Properties

Label 441.2.bg.a.395.7
Level $441$
Weight $2$
Character 441.395
Analytic conductor $3.521$
Analytic rank $0$
Dimension $216$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 395.7
Character \(\chi\) \(=\) 441.395
Dual form 441.2.bg.a.278.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.811510 - 0.318494i) q^{2} +(-0.908993 - 0.843422i) q^{4} +(0.228773 + 0.155975i) q^{5} +(-2.58038 + 0.584516i) q^{7} +(1.22553 + 2.54484i) q^{8} +O(q^{10})\) \(q+(-0.811510 - 0.318494i) q^{2} +(-0.908993 - 0.843422i) q^{4} +(0.228773 + 0.155975i) q^{5} +(-2.58038 + 0.584516i) q^{7} +(1.22553 + 2.54484i) q^{8} +(-0.135974 - 0.199438i) q^{10} +(0.640710 + 4.25083i) q^{11} +(3.73796 - 2.98092i) q^{13} +(2.28017 + 0.347495i) q^{14} +(0.00131931 + 0.0176050i) q^{16} +(5.10459 + 1.57456i) q^{17} +(1.61087 - 0.930035i) q^{19} +(-0.0764004 - 0.334732i) q^{20} +(0.833924 - 3.65366i) q^{22} +(0.312885 + 1.01435i) q^{23} +(-1.79870 - 4.58300i) q^{25} +(-3.98280 + 1.22853i) q^{26} +(2.83854 + 1.64503i) q^{28} +(3.23196 - 0.737675i) q^{29} +(4.59195 + 2.65116i) q^{31} +(1.66964 - 5.41284i) q^{32} +(-3.64094 - 2.90355i) q^{34} +(-0.681490 - 0.268752i) q^{35} +(-5.88543 + 5.46088i) q^{37} +(-1.60345 + 0.241681i) q^{38} +(-0.116562 + 0.773341i) q^{40} +(5.58866 - 2.69136i) q^{41} +(9.74651 + 4.69367i) q^{43} +(3.00285 - 4.40437i) q^{44} +(0.0691548 - 0.922807i) q^{46} +(-3.78553 + 9.64538i) q^{47} +(6.31668 - 3.01654i) q^{49} +4.29203i q^{50} +(-5.91196 - 0.443040i) q^{52} +(2.18512 - 2.35500i) q^{53} +(-0.516445 + 1.07241i) q^{55} +(-4.64982 - 5.85029i) q^{56} +(-2.85772 - 0.430732i) q^{58} +(-10.0364 + 6.84272i) q^{59} +(5.45959 + 5.88404i) q^{61} +(-2.88203 - 3.61396i) q^{62} +(-3.05688 + 3.83320i) q^{64} +(1.32009 - 0.0989272i) q^{65} +(3.64950 - 6.32111i) q^{67} +(-3.31202 - 5.73658i) q^{68} +(0.467440 + 0.435146i) q^{70} +(4.23060 + 0.965606i) q^{71} +(-4.31759 + 1.69453i) q^{73} +(6.51535 - 2.55708i) q^{74} +(-2.24868 - 0.513247i) q^{76} +(-4.13795 - 10.5942i) q^{77} +(1.86308 + 3.22695i) q^{79} +(-0.00244411 + 0.00423332i) q^{80} +(-5.39244 + 0.404107i) q^{82} +(-0.641843 + 0.804845i) q^{83} +(0.922200 + 1.15640i) q^{85} +(-6.41449 - 6.91317i) q^{86} +(-10.0325 + 6.84002i) q^{88} +(-15.0504 - 2.26848i) q^{89} +(-7.90295 + 9.87680i) q^{91} +(0.571114 - 1.18593i) q^{92} +(6.14400 - 6.62166i) q^{94} +(0.513585 + 0.0384879i) q^{95} -10.6247i q^{97} +(-6.08681 + 0.436126i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q - 16q^{4} + 2q^{7} + O(q^{10}) \) \( 216q - 16q^{4} + 2q^{7} + 12q^{10} + 12q^{16} - 6q^{19} + 44q^{22} + 26q^{25} + 84q^{28} - 6q^{31} - 112q^{34} + 60q^{37} - 304q^{40} + 20q^{43} - 20q^{46} - 86q^{49} - 168q^{52} - 84q^{55} - 120q^{58} - 2q^{61} + 32q^{64} + 22q^{67} - 136q^{70} - 6q^{73} + 84q^{76} + 2q^{79} - 104q^{82} + 96q^{85} - 12q^{88} + 58q^{91} + 52q^{94} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.811510 0.318494i −0.573825 0.225210i 0.0606424 0.998160i \(-0.480685\pi\)
−0.634467 + 0.772950i \(0.718780\pi\)
\(3\) 0 0
\(4\) −0.908993 0.843422i −0.454497 0.421711i
\(5\) 0.228773 + 0.155975i 0.102310 + 0.0697540i 0.613395 0.789777i \(-0.289804\pi\)
−0.511084 + 0.859531i \(0.670756\pi\)
\(6\) 0 0
\(7\) −2.58038 + 0.584516i −0.975291 + 0.220926i
\(8\) 1.22553 + 2.54484i 0.433290 + 0.899735i
\(9\) 0 0
\(10\) −0.135974 0.199438i −0.0429989 0.0630678i
\(11\) 0.640710 + 4.25083i 0.193181 + 1.28167i 0.849660 + 0.527330i \(0.176807\pi\)
−0.656479 + 0.754344i \(0.727955\pi\)
\(12\) 0 0
\(13\) 3.73796 2.98092i 1.03672 0.826760i 0.0516106 0.998667i \(-0.483565\pi\)
0.985113 + 0.171908i \(0.0549931\pi\)
\(14\) 2.28017 + 0.347495i 0.609400 + 0.0928719i
\(15\) 0 0
\(16\) 0.00131931 + 0.0176050i 0.000329828 + 0.00440124i
\(17\) 5.10459 + 1.57456i 1.23804 + 0.381886i 0.843569 0.537021i \(-0.180450\pi\)
0.394475 + 0.918907i \(0.370927\pi\)
\(18\) 0 0
\(19\) 1.61087 0.930035i 0.369558 0.213365i −0.303707 0.952765i \(-0.598224\pi\)
0.673266 + 0.739401i \(0.264891\pi\)
\(20\) −0.0764004 0.334732i −0.0170837 0.0748484i
\(21\) 0 0
\(22\) 0.833924 3.65366i 0.177793 0.778963i
\(23\) 0.312885 + 1.01435i 0.0652411 + 0.211506i 0.982323 0.187191i \(-0.0599385\pi\)
−0.917082 + 0.398698i \(0.869462\pi\)
\(24\) 0 0
\(25\) −1.79870 4.58300i −0.359739 0.916601i
\(26\) −3.98280 + 1.22853i −0.781092 + 0.240935i
\(27\) 0 0
\(28\) 2.83854 + 1.64503i 0.536433 + 0.310881i
\(29\) 3.23196 0.737675i 0.600161 0.136983i 0.0883624 0.996088i \(-0.471837\pi\)
0.511798 + 0.859106i \(0.328980\pi\)
\(30\) 0 0
\(31\) 4.59195 + 2.65116i 0.824738 + 0.476163i 0.852048 0.523464i \(-0.175361\pi\)
−0.0273093 + 0.999627i \(0.508694\pi\)
\(32\) 1.66964 5.41284i 0.295154 0.956864i
\(33\) 0 0
\(34\) −3.64094 2.90355i −0.624416 0.497955i
\(35\) −0.681490 0.268752i −0.115193 0.0454274i
\(36\) 0 0
\(37\) −5.88543 + 5.46088i −0.967558 + 0.897763i −0.994798 0.101866i \(-0.967519\pi\)
0.0272397 + 0.999629i \(0.491328\pi\)
\(38\) −1.60345 + 0.241681i −0.260113 + 0.0392058i
\(39\) 0 0
\(40\) −0.116562 + 0.773341i −0.0184301 + 0.122276i
\(41\) 5.58866 2.69136i 0.872802 0.420319i 0.0568115 0.998385i \(-0.481907\pi\)
