Properties

Label 3150.2.bf.f.1151.15
Level 3150
Weight 2
Character 3150.1151
Analytic conductor 25.153
Analytic rank 0
Dimension 32
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1151.15
Character \(\chi\) = 3150.1151
Dual form 3150.2.bf.f.1601.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.24547 + 1.39924i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.24547 + 1.39924i) q^{7} -1.00000i q^{8} +(-1.37897 - 0.796151i) q^{11} -0.925091i q^{13} +(-1.24501 + 2.33451i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.97883 + 3.42743i) q^{17} +(-0.541679 + 0.312739i) q^{19} -1.59230 q^{22} +(6.74256 - 3.89282i) q^{23} +(-0.462546 - 0.801153i) q^{26} +(0.0890445 + 2.64425i) q^{28} +9.34805i q^{29} +(8.94618 + 5.16508i) q^{31} +(-0.866025 - 0.500000i) q^{32} +3.95765i q^{34} +(-0.213192 - 0.369259i) q^{37} +(-0.312739 + 0.541679i) q^{38} +8.35463 q^{41} -6.27133 q^{43} +(-1.37897 + 0.796151i) q^{44} +(3.89282 - 6.74256i) q^{46} +(1.39065 + 2.40868i) q^{47} +(3.08425 - 6.28390i) q^{49} +(-0.801153 - 0.462546i) q^{52} +(2.90217 + 1.67557i) q^{53} +(1.39924 + 2.24547i) q^{56} +(4.67403 + 8.09565i) q^{58} +(3.10680 - 5.38113i) q^{59} +(9.52671 - 5.50025i) q^{61} +10.3302 q^{62} -1.00000 q^{64} +(0.178089 - 0.308459i) q^{67} +(1.97883 + 3.42743i) q^{68} +9.07975i q^{71} +(5.91515 + 3.41511i) q^{73} +(-0.369259 - 0.213192i) q^{74} +0.625477i q^{76} +(4.21045 - 0.141786i) q^{77} +(4.52582 + 7.83895i) q^{79} +(7.23532 - 4.17731i) q^{82} -0.809898 q^{83} +(-5.43113 + 3.13566i) q^{86} +(-0.796151 + 1.37897i) q^{88} +(2.00721 + 3.47659i) q^{89} +(1.29443 + 2.07726i) q^{91} -7.78564i q^{92} +(2.40868 + 1.39065i) q^{94} +7.87721i q^{97} +(-0.470912 - 6.98414i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 16q^{4} + O(q^{10}) \) \( 32q + 16q^{4} - 16q^{16} - 48q^{19} + 24q^{31} - 16q^{46} + 56q^{49} + 48q^{61} - 32q^{64} - 8q^{79} - 56q^{91} + 120q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −2.24547 + 1.39924i −0.848707 + 0.528863i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) −1.37897 0.796151i −0.415776 0.240049i 0.277492 0.960728i \(-0.410497\pi\)
−0.693269 + 0.720679i \(0.743830\pi\)
\(12\) 0 0
\(13\) 0.925091i 0.256574i −0.991737 0.128287i \(-0.959052\pi\)
0.991737 0.128287i \(-0.0409479\pi\)
\(14\) −1.24501 + 2.33451i −0.332743 + 0.623925i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.97883 + 3.42743i −0.479936 + 0.831273i −0.999735 0.0230153i \(-0.992673\pi\)
0.519799 + 0.854288i \(0.326007\pi\)
\(18\) 0 0
\(19\) −0.541679 + 0.312739i −0.124270 + 0.0717472i −0.560846 0.827920i \(-0.689524\pi\)
0.436577 + 0.899667i \(0.356191\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.59230 −0.339480
\(23\) 6.74256 3.89282i 1.40592 0.811709i 0.410930 0.911667i \(-0.365204\pi\)
0.994992 + 0.0999578i \(0.0318708\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −0.462546 0.801153i −0.0907127 0.157119i
\(27\) 0 0
\(28\) 0.0890445 + 2.64425i 0.0168278 + 0.499717i
\(29\) 9.34805i 1.73589i 0.496661 + 0.867945i \(0.334559\pi\)
−0.496661 + 0.867945i \(0.665441\pi\)
\(30\) 0 0
\(31\) 8.94618 + 5.16508i 1.60678 + 0.927675i 0.990084 + 0.140474i \(0.0448626\pi\)
0.616696 + 0.787201i \(0.288471\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 3.95765i 0.678732i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.213192 0.369259i −0.0350485 0.0607058i 0.847969 0.530046i \(-0.177825\pi\)
−0.883018 + 0.469340i \(0.844492\pi\)
\(38\) −0.312739 + 0.541679i −0.0507329 + 0.0878720i
\(39\) 0 0
\(40\) 0 0
\(41\) 8.35463 1.30477 0.652387 0.757886i \(-0.273768\pi\)
0.652387 + 0.757886i \(0.273768\pi\)
\(42\) 0 0
\(43\) −6.27133 −0.956369 −0.478184 0.878259i \(-0.658705\pi\)
−0.478184 + 0.878259i \(0.658705\pi\)
\(44\) −1.37897 + 0.796151i −0.207888 + 0.120024i
\(45\) 0 0
\(46\) 3.89282 6.74256i 0.573965 0.994137i
\(47\) 1.39065 + 2.40868i 0.202847 + 0.351342i 0.949445 0.313934i \(-0.101647\pi\)
−0.746597 + 0.665276i \(0.768314\pi\)
\(48\) 0 0
\(49\) 3.08425 6.28390i 0.440607 0.897700i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.801153 0.462546i −0.111100 0.0641435i
\(53\) 2.90217 + 1.67557i 0.398644 + 0.230157i 0.685899 0.727697i \(-0.259409\pi\)
−0.287255 + 0.957854i \(0.592743\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.39924 + 2.24547i 0.186981 + 0.300063i
