Properties

Label 804.2.y.b.121.5
Level 804
Weight 2
Character 804.121
Analytic conductor 6.420
Analytic rank 0
Dimension 120
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(6\) over \(\Q(\zeta_{33})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 121.5
Character \(\chi\) = 804.121
Dual form 804.2.y.b.505.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.654861 - 0.755750i) q^{3} +(2.24994 - 1.44595i) q^{5} +(2.21379 + 0.886268i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\) \(q+(0.654861 - 0.755750i) q^{3} +(2.24994 - 1.44595i) q^{5} +(2.21379 + 0.886268i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(0.240925 + 5.05764i) q^{11} +(3.25247 - 0.310573i) q^{13} +(0.380622 - 2.64728i) q^{15} +(0.620152 + 2.55630i) q^{17} +(-0.689895 + 0.276192i) q^{19} +(2.11952 - 1.09269i) q^{21} +(0.936879 + 0.180569i) q^{23} +(0.894377 - 1.95841i) q^{25} +(-0.841254 - 0.540641i) q^{27} +(0.974121 - 1.68723i) q^{29} +(-7.90618 - 0.754949i) q^{31} +(3.98008 + 3.12997i) q^{33} +(6.26239 - 1.20698i) q^{35} +(-3.51395 - 6.08634i) q^{37} +(1.89520 - 2.66143i) q^{39} +(-1.77758 + 1.69491i) q^{41} +(2.03516 + 0.597576i) q^{43} +(-1.75143 - 2.02126i) q^{45} +(-4.00788 - 11.5800i) q^{47} +(-0.950738 - 0.906526i) q^{49} +(2.33804 + 1.20534i) q^{51} +(-4.25911 + 1.25059i) q^{53} +(7.85514 + 11.0310i) q^{55} +(-0.243053 + 0.702255i) q^{57} +(5.12694 + 11.2264i) q^{59} +(0.457763 - 9.60964i) q^{61} +(0.562192 - 2.31739i) q^{63} +(6.86877 - 5.40166i) q^{65} +(2.69049 - 7.73054i) q^{67} +(0.749990 - 0.589798i) q^{69} +(-2.64422 + 10.8996i) q^{71} +(0.635094 - 13.3323i) q^{73} +(-0.894377 - 1.95841i) q^{75} +(-3.94907 + 11.4101i) q^{77} +(3.59430 + 5.04749i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-1.66036 - 0.855976i) q^{83} +(5.09158 + 4.85481i) q^{85} +(-0.637207 - 1.84109i) q^{87} +(2.92096 + 3.37097i) q^{89} +(7.47553 + 2.19501i) q^{91} +(-5.74800 + 5.48071i) q^{93} +(-1.15286 + 1.61897i) q^{95} +(0.507256 + 0.878592i) q^{97} +(4.97187 - 0.958250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + O(q^{10}) \) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + 11q^{11} + 2q^{13} - 9q^{15} + 48q^{17} - 4q^{19} - q^{21} + 22q^{23} - 42q^{25} + 12q^{27} - q^{29} + 27q^{31} + 17q^{35} - 8q^{37} - 2q^{39} - 58q^{41} - 17q^{43} - 2q^{45} - 84q^{47} + 101q^{49} - 26q^{51} + 28q^{53} - 9q^{55} + 26q^{57} + 34q^{59} + 16q^{61} + 12q^{63} + 144q^{65} + 23q^{67} + 11q^{69} + 173q^{71} - 2q^{73} + 42q^{75} + 128q^{77} + 31q^{79} - 12q^{81} + 47q^{83} - 75q^{85} - 10q^{87} - 67q^{89} + 16q^{91} + 6q^{93} - 79q^{95} + 10q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{26}{33}\right)\) \(1\)

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 0
\(3\) 0.654861 0.755750i 0.378084 0.436332i
\(4\) 0 0
\(5\) 2.24994 1.44595i 1.00620 0.646647i 0.0697946 0.997561i \(-0.477766\pi\)
0.936407 + 0.350915i \(0.114129\pi\)
\(6\) 0 0
\(7\) 2.21379 + 0.886268i 0.836734 + 0.334978i 0.750151 0.661267i \(-0.229981\pi\)
0.0865836 + 0.996245i \(0.472405\pi\)
\(8\) 0 0
\(9\) −0.142315 0.989821i −0.0474383 0.329940i
\(10\) 0 0
\(11\) 0.240925 + 5.05764i 0.0726417 + 1.52494i 0.681595 + 0.731730i \(0.261287\pi\)
−0.608953 + 0.793206i \(0.708410\pi\)
\(12\) 0 0
\(13\) 3.25247 0.310573i 0.902072 0.0861374i 0.366297 0.930498i \(-0.380626\pi\)
0.535775 + 0.844361i \(0.320019\pi\)
\(14\) 0 0
\(15\) 0.380622 2.64728i 0.0982761 0.683525i
\(16\) 0 0
\(17\) 0.620152 + 2.55630i 0.150409 + 0.619995i 0.996247 + 0.0865547i \(0.0275857\pi\)
−0.845838 + 0.533440i \(0.820899\pi\)
\(18\) 0 0
\(19\) −0.689895 + 0.276192i −0.158273 + 0.0633628i −0.449446 0.893307i \(-0.648379\pi\)
0.291173 + 0.956670i \(0.405954\pi\)
\(20\) 0 0
\(21\) 2.11952 1.09269i 0.462518 0.238444i
\(22\) 0 0
\(23\) 0.936879 + 0.180569i 0.195353 + 0.0376511i 0.285989 0.958233i \(-0.407678\pi\)
−0.0906362 + 0.995884i \(0.528890\pi\)
\(24\) 0 0
\(25\) 0.894377 1.95841i 0.178875 0.391683i
\(26\) 0 0
\(27\) −0.841254 0.540641i −0.161899 0.104046i
\(28\) 0 0
\(29\) 0.974121 1.68723i 0.180890 0.313310i −0.761294 0.648407i \(-0.775436\pi\)
0.942184 + 0.335097i \(0.108769\pi\)
\(30\) 0 0
\(31\) −7.90618 0.754949i −1.41999 0.135593i −0.643368 0.765557i \(-0.722464\pi\)
−0.776624 + 0.629964i \(0.783070\pi\)
\(32\) 0 0
\(33\) 3.98008 + 3.12997i 0.692843 + 0.544858i
\(34\) 0 0
\(35\) 6.26239 1.20698i 1.05854 0.204016i
\(36\) 0 0
\(37\) −3.51395 6.08634i −0.577689 1.00059i −0.995744 0.0921655i \(-0.970621\pi\)
