Properties

Label 784.2.m.h.197.3
Level $784$
Weight $2$
Character 784.197
Analytic conductor $6.260$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.20138089353117696.1
Defining polynomial: \(x^{12} - 3 x^{10} - 2 x^{9} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 8 x^{5} + 8 x^{4} - 16 x^{3} - 48 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 197.3
Root \(-1.40471 + 0.163666i\) of defining polynomial
Character \(\chi\) \(=\) 784.197
Dual form 784.2.m.h.589.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.163666 - 1.40471i) q^{2} +(2.05500 - 2.05500i) q^{3} +(-1.94643 - 0.459808i) q^{4} +(-2.72766 - 2.72766i) q^{5} +(-2.55034 - 3.22301i) q^{6} +(-0.964462 + 2.65891i) q^{8} -5.44602i q^{9} +O(q^{10})\) \(q+(0.163666 - 1.40471i) q^{2} +(2.05500 - 2.05500i) q^{3} +(-1.94643 - 0.459808i) q^{4} +(-2.72766 - 2.72766i) q^{5} +(-2.55034 - 3.22301i) q^{6} +(-0.964462 + 2.65891i) q^{8} -5.44602i q^{9} +(-4.27801 + 3.38515i) q^{10} +(0.919616 + 0.919616i) q^{11} +(-4.94480 + 3.05500i) q^{12} +(1.12607 - 1.12607i) q^{13} -11.2107 q^{15} +(3.57715 + 1.78996i) q^{16} +1.50885 q^{17} +(-7.65008 - 0.891330i) q^{18} +(-1.46271 + 1.46271i) q^{19} +(4.05500 + 6.56340i) q^{20} +(1.44230 - 1.14128i) q^{22} -4.77031i q^{23} +(3.48209 + 7.44602i) q^{24} +9.88030i q^{25} +(-1.39751 - 1.76611i) q^{26} +(-5.02656 - 5.02656i) q^{27} +(4.10069 - 4.10069i) q^{29} +(-1.83481 + 15.7478i) q^{30} -4.10999 q^{31} +(3.09984 - 4.73191i) q^{32} +3.77961 q^{33} +(0.246948 - 2.11950i) q^{34} +(-2.50412 + 10.6003i) q^{36} +(-1.65467 - 1.65467i) q^{37} +(1.81529 + 2.29409i) q^{38} -4.62815i q^{39} +(9.88334 - 4.62189i) q^{40} +7.45533i q^{41} +(5.68992 + 5.68992i) q^{43} +(-1.36712 - 2.21281i) q^{44} +(-14.8549 + 14.8549i) q^{45} +(-6.70090 - 0.780738i) q^{46} -3.59748 q^{47} +(11.0294 - 3.67267i) q^{48} +(13.8790 + 1.61707i) q^{50} +(3.10069 - 3.10069i) q^{51} +(-2.70960 + 1.67404i) q^{52} +(-0.675714 - 0.675714i) q^{53} +(-7.88355 + 6.23819i) q^{54} -5.01680i q^{55} +6.01174i q^{57} +(-5.08913 - 6.43142i) q^{58} +(-1.13843 - 1.13843i) q^{59} +(21.8208 + 5.15476i) q^{60} +(3.21881 - 3.21881i) q^{61} +(-0.672667 + 5.77335i) q^{62} +(-6.13963 - 5.12884i) q^{64} -6.14310 q^{65} +(0.618595 - 5.30926i) q^{66} +(-1.52640 + 1.52640i) q^{67} +(-2.93687 - 0.693782i) q^{68} +(-9.80296 - 9.80296i) q^{69} -13.8202i q^{71} +(14.4805 + 5.25248i) q^{72} -14.4749i q^{73} +(-2.59514 + 2.05351i) q^{74} +(20.3040 + 20.3040i) q^{75} +(3.51963 - 2.17450i) q^{76} +(-6.50122 - 0.757473i) q^{78} -1.77961 q^{79} +(-4.87485 - 14.6397i) q^{80} -4.32107 q^{81} +(10.4726 + 1.22019i) q^{82} +(7.16133 - 7.16133i) q^{83} +(-4.11564 - 4.11564i) q^{85} +(8.92394 - 7.06145i) q^{86} -16.8538i q^{87} +(-3.33211 + 1.55824i) q^{88} -8.45899i q^{89} +(18.4356 + 23.2981i) q^{90} +(-2.19342 + 9.28505i) q^{92} +(-8.44602 + 8.44602i) q^{93} +(-0.588786 + 5.05342i) q^{94} +7.97958 q^{95} +(-3.35389 - 16.0942i) q^{96} -16.2227 q^{97} +(5.00824 - 5.00824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} - 4q^{3} - 6q^{4} - 4q^{5} - 4q^{6} - 4q^{8} + O(q^{10}) \) \( 12q + 2q^{2} - 4q^{3} - 6q^{4} - 4q^{5} - 4q^{6} - 4q^{8} + 4q^{10} - 8q^{12} - 24q^{15} + 10q^{16} + 8q^{17} + 20q^{20} + 14q^{22} + 8q^{24} + 20q^{26} - 4q^{27} - 4q^{29} - 28q^{30} + 8q^{31} + 12q^{32} - 8q^{34} - 16q^{36} - 20q^{37} - 16q^{38} + 8q^{40} + 16q^{43} + 14q^{44} - 40q^{45} - 28q^{46} - 16q^{47} - 16q^{48} + 44q^{50} - 16q^{51} + 16q^{52} + 4q^{53} - 64q^{54} + 14q^{58} + 16q^{59} + 60q^{60} + 20q^{61} - 8q^{62} - 18q^{64} + 32q^{65} - 12q^{66} + 24q^{67} + 28q^{68} + 4q^{69} + 6q^{72} - 38q^{74} + 40q^{75} - 48q^{76} - 76q^{78} + 24q^{79} - 24q^{80} - 44q^{81} + 16q^{82} + 20q^{83} - 8q^{85} + 38q^{86} - 14q^{88} + 40q^{90} + 32q^{92} - 48q^{93} + 24q^{94} + 16q^{96} - 48q^{97} + 32q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.163666 1.40471i 0.115730 0.993281i
\(3\) 2.05500 2.05500i 1.18645 1.18645i 0.208411 0.978041i \(-0.433171\pi\)
0.978041 0.208411i \(-0.0668293\pi\)
\(4\) −1.94643 0.459808i −0.973213 0.229904i
\(5\) −2.72766 2.72766i −1.21985 1.21985i −0.967685 0.252164i \(-0.918858\pi\)
−0.252164 0.967685i \(-0.581142\pi\)
\(6\) −2.55034 3.22301i −1.04117 1.31579i
\(7\) 0 0
\(8\) −0.964462 + 2.65891i −0.340989 + 0.940067i
\(9\) 5.44602i 1.81534i
\(10\) −4.27801 + 3.38515i −1.35282 + 1.07048i
\(11\) 0.919616 + 0.919616i 0.277275 + 0.277275i 0.832020 0.554746i \(-0.187184\pi\)
−0.554746 + 0.832020i \(0.687184\pi\)
\(12\) −4.94480 + 3.05500i −1.42744 + 0.881901i
\(13\) 1.12607 1.12607i 0.312316 0.312316i −0.533490 0.845806i \(-0.679120\pi\)
0.845806 + 0.533490i \(0.179120\pi\)
\(14\) 0 0
\(15\) −11.2107 −2.89458
\(16\) 3.57715 + 1.78996i 0.894288 + 0.447491i
\(17\) 1.50885 0.365950 0.182975 0.983118i \(-0.441427\pi\)
0.182975 + 0.983118i \(0.441427\pi\)
\(18\) −7.65008 0.891330i −1.80314 0.210088i
\(19\) −1.46271 + 1.46271i −0.335569 + 0.335569i −0.854697 0.519127i \(-0.826257\pi\)
0.519127 + 0.854697i \(0.326257\pi\)
\(20\) 4.05500 + 6.56340i 0.906725 + 1.46762i
\(21\) 0 0
\(22\) 1.44230 1.14128i 0.307500 0.243323i
\(23\) 4.77031i 0.994677i −0.867556 0.497339i \(-0.834311\pi\)
0.867556 0.497339i \(-0.165689\pi\)
\(24\) 3.48209 + 7.44602i 0.710779 + 1.51991i
\(25\) 9.88030i 1.97606i
\(26\) −1.39751 1.76611i −0.274074 0.346362i
\(27\) −5.02656 5.02656i −0.967362 0.967362i
\(28\) 0 0
\(29\) 4.10069 4.10069i 0.761478 0.761478i −0.215111 0.976590i \(-0.569011\pi\)
