Properties

Label 1110.2.o.a.253.12
Level $1110$
Weight $2$
Character 1110.253
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.12
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.12

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.407420 + 2.19864i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.64494 - 1.64494i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.407420 + 2.19864i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.64494 - 1.64494i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-0.407420 - 2.19864i) q^{10} -5.09841i q^{11} +(0.707107 - 0.707107i) q^{12} -5.90090 q^{13} +(-1.64494 + 1.64494i) q^{14} +(1.84276 + 1.26658i) q^{15} +1.00000 q^{16} -0.720684i q^{17} +1.00000i q^{18} +(-5.20267 - 5.20267i) q^{19} +(0.407420 + 2.19864i) q^{20} -2.32629i q^{21} +5.09841i q^{22} +2.47151 q^{23} +(-0.707107 + 0.707107i) q^{24} +(-4.66802 + 1.79154i) q^{25} +5.90090 q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.64494 - 1.64494i) q^{28} +(-2.09433 + 2.09433i) q^{29} +(-1.84276 - 1.26658i) q^{30} +(-6.99049 - 6.99049i) q^{31} -1.00000 q^{32} +(-3.60512 - 3.60512i) q^{33} +0.720684i q^{34} +(4.28681 + 2.94644i) q^{35} -1.00000i q^{36} +(0.654393 - 6.04746i) q^{37} +(5.20267 + 5.20267i) q^{38} +(-4.17257 + 4.17257i) q^{39} +(-0.407420 - 2.19864i) q^{40} +6.58809i q^{41} +2.32629i q^{42} +10.4051 q^{43} -5.09841i q^{44} +(2.19864 - 0.407420i) q^{45} -2.47151 q^{46} +(6.69776 - 6.69776i) q^{47} +(0.707107 - 0.707107i) q^{48} +1.58835i q^{49} +(4.66802 - 1.79154i) q^{50} +(-0.509601 - 0.509601i) q^{51} -5.90090 q^{52} +(6.02669 + 6.02669i) q^{53} +(0.707107 + 0.707107i) q^{54} +(11.2096 - 2.07719i) q^{55} +(-1.64494 + 1.64494i) q^{56} -7.35769 q^{57} +(2.09433 - 2.09433i) q^{58} +(-1.31697 - 1.31697i) q^{59} +(1.84276 + 1.26658i) q^{60} +(-0.136297 - 0.136297i) q^{61} +(6.99049 + 6.99049i) q^{62} +(-1.64494 - 1.64494i) q^{63} +1.00000 q^{64} +(-2.40415 - 12.9740i) q^{65} +(3.60512 + 3.60512i) q^{66} +(-8.82528 - 8.82528i) q^{67} -0.720684i q^{68} +(1.74762 - 1.74762i) q^{69} +(-4.28681 - 2.94644i) q^{70} +0.630243 q^{71} +1.00000i q^{72} +(0.800728 - 0.800728i) q^{73} +(-0.654393 + 6.04746i) q^{74} +(-2.03398 + 4.56760i) q^{75} +(-5.20267 - 5.20267i) q^{76} +(-8.38658 - 8.38658i) q^{77} +(4.17257 - 4.17257i) q^{78} +(1.35715 + 1.35715i) q^{79} +(0.407420 + 2.19864i) q^{80} -1.00000 q^{81} -6.58809i q^{82} +(0.0877629 + 0.0877629i) q^{83} -2.32629i q^{84} +(1.58452 - 0.293621i) q^{85} -10.4051 q^{86} +2.96182i q^{87} +5.09841i q^{88} +(0.651916 - 0.651916i) q^{89} +(-2.19864 + 0.407420i) q^{90} +(-9.70663 + 9.70663i) q^{91} +2.47151 q^{92} -9.88605 q^{93} +(-6.69776 + 6.69776i) q^{94} +(9.31912 - 13.5585i) q^{95} +(-0.707107 + 0.707107i) q^{96} +5.99946i q^{97} -1.58835i q^{98} -5.09841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} + O(q^{10}) \) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} - 4q^{10} - 8q^{13} - 4q^{14} + 36q^{16} - 4q^{19} + 4q^{20} + 4q^{25} + 8q^{26} + 4q^{28} - 36q^{29} - 4q^{31} - 36q^{32} + 4q^{33} + 28q^{35} + 28q^{37} + 4q^{38} - 4q^{39} - 4q^{40} - 32q^{43} + 16q^{47} - 4q^{50} - 8q^{52} - 8q^{53} - 8q^{55} - 4q^{56} - 8q^{57} + 36q^{58} + 4q^{59} - 4q^{61} + 4q^{62} - 4q^{63} + 36q^{64} - 52q^{65} - 4q^{66} - 16q^{67} + 8q^{69} - 28q^{70} - 8q^{71} + 4q^{73} - 28q^{74} + 16q^{75} - 4q^{76} - 8q^{77} + 4q^{78} + 12q^{79} + 4q^{80} - 36q^{81} + 8q^{83} - 8q^{85} + 32q^{86} + 24q^{89} + 56q^{91} - 8q^{93} - 16q^{94} + 20q^{95} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000 0.500000
\(5\) 0.407420 + 2.19864i 0.182204 + 0.983261i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) 1.64494 1.64494i 0.621728 0.621728i −0.324245 0.945973i \(-0.605110\pi\)
0.945973 + 0.324245i \(0.105110\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) −0.407420 2.19864i −0.128837 0.695270i
\(11\) 5.09841i 1.53723i −0.639712 0.768614i \(-0.720947\pi\)
0.639712 0.768614i \(-0.279053\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) −5.90090 −1.63662 −0.818308 0.574780i \(-0.805088\pi\)
−0.818308 + 0.574780i \(0.805088\pi\)
\(14\) −1.64494 + 1.64494i −0.439628 + 0.439628i
\(15\) 1.84276 + 1.26658i 0.475799 + 0.327030i
\(16\) 1.00000 0.250000
\(17\) 0.720684i 0.174792i −0.996174 0.0873958i \(-0.972146\pi\)
0.996174 0.0873958i \(-0.0278545\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −5.20267 5.20267i −1.19357 1.19357i −0.976056 0.217519i \(-0.930204\pi\)
−0.217519 0.976056i \(-0.569796\pi\)
\(20\) 0.407420 + 2.19864i 0.0911019 + 0.491630i
\(21\) 2.32629i 0.507639i
\(22\) 5.09841i 1.08698i
\(23\) 2.47151 0.515346 0.257673 0.966232i \(-0.417044\pi\)
0.257673 + 0.966232i \(0.417044\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) −4.66802 + 1.79154i −0.933604 + 0.358308i
\(26\) 5.90090 1.15726
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 1.64494 1.64494i 0.310864 0.310864i
\(29\) −2.09433 + 2.09433i −0.388907 + 0.388907i −0.874297 0.485391i \(-0.838677\pi\)
0.485391 + 0.874297i \(0.338677\pi\)
\(30\) −1.84276 1.26658i −0.336441 0.231245i
\(31\) −6.99049 6.99049i −1.25553 1.25553i −0.953205 0.302324i \(-0.902238\pi\)
−0.302324 0.953205i \(-0.597762\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.60512 3.60512i −0.627571 0.627571i
\(34\) 0.720684i 0.123596i
\(35\) 4.28681 + 2.94644i 0.724602 + 0.498040i
\(36\) 1.00000i 0.166667i
\(37\) 0.654393 6.04746i 0.107582 0.994196i
\(38\) 5.20267 + 5.20267i 0.843985 + 0.843985i
\(39\) −4.17257 + 4.17257i −0.668146 + 0.668146i
\(40\) −0.407420 2.19864i −0.0644187 0.347635i
