Properties

Label 405.2.r.a.152.13
Level $405$
Weight $2$
Character 405.152
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 152.13
Character \(\chi\) \(=\) 405.152
Dual form 405.2.r.a.8.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.42277 + 0.996232i) q^{2} +(0.347747 + 0.955427i) q^{4} +(0.893670 - 2.04972i) q^{5} +(0.429055 + 0.920112i) q^{7} +(0.442010 - 1.64960i) q^{8} +O(q^{10})\) \(q+(1.42277 + 0.996232i) q^{2} +(0.347747 + 0.955427i) q^{4} +(0.893670 - 2.04972i) q^{5} +(0.429055 + 0.920112i) q^{7} +(0.442010 - 1.64960i) q^{8} +(3.31348 - 2.02597i) q^{10} +(0.759141 + 0.904709i) q^{11} +(2.21505 + 3.16342i) q^{13} +(-0.306200 + 1.73654i) q^{14} +(3.83001 - 3.21376i) q^{16} +(-0.144887 - 0.540727i) q^{17} +(3.83587 - 2.21464i) q^{19} +(2.26913 + 0.141052i) q^{20} +(0.178781 + 2.04347i) q^{22} +(-4.21975 - 1.96770i) q^{23} +(-3.40271 - 3.66355i) q^{25} +6.70752i q^{26} +(-0.729897 + 0.729897i) q^{28} +(1.44060 + 8.17007i) q^{29} +(-7.51688 + 2.73592i) q^{31} +(5.24827 - 0.459164i) q^{32} +(0.332549 - 0.913671i) q^{34} +(2.26941 - 0.0571670i) q^{35} +(-5.30076 + 1.42034i) q^{37} +(7.66385 + 0.670500i) q^{38} +(-2.98621 - 2.38020i) q^{40} +(-5.46773 - 0.964109i) q^{41} +(0.0660161 - 0.754568i) q^{43} +(-0.600395 + 1.03991i) q^{44} +(-4.04344 - 7.00343i) q^{46} +(-11.1364 + 5.19301i) q^{47} +(3.83700 - 4.57275i) q^{49} +(-1.19152 - 8.60226i) q^{50} +(-2.25214 + 3.21639i) q^{52} +(5.40763 + 5.40763i) q^{53} +(2.53282 - 0.747516i) q^{55} +(1.70747 - 0.301072i) q^{56} +(-6.08964 + 13.0593i) q^{58} +(-6.20310 - 5.20502i) q^{59} +(10.5365 + 3.83498i) q^{61} +(-13.4204 - 3.59598i) q^{62} +(-0.735277 - 0.424512i) q^{64} +(8.46365 - 1.71318i) q^{65} +(-1.29416 + 0.906180i) q^{67} +(0.466241 - 0.326466i) q^{68} +(3.28579 + 2.17952i) q^{70} +(-6.95937 - 4.01800i) q^{71} +(-5.11087 - 1.36945i) q^{73} +(-8.95674 - 3.25999i) q^{74} +(3.44984 + 2.89476i) q^{76} +(-0.506721 + 1.08667i) q^{77} +(6.62789 - 1.16868i) q^{79} +(-3.16454 - 10.7225i) q^{80} +(-6.81884 - 6.81884i) q^{82} +(-0.172108 + 0.245796i) q^{83} +(-1.23782 - 0.186253i) q^{85} +(0.845650 - 1.00781i) q^{86} +(1.82796 - 0.852391i) q^{88} +(5.41601 + 9.38081i) q^{89} +(-1.96032 + 3.39538i) q^{91} +(0.412590 - 4.71593i) q^{92} +(-21.0180 - 3.70604i) q^{94} +(-1.11139 - 9.84163i) q^{95} +(-5.10194 - 0.446362i) q^{97} +(10.0147 - 2.68342i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.42277 + 0.996232i 1.00605 + 0.704443i 0.955716 0.294290i \(-0.0950832\pi\)
0.0503320 + 0.998733i \(0.483972\pi\)
\(3\) 0 0
\(4\) 0.347747 + 0.955427i 0.173874 + 0.477714i
\(5\) 0.893670 2.04972i 0.399661 0.916663i
\(6\) 0 0
\(7\) 0.429055 + 0.920112i 0.162168 + 0.347770i 0.970554 0.240882i \(-0.0774367\pi\)
−0.808387 + 0.588652i \(0.799659\pi\)
\(8\) 0.442010 1.64960i 0.156274 0.583223i
\(9\) 0 0
\(10\) 3.31348 2.02597i 1.04781 0.640669i
\(11\) 0.759141 + 0.904709i 0.228890 + 0.272780i 0.868250 0.496127i \(-0.165245\pi\)
−0.639360 + 0.768908i \(0.720801\pi\)
\(12\) 0 0
\(13\) 2.21505 + 3.16342i 0.614345 + 0.877375i 0.998955 0.0457040i \(-0.0145531\pi\)
−0.384610 + 0.923079i \(0.625664\pi\)
\(14\) −0.306200 + 1.73654i −0.0818353 + 0.464111i
\(15\) 0 0
\(16\) 3.83001 3.21376i 0.957502 0.803439i
\(17\) −0.144887 0.540727i −0.0351404 0.131146i 0.946127 0.323795i \(-0.104959\pi\)
−0.981268 + 0.192649i \(0.938292\pi\)
\(18\) 0 0
\(19\) 3.83587 2.21464i 0.880010 0.508074i 0.00934815 0.999956i \(-0.497024\pi\)
0.870662 + 0.491882i \(0.163691\pi\)
\(20\) 2.26913 + 0.141052i 0.507393 + 0.0315402i
\(21\) 0 0
\(22\) 0.178781 + 2.04347i 0.0381162 + 0.435670i
\(23\) −4.21975 1.96770i −0.879879 0.410294i −0.0704523 0.997515i \(-0.522444\pi\)
−0.809427 + 0.587221i \(0.800222\pi\)
\(24\) 0 0
\(25\) −3.40271 3.66355i −0.680542 0.732709i
\(26\) 6.70752i 1.31545i
\(27\) 0 0
\(28\) −0.729897 + 0.729897i −0.137938 + 0.137938i
\(29\) 1.44060 + 8.17007i 0.267513 + 1.51714i 0.761782 + 0.647834i \(0.224325\pi\)
−0.494268 + 0.869309i \(0.664564\pi\)
\(30\) 0 0
\(31\) −7.51688 + 2.73592i −1.35007 + 0.491386i −0.912970 0.408026i \(-0.866217\pi\)
−0.437102 + 0.899412i \(0.643995\pi\)
\(32\) 5.24827 0.459164i 0.927771 0.0811694i
\(33\) 0 0
\(34\) 0.332549 0.913671i 0.0570317 0.156693i
\(35\) 2.26941 0.0571670i 0.383600 0.00966299i
\(36\) 0 0
\(37\) −5.30076 + 1.42034i −0.871440 + 0.233502i −0.666710 0.745317i \(-0.732298\pi\)
−0.204730 + 0.978819i \(0.565632\pi\)
\(38\) 7.66385 + 0.670500i 1.24324 + 0.108770i
\(39\) 0 0
\(40\) −2.98621 2.38020i −0.472162 0.376342i
\(41\) −5.46773 0.964109i −0.853917 0.150569i −0.270478 0.962726i \(-0.587182\pi\)
−0.583438 + 0.812157i \(0.698293\pi\)
\(42\) 0 0
\(43\) 0.0660161 0.754568i 0.0100674 0.115070i −0.989498 0.144546i \(-0.953828\pi\)
0.999566 + 0.0294750i \(0.00938355\pi\)
\(44\) −0.600395 + 1.03991i −0.0905129 + 0.156773i
\(45\) 0 0
\(46\) −4.04344 7.00343i −0.596172 1.03260i
\(47\) −11.1364 + 5.19301i −1.62442 + 0.757478i −0.999726 0.0233932i \(-0.992553\pi\)
−0.624691 + 0.780872i \(0.714775\pi\)
\(48\) 0 0