0.815990 + 0.578066i \(0.196192\pi\)
\(42\) 0 0
\(43\) 9.74651 + 4.69367i 1.48633 + 0.715778i 0.988461 0.151475i \(-0.0484023\pi\)
0.497867 + 0.867253i \(0.334117\pi\)
\(44\) 3.00285 4.40437i 0.452696 0.663983i
\(45\) 0 0
\(46\) 0.0691548 0.922807i 0.0101963 0.136060i
\(47\) −3.78553 + 9.64538i −0.552177 + 1.40692i 0.333557 + 0.942730i \(0.391751\pi\)
−0.885734 + 0.464194i \(0.846344\pi\)
\(48\) 0 0
\(49\) 6.31668 3.01654i 0.902383 0.430934i
\(50\) 4.29203i 0.606985i
\(51\) 0 0
\(52\) −5.91196 0.443040i −0.819841 0.0614386i
\(53\) 2.18512 2.35500i 0.300149 0.323484i −0.564911 0.825152i \(-0.691089\pi\)
0.865060 + 0.501668i \(0.167280\pi\)
\(54\) 0 0
\(55\) −0.516445 + 1.07241i −0.0696375 + 0.144604i
\(56\) −4.64982 5.85029i −0.621358 0.781778i
\(57\) 0 0
\(58\) −2.85772 0.430732i −0.375237 0.0565578i
\(59\) −10.0364 + 6.84272i −1.30663 + 0.890847i −0.998175 0.0603916i \(-0.980765\pi\)
−0.308457 + 0.951238i \(0.599813\pi\)
\(60\) 0 0
\(61\) 5.45959 + 5.88404i 0.699029 + 0.753374i 0.978380 0.206815i \(-0.0663098\pi\)
−0.279351 + 0.960189i \(0.590119\pi\)
\(62\) −2.88203 3.61396i −0.366019 0.458973i
\(63\) 0 0
\(64\) −3.05688 + 3.83320i −0.382109 + 0.479150i
\(65\) 1.32009 0.0989272i 0.163737 0.0122704i
\(66\) 0 0
\(67\) 3.64950 6.32111i 0.445857 0.772247i −0.552255 0.833676i \(-0.686232\pi\)
0.998111 + 0.0614287i \(0.0195657\pi\)
\(68\) −3.31202 5.73658i −0.401641 0.695663i
\(69\) 0 0
\(70\) 0.467440 + 0.435146i 0.0558698 + 0.0520099i
\(71\) 4.23060 + 0.965606i 0.502080 + 0.114596i 0.466057 0.884755i \(-0.345674\pi\)
0.0360224 + 0.999351i \(0.488531\pi\)
\(72\) 0 0
\(73\) −4.31759 + 1.69453i −0.505336 + 0.198330i −0.604293 0.796762i \(-0.706544\pi\)
0.0989576 + 0.995092i \(0.468449\pi\)
\(74\) 6.51535 2.55708i 0.757394 0.297255i
\(75\) 0 0
\(76\) −2.24868 0.513247i −0.257941 0.0588734i
\(77\) −4.13795 10.5942i −0.471563 1.20733i
\(78\) 0 0
\(79\) 1.86308 + 3.22695i 0.209613 + 0.363060i 0.951593 0.307362i \(-0.0994463\pi\)
−0.741980 + 0.670422i \(0.766113\pi\)
\(80\) −0.00244411 + 0.00423332i −0.000273259 + 0.000473299i
\(81\) 0 0
\(82\) −5.39244 + 0.404107i −0.595495 + 0.0446262i
\(83\) −0.641843 + 0.804845i −0.0704514 + 0.0883433i −0.815808 0.578322i \(-0.803708\pi\)
0.745357 + 0.666666i \(0.232279\pi\)
\(84\) 0 0
\(85\) 0.922200 + 1.15640i 0.100027 + 0.125429i
\(86\) −6.41449 6.91317i −0.691692 0.745466i
\(87\) 0 0
\(88\) −10.0325 + 6.84002i −1.06946 + 0.729148i
\(89\) −15.0504 2.26848i −1.59534 0.240459i −0.709587 0.704617i \(-0.751119\pi\)
−0.885752 + 0.464159i \(0.846357\pi\)
\(90\) 0 0
\(91\) −7.90295 + 9.87680i −0.828454 + 1.03537i
\(92\) 0.571114 1.18593i 0.0595427 0.123642i
\(93\) 0 0
\(94\) 6.14400 6.62166i 0.633705 0.682972i
\(95\) 0.513585 + 0.0384879i 0.0526927 + 0.00394877i
\(96\) 0 0
\(97\) 10.6247i 1.07877i −0.842059 0.539385i \(-0.818657\pi\)
0.842059 0.539385i \(-0.181343\pi\)
\(98\) −6.08681 + 0.436126i −0.614860 + 0.0440554i
\(99\) 0 0
\(100\) −2.23041 + 5.68298i −0.223041 + 0.568298i
\(101\) −1.24376 + 16.5969i −0.123759 + 1.65145i 0.497220 + 0.867624i \(0.334354\pi\)
−0.620979 + 0.783827i \(0.713265\pi\)
\(102\) 0 0
\(103\) 1.06150 1.55694i 0.104593 0.153410i −0.770374 0.637592i \(-0.779931\pi\)
0.874967 + 0.484183i \(0.160883\pi\)
\(104\) 12.1669 + 5.85929i 1.19307 + 0.574550i
\(105\) 0 0
\(106\) −2.52330 + 1.21516i −0.245085 + 0.118027i
\(107\) 2.47659 16.4311i 0.239421 1.58845i −0.469350 0.883012i \(-0.655512\pi\)
0.708770 0.705439i \(-0.249250\pi\)
\(108\) 0 0
\(109\) −14.3027 + 2.15578i −1.36995 + 0.206487i −0.792466 0.609916i \(-0.791203\pi\)
−0.577483 + 0.816402i \(0.695965\pi\)
\(110\) 0.760657 0.705787i 0.0725258 0.0672941i
\(111\) 0 0
\(112\) −0.0136947 0.0446563i −0.00129403 0.00421962i
\(113\) 9.63490 + 7.68357i 0.906375 + 0.722810i 0.961248 0.275683i \(-0.0889042\pi\)
−0.0548736 + 0.998493i \(0.517476\pi\)
\(114\) 0 0
\(115\) −0.0866331 + 0.280858i −0.00807858 + 0.0261901i
\(116\) −3.56000 2.05537i −0.330538 0.190836i
\(117\) 0 0
\(118\) 10.3240 2.35639i 0.950405 0.216924i
\(119\) −14.0921 1.07924i −1.29182 0.0989335i
\(120\) 0 0
\(121\) −7.14777 + 2.20480i −0.649798 + 0.200436i
\(122\) −2.55648 6.51381i −0.231453 0.589733i
\(123\) 0 0
\(124\) −1.93800 6.28284i −0.174038 0.564216i
\(125\) 0.611403 2.67873i 0.0546855 0.239593i
\(126\) 0 0
\(127\) −2.70552 11.8537i −0.240077 1.05184i −0.940947 0.338555i \(-0.890062\pi\)
0.700870 0.713289i \(-0.252795\pi\)
\(128\) −6.10966 + 3.52741i −0.540023 + 0.311782i
\(129\) 0 0
\(130\) −1.10278 0.340162i −0.0967199 0.0298341i
\(131\) −0.180600 2.40993i −0.0157791 0.210557i −0.999520 0.0309660i \(-0.990142\pi\)
0.983741 0.179591i \(-0.0574774\pi\)
\(132\) 0 0
\(133\) −3.61303 + 3.34142i −0.313289 + 0.289738i
\(134\) −4.97484 + 3.96731i −0.429761 + 0.342723i
\(135\) 0 0
\(136\) 2.24883 + 14.9200i 0.192835 + 1.27938i
\(137\) −5.24492 7.69289i −0.448104 0.657248i 0.534022 0.845470i \(-0.320680\pi\)
−0.982126 + 0.188222i \(0.939727\pi\)
\(138\) 0 0
\(139\) 0.735987 + 1.52829i 0.0624256 + 0.129628i 0.929847 0.367946i \(-0.119939\pi\)
−0.867422 + 0.497574i \(0.834224\pi\)
\(140\) 0.392798 + 0.819077i 0.0331975 + 0.0692247i
\(141\) 0 0