\(57\) 0 0
\(58\) 4.67403 + 8.09565i 0.613730 + 1.06301i
\(59\) 3.10680 5.38113i 0.404471 0.700564i −0.589789 0.807557i \(-0.700789\pi\)
0.994260 + 0.106994i \(0.0341224\pi\)
\(60\) 0 0
\(61\) 9.52671 5.50025i 1.21977 0.704235i 0.254902 0.966967i \(-0.417957\pi\)
0.964869 + 0.262732i \(0.0846236\pi\)
\(62\) 10.3302 1.31193
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 0.178089 0.308459i 0.0217570 0.0376843i −0.854942 0.518724i \(-0.826407\pi\)
0.876699 + 0.481039i \(0.159741\pi\)
\(68\) 1.97883 + 3.42743i 0.239968 + 0.415637i
\(69\) 0 0
\(70\) 0 0
\(71\) 9.07975i 1.07757i 0.842444 + 0.538784i \(0.181116\pi\)
−0.842444 + 0.538784i \(0.818884\pi\)
\(72\) 0 0
\(73\) 5.91515 + 3.41511i 0.692316 + 0.399709i 0.804479 0.593981i \(-0.202445\pi\)
−0.112163 + 0.993690i \(0.535778\pi\)
\(74\) −0.369259 0.213192i −0.0429255 0.0247830i
\(75\) 0 0
\(76\) 0.625477i 0.0717472i
\(77\) 4.21045 0.141786i 0.479825 0.0161580i
\(78\) 0 0
\(79\) 4.52582 + 7.83895i 0.509195 + 0.881951i 0.999943 + 0.0106498i \(0.00339001\pi\)
−0.490749 + 0.871301i \(0.663277\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 7.23532 4.17731i 0.799007 0.461307i
\(83\) −0.809898 −0.0888978 −0.0444489 0.999012i \(-0.514153\pi\)
−0.0444489 + 0.999012i \(0.514153\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −5.43113 + 3.13566i −0.585654 + 0.338127i
\(87\) 0 0
\(88\) −0.796151 + 1.37897i −0.0848700 + 0.146999i
\(89\) 2.00721 + 3.47659i 0.212764 + 0.368518i 0.952579 0.304293i \(-0.0984201\pi\)
−0.739815 + 0.672811i \(0.765087\pi\)
\(90\) 0 0
\(91\) 1.29443 + 2.07726i 0.135693 + 0.217756i
\(92\) 7.78564i 0.811709i
\(93\) 0 0
\(94\) 2.40868 + 1.39065i 0.248436 + 0.143435i
\(95\) 0 0
\(96\) 0 0
\(97\) 7.87721i 0.799809i 0.916557 + 0.399905i \(0.130957\pi\)
−0.916557 + 0.399905i \(0.869043\pi\)
\(98\) −0.470912 6.98414i −0.0475693 0.705505i
\(99\) 0 0
\(100\) 0 0
\(101\) −3.76411 + 6.51962i −0.374543 + 0.648727i −0.990258 0.139241i \(-0.955534\pi\)
0.615716 + 0.787968i \(0.288867\pi\)
\(102\) 0 0
\(103\) −1.44073 + 0.831805i −0.141959 + 0.0819601i −0.569297 0.822132i \(-0.692785\pi\)
0.427338 + 0.904092i \(0.359451\pi\)
\(104\) −0.925091 −0.0907127
\(105\) 0 0
\(106\) 3.35114 0.325492
\(107\) −16.8033 + 9.70139i −1.62444 + 0.937869i −0.638724 + 0.769436i \(0.720537\pi\)
−0.985713 + 0.168433i \(0.946129\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.33451 + 1.24501i 0.220591 + 0.117643i
\(113\) 16.0750i 1.51221i 0.654451 + 0.756104i \(0.272900\pi\)
−0.654451 + 0.756104i \(0.727100\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 8.09565 + 4.67403i 0.751662 + 0.433972i
\(117\) 0 0
\(118\) 6.21360i 0.572008i
\(119\) −0.352407 10.4650i −0.0323051 0.959328i
\(120\) 0 0
\(121\) −4.23229 7.33053i −0.384753 0.666412i
\(122\) 5.50025 9.52671i 0.497969 0.862508i
\(123\) 0 0
\(124\) 8.94618 5.16508i 0.803390 0.463838i
\(125\) 0 0
\(126\) 0 0
\(127\) 13.2173 1.17285 0.586424 0.810004i \(-0.300535\pi\)
0.586424 + 0.810004i \(0.300535\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) 4.70080 + 8.14203i 0.410711 + 0.711372i 0.994968 0.100197i \(-0.0319472\pi\)
−0.584257 + 0.811569i \(0.698614\pi\)
\(132\) 0 0
\(133\) 0.778726 1.46018i 0.0675241 0.126614i
\(134\) 0.356178i 0.0307691i
\(135\) 0 0
\(136\) 3.42743 + 1.97883i 0.293899 + 0.169683i
\(137\) −8.11701 4.68636i −0.693483 0.400382i 0.111433 0.993772i \(-0.464456\pi\)
−0.804915 + 0.593390i \(0.797789\pi\)
\(138\) 0 0
\(139\) 14.1106i 1.19685i −0.801180 0.598423i \(-0.795794\pi\)
0.801180 0.598423i \(-0.204206\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4.53988 + 7.86330i 0.380978 + 0.659873i
\(143\) −0.736513 + 1.27568i −0.0615903 + 0.106678i
\(144\) 0 0
\(145\) 0 0
\(146\) 6.83023 0.565274
\(147\) 0 0
\(148\) −0.426383 −0.0350485
\(149\) 2.14103 1.23612i 0.175400 0.101267i −0.409730 0.912207i \(-0.634377\pi\)
0.585130 + 0.810940i \(0.301044\pi\)
\(150\) 0 0
\(151\) 10.4425 18.0869i 0.849796 1.47189i −0.0315949 0.999501i \(-0.510059\pi\)
0.881391 0.472388i \(-0.156608\pi\)
\(152\) 0.312739 + 0.541679i 0.0253664 + 0.0439360i
\(153\) 0 0
\(154\) 3.57546 2.22802i 0.288119 0.179539i
\(155\) 0 0
\(156\) 0 0
\(157\) −21.1722 12.2238i −1.68972 0.975563i −0.954723 0.297498i \(-0.903848\pi\)
