Properties

Label 936.2.m.h.181.1
Level $936$
Weight $2$
Character 936.181
Analytic conductor $7.474$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 936.m (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.47399762919\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 181.1
Root \(-0.556839 - 1.81878i\) of defining polynomial
Character \(\chi\) \(=\) 936.181
Dual form 936.2.m.h.181.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.34500 - 0.437016i) q^{2} +(1.61803 + 1.17557i) q^{4} -1.66251 q^{5} -3.57266i q^{7} +(-1.66251 - 2.28825i) q^{8} +O(q^{10})\) \(q+(-1.34500 - 0.437016i) q^{2} +(1.61803 + 1.17557i) q^{4} -1.66251 q^{5} -3.57266i q^{7} +(-1.66251 - 2.28825i) q^{8} +(2.23607 + 0.726543i) q^{10} -1.02749 q^{11} +(1.87826 - 3.07768i) q^{13} +(-1.56131 + 4.80522i) q^{14} +(1.23607 + 3.80423i) q^{16} +5.05251 q^{17} +1.16083 q^{19} +(-2.68999 - 1.95440i) q^{20} +(1.38197 + 0.449028i) q^{22} -8.17513 q^{23} -2.23607 q^{25} +(-3.87125 + 3.31865i) q^{26} +(4.19992 - 5.78069i) q^{28} +4.29792i q^{29} +7.98872i q^{31} -5.65685i q^{32} +(-6.79561 - 2.20803i) q^{34} +5.93958i q^{35} -9.83470 q^{37} +(-1.56131 - 0.507301i) q^{38} +(2.76393 + 3.80423i) q^{40} -1.62054i q^{41} -2.35114i q^{43} +(-1.66251 - 1.20788i) q^{44} +(10.9955 + 3.57266i) q^{46} -7.73877i q^{47} -5.76393 q^{49} +(3.00750 + 0.977198i) q^{50} +(6.65712 - 2.77177i) q^{52} -11.2521i q^{53} +1.70820 q^{55} +(-8.17513 + 5.93958i) q^{56} +(1.87826 - 5.78069i) q^{58} -9.73249 q^{59} -11.4127i q^{61} +(3.49120 - 10.7448i) q^{62} +(-2.47214 + 7.60845i) q^{64} +(-3.12262 + 5.11667i) q^{65} -7.23901 q^{67} +(8.17513 + 5.93958i) q^{68} +(2.59569 - 7.98872i) q^{70} -10.5672i q^{71} +4.41606i q^{73} +(13.2276 + 4.29792i) q^{74} +(1.87826 + 1.36464i) q^{76} +3.67086i q^{77} -6.94427 q^{79} +(-2.05497 - 6.32456i) q^{80} +(-0.708204 + 2.17963i) q^{82} -2.29753 q^{83} -8.39984 q^{85} +(-1.02749 + 3.16228i) q^{86} +(1.70820 + 2.35114i) q^{88} +9.02546i q^{89} +(-10.9955 - 6.71040i) q^{91} +(-13.2276 - 9.61045i) q^{92} +(-3.38197 + 10.4086i) q^{94} -1.92989 q^{95} +11.5614i q^{97} +(7.75247 + 2.51893i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 16 q^{16} + 40 q^{22} + 80 q^{40} - 128 q^{49} + 40 q^{52} - 80 q^{55} + 32 q^{64} + 32 q^{79} + 96 q^{82} - 80 q^{88} - 72 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/936\mathbb{Z}\right)^\times\).

\(n\) \(145\) \(209\) \(469\) \(703\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34500 0.437016i −0.951057 0.309017i
\(3\) 0 0
\(4\) 1.61803 + 1.17557i 0.809017 + 0.587785i
\(5\) −1.66251 −0.743496 −0.371748 0.928334i \(-0.621241\pi\)
−0.371748 + 0.928334i \(0.621241\pi\)
\(6\) 0 0
\(7\) 3.57266i 1.35034i −0.737662 0.675170i \(-0.764070\pi\)
0.737662 0.675170i \(-0.235930\pi\)
\(8\) −1.66251 2.28825i −0.587785 0.809017i
\(9\) 0 0
\(10\) 2.23607 + 0.726543i 0.707107 + 0.229753i
\(11\) −1.02749 −0.309799 −0.154899 0.987930i \(-0.549505\pi\)
−0.154899 + 0.987930i \(0.549505\pi\)
\(12\) 0 0
\(13\) 1.87826 3.07768i 0.520936 0.853596i
\(14\) −1.56131 + 4.80522i −0.417278 + 1.28425i
\(15\) 0 0
\(16\) 1.23607 + 3.80423i 0.309017 + 0.951057i
\(17\) 5.05251 1.22541 0.612707 0.790310i \(-0.290081\pi\)
0.612707 + 0.790310i \(0.290081\pi\)
\(18\) 0 0
\(19\) 1.16083 0.266312 0.133156 0.991095i \(-0.457489\pi\)
0.133156 + 0.991095i \(0.457489\pi\)
\(20\) −2.68999 1.95440i −0.601501 0.437016i
\(21\) 0 0
\(22\) 1.38197 + 0.449028i 0.294636 + 0.0957331i
\(23\) −8.17513 −1.70463 −0.852317 0.523026i \(-0.824803\pi\)
−0.852317 + 0.523026i \(0.824803\pi\)
\(24\) 0 0
\(25\) −2.23607 −0.447214
\(26\) −3.87125 + 3.31865i −0.759215 + 0.650840i
\(27\) 0 0
\(28\) 4.19992 5.78069i 0.793710 1.09245i
\(29\) 4.29792i 0.798104i 0.916928 + 0.399052i \(0.130661\pi\)
−0.916928 + 0.399052i \(0.869339\pi\)
\(30\) 0 0
\(31\) 7.98872i 1.43482i 0.696653 + 0.717408i \(0.254672\pi\)
−0.696653 + 0.717408i \(0.745328\pi\)
\(32\) 5.65685i 1.00000i
\(33\) 0 0
\(34\) −6.79561 2.20803i −1.16544 0.378674i
\(35\) 5.93958i 1.00397i
\(36\) 0 0
\(37\) −9.83470 −1.61682 −0.808408 0.588623i \(-0.799670\pi\)
−0.808408 + 0.588623i \(0.799670\pi\)
\(38\) −1.56131 0.507301i −0.253278 0.0822951i
\(39\) 0 0
\(40\) 2.76393 + 3.80423i 0.437016 + 0.601501i
\(41\) 1.62054i 0.253087i −0.991961 0.126543i \(-0.959612\pi\)
0.991961 0.126543i \(-0.0403883\pi\)
\(42\) 0 0
\(43\) 2.35114i 0.358546i −0.983799 0.179273i \(-0.942626\pi\)
