Properties

Label 252.2.w.a.101.5
Level $252$
Weight $2$
Character 252.101
Analytic conductor $2.012$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.w (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.5
Root \(-0.213160 + 1.71888i\) of defining polynomial
Character \(\chi\) \(=\) 252.101
Dual form 252.2.w.a.5.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.106783 - 1.72876i) q^{3} +(1.43402 - 2.48379i) q^{5} +(2.56899 + 0.632668i) q^{7} +(-2.97719 - 0.369204i) q^{9} +O(q^{10})\) \(q+(0.106783 - 1.72876i) q^{3} +(1.43402 - 2.48379i) q^{5} +(2.56899 + 0.632668i) q^{7} +(-2.97719 - 0.369204i) q^{9} +(-2.34941 + 1.35643i) q^{11} +(-3.18987 + 1.84167i) q^{13} +(-4.14074 - 2.74429i) q^{15} +(3.22192 - 5.58052i) q^{17} +(2.73867 - 1.58117i) q^{19} +(1.36805 - 4.37361i) q^{21} +(2.59068 + 1.49573i) q^{23} +(-1.61282 - 2.79348i) q^{25} +(-0.956179 + 5.10742i) q^{27} +(-2.48332 - 1.43375i) q^{29} +9.54636i q^{31} +(2.09406 + 4.20639i) q^{33} +(5.25540 - 5.47359i) q^{35} +(-1.70640 - 2.95556i) q^{37} +(2.84318 + 5.71117i) q^{39} +(-0.794538 - 1.37618i) q^{41} +(-4.67828 + 8.10302i) q^{43} +(-5.18638 + 6.86529i) q^{45} +11.3074 q^{47} +(6.19946 + 3.25064i) q^{49} +(-9.30332 - 6.16581i) q^{51} +(2.16419 + 1.24950i) q^{53} +7.78058i q^{55} +(-2.44102 - 4.90333i) q^{57} -8.67361 q^{59} +0.654617i q^{61} +(-7.41481 - 2.83206i) q^{63} +10.5640i q^{65} +7.72292 q^{67} +(2.86240 - 4.31894i) q^{69} -7.86582i q^{71} +(11.0769 + 6.39527i) q^{73} +(-5.00146 + 2.48987i) q^{75} +(-6.89378 + 1.99827i) q^{77} +5.19132 q^{79} +(8.72738 + 2.19839i) q^{81} +(-7.92948 + 13.7343i) q^{83} +(-9.24057 - 16.0051i) q^{85} +(-2.74378 + 4.13996i) q^{87} +(3.14826 + 5.45295i) q^{89} +(-9.35993 + 2.71312i) q^{91} +(16.5033 + 1.01939i) q^{93} -9.06971i q^{95} +(-13.2065 - 7.62477i) q^{97} +(7.49544 - 3.17095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - q^{7} + 6q^{9} + O(q^{10}) \) \( 16q - q^{7} + 6q^{9} - 6q^{11} - 3q^{13} - 3q^{15} + 9q^{17} + 6q^{21} + 21q^{23} - 8q^{25} + 9q^{27} + 6q^{29} - 15q^{35} + q^{37} - 3q^{39} - 6q^{41} - 2q^{43} - 30q^{45} - 36q^{47} - 5q^{49} - 33q^{51} + 15q^{57} - 30q^{59} - 15q^{63} + 14q^{67} + 21q^{69} - 57q^{75} + 3q^{77} + 2q^{79} + 18q^{81} + 6q^{85} + 48q^{87} + 21q^{89} + 9q^{91} + 21q^{93} - 3q^{97} - 9q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.106783 1.72876i 0.0616513 0.998098i
\(4\) 0 0
\(5\) 1.43402 2.48379i 0.641312 1.11079i −0.343828 0.939033i \(-0.611724\pi\)
0.985140 0.171753i \(-0.0549431\pi\)
\(6\) 0 0
\(7\) 2.56899 + 0.632668i 0.970989 + 0.239126i
\(8\) 0 0
\(9\) −2.97719 0.369204i −0.992398 0.123068i
\(10\) 0 0
\(11\) −2.34941 + 1.35643i −0.708373 + 0.408979i −0.810458 0.585797i \(-0.800782\pi\)
0.102086 + 0.994776i \(0.467448\pi\)
\(12\) 0 0
\(13\) −3.18987 + 1.84167i −0.884712 + 0.510789i −0.872209 0.489133i \(-0.837313\pi\)
−0.0125026 + 0.999922i \(0.503980\pi\)
\(14\) 0 0
\(15\) −4.14074 2.74429i −1.06913 0.708574i
\(16\) 0 0
\(17\) 3.22192 5.58052i 0.781429 1.35348i −0.149680 0.988735i \(-0.547824\pi\)
0.931109 0.364741i \(-0.118842\pi\)
\(18\) 0 0
\(19\) 2.73867 1.58117i 0.628294 0.362746i −0.151797 0.988412i \(-0.548506\pi\)
0.780091 + 0.625666i \(0.215173\pi\)
\(20\) 0 0
\(21\) 1.36805 4.37361i 0.298534 0.954399i
\(22\) 0 0
\(23\) 2.59068 + 1.49573i 0.540195 + 0.311882i 0.745158 0.666888i \(-0.232374\pi\)
−0.204963 + 0.978770i \(0.565707\pi\)
\(24\) 0 0
\(25\) −1.61282 2.79348i −0.322563 0.558696i
\(26\) 0 0
\(27\) −0.956179 + 5.10742i −0.184017 + 0.982923i
\(28\) 0 0
\(29\) −2.48332 1.43375i −0.461142 0.266240i 0.251383 0.967888i \(-0.419115\pi\)
−0.712524 + 0.701648i \(0.752448\pi\)
\(30\) 0 0
\(31\) 9.54636i 1.71458i 0.514836 + 0.857289i \(0.327853\pi\)
−0.514836 + 0.857289i \(0.672147\pi\)
\(32\) 0 0
\(33\) 2.09406 + 4.20639i 0.364529 + 0.732239i
\(34\) 0 0
\(35\) 5.25540 5.47359i 0.888325 0.925205i
\(36\) 0 0
\(37\) −1.70640 2.95556i −0.280530 0.485892i 0.690986 0.722868i \(-0.257177\pi\)
−0.971515 + 0.236977i \(0.923843\pi\)
\(38\) 0 0
\(39\) 2.84318 + 5.71117i 0.455273 + 0.914520i
\(40\) 0 0
\(41\) −0.794538 1.37618i −0.124086 0.214923i 0.797289 0.603597i \(-0.206267\pi\)
−0.921375 + 0.388674i \(0.872933\pi\)
\(42\) 0 0
\(43\) −4.67828 + 8.10302i −0.713431 + 1.23570i 0.250131 + 0.968212i \(0.419526\pi\)
−0.963562 + 0.267487i \(0.913807\pi\)