\(142\) −3.12563 2.13102i −0.262297 0.178831i
\(143\) 15.0664 + 13.9795i 1.25991 + 1.16903i
\(144\) 0 0
\(145\) 0.854444 + 0.335345i 0.0709577 + 0.0278489i
\(146\) 4.04347 0.334640
\(147\) 0 0
\(148\) 9.95564 0.818349
\(149\) 3.50677 + 1.37630i 0.287286 + 0.112751i 0.504608 0.863349i \(-0.331637\pi\)
−0.217322 + 0.976100i \(0.569732\pi\)
\(150\) 0 0
\(151\) 4.76478 + 4.42107i 0.387752 + 0.359782i 0.849829 0.527058i \(-0.176705\pi\)
−0.462077 + 0.886840i \(0.652896\pi\)
\(152\) 4.34095 + 2.95961i 0.352098 + 0.240056i
\(153\) 0 0
\(154\) −0.0162164 + 9.91525i −0.00130675 + 0.798994i
\(155\) 0.636999 + 1.32274i 0.0511650 + 0.106245i
\(156\) 0 0
\(157\) −1.64517 2.41302i −0.131299 0.192580i 0.754959 0.655772i \(-0.227657\pi\)
−0.886258 + 0.463191i \(0.846704\pi\)
\(158\) −0.484144 3.21208i −0.0385164 0.255540i
\(159\) 0 0
\(160\) 1.22623 0.977890i 0.0969424 0.0773090i
\(161\) −1.40026 2.43451i −0.110356 0.191867i
\(162\) 0 0
\(163\) −0.954846 12.7415i −0.0747893 0.997994i −0.900770 0.434296i \(-0.856997\pi\)
0.825981 0.563698i \(-0.190622\pi\)
\(164\) −7.35000 2.26718i −0.573939 0.177037i
\(165\) 0 0
\(166\) 0.777201 0.448717i 0.0603225 0.0348272i
\(167\) 1.13054 + 4.95320i 0.0874835 + 0.383290i 0.999648 0.0265343i \(-0.00844713\pi\)
−0.912164 + 0.409824i \(0.865590\pi\)
\(168\) 0 0
\(169\) 2.19367 9.61109i 0.168744 0.739314i
\(170\) −0.380067 1.23215i −0.0291498 0.0945014i
\(171\) 0 0
\(172\) −4.90076 12.4869i −0.373680 0.952120i
\(173\) −11.6361 + 3.58926i −0.884676 + 0.272886i −0.703612 0.710585i \(-0.748430\pi\)
−0.181065 + 0.983471i \(0.557954\pi\)
\(174\) 0 0
\(175\) 7.32015 + 10.7745i 0.553351 + 0.814476i
\(176\) −0.0739905 + 0.0168878i −0.00557724 + 0.00127297i
\(177\) 0 0
\(178\) 11.4911 + 6.63437i 0.861291 + 0.497267i
\(179\) −3.24820 + 10.5304i −0.242782 + 0.787081i 0.749382 + 0.662138i \(0.230351\pi\)
−0.992164 + 0.124942i \(0.960125\pi\)
\(180\) 0 0
\(181\) 5.36313 + 4.27695i 0.398638 + 0.317903i 0.802207 0.597046i \(-0.203659\pi\)
−0.403569 + 0.914949i \(0.632230\pi\)
\(182\) 9.55903 5.49808i 0.708562 0.407545i
\(183\) 0 0
\(184\) −2.19790 + 2.03935i −0.162031 + 0.150343i
\(185\) −2.19818 + 0.331323i −0.161614 + 0.0243594i
\(186\) 0 0
\(187\) −3.42262 + 22.7076i −0.250287 + 1.66054i
\(188\) 11.5762 5.57478i 0.844278 0.406583i
\(189\) 0 0
\(190\) −0.404521 0.194807i −0.0293471 0.0141328i
\(191\) 5.80719 8.51758i 0.420193 0.616311i −0.556526 0.830830i \(-0.687866\pi\)
0.976720 + 0.214519i \(0.0688185\pi\)
\(192\) 0 0
\(193\) 1.73566 23.1608i 0.124936 1.66715i −0.484860 0.874592i \(-0.661130\pi\)
0.609796 0.792558i \(-0.291251\pi\)
\(194\) −3.38389 + 8.62202i −0.242949 + 0.619025i
\(195\) 0 0
\(196\) −8.28604 2.58562i −0.591860 0.184687i
\(197\) 12.5738i 0.895847i −0.894072 0.447923i \(-0.852164\pi\)
0.894072 0.447923i \(-0.147836\pi\)
\(198\) 0 0
\(199\) 22.3916 + 1.67802i 1.58730 + 0.118952i 0.838896 0.544292i \(-0.183201\pi\)
0.748404 + 0.663243i \(0.230821\pi\)
\(200\) 9.45864 10.1940i 0.668827 0.720824i
\(201\) 0 0
\(202\) 6.29534 13.0724i 0.442939 0.919772i
\(203\) −7.90850 + 3.79261i −0.555068 + 0.266189i
\(204\) 0 0
\(205\) 1.69832 + 0.255980i 0.118616 + 0.0178784i
\(206\) −1.35730 + 0.925388i −0.0945673 + 0.0644749i
\(207\) 0 0
\(208\) 0.0574106 + 0.0618739i 0.00398071 + 0.00429018i
\(209\) 4.98552 + 6.25165i 0.344856 + 0.432436i
\(210\) 0 0
\(211\) 6.35501 7.96894i 0.437497 0.548604i −0.513384 0.858159i \(-0.671609\pi\)
0.950882 + 0.309555i \(0.100180\pi\)
\(212\) −3.97252 + 0.297699i −0.272834 + 0.0204461i
\(213\) 0 0
\(214\) −7.24298 + 12.5452i −0.495120 + 0.857573i
\(215\) 1.49764 + 2.59399i 0.102138 + 0.176909i
\(216\) 0 0
\(217\) −13.3986 4.15693i −0.909556 0.282191i
\(218\) 12.2934 + 2.80589i 0.832613 + 0.190039i
\(219\) 0 0
\(220\) 1.37394 0.539232i 0.0926310 0.0363550i
\(221\) 23.7744 9.33075i 1.59924 0.627654i
\(222\) 0 0
\(223\) −12.5054 2.85429i −0.837426 0.191137i −0.217760 0.976002i \(-0.569875\pi\)
−0.619666 + 0.784865i \(0.712732\pi\)
\(224\) −1.14441 + 14.9431i −0.0764641 + 0.998428i
\(225\) 0 0
\(226\) −5.37164 9.30396i −0.357316 0.618890i
\(227\) −1.71216 + 2.96554i −0.113640 + 0.196830i −0.917235 0.398346i \(-0.869584\pi\)
0.803595 + 0.595176i \(0.202918\pi\)
\(228\) 0 0
\(229\) 19.3879 1.45292i 1.28119 0.0960118i 0.583323 0.812241i \(-0.301752\pi\)
0.697866 + 0.716229i \(0.254133\pi\)
\(230\) 0.159755 0.200327i 0.0105339 0.0132092i
\(231\) 0 0
\(232\) 5.83812 + 7.32078i 0.383292 + 0.480633i
\(233\) 11.1624 + 12.0302i 0.731274 + 0.788126i 0.983763 0.179474i \(-0.0574396\pi\)
−0.252489 + 0.967600i \(0.581249\pi\)
\(234\) 0 0
\(235\) −2.37046 + 1.61615i −0.154632 + 0.105426i
\(236\) 14.8944 + 2.24496i 0.969540 + 0.146135i
\(237\) 0 0
\(238\) 11.0922 + 5.36407i 0.718998 + 0.347701i
\(239\) −8.73850 + 18.1457i −0.565247 + 1.17375i 0.400988 + 0.916083i \(0.368667\pi\)
−0.966235 + 0.257664i \(0.917047\pi\)
\(240\) 0 0
\(241\) 4.89741 5.27815i 0.315470 0.339996i −0.555333 0.831628i \(-0.687409\pi\)
0.870803 + 0.491632i \(0.163600\pi\)
\(242\) 6.50271 + 0.487311i 0.418010 + 0.0313255i
\(243\) 0 0
\(244\) 9.95329i 0.637194i
\(245\) 1.91559 + 0.295140i 0.122383 + 0.0188558i
