Properties

Label 225.2.k.b.124.3
Level $225$
Weight $2$
Character 225.124
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 124.3
Root \(-0.403293 - 1.50511i\) of defining polynomial
Character \(\chi\) \(=\) 225.124
Dual form 225.2.k.b.49.3

$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 \(-0.398152\pi\)
−0.664805 + 0.747017i \(0.731486\pi\)
\(3\) −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 \(-0.420313\pi\)
−0.715161 + 0.698960i \(0.753647\pi\)
\(8\) 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 −0.994080 0.108653i \(-0.965346\pi\)
0.591136 + 0.806572i \(0.298679\pi\)
\(12\) 1.01450 + 2.71400i 0.292860 + 0.783465i
\(13\) −4.04678 + 2.33641i −1.12238 + 0.648004i −0.942006 0.335595i \(-0.891063\pi\)
−0.180370 + 0.983599i \(0.557729\pi\)
\(14\) 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 \(-0.455032\pi\)
0.927799 + 0.373081i \(0.121699\pi\)
\(24\) 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 −0.0309603 + 0.999521i \(0.509857\pi\)
−0.850130 + 0.526573i \(0.823477\pi\)
\(30\) 0 0
\(31\) −3.48040 6.02823i −0.625098 1.08270i −0.988522 0.151078i \(-0.951726\pi\)
0.363424 0.931624i \(-0.381608\pi\)
\(32\) 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 0.917731 0.397202i \(-0.130019\pi\)
−0.802853 + 0.596177i \(0.796685\pi\)
\(42\) −0.495361 1.32520i −0.0764358 0.204483i
\(43\) 0.408039 + 0.235581i 0.0622254 + 0.0359258i 0.530790 0.847503i \(-0.321895\pi\)
−0.468565 + 0.883429i \(0.655229\pi\)
\(44\) 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 \(-0.502719\pi\)
−0.870265 + 0.492584i \(0.836053\pi\)
\(48\) 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 0.826387 0.563102i \(-0.190392\pi\)
−0.900854 + 0.434121i \(0.857059\pi\)
\(60\) 0 0
\(61\) 1.26442 2.19004i 0.161892 0.280406i −0.773655 0.633607i \(-0.781574\pi\)
0.935547 + 0.353201i \(0.114907\pi\)
\(62\) 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 \(-0.798552\pi\)
0.109051 + 0.994036i \(0.465219\pi\)
\(68\) 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 −0.874012 0.485905i \(-0.838490\pi\)
0.857812 + 0.513964i \(0.171823\pi\)
\(80\) 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 \(-0.408880\pi\)
−0.689600 + 0.724190i \(0.742214\pi\)
\(84\) 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 \(-0.463551\pi\)
−0.803225 + 0.595675i \(0.796885\pi\)
\(98\) 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 −0.742372 0.669988i \(-0.766299\pi\)
0.951413 + 0.307919i \(0.0996326\pi\)
\(102\) −1.68450 + 2.04316i −0.166790 + 0.202303i
\(103\) 1.57340 0.908405i 0.155032 0.0895078i −0.420477 0.907303i \(-0.638137\pi\)
0.575509 + 0.817795i \(0.304804\pi\)
\(104\) −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 −0.658384 + 0.752682i \(0.728760\pi\)
−0.981034 + 0.193836i \(0.937907\pi\)
\(114\) −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 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) −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 \(-0.189801\pi\)
−0.0726153 + 0.997360i \(0.523135\pi\)
\(138\) 5.78226 + 0.968056i 0.492218 + 0.0824064i
\(139\) 4.00000 + 6.92820i 0.339276 + 0.587643i 0.984297 0.176522i \(-0.0564848\pi\)
−0.645021 + 0.764165i \(0.723151\pi\)
\(140\) 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 −0.903927 0.427687i \(-0.859329\pi\)
0.0815762 0.996667i \(-0.474005\pi\)
\(150\) 0 0
\(151\) −1.51960 + 2.63203i −0.123663 + 0.214191i −0.921210 0.389066i \(-0.872798\pi\)
0.797546 + 0.603258i \(0.206131\pi\)
\(152\) 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 \(-0.664105\pi\)
0.506953 + 0.861974i \(0.330772\pi\)
\(158\) 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 \(-0.482977\pi\)
0.891514 + 0.452993i \(0.149644\pi\)
\(168\) −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 \(-0.280253\pi\)
−0.349317 + 0.937005i \(0.613586\pi\)
\(174\) −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 −0.810121 0.586263i \(-0.800598\pi\)
0.912779 + 0.408453i \(0.133932\pi\)
\(192\) −2.02121 0.338388i −0.145869 0.0244211i
\(193\) 16.2710 9.39409i 1.17121 0.676201i 0.217249 0.976116i \(-0.430292\pi\)
0.953966 + 0.299915i \(0.0969584\pi\)
