Properties

Label 441.2.bg.a.395.14
Level $441$
Weight $2$
Character 441.395
Analytic conductor $3.521$
Analytic rank $0$
Dimension $216$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bg (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 395.14
Character \(\chi\) \(=\) 441.395
Dual form 441.2.bg.a.278.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50023 + 0.588795i) q^{2} +(0.437895 + 0.406307i) q^{4} +(-3.18030 - 2.16829i) q^{5} +(2.37141 - 1.17321i) q^{7} +(-0.980812 - 2.03668i) q^{8} +O(q^{10})\) \(q+(1.50023 + 0.588795i) q^{2} +(0.437895 + 0.406307i) q^{4} +(-3.18030 - 2.16829i) q^{5} +(2.37141 - 1.17321i) q^{7} +(-0.980812 - 2.03668i) q^{8} +(-3.49449 - 5.12548i) q^{10} +(-0.655355 - 4.34800i) q^{11} +(-3.43618 + 2.74026i) q^{13} +(4.24843 - 0.363804i) q^{14} +(-0.361535 - 4.82435i) q^{16} +(3.21706 + 0.992330i) q^{17} +(-0.776988 + 0.448594i) q^{19} +(-0.511645 - 2.24166i) q^{20} +(1.57690 - 6.90885i) q^{22} +(-0.732111 - 2.37344i) q^{23} +(3.58612 + 9.13730i) q^{25} +(-6.76850 + 2.08781i) q^{26} +(1.51511 + 0.449778i) q^{28} +(8.30122 - 1.89470i) q^{29} +(4.67386 + 2.69846i) q^{31} +(0.965559 - 3.13027i) q^{32} +(4.24203 + 3.38291i) q^{34} +(-10.0857 - 1.41075i) q^{35} +(5.45716 - 5.06350i) q^{37} +(-1.42979 + 0.215506i) q^{38} +(-1.29684 + 8.60394i) q^{40} +(-5.36277 + 2.58258i) q^{41} +(-2.54826 - 1.22718i) q^{43} +(1.47965 - 2.17024i) q^{44} +(0.299142 - 3.99177i) q^{46} +(1.55456 - 3.96096i) q^{47} +(4.24716 - 5.56432i) q^{49} +15.8195i q^{50} +(-2.61807 - 0.196198i) q^{52} +(-8.87284 + 9.56264i) q^{53} +(-7.34351 + 15.2490i) q^{55} +(-4.71536 - 3.67910i) q^{56} +(13.5693 + 2.04524i) q^{58} +(-6.88259 + 4.69247i) q^{59} +(2.93497 + 3.16315i) q^{61} +(5.42301 + 6.80024i) q^{62} +(-2.74110 + 3.43722i) q^{64} +(16.8698 - 1.26422i) q^{65} +(-1.42922 + 2.47548i) q^{67} +(1.00554 + 1.74165i) q^{68} +(-14.3001 - 8.05484i) q^{70} +(7.30694 + 1.66776i) q^{71} +(3.88677 - 1.52545i) q^{73} +(11.1683 - 4.38325i) q^{74} +(-0.522506 - 0.119259i) q^{76} +(-6.65522 - 9.54201i) q^{77} +(-1.80778 - 3.13117i) q^{79} +(-9.31082 + 16.1268i) q^{80} +(-9.56598 + 0.716871i) q^{82} +(8.34856 - 10.4688i) q^{83} +(-8.07955 - 10.1314i) q^{85} +(-3.10041 - 3.34145i) q^{86} +(-8.21269 + 5.59932i) q^{88} +(-3.95521 - 0.596152i) q^{89} +(-4.93369 + 10.5296i) q^{91} +(0.643760 - 1.33678i) q^{92} +(4.66439 - 5.02702i) q^{94} +(3.44374 + 0.258073i) q^{95} -18.1405i q^{97} +(9.64795 - 5.84702i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{42}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50023 + 0.588795i 1.06082 + 0.416341i 0.830642 0.556807i \(-0.187974\pi\)
0.230178 + 0.973148i \(0.426069\pi\)
\(3\) 0 0
\(4\) 0.437895 + 0.406307i 0.218947 + 0.203154i
\(5\) −3.18030 2.16829i −1.42227 0.969691i −0.997938 0.0641862i \(-0.979555\pi\)
−0.424337 0.905504i \(-0.639493\pi\)
\(6\) 0 0
\(7\) 2.37141 1.17321i 0.896308 0.443431i
\(8\) −0.980812 2.03668i −0.346770 0.720074i
\(9\) 0 0
\(10\) −3.49449 5.12548i −1.10506 1.62082i
\(11\) −0.655355 4.34800i −0.197597 1.31097i −0.839153 0.543895i \(-0.816949\pi\)
0.641556 0.767076i \(-0.278289\pi\)
\(12\) 0 0
\(13\) −3.43618 + 2.74026i −0.953025 + 0.760012i −0.970815 0.239830i \(-0.922908\pi\)
0.0177899 + 0.999842i \(0.494337\pi\)
\(14\) 4.24843 0.363804i 1.13544 0.0972306i
\(15\) 0 0
\(16\) −0.361535 4.82435i −0.0903838 1.20609i
\(17\) 3.21706 + 0.992330i 0.780250 + 0.240675i 0.659197 0.751971i \(-0.270896\pi\)
0.121054 + 0.992646i \(0.461373\pi\)
\(18\) 0 0
\(19\) −0.776988 + 0.448594i −0.178253 + 0.102915i −0.586472 0.809970i \(-0.699483\pi\)
0.408218 + 0.912884i \(0.366150\pi\)
\(20\) −0.511645 2.24166i −0.114407 0.501251i
\(21\) 0 0
\(22\) 1.57690 6.90885i 0.336196 1.47297i
\(23\) −0.732111 2.37344i −0.152656 0.494897i 0.846650 0.532150i \(-0.178616\pi\)
−0.999306 + 0.0372524i \(0.988139\pi\)
\(24\) 0 0
\(25\) 3.58612 + 9.13730i 0.717225 + 1.82746i
\(26\) −6.76850 + 2.08781i −1.32741 + 0.409453i
\(27\) 0 0
\(28\) 1.51511 + 0.449778i 0.286329 + 0.0850001i
\(29\) 8.30122 1.89470i 1.54150 0.351837i 0.634484 0.772936i \(-0.281213\pi\)
0.907015 + 0.421099i \(0.138356\pi\)
\(30\) 0 0
\(31\) 4.67386 + 2.69846i 0.839451 + 0.484657i 0.857077 0.515188i \(-0.172278\pi\)
−0.0176268 + 0.999845i \(0.505611\pi\)
\(32\) 0.965559 3.13027i 0.170688 0.553358i
\(33\) 0 0
\(34\) 4.24203 + 3.38291i 0.727502 + 0.580164i
\(35\) −10.0857 1.41075i −1.70479 0.238461i
\(36\) 0 0
\(37\) 5.45716 5.06350i 0.897151 0.832435i −0.0893816 0.995997i \(-0.528489\pi\)
0.986533 + 0.163563i \(0.0522986\pi\)
\(38\) −1.42979 + 0.215506i −0.231942 + 0.0349597i
\(39\) 0 0
\(40\) −1.29684 + 8.60394i −0.205048 + 1.36040i
\(41\) −5.36277 + 2.58258i −0.837524 + 0.403331i −0.802932 0.596071i \(-0.796728\pi\)
−0.0345927 + 0.999401i \(0.511013\pi\)
\(42\) 0 0
\(43\) −2.54826 1.22718i −0.388606 0.187143i 0.229371 0.973339i \(-0.426333\pi\)
−0.617977 + 0.786196i \(0.712047\pi\)
\(44\) 1.47965 2.17024i 0.223065 0.327176i
\(45\) 0 0
\(46\) 0.299142 3.99177i 0.0441060 0.588554i
