) 20.3101 + 72.1977i 0.0902670 + 0.320878i
\(226\) 34.8283 0.154108
\(227\) −106.842 106.842i −0.470670 0.470670i 0.431461 0.902132i \(-0.357998\pi\)
−0.902132 + 0.431461i \(0.857998\pi\)
\(228\) 164.058 164.058i 0.719551 0.719551i
\(229\) 88.3402i 0.385765i −0.981222 0.192883i \(-0.938216\pi\)
0.981222 0.192883i \(-0.0617836\pi\)
\(230\) −91.1646 660.717i −0.396368 2.87268i
\(231\) −50.1017 −0.216890
\(232\) −285.818 285.818i −1.23198 1.23198i
\(233\) −260.550 + 260.550i −1.11824 + 1.11824i −0.126242 + 0.991999i \(0.540292\pi\)
−0.991999 + 0.126242i \(0.959708\pi\)
\(234\) 133.367i 0.569942i
\(235\) −231.267 + 305.302i −0.984116 + 1.29916i
\(236\) 490.420 2.07805
\(237\) −84.2626 84.2626i −0.355538 0.355538i
\(238\) 56.5405 56.5405i 0.237565 0.237565i
\(239\) 166.308i 0.695851i 0.937522 + 0.347925i \(0.113114\pi\)
−0.937522 + 0.347925i \(0.886886\pi\)
\(240\) −426.265 322.897i −1.77610 1.34540i
\(241\) −309.962 −1.28615 −0.643075 0.765804i \(-0.722342\pi\)
−0.643075 + 0.765804i \(0.722342\pi\)
\(242\) −4.02490 4.02490i −0.0166318 0.0166318i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 932.391i 3.82127i
\(245\) 34.6715 4.78391i 0.141516 0.0195262i
\(246\) −215.614 −0.876480
\(247\) 98.3306 + 98.3306i 0.398100 + 0.398100i
\(248\) 155.889 155.889i 0.628586 0.628586i
\(249\) 174.994i 0.702787i
\(250\) −177.142 + 451.269i −0.708569 + 1.80508i
\(251\) −403.709 −1.60840 −0.804201 0.594358i \(-0.797406\pi\)
−0.804201 + 0.594358i \(0.797406\pi\)
\(252\) 61.9701 + 61.9701i 0.245913 + 0.245913i
\(253\) 265.903 265.903i 1.05100 1.05100i
\(254\) 111.242i 0.437960i
\(255\) −9.22415 66.8522i −0.0361731 0.262166i
\(256\) 829.683 3.24095
\(257\) 109.310 + 109.310i 0.425332 + 0.425332i 0.887035 0.461703i \(-0.152761\pi\)
−0.461703 + 0.887035i \(0.652761\pi\)
\(258\) 87.7726 87.7726i 0.340204 0.340204i
\(259\) 129.581i 0.500312i
\(260\) 382.107 504.430i 1.46964 1.94012i
\(261\) 44.4035 0.170128
\(262\) 213.124 + 213.124i 0.813449 + 0.813449i
\(263\) 207.442 207.442i 0.788754 0.788754i −0.192536 0.981290i \(-0.561671\pi\)
0.981290 + 0.192536i \(0.0616713\pi\)
\(264\) 517.145i 1.95888i
\(265\) −38.1332 28.8860i −0.143899 0.109004i
\(266\) −124.485 −0.467989
\(267\) −51.0198 51.0198i −0.191086 0.191086i
\(268\) −7.30830 + 7.30830i −0.0272698 + 0.0272698i
\(269\) 31.5174i 0.117165i −0.998283 0.0585825i \(-0.981342\pi\)
0.998283 0.0585825i \(-0.0186581\pi\)
\(270\) 99.8164 13.7725i 0.369690 0.0510092i
\(271\) −92.6505 −0.341884 −0.170942 0.985281i \(-0.554681\pi\)
−0.170942 + 0.985281i \(0.554681\pi\)
\(272\) 340.244 + 340.244i 1.25090 + 1.25090i
\(273\) −37.1428 + 37.1428i −0.136054 + 0.136054i
\(274\) 805.553i 2.93997i
\(275\) −263.114 + 74.0172i −0.956779 + 0.269154i
\(276\) −657.784 −2.38328
\(277\) −29.1214 29.1214i −0.105131 0.105131i 0.652585 0.757716i \(-0.273685\pi\)
−0.757716 + 0.652585i \(0.773685\pi\)
\(278\) −401.274 + 401.274i −1.44343 + 1.44343i
\(279\) 24.2183i 0.0868039i
\(280\) 49.3791 + 357.876i 0.176354 + 1.27813i
\(281\) −186.605 −0.664075 −0.332038 0.943266i \(-0.607736\pi\)
−0.332038 + 0.943266i \(0.607736\pi\)
\(282\) 363.854 + 363.854i 1.29026 + 1.29026i
\(283\) 199.836 199.836i 0.706135 0.706135i −0.259585 0.965720i \(-0.583586\pi\)
0.965720 + 0.259585i \(0.0835859\pi\)
\(284\) 1142.01i 4.02115i
\(285\) −63.4399 + 83.7487i −0.222596 + 0.293855i
\(286\) 486.036 1.69943
\(287\) 60.0489 + 60.0489i 0.209230 + 0.209230i
\(288\) −276.289 + 276.289i −0.959336 + 0.959336i
\(289\) 228.276i 0.789882i