\(49\) 3.83700 4.57275i 0.548142 0.653250i
\(50\) −1.19152 8.60226i −0.168506 1.21654i
\(51\) 0 0
\(52\) −2.25214 + 3.21639i −0.312316 + 0.446033i
\(53\) 5.40763 + 5.40763i 0.742795 + 0.742795i 0.973115 0.230320i \(-0.0739772\pi\)
−0.230320 + 0.973115i \(0.573977\pi\)
\(54\) 0 0
\(55\) 2.53282 0.747516i 0.341526 0.100795i
\(56\) 1.70747 0.301072i 0.228170 0.0402325i
\(57\) 0 0
\(58\) −6.08964 + 13.0593i −0.799609 + 1.71477i
\(59\) −6.20310 5.20502i −0.807575 0.677636i 0.142453 0.989802i \(-0.454501\pi\)
−0.950028 + 0.312166i \(0.898946\pi\)
\(60\) 0 0
\(61\) 10.5365 + 3.83498i 1.34906 + 0.491018i 0.912655 0.408731i \(-0.134029\pi\)
0.436407 + 0.899749i \(0.356251\pi\)
\(62\) −13.4204 3.59598i −1.70439 0.456690i
\(63\) 0 0
\(64\) −0.735277 0.424512i −0.0919096 0.0530640i
\(65\) 8.46365 1.71318i 1.04979 0.212494i
\(66\) 0 0
\(67\) −1.29416 + 0.906180i −0.158107 + 0.110707i −0.649953 0.759975i \(-0.725211\pi\)
0.491846 + 0.870682i \(0.336322\pi\)
\(68\) 0.466241 0.326466i 0.0565401 0.0395898i
\(69\) 0 0
\(70\) 3.28579 + 2.17952i 0.392727 + 0.260503i
\(71\) −6.95937 4.01800i −0.825926 0.476849i 0.0265298 0.999648i \(-0.491554\pi\)
−0.852456 + 0.522800i \(0.824888\pi\)
\(72\) 0 0
\(73\) −5.11087 1.36945i −0.598182 0.160282i −0.0529922 0.998595i \(-0.516876\pi\)
−0.545190 + 0.838312i \(0.683543\pi\)
\(74\) −8.95674 3.25999i −1.04120 0.378966i
\(75\) 0 0
\(76\) 3.44984 + 2.89476i 0.395724 + 0.332052i
\(77\) −0.506721 + 1.08667i −0.0577462 + 0.123837i
\(78\) 0 0
\(79\) 6.62789 1.16868i 0.745696 0.131486i 0.212126 0.977242i \(-0.431961\pi\)
0.533570 + 0.845756i \(0.320850\pi\)
\(80\) −3.16454 10.7225i −0.353807 1.19881i
\(81\) 0 0
\(82\) −6.81884 6.81884i −0.753014 0.753014i
\(83\) −0.172108 + 0.245796i −0.0188913 + 0.0269796i −0.828487 0.560009i \(-0.810798\pi\)
0.809595 + 0.586988i \(0.199687\pi\)
\(84\) 0 0
\(85\) −1.23782 0.186253i −0.134261 0.0202020i
\(86\) 0.845650 1.00781i 0.0911888 0.108675i
\(87\) 0 0
\(88\) 1.82796 0.852391i 0.194861 0.0908652i
\(89\) 5.41601 + 9.38081i 0.574096 + 0.994364i 0.996139 + 0.0877879i \(0.0279798\pi\)
−0.422043 + 0.906576i \(0.638687\pi\)
\(90\) 0 0
\(91\) −1.96032 + 3.39538i −0.205498 + 0.355932i
\(92\) 0.412590 4.71593i 0.0430155 0.491670i
\(93\) 0 0
\(94\) −21.0180 3.70604i −2.16784 0.382249i
\(95\) −1.11139 9.84163i −0.114027 1.00973i
\(96\) 0 0
\(97\) −5.10194 0.446362i −0.518023 0.0453212i −0.174853 0.984595i \(-0.555945\pi\)
−0.343170 + 0.939273i \(0.611501\pi\)
\(98\) 10.0147 2.68342i 1.01163 0.271067i
\(99\) 0 0
\(100\) 2.31697 4.52503i 0.231697 0.452503i
\(101\) 6.63190 18.2210i 0.659899 1.81306i 0.0825062 0.996591i \(-0.473708\pi\)
0.577393 0.816467i \(-0.304070\pi\)
\(102\) 0 0
\(103\) 14.8525 1.29943i 1.46346 0.128036i 0.672589 0.740016i \(-0.265182\pi\)
0.790873 + 0.611980i \(0.209627\pi\)
\(104\) 6.19746 2.25569i 0.607711 0.221189i
\(105\) 0 0
\(106\) 2.30654 + 13.0811i 0.224031 + 1.27054i
\(107\) −3.20052 + 3.20052i −0.309406 + 0.309406i −0.844679 0.535273i \(-0.820209\pi\)
0.535273 + 0.844679i \(0.320209\pi\)
\(108\) 0 0
\(109\) 10.7258i 1.02735i 0.857986 + 0.513673i \(0.171716\pi\)
−0.857986 + 0.513673i \(0.828284\pi\)
\(110\) 4.34832 + 1.45974i 0.414596 + 0.139181i
\(111\) 0 0
\(112\) 4.60030 + 2.14516i 0.434688 + 0.202698i
\(113\) 1.10011 + 12.5744i 0.103490 + 1.18290i 0.853364 + 0.521316i \(0.174559\pi\)
−0.749874 + 0.661581i \(0.769886\pi\)
\(114\) 0 0
\(115\) −7.80431 + 6.89084i −0.727755 + 0.642574i
\(116\) −7.30494 + 4.21751i −0.678247 + 0.391586i
\(117\) 0 0
\(118\) −3.64016 13.5853i −0.335104 1.25062i
\(119\) 0.435365 0.365315i 0.0399099 0.0334883i
\(120\) 0 0
\(121\) 1.66793 9.45928i 0.151630 0.859935i
\(122\) 11.1705 + 15.9531i 1.01133 + 1.44432i
\(123\) 0 0
\(124\) −5.22795 6.23043i −0.469484 0.559509i
\(125\) −10.5501 + 3.70060i −0.943634 + 0.330992i
\(126\) 0 0
\(127\) −4.56717 + 17.0449i −0.405270 + 1.51249i 0.398286 + 0.917261i \(0.369605\pi\)
−0.803556 + 0.595229i \(0.797061\pi\)
\(128\) −5.07618 10.8859i −0.448676 0.962188i
\(129\) 0 0
\(130\) 13.7485 + 5.99430i 1.20583 + 0.525735i
\(131\) 0.988469 + 2.71580i 0.0863629 + 0.237280i 0.975355 0.220643i \(-0.0708156\pi\)
−0.888992 + 0.457923i \(0.848593\pi\)
\(132\) 0 0
\(133\) 3.68352 + 2.57923i 0.319402 + 0.223648i
\(134\) −2.74405 −0.237050
\(135\) 0 0
\(136\) −0.956027 −0.0819787
\(137\) 6.89836 + 4.83028i 0.589367 + 0.412679i 0.829860 0.557972i \(-0.188420\pi\)
−0.240493 + 0.970651i \(0.577309\pi\)
\(138\) 0 0
\(139\) −3.42050 9.39775i −0.290123 0.797107i −0.996048 0.0888198i \(-0.971690\pi\)
0.705925 0.708287i \(-0.250532\pi\)
\(140\) 0.843798 + 2.14837i 0.0713140 + 0.181571i
\(141\) 0 0
\(142\) −5.89871 12.6498i −0.495009 1.06155i
\(143\) −1.18044 + 4.40546i −0.0987133 + 0.368403i
\(144\) 0 0
\(145\) 18.0338 + 4.34851i 1.49762 + 0.361124i
\(146\) −5.90728 7.04003i −0.488890 0.582637i
\(147\) 0 0
\(148\) −3.20035 4.57058i −0.263067 0.375699i
\(149\) 2.48868 14.1140i 0.203881 1.15626i −0.695311 0.718709i \(-0.744733\pi\)
0.899191 0.437555i \(-0.144156\pi\)
\(150\) 0 0
