Properties

Label 819.2.n.d.172.4
Level $819$
Weight $2$
Character 819.172
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
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.n (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 172.4
Root \(-0.437442 - 0.757672i\) of defining polynomial
Character \(\chi\) \(=\) 819.172
Dual form 819.2.n.d.100.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.134063 + 0.232203i) q^{2} +(0.964054 + 1.66979i) q^{4} +(-1.28088 - 2.21854i) q^{5} +(0.773854 - 2.53005i) q^{7} -1.05323 q^{8} +O(q^{10})\) \(q+(-0.134063 + 0.232203i) q^{2} +(0.964054 + 1.66979i) q^{4} +(-1.28088 - 2.21854i) q^{5} +(0.773854 - 2.53005i) q^{7} -1.05323 q^{8} +0.686871 q^{10} -3.94600 q^{11} +(-3.15374 - 1.74755i) q^{13} +(0.483741 + 0.518876i) q^{14} +(-1.78691 + 3.09502i) q^{16} +(0.392550 + 0.679916i) q^{17} -7.49527 q^{19} +(2.46967 - 4.27760i) q^{20} +(0.529011 - 0.916274i) q^{22} +(-3.97759 + 6.88938i) q^{23} +(-0.781294 + 1.35324i) q^{25} +(0.828585 - 0.498028i) q^{26} +(4.97069 - 1.14693i) q^{28} +(1.17586 + 2.03666i) q^{29} +(1.27718 - 2.21215i) q^{31} +(-1.53234 - 2.65409i) q^{32} -0.210505 q^{34} +(-6.60424 + 1.52385i) q^{35} +(-3.37858 + 5.85187i) q^{37} +(1.00484 - 1.74043i) q^{38} +(1.34905 + 2.33663i) q^{40} +(-1.21874 - 2.11091i) q^{41} +(1.12473 - 1.94809i) q^{43} +(-3.80416 - 6.58900i) q^{44} +(-1.06649 - 1.84722i) q^{46} +(0.658276 + 1.14017i) q^{47} +(-5.80230 - 3.91578i) q^{49} +(-0.209485 - 0.362838i) q^{50} +(-0.122340 - 6.95082i) q^{52} +(4.63977 - 8.03632i) q^{53} +(5.05434 + 8.75438i) q^{55} +(-0.815042 + 2.66471i) q^{56} -0.630558 q^{58} +(-4.48335 - 7.76540i) q^{59} +9.44547 q^{61} +(0.342445 + 0.593132i) q^{62} -6.32592 q^{64} +(0.162546 + 9.23511i) q^{65} -1.35256 q^{67} +(-0.756879 + 1.31095i) q^{68} +(0.531538 - 1.73782i) q^{70} +(6.15808 - 10.6661i) q^{71} +(-0.384295 + 0.665619i) q^{73} +(-0.905882 - 1.56903i) q^{74} +(-7.22585 - 12.5155i) q^{76} +(-3.05363 + 9.98358i) q^{77} +(-3.09642 - 5.36316i) q^{79} +9.15525 q^{80} +0.653548 q^{82} +1.07292 q^{83} +(1.00562 - 1.74178i) q^{85} +(0.301568 + 0.522332i) q^{86} +4.15603 q^{88} +(3.83149 - 6.63634i) q^{89} +(-6.86191 + 6.62678i) q^{91} -15.3384 q^{92} -0.353001 q^{94} +(9.60052 + 16.6286i) q^{95} +(1.18601 - 2.05423i) q^{97} +(1.68713 - 0.822354i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} + O(q^{10}) \) \( 12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} - 8q^{10} + 8q^{11} - 2q^{13} + 2q^{14} + 8q^{16} - 5q^{17} + 2q^{19} + q^{20} - 5q^{22} + q^{23} + 7q^{25} - 5q^{26} - 7q^{28} - 3q^{29} + 16q^{31} - 8q^{32} + 32q^{34} - 8q^{35} - 13q^{37} + 17q^{38} - 5q^{40} + 8q^{41} - 11q^{43} - 21q^{44} + 16q^{46} + q^{47} - 3q^{49} - 6q^{50} - 25q^{52} + 2q^{53} + 9q^{55} + 18q^{56} + 16q^{58} - 13q^{59} + 10q^{61} - 5q^{62} - 30q^{64} - 19q^{65} + 22q^{67} - 29q^{68} - 39q^{70} - 6q^{71} - 30q^{73} + 3q^{74} - 9q^{76} - 11q^{77} + 7q^{79} - 14q^{80} - 2q^{82} + 54q^{83} - q^{85} + 7q^{86} - 4q^{89} - 20q^{91} - 54q^{92} - 90q^{94} + 6q^{95} - 35q^{97} - 62q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.134063 + 0.232203i −0.0947966 + 0.164193i −0.909524 0.415652i \(-0.863553\pi\)
0.814727 + 0.579845i \(0.196887\pi\)
\(3\) 0 0
\(4\) 0.964054 + 1.66979i 0.482027 + 0.834896i
\(5\) −1.28088 2.21854i −0.572826 0.992163i −0.996274 0.0862431i \(-0.972514\pi\)
0.423448 0.905920i \(-0.360820\pi\)
\(6\) 0 0
\(7\) 0.773854 2.53005i 0.292489 0.956269i
\(8\) −1.05323 −0.372371
\(9\) 0 0
\(10\) 0.686871 0.217208
\(11\) −3.94600 −1.18976 −0.594882 0.803813i \(-0.702801\pi\)
−0.594882 + 0.803813i \(0.702801\pi\)
\(12\) 0 0
\(13\) −3.15374 1.74755i −0.874690 0.484682i
\(14\) 0.483741 + 0.518876i 0.129285 + 0.138676i
\(15\) 0 0
\(16\) −1.78691 + 3.09502i −0.446728 + 0.773755i
\(17\) 0.392550 + 0.679916i 0.0952073 + 0.164904i 0.909695 0.415277i \(-0.136315\pi\)
−0.814488 + 0.580181i \(0.802982\pi\)
\(18\) 0 0
\(19\) −7.49527 −1.71953 −0.859767 0.510687i \(-0.829391\pi\)
−0.859767 + 0.510687i \(0.829391\pi\)
\(20\) 2.46967 4.27760i 0.552235 0.956500i
\(21\) 0 0
\(22\) 0.529011 0.916274i 0.112786 0.195350i
\(23\) −3.97759 + 6.88938i −0.829384 + 1.43654i 0.0691375 + 0.997607i \(0.477975\pi\)
−0.898522 + 0.438929i \(0.855358\pi\)
\(24\) 0 0
\(25\) −0.781294 + 1.35324i −0.156259 + 0.270648i
\(26\) 0.828585 0.498028i 0.162499 0.0976714i
\(27\) 0 0
\(28\) 4.97069 1.14693i 0.939372 0.216750i
\(29\) 1.17586 + 2.03666i 0.218353 + 0.378198i 0.954304 0.298836i \(-0.0965984\pi\)
−0.735952 + 0.677034i \(0.763265\pi\)
\(30\) 0 0
\(31\) 1.27718 2.21215i 0.229389 0.397313i −0.728238 0.685324i \(-0.759661\pi\)
0.957627 + 0.288011i \(0.0929939\pi\)
\(32\) −1.53234 2.65409i −0.270882 0.469182i
\(33\) 0 0
\(34\) −0.210505 −0.0361013
\(35\) −6.60424 + 1.52385i −1.11632 + 0.257578i
\(36\) 0 0