\(47\) 1.55456 3.96096i 0.226756 0.577765i −0.771536 0.636186i \(-0.780511\pi\)
0.998292 + 0.0584204i \(0.0186064\pi\)
\(48\) 0 0
\(49\) 4.24716 5.56432i 0.606738 0.794902i
\(50\) 15.8195i 2.23722i
\(51\) 0 0
\(52\) −2.61807 0.196198i −0.363062 0.0272077i
\(53\) −8.87284 + 9.56264i −1.21878 + 1.31353i −0.283775 + 0.958891i \(0.591587\pi\)
−0.935003 + 0.354639i \(0.884604\pi\)
\(54\) 0 0
\(55\) −7.34351 + 15.2490i −0.990199 + 2.05617i
\(56\) −4.71536 3.67910i −0.630116 0.491640i
\(57\) 0 0
\(58\) 13.5693 + 2.04524i 1.78174 + 0.268554i
\(59\) −6.88259 + 4.69247i −0.896037 + 0.610908i −0.921334 0.388772i \(-0.872899\pi\)
0.0252968 + 0.999680i \(0.491947\pi\)
\(60\) 0 0
\(61\) 2.93497 + 3.16315i 0.375784 + 0.404999i 0.892420 0.451206i \(-0.149006\pi\)
−0.516635 + 0.856206i \(0.672816\pi\)
\(62\) 5.42301 + 6.80024i 0.688723 + 0.863632i
\(63\) 0 0
\(64\) −2.74110 + 3.43722i −0.342637 + 0.429653i
\(65\) 16.8698 1.26422i 2.09244 0.156807i
\(66\) 0 0
\(67\) −1.42922 + 2.47548i −0.174607 + 0.302428i −0.940025 0.341105i \(-0.889199\pi\)
0.765418 + 0.643533i \(0.222532\pi\)
\(68\) 1.00554 + 1.74165i 0.121940 + 0.211206i
\(69\) 0 0
\(70\) −14.3001 8.05484i −1.70919 0.962737i
\(71\) 7.30694 + 1.66776i 0.867175 + 0.197927i 0.632891 0.774241i \(-0.281868\pi\)
0.234284 + 0.972168i \(0.424725\pi\)
\(72\) 0 0
\(73\) 3.88677 1.52545i 0.454912 0.178540i −0.126811 0.991927i \(-0.540474\pi\)
0.581723 + 0.813387i \(0.302379\pi\)
\(74\) 11.1683 4.38325i 1.29829 0.509543i
\(75\) 0 0
\(76\) −0.522506 0.119259i −0.0599356 0.0136799i
\(77\) −6.65522 9.54201i −0.758433 1.08741i
\(78\) 0 0
\(79\) −1.80778 3.13117i −0.203391 0.352284i 0.746228 0.665691i \(-0.231863\pi\)
−0.949619 + 0.313407i \(0.898530\pi\)
\(80\) −9.31082 + 16.1268i −1.04098 + 1.80303i
\(81\) 0 0
\(82\) −9.56598 + 0.716871i −1.05639 + 0.0791652i
\(83\) 8.34856 10.4688i 0.916373 1.14910i −0.0720540 0.997401i \(-0.522955\pi\)
0.988427 0.151695i \(-0.0484732\pi\)
\(84\) 0 0
\(85\) −8.07955 10.1314i −0.876350 1.09891i
\(86\) −3.10041 3.34145i −0.334326 0.360318i
\(87\) 0 0
\(88\) −8.21269 + 5.59932i −0.875476 + 0.596889i
\(89\) −3.95521 0.596152i −0.419251 0.0631919i −0.0639709 0.997952i \(-0.520376\pi\)
−0.355280 + 0.934760i \(0.615615\pi\)
\(90\) 0 0
\(91\) −4.93369 + 10.5296i −0.517191 + 1.10381i
\(92\) 0.643760 1.33678i 0.0671166 0.139369i
\(93\) 0 0
\(94\) 4.66439 5.02702i 0.481095 0.518497i
\(95\) 3.44374 + 0.258073i 0.353320 + 0.0264777i
\(96\) 0 0
\(97\) 18.1405i 1.84189i −0.389690 0.920946i \(-0.627418\pi\)
0.389690 0.920946i \(-0.372582\pi\)
\(98\) 9.64795 5.84702i 0.974590 0.590638i
\(99\) 0 0
\(100\) −2.14220 + 5.45824i −0.214220 + 0.545824i
\(101\) −0.182498 + 2.43527i −0.0181593 + 0.242319i 0.980736 + 0.195336i \(0.0625797\pi\)
−0.998896 + 0.0469828i \(0.985039\pi\)
\(102\) 0 0
\(103\) 10.6815 15.6669i 1.05248 1.54370i 0.231424 0.972853i \(-0.425662\pi\)
0.821055 0.570849i \(-0.193386\pi\)
\(104\) 8.95128 + 4.31071i 0.877745 + 0.422700i
\(105\) 0 0
\(106\) −18.9417 + 9.12184i −1.83978 + 0.885992i
\(107\) 0.405749 2.69197i 0.0392252 0.260242i −0.960619 0.277867i \(-0.910372\pi\)
0.999845 + 0.0176251i \(0.00561054\pi\)
\(108\) 0 0
\(109\) 11.5445 1.74005i 1.10576 0.166667i 0.429313 0.903156i \(-0.358756\pi\)
0.676449 + 0.736489i \(0.263518\pi\)
\(110\) −19.9954 + 18.5531i −1.90649 + 1.76896i
\(111\) 0 0
\(112\) −6.51732 11.0164i −0.615829 1.04095i
\(113\) 9.04782 + 7.21539i 0.851147 + 0.678767i 0.948602 0.316473i \(-0.102499\pi\)
−0.0974544 + 0.995240i \(0.531070\pi\)
\(114\) 0 0
\(115\) −2.81799 + 9.13570i −0.262779 + 0.851909i
\(116\) 4.40489 + 2.54317i 0.408984 + 0.236127i
\(117\) 0 0
\(118\) −13.0883 + 2.98733i −1.20488 + 0.275006i
\(119\) 8.79316 1.42106i 0.806068 0.130268i
\(120\) 0 0
\(121\) −7.96429 + 2.45666i −0.724026 + 0.223333i
\(122\) 2.54067 + 6.47353i 0.230022 + 0.586086i
\(123\) 0 0
\(124\) 0.950259 + 3.08066i 0.0853358 + 0.276652i
\(125\) 4.12482 18.0720i 0.368935 1.61641i
\(126\) 0 0
\(127\) 2.54710 + 11.1596i 0.226018 + 0.990251i 0.952852 + 0.303437i \(0.0981342\pi\)
−0.726833 + 0.686814i \(0.759009\pi\)
\(128\) −11.8099 + 6.81847i −1.04386 + 0.602673i
\(129\) 0 0
\(130\) 26.0529 + 8.03625i 2.28499 + 0.704825i
\(131\) −0.421231 5.62093i −0.0368031 0.491103i −0.984900 0.173123i \(-0.944614\pi\)
0.948097 0.317981i \(-0.103005\pi\)
\(132\) 0 0
\(133\) −1.31626 + 1.97537i −0.114134 + 0.171286i
\(134\) −3.60170 + 2.87226i −0.311139 + 0.248125i
\(135\) 0 0
\(136\) −1.13427 7.52539i −0.0972629 0.645297i
\(137\) 10.1322 + 14.8611i 0.865648 + 1.26967i 0.961647 + 0.274291i \(0.0884433\pi\)
−0.0959983 + 0.995381i \(0.530604\pi\)
\(138\) 0 0
\(139\) 2.66447 + 5.53282i 0.225997 + 0.469288i 0.982876 0.184267i \(-0.0589911\pi\)
−0.756879 + 0.653555i \(0.773277\pi\)
\(140\) −3.84326 4.71564i −0.324815 0.398544i
\(141\) 0 0
\(142\) 9.98010 + 6.80431i 0.837511 + 0.571005i
\(143\) 14.1666 + 13.1447i 1.18467 + 1.09921i
\(144\) 0 0
\(145\) −30.5087 11.9738i −2.53361 0.994368i
\(146\) 6.72921 0.556913
\(147\) 0 0
\(148\) 4.44700 0.365541
