Properties

Label 495.2.n.h.91.3
Level $495$
Weight $2$
Character 495.91
Analytic conductor $3.953$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.n (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.95259490005\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 47 x^{12} + 32 x^{11} + 171 x^{10} + 26 x^{9} + 360 x^{8} - 172 x^{7} + 471 x^{6} - 430 x^{5} + 383 x^{4} + 70 x^{3} + 17 x^{2} + 4 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.3
Root \(0.0698401 - 0.214946i\) of defining polynomial
Character \(\chi\) \(=\) 495.91
Dual form 495.2.n.h.136.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.991861 - 0.720629i) q^{2} +(-0.153553 + 0.472586i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.139581 + 0.429587i) q^{7} +(0.945971 + 2.91140i) q^{8} +O(q^{10})\) \(q+(0.991861 - 0.720629i) q^{2} +(-0.153553 + 0.472586i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.139581 + 0.429587i) q^{7} +(0.945971 + 2.91140i) q^{8} +1.22601 q^{10} +(-1.55234 + 2.93091i) q^{11} +(3.91592 - 2.84508i) q^{13} +(0.171128 + 0.526677i) q^{14} +(2.23230 + 1.62186i) q^{16} +(-0.598736 - 0.435007i) q^{17} +(2.10247 + 6.47075i) q^{19} +(-0.402006 + 0.292074i) q^{20} +(0.572395 + 4.02572i) q^{22} -0.00634166 q^{23} +(0.309017 + 0.951057i) q^{25} +(1.83380 - 5.64385i) q^{26} +(-0.181584 - 0.131928i) q^{28} +(-0.100091 + 0.308048i) q^{29} +(4.53521 - 3.29503i) q^{31} -2.73956 q^{32} -0.907341 q^{34} +(-0.365429 + 0.265500i) q^{35} +(2.27713 - 7.00828i) q^{37} +(6.74837 + 4.90298i) q^{38} +(-0.945971 + 2.91140i) q^{40} +(-3.39006 - 10.4335i) q^{41} -1.80668 q^{43} +(-1.14674 - 1.18366i) q^{44} +(-0.00629004 + 0.00456998i) q^{46} +(-0.518988 - 1.59728i) q^{47} +(5.49806 + 3.99457i) q^{49} +(0.991861 + 0.720629i) q^{50} +(0.743247 + 2.28748i) q^{52} +(-6.98948 + 5.07816i) q^{53} +(-2.97862 + 1.45871i) q^{55} -1.38274 q^{56} +(0.122712 + 0.377669i) q^{58} +(-0.463691 + 1.42709i) q^{59} +(-10.5540 - 7.66790i) q^{61} +(2.12381 - 6.53641i) q^{62} +(-7.18186 + 5.21793i) q^{64} +4.84034 q^{65} +9.60773 q^{67} +(0.297516 - 0.216158i) q^{68} +(-0.171128 + 0.526677i) q^{70} +(-9.23296 - 6.70814i) q^{71} +(3.16430 - 9.73870i) q^{73} +(-2.79178 - 8.59220i) q^{74} -3.38083 q^{76} +(-1.04241 - 1.07597i) q^{77} +(1.69866 - 1.23415i) q^{79} +(0.852662 + 2.62422i) q^{80} +(-10.8812 - 7.90563i) q^{82} +(12.8589 + 9.34255i) q^{83} +(-0.228697 - 0.703856i) q^{85} +(-1.79197 + 1.30194i) q^{86} +(-10.0015 - 1.74692i) q^{88} -9.36925 q^{89} +(0.675622 + 2.07935i) q^{91} +(0.000973778 - 0.00299698i) q^{92} +(-1.66581 - 1.21028i) q^{94} +(-2.10247 + 6.47075i) q^{95} +(-4.75689 + 3.45608i) q^{97} +8.33191 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} + O(q^{10}) \) \( 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} + 8 q^{10} - 4 q^{11} + 2 q^{13} + 22 q^{14} + 8 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 28 q^{22} - 8 q^{23} - 4 q^{25} - 6 q^{26} - 2 q^{28} + 26 q^{29} - 10 q^{31} - 56 q^{32} - 4 q^{34} + 4 q^{35} + 22 q^{37} + 30 q^{38} - 6 q^{40} + 6 q^{41} + 28 q^{43} - 68 q^{44} + 16 q^{46} + 20 q^{47} + 10 q^{49} + 2 q^{50} + 30 q^{52} - 14 q^{53} - 6 q^{55} - 68 q^{56} - 6 q^{58} + 16 q^{59} - 38 q^{61} + 20 q^{62} + 10 q^{64} - 12 q^{65} + 20 q^{67} + 48 q^{68} - 22 q^{70} + 54 q^{71} + 2 q^{73} - 28 q^{74} - 44 q^{76} - 34 q^{77} - 12 q^{79} + 22 q^{80} + 30 q^{82} + 28 q^{83} - 4 q^{85} - 74 q^{86} + 46 q^{88} - 76 q^{89} - 34 q^{91} + 8 q^{92} - 10 q^{94} + 4 q^{95} - 18 q^{97} - 8 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.991861 0.720629i 0.701351 0.509562i −0.179021 0.983845i \(-0.557293\pi\)
0.880372 + 0.474284i \(0.157293\pi\)
\(3\) 0 0
\(4\) −0.153553 + 0.472586i −0.0767763 + 0.236293i
\(5\) 0.809017 + 0.587785i 0.361803 + 0.262866i
\(6\) 0 0
\(7\) −0.139581 + 0.429587i −0.0527568 + 0.162369i −0.973964 0.226705i \(-0.927205\pi\)
0.921207 + 0.389073i \(0.127205\pi\)
\(8\) 0.945971 + 2.91140i 0.334451 + 1.02933i
\(9\) 0 0
\(10\) 1.22601 0.387698
\(11\) −1.55234 + 2.93091i −0.468048 + 0.883703i
\(12\) 0 0
\(13\) 3.91592 2.84508i 1.08608 0.789084i 0.107348 0.994222i \(-0.465764\pi\)
0.978733 + 0.205138i \(0.0657643\pi\)
\(14\) 0.171128 + 0.526677i 0.0457358 + 0.140760i
\(15\) 0 0
\(16\) 2.23230 + 1.62186i 0.558074 + 0.405465i
\(17\) −0.598736 0.435007i −0.145215 0.105505i 0.512806 0.858505i \(-0.328606\pi\)
−0.658021 + 0.753000i \(0.728606\pi\)
\(18\) 0 0
\(19\) 2.10247 + 6.47075i 0.482340 + 1.48449i 0.835796 + 0.549040i \(0.185007\pi\)
−0.353456 + 0.935451i \(0.614993\pi\)
\(20\) −0.402006 + 0.292074i −0.0898912 + 0.0653098i
\(21\) 0 0
\(22\) 0.572395 + 4.02572i 0.122035 + 0.858286i
\(23\) −0.00634166 −0.00132233 −0.000661164 1.00000i \(-0.500210\pi\)
−0.000661164 1.00000i \(0.500210\pi\)
\(24\) 0 0
\(25\) 0.309017 + 0.951057i 0.0618034 + 0.190211i
\(26\) 1.83380 5.64385i 0.359637 1.10685i
\(27\) 0 0
\(28\) −0.181584 0.131928i −0.0343162 0.0249321i
\(29\) −0.100091 + 0.308048i −0.0185864 + 0.0572030i −0.959920 0.280276i \(-0.909574\pi\)
