Properties

Label 105.3.l.a.22.1
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 22.1
Character \(\chi\) \(=\) 105.22
Dual form 105.3.l.a.43.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.72310 - 2.72310i) q^{2} +(-1.22474 + 1.22474i) q^{3} +10.8306i q^{4} +(4.39513 - 2.38387i) q^{5} +6.67022 q^{6} +(-1.87083 - 1.87083i) q^{7} +(18.6004 - 18.6004i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-2.72310 - 2.72310i) q^{2} +(-1.22474 + 1.22474i) q^{3} +10.8306i q^{4} +(4.39513 - 2.38387i) q^{5} +6.67022 q^{6} +(-1.87083 - 1.87083i) q^{7} +(18.6004 - 18.6004i) q^{8} -3.00000i q^{9} +(-18.4599 - 5.47689i) q^{10} +3.42164 q^{11} +(-13.2647 - 13.2647i) q^{12} +(7.98120 - 7.98120i) q^{13} +10.1889i q^{14} +(-2.46329 + 8.30254i) q^{15} -57.9794 q^{16} +(-16.5713 - 16.5713i) q^{17} +(-8.16931 + 8.16931i) q^{18} +1.38069i q^{19} +(25.8187 + 47.6019i) q^{20} +4.58258 q^{21} +(-9.31750 - 9.31750i) q^{22} +(18.8473 - 18.8473i) q^{23} +45.5616i q^{24} +(13.6344 - 20.9548i) q^{25} -43.4673 q^{26} +(3.67423 + 3.67423i) q^{27} +(20.2622 - 20.2622i) q^{28} -45.7370i q^{29} +(29.3165 - 15.9009i) q^{30} +43.2632 q^{31} +(83.4823 + 83.4823i) q^{32} +(-4.19064 + 4.19064i) q^{33} +90.2505i q^{34} +(-12.6823 - 3.76274i) q^{35} +32.4918 q^{36} +(2.18941 + 2.18941i) q^{37} +(3.75977 - 3.75977i) q^{38} +19.5499i q^{39} +(37.4104 - 126.092i) q^{40} +6.61005 q^{41} +(-12.4788 - 12.4788i) q^{42} +(-44.1187 + 44.1187i) q^{43} +37.0585i q^{44} +(-7.15160 - 13.1854i) q^{45} -102.646 q^{46} +(14.2193 + 14.2193i) q^{47} +(71.0100 - 71.0100i) q^{48} +7.00000i q^{49} +(-94.1899 + 19.9343i) q^{50} +40.5911 q^{51} +(86.4412 + 86.4412i) q^{52} +(-44.4359 + 44.4359i) q^{53} -20.0106i q^{54} +(15.0386 - 8.15674i) q^{55} -69.5964 q^{56} +(-1.69100 - 1.69100i) q^{57} +(-124.547 + 124.547i) q^{58} +17.2928i q^{59} +(-89.9215 - 26.6789i) q^{60} +48.0848 q^{61} +(-117.810 - 117.810i) q^{62} +(-5.61249 + 5.61249i) q^{63} -222.745i q^{64} +(16.0523 - 54.1046i) q^{65} +22.8231 q^{66} +(40.9435 + 40.9435i) q^{67} +(179.477 - 179.477i) q^{68} +46.1662i q^{69} +(24.2890 + 44.7817i) q^{70} -38.7743 q^{71} +(-55.8013 - 55.8013i) q^{72} +(66.4788 - 66.4788i) q^{73} -11.9240i q^{74} +(8.96566 + 42.3629i) q^{75} -14.9537 q^{76} +(-6.40131 - 6.40131i) q^{77} +(53.2363 - 53.2363i) q^{78} -5.30864i q^{79} +(-254.827 + 138.215i) q^{80} -9.00000 q^{81} +(-17.9999 - 17.9999i) q^{82} +(-62.5835 + 62.5835i) q^{83} +49.6320i q^{84} +(-112.337 - 33.3292i) q^{85} +240.280 q^{86} +(56.0161 + 56.0161i) q^{87} +(63.6441 - 63.6441i) q^{88} +44.8163i q^{89} +(-16.4307 + 55.3798i) q^{90} -29.8629 q^{91} +(204.127 + 204.127i) q^{92} +(-52.9864 + 52.9864i) q^{93} -77.4411i q^{94} +(3.29139 + 6.06833i) q^{95} -204.489 q^{96} +(-30.5196 - 30.5196i) q^{97} +(19.0617 - 19.0617i) q^{98} -10.2649i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.72310 2.72310i −1.36155 1.36155i −0.871941 0.489612i \(-0.837139\pi\)
−0.489612 0.871941i \(-0.662861\pi\)
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 10.8306i 2.70765i
\(5\) 4.39513 2.38387i 0.879026 0.476773i
\(6\) 6.67022 1.11170
\(7\) −1.87083 1.87083i −0.267261 0.267261i
\(8\) 18.6004 18.6004i 2.32505 2.32505i
\(9\) 3.00000i 0.333333i
\(10\) −18.4599 5.47689i −1.84599 0.547689i
\(11\) 3.42164 0.311059 0.155529 0.987831i \(-0.450292\pi\)
0.155529 + 0.987831i \(0.450292\pi\)
\(12\) −13.2647 13.2647i −1.10539 1.10539i
\(13\) 7.98120 7.98120i 0.613939 0.613939i −0.330031 0.943970i \(-0.607059\pi\)
0.943970 + 0.330031i \(0.107059\pi\)
\(14\) 10.1889i 0.727780i
\(15\) −2.46329 + 8.30254i −0.164219 + 0.553503i
\(16\) −57.9794 −3.62371
\(17\) −16.5713 16.5713i −0.974780 0.974780i 0.0249097 0.999690i \(-0.492070\pi\)
−0.999690 + 0.0249097i \(0.992070\pi\)
\(18\) −8.16931 + 8.16931i −0.453851 + 0.453851i
\(19\) 1.38069i 0.0726681i 0.999340 + 0.0363341i \(0.0115680\pi\)
−0.999340 + 0.0363341i \(0.988432\pi\)
\(20\) 25.8187 + 47.6019i 1.29093 + 2.38010i
\(21\) 4.58258 0.218218
\(22\) −9.31750 9.31750i −0.423523 0.423523i
\(23\) 18.8473 18.8473i 0.819447 0.819447i −0.166581 0.986028i \(-0.553273\pi\)
0.986028 + 0.166581i \(0.0532728\pi\)
\(24\) 45.5616i 1.89840i
\(25\) 13.6344 20.9548i 0.545375 0.838192i
\(26\) −43.4673 −1.67182
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 20.2622 20.2622i 0.723650 0.723650i
\(29\) 45.7370i 1.57714i −0.614947 0.788568i \(-0.710823\pi\)
0.614947 0.788568i \(-0.289177\pi\)
\(30\) 29.3165 15.9009i 0.977216 0.530030i
\(31\) 43.2632 1.39559 0.697793 0.716299i \(-0.254165\pi\)
0.697793 + 0.716299i \(0.254165\pi\)
\(32\) 83.4823 + 83.4823i 2.60882 + 2.60882i
\(33\) −4.19064 + 4.19064i −0.126989 + 0.126989i
\(34\) 90.2505i 2.65443i
\(35\) −12.6823 3.76274i −0.362353 0.107507i
\(36\) 32.4918 0.902550
\(37\) 2.18941 + 2.18941i 0.0591732 + 0.0591732i 0.736074 0.676901i \(-0.236677\pi\)
−0.676901 + 0.736074i \(0.736677\pi\)
\(38\) 3.75977 3.75977i 0.0989414 0.0989414i
\(39\) 19.5499i 0.501279i
\(40\) 37.4104 126.092i 0.935260 3.15231i
\(41\) 6.61005 0.161221 0.0806104 0.996746i \(-0.474313\pi\)
0.0806104 + 0.996746i \(0.474313\pi\)
\(42\) −12.4788 12.4788i −0.297115 0.297115i
\(43\) −44.1187 + 44.1187i −1.02602 + 1.02602i −0.0263634 + 0.999652i \(0.508393\pi\)
−0.999652 + 0.0263634i \(0.991607\pi\)
\(44\) 37.0585i 0.842238i
\(45\) −7.15160 13.1854i −0.158924 0.293009i
\(46\) −102.646 −2.23144
