Properties

Label 380.2.i.b.121.3
Level $380$
Weight $2$
Character 380.121
Analytic conductor $3.034$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1783323.2
Defining polynomial: \(x^{6} - x^{5} + 5 x^{4} - 2 x^{3} + 19 x^{2} - 12 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.3
Root \(0.356769 - 0.617942i\) of defining polynomial
Character \(\chi\) \(=\) 380.121
Dual form 380.2.i.b.201.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.60220 + 2.77509i) q^{3} +(0.500000 + 0.866025i) q^{5} -2.20440 q^{7} +(-3.63409 + 6.29444i) q^{9} +O(q^{10})\) \(q+(1.60220 + 2.77509i) q^{3} +(0.500000 + 0.866025i) q^{5} -2.20440 q^{7} +(-3.63409 + 6.29444i) q^{9} -1.20440 q^{11} +(0.500000 - 0.866025i) q^{13} +(-1.60220 + 2.77509i) q^{15} +(1.07031 + 1.85383i) q^{17} +(4.30660 - 0.673184i) q^{19} +(-3.53189 - 6.11742i) q^{21} +(4.63409 - 8.02649i) q^{23} +(-0.500000 + 0.866025i) q^{25} -13.6770 q^{27} +(-4.16599 + 7.21570i) q^{29} +8.26819 q^{31} +(-1.92969 - 3.34233i) q^{33} +(-1.10220 - 1.90907i) q^{35} -2.20440 q^{37} +3.20440 q^{39} +(3.30660 + 5.72720i) q^{41} +(-1.17251 - 2.03084i) q^{43} -7.26819 q^{45} +(4.16599 - 7.21570i) q^{47} -2.14061 q^{49} +(-3.42969 + 5.94040i) q^{51} +(-0.134095 + 0.232259i) q^{53} +(-0.602201 - 1.04304i) q^{55} +(8.76819 + 10.8726i) q^{57} +(4.16599 + 7.21570i) q^{59} +(1.70440 - 2.95211i) q^{61} +(8.01100 - 13.8755i) q^{63} +1.00000 q^{65} +(1.06379 - 1.84253i) q^{67} +29.6990 q^{69} +(5.23630 + 9.06953i) q^{71} +(2.42969 + 4.20835i) q^{73} -3.20440 q^{75} +2.65498 q^{77} +(-8.20440 - 14.2104i) q^{79} +(-11.0110 - 19.0716i) q^{81} -5.73181 q^{83} +(-1.07031 + 1.85383i) q^{85} -26.6990 q^{87} +(5.40880 - 9.36832i) q^{89} +(-1.10220 + 1.90907i) q^{91} +(13.2473 + 22.9450i) q^{93} +(2.73630 + 3.39304i) q^{95} +(-7.87039 - 13.6319i) q^{97} +(4.37691 - 7.58103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{3} + 3q^{5} + 4q^{7} - 8q^{9} + O(q^{10}) \) \( 6q + q^{3} + 3q^{5} + 4q^{7} - 8q^{9} + 10q^{11} + 3q^{13} - q^{15} + 3q^{17} - 16q^{21} + 14q^{23} - 3q^{25} - 20q^{27} - 6q^{29} + 22q^{31} - 15q^{33} + 2q^{35} + 4q^{37} + 2q^{39} - 6q^{41} + 5q^{43} - 16q^{45} + 6q^{47} - 6q^{49} - 24q^{51} + 13q^{53} + 5q^{55} + 25q^{57} + 6q^{59} - 7q^{61} + 5q^{63} + 6q^{65} - 4q^{67} + 30q^{69} + 9q^{71} + 18q^{73} - 2q^{75} + 40q^{77} - 32q^{79} - 23q^{81} - 62q^{83} - 3q^{85} - 12q^{87} - 2q^{89} + 2q^{91} + 14q^{93} - 6q^{95} - 11q^{97} - 3q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(3\) 1.60220 + 2.77509i 0.925031 + 1.60220i 0.791511 + 0.611155i \(0.209295\pi\)
0.133520 + 0.991046i \(0.457372\pi\)
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −2.20440 −0.833185 −0.416593 0.909093i \(-0.636776\pi\)
−0.416593 + 0.909093i \(0.636776\pi\)
\(8\) 0 0
\(9\) −3.63409 + 6.29444i −1.21136 + 2.09815i
\(10\) 0 0
\(11\) −1.20440 −0.363141 −0.181570 0.983378i \(-0.558118\pi\)
−0.181570 + 0.983378i \(0.558118\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0 0
\(15\) −1.60220 + 2.77509i −0.413686 + 0.716526i
\(16\) 0 0
\(17\) 1.07031 + 1.85383i 0.259588 + 0.449619i 0.966131 0.258050i \(-0.0830801\pi\)
−0.706544 + 0.707669i \(0.749747\pi\)
\(18\) 0 0
\(19\) 4.30660 0.673184i 0.988002 0.154439i
\(20\) 0 0
\(21\) −3.53189 6.11742i −0.770722 1.33493i
\(22\) 0 0
\(23\) 4.63409 8.02649i 0.966276 1.67364i 0.260127 0.965574i \(-0.416235\pi\)
0.706148 0.708064i \(-0.250431\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) −13.6770 −2.63214
\(28\) 0 0
\(29\) −4.16599 + 7.21570i −0.773605 + 1.33992i 0.161971 + 0.986796i \(0.448215\pi\)
−0.935575 + 0.353127i \(0.885118\pi\)
\(30\) 0 0
\(31\) 8.26819 1.48501 0.742505 0.669840i \(-0.233637\pi\)
0.742505 + 0.669840i \(0.233637\pi\)
\(32\) 0 0
\(33\) −1.92969 3.34233i −0.335916 0.581824i
\(34\) 0 0
\(35\) −1.10220 1.90907i −0.186306 0.322691i
\(36\) 0 0
\(37\) −2.20440 −0.362401 −0.181201 0.983446i \(-0.557998\pi\)
−0.181201 + 0.983446i \(0.557998\pi\)
\(38\) 0 0
\(39\) 3.20440 0.513115
\(40\) 0 0
\(41\) 3.30660 + 5.72720i 0.516405 + 0.894439i 0.999819 + 0.0190471i \(0.00606323\pi\)
−0.483414 + 0.875392i \(0.660603\pi\)
\(42\) 0 0
\(43\) −1.17251 2.03084i −0.178806 0.309701i 0.762666 0.646793i \(-0.223890\pi\)