0.976590 + 0.215111i \(0.0690115\pi\)
\(30\) −1.83481 + 15.7478i −0.334989 + 2.87514i
\(31\) −4.10999 −0.738176 −0.369088 0.929394i \(-0.620330\pi\)
−0.369088 + 0.929394i \(0.620330\pi\)
\(32\) 3.09984 4.73191i 0.547980 0.836492i
\(33\) 3.77961 0.657946
\(34\) 0.246948 2.11950i 0.0423513 0.363491i
\(35\) 0 0
\(36\) −2.50412 + 10.6003i −0.417354 + 1.76671i
\(37\) −1.65467 1.65467i −0.272025 0.272025i 0.557890 0.829915i \(-0.311611\pi\)
−0.829915 + 0.557890i \(0.811611\pi\)
\(38\) 1.81529 + 2.29409i 0.294479 + 0.372150i
\(39\) 4.62815i 0.741097i
\(40\) 9.88334 4.62189i 1.56269 0.730785i
\(41\) 7.45533i 1.16433i 0.813072 + 0.582163i \(0.197794\pi\)
−0.813072 + 0.582163i \(0.802206\pi\)
\(42\) 0 0
\(43\) 5.68992 + 5.68992i 0.867705 + 0.867705i 0.992218 0.124513i \(-0.0397369\pi\)
−0.124513 + 0.992218i \(0.539737\pi\)
\(44\) −1.36712 2.21281i −0.206101 0.333594i
\(45\) −14.8549 + 14.8549i −2.21444 + 2.21444i
\(46\) −6.70090 0.780738i −0.987994 0.115114i
\(47\) −3.59748 −0.524747 −0.262373 0.964966i \(-0.584505\pi\)
−0.262373 + 0.964966i \(0.584505\pi\)
\(48\) 11.0294 3.67267i 1.59196 0.530104i
\(49\) 0 0
\(50\) 13.8790 + 1.61707i 1.96278 + 0.228689i
\(51\) 3.10069 3.10069i 0.434183 0.434183i
\(52\) −2.70960 + 1.67404i −0.375753 + 0.232148i
\(53\) −0.675714 0.675714i −0.0928165 0.0928165i 0.659174 0.751990i \(-0.270906\pi\)
−0.751990 + 0.659174i \(0.770906\pi\)
\(54\) −7.88355 + 6.23819i −1.07281 + 0.848910i
\(55\) 5.01680i 0.676466i
\(56\) 0 0
\(57\) 6.01174i 0.796275i
\(58\) −5.08913 6.43142i −0.668236 0.844487i
\(59\) −1.13843 1.13843i −0.148211 0.148211i 0.629108 0.777318i \(-0.283420\pi\)
−0.777318 + 0.629108i \(0.783420\pi\)
\(60\) 21.8208 + 5.15476i 2.81705 + 0.665476i
\(61\) 3.21881 3.21881i 0.412127 0.412127i −0.470352 0.882479i \(-0.655873\pi\)
0.882479 + 0.470352i \(0.155873\pi\)
\(62\) −0.672667 + 5.77335i −0.0854288 + 0.733216i
\(63\) 0 0
\(64\) −6.13963 5.12884i −0.767453 0.641105i
\(65\) −6.14310 −0.761957
\(66\) 0.618595 5.30926i 0.0761438 0.653525i
\(67\) −1.52640 + 1.52640i −0.186480 + 0.186480i −0.794172 0.607692i \(-0.792095\pi\)
0.607692 + 0.794172i \(0.292095\pi\)
\(68\) −2.93687 0.693782i −0.356148 0.0841334i
\(69\) −9.80296 9.80296i −1.18014 1.18014i
\(70\) 0 0
\(71\) 13.8202i 1.64016i −0.572251 0.820079i \(-0.693930\pi\)
0.572251 0.820079i \(-0.306070\pi\)
\(72\) 14.4805 + 5.25248i 1.70654 + 0.619010i
\(73\) 14.4749i 1.69416i −0.531468 0.847078i \(-0.678359\pi\)
0.531468 0.847078i \(-0.321641\pi\)
\(74\) −2.59514 + 2.05351i −0.301679 + 0.238716i
\(75\) 20.3040 + 20.3040i 2.34450 + 2.34450i
\(76\) 3.51963 2.17450i 0.403729 0.249432i
\(77\) 0 0
\(78\) −6.50122 0.757473i −0.736118 0.0857669i
\(79\) −1.77961 −0.200222 −0.100111 0.994976i \(-0.531920\pi\)
−0.100111 + 0.994976i \(0.531920\pi\)
\(80\) −4.87485 14.6397i −0.545025 1.63677i
\(81\) −4.32107 −0.480119
\(82\) 10.4726 + 1.22019i 1.15650 + 0.134747i
\(83\) 7.16133 7.16133i 0.786058 0.786058i −0.194787 0.980845i \(-0.562402\pi\)
0.980845 + 0.194787i \(0.0624017\pi\)
\(84\) 0 0
\(85\) −4.11564 4.11564i −0.446404 0.446404i
\(86\) 8.92394 7.06145i 0.962294 0.761455i
\(87\) 16.8538i 1.80692i
\(88\) −3.33211 + 1.55824i −0.355204 + 0.166109i
\(89\) 8.45899i 0.896651i −0.893870 0.448325i \(-0.852021\pi\)
0.893870 0.448325i \(-0.147979\pi\)
\(90\) 18.4356 + 23.2981i 1.94328 + 2.45584i
\(91\) 0 0
\(92\) −2.19342 + 9.28505i −0.228680 + 0.968033i
\(93\) −8.44602 + 8.44602i −0.875811 + 0.875811i
\(94\) −0.588786 + 5.05342i −0.0607287 + 0.521221i
\(95\) 7.97958 0.818688
\(96\) −3.35389 16.0942i −0.342305 1.64261i
\(97\) −16.2227 −1.64717 −0.823585 0.567194i \(-0.808029\pi\)
−0.823585 + 0.567194i \(0.808029\pi\)
\(98\) 0 0
\(99\) 5.00824 5.00824i 0.503348 0.503348i
\(100\) 4.54304 19.2313i 0.454304 1.92313i
\(101\) 11.5664 + 11.5664i 1.15090 + 1.15090i 0.986372 + 0.164533i \(0.0526116\pi\)
0.164533 + 0.986372i \(0.447388\pi\)
\(102\) −3.84809 4.86304i −0.381018 0.481513i
\(103\) 17.1875i 1.69354i 0.531963 + 0.846768i \(0.321455\pi\)
−0.531963 + 0.846768i \(0.678545\pi\)
\(104\) 1.90808 + 4.08018i 0.187102 + 0.400095i
\(105\) 0 0
\(106\) −1.05977 + 0.838591i −0.102934 + 0.0814512i
\(107\) 4.10143 + 4.10143i 0.396501 + 0.396501i 0.876997 0.480496i \(-0.159543\pi\)
−0.480496 + 0.876997i \(0.659543\pi\)
\(108\) 7.47258 + 12.0951i 0.719049 + 1.16385i
\(109\) −3.27351 + 3.27351i −0.313545 + 0.313545i −0.846281 0.532736i \(-0.821164\pi\)
0.532736 + 0.846281i \(0.321164\pi\)
\(110\) −7.04716 0.821082i −0.671920 0.0782871i
\(111\) −6.80066 −0.645490
\(112\) 0 0
\(113\) −9.17193 −0.862822 −0.431411 0.902155i \(-0.641984\pi\)
−0.431411 + 0.902155i \(0.641984\pi\)
\(114\) 8.44476 + 0.983920i 0.790924 + 0.0921525i
\(115\) −13.0118 + 13.0118i −1.21336 + 1.21336i
\(116\) −9.86721 + 6.09616i −0.916147 + 0.566014i
\(117\) −6.13262 6.13262i −0.566961 0.566961i
\(118\) −1.78548 + 1.41284i −0.164367 + 0.130062i
\(119\) 0 0
\(120\) 10.8123 29.8082i 0.987021 2.72110i
\(121\) 9.30861i 0.846238i
\(122\) −3.99469 5.04831i −0.361662 0.457053i
\(123\) 15.3207 + 15.3207i 1.38142 + 1.38142i
\(124\) 7.99980 + 1.88981i 0.718403 + 0.169710i
\(125\) 13.3118 13.3118i 1.19064 1.19064i
\(126\) 0 0
\(127\) −12.9787 −1.15167 −0.575835 0.817566i \(-0.695323\pi\)
−0.575835 + 0.817566i \(0.695323\pi\)
\(128\) −8.20939 + 7.78499i −0.725614 + 0.688102i
\(129\) 23.3855 2.05898
\(130\) −1.00542 + 8.62928i −0.0881810 + 0.756838i