0.941333 + 0.337479i \(0.109574\pi\)
\(30\) 0 0
\(31\) 4.53521 3.29503i 0.814548 0.591804i −0.100597 0.994927i \(-0.532075\pi\)
0.915146 + 0.403123i \(0.132075\pi\)
\(32\) −2.73956 −0.484291
\(33\) 0 0
\(34\) −0.907341 −0.155608
\(35\) −0.365429 + 0.265500i −0.0617688 + 0.0448776i
\(36\) 0 0
\(37\) 2.27713 7.00828i 0.374358 1.15215i −0.569553 0.821954i \(-0.692884\pi\)
0.943911 0.330200i \(-0.107116\pi\)
\(38\) 6.74837 + 4.90298i 1.09473 + 0.795368i
\(39\) 0 0
\(40\) −0.945971 + 2.91140i −0.149571 + 0.460332i
\(41\) −3.39006 10.4335i −0.529438 1.62944i −0.755369 0.655299i \(-0.772543\pi\)
0.225931 0.974143i \(-0.427457\pi\)
\(42\) 0 0
\(43\) −1.80668 −0.275516 −0.137758 0.990466i \(-0.543990\pi\)
−0.137758 + 0.990466i \(0.543990\pi\)
\(44\) −1.14674 1.18366i −0.172878 0.178444i
\(45\) 0 0
\(46\) −0.00629004 + 0.00456998i −0.000927416 + 0.000673807i
\(47\) −0.518988 1.59728i −0.0757022 0.232987i 0.906044 0.423184i \(-0.139088\pi\)
−0.981746 + 0.190196i \(0.939088\pi\)
\(48\) 0 0
\(49\) 5.49806 + 3.99457i 0.785437 + 0.570653i
\(50\) 0.991861 + 0.720629i 0.140270 + 0.101912i
\(51\) 0 0
\(52\) 0.743247 + 2.28748i 0.103070 + 0.317216i
\(53\) −6.98948 + 5.07816i −0.960079 + 0.697539i −0.953169 0.302438i \(-0.902200\pi\)
−0.00691024 + 0.999976i \(0.502200\pi\)
\(54\) 0 0
\(55\) −2.97862 + 1.45871i −0.401636 + 0.196693i
\(56\) −1.38274 −0.184776
\(57\) 0 0
\(58\) 0.122712 + 0.377669i 0.0161129 + 0.0495903i
\(59\) −0.463691 + 1.42709i −0.0603674 + 0.185792i −0.976692 0.214643i \(-0.931141\pi\)
0.916325 + 0.400435i \(0.131141\pi\)
\(60\) 0 0
\(61\) −10.5540 7.66790i −1.35130 0.981774i −0.998946 0.0459057i \(-0.985383\pi\)
−0.352350 0.935868i \(-0.614617\pi\)
\(62\) 2.12381 6.53641i 0.269724 0.830125i
\(63\) 0 0
\(64\) −7.18186 + 5.21793i −0.897733 + 0.652241i
\(65\) 4.84034 0.600371
\(66\) 0 0
\(67\) 9.60773 1.17377 0.586885 0.809670i \(-0.300354\pi\)
0.586885 + 0.809670i \(0.300354\pi\)
\(68\) 0.297516 0.216158i 0.0360791 0.0262130i
\(69\) 0 0
\(70\) −0.171128 + 0.526677i −0.0204537 + 0.0629500i
\(71\) −9.23296 6.70814i −1.09575 0.796110i −0.115390 0.993320i \(-0.536812\pi\)
−0.980361 + 0.197211i \(0.936812\pi\)
\(72\) 0 0
\(73\) 3.16430 9.73870i 0.370353 1.13983i −0.576208 0.817303i \(-0.695468\pi\)
0.946561 0.322526i \(-0.104532\pi\)
\(74\) −2.79178 8.59220i −0.324537 0.998823i
\(75\) 0 0
\(76\) −3.38083 −0.387807
\(77\) −1.04241 1.07597i −0.118793 0.122618i
\(78\) 0 0
\(79\) 1.69866 1.23415i 0.191114 0.138852i −0.488114 0.872780i \(-0.662315\pi\)
0.679228 + 0.733928i \(0.262315\pi\)
\(80\) 0.852662 + 2.62422i 0.0953305 + 0.293397i
\(81\) 0 0
\(82\) −10.8812 7.90563i −1.20162 0.873030i
\(83\) 12.8589 + 9.34255i 1.41145 + 1.02548i 0.993110 + 0.117187i \(0.0373876\pi\)
0.418339 + 0.908291i \(0.362612\pi\)
\(84\) 0 0
\(85\) −0.228697 0.703856i −0.0248056 0.0763439i
\(86\) −1.79197 + 1.30194i −0.193233 + 0.140392i
\(87\) 0 0
\(88\) −10.0015 1.74692i −1.06617 0.186223i
\(89\) −9.36925 −0.993138 −0.496569 0.867997i \(-0.665407\pi\)
−0.496569 + 0.867997i \(0.665407\pi\)
\(90\) 0 0
\(91\) 0.675622 + 2.07935i 0.0708244 + 0.217975i
\(92\) 0.000973778 0.00299698i 0.000101523 0.000312457i
\(93\) 0 0
\(94\) −1.66581 1.21028i −0.171815 0.124831i
\(95\) −2.10247 + 6.47075i −0.215709 + 0.663885i
\(96\) 0 0
\(97\) −4.75689 + 3.45608i −0.482989 + 0.350912i −0.802482 0.596677i \(-0.796487\pi\)
0.319493 + 0.947589i \(0.396487\pi\)
\(98\) 8.33191 0.841650
\(99\) 0 0
\(100\) −0.496906 −0.0496906
\(101\) 1.78628 1.29781i 0.177742 0.129137i −0.495357 0.868689i \(-0.664963\pi\)
0.673099 + 0.739552i \(0.264963\pi\)
\(102\) 0 0
\(103\) 2.99111 9.20568i 0.294723 0.907063i −0.688592 0.725149i \(-0.741771\pi\)
0.983314 0.181914i \(-0.0582292\pi\)
\(104\) 11.9875 + 8.70944i 1.17547 + 0.854031i
\(105\) 0 0
\(106\) −3.27313 + 10.0736i −0.317914 + 0.978439i
\(107\) −3.63294 11.1810i −0.351210 1.08091i −0.958175 0.286184i \(-0.907613\pi\)
0.606965 0.794729i \(-0.292387\pi\)
\(108\) 0 0
\(109\) −12.5091 −1.19816 −0.599078 0.800691i \(-0.704466\pi\)
−0.599078 + 0.800691i \(0.704466\pi\)
\(110\) −1.90318 + 3.59332i −0.181461 + 0.342609i
\(111\) 0 0
\(112\) −1.00832 + 0.732586i −0.0952771 + 0.0692228i
\(113\) 3.06115 + 9.42124i 0.287968 + 0.886276i 0.985493 + 0.169715i \(0.0542847\pi\)
−0.697525 + 0.716561i \(0.745715\pi\)
\(114\) 0 0
\(115\) −0.00513051 0.00372753i −0.000478422 0.000347594i
\(116\) −0.130210 0.0946030i −0.0120897 0.00878367i
\(117\) 0 0
\(118\) 0.568489 + 1.74963i 0.0523336 + 0.161066i
\(119\) 0.270446 0.196491i 0.0247917 0.0180123i
\(120\) 0 0
\(121\) −6.18048 9.09954i −0.561862 0.827231i
\(122\) −15.9938 −1.44801
\(123\) 0 0
\(124\) 0.860790 + 2.64924i 0.0773012 + 0.237909i
\(125\) −0.309017 + 0.951057i −0.0276393 + 0.0850651i
\(126\) 0 0
\(127\) 0.454312 + 0.330077i 0.0403137 + 0.0292896i 0.607760 0.794121i \(-0.292068\pi\)
−0.567446 + 0.823411i \(0.692068\pi\)
\(128\) −1.67007 + 5.13995i −0.147615 + 0.454312i
\(129\) 0 0
\(130\) 4.80095 3.48809i 0.421071 0.305926i
\(131\) 3.03500 0.265170 0.132585 0.991172i \(-0.457672\pi\)
