Properties

Label 576.2.bd.a.109.4
Level $576$
Weight $2$
Character 576.109
Analytic conductor $4.599$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bd (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(7\) over \(\Q(\zeta_{16})\)
Twist minimal: no (minimal twist has level 64)
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 109.4
Character \(\chi\) \(=\) 576.109
Dual form 576.2.bd.a.37.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.466807 + 1.33495i) q^{2} +(-1.56418 + 1.24633i) q^{4} +(0.690473 + 3.47124i) q^{5} +(0.983337 + 2.37399i) q^{7} +(-2.39396 - 1.50631i) q^{8} +O(q^{10})\) \(q+(0.466807 + 1.33495i) q^{2} +(-1.56418 + 1.24633i) q^{4} +(0.690473 + 3.47124i) q^{5} +(0.983337 + 2.37399i) q^{7} +(-2.39396 - 1.50631i) q^{8} +(-4.31162 + 2.54215i) q^{10} +(-1.29020 - 0.862086i) q^{11} +(-0.115716 + 0.581745i) q^{13} +(-2.71012 + 2.42090i) q^{14} +(0.893330 - 3.89897i) q^{16} +(-4.30936 - 4.30936i) q^{17} +(3.59299 + 0.714690i) q^{19} +(-5.40633 - 4.56910i) q^{20} +(0.548565 - 2.12478i) q^{22} +(7.79200 + 3.22755i) q^{23} +(-6.95338 + 2.88018i) q^{25} +(-0.830617 + 0.117087i) q^{26} +(-4.49689 - 2.48779i) q^{28} +(0.373179 - 0.249351i) q^{29} +1.08345i q^{31} +(5.62194 - 0.627516i) q^{32} +(3.74114 - 7.76442i) q^{34} +(-7.56172 + 5.05258i) q^{35} +(-4.16040 + 0.827556i) q^{37} +(0.723158 + 5.13008i) q^{38} +(3.57580 - 9.35007i) q^{40} +(-5.15990 - 2.13730i) q^{41} +(-1.55896 + 2.33315i) q^{43} +(3.09255 - 0.259557i) q^{44} +(-0.671258 + 11.9086i) q^{46} +(-6.43269 - 6.43269i) q^{47} +(0.280888 - 0.280888i) q^{49} +(-7.09079 - 7.93792i) q^{50} +(-0.544044 - 1.05417i) q^{52} +(1.22184 + 0.816410i) q^{53} +(2.10166 - 5.07385i) q^{55} +(1.22189 - 7.16443i) q^{56} +(0.507073 + 0.381777i) q^{58} +(1.46423 + 7.36119i) q^{59} +(6.45980 + 9.66777i) q^{61} +(-1.44635 + 0.505761i) q^{62} +(3.46207 + 7.21208i) q^{64} -2.09928 q^{65} +(3.30637 + 4.94834i) q^{67} +(12.1115 + 1.36974i) q^{68} +(-10.2748 - 7.73593i) q^{70} +(3.75143 + 9.05676i) q^{71} +(-1.19724 + 2.89039i) q^{73} +(-3.04685 - 5.16762i) q^{74} +(-6.51083 + 3.36014i) q^{76} +(0.777876 - 3.91064i) q^{77} +(-0.934789 + 0.934789i) q^{79} +(14.1511 + 0.408832i) q^{80} +(0.444510 - 7.88591i) q^{82} +(16.5833 + 3.29862i) q^{83} +(11.9833 - 17.9343i) q^{85} +(-3.84237 - 0.992002i) q^{86} +(1.79012 + 4.00724i) q^{88} +(6.15337 - 2.54881i) q^{89} +(-1.49484 + 0.297343i) q^{91} +(-16.2107 + 4.66291i) q^{92} +(5.58449 - 11.5901i) q^{94} +12.9656i q^{95} -5.79443i q^{97} +(0.506092 + 0.243851i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} + O(q^{10}) \) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} - 8q^{10} + 8q^{11} - 8q^{13} + 8q^{14} - 8q^{16} + 8q^{17} - 8q^{19} + 8q^{20} + 8q^{23} - 8q^{25} - 32q^{26} + 32q^{28} + 8q^{29} - 32q^{32} + 32q^{34} + 8q^{35} - 8q^{37} - 32q^{38} + 32q^{40} + 8q^{41} - 8q^{43} - 8q^{46} + 8q^{47} - 8q^{49} + 32q^{50} - 56q^{52} + 8q^{53} + 56q^{55} + 64q^{56} - 80q^{58} - 56q^{59} - 8q^{61} + 40q^{62} - 104q^{64} + 16q^{65} + 72q^{67} + 56q^{68} - 104q^{70} - 56q^{71} - 8q^{73} + 64q^{74} - 72q^{76} + 8q^{77} + 24q^{79} - 32q^{80} + 72q^{82} + 8q^{83} - 8q^{85} - 96q^{86} + 72q^{88} + 8q^{89} - 8q^{91} - 144q^{92} + 88q^{94} - 128q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{16}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.466807 + 1.33495i 0.330083 + 0.943952i
\(3\) 0 0
\(4\) −1.56418 + 1.24633i −0.782091 + 0.623164i
\(5\) 0.690473 + 3.47124i 0.308789 + 1.55239i 0.753947 + 0.656935i \(0.228147\pi\)
−0.445158 + 0.895452i \(0.646853\pi\)
\(6\) 0 0
\(7\) 0.983337 + 2.37399i 0.371667 + 0.897283i 0.993468 + 0.114108i \(0.0364010\pi\)
−0.621802 + 0.783175i \(0.713599\pi\)
\(8\) −2.39396 1.50631i −0.846392 0.532561i
\(9\) 0 0
\(10\) −4.31162 + 2.54215i −1.36345 + 0.803898i
\(11\) −1.29020 0.862086i −0.389011 0.259929i 0.345650 0.938364i \(-0.387659\pi\)
−0.734660 + 0.678435i \(0.762659\pi\)
\(12\) 0 0
\(13\) −0.115716 + 0.581745i −0.0320939 + 0.161347i −0.993509 0.113756i \(-0.963712\pi\)
0.961415 + 0.275103i \(0.0887119\pi\)
\(14\) −2.71012 + 2.42090i −0.724311 + 0.647013i
\(15\) 0 0
\(16\) 0.893330 3.89897i 0.223333 0.974742i
\(17\) −4.30936 4.30936i −1.04517 1.04517i −0.998930 0.0462432i \(-0.985275\pi\)
−0.0462432 0.998930i \(-0.514725\pi\)
\(18\) 0 0
\(19\) 3.59299 + 0.714690i 0.824288 + 0.163961i 0.589174 0.808006i \(-0.299453\pi\)
0.235115 + 0.971968i \(0.424453\pi\)
\(20\) −5.40633 4.56910i −1.20889 1.02168i
\(21\) 0 0
\(22\) 0.548565 2.12478i 0.116955 0.453005i
\(23\) 7.79200 + 3.22755i 1.62474 + 0.672991i 0.994628 0.103510i \(-0.0330075\pi\)
0.630116 + 0.776501i \(0.283007\pi\)
\(24\) 0 0
\(25\) −6.95338 + 2.88018i −1.39068 + 0.576037i
\(26\) −0.830617 + 0.117087i −0.162897 + 0.0229627i
\(27\) 0 0
\(28\) −4.49689 2.48779i −0.849832 0.470147i
\(29\) 0.373179 0.249351i 0.0692977 0.0463032i −0.520439 0.853899i \(-0.674232\pi\)
0.589736 + 0.807596i \(0.299232\pi\)
\(30\) 0 0
\(31\) 1.08345i 0.194593i 0.995255 + 0.0972963i \(0.0310195\pi\)
−0.995255 + 0.0972963i \(0.968981\pi\)
\(32\) 5.62194 0.627516i 0.993828 0.110930i
\(33\) 0 0
\(34\) 3.74114 7.76442i 0.641600 1.33159i
