Properties

Label 225.2.k.b.49.4
Level $225$
Weight $2$
Character 225.49
Analytic conductor $1.797$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.4
Root \(-1.50511 - 0.403293i\) of defining polynomial
Character \(\chi\) \(=\) 225.49
Dual form 225.2.k.b.124.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.495361 - 0.285997i) q^{2} +(1.70828 - 0.285997i) q^{3} +(-0.836412 + 1.44871i) q^{4} +(0.764419 - 0.630233i) q^{6} +(1.23669 - 0.714003i) q^{7} +2.10083i q^{8} +(2.83641 - 0.977122i) q^{9} +O(q^{10})\) \(q+(0.495361 - 0.285997i) q^{2} +(1.70828 - 0.285997i) q^{3} +(-0.836412 + 1.44871i) q^{4} +(0.764419 - 0.630233i) q^{6} +(1.23669 - 0.714003i) q^{7} +2.10083i q^{8} +(2.83641 - 0.977122i) q^{9} +(-1.33641 - 2.31473i) q^{11} +(-1.01450 + 2.71400i) q^{12} +(4.04678 + 2.33641i) q^{13} +(0.408405 - 0.707378i) q^{14} +(-1.07199 - 1.85675i) q^{16} +2.67282i q^{17} +(1.12559 - 1.29523i) q^{18} -4.67282 q^{19} +(1.90841 - 1.57340i) q^{21} +(-1.32401 - 0.764419i) q^{22} +(-5.12483 - 2.95882i) q^{23} +(0.600830 + 3.58880i) q^{24} +2.67282 q^{26} +(4.56592 - 2.48040i) q^{27} +2.38880i q^{28} +(-4.74482 - 8.21826i) q^{29} +(-3.48040 + 6.02823i) q^{31} +(-4.70079 - 2.71400i) q^{32} +(-2.94497 - 3.57199i) q^{33} +(0.764419 + 1.32401i) q^{34} +(-0.956844 + 4.92641i) q^{36} -1.81681i q^{37} +(-2.31473 + 1.33641i) q^{38} +(7.58123 + 2.83387i) q^{39} +(0.735581 - 1.27406i) q^{41} +(0.495361 - 1.32520i) q^{42} +(-0.408039 + 0.235581i) q^{43} +4.47116 q^{44} -3.38485 q^{46} +(6.02480 - 3.47842i) q^{47} +(-2.36228 - 2.86525i) q^{48} +(-2.48040 + 4.29618i) q^{49} +(0.764419 + 4.56592i) q^{51} +(-6.76956 + 3.90841i) q^{52} +1.14399i q^{53} +(1.55239 - 2.53453i) q^{54} +(1.50000 + 2.59808i) q^{56} +(-7.98247 + 1.33641i) q^{57} +(-4.70079 - 2.71400i) q^{58} +(-0.571993 + 0.990721i) q^{59} +(1.26442 + 2.19004i) q^{61} +3.98153i q^{62} +(2.81009 - 3.23360i) q^{63} +1.18319 q^{64} +(-2.48040 - 0.927175i) q^{66} +(5.70751 + 3.29523i) q^{67} +(-3.87214 - 2.23558i) q^{68} +(-9.60083 - 3.58880i) q^{69} -12.8745 q^{71} +(2.05277 + 5.95882i) q^{72} +1.71203i q^{73} +(-0.519602 - 0.899976i) q^{74} +(3.90841 - 6.76956i) q^{76} +(-3.30545 - 1.90841i) q^{77} +(4.56592 - 0.764419i) q^{78} +(-0.143987 - 0.249392i) q^{79} +(7.09046 - 5.54304i) q^{81} -0.841495i q^{82} +(3.71007 - 2.14201i) q^{83} +(0.683190 + 4.08074i) q^{84} +(-0.134751 + 0.233396i) q^{86} +(-10.4559 - 12.6821i) q^{87} +(4.86286 - 2.80757i) q^{88} +3.00000 q^{89} +6.67282 q^{91} +(8.57293 - 4.94958i) q^{92} +(-4.22143 + 11.2933i) q^{93} +(1.98963 - 3.44615i) q^{94} +(-8.80644 - 3.29186i) q^{96} +(6.78555 - 3.91764i) q^{97} +2.83754i q^{98} +(-6.05239 - 5.25970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9} + 4 q^{11} - 18 q^{14} - 10 q^{16} - 16 q^{19} - 30 q^{24} - 8 q^{26} - 14 q^{29} - 16 q^{31} - 8 q^{34} + 20 q^{36} + 28 q^{39} + 26 q^{41} + 88 q^{44} - 12 q^{46} - 4 q^{49} - 8 q^{51} - 10 q^{54} + 18 q^{56} - 4 q^{59} - 2 q^{61} + 60 q^{64} - 4 q^{66} - 78 q^{69} - 40 q^{71} - 32 q^{74} + 24 q^{76} + 4 q^{79} - 38 q^{81} + 54 q^{84} - 56 q^{86} + 36 q^{89} + 40 q^{91} - 62 q^{94} + 26 q^{96} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.495361 0.285997i 0.350273 0.202230i −0.314533 0.949247i \(-0.601848\pi\)
0.664805 + 0.747017i \(0.268514\pi\)
\(3\) 1.70828 0.285997i 0.986273 0.165120i
\(4\) −0.836412 + 1.44871i −0.418206 + 0.724354i
\(5\) 0 0
\(6\) 0.764419 0.630233i 0.312073 0.257291i
\(7\) 1.23669 0.714003i 0.467425 0.269868i −0.247736 0.968828i \(-0.579687\pi\)
0.715161 + 0.698960i \(0.246353\pi\)
\(8\) 2.10083i 0.742756i
\(9\) 2.83641 0.977122i 0.945471 0.325707i
\(10\) 0 0
\(11\) −1.33641 2.31473i −0.402943 0.697918i 0.591136 0.806572i \(-0.298679\pi\)
−0.994080 + 0.108653i \(0.965346\pi\)
\(12\) −1.01450 + 2.71400i −0.292860 + 0.783465i
\(13\) 4.04678 + 2.33641i 1.12238 + 0.648004i 0.942006 0.335595i \(-0.108937\pi\)
0.180370 + 0.983599i \(0.442271\pi\)
\(14\) 0.408405 0.707378i 0.109151 0.189055i
\(15\) 0 0
\(16\) −1.07199 1.85675i −0.267998 0.464187i
\(17\) 2.67282i 0.648255i 0.946013 + 0.324127i \(0.105071\pi\)
−0.946013 + 0.324127i \(0.894929\pi\)
\(18\) 1.12559 1.29523i 0.265305 0.305289i
\(19\) −4.67282 −1.07202 −0.536010 0.844212i \(-0.680069\pi\)
−0.536010 + 0.844212i \(0.680069\pi\)
\(20\) 0 0
\(21\) 1.90841 1.57340i 0.416448 0.343345i
\(22\) −1.32401 0.764419i −0.282280 0.162975i
\(23\) −5.12483 2.95882i −1.06860 0.616957i −0.140802 0.990038i \(-0.544968\pi\)
−0.927799 + 0.373081i \(0.878301\pi\)
\(24\) 0.600830 + 3.58880i 0.122644 + 0.732560i
\(25\) 0 0
\(26\) 2.67282 0.524184
\(27\) 4.56592 2.48040i 0.878712 0.477353i
\(28\) 2.38880i 0.451441i
\(29\) −4.74482 8.21826i −0.881090 1.52609i −0.850130 0.526573i \(-0.823477\pi\)
−0.0309603 0.999521i \(-0.509857\pi\)
\(30\) 0 0
\(31\) −3.48040 + 6.02823i −0.625098 + 1.08270i 0.363424 + 0.931624i \(0.381608\pi\)
−0.988522 + 0.151078i \(0.951726\pi\)
\(32\) −4.70079 2.71400i −0.830990 0.479773i
\(33\) −2.94497 3.57199i −0.512653 0.621804i
\(34\) 0.764419 + 1.32401i 0.131097 + 0.227066i
\(35\) 0 0
\(36\) −0.956844 + 4.92641i −0.159474 + 0.821068i
\(37\) 1.81681i 0.298682i −0.988786 0.149341i \(-0.952285\pi\)
0.988786 0.149341i \(-0.0477152\pi\)
