Properties

Label 819.2.et.c.145.2
Level $819$
Weight $2$
Character 819.145
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 145.2
Character \(\chi\) \(=\) 819.145
Dual form 819.2.et.c.514.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.55654 + 1.55654i) q^{2} -2.84566i q^{4} +(-3.12520 + 0.837395i) q^{5} +(1.93981 + 1.79920i) q^{7} +(1.31631 + 1.31631i) q^{8} +O(q^{10})\) \(q+(-1.55654 + 1.55654i) q^{2} -2.84566i q^{4} +(-3.12520 + 0.837395i) q^{5} +(1.93981 + 1.79920i) q^{7} +(1.31631 + 1.31631i) q^{8} +(3.56107 - 6.16796i) q^{10} +(3.89463 - 1.04356i) q^{11} +(-2.61925 - 2.47781i) q^{13} +(-5.81994 + 0.218864i) q^{14} +1.59353 q^{16} +7.61003 q^{17} +(-0.714314 + 2.66585i) q^{19} +(2.38294 + 8.89327i) q^{20} +(-4.43782 + 7.68652i) q^{22} -4.49695i q^{23} +(4.73553 - 2.73406i) q^{25} +(7.93380 - 0.220148i) q^{26} +(5.11992 - 5.52005i) q^{28} +(-1.49169 - 2.58368i) q^{29} +(0.691794 - 2.58181i) q^{31} +(-5.11302 + 5.11302i) q^{32} +(-11.8454 + 11.8454i) q^{34} +(-7.56895 - 3.99848i) q^{35} +(1.20113 + 1.20113i) q^{37} +(-3.03766 - 5.26138i) q^{38} +(-5.21601 - 3.01147i) q^{40} +(-2.95120 + 11.0140i) q^{41} +(6.30996 + 3.64306i) q^{43} +(-2.96963 - 11.0828i) q^{44} +(6.99971 + 6.99971i) q^{46} +(0.666302 + 2.48667i) q^{47} +(0.525739 + 6.98023i) q^{49} +(-3.11538 + 11.6267i) q^{50} +(-7.05102 + 7.45349i) q^{52} +(3.91287 + 6.77729i) q^{53} +(-11.2976 + 6.52269i) q^{55} +(0.185085 + 4.92171i) q^{56} +(6.34349 + 1.69973i) q^{58} +(5.78594 - 5.78594i) q^{59} +(-7.97503 + 4.60439i) q^{61} +(2.94189 + 5.09551i) q^{62} -12.7302i q^{64} +(10.2606 + 5.55032i) q^{65} +(2.02258 + 7.54839i) q^{67} -21.6556i q^{68} +(18.0052 - 5.55759i) q^{70} +(0.721147 + 2.69136i) q^{71} +(1.69255 + 0.453517i) q^{73} -3.73923 q^{74} +(7.58612 + 2.03270i) q^{76} +(9.43244 + 4.98292i) q^{77} +(4.31023 - 7.46554i) q^{79} +(-4.98010 + 1.33441i) q^{80} +(-12.5501 - 21.7375i) q^{82} +(-1.63865 - 1.63865i) q^{83} +(-23.7829 + 6.37260i) q^{85} +(-15.4923 + 4.15115i) q^{86} +(6.50021 + 3.75290i) q^{88} +(-12.7524 + 12.7524i) q^{89} +(-0.622758 - 9.51904i) q^{91} -12.7968 q^{92} +(-4.90774 - 2.83349i) q^{94} -8.92950i q^{95} +(12.7508 - 3.41658i) q^{97} +(-11.6834 - 10.0467i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.55654 + 1.55654i −1.10064 + 1.10064i −0.106310 + 0.994333i \(0.533904\pi\)
−0.994333 + 0.106310i \(0.966096\pi\)
\(3\) 0 0
\(4\) 2.84566i 1.42283i
\(5\) −3.12520 + 0.837395i −1.39763 + 0.374495i −0.877494 0.479587i \(-0.840786\pi\)
−0.520139 + 0.854082i \(0.674120\pi\)
\(6\) 0 0
\(7\) 1.93981 + 1.79920i 0.733180 + 0.680035i
\(8\) 1.31631 + 1.31631i 0.465386 + 0.465386i
\(9\) 0 0
\(10\) 3.56107 6.16796i 1.12611 1.95048i
\(11\) 3.89463 1.04356i 1.17428 0.314646i 0.381622 0.924318i \(-0.375366\pi\)
0.792654 + 0.609672i \(0.208699\pi\)
\(12\) 0 0
\(13\) −2.61925 2.47781i −0.726448 0.687221i
\(14\) −5.81994 + 0.218864i −1.55545 + 0.0584939i
\(15\) 0 0
\(16\) 1.59353 0.398382
\(17\) 7.61003 1.84570 0.922852 0.385156i \(-0.125852\pi\)
0.922852 + 0.385156i \(0.125852\pi\)
\(18\) 0 0
\(19\) −0.714314 + 2.66585i −0.163875 + 0.611589i 0.834306 + 0.551301i \(0.185869\pi\)
−0.998181 + 0.0602878i \(0.980798\pi\)
\(20\) 2.38294 + 8.89327i 0.532843 + 1.98860i
\(21\) 0 0
\(22\) −4.43782 + 7.68652i −0.946146 + 1.63877i
\(23\) 4.49695i 0.937679i −0.883283 0.468840i \(-0.844672\pi\)
0.883283 0.468840i \(-0.155328\pi\)
\(24\) 0 0
\(25\) 4.73553 2.73406i 0.947106 0.546812i
\(26\) 7.93380 0.220148i 1.55595 0.0431746i
\(27\) 0 0
\(28\) 5.11992 5.52005i 0.967575 1.04319i
\(29\) −1.49169 2.58368i −0.276999 0.479777i 0.693638 0.720323i \(-0.256007\pi\)
−0.970638 + 0.240547i \(0.922673\pi\)
\(30\) 0 0
\(31\) 0.691794 2.58181i 0.124250 0.463707i −0.875562 0.483106i \(-0.839509\pi\)
0.999812 + 0.0193991i \(0.00617531\pi\)
\(32\) −5.11302 + 5.11302i −0.903863 + 0.903863i
\(33\) 0 0
\(34\) −11.8454 + 11.8454i −2.03146 + 2.03146i
\(35\) −7.56895 3.99848i −1.27939 0.675867i
\(36\) 0 0
\(37\) 1.20113 + 1.20113i 0.197465 + 0.197465i 0.798912 0.601447i \(-0.205409\pi\)
−0.601447 + 0.798912i \(0.705409\pi\)
\(38\) −3.03766 5.26138i −0.492774 0.853509i
\(39\) 0 0
\(40\) −5.21601 3.01147i −0.824724 0.476155i
\(41\) −2.95120 + 11.0140i −0.460900 + 1.72010i 0.209239 + 0.977865i \(0.432901\pi\)
−0.670138 + 0.742236i \(0.733765\pi\)
\(42\) 0 0
\(43\) 6.30996 + 3.64306i 0.962260 + 0.555561i 0.896868 0.442298i \(-0.145837\pi\)
0.0653923 + 0.997860i \(0.479170\pi\)
\(44\) −2.96963 11.0828i −0.447689 1.67080i
\(45\) 0 0
\(46\) 6.99971 + 6.99971i 1.03205 + 1.03205i
\(47\) 0.666302 + 2.48667i 0.0971901 + 0.362718i 0.997342 0.0728569i \(-0.0232116\pi\)
−0.900152 + 0.435575i \(0.856545\pi\)
\(48\) 0 0
\(49\) 0.525739 + 6.98023i 0.0751056 + 0.997176i
\(50\) −3.11538 + 11.6267i −0.440581 + 1.64427i
\(51\) 0 0
\(52\) −7.05102 + 7.45349i −0.977800 + 1.03361i