\(35\) −7.56172 + 5.05258i −1.27816 + 0.854041i
\(36\) 0 0
\(37\) −4.16040 + 0.827556i −0.683966 + 0.136049i −0.524830 0.851207i \(-0.675871\pi\)
−0.159136 + 0.987257i \(0.550871\pi\)
\(38\) 0.723158 + 5.13008i 0.117312 + 0.832209i
\(39\) 0 0
\(40\) 3.57580 9.35007i 0.565384 1.47838i
\(41\) −5.15990 2.13730i −0.805841 0.333790i −0.0585477 0.998285i \(-0.518647\pi\)
−0.747293 + 0.664494i \(0.768647\pi\)
\(42\) 0 0
\(43\) −1.55896 + 2.33315i −0.237739 + 0.355802i −0.931084 0.364804i \(-0.881136\pi\)
0.693345 + 0.720605i \(0.256136\pi\)
\(44\) 3.09255 0.259557i 0.466220 0.0391297i
\(45\) 0 0
\(46\) −0.671258 + 11.9086i −0.0989715 + 1.75582i
\(47\) −6.43269 6.43269i −0.938304 0.938304i 0.0599006 0.998204i \(-0.480922\pi\)
−0.998204 + 0.0599006i \(0.980922\pi\)
\(48\) 0 0
\(49\) 0.280888 0.280888i 0.0401268 0.0401268i
\(50\) −7.09079 7.93792i −1.00279 1.12259i
\(51\) 0 0
\(52\) −0.544044 1.05417i −0.0754453 0.146188i
\(53\) 1.22184 + 0.816410i 0.167833 + 0.112143i 0.636650 0.771153i \(-0.280320\pi\)
−0.468817 + 0.883295i \(0.655320\pi\)
\(54\) 0 0
\(55\) 2.10166 5.07385i 0.283388 0.684158i
\(56\) 1.22189 7.16443i 0.163282 0.957388i
\(57\) 0 0
\(58\) 0.507073 + 0.381777i 0.0665820 + 0.0501298i
\(59\) 1.46423 + 7.36119i 0.190627 + 0.958345i 0.951078 + 0.308950i \(0.0999776\pi\)
−0.760452 + 0.649395i \(0.775022\pi\)
\(60\) 0 0
\(61\) 6.45980 + 9.66777i 0.827092 + 1.23783i 0.968781 + 0.247920i \(0.0797470\pi\)
−0.141688 + 0.989911i \(0.545253\pi\)
\(62\) −1.44635 + 0.505761i −0.183686 + 0.0642317i
\(63\) 0 0
\(64\) 3.46207 + 7.21208i 0.432758 + 0.901510i
\(65\) −2.09928 −0.260383
\(66\) 0 0
\(67\) 3.30637 + 4.94834i 0.403938 + 0.604535i 0.976550 0.215291i \(-0.0690700\pi\)
−0.572612 + 0.819826i \(0.694070\pi\)
\(68\) 12.1115 + 1.36974i 1.46874 + 0.166106i
\(69\) 0 0
\(70\) −10.2748 7.73593i −1.22807 0.924621i
\(71\) 3.75143 + 9.05676i 0.445213 + 1.07484i 0.974094 + 0.226143i \(0.0726118\pi\)
−0.528881 + 0.848696i \(0.677388\pi\)
\(72\) 0 0
\(73\) −1.19724 + 2.89039i −0.140126 + 0.338295i −0.978327 0.207068i \(-0.933608\pi\)
0.838200 + 0.545362i \(0.183608\pi\)
\(74\) −3.04685 5.16762i −0.354189 0.600724i
\(75\) 0 0
\(76\) −6.51083 + 3.36014i −0.746843 + 0.385435i
\(77\) 0.777876 3.91064i 0.0886472 0.445659i
\(78\) 0 0
\(79\) −0.934789 + 0.934789i −0.105172 + 0.105172i −0.757735 0.652563i \(-0.773694\pi\)
0.652563 + 0.757735i \(0.273694\pi\)
\(80\) 14.1511 + 0.408832i 1.58214 + 0.0457088i
\(81\) 0 0
\(82\) 0.444510 7.88591i 0.0490879 0.870854i
\(83\) 16.5833 + 3.29862i 1.82025 + 0.362070i 0.982834 0.184494i \(-0.0590645\pi\)
0.837417 + 0.546564i \(0.184064\pi\)
\(84\) 0 0
\(85\) 11.9833 17.9343i 1.29978 1.94525i
\(86\) −3.84237 0.992002i −0.414333 0.106970i
\(87\) 0 0
\(88\) 1.79012 + 4.00724i 0.190828 + 0.427173i
\(89\) 6.15337 2.54881i 0.652256 0.270173i −0.0319199 0.999490i \(-0.510162\pi\)
0.684176 + 0.729317i \(0.260162\pi\)
\(90\) 0 0
\(91\) −1.49484 + 0.297343i −0.156702 + 0.0311700i
\(92\) −16.2107 + 4.66291i −1.69008 + 0.486142i
\(93\) 0 0
\(94\) 5.58449 11.5901i 0.575996 1.19543i
\(95\) 12.9656i 1.33024i
\(96\) 0 0
\(97\) 5.79443i 0.588336i −0.955754 0.294168i \(-0.904958\pi\)
0.955754 0.294168i \(-0.0950425\pi\)
\(98\) 0.506092 + 0.243851i 0.0511230 + 0.0246326i
\(99\) 0 0
\(100\) 7.28669 13.1713i 0.728669 1.31713i
\(101\) −0.921112 + 0.183220i −0.0916540 + 0.0182311i −0.240704 0.970599i \(-0.577378\pi\)
0.149050 + 0.988830i \(0.452378\pi\)
\(102\) 0 0
\(103\) 12.7902 5.29788i 1.26026 0.522015i 0.350268 0.936649i \(-0.386090\pi\)
0.909988 + 0.414634i \(0.136090\pi\)
\(104\) 1.15331 1.21837i 0.113091 0.119471i
\(105\) 0 0
\(106\) −0.519501 + 2.01221i −0.0504584 + 0.195443i
\(107\) 8.24793 12.3439i 0.797358 1.19333i −0.180400 0.983593i \(-0.557739\pi\)
0.977758 0.209737i \(-0.0672608\pi\)
\(108\) 0 0
\(109\) −6.63883 1.32055i −0.635885 0.126485i −0.133387 0.991064i \(-0.542585\pi\)
−0.502497 + 0.864579i \(0.667585\pi\)
\(110\) 7.75441 + 0.437097i 0.739354 + 0.0416756i
\(111\) 0 0
\(112\) 10.1345 1.71325i 0.957625 0.161887i
\(113\) 3.62032 3.62032i 0.340571 0.340571i −0.516011 0.856582i \(-0.672584\pi\)
0.856582 + 0.516011i \(0.172584\pi\)
\(114\) 0 0
\(115\) −5.82345 + 29.2765i −0.543039 + 2.73004i
\(116\) −0.272948 + 0.855134i −0.0253426 + 0.0793972i
\(117\) 0 0
\(118\) −9.14330 + 5.39093i −0.841709 + 0.496275i
\(119\) 5.99281 14.4679i 0.549360 1.32627i
\(120\) 0 0
\(121\) −3.28809 7.93814i −0.298917 0.721649i
\(122\) −9.89051 + 13.1365i −0.895445 + 1.18932i
\(123\) 0 0
\(124\) −1.35033 1.69471i −0.121263 0.152189i
\(125\) −4.96743 7.43428i −0.444300 0.664942i
\(126\) 0 0
\(127\) −5.27774 −0.468324 −0.234162 0.972198i \(-0.575235\pi\)
−0.234162 + 0.972198i \(0.575235\pi\)
\(128\) −8.01165 + 7.98834i −0.708136 + 0.706076i
\(129\) 0 0
\(130\) −0.979957 2.80243i −0.0859479 0.245789i
\(131\) 3.19779 + 4.78583i 0.279392 + 0.418140i 0.944452 0.328651i \(-0.106594\pi\)
−0.665060 + 0.746790i \(0.731594\pi\)
\(132\) 0 0
\(133\) 1.83646 + 9.23249i 0.159241 + 0.800558i
\(134\) −5.06234 + 6.72376i −0.437320 + 0.580844i
\(135\) 0 0
\(136\) 3.82520 + 16.8077i 0.328008 + 1.44124i