0.418054 0.908422i \(-0.362712\pi\)
\(38\) 0 0
\(39\) 1.89520 2.66143i 0.303474 0.426170i
\(40\) 0 0
\(41\) −1.77758 + 1.69491i −0.277611 + 0.264701i −0.816074 0.577948i \(-0.803854\pi\)
0.538463 + 0.842649i \(0.319005\pi\)
\(42\) 0 0
\(43\) 2.03516 + 0.597576i 0.310358 + 0.0911295i 0.433203 0.901296i \(-0.357383\pi\)
−0.122844 + 0.992426i \(0.539202\pi\)
\(44\) 0 0
\(45\) −1.75143 2.02126i −0.261087 0.301311i
\(46\) 0 0
\(47\) −4.00788 11.5800i −0.584610 1.68912i −0.716269 0.697824i \(-0.754152\pi\)
0.131659 0.991295i \(-0.457969\pi\)
\(48\) 0 0
\(49\) −0.950738 0.906526i −0.135820 0.129504i
\(50\) 0 0
\(51\) 2.33804 + 1.20534i 0.327391 + 0.168782i
\(52\) 0 0
\(53\) −4.25911 + 1.25059i −0.585034 + 0.171781i −0.560838 0.827926i \(-0.689521\pi\)
−0.0241963 + 0.999707i \(0.507703\pi\)
\(54\) 0 0
\(55\) 7.85514 + 11.0310i 1.05919 + 1.48742i
\(56\) 0 0
\(57\) −0.243053 + 0.702255i −0.0321931 + 0.0930160i
\(58\) 0 0
\(59\) 5.12694 + 11.2264i 0.667471 + 1.46156i 0.875393 + 0.483412i \(0.160603\pi\)
−0.207922 + 0.978145i \(0.566670\pi\)
\(60\) 0 0
\(61\) 0.457763 9.60964i 0.0586106 1.23039i −0.757633 0.652680i \(-0.773644\pi\)
0.816244 0.577707i \(-0.196053\pi\)
\(62\) 0 0
\(63\) 0.562192 2.31739i 0.0708295 0.291963i
\(64\) 0 0
\(65\) 6.86877 5.40166i 0.851966 0.669993i
\(66\) 0 0
\(67\) 2.69049 7.73054i 0.328696 0.944436i
\(68\) 0 0
\(69\) 0.749990 0.589798i 0.0902881 0.0710034i
\(70\) 0 0
\(71\) −2.64422 + 10.8996i −0.313811 + 1.29355i 0.568423 + 0.822736i \(0.307554\pi\)
−0.882234 + 0.470810i \(0.843962\pi\)
\(72\) 0 0
\(73\) 0.635094 13.3323i 0.0743321 1.56042i −0.586538 0.809922i \(-0.699509\pi\)
0.660870 0.750501i \(-0.270188\pi\)
\(74\) 0 0
\(75\) −0.894377 1.95841i −0.103274 0.226138i
\(76\) 0 0
\(77\) −3.94907 + 11.4101i −0.450038 + 1.30030i
\(78\) 0 0
\(79\) 3.59430 + 5.04749i 0.404391 + 0.567887i 0.965681 0.259732i \(-0.0836342\pi\)
−0.561290 + 0.827619i \(0.689695\pi\)
\(80\) 0 0
\(81\) −0.959493 + 0.281733i −0.106610 + 0.0313036i
\(82\) 0 0
\(83\) −1.66036 0.855976i −0.182248 0.0939556i 0.364688 0.931130i \(-0.381176\pi\)
−0.546936 + 0.837174i \(0.684206\pi\)
\(84\) 0 0
\(85\) 5.09158 + 4.85481i 0.552259 + 0.526578i
\(86\) 0 0
\(87\) −0.637207 1.84109i −0.0683158 0.197386i
\(88\) 0 0
\(89\) 2.92096 + 3.37097i 0.309621 + 0.357322i 0.889139 0.457638i \(-0.151304\pi\)
−0.579517 + 0.814960i \(0.696759\pi\)
\(90\) 0 0
\(91\) 7.47553 + 2.19501i 0.783649 + 0.230100i
\(92\) 0 0
\(93\) −5.74800 + 5.48071i −0.596040 + 0.568323i
\(94\) 0 0
\(95\) −1.15286 + 1.61897i −0.118281 + 0.166102i
\(96\) 0 0
\(97\) 0.507256 + 0.878592i 0.0515040 + 0.0892075i 0.890628 0.454733i \(-0.150265\pi\)
−0.839124 + 0.543940i \(0.816932\pi\)
\(98\) 0 0
\(99\) 4.97187 0.958250i 0.499692 0.0963078i
\(100\) 0 0
\(101\) −14.2592 11.2136i −1.41884 1.11579i −0.975642 0.219370i \(-0.929600\pi\)
−0.443203 0.896421i \(-0.646158\pi\)
\(102\) 0 0
\(103\) 13.5261 + 1.29159i 1.33277 + 0.127264i 0.737001 0.675892i \(-0.236241\pi\)
0.595769 + 0.803156i \(0.296847\pi\)
\(104\) 0 0
\(105\) 3.18882 5.52320i 0.311197 0.539009i
\(106\) 0 0
\(107\) −3.63634 2.33693i −0.351538 0.225920i 0.352939 0.935646i \(-0.385182\pi\)
−0.704477 + 0.709726i \(0.748819\pi\)
\(108\) 0 0
\(109\) 2.53865 5.55888i 0.243159 0.532444i −0.748223 0.663447i \(-0.769093\pi\)
0.991382 + 0.131004i \(0.0418199\pi\)
\(110\) 0 0
\(111\) −6.90089 1.33004i −0.655004 0.126242i
\(112\) 0 0
\(113\) −12.6800 + 6.53699i −1.19283 + 0.614948i −0.936168 0.351553i \(-0.885654\pi\)
−0.256664 + 0.966501i \(0.582623\pi\)
\(114\) 0 0
\(115\) 2.36901 0.948408i 0.220911 0.0884395i
\(116\) 0 0
\(117\) −0.770286 3.17516i −0.0712129 0.293544i
\(118\) 0 0
\(119\) −0.892682 + 6.20874i −0.0818321 + 0.569155i
\(120\) 0 0
\(121\) −14.5715 + 1.39141i −1.32468 + 0.126492i
\(122\) 0 0
\(123\) 0.116867 + 2.45333i 0.0105375 + 0.221210i
\(124\) 0 0
\(125\) 1.08364 + 7.53688i 0.0969237 + 0.674119i
\(126\) 0 0
\(127\) −4.40765 1.76456i −0.391116 0.156579i 0.167765 0.985827i \(-0.446345\pi\)
−0.558881 + 0.829248i \(0.688769\pi\)
\(128\) 0 0
\(129\) 1.78436 1.14674i 0.157104 0.100965i
\(130\) 0 0
\(131\) −7.83709 + 9.04448i −0.684729 + 0.790220i −0.986605 0.163127i \(-0.947842\pi\)
0.301876 + 0.953347i \(0.402387\pi\)
\(132\) 0 0
\(133\) −1.77206 −0.153657
\(134\) 0 0
\(135\) −2.67450 −0.230185
\(136\) 0 0
\(137\) 1.69887 1.96060i 0.145144 0.167505i −0.678522 0.734580i \(-0.737379\pi\)
0.823667 + 0.567074i \(0.191925\pi\)
\(138\) 0 0