\(131\) 6.81965 6.81965i 0.595836 0.595836i −0.343366 0.939202i \(-0.611567\pi\)
0.939202 + 0.343366i \(0.111567\pi\)
\(132\) −7.35674 1.73790i −0.640322 0.151264i
\(133\) 0 0
\(134\) 1.89434 + 2.39398i 0.163646 + 0.206808i
\(135\) 27.4215i 2.36007i
\(136\) −1.45523 + 4.01190i −0.124785 + 0.344018i
\(137\) 22.6543i 1.93548i −0.251943 0.967742i \(-0.581069\pi\)
0.251943 0.967742i \(-0.418931\pi\)
\(138\) −15.3747 + 12.1659i −1.30878 + 1.03563i
\(139\) 6.64728 + 6.64728i 0.563815 + 0.563815i 0.930389 0.366574i \(-0.119469\pi\)
−0.366574 + 0.930389i \(0.619469\pi\)
\(140\) 0 0
\(141\) −7.39281 + 7.39281i −0.622587 + 0.622587i
\(142\) −19.4134 2.26190i −1.62914 0.189815i
\(143\) 2.07111 0.173195
\(144\) 9.74818 19.4812i 0.812348 1.62344i
\(145\) −22.3706 −1.85778
\(146\) −20.3330 2.36905i −1.68277 0.196064i
\(147\) 0 0
\(148\) 2.45986 + 3.98151i 0.202199 + 0.327278i
\(149\) 7.77031 + 7.77031i 0.636568 + 0.636568i 0.949707 0.313139i \(-0.101381\pi\)
−0.313139 + 0.949707i \(0.601381\pi\)
\(150\) 31.8443 25.1981i 2.60008 2.05742i
\(151\) 5.46829i 0.445004i 0.974932 + 0.222502i \(0.0714223\pi\)
−0.974932 + 0.222502i \(0.928578\pi\)
\(152\) −2.47850 5.29996i −0.201033 0.429883i
\(153\) 8.21724i 0.664324i
\(154\) 0 0
\(155\) 11.2107 + 11.2107i 0.900463 + 0.900463i
\(156\) −2.12806 + 9.00836i −0.170381 + 0.721246i
\(157\) 5.61722 5.61722i 0.448303 0.448303i −0.446487 0.894790i \(-0.647325\pi\)
0.894790 + 0.446487i \(0.147325\pi\)
\(158\) −0.291263 + 2.49984i −0.0231716 + 0.198877i
\(159\) −2.77718 −0.220245
\(160\) −21.3624 + 4.45173i −1.68885 + 0.351940i
\(161\) 0 0
\(162\) −0.707214 + 6.06986i −0.0555640 + 0.476893i
\(163\) −6.31758 + 6.31758i −0.494831 + 0.494831i −0.909824 0.414994i \(-0.863784\pi\)
0.414994 + 0.909824i \(0.363784\pi\)
\(164\) 3.42802 14.5112i 0.267683 1.13314i
\(165\) −10.3095 10.3095i −0.802595 0.802595i
\(166\) −8.88753 11.2317i −0.689806 0.871746i
\(167\) 11.8175i 0.914463i 0.889348 + 0.457231i \(0.151159\pi\)
−0.889348 + 0.457231i \(0.848841\pi\)
\(168\) 0 0
\(169\) 10.4639i 0.804917i
\(170\) −6.45488 + 5.10769i −0.495067 + 0.391742i
\(171\) 7.96597 + 7.96597i 0.609173 + 0.609173i
\(172\) −8.45874 13.6913i −0.644973 1.04395i
\(173\) −5.63858 + 5.63858i −0.428694 + 0.428694i −0.888183 0.459490i \(-0.848032\pi\)
0.459490 + 0.888183i \(0.348032\pi\)
\(174\) −23.6747 2.75840i −1.79477 0.209114i
\(175\) 0 0
\(176\) 1.64353 + 4.93569i 0.123886 + 0.372041i
\(177\) −4.67893 −0.351690
\(178\) −11.8824 1.38445i −0.890626 0.103769i
\(179\) 11.7278 11.7278i 0.876575 0.876575i −0.116604 0.993179i \(-0.537201\pi\)
0.993179 + 0.116604i \(0.0372007\pi\)
\(180\) 35.7444 22.0836i 2.66423 1.64601i
\(181\) 4.18574 + 4.18574i 0.311124 + 0.311124i 0.845345 0.534221i \(-0.179395\pi\)
−0.534221 + 0.845345i \(0.679395\pi\)
\(182\) 0 0
\(183\) 13.2293i 0.977937i
\(184\) 12.6838 + 4.60078i 0.935064 + 0.339174i
\(185\) 9.02674i 0.663659i
\(186\) 10.4819 + 13.2465i 0.768569 + 0.971284i
\(187\) 1.38756 + 1.38756i 0.101469 + 0.101469i
\(188\) 7.00223 + 1.65415i 0.510690 + 0.120641i
\(189\) 0 0
\(190\) 1.30599 11.2090i 0.0947464 0.813187i
\(191\) 12.3676 0.894891 0.447445 0.894311i \(-0.352334\pi\)
0.447445 + 0.894311i \(0.352334\pi\)
\(192\) −23.1567 + 2.07717i −1.67119 + 0.149907i
\(193\) 23.6837 1.70479 0.852395 0.522898i \(-0.175149\pi\)
0.852395 + 0.522898i \(0.175149\pi\)
\(194\) −2.65512 + 22.7883i −0.190626 + 1.63610i
\(195\) −12.6240 + 12.6240i −0.904026 + 0.904026i
\(196\) 0 0
\(197\) −11.4195 11.4195i −0.813606 0.813606i 0.171566 0.985173i \(-0.445117\pi\)
−0.985173 + 0.171566i \(0.945117\pi\)
\(198\) −6.21546 7.85482i −0.441713 0.558218i
\(199\) 5.49683i 0.389660i −0.980837 0.194830i \(-0.937585\pi\)
0.980837 0.194830i \(-0.0624155\pi\)
\(200\) −26.2708 9.52917i −1.85763 0.673814i
\(201\) 6.27351i 0.442499i
\(202\) 18.1406 14.3545i 1.27636 1.00998i
\(203\) 0 0
\(204\) −7.46098 + 4.60954i −0.522373 + 0.322732i
\(205\) 20.3356 20.3356i 1.42030 1.42030i
\(206\) 24.1435 + 2.81302i 1.68216 + 0.195992i
\(207\) −25.9792 −1.80568
\(208\) 6.04377 2.01251i 0.419060 0.139542i
\(209\) −2.69027 −0.186090
\(210\) 0 0
\(211\) 0.907874 0.907874i 0.0625007 0.0625007i −0.675166 0.737666i \(-0.735928\pi\)
0.737666 + 0.675166i \(0.235928\pi\)
\(212\) 1.00453 + 1.62593i 0.0689914 + 0.111669i
\(213\) −28.4005 28.4005i −1.94597 1.94597i
\(214\) 6.43260 5.09006i 0.439723 0.347949i
\(215\) 31.0404i 2.11694i
\(216\) 18.2131 8.51726i 1.23925 0.579526i
\(217\) 0 0
\(218\) 4.06257 + 5.13410i 0.275152 + 0.347725i
\(219\) −29.7458 29.7458i −2.01004 2.01004i
\(220\) −2.30677 + 9.76484i −0.155522 + 0.658345i
\(221\) 1.69908 1.69908i 0.114292 0.114292i
\(222\) −1.11304 + 9.55297i −0.0747023 + 0.641153i
\(223\) 3.20318 0.214501 0.107250 0.994232i \(-0.465795\pi\)
0.107250 + 0.994232i \(0.465795\pi\)
\(224\) 0 0
\(225\) 53.8083 3.58722
\(226\) −1.50114 + 12.8839i −0.0998540 + 0.857025i
\(227\) 13.7931 13.7931i 0.915480 0.915480i −0.0812167 0.996696i \(-0.525881\pi\)
0.996696 + 0.0812167i \(0.0258806\pi\)
\(228\) 2.76425 11.7014i 0.183067 0.774945i
\(229\) −7.02177 7.02177i −0.464012 0.464012i 0.435956 0.899968i \(-0.356410\pi\)
−0.899968 + 0.435956i \(0.856410\pi\)
\(230\) 16.1482 + 20.4074i 1.06478 + 1.34562i
\(231\) 0 0
\(232\) 6.94841 + 14.8583i 0.456185 + 0.975496i
\(233\) 2.93857i 0.192512i 0.995357 + 0.0962561i \(0.0306868\pi\)
−0.995357 + 0.0962561i \(0.969313\pi\)
\(234\) −9.61826 + 7.61085i −0.628765 + 0.497537i