0.983799 0.179273i \(-0.0573745\pi\)
\(44\) −1.66251 1.20788i −0.250632 0.182095i
\(45\) 0 0
\(46\) 10.9955 + 3.57266i 1.62120 + 0.526761i
\(47\) 7.73877i 1.12882i −0.825496 0.564408i \(-0.809105\pi\)
0.825496 0.564408i \(-0.190895\pi\)
\(48\) 0 0
\(49\) −5.76393 −0.823419
\(50\) 3.00750 + 0.977198i 0.425325 + 0.138197i
\(51\) 0 0
\(52\) 6.65712 2.77177i 0.923177 0.384375i
\(53\) 11.2521i 1.54560i −0.634652 0.772798i \(-0.718857\pi\)
0.634652 0.772798i \(-0.281143\pi\)
\(54\) 0 0
\(55\) 1.70820 0.230334
\(56\) −8.17513 + 5.93958i −1.09245 + 0.793710i
\(57\) 0 0
\(58\) 1.87826 5.78069i 0.246628 0.759042i
\(59\) −9.73249 −1.26706 −0.633531 0.773717i \(-0.718395\pi\)
−0.633531 + 0.773717i \(0.718395\pi\)
\(60\) 0 0
\(61\) 11.4127i 1.46124i −0.682782 0.730622i \(-0.739230\pi\)
0.682782 0.730622i \(-0.260770\pi\)
\(62\) 3.49120 10.7448i 0.443383 1.36459i
\(63\) 0 0
\(64\) −2.47214 + 7.60845i −0.309017 + 0.951057i
\(65\) −3.12262 + 5.11667i −0.387314 + 0.634645i
\(66\) 0 0
\(67\) −7.23901 −0.884386 −0.442193 0.896920i \(-0.645799\pi\)
−0.442193 + 0.896920i \(0.645799\pi\)
\(68\) 8.17513 + 5.93958i 0.991381 + 0.720280i
\(69\) 0 0
\(70\) 2.59569 7.98872i 0.310245 0.954835i
\(71\) 10.5672i 1.25410i −0.778981 0.627048i \(-0.784263\pi\)
0.778981 0.627048i \(-0.215737\pi\)
\(72\) 0 0
\(73\) 4.41606i 0.516860i 0.966030 + 0.258430i \(0.0832052\pi\)
−0.966030 + 0.258430i \(0.916795\pi\)
\(74\) 13.2276 + 4.29792i 1.53768 + 0.499623i
\(75\) 0 0
\(76\) 1.87826 + 1.36464i 0.215451 + 0.156535i
\(77\) 3.67086i 0.418334i
\(78\) 0 0
\(79\) −6.94427 −0.781292 −0.390646 0.920541i \(-0.627748\pi\)
−0.390646 + 0.920541i \(0.627748\pi\)
\(80\) −2.05497 6.32456i −0.229753 0.707107i
\(81\) 0 0
\(82\) −0.708204 + 2.17963i −0.0782080 + 0.240700i
\(83\) −2.29753 −0.252187 −0.126093 0.992018i \(-0.540244\pi\)
−0.126093 + 0.992018i \(0.540244\pi\)
\(84\) 0 0
\(85\) −8.39984 −0.911090
\(86\) −1.02749 + 3.16228i −0.110797 + 0.340997i
\(87\) 0 0
\(88\) 1.70820 + 2.35114i 0.182095 + 0.250632i
\(89\) 9.02546i 0.956697i 0.878170 + 0.478349i \(0.158764\pi\)
−0.878170 + 0.478349i \(0.841236\pi\)
\(90\) 0 0
\(91\) −10.9955 6.71040i −1.15264 0.703441i
\(92\) −13.2276 9.61045i −1.37908 1.00196i
\(93\) 0 0
\(94\) −3.38197 + 10.4086i −0.348823 + 1.07357i
\(95\) −1.92989 −0.198002
\(96\) 0 0
\(97\) 11.5614i 1.17388i 0.809630 + 0.586940i \(0.199668\pi\)
−0.809630 + 0.586940i \(0.800332\pi\)
\(98\) 7.75247 + 2.51893i 0.783118 + 0.254450i
\(99\) 0 0
\(100\) −3.61803 2.62866i −0.361803 0.262866i
\(101\) 7.96879i 0.792924i 0.918051 + 0.396462i \(0.129762\pi\)
−0.918051 + 0.396462i \(0.870238\pi\)
\(102\) 0 0
\(103\) −11.7082 −1.15364 −0.576822 0.816870i \(-0.695707\pi\)
−0.576822 + 0.816870i \(0.695707\pi\)
\(104\) −10.1651 + 0.818750i −0.996772 + 0.0802851i
\(105\) 0 0
\(106\) −4.91735 + 15.1340i −0.477615 + 1.46995i
\(107\) 2.65626i 0.256791i −0.991723 0.128395i \(-0.959017\pi\)
0.991723 0.128395i \(-0.0409826\pi\)
\(108\) 0 0
\(109\) 12.1564 1.16437 0.582184 0.813057i \(-0.302198\pi\)
0.582184 + 0.813057i \(0.302198\pi\)
\(110\) −2.29753 0.746512i −0.219061 0.0711772i
\(111\) 0 0
\(112\) 13.5912 4.41606i 1.28425 0.417278i
\(113\) 5.05251 0.475300 0.237650 0.971351i \(-0.423623\pi\)
0.237650 + 0.971351i \(0.423623\pi\)
\(114\) 0 0
\(115\) 13.5912 1.26739
\(116\) −5.05251 + 6.95418i −0.469114 + 0.645680i
\(117\) 0 0
\(118\) 13.0902 + 4.25325i 1.20505 + 0.391544i
\(119\) 18.0509i 1.65473i
\(120\) 0 0
\(121\) −9.94427 −0.904025
\(122\) −4.98752 + 15.3500i −0.451549 + 1.38973i
\(123\) 0 0
\(124\) −9.39130 + 12.9260i −0.843364 + 1.16079i
\(125\) 12.0300 1.07600
\(126\) 0 0
\(127\) −6.00000 −0.532414 −0.266207 0.963916i \(-0.585770\pi\)
−0.266207 + 0.963916i \(0.585770\pi\)
\(128\) 6.65003 9.15298i 0.587785 0.809017i
\(129\) 0 0
\(130\) 6.43599 5.51727i 0.564473 0.483897i
\(131\) 16.5646i 1.44726i 0.690189 + 0.723629i \(0.257527\pi\)
−0.690189 + 0.723629i \(0.742473\pi\)
\(132\) 0 0
\(133\) 4.14725i 0.359612i
\(134\) 9.73645 + 3.16356i 0.841101 + 0.273290i
\(135\) 0 0
\(136\) −8.39984 11.5614i −0.720280 0.991381i
\(137\) 13.6020i 1.16209i 0.813870 + 0.581047i \(0.197357\pi\)
−0.813870 + 0.581047i \(0.802643\pi\)
\(138\) 0 0
\(139\) 19.3642i 1.64245i −0.570607 0.821223i \(-0.693292\pi\)
0.570607 0.821223i \(-0.306708\pi\)
\(140\) −6.98240 + 9.61045i −0.590120 + 0.812231i
\(141\) 0 0
\(142\) −4.61803 + 14.2128i −0.387537 + 1.19272i
\(143\) −1.92989 + 3.16228i −0.161385 + 0.264443i