\(139\) −10.4574 + 6.72053i −0.886981 + 0.570028i −0.902903 0.429845i \(-0.858568\pi\)
0.0159214 + 0.999873i \(0.494932\pi\)
\(140\) 0 0
\(141\) −11.3762 4.55434i −0.958049 0.383545i
\(142\) 0 0
\(143\) 2.35437 + 16.3750i 0.196882 + 1.36934i
\(144\) 0 0
\(145\) −0.247929 5.20468i −0.0205894 0.432225i
\(146\) 0 0
\(147\) −1.30771 + 0.124871i −0.107858 + 0.0102992i
\(148\) 0 0
\(149\) −0.128389 + 0.892962i −0.0105180 + 0.0731543i −0.994404 0.105640i \(-0.966311\pi\)
0.983886 + 0.178795i \(0.0572198\pi\)
\(150\) 0 0
\(151\) −5.73097 23.6234i −0.466380 1.92244i −0.376268 0.926511i \(-0.622793\pi\)
−0.0901118 0.995932i \(-0.528722\pi\)
\(152\) 0 0
\(153\) 2.44203 0.977640i 0.197426 0.0790375i
\(154\) 0 0
\(155\) −18.8800 + 9.73333i −1.51648 + 0.781800i
\(156\) 0 0
\(157\) 15.4862 + 2.98471i 1.23593 + 0.238206i 0.765038 0.643985i \(-0.222720\pi\)
0.470892 + 0.882191i \(0.343932\pi\)
\(158\) 0 0
\(159\) −1.84399 + 4.03778i −0.146238 + 0.320217i
\(160\) 0 0
\(161\) 1.91402 + 1.23007i 0.150846 + 0.0969429i
\(162\) 0 0
\(163\) −6.78331 + 11.7490i −0.531310 + 0.920256i 0.468022 + 0.883717i \(0.344967\pi\)
−0.999332 + 0.0365391i \(0.988367\pi\)
\(164\) 0 0
\(165\) 13.4807 + 1.28725i 1.04947 + 0.100212i
\(166\) 0 0
\(167\) 8.50664 + 6.68969i 0.658263 + 0.517664i 0.890493 0.454997i \(-0.150360\pi\)
−0.232230 + 0.972661i \(0.574602\pi\)
\(168\) 0 0
\(169\) −2.28299 + 0.440011i −0.175615 + 0.0338470i
\(170\) 0 0
\(171\) 0.371563 + 0.643566i 0.0284141 + 0.0492147i
\(172\) 0 0
\(173\) −3.88923 + 5.46166i −0.295693 + 0.415242i −0.935519 0.353278i \(-0.885067\pi\)
0.639826 + 0.768520i \(0.279006\pi\)
\(174\) 0 0
\(175\) 3.71564 3.54286i 0.280876 0.267815i
\(176\) 0 0
\(177\) 11.8418 + 3.47707i 0.890085 + 0.261352i
\(178\) 0 0
\(179\) 5.96575 + 6.88484i 0.445901 + 0.514597i 0.933552 0.358441i \(-0.116692\pi\)
−0.487651 + 0.873039i \(0.662146\pi\)
\(180\) 0 0
\(181\) 2.20978 + 6.38473i 0.164251 + 0.474573i 0.996851 0.0793027i \(-0.0252694\pi\)
−0.832599 + 0.553876i \(0.813148\pi\)
\(182\) 0 0
\(183\) −6.96271 6.63893i −0.514698 0.490764i
\(184\) 0 0
\(185\) −16.7067 8.61289i −1.22830 0.633232i
\(186\) 0 0
\(187\) −12.7795 + 3.75239i −0.934526 + 0.274402i
\(188\) 0 0
\(189\) −1.38321 1.94244i −0.100614 0.141292i
\(190\) 0 0
\(191\) 4.50342 13.0118i 0.325856 0.941498i −0.656475 0.754347i \(-0.727953\pi\)
0.982331 0.187151i \(-0.0599253\pi\)
\(192\) 0 0
\(193\) −6.42870 14.0769i −0.462748 1.01328i −0.986853 0.161623i \(-0.948327\pi\)
0.524105 0.851654i \(-0.324400\pi\)
\(194\) 0 0
\(195\) 0.415785 8.72840i 0.0297750 0.625054i
\(196\) 0 0
\(197\) 2.23568 9.21560i 0.159286 0.656584i −0.835039 0.550191i \(-0.814555\pi\)
0.994324 0.106393i \(-0.0339301\pi\)
\(198\) 0 0
\(199\) −16.7167 + 13.1461i −1.18501 + 0.931904i −0.998719 0.0505904i \(-0.983890\pi\)
−0.186293 + 0.982494i \(0.559647\pi\)
\(200\) 0 0
\(201\) −4.08045 7.09577i −0.287813 0.500497i
\(202\) 0 0
\(203\) 3.65184 2.87184i 0.256309 0.201563i
\(204\) 0 0
\(205\) −1.54868 + 6.38373i −0.108164 + 0.445859i
\(206\) 0 0
\(207\) 0.0453989 0.953040i 0.00315544 0.0662409i
\(208\) 0 0
\(209\) −1.56309 3.42270i −0.108121 0.236753i
\(210\) 0 0
\(211\) 1.98318 5.73002i 0.136528 0.394471i −0.855925 0.517100i \(-0.827011\pi\)
0.992453 + 0.122629i \(0.0391327\pi\)
\(212\) 0 0
\(213\) 6.50579 + 9.13610i 0.445769 + 0.625995i
\(214\) 0 0
\(215\) 5.44303 1.59822i 0.371212 0.108998i
\(216\) 0 0
\(217\) −16.8336 8.67830i −1.14274 0.589121i
\(218\) 0 0
\(219\) −9.65995 9.21074i −0.652759 0.622404i
\(220\) 0 0
\(221\) 2.81094 + 8.12169i 0.189084 + 0.546324i
\(222\) 0 0
\(223\) 9.53681 + 11.0061i 0.638632 + 0.737020i 0.979132 0.203224i \(-0.0651419\pi\)
−0.340500 + 0.940244i \(0.610596\pi\)
\(224\) 0 0
\(225\) −2.06576 0.606563i −0.137718 0.0404375i
\(226\) 0 0
\(227\) −14.7519 + 14.0659i −0.979120 + 0.933589i −0.997804 0.0662360i \(-0.978901\pi\)
0.0186835 + 0.999825i \(0.494052\pi\)
\(228\) 0 0
\(229\) −5.04518 + 7.08497i −0.333395 + 0.468188i −0.946912 0.321494i \(-0.895815\pi\)
0.613516 + 0.789682i \(0.289754\pi\)
\(230\) 0 0
\(231\) 6.03708 + 10.4565i 0.397210 + 0.687989i
\(232\) 0 0
\(233\) 11.3034 2.17855i 0.740508 0.142721i 0.194972 0.980809i \(-0.437538\pi\)
0.545536 + 0.838087i \(0.316326\pi\)
\(234\) 0 0
\(235\) −25.7616 20.2591i −1.68050 1.32156i
\(236\) 0 0
\(237\) 6.16841 + 0.589011i 0.400681 + 0.0382604i
\(238\) 0 0
\(239\) 3.30688 5.72769i 0.213904 0.370493i −0.739029 0.673674i \(-0.764715\pi\)
0.952933 + 0.303181i \(0.0980486\pi\)
\(240\) 0 0