−0.735002 0.678065i \(-0.762819\pi\)
\(158\) 7.83895 + 4.52582i 0.623634 + 0.360055i
\(159\) 0 0
\(160\) 0 0
\(161\) −9.69321 + 18.1757i −0.763932 + 1.43244i
\(162\) 0 0
\(163\) −2.95758 5.12267i −0.231655 0.401239i 0.726640 0.687018i \(-0.241081\pi\)
−0.958295 + 0.285780i \(0.907747\pi\)
\(164\) 4.17731 7.23532i 0.326193 0.564983i
\(165\) 0 0
\(166\) −0.701392 + 0.404949i −0.0544386 + 0.0314301i
\(167\) 12.1440 0.939733 0.469867 0.882737i \(-0.344302\pi\)
0.469867 + 0.882737i \(0.344302\pi\)
\(168\) 0 0
\(169\) 12.1442 0.934170
\(170\) 0 0
\(171\) 0 0
\(172\) −3.13566 + 5.43113i −0.239092 + 0.414120i
\(173\) 8.19918 + 14.2014i 0.623372 + 1.07971i 0.988853 + 0.148893i \(0.0475711\pi\)
−0.365481 + 0.930819i \(0.619096\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.59230i 0.120024i
\(177\) 0 0
\(178\) 3.47659 + 2.00721i 0.260581 + 0.150447i
\(179\) 2.73398 + 1.57846i 0.204347 + 0.117980i 0.598682 0.800987i \(-0.295691\pi\)
−0.394334 + 0.918967i \(0.629025\pi\)
\(180\) 0 0
\(181\) 8.17916i 0.607952i 0.952680 + 0.303976i \(0.0983143\pi\)
−0.952680 + 0.303976i \(0.901686\pi\)
\(182\) 2.15964 + 1.15175i 0.160083 + 0.0853733i
\(183\) 0 0
\(184\) −3.89282 6.74256i −0.286983 0.497068i
\(185\) 0 0
\(186\) 0 0
\(187\) 5.45750 3.15089i 0.399092 0.230416i
\(188\) 2.78130 0.202847
\(189\) 0 0
\(190\) 0 0
\(191\) −2.44949 + 1.41421i −0.177239 + 0.102329i −0.585995 0.810315i \(-0.699296\pi\)
0.408756 + 0.912644i \(0.365963\pi\)
\(192\) 0 0
\(193\) −8.85772 + 15.3420i −0.637593 + 1.10434i 0.348367 + 0.937358i \(0.386736\pi\)
−0.985959 + 0.166985i \(0.946597\pi\)
\(194\) 3.93860 + 6.82186i 0.282775 + 0.489781i
\(195\) 0 0
\(196\) −3.89989 5.81299i −0.278564 0.415213i
\(197\) 4.30350i 0.306612i −0.988179 0.153306i \(-0.951008\pi\)
0.988179 0.153306i \(-0.0489919\pi\)
\(198\) 0 0
\(199\) 3.00000 + 1.73205i 0.212664 + 0.122782i 0.602549 0.798082i \(-0.294152\pi\)
−0.389885 + 0.920864i \(0.627485\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 7.52821i 0.529683i
\(203\) −13.0802 20.9907i −0.918048 1.47326i
\(204\) 0 0
\(205\) 0 0
\(206\) −0.831805 + 1.44073i −0.0579546 + 0.100380i
\(207\) 0 0
\(208\) −0.801153 + 0.462546i −0.0555499 + 0.0320718i
\(209\) 0.995949 0.0688912
\(210\) 0 0
\(211\) 10.3886 0.715183 0.357592 0.933878i \(-0.383598\pi\)
0.357592 + 0.933878i \(0.383598\pi\)
\(212\) 2.90217 1.67557i 0.199322 0.115079i
\(213\) 0 0
\(214\) −9.70139 + 16.8033i −0.663173 + 1.14865i
\(215\) 0 0
\(216\) 0 0
\(217\) −27.3155 + 0.919844i −1.85430 + 0.0624431i
\(218\) 2.00000i 0.135457i
\(219\) 0 0
\(220\) 0 0
\(221\) 3.17068 + 1.83059i 0.213283 + 0.123139i
\(222\) 0 0
\(223\) 18.3555i 1.22918i −0.788848 0.614589i \(-0.789322\pi\)
0.788848 0.614589i \(-0.210678\pi\)
\(224\) 2.64425 0.0890445i 0.176677 0.00594954i
\(225\) 0 0
\(226\) 8.03750 + 13.9214i 0.534646 + 0.926035i
\(227\) −1.51152 + 2.61803i −0.100323 + 0.173765i −0.911818 0.410595i \(-0.865321\pi\)
0.811495 + 0.584360i \(0.198654\pi\)
\(228\) 0 0
\(229\) −9.22014 + 5.32325i −0.609284 + 0.351770i −0.772685 0.634789i \(-0.781087\pi\)
0.163401 + 0.986560i \(0.447754\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 9.34805 0.613730
\(233\) −3.45185 + 1.99293i −0.226138 + 0.130561i −0.608789 0.793332i \(-0.708345\pi\)
0.382651 + 0.923893i \(0.375011\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3.10680 5.38113i −0.202235 0.350282i
\(237\) 0 0
\(238\) −5.53771 8.88678i −0.358956 0.576044i
\(239\) 8.24699i 0.533453i 0.963772 + 0.266727i \(0.0859421\pi\)
−0.963772 + 0.266727i \(0.914058\pi\)
\(240\) 0 0
\(241\) −9.48785 5.47782i −0.611166 0.352857i 0.162255 0.986749i \(-0.448123\pi\)
−0.773422 + 0.633892i \(0.781456\pi\)
\(242\) −7.33053 4.23229i −0.471225 0.272062i
\(243\) 0 0
\(244\) 11.0005i 0.704235i
\(245\) 0 0
\(246\) 0 0
\(247\) 0.289312 + 0.501103i 0.0184085 + 0.0318844i
\(248\) 5.16508 8.94618i 0.327983 0.568083i
\(249\) 0 0
\(250\) 0 0
\(251\) 21.7369 1.37202 0.686012 0.727590i \(-0.259360\pi\)
0.686012 + 0.727590i \(0.259360\pi\)
\(252\) 0 0
\(253\) −12.3971 −0.779399
\(254\) 11.4465 6.60867i 0.718220 0.414665i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 8.71758 + 15.0993i 0.543787 + 0.941868i 0.998682 + 0.0513223i \(0.0163436\pi\)