\(246\) 0 0
\(247\) 3.24900 8.27831i 0.206729 0.526736i
\(248\) −1.11921 + 14.9348i −0.0710700 + 0.948363i
\(249\) 0 0
\(250\) −1.34932 + 1.97909i −0.0853385 + 0.125169i
\(251\) 13.6920 + 6.59370i 0.864229 + 0.416191i 0.812839 0.582488i \(-0.197921\pi\)
0.0513894 + 0.998679i \(0.483635\pi\)
\(252\) 0 0
\(253\) −4.11136 + 1.97993i −0.258479 + 0.124477i
\(254\) −1.57977 + 10.4811i −0.0991235 + 0.657641i
\(255\) 0 0
\(256\) 15.7777 2.37810i 0.986106 0.148632i
\(257\) 11.8368 10.9830i 0.738361 0.685099i −0.218437 0.975851i \(-0.570096\pi\)
0.956799 + 0.290752i \(0.0939054\pi\)
\(258\) 0 0
\(259\) 11.9946 17.5312i 0.745311 1.08934i
\(260\) −1.28339 1.02347i −0.0795926 0.0634730i
\(261\) 0 0
\(262\) −0.620992 + 2.01321i −0.0383650 + 0.124376i
\(263\) −11.2661 6.50450i −0.694699 0.401084i 0.110671 0.993857i \(-0.464700\pi\)
−0.805370 + 0.592773i \(0.798033\pi\)
\(264\) 0 0
\(265\) 0.867217 0.197937i 0.0532727 0.0121591i
\(266\) 3.99623 1.56087i 0.245025 0.0957029i
\(267\) 0 0
\(268\) −8.64874 + 2.66778i −0.528306 + 0.162961i
\(269\) −2.21024 5.63160i −0.134761 0.343365i 0.847525 0.530756i \(-0.178092\pi\)
−0.982285 + 0.187391i \(0.939997\pi\)
\(270\) 0 0
\(271\) 2.34986 + 7.61806i 0.142744 + 0.462764i 0.998508 0.0546014i \(-0.0173888\pi\)
−0.855764 + 0.517366i \(0.826913\pi\)
\(272\) −0.0209855 + 0.0919434i −0.00127243 + 0.00557489i
\(273\) 0 0
\(274\) 1.80617 + 7.91334i 0.109115 + 0.478062i
\(275\) 18.3291 10.5823i 1.10529 0.638139i
\(276\) 0 0
\(277\) 14.6743 + 4.52643i 0.881695 + 0.271967i 0.702360 0.711821i \(-0.252129\pi\)
0.179334 + 0.983788i \(0.442606\pi\)
\(278\) −0.110509 1.47463i −0.00662786 0.0884427i
\(279\) 0 0
\(280\) −0.151255 2.06364i −0.00903921 0.123326i
\(281\) 7.00086 5.58300i 0.417636 0.333054i −0.392022 0.919956i \(-0.628224\pi\)
0.809658 + 0.586902i \(0.199653\pi\)
\(282\) 0 0
\(283\) −2.90781 19.2921i −0.172852 1.14680i −0.892032 0.451972i \(-0.850721\pi\)
0.719181 0.694823i \(-0.244517\pi\)
\(284\) −3.03117 4.44591i −0.179867 0.263816i
\(285\) 0 0
\(286\) −7.77410 16.1431i −0.459692 0.954561i
\(287\) −12.8477 + 10.2114i −0.758376 + 0.602758i
\(288\) 0 0
\(289\) 9.53151 + 6.49847i 0.560677 + 0.382263i
\(290\) −0.586585 0.544271i −0.0344455 0.0319607i
\(291\) 0 0
\(292\) 5.35386 + 2.10124i 0.313311 + 0.122966i
\(293\) −23.9976 −1.40195 −0.700977 0.713183i \(-0.747253\pi\)
−0.700977 + 0.713183i \(0.747253\pi\)
\(294\) 0 0
\(295\) −3.36335 −0.195822
\(296\) −21.1098 8.28499i −1.22698 0.481555i
\(297\) 0 0
\(298\) −2.40743 2.23377i −0.139459 0.129399i
\(299\) 4.19325 + 2.85891i 0.242502 + 0.165335i
\(300\) 0 0
\(301\) −27.8932 6.41445i −1.60774 0.369723i
\(302\) −2.45858 5.10530i −0.141476 0.293777i
\(303\) 0 0
\(304\) 0.0184985 + 0.0271323i 0.00106096 + 0.00155614i
\(305\) 0.331245 + 2.19767i 0.0189670 + 0.125838i
\(306\) 0 0
\(307\) −21.5006 + 17.1462i −1.22711 + 0.978584i −0.227116 + 0.973868i \(0.572930\pi\)
−0.999989 + 0.00471621i \(0.998499\pi\)
\(308\) −5.17405 + 13.1201i −0.294819 + 0.747589i
\(309\) 0 0
\(310\) −0.0956454 1.27630i −0.00543229 0.0724889i
\(311\) −15.0023 4.62759i −0.850701 0.262407i −0.161407 0.986888i \(-0.551603\pi\)
−0.689294 + 0.724481i \(0.742079\pi\)
\(312\) 0 0
\(313\) −15.8489 + 9.15035i −0.895831 + 0.517209i −0.875845 0.482592i \(-0.839696\pi\)
−0.0199860 + 0.999800i \(0.506362\pi\)
\(314\) 0.566539 + 2.48217i 0.0319717 + 0.140077i
\(315\) 0 0
\(316\) 1.02815 4.50464i 0.0578382 0.253406i
\(317\) −4.14770 13.4465i −0.232958 0.755231i −0.994275 0.106851i \(-0.965923\pi\)
0.761317 0.648380i \(-0.224553\pi\)
\(318\) 0 0
\(319\) 5.20648 + 13.2659i 0.291507 + 0.742748i
\(320\) −1.29721 + 0.400137i −0.0725164 + 0.0223683i
\(321\) 0 0
\(322\) 0.360950 + 2.42161i 0.0201149 + 0.134951i
\(323\) 9.68721 2.21104i 0.539011 0.123026i
\(324\) 0 0
\(325\) −20.3850 11.7693i −1.13076 0.652844i
\(326\) −3.28324 + 10.6440i −0.181842 + 0.589517i
\(327\) 0 0
\(328\) 13.6981 + 10.9239i 0.756352 + 0.603171i
\(329\) 4.13022 27.1014i 0.227707 1.49415i
\(330\) 0 0
\(331\) −5.68394 + 5.27393i −0.312418 + 0.289881i −0.820759 0.571274i \(-0.806449\pi\)
0.508341 + 0.861156i \(0.330259\pi\)
\(332\) 1.26226 0.190254i 0.0692753 0.0104416i
\(333\) 0 0
\(334\) 0.660125 4.37964i 0.0361204 0.239643i
\(335\) 1.82084 0.876870i 0.0994831 0.0479085i
\(336\) 0 0
\(337\) −14.8709 7.16145i −0.810070 0.390109i −0.0174669 0.999847i \(-0.505560\pi\)
−0.792603 + 0.609739i \(0.791274\pi\)
\(338\) −4.84126 + 7.10083i −0.263330 + 0.386234i
\(339\) 0 0
\(340\) 0.137062 1.82897i 0.00743323 0.0991896i
\(341\) −8.32754 + 21.2182i −0.450962 + 1.14903i
\(342\) 0 0
\(343\) −14.5362 + 11.4760i −0.784881 + 0.619646i
\(344\) 30.5555i 1.64744i
\(345\) 0 0
\(346\) 10.5860 + 0.793309i 0.569105 + 0.0426486i
\(347\) −4.50396 + 4.85411i −0.241785 + 0.260582i −0.842273 0.539052i \(-0.818783\pi\)
0.600488 + 0.799634i \(0.294973\pi\)
\(348\) 0 0
\(349\) −14.2030 + 29.4929i −0.760270 + 1.57872i 0.0542126 + 0.998529i \(0.482735\pi\)
−0.814483 + 0.580188i \(0.802979\pi\)
\(350\) −2.50876 11.0751i −0.134099 0.591986i
\(351\) 0 0
\(352\) 24.0788 + 3.62930i 1.28341 + 0.193442i
\(353\) 21.2098 14.4606i 1.12889 0.769661i 0.153061 0.988217i \(-0.451087\pi\)