\(137\) −3.78991 + 9.14965i −0.323794 + 0.781707i 0.675233 + 0.737604i \(0.264043\pi\)
−0.999027 + 0.0441030i \(0.985957\pi\)
\(138\) 0 0
\(139\) −1.75609 1.17338i −0.148950 0.0995250i 0.478862 0.877890i \(-0.341049\pi\)
−0.627812 + 0.778365i \(0.716049\pi\)
\(140\) 5.53073 17.3275i 0.467432 1.46444i
\(141\) 0 0
\(142\) −10.3391 + 9.23573i −0.867640 + 0.775046i
\(143\) 0.650811 0.650811i 0.0544236 0.0544236i
\(144\) 0 0
\(145\) 1.12323 + 1.12323i 0.0932789 + 0.0932789i
\(146\) −4.41740 0.248998i −0.365587 0.0206073i
\(147\) 0 0
\(148\) 5.47622 6.47968i 0.450143 0.532626i
\(149\) 10.0124 14.9845i 0.820244 1.22758i −0.150772 0.988569i \(-0.548176\pi\)
0.971016 0.239013i \(-0.0768240\pi\)
\(150\) 0 0
\(151\) −4.99222 2.06785i −0.406261 0.168279i 0.170188 0.985412i \(-0.445562\pi\)
−0.576450 + 0.817133i \(0.695562\pi\)
\(152\) −7.52492 7.12309i −0.610352 0.577759i
\(153\) 0 0
\(154\) 5.58363 0.787093i 0.449942 0.0634257i
\(155\) −3.76090 + 0.748090i −0.302083 + 0.0600881i
\(156\) 0 0
\(157\) 7.04496 4.70729i 0.562249 0.375683i −0.241727 0.970344i \(-0.577714\pi\)
0.803976 + 0.594662i \(0.202714\pi\)
\(158\) −1.68426 0.811530i −0.133993 0.0645619i
\(159\) 0 0
\(160\) 6.06006 + 19.0818i 0.479090 + 1.50855i
\(161\) 21.6719i 1.70798i
\(162\) 0 0
\(163\) 0.919897 0.614656i 0.0720519 0.0481435i −0.519023 0.854761i \(-0.673704\pi\)
0.591074 + 0.806617i \(0.298704\pi\)
\(164\) 10.7348 3.08780i 0.838247 0.241117i
\(165\) 0 0
\(166\) 3.33770 + 23.6777i 0.259056 + 1.83774i
\(167\) 2.61833 1.08455i 0.202612 0.0839247i −0.279070 0.960271i \(-0.590026\pi\)
0.481682 + 0.876346i \(0.340026\pi\)
\(168\) 0 0
\(169\) 11.6854 + 4.84025i 0.898877 + 0.372327i
\(170\) 29.5353 + 7.62528i 2.26526 + 0.584832i
\(171\) 0 0
\(172\) −0.469373 5.59244i −0.0357893 0.426420i
\(173\) −10.2464 2.03813i −0.779016 0.154956i −0.210462 0.977602i \(-0.567497\pi\)
−0.568554 + 0.822646i \(0.692497\pi\)
\(174\) 0 0
\(175\) −13.6750 13.6750i −1.03374 1.03374i
\(176\) −4.51382 + 4.26033i −0.340242 + 0.321135i
\(177\) 0 0
\(178\) 6.27497 + 7.02464i 0.470329 + 0.526519i
\(179\) −3.79507 + 19.0791i −0.283657 + 1.42604i 0.531627 + 0.846979i \(0.321581\pi\)
−0.815284 + 0.579061i \(0.803419\pi\)
\(180\) 0 0
\(181\) 3.32947 + 2.22468i 0.247477 + 0.165359i 0.673122 0.739531i \(-0.264953\pi\)
−0.425645 + 0.904890i \(0.639953\pi\)
\(182\) −1.09474 1.85674i −0.0811476 0.137631i
\(183\) 0 0
\(184\) −13.7920 19.4638i −1.01676 1.43489i
\(185\) −5.74529 13.8704i −0.422402 1.01977i
\(186\) 0 0
\(187\) 1.84491 + 9.27499i 0.134913 + 0.678254i
\(188\) 18.0791 + 2.04465i 1.31856 + 0.149121i
\(189\) 0 0
\(190\) −17.3084 + 6.05244i −1.25569 + 0.439090i
\(191\) −16.2586 −1.17643 −0.588215 0.808704i \(-0.700169\pi\)
−0.588215 + 0.808704i \(0.700169\pi\)
\(192\) 0 0
\(193\) −24.9345 −1.79482 −0.897411 0.441196i \(-0.854554\pi\)
−0.897411 + 0.441196i \(0.854554\pi\)
\(194\) 7.73528 2.70488i 0.555361 0.194199i
\(195\) 0 0
\(196\) −0.0892812 + 0.789438i −0.00637723 + 0.0563885i
\(197\) 0.816489 + 4.10477i 0.0581724 + 0.292452i 0.998910 0.0466836i \(-0.0148653\pi\)
−0.940737 + 0.339136i \(0.889865\pi\)
\(198\) 0 0
\(199\) −0.744172 1.79659i −0.0527529 0.127357i 0.895306 0.445452i \(-0.146957\pi\)
−0.948059 + 0.318095i \(0.896957\pi\)
\(200\) 20.9845 + 3.57890i 1.48383 + 0.253066i
\(201\) 0 0
\(202\) −0.674572 1.14411i −0.0474627 0.0804992i
\(203\) 0.958916 + 0.640727i 0.0673027 + 0.0449702i
\(204\) 0 0
\(205\) 3.85632 19.3870i 0.269337 1.35405i
\(206\) 13.0430 + 14.6012i 0.908746 + 1.01731i
\(207\) 0 0
\(208\) 2.16483 + 0.970864i 0.150104 + 0.0673173i
\(209\) −4.01956 4.01956i −0.278039 0.278039i
\(210\) 0 0
\(211\) 14.6646 + 2.91696i 1.00955 + 0.200812i 0.672044 0.740511i \(-0.265416\pi\)
0.337507 + 0.941323i \(0.390416\pi\)
\(212\) −2.92870 + 0.245805i −0.201144 + 0.0168820i
\(213\) 0 0
\(214\) 20.3287 + 5.24835i 1.38964 + 0.358770i
\(215\) −9.17534 3.80055i −0.625753 0.259195i
\(216\) 0 0
\(217\) −2.57209 + 1.06539i −0.174605 + 0.0723236i
\(218\) −1.33619 9.47894i −0.0904984 0.641995i
\(219\) 0 0
\(220\) 3.03631 + 10.5558i 0.204708 + 0.711671i
\(221\) 3.00561 2.00828i 0.202179 0.135092i
\(222\) 0 0
\(223\) 14.8634i 0.995330i −0.867369 0.497665i \(-0.834191\pi\)
0.867369 0.497665i \(-0.165809\pi\)
\(224\) 7.01798 + 12.7294i 0.468909 + 0.850516i
\(225\) 0 0
\(226\) 6.52294 + 3.14296i 0.433900 + 0.209066i
\(227\) 6.90248 4.61209i 0.458133 0.306115i −0.305004 0.952351i \(-0.598658\pi\)
0.763138 + 0.646236i \(0.223658\pi\)
\(228\) 0 0
\(229\) −3.63468 + 0.722983i −0.240187 + 0.0477761i −0.313716 0.949517i \(-0.601574\pi\)
0.0735290 + 0.997293i \(0.476574\pi\)
\(230\) −41.8010 + 5.89245i −2.75628 + 0.388537i
\(231\) 0 0
\(232\) −1.26897 + 0.0348110i −0.0833123 + 0.00228546i
\(233\) −17.7828 7.36589i −1.16499 0.482556i −0.285458 0.958391i \(-0.592146\pi\)
−0.879534 + 0.475836i \(0.842146\pi\)
\(234\) 0 0
\(235\) 17.8878 26.7710i 1.16687 1.74635i
\(236\) −11.4648 9.68932i −0.746294 0.630721i
\(237\) 0 0
\(238\) 22.1114 + 1.24637i 1.43327 + 0.0807901i
\(239\) 1.69651 + 1.69651i 0.109738 + 0.109738i 0.759844 0.650106i \(-0.225275\pi\)
−0.650106 + 0.759844i \(0.725275\pi\)