−0.454895 + 0.890545i \(0.650323\pi\)
\(258\) 0 0
\(259\) 0.995397 + 0.530852i 0.0618510 + 0.0329856i
\(260\) 0 0
\(261\) 0 0
\(262\) 8.14203 + 4.70080i 0.503016 + 0.290417i
\(263\) −15.8926 9.17557i −0.979977 0.565790i −0.0777137 0.996976i \(-0.524762\pi\)
−0.902263 + 0.431186i \(0.858095\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.0556953 1.65392i −0.00341490 0.101408i
\(267\) 0 0
\(268\) −0.178089 0.308459i −0.0108785 0.0188422i
\(269\) −12.4185 + 21.5095i −0.757171 + 1.31146i 0.187117 + 0.982338i \(0.440086\pi\)
−0.944288 + 0.329121i \(0.893248\pi\)
\(270\) 0 0
\(271\) 21.1663 12.2204i 1.28576 0.742335i 0.307867 0.951430i \(-0.400385\pi\)
0.977895 + 0.209094i \(0.0670516\pi\)
\(272\) 3.95765 0.239968
\(273\) 0 0
\(274\) −9.37271 −0.566226
\(275\) 0 0
\(276\) 0 0
\(277\) 11.5985 20.0892i 0.696888 1.20704i −0.272653 0.962113i \(-0.587901\pi\)
0.969540 0.244932i \(-0.0787657\pi\)
\(278\) −7.05530 12.2201i −0.423149 0.732915i
\(279\) 0 0
\(280\) 0 0
\(281\) 14.0801i 0.839949i −0.907536 0.419974i \(-0.862039\pi\)
0.907536 0.419974i \(-0.137961\pi\)
\(282\) 0 0
\(283\) −2.42331 1.39910i −0.144051 0.0831677i 0.426242 0.904609i \(-0.359837\pi\)
−0.570293 + 0.821441i \(0.693170\pi\)
\(284\) 7.86330 + 4.53988i 0.466601 + 0.269392i
\(285\) 0 0
\(286\) 1.47303i 0.0871018i
\(287\) −18.7600 + 11.6901i −1.10737 + 0.690047i
\(288\) 0 0
\(289\) 0.668498 + 1.15787i 0.0393234 + 0.0681101i
\(290\) 0 0
\(291\) 0 0
\(292\) 5.91515 3.41511i 0.346158 0.199854i
\(293\) −25.5598 −1.49322 −0.746609 0.665263i \(-0.768319\pi\)
−0.746609 + 0.665263i \(0.768319\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.369259 + 0.213192i −0.0214627 + 0.0123915i
\(297\) 0 0
\(298\) 1.23612 2.14103i 0.0716068 0.124027i
\(299\) −3.60121 6.23749i −0.208264 0.360723i
\(300\) 0 0
\(301\) 14.0821 8.77510i 0.811677 0.505788i
\(302\) 20.8849i 1.20179i
\(303\) 0 0
\(304\) 0.541679 + 0.312739i 0.0310674 + 0.0179368i
\(305\) 0 0
\(306\) 0 0
\(307\) 34.2860i 1.95681i −0.206704 0.978403i \(-0.566274\pi\)
0.206704 0.978403i \(-0.433726\pi\)
\(308\) 1.98243 3.71725i 0.112960 0.211810i
\(309\) 0 0
\(310\) 0 0
\(311\) 4.34021 7.51746i 0.246110 0.426276i −0.716333 0.697759i \(-0.754181\pi\)
0.962443 + 0.271483i \(0.0875141\pi\)
\(312\) 0 0
\(313\) 25.9992 15.0106i 1.46956 0.848452i 0.470145 0.882589i \(-0.344202\pi\)
0.999417 + 0.0341376i \(0.0108684\pi\)
\(314\) −24.4475 −1.37965
\(315\) 0 0
\(316\) 9.05164 0.509195
\(317\) −24.0111 + 13.8628i −1.34860 + 0.778613i −0.988051 0.154128i \(-0.950743\pi\)
−0.360547 + 0.932741i \(0.617410\pi\)
\(318\) 0 0
\(319\) 7.44246 12.8907i 0.416698 0.721742i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.693269 + 20.5872i 0.0386344 + 1.14728i
\(323\) 2.47542i 0.137736i
\(324\) 0 0
\(325\) 0 0
\(326\) −5.12267 2.95758i −0.283719 0.163805i
\(327\) 0 0
\(328\) 8.35463i 0.461307i
\(329\) −6.49298 3.46275i −0.357970 0.190908i
\(330\) 0 0
\(331\) −3.15175 5.45899i −0.173236 0.300053i 0.766314 0.642467i \(-0.222089\pi\)
−0.939549 + 0.342414i \(0.888756\pi\)
\(332\) −0.404949 + 0.701392i −0.0222245 + 0.0384939i
\(333\) 0 0
\(334\) 10.5170 6.07201i 0.575467 0.332246i
\(335\) 0 0
\(336\) 0 0
\(337\) −27.4097 −1.49310 −0.746550 0.665329i \(-0.768291\pi\)
−0.746550 + 0.665329i \(0.768291\pi\)
\(338\) 10.5172 6.07210i 0.572060 0.330279i
\(339\) 0 0
\(340\) 0 0
\(341\) −8.22437 14.2450i −0.445374 0.771411i
\(342\) 0 0
\(343\) 1.86711 + 18.4259i 0.100815 + 0.994905i
\(344\) 6.27133i 0.338127i
\(345\) 0 0
\(346\) 14.2014 + 8.19918i 0.763472 + 0.440791i
\(347\) 7.07258 + 4.08336i 0.379676 + 0.219206i 0.677677 0.735359i \(-0.262987\pi\)
−0.298001 + 0.954566i \(0.596320\pi\)
\(348\) 0 0
\(349\) 27.5885i 1.47678i 0.674374 + 0.738390i \(0.264413\pi\)
−0.674374 + 0.738390i \(0.735587\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.796151 + 1.37897i 0.0424350 + 0.0734996i
\(353\) −3.52142 + 6.09929i −0.187426 + 0.324632i −0.944391 0.328823i \(-0.893348\pi\)
0.756965 + 0.653455i \(0.226681\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 4.01442 0.212764
\(357\) 0 0
\(358\) 3.15693 0.166849
\(359\) −14.1545 + 8.17213i −0.747048 + 0.431308i −0.824626 0.565678i \(-0.808615\pi\)
0.0775782 + 0.996986i \(0.475281\pi\)
\(360\) 0 0
\(361\) −9.30439 + 16.1157i −0.489705 + 0.848193i
