Properties

Label 70.2.g.a.27.4
Level $70$
Weight $2$
Character 70.27
Analytic conductor $0.559$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 70.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.558952814149\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{16})\)
Defining polynomial: \(x^{8} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 27.4
Root \(0.923880 - 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 70.27
Dual form 70.2.g.a.13.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(0.541196 + 0.541196i) q^{3} +1.00000i q^{4} +(-2.23044 + 0.158513i) q^{5} +0.765367i q^{6} +(1.55487 - 2.14065i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.41421i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(0.541196 + 0.541196i) q^{3} +1.00000i q^{4} +(-2.23044 + 0.158513i) q^{5} +0.765367i q^{6} +(1.55487 - 2.14065i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.41421i q^{9} +(-1.68925 - 1.46508i) q^{10} -2.82843 q^{11} +(-0.541196 + 0.541196i) q^{12} +(2.83730 + 2.83730i) q^{13} +(2.61313 - 0.414214i) q^{14} +(-1.29289 - 1.12132i) q^{15} -1.00000 q^{16} +(1.53073 - 1.53073i) q^{17} +(1.70711 - 1.70711i) q^{18} -7.07401 q^{19} +(-0.158513 - 2.23044i) q^{20} +(2.00000 - 0.317025i) q^{21} +(-2.00000 - 2.00000i) q^{22} +(-2.41421 + 2.41421i) q^{23} -0.765367 q^{24} +(4.94975 - 0.707107i) q^{25} +4.01254i q^{26} +(2.93015 - 2.93015i) q^{27} +(2.14065 + 1.55487i) q^{28} +4.82843i q^{29} +(-0.121320 - 1.70711i) q^{30} +3.69552i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.53073 - 1.53073i) q^{33} +2.16478 q^{34} +(-3.12872 + 5.02107i) q^{35} +2.41421 q^{36} +(5.41421 + 5.41421i) q^{37} +(-5.00208 - 5.00208i) q^{38} +3.07107i q^{39} +(1.46508 - 1.68925i) q^{40} -1.53073i q^{41} +(1.63838 + 1.19004i) q^{42} +(4.00000 - 4.00000i) q^{43} -2.82843i q^{44} +(0.382683 + 5.38476i) q^{45} -3.41421 q^{46} +(-2.61313 + 2.61313i) q^{47} +(-0.541196 - 0.541196i) q^{48} +(-2.16478 - 6.65685i) q^{49} +(4.00000 + 3.00000i) q^{50} +1.65685 q^{51} +(-2.83730 + 2.83730i) q^{52} +(0.242641 - 0.242641i) q^{53} +4.14386 q^{54} +(6.30864 - 0.448342i) q^{55} +(0.414214 + 2.61313i) q^{56} +(-3.82843 - 3.82843i) q^{57} +(-3.41421 + 3.41421i) q^{58} +3.82683 q^{59} +(1.12132 - 1.29289i) q^{60} -10.3212i q^{61} +(-2.61313 + 2.61313i) q^{62} +(-5.16799 - 3.75378i) q^{63} -1.00000i q^{64} +(-6.77817 - 5.87868i) q^{65} -2.16478i q^{66} +(-6.48528 - 6.48528i) q^{67} +(1.53073 + 1.53073i) q^{68} -2.61313 q^{69} +(-5.76277 + 1.33809i) q^{70} -3.41421 q^{71} +(1.70711 + 1.70711i) q^{72} +(4.77791 + 4.77791i) q^{73} +7.65685i q^{74} +(3.06147 + 2.29610i) q^{75} -7.07401i q^{76} +(-4.39782 + 6.05468i) q^{77} +(-2.17157 + 2.17157i) q^{78} -9.07107i q^{79} +(2.23044 - 0.158513i) q^{80} -4.07107 q^{81} +(1.08239 - 1.08239i) q^{82} +(-5.45042 - 5.45042i) q^{83} +(0.317025 + 2.00000i) q^{84} +(-3.17157 + 3.65685i) q^{85} +5.65685 q^{86} +(-2.61313 + 2.61313i) q^{87} +(2.00000 - 2.00000i) q^{88} +16.9469 q^{89} +(-3.53701 + 4.07820i) q^{90} +(10.4853 - 1.66205i) q^{91} +(-2.41421 - 2.41421i) q^{92} +(-2.00000 + 2.00000i) q^{93} -3.69552 q^{94} +(15.7782 - 1.12132i) q^{95} -0.765367i q^{96} +(-11.0866 + 11.0866i) q^{97} +(3.17637 - 6.23784i) q^{98} +6.82843i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{7} + O(q^{10}) \) \( 8 q - 8 q^{7} - 16 q^{15} - 8 q^{16} + 8 q^{18} + 16 q^{21} - 16 q^{22} - 8 q^{23} + 8 q^{28} + 16 q^{30} - 8 q^{35} + 8 q^{36} + 32 q^{37} + 32 q^{43} - 16 q^{46} + 32 q^{50} - 32 q^{51} - 32 q^{53} - 8 q^{56} - 8 q^{57} - 16 q^{58} - 8 q^{60} + 8 q^{65} + 16 q^{67} - 24 q^{70} - 16 q^{71} + 8 q^{72} - 16 q^{77} - 40 q^{78} + 24 q^{81} - 48 q^{85} + 16 q^{88} + 16 q^{91} - 8 q^{92} - 16 q^{93} + 64 q^{95} + 32 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(57\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0.541196 + 0.541196i 0.312460 + 0.312460i 0.845862 0.533402i \(-0.179087\pi\)
−0.533402 + 0.845862i \(0.679087\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −2.23044 + 0.158513i −0.997484 + 0.0708890i
\(6\) 0.765367i 0.312460i
\(7\) 1.55487 2.14065i 0.587684 0.809091i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 2.41421i 0.804738i
\(10\) −1.68925 1.46508i −0.534187 0.463298i
\(11\) −2.82843 −0.852803 −0.426401 0.904534i \(-0.640219\pi\)
−0.426401 + 0.904534i \(0.640219\pi\)
\(12\) −0.541196 + 0.541196i −0.156230 + 0.156230i
\(13\) 2.83730 + 2.83730i 0.786925 + 0.786925i 0.980989 0.194064i \(-0.0621670\pi\)
−0.194064 + 0.980989i \(0.562167\pi\)
\(14\) 2.61313 0.414214i 0.698387 0.110703i
\(15\) −1.29289 1.12132i −0.333824 0.289524i
\(16\) −1.00000 −0.250000
\(17\) 1.53073 1.53073i 0.371257 0.371257i −0.496678 0.867935i \(-0.665447\pi\)
0.867935 + 0.496678i \(0.165447\pi\)
\(18\) 1.70711 1.70711i 0.402369 0.402369i
\(19\) −7.07401 −1.62289 −0.811445 0.584429i \(-0.801318\pi\)
−0.811445 + 0.584429i \(0.801318\pi\)
\(20\) −0.158513 2.23044i −0.0354445 0.498742i
\(21\) 2.00000 0.317025i 0.436436 0.0691806i
\(22\) −2.00000 2.00000i −0.426401 0.426401i
\(23\) −2.41421 + 2.41421i −0.503398 + 0.503398i −0.912492 0.409094i \(-0.865845\pi\)
0.409094 + 0.912492i \(0.365845\pi\)
\(24\) −0.765367 −0.156230
\(25\) 4.94975 0.707107i 0.989949 0.141421i
\(26\) 4.01254i 0.786925i
\(27\) 2.93015 2.93015i 0.563908 0.563908i
\(28\) 2.14065 + 1.55487i 0.404545 + 0.293842i
\(29\) 4.82843i 0.896616i 0.893879 + 0.448308i \(0.147973\pi\)
−0.893879 + 0.448308i \(0.852027\pi\)
\(30\) −0.121320 1.70711i −0.0221500 0.311674i
\(31\) 3.69552i 0.663735i 0.943326 + 0.331867i \(0.107679\pi\)
−0.943326 + 0.331867i \(0.892321\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −1.53073 1.53073i −0.266467 0.266467i