\(149\) −6.21653 2.43981i −0.509278 0.199877i 0.0967671 0.995307i \(-0.469150\pi\)
−0.606045 + 0.795430i \(0.707245\pi\)
\(150\) 0 0
\(151\) 8.46747 + 7.85666i 0.689073 + 0.639366i 0.944901 0.327356i \(-0.106158\pi\)
−0.255828 + 0.966722i \(0.582348\pi\)
\(152\) 1.67572 + 1.14249i 0.135919 + 0.0926680i
\(153\) 0 0
\(154\) −4.36605 18.2337i −0.351826 1.46932i
\(155\) −9.01326 18.7162i −0.723962 1.50332i
\(156\) 0 0
\(157\) 2.61302 + 3.83259i 0.208541 + 0.305874i 0.916232 0.400649i \(-0.131215\pi\)
−0.707690 + 0.706523i \(0.750263\pi\)
\(158\) −0.868463 5.76187i −0.0690912 0.458390i
\(159\) 0 0
\(160\) −9.85811 + 7.86158i −0.779352 + 0.621512i
\(161\) −4.52068 4.76949i −0.356279 0.375888i
\(162\) 0 0
\(163\) −0.887218 11.8391i −0.0694923 0.927310i −0.917605 0.397494i \(-0.869880\pi\)
0.848112 0.529816i \(-0.177739\pi\)
\(164\) −3.39765 1.04804i −0.265312 0.0818379i
\(165\) 0 0
\(166\) 18.6887 10.7899i 1.45052 0.837460i
\(167\) 5.11430 + 22.4072i 0.395756 + 1.73392i 0.643819 + 0.765177i \(0.277349\pi\)
−0.248063 + 0.968744i \(0.579794\pi\)
\(168\) 0 0
\(169\) 1.40553 6.15801i 0.108117 0.473693i
\(170\) −6.15581 19.9566i −0.472129 1.53060i
\(171\) 0 0
\(172\) −0.617260 1.57275i −0.0470656 0.119921i
\(173\) −12.5556 + 3.87288i −0.954583 + 0.294450i −0.732645 0.680611i \(-0.761715\pi\)
−0.221938 + 0.975061i \(0.571238\pi\)
\(174\) 0 0
\(175\) 19.2241 + 17.4610i 1.45321 + 1.31993i
\(176\) −20.7393 + 4.73362i −1.56329 + 0.356810i
\(177\) 0 0
\(178\) −5.58269 3.22317i −0.418441 0.241587i
\(179\) 5.16876 16.7567i 0.386331 1.25246i −0.528609 0.848866i \(-0.677286\pi\)
0.914940 0.403590i \(-0.132238\pi\)
\(180\) 0 0
\(181\) −4.95113 3.94840i −0.368015 0.293482i 0.421968 0.906611i \(-0.361339\pi\)
−0.789983 + 0.613129i \(0.789911\pi\)
\(182\) −13.6015 + 12.8919i −1.00821 + 0.955612i
\(183\) 0 0
\(184\) −4.11588 + 3.81898i −0.303427 + 0.281539i
\(185\) −28.3346 + 4.27075i −2.08320 + 0.313992i
\(186\) 0 0
\(187\) 2.20633 14.6381i 0.161343 1.07044i
\(188\) 2.29010 1.10285i 0.167023 0.0804339i
\(189\) 0 0
\(190\) 5.01444 + 2.41483i 0.363786 + 0.175190i
\(191\) 2.58021 3.78448i 0.186698 0.273835i −0.721467 0.692449i \(-0.756532\pi\)
0.908164 + 0.418614i \(0.137484\pi\)
\(192\) 0 0
\(193\) 0.0550106 0.734065i 0.00395975 0.0528392i −0.994874 0.101123i \(-0.967756\pi\)
0.998834 + 0.0482843i \(0.0153753\pi\)
\(194\) 10.6811 27.2149i 0.766856 1.95392i
\(195\) 0 0
\(196\) 4.12063 0.710933i 0.294331 0.0507809i
\(197\) 5.02513i 0.358025i 0.983847 + 0.179013i \(0.0572903\pi\)
−0.983847 + 0.179013i \(0.942710\pi\)
\(198\) 0 0
\(199\) 1.83712 + 0.137673i 0.130230 + 0.00975937i 0.139685 0.990196i \(-0.455391\pi\)
−0.00945574 + 0.999955i \(0.503010\pi\)
\(200\) 15.0924 16.2658i 1.06719 1.15016i
\(201\) 0 0
\(202\) −1.70767 + 3.54600i −0.120151 + 0.249496i
\(203\) 17.4627 14.2322i 1.22564 0.998903i
\(204\) 0 0
\(205\) 22.6550 + 3.41470i 1.58230 + 0.238493i
\(206\) 25.2492 17.2146i 1.75920 1.19940i
\(207\) 0 0
\(208\) 14.4623 + 15.5866i 1.00278 + 1.08074i
\(209\) 2.45969 + 3.08435i 0.170140 + 0.213349i
\(210\) 0 0
\(211\) −7.68161 + 9.63244i −0.528824 + 0.663124i −0.972456 0.233084i \(-0.925118\pi\)
0.443632 + 0.896209i \(0.353690\pi\)
\(212\) −7.77074 + 0.582336i −0.533697 + 0.0399950i
\(213\) 0 0
\(214\) 2.19373 3.79966i 0.149960 0.259739i
\(215\) 5.44336 + 9.42818i 0.371234 + 0.642997i
\(216\) 0 0
\(217\) 14.2495 + 0.915727i 0.967319 + 0.0621636i
\(218\) 18.3439 + 4.18687i 1.24240 + 0.283571i
\(219\) 0 0
\(220\) −9.41144 + 3.69372i −0.634519 + 0.249031i
\(221\) −13.7736 + 5.40575i −0.926514 + 0.363630i
\(222\) 0 0
\(223\) −0.0216823 0.00494884i −0.00145195 0.000331399i 0.221795 0.975093i \(-0.428808\pi\)
−0.223247 + 0.974762i \(0.571666\pi\)
\(224\) −1.38272 8.55594i −0.0923868 0.571668i
\(225\) 0 0
\(226\) 9.32538 + 16.1520i 0.620315 + 1.07442i
\(227\) −4.56676 + 7.90986i −0.303106 + 0.524996i −0.976838 0.213980i \(-0.931357\pi\)
0.673732 + 0.738976i \(0.264690\pi\)
\(228\) 0 0
\(229\) −3.95603 + 0.296463i −0.261422 + 0.0195908i −0.204796 0.978805i \(-0.565653\pi\)
−0.0566254 + 0.998395i \(0.518034\pi\)
\(230\) −9.60668 + 12.0464i −0.633446 + 0.794316i
\(231\) 0 0
\(232\) −12.0008 15.0486i −0.787893 0.987987i
\(233\) −10.0603 10.8424i −0.659069 0.710307i 0.311738 0.950168i \(-0.399089\pi\)
−0.970807 + 0.239861i \(0.922898\pi\)
\(234\) 0 0
\(235\) −13.5325 + 9.22631i −0.882763 + 0.601858i
\(236\) −4.92044 0.741636i −0.320293 0.0482764i
\(237\) 0 0
\(238\) 14.0284 + 3.04547i 0.909329 + 0.197408i
\(239\) −5.51570 + 11.4535i −0.356781 + 0.740863i −0.999685 0.0250833i \(-0.992015\pi\)
0.642905 + 0.765946i \(0.277729\pi\)
\(240\) 0 0
\(241\) −8.72384 + 9.40207i −0.561952 + 0.605640i −0.948558 0.316605i \(-0.897457\pi\)
0.386605 + 0.922245i \(0.373648\pi\)
\(242\) −13.3947 1.00379i −0.861044 0.0645264i
\(243\) 0 0
\(244\) 2.57762i 0.165015i
\(245\) −25.5723 + 8.48711i −1.63376 + 0.542222i
\(246\) 0 0
\(247\) 1.44061 3.67060i 0.0916635 0.233555i
\(248\) 0.911703 12.1658i 0.0578932 0.772531i
\(249\) 0 0
\(250\) 16.8289 24.6834i 1.06435 1.56112i