\(240\) 0 0
\(241\) −12.7520 + 12.7520i −0.821432 + 0.821432i −0.986313 0.164882i \(-0.947276\pi\)
0.164882 + 0.986313i \(0.447276\pi\)
\(242\) 9.06212 8.09501i 0.582535 0.520367i
\(243\) 0 0
\(244\) −22.1535 7.07112i −1.41823 0.452682i
\(245\) 1.16898 + 0.781085i 0.0746831 + 0.0499017i
\(246\) 0 0
\(247\) −0.831534 + 2.00750i −0.0529093 + 0.127734i
\(248\) 1.63200 2.59372i 0.103632 0.164702i
\(249\) 0 0
\(250\) 7.60556 10.1016i 0.481018 0.638884i
\(251\) −0.0325488 0.163634i −0.00205446 0.0103285i 0.979744 0.200252i \(-0.0641760\pi\)
−0.981799 + 0.189923i \(0.939176\pi\)
\(252\) 0 0
\(253\) −7.27083 10.8816i −0.457113 0.684118i
\(254\) −2.46369 7.04552i −0.154586 0.442076i
\(255\) 0 0
\(256\) −14.4039 6.96613i −0.900245 0.435383i
\(257\) −1.30561 −0.0814417 −0.0407209 0.999171i \(-0.512965\pi\)
−0.0407209 + 0.999171i \(0.512965\pi\)
\(258\) 0 0
\(259\) −6.05569 9.06297i −0.376282 0.563146i
\(260\) 3.28365 2.61639i 0.203643 0.162261i
\(261\) 0 0
\(262\) −4.89609 + 6.50295i −0.302481 + 0.401753i
\(263\) −4.45700 10.7602i −0.274831 0.663500i 0.724846 0.688910i \(-0.241911\pi\)
−0.999677 + 0.0254106i \(0.991911\pi\)
\(264\) 0 0
\(265\) −1.99031 + 4.80503i −0.122264 + 0.295170i
\(266\) −11.4676 + 6.76137i −0.703126 + 0.414566i
\(267\) 0 0
\(268\) −11.3390 3.61927i −0.692641 0.221082i
\(269\) 2.48406 12.4882i 0.151456 0.761419i −0.828153 0.560502i \(-0.810608\pi\)
0.979608 0.200916i \(-0.0643919\pi\)
\(270\) 0 0
\(271\) 5.90740 5.90740i 0.358849 0.358849i −0.504540 0.863389i \(-0.668338\pi\)
0.863389 + 0.504540i \(0.168338\pi\)
\(272\) −20.6517 + 12.9524i −1.25220 + 0.785354i
\(273\) 0 0
\(274\) −13.9835 0.788215i −0.844773 0.0476178i
\(275\) 11.4542 + 2.27839i 0.690716 + 0.137392i
\(276\) 0 0
\(277\) −0.0619322 + 0.0926880i −0.00372114 + 0.00556908i −0.833326 0.552783i \(-0.813566\pi\)
0.829604 + 0.558352i \(0.188566\pi\)
\(278\) 0.746651 2.89204i 0.0447811 0.173453i
\(279\) 0 0
\(280\) 25.7132 0.705374i 1.53666 0.0421542i
\(281\) 8.41645 3.48621i 0.502083 0.207970i −0.117243 0.993103i \(-0.537406\pi\)
0.619327 + 0.785133i \(0.287406\pi\)
\(282\) 0 0
\(283\) 11.6331 2.31397i 0.691518 0.137551i 0.163193 0.986594i \(-0.447821\pi\)
0.528324 + 0.849043i \(0.322821\pi\)
\(284\) −17.1556 9.49090i −1.01800 0.563181i
\(285\) 0 0
\(286\) 1.17260 + 0.564997i 0.0693375 + 0.0334090i
\(287\) 14.3512i 0.847126i
\(288\) 0 0
\(289\) 20.1412i 1.18478i
\(290\) −0.975121 + 2.02378i −0.0572611 + 0.118841i
\(291\) 0 0
\(292\) −1.72968 6.01325i −0.101222 0.351899i
\(293\) −0.100300 + 0.0199510i −0.00585961 + 0.00116555i −0.198019 0.980198i \(-0.563451\pi\)
0.192160 + 0.981364i \(0.438451\pi\)
\(294\) 0 0
\(295\) −24.5415 + 10.1654i −1.42886 + 0.591853i
\(296\) 11.2064 + 4.28572i 0.651358 + 0.249102i
\(297\) 0 0
\(298\) 24.6775 + 6.37109i 1.42953 + 0.369068i
\(299\) −2.77927 + 4.15947i −0.160729 + 0.240549i
\(300\) 0 0
\(301\) −7.07185 1.40668i −0.407614 0.0810795i
\(302\) 0.430065 7.62965i 0.0247475 0.439037i
\(303\) 0 0
\(304\) 5.99628 13.3705i 0.343910 0.766851i
\(305\) −29.0989 + 29.0989i −1.66620 + 1.66620i
\(306\) 0 0
\(307\) 4.46728 22.4585i 0.254961 1.28178i −0.614950 0.788566i \(-0.710824\pi\)
0.869911 0.493209i \(-0.164176\pi\)
\(308\) 3.65721 + 7.08645i 0.208389 + 0.403788i
\(309\) 0 0
\(310\) −2.75428 4.67140i −0.156433 0.265318i
\(311\) 6.48708 15.6612i 0.367848 0.888064i −0.626254 0.779619i \(-0.715413\pi\)
0.994102 0.108445i \(-0.0345873\pi\)
\(312\) 0 0
\(313\) −6.94583 16.7687i −0.392602 0.947824i −0.989371 0.145411i \(-0.953549\pi\)
0.596770 0.802413i \(-0.296451\pi\)
\(314\) 9.57264 + 7.20727i 0.540215 + 0.406730i
\(315\) 0 0
\(316\) 0.297126 2.62724i 0.0167146 0.147794i
\(317\) 10.9936 + 16.4530i 0.617459 + 0.924093i 1.00000 0.000154534i \(4.91898e-5\pi\)
−0.382541 + 0.923939i \(0.624951\pi\)
\(318\) 0 0
\(319\) −0.696439 −0.0389931
\(320\) −22.6444 + 16.9974i −1.26586 + 0.950185i
\(321\) 0 0
\(322\) −28.9309 + 10.1166i −1.61225 + 0.563775i
\(323\) −12.4036 18.5633i −0.690156 1.03289i
\(324\) 0 0
\(325\) −0.870913 4.37837i −0.0483095 0.242868i
\(326\) 1.24995 + 0.941091i 0.0692283 + 0.0521222i
\(327\) 0 0
\(328\) 9.13315 + 12.8890i 0.504294 + 0.711677i
\(329\) 8.94561 21.5966i 0.493187 1.19066i
\(330\) 0 0
\(331\) −5.97462 3.99211i −0.328395 0.219426i 0.380432 0.924809i \(-0.375775\pi\)
−0.708827 + 0.705382i \(0.750775\pi\)
\(332\) −30.0504 + 15.5086i −1.64923 + 0.851143i
\(333\) 0 0
\(334\) 2.67007 + 2.98906i 0.146100 + 0.163554i
\(335\) −14.8939 + 14.8939i −0.813741 + 0.813741i
\(336\) 0 0
\(337\) −18.4718 18.4718i −1.00622 1.00622i −0.999981 0.00624304i \(-0.998013\pi\)
−0.00624304 0.999981i \(-0.501987\pi\)
\(338\) −1.00666 + 17.8589i −0.0547552 + 0.971395i
\(339\) 0 0
\(340\) 3.60795 + 42.9877i 0.195669 + 2.33134i
\(341\) 0.934023 1.39786i 0.0505802 0.0756986i
\(342\) 0 0
\(343\) 17.5609 + 7.27398i 0.948201 + 0.392758i
\(344\) 7.24653 3.23718i 0.390706 0.174537i
\(345\) 0 0
\(346\) −2.06228 14.6298i −0.110869 0.786502i
\(347\) −9.12297 + 1.81467i −0.489747 + 0.0974167i −0.433785 0.901016i \(-0.642822\pi\)
−0.0559615 + 0.998433i \(0.517822\pi\)
\(348\) 0 0