\(235\) 9.81272 + 9.81272i 0.640111 + 0.640111i
\(236\) 1.69241 + 2.73932i 0.110166 + 0.178315i
\(237\) −3.65710 + 3.65710i −0.237554 + 0.237554i
\(238\) 0 0
\(239\) 16.2109 1.04859 0.524297 0.851536i \(-0.324328\pi\)
0.524297 + 0.851536i \(0.324328\pi\)
\(240\) −40.1023 20.0667i −2.58859 1.29530i
\(241\) 14.1166 0.909329 0.454665 0.890663i \(-0.349759\pi\)
0.454665 + 0.890663i \(0.349759\pi\)
\(242\) −13.0759 1.52351i −0.840552 0.0979347i
\(243\) 6.19990 6.19990i 0.397724 0.397724i
\(244\) −7.74522 + 4.78515i −0.495837 + 0.306338i
\(245\) 0 0
\(246\) 24.0286 19.0136i 1.53201 1.21227i
\(247\) 3.29424i 0.209608i
\(248\) 3.96393 10.9281i 0.251710 0.693936i
\(249\) 29.4330i 1.86524i
\(250\) −16.5206 20.8779i −1.04485 1.32044i
\(251\) 14.1967 + 14.1967i 0.896091 + 0.896091i 0.995088 0.0989969i \(-0.0315634\pi\)
−0.0989969 + 0.995088i \(0.531563\pi\)
\(252\) 0 0
\(253\) 4.38685 4.38685i 0.275799 0.275799i
\(254\) −2.12417 + 18.2313i −0.133282 + 1.14393i
\(255\) −16.9153 −1.05927
\(256\) 9.59206 + 12.8060i 0.599503 + 0.800372i
\(257\) 3.23679 0.201905 0.100953 0.994891i \(-0.467811\pi\)
0.100953 + 0.994891i \(0.467811\pi\)
\(258\) 3.82742 32.8499i 0.238285 2.04515i
\(259\) 0 0
\(260\) 11.9571 + 2.82464i 0.741547 + 0.175177i
\(261\) −22.3324 22.3324i −1.38234 1.38234i
\(262\) −8.46350 10.6958i −0.522877 0.660788i
\(263\) 24.0161i 1.48090i 0.672114 + 0.740448i \(0.265386\pi\)
−0.672114 + 0.740448i \(0.734614\pi\)
\(264\) −3.64529 + 10.0497i −0.224352 + 0.618514i
\(265\) 3.68624i 0.226444i
\(266\) 0 0
\(267\) −17.3832 17.3832i −1.06383 1.06383i
\(268\) 3.67289 2.26918i 0.224357 0.138612i
\(269\) 0.0875040 0.0875040i 0.00533521 0.00533521i −0.704434 0.709769i \(-0.748799\pi\)
0.709769 + 0.704434i \(0.248799\pi\)
\(270\) 38.5193 + 4.48798i 2.34421 + 0.273130i
\(271\) 10.1138 0.614372 0.307186 0.951650i \(-0.400613\pi\)
0.307186 + 0.951650i \(0.400613\pi\)
\(272\) 5.39739 + 2.70079i 0.327265 + 0.163760i
\(273\) 0 0
\(274\) −31.8227 3.70774i −1.92248 0.223993i
\(275\) −9.08608 + 9.08608i −0.547911 + 0.547911i
\(276\) 14.5733 + 23.5882i 0.877208 + 1.41984i
\(277\) −11.0080 11.0080i −0.661406 0.661406i 0.294305 0.955711i \(-0.404912\pi\)
−0.955711 + 0.294305i \(0.904912\pi\)
\(278\) 10.4254 8.24957i 0.625277 0.494776i
\(279\) 22.3831i 1.34004i
\(280\) 0 0
\(281\) 4.21999i 0.251743i −0.992047 0.125872i \(-0.959827\pi\)
0.992047 0.125872i \(-0.0401727\pi\)
\(282\) 9.17481 + 11.5947i 0.546352 + 0.690455i
\(283\) 16.5834 + 16.5834i 0.985781 + 0.985781i 0.999900 0.0141195i \(-0.00449452\pi\)
−0.0141195 + 0.999900i \(0.504495\pi\)
\(284\) −6.35464 + 26.9000i −0.377079 + 1.59622i
\(285\) 16.3980 16.3980i 0.971334 0.971334i
\(286\) 0.338971 2.90931i 0.0200438 0.172031i
\(287\) 0 0
\(288\) −25.7701 16.8818i −1.51852 0.994770i
\(289\) −14.7234 −0.866080
\(290\) −3.66131 + 31.4242i −0.215000 + 1.84529i
\(291\) −33.3377 + 33.3377i −1.95429 + 1.95429i
\(292\) −6.65566 + 28.1743i −0.389493 + 1.64878i
\(293\) 13.5242 + 13.5242i 0.790093 + 0.790093i 0.981509 0.191416i \(-0.0613079\pi\)
−0.191416 + 0.981509i \(0.561308\pi\)
\(294\) 0 0
\(295\) 6.21049i 0.361589i
\(296\) 5.99547 2.80375i 0.348480 0.162965i
\(297\) 9.24501i 0.536450i
\(298\) 12.1868 9.64330i 0.705961 0.558621i
\(299\) −5.37171 5.37171i −0.310654 0.310654i
\(300\) −30.1843 48.8561i −1.74269 2.82071i
\(301\) 0 0
\(302\) 7.68137 + 0.894976i 0.442013 + 0.0515001i
\(303\) 47.5380 2.73099
\(304\) −7.85056 + 2.61415i −0.450260 + 0.149932i
\(305\) −17.5597 −1.00546
\(306\) −11.5428 1.34488i −0.659860 0.0768820i
\(307\) 8.93389 8.93389i 0.509884 0.509884i −0.404607 0.914491i \(-0.632592\pi\)
0.914491 + 0.404607i \(0.132592\pi\)
\(308\) 0 0
\(309\) 35.3203 + 35.3203i 2.00930 + 2.00930i
\(310\) 17.5826 13.9130i 0.998623 0.790203i
\(311\) 19.7737i 1.12126i −0.828066 0.560631i \(-0.810558\pi\)
0.828066 0.560631i \(-0.189442\pi\)
\(312\) 12.3058 + 4.46368i 0.696682 + 0.252706i
\(313\) 8.72743i 0.493303i −0.969104 0.246652i \(-0.920670\pi\)
0.969104 0.246652i \(-0.0793304\pi\)
\(314\) −6.97122 8.80992i −0.393409 0.497173i
\(315\) 0 0
\(316\) 3.46389 + 0.818280i 0.194859 + 0.0460319i
\(317\) 19.0197 19.0197i 1.06825 1.06825i 0.0707615 0.997493i \(-0.477457\pi\)
0.997493 0.0707615i \(-0.0225429\pi\)
\(318\) −0.454531 + 3.90114i −0.0254888 + 0.218765i
\(319\) 7.54211 0.422277
\(320\) 2.75710 + 30.7366i 0.154126 + 1.71823i
\(321\) 16.8569 0.940858
\(322\) 0 0
\(323\) −2.20702 + 2.20702i −0.122802 + 0.122802i
\(324\) 8.41065 + 1.98686i 0.467258 + 0.110381i
\(325\) 11.1259 + 11.1259i 0.617156 + 0.617156i
\(326\) 7.84039 + 9.90834i 0.434239 + 0.548772i
\(327\) 13.4541i 0.744013i
\(328\) −19.8231 7.19038i −1.09455 0.397022i
\(329\) 0 0
\(330\) −16.1692 + 12.7946i −0.890086 + 0.704318i
\(331\) 22.3328 + 22.3328i 1.22752 + 1.22752i 0.964899 + 0.262620i \(0.0845866\pi\)
0.262620 + 0.964899i \(0.415413\pi\)
\(332\) −17.2318 + 10.6462i −0.945720 + 0.584284i
\(333\) −9.01134 + 9.01134i −0.493818 + 0.493818i
\(334\) 16.6001 + 1.93412i 0.908318 + 0.105830i
\(335\) 8.32703 0.454954
\(336\) 0 0
\(337\) −23.4825 −1.27918 −0.639588 0.768718i \(-0.720895\pi\)
−0.639588 + 0.768718i \(0.720895\pi\)
\(338\) 14.6988 + 1.71259i 0.799508 + 0.0931527i
\(339\) −18.8483 + 18.8483i −1.02370 + 1.02370i
\(340\) 6.11839 + 9.90320i 0.331816 + 0.537076i
\(341\) −3.77961 3.77961i −0.204678 0.204678i
\(342\) 12.4936 9.88612i 0.675579 0.534580i
\(343\) 0 0