\(144\) 0 0
\(145\) 7.14533i 0.593387i
\(146\) 1.92989 5.93958i 0.159719 0.491563i
\(147\) 0 0
\(148\) −15.9129 11.5614i −1.30803 0.950340i
\(149\) −7.04250 −0.576944 −0.288472 0.957488i \(-0.593147\pi\)
−0.288472 + 0.957488i \(0.593147\pi\)
\(150\) 0 0
\(151\) 3.57266i 0.290739i 0.989377 + 0.145370i \(0.0464371\pi\)
−0.989377 + 0.145370i \(0.953563\pi\)
\(152\) −1.92989 2.65626i −0.156535 0.215451i
\(153\) 0 0
\(154\) 1.60423 4.93730i 0.129272 0.397859i
\(155\) 13.2813i 1.06678i
\(156\) 0 0
\(157\) 0.555029i 0.0442961i −0.999755 0.0221481i \(-0.992949\pi\)
0.999755 0.0221481i \(-0.00705053\pi\)
\(158\) 9.34003 + 3.03476i 0.743052 + 0.241432i
\(159\) 0 0
\(160\) 9.40456i 0.743496i
\(161\) 29.2070i 2.30183i
\(162\) 0 0
\(163\) −7.23901 −0.567003 −0.283501 0.958972i \(-0.591496\pi\)
−0.283501 + 0.958972i \(0.591496\pi\)
\(164\) 1.90506 2.62210i 0.148761 0.204751i
\(165\) 0 0
\(166\) 3.09017 + 1.00406i 0.239844 + 0.0779299i
\(167\) 7.32611i 0.566911i −0.958985 0.283456i \(-0.908519\pi\)
0.958985 0.283456i \(-0.0914809\pi\)
\(168\) 0 0
\(169\) −5.94427 11.5614i −0.457252 0.889337i
\(170\) 11.2978 + 3.67086i 0.866498 + 0.281542i
\(171\) 0 0
\(172\) 2.76393 3.80423i 0.210748 0.290070i
\(173\) 11.2521i 0.855482i −0.903901 0.427741i \(-0.859310\pi\)
0.903901 0.427741i \(-0.140690\pi\)
\(174\) 0 0
\(175\) 7.98872i 0.603891i
\(176\) −1.27004 3.90879i −0.0957331 0.294636i
\(177\) 0 0
\(178\) 3.94427 12.1392i 0.295636 0.909873i
\(179\) 21.8772i 1.63518i −0.575804 0.817588i \(-0.695311\pi\)
0.575804 0.817588i \(-0.304689\pi\)
\(180\) 0 0
\(181\) 12.8658i 0.956305i 0.878277 + 0.478152i \(0.158693\pi\)
−0.878277 + 0.478152i \(0.841307\pi\)
\(182\) 11.8564 + 13.8307i 0.878855 + 1.02520i
\(183\) 0 0
\(184\) 13.5912 + 18.7067i 1.00196 + 1.37908i
\(185\) 16.3503 1.20210
\(186\) 0 0
\(187\) −5.19139 −0.379632
\(188\) 9.09747 12.5216i 0.663501 0.913231i
\(189\) 0 0
\(190\) 2.59569 + 0.843392i 0.188311 + 0.0611861i
\(191\) −1.92989 −0.139642 −0.0698209 0.997560i \(-0.522243\pi\)
−0.0698209 + 0.997560i \(0.522243\pi\)
\(192\) 0 0
\(193\) 4.41606i 0.317875i 0.987289 + 0.158937i \(0.0508068\pi\)
−0.987289 + 0.158937i \(0.949193\pi\)
\(194\) 5.05251 15.5500i 0.362749 1.11643i
\(195\) 0 0
\(196\) −9.32624 6.77591i −0.666160 0.483993i
\(197\) 23.1825 1.65168 0.825841 0.563903i \(-0.190701\pi\)
0.825841 + 0.563903i \(0.190701\pi\)
\(198\) 0 0
\(199\) 18.0000 1.27599 0.637993 0.770042i \(-0.279765\pi\)
0.637993 + 0.770042i \(0.279765\pi\)
\(200\) 3.71748 + 5.11667i 0.262866 + 0.361803i
\(201\) 0 0
\(202\) 3.48249 10.7180i 0.245027 0.754115i
\(203\) 15.3550 1.07771
\(204\) 0 0
\(205\) 2.69417i 0.188169i
\(206\) 15.7475 + 5.11667i 1.09718 + 0.356495i
\(207\) 0 0
\(208\) 14.0299 + 3.34110i 0.972796 + 0.231664i
\(209\) −1.19274 −0.0825033
\(210\) 0 0
\(211\) 10.5146i 0.723856i −0.932206 0.361928i \(-0.882119\pi\)
0.932206 0.361928i \(-0.117881\pi\)
\(212\) 13.2276 18.2063i 0.908478 1.25041i
\(213\) 0 0
\(214\) −1.16083 + 3.57266i −0.0793526 + 0.244222i
\(215\) 3.90879i 0.266577i
\(216\) 0 0
\(217\) 28.5410 1.93749
\(218\) −16.3503 5.31252i −1.10738 0.359810i
\(219\) 0 0
\(220\) 2.76393 + 2.00811i 0.186344 + 0.135387i
\(221\) 9.48993 15.5500i 0.638362 1.04601i
\(222\) 0 0
\(223\) 7.98872i 0.534964i −0.963563 0.267482i \(-0.913808\pi\)
0.963563 0.267482i \(-0.0861916\pi\)
\(224\) −20.2100 −1.35034
\(225\) 0 0
\(226\) −6.79561 2.20803i −0.452037 0.146876i
\(227\) 4.35250 0.288886 0.144443 0.989513i \(-0.453861\pi\)
0.144443 + 0.989513i \(0.453861\pi\)
\(228\) 0 0
\(229\) −1.43486 −0.0948185 −0.0474092 0.998876i \(-0.515096\pi\)
−0.0474092 + 0.998876i \(0.515096\pi\)
\(230\) −18.2802 5.93958i −1.20536 0.391644i
\(231\) 0 0
\(232\) 9.83470 7.14533i 0.645680 0.469114i
\(233\) 16.3503 1.07114 0.535571 0.844490i \(-0.320096\pi\)
0.535571 + 0.844490i \(0.320096\pi\)
\(234\) 0 0
\(235\) 12.8658i 0.839270i
\(236\) −15.7475 11.4412i −1.02507 0.744761i
\(237\) 0 0
\(238\) −7.88854 + 24.2784i −0.511338 + 1.57374i
\(239\) 7.07107i 0.457389i 0.973498 + 0.228695i \(0.0734457\pi\)
−0.973498 + 0.228695i \(0.926554\pi\)
\(240\) 0 0
\(241\) 15.9774i 1.02920i −0.857431 0.514599i \(-0.827941\pi\)
0.857431 0.514599i \(-0.172059\pi\)
\(242\) 13.3750 + 4.34581i 0.859779 + 0.279359i
\(243\) 0 0
\(244\) 13.4164 18.4661i 0.858898 1.18217i
\(245\) 9.58258 0.612209
\(246\) 0 0
\(247\) 2.18034 3.57266i 0.138732 0.227323i
\(248\) 18.2802 13.2813i 1.16079 0.843364i
