Properties

Label 300.2.x.a.53.1
Level $300$
Weight $2$
Character 300.53
Analytic conductor $2.396$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.x (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 53.1
Character \(\chi\) \(=\) 300.53
Dual form 300.2.x.a.17.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.73066 + 0.0694365i) q^{3} +(0.354250 - 2.20783i) q^{5} +(-1.67035 + 1.67035i) q^{7} +(2.99036 - 0.240342i) q^{9} +O(q^{10})\) \(q+(-1.73066 + 0.0694365i) q^{3} +(0.354250 - 2.20783i) q^{5} +(-1.67035 + 1.67035i) q^{7} +(2.99036 - 0.240342i) q^{9} +(-5.27981 - 1.71551i) q^{11} +(-1.00207 + 1.96667i) q^{13} +(-0.459783 + 3.84559i) q^{15} +(-4.25837 - 0.674459i) q^{17} +(-4.59013 - 6.31777i) q^{19} +(2.77483 - 3.00680i) q^{21} +(1.53667 + 3.01588i) q^{23} +(-4.74901 - 1.56425i) q^{25} +(-5.15860 + 0.623589i) q^{27} +(0.409155 + 0.297269i) q^{29} +(2.41697 - 1.75603i) q^{31} +(9.25666 + 2.60236i) q^{33} +(3.09613 + 4.27958i) q^{35} +(-7.68210 - 3.91423i) q^{37} +(1.59768 - 3.47321i) q^{39} +(4.48088 - 1.45593i) q^{41} +(5.88737 + 5.88737i) q^{43} +(0.528702 - 6.68734i) q^{45} +(-0.527820 - 3.33252i) q^{47} +1.41984i q^{49} +(7.41661 + 0.871573i) q^{51} +(5.21091 - 0.825328i) q^{53} +(-5.65793 + 11.0492i) q^{55} +(8.38263 + 10.6152i) q^{57} +(3.17139 + 9.76054i) q^{59} +(1.65928 - 5.10673i) q^{61} +(-4.59350 + 5.39641i) q^{63} +(3.98709 + 2.90909i) q^{65} +(0.707187 - 4.46500i) q^{67} +(-2.86886 - 5.11276i) q^{69} +(-6.04875 + 8.32540i) q^{71} +(-1.93067 + 0.983727i) q^{73} +(8.32754 + 2.37742i) q^{75} +(11.6847 - 5.95363i) q^{77} +(10.1110 - 13.9166i) q^{79} +(8.88447 - 1.43741i) q^{81} +(1.93251 - 12.2014i) q^{83} +(-2.99762 + 9.16282i) q^{85} +(-0.728750 - 0.486061i) q^{87} +(1.43321 - 4.41098i) q^{89} +(-1.61123 - 4.95884i) q^{91} +(-4.06102 + 3.20692i) q^{93} +(-15.5746 + 7.89614i) q^{95} +(-15.9942 + 2.53324i) q^{97} +(-16.2008 - 3.86104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\)

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
\(3\) −1.73066 + 0.0694365i −0.999196 + 0.0400892i
\(4\) 0 0
\(5\) 0.354250 2.20783i 0.158426 0.987371i
\(6\) 0 0
\(7\) −1.67035 + 1.67035i −0.631334 + 0.631334i −0.948403 0.317068i \(-0.897302\pi\)
0.317068 + 0.948403i \(0.397302\pi\)
\(8\) 0 0
\(9\) 2.99036 0.240342i 0.996786 0.0801139i
\(10\) 0 0
\(11\) −5.27981 1.71551i −1.59192 0.517247i −0.626830 0.779156i \(-0.715648\pi\)
−0.965092 + 0.261910i \(0.915648\pi\)
\(12\) 0 0
\(13\) −1.00207 + 1.96667i −0.277924 + 0.545456i −0.987202 0.159472i \(-0.949021\pi\)
0.709279 + 0.704928i \(0.249021\pi\)
\(14\) 0 0
\(15\) −0.459783 + 3.84559i −0.118715 + 0.992928i
\(16\) 0 0
\(17\) −4.25837 0.674459i −1.03281 0.163580i −0.383053 0.923726i \(-0.625128\pi\)
−0.649753 + 0.760146i \(0.725128\pi\)
\(18\) 0 0
\(19\) −4.59013 6.31777i −1.05305 1.44940i −0.886137 0.463423i \(-0.846621\pi\)
−0.166911 0.985972i \(-0.553379\pi\)
\(20\) 0 0
\(21\) 2.77483 3.00680i 0.605517 0.656136i
\(22\) 0 0
\(23\) 1.53667 + 3.01588i 0.320418 + 0.628855i 0.993892 0.110355i \(-0.0351989\pi\)
−0.673475 + 0.739210i \(0.735199\pi\)
\(24\) 0 0
\(25\) −4.74901 1.56425i −0.949803 0.312850i
\(26\) 0 0
\(27\) −5.15860 + 0.623589i −0.992773 + 0.120010i
\(28\) 0 0
\(29\) 0.409155 + 0.297269i 0.0759783 + 0.0552014i 0.625126 0.780524i \(-0.285048\pi\)
−0.549148 + 0.835725i \(0.685048\pi\)
\(30\) 0 0
\(31\) 2.41697 1.75603i 0.434101 0.315393i −0.349186 0.937054i \(-0.613542\pi\)
0.783287 + 0.621661i \(0.213542\pi\)
\(32\) 0 0
\(33\) 9.25666 + 2.60236i 1.61138 + 0.453012i
\(34\) 0 0
\(35\) 3.09613 + 4.27958i 0.523342 + 0.723381i
\(36\) 0 0
\(37\) −7.68210 3.91423i −1.26293 0.643495i −0.311174 0.950353i \(-0.600722\pi\)
−0.951755 + 0.306858i \(0.900722\pi\)
\(38\) 0 0
\(39\) 1.59768 3.47321i 0.255833 0.556159i
\(40\) 0 0
\(41\) 4.48088 1.45593i 0.699796 0.227377i 0.0625543 0.998042i \(-0.480075\pi\)
0.637242 + 0.770664i \(0.280075\pi\)
\(42\) 0 0
\(43\) 5.88737 + 5.88737i 0.897816 + 0.897816i 0.995243 0.0974269i \(-0.0310612\pi\)
−0.0974269 + 0.995243i \(0.531061\pi\)
\(44\) 0 0
\(45\) 0.528702 6.68734i 0.0788143 0.996889i
\(46\) 0 0
\(47\) −0.527820 3.33252i −0.0769905 0.486099i −0.995812 0.0914252i \(-0.970858\pi\)
0.918821 0.394673i \(-0.129142\pi\)
\(48\) 0 0
\(49\) 1.41984i 0.202834i
\(50\) 0 0
\(51\) 7.41661 + 0.871573i 1.03853 + 0.122045i
\(52\) 0 0
\(53\) 5.21091 0.825328i 0.715774 0.113367i 0.212083 0.977252i \(-0.431975\pi\)