0.975824 + 0.218556i \(0.0701346\pi\)
\(354\) 0 0
\(355\) 0.817236 + 0.880771i 0.0433744 + 0.0467464i
\(356\) 11.7674 + 14.7559i 0.623672 + 0.782060i
\(357\) 0 0
\(358\) 5.98983 7.51101i 0.316572 0.396969i
\(359\) −34.3431 + 2.57366i −1.81256 + 0.135833i −0.937456 0.348103i \(-0.886826\pi\)
−0.875103 + 0.483936i \(0.839207\pi\)
\(360\) 0 0
\(361\) −7.77007 + 13.4582i −0.408951 + 0.708324i
\(362\) −2.99005 5.17892i −0.157153 0.272198i
\(363\) 0 0
\(364\) 15.5140 2.31242i 0.813157 0.121204i
\(365\) −1.25205 0.285772i −0.0655353 0.0149580i
\(366\) 0 0
\(367\) −1.39443 + 0.547272i −0.0727885 + 0.0285674i −0.401456 0.915878i \(-0.631496\pi\)
0.328667 + 0.944446i \(0.393400\pi\)
\(368\) −0.0174448 + 0.00684657i −0.000909372 + 0.000356902i
\(369\) 0 0
\(370\) 1.88937 + 0.431237i 0.0982239 + 0.0224190i
\(371\) −4.26190 + 7.35402i −0.221267 + 0.381802i
\(372\) 0 0
\(373\) −7.15901 12.3998i −0.370680 0.642036i 0.618991 0.785398i \(-0.287542\pi\)
−0.989670 + 0.143362i \(0.954209\pi\)
\(374\) 10.0097 17.3374i 0.517591 0.896493i
\(375\) 0 0
\(376\) −29.1852 + 2.18713i −1.50511 + 0.112792i
\(377\) 9.88200 12.3916i 0.508949 0.638202i
\(378\) 0 0
\(379\) −12.2500 15.3610i −0.629241 0.789043i 0.360371 0.932809i \(-0.382650\pi\)
−0.989612 + 0.143766i \(0.954079\pi\)
\(380\) −0.434384 0.468154i −0.0222834 0.0240158i
\(381\) 0 0
\(382\) −7.42540 + 5.06255i −0.379916 + 0.259023i
\(383\) −38.4974 5.80256i −1.96713 0.296497i −0.998927 0.0463217i \(-0.985250\pi\)
−0.968201 0.250175i \(-0.919512\pi\)
\(384\) 0 0
\(385\) 0.705783 3.06909i 0.0359700 0.156415i
\(386\) −8.78509 + 18.2424i −0.447149 + 0.928515i
\(387\) 0 0
\(388\) −8.96108 + 9.65774i −0.454930 + 0.490298i
\(389\) 18.9964 + 1.42358i 0.963155 + 0.0721785i 0.547016 0.837122i \(-0.315764\pi\)
0.416140 + 0.909301i \(0.363383\pi\)
\(390\) 0 0
\(391\) 5.67048i 0.286769i
\(392\) 15.4179 + 12.3781i 0.778720 + 0.625187i
\(393\) 0 0
\(394\) −4.00469 + 10.2038i −0.201753 + 0.514059i
\(395\) −0.0771003 + 1.02883i −0.00387934 + 0.0517662i
\(396\) 0 0
\(397\) 21.3628 31.3335i 1.07217 1.57258i 0.282284 0.959331i \(-0.408908\pi\)
0.789886 0.613254i \(-0.210140\pi\)
\(398\) −17.6366 8.49334i −0.884043 0.425733i
\(399\) 0 0
\(400\) 0.0783106 0.0377124i 0.00391553 0.00188562i
\(401\) 1.67231 11.0951i 0.0835112 0.554060i −0.907476 0.420104i \(-0.861994\pi\)
0.990987 0.133957i \(-0.0427683\pi\)
\(402\) 0 0
\(403\) 25.0674 3.77831i 1.24870 0.188211i
\(404\) 15.1288 14.0374i 0.752684 0.698388i
\(405\) 0 0
\(406\) 7.62576 0.558931i 0.378460 0.0277393i
\(407\) −26.9841 21.5191i −1.33755 1.06666i
\(408\) 0 0
\(409\) −2.17430 + 7.04892i −0.107512 + 0.348547i −0.993303 0.115538i \(-0.963141\pi\)
0.885791 + 0.464085i \(0.153617\pi\)
\(410\) −1.29667 0.748635i −0.0640381 0.0369724i
\(411\) 0 0
\(412\) −2.27805 + 0.519951i −0.112232 + 0.0256161i
\(413\) 21.8981 23.5232i 1.07753 1.15750i
\(414\) 0 0
\(415\) −0.272372 + 0.0840155i −0.0133702 + 0.00412416i
\(416\) −9.89422 25.2101i −0.485104 1.23602i
\(417\) 0 0
\(418\) −2.05469 6.66114i −0.100498 0.325807i
\(419\) −3.14968 + 13.7996i −0.153872 + 0.674156i 0.837866 + 0.545876i \(0.183803\pi\)
−0.991738 + 0.128280i \(0.959054\pi\)
\(420\) 0 0
\(421\) −0.174136 0.762941i −0.00848688 0.0371835i 0.970507 0.241072i \(-0.0774991\pi\)
−0.978994 + 0.203889i \(0.934642\pi\)
\(422\) −7.69522 + 4.44284i −0.374598 + 0.216274i
\(423\) 0 0
\(424\) 8.67102 + 2.67465i 0.421102 + 0.129893i
\(425\) −1.96540 26.2265i −0.0953360 1.27217i
\(426\) 0 0
\(427\) −17.5271 11.9918i −0.848196 0.580325i
\(428\) −16.1095 + 12.8469i −0.778684 + 0.620980i
\(429\) 0 0
\(430\) −0.389180 2.58204i −0.0187679 0.124517i
\(431\) −9.82949 14.4172i −0.473470 0.694453i 0.513001 0.858388i \(-0.328534\pi\)
−0.986471 + 0.163935i \(0.947581\pi\)
\(432\) 0 0
\(433\) 13.1419 + 27.2894i 0.631558 + 1.31144i 0.933658 + 0.358167i \(0.116598\pi\)
−0.302100 + 0.953276i \(0.597688\pi\)
\(434\) 9.54915 + 7.64077i 0.458374 + 0.366769i
\(435\) 0 0
\(436\) 14.8193 + 10.1036i 0.709715 + 0.483876i
\(437\) 1.44740 + 1.34299i 0.0692384 + 0.0642438i
\(438\) 0 0
\(439\) 10.1890 + 3.99890i 0.486296 + 0.190857i 0.595806 0.803129i \(-0.296833\pi\)
−0.109510 + 0.993986i \(0.534928\pi\)
\(440\) −3.36202 −0.160278
\(441\) 0 0
\(442\) −22.2649 −1.05904
\(443\) 16.2878 + 6.39250i 0.773858 + 0.303717i 0.719214 0.694789i \(-0.244502\pi\)
0.0546446 + 0.998506i \(0.482597\pi\)
\(444\) 0 0
\(445\) −3.08930 2.86645i −0.146447 0.135883i
\(446\) 9.23922 + 6.29919i 0.437490 + 0.298276i
\(447\) 0 0
\(448\) 5.64732 11.6779i 0.266811 0.551729i
\(449\) −8.43206 17.5094i −0.397933 0.826317i −0.999619 0.0275846i \(-0.991218\pi\)
0.601686 0.798733i \(-0.294496\pi\)
\(450\) 0 0
\(451\) 15.0212 + 22.0321i 0.707321 + 1.03745i
\(452\) −2.27756 15.1106i −0.107127 0.710743i
\(453\) 0 0
\(454\) 2.33394 1.86126i 0.109537 0.0873531i
\(455\) −3.34851 + 1.02688i −0.156981 + 0.0481411i
\(456\) 0 0
\(457\) −0.462572 6.17260i −0.0216382 0.288742i −0.997517 0.0704283i \(-0.977563\pi\)
0.975879 0.218314i \(-0.0700556\pi\)
\(458\) −16.1962 4.99587i −0.756800 0.233442i
\(459\) 0 0
\(460\) 0.315630 0.182229i 0.0147163 0.00849649i