\(249\) 0 0
\(250\) −16.1803 5.25731i −1.02333 0.332502i
\(251\) 22.5042i 1.42045i 0.703973 + 0.710227i \(0.251408\pi\)
−0.703973 + 0.710227i \(0.748592\pi\)
\(252\) 0 0
\(253\) 8.39984 0.528093
\(254\) 8.06998 + 2.62210i 0.506356 + 0.164525i
\(255\) 0 0
\(256\) −12.9443 + 9.40456i −0.809017 + 0.587785i
\(257\) 22.5955 1.40947 0.704735 0.709471i \(-0.251066\pi\)
0.704735 + 0.709471i \(0.251066\pi\)
\(258\) 0 0
\(259\) 35.1361i 2.18325i
\(260\) −11.0675 + 4.60809i −0.686378 + 0.285781i
\(261\) 0 0
\(262\) 7.23901 22.2794i 0.447227 1.37642i
\(263\) −16.3503 −1.00820 −0.504100 0.863645i \(-0.668176\pi\)
−0.504100 + 0.863645i \(0.668176\pi\)
\(264\) 0 0
\(265\) 18.7067i 1.14914i
\(266\) −1.81242 + 5.57804i −0.111126 + 0.342012i
\(267\) 0 0
\(268\) −11.7130 8.50997i −0.715483 0.519829i
\(269\) 7.58124i 0.462237i −0.972926 0.231118i \(-0.925762\pi\)
0.972926 0.231118i \(-0.0742384\pi\)
\(270\) 0 0
\(271\) 7.98872i 0.485280i −0.970116 0.242640i \(-0.921987\pi\)
0.970116 0.242640i \(-0.0780134\pi\)
\(272\) 6.24525 + 19.2209i 0.378674 + 1.16544i
\(273\) 0 0
\(274\) 5.94427 18.2946i 0.359107 1.10522i
\(275\) 2.29753 0.138546
\(276\) 0 0
\(277\) 18.1231i 1.08891i 0.838790 + 0.544455i \(0.183263\pi\)
−0.838790 + 0.544455i \(0.816737\pi\)
\(278\) −8.46245 + 26.0447i −0.507544 + 1.56206i
\(279\) 0 0
\(280\) 13.5912 9.87460i 0.812231 0.590120i
\(281\) 6.19704i 0.369684i −0.982768 0.184842i \(-0.940823\pi\)
0.982768 0.184842i \(-0.0591774\pi\)
\(282\) 0 0
\(283\) 2.90617i 0.172754i −0.996263 0.0863769i \(-0.972471\pi\)
0.996263 0.0863769i \(-0.0275289\pi\)
\(284\) 12.4225 17.0981i 0.737139 1.01458i
\(285\) 0 0
\(286\) 3.97766 3.40986i 0.235204 0.201629i
\(287\) −5.78966 −0.341753
\(288\) 0 0
\(289\) 8.52786 0.501639
\(290\) −3.12262 + 9.61045i −0.183367 + 0.564345i
\(291\) 0 0
\(292\) −5.19139 + 7.14533i −0.303803 + 0.418149i
\(293\) −0.877578 −0.0512687 −0.0256343 0.999671i \(-0.508161\pi\)
−0.0256343 + 0.999671i \(0.508161\pi\)
\(294\) 0 0
\(295\) 16.1803 0.942056
\(296\) 16.3503 + 22.5042i 0.950340 + 1.30803i
\(297\) 0 0
\(298\) 9.47214 + 3.07768i 0.548706 + 0.178285i
\(299\) −15.3550 + 25.1605i −0.888005 + 1.45507i
\(300\) 0 0
\(301\) −8.39984 −0.484159
\(302\) 1.56131 4.80522i 0.0898434 0.276510i
\(303\) 0 0
\(304\) 1.43486 + 4.41606i 0.0822951 + 0.253278i
\(305\) 18.9737i 1.08643i
\(306\) 0 0
\(307\) 14.7521 0.841944 0.420972 0.907074i \(-0.361689\pi\)
0.420972 + 0.907074i \(0.361689\pi\)
\(308\) −4.31536 + 5.93958i −0.245890 + 0.338439i
\(309\) 0 0
\(310\) −5.80415 + 17.8633i −0.329653 + 1.01457i
\(311\) −24.5254 −1.39071 −0.695354 0.718667i \(-0.744752\pi\)
−0.695354 + 0.718667i \(0.744752\pi\)
\(312\) 0 0
\(313\) 6.47214 0.365827 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(314\) −0.242557 + 0.746512i −0.0136883 + 0.0421281i
\(315\) 0 0
\(316\) −11.2361 8.16348i −0.632078 0.459232i
\(317\) −31.1025 −1.74689 −0.873446 0.486921i \(-0.838120\pi\)
−0.873446 + 0.486921i \(0.838120\pi\)
\(318\) 0 0
\(319\) 4.41606i 0.247252i
\(320\) 4.10995 12.6491i 0.229753 0.707107i
\(321\) 0 0
\(322\) 12.7639 39.2833i 0.711306 2.18918i
\(323\) 5.86510 0.326343
\(324\) 0 0
\(325\) −4.19992 + 6.88191i −0.232970 + 0.381740i
\(326\) 9.73645 + 3.16356i 0.539252 + 0.175214i
\(327\) 0 0
\(328\) −3.70820 + 2.69417i −0.204751 + 0.148761i
\(329\) −27.6480 −1.52428
\(330\) 0 0
\(331\) 10.9955 0.604369 0.302185 0.953249i \(-0.402284\pi\)
0.302185 + 0.953249i \(0.402284\pi\)
\(332\) −3.71748 2.70091i −0.204023 0.148232i
\(333\) 0 0
\(334\) −3.20163 + 9.85359i −0.175185 + 0.539165i
\(335\) 12.0349 0.657537
\(336\) 0 0
\(337\) 5.52786 0.301122 0.150561 0.988601i \(-0.451892\pi\)
0.150561 + 0.988601i \(0.451892\pi\)
\(338\) 2.94252 + 18.1478i 0.160052 + 0.987109i
\(339\) 0 0
\(340\) −13.5912 9.87460i −0.737088 0.535525i
\(341\) 8.20830i 0.444504i
\(342\) 0 0
\(343\) 4.41606i 0.238445i
\(344\) −5.37999 + 3.90879i −0.290070 + 0.210748i
\(345\) 0 0
\(346\) −4.91735 + 15.1340i −0.264358 + 0.813612i
\(347\) 20.4750i 1.09916i −0.835442 0.549578i \(-0.814788\pi\)
0.835442 0.549578i \(-0.185212\pi\)
\(348\) 0 0
\(349\) 13.5912 0.727522 0.363761 0.931492i \(-0.381493\pi\)
0.363761 + 0.931492i \(0.381493\pi\)
\(350\) 3.49120 10.7448i 0.186612 0.574334i
\(351\) 0 0
\(352\) 5.81234i 0.309799i
\(353\) 20.5942i 1.09612i −0.836439 0.548060i \(-0.815367\pi\)
0.836439 0.548060i \(-0.184633\pi\)
\(354\) 0 0
\(355\) 17.5680i 0.932415i