−0.941472 + 0.337092i \(0.890557\pi\)
\(44\) 0 0
\(45\) −7.26819 −1.08348
\(46\) 0 0
\(47\) 4.16599 7.21570i 0.607672 1.05252i −0.383951 0.923353i \(-0.625437\pi\)
0.991623 0.129165i \(-0.0412297\pi\)
\(48\) 0 0
\(49\) −2.14061 −0.305802
\(50\) 0 0
\(51\) −3.42969 + 5.94040i −0.480253 + 0.831823i
\(52\) 0 0
\(53\) −0.134095 + 0.232259i −0.0184193 + 0.0319032i −0.875088 0.483964i \(-0.839197\pi\)
0.856669 + 0.515867i \(0.172530\pi\)
\(54\) 0 0
\(55\) −0.602201 1.04304i −0.0812007 0.140644i
\(56\) 0 0
\(57\) 8.76819 + 10.8726i 1.16138 + 1.44012i
\(58\) 0 0
\(59\) 4.16599 + 7.21570i 0.542366 + 0.939405i 0.998768 + 0.0496310i \(0.0158045\pi\)
−0.456402 + 0.889774i \(0.650862\pi\)
\(60\) 0 0
\(61\) 1.70440 2.95211i 0.218226 0.377979i −0.736040 0.676939i \(-0.763306\pi\)
0.954266 + 0.298960i \(0.0966396\pi\)
\(62\) 0 0
\(63\) 8.01100 13.8755i 1.00929 1.74814i
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 1.06379 1.84253i 0.129962 0.225101i −0.793699 0.608310i \(-0.791848\pi\)
0.923662 + 0.383209i \(0.125181\pi\)
\(68\) 0 0
\(69\) 29.6990 3.57534
\(70\) 0 0
\(71\) 5.23630 + 9.06953i 0.621434 + 1.07636i 0.989219 + 0.146444i \(0.0467829\pi\)
−0.367785 + 0.929911i \(0.619884\pi\)
\(72\) 0 0
\(73\) 2.42969 + 4.20835i 0.284374 + 0.492550i 0.972457 0.233082i \(-0.0748809\pi\)
−0.688083 + 0.725632i \(0.741548\pi\)
\(74\) 0 0
\(75\) −3.20440 −0.370012
\(76\) 0 0
\(77\) 2.65498 0.302564
\(78\) 0 0
\(79\) −8.20440 14.2104i −0.923067 1.59880i −0.794640 0.607080i \(-0.792341\pi\)
−0.128427 0.991719i \(-0.540993\pi\)
\(80\) 0 0
\(81\) −11.0110 19.0716i −1.22344 2.11907i
\(82\) 0 0
\(83\) −5.73181 −0.629148 −0.314574 0.949233i \(-0.601862\pi\)
−0.314574 + 0.949233i \(0.601862\pi\)
\(84\) 0 0
\(85\) −1.07031 + 1.85383i −0.116091 + 0.201076i
\(86\) 0 0
\(87\) −26.6990 −2.86243
\(88\) 0 0
\(89\) 5.40880 9.36832i 0.573332 0.993040i −0.422889 0.906182i \(-0.638984\pi\)
0.996221 0.0868585i \(-0.0276828\pi\)
\(90\) 0 0
\(91\) −1.10220 + 1.90907i −0.115542 + 0.200125i
\(92\) 0 0
\(93\) 13.2473 + 22.9450i 1.37368 + 2.37929i
\(94\) 0 0
\(95\) 2.73630 + 3.39304i 0.280738 + 0.348118i
\(96\) 0 0
\(97\) −7.87039 13.6319i −0.799117 1.38411i −0.920192 0.391468i \(-0.871967\pi\)
0.121075 0.992643i \(-0.461366\pi\)
\(98\) 0 0
\(99\) 4.37691 7.58103i 0.439896 0.761922i
\(100\) 0 0
\(101\) 5.27471 9.13606i 0.524853 0.909072i −0.474728 0.880133i \(-0.657454\pi\)
0.999581 0.0289397i \(-0.00921308\pi\)
\(102\) 0 0
\(103\) −0.731811 −0.0721075 −0.0360537 0.999350i \(-0.511479\pi\)
−0.0360537 + 0.999350i \(0.511479\pi\)
\(104\) 0 0
\(105\) 3.53189 6.11742i 0.344678 0.596999i
\(106\) 0 0
\(107\) −13.3958 −1.29502 −0.647509 0.762058i \(-0.724189\pi\)
−0.647509 + 0.762058i \(0.724189\pi\)
\(108\) 0 0
\(109\) −2.96811 5.14091i −0.284293 0.492410i 0.688144 0.725574i \(-0.258426\pi\)
−0.972437 + 0.233164i \(0.925092\pi\)
\(110\) 0 0
\(111\) −3.53189 6.11742i −0.335233 0.580640i
\(112\) 0 0
\(113\) 15.6132 1.46877 0.734383 0.678735i \(-0.237471\pi\)
0.734383 + 0.678735i \(0.237471\pi\)
\(114\) 0 0
\(115\) 9.26819 0.864263
\(116\) 0 0
\(117\) 3.63409 + 6.29444i 0.335972 + 0.581921i
\(118\) 0 0
\(119\) −2.35939 4.08658i −0.216285 0.374616i
\(120\) 0 0
\(121\) −9.54942 −0.868129
\(122\) 0 0
\(123\) −10.5957 + 18.3523i −0.955380 + 1.65477i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 7.67699 13.2969i 0.681223 1.17991i −0.293385 0.955994i \(-0.594782\pi\)
0.974608 0.223918i \(-0.0718849\pi\)
\(128\) 0 0
\(129\) 3.75719 6.50764i 0.330802 0.572965i
\(130\) 0 0
\(131\) 3.89780 + 6.75119i 0.340552 + 0.589854i 0.984535 0.175186i \(-0.0560526\pi\)
−0.643983 + 0.765040i \(0.722719\pi\)
\(132\) 0 0
\(133\) −9.49348 + 1.48397i −0.823189 + 0.128676i
\(134\) 0 0
\(135\) −6.83850 11.8446i −0.588564 1.01942i
\(136\) 0 0
\(137\) −8.23630 + 14.2657i −0.703674 + 1.21880i 0.263494 + 0.964661i \(0.415125\pi\)
−0.967168 + 0.254138i \(0.918208\pi\)
\(138\) 0 0
\(139\) 9.76819 16.9190i 0.828527 1.43505i −0.0706667 0.997500i \(-0.522513\pi\)
0.899194 0.437551i \(-0.144154\pi\)
\(140\) 0 0
\(141\) 26.6990 2.24846
\(142\) 0 0
\(143\) −0.602201 + 1.04304i −0.0503586 + 0.0872236i