0.503691 + 0.863884i \(0.331975\pi\)
\(54\) 0 0
\(55\) −5.65793 + 11.0492i −0.762916 + 1.48987i
\(56\) 0 0
\(57\) 8.38263 + 10.6152i 1.11031 + 1.40601i
\(58\) 0 0
\(59\) 3.17139 + 9.76054i 0.412880 + 1.27071i 0.914134 + 0.405413i \(0.132872\pi\)
−0.501254 + 0.865300i \(0.667128\pi\)
\(60\) 0 0
\(61\) 1.65928 5.10673i 0.212449 0.653850i −0.786876 0.617111i \(-0.788303\pi\)
0.999325 0.0367391i \(-0.0116970\pi\)
\(62\) 0 0
\(63\) −4.59350 + 5.39641i −0.578726 + 0.679884i
\(64\) 0 0
\(65\) 3.98709 + 2.90909i 0.494537 + 0.360828i
\(66\) 0 0
\(67\) 0.707187 4.46500i 0.0863966 0.545487i −0.906085 0.423095i \(-0.860944\pi\)
0.992482 0.122392i \(-0.0390564\pi\)
\(68\) 0 0
\(69\) −2.86886 5.11276i −0.345370 0.615504i
\(70\) 0 0
\(71\) −6.04875 + 8.32540i −0.717855 + 0.988043i 0.281737 + 0.959492i \(0.409089\pi\)
−0.999592 + 0.0285511i \(0.990911\pi\)
\(72\) 0 0
\(73\) −1.93067 + 0.983727i −0.225968 + 0.115136i −0.563310 0.826246i \(-0.690472\pi\)
0.337342 + 0.941382i \(0.390472\pi\)
\(74\) 0 0
\(75\) 8.32754 + 2.37742i 0.961581 + 0.274521i
\(76\) 0 0
\(77\) 11.6847 5.95363i 1.33159 0.678479i
\(78\) 0 0
\(79\) 10.1110 13.9166i 1.13757 1.56574i 0.364764 0.931100i \(-0.381150\pi\)
0.772811 0.634637i \(-0.218850\pi\)
\(80\) 0 0
\(81\) 8.88447 1.43741i 0.987164 0.159713i
\(82\) 0 0
\(83\) 1.93251 12.2014i 0.212121 1.33928i −0.619964 0.784630i \(-0.712853\pi\)
0.832085 0.554648i \(-0.187147\pi\)
\(84\) 0 0
\(85\) −2.99762 + 9.16282i −0.325137 + 0.993847i
\(86\) 0 0
\(87\) −0.728750 0.486061i −0.0781302 0.0521112i
\(88\) 0 0
\(89\) 1.43321 4.41098i 0.151920 0.467563i −0.845915 0.533317i \(-0.820945\pi\)
0.997836 + 0.0657541i \(0.0209453\pi\)
\(90\) 0 0
\(91\) −1.61123 4.95884i −0.168902 0.519828i
\(92\) 0 0
\(93\) −4.06102 + 3.20692i −0.421108 + 0.332542i
\(94\) 0 0
\(95\) −15.5746 + 7.89614i −1.59792 + 0.810127i
\(96\) 0 0
\(97\) −15.9942 + 2.53324i −1.62397 + 0.257211i −0.901048 0.433720i \(-0.857201\pi\)
−0.722921 + 0.690931i \(0.757201\pi\)
\(98\) 0 0
\(99\) −16.2008 3.86104i −1.62824 0.388049i
\(100\) 0 0
\(101\) 4.67239i 0.464920i −0.972606 0.232460i \(-0.925322\pi\)
0.972606 0.232460i \(-0.0746775\pi\)
\(102\) 0 0
\(103\) −1.07022 6.75713i −0.105452 0.665800i −0.982622 0.185619i \(-0.940571\pi\)
0.877169 0.480181i \(-0.159429\pi\)
\(104\) 0 0
\(105\) −5.65550 7.19150i −0.551921 0.701819i
\(106\) 0 0
\(107\) −2.84075 2.84075i −0.274626 0.274626i 0.556334 0.830959i \(-0.312208\pi\)
−0.830959 + 0.556334i \(0.812208\pi\)
\(108\) 0 0
\(109\) −10.7758 + 3.50126i −1.03213 + 0.335360i −0.775633 0.631185i \(-0.782569\pi\)
−0.256499 + 0.966544i \(0.582569\pi\)
\(110\) 0 0
\(111\) 13.5669 + 6.24077i 1.28771 + 0.592348i
\(112\) 0 0
\(113\) 3.85613 + 1.96480i 0.362754 + 0.184833i 0.625862 0.779934i \(-0.284747\pi\)
−0.263108 + 0.964767i \(0.584747\pi\)
\(114\) 0 0
\(115\) 7.20292 2.32432i 0.671675 0.216744i
\(116\) 0 0
\(117\) −2.52387 + 6.12188i −0.233332 + 0.565968i
\(118\) 0 0
\(119\) 8.23957 5.98640i 0.755320 0.548772i
\(120\) 0 0
\(121\) 16.0342 + 11.6495i 1.45765 + 1.05905i
\(122\) 0 0
\(123\) −7.65378 + 2.83085i −0.690118 + 0.255249i
\(124\) 0 0
\(125\) −5.13593 + 9.93087i −0.459372 + 0.888244i
\(126\) 0 0
\(127\) −0.759425 1.49046i −0.0673881 0.132257i 0.854855 0.518867i \(-0.173646\pi\)
−0.922243 + 0.386610i \(0.873646\pi\)
\(128\) 0 0
\(129\) −10.5978 9.78023i −0.933087 0.861101i
\(130\) 0 0
\(131\) −2.70065 3.71712i −0.235957 0.324767i 0.674575 0.738207i \(-0.264327\pi\)
−0.910531 + 0.413440i \(0.864327\pi\)
\(132\) 0 0
\(133\) 18.2200 + 2.88577i 1.57988 + 0.250228i
\(134\) 0 0
\(135\) −0.450658 + 11.6102i −0.0387865 + 0.999248i
\(136\) 0 0
\(137\) −4.03906 + 7.92710i −0.345080 + 0.677258i −0.996690 0.0812966i \(-0.974094\pi\)
0.651610 + 0.758554i \(0.274094\pi\)
\(138\) 0 0
\(139\) 3.53260 + 1.14781i 0.299631 + 0.0973561i 0.454975 0.890504i \(-0.349648\pi\)
−0.155343 + 0.987861i \(0.549648\pi\)
\(140\) 0 0
\(141\) 1.14487 + 5.73081i 0.0964158 + 0.482621i
\(142\) 0 0
\(143\) 8.66458 8.66458i 0.724568 0.724568i
\(144\) 0 0
\(145\) 0.801262 0.798037i 0.0665412 0.0662734i
\(146\) 0 0
\(147\) −0.0985885 2.45725i −0.00813144 0.202671i
\(148\) 0 0
\(149\) −16.5291 −1.35411 −0.677057 0.735931i \(-0.736745\pi\)
−0.677057 + 0.735931i \(0.736745\pi\)
\(150\) 0 0
\(151\) −5.27383 −0.429178 −0.214589 0.976704i \(-0.568841\pi\)
−0.214589 + 0.976704i \(0.568841\pi\)
\(152\) 0 0
\(153\) −12.8961 0.993411i −1.04259 0.0803125i