\(344\) −20.6167 + 9.64129i −1.11158 + 0.519824i
\(345\) 53.4784i 2.87918i
\(346\) 6.99774 + 8.84343i 0.376201 + 0.475426i
\(347\) −6.29716 6.29716i −0.338049 0.338049i 0.517584 0.855633i \(-0.326832\pi\)
−0.855633 + 0.517584i \(0.826832\pi\)
\(348\) −7.74950 + 32.8047i −0.415417 + 1.75851i
\(349\) −6.94033 + 6.94033i −0.371507 + 0.371507i −0.868026 0.496519i \(-0.834611\pi\)
0.496519 + 0.868026i \(0.334611\pi\)
\(350\) 0 0
\(351\) −11.3206 −0.604246
\(352\) 7.20220 1.50088i 0.383879 0.0799969i
\(353\) −30.0934 −1.60171 −0.800856 0.598857i \(-0.795622\pi\)
−0.800856 + 0.598857i \(0.795622\pi\)
\(354\) −0.765783 + 6.57254i −0.0407009 + 0.349327i
\(355\) −37.6969 + 37.6969i −2.00074 + 2.00074i
\(356\) −3.88951 + 16.4648i −0.206144 + 0.872633i
\(357\) 0 0
\(358\) −14.5547 18.3936i −0.769239 0.972131i
\(359\) 10.3716i 0.547394i 0.961816 + 0.273697i \(0.0882465\pi\)
−0.961816 + 0.273697i \(0.911754\pi\)
\(360\) −25.1709 53.8249i −1.32662 2.83682i
\(361\) 14.7209i 0.774786i
\(362\) 6.56482 5.19469i 0.345039 0.273027i
\(363\) −19.1292 19.1292i −1.00402 1.00402i
\(364\) 0 0
\(365\) −39.4826 + 39.4826i −2.06661 + 2.06661i
\(366\) −18.5833 2.16519i −0.971366 0.113176i
\(367\) 8.12973 0.424368 0.212184 0.977230i \(-0.431942\pi\)
0.212184 + 0.977230i \(0.431942\pi\)
\(368\) 8.53868 17.0641i 0.445109 0.889529i
\(369\) 40.6019 2.11365
\(370\) 12.6800 + 1.47737i 0.659200 + 0.0768050i
\(371\) 0 0
\(372\) 20.3231 12.5560i 1.05370 0.650999i
\(373\) −3.18688 3.18688i −0.165010 0.165010i 0.619772 0.784782i \(-0.287225\pi\)
−0.784782 + 0.619772i \(0.787225\pi\)
\(374\) 2.17622 1.72203i 0.112530 0.0890440i
\(375\) 54.7115i 2.82529i
\(376\) 3.46963 9.56539i 0.178933 0.493297i
\(377\) 9.23534i 0.475644i
\(378\) 0 0
\(379\) −0.839080 0.839080i −0.0431006 0.0431006i 0.685228 0.728329i \(-0.259703\pi\)
−0.728329 + 0.685228i \(0.759703\pi\)
\(380\) −15.5317 3.66907i −0.796758 0.188219i
\(381\) −26.6711 + 26.6711i −1.36640 + 1.36640i
\(382\) 2.02417 17.3730i 0.103565 0.888878i
\(383\) 34.3749 1.75647 0.878237 0.478225i \(-0.158720\pi\)
0.878237 + 0.478225i \(0.158720\pi\)
\(384\) −0.872140 + 32.8684i −0.0445062 + 1.67731i
\(385\) 0 0
\(386\) 3.87623 33.2688i 0.197295 1.69334i
\(387\) 30.9874 30.9874i 1.57518 1.57518i
\(388\) 31.5764 + 7.45934i 1.60305 + 0.378691i
\(389\) 10.9633 + 10.9633i 0.555860 + 0.555860i 0.928126 0.372266i \(-0.121419\pi\)
−0.372266 + 0.928126i \(0.621419\pi\)
\(390\) 15.6670 + 19.7993i 0.793329 + 1.00257i
\(391\) 7.19768i 0.364003i
\(392\) 0 0
\(393\) 28.0287i 1.41386i
\(394\) −17.9101 + 14.1721i −0.902298 + 0.713981i
\(395\) 4.85419 + 4.85419i 0.244241 + 0.244241i
\(396\) −12.0510 + 7.44535i −0.605586 + 0.374143i
\(397\) −26.4375 + 26.4375i −1.32686 + 1.32686i −0.418764 + 0.908095i \(0.637537\pi\)
−0.908095 + 0.418764i \(0.862463\pi\)
\(398\) −7.72146 0.899646i −0.387042 0.0450952i
\(399\) 0 0
\(400\) −17.6854 + 35.3433i −0.884269 + 1.76717i
\(401\) 4.97625 0.248502 0.124251 0.992251i \(-0.460347\pi\)
0.124251 + 0.992251i \(0.460347\pi\)
\(402\) 8.81247 + 1.02676i 0.439526 + 0.0512102i
\(403\) −4.62815 + 4.62815i −0.230545 + 0.230545i
\(404\) −17.1949 27.8316i −0.855478 1.38467i
\(405\) 11.7864 + 11.7864i 0.585672 + 0.585672i
\(406\) 0 0
\(407\) 3.04331i 0.150851i
\(408\) 5.25396 + 11.2349i 0.260110 + 0.556212i
\(409\) 4.06359i 0.200932i −0.994941 0.100466i \(-0.967967\pi\)
0.994941 0.100466i \(-0.0320333\pi\)
\(410\) −25.2374 31.8939i −1.24639 1.57513i
\(411\) −46.5544 46.5544i −2.29636 2.29636i
\(412\) 7.90295 33.4542i 0.389350 1.64817i
\(413\) 0 0
\(414\) −4.25192 + 36.4932i −0.208970 + 1.79354i
\(415\) −39.0674 −1.91774
\(416\) −1.83783 8.81913i −0.0901069 0.432393i
\(417\) 27.3203 1.33788
\(418\) −0.440306 + 3.77905i −0.0215361 + 0.184839i
\(419\) −0.552238 + 0.552238i −0.0269786 + 0.0269786i −0.720467 0.693489i \(-0.756073\pi\)
0.693489 + 0.720467i \(0.256073\pi\)
\(420\) 0 0
\(421\) −3.77763 3.77763i −0.184110 0.184110i 0.609034 0.793144i \(-0.291557\pi\)
−0.793144 + 0.609034i \(0.791557\pi\)
\(422\) −1.12671 1.42389i −0.0548475 0.0693139i
\(423\) 19.5920i 0.952593i
\(424\) 2.44836 1.14496i 0.118903 0.0556044i
\(425\) 14.9079i 0.723140i
\(426\) −44.5427 + 35.2463i −2.15810 + 1.70769i
\(427\) 0 0
\(428\) −6.09727 9.86901i −0.294723 0.477037i
\(429\) 4.25612 4.25612i 0.205487 0.205487i
\(430\) −43.6028 5.08027i −2.10271 0.244992i
\(431\) 1.18186 0.0569283 0.0284641 0.999595i \(-0.490938\pi\)
0.0284641 + 0.999595i \(0.490938\pi\)
\(432\) −8.98342 26.9781i −0.432215 1.29799i
\(433\) 15.2584 0.733273 0.366637 0.930364i \(-0.380509\pi\)
0.366637 + 0.930364i \(0.380509\pi\)
\(434\) 0 0
\(435\) −45.9715 + 45.9715i −2.20416 + 2.20416i
\(436\) 7.87683 4.86646i 0.377232 0.233061i
\(437\) 6.97759 + 6.97759i 0.333783 + 0.333783i
\(438\) −46.6527 + 36.9159i −2.22915 + 1.76391i
\(439\) 4.34502i 0.207376i −0.994610 0.103688i \(-0.966936\pi\)
0.994610 0.103688i \(-0.0330644\pi\)
\(440\) 13.3392 + 4.83851i 0.635923 + 0.230667i
\(441\) 0 0
\(442\) −2.10863 2.66479i −0.100297 0.126751i
\(443\) −4.31392 4.31392i −0.204961 0.204961i 0.597161 0.802121i \(-0.296295\pi\)
−0.802121 + 0.597161i \(0.796295\pi\)
\(444\) 13.2370 + 3.12700i 0.628200 + 0.148401i
\(445\) −23.0733 + 23.0733i −1.09378 + 1.09378i
\(446\) 0.524253 4.49954i 0.0248241 0.213060i
\(447\) 31.9359 1.51052
\(448\) 0 0
\(449\) 3.72499 0.175793 0.0878967 0.996130i \(-0.471985\pi\)
0.0878967 + 0.996130i \(0.471985\pi\)