\(151\) 4.12708 3.46303i 0.335857 0.281818i −0.459224 0.888320i \(-0.651873\pi\)
0.795081 + 0.606503i \(0.207428\pi\)
\(152\) −1.95779 7.30656i −0.158798 0.592640i
\(153\) 0 0
\(154\) −1.80352 + 1.04126i −0.145332 + 0.0839072i
\(155\) −1.10974 + 17.8525i −0.0891362 + 1.43395i
\(156\) 0 0
\(157\) −0.694063 7.93317i −0.0553922 0.633136i −0.972253 0.233930i \(-0.924841\pi\)
0.916861 0.399206i \(-0.130714\pi\)
\(158\) 10.5942 + 4.94016i 0.842831 + 0.393018i
\(159\) 0 0
\(160\) 3.74906 11.1678i 0.296389 0.882893i
\(161\) 4.72690i 0.372532i
\(162\) 0 0
\(163\) −11.3432 + 11.3432i −0.888466 + 0.888466i −0.994376 0.105910i \(-0.966224\pi\)
0.105910 + 0.994376i \(0.466224\pi\)
\(164\) −0.980253 5.55929i −0.0765449 0.434108i
\(165\) 0 0
\(166\) −0.489740 + 0.178251i −0.0380112 + 0.0138349i
\(167\) 0.422026 0.0369225i 0.0326574 0.00285715i −0.0708153 0.997489i \(-0.522560\pi\)
0.103473 + 0.994632i \(0.467005\pi\)
\(168\) 0 0
\(169\) −0.654517 + 1.79827i −0.0503475 + 0.138329i
\(170\) −1.57558 1.49815i −0.120842 0.114903i
\(171\) 0 0
\(172\) 0.743891 0.199325i 0.0567212 0.0151984i
\(173\) 8.04840 + 0.704144i 0.611909 + 0.0535351i 0.388898 0.921281i \(-0.372856\pi\)
0.223011 + 0.974816i \(0.428411\pi\)
\(174\) 0 0
\(175\) 1.91092 4.70274i 0.144452 0.355494i
\(176\) 5.81503 + 1.02535i 0.438325 + 0.0772885i
\(177\) 0 0
\(178\) −1.63974 + 18.7423i −0.122904 + 1.40480i
\(179\) −6.38218 + 11.0543i −0.477026 + 0.826234i −0.999653 0.0263277i \(-0.991619\pi\)
0.522627 + 0.852561i \(0.324952\pi\)
\(180\) 0 0
\(181\) −9.24880 16.0194i −0.687458 1.19071i −0.972657 0.232244i \(-0.925393\pi\)
0.285199 0.958468i \(-0.407940\pi\)
\(182\) −6.17167 + 2.87790i −0.457474 + 0.213324i
\(183\) 0 0
\(184\) −5.11110 + 6.09117i −0.376795 + 0.449047i
\(185\) −1.82584 + 12.1344i −0.134239 + 0.892139i
\(186\) 0 0
\(187\) 0.379211 0.541570i 0.0277307 0.0396035i
\(188\) −8.83421 8.83421i −0.644301 0.644301i
\(189\) 0 0
\(190\) 8.22329 15.1096i 0.596580 1.09616i
\(191\) −4.20349 + 0.741189i −0.304154 + 0.0536306i −0.323642 0.946180i \(-0.604907\pi\)
0.0194882 + 0.999810i \(0.493796\pi\)
\(192\) 0 0
\(193\) −4.28212 + 9.18304i −0.308234 + 0.661010i −0.998013 0.0630104i \(-0.979930\pi\)
0.689779 + 0.724020i \(0.257708\pi\)
\(194\) −6.81419 5.71778i −0.489230 0.410513i
\(195\) 0 0
\(196\) 5.70324 + 2.07581i 0.407374 + 0.148272i
\(197\) 11.4519 + 3.06853i 0.815916 + 0.218624i 0.642560 0.766235i \(-0.277872\pi\)
0.173356 + 0.984859i \(0.444539\pi\)
\(198\) 0 0
\(199\) 5.06551 + 2.92457i 0.359084 + 0.207317i 0.668679 0.743551i \(-0.266860\pi\)
−0.309595 + 0.950869i \(0.600193\pi\)
\(200\) −7.54743 + 3.99379i −0.533684 + 0.282404i
\(201\) 0 0
\(202\) 27.5880 19.3173i 1.94108 1.35916i
\(203\) −6.89928 + 4.83093i −0.484234 + 0.339065i
\(204\) 0 0
\(205\) −6.86250 + 10.3457i −0.479298 + 0.722577i
\(206\) 22.4262 + 12.9478i 1.56251 + 0.902114i
\(207\) 0 0
\(208\) 18.6501 + 4.99729i 1.29315 + 0.346500i
\(209\) 4.91558 + 1.78912i 0.340018 + 0.123756i
\(210\) 0 0
\(211\) −5.44373 4.56783i −0.374762 0.314462i 0.435880 0.900005i \(-0.356437\pi\)
−0.810642 + 0.585542i \(0.800882\pi\)
\(212\) −3.28611 + 7.04709i −0.225691 + 0.483996i
\(213\) 0 0
\(214\) −7.74205 + 1.36513i −0.529236 + 0.0933186i
\(215\) −1.48766 0.809649i −0.101457 0.0552176i
\(216\) 0 0
\(217\) −5.74251 5.74251i −0.389827 0.389827i
\(218\) −10.6854 + 15.2603i −0.723707 + 1.03356i
\(219\) 0 0
\(220\) 1.59498 + 2.15998i 0.107533 + 0.145626i
\(221\) 1.38961 1.65608i 0.0934756 0.111400i
\(222\) 0 0
\(223\) 2.00892 0.936774i 0.134527 0.0627310i −0.354189 0.935174i \(-0.615243\pi\)
0.488716 + 0.872443i \(0.337465\pi\)
\(224\) 2.67428 + 4.63199i 0.178683 + 0.309488i
\(225\) 0 0
\(226\) −10.9618 + 18.9864i −0.729167 + 1.26295i
\(227\) 0.837726 9.57526i 0.0556018 0.635532i −0.916354 0.400369i \(-0.868882\pi\)
0.971956 0.235163i \(-0.0755624\pi\)
\(228\) 0 0
\(229\) −9.88832 1.74358i −0.653438 0.115219i −0.162906 0.986642i \(-0.552087\pi\)
−0.490533 + 0.871423i \(0.663198\pi\)
\(230\) −17.9686 + 2.02915i −1.18481 + 0.133798i
\(231\) 0 0
\(232\) 14.1141 + 1.23483i 0.926638 + 0.0810703i
\(233\) 11.6282 3.11576i 0.761788 0.204120i 0.143047 0.989716i \(-0.454310\pi\)
0.618741 + 0.785595i \(0.287643\pi\)
\(234\) 0 0
\(235\) 0.691913 + 27.4674i 0.0451354 + 1.79178i
\(236\) 2.81591 7.73664i 0.183300 0.503613i
\(237\) 0 0
\(238\) 0.983361 0.0860330i 0.0637418 0.00557669i
\(239\) 1.69787 0.617976i 0.109826 0.0399735i −0.286522 0.958074i \(-0.592499\pi\)
0.396349 + 0.918100i \(0.370277\pi\)
\(240\) 0 0
\(241\) −2.79425 15.8470i −0.179994 1.02079i −0.932221 0.361890i \(-0.882131\pi\)
0.752227 0.658904i \(-0.228980\pi\)
\(242\) 11.7967 11.7967i 0.758321 0.758321i
\(243\) 0 0
\(244\) 11.4005i 0.729840i
\(245\) −5.94386 11.9513i −0.379739 0.763541i
\(246\) 0 0
\(247\) 15.5025 + 7.22894i 0.986401 + 0.459966i
\(248\) 1.19065 + 13.6092i 0.0756063 + 0.864184i
\(249\) 0 0
\(250\) −18.6971 5.24530i −1.18251 0.331742i
\(251\) 15.8224 9.13506i 0.998700 0.576600i 0.0908365 0.995866i \(-0.471046\pi\)
0.907863 + 0.419266i \(0.137713\pi\)