\(47\) 14.2193 + 14.2193i 0.302538 + 0.302538i 0.842006 0.539468i \(-0.181375\pi\)
−0.539468 + 0.842006i \(0.681375\pi\)
\(48\) 71.0100 71.0100i 1.47938 1.47938i
\(49\) 7.00000i 0.142857i
\(50\) −94.1899 + 19.9343i −1.88380 + 0.398686i
\(51\) 40.5911 0.795905
\(52\) 86.4412 + 86.4412i 1.66233 + 1.66233i
\(53\) −44.4359 + 44.4359i −0.838413 + 0.838413i −0.988650 0.150237i \(-0.951996\pi\)
0.150237 + 0.988650i \(0.451996\pi\)
\(54\) 20.0106i 0.370568i
\(55\) 15.0386 8.15674i 0.273429 0.148304i
\(56\) −69.5964 −1.24279
\(57\) −1.69100 1.69100i −0.0296666 0.0296666i
\(58\) −124.547 + 124.547i −2.14735 + 2.14735i
\(59\) 17.2928i 0.293099i 0.989203 + 0.146549i \(0.0468167\pi\)
−0.989203 + 0.146549i \(0.953183\pi\)
\(60\) −89.9215 26.6789i −1.49869 0.444648i
\(61\) 48.0848 0.788276 0.394138 0.919051i \(-0.371043\pi\)
0.394138 + 0.919051i \(0.371043\pi\)
\(62\) −117.810 117.810i −1.90016 1.90016i
\(63\) −5.61249 + 5.61249i −0.0890871 + 0.0890871i
\(64\) 222.745i 3.48038i
\(65\) 16.0523 54.1046i 0.246959 0.832378i
\(66\) 22.8231 0.345805
\(67\) 40.9435 + 40.9435i 0.611097 + 0.611097i 0.943232 0.332135i \(-0.107769\pi\)
−0.332135 + 0.943232i \(0.607769\pi\)
\(68\) 179.477 179.477i 2.63936 2.63936i
\(69\) 46.1662i 0.669075i
\(70\) 24.2890 + 44.7817i 0.346986 + 0.639738i
\(71\) −38.7743 −0.546118 −0.273059 0.961997i \(-0.588035\pi\)
−0.273059 + 0.961997i \(0.588035\pi\)
\(72\) −55.8013 55.8013i −0.775018 0.775018i
\(73\) 66.4788 66.4788i 0.910668 0.910668i −0.0856565 0.996325i \(-0.527299\pi\)
0.996325 + 0.0856565i \(0.0272988\pi\)
\(74\) 11.9240i 0.161135i
\(75\) 8.96566 + 42.3629i 0.119542 + 0.564839i
\(76\) −14.9537 −0.196760
\(77\) −6.40131 6.40131i −0.0831339 0.0831339i
\(78\) 53.2363 53.2363i 0.682517 0.682517i
\(79\) 5.30864i 0.0671980i −0.999435 0.0335990i \(-0.989303\pi\)
0.999435 0.0335990i \(-0.0106969\pi\)
\(80\) −254.827 + 138.215i −3.18534 + 1.72769i
\(81\) −9.00000 −0.111111
\(82\) −17.9999 17.9999i −0.219511 0.219511i
\(83\) −62.5835 + 62.5835i −0.754017 + 0.754017i −0.975226 0.221209i \(-0.929000\pi\)
0.221209 + 0.975226i \(0.429000\pi\)
\(84\) 49.6320i 0.590857i
\(85\) −112.337 33.3292i −1.32161 0.392109i
\(86\) 240.280 2.79395
\(87\) 56.0161 + 56.0161i 0.643863 + 0.643863i
\(88\) 63.6441 63.6441i 0.723228 0.723228i
\(89\) 44.8163i 0.503554i 0.967785 + 0.251777i \(0.0810149\pi\)
−0.967785 + 0.251777i \(0.918985\pi\)
\(90\) −16.4307 + 55.3798i −0.182563 + 0.615331i
\(91\) −29.8629 −0.328164
\(92\) 204.127 + 204.127i 2.21877 + 2.21877i
\(93\) −52.9864 + 52.9864i −0.569746 + 0.569746i
\(94\) 77.4411i 0.823842i
\(95\) 3.29139 + 6.06833i 0.0346462 + 0.0638772i
\(96\) −204.489 −2.13010
\(97\) −30.5196 30.5196i −0.314635 0.314635i 0.532067 0.846702i \(-0.321415\pi\)
−0.846702 + 0.532067i \(0.821415\pi\)
\(98\) 19.0617 19.0617i 0.194507 0.194507i
\(99\) 10.2649i 0.103686i
\(100\) 226.953 + 147.668i 2.26953 + 1.47668i
\(101\) 115.859 1.14712 0.573561 0.819163i \(-0.305561\pi\)
0.573561 + 0.819163i \(0.305561\pi\)
\(102\) −110.534 110.534i −1.08367 1.08367i
\(103\) −36.9871 + 36.9871i −0.359098 + 0.359098i −0.863480 0.504382i \(-0.831720\pi\)
0.504382 + 0.863480i \(0.331720\pi\)
\(104\) 296.908i 2.85488i
\(105\) 20.1410 10.9242i 0.191819 0.104040i
\(106\) 242.007 2.28309
\(107\) −105.863 105.863i −0.989371 0.989371i 0.0105734 0.999944i \(-0.496634\pi\)
−0.999944 + 0.0105734i \(0.996634\pi\)
\(108\) −39.7942 + 39.7942i −0.368464 + 0.368464i
\(109\) 41.7489i 0.383017i −0.981491 0.191509i \(-0.938662\pi\)
0.981491 0.191509i \(-0.0613380\pi\)
\(110\) −63.1633 18.7400i −0.574212 0.170363i
\(111\) −5.36293 −0.0483147
\(112\) 108.470 + 108.470i 0.968478 + 0.968478i
\(113\) −154.947 + 154.947i −1.37121 + 1.37121i −0.512554 + 0.858655i \(0.671300\pi\)
−0.858655 + 0.512554i \(0.828700\pi\)
\(114\) 9.20953i 0.0807853i
\(115\) 37.9069 127.766i 0.329625 1.11101i
\(116\) 495.358 4.27033
\(117\) −23.9436 23.9436i −0.204646 0.204646i
\(118\) 47.0902 47.0902i 0.399069 0.399069i
\(119\) 62.0040i 0.521042i
\(120\) 108.613 + 200.249i 0.905105 + 1.66874i
\(121\) −109.292 −0.903243
\(122\) −130.940 130.940i −1.07328 1.07328i
\(123\) −8.09563 + 8.09563i −0.0658181 + 0.0658181i
\(124\) 468.566i 3.77876i
\(125\) 9.97143 124.602i 0.0797714 0.996813i
\(126\) 30.5668 0.242593
\(127\) 84.5679 + 84.5679i 0.665889 + 0.665889i 0.956762 0.290873i \(-0.0939456\pi\)
−0.290873 + 0.956762i \(0.593946\pi\)
\(128\) −272.627 + 272.627i −2.12990 + 2.12990i
\(129\) 108.068i 0.837738i
\(130\) −191.045 + 103.620i −1.46957 + 0.797078i
\(131\) 75.1775 0.573874 0.286937 0.957949i \(-0.407363\pi\)
0.286937 + 0.957949i \(0.407363\pi\)
\(132\) −45.3872 45.3872i −0.343842 0.343842i
\(133\) 2.58304 2.58304i 0.0194214 0.0194214i
\(134\) 222.987i 1.66408i
\(135\) 24.9076 + 7.38987i 0.184501 + 0.0547397i
\(136\) −616.465 −4.53283
\(137\) −1.34004 1.34004i −0.00978134 0.00978134i 0.702199 0.711981i \(-0.252202\pi\)
−0.711981 + 0.702199i \(0.752202\pi\)
\(138\) 125.715 125.715i 0.910981 0.910981i
\(139\) 14.7459i 0.106086i 0.998592 + 0.0530429i \(0.0168920\pi\)
−0.998592 + 0.0530429i \(0.983108\pi\)
\(140\) 40.7527 137.357i 0.291090 0.981124i
\(141\) −34.8300 −0.247021
\(142\) 105.587 + 105.587i 0.743568 + 0.743568i
\(143\) 27.3088 27.3088i 0.190971 0.190971i
\(144\) 173.938i 1.20790i
\(145\) −109.031 201.020i −0.751936 1.38634i
\(146\) −362.057 −2.47984
\(147\) −8.57321 8.57321i −0.0583212 0.0583212i