\(37\) −3.37858 + 5.85187i −0.555435 + 0.962041i 0.442435 + 0.896801i \(0.354115\pi\)
−0.997870 + 0.0652406i \(0.979219\pi\)
\(38\) 1.00484 1.74043i 0.163006 0.282334i
\(39\) 0 0
\(40\) 1.34905 + 2.33663i 0.213304 + 0.369453i
\(41\) −1.21874 2.11091i −0.190335 0.329669i 0.755027 0.655694i \(-0.227624\pi\)
−0.945361 + 0.326025i \(0.894291\pi\)
\(42\) 0 0
\(43\) 1.12473 1.94809i 0.171520 0.297081i −0.767432 0.641131i \(-0.778466\pi\)
0.938951 + 0.344050i \(0.111799\pi\)
\(44\) −3.80416 6.58900i −0.573499 0.993329i
\(45\) 0 0
\(46\) −1.06649 1.84722i −0.157246 0.272357i
\(47\) 0.658276 + 1.14017i 0.0960195 + 0.166311i 0.910034 0.414534i \(-0.136056\pi\)
−0.814014 + 0.580845i \(0.802722\pi\)
\(48\) 0 0
\(49\) −5.80230 3.91578i −0.828900 0.559397i
\(50\) −0.209485 0.362838i −0.0296256 0.0513130i
\(51\) 0 0
\(52\) −0.122340 6.95082i −0.0169655 0.963905i
\(53\) 4.63977 8.03632i 0.637321 1.10387i −0.348697 0.937236i \(-0.613376\pi\)
0.986018 0.166637i \(-0.0532909\pi\)
\(54\) 0 0
\(55\) 5.05434 + 8.75438i 0.681528 + 1.18044i
\(56\) −0.815042 + 2.66471i −0.108915 + 0.356087i
\(57\) 0 0
\(58\) −0.630558 −0.0827963
\(59\) −4.48335 7.76540i −0.583683 1.01097i −0.995038 0.0994935i \(-0.968278\pi\)
0.411355 0.911475i \(-0.365056\pi\)
\(60\) 0 0
\(61\) 9.44547 1.20937 0.604684 0.796465i \(-0.293299\pi\)
0.604684 + 0.796465i \(0.293299\pi\)
\(62\) 0.342445 + 0.593132i 0.0434906 + 0.0753279i
\(63\) 0 0
\(64\) −6.32592 −0.790741
\(65\) 0.162546 + 9.23511i 0.0201613 + 1.14547i
\(66\) 0 0
\(67\) −1.35256 −0.165242 −0.0826209 0.996581i \(-0.526329\pi\)
−0.0826209 + 0.996581i \(0.526329\pi\)
\(68\) −0.756879 + 1.31095i −0.0917851 + 0.158976i
\(69\) 0 0
\(70\) 0.531538 1.73782i 0.0635309 0.207709i
\(71\) 6.15808 10.6661i 0.730829 1.26583i −0.225700 0.974197i \(-0.572467\pi\)
0.956529 0.291637i \(-0.0941998\pi\)
\(72\) 0 0
\(73\) −0.384295 + 0.665619i −0.0449783 + 0.0779048i −0.887638 0.460542i \(-0.847655\pi\)
0.842660 + 0.538446i \(0.180989\pi\)
\(74\) −0.905882 1.56903i −0.105307 0.182396i
\(75\) 0 0
\(76\) −7.22585 12.5155i −0.828862 1.43563i
\(77\) −3.05363 + 9.98358i −0.347993 + 1.13773i
\(78\) 0 0
\(79\) −3.09642 5.36316i −0.348375 0.603402i 0.637586 0.770379i \(-0.279933\pi\)
−0.985961 + 0.166976i \(0.946600\pi\)
\(80\) 9.15525 1.02359
\(81\) 0 0
\(82\) 0.653548 0.0721723
\(83\) 1.07292 0.117768 0.0588841 0.998265i \(-0.481246\pi\)
0.0588841 + 0.998265i \(0.481246\pi\)
\(84\) 0 0
\(85\) 1.00562 1.74178i 0.109074 0.188922i
\(86\) 0.301568 + 0.522332i 0.0325190 + 0.0563245i
\(87\) 0 0
\(88\) 4.15603 0.443034
\(89\) 3.83149 6.63634i 0.406138 0.703451i −0.588316 0.808631i \(-0.700209\pi\)
0.994453 + 0.105180i \(0.0335420\pi\)
\(90\) 0 0
\(91\) −6.86191 + 6.62678i −0.719324 + 0.694675i
\(92\) −15.3384 −1.59914
\(93\) 0 0
\(94\) −0.353001 −0.0364093
\(95\) 9.60052 + 16.6286i 0.984993 + 1.70606i
\(96\) 0 0
\(97\) 1.18601 2.05423i 0.120421 0.208575i −0.799513 0.600649i \(-0.794909\pi\)
0.919934 + 0.392074i \(0.128242\pi\)
\(98\) 1.68713 0.822354i 0.170426 0.0830703i
\(99\) 0 0
\(100\) −3.01284 −0.301284
\(101\) 0.797330 0.0793373 0.0396686 0.999213i \(-0.487370\pi\)
0.0396686 + 0.999213i \(0.487370\pi\)
\(102\) 0 0
\(103\) −1.08309 1.87597i −0.106720 0.184844i 0.807720 0.589567i \(-0.200701\pi\)
−0.914440 + 0.404722i \(0.867368\pi\)
\(104\) 3.32160 + 1.84056i 0.325710 + 0.180482i
\(105\) 0 0
\(106\) 1.24404 + 2.15474i 0.120832 + 0.209287i
\(107\) −5.76311 + 9.98201i −0.557141 + 0.964997i 0.440592 + 0.897707i \(0.354768\pi\)
−0.997733 + 0.0672896i \(0.978565\pi\)
\(108\) 0 0
\(109\) −4.03912 + 6.99595i −0.386877 + 0.670091i −0.992028 0.126020i \(-0.959780\pi\)
0.605151 + 0.796111i \(0.293113\pi\)
\(110\) −2.71039 −0.258426
\(111\) 0 0
\(112\) 6.44775 + 6.91607i 0.609255 + 0.653507i
\(113\) 4.02067 6.96401i 0.378233 0.655119i −0.612572 0.790415i \(-0.709865\pi\)
0.990805 + 0.135296i \(0.0431984\pi\)
\(114\) 0 0
\(115\) 20.3792 1.90037
\(116\) −2.26719 + 3.92690i −0.210504 + 0.364603i
\(117\) 0 0
\(118\) 2.40420 0.221325
\(119\) 2.02400 0.467015i 0.185540 0.0428112i
\(120\) 0 0
\(121\) 4.57093 0.415539
\(122\) −1.26628 + 2.19327i −0.114644 + 0.198569i
\(123\) 0 0
\(124\) 4.92510 0.442287
\(125\) −8.80581 −0.787615
\(126\) 0 0
\(127\) −0.894023 1.54849i −0.0793317 0.137406i 0.823630 0.567127i \(-0.191945\pi\)
−0.902962 + 0.429721i \(0.858612\pi\)
\(128\) 3.91275 6.77709i 0.345842 0.599015i
\(129\) 0 0
\(130\) −2.16621 1.20034i −0.189989 0.105277i
\(131\) −3.19545 5.53469i −0.279188 0.483568i 0.691995 0.721902i \(-0.256732\pi\)
−0.971183 + 0.238334i \(0.923399\pi\)
\(132\) 0 0
\(133\) −5.80024 + 18.9634i −0.502945 + 1.64434i
\(134\) 0.181328 0.314069i 0.0156644 0.0271315i
\(135\) 0 0
\(136\) −0.413443 0.716105i −0.0354525 0.0614055i
\(137\) 5.01827 + 8.69190i 0.428740 + 0.742599i 0.996762 0.0804144i \(-0.0256244\pi\)
−0.568022 + 0.823014i \(0.692291\pi\)