\(362\) 4.08958 + 7.08336i 0.214943 + 0.372293i
\(363\) 0 0
\(364\) 2.44618 0.0823743i 0.128214 0.00431759i
\(365\) 0 0
\(366\) 0 0
\(367\) −2.60498 1.50399i −0.135979 0.0785076i 0.430467 0.902606i \(-0.358349\pi\)
−0.566446 + 0.824099i \(0.691682\pi\)
\(368\) −6.74256 3.89282i −0.351480 0.202927i
\(369\) 0 0
\(370\) 0 0
\(371\) −8.86126 + 0.298401i −0.460054 + 0.0154922i
\(372\) 0 0
\(373\) 11.5985 + 20.0892i 0.600549 + 1.04018i 0.992738 + 0.120296i \(0.0383844\pi\)
−0.392189 + 0.919884i \(0.628282\pi\)
\(374\) 3.15089 5.45750i 0.162929 0.282201i
\(375\) 0 0
\(376\) 2.40868 1.39065i 0.124218 0.0717174i
\(377\) 8.64780 0.445384
\(378\) 0 0
\(379\) −27.2718 −1.40086 −0.700429 0.713722i \(-0.747008\pi\)
−0.700429 + 0.713722i \(0.747008\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.41421 + 2.44949i −0.0723575 + 0.125327i
\(383\) −2.13098 3.69096i −0.108888 0.188599i 0.806432 0.591327i \(-0.201396\pi\)
−0.915320 + 0.402727i \(0.868062\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 17.7154i 0.901692i
\(387\) 0 0
\(388\) 6.82186 + 3.93860i 0.346327 + 0.199952i
\(389\) 1.80282 + 1.04086i 0.0914066 + 0.0527736i 0.545007 0.838432i \(-0.316527\pi\)
−0.453600 + 0.891205i \(0.649860\pi\)
\(390\) 0 0
\(391\) 30.8129i 1.55827i
\(392\) −6.28390 3.08425i −0.317385 0.155778i
\(393\) 0 0
\(394\) −2.15175 3.72694i −0.108404 0.187760i
\(395\) 0 0
\(396\) 0 0
\(397\) 19.3791 11.1885i 0.972610 0.561537i 0.0725790 0.997363i \(-0.476877\pi\)
0.900031 + 0.435826i \(0.143544\pi\)
\(398\) 3.46410 0.173640
\(399\) 0 0
\(400\) 0 0
\(401\) 17.0295 9.83196i 0.850411 0.490985i −0.0103787 0.999946i \(-0.503304\pi\)
0.860789 + 0.508961i \(0.169970\pi\)
\(402\) 0 0
\(403\) 4.77817 8.27603i 0.238017 0.412258i
\(404\) 3.76411 + 6.51962i 0.187271 + 0.324363i
\(405\) 0 0
\(406\) −21.8231 11.6384i −1.08306 0.577606i
\(407\) 0.678932i 0.0336534i
\(408\) 0 0
\(409\) −2.19932 1.26978i −0.108750 0.0627866i 0.444639 0.895710i \(-0.353332\pi\)
−0.553388 + 0.832923i \(0.686665\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.66361i 0.0819601i
\(413\) 0.553287 + 16.4303i 0.0272255 + 0.808483i
\(414\) 0 0
\(415\) 0 0
\(416\) −0.462546 + 0.801153i −0.0226782 + 0.0392797i
\(417\) 0 0
\(418\) 0.862517 0.497974i 0.0421871 0.0243567i
\(419\) 32.0568 1.56608 0.783039 0.621973i \(-0.213669\pi\)
0.783039 + 0.621973i \(0.213669\pi\)
\(420\) 0 0
\(421\) −25.2201 −1.22915 −0.614577 0.788857i \(-0.710673\pi\)
−0.614577 + 0.788857i \(0.710673\pi\)
\(422\) 8.99682 5.19432i 0.437959 0.252855i
\(423\) 0 0
\(424\) 1.67557 2.90217i 0.0813729 0.140942i
\(425\) 0 0
\(426\) 0 0
\(427\) −13.6957 + 25.6808i −0.662784 + 1.24278i
\(428\) 19.4028i 0.937869i
\(429\) 0 0
\(430\) 0 0
\(431\) −29.1599 16.8355i −1.40458 0.810937i −0.409726 0.912209i \(-0.634376\pi\)
−0.994859 + 0.101271i \(0.967709\pi\)
\(432\) 0 0
\(433\) 22.7610i 1.09382i −0.837190 0.546912i \(-0.815803\pi\)
0.837190 0.546912i \(-0.184197\pi\)
\(434\) −23.1960 + 14.4544i −1.11344 + 0.693832i
\(435\) 0 0
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) −2.43487 + 4.21732i −0.116476 + 0.201742i
\(438\) 0 0
\(439\) −1.86282 + 1.07550i −0.0889074 + 0.0513307i −0.543795 0.839218i \(-0.683013\pi\)
0.454887 + 0.890549i \(0.349680\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 3.66119 0.174145
\(443\) −6.63790 + 3.83239i −0.315376 + 0.182082i −0.649330 0.760507i \(-0.724950\pi\)
0.333954 + 0.942590i \(0.391617\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −9.17777 15.8964i −0.434580 0.752715i
\(447\) 0 0
\(448\) 2.24547 1.39924i 0.106088 0.0661079i
\(449\) 18.8337i 0.888817i 0.895824 + 0.444408i \(0.146586\pi\)
−0.895824 + 0.444408i \(0.853414\pi\)
\(450\) 0 0
\(451\) −11.5208 6.65155i −0.542494 0.313209i
\(452\) 13.9214 + 8.03750i 0.654805 + 0.378052i
\(453\) 0 0
\(454\) 3.02304i 0.141879i
\(455\) 0 0
\(456\) 0 0
\(457\) 14.6325 + 25.3442i 0.684478 + 1.18555i 0.973601 + 0.228258i \(0.0733031\pi\)
−0.289123 + 0.957292i \(0.593364\pi\)
\(458\) −5.32325 + 9.22014i −0.248739 + 0.430829i
\(459\) 0 0
\(460\) 0 0
\(461\) 14.1963 0.661188 0.330594 0.943773i \(-0.392751\pi\)
0.330594 + 0.943773i \(0.392751\pi\)
\(462\) 0 0
\(463\) 7.65787 0.355891 0.177946 0.984040i \(-0.443055\pi\)
0.177946 + 0.984040i \(0.443055\pi\)