\(34\) 2.16478 0.371257
\(35\) −3.12872 + 5.02107i −0.528850 + 0.848715i
\(36\) 2.41421 0.402369
\(37\) 5.41421 + 5.41421i 0.890091 + 0.890091i 0.994531 0.104440i \(-0.0333050\pi\)
−0.104440 + 0.994531i \(0.533305\pi\)
\(38\) −5.00208 5.00208i −0.811445 0.811445i
\(39\) 3.07107i 0.491764i
\(40\) 1.46508 1.68925i 0.231649 0.267093i
\(41\) 1.53073i 0.239060i −0.992831 0.119530i \(-0.961861\pi\)
0.992831 0.119530i \(-0.0381388\pi\)
\(42\) 1.63838 + 1.19004i 0.252808 + 0.183628i
\(43\) 4.00000 4.00000i 0.609994 0.609994i −0.332950 0.942944i \(-0.608044\pi\)
0.942944 + 0.332950i \(0.108044\pi\)
\(44\) 2.82843i 0.426401i
\(45\) 0.382683 + 5.38476i 0.0570471 + 0.802713i
\(46\) −3.41421 −0.503398
\(47\) −2.61313 + 2.61313i −0.381164 + 0.381164i −0.871521 0.490358i \(-0.836866\pi\)
0.490358 + 0.871521i \(0.336866\pi\)
\(48\) −0.541196 0.541196i −0.0781149 0.0781149i
\(49\) −2.16478 6.65685i −0.309255 0.950979i
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) 1.65685 0.232006
\(52\) −2.83730 + 2.83730i −0.393462 + 0.393462i
\(53\) 0.242641 0.242641i 0.0333293 0.0333293i −0.690246 0.723575i \(-0.742498\pi\)
0.723575 + 0.690246i \(0.242498\pi\)
\(54\) 4.14386 0.563908
\(55\) 6.30864 0.448342i 0.850657 0.0604544i
\(56\) 0.414214 + 2.61313i 0.0553516 + 0.349194i
\(57\) −3.82843 3.82843i −0.507088 0.507088i
\(58\) −3.41421 + 3.41421i −0.448308 + 0.448308i
\(59\) 3.82683 0.498211 0.249106 0.968476i \(-0.419863\pi\)
0.249106 + 0.968476i \(0.419863\pi\)
\(60\) 1.12132 1.29289i 0.144762 0.166912i
\(61\) 10.3212i 1.32149i −0.750609 0.660746i \(-0.770240\pi\)
0.750609 0.660746i \(-0.229760\pi\)
\(62\) −2.61313 + 2.61313i −0.331867 + 0.331867i
\(63\) −5.16799 3.75378i −0.651106 0.472932i
\(64\) 1.00000i 0.125000i
\(65\) −6.77817 5.87868i −0.840729 0.729160i
\(66\) 2.16478i 0.266467i
\(67\) −6.48528 6.48528i −0.792303 0.792303i 0.189565 0.981868i \(-0.439292\pi\)
−0.981868 + 0.189565i \(0.939292\pi\)
\(68\) 1.53073 + 1.53073i 0.185629 + 0.185629i
\(69\) −2.61313 −0.314583
\(70\) −5.76277 + 1.33809i −0.688783 + 0.159933i
\(71\) −3.41421 −0.405193 −0.202596 0.979262i \(-0.564938\pi\)
−0.202596 + 0.979262i \(0.564938\pi\)
\(72\) 1.70711 + 1.70711i 0.201184 + 0.201184i
\(73\) 4.77791 + 4.77791i 0.559212 + 0.559212i 0.929083 0.369871i \(-0.120598\pi\)
−0.369871 + 0.929083i \(0.620598\pi\)
\(74\) 7.65685i 0.890091i
\(75\) 3.06147 + 2.29610i 0.353508 + 0.265131i
\(76\) 7.07401i 0.811445i
\(77\) −4.39782 + 6.05468i −0.501179 + 0.689995i
\(78\) −2.17157 + 2.17157i −0.245882 + 0.245882i
\(79\) 9.07107i 1.02057i −0.860004 0.510287i \(-0.829539\pi\)
0.860004 0.510287i \(-0.170461\pi\)
\(80\) 2.23044 0.158513i 0.249371 0.0177223i
\(81\) −4.07107 −0.452341
\(82\) 1.08239 1.08239i 0.119530 0.119530i
\(83\) −5.45042 5.45042i −0.598262 0.598262i 0.341588 0.939850i \(-0.389035\pi\)
−0.939850 + 0.341588i \(0.889035\pi\)
\(84\) 0.317025 + 2.00000i 0.0345903 + 0.218218i
\(85\) −3.17157 + 3.65685i −0.344005 + 0.396642i
\(86\) 5.65685 0.609994
\(87\) −2.61313 + 2.61313i −0.280157 + 0.280157i
\(88\) 2.00000 2.00000i 0.213201 0.213201i
\(89\) 16.9469 1.79636 0.898182 0.439625i \(-0.144889\pi\)
0.898182 + 0.439625i \(0.144889\pi\)
\(90\) −3.53701 + 4.07820i −0.372833 + 0.429880i
\(91\) 10.4853 1.66205i 1.09916 0.174230i
\(92\) −2.41421 2.41421i −0.251699 0.251699i
\(93\) −2.00000 + 2.00000i −0.207390 + 0.207390i
\(94\) −3.69552 −0.381164
\(95\) 15.7782 1.12132i 1.61881 0.115045i
\(96\) 0.765367i 0.0781149i
\(97\) −11.0866 + 11.0866i −1.12567 + 1.12567i −0.134796 + 0.990873i \(0.543038\pi\)
−0.990873 + 0.134796i \(0.956962\pi\)
\(98\) 3.17637 6.23784i 0.320862 0.630117i
\(99\) 6.82843i 0.686283i
\(100\) 0.707107 + 4.94975i 0.0707107 + 0.494975i
\(101\) 11.8519i 1.17931i −0.807655 0.589655i \(-0.799264\pi\)
0.807655 0.589655i \(-0.200736\pi\)
\(102\) 1.17157 + 1.17157i 0.116003 + 0.116003i
\(103\) 1.97908 + 1.97908i 0.195004 + 0.195004i 0.797854 0.602850i \(-0.205968\pi\)
−0.602850 + 0.797854i \(0.705968\pi\)
\(104\) −4.01254 −0.393462
\(105\) −4.41063 + 1.02413i −0.430434 + 0.0999451i
\(106\) 0.343146 0.0333293
\(107\) 7.65685 + 7.65685i 0.740216 + 0.740216i 0.972619 0.232403i \(-0.0746590\pi\)
−0.232403 + 0.972619i \(0.574659\pi\)
\(108\) 2.93015 + 2.93015i 0.281954 + 0.281954i
\(109\) 16.1421i 1.54614i 0.634323 + 0.773068i \(0.281279\pi\)
−0.634323 + 0.773068i \(0.718721\pi\)
\(110\) 4.77791 + 4.14386i 0.455556 + 0.395102i
\(111\) 5.86030i 0.556235i
\(112\) −1.55487 + 2.14065i −0.146921 + 0.202273i
\(113\) 6.82843 6.82843i 0.642364 0.642364i −0.308772 0.951136i \(-0.599918\pi\)
0.951136 + 0.308772i \(0.0999179\pi\)
\(114\) 5.41421i 0.507088i
\(115\) 5.00208 5.76745i 0.466446 0.537817i
\(116\) −4.82843 −0.448308
\(117\) 6.84984 6.84984i 0.633268 0.633268i
\(118\) 2.70598 + 2.70598i 0.249106 + 0.249106i
\(119\) −0.896683 5.65685i −0.0821988 0.518563i
\(120\) 1.70711 0.121320i 0.155837 0.0110750i
\(121\) −3.00000 −0.272727
\(122\) 7.29818 7.29818i 0.660746 0.660746i
\(123\) 0.828427 0.828427i 0.0746968 0.0746968i
\(124\) −3.69552 −0.331867
\(125\) −10.9280 + 2.36176i −0.977434 + 0.211242i
\(126\) −1.00000 6.30864i −0.0890871 0.562019i
\(127\) 6.41421 + 6.41421i 0.569169 + 0.569169i 0.931896 0.362726i \(-0.118154\pi\)
−0.362726 + 0.931896i \(0.618154\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 4.32957 0.381197
\(130\) −0.636039 8.94975i −0.0557843 0.784945i
\(131\) 16.8925i 1.47590i 0.674855 + 0.737951i \(0.264206\pi\)
−0.674855 + 0.737951i \(0.735794\pi\)
\(132\) 1.53073 1.53073i 0.133233 0.133233i
\(133\) −10.9991 + 15.1430i −0.953746 + 1.31306i
\(134\) 9.17157i 0.792303i
\(135\) −6.07107 + 7.00000i −0.522514 + 0.602464i