\(41\) 6.58809i 1.02889i 0.857524 + 0.514444i \(0.172001\pi\)
−0.857524 + 0.514444i \(0.827999\pi\)
\(42\) 2.32629i 0.358955i
\(43\) 10.4051 1.58676 0.793380 0.608726i \(-0.208319\pi\)
0.793380 + 0.608726i \(0.208319\pi\)
\(44\) 5.09841i 0.768614i
\(45\) 2.19864 0.407420i 0.327754 0.0607346i
\(46\) −2.47151 −0.364405
\(47\) 6.69776 6.69776i 0.976969 0.976969i −0.0227714 0.999741i \(-0.507249\pi\)
0.999741 + 0.0227714i \(0.00724897\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 1.58835i 0.226907i
\(50\) 4.66802 1.79154i 0.660157 0.253362i
\(51\) −0.509601 0.509601i −0.0713584 0.0713584i
\(52\) −5.90090 −0.818308
\(53\) 6.02669 + 6.02669i 0.827829 + 0.827829i 0.987216 0.159387i \(-0.0509518\pi\)
−0.159387 + 0.987216i \(0.550952\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) 11.2096 2.07719i 1.51150 0.280089i
\(56\) −1.64494 + 1.64494i −0.219814 + 0.219814i
\(57\) −7.35769 −0.974550
\(58\) 2.09433 2.09433i 0.274999 0.274999i
\(59\) −1.31697 1.31697i −0.171455 0.171455i 0.616163 0.787619i \(-0.288686\pi\)
−0.787619 + 0.616163i \(0.788686\pi\)
\(60\) 1.84276 + 1.26658i 0.237899 + 0.163515i
\(61\) −0.136297 0.136297i −0.0174510 0.0174510i 0.698327 0.715778i \(-0.253928\pi\)
−0.715778 + 0.698327i \(0.753928\pi\)
\(62\) 6.99049 + 6.99049i 0.887793 + 0.887793i
\(63\) −1.64494 1.64494i −0.207243 0.207243i
\(64\) 1.00000 0.125000
\(65\) −2.40415 12.9740i −0.298198 1.60922i
\(66\) 3.60512 + 3.60512i 0.443760 + 0.443760i
\(67\) −8.82528 8.82528i −1.07818 1.07818i −0.996673 0.0815072i \(-0.974027\pi\)
−0.0815072 0.996673i \(-0.525973\pi\)
\(68\) 0.720684i 0.0873958i
\(69\) 1.74762 1.74762i 0.210389 0.210389i
\(70\) −4.28681 2.94644i −0.512371 0.352167i
\(71\) 0.630243 0.0747961 0.0373980 0.999300i \(-0.488093\pi\)
0.0373980 + 0.999300i \(0.488093\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 0.800728 0.800728i 0.0937181 0.0937181i −0.658693 0.752411i \(-0.728891\pi\)
0.752411 + 0.658693i \(0.228891\pi\)
\(74\) −0.654393 + 6.04746i −0.0760717 + 0.703003i
\(75\) −2.03398 + 4.56760i −0.234864 + 0.527421i
\(76\) −5.20267 5.20267i −0.596787 0.596787i
\(77\) −8.38658 8.38658i −0.955739 0.955739i
\(78\) 4.17257 4.17257i 0.472451 0.472451i
\(79\) 1.35715 + 1.35715i 0.152691 + 0.152691i 0.779319 0.626628i \(-0.215565\pi\)
−0.626628 + 0.779319i \(0.715565\pi\)
\(80\) 0.407420 + 2.19864i 0.0455509 + 0.245815i
\(81\) −1.00000 −0.111111
\(82\) 6.58809i 0.727533i
\(83\) 0.0877629 + 0.0877629i 0.00963323 + 0.00963323i 0.711907 0.702274i \(-0.247832\pi\)
−0.702274 + 0.711907i \(0.747832\pi\)
\(84\) 2.32629i 0.253820i
\(85\) 1.58452 0.293621i 0.171866 0.0318477i
\(86\) −10.4051 −1.12201
\(87\) 2.96182i 0.317541i
\(88\) 5.09841i 0.543492i
\(89\) 0.651916 0.651916i 0.0691030 0.0691030i −0.671711 0.740814i \(-0.734440\pi\)
0.740814 + 0.671711i \(0.234440\pi\)
\(90\) −2.19864 + 0.407420i −0.231757 + 0.0429458i
\(91\) −9.70663 + 9.70663i −1.01753 + 1.01753i
\(92\) 2.47151 0.257673
\(93\) −9.88605 −1.02514
\(94\) −6.69776 + 6.69776i −0.690822 + 0.690822i
\(95\) 9.31912 13.5585i 0.956122 1.39107i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) 5.99946i 0.609153i 0.952488 + 0.304577i \(0.0985150\pi\)
−0.952488 + 0.304577i \(0.901485\pi\)
\(98\) 1.58835i 0.160448i
\(99\) −5.09841 −0.512410
\(100\) −4.66802 + 1.79154i −0.466802 + 0.179154i
\(101\) 0.764728i 0.0760932i −0.999276 0.0380466i \(-0.987886\pi\)
0.999276 0.0380466i \(-0.0121135\pi\)
\(102\) 0.509601 + 0.509601i 0.0504580 + 0.0504580i
\(103\) 2.86283i 0.282083i 0.990004 + 0.141041i \(0.0450451\pi\)
−0.990004 + 0.141041i \(0.954955\pi\)
\(104\) 5.90090 0.578631
\(105\) 5.11468 0.947779i 0.499142 0.0924938i
\(106\) −6.02669 6.02669i −0.585363 0.585363i
\(107\) 7.65897 7.65897i 0.740421 0.740421i −0.232238 0.972659i \(-0.574605\pi\)
0.972659 + 0.232238i \(0.0746048\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) −1.40152 1.40152i −0.134241 0.134241i 0.636793 0.771034i \(-0.280260\pi\)
−0.771034 + 0.636793i \(0.780260\pi\)
\(110\) −11.2096 + 2.07719i −1.06879 + 0.198053i
\(111\) −3.81347 4.73893i −0.361959 0.449799i
\(112\) 1.64494 1.64494i 0.155432 0.155432i
\(113\) 15.5998i 1.46751i 0.679416 + 0.733753i \(0.262233\pi\)
−0.679416 + 0.733753i \(0.737767\pi\)
\(114\) 7.35769 0.689111
\(115\) 1.00694 + 5.43396i 0.0938980 + 0.506720i
\(116\) −2.09433 + 2.09433i −0.194453 + 0.194453i
\(117\) 5.90090i 0.545539i
\(118\) 1.31697 + 1.31697i 0.121237 + 0.121237i
\(119\) −1.18548 1.18548i −0.108673 0.108673i
\(120\) −1.84276 1.26658i −0.168220 0.115623i
\(121\) −14.9938 −1.36307
\(122\) 0.136297 + 0.136297i 0.0123397 + 0.0123397i
\(123\) 4.65848 + 4.65848i 0.420041 + 0.420041i
\(124\) −6.99049 6.99049i −0.627765 0.627765i
\(125\) −5.84079 9.53337i −0.522416 0.852691i
\(126\) 1.64494 + 1.64494i 0.146543 + 0.146543i
\(127\) 14.2375 14.2375i 1.26337 1.26337i 0.313928 0.949447i \(-0.398355\pi\)
0.949447 0.313928i \(-0.101645\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 7.35750 7.35750i 0.647792 0.647792i
\(130\) 2.40415 + 12.9740i 0.210858 + 1.13789i
\(131\) −9.64243 9.64243i −0.842463 0.842463i 0.146716 0.989179i \(-0.453130\pi\)
−0.989179 + 0.146716i \(0.953130\pi\)
\(132\) −3.60512 3.60512i −0.313786 0.313786i
\(133\) −17.1162 −1.48416
\(134\) 8.82528 + 8.82528i 0.762388 + 0.762388i
\(135\) 1.26658 1.84276i 0.109010 0.158600i
\(136\) 0.720684i 0.0617982i
\(137\) −5.63532 + 5.63532i −0.481458 + 0.481458i −0.905597 0.424139i \(-0.860577\pi\)
0.424139 + 0.905597i \(0.360577\pi\)
\(138\) −1.74762 + 1.74762i −0.148768 + 0.148768i