0.132585 + 0.991172i \(0.457672\pi\)
\(132\) 0 0
\(133\) −3.07322 −0.266482
\(134\) 9.52953 6.92361i 0.823226 0.598108i
\(135\) 0 0
\(136\) 0.700092 2.15466i 0.0600324 0.184761i
\(137\) 16.7469 + 12.1674i 1.43079 + 1.03953i 0.989869 + 0.141981i \(0.0453471\pi\)
0.440918 + 0.897547i \(0.354653\pi\)
\(138\) 0 0
\(139\) 1.09662 3.37504i 0.0930139 0.286267i −0.893717 0.448631i \(-0.851912\pi\)
0.986731 + 0.162364i \(0.0519117\pi\)
\(140\) −0.0693589 0.213465i −0.00586190 0.0180411i
\(141\) 0 0
\(142\) −13.9919 −1.17417
\(143\) 2.25985 + 15.8937i 0.188978 + 1.32910i
\(144\) 0 0
\(145\) −0.262041 + 0.190384i −0.0217613 + 0.0158105i
\(146\) −3.87945 11.9397i −0.321065 0.988138i
\(147\) 0 0
\(148\) 2.96236 + 2.15228i 0.243504 + 0.176916i
\(149\) −5.10052 3.70575i −0.417851 0.303587i 0.358921 0.933368i \(-0.383145\pi\)
−0.776773 + 0.629781i \(0.783145\pi\)
\(150\) 0 0
\(151\) −1.13852 3.50400i −0.0926512 0.285151i 0.893983 0.448100i \(-0.147899\pi\)
−0.986634 + 0.162949i \(0.947899\pi\)
\(152\) −16.8500 + 12.2423i −1.36672 + 0.992980i
\(153\) 0 0
\(154\) −1.80929 0.316022i −0.145797 0.0254657i
\(155\) 5.60583 0.450271
\(156\) 0 0
\(157\) 0.874113 + 2.69024i 0.0697618 + 0.214705i 0.979859 0.199690i \(-0.0639934\pi\)
−0.910097 + 0.414394i \(0.863993\pi\)
\(158\) 0.795469 2.44820i 0.0632841 0.194768i
\(159\) 0 0
\(160\) −2.21635 1.61028i −0.175218 0.127303i
\(161\) 0.000885178 0.00272430i 6.97618e−5 0.000214705i
\(162\) 0 0
\(163\) −7.16094 + 5.20273i −0.560888 + 0.407509i −0.831784 0.555099i \(-0.812680\pi\)
0.270896 + 0.962609i \(0.412680\pi\)
\(164\) 5.45129 0.425674
\(165\) 0 0
\(166\) 19.4868 1.51247
\(167\) 15.9249 11.5701i 1.23230 0.895320i 0.235241 0.971937i \(-0.424412\pi\)
0.997061 + 0.0766171i \(0.0244119\pi\)
\(168\) 0 0
\(169\) 3.22271 9.91849i 0.247901 0.762961i
\(170\) −0.734054 0.533322i −0.0562994 0.0409039i
\(171\) 0 0
\(172\) 0.277420 0.853811i 0.0211531 0.0651025i
\(173\) −0.899661 2.76887i −0.0684000 0.210513i 0.911014 0.412375i \(-0.135301\pi\)
−0.979414 + 0.201862i \(0.935301\pi\)
\(174\) 0 0
\(175\) −0.451695 −0.0341449
\(176\) −8.21881 + 4.02499i −0.619516 + 0.303395i
\(177\) 0 0
\(178\) −9.29299 + 6.75175i −0.696539 + 0.506065i
\(179\) 1.94467 + 5.98508i 0.145352 + 0.447346i 0.997056 0.0766763i \(-0.0244308\pi\)
−0.851704 + 0.524022i \(0.824431\pi\)
\(180\) 0 0
\(181\) 9.03200 + 6.56213i 0.671343 + 0.487759i 0.870475 0.492213i \(-0.163812\pi\)
−0.199131 + 0.979973i \(0.563812\pi\)
\(182\) 2.16856 + 1.57555i 0.160745 + 0.116788i
\(183\) 0 0
\(184\) −0.00599902 0.0184631i −0.000442254 0.00136112i
\(185\) 5.96160 4.33136i 0.438306 0.318448i
\(186\) 0 0
\(187\) 2.20441 1.07956i 0.161202 0.0789455i
\(188\) 0.834545 0.0608655
\(189\) 0 0
\(190\) 2.57765 + 7.93318i 0.187002 + 0.575534i
\(191\) 6.30228 19.3964i 0.456017 1.40348i −0.413920 0.910313i \(-0.635841\pi\)
0.869937 0.493163i \(-0.164159\pi\)
\(192\) 0 0
\(193\) 2.40629 + 1.74827i 0.173208 + 0.125843i 0.671012 0.741447i \(-0.265860\pi\)
−0.497804 + 0.867290i \(0.665860\pi\)
\(194\) −2.22762 + 6.85590i −0.159934 + 0.492225i
\(195\) 0 0
\(196\) −2.73202 + 1.98493i −0.195144 + 0.141781i
\(197\) −5.20127 −0.370575 −0.185288 0.982684i \(-0.559322\pi\)
−0.185288 + 0.982684i \(0.559322\pi\)
\(198\) 0 0
\(199\) 8.10264 0.574381 0.287191 0.957873i \(-0.407279\pi\)
0.287191 + 0.957873i \(0.407279\pi\)
\(200\) −2.47658 + 1.79934i −0.175121 + 0.127233i
\(201\) 0 0
\(202\) 0.836505 2.57450i 0.0588563 0.181141i
\(203\) −0.118363 0.0859955i −0.00830743 0.00603570i
\(204\) 0 0
\(205\) 3.39006 10.4335i 0.236772 0.728709i
\(206\) −3.66712 11.2862i −0.255500 0.786349i
\(207\) 0 0
\(208\) 13.3558 0.926059
\(209\) −22.2289 3.88264i −1.53761 0.268568i
\(210\) 0 0
\(211\) 1.06252 0.771967i 0.0731470 0.0531444i −0.550611 0.834762i \(-0.685605\pi\)
0.623758 + 0.781618i \(0.285605\pi\)
\(212\) −1.32661 4.08290i −0.0911122 0.280415i
\(213\) 0 0
\(214\) −11.6608 8.47204i −0.797113 0.579137i
\(215\) −1.46163 1.06194i −0.0996826 0.0724236i
\(216\) 0 0
\(217\) 0.782470 + 2.40820i 0.0531175 + 0.163479i
\(218\) −12.4073 + 9.01443i −0.840328 + 0.610534i
\(219\) 0 0
\(220\) −0.231994 1.63164i −0.0156411 0.110005i
\(221\) −3.58223 −0.240967
\(222\) 0 0
\(223\) 8.84861 + 27.2332i 0.592547 + 1.82367i 0.566577 + 0.824009i \(0.308267\pi\)
0.0259701 + 0.999663i \(0.491733\pi\)
\(224\) 0.382392 1.17688i 0.0255497 0.0786338i
\(225\) 0 0
\(226\) 9.82545 + 7.13861i 0.653579 + 0.474853i
\(227\) 2.43074 7.48104i 0.161334 0.496534i −0.837414 0.546570i \(-0.815933\pi\)
0.998747 + 0.0500354i \(0.0159334\pi\)
\(228\) 0 0
\(229\) 13.0664 9.49331i 0.863453 0.627336i −0.0653689 0.997861i \(-0.520822\pi\)
0.928822 + 0.370526i \(0.120822\pi\)
\(230\) −0.00777492 −0.000512663
\(231\) 0 0
\(232\) −0.991532 −0.0650973
\(233\) 14.9138 10.8355i 0.977035 0.709858i 0.0199914 0.999800i \(-0.493636\pi\)
0.957044 + 0.289942i \(0.0936361\pi\)
\(234\) 0 0
\(235\) 0.518988 1.59728i 0.0338551 0.104195i
\(236\) −0.603224 0.438268i −0.0392665 0.0285288i
\(237\) 0 0