\(154\) 0 0
\(155\) −3.02081 5.95833i −0.242637 0.478585i
\(156\) 0 0
\(157\) 7.79069 7.79069i 0.621765 0.621765i −0.324218 0.945982i \(-0.605101\pi\)
0.945982 + 0.324218i \(0.105101\pi\)
\(158\) 0 0
\(159\) −8.96100 + 1.79019i −0.710654 + 0.141971i
\(160\) 0 0
\(161\) −7.60437 2.47081i −0.599308 0.194727i
\(162\) 0 0
\(163\) −7.02791 + 13.7931i −0.550469 + 1.08036i 0.433356 + 0.901223i \(0.357329\pi\)
−0.983825 + 0.179133i \(0.942671\pi\)
\(164\) 0 0
\(165\) 9.02473 19.5152i 0.702575 1.51926i
\(166\) 0 0
\(167\) −9.92370 1.57176i −0.767919 0.121626i −0.239829 0.970815i \(-0.577092\pi\)
−0.528090 + 0.849189i \(0.677092\pi\)
\(168\) 0 0
\(169\) 4.77756 + 6.57575i 0.367505 + 0.505827i
\(170\) 0 0
\(171\) −15.2445 17.7892i −1.16578 1.36037i
\(172\) 0 0
\(173\) −6.65343 13.0581i −0.505851 0.992789i −0.992848 0.119385i \(-0.961908\pi\)
0.486997 0.873404i \(-0.338092\pi\)
\(174\) 0 0
\(175\) 10.5454 5.31968i 0.797156 0.402130i
\(176\) 0 0
\(177\) −6.16633 16.6719i −0.463490 1.25314i
\(178\) 0 0
\(179\) 12.3066 + 8.94125i 0.919837 + 0.668301i 0.943483 0.331420i \(-0.107528\pi\)
−0.0236465 + 0.999720i \(0.507528\pi\)
\(180\) 0 0
\(181\) 0.447095 0.324833i 0.0332323 0.0241447i −0.571045 0.820919i \(-0.693462\pi\)
0.604277 + 0.796774i \(0.293462\pi\)
\(182\) 0 0
\(183\) −2.51705 + 8.95322i −0.186066 + 0.661841i
\(184\) 0 0
\(185\) −11.3633 + 15.5741i −0.835448 + 1.14503i
\(186\) 0 0
\(187\) 21.3263 + 10.8663i 1.55954 + 0.794623i
\(188\) 0 0
\(189\) 7.57507 9.65830i 0.551005 0.702538i
\(190\) 0 0
\(191\) −20.5690 + 6.68327i −1.48832 + 0.483585i −0.936587 0.350435i \(-0.886034\pi\)
−0.551734 + 0.834020i \(0.686034\pi\)
\(192\) 0 0
\(193\) −3.71609 3.71609i −0.267490 0.267490i 0.560598 0.828088i \(-0.310571\pi\)
−0.828088 + 0.560598i \(0.810571\pi\)
\(194\) 0 0
\(195\) −7.10228 4.75779i −0.508605 0.340712i
\(196\) 0 0
\(197\) −3.06376 19.3438i −0.218284 1.37819i −0.816726 0.577026i \(-0.804213\pi\)
0.598442 0.801166i \(-0.295787\pi\)
\(198\) 0 0
\(199\) 1.77115i 0.125553i 0.998028 + 0.0627766i \(0.0199956\pi\)
−0.998028 + 0.0627766i \(0.980004\pi\)
\(200\) 0 0
\(201\) −0.913865 + 7.77649i −0.0644590 + 0.548512i
\(202\) 0 0
\(203\) −1.17998 + 0.186890i −0.0828182 + 0.0131171i
\(204\) 0 0
\(205\) −1.62708 10.4088i −0.113640 0.726980i
\(206\) 0 0
\(207\) 5.32003 + 8.64924i 0.369768 + 0.601164i
\(208\) 0 0
\(209\) 13.3968 + 41.2310i 0.926674 + 2.85201i
\(210\) 0 0
\(211\) 0.990096 3.04720i 0.0681610 0.209778i −0.911174 0.412021i \(-0.864823\pi\)
0.979335 + 0.202243i \(0.0648230\pi\)
\(212\) 0 0
\(213\) 9.89024 14.8284i 0.677668 1.01603i
\(214\) 0 0
\(215\) 15.0839 10.9127i 1.02871 0.744240i
\(216\) 0 0
\(217\) −1.10400 + 6.97039i −0.0749445 + 0.473181i
\(218\) 0 0
\(219\) 3.27303 1.83655i 0.221171 0.124103i
\(220\) 0 0
\(221\) 5.59361 7.69895i 0.376267 0.517887i
\(222\) 0 0
\(223\) −2.15039 + 1.09568i −0.144001 + 0.0733720i −0.524506 0.851407i \(-0.675750\pi\)
0.380505 + 0.924779i \(0.375750\pi\)
\(224\) 0 0
\(225\) −14.5772 3.53628i −0.971813 0.235752i
\(226\) 0 0
\(227\) 14.3886 7.33136i 0.955005 0.486599i 0.0942105 0.995552i \(-0.469967\pi\)
0.860794 + 0.508953i \(0.169967\pi\)
\(228\) 0 0
\(229\) −10.1726 + 14.0013i −0.672222 + 0.925235i −0.999808 0.0195869i \(-0.993765\pi\)
0.327586 + 0.944821i \(0.393765\pi\)
\(230\) 0 0
\(231\) −19.8088 + 11.1150i −1.30332 + 0.731316i
\(232\) 0 0
\(233\) −2.40288 + 15.1712i −0.157418 + 0.993898i 0.774854 + 0.632140i \(0.217823\pi\)
−0.932272 + 0.361758i \(0.882177\pi\)
\(234\) 0 0
\(235\) −7.54462 0.0152120i −0.492157 0.000992319i
\(236\) 0 0
\(237\) −16.5323 + 24.7869i −1.07389 + 1.61008i
\(238\) 0 0
\(239\) 6.17815 19.0144i 0.399631 1.22994i −0.525664 0.850692i \(-0.676183\pi\)
0.925296 0.379247i \(-0.123817\pi\)
\(240\) 0 0
\(241\) 1.32659 + 4.08282i 0.0854532 + 0.262998i 0.984648 0.174550i \(-0.0558471\pi\)
−0.899195 + 0.437548i \(0.855847\pi\)
\(242\) 0 0
\(243\) −15.2762 + 3.10458i −0.979967 + 0.199159i
\(244\) 0 0
\(245\) 3.13476 + 0.502978i 0.200272 + 0.0321341i
\(246\) 0 0
\(247\) 17.0246 2.69643i 1.08325 0.171570i
\(248\) 0 0
\(249\) −2.49730 + 21.2506i −0.158260 + 1.34671i
\(250\) 0 0
\(251\) 7.64733i 0.482695i −0.970439 0.241347i \(-0.922411\pi\)
0.970439 0.241347i \(-0.0775893\pi\)
\(252\) 0 0
\(253\) −2.93953 18.5595i −0.184807 1.16682i
\(254\) 0 0
\(255\) 4.55162 16.0659i 0.285034 1.00608i
\(256\) 0 0
\(257\) −6.23777 6.23777i −0.389101 0.389101i 0.485266 0.874367i \(-0.338723\pi\)