\(139\) −18.1510 −1.53955 −0.769775 0.638315i \(-0.779632\pi\)
−0.769775 + 0.638315i \(0.779632\pi\)
\(140\) 4.28681 + 2.94644i 0.362301 + 0.249020i
\(141\) 9.47207i 0.797692i
\(142\) −0.630243 −0.0528888
\(143\) 30.0852i 2.51585i
\(144\) 1.00000i 0.0833333i
\(145\) −5.45794 3.75140i −0.453257 0.311536i
\(146\) −0.800728 + 0.800728i −0.0662687 + 0.0662687i
\(147\) 1.12313 + 1.12313i 0.0926346 + 0.0926346i
\(148\) 0.654393 6.04746i 0.0537908 0.497098i
\(149\) 19.7092i 1.61464i −0.590112 0.807322i \(-0.700916\pi\)
0.590112 0.807322i \(-0.299084\pi\)
\(150\) 2.03398 4.56760i 0.166074 0.372943i
\(151\) 5.28263i 0.429895i 0.976626 + 0.214947i \(0.0689580\pi\)
−0.976626 + 0.214947i \(0.931042\pi\)
\(152\) 5.20267 + 5.20267i 0.421992 + 0.421992i
\(153\) −0.720684 −0.0582639
\(154\) 8.38658 + 8.38658i 0.675809 + 0.675809i
\(155\) 12.5215 18.2176i 1.00575 1.46327i
\(156\) −4.17257 + 4.17257i −0.334073 + 0.334073i
\(157\) 16.6599 16.6599i 1.32961 1.32961i 0.423893 0.905712i \(-0.360663\pi\)
0.905712 0.423893i \(-0.139337\pi\)
\(158\) −1.35715 1.35715i −0.107969 0.107969i
\(159\) 8.52302 0.675920
\(160\) −0.407420 2.19864i −0.0322094 0.173818i
\(161\) 4.06549 4.06549i 0.320405 0.320405i
\(162\) 1.00000 0.0785674
\(163\) 15.8733i 1.24330i 0.783297 + 0.621648i \(0.213537\pi\)
−0.783297 + 0.621648i \(0.786463\pi\)
\(164\) 6.58809i 0.514444i
\(165\) 6.45756 9.39515i 0.502720 0.731412i
\(166\) −0.0877629 0.0877629i −0.00681172 0.00681172i
\(167\) 16.1399i 1.24894i 0.781048 + 0.624471i \(0.214686\pi\)
−0.781048 + 0.624471i \(0.785314\pi\)
\(168\) 2.32629i 0.179478i
\(169\) 21.8207 1.67851
\(170\) −1.58452 + 0.293621i −0.121527 + 0.0225197i
\(171\) −5.20267 + 5.20267i −0.397858 + 0.397858i
\(172\) 10.4051 0.793380
\(173\) 7.18619 7.18619i 0.546356 0.546356i −0.379029 0.925385i \(-0.623742\pi\)
0.925385 + 0.379029i \(0.123742\pi\)
\(174\) 2.96182i 0.224535i
\(175\) −4.73163 + 10.6256i −0.357678 + 0.803218i
\(176\) 5.09841i 0.384307i
\(177\) −1.86248 −0.139993
\(178\) −0.651916 + 0.651916i −0.0488632 + 0.0488632i
\(179\) 1.27828 1.27828i 0.0955432 0.0955432i −0.657720 0.753263i \(-0.728479\pi\)
0.753263 + 0.657720i \(0.228479\pi\)
\(180\) 2.19864 0.407420i 0.163877 0.0303673i
\(181\) 6.63253 0.492992 0.246496 0.969144i \(-0.420721\pi\)
0.246496 + 0.969144i \(0.420721\pi\)
\(182\) 9.70663 9.70663i 0.719503 0.719503i
\(183\) −0.192753 −0.0142487
\(184\) −2.47151 −0.182202
\(185\) 13.5628 1.02508i 0.997156 0.0753655i
\(186\) 9.88605 0.724880
\(187\) −3.67435 −0.268695
\(188\) 6.69776 6.69776i 0.488485 0.488485i
\(189\) −2.32629 −0.169213
\(190\) −9.31912 + 13.5585i −0.676080 + 0.983634i
\(191\) 13.4202 13.4202i 0.971054 0.971054i −0.0285382 0.999593i \(-0.509085\pi\)
0.999593 + 0.0285382i \(0.00908524\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) 9.65236 0.694792 0.347396 0.937719i \(-0.387066\pi\)
0.347396 + 0.937719i \(0.387066\pi\)
\(194\) 5.99946i 0.430736i
\(195\) −10.8740 7.47398i −0.778700 0.535223i
\(196\) 1.58835i 0.113454i
\(197\) 1.88877 1.88877i 0.134569 0.134569i −0.636614 0.771183i \(-0.719665\pi\)
0.771183 + 0.636614i \(0.219665\pi\)
\(198\) 5.09841 0.362328
\(199\) 5.38735 5.38735i 0.381899 0.381899i −0.489887 0.871786i \(-0.662962\pi\)
0.871786 + 0.489887i \(0.162962\pi\)
\(200\) 4.66802 1.79154i 0.330079 0.126681i
\(201\) −12.4808 −0.880330
\(202\) 0.764728i 0.0538060i
\(203\) 6.89008i 0.483589i
\(204\) −0.509601 0.509601i −0.0356792 0.0356792i
\(205\) −14.4848 + 2.68412i −1.01166 + 0.187467i
\(206\) 2.86283i 0.199463i
\(207\) 2.47151i 0.171782i
\(208\) −5.90090 −0.409154
\(209\) −26.5254 + 26.5254i −1.83480 + 1.83480i
\(210\) −5.11468 + 0.947779i −0.352946 + 0.0654030i
\(211\) −2.70038 −0.185902 −0.0929510 0.995671i \(-0.529630\pi\)
−0.0929510 + 0.995671i \(0.529630\pi\)
\(212\) 6.02669 + 6.02669i 0.413914 + 0.413914i
\(213\) 0.445649 0.445649i 0.0305354 0.0305354i
\(214\) −7.65897 + 7.65897i −0.523557 + 0.523557i
\(215\) 4.23924 + 22.8770i 0.289114 + 1.56020i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) −22.9979 −1.56120
\(218\) 1.40152 + 1.40152i 0.0949228 + 0.0949228i
\(219\) 1.13240i 0.0765205i
\(220\) 11.2096 2.07719i 0.755748 0.140044i
\(221\) 4.25269i 0.286067i
\(222\) 3.81347 + 4.73893i 0.255944 + 0.318056i
\(223\) 0.836925 + 0.836925i 0.0560447 + 0.0560447i 0.734574 0.678529i \(-0.237382\pi\)
−0.678529 + 0.734574i \(0.737382\pi\)
\(224\) −1.64494 + 1.64494i −0.109907 + 0.109907i
\(225\) 1.79154 + 4.66802i 0.119436 + 0.311201i
\(226\) 15.5998i 1.03768i
\(227\) 2.55431i 0.169535i 0.996401 + 0.0847677i \(0.0270148\pi\)
−0.996401 + 0.0847677i \(0.972985\pi\)
\(228\) −7.35769 −0.487275
\(229\) 2.55867i 0.169082i 0.996420 + 0.0845409i \(0.0269424\pi\)
−0.996420 + 0.0845409i \(0.973058\pi\)
\(230\) −1.00694 5.43396i −0.0663959 0.358305i
\(231\) −11.8604 −0.780358
\(232\) 2.09433 2.09433i 0.137499 0.137499i
\(233\) 5.68879 5.68879i 0.372685 0.372685i −0.495769 0.868454i \(-0.665114\pi\)
0.868454 + 0.495769i \(0.165114\pi\)
\(234\) 5.90090i 0.385754i
\(235\) 17.4548 + 11.9972i 1.13862 + 0.782608i
\(236\) −1.31697 1.31697i −0.0857277 0.0857277i
\(237\) 1.91930 0.124672
\(238\) 1.18548 + 1.18548i 0.0768434 + 0.0768434i
\(239\) −8.30333 8.30333i −0.537098 0.537098i 0.385577 0.922675i \(-0.374002\pi\)
−0.922675 + 0.385577i \(0.874002\pi\)
\(240\) 1.84276 + 1.26658i 0.118950 + 0.0817575i
\(241\) 2.03835 2.03835i 0.131302 0.131302i −0.638402 0.769703i \(-0.720404\pi\)
0.769703 + 0.638402i \(0.220404\pi\)
\(242\) 14.9938 0.963838
