Properties

Label 432.2.be.b.191.1
Level $432$
Weight $2$
Character 432.191
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 191.1
Character \(\chi\) \(=\) 432.191
Dual form 432.2.be.b.95.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22376 - 1.22573i) q^{3} +(1.15344 + 1.37462i) q^{5} +(-0.0374696 - 0.102947i) q^{7} +(-0.00480931 + 3.00000i) q^{9} +O(q^{10})\) \(q+(-1.22376 - 1.22573i) q^{3} +(1.15344 + 1.37462i) q^{5} +(-0.0374696 - 0.102947i) q^{7} +(-0.00480931 + 3.00000i) q^{9} +(1.39140 + 1.16752i) q^{11} +(0.628601 + 3.56497i) q^{13} +(0.273367 - 3.09601i) q^{15} +(3.51663 - 2.03033i) q^{17} +(-0.846129 - 0.488513i) q^{19} +(-0.0803308 + 0.171910i) q^{21} +(5.93514 + 2.16021i) q^{23} +(0.309093 - 1.75296i) q^{25} +(3.68306 - 3.66539i) q^{27} +(0.912843 + 0.160959i) q^{29} +(0.185026 - 0.508354i) q^{31} +(-0.271680 - 3.13425i) q^{33} +(0.0982937 - 0.170250i) q^{35} +(4.79618 + 8.30722i) q^{37} +(3.60042 - 5.13318i) q^{39} +(0.0246348 - 0.00434378i) q^{41} +(-6.93075 + 8.25975i) q^{43} +(-4.12940 + 3.45371i) q^{45} +(7.54426 - 2.74589i) q^{47} +(5.35312 - 4.49180i) q^{49} +(-6.79215 - 1.82579i) q^{51} -11.7054i q^{53} +3.25932i q^{55} +(0.436678 + 1.63495i) q^{57} +(1.98032 - 1.66168i) q^{59} +(-5.80843 + 2.11410i) q^{61} +(0.309021 - 0.111914i) q^{63} +(-4.17542 + 4.97608i) q^{65} +(-13.5924 + 2.39670i) q^{67} +(-4.61537 - 9.91844i) q^{69} +(0.650941 + 1.12746i) q^{71} +(-3.34757 + 5.79815i) q^{73} +(-2.52690 + 1.76634i) q^{75} +(0.0680578 - 0.186987i) q^{77} +(-8.71473 - 1.53664i) q^{79} +(-8.99995 - 0.0288558i) q^{81} +(-3.02146 + 17.1355i) q^{83} +(6.84715 + 2.49216i) q^{85} +(-0.919812 - 1.31587i) q^{87} +(-4.27071 - 2.46569i) q^{89} +(0.343450 - 0.198291i) q^{91} +(-0.849530 + 0.395314i) q^{93} +(-0.304442 - 1.72657i) q^{95} +(-10.6279 - 8.91789i) q^{97} +(-3.50926 + 4.16859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.22376 1.22573i −0.706540 0.707673i
\(4\) 0 0
\(5\) 1.15344 + 1.37462i 0.515835 + 0.614748i 0.959591 0.281400i \(-0.0907987\pi\)
−0.443756 + 0.896148i \(0.646354\pi\)
\(6\) 0 0
\(7\) −0.0374696 0.102947i −0.0141622 0.0389103i 0.932410 0.361402i \(-0.117702\pi\)
−0.946572 + 0.322492i \(0.895480\pi\)
\(8\) 0 0
\(9\) −0.00480931 + 3.00000i −0.00160310 + 0.999999i
\(10\) 0 0
\(11\) 1.39140 + 1.16752i 0.419523 + 0.352022i 0.827982 0.560755i \(-0.189489\pi\)
−0.408458 + 0.912777i \(0.633933\pi\)
\(12\) 0 0
\(13\) 0.628601 + 3.56497i 0.174343 + 0.988746i 0.938900 + 0.344190i \(0.111847\pi\)
−0.764557 + 0.644556i \(0.777042\pi\)
\(14\) 0 0
\(15\) 0.273367 3.09601i 0.0705829 0.799386i
\(16\) 0 0
\(17\) 3.51663 2.03033i 0.852908 0.492427i −0.00872297 0.999962i \(-0.502777\pi\)
0.861631 + 0.507535i \(0.169443\pi\)
\(18\) 0 0
\(19\) −0.846129 0.488513i −0.194115 0.112073i 0.399792 0.916606i \(-0.369082\pi\)
−0.593908 + 0.804533i \(0.702416\pi\)
\(20\) 0 0
\(21\) −0.0803308 + 0.171910i −0.0175296 + 0.0375139i
\(22\) 0 0
\(23\) 5.93514 + 2.16021i 1.23756 + 0.450436i 0.876181 0.481983i \(-0.160083\pi\)
0.361381 + 0.932418i \(0.382305\pi\)
\(24\) 0 0
\(25\) 0.309093 1.75296i 0.0618187 0.350591i
\(26\) 0 0
\(27\) 3.68306 3.66539i 0.708805 0.705404i
\(28\) 0 0
\(29\) 0.912843 + 0.160959i 0.169511 + 0.0298893i 0.257759 0.966209i \(-0.417016\pi\)
−0.0882486 + 0.996098i \(0.528127\pi\)
\(30\) 0 0
\(31\) 0.185026 0.508354i 0.0332316 0.0913030i −0.921967 0.387268i \(-0.873419\pi\)
0.955199 + 0.295965i \(0.0956411\pi\)
\(32\) 0 0
\(33\) −0.271680 3.13425i −0.0472934 0.545603i
\(34\) 0 0
\(35\) 0.0982937 0.170250i 0.0166147 0.0287775i
\(36\) 0 0
\(37\) 4.79618 + 8.30722i 0.788486 + 1.36570i 0.926894 + 0.375323i \(0.122468\pi\)
−0.138408 + 0.990375i \(0.544198\pi\)
\(38\) 0 0
\(39\) 3.60042 5.13318i 0.576529 0.821966i
\(40\) 0 0
\(41\) 0.0246348 0.00434378i 0.00384731 0.000678384i −0.171724 0.985145i \(-0.554934\pi\)
0.175571 + 0.984467i \(0.443823\pi\)
\(42\) 0 0
\(43\) −6.93075 + 8.25975i −1.05693 + 1.25960i −0.0923729 + 0.995724i \(0.529445\pi\)
−0.964557 + 0.263875i \(0.914999\pi\)
\(44\) 0 0
\(45\) −4.12940 + 3.45371i −0.615574 + 0.514849i
\(46\) 0 0
\(47\) 7.54426 2.74589i 1.10044 0.400529i 0.272964 0.962024i \(-0.411996\pi\)
0.827480 + 0.561496i \(0.189774\pi\)
\(48\) 0 0
\(49\) 5.35312 4.49180i 0.764731 0.641685i
\(50\) 0 0
\(51\) −6.79215 1.82579i −0.951091 0.255661i
\(52\) 0 0
\(53\) 11.7054i 1.60786i −0.594726 0.803928i \(-0.702740\pi\)
0.594726 0.803928i \(-0.297260\pi\)
\(54\) 0 0