\(148\) −23.7126 + 23.7126i −0.160220 + 0.160220i
\(149\) 13.4239i 0.0900930i −0.998985 0.0450465i \(-0.985656\pi\)
0.998985 0.0450465i \(-0.0143436\pi\)
\(150\) 90.9442 139.773i 0.606295 0.931821i
\(151\) −133.609 −0.884826 −0.442413 0.896811i \(-0.645877\pi\)
−0.442413 + 0.896811i \(0.645877\pi\)
\(152\) 25.6815 + 25.6815i 0.168957 + 0.168957i
\(153\) −49.7138 + 49.7138i −0.324927 + 0.324927i
\(154\) 34.8629i 0.226382i
\(155\) 190.147 103.134i 1.22676 0.665378i
\(156\) −211.737 −1.35729
\(157\) 144.591 + 144.591i 0.920959 + 0.920959i 0.997097 0.0761383i \(-0.0242590\pi\)
−0.0761383 + 0.997097i \(0.524259\pi\)
\(158\) −14.4560 + 14.4560i −0.0914936 + 0.0914936i
\(159\) 108.845i 0.684561i
\(160\) 565.927 + 167.905i 3.53704 + 1.04941i
\(161\) −70.5200 −0.438013
\(162\) 24.5079 + 24.5079i 0.151284 + 0.151284i
\(163\) 141.760 141.760i 0.869693 0.869693i −0.122746 0.992438i \(-0.539170\pi\)
0.992438 + 0.122746i \(0.0391699\pi\)
\(164\) 71.5908i 0.436529i
\(165\) −8.42850 + 28.4084i −0.0510818 + 0.172172i
\(166\) 340.843 2.05327
\(167\) 119.348 + 119.348i 0.714660 + 0.714660i 0.967506 0.252847i \(-0.0813668\pi\)
−0.252847 + 0.967506i \(0.581367\pi\)
\(168\) 85.2379 85.2379i 0.507368 0.507368i
\(169\) 41.6008i 0.246159i
\(170\) 215.145 + 396.663i 1.26556 + 2.33331i
\(171\) 4.14208 0.0242227
\(172\) −477.832 477.832i −2.77809 2.77809i
\(173\) 6.11726 6.11726i 0.0353599 0.0353599i −0.689206 0.724566i \(-0.742040\pi\)
0.724566 + 0.689206i \(0.242040\pi\)
\(174\) 305.075i 1.75331i
\(175\) −64.7104 + 13.6953i −0.369774 + 0.0782587i
\(176\) −198.385 −1.12719
\(177\) −21.1793 21.1793i −0.119657 0.119657i
\(178\) 122.039 122.039i 0.685615 0.685615i
\(179\) 234.919i 1.31240i 0.754588 + 0.656199i \(0.227837\pi\)
−0.754588 + 0.656199i \(0.772163\pi\)
\(180\) 142.806 77.4561i 0.793365 0.430311i
\(181\) 128.874 0.712013 0.356007 0.934483i \(-0.384138\pi\)
0.356007 + 0.934483i \(0.384138\pi\)
\(182\) 81.3199 + 81.3199i 0.446812 + 0.446812i
\(183\) −58.8917 + 58.8917i −0.321812 + 0.321812i
\(184\) 701.135i 3.81051i
\(185\) 14.8420 + 4.40348i 0.0802270 + 0.0238026i
\(186\) 288.575 1.55148
\(187\) −56.7010 56.7010i −0.303214 0.303214i
\(188\) −154.003 + 154.003i −0.819166 + 0.819166i
\(189\) 13.7477i 0.0727393i
\(190\) 7.56191 25.4875i 0.0397995 0.134145i
\(191\) 73.4776 0.384699 0.192350 0.981326i \(-0.438389\pi\)
0.192350 + 0.981326i \(0.438389\pi\)
\(192\) 272.805 + 272.805i 1.42086 + 1.42086i
\(193\) 120.661 120.661i 0.625187 0.625187i −0.321666 0.946853i \(-0.604243\pi\)
0.946853 + 0.321666i \(0.104243\pi\)
\(194\) 166.216i 0.856783i
\(195\) 46.6043 + 85.9243i 0.238996 + 0.440637i
\(196\) −75.8142 −0.386807
\(197\) −34.8422 34.8422i −0.176864 0.176864i 0.613123 0.789987i \(-0.289913\pi\)
−0.789987 + 0.613123i \(0.789913\pi\)
\(198\) −27.9525 + 27.9525i −0.141174 + 0.141174i
\(199\) 22.8910i 0.115030i 0.998345 + 0.0575151i \(0.0183177\pi\)
−0.998345 + 0.0575151i \(0.981682\pi\)
\(200\) −136.163 643.373i −0.680816 3.21687i
\(201\) −100.291 −0.498959
\(202\) −315.497 315.497i −1.56187 1.56187i
\(203\) −85.5660 + 85.5660i −0.421507 + 0.421507i
\(204\) 439.626i 2.15503i
\(205\) 29.0521 15.7575i 0.141717 0.0768657i
\(206\) 201.439 0.977861
\(207\) −56.5418 56.5418i −0.273149 0.273149i
\(208\) −462.746 + 462.746i −2.22474 + 2.22474i
\(209\) 4.72425i 0.0226040i
\(210\) −84.5940 25.0983i −0.402828 0.119516i
\(211\) −216.288 −1.02506 −0.512531 0.858668i \(-0.671292\pi\)
−0.512531 + 0.858668i \(0.671292\pi\)
\(212\) −481.267 481.267i −2.27013 2.27013i
\(213\) 47.4887 47.4887i 0.222952 0.222952i
\(214\) 576.550i 2.69416i
\(215\) −88.7344 + 299.080i −0.412718 + 1.39107i
\(216\) 136.685 0.632799
\(217\) −80.9380 80.9380i −0.372986 0.372986i
\(218\) −113.687 + 113.687i −0.521498 + 0.521498i
\(219\) 162.839i 0.743557i
\(220\) 88.3424 + 162.877i 0.401556 + 0.740349i
\(221\) −264.517 −1.19691
\(222\) 14.6038 + 14.6038i 0.0657830 + 0.0657830i
\(223\) −55.1194 + 55.1194i −0.247172 + 0.247172i −0.819809 0.572637i \(-0.805921\pi\)
0.572637 + 0.819809i \(0.305921\pi\)
\(224\) 312.362i 1.39447i
\(225\) −62.8644 40.9031i −0.279397 0.181792i
\(226\) 843.872 3.73395
\(227\) 163.968 + 163.968i 0.722327 + 0.722327i 0.969079 0.246752i \(-0.0793633\pi\)
−0.246752 + 0.969079i \(0.579363\pi\)
\(228\) 18.3145 18.3145i 0.0803268 0.0803268i
\(229\) 161.221i 0.704022i −0.935996 0.352011i \(-0.885498\pi\)
0.935996 0.352011i \(-0.114502\pi\)
\(230\) −451.143 + 244.695i −1.96149 + 1.06389i
\(231\) 15.6799 0.0678786
\(232\) −850.727 850.727i −3.66693 3.66693i
\(233\) 8.28891 8.28891i 0.0355747 0.0355747i −0.689096 0.724670i \(-0.741992\pi\)
0.724670 + 0.689096i \(0.241992\pi\)
\(234\) 130.402i 0.557273i
\(235\) 96.3924 + 28.5987i 0.410180 + 0.121697i
\(236\) −187.292 −0.793608
\(237\) 6.50173 + 6.50173i 0.0274335 + 0.0274335i
\(238\) 168.843 168.843i 0.709426 0.709426i
\(239\) 66.4975i 0.278232i −0.990276 0.139116i \(-0.955574\pi\)
0.990276 0.139116i \(-0.0444261\pi\)
\(240\) 142.820 481.377i 0.595084 2.00574i
\(241\) −152.923 −0.634535 −0.317267 0.948336i \(-0.602765\pi\)
−0.317267 + 0.948336i \(0.602765\pi\)
\(242\) 297.614 + 297.614i 1.22981 + 1.22981i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 520.788i 2.13438i
\(245\) 16.6871 + 30.7659i 0.0681104 + 0.125575i
\(246\) 44.0905 0.179230
\(247\) 11.0196 + 11.0196i 0.0446138 + 0.0446138i