\(136\) 2.16478i 0.185629i
\(137\) −13.8284 13.8284i −1.18144 1.18144i −0.979371 0.202071i \(-0.935233\pi\)
−0.202071 0.979371i \(-0.564767\pi\)
\(138\) −1.84776 1.84776i −0.157292 0.157292i
\(139\) −5.09494 −0.432147 −0.216073 0.976377i \(-0.569325\pi\)
−0.216073 + 0.976377i \(0.569325\pi\)
\(140\) −5.02107 3.12872i −0.424358 0.264425i
\(141\) −2.82843 −0.238197
\(142\) −2.41421 2.41421i −0.202596 0.202596i
\(143\) −8.02509 8.02509i −0.671091 0.671091i
\(144\) 2.41421i 0.201184i
\(145\) −0.765367 10.7695i −0.0635603 0.894361i
\(146\) 6.75699i 0.559212i
\(147\) 2.43109 4.77424i 0.200513 0.393772i
\(148\) −5.41421 + 5.41421i −0.445046 + 0.445046i
\(149\) 5.31371i 0.435316i −0.976025 0.217658i \(-0.930158\pi\)
0.976025 0.217658i \(-0.0698417\pi\)
\(150\) 0.541196 + 3.78837i 0.0441885 + 0.309319i
\(151\) −3.17157 −0.258099 −0.129049 0.991638i \(-0.541193\pi\)
−0.129049 + 0.991638i \(0.541193\pi\)
\(152\) 5.00208 5.00208i 0.405722 0.405722i
\(153\) −3.69552 3.69552i −0.298765 0.298765i
\(154\) −7.39104 + 1.17157i −0.595587 + 0.0944080i
\(155\) −0.585786 8.24264i −0.0470515 0.662065i
\(156\) −3.07107 −0.245882
\(157\) 1.17525 1.17525i 0.0937949 0.0937949i −0.658652 0.752447i \(-0.728873\pi\)
0.752447 + 0.658652i \(0.228873\pi\)
\(158\) 6.41421 6.41421i 0.510287 0.510287i
\(159\) 0.262632 0.0208281
\(160\) 1.68925 + 1.46508i 0.133547 + 0.115824i
\(161\) 1.41421 + 8.92177i 0.111456 + 0.703134i
\(162\) −2.87868 2.87868i −0.226170 0.226170i
\(163\) 2.34315 2.34315i 0.183529 0.183529i −0.609362 0.792892i \(-0.708575\pi\)
0.792892 + 0.609362i \(0.208575\pi\)
\(164\) 1.53073 0.119530
\(165\) 3.65685 + 3.17157i 0.284686 + 0.246907i
\(166\) 7.70806i 0.598262i
\(167\) 11.5349 11.5349i 0.892597 0.892597i −0.102170 0.994767i \(-0.532579\pi\)
0.994767 + 0.102170i \(0.0325785\pi\)
\(168\) −1.19004 + 1.63838i −0.0918138 + 0.126404i
\(169\) 3.10051i 0.238500i
\(170\) −4.82843 + 0.343146i −0.370323 + 0.0263181i
\(171\) 17.0782i 1.30600i
\(172\) 4.00000 + 4.00000i 0.304997 + 0.304997i
\(173\) 8.56628 + 8.56628i 0.651282 + 0.651282i 0.953302 0.302019i \(-0.0976607\pi\)
−0.302019 + 0.953302i \(0.597661\pi\)
\(174\) −3.69552 −0.280157
\(175\) 6.18252 11.6951i 0.467355 0.884070i
\(176\) 2.82843 0.213201
\(177\) 2.07107 + 2.07107i 0.155671 + 0.155671i
\(178\) 11.9832 + 11.9832i 0.898182 + 0.898182i
\(179\) 2.34315i 0.175135i −0.996159 0.0875675i \(-0.972091\pi\)
0.996159 0.0875675i \(-0.0279093\pi\)
\(180\) −5.38476 + 0.382683i −0.401357 + 0.0285235i
\(181\) 10.1355i 0.753364i 0.926343 + 0.376682i \(0.122935\pi\)
−0.926343 + 0.376682i \(0.877065\pi\)
\(182\) 8.58946 + 6.23897i 0.636693 + 0.462463i
\(183\) 5.58579 5.58579i 0.412913 0.412913i
\(184\) 3.41421i 0.251699i
\(185\) −12.9343 11.2179i −0.950950 0.824754i
\(186\) −2.82843 −0.207390
\(187\) −4.32957 + 4.32957i −0.316609 + 0.316609i
\(188\) −2.61313 2.61313i −0.190582 0.190582i
\(189\) −1.71644 10.8284i −0.124853 0.787652i
\(190\) 11.9497 + 10.3640i 0.866926 + 0.751881i
\(191\) 10.2426 0.741131 0.370566 0.928806i \(-0.379164\pi\)
0.370566 + 0.928806i \(0.379164\pi\)
\(192\) 0.541196 0.541196i 0.0390575 0.0390575i
\(193\) −0.242641 + 0.242641i −0.0174657 + 0.0174657i −0.715786 0.698320i \(-0.753931\pi\)
0.698320 + 0.715786i \(0.253931\pi\)
\(194\) −15.6788 −1.12567
\(195\) −0.486803 6.84984i −0.0348607 0.490527i
\(196\) 6.65685 2.16478i 0.475490 0.154627i
\(197\) 3.41421 + 3.41421i 0.243253 + 0.243253i 0.818194 0.574942i \(-0.194975\pi\)
−0.574942 + 0.818194i \(0.694975\pi\)
\(198\) −4.82843 + 4.82843i −0.343141 + 0.343141i
\(199\) −15.9414 −1.13006 −0.565028 0.825072i \(-0.691134\pi\)
−0.565028 + 0.825072i \(0.691134\pi\)
\(200\) −3.00000 + 4.00000i −0.212132 + 0.282843i
\(201\) 7.01962i 0.495126i
\(202\) 8.38057 8.38057i 0.589655 0.589655i
\(203\) 10.3360 + 7.50756i 0.725444 + 0.526927i
\(204\) 1.65685i 0.116003i
\(205\) 0.242641 + 3.41421i 0.0169468 + 0.238459i
\(206\) 2.79884i 0.195004i
\(207\) 5.82843 + 5.82843i 0.405104 + 0.405104i
\(208\) −2.83730 2.83730i −0.196731 0.196731i
\(209\) 20.0083 1.38400
\(210\) −3.84296 2.39462i −0.265189 0.165244i
\(211\) −21.6569 −1.49092 −0.745460 0.666551i \(-0.767770\pi\)
−0.745460 + 0.666551i \(0.767770\pi\)
\(212\) 0.242641 + 0.242641i 0.0166646 + 0.0166646i
\(213\) −1.84776 1.84776i −0.126606 0.126606i
\(214\) 10.8284i 0.740216i
\(215\) −8.28772 + 9.55582i −0.565218 + 0.651702i
\(216\) 4.14386i 0.281954i
\(217\) 7.91082 + 5.74603i 0.537021 + 0.390066i
\(218\) −11.4142 + 11.4142i −0.773068 + 0.773068i
\(219\) 5.17157i 0.349463i
\(220\) 0.448342 + 6.30864i 0.0302272 + 0.425329i
\(221\) 8.68629 0.584303
\(222\) −4.14386 + 4.14386i −0.278118 + 0.278118i
\(223\) 5.86030 + 5.86030i 0.392435 + 0.392435i 0.875554 0.483120i \(-0.160496\pi\)
−0.483120 + 0.875554i \(0.660496\pi\)
\(224\) −2.61313 + 0.414214i −0.174597 + 0.0276758i
\(225\) −1.70711 11.9497i −0.113807 0.796650i
\(226\) 9.65685 0.642364
\(227\) −1.94061 + 1.94061i −0.128803 + 0.128803i −0.768569 0.639766i \(-0.779031\pi\)
0.639766 + 0.768569i \(0.279031\pi\)
\(228\) 3.82843 3.82843i 0.253544 0.253544i
\(229\) −7.52235 −0.497091 −0.248546 0.968620i \(-0.579953\pi\)
−0.248546 + 0.968620i \(0.579953\pi\)
\(230\) 7.61521 0.541196i 0.502132 0.0356854i
\(231\) −5.65685 + 0.896683i −0.372194 + 0.0589974i
\(232\) −3.41421 3.41421i −0.224154 0.224154i
\(233\) 3.00000 3.00000i 0.196537 0.196537i −0.601977 0.798513i \(-0.705620\pi\)
0.798513 + 0.601977i \(0.205620\pi\)
\(234\) 9.68714 0.633268
\(235\) 5.41421 6.24264i 0.353184 0.407225i
\(236\) 3.82683i 0.249106i
\(237\) 4.90923 4.90923i 0.318889 0.318889i
\(238\) 3.36595 4.63405i 0.218182 0.300381i
\(239\) 10.4853i 0.678236i 0.940744 + 0.339118i \(0.110129\pi\)