\(138\) 0 0
\(139\) 2.77278 4.80260i 0.235184 0.407351i −0.724142 0.689651i \(-0.757764\pi\)
0.959326 + 0.282300i \(0.0910972\pi\)
\(140\) −8.91137 9.55862i −0.753148 0.807851i
\(141\) 0 0
\(142\) 1.65114 + 2.85985i 0.138560 + 0.239993i
\(143\) 12.4447 + 6.89582i 1.04068 + 0.576658i
\(144\) 0 0
\(145\) 3.01228 5.21742i 0.250156 0.433283i
\(146\) −0.103039 0.178469i −0.00852759 0.0147702i
\(147\) 0 0
\(148\) −13.0285 −1.07094
\(149\) −18.4651 −1.51272 −0.756359 0.654157i \(-0.773024\pi\)
−0.756359 + 0.654157i \(0.773024\pi\)
\(150\) 0 0
\(151\) −0.803678 + 1.39201i −0.0654024 + 0.113280i −0.896872 0.442289i \(-0.854166\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(152\) 7.89421 0.640305
\(153\) 0 0
\(154\) −1.90884 2.04749i −0.153819 0.164991i
\(155\) −6.54366 −0.525600
\(156\) 0 0
\(157\) 0.822967 1.42542i 0.0656799 0.113761i −0.831315 0.555801i \(-0.812412\pi\)
0.896995 + 0.442040i \(0.145745\pi\)
\(158\) 1.66046 0.132099
\(159\) 0 0
\(160\) −3.92548 + 6.79913i −0.310337 + 0.537519i
\(161\) 14.3524 + 15.3949i 1.13113 + 1.21329i
\(162\) 0 0
\(163\) −6.54819 −0.512894 −0.256447 0.966558i \(-0.582552\pi\)
−0.256447 + 0.966558i \(0.582552\pi\)
\(164\) 2.34986 4.07007i 0.183493 0.317819i
\(165\) 0 0
\(166\) −0.143838 + 0.249135i −0.0111640 + 0.0193367i
\(167\) 4.77440 + 8.26950i 0.369454 + 0.639913i 0.989480 0.144668i \(-0.0462114\pi\)
−0.620026 + 0.784581i \(0.712878\pi\)
\(168\) 0 0
\(169\) 6.89216 + 11.0226i 0.530166 + 0.847894i
\(170\) 0.269631 + 0.467015i 0.0206798 + 0.0358184i
\(171\) 0 0
\(172\) 4.33720 0.330709
\(173\) −11.1316 −0.846322 −0.423161 0.906054i \(-0.639080\pi\)
−0.423161 + 0.906054i \(0.639080\pi\)
\(174\) 0 0
\(175\) 2.81916 + 3.02392i 0.213108 + 0.228587i
\(176\) 7.05115 12.2130i 0.531501 0.920586i
\(177\) 0 0
\(178\) 1.02732 + 1.77937i 0.0770009 + 0.133369i
\(179\) 12.6435 0.945017 0.472508 0.881326i \(-0.343349\pi\)
0.472508 + 0.881326i \(0.343349\pi\)
\(180\) 0 0
\(181\) 14.9158 1.10868 0.554341 0.832289i \(-0.312970\pi\)
0.554341 + 0.832289i \(0.312970\pi\)
\(182\) −0.618833 2.48176i −0.0458709 0.183960i
\(183\) 0 0
\(184\) 4.18930 7.25607i 0.308839 0.534925i
\(185\) 17.3102 1.27267
\(186\) 0 0
\(187\) −1.54900 2.68295i −0.113274 0.196197i
\(188\) −1.26923 + 2.19837i −0.0925680 + 0.160332i
\(189\) 0 0
\(190\) −5.14829 −0.373496
\(191\) 14.1306 1.02245 0.511226 0.859447i \(-0.329192\pi\)
0.511226 + 0.859447i \(0.329192\pi\)
\(192\) 0 0
\(193\) 3.89454 0.280335 0.140167 0.990128i \(-0.455236\pi\)
0.140167 + 0.990128i \(0.455236\pi\)
\(194\) 0.317999 + 0.550790i 0.0228310 + 0.0395444i
\(195\) 0 0
\(196\) 0.944795 13.4637i 0.0674853 0.961689i
\(197\) −5.85445 10.1402i −0.417112 0.722459i 0.578536 0.815657i \(-0.303624\pi\)
−0.995648 + 0.0931979i \(0.970291\pi\)
\(198\) 0 0
\(199\) −1.74842 3.02835i −0.123942 0.214674i 0.797377 0.603482i \(-0.206220\pi\)
−0.921319 + 0.388808i \(0.872887\pi\)
\(200\) 0.822878 1.42527i 0.0581863 0.100782i
\(201\) 0 0
\(202\) −0.106892 + 0.185143i −0.00752090 + 0.0130266i
\(203\) 6.06279 1.39892i 0.425524 0.0981850i
\(204\) 0 0
\(205\) −3.12210 + 5.40764i −0.218057 + 0.377686i
\(206\) 0.580807 0.0404667
\(207\) 0 0
\(208\) 11.0441 6.63818i 0.765774 0.460275i
\(209\) 29.5764 2.04584
\(210\) 0 0
\(211\) −9.50258 16.4589i −0.654184 1.13308i −0.982098 0.188373i \(-0.939679\pi\)
0.327913 0.944708i \(-0.393655\pi\)
\(212\) 17.8920 1.22882
\(213\) 0 0
\(214\) −1.54524 2.67643i −0.105630 0.182957i
\(215\) −5.76256 −0.393004
\(216\) 0 0
\(217\) −4.60849 4.94321i −0.312844 0.335567i
\(218\) −1.08299 1.87579i −0.0733492 0.127045i
\(219\) 0 0
\(220\) −9.74533 + 16.8794i −0.657030 + 1.13801i
\(221\) −0.0498153 2.83028i −0.00335094 0.190385i
\(222\) 0 0
\(223\) 5.98311 + 10.3630i 0.400658 + 0.693961i 0.993805 0.111133i \(-0.0354481\pi\)
−0.593147 + 0.805094i \(0.702115\pi\)
\(224\) −7.90079 + 1.82302i −0.527894 + 0.121806i
\(225\) 0 0
\(226\) 1.07804 + 1.86723i 0.0717104 + 0.124206i
\(227\) 7.69209 + 13.3231i 0.510542 + 0.884284i 0.999925 + 0.0122157i \(0.00388847\pi\)
−0.489384 + 0.872069i \(0.662778\pi\)
\(228\) 0 0
\(229\) −4.33084 7.50123i −0.286190 0.495695i 0.686707 0.726934i \(-0.259055\pi\)
−0.972897 + 0.231239i \(0.925722\pi\)
\(230\) −2.73209 + 4.73212i −0.180149 + 0.312027i
\(231\) 0 0
\(232\) −1.23845 2.14506i −0.0813082 0.140830i
\(233\) 10.1253 + 17.5376i 0.663333 + 1.14893i 0.979734 + 0.200301i \(0.0641919\pi\)
−0.316402 + 0.948625i \(0.602475\pi\)
\(234\) 0 0
\(235\) 1.68634 2.92083i 0.110005 0.190534i
\(236\) 8.64440 14.9725i 0.562702 0.974629i
\(237\) 0 0
\(238\) −0.162900 + 0.532588i −0.0105592 + 0.0345226i
\(239\) −16.5526 −1.07070 −0.535350 0.844630i \(-0.679820\pi\)
−0.535350 + 0.844630i \(0.679820\pi\)
\(240\) 0 0
\(241\) 8.20038 + 14.2035i 0.528233 + 0.914926i 0.999458 + 0.0329132i \(0.0104785\pi\)