\(450\) 8.80661 75.5851i 0.415147 3.56312i
\(451\) −6.85604 + 6.85604i −0.322838 + 0.322838i
\(452\) 17.8525 + 4.21732i 0.839710 + 0.198366i
\(453\) 11.2373 + 11.2373i 0.527976 + 0.527976i
\(454\) −17.1178 21.6328i −0.803380 1.01528i
\(455\) 0 0
\(456\) −15.9847 5.79809i −0.748552 0.271521i
\(457\) 10.7451i 0.502636i 0.967905 + 0.251318i \(0.0808640\pi\)
−0.967905 + 0.251318i \(0.919136\pi\)
\(458\) −11.0128 + 8.71433i −0.514594 + 0.407194i
\(459\) −7.58434 7.58434i −0.354007 0.354007i
\(460\) 31.3094 19.3436i 1.45981 0.901899i
\(461\) −7.88785 + 7.88785i −0.367374 + 0.367374i −0.866519 0.499145i \(-0.833648\pi\)
0.499145 + 0.866519i \(0.333648\pi\)
\(462\) 0 0
\(463\) 27.3485 1.27099 0.635496 0.772104i \(-0.280796\pi\)
0.635496 + 0.772104i \(0.280796\pi\)
\(464\) 22.0089 7.32870i 1.02174 0.340226i
\(465\) 46.0758 2.13671
\(466\) 4.12784 + 0.480945i 0.191219 + 0.0222794i
\(467\) −11.3915 + 11.3915i −0.527135 + 0.527135i −0.919717 0.392582i \(-0.871582\pi\)
0.392582 + 0.919717i \(0.371582\pi\)
\(468\) 9.11686 + 14.7565i 0.421427 + 0.682120i
\(469\) 0 0
\(470\) 15.3900 12.1780i 0.709890 0.561730i
\(471\) 23.0867i 1.06378i
\(472\) 4.12495 1.92901i 0.189866 0.0887898i
\(473\) 10.4651i 0.481185i
\(474\) 4.53862 + 5.73571i 0.208466 + 0.263450i
\(475\) −14.4520 14.4520i −0.663105 0.663105i
\(476\) 0 0
\(477\) −3.67995 + 3.67995i −0.168493 + 0.168493i
\(478\) 2.65317 22.7716i 0.121353 1.04155i
\(479\) −11.3880 −0.520330 −0.260165 0.965564i \(-0.583777\pi\)
−0.260165 + 0.965564i \(0.583777\pi\)
\(480\) −34.7513 + 53.0479i −1.58617 + 2.42130i
\(481\) −3.72655 −0.169916
\(482\) 2.31041 19.8297i 0.105236 0.903219i
\(483\) 0 0
\(484\) −4.28017 + 18.1185i −0.194553 + 0.823570i
\(485\) 44.2502 + 44.2502i 2.00930 + 2.00930i
\(486\) −7.69435 9.72378i −0.349023 0.441080i
\(487\) 31.3531i 1.42075i −0.703826 0.710373i \(-0.748526\pi\)
0.703826 0.710373i \(-0.251474\pi\)
\(488\) 5.45412 + 11.6630i 0.246896 + 0.527957i
\(489\) 25.9652i 1.17419i
\(490\) 0 0
\(491\) 20.2775 + 20.2775i 0.915112 + 0.915112i 0.996669 0.0815572i \(-0.0259893\pi\)
−0.0815572 + 0.996669i \(0.525989\pi\)
\(492\) −22.7760 36.8651i −1.02682 1.66201i
\(493\) 6.18733 6.18733i 0.278663 0.278663i
\(494\) 4.62746 + 0.539157i 0.208199 + 0.0242578i
\(495\) −27.3216 −1.22802
\(496\) −14.7021 7.35674i −0.660143 0.330327i
\(497\) 0 0
\(498\) −41.3449 4.81719i −1.85271 0.215864i
\(499\) −18.5167 + 18.5167i −0.828921 + 0.828921i −0.987368 0.158446i \(-0.949351\pi\)
0.158446 + 0.987368i \(0.449351\pi\)
\(500\) −32.0313 + 19.7896i −1.43249 + 0.885017i
\(501\) 24.2848 + 24.2848i 1.08497 + 1.08497i
\(502\) 22.2659 17.6188i 0.993774 0.786366i
\(503\) 31.9854i 1.42616i 0.701082 + 0.713080i \(0.252701\pi\)
−0.701082 + 0.713080i \(0.747299\pi\)
\(504\) 0 0
\(505\) 63.0987i 2.80786i
\(506\) −5.44427 6.88023i −0.242028 0.305864i
\(507\) 21.5033 + 21.5033i 0.954996 + 0.954996i
\(508\) 25.2620 + 5.96769i 1.12082 + 0.264774i
\(509\) −12.1644 + 12.1644i −0.539176 + 0.539176i −0.923287 0.384111i \(-0.874508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(510\) −2.76846 + 23.7610i −0.122589 + 1.05216i
\(511\) 0 0
\(512\) 19.5586 11.3782i 0.864375 0.502849i
\(513\) 14.7048 0.649234
\(514\) 0.529753 4.54675i 0.0233664 0.200549i
\(515\) 46.8817 46.8817i 2.06586 2.06586i
\(516\) −45.5182 10.7529i −2.00383 0.473368i
\(517\) −3.30830 3.30830i −0.145499 0.145499i
\(518\) 0 0
\(519\) 23.1745i 1.01725i
\(520\) 5.92478 16.3340i 0.259819 0.716291i
\(521\) 34.4322i 1.50850i 0.656586 + 0.754251i \(0.272000\pi\)
−0.656586 + 0.754251i \(0.728000\pi\)
\(522\) −35.0257 + 27.7155i −1.53303 + 1.21308i
\(523\) 15.4031 + 15.4031i 0.673530 + 0.673530i 0.958528 0.284998i \(-0.0919929\pi\)
−0.284998 + 0.958528i \(0.591993\pi\)
\(524\) −16.4097 + 10.1382i −0.716861 + 0.442890i
\(525\) 0 0
\(526\) 33.7357 + 3.93062i 1.47094 + 0.171383i
\(527\) −6.20137 −0.270136
\(528\) 13.5203 + 6.76537i 0.588394 + 0.294425i
\(529\) 0.244184 0.0106167
\(530\) 5.17810 + 0.603314i 0.224922 + 0.0262063i
\(531\) −6.19990 + 6.19990i −0.269053 + 0.269053i
\(532\) 0 0
\(533\) 8.39524 + 8.39524i 0.363638 + 0.363638i
\(534\) −27.2634 + 21.5733i −1.17980 + 0.933569i
\(535\) 22.3747i 0.967341i
\(536\) −2.58642 5.53073i −0.111716 0.238891i
\(537\) 48.2011i 2.08003i
\(538\) −0.108596 0.137239i −0.00468192 0.00591681i
\(539\) 0 0
\(540\) 12.6086 53.3740i 0.542589 2.29685i
\(541\) −23.7164 + 23.7164i −1.01965 + 1.01965i −0.0198437 + 0.999803i \(0.506317\pi\)
−0.999803 + 0.0198437i \(0.993683\pi\)
\(542\) 1.65529 14.2070i 0.0711010 0.610244i
\(543\) 17.2034 0.738267
\(544\) 4.67720 7.13975i 0.200533 0.306114i
\(545\) 17.8581 0.764956
\(546\) 0 0
\(547\) 27.8819 27.8819i 1.19214 1.19214i 0.215680 0.976464i \(-0.430803\pi\)
0.976464 0.215680i \(-0.0691967\pi\)
\(548\) −10.4166 + 44.0949i −0.444975 + 1.88364i
\(549\) −17.5297 17.5297i −0.748150 0.748150i
\(550\) 11.2762 + 14.2504i 0.480820 + 0.607639i
\(551\) 11.9963i 0.511058i
\(552\) 35.5198 16.6106i 1.51182 0.706995i
\(553\) 0 0
\(554\) −17.2647 + 13.6614i −0.733506 + 0.580418i
\(555\) 18.5499 + 18.5499i 0.787400 + 0.787400i
\(556\) −9.88197 15.9949i −0.419089 0.678335i
\(557\) 0.275943 0.275943i 0.0116921 0.0116921i −0.701237 0.712929i \(-0.747368\pi\)
0.712929 + 0.701237i \(0.247368\pi\)
\(558\) 31.4418 + 3.66336i 1.33104 + 0.155082i
\(559\) 12.8145 0.541997
\(560\) 0 0
\(561\) 5.70288 0.240776
\(562\) −5.92786 0.690669i −0.250052 0.0291341i