−0.940744 + 0.339118i \(0.889871\pi\)
\(240\) 1.29289 + 1.12132i 0.0834559 + 0.0723809i
\(241\) 5.86030i 0.377495i −0.982026 0.188748i \(-0.939557\pi\)
0.982026 0.188748i \(-0.0604428\pi\)
\(242\) −2.12132 2.12132i −0.136364 0.136364i
\(243\) −10.9937 10.9937i −0.705246 0.705246i
\(244\) 10.3212 0.660746
\(245\) 5.88362 + 14.5046i 0.375891 + 0.926664i
\(246\) 1.17157 0.0746968
\(247\) −20.0711 20.0711i −1.27709 1.27709i
\(248\) −2.61313 2.61313i −0.165934 0.165934i
\(249\) 5.89949i 0.373865i
\(250\) −9.39731 6.05728i −0.594338 0.383096i
\(251\) 28.7988i 1.81776i −0.417055 0.908881i \(-0.636938\pi\)
0.417055 0.908881i \(-0.363062\pi\)
\(252\) 3.75378 5.16799i 0.236466 0.325553i
\(253\) 6.82843 6.82843i 0.429300 0.429300i
\(254\) 9.07107i 0.569169i
\(255\) −3.69552 + 0.262632i −0.231422 + 0.0164467i
\(256\) 1.00000 0.0625000
\(257\) −3.24718 + 3.24718i −0.202553 + 0.202553i −0.801093 0.598540i \(-0.795748\pi\)
0.598540 + 0.801093i \(0.295748\pi\)
\(258\) 3.06147 + 3.06147i 0.190599 + 0.190599i
\(259\) 20.0083 3.17157i 1.24326 0.197072i
\(260\) 5.87868 6.77817i 0.364580 0.420365i
\(261\) 11.6569 0.721541
\(262\) −11.9448 + 11.9448i −0.737951 + 0.737951i
\(263\) −16.5858 + 16.5858i −1.02272 + 1.02272i −0.0229877 + 0.999736i \(0.507318\pi\)
−0.999736 + 0.0229877i \(0.992682\pi\)
\(264\) 2.16478 0.133233
\(265\) −0.502734 + 0.579658i −0.0308827 + 0.0356081i
\(266\) −18.4853 + 2.93015i −1.13341 + 0.179659i
\(267\) 9.17157 + 9.17157i 0.561291 + 0.561291i
\(268\) 6.48528 6.48528i 0.396152 0.396152i
\(269\) −12.6717 −0.772606 −0.386303 0.922372i \(-0.626248\pi\)
−0.386303 + 0.922372i \(0.626248\pi\)
\(270\) −9.24264 + 0.656854i −0.562489 + 0.0399749i
\(271\) 13.8854i 0.843477i 0.906717 + 0.421739i \(0.138580\pi\)
−0.906717 + 0.421739i \(0.861420\pi\)
\(272\) −1.53073 + 1.53073i −0.0928144 + 0.0928144i
\(273\) 6.57409 + 4.77510i 0.397882 + 0.289002i
\(274\) 19.5563i 1.18144i
\(275\) −14.0000 + 2.00000i −0.844232 + 0.120605i
\(276\) 2.61313i 0.157292i
\(277\) −10.2426 10.2426i −0.615421 0.615421i 0.328933 0.944353i \(-0.393311\pi\)
−0.944353 + 0.328933i \(0.893311\pi\)
\(278\) −3.60266 3.60266i −0.216073 0.216073i
\(279\) 8.92177 0.534132
\(280\) −1.33809 5.76277i −0.0799664 0.344391i
\(281\) 5.65685 0.337460 0.168730 0.985662i \(-0.446033\pi\)
0.168730 + 0.985662i \(0.446033\pi\)
\(282\) −2.00000 2.00000i −0.119098 0.119098i
\(283\) −0.224171 0.224171i −0.0133256 0.0133256i 0.700413 0.713738i \(-0.252999\pi\)
−0.713738 + 0.700413i \(0.752999\pi\)
\(284\) 3.41421i 0.202596i
\(285\) 9.14594 + 7.93223i 0.541759 + 0.469865i
\(286\) 11.3492i 0.671091i
\(287\) −3.27677 2.38009i −0.193422 0.140492i
\(288\) −1.70711 + 1.70711i −0.100592 + 0.100592i
\(289\) 12.3137i 0.724336i
\(290\) 7.07401 8.15640i 0.415400 0.478960i
\(291\) −12.0000 −0.703452
\(292\) −4.77791 + 4.77791i −0.279606 + 0.279606i
\(293\) 2.07193 + 2.07193i 0.121043 + 0.121043i 0.765034 0.643990i \(-0.222722\pi\)
−0.643990 + 0.765034i \(0.722722\pi\)
\(294\) 5.09494 1.65685i 0.297143 0.0966297i
\(295\) −8.53553 + 0.606602i −0.496958 + 0.0353177i
\(296\) −7.65685 −0.445046
\(297\) −8.28772 + 8.28772i −0.480902 + 0.480902i
\(298\) 3.75736 3.75736i 0.217658 0.217658i
\(299\) −13.6997 −0.792273
\(300\) −2.29610 + 3.06147i −0.132565 + 0.176754i
\(301\) −2.34315 14.7821i −0.135057 0.852024i
\(302\) −2.24264 2.24264i −0.129049 0.129049i
\(303\) 6.41421 6.41421i 0.368487 0.368487i
\(304\) 7.07401 0.405722
\(305\) 1.63604 + 23.0208i 0.0936793 + 1.31817i
\(306\) 5.22625i 0.298765i
\(307\) −4.18232 + 4.18232i −0.238698 + 0.238698i −0.816311 0.577613i \(-0.803984\pi\)
0.577613 + 0.816311i \(0.303984\pi\)
\(308\) −6.05468 4.39782i −0.344997 0.250589i
\(309\) 2.14214i 0.121862i
\(310\) 5.41421 6.24264i 0.307507 0.354558i
\(311\) 23.0698i 1.30817i −0.756422 0.654084i \(-0.773054\pi\)
0.756422 0.654084i \(-0.226946\pi\)
\(312\) −2.17157 2.17157i −0.122941 0.122941i
\(313\) −5.86030 5.86030i −0.331244 0.331244i 0.521815 0.853059i \(-0.325255\pi\)
−0.853059 + 0.521815i \(0.825255\pi\)
\(314\) 1.66205 0.0937949
\(315\) 12.1219 + 7.55339i 0.682993 + 0.425586i
\(316\) 9.07107 0.510287
\(317\) 2.10051 + 2.10051i 0.117976 + 0.117976i 0.763630 0.645654i \(-0.223415\pi\)
−0.645654 + 0.763630i \(0.723415\pi\)
\(318\) 0.185709 + 0.185709i 0.0104141 + 0.0104141i
\(319\) 13.6569i 0.764637i
\(320\) 0.158513 + 2.23044i 0.00886113 + 0.124686i
\(321\) 8.28772i 0.462575i
\(322\) −5.30864 + 7.30864i −0.295839 + 0.407295i
\(323\) −10.8284 + 10.8284i −0.602510 + 0.602510i
\(324\) 4.07107i 0.226170i
\(325\) 16.0502 + 12.0376i 0.890303 + 0.667728i
\(326\) 3.31371 0.183529
\(327\) −8.73606 + 8.73606i −0.483105 + 0.483105i
\(328\) 1.08239 + 1.08239i 0.0597651 + 0.0597651i
\(329\) 1.53073 + 9.65685i 0.0843921 + 0.532400i
\(330\) 0.343146 + 4.82843i 0.0188896 + 0.265796i
\(331\) 0.686292 0.0377220 0.0188610 0.999822i \(-0.493996\pi\)
0.0188610 + 0.999822i \(0.493996\pi\)
\(332\) 5.45042 5.45042i 0.299131 0.299131i
\(333\) 13.0711 13.0711i 0.716290 0.716290i
\(334\) 16.3128 0.892597
\(335\) 15.4930 + 13.4370i 0.846476 + 0.734144i
\(336\) −2.00000 + 0.317025i −0.109109 + 0.0172951i
\(337\) 12.2426 + 12.2426i 0.666899 + 0.666899i 0.956997 0.290098i \(-0.0936879\pi\)
−0.290098 + 0.956997i \(0.593688\pi\)
\(338\) −2.19239 + 2.19239i −0.119250 + 0.119250i
\(339\) 7.39104 0.401426
\(340\) −3.65685 3.17157i −0.198321 0.172003i
\(341\) 10.4525i 0.566035i
\(342\) −12.0761 + 12.0761i −0.653000 + 0.653000i
\(343\) −17.6160 5.71646i −0.951172 0.308660i
\(344\) 5.65685i 0.304997i
\(345\) 5.82843 0.414214i 0.313792 0.0223005i
\(346\) 12.1146i 0.651282i
\(347\) 17.3137 + 17.3137i 0.929449 + 0.929449i 0.997670 0.0682216i \(-0.0217325\pi\)