−0.471225 + 0.882013i \(0.656188\pi\)
\(242\) −0.612791 + 1.06138i −0.0393917 + 0.0682284i
\(243\) 0 0
\(244\) 9.10595 + 15.7720i 0.582949 + 1.00970i
\(245\) −1.25529 + 17.8883i −0.0801974 + 1.14284i
\(246\) 0 0
\(247\) 23.6381 + 13.0983i 1.50406 + 0.833427i
\(248\) −1.34516 + 2.32989i −0.0854178 + 0.147948i
\(249\) 0 0
\(250\) 1.18053 2.04474i 0.0746632 0.129321i
\(251\) −10.2154 + 17.6935i −0.644788 + 1.11681i 0.339563 + 0.940583i \(0.389721\pi\)
−0.984350 + 0.176222i \(0.943612\pi\)
\(252\) 0 0
\(253\) 15.6956 27.1855i 0.986772 1.70914i
\(254\) 0.479420 0.0300815
\(255\) 0 0
\(256\) −5.27682 9.13972i −0.329801 0.571232i
\(257\) 6.88895 11.9320i 0.429721 0.744299i −0.567127 0.823630i \(-0.691945\pi\)
0.996848 + 0.0793315i \(0.0252786\pi\)
\(258\) 0 0
\(259\) 12.1910 + 13.0765i 0.757511 + 0.812532i
\(260\) −15.2640 + 9.17456i −0.946633 + 0.568982i
\(261\) 0 0
\(262\) 1.71356 0.105864
\(263\) −25.9173 −1.59813 −0.799065 0.601244i \(-0.794672\pi\)
−0.799065 + 0.601244i \(0.794672\pi\)
\(264\) 0 0
\(265\) −23.7719 −1.46030
\(266\) −3.62577 3.88912i −0.222310 0.238457i
\(267\) 0 0
\(268\) −1.30394 2.25850i −0.0796510 0.137960i
\(269\) −15.0333 26.0384i −0.916596 1.58759i −0.804547 0.593889i \(-0.797592\pi\)
−0.112050 0.993703i \(-0.535742\pi\)
\(270\) 0 0
\(271\) −7.22527 + 12.5145i −0.438904 + 0.760204i −0.997605 0.0691651i \(-0.977966\pi\)
0.558701 + 0.829369i \(0.311300\pi\)
\(272\) −2.80581 −0.170127
\(273\) 0 0
\(274\) −2.69105 −0.162572
\(275\) 3.08299 5.33989i 0.185911 0.322008i
\(276\) 0 0
\(277\) 7.66274 + 13.2723i 0.460409 + 0.797452i 0.998981 0.0451272i \(-0.0143693\pi\)
−0.538572 + 0.842580i \(0.681036\pi\)
\(278\) 0.743453 + 1.28770i 0.0445894 + 0.0772310i
\(279\) 0 0
\(280\) 6.95575 1.60496i 0.415686 0.0959148i
\(281\) −5.29279 −0.315741 −0.157871 0.987460i \(-0.550463\pi\)
−0.157871 + 0.987460i \(0.550463\pi\)
\(282\) 0 0
\(283\) −30.7845 −1.82995 −0.914975 0.403511i \(-0.867790\pi\)
−0.914975 + 0.403511i \(0.867790\pi\)
\(284\) 23.7469 1.40912
\(285\) 0 0
\(286\) −3.26960 + 1.96522i −0.193335 + 0.116206i
\(287\) −6.28384 + 1.44992i −0.370923 + 0.0855864i
\(288\) 0 0
\(289\) 8.19181 14.1886i 0.481871 0.834625i
\(290\) 0.807667 + 1.39892i 0.0474279 + 0.0821474i
\(291\) 0 0
\(292\) −1.48193 −0.0867231
\(293\) −8.75864 + 15.1704i −0.511685 + 0.886265i 0.488223 + 0.872719i \(0.337645\pi\)
−0.999908 + 0.0135461i \(0.995688\pi\)
\(294\) 0 0
\(295\) −11.4853 + 19.8930i −0.668697 + 1.15822i
\(296\) 3.55840 6.16333i 0.206828 0.358237i
\(297\) 0 0
\(298\) 2.47548 4.28765i 0.143400 0.248377i
\(299\) 24.5838 14.7763i 1.42172 0.854536i
\(300\) 0 0
\(301\) −4.05839 4.35316i −0.233921 0.250912i
\(302\) −0.215486 0.373233i −0.0123998 0.0214772i
\(303\) 0 0
\(304\) 13.3934 23.1980i 0.768163 1.33050i
\(305\) −12.0985 20.9552i −0.692757 1.19989i
\(306\) 0 0
\(307\) −8.63573 −0.492867 −0.246434 0.969160i \(-0.579259\pi\)
−0.246434 + 0.969160i \(0.579259\pi\)
\(308\) −19.6144 + 4.52579i −1.11763 + 0.257881i
\(309\) 0 0
\(310\) 0.877260 1.51946i 0.0498250 0.0862995i
\(311\) −8.21130 + 14.2224i −0.465620 + 0.806478i −0.999229 0.0392535i \(-0.987502\pi\)
0.533609 + 0.845731i \(0.320835\pi\)
\(312\) 0 0
\(313\) −5.02308 8.70024i −0.283921 0.491766i 0.688426 0.725307i \(-0.258302\pi\)
−0.972347 + 0.233541i \(0.924969\pi\)
\(314\) 0.220658 + 0.382191i 0.0124525 + 0.0215683i
\(315\) 0 0
\(316\) 5.97024 10.3408i 0.335852 0.581713i
\(317\) 5.07249 + 8.78581i 0.284899 + 0.493460i 0.972585 0.232549i \(-0.0747064\pi\)
−0.687685 + 0.726009i \(0.741373\pi\)
\(318\) 0 0
\(319\) −4.63996 8.03665i −0.259788 0.449966i
\(320\) 8.10273 + 14.0343i 0.452957 + 0.784544i
\(321\) 0 0
\(322\) −5.49886 + 1.26880i −0.306440 + 0.0707075i
\(323\) −2.94227 5.09616i −0.163712 0.283558i
\(324\) 0 0
\(325\) 4.82885 2.90242i 0.267856 0.160998i
\(326\) 0.877867 1.52051i 0.0486206 0.0842133i
\(327\) 0 0
\(328\) 1.28360 + 2.22327i 0.0708751 + 0.122759i
\(329\) 3.39409 0.783149i 0.187122 0.0431764i
\(330\) 0 0
\(331\) 2.31916 0.127473 0.0637363 0.997967i \(-0.479698\pi\)
0.0637363 + 0.997967i \(0.479698\pi\)
\(332\) 1.03435 + 1.79155i 0.0567675 + 0.0983242i
\(333\) 0 0
\(334\) −2.56027 −0.140092
\(335\) 1.73247 + 3.00072i 0.0946547 + 0.163947i
\(336\) 0 0
\(337\) −15.9998 −0.871565 −0.435783 0.900052i \(-0.643528\pi\)
−0.435783 + 0.900052i \(0.643528\pi\)
\(338\) −3.48347 + 0.122662i −0.189476 + 0.00667193i
\(339\) 0 0
\(340\) 3.87788 0.210307
\(341\) −5.03977 + 8.72913i −0.272919 + 0.472709i
\(342\) 0 0
\(343\) −14.3972 + 11.6499i −0.777378 + 0.629034i
\(344\) −1.18459 + 2.05178i −0.0638690 + 0.110624i
\(345\) 0 0
\(346\) 1.49234 2.58480i 0.0802285 0.138960i
\(347\) −11.4104 19.7634i −0.612543 1.06096i −0.990810 0.135259i \(-0.956813\pi\)
0.378267 0.925696i \(-0.376520\pi\)
\(348\) 0 0
\(349\) 11.3511 + 19.6607i 0.607612 + 1.05241i 0.991633 + 0.129090i \(0.0412056\pi\)