\(349\) 9.46721 6.32579i 0.506768 0.338612i −0.275760 0.961226i \(-0.588930\pi\)
0.782528 + 0.622615i \(0.213930\pi\)
\(350\) 11.8719 24.6391i 0.634578 1.31701i
\(351\) 0 0
\(352\) −7.79442 4.03697i −0.415444 0.215171i
\(353\) 12.2587i 0.652465i −0.945290 0.326233i \(-0.894221\pi\)
0.945290 0.326233i \(-0.105779\pi\)
\(354\) 0 0
\(355\) −28.8479 + 19.2756i −1.53109 + 1.02304i
\(356\) −6.44834 + 11.6559i −0.341761 + 0.617763i
\(357\) 0 0
\(358\) −27.2412 + 3.84004i −1.43974 + 0.202952i
\(359\) 6.95121 2.87929i 0.366871 0.151963i −0.191629 0.981467i \(-0.561377\pi\)
0.558500 + 0.829505i \(0.311377\pi\)
\(360\) 0 0
\(361\) −5.15492 2.13524i −0.271311 0.112381i
\(362\) −1.41562 + 5.48317i −0.0744031 + 0.288189i
\(363\) 0 0
\(364\) 1.96762 2.32816i 0.103131 0.122029i
\(365\) −10.8599 2.16017i −0.568433 0.113068i
\(366\) 0 0
\(367\) −1.10049 1.10049i −0.0574452 0.0574452i 0.677801 0.735246i \(-0.262933\pi\)
−0.735246 + 0.677801i \(0.762933\pi\)
\(368\) 19.5450 27.4975i 1.01885 1.43341i
\(369\) 0 0
\(370\) 15.8343 14.1445i 0.823186 0.735336i
\(371\) −0.736662 + 3.70345i −0.0382456 + 0.192273i
\(372\) 0 0
\(373\) 29.9517 + 20.0131i 1.55084 + 1.03624i 0.975946 + 0.218014i \(0.0699579\pi\)
0.574897 + 0.818226i \(0.305042\pi\)
\(374\) −11.5204 + 6.79249i −0.595707 + 0.351231i
\(375\) 0 0
\(376\) 5.70996 + 25.0892i 0.294469 + 1.29388i
\(377\) 0.101875 + 0.245949i 0.00524685 + 0.0126670i
\(378\) 0 0
\(379\) 3.70680 + 18.6353i 0.190405 + 0.957233i 0.951279 + 0.308332i \(0.0997708\pi\)
−0.760873 + 0.648900i \(0.775229\pi\)
\(380\) −16.1594 20.2806i −0.828961 1.04037i
\(381\) 0 0
\(382\) −7.58963 21.7044i −0.388319 1.11049i
\(383\) 22.9884 1.17465 0.587327 0.809350i \(-0.300180\pi\)
0.587327 + 0.809350i \(0.300180\pi\)
\(384\) 0 0
\(385\) 14.1119 0.719209
\(386\) −11.6396 33.2863i −0.592439 1.69423i
\(387\) 0 0
\(388\) 7.22177 + 9.06355i 0.366630 + 0.460132i
\(389\) 5.01123 + 25.1931i 0.254079 + 1.27734i 0.871377 + 0.490614i \(0.163227\pi\)
−0.617298 + 0.786729i \(0.711773\pi\)
\(390\) 0 0
\(391\) −19.6698 47.4872i −0.994747 2.40153i
\(392\) −1.09554 + 0.249330i −0.0553330 + 0.0125931i
\(393\) 0 0
\(394\) −5.09851 + 3.00611i −0.256859 + 0.151445i
\(395\) −3.89033 2.59943i −0.195744 0.130792i
\(396\) 0 0
\(397\) 0.319222 1.60484i 0.0160213 0.0805445i −0.971947 0.235198i \(-0.924426\pi\)
0.987969 + 0.154654i \(0.0494261\pi\)
\(398\) 2.05097 1.83209i 0.102806 0.0918345i
\(399\) 0 0
\(400\) 5.01808 + 29.6840i 0.250904 + 1.48420i
\(401\) 21.7278 + 21.7278i 1.08503 + 1.08503i 0.996031 + 0.0890025i \(0.0283679\pi\)
0.0890025 + 0.996031i \(0.471632\pi\)
\(402\) 0 0
\(403\) −0.630289 0.125372i −0.0313969 0.00624524i
\(404\) 1.21243 1.43460i 0.0603208 0.0713739i
\(405\) 0 0
\(406\) −0.407710 + 1.57920i −0.0202343 + 0.0783744i
\(407\) 6.08119 + 2.51891i 0.301433 + 0.124858i
\(408\) 0 0
\(409\) 17.9000 7.41442i 0.885097 0.366619i 0.106626 0.994299i \(-0.465995\pi\)
0.778472 + 0.627680i \(0.215995\pi\)
\(410\) 27.6808 3.90201i 1.36706 0.192707i
\(411\) 0 0
\(412\) −13.4033 + 24.2276i −0.660334 + 1.19361i
\(413\) −16.0355 + 10.7146i −0.789056 + 0.527231i
\(414\) 0 0
\(415\) 59.8422i 2.93754i
\(416\) −0.285495 + 3.34315i −0.0139976 + 0.163911i
\(417\) 0 0
\(418\) 3.48955 7.24227i 0.170680 0.354231i
\(419\) −27.8129 + 18.5840i −1.35875 + 0.907886i −0.999677 0.0254236i \(-0.991907\pi\)
−0.359071 + 0.933310i \(0.616907\pi\)
\(420\) 0 0
\(421\) 19.7735 3.93320i 0.963703 0.191693i 0.311929 0.950105i \(-0.399025\pi\)
0.651774 + 0.758413i \(0.274025\pi\)
\(422\) 2.95153 + 20.9381i 0.143678 + 1.01925i
\(423\) 0 0
\(424\) −1.69528 3.79493i −0.0823299 0.184298i
\(425\) 42.3764 + 17.5529i 2.05556 + 0.851439i
\(426\) 0 0
\(427\) −16.5990 + 24.8422i −0.803282 + 1.20220i
\(428\) 2.48329 + 29.5878i 0.120035 + 1.43018i
\(429\) 0 0
\(430\) 0.790429 14.0227i 0.0381178 0.676237i
\(431\) −13.5229 13.5229i −0.651373 0.651373i 0.301950 0.953324i \(-0.402362\pi\)
−0.953324 + 0.301950i \(0.902362\pi\)
\(432\) 0 0
\(433\) −17.9120 + 17.9120i −0.860797 + 0.860797i −0.991431 0.130634i \(-0.958299\pi\)
0.130634 + 0.991431i \(0.458299\pi\)
\(434\) −2.62291 2.93627i −0.125904 0.140946i
\(435\) 0 0
\(436\) 12.0302 6.20859i 0.576141 0.297338i
\(437\) 25.6899 + 17.1654i 1.22891 + 0.821134i
\(438\) 0 0
\(439\) 2.81785 6.80290i 0.134489 0.324685i −0.842260 0.539071i \(-0.818775\pi\)
0.976749 + 0.214387i \(0.0687753\pi\)
\(440\) −12.6741 + 8.98084i −0.604213 + 0.428145i
\(441\) 0 0
\(442\) 4.08400 + 3.07486i 0.194256 + 0.146256i
\(443\) −5.64485 28.3786i −0.268195 1.34831i −0.846458 0.532456i \(-0.821269\pi\)
0.578263 0.815850i \(-0.303731\pi\)
\(444\) 0 0
\(445\) 13.0963 + 19.6000i 0.620823 + 0.929127i
\(446\) 19.8419 6.93836i 0.939543 0.328541i
\(447\) 0 0
\(448\) −13.7170 + 15.3108i −0.648067 + 0.723368i
\(449\) 0.0955370 0.00450867 0.00225433 0.999997i \(-0.499282\pi\)
0.00225433 + 0.999997i \(0.499282\pi\)
\(450\) 0 0
\(451\) 4.81478 + 7.20583i 0.226719 + 0.339309i
\(452\) −1.15073 + 10.1750i −0.0541259 + 0.478590i
\(453\) 0 0
\(454\) 9.37903 + 7.06150i 0.440180 + 0.331413i
\(455\) −2.06430 4.98365i −0.0967757 0.233637i
\(456\) 0 0
