Properties

Label 432.2.be.a.335.4
Level $432$
Weight $2$
Character 432.335
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 335.4
Character \(\chi\) \(=\) 432.335
Dual form 432.2.be.a.383.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.265485 - 1.71158i) q^{3} +(0.601308 - 1.65208i) q^{5} +(-3.31695 - 0.584867i) q^{7} +(-2.85904 - 0.908799i) q^{9} +O(q^{10})\) \(q+(0.265485 - 1.71158i) q^{3} +(0.601308 - 1.65208i) q^{5} +(-3.31695 - 0.584867i) q^{7} +(-2.85904 - 0.908799i) q^{9} +(-1.91444 + 0.696801i) q^{11} +(3.10802 - 2.60794i) q^{13} +(-2.66804 - 1.46779i) q^{15} +(-2.93090 + 1.69216i) q^{17} +(-2.04178 - 1.17882i) q^{19} +(-1.88165 + 5.52196i) q^{21} +(-0.695477 - 3.94425i) q^{23} +(1.46242 + 1.22712i) q^{25} +(-2.31452 + 4.65220i) q^{27} +(1.89297 - 2.25596i) q^{29} +(4.69332 - 0.827559i) q^{31} +(0.684376 + 3.46172i) q^{33} +(-2.96076 + 5.12818i) q^{35} +(4.41679 + 7.65010i) q^{37} +(-3.63857 - 6.01200i) q^{39} +(-6.67751 - 7.95795i) q^{41} +(-1.29292 - 3.55227i) q^{43} +(-3.22057 + 4.17689i) q^{45} +(2.19570 - 12.4524i) q^{47} +(4.08223 + 1.48581i) q^{49} +(2.11816 + 5.46573i) q^{51} -10.0071i q^{53} +3.58181i q^{55} +(-2.55971 + 3.18171i) q^{57} +(-6.19943 - 2.25641i) q^{59} +(-0.0727139 + 0.412381i) q^{61} +(8.95174 + 4.68660i) q^{63} +(-2.43965 - 6.70287i) q^{65} +(7.81114 + 9.30896i) q^{67} +(-6.93555 + 0.143229i) q^{69} +(7.57186 + 13.1148i) q^{71} +(5.87873 - 10.1823i) q^{73} +(2.48857 - 2.17728i) q^{75} +(6.75765 - 1.19156i) q^{77} +(5.00952 - 5.97012i) q^{79} +(7.34817 + 5.19658i) q^{81} +(12.5809 + 10.5566i) q^{83} +(1.03320 + 5.85959i) q^{85} +(-3.35870 - 3.83890i) q^{87} +(-2.81064 - 1.62273i) q^{89} +(-11.8344 + 6.83262i) q^{91} +(-0.170430 - 8.25272i) q^{93} +(-3.17524 + 2.66435i) q^{95} +(10.7401 - 3.90906i) q^{97} +(6.10672 - 0.252332i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 6 q^{5} - 12 q^{9} + O(q^{10}) \) \( 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.265485 1.71158i 0.153278 0.988183i
\(4\) 0 0
\(5\) 0.601308 1.65208i 0.268913 0.738833i −0.729577 0.683899i \(-0.760283\pi\)
0.998490 0.0549340i \(-0.0174948\pi\)
\(6\) 0 0
\(7\) −3.31695 0.584867i −1.25369 0.221059i −0.492916 0.870077i \(-0.664069\pi\)
−0.760773 + 0.649018i \(0.775180\pi\)
\(8\) 0 0
\(9\) −2.85904 0.908799i −0.953012 0.302933i
\(10\) 0 0
\(11\) −1.91444 + 0.696801i −0.577227 + 0.210093i −0.614102 0.789227i \(-0.710482\pi\)
0.0368755 + 0.999320i \(0.488260\pi\)
\(12\) 0 0
\(13\) 3.10802 2.60794i 0.862010 0.723312i −0.100390 0.994948i \(-0.532009\pi\)
0.962400 + 0.271636i \(0.0875647\pi\)
\(14\) 0 0
\(15\) −2.66804 1.46779i −0.688884 0.378982i
\(16\) 0 0
\(17\) −2.93090 + 1.69216i −0.710848 + 0.410408i −0.811375 0.584526i \(-0.801280\pi\)
0.100527 + 0.994934i \(0.467947\pi\)
\(18\) 0 0
\(19\) −2.04178 1.17882i −0.468416 0.270440i 0.247160 0.968975i \(-0.420503\pi\)
−0.715576 + 0.698534i \(0.753836\pi\)
\(20\) 0 0
\(21\) −1.88165 + 5.52196i −0.410610 + 1.20499i
\(22\) 0 0
\(23\) −0.695477 3.94425i −0.145017 0.822433i −0.967353 0.253431i \(-0.918441\pi\)
0.822336 0.569002i \(-0.192670\pi\)
\(24\) 0 0
\(25\) 1.46242 + 1.22712i 0.292485 + 0.245424i
\(26\) 0 0
\(27\) −2.31452 + 4.65220i −0.445429 + 0.895317i
\(28\) 0 0
\(29\) 1.89297 2.25596i 0.351516 0.418921i −0.561094 0.827752i \(-0.689619\pi\)
0.912610 + 0.408832i \(0.134064\pi\)
\(30\) 0 0
\(31\) 4.69332 0.827559i 0.842946 0.148634i 0.264531 0.964377i \(-0.414783\pi\)
0.578414 + 0.815743i \(0.303672\pi\)
\(32\) 0 0
\(33\) 0.684376 + 3.46172i 0.119135 + 0.602608i
\(34\) 0 0
\(35\) −2.96076 + 5.12818i −0.500459 + 0.866821i
\(36\) 0 0
\(37\) 4.41679 + 7.65010i 0.726115 + 1.25767i 0.958513 + 0.285047i \(0.0920093\pi\)
−0.232398 + 0.972621i \(0.574657\pi\)
\(38\) 0 0
\(39\) −3.63857 6.01200i −0.582638 0.962691i
\(40\) 0 0
\(41\) −6.67751 7.95795i −1.04285 1.24282i −0.969390 0.245525i \(-0.921040\pi\)
−0.0734622 0.997298i \(-0.523405\pi\)
\(42\) 0 0
\(43\) −1.29292 3.55227i −0.197169 0.541717i 0.801226 0.598362i \(-0.204182\pi\)
−0.998394 + 0.0566457i \(0.981959\pi\)
\(44\) 0 0
\(45\) −3.22057 + 4.17689i −0.480094 + 0.622654i
\(46\) 0 0
\(47\) 2.19570 12.4524i 0.320276 1.81637i −0.220706 0.975340i \(-0.570836\pi\)
0.540982 0.841034i \(-0.318053\pi\)
\(48\) 0 0
\(49\) 4.08223 + 1.48581i 0.583175 + 0.212258i
\(50\) 0 0
\(51\) 2.11816 + 5.46573i 0.296601 + 0.765355i
\(52\) 0 0
\(53\) 10.0071i 1.37457i −0.726386 0.687287i \(-0.758801\pi\)
