Properties

Label 819.2.fm.e.496.7
Level $819$
Weight $2$
Character 819.496
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 496.7
Character \(\chi\) \(=\) 819.496
Dual form 819.2.fm.e.748.7

$q$-expansion

\(f(q)\) \(=\) \(q+(2.11902 + 0.567791i) q^{2} +(2.43582 + 1.40632i) q^{4} +(3.00219 + 3.00219i) q^{5} +(-2.60148 + 0.481982i) q^{7} +(1.26060 + 1.26060i) q^{8} +O(q^{10})\) \(q+(2.11902 + 0.567791i) q^{2} +(2.43582 + 1.40632i) q^{4} +(3.00219 + 3.00219i) q^{5} +(-2.60148 + 0.481982i) q^{7} +(1.26060 + 1.26060i) q^{8} +(4.65710 + 8.06633i) q^{10} +(0.698323 - 2.60618i) q^{11} +(0.373866 + 3.58612i) q^{13} +(-5.78626 - 0.455764i) q^{14} +(-0.857159 - 1.48464i) q^{16} +(-0.599399 + 1.03819i) q^{17} +(1.89568 - 0.507945i) q^{19} +(3.09075 + 11.5349i) q^{20} +(2.95953 - 5.12605i) q^{22} +(4.65282 - 2.68631i) q^{23} +13.0263i q^{25} +(-1.24393 + 7.81134i) q^{26} +(-7.01456 - 2.48450i) q^{28} +(-1.47928 - 2.56220i) q^{29} +(-3.36721 - 3.36721i) q^{31} +(-1.89620 - 7.07671i) q^{32} +(-1.85961 + 1.85961i) q^{34} +(-9.25714 - 6.36314i) q^{35} +(-1.03769 + 3.87273i) q^{37} +4.30539 q^{38} +7.56914i q^{40} +(1.42770 - 5.32825i) q^{41} +(-9.78317 - 5.64832i) q^{43} +(5.36612 - 5.36612i) q^{44} +(11.3847 - 3.05052i) q^{46} +(2.97828 - 2.97828i) q^{47} +(6.53539 - 2.50773i) q^{49} +(-7.39621 + 27.6030i) q^{50} +(-4.13256 + 9.26092i) q^{52} +11.0603 q^{53} +(9.92075 - 5.72775i) q^{55} +(-3.88702 - 2.67184i) q^{56} +(-1.67985 - 6.26927i) q^{58} +(3.14721 + 11.7455i) q^{59} +(-4.55683 - 2.63089i) q^{61} +(-5.22332 - 9.04706i) q^{62} -12.6437i q^{64} +(-9.64379 + 11.8886i) q^{65} +(4.15530 + 1.11341i) q^{67} +(-2.92006 + 1.68590i) q^{68} +(-16.0032 - 18.7397i) q^{70} +(-0.800761 - 2.98848i) q^{71} +(4.78407 - 4.78407i) q^{73} +(-4.39780 + 7.61721i) q^{74} +(5.33186 + 1.42867i) q^{76} +(-0.560542 + 7.11650i) q^{77} -1.16895 q^{79} +(1.88383 - 7.03054i) q^{80} +(6.05066 - 10.4801i) q^{82} +(3.24002 + 3.24002i) q^{83} +(-4.91635 + 1.31733i) q^{85} +(-17.5237 - 17.5237i) q^{86} +(4.16566 - 2.40505i) q^{88} +(-4.80209 - 1.28672i) q^{89} +(-2.70105 - 9.14901i) q^{91} +15.1113 q^{92} +(8.00209 - 4.62001i) q^{94} +(7.21613 + 4.16623i) q^{95} +(-14.7483 + 3.95180i) q^{97} +(15.2725 - 1.60321i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.11902 + 0.567791i 1.49838 + 0.401489i 0.912556 0.408953i \(-0.134106\pi\)
0.585820 + 0.810441i \(0.300773\pi\)
\(3\) 0 0
\(4\) 2.43582 + 1.40632i 1.21791 + 0.703161i
\(5\) 3.00219 + 3.00219i 1.34262 + 1.34262i 0.893442 + 0.449179i \(0.148283\pi\)
0.449179 + 0.893442i \(0.351717\pi\)
\(6\) 0 0
\(7\) −2.60148 + 0.481982i −0.983267 + 0.182172i
\(8\) 1.26060 + 1.26060i 0.445690 + 0.445690i
\(9\) 0 0
\(10\) 4.65710 + 8.06633i 1.47270 + 2.55080i
\(11\) 0.698323 2.60618i 0.210552 0.785792i −0.777133 0.629337i \(-0.783327\pi\)
0.987685 0.156455i \(-0.0500068\pi\)
\(12\) 0 0
\(13\) 0.373866 + 3.58612i 0.103692 + 0.994609i
\(14\) −5.78626 0.455764i −1.54644 0.121808i
\(15\) 0 0
\(16\) −0.857159 1.48464i −0.214290 0.371161i
\(17\) −0.599399 + 1.03819i −0.145376 + 0.251798i −0.929513 0.368789i \(-0.879772\pi\)
0.784137 + 0.620587i \(0.213106\pi\)
\(18\) 0 0
\(19\) 1.89568 0.507945i 0.434898 0.116531i −0.0347266 0.999397i \(-0.511056\pi\)
0.469624 + 0.882866i \(0.344389\pi\)
\(20\) 3.09075 + 11.5349i 0.691114 + 2.57927i
\(21\) 0 0
\(22\) 2.95953 5.12605i 0.630973 1.09288i
\(23\) 4.65282 2.68631i 0.970181 0.560134i 0.0708893 0.997484i \(-0.477416\pi\)
0.899291 + 0.437350i \(0.144083\pi\)
\(24\) 0 0
\(25\) 13.0263i 2.60526i
\(26\) −1.24393 + 7.81134i −0.243955 + 1.53193i
\(27\) 0 0
\(28\) −7.01456 2.48450i −1.32563 0.469526i
\(29\) −1.47928 2.56220i −0.274696 0.475788i 0.695362 0.718659i \(-0.255244\pi\)
−0.970058 + 0.242872i \(0.921911\pi\)
\(30\) 0 0
\(31\) −3.36721 3.36721i −0.604768 0.604768i 0.336806 0.941574i \(-0.390653\pi\)
−0.941574 + 0.336806i \(0.890653\pi\)
\(32\) −1.89620 7.07671i −0.335204 1.25100i
\(33\) 0 0
\(34\) −1.85961 + 1.85961i −0.318921 + 0.318921i
\(35\) −9.25714 6.36314i −1.56474 1.07557i
\(36\) 0 0
\(37\) −1.03769 + 3.87273i −0.170596 + 0.636673i 0.826664 + 0.562696i \(0.190236\pi\)
−0.997260 + 0.0739770i \(0.976431\pi\)
\(38\) 4.30539 0.698426
\(39\) 0 0
\(40\) 7.56914i 1.19679i
\(41\) 1.42770 5.32825i 0.222969 0.832133i −0.760239 0.649644i \(-0.774918\pi\)
0.983208 0.182489i \(-0.0584154\pi\)
\(42\) 0 0
\(43\) −9.78317 5.64832i −1.49192 0.861360i −0.491963 0.870616i \(-0.663720\pi\)
−0.999957 + 0.00925580i \(0.997054\pi\)
\(44\) 5.36612 5.36612i 0.808973 0.808973i
\(45\) 0 0
\(46\) 11.3847 3.05052i 1.67858 0.449775i
\(47\) 2.97828 2.97828i 0.434427 0.434427i −0.455704 0.890131i \(-0.650613\pi\)
0.890131 + 0.455704i \(0.150613\pi\)
\(48\) 0 0
\(49\) 6.53539 2.50773i 0.933627 0.358248i
\(50\) −7.39621 + 27.6030i −1.04598 + 3.90366i
\(51\) 0 0
\(52\) −4.13256 + 9.26092i −0.573084 + 1.28426i