−0.384021 + 0.923324i \(0.625461\pi\)
\(350\) −1.08011 + 0.249223i −0.0577342 + 0.0133215i
\(351\) 0 0
\(352\) 6.04662 + 10.4731i 0.322286 + 0.558216i
\(353\) 27.2644 1.45114 0.725568 0.688150i \(-0.241577\pi\)
0.725568 + 0.688150i \(0.241577\pi\)
\(354\) 0 0
\(355\) −31.5510 −1.67455
\(356\) 14.7751 0.783077
\(357\) 0 0
\(358\) −1.69502 + 2.93585i −0.0895844 + 0.155165i
\(359\) −7.21309 12.4934i −0.380692 0.659378i 0.610469 0.792040i \(-0.290981\pi\)
−0.991161 + 0.132662i \(0.957648\pi\)
\(360\) 0 0
\(361\) 37.1791 1.95679
\(362\) −1.99965 + 3.46350i −0.105099 + 0.182037i
\(363\) 0 0
\(364\) −17.6806 5.06939i −0.926715 0.265708i
\(365\) 1.96894 0.103059
\(366\) 0 0
\(367\) −11.3917 −0.594643 −0.297322 0.954777i \(-0.596093\pi\)
−0.297322 + 0.954777i \(0.596093\pi\)
\(368\) −14.2152 24.6214i −0.741018 1.28348i
\(369\) 0 0
\(370\) −2.32065 + 4.01948i −0.120645 + 0.208963i
\(371\) −16.7418 17.9578i −0.869190 0.932321i
\(372\) 0 0
\(373\) −30.9629 −1.60320 −0.801599 0.597862i \(-0.796017\pi\)
−0.801599 + 0.597862i \(0.796017\pi\)
\(374\) 0.830653 0.0429521
\(375\) 0 0
\(376\) −0.693313 1.20085i −0.0357549 0.0619293i
\(377\) −0.149219 8.47796i −0.00768518 0.436637i
\(378\) 0 0
\(379\) −5.29330 9.16826i −0.271898 0.470942i 0.697450 0.716634i \(-0.254318\pi\)
−0.969348 + 0.245692i \(0.920985\pi\)
\(380\) −18.5109 + 32.0617i −0.949587 + 1.64473i
\(381\) 0 0
\(382\) −1.89438 + 3.28116i −0.0969249 + 0.167879i
\(383\) −30.7517 −1.57134 −0.785668 0.618648i \(-0.787681\pi\)
−0.785668 + 0.618648i \(0.787681\pi\)
\(384\) 0 0
\(385\) 26.0603 6.01313i 1.32816 0.306458i
\(386\) −0.522112 + 0.904324i −0.0265748 + 0.0460289i
\(387\) 0 0
\(388\) 4.57351 0.232185
\(389\) −8.18978 + 14.1851i −0.415239 + 0.719214i −0.995453 0.0952492i \(-0.969635\pi\)
0.580215 + 0.814463i \(0.302969\pi\)
\(390\) 0 0
\(391\) −6.24561 −0.315854
\(392\) 6.11113 + 4.12419i 0.308659 + 0.208303i
\(393\) 0 0
\(394\) 3.13945 0.158163
\(395\) −7.93227 + 13.7391i −0.399116 + 0.691289i
\(396\) 0 0
\(397\) −15.8827 −0.797127 −0.398564 0.917141i \(-0.630491\pi\)
−0.398564 + 0.917141i \(0.630491\pi\)
\(398\) 0.937591 0.0469972
\(399\) 0 0
\(400\) −2.79221 4.83624i −0.139610 0.241812i
\(401\) 3.31787 5.74671i 0.165686 0.286977i −0.771212 0.636578i \(-0.780349\pi\)
0.936899 + 0.349601i \(0.113683\pi\)
\(402\) 0 0
\(403\) −7.89373 + 4.74460i −0.393215 + 0.236345i
\(404\) 0.768670 + 1.33137i 0.0382427 + 0.0662384i
\(405\) 0 0
\(406\) −0.487959 + 1.59534i −0.0242170 + 0.0791755i
\(407\) 13.3319 23.0915i 0.660836 1.14460i
\(408\) 0 0
\(409\) −2.93617 5.08560i −0.145184 0.251467i 0.784257 0.620436i \(-0.213044\pi\)
−0.929442 + 0.368969i \(0.879711\pi\)
\(410\) −0.837115 1.44992i −0.0413421 0.0716067i
\(411\) 0 0
\(412\) 2.08831 3.61707i 0.102884 0.178200i
\(413\) −23.1163 + 5.33383i −1.13748 + 0.262460i
\(414\) 0 0
\(415\) −1.37428 2.38032i −0.0674607 0.116845i
\(416\) 0.194457 + 11.0482i 0.00953403 + 0.541680i
\(417\) 0 0
\(418\) −3.96508 + 6.86773i −0.193939 + 0.335911i
\(419\) −15.0712 26.1040i −0.736274 1.27526i −0.954162 0.299290i \(-0.903250\pi\)
0.217888 0.975974i \(-0.430083\pi\)
\(420\) 0 0
\(421\) 40.0580 1.95231 0.976153 0.217083i \(-0.0696543\pi\)
0.976153 + 0.217083i \(0.0696543\pi\)
\(422\) 5.09576 0.248058
\(423\) 0 0
\(424\) −4.88672 + 8.46405i −0.237320 + 0.411051i
\(425\) −1.22679 −0.0595079
\(426\) 0 0
\(427\) 7.30941 23.8975i 0.353727 1.15648i
\(428\) −22.2238 −1.07423
\(429\) 0 0
\(430\) 0.772544 1.33809i 0.0372554 0.0645282i
\(431\) 3.91587 0.188621 0.0943104 0.995543i \(-0.469935\pi\)
0.0943104 + 0.995543i \(0.469935\pi\)
\(432\) 0 0
\(433\) 20.3963 35.3274i 0.980182 1.69772i 0.318532 0.947912i \(-0.396810\pi\)
0.661650 0.749813i \(-0.269856\pi\)
\(434\) 1.76566 0.407405i 0.0847542 0.0195561i
\(435\) 0 0
\(436\) −15.5757 −0.745941
\(437\) 29.8131 51.6378i 1.42615 2.47017i
\(438\) 0 0
\(439\) 12.7811 22.1376i 0.610010 1.05657i −0.381228 0.924481i \(-0.624499\pi\)
0.991238 0.132087i \(-0.0421680\pi\)
\(440\) −5.32336 9.22033i −0.253781 0.439562i
\(441\) 0 0
\(442\) 0.663878 + 0.367867i 0.0315775 + 0.0174977i
\(443\) −13.7282 23.7779i −0.652247 1.12972i −0.982576 0.185859i \(-0.940493\pi\)
0.330330 0.943866i \(-0.392840\pi\)
\(444\) 0 0
\(445\) −19.6307 −0.930584
\(446\) −3.20844 −0.151924
\(447\) 0 0
\(448\) −4.89534 + 16.0049i −0.231283 + 0.756161i
\(449\) −7.40181 + 12.8203i −0.349313 + 0.605028i −0.986128 0.165989i \(-0.946918\pi\)
0.636815 + 0.771017i \(0.280252\pi\)
\(450\) 0 0
\(451\) 4.80913 + 8.32966i 0.226453 + 0.392229i
\(452\) 15.5046 0.729275
\(453\) 0 0
\(454\) −4.12489 −0.193590
\(455\) 23.4911 + 6.73537i 1.10128 + 0.315759i
\(456\) 0 0
\(457\) 0.325975 0.564606i 0.0152485 0.0264112i −0.858300 0.513147i \(-0.828479\pi\)
0.873549 + 0.486736i \(0.161813\pi\)
\(458\) 2.32241 0.108519
\(459\) 0 0