\(461\) −5.60182 24.5432i −0.260903 1.14309i −0.920275 0.391273i \(-0.872035\pi\)
0.659372 0.751817i \(-0.270822\pi\)
\(462\) 0 0
\(463\) −6.45210 + 28.2685i −0.299854 + 1.31375i 0.570490 + 0.821304i \(0.306753\pi\)
−0.870344 + 0.492443i \(0.836104\pi\)
\(464\) 0.0172507 + 0.0559254i 0.000800844 + 0.00259627i
\(465\) 0 0
\(466\) −5.22686 13.3178i −0.242129 0.616936i
\(467\) 30.4671 9.39786i 1.40985 0.434881i 0.505927 0.862576i \(-0.331150\pi\)
0.903923 + 0.427695i \(0.140674\pi\)
\(468\) 0 0
\(469\) −5.72228 + 18.4440i −0.264231 + 0.851667i
\(470\) 2.43839 0.556547i 0.112475 0.0256716i
\(471\) 0 0
\(472\) −29.7135 17.1551i −1.36768 0.789628i
\(473\) −13.7073 + 44.4381i −0.630264 + 2.04326i
\(474\) 0 0
\(475\) −7.15982 5.70976i −0.328515 0.261982i
\(476\) 11.8994 + 12.8666i 0.545407 + 0.589740i
\(477\) 0 0
\(478\) 12.8707 11.9423i 0.588692 0.546226i
\(479\) 13.8989 2.09492i 0.635057 0.0957195i 0.176380 0.984322i \(-0.443561\pi\)
0.458678 + 0.888603i \(0.348323\pi\)
\(480\) 0 0
\(481\) −5.72103 + 37.9566i −0.260857 + 1.73067i
\(482\) −5.65536 + 2.72348i −0.257595 + 0.124051i
\(483\) 0 0
\(484\) 8.35685 + 4.02445i 0.379857 + 0.182929i
\(485\) 1.65718 2.43063i 0.0752486 0.110369i
\(486\) 0 0
\(487\) −1.41125 + 18.8319i −0.0639500 + 0.853353i 0.869336 + 0.494221i \(0.164547\pi\)
−0.933286 + 0.359133i \(0.883073\pi\)
\(488\) −8.28303 + 21.1048i −0.374955 + 0.955370i
\(489\) 0 0
\(490\) −1.46052 0.849614i −0.0659796 0.0383816i
\(491\) 23.3060i 1.05179i −0.850550 0.525894i \(-0.823731\pi\)
0.850550 0.525894i \(-0.176269\pi\)
\(492\) 0 0
\(493\) 17.6593 + 1.32339i 0.795337 + 0.0596023i
\(494\) −5.27319 + 5.68315i −0.237252 + 0.255697i
\(495\) 0 0
\(496\) −0.0406154 + 0.0843388i −0.00182369 + 0.00378693i
\(497\) −11.4809 0.0187771i −0.514991 0.000842266i
\(498\) 0 0
\(499\) 1.48858 + 0.224367i 0.0666379 + 0.0100441i 0.182277 0.983247i \(-0.441653\pi\)
−0.115639 + 0.993291i \(0.536891\pi\)
\(500\) −2.81506 + 1.91928i −0.125893 + 0.0858327i
\(501\) 0 0
\(502\) −9.01111 9.71167i −0.402186 0.433453i
\(503\) −26.3252 33.0107i −1.17378 1.47187i −0.850816 0.525464i \(-0.823892\pi\)
−0.322965 0.946411i \(-0.604680\pi\)
\(504\) 0 0
\(505\) −2.87323 + 3.60292i −0.127857 + 0.160328i
\(506\) 3.96701 0.297286i 0.176355 0.0132160i
\(507\) 0 0
\(508\) −7.53836 + 13.0568i −0.334460 + 0.579302i
\(509\) 7.79004 + 13.4927i 0.345287 + 0.598055i 0.985406 0.170221i \(-0.0544481\pi\)
−0.640118 + 0.768276i \(0.721115\pi\)
\(510\) 0 0
\(511\) 10.1505 6.89622i 0.449033 0.305071i
\(512\) 0.194726 + 0.0444450i 0.00860578 + 0.00196421i
\(513\) 0 0
\(514\) −13.1037 + 5.14284i −0.577981 + 0.226841i
\(515\) 0.485686 0.190618i 0.0214019 0.00839961i
\(516\) 0 0
\(517\) −43.4263 9.91178i −1.90989 0.435920i
\(518\) −15.3174 + 10.4066i −0.673007 + 0.457238i
\(519\) 0 0
\(520\) 1.86956 + 3.23818i 0.0819858 + 0.142004i
\(521\) 4.91771 8.51773i 0.215449 0.373168i −0.737962 0.674842i \(-0.764212\pi\)
0.953411 + 0.301673i \(0.0975452\pi\)
\(522\) 0 0
\(523\) 4.35373 0.326267i 0.190375 0.0142667i 0.0207989 0.999784i \(-0.493379\pi\)
0.169577 + 0.985517i \(0.445760\pi\)
\(524\) −1.86843 + 2.34294i −0.0816227 + 0.102352i
\(525\) 0 0
\(526\) 7.07093 + 8.86666i 0.308307 + 0.386605i
\(527\) 19.2656 + 20.7634i 0.839222 + 0.904467i
\(528\) 0 0
\(529\) 18.0725 12.3216i 0.785760 0.535722i
\(530\) −0.766797 0.115576i −0.0333075 0.00502030i
\(531\) 0 0
\(532\) 6.10244 + 0.00998053i 0.264574 + 0.000432711i
\(533\) 12.8675 26.7195i 0.557351 1.15735i
\(534\) 0 0
\(535\) 3.12941 3.37270i 0.135296 0.145814i
\(536\) 20.5588 + 1.54067i 0.888003 + 0.0665466i
\(537\) 0 0
\(538\) 5.27405i 0.227381i
\(539\) 16.8700 + 24.9184i 0.726641 + 1.07331i
\(540\) 0 0
\(541\) 8.74975 22.2940i 0.376181 0.958494i −0.609937 0.792450i \(-0.708805\pi\)
0.986118 0.166044i \(-0.0530995\pi\)
\(542\) 0.519373 6.93056i 0.0223090 0.297693i
\(543\) 0 0
\(544\) 17.0456 25.0014i 0.730826 1.07192i
\(545\) −3.60832 1.73767i −0.154563 0.0744337i
\(546\) 0 0
\(547\) 6.46836 3.11500i 0.276567 0.133188i −0.290459 0.956887i \(-0.593808\pi\)
0.567026 + 0.823700i \(0.308094\pi\)
\(548\) −1.72076 + 11.4165i −0.0735071 + 0.487688i
\(549\) 0 0
\(550\) −18.2447 + 2.74995i −0.777957 + 0.117258i
\(551\) 4.52020 4.19414i 0.192567 0.178676i
\(552\) 0 0
\(553\) −6.69365 7.23775i −0.284643 0.307780i
\(554\) −10.4667 8.34693i −0.444688 0.354627i
\(555\) 0 0
\(556\) 0.619990 2.00996i 0.0262934 0.0852411i
\(557\) −24.1717 13.9555i −1.02419 0.591315i −0.108873 0.994056i \(-0.534724\pi\)
−0.915314 + 0.402741i \(0.868058\pi\)
\(558\) 0 0
\(559\) 50.4235 11.5088i 2.13269 0.486772i
\(560\) 0.00383228 0.0123522i 0.000161943 0.000521975i
\(561\) 0 0
\(562\) −7.45942 + 2.30093i −0.314657 + 0.0970588i
\(563\) 2.96369 + 7.55137i 0.124905 + 0.318252i 0.979625 0.200837i \(-0.0643663\pi\)
−0.854720 + 0.519090i \(0.826271\pi\)
\(564\) 0 0
\(565\) 1.00576 + 3.26059i 0.0423126 + 0.137174i
\(566\) −3.78470 + 16.5818i −0.159083 + 0.696987i
\(567\) 0 0
\(568\) 2.72741 + 11.9496i 0.114439 + 0.501392i
\(569\) −25.8002 + 14.8957i −1.08160 + 0.624462i −0.931328 0.364183i \(-0.881348\pi\)
−0.150272 + 0.988645i \(0.548015\pi\)