\(53\) 3.91287 + 6.77729i 0.537474 + 0.930933i 0.999039 + 0.0438262i \(0.0139548\pi\)
−0.461565 + 0.887106i \(0.652712\pi\)
\(54\) 0 0
\(55\) −11.2976 + 6.52269i −1.52337 + 0.879520i
\(56\) 0.185085 + 4.92171i 0.0247331 + 0.657691i
\(57\) 0 0
\(58\) 6.34349 + 1.69973i 0.832941 + 0.223186i
\(59\) 5.78594 5.78594i 0.753265 0.753265i −0.221822 0.975087i \(-0.571200\pi\)
0.975087 + 0.221822i \(0.0712003\pi\)
\(60\) 0 0
\(61\) −7.97503 + 4.60439i −1.02110 + 0.589531i −0.914422 0.404763i \(-0.867354\pi\)
−0.106676 + 0.994294i \(0.534021\pi\)
\(62\) 2.94189 + 5.09551i 0.373621 + 0.647130i
\(63\) 0 0
\(64\) 12.7302i 1.59128i
\(65\) 10.2606 + 5.55032i 1.27267 + 0.688432i
\(66\) 0 0
\(67\) 2.02258 + 7.54839i 0.247098 + 0.922182i 0.972317 + 0.233664i \(0.0750717\pi\)
−0.725219 + 0.688518i \(0.758262\pi\)
\(68\) 21.6556i 2.62612i
\(69\) 0 0
\(70\) 18.0052 5.55759i 2.15204 0.664259i
\(71\) 0.721147 + 2.69136i 0.0855844 + 0.319405i 0.995424 0.0955544i \(-0.0304624\pi\)
−0.909840 + 0.414960i \(0.863796\pi\)
\(72\) 0 0
\(73\) 1.69255 + 0.453517i 0.198098 + 0.0530802i 0.356504 0.934294i \(-0.383969\pi\)
−0.158406 + 0.987374i \(0.550635\pi\)
\(74\) −3.73923 −0.434677
\(75\) 0 0
\(76\) 7.58612 + 2.03270i 0.870188 + 0.233166i
\(77\) 9.43244 + 4.98292i 1.07493 + 0.567856i
\(78\) 0 0
\(79\) 4.31023 7.46554i 0.484939 0.839939i −0.514911 0.857244i \(-0.672175\pi\)
0.999850 + 0.0173043i \(0.00550840\pi\)
\(80\) −4.98010 + 1.33441i −0.556792 + 0.149192i
\(81\) 0 0
\(82\) −12.5501 21.7375i −1.38593 2.40050i
\(83\) −1.63865 1.63865i −0.179865 0.179865i 0.611432 0.791297i \(-0.290594\pi\)
−0.791297 + 0.611432i \(0.790594\pi\)
\(84\) 0 0
\(85\) −23.7829 + 6.37260i −2.57962 + 0.691206i
\(86\) −15.4923 + 4.15115i −1.67058 + 0.447631i
\(87\) 0 0
\(88\) 6.50021 + 3.75290i 0.692924 + 0.400060i
\(89\) −12.7524 + 12.7524i −1.35175 + 1.35175i −0.468049 + 0.883703i \(0.655043\pi\)
−0.883703 + 0.468049i \(0.844957\pi\)
\(90\) 0 0
\(91\) −0.622758 9.51904i −0.0652827 0.997867i
\(92\) −12.7968 −1.33416
\(93\) 0 0
\(94\) −4.90774 2.83349i −0.506195 0.292252i
\(95\) 8.92950i 0.916147i
\(96\) 0 0
\(97\) 12.7508 3.41658i 1.29465 0.346901i 0.455226 0.890376i \(-0.349559\pi\)
0.839425 + 0.543475i \(0.182892\pi\)
\(98\) −11.6834 10.0467i −1.18020 1.01487i
\(99\) 0 0
\(100\) −7.78021 13.4757i −0.778021 1.34757i
\(101\) −1.98582 + 3.43954i −0.197597 + 0.342247i −0.947749 0.319018i \(-0.896647\pi\)
0.750152 + 0.661265i \(0.229980\pi\)
\(102\) 0 0
\(103\) −1.90417 + 3.29812i −0.187623 + 0.324973i −0.944457 0.328634i \(-0.893412\pi\)
0.756834 + 0.653607i \(0.226745\pi\)
\(104\) −0.186171 6.70932i −0.0182556 0.657903i
\(105\) 0 0
\(106\) −16.6397 4.45860i −1.61619 0.433057i
\(107\) 6.86597 0.663758 0.331879 0.943322i \(-0.392317\pi\)
0.331879 + 0.943322i \(0.392317\pi\)
\(108\) 0 0
\(109\) −4.71023 1.26210i −0.451158 0.120887i 0.0260833 0.999660i \(-0.491696\pi\)
−0.477241 + 0.878772i \(0.658363\pi\)
\(110\) 7.43241 27.7381i 0.708653 2.64473i
\(111\) 0 0
\(112\) 3.09115 + 2.86708i 0.292086 + 0.270914i
\(113\) 4.45378 7.71418i 0.418977 0.725689i −0.576860 0.816843i \(-0.695722\pi\)
0.995837 + 0.0911542i \(0.0290556\pi\)
\(114\) 0 0
\(115\) 3.76573 + 14.0539i 0.351156 + 1.31053i
\(116\) −7.35227 + 4.24484i −0.682642 + 0.394123i
\(117\) 0 0
\(118\) 18.0122i 1.65815i
\(119\) 14.7620 + 13.6920i 1.35323 + 1.25514i
\(120\) 0 0
\(121\) 4.55286 2.62860i 0.413896 0.238963i
\(122\) 5.24656 19.5804i 0.475001 1.77273i
\(123\) 0 0
\(124\) −7.34696 1.96861i −0.659776 0.176787i
\(125\) −1.07096 + 1.07096i −0.0957897 + 0.0957897i
\(126\) 0 0
\(127\) 5.06664 2.92523i 0.449592 0.259572i −0.258066 0.966127i \(-0.583085\pi\)
0.707658 + 0.706555i \(0.249752\pi\)
\(128\) 9.58914 + 9.58914i 0.847568 + 0.847568i
\(129\) 0 0
\(130\) −24.6104 + 7.33173i −2.15847 + 0.643035i
\(131\) −2.26616 1.30837i −0.197995 0.114313i 0.397725 0.917505i \(-0.369800\pi\)
−0.595720 + 0.803192i \(0.703133\pi\)
\(132\) 0 0
\(133\) −6.18205 + 3.88606i −0.536051 + 0.336964i
\(134\) −14.8976 8.60116i −1.28696 0.743027i
\(135\) 0 0
\(136\) 10.0172 + 10.0172i 0.858965 + 0.858965i
\(137\) 7.97460 + 7.97460i 0.681316 + 0.681316i 0.960297 0.278981i \(-0.0899966\pi\)
−0.278981 + 0.960297i \(0.589997\pi\)
\(138\) 0 0
\(139\) −2.50525 1.44641i −0.212493 0.122683i 0.389977 0.920825i \(-0.372483\pi\)
−0.602469 + 0.798142i \(0.705816\pi\)
\(140\) −11.3783 + 21.5387i −0.961645 + 1.82035i
\(141\) 0 0
\(142\) −5.31171 3.06672i −0.445749 0.257353i
\(143\) −12.7868 6.91682i −1.06928 0.578413i
\(144\) 0 0
\(145\) 6.82538 + 6.82538i 0.566817 + 0.566817i
\(146\) −3.34045 + 1.92861i −0.276458 + 0.159613i
\(147\) 0 0
\(148\) 3.41802 3.41802i 0.280959 0.280959i
\(149\) −1.38788 0.371881i −0.113699 0.0304657i 0.201521 0.979484i \(-0.435412\pi\)
−0.315220 + 0.949019i \(0.602078\pi\)
\(150\) 0 0
\(151\) 2.07821 7.75599i 0.169122 0.631174i −0.828356 0.560202i \(-0.810723\pi\)