\(38\) −2.31473 + 1.33641i −0.375499 + 0.216795i
\(39\) 7.58123 + 2.83387i 1.21397 + 0.453782i
\(40\) 0 0
\(41\) 0.735581 1.27406i 0.114879 0.198975i −0.802853 0.596177i \(-0.796685\pi\)
0.917731 + 0.397202i \(0.130019\pi\)
\(42\) 0.495361 1.32520i 0.0764358 0.204483i
\(43\) −0.408039 + 0.235581i −0.0622254 + 0.0359258i −0.530790 0.847503i \(-0.678105\pi\)
0.468565 + 0.883429i \(0.344771\pi\)
\(44\) 4.47116 0.674053
\(45\) 0 0
\(46\) −3.38485 −0.499069
\(47\) 6.02480 3.47842i 0.878808 0.507380i 0.00854274 0.999964i \(-0.497281\pi\)
0.870265 + 0.492584i \(0.163947\pi\)
\(48\) −2.36228 2.86525i −0.340966 0.413563i
\(49\) −2.48040 + 4.29618i −0.354343 + 0.613739i
\(50\) 0 0
\(51\) 0.764419 + 4.56592i 0.107040 + 0.639357i
\(52\) −6.76956 + 3.90841i −0.938769 + 0.541998i
\(53\) 1.14399i 0.157139i 0.996909 + 0.0785693i \(0.0250352\pi\)
−0.996909 + 0.0785693i \(0.974965\pi\)
\(54\) 1.55239 2.53453i 0.211254 0.344906i
\(55\) 0 0
\(56\) 1.50000 + 2.59808i 0.200446 + 0.347183i
\(57\) −7.98247 + 1.33641i −1.05730 + 0.177012i
\(58\) −4.70079 2.71400i −0.617244 0.356366i
\(59\) −0.571993 + 0.990721i −0.0744672 + 0.128981i −0.900854 0.434121i \(-0.857059\pi\)
0.826387 + 0.563102i \(0.190392\pi\)
\(60\) 0 0
\(61\) 1.26442 + 2.19004i 0.161892 + 0.280406i 0.935547 0.353201i \(-0.114907\pi\)
−0.773655 + 0.633607i \(0.781574\pi\)
\(62\) 3.98153i 0.505655i
\(63\) 2.81009 3.23360i 0.354039 0.407396i
\(64\) 1.18319 0.147899
\(65\) 0 0
\(66\) −2.48040 0.927175i −0.305316 0.114127i
\(67\) 5.70751 + 3.29523i 0.697283 + 0.402577i 0.806335 0.591459i \(-0.201448\pi\)
−0.109051 + 0.994036i \(0.534781\pi\)
\(68\) −3.87214 2.23558i −0.469566 0.271104i
\(69\) −9.60083 3.58880i −1.15580 0.432040i
\(70\) 0 0
\(71\) −12.8745 −1.52792 −0.763960 0.645263i \(-0.776748\pi\)
−0.763960 + 0.645263i \(0.776748\pi\)
\(72\) 2.05277 + 5.95882i 0.241921 + 0.702254i
\(73\) 1.71203i 0.200378i 0.994968 + 0.100189i \(0.0319447\pi\)
−0.994968 + 0.100189i \(0.968055\pi\)
\(74\) −0.519602 0.899976i −0.0604025 0.104620i
\(75\) 0 0
\(76\) 3.90841 6.76956i 0.448325 0.776521i
\(77\) −3.30545 1.90841i −0.376692 0.217483i
\(78\) 4.56592 0.764419i 0.516989 0.0865534i
\(79\) −0.143987 0.249392i −0.0161998 0.0280588i 0.857812 0.513964i \(-0.171823\pi\)
−0.874012 + 0.485905i \(0.838490\pi\)
\(80\) 0 0
\(81\) 7.09046 5.54304i 0.787829 0.615894i
\(82\) 0.841495i 0.0929276i
\(83\) 3.71007 2.14201i 0.407233 0.235116i −0.282367 0.959306i \(-0.591120\pi\)
0.689600 + 0.724190i \(0.257786\pi\)
\(84\) 0.683190 + 4.08074i 0.0745421 + 0.445245i
\(85\) 0 0
\(86\) −0.134751 + 0.233396i −0.0145306 + 0.0251677i
\(87\) −10.4559 12.6821i −1.12098 1.35966i
\(88\) 4.86286 2.80757i 0.518383 0.299288i
\(89\) 3.00000 0.317999 0.159000 0.987279i \(-0.449173\pi\)
0.159000 + 0.987279i \(0.449173\pi\)
\(90\) 0 0
\(91\) 6.67282 0.699502
\(92\) 8.57293 4.94958i 0.893790 0.516030i
\(93\) −4.22143 + 11.2933i −0.437742 + 1.17106i
\(94\) 1.98963 3.44615i 0.205215 0.355443i
\(95\) 0 0
\(96\) −8.80644 3.29186i −0.898804 0.335974i
\(97\) 6.78555 3.91764i 0.688968 0.397776i −0.114257 0.993451i \(-0.536449\pi\)
0.803225 + 0.595675i \(0.203115\pi\)
\(98\) 2.83754i 0.286635i
\(99\) −6.05239 5.25970i −0.608288 0.528620i
\(100\) 0 0
\(101\) 2.10083 + 3.63875i 0.209040 + 0.362069i 0.951413 0.307919i \(-0.0996326\pi\)
−0.742372 + 0.669988i \(0.766299\pi\)
\(102\) 1.68450 + 2.04316i 0.166790 + 0.202303i
\(103\) −1.57340 0.908405i −0.155032 0.0895078i 0.420477 0.907303i \(-0.361863\pi\)
−0.575509 + 0.817795i \(0.695196\pi\)
\(104\) −4.90841 + 8.50161i −0.481309 + 0.833651i
\(105\) 0 0
\(106\) 0.327176 + 0.566686i 0.0317782 + 0.0550414i
\(107\) 11.9176i 1.15212i 0.817407 + 0.576061i \(0.195411\pi\)
−0.817407 + 0.576061i \(0.804589\pi\)
\(108\) −0.225617 + 8.68932i −0.0217100 + 0.836130i
\(109\) 16.6521 1.59498 0.797491 0.603331i \(-0.206160\pi\)
0.797491 + 0.603331i \(0.206160\pi\)
\(110\) 0 0
\(111\) −0.519602 3.10361i −0.0493184 0.294582i
\(112\) −2.65145 1.53081i −0.250538 0.144648i
\(113\) 17.4272 + 10.0616i 1.63942 + 0.946518i 0.981034 + 0.193836i \(0.0620929\pi\)
0.658384 + 0.752682i \(0.271240\pi\)
\(114\) −3.57199 + 2.94497i −0.334548 + 0.275821i
\(115\) 0 0
\(116\) 15.8745 1.47391
\(117\) 13.7613 + 2.67282i 1.27223 + 0.247103i
\(118\) 0.654353i 0.0602380i
\(119\) 1.90841 + 3.30545i 0.174943 + 0.303011i
\(120\) 0 0
\(121\) 1.92801 3.33941i 0.175273 0.303582i
\(122\) 1.25269 + 0.723239i 0.113413 + 0.0654790i
\(123\) 0.892198 2.38683i 0.0804468 0.215213i
\(124\) −5.82209 10.0842i −0.522839 0.905584i
\(125\) 0 0
\(126\) 0.467210 2.40548i 0.0416224 0.214297i
\(127\) 2.18714i 0.194078i 0.995281 + 0.0970388i \(0.0309371\pi\)
−0.995281 + 0.0970388i \(0.969063\pi\)
\(128\) 9.98769 5.76640i 0.882795 0.509682i
\(129\) −0.629668 + 0.519136i −0.0554391 + 0.0457074i
\(130\) 0 0
\(131\) 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) 7.63798 1.27874i 0.664801 0.111300i
\(133\) −5.77883 + 3.33641i −0.501089 + 0.289304i
\(134\) 3.76970 0.325653
\(135\) 0 0
\(136\) −5.61515 −0.481495
\(137\) −8.83490 + 5.10083i −0.754816 + 0.435793i −0.827431 0.561567i \(-0.810199\pi\)
0.0726153 + 0.997360i \(0.476865\pi\)
\(138\) −5.78226 + 0.968056i −0.492218 + 0.0824064i
\(139\) 4.00000 6.92820i 0.339276 0.587643i −0.645021 0.764165i \(-0.723151\pi\)