\(55\) 3.25932i 0.439486i
\(56\) 0 0
\(57\) 0.436678 + 1.63495i 0.0578394 + 0.216554i
\(58\) 0 0
\(59\) 1.98032 1.66168i 0.257815 0.216333i −0.504714 0.863287i \(-0.668402\pi\)
0.762529 + 0.646954i \(0.223957\pi\)
\(60\) 0 0
\(61\) −5.80843 + 2.11410i −0.743694 + 0.270682i −0.685950 0.727649i \(-0.740613\pi\)
−0.0577441 + 0.998331i \(0.518391\pi\)
\(62\) 0 0
\(63\) 0.309021 0.111914i 0.0389329 0.0140998i
\(64\) 0 0
\(65\) −4.17542 + 4.97608i −0.517897 + 0.617206i
\(66\) 0 0
\(67\) −13.5924 + 2.39670i −1.66057 + 0.292804i −0.923669 0.383192i \(-0.874825\pi\)
−0.736905 + 0.675996i \(0.763714\pi\)
\(68\) 0 0
\(69\) −4.61537 9.91844i −0.555625 1.19404i
\(70\) 0 0
\(71\) 0.650941 + 1.12746i 0.0772525 + 0.133805i 0.902064 0.431603i \(-0.142052\pi\)
−0.824811 + 0.565408i \(0.808719\pi\)
\(72\) 0 0
\(73\) −3.34757 + 5.79815i −0.391803 + 0.678623i −0.992687 0.120713i \(-0.961482\pi\)
0.600884 + 0.799336i \(0.294815\pi\)
\(74\) 0 0
\(75\) −2.52690 + 1.76634i −0.291781 + 0.203959i
\(76\) 0 0
\(77\) 0.0680578 0.186987i 0.00775591 0.0213092i
\(78\) 0 0
\(79\) −8.71473 1.53664i −0.980484 0.172886i −0.339639 0.940556i \(-0.610305\pi\)
−0.640845 + 0.767670i \(0.721416\pi\)
\(80\) 0 0
\(81\) −8.99995 0.0288558i −0.999995 0.00320620i
\(82\) 0 0
\(83\) −3.02146 + 17.1355i −0.331648 + 1.88087i 0.126460 + 0.991972i \(0.459638\pi\)
−0.458108 + 0.888897i \(0.651473\pi\)
\(84\) 0 0
\(85\) 6.84715 + 2.49216i 0.742678 + 0.270313i
\(86\) 0 0
\(87\) −0.919812 1.31587i −0.0986141 0.141076i
\(88\) 0 0
\(89\) −4.27071 2.46569i −0.452694 0.261363i 0.256273 0.966604i \(-0.417505\pi\)
−0.708967 + 0.705241i \(0.750839\pi\)
\(90\) 0 0
\(91\) 0.343450 0.198291i 0.0360033 0.0207865i
\(92\) 0 0
\(93\) −0.849530 + 0.395314i −0.0880921 + 0.0409921i
\(94\) 0 0
\(95\) −0.304442 1.72657i −0.0312351 0.177143i
\(96\) 0 0
\(97\) −10.6279 8.91789i −1.07910 0.905475i −0.0832569 0.996528i \(-0.526532\pi\)
−0.995846 + 0.0910532i \(0.970977\pi\)
\(98\) 0 0
\(99\) −3.50926 + 4.16859i −0.352694 + 0.418959i
\(100\) 0 0
\(101\) −4.68279 12.8659i −0.465955 1.28020i −0.920941 0.389703i \(-0.872578\pi\)
0.454985 0.890499i \(-0.349645\pi\)
\(102\) 0 0
\(103\) 2.07621 + 2.47433i 0.204575 + 0.243803i 0.858571 0.512695i \(-0.171353\pi\)
−0.653995 + 0.756499i \(0.726908\pi\)
\(104\) 0 0
\(105\) −0.328968 + 0.0878641i −0.0321040 + 0.00857466i
\(106\) 0 0
\(107\) −0.288606 −0.0279006 −0.0139503 0.999903i \(-0.504441\pi\)
−0.0139503 + 0.999903i \(0.504441\pi\)
\(108\) 0 0
\(109\) −3.08753 −0.295732 −0.147866 0.989007i \(-0.547240\pi\)
−0.147866 + 0.989007i \(0.547240\pi\)
\(110\) 0 0
\(111\) 4.31300 16.0449i 0.409371 1.52291i
\(112\) 0 0
\(113\) 7.46015 + 8.89065i 0.701791 + 0.836362i 0.992728 0.120380i \(-0.0384113\pi\)
−0.290936 + 0.956742i \(0.593967\pi\)
\(114\) 0 0
\(115\) 3.87637 + 10.6502i 0.361473 + 0.993139i
\(116\) 0 0
\(117\) −10.6979 + 1.86866i −0.989024 + 0.172757i
\(118\) 0 0
\(119\) −0.340783 0.285951i −0.0312395 0.0262131i
\(120\) 0 0
\(121\) −1.33724 7.58389i −0.121568 0.689445i
\(122\) 0 0
\(123\) −0.0354714 0.0248797i −0.00319835 0.00224333i
\(124\) 0 0
\(125\) 10.5363 6.08314i 0.942396 0.544092i
\(126\) 0 0
\(127\) 6.76517 + 3.90587i 0.600312 + 0.346590i 0.769164 0.639051i \(-0.220673\pi\)
−0.168853 + 0.985641i \(0.554006\pi\)
\(128\) 0 0
\(129\) 18.6058 1.61277i 1.63815 0.141996i
\(130\) 0 0
\(131\) 3.17078 + 1.15407i 0.277032 + 0.100831i 0.476800 0.879012i \(-0.341797\pi\)
−0.199768 + 0.979843i \(0.564019\pi\)
\(132\) 0 0
\(133\) −0.0185868 + 0.105411i −0.00161168 + 0.00914028i
\(134\) 0 0
\(135\) 9.28670 + 0.834988i 0.799272 + 0.0718643i
\(136\) 0 0
\(137\) −17.7688 3.13311i −1.51809 0.267680i −0.648407 0.761294i \(-0.724564\pi\)
−0.869681 + 0.493614i \(0.835675\pi\)
\(138\) 0 0
\(139\) 5.84789 16.0669i 0.496012 1.36278i −0.399087 0.916913i \(-0.630673\pi\)
0.895099 0.445868i \(-0.147105\pi\)
\(140\) 0 0
\(141\) −12.5981 5.88688i −1.06095 0.495765i
\(142\) 0 0
\(143\) −3.28756 + 5.69422i −0.274920 + 0.476175i
\(144\) 0 0
\(145\) 0.831654 + 1.44047i 0.0690651 + 0.119624i
\(146\) 0 0
\(147\) −12.0567 1.06456i −0.994417 0.0878034i
\(148\) 0 0
\(149\) 17.4360 3.07444i 1.42841 0.251868i 0.594648 0.803986i \(-0.297291\pi\)
0.833766 + 0.552118i \(0.186180\pi\)
\(150\) 0 0
\(151\) 3.97337 4.73527i 0.323348 0.385351i −0.579744 0.814799i \(-0.696847\pi\)
0.903092 + 0.429448i \(0.141292\pi\)
\(152\) 0 0
\(153\) 6.07406 + 10.5596i 0.491059 + 0.853696i
\(154\) 0 0