\(290\) 228.789 + 173.308i 0.788928 + 0.597615i
\(291\) −61.8516 −0.212548
\(292\) −609.461 609.461i −2.08720 2.08720i
\(293\) −118.656 + 118.656i −0.404969 + 0.404969i −0.879980 0.475011i \(-0.842444\pi\)
0.475011 + 0.879980i \(0.342444\pi\)
\(294\) 47.0223i 0.159940i
\(295\) −219.996 + 30.3547i −0.745751 + 0.102897i
\(296\) 1337.52 4.51865
\(297\) 40.1707 + 40.1707i 0.135255 + 0.135255i
\(298\) 392.774 392.774i 1.31803 1.31803i
\(299\) 394.254i 1.31857i
\(300\) 416.994 + 233.892i 1.38998 + 0.779639i
\(301\) −48.8897 −0.162424
\(302\) 560.626 + 560.626i 1.85638 + 1.85638i
\(303\) −65.8024 + 65.8024i −0.217170 + 0.217170i
\(304\) 749.115i 2.46419i
\(305\) 57.7107 + 418.259i 0.189215 + 1.37134i
\(306\) −90.6665 −0.296296
\(307\) 315.593 + 315.593i 1.02799 + 1.02799i 0.999597 + 0.0283934i \(0.00903913\pi\)
0.0283934 + 0.999597i \(0.490961\pi\)
\(308\) −225.842 + 225.842i −0.733252 + 0.733252i
\(309\) 97.1948i 0.314546i
\(310\) −94.5248 + 124.785i −0.304919 + 0.402531i
\(311\) 569.702 1.83184 0.915919 0.401362i \(-0.131463\pi\)
0.915919 + 0.401362i \(0.131463\pi\)
\(312\) −383.385 383.385i −1.22880 1.22880i
\(313\) 222.379 222.379i 0.710475 0.710475i −0.256160 0.966634i \(-0.582457\pi\)
0.966634 + 0.256160i \(0.0824574\pi\)
\(314\) 926.518i 2.95069i
\(315\) −31.6347 23.9634i −0.100428 0.0760743i
\(316\) −759.655 −2.40397
\(317\) −183.394 183.394i −0.578530 0.578530i 0.355968 0.934498i \(-0.384151\pi\)
−0.934498 + 0.355968i \(0.884151\pi\)
\(318\) −45.4464 + 45.4464i −0.142913 + 0.142913i
\(319\) 161.822i 0.507281i
\(320\) −1278.56 + 176.414i −3.99551 + 0.551294i
\(321\) 167.476 0.521731
\(322\) 249.560 + 249.560i 0.775031 + 0.775031i
\(323\) 66.8481 66.8481i 0.206960 0.206960i
\(324\) 99.3733i 0.306708i
\(325\) −140.187 + 249.932i −0.431344 + 0.769022i
\(326\) 918.008 2.81597
\(327\) −165.922 165.922i −0.507408 0.507408i
\(328\) −619.819 + 619.819i −1.88969 + 1.88969i
\(329\) 202.668i 0.616012i
\(330\) 50.1919 + 363.767i 0.152097 + 1.10232i
\(331\) −215.246 −0.650291 −0.325146 0.945664i \(-0.605413\pi\)
−0.325146 + 0.945664i \(0.605413\pi\)
\(332\) −788.814 788.814i −2.37595 2.37595i
\(333\) −103.896 + 103.896i −0.311999 + 0.311999i
\(334\) 440.638i 1.31927i
\(335\) 2.82606 3.73076i 0.00843601 0.0111366i
\(336\) 282.966 0.842161
\(337\) −401.198 401.198i −1.19050 1.19050i −0.976927 0.213571i \(-0.931490\pi\)
−0.213571 0.976927i \(-0.568510\pi\)
\(338\) −103.143 + 103.143i −0.305157 + 0.305157i
\(339\) 15.5542i 0.0458827i
\(340\) −342.927 259.768i −1.00861 0.764024i
\(341\) −88.2602 −0.258828
\(342\) 99.8102 + 99.8102i 0.291843 + 0.291843i
\(343\) −13.0958 + 13.0958i −0.0381802 + 0.0381802i
\(344\) 504.635i 1.46696i
\(345\) 295.074 40.7138i 0.855287 0.118011i
\(346\) −417.012 −1.20524
\(347\) −122.535 122.535i −0.353126 0.353126i 0.508145 0.861271i \(-0.330331\pi\)
−0.861271 + 0.508145i \(0.830331\pi\)
\(348\) 200.156 200.156i 0.575161 0.575161i
\(349\) 18.8032i 0.0538774i 0.999637 + 0.0269387i \(0.00857589\pi\)
−0.999637 + 0.0269387i \(0.991424\pi\)
\(350\) −69.4679 246.943i −0.198480 0.705550i
\(351\) 59.5610 0.169690
\(352\) −1006.90 1006.90i −2.86050 2.86050i
\(353\) 242.291 242.291i 0.686377 0.686377i −0.275052 0.961429i \(-0.588695\pi\)
0.961429 + 0.275052i \(0.0886951\pi\)
\(354\) 298.364i 0.842837i
\(355\) −70.6850 512.291i −0.199113 1.44307i
\(356\) −459.961 −1.29202
\(357\) 25.2508 + 25.2508i 0.0707305 + 0.0707305i
\(358\) 199.655 199.655i 0.557697 0.557697i
\(359\) 228.420i 0.636268i 0.948046 + 0.318134i \(0.103056\pi\)