\(53\) 11.0603 1.51925 0.759627 0.650359i \(-0.225382\pi\)
0.759627 + 0.650359i \(0.225382\pi\)
\(54\) 0 0
\(55\) 9.92075 5.72775i 1.33771 0.772329i
\(56\) −3.88702 2.67184i −0.519424 0.357040i
\(57\) 0 0
\(58\) −1.67985 6.26927i −0.220575 0.823196i
\(59\) 3.14721 + 11.7455i 0.409731 + 1.52914i 0.795160 + 0.606400i \(0.207387\pi\)
−0.385428 + 0.922738i \(0.625946\pi\)
\(60\) 0 0
\(61\) −4.55683 2.63089i −0.583442 0.336851i 0.179058 0.983839i \(-0.442695\pi\)
−0.762500 + 0.646988i \(0.776028\pi\)
\(62\) −5.22332 9.04706i −0.663362 1.14898i
\(63\) 0 0
\(64\) 12.6437i 1.58046i
\(65\) −9.64379 + 11.8886i −1.19616 + 1.47460i
\(66\) 0 0
\(67\) 4.15530 + 1.11341i 0.507651 + 0.136025i 0.503549 0.863967i \(-0.332028\pi\)
0.00410235 + 0.999992i \(0.498694\pi\)
\(68\) −2.92006 + 1.68590i −0.354109 + 0.204445i
\(69\) 0 0
\(70\) −16.0032 18.7397i −1.91274 2.23983i
\(71\) −0.800761 2.98848i −0.0950329 0.354668i 0.901992 0.431754i \(-0.142105\pi\)
−0.997024 + 0.0770861i \(0.975438\pi\)
\(72\) 0 0
\(73\) 4.78407 4.78407i 0.559933 0.559933i −0.369355 0.929288i \(-0.620421\pi\)
0.929288 + 0.369355i \(0.120421\pi\)
\(74\) −4.39780 + 7.61721i −0.511234 + 0.885483i
\(75\) 0 0
\(76\) 5.33186 + 1.42867i 0.611607 + 0.163879i
\(77\) −0.560542 + 7.11650i −0.0638797 + 0.811000i
\(78\) 0 0
\(79\) −1.16895 −0.131517 −0.0657584 0.997836i \(-0.520947\pi\)
−0.0657584 + 0.997836i \(0.520947\pi\)
\(80\) 1.88383 7.03054i 0.210618 0.786038i
\(81\) 0 0
\(82\) 6.05066 10.4801i 0.668184 1.15733i
\(83\) 3.24002 + 3.24002i 0.355639 + 0.355639i 0.862202 0.506564i \(-0.169085\pi\)
−0.506564 + 0.862202i \(0.669085\pi\)
\(84\) 0 0
\(85\) −4.91635 + 1.31733i −0.533253 + 0.142885i
\(86\) −17.5237 17.5237i −1.88963 1.88963i
\(87\) 0 0
\(88\) 4.16566 2.40505i 0.444061 0.256379i
\(89\) −4.80209 1.28672i −0.509020 0.136392i −0.00483713 0.999988i \(-0.501540\pi\)
−0.504183 + 0.863597i \(0.668206\pi\)
\(90\) 0 0
\(91\) −2.70105 9.14901i −0.283147 0.959077i
\(92\) 15.1113 1.57546
\(93\) 0 0
\(94\) 8.00209 4.62001i 0.825352 0.476517i
\(95\) 7.21613 + 4.16623i 0.740359 + 0.427447i
\(96\) 0 0
\(97\) −14.7483 + 3.95180i −1.49746 + 0.401244i −0.912250 0.409634i \(-0.865656\pi\)
−0.585214 + 0.810879i \(0.698990\pi\)
\(98\) 15.2725 1.60321i 1.54276 0.161949i
\(99\) 0 0
\(100\) −18.3192 + 31.7298i −1.83192 + 3.17298i
\(101\) 0.803086 + 1.39099i 0.0799101 + 0.138408i 0.903211 0.429197i \(-0.141203\pi\)
−0.823301 + 0.567605i \(0.807870\pi\)
\(102\) 0 0
\(103\) −14.4997 −1.42870 −0.714351 0.699787i \(-0.753278\pi\)
−0.714351 + 0.699787i \(0.753278\pi\)
\(104\) −4.04937 + 4.99196i −0.397073 + 0.489502i
\(105\) 0 0
\(106\) 23.4371 + 6.27995i 2.27641 + 0.609963i
\(107\) −1.91021 3.30858i −0.184667 0.319852i 0.758797 0.651327i \(-0.225787\pi\)
−0.943464 + 0.331475i \(0.892454\pi\)
\(108\) 0 0
\(109\) 9.59246 9.59246i 0.918791 0.918791i −0.0781507 0.996942i \(-0.524902\pi\)
0.996942 + 0.0781507i \(0.0249015\pi\)
\(110\) 24.2745 6.50432i 2.31448 0.620163i
\(111\) 0 0
\(112\) 2.94545 + 3.44913i 0.278319 + 0.325912i
\(113\) 1.57880 2.73457i 0.148521 0.257247i −0.782160 0.623078i \(-0.785882\pi\)
0.930681 + 0.365831i \(0.119215\pi\)
\(114\) 0 0
\(115\) 22.0335 + 5.90385i 2.05463 + 0.550537i
\(116\) 8.32140i 0.772623i
\(117\) 0 0
\(118\) 26.6760i 2.45573i
\(119\) 1.05893 2.98973i 0.0970724 0.274068i
\(120\) 0 0
\(121\) 3.22177 + 1.86009i 0.292888 + 0.169099i
\(122\) −8.16224 8.16224i −0.738974 0.738974i
\(123\) 0 0
\(124\) −3.46654 12.9373i −0.311304 1.16180i
\(125\) −24.0965 + 24.0965i −2.15526 + 2.15526i
\(126\) 0 0
\(127\) 5.77265 3.33284i 0.512240 0.295742i −0.221514 0.975157i \(-0.571100\pi\)
0.733754 + 0.679415i \(0.237767\pi\)
\(128\) 3.38658 12.6389i 0.299335 1.11713i
\(129\) 0 0
\(130\) −27.1857 + 19.7166i −2.38434 + 1.72926i
\(131\) 9.80212i 0.856415i −0.903680 0.428207i \(-0.859145\pi\)
0.903680 0.428207i \(-0.140855\pi\)
\(132\) 0 0
\(133\) −4.68674 + 2.23509i −0.406392 + 0.193807i
\(134\) 8.17300 + 4.71868i 0.706039 + 0.407632i
\(135\) 0 0
\(136\) −2.06435 + 0.553140i −0.177016 + 0.0474314i
\(137\) −6.48757 + 1.73834i −0.554271 + 0.148516i −0.525073 0.851057i \(-0.675962\pi\)
−0.0291978 + 0.999574i \(0.509295\pi\)
\(138\) 0 0
\(139\) −0.304839 0.175999i −0.0258561 0.0149280i 0.487016 0.873393i \(-0.338085\pi\)
−0.512872 + 0.858465i \(0.671419\pi\)
\(140\) −13.6001 28.5180i −1.14942 2.41021i
\(141\) 0 0
\(142\) 6.78733i 0.569580i
\(143\) 9.60714 + 1.52991i 0.803389 + 0.127937i
\(144\) 0 0
\(145\) 3.25111 12.1333i 0.269990 1.00762i
\(146\) 12.8539 7.42121i 1.06380 0.614184i
\(147\) 0 0
\(148\) −7.97395 + 7.97395i −0.655455 + 0.655455i
\(149\) −3.05452 11.3996i −0.250236 0.933892i −0.970679 0.240379i \(-0.922728\pi\)
0.720443 0.693514i \(-0.243938\pi\)
\(150\) 0 0
\(151\) −12.2745 12.2745i −0.998884 0.998884i 0.00111530 0.999999i \(-0.499645\pi\)
−0.999999 + 0.00111530i \(0.999645\pi\)