\(248\) 804.714 804.714i 3.24481 3.24481i
\(249\) 153.298i 0.615653i
\(250\) −366.457 + 312.150i −1.46583 + 1.24860i
\(251\) 462.911 1.84427 0.922134 0.386871i \(-0.126444\pi\)
0.922134 + 0.386871i \(0.126444\pi\)
\(252\) −60.7866 60.7866i −0.241217 0.241217i
\(253\) 64.4887 64.4887i 0.254896 0.254896i
\(254\) 460.575i 1.81329i
\(255\) 178.403 96.7638i 0.699621 0.379466i
\(256\) 593.807 2.31956
\(257\) 54.4719 + 54.4719i 0.211953 + 0.211953i 0.805097 0.593144i \(-0.202113\pi\)
−0.593144 + 0.805097i \(0.702113\pi\)
\(258\) −294.281 + 294.281i −1.14062 + 1.14062i
\(259\) 8.19201i 0.0316294i
\(260\) 585.985 + 173.856i 2.25379 + 0.668678i
\(261\) −137.211 −0.525712
\(262\) −204.716 204.716i −0.781360 0.781360i
\(263\) −132.088 + 132.088i −0.502236 + 0.502236i −0.912132 0.409896i \(-0.865565\pi\)
0.409896 + 0.912132i \(0.365565\pi\)
\(264\) 155.895i 0.590513i
\(265\) −89.3724 + 301.231i −0.337254 + 1.13672i
\(266\) −14.0678 −0.0528864
\(267\) −54.8885 54.8885i −0.205575 0.205575i
\(268\) −443.443 + 443.443i −1.65464 + 1.65464i
\(269\) 200.132i 0.743985i 0.928236 + 0.371993i \(0.121325\pi\)
−0.928236 + 0.371993i \(0.878675\pi\)
\(270\) −47.7027 87.9494i −0.176677 0.325739i
\(271\) −119.987 −0.442758 −0.221379 0.975188i \(-0.571056\pi\)
−0.221379 + 0.975188i \(0.571056\pi\)
\(272\) 960.792 + 960.792i 3.53232 + 3.53232i
\(273\) 36.5745 36.5745i 0.133972 0.133972i
\(274\) 7.29816i 0.0266356i
\(275\) 46.6520 71.6999i 0.169644 0.260727i
\(276\) −500.007 −1.81162
\(277\) 202.673 + 202.673i 0.731672 + 0.731672i 0.970951 0.239279i \(-0.0769110\pi\)
−0.239279 + 0.970951i \(0.576911\pi\)
\(278\) 40.1547 40.1547i 0.144441 0.144441i
\(279\) 129.790i 0.465196i
\(280\) −305.885 + 165.909i −1.09245 + 0.592530i
\(281\) −283.806 −1.00999 −0.504994 0.863123i \(-0.668505\pi\)
−0.504994 + 0.863123i \(0.668505\pi\)
\(282\) 94.8456 + 94.8456i 0.336332 + 0.336332i
\(283\) 19.2062 19.2062i 0.0678664 0.0678664i −0.672359 0.740225i \(-0.734719\pi\)
0.740225 + 0.672359i \(0.234719\pi\)
\(284\) 419.949i 1.47869i
\(285\) −11.4633 3.40105i −0.0402220 0.0119335i
\(286\) −148.730 −0.520034
\(287\) −12.3663 12.3663i −0.0430881 0.0430881i
\(288\) 250.447 250.447i 0.869608 0.869608i
\(289\) 260.213i 0.900392i
\(290\) −250.496 + 844.300i −0.863780 + 2.91138i
\(291\) 74.7573 0.256898
\(292\) 720.005 + 720.005i 2.46577 + 2.46577i
\(293\) 276.326 276.326i 0.943093 0.943093i −0.0553728 0.998466i \(-0.517635\pi\)
0.998466 + 0.0553728i \(0.0176347\pi\)
\(294\) 46.6915i 0.158815i
\(295\) 41.2237 + 76.0042i 0.139742 + 0.257641i
\(296\) 81.4478 0.275162
\(297\) 12.5719 + 12.5719i 0.0423297 + 0.0423297i
\(298\) −36.5546 + 36.5546i −0.122666 + 0.122666i
\(299\) 300.848i 1.00618i
\(300\) −458.816 + 97.1035i −1.52939 + 0.323678i
\(301\) 165.077 0.548429
\(302\) 363.830 + 363.830i 1.20474 + 1.20474i
\(303\) −141.898 + 141.898i −0.468311 + 0.468311i
\(304\) 80.0519i 0.263328i
\(305\) 211.339 114.628i 0.692916 0.375829i
\(306\) 270.752 0.884809
\(307\) 84.0526 + 84.0526i 0.273787 + 0.273787i 0.830623 0.556836i \(-0.187985\pi\)
−0.556836 + 0.830623i \(0.687985\pi\)
\(308\) 69.3300 69.3300i 0.225097 0.225097i
\(309\) 90.5995i 0.293202i
\(310\) −798.635 236.948i −2.57624 0.764347i
\(311\) −228.140 −0.733569 −0.366785 0.930306i \(-0.619541\pi\)
−0.366785 + 0.930306i \(0.619541\pi\)
\(312\) 363.636 + 363.636i 1.16550 + 1.16550i
\(313\) 415.710 415.710i 1.32815 1.32815i 0.421163 0.906985i \(-0.361622\pi\)
0.906985 0.421163i \(-0.138378\pi\)
\(314\) 787.470i 2.50787i
\(315\) −11.2882 + 38.0470i −0.0358356 + 0.120784i
\(316\) 57.4958 0.181949
\(317\) −167.997 167.997i −0.529960 0.529960i 0.390600 0.920560i \(-0.372267\pi\)
−0.920560 + 0.390600i \(0.872267\pi\)
\(318\) −296.397 + 296.397i −0.932066 + 0.932066i
\(319\) 156.496i 0.490582i
\(320\) −530.993 978.992i −1.65935 3.05935i
\(321\) 259.310 0.807818
\(322\) 192.033 + 192.033i 0.596377 + 0.596377i
\(323\) 22.8798 22.8798i 0.0708354 0.0708354i
\(324\) 97.4754i 0.300850i
\(325\) −58.4259 276.063i −0.179772 0.849425i
\(326\) −772.054 −2.36826
\(327\) 51.1317 + 51.1317i 0.156366 + 0.156366i
\(328\) 122.950 122.950i 0.374847 0.374847i
\(329\) 53.2036i 0.161713i
\(330\) 100.311 54.4072i 0.303971 0.164870i
\(331\) −379.871 −1.14765 −0.573823 0.818979i \(-0.694540\pi\)
−0.573823 + 0.818979i \(0.694540\pi\)
\(332\) −677.816 677.816i −2.04161 2.04161i
\(333\) 6.56822 6.56822i 0.0197244 0.0197244i
\(334\) 649.995i 1.94609i
\(335\) 277.556 + 82.3483i 0.828525 + 0.245816i
\(336\) −265.695 −0.790759
\(337\) 251.400 + 251.400i 0.745994 + 0.745994i 0.973724 0.227730i \(-0.0731305\pi\)
−0.227730 + 0.973724i \(0.573130\pi\)
\(338\) 113.283 113.283i 0.335158 0.335158i
\(339\) 379.540i 1.11959i
\(340\) 360.975 1216.67i 1.06169 3.57845i
\(341\) 148.031 0.434109
\(342\) −11.2793 11.2793i −0.0329805 0.0329805i
\(343\) 13.0958 13.0958i 0.0381802 0.0381802i
\(344\) 1641.25i 4.77108i
\(345\) 110.054 + 202.907i 0.318997 + 0.588135i
\(346\) −33.3159 −0.0962886
\(347\) 234.925 + 234.925i 0.677016 + 0.677016i 0.959324 0.282308i \(-0.0910999\pi\)
−0.282308 + 0.959324i \(0.591100\pi\)
\(348\) −606.688 + 606.688i −1.74336 + 1.74336i
\(349\) 497.584i 1.42574i 0.701295 + 0.712871i \(0.252605\pi\)
−0.701295 + 0.712871i \(0.747395\pi\)
\(350\) 213.507 + 138.920i 0.610020 + 0.396913i
\(351\) 58.6496 0.167093
\(352\) 285.647 + 285.647i 0.811497 + 0.811497i