\(356\) −10.6101 + 14.6035i −0.562332 + 0.773984i
\(357\) 0 0
\(358\) −9.56067 + 29.4247i −0.505297 + 1.55514i
\(359\) 32.1142i 1.69493i −0.530855 0.847463i \(-0.678129\pi\)
0.530855 0.847463i \(-0.321871\pi\)
\(360\) 0 0
\(361\) −17.6525 −0.929078
\(362\) 5.62254 17.3044i 0.295514 0.909500i
\(363\) 0 0
\(364\) −9.90260 23.7837i −0.519037 1.24660i
\(365\) 7.34173i 0.384284i
\(366\) 0 0
\(367\) 31.1246 1.62469 0.812346 0.583176i \(-0.198190\pi\)
0.812346 + 0.583176i \(0.198190\pi\)
\(368\) −10.1050 31.1001i −0.526761 1.62120i
\(369\) 0 0
\(370\) −21.9911 7.14533i −1.14326 0.371468i
\(371\) −40.2000 −2.08708
\(372\) 0 0
\(373\) 26.0746i 1.35009i −0.737777 0.675045i \(-0.764124\pi\)
0.737777 0.675045i \(-0.235876\pi\)
\(374\) 6.98240 + 2.26872i 0.361051 + 0.117313i
\(375\) 0 0
\(376\) −17.7082 + 12.8658i −0.913231 + 0.663501i
\(377\) 13.2276 + 8.07262i 0.681258 + 0.415761i
\(378\) 0 0
\(379\) 19.3954 0.996273 0.498137 0.867099i \(-0.334018\pi\)
0.498137 + 0.867099i \(0.334018\pi\)
\(380\) −3.12262 2.26872i −0.160187 0.116383i
\(381\) 0 0
\(382\) 2.59569 + 0.843392i 0.132807 + 0.0431517i
\(383\) 3.57494i 0.182671i 0.995820 + 0.0913354i \(0.0291135\pi\)
−0.995820 + 0.0913354i \(0.970886\pi\)
\(384\) 0 0
\(385\) 6.10284i 0.311030i
\(386\) 1.92989 5.93958i 0.0982287 0.302317i
\(387\) 0 0
\(388\) −13.5912 + 18.7067i −0.689990 + 0.949690i
\(389\) 35.3980i 1.79475i 0.441270 + 0.897374i \(0.354528\pi\)
−0.441270 + 0.897374i \(0.645472\pi\)
\(390\) 0 0
\(391\) −41.3050 −2.08888
\(392\) 9.58258 + 13.1893i 0.483993 + 0.666160i
\(393\) 0 0
\(394\) −31.1803 10.1311i −1.57084 0.510398i
\(395\) 11.5449 0.580887
\(396\) 0 0
\(397\) 20.5562 1.03169 0.515843 0.856683i \(-0.327479\pi\)
0.515843 + 0.856683i \(0.327479\pi\)
\(398\) −24.2099 7.86629i −1.21353 0.394301i
\(399\) 0 0
\(400\) −2.76393 8.50651i −0.138197 0.425325i
\(401\) 30.4149i 1.51885i −0.650596 0.759424i \(-0.725481\pi\)
0.650596 0.759424i \(-0.274519\pi\)
\(402\) 0 0
\(403\) 24.5868 + 15.0049i 1.22475 + 0.747447i
\(404\) −9.36787 + 12.8938i −0.466069 + 0.641489i
\(405\) 0 0
\(406\) −20.6525 6.71040i −1.02497 0.333031i
\(407\) 10.1050 0.500887
\(408\) 0 0
\(409\) 34.6842i 1.71502i −0.514466 0.857511i \(-0.672010\pi\)
0.514466 0.857511i \(-0.327990\pi\)
\(410\) 1.17739 3.62365i 0.0581474 0.178959i
\(411\) 0 0
\(412\) −18.9443 13.7638i −0.933317 0.678095i
\(413\) 34.7709i 1.71097i
\(414\) 0 0
\(415\) 3.81966 0.187500
\(416\) −17.4100 10.6250i −0.853596 0.520936i
\(417\) 0 0
\(418\) 1.60423 + 0.521245i 0.0784653 + 0.0254949i
\(419\) 7.96879i 0.389301i −0.980873 0.194650i \(-0.937643\pi\)
0.980873 0.194650i \(-0.0623572\pi\)
\(420\) 0 0
\(421\) −8.39984 −0.409383 −0.204692 0.978827i \(-0.565619\pi\)
−0.204692 + 0.978827i \(0.565619\pi\)
\(422\) −4.59506 + 14.1421i −0.223684 + 0.688428i
\(423\) 0 0
\(424\) −25.7476 + 18.7067i −1.25041 + 0.908478i
\(425\) −11.2978 −0.548022
\(426\) 0 0
\(427\) −40.7737 −1.97318
\(428\) 3.12262 4.29792i 0.150938 0.207748i
\(429\) 0 0
\(430\) 1.70820 5.25731i 0.0823769 0.253530i
\(431\) 1.82688i 0.0879975i 0.999032 + 0.0439987i \(0.0140098\pi\)
−0.999032 + 0.0439987i \(0.985990\pi\)
\(432\) 0 0
\(433\) −8.18034 −0.393122 −0.196561 0.980492i \(-0.562977\pi\)
−0.196561 + 0.980492i \(0.562977\pi\)
\(434\) −38.3876 12.4729i −1.84266 0.598718i
\(435\) 0 0
\(436\) 19.6694 + 14.2907i 0.941994 + 0.684398i
\(437\) −9.48993 −0.453965
\(438\) 0 0
\(439\) 1.81966 0.0868476 0.0434238 0.999057i \(-0.486173\pi\)
0.0434238 + 0.999057i \(0.486173\pi\)
\(440\) −2.83990 3.90879i −0.135387 0.186344i
\(441\) 0 0
\(442\) −19.5595 + 16.7675i −0.930353 + 0.797548i
\(443\) 11.2521i 0.534604i 0.963613 + 0.267302i \(0.0861321\pi\)
−0.963613 + 0.267302i \(0.913868\pi\)
\(444\) 0 0
\(445\) 15.0049i 0.711301i
\(446\) −3.49120 + 10.7448i −0.165313 + 0.508781i
\(447\) 0 0
\(448\) 27.1824 + 8.83211i 1.28425 + 0.417278i
\(449\) 4.86163i 0.229435i 0.993398 + 0.114717i \(0.0365962\pi\)
−0.993398 + 0.114717i \(0.963404\pi\)
\(450\) 0 0
\(451\) 1.66509i 0.0784059i
\(452\) 8.17513 + 5.93958i 0.384526 + 0.279374i
\(453\) 0 0
\(454\) −5.85410 1.90211i −0.274747 0.0892706i
\(455\) 18.2802 + 11.1561i 0.856987 + 0.523005i
\(456\) 0 0
\(457\) 17.0199i 0.796159i 0.917351 + 0.398079i \(0.130323\pi\)
−0.917351 + 0.398079i \(0.869677\pi\)
\(458\) 1.92989 + 0.627058i 0.0901777 + 0.0293005i
\(459\) 0 0
\(460\) 21.9911 + 15.9774i 1.02534 + 0.744952i
\(461\) −21.9124 −1.02056 −0.510282 0.860007i \(-0.670459\pi\)