\(144\) 0 0
\(145\) −8.33198 −0.691933
\(146\) 0 0
\(147\) −3.42969 5.94040i −0.282876 0.489956i
\(148\) 0 0
\(149\) 2.83850 + 4.91642i 0.232539 + 0.402769i 0.958555 0.284909i \(-0.0919634\pi\)
−0.726016 + 0.687678i \(0.758630\pi\)
\(150\) 0 0
\(151\) −14.2264 −1.15773 −0.578864 0.815424i \(-0.696504\pi\)
−0.578864 + 0.815424i \(0.696504\pi\)
\(152\) 0 0
\(153\) −15.5584 −1.25782
\(154\) 0 0
\(155\) 4.13409 + 7.16046i 0.332058 + 0.575142i
\(156\) 0 0
\(157\) 0.327492 + 0.567233i 0.0261367 + 0.0452701i 0.878798 0.477194i \(-0.158346\pi\)
−0.852661 + 0.522464i \(0.825013\pi\)
\(158\) 0 0
\(159\) −0.859386 −0.0681538
\(160\) 0 0
\(161\) −10.2154 + 17.6936i −0.805087 + 1.39445i
\(162\) 0 0
\(163\) −12.6770 −0.992939 −0.496469 0.868054i \(-0.665370\pi\)
−0.496469 + 0.868054i \(0.665370\pi\)
\(164\) 0 0
\(165\) 1.92969 3.34233i 0.150226 0.260200i
\(166\) 0 0
\(167\) 3.89780 6.75119i 0.301621 0.522422i −0.674882 0.737925i \(-0.735806\pi\)
0.976503 + 0.215503i \(0.0691390\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 0 0
\(171\) −11.4133 + 29.5540i −0.872796 + 2.26005i
\(172\) 0 0
\(173\) 5.37039 + 9.30179i 0.408303 + 0.707202i 0.994700 0.102822i \(-0.0327873\pi\)
−0.586397 + 0.810024i \(0.699454\pi\)
\(174\) 0 0
\(175\) 1.10220 1.90907i 0.0833185 0.144312i
\(176\) 0 0
\(177\) −13.3495 + 23.1220i −1.00341 + 1.73796i
\(178\) 0 0
\(179\) −1.54942 −0.115809 −0.0579044 0.998322i \(-0.518442\pi\)
−0.0579044 + 0.998322i \(0.518442\pi\)
\(180\) 0 0
\(181\) 4.11320 7.12428i 0.305732 0.529544i −0.671692 0.740831i \(-0.734432\pi\)
0.977424 + 0.211287i \(0.0677655\pi\)
\(182\) 0 0
\(183\) 10.9232 0.807464
\(184\) 0 0
\(185\) −1.10220 1.90907i −0.0810354 0.140357i
\(186\) 0 0
\(187\) −1.28908 2.23275i −0.0942668 0.163275i
\(188\) 0 0
\(189\) 30.1496 2.19306
\(190\) 0 0
\(191\) 16.2812 1.17807 0.589034 0.808108i \(-0.299508\pi\)
0.589034 + 0.808108i \(0.299508\pi\)
\(192\) 0 0
\(193\) −8.60669 14.9072i −0.619523 1.07304i −0.989573 0.144033i \(-0.953993\pi\)
0.370050 0.929012i \(-0.379341\pi\)
\(194\) 0 0
\(195\) 1.60220 + 2.77509i 0.114736 + 0.198729i
\(196\) 0 0
\(197\) −10.2044 −0.727034 −0.363517 0.931588i \(-0.618424\pi\)
−0.363517 + 0.931588i \(0.618424\pi\)
\(198\) 0 0
\(199\) −5.03189 + 8.71550i −0.356701 + 0.617825i −0.987408 0.158197i \(-0.949432\pi\)
0.630706 + 0.776022i \(0.282765\pi\)
\(200\) 0 0
\(201\) 6.81761 0.480877
\(202\) 0 0
\(203\) 9.18351 15.9063i 0.644556 1.11640i
\(204\) 0 0
\(205\) −3.30660 + 5.72720i −0.230943 + 0.400005i
\(206\) 0 0
\(207\) 33.6815 + 58.3380i 2.34102 + 4.05477i
\(208\) 0 0
\(209\) −5.18688 + 0.810784i −0.358784 + 0.0560831i
\(210\) 0 0
\(211\) 6.12758 + 10.6133i 0.421840 + 0.730648i 0.996119 0.0880113i \(-0.0280512\pi\)
−0.574280 + 0.818659i \(0.694718\pi\)
\(212\) 0 0
\(213\) −16.7792 + 29.0624i −1.14969 + 1.99132i
\(214\) 0 0
\(215\) 1.17251 2.03084i 0.0799644 0.138502i
\(216\) 0 0
\(217\) −18.2264 −1.23729
\(218\) 0 0
\(219\) −7.78571 + 13.4852i −0.526110 + 0.911249i
\(220\) 0 0
\(221\) 2.14061 0.143993
\(222\) 0 0
\(223\) 10.0748 + 17.4501i 0.674658 + 1.16854i 0.976569 + 0.215206i \(0.0690422\pi\)
−0.301911 + 0.953336i \(0.597624\pi\)
\(224\) 0 0
\(225\) −3.63409 6.29444i −0.242273 0.419629i
\(226\) 0 0
\(227\) −8.25515 −0.547914 −0.273957 0.961742i \(-0.588333\pi\)
−0.273957 + 0.961742i \(0.588333\pi\)
\(228\) 0 0
\(229\) −26.6860 −1.76346 −0.881729 0.471756i \(-0.843620\pi\)
−0.881729 + 0.471756i \(0.843620\pi\)
\(230\) 0 0
\(231\) 4.25382 + 7.36783i 0.279881 + 0.484768i
\(232\) 0 0
\(233\) −7.00448 12.1321i −0.458879 0.794802i 0.540023 0.841650i \(-0.318416\pi\)
−0.998902 + 0.0468485i \(0.985082\pi\)
\(234\) 0 0
\(235\) 8.33198 0.543518
\(236\) 0 0
\(237\) 26.2902 45.5360i 1.70773 2.95788i
\(238\) 0 0
\(239\) −12.2682 −0.793563 −0.396782 0.917913i \(-0.629873\pi\)
−0.396782 + 0.917913i \(0.629873\pi\)
\(240\) 0 0
\(241\) −4.93621 + 8.54977i −0.317969 + 0.550739i −0.980064 0.198681i \(-0.936334\pi\)
0.662095 + 0.749420i \(0.269668\pi\)
\(242\) 0 0
\(243\) 14.7682 25.5793i 0.947380 1.64091i
\(244\) 0 0
\(245\) −1.07031 1.85383i −0.0683794 0.118437i
\(246\) 0 0
\(247\) 1.57031 4.06622i 0.0999162 0.258727i
\(248\) 0 0