−0.948046 + 0.318134i \(0.896944\pi\)
\(360\) 247.348 326.531i 0.687078 0.907030i
\(361\) 213.821 0.592301
\(362\) 318.176 + 318.176i 0.878938 + 0.878938i
\(363\) 1.79750 1.79750i 0.00495180 0.00495180i
\(364\) 334.855i 0.919931i
\(365\) 311.120 + 235.674i 0.852383 + 0.645682i
\(366\) 567.253 1.54987
\(367\) 490.375 + 490.375i 1.33617 + 1.33617i 0.899735 + 0.436437i \(0.143760\pi\)
0.436437 + 0.899735i \(0.356240\pi\)
\(368\) −1501.78 + 1501.78i −4.08092 + 4.08092i
\(369\) 96.2925i 0.260955i
\(370\) −940.831 + 129.814i −2.54279 + 0.350849i
\(371\) 25.3138 0.0682314
\(372\) 109.168 + 109.168i 0.293462 + 0.293462i
\(373\) 282.198 282.198i 0.756562 0.756562i −0.219133 0.975695i \(-0.570323\pi\)
0.975695 + 0.219133i \(0.0703229\pi\)
\(374\) 330.422i 0.883480i
\(375\) −201.535 79.1111i −0.537427 0.210963i
\(376\) 2091.92 5.56362
\(377\) 119.967 + 119.967i 0.318215 + 0.318215i
\(378\) −37.7017 + 37.7017i −0.0997400 + 0.0997400i
\(379\) 389.970i 1.02895i 0.857507 + 0.514473i \(0.172012\pi\)
−0.857507 + 0.514473i \(0.827988\pi\)
\(380\) 91.5453 + 663.476i 0.240909 + 1.74599i
\(381\) −49.6802 −0.130394
\(382\) −368.406 368.406i −0.964412 0.964412i
\(383\) 330.663 330.663i 0.863350 0.863350i −0.128376 0.991726i \(-0.540976\pi\)
0.991726 + 0.128376i \(0.0409764\pi\)
\(384\) 831.663i 2.16579i
\(385\) 87.3313 115.288i 0.226834 0.299450i
\(386\) −27.4614 −0.0711435
\(387\) 39.1989 + 39.1989i 0.101289 + 0.101289i
\(388\) −278.806 + 278.806i −0.718572 + 0.718572i
\(389\) 491.789i 1.26424i −0.774871 0.632119i \(-0.782185\pi\)
0.774871 0.632119i \(-0.217815\pi\)
\(390\) 306.888 + 232.469i 0.786892 + 0.596073i
\(391\) −268.025 −0.685487
\(392\) −135.174 135.174i −0.344831 0.344831i
\(393\) −95.1803 + 95.1803i −0.242189 + 0.242189i
\(394\) 1136.56i 2.88468i
\(395\) 340.772 47.0191i 0.862714 0.119036i
\(396\) 362.152 0.914526
\(397\) 546.007 + 546.007i 1.37533 + 1.37533i 0.852333 + 0.523000i \(0.175187\pi\)
0.523000 + 0.852333i \(0.324813\pi\)
\(398\) −317.299 + 317.299i −0.797234 + 0.797234i
\(399\) 55.5947i 0.139335i
\(400\) 1486.03 418.037i 3.71507 1.04509i
\(401\) −631.914 −1.57585 −0.787923 0.615774i \(-0.788843\pi\)
−0.787923 + 0.615774i \(0.788843\pi\)
\(402\) −4.44626 4.44626i −0.0110603 0.0110603i
\(403\) −65.4316 + 65.4316i −0.162361 + 0.162361i
\(404\) 593.230i 1.46839i
\(405\) 6.15075 + 44.5777i 0.0151870 + 0.110068i
\(406\) −151.876 −0.374080
\(407\) −378.634 378.634i −0.930304 0.930304i
\(408\) −260.636 + 260.636i −0.638815 + 0.638815i
\(409\) 72.2476i 0.176645i 0.996092 + 0.0883223i \(0.0281505\pi\)
−0.996092 + 0.0883223i \(0.971849\pi\)
\(410\) 375.833 496.147i 0.916665 1.21011i
\(411\) −359.757 −0.875321
\(412\) 438.121 + 438.121i 1.06340 + 1.06340i
\(413\) 83.0950 83.0950i 0.201199 0.201199i
\(414\) 400.186i 0.966633i
\(415\) 402.677 + 305.029i 0.970305 + 0.735009i
\(416\) −1492.92 −3.58876
\(417\) −179.207 179.207i −0.429754 0.429754i
\(418\) −363.744 + 363.744i −0.870202 + 0.870202i
\(419\) 334.155i 0.797506i −0.917058 0.398753i \(-0.869443\pi\)
0.917058 0.398753i \(-0.130557\pi\)
\(420\) −250.618 + 34.5798i −0.596709 + 0.0823328i
\(421\) 316.485 0.751746 0.375873 0.926671i \(-0.377343\pi\)
0.375873 + 0.926671i \(0.377343\pi\)
\(422\) 181.581 + 181.581i 0.430286 + 0.430286i
\(423\) −162.496 + 162.496i −0.384151 + 0.384151i
\(424\) 261.287i 0.616243i
\(425\) 169.911 + 95.3033i 0.399791 + 0.224243i
\(426\) −694.781 −1.63094
\(427\) −157.981 157.981i −0.369979 0.369979i