−0.0682216 + 0.997670i \(0.521732\pi\)
\(348\) −2.61313 2.61313i −0.140078 0.140078i
\(349\) −24.9176 −1.33381 −0.666903 0.745145i \(-0.732380\pi\)
−0.666903 + 0.745145i \(0.732380\pi\)
\(350\) 12.6414 3.89801i 0.675712 0.208357i
\(351\) 16.6274 0.887506
\(352\) 2.00000 + 2.00000i 0.106600 + 0.106600i
\(353\) −5.67459 5.67459i −0.302028 0.302028i 0.539779 0.841807i \(-0.318508\pi\)
−0.841807 + 0.539779i \(0.818508\pi\)
\(354\) 2.92893i 0.155671i
\(355\) 7.61521 0.541196i 0.404173 0.0287237i
\(356\) 16.9469i 0.898182i
\(357\) 2.57619 3.54675i 0.136346 0.187714i
\(358\) 1.65685 1.65685i 0.0875675 0.0875675i
\(359\) 16.9706i 0.895672i 0.894116 + 0.447836i \(0.147805\pi\)
−0.894116 + 0.447836i \(0.852195\pi\)
\(360\) −4.07820 3.53701i −0.214940 0.186417i
\(361\) 31.0416 1.63377
\(362\) −7.16687 + 7.16687i −0.376682 + 0.376682i
\(363\) −1.62359 1.62359i −0.0852163 0.0852163i
\(364\) 1.66205 + 10.4853i 0.0871151 + 0.549578i
\(365\) −11.4142 9.89949i −0.597447 0.518163i
\(366\) 7.89949 0.412913
\(367\) 7.39104 7.39104i 0.385809 0.385809i −0.487381 0.873190i \(-0.662048\pi\)
0.873190 + 0.487381i \(0.162048\pi\)
\(368\) 2.41421 2.41421i 0.125850 0.125850i
\(369\) −3.69552 −0.192381
\(370\) −1.21371 17.0782i −0.0630977 0.887852i
\(371\) −0.142136 0.896683i −0.00737931 0.0465535i
\(372\) −2.00000 2.00000i −0.103695 0.103695i
\(373\) −0.928932 + 0.928932i −0.0480983 + 0.0480983i −0.730747 0.682649i \(-0.760828\pi\)
0.682649 + 0.730747i \(0.260828\pi\)
\(374\) −6.12293 −0.316609
\(375\) −7.19239 4.63604i −0.371413 0.239404i
\(376\) 3.69552i 0.190582i
\(377\) −13.6997 + 13.6997i −0.705569 + 0.705569i
\(378\) 6.44315 8.87056i 0.331400 0.456253i
\(379\) 22.1421i 1.13737i −0.822557 0.568683i \(-0.807453\pi\)
0.822557 0.568683i \(-0.192547\pi\)
\(380\) 1.12132 + 15.7782i 0.0575225 + 0.809403i
\(381\) 6.94269i 0.355685i
\(382\) 7.24264 + 7.24264i 0.370566 + 0.370566i
\(383\) 10.9008 + 10.9008i 0.557007 + 0.557007i 0.928454 0.371447i \(-0.121138\pi\)
−0.371447 + 0.928454i \(0.621138\pi\)
\(384\) 0.765367 0.0390575
\(385\) 8.84935 14.2017i 0.451005 0.723787i
\(386\) −0.343146 −0.0174657
\(387\) −9.65685 9.65685i −0.490885 0.490885i
\(388\) −11.0866 11.0866i −0.562835 0.562835i
\(389\) 28.1421i 1.42686i −0.700725 0.713431i \(-0.747140\pi\)
0.700725 0.713431i \(-0.252860\pi\)
\(390\) 4.49935 5.18779i 0.227833 0.262694i
\(391\) 7.39104i 0.373781i
\(392\) 6.23784 + 3.17637i 0.315059 + 0.160431i
\(393\) −9.14214 + 9.14214i −0.461160 + 0.461160i
\(394\) 4.82843i 0.243253i
\(395\) 1.43788 + 20.2325i 0.0723476 + 1.01801i
\(396\) −6.82843 −0.343141
\(397\) 15.7716 15.7716i 0.791554 0.791554i −0.190192 0.981747i \(-0.560911\pi\)
0.981747 + 0.190192i \(0.0609112\pi\)
\(398\) −11.2723 11.2723i −0.565028 0.565028i
\(399\) −14.1480 + 2.24264i −0.708287 + 0.112272i
\(400\) −4.94975 + 0.707107i −0.247487 + 0.0353553i
\(401\) −28.2426 −1.41037 −0.705185 0.709023i \(-0.749136\pi\)
−0.705185 + 0.709023i \(0.749136\pi\)
\(402\) 4.96362 4.96362i 0.247563 0.247563i
\(403\) −10.4853 + 10.4853i −0.522309 + 0.522309i
\(404\) 11.8519 0.589655
\(405\) 9.08028 0.645316i 0.451203 0.0320660i
\(406\) 2.00000 + 12.6173i 0.0992583 + 0.626185i
\(407\) −15.3137 15.3137i −0.759072 0.759072i
\(408\) −1.17157 + 1.17157i −0.0580015 + 0.0580015i
\(409\) 23.3324 1.15371 0.576857 0.816845i \(-0.304279\pi\)
0.576857 + 0.816845i \(0.304279\pi\)
\(410\) −2.24264 + 2.58579i −0.110756 + 0.127703i
\(411\) 14.9678i 0.738306i
\(412\) −1.97908 + 1.97908i −0.0975020 + 0.0975020i
\(413\) 5.95021 8.19192i 0.292791 0.403098i
\(414\) 8.24264i 0.405104i
\(415\) 13.0208 + 11.2929i 0.639167 + 0.554346i
\(416\) 4.01254i 0.196731i
\(417\) −2.75736 2.75736i −0.135028 0.135028i
\(418\) 14.1480 + 14.1480i 0.692002 + 0.692002i
\(419\) −24.2835 −1.18633 −0.593163 0.805082i \(-0.702121\pi\)
−0.593163 + 0.805082i \(0.702121\pi\)
\(420\) −1.02413 4.41063i −0.0499725 0.215217i
\(421\) −21.7990 −1.06242 −0.531209 0.847241i \(-0.678262\pi\)
−0.531209 + 0.847241i \(0.678262\pi\)
\(422\) −15.3137 15.3137i −0.745460 0.745460i
\(423\) 6.30864 + 6.30864i 0.306737 + 0.306737i
\(424\) 0.343146i 0.0166646i
\(425\) 6.49435 8.65914i 0.315022 0.420030i
\(426\) 2.61313i 0.126606i
\(427\) −22.0941 16.0481i −1.06921 0.776620i
\(428\) −7.65685 + 7.65685i −0.370108 + 0.370108i
\(429\) 8.68629i 0.419378i
\(430\) −12.6173 + 0.896683i −0.608460 + 0.0432419i
\(431\) −5.65685 −0.272481 −0.136241 0.990676i \(-0.543502\pi\)
−0.136241 + 0.990676i \(0.543502\pi\)
\(432\) −2.93015 + 2.93015i −0.140977 + 0.140977i
\(433\) −4.32957 4.32957i −0.208066 0.208066i 0.595379 0.803445i \(-0.297002\pi\)
−0.803445 + 0.595379i \(0.797002\pi\)
\(434\) 1.53073 + 9.65685i 0.0734776 + 0.463544i
\(435\) 5.41421 6.24264i 0.259592 0.299312i
\(436\) −16.1421 −0.773068
\(437\) 17.0782 17.0782i 0.816960 0.816960i
\(438\) −3.65685 + 3.65685i −0.174731 + 0.174731i
\(439\) 18.7402 0.894422 0.447211 0.894428i \(-0.352417\pi\)
0.447211 + 0.894428i \(0.352417\pi\)
\(440\) −4.14386 + 4.77791i −0.197551 + 0.227778i
\(441\) −16.0711 + 5.22625i −0.765289 + 0.248869i
\(442\) 6.14214 + 6.14214i 0.292152 + 0.292152i
\(443\) 24.1421 24.1421i 1.14703 1.14703i 0.159893 0.987134i \(-0.448885\pi\)
0.987134 0.159893i \(-0.0511150\pi\)
\(444\) −5.86030 −0.278118
\(445\) −37.7990 + 2.68629i −1.79184 + 0.127342i
\(446\) 8.28772i 0.392435i
\(447\) 2.87576 2.87576i 0.136019 0.136019i
\(448\) −2.14065 1.55487i −0.101136 0.0734605i
\(449\) 14.3431i 0.676895i 0.940985 + 0.338447i \(0.109902\pi\)
−0.940985 + 0.338447i \(0.890098\pi\)
\(450\) 7.24264 9.65685i 0.341421 0.455228i
\(451\) 4.32957i 0.203871i
\(452\) 6.82843 + 6.82843i 0.321182 + 0.321182i