0.726386 0.687287i \(-0.241199\pi\)
\(54\) 0 0
\(55\) 3.58181i 0.482971i
\(56\) 0 0
\(57\) −2.55971 + 3.18171i −0.339042 + 0.421428i
\(58\) 0 0
\(59\) −6.19943 2.25641i −0.807097 0.293759i −0.0946731 0.995508i \(-0.530181\pi\)
−0.712424 + 0.701749i \(0.752403\pi\)
\(60\) 0 0
\(61\) −0.0727139 + 0.412381i −0.00931006 + 0.0528000i −0.989109 0.147186i \(-0.952978\pi\)
0.979799 + 0.199986i \(0.0640896\pi\)
\(62\) 0 0
\(63\) 8.95174 + 4.68660i 1.12781 + 0.590456i
\(64\) 0 0
\(65\) −2.43965 6.70287i −0.302601 0.831389i
\(66\) 0 0
\(67\) 7.81114 + 9.30896i 0.954283 + 1.13727i 0.990443 + 0.137924i \(0.0440430\pi\)
−0.0361600 + 0.999346i \(0.511513\pi\)
\(68\) 0 0
\(69\) −6.93555 + 0.143229i −0.834942 + 0.0172427i
\(70\) 0 0
\(71\) 7.57186 + 13.1148i 0.898615 + 1.55645i 0.829266 + 0.558854i \(0.188759\pi\)
0.0693485 + 0.997592i \(0.477908\pi\)
\(72\) 0 0
\(73\) 5.87873 10.1823i 0.688054 1.19174i −0.284413 0.958702i \(-0.591799\pi\)
0.972467 0.233042i \(-0.0748681\pi\)
\(74\) 0 0
\(75\) 2.48857 2.17728i 0.287355 0.251410i
\(76\) 0 0
\(77\) 6.75765 1.19156i 0.770106 0.135790i
\(78\) 0 0
\(79\) 5.00952 5.97012i 0.563615 0.671691i −0.406692 0.913565i \(-0.633318\pi\)
0.970308 + 0.241875i \(0.0777623\pi\)
\(80\) 0 0
\(81\) 7.34817 + 5.19658i 0.816463 + 0.577398i
\(82\) 0 0
\(83\) 12.5809 + 10.5566i 1.38093 + 1.15874i 0.968866 + 0.247587i \(0.0796374\pi\)
0.412067 + 0.911154i \(0.364807\pi\)
\(84\) 0 0
\(85\) 1.03320 + 5.85959i 0.112067 + 0.635562i
\(86\) 0 0
\(87\) −3.35870 3.83890i −0.360091 0.411574i
\(88\) 0 0
\(89\) −2.81064 1.62273i −0.297928 0.172009i 0.343584 0.939122i \(-0.388359\pi\)
−0.641512 + 0.767113i \(0.721692\pi\)
\(90\) 0 0
\(91\) −11.8344 + 6.83262i −1.24059 + 0.716253i
\(92\) 0 0
\(93\) −0.170430 8.25272i −0.0176728 0.855767i
\(94\) 0 0
\(95\) −3.17524 + 2.66435i −0.325773 + 0.273356i
\(96\) 0 0
\(97\) 10.7401 3.90906i 1.09049 0.396905i 0.266686 0.963783i \(-0.414071\pi\)
0.823802 + 0.566878i \(0.191849\pi\)
\(98\) 0 0
\(99\) 6.10672 0.252332i 0.613748 0.0253603i
\(100\) 0 0
\(101\) −5.82407 1.02694i −0.579516 0.102184i −0.123796 0.992308i \(-0.539507\pi\)
−0.455720 + 0.890123i \(0.650618\pi\)
\(102\) 0 0
\(103\) 1.09855 3.01824i 0.108243 0.297396i −0.873731 0.486409i \(-0.838307\pi\)
0.981975 + 0.189013i \(0.0605288\pi\)
\(104\) 0 0
\(105\) 7.99127 + 6.42904i 0.779868 + 0.627410i
\(106\) 0 0
\(107\) 2.38343 0.230415 0.115208 0.993341i \(-0.463247\pi\)
0.115208 + 0.993341i \(0.463247\pi\)
\(108\) 0 0
\(109\) −4.67235 −0.447530 −0.223765 0.974643i \(-0.571835\pi\)
−0.223765 + 0.974643i \(0.571835\pi\)
\(110\) 0 0
\(111\) 14.2664 5.52871i 1.35410 0.524762i
\(112\) 0 0
\(113\) −5.25158 + 14.4286i −0.494027 + 1.35733i 0.402938 + 0.915227i \(0.367989\pi\)
−0.896965 + 0.442101i \(0.854233\pi\)
\(114\) 0 0
\(115\) −6.93441 1.22272i −0.646637 0.114020i
\(116\) 0 0
\(117\) −11.2560 + 4.63162i −1.04062 + 0.428194i
\(118\) 0 0
\(119\) 10.7113 3.89861i 0.981907 0.357385i
\(120\) 0 0
\(121\) −5.24692 + 4.40269i −0.476993 + 0.400245i
\(122\) 0 0
\(123\) −15.3935 + 9.31641i −1.38798 + 0.840032i
\(124\) 0 0
\(125\) 10.5195 6.07343i 0.940892 0.543224i
\(126\) 0 0
\(127\) 7.33037 + 4.23219i 0.650465 + 0.375546i 0.788634 0.614863i \(-0.210789\pi\)
−0.138169 + 0.990409i \(0.544122\pi\)
\(128\) 0 0
\(129\) −6.42326 + 1.26987i −0.565537 + 0.111806i
\(130\) 0 0
\(131\) −0.590649 3.34974i −0.0516053 0.292668i 0.948072 0.318054i \(-0.103029\pi\)
−0.999678 + 0.0253865i \(0.991918\pi\)
\(132\) 0 0
\(133\) 6.08302 + 5.10426i 0.527464 + 0.442595i
\(134\) 0 0
\(135\) 6.29408 + 6.62118i 0.541708 + 0.569860i
\(136\) 0 0
\(137\) −3.87409 + 4.61696i −0.330986 + 0.394454i −0.905713 0.423891i \(-0.860664\pi\)
0.574727 + 0.818345i \(0.305108\pi\)
\(138\) 0 0
\(139\) 18.5190 3.26539i 1.57076 0.276967i 0.680612 0.732644i \(-0.261714\pi\)
0.890145 + 0.455677i \(0.150603\pi\)
\(140\) 0 0
\(141\) −20.7305 7.06406i −1.74582 0.594901i
\(142\) 0 0
\(143\) −4.13292 + 7.15842i −0.345612 + 0.598617i
\(144\) 0 0
\(145\) −2.58876 4.48387i −0.214985 0.372365i
\(146\) 0 0
\(147\) 3.62686 6.59261i 0.299138 0.543749i
\(148\) 0 0
\(149\) −0.977398 1.16482i −0.0800716 0.0954256i 0.724521 0.689252i \(-0.242061\pi\)
−0.804593 + 0.593827i \(0.797616\pi\)
\(150\) 0 0
\(151\) −5.98184 16.4350i −0.486795 1.33746i −0.903567 0.428447i \(-0.859061\pi\)
0.416771 0.909011i \(-0.363162\pi\)
\(152\) 0 0