\(241\) 10.9208 + 7.01838i 0.703472 + 0.452094i 0.842852 0.538145i \(-0.180875\pi\)
−0.139381 + 0.990239i \(0.544511\pi\)
\(242\) 0 0
\(243\) −0.415415 + 0.909632i −0.0266489 + 0.0583529i
\(244\) 0 0
\(245\) −3.44989 0.664911i −0.220405 0.0424796i
\(246\) 0 0
\(247\) −2.15808 + 1.11257i −0.137315 + 0.0707910i
\(248\) 0 0
\(249\) −1.73421 + 0.694273i −0.109901 + 0.0439978i
\(250\) 0 0
\(251\) 4.40650 + 18.1638i 0.278136 + 1.14649i 0.923802 + 0.382871i \(0.125065\pi\)
−0.645666 + 0.763620i \(0.723420\pi\)
\(252\) 0 0
\(253\) −0.687533 + 4.78190i −0.0432248 + 0.300635i
\(254\) 0 0
\(255\) 7.00330 0.668734i 0.438563 0.0418777i
\(256\) 0 0
\(257\) −0.690702 14.4996i −0.0430848 0.904461i −0.912173 0.409805i \(-0.865597\pi\)
0.869088 0.494657i \(-0.164706\pi\)
\(258\) 0 0
\(259\) −2.38502 16.5882i −0.148198 1.03074i
\(260\) 0 0
\(261\) −1.80869 0.724088i −0.111955 0.0448199i
\(262\) 0 0
\(263\) 4.32231 2.77778i 0.266525 0.171285i −0.400552 0.916274i \(-0.631182\pi\)
0.667077 + 0.744989i \(0.267545\pi\)
\(264\) 0 0
\(265\) −7.77445 + 8.97219i −0.477581 + 0.551157i
\(266\) 0 0
\(267\) 4.46043 0.272974
\(268\) 0 0
\(269\) −15.4431 −0.941580 −0.470790 0.882245i \(-0.656031\pi\)
−0.470790 + 0.882245i \(0.656031\pi\)
\(270\) 0 0
\(271\) −5.06837 + 5.84921i −0.307881 + 0.355314i −0.888512 0.458853i \(-0.848260\pi\)
0.580631 + 0.814167i \(0.302806\pi\)
\(272\) 0 0
\(273\) 6.55431 4.21220i 0.396685 0.254934i
\(274\) 0 0
\(275\) 10.1204 + 4.05161i 0.610285 + 0.244321i
\(276\) 0 0
\(277\) 2.27102 + 15.7953i 0.136452 + 0.949046i 0.936888 + 0.349628i \(0.113692\pi\)
−0.800436 + 0.599418i \(0.795399\pi\)
\(278\) 0 0
\(279\) 0.377903 + 7.93315i 0.0226244 + 0.474945i
\(280\) 0 0
\(281\) 1.05447 0.100689i 0.0629043 0.00600663i −0.0635564 0.997978i \(-0.520244\pi\)
0.126461 + 0.991972i \(0.459638\pi\)
\(282\) 0 0
\(283\) −1.82141 + 12.6682i −0.108272 + 0.753047i 0.861275 + 0.508140i \(0.169667\pi\)
−0.969546 + 0.244907i \(0.921242\pi\)
\(284\) 0 0
\(285\) 0.468570 + 1.93147i 0.0277557 + 0.114410i
\(286\) 0 0
\(287\) −5.43733 + 2.17678i −0.320955 + 0.128491i
\(288\) 0 0
\(289\) 8.96011 4.61926i 0.527065 0.271721i
\(290\) 0 0
\(291\) 0.996178 + 0.191997i 0.0583970 + 0.0112551i
\(292\) 0 0
\(293\) −5.53173 + 12.1128i −0.323167 + 0.707638i −0.999583 0.0288826i \(-0.990805\pi\)
0.676416 + 0.736520i \(0.263532\pi\)
\(294\) 0 0
\(295\) 27.7681 + 17.8455i 1.61672 + 1.03900i
\(296\) 0 0
\(297\) 2.53169 4.38501i 0.146903 0.254444i
\(298\) 0 0
\(299\) 3.10325 + 0.296324i 0.179465 + 0.0171369i
\(300\) 0 0
\(301\) 3.97580 + 3.12660i 0.229161 + 0.180214i
\(302\) 0 0
\(303\) −17.8124 + 3.43307i −1.02330 + 0.197225i
\(304\) 0 0
\(305\) −12.8651 22.2830i −0.736652 1.27592i
\(306\) 0 0
\(307\) 1.11409 1.56452i 0.0635846 0.0892920i −0.781559 0.623831i \(-0.785575\pi\)
0.845144 + 0.534539i \(0.179515\pi\)
\(308\) 0 0
\(309\) 9.83385 9.37656i 0.559428 0.533414i
\(310\) 0 0
\(311\) 27.3417 + 8.02825i 1.55041 + 0.455240i 0.941222 0.337788i \(-0.109679\pi\)
0.609184 + 0.793029i \(0.291497\pi\)
\(312\) 0 0
\(313\) −0.304085 0.350933i −0.0171879 0.0198359i 0.747091 0.664722i \(-0.231450\pi\)
−0.764278 + 0.644886i \(0.776905\pi\)
\(314\) 0 0
\(315\) −2.08592 6.02687i −0.117528 0.339576i
\(316\) 0 0
\(317\) 1.79202 + 1.70868i 0.100650 + 0.0959693i 0.738734 0.673998i \(-0.235424\pi\)
−0.638084 + 0.769967i \(0.720273\pi\)
\(318\) 0 0
\(319\) 8.76808 + 4.52026i 0.490918 + 0.253086i
\(320\) 0 0
\(321\) −4.14743 + 1.21780i −0.231487 + 0.0679707i
\(322\) 0 0
\(323\) −1.13387 1.59230i −0.0630903 0.0885979i
\(324\) 0 0
\(325\) 2.30070 6.64744i 0.127620 0.368734i
\(326\) 0 0
\(327\) −2.53865 5.55888i −0.140388 0.307407i
\(328\) 0 0
\(329\) 1.39039 29.1878i 0.0766545 1.60918i
\(330\) 0 0
\(331\) 7.35654 30.3241i 0.404352 1.66676i −0.297718 0.954654i \(-0.596225\pi\)
0.702070 0.712108i \(-0.252259\pi\)
\(332\) 0 0
\(333\) −5.52430 + 4.34436i −0.302730 + 0.238069i
\(334\) 0 0
\(335\) −5.12450 21.2835i −0.279982 1.16284i
\(336\) 0 0
\(337\) 2.89269 2.27484i 0.157575 0.123918i −0.536259 0.844054i \(-0.680163\pi\)
0.693833 + 0.720135i \(0.255920\pi\)
\(338\) 0 0
\(339\) −3.36330 + 13.8637i −0.182669 + 0.752973i
\(340\) 0 0
\(341\) 1.91346 40.1685i 0.103620 2.17525i
\(342\) 0 0
\(343\) −8.23552 18.0333i −0.444676 0.973705i
\(344\) 0 0
\(345\) 0.834612 2.41145i 0.0449340 0.129828i
\(346\) 0 0
\(347\) 2.56959 + 3.60849i 0.137943 + 0.193714i 0.877769 0.479085i \(-0.159031\pi\)
−0.739826 + 0.672799i \(0.765092\pi\)
\(348\) 0 0