\(251\) −14.8498 7.15128i −0.937310 0.451385i −0.0980903 0.995178i \(-0.531273\pi\)
−0.839219 + 0.543793i \(0.816988\pi\)
\(252\) 0 0
\(253\) −9.83994 + 4.73866i −0.618632 + 0.297917i
\(254\) −2.74948 + 18.2416i −0.172517 + 1.14458i
\(255\) 0 0
\(256\) −13.0377 + 1.96512i −0.814857 + 0.122820i
\(257\) −8.36052 + 7.75743i −0.521515 + 0.483895i −0.896443 0.443159i \(-0.853858\pi\)
0.374928 + 0.927054i \(0.377667\pi\)
\(258\) 0 0
\(259\) 7.00061 18.4100i 0.434997 1.14394i
\(260\) 7.90086 + 6.30072i 0.489990 + 0.390754i
\(261\) 0 0
\(262\) 2.67764 8.68069i 0.165425 0.536295i
\(263\) 6.94717 + 4.01095i 0.428381 + 0.247326i 0.698657 0.715457i \(-0.253782\pi\)
−0.270276 + 0.962783i \(0.587115\pi\)
\(264\) 0 0
\(265\) 48.9529 11.1732i 3.00715 0.686363i
\(266\) −3.13778 + 2.18849i −0.192390 + 0.134185i
\(267\) 0 0
\(268\) −1.63165 + 0.503298i −0.0996689 + 0.0307438i
\(269\) 0.0713278 + 0.181740i 0.00434893 + 0.0110809i 0.933032 0.359794i \(-0.117153\pi\)
−0.928683 + 0.370875i \(0.879058\pi\)
\(270\) 0 0
\(271\) −0.693161 2.24717i −0.0421065 0.136506i 0.932079 0.362255i \(-0.117993\pi\)
−0.974185 + 0.225749i \(0.927517\pi\)
\(272\) 3.62427 15.8790i 0.219754 0.962804i
\(273\) 0 0
\(274\) 6.45035 + 28.2608i 0.389680 + 1.70730i
\(275\) 37.3788 21.5806i 2.25402 1.30136i
\(276\) 0 0
\(277\) −22.3119 6.88231i −1.34059 0.413518i −0.460221 0.887804i \(-0.652230\pi\)
−0.880371 + 0.474286i \(0.842706\pi\)
\(278\) 0.739603 + 9.86931i 0.0443584 + 0.591922i
\(279\) 0 0
\(280\) 7.01889 + 21.9249i 0.419459 + 1.31027i
\(281\) 7.57759 6.04292i 0.452041 0.360491i −0.370847 0.928694i \(-0.620933\pi\)
0.822888 + 0.568203i \(0.192361\pi\)
\(282\) 0 0
\(283\) −1.79996 11.9419i −0.106996 0.709874i −0.976432 0.215827i \(-0.930755\pi\)
0.869435 0.494047i \(-0.164483\pi\)
\(284\) 2.52205 + 3.69917i 0.149656 + 0.219505i
\(285\) 0 0
\(286\) 13.5136 + 28.0612i 0.799073 + 1.65929i
\(287\) −9.68743 + 12.4160i −0.571831 + 0.732893i
\(288\) 0 0
\(289\) −4.68133 3.19168i −0.275373 0.187746i
\(290\) −38.7198 35.9267i −2.27371 2.10969i
\(291\) 0 0
\(292\) 2.32180 + 0.911238i 0.135873 + 0.0533262i
\(293\) 11.9276 0.696817 0.348409 0.937343i \(-0.386722\pi\)
0.348409 + 0.937343i \(0.386722\pi\)
\(294\) 0 0
\(295\) 32.0634 1.86680
\(296\) −15.6652 6.14813i −0.910520 0.357353i
\(297\) 0 0
\(298\) −7.88966 7.32053i −0.457036 0.424067i
\(299\) 9.01952 + 6.14941i 0.521613 + 0.355629i
\(300\) 0 0
\(301\) −7.48271 + 0.0795013i −0.431296 + 0.00458238i
\(302\) 8.07715 + 16.7724i 0.464788 + 0.965142i
\(303\) 0 0
\(304\) 2.44509 + 3.58628i 0.140235 + 0.205687i
\(305\) −2.47547 16.4236i −0.141745 0.940415i
\(306\) 0 0
\(307\) 22.0802 17.6084i 1.26018 1.00496i 0.260968 0.965347i \(-0.415958\pi\)
0.999215 0.0396152i \(-0.0126132\pi\)
\(308\) 0.962699 6.88246i 0.0548549 0.392165i
\(309\) 0 0
\(310\) −2.50190 33.3855i −0.142098 1.89617i
\(311\) 18.2667 + 5.63452i 1.03581 + 0.319504i 0.765613 0.643301i \(-0.222436\pi\)
0.270195 + 0.962806i \(0.412912\pi\)
\(312\) 0 0
\(313\) −29.5626 + 17.0680i −1.67098 + 0.964739i −0.703885 + 0.710314i \(0.748553\pi\)
−0.967093 + 0.254425i \(0.918114\pi\)
\(314\) 1.66350 + 7.28829i 0.0938770 + 0.411302i
\(315\) 0 0
\(316\) 0.480598 2.10564i 0.0270357 0.118451i
\(317\) 2.40572 + 7.79916i 0.135119 + 0.438044i 0.997693 0.0678861i \(-0.0216255\pi\)
−0.862574 + 0.505930i \(0.831149\pi\)
\(318\) 0 0
\(319\) −13.6784 34.8520i −0.765843 1.95134i
\(320\) 16.1704 4.98792i 0.903954 0.278833i
\(321\) 0 0
\(322\) −3.97379 9.81707i −0.221451 0.547084i
\(323\) −2.94477 + 0.672124i −0.163851 + 0.0373980i
\(324\) 0 0
\(325\) −37.3612 21.5705i −2.07242 1.19651i
\(326\) 5.63978 18.2837i 0.312359 1.01264i
\(327\) 0 0
\(328\) 10.5197 + 8.38922i 0.580856 + 0.463217i
\(329\) −0.960530 11.2169i −0.0529557 0.618407i
\(330\) 0 0
\(331\) −22.0820 + 20.4891i −1.21374 + 1.12618i −0.225341 + 0.974280i \(0.572350\pi\)
−0.988395 + 0.151903i \(0.951460\pi\)
\(332\) 7.90932 1.19214i 0.434081 0.0654271i
\(333\) 0 0
\(334\) −5.52065 + 36.6271i −0.302077 + 2.00415i
\(335\) 9.91290 4.77380i 0.541600 0.260821i
\(336\) 0 0
\(337\) −26.1851 12.6101i −1.42640 0.686916i −0.448072 0.893998i \(-0.647889\pi\)
−0.978324 + 0.207082i \(0.933603\pi\)
\(338\) 5.73442 8.41085i 0.311911 0.457490i
\(339\) 0 0
\(340\) 0.578480 7.71928i 0.0313725 0.418637i
\(341\) 8.66984 22.0904i 0.469498 1.19626i
\(342\) 0 0
\(343\) 3.54366 18.1781i 0.191339 0.981524i
\(344\) 6.39362i 0.344721i
\(345\) 0 0
\(346\) −21.1166 1.58247i −1.13523 0.0850739i
\(347\) 8.34219 8.99074i 0.447832 0.482648i −0.468275 0.883583i \(-0.655124\pi\)
0.916107 + 0.400935i \(0.131315\pi\)
\(348\) 0 0
\(349\) −1.40591 + 2.91940i −0.0752565 + 0.156272i −0.935203 0.354113i \(-0.884783\pi\)
0.859946 + 0.510385i \(0.170497\pi\)
\(350\) 18.5596 + 37.5145i 0.992051 + 2.00524i
\(351\) 0 0
\(352\) −14.2432 2.14681i −0.759163 0.114425i
\(353\) −4.43190 + 3.02162i −0.235886 + 0.160824i −0.675494 0.737365i \(-0.736070\pi\)
0.439608 + 0.898190i \(0.355117\pi\)
\(354\) 0 0
\(355\) −19.6221 21.1476i −1.04143 1.12240i
\(356\) −1.48974 1.86808i −0.0789563 0.0990081i