\(194\) 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 0.684862 0.728673i \(-0.259863\pi\)
−0.973480 + 0.228771i \(0.926529\pi\)
\(212\) 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 \(-0.234037\pi\)
−0.210073 + 0.977686i \(0.567370\pi\)
\(224\) −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 \(-0.305062\pi\)
−0.421212 + 0.906962i \(0.638395\pi\)
\(228\) −4.74056 12.6821i −0.313951 0.839890i
\(229\) 1.27365 + 2.20603i 0.0841654 + 0.145779i 0.905035 0.425336i \(-0.139844\pi\)
−0.820870 + 0.571115i \(0.806511\pi\)
\(230\) 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 0.966965 0.254909i \(-0.0820455\pi\)
−0.704240 + 0.709962i \(0.748712\pi\)
\(240\) 0 0
\(241\) 13.1821 22.8320i 0.849131 1.47074i −0.0328536 0.999460i \(-0.510460\pi\)
0.881985 0.471278i \(-0.156207\pi\)
\(242\) 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 \(-0.856405\pi\)
−0.0724199 + 0.997374i \(0.523072\pi\)
\(258\) 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 \(-0.213805\pi\)
−0.147550 + 0.989055i \(0.547139\pi\)
\(264\) 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 \(-0.183716\pi\)
−0.0535366 + 0.998566i \(0.517049\pi\)
\(278\) 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 −0.948015 0.318226i \(-0.896913\pi\)
0.749599 + 0.661892i \(0.230246\pi\)
\(282\) −2.41326 6.45600i −0.143707 0.384449i
\(283\) −23.2934 + 13.4485i −1.38465 + 0.799428i −0.992706 0.120562i \(-0.961530\pi\)
−0.391943 + 0.919989i \(0.628197\pi\)
\(284\) 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 \(-0.784493\pi\)
0.152837 + 0.988251i \(0.451159\pi\)
\(294\) 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 0.972900 + 0.231228i \(0.0742742\pi\)
−0.286201 + 0.958170i \(0.592392\pi\)
\(312\) 5.95348 + 15.9269i 0.337049 + 0.901682i
\(313\) −30.3837 17.5420i −1.71739 0.991534i −0.923618 0.383315i \(-0.874782\pi\)
−0.793770 0.608219i \(-0.791884\pi\)
\(314\) −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 \(-0.238327\pi\)
−0.223231 + 0.974766i \(0.571660\pi\)
\(318\) −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 −0.999016 0.0443606i \(-0.985875\pi\)
0.537925 + 0.842993i \(0.319208\pi\)
\(332\) 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 \(-0.931993\pi\)
−0.305008 + 0.952350i \(0.598659\pi\)
\(338\) −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 \(-0.884654\pi\)
−0.160530 + 0.987031i \(0.551320\pi\)
\(348\) −27.1180 4.54005i −1.45368 0.243372i
\(349\) −5.35601 + 9.27689i −0.286701 + 0.496580i −0.973020 0.230720i \(-0.925892\pi\)
0.686319 + 0.727300i \(0.259225\pi\)
\(350\) 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 \(-0.0748751\pi\)
0.284392 + 0.958708i \(0.408208\pi\)
\(354\) 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 \(-0.262370\pi\)
−0.296152 + 0.955141i \(0.595703\pi\)
\(368\) 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 \(-0.751075\pi\)
0.255554 + 0.966795i \(0.417742\pi\)
\(374\) 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 \(-0.747363\pi\)
0.266813 + 0.963748i \(0.414030\pi\)
\(384\) 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 −0.725166 0.688574i \(-0.758237\pi\)
0.958906 + 0.283725i \(0.0915703\pi\)
\(390\) 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 0.970461 0.241259i \(-0.0775602\pi\)
−0.694167 + 0.719814i \(0.744227\pi\)
\(402\) −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 0.561411 0.827537i \(-0.310259\pi\)
−0.997374 + 0.0724270i \(0.976926\pi\)
\(410\) 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 0.821411 + 0.570336i \(0.193187\pi\)
0.0832199 + 0.996531i \(0.473480\pi\)
\(420\) 0 0
\(421\) −2.52884 + 4.38007i −0.123248 + 0.213472i −0.921047 0.389452i \(-0.872664\pi\)
0.797799 + 0.602924i \(0.205998\pi\)
\(422\) 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 −0.999267 0.0382924i \(-0.987808\pi\)
0.532796 + 0.846244i \(0.321141\pi\)
\(440\) 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 \(-0.253056\pi\)
−0.268081 + 0.963396i \(0.586389\pi\)
\(444\) 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 \(-0.226937\pi\)
−0.188217 + 0.982127i \(0.560271\pi\)