\(349\) 5.16556 1.51674i 0.276506 0.0811894i −0.140540 0.990075i \(-0.544884\pi\)
0.417045 + 0.908886i \(0.363066\pi\)
\(350\) 0 0
\(351\) −2.90406 1.49715i −0.155007 0.0799117i
\(352\) 0 0
\(353\) −1.12975 1.07722i −0.0601306 0.0573344i 0.659418 0.751776i \(-0.270803\pi\)
−0.719549 + 0.694442i \(0.755651\pi\)
\(354\) 0 0
\(355\) 9.81094 + 28.3468i 0.520710 + 1.50449i
\(356\) 0 0
\(357\) 4.10767 + 4.74051i 0.217401 + 0.250894i
\(358\) 0 0
\(359\) 17.9989 + 5.28495i 0.949945 + 0.278929i 0.719764 0.694219i \(-0.244250\pi\)
0.230181 + 0.973148i \(0.426068\pi\)
\(360\) 0 0
\(361\) −13.3513 + 12.7304i −0.702699 + 0.670022i
\(362\) 0 0
\(363\) −8.49074 + 11.9236i −0.445648 + 0.625825i
\(364\) 0 0
\(365\) −17.8488 30.9150i −0.934249 1.61817i
\(366\) 0 0
\(367\) 2.63124 0.507130i 0.137350 0.0264720i −0.120113 0.992760i \(-0.538326\pi\)
0.257463 + 0.966288i \(0.417114\pi\)
\(368\) 0 0
\(369\) 1.93064 + 1.51827i 0.100505 + 0.0790380i
\(370\) 0 0
\(371\) −10.5371 1.00618i −0.547061 0.0522380i
\(372\) 0 0
\(373\) 10.1800 17.6323i 0.527101 0.912965i −0.472401 0.881384i \(-0.656612\pi\)
0.999501 0.0315811i \(-0.0100543\pi\)
\(374\) 0 0
\(375\) 6.40563 + 4.11665i 0.330785 + 0.212583i
\(376\) 0 0
\(377\) 2.64429 5.79018i 0.136188 0.298210i
\(378\) 0 0
\(379\) −22.7439 4.38353i −1.16828 0.225167i −0.432016 0.901866i \(-0.642198\pi\)
−0.736260 + 0.676699i \(0.763410\pi\)
\(380\) 0 0
\(381\) −4.21996 + 2.17554i −0.216195 + 0.111456i
\(382\) 0 0
\(383\) 17.8400 7.14206i 0.911582 0.364942i 0.132005 0.991249i \(-0.457858\pi\)
0.779577 + 0.626307i \(0.215434\pi\)
\(384\) 0 0
\(385\) 7.61322 + 31.3821i 0.388005 + 1.59938i
\(386\) 0 0
\(387\) 0.301860 2.09949i 0.0153444 0.106723i
\(388\) 0 0
\(389\) 9.16497 0.875149i 0.464683 0.0443718i 0.139911 0.990164i \(-0.455318\pi\)
0.324772 + 0.945792i \(0.394712\pi\)
\(390\) 0 0
\(391\) 0.119420 + 2.50693i 0.00603931 + 0.126781i
\(392\) 0 0
\(393\) 1.70316 + 11.8458i 0.0859131 + 0.597539i
\(394\) 0 0
\(395\) 15.3854 + 6.15937i 0.774121 + 0.309911i
\(396\) 0 0
\(397\) 13.9858 8.98815i 0.701929 0.451102i −0.140380 0.990098i \(-0.544832\pi\)
0.842309 + 0.538995i \(0.181196\pi\)
\(398\) 0 0
\(399\) −1.16045 + 1.33924i −0.0580954 + 0.0670457i
\(400\) 0 0
\(401\) 19.6771 0.982626 0.491313 0.870983i \(-0.336517\pi\)
0.491313 + 0.870983i \(0.336517\pi\)
\(402\) 0 0
\(403\) −25.9491 −1.29261
\(404\) 0 0
\(405\) −1.75143 + 2.02126i −0.0870291 + 0.100437i
\(406\) 0 0
\(407\) 29.9359 19.2386i 1.48387 0.953624i
\(408\) 0 0
\(409\) 30.7765 + 12.3210i 1.52180 + 0.609237i 0.973833 0.227264i \(-0.0729780\pi\)
0.547966 + 0.836500i \(0.315402\pi\)
\(410\) 0 0
\(411\) −0.369200 2.56784i −0.0182113 0.126662i
\(412\) 0 0
\(413\) 1.40034 + 29.3968i 0.0689064 + 1.44652i
\(414\) 0 0
\(415\) −4.97340 + 0.474903i −0.244135 + 0.0233120i
\(416\) 0 0
\(417\) −1.76907 + 12.3042i −0.0866318 + 0.602537i
\(418\) 0 0
\(419\) −1.72282 7.10156i −0.0841652 0.346934i 0.914122 0.405440i \(-0.132882\pi\)
−0.998287 + 0.0585058i \(0.981366\pi\)
\(420\) 0 0
\(421\) 27.0054 10.8113i 1.31616 0.526912i 0.395929 0.918281i \(-0.370422\pi\)
0.920234 + 0.391369i \(0.127998\pi\)
\(422\) 0 0
\(423\) −10.8918 + 5.61510i −0.529576 + 0.273015i
\(424\) 0 0
\(425\) 5.56095 + 1.07178i 0.269746 + 0.0519892i
\(426\) 0 0
\(427\) 9.53011 20.8680i 0.461194 1.00987i
\(428\) 0 0
\(429\) 13.9172 + 8.94402i 0.671927 + 0.431821i
\(430\) 0 0
\(431\) −12.3344 + 21.3637i −0.594125 + 1.02905i 0.399545 + 0.916714i \(0.369168\pi\)
−0.993670 + 0.112341i \(0.964165\pi\)
\(432\) 0 0
\(433\) 16.8617 + 1.61010i 0.810324 + 0.0773766i 0.491989 0.870602i \(-0.336270\pi\)
0.318335 + 0.947978i \(0.396876\pi\)
\(434\) 0 0
\(435\) −4.09579 3.22097i −0.196378 0.154434i
\(436\) 0 0
\(437\) −0.696219 + 0.134185i −0.0333047 + 0.00641895i
\(438\) 0 0
\(439\) 5.78112 + 10.0132i 0.275918 + 0.477904i 0.970366 0.241639i \(-0.0776849\pi\)
−0.694448 + 0.719542i \(0.744352\pi\)
\(440\) 0 0
\(441\) −0.761995 + 1.07007i −0.0362855 + 0.0509558i
\(442\) 0 0
\(443\) −9.60770 + 9.16092i −0.456475 + 0.435248i −0.883103 0.469179i \(-0.844550\pi\)
0.426628 + 0.904427i \(0.359701\pi\)
\(444\) 0 0
\(445\) 11.4462 + 3.36091i 0.542603 + 0.159322i
\(446\) 0 0
\(447\) 0.590779 + 0.681795i 0.0279429 + 0.0322478i
\(448\) 0 0
\(449\) −7.55479 21.8281i −0.356533 1.03013i −0.970562 0.240851i \(-0.922574\pi\)
0.614029 0.789283i \(-0.289548\pi\)
\(450\) 0 0
\(451\) −9.00053 8.58199i −0.423818 0.404110i
\(452\) 0 0
\(453\) −21.6063 11.1388i −1.01515 0.523348i