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) −0.136297 0.136297i −0.00872550 0.00872550i
\(245\) −3.49221 + 0.647126i −0.223109 + 0.0413434i
\(246\) −4.65848 4.65848i −0.297014 0.297014i
\(247\) 30.7005 + 30.7005i 1.95342 + 1.95342i
\(248\) 6.99049 + 6.99049i 0.443897 + 0.443897i
\(249\) 0.124116 0.00786550
\(250\) 5.84079 + 9.53337i 0.369404 + 0.602943i
\(251\) 18.1430 + 18.1430i 1.14518 + 1.14518i 0.987489 + 0.157690i \(0.0504048\pi\)
0.157690 + 0.987489i \(0.449595\pi\)
\(252\) −1.64494 1.64494i −0.103621 0.103621i
\(253\) 12.6008i 0.792205i
\(254\) −14.2375 + 14.2375i −0.893341 + 0.893341i
\(255\) 0.912806 1.32805i 0.0571621 0.0831657i
\(256\) 1.00000 0.0625000
\(257\) 13.8117i 0.861552i 0.902459 + 0.430776i \(0.141760\pi\)
−0.902459 + 0.430776i \(0.858240\pi\)
\(258\) −7.35750 + 7.35750i −0.458058 + 0.458058i
\(259\) −8.87127 11.0241i −0.551234 0.685007i
\(260\) −2.40415 12.9740i −0.149099 0.804610i
\(261\) 2.09433 + 2.09433i 0.129636 + 0.129636i
\(262\) 9.64243 + 9.64243i 0.595711 + 0.595711i
\(263\) −14.0744 + 14.0744i −0.867867 + 0.867867i −0.992236 0.124369i \(-0.960309\pi\)
0.124369 + 0.992236i \(0.460309\pi\)
\(264\) 3.60512 + 3.60512i 0.221880 + 0.221880i
\(265\) −10.7951 + 15.7059i −0.663138 + 0.964805i
\(266\) 17.1162 1.04946
\(267\) 0.921949i 0.0564224i
\(268\) −8.82528 8.82528i −0.539090 0.539090i
\(269\) 18.2296i 1.11148i 0.831357 + 0.555738i \(0.187564\pi\)
−0.831357 + 0.555738i \(0.812436\pi\)
\(270\) −1.26658 + 1.84276i −0.0770818 + 0.112147i
\(271\) −12.8081 −0.778034 −0.389017 0.921231i \(-0.627185\pi\)
−0.389017 + 0.921231i \(0.627185\pi\)
\(272\) 0.720684i 0.0436979i
\(273\) 13.7272i 0.830811i
\(274\) 5.63532 5.63532i 0.340442 0.340442i
\(275\) 9.13400 + 23.7995i 0.550801 + 1.43516i
\(276\) 1.74762 1.74762i 0.105195 0.105195i
\(277\) 30.4939 1.83220 0.916099 0.400952i \(-0.131321\pi\)
0.916099 + 0.400952i \(0.131321\pi\)
\(278\) 18.1510 1.08863
\(279\) −6.99049 + 6.99049i −0.418510 + 0.418510i
\(280\) −4.28681 2.94644i −0.256186 0.176084i
\(281\) −7.94084 + 7.94084i −0.473711 + 0.473711i −0.903113 0.429402i \(-0.858724\pi\)
0.429402 + 0.903113i \(0.358724\pi\)
\(282\) 9.47207i 0.564054i
\(283\) 3.46807i 0.206155i 0.994673 + 0.103078i \(0.0328690\pi\)
−0.994673 + 0.103078i \(0.967131\pi\)
\(284\) 0.630243 0.0373980
\(285\) −2.99767 16.1769i −0.177567 0.958237i
\(286\) 30.0852i 1.77898i
\(287\) 10.8370 + 10.8370i 0.639688 + 0.639688i
\(288\) 1.00000i 0.0589256i
\(289\) 16.4806 0.969448
\(290\) 5.45794 + 3.75140i 0.320501 + 0.220290i
\(291\) 4.24226 + 4.24226i 0.248686 + 0.248686i
\(292\) 0.800728 0.800728i 0.0468590 0.0468590i
\(293\) 6.68632 + 6.68632i 0.390619 + 0.390619i 0.874908 0.484289i \(-0.160922\pi\)
−0.484289 + 0.874908i \(0.660922\pi\)
\(294\) −1.12313 1.12313i −0.0655025 0.0655025i
\(295\) 2.35899 3.43211i 0.137346 0.199825i
\(296\) −0.654393 + 6.04746i −0.0380358 + 0.351501i
\(297\) −3.60512 + 3.60512i −0.209190 + 0.209190i
\(298\) 19.7092i 1.14173i
\(299\) −14.5842 −0.843424
\(300\) −2.03398 + 4.56760i −0.117432 + 0.263710i
\(301\) 17.1157 17.1157i 0.986534 0.986534i
\(302\) 5.28263i 0.303981i
\(303\) −0.540744 0.540744i −0.0310649 0.0310649i
\(304\) −5.20267 5.20267i −0.298394 0.298394i
\(305\) 0.244137 0.355197i 0.0139792 0.0203385i
\(306\) 0.720684 0.0411988
\(307\) −24.0972 24.0972i −1.37530 1.37530i −0.852382 0.522919i \(-0.824843\pi\)
−0.522919 0.852382i \(-0.675157\pi\)
\(308\) −8.38658 8.38658i −0.477869 0.477869i
\(309\) 2.02432 + 2.02432i 0.115160 + 0.115160i
\(310\) −12.5215 + 18.2176i −0.711173 + 1.03469i
\(311\) 7.00421 + 7.00421i 0.397172 + 0.397172i 0.877234 0.480062i \(-0.159386\pi\)
−0.480062 + 0.877234i \(0.659386\pi\)
\(312\) 4.17257 4.17257i 0.236225 0.236225i
\(313\) 0.610621 0.0345144 0.0172572 0.999851i \(-0.494507\pi\)
0.0172572 + 0.999851i \(0.494507\pi\)
\(314\) −16.6599 + 16.6599i −0.940173 + 0.940173i
\(315\) 2.94644 4.28681i 0.166013 0.241534i
\(316\) 1.35715 + 1.35715i 0.0763455 + 0.0763455i
\(317\) 13.6669 + 13.6669i 0.767608 + 0.767608i 0.977685 0.210077i \(-0.0673715\pi\)
−0.210077 + 0.977685i \(0.567372\pi\)
\(318\) −8.52302 −0.477947
\(319\) 10.6777 + 10.6777i 0.597839 + 0.597839i
\(320\) 0.407420 + 2.19864i 0.0227755 + 0.122908i
\(321\) 10.8314i 0.604551i
\(322\) −4.06549 + 4.06549i −0.226561 + 0.226561i
\(323\) −3.74948 + 3.74948i −0.208627 + 0.208627i
\(324\) −1.00000 −0.0555556
\(325\) 27.5455 10.5717i 1.52795 0.586412i
\(326\) 15.8733i 0.879143i
\(327\) −1.98205 −0.109607
\(328\) 6.58809i 0.363767i
\(329\) 22.0348i 1.21482i
\(330\) −6.45756 + 9.39515i −0.355477 + 0.517186i
\(331\) −4.46154 + 4.46154i −0.245228 + 0.245228i −0.819009 0.573781i \(-0.805476\pi\)
0.573781 + 0.819009i \(0.305476\pi\)
\(332\) 0.0877629 + 0.0877629i 0.00481662 + 0.00481662i
\(333\) −6.04746 0.654393i −0.331399 0.0358605i
\(334\) 16.1399i 0.883136i
\(335\) 15.8080 22.9992i 0.863684 1.25658i
\(336\) 2.32629i 0.126910i
\(337\) 0.254872 + 0.254872i 0.0138838 + 0.0138838i 0.714015 0.700131i \(-0.246875\pi\)
−0.700131 + 0.714015i \(0.746875\pi\)
\(338\) −21.8207 −1.18689
\(339\) 11.0307 + 11.0307i 0.599107 + 0.599107i
\(340\) 1.58452 0.293621i 0.0859329 0.0159238i
\(341\) −35.6404 + 35.6404i −1.93004 + 1.93004i
\(342\) 5.20267 5.20267i 0.281328 0.281328i
\(343\) 14.1273 + 14.1273i 0.762803 + 0.762803i
\(344\) −10.4051 −0.561004
\(345\) 4.55441 + 3.13038i 0.245201 + 0.168534i
\(346\) −7.18619 + 7.18619i −0.386332 + 0.386332i
\(347\) −28.6170 −1.53624 −0.768122 0.640304i \(-0.778808\pi\)
−0.768122 + 0.640304i \(0.778808\pi\)
\(348\) 2.96182i 0.158770i