\(357\) 0 0
\(358\) 17.6206 22.0955i 0.931277 1.16778i
\(359\) 31.7494 2.37929i 1.67567 0.125574i 0.797307 0.603574i \(-0.206257\pi\)
0.878360 + 0.478000i \(0.158638\pi\)
\(360\) 0 0
\(361\) −9.09753 + 15.7574i −0.478817 + 0.829336i
\(362\) −5.10302 8.83869i −0.268209 0.464551i
\(363\) 0 0
\(364\) −6.43871 + 2.60628i −0.337480 + 0.136606i
\(365\) −15.6687 3.57628i −0.820139 0.187191i
\(366\) 0 0
\(367\) −9.53927 + 3.74389i −0.497946 + 0.195429i −0.601004 0.799246i \(-0.705232\pi\)
0.103058 + 0.994675i \(0.467137\pi\)
\(368\) −11.1856 + 4.39004i −0.583092 + 0.228847i
\(369\) 0 0
\(370\) −45.0229 10.2762i −2.34063 0.534233i
\(371\) −9.82215 + 33.0866i −0.509941 + 1.71777i
\(372\) 0 0
\(373\) 6.35426 + 11.0059i 0.329011 + 0.569864i 0.982316 0.187231i \(-0.0599512\pi\)
−0.653305 + 0.757095i \(0.726618\pi\)
\(374\) 11.9288 20.6613i 0.616825 1.06837i
\(375\) 0 0
\(376\) −9.59193 + 0.718816i −0.494666 + 0.0370701i
\(377\) −23.3325 + 29.2581i −1.20169 + 1.50687i
\(378\) 0 0
\(379\) 23.0179 + 28.8635i 1.18235 + 1.48262i 0.839610 + 0.543190i \(0.182784\pi\)
0.342740 + 0.939430i \(0.388645\pi\)
\(380\) 1.40314 + 1.51223i 0.0719796 + 0.0775755i
\(381\) 0 0
\(382\) 6.09919 4.15836i 0.312062 0.212760i
\(383\) −2.39721 0.361321i −0.122492 0.0184627i 0.0875103 0.996164i \(-0.472109\pi\)
−0.210002 + 0.977701i \(0.567347\pi\)
\(384\) 0 0
\(385\) 0.475741 + 44.7770i 0.0242460 + 2.28205i
\(386\) 0.514742 1.06887i 0.0261997 0.0544042i
\(387\) 0 0
\(388\) 7.37063 7.94365i 0.374187 0.403278i
\(389\) 3.19974 + 0.239787i 0.162233 + 0.0121577i 0.155599 0.987820i \(-0.450269\pi\)
0.00663415 + 0.999978i \(0.497888\pi\)
\(390\) 0 0
\(391\) 8.36200i 0.422884i
\(392\) −15.4984 3.19255i −0.782787 0.161248i
\(393\) 0 0
\(394\) −2.95877 + 7.53883i −0.149061 + 0.379801i
\(395\) −1.04000 + 13.8779i −0.0523282 + 0.698271i
\(396\) 0 0
\(397\) 17.6855 25.9398i 0.887608 1.30188i −0.0650632 0.997881i \(-0.520725\pi\)
0.952672 0.304001i \(-0.0983227\pi\)
\(398\) 2.67503 + 1.28823i 0.134087 + 0.0645729i
\(399\) 0 0
\(400\) 42.7850 20.6042i 2.13925 1.03021i
\(401\) −3.40985 + 22.6229i −0.170280 + 1.12973i 0.726471 + 0.687197i \(0.241159\pi\)
−0.896751 + 0.442535i \(0.854079\pi\)
\(402\) 0 0
\(403\) −23.4547 + 3.53523i −1.16836 + 0.176102i
\(404\) −1.06938 + 0.992243i −0.0532038 + 0.0493659i
\(405\) 0 0
\(406\) 34.5779 11.0695i 1.71607 0.549371i
\(407\) −25.5925 20.4093i −1.26857 1.01165i
\(408\) 0 0
\(409\) −0.786141 + 2.54861i −0.0388721 + 0.126020i −0.972929 0.231103i \(-0.925766\pi\)
0.934057 + 0.357124i \(0.116243\pi\)
\(410\) 31.9771 + 18.4620i 1.57924 + 0.911773i
\(411\) 0 0
\(412\) 11.0429 2.52048i 0.544046 0.124175i
\(413\) −10.8162 + 19.2025i −0.532230 + 0.944893i
\(414\) 0 0
\(415\) −49.2503 + 15.1917i −2.41760 + 0.745732i
\(416\) 5.25991 + 13.4020i 0.257889 + 0.657089i
\(417\) 0 0
\(418\) 1.87404 + 6.07548i 0.0916622 + 0.297162i
\(419\) −7.01996 + 30.7565i −0.342947 + 1.50255i 0.449871 + 0.893093i \(0.351470\pi\)
−0.792819 + 0.609458i \(0.791387\pi\)
\(420\) 0 0
\(421\) 2.52739 + 11.0732i 0.123178 + 0.539676i 0.998430 + 0.0560100i \(0.0178379\pi\)
−0.875253 + 0.483666i \(0.839305\pi\)
\(422\) −17.1957 + 9.92794i −0.837073 + 0.483284i
\(423\) 0 0
\(424\) 28.1786 + 8.69195i 1.36847 + 0.422118i
\(425\) 2.46955 + 32.9538i 0.119791 + 1.59849i
\(426\) 0 0
\(427\) 10.6710 + 4.05778i 0.516408 + 0.196370i
\(428\) 1.27144 1.01394i 0.0614574 0.0490106i
\(429\) 0 0
\(430\) 2.61501 + 17.3494i 0.126107 + 0.836664i
\(431\) −4.08471 5.99117i −0.196754 0.288585i 0.715165 0.698956i \(-0.246352\pi\)
−0.911919 + 0.410371i \(0.865399\pi\)
\(432\) 0 0
\(433\) −5.40026 11.2138i −0.259520 0.538899i 0.729974 0.683475i \(-0.239532\pi\)
−0.989494 + 0.144577i \(0.953818\pi\)
\(434\) 20.8383 + 9.76383i 1.00027 + 0.468679i
\(435\) 0 0
\(436\) 5.76227 + 3.92865i 0.275963 + 0.188148i
\(437\) 1.63355 + 1.51572i 0.0781435 + 0.0725066i
\(438\) 0 0
\(439\) 34.4035 + 13.5024i 1.64199 + 0.644433i 0.993188 0.116525i \(-0.0371754\pi\)
0.648801 + 0.760958i \(0.275271\pi\)
\(440\) 38.2598 1.82396
\(441\) 0 0
\(442\) −23.8464 −1.13426
\(443\) −9.19111 3.60724i −0.436683 0.171385i 0.136808 0.990598i \(-0.456316\pi\)
−0.573490 + 0.819212i \(0.694411\pi\)
\(444\) 0 0
\(445\) 11.2861 + 10.4720i 0.535014 + 0.496420i
\(446\) −0.0296145 0.0201908i −0.00140229 0.000956063i
\(447\) 0 0
\(448\) −2.46768 + 11.3669i −0.116587 + 0.537038i
\(449\) 2.05379 + 4.26475i 0.0969245 + 0.201266i 0.943793 0.330536i \(-0.107229\pi\)
−0.846869 + 0.531802i \(0.821515\pi\)
\(450\) 0 0
\(451\) 14.7436 + 21.6248i 0.694247 + 1.01827i
\(452\) 1.03033 + 6.83578i 0.0484625 + 0.321528i
\(453\) 0 0
\(454\) −11.5085 + 9.17769i −0.540119 + 0.430730i
\(455\) 38.5220 22.7898i 1.80594 1.06840i
\(456\) 0 0
\(457\) −1.23467 16.4756i −0.0577556 0.770695i −0.948618 0.316423i \(-0.897518\pi\)
0.890863 0.454273i \(-0.150101\pi\)
\(458\) −6.10949 1.88453i −0.285478 0.0880582i
\(459\) 0 0
\(460\) −4.94589 + 2.85551i −0.230603 + 0.133139i
\(461\) 2.95601 + 12.9511i 0.137675 + 0.603194i 0.995943 + 0.0899916i \(0.0286840\pi\)
