Properties

Label 1170.2.bs.f.361.2
Level $1170$
Weight $2$
Character 1170.361
Analytic conductor $9.342$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.17284886784.1
Defining polynomial: \(x^{8} - 2 x^{7} + 2 x^{6} + 30 x^{5} + 185 x^{4} + 36 x^{3} + 8 x^{2} + 208 x + 2704\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.2
Root \(-1.70006 + 1.70006i\) of defining polynomial
Character \(\chi\) \(=\) 1170.361
Dual form 1170.2.bs.f.901.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(4.02239 + 2.32233i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(4.02239 + 2.32233i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(-3.81062 + 2.20006i) q^{11} +(-3.35432 + 1.32233i) q^{13} -4.64466 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-6.96699 - 4.02239i) q^{19} +(0.866025 + 0.500000i) q^{20} +(2.20006 - 3.81062i) q^{22} +(0.488292 + 0.845746i) q^{23} -1.00000 q^{25} +(2.24376 - 2.82233i) q^{26} +(4.02239 - 2.32233i) q^{28} +(-2.15637 - 3.73494i) q^{29} +6.44069i q^{31} +(0.866025 + 0.500000i) q^{32} -4.00000i q^{34} +(-2.32233 + 4.02239i) q^{35} +(3.28745 - 1.89801i) q^{37} +8.04479 q^{38} -1.00000 q^{40} +(6.31274 - 3.64466i) q^{41} +(0.358228 - 0.620469i) q^{43} +4.40013i q^{44} +(-0.845746 - 0.488292i) q^{46} -9.75342i q^{47} +(7.28643 + 12.6205i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-0.531987 + 3.56609i) q^{52} -13.5089 q^{53} +(-2.20006 - 3.81062i) q^{55} +(-2.32233 + 4.02239i) q^{56} +(3.73494 + 2.15637i) q^{58} +(1.88842 + 1.09028i) q^{59} +(-3.73205 + 6.46410i) q^{61} +(-3.22034 - 5.57780i) q^{62} -1.00000 q^{64} +(-1.32233 - 3.35432i) q^{65} +(-1.58068 + 0.912609i) q^{67} +(2.00000 + 3.46410i) q^{68} -4.64466i q^{70} +(6.88764 + 3.97658i) q^{71} -4.36112i q^{73} +(-1.89801 + 3.28745i) q^{74} +(-6.96699 + 4.02239i) q^{76} -20.4371 q^{77} -14.9340 q^{79} +(0.866025 - 0.500000i) q^{80} +(-3.64466 + 6.31274i) q^{82} -3.51093i q^{83} +(-3.46410 - 2.00000i) q^{85} +0.716456i q^{86} +(-2.20006 - 3.81062i) q^{88} +(-7.07780 + 4.08637i) q^{89} +(-16.5633 - 2.47090i) q^{91} +0.976584 q^{92} +(4.87671 + 8.44671i) q^{94} +(4.02239 - 6.96699i) q^{95} +(11.9730 + 6.91261i) q^{97} +(-12.6205 - 7.28643i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + O(q^{10}) \) \( 8 q + 4 q^{4} - 4 q^{10} - 6 q^{11} - 12 q^{13} - 4 q^{14} - 4 q^{16} - 16 q^{17} - 6 q^{19} + 2 q^{22} - 4 q^{23} - 8 q^{25} + 12 q^{26} + 8 q^{29} - 2 q^{35} + 30 q^{37} - 8 q^{40} + 14 q^{43} - 6 q^{46} + 14 q^{49} - 6 q^{52} - 16 q^{53} - 2 q^{55} - 2 q^{56} - 6 q^{58} - 24 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} + 6 q^{65} + 24 q^{67} + 16 q^{68} + 12 q^{71} - 10 q^{74} - 6 q^{76} - 16 q^{77} - 20 q^{79} + 4 q^{82} - 2 q^{88} - 42 q^{89} - 10 q^{91} - 8 q^{92} - 8 q^{94} - 24 q^{97} - 48 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 4.02239 + 2.32233i 1.52032 + 0.877758i 0.999713 + 0.0239629i \(0.00762835\pi\)
0.520609 + 0.853795i \(0.325705\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −3.81062 + 2.20006i −1.14895 + 0.663344i −0.948630 0.316387i \(-0.897530\pi\)
−0.200316 + 0.979731i \(0.564197\pi\)
\(12\) 0 0
\(13\) −3.35432 + 1.32233i −0.930320 + 0.366748i
\(14\) −4.64466 −1.24134
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 0 0
\(19\) −6.96699 4.02239i −1.59834 0.922800i −0.991808 0.127739i \(-0.959228\pi\)
−0.606529 0.795061i \(-0.707439\pi\)
\(20\) 0.866025 + 0.500000i 0.193649 + 0.111803i
\(21\) 0 0
\(22\) 2.20006 3.81062i 0.469055 0.812427i
\(23\) 0.488292 + 0.845746i 0.101816 + 0.176350i 0.912433 0.409226i \(-0.134201\pi\)
−0.810617 + 0.585577i \(0.800868\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 2.24376 2.82233i 0.440037 0.553504i
\(27\) 0 0
\(28\) 4.02239 2.32233i 0.760161 0.438879i
\(29\) −2.15637 3.73494i −0.400427 0.693561i 0.593350 0.804945i \(-0.297805\pi\)
−0.993777 + 0.111384i \(0.964472\pi\)
\(30\) 0 0
\(31\) 6.44069i 1.15678i 0.815760 + 0.578391i \(0.196319\pi\)
−0.815760 + 0.578391i \(0.803681\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 4.00000i 0.685994i
\(35\) −2.32233 + 4.02239i −0.392545 + 0.679909i
\(36\) 0 0
\(37\) 3.28745 1.89801i 0.540454 0.312031i −0.204809 0.978802i \(-0.565657\pi\)
0.745263 + 0.666771i \(0.232324\pi\)
\(38\) 8.04479 1.30504
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) 6.31274 3.64466i 0.985884 0.569200i 0.0818424 0.996645i \(-0.473920\pi\)
0.904041 + 0.427445i \(0.140586\pi\)
\(42\) 0 0
\(43\) 0.358228 0.620469i 0.0546293 0.0946207i −0.837418 0.546564i \(-0.815936\pi\)
0.892047 + 0.451943i \(0.149269\pi\)
\(44\) 4.40013i 0.663344i
\(45\) 0 0
\(46\) −0.845746 0.488292i −0.124698 0.0719947i
\(47\) 9.75342i 1.42268i −0.702847 0.711341i \(-0.748088\pi\)