\(44\) 0 0
\(45\) −5.18638 + 6.86529i −0.773140 + 1.02342i
\(46\) 0 0
\(47\) 11.3074 1.64936 0.824680 0.565599i \(-0.191355\pi\)
0.824680 + 0.565599i \(0.191355\pi\)
\(48\) 0 0
\(49\) 6.19946 + 3.25064i 0.885637 + 0.464378i
\(50\) 0 0
\(51\) −9.30332 6.16581i −1.30272 0.863387i
\(52\) 0 0
\(53\) 2.16419 + 1.24950i 0.297275 + 0.171632i 0.641218 0.767359i \(-0.278429\pi\)
−0.343943 + 0.938990i \(0.611763\pi\)
\(54\) 0 0
\(55\) 7.78058i 1.04913i
\(56\) 0 0
\(57\) −2.44102 4.90333i −0.323320 0.649462i
\(58\) 0 0
\(59\) −8.67361 −1.12921 −0.564604 0.825362i \(-0.690971\pi\)
−0.564604 + 0.825362i \(0.690971\pi\)
\(60\) 0 0
\(61\) 0.654617i 0.0838151i 0.999121 + 0.0419075i \(0.0133435\pi\)
−0.999121 + 0.0419075i \(0.986657\pi\)
\(62\) 0 0
\(63\) −7.41481 2.83206i −0.934178 0.356806i
\(64\) 0 0
\(65\) 10.5640i 1.31030i
\(66\) 0 0
\(67\) 7.72292 0.943505 0.471752 0.881731i \(-0.343622\pi\)
0.471752 + 0.881731i \(0.343622\pi\)
\(68\) 0 0
\(69\) 2.86240 4.31894i 0.344592 0.519939i
\(70\) 0 0
\(71\) 7.86582i 0.933501i −0.884389 0.466750i \(-0.845425\pi\)
0.884389 0.466750i \(-0.154575\pi\)
\(72\) 0 0
\(73\) 11.0769 + 6.39527i 1.29646 + 0.748510i 0.979790 0.200027i \(-0.0641028\pi\)
0.316667 + 0.948537i \(0.397436\pi\)
\(74\) 0 0
\(75\) −5.00146 + 2.48987i −0.577519 + 0.287505i
\(76\) 0 0
\(77\) −6.89378 + 1.99827i −0.785619 + 0.227724i
\(78\) 0 0
\(79\) 5.19132 0.584069 0.292034 0.956408i \(-0.405668\pi\)
0.292034 + 0.956408i \(0.405668\pi\)
\(80\) 0 0
\(81\) 8.72738 + 2.19839i 0.969708 + 0.244265i
\(82\) 0 0
\(83\) −7.92948 + 13.7343i −0.870373 + 1.50753i −0.00876173 + 0.999962i \(0.502789\pi\)
−0.861611 + 0.507569i \(0.830544\pi\)
\(84\) 0 0
\(85\) −9.24057 16.0051i −1.00228 1.73600i
\(86\) 0 0
\(87\) −2.74378 + 4.13996i −0.294164 + 0.443850i
\(88\) 0 0
\(89\) 3.14826 + 5.45295i 0.333715 + 0.578012i 0.983237 0.182331i \(-0.0583643\pi\)
−0.649522 + 0.760343i \(0.725031\pi\)
\(90\) 0 0
\(91\) −9.35993 + 2.71312i −0.981188 + 0.284412i
\(92\) 0 0
\(93\) 16.5033 + 1.01939i 1.71132 + 0.105706i
\(94\) 0 0
\(95\) 9.06971i 0.930533i
\(96\) 0 0
\(97\) −13.2065 7.62477i −1.34092 0.774178i −0.353974 0.935255i \(-0.615170\pi\)
−0.986942 + 0.161077i \(0.948503\pi\)
\(98\) 0 0
\(99\) 7.49544 3.17095i 0.753320 0.318692i
\(100\) 0 0
\(101\) −1.74451 3.02158i −0.173585 0.300658i 0.766086 0.642739i \(-0.222202\pi\)
−0.939671 + 0.342080i \(0.888869\pi\)
\(102\) 0 0
\(103\) −2.89161 1.66947i −0.284919 0.164498i 0.350729 0.936477i \(-0.385934\pi\)
−0.635648 + 0.771979i \(0.719267\pi\)
\(104\) 0 0
\(105\) −8.90131 9.66979i −0.868679 0.943675i
\(106\) 0 0
\(107\) −3.10776 + 1.79427i −0.300439 + 0.173458i −0.642640 0.766168i \(-0.722161\pi\)
0.342201 + 0.939627i \(0.388828\pi\)
\(108\) 0 0
\(109\) 6.89673 11.9455i 0.660587 1.14417i −0.319875 0.947460i \(-0.603641\pi\)
0.980462 0.196710i \(-0.0630258\pi\)
\(110\) 0 0
\(111\) −5.29166 + 2.63434i −0.502262 + 0.250040i
\(112\) 0 0
\(113\) −5.28607 + 3.05191i −0.497271 + 0.287100i −0.727586 0.686016i \(-0.759358\pi\)
0.230315 + 0.973116i \(0.426024\pi\)
\(114\) 0 0
\(115\) 7.43018 4.28981i 0.692867 0.400027i
\(116\) 0 0
\(117\) 10.1768 4.30531i 0.940848 0.398026i
\(118\) 0 0
\(119\) 11.8077 12.2979i 1.08241 1.12735i
\(120\) 0 0
\(121\) −1.82019 + 3.15267i −0.165472 + 0.286606i
\(122\) 0 0
\(123\) −2.46392 + 1.22661i −0.222164 + 0.110600i
\(124\) 0 0
\(125\) 5.08895 0.455170
\(126\) 0 0
\(127\) −13.3819 −1.18745 −0.593727 0.804666i \(-0.702344\pi\)
−0.593727 + 0.804666i \(0.702344\pi\)
\(128\) 0 0
\(129\) 13.5086 + 8.95287i 1.18936 + 0.788256i
\(130\) 0 0
\(131\) −0.388964 + 0.673705i −0.0339839 + 0.0588619i −0.882517 0.470280i \(-0.844153\pi\)
0.848533 + 0.529142i \(0.177486\pi\)
\(132\) 0 0
\(133\) 8.03598 2.32935i 0.696808 0.201980i
\(134\) 0 0
\(135\) 11.3146 + 9.69908i 0.973805 + 0.834764i
\(136\) 0 0
\(137\) −14.3082 + 8.26083i −1.22243 + 0.705771i −0.965435 0.260642i \(-0.916066\pi\)
−0.256995 + 0.966413i \(0.582732\pi\)
\(138\) 0 0
\(139\) 9.91826 5.72631i 0.841256 0.485699i −0.0164348 0.999865i \(-0.505232\pi\)
0.857691 + 0.514165i \(0.171898\pi\)
\(140\) 0 0
\(141\) 1.20745 19.5478i 0.101685 1.64622i
\(142\) 0 0
\(143\) 4.99620 8.65368i 0.417804 0.723657i
\(144\) 0 0
\(145\) −7.12226 + 4.11204i −0.591472 + 0.341486i
\(146\) 0 0
\(147\) 6.28157 10.3702i 0.518095 0.855323i