\(458\) 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 −0.436102 0.899897i \(-0.643641\pi\)
0.997385 0.0722736i \(-0.0230255\pi\)
\(462\) 3.72949 + 0.624385i 0.173512 + 0.0290490i
\(463\) 29.3930 16.9700i 1.36601 0.788664i 0.375591 0.926785i \(-0.377440\pi\)
0.990415 + 0.138121i \(0.0441063\pi\)
\(464\) −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 −0.800076 0.599898i \(-0.795208\pi\)
0.919565 + 0.392937i \(0.128541\pi\)
\(480\) 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 0.649734 0.760161i \(-0.274880\pi\)
−0.983186 + 0.182606i \(0.941547\pi\)
\(492\) −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 0.997797 + 0.0663440i \(0.0211335\pi\)
−0.441443 + 0.897289i \(0.645533\pi\)
\(500\) 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 0.887548 0.460715i \(-0.152407\pi\)
−0.842765 + 0.538282i \(0.819073\pi\)
\(510\) 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 \(-0.660399\pi\)
−0.999806 + 0.0196900i \(0.993732\pi\)
\(548\) 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 \(-0.879071\pi\)
−0.143196 + 0.989694i \(0.545738\pi\)
\(564\) 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 0.323062 0.946378i \(-0.395288\pi\)
0.658056 0.752969i \(-0.271379\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) −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 \(-0.455062\pi\)
−0.787056 + 0.616882i \(0.788396\pi\)
\(588\) 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 −0.996522 0.0833249i \(-0.973446\pi\)
0.426100 0.904676i \(-0.359887\pi\)
\(600\) 0 0
\(601\) −19.2201 + 33.2902i −0.784006 + 1.35794i 0.145586 + 0.989346i \(0.453493\pi\)
−0.929591 + 0.368592i \(0.879840\pi\)
\(602\) 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 \(-0.670800\pi\)
0.488712 + 0.872445i \(0.337467\pi\)
\(608\) −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 \(-0.527019\pi\)
0.820517 + 0.571622i \(0.193686\pi\)
\(618\) 1.77525 + 0.297209i 0.0714109 + 0.0119555i
\(619\) −6.82605 + 11.8231i −0.274362 + 0.475209i −0.969974 0.243209i \(-0.921800\pi\)
0.695612 + 0.718418i \(0.255133\pi\)
\(620\) 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 0.480642 + 0.876917i \(0.340404\pi\)
−0.999753 + 0.0222106i \(0.992930\pi\)
\(642\) −7.51089 + 9.11007i −0.296431 + 0.359546i
\(643\) −17.8250 + 10.2913i −0.702950 + 0.405848i −0.808445 0.588571i \(-0.799691\pi\)
0.105495 + 0.994420i \(0.466357\pi\)
\(644\) 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 \(-0.786299\pi\)
0.147225 + 0.989103i \(0.452966\pi\)
\(654\) 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 −0.868740 0.495268i \(-0.835070\pi\)
0.863285 + 0.504717i \(0.168403\pi\)
\(660\) 0 0
\(661\) 19.8930 + 34.4556i 0.773746 + 1.34017i 0.935496 + 0.353336i \(0.114953\pi\)
−0.161750 + 0.986832i \(0.551714\pi\)
\(662\) 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 \(-0.109682\pi\)
0.178068 + 0.984018i \(0.443015\pi\)
\(674\) 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 \(-0.510471\pi\)
−0.882002 + 0.471246i \(0.843804\pi\)
\(678\) −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 0.160282 + 0.987071i \(0.448760\pi\)
−0.934970 + 0.354727i \(0.884574\pi\)
\(692\) 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 −0.688904 0.724853i \(-0.741908\pi\)
0.972193 + 0.234182i \(0.0752410\pi\)
\(710\) 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 \(-0.102470\pi\)
0.200315 + 0.979732i \(0.435803\pi\)
\(728\) 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 \(-0.533487\pi\)
0.808732 + 0.588177i \(0.200154\pi\)
\(734\) −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 \(-0.511718\pi\)
0.847036 + 0.531536i \(0.178385\pi\)
\(744\) −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 0.983596 0.180384i \(-0.0577342\pi\)
−0.648016 + 0.761627i \(0.724401\pi\)
\(752\) 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 0.929179 0.369630i \(-0.120515\pi\)
−0.784698 + 0.619878i \(0.787182\pi\)
\(762\) −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 0.915244 0.402901i \(-0.131998\pi\)
−0.806544 + 0.591174i \(0.798665\pi\)
\(770\) 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