\(155\) 0.912208 0.332017i 0.0732703 0.0266682i
\(156\) 0 0
\(157\) 13.5145 11.3400i 1.07857 0.905032i 0.0827730 0.996568i \(-0.473622\pi\)
0.995802 + 0.0915368i \(0.0291779\pi\)
\(158\) 0 0
\(159\) −14.3476 + 14.3246i −1.13784 + 1.13601i
\(160\) 0 0
\(161\) 0.691947i 0.0545330i
\(162\) 0 0
\(163\) 0.563744i 0.0441559i −0.999756 0.0220779i \(-0.992972\pi\)
0.999756 0.0220779i \(-0.00702820\pi\)
\(164\) 0 0
\(165\) 3.99503 3.98863i 0.311013 0.310515i
\(166\) 0 0
\(167\) 13.0407 10.9424i 1.00912 0.846750i 0.0208959 0.999782i \(-0.493348\pi\)
0.988221 + 0.153032i \(0.0489037\pi\)
\(168\) 0 0
\(169\) −0.0978970 + 0.0356316i −0.00753054 + 0.00274089i
\(170\) 0 0
\(171\) 1.46961 2.53603i 0.112384 0.193935i
\(172\) 0 0
\(173\) −11.8795 + 14.1575i −0.903184 + 1.07637i 0.0935494 + 0.995615i \(0.470179\pi\)
−0.996734 + 0.0807585i \(0.974266\pi\)
\(174\) 0 0
\(175\) −0.192043 + 0.0338624i −0.0145171 + 0.00255976i
\(176\) 0 0
\(177\) −4.46021 0.393820i −0.335250 0.0296013i
\(178\) 0 0
\(179\) −7.48642 12.9669i −0.559561 0.969188i −0.997533 0.0701997i \(-0.977636\pi\)
0.437972 0.898989i \(-0.355697\pi\)
\(180\) 0 0
\(181\) −9.67055 + 16.7499i −0.718806 + 1.24501i 0.242667 + 0.970110i \(0.421978\pi\)
−0.961473 + 0.274899i \(0.911356\pi\)
\(182\) 0 0
\(183\) 9.69945 + 4.53240i 0.717004 + 0.335044i
\(184\) 0 0
\(185\) −5.88715 + 16.1748i −0.432832 + 1.18920i
\(186\) 0 0
\(187\) 7.26350 + 1.28075i 0.531160 + 0.0936578i
\(188\) 0 0
\(189\) −0.515344 0.241819i −0.0374857 0.0175897i
\(190\) 0 0
\(191\) −2.44661 + 13.8754i −0.177031 + 1.00399i 0.758743 + 0.651390i \(0.225814\pi\)
−0.935774 + 0.352601i \(0.885297\pi\)
\(192\) 0 0
\(193\) 2.31451 + 0.842411i 0.166602 + 0.0606381i 0.423975 0.905674i \(-0.360635\pi\)
−0.257373 + 0.966312i \(0.582857\pi\)
\(194\) 0 0
\(195\) 11.2090 0.971611i 0.802696 0.0695785i
\(196\) 0 0
\(197\) 7.93614 + 4.58193i 0.565426 + 0.326449i 0.755321 0.655355i \(-0.227481\pi\)
−0.189894 + 0.981805i \(0.560814\pi\)
\(198\) 0 0
\(199\) 7.82997 4.52063i 0.555052 0.320459i −0.196105 0.980583i \(-0.562829\pi\)
0.751157 + 0.660124i \(0.229496\pi\)
\(200\) 0 0
\(201\) 19.5716 + 13.7275i 1.38047 + 0.968266i
\(202\) 0 0
\(203\) −0.0176337 0.100005i −0.00123764 0.00701901i
\(204\) 0 0
\(205\) 0.0343858 + 0.0288531i 0.00240161 + 0.00201519i
\(206\) 0 0
\(207\) −6.50918 + 17.7950i −0.452419 + 1.23684i
\(208\) 0 0
\(209\) −0.606955 1.66759i −0.0419839 0.115350i
\(210\) 0 0
\(211\) −10.9596 13.0612i −0.754492 0.899169i 0.242994 0.970028i \(-0.421870\pi\)
−0.997486 + 0.0708592i \(0.977426\pi\)
\(212\) 0 0
\(213\) 0.585363 2.17762i 0.0401084 0.149208i
\(214\) 0 0
\(215\) −19.3482 −1.31954
\(216\) 0 0
\(217\) −0.0592663 −0.00402326
\(218\) 0 0
\(219\) 11.2036 2.99237i 0.757068 0.202205i
\(220\) 0 0
\(221\) 9.44862 + 11.2604i 0.635583 + 0.757458i
\(222\) 0 0
\(223\) −2.45483 6.74460i −0.164388 0.451651i 0.829960 0.557823i \(-0.188363\pi\)
−0.994348 + 0.106171i \(0.966141\pi\)
\(224\) 0 0
\(225\) 5.25737 + 0.935710i 0.350492 + 0.0623806i
\(226\) 0 0
\(227\) −20.2092 16.9575i −1.34133 1.12551i −0.981281 0.192580i \(-0.938315\pi\)
−0.360052 0.932932i \(-0.617241\pi\)
\(228\) 0 0
\(229\) 0.294614 + 1.67084i 0.0194686 + 0.110412i 0.992993 0.118169i \(-0.0377025\pi\)
−0.973525 + 0.228581i \(0.926591\pi\)
\(230\) 0 0
\(231\) −0.312482 + 0.145408i −0.0205598 + 0.00956714i
\(232\) 0 0
\(233\) −3.85496 + 2.22566i −0.252547 + 0.145808i −0.620930 0.783866i \(-0.713245\pi\)
0.368383 + 0.929674i \(0.379912\pi\)
\(234\) 0 0
\(235\) 12.4764 + 7.20326i 0.813871 + 0.469889i
\(236\) 0 0
\(237\) 8.78126 + 12.5624i 0.570404 + 0.816013i
\(238\) 0 0
\(239\) −23.7297 8.63692i −1.53495 0.558676i −0.570122 0.821560i \(-0.693104\pi\)
−0.964827 + 0.262884i \(0.915326\pi\)
\(240\) 0 0
\(241\) 0.665669 3.77520i 0.0428795 0.243182i −0.955833 0.293911i \(-0.905043\pi\)
0.998712 + 0.0507286i \(0.0161543\pi\)
\(242\) 0 0
\(243\) 10.9784 + 11.0668i 0.704267 + 0.709935i
\(244\) 0 0
\(245\) 12.3490 + 2.17746i 0.788950 + 0.139113i
\(246\) 0 0
\(247\) 1.20966 3.32351i 0.0769687 0.211470i
\(248\) 0 0
\(249\) 24.7010 17.2663i 1.56536 1.09421i
\(250\) 0 0
\(251\) 9.34108 16.1792i 0.589604 1.02122i −0.404680 0.914458i \(-0.632617\pi\)
0.994284 0.106766i \(-0.0340494\pi\)
\(252\) 0 0
\(253\) 5.73606 + 9.93515i 0.360623 + 0.624617i
\(254\) 0 0
\(255\) −5.32458 11.4425i −0.333438 0.716560i
\(256\) 0 0
\(257\) −1.33829 + 0.235977i −0.0834802 + 0.0147198i −0.215232 0.976563i \(-0.569051\pi\)