−0.874367 + 0.485266i \(0.838723\pi\)
\(258\) 0 0
\(259\) 19.3700 6.29368i 1.20359 0.391070i
\(260\) 0 0
\(261\) 1.29497 + 0.790603i 0.0801564 + 0.0489371i
\(262\) 0 0
\(263\) 15.4727 + 7.88374i 0.954088 + 0.486132i 0.860484 0.509478i \(-0.170161\pi\)
0.0936037 + 0.995610i \(0.470161\pi\)
\(264\) 0 0
\(265\) 0.0237862 11.7972i 0.00146118 0.724695i
\(266\) 0 0
\(267\) −2.17412 + 7.73342i −0.133054 + 0.473277i
\(268\) 0 0
\(269\) 17.2020 12.4980i 1.04883 0.762017i 0.0768379 0.997044i \(-0.475518\pi\)
0.971989 + 0.235026i \(0.0755176\pi\)
\(270\) 0 0
\(271\) −7.79739 5.66514i −0.473658 0.344133i 0.325207 0.945643i \(-0.394566\pi\)
−0.798865 + 0.601510i \(0.794566\pi\)
\(272\) 0 0
\(273\) 3.13280 + 8.47018i 0.189606 + 0.512639i
\(274\) 0 0
\(275\) 22.3904 + 16.4059i 1.35019 + 0.989315i
\(276\) 0 0
\(277\) 14.6228 + 28.6988i 0.878596 + 1.72434i 0.664141 + 0.747608i \(0.268798\pi\)
0.214455 + 0.976734i \(0.431202\pi\)
\(278\) 0 0
\(279\) 6.80556 5.83206i 0.407438 0.349157i
\(280\) 0 0
\(281\) −1.62290 2.23373i −0.0968141 0.133253i 0.757862 0.652415i \(-0.226244\pi\)
−0.854676 + 0.519162i \(0.826244\pi\)
\(282\) 0 0
\(283\) −15.0519 2.38398i −0.894741 0.141713i −0.307903 0.951418i \(-0.599627\pi\)
−0.586838 + 0.809705i \(0.699627\pi\)
\(284\) 0 0
\(285\) 26.4060 14.7470i 1.56416 0.873535i
\(286\) 0 0
\(287\) −5.05274 + 9.91657i −0.298254 + 0.585356i
\(288\) 0 0
\(289\) 1.51085 + 0.490904i 0.0888733 + 0.0288767i
\(290\) 0 0
\(291\) 27.5047 5.49475i 1.61235 0.322108i
\(292\) 0 0
\(293\) 7.47364 7.47364i 0.436615 0.436615i −0.454256 0.890871i \(-0.650095\pi\)
0.890871 + 0.454256i \(0.150095\pi\)
\(294\) 0 0
\(295\) 22.6731 3.54421i 1.32008 0.206352i
\(296\) 0 0
\(297\) 28.3062 + 5.55722i 1.64249 + 0.322462i
\(298\) 0 0
\(299\) −7.47109 −0.432064
\(300\) 0 0
\(301\) −19.6680 −1.13364
\(302\) 0 0
\(303\) 0.324434 + 8.08631i 0.0186383 + 0.464547i
\(304\) 0 0
\(305\) −10.6870 5.47246i −0.611935 0.313352i
\(306\) 0 0
\(307\) 3.64430 3.64430i 0.207991 0.207991i −0.595422 0.803413i \(-0.703015\pi\)
0.803413 + 0.595422i \(0.203015\pi\)
\(308\) 0 0
\(309\) 2.32139 + 11.6200i 0.132059 + 0.661038i
\(310\) 0 0
\(311\) 7.97750 + 2.59205i 0.452363 + 0.146982i 0.526332 0.850279i \(-0.323567\pi\)
−0.0739696 + 0.997260i \(0.523567\pi\)
\(312\) 0 0
\(313\) 4.02979 7.90891i 0.227777 0.447038i −0.748626 0.662992i \(-0.769286\pi\)
0.976403 + 0.215954i \(0.0692863\pi\)
\(314\) 0 0
\(315\) 10.2871 + 12.0533i 0.579612 + 0.679129i
\(316\) 0 0
\(317\) −14.6748 2.32426i −0.824218 0.130543i −0.269943 0.962876i \(-0.587005\pi\)
−0.554276 + 0.832333i \(0.687005\pi\)
\(318\) 0 0
\(319\) −1.65029 2.27143i −0.0923987 0.127176i
\(320\) 0 0
\(321\) 5.11362 + 4.71911i 0.285414 + 0.263395i
\(322\) 0 0
\(323\) 15.2854 + 29.9992i 0.850501 + 1.66920i
\(324\) 0 0
\(325\) 7.83519 7.77226i 0.434618 0.431127i
\(326\) 0 0
\(327\) 18.4061 6.80772i 1.01786 0.376468i
\(328\) 0 0
\(329\) 6.44814 + 4.68485i 0.355497 + 0.258284i
\(330\) 0 0
\(331\) −9.59179 + 6.96885i −0.527213 + 0.383042i −0.819314 0.573345i \(-0.805646\pi\)
0.292101 + 0.956387i \(0.405646\pi\)
\(332\) 0 0
\(333\) −23.9130 9.85860i −1.31042 0.540248i
\(334\) 0 0
\(335\) −9.60743 3.14307i −0.524910 0.171725i
\(336\) 0 0
\(337\) −9.98022 5.08518i −0.543657 0.277007i 0.160519 0.987033i \(-0.448683\pi\)
−0.704176 + 0.710026i \(0.748683\pi\)
\(338\) 0 0
\(339\) −6.81007 3.13264i −0.369872 0.170141i
\(340\) 0 0
\(341\) −15.7736 + 5.12517i −0.854191 + 0.277543i
\(342\) 0 0
\(343\) −14.0641 14.0641i −0.759390 0.759390i
\(344\) 0 0
\(345\) −12.3044 + 4.52276i −0.662446 + 0.243497i
\(346\) 0 0
\(347\) −4.46050 28.1625i −0.239452 1.51184i −0.755424 0.655236i \(-0.772569\pi\)
0.515972 0.856606i \(-0.327431\pi\)
\(348\) 0 0
\(349\) 24.5531i 1.31430i 0.753761 + 0.657149i \(0.228238\pi\)
−0.753761 + 0.657149i \(0.771762\pi\)
\(350\) 0 0
\(351\) 3.94287 10.7701i 0.210455 0.574867i
\(352\) 0 0
\(353\) 7.23776 1.14635i 0.385227 0.0610140i 0.0391827 0.999232i \(-0.487525\pi\)
0.346045 + 0.938218i \(0.387525\pi\)
\(354\) 0 0
\(355\) 16.2383 + 16.3039i 0.861838 + 0.865320i
\(356\) 0 0
\(357\) −13.8442 + 10.9325i −0.732713 + 0.578611i
\(358\) 0 0
\(359\) 3.41890 + 10.5223i 0.180443 + 0.555345i 0.999840 0.0178804i \(-0.00569180\pi\)
−0.819397 + 0.573226i \(0.805692\pi\)
\(360\) 0 0
\(361\) −12.9736 + 39.9287i −0.682821 + 2.10151i
\(362\) 0 0
\(363\) −28.5586 19.0480i −1.49894 0.999760i