\(460\) 19.6467 + 34.0290i 0.916031 + 1.58661i
\(461\) 6.24774 10.8214i 0.290986 0.504003i −0.683057 0.730365i \(-0.739350\pi\)
0.974043 + 0.226362i \(0.0726833\pi\)
\(462\) 0 0
\(463\) −0.309503 −0.0143838 −0.00719190 0.999974i \(-0.502289\pi\)
−0.00719190 + 0.999974i \(0.502289\pi\)
\(464\) −8.40466 −0.390176
\(465\) 0 0
\(466\) −5.42972 −0.251527
\(467\) 12.2387 + 21.1980i 0.566338 + 0.980926i 0.996924 + 0.0783762i \(0.0249735\pi\)
−0.430586 + 0.902549i \(0.641693\pi\)
\(468\) 0 0
\(469\) −1.04668 + 3.42205i −0.0483314 + 0.158016i
\(470\) 0.452151 + 0.783149i 0.0208562 + 0.0361240i
\(471\) 0 0
\(472\) 4.72198 + 8.17871i 0.217347 + 0.376456i
\(473\) −4.43818 + 7.68716i −0.204068 + 0.353456i
\(474\) 0 0
\(475\) 5.85601 10.1429i 0.268692 0.465389i
\(476\) 2.73106 + 2.92943i 0.125178 + 0.134270i
\(477\) 0 0
\(478\) 2.21909 3.84357i 0.101499 0.175801i
\(479\) −8.13850 −0.371858 −0.185929 0.982563i \(-0.559529\pi\)
−0.185929 + 0.982563i \(0.559529\pi\)
\(480\) 0 0
\(481\) 20.8816 12.5511i 0.952118 0.572279i
\(482\) −4.39746 −0.200299
\(483\) 0 0
\(484\) 4.40662 + 7.63250i 0.200301 + 0.346932i
\(485\) −6.07653 −0.275921
\(486\) 0 0
\(487\) −2.30480 3.99203i −0.104440 0.180896i 0.809069 0.587714i \(-0.199972\pi\)
−0.913509 + 0.406817i \(0.866638\pi\)
\(488\) −9.94821 −0.450334
\(489\) 0 0
\(490\) −3.98543 2.68963i −0.180044 0.121505i
\(491\) 6.50947 + 11.2747i 0.293768 + 0.508822i 0.974698 0.223527i \(-0.0717572\pi\)
−0.680929 + 0.732349i \(0.738424\pi\)
\(492\) 0 0
\(493\) −0.923171 + 1.59898i −0.0415775 + 0.0720144i
\(494\) −6.21047 + 3.73286i −0.279422 + 0.167949i
\(495\) 0 0
\(496\) 4.56443 + 7.90582i 0.204949 + 0.354982i
\(497\) −22.2203 23.8342i −0.996718 1.06911i
\(498\) 0 0
\(499\) 16.1603 + 27.9905i 0.723436 + 1.25303i 0.959614 + 0.281319i \(0.0907717\pi\)
−0.236178 + 0.971710i \(0.575895\pi\)
\(500\) −8.48928 14.7039i −0.379652 0.657577i
\(501\) 0 0
\(502\) −2.73900 4.74408i −0.122247 0.211739i
\(503\) −15.9126 + 27.5615i −0.709509 + 1.22891i 0.255531 + 0.966801i \(0.417750\pi\)
−0.965039 + 0.262105i \(0.915583\pi\)
\(504\) 0 0
\(505\) −1.02128 1.76891i −0.0454465 0.0787156i
\(506\) 4.20838 + 7.28912i 0.187085 + 0.324041i
\(507\) 0 0
\(508\) 1.72377 2.98566i 0.0764801 0.132467i
\(509\) 1.12788 1.95354i 0.0499922 0.0865891i −0.839946 0.542669i \(-0.817414\pi\)
0.889939 + 0.456080i \(0.150747\pi\)
\(510\) 0 0
\(511\) 1.38666 + 1.48738i 0.0613422 + 0.0657977i
\(512\) 18.4807 0.816739
\(513\) 0 0
\(514\) 1.84710 + 3.19927i 0.0814722 + 0.141114i
\(515\) −2.77461 + 4.80576i −0.122264 + 0.211767i
\(516\) 0 0
\(517\) −2.59756 4.49911i −0.114241 0.197870i
\(518\) −4.67075 + 1.07772i −0.205221 + 0.0473525i
\(519\) 0 0
\(520\) −0.171197 9.72665i −0.00750749 0.426542i
\(521\) 5.38562 9.32817i 0.235948 0.408675i −0.723600 0.690220i \(-0.757514\pi\)
0.959548 + 0.281546i \(0.0908471\pi\)
\(522\) 0 0
\(523\) −3.70397 + 6.41546i −0.161963 + 0.280528i −0.935573 0.353134i \(-0.885116\pi\)
0.773610 + 0.633663i \(0.218449\pi\)
\(524\) 6.16118 10.6715i 0.269152 0.466186i
\(525\) 0 0
\(526\) 3.47454 6.01809i 0.151497 0.262401i
\(527\) 2.00543 0.0873580
\(528\) 0 0
\(529\) −20.1424 34.8877i −0.875757 1.51686i
\(530\) 3.18692 5.51991i 0.138431 0.239770i
\(531\) 0 0
\(532\) −37.2567 + 8.59656i −1.61528 + 0.372708i
\(533\) 0.154660 + 8.78707i 0.00669906 + 0.380610i
\(534\) 0 0
\(535\) 29.5274 1.27658
\(536\) 1.42455 0.0615313
\(537\) 0 0
\(538\) 8.06161 0.347561
\(539\) 22.8959 + 15.4517i 0.986196 + 0.665550i
\(540\) 0 0
\(541\) −16.2741 28.1875i −0.699676 1.21188i −0.968579 0.248708i \(-0.919994\pi\)
0.268902 0.963168i \(-0.413339\pi\)
\(542\) −1.93728 3.35546i −0.0832132 0.144129i
\(543\) 0 0
\(544\) 1.20304 2.08373i 0.0515799 0.0893391i
\(545\) 20.6944 0.886453
\(546\) 0 0
\(547\) −13.4997 −0.577206 −0.288603 0.957449i \(-0.593191\pi\)
−0.288603 + 0.957449i \(0.593191\pi\)
\(548\) −9.67577 + 16.7589i −0.413329 + 0.715906i
\(549\) 0 0
\(550\) 0.826627 + 1.43176i 0.0352475 + 0.0610504i
\(551\) −8.81342 15.2653i −0.375464 0.650323i
\(552\) 0 0
\(553\) −15.9652 + 3.68380i −0.678911 + 0.156651i
\(554\) −4.10915 −0.174581
\(555\) 0 0
\(556\) 10.6925 0.453461
\(557\) 29.7703 1.26141 0.630703 0.776024i \(-0.282767\pi\)
0.630703 + 0.776024i \(0.282767\pi\)
\(558\) 0 0
\(559\) −6.95148 + 4.17825i −0.294016 + 0.176721i
\(560\) 7.08483 23.1632i 0.299389 0.978826i
\(561\) 0 0
\(562\) 0.709566 1.22900i 0.0299312 0.0518424i
\(563\) 7.06629 + 12.2392i 0.297809 + 0.515819i 0.975634 0.219403i \(-0.0704110\pi\)
−0.677826 + 0.735223i \(0.737078\pi\)
\(564\) 0 0
\(565\) −20.6000 −0.866647
\(566\) 4.12705 7.14826i 0.173473 0.300464i
\(567\) 0 0
\(568\) −6.48584 + 11.2338i −0.272140 + 0.471360i
\(569\) −12.1270 + 21.0046i −0.508391 + 0.880558i 0.491562 + 0.870842i \(0.336426\pi\)
−0.999953 + 0.00971585i \(0.996907\pi\)
\(570\) 0 0