0.131752 + 0.991283i \(0.457940\pi\)
\(258\) 0 0
\(259\) 0.675492 0.805020i 0.0419730 0.0500215i
\(260\) 0 0
\(261\) −0.487266 + 2.73775i −0.0301610 + 0.169463i
\(262\) 0 0
\(263\) 22.8321 8.31021i 1.40789 0.512429i 0.477379 0.878698i \(-0.341587\pi\)
0.930509 + 0.366268i \(0.119365\pi\)
\(264\) 0 0
\(265\) 16.0904 13.5015i 0.988426 0.829388i
\(266\) 0 0
\(267\) 2.20407 + 8.25215i 0.134887 + 0.505023i
\(268\) 0 0
\(269\) 7.63814i 0.465706i −0.972512 0.232853i \(-0.925194\pi\)
0.972512 0.232853i \(-0.0748061\pi\)
\(270\) 0 0
\(271\) 6.51576i 0.395804i −0.980222 0.197902i \(-0.936587\pi\)
0.980222 0.197902i \(-0.0634128\pi\)
\(272\) 0 0
\(273\) −0.663351 0.178314i −0.0401479 0.0107921i
\(274\) 0 0
\(275\) 2.47669 2.07819i 0.149350 0.125320i
\(276\) 0 0
\(277\) −15.3821 + 5.59863i −0.924221 + 0.336389i −0.759916 0.650021i \(-0.774760\pi\)
−0.164304 + 0.986410i \(0.552538\pi\)
\(278\) 0 0
\(279\) 1.52417 + 0.557521i 0.0912496 + 0.0333779i
\(280\) 0 0
\(281\) −18.6722 + 22.2527i −1.11389 + 1.32748i −0.174492 + 0.984659i \(0.555828\pi\)
−0.939399 + 0.342825i \(0.888616\pi\)
\(282\) 0 0
\(283\) 14.3442 2.52928i 0.852677 0.150350i 0.269806 0.962915i \(-0.413040\pi\)
0.582871 + 0.812565i \(0.301929\pi\)
\(284\) 0 0
\(285\) −1.74374 + 2.48608i −0.103290 + 0.147263i
\(286\) 0 0
\(287\) −0.00137023 0.00237332i −8.08824e−5 0.000140092i
\(288\) 0 0
\(289\) −0.255543 + 0.442614i −0.0150320 + 0.0260361i
\(290\) 0 0
\(291\) 2.07517 + 23.9403i 0.121649 + 1.40341i
\(292\) 0 0
\(293\) −0.657295 + 1.80590i −0.0383996 + 0.105502i −0.957411 0.288730i \(-0.906767\pi\)
0.919011 + 0.394232i \(0.128989\pi\)
\(294\) 0 0
\(295\) 4.56836 + 0.805525i 0.265980 + 0.0468995i
\(296\) 0 0
\(297\) 9.40405 0.799966i 0.545678 0.0464187i
\(298\) 0 0
\(299\) −3.97027 + 22.5165i −0.229607 + 1.30216i
\(300\) 0 0
\(301\) 1.11001 + 0.404010i 0.0639798 + 0.0232868i
\(302\) 0 0
\(303\) −10.0394 + 21.4846i −0.576749 + 1.23426i
\(304\) 0 0
\(305\) −9.60576 5.54589i −0.550024 0.317557i
\(306\) 0 0
\(307\) 23.7774 13.7279i 1.35705 0.783492i 0.367822 0.929896i \(-0.380103\pi\)
0.989225 + 0.146405i \(0.0467701\pi\)
\(308\) 0 0
\(309\) 0.492064 5.57287i 0.0279925 0.317029i
\(310\) 0 0
\(311\) −3.16971 17.9763i −0.179738 1.01934i −0.932532 0.361087i \(-0.882406\pi\)
0.752794 0.658256i \(-0.228705\pi\)
\(312\) 0 0
\(313\) −23.3508 19.5937i −1.31987 1.10750i −0.986334 0.164761i \(-0.947315\pi\)
−0.333533 0.942738i \(-0.608241\pi\)
\(314\) 0 0
\(315\) 0.510276 + 0.295700i 0.0287508 + 0.0166608i
\(316\) 0 0
\(317\) −4.40578 12.1048i −0.247453 0.679872i −0.999778 0.0210792i \(-0.993290\pi\)
0.752325 0.658792i \(-0.228932\pi\)
\(318\) 0 0
\(319\) 1.08221 + 1.28972i 0.0605920 + 0.0722107i
\(320\) 0 0
\(321\) 0.353186 + 0.353752i 0.0197129 + 0.0197445i
\(322\) 0 0
\(323\) −3.96736 −0.220750
\(324\) 0 0
\(325\) 6.44354 0.357423
\(326\) 0 0
\(327\) 3.77841 + 3.78447i 0.208946 + 0.209282i
\(328\) 0 0
\(329\) −0.565361 0.673771i −0.0311694 0.0371462i
\(330\) 0 0
\(331\) 3.04766 + 8.37337i 0.167514 + 0.460242i 0.994837 0.101485i \(-0.0323594\pi\)
−0.827323 + 0.561727i \(0.810137\pi\)
\(332\) 0 0
\(333\) −24.9447 + 14.3486i −1.36696 + 0.786296i
\(334\) 0 0
\(335\) −18.9726 15.9199i −1.03658 0.869796i
\(336\) 0 0
\(337\) −1.58582 8.99362i −0.0863850 0.489913i −0.997049 0.0767661i \(-0.975541\pi\)
0.910664 0.413147i \(-0.135571\pi\)
\(338\) 0 0
\(339\) 1.76806 20.0241i 0.0960279 1.08756i
\(340\) 0 0
\(341\) 0.850961 0.491302i 0.0460821 0.0266055i
\(342\) 0 0
\(343\) −1.32713 0.766220i −0.0716584 0.0413720i
\(344\) 0 0
\(345\) 8.31051 17.7847i 0.447423 0.957497i
\(346\) 0 0
\(347\) 17.6125 + 6.41042i 0.945487 + 0.344129i 0.768330 0.640054i \(-0.221088\pi\)
0.177157 + 0.984183i \(0.443310\pi\)
\(348\) 0 0
\(349\) 3.31068 18.7758i 0.177217 1.00505i −0.758338 0.651862i \(-0.773988\pi\)
0.935554 0.353183i \(-0.114901\pi\)
\(350\) 0 0
\(351\) 15.3822 + 10.8259i 0.821041 + 0.577846i
\(352\) 0 0
\(353\) 12.6087 + 2.22326i 0.671094 + 0.118332i 0.498805 0.866714i \(-0.333772\pi\)
0.172290 + 0.985046i \(0.444884\pi\)
\(354\) 0 0
\(355\) −0.799008 + 2.19526i −0.0424070 + 0.116512i
\(356\) 0 0
\(357\) 0.0665400 + 0.767642i 0.00352167 + 0.0406279i
\(358\) 0 0
\(359\) −14.9673 + 25.9241i −0.789945 + 1.36822i 0.136056 + 0.990701i \(0.456557\pi\)
−0.926000 + 0.377523i \(0.876776\pi\)
\(360\) 0 0
\(361\) −9.02271 15.6278i −0.474880 0.822515i
\(362\) 0 0