\(453\) −1.71644 1.71644i −0.0806455 0.0806455i
\(454\) −2.74444 −0.128803
\(455\) −23.1234 + 5.36916i −1.08404 + 0.251710i
\(456\) 5.41421 0.253544
\(457\) 9.65685 + 9.65685i 0.451729 + 0.451729i 0.895928 0.444199i \(-0.146512\pi\)
−0.444199 + 0.895928i \(0.646512\pi\)
\(458\) −5.31911 5.31911i −0.248546 0.248546i
\(459\) 8.97056i 0.418710i
\(460\) 5.76745 + 5.00208i 0.268909 + 0.233223i
\(461\) 11.9288i 0.555582i −0.960642 0.277791i \(-0.910398\pi\)
0.960642 0.277791i \(-0.0896022\pi\)
\(462\) −4.63405 3.36595i −0.215596 0.156598i
\(463\) 20.9706 20.9706i 0.974585 0.974585i −0.0251002 0.999685i \(-0.507990\pi\)
0.999685 + 0.0251002i \(0.00799049\pi\)
\(464\) 4.82843i 0.224154i
\(465\) 4.14386 4.77791i 0.192167 0.221570i
\(466\) 4.24264 0.196537
\(467\) 13.3442 13.3442i 0.617496 0.617496i −0.327393 0.944888i \(-0.606170\pi\)
0.944888 + 0.327393i \(0.106170\pi\)
\(468\) 6.84984 + 6.84984i 0.316634 + 0.316634i
\(469\) −23.9665 + 3.79899i −1.10667 + 0.175421i
\(470\) 8.24264 0.585786i 0.380205 0.0270203i
\(471\) 1.27208 0.0586143
\(472\) −2.70598 + 2.70598i −0.124553 + 0.124553i
\(473\) −11.3137 + 11.3137i −0.520205 + 0.520205i
\(474\) 6.94269 0.318889
\(475\) −35.0146 + 5.00208i −1.60658 + 0.229511i
\(476\) 5.65685 0.896683i 0.259281 0.0410994i
\(477\) −0.585786 0.585786i −0.0268213 0.0268213i
\(478\) −7.41421 + 7.41421i −0.339118 + 0.339118i
\(479\) 4.59220 0.209823 0.104912 0.994482i \(-0.466544\pi\)
0.104912 + 0.994482i \(0.466544\pi\)
\(480\) 0.121320 + 1.70711i 0.00553749 + 0.0779184i
\(481\) 30.7235i 1.40087i
\(482\) 4.14386 4.14386i 0.188748 0.188748i
\(483\) −4.06306 + 5.59379i −0.184876 + 0.254526i
\(484\) 3.00000i 0.136364i
\(485\) 22.9706 26.4853i 1.04304 1.20263i
\(486\) 15.5474i 0.705246i
\(487\) 20.8995 + 20.8995i 0.947047 + 0.947047i 0.998667 0.0516203i \(-0.0164385\pi\)
−0.0516203 + 0.998667i \(0.516439\pi\)
\(488\) 7.29818 + 7.29818i 0.330373 + 0.330373i
\(489\) 2.53620 0.114691
\(490\) −6.09594 + 14.4166i −0.275387 + 0.651277i
\(491\) 30.8284 1.39127 0.695634 0.718397i \(-0.255124\pi\)
0.695634 + 0.718397i \(0.255124\pi\)
\(492\) 0.828427 + 0.828427i 0.0373484 + 0.0373484i
\(493\) 7.39104 + 7.39104i 0.332876 + 0.332876i
\(494\) 28.3848i 1.27709i
\(495\) −1.08239 15.2304i −0.0486499 0.684556i
\(496\) 3.69552i 0.165934i
\(497\) −5.30864 + 7.30864i −0.238125 + 0.327837i
\(498\) 4.17157 4.17157i 0.186933 0.186933i
\(499\) 24.4853i 1.09611i 0.836442 + 0.548056i \(0.184632\pi\)
−0.836442 + 0.548056i \(0.815368\pi\)
\(500\) −2.36176 10.9280i −0.105621 0.488717i
\(501\) 12.4853 0.557801
\(502\) 20.3638 20.3638i 0.908881 0.908881i
\(503\) 22.8072 + 22.8072i 1.01692 + 1.01692i 0.999854 + 0.0170666i \(0.00543274\pi\)
0.0170666 + 0.999854i \(0.494567\pi\)
\(504\) 6.30864 1.00000i 0.281009 0.0445435i
\(505\) 1.87868 + 26.4350i 0.0836001 + 1.17634i
\(506\) 9.65685 0.429300
\(507\) −1.67798 + 1.67798i −0.0745218 + 0.0745218i
\(508\) −6.41421 + 6.41421i −0.284585 + 0.284585i
\(509\) −1.66205 −0.0736691 −0.0368345 0.999321i \(-0.511727\pi\)
−0.0368345 + 0.999321i \(0.511727\pi\)
\(510\) −2.79884 2.42742i −0.123935 0.107488i
\(511\) 17.6569 2.79884i 0.781093 0.123813i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −20.7279 + 20.7279i −0.915160 + 0.915160i
\(514\) −4.59220 −0.202553
\(515\) −4.72792 4.10051i −0.208337 0.180690i
\(516\) 4.32957i 0.190599i
\(517\) 7.39104 7.39104i 0.325057 0.325057i
\(518\) 16.3907 + 11.9054i 0.720164 + 0.523092i
\(519\) 9.27208i 0.406999i
\(520\) 8.94975 0.636039i 0.392472 0.0278922i
\(521\) 36.8464i 1.61427i 0.590367 + 0.807135i \(0.298983\pi\)
−0.590367 + 0.807135i \(0.701017\pi\)
\(522\) 8.24264 + 8.24264i 0.360771 + 0.360771i
\(523\) 6.84984 + 6.84984i 0.299523 + 0.299523i 0.840827 0.541304i \(-0.182069\pi\)
−0.541304 + 0.840827i \(0.682069\pi\)
\(524\) −16.8925 −0.737951
\(525\) 9.67532 2.98341i 0.422266 0.130207i
\(526\) −23.4558 −1.02272
\(527\) 5.65685 + 5.65685i 0.246416 + 0.246416i
\(528\) 1.53073 + 1.53073i 0.0666166 + 0.0666166i
\(529\) 11.3431i 0.493180i
\(530\) −0.765367 + 0.0543929i −0.0332454 + 0.00236268i
\(531\) 9.23880i 0.400930i
\(532\) −15.1430 10.9991i −0.656532 0.476873i
\(533\) 4.34315 4.34315i 0.188123 0.188123i
\(534\) 12.9706i 0.561291i
\(535\) −18.2919 15.8645i −0.790827 0.685881i
\(536\) 9.17157 0.396152
\(537\) 1.26810 1.26810i 0.0547226 0.0547226i
\(538\) −8.96023 8.96023i −0.386303 0.386303i
\(539\) 6.12293 + 18.8284i 0.263733 + 0.810998i
\(540\) −7.00000 6.07107i −0.301232 0.261257i
\(541\) −22.9706 −0.987582 −0.493791 0.869581i \(-0.664389\pi\)
−0.493791 + 0.869581i \(0.664389\pi\)
\(542\) −9.81845 + 9.81845i −0.421739 + 0.421739i
\(543\) −5.48528 + 5.48528i −0.235396 + 0.235396i
\(544\) −2.16478 −0.0928144
\(545\) −2.55873 36.0041i −0.109604 1.54225i
\(546\) 1.27208 + 8.02509i 0.0544399 + 0.343442i
\(547\) 14.6274 + 14.6274i 0.625423 + 0.625423i 0.946913 0.321490i \(-0.104184\pi\)
−0.321490 + 0.946913i \(0.604184\pi\)
\(548\) 13.8284 13.8284i 0.590721 0.590721i
\(549\) −24.9176 −1.06346
\(550\) −11.3137 8.48528i −0.482418 0.361814i
\(551\) 34.1563i 1.45511i
\(552\) 1.84776 1.84776i 0.0786458 0.0786458i
\(553\) −19.4180 14.1043i −0.825737 0.599776i
\(554\) 14.4853i 0.615421i
\(555\) −0.928932 13.0711i −0.0394310 0.554836i
\(556\) 5.09494i 0.216073i
\(557\) −1.27208 1.27208i −0.0538997 0.0538997i 0.679643 0.733543i \(-0.262135\pi\)
−0.733543 + 0.679643i \(0.762135\pi\)
\(558\) 6.30864 + 6.30864i 0.267066 + 0.267066i
\(559\) 22.6984 0.960039
\(560\) 3.12872 5.02107i 0.132212 0.212179i
\(561\) −4.68629 −0.197855
\(562\) 4.00000 + 4.00000i 0.168730 + 0.168730i
\(563\) 32.0844 + 32.0844i 1.35220 + 1.35220i 0.883200 + 0.468997i \(0.155385\pi\)