\(252\) 0 0
\(253\) −1.42319 5.31141i −0.0894751 0.333926i
\(254\) −23.4787 + 19.7010i −1.47318 + 1.23615i
\(255\) 0 0
\(256\) 3.32781 18.8729i 0.207988 1.17956i
\(257\) 8.13228 + 11.6141i 0.507278 + 0.724468i 0.988347 0.152215i \(-0.0486405\pi\)
−0.481070 + 0.876682i \(0.659752\pi\)
\(258\) 0 0
\(259\) −3.58119 4.26790i −0.222524 0.265194i
\(260\) 4.58003 + 7.49065i 0.284041 + 0.464550i
\(261\) 0 0
\(262\) −1.29920 + 4.84869i −0.0802650 + 0.299553i
\(263\) 1.55072 + 3.32553i 0.0956215 + 0.205061i 0.948300 0.317375i \(-0.102801\pi\)
−0.852679 + 0.522436i \(0.825023\pi\)
\(264\) 0 0
\(265\) 15.9168 6.25149i 0.977759 0.384026i
\(266\) 2.67128 + 7.33929i 0.163787 + 0.450000i
\(267\) 0 0
\(268\) −1.31583 0.921353i −0.0803770 0.0562806i
\(269\) 11.1677 0.680904 0.340452 0.940262i \(-0.389420\pi\)
0.340452 + 0.940262i \(0.389420\pi\)
\(270\) 0 0
\(271\) 23.0328 1.39914 0.699572 0.714562i \(-0.253374\pi\)
0.699572 + 0.714562i \(0.253374\pi\)
\(272\) −2.29269 1.60536i −0.139015 0.0973390i
\(273\) 0 0
\(274\) 5.00267 + 13.7447i 0.302223 + 0.830350i
\(275\) 0.731309 5.85961i 0.0440996 0.353348i
\(276\) 0 0
\(277\) 5.25770 + 11.2752i 0.315905 + 0.677460i 0.998581 0.0532613i \(-0.0169616\pi\)
−0.682676 + 0.730721i \(0.739184\pi\)
\(278\) 4.49577 16.7784i 0.269638 1.00630i
\(279\) 0 0
\(280\) 0.908797 3.76889i 0.0543110 0.225234i
\(281\) −5.39196 6.42589i −0.321657 0.383336i 0.580850 0.814011i \(-0.302720\pi\)
−0.902507 + 0.430674i \(0.858276\pi\)
\(282\) 0 0
\(283\) −6.92088 9.88404i −0.411404 0.587545i 0.558960 0.829195i \(-0.311201\pi\)
−0.970364 + 0.241649i \(0.922312\pi\)
\(284\) 1.41880 8.04642i 0.0841904 0.477467i
\(285\) 0 0
\(286\) −6.06835 + 5.09195i −0.358829 + 0.301093i
\(287\) −1.45887 5.44459i −0.0861145 0.321384i
\(288\) 0 0
\(289\) 14.4510 8.34331i 0.850061 0.490783i
\(290\) 21.3257 + 24.1527i 1.25229 + 1.41830i
\(291\) 0 0
\(292\) −0.468877 5.35929i −0.0274390 0.313629i
\(293\) −19.4978 9.09195i −1.13907 0.531157i −0.240789 0.970577i \(-0.577406\pi\)
−0.898282 + 0.439420i \(0.855184\pi\)
\(294\) 0 0
\(295\) −16.2124 + 8.06305i −0.943920 + 0.469449i
\(296\) 9.37196i 0.544734i
\(297\) 0 0
\(298\) 17.6016 17.6016i 1.01964 1.01964i
\(299\) −3.12229 17.7074i −0.180567 1.02405i
\(300\) 0 0
\(301\) 0.722611 0.263009i 0.0416506 0.0151596i
\(302\) 9.32186 0.815557i 0.536413 0.0469301i
\(303\) 0 0
\(304\) 7.57410 20.8097i 0.434404 1.19352i
\(305\) 17.2768 18.1697i 0.989266 1.04039i
\(306\) 0 0
\(307\) −11.9453 + 3.20074i −0.681757 + 0.182676i −0.583045 0.812440i \(-0.698139\pi\)
−0.0987117 + 0.995116i \(0.531472\pi\)
\(308\) −1.21444 0.106250i −0.0691992 0.00605414i
\(309\) 0 0
\(310\) −19.3642 + 24.2944i −1.09981 + 1.37983i
\(311\) 13.5294 + 2.38560i 0.767181 + 0.135275i 0.543524 0.839393i \(-0.317090\pi\)
0.223656 + 0.974668i \(0.428201\pi\)
\(312\) 0 0
\(313\) 2.60145 29.7347i 0.147043 1.68071i −0.461465 0.887159i \(-0.652676\pi\)
0.608507 0.793548i \(-0.291769\pi\)
\(314\) 6.91579 11.9785i 0.390281 0.675986i
\(315\) 0 0
\(316\) 3.42141 + 5.92606i 0.192470 + 0.333367i
\(317\) 19.3873 9.04044i 1.08890 0.507762i 0.206588 0.978428i \(-0.433764\pi\)
0.882311 + 0.470666i \(0.155986\pi\)
\(318\) 0 0
\(319\) −6.29792 + 7.50556i −0.352616 + 0.420231i
\(320\) −1.52723 + 1.12774i −0.0853745 + 0.0630425i
\(321\) 0 0
\(322\) 4.70909 6.72527i 0.262427 0.374785i
\(323\) −1.75329 1.75329i −0.0975556 0.0975556i
\(324\) 0 0
\(325\) 4.05217 18.8791i 0.224774 1.04723i
\(326\) −27.4391 + 4.83826i −1.51971 + 0.267966i
\(327\) 0 0
\(328\) −4.00719 + 8.59345i −0.221260 + 0.474494i
\(329\) −9.55630 8.01869i −0.526856 0.442085i
\(330\) 0 0
\(331\) −24.1329 8.78365i −1.32646 0.482793i −0.420939 0.907089i \(-0.638299\pi\)
−0.905524 + 0.424296i \(0.860522\pi\)
\(332\) −0.294691 0.0789621i −0.0161732 0.00433361i
\(333\) 0 0
\(334\) 0.637228 + 0.367904i 0.0348676 + 0.0201308i
\(335\) 0.700864 + 3.46249i 0.0382923 + 0.189176i
\(336\) 0 0
\(337\) −0.778831 + 0.545344i −0.0424256 + 0.0297068i −0.594597 0.804024i \(-0.702688\pi\)
0.552171 + 0.833731i \(0.313799\pi\)
\(338\) −2.72272 + 1.90647i −0.148096 + 0.103698i
\(339\) 0 0
\(340\) −0.252498 1.24742i −0.0136936 0.0676507i
\(341\) −8.18159 4.72364i −0.443058 0.255800i
\(342\) 0 0
\(343\) 12.7182 + 3.40783i 0.686718 + 0.184006i
\(344\) −1.21556 0.442427i −0.0655385 0.0238540i
\(345\) 0 0
\(346\) 10.7495 + 9.01991i 0.577897 + 0.484913i
\(347\) −0.861237 + 1.84693i −0.0462336 + 0.0991483i −0.928068 0.372411i \(-0.878531\pi\)
0.881834 + 0.471560i \(0.156309\pi\)
\(348\) 0 0
\(349\) 13.3172 2.34817i 0.712851 0.125695i 0.194549 0.980893i \(-0.437676\pi\)
0.518302 + 0.855198i \(0.326564\pi\)
\(350\) 7.40382 4.78718i 0.395751 0.255885i
\(351\) 0 0
\(352\) 4.39958 + 4.39958i 0.234499 + 0.234499i
\(353\) 4.28254 6.11610i 0.227936 0.325527i −0.688851 0.724903i \(-0.741884\pi\)
0.916787 + 0.399376i \(0.130773\pi\)
\(354\) 0 0
\(355\) −14.4552 + 10.6740i −0.767200 + 0.566518i
\(356\) −7.07928 + 8.43675i −0.375201 + 0.447147i
\(357\) 0 0
\(358\) −20.0930 + 9.36950i −1.06195 + 0.495193i