0.702847 0.711341i \(-0.251912\pi\)
\(48\) 0 0
\(49\) 7.28643 + 12.6205i 1.04092 + 1.80292i
\(50\) 0.866025 0.500000i 0.122474 0.0707107i
\(51\) 0 0
\(52\) −0.531987 + 3.56609i −0.0737734 + 0.494528i
\(53\) −13.5089 −1.85559 −0.927794 0.373092i \(-0.878297\pi\)
−0.927794 + 0.373092i \(0.878297\pi\)
\(54\) 0 0
\(55\) −2.20006 3.81062i −0.296656 0.513824i
\(56\) −2.32233 + 4.02239i −0.310334 + 0.537515i
\(57\) 0 0
\(58\) 3.73494 + 2.15637i 0.490421 + 0.283145i
\(59\) 1.88842 + 1.09028i 0.245851 + 0.141942i 0.617863 0.786286i \(-0.287999\pi\)
−0.372012 + 0.928228i \(0.621332\pi\)
\(60\) 0 0
\(61\) −3.73205 + 6.46410i −0.477840 + 0.827643i −0.999677 0.0254017i \(-0.991914\pi\)
0.521837 + 0.853045i \(0.325247\pi\)
\(62\) −3.22034 5.57780i −0.408984 0.708381i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −1.32233 3.35432i −0.164015 0.416052i
\(66\) 0 0
\(67\) −1.58068 + 0.912609i −0.193111 + 0.111493i −0.593438 0.804879i \(-0.702230\pi\)
0.400327 + 0.916372i \(0.368897\pi\)
\(68\) 2.00000 + 3.46410i 0.242536 + 0.420084i
\(69\) 0 0
\(70\) 4.64466i 0.555143i
\(71\) 6.88764 + 3.97658i 0.817413 + 0.471934i 0.849524 0.527551i \(-0.176890\pi\)
−0.0321105 + 0.999484i \(0.510223\pi\)
\(72\) 0 0
\(73\) 4.36112i 0.510430i −0.966884 0.255215i \(-0.917854\pi\)
0.966884 0.255215i \(-0.0821463\pi\)
\(74\) −1.89801 + 3.28745i −0.220640 + 0.382159i
\(75\) 0 0
\(76\) −6.96699 + 4.02239i −0.799168 + 0.461400i
\(77\) −20.4371 −2.32902
\(78\) 0 0
\(79\) −14.9340 −1.68020 −0.840102 0.542429i \(-0.817505\pi\)
−0.840102 + 0.542429i \(0.817505\pi\)
\(80\) 0.866025 0.500000i 0.0968246 0.0559017i
\(81\) 0 0
\(82\) −3.64466 + 6.31274i −0.402485 + 0.697125i
\(83\) 3.51093i 0.385375i −0.981260 0.192688i \(-0.938280\pi\)
0.981260 0.192688i \(-0.0617204\pi\)
\(84\) 0 0
\(85\) −3.46410 2.00000i −0.375735 0.216930i
\(86\) 0.716456i 0.0772575i
\(87\) 0 0
\(88\) −2.20006 3.81062i −0.234528 0.406214i
\(89\) −7.07780 + 4.08637i −0.750245 + 0.433154i −0.825782 0.563989i \(-0.809266\pi\)
0.0755374 + 0.997143i \(0.475933\pi\)
\(90\) 0 0
\(91\) −16.5633 2.47090i −1.73630 0.259021i
\(92\) 0.976584 0.101816
\(93\) 0 0
\(94\) 4.87671 + 8.44671i 0.502994 + 0.871212i
\(95\) 4.02239 6.96699i 0.412689 0.714798i
\(96\) 0 0
\(97\) 11.9730 + 6.91261i 1.21567 + 0.701869i 0.963989 0.265941i \(-0.0856825\pi\)
0.251683 + 0.967810i \(0.419016\pi\)
\(98\) −12.6205 7.28643i −1.27486 0.736041i
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 3.40013 + 5.88919i 0.338325 + 0.585997i 0.984118 0.177516i \(-0.0568063\pi\)
−0.645793 + 0.763513i \(0.723473\pi\)
\(102\) 0 0
\(103\) −5.29137 −0.521374 −0.260687 0.965423i \(-0.583949\pi\)
−0.260687 + 0.965423i \(0.583949\pi\)
\(104\) −1.32233 3.35432i −0.129665 0.328918i
\(105\) 0 0
\(106\) 11.6990 6.75444i 1.13631 0.656050i
\(107\) 8.46410 + 14.6603i 0.818256 + 1.41726i 0.906966 + 0.421203i \(0.138392\pi\)
−0.0887109 + 0.996057i \(0.528275\pi\)
\(108\) 0 0
\(109\) 12.8003i 1.22604i 0.790067 + 0.613021i \(0.210046\pi\)
−0.790067 + 0.613021i \(0.789954\pi\)
\(110\) 3.81062 + 2.20006i 0.363329 + 0.209768i
\(111\) 0 0
\(112\) 4.64466i 0.438879i
\(113\) 6.53308 11.3156i 0.614580 1.06448i −0.375878 0.926669i \(-0.622659\pi\)
0.990458 0.137815i \(-0.0440079\pi\)
\(114\) 0 0
\(115\) −0.845746 + 0.488292i −0.0788662 + 0.0455334i
\(116\) −4.31274 −0.400427
\(117\) 0 0
\(118\) −2.18056 −0.200737
\(119\) −16.0896 + 9.28932i −1.47493 + 0.851550i
\(120\) 0 0
\(121\) 4.18056 7.24094i 0.380051 0.658267i
\(122\) 7.46410i 0.675768i
\(123\) 0 0
\(124\) 5.57780 + 3.22034i 0.500901 + 0.289195i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 6.10978 + 10.5825i 0.542156 + 0.939041i 0.998780 + 0.0493816i \(0.0157250\pi\)
−0.456624 + 0.889660i \(0.650942\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 2.82233 + 2.24376i 0.247535 + 0.196791i
\(131\) 0.378757 0.0330921 0.0165461 0.999863i \(-0.494733\pi\)
0.0165461 + 0.999863i \(0.494733\pi\)
\(132\) 0 0
\(133\) −18.6826 32.3593i −1.61999 2.80591i
\(134\) 0.912609 1.58068i 0.0788374 0.136550i
\(135\) 0 0
\(136\) −3.46410 2.00000i −0.297044 0.171499i
\(137\) 1.08457 + 0.626177i 0.0926612 + 0.0534979i 0.545615 0.838036i \(-0.316296\pi\)
−0.452953 + 0.891534i \(0.649630\pi\)
\(138\) 0 0
\(139\) −1.67767 + 2.90581i −0.142298 + 0.246468i −0.928362 0.371678i \(-0.878783\pi\)
0.786064 + 0.618146i \(0.212116\pi\)
\(140\) 2.32233 + 4.02239i 0.196273 + 0.339954i
\(141\) 0 0
\(142\) −7.95317 −0.667415
\(143\) 9.87282 12.4186i 0.825607 1.03850i
\(144\) 0 0
\(145\) 3.73494 2.15637i 0.310170 0.179077i
\(146\) 2.18056 + 3.77684i 0.180464 + 0.312573i
\(147\) 0 0
\(148\) 3.79603i 0.312031i