\(349\) 15.9860i 0.855710i −0.903847 0.427855i \(-0.859269\pi\)
0.903847 0.427855i \(-0.140731\pi\)
\(350\) 4.73163 10.6256i 0.252916 0.567961i
\(351\) 4.17257 + 4.17257i 0.222715 + 0.222715i
\(352\) 5.09841i 0.271746i
\(353\) 16.4429i 0.875170i −0.899177 0.437585i \(-0.855834\pi\)
0.899177 0.437585i \(-0.144166\pi\)
\(354\) 1.86248 0.0989899
\(355\) 0.256774 + 1.38568i 0.0136281 + 0.0735440i
\(356\) 0.651916 0.651916i 0.0345515 0.0345515i
\(357\) −1.67652 −0.0887311
\(358\) −1.27828 + 1.27828i −0.0675593 + 0.0675593i
\(359\) 17.3539i 0.915904i −0.888977 0.457952i \(-0.848583\pi\)
0.888977 0.457952i \(-0.151417\pi\)
\(360\) −2.19864 + 0.407420i −0.115878 + 0.0214729i
\(361\) 35.1356i 1.84924i
\(362\) −6.63253 −0.348598
\(363\) −10.6022 + 10.6022i −0.556472 + 0.556472i
\(364\) −9.70663 + 9.70663i −0.508766 + 0.508766i
\(365\) 2.08674 + 1.43428i 0.109225 + 0.0750735i
\(366\) 0.192753 0.0100753
\(367\) −9.80219 + 9.80219i −0.511670 + 0.511670i −0.915038 0.403368i \(-0.867840\pi\)
0.403368 + 0.915038i \(0.367840\pi\)
\(368\) 2.47151 0.128837
\(369\) 6.58809 0.342962
\(370\) −13.5628 + 1.02508i −0.705096 + 0.0532915i
\(371\) 19.8271 1.02937
\(372\) −9.88605 −0.512568
\(373\) −1.82136 + 1.82136i −0.0943063 + 0.0943063i −0.752686 0.658380i \(-0.771242\pi\)
0.658380 + 0.752686i \(0.271242\pi\)
\(374\) 3.67435 0.189996
\(375\) −10.8712 2.61105i −0.561385 0.134834i
\(376\) −6.69776 + 6.69776i −0.345411 + 0.345411i
\(377\) 12.3584 12.3584i 0.636491 0.636491i
\(378\) 2.32629 0.119652
\(379\) 23.5189i 1.20808i 0.796953 + 0.604041i \(0.206444\pi\)
−0.796953 + 0.604041i \(0.793556\pi\)
\(380\) 9.31912 13.5585i 0.478061 0.695535i
\(381\) 20.1349i 1.03154i
\(382\) −13.4202 + 13.4202i −0.686639 + 0.686639i
\(383\) −31.0387 −1.58600 −0.793001 0.609220i \(-0.791482\pi\)
−0.793001 + 0.609220i \(0.791482\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) 15.0222 21.8559i 0.765601 1.11388i
\(386\) −9.65236 −0.491292
\(387\) 10.4051i 0.528920i
\(388\) 5.99946i 0.304577i
\(389\) 23.1210 + 23.1210i 1.17228 + 1.17228i 0.981665 + 0.190615i \(0.0610484\pi\)
0.190615 + 0.981665i \(0.438952\pi\)
\(390\) 10.8740 + 7.47398i 0.550624 + 0.378460i
\(391\) 1.78118i 0.0900782i
\(392\) 1.58835i 0.0802239i
\(393\) −13.6365 −0.687868
\(394\) −1.88877 + 1.88877i −0.0951547 + 0.0951547i
\(395\) −2.43095 + 3.53681i −0.122314 + 0.177956i
\(396\) −5.09841 −0.256205
\(397\) −6.35301 6.35301i −0.318848 0.318848i 0.529476 0.848325i \(-0.322388\pi\)
−0.848325 + 0.529476i \(0.822388\pi\)
\(398\) −5.38735 + 5.38735i −0.270043 + 0.270043i
\(399\) −12.1030 + 12.1030i −0.605905 + 0.605905i
\(400\) −4.66802 + 1.79154i −0.233401 + 0.0895769i
\(401\) −23.0255 23.0255i −1.14984 1.14984i −0.986584 0.163256i \(-0.947800\pi\)
−0.163256 0.986584i \(-0.552200\pi\)
\(402\) 12.4808 0.622487
\(403\) 41.2502 + 41.2502i 2.05482 + 2.05482i
\(404\) 0.764728i 0.0380466i
\(405\) −0.407420 2.19864i −0.0202449 0.109251i
\(406\) 6.89008i 0.341949i
\(407\) −30.8324 3.33637i −1.52831 0.165377i
\(408\) 0.509601 + 0.509601i 0.0252290 + 0.0252290i
\(409\) 2.34868 2.34868i 0.116135 0.116135i −0.646651 0.762786i \(-0.723831\pi\)
0.762786 + 0.646651i \(0.223831\pi\)
\(410\) 14.4848 2.68412i 0.715355 0.132559i
\(411\) 7.96955i 0.393109i
\(412\) 2.86283i 0.141041i
\(413\) −4.33269 −0.213197
\(414\) 2.47151i 0.121468i
\(415\) −0.157203 + 0.228715i −0.00771677 + 0.0112272i
\(416\) 5.90090 0.289316
\(417\) −12.8347 + 12.8347i −0.628519 + 0.628519i
\(418\) 26.5254 26.5254i 1.29740 1.29740i
\(419\) 11.9631i 0.584434i 0.956352 + 0.292217i \(0.0943930\pi\)
−0.956352 + 0.292217i \(0.905607\pi\)
\(420\) 5.11468 0.947779i 0.249571 0.0462469i
\(421\) −18.2560 18.2560i −0.889744 0.889744i 0.104754 0.994498i \(-0.466594\pi\)
−0.994498 + 0.104754i \(0.966594\pi\)
\(422\) 2.70038 0.131453
\(423\) −6.69776 6.69776i −0.325656 0.325656i
\(424\) −6.02669 6.02669i −0.292682 0.292682i
\(425\) 1.29113 + 3.36417i 0.0626292 + 0.163186i
\(426\) −0.445649 + 0.445649i −0.0215918 + 0.0215918i
\(427\) −0.448399 −0.0216996
\(428\) 7.65897 7.65897i 0.370210 0.370210i
\(429\) 21.2735 + 21.2735i 1.02709 + 1.02709i
\(430\) −4.23924 22.8770i −0.204434 1.10323i
\(431\) −13.3451 13.3451i −0.642811 0.642811i 0.308435 0.951245i \(-0.400195\pi\)
−0.951245 + 0.308435i \(0.900195\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) −12.4634 12.4634i −0.598952 0.598952i 0.341082 0.940034i \(-0.389207\pi\)
−0.940034 + 0.341082i \(0.889207\pi\)
\(434\) 22.9979 1.10393
\(435\) −6.51198 + 1.20671i −0.312226 + 0.0578572i
\(436\) −1.40152 1.40152i −0.0671206 0.0671206i
\(437\) −12.8585 12.8585i −0.615104 0.615104i
\(438\) 1.13240i 0.0541082i
\(439\) 24.4496 24.4496i 1.16692 1.16692i 0.183987 0.982929i \(-0.441100\pi\)
0.982929 0.183987i \(-0.0589005\pi\)
\(440\) −11.2096 + 2.07719i −0.534395 + 0.0990264i
\(441\) 1.58835 0.0756358
\(442\) 4.25269i 0.202280i
\(443\) 19.6237 19.6237i 0.932352 0.932352i −0.0655007 0.997853i \(-0.520864\pi\)
0.997853 + 0.0655007i \(0.0208645\pi\)
\(444\) −3.81347 4.73893i −0.180979 0.224899i
\(445\) 1.69893 + 1.16772i 0.0805371 + 0.0553555i
\(446\) −0.836925 0.836925i −0.0396296 0.0396296i
\(447\) −13.9365 13.9365i −0.659175 0.659175i
\(448\) 1.64494 1.64494i 0.0777161 0.0777161i
\(449\) 26.1134 + 26.1134i 1.23237 + 1.23237i 0.963052 + 0.269315i \(0.0867974\pi\)
0.269315 + 0.963052i \(0.413203\pi\)
\(450\) −1.79154 4.66802i −0.0844539 0.220052i
\(451\) 33.5888 1.58163
\(452\) 15.5998i 0.733753i
\(453\) 3.73539 + 3.73539i 0.175504 + 0.175504i
\(454\) 2.55431i 0.119880i
\(455\) −25.2960 17.3867i −1.18590 0.815100i