\(454\) 0 0
\(455\) 19.9933 5.87058i 0.937302 0.275217i
\(456\) 0 0
\(457\) 20.1748 + 28.3316i 0.943738 + 1.32529i 0.945612 + 0.325297i \(0.105464\pi\)
−0.00187373 + 0.999998i \(0.500596\pi\)
\(458\) 0 0
\(459\) 0.860336 2.48578i 0.0401571 0.116026i
\(460\) 0 0
\(461\) 8.78276 + 19.2316i 0.409054 + 0.895703i 0.996271 + 0.0862742i \(0.0274961\pi\)
−0.587217 + 0.809429i \(0.699777\pi\)
\(462\) 0 0
\(463\) −0.844970 + 17.7381i −0.0392691 + 0.824359i 0.890225 + 0.455522i \(0.150547\pi\)
−0.929494 + 0.368838i \(0.879756\pi\)
\(464\) 0 0
\(465\) −5.00783 + 20.6425i −0.232232 + 0.957275i
\(466\) 0 0
\(467\) 14.9888 11.7873i 0.693597 0.545451i −0.207946 0.978140i \(-0.566678\pi\)
0.901543 + 0.432689i \(0.142435\pi\)
\(468\) 0 0
\(469\) 12.8075 14.7293i 0.591397 0.680136i
\(470\) 0 0
\(471\) 12.3970 9.74909i 0.571223 0.449214i
\(472\) 0 0
\(473\) −2.53200 + 10.4371i −0.116422 + 0.479897i
\(474\) 0 0
\(475\) −0.0761278 + 1.59812i −0.00349298 + 0.0733267i
\(476\) 0 0
\(477\) 1.84399 + 4.03778i 0.0844307 + 0.184877i
\(478\) 0 0
\(479\) 0.804151 2.32344i 0.0367426 0.106161i −0.925138 0.379632i \(-0.876051\pi\)
0.961880 + 0.273471i \(0.0881718\pi\)
\(480\) 0 0
\(481\) −13.3192 18.7043i −0.607305 0.852841i
\(482\) 0 0
\(483\) 2.18304 0.640998i 0.0993318 0.0291664i
\(484\) 0 0
\(485\) 2.41169 + 1.24331i 0.109509 + 0.0564559i
\(486\) 0 0
\(487\) 2.86359 + 2.73042i 0.129761 + 0.123727i 0.752181 0.658956i \(-0.229002\pi\)
−0.622420 + 0.782684i \(0.713850\pi\)
\(488\) 0 0
\(489\) 4.43721 + 12.8205i 0.200657 + 0.579762i
\(490\) 0 0
\(491\) −1.69045 1.95088i −0.0762889 0.0880421i 0.716322 0.697770i \(-0.245824\pi\)
−0.792611 + 0.609728i \(0.791279\pi\)
\(492\) 0 0
\(493\) 4.91717 + 1.44381i 0.221458 + 0.0650259i
\(494\) 0 0
\(495\) 9.80082 9.34506i 0.440514 0.420029i
\(496\) 0 0
\(497\) −15.5137 + 21.7860i −0.695886 + 0.977235i
\(498\) 0 0
\(499\) −2.68230 4.64588i −0.120076 0.207978i 0.799721 0.600371i \(-0.204981\pi\)
−0.919798 + 0.392393i \(0.871647\pi\)
\(500\) 0 0
\(501\) 10.6264 2.04807i 0.474752 0.0915010i
\(502\) 0 0
\(503\) 32.0300 + 25.1886i 1.42815 + 1.12311i 0.972489 + 0.232950i \(0.0748379\pi\)
0.455657 + 0.890156i \(0.349405\pi\)
\(504\) 0 0
\(505\) −48.2965 4.61176i −2.14917 0.205221i
\(506\) 0 0
\(507\) −1.16250 + 2.01352i −0.0516287 + 0.0894235i
\(508\) 0 0
\(509\) −24.1414 15.5147i −1.07005 0.687678i −0.117810 0.993036i \(-0.537587\pi\)
−0.952237 + 0.305358i \(0.901224\pi\)
\(510\) 0 0
\(511\) 13.2219 28.9520i 0.584903 1.28076i
\(512\) 0 0
\(513\) 0.729697 + 0.140638i 0.0322169 + 0.00620930i
\(514\) 0 0
\(515\) 32.3005 16.6521i 1.42333 0.733778i
\(516\) 0 0
\(517\) 57.6020 23.0603i 2.53333 1.01419i
\(518\) 0 0
\(519\) 1.58074 + 6.51591i 0.0693869 + 0.286017i
\(520\) 0 0
\(521\) 5.39421 37.5176i 0.236325 1.64367i −0.433499 0.901154i \(-0.642721\pi\)
0.669824 0.742520i \(-0.266370\pi\)
\(522\) 0 0
\(523\) −30.0475 + 2.86919i −1.31389 + 0.125461i −0.728361 0.685193i \(-0.759718\pi\)
−0.585525 + 0.810654i \(0.699112\pi\)
\(524\) 0 0
\(525\) −0.244285 5.12818i −0.0106615 0.223812i
\(526\) 0 0
\(527\) −2.97316 20.6788i −0.129513 0.900782i
\(528\) 0 0
\(529\) −20.5073 8.20989i −0.891623 0.356952i
\(530\) 0 0
\(531\) 10.3825 6.67244i 0.450563 0.289559i
\(532\) 0 0
\(533\) −5.25511 + 6.06472i −0.227624 + 0.262692i
\(534\) 0 0
\(535\) −11.5606 −0.499809
\(536\) 0 0
\(537\) 9.10995 0.393123
\(538\) 0 0
\(539\) 4.35583 5.02689i 0.187619 0.216524i
\(540\) 0 0
\(541\) −18.1215 + 11.6460i −0.779104 + 0.500700i −0.868736 0.495275i \(-0.835067\pi\)
0.0896323 + 0.995975i \(0.471431\pi\)
\(542\) 0 0
\(543\) 6.27235 + 2.51107i 0.269172 + 0.107760i
\(544\) 0 0
\(545\) −2.32603 16.1779i −0.0996361 0.692984i
\(546\) 0 0
\(547\) −1.11299 23.3646i −0.0475881 0.998998i −0.888801 0.458294i \(-0.848461\pi\)
0.841213 0.540704i \(-0.181842\pi\)
\(548\) 0 0
\(549\) −9.57697 + 0.914490i −0.408735 + 0.0390295i
\(550\) 0 0
\(551\) −0.206042 + 1.43305i −0.00877768 + 0.0610501i
\(552\) 0 0
\(553\) 3.48360 + 14.3596i 0.148138 + 0.610633i
\(554\) 0 0
\(555\) −17.4497 + 6.98582i −0.740700 + 0.296531i
\(556\) 0 0
\(557\) −4.71880 + 2.43271i −0.199942 + 0.103077i −0.555290 0.831657i \(-0.687393\pi\)
0.355348 + 0.934734i \(0.384362\pi\)
\(558\) 0 0
\(559\) 6.80487 + 1.31153i 0.287815 + 0.0554718i
\(560\) 0 0
\(561\) −5.53290 + 12.1154i −0.233599 + 0.511511i
\(562\) 0 0
\(563\) −21.7994 14.0097i −0.918737 0.590436i −0.00644607 0.999979i \(-0.502052\pi\)
−0.912291 + 0.409543i \(0.865688\pi\)