\(570\) 0 0
\(571\) 23.9608 + 7.39093i 1.00273 + 0.309301i 0.752291 0.658832i \(-0.228949\pi\)
0.250439 + 0.968132i \(0.419425\pi\)
\(572\) −1.90456 25.4146i −0.0796337 1.06264i
\(573\) 0 0
\(574\) 13.6783 4.19471i 0.570921 0.175084i
\(575\) 4.08598 3.25846i 0.170397 0.135887i
\(576\) 0 0
\(577\) −1.36164 9.03390i −0.0566859 0.376086i −0.999129 0.0417207i \(-0.986716\pi\)
0.942443 0.334366i \(-0.108522\pi\)
\(578\) −5.66519 8.30931i −0.235641 0.345622i
\(579\) 0 0
\(580\) −0.493847 1.02548i −0.0205059 0.0425809i
\(581\) 1.18575 2.45197i 0.0491932 0.101725i
\(582\) 0 0
\(583\) 11.4107 + 7.77971i 0.472585 + 0.322203i
\(584\) −9.60362 8.91086i −0.397401 0.368734i
\(585\) 0 0
\(586\) 19.4743 + 7.64310i 0.804476 + 0.315734i
\(587\) 1.41804 0.0585289 0.0292645 0.999572i \(-0.490684\pi\)
0.0292645 + 0.999572i \(0.490684\pi\)
\(588\) 0 0
\(589\) 9.86270 0.406385
\(590\) 2.72940 + 1.07121i 0.112367 + 0.0441010i
\(591\) 0 0
\(592\) −0.103903 0.0964082i −0.00427040 0.00396235i
\(593\) 36.0642 + 24.5882i 1.48098 + 1.00971i 0.990387 + 0.138326i \(0.0441721\pi\)
0.490593 + 0.871389i \(0.336780\pi\)
\(594\) 0 0
\(595\) −3.05556 2.44491i −0.125266 0.100232i
\(596\) −2.02682 4.20874i −0.0830218 0.172397i
\(597\) 0 0
\(598\) −2.49232 3.65556i −0.101918 0.149487i
\(599\) 6.45351 + 42.8162i 0.263683 + 1.74942i 0.592999 + 0.805203i \(0.297944\pi\)
−0.329315 + 0.944220i \(0.606818\pi\)
\(600\) 0 0
\(601\) −2.02198 + 1.61248i −0.0824784 + 0.0657743i −0.663861 0.747856i \(-0.731083\pi\)
0.581383 + 0.813630i \(0.302512\pi\)
\(602\) 20.5926 + 14.0892i 0.839293 + 0.574234i
\(603\) 0 0
\(604\) −0.602323 8.03745i −0.0245082 0.327039i
\(605\) −1.97911 0.610474i −0.0804622 0.0248193i
\(606\) 0 0
\(607\) −34.4840 + 19.9093i −1.39966 + 0.808095i −0.994357 0.106087i \(-0.966168\pi\)
−0.405304 + 0.914182i \(0.632834\pi\)
\(608\) −2.34456 10.2722i −0.0950846 0.416593i
\(609\) 0 0
\(610\) 0.431136 1.88893i 0.0174562 0.0764805i
\(611\) 14.6020 + 47.3384i 0.590733 + 1.91511i
\(612\) 0 0
\(613\) −12.6903 32.3343i −0.512555 1.30597i −0.919706 0.392607i \(-0.871573\pi\)
0.407151 0.913361i \(-0.366522\pi\)
\(614\) 22.9089 7.06647i 0.924530 0.285180i
\(615\) 0 0
\(616\) 21.8894 23.5140i 0.881950 0.947404i
\(617\) 11.6915 2.66851i 0.470682 0.107430i 0.0194008 0.999812i \(-0.493824\pi\)
0.451282 + 0.892382i \(0.350967\pi\)
\(618\) 0 0
\(619\) −30.5798 17.6553i −1.22911 0.709625i −0.262263 0.964996i \(-0.584469\pi\)
−0.966843 + 0.255372i \(0.917802\pi\)
\(620\) 0.536602 1.73962i 0.0215505 0.0698649i
\(621\) 0 0
\(622\) 10.7006 + 8.53348i 0.429057 + 0.342161i
\(623\) 40.1617 2.94366i 1.60904 0.117935i
\(624\) 0 0
\(625\) −17.4876 + 16.2261i −0.699505 + 0.649045i
\(626\) 15.7759 2.37783i 0.630530 0.0950372i
\(627\) 0 0
\(628\) −0.539748 + 3.58100i −0.0215383 + 0.142897i
\(629\) −38.6411 + 18.6086i −1.54072 + 0.741973i
\(630\) 0 0
\(631\) −10.0804 4.85448i −0.401295 0.193254i 0.222340 0.974969i \(-0.428631\pi\)
−0.623635 + 0.781716i \(0.714345\pi\)
\(632\) −5.92880 + 8.69595i −0.235835 + 0.345906i
\(633\) 0 0
\(634\) −0.916736 + 12.2330i −0.0364083 + 0.485834i
\(635\) 1.22992 3.13379i 0.0488080 0.124361i
\(636\) 0 0
\(637\) 14.6194 30.1053i 0.579243 1.19281i
\(638\) 12.4237i 0.491857i
\(639\) 0 0
\(640\) −1.94791 0.145976i −0.0769980 0.00577020i
\(641\) −27.6812 + 29.8332i −1.09334 + 1.17834i −0.110503 + 0.993876i \(0.535246\pi\)
−0.982839 + 0.184466i \(0.940944\pi\)
\(642\) 0 0
\(643\) 2.78693 5.78711i 0.109906 0.228221i −0.838761 0.544500i \(-0.816719\pi\)
0.948666 + 0.316279i \(0.102434\pi\)
\(644\) −0.780494 + 3.39397i −0.0307558 + 0.133741i
\(645\) 0 0
\(646\) −8.56547 1.29104i −0.337004 0.0507952i
\(647\) 0.889227 0.606265i 0.0349591 0.0238347i −0.545714 0.837971i \(-0.683742\pi\)
0.580674 + 0.814136i \(0.302789\pi\)
\(648\) 0 0
\(649\) −35.5177 38.2790i −1.39419 1.50258i
\(650\) 12.7942 + 16.0434i 0.501830 + 0.629275i
\(651\) 0 0
\(652\) −9.87855 + 12.3873i −0.386874 + 0.485125i
\(653\) 28.3505 2.12457i 1.10944 0.0831410i 0.492619 0.870245i \(-0.336040\pi\)
0.616820 + 0.787104i \(0.288421\pi\)
\(654\) 0 0
\(655\) 0.334572 0.579496i 0.0130728 0.0226428i
\(656\) 0.0547544 + 0.0948374i 0.00213780 + 0.00370278i
\(657\) 0 0
\(658\) −11.9834 + 20.6776i −0.467160 + 0.806098i
\(659\) −21.2058 4.84008i −0.826060 0.188543i −0.211465 0.977386i \(-0.567823\pi\)
−0.614595 + 0.788843i \(0.710681\pi\)
\(660\) 0 0
\(661\) −15.9421 + 6.25682i −0.620077 + 0.243362i −0.654520 0.756044i \(-0.727129\pi\)
0.0344436 + 0.999407i \(0.489034\pi\)
\(662\) 6.29230 2.46954i 0.244557 0.0959816i
\(663\) 0 0
\(664\) −2.83480 0.647024i −0.110011 0.0251094i
\(665\) −1.34774 + 0.200885i −0.0522631 + 0.00778999i
\(666\) 0 0
\(667\) 1.75949 + 3.04753i 0.0681278 + 0.118001i
\(668\) 3.14999 5.45594i 0.121877 0.211097i
\(669\) 0 0
\(670\) −1.75691 + 0.131662i −0.0678753 + 0.00508655i
\(671\) −21.5141 + 26.9778i −0.830541 + 1.04147i
\(672\) 0 0
\(673\) −2.48969 3.12198i −0.0959706 0.120343i 0.731527 0.681812i \(-0.238808\pi\)
−0.827498 + 0.561469i \(0.810236\pi\)
\(674\) 9.78701 + 10.5479i 0.376982 + 0.406289i
\(675\) 0 0
\(676\) −10.1002 + 6.88622i −0.388471 + 0.264855i