\(249\) −9.18351 15.9063i −0.581981 1.00802i
\(250\) 0 0
\(251\) −14.4198 + 24.9758i −0.910170 + 1.57646i −0.0963474 + 0.995348i \(0.530716\pi\)
−0.813823 + 0.581113i \(0.802617\pi\)
\(252\) 0 0
\(253\) −5.58131 + 9.66711i −0.350894 + 0.607766i
\(254\) 0 0
\(255\) −6.85939 −0.429551
\(256\) 0 0
\(257\) 2.39780 4.15311i 0.149571 0.259064i −0.781498 0.623907i \(-0.785544\pi\)
0.931069 + 0.364844i \(0.118878\pi\)
\(258\) 0 0
\(259\) 4.85939 0.301948
\(260\) 0 0
\(261\) −30.2792 52.4451i −1.87424 3.24627i
\(262\) 0 0
\(263\) −10.2044 17.6745i −0.629230 1.08986i −0.987706 0.156320i \(-0.950037\pi\)
0.358476 0.933539i \(-0.383296\pi\)
\(264\) 0 0
\(265\) −0.268189 −0.0164747
\(266\) 0 0
\(267\) 34.6640 2.12140
\(268\) 0 0
\(269\) −0.563788 0.976509i −0.0343747 0.0595388i 0.848326 0.529474i \(-0.177611\pi\)
−0.882701 + 0.469935i \(0.844277\pi\)
\(270\) 0 0
\(271\) −9.83850 17.0408i −0.597646 1.03515i −0.993168 0.116697i \(-0.962769\pi\)
0.395522 0.918457i \(-0.370564\pi\)
\(272\) 0 0
\(273\) −7.06379 −0.427520
\(274\) 0 0
\(275\) 0.602201 1.04304i 0.0363141 0.0628978i
\(276\) 0 0
\(277\) 7.35398 0.441858 0.220929 0.975290i \(-0.429091\pi\)
0.220929 + 0.975290i \(0.429091\pi\)
\(278\) 0 0
\(279\) −30.0474 + 52.0436i −1.79889 + 3.11577i
\(280\) 0 0
\(281\) −6.73630 + 11.6676i −0.401854 + 0.696031i −0.993950 0.109836i \(-0.964967\pi\)
0.592096 + 0.805867i \(0.298301\pi\)
\(282\) 0 0
\(283\) −10.6595 18.4627i −0.633640 1.09750i −0.986802 0.161934i \(-0.948227\pi\)
0.353162 0.935562i \(-0.385106\pi\)
\(284\) 0 0
\(285\) −5.03189 + 13.0298i −0.298064 + 0.771819i
\(286\) 0 0
\(287\) −7.28908 12.6251i −0.430261 0.745233i
\(288\) 0 0
\(289\) 6.20889 10.7541i 0.365229 0.632594i
\(290\) 0 0
\(291\) 25.2199 43.6821i 1.47842 2.56069i
\(292\) 0 0
\(293\) 8.08580 0.472377 0.236189 0.971707i \(-0.424102\pi\)
0.236189 + 0.971707i \(0.424102\pi\)
\(294\) 0 0
\(295\) −4.16599 + 7.21570i −0.242553 + 0.420115i
\(296\) 0 0
\(297\) 16.4726 0.955837
\(298\) 0 0
\(299\) −4.63409 8.02649i −0.267997 0.464184i
\(300\) 0 0
\(301\) 2.58468 + 4.47679i 0.148978 + 0.258038i
\(302\) 0 0
\(303\) 33.8046 1.94202
\(304\) 0 0
\(305\) 3.40880 0.195187
\(306\) 0 0
\(307\) −14.2922 24.7549i −0.815701 1.41284i −0.908824 0.417180i \(-0.863018\pi\)
0.0931229 0.995655i \(-0.470315\pi\)
\(308\) 0 0
\(309\) −1.17251 2.03084i −0.0667016 0.115531i
\(310\) 0 0
\(311\) −10.7408 −0.609054 −0.304527 0.952504i \(-0.598498\pi\)
−0.304527 + 0.952504i \(0.598498\pi\)
\(312\) 0 0
\(313\) −5.71092 + 9.89160i −0.322800 + 0.559107i −0.981065 0.193680i \(-0.937958\pi\)
0.658264 + 0.752787i \(0.271291\pi\)
\(314\) 0 0
\(315\) 16.0220 0.902738
\(316\) 0 0
\(317\) −1.62309 + 2.81128i −0.0911619 + 0.157897i −0.908000 0.418970i \(-0.862391\pi\)
0.816838 + 0.576867i \(0.195725\pi\)
\(318\) 0 0
\(319\) 5.01752 8.69060i 0.280927 0.486580i
\(320\) 0 0
\(321\) −21.4627 37.1745i −1.19793 2.07488i
\(322\) 0 0
\(323\) 5.85735 + 7.26318i 0.325912 + 0.404134i
\(324\) 0 0
\(325\) 0.500000 + 0.866025i 0.0277350 + 0.0480384i
\(326\) 0 0
\(327\) 9.51100 16.4735i 0.525960 0.910989i
\(328\) 0 0
\(329\) −9.18351 + 15.9063i −0.506303 + 0.876943i
\(330\) 0 0
\(331\) 35.1208 1.93042 0.965208 0.261483i \(-0.0842116\pi\)
0.965208 + 0.261483i \(0.0842116\pi\)
\(332\) 0 0
\(333\) 8.01100 13.8755i 0.439000 0.760371i
\(334\) 0 0
\(335\) 2.12758 0.116242
\(336\) 0 0
\(337\) −7.93621 13.7459i −0.432313 0.748788i 0.564759 0.825256i \(-0.308969\pi\)
−0.997072 + 0.0764677i \(0.975636\pi\)
\(338\) 0 0
\(339\) 25.0155 + 43.3281i 1.35865 + 2.35326i
\(340\) 0 0
\(341\) −9.95822 −0.539268
\(342\) 0 0
\(343\) 20.1496 1.08798
\(344\) 0 0
\(345\) 14.8495 + 25.7201i 0.799470 + 1.38472i
\(346\) 0 0
\(347\) 16.3221 + 28.2707i 0.876216 + 1.51765i 0.855462 + 0.517866i \(0.173273\pi\)
0.0207537 + 0.999785i \(0.493393\pi\)
\(348\) 0 0
\(349\) −21.7538 −1.16446 −0.582228 0.813026i \(-0.697819\pi\)
−0.582228 + 0.813026i \(0.697819\pi\)
\(350\) 0 0
\(351\) −6.83850 + 11.8446i −0.365012 + 0.632219i
\(352\) 0 0
\(353\) 8.67699 0.461830 0.230915 0.972974i \(-0.425828\pi\)
0.230915 + 0.972974i \(0.425828\pi\)
\(354\) 0 0
\(355\) −5.23630 + 9.06953i −0.277914 + 0.481361i
\(356\) 0 0