\(152\) 3.03001 + 1.74938i 0.245766 + 0.141893i
\(153\) 0 0
\(154\) −5.22848 + 14.7618i −0.421323 + 1.18954i
\(155\) 20.2180i 1.62395i
\(156\) 0 0
\(157\) 4.41109i 0.352043i 0.984386 + 0.176022i \(0.0563228\pi\)
−0.984386 + 0.176022i \(0.943677\pi\)
\(158\) −2.47702 0.663716i −0.197061 0.0528024i
\(159\) 0 0
\(160\) 15.5529 26.9384i 1.22956 2.12967i
\(161\) −10.8095 + 9.23095i −0.851905 + 0.727501i
\(162\) 0 0
\(163\) −0.610931 + 0.163698i −0.0478518 + 0.0128219i −0.282666 0.959219i \(-0.591219\pi\)
0.234814 + 0.972040i \(0.424552\pi\)
\(164\) 10.9709 10.9709i 0.856680 0.856680i
\(165\) 0 0
\(166\) 5.02603 + 8.70534i 0.390096 + 0.675665i
\(167\) 16.3769 + 4.38817i 1.26728 + 0.339567i 0.828988 0.559266i \(-0.188917\pi\)
0.438292 + 0.898833i \(0.355584\pi\)
\(168\) 0 0
\(169\) −12.7204 + 2.68145i −0.978496 + 0.206266i
\(170\) −11.1658 −0.856380
\(171\) 0 0
\(172\) −15.8867 27.5166i −1.21135 2.09812i
\(173\) −4.60670 + 7.97903i −0.350241 + 0.606634i −0.986291 0.165013i \(-0.947234\pi\)
0.636051 + 0.771647i \(0.280567\pi\)
\(174\) 0 0
\(175\) −6.27845 33.8877i −0.474606 2.56167i
\(176\) −4.46782 + 1.19715i −0.336774 + 0.0902384i
\(177\) 0 0
\(178\) −9.44515 5.45316i −0.707944 0.408732i
\(179\) −2.35631 + 1.36042i −0.176119 + 0.101682i −0.585468 0.810696i \(-0.699089\pi\)
0.409349 + 0.912378i \(0.365756\pi\)
\(180\) 0 0
\(181\) −15.4525 −1.14858 −0.574288 0.818653i \(-0.694721\pi\)
−0.574288 + 0.818653i \(0.694721\pi\)
\(182\) −0.528864 20.9206i −0.0392020 1.55074i
\(183\) 0 0
\(184\) 9.25172 + 2.47899i 0.682046 + 0.182754i
\(185\) −14.7420 + 8.51132i −1.08386 + 0.625765i
\(186\) 0 0
\(187\) 2.28713 + 2.28713i 0.167252 + 0.167252i
\(188\) 11.4430 3.06614i 0.834566 0.223621i
\(189\) 0 0
\(190\) 12.9256 + 12.9256i 0.937721 + 0.937721i
\(191\) −1.63770 + 2.83658i −0.118500 + 0.205248i −0.919173 0.393853i \(-0.871142\pi\)
0.800673 + 0.599101i \(0.204475\pi\)
\(192\) 0 0
\(193\) −5.44447 + 20.3190i −0.391901 + 1.46260i 0.435093 + 0.900385i \(0.356715\pi\)
−0.826995 + 0.562210i \(0.809951\pi\)
\(194\) −33.4958 −2.40486
\(195\) 0 0
\(196\) 19.4457 + 3.08247i 1.38898 + 0.220176i
\(197\) −20.1959 5.41149i −1.43890 0.385553i −0.546753 0.837294i \(-0.684136\pi\)
−0.892149 + 0.451741i \(0.850803\pi\)
\(198\) 0 0
\(199\) −12.4685 + 21.5960i −0.883867 + 1.53090i −0.0368601 + 0.999320i \(0.511736\pi\)
−0.847007 + 0.531582i \(0.821598\pi\)
\(200\) −16.4210 + 16.4210i −1.16114 + 1.16114i
\(201\) 0 0
\(202\) 0.911969 + 3.40352i 0.0641659 + 0.239471i
\(203\) 5.08326 + 5.95251i 0.356775 + 0.417784i
\(204\) 0 0
\(205\) 20.2827 11.7102i 1.41660 0.817876i
\(206\) −30.7253 8.23282i −2.14073 0.573608i
\(207\) 0 0
\(208\) 5.00364 3.62893i 0.346940 0.251621i
\(209\) 5.29518i 0.366275i
\(210\) 0 0
\(211\) 5.46157 + 9.45972i 0.375990 + 0.651234i 0.990475 0.137695i \(-0.0439694\pi\)
−0.614485 + 0.788929i \(0.710636\pi\)
\(212\) 26.9410 + 15.5544i 1.85032 + 1.06828i
\(213\) 0 0
\(214\) −2.16919 8.09554i −0.148283 0.553400i
\(215\) −12.4136 46.3283i −0.846602 3.15956i
\(216\) 0 0
\(217\) 10.3827 + 7.13678i 0.704820 + 0.484476i
\(218\) 25.7731 14.8801i 1.74558 1.00781i
\(219\) 0 0
\(220\) 32.2202 2.17229
\(221\) −3.94716 1.76137i −0.265515 0.118483i
\(222\) 0 0
\(223\) −3.99267 + 14.9009i −0.267369 + 0.997835i 0.693415 + 0.720538i \(0.256105\pi\)
−0.960784 + 0.277297i \(0.910561\pi\)
\(224\) 8.34376 + 17.4960i 0.557491 + 1.16900i
\(225\) 0 0
\(226\) 4.89819 4.89819i 0.325823 0.325823i
\(227\) 18.6556 4.99875i 1.23822 0.331779i 0.420442 0.907319i \(-0.361875\pi\)
0.817773 + 0.575541i \(0.195208\pi\)
\(228\) 0 0
\(229\) 12.6136 12.6136i 0.833528 0.833528i −0.154470 0.987998i \(-0.549367\pi\)
0.987998 + 0.154470i \(0.0493669\pi\)
\(230\) 43.3373 + 25.0208i 2.85758 + 1.64982i
\(231\) 0 0
\(232\) 1.36512 5.09470i 0.0896245 0.334483i
\(233\) 24.9418i 1.63399i 0.576643 + 0.816996i \(0.304362\pi\)
−0.576643 + 0.816996i \(0.695638\pi\)
\(234\) 0 0
\(235\) 17.8827 1.16654
\(236\) −8.85197 + 33.0360i −0.576214 + 2.15046i
\(237\) 0 0
\(238\) 3.94145 5.73405i 0.255486 0.371683i
\(239\) 4.67931 4.67931i 0.302680 0.302680i −0.539382 0.842061i \(-0.681342\pi\)
0.842061 + 0.539382i \(0.181342\pi\)
\(240\) 0 0
\(241\) −0.169033 0.630839i −0.0108884 0.0406359i 0.960268 0.279080i \(-0.0900294\pi\)
−0.971156 + 0.238444i \(0.923363\pi\)
\(242\) 5.77086 + 5.77086i 0.370965 + 0.370965i
\(243\) 0 0
\(244\) −7.39975 12.8167i −0.473721 0.820508i
\(245\) 27.1492 + 12.0918i 1.73450 + 0.772516i
\(246\) 0 0
\(247\) 2.53028 + 6.60821i 0.160998 + 0.420470i
\(248\) 8.48941i 0.539078i
\(249\) 0 0
\(250\) −64.7428 + 37.3793i −4.09470 + 2.36407i
\(251\) −9.89477 + 17.1382i −0.624552 + 1.08176i 0.364075 + 0.931370i \(0.381385\pi\)
−0.988627 + 0.150386i \(0.951948\pi\)
\(252\) 0 0
\(253\) −3.75182 14.0020i −0.235875 0.880298i
\(254\) 14.1247 3.78471i 0.886265 0.237474i
\(255\) 0 0