\(148\) 0 0
\(149\) −4.24781 2.45247i −0.347994 0.200914i 0.315807 0.948823i \(-0.397725\pi\)
−0.663801 + 0.747909i \(0.731058\pi\)
\(150\) 0 0
\(151\) −4.92814 8.53579i −0.401047 0.694633i 0.592806 0.805345i \(-0.298020\pi\)
−0.993852 + 0.110712i \(0.964687\pi\)
\(152\) 0 0
\(153\) −11.6526 + 15.4248i −0.942059 + 1.24702i
\(154\) 0 0
\(155\) 23.7112 + 13.6897i 1.90453 + 1.09958i
\(156\) 0 0
\(157\) 15.4169i 1.23040i −0.788371 0.615200i \(-0.789075\pi\)
0.788371 0.615200i \(-0.210925\pi\)
\(158\) 0 0
\(159\) 2.39118 3.60794i 0.189633 0.286128i
\(160\) 0 0
\(161\) 5.70915 + 5.48157i 0.449944 + 0.432008i
\(162\) 0 0
\(163\) −5.72053 9.90825i −0.448066 0.776074i 0.550194 0.835037i \(-0.314554\pi\)
−0.998260 + 0.0589632i \(0.981221\pi\)
\(164\) 0 0
\(165\) 13.4507 + 0.830835i 1.04714 + 0.0646805i
\(166\) 0 0
\(167\) −6.49103 11.2428i −0.502291 0.869993i −0.999996 0.00264735i \(-0.999157\pi\)
0.497706 0.867346i \(-0.334176\pi\)
\(168\) 0 0
\(169\) 0.283528 0.491084i 0.0218098 0.0377757i
\(170\) 0 0
\(171\) −8.73733 + 3.69633i −0.668160 + 0.282665i
\(172\) 0 0
\(173\) −19.5997 −1.49014 −0.745068 0.666988i \(-0.767583\pi\)
−0.745068 + 0.666988i \(0.767583\pi\)
\(174\) 0 0
\(175\) −2.37597 8.19681i −0.179606 0.619620i
\(176\) 0 0
\(177\) −0.926196 + 14.9945i −0.0696171 + 1.12706i
\(178\) 0 0
\(179\) −16.2630 9.38942i −1.21555 0.701799i −0.251588 0.967835i \(-0.580953\pi\)
−0.963963 + 0.266036i \(0.914286\pi\)
\(180\) 0 0
\(181\) 4.47775i 0.332829i −0.986056 0.166414i \(-0.946781\pi\)
0.986056 0.166414i \(-0.0532190\pi\)
\(182\) 0 0
\(183\) 1.13167 + 0.0699021i 0.0836556 + 0.00516731i
\(184\) 0 0
\(185\) −9.78801 −0.719629
\(186\) 0 0
\(187\) 17.4812i 1.27835i
\(188\) 0 0
\(189\) −5.68772 + 12.5160i −0.413721 + 0.910404i
\(190\) 0 0
\(191\) 6.81331i 0.492994i −0.969144 0.246497i \(-0.920720\pi\)
0.969144 0.246497i \(-0.0792795\pi\)
\(192\) 0 0
\(193\) −15.9539 −1.14839 −0.574193 0.818720i \(-0.694684\pi\)
−0.574193 + 0.818720i \(0.694684\pi\)
\(194\) 0 0
\(195\) 18.2625 + 1.12806i 1.30781 + 0.0807817i
\(196\) 0 0
\(197\) 25.9511i 1.84894i 0.381254 + 0.924470i \(0.375492\pi\)
−0.381254 + 0.924470i \(0.624508\pi\)
\(198\) 0 0
\(199\) 2.75706 + 1.59179i 0.195443 + 0.112839i 0.594528 0.804075i \(-0.297339\pi\)
−0.399085 + 0.916914i \(0.630672\pi\)
\(200\) 0 0
\(201\) 0.824678 13.3510i 0.0581683 0.941710i
\(202\) 0 0
\(203\) −5.47256 5.25441i −0.384098 0.368787i
\(204\) 0 0
\(205\) −4.55752 −0.318311
\(206\) 0 0
\(207\) −7.16074 5.40958i −0.497706 0.375992i
\(208\) 0 0
\(209\) −4.28950 + 7.42963i −0.296711 + 0.513918i
\(210\) 0 0
\(211\) −0.0552411 0.0956804i −0.00380295 0.00658691i 0.864118 0.503290i \(-0.167877\pi\)
−0.867921 + 0.496703i \(0.834544\pi\)
\(212\) 0 0
\(213\) −13.5981 0.839937i −0.931725 0.0575516i
\(214\) 0 0
\(215\) 13.4175 + 23.2397i 0.915064 + 1.58494i
\(216\) 0 0
\(217\) −6.03968 + 24.5245i −0.410000 + 1.66483i
\(218\) 0 0
\(219\) 12.2387 18.4664i 0.827015 1.24784i
\(220\) 0 0
\(221\) 23.7349i 1.59658i
\(222\) 0 0
\(223\) 11.3064 + 6.52775i 0.757132 + 0.437130i 0.828265 0.560336i \(-0.189328\pi\)
−0.0711331 + 0.997467i \(0.522661\pi\)
\(224\) 0 0
\(225\) 3.77030 + 8.91219i 0.251353 + 0.594146i
\(226\) 0 0
\(227\) 4.63392 + 8.02618i 0.307564 + 0.532716i 0.977829 0.209406i \(-0.0671529\pi\)
−0.670265 + 0.742122i \(0.733820\pi\)
\(228\) 0 0
\(229\) 11.6204 + 6.70902i 0.767895 + 0.443344i 0.832123 0.554591i \(-0.187125\pi\)
−0.0642281 + 0.997935i \(0.520459\pi\)
\(230\) 0 0
\(231\) 2.71837 + 12.1310i 0.178856 + 0.798164i
\(232\) 0 0
\(233\) −18.3415 + 10.5895i −1.20159 + 0.693738i −0.960909 0.276866i \(-0.910704\pi\)
−0.240681 + 0.970604i \(0.577371\pi\)
\(234\) 0 0
\(235\) 16.2151 28.0853i 1.05776 1.83209i
\(236\) 0 0
\(237\) 0.554346 8.97452i 0.0360086 0.582958i
\(238\) 0 0
\(239\) −7.73342 + 4.46489i −0.500233 + 0.288810i −0.728810 0.684716i \(-0.759926\pi\)
0.228577 + 0.973526i \(0.426593\pi\)
\(240\) 0 0
\(241\) 15.9430 9.20469i 1.02698 0.592926i 0.110860 0.993836i \(-0.464639\pi\)
0.916117 + 0.400910i \(0.131306\pi\)
\(242\) 0 0
\(243\) 4.73241 14.8528i 0.303584 0.952805i
\(244\) 0 0
\(245\) 16.9641 10.7367i 1.08379 0.685942i
\(246\) 0 0
\(247\) −5.82401 + 10.0875i −0.370573 + 0.641851i
\(248\) 0 0
\(249\) 22.8964 + 15.1747i 1.45100 + 0.961659i
\(250\) 0 0