\(364\) 0 0
\(365\) 1.48796 + 4.61108i 0.0778833 + 0.241355i
\(366\) 0 0
\(367\) 5.39806 34.0820i 0.281776 1.77907i −0.288366 0.957520i \(-0.593112\pi\)
0.570142 0.821546i \(-0.306888\pi\)
\(368\) 0 0
\(369\) 13.0495 5.43068i 0.679330 0.282710i
\(370\) 0 0
\(371\) −7.32548 + 10.0827i −0.380320 + 0.523465i
\(372\) 0 0
\(373\) 14.7942 7.53802i 0.766014 0.390304i −0.0268992 0.999638i \(-0.508563\pi\)
0.792913 + 0.609335i \(0.208563\pi\)
\(374\) 0 0
\(375\) 8.19898 17.5436i 0.423393 0.905946i
\(376\) 0 0
\(377\) −0.994631 + 0.506790i −0.0512261 + 0.0261010i
\(378\) 0 0
\(379\) −20.3628 + 28.0270i −1.04597 + 1.43965i −0.153711 + 0.988116i \(0.549122\pi\)
−0.892255 + 0.451532i \(0.850878\pi\)
\(380\) 0 0
\(381\) 1.41780 + 2.52674i 0.0726359 + 0.129449i
\(382\) 0 0
\(383\) 3.45899 21.8392i 0.176746 1.11593i −0.726613 0.687047i \(-0.758906\pi\)
0.903359 0.428885i \(-0.141094\pi\)
\(384\) 0 0
\(385\) −9.00530 27.9068i −0.458953 1.42226i
\(386\) 0 0
\(387\) 19.0203 + 16.1904i 0.966857 + 0.823003i
\(388\) 0 0
\(389\) 0.876383 2.69723i 0.0444344 0.136755i −0.926378 0.376595i \(-0.877095\pi\)
0.970812 + 0.239840i \(0.0770949\pi\)
\(390\) 0 0
\(391\) −4.50961 13.8792i −0.228061 0.701899i
\(392\) 0 0
\(393\) 4.93200 + 6.24555i 0.248787 + 0.315046i
\(394\) 0 0
\(395\) −27.1436 27.2533i −1.36574 1.37126i
\(396\) 0 0
\(397\) −29.9879 + 4.74962i −1.50505 + 0.238377i −0.853846 0.520525i \(-0.825736\pi\)
−0.651205 + 0.758902i \(0.725736\pi\)
\(398\) 0 0
\(399\) −31.7331 3.72915i −1.58864 0.186691i
\(400\) 0 0
\(401\) 33.3974i 1.66779i 0.551925 + 0.833894i \(0.313893\pi\)
−0.551925 + 0.833894i \(0.686107\pi\)
\(402\) 0 0
\(403\) 1.03157 + 6.51305i 0.0513859 + 0.324438i
\(404\) 0 0
\(405\) −0.0262368 20.1246i −0.00130372 0.999999i
\(406\) 0 0
\(407\) 33.8451 + 33.8451i 1.67764 + 1.67764i
\(408\) 0 0
\(409\) 15.7176 5.10695i 0.777184 0.252522i 0.106547 0.994308i \(-0.466021\pi\)
0.670637 + 0.741785i \(0.266021\pi\)
\(410\) 0 0
\(411\) 6.43980 13.9996i 0.317652 0.690547i
\(412\) 0 0
\(413\) −21.6009 11.0062i −1.06291 0.541580i
\(414\) 0 0
\(415\) −26.2540 8.58901i −1.28876 0.421618i
\(416\) 0 0
\(417\) −6.19343 1.74118i −0.303293 0.0852659i
\(418\) 0 0
\(419\) −0.401580 + 0.291765i −0.0196184 + 0.0142536i −0.597551 0.801831i \(-0.703860\pi\)
0.577933 + 0.816084i \(0.303860\pi\)
\(420\) 0 0
\(421\) −5.08407 3.69379i −0.247782 0.180025i 0.456961 0.889487i \(-0.348938\pi\)
−0.704743 + 0.709462i \(0.748938\pi\)
\(422\) 0 0
\(423\) −2.37931 9.83858i −0.115686 0.478368i
\(424\) 0 0
\(425\) 19.1680 + 9.86416i 0.929786 + 0.478482i
\(426\) 0 0
\(427\) 5.75847 + 11.3016i 0.278672 + 0.546924i
\(428\) 0 0
\(429\) −14.3938 + 15.5971i −0.694938 + 0.753033i
\(430\) 0 0
\(431\) −7.36561 10.1379i −0.354789 0.488325i 0.593899 0.804540i \(-0.297588\pi\)
−0.948688 + 0.316215i \(0.897588\pi\)
\(432\) 0 0
\(433\) −26.6433 4.21988i −1.28039 0.202795i −0.521074 0.853512i \(-0.674468\pi\)
−0.759320 + 0.650717i \(0.774468\pi\)
\(434\) 0 0
\(435\) −1.33130 + 1.43677i −0.0638309 + 0.0688877i
\(436\) 0 0
\(437\) 12.0001 23.5516i 0.574045 1.12663i
\(438\) 0 0
\(439\) −10.8500 3.52537i −0.517841 0.168257i 0.0384243 0.999262i \(-0.487766\pi\)
−0.556265 + 0.831005i \(0.687766\pi\)
\(440\) 0 0
\(441\) 0.341246 + 4.24582i 0.0162498 + 0.202182i
\(442\) 0 0
\(443\) −15.4331 + 15.4331i −0.733251 + 0.733251i −0.971262 0.238011i \(-0.923504\pi\)
0.238011 + 0.971262i \(0.423504\pi\)
\(444\) 0 0
\(445\) −9.23097 4.72688i −0.437590 0.224076i
\(446\) 0 0
\(447\) 28.6062 1.14772i 1.35303 0.0542853i
\(448\) 0 0
\(449\) −34.8771 −1.64595 −0.822975 0.568077i \(-0.807688\pi\)
−0.822975 + 0.568077i \(0.807688\pi\)
\(450\) 0 0
\(451\) −26.1558 −1.23163
\(452\) 0 0
\(453\) 9.12719 0.366196i 0.428833 0.0172054i
\(454\) 0 0
\(455\) −11.5190 + 1.80064i −0.540021 + 0.0844152i
\(456\) 0 0
\(457\) 23.6405 23.6405i 1.10585 1.10585i 0.112165 0.993690i \(-0.464221\pi\)
0.993690 0.112165i \(-0.0357786\pi\)
\(458\) 0 0
\(459\) 22.3878 + 0.823793i 1.04497 + 0.0384514i
\(460\) 0 0
\(461\) −11.6988 3.80117i −0.544868 0.177038i 0.0236333 0.999721i \(-0.492477\pi\)
−0.568501 + 0.822682i \(0.692477\pi\)
\(462\) 0 0
\(463\) 8.22226 16.1371i 0.382121 0.749955i −0.617200 0.786806i \(-0.711733\pi\)
0.999321 + 0.0368518i \(0.0117330\pi\)
\(464\) 0 0
\(465\) 5.64171 + 10.1021i 0.261628 + 0.468473i
\(466\) 0 0
\(467\) −16.3946 2.59664i −0.758650 0.120158i −0.234887 0.972023i \(-0.575472\pi\)