0.984297 + 0.176522i \(0.0564848\pi\)
\(140\) 0 0
\(141\) 9.29721 7.66518i 0.782966 0.645524i
\(142\) −6.37751 + 3.68206i −0.535189 + 0.308992i
\(143\) 12.4896i 1.04444i
\(144\) −4.85488 4.21903i −0.404574 0.351586i
\(145\) 0 0
\(146\) 0.489634 + 0.848071i 0.0405224 + 0.0701868i
\(147\) −3.00851 + 8.04844i −0.248138 + 0.663824i
\(148\) 2.63203 + 1.51960i 0.216351 + 0.124910i
\(149\) −10.0381 + 17.3865i −0.822351 + 1.42435i 0.0815762 + 0.996667i \(0.474005\pi\)
−0.903927 + 0.427687i \(0.859329\pi\)
\(150\) 0 0
\(151\) −1.51960 2.63203i −0.123663 0.214191i 0.797546 0.603258i \(-0.206131\pi\)
−0.921210 + 0.389066i \(0.872798\pi\)
\(152\) 9.81681i 0.796248i
\(153\) 2.61168 + 7.58123i 0.211141 + 0.612906i
\(154\) −2.18319 −0.175926
\(155\) 0 0
\(156\) −10.4465 + 8.61270i −0.836388 + 0.689568i
\(157\) −0.174643 0.100830i −0.0139381 0.00804714i 0.493015 0.870021i \(-0.335895\pi\)
−0.506953 + 0.861974i \(0.669228\pi\)
\(158\) −0.142651 0.0823593i −0.0113487 0.00655216i
\(159\) 0.327176 + 1.95424i 0.0259468 + 0.154982i
\(160\) 0 0
\(161\) −8.45043 −0.665987
\(162\) 1.92705 4.77365i 0.151403 0.375054i
\(163\) 17.8168i 1.39552i −0.716331 0.697760i \(-0.754180\pi\)
0.716331 0.697760i \(-0.245820\pi\)
\(164\) 1.23050 + 2.13129i 0.0960858 + 0.166425i
\(165\) 0 0
\(166\) 1.22522 2.12214i 0.0950952 0.164710i
\(167\) −12.2117 7.05042i −0.944968 0.545578i −0.0534538 0.998570i \(-0.517023\pi\)
−0.891514 + 0.452993i \(0.850356\pi\)
\(168\) 3.30545 + 4.00924i 0.255021 + 0.309319i
\(169\) 4.41764 + 7.65158i 0.339819 + 0.588583i
\(170\) 0 0
\(171\) −13.2541 + 4.56592i −1.01356 + 0.349165i
\(172\) 0.788172i 0.0600976i
\(173\) −3.78140 + 2.18319i −0.287494 + 0.165985i −0.636811 0.771020i \(-0.719747\pi\)
0.349317 + 0.937005i \(0.386414\pi\)
\(174\) −8.80644 3.29186i −0.667615 0.249555i
\(175\) 0 0
\(176\) −2.86525 + 4.96276i −0.215976 + 0.374082i
\(177\) −0.693779 + 1.85601i −0.0521476 + 0.139507i
\(178\) 1.48608 0.857990i 0.111387 0.0643091i
\(179\) 15.1625 1.13330 0.566648 0.823960i \(-0.308240\pi\)
0.566648 + 0.823960i \(0.308240\pi\)
\(180\) 0 0
\(181\) 3.20166 0.237978 0.118989 0.992896i \(-0.462035\pi\)
0.118989 + 0.992896i \(0.462035\pi\)
\(182\) 3.30545 1.90841i 0.245017 0.141460i
\(183\) 2.78632 + 3.37957i 0.205971 + 0.249825i
\(184\) 6.21598 10.7664i 0.458248 0.793709i
\(185\) 0 0
\(186\) 1.13870 + 6.80155i 0.0834938 + 0.498714i
\(187\) 6.18687 3.57199i 0.452429 0.261210i
\(188\) 11.6376i 0.848757i
\(189\) 3.87562 6.32757i 0.281910 0.460263i
\(190\) 0 0
\(191\) 1.41877 + 2.45738i 0.102659 + 0.177810i 0.912779 0.408453i \(-0.133932\pi\)
−0.810121 + 0.586263i \(0.800598\pi\)
\(192\) 2.02121 0.338388i 0.145869 0.0244211i
\(193\) −16.2710 9.39409i −1.17121 0.676201i −0.217249 0.976116i \(-0.569708\pi\)
−0.953966 + 0.299915i \(0.903042\pi\)
\(194\) 2.24086 3.88129i 0.160885 0.278660i
\(195\) 0 0
\(196\) −4.14927 7.18675i −0.296376 0.513339i
\(197\) 5.83528i 0.415747i 0.978156 + 0.207873i \(0.0666542\pi\)
−0.978156 + 0.207873i \(0.933346\pi\)
\(198\) −4.50237 0.874485i −0.319970 0.0621469i
\(199\) −13.0761 −0.926943 −0.463472 0.886112i \(-0.653396\pi\)
−0.463472 + 0.886112i \(0.653396\pi\)
\(200\) 0 0
\(201\) 10.6924 + 3.99684i 0.754186 + 0.281915i
\(202\) 2.08134 + 1.20166i 0.146442 + 0.0845486i
\(203\) −11.7357 6.77563i −0.823687 0.475556i
\(204\) −7.25405 2.71157i −0.507885 0.189848i
\(205\) 0 0
\(206\) −1.03920 −0.0724047
\(207\) −17.4272 3.38485i −1.21128 0.235263i
\(208\) 10.0185i 0.694656i
\(209\) 6.24482 + 10.8163i 0.431963 + 0.748182i
\(210\) 0 0
\(211\) −4.19243 + 7.26149i −0.288618 + 0.499902i −0.973480 0.228771i \(-0.926529\pi\)
0.684862 + 0.728673i \(0.259863\pi\)
\(212\) −1.65730 0.956844i −0.113824 0.0657163i
\(213\) −21.9932 + 3.68206i −1.50695 + 0.252291i
\(214\) 3.40841 + 5.90353i 0.232994 + 0.403557i
\(215\) 0 0
\(216\) 5.21090 + 9.59222i 0.354557 + 0.652668i
\(217\) 9.94006i 0.674776i
\(218\) 8.24879 4.76244i 0.558679 0.322553i
\(219\) 0.489634 + 2.92461i 0.0330864 + 0.197627i
\(220\) 0 0
\(221\) −6.24482 + 10.8163i −0.420072 + 0.727586i
\(222\) −1.14501 1.38880i −0.0768482 0.0932104i
\(223\) −7.93834 + 4.58321i −0.531591 + 0.306914i −0.741664 0.670772i \(-0.765963\pi\)
0.210073 + 0.977686i \(0.432630\pi\)
\(224\) −7.75123 −0.517901
\(225\) 0 0
\(226\) 11.5104 0.765658
\(227\) −2.31473 + 1.33641i −0.153634 + 0.0887008i −0.574846 0.818261i \(-0.694938\pi\)
0.421212 + 0.906962i \(0.361605\pi\)
\(228\) 4.74056 12.6821i 0.313951 0.839890i
\(229\) 1.27365 2.20603i 0.0841654 0.145779i −0.820870 0.571115i \(-0.806511\pi\)
0.905035 + 0.425336i \(0.139844\pi\)
\(230\) 0 0
\(231\) −6.19243 2.31473i −0.407432 0.152298i
\(232\) 17.2652 9.96806i 1.13351 0.654435i
\(233\) 6.22013i 0.407494i 0.979024 + 0.203747i \(0.0653121\pi\)
−0.979024 + 0.203747i \(0.934688\pi\)
\(234\) 7.58123 2.61168i 0.495600 0.170731i
\(235\) 0 0
\(236\) −0.956844 1.65730i −0.0622852 0.107881i
\(237\) −0.317294 0.384851i −0.0206105 0.0249987i
\(238\) 1.89070 + 1.09159i 0.122556 + 0.0707576i
\(239\) 4.06163 7.03494i 0.262725 0.455053i −0.704240 0.709962i \(-0.748712\pi\)
0.966965 + 0.254909i \(0.0820455\pi\)
\(240\) 0 0
\(241\) 13.1821 + 22.8320i 0.849131 + 1.47074i 0.881985 + 0.471278i \(0.156207\pi\)