\(238\) 0.126648 0.389782i 0.00820937 0.0252658i
\(239\) −6.91081 21.2693i −0.447023 1.37579i −0.880250 0.474510i \(-0.842625\pi\)
0.433227 0.901285i \(-0.357375\pi\)
\(240\) 0 0
\(241\) −13.2213 −0.851662 −0.425831 0.904803i \(-0.640018\pi\)
−0.425831 + 0.904803i \(0.640018\pi\)
\(242\) −12.6876 4.57164i −0.815588 0.293876i
\(243\) 0 0
\(244\) 5.24433 3.81023i 0.335734 0.243925i
\(245\) 2.10007 + 6.46335i 0.134169 + 0.412928i
\(246\) 0 0
\(247\) 26.6429 + 19.3572i 1.69525 + 1.23167i
\(248\) 13.8833 + 10.0868i 0.881591 + 0.640513i
\(249\) 0 0
\(250\) 0.378857 + 1.16600i 0.0239610 + 0.0737444i
\(251\) −16.9919 + 12.3454i −1.07252 + 0.779232i −0.976364 0.216134i \(-0.930655\pi\)
−0.0961569 + 0.995366i \(0.530655\pi\)
\(252\) 0 0
\(253\) 0.00984441 0.0185868i 0.000618913 0.00116854i
\(254\) 0.688477 0.0431989
\(255\) 0 0
\(256\) −3.43893 10.5839i −0.214933 0.661497i
\(257\) 1.04068 3.20289i 0.0649160 0.199791i −0.913338 0.407203i \(-0.866504\pi\)
0.978254 + 0.207412i \(0.0665041\pi\)
\(258\) 0 0
\(259\) 2.69283 + 1.95645i 0.167324 + 0.121568i
\(260\) −0.743247 + 2.28748i −0.0460942 + 0.141863i
\(261\) 0 0
\(262\) 3.01030 2.18711i 0.185977 0.135120i
\(263\) −21.0450 −1.29769 −0.648845 0.760920i \(-0.724748\pi\)
−0.648845 + 0.760920i \(0.724748\pi\)
\(264\) 0 0
\(265\) −8.63948 −0.530719
\(266\) −3.04820 + 2.21465i −0.186897 + 0.135789i
\(267\) 0 0
\(268\) −1.47529 + 4.54048i −0.0901177 + 0.277354i
\(269\) 18.9161 + 13.7434i 1.15334 + 0.837947i 0.988921 0.148444i \(-0.0474265\pi\)
0.164415 + 0.986391i \(0.447427\pi\)
\(270\) 0 0
\(271\) −6.34951 + 19.5418i −0.385705 + 1.18708i 0.550262 + 0.834992i \(0.314528\pi\)
−0.935967 + 0.352087i \(0.885472\pi\)
\(272\) −0.631036 1.94213i −0.0382622 0.117759i
\(273\) 0 0
\(274\) 25.3788 1.53319
\(275\) −3.26716 0.570661i −0.197017 0.0344122i
\(276\) 0 0
\(277\) 15.8420 11.5099i 0.951856 0.691564i 0.000611096 1.00000i \(-0.499805\pi\)
0.951245 + 0.308436i \(0.0998055\pi\)
\(278\) −1.34446 4.13783i −0.0806354 0.248170i
\(279\) 0 0
\(280\) −1.11866 0.812754i −0.0668527 0.0485714i
\(281\) 11.1585 + 8.10711i 0.665659 + 0.483630i 0.868569 0.495567i \(-0.165040\pi\)
−0.202910 + 0.979197i \(0.565040\pi\)
\(282\) 0 0
\(283\) 9.73949 + 29.9751i 0.578953 + 1.78183i 0.622306 + 0.782774i \(0.286196\pi\)
−0.0433533 + 0.999060i \(0.513804\pi\)
\(284\) 4.58792 3.33332i 0.272243 0.197796i
\(285\) 0 0
\(286\) 13.6949 + 14.1359i 0.809799 + 0.835872i
\(287\) 4.95530 0.292502
\(288\) 0 0
\(289\) −5.08404 15.6471i −0.299061 0.920415i
\(290\) −0.122712 + 0.377669i −0.00720589 + 0.0221775i
\(291\) 0 0
\(292\) 4.11649 + 2.99080i 0.240899 + 0.175024i
\(293\) 7.20413 22.1720i 0.420870 1.29530i −0.486024 0.873945i \(-0.661553\pi\)
0.906894 0.421359i \(-0.138447\pi\)
\(294\) 0 0
\(295\) −1.21396 + 0.881993i −0.0706794 + 0.0513516i
\(296\) 22.5580 1.31116
\(297\) 0 0
\(298\) −7.72948 −0.447757
\(299\) −0.0248334 + 0.0180425i −0.00143615 + 0.00104343i
\(300\) 0 0
\(301\) 0.252179 0.776126i 0.0145353 0.0447352i
\(302\) −3.65433 2.65503i −0.210283 0.152780i
\(303\) 0 0
\(304\) −5.80129 + 17.8545i −0.332727 + 1.02403i
\(305\) −4.03125 12.4069i −0.230829 0.710418i
\(306\) 0 0
\(307\) −10.0938 −0.576083 −0.288042 0.957618i \(-0.593004\pi\)
−0.288042 + 0.957618i \(0.593004\pi\)
\(308\) 0.668551 0.327409i 0.0380942 0.0186558i
\(309\) 0 0
\(310\) 5.56020 4.03972i 0.315798 0.229441i
\(311\) 4.11778 + 12.6732i 0.233498 + 0.718632i 0.997317 + 0.0732020i \(0.0233218\pi\)
−0.763819 + 0.645430i \(0.776678\pi\)
\(312\) 0 0
\(313\) −18.7435 13.6180i −1.05945 0.769732i −0.0854599 0.996342i \(-0.527236\pi\)
−0.973986 + 0.226609i \(0.927236\pi\)
\(314\) 2.80566 + 2.03843i 0.158333 + 0.115036i
\(315\) 0 0
\(316\) 0.322407 + 0.992267i 0.0181368 + 0.0558194i
\(317\) 5.60802 4.07446i 0.314978 0.228845i −0.419052 0.907962i \(-0.637637\pi\)
0.734029 + 0.679118i \(0.237637\pi\)
\(318\) 0 0
\(319\) −0.747485 0.771552i −0.0418512 0.0431986i
\(320\) −8.87727 −0.496254
\(321\) 0 0
\(322\) −0.00108523 0.00334001i −6.04777e−5 0.000186131i
\(323\) 1.55599 4.78886i 0.0865779 0.266459i
\(324\) 0 0
\(325\) 3.91592 + 2.84508i 0.217216 + 0.157817i
\(326\) −3.35342 + 10.3208i −0.185729 + 0.571614i
\(327\) 0 0
\(328\) 27.1692 19.7396i 1.50017 1.08994i
\(329\) 0.758613 0.0418237
\(330\) 0 0
\(331\) −10.5717 −0.581075 −0.290538 0.956864i \(-0.593834\pi\)
−0.290538 + 0.956864i \(0.593834\pi\)
\(332\) −6.38968 + 4.64237i −0.350679 + 0.254783i
\(333\) 0 0
\(334\) 7.45750 22.9518i 0.408056 1.25587i
\(335\) 7.77281 + 5.64728i 0.424674 + 0.308544i
\(336\) 0 0
\(337\) −1.96123 + 6.03605i −0.106835 + 0.328805i −0.990157 0.139963i \(-0.955302\pi\)
0.883322 + 0.468767i \(0.155302\pi\)
\(338\) −3.95107 12.1601i −0.214910 0.661424i
\(339\) 0 0
\(340\) 0.367750 0.0199440
\(341\) 2.61724 + 18.4073i 0.141731 + 0.996811i
\(342\) 0 0
\(343\) −5.04145 + 3.66283i −0.272213 + 0.197774i
\(344\) −1.70906 5.25996i −0.0921466 0.283598i
\(345\) 0 0
\(346\) −2.88767 2.09801i −0.155242 0.112790i