\(153\) 9.91738 2.17433i 0.801773 0.175785i
\(154\) 0 0
\(155\) 1.45494 8.25137i 0.116863 0.662766i
\(156\) 0 0
\(157\) 2.00637 + 0.730259i 0.160126 + 0.0582810i 0.420839 0.907135i \(-0.361736\pi\)
−0.260714 + 0.965416i \(0.583958\pi\)
\(158\) 0 0
\(159\) −17.1279 2.65672i −1.35833 0.210692i
\(160\) 0 0
\(161\) 13.4896i 1.06313i
\(162\) 0 0
\(163\) 23.0331i 1.80409i 0.431640 + 0.902046i \(0.357935\pi\)
−0.431640 + 0.902046i \(0.642065\pi\)
\(164\) 0 0
\(165\) 6.13056 + 0.950916i 0.477264 + 0.0740287i
\(166\) 0 0
\(167\) −22.1988 8.07970i −1.71779 0.625226i −0.720150 0.693819i \(-0.755927\pi\)
−0.997645 + 0.0685925i \(0.978149\pi\)
\(168\) 0 0
\(169\) 0.601020 3.40855i 0.0462323 0.262196i
\(170\) 0 0
\(171\) 4.76620 + 5.22586i 0.364481 + 0.399631i
\(172\) 0 0
\(173\) 1.26759 + 3.48267i 0.0963728 + 0.264782i 0.978506 0.206218i \(-0.0661155\pi\)
−0.882133 + 0.471000i \(0.843893\pi\)
\(174\) 0 0
\(175\) −4.13308 4.92561i −0.312432 0.372341i
\(176\) 0 0
\(177\) −5.50789 + 10.0118i −0.413998 + 0.752533i
\(178\) 0 0
\(179\) −4.88951 8.46888i −0.365459 0.632994i 0.623391 0.781911i \(-0.285755\pi\)
−0.988850 + 0.148917i \(0.952421\pi\)
\(180\) 0 0
\(181\) −2.23147 + 3.86501i −0.165864 + 0.287284i −0.936962 0.349432i \(-0.886374\pi\)
0.771098 + 0.636716i \(0.219708\pi\)
\(182\) 0 0
\(183\) 0.686520 + 0.233937i 0.0507490 + 0.0172931i
\(184\) 0 0
\(185\) 15.2944 2.69682i 1.12447 0.198274i
\(186\) 0 0
\(187\) 4.43195 5.28179i 0.324096 0.386243i
\(188\) 0 0
\(189\) 10.3981 14.0774i 0.756347 1.02398i
\(190\) 0 0
\(191\) −1.11424 0.934959i −0.0806236 0.0676513i 0.601585 0.798809i \(-0.294536\pi\)
−0.682209 + 0.731157i \(0.738980\pi\)
\(192\) 0 0
\(193\) −2.89413 16.4134i −0.208324 1.18146i −0.892122 0.451794i \(-0.850784\pi\)
0.683798 0.729671i \(-0.260327\pi\)
\(194\) 0 0
\(195\) −12.1202 + 2.39615i −0.867947 + 0.171592i
\(196\) 0 0
\(197\) 0.492249 + 0.284200i 0.0350713 + 0.0202484i 0.517433 0.855724i \(-0.326888\pi\)
−0.482362 + 0.875972i \(0.660221\pi\)
\(198\) 0 0
\(199\) −13.9651 + 8.06276i −0.989960 + 0.571554i −0.905262 0.424853i \(-0.860326\pi\)
−0.0846975 + 0.996407i \(0.526992\pi\)
\(200\) 0 0
\(201\) 18.0068 10.8980i 1.27010 0.768688i
\(202\) 0 0
\(203\) −7.59833 + 6.37575i −0.533298 + 0.447490i
\(204\) 0 0
\(205\) −17.1624 + 6.24661i −1.19868 + 0.436282i
\(206\) 0 0
\(207\) −1.59614 + 11.9088i −0.110939 + 0.827719i
\(208\) 0 0
\(209\) 4.73027 + 0.834075i 0.327200 + 0.0576942i
\(210\) 0 0
\(211\) 2.10308 5.77817i 0.144782 0.397786i −0.846012 0.533164i \(-0.821003\pi\)
0.990794 + 0.135378i \(0.0432250\pi\)
\(212\) 0 0
\(213\) 24.4574 9.47808i 1.67579 0.649427i
\(214\) 0 0
\(215\) −6.64609 −0.453259
\(216\) 0 0
\(217\) −16.0515 −1.08965
\(218\) 0 0
\(219\) −15.8671 12.7652i −1.07220 0.862591i
\(220\) 0 0
\(221\) −4.69626 + 12.9029i −0.315905 + 0.867941i
\(222\) 0 0
\(223\) 6.78099 + 1.19567i 0.454088 + 0.0800680i 0.396015 0.918244i \(-0.370393\pi\)
0.0580739 + 0.998312i \(0.481504\pi\)
\(224\) 0 0
\(225\) −3.06592 4.83743i −0.204394 0.322495i
\(226\) 0 0
\(227\) 19.2009 6.98854i 1.27441 0.463846i 0.385827 0.922571i \(-0.373916\pi\)
0.888578 + 0.458725i \(0.151694\pi\)
\(228\) 0 0
\(229\) −3.69275 + 3.09858i −0.244024 + 0.204760i −0.756594 0.653885i \(-0.773138\pi\)
0.512570 + 0.858645i \(0.328693\pi\)
\(230\) 0 0
\(231\) −0.245393 11.8826i −0.0161456 0.781819i
\(232\) 0 0
\(233\) −5.70605 + 3.29439i −0.373816 + 0.215823i −0.675124 0.737704i \(-0.735910\pi\)
0.301308 + 0.953527i \(0.402577\pi\)
\(234\) 0 0
\(235\) −19.2521 11.1152i −1.25587 0.725077i
\(236\) 0 0
\(237\) −8.88840 10.1592i −0.577364 0.659910i
\(238\) 0 0
\(239\) −1.78098 10.1005i −0.115202 0.653344i −0.986650 0.162856i \(-0.947930\pi\)
0.871448 0.490488i \(-0.163182\pi\)
\(240\) 0 0
\(241\) −16.6341 13.9577i −1.07150 0.899092i −0.0763084 0.997084i \(-0.524313\pi\)
−0.995187 + 0.0979927i \(0.968758\pi\)
\(242\) 0 0
\(243\) 10.8452 11.1974i 0.695720 0.718313i
\(244\) 0 0
\(245\) 4.90935 5.85074i 0.313647 0.373790i
\(246\) 0 0
\(247\) −9.42018 + 1.66103i −0.599392 + 0.105689i
\(248\) 0 0
\(249\) 21.4086 18.7306i 1.35671 1.18701i
\(250\) 0 0
\(251\) −7.00303 + 12.1296i −0.442027 + 0.765614i −0.997840 0.0656939i \(-0.979074\pi\)
0.555813 + 0.831308i \(0.312407\pi\)
\(252\) 0 0
\(253\) 4.07981 + 7.06644i 0.256495 + 0.444263i
\(254\) 0 0
\(255\) 10.3035 0.212781i 0.645229 0.0133249i
\(256\) 0 0