\(256\) 1.70879 2.95971i 0.106799 0.184982i
\(257\) 7.97194 + 13.8078i 0.497276 + 0.861307i 0.999995 0.00314245i \(-0.00100027\pi\)
−0.502719 + 0.864450i \(0.667667\pi\)
\(258\) 0 0
\(259\) 0.832955 10.5750i 0.0517573 0.657097i
\(260\) −40.2098 + 15.3963i −2.49371 + 0.954838i
\(261\) 0 0
\(262\) 5.56555 20.7709i 0.343841 1.28323i
\(263\) 0.217727 + 0.377114i 0.0134256 + 0.0232538i 0.872660 0.488328i \(-0.162393\pi\)
−0.859235 + 0.511582i \(0.829060\pi\)
\(264\) 0 0
\(265\) 33.2052 + 33.2052i 2.03978 + 2.03978i
\(266\) −11.2004 + 2.07512i −0.686739 + 0.127234i
\(267\) 0 0
\(268\) 8.55576 + 8.55576i 0.522626 + 0.522626i
\(269\) −14.2630 8.23477i −0.869633 0.502083i −0.00240680 0.999997i \(-0.500766\pi\)
−0.867226 + 0.497914i \(0.834099\pi\)
\(270\) 0 0
\(271\) −22.4966 6.02794i −1.36657 0.366171i −0.500345 0.865826i \(-0.666793\pi\)
−0.866224 + 0.499655i \(0.833460\pi\)
\(272\) 2.05512 0.124610
\(273\) 0 0
\(274\) −14.7343 −0.890133
\(275\) 33.9489 + 9.09658i 2.04719 + 0.548544i
\(276\) 0 0
\(277\) 7.08167 + 4.08860i 0.425496 + 0.245660i 0.697426 0.716657i \(-0.254329\pi\)
−0.271930 + 0.962317i \(0.587662\pi\)
\(278\) −0.546031 0.546031i −0.0327488 0.0327488i
\(279\) 0 0
\(280\) −3.64819 19.6909i −0.218021 1.17676i
\(281\) −3.14177 3.14177i −0.187422 0.187422i 0.607159 0.794581i \(-0.292309\pi\)
−0.794581 + 0.607159i \(0.792309\pi\)
\(282\) 0 0
\(283\) 6.35147 + 11.0011i 0.377555 + 0.653945i 0.990706 0.136021i \(-0.0434314\pi\)
−0.613151 + 0.789966i \(0.710098\pi\)
\(284\) 2.25226 8.40554i 0.133647 0.498777i
\(285\) 0 0
\(286\) 19.4891 + 8.69675i 1.15241 + 0.514250i
\(287\) −1.14601 + 14.5495i −0.0676469 + 0.858827i
\(288\) 0 0
\(289\) 7.78144 + 13.4779i 0.457732 + 0.792815i
\(290\) 13.7783 23.8648i 0.809092 1.40139i
\(291\) 0 0
\(292\) 18.3811 4.92520i 1.07567 0.288226i
\(293\) 1.47718 + 5.51290i 0.0862977 + 0.322067i 0.995557 0.0941633i \(-0.0300176\pi\)
−0.909259 + 0.416231i \(0.863351\pi\)
\(294\) 0 0
\(295\) −25.8138 + 44.7109i −1.50294 + 2.60317i
\(296\) −6.19009 + 3.57385i −0.359792 + 0.207726i
\(297\) 0 0
\(298\) 25.8904i 1.49979i
\(299\) 11.3729 + 15.6812i 0.657714 + 0.906870i
\(300\) 0 0
\(301\) 28.1731 + 9.97867i 1.62387 + 0.575161i
\(302\) −19.0406 32.9793i −1.09566 1.89774i
\(303\) 0 0
\(304\) −2.37901 2.37901i −0.136446 0.136446i
\(305\) −5.78205 21.5789i −0.331079 1.23560i
\(306\) 0 0
\(307\) 10.2283 10.2283i 0.583760 0.583760i −0.352174 0.935934i \(-0.614558\pi\)
0.935934 + 0.352174i \(0.114558\pi\)
\(308\) −11.3735 + 16.5462i −0.648064 + 0.942808i
\(309\) 0 0
\(310\) 11.4796 42.8424i 0.651997 2.43328i
\(311\) −14.6147 −0.828724 −0.414362 0.910112i \(-0.635995\pi\)
−0.414362 + 0.910112i \(0.635995\pi\)
\(312\) 0 0
\(313\) 17.9984i 1.01733i −0.860965 0.508665i \(-0.830139\pi\)
0.860965 0.508665i \(-0.169861\pi\)
\(314\) −2.50457 + 9.34720i −0.141341 + 0.527493i
\(315\) 0 0
\(316\) −2.84734 1.64392i −0.160176 0.0924775i
\(317\) 12.0835 12.0835i 0.678674 0.678674i −0.281026 0.959700i \(-0.590675\pi\)
0.959700 + 0.281026i \(0.0906747\pi\)
\(318\) 0 0
\(319\) −7.71056 + 2.06604i −0.431708 + 0.115676i
\(320\) 37.9588 37.9588i 2.12196 2.12196i
\(321\) 0 0
\(322\) −28.1468 + 13.4231i −1.56856 + 0.748040i
\(323\) −0.608923 + 2.27253i −0.0338814 + 0.126447i
\(324\) 0 0
\(325\) −46.7138 + 4.87009i −2.59122 + 0.270144i
\(326\) −1.38752 −0.0768478
\(327\) 0 0
\(328\) 8.51656 4.91704i 0.470248 0.271498i
\(329\) −6.31246 + 9.18341i −0.348017 + 0.506298i
\(330\) 0 0
\(331\) 2.57122 + 9.59594i 0.141327 + 0.527441i 0.999891 + 0.0147345i \(0.00469030\pi\)
−0.858564 + 0.512706i \(0.828643\pi\)
\(332\) 3.33560 + 12.4486i 0.183065 + 0.683208i
\(333\) 0 0
\(334\) 32.2114 + 18.5973i 1.76253 + 1.01760i
\(335\) 9.13234 + 15.8177i 0.498953 + 0.864212i
\(336\) 0 0
\(337\) 6.44780i 0.351234i −0.984459 0.175617i \(-0.943808\pi\)
0.984459 0.175617i \(-0.0561920\pi\)
\(338\) −28.4774 1.54049i −1.54897 0.0837915i
\(339\) 0 0
\(340\) −13.8280 3.70519i −0.749926 0.200942i
\(341\) −11.1269 + 6.42414i −0.602558 + 0.347887i
\(342\) 0 0
\(343\) −15.7930 + 9.67375i −0.852741 + 0.522334i
\(344\) −5.21241 19.4530i −0.281034 1.04883i
\(345\) 0 0
\(346\) −14.2921 + 14.2921i −0.768349 + 0.768349i
\(347\) −6.00501 + 10.4010i −0.322366 + 0.558354i −0.980976 0.194131i \(-0.937811\pi\)
0.658610 + 0.752484i \(0.271145\pi\)
\(348\) 0 0
\(349\) 24.5954 + 6.59031i 1.31656 + 0.352771i 0.847688 0.530495i \(-0.177994\pi\)
0.468872 + 0.883266i \(0.344661\pi\)
\(350\) 5.93692 75.3736i 0.317342 4.02889i
\(351\) 0 0
\(352\) −19.7673 −1.05360
\(353\) −2.43053 + 9.07084i −0.129364 + 0.482792i −0.999958 0.00921021i \(-0.997068\pi\)
0.870594 + 0.492003i \(0.163735\pi\)
\(354\) 0 0
\(355\) 6.56796 11.3760i 0.348591 0.603777i
\(356\) −9.88750 9.88750i −0.524036 0.524036i
\(357\) 0 0
\(358\) −5.76551 + 1.54486i −0.304716 + 0.0816485i
\(359\) 16.2790 + 16.2790i 0.859171 + 0.859171i 0.991240 0.132070i \(-0.0421622\pi\)