\(464\) 8.09565 4.67403i 0.375831 0.216986i
\(465\) 0 0
\(466\) −1.99293 + 3.45185i −0.0923206 + 0.159904i
\(467\) −8.85713 15.3410i −0.409859 0.709897i 0.585015 0.811023i \(-0.301089\pi\)
−0.994874 + 0.101126i \(0.967755\pi\)
\(468\) 0 0
\(469\) 0.0317157 + 0.941825i 0.00146450 + 0.0434894i
\(470\) 0 0
\(471\) 0 0
\(472\) −5.38113 3.10680i −0.247687 0.143002i
\(473\) 8.64800 + 4.99293i 0.397636 + 0.229575i
\(474\) 0 0
\(475\) 0 0
\(476\) −9.23918 4.92732i −0.423477 0.225843i
\(477\) 0 0
\(478\) 4.12349 + 7.14210i 0.188604 + 0.326672i
\(479\) 6.41996 11.1197i 0.293336 0.508072i −0.681261 0.732041i \(-0.738568\pi\)
0.974596 + 0.223969i \(0.0719013\pi\)
\(480\) 0 0
\(481\) −0.341598 + 0.197222i −0.0155755 + 0.00899254i
\(482\) −10.9556 −0.499015
\(483\) 0 0
\(484\) −8.46457 −0.384753
\(485\) 0 0
\(486\) 0 0
\(487\) 1.88929 3.27235i 0.0856119 0.148284i −0.820040 0.572306i \(-0.806049\pi\)
0.905652 + 0.424022i \(0.139382\pi\)
\(488\) −5.50025 9.52671i −0.248985 0.431254i
\(489\) 0 0
\(490\) 0 0
\(491\) 32.1664i 1.45165i 0.687880 + 0.725824i \(0.258541\pi\)
−0.687880 + 0.725824i \(0.741459\pi\)
\(492\) 0 0
\(493\) −32.0398 18.4982i −1.44300 0.833115i
\(494\) 0.501103 + 0.289312i 0.0225457 + 0.0130168i
\(495\) 0 0
\(496\) 10.3302i 0.463838i
\(497\) −12.7048 20.3883i −0.569886 0.914540i
\(498\) 0 0
\(499\) 15.9683 + 27.6579i 0.714839 + 1.23814i 0.963022 + 0.269424i \(0.0868332\pi\)
−0.248183 + 0.968713i \(0.579833\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 18.8247 10.8685i 0.840190 0.485084i
\(503\) −5.29834 −0.236241 −0.118121 0.992999i \(-0.537687\pi\)
−0.118121 + 0.992999i \(0.537687\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −10.7362 + 6.19855i −0.477282 + 0.275559i
\(507\) 0 0
\(508\) 6.60867 11.4465i 0.293212 0.507858i
\(509\) −18.6321 32.2718i −0.825854 1.43042i −0.901265 0.433269i \(-0.857360\pi\)
0.0754100 0.997153i \(-0.475973\pi\)
\(510\) 0 0
\(511\) −18.0608 + 0.608195i −0.798965 + 0.0269049i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 15.0993 + 8.71758i 0.666001 + 0.384516i
\(515\) 0 0
\(516\) 0 0
\(517\) 4.42867i 0.194773i
\(518\) 1.12747 0.0379671i 0.0495380 0.00166818i
\(519\) 0 0
\(520\) 0 0
\(521\) 6.00676 10.4040i 0.263161 0.455808i −0.703919 0.710280i \(-0.748568\pi\)
0.967080 + 0.254472i \(0.0819017\pi\)
\(522\) 0 0
\(523\) 23.4136 13.5178i 1.02380 0.591093i 0.108600 0.994085i \(-0.465363\pi\)
0.915203 + 0.402992i \(0.132030\pi\)
\(524\) 9.40160 0.410711
\(525\) 0 0
\(526\) −18.3511 −0.800148
\(527\) −35.4058 + 20.4416i −1.54230 + 0.890449i
\(528\) 0 0
\(529\) 18.8081 32.5766i 0.817744 1.41637i
\(530\) 0 0
\(531\) 0 0
\(532\) −0.875193 1.40449i −0.0379444 0.0608923i
\(533\) 7.72879i 0.334771i
\(534\) 0 0
\(535\) 0 0
\(536\) −0.308459 0.178089i −0.0133234 0.00769228i
\(537\) 0 0
\(538\) 24.8371i 1.07080i
\(539\) −9.25604 + 6.20981i −0.398686 + 0.267475i
\(540\) 0 0
\(541\) 5.85450 + 10.1403i 0.251705 + 0.435965i 0.963995 0.265919i \(-0.0856755\pi\)
−0.712291 + 0.701885i \(0.752342\pi\)
\(542\) 12.2204 21.1663i 0.524910 0.909171i
\(543\) 0 0
\(544\) 3.42743 1.97883i 0.146950 0.0848415i
\(545\) 0 0
\(546\) 0 0
\(547\) −17.6050 −0.752737 −0.376369 0.926470i \(-0.622827\pi\)
−0.376369 + 0.926470i \(0.622827\pi\)
\(548\) −8.11701 + 4.68636i −0.346741 + 0.200191i
\(549\) 0 0
\(550\) 0 0
\(551\) −2.92350 5.06364i −0.124545 0.215718i
\(552\) 0 0
\(553\) −21.1312 11.2694i −0.898589 0.479224i
\(554\) 23.1970i 0.985548i
\(555\) 0 0
\(556\) −12.2201 7.05530i −0.518249 0.299211i
\(557\) 17.3913 + 10.0409i 0.736892 + 0.425445i 0.820938 0.571017i \(-0.193451\pi\)
−0.0840462 + 0.996462i \(0.526784\pi\)
\(558\) 0 0
\(559\) 5.80155i 0.245380i
\(560\) 0 0
\(561\) 0 0
\(562\) −7.04005 12.1937i −0.296967 0.514361i
\(563\) 11.9038 20.6180i 0.501687 0.868947i −0.498312 0.866998i \(-0.666046\pi\)
0.999998 0.00194851i \(-0.000620229\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −2.79820 −0.117617
\(567\) 0 0
\(568\) 9.07975 0.380978
\(569\) 35.8766 20.7134i 1.50403 0.868350i 0.504037 0.863682i \(-0.331848\pi\)
0.999989 0.00466765i \(-0.00148577\pi\)
\(570\) 0 0
\(571\) −20.5784 + 35.6428i −0.861177 + 1.49160i 0.00961607 + 0.999954i \(0.496939\pi\)
−0.870793 + 0.491649i \(0.836394\pi\)
\(572\) 0.736513 + 1.27568i 0.0307951 + 0.0533388i