\(251\) −6.33194 −0.399669 −0.199834 0.979830i \(-0.564040\pi\)
−0.199834 + 0.979830i \(0.564040\pi\)
\(252\) 0 0
\(253\) −8.11542 −0.510212
\(254\) 0 0
\(255\) −28.6557 + 14.2656i −1.79449 + 0.893347i
\(256\) 0 0
\(257\) 8.19283 14.1904i 0.511054 0.885172i −0.488863 0.872360i \(-0.662588\pi\)
0.999918 0.0128120i \(-0.00407829\pi\)
\(258\) 0 0
\(259\) −2.51383 8.67241i −0.156202 0.538877i
\(260\) 0 0
\(261\) 6.86399 + 5.18540i 0.424870 + 0.320968i
\(262\) 0 0
\(263\) −10.4663 + 6.04270i −0.645377 + 0.372609i −0.786683 0.617357i \(-0.788203\pi\)
0.141306 + 0.989966i \(0.454870\pi\)
\(264\) 0 0
\(265\) 6.20698 3.58360i 0.381292 0.220139i
\(266\) 0 0
\(267\) 9.76300 4.86029i 0.597486 0.297445i
\(268\) 0 0
\(269\) 12.6652 21.9368i 0.772212 1.33751i −0.164136 0.986438i \(-0.552484\pi\)
0.936348 0.351072i \(-0.114183\pi\)
\(270\) 0 0
\(271\) −0.195591 + 0.112924i −0.0118813 + 0.00685967i −0.505929 0.862575i \(-0.668850\pi\)
0.494048 + 0.869435i \(0.335517\pi\)
\(272\) 0 0
\(273\) 3.69084 + 16.4708i 0.223380 + 0.996856i
\(274\) 0 0
\(275\) 7.57832 + 4.37534i 0.456990 + 0.263843i
\(276\) 0 0
\(277\) 10.2170 + 17.6963i 0.613878 + 1.06327i 0.990580 + 0.136934i \(0.0437248\pi\)
−0.376702 + 0.926335i \(0.622942\pi\)
\(278\) 0 0
\(279\) 3.52456 28.4214i 0.211010 1.70154i
\(280\) 0 0
\(281\) 8.96635 + 5.17672i 0.534887 + 0.308817i 0.743004 0.669287i \(-0.233400\pi\)
−0.208117 + 0.978104i \(0.566733\pi\)
\(282\) 0 0
\(283\) 13.7157i 0.815311i 0.913136 + 0.407656i \(0.133654\pi\)
−0.913136 + 0.407656i \(0.866346\pi\)
\(284\) 0 0
\(285\) −15.6793 0.968493i −0.928763 0.0573686i
\(286\) 0 0
\(287\) −1.17050 4.03808i −0.0690923 0.238360i
\(288\) 0 0
\(289\) −12.2615 21.2375i −0.721264 1.24927i
\(290\) 0 0
\(291\) −14.5916 + 22.0166i −0.855375 + 1.29064i
\(292\) 0 0
\(293\) 4.21527 + 7.30105i 0.246258 + 0.426532i 0.962485 0.271336i \(-0.0874655\pi\)
−0.716226 + 0.697868i \(0.754132\pi\)
\(294\) 0 0
\(295\) −12.4381 + 21.5434i −0.724175 + 1.25431i
\(296\) 0 0
\(297\) −4.68140 13.2964i −0.271643 0.771535i
\(298\) 0 0
\(299\) −11.0186 −0.637222
\(300\) 0 0
\(301\) −17.1450 + 17.8568i −0.988221 + 1.02925i
\(302\) 0 0
\(303\) −5.40986 + 2.69318i −0.310788 + 0.154719i
\(304\) 0 0
\(305\) 1.62593 + 0.938732i 0.0931006 + 0.0537516i
\(306\) 0 0
\(307\) 5.34345i 0.304967i 0.988306 + 0.152484i \(0.0487271\pi\)
−0.988306 + 0.152484i \(0.951273\pi\)
\(308\) 0 0
\(309\) −3.19488 + 4.82061i −0.181751 + 0.274235i
\(310\) 0 0
\(311\) −9.41734 −0.534008 −0.267004 0.963695i \(-0.586034\pi\)
−0.267004 + 0.963695i \(0.586034\pi\)
\(312\) 0 0
\(313\) 16.5523i 0.935590i −0.883837 0.467795i \(-0.845049\pi\)
0.883837 0.467795i \(-0.154951\pi\)
\(314\) 0 0
\(315\) −17.6672 + 14.3556i −0.995435 + 0.808848i
\(316\) 0 0
\(317\) 26.5264i 1.48987i −0.667138 0.744934i \(-0.732481\pi\)
0.667138 0.744934i \(-0.267519\pi\)
\(318\) 0 0
\(319\) 7.77911 0.435547
\(320\) 0 0
\(321\) 2.76999 + 5.56416i 0.154606 + 0.310561i
\(322\) 0 0
\(323\) 20.3776i 1.13384i
\(324\) 0 0
\(325\) 10.2894 + 5.94056i 0.570751 + 0.329523i
\(326\) 0 0
\(327\) −19.9144 13.1983i −1.10127 0.729870i
\(328\) 0 0
\(329\) 29.0488 + 7.15386i 1.60151 + 0.394405i
\(330\) 0 0
\(331\) −17.6400 −0.969582 −0.484791 0.874630i \(-0.661104\pi\)
−0.484791 + 0.874630i \(0.661104\pi\)
\(332\) 0 0
\(333\) 3.98906 + 9.42930i 0.218599 + 0.516722i
\(334\) 0 0
\(335\) 11.0748 19.1821i 0.605081 1.04803i
\(336\) 0 0
\(337\) 7.31169 + 12.6642i 0.398293 + 0.689864i 0.993515 0.113697i \(-0.0362694\pi\)
−0.595222 + 0.803561i \(0.702936\pi\)
\(338\) 0 0
\(339\) 4.71155 + 9.46421i 0.255896 + 0.514026i
\(340\) 0 0
\(341\) −12.9490 22.4283i −0.701226 1.21456i
\(342\) 0 0
\(343\) 13.8698 + 12.2731i 0.748899 + 0.662684i
\(344\) 0 0
\(345\) −6.62262 13.3030i −0.356550 0.716212i
\(346\) 0 0
\(347\) 1.21893i 0.0654358i −0.999465 0.0327179i \(-0.989584\pi\)
0.999465 0.0327179i \(-0.0104163\pi\)
\(348\) 0 0
\(349\) −10.6857 6.16942i −0.571995 0.330241i 0.185951 0.982559i \(-0.440463\pi\)
−0.757946 + 0.652318i \(0.773797\pi\)
\(350\) 0 0
\(351\) −6.35611 18.0530i −0.339264 0.963597i
\(352\) 0 0
\(353\) −11.1484 19.3097i −0.593372 1.02775i −0.993774 0.111411i \(-0.964463\pi\)
0.400402 0.916339i \(-0.368870\pi\)
\(354\) 0 0
\(355\) −19.5371 11.2797i −1.03692 0.598666i
\(356\) 0 0
\(357\) −19.9992 21.7259i −1.05847 1.14985i
\(358\) 0 0