0.468997 + 0.883200i \(0.344615\pi\)
\(564\) 2.82843i 0.119098i
\(565\) −14.1480 + 16.3128i −0.595212 + 0.686285i
\(566\) 0.317025i 0.0133256i
\(567\) −6.32996 + 8.71474i −0.265834 + 0.365985i
\(568\) 2.41421 2.41421i 0.101298 0.101298i
\(569\) 1.41421i 0.0592869i −0.999561 0.0296435i \(-0.990563\pi\)
0.999561 0.0296435i \(-0.00943719\pi\)
\(570\) 0.858221 + 12.0761i 0.0359469 + 0.505812i
\(571\) 25.4558 1.06529 0.532647 0.846338i \(-0.321197\pi\)
0.532647 + 0.846338i \(0.321197\pi\)
\(572\) 8.02509 8.02509i 0.335546 0.335546i
\(573\) 5.54328 + 5.54328i 0.231574 + 0.231574i
\(574\) −0.634051 4.00000i −0.0264648 0.166957i
\(575\) −10.2426 + 13.6569i −0.427148 + 0.569530i
\(576\) −2.41421 −0.100592
\(577\) 4.40649 4.40649i 0.183445 0.183445i −0.609410 0.792855i \(-0.708594\pi\)
0.792855 + 0.609410i \(0.208594\pi\)
\(578\) −8.70711 + 8.70711i −0.362168 + 0.362168i
\(579\) −0.262632 −0.0109146
\(580\) 10.7695 0.765367i 0.447180 0.0317801i
\(581\) −20.1421 + 3.19278i −0.835637 + 0.132459i
\(582\) −8.48528 8.48528i −0.351726 0.351726i
\(583\) −0.686292 + 0.686292i −0.0284233 + 0.0284233i
\(584\) −6.75699 −0.279606
\(585\) −14.1924 + 16.3640i −0.586783 + 0.676567i
\(586\) 2.93015i 0.121043i
\(587\) −5.58174 + 5.58174i −0.230383 + 0.230383i −0.812853 0.582470i \(-0.802087\pi\)
0.582470 + 0.812853i \(0.302087\pi\)
\(588\) 4.77424 + 2.43109i 0.196886 + 0.100256i
\(589\) 26.1421i 1.07717i
\(590\) −6.46447 5.60660i −0.266138 0.230820i
\(591\) 3.69552i 0.152013i
\(592\) −5.41421 5.41421i −0.222523 0.222523i
\(593\) −18.6633 18.6633i −0.766410 0.766410i 0.211063 0.977473i \(-0.432308\pi\)
−0.977473 + 0.211063i \(0.932308\pi\)
\(594\) −11.7206 −0.480902
\(595\) 2.89668 + 12.4752i 0.118752 + 0.511431i
\(596\) 5.31371 0.217658
\(597\) −8.62742 8.62742i −0.353097 0.353097i
\(598\) −9.68714 9.68714i −0.396136 0.396136i
\(599\) 46.5269i 1.90104i −0.310666 0.950519i \(-0.600552\pi\)
0.310666 0.950519i \(-0.399448\pi\)
\(600\) −3.78837 + 0.541196i −0.154660 + 0.0220942i
\(601\) 19.1116i 0.779580i 0.920904 + 0.389790i \(0.127452\pi\)
−0.920904 + 0.389790i \(0.872548\pi\)
\(602\) 8.79565 12.1094i 0.358484 0.493541i
\(603\) −15.6569 + 15.6569i −0.637596 + 0.637596i
\(604\) 3.17157i 0.129049i
\(605\) 6.69133 0.475538i 0.272041 0.0193334i
\(606\) 9.07107 0.368487
\(607\) 0.262632 0.262632i 0.0106599 0.0106599i −0.701757 0.712417i \(-0.747601\pi\)
0.712417 + 0.701757i \(0.247601\pi\)
\(608\) 5.00208 + 5.00208i 0.202861 + 0.202861i
\(609\) 1.53073 + 9.65685i 0.0620285 + 0.391315i
\(610\) −15.1213 + 17.4350i −0.612244 + 0.705924i
\(611\) −14.8284 −0.599894
\(612\) 3.69552 3.69552i 0.149382 0.149382i
\(613\) 0.100505 0.100505i 0.00405936 0.00405936i −0.705074 0.709134i \(-0.749086\pi\)
0.709134 + 0.705074i \(0.249086\pi\)
\(614\) −5.91470 −0.238698
\(615\) −1.71644 + 1.97908i −0.0692137 + 0.0798040i
\(616\) −1.17157 7.39104i −0.0472040 0.297793i
\(617\) −11.5147 11.5147i −0.463565 0.463565i 0.436257 0.899822i \(-0.356304\pi\)
−0.899822 + 0.436257i \(0.856304\pi\)
\(618\) −1.51472 + 1.51472i −0.0609309 + 0.0609309i
\(619\) 34.9217 1.40362 0.701811 0.712363i \(-0.252375\pi\)
0.701811 + 0.712363i \(0.252375\pi\)
\(620\) 8.24264 0.585786i 0.331032 0.0235257i
\(621\) 14.1480i 0.567741i
\(622\) 16.3128 16.3128i 0.654084 0.654084i
\(623\) 26.3501 36.2773i 1.05569 1.45342i
\(624\) 3.07107i 0.122941i
\(625\) 24.0000 7.00000i 0.960000 0.280000i
\(626\) 8.28772i 0.331244i
\(627\) 10.8284 + 10.8284i 0.432446 + 0.432446i
\(628\) 1.17525 + 1.17525i 0.0468975 + 0.0468975i
\(629\) 16.5754 0.660906
\(630\) 3.23044 + 13.9126i 0.128704 + 0.554289i
\(631\) −29.3553 −1.16862 −0.584309 0.811531i \(-0.698634\pi\)
−0.584309 + 0.811531i \(0.698634\pi\)
\(632\) 6.41421 + 6.41421i 0.255144 + 0.255144i
\(633\) −11.7206 11.7206i −0.465852 0.465852i
\(634\) 2.97056i 0.117976i
\(635\) −15.3233 13.2898i −0.608085 0.527390i
\(636\) 0.262632i 0.0104141i
\(637\) 12.7453 25.0296i 0.504989 0.991709i
\(638\) 9.65685 9.65685i 0.382319 0.382319i
\(639\) 8.24264i 0.326074i
\(640\) −1.46508 + 1.68925i −0.0579122 + 0.0667733i
\(641\) 5.21320 0.205909 0.102955 0.994686i \(-0.467170\pi\)
0.102955 + 0.994686i \(0.467170\pi\)
\(642\) −5.86030 + 5.86030i −0.231288 + 0.231288i
\(643\) −27.0439 27.0439i −1.06651 1.06651i −0.997625 0.0688814i \(-0.978057\pi\)
−0.0688814 0.997625i \(-0.521943\pi\)
\(644\) −8.92177 + 1.41421i −0.351567 + 0.0557278i
\(645\) −9.65685 + 0.686292i −0.380238 + 0.0270227i
\(646\) −15.3137 −0.602510
\(647\) −20.7193 + 20.7193i −0.814560 + 0.814560i −0.985314 0.170754i \(-0.945380\pi\)
0.170754 + 0.985314i \(0.445380\pi\)
\(648\) 2.87868 2.87868i 0.113085 0.113085i
\(649\) −10.8239 −0.424876
\(650\) 2.83730 + 19.8611i 0.111288 + 0.779016i
\(651\) 1.17157 + 7.39104i 0.0459176 + 0.289678i
\(652\) 2.34315 + 2.34315i 0.0917647 + 0.0917647i
\(653\) −16.7279 + 16.7279i −0.654614 + 0.654614i −0.954101 0.299486i \(-0.903185\pi\)
0.299486 + 0.954101i \(0.403185\pi\)
\(654\) −12.3547 −0.483105
\(655\) −2.67767 37.6777i −0.104625 1.47219i
\(656\) 1.53073i 0.0597651i
\(657\) 11.5349 11.5349i 0.450019 0.450019i
\(658\) −5.74603 + 7.91082i −0.224004 + 0.308396i
\(659\) 18.3431i 0.714548i −0.934000 0.357274i \(-0.883706\pi\)
0.934000 0.357274i \(-0.116294\pi\)
\(660\) −3.17157 + 3.65685i −0.123453 + 0.142343i
\(661\) 0.208239i 0.00809958i −0.999992 0.00404979i \(-0.998711\pi\)
0.999992 0.00404979i \(-0.00128909\pi\)
\(662\) 0.485281 + 0.485281i 0.0188610 + 0.0188610i
\(663\) 4.70099 + 4.70099i 0.182571 + 0.182571i
\(664\) 7.70806 0.299131
\(665\) 22.1326 35.5191i 0.858265 1.37737i
\(666\) 18.4853 0.716290
\(667\) −11.6569 11.6569i −0.451355 0.451355i