\(257\) −16.2302 19.3424i −1.01241 1.20655i −0.978313 0.207130i \(-0.933588\pi\)
−0.0341011 0.999418i \(-0.510857\pi\)
\(258\) 0 0
\(259\) −10.1760 27.9582i −0.632303 1.73724i
\(260\) 0 0
\(261\) −7.46229 + 4.72953i −0.461904 + 0.292750i
\(262\) 0 0
\(263\) 0.542765 3.07817i 0.0334683 0.189808i −0.963490 0.267744i \(-0.913722\pi\)
0.996958 + 0.0779359i \(0.0248330\pi\)
\(264\) 0 0
\(265\) −16.5325 6.01732i −1.01558 0.369641i
\(266\) 0 0
\(267\) −3.52362 + 4.37984i −0.215642 + 0.268042i
\(268\) 0 0
\(269\) 21.1146i 1.28738i 0.765287 + 0.643689i \(0.222597\pi\)
−0.765287 + 0.643689i \(0.777403\pi\)
\(270\) 0 0
\(271\) 1.60064i 0.0972320i −0.998818 0.0486160i \(-0.984519\pi\)
0.998818 0.0486160i \(-0.0154811\pi\)
\(272\) 0 0
\(273\) 8.55273 + 22.0696i 0.517635 + 1.33571i
\(274\) 0 0
\(275\) −3.65479 1.33023i −0.220392 0.0802161i
\(276\) 0 0
\(277\) −1.63119 + 9.25096i −0.0980090 + 0.555836i 0.895775 + 0.444508i \(0.146622\pi\)
−0.993784 + 0.111328i \(0.964490\pi\)
\(278\) 0 0
\(279\) −14.1705 1.89927i −0.848363 0.113706i
\(280\) 0 0
\(281\) 8.00459 + 21.9924i 0.477514 + 1.31196i 0.911597 + 0.411085i \(0.134850\pi\)
−0.434083 + 0.900873i \(0.642928\pi\)
\(282\) 0 0
\(283\) 12.4967 + 14.8930i 0.742853 + 0.885297i 0.996635 0.0819641i \(-0.0261193\pi\)
−0.253783 + 0.967261i \(0.581675\pi\)
\(284\) 0 0
\(285\) 3.71727 + 6.14204i 0.220192 + 0.363823i
\(286\) 0 0
\(287\) 17.4946 + 30.3016i 1.03267 + 1.78865i
\(288\) 0 0
\(289\) −2.77321 + 4.80334i −0.163130 + 0.282549i
\(290\) 0 0
\(291\) −3.83936 19.4203i −0.225067 1.13844i
\(292\) 0 0
\(293\) 31.0155 5.46886i 1.81194 0.319494i 0.837894 0.545833i \(-0.183787\pi\)
0.974049 + 0.226339i \(0.0726756\pi\)
\(294\) 0 0
\(295\) −7.45554 + 8.88516i −0.434078 + 0.517314i
\(296\) 0 0
\(297\) 1.18935 10.5191i 0.0690133 0.610383i
\(298\) 0 0
\(299\) −12.4479 10.4450i −0.719882 0.604052i
\(300\) 0 0
\(301\) 2.21095 + 12.5389i 0.127437 + 0.722730i
\(302\) 0 0
\(303\) −3.30390 + 9.69574i −0.189804 + 0.557006i
\(304\) 0 0
\(305\) 0.637563 + 0.368097i 0.0365068 + 0.0210772i
\(306\) 0 0
\(307\) −1.54525 + 0.892151i −0.0881921 + 0.0509177i −0.543447 0.839443i \(-0.682881\pi\)
0.455255 + 0.890361i \(0.349548\pi\)
\(308\) 0 0
\(309\) −4.87431 2.68155i −0.277290 0.152548i
\(310\) 0 0
\(311\) −8.43637 + 7.07896i −0.478383 + 0.401411i −0.849841 0.527039i \(-0.823302\pi\)
0.371458 + 0.928450i \(0.378858\pi\)
\(312\) 0 0
\(313\) −18.0684 + 6.57635i −1.02129 + 0.371718i −0.797757 0.602980i \(-0.793980\pi\)
−0.223529 + 0.974697i \(0.571758\pi\)
\(314\) 0 0
\(315\) 13.1254 11.9709i 0.739532 0.674485i
\(316\) 0 0
\(317\) 21.7504 + 3.83518i 1.22162 + 0.215405i 0.747024 0.664797i \(-0.231482\pi\)
0.474600 + 0.880202i \(0.342593\pi\)
\(318\) 0 0
\(319\) −2.05204 + 5.63793i −0.114892 + 0.315663i
\(320\) 0 0
\(321\) 0.632766 4.07945i 0.0353176 0.227693i
\(322\) 0 0
\(323\) 7.97900 0.443963
\(324\) 0 0
\(325\) 7.74549 0.429643
\(326\) 0 0
\(327\) −1.24044 + 7.99712i −0.0685964 + 0.442242i
\(328\) 0 0
\(329\) −14.5661 + 40.0199i −0.803052 + 2.20637i
\(330\) 0 0
\(331\) −13.3244 2.34946i −0.732377 0.129138i −0.204991 0.978764i \(-0.565717\pi\)
−0.527386 + 0.849626i \(0.676828\pi\)
\(332\) 0 0
\(333\) −5.67534 25.8859i −0.311007 1.41854i
\(334\) 0 0
\(335\) 20.0760 7.30708i 1.09687 0.399229i
\(336\) 0 0
\(337\) 10.8570 9.11008i 0.591417 0.496258i −0.297257 0.954798i \(-0.596072\pi\)
0.888674 + 0.458540i \(0.151627\pi\)
\(338\) 0 0
\(339\) 23.3015 + 12.8191i 1.26557 + 0.696238i
\(340\) 0 0
\(341\) −8.40846 + 4.85463i −0.455344 + 0.262893i
\(342\) 0 0
\(343\) 7.74659 + 4.47250i 0.418277 + 0.241492i
\(344\) 0 0
\(345\) −3.93378 + 11.5442i −0.211787 + 0.621519i
\(346\) 0 0
\(347\) −2.54597 14.4389i −0.136675 0.775121i −0.973679 0.227924i \(-0.926806\pi\)
0.837004 0.547196i \(-0.184305\pi\)
\(348\) 0 0
\(349\) −8.88139 7.45237i −0.475410 0.398916i 0.373354 0.927689i \(-0.378208\pi\)
−0.848763 + 0.528773i \(0.822652\pi\)
\(350\) 0 0
\(351\) 4.93910 + 20.4953i 0.263630 + 1.09396i
\(352\) 0 0
\(353\) −12.3110 + 14.6717i −0.655249 + 0.780895i −0.986696 0.162579i \(-0.948019\pi\)
0.331447 + 0.943474i \(0.392463\pi\)
\(354\) 0 0
\(355\) 26.2198 4.62326i 1.39160 0.245377i
\(356\) 0 0
\(357\) −3.82909 19.3684i −0.202657 1.02508i
\(358\) 0 0
\(359\) 1.56411 2.70911i 0.0825504 0.142982i −0.821794 0.569784i \(-0.807027\pi\)
0.904345 + 0.426803i \(0.140360\pi\)
\(360\) 0 0
\(361\) −6.72076 11.6407i −0.353724 0.612668i