\(149\) 4.00077 + 2.30985i 0.327756 + 0.189230i 0.654844 0.755764i \(-0.272734\pi\)
−0.327088 + 0.944994i \(0.606067\pi\)
\(150\) 0 0
\(151\) 11.2425i 0.914901i 0.889235 + 0.457450i \(0.151237\pi\)
−0.889235 + 0.457450i \(0.848763\pi\)
\(152\) 4.02239 6.96699i 0.326259 0.565097i
\(153\) 0 0
\(154\) 17.6990 10.2185i 1.42623 0.823434i
\(155\) −6.44069 −0.517328
\(156\) 0 0
\(157\) −1.50311 −0.119961 −0.0599807 0.998200i \(-0.519104\pi\)
−0.0599807 + 0.998200i \(0.519104\pi\)
\(158\) 12.9332 7.46699i 1.02891 0.594042i
\(159\) 0 0
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 4.53590i 0.357479i
\(162\) 0 0
\(163\) −0.152706 0.0881650i −0.0119609 0.00690561i 0.494008 0.869458i \(-0.335531\pi\)
−0.505969 + 0.862552i \(0.668865\pi\)
\(164\) 7.28932i 0.569200i
\(165\) 0 0
\(166\) 1.75547 + 3.04056i 0.136251 + 0.235993i
\(167\) −7.51851 + 4.34081i −0.581800 + 0.335902i −0.761848 0.647756i \(-0.775708\pi\)
0.180049 + 0.983658i \(0.442374\pi\)
\(168\) 0 0
\(169\) 9.50289 8.87103i 0.730991 0.682387i
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) −0.358228 0.620469i −0.0273146 0.0473103i
\(173\) −0.890216 + 1.54190i −0.0676818 + 0.117228i −0.897880 0.440239i \(-0.854894\pi\)
0.830199 + 0.557468i \(0.188227\pi\)
\(174\) 0 0
\(175\) −4.02239 2.32233i −0.304064 0.175552i
\(176\) 3.81062 + 2.20006i 0.287236 + 0.165836i
\(177\) 0 0
\(178\) 4.08637 7.07780i 0.306286 0.530503i
\(179\) 8.70786 + 15.0825i 0.650856 + 1.12732i 0.982916 + 0.184057i \(0.0589232\pi\)
−0.332059 + 0.943258i \(0.607743\pi\)
\(180\) 0 0
\(181\) −10.3611 −0.770136 −0.385068 0.922888i \(-0.625822\pi\)
−0.385068 + 0.922888i \(0.625822\pi\)
\(182\) 15.5797 6.14177i 1.15484 0.455258i
\(183\) 0 0
\(184\) −0.845746 + 0.488292i −0.0623492 + 0.0359973i
\(185\) 1.89801 + 3.28745i 0.139545 + 0.241698i
\(186\) 0 0
\(187\) 17.6005i 1.28708i
\(188\) −8.44671 4.87671i −0.616040 0.355671i
\(189\) 0 0
\(190\) 8.04479i 0.583630i
\(191\) −0.448507 + 0.776837i −0.0324528 + 0.0562100i −0.881796 0.471632i \(-0.843665\pi\)
0.849343 + 0.527842i \(0.176999\pi\)
\(192\) 0 0
\(193\) 17.5494 10.1322i 1.26324 0.729330i 0.289537 0.957167i \(-0.406499\pi\)
0.973699 + 0.227837i \(0.0731652\pi\)
\(194\) −13.8252 −0.992593
\(195\) 0 0
\(196\) 14.5729 1.04092
\(197\) −7.95060 + 4.59028i −0.566457 + 0.327044i −0.755733 0.654880i \(-0.772719\pi\)
0.189276 + 0.981924i \(0.439386\pi\)
\(198\) 0 0
\(199\) −8.10876 + 14.0448i −0.574815 + 0.995609i 0.421247 + 0.906946i \(0.361593\pi\)
−0.996062 + 0.0886625i \(0.971741\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) −5.88919 3.40013i −0.414362 0.239232i
\(203\) 20.0312i 1.40591i
\(204\) 0 0
\(205\) 3.64466 + 6.31274i 0.254554 + 0.440901i
\(206\) 4.58246 2.64568i 0.319275 0.184333i
\(207\) 0 0
\(208\) 2.82233 + 2.24376i 0.195693 + 0.155577i
\(209\) 35.3981 2.44854
\(210\) 0 0
\(211\) 0.809848 + 1.40270i 0.0557522 + 0.0965657i 0.892555 0.450939i \(-0.148911\pi\)
−0.836802 + 0.547505i \(0.815578\pi\)
\(212\) −6.75444 + 11.6990i −0.463897 + 0.803493i
\(213\) 0 0
\(214\) −14.6603 8.46410i −1.00215 0.578594i
\(215\) 0.620469 + 0.358228i 0.0423157 + 0.0244310i
\(216\) 0 0
\(217\) −14.9574 + 25.9070i −1.01537 + 1.75868i
\(218\) −6.40013 11.0853i −0.433471 0.750794i
\(219\) 0 0
\(220\) −4.40013 −0.296656
\(221\) 2.12795 14.2644i 0.143141 0.959524i
\(222\) 0 0
\(223\) 1.93705 1.11836i 0.129714 0.0748906i −0.433739 0.901039i \(-0.642806\pi\)
0.563453 + 0.826148i \(0.309473\pi\)
\(224\) 2.32233 + 4.02239i 0.155167 + 0.268757i
\(225\) 0 0
\(226\) 13.0662i 0.869148i
\(227\) 13.2679 + 7.66025i 0.880625 + 0.508429i 0.870864 0.491523i \(-0.163560\pi\)
0.00976038 + 0.999952i \(0.496893\pi\)
\(228\) 0 0
\(229\) 10.1279i 0.669274i −0.942347 0.334637i \(-0.891386\pi\)
0.942347 0.334637i \(-0.108614\pi\)
\(230\) 0.488292 0.845746i 0.0321970 0.0557669i
\(231\) 0 0
\(232\) 3.73494 2.15637i 0.245211 0.141572i
\(233\) −20.7519 −1.35950 −0.679750 0.733444i \(-0.737912\pi\)
−0.679750 + 0.733444i \(0.737912\pi\)
\(234\) 0 0
\(235\) 9.75342 0.636243
\(236\) 1.88842 1.09028i 0.122926 0.0709711i
\(237\) 0 0
\(238\) 9.28932 16.0896i 0.602137 1.04293i
\(239\) 24.3539i 1.57532i 0.616107 + 0.787662i \(0.288709\pi\)
−0.616107 + 0.787662i \(0.711291\pi\)
\(240\) 0 0
\(241\) −17.2066 9.93423i −1.10837 0.639920i −0.169966 0.985450i \(-0.554366\pi\)
−0.938408 + 0.345530i \(0.887699\pi\)
\(242\) 8.36112i 0.537473i
\(243\) 0 0
\(244\) 3.73205 + 6.46410i 0.238920 + 0.413822i
\(245\) −12.6205 + 7.28643i −0.806292 + 0.465513i
\(246\) 0 0
\(247\) 28.6884 + 4.27973i 1.82540 + 0.272312i
\(248\) −6.44069 −0.408984
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) −6.78566 + 11.7531i −0.428307 + 0.741849i −0.996723 0.0808920i \(-0.974223\pi\)