\(571\) −0.604159 + 1.04643i −0.0252832 + 0.0437919i −0.878390 0.477944i \(-0.841382\pi\)
0.853107 + 0.521736i \(0.174715\pi\)
\(572\) 0.482755 + 27.4279i 0.0201850 + 1.14682i
\(573\) 0 0
\(574\) 0.505750 1.65351i 0.0211096 0.0690161i
\(575\) −6.21533 10.7653i −0.259197 0.448943i
\(576\) 0 0
\(577\) 7.30518 12.6529i 0.304119 0.526749i −0.672946 0.739692i \(-0.734971\pi\)
0.977065 + 0.212943i \(0.0683047\pi\)
\(578\) 2.19643 + 3.80433i 0.0913595 + 0.158239i
\(579\) 0 0
\(580\) 11.6160 0.482328
\(581\) 0.830283 2.71454i 0.0344459 0.112618i
\(582\) 0 0
\(583\) −18.3085 + 31.7113i −0.758262 + 1.31335i
\(584\) 0.404749 0.701046i 0.0167486 0.0290095i
\(585\) 0 0
\(586\) −2.34841 4.06757i −0.0970120 0.168030i
\(587\) 10.7548 + 18.6278i 0.443897 + 0.768852i 0.997975 0.0636132i \(-0.0202624\pi\)
−0.554078 + 0.832465i \(0.686929\pi\)
\(588\) 0 0
\(589\) −9.57284 + 16.5806i −0.394442 + 0.683193i
\(590\) −3.07949 5.33383i −0.126780 0.219590i
\(591\) 0 0
\(592\) −12.0744 20.9135i −0.496256 0.859541i
\(593\) −1.32429 2.29373i −0.0543820 0.0941923i 0.837553 0.546356i \(-0.183986\pi\)
−0.891935 + 0.452164i \(0.850652\pi\)
\(594\) 0 0
\(595\) −3.62859 3.89214i −0.148758 0.159562i
\(596\) −17.8013 30.8328i −0.729171 1.26296i
\(597\) 0 0
\(598\) 0.135340 + 7.68939i 0.00553445 + 0.314443i
\(599\) −20.1250 + 34.8576i −0.822287 + 1.42424i 0.0816889 + 0.996658i \(0.473969\pi\)
−0.903975 + 0.427584i \(0.859365\pi\)
\(600\) 0 0
\(601\) −19.1725 33.2077i −0.782061 1.35457i −0.930739 0.365683i \(-0.880835\pi\)
0.148679 0.988886i \(-0.452498\pi\)
\(602\) 1.55490 0.358775i 0.0633728 0.0146226i
\(603\) 0 0
\(604\) −3.09916 −0.126103
\(605\) −5.85480 10.1408i −0.238031 0.412283i
\(606\) 0 0
\(607\) 42.5547 1.72724 0.863620 0.504143i \(-0.168192\pi\)
0.863620 + 0.504143i \(0.168192\pi\)
\(608\) 11.4853 + 19.8931i 0.465791 + 0.806773i
\(609\) 0 0
\(610\) 6.48782 0.262684
\(611\) −0.0835364 4.74616i −0.00337952 0.192009i
\(612\) 0 0
\(613\) 15.2652 0.616556 0.308278 0.951296i \(-0.400247\pi\)
0.308278 + 0.951296i \(0.400247\pi\)
\(614\) 1.15773 2.00524i 0.0467221 0.0809251i
\(615\) 0 0
\(616\) 3.21616 10.5150i 0.129583 0.423660i
\(617\) 6.99061 12.1081i 0.281431 0.487453i −0.690306 0.723517i \(-0.742524\pi\)
0.971737 + 0.236064i \(0.0758575\pi\)
\(618\) 0 0
\(619\) 4.25792 7.37494i 0.171140 0.296424i −0.767678 0.640835i \(-0.778588\pi\)
0.938819 + 0.344411i \(0.111921\pi\)
\(620\) −6.30845 10.9265i −0.253353 0.438821i
\(621\) 0 0
\(622\) −2.20166 3.81338i −0.0882784 0.152903i
\(623\) −13.8253 14.8294i −0.553897 0.594129i
\(624\) 0 0
\(625\) 15.1856 + 26.3023i 0.607425 + 1.05209i
\(626\) 2.69363 0.107659
\(627\) 0 0
\(628\) 3.17354 0.126638
\(629\) −5.30504 −0.211526
\(630\) 0 0
\(631\) −18.4146 + 31.8950i −0.733074 + 1.26972i 0.222490 + 0.974935i \(0.428582\pi\)
−0.955563 + 0.294786i \(0.904752\pi\)
\(632\) 3.26123 + 5.64861i 0.129725 + 0.224690i
\(633\) 0 0
\(634\) −2.72013 −0.108030
\(635\) −2.29027 + 3.96686i −0.0908865 + 0.157420i
\(636\) 0 0
\(637\) 11.4560 + 22.4891i 0.453901 + 0.891052i
\(638\) 2.48818 0.0985081
\(639\) 0 0
\(640\) −20.0470 −0.792428
\(641\) 12.9374 + 22.4082i 0.510996 + 0.885070i 0.999919 + 0.0127435i \(0.00405649\pi\)
−0.488923 + 0.872327i \(0.662610\pi\)
\(642\) 0 0
\(643\) −20.2626 + 35.0958i −0.799078 + 1.38404i 0.121139 + 0.992636i \(0.461345\pi\)
−0.920217 + 0.391408i \(0.871988\pi\)
\(644\) −11.8697 + 38.8070i −0.467732 + 1.52921i
\(645\) 0 0
\(646\) 1.57779 0.0620774
\(647\) −1.78400 −0.0701364 −0.0350682 0.999385i \(-0.511165\pi\)
−0.0350682 + 0.999385i \(0.511165\pi\)
\(648\) 0 0
\(649\) 17.6913 + 30.6423i 0.694445 + 1.20281i
\(650\) 0.0265840 + 1.51038i 0.00104271 + 0.0592420i
\(651\) 0 0
\(652\) −6.31281 10.9341i −0.247229 0.428213i
\(653\) 6.20210 10.7424i 0.242707 0.420381i −0.718778 0.695240i \(-0.755298\pi\)
0.961484 + 0.274860i \(0.0886313\pi\)
\(654\) 0 0
\(655\) −8.18597 + 14.1785i −0.319852 + 0.554000i
\(656\) 8.71109 0.340111
\(657\) 0 0
\(658\) −0.273171 + 0.893110i −0.0106493 + 0.0348171i
\(659\) −0.564336 + 0.977458i −0.0219834 + 0.0380764i −0.876808 0.480841i \(-0.840331\pi\)
0.854824 + 0.518917i \(0.173665\pi\)
\(660\) 0 0
\(661\) −28.9254 −1.12507 −0.562534 0.826774i \(-0.690174\pi\)
−0.562534 + 0.826774i \(0.690174\pi\)
\(662\) −0.310913 + 0.538517i −0.0120840 + 0.0209301i
\(663\) 0 0
\(664\) −1.13003 −0.0438535
\(665\) 49.5006 11.4217i 1.91955 0.442915i
\(666\) 0 0
\(667\) −18.7084 −0.724393
\(668\) −9.20556 + 15.9445i −0.356174 + 0.616911i
\(669\) 0 0
\(670\) −0.929036 −0.0358918
\(671\) −37.2718 −1.43886
\(672\) 0 0
\(673\) 3.54980 + 6.14843i 0.136835 + 0.237005i 0.926297 0.376795i \(-0.122974\pi\)
−0.789462 + 0.613799i \(0.789640\pi\)
\(674\) 2.14498 3.71521i 0.0826214 0.143104i
\(675\) 0 0
\(676\) −11.7610 + 22.1349i −0.452348 + 0.851341i