\(363\) −7.65930 + 10.9200i −0.402009 + 0.573150i
\(364\) 0 0
\(365\) −11.8315 + 2.08621i −0.619287 + 0.109197i
\(366\) 0 0
\(367\) −7.71474 + 9.19407i −0.402706 + 0.479927i −0.928843 0.370473i \(-0.879196\pi\)
0.526137 + 0.850400i \(0.323640\pi\)
\(368\) 0 0
\(369\) 0.0129128 + 0.0739251i 0.000672215 + 0.00384839i
\(370\) 0 0
\(371\) −1.20503 + 0.438596i −0.0625622 + 0.0227708i
\(372\) 0 0
\(373\) −20.3745 + 17.0962i −1.05495 + 0.885209i −0.993605 0.112908i \(-0.963984\pi\)
−0.0613456 + 0.998117i \(0.519539\pi\)
\(374\) 0 0
\(375\) −20.3502 5.47031i −1.05088 0.282485i
\(376\) 0 0
\(377\) 3.35544i 0.172814i
\(378\) 0 0
\(379\) 22.5119i 1.15636i −0.815910 0.578179i \(-0.803764\pi\)
0.815910 0.578179i \(-0.196236\pi\)
\(380\) 0 0
\(381\) −3.49143 13.0721i −0.178871 0.669704i
\(382\) 0 0
\(383\) −22.3710 + 18.7715i −1.14310 + 0.959177i −0.999536 0.0304640i \(-0.990301\pi\)
−0.143566 + 0.989641i \(0.545857\pi\)
\(384\) 0 0
\(385\) 0.335537 0.122125i 0.0171005 0.00622409i
\(386\) 0 0
\(387\) −24.7459 20.8320i −1.25790 1.05895i
\(388\) 0 0
\(389\) −1.76256 + 2.10053i −0.0893651 + 0.106501i −0.808874 0.587982i \(-0.799923\pi\)
0.719509 + 0.694483i \(0.244367\pi\)
\(390\) 0 0
\(391\) 25.2576 4.45360i 1.27733 0.225228i
\(392\) 0 0
\(393\) −2.46571 5.29881i −0.124378 0.267290i
\(394\) 0 0
\(395\) −7.93964 13.7519i −0.399487 0.691931i
\(396\) 0 0
\(397\) 3.91367 6.77868i 0.196422 0.340212i −0.750944 0.660366i \(-0.770401\pi\)
0.947366 + 0.320154i \(0.103735\pi\)
\(398\) 0 0
\(399\) 0.151951 0.106216i 0.00760704 0.00531743i
\(400\) 0 0
\(401\) −2.67952 + 7.36193i −0.133809 + 0.367637i −0.988443 0.151594i \(-0.951559\pi\)
0.854634 + 0.519231i \(0.173782\pi\)
\(402\) 0 0
\(403\) 1.92857 + 0.340060i 0.0960692 + 0.0169396i
\(404\) 0 0
\(405\) −10.3413 12.4048i −0.513861 0.616399i
\(406\) 0 0
\(407\) −3.02548 + 17.1583i −0.149967 + 0.850507i
\(408\) 0 0
\(409\) −5.15878 1.87764i −0.255085 0.0928434i 0.211313 0.977419i \(-0.432226\pi\)
−0.466398 + 0.884575i \(0.654448\pi\)
\(410\) 0 0
\(411\) 17.9044 + 25.6138i 0.883159 + 1.26344i
\(412\) 0 0
\(413\) −0.245267 0.141605i −0.0120688 0.00696792i
\(414\) 0 0
\(415\) −27.0399 + 15.6115i −1.32734 + 0.766337i
\(416\) 0 0
\(417\) −26.8501 + 12.4942i −1.31486 + 0.611845i
\(418\) 0 0
\(419\) 2.24813 + 12.7498i 0.109829 + 0.622868i 0.989181 + 0.146698i \(0.0468645\pi\)
−0.879353 + 0.476171i \(0.842024\pi\)
\(420\) 0 0
\(421\) 10.1658 + 8.53012i 0.495451 + 0.415733i 0.855975 0.517017i \(-0.172958\pi\)
−0.360524 + 0.932750i \(0.617402\pi\)
\(422\) 0 0
\(423\) 8.20137 + 22.6460i 0.398764 + 1.10108i
\(424\) 0 0
\(425\) −2.47211 6.79206i −0.119915 0.329463i
\(426\) 0 0
\(427\) 0.435280 + 0.518746i 0.0210647 + 0.0251039i
\(428\) 0 0
\(429\) 11.0027 2.93873i 0.531218 0.141883i
\(430\) 0 0
\(431\) −3.50754 −0.168952 −0.0844762 0.996425i \(-0.526922\pi\)
−0.0844762 + 0.996425i \(0.526922\pi\)
\(432\) 0 0
\(433\) −6.80047 −0.326810 −0.163405 0.986559i \(-0.552248\pi\)
−0.163405 + 0.986559i \(0.552248\pi\)
\(434\) 0 0
\(435\) 0.747871 2.78217i 0.0358577 0.133395i
\(436\) 0 0
\(437\) −3.96660 4.72721i −0.189748 0.226133i
\(438\) 0 0
\(439\) −9.11906 25.0544i −0.435229 1.19578i −0.942562 0.334032i \(-0.891591\pi\)
0.507333 0.861750i \(-0.330632\pi\)
\(440\) 0 0
\(441\) 13.4496 + 16.0809i 0.640459 + 0.765759i
\(442\) 0 0
\(443\) −10.2936 8.63732i −0.489062 0.410371i 0.364628 0.931153i \(-0.381196\pi\)
−0.853690 + 0.520782i \(0.825641\pi\)
\(444\) 0 0
\(445\) −1.53662 8.71463i −0.0728430 0.413113i
\(446\) 0 0
\(447\) −25.1060 17.6094i −1.18747 0.832896i
\(448\) 0 0
\(449\) 15.8947 9.17681i 0.750117 0.433081i −0.0756189 0.997137i \(-0.524093\pi\)
0.825736 + 0.564056i \(0.190760\pi\)
\(450\) 0 0
\(451\) 0.0393483 + 0.0227178i 0.00185284 + 0.00106974i
\(452\) 0 0
\(453\) −10.6666 + 0.924592i −0.501161 + 0.0434411i
\(454\) 0 0
\(455\) 0.668723 + 0.243395i 0.0313502 + 0.0114106i
\(456\) 0 0
\(457\) 0.210261 1.19245i 0.00983562 0.0557806i −0.979495 0.201469i \(-0.935429\pi\)
0.989331 + 0.145688i \(0.0465396\pi\)
\(458\) 0 0
\(459\) 5.51002 20.3676i 0.257186 0.950680i
\(460\) 0 0
\(461\) 3.12039 + 0.550208i 0.145331 + 0.0256257i 0.245840 0.969310i \(-0.420936\pi\)
−0.100509 + 0.994936i \(0.532047\pi\)
\(462\) 0 0
\(463\) −6.53132 + 17.9447i −0.303536 + 0.833959i 0.690342 + 0.723483i \(0.257460\pi\)
−0.993879 + 0.110476i \(0.964762\pi\)
\(464\) 0 0
\(465\) −1.52329 0.711808i −0.0706408 0.0330093i
\(466\) 0 0