\(564\) 0 0
\(565\) −19.0770 + 33.0424i −0.802576 + 1.39010i
\(566\) 0 0
\(567\) −2.37381 0.226671i −0.0996906 0.00951929i
\(568\) 0 0
\(569\) 26.4546 + 20.8041i 1.10904 + 0.872155i 0.992647 0.121049i \(-0.0386258\pi\)
0.116389 + 0.993204i \(0.462868\pi\)
\(570\) 0 0
\(571\) 26.9558 5.19530i 1.12806 0.217417i 0.409118 0.912482i \(-0.365837\pi\)
0.718947 + 0.695065i \(0.244624\pi\)
\(572\) 0 0
\(573\) −6.88453 11.9243i −0.287605 0.498147i
\(574\) 0 0
\(575\) 1.19155 1.67330i 0.0496911 0.0697814i
\(576\) 0 0
\(577\) −26.7774 + 25.5322i −1.11476 + 1.06292i −0.117200 + 0.993108i \(0.537392\pi\)
−0.997560 + 0.0698129i \(0.977760\pi\)
\(578\) 0 0
\(579\) −14.8485 4.35991i −0.617083 0.181192i
\(580\) 0 0
\(581\) −2.91707 3.36648i −0.121020 0.139665i
\(582\) 0 0
\(583\) −7.35115 21.2398i −0.304454 0.879661i
\(584\) 0 0
\(585\) −6.32421 6.03012i −0.261474 0.249315i
\(586\) 0 0
\(587\) −24.4175 12.5881i −1.00782 0.519566i −0.126437 0.991975i \(-0.540354\pi\)
−0.881379 + 0.472409i \(0.843385\pi\)
\(588\) 0 0
\(589\) 5.66295 1.66279i 0.233338 0.0685141i
\(590\) 0 0
\(591\) −5.50063 7.72455i −0.226266 0.317746i
\(592\) 0 0
\(593\) −13.5097 + 39.0337i −0.554777 + 1.60292i 0.223298 + 0.974750i \(0.428318\pi\)
−0.778074 + 0.628172i \(0.783803\pi\)
\(594\) 0 0
\(595\) 6.96903 + 15.2600i 0.285702 + 0.625601i
\(596\) 0 0
\(597\) −1.01190 + 21.2425i −0.0414145 + 0.869397i
\(598\) 0 0
\(599\) 4.91003 20.2394i 0.200618 0.826960i −0.779152 0.626835i \(-0.784350\pi\)
0.979770 0.200125i \(-0.0641349\pi\)
\(600\) 0 0
\(601\) −8.13788 + 6.39970i −0.331951 + 0.261049i −0.770197 0.637806i \(-0.779842\pi\)
0.438246 + 0.898855i \(0.355600\pi\)
\(602\) 0 0
\(603\) −8.03475 1.56294i −0.327200 0.0636478i
\(604\) 0 0
\(605\) −30.7730 + 24.2002i −1.25110 + 0.983877i
\(606\) 0 0
\(607\) 11.0691 45.6273i 0.449279 1.85195i −0.0702907 0.997527i \(-0.522393\pi\)
0.519570 0.854428i \(-0.326092\pi\)
\(608\) 0 0
\(609\) 0.221056 4.64053i 0.00895762 0.188044i
\(610\) 0 0
\(611\) −16.6319 36.4189i −0.672856 1.47335i
\(612\) 0 0
\(613\) −8.69536 + 25.1236i −0.351202 + 1.01473i 0.621648 + 0.783297i \(0.286464\pi\)
−0.972850 + 0.231436i \(0.925658\pi\)
\(614\) 0 0
\(615\) 3.81033 + 5.35086i 0.153647 + 0.215768i
\(616\) 0 0
\(617\) 16.9187 4.96779i 0.681123 0.199996i 0.0771725 0.997018i \(-0.475411\pi\)
0.603950 + 0.797022i \(0.293593\pi\)
\(618\) 0 0
\(619\) −26.5830 13.7045i −1.06846 0.550831i −0.168010 0.985785i \(-0.553734\pi\)
−0.900452 + 0.434955i \(0.856764\pi\)
\(620\) 0 0
\(621\) −0.690530 0.658419i −0.0277100 0.0264214i
\(622\) 0 0
\(623\) 3.47881 + 10.0514i 0.139376 + 0.402700i
\(624\) 0 0
\(625\) 20.3855 + 23.5262i 0.815421 + 0.941046i
\(626\) 0 0
\(627\) −3.61031 1.06008i −0.144182 0.0423356i
\(628\) 0 0
\(629\) 13.3793 12.7572i 0.533469 0.508662i
\(630\) 0 0
\(631\) 15.1548 21.2819i 0.603302 0.847220i −0.394114 0.919062i \(-0.628948\pi\)
0.997416 + 0.0718420i \(0.0228877\pi\)
\(632\) 0 0
\(633\) −3.03175 5.25115i −0.120501 0.208715i
\(634\) 0 0
\(635\) −12.4684 + 2.40309i −0.494793 + 0.0953636i
\(636\) 0 0
\(637\) −3.37378 2.65317i −0.133674 0.105123i
\(638\) 0 0
\(639\) 11.1650 + 1.06613i 0.441680 + 0.0421753i
\(640\) 0 0
\(641\) 14.9380 25.8734i 0.590017 1.02194i −0.404212 0.914665i \(-0.632454\pi\)
0.994229 0.107274i \(-0.0342123\pi\)
\(642\) 0 0
\(643\) 20.6119 + 13.2465i 0.812855 + 0.522390i 0.879787 0.475367i \(-0.157685\pi\)
−0.0669326 + 0.997758i \(0.521321\pi\)
\(644\) 0 0
\(645\) 2.35658 5.16018i 0.0927901 0.203182i
\(646\) 0 0
\(647\) −13.8587 2.67104i −0.544841 0.105009i −0.0905983 0.995888i \(-0.528878\pi\)
−0.454243 + 0.890878i \(0.650090\pi\)
\(648\) 0 0
\(649\) −55.5441 + 28.6350i −2.18030 + 1.12402i
\(650\) 0 0
\(651\) −17.5823 + 7.03887i −0.689103 + 0.275875i
\(652\) 0 0
\(653\) 7.58525 + 31.2668i 0.296834 + 1.22356i 0.903493 + 0.428603i \(0.140994\pi\)
−0.606659 + 0.794962i \(0.707491\pi\)
\(654\) 0 0
\(655\) −4.55511 + 31.6815i −0.177983 + 1.23790i
\(656\) 0 0
\(657\) −13.2869 + 1.26875i −0.518373 + 0.0494986i
\(658\) 0 0
\(659\) −2.24079 47.0400i −0.0872888 1.83242i −0.441510 0.897256i \(-0.645557\pi\)
0.354222 0.935161i \(-0.384746\pi\)
\(660\) 0 0
\(661\) −1.34019 9.32121i −0.0521273 0.362553i −0.999144 0.0413687i \(-0.986828\pi\)
0.947017 0.321184i \(-0.104081\pi\)
\(662\) 0 0
\(663\) 7.97874 + 3.19420i 0.309868 + 0.124053i
\(664\) 0 0
\(665\) −3.98703 + 2.56231i −0.154610 + 0.0993621i
\(666\) 0 0
\(667\) 1.21729 1.40483i 0.0471338 0.0543953i
\(668\) 0 0