\(359\) 10.4819 6.05173i 0.553214 0.319398i −0.197204 0.980363i \(-0.563186\pi\)
0.750417 + 0.660965i \(0.229853\pi\)
\(360\) 0 0
\(361\) −4.49979 + 7.79387i −0.236831 + 0.410204i
\(362\) 0 0
\(363\) 5.25583 + 3.48333i 0.275860 + 0.182827i
\(364\) 0 0
\(365\) 31.7691 18.3419i 1.66287 0.960058i
\(366\) 0 0
\(367\) 12.7544 7.36375i 0.665774 0.384385i −0.128700 0.991684i \(-0.541080\pi\)
0.794473 + 0.607299i \(0.207747\pi\)
\(368\) 0 0
\(369\) 1.85740 + 4.39050i 0.0966925 + 0.228560i
\(370\) 0 0
\(371\) 4.76928 + 4.57917i 0.247609 + 0.237739i
\(372\) 0 0
\(373\) 4.54279 7.86834i 0.235217 0.407407i −0.724119 0.689675i \(-0.757753\pi\)
0.959336 + 0.282268i \(0.0910867\pi\)
\(374\) 0 0
\(375\) 0.543415 8.79756i 0.0280618 0.454304i
\(376\) 0 0
\(377\) 10.5620 0.543970
\(378\) 0 0
\(379\) 21.2298 1.09050 0.545250 0.838273i \(-0.316435\pi\)
0.545250 + 0.838273i \(0.316435\pi\)
\(380\) 0 0
\(381\) −1.42897 + 23.1341i −0.0732082 + 1.18520i
\(382\) 0 0
\(383\) 3.35227 5.80630i 0.171293 0.296688i −0.767579 0.640954i \(-0.778539\pi\)
0.938872 + 0.344266i \(0.111872\pi\)
\(384\) 0 0
\(385\) −4.92253 + 19.9883i −0.250875 + 1.01870i
\(386\) 0 0
\(387\) 16.9198 22.3970i 0.860083 1.13850i
\(388\) 0 0
\(389\) −6.66661 + 3.84897i −0.338011 + 0.195151i −0.659392 0.751799i \(-0.729186\pi\)
0.321381 + 0.946950i \(0.395853\pi\)
\(390\) 0 0
\(391\) 16.6939 9.63825i 0.844249 0.487427i
\(392\) 0 0
\(393\) 1.12314 + 0.744364i 0.0566548 + 0.0375482i
\(394\) 0 0
\(395\) 7.44444 12.8942i 0.374571 0.648775i
\(396\) 0 0
\(397\) −0.0428112 + 0.0247170i −0.00214863 + 0.00124051i −0.501074 0.865404i \(-0.667062\pi\)
0.498925 + 0.866645i \(0.333728\pi\)
\(398\) 0 0
\(399\) −3.16877 14.1410i −0.158637 0.707935i
\(400\) 0 0
\(401\) 17.6039 + 10.1636i 0.879096 + 0.507546i 0.870360 0.492416i \(-0.163886\pi\)
0.00873572 + 0.999962i \(0.497219\pi\)
\(402\) 0 0
\(403\) −17.5813 30.4517i −0.875786 1.51691i
\(404\) 0 0
\(405\) 17.9755 18.5245i 0.893212 0.920488i
\(406\) 0 0
\(407\) 8.01803 + 4.62921i 0.397439 + 0.229461i
\(408\) 0 0
\(409\) 13.9886i 0.691689i 0.938292 + 0.345845i \(0.112408\pi\)
−0.938292 + 0.345845i \(0.887592\pi\)
\(410\) 0 0
\(411\) 12.7531 + 25.6175i 0.629064 + 1.26362i
\(412\) 0 0
\(413\) −22.2824 5.48752i −1.09645 0.270023i
\(414\) 0 0
\(415\) 22.7420 + 39.3903i 1.11636 + 1.93360i
\(416\) 0 0
\(417\) −8.84029 17.7577i −0.432911 0.869600i
\(418\) 0 0
\(419\) 10.6718 + 18.4842i 0.521353 + 0.903010i 0.999692 + 0.0248344i \(0.00790585\pi\)
−0.478339 + 0.878176i \(0.658761\pi\)
\(420\) 0 0
\(421\) 3.97287 6.88121i 0.193626 0.335370i −0.752823 0.658223i \(-0.771309\pi\)
0.946449 + 0.322853i \(0.104642\pi\)
\(422\) 0 0
\(423\) −33.6645 4.17476i −1.63682 0.202984i
\(424\) 0 0
\(425\) −20.7854 −1.00824
\(426\) 0 0
\(427\) −0.414155 + 1.68171i −0.0200424 + 0.0813835i
\(428\) 0 0
\(429\) −14.4266 9.56129i −0.696522 0.461623i
\(430\) 0 0
\(431\) −27.6515 15.9646i −1.33193 0.768989i −0.346333 0.938112i \(-0.612573\pi\)
−0.985595 + 0.169123i \(0.945907\pi\)
\(432\) 0 0
\(433\) 18.5300i 0.890493i −0.895408 0.445247i \(-0.853116\pi\)
0.895408 0.445247i \(-0.146884\pi\)
\(434\) 0 0
\(435\) 6.34817 + 12.7517i 0.304372 + 0.611400i
\(436\) 0 0
\(437\) 9.46004 0.452535
\(438\) 0 0
\(439\) 2.08211i 0.0993739i −0.998765 0.0496869i \(-0.984178\pi\)
0.998765 0.0496869i \(-0.0158224\pi\)
\(440\) 0 0
\(441\) −17.2569 11.9667i −0.821755 0.569841i
\(442\) 0 0
\(443\) 2.46985i 0.117346i 0.998277 + 0.0586731i \(0.0186870\pi\)
−0.998277 + 0.0586731i \(0.981313\pi\)
\(444\) 0 0
\(445\) 18.0587 0.856063
\(446\) 0 0
\(447\) −4.69332 + 7.08154i −0.221986 + 0.334945i
\(448\) 0 0
\(449\) 37.5094i 1.77018i 0.465424 + 0.885088i \(0.345902\pi\)
−0.465424 + 0.885088i \(0.654098\pi\)
\(450\) 0 0
\(451\) 3.73338 + 2.15547i 0.175798 + 0.101497i
\(452\) 0 0
\(453\) −15.2825 + 7.60808i −0.718037 + 0.357459i
\(454\) 0 0
\(455\) −6.68349 + 27.1388i −0.313327 + 1.27229i
\(456\) 0 0
\(457\) 5.84690 0.273506 0.136753 0.990605i \(-0.456333\pi\)
0.136753 + 0.990605i \(0.456333\pi\)
\(458\) 0 0
\(459\) 25.4213 + 21.7916i 1.18657 + 1.01715i
\(460\) 0 0
\(461\) 3.82830 6.63081i 0.178302 0.308827i −0.762997 0.646402i \(-0.776273\pi\)
0.941299 + 0.337574i \(0.109606\pi\)
\(462\) 0 0
\(463\) 4.89449 + 8.47751i 0.227466 + 0.393983i 0.957057 0.289901i \(-0.0936225\pi\)
−0.729590 + 0.683885i \(0.760289\pi\)