\(467\) 6.32468 10.9547i 0.292672 0.506922i −0.681769 0.731567i \(-0.738789\pi\)
0.974441 + 0.224646i \(0.0721224\pi\)
\(468\) 0 0
\(469\) 0.756035 + 1.30949i 0.0349104 + 0.0604667i
\(470\) 0 0
\(471\) −30.4383 2.68759i −1.40252 0.123838i
\(472\) 0 0
\(473\) −19.2869 + 3.40080i −0.886814 + 0.156369i
\(474\) 0 0
\(475\) −1.11787 + 1.33223i −0.0512916 + 0.0611269i
\(476\) 0 0
\(477\) 35.1161 + 0.0562948i 1.60785 + 0.00257756i
\(478\) 0 0
\(479\) 31.0456 11.2997i 1.41851 0.516296i 0.484896 0.874572i \(-0.338858\pi\)
0.933616 + 0.358276i \(0.116635\pi\)
\(480\) 0 0
\(481\) −26.6001 + 22.3202i −1.21286 + 1.01771i
\(482\) 0 0
\(483\) −0.848137 + 0.846779i −0.0385916 + 0.0385298i
\(484\) 0 0
\(485\) 24.8956i 1.13045i
\(486\) 0 0
\(487\) 39.0120i 1.76780i 0.467673 + 0.883901i \(0.345092\pi\)
−0.467673 + 0.883901i \(0.654908\pi\)
\(488\) 0 0
\(489\) −0.690996 + 0.689889i −0.0312479 + 0.0311979i
\(490\) 0 0
\(491\) 4.73374 3.97208i 0.213631 0.179257i −0.529693 0.848190i \(-0.677693\pi\)
0.743323 + 0.668932i \(0.233248\pi\)
\(492\) 0 0
\(493\) 3.53693 1.28734i 0.159295 0.0579787i
\(494\) 0 0
\(495\) −9.77794 0.0156751i −0.439486 0.000704542i
\(496\) 0 0
\(497\) 0.0916783 0.109258i 0.00411234 0.00490089i
\(498\) 0 0
\(499\) −29.7454 + 5.24491i −1.33159 + 0.234794i −0.793744 0.608252i \(-0.791871\pi\)
−0.537841 + 0.843046i \(0.680760\pi\)
\(500\) 0 0
\(501\) −29.3711 2.59336i −1.31220 0.115863i
\(502\) 0 0
\(503\) 5.66137 + 9.80578i 0.252428 + 0.437218i 0.964194 0.265199i \(-0.0854376\pi\)
−0.711766 + 0.702417i \(0.752104\pi\)
\(504\) 0 0
\(505\) 12.2843 21.2771i 0.546646 0.946818i
\(506\) 0 0
\(507\) 0.163477 + 0.0763903i 0.00726028 + 0.00339261i
\(508\) 0 0
\(509\) 6.79275 18.6629i 0.301083 0.827219i −0.693229 0.720717i \(-0.743813\pi\)
0.994312 0.106502i \(-0.0339651\pi\)
\(510\) 0 0
\(511\) 0.722334 + 0.127367i 0.0319542 + 0.00563439i
\(512\) 0 0
\(513\) −4.90693 + 1.30217i −0.216646 + 0.0574922i
\(514\) 0 0
\(515\) −1.00647 + 5.70800i −0.0443506 + 0.251524i
\(516\) 0 0
\(517\) 13.7030 + 4.98748i 0.602657 + 0.219349i
\(518\) 0 0
\(519\) 31.8909 2.76434i 1.39986 0.121341i
\(520\) 0 0
\(521\) −5.13805 2.96646i −0.225102 0.129963i 0.383208 0.923662i \(-0.374819\pi\)
−0.608311 + 0.793699i \(0.708152\pi\)
\(522\) 0 0
\(523\) 17.2055 9.93358i 0.752343 0.434365i −0.0741971 0.997244i \(-0.523639\pi\)
0.826540 + 0.562878i \(0.190306\pi\)
\(524\) 0 0
\(525\) 0.276521 + 0.193953i 0.0120684 + 0.00846479i
\(526\) 0 0
\(527\) −0.381458 2.16335i −0.0166166 0.0942372i
\(528\) 0 0
\(529\) 12.9403 + 10.8582i 0.562622 + 0.472096i
\(530\) 0 0
\(531\) 4.97552 + 5.94893i 0.215919 + 0.258162i
\(532\) 0 0
\(533\) 0.0309709 + 0.0850918i 0.00134150 + 0.00368574i
\(534\) 0 0
\(535\) −0.332890 0.396723i −0.0143921 0.0171518i
\(536\) 0 0
\(537\) −6.73222 + 25.0447i −0.290517 + 1.08076i
\(538\) 0 0
\(539\) 12.6926 0.546710
\(540\) 0 0
\(541\) −1.88488 −0.0810372 −0.0405186 0.999179i \(-0.512901\pi\)
−0.0405186 + 0.999179i \(0.512901\pi\)
\(542\) 0 0
\(543\) 32.3652 8.64444i 1.38892 0.370968i
\(544\) 0 0
\(545\) −3.56129 4.24418i −0.152549 0.181801i
\(546\) 0 0
\(547\) 7.60406 + 20.8920i 0.325126 + 0.893277i 0.989326 + 0.145722i \(0.0465504\pi\)
−0.664199 + 0.747556i \(0.731227\pi\)
\(548\) 0 0
\(549\) −6.31435 17.4354i −0.269490 0.744127i
\(550\) 0 0
\(551\) −0.693752 0.582127i −0.0295548 0.0247995i
\(552\) 0 0
\(553\) 0.168345 + 0.954733i 0.00715876 + 0.0405994i
\(554\) 0 0
\(555\) 27.0303 12.5781i 1.14737 0.533910i
\(556\) 0 0
\(557\) −29.9947 + 17.3175i −1.27092 + 0.733764i −0.975160 0.221499i \(-0.928905\pi\)
−0.295756 + 0.955264i \(0.595572\pi\)
\(558\) 0 0
\(559\) −33.8025 19.5159i −1.42969 0.825433i
\(560\) 0 0
\(561\) −7.31895 10.4704i −0.309006 0.442061i
\(562\) 0 0
\(563\) 18.6994 + 6.80604i 0.788087 + 0.286840i 0.704541 0.709664i \(-0.251153\pi\)
0.0835464 + 0.996504i \(0.473375\pi\)
\(564\) 0 0
\(565\) −3.61641 + 20.5097i −0.152144 + 0.862850i
\(566\) 0 0
\(567\) 0.334254 + 0.927599i 0.0140374 + 0.0389555i
\(568\) 0 0
\(569\) 38.9668 + 6.87090i 1.63357 + 0.288043i 0.913799 0.406166i \(-0.133134\pi\)
0.719774 + 0.694209i \(0.244246\pi\)
\(570\) 0 0
\(571\) −7.36266 + 20.2288i −0.308118 + 0.846547i 0.684906 + 0.728632i \(0.259843\pi\)
−0.993024 + 0.117915i \(0.962379\pi\)
\(572\) 0 0
\(573\) 20.0016 13.9814i 0.835577 0.584080i
\(574\) 0 0
\(575\) 5.62127 9.73633i 0.234423 0.406033i
\(576\) 0 0
\(577\) 15.4075 + 26.6866i 0.641424 + 1.11098i 0.985115 + 0.171896i \(0.0549892\pi\)