−0.510282 + 0.860007i \(0.670459\pi\)
\(462\) 0 0
\(463\) 3.57266i 0.166036i −0.996548 0.0830179i \(-0.973544\pi\)
0.996548 0.0830179i \(-0.0264559\pi\)
\(464\) −16.3503 + 5.31252i −0.759042 + 0.246628i
\(465\) 0 0
\(466\) −21.9911 7.14533i −1.01872 0.331001i
\(467\) 8.59584i 0.397768i −0.980023 0.198884i \(-0.936268\pi\)
0.980023 0.198884i \(-0.0637317\pi\)
\(468\) 0 0
\(469\) 25.8626i 1.19422i
\(470\) 5.62254 17.3044i 0.259349 0.798193i
\(471\) 0 0
\(472\) 16.1803 + 22.2703i 0.744761 + 1.02507i
\(473\) 2.41577i 0.111077i
\(474\) 0 0
\(475\) −2.59569 −0.119099
\(476\) 21.2201 29.2070i 0.972623 1.33870i
\(477\) 0 0
\(478\) 3.09017 9.51057i 0.141341 0.435003i
\(479\) 29.2858i 1.33810i −0.743216 0.669052i \(-0.766700\pi\)
0.743216 0.669052i \(-0.233300\pi\)
\(480\) 0 0
\(481\) −18.4721 + 30.2681i −0.842257 + 1.38011i
\(482\) −6.98240 + 21.4896i −0.318040 + 0.978825i
\(483\) 0 0
\(484\) −16.0902 11.6902i −0.731371 0.531372i
\(485\) 19.2209i 0.872776i
\(486\) 0 0
\(487\) 0.843392i 0.0382177i −0.999817 0.0191089i \(-0.993917\pi\)
0.999817 0.0191089i \(-0.00608291\pi\)
\(488\) −26.1150 + 18.9737i −1.18217 + 0.858898i
\(489\) 0 0
\(490\) −12.8885 4.18774i −0.582245 0.189183i
\(491\) 2.02920i 0.0915767i −0.998951 0.0457883i \(-0.985420\pi\)
0.998951 0.0457883i \(-0.0145800\pi\)
\(492\) 0 0
\(493\) 21.7153i 0.978008i
\(494\) −4.49386 + 3.85238i −0.202188 + 0.173327i
\(495\) 0 0
\(496\) −30.3909 + 9.87460i −1.36459 + 0.443383i
\(497\) −37.7530 −1.69346
\(498\) 0 0
\(499\) 33.5347 1.50122 0.750609 0.660747i \(-0.229760\pi\)
0.750609 + 0.660747i \(0.229760\pi\)
\(500\) 19.4650 + 14.1421i 0.870500 + 0.632456i
\(501\) 0 0
\(502\) 9.83470 30.2681i 0.438944 1.35093i
\(503\) −6.24525 −0.278462 −0.139231 0.990260i \(-0.544463\pi\)
−0.139231 + 0.990260i \(0.544463\pi\)
\(504\) 0 0
\(505\) 13.2482i 0.589536i
\(506\) −11.2978 3.67086i −0.502247 0.163190i
\(507\) 0 0
\(508\) −9.70820 7.05342i −0.430732 0.312945i
\(509\) 9.58258 0.424740 0.212370 0.977189i \(-0.431882\pi\)
0.212370 + 0.977189i \(0.431882\pi\)
\(510\) 0 0
\(511\) 15.7771 0.697937
\(512\) 21.5200 6.99226i 0.951057 0.309017i
\(513\) 0 0
\(514\) −30.3909 9.87460i −1.34049 0.435550i
\(515\) 19.4650 0.857729
\(516\) 0 0
\(517\) 7.95148i 0.349706i
\(518\) 15.3550 47.2579i 0.674661 2.07639i
\(519\) 0 0
\(520\) 16.8996 1.36118i 0.741096 0.0596916i
\(521\) −1.19274 −0.0522547 −0.0261274 0.999659i \(-0.508318\pi\)
−0.0261274 + 0.999659i \(0.508318\pi\)
\(522\) 0 0
\(523\) 24.0664i 1.05235i −0.850376 0.526176i \(-0.823625\pi\)
0.850376 0.526176i \(-0.176375\pi\)
\(524\) −19.4729 + 26.8021i −0.850677 + 1.17086i
\(525\) 0 0
\(526\) 21.9911 + 7.14533i 0.958856 + 0.311551i
\(527\) 40.3631i 1.75824i
\(528\) 0 0
\(529\) 43.8328 1.90577
\(530\) 8.17513 25.1605i 0.355105 1.09290i
\(531\) 0 0
\(532\) 4.87539 6.71040i 0.211375 0.290933i
\(533\) −4.98752 3.04381i −0.216034 0.131842i
\(534\) 0 0
\(535\) 4.41606i 0.190923i
\(536\) 12.0349 + 16.5646i 0.519829 + 0.715483i
\(537\) 0 0
\(538\) −3.31312 + 10.1967i −0.142839 + 0.439613i
\(539\) 5.92236 0.255094
\(540\) 0 0
\(541\) −3.20845 −0.137942 −0.0689711 0.997619i \(-0.521972\pi\)
−0.0689711 + 0.997619i \(0.521972\pi\)
\(542\) −3.49120 + 10.7448i −0.149960 + 0.461529i
\(543\) 0 0
\(544\) 28.5813i 1.22541i
\(545\) −20.2100 −0.865703
\(546\) 0 0
\(547\) 42.1895i 1.80389i 0.431847 + 0.901947i \(0.357862\pi\)
−0.431847 + 0.901947i \(0.642138\pi\)
\(548\) −15.9901 + 22.0084i −0.683061 + 0.940153i
\(549\) 0 0
\(550\) −3.09017 1.00406i −0.131765 0.0428131i
\(551\) 4.98915i 0.212545i
\(552\) 0 0
\(553\) 24.8096i 1.05501i
\(554\) 7.92007 24.3755i 0.336492 1.03561i
\(555\) 0 0
\(556\) 22.7639 31.3319i 0.965406 1.32877i
\(557\) 24.4525 1.03609 0.518043 0.855355i \(-0.326661\pi\)
0.518043 + 0.855355i \(0.326661\pi\)
\(558\) 0 0
\(559\) −7.23607 4.41606i −0.306053 0.186779i
\(560\) −22.5955 + 7.34173i −0.954835 + 0.310245i
\(561\) 0 0
\(562\) −2.70820 + 8.33499i −0.114239 + 0.351591i
\(563\) 0.627058i 0.0264274i −0.999913 0.0132137i \(-0.995794\pi\)
0.999913 0.0132137i \(-0.00420617\pi\)
\(564\) 0 0
\(565\) −8.39984 −0.353384
\(566\) −1.27004 + 3.90879i −0.0533839 + 0.164299i
\(567\) 0 0
\(568\) −24.1803 + 17.5680i −1.01458 + 0.737139i
\(569\) −26.4553 −1.10906 −0.554532 0.832163i \(-0.687103\pi\)
−0.554532 + 0.832163i \(0.687103\pi\)
\(570\) 0 0
\(571\) 24.6215i 1.03038i −0.857077 0.515188i \(-0.827722\pi\)