\(669\) 14.5631 0.563042
\(670\) 0 0
\(671\) 48.7124 1.88052
\(672\) 0 0
\(673\) −28.3361 + 32.7016i −1.09227 + 1.26055i −0.129113 + 0.991630i \(0.541213\pi\)
−0.963162 + 0.268922i \(0.913332\pi\)
\(674\) 0 0
\(675\) −1.81120 + 1.16399i −0.0697130 + 0.0448018i
\(676\) 0 0
\(677\) −34.8171 13.9387i −1.33813 0.535706i −0.411406 0.911452i \(-0.634962\pi\)
−0.926723 + 0.375746i \(0.877387\pi\)
\(678\) 0 0
\(679\) 0.344289 + 2.39458i 0.0132126 + 0.0918957i
\(680\) 0 0
\(681\) 0.969867 + 20.3600i 0.0371654 + 0.780197i
\(682\) 0 0
\(683\) −2.41541 + 0.230644i −0.0924232 + 0.00882534i −0.141165 0.989986i \(-0.545085\pi\)
0.0487420 + 0.998811i \(0.484479\pi\)
\(684\) 0 0
\(685\) 0.987426 6.86770i 0.0377276 0.262401i
\(686\) 0 0
\(687\) 2.05057 + 8.45257i 0.0782341 + 0.322485i
\(688\) 0 0
\(689\) −13.4642 + 5.39026i −0.512946 + 0.205353i
\(690\) 0 0
\(691\) −45.5027 + 23.4583i −1.73100 + 0.892394i −0.761195 + 0.648523i \(0.775387\pi\)
−0.969808 + 0.243871i \(0.921583\pi\)
\(692\) 0 0
\(693\) 11.8560 + 2.28505i 0.450371 + 0.0868018i
\(694\) 0 0
\(695\) −13.8109 + 30.2415i −0.523875 + 1.14713i
\(696\) 0 0
\(697\) −5.43508 3.49292i −0.205868 0.132304i
\(698\) 0 0
\(699\) 5.75570 9.96916i 0.217700 0.377068i
\(700\) 0 0
\(701\) −34.9099 3.33349i −1.31853 0.125904i −0.588041 0.808831i \(-0.700101\pi\)
−0.730486 + 0.682927i \(0.760707\pi\)
\(702\) 0 0
\(703\) 4.10525 + 3.22841i 0.154833 + 0.121762i
\(704\) 0 0
\(705\) −32.1811 + 6.20239i −1.21201 + 0.233596i
\(706\) 0 0
\(707\) −21.6287 37.4620i −0.813430 1.40890i
\(708\) 0 0
\(709\) −5.76058 + 8.08960i −0.216343 + 0.303811i −0.908458 0.417976i \(-0.862740\pi\)
0.692115 + 0.721787i \(0.256679\pi\)
\(710\) 0 0
\(711\) 4.48459 4.27605i 0.168185 0.160364i
\(712\) 0 0
\(713\) −7.27081 2.13490i −0.272294 0.0799528i
\(714\) 0 0
\(715\) 28.9745 + 33.4384i 1.08359 + 1.25052i
\(716\) 0 0
\(717\) −2.16315 6.25001i −0.0807843 0.233411i
\(718\) 0 0
\(719\) −9.66483 9.21539i −0.360437 0.343676i 0.488123 0.872775i \(-0.337682\pi\)
−0.848560 + 0.529099i \(0.822530\pi\)
\(720\) 0 0
\(721\) 28.7994 + 14.8471i 1.07254 + 0.552935i
\(722\) 0 0
\(723\) 12.4558 3.65734i 0.463235 0.136018i
\(724\) 0 0
\(725\) −2.43306 3.41675i −0.0903614 0.126895i
\(726\) 0 0
\(727\) 3.23077 9.33469i 0.119823 0.346205i −0.869100 0.494636i \(-0.835301\pi\)
0.988923 + 0.148432i \(0.0474225\pi\)
\(728\) 0 0
\(729\) 0.415415 + 0.909632i 0.0153857 + 0.0336901i
\(730\) 0 0
\(731\) −0.265478 + 5.57306i −0.00981905 + 0.206127i
\(732\) 0 0
\(733\) −12.7067 + 52.3776i −0.469332 + 1.93461i −0.141194 + 0.989982i \(0.545094\pi\)
−0.328138 + 0.944630i \(0.606421\pi\)
\(734\) 0 0
\(735\) −2.76170 + 2.17183i −0.101867 + 0.0801090i
\(736\) 0 0
\(737\) 39.7465 + 11.7451i 1.46408 + 0.432635i
\(738\) 0 0
\(739\) −11.5553 + 9.08715i −0.425067 + 0.334276i −0.807668 0.589637i \(-0.799271\pi\)
0.382601 + 0.923914i \(0.375028\pi\)
\(740\) 0 0
\(741\) −0.572420 + 2.35955i −0.0210284 + 0.0866801i
\(742\) 0 0
\(743\) 0.123349 2.58942i 0.00452525 0.0949967i −0.995475 0.0950265i \(-0.969706\pi\)
1.00000 2.97169e-5i \(9.45918e-6\pi\)
\(744\) 0 0
\(745\) 1.00231 + 2.19475i 0.0367217 + 0.0804094i
\(746\) 0 0
\(747\) −0.610969 + 1.76528i −0.0223542 + 0.0645882i
\(748\) 0 0
\(749\) −5.97895 8.39626i −0.218466 0.306793i
\(750\) 0 0
\(751\) −40.3993 + 11.8623i −1.47419 + 0.432862i −0.917459 0.397830i \(-0.869763\pi\)
−0.556732 + 0.830692i \(0.687945\pi\)
\(752\) 0 0
\(753\) 16.6130 + 8.56457i 0.605410 + 0.312110i
\(754\) 0 0
\(755\) −47.0524 44.8644i −1.71241 1.63278i
\(756\) 0 0
\(757\) −9.30545 26.8863i −0.338212 0.977201i −0.977992 0.208642i \(-0.933096\pi\)
0.639780 0.768558i \(-0.279026\pi\)
\(758\) 0 0
\(759\) 3.16368 + 3.65108i 0.114834 + 0.132526i
\(760\) 0 0
\(761\) 16.5705 + 4.86553i 0.600679 + 0.176375i 0.567914 0.823088i \(-0.307751\pi\)
0.0327651 + 0.999463i \(0.489569\pi\)
\(762\) 0 0
\(763\) 10.5467 10.0563i 0.381816 0.364061i
\(764\) 0 0
\(765\) 4.08079 5.73067i 0.147541 0.207193i
\(766\) 0 0
\(767\) 20.1618 + 34.9213i 0.728001 + 1.26094i
\(768\) 0 0
\(769\) 24.9858 4.81562i 0.901010 0.173656i 0.282348 0.959312i \(-0.408887\pi\)
0.618663 + 0.785657i \(0.287675\pi\)
\(770\) 0 0
\(771\) −11.4104 8.97323i −0.410935 0.323163i
\(772\) 0 0
\(773\) 42.5346 + 4.06156i 1.52986 + 0.146084i 0.825763 0.564017i \(-0.190745\pi\)
0.704099 + 0.710102i \(0.251351\pi\)
\(774\) 0 0
\(775\) −8.54961 + 14.8084i −0.307111 + 0.531932i
\(776\) 0 0
\(777\) −14.0984 9.06047i −0.505776 0.325043i
\(778\) 0