\(456\) 7.35769 0.344555
\(457\) 0.148390i 0.00694138i 0.999994 + 0.00347069i \(0.00110476\pi\)
−0.999994 + 0.00347069i \(0.998895\pi\)
\(458\) 2.55867i 0.119559i
\(459\) −0.509601 + 0.509601i −0.0237861 + 0.0237861i
\(460\) 1.00694 + 5.43396i 0.0469490 + 0.253360i
\(461\) 20.8196 20.8196i 0.969665 0.969665i −0.0298885 0.999553i \(-0.509515\pi\)
0.999553 + 0.0298885i \(0.00951521\pi\)
\(462\) 11.8604 0.551796
\(463\) 29.5512 1.37336 0.686681 0.726959i \(-0.259067\pi\)
0.686681 + 0.726959i \(0.259067\pi\)
\(464\) −2.09433 + 2.09433i −0.0972267 + 0.0972267i
\(465\) −4.02777 21.7358i −0.186783 1.00798i
\(466\) −5.68879 + 5.68879i −0.263528 + 0.263528i
\(467\) 12.6036i 0.583225i −0.956537 0.291613i \(-0.905808\pi\)
0.956537 0.291613i \(-0.0941918\pi\)
\(468\) 5.90090i 0.272769i
\(469\) −29.0341 −1.34067
\(470\) −17.4548 11.9972i −0.805128 0.553388i
\(471\) 23.5607i 1.08562i
\(472\) 1.31697 + 1.31697i 0.0606187 + 0.0606187i
\(473\) 53.0494i 2.43921i
\(474\) −1.91930 −0.0881562
\(475\) 33.6070 + 14.9654i 1.54199 + 0.686659i
\(476\) −1.18548 1.18548i −0.0543365 0.0543365i
\(477\) 6.02669 6.02669i 0.275943 0.275943i
\(478\) 8.30333 + 8.30333i 0.379786 + 0.379786i
\(479\) −0.298466 0.298466i −0.0136373 0.0136373i 0.700255 0.713893i \(-0.253070\pi\)
−0.713893 + 0.700255i \(0.753070\pi\)
\(480\) −1.84276 1.26658i −0.0841102 0.0578113i
\(481\) −3.86151 + 35.6855i −0.176070 + 1.62712i
\(482\) −2.03835 + 2.03835i −0.0928442 + 0.0928442i
\(483\) 5.74947i 0.261610i
\(484\) −14.9938 −0.681536
\(485\) −13.1906 + 2.44430i −0.598957 + 0.110990i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 13.5324i 0.613209i 0.951837 + 0.306605i \(0.0991930\pi\)
−0.951837 + 0.306605i \(0.900807\pi\)
\(488\) 0.136297 + 0.136297i 0.00616986 + 0.00616986i
\(489\) 11.2241 + 11.2241i 0.507573 + 0.507573i
\(490\) 3.49221 0.647126i 0.157762 0.0292342i
\(491\) 0.261520 0.0118022 0.00590111 0.999983i \(-0.498122\pi\)
0.00590111 + 0.999983i \(0.498122\pi\)
\(492\) 4.65848 + 4.65848i 0.210021 + 0.210021i
\(493\) 1.50935 + 1.50935i 0.0679776 + 0.0679776i
\(494\) −30.7005 30.7005i −1.38128 1.38128i
\(495\) −2.07719 11.2096i −0.0933629 0.503832i
\(496\) −6.99049 6.99049i −0.313882 0.313882i
\(497\) 1.03671 1.03671i 0.0465028 0.0465028i
\(498\) −0.124116 −0.00556175
\(499\) 11.3438 11.3438i 0.507819 0.507819i −0.406037 0.913856i \(-0.633090\pi\)
0.913856 + 0.406037i \(0.133090\pi\)
\(500\) −5.84079 9.53337i −0.261208 0.426345i
\(501\) 11.4126 + 11.4126i 0.509879 + 0.509879i
\(502\) −18.1430 18.1430i −0.809764 0.809764i
\(503\) −40.5994 −1.81024 −0.905118 0.425160i \(-0.860218\pi\)
−0.905118 + 0.425160i \(0.860218\pi\)
\(504\) 1.64494 + 1.64494i 0.0732714 + 0.0732714i
\(505\) 1.68136 0.311565i 0.0748195 0.0138645i
\(506\) 12.6008i 0.560174i
\(507\) 15.4295 15.4295i 0.685250 0.685250i
\(508\) 14.2375 14.2375i 0.631687 0.631687i
\(509\) 19.0305 0.843513 0.421756 0.906709i \(-0.361414\pi\)
0.421756 + 0.906709i \(0.361414\pi\)
\(510\) −0.912806 + 1.32805i −0.0404197 + 0.0588070i
\(511\) 2.63430i 0.116534i
\(512\) −1.00000 −0.0441942
\(513\) 7.35769i 0.324850i
\(514\) 13.8117i 0.609209i
\(515\) −6.29432 + 1.16637i −0.277361 + 0.0513965i
\(516\) 7.35750 7.35750i 0.323896 0.323896i
\(517\) −34.1480 34.1480i −1.50183 1.50183i
\(518\) 8.87127 + 11.0241i 0.389781 + 0.484373i
\(519\) 10.1628i 0.446098i
\(520\) 2.40415 + 12.9740i 0.105429 + 0.568946i
\(521\) 28.7069i 1.25767i −0.777539 0.628835i \(-0.783532\pi\)
0.777539 0.628835i \(-0.216468\pi\)
\(522\) −2.09433 2.09433i −0.0916662 0.0916662i
\(523\) 19.7783 0.864845 0.432423 0.901671i \(-0.357659\pi\)
0.432423 + 0.901671i \(0.357659\pi\)
\(524\) −9.64243 9.64243i −0.421231 0.421231i
\(525\) 4.16765 + 10.8592i 0.181891 + 0.473934i
\(526\) 14.0744 14.0744i 0.613674 0.613674i
\(527\) −5.03794 + 5.03794i −0.219456 + 0.219456i
\(528\) −3.60512 3.60512i −0.156893 0.156893i
\(529\) −16.8916 −0.734418
\(530\) 10.7951 15.7059i 0.468910 0.682220i
\(531\) −1.31697 + 1.31697i −0.0571518 + 0.0571518i
\(532\) −17.1162 −0.742080
\(533\) 38.8757i 1.68389i
\(534\) 0.921949i 0.0398966i
\(535\) 19.9597 + 13.7189i 0.862934 + 0.593119i
\(536\) 8.82528 + 8.82528i 0.381194 + 0.381194i
\(537\) 1.80776i 0.0780107i
\(538\) 18.2296i 0.785932i
\(539\) 8.09807 0.348809
\(540\) 1.26658 1.84276i 0.0545050 0.0792998i
\(541\) 13.1613 13.1613i 0.565851 0.565851i −0.365113 0.930963i \(-0.618970\pi\)
0.930963 + 0.365113i \(0.118970\pi\)
\(542\) 12.8081 0.550153
\(543\) 4.68991 4.68991i 0.201263 0.201263i
\(544\) 0.720684i 0.0308991i
\(545\) 2.51043 3.65244i 0.107535 0.156453i
\(546\) 13.7272i 0.587472i
\(547\) 25.1974 1.07736 0.538682 0.842509i \(-0.318923\pi\)
0.538682 + 0.842509i \(0.318923\pi\)
\(548\) −5.63532 + 5.63532i −0.240729 + 0.240729i
\(549\) −0.136297 + 0.136297i −0.00581700 + 0.00581700i
\(550\) −9.13400 23.7995i −0.389475 1.01481i
\(551\) 21.7922 0.928378
\(552\) −1.74762 + 1.74762i −0.0743838 + 0.0743838i
\(553\) 4.46485 0.189865
\(554\) −30.4939 −1.29556
\(555\) 8.86550 10.3152i 0.376319 0.437855i
\(556\) −18.1510 −0.769775
\(557\) 7.96504 0.337490 0.168745 0.985660i \(-0.446029\pi\)
0.168745 + 0.985660i \(0.446029\pi\)
\(558\) 6.99049 6.99049i 0.295931 0.295931i
\(559\) −61.3994 −2.59692
\(560\) 4.28681 + 2.94644i 0.181151 + 0.124510i
\(561\) −2.59815 + 2.59815i −0.109694 + 0.109694i
\(562\) 7.94084 7.94084i 0.334964 0.334964i
\(563\) −19.0142 −0.801352 −0.400676 0.916220i \(-0.631225\pi\)
−0.400676 + 0.916220i \(0.631225\pi\)
\(564\) 9.47207i 0.398846i
\(565\) −34.2983 + 6.35567i −1.44294 + 0.267385i