−0.858267 + 0.513203i \(0.828459\pi\)
\(462\) 0 0
\(463\) −8.14915 + 35.7038i −0.378723 + 1.65929i 0.322664 + 0.946514i \(0.395422\pi\)
−0.701387 + 0.712781i \(0.747435\pi\)
\(464\) −12.1419 39.3630i −0.563673 1.82738i
\(465\) 0 0
\(466\) −8.70871 22.1894i −0.403423 1.02791i
\(467\) −6.35492 + 1.96023i −0.294071 + 0.0907088i −0.438280 0.898838i \(-0.644412\pi\)
0.144210 + 0.989547i \(0.453936\pi\)
\(468\) 0 0
\(469\) −0.485008 + 7.54714i −0.0223956 + 0.348494i
\(470\) −25.7342 + 5.87367i −1.18703 + 0.270932i
\(471\) 0 0
\(472\) 16.3076 + 9.41519i 0.750617 + 0.433369i
\(473\) −3.66575 + 11.8841i −0.168551 + 0.546430i
\(474\) 0 0
\(475\) −6.88531 5.49085i −0.315920 0.251938i
\(476\) 4.42787 + 2.95045i 0.202951 + 0.135234i
\(477\) 0 0
\(478\) −15.0185 + 13.9352i −0.686932 + 0.637380i
\(479\) 19.8784 2.99619i 0.908268 0.136899i 0.321740 0.946828i \(-0.395732\pi\)
0.586528 + 0.809929i \(0.300494\pi\)
\(480\) 0 0
\(481\) −4.87645 + 32.3532i −0.222347 + 1.47518i
\(482\) −18.6236 + 8.96867i −0.848283 + 0.408512i
\(483\) 0 0
\(484\) −4.48568 2.16019i −0.203895 0.0981905i
\(485\) −39.3340 + 57.6924i −1.78607 + 2.61968i
\(486\) 0 0
\(487\) −0.296814 + 3.96071i −0.0134499 + 0.179477i 0.986433 + 0.164165i \(0.0524931\pi\)
−0.999883 + 0.0153116i \(0.995126\pi\)
\(488\) 3.56365 9.08004i 0.161319 0.411034i
\(489\) 0 0
\(490\) −43.3615 2.32428i −1.95887 0.105000i
\(491\) 11.1315i 0.502357i −0.967941 0.251179i \(-0.919182\pi\)
0.967941 0.251179i \(-0.0808182\pi\)
\(492\) 0 0
\(493\) 28.5857 + 2.14220i 1.28743 + 0.0964798i
\(494\) 4.32247 4.65851i 0.194477 0.209596i
\(495\) 0 0
\(496\) 11.3285 23.5240i 0.508666 1.05626i
\(497\) 19.2844 4.61762i 0.865023 0.207129i
\(498\) 0 0
\(499\) 29.2283 + 4.40545i 1.30844 + 0.197215i 0.765978 0.642867i \(-0.222255\pi\)
0.542459 + 0.840082i \(0.317493\pi\)
\(500\) 9.14902 6.23770i 0.409157 0.278958i
\(501\) 0 0
\(502\) −18.0674 19.4720i −0.806387 0.869079i
\(503\) −19.4052 24.3333i −0.865235 1.08497i −0.995619 0.0935062i \(-0.970192\pi\)
0.130384 0.991464i \(-0.458379\pi\)
\(504\) 0 0
\(505\) 5.86079 7.34919i 0.260802 0.327035i
\(506\) −17.5522 + 1.31536i −0.780292 + 0.0584748i
\(507\) 0 0
\(508\) −3.41885 + 5.92162i −0.151687 + 0.262729i
\(509\) −7.33336 12.7017i −0.325045 0.562995i 0.656476 0.754347i \(-0.272046\pi\)
−0.981522 + 0.191352i \(0.938713\pi\)
\(510\) 0 0
\(511\) 7.42746 8.17745i 0.328571 0.361749i
\(512\) 5.87349 + 1.34059i 0.259574 + 0.0592461i
\(513\) 0 0
\(514\) −17.1102 + 6.71527i −0.754699 + 0.296198i
\(515\) −67.9408 + 26.6648i −2.99383 + 1.17499i
\(516\) 0 0
\(517\) −18.2410 4.16340i −0.802240 0.183106i
\(518\) 21.3422 23.4973i 0.937724 1.03241i
\(519\) 0 0
\(520\) −19.1209 33.1184i −0.838507 1.45234i
\(521\) 10.3784 17.9759i 0.454686 0.787540i −0.543984 0.839096i \(-0.683085\pi\)
0.998670 + 0.0515557i \(0.0164180\pi\)
\(522\) 0 0
\(523\) 27.5060 2.06129i 1.20275 0.0901340i 0.541765 0.840530i \(-0.317756\pi\)
0.660989 + 0.750396i \(0.270137\pi\)
\(524\) 2.09937 2.63253i 0.0917114 0.115002i
\(525\) 0 0
\(526\) 8.06069 + 10.1078i 0.351463 + 0.440721i
\(527\) 12.3583 + 13.3191i 0.538337 + 0.580189i
\(528\) 0 0
\(529\) 13.9062 9.48111i 0.604619 0.412222i
\(530\) 80.0192 + 12.0610i 3.47581 + 0.523894i
\(531\) 0 0
\(532\) −1.37899 + 0.330198i −0.0597868 + 0.0143159i
\(533\) 11.3505 23.5696i 0.491646 1.02091i
\(534\) 0 0
\(535\) −7.12738 + 7.68149i −0.308143 + 0.332100i
\(536\) 6.44354 + 0.482877i 0.278319 + 0.0208571i
\(537\) 0 0
\(538\) 0.314649i 0.0135655i
\(539\) −26.9770 14.8200i −1.16198 0.638345i
\(540\) 0 0
\(541\) −3.00765 + 7.66336i −0.129309 + 0.329474i −0.980835 0.194838i \(-0.937582\pi\)
0.851527 + 0.524311i \(0.175677\pi\)
\(542\) 0.283227 3.77940i 0.0121656 0.162339i
\(543\) 0 0
\(544\) 6.21251 9.11208i 0.266359 0.390677i
\(545\) −40.4879 19.4980i −1.73431 0.835201i
\(546\) 0 0
\(547\) −30.9935 + 14.9257i −1.32519 + 0.638177i −0.956597 0.291415i \(-0.905874\pi\)
−0.368591 + 0.929592i \(0.620160\pi\)
\(548\) −1.60137 + 10.6244i −0.0684071 + 0.453851i
\(549\) 0 0
\(550\) 68.7832 10.3674i 2.93292 0.442067i
\(551\) −5.60000 + 5.19604i −0.238568 + 0.221359i
\(552\) 0 0
\(553\) −7.96050 5.30438i −0.338515 0.225565i
\(554\) −29.4206 23.4622i −1.24996 0.996812i
\(555\) 0 0
\(556\) −1.08127 + 3.50539i −0.0458560 + 0.148662i
\(557\) −13.2494 7.64952i −0.561394 0.324121i 0.192311 0.981334i \(-0.438402\pi\)
−0.753705 + 0.657213i \(0.771735\pi\)
\(558\) 0 0
\(559\) 12.1191 2.76610i 0.512582 0.116994i
\(560\) −3.15965 + 49.1668i −0.133519 + 2.07768i
\(561\) 0 0
\(562\) 14.9261 4.60410i 0.629621 0.194212i
\(563\) 6.01917 + 15.3366i 0.253678 + 0.646360i 0.999811 0.0194364i \(-0.00618720\pi\)
−0.746134 + 0.665796i \(0.768092\pi\)
\(564\) 0 0
\(565\) −13.1297 42.5655i −0.552371 1.79074i
\(566\) 4.33101 18.9754i 0.182046 0.797596i
\(567\) 0 0
\(568\) −3.77005 16.5177i −0.158188 0.693065i
\(569\) −13.2052 + 7.62404i −0.553592 + 0.319616i −0.750569 0.660792i \(-0.770221\pi\)
0.196978 + 0.980408i \(0.436887\pi\)
\(570\) 0 0