0.997478 0.0709714i \(-0.0226099\pi\)
\(152\) −4.44936 + 2.56884i −0.360890 + 0.208360i
\(153\) 0 0
\(154\) −22.4381 + 6.92588i −1.80812 + 0.558103i
\(155\) 8.64798i 0.694623i
\(156\) 0 0
\(157\) −1.71529 + 0.990321i −0.136895 + 0.0790362i −0.566883 0.823798i \(-0.691851\pi\)
0.429989 + 0.902834i \(0.358518\pi\)
\(158\) 4.91138 + 18.3295i 0.390728 + 1.45822i
\(159\) 0 0
\(160\) 11.6976 20.2609i 0.924777 1.60176i
\(161\) 8.09093 8.72324i 0.637654 0.687488i
\(162\) 0 0
\(163\) −0.0288858 + 0.107803i −0.00226251 + 0.00844379i −0.967048 0.254595i \(-0.918058\pi\)
0.964785 + 0.263038i \(0.0847246\pi\)
\(164\) 31.3422 + 8.39811i 2.44741 + 0.655782i
\(165\) 0 0
\(166\) 5.10125 0.395934
\(167\) 21.7275 + 5.82186i 1.68132 + 0.450509i 0.968128 0.250456i \(-0.0805805\pi\)
0.713195 + 0.700965i \(0.247247\pi\)
\(168\) 0 0
\(169\) 0.720896 + 12.9800i 0.0554536 + 0.998461i
\(170\) 27.0999 46.9384i 2.07847 3.60001i
\(171\) 0 0
\(172\) 10.3669 17.9560i 0.790470 1.36913i
\(173\) −2.36409 4.09472i −0.179738 0.311316i 0.762053 0.647515i \(-0.224192\pi\)
−0.941791 + 0.336199i \(0.890858\pi\)
\(174\) 0 0
\(175\) 14.1052 + 3.21662i 1.06625 + 0.243153i
\(176\) 6.20621 1.66295i 0.467811 0.125350i
\(177\) 0 0
\(178\) 39.6994i 2.97559i
\(179\) −19.8416 11.4556i −1.48303 0.856228i −0.483217 0.875501i \(-0.660532\pi\)
−0.999814 + 0.0192725i \(0.993865\pi\)
\(180\) 0 0
\(181\) 4.84056 0.359796 0.179898 0.983685i \(-0.442423\pi\)
0.179898 + 0.983685i \(0.442423\pi\)
\(182\) 15.7862 + 13.8475i 1.17015 + 1.02644i
\(183\) 0 0
\(184\) 5.91939 5.91939i 0.436383 0.436383i
\(185\) −4.75961 2.74796i −0.349933 0.202034i
\(186\) 0 0
\(187\) 29.6383 7.94155i 2.16737 0.580744i
\(188\) 7.07623 1.89607i 0.516087 0.138285i
\(189\) 0 0
\(190\) 13.8992 + 13.8992i 1.00835 + 1.00835i
\(191\) 7.41350 + 12.8406i 0.536422 + 0.929111i 0.999093 + 0.0425804i \(0.0135579\pi\)
−0.462671 + 0.886530i \(0.653109\pi\)
\(192\) 0 0
\(193\) 15.1925 4.07082i 1.09358 0.293024i 0.333433 0.942774i \(-0.391793\pi\)
0.760148 + 0.649750i \(0.225126\pi\)
\(194\) −14.5292 + 25.1653i −1.04313 + 1.80676i
\(195\) 0 0
\(196\) 19.8634 1.49608i 1.41881 0.106863i
\(197\) 8.62996 + 2.31239i 0.614859 + 0.164751i 0.552790 0.833321i \(-0.313563\pi\)
0.0620697 + 0.998072i \(0.480230\pi\)
\(198\) 0 0
\(199\) 6.81178 0.482874 0.241437 0.970416i \(-0.422381\pi\)
0.241437 + 0.970416i \(0.422381\pi\)
\(200\) 9.83230 + 2.63456i 0.695249 + 0.186291i
\(201\) 0 0
\(202\) −2.26278 8.44483i −0.159209 0.594176i
\(203\) 1.75497 7.69569i 0.123175 0.540132i
\(204\) 0 0
\(205\) 36.8924i 2.57667i
\(206\) −2.16974 8.09759i −0.151173 0.564186i
\(207\) 0 0
\(208\) −4.17385 3.94847i −0.289404 0.273777i
\(209\) 11.1280i 0.769737i
\(210\) 0 0
\(211\) −1.65897 2.87342i −0.114208 0.197814i 0.803255 0.595636i \(-0.203100\pi\)
−0.917463 + 0.397821i \(0.869766\pi\)
\(212\) 19.2859 11.1347i 1.32456 0.764735i
\(213\) 0 0
\(214\) −10.6872 + 10.6872i −0.730561 + 0.730561i
\(215\) −22.7706 6.10136i −1.55294 0.416109i
\(216\) 0 0
\(217\) 5.98715 3.76355i 0.406434 0.255486i
\(218\) 9.29619 5.36716i 0.629618 0.363510i
\(219\) 0 0
\(220\) 18.5614 + 32.1493i 1.25141 + 2.16750i
\(221\) −19.9325 18.8562i −1.34081 1.26841i
\(222\) 0 0
\(223\) −5.97866 + 22.3127i −0.400361 + 1.49417i 0.412094 + 0.911141i \(0.364798\pi\)
−0.812455 + 0.583024i \(0.801869\pi\)
\(224\) −19.1177 + 0.718937i −1.27735 + 0.0480360i
\(225\) 0 0
\(226\) 5.07495 + 18.9400i 0.337581 + 1.25987i
\(227\) 12.2034 + 12.2034i 0.809965 + 0.809965i 0.984628 0.174663i \(-0.0558836\pi\)
−0.174663 + 0.984628i \(0.555884\pi\)
\(228\) 0 0
\(229\) 1.95525 + 7.29710i 0.129207 + 0.482206i 0.999955 0.00952370i \(-0.00303153\pi\)
−0.870748 + 0.491730i \(0.836365\pi\)
\(230\) −27.7370 16.0140i −1.82892 1.05593i
\(231\) 0 0
\(232\) 1.43740 5.36445i 0.0943699 0.352193i
\(233\) 18.4325 + 10.6420i 1.20755 + 0.697181i 0.962224 0.272258i \(-0.0877705\pi\)
0.245330 + 0.969440i \(0.421104\pi\)
\(234\) 0 0
\(235\) −4.16465 7.21339i −0.271672 0.470550i
\(236\) −16.4648 16.4648i −1.07177 1.07177i
\(237\) 0 0
\(238\) −44.2899 + 1.66556i −2.87089 + 0.107962i
\(239\) 14.8128 14.8128i 0.958161 0.958161i −0.0409982 0.999159i \(-0.513054\pi\)
0.999159 + 0.0409982i \(0.0130538\pi\)
\(240\) 0 0
\(241\) −3.26162 + 3.26162i −0.210100 + 0.210100i −0.804310 0.594210i \(-0.797465\pi\)
0.594210 + 0.804310i \(0.297465\pi\)
\(242\) −2.99521 + 11.1783i −0.192539 + 0.718566i
\(243\) 0 0
\(244\) 13.1025 + 22.6942i 0.838804 + 1.45285i
\(245\) −7.48825 21.3744i −0.478407 1.36556i
\(246\) 0 0
\(247\) 8.47645 5.21259i 0.539344 0.331669i
\(248\) 4.30908 2.48785i 0.273627 0.157979i
\(249\) 0 0
\(250\) 3.33400i 0.210861i
\(251\) −7.81358 + 13.5335i −0.493189 + 0.854228i −0.999969 0.00784717i \(-0.997502\pi\)
0.506780 + 0.862075i \(0.330835\pi\)
\(252\) 0 0
\(253\) −4.69286 17.5140i −0.295037 1.10109i
\(254\) −3.33321 + 12.4397i −0.209144 + 0.780536i