\(566\) 3.46807i 0.145774i
\(567\) −1.64494 + 1.64494i −0.0690809 + 0.0690809i
\(568\) −0.630243 −0.0264444
\(569\) −0.615232 + 0.615232i −0.0257918 + 0.0257918i −0.719885 0.694093i \(-0.755806\pi\)
0.694093 + 0.719885i \(0.255806\pi\)
\(570\) 2.99767 + 16.1769i 0.125559 + 0.677576i
\(571\) −42.1498 −1.76391 −0.881957 0.471330i \(-0.843774\pi\)
−0.881957 + 0.471330i \(0.843774\pi\)
\(572\) 30.0852i 1.25793i
\(573\) 18.9791i 0.792863i
\(574\) −10.8370 10.8370i −0.452328 0.452328i
\(575\) −11.5371 + 4.42781i −0.481129 + 0.184652i
\(576\) 1.00000i 0.0416667i
\(577\) 7.37152i 0.306881i 0.988158 + 0.153440i \(0.0490353\pi\)
−0.988158 + 0.153440i \(0.950965\pi\)
\(578\) −16.4806 −0.685503
\(579\) 6.82525 6.82525i 0.283648 0.283648i
\(580\) −5.45794 3.75140i −0.226628 0.155768i
\(581\) 0.288729 0.0119785
\(582\) −4.24226 4.24226i −0.175847 0.175847i
\(583\) 30.7265 30.7265i 1.27256 1.27256i
\(584\) −0.800728 + 0.800728i −0.0331343 + 0.0331343i
\(585\) −12.9740 + 2.40415i −0.536407 + 0.0993992i
\(586\) −6.68632 6.68632i −0.276209 0.276209i
\(587\) 44.0572 1.81844 0.909218 0.416319i \(-0.136680\pi\)
0.909218 + 0.416319i \(0.136680\pi\)
\(588\) 1.12313 + 1.12313i 0.0463173 + 0.0463173i
\(589\) 72.7385i 2.99714i
\(590\) −2.35899 + 3.43211i −0.0971180 + 0.141298i
\(591\) 2.67112i 0.109875i
\(592\) 0.654393 6.04746i 0.0268954 0.248549i
\(593\) −4.89452 4.89452i −0.200994 0.200994i 0.599432 0.800426i \(-0.295393\pi\)
−0.800426 + 0.599432i \(0.795393\pi\)
\(594\) 3.60512 3.60512i 0.147920 0.147920i
\(595\) 2.12346 3.08943i 0.0870532 0.126654i
\(596\) 19.7092i 0.807322i
\(597\) 7.61886i 0.311819i
\(598\) 14.5842 0.596391
\(599\) 34.6454i 1.41557i 0.706427 + 0.707785i \(0.250306\pi\)
−0.706427 + 0.707785i \(0.749694\pi\)
\(600\) 2.03398 4.56760i 0.0830368 0.186471i
\(601\) −3.11150 −0.126921 −0.0634604 0.997984i \(-0.520214\pi\)
−0.0634604 + 0.997984i \(0.520214\pi\)
\(602\) −17.1157 + 17.1157i −0.697585 + 0.697585i
\(603\) −8.82528 + 8.82528i −0.359393 + 0.359393i
\(604\) 5.28263i 0.214947i
\(605\) −6.10877 32.9659i −0.248357 1.34026i
\(606\) 0.540744 + 0.540744i 0.0219662 + 0.0219662i
\(607\) −38.6760 −1.56981 −0.784906 0.619615i \(-0.787289\pi\)
−0.784906 + 0.619615i \(0.787289\pi\)
\(608\) 5.20267 + 5.20267i 0.210996 + 0.210996i
\(609\) 4.87202 + 4.87202i 0.197424 + 0.197424i
\(610\) −0.244137 + 0.355197i −0.00988482 + 0.0143815i
\(611\) −39.5229 + 39.5229i −1.59892 + 1.59892i
\(612\) −0.720684 −0.0291319
\(613\) −19.7218 + 19.7218i −0.796557 + 0.796557i −0.982551 0.185994i \(-0.940449\pi\)
0.185994 + 0.982551i \(0.440449\pi\)
\(614\) 24.0972 + 24.0972i 0.972485 + 0.972485i
\(615\) −8.34436 + 12.1403i −0.336477 + 0.489543i
\(616\) 8.38658 + 8.38658i 0.337905 + 0.337905i
\(617\) 23.5004 + 23.5004i 0.946091 + 0.946091i 0.998619 0.0525282i \(-0.0167280\pi\)
−0.0525282 + 0.998619i \(0.516728\pi\)
\(618\) −2.02432 2.02432i −0.0814303 0.0814303i
\(619\) 31.4805 1.26531 0.632654 0.774434i \(-0.281965\pi\)
0.632654 + 0.774434i \(0.281965\pi\)
\(620\) 12.5215 18.2176i 0.502875 0.731637i
\(621\) −1.74762 1.74762i −0.0701297 0.0701297i
\(622\) −7.00421 7.00421i −0.280843 0.280843i
\(623\) 2.14473i 0.0859266i
\(624\) −4.17257 + 4.17257i −0.167036 + 0.167036i
\(625\) 18.5808 16.7259i 0.743231 0.669034i
\(626\) −0.610621 −0.0244053
\(627\) 37.5125i 1.49811i
\(628\) 16.6599 16.6599i 0.664803 0.664803i
\(629\) −4.35831 0.471611i −0.173777 0.0188044i
\(630\) −2.94644 + 4.28681i −0.117389 + 0.170790i
\(631\) 23.3413 + 23.3413i 0.929204 + 0.929204i 0.997654 0.0684508i \(-0.0218056\pi\)
−0.0684508 + 0.997654i \(0.521806\pi\)
\(632\) −1.35715 1.35715i −0.0539844 0.0539844i
\(633\) −1.90946 + 1.90946i −0.0758942 + 0.0758942i
\(634\) −13.6669 13.6669i −0.542781 0.542781i
\(635\) 37.1038 + 25.5025i 1.47242 + 1.01204i
\(636\) 8.52302 0.337960
\(637\) 9.37271i 0.371360i
\(638\) −10.6777 10.6777i −0.422736 0.422736i
\(639\) 0.630243i 0.0249320i
\(640\) −0.407420 2.19864i −0.0161047 0.0869088i
\(641\) 9.30102 0.367368 0.183684 0.982985i \(-0.441198\pi\)
0.183684 + 0.982985i \(0.441198\pi\)
\(642\) 10.8314i 0.427482i
\(643\) 17.5936i 0.693823i 0.937898 + 0.346911i \(0.112770\pi\)
−0.937898 + 0.346911i \(0.887230\pi\)
\(644\) 4.06549 4.06549i 0.160203 0.160203i
\(645\) 19.1741 + 13.1789i 0.754979 + 0.518919i
\(646\) 3.74948 3.74948i 0.147521 0.147521i
\(647\) −38.2288 −1.50293 −0.751466 0.659772i \(-0.770653\pi\)
−0.751466 + 0.659772i \(0.770653\pi\)
\(648\) 1.00000 0.0392837
\(649\) −6.71448 + 6.71448i −0.263566 + 0.263566i
\(650\) −27.5455 + 10.5717i −1.08042 + 0.414656i
\(651\) −16.2619 + 16.2619i −0.637356 + 0.637356i
\(652\) 15.8733i 0.621648i
\(653\) 2.43786i 0.0954008i −0.998862 0.0477004i \(-0.984811\pi\)
0.998862 0.0477004i \(-0.0151893\pi\)
\(654\) 1.98205 0.0775041
\(655\) 17.2717 25.1287i 0.674861 0.981861i
\(656\) 6.58809i 0.257222i
\(657\) −0.800728 0.800728i −0.0312394 0.0312394i
\(658\) 22.0348i 0.859007i
\(659\) −10.7505 −0.418779 −0.209390 0.977832i \(-0.567148\pi\)
−0.209390 + 0.977832i \(0.567148\pi\)
\(660\) 6.45756 9.39515i 0.251360 0.365706i
\(661\) −28.1910 28.1910i −1.09650 1.09650i −0.994817 0.101686i \(-0.967576\pi\)
−0.101686 0.994817i \(-0.532424\pi\)
\(662\) 4.46154 4.46154i 0.173403 0.173403i
\(663\) 3.00711 + 3.00711i 0.116786 + 0.116786i
\(664\) −0.0877629 0.0877629i −0.00340586 0.00340586i
\(665\) −6.97346 37.6322i −0.270419 1.45932i
\(666\) 6.04746 + 0.654393i 0.234334 + 0.0253572i
\(667\) −5.17616 + 5.17616i −0.200422 + 0.200422i
\(668\) 16.1399i 0.624471i
\(669\) 1.18359 0.0457603