\(362\) 0 0
\(363\) 6.14259 + 10.1494i 0.322403 + 0.532705i
\(364\) 0 0
\(365\) −13.2870 15.8348i −0.695473 0.828833i
\(366\) 0 0
\(367\) 11.9355 + 32.7926i 0.623030 + 1.71176i 0.699446 + 0.714686i \(0.253430\pi\)
−0.0764152 + 0.997076i \(0.524347\pi\)
\(368\) 0 0
\(369\) 11.8591 + 28.8206i 0.617358 + 1.50034i
\(370\) 0 0
\(371\) −5.85280 + 33.1929i −0.303862 + 1.72329i
\(372\) 0 0
\(373\) −17.5314 6.38090i −0.907740 0.330391i −0.154390 0.988010i \(-0.549341\pi\)
−0.753350 + 0.657619i \(0.771564\pi\)
\(374\) 0 0
\(375\) −7.60242 19.6174i −0.392587 1.01304i
\(376\) 0 0
\(377\) 11.9483i 0.615369i
\(378\) 0 0
\(379\) 4.52212i 0.232285i −0.993233 0.116143i \(-0.962947\pi\)
0.993233 0.116143i \(-0.0370530\pi\)
\(380\) 0 0
\(381\) 9.18985 11.4230i 0.470810 0.585216i
\(382\) 0 0
\(383\) 7.58521 + 2.76079i 0.387586 + 0.141070i 0.528461 0.848958i \(-0.322769\pi\)
−0.140875 + 0.990027i \(0.544991\pi\)
\(384\) 0 0
\(385\) 2.09488 11.8807i 0.106765 0.605495i
\(386\) 0 0
\(387\) 0.468205 + 11.3311i 0.0238002 + 0.575991i
\(388\) 0 0
\(389\) 2.93943 + 8.07603i 0.149035 + 0.409471i 0.991636 0.129068i \(-0.0411986\pi\)
−0.842600 + 0.538539i \(0.818976\pi\)
\(390\) 0 0
\(391\) 8.71266 + 10.3833i 0.440618 + 0.525109i
\(392\) 0 0
\(393\) −5.89016 + 0.121640i −0.297119 + 0.00613593i
\(394\) 0 0
\(395\) −6.85085 11.8660i −0.344704 0.597044i
\(396\) 0 0
\(397\) −8.36056 + 14.4809i −0.419605 + 0.726776i −0.995900 0.0904653i \(-0.971165\pi\)
0.576295 + 0.817242i \(0.304498\pi\)
\(398\) 0 0
\(399\) 10.3513 9.05649i 0.518214 0.453391i
\(400\) 0 0
\(401\) 10.7406 1.89386i 0.536360 0.0945747i 0.101094 0.994877i \(-0.467766\pi\)
0.435266 + 0.900302i \(0.356654\pi\)
\(402\) 0 0
\(403\) 12.4287 14.8120i 0.619119 0.737837i
\(404\) 0 0
\(405\) 13.0037 9.01502i 0.646158 0.447960i
\(406\) 0 0
\(407\) −13.7863 11.5681i −0.683361 0.573408i
\(408\) 0 0
\(409\) −1.98786 11.2737i −0.0982932 0.557449i −0.993688 0.112176i \(-0.964218\pi\)
0.895395 0.445273i \(-0.146893\pi\)
\(410\) 0 0
\(411\) 6.87380 + 7.85656i 0.339060 + 0.387536i
\(412\) 0 0
\(413\) 19.2435 + 11.1102i 0.946911 + 0.546699i
\(414\) 0 0
\(415\) 25.0054 14.4369i 1.22747 0.708678i
\(416\) 0 0
\(417\) −0.672485 32.5636i −0.0329317 1.59465i
\(418\) 0 0
\(419\) 29.6189 24.8532i 1.44698 1.21416i 0.512226 0.858851i \(-0.328821\pi\)
0.934750 0.355306i \(-0.115623\pi\)
\(420\) 0 0
\(421\) 22.9468 8.35196i 1.11836 0.407050i 0.284306 0.958733i \(-0.408237\pi\)
0.834053 + 0.551684i \(0.186014\pi\)
\(422\) 0 0
\(423\) −17.5944 + 33.6065i −0.855467 + 1.63400i
\(424\) 0 0
\(425\) −6.36270 1.12192i −0.308636 0.0544209i
\(426\) 0 0
\(427\) 0.482377 1.32532i 0.0233438 0.0641367i
\(428\) 0 0
\(429\) 11.1550 + 8.97429i 0.538569 + 0.433283i
\(430\) 0 0
\(431\) 1.83273 0.0882794 0.0441397 0.999025i \(-0.485945\pi\)
0.0441397 + 0.999025i \(0.485945\pi\)
\(432\) 0 0
\(433\) 24.3880 1.17201 0.586006 0.810306i \(-0.300699\pi\)
0.586006 + 0.810306i \(0.300699\pi\)
\(434\) 0 0
\(435\) −8.36179 + 3.24048i −0.400917 + 0.155369i
\(436\) 0 0
\(437\) −3.22955 + 8.87312i −0.154490 + 0.424459i
\(438\) 0 0
\(439\) −6.79585 1.19829i −0.324348 0.0571913i 0.00910346 0.999959i \(-0.497102\pi\)
−0.333452 + 0.942767i \(0.608213\pi\)
\(440\) 0 0
\(441\) −10.3209 7.95791i −0.491473 0.378948i
\(442\) 0 0
\(443\) −12.8196 + 4.66594i −0.609076 + 0.221686i −0.628099 0.778133i \(-0.716167\pi\)
0.0190226 + 0.999819i \(0.493945\pi\)
\(444\) 0 0
\(445\) −4.37094 + 3.66765i −0.207202 + 0.173863i
\(446\) 0 0
\(447\) −2.25317 + 1.36366i −0.106571 + 0.0644987i
\(448\) 0 0
\(449\) −2.16633 + 1.25073i −0.102235 + 0.0590255i −0.550246 0.835003i \(-0.685466\pi\)
0.448011 + 0.894028i \(0.352133\pi\)
\(450\) 0 0
\(451\) 18.3288 + 10.5822i 0.863071 + 0.498294i
\(452\) 0 0
\(453\) −29.7179 + 5.87518i −1.39627 + 0.276040i
\(454\) 0 0
\(455\) 4.17189 + 23.6600i 0.195581 + 1.10920i
\(456\) 0 0
\(457\) 12.1416 + 10.1880i 0.567961 + 0.476576i 0.880969 0.473175i \(-0.156892\pi\)
−0.313008 + 0.949751i \(0.601337\pi\)
\(458\) 0 0
\(459\) −1.08864 17.5517i −0.0508133 0.819242i
\(460\) 0 0
\(461\) 13.3795 15.9451i 0.623147 0.742637i −0.358461 0.933545i \(-0.616699\pi\)
0.981608 + 0.190907i \(0.0611430\pi\)
\(462\) 0 0
\(463\) −4.07709 + 0.718900i −0.189478 + 0.0334101i −0.267582 0.963535i \(-0.586225\pi\)
0.0781036 + 0.996945i \(0.475113\pi\)
\(464\) 0 0
\(465\) −13.7366 4.68086i −0.637021 0.217070i
\(466\) 0 0