\(255\) 0 0
\(256\) −4.39137 −0.274461
\(257\) 3.90912 0.243844 0.121922 0.992540i \(-0.461094\pi\)
0.121922 + 0.992540i \(0.461094\pi\)
\(258\) 0 0
\(259\) 0.168890 + 4.49105i 0.0104943 + 0.279060i
\(260\) 15.7943 29.1981i 0.979523 1.81079i
\(261\) 0 0
\(262\) 5.56391 1.49084i 0.343739 0.0921047i
\(263\) 0.922323 1.59751i 0.0568729 0.0985067i −0.836187 0.548444i \(-0.815220\pi\)
0.893060 + 0.449937i \(0.148554\pi\)
\(264\) 0 0
\(265\) −17.9038 17.9038i −1.09982 1.09982i
\(266\) 3.57380 15.6715i 0.219124 0.960879i
\(267\) 0 0
\(268\) 21.4802 5.75559i 1.31211 0.351579i
\(269\) 0.812046i 0.0495113i 0.999694 + 0.0247557i \(0.00788078\pi\)
−0.999694 + 0.0247557i \(0.992119\pi\)
\(270\) 0 0
\(271\) 4.86056 4.86056i 0.295258 0.295258i −0.543895 0.839153i \(-0.683051\pi\)
0.839153 + 0.543895i \(0.183051\pi\)
\(272\) 12.1268 0.735296
\(273\) 0 0
\(274\) −24.8256 −1.49977
\(275\) 15.5900 15.5900i 0.940111 0.940111i
\(276\) 0 0
\(277\) 19.0090i 1.14214i −0.820902 0.571070i \(-0.806529\pi\)
0.820902 0.571070i \(-0.193471\pi\)
\(278\) 6.15093 1.64814i 0.368908 0.0988487i
\(279\) 0 0
\(280\) −4.69984 15.2263i −0.280869 0.909948i
\(281\) −3.58709 3.58709i −0.213988 0.213988i 0.591971 0.805959i \(-0.298350\pi\)
−0.805959 + 0.591971i \(0.798350\pi\)
\(282\) 0 0
\(283\) −7.04222 + 12.1975i −0.418616 + 0.725065i −0.995801 0.0915492i \(-0.970818\pi\)
0.577184 + 0.816614i \(0.304151\pi\)
\(284\) 7.65869 2.05214i 0.454460 0.121772i
\(285\) 0 0
\(286\) 30.6695 9.13682i 1.81353 0.540271i
\(287\) −25.5412 + 16.0553i −1.50765 + 0.947716i
\(288\) 0 0
\(289\) 40.9126 2.40662
\(290\) −21.2480 −1.24773
\(291\) 0 0
\(292\) 1.29056 4.81642i 0.0755241 0.281860i
\(293\) −7.18612 26.8190i −0.419818 1.56678i −0.774985 0.631979i \(-0.782243\pi\)
0.355168 0.934803i \(-0.384424\pi\)
\(294\) 0 0
\(295\) −13.2371 + 22.9274i −0.770695 + 1.33488i
\(296\) 3.16213i 0.183795i
\(297\) 0 0
\(298\) 2.73914 1.58145i 0.158674 0.0916107i
\(299\) −11.1426 + 11.7786i −0.644393 + 0.681175i
\(300\) 0 0
\(301\) 5.68554 + 18.4197i 0.327709 + 1.06170i
\(302\) 8.83772 + 15.3074i 0.508553 + 0.880840i
\(303\) 0 0
\(304\) −1.13828 + 4.24812i −0.0652848 + 0.243646i
\(305\) 21.0679 21.0679i 1.20634 1.20634i
\(306\) 0 0
\(307\) −20.3066 + 20.3066i −1.15896 + 1.15896i −0.174260 + 0.984700i \(0.555753\pi\)
−0.984700 + 0.174260i \(0.944247\pi\)
\(308\) 14.1797 26.8415i 0.807963 1.52944i
\(309\) 0 0
\(310\) −13.4610 13.4610i −0.764532 0.764532i
\(311\) 3.76230 + 6.51650i 0.213341 + 0.369517i 0.952758 0.303731i \(-0.0982323\pi\)
−0.739417 + 0.673247i \(0.764899\pi\)
\(312\) 0 0
\(313\) 21.8314 + 12.6043i 1.23398 + 0.712439i 0.967857 0.251500i \(-0.0809237\pi\)
0.266124 + 0.963939i \(0.414257\pi\)
\(314\) 1.12844 4.21140i 0.0636816 0.237663i
\(315\) 0 0
\(316\) −21.2444 12.2655i −1.19509 0.689987i
\(317\) −1.93925 7.23738i −0.108919 0.406492i 0.889841 0.456270i \(-0.150815\pi\)
−0.998760 + 0.0497787i \(0.984148\pi\)
\(318\) 0 0
\(319\) −8.50581 8.50581i −0.476234 0.476234i
\(320\) 10.6602 + 39.7846i 0.595926 + 2.22402i
\(321\) 0 0
\(322\) 0.984222 + 26.1720i 0.0548485 + 1.45851i
\(323\) −5.43595 + 20.2872i −0.302464 + 1.12881i
\(324\) 0 0
\(325\) −19.1780 4.57258i −1.06380 0.253641i
\(326\) −0.122838 0.212762i −0.00680339 0.0117838i
\(327\) 0 0
\(328\) −18.3826 + 10.6132i −1.01501 + 0.586015i
\(329\) −3.18153 + 6.02249i −0.175403 + 0.332030i
\(330\) 0 0
\(331\) −26.7149 7.15824i −1.46838 0.393452i −0.566008 0.824400i \(-0.691513\pi\)
−0.902377 + 0.430948i \(0.858179\pi\)
\(332\) −4.66303 + 4.66303i −0.255917 + 0.255917i
\(333\) 0 0
\(334\) −42.8818 + 24.7578i −2.34639 + 1.35469i
\(335\) −12.6420 21.8965i −0.690704 1.19634i
\(336\) 0 0
\(337\) 15.1198i 0.823630i −0.911267 0.411815i \(-0.864895\pi\)
0.911267 0.411815i \(-0.135105\pi\)
\(338\) −21.3261 19.0818i −1.15998 1.03792i
\(339\) 0 0
\(340\) 18.1343 + 67.6780i 0.983469 + 3.67036i
\(341\) 10.7771i 0.583614i
\(342\) 0 0
\(343\) −11.5390 + 14.4862i −0.623048 + 0.782184i
\(344\) 3.51048 + 13.1013i 0.189272 + 0.706373i
\(345\) 0 0
\(346\) 10.0534 + 2.69381i 0.540475 + 0.144820i
\(347\) −0.255152 −0.0136973 −0.00684864 0.999977i \(-0.502180\pi\)
−0.00684864 + 0.999977i \(0.502180\pi\)
\(348\) 0 0
\(349\) 23.4871 + 6.29335i 1.25723 + 0.336875i 0.825127 0.564947i \(-0.191103\pi\)
0.432108 + 0.901822i \(0.357770\pi\)
\(350\) −26.9621 + 16.9485i −1.44119 + 0.905936i
\(351\) 0 0
\(352\) −14.5776 + 25.2491i −0.776988 + 1.34578i
\(353\) −9.33450 + 2.50117i −0.496825 + 0.133124i −0.498526 0.866875i \(-0.666125\pi\)
0.00170096 + 0.999999i \(0.499459\pi\)
\(354\) 0 0
\(355\) −4.50746 7.80715i −0.239231 0.414360i
\(356\) 36.2890 + 36.2890i 1.92331 + 1.92331i
\(357\) 0 0
\(358\) 48.7154 13.0533i 2.57469 0.689886i
\(359\) −19.6234 + 5.25807i −1.03568 + 0.277510i −0.736323 0.676630i \(-0.763440\pi\)
−0.299360 + 0.954140i \(0.596773\pi\)
\(360\) 0 0