\(573\) 0 0
\(574\) −10.4016 + 19.5040i −0.434155 + 0.814080i
\(575\) 0 0
\(576\) 0 0
\(577\) −10.7532 6.20835i −0.447661 0.258457i 0.259181 0.965829i \(-0.416547\pi\)
−0.706842 + 0.707372i \(0.749881\pi\)
\(578\) 1.15787 + 0.668498i 0.0481611 + 0.0278058i
\(579\) 0 0
\(580\) 0 0
\(581\) 1.81860 1.13324i 0.0754482 0.0470148i
\(582\) 0 0
\(583\) −2.66802 4.62114i −0.110498 0.191388i
\(584\) 3.41511 5.91515i 0.141318 0.244771i
\(585\) 0 0
\(586\) −22.1354 + 12.7799i −0.914406 + 0.527932i
\(587\) 4.01980 0.165915 0.0829575 0.996553i \(-0.473563\pi\)
0.0829575 + 0.996553i \(0.473563\pi\)
\(588\) 0 0
\(589\) −6.46127 −0.266232
\(590\) 0 0
\(591\) 0 0
\(592\) −0.213192 + 0.369259i −0.00876213 + 0.0151764i
\(593\) 21.7667 + 37.7010i 0.893850 + 1.54819i 0.835221 + 0.549914i \(0.185340\pi\)
0.0586292 + 0.998280i \(0.481327\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2.47225i 0.101267i
\(597\) 0 0
\(598\) −6.23749 3.60121i −0.255070 0.147265i
\(599\) −27.8218 16.0629i −1.13677 0.656314i −0.191141 0.981563i \(-0.561219\pi\)
−0.945629 + 0.325249i \(0.894552\pi\)
\(600\) 0 0
\(601\) 8.21681i 0.335171i 0.985858 + 0.167585i \(0.0535970\pi\)
−0.985858 + 0.167585i \(0.946403\pi\)
\(602\) 7.80788 14.6405i 0.318225 0.596702i
\(603\) 0 0
\(604\) −10.4425 18.0869i −0.424898 0.735945i
\(605\) 0 0
\(606\) 0 0
\(607\) 24.4532 14.1180i 0.992523 0.573034i 0.0864957 0.996252i \(-0.472433\pi\)
0.906028 + 0.423219i \(0.139100\pi\)
\(608\) 0.625477 0.0253664
\(609\) 0 0
\(610\) 0 0
\(611\) 2.22825 1.28648i 0.0901452 0.0520454i
\(612\) 0 0
\(613\) −15.3962 + 26.6670i −0.621846 + 1.07707i 0.367296 + 0.930104i \(0.380284\pi\)
−0.989142 + 0.146965i \(0.953050\pi\)
\(614\) −17.1430 29.6926i −0.691836 1.19829i
\(615\) 0 0
\(616\) −0.141786 4.21045i −0.00571272 0.169644i
\(617\) 4.42613i 0.178189i 0.996023 + 0.0890947i \(0.0283974\pi\)
−0.996023 + 0.0890947i \(0.971603\pi\)
\(618\) 0 0
\(619\) −9.47047 5.46778i −0.380650 0.219768i 0.297451 0.954737i \(-0.403864\pi\)
−0.678101 + 0.734969i \(0.737197\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 8.68041i 0.348053i
\(623\) −9.37171 4.99800i −0.375470 0.200241i
\(624\) 0 0
\(625\) 0 0
\(626\) 15.0106 25.9992i 0.599946 1.03914i
\(627\) 0 0
\(628\) −21.1722 + 12.2238i −0.844862 + 0.487781i
\(629\) 1.68748 0.0672841
\(630\) 0 0
\(631\) −38.2293 −1.52189 −0.760943 0.648819i \(-0.775263\pi\)
−0.760943 + 0.648819i \(0.775263\pi\)
\(632\) 7.83895 4.52582i 0.311817 0.180028i
\(633\) 0 0
\(634\) −13.8628 + 24.0111i −0.550563 + 0.953603i
\(635\) 0 0
\(636\) 0 0
\(637\) −5.81318 2.85321i −0.230327 0.113048i
\(638\) 14.8849i 0.589300i
\(639\) 0 0
\(640\) 0 0
\(641\) −29.0339 16.7627i −1.14677 0.662088i −0.198671 0.980066i \(-0.563663\pi\)
−0.948098 + 0.317979i \(0.896996\pi\)
\(642\) 0 0
\(643\) 17.4072i 0.686474i 0.939249 + 0.343237i \(0.111523\pi\)
−0.939249 + 0.343237i \(0.888477\pi\)
\(644\) 10.8940 + 17.4824i 0.429283 + 0.688903i
\(645\) 0 0
\(646\) −1.23771 2.14378i −0.0486971 0.0843458i
\(647\) 19.1301 33.1343i 0.752082 1.30264i −0.194730 0.980857i \(-0.562383\pi\)
0.946812 0.321787i \(-0.104284\pi\)
\(648\) 0 0
\(649\) −8.56839 + 4.94696i −0.336339 + 0.194185i
\(650\) 0 0
\(651\) 0 0
\(652\) −5.91515 −0.231655
\(653\) −28.0023 + 16.1671i −1.09581 + 0.632669i −0.935119 0.354335i \(-0.884707\pi\)
−0.160696 + 0.987004i \(0.551374\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −4.17731 7.23532i −0.163097 0.282492i
\(657\) 0 0
\(658\) −7.35446 + 0.247660i −0.286707 + 0.00965478i
\(659\) 16.4516i 0.640865i −0.947271 0.320433i \(-0.896172\pi\)
0.947271 0.320433i \(-0.103828\pi\)
\(660\) 0 0
\(661\) −2.14550 1.23870i −0.0834502 0.0481800i 0.457694 0.889110i \(-0.348675\pi\)
−0.541144 + 0.840930i \(0.682009\pi\)
\(662\) −5.45899 3.15175i −0.212170 0.122496i
\(663\) 0 0
\(664\) 0.809898i 0.0314301i
\(665\) 0 0
\(666\) 0 0
\(667\) 36.3903 + 63.0298i 1.40904 + 2.44052i
\(668\) 6.07201 10.5170i 0.234933 0.406916i
\(669\) 0 0
\(670\) 0 0
\(671\) −17.5161 −0.676202
\(672\) 0 0
\(673\) −17.0784 −0.658326 −0.329163 0.944273i \(-0.606767\pi\)
−0.329163 + 0.944273i \(0.606767\pi\)
\(674\) −23.7375 + 13.7048i −0.914333 + 0.527891i
\(675\) 0 0
\(676\) 6.07210 10.5172i 0.233542 0.404507i