−0.132070 + 0.991240i \(0.542162\pi\)
\(360\) 0 0
\(361\) −13.1189 + 7.57420i −0.690469 + 0.398642i
\(362\) −32.7442 8.77379i −1.72100 0.461140i
\(363\) 0 0
\(364\) 6.28718 26.0839i 0.329538 1.36717i
\(365\) 28.7254 1.50356
\(366\) 0 0
\(367\) 19.6200 11.3276i 1.02416 0.591297i 0.108851 0.994058i \(-0.465283\pi\)
0.915305 + 0.402761i \(0.131949\pi\)
\(368\) −7.97642 4.60519i −0.415799 0.240062i
\(369\) 0 0
\(370\) −36.0714 + 9.66529i −1.87526 + 0.502475i
\(371\) −28.7732 + 5.33088i −1.49383 + 0.276766i
\(372\) 0 0
\(373\) 11.0535 19.1453i 0.572330 0.991305i −0.423996 0.905664i \(-0.639373\pi\)
0.996326 0.0856409i \(-0.0272938\pi\)
\(374\) 3.54787 + 6.14510i 0.183456 + 0.317755i
\(375\) 0 0
\(376\) 7.50885 0.387240
\(377\) 8.63527 6.26280i 0.444739 0.322551i
\(378\) 0 0
\(379\) −1.03041 0.276097i −0.0529284 0.0141821i 0.232258 0.972654i \(-0.425389\pi\)
−0.285186 + 0.958472i \(0.592055\pi\)
\(380\) 11.7181 + 20.2964i 0.601128 + 1.04118i
\(381\) 0 0
\(382\) −5.08092 + 5.08092i −0.259962 + 0.259962i
\(383\) −12.0580 + 3.23092i −0.616133 + 0.165092i −0.553369 0.832936i \(-0.686658\pi\)
−0.0627635 + 0.998028i \(0.519991\pi\)
\(384\) 0 0
\(385\) −23.0479 + 19.6822i −1.17463 + 1.00310i
\(386\) −23.0739 + 39.9652i −1.17443 + 2.03417i
\(387\) 0 0
\(388\) −41.4818 11.1150i −2.10592 0.564279i
\(389\) 19.0137i 0.964031i 0.876163 + 0.482015i \(0.160095\pi\)
−0.876163 + 0.482015i \(0.839905\pi\)
\(390\) 0 0
\(391\) 6.44068i 0.325719i
\(392\) 11.3998 + 5.07727i 0.575775 + 0.256441i
\(393\) 0 0
\(394\) −39.7231 22.9341i −2.00122 1.15541i
\(395\) −3.50940 3.50940i −0.176577 0.176577i
\(396\) 0 0
\(397\) −0.702815 2.62294i −0.0352733 0.131642i 0.946044 0.324038i \(-0.105041\pi\)
−0.981317 + 0.192397i \(0.938374\pi\)
\(398\) −38.6830 + 38.6830i −1.93900 + 1.93900i
\(399\) 0 0
\(400\) 19.3394 11.1656i 0.966970 0.558281i
\(401\) −0.821135 + 3.06452i −0.0410055 + 0.153035i −0.983393 0.181488i \(-0.941909\pi\)
0.942388 + 0.334523i \(0.108575\pi\)
\(402\) 0 0
\(403\) 10.8163 13.3341i 0.538799 0.664218i
\(404\) 4.51759i 0.224759i
\(405\) 0 0
\(406\) 7.39177 + 15.4997i 0.366847 + 0.769239i
\(407\) 9.36838 + 5.40884i 0.464373 + 0.268106i
\(408\) 0 0
\(409\) −2.97815 + 0.797992i −0.147260 + 0.0394582i −0.331696 0.943386i \(-0.607621\pi\)
0.184436 + 0.982845i \(0.440954\pi\)
\(410\) 49.6284 13.2979i 2.45097 0.656735i
\(411\) 0 0
\(412\) −35.3188 20.3913i −1.74003 1.00461i
\(413\) −13.8485 29.0389i −0.681442 1.42891i
\(414\) 0 0
\(415\) 19.4543i 0.954976i
\(416\) 24.6690 9.44572i 1.20950 0.463115i
\(417\) 0 0
\(418\) 3.00655 11.2206i 0.147055 0.548818i
\(419\) 29.0623 16.7791i 1.41979 0.819715i 0.423508 0.905893i \(-0.360799\pi\)
0.996280 + 0.0861779i \(0.0274653\pi\)
\(420\) 0 0
\(421\) 18.2634 18.2634i 0.890104 0.890104i −0.104429 0.994532i \(-0.533301\pi\)
0.994532 + 0.104429i \(0.0333014\pi\)
\(422\) 6.20205 + 23.1464i 0.301911 + 1.12675i
\(423\) 0 0
\(424\) 13.9427 + 13.9427i 0.677116 + 0.677116i
\(425\) −13.5238 7.80795i −0.655999 0.378741i
\(426\) 0 0
\(427\) 13.1225 + 4.64789i 0.635044 + 0.224927i
\(428\) 10.7455i 0.519402i
\(429\) 0 0
\(430\) 105.219i 5.07411i
\(431\) 16.9380 + 4.53851i 0.815873 + 0.218612i 0.642541 0.766251i \(-0.277880\pi\)
0.173331 + 0.984864i \(0.444547\pi\)
\(432\) 0 0
\(433\) −17.6656 + 30.5978i −0.848957 + 1.47044i 0.0331835 + 0.999449i \(0.489435\pi\)
−0.882140 + 0.470987i \(0.843898\pi\)
\(434\) 17.9489 + 21.0182i 0.861574 + 1.00890i
\(435\) 0 0
\(436\) 36.8556 9.87543i 1.76506 0.472947i
\(437\) 7.45575 7.45575i 0.356657 0.356657i
\(438\) 0 0
\(439\) −9.35887 16.2100i −0.446674 0.773663i 0.551493 0.834180i \(-0.314058\pi\)
−0.998167 + 0.0605168i \(0.980725\pi\)
\(440\) 19.7265 + 5.28570i 0.940425 + 0.251986i
\(441\) 0 0
\(442\) −7.36404 5.97354i −0.350272 0.284133i
\(443\) −30.4948 −1.44885 −0.724426 0.689353i \(-0.757895\pi\)
−0.724426 + 0.689353i \(0.757895\pi\)
\(444\) 0 0
\(445\) −10.5538 18.2798i −0.500299 0.866544i
\(446\) −16.9211 + 29.3083i −0.801239 + 1.38779i
\(447\) 0 0
\(448\) 6.09404 + 32.8924i 0.287917 + 1.55402i
\(449\) 19.0888 5.11484i 0.900859 0.241384i 0.221474 0.975166i \(-0.428913\pi\)
0.679385 + 0.733782i \(0.262247\pi\)
\(450\) 0 0
\(451\) −12.8894 7.44168i −0.606937 0.350415i
\(452\) 7.69138 4.44062i 0.361772 0.208869i
\(453\) 0 0
\(454\) 42.3699 1.98852
\(455\) 19.3580 35.5761i 0.907517 1.66784i
\(456\) 0 0
\(457\) 7.87442 + 2.10994i 0.368350 + 0.0986990i 0.438246 0.898855i \(-0.355600\pi\)
−0.0698958 + 0.997554i \(0.522267\pi\)
\(458\) 33.8903 19.5666i 1.58359 0.914286i
\(459\) 0 0
\(460\) 45.3669 + 45.3669i 2.11524 + 2.11524i
\(461\) −32.2015 + 8.62836i −1.49977 + 0.401863i −0.913024 0.407907i \(-0.866259\pi\)
−0.586748 + 0.809769i \(0.699592\pi\)
\(462\) 0 0
\(463\) 1.66118 + 1.66118i 0.0772018 + 0.0772018i 0.744653 0.667452i \(-0.232615\pi\)