−0.0328536 + 0.999460i \(0.510460\pi\)
\(242\) 2.20561i 0.141782i
\(243\) 10.5272 11.4969i 0.675319 0.737526i
\(244\) −4.23030 −0.270817
\(245\) 0 0
\(246\) −0.240665 1.43751i −0.0153442 0.0916520i
\(247\) −18.9099 10.9176i −1.20321 0.694673i
\(248\) −12.6643 7.31173i −0.804183 0.464295i
\(249\) 5.72522 4.72021i 0.362821 0.299131i
\(250\) 0 0
\(251\) −0.549569 −0.0346885 −0.0173443 0.999850i \(-0.505521\pi\)
−0.0173443 + 0.999850i \(0.505521\pi\)
\(252\) 2.33415 + 6.77563i 0.147038 + 0.426825i
\(253\) 15.8168i 0.994394i
\(254\) 0.625515 + 1.08342i 0.0392483 + 0.0679801i
\(255\) 0 0
\(256\) 2.11515 3.66355i 0.132197 0.228972i
\(257\) 15.5885 + 9.00000i 0.972381 + 0.561405i 0.899961 0.435970i \(-0.143595\pi\)
0.0724199 + 0.997374i \(0.476928\pi\)
\(258\) −0.163441 + 0.437242i −0.0101754 + 0.0272215i
\(259\) −1.29721 2.24683i −0.0806046 0.139611i
\(260\) 0 0
\(261\) −21.4885 18.6741i −1.33010 1.15590i
\(262\) 3.43196i 0.212027i
\(263\) −10.3016 + 5.94761i −0.635221 + 0.366745i −0.782771 0.622309i \(-0.786195\pi\)
0.147550 + 0.989055i \(0.452861\pi\)
\(264\) 7.50415 6.18687i 0.461849 0.380776i
\(265\) 0 0
\(266\) −1.90841 + 3.30545i −0.117012 + 0.202670i
\(267\) 5.12483 0.857990i 0.313634 0.0525081i
\(268\) −9.54766 + 5.51234i −0.583216 + 0.336720i
\(269\) −28.5737 −1.74217 −0.871084 0.491134i \(-0.836583\pi\)
−0.871084 + 0.491134i \(0.836583\pi\)
\(270\) 0 0
\(271\) −23.3641 −1.41927 −0.709635 0.704570i \(-0.751140\pi\)
−0.709635 + 0.704570i \(0.751140\pi\)
\(272\) 4.96276 2.86525i 0.300911 0.173731i
\(273\) 11.3990 1.90841i 0.689900 0.115502i
\(274\) −2.91764 + 5.05350i −0.176261 + 0.305293i
\(275\) 0 0
\(276\) 13.2294 10.9071i 0.796314 0.656529i
\(277\) −13.0563 + 7.53807i −0.784479 + 0.452919i −0.838015 0.545647i \(-0.816284\pi\)
0.0535366 + 0.998566i \(0.482951\pi\)
\(278\) 4.57595i 0.274447i
\(279\) −3.98153 + 20.4993i −0.238368 + 1.22726i
\(280\) 0 0
\(281\) −3.32605 5.76088i −0.198415 0.343665i 0.749599 0.661892i \(-0.230246\pi\)
−0.948015 + 0.318226i \(0.896913\pi\)
\(282\) 2.41326 6.45600i 0.143707 0.384449i
\(283\) 23.2934 + 13.4485i 1.38465 + 0.799428i 0.992706 0.120562i \(-0.0384696\pi\)
0.391943 + 0.919989i \(0.371803\pi\)
\(284\) 10.7684 18.6514i 0.638985 1.10675i
\(285\) 0 0
\(286\) −3.57199 6.18687i −0.211216 0.365838i
\(287\) 2.10083i 0.124008i
\(288\) −15.9853 3.10478i −0.941943 0.182951i
\(289\) 9.85601 0.579765
\(290\) 0 0
\(291\) 10.4712 8.63306i 0.613830 0.506079i
\(292\) −2.48023 1.43196i −0.145144 0.0837991i
\(293\) 10.7256 + 6.19243i 0.626596 + 0.361765i 0.779433 0.626486i \(-0.215507\pi\)
−0.152837 + 0.988251i \(0.548841\pi\)
\(294\) 0.811528 + 4.84730i 0.0473292 + 0.282701i
\(295\) 0 0
\(296\) 3.81681 0.221848
\(297\) −11.8434 7.25405i −0.687224 0.420923i
\(298\) 11.4834i 0.665217i
\(299\) −13.8260 23.9474i −0.799581 1.38491i
\(300\) 0 0
\(301\) −0.336412 + 0.582682i −0.0193905 + 0.0335853i
\(302\) −1.50550 0.869202i −0.0866319 0.0500169i
\(303\) 4.62947 + 5.61515i 0.265956 + 0.322582i
\(304\) 5.00924 + 8.67625i 0.287299 + 0.497617i
\(305\) 0 0
\(306\) 3.46193 + 3.00851i 0.197905 + 0.171985i
\(307\) 2.49359i 0.142317i −0.997465 0.0711583i \(-0.977330\pi\)
0.997465 0.0711583i \(-0.0226695\pi\)
\(308\) 5.52944 3.19243i 0.315069 0.181905i
\(309\) −2.94761 1.10182i −0.167684 0.0626802i
\(310\) 0 0
\(311\) 12.1101 20.9752i 0.686699 1.18940i −0.286201 0.958170i \(-0.592392\pi\)
0.972900 0.231228i \(-0.0742742\pi\)
\(312\) −5.95348 + 15.9269i −0.337049 + 0.901682i
\(313\) 30.3837 17.5420i 1.71739 0.991534i 0.793770 0.608219i \(-0.208116\pi\)
0.923618 0.383315i \(-0.125218\pi\)
\(314\) −0.115349 −0.00650950
\(315\) 0 0
\(316\) 0.481728 0.0270993
\(317\) −9.06829 + 5.23558i −0.509326 + 0.294060i −0.732557 0.680706i \(-0.761673\pi\)
0.223231 + 0.974766i \(0.428340\pi\)
\(318\) 0.720978 + 0.874485i 0.0404304 + 0.0490387i
\(319\) −12.6821 + 21.9660i −0.710059 + 1.22986i
\(320\) 0 0
\(321\) 3.40841 + 20.3586i 0.190239 + 1.13631i
\(322\) −4.18601 + 2.41679i −0.233277 + 0.134683i
\(323\) 12.4896i 0.694942i
\(324\) 2.09970 + 14.9083i 0.116650 + 0.828238i
\(325\) 0 0
\(326\) −5.09555 8.82575i −0.282216 0.488813i
\(327\) 28.4464 4.76244i 1.57309 0.263364i
\(328\) 2.67659 + 1.54533i 0.147790 + 0.0853267i
\(329\) 4.96721 8.60346i 0.273851 0.474324i
\(330\) 0 0
\(331\) −8.38880 14.5298i −0.461090 0.798632i 0.537925 0.842993i \(-0.319208\pi\)
−0.999016 + 0.0443606i \(0.985875\pi\)
\(332\) 7.16641i 0.393308i
\(333\) −1.77525 5.15322i −0.0972829 0.282395i
\(334\) −8.06558 −0.441329
\(335\) 0 0
\(336\) −4.96721 1.85675i −0.270984 0.101294i
\(337\) 23.5394 + 13.5905i 1.28227 + 0.740320i 0.977263 0.212030i \(-0.0680074\pi\)
0.305008 + 0.952350i \(0.401341\pi\)
\(338\) 4.37665 + 2.52686i 0.238058 + 0.137443i
\(339\) 32.6481 + 12.2039i 1.77320 + 0.662825i
\(340\) 0 0
\(341\) 18.6050 1.00752
\(342\) −5.25970 + 6.05239i −0.284412 + 0.327276i
\(343\) 17.0801i 0.922239i
\(344\) −0.494917 0.857221i −0.0266841 0.0462182i
\(345\) 0 0
\(346\) −1.24877 + 2.16293i −0.0671343 + 0.116280i
\(347\) 20.4086 + 11.7829i 1.09559 + 0.632539i 0.935059 0.354492i \(-0.115346\pi\)
0.160530 + 0.987031i \(0.448680\pi\)
\(348\) 27.1180 4.54005i 1.45368 0.243372i
\(349\) −5.35601 9.27689i −0.286701 0.496580i 0.686319 0.727300i \(-0.259225\pi\)