\(357\) 7.56042 13.0950i 0.400140 0.693063i
\(358\) 0 0
\(359\) −5.81109 10.0651i −0.306697 0.531216i 0.670940 0.741511i \(-0.265891\pi\)
−0.977638 + 0.210296i \(0.932557\pi\)
\(360\) 0 0
\(361\) 18.0936 5.79827i 0.952297 0.305172i
\(362\) 0 0
\(363\) −15.3001 26.5005i −0.803046 1.39092i
\(364\) 0 0
\(365\) −2.42969 + 4.20835i −0.127176 + 0.220275i
\(366\) 0 0
\(367\) −15.3046 + 26.5083i −0.798892 + 1.38372i 0.121446 + 0.992598i \(0.461247\pi\)
−0.920338 + 0.391123i \(0.872087\pi\)
\(368\) 0 0
\(369\) −48.0660 −2.50222
\(370\) 0 0
\(371\) 0.295598 0.511992i 0.0153467 0.0265813i
\(372\) 0 0
\(373\) 4.70980 0.243864 0.121932 0.992538i \(-0.461091\pi\)
0.121932 + 0.992538i \(0.461091\pi\)
\(374\) 0 0
\(375\) −1.60220 2.77509i −0.0827373 0.143305i
\(376\) 0 0
\(377\) 4.16599 + 7.21570i 0.214559 + 0.371628i
\(378\) 0 0
\(379\) 10.0638 0.516942 0.258471 0.966019i \(-0.416781\pi\)
0.258471 + 0.966019i \(0.416781\pi\)
\(380\) 0 0
\(381\) 49.2003 2.52061
\(382\) 0 0
\(383\) −13.7219 23.7671i −0.701158 1.21444i −0.968060 0.250717i \(-0.919334\pi\)
0.266903 0.963723i \(-0.414000\pi\)
\(384\) 0 0
\(385\) 1.32749 + 2.29928i 0.0676553 + 0.117182i
\(386\) 0 0
\(387\) 17.0440 0.866396
\(388\) 0 0
\(389\) −0.257185 + 0.445458i −0.0130398 + 0.0225856i −0.872472 0.488665i \(-0.837484\pi\)
0.859432 + 0.511250i \(0.170817\pi\)
\(390\) 0 0
\(391\) 19.8396 1.00333
\(392\) 0 0
\(393\) −12.4901 + 21.6335i −0.630043 + 1.09127i
\(394\) 0 0
\(395\) 8.20440 14.2104i 0.412808 0.715005i
\(396\) 0 0
\(397\) −1.55278 2.68950i −0.0779320 0.134982i 0.824426 0.565970i \(-0.191498\pi\)
−0.902358 + 0.430988i \(0.858165\pi\)
\(398\) 0 0
\(399\) −19.3286 23.9677i −0.967641 1.19988i
\(400\) 0 0
\(401\) 6.51752 + 11.2887i 0.325470 + 0.563730i 0.981607 0.190911i \(-0.0611443\pi\)
−0.656138 + 0.754641i \(0.727811\pi\)
\(402\) 0 0
\(403\) 4.13409 7.16046i 0.205934 0.356688i
\(404\) 0 0
\(405\) 11.0110 19.0716i 0.547141 0.947676i
\(406\) 0 0
\(407\) 2.65498 0.131603
\(408\) 0 0
\(409\) −13.7747 + 23.8585i −0.681115 + 1.17973i 0.293525 + 0.955951i \(0.405172\pi\)
−0.974641 + 0.223775i \(0.928162\pi\)
\(410\) 0 0
\(411\) −52.7848 −2.60368
\(412\) 0 0
\(413\) −9.18351 15.9063i −0.451891 0.782698i
\(414\) 0 0
\(415\) −2.86591 4.96389i −0.140682 0.243668i
\(416\) 0 0
\(417\) 62.6024 3.06565
\(418\) 0 0
\(419\) 16.5494 0.808492 0.404246 0.914650i \(-0.367534\pi\)
0.404246 + 0.914650i \(0.367534\pi\)
\(420\) 0 0
\(421\) 7.93418 + 13.7424i 0.386688 + 0.669764i 0.992002 0.126223i \(-0.0402856\pi\)
−0.605314 + 0.795987i \(0.706952\pi\)
\(422\) 0 0
\(423\) 30.2792 + 52.4451i 1.47222 + 2.54997i
\(424\) 0 0
\(425\) −2.14061 −0.103835
\(426\) 0 0
\(427\) −3.75719 + 6.50764i −0.181823 + 0.314927i
\(428\) 0 0
\(429\) −3.85939 −0.186333
\(430\) 0 0
\(431\) −11.4472 + 19.8272i −0.551393 + 0.955041i 0.446781 + 0.894643i \(0.352570\pi\)
−0.998174 + 0.0603975i \(0.980763\pi\)
\(432\) 0 0
\(433\) 10.6660 18.4740i 0.512575 0.887805i −0.487319 0.873224i \(-0.662025\pi\)
0.999894 0.0145814i \(-0.00464157\pi\)
\(434\) 0 0
\(435\) −13.3495 23.1220i −0.640060 1.10862i
\(436\) 0 0
\(437\) 14.5539 37.6865i 0.696208 1.80279i
\(438\) 0 0
\(439\) 5.08783 + 8.81238i 0.242829 + 0.420592i 0.961519 0.274739i \(-0.0885913\pi\)
−0.718690 + 0.695331i \(0.755258\pi\)
\(440\) 0 0
\(441\) 7.77919 13.4740i 0.370438 0.641617i
\(442\) 0 0
\(443\) 3.30660 5.72720i 0.157101 0.272108i −0.776721 0.629845i \(-0.783118\pi\)
0.933822 + 0.357737i \(0.116452\pi\)
\(444\) 0 0
\(445\) 10.8176 0.512804
\(446\) 0 0
\(447\) −9.09568 + 15.7542i −0.430211 + 0.745147i
\(448\) 0 0
\(449\) 10.9870 0.518507 0.259253 0.965809i \(-0.416524\pi\)
0.259253 + 0.965809i \(0.416524\pi\)
\(450\) 0 0
\(451\) −3.98248 6.89785i −0.187528 0.324807i
\(452\) 0 0
\(453\) −22.7936 39.4796i −1.07094 1.85491i
\(454\) 0 0
\(455\) −2.20440 −0.103344
\(456\) 0 0
\(457\) 12.5494 0.587037 0.293518 0.955953i \(-0.405174\pi\)
0.293518 + 0.955953i \(0.405174\pi\)
\(458\) 0 0
\(459\) −14.6386 25.3548i −0.683270 1.18346i
\(460\) 0 0
\(461\) 11.6386 + 20.1586i 0.542063 + 0.938880i 0.998785 + 0.0492710i \(0.0156898\pi\)
−0.456723 + 0.889609i \(0.650977\pi\)
\(462\) 0 0