\(428\) 754.924 754.924i 1.76384 1.76384i
\(429\) 217.062i 0.505972i
\(430\) 48.9777 + 354.967i 0.113902 + 0.825505i
\(431\) −431.234 −1.00054 −0.500272 0.865869i \(-0.666766\pi\)
−0.500272 + 0.865869i \(0.666766\pi\)
\(432\) −226.878 226.878i −0.525180 0.525180i
\(433\) −13.1404 + 13.1404i −0.0303474 + 0.0303474i −0.722118 0.691770i \(-0.756831\pi\)
0.691770 + 0.722118i \(0.256831\pi\)
\(434\) 82.8355i 0.190865i
\(435\) −77.3989 + 102.176i −0.177929 + 0.234888i
\(436\) −1495.84 −3.43084
\(437\) 295.056 + 295.056i 0.675185 + 0.675185i
\(438\) 370.787 370.787i 0.846546 0.846546i
\(439\) 426.469i 0.971457i 0.874110 + 0.485728i \(0.161446\pi\)
−0.874110 + 0.485728i \(0.838554\pi\)
\(440\) 1190.00 + 901.425i 2.70454 + 2.04869i
\(441\) 21.0000 0.0476190
\(442\) −244.958 244.958i −0.554203 0.554203i
\(443\) 334.181 334.181i 0.754360 0.754360i −0.220930 0.975290i \(-0.570909\pi\)
0.975290 + 0.220930i \(0.0709093\pi\)
\(444\) 936.655i 2.10958i
\(445\) 206.333 28.4694i 0.463669 0.0639762i
\(446\) −281.721 −0.631662
\(447\) 175.412 + 175.412i 0.392420 + 0.392420i
\(448\) 482.927 482.927i 1.07796 1.07796i
\(449\) 463.309i 1.03187i −0.856628 0.515935i \(-0.827445\pi\)
0.856628 0.515935i \(-0.172555\pi\)
\(450\) −142.296 + 253.693i −0.316214 + 0.563762i
\(451\) 350.925 0.778104
\(452\) 70.1132 + 70.1132i 0.155118 + 0.155118i
\(453\) −250.374 + 250.374i −0.552702 + 0.552702i
\(454\) 586.007i 1.29076i
\(455\) −20.7260 150.212i −0.0455516 0.330136i
\(456\) 573.843 1.25843
\(457\) 356.971 + 356.971i 0.781119 + 0.781119i 0.980020 0.198901i \(-0.0637372\pi\)
−0.198901 + 0.980020i \(0.563737\pi\)
\(458\) 242.264 242.264i 0.528960 0.528960i
\(459\) 40.4914i 0.0882165i
\(460\) 1146.57 1513.62i 2.49255 3.29048i
\(461\) −126.296 −0.273960 −0.136980 0.990574i \(-0.543740\pi\)
−0.136980 + 0.990574i \(0.543740\pi\)
\(462\) −137.399 137.399i −0.297400 0.297400i
\(463\) −40.0934 + 40.0934i −0.0865947 + 0.0865947i −0.749077 0.662483i \(-0.769503\pi\)
0.662483 + 0.749077i \(0.269503\pi\)
\(464\) 913.947i 1.96971i
\(465\) −55.7284 42.2144i −0.119846 0.0907837i
\(466\) −1429.06 −3.06666
\(467\) 494.819 + 494.819i 1.05957 + 1.05957i 0.998110 + 0.0614589i \(0.0195753\pi\)
0.0614589 + 0.998110i \(0.480425\pi\)
\(468\) 268.481 268.481i 0.573678 0.573678i
\(469\) 2.47658i 0.00528056i
\(470\) −1471.49 + 203.033i −3.13082 + 0.431985i
\(471\) 413.780 0.878513
\(472\) 857.699 + 857.699i 1.81716 + 1.81716i
\(473\) −142.855 + 142.855i −0.302019 + 0.302019i
\(474\) 462.163i 0.975027i
\(475\) −82.1322 291.961i −0.172910 0.614655i
\(476\) 227.644 0.478244
\(477\) −20.2962 20.2962i −0.0425497 0.0425497i
\(478\) −456.083 + 456.083i −0.954149 + 0.954149i
\(479\) 854.008i 1.78290i 0.453121 + 0.891449i \(0.350311\pi\)
−0.453121 + 0.891449i \(0.649689\pi\)
\(480\) −154.171 1117.36i −0.321190 2.32783i
\(481\) −561.399 −1.16715
\(482\) −850.039 850.039i −1.76357 1.76357i
\(483\) −111.453 + 111.453i −0.230751 + 0.230751i
\(484\) 16.2051i 0.0334816i
\(485\) 107.812 142.326i 0.222293 0.293455i
\(486\) 60.4572 0.124398
\(487\) 401.669 + 401.669i 0.824782 + 0.824782i 0.986790 0.162007i \(-0.0517968\pi\)
−0.162007 + 0.986790i \(0.551797\pi\)
\(488\) 1630.66 1630.66i 3.34153 3.34153i
\(489\) 409.979i 0.838403i
\(490\) 108.202 + 81.9637i 0.220821 + 0.167273i
\(491\) −250.314 −0.509805 −0.254903 0.966967i \(-0.582043\pi\)
−0.254903 + 0.966967i \(0.582043\pi\)
\(492\) −434.054 434.054i −0.882224 0.882224i
\(493\) 81.5571 81.5571i 0.165430 0.165430i
\(494\) 539.323i 1.09175i