\(457\) 11.4359 27.6087i 0.534949 1.29148i −0.393262 0.919426i \(-0.628654\pi\)
0.928211 0.372054i \(-0.121346\pi\)
\(458\) −2.66184 4.51463i −0.124380 0.210955i
\(459\) 0 0
\(460\) −27.3792 53.0516i −1.27656 2.47355i
\(461\) 5.29789 26.6343i 0.246747 1.24048i −0.636390 0.771368i \(-0.719573\pi\)
0.883137 0.469115i \(-0.155427\pi\)
\(462\) 0 0
\(463\) 21.3463 21.3463i 0.992048 0.992048i −0.00792071 0.999969i \(-0.502521\pi\)
0.999969 + 0.00792071i \(0.00252127\pi\)
\(464\) −0.638838 1.67777i −0.0296573 0.0778884i
\(465\) 0 0
\(466\) 1.53194 27.1776i 0.0709657 1.25898i
\(467\) −32.0458 6.37431i −1.48290 0.294968i −0.613746 0.789503i \(-0.710338\pi\)
−0.869157 + 0.494535i \(0.835338\pi\)
\(468\) 0 0
\(469\) −8.49600 + 12.7152i −0.392309 + 0.587132i
\(470\) 44.0881 + 11.3824i 2.03363 + 0.525033i
\(471\) 0 0
\(472\) 7.58291 19.8280i 0.349032 0.912655i
\(473\) 4.02275 1.66628i 0.184966 0.0766155i
\(474\) 0 0
\(475\) −27.0418 + 5.37896i −1.24077 + 0.246804i
\(476\) 8.65794 + 30.0995i 0.396836 + 1.37961i
\(477\) 0 0
\(478\) −1.47281 + 3.05670i −0.0673649 + 0.139810i
\(479\) 0.620601i 0.0283560i 0.999899 + 0.0141780i \(0.00451315\pi\)
−0.999899 + 0.0141780i \(0.995487\pi\)
\(480\) 0 0
\(481\) 2.51605i 0.114722i
\(482\) −22.9761 11.0706i −1.04653 0.504252i
\(483\) 0 0
\(484\) 15.0367 + 8.31866i 0.683486 + 0.378121i
\(485\) 20.1139 4.00090i 0.913325 0.181672i
\(486\) 0 0
\(487\) −11.7418 + 4.86361i −0.532072 + 0.220391i −0.632510 0.774552i \(-0.717975\pi\)
0.100439 + 0.994943i \(0.467975\pi\)
\(488\) −0.901832 32.8747i −0.0408240 1.48817i
\(489\) 0 0
\(490\) −0.497022 + 1.92514i −0.0224532 + 0.0869689i
\(491\) 11.9335 17.8598i 0.538553 0.806002i −0.458000 0.888952i \(-0.651434\pi\)
0.996554 + 0.0829501i \(0.0264342\pi\)
\(492\) 0 0
\(493\) −2.68271 0.533623i −0.120823 0.0240332i
\(494\) −3.06808 0.172940i −0.138039 0.00778095i
\(495\) 0 0
\(496\) 4.22432 + 0.967875i 0.189678 + 0.0434589i
\(497\) −17.8117 + 17.8117i −0.798964 + 0.798964i
\(498\) 0 0
\(499\) 5.81742 29.2462i 0.260424 1.30924i −0.600140 0.799895i \(-0.704888\pi\)
0.860564 0.509343i \(-0.170112\pi\)
\(500\) 17.0355 + 5.43752i 0.761852 + 0.243173i
\(501\) 0 0
\(502\) 0.203249 0.119836i 0.00907144 0.00534856i
\(503\) −10.2519 + 24.7502i −0.457108 + 1.10356i 0.512455 + 0.858714i \(0.328736\pi\)
−0.969563 + 0.244842i \(0.921264\pi\)
\(504\) 0 0
\(505\) −1.27201 3.07089i −0.0566035 0.136653i
\(506\) 11.1323 14.7858i 0.494890 0.657308i
\(507\) 0 0
\(508\) 8.25535 6.57780i 0.366272 0.291843i
\(509\) 3.45815 + 5.17549i 0.153280 + 0.229399i 0.900160 0.435559i \(-0.143449\pi\)
−0.746880 + 0.664958i \(0.768449\pi\)
\(510\) 0 0
\(511\) −8.03904 −0.355626
\(512\) 2.57558 22.4804i 0.113826 0.993501i
\(513\) 0 0
\(514\) −0.609468 1.74292i −0.0268825 0.0768771i
\(515\) 27.2215 + 40.7399i 1.19952 + 1.79521i
\(516\) 0 0
\(517\) 2.75394 + 13.8450i 0.121118 + 0.608902i
\(518\) 9.27178 12.3147i 0.407378 0.541077i
\(519\) 0 0
\(520\) 5.02558 + 3.16216i 0.220386 + 0.138670i
\(521\) 13.3796 32.3011i 0.586169 1.41514i −0.300969 0.953634i \(-0.597310\pi\)
0.887138 0.461504i \(-0.152690\pi\)
\(522\) 0 0
\(523\) −29.7773 19.8966i −1.30207 0.870016i −0.305455 0.952207i \(-0.598808\pi\)
−0.996617 + 0.0821904i \(0.973808\pi\)
\(524\) −10.9666 3.50041i −0.479080 0.152916i
\(525\) 0 0
\(526\) 12.2837 10.9728i 0.535595 0.478437i
\(527\) 4.66896 4.66896i 0.203383 0.203383i
\(528\) 0 0
\(529\) 34.0347 + 34.0347i 1.47977 + 1.47977i
\(530\) −7.34356 0.413939i −0.318984 0.0179803i
\(531\) 0 0
\(532\) −14.3793 12.1525i −0.623420 0.526876i
\(533\) 1.84045 2.75442i 0.0797186 0.119307i
\(534\) 0 0
\(535\) 48.5437 + 20.1074i 2.09873 + 0.869321i
\(536\) −0.461592 16.8265i −0.0199377 0.726795i
\(537\) 0 0
\(538\) 17.8307 2.51349i 0.768735 0.108364i
\(539\) −0.604552 + 0.120253i −0.0260399 + 0.00517966i
\(540\) 0 0
\(541\) −33.4281 + 22.3359i −1.43718 + 0.960296i −0.439099 + 0.898439i \(0.644702\pi\)
−0.998085 + 0.0618571i \(0.980298\pi\)
\(542\) 10.6437 + 5.12847i 0.457186 + 0.220287i
\(543\) 0 0
\(544\) −26.9312 21.5228i −1.15466 0.922781i
\(545\) 23.9568i 1.02620i
\(546\) 0 0
\(547\) −2.75272 + 1.83931i −0.117698 + 0.0786432i −0.613026 0.790063i \(-0.710048\pi\)
0.495328 + 0.868706i \(0.335048\pi\)
\(548\) −5.47536 19.0352i −0.233896 0.813143i
\(549\) 0 0
\(550\) 2.30538 + 16.3544i 0.0983019 + 0.697353i
\(551\) 1.51904 0.629206i 0.0647132 0.0268051i
\(552\) 0 0
\(553\) −3.13839 1.29996i −0.133458 0.0552801i
\(554\) −0.152644 0.0394089i −0.00648523 0.00167432i
\(555\) 0 0
\(556\) 4.20927 0.353283i 0.178513 0.0149825i
\(557\) −42.1945 8.39301i −1.78784 0.355623i −0.813650 0.581355i \(-0.802523\pi\)
−0.974190 + 0.225731i \(0.927523\pi\)
\(558\) 0 0
\(559\) −1.17690 1.17690i −0.0497775 0.0497775i
\(560\) 12.9447 + 33.9965i 0.547015 + 1.43662i
\(561\) 0 0
\(562\) 8.58278 + 9.60815i 0.362043 + 0.405296i
\(563\) 2.34500 11.7891i 0.0988299 0.496852i −0.899387 0.437154i \(-0.855986\pi\)
0.998217 0.0596975i \(-0.0190136\pi\)
\(564\) 0 0
\(565\) 15.0668 + 10.0673i 0.633863 + 0.423534i
\(566\) 8.51947 + 14.4495i 0.358100 + 0.607356i
\(567\) 0 0
\(568\) 4.66151 27.3323i 0.195592 1.14684i