\(463\) −23.3958 −1.08729 −0.543647 0.839314i \(-0.682957\pi\)
−0.543647 + 0.839314i \(0.682957\pi\)
\(464\) 0 0
\(465\) −13.2473 + 22.9450i −0.614329 + 1.06405i
\(466\) 0 0
\(467\) −12.6352 −0.584688 −0.292344 0.956313i \(-0.594435\pi\)
−0.292344 + 0.956313i \(0.594435\pi\)
\(468\) 0 0
\(469\) −2.34502 + 4.06169i −0.108283 + 0.187551i
\(470\) 0 0
\(471\) −1.04942 + 1.81764i −0.0483546 + 0.0837526i
\(472\) 0 0
\(473\) 1.41217 + 2.44595i 0.0649316 + 0.112465i
\(474\) 0 0
\(475\) −1.57031 + 4.06622i −0.0720506 + 0.186571i
\(476\) 0 0
\(477\) −0.974625 1.68810i −0.0446250 0.0772928i
\(478\) 0 0
\(479\) −2.01752 + 3.49445i −0.0921830 + 0.159666i −0.908429 0.418038i \(-0.862718\pi\)
0.816246 + 0.577704i \(0.196051\pi\)
\(480\) 0 0
\(481\) −1.10220 + 1.90907i −0.0502560 + 0.0870460i
\(482\) 0 0
\(483\) −65.4685 −2.97892
\(484\) 0 0
\(485\) 7.87039 13.6319i 0.357376 0.618993i
\(486\) 0 0
\(487\) 6.54942 0.296782 0.148391 0.988929i \(-0.452591\pi\)
0.148391 + 0.988929i \(0.452591\pi\)
\(488\) 0 0
\(489\) −20.3111 35.1798i −0.918499 1.59089i
\(490\) 0 0
\(491\) −1.04290 1.80635i −0.0470653 0.0815195i 0.841533 0.540206i \(-0.181654\pi\)
−0.888598 + 0.458686i \(0.848320\pi\)
\(492\) 0 0
\(493\) −17.8355 −0.803273
\(494\) 0 0
\(495\) 8.75382 0.393455
\(496\) 0 0
\(497\) −11.5429 19.9929i −0.517770 0.896803i
\(498\) 0 0
\(499\) 12.0539 + 20.8780i 0.539607 + 0.934626i 0.998925 + 0.0463546i \(0.0147604\pi\)
−0.459318 + 0.888272i \(0.651906\pi\)
\(500\) 0 0
\(501\) 24.9802 1.11603
\(502\) 0 0
\(503\) 4.13858 7.16823i 0.184530 0.319616i −0.758888 0.651221i \(-0.774257\pi\)
0.943418 + 0.331606i \(0.107590\pi\)
\(504\) 0 0
\(505\) 10.5494 0.469443
\(506\) 0 0
\(507\) −19.2264 + 33.3011i −0.853875 + 1.47895i
\(508\) 0 0
\(509\) 2.86591 4.96389i 0.127029 0.220021i −0.795495 0.605960i \(-0.792789\pi\)
0.922524 + 0.385939i \(0.126123\pi\)
\(510\) 0 0
\(511\) −5.35602 9.27690i −0.236936 0.410386i
\(512\) 0 0
\(513\) −58.9014 + 9.20713i −2.60056 + 0.406505i
\(514\) 0 0
\(515\) −0.365905 0.633767i −0.0161237 0.0279271i
\(516\) 0 0
\(517\) −5.01752 + 8.69060i −0.220670 + 0.382212i
\(518\) 0 0
\(519\) −17.2089 + 29.8067i −0.755386 + 1.30837i
\(520\) 0 0
\(521\) 14.8086 0.648778 0.324389 0.945924i \(-0.394841\pi\)
0.324389 + 0.945924i \(0.394841\pi\)
\(522\) 0 0
\(523\) −7.79356 + 13.4988i −0.340789 + 0.590263i −0.984579 0.174938i \(-0.944027\pi\)
0.643791 + 0.765202i \(0.277361\pi\)
\(524\) 0 0
\(525\) 7.06379 0.308289
\(526\) 0 0
\(527\) 8.84950 + 15.3278i 0.385490 + 0.667689i
\(528\) 0 0
\(529\) −31.4497 54.4724i −1.36738 2.36837i
\(530\) 0 0
\(531\) −60.5584 −2.62801
\(532\) 0 0
\(533\) 6.61320 0.286450
\(534\) 0 0
\(535\) −6.69788 11.6011i −0.289575 0.501558i
\(536\) 0 0
\(537\) −2.48248 4.29978i −0.107127 0.185549i
\(538\) 0 0
\(539\) 2.57816 0.111049
\(540\) 0 0
\(541\) −14.0539 + 24.3421i −0.604224 + 1.04655i 0.387949 + 0.921681i \(0.373184\pi\)
−0.992174 + 0.124867i \(0.960150\pi\)
\(542\) 0 0
\(543\) 26.3607 1.13125
\(544\) 0 0
\(545\) 2.96811 5.14091i 0.127140 0.220212i
\(546\) 0 0
\(547\) 21.6835 37.5569i 0.927120 1.60582i 0.139004 0.990292i \(-0.455610\pi\)
0.788116 0.615527i \(-0.211057\pi\)
\(548\) 0 0
\(549\) 12.3879 + 21.4565i 0.528703 + 0.915741i
\(550\) 0 0
\(551\) −13.0838 + 33.8796i −0.557387 + 1.44332i
\(552\) 0 0
\(553\) 18.0858 + 31.3255i 0.769086 + 1.33210i
\(554\) 0 0
\(555\) 3.53189 6.11742i 0.149921 0.259670i
\(556\) 0 0
\(557\) −8.65814 + 14.9963i −0.366857 + 0.635415i −0.989072 0.147431i \(-0.952900\pi\)
0.622215 + 0.782846i \(0.286233\pi\)
\(558\) 0 0
\(559\) −2.34502 −0.0991836
\(560\) 0 0
\(561\) 4.13073 7.15463i 0.174399 0.302069i
\(562\) 0 0
\(563\) 8.35398 0.352078 0.176039 0.984383i \(-0.443671\pi\)
0.176039 + 0.984383i \(0.443671\pi\)
\(564\) 0 0
\(565\) 7.80660 + 13.5214i 0.328426 + 0.568851i
\(566\) 0 0
\(567\) 24.2727 + 42.0415i 1.01936 + 1.76558i
\(568\) 0 0
\(569\) −10.6640 −0.447056 −0.223528 0.974697i \(-0.571757\pi\)
−0.223528 + 0.974697i \(0.571757\pi\)
\(570\) 0 0
\(571\) −2.56512 −0.107347 −0.0536735 0.998559i \(-0.517093\pi\)
−0.0536735 + 0.998559i \(0.517093\pi\)
\(572\) 0 0
\(573\) 26.0858 + 45.1819i 1.08975 + 1.88750i
\(574\) 0 0