\(495\) −162.457 + 22.4155i −0.328196 + 0.0452839i
\(496\) 498.480 1.00500
\(497\) 193.498 + 193.498i 0.389332 + 0.389332i
\(498\) 479.903 479.903i 0.963661 0.963661i
\(499\) 293.789i 0.588756i 0.955689 + 0.294378i \(0.0951125\pi\)
−0.955689 + 0.294378i \(0.904888\pi\)
\(500\) −1265.06 + 551.847i −2.53012 + 1.10369i
\(501\) −196.787 −0.392789
\(502\) −1107.13 1107.13i −2.20544 2.20544i
\(503\) −301.845 + 301.845i −0.600090 + 0.600090i −0.940336 0.340246i \(-0.889490\pi\)
0.340246 + 0.940336i \(0.389490\pi\)
\(504\) 216.760i 0.430079i
\(505\) −36.7182 266.116i −0.0727093 0.526962i
\(506\) 1458.42 2.88226
\(507\) −46.0633 46.0633i −0.0908546 0.0908546i
\(508\) −223.942 + 223.942i −0.440830 + 0.440830i
\(509\) 495.550i 0.973575i −0.873520 0.486787i \(-0.838169\pi\)
0.873520 0.486787i \(-0.161831\pi\)
\(510\) 158.039 208.632i 0.309881 0.409082i
\(511\) −206.530 −0.404168
\(512\) 917.219 + 917.219i 1.79144 + 1.79144i
\(513\) −44.5749 + 44.5749i −0.0868906 + 0.0868906i
\(514\) 599.544i 1.16643i
\(515\) −223.654 169.418i −0.434279 0.328968i
\(516\) 353.391 0.684867
\(517\) −592.194 592.194i −1.14544 1.14544i
\(518\) 355.362 355.362i 0.686027 0.686027i
\(519\) 186.236i 0.358837i
\(520\) 1550.47 213.931i 2.98168 0.411407i
\(521\) 375.437 0.720609 0.360304 0.932835i \(-0.382673\pi\)
0.360304 + 0.932835i \(0.382673\pi\)
\(522\) 121.772 + 121.772i 0.233280 + 0.233280i
\(523\) −671.097 + 671.097i −1.28317 + 1.28317i −0.344314 + 0.938855i \(0.611889\pi\)
−0.938855 + 0.344314i \(0.888111\pi\)
\(524\) 858.082i 1.63756i
\(525\) 110.284 31.0241i 0.210064 0.0590936i
\(526\) 1137.78 2.16308
\(527\) 44.4824 + 44.4824i 0.0844068 + 0.0844068i
\(528\) 826.825 826.825i 1.56596 1.56596i
\(529\) 654.018i 1.23633i
\(530\) −25.3594 183.793i −0.0478480 0.346779i
\(531\) −133.248 −0.250939
\(532\) −250.602 250.602i −0.471057 0.471057i
\(533\) 260.158 260.158i 0.488101 0.488101i
\(534\) 279.833i 0.524032i
\(535\) −291.924 + 385.376i −0.545651 + 0.720329i
\(536\) −25.5631 −0.0476923
\(537\) 89.1654 + 89.1654i 0.166044 + 0.166044i
\(538\) 86.4331 86.4331i 0.160656 0.160656i
\(539\) 76.5316i 0.141988i
\(540\) 228.667 + 173.216i 0.423457 + 0.320770i
\(541\) 557.721 1.03091 0.515454 0.856917i \(-0.327623\pi\)
0.515454 + 0.856917i \(0.327623\pi\)
\(542\) −254.084 254.084i −0.468790 0.468790i
\(543\) −142.096 + 142.096i −0.261687 + 0.261687i
\(544\) 1014.93i 1.86569i
\(545\) 671.018 92.5858i 1.23123 0.169882i
\(546\) −203.721 −0.373115
\(547\) −656.108 656.108i −1.19947 1.19947i −0.974326 0.225141i \(-0.927716\pi\)
−0.225141 0.974326i \(-0.572284\pi\)
\(548\) −1621.66 + 1621.66i −2.95924 + 2.95924i
\(549\) 253.333i 0.461445i
\(550\) −924.548 518.579i −1.68100 0.942871i
\(551\) −179.564 −0.325888
\(552\) −1150.40 1150.40i −2.08406 2.08406i
\(553\) −128.713 + 128.713i −0.232754 + 0.232754i
\(554\) 159.725i 0.288312i
\(555\) −57.9746 420.172i −0.104459 0.757067i
\(556\) −1615.61 −2.90578
\(557\) 77.0795 + 77.0795i 0.138383 + 0.138383i 0.772905 0.634522i \(-0.218803\pi\)
−0.634522 + 0.772905i \(0.718803\pi\)
\(558\) −66.4162 + 66.4162i −0.119025 + 0.119025i
\(559\) 211.811i 0.378910i
\(560\) −493.233 + 651.130i −0.880773 + 1.16273i
\(561\) 147.565 0.263040
\(562\) −511.745 511.745i −0.910579 0.910579i
\(563\) 100.072 100.072i 0.177747 0.177747i −0.612626 0.790373i \(-0.709887\pi\)
0.790373 + 0.612626i \(0.209887\pi\)
\(564\) 1464.95i 2.59744i
\(565\) −35.7916 27.1123i −0.0633480 0.0479863i
\(566\) 1096.06 1.93650
\(567\) −16.8375 16.8375i −0.0296957 0.0296957i