\(464\) 0 0
\(465\) 26.1980 39.5290i 1.21490 1.83311i
\(466\) 0 0
\(467\) 14.0806 + 24.3883i 0.651572 + 1.12856i 0.982741 + 0.184985i \(0.0592235\pi\)
−0.331169 + 0.943571i \(0.607443\pi\)
\(468\) 0 0
\(469\) 19.8401 + 4.88605i 0.916132 + 0.225617i
\(470\) 0 0
\(471\) −26.6520 1.64626i −1.22806 0.0758558i
\(472\) 0 0
\(473\) 25.3830i 1.16711i
\(474\) 0 0
\(475\) −8.83394 5.10028i −0.405329 0.234017i
\(476\) 0 0
\(477\) −5.98190 4.51903i −0.273893 0.206912i
\(478\) 0 0
\(479\) −14.8053 25.6435i −0.676470 1.17168i −0.976037 0.217605i \(-0.930175\pi\)
0.299567 0.954075i \(-0.403158\pi\)
\(480\) 0 0
\(481\) 10.8864 + 6.28525i 0.496376 + 0.286583i
\(482\) 0 0
\(483\) 10.0859 9.28439i 0.458926 0.422454i
\(484\) 0 0
\(485\) −37.8767 + 21.8681i −1.71989 + 0.992980i
\(486\) 0 0
\(487\) −14.6701 + 25.4094i −0.664767 + 1.15141i 0.314582 + 0.949230i \(0.398136\pi\)
−0.979348 + 0.202180i \(0.935198\pi\)
\(488\) 0 0
\(489\) −17.7398 + 8.83136i −0.802221 + 0.399368i
\(490\) 0 0
\(491\) −8.63745 + 4.98683i −0.389803 + 0.225053i −0.682075 0.731283i \(-0.738922\pi\)
0.292272 + 0.956335i \(0.405589\pi\)
\(492\) 0 0
\(493\) −16.0021 + 9.23883i −0.720699 + 0.416096i
\(494\) 0 0
\(495\) 2.87262 23.1643i 0.129115 1.04116i
\(496\) 0 0
\(497\) 4.97645 20.2072i 0.223224 0.906419i
\(498\) 0 0
\(499\) 9.79784 16.9704i 0.438611 0.759697i −0.558971 0.829187i \(-0.688804\pi\)
0.997583 + 0.0694898i \(0.0221371\pi\)
\(500\) 0 0
\(501\) −20.1292 + 10.0209i −0.899305 + 0.447699i
\(502\) 0 0
\(503\) 21.2907 0.949304 0.474652 0.880174i \(-0.342574\pi\)
0.474652 + 0.880174i \(0.342574\pi\)
\(504\) 0 0
\(505\) −10.0066 −0.445289
\(506\) 0 0
\(507\) −0.818689 0.542590i −0.0363593 0.0240973i
\(508\) 0 0
\(509\) 21.8307 37.8119i 0.967630 1.67598i 0.265252 0.964179i \(-0.414545\pi\)
0.702378 0.711804i \(-0.252122\pi\)
\(510\) 0 0
\(511\) 24.4105 + 23.4374i 1.07986 + 1.03681i
\(512\) 0 0
\(513\) 5.45705 + 15.4994i 0.240935 + 0.684316i
\(514\) 0 0
\(515\) −8.29324 + 4.78810i −0.365444 + 0.210989i
\(516\) 0 0
\(517\) −26.5658 + 15.3378i −1.16836 + 0.674554i
\(518\) 0 0
\(519\) −2.09292 + 33.8831i −0.0918689 + 1.48730i
\(520\) 0 0
\(521\) 2.60043 4.50408i 0.113927 0.197327i −0.803423 0.595408i \(-0.796990\pi\)
0.917350 + 0.398081i \(0.130324\pi\)
\(522\) 0 0
\(523\) −34.7043 + 20.0365i −1.51751 + 0.876137i −0.517726 + 0.855547i \(0.673221\pi\)
−0.999788 + 0.0205902i \(0.993445\pi\)
\(524\) 0 0
\(525\) −14.4240 + 3.23219i −0.629515 + 0.141064i
\(526\) 0 0
\(527\) 53.2737 + 30.7576i 2.32064 + 1.33982i
\(528\) 0 0
\(529\) −7.02557 12.1686i −0.305460 0.529072i
\(530\) 0 0
\(531\) 25.8230 + 3.20233i 1.12062 + 0.138969i
\(532\) 0 0
\(533\) 5.06895 + 2.92656i 0.219561 + 0.126763i
\(534\) 0 0
\(535\) 10.2920i 0.444964i
\(536\) 0 0
\(537\) −17.9686 + 27.1121i −0.775404 + 1.16997i
\(538\) 0 0
\(539\) −18.9743 + 0.772057i −0.817282 + 0.0332549i
\(540\) 0 0
\(541\) −4.12096 7.13771i −0.177174 0.306874i 0.763738 0.645527i \(-0.223362\pi\)
−0.940911 + 0.338653i \(0.890029\pi\)
\(542\) 0 0
\(543\) −7.74094 0.478149i −0.332196 0.0205193i
\(544\) 0 0
\(545\) −19.7801 34.2601i −0.847285 1.46754i
\(546\) 0 0
\(547\) −2.53756 + 4.39518i −0.108498 + 0.187925i −0.915162 0.403086i \(-0.867938\pi\)
0.806664 + 0.591011i \(0.201271\pi\)
\(548\) 0 0
\(549\) 0.241687 1.94892i 0.0103150 0.0831779i
\(550\) 0 0
\(551\) −9.06800 −0.386310
\(552\) 0 0
\(553\) 13.3365 + 3.28438i 0.567124 + 0.139666i
\(554\) 0 0
\(555\) −1.04519 + 16.9211i −0.0443660 + 0.718260i
\(556\) 0 0
\(557\) 37.6102 + 21.7142i 1.59359 + 0.920062i 0.992684 + 0.120745i \(0.0385285\pi\)
0.600910 + 0.799316i \(0.294805\pi\)
\(558\) 0 0
\(559\) 34.4635i 1.45765i
\(560\) 0 0
\(561\) 30.2208 + 1.86670i 1.27592 + 0.0788122i
\(562\) 0 0
\(563\) −9.98237 −0.420707 −0.210353 0.977625i \(-0.567461\pi\)
−0.210353 + 0.977625i \(0.567461\pi\)
\(564\) 0 0
\(565\) 17.5060i 0.736483i
\(566\) 0 0
\(567\) 21.0297 + 11.1692i 0.883166 + 0.469061i
\(568\) 0 0
\(569\) 16.2348i 0.680598i −0.940317 0.340299i \(-0.889472\pi\)
0.940317 0.340299i \(-0.110528\pi\)
\(570\) 0 0
\(571\) −12.6206 −0.528154 −0.264077 0.964502i \(-0.585067\pi\)
−0.264077 + 0.964502i \(0.585067\pi\)
\(572\) 0 0
\(573\) −11.7785 0.727547i −0.492056 0.0303937i
\(574\) 0 0
\(575\) 9.64936i 0.402406i
\(576\) 0 0
\(577\) −4.18012 2.41339i −0.174020 0.100471i 0.410460 0.911879i \(-0.365368\pi\)