\(361\) 9.85794 + 5.69149i 0.518839 + 0.299552i
\(362\) −7.53454 + 7.53454i −0.396007 + 0.396007i
\(363\) 0 0
\(364\) −27.0880 + 1.77216i −1.41980 + 0.0928863i
\(365\) −5.66933 −0.296746
\(366\) 0 0
\(367\) −18.8485 10.8822i −0.983886 0.568047i −0.0804448 0.996759i \(-0.525634\pi\)
−0.903441 + 0.428712i \(0.858967\pi\)
\(368\) 7.16603i 0.373555i
\(369\) 0 0
\(370\) 11.6859 3.13122i 0.607519 0.162784i
\(371\) −4.60349 + 20.1867i −0.239001 + 1.04804i
\(372\) 0 0
\(373\) −7.76385 13.4474i −0.401997 0.696279i 0.591970 0.805960i \(-0.298350\pi\)
−0.993967 + 0.109681i \(0.965017\pi\)
\(374\) −33.7719 + 58.4947i −1.74630 + 3.02469i
\(375\) 0 0
\(376\) −2.39617 + 4.15030i −0.123573 + 0.214035i
\(377\) −2.49477 + 10.4634i −0.128487 + 0.538893i
\(378\) 0 0
\(379\) 22.4101 + 6.00477i 1.15113 + 0.308444i 0.783418 0.621495i \(-0.213474\pi\)
0.367712 + 0.929940i \(0.380141\pi\)
\(380\) −25.4103 −1.30352
\(381\) 0 0
\(382\) −31.5264 8.44746i −1.61303 0.432210i
\(383\) 0.417833 1.55937i 0.0213503 0.0796803i −0.954429 0.298439i \(-0.903534\pi\)
0.975779 + 0.218759i \(0.0702007\pi\)
\(384\) 0 0
\(385\) −33.6509 7.67394i −1.71501 0.391100i
\(386\) −17.3114 + 29.9842i −0.881127 + 1.52616i
\(387\) 0 0
\(388\) −9.72242 36.2846i −0.493581 1.84207i
\(389\) −14.1958 + 8.19595i −0.719756 + 0.415551i −0.814663 0.579935i \(-0.803078\pi\)
0.0949069 + 0.995486i \(0.469745\pi\)
\(390\) 0 0
\(391\) 34.2219i 1.73068i
\(392\) −8.49612 + 9.88019i −0.429119 + 0.499025i
\(393\) 0 0
\(394\) −17.0323 + 9.83358i −0.858073 + 0.495409i
\(395\) −7.21874 + 26.9407i −0.363214 + 1.35553i
\(396\) 0 0
\(397\) −33.4523 8.96351i −1.67892 0.449866i −0.711428 0.702759i \(-0.751951\pi\)
−0.967494 + 0.252894i \(0.918618\pi\)
\(398\) −10.6028 + 10.6028i −0.531472 + 0.531472i
\(399\) 0 0
\(400\) 7.54620 4.35680i 0.377310 0.217840i
\(401\) −25.6135 25.6135i −1.27908 1.27908i −0.941184 0.337895i \(-0.890285\pi\)
−0.337895 0.941184i \(-0.609715\pi\)
\(402\) 0 0
\(403\) −8.20922 + 5.04826i −0.408930 + 0.251472i
\(404\) 9.78778 + 5.65098i 0.486960 + 0.281147i
\(405\) 0 0
\(406\) 9.24701 + 14.7104i 0.458921 + 0.730064i
\(407\) 5.93143 + 3.42451i 0.294010 + 0.169747i
\(408\) 0 0
\(409\) −15.6288 15.6288i −0.772795 0.772795i 0.205799 0.978594i \(-0.434021\pi\)
−0.978594 + 0.205799i \(0.934021\pi\)
\(410\) 57.4246 + 57.4246i 2.83600 + 2.83600i
\(411\) 0 0
\(412\) 9.38533 + 5.41862i 0.462382 + 0.266956i
\(413\) 21.6337 0.813555i 1.06453 0.0400324i
\(414\) 0 0
\(415\) 6.49329 + 3.74890i 0.318743 + 0.184026i
\(416\) 26.0614 0.723154i 1.27776 0.0354556i
\(417\) 0 0
\(418\) −17.3212 17.3212i −0.847206 0.847206i
\(419\) −6.99593 + 4.03910i −0.341774 + 0.197323i −0.661056 0.750336i \(-0.729891\pi\)
0.319282 + 0.947660i \(0.396558\pi\)
\(420\) 0 0
\(421\) 5.31808 5.31808i 0.259187 0.259187i −0.565536 0.824724i \(-0.691331\pi\)
0.824724 + 0.565536i \(0.191331\pi\)
\(422\) 7.05487 + 1.89035i 0.343425 + 0.0920206i
\(423\) 0 0
\(424\) −3.77047 + 14.0716i −0.183110 + 0.683377i
\(425\) 36.0375 20.8063i 1.74808 1.00925i
\(426\) 0 0
\(427\) −23.7543 5.41706i −1.14955 0.262150i
\(428\) 19.5382i 0.944416i
\(429\) 0 0
\(430\) 44.9405 25.9464i 2.16722 1.25125i
\(431\) 2.71448 + 10.1306i 0.130752 + 0.487973i 0.999979 0.00643990i \(-0.00204990\pi\)
−0.869227 + 0.494413i \(0.835383\pi\)
\(432\) 0 0
\(433\) 2.59289 4.49102i 0.124607 0.215825i −0.796973 0.604016i \(-0.793566\pi\)
0.921579 + 0.388191i \(0.126900\pi\)
\(434\) −3.46114 + 15.1774i −0.166140 + 0.728538i
\(435\) 0 0
\(436\) −3.59151 + 13.4037i −0.172002 + 0.641921i
\(437\) 11.9882 + 3.21223i 0.573474 + 0.153662i
\(438\) 0 0
\(439\) 8.67818 0.414187 0.207093 0.978321i \(-0.433600\pi\)
0.207093 + 0.978321i \(0.433600\pi\)
\(440\) −23.4571 6.28531i −1.11827 0.299641i
\(441\) 0 0
\(442\) 60.3764 1.67533i 2.87181 0.0796875i
\(443\) −5.13279 + 8.89025i −0.243866 + 0.422388i −0.961812 0.273710i \(-0.911749\pi\)
0.717946 + 0.696099i \(0.245082\pi\)
\(444\) 0 0
\(445\) 29.1750 50.5326i 1.38303 2.39548i
\(446\) −25.4246 44.0367i −1.20389 2.08520i
\(447\) 0 0
\(448\) 22.9043 24.6943i 1.08213 1.16669i
\(449\) −7.73538 + 2.07269i −0.365055 + 0.0978162i −0.436684 0.899615i \(-0.643847\pi\)
0.0716285 + 0.997431i \(0.477180\pi\)
\(450\) 0 0
\(451\) 45.9753i 2.16489i
\(452\) −21.9519 12.6740i −1.03253 0.596133i
\(453\) 0 0
\(454\) −37.9901 −1.78297
\(455\) 9.91744 + 29.2274i 0.464937 + 1.37020i
\(456\) 0 0
\(457\) −18.3530 + 18.3530i −0.858515 + 0.858515i −0.991163 0.132648i \(-0.957652\pi\)
0.132648 + 0.991163i \(0.457652\pi\)
\(458\) −14.4017 8.31482i −0.672947 0.388526i
\(459\) 0 0
\(460\) 39.9926 10.7160i 1.86466 0.499635i
\(461\) −14.2955 + 3.83046i −0.665807 + 0.178402i −0.575865 0.817545i \(-0.695335\pi\)
−0.0899418 + 0.995947i \(0.528668\pi\)
\(462\) 0 0
\(463\) 6.69179 + 6.69179i 0.310994 + 0.310994i 0.845294 0.534301i \(-0.179425\pi\)
−0.534301 + 0.845294i \(0.679425\pi\)