0.568416 + 0.822741i \(0.307556\pi\)
\(252\) 0 0
\(253\) −3.72139 2.14855i −0.233962 0.135078i
\(254\) −10.5825 6.10978i −0.664002 0.383362i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.331150 0.573569i −0.0206566 0.0357783i 0.855512 0.517782i \(-0.173242\pi\)
−0.876169 + 0.482004i \(0.839909\pi\)
\(258\) 0 0
\(259\) 17.6312 1.09555
\(260\) −3.56609 0.531987i −0.221159 0.0329925i
\(261\) 0 0
\(262\) −0.328013 + 0.189378i −0.0202647 + 0.0116998i
\(263\) 15.3749 + 26.6301i 0.948058 + 1.64208i 0.749510 + 0.661993i \(0.230289\pi\)
0.198548 + 0.980091i \(0.436377\pi\)
\(264\) 0 0
\(265\) 13.5089i 0.829844i
\(266\) 32.3593 + 18.6826i 1.98408 + 1.14551i
\(267\) 0 0
\(268\) 1.82522i 0.111493i
\(269\) −1.87205 + 3.24249i −0.114141 + 0.197698i −0.917436 0.397883i \(-0.869745\pi\)
0.803295 + 0.595581i \(0.203078\pi\)
\(270\) 0 0
\(271\) 24.0419 13.8806i 1.46044 0.843186i 0.461410 0.887187i \(-0.347344\pi\)
0.999031 + 0.0440009i \(0.0140104\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) −1.25235 −0.0756575
\(275\) 3.81062 2.20006i 0.229789 0.132669i
\(276\) 0 0
\(277\) 5.99609 10.3855i 0.360270 0.624006i −0.627735 0.778427i \(-0.716018\pi\)
0.988005 + 0.154421i \(0.0493512\pi\)
\(278\) 3.35534i 0.201240i
\(279\) 0 0
\(280\) −4.02239 2.32233i −0.240384 0.138786i
\(281\) 3.63888i 0.217078i −0.994092 0.108539i \(-0.965383\pi\)
0.994092 0.108539i \(-0.0346172\pi\)
\(282\) 0 0
\(283\) 2.42220 + 4.19538i 0.143985 + 0.249389i 0.928994 0.370095i \(-0.120675\pi\)
−0.785009 + 0.619485i \(0.787342\pi\)
\(284\) 6.88764 3.97658i 0.408707 0.235967i
\(285\) 0 0
\(286\) −2.34081 + 15.6912i −0.138415 + 0.927843i
\(287\) 33.8564 1.99848
\(288\) 0 0
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) −2.15637 + 3.73494i −0.126626 + 0.219323i
\(291\) 0 0
\(292\) −3.77684 2.18056i −0.221023 0.127608i
\(293\) −3.20500 1.85041i −0.187238 0.108102i 0.403451 0.915001i \(-0.367811\pi\)
−0.590689 + 0.806899i \(0.701144\pi\)
\(294\) 0 0
\(295\) −1.09028 + 1.88842i −0.0634785 + 0.109948i
\(296\) 1.89801 + 3.28745i 0.110320 + 0.191079i
\(297\) 0 0
\(298\) −4.61970 −0.267612
\(299\) −2.75624 2.19122i −0.159398 0.126721i
\(300\) 0 0
\(301\) 2.88187 1.66385i 0.166108 0.0959026i
\(302\) −5.62124 9.73628i −0.323466 0.560260i
\(303\) 0 0
\(304\) 8.04479i 0.461400i
\(305\) −6.46410 3.73205i −0.370133 0.213697i
\(306\) 0 0
\(307\) 7.11454i 0.406048i −0.979174 0.203024i \(-0.934923\pi\)
0.979174 0.203024i \(-0.0650770\pi\)
\(308\) −10.2185 + 17.6990i −0.582256 + 1.00850i
\(309\) 0 0
\(310\) 5.57780 3.22034i 0.316798 0.182903i
\(311\) 19.9148 1.12926 0.564632 0.825343i \(-0.309018\pi\)
0.564632 + 0.825343i \(0.309018\pi\)
\(312\) 0 0
\(313\) 6.13950 0.347025 0.173513 0.984832i \(-0.444488\pi\)
0.173513 + 0.984832i \(0.444488\pi\)
\(314\) 1.30173 0.751556i 0.0734611 0.0424128i
\(315\) 0 0
\(316\) −7.46699 + 12.9332i −0.420051 + 0.727550i
\(317\) 7.85286i 0.441061i −0.975380 0.220530i \(-0.929221\pi\)
0.975380 0.220530i \(-0.0707788\pi\)
\(318\) 0 0
\(319\) 16.4342 + 9.48829i 0.920139 + 0.531242i
\(320\) 1.00000i 0.0559017i
\(321\) 0 0
\(322\) −2.26795 3.92820i −0.126388 0.218910i
\(323\) 27.8680 16.0896i 1.55061 0.895248i
\(324\) 0 0
\(325\) 3.35432 1.32233i 0.186064 0.0733497i
\(326\) 0.176330 0.00976601
\(327\) 0 0
\(328\) 3.64466 + 6.31274i 0.201243 + 0.348563i
\(329\) 22.6507 39.2321i 1.24877 2.16294i
\(330\) 0 0
\(331\) 27.7093 + 15.9980i 1.52304 + 0.879327i 0.999629 + 0.0272463i \(0.00867385\pi\)
0.523410 + 0.852081i \(0.324659\pi\)
\(332\) −3.04056 1.75547i −0.166872 0.0963438i
\(333\) 0 0
\(334\) 4.34081 7.51851i 0.237519 0.411394i
\(335\) −0.912609 1.58068i −0.0498611 0.0863620i
\(336\) 0 0
\(337\) −35.6432 −1.94161 −0.970806 0.239867i \(-0.922896\pi\)
−0.970806 + 0.239867i \(0.922896\pi\)
\(338\) −3.79423 + 12.4340i −0.206379 + 0.676319i
\(339\) 0 0
\(340\) −3.46410 + 2.00000i −0.187867 + 0.108465i
\(341\) −14.1699 24.5430i −0.767344 1.32908i
\(342\) 0 0
\(343\) 35.1734i 1.89918i
\(344\) 0.620469 + 0.358228i 0.0334535 + 0.0193144i
\(345\) 0 0
\(346\) 1.78043i 0.0957166i
\(347\) −3.44851 + 5.97299i −0.185126 + 0.320647i −0.943619 0.331034i \(-0.892603\pi\)
0.758493 + 0.651681i \(0.225936\pi\)
\(348\) 0 0
\(349\) 16.7321 9.66025i 0.895646 0.517102i 0.0198610 0.999803i \(-0.493678\pi\)
0.875785 + 0.482701i \(0.160344\pi\)
\(350\) 4.64466 0.248267
\(351\) 0 0
\(352\) −4.40013 −0.234528
\(353\) 23.7441 13.7086i 1.26377 0.729637i 0.289967 0.957037i \(-0.406356\pi\)
0.973802 + 0.227400i \(0.0730224\pi\)
\(354\) 0 0
\(355\) −3.97658 + 6.88764i −0.211055 + 0.365558i
\(356\) 8.17274i 0.433154i
\(357\) 0 0
\(358\) −15.0825 8.70786i −0.797133 0.460225i