\(467\) 1.51667 2.62696i 0.0701833 0.121561i −0.828798 0.559548i \(-0.810975\pi\)
0.898982 + 0.437987i \(0.144308\pi\)
\(468\) 0 0
\(469\) −20.4646 35.4458i −0.944970 1.63674i
\(470\) 0 0
\(471\) 1.78256 3.24019i 0.0821360 0.149300i
\(472\) 0 0
\(473\) 4.95045 + 5.89972i 0.227622 + 0.271269i
\(474\) 0 0
\(475\) −1.53939 4.22944i −0.0706321 0.194060i
\(476\) 0 0
\(477\) −9.09441 + 28.6105i −0.416404 + 1.30999i
\(478\) 0 0
\(479\) 0.400967 2.27400i 0.0183207 0.103902i −0.974276 0.225357i \(-0.927645\pi\)
0.992597 + 0.121456i \(0.0387562\pi\)
\(480\) 0 0
\(481\) 33.6784 + 12.2579i 1.53560 + 0.558914i
\(482\) 0 0
\(483\) 23.0886 + 3.58129i 1.05057 + 0.162955i
\(484\) 0 0
\(485\) 20.0940i 0.912421i
\(486\) 0 0
\(487\) 10.8187i 0.490242i −0.969492 0.245121i \(-0.921172\pi\)
0.969492 0.245121i \(-0.0788277\pi\)
\(488\) 0 0
\(489\) 39.4231 + 6.11495i 1.78277 + 0.276527i
\(490\) 0 0
\(491\) 37.8763 + 13.7858i 1.70933 + 0.622146i 0.996833 0.0795275i \(-0.0253411\pi\)
0.712499 + 0.701673i \(0.247563\pi\)
\(492\) 0 0
\(493\) −1.73068 + 9.81519i −0.0779461 + 0.442054i
\(494\) 0 0
\(495\) 3.25515 10.2405i 0.146308 0.460277i
\(496\) 0 0
\(497\) −17.4450 47.9298i −0.782516 2.14995i
\(498\) 0 0
\(499\) −12.0797 14.3960i −0.540760 0.644452i 0.424598 0.905382i \(-0.360415\pi\)
−0.965358 + 0.260930i \(0.915971\pi\)
\(500\) 0 0
\(501\) −19.7225 + 35.8501i −0.881138 + 1.60166i
\(502\) 0 0
\(503\) 4.44979 + 7.70726i 0.198406 + 0.343650i 0.948012 0.318235i \(-0.103090\pi\)
−0.749606 + 0.661885i \(0.769757\pi\)
\(504\) 0 0
\(505\) −5.19865 + 9.00432i −0.231337 + 0.400687i
\(506\) 0 0
\(507\) −5.67446 1.93361i −0.252012 0.0858748i
\(508\) 0 0
\(509\) 16.1048 2.83970i 0.713831 0.125868i 0.195073 0.980789i \(-0.437506\pi\)
0.518758 + 0.854921i \(0.326395\pi\)
\(510\) 0 0
\(511\) −25.4547 + 30.3358i −1.12605 + 1.34198i
\(512\) 0 0
\(513\) 10.2098 6.77037i 0.450776 0.298919i
\(514\) 0 0
\(515\) −4.32580 3.62978i −0.190618 0.159947i
\(516\) 0 0
\(517\) 4.47332 + 25.3695i 0.196736 + 1.11575i
\(518\) 0 0
\(519\) 6.29740 1.24498i 0.276425 0.0546488i
\(520\) 0 0
\(521\) 5.28398 + 3.05071i 0.231495 + 0.133654i 0.611262 0.791429i \(-0.290662\pi\)
−0.379766 + 0.925082i \(0.623996\pi\)
\(522\) 0 0
\(523\) −26.2053 + 15.1297i −1.14588 + 0.661574i −0.947880 0.318628i \(-0.896778\pi\)
−0.198000 + 0.980202i \(0.563445\pi\)
\(524\) 0 0
\(525\) −9.52787 + 5.76644i −0.415830 + 0.251668i
\(526\) 0 0
\(527\) −12.3553 + 10.3673i −0.538206 + 0.451608i
\(528\) 0 0
\(529\) 6.53952 2.38019i 0.284327 0.103487i
\(530\) 0 0
\(531\) 15.6738 + 12.0852i 0.680184 + 0.524453i
\(532\) 0 0
\(533\) −41.5077 7.31893i −1.79790 0.317018i
\(534\) 0 0
\(535\) 1.43318 3.93763i 0.0619617 0.170238i
\(536\) 0 0
\(537\) −15.7933 + 6.12044i −0.681530 + 0.264117i
\(538\) 0 0
\(539\) −8.85051 −0.381218
\(540\) 0 0
\(541\) −7.88737 −0.339105 −0.169552 0.985521i \(-0.554232\pi\)
−0.169552 + 0.985521i \(0.554232\pi\)
\(542\) 0 0
\(543\) 6.02287 + 4.84545i 0.258466 + 0.207938i
\(544\) 0 0
\(545\) −2.80952 + 7.71910i −0.120347 + 0.330650i
\(546\) 0 0
\(547\) 18.7310 + 3.30278i 0.800878 + 0.141216i 0.559084 0.829111i \(-0.311153\pi\)
0.241794 + 0.970327i \(0.422264\pi\)
\(548\) 0 0
\(549\) 0.582663 1.11293i 0.0248675 0.0474987i
\(550\) 0 0
\(551\) −6.52440 + 2.37469i −0.277949 + 0.101165i
\(552\) 0 0
\(553\) −20.1081 + 16.8727i −0.855081 + 0.717499i
\(554\) 0 0
\(555\) −0.555391 26.8936i −0.0235750 1.14157i
\(556\) 0 0
\(557\) 3.52729 2.03648i 0.149456 0.0862886i −0.423407 0.905940i \(-0.639166\pi\)
0.572863 + 0.819651i \(0.305833\pi\)
\(558\) 0 0
\(559\) −13.2825 7.66868i −0.561792 0.324351i
\(560\) 0 0
\(561\) −7.86362 8.98789i −0.332002 0.379469i
\(562\) 0 0
\(563\) 1.67761 + 9.51422i 0.0707030 + 0.400976i 0.999535 + 0.0304766i \(0.00970249\pi\)
−0.928833 + 0.370500i \(0.879186\pi\)
\(564\) 0 0
\(565\) 20.6794 + 17.3521i 0.869989 + 0.730007i
\(566\) 0 0
\(567\) −21.3342 21.5345i −0.895951 0.904364i
\(568\) 0 0
\(569\) −18.7820 + 22.3835i −0.787382 + 0.938365i −0.999242 0.0389352i \(-0.987603\pi\)
0.211860 + 0.977300i \(0.432048\pi\)
\(570\) 0 0
\(571\) −29.7351 + 5.24311i −1.24438 + 0.219417i −0.756791 0.653657i \(-0.773234\pi\)
−0.487587 + 0.873075i \(0.662123\pi\)
\(572\) 0 0
\(573\) −1.89607 + 1.65890i −0.0792096 + 0.0693015i
\(574\) 0 0
\(575\) 3.82298 6.62160i 0.159429 0.276140i
\(576\) 0 0
\(577\) 11.3102 + 19.5898i 0.470848 + 0.815532i 0.999444 0.0333411i \(-0.0106148\pi\)