−0.343692 + 0.939083i \(0.611677\pi\)
\(578\) 0 0
\(579\) −1.79984 3.86786i −0.0747988 0.160743i
\(580\) 0 0
\(581\) 1.87726 0.331012i 0.0778820 0.0137327i
\(582\) 0 0
\(583\) 13.6663 16.2869i 0.566001 0.674534i
\(584\) 0 0
\(585\) −14.9081 12.5502i −0.616375 0.518886i
\(586\) 0 0
\(587\) 35.5365 12.9342i 1.46675 0.533853i 0.519533 0.854451i \(-0.326106\pi\)
0.947215 + 0.320598i \(0.103884\pi\)
\(588\) 0 0
\(589\) −0.404893 + 0.339745i −0.0166833 + 0.0139990i
\(590\) 0 0
\(591\) −4.09576 15.3347i −0.168477 0.630787i
\(592\) 0 0
\(593\) 46.2503i 1.89927i 0.313355 + 0.949636i \(0.398547\pi\)
−0.313355 + 0.949636i \(0.601453\pi\)
\(594\) 0 0
\(595\) 0.798274i 0.0327260i
\(596\) 0 0
\(597\) −15.1231 4.06521i −0.618946 0.166378i
\(598\) 0 0
\(599\) −1.69945 + 1.42601i −0.0694377 + 0.0582651i −0.676846 0.736125i \(-0.736654\pi\)
0.607408 + 0.794390i \(0.292209\pi\)
\(600\) 0 0
\(601\) 31.3863 11.4237i 1.28027 0.465981i 0.389750 0.920921i \(-0.372561\pi\)
0.890522 + 0.454940i \(0.150339\pi\)
\(602\) 0 0
\(603\) −7.12473 40.7886i −0.290141 1.66104i
\(604\) 0 0
\(605\) 8.88252 10.5858i 0.361126 0.430373i
\(606\) 0 0
\(607\) 24.0862 4.24704i 0.977628 0.172382i 0.338067 0.941122i \(-0.390227\pi\)
0.639561 + 0.768740i \(0.279116\pi\)
\(608\) 0 0
\(609\) −0.101000 + 0.143997i −0.00409272 + 0.00583505i
\(610\) 0 0
\(611\) 14.5313 + 25.1690i 0.587875 + 1.01823i
\(612\) 0 0
\(613\) −1.57336 + 2.72514i −0.0635474 + 0.110067i −0.896049 0.443956i \(-0.853575\pi\)
0.832501 + 0.554023i \(0.186908\pi\)
\(614\) 0 0
\(615\) −0.00671405 0.0774569i −0.000270737 0.00312337i
\(616\) 0 0
\(617\) 9.26016 25.4421i 0.372800 1.02426i −0.601474 0.798893i \(-0.705420\pi\)
0.974274 0.225367i \(-0.0723582\pi\)
\(618\) 0 0
\(619\) −24.1567 4.25949i −0.970942 0.171203i −0.334388 0.942436i \(-0.608530\pi\)
−0.636554 + 0.771232i \(0.719641\pi\)
\(620\) 0 0
\(621\) 29.7775 13.7984i 1.19493 0.553710i
\(622\) 0 0
\(623\) −0.0938139 + 0.532045i −0.00375858 + 0.0213159i
\(624\) 0 0
\(625\) 12.1517 + 4.42287i 0.486070 + 0.176915i
\(626\) 0 0
\(627\) −1.30125 + 2.78470i −0.0519667 + 0.111210i
\(628\) 0 0
\(629\) 33.7327 + 19.4756i 1.34501 + 0.776544i
\(630\) 0 0
\(631\) −39.8629 + 23.0148i −1.58692 + 0.916206i −0.593105 + 0.805125i \(0.702098\pi\)
−0.993811 + 0.111081i \(0.964569\pi\)
\(632\) 0 0
\(633\) −2.59744 + 29.4173i −0.103239 + 1.16923i
\(634\) 0 0
\(635\) 2.43414 + 13.8047i 0.0965961 + 0.547823i
\(636\) 0 0
\(637\) 19.3781 + 16.2602i 0.767789 + 0.644252i
\(638\) 0 0
\(639\) −3.38551 + 1.94740i −0.133929 + 0.0770379i
\(640\) 0 0
\(641\) −10.3755 28.5064i −0.409807 1.12593i −0.957293 0.289120i \(-0.906637\pi\)
0.547486 0.836815i \(-0.315585\pi\)
\(642\) 0 0
\(643\) −15.9458 19.0034i −0.628840 0.749422i 0.353723 0.935350i \(-0.384915\pi\)
−0.982563 + 0.185928i \(0.940471\pi\)
\(644\) 0 0
\(645\) 23.6776 + 23.7156i 0.932306 + 0.933801i
\(646\) 0 0
\(647\) 39.5989 1.55679 0.778397 0.627772i \(-0.216033\pi\)
0.778397 + 0.627772i \(0.216033\pi\)
\(648\) 0 0
\(649\) 4.69547 0.184313
\(650\) 0 0
\(651\) 0.0725279 + 0.0726443i 0.00284259 + 0.00284715i
\(652\) 0 0
\(653\) −16.5273 19.6964i −0.646762 0.770781i 0.338660 0.940909i \(-0.390026\pi\)
−0.985422 + 0.170128i \(0.945582\pi\)
\(654\) 0 0
\(655\) 2.07090 + 5.68976i 0.0809168 + 0.222317i
\(656\) 0 0
\(657\) −17.3783 10.0706i −0.677994 0.392890i
\(658\) 0 0
\(659\) −38.2134 32.0648i −1.48858 1.24907i −0.896385 0.443276i \(-0.853816\pi\)
−0.592198 0.805793i \(-0.701739\pi\)
\(660\) 0 0
\(661\) 4.10673 + 23.2904i 0.159733 + 0.905893i 0.954330 + 0.298755i \(0.0965714\pi\)
−0.794596 + 0.607138i \(0.792317\pi\)
\(662\) 0 0
\(663\) 2.23933 25.3615i 0.0869684 0.984960i
\(664\) 0 0
\(665\) −0.166338 + 0.0960355i −0.00645032 + 0.00372410i
\(666\) 0 0
\(667\) 5.07014 + 2.92725i 0.196317 + 0.113343i
\(668\) 0 0
\(669\) −5.26289 + 11.2627i −0.203475 + 0.435443i
\(670\) 0 0
\(671\) −10.5501 3.83993i −0.407283 0.148239i
\(672\) 0 0
\(673\) −7.07247 + 40.1100i −0.272624 + 1.54613i 0.473787 + 0.880640i \(0.342887\pi\)
−0.746410 + 0.665486i \(0.768224\pi\)
\(674\) 0 0
\(675\) −5.28686 7.58919i −0.203491 0.292108i
\(676\) 0 0
\(677\) 27.5622 + 4.85995i 1.05930 + 0.186783i 0.676046 0.736860i \(-0.263692\pi\)
0.383254 + 0.923643i \(0.374803\pi\)
\(678\) 0 0
\(679\) −0.519845 + 1.42826i −0.0199498 + 0.0548117i
\(680\) 0 0
\(681\) 3.94598 + 45.5230i 0.151210 + 1.74444i
\(682\) 0 0