−0.667452 + 0.744653i \(0.732615\pi\)
\(464\) −2.53596 + 4.39242i −0.117729 + 0.203913i
\(465\) 0 0
\(466\) −14.1617 + 52.8523i −0.656029 + 2.44833i
\(467\) 12.2930 0.568854 0.284427 0.958698i \(-0.408197\pi\)
0.284427 + 0.958698i \(0.408197\pi\)
\(468\) 0 0
\(469\) −11.3466 0.893731i −0.523936 0.0412687i
\(470\) 37.8939 + 10.1537i 1.74792 + 0.468353i
\(471\) 0 0
\(472\) −10.8391 + 18.7738i −0.498908 + 0.864135i
\(473\) −21.5523 + 21.5523i −0.990978 + 0.990978i
\(474\) 0 0
\(475\) 6.61664 + 24.6937i 0.303592 + 1.13302i
\(476\) 6.78390 5.79324i 0.310939 0.265533i
\(477\) 0 0
\(478\) 12.5724 7.25871i 0.575050 0.332005i
\(479\) −22.8035 6.11018i −1.04192 0.279181i −0.303010 0.952987i \(-0.597992\pi\)
−0.738908 + 0.673806i \(0.764658\pi\)
\(480\) 0 0
\(481\) −14.2760 2.27341i −0.650930 0.103659i
\(482\) 1.43274i 0.0652594i
\(483\) 0 0
\(484\) 5.23177 + 9.06169i 0.237808 + 0.411895i
\(485\) −56.1413 32.4132i −2.54925 1.47181i
\(486\) 0 0
\(487\) −2.73616 10.2115i −0.123987 0.462726i 0.875814 0.482648i \(-0.160325\pi\)
−0.999802 + 0.0199217i \(0.993658\pi\)
\(488\) −2.42785 9.06085i −0.109903 0.410165i
\(489\) 0 0
\(490\) 50.6641 + 41.0378i 2.28877 + 1.85390i
\(491\) −9.46863 + 5.46672i −0.427313 + 0.246710i −0.698201 0.715901i \(-0.746016\pi\)
0.270888 + 0.962611i \(0.412683\pi\)
\(492\) 0 0
\(493\) 3.54672 0.159736
\(494\) 1.60964 + 15.4396i 0.0724210 + 0.694661i
\(495\) 0 0
\(496\) −2.11287 + 7.88533i −0.0948705 + 0.354062i
\(497\) 3.52356 + 7.38852i 0.158053 + 0.331420i
\(498\) 0 0
\(499\) −21.1483 + 21.1483i −0.946727 + 0.946727i −0.998651 0.0519238i \(-0.983465\pi\)
0.0519238 + 0.998651i \(0.483465\pi\)
\(500\) −92.5823 + 24.8073i −4.14041 + 1.10942i
\(501\) 0 0
\(502\) −30.6982 + 30.6982i −1.37013 + 1.37013i
\(503\) 6.00891 + 3.46924i 0.267924 + 0.154686i 0.627944 0.778259i \(-0.283897\pi\)
−0.360020 + 0.932945i \(0.617230\pi\)
\(504\) 0 0
\(505\) −1.76499 + 6.58703i −0.0785409 + 0.293119i
\(506\) 31.8008i 1.41372i
\(507\) 0 0
\(508\) 18.7482 0.831817
\(509\) 2.48325 9.26762i 0.110068 0.410780i −0.888803 0.458290i \(-0.848462\pi\)
0.998871 + 0.0475103i \(0.0151287\pi\)
\(510\) 0 0
\(511\) −10.1398 + 14.7515i −0.448560 + 0.652568i
\(512\) −13.2032 + 13.2032i −0.583504 + 0.583504i
\(513\) 0 0
\(514\) 9.05279 + 33.7855i 0.399301 + 1.49021i
\(515\) −43.5310 43.5310i −1.91821 1.91821i
\(516\) 0 0
\(517\) −5.68213 9.84174i −0.249900 0.432839i
\(518\) 7.76942 21.9357i 0.341369 0.963798i
\(519\) 0 0
\(520\) −27.1438 + 2.82984i −1.19033 + 0.124097i
\(521\) 17.8193i 0.780676i 0.920672 + 0.390338i \(0.127642\pi\)
−0.920672 + 0.390338i \(0.872358\pi\)
\(522\) 0 0
\(523\) 6.40070 3.69545i 0.279883 0.161591i −0.353487 0.935439i \(-0.615004\pi\)
0.633370 + 0.773849i \(0.281671\pi\)
\(524\) 13.7849 23.8762i 0.602198 1.04304i
\(525\) 0 0
\(526\) 0.247246 + 0.922736i 0.0107805 + 0.0402332i
\(527\) 5.51410 1.47750i 0.240198 0.0643608i
\(528\) 0 0
\(529\) 2.93251 5.07925i 0.127500 0.220837i
\(530\) 51.5090 + 89.2163i 2.23741 + 3.87531i
\(531\) 0 0
\(532\) −14.5593 1.14679i −0.631227 0.0497196i
\(533\) 19.6415 + 3.12785i 0.850767 + 0.135482i
\(534\) 0 0
\(535\) 4.19817 15.6678i 0.181503 0.677377i
\(536\) 3.83461 + 6.64175i 0.165630 + 0.286880i
\(537\) 0 0
\(538\) −25.5481 25.5481i −1.10146 1.10146i
\(539\) −1.97179 18.7836i −0.0849308 0.809067i
\(540\) 0 0
\(541\) −17.3442 17.3442i −0.745687 0.745687i 0.227979 0.973666i \(-0.426788\pi\)
−0.973666 + 0.227979i \(0.926788\pi\)
\(542\) −44.2481 25.5467i −1.90062 1.09732i
\(543\) 0 0
\(544\) 8.48354 + 2.27316i 0.363729 + 0.0974608i
\(545\) 57.5968 2.46718
\(546\) 0 0
\(547\) 26.8037 1.14604 0.573022 0.819540i \(-0.305771\pi\)
0.573022 + 0.819540i \(0.305771\pi\)
\(548\) −18.2472 4.88933i −0.779483 0.208862i
\(549\) 0 0
\(550\) 66.7735 + 38.5517i 2.84723 + 1.64385i
\(551\) −4.10570 4.10570i −0.174909 0.174909i
\(552\) 0 0
\(553\) 3.04099 0.563411i 0.129316 0.0239587i
\(554\) 12.6847 + 12.6847i 0.538923 + 0.538923i
\(555\) 0 0
\(556\) −0.495023 0.857405i −0.0209936 0.0363621i
\(557\) 3.42508 12.7826i 0.145125 0.541615i −0.854624 0.519247i \(-0.826213\pi\)
0.999750 0.0223686i \(-0.00712072\pi\)
\(558\) 0 0
\(559\) 16.5979 37.1953i 0.702017 1.57319i
\(560\) −1.51214 + 19.1978i −0.0638997 + 0.811254i
\(561\) 0 0
\(562\) −4.87361 8.44134i −0.205581 0.356077i
\(563\) 8.52959 14.7737i 0.359479 0.622636i −0.628395 0.777895i \(-0.716288\pi\)
0.987874 + 0.155258i \(0.0496210\pi\)
\(564\) 0 0
\(565\) 12.9496 3.46983i 0.544793 0.145977i
\(566\) 7.21260 + 26.9178i 0.303168 + 1.13144i
\(567\) 0 0
\(568\) 2.75784 4.77673i 0.115717 0.200427i
\(569\) 26.6276 15.3735i 1.11629 0.644489i 0.175837 0.984419i \(-0.443737\pi\)
0.940450 + 0.339931i \(0.110404\pi\)
\(570\) 0 0
\(571\) 4.14822i 0.173598i 0.996226 + 0.0867988i \(0.0276637\pi\)
−0.996226 + 0.0867988i \(0.972336\pi\)
\(572\) 21.2497 + 17.2373i 0.888496 + 0.720728i