\(575\) 4.63409 + 8.02649i 0.193255 + 0.334728i
\(576\) 0 0
\(577\) 20.4218 0.850172 0.425086 0.905153i \(-0.360244\pi\)
0.425086 + 0.905153i \(0.360244\pi\)
\(578\) 0 0
\(579\) 27.5793 47.7687i 1.14616 1.98520i
\(580\) 0 0
\(581\) 12.6352 0.524197
\(582\) 0 0
\(583\) 0.161504 0.279733i 0.00668880 0.0115853i
\(584\) 0 0
\(585\) −3.63409 + 6.29444i −0.150251 + 0.260243i
\(586\) 0 0
\(587\) 4.40432 + 7.62850i 0.181786 + 0.314862i 0.942489 0.334238i \(-0.108479\pi\)
−0.760703 + 0.649100i \(0.775146\pi\)
\(588\) 0 0
\(589\) 35.6078 5.56601i 1.46719 0.229343i
\(590\) 0 0
\(591\) −16.3495 28.3182i −0.672529 1.16485i
\(592\) 0 0
\(593\) −16.4726 + 28.5314i −0.676448 + 1.17164i 0.299595 + 0.954066i \(0.403148\pi\)
−0.976043 + 0.217576i \(0.930185\pi\)
\(594\) 0 0
\(595\) 2.35939 4.08658i 0.0967254 0.167533i
\(596\) 0 0
\(597\) −32.2484 −1.31984
\(598\) 0 0
\(599\) 9.56379 16.5650i 0.390766 0.676826i −0.601785 0.798658i \(-0.705544\pi\)
0.992551 + 0.121832i \(0.0388769\pi\)
\(600\) 0 0
\(601\) 19.3100 0.787670 0.393835 0.919181i \(-0.371148\pi\)
0.393835 + 0.919181i \(0.371148\pi\)
\(602\) 0 0
\(603\) 7.73181 + 13.3919i 0.314864 + 0.545360i
\(604\) 0 0
\(605\) −4.77471 8.27004i −0.194120 0.336225i
\(606\) 0 0
\(607\) 36.8773 1.49680 0.748402 0.663245i \(-0.230821\pi\)
0.748402 + 0.663245i \(0.230821\pi\)
\(608\) 0 0
\(609\) 58.8553 2.38494
\(610\) 0 0
\(611\) −4.16599 7.21570i −0.168538 0.291916i
\(612\) 0 0
\(613\) 14.2603 + 24.6996i 0.575970 + 0.997609i 0.995936 + 0.0900688i \(0.0287087\pi\)
−0.419966 + 0.907540i \(0.637958\pi\)
\(614\) 0 0
\(615\) −21.1914 −0.854518
\(616\) 0 0
\(617\) 5.64713 9.78112i 0.227345 0.393773i −0.729675 0.683794i \(-0.760329\pi\)
0.957020 + 0.290021i \(0.0936622\pi\)
\(618\) 0 0
\(619\) 27.2044 1.09344 0.546719 0.837316i \(-0.315877\pi\)
0.546719 + 0.837316i \(0.315877\pi\)
\(620\) 0 0
\(621\) −63.3805 + 109.778i −2.54337 + 4.40525i
\(622\) 0 0
\(623\) −11.9232 + 20.6515i −0.477692 + 0.827387i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) −10.5604 13.0950i −0.421743 0.522965i
\(628\) 0 0
\(629\) −2.35939 4.08658i −0.0940749 0.162942i
\(630\) 0 0
\(631\) −4.19136 + 7.25965i −0.166856 + 0.289002i −0.937313 0.348490i \(-0.886695\pi\)
0.770457 + 0.637492i \(0.220028\pi\)
\(632\) 0 0
\(633\) −19.6352 + 34.0092i −0.780430 + 1.35174i
\(634\) 0 0
\(635\) 15.3540 0.609304
\(636\) 0 0
\(637\) −1.07031 + 1.85383i −0.0424071 + 0.0734513i
\(638\) 0 0
\(639\) −76.1168 −3.01113
\(640\) 0 0
\(641\) −9.55594 16.5514i −0.377437 0.653740i 0.613252 0.789888i \(-0.289861\pi\)
−0.990689 + 0.136148i \(0.956528\pi\)
\(642\) 0 0
\(643\) 24.1112 + 41.7618i 0.950852 + 1.64692i 0.743588 + 0.668638i \(0.233123\pi\)
0.207264 + 0.978285i \(0.433544\pi\)
\(644\) 0 0
\(645\) 7.51437 0.295878
\(646\) 0 0
\(647\) −30.0817 −1.18263 −0.591317 0.806439i \(-0.701392\pi\)
−0.591317 + 0.806439i \(0.701392\pi\)
\(648\) 0 0
\(649\) −5.01752 8.69060i −0.196955 0.341136i
\(650\) 0 0
\(651\) −29.2024 50.5800i −1.14453 1.98239i
\(652\) 0 0
\(653\) 41.9124 1.64016 0.820079 0.572250i \(-0.193929\pi\)
0.820079 + 0.572250i \(0.193929\pi\)
\(654\) 0 0
\(655\) −3.89780 + 6.75119i −0.152300 + 0.263791i
\(656\) 0 0
\(657\) −35.3189 −1.37792
\(658\) 0 0
\(659\) 20.0936 34.8032i 0.782737 1.35574i −0.147604 0.989047i \(-0.547156\pi\)
0.930341 0.366694i \(-0.119511\pi\)
\(660\) 0 0
\(661\) 0.757185 1.31148i 0.0294511 0.0510108i −0.850924 0.525289i \(-0.823957\pi\)
0.880375 + 0.474278i \(0.157291\pi\)
\(662\) 0 0
\(663\) 3.42969 + 5.94040i 0.133198 + 0.230706i
\(664\) 0 0
\(665\) −6.03189 7.47961i −0.233907 0.290047i
\(666\) 0 0
\(667\) 38.6112 + 66.8765i 1.49503 + 2.58947i
\(668\) 0 0
\(669\) −32.2837 + 55.9170i −1.24816 + 2.16187i
\(670\) 0 0
\(671\) −2.05278 + 3.55553i −0.0792468 + 0.137260i
\(672\) 0 0
\(673\) −7.76686 −0.299390 −0.149695 0.988732i \(-0.547829\pi\)
−0.149695 + 0.988732i \(0.547829\pi\)
\(674\) 0 0
\(675\) 6.83850 11.8446i 0.263214 0.455900i
\(676\) 0 0
\(677\) 6.19136 0.237953 0.118977 0.992897i \(-0.462039\pi\)
0.118977 + 0.992897i \(0.462039\pi\)
\(678\) 0 0
\(679\) 17.3495 + 30.0502i 0.665813 + 1.15322i
\(680\) 0 0
\(681\) −13.2264 22.9088i −0.506837 0.877868i
\(682\) 0 0