\(677\) 19.0605 + 2.87290i 0.732553 + 0.110415i 0.504717 0.863285i \(-0.331597\pi\)
0.227836 + 0.973699i \(0.426835\pi\)
\(678\) 0 0
\(679\) 6.21028 + 27.4156i 0.238329 + 1.05211i
\(680\) −1.81267 + 3.76405i −0.0695127 + 0.144345i
\(681\) 0 0
\(682\) 13.5158 14.5665i 0.517546 0.557782i
\(683\) −16.0986 1.20642i −0.615994 0.0461624i −0.236921 0.971529i \(-0.576138\pi\)
−0.379074 + 0.925367i \(0.623757\pi\)
\(684\) 0 0
\(685\) 2.57800i 0.0985003i
\(686\) 15.4513 4.68320i 0.589934 0.178806i
\(687\) 0 0
\(688\) −0.0697733 + 0.177779i −0.00266008 + 0.00677778i
\(689\) 1.14782 15.3166i 0.0437284 0.583515i
\(690\) 0 0
\(691\) 18.8400 27.6332i 0.716708 1.05122i −0.279146 0.960249i \(-0.590051\pi\)
0.995854 0.0909687i \(-0.0289963\pi\)
\(692\) 13.6044 + 6.55153i 0.517162 + 0.249052i
\(693\) 0 0
\(694\) 5.20101 2.50468i 0.197428 0.0950762i
\(695\) −0.0700012 + 0.464427i −0.00265530 + 0.0176167i
\(696\) 0 0
\(697\) 32.7655 4.93860i 1.24108 0.187063i
\(698\) 20.9192 19.4102i 0.791804 0.734687i
\(699\) 0 0
\(700\) 2.43349 15.9679i 0.0919774 0.603531i
\(701\) 26.7063 + 21.2976i 1.00868 + 0.804398i 0.980761 0.195212i \(-0.0625395\pi\)
0.0279223 + 0.999610i \(0.491111\pi\)
\(702\) 0 0
\(703\) −4.40184 + 14.2704i −0.166018 + 0.538219i
\(704\) −18.2529 10.5383i −0.687931 0.397177i
\(705\) 0 0
\(706\) −21.8176 + 4.97973i −0.821117 + 0.187415i
\(707\) −6.49176 43.5532i −0.244148 1.63799i
\(708\) 0 0
\(709\) 19.0917 5.88901i 0.717004 0.221167i 0.0852770 0.996357i \(-0.472822\pi\)
0.631727 + 0.775191i \(0.282346\pi\)
\(710\) −0.382675 0.975039i −0.0143615 0.0365926i
\(711\) 0 0
\(712\) −12.6718 41.0809i −0.474895 1.53957i
\(713\) −1.25245 + 5.48735i −0.0469047 + 0.205503i
\(714\) 0 0
\(715\) 1.26632 + 5.54811i 0.0473577 + 0.207488i
\(716\) 11.8342 6.83247i 0.442264 0.255341i
\(717\) 0 0
\(718\) 28.6895 + 8.84953i 1.07068 + 0.330262i
\(719\) −0.768305 10.2523i −0.0286529 0.382347i −0.993034 0.117829i \(-0.962406\pi\)
0.964381 0.264517i \(-0.0852126\pi\)
\(720\) 0 0
\(721\) −1.82902 + 4.63795i −0.0681163 + 0.172726i
\(722\) 10.5918 8.44671i 0.394187 0.314354i
\(723\) 0 0
\(724\) −1.26777 8.41110i −0.0471163 0.312596i
\(725\) −9.19409 13.4852i −0.341460 0.500830i
\(726\) 0 0
\(727\) 8.03723 + 16.6895i 0.298084 + 0.618978i 0.995187 0.0979928i \(-0.0312422\pi\)
−0.697103 + 0.716971i \(0.745528\pi\)
\(728\) −34.8201 8.00740i −1.29052 0.296774i
\(729\) 0 0
\(730\) 0.925035 + 0.630678i 0.0342371 + 0.0233425i
\(731\) 42.3614 + 39.3057i 1.56679 + 1.45377i
\(732\) 0 0
\(733\) 2.10783 + 0.827261i 0.0778544 + 0.0305556i 0.403949 0.914782i \(-0.367637\pi\)
−0.326094 + 0.945337i \(0.605733\pi\)
\(734\) 1.30590 0.0482015
\(735\) 0 0
\(736\) 6.01291 0.221639
\(737\) 29.2083 + 11.4634i 1.07590 + 0.422260i
\(738\) 0 0
\(739\) −2.56600 2.38090i −0.0943920 0.0875830i 0.631566 0.775322i \(-0.282413\pi\)
−0.725958 + 0.687739i \(0.758603\pi\)
\(740\) 2.27758 + 1.55283i 0.0837255 + 0.0570831i
\(741\) 0 0
\(742\) 5.80079 4.61048i 0.212954 0.169256i
\(743\) −7.79526 16.1870i −0.285980 0.593844i 0.707646 0.706567i \(-0.249757\pi\)
−0.993626 + 0.112723i \(0.964043\pi\)
\(744\) 0 0
\(745\) 0.587584 + 0.861828i 0.0215274 + 0.0315749i
\(746\) 1.86036 + 12.3427i 0.0681124 + 0.451897i
\(747\) 0 0
\(748\) 22.2632 17.7543i 0.814024 0.649162i
\(749\) 3.21370 + 43.8459i 0.117426 + 1.60210i
\(750\) 0 0
\(751\) −2.07448 27.6821i −0.0756990 1.01013i −0.897689 0.440630i \(-0.854755\pi\)
0.821990 0.569502i \(-0.192864\pi\)
\(752\) −0.174801 0.0539189i −0.00637433 0.00196622i
\(753\) 0 0
\(754\) −11.9660 + 6.90858i −0.435777 + 0.251596i
\(755\) 0.400477 + 1.75461i 0.0145749 + 0.0638566i
\(756\) 0 0
\(757\) 4.94805 21.6788i 0.179840 0.787930i −0.801863 0.597508i \(-0.796157\pi\)
0.981702 0.190421i \(-0.0609854\pi\)
\(758\) 5.04861 + 16.3672i 0.183374 + 0.594483i
\(759\) 0 0
\(760\) 0.531467 + 1.35416i 0.0192783 + 0.0491204i
\(761\) −30.5910 + 9.43607i −1.10892 + 0.342057i −0.794523 0.607234i \(-0.792279\pi\)
−0.314399 + 0.949291i \(0.601803\pi\)
\(762\) 0 0
\(763\) 35.6462 13.9229i 1.29048 0.504042i
\(764\) −12.4626 + 2.84451i −0.450882 + 0.102911i
\(765\) 0 0
\(766\) 29.3930 + 16.9701i 1.06201 + 0.613153i
\(767\) −17.1181 + 55.4957i −0.618100 + 2.00383i
\(768\) 0 0
\(769\) 7.26818 + 5.79618i 0.262097 + 0.209016i 0.745717 0.666262i \(-0.232107\pi\)
−0.483620 + 0.875278i \(0.660678\pi\)
\(770\) −1.55024 + 2.26581i −0.0558667 + 0.0816542i
\(771\) 0 0
\(772\) −21.1120 + 19.5891i −0.759839 + 0.705027i
\(773\) 16.0242 2.41526i 0.576350 0.0868708i 0.145602 0.989343i \(-0.453488\pi\)
0.430748 + 0.902472i \(0.358250\pi\)
\(774\) 0 0
\(775\) 3.89077 25.8136i 0.139760 0.927250i
\(776\) 27.0380 13.0208i 0.970608 0.467420i
\(777\) 0 0
\(778\) −14.9624 7.20550i −0.536427 0.258330i
\(779\) 6.49954 9.53307i 0.232870 0.341558i
\(780\) 0 0
\(781\) −1.39405 + 18.6022i −0.0498829 + 0.665640i
\(782\) 1.80602 4.60166i 0.0645830 0.164555i
\(783\) 0 0
\(784\) 0.0614398 + 0.107225i 0.00219428 + 0.00382947i
\(785\) 0.808639i 0.0288616i
\(786\) 0 0
\(787\) −22.4776 1.68446i −0.801239 0.0600446i −0.332185 0.943214i \(-0.607786\pi\)
−0.469054 + 0.883170i \(0.655405\pi\)