\(347\) 20.4210 + 14.8367i 1.09626 + 0.796477i 0.980445 0.196794i \(-0.0630532\pi\)
0.115811 + 0.993271i \(0.463053\pi\)
\(348\) 0 0
\(349\) −3.43118 10.5601i −0.183667 0.565269i 0.816256 0.577691i \(-0.196046\pi\)
−0.999923 + 0.0124217i \(0.996046\pi\)
\(350\) −0.448019 + 0.325504i −0.0239476 + 0.0173989i
\(351\) 0 0
\(352\) 4.25273 8.02942i 0.226672 0.427970i
\(353\) −18.8552 −1.00356 −0.501780 0.864996i \(-0.667321\pi\)
−0.501780 + 0.864996i \(0.667321\pi\)
\(354\) 0 0
\(355\) −3.52668 10.8540i −0.187177 0.576070i
\(356\) 1.43867 4.42778i 0.0762494 0.234672i
\(357\) 0 0
\(358\) 6.24187 + 4.53498i 0.329893 + 0.239681i
\(359\) −6.57983 + 20.2506i −0.347270 + 1.06879i 0.613087 + 0.790016i \(0.289928\pi\)
−0.960357 + 0.278773i \(0.910072\pi\)
\(360\) 0 0
\(361\) −22.0789 + 16.0412i −1.16205 + 0.844275i
\(362\) 13.6873 0.719391
\(363\) 0 0
\(364\) −1.08642 −0.0569437
\(365\) 8.28423 6.01885i 0.433617 0.315041i
\(366\) 0 0
\(367\) −9.66781 + 29.7545i −0.504656 + 1.55317i 0.296693 + 0.954973i \(0.404116\pi\)
−0.801349 + 0.598197i \(0.795884\pi\)
\(368\) −0.0141565 0.0102853i −0.000737957 0.000536157i
\(369\) 0 0
\(370\) 2.79178 8.59220i 0.145138 0.446687i
\(371\) −1.20591 3.71141i −0.0626078 0.192687i
\(372\) 0 0
\(373\) 9.39368 0.486386 0.243193 0.969978i \(-0.421805\pi\)
0.243193 + 0.969978i \(0.421805\pi\)
\(374\) 1.40850 2.65934i 0.0728319 0.137511i
\(375\) 0 0
\(376\) 4.15938 3.02196i 0.214503 0.155846i
\(377\) 0.484473 + 1.49106i 0.0249517 + 0.0767933i
\(378\) 0 0
\(379\) 6.63173 + 4.81823i 0.340649 + 0.247496i 0.744936 0.667136i \(-0.232480\pi\)
−0.404287 + 0.914632i \(0.632480\pi\)
\(380\) −2.73515 1.98720i −0.140310 0.101941i
\(381\) 0 0
\(382\) −7.72664 23.7802i −0.395329 1.21670i
\(383\) −27.2501 + 19.7984i −1.39242 + 1.01165i −0.396820 + 0.917897i \(0.629886\pi\)
−0.995596 + 0.0937524i \(0.970114\pi\)
\(384\) 0 0
\(385\) −0.210886 1.48319i −0.0107478 0.0755901i
\(386\) 3.64656 0.185605
\(387\) 0 0
\(388\) −0.902863 2.77873i −0.0458359 0.141069i
\(389\) −10.1771 + 31.3219i −0.515999 + 1.58808i 0.265457 + 0.964123i \(0.414477\pi\)
−0.781456 + 0.623960i \(0.785523\pi\)
\(390\) 0 0
\(391\) 0.00379698 + 0.00275867i 0.000192021 + 0.000139512i
\(392\) −6.42879 + 19.7858i −0.324703 + 0.999333i
\(393\) 0 0
\(394\) −5.15894 + 3.74819i −0.259904 + 0.188831i
\(395\) 2.09965 0.105645
\(396\) 0 0
\(397\) −15.3865 −0.772228 −0.386114 0.922451i \(-0.626183\pi\)
−0.386114 + 0.922451i \(0.626183\pi\)
\(398\) 8.03669 5.83900i 0.402843 0.292683i
\(399\) 0 0
\(400\) −0.852662 + 2.62422i −0.0426331 + 0.131211i
\(401\) 5.37426 + 3.90463i 0.268378 + 0.194988i 0.713832 0.700317i \(-0.246958\pi\)
−0.445455 + 0.895305i \(0.646958\pi\)
\(402\) 0 0
\(403\) 8.38491 25.8061i 0.417682 1.28549i
\(404\) 0.339039 + 1.04346i 0.0168678 + 0.0519138i
\(405\) 0 0
\(406\) −0.179370 −0.00890198
\(407\) 17.0058 + 17.5533i 0.842945 + 0.870085i
\(408\) 0 0
\(409\) −19.8088 + 14.3919i −0.979482 + 0.711636i −0.957593 0.288125i \(-0.906968\pi\)
−0.0218895 + 0.999760i \(0.506968\pi\)
\(410\) −4.15623 12.7916i −0.205262 0.631731i
\(411\) 0 0
\(412\) 3.89119 + 2.82711i 0.191705 + 0.139282i
\(413\) −0.548339 0.398392i −0.0269820 0.0196036i
\(414\) 0 0
\(415\) 4.91167 + 15.1166i 0.241104 + 0.742043i
\(416\) −10.7279 + 7.79428i −0.525979 + 0.382146i
\(417\) 0 0
\(418\) −24.8459 + 12.1678i −1.21526 + 0.595146i
\(419\) −20.8656 −1.01935 −0.509676 0.860367i \(-0.670235\pi\)
−0.509676 + 0.860367i \(0.670235\pi\)
\(420\) 0 0
\(421\) −5.23200 16.1025i −0.254992 0.784785i −0.993831 0.110903i \(-0.964626\pi\)
0.738839 0.673882i \(-0.235374\pi\)
\(422\) 0.497571 1.53137i 0.0242214 0.0745458i
\(423\) 0 0
\(424\) −21.3964 15.5454i −1.03910 0.754951i
\(425\) 0.228697 0.703856i 0.0110934 0.0341420i
\(426\) 0 0
\(427\) 4.76717 3.46355i 0.230700 0.167613i
\(428\) 5.84186 0.282377
\(429\) 0 0
\(430\) −2.21500 −0.106817
\(431\) 21.1677 15.3792i 1.01961 0.740791i 0.0534080 0.998573i \(-0.482992\pi\)
0.966203 + 0.257782i \(0.0829916\pi\)
\(432\) 0 0
\(433\) −7.74375 + 23.8328i −0.372141 + 1.14533i 0.573246 + 0.819383i \(0.305684\pi\)
−0.945387 + 0.325949i \(0.894316\pi\)
\(434\) 2.51152 + 1.82472i 0.120557 + 0.0875895i
\(435\) 0 0
\(436\) 1.92081 5.91163i 0.0919899 0.283116i
\(437\) −0.0133332 0.0410353i −0.000637812 0.00196298i
\(438\) 0 0
\(439\) 5.11234 0.243999 0.121999 0.992530i \(-0.461069\pi\)
0.121999 + 0.992530i \(0.461069\pi\)
\(440\) −7.06458 7.29203i −0.336791 0.347634i
\(441\) 0 0
\(442\) −3.55307 + 2.58146i −0.169003 + 0.122788i
\(443\) −8.67635 26.7031i −0.412226 1.26870i −0.914709 0.404113i \(-0.867580\pi\)
0.502483 0.864587i \(-0.332420\pi\)
\(444\) 0 0
\(445\) −7.57988 5.50711i −0.359321 0.261062i
\(446\) 28.4016 + 20.6350i 1.34486 + 0.977096i
\(447\) 0 0
\(448\) −1.23910 3.81356i −0.0585421 0.180174i
\(449\) 29.9297 21.7452i 1.41247 1.02622i 0.419510 0.907751i \(-0.362202\pi\)
0.992958 0.118467i \(-0.0377981\pi\)
\(450\) 0 0
\(451\) 35.8422 + 6.26041i 1.68775 + 0.294791i
\(452\) −4.92239 −0.231530
\(453\) 0 0
\(454\) −2.98010 9.17181i −0.139863 0.430454i