\(568\) −1997.27 + 1997.27i −3.51631 + 3.51631i
\(569\) 73.3966i 0.128992i 0.997918 + 0.0644961i \(0.0205440\pi\)
−0.997918 + 0.0644961i \(0.979456\pi\)
\(570\) −403.649 + 55.6948i −0.708157 + 0.0977102i
\(571\) −131.618 −0.230504 −0.115252 0.993336i \(-0.536768\pi\)
−0.115252 + 0.993336i \(0.536768\pi\)
\(572\) 978.442 + 978.442i 1.71056 + 1.71056i
\(573\) 164.529 164.529i 0.287136 0.287136i
\(574\) 329.356i 0.573791i
\(575\) −420.652 + 749.959i −0.731568 + 1.30428i
\(576\) −774.407 −1.34446
\(577\) −614.754 614.754i −1.06543 1.06543i −0.997704 0.0677285i \(-0.978425\pi\)
−0.0677285 0.997704i \(-0.521575\pi\)
\(578\) 626.023 626.023i 1.08308 1.08308i
\(579\) 12.2642i 0.0211816i
\(580\) 111.689 + 809.465i 0.192566 + 1.39563i
\(581\) −267.308 −0.460082
\(582\) −169.622 169.622i −0.291446 0.291446i
\(583\) 73.9668 73.9668i 0.126873 0.126873i
\(584\) 2131.78i 3.65031i
\(585\) −103.820 + 137.055i −0.177470 + 0.234282i
\(586\) −650.803 −1.11059
\(587\) −328.506 328.506i −0.559636 0.559636i 0.369568 0.929204i \(-0.379506\pi\)
−0.929204 + 0.369568i \(0.879506\pi\)
\(588\) 94.6609 94.6609i 0.160988 0.160988i
\(589\) 97.9368i 0.166276i
\(590\) −686.562 520.073i −1.16366 0.881480i
\(591\) 507.586 0.858860
\(592\) 2138.46 + 2138.46i 3.61227 + 3.61227i
\(593\) −46.4495 + 46.4495i −0.0783298 + 0.0783298i −0.745186 0.666856i \(-0.767639\pi\)
0.666856 + 0.745186i \(0.267639\pi\)
\(594\) 220.328i 0.370923i
\(595\) −102.118 + 14.0901i −0.171628 + 0.0236809i
\(596\) 1581.39 2.65334
\(597\) −141.705 141.705i −0.237361 0.237361i
\(598\) 1081.20 1081.20i 1.80803 1.80803i
\(599\) 256.090i 0.427529i 0.976885 + 0.213764i \(0.0685724\pi\)
−0.976885 + 0.213764i \(0.931428\pi\)
\(600\) 320.228 + 1138.34i 0.533714 + 1.89723i
\(601\) 433.545 0.721372 0.360686 0.932687i \(-0.382543\pi\)
0.360686 + 0.932687i \(0.382543\pi\)
\(602\) −134.075 134.075i −0.222716 0.222716i
\(603\) 1.98568 1.98568i 0.00329301 0.00329301i
\(604\) 2257.20i 3.73709i
\(605\) 1.00302 + 7.26941i 0.00165788 + 0.0120156i
\(606\) −360.913 −0.595565
\(607\) 788.344 + 788.344i 1.29875 + 1.29875i 0.929215 + 0.369540i \(0.120485\pi\)
0.369540 + 0.929215i \(0.379515\pi\)
\(608\) 1117.29 1117.29i 1.83765 1.83765i
\(609\) 67.8275i 0.111375i
\(610\) −988.767 + 1305.30i −1.62093 + 2.13983i
\(611\) −878.045 −1.43706
\(612\) −182.521 182.521i −0.298238 0.298238i
\(613\) 143.879 143.879i 0.234712 0.234712i −0.579944 0.814656i \(-0.696926\pi\)
0.814656 + 0.579944i \(0.196926\pi\)
\(614\) 1730.96i 2.81916i
\(615\) 221.577 + 167.846i 0.360289 + 0.272920i
\(616\) −789.952 −1.28239
\(617\) −280.216 280.216i −0.454159 0.454159i 0.442573 0.896732i \(-0.354066\pi\)
−0.896732 + 0.442573i \(0.854066\pi\)
\(618\) −266.547 + 266.547i −0.431305 + 0.431305i
\(619\) 438.884i 0.709020i −0.935052 0.354510i \(-0.884648\pi\)
0.935052 0.354510i \(-0.115352\pi\)
\(620\) −441.493 + 60.9165i −0.712086 + 0.0982524i
\(621\) 178.722 0.287797
\(622\) 1562.35 + 1562.35i 2.51181 + 2.51181i
\(623\) −77.9341 + 77.9341i −0.125095 + 0.125095i
\(624\) 1225.93i 1.96463i
\(625\) 533.334 325.853i 0.853334 0.521365i
\(626\) 1219.70 1.94840
\(627\) −162.447 162.447i −0.259086 0.259086i
\(628\) 1865.18 1865.18i 2.97003 2.97003i
\(629\) 381.656i 0.606766i
\(630\) −21.0378 152.472i −0.0333934 0.242019i
\(631\) 601.250 0.952852 0.476426 0.879215i \(-0.341932\pi\)
0.476426 + 0.879215i \(0.341932\pi\)
\(632\) −1328.57 1328.57i −2.10216 2.10216i
\(633\) −81.0933 + 81.0933i −0.128109 + 0.128109i