\(359\) 14.3611i 0.757951i −0.925407 0.378975i \(-0.876277\pi\)
0.925407 0.378975i \(-0.123723\pi\)
\(360\) 0 0
\(361\) 22.8593 + 39.5935i 1.20312 + 2.08387i
\(362\) 8.97299 5.18056i 0.471610 0.272284i
\(363\) 0 0
\(364\) −10.4215 + 13.1088i −0.546235 + 0.687086i
\(365\) 4.36112 0.228271
\(366\) 0 0
\(367\) 6.88764 + 11.9298i 0.359532 + 0.622728i 0.987883 0.155202i \(-0.0496030\pi\)
−0.628351 + 0.777930i \(0.716270\pi\)
\(368\) 0.488292 0.845746i 0.0254540 0.0440876i
\(369\) 0 0
\(370\) −3.28745 1.89801i −0.170907 0.0986730i
\(371\) −54.3381 31.3721i −2.82109 1.62876i
\(372\) 0 0
\(373\) 16.7313 28.9795i 0.866316 1.50050i 0.000581860 1.00000i \(-0.499815\pi\)
0.865734 0.500504i \(-0.166852\pi\)
\(374\) 8.80025 + 15.2425i 0.455050 + 0.788170i
\(375\) 0 0
\(376\) 9.75342 0.502994
\(377\) 12.1720 + 9.67674i 0.626888 + 0.498377i
\(378\) 0 0
\(379\) −28.9052 + 16.6884i −1.48476 + 0.857227i −0.999850 0.0173371i \(-0.994481\pi\)
−0.484910 + 0.874564i \(0.661148\pi\)
\(380\) −4.02239 6.96699i −0.206344 0.357399i
\(381\) 0 0
\(382\) 0.897014i 0.0458952i
\(383\) −6.34829 3.66519i −0.324383 0.187282i 0.328962 0.944343i \(-0.393301\pi\)
−0.653344 + 0.757061i \(0.726635\pi\)
\(384\) 0 0
\(385\) 20.4371i 1.04157i
\(386\) −10.1322 + 17.5494i −0.515714 + 0.893243i
\(387\) 0 0
\(388\) 11.9730 6.91261i 0.607836 0.350935i
\(389\) 32.6198 1.65389 0.826946 0.562282i \(-0.190076\pi\)
0.826946 + 0.562282i \(0.190076\pi\)
\(390\) 0 0
\(391\) −3.90633 −0.197552
\(392\) −12.6205 + 7.28643i −0.637430 + 0.368020i
\(393\) 0 0
\(394\) 4.59028 7.95060i 0.231255 0.400545i
\(395\) 14.9340i 0.751410i
\(396\) 0 0
\(397\) 12.5299 + 7.23416i 0.628860 + 0.363072i 0.780310 0.625392i \(-0.215061\pi\)
−0.151451 + 0.988465i \(0.548394\pi\)
\(398\) 16.2175i 0.812911i
\(399\) 0 0
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) 6.31096 3.64364i 0.315154 0.181955i −0.334076 0.942546i \(-0.608424\pi\)
0.649231 + 0.760592i \(0.275091\pi\)
\(402\) 0 0
\(403\) −8.51671 21.6041i −0.424248 1.07618i
\(404\) 6.80025 0.338325
\(405\) 0 0
\(406\) 10.0156 + 17.3475i 0.497066 + 0.860943i
\(407\) −8.35150 + 14.4652i −0.413968 + 0.717014i
\(408\) 0 0
\(409\) −21.2840 12.2883i −1.05242 0.607617i −0.129097 0.991632i \(-0.541208\pi\)
−0.923327 + 0.384015i \(0.874541\pi\)
\(410\) −6.31274 3.64466i −0.311764 0.179997i
\(411\) 0 0
\(412\) −2.64568 + 4.58246i −0.130343 + 0.225761i
\(413\) 5.06397 + 8.77106i 0.249182 + 0.431596i
\(414\) 0 0
\(415\) 3.51093 0.172345
\(416\) −3.56609 0.531987i −0.174842 0.0260828i
\(417\) 0 0
\(418\) −30.6556 + 17.6990i −1.49942 + 0.865688i
\(419\) 7.77684 + 13.4699i 0.379923 + 0.658047i 0.991051 0.133486i \(-0.0426170\pi\)
−0.611127 + 0.791532i \(0.709284\pi\)
\(420\) 0 0
\(421\) 22.3143i 1.08753i −0.839237 0.543766i \(-0.816998\pi\)
0.839237 0.543766i \(-0.183002\pi\)
\(422\) −1.40270 0.809848i −0.0682822 0.0394228i
\(423\) 0 0
\(424\) 13.5089i 0.656050i
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) 0 0
\(427\) −30.0236 + 17.3341i −1.45294 + 0.838856i
\(428\) 16.9282 0.818256
\(429\) 0 0
\(430\) −0.716456 −0.0345506
\(431\) −21.0135 + 12.1322i −1.01219 + 0.584386i −0.911831 0.410565i \(-0.865331\pi\)
−0.100356 + 0.994952i \(0.531998\pi\)
\(432\) 0 0
\(433\) −11.5494 + 20.0042i −0.555031 + 0.961342i 0.442870 + 0.896586i \(0.353960\pi\)
−0.997901 + 0.0647561i \(0.979373\pi\)
\(434\) 29.9148i 1.43596i
\(435\) 0 0
\(436\) 11.0853 + 6.40013i 0.530892 + 0.306510i
\(437\) 7.85641i 0.375823i
\(438\) 0 0
\(439\) −19.9980 34.6375i −0.954450 1.65316i −0.735621 0.677393i \(-0.763110\pi\)
−0.218829 0.975763i \(-0.570224\pi\)
\(440\) 3.81062 2.20006i 0.181664 0.104884i
\(441\) 0 0
\(442\) 5.28932 + 13.4173i 0.251587 + 0.638194i
\(443\) 15.6036 0.741350 0.370675 0.928763i \(-0.379126\pi\)
0.370675 + 0.928763i \(0.379126\pi\)
\(444\) 0 0
\(445\) −4.08637 7.07780i −0.193712 0.335520i
\(446\) −1.11836 + 1.93705i −0.0529557 + 0.0917219i
\(447\) 0 0
\(448\) −4.02239 2.32233i −0.190040 0.109720i
\(449\) −23.3863 13.5021i −1.10367 0.637203i −0.166486 0.986044i \(-0.553242\pi\)
−0.937182 + 0.348841i \(0.886575\pi\)
\(450\) 0 0
\(451\) −16.0370 + 27.7768i −0.755151 + 1.30796i
\(452\) −6.53308 11.3156i −0.307290 0.532242i
\(453\) 0 0
\(454\) −15.3205 −0.719027
\(455\) 2.47090 16.5633i 0.115838 0.776498i
\(456\) 0 0
\(457\) 15.4039 8.89342i 0.720562 0.416017i −0.0943975 0.995535i \(-0.530092\pi\)
0.814959 + 0.579518i \(0.196759\pi\)
\(458\) 5.06397 + 8.77106i 0.236624 + 0.409845i
\(459\) 0 0
\(460\) 0.976584i 0.0455334i
\(461\) −21.6205 12.4826i −1.00697 0.581372i −0.0966638 0.995317i \(-0.530817\pi\)
−0.910302 + 0.413945i \(0.864151\pi\)
\(462\) 0 0
\(463\) 15.6389i 0.726801i 0.931633 + 0.363400i \(0.118384\pi\)