0.857077 0.515188i \(-0.172278\pi\)
\(572\) −6.84010 + 2.84795i −0.285999 + 0.119079i
\(573\) 0 0
\(574\) 7.78708 + 2.53018i 0.325026 + 0.105607i
\(575\) 18.2802 0.762335
\(576\) 0 0
\(577\) 44.5588i 1.85501i −0.373816 0.927503i \(-0.621951\pi\)
0.373816 0.927503i \(-0.378049\pi\)
\(578\) −11.4700 3.72681i −0.477087 0.155015i
\(579\) 0 0
\(580\) 8.39984 11.5614i 0.348784 0.480060i
\(581\) 8.20830i 0.340538i
\(582\) 0 0
\(583\) 11.5614i 0.478824i
\(584\) 10.1050 7.34173i 0.418149 0.303803i
\(585\) 0 0
\(586\) 1.18034 + 0.383516i 0.0487594 + 0.0158429i
\(587\) −10.5174 −0.434100 −0.217050 0.976160i \(-0.569644\pi\)
−0.217050 + 0.976160i \(0.569644\pi\)
\(588\) 0 0
\(589\) 9.27354i 0.382110i
\(590\) −21.7625 7.07107i −0.895948 0.291111i
\(591\) 0 0
\(592\) −12.1564 37.4134i −0.499623 1.53768i
\(593\) 26.6637i 1.09495i −0.836823 0.547474i \(-0.815589\pi\)
0.836823 0.547474i \(-0.184411\pi\)
\(594\) 0 0
\(595\) 30.0098i 1.23028i
\(596\) −11.3950 8.27895i −0.466757 0.339119i
\(597\) 0 0
\(598\) 31.6480 27.1304i 1.29418 1.10944i
\(599\) 46.6653 1.90669 0.953347 0.301877i \(-0.0976132\pi\)
0.953347 + 0.301877i \(0.0976132\pi\)
\(600\) 0 0
\(601\) 19.4164 0.792012 0.396006 0.918248i \(-0.370396\pi\)
0.396006 + 0.918248i \(0.370396\pi\)
\(602\) 11.2978 + 3.67086i 0.460462 + 0.149613i
\(603\) 0 0
\(604\) −4.19992 + 5.78069i −0.170892 + 0.235213i
\(605\) 16.5324 0.672139
\(606\) 0 0
\(607\) 15.7082 0.637576 0.318788 0.947826i \(-0.396724\pi\)
0.318788 + 0.947826i \(0.396724\pi\)
\(608\) 6.56664i 0.266312i
\(609\) 0 0
\(610\) 8.29180 25.5195i 0.335725 1.03326i
\(611\) −23.8175 14.5354i −0.963552 0.588040i
\(612\) 0 0
\(613\) 6.96497 0.281313 0.140656 0.990058i \(-0.455079\pi\)
0.140656 + 0.990058i \(0.455079\pi\)
\(614\) −19.8415 6.44688i −0.800736 0.260175i
\(615\) 0 0
\(616\) 8.39984 6.10284i 0.338439 0.245890i
\(617\) 3.36861i 0.135615i −0.997698 0.0678075i \(-0.978400\pi\)
0.997698 0.0678075i \(-0.0216004\pi\)
\(618\) 0 0
\(619\) −29.7781 −1.19688 −0.598442 0.801166i \(-0.704213\pi\)
−0.598442 + 0.801166i \(0.704213\pi\)
\(620\) 15.6131 21.4896i 0.627038 0.863044i
\(621\) 0 0
\(622\) 32.9866 + 10.7180i 1.32264 + 0.429752i
\(623\) 32.2450 1.29187
\(624\) 0 0
\(625\) −8.81966 −0.352786
\(626\) −8.70500 2.82843i −0.347922 0.113047i
\(627\) 0 0
\(628\) 0.652476 0.898056i 0.0260366 0.0358363i
\(629\) −49.6899 −1.98127
\(630\) 0 0
\(631\) 22.2794i 0.886928i 0.896292 + 0.443464i \(0.146251\pi\)
−0.896292 + 0.443464i \(0.853749\pi\)
\(632\) 11.5449 + 15.8902i 0.459232 + 0.632078i
\(633\) 0 0
\(634\) 41.8328 + 13.5923i 1.66139 + 0.539819i
\(635\) 9.97505 0.395848
\(636\) 0 0
\(637\) −10.8262 + 17.7396i −0.428948 + 0.702867i
\(638\) −1.92989 + 5.93958i −0.0764050 + 0.235150i
\(639\) 0 0
\(640\) −11.0557 + 15.2169i −0.437016 + 0.601501i
\(641\) 43.9983 1.73783 0.868914 0.494963i \(-0.164818\pi\)
0.868914 + 0.494963i \(0.164818\pi\)
\(642\) 0 0
\(643\) −33.8734 −1.33584 −0.667918 0.744235i \(-0.732814\pi\)
−0.667918 + 0.744235i \(0.732814\pi\)
\(644\) −34.3349 + 47.2579i −1.35298 + 1.86222i
\(645\) 0 0
\(646\) −7.88854 2.56314i −0.310371 0.100846i
\(647\) −36.5603 −1.43733 −0.718667 0.695354i \(-0.755247\pi\)
−0.718667 + 0.695354i \(0.755247\pi\)
\(648\) 0 0
\(649\) 10.0000 0.392534
\(650\) 8.65638 7.42072i 0.339531 0.291064i
\(651\) 0 0
\(652\) −11.7130 8.50997i −0.458715 0.333276i
\(653\) 33.3688i 1.30582i 0.757435 + 0.652911i \(0.226452\pi\)
−0.757435 + 0.652911i \(0.773548\pi\)
\(654\) 0 0
\(655\) 27.5388i 1.07603i
\(656\) 6.16492 2.00310i 0.240700 0.0782080i
\(657\) 0 0
\(658\) 37.1865 + 12.0826i 1.44968 + 0.471030i
\(659\) 36.4126i 1.41843i 0.704991 + 0.709216i \(0.250951\pi\)
−0.704991 + 0.709216i \(0.749049\pi\)
\(660\) 0 0
\(661\) 46.3038 1.80101 0.900504 0.434847i \(-0.143198\pi\)
0.900504 + 0.434847i \(0.143198\pi\)
\(662\) −14.7890 4.80522i −0.574789 0.186760i
\(663\) 0 0
\(664\) 3.81966 + 5.25731i 0.148232 + 0.204023i
\(665\) 6.89484i 0.267370i
\(666\) 0 0
\(667\) 35.1361i 1.36047i
\(668\) 8.61236 11.8539i 0.333222 0.458641i
\(669\) 0 0
\(670\) −16.1869 5.25945i −0.625355 0.203190i
\(671\) 11.7264i 0.452692i
\(672\) 0 0
\(673\) −12.6525 −0.487717 −0.243859 0.969811i \(-0.578413\pi\)
−0.243859 + 0.969811i \(0.578413\pi\)
\(674\) −7.43496 2.41577i −0.286384 0.0930518i
\(675\) 0 0
\(676\) 3.97319 25.6946i 0.152815 0.988255i
\(677\) 17.8187i 0.684830i −0.939549 0.342415i \(-0.888755\pi\)
0.939549 0.342415i \(-0.111245\pi\)