\(670\) −15.8080 + 22.9992i −0.610717 + 0.888537i
\(671\) −0.694897 + 0.694897i −0.0268262 + 0.0268262i
\(672\) 2.32629i 0.0897388i
\(673\) −9.84759 9.84759i −0.379597 0.379597i 0.491360 0.870957i \(-0.336500\pi\)
−0.870957 + 0.491360i \(0.836500\pi\)
\(674\) −0.254872 0.254872i −0.00981731 0.00981731i
\(675\) 4.56760 + 2.03398i 0.175807 + 0.0782879i
\(676\) 21.8207 0.839257
\(677\) −2.68587 2.68587i −0.103226 0.103226i 0.653607 0.756834i \(-0.273255\pi\)
−0.756834 + 0.653607i \(0.773255\pi\)
\(678\) −11.0307 11.0307i −0.423632 0.423632i
\(679\) 9.86875 + 9.86875i 0.378728 + 0.378728i
\(680\) −1.58452 + 0.293621i −0.0607637 + 0.0112599i
\(681\) 1.80617 + 1.80617i 0.0692125 + 0.0692125i
\(682\) 35.6404 35.6404i 1.36474 1.36474i
\(683\) −21.4016 −0.818910 −0.409455 0.912330i \(-0.634281\pi\)
−0.409455 + 0.912330i \(0.634281\pi\)
\(684\) −5.20267 + 5.20267i −0.198929 + 0.198929i
\(685\) −14.6860 10.0941i −0.561123 0.385676i
\(686\) −14.1273 14.1273i −0.539383 0.539383i
\(687\) 1.80926 + 1.80926i 0.0690274 + 0.0690274i
\(688\) 10.4051 0.396690
\(689\) −35.5629 35.5629i −1.35484 1.35484i
\(690\) −4.55441 3.13038i −0.173383 0.119171i
\(691\) 2.78114i 0.105800i −0.998600 0.0528998i \(-0.983154\pi\)
0.998600 0.0528998i \(-0.0168464\pi\)
\(692\) 7.18619 7.18619i 0.273178 0.273178i
\(693\) −8.38658 + 8.38658i −0.318580 + 0.318580i
\(694\) 28.6170 1.08629
\(695\) −7.39509 39.9075i −0.280512 1.51378i
\(696\) 2.96182i 0.112268i
\(697\) 4.74793 0.179841
\(698\) 15.9860i 0.605078i
\(699\) 8.04517i 0.304296i
\(700\) −4.73163 + 10.6256i −0.178839 + 0.401609i
\(701\) −0.336016 + 0.336016i −0.0126911 + 0.0126911i −0.713424 0.700733i \(-0.752857\pi\)
0.700733 + 0.713424i \(0.252857\pi\)
\(702\) −4.17257 4.17257i −0.157484 0.157484i
\(703\) −34.8675 + 28.0584i −1.31505 + 1.05824i
\(704\) 5.09841i 0.192154i
\(705\) 20.8257 3.85911i 0.784339 0.145342i
\(706\) 16.4429i 0.618839i
\(707\) −1.25793 1.25793i −0.0473093 0.0473093i
\(708\) −1.86248 −0.0699964
\(709\) −34.2461 34.2461i −1.28614 1.28614i −0.937114 0.349024i \(-0.886513\pi\)
−0.349024 0.937114i \(-0.613487\pi\)
\(710\) −0.256774 1.38568i −0.00963654 0.0520035i
\(711\) 1.35715 1.35715i 0.0508970 0.0508970i
\(712\) −0.651916 + 0.651916i −0.0244316 + 0.0244316i
\(713\) −17.2771 17.2771i −0.647032 0.647032i
\(714\) 1.67652 0.0627423
\(715\) −66.1466 + 12.2573i −2.47374 + 0.458398i
\(716\) 1.27828 1.27828i 0.0477716 0.0477716i
\(717\) −11.7427 −0.438539
\(718\) 17.3539i 0.647642i
\(719\) 7.34855i 0.274055i −0.990567 0.137027i \(-0.956245\pi\)
0.990567 0.137027i \(-0.0437548\pi\)
\(720\) 2.19864 0.407420i 0.0819384 0.0151836i
\(721\) 4.70918 + 4.70918i 0.175379 + 0.175379i
\(722\) 35.1356i 1.30761i
\(723\) 2.88266i 0.107207i
\(724\) 6.63253 0.246496
\(725\) 6.02429 13.5284i 0.223736 0.502433i
\(726\) 10.6022 10.6022i 0.393485 0.393485i
\(727\) 46.5833 1.72768 0.863839 0.503768i \(-0.168053\pi\)
0.863839 + 0.503768i \(0.168053\pi\)
\(728\) 9.70663 9.70663i 0.359752 0.359752i
\(729\) 1.00000i 0.0370370i
\(730\) −2.08674 1.43428i −0.0772338 0.0530850i
\(731\) 7.49878i 0.277352i
\(732\) −0.192753 −0.00712434
\(733\) 12.4565 12.4565i 0.460092 0.460092i −0.438594 0.898685i \(-0.644523\pi\)
0.898685 + 0.438594i \(0.144523\pi\)
\(734\) 9.80219 9.80219i 0.361805 0.361805i
\(735\) −2.01178 + 2.92695i −0.0742056 + 0.107962i
\(736\) −2.47151 −0.0911012
\(737\) −44.9949 + 44.9949i −1.65741 + 1.65741i
\(738\) −6.58809 −0.242511
\(739\) −27.0728 −0.995889 −0.497945 0.867209i \(-0.665912\pi\)
−0.497945 + 0.867209i \(0.665912\pi\)
\(740\) 13.5628 1.02508i 0.498578 0.0376828i
\(741\) 43.4170 1.59496
\(742\) −19.8271 −0.727874
\(743\) −21.9556 + 21.9556i −0.805471 + 0.805471i −0.983945 0.178474i \(-0.942884\pi\)
0.178474 + 0.983945i \(0.442884\pi\)
\(744\) 9.88605 0.362440
\(745\) 43.3335 8.02993i 1.58762 0.294194i
\(746\) 1.82136 1.82136i 0.0666846 0.0666846i
\(747\) 0.0877629 0.0877629i 0.00321108 0.00321108i
\(748\) −3.67435 −0.134347
\(749\) 25.1971i 0.920682i
\(750\) 10.8712 + 2.61105i 0.396959 + 0.0953422i
\(751\) 8.35224i 0.304778i −0.988321 0.152389i \(-0.951303\pi\)
0.988321 0.152389i \(-0.0486966\pi\)
\(752\) 6.69776 6.69776i 0.244242 0.244242i
\(753\) 25.6581 0.935035
\(754\) −12.3584 + 12.3584i −0.450067 + 0.450067i
\(755\) −11.6146 + 2.15225i −0.422698 + 0.0783284i
\(756\) −2.32629 −0.0846065
\(757\) 6.78896i 0.246749i −0.992360 0.123374i \(-0.960628\pi\)
0.992360 0.123374i \(-0.0393716\pi\)
\(758\) 23.5189i 0.854244i
\(759\) −8.91011 8.91011i −0.323416 0.323416i
\(760\) −9.31912 + 13.5585i −0.338040 + 0.491817i
\(761\) 11.1352i 0.403651i −0.979421 0.201826i \(-0.935313\pi\)
0.979421 0.201826i \(-0.0646874\pi\)
\(762\) 20.1349i 0.729410i
\(763\) −4.61082 −0.166923
\(764\) 13.4202 13.4202i 0.485527 0.485527i
\(765\) −0.293621 1.58452i −0.0106159 0.0572886i
\(766\) 31.0387 1.12147
\(767\) 7.77134 + 7.77134i 0.280607 + 0.280607i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) −26.8144 + 26.8144i −0.966950 + 0.966950i −0.999471 0.0325207i \(-0.989647\pi\)
0.0325207 + 0.999471i \(0.489647\pi\)
\(770\) −15.0222 + 21.8559i −0.541362 + 0.787632i
\(771\) 9.76637 + 9.76637i 0.351727 + 0.351727i
\(772\) 9.65236 0.347396
\(773\) 25.7542 + 25.7542i 0.926315 + 0.926315i 0.997466 0.0711506i \(-0.0226671\pi\)
−0.0711506 + 0.997466i \(0.522667\pi\)
\(774\) 10.4051i 0.374003i
\(775\) 45.1555 + 20.1080i 1.62203 + 0.722301i
\(776\) 5.99946i 0.215368i
\(777\) −14.0682 1.52231i −0.504693 0.0546126i
\(778\) −23.1210 23.1210i −0.828927 0.828927i
\(779\) 34.2757 34.2757i 1.22805 1.22805i