\(683\) 2.92317 0.111852 0.0559261 0.998435i \(-0.482189\pi\)
0.0559261 + 0.998435i \(0.482189\pi\)
\(684\) 0 0
\(685\) −16.4726 −0.629385
\(686\) 0 0
\(687\) −42.7563 74.0560i −1.63125 2.82541i
\(688\) 0 0
\(689\) 0.134095 + 0.232259i 0.00510860 + 0.00884835i
\(690\) 0 0
\(691\) −2.35805 −0.0897046 −0.0448523 0.998994i \(-0.514282\pi\)
−0.0448523 + 0.998994i \(0.514282\pi\)
\(692\) 0 0
\(693\) −9.64847 + 16.7116i −0.366515 + 0.634822i
\(694\) 0 0
\(695\) 19.5364 0.741057
\(696\) 0 0
\(697\) −7.07816 + 12.2597i −0.268104 + 0.464370i
\(698\) 0 0
\(699\) 22.4452 38.8762i 0.848955 1.47043i
\(700\) 0 0
\(701\) −12.2792 21.2682i −0.463779 0.803288i 0.535367 0.844620i \(-0.320173\pi\)
−0.999145 + 0.0413314i \(0.986840\pi\)
\(702\) 0 0
\(703\) −9.49348 + 1.48397i −0.358053 + 0.0559689i
\(704\) 0 0
\(705\) 13.3495 + 23.1220i 0.502771 + 0.870825i
\(706\) 0 0
\(707\) −11.6276 + 20.1396i −0.437300 + 0.757426i
\(708\) 0 0
\(709\) −3.63858 + 6.30220i −0.136650 + 0.236684i −0.926226 0.376968i \(-0.876967\pi\)
0.789577 + 0.613652i \(0.210300\pi\)
\(710\) 0 0
\(711\) 119.262 4.47269
\(712\) 0 0
\(713\) 38.3156 66.3645i 1.43493 2.48537i
\(714\) 0 0
\(715\) −1.20440 −0.0450421
\(716\) 0 0
\(717\) −19.6561 34.0454i −0.734071 1.27145i
\(718\) 0 0
\(719\) −16.4452 28.4839i −0.613302 1.06227i −0.990680 0.136211i \(-0.956508\pi\)
0.377378 0.926059i \(-0.376826\pi\)
\(720\) 0 0
\(721\) 1.61320 0.0600789
\(722\) 0 0
\(723\) −31.6352 −1.17653
\(724\) 0 0
\(725\) −4.16599 7.21570i −0.154721 0.267985i
\(726\) 0 0
\(727\) −13.9551 24.1709i −0.517565 0.896449i −0.999792 0.0204023i \(-0.993505\pi\)
0.482227 0.876046i \(-0.339828\pi\)
\(728\) 0 0
\(729\) 28.5804 1.05853
\(730\) 0 0
\(731\) 2.50989 4.34725i 0.0928315 0.160789i
\(732\) 0 0
\(733\) −4.89710 −0.180878 −0.0904392 0.995902i \(-0.528827\pi\)
−0.0904392 + 0.995902i \(0.528827\pi\)
\(734\) 0 0
\(735\) 3.42969 5.94040i 0.126506 0.219115i
\(736\) 0 0
\(737\) −1.28123 + 2.21915i −0.0471946 + 0.0817435i
\(738\) 0 0
\(739\) 11.5936 + 20.0808i 0.426479 + 0.738684i 0.996557 0.0829069i \(-0.0264204\pi\)
−0.570078 + 0.821591i \(0.693087\pi\)
\(740\) 0 0
\(741\) 13.8001 2.15715i 0.506959 0.0792449i
\(742\) 0 0
\(743\) −19.9901 34.6239i −0.733366 1.27023i −0.955436 0.295197i \(-0.904615\pi\)
0.222070 0.975031i \(-0.428719\pi\)
\(744\) 0 0
\(745\) −2.83850 + 4.91642i −0.103994 + 0.180124i
\(746\) 0 0
\(747\) 20.8299 36.0785i 0.762128 1.32004i
\(748\) 0 0
\(749\) 29.5296 1.07899
\(750\) 0 0
\(751\) 10.2936 17.8290i 0.375617 0.650589i −0.614802 0.788682i \(-0.710764\pi\)
0.990419 + 0.138093i \(0.0440973\pi\)
\(752\) 0 0
\(753\) −92.4137 −3.36774
\(754\) 0 0
\(755\) −7.11320 12.3204i −0.258876 0.448386i
\(756\) 0 0
\(757\) 17.3176 + 29.9950i 0.629419 + 1.09019i 0.987668 + 0.156560i \(0.0500404\pi\)
−0.358249 + 0.933626i \(0.616626\pi\)
\(758\) 0 0
\(759\) −35.7695 −1.29835
\(760\) 0 0
\(761\) 24.3890 0.884102 0.442051 0.896990i \(-0.354251\pi\)
0.442051 + 0.896990i \(0.354251\pi\)
\(762\) 0 0
\(763\) 6.54290 + 11.3326i 0.236869 + 0.410269i
\(764\) 0 0
\(765\) −7.77919 13.4740i −0.281257 0.487152i
\(766\) 0 0
\(767\) 8.33198 0.300850
\(768\) 0 0
\(769\) −3.27471 + 5.67196i −0.118089 + 0.204536i −0.919010 0.394233i \(-0.871010\pi\)
0.800921 + 0.598770i \(0.204343\pi\)
\(770\) 0 0
\(771\) 15.3670 0.553430
\(772\) 0 0
\(773\) 18.7363 32.4522i 0.673898 1.16723i −0.302892 0.953025i \(-0.597952\pi\)
0.976790 0.214200i \(-0.0687145\pi\)
\(774\) 0 0
\(775\) −4.13409 + 7.16046i −0.148501 + 0.257211i
\(776\) 0 0
\(777\) 7.78571 + 13.4852i 0.279311 + 0.483781i
\(778\) 0 0
\(779\) 18.0957 + 22.4388i 0.648345 + 0.803955i
\(780\) 0 0
\(781\) −6.30660 10.9234i −0.225668 0.390868i
\(782\) 0 0
\(783\) 56.9782 98.6891i 2.03623 3.52686i
\(784\) 0 0
\(785\) −0.327492 + 0.567233i −0.0116887 + 0.0202454i
\(786\) 0 0
\(787\) −12.8306 −0.457363 −0.228682 0.973501i \(-0.573441\pi\)
−0.228682 + 0.973501i \(0.573441\pi\)
\(788\) 0 0
\(789\) 32.6990 56.6363i 1.16412 2.01631i
\(790\) 0 0
\(791\) −34.4178 −1.22376
\(792\) 0 0
\(793\) −1.70440 2.95211i −0.0605251 0.104833i
\(794\) 0 0
\(795\) −0.429693 0.744250i −0.0152396 0.0263958i
\(796\) 0 0
\(797\) −28.3032 −1.00255