\(677\) −25.2010 43.6494i −0.968552 1.67758i −0.699752 0.714386i \(-0.746706\pi\)
−0.268800 0.963196i \(-0.586627\pi\)
\(678\) 0 0
\(679\) −4.27950 4.59033i −0.164232 0.176161i
\(680\) −1.05914 + 1.83449i −0.0406162 + 0.0703493i
\(681\) 0 0
\(682\) −1.35129 2.34050i −0.0517435 0.0896224i
\(683\) 13.7641 + 23.8401i 0.526669 + 0.912217i 0.999517 + 0.0310735i \(0.00989259\pi\)
−0.472848 + 0.881144i \(0.656774\pi\)
\(684\) 0 0
\(685\) 12.8556 22.2665i 0.491186 0.850760i
\(686\) −0.775007 4.90490i −0.0295899 0.187270i
\(687\) 0 0
\(688\) 4.01958 + 6.96212i 0.153245 + 0.265428i
\(689\) −28.6765 + 17.2362i −1.09249 + 0.656649i
\(690\) 0 0
\(691\) 12.1669 21.0737i 0.462851 0.801682i −0.536251 0.844059i \(-0.680160\pi\)
0.999102 + 0.0423772i \(0.0134931\pi\)
\(692\) −10.7315 18.5875i −0.407950 0.706591i
\(693\) 0 0
\(694\) 6.11884 0.232268
\(695\) −14.2064 −0.538879
\(696\) 0 0
\(697\) 0.956829 1.65728i 0.0362425 0.0627738i
\(698\) −6.08704 −0.230398
\(699\) 0 0
\(700\) −2.33150 + 7.62263i −0.0881223 + 0.288108i
\(701\) 20.5588 0.776495 0.388248 0.921555i \(-0.373081\pi\)
0.388248 + 0.921555i \(0.373081\pi\)
\(702\) 0 0
\(703\) 25.3234 43.8613i 0.955088 1.65426i
\(704\) 24.9621 0.940795
\(705\) 0 0
\(706\) −3.65513 + 6.33088i −0.137563 + 0.238266i
\(707\) 0.617017 2.01728i 0.0232053 0.0758678i
\(708\) 0 0
\(709\) 40.9089 1.53637 0.768183 0.640230i \(-0.221161\pi\)
0.768183 + 0.640230i \(0.221161\pi\)
\(710\) 4.22981 7.32624i 0.158742 0.274949i
\(711\) 0 0
\(712\) −4.03543 + 6.98956i −0.151234 + 0.261945i
\(713\) 10.1602 + 17.5980i 0.380503 + 0.659051i
\(714\) 0 0
\(715\) −0.641405 36.4418i −0.0239872 1.36284i
\(716\) 12.1890 + 21.1119i 0.455524 + 0.788990i
\(717\) 0 0
\(718\) 3.86802 0.144353
\(719\) 1.19947 0.0447326 0.0223663 0.999750i \(-0.492880\pi\)
0.0223663 + 0.999750i \(0.492880\pi\)
\(720\) 0 0
\(721\) −5.58444 + 1.28855i −0.207975 + 0.0479880i
\(722\) −4.98433 + 8.63311i −0.185497 + 0.321291i
\(723\) 0 0
\(724\) 14.3796 + 24.9063i 0.534415 + 0.925634i
\(725\) −3.67478 −0.136478
\(726\) 0 0
\(727\) −2.06230 −0.0764865 −0.0382433 0.999268i \(-0.512176\pi\)
−0.0382433 + 0.999268i \(0.512176\pi\)
\(728\) 7.22714 6.97949i 0.267856 0.258677i
\(729\) 0 0
\(730\) −0.263961 + 0.457194i −0.00976964 + 0.0169215i
\(731\) 1.76605 0.0653197
\(732\) 0 0
\(733\) −15.0310 26.0345i −0.555184 0.961606i −0.997889 0.0649392i \(-0.979315\pi\)
0.442706 0.896667i \(-0.354019\pi\)
\(734\) 1.52720 2.64520i 0.0563702 0.0976360i
\(735\) 0 0
\(736\) 24.3801 0.898662
\(737\) 5.33721 0.196599
\(738\) 0 0
\(739\) 44.2548 1.62794 0.813969 0.580908i \(-0.197303\pi\)
0.813969 + 0.580908i \(0.197303\pi\)
\(740\) 16.6880 + 28.9044i 0.613461 + 1.06255i
\(741\) 0 0
\(742\) 6.41430 1.48003i 0.235476 0.0543335i
\(743\) −4.31326 7.47078i −0.158238 0.274076i 0.775995 0.630739i \(-0.217248\pi\)
−0.934233 + 0.356662i \(0.883915\pi\)
\(744\) 0 0
\(745\) 23.6515 + 40.9656i 0.866524 + 1.50086i
\(746\) 4.15097 7.18969i 0.151978 0.263233i
\(747\) 0 0
\(748\) 2.98665 5.17302i 0.109203 0.189144i
\(749\) 20.7952 + 22.3056i 0.759839 + 0.815028i
\(750\) 0 0
\(751\) −2.86105 + 4.95549i −0.104401 + 0.180828i −0.913493 0.406853i \(-0.866626\pi\)
0.809092 + 0.587682i \(0.199959\pi\)
\(752\) −4.70512 −0.171578
\(753\) 0 0
\(754\) 1.98862 + 1.10193i 0.0724211 + 0.0401299i
\(755\) 4.11765 0.149857
\(756\) 0 0
\(757\) 17.3611 + 30.0703i 0.631000 + 1.09292i 0.987348 + 0.158571i \(0.0506887\pi\)
−0.356347 + 0.934354i \(0.615978\pi\)
\(758\) 2.83853 0.103100
\(759\) 0 0
\(760\) −10.1115 17.5137i −0.366783 0.635287i
\(761\) 53.1735 1.92754 0.963768 0.266741i \(-0.0859467\pi\)
0.963768 + 0.266741i \(0.0859467\pi\)
\(762\) 0 0
\(763\) 14.5744 + 15.6330i 0.527630 + 0.565953i
\(764\) 13.6226 + 23.5951i 0.492849 + 0.853640i
\(765\) 0 0
\(766\) 4.12265 7.14063i 0.148957 0.258002i
\(767\) 0.568946 + 32.3249i 0.0205434 + 1.16719i
\(768\) 0 0
\(769\) −2.45578 4.25354i −0.0885578 0.153387i 0.818344 0.574729i \(-0.194892\pi\)
−0.906902 + 0.421342i \(0.861559\pi\)
\(770\) −2.09745 + 6.85743i −0.0755868 + 0.247125i
\(771\) 0 0
\(772\) 3.75455 + 6.50306i 0.135129 + 0.234050i
\(773\) −11.4903 19.9018i −0.413279 0.715819i 0.581967 0.813212i \(-0.302283\pi\)
−0.995246 + 0.0973926i \(0.968950\pi\)
\(774\) 0 0
\(775\) 1.99571 + 3.45667i 0.0716881 + 0.124167i
\(776\) −1.24913 + 2.16356i −0.0448413 + 0.0776674i
\(777\) 0 0
\(778\) −2.19589 3.80339i −0.0787264 0.136358i
\(779\) 9.13476 + 15.8219i 0.327287 + 0.566877i
\(780\) 0 0
\(781\) −24.2998 + 42.0885i −0.869515 + 1.50604i
\(782\) 0.837302 1.45025i 0.0299419 0.0518608i
\(783\) 0 0
\(784\) 22.4876 10.9611i 0.803129 0.391468i
\(785\) −4.21648 −0.150493
\(786\) 0 0
\(787\) 1.59387 + 2.76067i 0.0568154 + 0.0984071i 0.893034 0.449989i \(-0.148572\pi\)
−0.836219 + 0.548396i \(0.815239\pi\)
\(788\) 11.2880 19.5514i 0.402119 0.696490i
\(789\) 0 0
\(790\) &minus