\(359\) −4.40107 7.62287i −0.232279 0.402320i 0.726199 0.687484i \(-0.241285\pi\)
−0.958479 + 0.285165i \(0.907952\pi\)
\(360\) 0 0
\(361\) 0.309285 0.535697i 0.0162782 0.0281946i
\(362\) 2.80015 32.0058i 0.147172 1.68219i
\(363\) 0 0
\(364\) −3.92573 0.692213i −0.205764 0.0362818i
\(365\) −7.37443 + 9.25202i −0.385995 + 0.484273i
\(366\) 0 0
\(367\) −27.1913 2.37893i −1.41938 0.124179i −0.648524 0.761194i \(-0.724613\pi\)
−0.770852 + 0.637015i \(0.780169\pi\)
\(368\) −22.4854 + 6.02494i −1.17213 + 0.314072i
\(369\) 0 0
\(370\) −14.6864 + 15.4455i −0.763511 + 0.802971i
\(371\) −2.65545 + 7.29580i −0.137864 + 0.378779i
\(372\) 0 0
\(373\) 12.1103 1.05951i 0.627046 0.0548594i 0.230796 0.973002i \(-0.425867\pi\)
0.396250 + 0.918143i \(0.370311\pi\)
\(374\) 1.07906 0.392745i 0.0557968 0.0203084i
\(375\) 0 0
\(376\) 3.64399 + 20.6661i 0.187924 + 1.06577i
\(377\) −22.6543 + 22.6543i −1.16676 + 1.16676i
\(378\) 0 0
\(379\) 22.6602i 1.16398i 0.813198 + 0.581988i \(0.197725\pi\)
−0.813198 + 0.581988i \(0.802275\pi\)
\(380\) 9.01648 4.48425i 0.462535 0.230037i
\(381\) 0 0
\(382\) −6.71899 3.13312i −0.343773 0.160304i
\(383\) −1.66185 18.9950i −0.0849166 0.970601i −0.912451 0.409186i \(-0.865813\pi\)
0.827534 0.561415i \(-0.189743\pi\)
\(384\) 0 0
\(385\) 1.77452 + 2.00976i 0.0904379 + 0.102427i
\(386\) −15.2409 + 8.79934i −0.775741 + 0.447874i
\(387\) 0 0
\(388\) −1.34772 5.02975i −0.0684200 0.255347i
\(389\) −11.9485 + 10.0260i −0.605814 + 0.508338i −0.893309 0.449444i \(-0.851622\pi\)
0.287495 + 0.957782i \(0.407178\pi\)
\(390\) 0 0
\(391\) −0.452602 + 2.56683i −0.0228890 + 0.129810i
\(392\) −5.84724 8.35072i −0.295330 0.421775i
\(393\) 0 0
\(394\) 13.2364 + 15.7746i 0.666842 + 0.794712i
\(395\) 3.52769 14.6297i 0.177497 0.736102i
\(396\) 0 0
\(397\) 2.30277 8.59405i 0.115573 0.431323i −0.883756 0.467947i \(-0.844994\pi\)
0.999329 + 0.0366240i \(0.0116604\pi\)
\(398\) 4.29348 + 9.20740i 0.215213 + 0.461525i
\(399\) 0 0
\(400\) −24.8062 3.09593i −1.24031 0.154797i
\(401\) 0.377837 + 1.03810i 0.0188683 + 0.0518401i 0.948769 0.315970i \(-0.102330\pi\)
−0.929901 + 0.367810i \(0.880108\pi\)
\(402\) 0 0
\(403\) −25.3051 17.7189i −1.26054 0.882639i
\(404\) 19.7151 0.980861
\(405\) 0 0
\(406\) −14.6288 −0.726015
\(407\) −5.30902 3.71742i −0.263158 0.184265i
\(408\) 0 0
\(409\) −0.248916 0.683891i −0.0123081 0.0338162i 0.933386 0.358873i \(-0.116839\pi\)
−0.945695 + 0.325057i \(0.894617\pi\)
\(410\) −20.0705 + 7.88292i −0.991211 + 0.389310i
\(411\) 0 0
\(412\) 6.40643 + 13.7386i 0.315622 + 0.676854i
\(413\) 2.12773 7.94079i 0.104699 0.390741i
\(414\) 0 0
\(415\) 0.350005 + 0.572435i 0.0171811 + 0.0280997i
\(416\) 13.0777 + 15.5854i 0.641187 + 0.764137i
\(417\) 0 0
\(418\) 5.21134 + 7.44256i 0.254895 + 0.364028i
\(419\) 3.40845 19.3303i 0.166514 0.944347i −0.780976 0.624561i \(-0.785278\pi\)
0.947490 0.319786i \(-0.103611\pi\)
\(420\) 0 0
\(421\) −8.09926 + 6.79608i −0.394734 + 0.331221i −0.818454 0.574572i \(-0.805168\pi\)
0.423720 + 0.905793i \(0.360724\pi\)
\(422\) −3.19454 11.9222i −0.155508 0.580362i
\(423\) 0 0
\(424\) 11.3107 6.53022i 0.549295 0.317135i
\(425\) −1.48797 + 2.37074i −0.0721772 + 0.114998i
\(426\) 0 0
\(427\) 0.992138 + 11.3402i 0.0480129 + 0.548790i
\(428\) −4.17083 1.94489i −0.201605 0.0940099i
\(429\) 0 0
\(430\) −1.30999 2.63399i −0.0631733 0.127022i
\(431\) 16.6095i 0.800052i 0.916504 + 0.400026i \(0.130999\pi\)
−0.916504 + 0.400026i \(0.869001\pi\)
\(432\) 0 0
\(433\) −14.3203 + 14.3203i −0.688189 + 0.688189i −0.961831 0.273643i \(-0.911771\pi\)
0.273643 + 0.961831i \(0.411771\pi\)
\(434\) −2.44938 13.8911i −0.117574 0.666796i
\(435\) 0 0
\(436\) −10.2477 + 3.72987i −0.490778 + 0.178628i
\(437\) −20.5442 + 1.79738i −0.982762 + 0.0859805i
\(438\) 0 0
\(439\) 4.05583 11.1433i 0.193574 0.531840i −0.804495 0.593960i \(-0.797564\pi\)
0.998069 + 0.0621195i \(0.0197860\pi\)
\(440\) −0.113572 4.50856i −0.00541434 0.214937i
\(441\) 0 0
\(442\) 3.62694 0.971835i 0.172516 0.0462255i
\(443\) −22.1937 1.94169i −1.05445 0.0922527i −0.453277 0.891369i \(-0.649745\pi\)
−0.601176 + 0.799117i \(0.705301\pi\)
\(444\) 0 0
\(445\) 24.0682 2.71797i 1.14094 0.128844i
\(446\) 3.79147 + 0.668538i 0.179531 + 0.0316562i
\(447\) 0 0
\(448\) 0.0751244 0.858676i 0.00354930 0.0405686i
\(449\) −2.63657 + 4.56667i −0.124427 + 0.215514i −0.921509 0.388357i \(-0.873043\pi\)
0.797082 + 0.603872i \(0.206376\pi\)
\(450\) 0 0
\(451\) −3.27855 5.67861i −0.154381 0.267395i
\(452\) −11.6313 + 5.42378i −0.547092 + 0.255113i
\(453\) 0 0
\(454\) 10.7311 12.7888i 0.503634 0.600208i
\(455\) 5.20769 + 7.05246i 0.244140 + 0.330624i
\(456\) 0 0
\(457\) −5.51211 + 7.87211i −0.257846 + 0.368242i −0.927114 0.374779i \(-0.877719\pi\)
0.669269 + 0.743021i \(0.266608\pi\)
\(458\) −12.3318 12.3318i −0.576225 0.576225i
\(459\) 0 0
\(460\) −9.29762 5.06018i −0.433504 0.235932i
\(461\) −10.5760 + 1.86484i −0.492575 + 0.0868543i −0.414418 0.910087i \(-0.636015\pi\)
−0.0781574 + 0.996941i \(0.524904\pi\)
\(462\) 0 0