\(569\) 2.83292 + 6.83927i 0.118762 + 0.286717i 0.972070 0.234690i \(-0.0754074\pi\)
−0.853308 + 0.521407i \(0.825407\pi\)
\(570\) 0 0
\(571\) 6.93430 + 34.8611i 0.290191 + 1.45889i 0.800725 + 0.599032i \(0.204448\pi\)
−0.510534 + 0.859858i \(0.670552\pi\)
\(572\) −0.206862 + 1.82911i −0.00864936 + 0.0764790i
\(573\) 0 0
\(574\) 19.1582 6.69925i 0.799646 0.279621i
\(575\) −63.4766 −2.64716
\(576\) 0 0
\(577\) 24.2433 1.00926 0.504632 0.863335i \(-0.331628\pi\)
0.504632 + 0.863335i \(0.331628\pi\)
\(578\) −26.8875 + 9.40205i −1.11837 + 0.391074i
\(579\) 0 0
\(580\) −3.15684 0.357021i −0.131081 0.0148245i
\(581\) 8.47608 + 42.6121i 0.351647 + 1.76785i
\(582\) 0 0
\(583\) −0.872611 2.10667i −0.0361398 0.0872493i
\(584\) 7.21996 5.11606i 0.298764 0.211704i
\(585\) 0 0
\(586\) −0.0734546 0.124583i −0.00303438 0.00514647i
\(587\) −12.8222 8.56752i −0.529229 0.353619i 0.262070 0.965049i \(-0.415595\pi\)
−0.791299 + 0.611429i \(0.790595\pi\)
\(588\) 0 0
\(589\) −0.774328 + 3.89281i −0.0319056 + 0.160400i
\(590\) −25.0264 28.0163i −1.03032 1.15341i
\(591\) 0 0
\(592\) −0.489999 + 16.9606i −0.0201389 + 0.697075i
\(593\) 7.17902 + 7.17902i 0.294807 + 0.294807i 0.838976 0.544169i \(-0.183155\pi\)
−0.544169 + 0.838976i \(0.683155\pi\)
\(594\) 0 0
\(595\) 54.3595 + 10.8128i 2.22852 + 0.443281i
\(596\) 3.01453 + 35.9172i 0.123480 + 1.47123i
\(597\) 0 0
\(598\) −6.85007 1.76852i −0.280120 0.0723200i
\(599\) 37.8559 + 15.6804i 1.54675 + 0.640685i 0.982725 0.185073i \(-0.0592522\pi\)
0.564025 + 0.825758i \(0.309252\pi\)
\(600\) 0 0
\(601\) −32.5429 + 13.4797i −1.32745 + 0.549850i −0.929928 0.367741i \(-0.880131\pi\)
−0.397526 + 0.917591i \(0.630131\pi\)
\(602\) −1.42335 10.0972i −0.0580112 0.411531i
\(603\) 0 0
\(604\) 10.3860 2.98746i 0.422599 0.121558i
\(605\) 25.2849 16.8948i 1.02798 0.686872i
\(606\) 0 0
\(607\) 37.4709i 1.52090i −0.649399 0.760448i \(-0.724979\pi\)
0.649399 0.760448i \(-0.275021\pi\)
\(608\) 20.6481 + 1.76329i 0.837389 + 0.0715107i
\(609\) 0 0
\(610\) −52.4291 25.2620i −2.12279 1.02283i
\(611\) 4.48655 2.99781i 0.181506 0.121279i
\(612\) 0 0
\(613\) 3.83710 0.763246i 0.154979 0.0308272i −0.116991 0.993133i \(-0.537325\pi\)
0.271970 + 0.962306i \(0.412325\pi\)
\(614\) 32.0664 4.52021i 1.29409 0.182421i
\(615\) 0 0
\(616\) −7.75284 + 8.19020i −0.312371 + 0.329992i
\(617\) 37.8776 + 15.6894i 1.52490 + 0.631633i 0.978565 0.205937i \(-0.0660241\pi\)
0.546331 + 0.837569i \(0.316024\pi\)
\(618\) 0 0
\(619\) 22.0632 33.0200i 0.886796 1.32718i −0.0575877 0.998340i \(-0.518341\pi\)
0.944384 0.328844i \(-0.106659\pi\)
\(620\) 4.95037 5.85747i 0.198812 0.235242i
\(621\) 0 0
\(622\) 23.9351 + 1.34916i 0.959711 + 0.0540966i
\(623\) 12.1017 + 12.1017i 0.484843 + 0.484843i
\(624\) 0 0
\(625\) −4.23310 + 4.23310i −0.169324 + 0.169324i
\(626\) 19.1430 17.1001i 0.765109 0.683457i
\(627\) 0 0
\(628\) −5.15277 + 16.1434i −0.205618 + 0.644192i
\(629\) 21.4949 + 14.3624i 0.857058 + 0.572668i
\(630\) 0 0
\(631\) −0.295581 + 0.713596i −0.0117669 + 0.0284078i −0.929654 0.368434i \(-0.879894\pi\)
0.917887 + 0.396842i \(0.129894\pi\)
\(632\) 3.64593 0.829765i 0.145027 0.0330063i
\(633\) 0 0
\(634\) −16.8321 + 22.3562i −0.668487 + 0.887879i
\(635\) −3.64414 18.3203i −0.144613 0.727020i
\(636\) 0 0
\(637\) 0.130902 + 0.195908i 0.00518652 + 0.00776217i
\(638\) −0.325103 0.929711i −0.0128709 0.0368076i
\(639\) 0 0
\(640\) −33.2613 22.2946i −1.31477 0.881273i
\(641\) −20.3094 −0.802172 −0.401086 0.916040i \(-0.631367\pi\)
−0.401086 + 0.916040i \(0.631367\pi\)
\(642\) 0 0
\(643\) −6.26132 9.37072i −0.246922 0.369545i 0.687218 0.726451i \(-0.258832\pi\)
−0.934140 + 0.356906i \(0.883832\pi\)
\(644\) −27.0103 33.8988i −1.06435 1.33580i
\(645\) 0 0
\(646\) 18.9910 25.2237i 0.747192 0.992414i
\(647\) 0.189930 + 0.458531i 0.00746691 + 0.0180267i 0.927569 0.373652i \(-0.121895\pi\)
−0.920102 + 0.391679i \(0.871895\pi\)
\(648\) 0 0
\(649\) 4.45682 10.7597i 0.174945 0.422356i
\(650\) 5.43836 3.20648i 0.213310 0.125769i
\(651\) 0 0
\(652\) −0.672824 + 2.10793i −0.0263498 + 0.0825528i
\(653\) −4.73978 + 23.8285i −0.185482 + 0.932481i 0.770138 + 0.637878i \(0.220187\pi\)
−0.955620 + 0.294603i \(0.904813\pi\)
\(654\) 0 0
\(655\) −14.4048 + 14.4048i −0.562842 + 0.562842i
\(656\) −12.9428 + 18.2090i −0.505330 + 0.710941i
\(657\) 0 0
\(658\) 33.0063 + 1.86048i 1.28672 + 0.0725292i
\(659\) 38.0620 + 7.57099i 1.48268 + 0.294924i 0.869073 0.494685i \(-0.164716\pi\)
0.613611 + 0.789609i \(0.289716\pi\)
\(660\) 0 0
\(661\) 5.84250 8.74392i 0.227247 0.340099i −0.700271 0.713877i \(-0.746938\pi\)
0.927518 + 0.373778i \(0.121938\pi\)
\(662\) 2.54027 9.83937i 0.0987306 0.382418i
\(663\) 0 0
\(664\) −34.7309 32.8763i −1.34782 1.27585i
\(665\) −30.7802 + 12.7496i −1.19360 + 0.494407i
\(666\) 0 0
\(667\) 3.71261 0.738483i 0.143753 0.0285942i
\(668\) −2.74384 + 4.95972i −0.106162 + 0.191898i
\(669\) 0 0
\(670\) −26.8352 12.9300i −1.03673 0.499531i
\(671\) 18.0423i 0.696515i
\(672\) 0 0
\(673\) 40.4801i 1.56039i −0.625534 0.780197i \(-0.715119\pi\)
0.625534 0.780197i \(-0.284881\pi\)
\(674\) 16.0362 33.2817i 0.617690 1.28196i
\(675\) 0 0
\(676\) −24.3106 + 6.99281i −0.935024 + 0.268954i