\(353\) −217.500 + 217.500i −0.616146 + 0.616146i −0.944541 0.328394i \(-0.893492\pi\)
0.328394 + 0.944541i \(0.393492\pi\)
\(354\) 115.347i 0.325839i
\(355\) −170.418 + 92.4328i −0.480052 + 0.260374i
\(356\) −485.387 −1.36345
\(357\) −75.9391 75.9391i −0.212714 0.212714i
\(358\) 639.709 639.709i 1.78690 1.78690i
\(359\) 531.115i 1.47943i −0.672921 0.739714i \(-0.734961\pi\)
0.672921 0.739714i \(-0.265039\pi\)
\(360\) −378.277 112.231i −1.05077 0.311753i
\(361\) 359.094 0.994719
\(362\) −350.938 350.938i −0.969443 0.969443i
\(363\) 133.855 133.855i 0.368747 0.368747i
\(364\) 323.433i 0.888553i
\(365\) 133.707 450.659i 0.366319 1.23468i
\(366\) 320.736 0.876329
\(367\) −190.791 190.791i −0.519867 0.519867i 0.397664 0.917531i \(-0.369821\pi\)
−0.917531 + 0.397664i \(0.869821\pi\)
\(368\) −1092.75 + 1092.75i −2.96944 + 2.96944i
\(369\) 19.8302i 0.0537403i
\(370\) −28.4251 52.4074i −0.0768247 0.141642i
\(371\) 166.264 0.448151
\(372\) −573.874 573.874i −1.54267 1.54267i
\(373\) −178.025 + 178.025i −0.477279 + 0.477279i −0.904260 0.426981i \(-0.859577\pi\)
0.426981 + 0.904260i \(0.359577\pi\)
\(374\) 308.805i 0.825683i
\(375\) 140.393 + 164.818i 0.374381 + 0.439514i
\(376\) 528.969 1.40683
\(377\) −365.036 365.036i −0.968265 0.968265i
\(378\) −37.4365 + 37.4365i −0.0990384 + 0.0990384i
\(379\) 427.303i 1.12745i −0.825963 0.563725i \(-0.809368\pi\)
0.825963 0.563725i \(-0.190632\pi\)
\(380\) −65.7237 + 35.6477i −0.172957 + 0.0938098i
\(381\) −207.148 −0.543696
\(382\) −200.087 200.087i −0.523788 0.523788i
\(383\) −408.586 + 408.586i −1.06680 + 1.06680i −0.0692020 + 0.997603i \(0.522045\pi\)
−0.997603 + 0.0692020i \(0.977955\pi\)
\(384\) 667.798i 1.73906i
\(385\) −43.3945 12.8747i −0.112713 0.0334409i
\(386\) −657.146 −1.70245
\(387\) 132.356 + 132.356i 0.342005 + 0.342005i
\(388\) 330.545 330.545i 0.851920 0.851920i
\(389\) 380.438i 0.977990i −0.872286 0.488995i \(-0.837364\pi\)
0.872286 0.488995i \(-0.162636\pi\)
\(390\) 107.072 360.889i 0.274545 0.925357i
\(391\) −624.646 −1.59756
\(392\) 130.203 + 130.203i 0.332150 + 0.332150i
\(393\) −92.0733 + 92.0733i −0.234283 + 0.234283i
\(394\) 189.758i 0.481619i
\(395\) −12.6551 23.3322i −0.0320382 0.0590688i
\(396\) 111.175 0.280746
\(397\) 419.765 + 419.765i 1.05734 + 1.05734i 0.998253 + 0.0590903i \(0.0188200\pi\)
0.0590903 + 0.998253i \(0.481180\pi\)
\(398\) 62.3346 62.3346i 0.156620 0.156620i
\(399\) 6.32714i 0.0158575i
\(400\) −790.513 + 1214.95i −1.97628 + 3.03737i
\(401\) −116.260 −0.289926 −0.144963 0.989437i \(-0.546306\pi\)
−0.144963 + 0.989437i \(0.546306\pi\)
\(402\) 273.102 + 273.102i 0.679359 + 0.679359i
\(403\) 345.292 345.292i 0.856805 0.856805i
\(404\) 1254.83i 3.10600i
\(405\) −39.5562 + 21.4548i −0.0976696 + 0.0529748i
\(406\) 466.010 1.14781
\(407\) 7.49137 + 7.49137i 0.0184063 + 0.0184063i
\(408\) 755.012 755.012i 1.85052 1.85052i
\(409\) 510.537i 1.24826i 0.781322 + 0.624129i \(0.214546\pi\)
−0.781322 + 0.624129i \(0.785454\pi\)
\(410\) −122.021 36.2025i −0.297612 0.0882988i
\(411\) 3.28242 0.00798643
\(412\) −400.592 400.592i −0.972311 0.972311i
\(413\) 32.3519 32.3519i 0.0783339 0.0783339i
\(414\) 307.939i 0.743813i
\(415\) −125.872 + 424.253i −0.303306 + 1.02230i
\(416\) 1332.58 3.20331
\(417\) −18.0600 18.0600i −0.0433093 0.0433093i
\(418\) 12.8646 12.8646i 0.0307766 0.0307766i
\(419\) 421.546i 1.00608i −0.864265 0.503038i \(-0.832216\pi\)
0.864265 0.503038i \(-0.167784\pi\)
\(420\) 118.316 + 218.139i 0.281705 + 0.519379i
\(421\) −617.382 −1.46646 −0.733232 0.679978i \(-0.761989\pi\)
−0.733232 + 0.679978i \(0.761989\pi\)
\(422\) 588.976 + 588.976i 1.39568 + 1.39568i
\(423\) 42.6578 42.6578i 0.100846 0.100846i
\(424\) 1653.05i 3.89871i
\(425\) −573.186 + 121.309i −1.34867 + 0.285433i
\(426\) −258.633 −0.607120
\(427\) −89.9585 89.9585i −0.210676 0.210676i
\(428\) 1146.56 1146.56i 2.67887 2.67887i
\(429\) 66.8927i 0.155927i
\(430\) 1056.06 572.794i 2.45595 1.33208i
\(431\) −13.8516 −0.0321382 −0.0160691 0.999871i \(-0.505115\pi\)
−0.0160691 + 0.999871i \(0.505115\pi\)
\(432\) −213.030 213.030i −0.493125 0.493125i
\(433\) 539.624 539.624i 1.24624 1.24624i 0.288879 0.957366i \(-0.406718\pi\)
0.957366 0.288879i \(-0.0932824\pi\)
\(434\) 440.805i 1.01568i
\(435\) 379.733 + 112.663i 0.872949 + 0.258996i
\(436\) 452.165 1.03708
\(437\) 26.0223 + 26.0223i 0.0595476 + 0.0595476i
\(438\) 443.428 443.428i 1.01239 1.01239i
\(439\) 41.4994i 0.0945318i −0.998882 0.0472659i \(-0.984949\pi\)
0.998882 0.0472659i \(-0.0150508\pi\)
\(440\) 128.005 431.443i 0.290921 0.980552i
\(441\) 21.0000 0.0476190
\(442\) 720.308 + 720.308i 1.62966 + 1.62966i
\(443\) 577.471 577.471i 1.30355 1.30355i 0.377563 0.925984i \(-0.376762\pi\)
0.925984 0.377563i \(-0.123238\pi\)
\(444\) 58.0837i 0.130819i
\(445\) 106.836 + 196.973i 0.240081 + 0.442637i
\(446\) 300.192 0.673076
\(447\) 16.4408 + 16.4408i 0.0367803 + 0.0367803i
\(448\) −416.717 + 416.717i −0.930172 + 0.930172i
\(449\) 234.581i 0.522451i −0.965278 0.261226i \(-0.915873\pi\)
0.965278 0.261226i \(-0.0841266\pi\)
\(450\) 59.8029 + 282.570i 0.132895 + 0.627933i
\(451\) 22.6173 0.0501491
\(452\) −1678.16 1678.16i −3.71275 3.71275i
\(453\) 163.637 163.637i 0.361229 0.361229i
\(454\) 893.005i 1.96697i
\(455\) −131.252 + 71.1892i −0.288465 + 0.156460i
\(456\) −62.9066 −0.137953
\(457\) 153.225 + 153.225i 0.335284 + 0.335284i 0.854589 0.519305i \(-0.173809\pi\)