\(464\) −2.37705 4.11717i −0.110352 0.191135i
\(465\) 0 0
\(466\) −45.2558 + 12.1263i −2.09643 + 0.561738i
\(467\) 15.6442 27.0965i 0.723925 1.25388i −0.235490 0.971877i \(-0.575669\pi\)
0.959415 0.281998i \(-0.0909973\pi\)
\(468\) 0 0
\(469\) −9.65765 + 18.2815i −0.445949 + 0.844161i
\(470\) 17.7104 + 4.74550i 0.816922 + 0.218894i
\(471\) 0 0
\(472\) 15.2322 0.701119
\(473\) 28.3767 + 7.60353i 1.30476 + 0.349611i
\(474\) 0 0
\(475\) 3.90595 + 14.5772i 0.179217 + 0.668848i
\(476\) 38.9628 42.0077i 1.78586 1.92542i
\(477\) 0 0
\(478\) 46.1136i 2.10919i
\(479\) −8.45059 31.5380i −0.386117 1.44101i −0.836398 0.548123i \(-0.815343\pi\)
0.450280 0.892887i \(-0.351324\pi\)
\(480\) 0 0
\(481\) −0.169881 6.12224i −0.00774590 0.279150i
\(482\) 10.1537i 0.462489i
\(483\) 0 0
\(484\) −7.48010 12.9559i −0.340004 0.588905i
\(485\) −36.9879 + 21.3550i −1.67953 + 0.969679i
\(486\) 0 0
\(487\) 0.388513 0.388513i 0.0176052 0.0176052i −0.698249 0.715855i \(-0.746037\pi\)
0.715855 + 0.698249i \(0.246037\pi\)
\(488\) −16.5584 4.43682i −0.749565 0.200845i
\(489\) 0 0
\(490\) 44.9260 + 21.6144i 2.02955 + 0.976438i
\(491\) 11.1482 6.43644i 0.503113 0.290472i −0.226885 0.973921i \(-0.572854\pi\)
0.729998 + 0.683449i \(0.239521\pi\)
\(492\) 0 0
\(493\) −11.3518 19.6619i −0.511259 0.885526i
\(494\) −5.08034 + 21.3076i −0.228575 + 0.958675i
\(495\) 0 0
\(496\) 1.10239 4.11419i 0.0494989 0.184733i
\(497\) −3.44341 + 6.51821i −0.154458 + 0.292382i
\(498\) 0 0
\(499\) 0.964321 + 3.59890i 0.0431689 + 0.161109i 0.984145 0.177363i \(-0.0567567\pi\)
−0.940977 + 0.338472i \(0.890090\pi\)
\(500\) 3.04760 + 3.04760i 0.136293 + 0.136293i
\(501\) 0 0
\(502\) −8.90334 33.2277i −0.397375 1.48303i
\(503\) −12.0422 6.95256i −0.536935 0.309999i 0.206901 0.978362i \(-0.433662\pi\)
−0.743836 + 0.668362i \(0.766996\pi\)
\(504\) 0 0
\(505\) 3.32584 12.4122i 0.147998 0.552335i
\(506\) 34.5659 + 19.9566i 1.53664 + 0.887181i
\(507\) 0 0
\(508\) −8.32421 14.4179i −0.369327 0.639693i
\(509\) −13.0210 13.0210i −0.577144 0.577144i 0.356971 0.934115i \(-0.383809\pi\)
−0.934115 + 0.356971i \(0.883809\pi\)
\(510\) 0 0
\(511\) 2.46726 + 3.92498i 0.109145 + 0.173631i
\(512\) −12.3429 + 12.3429i −0.545485 + 0.545485i
\(513\) 0 0
\(514\) −6.08472 + 6.08472i −0.268386 + 0.268386i
\(515\) 3.18908 11.9018i 0.140528 0.524457i
\(516\) 0 0
\(517\) 5.19000 + 8.98935i 0.228256 + 0.395351i
\(518\) −7.25341 6.72764i −0.318697 0.295596i
\(519\) 0 0
\(520\) 6.20017 + 20.8121i 0.271896 + 0.912670i
\(521\) −2.00007 + 1.15474i −0.0876246 + 0.0505901i −0.543172 0.839621i \(-0.682777\pi\)
0.455547 + 0.890211i \(0.349444\pi\)
\(522\) 0 0
\(523\) 0.544569i 0.0238124i 0.999929 + 0.0119062i \(0.00378994\pi\)
−0.999929 + 0.0119062i \(0.996210\pi\)
\(524\) −3.72317 + 6.44872i −0.162647 + 0.281714i
\(525\) 0 0
\(526\) 1.05096 + 3.92223i 0.0458240 + 0.171017i
\(527\) 5.26457 19.6476i 0.229328 0.855865i
\(528\) 0 0
\(529\) 2.77742 0.120757
\(530\) 55.7361 2.42102
\(531\) 0 0
\(532\) 11.0584 + 17.5920i 0.479443 + 0.762711i
\(533\) 35.0206 21.5359i 1.51691 0.932824i
\(534\) 0 0
\(535\) −21.4575 + 5.74953i −0.927690 + 0.248574i
\(536\) −7.27368 + 12.5984i −0.314175 + 0.544167i
\(537\) 0 0
\(538\) −1.26399 1.26399i −0.0544943 0.0544943i
\(539\) 9.33187 + 26.6368i 0.401952 + 1.14733i
\(540\) 0 0
\(541\) 35.8145 9.59647i 1.53979 0.412584i 0.613589 0.789626i \(-0.289725\pi\)
0.926196 + 0.377041i \(0.123059\pi\)
\(542\) 15.1314i 0.649948i
\(543\) 0 0
\(544\) −38.9103 + 38.9103i −1.66826 + 1.66826i
\(545\) 15.7773 0.675825
\(546\) 0 0
\(547\) −11.4043 −0.487613 −0.243806 0.969824i \(-0.578396\pi\)
−0.243806 + 0.969824i \(0.578396\pi\)
\(548\) 22.6930 22.6930i 0.969397 0.969397i
\(549\) 0 0
\(550\) 48.5330i 2.06945i
\(551\) 7.95324 2.13106i 0.338819 0.0907864i
\(552\) 0 0
\(553\) 21.7931 6.72676i 0.926736 0.286051i
\(554\) 29.5883 + 29.5883i 1.25709 + 1.25709i
\(555\) 0 0
\(556\) −4.11599 + 7.12910i −0.174557 + 0.302341i
\(557\) 2.44687 0.655638i 0.103677 0.0277803i −0.206607 0.978424i \(-0.566242\pi\)
0.310285 + 0.950644i \(0.399576\pi\)
\(558\) 0 0
\(559\) −7.50053 25.1770i −0.317239 1.06487i
\(560\) −12.0613 6.37170i −0.509685 0.269253i
\(561\) 0 0
\(562\) 11.1669 0.471048
\(563\) 14.6059 0.615564 0.307782 0.951457i \(-0.400413\pi\)
0.307782 + 0.951457i \(0.400413\pi\)
\(564\) 0 0
\(565\) −7.45915 + 27.8379i −0.313809 + 1.17115i
\(566\) −8.02439 29.9474i −0.337290 1.25879i
\(567\) 0 0
\(568\) −2.59341 + 4.49192i −0.108817 + 0.188477i
\(569\) 17.4403i 0.731137i 0.930784 + 0.365568i \(0.119125\pi\)
−0.930784 + 0.365568i \(0.880875\pi\)
\(570\) 0 0
\(571\) −30.0741 + 17.3633i −1.25856 + 0.726630i −0.972795 0.231669i \(-0.925581\pi\)
−0.285766 + 0.958299i \(0.592248\pi\)
\(572\) −19.6829 + 36.3868i −0.822985 + 1.52141i
\(573\) 0 0
\(574\) 14.7652 64.7469i 0.616289 2.70248i
\(575\) −12.2949 21.2954i −0.512734 0.888081i
\(576\) 0 0