−0.523763 + 0.851864i \(0.675472\pi\)
\(468\) 0 0
\(469\) 6.27688 + 8.63938i 0.289839 + 0.398930i
\(470\) 0 0
\(471\) −12.9421 + 14.0240i −0.596339 + 0.646191i
\(472\) 0 0
\(473\) −20.9843 41.1841i −0.964860 1.89365i
\(474\) 0 0
\(475\) 11.9160 + 37.1833i 0.546744 + 1.70609i
\(476\) 0 0
\(477\) 15.3841 3.72042i 0.704391 0.170346i
\(478\) 0 0
\(479\) −21.0507 15.2942i −0.961831 0.698811i −0.00825583 0.999966i \(-0.502628\pi\)
−0.953575 + 0.301155i \(0.902628\pi\)
\(480\) 0 0
\(481\) 15.3960 11.1858i 0.701996 0.510030i
\(482\) 0 0
\(483\) 13.3321 + 3.74811i 0.606633 + 0.170545i
\(484\) 0 0
\(485\) −0.0730088 + 36.2099i −0.00331516 + 1.64421i
\(486\) 0 0
\(487\) 12.2935 + 6.26384i 0.557071 + 0.283842i 0.709773 0.704430i \(-0.248797\pi\)
−0.152702 + 0.988272i \(0.548797\pi\)
\(488\) 0 0
\(489\) 11.2052 24.3591i 0.506716 1.10156i
\(490\) 0 0
\(491\) 21.5354 6.99728i 0.971879 0.315783i 0.220305 0.975431i \(-0.429295\pi\)
0.751574 + 0.659648i \(0.229295\pi\)
\(492\) 0 0
\(493\) −1.54184 1.54184i −0.0694409 0.0694409i
\(494\) 0 0
\(495\) −14.2637 + 34.4009i −0.641104 + 1.54620i
\(496\) 0 0
\(497\) −3.80280 24.0099i −0.170579 1.07699i
\(498\) 0 0
\(499\) 7.12077i 0.318770i −0.987217 0.159385i \(-0.949049\pi\)
0.987217 0.159385i \(-0.0509511\pi\)
\(500\) 0 0
\(501\) 17.2837 + 2.03111i 0.772178 + 0.0907434i
\(502\) 0 0
\(503\) 20.1311 3.18846i 0.897602 0.142166i 0.309449 0.950916i \(-0.399855\pi\)
0.588153 + 0.808750i \(0.299855\pi\)
\(504\) 0 0
\(505\) −10.3158 1.65520i −0.459049 0.0736553i
\(506\) 0 0
\(507\) −8.72492 11.0486i −0.387487 0.490687i
\(508\) 0 0
\(509\) −0.874684 2.69200i −0.0387697 0.119321i 0.929799 0.368069i \(-0.119981\pi\)
−0.968568 + 0.248748i \(0.919981\pi\)
\(510\) 0 0
\(511\) 1.58173 4.86808i 0.0699718 0.215351i
\(512\) 0 0
\(513\) 27.6183 + 29.7285i 1.21938 + 1.31254i
\(514\) 0 0
\(515\) −15.2977 0.0308443i −0.674098 0.00135916i
\(516\) 0 0
\(517\) −2.93020 + 18.5006i −0.128870 + 0.813654i
\(518\) 0 0
\(519\) 12.4215 + 22.1371i 0.545245 + 0.971711i
\(520\) 0 0
\(521\) 21.4218 29.4846i 0.938507 1.29174i −0.0179402 0.999839i \(-0.505711\pi\)
0.956447 0.291905i \(-0.0942892\pi\)
\(522\) 0 0
\(523\) −12.8556 + 6.55024i −0.562135 + 0.286422i −0.711878 0.702303i \(-0.752155\pi\)
0.149743 + 0.988725i \(0.452155\pi\)
\(524\) 0 0
\(525\) −17.8811 + 9.93879i −0.780394 + 0.433764i
\(526\) 0 0
\(527\) −11.4767 + 5.84769i −0.499934 + 0.254729i
\(528\) 0 0
\(529\) 6.78486 9.33856i 0.294994 0.406025i
\(530\) 0 0
\(531\) 11.8295 + 28.4253i 0.513354 + 1.23355i
\(532\) 0 0
\(533\) −1.62682 + 10.2713i −0.0704655 + 0.444901i
\(534\) 0 0
\(535\) −7.27822 + 5.26555i −0.314665 + 0.227650i
\(536\) 0 0
\(537\) −21.9193 14.6197i −0.945889 0.630888i
\(538\) 0 0
\(539\) 2.43575 7.49647i 0.104915 0.322896i
\(540\) 0 0
\(541\) −9.28677 28.5817i −0.399269 1.22882i −0.925586 0.378536i \(-0.876428\pi\)
0.526317 0.850288i \(-0.323572\pi\)
\(542\) 0 0
\(543\) −0.751213 + 0.593220i −0.0322376 + 0.0254575i
\(544\) 0 0
\(545\) 3.91286 + 25.0314i 0.167609 + 1.07223i
\(546\) 0 0
\(547\) −32.6302 + 5.16812i −1.39517 + 0.220973i −0.808329 0.588731i \(-0.799628\pi\)
−0.586839 + 0.809704i \(0.699628\pi\)
\(548\) 0 0
\(549\) 3.73447 15.6697i 0.159383 0.668769i
\(550\) 0 0
\(551\) 3.94945i 0.168252i
\(552\) 0 0
\(553\) 6.35668 + 40.1345i 0.270314 + 1.70669i
\(554\) 0 0
\(555\) 18.5846 27.7426i 0.788873 1.17761i
\(556\) 0 0
\(557\) 21.8255 + 21.8255i 0.924778 + 0.924778i 0.997362 0.0725847i \(-0.0231247\pi\)
−0.0725847 + 0.997362i \(0.523125\pi\)
\(558\) 0 0
\(559\) −17.4781 + 5.67897i −0.739243 + 0.240195i
\(560\) 0 0
\(561\) −37.6631 17.3250i −1.59014 0.731464i
\(562\) 0 0
\(563\) −1.53782 0.783556i −0.0648112 0.0330230i 0.421285 0.906929i \(-0.361579\pi\)
−0.486096 + 0.873906i \(0.661579\pi\)
\(564\) 0 0
\(565\) 5.70397 7.81765i 0.239968 0.328891i
\(566\) 0 0
\(567\) −12.4392 + 17.2412i −0.522398 + 0.724062i
\(568\) 0 0
\(569\) 10.8632 7.89256i 0.455408 0.330873i −0.336319 0.941748i \(-0.609182\pi\)
0.791727 + 0.610875i \(0.209182\pi\)
\(570\) 0 0
\(571\) 13.8833 + 10.0868i 0.580999 + 0.422121i 0.839084 0.544001i \(-0.183091\pi\)
−0.258085 + 0.966122i \(0.583091\pi\)
\(572\) 0 0
\(573\) 35.1339 12.9947i 1.46774 0.542862i
\(574\) 0 0
\(575\) −2.58007 16.7262i −0.107596 0.697531i
\(576\) 0 0
\(577\) −5.02409 9.86033i −0.209156 0.410491i 0.762467 0.647027i \(-0.223988\pi\)
−0.971623 + 0.236536i \(0.923988\pi\)
\(578\) 0 0