\(455\) −0.675622 + 2.07935i −0.0316736 + 0.0974815i
\(456\) 0 0
\(457\) −29.8092 21.6576i −1.39441 1.01310i −0.995365 0.0961719i \(-0.969340\pi\)
−0.399050 0.916929i \(-0.630660\pi\)
\(458\) 6.11891 18.8321i 0.285918 0.879965i
\(459\) 0 0
\(460\) 0.00254938 0.00185224i 0.000118866 8.63609e-5i
\(461\) −23.0013 −1.07128 −0.535640 0.844447i \(-0.679929\pi\)
−0.535640 + 0.844447i \(0.679929\pi\)
\(462\) 0 0
\(463\) −36.1571 −1.68036 −0.840181 0.542306i \(-0.817551\pi\)
−0.840181 + 0.542306i \(0.817551\pi\)
\(464\) −0.723042 + 0.525321i −0.0335664 + 0.0243874i
\(465\) 0 0
\(466\) 6.98403 21.4946i 0.323529 0.995720i
\(467\) −1.83240 1.33132i −0.0847935 0.0616061i 0.544581 0.838708i \(-0.316689\pi\)
−0.629374 + 0.777102i \(0.716689\pi\)
\(468\) 0 0
\(469\) −1.34106 + 4.12736i −0.0619244 + 0.190584i
\(470\) −0.636283 1.95828i −0.0293496 0.0903287i
\(471\) 0 0
\(472\) −4.59348 −0.211432
\(473\) 2.80458 5.29521i 0.128955 0.243474i
\(474\) 0 0
\(475\) −5.50435 + 3.99914i −0.252557 + 0.183493i
\(476\) 0.0513310 + 0.157981i 0.00235275 + 0.00724103i
\(477\) 0 0
\(478\) −22.1818 16.1160i −1.01457 0.737130i
\(479\) −24.7000 17.9456i −1.12857 0.819954i −0.143084 0.989711i \(-0.545702\pi\)
−0.985486 + 0.169756i \(0.945702\pi\)
\(480\) 0 0
\(481\) −11.0221 33.9225i −0.502564 1.54673i
\(482\) −13.1137 + 9.52768i −0.597314 + 0.433974i
\(483\) 0 0
\(484\) 5.24935 1.52355i 0.238607 0.0692524i
\(485\) −5.87983 −0.266989
\(486\) 0 0
\(487\) −4.99195 15.3636i −0.226207 0.696193i −0.998167 0.0605221i \(-0.980723\pi\)
0.771960 0.635671i \(-0.219277\pi\)
\(488\) 12.3406 37.9804i 0.558632 1.71929i
\(489\) 0 0
\(490\) 6.74066 + 4.89737i 0.304512 + 0.221241i
\(491\) 3.60828 11.1051i 0.162839 0.501168i −0.836031 0.548682i \(-0.815130\pi\)
0.998871 + 0.0475137i \(0.0151298\pi\)
\(492\) 0 0
\(493\) 0.193931 0.140899i 0.00873420 0.00634577i
\(494\) 40.3754 1.81658
\(495\) 0 0
\(496\) 15.4680 0.694534
\(497\) 4.17048 3.03003i 0.187072 0.135916i
\(498\) 0 0
\(499\) −12.6501 + 38.9330i −0.566296 + 1.74288i 0.0977712 + 0.995209i \(0.468829\pi\)
−0.664068 + 0.747672i \(0.731171\pi\)
\(500\) −0.402006 0.292074i −0.0179782 0.0130620i
\(501\) 0 0
\(502\) −7.95720 + 24.4897i −0.355147 + 1.09303i
\(503\) 0.131171 + 0.403703i 0.00584863 + 0.0180002i 0.953938 0.300003i \(-0.0969877\pi\)
−0.948090 + 0.318003i \(0.896988\pi\)
\(504\) 0 0
\(505\) 2.20797 0.0982533
\(506\) −0.00362993 0.0255297i −0.000161370 0.00113493i
\(507\) 0 0
\(508\) −0.225751 + 0.164017i −0.0100161 + 0.00727710i
\(509\) 6.12017 + 18.8360i 0.271272 + 0.834889i 0.990182 + 0.139786i \(0.0446414\pi\)
−0.718910 + 0.695103i \(0.755359\pi\)
\(510\) 0 0
\(511\) 3.74195 + 2.71868i 0.165534 + 0.120267i
\(512\) −19.7827 14.3729i −0.874278 0.635200i
\(513\) 0 0
\(514\) −1.27588 3.92677i −0.0562769 0.173202i
\(515\) 7.83082 5.68943i 0.345067 0.250706i
\(516\) 0 0
\(517\) 5.48714 + 0.958415i 0.241324 + 0.0421510i
\(518\) 4.08078 0.179299
\(519\) 0 0
\(520\) 4.57882 + 14.0922i 0.200795 + 0.617982i
\(521\) −11.3748 + 35.0079i −0.498337 + 1.53372i 0.313353 + 0.949637i \(0.398548\pi\)
−0.811690 + 0.584088i \(0.801452\pi\)
\(522\) 0 0
\(523\) 8.49589 + 6.17262i 0.371499 + 0.269910i 0.757832 0.652449i \(-0.226258\pi\)
−0.386333 + 0.922359i \(0.626258\pi\)
\(524\) −0.466033 + 1.43430i −0.0203587 + 0.0626577i
\(525\) 0 0
\(526\) −20.8737 + 15.1656i −0.910137 + 0.661253i
\(527\) −4.14875 −0.180723
\(528\) 0 0
\(529\) −23.0000 −0.999998
\(530\) −8.56916 + 6.22586i −0.372220 + 0.270434i
\(531\) 0 0
\(532\) 0.471900 1.45236i 0.0204595 0.0629678i
\(533\) −42.9594 31.2118i −1.86078 1.35193i
\(534\) 0 0
\(535\) 3.63294 11.1810i 0.157066 0.483399i
\(536\) 9.08863 + 27.9719i 0.392569 + 1.20820i
\(537\) 0 0
\(538\) 28.6660 1.23588
\(539\) −20.2426 + 9.91338i −0.871910 + 0.427000i
\(540\) 0 0
\(541\) −0.529593 + 0.384772i −0.0227690 + 0.0165426i −0.599112 0.800666i \(-0.704479\pi\)
0.576343 + 0.817208i \(0.304479\pi\)
\(542\) 7.78454 + 23.9584i 0.334375 + 1.02910i
\(543\) 0 0
\(544\) 1.64028 + 1.19173i 0.0703262 + 0.0510950i
\(545\) −10.1201 7.35267i −0.433497 0.314954i
\(546\) 0 0
\(547\) −4.14573 12.7592i −0.177259 0.545546i 0.822471 0.568807i \(-0.192595\pi\)
−0.999729 + 0.0232616i \(0.992595\pi\)
\(548\) −8.32166 + 6.04604i −0.355484 + 0.258274i
\(549\) 0 0
\(550\) −3.65180 + 1.78839i −0.155713 + 0.0762574i
\(551\) −2.20374 −0.0938823
\(552\) 0 0
\(553\) 0.293073 + 0.901985i 0.0124627 + 0.0383563i
\(554\) 7.41872 22.8325i 0.315191 0.970059i
\(555\) 0 0
\(556\) 1.42661 + 1.03649i 0.0605017 + 0.0439571i
\(557\) 4.09205 12.5940i 0.173386 0.533626i −0.826171 0.563420i \(-0.809485\pi\)
0.999556 + 0.0297943i \(0.00948523\pi\)
\(558\) 0 0
\(559\) −7.07481 + 5.14015i −0.299232 + 0.217405i
\(560\) −1.24635 −0.0526679
\(561\) 0 0
\(562\) 16.9099 0.713300
\(563\) −17.2822 + 12.5562i −0.728356 + 0.529182i −0.889043 0.457824i \(-0.848629\pi\)
0.160687 + 0.987005i \(0.448629\pi\)
\(564\) 0 0
\(565\) −3.06115 + 9.42124i −0.128783 + 0.396355i
\(566\) 31.2611 + 22.7125i 1.31400 + 0.954679i