\(573\) 0 0
\(574\) −10.6895 + 30.1799i −0.446170 + 1.25969i
\(575\) 34.9927 + 60.6091i 1.45930 + 2.52757i
\(576\) 0 0
\(577\) 8.22860 + 8.22860i 0.342561 + 0.342561i 0.857329 0.514768i \(-0.172122\pi\)
−0.514768 + 0.857329i \(0.672122\pi\)
\(578\) 8.83646 + 32.9781i 0.367548 + 1.37171i
\(579\) 0 0
\(580\) 24.9824 24.9824i 1.03734 1.03734i
\(581\) −9.99049 6.86722i −0.414475 0.284900i
\(582\) 0 0
\(583\) 7.72369 28.8252i 0.319883 1.19382i
\(584\) 12.0616 0.499113
\(585\) 0 0
\(586\) 12.5207i 0.517225i
\(587\) −2.86420 + 10.6893i −0.118218 + 0.441196i −0.999508 0.0313808i \(-0.990010\pi\)
0.881289 + 0.472577i \(0.156676\pi\)
\(588\) 0 0
\(589\) −8.09348 4.67278i −0.333486 0.192538i
\(590\) −80.0865 + 80.0865i −3.29711 + 3.29711i
\(591\) 0 0
\(592\) 6.63909 1.77894i 0.272865 0.0731139i
\(593\) 9.97769 9.97769i 0.409734 0.409734i −0.471911 0.881646i \(-0.656436\pi\)
0.881646 + 0.471911i \(0.156436\pi\)
\(594\) 0 0
\(595\) 12.1549 5.79661i 0.498301 0.237638i
\(596\) 8.59127 32.0631i 0.351912 1.31335i
\(597\) 0 0
\(598\) 15.1959 + 39.6864i 0.621406 + 1.62290i
\(599\) −34.7079 −1.41813 −0.709063 0.705145i \(-0.750882\pi\)
−0.709063 + 0.705145i \(0.750882\pi\)
\(600\) 0 0
\(601\) −11.2636 + 6.50302i −0.459450 + 0.265264i −0.711813 0.702369i \(-0.752126\pi\)
0.252363 + 0.967633i \(0.418792\pi\)
\(602\) 54.0337 + 37.1414i 2.20225 + 1.51377i
\(603\) 0 0
\(604\) −12.6366 47.1604i −0.514175 1.91893i
\(605\) 4.08802 + 15.2567i 0.166202 + 0.620273i
\(606\) 0 0
\(607\) 18.9672 + 10.9507i 0.769856 + 0.444477i 0.832823 0.553539i \(-0.186723\pi\)
−0.0629670 + 0.998016i \(0.520056\pi\)
\(608\) −7.18915 12.4520i −0.291559 0.504994i
\(609\) 0 0
\(610\) 49.0092i 1.98432i
\(611\) 11.7939 + 9.56698i 0.477132 + 0.387039i
\(612\) 0 0
\(613\) −10.3087 2.76221i −0.416365 0.111565i 0.0445537 0.999007i \(-0.485813\pi\)
−0.460919 + 0.887442i \(0.652480\pi\)
\(614\) 27.4815 15.8665i 1.10906 0.640319i
\(615\) 0 0
\(616\) −9.67769 + 8.26445i −0.389925 + 0.332984i
\(617\) −5.78797 21.6010i −0.233015 0.869624i −0.979034 0.203699i \(-0.934704\pi\)
0.746019 0.665925i \(-0.231963\pi\)
\(618\) 0 0
\(619\) 5.50453 5.50453i 0.221246 0.221246i −0.587777 0.809023i \(-0.699997\pi\)
0.809023 + 0.587777i \(0.199997\pi\)
\(620\) 28.4330 49.2474i 1.14190 1.97782i
\(621\) 0 0
\(622\) −30.9689 8.29810i −1.24174 0.332723i
\(623\) 13.1127 + 1.03284i 0.525349 + 0.0413800i
\(624\) 0 0
\(625\) −79.5531 −3.18213
\(626\) 10.2193 38.1390i 0.408446 1.52434i
\(627\) 0 0
\(628\) −6.20341 + 10.7446i −0.247543 + 0.428757i
\(629\) −3.39863 3.39863i −0.135512 0.135512i
\(630\) 0 0
\(631\) −20.7278 + 5.55399i −0.825160 + 0.221101i −0.646601 0.762828i \(-0.723810\pi\)
−0.178559 + 0.983929i \(0.557143\pi\)
\(632\) −1.47358 1.47358i −0.0586157 0.0586157i
\(633\) 0 0
\(634\) 32.4660 18.7442i 1.28939 0.744429i
\(635\) 27.3364 + 7.32477i 1.08481 + 0.290675i
\(636\) 0 0
\(637\) 11.4364 + 22.4991i 0.453126 + 0.891447i
\(638\) −17.5119 −0.693304
\(639\) 0 0
\(640\) 48.1116 27.7772i 1.90178 1.09799i
\(641\) 40.6530 + 23.4710i 1.60570 + 0.927050i 0.990318 + 0.138818i \(0.0443304\pi\)
0.615379 + 0.788231i \(0.289003\pi\)
\(642\) 0 0
\(643\) −22.4152 + 6.00613i −0.883968 + 0.236859i −0.672118 0.740444i \(-0.734615\pi\)
−0.211850 + 0.977302i \(0.567949\pi\)
\(644\) −39.3116 + 7.28336i −1.54910 + 0.287005i
\(645\) 0 0
\(646\) −2.58064 + 4.46981i −0.101534 + 0.175862i
\(647\) −6.98028 12.0902i −0.274423 0.475315i 0.695566 0.718462i \(-0.255154\pi\)
−0.969989 + 0.243147i \(0.921820\pi\)
\(648\) 0 0
\(649\) 32.8087 1.28786
\(650\) −101.753 16.2038i −3.99108 0.635567i
\(651\) 0 0
\(652\) −1.71833 0.460426i −0.0672951 0.0180317i
\(653\) 13.4921 + 23.3689i 0.527985 + 0.914497i 0.999468 + 0.0326216i \(0.0103856\pi\)
−0.471483 + 0.881875i \(0.656281\pi\)
\(654\) 0 0
\(655\) 29.4278 29.4278i 1.14984 1.14984i
\(656\) −9.13431 + 2.44753i −0.356635 + 0.0955601i
\(657\) 0 0
\(658\) −18.5905 + 15.8757i −0.724733 + 0.618900i
\(659\) −2.76889 + 4.79586i −0.107861 + 0.186820i −0.914903 0.403673i \(-0.867733\pi\)
0.807043 + 0.590493i \(0.201067\pi\)
\(660\) 0 0
\(661\) −36.8331 9.86941i −1.43264 0.383875i −0.542692 0.839932i \(-0.682595\pi\)
−0.889951 + 0.456057i \(0.849261\pi\)
\(662\) 21.7939i 0.847046i
\(663\) 0 0
\(664\) 8.16876i 0.317009i
\(665\) −20.7807 7.36032i −0.805839 0.285421i
\(666\) 0 0
\(667\) −13.7657 7.94763i −0.533010 0.307733i
\(668\) 33.7200 + 33.7200i 1.30466 + 1.30466i
\(669\) 0 0
\(670\) 10.3705 + 38.7033i 0.400648 + 1.49524i
\(671\) −10.0387 + 10.0387i −0.387540 + 0.387540i
\(672\) 0 0
\(673\) 5.72219 3.30371i 0.220574 0.127349i −0.385642 0.922649i \(-0.626020\pi\)
0.606216 + 0.795300i \(0.292687\pi\)
\(674\) 3.66100 13.6630i 0.141016 0.526281i
\(675\) 0 0
\(676\) −34.7557 11.3575i −1.33676 0.436827i
\(677\) 21.3320i 0.819855i −0.912118 0.409928i \(-0.865554\pi\)
0.912118 0.409928i \(-0.134446\pi\)