\(571\) −38.7414 11.9502i −1.62128 0.500098i −0.654575 0.755997i \(-0.727153\pi\)
−0.966704 + 0.255899i \(0.917629\pi\)
\(572\) 0.862702 + 11.5120i 0.0360714 + 0.481339i
\(573\) 0 0
\(574\) −21.8438 + 12.9229i −0.911743 + 0.539391i
\(575\) 19.0614 15.2010i 0.794916 0.633925i
\(576\) 0 0
\(577\) −3.75825 24.9343i −0.156458 1.03803i −0.919900 0.392154i \(-0.871730\pi\)
0.763442 0.645877i \(-0.223508\pi\)
\(578\) −5.14381 7.54459i −0.213954 0.313814i
\(579\) 0 0
\(580\) −8.49456 17.6391i −0.352718 0.732426i
\(581\) 7.51581 34.6203i 0.311808 1.43629i
\(582\) 0 0
\(583\) 47.3932 + 32.3121i 1.96283 + 1.33823i
\(584\) −6.91903 6.41993i −0.286312 0.265658i
\(585\) 0 0
\(586\) 17.8941 + 7.02291i 0.739198 + 0.290114i
\(587\) 2.24197 0.0925360 0.0462680 0.998929i \(-0.485267\pi\)
0.0462680 + 0.998929i \(0.485267\pi\)
\(588\) 0 0
\(589\) −4.84205 −0.199513
\(590\) 48.1023 + 18.8788i 1.98034 + 0.777227i
\(591\) 0 0
\(592\) −26.4011 24.4966i −1.08508 1.00680i
\(593\) −32.4557 22.1279i −1.33279 0.908684i −0.333376 0.942794i \(-0.608188\pi\)
−0.999418 + 0.0341103i \(0.989140\pi\)
\(594\) 0 0
\(595\) −31.0462 14.5468i −1.27277 0.596360i
\(596\) −1.73088 3.59420i −0.0708995 0.147224i
\(597\) 0 0
\(598\) 9.91058 + 14.5362i 0.405274 + 0.594428i
\(599\) 4.17473 + 27.6976i 0.170575 + 1.13169i 0.896216 + 0.443618i \(0.146305\pi\)
−0.725641 + 0.688074i \(0.758457\pi\)
\(600\) 0 0
\(601\) 19.9039 15.8728i 0.811896 0.647466i −0.126909 0.991914i \(-0.540506\pi\)
0.938805 + 0.344449i \(0.111934\pi\)
\(602\) −11.2726 4.28651i −0.459435 0.174705i
\(603\) 0 0
\(604\) 0.515643 + 6.88078i 0.0209812 + 0.279975i
\(605\) 30.6556 + 9.45601i 1.24633 + 0.384441i
\(606\) 0 0
\(607\) −11.0459 + 6.37734i −0.448338 + 0.258848i −0.707128 0.707086i \(-0.750010\pi\)
0.258790 + 0.965934i \(0.416676\pi\)
\(608\) 0.653991 + 2.86532i 0.0265228 + 0.116204i
\(609\) 0 0
\(610\) 5.95641 26.0967i 0.241168 1.05663i
\(611\) 5.51231 + 17.8705i 0.223004 + 0.722962i
\(612\) 0 0
\(613\) −5.50861 14.0357i −0.222491 0.566897i 0.775424 0.631441i \(-0.217536\pi\)
−0.997915 + 0.0645435i \(0.979441\pi\)
\(614\) 43.4930 13.4158i 1.75524 0.541418i
\(615\) 0 0
\(616\) −12.9065 + 22.9135i −0.520017 + 0.923210i
\(617\) 28.8631 6.58782i 1.16199 0.265216i 0.402301 0.915507i \(-0.368210\pi\)
0.759685 + 0.650292i \(0.225353\pi\)
\(618\) 0 0
\(619\) 19.2524 + 11.1154i 0.773819 + 0.446765i 0.834235 0.551409i \(-0.185910\pi\)
−0.0604163 + 0.998173i \(0.519243\pi\)
\(620\) 3.65767 11.8579i 0.146896 0.476224i
\(621\) 0 0
\(622\) 24.0865 + 19.2084i 0.965783 + 0.770186i
\(623\) −10.0788 + 3.22656i −0.403800 + 0.129270i
\(624\) 0 0
\(625\) −16.3260 + 15.1484i −0.653042 + 0.605934i
\(626\) −54.4001 + 8.19950i −2.17427 + 0.327718i
\(627\) 0 0
\(628\) −0.412982 + 2.73996i −0.0164798 + 0.109336i
\(629\) 22.5806 10.8743i 0.900349 0.433585i
\(630\) 0 0
\(631\) 6.82205 + 3.28533i 0.271582 + 0.130787i 0.564718 0.825284i \(-0.308985\pi\)
−0.293137 + 0.956071i \(0.594699\pi\)
\(632\) −4.60409 + 6.75296i −0.183141 + 0.268618i
\(633\) 0 0
\(634\) −0.982981 + 13.1170i −0.0390392 + 0.520942i
\(635\) 16.0967 41.0136i 0.638777 1.62758i
\(636\) 0 0
\(637\) 0.653668 + 30.7583i 0.0258993 + 1.21869i
\(638\) 60.3396i 2.38887i
\(639\) 0 0
\(640\) 52.3436 + 3.92261i 2.06906 + 0.155055i
\(641\) −5.33852 + 5.75356i −0.210859 + 0.227252i −0.829622 0.558326i \(-0.811444\pi\)
0.618763 + 0.785578i \(0.287634\pi\)
\(642\) 0 0
\(643\) −13.2286 + 27.4694i −0.521684 + 1.08329i 0.459135 + 0.888367i \(0.348160\pi\)
−0.980819 + 0.194922i \(0.937555\pi\)
\(644\) −0.0417052 3.92532i −0.00164342 0.154679i
\(645\) 0 0
\(646\) −4.81356 0.725527i −0.189387 0.0285455i
\(647\) −7.77763 + 5.30270i −0.305770 + 0.208471i −0.706478 0.707736i \(-0.749717\pi\)
0.400707 + 0.916206i \(0.368764\pi\)
\(648\) 0 0
\(649\) 24.9134 + 26.8503i 0.977936 + 1.05396i
\(650\) −43.3496 54.3587i −1.70031 2.13212i
\(651\) 0 0
\(652\) 4.42181 5.54477i 0.173171 0.217150i
\(653\) 12.8389 0.962144i 0.502426 0.0376516i 0.178893 0.983869i \(-0.442748\pi\)
0.323533 + 0.946217i \(0.395129\pi\)
\(654\) 0 0
\(655\) −10.8482 + 18.7896i −0.423874 + 0.734171i
\(656\) 14.3981 + 24.9382i 0.562151 + 0.973674i
\(657\) 0 0
\(658\) 5.16344 17.3934i 0.201292 0.678066i
\(659\) −1.07593 0.245573i −0.0419121 0.00956617i 0.201513 0.979486i \(-0.435414\pi\)
−0.243426 + 0.969920i \(0.578271\pi\)
\(660\) 0 0
\(661\) 23.8238 9.35014i 0.926637 0.363678i 0.146445 0.989219i \(-0.453217\pi\)
0.780192 + 0.625541i \(0.215122\pi\)
\(662\) −45.1919 + 17.7365i −1.75643 + 0.689349i
\(663\) 0 0
\(664\) −29.5099 6.73543i −1.14520 0.261386i
\(665\) 8.46929 3.42823i 0.328425 0.132941i
\(666\) 0 0
\(667\) −10.5744 18.3154i −0.409441 0.709173i
\(668\) −6.86468 + 11.8900i −0.265602 + 0.460037i
\(669\) 0 0
\(670\) 17.6824 1.32511i 0.683130 0.0511935i
\(671\) 11.8299 14.8342i 0.456688 0.572669i
\(672\) 0 0
\(673\) −10.2056 12.7974i −0.393395 0.493302i 0.545208 0.838301i \(-0.316451\pi\)
−0.938603 + 0.344999i \(0.887879\pi\)
\(674\) −31.8589 34.3357i −1.22716 1.32256i
\(675\) 0 0
\(676\) 3.11752 2.12549i 0.119905 0.0817495i