−0.973020 + 0.230720i \(0.925892\pi\)
\(350\) 0 0
\(351\) 24.2725 + 0.630233i 1.29557 + 0.0336393i
\(352\) 14.5081i 0.773285i
\(353\) −23.6141 + 13.6336i −1.25685 + 0.725644i −0.972461 0.233064i \(-0.925125\pi\)
−0.284392 + 0.958708i \(0.591792\pi\)
\(354\) 0.187143 + 1.11781i 0.00994652 + 0.0594112i
\(355\) 0 0
\(356\) −2.50924 + 4.34612i −0.132989 + 0.230344i
\(357\) 4.20543 + 5.10083i 0.222575 + 0.269965i
\(358\) 7.51089 4.33641i 0.396963 0.229186i
\(359\) 10.6807 0.563707 0.281854 0.959457i \(-0.409051\pi\)
0.281854 + 0.959457i \(0.409051\pi\)
\(360\) 0 0
\(361\) 2.83528 0.149225
\(362\) 1.58598 0.915664i 0.0833571 0.0481262i
\(363\) 2.33851 6.25603i 0.122740 0.328356i
\(364\) −5.58123 + 9.66697i −0.292536 + 0.506687i
\(365\) 0 0
\(366\) 2.34678 + 0.877227i 0.122668 + 0.0458534i
\(367\) −7.33624 + 4.23558i −0.382949 + 0.221096i −0.679100 0.734045i \(-0.737630\pi\)
0.296152 + 0.955141i \(0.404297\pi\)
\(368\) 12.6873i 0.661373i
\(369\) 0.841495 4.33252i 0.0438065 0.225542i
\(370\) 0 0
\(371\) 0.816810 + 1.41476i 0.0424067 + 0.0734505i
\(372\) −12.8298 15.5614i −0.665193 0.806822i
\(373\) 8.76700 + 5.06163i 0.453938 + 0.262081i 0.709492 0.704714i \(-0.248925\pi\)
−0.255554 + 0.966795i \(0.582258\pi\)
\(374\) 2.04316 3.53885i 0.105649 0.182990i
\(375\) 0 0
\(376\) 7.30757 + 12.6571i 0.376859 + 0.652740i
\(377\) 44.3434i 2.28380i
\(378\) 0.110165 4.24284i 0.00566626 0.218228i
\(379\) −11.9216 −0.612371 −0.306186 0.951972i \(-0.599053\pi\)
−0.306186 + 0.951972i \(0.599053\pi\)
\(380\) 0 0
\(381\) 0.625515 + 3.73624i 0.0320461 + 0.191414i
\(382\) 1.40561 + 0.811528i 0.0719171 + 0.0415214i
\(383\) 8.50161 + 4.90841i 0.434412 + 0.250808i 0.701224 0.712941i \(-0.252637\pi\)
−0.266813 + 0.963748i \(0.585970\pi\)
\(384\) 15.4126 12.7070i 0.786519 0.648453i
\(385\) 0 0
\(386\) −10.7467 −0.546993
\(387\) −0.927175 + 1.06691i −0.0471309 + 0.0542341i
\(388\) 13.1070i 0.665409i
\(389\) 4.61007 + 7.98487i 0.233740 + 0.404849i 0.958906 0.283725i \(-0.0915703\pi\)
−0.725166 + 0.688574i \(0.758237\pi\)
\(390\) 0 0
\(391\) 7.90841 13.6978i 0.399945 0.692725i
\(392\) −9.02554 5.21090i −0.455858 0.263190i
\(393\) 3.63875 9.73445i 0.183550 0.491038i
\(394\) 1.66887 + 2.89057i 0.0840765 + 0.145625i
\(395\) 0 0
\(396\) 12.6821 4.36887i 0.637297 0.219544i
\(397\) 22.9793i 1.15330i −0.816993 0.576648i \(-0.804360\pi\)
0.816993 0.576648i \(-0.195640\pi\)
\(398\) −6.47741 + 3.73973i −0.324683 + 0.187456i
\(399\) −8.91764 + 7.35224i −0.446440 + 0.368072i
\(400\) 0 0
\(401\) 5.53279 9.58307i 0.276294 0.478556i −0.694167 0.719814i \(-0.744227\pi\)
0.970461 + 0.241259i \(0.0775602\pi\)
\(402\) 6.43969 1.07812i 0.321183 0.0537718i
\(403\) −28.1688 + 16.2633i −1.40319 + 0.810132i
\(404\) −7.02864 −0.349688
\(405\) 0 0
\(406\) −7.75123 −0.384687
\(407\) −4.20543 + 2.42801i −0.208455 + 0.120352i
\(408\) −9.59222 + 1.60591i −0.474886 + 0.0795046i
\(409\) −8.81681 + 15.2712i −0.435963 + 0.755110i −0.997374 0.0724270i \(-0.976926\pi\)
0.561411 + 0.827537i \(0.310259\pi\)
\(410\) 0 0
\(411\) −13.6336 + 11.2404i −0.672497 + 0.554447i
\(412\) 2.63203 1.51960i 0.129671 0.0748654i
\(413\) 1.63362i 0.0803852i
\(414\) −9.60083 + 3.30741i −0.471855 + 0.162550i
\(415\) 0 0
\(416\) −12.6821 21.9660i −0.621789 1.07697i
\(417\) 4.85166 12.9793i 0.237587 0.635597i
\(418\) 6.18687 + 3.57199i 0.302610 + 0.174712i
\(419\) 18.5173 32.0730i 0.904631 1.56687i 0.0832199 0.996531i \(-0.473480\pi\)
0.821411 0.570336i \(-0.193187\pi\)
\(420\) 0 0
\(421\) −2.52884 4.38007i −0.123248 0.213472i 0.797799 0.602924i \(-0.205998\pi\)
−0.921047 + 0.389452i \(0.872664\pi\)
\(422\) 4.79608i 0.233469i
\(423\) 13.6900 15.7532i 0.665630 0.765947i
\(424\) −2.40332 −0.116716
\(425\) 0 0
\(426\) −9.84150 + 8.11392i −0.476822 + 0.393121i
\(427\) 3.12739 + 1.80560i 0.151345 + 0.0873790i
\(428\) −17.2652 9.96806i −0.834544 0.481824i
\(429\) −3.57199 21.3357i −0.172457 1.03010i
\(430\) 0 0
\(431\) −5.23030 −0.251935 −0.125967 0.992034i \(-0.540203\pi\)
−0.125967 + 0.992034i \(0.540203\pi\)
\(432\) −9.50011 5.81879i −0.457074 0.279957i
\(433\) 34.3434i 1.65044i −0.564813 0.825219i \(-0.691052\pi\)
0.564813 0.825219i \(-0.308948\pi\)
\(434\) 2.84283 + 4.92392i 0.136460 + 0.236356i
\(435\) 0 0
\(436\) −13.9280 + 24.1240i −0.667031 + 1.15533i
\(437\) 23.9474 + 13.8260i 1.14556 + 0.661389i
\(438\) 1.07898 + 1.30871i 0.0515554 + 0.0625324i
\(439\) −9.77365 16.9285i −0.466471 0.807952i 0.532796 0.846244i \(-0.321141\pi\)
−0.999267 + 0.0382924i \(0.987808\pi\)
\(440\) 0 0
\(441\) −2.83754 + 14.6094i −0.135121 + 0.695685i
\(442\) 7.14399i 0.339805i
\(443\) −9.09686 + 5.25208i −0.432205 + 0.249534i −0.700286 0.713863i \(-0.746944\pi\)
0.268081 + 0.963396i \(0.413611\pi\)
\(444\) 4.93083 + 1.84315i 0.234007 + 0.0874719i
\(445\) 0 0
\(446\) −2.62156 + 4.54068i −0.124135 + 0.215007i
\(447\) −12.1753 + 32.5717i −0.575873 + 1.54059i
\(448\) 1.46324 0.844801i 0.0691315 0.0399131i
\(449\) −22.8560 −1.07864 −0.539321 0.842100i \(-0.681319\pi\)
−0.539321 + 0.842100i \(0.681319\pi\)
\(450\) 0 0
\(451\) −3.93216 −0.185158
\(452\) −29.1527 + 16.8313i −1.37123 + 0.791679i
\(453\) −3.34865 4.06163i −0.157333 0.190832i
\(454\) −0.764419 + 1.32401i −0.0358759 + 0.0621390i