\(678\) 0 0
\(679\) 41.3050 1.58514
\(680\) 13.9648 + 19.2209i 0.535525 + 0.737088i
\(681\) 0 0
\(682\) −3.58716 + 11.0401i −0.137359 + 0.422749i
\(683\) −10.5174 −0.402438 −0.201219 0.979546i \(-0.564490\pi\)
−0.201219 + 0.979546i \(0.564490\pi\)
\(684\) 0 0
\(685\) 22.6134i 0.864012i
\(686\) −1.92989 + 5.93958i −0.0736834 + 0.226774i
\(687\) 0 0
\(688\) 8.94427 2.90617i 0.340997 0.110797i
\(689\) −34.6304 21.1344i −1.31931 0.805156i
\(690\) 0 0
\(691\) 4.91735 0.187065 0.0935324 0.995616i \(-0.470184\pi\)
0.0935324 + 0.995616i \(0.470184\pi\)
\(692\) 13.2276 18.2063i 0.502840 0.692099i
\(693\) 0 0
\(694\) −8.94791 + 27.5388i −0.339658 + 1.04536i
\(695\) 32.1931i 1.22115i
\(696\) 0 0
\(697\) 8.18782i 0.310136i
\(698\) −18.2802 5.93958i −0.691914 0.224817i
\(699\) 0 0
\(700\) −9.39130 + 12.9260i −0.354958 + 0.488558i
\(701\) 26.8021i 1.01230i −0.862445 0.506151i \(-0.831068\pi\)
0.862445 0.506151i \(-0.168932\pi\)
\(702\) 0 0
\(703\) −11.4164 −0.430578
\(704\) 2.54009 7.81758i 0.0957331 0.294636i
\(705\) 0 0
\(706\) −9.00000 + 27.6992i −0.338719 + 1.04247i
\(707\) 28.4698 1.07072
\(708\) 0 0
\(709\) 8.39984 0.315463 0.157731 0.987482i \(-0.449582\pi\)
0.157731 + 0.987482i \(0.449582\pi\)
\(710\) 7.67752 23.6290i 0.288132 0.886779i
\(711\) 0 0
\(712\) 20.6525 15.0049i 0.773984 0.562332i
\(713\) 65.3089i 2.44584i
\(714\) 0 0
\(715\) 3.20845 5.25731i 0.119989 0.196612i
\(716\) 25.7181 35.3980i 0.961132 1.32288i
\(717\) 0 0
\(718\) −14.0344 + 43.1936i −0.523761 + 1.61197i
\(719\) −12.0349 −0.448826 −0.224413 0.974494i \(-0.572047\pi\)
−0.224413 + 0.974494i \(0.572047\pi\)
\(720\) 0 0
\(721\) 41.8295i 1.55781i
\(722\) 23.7425 + 7.71441i 0.883605 + 0.287101i
\(723\) 0 0
\(724\) −15.1246 + 20.8172i −0.562102 + 0.773667i
\(725\) 9.61045i 0.356923i
\(726\) 0 0
\(727\) −22.3607 −0.829312 −0.414656 0.909978i \(-0.636098\pi\)
−0.414656 + 0.909978i \(0.636098\pi\)
\(728\) 2.92512 + 36.3166i 0.108412 + 1.34598i
\(729\) 0 0
\(730\) −3.20845 + 9.87460i −0.118750 + 0.365475i
\(731\) 11.8792i 0.439367i
\(732\) 0 0
\(733\) −46.8519 −1.73051 −0.865256 0.501330i \(-0.832844\pi\)
−0.865256 + 0.501330i \(0.832844\pi\)
\(734\) −41.8625 13.6020i −1.54517 0.502057i
\(735\) 0 0
\(736\) 46.2455i 1.70463i
\(737\) 7.43798 0.273982
\(738\) 0 0
\(739\) 19.9434 0.733631 0.366816 0.930294i \(-0.380448\pi\)
0.366816 + 0.930294i \(0.380448\pi\)
\(740\) 26.4553 + 19.2209i 0.972516 + 0.706574i
\(741\) 0 0
\(742\) 54.0689 + 17.5680i 1.98493 + 0.644943i
\(743\) 47.5918i 1.74597i 0.487744 + 0.872987i \(0.337820\pi\)
−0.487744 + 0.872987i \(0.662180\pi\)
\(744\) 0 0
\(745\) 11.7082 0.428955
\(746\) −11.3950 + 35.0702i −0.417201 + 1.28401i
\(747\) 0 0
\(748\) −8.39984 6.10284i −0.307129 0.223142i
\(749\) −9.48993 −0.346755
\(750\) 0 0
\(751\) −54.5410 −1.99023 −0.995115 0.0987222i \(-0.968524\pi\)
−0.995115 + 0.0987222i \(0.968524\pi\)
\(752\) 29.4400 9.56564i 1.07357 0.348823i
\(753\) 0 0
\(754\) −14.2633 16.6383i −0.519438 0.605933i
\(755\) 5.93958i 0.216164i
\(756\) 0 0
\(757\) 8.50651i 0.309174i −0.987979 0.154587i \(-0.950595\pi\)
0.987979 0.154587i \(-0.0494047\pi\)
\(758\) −26.0867 8.47609i −0.947512 0.307865i
\(759\) 0 0
\(760\) 3.20845 + 4.41606i 0.116383 + 0.160187i
\(761\) 16.4304i 0.595601i −0.954628 0.297800i \(-0.903747\pi\)
0.954628 0.297800i \(-0.0962530\pi\)
\(762\) 0 0
\(763\) 43.4306i 1.57229i
\(764\) −3.12262 2.26872i −0.112973 0.0820794i
\(765\) 0 0
\(766\) 1.56231 4.80828i 0.0564484 0.173730i
\(767\) −18.2802 + 29.9535i −0.660058 + 1.08156i
\(768\) 0 0
\(769\) 24.1653i 0.871422i −0.900087 0.435711i \(-0.856497\pi\)
0.900087 0.435711i \(-0.143503\pi\)
\(770\) −2.66704 + 8.20830i −0.0961134 + 0.295807i
\(771\) 0 0
\(772\) −5.19139 + 7.14533i −0.186842 + 0.257166i
\(773\) −30.3176 −1.09045 −0.545224 0.838290i \(-0.683555\pi\)
−0.545224 + 0.838290i \(0.683555\pi\)
\(774\) 0 0
\(775\) 17.8633i 0.641669i
\(776\) 26.4553 19.2209i 0.949690 0.689990i
\(777\) 0 0
\(778\) 15.4695 47.6102i 0.554608 1.70691i
\(779\) 1.88118i 0.0674001i
\(780\) 0 0
\(781\) 10.8576i 0.388517i
\(782\) 55.5550 + 18.0509i 1.98664 + 0.645500i
\(783\) 0 0
\(784\) −7.12461 21.9273i −0.254450 0.783118i
\(785\) 0.922740i 0.0329340i
\(786\) 0 0
\(787\) 40.4996 1.44366 0.721828 0.692072i \(-0.243302\pi\)
0.721828 + 0.692072i \(0.243302\pi\)
\(788\) 37.5100 + 27.2526i 1.33624 + 0.970834i
\(789\) 0 0
\(790\) −15.5279 5.04531i −0.552457 0.179504i
\(791\)