−0.519305 + 0.854589i \(0.673809\pi\)
\(458\) −439.022 + 439.022i −0.958562 + 0.958562i
\(459\) 121.773i 0.265302i
\(460\) 1383.78 + 410.554i 3.00821 + 0.892509i
\(461\) 623.452 1.35239 0.676195 0.736723i \(-0.263628\pi\)
0.676195 + 0.736723i \(0.263628\pi\)
\(462\) −42.6981 42.6981i −0.0924202 0.0924202i
\(463\) −613.771 + 613.771i −1.32564 + 1.32564i −0.416506 + 0.909133i \(0.636745\pi\)
−0.909133 + 0.416506i \(0.863255\pi\)
\(464\) 2651.80i 5.71509i
\(465\) −106.570 + 359.194i −0.229182 + 0.772461i
\(466\) −45.1431 −0.0968737
\(467\) −439.249 439.249i −0.940575 0.940575i 0.0577556 0.998331i \(-0.481606\pi\)
−0.998331 + 0.0577556i \(0.981606\pi\)
\(468\) 259.324 259.324i 0.554110 0.554110i
\(469\) 153.197i 0.326645i
\(470\) −184.609 340.364i −0.392786 0.724179i
\(471\) −354.173 −0.751960
\(472\) 321.654 + 321.654i 0.681470 + 0.681470i
\(473\) −150.958 + 150.958i −0.319151 + 0.319151i
\(474\) 35.4098i 0.0747042i
\(475\) 28.9322 + 18.8249i 0.0609099 + 0.0396314i
\(476\) −671.540 −1.41080
\(477\) 133.308 + 133.308i 0.279471 + 0.279471i
\(478\) −181.080 + 181.080i −0.378828 + 0.378828i
\(479\) 15.2748i 0.0318889i −0.999873 0.0159445i \(-0.994925\pi\)
0.999873 0.0159445i \(-0.00507549\pi\)
\(480\) −898.757 + 487.475i −1.87241 + 1.01557i
\(481\) 34.9482 0.0726574
\(482\) 416.425 + 416.425i 0.863952 + 0.863952i
\(483\) 86.3690 86.3690i 0.178818 0.178818i
\(484\) 1183.70i 2.44566i
\(485\) −206.892 61.3830i −0.426581 0.126563i
\(486\) −60.0319 −0.123523
\(487\) −170.456 170.456i −0.350013 0.350013i 0.510101 0.860114i \(-0.329608\pi\)
−0.860114 + 0.510101i \(0.829608\pi\)
\(488\) 894.399 894.399i 1.83278 1.83278i
\(489\) 347.239i 0.710101i
\(490\) 38.3382 129.219i 0.0782413 0.263713i
\(491\) 539.988 1.09977 0.549886 0.835239i \(-0.314671\pi\)
0.549886 + 0.835239i \(0.314671\pi\)
\(492\) −87.6805 87.6805i −0.178212 0.178212i
\(493\) −757.919 + 757.919i −1.53736 + 1.53736i
\(494\) 60.0150i 0.121488i
\(495\) −24.4702 45.1157i −0.0494348 0.0911429i
\(496\) −2508.38 −5.05721
\(497\) 72.5402 + 72.5402i 0.145956 + 0.145956i
\(498\) −417.445 + 417.445i −0.838243 + 0.838243i
\(499\) 594.406i 1.19119i 0.803284 + 0.595597i \(0.203084\pi\)
−0.803284 + 0.595597i \(0.796916\pi\)
\(500\) 1349.51 + 107.996i 2.69902 + 0.215993i
\(501\) −292.342 −0.583517
\(502\) −1260.56 1260.56i −2.51107 2.51107i
\(503\) −416.709 + 416.709i −0.828447 + 0.828447i −0.987302 0.158855i \(-0.949220\pi\)
0.158855 + 0.987302i \(0.449220\pi\)
\(504\) 208.789i 0.414264i
\(505\) 509.217 276.193i 1.00835 0.546917i
\(506\) −351.219 −0.694108
\(507\) −50.9504 50.9504i −0.100494 0.100494i
\(508\) −915.921 + 915.921i −1.80299 + 1.80299i
\(509\) 932.017i 1.83107i 0.402234 + 0.915537i \(0.368234\pi\)
−0.402234 + 0.915537i \(0.631766\pi\)
\(510\) −749.309 222.313i −1.46923 0.435908i
\(511\) −248.741 −0.486773
\(512\) −526.490 526.490i −1.02830 1.02830i
\(513\) −5.07299 + 5.07299i −0.00988888 + 0.00988888i
\(514\) 296.665i 0.577170i
\(515\) −74.3909 + 250.735i −0.144448 + 0.486865i
\(516\) 1170.44 2.26830
\(517\) 48.6533 + 48.6533i 0.0941069 + 0.0941069i
\(518\) −22.3077 + 22.3077i −0.0430651 + 0.0430651i
\(519\) 14.9842i 0.0288712i
\(520\) −707.788 1304.95i −1.36113 2.50952i
\(521\) −536.572 −1.02989 −0.514945 0.857223i \(-0.672188\pi\)
−0.514945 + 0.857223i \(0.672188\pi\)
\(522\) 373.640 + 373.640i 0.715785 + 0.715785i
\(523\) 151.430 151.430i 0.289542 0.289542i −0.547357 0.836899i \(-0.684366\pi\)
0.836899 + 0.547357i \(0.184366\pi\)
\(524\) 814.217i 1.55385i
\(525\) 62.4805 96.0270i 0.119011 0.182909i
\(526\) 719.379 1.36764
\(527\) −716.926 716.926i −1.36039 1.36039i
\(528\) 242.971 242.971i 0.460172 0.460172i
\(529\) 181.439i 0.342985i
\(530\) 1063.65 576.912i 2.00689 1.08851i
\(531\) 51.8785 0.0976995
\(532\) 27.9759 + 27.9759i 0.0525863 + 0.0525863i
\(533\) 52.7562 52.7562i 0.0989797 0.0989797i
\(534\) 298.934i 0.559802i
\(535\) −717.643 212.918i −1.34139 0.397978i
\(536\) 1523.13 2.84167
\(537\) −287.716 287.716i −0.535784 0.535784i
\(538\) 544.981 544.981i 1.01298 1.01298i
\(539\) 23.9515i 0.0444369i
\(540\) −80.0367 + 269.764i −0.148216 + 0.499564i
\(541\) 363.668 0.672215 0.336107 0.941824i \(-0.390890\pi\)
0.336107 + 0.941824i \(0.390890\pi\)
\(542\) 326.738 + 326.738i 0.602838 + 0.602838i
\(543\) −157.838 + 157.838i −0.290678 + 0.290678i
\(544\) 2766.82i 5.08606i
\(545\) −99.5237 183.492i −0.182612 0.336682i
\(546\) −199.192 −0.364821
\(547\) 426.746 + 426.746i 0.780158 + 0.780158i 0.979857 0.199699i \(-0.0639965\pi\)
−0.199699 + 0.979857i \(0.563997\pi\)
\(548\) 14.5135 14.5135i 0.0264844 0.0264844i
\(549\) 144.255i 0.262759i
\(550\) −322.285 + 68.2081i −0.585972 + 0.124015i
\(551\) 63.1487 0.114608
\(552\) 858.711 + 858.711i 1.55564 + 1.55564i
\(553\) −9.93156 + 9.93156i −0.0179594 + 0.0179594i
\(554\) 1103.80i 1.99242i
\(555\) −23.5708 + 12.7845i −0.0424699 + 0.0230351i
\(556\) −159.707 −0.287243
\(557\) 199.988 + 199.988i 0.359045 + 0.359045i 0.863461 0.504416i \(-0.168292\pi\)
−0.504416 + 0.863461i \(0.668292\pi\)
\(558\) −353.431 + 353.431i −0.633388 + 0.633388i
\(559\) 704.240i 1.25982i
\(560\) 735.315 + 218.161i 1.31306 + 0.389574i
\(561\) 138.888 0.247573
\(562\) 772.835 + 772.835i 1.37515 + 1.37515i
\(563\) −85.4562 + 85.4562i −0.151787 + 0.151787i −0.778916 0.627129i \(-0.784230\pi\)
0.627129 + 0.778916i \(0.284230\pi\)
\(564\) 377.229i 0.668846i