\(455\) 0 0
\(456\) −2.80757 16.7698i −0.131477 0.785319i
\(457\) −12.1472 + 7.01319i −0.568222 + 0.328063i −0.756439 0.654064i \(-0.773063\pi\)
0.188217 + 0.982127i \(0.439729\pi\)
\(458\) 1.45704i 0.0680832i
\(459\) 6.62967 + 12.2039i 0.309446 + 0.569629i
\(460\) 0 0
\(461\) 12.0513 + 20.8734i 0.561283 + 0.972171i 0.997385 + 0.0722736i \(0.0230255\pi\)
−0.436102 + 0.899897i \(0.643641\pi\)
\(462\) −3.72949 + 0.624385i −0.173512 + 0.0290490i
\(463\) −29.3930 16.9700i −1.36601 0.788664i −0.375591 0.926785i \(-0.622560\pi\)
−0.990415 + 0.138121i \(0.955894\pi\)
\(464\) −10.1728 + 17.6198i −0.472261 + 0.817981i
\(465\) 0 0
\(466\) 1.77894 + 3.08121i 0.0824077 + 0.142734i
\(467\) 27.3720i 1.26663i −0.773896 0.633313i \(-0.781695\pi\)
0.773896 0.633313i \(-0.218305\pi\)
\(468\) −15.3823 + 17.7005i −0.711045 + 0.818207i
\(469\) 9.41123 0.434570
\(470\) 0 0
\(471\) −0.327176 0.122299i −0.0150755 0.00563523i
\(472\) −2.08134 1.20166i −0.0958013 0.0553109i
\(473\) 1.09062 + 0.629668i 0.0501466 + 0.0289521i
\(474\) −0.267241 0.0998949i −0.0122748 0.00458832i
\(475\) 0 0
\(476\) −6.38485 −0.292649
\(477\) 1.11781 + 3.24482i 0.0511812 + 0.148570i
\(478\) 4.64645i 0.212524i
\(479\) 2.61515 + 4.52957i 0.119489 + 0.206961i 0.919565 0.392937i \(-0.128541\pi\)
−0.800076 + 0.599898i \(0.795208\pi\)
\(480\) 0 0
\(481\) 4.24482 7.35224i 0.193547 0.335233i
\(482\) 13.0597 + 7.54005i 0.594855 + 0.343440i
\(483\) −14.4357 + 2.41679i −0.656846 + 0.109968i
\(484\) 3.22522 + 5.58624i 0.146601 + 0.253920i
\(485\) 0 0
\(486\) 1.92668 8.70585i 0.0873958 0.394905i
\(487\) 24.0185i 1.08838i −0.838962 0.544190i \(-0.816837\pi\)
0.838962 0.544190i \(-0.183163\pi\)
\(488\) −4.60090 + 2.65633i −0.208273 + 0.120246i
\(489\) −5.09555 30.4360i −0.230429 1.37636i
\(490\) 0 0
\(491\) −7.38880 + 12.7978i −0.333452 + 0.577556i −0.983186 0.182606i \(-0.941547\pi\)
0.649734 + 0.760161i \(0.274880\pi\)
\(492\) 2.71157 + 3.28890i 0.122247 + 0.148275i
\(493\) 21.9660 12.6821i 0.989298 0.571171i
\(494\) −12.4896 −0.561935
\(495\) 0 0
\(496\) 14.9239 0.670101
\(497\) −15.9217 + 9.19243i −0.714188 + 0.412337i
\(498\) 1.48608 3.97560i 0.0665929 0.178151i
\(499\) 12.4280 21.5259i 0.556354 0.963633i −0.441443 0.897289i \(-0.645533\pi\)
0.997797 0.0663440i \(-0.0211335\pi\)
\(500\) 0 0
\(501\) −22.8773 8.55155i −1.02208 0.382055i
\(502\) −0.272235 + 0.157175i −0.0121504 + 0.00701506i
\(503\) 38.9154i 1.73515i −0.497305 0.867576i \(-0.665677\pi\)
0.497305 0.867576i \(-0.334323\pi\)
\(504\) 6.79326 + 5.90353i 0.302596 + 0.262964i
\(505\) 0 0
\(506\) 4.52355 + 7.83503i 0.201097 + 0.348309i
\(507\) 9.73487 + 11.8076i 0.432341 + 0.524393i
\(508\) −3.16853 1.82935i −0.140581 0.0811644i
\(509\) 1.01037 1.75001i 0.0447837 0.0775676i −0.842765 0.538282i \(-0.819073\pi\)
0.887548 + 0.460715i \(0.152407\pi\)
\(510\) 0 0
\(511\) 1.22239 + 2.11725i 0.0540755 + 0.0936615i
\(512\) 20.6459i 0.912428i
\(513\) −21.3357 + 11.5905i −0.941996 + 0.511732i
\(514\) 10.2959 0.454132
\(515\) 0 0
\(516\) −0.225415 1.34642i −0.00992333 0.0592726i
\(517\) −16.1032 9.29721i −0.708220 0.408891i
\(518\) −1.28517 0.741995i −0.0564672 0.0326014i
\(519\) −5.83528 + 4.81096i −0.256140 + 0.211178i
\(520\) 0 0
\(521\) −23.0290 −1.00892 −0.504460 0.863435i \(-0.668308\pi\)
−0.504460 + 0.863435i \(0.668308\pi\)
\(522\) −15.9853 3.10478i −0.699657 0.135893i
\(523\) 41.1170i 1.79792i 0.438028 + 0.898961i \(0.355677\pi\)
−0.438028 + 0.898961i \(0.644323\pi\)
\(524\) 5.01847 + 8.69225i 0.219233 + 0.379723i
\(525\) 0 0
\(526\) −3.40199 + 5.89242i −0.148334 + 0.256922i
\(527\) −16.1124 9.30249i −0.701867 0.405223i
\(528\) −3.47530 + 9.29721i −0.151243 + 0.404609i
\(529\) 6.00924 + 10.4083i 0.261271 + 0.452535i
\(530\) 0 0
\(531\) −0.654353 + 3.36900i −0.0283965 + 0.146202i
\(532\) 11.1625i 0.483954i
\(533\) 5.95348 3.43724i 0.257874 0.148883i
\(534\) 2.29326 1.89070i 0.0992389 0.0818185i
\(535\) 0 0
\(536\) −6.92272 + 11.9905i −0.299016 + 0.517911i
\(537\) 25.9017 4.33641i 1.11774 0.187130i
\(538\) −14.1543 + 8.17198i −0.610234 + 0.352319i
\(539\) 13.2593 0.571120
\(540\) 0 0
\(541\) 5.20957 0.223977 0.111988 0.993710i \(-0.464278\pi\)
0.111988 + 0.993710i \(0.464278\pi\)
\(542\) −11.5737 + 6.68206i −0.497132 + 0.287019i
\(543\) 5.46932 0.915664i 0.234711 0.0392949i
\(544\) 7.25405 12.5644i 0.311015 0.538694i
\(545\) 0 0
\(546\) 5.10083 4.20543i 0.218295 0.179976i
\(547\) 34.6764 20.0204i 1.48266 0.856013i 0.482851 0.875702i \(-0.339601\pi\)
0.999806 + 0.0196900i \(0.00626792\pi\)
\(548\) 17.0656i 0.729005i
\(549\) 5.72635 + 4.97636i 0.244394 + 0.212386i
\(550\) 0 0
\(551\) 22.1717 + 38.4025i 0.944546 + 1.63600i
\(552\) 7.53946 20.1697i 0.320901 0.858480i
\(553\) −0.356133 0.205614i −0.0151443 0.00874359i
\(554\) −4.31173 + 7.46813i −0.183188 + 0.317290i
\(555\) 0 0
\(556\) 6.69129 + 11.5897i 0.283774 + 0.491511i
\(557\) 14.4033i 0.610288i −0.952306 0.305144i \(-0.901295\pi\)
0.952306 0.305144i \(-0.0987047\pi\)
\(558\) 3.89044 + 11.2933i 0.164695 + 0.478082i
\(559\) −2.20166 −0.0931203
\(560\) 0 0
\(561\) 9.54731 7.87137i 0.403088 0.332330i
\(562\) −3.29518 1.90248i −0.138999 0.0802511i
\(563\) 25.4335 + 14.6840i 1.07189 + 0.618858i 0.928698 0.370836i \(-0.120929\pi\)