−0.931633 + 0.363400i \(0.881616\pi\)
\(464\) −2.15637 + 3.73494i −0.100107 + 0.173390i
\(465\) 0 0
\(466\) 17.9716 10.3759i 0.832521 0.480656i
\(467\) 2.43914 0.112870 0.0564349 0.998406i \(-0.482027\pi\)
0.0564349 + 0.998406i \(0.482027\pi\)
\(468\) 0 0
\(469\) −8.47751 −0.391455
\(470\) −8.44671 + 4.87671i −0.389618 + 0.224946i
\(471\) 0 0
\(472\) −1.09028 + 1.88842i −0.0501842 + 0.0869215i
\(473\) 3.15250i 0.144952i
\(474\) 0 0
\(475\) 6.96699 + 4.02239i 0.319667 + 0.184560i
\(476\) 18.5786i 0.851550i
\(477\) 0 0
\(478\) −12.1770 21.0911i −0.556961 0.964685i
\(479\) −12.2857 + 7.09317i −0.561349 + 0.324095i −0.753687 0.657234i \(-0.771726\pi\)
0.192338 + 0.981329i \(0.438393\pi\)
\(480\) 0 0
\(481\) −8.51737 + 10.7136i −0.388358 + 0.488500i
\(482\) 19.8685 0.904983
\(483\) 0 0
\(484\) −4.18056 7.24094i −0.190025 0.329134i
\(485\) −6.91261 + 11.9730i −0.313885 + 0.543665i
\(486\) 0 0
\(487\) 4.99115 + 2.88164i 0.226171 + 0.130580i 0.608804 0.793320i \(-0.291649\pi\)
−0.382633 + 0.923900i \(0.624983\pi\)
\(488\) −6.46410 3.73205i −0.292616 0.168942i
\(489\) 0 0
\(490\) 7.28643 12.6205i 0.329167 0.570135i
\(491\) 0.537671 + 0.931273i 0.0242647 + 0.0420278i 0.877903 0.478839i \(-0.158942\pi\)
−0.853638 + 0.520867i \(0.825609\pi\)
\(492\) 0 0
\(493\) 17.2509 0.776943
\(494\) −26.9848 + 10.6379i −1.21410 + 0.478620i
\(495\) 0 0
\(496\) 5.57780 3.22034i 0.250450 0.144598i
\(497\) 18.4699 + 31.9908i 0.828487 + 1.43498i
\(498\) 0 0
\(499\) 14.7534i 0.660454i 0.943902 + 0.330227i \(0.107125\pi\)
−0.943902 + 0.330227i \(0.892875\pi\)
\(500\) −0.866025 0.500000i −0.0387298 0.0223607i
\(501\) 0 0
\(502\) 13.5713i 0.605717i
\(503\) −13.3309 + 23.0898i −0.594395 + 1.02952i 0.399236 + 0.916848i \(0.369275\pi\)
−0.993632 + 0.112675i \(0.964058\pi\)
\(504\) 0 0
\(505\) −5.88919 + 3.40013i −0.262066 + 0.151304i
\(506\) 4.29709 0.191029
\(507\) 0 0
\(508\) 12.2196 0.542156
\(509\) −12.2807 + 7.09028i −0.544333 + 0.314271i −0.746833 0.665011i \(-0.768427\pi\)
0.202500 + 0.979282i \(0.435093\pi\)
\(510\) 0 0
\(511\) 10.1279 17.5421i 0.448034 0.776018i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 0.573569 + 0.331150i 0.0252990 + 0.0146064i
\(515\) 5.29137i 0.233165i
\(516\) 0 0
\(517\) 21.4581 + 37.1666i 0.943728 + 1.63459i
\(518\) −15.2691 + 8.81562i −0.670886 + 0.387336i
\(519\) 0 0
\(520\) 3.35432 1.32233i 0.147097 0.0579880i
\(521\) −23.7476 −1.04040 −0.520202 0.854043i \(-0.674143\pi\)
−0.520202 + 0.854043i \(0.674143\pi\)
\(522\) 0 0
\(523\) −6.92532 11.9950i −0.302823 0.524505i 0.673951 0.738776i \(-0.264596\pi\)
−0.976774 + 0.214271i \(0.931262\pi\)
\(524\) 0.189378 0.328013i 0.00827303 0.0143293i
\(525\) 0 0
\(526\) −26.6301 15.3749i −1.16113 0.670378i
\(527\) −22.3112 12.8814i −0.971891 0.561121i
\(528\) 0 0
\(529\) 11.0231 19.0926i 0.479267 0.830115i
\(530\) 6.75444 + 11.6990i 0.293394 + 0.508174i
\(531\) 0 0
\(532\) −37.3653 −1.61999
\(533\) −16.3555 + 20.5729i −0.708434 + 0.891110i
\(534\) 0 0
\(535\) −14.6603 + 8.46410i −0.633818 + 0.365935i
\(536\) −0.912609 1.58068i −0.0394187 0.0682752i
\(537\) 0 0
\(538\) 3.74410i 0.161420i
\(539\) −55.5317 32.0612i −2.39192 1.38097i
\(540\) 0 0
\(541\) 14.8898i 0.640164i 0.947390 + 0.320082i \(0.103710\pi\)
−0.947390 + 0.320082i \(0.896290\pi\)
\(542\) −13.8806 + 24.0419i −0.596223 + 1.03269i
\(543\) 0 0
\(544\) −3.46410 + 2.00000i −0.148522 + 0.0857493i
\(545\) −12.8003 −0.548303
\(546\) 0 0
\(547\) −22.2019 −0.949284 −0.474642 0.880179i \(-0.657422\pi\)
−0.474642 + 0.880179i \(0.657422\pi\)
\(548\) 1.08457 0.626177i 0.0463306 0.0267490i
\(549\) 0 0
\(550\) −2.20006 + 3.81062i −0.0938110 + 0.162485i
\(551\) 34.6950i 1.47806i
\(552\) 0 0
\(553\) −60.0703 34.6816i −2.55445 1.47481i
\(554\) 11.9922i 0.509499i
\(555\) 0 0
\(556\) 1.67767 + 2.90581i 0.0711491 + 0.123234i
\(557\) −1.64518 + 0.949847i −0.0697087 + 0.0402463i −0.534449 0.845201i \(-0.679481\pi\)
0.464741 + 0.885447i \(0.346148\pi\)
\(558\) 0 0
\(559\) −0.381146 + 2.55495i −0.0161207 + 0.108063i
\(560\) 4.64466 0.196273
\(561\) 0 0
\(562\) 1.81944 + 3.15137i 0.0767485 + 0.132932i
\(563\) 0.860000 1.48956i 0.0362447 0.0627777i −0.847334 0.531060i \(-0.821794\pi\)
0.883579 + 0.468283i \(0.155127\pi\)
\(564\) 0 0
\(565\) 11.3156 + 6.53308i 0.476052 + 0.274849i
\(566\) −4.19538 2.42220i −0.176345 0.101813i
\(567\) 0 0
\(568\) −3.97658 + 6.88764i −0.166854 + 0.288999i
\(569\) 0.300960 + 0.521278i 0.0126169 + 0.0218531i 0.872265 0.489034i \(-0.162650\pi\)
−0.859648 + 0.510887i \(0.829317\pi\)
\(570\) 0 0
\(571\) 11.9808 0.501381 0.250691 0.968067i \(-0.419342\pi\)
0.250691 + 0.968067i \(0.419342\pi\)
\(572\) −5.81842 14.7594i −0.243280 0.617122i