\(463\) 15.1325 32.4518i 0.703268 1.50816i −0.151113 0.988516i \(-0.548286\pi\)
0.854381 0.519647i \(-0.173936\pi\)
\(464\) 31.7741 + 26.6617i 1.47508 + 1.23774i
\(465\) 0 0
\(466\) 19.6482 + 7.15137i 0.910187 + 0.331281i
\(467\) −23.5963 6.32261i −1.09191 0.292575i −0.332441 0.943124i \(-0.607872\pi\)
−0.759465 + 0.650549i \(0.774539\pi\)
\(468\) 0 0
\(469\) −1.38905 0.801970i −0.0641405 0.0370315i
\(470\) −26.3795 + 39.7691i −1.21680 + 1.83441i
\(471\) 0 0
\(472\) −11.3280 + 7.93199i −0.521416 + 0.365099i
\(473\) 0.732780 0.513098i 0.0336933 0.0235923i
\(474\) 0 0
\(475\) −21.1658 6.51712i −0.971154 0.299026i
\(476\) 0.500429 + 0.288923i 0.0229371 + 0.0132427i
\(477\) 0 0
\(478\) 3.03133 + 0.812242i 0.138650 + 0.0371511i
\(479\) 38.3549 + 13.9601i 1.75248 + 0.637851i 0.999789 0.0205215i \(-0.00653265\pi\)
0.752692 + 0.658373i \(0.228755\pi\)
\(480\) 0 0
\(481\) −16.2346 13.6224i −0.740233 0.621129i
\(482\) 11.8117 25.3303i 0.538009 1.15376i
\(483\) 0 0
\(484\) 9.61767 1.69585i 0.437167 0.0770843i
\(485\) −5.47436 + 10.0586i −0.248578 + 0.456739i
\(486\) 0 0
\(487\) −23.5238 23.5238i −1.06596 1.06596i −0.997665 0.0682997i \(-0.978243\pi\)
−0.0682997 0.997665i \(-0.521757\pi\)
\(488\) 10.9834 15.6860i 0.497196 0.710070i
\(489\) 0 0
\(490\) 3.44954 22.9254i 0.155834 1.03566i
\(491\) 3.19936 3.81285i 0.144385 0.172071i −0.689005 0.724756i \(-0.741952\pi\)
0.833390 + 0.552685i \(0.186397\pi\)
\(492\) 0 0
\(493\) 4.20905 1.96271i 0.189566 0.0883962i
\(494\) 14.8548 + 25.7292i 0.668347 + 1.15761i
\(495\) 0 0
\(496\) −19.9971 + 34.6360i −0.897897 + 1.55520i
\(497\) 0.711051 8.12735i 0.0318950 0.364561i
\(498\) 0 0
\(499\) 6.36453 + 1.12224i 0.284916 + 0.0502383i 0.314280 0.949330i \(-0.398237\pi\)
−0.0293640 + 0.999569i \(0.509348\pi\)
\(500\) −7.20444 8.79302i −0.322192 0.393236i
\(501\) 0 0
\(502\) 31.6122 + 2.76571i 1.41092 + 0.123440i
\(503\) −24.7077 + 6.62040i −1.10166 + 0.295189i −0.763441 0.645878i \(-0.776491\pi\)
−0.338220 + 0.941067i \(0.609825\pi\)
\(504\) 0 0
\(505\) −31.4212 29.8771i −1.39823 1.32951i
\(506\) 3.26654 8.97473i 0.145215 0.398975i
\(507\) 0 0
\(508\) −17.8734 + 1.56372i −0.793003 + 0.0693788i
\(509\) 22.5637 8.21250i 1.00012 0.364013i 0.210487 0.977597i \(-0.432495\pi\)
0.789630 + 0.613584i \(0.210273\pi\)
\(510\) 0 0
\(511\) −0.932796 5.29015i −0.0412644 0.234022i
\(512\) 6.55000 6.55000i 0.289472 0.289472i
\(513\) 0 0
\(514\) 24.6258i 1.08620i
\(515\) 10.6098 31.6048i 0.467523 1.39267i
\(516\) 0 0
\(517\) −13.1523 6.13302i −0.578438 0.269730i
\(518\) −0.843383 9.63992i −0.0370561 0.423554i
\(519\) 0 0
\(520\) 0.914947 14.7189i 0.0401231 0.645467i
\(521\) −10.1059 + 5.83464i −0.442747 + 0.255620i −0.704762 0.709444i \(-0.748946\pi\)
0.262015 + 0.965064i \(0.415613\pi\)
\(522\) 0 0
\(523\) −9.07224 33.8581i −0.396701 1.48051i −0.818863 0.573989i \(-0.805395\pi\)
0.422162 0.906521i \(-0.361272\pi\)
\(524\) −2.25101 + 1.88882i −0.0983358 + 0.0825135i
\(525\) 0 0
\(526\) −1.10669 + 6.27633i −0.0482539 + 0.273661i
\(527\) 2.56849 + 3.66818i 0.111885 + 0.159789i
\(528\) 0 0
\(529\) −0.849663 1.01259i −0.0369419 0.0440256i
\(530\) 28.8738 + 6.96238i 1.25420 + 0.302426i
\(531\) 0 0
\(532\) −1.18333 + 4.41626i −0.0513040 + 0.191469i
\(533\) −9.06143 19.4323i −0.392494 0.841706i
\(534\) 0 0
\(535\) 3.69996 + 9.42038i 0.159963 + 0.407278i
\(536\) 0.922806 + 2.53539i 0.0398591 + 0.109512i
\(537\) 0 0
\(538\) 15.8890 + 11.1256i 0.685022 + 0.479658i
\(539\) 7.04983 0.303658
\(540\) 0 0
\(541\) 32.8530 1.41246 0.706230 0.707983i \(-0.250394\pi\)
0.706230 + 0.707983i \(0.250394\pi\)
\(542\) 32.7703 + 22.9460i 1.40761 + 0.985617i
\(543\) 0 0
\(544\) −1.00869 2.77135i −0.0432472 0.118821i
\(545\) 21.9849 + 9.58534i 0.941731 + 0.410591i
\(546\) 0 0
\(547\) 18.7126 + 40.1294i 0.800094 + 1.71581i 0.692271 + 0.721638i \(0.256610\pi\)
0.107823 + 0.994170i \(0.465612\pi\)
\(548\) −2.21610 + 8.27060i −0.0946671 + 0.353302i
\(549\) 0 0
\(550\) 6.87802 7.60831i 0.293280 0.324419i
\(551\) 23.6198 + 28.1489i 1.00624 + 1.19918i
\(552\) 0 0
\(553\) 3.91904 + 5.59698i 0.166655 + 0.238008i
\(554\) −3.75221 + 21.2799i −0.159416 + 0.904094i
\(555\) 0 0
\(556\) 7.78940 6.53608i 0.330344 0.277192i
\(557\) 9.87492 + 36.8537i 0.418414 + 1.56154i 0.777898 + 0.628391i \(0.216286\pi\)
−0.359484 + 0.933151i \(0.617047\pi\)
\(558\) 0 0
\(559\) 2.53324 1.46257i 0.107145 0.0618601i
\(560\) 8.50812 7.51227i 0.359534 0.317451i
\(561\) 0 0
\(562\) −1.26983 14.5142i −0.0535644 0.612244i
\(563\) −7.65616 3.57013i −0.322669 0.150463i 0.254534 0.967064i \(-0.418078\pi\)
−0.577203 + 0.816601i \(0.695856\pi\)
\(564\) 0 0
\(565\) 26.7571 + 8.98241i 1.12568 + 0.377893i
\(566\) 20.9575i 0.880909i
\(567\) 0 0
\(568\) −9.70421 + 9.70421i −0.407180 + 0.407180i
\(569\) −0.364320 2.06616i −0.0152731 0.0866180i 0.976218 0.216789i \(-0.0695584\pi\)
−0.991492 + 0.130171i \(0.958447\pi\)
\(570\) 0 0
\(571\) 39.5609 14.3990i 1.65557 0.602578i 0.665913 0.746029i \(-0.268042\pi\)
0.989657 + 0.143451i \(0.0458200\pi\)