\(577\) 4.83633 18.0494i 0.201339 0.751407i −0.789196 0.614142i \(-0.789502\pi\)
0.990534 0.137265i \(-0.0438311\pi\)
\(578\) −63.6822 + 63.6822i −2.64883 + 2.64883i
\(579\) 0 0
\(580\) 19.4227 19.4227i 0.806485 0.806485i
\(581\) −0.230408 6.12692i −0.00955895 0.254187i
\(582\) 0 0
\(583\) 22.3117 + 22.3117i 0.924058 + 0.924058i
\(584\) 1.63095 + 2.82489i 0.0674893 + 0.116895i
\(585\) 0 0
\(586\) 52.9305 + 30.5594i 2.18654 + 1.26240i
\(587\) 8.61022 32.1338i 0.355382 1.32630i −0.524622 0.851335i \(-0.675793\pi\)
0.880004 0.474967i \(-0.157540\pi\)
\(588\) 0 0
\(589\) 6.38857 + 3.68844i 0.263237 + 0.151980i
\(590\) −15.0833 56.2916i −0.620969 2.31749i
\(591\) 0 0
\(592\) 1.91404 + 1.91404i 0.0786666 + 0.0786666i
\(593\) −1.18632 4.42742i −0.0487164 0.181812i 0.937280 0.348576i \(-0.113335\pi\)
−0.985997 + 0.166764i \(0.946668\pi\)
\(594\) 0 0
\(595\) −57.5999 30.4286i −2.36137 1.24745i
\(596\) −1.05825 + 3.94943i −0.0433475 + 0.161775i
\(597\) 0 0
\(598\) −0.989995 35.6779i −0.0404839 1.45898i
\(599\) 9.84386 + 17.0501i 0.402209 + 0.696646i 0.993992 0.109451i \(-0.0349092\pi\)
−0.591783 + 0.806097i \(0.701576\pi\)
\(600\) 0 0
\(601\) −10.6224 + 6.13284i −0.433296 + 0.250164i −0.700750 0.713407i \(-0.747151\pi\)
0.267454 + 0.963571i \(0.413818\pi\)
\(602\) −37.5210 19.8214i −1.52924 0.807859i
\(603\) 0 0
\(604\) −22.0709 5.91389i −0.898054 0.240633i
\(605\) −12.0274 + 12.0274i −0.488985 + 0.488985i
\(606\) 0 0
\(607\) 20.8458 12.0353i 0.846105 0.488499i −0.0132296 0.999912i \(-0.504211\pi\)
0.859335 + 0.511413i \(0.170878\pi\)
\(608\) −9.97828 17.2829i −0.404672 0.700913i
\(609\) 0 0
\(610\) 65.5862i 2.65551i
\(611\) 4.41630 8.16418i 0.178664 0.330287i
\(612\) 0 0
\(613\) −12.5294 46.7603i −0.506057 1.88863i −0.456206 0.889874i \(-0.650792\pi\)
−0.0498516 0.998757i \(-0.515875\pi\)
\(614\) 63.2163i 2.55120i
\(615\) 0 0
\(616\) 5.85696 + 18.9751i 0.235983 + 0.764529i
\(617\) −4.83334 18.0383i −0.194583 0.726194i −0.992374 0.123260i \(-0.960665\pi\)
0.797791 0.602934i \(-0.206002\pi\)
\(618\) 0 0
\(619\) 9.70855 + 2.60140i 0.390219 + 0.104559i 0.448594 0.893736i \(-0.351925\pi\)
−0.0583743 + 0.998295i \(0.518592\pi\)
\(620\) 24.6092 0.988331
\(621\) 0 0
\(622\) −15.9994 4.28703i −0.641518 0.171894i
\(623\) −47.6814 + 1.79310i −1.91032 + 0.0718391i
\(624\) 0 0
\(625\) −11.2201 + 19.4339i −0.448806 + 0.777354i
\(626\) −53.6007 + 14.3623i −2.14231 + 0.574031i
\(627\) 0 0
\(628\) 2.81812 + 4.88112i 0.112455 + 0.194778i
\(629\) 9.14066 + 9.14066i 0.364462 + 0.364462i
\(630\) 0 0
\(631\) 8.95627 2.39983i 0.356543 0.0955355i −0.0761011 0.997100i \(-0.524247\pi\)
0.432645 + 0.901565i \(0.357581\pi\)
\(632\) 15.5006 4.15337i 0.616580 0.165212i
\(633\) 0 0
\(634\) 14.2838 + 8.24678i 0.567284 + 0.327521i
\(635\) −13.3847 + 13.3847i −0.531156 + 0.531156i
\(636\) 0 0
\(637\) 15.9187 19.5856i 0.630720 0.776010i
\(638\) 26.4793 1.04833
\(639\) 0 0
\(640\) −37.9979 21.9381i −1.50200 0.867179i
\(641\) 32.1058i 1.26810i −0.773291 0.634052i \(-0.781391\pi\)
0.773291 0.634052i \(-0.218609\pi\)
\(642\) 0 0
\(643\) 7.89631 2.11581i 0.311400 0.0834393i −0.0997345 0.995014i \(-0.531799\pi\)
0.411134 + 0.911575i \(0.365133\pi\)
\(644\) −24.8234 23.0241i −0.978179 0.907275i
\(645\) 0 0
\(646\) −23.1167 40.0393i −0.909514 1.57532i
\(647\) −4.00052 + 6.92910i −0.157276 + 0.272411i −0.933886 0.357572i \(-0.883605\pi\)
0.776609 + 0.629983i \(0.216938\pi\)
\(648\) 0 0
\(649\) 16.4961 28.5721i 0.647529 1.12155i
\(650\) 36.9688 22.7340i 1.45004 0.891700i
\(651\) 0 0
\(652\) 0.306771 + 0.0821991i 0.0120141 + 0.00321917i
\(653\) 45.0155 1.76159 0.880797 0.473495i \(-0.157008\pi\)
0.880797 + 0.473495i \(0.157008\pi\)
\(654\) 0 0
\(655\) 8.17782 + 2.19124i 0.319534 + 0.0856189i
\(656\) −4.70282 + 17.5512i −0.183614 + 0.685258i
\(657\) 0 0
\(658\) −4.42208 14.3265i −0.172391 0.558504i
\(659\) −15.9656 + 27.6532i −0.621930 + 1.07721i 0.367196 + 0.930144i \(0.380318\pi\)
−0.989126 + 0.147071i \(0.953015\pi\)
\(660\) 0 0
\(661\) 4.10014 + 15.3019i 0.159477 + 0.595175i 0.998680 + 0.0513580i \(0.0163549\pi\)
−0.839204 + 0.543817i \(0.816978\pi\)
\(662\) 52.7251 30.4408i 2.04922 1.18312i
\(663\) 0 0
\(664\) 4.31394i 0.167413i
\(665\) 16.0660 17.3215i 0.623012 0.671701i
\(666\) 0 0
\(667\) −11.6187 + 6.70804i −0.449877 + 0.259737i
\(668\) 16.5671 61.8291i 0.640999 2.39224i
\(669\) 0 0
\(670\) 53.7607 + 14.4051i 2.07696 + 0.556519i
\(671\) −26.2548 + 26.2548i −1.01356 + 1.01356i
\(672\) 0 0
\(673\) −2.46102 + 1.42087i −0.0948654 + 0.0547706i −0.546682 0.837340i \(-0.684109\pi\)
0.451817 + 0.892111i \(0.350776\pi\)
\(674\) 23.5347 + 23.5347i 0.906523 + 0.906523i
\(675\) 0 0
\(676\) 36.9367 2.05143i 1.42064 0.0789011i
\(677\) −5.65487 3.26484i −0.217334 0.125478i 0.387381 0.921920i \(-0.373380\pi\)
−0.604715 + 0.796442i \(0.706713\pi\)
\(678\) 0 0
\(679\) 30.8813 + 16.3138i 1.18512 + 0.626067i