−0.528596 + 0.848873i \(0.677281\pi\)
\(578\) 0 0
\(579\) −28.8613 + 0.596026i −1.19944 + 0.0247700i
\(580\) 0 0
\(581\) −35.5560 42.3739i −1.47511 1.75797i
\(582\) 0 0
\(583\) 6.97292 + 19.1580i 0.288789 + 0.793441i
\(584\) 0 0
\(585\) 0.883468 + 21.3809i 0.0365269 + 0.883992i
\(586\) 0 0
\(587\) −2.91625 + 16.5389i −0.120367 + 0.682633i 0.863586 + 0.504202i \(0.168213\pi\)
−0.983952 + 0.178431i \(0.942898\pi\)
\(588\) 0 0
\(589\) −10.5583 3.84290i −0.435046 0.158344i
\(590\) 0 0
\(591\) 0.617118 0.767075i 0.0253848 0.0315533i
\(592\) 0 0
\(593\) 29.7423i 1.22137i −0.791874 0.610685i \(-0.790894\pi\)
0.791874 0.610685i \(-0.209106\pi\)
\(594\) 0 0
\(595\) 20.0403i 0.821570i
\(596\) 0 0
\(597\) 10.0926 + 26.0430i 0.413061 + 1.06587i
\(598\) 0 0
\(599\) −37.6477 13.7027i −1.53824 0.559875i −0.572621 0.819820i \(-0.694073\pi\)
−0.965624 + 0.259945i \(0.916296\pi\)
\(600\) 0 0
\(601\) 0.169116 0.959102i 0.00689837 0.0391226i −0.981164 0.193175i \(-0.938121\pi\)
0.988063 + 0.154053i \(0.0492325\pi\)
\(602\) 0 0
\(603\) −13.8724 33.7134i −0.564926 1.37292i
\(604\) 0 0
\(605\) 4.11858 + 11.3157i 0.167444 + 0.460049i
\(606\) 0 0
\(607\) −26.7728 31.9065i −1.08667 1.29505i −0.952651 0.304067i \(-0.901655\pi\)
−0.134022 0.990978i \(-0.542789\pi\)
\(608\) 0 0
\(609\) 8.89539 + 14.6978i 0.360459 + 0.595586i
\(610\) 0 0
\(611\) −25.6509 44.4287i −1.03772 1.79739i
\(612\) 0 0
\(613\) 11.4932 19.9068i 0.464207 0.804029i −0.534959 0.844878i \(-0.679673\pi\)
0.999165 + 0.0408488i \(0.0130062\pi\)
\(614\) 0 0
\(615\) 6.13523 + 31.0333i 0.247396 + 1.25138i
\(616\) 0 0
\(617\) 40.0276 7.05794i 1.61145 0.284142i 0.705877 0.708334i \(-0.250553\pi\)
0.905572 + 0.424192i \(0.139442\pi\)
\(618\) 0 0
\(619\) 17.5190 20.8783i 0.704147 0.839169i −0.288842 0.957377i \(-0.593270\pi\)
0.992989 + 0.118207i \(0.0377148\pi\)
\(620\) 0 0
\(621\) 19.9591 + 5.89353i 0.800933 + 0.236499i
\(622\) 0 0
\(623\) 8.37368 + 7.02635i 0.335484 + 0.281505i
\(624\) 0 0
\(625\) −2.05082 11.6308i −0.0820328 0.465231i
\(626\) 0 0
\(627\) 2.68341 7.87482i 0.107165 0.314490i
\(628\) 0 0
\(629\) −25.8903 14.9478i −1.03231 0.596007i
\(630\) 0 0
\(631\) 34.4360 19.8817i 1.37088 0.791476i 0.379839 0.925053i \(-0.375980\pi\)
0.991039 + 0.133577i \(0.0426462\pi\)
\(632\) 0 0
\(633\) −9.33149 5.13362i −0.370893 0.204043i
\(634\) 0 0
\(635\) 11.3997 9.56551i 0.452384 0.379596i
\(636\) 0 0
\(637\) 16.5625 6.02827i 0.656232 0.238849i
\(638\) 0 0
\(639\) −9.72945 44.3771i −0.384891 1.75553i
\(640\) 0 0
\(641\) 16.0784 + 2.83506i 0.635060 + 0.111978i 0.481904 0.876224i \(-0.339945\pi\)
0.153156 + 0.988202i \(0.451056\pi\)
\(642\) 0 0
\(643\) −12.5805 + 34.5646i −0.496126 + 1.36309i 0.398865 + 0.917010i \(0.369404\pi\)
−0.894991 + 0.446084i \(0.852818\pi\)
\(644\) 0 0
\(645\) −1.76444 + 11.3753i −0.0694746 + 0.447903i
\(646\) 0 0
\(647\) 16.3460 0.642627 0.321314 0.946973i \(-0.395876\pi\)
0.321314 + 0.946973i \(0.395876\pi\)
\(648\) 0 0
\(649\) 13.4407 0.527595
\(650\) 0 0
\(651\) −4.26144 + 27.4735i −0.167019 + 1.07677i
\(652\) 0 0
\(653\) −14.5391 + 39.9459i −0.568960 + 1.56320i 0.237172 + 0.971468i \(0.423779\pi\)
−0.806132 + 0.591736i \(0.798443\pi\)
\(654\) 0 0
\(655\) −5.88920 1.03842i −0.230110 0.0405746i
\(656\) 0 0
\(657\) −26.0612 + 23.7689i −1.01674 + 0.927312i
\(658\) 0 0
\(659\) −38.5139 + 14.0179i −1.50029 + 0.546060i −0.956135 0.292926i \(-0.905371\pi\)
−0.544153 + 0.838986i \(0.683149\pi\)
\(660\) 0 0
\(661\) 24.6279 20.6653i 0.957916 0.803787i −0.0226971 0.999742i \(-0.507225\pi\)
0.980613 + 0.195956i \(0.0627809\pi\)
\(662\) 0 0
\(663\) 20.8376 + 11.4636i 0.809263 + 0.445208i
\(664\) 0 0
\(665\) 12.0904 6.98040i 0.468846 0.270688i
\(666\) 0 0
\(667\) −10.2146 5.89739i −0.395510 0.228348i
\(668\) 0 0
\(669\) 3.84674 11.2888i 0.148724 0.436450i
\(670\) 0 0
\(671\) −0.148141 0.840148i −0.00571891 0.0324335i
\(672\) 0 0
\(673\) 14.3659 + 12.0545i 0.553767 + 0.464665i 0.876214 0.481922i \(-0.160061\pi\)
−0.322447 + 0.946587i \(0.604506\pi\)
\(674\) 0 0
\(675\) −9.09361 + 3.96331i −0.350013 + 0.152548i
\(676\) 0 0
\(677\) 29.7738 35.4831i 1.14430 1.36373i 0.223027 0.974812i \(-0.428406\pi\)
0.921275 0.388913i \(-0.127149\pi\)
\(678\) 0 0
\(679\) −37.9105 + 6.68465i −1.45487 + 0.256533i
\(680\) 0 0
\(681\) −6.86393 34.7192i −0.263026 1.33044i
\(682\) 0 0
\(683\) 11.4472 19.8272i 0.438016 0.758666i −0.559520 0.828817i \(-0.689015\pi\)