0.143196 + 0.989694i \(0.454262\pi\)
\(564\) 3.32831 + 19.8802i 0.140147 + 0.837107i
\(565\) 0 0
\(566\) 15.3849 0.646674
\(567\) 4.81096 11.9176i 0.202041 0.500494i
\(568\) 27.0471i 1.13487i
\(569\) 23.4033 + 40.5357i 0.981118 + 1.69935i 0.658056 + 0.752969i \(0.271379\pi\)
0.323062 + 0.946378i \(0.395288\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) 18.0938 + 10.4465i 0.756541 + 0.436789i
\(573\) 3.12646 + 3.79213i 0.130610 + 0.158418i
\(574\) −0.600830 1.04067i −0.0250782 0.0434367i
\(575\) 0 0
\(576\) 3.35601 1.15612i 0.139834 0.0481717i
\(577\) 28.2386i 1.17559i 0.809010 + 0.587794i \(0.200004\pi\)
−0.809010 + 0.587794i \(0.799996\pi\)
\(578\) 4.88228 2.81879i 0.203076 0.117246i
\(579\) −30.4821 11.3942i −1.26679 0.473528i
\(580\) 0 0
\(581\) 3.05880 5.29801i 0.126901 0.219798i
\(582\) 2.71798 7.27119i 0.112664 0.301401i
\(583\) 2.64802 1.52884i 0.109670 0.0633180i
\(584\) −3.59668 −0.148832
\(585\) 0 0
\(586\) 7.08405 0.292639
\(587\) 15.6598 9.04118i 0.646348 0.373169i −0.140707 0.990051i \(-0.544938\pi\)
0.787056 + 0.616882i \(0.211604\pi\)
\(588\) −9.14348 11.0903i −0.377071 0.457355i
\(589\) 16.2633 28.1688i 0.670117 1.16068i
\(590\) 0 0
\(591\) 1.66887 + 9.96827i 0.0686482 + 0.410040i
\(592\) −3.37336 + 1.94761i −0.138644 + 0.0800462i
\(593\) 7.73840i 0.317778i 0.987296 + 0.158889i \(0.0507912\pi\)
−0.987296 + 0.158889i \(0.949209\pi\)
\(594\) −7.94139 0.206197i −0.325839 0.00846037i
\(595\) 0 0
\(596\) −16.7919 29.0845i −0.687824 1.19135i
\(597\) −22.3377 + 3.73973i −0.914220 + 0.153057i
\(598\) −13.6978 7.90841i −0.560143 0.323399i
\(599\) −13.9608 + 24.1808i −0.570423 + 0.988001i 0.426100 + 0.904676i \(0.359887\pi\)
−0.996522 + 0.0833249i \(0.973446\pi\)
\(600\) 0 0
\(601\) −19.2201 33.2902i −0.784006 1.35794i −0.929591 0.368592i \(-0.879840\pi\)
0.145586 0.989346i \(-0.453493\pi\)
\(602\) 0.384851i 0.0156853i
\(603\) 19.4087 + 3.76970i 0.790383 + 0.153514i
\(604\) 5.08405 0.206867
\(605\) 0 0
\(606\) 3.89917 + 1.45751i 0.158393 + 0.0592074i
\(607\) 0.554113 + 0.319917i 0.0224907 + 0.0129850i 0.511203 0.859460i \(-0.329200\pi\)
−0.488712 + 0.872445i \(0.662533\pi\)
\(608\) 21.9660 + 12.6821i 0.890838 + 0.514325i
\(609\) −21.9857 8.21826i −0.890905 0.333021i
\(610\) 0 0
\(611\) 32.5081 1.31514
\(612\) −13.1674 2.55748i −0.532261 0.103380i
\(613\) 42.7467i 1.72652i −0.504757 0.863262i \(-0.668418\pi\)
0.504757 0.863262i \(-0.331582\pi\)
\(614\) −0.713157 1.23522i −0.0287807 0.0498496i
\(615\) 0 0
\(616\) 4.00924 6.94420i 0.161537 0.279790i
\(617\) −18.2753 10.5513i −0.735737 0.424778i 0.0847805 0.996400i \(-0.472981\pi\)
−0.820517 + 0.571622i \(0.806314\pi\)
\(618\) −1.77525 + 0.297209i −0.0714109 + 0.0119555i
\(619\) −6.82605 11.8231i −0.274362 0.475209i 0.695612 0.718418i \(-0.255133\pi\)
−0.969974 + 0.243209i \(0.921800\pi\)
\(620\) 0 0
\(621\) −30.7386 0.798123i −1.23350 0.0320276i
\(622\) 13.8538i 0.555485i
\(623\) 3.71007 2.14201i 0.148641 0.0858178i
\(624\) −2.86525 17.1143i −0.114702 0.685121i
\(625\) 0 0
\(626\) 10.0339 17.3793i 0.401036 0.694615i
\(627\) 13.7613 + 16.6913i 0.549574 + 0.666586i
\(628\) 0.292148 0.168672i 0.0116580 0.00673073i
\(629\) 4.85601 0.193622
\(630\) 0 0
\(631\) 33.2593 1.32403 0.662017 0.749489i \(-0.269701\pi\)
0.662017 + 0.749489i \(0.269701\pi\)
\(632\) 0.523930 0.302491i 0.0208408 0.0120325i
\(633\) −5.08506 + 13.6037i −0.202113 + 0.540697i
\(634\) −2.99472 + 5.18700i −0.118935 + 0.206002i
\(635\) 0 0
\(636\) −3.10478 1.16057i −0.123113 0.0460196i
\(637\) −20.0753 + 11.5905i −0.795411 + 0.459231i
\(638\) 14.5081i 0.574381i
\(639\) −36.5173 + 12.5799i −1.44460 + 0.497655i
\(640\) 0 0
\(641\) −13.1429 22.7641i −0.519112 0.899128i −0.999753 0.0222106i \(-0.992930\pi\)
0.480642 0.876917i \(-0.340404\pi\)
\(642\) 7.51089 + 9.11007i 0.296431 + 0.359546i
\(643\) 17.8250 + 10.2913i 0.702950 + 0.405848i 0.808445 0.588571i \(-0.200309\pi\)
−0.105495 + 0.994420i \(0.533643\pi\)
\(644\) 7.06804 12.2422i 0.278520 0.482410i
\(645\) 0 0
\(646\) −3.57199 6.18687i −0.140538 0.243419i
\(647\) 23.2527i 0.914159i 0.889426 + 0.457079i \(0.151104\pi\)
−0.889426 + 0.457079i \(0.848896\pi\)
\(648\) 11.6450 + 14.8959i 0.457458 + 0.585165i
\(649\) 3.05767 0.120024
\(650\) 0 0
\(651\) 2.84283 + 16.9804i 0.111419 + 0.665513i
\(652\) 25.8114 + 14.9022i 1.01085 + 0.583615i
\(653\) 16.2459 + 9.37957i 0.635751 + 0.367051i 0.782976 0.622052i \(-0.213701\pi\)
−0.147225 + 0.989103i \(0.547034\pi\)
\(654\) 12.7292 10.4947i 0.497750 0.410375i
\(655\) 0 0
\(656\) −3.15415 −0.123149
\(657\) 1.67286 + 4.85601i 0.0652645 + 0.189451i
\(658\) 5.68242i 0.221524i
\(659\) −0.140034 0.242545i −0.00545494 0.00944823i 0.863285 0.504717i \(-0.168403\pi\)
−0.868740 + 0.495268i \(0.835070\pi\)
\(660\) 0 0
\(661\) 19.8930 34.4556i 0.773746 1.34017i −0.161750 0.986832i \(-0.551714\pi\)
0.935496 0.353336i \(-0.114953\pi\)
\(662\) −8.31097 4.79834i −0.323015 0.186493i
\(663\) −7.57443 + 20.2633i −0.294167 + 0.786961i
\(664\) 4.50000 + 7.79423i 0.174634 + 0.302475i
\(665\) 0 0
\(666\) −2.35319 2.04499i −0.0911843 0.0792417i
\(667\) 56.1562i 2.17438i
\(668\) 20.4280 11.7941i 0.790382 0.456327i
\(669\) −12.2501 + 10.0997i −0.473616 + 0.390478i
\(670\) 0 0
\(671\) 3.37957 5.85358i 0.130467 0.225975i