\(634\) 1005.88i 1.58656i
\(635\) 86.5966 114.319i 0.136373 0.180029i
\(636\) −182.977 −0.287700
\(637\) 56.7366 + 56.7366i 0.0890685 + 0.0890685i
\(638\) −443.781 + 443.781i −0.695582 + 0.695582i
\(639\) 310.287i 0.485582i
\(640\) −1913.73 1449.66i −2.99020 2.26509i
\(641\) 803.007 1.25274 0.626371 0.779525i \(-0.284540\pi\)
0.626371 + 0.779525i \(0.284540\pi\)
\(642\) 459.285 + 459.285i 0.715397 + 0.715397i
\(643\) −164.070 + 164.070i −0.255163 + 0.255163i −0.823084 0.567920i \(-0.807748\pi\)
0.567920 + 0.823084i \(0.307748\pi\)
\(644\) 1004.78i 1.56022i
\(645\) −158.527 + 21.8733i −0.245778 + 0.0339121i
\(646\) 366.648 0.567566
\(647\) 495.936 + 495.936i 0.766517 + 0.766517i 0.977491 0.210975i \(-0.0676638\pi\)
−0.210975 + 0.977491i \(0.567664\pi\)
\(648\) 173.795 173.795i 0.268202 0.268202i
\(649\) 485.606i 0.748237i
\(650\) −1069.86 + 300.965i −1.64594 + 0.463023i
\(651\) 36.9941 0.0568265
\(652\) 1848.05 + 1848.05i 2.83443 + 2.83443i
\(653\) −812.931 + 812.931i −1.24492 + 1.24492i −0.286982 + 0.957936i \(0.592652\pi\)
−0.957936 + 0.286982i \(0.907348\pi\)
\(654\) 910.050i 1.39151i
\(655\) −53.1113 384.925i −0.0810859 0.587672i
\(656\) −1981.97 −3.02129
\(657\) 165.592 + 165.592i 0.252043 + 0.252043i
\(658\) 555.796 555.796i 0.844675 0.844675i
\(659\) 135.081i 0.204979i 0.994734 + 0.102490i \(0.0326808\pi\)
−0.994734 + 0.102490i \(0.967319\pi\)
\(660\) −631.260 + 833.344i −0.956455 + 1.26264i
\(661\) −128.892 −0.194996 −0.0974980 0.995236i \(-0.531084\pi\)
−0.0974980 + 0.995236i \(0.531084\pi\)
\(662\) −590.291 590.291i −0.891678 0.891678i
\(663\) 109.397 109.397i 0.165003 0.165003i
\(664\) 2759.13i 4.15531i
\(665\) 127.928 + 96.9060i 0.192373 + 0.145723i
\(666\) −569.847 −0.855626
\(667\) 359.979 + 359.979i 0.539698 + 0.539698i
\(668\) −887.051 + 887.051i −1.32792 + 1.32792i
\(669\) 125.816i 0.188065i
\(670\) 17.9814 2.48104i 0.0268379 0.00370305i
\(671\) −923.237 −1.37591
\(672\) 422.038 + 422.038i 0.628033 + 0.628033i
\(673\) −217.545 + 217.545i −0.323246 + 0.323246i −0.850011 0.526765i \(-0.823405\pi\)
0.526765 + 0.850011i \(0.323405\pi\)
\(674\) 2200.49i 3.26482i
\(675\) −113.298 63.5491i −0.167849 0.0941468i
\(676\) −415.276 −0.614313
\(677\) −601.143 601.143i −0.887952 0.887952i 0.106374 0.994326i \(-0.466076\pi\)
−0.994326 + 0.106374i \(0.966076\pi\)
\(678\) −42.6558 + 42.6558i −0.0629142 + 0.0629142i
\(679\) 94.4798i 0.139146i
\(680\) −145.437 1054.06i −0.213878 1.55008i
\(681\) 261.709 0.384301
\(682\) −242.045 242.045i −0.354904 0.354904i
\(683\) −16.6370 + 16.6370i −0.0243587 + 0.0243587i −0.719181 0.694823i \(-0.755483\pi\)
0.694823 + 0.719181i \(0.255483\pi\)
\(684\) 401.857i 0.587511i
\(685\) 627.086 827.833i 0.915453 1.20851i
\(686\) −71.8278 −0.104705
\(687\) 108.194 + 108.194i 0.157488 + 0.157488i
\(688\) 806.823 806.823i 1.17271 1.17271i
\(689\) 109.670i 0.159173i
\(690\) 920.863 + 697.557i 1.33458 + 1.01095i
\(691\) 333.673 0.482884 0.241442 0.970415i \(-0.422380\pi\)
0.241442 + 0.970415i \(0.422380\pi\)
\(692\) −839.490 839.490i −1.21314 1.21314i
\(693\) 61.3618 61.3618i 0.0885451 0.0885451i
\(694\) 672.077i 0.968411i
\(695\) 724.745 99.9990i 1.04280 0.143883i
\(696\) 700.109 1.00590
\(697\) −176.863 176.863i −0.253749 0.253749i
\(698\) −51.5659 + 51.5659i −0.0738766 + 0.0738766i
\(699\) 638.215i 0.913040i
\(700\) 357.276 636.968i 0.510394 0.909955i
\(701\) 978.544 1.39593 0.697963 0.716134i \(-0.254090\pi\)
0.697963 + 0.716134i \(0.254090\pi\)
\(702\) 163.340 + 163.340i 0.232678 + 0.232678i