\(572\) −4.61959 + 0.404162i −0.193155 + 0.0168989i
\(573\) 0 0
\(574\) 3.34844 9.19975i 0.139761 0.383990i
\(575\) 7.14981 + 22.1548i 0.298168 + 0.923918i
\(576\) 0 0
\(577\) 39.4191 10.5623i 1.64104 0.439715i 0.683955 0.729525i \(-0.260259\pi\)
0.957084 + 0.289810i \(0.0935920\pi\)
\(578\) 28.8723 + 2.52600i 1.20093 + 0.105068i
\(579\) 0 0
\(580\) 2.11651 + 18.7421i 0.0878833 + 0.778225i
\(581\) −0.300004 0.0528988i −0.0124463 0.00219461i
\(582\) 0 0
\(583\) −0.787178 + 8.99749i −0.0326016 + 0.372638i
\(584\) −4.51811 + 7.82560i −0.186961 + 0.323825i
\(585\) 0 0
\(586\) −18.6831 32.3600i −0.771790 1.33678i
\(587\) −11.5098 + 5.36709i −0.475059 + 0.221524i −0.645375 0.763866i \(-0.723299\pi\)
0.170316 + 0.985389i \(0.445521\pi\)
\(588\) 0 0
\(589\) −22.7747 + 27.1419i −0.938416 + 1.11836i
\(590\) −31.0991 4.67943i −1.28033 0.192649i
\(591\) 0 0
\(592\) −15.7374 + 22.4753i −0.646801 + 0.923728i
\(593\) 6.50749 + 6.50749i 0.267230 + 0.267230i 0.827983 0.560753i \(-0.189488\pi\)
−0.560753 + 0.827983i \(0.689488\pi\)
\(594\) 0 0
\(595\) −0.359720 1.21885i −0.0147471 0.0499679i
\(596\) 14.3503 2.53035i 0.587813 0.103647i
\(597\) 0 0
\(598\) 13.1984 28.3041i 0.539723 1.15744i
\(599\) 7.62396 + 6.39726i 0.311507 + 0.261385i 0.785114 0.619351i \(-0.212604\pi\)
−0.473608 + 0.880736i \(0.657049\pi\)
\(600\) 0 0
\(601\) 24.7845 + 9.02082i 1.01098 + 0.367967i 0.793809 0.608167i \(-0.208095\pi\)
0.217171 + 0.976134i \(0.430317\pi\)
\(602\) 1.29013 + 0.345688i 0.0525816 + 0.0140892i
\(603\) 0 0
\(604\) 4.74386 + 2.73887i 0.193025 + 0.111443i
\(605\) −17.8983 11.8723i −0.727670 0.482676i
\(606\) 0 0
\(607\) −5.73315 + 4.01440i −0.232701 + 0.162939i −0.684112 0.729377i \(-0.739810\pi\)
0.451410 + 0.892316i \(0.350921\pi\)
\(608\) 19.1148 13.3843i 0.775207 0.542806i
\(609\) 0 0
\(610\) 42.6821 8.63955i 1.72815 0.349805i
\(611\) −41.0955 23.7265i −1.66254 0.959871i
\(612\) 0 0
\(613\) −3.76248 1.00815i −0.151965 0.0407189i 0.182034 0.983292i \(-0.441732\pi\)
−0.334000 + 0.942573i \(0.608398\pi\)
\(614\) −20.1841 7.34642i −0.814565 0.296477i
\(615\) 0 0
\(616\) 1.56859 + 1.31620i 0.0632004 + 0.0530314i
\(617\) 1.85144 3.97043i 0.0745363 0.159844i −0.865509 0.500894i \(-0.833005\pi\)
0.940045 + 0.341050i \(0.110783\pi\)
\(618\) 0 0
\(619\) 33.2378 5.86071i 1.33594 0.235562i 0.540371 0.841427i \(-0.318284\pi\)
0.795567 + 0.605865i \(0.207173\pi\)
\(620\) −17.4427 + 5.14789i −0.700515 + 0.206744i
\(621\) 0 0
\(622\) 16.8726 + 16.8726i 0.676528 + 0.676528i
\(623\) −6.30763 + 9.00822i −0.252710 + 0.360907i
\(624\) 0 0
\(625\) −1.84315 + 24.9320i −0.0737261 + 0.997279i
\(626\) 33.3240 39.7140i 1.33189 1.58729i
\(627\) 0 0
\(628\) 7.33821 3.42186i 0.292827 0.136547i
\(629\) 1.53603 + 2.66048i 0.0612455 + 0.106080i
\(630\) 0 0
\(631\) −17.7304 + 30.7100i −0.705837 + 1.22255i 0.260552 + 0.965460i \(0.416096\pi\)
−0.966389 + 0.257086i \(0.917238\pi\)
\(632\) 1.00174 11.4500i 0.0398471 0.455455i
\(633\) 0 0
\(634\) 36.5900 + 6.45180i 1.45317 + 0.256234i
\(635\) 30.8557 + 24.5939i 1.22447 + 0.975980i
\(636\) 0 0
\(637\) 22.9647 + 2.00915i 0.909894 + 0.0796054i
\(638\) −16.4377 + 4.40448i −0.650777 + 0.174375i
\(639\) 0 0
\(640\) −26.8495 + 0.676347i −1.06132 + 0.0267350i
\(641\) 9.20207 25.2825i 0.363460 0.998598i −0.614337 0.789044i \(-0.710577\pi\)
0.977797 0.209554i \(-0.0672013\pi\)
\(642\) 0 0
\(643\) −16.3427 + 1.42980i −0.644495 + 0.0563860i −0.404717 0.914442i \(-0.632630\pi\)
−0.239778 + 0.970828i \(0.577075\pi\)
\(644\) 4.51621 1.64377i 0.177964 0.0647734i
\(645\) 0 0
\(646\) −0.747838 4.24120i −0.0294233 0.166868i
\(647\) −6.34739 + 6.34739i −0.249542 + 0.249542i −0.820783 0.571241i \(-0.806462\pi\)
0.571241 + 0.820783i \(0.306462\pi\)
\(648\) 0 0
\(649\) 9.56335i 0.375394i
\(650\) 24.5733 22.8237i 0.963844 0.895220i
\(651\) 0 0
\(652\) −14.7821 6.89302i −0.578913 0.269951i
\(653\) −1.09427 12.5076i −0.0428222 0.489460i −0.987077 0.160245i \(-0.948772\pi\)
0.944255 0.329215i \(-0.106784\pi\)
\(654\) 0 0
\(655\) 6.44999 + 0.400940i 0.252022 + 0.0156660i
\(656\) −24.0399 + 13.8794i −0.938600 + 0.541901i
\(657\) 0 0
\(658\) −5.60792 20.9290i −0.218619 0.815898i
\(659\) −7.46847 + 6.26679i −0.290930 + 0.244120i −0.776557 0.630047i \(-0.783036\pi\)
0.485627 + 0.874166i \(0.338591\pi\)
\(660\) 0 0
\(661\) −7.28597 + 41.3208i −0.283391 + 1.60719i 0.427584 + 0.903976i \(0.359365\pi\)
−0.710975 + 0.703217i \(0.751746\pi\)
\(662\) −25.5849 36.5390i −0.994386 1.42013i
\(663\) 0 0
\(664\) 0.329393 + 0.392555i 0.0127829 + 0.0152341i
\(665\) 8.57855 5.24521i 0.332662 0.203401i
\(666\) 0 0
\(667\) 9.99727 37.3103i 0.387096 1.44466i
\(668\) 0.182035 + 0.390376i 0.00704315 + 0.0151041i
\(669\) 0 0
\(670\) −2.45228 + 5.62454i −0.0947397 + 0.217295i
\(671\) 4.52916 + 12.4438i 0.174846 + 0.480386i
\(672\) 0 0
\(673\) 7.99252 + 5.59642i 0.308089 + 0.215726i 0.717388 0.696674i \(-0.245338\pi\)
−0.409299 + 0.912401i \(0.634227\pi\)
\(674\) −1.65138 −0.0636089
\(675\) 0 0
\(676\) −1.94572 −0.0748355
\(677\) 34.3309 + 24.0388i 1.31944 + 0.923885i 0.999721 0.0236257i \(-0.00752099\pi\)