\(680\) −39.6940 22.9173i −1.52220 0.878840i
\(681\) 0 0
\(682\) 16.7751 + 16.7751i 0.642351 + 0.642351i
\(683\) 23.0449 + 23.0449i 0.881789 + 0.881789i 0.993716 0.111928i \(-0.0357025\pi\)
−0.111928 + 0.993716i \(0.535703\pi\)
\(684\) 0 0
\(685\) −31.6001 18.2443i −1.20738 0.697080i
\(686\) −4.58749 40.5095i −0.175151 1.54666i
\(687\) 0 0
\(688\) 10.0551 + 5.80532i 0.383347 + 0.221326i
\(689\) 6.54408 27.4468i 0.249310 1.04564i
\(690\) 0 0
\(691\) −18.4648 18.4648i −0.702433 0.702433i 0.262500 0.964932i \(-0.415453\pi\)
−0.964932 + 0.262500i \(0.915453\pi\)
\(692\) −11.6522 + 6.72739i −0.442950 + 0.255737i
\(693\) 0 0
\(694\) 0.397155 0.397155i 0.0150758 0.0150758i
\(695\) 9.04063 + 2.42243i 0.342931 + 0.0918880i
\(696\) 0 0
\(697\) −22.4587 + 83.8170i −0.850684 + 3.17480i
\(698\) −46.3546 + 26.7628i −1.75455 + 1.01299i
\(699\) 0 0
\(700\) 9.15341 40.1385i 0.345966 1.51709i
\(701\) 41.5208i 1.56822i 0.620623 + 0.784109i \(0.286880\pi\)
−0.620623 + 0.784109i \(0.713120\pi\)
\(702\) 0 0
\(703\) −4.06003 + 2.34406i −0.153127 + 0.0884079i
\(704\) −13.2848 49.5796i −0.500690 1.86860i
\(705\) 0 0
\(706\) 10.6364 18.4227i 0.400305 0.693349i
\(707\) −10.0406 + 3.09917i −0.377614 + 0.116556i
\(708\) 0 0
\(709\) −11.8453 + 44.2073i −0.444860 + 1.66024i 0.271445 + 0.962454i \(0.412499\pi\)
−0.716305 + 0.697787i \(0.754168\pi\)
\(710\) 19.1682 + 5.13611i 0.719371 + 0.192755i
\(711\) 0 0
\(712\) −33.5723 −1.25817
\(713\) −11.6103 3.11096i −0.434808 0.116507i
\(714\) 0 0
\(715\) 45.7533 + 10.9089i 1.71108 + 0.407969i
\(716\) −32.5986 + 56.4625i −1.21827 + 2.11010i
\(717\) 0 0
\(718\) 22.3603 38.7291i 0.834478 1.44536i
\(719\) 21.2541 + 36.8132i 0.792645 + 1.37290i 0.924324 + 0.381608i \(0.124630\pi\)
−0.131679 + 0.991292i \(0.542037\pi\)
\(720\) 0 0
\(721\) −9.62771 + 2.97174i −0.358555 + 0.110673i
\(722\) −24.2034 + 6.48528i −0.900757 + 0.241357i
\(723\) 0 0
\(724\) 13.7746i 0.511929i
\(725\) −14.1279 8.15672i −0.524695 0.302933i
\(726\) 0 0
\(727\) 44.5147 1.65096 0.825479 0.564433i \(-0.190905\pi\)
0.825479 + 0.564433i \(0.190905\pi\)
\(728\) 11.7103 13.3498i 0.434012 0.494775i
\(729\) 0 0
\(730\) 8.82457 8.82457i 0.326612 0.326612i
\(731\) 48.0190 + 27.7238i 1.77605 + 1.02540i
\(732\) 0 0
\(733\) 0.0758491 0.0203237i 0.00280155 0.000750673i −0.257418 0.966300i \(-0.582872\pi\)
0.260220 + 0.965549i \(0.416205\pi\)
\(734\) 46.2772 12.3999i 1.70812 0.457691i
\(735\) 0 0
\(736\) 22.9930 + 22.9930i 0.847534 + 0.847534i
\(737\) 15.7544 + 27.2875i 0.580322 + 1.00515i
\(738\) 0 0
\(739\) 39.9436 10.7028i 1.46935 0.393711i 0.566640 0.823965i \(-0.308243\pi\)
0.902708 + 0.430255i \(0.141576\pi\)
\(740\) −7.81977 + 13.5442i −0.287460 + 0.497896i
\(741\) 0 0
\(742\) −24.2560 38.5871i −0.890466 1.41658i
\(743\) −28.0978 7.52879i −1.03081 0.276205i −0.296510 0.955030i \(-0.595823\pi\)
−0.734300 + 0.678825i \(0.762489\pi\)
\(744\) 0 0
\(745\) 4.64881 0.170319
\(746\) 33.0162 + 8.84667i 1.20881 + 0.323900i
\(747\) 0 0
\(748\) −22.5990 84.3405i −0.826300 3.08380i
\(749\) 13.3187 + 12.3533i 0.486654 + 0.451379i
\(750\) 0 0
\(751\) 1.29328i 0.0471923i −0.999722 0.0235961i \(-0.992488\pi\)
0.999722 0.0235961i \(-0.00751158\pi\)
\(752\) 1.06177 + 3.96258i 0.0387188 + 0.144501i
\(753\) 0 0
\(754\) −12.4035 20.1700i −0.451710 0.734547i
\(755\) 25.9793i 0.945484i
\(756\) 0 0
\(757\) 23.6428 + 40.9506i 0.859313 + 1.48837i 0.872586 + 0.488461i \(0.162442\pi\)
−0.0132729 + 0.999912i \(0.504225\pi\)
\(758\) −44.2290 + 25.5356i −1.60647 + 0.927496i
\(759\) 0 0
\(760\) 11.7540 11.7540i 0.426362 0.426362i
\(761\) −20.6122 5.52303i −0.747193 0.200210i −0.134920 0.990856i \(-0.543078\pi\)
−0.612273 + 0.790647i \(0.709744\pi\)
\(762\) 0 0
\(763\) −6.86617 10.9229i −0.248572 0.395435i
\(764\) 36.5399 21.0963i 1.32197 0.763238i
\(765\) 0 0
\(766\) 1.77686 + 3.07761i 0.0642005 + 0.111199i
\(767\) −29.4913 + 0.818328i −1.06487 + 0.0295481i
\(768\) 0 0
\(769\) −6.12447 + 22.8568i −0.220854 + 0.824238i 0.763169 + 0.646198i \(0.223642\pi\)
−0.984023 + 0.178040i \(0.943024\pi\)
\(770\) 64.3240 40.4344i 2.31808 1.45715i
\(771\) 0 0
\(772\) −11.5842 43.2327i −0.416924 1.55598i
\(773\) −35.7559 35.7559i −1.28605 1.28605i −0.937165 0.348887i \(-0.886560\pi\)
−0.348887 0.937165i \(-0.613440\pi\)
\(774\) 0 0
\(775\) −3.78281 14.1176i −0.135883 0.507121i
\(776\) 21.2813 + 12.2868i 0.763956 + 0.441070i
\(777\) 0 0
\(778\) 9.33904 34.8538i 0.334821 1.24957i
\(779\) −27.2537 15.7349i −0.976465 0.563762i
\(780\) 0 0
\(781\) 5.61720 + 9.72928i 0.200999 + 0.348141i
\(782\) 53.2680 + 53.2680i 1.90486 + 1.90486i
\(783\) 0 0
\(784\) 0.837781 + 11.1232i 0.0299207 + 0.397257i
\(785\) 4.53132 4.53132i 0.161730 0.161730i
\(786\) 0 0
\(787\) −30.7868 + 30.7868i −1.09743 + 1.09743i −0.102719 + 0.994710i \(0.532754\pi\)
−0.994710 + 0.102719i \(0.967246\pi\)
\(788\) 6.58029 24.5580i 0.234413 0.874841i