\(668\) 11.5349 + 11.5349i 0.446299 + 0.446299i
\(669\) 6.34315i 0.245240i
\(670\) 1.45381 + 20.4567i 0.0561656 + 0.790310i
\(671\) 29.1927i 1.12697i
\(672\) −1.63838 1.19004i −0.0632020 0.0459069i
\(673\) 16.7990 16.7990i 0.647553 0.647553i −0.304848 0.952401i \(-0.598606\pi\)
0.952401 + 0.304848i \(0.0986055\pi\)
\(674\) 17.3137i 0.666899i
\(675\) 12.4316 16.5754i 0.478492 0.637989i
\(676\) −3.10051 −0.119250
\(677\) −30.7394 + 30.7394i −1.18141 + 1.18141i −0.202032 + 0.979379i \(0.564754\pi\)
−0.979379 + 0.202032i \(0.935246\pi\)
\(678\) 5.22625 + 5.22625i 0.200713 + 0.200713i
\(679\) 6.49435 + 40.9706i 0.249230 + 1.57231i
\(680\) −0.343146 4.82843i −0.0131590 0.185162i
\(681\) −2.10051 −0.0804915
\(682\) 7.39104 7.39104i 0.283017 0.283017i
\(683\) −2.68629 + 2.68629i −0.102788 + 0.102788i −0.756631 0.653843i \(-0.773156\pi\)
0.653843 + 0.756631i \(0.273156\pi\)
\(684\) −17.0782 −0.653000
\(685\) 33.0355 + 28.6515i 1.26222 + 1.09472i
\(686\) −8.41421 16.4985i −0.321256 0.629916i
\(687\) −4.07107 4.07107i −0.155321 0.155321i
\(688\) −4.00000 + 4.00000i −0.152499 + 0.152499i
\(689\) 1.37689 0.0524552
\(690\) 4.41421 + 3.82843i 0.168046 + 0.145746i
\(691\) 12.5629i 0.477915i −0.971030 0.238958i \(-0.923194\pi\)
0.971030 0.238958i \(-0.0768057\pi\)
\(692\) −8.56628 + 8.56628i −0.325641 + 0.325641i
\(693\) 14.6173 + 10.6173i 0.555265 + 0.403317i
\(694\) 24.4853i 0.929449i
\(695\) 11.3640 0.807612i 0.431060 0.0306345i
\(696\) 3.69552i 0.140078i
\(697\) −2.34315 2.34315i −0.0887530 0.0887530i
\(698\) −17.6194 17.6194i −0.666903 0.666903i
\(699\) 3.24718 0.122819
\(700\) 11.6951 + 6.18252i 0.442035 + 0.233677i
\(701\) 49.1127 1.85496 0.927481 0.373872i \(-0.121970\pi\)
0.927481 + 0.373872i \(0.121970\pi\)
\(702\) 11.7574 + 11.7574i 0.443753 + 0.443753i
\(703\) −38.3002 38.3002i −1.44452 1.44452i
\(704\) 2.82843i 0.106600i
\(705\) 6.30864 0.448342i 0.237597 0.0168855i
\(706\) 8.02509i 0.302028i
\(707\) −25.3708 18.4281i −0.954169 0.693062i
\(708\) −2.07107 + 2.07107i −0.0778355 + 0.0778355i
\(709\) 18.6863i 0.701778i −0.936417 0.350889i \(-0.885879\pi\)
0.936417 0.350889i \(-0.114121\pi\)
\(710\) 5.76745 + 5.00208i 0.216448 + 0.187725i
\(711\) −21.8995 −0.821295
\(712\) −11.9832 + 11.9832i −0.449091 + 0.449091i
\(713\) −8.92177 8.92177i −0.334123 0.334123i
\(714\) 4.32957 0.686292i 0.162030 0.0256838i
\(715\) 19.1716 + 16.6274i 0.716976 + 0.621830i
\(716\) 2.34315 0.0875675
\(717\) −5.67459 + 5.67459i −0.211922 + 0.211922i
\(718\) −12.0000 + 12.0000i −0.447836 + 0.447836i
\(719\) −9.44703 −0.352315 −0.176157 0.984362i \(-0.556367\pi\)
−0.176157 + 0.984362i \(0.556367\pi\)
\(720\) −0.382683 5.38476i −0.0142618 0.200678i
\(721\) 7.31371 1.15932i 0.272377 0.0431752i
\(722\) 21.9497 + 21.9497i 0.816885 + 0.816885i
\(723\) 3.17157 3.17157i 0.117952 0.117952i
\(724\) −10.1355 −0.376682
\(725\) 3.41421 + 23.8995i 0.126801 + 0.887605i
\(726\) 2.29610i 0.0852163i
\(727\) −18.6633 + 18.6633i −0.692183 + 0.692183i −0.962712 0.270528i \(-0.912802\pi\)
0.270528 + 0.962712i \(0.412802\pi\)
\(728\) −6.23897 + 8.58946i −0.231231 + 0.318347i
\(729\) 0.313708i 0.0116188i
\(730\) −1.07107 15.0711i −0.0396420 0.557805i
\(731\) 12.2459i 0.452930i
\(732\) 5.58579 + 5.58579i 0.206457 + 0.206457i
\(733\) −12.3387 12.3387i −0.455741 0.455741i 0.441513 0.897255i \(-0.354442\pi\)
−0.897255 + 0.441513i \(0.854442\pi\)
\(734\) 10.4525 0.385809
\(735\) −4.66563 + 11.0340i −0.172094 + 0.406996i
\(736\) 3.41421 0.125850
\(737\) 18.3431 + 18.3431i 0.675678 + 0.675678i
\(738\) −2.61313 2.61313i −0.0961905 0.0961905i
\(739\) 1.65685i 0.0609484i 0.999536 + 0.0304742i \(0.00970174\pi\)
−0.999536 + 0.0304742i \(0.990298\pi\)
\(740\) 11.2179 12.9343i 0.412377 0.475475i
\(741\) 21.7248i 0.798079i
\(742\) 0.533546 0.734556i 0.0195871 0.0269664i
\(743\) −21.0416 + 21.0416i −0.771943 + 0.771943i −0.978446 0.206503i \(-0.933792\pi\)
0.206503 + 0.978446i \(0.433792\pi\)
\(744\) 2.82843i 0.103695i
\(745\) 0.842290 + 11.8519i 0.0308591 + 0.434221i
\(746\) −1.31371 −0.0480983
\(747\) −13.1585 + 13.1585i −0.481444 + 0.481444i
\(748\) −4.32957 4.32957i −0.158305 0.158305i
\(749\) 28.2960 4.48528i 1.03391 0.163889i
\(750\) −1.80761 8.36396i −0.0660047 0.305409i
\(751\) 14.4853 0.528575 0.264288 0.964444i \(-0.414863\pi\)
0.264288 + 0.964444i \(0.414863\pi\)
\(752\) 2.61313 2.61313i 0.0952909 0.0952909i
\(753\) 15.5858 15.5858i 0.567978 0.567978i
\(754\) −19.3743 −0.705569
\(755\) 7.07401 0.502734i 0.257450 0.0182964i
\(756\) 10.8284 1.71644i 0.393826 0.0624264i
\(757\) −11.8995 11.8995i −0.432494 0.432494i 0.456982 0.889476i \(-0.348931\pi\)
−0.889476 + 0.456982i \(0.848931\pi\)
\(758\) 15.6569 15.6569i 0.568683 0.568683i
\(759\) 7.39104 0.268278
\(760\) −10.3640 + 11.9497i −0.375940 + 0.433463i
\(761\) 32.3630i 1.17316i 0.809892 + 0.586579i \(0.199525\pi\)
−0.809892 + 0.586579i \(0.800475\pi\)
\(762\) −4.90923 + 4.90923i −0.177843 + 0.177843i
\(763\) 34.5547 + 25.0989i 1.25096 + 0.908640i
\(764\) 10.2426i 0.370566i
\(765\) 8.82843 + 7.65685i 0.319192 + 0.276834i
\(766\) 15.4161i 0.557007i
\(767\) 10.8579 + 10.8579i 0.392055 + 0.392055i
\(768\) 0.541196 + 0.541196i 0.0195287 + 0.0195287i
\(769\) 20.2710 0.730989 0.365495 0.930813i \(-0.380900\pi\)
0.365495 + 0.930813i \(0.380900\pi\)
\(770\) 16.2996 3.78470i 0.587396 0.136391i
\(771\) −3.51472 −0.126579
\(772\) −0.242641 0.242641i −0.00873283 0.00873283i
\(773\) −1.49227 1.49227i −0.0536733 0.0536733i 0.679761 0.733434i \(-0.262084\pi\)
−0.733434 + 0.679761i \(0.762084\pi\)
\(774\) 13.6569i 0.490885i
\(775\) 2.61313 + 18.2919i 0.0938663 + 0.657064i
\(776\) 15.6788i 0.562835i
\(777\) 12.5449 + 9.11198i 0.450045 + 0.326891i