0.997536 + 0.0701505i \(0.0223480\pi\)
\(684\) 0 0
\(685\) 5.29807 + 9.17653i 0.202429 + 0.350617i
\(686\) 0 0
\(687\) 4.32312 + 7.14307i 0.164937 + 0.272525i
\(688\) 0 0
\(689\) −26.0978 31.1021i −0.994247 1.18490i
\(690\) 0 0
\(691\) 7.74396 + 21.2764i 0.294594 + 0.809391i 0.995380 + 0.0960186i \(0.0306108\pi\)
−0.700785 + 0.713372i \(0.747167\pi\)
\(692\) 0 0
\(693\) −20.4032 2.73465i −0.775055 0.103881i
\(694\) 0 0
\(695\) 5.74091 32.5583i 0.217765 1.23501i
\(696\) 0 0
\(697\) 33.0372 + 12.0246i 1.25137 + 0.455463i
\(698\) 0 0
\(699\) 4.12375 + 10.6410i 0.155975 + 0.402480i
\(700\) 0 0
\(701\) 4.91265i 0.185548i 0.995687 + 0.0927741i \(0.0295735\pi\)
−0.995687 + 0.0927741i \(0.970427\pi\)
\(702\) 0 0
\(703\) 20.8264i 0.785482i
\(704\) 0 0
\(705\) −24.1358 + 30.0007i −0.909006 + 1.12989i
\(706\) 0 0
\(707\) 18.7175 + 6.81261i 0.703944 + 0.256215i
\(708\) 0 0
\(709\) 2.99743 16.9993i 0.112571 0.638421i −0.875354 0.483483i \(-0.839371\pi\)
0.987924 0.154937i \(-0.0495176\pi\)
\(710\) 0 0
\(711\) −19.7480 + 12.5161i −0.740609 + 0.469391i
\(712\) 0 0
\(713\) −6.52820 17.9361i −0.244483 0.671712i
\(714\) 0 0
\(715\) 9.34114 + 11.1323i 0.349339 + 0.416326i
\(716\) 0 0
\(717\) −17.7606 + 0.366781i −0.663281 + 0.0136977i
\(718\) 0 0
\(719\) −13.2483 22.9467i −0.494077 0.855767i 0.505900 0.862592i \(-0.331161\pi\)
−0.999977 + 0.00682566i \(0.997827\pi\)
\(720\) 0 0
\(721\) −5.40910 + 9.36883i −0.201445 + 0.348913i
\(722\) 0 0
\(723\) −28.3058 + 24.7651i −1.05270 + 0.921023i
\(724\) 0 0
\(725\) 5.53665 0.976262i 0.205626 0.0362574i
\(726\) 0 0
\(727\) 12.7022 15.1379i 0.471098 0.561433i −0.477208 0.878791i \(-0.658351\pi\)
0.948306 + 0.317357i \(0.102795\pi\)
\(728\) 0 0
\(729\) −16.2860 21.5352i −0.603186 0.797601i
\(730\) 0 0
\(731\) 9.80043 + 8.22354i 0.362482 + 0.304159i
\(732\) 0 0
\(733\) −2.32265 13.1724i −0.0857892 0.486535i −0.997184 0.0750004i \(-0.976104\pi\)
0.911394 0.411534i \(-0.135007\pi\)
\(734\) 0 0
\(735\) −8.71067 9.95605i −0.321298 0.367234i
\(736\) 0 0
\(737\) −21.4405 12.3787i −0.789770 0.455974i
\(738\) 0 0
\(739\) 18.2507 10.5370i 0.671363 0.387611i −0.125230 0.992128i \(-0.539967\pi\)
0.796593 + 0.604516i \(0.206634\pi\)
\(740\) 0 0
\(741\) 0.342078 + 16.5644i 0.0125665 + 0.608509i
\(742\) 0 0
\(743\) −25.5261 + 21.4190i −0.936463 + 0.785786i −0.976966 0.213394i \(-0.931548\pi\)
0.0405033 + 0.999179i \(0.487104\pi\)
\(744\) 0 0
\(745\) −2.51209 + 0.914326i −0.0920358 + 0.0334983i
\(746\) 0 0
\(747\) −26.3754 41.6153i −0.965024 1.52262i
\(748\) 0 0
\(749\) −7.90573 1.39399i −0.288869 0.0509354i
\(750\) 0 0
\(751\) 13.9383 38.2951i 0.508615 1.39741i −0.374051 0.927408i \(-0.622031\pi\)
0.882666 0.470001i \(-0.155746\pi\)
\(752\) 0 0
\(753\) 18.9016 + 15.2065i 0.688814 + 0.554156i
\(754\) 0 0
\(755\) −30.7488 −1.11906
\(756\) 0 0
\(757\) 52.2535 1.89919 0.949593 0.313487i \(-0.101497\pi\)
0.949593 + 0.313487i \(0.101497\pi\)
\(758\) 0 0
\(759\) 13.1779 5.10690i 0.478328 0.185369i
\(760\) 0 0
\(761\) 9.53784 26.2050i 0.345746 0.949930i −0.637948 0.770080i \(-0.720216\pi\)
0.983694 0.179851i \(-0.0575614\pi\)
\(762\) 0 0
\(763\) 15.4979 + 2.73271i 0.561063 + 0.0989306i
\(764\) 0 0
\(765\) 2.37123 17.6918i 0.0857319 0.639647i
\(766\) 0 0
\(767\) −25.1525 + 9.15477i −0.908205 + 0.330560i
\(768\) 0 0
\(769\) 8.86910 7.44206i 0.319828 0.268368i −0.468712 0.883351i \(-0.655282\pi\)
0.788540 + 0.614983i \(0.210837\pi\)
\(770\) 0 0
\(771\) −37.4151 + 22.6443i −1.34747 + 0.815514i
\(772\) 0 0
\(773\) 2.47753 1.43040i 0.0891105 0.0514480i −0.454783 0.890603i \(-0.650283\pi\)
0.543893 + 0.839155i \(0.316950\pi\)
\(774\) 0 0
\(775\) 7.87914 + 4.54902i 0.283027 + 0.163406i
\(776\) 0 0
\(777\) −50.5544 + 9.99451i −1.81363 + 0.358551i
\(778\) 0 0
\(779\) 4.25300 + 24.1200i 0.152380 + 0.864187i
\(780\) 0 0
\(781\) −23.6343 19.8316i −0.845703 0.709629i
\(782\) 0 0
\(783\) 6.11385 + 14.0279i 0.218491 + 0.501318i
\(784\) 0 0
\(785\) 2.41289 2.87557i 0.0861198 0.102634i
\(786\) 0 0
\(787\) −20.8499 + 3.67640i −0.743219 + 0.131050i −0.532420 0.846480i \(-0.678717\pi\)
−0.210798 + 0.977530i \(0.567606\pi\)
\(788\) 0 0
\(789\) −5.12445 1.74620i −0.182435 0.0621662i
\(790\) 0 0
\(791\) 25.8580 44.7874i 0.919406 1.59246i
\(792\) 0 0
\(793\) 0.849468 + 1.47132i 0.0301655 + 0.0522482i
\(794\) 0 0
\(795\) −14.6883 + 26.6992i −0.520939 + 0.946922i