\(683\) −0.0671037 + 0.116227i −0.00256765 + 0.00444730i −0.867306 0.497775i \(-0.834151\pi\)
0.864739 + 0.502222i \(0.167484\pi\)
\(684\) 0 0
\(685\) −16.1884 28.0391i −0.618527 1.07132i
\(686\) 0 0
\(687\) 1.68745 2.40583i 0.0643803 0.0917880i
\(688\) 0 0
\(689\) 41.7294 7.35801i 1.58976 0.280318i
\(690\) 0 0
\(691\) −4.64904 + 5.54051i −0.176858 + 0.210771i −0.847190 0.531291i \(-0.821707\pi\)
0.670332 + 0.742061i \(0.266152\pi\)
\(692\) 0 0
\(693\) 0.560634 + 0.205072i 0.0212967 + 0.00779006i
\(694\) 0 0
\(695\) 28.8311 10.4937i 1.09363 0.398047i
\(696\) 0 0
\(697\) 0.0778121 0.0652921i 0.00294734 0.00247311i
\(698\) 0 0
\(699\) 7.44562 + 2.00144i 0.281619 + 0.0757016i
\(700\) 0 0
\(701\) 15.7113i 0.593407i 0.954970 + 0.296703i \(0.0958872\pi\)
−0.954970 + 0.296703i \(0.904113\pi\)
\(702\) 0 0
\(703\) 9.37197i 0.353471i
\(704\) 0 0
\(705\) −6.43894 24.1077i −0.242505 0.907950i
\(706\) 0 0
\(707\) −1.14904 + 0.964159i −0.0432141 + 0.0362609i
\(708\) 0 0
\(709\) 3.37957 1.23006i 0.126922 0.0461960i −0.277778 0.960645i \(-0.589598\pi\)
0.404701 + 0.914449i \(0.367376\pi\)
\(710\) 0 0
\(711\) 4.65183 26.1368i 0.174457 0.980206i
\(712\) 0 0
\(713\) 2.19630 2.61745i 0.0822523 0.0980244i
\(714\) 0 0
\(715\) −11.6194 + 2.04881i −0.434540 + 0.0766212i
\(716\) 0 0
\(717\) 18.4531 + 39.6557i 0.689143 + 1.48097i
\(718\) 0 0
\(719\) 21.2087 + 36.7345i 0.790950 + 1.36997i 0.925379 + 0.379042i \(0.123747\pi\)
−0.134429 + 0.990923i \(0.542920\pi\)
\(720\) 0 0
\(721\) 0.176930 0.306452i 0.00658923 0.0114129i
\(722\) 0 0
\(723\) −5.44198 + 3.80402i −0.202389 + 0.141473i
\(724\) 0 0
\(725\) 0.564307 1.55042i 0.0209579 0.0575812i
\(726\) 0 0
\(727\) −7.03446 1.24037i −0.260894 0.0460026i 0.0416711 0.999131i \(-0.486732\pi\)
−0.302565 + 0.953129i \(0.597843\pi\)
\(728\) 0 0
\(729\) 0.129851 26.9997i 0.00480930 0.999988i
\(730\) 0 0
\(731\) −7.60290 + 43.1182i −0.281203 + 1.59478i
\(732\) 0 0
\(733\) −25.3224 9.21661i −0.935305 0.340423i −0.170995 0.985272i \(-0.554698\pi\)
−0.764310 + 0.644849i \(0.776920\pi\)
\(734\) 0 0
\(735\) −12.4433 17.8012i −0.458978 0.656608i
\(736\) 0 0
\(737\) −21.7107 12.5347i −0.799723 0.461720i
\(738\) 0 0
\(739\) −8.02620 + 4.63393i −0.295249 + 0.170462i −0.640306 0.768120i \(-0.721193\pi\)
0.345058 + 0.938581i \(0.387859\pi\)
\(740\) 0 0
\(741\) −5.55404 + 2.58448i −0.204033 + 0.0949431i
\(742\) 0 0
\(743\) −2.56527 14.5484i −0.0941106 0.533728i −0.995016 0.0997127i \(-0.968208\pi\)
0.900906 0.434015i \(-0.142903\pi\)
\(744\) 0 0
\(745\) 24.3376 + 20.4217i 0.891661 + 0.748192i
\(746\) 0 0
\(747\) −51.3920 9.14676i −1.88033 0.334663i
\(748\) 0 0
\(749\) 0.0108140 + 0.0297111i 0.000395134 + 0.00108562i
\(750\) 0 0
\(751\) 22.7883 + 27.1580i 0.831556 + 0.991010i 0.999986 + 0.00529624i \(0.00168585\pi\)
−0.168430 + 0.985714i \(0.553870\pi\)
\(752\) 0 0
\(753\) −31.2626 + 8.34993i −1.13927 + 0.304288i
\(754\) 0 0
\(755\) 11.0922 0.403688
\(756\) 0 0
\(757\) 12.9971 0.472387 0.236194 0.971706i \(-0.424100\pi\)
0.236194 + 0.971706i \(0.424100\pi\)
\(758\) 0 0
\(759\) 5.15819 19.1891i 0.187231 0.696520i
\(760\) 0 0
\(761\) −9.68871 11.5466i −0.351215 0.418562i 0.561295 0.827616i \(-0.310303\pi\)
−0.912510 + 0.409054i \(0.865859\pi\)
\(762\) 0 0
\(763\) 0.115689 + 0.317852i 0.00418821 + 0.0115070i
\(764\) 0 0
\(765\) −7.50940 + 20.5294i −0.271503 + 0.742243i
\(766\) 0 0
\(767\) 7.16869 + 6.01524i 0.258846 + 0.217198i
\(768\) 0 0
\(769\) 3.04896 + 17.2915i 0.109948 + 0.623547i 0.989128 + 0.147057i \(0.0469801\pi\)
−0.879180 + 0.476490i \(0.841909\pi\)
\(770\) 0 0
\(771\) 1.92699 + 1.35160i 0.0693989 + 0.0486766i
\(772\) 0 0
\(773\) −28.6124 + 16.5194i −1.02912 + 0.594161i −0.916732 0.399503i \(-0.869183\pi\)
−0.112386 + 0.993665i \(0.535849\pi\)
\(774\) 0 0
\(775\) −0.833931 0.481471i −0.0299557 0.0172949i
\(776\) 0 0
\(777\) −1.81338 + 0.157185i −0.0650545 + 0.00563899i
\(778\) 0 0
\(779\) −0.0229662 0.00835901i −0.000822849 0.000299493i
\(780\) 0 0
\(781\) −0.410620 + 2.32874i −0.0146931 + 0.0833290i
\(782\) 0 0
\(783\) 3.95203 2.75310i 0.141234 0.0983879i
\(784\) 0 0
\(785\) 31.1764 + 5.49724i 1.11273 + 0.196205i
\(786\) 0 0
\(787\) −17.2840 + 47.4873i −0.616107 + 1.69274i 0.100211 + 0.994966i \(0.468048\pi\)
−0.716318 + 0.697774i \(0.754174\pi\)
\(788\) 0 0
\(789\) −38.1271 17.8162i −1.35736 0.634273i
\(790\) 0 0
\(791\) 0.635737 1.10113i 0.0226042 0.0391516i
\(792\) 0 0
\(793\) −11.1879 19.3780i −0.397294 0.688133i
\(794\) 0