\(563\) 13.8911 13.8911i 0.585438 0.585438i −0.350954 0.936393i \(-0.614143\pi\)
0.936393 + 0.350954i \(0.114143\pi\)
\(564\) 17.7888 10.9903i 0.749045 0.462775i
\(565\) 25.0179 + 25.0179i 1.05251 + 1.05251i
\(566\) 26.0090 20.5807i 1.09324 0.865073i
\(567\) 0 0
\(568\) 36.7467 + 13.3291i 1.54186 + 0.559275i
\(569\) 8.08076i 0.338763i −0.985551 0.169381i \(-0.945823\pi\)
0.985551 0.169381i \(-0.0541770\pi\)
\(570\) −20.3507 25.7183i −0.852395 1.07722i
\(571\) −7.55816 7.55816i −0.316299 0.316299i 0.531045 0.847344i \(-0.321800\pi\)
−0.847344 + 0.531045i \(0.821800\pi\)
\(572\) −4.03126 0.952312i −0.168556 0.0398182i
\(573\) 25.4154 25.4154i 1.06175 1.06175i
\(574\) 0 0
\(575\) 47.1320 1.96554
\(576\) −27.9317 + 33.4365i −1.16382 + 1.39319i
\(577\) −1.95969 −0.0815831 −0.0407915 0.999168i \(-0.512988\pi\)
−0.0407915 + 0.999168i \(0.512988\pi\)
\(578\) −2.40972 + 20.6821i −0.100231 + 0.860261i
\(579\) 48.6699 48.6699i 2.02265 2.02265i
\(580\) 43.5427 + 10.2862i 1.80801 + 0.427110i
\(581\) 0 0
\(582\) 41.3735 + 52.2860i 1.71499 + 2.16733i
\(583\) 1.24279i 0.0514713i
\(584\) 38.4874 + 13.9605i 1.59262 + 0.577688i
\(585\) 33.4554i 1.38321i
\(586\) 21.2111 16.7842i 0.876221 0.693347i
\(587\) −24.6131 24.6131i −1.01589 1.01589i −0.999872 0.0160192i \(-0.994901\pi\)
−0.0160192 0.999872i \(-0.505099\pi\)
\(588\) 0 0
\(589\) 6.01174 6.01174i 0.247709 0.247709i
\(590\) 8.72395 + 1.01645i 0.359159 + 0.0418465i
\(591\) −46.9341 −1.93061
\(592\) −2.95720 8.88078i −0.121540 0.364998i
\(593\) −16.5483 −0.679558 −0.339779 0.940505i \(-0.610352\pi\)
−0.339779 + 0.940505i \(0.610352\pi\)
\(594\) −12.9866 1.51310i −0.532845 0.0620831i
\(595\) 0 0
\(596\) −11.5515 18.6972i −0.473167 0.765866i
\(597\) −11.2960 11.2960i −0.462313 0.462313i
\(598\) −8.42487 + 6.66654i −0.344519 + 0.272615i
\(599\) 10.2649i 0.419412i 0.977764 + 0.209706i \(0.0672507\pi\)
−0.977764 + 0.209706i \(0.932749\pi\)
\(600\) −73.5689 + 34.4041i −3.00344 + 1.40454i
\(601\) 35.6586i 1.45455i −0.686348 0.727273i \(-0.740787\pi\)
0.686348 0.727273i \(-0.259213\pi\)
\(602\) 0 0
\(603\) 8.31283 + 8.31283i 0.338524 + 0.338524i
\(604\) 2.51436 10.6436i 0.102308 0.433083i
\(605\) −25.3908 + 25.3908i −1.03228 + 1.03228i
\(606\) 7.78037 66.7772i 0.316056 2.71264i
\(607\) −23.1111 −0.938052 −0.469026 0.883184i \(-0.655395\pi\)
−0.469026 + 0.883184i \(0.655395\pi\)
\(608\) 2.38725 + 11.4556i 0.0968157 + 0.464586i
\(609\) 0 0
\(610\) −2.87393 + 24.6663i −0.116362 + 0.998708i
\(611\) −4.05103 + 4.05103i −0.163887 + 0.163887i
\(612\) −3.77835 + 15.9942i −0.152731 + 0.646529i
\(613\) −26.9200 26.9200i −1.08729 1.08729i −0.995807 0.0914813i \(-0.970840\pi\)
−0.0914813 0.995807i \(-0.529160\pi\)
\(614\) −11.0874 14.0117i −0.447449 0.565467i
\(615\) 83.5793i 3.37024i
\(616\) 0 0
\(617\) 47.9337i 1.92974i 0.262732 + 0.964869i \(0.415377\pi\)
−0.262732 + 0.964869i \(0.584623\pi\)
\(618\) 55.3955 43.8340i 2.22833 1.76326i
\(619\) −4.05053 4.05053i −0.162805 0.162805i 0.621003 0.783808i \(-0.286725\pi\)
−0.783808 + 0.621003i \(0.786725\pi\)
\(620\) −16.6660 26.9755i −0.669323 1.08336i
\(621\) −23.9782 + 23.9782i −0.962213 + 0.962213i
\(622\) −27.7763 3.23629i −1.11373 0.129763i
\(623\) 0 0
\(624\) 8.28423 16.5556i 0.331634 0.662755i
\(625\) −23.2188 −0.928752
\(626\) −12.2595 1.42839i −0.489989 0.0570898i
\(627\) −5.52849 + 5.52849i −0.220787 + 0.220787i
\(628\) −13.5164 + 8.35067i −0.539361 + 0.333228i
\(629\) −2.49664 2.49664i −0.0995477 0.0995477i
\(630\) 0 0
\(631\) 2.35784i 0.0938640i 0.998898 + 0.0469320i \(0.0149444\pi\)
−0.998898 + 0.0469320i \(0.985056\pi\)
\(632\) 1.71637 4.73184i 0.0682735 0.188222i
\(633\) 3.73136i 0.148308i
\(634\) −23.6043 29.8301i −0.937448 1.18471i
\(635\) 35.4014 + 35.4014i 1.40486 + 1.40486i
\(636\) 5.40558 + 1.27697i 0.214345 + 0.0506351i
\(637\) 0 0
\(638\) 1.23439 10.5945i 0.0488699 0.419440i
\(639\) −75.2652 −2.97744
\(640\) 43.6273 + 1.15762i 1.72452 + 0.0457590i
\(641\) −49.8415 −1.96862 −0.984311 0.176440i \(-0.943542\pi\)
−0.984311 + 0.176440i \(0.943542\pi\)
\(642\) 2.75890 23.6790i 0.108885 0.934536i
\(643\) 6.07975 6.07975i 0.239762 0.239762i −0.576990 0.816751i \(-0.695773\pi\)
0.816751 + 0.576990i \(0.195773\pi\)
\(644\) 0 0
\(645\) −63.7879 63.7879i −2.51165 2.51165i
\(646\) 2.73901 + 3.46144i 0.107765 + 0.136188i
\(647\) 0.463264i 0.0182128i 0.999959 + 0.00910640i \(0.00289870\pi\)
−0.999959 + 0.00910640i \(0.997101\pi\)
\(648\) 4.16751 11.4894i 0.163715 0.451344i
\(649\) 2.09383i 0.0821901i
\(650\) 17.4497 13.8078i 0.684432 0.541586i
\(651\) 0 0
\(652\) 15.2016 9.39183i 0.595339 0.367812i
\(653\) 6.63668 6.63668i 0.259713 0.259713i −0.565224 0.824937i \(-0.691210\pi\)
0.824937 + 0.565224i \(0.191210\pi\)
\(654\) 18.8991 + 2.20198i 0.739014 + 0.0861044i
\(655\) −37.2034 −1.45366
\(656\) −13.3448 + 26.6689i −0.521026 + 1.04124i
\(657\) −78.8305 −3.07547
\(658\) 0 0
\(659\) −4.62922 + 4.62922i −0.180329 + 0.180329i −0.791499 0.611170i \(-0.790699\pi\)
0.611170 + 0.791499i \(0.290699\pi\)
\(660\) 15.3263 + 24.8071i 0.596576 + 0.965615i
\(661\) 2.25711 + 2.25711i 0.0877916 + 0.0877916i 0.749639 0.661847i \(-0.230227\pi\)
−0.661847 + 0.749639i \(0.730227\pi\)
\(662\) 35.0262 27.7160i 1.36133 1.07721i
\(663\) 6.98320i 0.271205i
\(664\) 12.1345 + 25.9482i 0.470911 + 1.00698i
\(665\) 0 0
\(666\) 11.1835 + 14.1332i 0.433351 + 0.547650i
\(667\) −19.5615 19.5615i −0.757425 0.757425i
\(668\) 5.43376 23.0018i 0.210239 0.889968i