\(677\) −28.0273 + 5.57498i −1.07718 + 0.214264i −0.701632 0.712540i \(-0.747545\pi\)
−0.375546 + 0.926804i \(0.622545\pi\)
\(678\) 0 0
\(679\) 13.7559 5.69788i 0.527903 0.218665i
\(680\) −55.7023 + 24.8834i −2.13608 + 0.954236i
\(681\) 0 0
\(682\) 2.30209 + 0.594341i 0.0881515 + 0.0227585i
\(683\) −10.1966 + 15.2603i −0.390163 + 0.583920i −0.973606 0.228234i \(-0.926705\pi\)
0.583443 + 0.812154i \(0.301705\pi\)
\(684\) 0 0
\(685\) −34.3775 6.83811i −1.31350 0.261271i
\(686\) −1.51282 + 26.8385i −0.0577598 + 1.02470i
\(687\) 0 0
\(688\) 7.70421 + 8.16261i 0.293720 + 0.311196i
\(689\) −0.616329 + 0.616329i −0.0234803 + 0.0234803i
\(690\) 0 0
\(691\) −0.695696 + 3.49750i −0.0264655 + 0.133051i −0.991759 0.128115i \(-0.959107\pi\)
0.965294 + 0.261167i \(0.0841072\pi\)
\(692\) 18.5673 9.58233i 0.705824 0.364265i
\(693\) 0 0
\(694\) −6.68117 11.3316i −0.253614 0.430142i
\(695\) 2.86056 6.90601i 0.108507 0.261960i
\(696\) 0 0
\(697\) 13.0255 + 31.4463i 0.493375 + 1.19111i
\(698\) 12.8640 + 9.68533i 0.486908 + 0.366595i
\(699\) 0 0
\(700\) 38.4338 + 4.34665i 1.45266 + 0.164288i
\(701\) −8.71090 13.0368i −0.329006 0.492393i 0.629681 0.776853i \(-0.283185\pi\)
−0.958688 + 0.284461i \(0.908185\pi\)
\(702\) 0 0
\(703\) −15.5397 −0.586092
\(704\) 1.75067 12.2896i 0.0659807 0.463183i
\(705\) 0 0
\(706\) 16.3648 5.72245i 0.615896 0.215367i
\(707\) −1.34073 2.00654i −0.0504232 0.0754637i
\(708\) 0 0
\(709\) −0.737183 3.70607i −0.0276855 0.139184i 0.964470 0.264191i \(-0.0851048\pi\)
−0.992156 + 0.125006i \(0.960105\pi\)
\(710\) −39.1984 29.5126i −1.47109 1.10759i
\(711\) 0 0
\(712\) −18.5702 3.16714i −0.695948 0.118693i
\(713\) −3.49688 + 8.44221i −0.130959 + 0.316163i
\(714\) 0 0
\(715\) 2.70849 + 1.80976i 0.101292 + 0.0676810i
\(716\) −17.8427 34.5731i −0.666812 1.29206i
\(717\) 0 0
\(718\) 7.08858 + 7.93544i 0.264543 + 0.296148i
\(719\) 36.7070 36.7070i 1.36894 1.36894i 0.506985 0.861955i \(-0.330760\pi\)
0.861955 0.506985i \(-0.169240\pi\)
\(720\) 0 0
\(721\) 25.1542 + 25.1542i 0.936790 + 0.936790i
\(722\) 0.444081 7.87830i 0.0165270 0.293200i
\(723\) 0 0
\(724\) −7.98058 + 0.669808i −0.296596 + 0.0248932i
\(725\) −1.87668 + 2.80865i −0.0696982 + 0.104311i
\(726\) 0 0
\(727\) −3.90063 1.61569i −0.144666 0.0599228i 0.309176 0.951005i \(-0.399947\pi\)
−0.453842 + 0.891082i \(0.649947\pi\)
\(728\) 4.02648 + 1.53987i 0.149231 + 0.0570713i
\(729\) 0 0
\(730\) −2.18577 15.5058i −0.0808988 0.573896i
\(731\) 16.7725 3.33626i 0.620353 0.123396i
\(732\) 0 0
\(733\) 10.5958 7.07991i 0.391366 0.261502i −0.344282 0.938866i \(-0.611878\pi\)
0.735648 + 0.677364i \(0.236878\pi\)
\(734\) 0.955384 1.98282i 0.0352639 0.0731872i
\(735\) 0 0
\(736\) 45.8315 + 13.2555i 1.68937 + 0.488604i
\(737\) 9.23473i 0.340166i
\(738\) 0 0
\(739\) −5.97439 + 3.99196i −0.219772 + 0.146847i −0.660583 0.750753i \(-0.729691\pi\)
0.440811 + 0.897600i \(0.354691\pi\)
\(740\) 26.2737 + 14.5352i 0.965841 + 0.534326i
\(741\) 0 0
\(742\) −5.28780 + 0.745390i −0.194121 + 0.0273641i
\(743\) 16.8050 6.96086i 0.616515 0.255369i −0.0524960 0.998621i \(-0.516718\pi\)
0.669011 + 0.743252i \(0.266718\pi\)
\(744\) 0 0
\(745\) 58.9283 + 24.4089i 2.15896 + 0.894272i
\(746\) −12.7348 + 49.3263i −0.466255 + 1.80597i
\(747\) 0 0
\(748\) −14.4455 12.2084i −0.528178 0.446383i
\(749\) 37.4148 + 7.44226i 1.36711 + 0.271934i
\(750\) 0 0
\(751\) 25.4171 + 25.4171i 0.927482 + 0.927482i 0.997543 0.0700603i \(-0.0223192\pi\)
−0.0700603 + 0.997543i \(0.522319\pi\)
\(752\) −30.8274 + 19.3343i −1.12416 + 0.705051i
\(753\) 0 0
\(754\) −0.280773 + 0.250809i −0.0102252 + 0.00913394i
\(755\) 3.73100 18.7570i 0.135785 0.682638i
\(756\) 0 0
\(757\) −28.3377 18.9346i −1.02995 0.688192i −0.0787918 0.996891i \(-0.525106\pi\)
−0.951160 + 0.308700i \(0.900106\pi\)
\(758\) −23.1469 + 13.6475i −0.840732 + 0.495699i
\(759\) 0 0
\(760\) 19.5302 31.0391i 0.708436 1.12591i
\(761\) −3.25313 7.85375i −0.117926 0.284698i 0.853884 0.520463i \(-0.174241\pi\)
−0.971810 + 0.235765i \(0.924241\pi\)
\(762\) 0 0
\(763\) −3.39325 17.0590i −0.122844 0.617578i
\(764\) 25.4314 20.2636i 0.920076 0.733110i
\(765\) 0 0
\(766\) 10.7312 + 30.6884i 0.387733 + 1.10882i
\(767\) −4.45177 −0.160744
\(768\) 0 0
\(769\) 0.673777 0.0242970 0.0121485 0.999926i \(-0.496133\pi\)
0.0121485 + 0.999926i \(0.496133\pi\)
\(770\) 6.58754 + 18.8387i 0.237398 + 0.678899i
\(771\) 0 0
\(772\) 39.0020 31.0765i 1.40371 1.11847i
\(773\) −9.93498 49.9465i −0.357336 1.79645i −0.572534 0.819881i \(-0.694040\pi\)
0.215198 0.976570i \(-0.430960\pi\)
\(774\) 0 0
\(775\) −3.12052 7.53361i −0.112092 0.270615i
\(776\) −8.72821 + 13.8716i −0.313324 + 0.497963i
\(777\) 0 0
\(778\) −31.2923 + 18.4501i −1.12188 + 0.661467i
\(779\) −17.0120 11.3670i −0.609517 0.407266i
\(780\) 0 0
\(781\) 2.96760 14.9191i 0.106189 0.533848i
\(782\) 54.2110 48.4256i 1.93858 1.73170i
\(783\) 0 0
\(784\) −0.844248 1.34610i −0.0301517 0.0480750i
\(785\) 21.2045 + 21.2045i 0.756821 + 0.756821i
\(786\) 0 0
\(787\) −50.7402 10.0929i −1.80869 0.359772i −0.828840 0.559486i \(-0.810999\pi\)
−0.979854 + 0.199715i \(0.935999\pi\)
\(788\) −6.39302