\(678\) 0 0
\(679\) 36.4627 17.3889i 1.39931 0.667326i
\(680\) −7.85819 4.53693i −0.301348 0.173983i
\(681\) 0 0
\(682\) −27.2258 + 7.29513i −1.04253 + 0.279345i
\(683\) 1.32430 0.354846i 0.0506730 0.0135778i −0.233393 0.972382i \(-0.574983\pi\)
0.284067 + 0.958805i \(0.408316\pi\)
\(684\) 0 0
\(685\) −24.6958 14.2581i −0.943576 0.544774i
\(686\) −38.9584 + 11.5318i −1.48744 + 0.440286i
\(687\) 0 0
\(688\) 19.3660i 0.738323i
\(689\) 4.13508 + 39.6636i 0.157534 + 1.51106i
\(690\) 0 0
\(691\) −8.87327 + 33.1155i −0.337555 + 1.25977i 0.563517 + 0.826104i \(0.309448\pi\)
−0.901072 + 0.433669i \(0.857219\pi\)
\(692\) −22.4422 + 12.9570i −0.853124 + 0.492551i
\(693\) 0 0
\(694\) −18.6303 + 18.6303i −0.707197 + 0.707197i
\(695\) −0.386803 1.44357i −0.0146723 0.0547577i
\(696\) 0 0
\(697\) 4.67597 + 4.67597i 0.177115 + 0.177115i
\(698\) 48.3762 + 27.9300i 1.83107 + 1.05717i
\(699\) 0 0
\(700\) 32.3638 91.3738i 1.22324 3.45361i
\(701\) 42.5906i 1.60862i −0.594208 0.804312i \(-0.702534\pi\)
0.594208 0.804312i \(-0.297466\pi\)
\(702\) 0 0
\(703\) 7.86853i 0.296767i
\(704\) −32.9518 8.82940i −1.24192 0.332771i
\(705\) 0 0
\(706\) −10.3007 + 17.8413i −0.387671 + 0.671466i
\(707\) −2.75964 3.23155i −0.103787 0.121535i
\(708\) 0 0
\(709\) 37.3239 10.0009i 1.40173 0.375592i 0.522764 0.852478i \(-0.324901\pi\)
0.878965 + 0.476886i \(0.158234\pi\)
\(710\) 20.3769 20.3769i 0.764730 0.764730i
\(711\) 0 0
\(712\) −4.43148 7.67556i −0.166077 0.287654i
\(713\) −24.7124 6.62166i −0.925486 0.247983i
\(714\) 0 0
\(715\) 24.2494 + 33.4355i 0.906876 + 1.25042i
\(716\) −7.65273 −0.285996
\(717\) 0 0
\(718\) 25.2525 + 43.7385i 0.942413 + 1.63231i
\(719\) 25.0297 43.3527i 0.933450 1.61678i 0.156076 0.987745i \(-0.450116\pi\)
0.777375 0.629038i \(-0.216551\pi\)
\(720\) 0 0
\(721\) 37.7208 6.98862i 1.40480 0.260270i
\(722\) −32.0998 + 8.60112i −1.19463 + 0.320101i
\(723\) 0 0
\(724\) −37.6396 21.7312i −1.39886 0.807634i
\(725\) 33.3759 19.2696i 1.23955 0.715655i
\(726\) 0 0
\(727\) −5.22923 −0.193941 −0.0969707 0.995287i \(-0.530915\pi\)
−0.0969707 + 0.995287i \(0.530915\pi\)
\(728\) 8.12831 14.9382i 0.301255 0.553647i
\(729\) 0 0
\(730\) 60.8698 + 16.3100i 2.25289 + 0.603661i
\(731\) 11.7280 6.77119i 0.433777 0.250442i
\(732\) 0 0
\(733\) 10.0406 + 10.0406i 0.370858 + 0.370858i 0.867790 0.496932i \(-0.165540\pi\)
−0.496932 + 0.867790i \(0.665540\pi\)
\(734\) 48.0070 12.8634i 1.77197 0.474798i
\(735\) 0 0
\(736\) −27.8329 27.8329i −1.02593 1.02593i
\(737\) 5.80349 10.0519i 0.213774 0.370268i
\(738\) 0 0
\(739\) −1.48318 + 5.53532i −0.0545598 + 0.203620i −0.987825 0.155567i \(-0.950279\pi\)
0.933265 + 0.359187i \(0.116946\pi\)
\(740\) −47.8786 −1.76005
\(741\) 0 0
\(742\) −63.9979 5.04090i −2.34944 0.185057i
\(743\) −0.617584 0.165481i −0.0226569 0.00607091i 0.247473 0.968895i \(-0.420400\pi\)
−0.270130 + 0.962824i \(0.587067\pi\)
\(744\) 0 0
\(745\) 25.0536 43.3941i 0.917892 1.58984i
\(746\) 34.2932 34.2932i 1.25556 1.25556i
\(747\) 0 0
\(748\) 2.35460 + 8.78749i 0.0860928 + 0.321303i
\(749\) 6.56404 + 7.68650i 0.239845 + 0.280859i
\(750\) 0 0
\(751\) −22.0888 + 12.7530i −0.806031 + 0.465362i −0.845576 0.533856i \(-0.820743\pi\)
0.0395448 + 0.999218i \(0.487409\pi\)
\(752\) −6.97454 1.86882i −0.254335 0.0681490i
\(753\) 0 0
\(754\) 21.8543 8.36799i 0.795887 0.304744i
\(755\) 73.7008i 2.68225i
\(756\) 0 0
\(757\) 8.06785 + 13.9739i 0.293231 + 0.507891i 0.974572 0.224075i \(-0.0719362\pi\)
−0.681341 + 0.731966i \(0.738603\pi\)
\(758\) −2.02669 1.17011i −0.0736127 0.0425003i
\(759\) 0 0
\(760\) 3.84470 + 14.3486i 0.139462 + 0.520479i
\(761\) −6.42639 23.9836i −0.232957 0.869406i −0.979059 0.203575i \(-0.934744\pi\)
0.746103 0.665831i \(-0.231923\pi\)
\(762\) 0 0
\(763\) −20.3312 + 29.5780i −0.736038 + 1.07079i
\(764\) −7.97831 + 4.60628i −0.288645 + 0.166649i
\(765\) 0 0
\(766\) −27.3856 −0.989481
\(767\) −40.9442 + 15.6775i −1.47841 + 0.566082i
\(768\) 0 0
\(769\) 3.09729 11.5592i 0.111691 0.416837i −0.887327 0.461141i \(-0.847440\pi\)
0.999018 + 0.0443040i \(0.0141070\pi\)
\(770\) −60.0145 + 28.6207i −2.16277 + 1.03142i
\(771\) 0 0
\(772\) −41.8368 + 41.8368i −1.50574 + 1.50574i
\(773\) 1.00730 0.269904i 0.0362299 0.00970777i −0.240659 0.970610i \(-0.577363\pi\)
0.276888 + 0.960902i \(0.410697\pi\)
\(774\) 0 0
\(775\) 43.8623 43.8623i 1.57558 1.57558i
\(776\) −23.5734 13.6101i −0.846235 0.488574i
\(777\) 0 0
\(778\) −10.7958 + 40.2904i −0.387047 + 1.44448i
\(779\) 10.8258i 0.387875i
\(780\) 0 0
\(781\) −8.34771 −0.298704
\(782\) −3.65696 + 13.6480i −0.130773 + 0.488050i
\(783\) 0 0
\(784\) −9.32495 7.55319i −0.333034 0.269757i
\(785\) −13.2429 + 13.2429i −0.472660 + 0.472660i
\(786\) 0 0
\(787\) −12.4106 46.3169i −0.442389 1.65102i −0.722738 0.691122i \(-0.757117\pi\)
0.280349 0.959898i \(-0.409550\pi\)
\(788\) −41.5834 41.5834i −1.48135 1.48135i