\(573\) 0 0
\(574\) −29.3205 + 16.9282i −1.22381 + 0.706570i
\(575\) −0.488292 0.845746i −0.0203632 0.0352701i
\(576\) 0 0
\(577\) 43.0293i 1.79133i −0.444725 0.895667i \(-0.646699\pi\)
0.444725 0.895667i \(-0.353301\pi\)
\(578\) −0.866025 0.500000i −0.0360219 0.0207973i
\(579\) 0 0
\(580\) 4.31274i 0.179077i
\(581\) 8.15355 14.1224i 0.338266 0.585894i
\(582\) 0 0
\(583\) 51.4773 29.7204i 2.13197 1.23089i
\(584\) 4.36112 0.180464
\(585\) 0 0
\(586\) 3.70081 0.152879
\(587\) 15.5147 8.95740i 0.640359 0.369711i −0.144394 0.989520i \(-0.546123\pi\)
0.784753 + 0.619809i \(0.212790\pi\)
\(588\) 0 0
\(589\) 25.9070 44.8722i 1.06748 1.84893i
\(590\) 2.18056i 0.0897722i
\(591\) 0 0
\(592\) −3.28745 1.89801i −0.135114 0.0780078i
\(593\) 0.669624i 0.0274981i −0.999905 0.0137491i \(-0.995623\pi\)
0.999905 0.0137491i \(-0.00437660\pi\)
\(594\) 0 0
\(595\) −9.28932 16.0896i −0.380825 0.659608i
\(596\) 4.00077 2.30985i 0.163878 0.0946151i
\(597\) 0 0
\(598\) 3.48258 + 0.519530i 0.142413 + 0.0212452i
\(599\) −1.29241 −0.0528066 −0.0264033 0.999651i \(-0.508405\pi\)
−0.0264033 + 0.999651i \(0.508405\pi\)
\(600\) 0 0
\(601\) 5.73671 + 9.93627i 0.234005 + 0.405309i 0.958983 0.283463i \(-0.0914834\pi\)
−0.724978 + 0.688772i \(0.758150\pi\)
\(602\) −1.66385 + 2.88187i −0.0678134 + 0.117456i
\(603\) 0 0
\(604\) 9.73628 + 5.62124i 0.396164 + 0.228725i
\(605\) 7.24094 + 4.18056i 0.294386 + 0.169964i
\(606\) 0 0
\(607\) 12.0672 20.9010i 0.489792 0.848344i −0.510139 0.860092i \(-0.670406\pi\)
0.999931 + 0.0117477i \(0.00373949\pi\)
\(608\) −4.02239 6.96699i −0.163130 0.282549i
\(609\) 0 0
\(610\) 7.46410 0.302213
\(611\) 12.8972 + 32.7161i 0.521766 + 1.32355i
\(612\) 0 0
\(613\) 25.0716 14.4751i 1.01263 0.584644i 0.100671 0.994920i \(-0.467901\pi\)
0.911961 + 0.410276i \(0.134568\pi\)
\(614\) 3.55727 + 6.16137i 0.143560 + 0.248653i
\(615\) 0 0
\(616\) 20.4371i 0.823434i
\(617\) 0.728597 + 0.420655i 0.0293322 + 0.0169349i 0.514594 0.857434i \(-0.327943\pi\)
−0.485262 + 0.874369i \(0.661276\pi\)
\(618\) 0 0
\(619\) 6.25076i 0.251239i −0.992078 0.125620i \(-0.959908\pi\)
0.992078 0.125620i \(-0.0400919\pi\)
\(620\) −3.22034 + 5.57780i −0.129332 + 0.224010i
\(621\) 0 0
\(622\) −17.2467 + 9.95740i −0.691530 + 0.399255i
\(623\) −37.9596 −1.52082
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −5.31696 + 3.06975i −0.212509 + 0.122692i
\(627\) 0 0
\(628\) −0.751556 + 1.30173i −0.0299904 + 0.0519448i
\(629\) 15.1841i 0.605430i
\(630\) 0 0
\(631\) 2.61970 + 1.51248i 0.104288 + 0.0602110i 0.551237 0.834349i \(-0.314156\pi\)
−0.446949 + 0.894560i \(0.647489\pi\)
\(632\) 14.9340i 0.594042i
\(633\) 0 0
\(634\) 3.92643 + 6.80078i 0.155938 + 0.270093i
\(635\) −10.5825 + 6.10978i −0.419952 + 0.242459i
\(636\) 0 0
\(637\) −41.1294 32.6980i −1.62961 1.29554i
\(638\) −18.9766 −0.751290
\(639\) 0 0
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −0.386305 + 0.669099i −0.0152581 + 0.0264278i −0.873554 0.486728i \(-0.838190\pi\)
0.858296 + 0.513156i \(0.171524\pi\)
\(642\) 0 0
\(643\) 16.7788 + 9.68726i 0.661693 + 0.382028i 0.792922 0.609324i \(-0.208559\pi\)
−0.131229 + 0.991352i \(0.541892\pi\)
\(644\) 3.92820 + 2.26795i 0.154793 + 0.0893697i
\(645\) 0 0
\(646\) −16.0896 + 27.8680i −0.633036 + 1.09645i
\(647\) 13.5953 + 23.5477i 0.534485 + 0.925755i 0.999188 + 0.0402882i \(0.0128276\pi\)
−0.464703 + 0.885466i \(0.653839\pi\)
\(648\) 0 0
\(649\) −9.59473 −0.376626
\(650\) −2.24376 + 2.82233i −0.0880075 + 0.110701i
\(651\) 0 0
\(652\) −0.152706 + 0.0881650i −0.00598044 + 0.00345281i
\(653\) 7.89799 + 13.6797i 0.309072 + 0.535329i 0.978160 0.207855i \(-0.0666482\pi\)
−0.669088 + 0.743184i \(0.733315\pi\)
\(654\) 0 0
\(655\) 0.378757i 0.0147993i
\(656\) −6.31274 3.64466i −0.246471 0.142300i
\(657\) 0 0
\(658\) 45.3013i 1.76603i
\(659\) 15.2381 26.3932i 0.593593 1.02813i −0.400151 0.916449i \(-0.631042\pi\)
0.993744 0.111684i \(-0.0356243\pi\)
\(660\) 0 0
\(661\) −24.1514 + 13.9438i −0.939379 + 0.542351i −0.889766 0.456418i \(-0.849132\pi\)
−0.0496136 + 0.998768i \(0.515799\pi\)
\(662\) −31.9959 −1.24356
\(663\) 0 0
\(664\) 3.51093 0.136251
\(665\) 32.3593 18.6826i 1.25484 0.724482i
\(666\) 0 0
\(667\) 2.10587 3.64748i 0.0815397 0.141231i
\(668\) 8.68162i 0.335902i
\(669\) 0 0
\(670\) 1.58068 + 0.912609i 0.0610672 + 0.0352572i
\(671\) 32.8430i 1.26789i
\(672\) 0 0
\(673\) −0.489066 0.847086i −0.0188521 0.0326528i 0.856445 0.516238i \(-0.172668\pi\)
−0.875298 + 0.483585i \(0.839334\pi\)
\(674\) 30.8680 17.8216i 1.18899 0.686463i
\(675\) 0 0
\(676\) −2.93109 12.6653i −0.112734 0.487125i
\(677\) 19.1926 0.737630 0.368815 0.929503i \(-0.379764\pi\)