\(565\) −311.639 + 1050.38i −0.551573 + 1.85908i
\(566\) −104.601 −0.184807
\(567\) 16.8375 + 16.8375i 0.0296957 + 0.0296957i
\(568\) −721.219 + 721.219i −1.26975 + 1.26975i
\(569\) 991.963i 1.74334i 0.490090 + 0.871672i \(0.336964\pi\)
−0.490090 + 0.871672i \(0.663036\pi\)
\(570\) 21.9543 + 40.4771i 0.0385163 + 0.0710125i
\(571\) 273.348 0.478719 0.239359 0.970931i \(-0.423063\pi\)
0.239359 + 0.970931i \(0.423063\pi\)
\(572\) 295.771 + 295.771i 0.517082 + 0.517082i
\(573\) −89.9913 + 89.9913i −0.157053 + 0.157053i
\(574\) 67.3493i 0.117333i
\(575\) −137.970 651.912i −0.239948 1.13376i
\(576\) −668.234 −1.16013
\(577\) 639.002 + 639.002i 1.10746 + 1.10746i 0.993484 + 0.113972i \(0.0363573\pi\)
0.113972 + 0.993484i \(0.463643\pi\)
\(578\) 708.588 708.588i 1.22593 1.22593i
\(579\) 295.558i 0.510463i
\(580\) 2177.17 1180.87i 3.75373 2.03598i
\(581\) 234.166 0.403039
\(582\) −203.572 203.572i −0.349780 0.349780i
\(583\) −152.044 + 152.044i −0.260796 + 0.260796i
\(584\) 2473.07i 4.23470i
\(585\) −162.314 48.1570i −0.277459 0.0823196i
\(586\) −1504.93 −2.56814
\(587\) −367.435 367.435i −0.625953 0.625953i 0.321094 0.947047i \(-0.395949\pi\)
−0.947047 + 0.321094i \(0.895949\pi\)
\(588\) 92.8530 92.8530i 0.157913 0.157913i
\(589\) 59.7332i 0.101415i
\(590\) 94.7108 319.224i 0.160527 0.541058i
\(591\) 85.3456 0.144409
\(592\) −126.941 126.941i −0.214427 0.214427i
\(593\) −319.591 + 319.591i −0.538939 + 0.538939i −0.923217 0.384278i \(-0.874450\pi\)
0.384278 + 0.923217i \(0.374450\pi\)
\(594\) 68.4693i 0.115268i
\(595\) 147.809 + 272.516i 0.248419 + 0.458010i
\(596\) 145.388 0.243940
\(597\) −28.0356 28.0356i −0.0469608 0.0469608i
\(598\) −819.240 + 819.240i −1.36997 + 1.36997i
\(599\) 119.408i 0.199346i −0.995020 0.0996730i \(-0.968220\pi\)
0.995020 0.0996730i \(-0.0317797\pi\)
\(600\) 954.734 + 621.203i 1.59122 + 1.03534i
\(601\) 183.966 0.306100 0.153050 0.988218i \(-0.451090\pi\)
0.153050 + 0.988218i \(0.451090\pi\)
\(602\) −449.522 449.522i −0.746714 0.746714i
\(603\) 122.831 122.831i 0.203699 0.203699i
\(604\) 1447.06i 2.39580i
\(605\) −480.354 + 260.538i −0.793974 + 0.430642i
\(606\) 772.807 1.27526
\(607\) −757.520 757.520i −1.24797 1.24797i −0.956614 0.291360i \(-0.905892\pi\)
−0.291360 0.956614i \(-0.594108\pi\)
\(608\) −115.264 + 115.264i −0.189578 + 0.189578i
\(609\) 209.593i 0.344159i
\(610\) −887.642 263.355i −1.45515 0.431730i
\(611\) 226.974 0.371479
\(612\) −538.430 538.430i −0.879787 0.879787i
\(613\) 584.336 584.336i 0.953239 0.953239i −0.0457151 0.998955i \(-0.514557\pi\)
0.998955 + 0.0457151i \(0.0145566\pi\)
\(614\) 457.768i 0.745550i
\(615\) −16.2825 + 54.8802i −0.0264756 + 0.0892362i
\(616\) −238.134 −0.386582
\(617\) 483.308 + 483.308i 0.783319 + 0.783319i 0.980389 0.197070i \(-0.0631428\pi\)
−0.197070 + 0.980389i \(0.563143\pi\)
\(618\) −246.712 + 246.712i −0.399210 + 0.399210i
\(619\) 1053.61i 1.70211i −0.525074 0.851056i \(-0.675962\pi\)
0.525074 0.851056i \(-0.324038\pi\)
\(620\) 1117.00 + 2059.41i 1.80161 + 3.32163i
\(621\) 138.499 0.223025
\(622\) 621.249 + 621.249i 0.998793 + 0.998793i
\(623\) 83.8436 83.8436i 0.134580 0.134580i
\(624\) 1133.49i 1.81649i
\(625\) −253.208 571.411i −0.405133 0.914258i
\(626\) −2264.05 −3.61669
\(627\) −5.78599 5.78599i −0.00922806 0.00922806i
\(628\) −1566.00 + 1566.00i −2.49363 + 2.49363i
\(629\) 72.5625i 0.115362i
\(630\) 134.345 72.8671i 0.213246 0.115662i
\(631\) −127.766 −0.202481 −0.101241 0.994862i \(-0.532281\pi\)
−0.101241 + 0.994862i \(0.532281\pi\)
\(632\) −98.7430 98.7430i −0.156239 0.156239i
\(633\) 264.898 264.898i 0.418480 0.418480i
\(634\) 914.949i 1.44314i
\(635\) 573.286 + 170.089i 0.902812 + 0.267856i
\(636\) 1178.86 1.85355
\(637\) 55.8684 + 55.8684i 0.0877055 + 0.0877055i
\(638\) −426.154 + 426.154i −0.667953 + 0.667953i
\(639\) 116.323i 0.182039i
\(640\) −548.326 + 1848.14i −0.856760 + 2.88772i
\(641\) 745.868 1.16360 0.581801 0.813331i \(-0.302348\pi\)
0.581801 + 0.813331i \(0.302348\pi\)
\(642\) −706.127 706.127i −1.09989 1.09989i
\(643\) 43.5132 43.5132i 0.0676721 0.0676721i −0.672461 0.740133i \(-0.734763\pi\)
0.740133 + 0.672461i \(0.234763\pi\)
\(644\) 763.774i 1.18598i
\(645\) −257.620 474.974i −0.399411 0.736394i
\(646\) −124.608 −0.192892
\(647\) 434.895 + 434.895i 0.672171 + 0.672171i 0.958216 0.286045i \(-0.0923407\pi\)
−0.286045 + 0.958216i \(0.592341\pi\)
\(648\) −167.404 + 167.404i −0.258339 + 0.258339i
\(649\) 59.1699i 0.0911708i
\(650\) −592.649 + 910.849i −0.911768 + 1.40131i
\(651\) 198.257 0.304542
\(652\) 1535.34 + 1535.34i 2.35482 + 2.35482i
\(653\) 495.522 495.522i 0.758839 0.758839i −0.217272 0.976111i \(-0.569716\pi\)
0.976111 + 0.217272i \(0.0697160\pi\)
\(654\) 278.474i 0.425801i
\(655\) 330.415 179.213i 0.504450 0.273608i
\(656\) −383.247 −0.584218
\(657\) −199.436 199.436i −0.303556 0.303556i
\(658\) −144.879 + 144.879i −0.220181 + 0.220181i
\(659\) 250.489i 0.380104i 0.981774 + 0.190052i \(0.0608657\pi\)
−0.981774 + 0.190052i \(0.939134\pi\)
\(660\) −307.679 91.2857i −0.466181 0.138312i
\(661\) 48.3637 0.0731674 0.0365837 0.999331i \(-0.488352\pi\)
0.0365837 + 0.999331i \(0.488352\pi\)
\(662\) 1034.43 + 1034.43i 1.56258 + 1.56258i
\(663\) 323.966 323.966i 0.488637 0.488637i
\(664\) 2328.16i 3.50626i
\(665\) 5.19519 17.5104i 0.00781231 0.0263315i
\(666\) −35.7719 −0.0537116
\(667\) −862.017 862.017i −1.29238 1.29238i