\(672\) −13.2412 + 2.21683i −0.510792 + 0.0855159i
\(673\) −29.0368 + 16.7644i −1.11929 + 0.646221i −0.941219 0.337797i \(-0.890318\pi\)
−0.178068 + 0.984018i \(0.556985\pi\)
\(674\) 15.5473 0.598860
\(675\) 0 0
\(676\) −14.7799 −0.568456
\(677\) 23.8048 13.7437i 0.914891 0.528213i 0.0328897 0.999459i \(-0.489529\pi\)
0.882002 + 0.471246i \(0.156196\pi\)
\(678\) 19.6629 3.29193i 0.755148 0.126426i
\(679\) 5.59442 9.68981i 0.214694 0.371861i
\(680\) 0 0
\(681\) −3.57199 + 2.94497i −0.136879 + 0.112851i
\(682\) 9.21618 5.32096i 0.352906 0.203750i
\(683\) 34.5865i 1.32342i 0.749762 + 0.661708i \(0.230168\pi\)
−0.749762 + 0.661708i \(0.769832\pi\)
\(684\) 4.47116 23.0202i 0.170959 0.880201i
\(685\) 0 0
\(686\) 4.88485 + 8.46081i 0.186504 + 0.323035i
\(687\) 1.54483 4.13277i 0.0589391 0.157675i
\(688\) 0.874830 + 0.505083i 0.0333526 + 0.0192561i
\(689\) −2.67282 + 4.62947i −0.101826 + 0.176369i
\(690\) 0 0
\(691\) −20.3641 35.2717i −0.774688 1.34180i −0.934970 0.354727i \(-0.884574\pi\)
0.160282 0.987071i \(-0.448760\pi\)
\(692\) 7.30418i 0.277663i
\(693\) −11.2404 2.18319i −0.426987 0.0829325i
\(694\) 13.4795 0.511674
\(695\) 0 0
\(696\) 26.6429 21.9660i 1.00989 0.832618i
\(697\) 3.40535 + 1.96608i 0.128987 + 0.0744706i
\(698\) −5.30632 3.06360i −0.200847 0.115959i
\(699\) 1.77894 + 10.6257i 0.0672856 + 0.401901i
\(700\) 0 0
\(701\) −19.4712 −0.735416 −0.367708 0.929941i \(-0.619857\pi\)
−0.367708 + 0.929941i \(0.619857\pi\)
\(702\) 12.2039 6.62967i 0.460606 0.250221i
\(703\) 8.48963i 0.320193i
\(704\) −1.58123 2.73877i −0.0595948 0.103221i
\(705\) 0 0
\(706\) −7.79834 + 13.5071i −0.293494 + 0.508347i
\(707\) 5.19615 + 3.00000i 0.195421 + 0.112827i
\(708\) −2.10854 2.55748i −0.0792436 0.0961158i
\(709\) 7.54316 + 13.0651i 0.283289 + 0.490671i 0.972193 0.234182i \(-0.0752410\pi\)
−0.688904 + 0.724853i \(0.741908\pi\)
\(710\) 0 0
\(711\) −0.652092 0.566686i −0.0244553 0.0212524i
\(712\) 6.30249i 0.236196i
\(713\) 35.6729 20.5957i 1.33596 0.771317i
\(714\) 3.54203 + 1.32401i 0.132557 + 0.0495499i
\(715\) 0 0
\(716\) −12.6821 + 21.9660i −0.473951 + 0.820907i
\(717\) 4.92641 13.1792i 0.183980 0.492188i
\(718\) 5.29081 3.05465i 0.197451 0.113999i
\(719\) 3.43196 0.127990 0.0639952 0.997950i \(-0.479616\pi\)
0.0639952 + 0.997950i \(0.479616\pi\)
\(720\) 0 0
\(721\) −2.59442 −0.0966211
\(722\) 1.40449 0.810881i 0.0522696 0.0301779i
\(723\) 29.0485 + 35.2333i 1.08032 + 1.31034i
\(724\) −2.67791 + 4.63827i −0.0995236 + 0.172380i
\(725\) 0 0
\(726\) −0.630798 3.76780i −0.0234111 0.139836i
\(727\) −30.9789 + 17.8857i −1.14895 + 0.663344i −0.948630 0.316388i \(-0.897530\pi\)
−0.200315 + 0.979732i \(0.564197\pi\)
\(728\) 14.0185i 0.519559i
\(729\) 14.6952 22.6506i 0.544268 0.838911i
\(730\) 0 0
\(731\) −0.629668 1.09062i −0.0232891 0.0403379i
\(732\) −7.22652 + 1.20985i −0.267100 + 0.0447174i
\(733\) −19.0526 11.0000i −0.703722 0.406294i 0.105010 0.994471i \(-0.466513\pi\)
−0.808732 + 0.588177i \(0.799846\pi\)
\(734\) −2.42272 + 4.19628i −0.0894244 + 0.154888i
\(735\) 0 0
\(736\) 16.0605 + 27.8176i 0.591998 + 1.02537i
\(737\) 17.6151i 0.648862i
\(738\) −0.822244 2.38683i −0.0302672 0.0878603i
\(739\) −6.08631 −0.223889 −0.111944 0.993714i \(-0.535708\pi\)
−0.111944 + 0.993714i \(0.535708\pi\)
\(740\) 0 0
\(741\) −35.4257 13.2422i −1.30140 0.486463i
\(742\) 0.809231 + 0.467210i 0.0297078 + 0.0171518i
\(743\) −22.0853 12.7509i −0.810231 0.467787i 0.0368054 0.999322i \(-0.488282\pi\)
−0.847036 + 0.531536i \(0.821615\pi\)
\(744\) −23.7252 8.86850i −0.869809 0.325135i
\(745\) 0 0
\(746\) 5.79043 0.212003
\(747\) 8.43028 9.70081i 0.308448 0.354934i
\(748\) 11.9506i 0.436958i
\(749\) 8.50924 + 14.7384i 0.310921 + 0.538530i
\(750\) 0 0
\(751\) 9.19638 15.9286i 0.335581 0.581243i −0.648016 0.761627i \(-0.724401\pi\)
0.983596 + 0.180384i \(0.0577342\pi\)
\(752\) −12.9171 7.45769i −0.471038 0.271954i
\(753\) −0.938816 + 0.157175i −0.0342124 + 0.00572777i
\(754\) −12.6821 21.9660i −0.461853 0.799953i
\(755\) 0 0
\(756\) 5.92518 + 10.9071i 0.215497 + 0.396687i
\(757\) 41.8986i 1.52283i −0.648264 0.761415i \(-0.724505\pi\)
0.648264 0.761415i \(-0.275495\pi\)
\(758\) −5.90549 + 3.40954i −0.214497 + 0.123840i
\(759\) 4.52355 + 27.0195i 0.164195 + 0.980745i
\(760\) 0 0
\(761\) 3.98568 6.90340i 0.144481 0.250248i −0.784698 0.619878i \(-0.787182\pi\)
0.929179 + 0.369630i \(0.120515\pi\)
\(762\) 1.37841 + 1.67189i 0.0499345 + 0.0605663i
\(763\) 20.5935 11.8896i 0.745534 0.430434i
\(764\) −4.74671 −0.171730
\(765\) 0 0
\(766\) 5.61515 0.202884
\(767\) −4.62947 + 2.67282i −0.167160 + 0.0965101i
\(768\) 2.56550 6.86327i 0.0925744 0.247657i
\(769\) 3.01432 5.22095i 0.108699 0.188272i −0.806544 0.591174i \(-0.798665\pi\)
0.915244 + 0.402901i \(0.131998\pi\)
\(770\) 0 0
\(771\) 29.2034 + 10.9162i 1.05173 + 0.393139i
\(772\) 27.2186 15.7147i 0.979618 0.565583i
\(773\) 44.4033i 1.59708i −0.601944 0.798538i \(-0.705607\pi\)
0.601944 0.798538i \(-0.294393\pi\)
\(774\) −0.154153 + 0.793674i −0.00554093 + 0.0285280i
\(775\) 0 0
\(776\) 8.23030 + 14.2553i 0.295451 + 0.511735i
\(777\) −2.85858 3.46721i −0.102551 0.124385i
\(778\) 4.56729 + 2.63693i 0.163745 + 0.0945384i
\(779\) −3.43724 + 5.95348i −0.123152 + 0.213305i
\(780\)