0.368815 + 0.929503i \(0.379764\pi\)
\(678\) 0 0
\(679\) 32.1067 + 55.6105i 1.23214 + 2.13413i
\(680\) 2.00000 3.46410i 0.0766965 0.132842i
\(681\) 0 0
\(682\) 24.5430 + 14.1699i 0.939801 + 0.542594i
\(683\) 1.30851 + 0.755467i 0.0500687 + 0.0289071i 0.524825 0.851210i \(-0.324131\pi\)
−0.474757 + 0.880117i \(0.657464\pi\)
\(684\) 0 0
\(685\) −0.626177 + 1.08457i −0.0239250 + 0.0414393i
\(686\) −17.5867 30.4610i −0.671463 1.16301i
\(687\) 0 0
\(688\) −0.716456 −0.0273146
\(689\) 45.3131 17.8632i 1.72629 0.680534i
\(690\) 0 0
\(691\) 28.6798 16.5583i 1.09103 0.629907i 0.157180 0.987570i \(-0.449760\pi\)
0.933851 + 0.357663i \(0.116426\pi\)
\(692\) 0.890216 + 1.54190i 0.0338409 + 0.0586142i
\(693\) 0 0
\(694\) 6.89701i 0.261807i
\(695\) −2.90581 1.67767i −0.110224 0.0636377i
\(696\) 0 0
\(697\) 29.1573i 1.10441i
\(698\) −9.66025 + 16.7321i −0.365646 + 0.633317i
\(699\) 0 0
\(700\) −4.02239 + 2.32233i −0.152032 + 0.0877758i
\(701\) −27.8695 −1.05262 −0.526308 0.850294i \(-0.676424\pi\)
−0.526308 + 0.850294i \(0.676424\pi\)
\(702\) 0 0
\(703\) −30.5382 −1.15177
\(704\) 3.81062 2.20006i 0.143618 0.0829180i
\(705\) 0 0
\(706\) −13.7086 + 23.7441i −0.515931 + 0.893619i
\(707\) 31.5849i 1.18787i
\(708\) 0 0
\(709\) −9.57491 5.52808i −0.359593 0.207611i 0.309309 0.950962i \(-0.399902\pi\)
−0.668902 + 0.743350i \(0.733236\pi\)
\(710\) 7.95317i 0.298477i
\(711\) 0 0
\(712\) −4.08637 7.07780i −0.153143 0.265252i
\(713\) −5.44719 + 3.14493i −0.203999 + 0.117779i
\(714\) 0 0
\(715\) 12.4186 + 9.87282i 0.464430 + 0.369223i
\(716\) 17.4157 0.650856
\(717\) 0 0
\(718\) 7.18056 + 12.4371i 0.267976 + 0.464148i
\(719\) −5.85641 + 10.1436i −0.218407 + 0.378292i −0.954321 0.298783i \(-0.903419\pi\)
0.735914 + 0.677075i \(0.236753\pi\)
\(720\) 0 0
\(721\) −21.2840 12.2883i −0.792656 0.457640i
\(722\) −39.5935 22.8593i −1.47352 0.850735i
\(723\) 0 0
\(724\) −5.18056 + 8.97299i −0.192534 + 0.333479i
\(725\) 2.15637 + 3.73494i 0.0800855 + 0.138712i
\(726\) 0 0
\(727\) −19.4152 −0.720071 −0.360035 0.932939i \(-0.617235\pi\)
−0.360035 + 0.932939i \(0.617235\pi\)
\(728\) 2.47090 16.5633i 0.0915777 0.613876i
\(729\) 0 0
\(730\) −3.77684 + 2.18056i −0.139787 + 0.0807061i
\(731\) 1.43291 + 2.48188i 0.0529982 + 0.0917956i
\(732\) 0 0
\(733\) 11.9340i 0.440792i 0.975411 + 0.220396i \(0.0707349\pi\)
−0.975411 + 0.220396i \(0.929265\pi\)
\(734\) −11.9298 6.88764i −0.440335 0.254228i
\(735\) 0 0
\(736\) 0.976584i 0.0359973i
\(737\) 4.01559 6.95521i 0.147916 0.256199i
\(738\) 0 0
\(739\) 17.2017 9.93141i 0.632775 0.365333i −0.149051 0.988830i \(-0.547622\pi\)
0.781826 + 0.623497i \(0.214289\pi\)
\(740\) 3.79603 0.139545
\(741\) 0 0
\(742\) 62.7442 2.30341
\(743\) −14.2787 + 8.24383i −0.523836 + 0.302437i −0.738503 0.674251i \(-0.764467\pi\)
0.214667 + 0.976687i \(0.431133\pi\)
\(744\) 0 0
\(745\) −2.30985 + 4.00077i −0.0846263 + 0.146577i
\(746\) 33.4627i 1.22516i
\(747\) 0 0
\(748\) −15.2425 8.80025i −0.557320 0.321769i
\(749\) 78.6257i 2.87292i
\(750\) 0 0
\(751\) −23.3312 40.4109i −0.851368 1.47461i −0.879974 0.475022i \(-0.842440\pi\)
0.0286056 0.999591i \(-0.490893\pi\)
\(752\) −8.44671 + 4.87671i −0.308020 + 0.177835i
\(753\) 0 0
\(754\) −15.3796 2.29432i −0.560092 0.0835542i
\(755\) −11.2425 −0.409156
\(756\) 0 0
\(757\) −1.31799 2.28282i −0.0479030 0.0829705i 0.841080 0.540911i \(-0.181921\pi\)
−0.888983 + 0.457941i \(0.848587\pi\)
\(758\) 16.6884 28.9052i 0.606151 1.04988i
\(759\) 0 0
\(760\) 6.96699 + 4.02239i 0.252719 + 0.145908i
\(761\) −0.0693410 0.0400340i −0.00251361 0.00145123i 0.498743 0.866750i \(-0.333795\pi\)
−0.501256 + 0.865299i \(0.667129\pi\)
\(762\) 0 0
\(763\) −29.7264 + 51.4877i −1.07617 + 1.86398i
\(764\) 0.448507 + 0.776837i 0.0162264 + 0.0281050i
\(765\) 0 0
\(766\) 7.33038 0.264857
\(767\) −7.77606 1.16003i −0.280777 0.0418862i
\(768\) 0 0
\(769\) 4.92177 2.84159i 0.177484 0.102470i −0.408626 0.912702i \(-0.633992\pi\)
0.586110 + 0.810232i \(0.300659\pi\)
\(770\) 10.2185 + 17.6990i 0.368251 + 0.637829i
\(771\) 0 0
\(772\) 20.2644i 0.729330i
\(773\) 6.57184 + 3.79425i 0.236373 + 0.136470i 0.613508 0.789688i \(-0.289758\pi\)
−0.377136 + 0.926158i \(0.623091\pi\)
\(774\) 0 0
\(775\) 6.44069i 0.231356i
\(776\) −6.91261 + 11.9730i −0.248148 + 0.429805i
\(777\) 0 0
\(778\) −28.2496 + 16.3099i −1.01280 + 0.584739i
\(779\) −58.6410 −2.10103
\(780\) 0 0
\(781\) −34.9949 −1.25222
\(782\) 3.38298 1.95317i 0.120975 0.0698451i
\(783\) 0 0
\(784\) 7.28643 12.6205i 0.260230 0.450731i
\(785\) 1.50311i 0.0536484i
\(786\) 0 0
\(787\) −4.10169 2.36811i −0.146210 0.0844142i 0.425111 0.905141i \(-0.360235\pi\)
−0.571320 + 0.820727i \(0.693569\pi\)
\(788\) 9.18056i 0.327044i
\(789\) 0 0