−0.584480 + 0.811408i \(0.698702\pi\)
\(578\) 0 0
\(579\) −1.70361 + 27.5804i −0.0707995 + 1.14620i
\(580\) 0 0
\(581\) −29.0600 + 30.2665i −1.20561 + 1.25567i
\(582\) 0 0
\(583\) −6.77942 −0.280775
\(584\) 0 0
\(585\) 3.90026 31.4510i 0.161256 1.30034i
\(586\) 0 0
\(587\) 5.26032 9.11114i 0.217117 0.376057i −0.736809 0.676101i \(-0.763668\pi\)
0.953925 + 0.300044i \(0.0970015\pi\)
\(588\) 0 0
\(589\) 15.0944 + 26.1443i 0.621955 + 1.07726i
\(590\) 0 0
\(591\) 44.8632 + 2.77114i 1.84542 + 0.113990i
\(592\) 0 0
\(593\) 14.7342 + 25.5205i 0.605063 + 1.04800i 0.992042 + 0.125911i \(0.0401853\pi\)
−0.386979 + 0.922089i \(0.626481\pi\)
\(594\) 0 0
\(595\) −13.6130 46.9633i −0.558080 1.92531i
\(596\) 0 0
\(597\) 3.04622 4.59630i 0.124673 0.188114i
\(598\) 0 0
\(599\) 8.21752i 0.335759i 0.985808 + 0.167879i \(0.0536919\pi\)
−0.985808 + 0.167879i \(0.946308\pi\)
\(600\) 0 0
\(601\) 32.7131 + 18.8869i 1.33439 + 0.770413i 0.985970 0.166924i \(-0.0533833\pi\)
0.348425 + 0.937337i \(0.386717\pi\)
\(602\) 0 0
\(603\) −22.9926 2.85133i −0.936333 0.116115i
\(604\) 0 0
\(605\) 5.22038 + 9.04197i 0.212239 + 0.367608i
\(606\) 0 0
\(607\) −30.8497 17.8111i −1.25215 0.722929i −0.280613 0.959821i \(-0.590538\pi\)
−0.971536 + 0.236892i \(0.923871\pi\)
\(608\) 0 0
\(609\) −9.66797 + 8.89963i −0.391766 + 0.360631i
\(610\) 0 0
\(611\) −36.0693 + 20.8246i −1.45921 + 0.842474i
\(612\) 0 0
\(613\) 11.9660 20.7256i 0.483301 0.837101i −0.516516 0.856278i \(-0.672771\pi\)
0.999816 + 0.0191767i \(0.00610451\pi\)
\(614\) 0 0
\(615\) −0.486667 + 7.87885i −0.0196243 + 0.317706i
\(616\) 0 0
\(617\) −1.98622 + 1.14675i −0.0799623 + 0.0461663i −0.539448 0.842019i \(-0.681367\pi\)
0.459486 + 0.888185i \(0.348034\pi\)
\(618\) 0 0
\(619\) −9.10806 + 5.25854i −0.366084 + 0.211359i −0.671746 0.740781i \(-0.734455\pi\)
0.305662 + 0.952140i \(0.401122\pi\)
\(620\) 0 0
\(621\) −10.1165 + 11.8015i −0.405961 + 0.473579i
\(622\) 0 0
\(623\) 4.63796 + 16.0004i 0.185816 + 0.641043i
\(624\) 0 0
\(625\) 15.3617 26.6073i 0.614469 1.06429i
\(626\) 0 0
\(627\) 12.3860 + 8.20885i 0.494648 + 0.327830i
\(628\) 0 0
\(629\) −21.9914 −0.876856
\(630\) 0 0
\(631\) −2.02836 −0.0807477 −0.0403739 0.999185i \(-0.512855\pi\)
−0.0403739 + 0.999185i \(0.512855\pi\)
\(632\) 0 0
\(633\) −0.171307 + 0.0852813i −0.00680884 + 0.00338963i
\(634\) 0 0
\(635\) −19.1899 + 33.2380i −0.761530 + 1.31901i
\(636\) 0 0
\(637\) −25.7621 + 1.04825i −1.02073 + 0.0415332i
\(638\) 0 0
\(639\) −2.90409 + 23.4181i −0.114884 + 0.926405i
\(640\) 0 0
\(641\) 10.7778 6.22257i 0.425698 0.245777i −0.271814 0.962350i \(-0.587624\pi\)
0.697512 + 0.716573i \(0.254290\pi\)
\(642\) 0 0
\(643\) −12.3358 + 7.12209i −0.486477 + 0.280868i −0.723112 0.690731i \(-0.757289\pi\)
0.236635 + 0.971599i \(0.423956\pi\)
\(644\) 0 0
\(645\) 41.6086 20.7139i 1.63834 0.815610i
\(646\) 0 0
\(647\) −10.1910 + 17.6513i −0.400649 + 0.693945i −0.993804 0.111143i \(-0.964549\pi\)
0.593155 + 0.805088i \(0.297882\pi\)
\(648\) 0 0
\(649\) 20.3778 11.7651i 0.799899 0.461822i
\(650\) 0 0
\(651\) 41.7520 + 13.0599i 1.63639 + 0.511860i
\(652\) 0 0
\(653\) 7.55335 + 4.36093i 0.295585 + 0.170656i 0.640458 0.767993i \(-0.278745\pi\)
−0.344873 + 0.938650i \(0.612078\pi\)
\(654\) 0 0
\(655\) 1.11556 + 1.93221i 0.0435887 + 0.0754978i
\(656\) 0 0
\(657\) −30.6170 23.1296i −1.19448 0.902373i
\(658\) 0 0
\(659\) −16.7524 9.67200i −0.652581 0.376768i 0.136864 0.990590i \(-0.456298\pi\)
−0.789444 + 0.613822i \(0.789631\pi\)
\(660\) 0 0
\(661\) 36.8289i 1.43248i −0.697854 0.716240i \(-0.745862\pi\)
0.697854 0.716240i \(-0.254138\pi\)
\(662\) 0 0
\(663\) 41.0318 + 2.53449i 1.59354 + 0.0984313i
\(664\) 0 0
\(665\) 5.73812 23.3000i 0.222515 0.903537i
\(666\) 0 0
\(667\) −4.28900 7.42877i −0.166071 0.287643i
\(668\) 0 0
\(669\) 12.4922 18.8489i 0.482977 0.728742i
\(670\) 0 0
\(671\) −0.887942 1.53796i −0.0342786 0.0593723i
\(672\) 0 0
\(673\) 8.79204 15.2283i 0.338908 0.587006i −0.645319 0.763913i \(-0.723276\pi\)
0.984228 + 0.176907i \(0.0566091\pi\)
\(674\) 0 0
\(675\) 15.8096 5.56626i 0.608512 0.214245i
\(676\) 0 0
\(677\) 40.8291 1.56919 0.784595 0.620009i \(-0.212871\pi\)
0.784595 + 0.620009i \(0.212871\pi\)
\(678\) 0 0
\(679\) −29.1035 27.9433i −1.11689 1.07237i
\(680\) 0 0
\(681\) 14.3701 7.15385i 0.550665 0.274136i