\(579\) 6.68932 + 6.17326i 0.277999 + 0.256552i
\(580\) 0 0
\(581\) 17.1527 + 23.6086i 0.711613 + 0.979451i
\(582\) 0 0
\(583\) −28.9285 4.58182i −1.19810 0.189760i
\(584\) 0 0
\(585\) 12.6220 + 7.74095i 0.521855 + 0.320049i
\(586\) 0 0
\(587\) −9.65285 + 18.9448i −0.398416 + 0.781935i −0.999856 0.0169832i \(-0.994594\pi\)
0.601440 + 0.798918i \(0.294594\pi\)
\(588\) 0 0
\(589\) −22.1884 7.20945i −0.914258 0.297060i
\(590\) 0 0
\(591\) 6.64550 + 33.2648i 0.273359 + 1.36833i
\(592\) 0 0
\(593\) 12.3241 12.3241i 0.506090 0.506090i −0.407234 0.913324i \(-0.633507\pi\)
0.913324 + 0.407234i \(0.133507\pi\)
\(594\) 0 0
\(595\) −10.2981 20.3122i −0.422180 0.832720i
\(596\) 0 0
\(597\) −0.122982 3.06525i −0.00503332 0.125452i
\(598\) 0 0
\(599\) −13.1359 −0.536716 −0.268358 0.963319i \(-0.586481\pi\)
−0.268358 + 0.963319i \(0.586481\pi\)
\(600\) 0 0
\(601\) 39.9534 1.62973 0.814867 0.579648i \(-0.196810\pi\)
0.814867 + 0.579648i \(0.196810\pi\)
\(602\) 0 0
\(603\) 1.04162 13.5219i 0.0424178 0.550655i
\(604\) 0 0
\(605\) 31.4003 31.2739i 1.27660 1.27147i
\(606\) 0 0
\(607\) −8.63234 + 8.63234i −0.350376 + 0.350376i −0.860249 0.509874i \(-0.829692\pi\)
0.509874 + 0.860249i \(0.329692\pi\)
\(608\) 0 0
\(609\) 2.02916 0.405377i 0.0822258 0.0164267i
\(610\) 0 0
\(611\) 7.08288 + 2.30137i 0.286543 + 0.0931034i
\(612\) 0 0
\(613\) 12.3185 24.1765i 0.497541 0.976480i −0.496558 0.868004i \(-0.665403\pi\)
0.994099 0.108476i \(-0.0345971\pi\)
\(614\) 0 0
\(615\) 3.53867 + 17.9011i 0.142693 + 0.721840i
\(616\) 0 0
\(617\) 16.2868 + 2.57957i 0.655681 + 0.103850i 0.475406 0.879766i \(-0.342301\pi\)
0.180275 + 0.983616i \(0.442301\pi\)
\(618\) 0 0
\(619\) −7.86705 10.8281i −0.316203 0.435216i 0.621100 0.783731i \(-0.286686\pi\)
−0.937303 + 0.348515i \(0.886686\pi\)
\(620\) 0 0
\(621\) −9.80773 14.5995i −0.393571 0.585857i
\(622\) 0 0
\(623\) 4.97392 + 9.76187i 0.199276 + 0.391101i
\(624\) 0 0
\(625\) 20.1063 + 14.8573i 0.804250 + 0.594291i
\(626\) 0 0
\(627\) −26.0482 70.4266i −1.04026 2.81257i
\(628\) 0 0
\(629\) 30.0732 + 21.8495i 1.19910 + 0.871196i
\(630\) 0 0
\(631\) 16.8778 12.2624i 0.671894 0.488160i −0.198764 0.980047i \(-0.563693\pi\)
0.870659 + 0.491887i \(0.163693\pi\)
\(632\) 0 0
\(633\) −1.50193 + 5.34242i −0.0596964 + 0.212342i
\(634\) 0 0
\(635\) −3.55970 + 1.14869i −0.141262 + 0.0455842i
\(636\) 0 0
\(637\) −2.79235 1.42277i −0.110637 0.0563723i
\(638\) 0 0
\(639\) −16.0870 + 26.3497i −0.636392 + 1.04238i
\(640\) 0 0
\(641\) 19.5368 6.34790i 0.771658 0.250727i 0.103383 0.994642i \(-0.467033\pi\)
0.668275 + 0.743915i \(0.267033\pi\)
\(642\) 0 0
\(643\) 20.8324 + 20.8324i 0.821549 + 0.821549i 0.986330 0.164781i \(-0.0526917\pi\)
−0.164781 + 0.986330i \(0.552692\pi\)
\(644\) 0 0
\(645\) −25.3474 + 19.9335i −0.998051 + 0.784882i
\(646\) 0 0
\(647\) 6.10259 + 38.5303i 0.239918 + 1.51478i 0.753905 + 0.656983i \(0.228168\pi\)
−0.513988 + 0.857798i \(0.671832\pi\)
\(648\) 0 0
\(649\) 56.9743i 2.23644i
\(650\) 0 0
\(651\) 1.42665 12.1400i 0.0559149 0.475805i
\(652\) 0 0
\(653\) −32.1247 + 5.08805i −1.25714 + 0.199111i −0.749235 0.662304i \(-0.769579\pi\)
−0.507901 + 0.861415i \(0.669579\pi\)
\(654\) 0 0
\(655\) −9.16347 + 4.64577i −0.358047 + 0.181525i
\(656\) 0 0
\(657\) −5.53697 + 3.40571i −0.216018 + 0.132870i
\(658\) 0 0
\(659\) 6.17031 + 18.9903i 0.240361 + 0.739755i 0.996365 + 0.0851880i \(0.0271491\pi\)
−0.756004 + 0.654567i \(0.772851\pi\)
\(660\) 0 0
\(661\) −4.21748 + 12.9801i −0.164041 + 0.504866i −0.998964 0.0455001i \(-0.985512\pi\)
0.834923 + 0.550366i \(0.185512\pi\)
\(662\) 0 0
\(663\) −9.14605 + 13.7127i −0.355203 + 0.532555i
\(664\) 0 0
\(665\) 12.8257 39.2044i 0.497361 1.52028i
\(666\) 0 0
\(667\) −0.267791 + 1.69077i −0.0103689 + 0.0654668i
\(668\) 0 0
\(669\) 3.64551 2.04556i 0.140943 0.0790859i
\(670\) 0 0
\(671\) −17.5213 + 24.1161i −0.676404 + 0.930990i
\(672\) 0 0
\(673\) −1.04272 + 0.531291i −0.0401938 + 0.0204798i −0.473972 0.880540i \(-0.657180\pi\)
0.433778 + 0.901020i \(0.357180\pi\)
\(674\) 0 0
\(675\) 25.4737 + 5.10790i 0.980483 + 0.196603i
\(676\) 0 0
\(677\) −2.46293 + 1.25493i −0.0946581 + 0.0482307i −0.500679 0.865633i \(-0.666916\pi\)
0.406020 + 0.913864i \(0.366916\pi\)
\(678\) 0 0
\(679\) 22.4846 30.9474i 0.862881 1.18765i
\(680\) 0 0
\(681\) −24.3927 + 13.6872i −0.934730 + 0.524493i
\(682\) 0 0
\(683\) −4.28310 + 27.0424i −0.163888 + 1.03475i 0.759395 + 0.650630i \(0.225495\pi\)