\(677\) 15.7345 + 2.37159i 0.604725 + 0.0911477i 0.444266 0.895895i \(-0.353464\pi\)
0.160459 + 0.987042i \(0.448703\pi\)
\(678\) 0 0
\(679\) −21.2826 43.0186i −0.816752 1.65090i
\(680\) −12.7099 + 26.3925i −0.487404 + 1.01211i
\(681\) 0 0
\(682\) 26.0134 28.0358i 0.996106 1.07355i
\(683\) −29.2178 2.18957i −1.11799 0.0837818i −0.497110 0.867688i \(-0.665605\pi\)
−0.620880 + 0.783906i \(0.713225\pi\)
\(684\) 0 0
\(685\) 69.2324i 2.64523i
\(686\) 16.0195 25.1847i 0.611626 0.961558i
\(687\) 0 0
\(688\) −4.99905 + 12.7374i −0.190587 + 0.485608i
\(689\) 4.28451 57.1729i 0.163227 2.17811i
\(690\) 0 0
\(691\) −0.376066 + 0.551588i −0.0143062 + 0.0209834i −0.833325 0.552783i \(-0.813566\pi\)
0.819019 + 0.573766i \(0.194518\pi\)
\(692\) −7.07161 3.40551i −0.268822 0.129458i
\(693\) 0 0
\(694\) 17.8089 8.57630i 0.676016 0.325552i
\(695\) 3.52297 23.3734i 0.133634 0.886604i
\(696\) 0 0
\(697\) −19.8151 + 2.98665i −0.750551 + 0.113127i
\(698\) −3.82811 + 3.55196i −0.144896 + 0.134444i
\(699\) 0 0
\(700\) 1.32362 + 15.4570i 0.0500281 + 0.584219i
\(701\) 14.6783 + 11.7056i 0.554394 + 0.442114i 0.860183 0.509985i \(-0.170349\pi\)
−0.305790 + 0.952099i \(0.598920\pi\)
\(702\) 0 0
\(703\) −1.96869 + 6.38233i −0.0742505 + 0.240714i
\(704\) 16.7414 + 9.66567i 0.630967 + 0.364289i
\(705\) 0 0
\(706\) −8.42796 + 1.92363i −0.317191 + 0.0723967i
\(707\) 2.42430 + 5.98913i 0.0911753 + 0.225245i
\(708\) 0 0
\(709\) 32.8575 10.1352i 1.23399 0.380635i 0.391917 0.920001i \(-0.371812\pi\)
0.842072 + 0.539366i \(0.181336\pi\)
\(710\) −16.9860 43.2796i −0.637472 1.62425i
\(711\) 0 0
\(712\) 2.66515 + 8.64020i 0.0998806 + 0.323805i
\(713\) 2.98285 13.0687i 0.111709 0.489427i
\(714\) 0 0
\(715\) −16.5525 72.5213i −0.619029 2.71214i
\(716\) 9.07174 5.23757i 0.339027 0.195737i
\(717\) 0 0
\(718\) 49.0321 + 15.1244i 1.82986 + 0.564438i
\(719\) 3.06099 + 40.8461i 0.114156 + 1.52330i 0.700741 + 0.713415i \(0.252853\pi\)
−0.586586 + 0.809887i \(0.699528\pi\)
\(720\) 0 0
\(721\) 6.94968 49.6842i 0.258819 1.85034i
\(722\) −22.9262 + 18.2830i −0.853226 + 0.680425i
\(723\) 0 0
\(724\) −0.563814 3.74066i −0.0209540 0.139021i
\(725\) 47.0816 + 69.0561i 1.74857 + 2.56468i
\(726\) 0 0
\(727\) 16.9262 + 35.1477i 0.627759 + 1.30356i 0.935917 + 0.352220i \(0.114573\pi\)
−0.308158 + 0.951335i \(0.599713\pi\)
\(728\) 26.2845 0.279264i 0.974169 0.0103502i
\(729\) 0 0
\(730\) −21.4009 14.5909i −0.792084 0.540034i
\(731\) −6.98013 6.47662i −0.258170 0.239546i
\(732\) 0 0
\(733\) −15.3173 6.01161i −0.565759 0.222044i 0.0651842 0.997873i \(-0.479237\pi\)
−0.630943 + 0.775829i \(0.717332\pi\)
\(734\) −16.5154 −0.609596
\(735\) 0 0
\(736\) −8.13641 −0.299912
\(737\) 11.7000 + 4.59192i 0.430975 + 0.169145i
\(738\) 0 0
\(739\) 16.0870 + 14.9265i 0.591769 + 0.549081i 0.918189 0.396144i \(-0.129652\pi\)
−0.326420 + 0.945225i \(0.605842\pi\)
\(740\) −14.1428 9.64240i −0.519900 0.354462i
\(741\) 0 0
\(742\) −34.2167 + 43.8542i −1.25613 + 1.60994i
\(743\) −6.05682 12.5771i −0.222203 0.461409i 0.759829 0.650123i \(-0.225283\pi\)
−0.982032 + 0.188713i \(0.939568\pi\)
\(744\) 0 0
\(745\) 14.4802 + 21.2386i 0.530515 + 0.778122i
\(746\) 3.05261 + 20.2527i 0.111764 + 0.741504i
\(747\) 0 0
\(748\) 6.91370 5.51349i 0.252790 0.201593i
\(749\) −2.19604 6.85978i −0.0802416 0.250651i
\(750\) 0 0
\(751\) 0.0540646 + 0.721442i 0.00197285 + 0.0263258i 0.998103 0.0615607i \(-0.0196078\pi\)
−0.996130 + 0.0878865i \(0.971989\pi\)
\(752\) −19.6711 6.06773i −0.717331 0.221267i
\(753\) 0 0
\(754\) −52.2311 + 30.1556i −1.90214 + 1.09820i
\(755\) −9.89356 43.3465i −0.360063 1.57754i
\(756\) 0 0
\(757\) −9.26950 + 40.6123i −0.336906 + 1.47608i 0.468556 + 0.883434i \(0.344774\pi\)
−0.805462 + 0.592647i \(0.798083\pi\)
\(758\) 17.5373 + 56.8547i 0.636985 + 2.06505i
\(759\) 0 0
\(760\) −2.85205 7.26691i −0.103455 0.263599i
\(761\) −13.4562 + 4.15068i −0.487786 + 0.150462i −0.528886 0.848693i \(-0.677390\pi\)
0.0410997 + 0.999155i \(0.486914\pi\)
\(762\) 0 0
\(763\) 25.3353 17.6705i 0.917198 0.639714i
\(764\) 2.66752 0.608845i 0.0965076 0.0220272i
\(765\) 0 0
\(766\) −3.38361 1.95353i −0.122255 0.0705839i
\(767\) 10.7912 34.9843i 0.389649 1.26321i
\(768\) 0 0
\(769\) −7.77227 6.19818i −0.280275 0.223512i 0.473255 0.880926i \(-0.343079\pi\)
−0.753530 + 0.657414i \(0.771650\pi\)
\(770\) −25.6508 + 67.4557i −0.924389 + 2.43093i
\(771\) 0 0
\(772\) 0.322345 0.299092i 0.0116014 0.0107646i
\(773\) 40.8349 6.15487i 1.46873 0.221375i 0.634555 0.772878i \(-0.281183\pi\)
0.834173 + 0.551503i \(0.185945\pi\)
\(774\) 0 0
\(775\) −7.89554 + 52.3835i −0.283616 + 1.88167i
\(776\) −36.9464 + 17.7925i −1.32630 + 0.638712i
\(777\) 0 0
\(778\) 4.65915 + 2.24373i 0.167038 + 0.0804415i
\(779\) 3.00828 4.41234i 0.107783 0.158088i
\(780\) 0 0
\(781\) 2.46278 32.8635i 0.0881253 1.17595i
\(782\) 4.92350 12.5449i 0.176064 0.448604i
\(783\) 0 0
\(784\) −28.3797 18.4781i −1.01356 0.659933i
\(785\) 17.8546i 0.637258i
\(786\) 0 0
\(787\) 27.0998 + 2.03085i 0.966004 + 0.0723920i 0.548381 &minus