\(567\) 0 0
\(568\) 10.7960 33.2265i 0.452988 1.39415i
\(569\) −14.0100 43.1185i −0.587332 1.80762i −0.589698 0.807624i \(-0.700753\pi\)
0.00236662 0.999997i \(-0.499247\pi\)
\(570\) 0 0
\(571\) −25.1544 −1.05268 −0.526339 0.850275i \(-0.676436\pi\)
−0.526339 + 0.850275i \(0.676436\pi\)
\(572\) −7.85817 1.37255i −0.328567 0.0573893i
\(573\) 0 0
\(574\) 4.91497 3.57093i 0.205147 0.149048i
\(575\) −0.00195968 0.00603127i −8.17243e−5 0.000251522i
\(576\) 0 0
\(577\) −6.16999 4.48276i −0.256860 0.186620i 0.451902 0.892068i \(-0.350746\pi\)
−0.708762 + 0.705448i \(0.750746\pi\)
\(578\) −16.3184 11.8560i −0.678755 0.493144i
\(579\) 0 0
\(580\) −0.0497357 0.153071i −0.00206516 0.00635592i
\(581\) −5.80831 + 4.21998i −0.240969 + 0.175074i
\(582\) 0 0
\(583\) −4.03358 28.3686i −0.167054 1.17491i
\(584\) 31.3466 1.29713
\(585\) 0 0
\(586\) −8.83232 27.1831i −0.364860 1.12292i
\(587\) 2.43760 7.50217i 0.100611 0.309648i −0.888065 0.459719i \(-0.847950\pi\)
0.988675 + 0.150071i \(0.0479502\pi\)
\(588\) 0 0
\(589\) 30.8564 + 22.4185i 1.27142 + 0.923739i
\(590\) −0.568489 + 1.74963i −0.0234043 + 0.0720310i
\(591\) 0 0
\(592\) 16.4497 11.9514i 0.676077 0.491199i
\(593\) −8.68507 −0.356653 −0.178327 0.983971i \(-0.557068\pi\)
−0.178327 + 0.983971i \(0.557068\pi\)
\(594\) 0 0
\(595\) 0.334290 0.0137045
\(596\) 2.53448 1.84141i 0.103816 0.0754271i
\(597\) 0 0
\(598\) −0.0116293 + 0.0357914i −0.000475558 + 0.00146362i
\(599\) 11.3275 + 8.22991i 0.462829 + 0.336265i 0.794640 0.607081i \(-0.207660\pi\)
−0.331811 + 0.943346i \(0.607660\pi\)
\(600\) 0 0
\(601\) −3.18091 + 9.78983i −0.129752 + 0.399335i −0.994737 0.102462i \(-0.967328\pi\)
0.864985 + 0.501798i \(0.167328\pi\)
\(602\) −0.309173 0.951537i −0.0126010 0.0387817i
\(603\) 0 0
\(604\) 1.83076 0.0744927
\(605\) 0.348460 10.9945i 0.0141669 0.446989i
\(606\) 0 0
\(607\) −22.2282 + 16.1497i −0.902214 + 0.655497i −0.939034 0.343825i \(-0.888277\pi\)
0.0368195 + 0.999322i \(0.488277\pi\)
\(608\) −5.75986 17.7270i −0.233593 0.718926i
\(609\) 0 0
\(610\) −12.9392 9.40090i −0.523894 0.380631i
\(611\) −6.57671 4.77826i −0.266065 0.193308i
\(612\) 0 0
\(613\) −3.35530 10.3266i −0.135519 0.417086i 0.860151 0.510039i \(-0.170369\pi\)
−0.995670 + 0.0929536i \(0.970369\pi\)
\(614\) −10.0116 + 7.27388i −0.404037 + 0.293550i
\(615\) 0 0
\(616\) 2.14648 4.05269i 0.0864842 0.163287i
\(617\) 18.2404 0.734330 0.367165 0.930156i \(-0.380329\pi\)
0.367165 + 0.930156i \(0.380329\pi\)
\(618\) 0 0
\(619\) 6.08144 + 18.7167i 0.244434 + 0.752289i 0.995729 + 0.0923233i \(0.0294293\pi\)
−0.751295 + 0.659966i \(0.770571\pi\)
\(620\) −0.860790 + 2.64924i −0.0345701 + 0.106396i
\(621\) 0 0
\(622\) 13.2169 + 9.60267i 0.529951 + 0.385032i
\(623\) 1.30777 4.02491i 0.0523948 0.161255i
\(624\) 0 0
\(625\) −0.809017 + 0.587785i −0.0323607 + 0.0235114i
\(626\) −28.4044 −1.13527
\(627\) 0 0
\(628\) −1.40559 −0.0560893
\(629\) −4.41205 + 3.20554i −0.175920 + 0.127813i
\(630\) 0 0
\(631\) −9.40181 + 28.9358i −0.374280 + 1.15192i 0.569683 + 0.821865i \(0.307066\pi\)
−0.943963 + 0.330051i \(0.892934\pi\)
\(632\) 5.19997 + 3.77800i 0.206844 + 0.150281i
\(633\) 0 0
\(634\) 2.62619 8.08260i 0.104300 0.321001i
\(635\) 0.173532 + 0.534076i 0.00688640 + 0.0211942i
\(636\) 0 0
\(637\) 32.8948 1.30334
\(638\) −1.29740 0.226612i −0.0513647 0.00897166i
\(639\) 0 0
\(640\) −4.37230 + 3.17666i −0.172830 + 0.125569i
\(641\) 11.5427 + 35.5247i 0.455908 + 1.40314i 0.870066 + 0.492935i \(0.164076\pi\)
−0.414159 + 0.910205i \(0.635924\pi\)
\(642\) 0 0
\(643\) −0.861554 0.625956i −0.0339764 0.0246853i 0.570667 0.821181i \(-0.306685\pi\)
−0.604644 + 0.796496i \(0.706685\pi\)
\(644\) 0.00115154 0.000836645i 4.53772e−5 3.29684e-5i
\(645\) 0 0
\(646\) −1.90766 5.87118i −0.0750559 0.230998i
\(647\) 12.7864 9.28987i 0.502686 0.365223i −0.307356 0.951595i \(-0.599444\pi\)
0.810042 + 0.586372i \(0.199444\pi\)
\(648\) 0 0
\(649\) −3.46288 3.57437i −0.135930 0.140306i
\(650\) 5.93429 0.232762
\(651\) 0 0
\(652\) −1.35916 4.18305i −0.0532287 0.163821i
\(653\) 10.9241 33.6210i 0.427495 1.31569i −0.473091 0.881014i \(-0.656862\pi\)
0.900585 0.434679i \(-0.143138\pi\)
\(654\) 0 0
\(655\) 2.45537 + 1.78393i 0.0959393 + 0.0697040i
\(656\) 9.35409 28.7889i 0.365216 1.12402i
\(657\) 0 0
\(658\) 0.752439 0.546679i 0.0293331 0.0213118i
\(659\) −28.4474 −1.10815 −0.554077 0.832465i \(-0.686929\pi\)
−0.554077 + 0.832465i \(0.686929\pi\)
\(660\) 0 0
\(661\) 39.5989 1.54022 0.770110 0.637911i \(-0.220201\pi\)
0.770110 + 0.637911i \(0.220201\pi\)
\(662\) −10.4857 + 7.61830i −0.407538 + 0.296094i
\(663\) 0 0
\(664\) −15.0357 + 46.2752i −0.583499 + 1.79583i
\(665\) −2.48629 1.80639i −0.0964140 0.0700489i
\(666\) 0 0
\(667\) 0.000634741 0.00195353i 2.45773e−5 7.56411e-5i
\(668\) 3.02256 + 9.30248i 0.116946 + 0.359924i
\(669\) 0 0
\(670\) 11.7791 0.455068
\(671\) 38.8573 19.0295i 1.50007 0.734627i
\(672\) 0 0
\(673\) 14.2080 10.3227i 0.547679 0.397912i −0.279250 0.960218i \(-0.590086\pi\)
0.826929 + 0.562306i \(0.190086\pi\)