−0.923283 + 0.384119i \(0.874505\pi\)
\(684\) 0 0
\(685\) 16.0708 + 11.7257i 0.614035 + 0.448017i
\(686\) 0 0
\(687\) 16.6330 24.9379i 0.634590 0.951440i
\(688\) 0 0
\(689\) −3.59854 + 11.0752i −0.137094 + 0.421931i
\(690\) 0 0
\(691\) 6.92199 + 21.3037i 0.263325 + 0.810430i 0.992075 + 0.125650i \(0.0401017\pi\)
−0.728750 + 0.684780i \(0.759898\pi\)
\(692\) 0 0
\(693\) 33.5104 20.6118i 1.27296 0.782977i
\(694\) 0 0
\(695\) 3.78560 7.39276i 0.143596 0.280424i
\(696\) 0 0
\(697\) −20.0632 + 3.17770i −0.759948 + 0.120364i
\(698\) 0 0
\(699\) 3.10513 26.4230i 0.117447 0.999410i
\(700\) 0 0
\(701\) 19.9094i 0.751969i −0.926626 0.375985i \(-0.877305\pi\)
0.926626 0.375985i \(-0.122695\pi\)
\(702\) 0 0
\(703\) 10.5326 + 66.5005i 0.397246 + 2.50811i
\(704\) 0 0
\(705\) 13.0582 0.497545i 0.491801 0.0187386i
\(706\) 0 0
\(707\) 7.80455 + 7.80455i 0.293520 + 0.293520i
\(708\) 0 0
\(709\) −16.9259 + 5.49956i −0.635666 + 0.206540i −0.609083 0.793106i \(-0.708463\pi\)
−0.0265827 + 0.999647i \(0.508463\pi\)
\(710\) 0 0
\(711\) 26.8907 44.0456i 1.00848 1.65184i
\(712\) 0 0
\(713\) 9.01008 + 4.59086i 0.337430 + 0.171929i
\(714\) 0 0
\(715\) −16.0605 22.1993i −0.600627 0.830208i
\(716\) 0 0
\(717\) −9.37198 + 33.3364i −0.350003 + 1.24497i
\(718\) 0 0
\(719\) 33.9545 24.6694i 1.26629 0.920014i 0.267242 0.963629i \(-0.413888\pi\)
0.999048 + 0.0436153i \(0.0138876\pi\)
\(720\) 0 0
\(721\) 13.0745 + 9.49915i 0.486918 + 0.353767i
\(722\) 0 0
\(723\) −2.57937 6.97386i −0.0959279 0.259361i
\(724\) 0 0
\(725\) −1.47808 2.05175i −0.0548946 0.0762002i
\(726\) 0 0
\(727\) 11.3404 + 22.2569i 0.420594 + 0.825462i 0.999946 + 0.0103844i \(0.00330552\pi\)
−0.579352 + 0.815077i \(0.696694\pi\)
\(728\) 0 0
\(729\) 26.2223 6.43369i 0.971195 0.238285i
\(730\) 0 0
\(731\) −21.0998 29.0414i −0.780405 1.07413i
\(732\) 0 0
\(733\) 30.1622 + 4.77723i 1.11407 + 0.176451i 0.686216 0.727398i \(-0.259270\pi\)
0.427852 + 0.903849i \(0.359270\pi\)
\(734\) 0 0
\(735\) −5.46012 0.652817i −0.201400 0.0240795i
\(736\) 0 0
\(737\) −11.3936 + 22.3612i −0.419688 + 0.823684i
\(738\) 0 0
\(739\) 18.0849 + 5.87616i 0.665266 + 0.216158i 0.622133 0.782911i \(-0.286266\pi\)
0.0431325 + 0.999069i \(0.486266\pi\)
\(740\) 0 0
\(741\) −29.2765 + 5.84872i −1.07550 + 0.214858i
\(742\) 0 0
\(743\) −21.7526 + 21.7526i −0.798025 + 0.798025i −0.982784 0.184759i \(-0.940850\pi\)
0.184759 + 0.982784i \(0.440850\pi\)
\(744\) 0 0
\(745\) −5.85543 + 36.4934i −0.214526 + 1.33701i
\(746\) 0 0
\(747\) 2.84640 36.9510i 0.104144 1.35197i
\(748\) 0 0
\(749\) 9.49011 0.346761
\(750\) 0 0
\(751\) −2.51184 −0.0916583 −0.0458292 0.998949i \(-0.514593\pi\)
−0.0458292 + 0.998949i \(0.514593\pi\)
\(752\) 0 0
\(753\) 0.531003 + 13.2349i 0.0193508 + 0.482307i
\(754\) 0 0
\(755\) −1.86826 + 11.6437i −0.0679928 + 0.423758i
\(756\) 0 0
\(757\) 10.6543 10.6543i 0.387238 0.387238i −0.486463 0.873701i \(-0.661713\pi\)
0.873701 + 0.486463i \(0.161713\pi\)
\(758\) 0 0
\(759\) 6.37602 + 31.9160i 0.231435 + 1.15848i
\(760\) 0 0
\(761\) 25.2259 + 8.19638i 0.914437 + 0.297119i 0.728183 0.685383i \(-0.240365\pi\)
0.186254 + 0.982502i \(0.440365\pi\)
\(762\) 0 0
\(763\) 12.1510 23.8477i 0.439896 0.863344i
\(764\) 0 0
\(765\) −6.76175 + 28.1206i −0.244471 + 1.01670i
\(766\) 0 0
\(767\) −22.3737 3.54365i −0.807867 0.127954i
\(768\) 0 0
\(769\) 12.4291 + 17.1072i 0.448206 + 0.616903i 0.972011 0.234935i \(-0.0754878\pi\)
−0.523805 + 0.851838i \(0.675488\pi\)
\(770\) 0 0
\(771\) 11.2286 + 10.3623i 0.404387 + 0.373190i
\(772\) 0 0
\(773\) 16.4953 + 32.3738i 0.593294 + 1.16441i 0.971134 + 0.238534i \(0.0766669\pi\)
−0.377840 + 0.925871i \(0.623333\pi\)
\(774\) 0 0
\(775\) −14.2251 + 4.55868i −0.510981 + 0.163753i
\(776\) 0 0
\(777\) −33.0858 + 12.2372i −1.18695 + 0.439007i
\(778\) 0 0
\(779\) −29.7660 21.6263i −1.06648 0.774842i
\(780\) 0 0
\(781\) 46.2186 33.5798i 1.65383 1.20158i
\(782\) 0 0
\(783\) −2.29604 1.27835i −0.0820539 0.0456843i
\(784\) 0 0
\(785\) −14.4406 19.9604i −0.515409 0.712416i
\(786\) 0 0
\(787\) −25.7846 13.1379i −0.919122 0.468316i −0.0706170 0.997504i \(-0.522497\pi\)
−0.848505 + 0.529188i \(0.822497\pi\)
\(788\) 0 0
\(789\) −27.3254 12.5697i −0.972809 0.447493i
\(790\) 0 0
\(791\) −9.72301 + 3.15920i −0.345710 + 0.112328i
\(792\) 0 0
\(793\) 8.38054 + 8.38054i 0.297602 + 0.297602i
\(794\) 0 0
\(795\) 0.777988 + 20.4185i 0.0275924 + 0.724171i
\(796\) 0 0
\(797\) 1.30431 +