\(677\) 23.3041 + 40.3639i 0.895650 + 1.55131i 0.832998 + 0.553276i \(0.186623\pi\)
0.0626524 + 0.998035i \(0.480044\pi\)
\(678\) 0 0
\(679\) −11.0221 17.6880i −0.422990 0.678803i
\(680\) 0 0
\(681\) 0 0
\(682\) −14.2450 8.22437i −0.545470 0.314927i
\(683\) −2.04994 1.18353i −0.0784388 0.0452867i 0.460268 0.887780i \(-0.347753\pi\)
−0.538706 + 0.842494i \(0.681087\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 10.8299 + 15.0237i 0.413488 + 0.573609i
\(687\) 0 0
\(688\) 3.13566 + 5.43113i 0.119546 + 0.207060i
\(689\) 1.55006 2.68478i 0.0590524 0.102282i
\(690\) 0 0
\(691\) −19.0534 + 11.0005i −0.724826 + 0.418479i −0.816527 0.577308i \(-0.804103\pi\)
0.0917001 + 0.995787i \(0.470770\pi\)
\(692\) 16.3984 0.623372
\(693\) 0 0
\(694\) 8.16672 0.310004
\(695\) 0 0
\(696\) 0 0
\(697\) −16.5323 + 28.6349i −0.626207 + 1.08462i
\(698\) 13.7943 + 23.8924i 0.522120 + 0.904339i
\(699\) 0 0
\(700\) 0 0
\(701\) 28.7909i 1.08742i 0.839274 + 0.543708i \(0.182980\pi\)
−0.839274 + 0.543708i \(0.817020\pi\)
\(702\) 0 0
\(703\) 0.230963 + 0.133347i 0.00871094 + 0.00502926i
\(704\) 1.37897 + 0.796151i 0.0519721 + 0.0300061i
\(705\) 0 0
\(706\) 7.04285i 0.265061i
\(707\) −0.670346 19.9065i −0.0252110 0.748661i
\(708\) 0 0
\(709\) −7.64049 13.2337i −0.286945 0.497003i 0.686134 0.727475i \(-0.259306\pi\)
−0.973079 + 0.230472i \(0.925973\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 3.47659 2.00721i 0.130291 0.0752234i
\(713\) 80.4269 3.01201
\(714\) 0 0
\(715\) 0 0
\(716\) 2.73398 1.57846i 0.102174 0.0589900i
\(717\) 0 0
\(718\) −8.17213 + 14.1545i −0.304981 + 0.528243i
\(719\) 8.33730 + 14.4406i 0.310929 + 0.538545i 0.978564 0.205944i \(-0.0660266\pi\)
−0.667635 + 0.744489i \(0.732693\pi\)
\(720\) 0 0
\(721\) 2.07121 3.88372i 0.0771360 0.144637i
\(722\) 18.6088i 0.692547i
\(723\) 0 0
\(724\) 7.08336 + 4.08958i 0.263251 + 0.151988i
\(725\) 0 0
\(726\) 0 0
\(727\) 32.4228i 1.20250i −0.799062 0.601248i \(-0.794670\pi\)
0.799062 0.601248i \(-0.205330\pi\)
\(728\) 2.07726 1.29443i 0.0769885 0.0479746i
\(729\) 0 0
\(730\) 0 0
\(731\) 12.4099 21.4945i 0.458996 0.795004i
\(732\) 0 0
\(733\) −40.1207 + 23.1637i −1.48189 + 0.855570i −0.999789 0.0205452i \(-0.993460\pi\)
−0.482102 + 0.876115i \(0.660126\pi\)
\(734\) −3.00798 −0.111026
\(735\) 0 0
\(736\) −7.78564 −0.286983
\(737\) −0.491161 + 0.283572i −0.0180921 + 0.0104455i
\(738\) 0 0
\(739\) −8.23689 + 14.2667i −0.302999 + 0.524809i −0.976814 0.214091i \(-0.931321\pi\)
0.673815 + 0.738900i \(0.264655\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −7.52488 + 4.68905i −0.276247 + 0.172141i
\(743\) 38.4778i 1.41161i −0.708405 0.705806i \(-0.750585\pi\)
0.708405 0.705806i \(-0.249415\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 20.0892 + 11.5985i 0.735519 + 0.424652i
\(747\) 0 0
\(748\) 6.30178i 0.230416i
\(749\) 24.1567 45.2960i 0.882666 1.65508i
\(750\) 0 0
\(751\) −18.9145 32.7608i −0.690198 1.19546i −0.971773 0.235919i \(-0.924190\pi\)
0.281574 0.959539i \(-0.409143\pi\)
\(752\) 1.39065 2.40868i 0.0507118 0.0878355i
\(753\) 0 0
\(754\) 7.48922 4.32390i 0.272741 0.157467i
\(755\) 0 0
\(756\) 0 0
\(757\) 11.1485 0.405197 0.202599 0.979262i \(-0.435061\pi\)
0.202599 + 0.979262i \(0.435061\pi\)
\(758\) −23.6181 + 13.6359i −0.857846 + 0.495278i
\(759\) 0 0
\(760\) 0 0
\(761\) −14.6239 25.3294i −0.530117 0.918189i −0.999383 0.0351321i \(-0.988815\pi\)
0.469266 0.883057i \(-0.344519\pi\)
\(762\) 0 0
\(763\) 0.178089 + 5.28850i 0.00644726 + 0.191457i
\(764\) 2.82843i 0.102329i
\(765\) 0 0
\(766\) −3.69096 2.13098i −0.133360 0.0769953i
\(767\) −4.97804 2.87407i −0.179747 0.103777i
\(768\) 0 0
\(769\) 0.892823i 0.0321960i −0.999870 0.0160980i \(-0.994876\pi\)
0.999870 0.0160980i \(-0.00512438\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 8.85772 + 15.3420i 0.318796 + 0.552172i
\(773\) 9.89011 17.1302i 0.355723 0.616130i −0.631519 0.775361i \(-0.717568\pi\)
0.987241 + 0.159231i \(0.0509014\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 7.87721 0.282775
\(777\) 0 0
\(778\) 2.08172 0.0746332
\(779\) −4.52553 + 2.61281i −0.162144 + 0.0936138i
\(780\) 0 0
\(781\) 7.22886 12.5207i 0.258669 0.448028i
\(782\) 15.4064 + 26.6847i 0.550933 + 0.954243i
\(783\) 0 0
\(784\) −6.98414 + 0.470912i −0.249434 + 0.0168183i
\(785\) 0 0
\(786\) 0 0