0.319724 + 0.947511i \(0.396410\pi\)
\(678\) 0 0
\(679\) −1.77831 4.88587i −0.0682453 0.187502i
\(680\) −0.854373 + 1.95959i −0.0327637 + 0.0751468i
\(681\) 0 0
\(682\) −6.93465 14.8714i −0.265542 0.569456i
\(683\) −5.59914 + 20.8963i −0.214245 + 0.799574i 0.772186 + 0.635397i \(0.219163\pi\)
−0.986431 + 0.164177i \(0.947503\pi\)
\(684\) 0 0
\(685\) 16.0656 9.82303i 0.613835 0.375319i
\(686\) 14.7000 + 17.5188i 0.561250 + 0.668872i
\(687\) 0 0
\(688\) −2.17216 3.10216i −0.0828127 0.118269i
\(689\) −5.12843 + 29.0848i −0.195378 + 1.10804i
\(690\) 0 0
\(691\) −19.0033 + 15.9457i −0.722921 + 0.606603i −0.928192 0.372102i \(-0.878637\pi\)
0.205270 + 0.978705i \(0.434193\pi\)
\(692\) 2.12605 + 7.93453i 0.0808203 + 0.301625i
\(693\) 0 0
\(694\) −3.06531 + 1.76976i −0.116358 + 0.0671791i
\(695\) −22.3196 1.38741i −0.846629 0.0526276i
\(696\) 0 0
\(697\) 0.270886 + 3.09624i 0.0102605 + 0.117279i
\(698\) 21.2865 + 9.92607i 0.805707 + 0.375707i
\(699\) 0 0
\(700\) 5.15764 + 0.190385i 0.194941 + 0.00719589i
\(701\) 3.89640i 0.147165i −0.997289 0.0735825i \(-0.976557\pi\)
0.997289 0.0735825i \(-0.0234432\pi\)
\(702\) 0 0
\(703\) −17.1875 + 17.1875i −0.648240 + 0.648240i
\(704\) −0.174119 0.987476i −0.00656235 0.0372169i
\(705\) 0 0
\(706\) 12.1861 4.43538i 0.458630 0.166928i
\(707\) 19.6108 1.71572i 0.737541 0.0645264i
\(708\) 0 0
\(709\) −7.07809 + 19.4469i −0.265823 + 0.730343i 0.732924 + 0.680310i \(0.238155\pi\)
−0.998748 + 0.0500331i \(0.984067\pi\)
\(710\) −31.2001 + 0.785940i −1.17092 + 0.0294958i
\(711\) 0 0
\(712\) 17.8685 4.78786i 0.669652 0.179433i
\(713\) 37.1029 + 3.24608i 1.38951 + 0.121567i
\(714\) 0 0
\(715\) 7.97504 + 6.35660i 0.298250 + 0.237723i
\(716\) −12.7809 2.25362i −0.477645 0.0842218i
\(717\) 0 0
\(718\) 1.33246 15.2301i 0.0497269 0.568381i
\(719\) 23.2328 40.2403i 0.866436 1.50071i 0.000822468 1.00000i \(-0.499738\pi\)
0.865614 0.500712i \(-0.166928\pi\)
\(720\) 0 0
\(721\) 7.56817 + 13.1085i 0.281853 + 0.488185i
\(722\) 0.973719 0.454053i 0.0362381 0.0168981i
\(723\) 0 0
\(724\) 12.0891 14.4073i 0.449289 0.535442i
\(725\) 25.0295 33.0781i 0.929571 1.22849i
\(726\) 0 0
\(727\) 14.7105 21.0088i 0.545584 0.779175i −0.447785 0.894141i \(-0.647787\pi\)
0.993369 + 0.114966i \(0.0366760\pi\)
\(728\) 4.73454 + 4.73454i 0.175474 + 0.175474i
\(729\) 0 0
\(730\) −19.7093 + 5.81682i −0.729472 + 0.215290i
\(731\) −0.417580 + 0.0736307i −0.0154448 + 0.00272333i
\(732\) 0 0
\(733\) 1.12205 2.40624i 0.0414438 0.0888766i −0.884496 0.466548i \(-0.845497\pi\)
0.925940 + 0.377672i \(0.123275\pi\)
\(734\) −36.3169 30.4735i −1.34048 1.12480i
\(735\) 0 0
\(736\) −23.0499 8.38947i −0.849630 0.309240i
\(737\) −1.80228 0.482919i −0.0663878 0.0177886i
\(738\) 0 0
\(739\) −19.4519 11.2305i −0.715548 0.413122i 0.0975639 0.995229i \(-0.468895\pi\)
−0.813112 + 0.582107i \(0.802228\pi\)
\(740\) −12.2285 + 2.47524i −0.449527 + 0.0909917i
\(741\) 0 0
\(742\) −11.0464 + 7.73477i −0.405526 + 0.283952i
\(743\) −25.2126 + 17.6540i −0.924960 + 0.647664i −0.935896 0.352276i \(-0.885408\pi\)
0.0109359 + 0.999940i \(0.496519\pi\)
\(744\) 0 0
\(745\) −26.7057 17.7144i −0.978422 0.649004i
\(746\) 18.2856 + 10.5572i 0.669484 + 0.386527i
\(747\) 0 0
\(748\) 0.649300 + 0.173979i 0.0237408 + 0.00636132i
\(749\) −4.31804 1.57164i −0.157778 0.0574264i
\(750\) 0 0
\(751\) 5.77858 + 4.84881i 0.210864 + 0.176936i 0.742102 0.670287i \(-0.233829\pi\)
−0.531239 + 0.847222i \(0.678273\pi\)
\(752\) −25.9636 + 55.6791i −0.946795 + 2.03041i
\(753\) 0 0
\(754\) −54.8008 + 9.66287i −1.99573 + 0.351901i
\(755\) −3.41000 11.5542i −0.124103 0.420499i
\(756\) 0 0
\(757\) −18.1781 18.1781i −0.660696 0.660696i 0.294848 0.955544i \(-0.404731\pi\)
−0.955544 + 0.294848i \(0.904731\pi\)
\(758\) −22.5748 + 32.2402i −0.819954 + 1.17102i
\(759\) 0 0
\(760\) −16.7260 2.51674i −0.606717 0.0912917i
\(761\) −19.2569 + 22.9494i −0.698061 + 0.831916i −0.992305 0.123814i \(-0.960487\pi\)
0.294245 + 0.955730i \(0.404932\pi\)
\(762\) 0 0
\(763\) −9.86895 + 4.60197i −0.357280 + 0.166602i
\(764\) −2.16991 3.75839i −0.0785044 0.135974i
\(765\) 0 0
\(766\) 16.5590 28.6811i 0.598302 1.03629i
\(767\) 2.72548 31.1524i 0.0984115 1.12485i
\(768\) 0 0
\(769\) 4.02410 + 0.709557i 0.145113 + 0.0255873i 0.245733 0.969338i \(-0.420971\pi\)
−0.100620 + 0.994925i \(0.532083\pi\)
\(770\) 0.522545 + 4.62725i 0.0188312 + 0.166754i
\(771\) 0 0
\(772\) −10.2628 0.897880i −0.369367 0.0323154i
\(773\) 38.4073 10.2912i 1.38141 0.370149i 0.509780 0.860305i \(-0.329727\pi\)
0.871635 + 0.490156i \(0.163060\pi\)
\(774\) 0 0
\(775\) 35.6009 + 18.2289i 1.27882 + 0.654802i
\(776\) −2.99143 + 8.21887i −0.107386 + 0.295040i
\(777\) 0 0
\(778\) −26.9882 + 2.36116i −0.967573 + 0.0846517i
\(779\) −23.1087 + 8.41088i −0.827955 + 0.301351i
\(780\) 0 0
\(781\) −1.64803 9.34644i −0.0589711 0.334442i
\(782\) −3.20111 + 3.20111i −0.114471 + 0.114471i
\(783\) 0 0
\(784\) 29.8449i 1.06589i
\(785\) −16.8811 5.66700i −0.602511 0.202264i
\(786\) 0 0
\(787\) 4.88315