\(674\) 2.40448 + 7.40024i 0.0926173 + 0.285047i
\(675\) 0 0
\(676\) 4.19248 + 3.04602i 0.161249 + 0.117155i
\(677\) 36.4616 + 26.4909i 1.40133 + 1.01813i 0.994512 + 0.104619i \(0.0333622\pi\)
0.406819 + 0.913509i \(0.366638\pi\)
\(678\) 0 0
\(679\) −0.820716 2.52590i −0.0314962 0.0969353i
\(680\) 1.83287 1.33165i 0.0702872 0.0510666i
\(681\) 0 0
\(682\) 15.8608 + 16.3714i 0.607340 + 0.626894i
\(683\) 15.7677 0.603334 0.301667 0.953413i \(-0.402457\pi\)
0.301667 + 0.953413i \(0.402457\pi\)
\(684\) 0 0
\(685\) 6.39676 + 19.6872i 0.244408 + 0.752210i
\(686\) −2.36087 + 7.26603i −0.0901386 + 0.277418i
\(687\) 0 0
\(688\) −4.03304 2.93018i −0.153758 0.111712i
\(689\) −12.9225 + 39.7713i −0.492307 + 1.51517i
\(690\) 0 0
\(691\) −2.39970 + 1.74348i −0.0912889 + 0.0663253i −0.632493 0.774566i \(-0.717968\pi\)
0.541205 + 0.840891i \(0.317968\pi\)
\(692\) 1.44668 0.0549944
\(693\) 0 0
\(694\) 30.9465 1.17471
\(695\) 2.87098 2.08589i 0.108903 0.0791224i
\(696\) 0 0
\(697\) −2.50891 + 7.72162i −0.0950316 + 0.292477i
\(698\) −11.0132 8.00153i −0.416854 0.302862i
\(699\) 0 0
\(700\) 0.0693589 0.213465i 0.00262152 0.00806821i
\(701\) 11.4738 + 35.3128i 0.433360 + 1.33375i 0.894757 + 0.446553i \(0.147348\pi\)
−0.461397 + 0.887194i \(0.652652\pi\)
\(702\) 0 0
\(703\) 50.1364 1.89093
\(704\) −4.14459 29.1494i −0.156205 1.09861i
\(705\) 0 0
\(706\) −18.7017 + 13.5876i −0.703848 + 0.511375i
\(707\) 0.308191 + 0.948516i 0.0115907 + 0.0356726i
\(708\) 0 0
\(709\) 25.6867 + 18.6625i 0.964683 + 0.700883i 0.954234 0.299062i \(-0.0966738\pi\)
0.0104495 + 0.999945i \(0.496674\pi\)
\(710\) −11.3197 8.22423i −0.424820 0.308650i
\(711\) 0 0
\(712\) −8.86303 27.2776i −0.332156 1.02227i
\(713\) −0.0287608 + 0.0208959i −0.00107710 + 0.000782558i
\(714\) 0 0
\(715\) −7.51386 + 14.1866i −0.281002 + 0.530549i
\(716\) −3.12708 −0.116864
\(717\) 0 0
\(718\) 8.06692 + 24.8274i 0.301055 + 0.926552i
\(719\) −9.85059 + 30.3170i −0.367365 + 1.13063i 0.581122 + 0.813816i \(0.302614\pi\)
−0.948487 + 0.316816i \(0.897386\pi\)
\(720\) 0 0
\(721\) 3.53714 + 2.56989i 0.131730 + 0.0957075i
\(722\) −10.3394 + 31.8213i −0.384792 + 1.18427i
\(723\) 0 0
\(724\) −4.48806 + 3.26077i −0.166797 + 0.121185i
\(725\) −0.323900 −0.0120294
\(726\) 0 0
\(727\) 41.4129 1.53592 0.767959 0.640499i \(-0.221272\pi\)
0.767959 + 0.640499i \(0.221272\pi\)
\(728\) −5.41470 + 3.93401i −0.200682 + 0.145804i
\(729\) 0 0
\(730\) 3.87945 11.9397i 0.143585 0.441909i
\(731\) 1.08172 + 0.785918i 0.0400090 + 0.0290682i
\(732\) 0 0
\(733\) 14.7376 45.3578i 0.544347 1.67533i −0.178189 0.983996i \(-0.557024\pi\)
0.722537 0.691333i \(-0.242976\pi\)
\(734\) 11.8528 + 36.4792i 0.437495 + 1.34647i
\(735\) 0 0
\(736\) 0.0173734 0.000640391
\(737\) −14.9145 + 28.1594i −0.549381 + 1.03726i
\(738\) 0 0
\(739\) 10.0777 7.32187i 0.370714 0.269339i −0.386793 0.922167i \(-0.626417\pi\)
0.757507 + 0.652827i \(0.226417\pi\)
\(740\) 1.13152 + 3.48246i 0.0415955 + 0.128018i
\(741\) 0 0
\(742\) −3.87065 2.81219i −0.142096 0.103239i
\(743\) 22.1446 + 16.0890i 0.812407 + 0.590249i 0.914528 0.404524i \(-0.132563\pi\)
−0.102120 + 0.994772i \(0.532563\pi\)
\(744\) 0 0
\(745\) −1.94823 5.99603i −0.0713775 0.219677i
\(746\) 9.31722 6.76936i 0.341128 0.247844i
\(747\) 0 0
\(748\) 0.171694 + 1.20754i 0.00627775 + 0.0441521i
\(749\) 5.31033 0.194035
\(750\) 0 0
\(751\) −12.9393 39.8231i −0.472162 1.45317i −0.849747 0.527191i \(-0.823245\pi\)
0.377585 0.925975i \(-0.376755\pi\)
\(752\) 1.43203 4.40733i 0.0522207 0.160719i
\(753\) 0 0
\(754\) 1.55503 + 1.12979i 0.0566308 + 0.0411447i
\(755\) 1.13852 3.50400i 0.0414349 0.127523i
\(756\) 0 0
\(757\) −13.0407 + 9.47464i −0.473973 + 0.344362i −0.798988 0.601347i \(-0.794631\pi\)
0.325015 + 0.945709i \(0.394631\pi\)
\(758\) 10.0499 0.365029
\(759\) 0 0
\(760\) −20.8278 −0.755504
\(761\) −8.83760 + 6.42090i −0.320363 + 0.232757i −0.736330 0.676622i \(-0.763443\pi\)
0.415967 + 0.909380i \(0.363443\pi\)
\(762\) 0 0
\(763\) 1.74604 5.37376i 0.0632109 0.194543i
\(764\) 8.19875 + 5.95674i 0.296620 + 0.215507i
\(765\) 0 0
\(766\) −12.7610 + 39.2744i −0.461075 + 1.41904i
\(767\) 2.24442 + 6.90762i 0.0810414 + 0.249420i
\(768\) 0 0
\(769\) −34.2074 −1.23355 −0.616775 0.787139i \(-0.711561\pi\)
−0.616775 + 0.787139i \(0.711561\pi\)
\(770\) −1.27800 1.31914i −0.0460558 0.0475386i
\(771\) 0 0
\(772\) −1.19570 + 0.868727i −0.0430342 + 0.0312662i
\(773\) −2.66894 8.21416i −0.0959952 0.295443i 0.891517 0.452988i \(-0.149642\pi\)
−0.987512 + 0.157545i \(0.949642\pi\)
\(774\) 0 0
\(775\) 4.53521 + 3.29503i 0.162910 + 0.118361i
\(776\) −14.5619 10.5798i −0.522742 0.379794i
\(777\) 0 0
\(778\) 12.4772 + 38.4009i 0.447329 + 1.37674i
\(779\) 60.3852 43.8724i 2.16352 1.57189i
\(780\) 0 0
\(781\) 33.9937 16.6477i 1.21639 0.595701i
\(782\) 0.00575405 0.000205764
\(783\) 0 0
\(784\) 5.79466 + 17.8341i 0.206952 + 0.636934i
\(785\) −0.874113 + 2.69024i −0.0311984 + 0.0960189i
\(786\) 0 0
\(787\) 18.6918 + 13.5804i 0.666291 + 0.484089i 0.868781 0.495196i \(-0.164904\pi\)