\(703\) 420.146 420.146i 0.597647 0.597647i
\(704\) 2822.22i 4.00883i
\(705\) −90.6739 657.161i −0.128615 0.932143i
\(706\) 1328.92 1.88232
\(707\) 100.515 + 100.515i 0.142171 + 0.142171i
\(708\) −600.639 + 600.639i −0.848361 + 0.848361i
\(709\) 775.664i 1.09402i 0.837125 + 0.547012i \(0.184235\pi\)
−0.837125 + 0.547012i \(0.815765\pi\)
\(710\) 1211.06 1598.75i 1.70572 2.25176i
\(711\) 206.400 0.290296
\(712\) −804.428 804.428i −1.12982 1.12982i
\(713\) −196.337 + 196.337i −0.275368 + 0.275368i
\(714\) 138.495i 0.193971i
\(715\) −499.478 378.356i −0.698571 0.529170i
\(716\) 803.856 1.12270
\(717\) −203.685 203.685i −0.284080 0.284080i
\(718\) −626.419 + 626.419i −0.872450 + 0.872450i
\(719\) 195.183i 0.271464i −0.990746 0.135732i \(-0.956661\pi\)
0.990746 0.135732i \(-0.0433386\pi\)
\(720\) 917.532 126.599i 1.27435 0.175832i
\(721\) 148.467 0.205919
\(722\) 586.381 + 586.381i 0.812162 + 0.812162i
\(723\) 379.624 379.624i 0.525068 0.525068i
\(724\) 1281.04i 1.76940i
\(725\) −100.204 356.203i −0.138213 0.491315i
\(726\) 9.85894 0.0135798
\(727\) −127.418 127.418i −0.175265 0.175265i 0.614023 0.789288i \(-0.289550\pi\)
−0.789288 + 0.614023i \(0.789550\pi\)
\(728\) −585.630 + 585.630i −0.804437 + 0.804437i
\(729\) 27.0000i 0.0370370i
\(730\) 206.902 + 1499.53i 0.283427 + 2.05414i
\(731\) 143.995 0.196984
\(732\) 1141.94 + 1141.94i 1.56003 + 1.56003i
\(733\) −657.079 + 657.079i −0.896425 + 0.896425i −0.995118 0.0986932i \(-0.968534\pi\)
0.0986932 + 0.995118i \(0.468534\pi\)
\(734\) 2689.61i 3.66431i
\(735\) −36.6047 + 48.3228i −0.0498023 + 0.0657454i
\(736\) −4479.74 −6.08660
\(737\) 7.23655 + 7.23655i 0.00981893 + 0.00981893i
\(738\) 264.072 264.072i 0.357821 0.357821i
\(739\) 1191.53i 1.61235i 0.591676 + 0.806176i \(0.298466\pi\)
−0.591676 + 0.806176i \(0.701534\pi\)
\(740\) −2155.32 1632.66i −2.91260 2.20630i
\(741\) −240.860 −0.325047
\(742\) 69.4206 + 69.4206i 0.0935588 + 0.0935588i
\(743\) 115.268 115.268i 0.155138 0.155138i −0.625270 0.780408i \(-0.715011\pi\)
0.780408 + 0.625270i \(0.215011\pi\)
\(744\) 381.849i 0.513238i
\(745\) −709.394 + 97.8809i −0.952207 + 0.131384i
\(746\) 1547.79 2.07479
\(747\) 214.323 + 214.323i 0.286912 + 0.286912i
\(748\) 665.174 665.174i 0.889270 0.889270i
\(749\) 255.823i 0.341553i
\(750\) −335.735 769.643i −0.447647 1.02619i
\(751\) −627.744 −0.835878 −0.417939 0.908475i \(-0.637247\pi\)
−0.417939 + 0.908475i \(0.637247\pi\)
\(752\) 3344.62 + 3344.62i 4.44763 + 4.44763i
\(753\) 494.440 494.440i 0.656627 0.656627i
\(754\) 657.994i 0.872671i
\(755\) −139.710 1012.55i −0.185047 1.34113i
\(756\) −151.795 −0.200787
\(757\) 117.159 + 117.159i 0.154767 + 0.154767i 0.780243 0.625476i \(-0.215095\pi\)
−0.625476 + 0.780243i \(0.715095\pi\)
\(758\) −1069.45 + 1069.45i −1.41089 + 1.41089i
\(759\) 651.327i 0.858138i
\(760\) −1000.25 + 1320.46i −1.31612 + 1.73745i
\(761\) 1272.61 1.67229 0.836145 0.548509i \(-0.184804\pi\)
0.836145 + 0.548509i \(0.184804\pi\)
\(762\) −136.243 136.243i −0.178796 0.178796i
\(763\) −253.451 + 253.451i −0.332176 + 0.332176i
\(764\) 1483.28i 1.94147i
\(765\) 93.1742 + 70.5797i 0.121796 + 0.0922610i
\(766\) 1813.62 2.36765
\(767\) −360.003 360.003i −0.469365 0.469365i
\(768\) −1016.15 + 1016.15i −1.32311 + 1.32311i
\(769\) 1506.02i 1.95842i −0.202857 0.979208i \(-0.565022\pi\)
0.202857 0.979208i \(-0.434978\pi\)
\(770\) 555.663 76.6694i 0.721641 0.0995707i
\(771\) −267.754 −0.347282
\(772\) −55.2827 55.2827i −0.0716097 0.0716097i
\(773\)