\(669\) 6.58253 6.58253i 0.254495 0.254495i
\(670\) 1.36286 11.6971i 0.0526517 0.451898i
\(671\) 5.92014 0.228544
\(672\) 0 0
\(673\) 6.82222 0.262977 0.131489 0.991318i \(-0.458024\pi\)
0.131489 + 0.991318i \(0.458024\pi\)
\(674\) −3.84330 + 32.9862i −0.148038 + 1.27058i
\(675\) 49.6639 49.6639i 1.91157 1.91157i
\(676\) 4.81139 20.3673i 0.185054 0.783356i
\(677\) −4.77844 4.77844i −0.183650 0.183650i 0.609294 0.792944i \(-0.291453\pi\)
−0.792944 + 0.609294i \(0.791453\pi\)
\(678\) 23.3916 + 29.5612i 0.898347 + 1.13529i
\(679\) 0 0
\(680\) 14.9125 6.97375i 0.571868 0.267431i
\(681\) 56.6895i 2.17235i
\(682\) −5.92786 + 4.69067i −0.226990 + 0.179615i
\(683\) −29.2736 29.2736i −1.12012 1.12012i −0.991723 0.128400i \(-0.959016\pi\)
−0.128400 0.991723i \(-0.540984\pi\)
\(684\) −11.8424 19.1680i −0.452804 0.732906i
\(685\) −61.7932 + 61.7932i −2.36100 + 2.36100i
\(686\) 0 0
\(687\) −28.8594 −1.10106
\(688\) 10.1690 + 30.5385i 0.387688 + 1.16427i
\(689\) −1.52181 −0.0579762
\(690\) 75.1216 + 8.75261i 2.85983 + 0.333206i
\(691\) 4.65064 4.65064i 0.176919 0.176919i −0.613092 0.790011i \(-0.710075\pi\)
0.790011 + 0.613092i \(0.210075\pi\)
\(692\) 13.5678 8.38243i 0.515769 0.318652i
\(693\) 0 0
\(694\) −9.87632 + 7.81505i −0.374900 + 0.296655i
\(695\) 36.2631i 1.37554i
\(696\) 44.8127 + 16.2548i 1.69862 + 0.616138i
\(697\) 11.2490i 0.426086i
\(698\) 8.61326 + 10.8851i 0.326017 + 0.412005i
\(699\) 6.03875 + 6.03875i 0.228407 + 0.228407i
\(700\) 0 0
\(701\) −4.01206 + 4.01206i −0.151533 + 0.151533i −0.778802 0.627269i \(-0.784173\pi\)
0.627269 + 0.778802i \(0.284173\pi\)
\(702\) −1.85279 + 15.9021i −0.0699292 + 0.600186i
\(703\) 4.84060 0.182567
\(704\) −0.929538 10.3627i −0.0350333 0.390557i
\(705\) 40.3302 1.51892
\(706\) −4.92528 + 42.2726i −0.185365 + 1.59095i
\(707\) 0 0
\(708\) 9.10719 + 2.15141i 0.342269 + 0.0808549i
\(709\) 36.0117 + 36.0117i 1.35245 + 1.35245i 0.882915 + 0.469533i \(0.155578\pi\)
0.469533 + 0.882915i \(0.344422\pi\)
\(710\) 46.7835 + 59.1230i 1.75575 + 2.21885i
\(711\) 9.69181i 0.363471i
\(712\) 22.4917 + 8.15837i 0.842912 + 0.305748i
\(713\) 19.6059i 0.734248i
\(714\) 0 0
\(715\) −5.64929 5.64929i −0.211271 0.211271i
\(716\) −28.2198 + 17.4347i −1.05462 + 0.651566i
\(717\) 33.3133 33.3133i 1.24411 1.24411i
\(718\) 14.5691 + 1.69749i 0.543716 + 0.0633496i
\(719\) −7.62249 −0.284271 −0.142135 0.989847i \(-0.545397\pi\)
−0.142135 + 0.989847i \(0.545397\pi\)
\(720\) −79.7281 + 26.5485i −2.97129 + 0.989406i
\(721\) 0 0
\(722\) 20.6787 + 2.40932i 0.769580 + 0.0896657i
\(723\) 29.0095 29.0095i 1.07888 1.07888i
\(724\) −6.22260 10.0719i −0.231261 0.374318i
\(725\) 40.5160 + 40.5160i 1.50473 + 1.50473i
\(726\) −30.0018 + 23.7402i −1.11347 + 0.881080i
\(727\) 25.4856i 0.945207i 0.881275 + 0.472604i \(0.156686\pi\)
−0.881275 + 0.472604i \(0.843314\pi\)
\(728\) 0 0
\(729\) 38.4448i 1.42388i
\(730\) 48.9997 + 61.9236i 1.81356 + 2.29190i
\(731\) 8.58525 + 8.58525i 0.317537 + 0.317537i
\(732\) −6.08293 + 25.7498i −0.224832 + 0.951742i
\(733\) 14.9748 14.9748i 0.553106 0.553106i −0.374230 0.927336i \(-0.622093\pi\)
0.927336 + 0.374230i \(0.122093\pi\)
\(734\) 1.33056 11.4199i 0.0491120 0.421517i
\(735\) 0 0
\(736\) −22.5727 14.7872i −0.832039 0.545063i
\(737\) −2.80741 −0.103412
\(738\) 6.64516 57.0339i 0.244612 2.09945i
\(739\) −12.3417 + 12.3417i −0.453996 + 0.453996i −0.896679 0.442682i \(-0.854027\pi\)
0.442682 + 0.896679i \(0.354027\pi\)
\(740\) 4.15057 17.5699i 0.152578 0.645882i
\(741\) 6.76966 + 6.76966i 0.248690 + 0.248690i
\(742\) 0 0
\(743\) 10.6724i 0.391531i 0.980651 + 0.195766i \(0.0627192\pi\)
−0.980651 + 0.195766i \(0.937281\pi\)
\(744\) −14.3114 30.6031i −0.524680 1.12196i
\(745\) 42.3896i 1.55303i
\(746\) −4.99823 + 3.95506i −0.182998 + 0.144805i
\(747\) −39.0007 39.0007i −1.42696 1.42696i
\(748\) −2.06278 3.33880i −0.0754226 0.122079i
\(749\) 0 0
\(750\) −76.8538 8.95442i −2.80630 0.326969i
\(751\) −2.82952 −0.103251 −0.0516254 0.998667i \(-0.516440\pi\)
−0.0516254 + 0.998667i \(0.516440\pi\)
\(752\) −12.8687 6.43936i −0.469275 0.234819i
\(753\) 58.3485 2.12634
\(754\) −12.9730 1.51151i −0.472448 0.0550461i
\(755\) 14.9157 14.9157i 0.542837 0.542837i
\(756\) 0 0
\(757\) 15.6590 + 15.6590i 0.569136 + 0.569136i 0.931886 0.362750i \(-0.118162\pi\)
−0.362750 + 0.931886i \(0.618162\pi\)
\(758\) −1.31599 + 1.04134i −0.0477990 + 0.0378230i
\(759\) 18.0299i 0.654444i
\(760\) −7.69600 + 21.2170i −0.279163 + 0.769622i
\(761\) 4.79367i 0.173770i −0.996218 0.0868852i \(-0.972309\pi\)
0.996218 0.0868852i \(-0.0276913\pi\)
\(762\) 33.1001 + 41.8304i 1.19909 + 1.51535i
\(763\) 0 0
\(764\) −24.0727 5.68674i −0.870920 0.205739i
\(765\) −22.4139 + 22.4139i −0.810375 + 0.810375i
\(766\) 5.62601 48.2868i 0.203276 1.74467i
\(767\) −2.56390 −0.0925772
\(768\) 46.0278 + 6.60455i 1.66089 + 0.238321i
\(769\) −13.5489 −0.488585 −0.244293 0.969702i \(-0.578556\pi\)
−0.244293 + 0.969702i \(0.578556\pi\)
\(770\) 0 0
\(771\) 6.65159 6.65159i 0.239551 0.239551i
\(772\) −46.0986 10.8900i −1.65913 0.391938i
\(773\) −18.7803 18.7803i −0.675480 0.675480i 0.283494 0.958974i \(-0.408506\pi\)
−0.958974 + 0.283494i \(0.908506\pi\)
\(774\) −38.4568 48.6000i −1.38230 1.74689i
\(775\) 40.6080i 1.45868i
\(776\) 15.6462 43.1348i 0.561666 1.54845i
\(777\) 0 0
\(778\) 17.1945 13.6059i 0.616454 0.487795i
\(779\) −10.9050 10.9050i −0.390712 0.390712i
\(780\) 30.3764 18.7671i 1.08765 0.671971i