\(682\) 0 0
\(683\) −8.56287 4.94377i −0.327649 0.189168i 0.327148 0.944973i \(-0.393912\pi\)
−0.654797 + 0.755805i \(0.727246\pi\)
\(684\) 0 0
\(685\) 47.3847i 1.81048i
\(686\) 0 0
\(687\) 12.8391 19.3724i 0.489843 0.739102i
\(688\) 0 0
\(689\) −9.20467 −0.350670
\(690\) 0 0
\(691\) 43.7882i 1.66578i −0.553436 0.832891i \(-0.686684\pi\)
0.553436 0.832891i \(-0.313316\pi\)
\(692\) 0 0
\(693\) 21.2619 3.40401i 0.807673 0.129308i
\(694\) 0 0
\(695\) 32.8465i 1.24594i
\(696\) 0 0
\(697\) −10.2397 −0.387858
\(698\) 0 0
\(699\) 16.3480 + 32.8387i 0.618339 + 1.24207i
\(700\) 0 0
\(701\) 29.6742i 1.12078i −0.828229 0.560389i \(-0.810651\pi\)
0.828229 0.560389i \(-0.189349\pi\)
\(702\) 0 0
\(703\) −9.34651 5.39621i −0.352510 0.203522i
\(704\) 0 0
\(705\) −46.8212 31.0310i −1.76339 1.16869i
\(706\) 0 0
\(707\) −2.56998 8.86612i −0.0966540 0.333445i
\(708\) 0 0
\(709\) 47.0538 1.76714 0.883572 0.468296i \(-0.155132\pi\)
0.883572 + 0.468296i \(0.155132\pi\)
\(710\) 0 0
\(711\) −15.4556 1.91666i −0.579629 0.0718802i
\(712\) 0 0
\(713\) −14.2788 + 24.7316i −0.534745 + 0.926206i
\(714\) 0 0
\(715\) −14.3293 24.8191i −0.535885 0.928180i
\(716\) 0 0
\(717\) 6.89291 + 13.8460i 0.257420 + 0.517087i
\(718\) 0 0
\(719\) 0.909148 + 1.57469i 0.0339055 + 0.0587261i 0.882480 0.470349i \(-0.155872\pi\)
−0.848575 + 0.529076i \(0.822539\pi\)
\(720\) 0 0
\(721\) −6.37230 6.11829i −0.237317 0.227857i
\(722\) 0 0
\(723\) −14.2102 28.5444i −0.528483 1.06158i
\(724\) 0 0
\(725\) 9.24948i 0.343517i
\(726\) 0 0
\(727\) 21.7854 + 12.5778i 0.807976 + 0.466485i 0.846252 0.532782i \(-0.178853\pi\)
−0.0382766 + 0.999267i \(0.512187\pi\)
\(728\) 0 0
\(729\) −25.1714 9.76721i −0.932276 0.361748i
\(730\) 0 0
\(731\) 30.1460 + 52.2145i 1.11499 + 1.93122i
\(732\) 0 0
\(733\) −3.84543 2.22016i −0.142034 0.0820034i 0.427299 0.904110i \(-0.359465\pi\)
−0.569333 + 0.822107i \(0.692799\pi\)
\(734\) 0 0
\(735\) −16.7496 30.4732i −0.617820 1.12402i
\(736\) 0 0
\(737\) −18.1443 + 10.4756i −0.668353 + 0.385874i
\(738\) 0 0
\(739\) −8.97608 + 15.5470i −0.330191 + 0.571907i −0.982549 0.186004i \(-0.940446\pi\)
0.652358 + 0.757911i \(0.273780\pi\)
\(740\) 0 0
\(741\) 16.8169 + 11.1455i 0.617783 + 0.409439i
\(742\) 0 0
\(743\) −31.3712 + 18.1122i −1.15090 + 0.664472i −0.949106 0.314956i \(-0.898010\pi\)
−0.201793 + 0.979428i \(0.564677\pi\)
\(744\) 0 0
\(745\) −12.1829 + 7.03378i −0.446345 + 0.257698i
\(746\) 0 0
\(747\) 28.6783 37.9620i 1.04929 1.38896i
\(748\) 0 0
\(749\) −9.11899 + 2.64328i −0.333201 + 0.0965833i
\(750\) 0 0
\(751\) −5.98210 + 10.3613i −0.218290 + 0.378089i −0.954285 0.298897i \(-0.903381\pi\)
0.735995 + 0.676986i \(0.236714\pi\)
\(752\) 0 0
\(753\) −0.676145 + 10.9464i −0.0246401 + 0.398908i
\(754\) 0 0
\(755\) −28.2682 −1.02878
\(756\) 0 0
\(757\) −49.4440 −1.79707 −0.898537 0.438898i \(-0.855369\pi\)
−0.898537 + 0.438898i \(0.855369\pi\)
\(758\) 0 0
\(759\) −0.866591 + 14.0296i −0.0314553 + 0.509242i
\(760\) 0 0
\(761\) 14.6192 25.3212i 0.529945 0.917892i −0.469445 0.882962i \(-0.655546\pi\)
0.999390 0.0349300i \(-0.0111208\pi\)
\(762\) 0 0
\(763\) 25.2752 26.3245i 0.915023 0.953012i
\(764\) 0 0
\(765\) 21.6018 + 51.0621i 0.781015 + 1.84615i
\(766\) 0 0
\(767\) 27.6677 15.9740i 0.999023 0.576786i
\(768\) 0 0
\(769\) −4.54689 + 2.62515i −0.163965 + 0.0946653i −0.579737 0.814804i \(-0.696845\pi\)
0.415772 + 0.909469i \(0.363511\pi\)
\(770\) 0 0
\(771\) −23.6569 15.6787i −0.851981 0.564654i
\(772\) 0 0
\(773\) −15.6829 + 27.1635i −0.564073 + 0.977003i 0.433062 + 0.901364i \(0.357433\pi\)
−0.997135 + 0.0756393i \(0.975900\pi\)
\(774\) 0 0
\(775\) 26.6676 15.3965i 0.957927 0.553059i
\(776\) 0 0
\(777\) −15.2609 + 3.41973i −0.547482 + 0.122682i
\(778\) 0 0
\(779\) −4.35195 2.51260i −0.155925 0.0900233i
\(780\) 0 0
\(781\) 10.6694 + 18.4800i 0.381782 + 0.661266i
\(782\) 0 0
\(783\) 9.69725 11.3125i 0.346551 0.404274i
\(784\) 0 0
\(785\) −38.2923 22.1081i −1.36671 0.789071i
\(786\) 0 0
\(787\) 1.83971i 0.0655786i −0.999462 0.0327893i \(-0.989561\pi\)
0.999462 0.0327893i \(-0.0104390\pi\)
\(788\) 0 0
\(789\) 9.32873 + 18.7389i 0.332112 + 0.667121i
\(790\) 0 0
\(791\) −15.5107 + 4.49602i −0.551498 + 0.159860i
\(792\) 0 0
\(793\) −1.20559 2.08814i −0.0428118 0.0741522i
\(794\) 0 0
\(795\) −5.53237 11.1130i −0.196213 0.394138i