\(668\) −1292.61 + 1292.61i −1.93505 + 1.93505i
\(669\) 135.014i 0.201815i
\(670\) −531.571 980.057i −0.793389 1.46277i
\(671\) 164.529 0.245200
\(672\) 382.564 + 382.564i 0.569292 + 0.569292i
\(673\) 621.928 621.928i 0.924113 0.924113i −0.0732040 0.997317i \(-0.523322\pi\)
0.997317 + 0.0732040i \(0.0233224\pi\)
\(674\) 1369.18i 2.03142i
\(675\) 127.089 26.8970i 0.188280 0.0398474i
\(676\) −450.562 −0.666511
\(677\) −446.844 446.844i −0.660035 0.660035i 0.295353 0.955388i \(-0.404563\pi\)
−0.955388 + 0.295353i \(0.904563\pi\)
\(678\) −1033.53 + 1033.53i −1.52438 + 1.52438i
\(679\) 114.194i 0.168179i
\(680\) −2709.45 + 1469.57i −3.98448 + 2.16113i
\(681\) −401.638 −0.589777
\(682\) −403.105 403.105i −0.591062 0.591062i
\(683\) −571.060 + 571.060i −0.836106 + 0.836106i −0.988344 0.152238i \(-0.951352\pi\)
0.152238 + 0.988344i \(0.451352\pi\)
\(684\) 44.8612i 0.0655866i
\(685\) −9.08415 2.69518i −0.0132615 0.00393458i
\(686\) −71.3225 −0.103969
\(687\) 197.455 + 197.455i 0.287416 + 0.287416i
\(688\) 2557.98 2557.98i 3.71799 3.71799i
\(689\) 709.304i 1.02947i
\(690\) 252.847 852.224i 0.366445 1.23511i
\(691\) 988.525 1.43057 0.715286 0.698832i \(-0.246296\pi\)
0.715286 + 0.698832i \(0.246296\pi\)
\(692\) 66.2535 + 66.2535i 0.0957421 + 0.0957421i
\(693\) −19.2039 + 19.2039i −0.0277113 + 0.0277113i
\(694\) 1279.45i 1.84359i
\(695\) 35.1523 + 64.8103i 0.0505788 + 0.0932522i
\(696\) 2083.85 2.99403
\(697\) −109.537 109.537i −0.157155 0.157155i
\(698\) 1354.97 1354.97i 1.94122 1.94122i
\(699\) 20.3036i 0.0290466i
\(700\) −148.328 700.853i −0.211897 1.00122i
\(701\) 271.597 0.387443 0.193721 0.981057i \(-0.437944\pi\)
0.193721 + 0.981057i \(0.437944\pi\)
\(702\) −159.709 159.709i −0.227506 0.227506i
\(703\) −3.02290 + 3.02290i −0.00430000 + 0.00430000i
\(704\) 762.153i 1.08260i
\(705\) −153.082 + 83.0299i −0.217138 + 0.117773i
\(706\) 1184.55 1.67783
\(707\) −216.753 216.753i −0.306581 0.306581i
\(708\) 229.384 229.384i 0.323989 0.323989i
\(709\) 181.787i 0.256400i 0.991748 + 0.128200i \(0.0409199\pi\)
−0.991748 + 0.128200i \(0.959080\pi\)
\(710\) 715.771 + 212.363i 1.00813 + 0.299103i
\(711\) −15.9259 −0.0223993
\(712\) 833.602 + 833.602i 1.17079 + 1.17079i
\(713\) 815.393 815.393i 1.14361 1.14361i
\(714\) 413.580i 0.579244i
\(715\) 54.9254 185.127i 0.0768187 0.258918i
\(716\) −2544.31 −3.55351
\(717\) 81.4424 + 81.4424i 0.113588 + 0.113588i
\(718\) −1446.28 + 1446.28i −2.01432 + 2.01432i
\(719\) 286.878i 0.398995i −0.979898 0.199498i \(-0.936069\pi\)
0.979898 0.199498i \(-0.0639310\pi\)
\(720\) 414.645 + 764.482i 0.575896 + 1.06178i
\(721\) 138.393 0.191946
\(722\) −977.850 977.850i −1.35436 1.35436i
\(723\) 187.291 187.291i 0.259048 0.259048i
\(724\) 1395.79i 1.92788i
\(725\) −958.409 623.595i −1.32194 0.860131i
\(726\) −729.004 −1.00414
\(727\) −857.435 857.435i −1.17941 1.17941i −0.979893 0.199521i \(-0.936061\pi\)
−0.199521 0.979893i \(-0.563939\pi\)
\(728\) −555.463 + 555.463i −0.762999 + 0.762999i
\(729\) 27.0000i 0.0370370i
\(730\) −1591.29 + 863.096i −2.17985 + 1.18232i
\(731\) 1462.20 2.00028
\(732\) −637.832 637.832i −0.871355 0.871355i
\(733\) 291.875 291.875i 0.398193 0.398193i −0.479402 0.877595i \(-0.659147\pi\)
0.877595 + 0.479402i \(0.159147\pi\)
\(734\) 1039.09i 1.41565i
\(735\) −58.1178 17.2430i −0.0790718 0.0234599i
\(736\) 3146.83 4.27558
\(737\) 140.094 + 140.094i 0.190087 + 0.190087i
\(738\) −53.9996 + 53.9996i −0.0731702 + 0.0731702i
\(739\) 1080.02i 1.46147i −0.682662 0.730734i \(-0.739178\pi\)
0.682662 0.730734i \(-0.260822\pi\)
\(740\) −47.6923 + 160.748i −0.0644491 + 0.217226i
\(741\) −26.9924 −0.0364270
\(742\) −452.754 452.754i −0.610181 0.610181i
\(743\) −821.950 + 821.950i −1.10626 + 1.10626i −0.112621 + 0.993638i \(0.535925\pi\)
−0.993638 + 0.112621i \(0.964075\pi\)
\(744\) 1971.14i 2.64938i
\(745\) −32.0007 58.9996i −0.0429539 0.0791942i
\(746\) 969.562 1.29968
\(747\) 187.750 + 187.750i 0.251339 + 0.251339i
\(748\) 614.105 614.105i 0.820996 0.820996i
\(749\) 396.102i 0.528841i
\(750\) 66.5116 831.120i 0.0886821 1.10816i
\(751\) 834.946 1.11178 0.555889 0.831256i \(-0.312378\pi\)
0.555889 + 0.831256i \(0.312378\pi\)
\(752\) −824.425 824.425i −1.09631 1.09631i
\(753\) −566.948 + 566.948i −0.752919 + 0.752919i
\(754\) 1988.06i 2.63669i
\(755\) −587.228 + 318.505i −0.777785 + 0.421861i
\(756\) 148.896 0.196952
\(757\) −192.396 192.396i −0.254156 0.254156i 0.568516 0.822672i \(-0.307518\pi\)
−0.822672 + 0.568516i \(0.807518\pi\)
\(758\) −1163.59 + 1163.59i −1.53508 + 1.53508i
\(759\) 157.964i 0.208122i
\(760\) 174.095 + 51.6523i 0.229072 + 0.0679636i
\(761\) 95.1019 0.124970 0.0624848 0.998046i \(-0.480097\pi\)
0.0624848 + 0.998046i \(0.480097\pi\)
\(762\) 564.086 + 564.086i 0.740271 + 0.740271i
\(763\) −78.1050 + 78.1050i −0.102366 + 0.102366i
\(764\) 795.806i 1.04163i
\(765\) −99.9877 + 337.010i −0.130703 + 0.440535i
\(766\) 2225.25 2.90502
\(767\) 138.017 + 138.017i 0.179945 + 0.179945i
\(768\) −727.262 + 727.262i −0.946956 + 0.946956i
\(769\) 368.887i 0.479697i −0.970810 0.239848i \(-0.922902\pi\)
0.970810 0.239848i \(-0.0770977\pi\)
\(770\) 83.1084 + 153.227i 0.107933 + 0.198996i
\(771\) −133.428 −0.173059
\(772\) 1306.83 + 1306.83i 1.69279 + 1.69279i
\(773\) −87.2860 + 87.2860i −0.112918 + 0.112918i −0.761308 0.648390i \(-0.775443\pi\)
0.648390 + 0.761308i \(0.275443\pi\) <