Properties

Label 280.2.q.e.81.1
Level $280$
Weight $2$
Character 280.81
Analytic conductor $2.236$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.11337408.1
Defining polynomial: \(x^{6} + 18 x^{4} + 81 x^{2} + 12\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 81.1
Root \(-0.391571i\) of defining polynomial
Character \(\chi\) \(=\) 280.81
Dual form 280.2.q.e.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.29211 + 2.23800i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.292113 + 2.62958i) q^{7} +(-1.83911 - 3.18543i) q^{9} +O(q^{10})\) \(q+(-1.29211 + 2.23800i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.292113 + 2.62958i) q^{7} +(-1.83911 - 3.18543i) q^{9} +(-0.839111 + 1.45338i) q^{11} -4.84667 q^{13} +2.58423 q^{15} +(-1.00000 + 1.73205i) q^{17} +(-3.42334 - 5.92939i) q^{19} +(-5.50756 - 4.05146i) q^{21} +(1.13122 + 1.95934i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.75268 q^{27} +3.32178 q^{29} +(-4.58423 + 7.94011i) q^{31} +(-2.16845 - 3.75587i) q^{33} +(2.42334 - 1.06181i) q^{35} +(1.42334 + 2.46529i) q^{37} +(6.26245 - 10.8469i) q^{39} +9.52489 q^{41} +6.58423 q^{43} +(-1.83911 + 3.18543i) q^{45} +(6.10156 + 10.5682i) q^{47} +(-6.82934 - 1.53627i) q^{49} +(-2.58423 - 4.47601i) q^{51} +(-3.74511 + 6.48673i) q^{53} +1.67822 q^{55} +17.6933 q^{57} +(-4.00000 + 6.92820i) q^{59} +(3.24511 + 5.62070i) q^{61} +(8.91357 - 3.90558i) q^{63} +(2.42334 + 4.19734i) q^{65} +(2.87634 - 4.98196i) q^{67} -5.84667 q^{69} +(5.84667 - 10.1267i) q^{73} +(-1.29211 - 2.23800i) q^{75} +(-3.57666 - 2.63106i) q^{77} +(-2.84667 - 4.93058i) q^{79} +(3.25268 - 5.63380i) q^{81} -12.5842 q^{83} +2.00000 q^{85} +(-4.29211 + 7.43416i) q^{87} +(2.92334 + 5.06337i) q^{89} +(1.41577 - 12.7447i) q^{91} +(-11.8467 - 20.5190i) q^{93} +(-3.42334 + 5.92939i) q^{95} -2.00000 q^{97} +6.17287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{5} + 6q^{7} - 9q^{9} + O(q^{10}) \) \( 6q - 3q^{5} + 6q^{7} - 9q^{9} - 3q^{11} + 6q^{13} - 6q^{17} - 3q^{19} - 3q^{23} - 3q^{25} - 36q^{27} + 24q^{29} - 12q^{31} + 18q^{33} - 3q^{35} - 9q^{37} + 18q^{39} + 18q^{41} + 24q^{43} - 9q^{45} + 15q^{47} - 12q^{49} - 9q^{53} + 6q^{55} + 36q^{57} - 24q^{59} + 6q^{61} + 9q^{63} - 3q^{65} - 6q^{67} - 39q^{77} + 18q^{79} - 27q^{81} - 60q^{83} + 12q^{85} - 18q^{87} + 24q^{91} - 36q^{93} - 3q^{95} - 12q^{97} + 126q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0
\(3\) −1.29211 + 2.23800i −0.746002 + 1.29211i 0.203724 + 0.979028i \(0.434696\pi\)
−0.949725 + 0.313084i \(0.898638\pi\)
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) −0.292113 + 2.62958i −0.110408 + 0.993886i
\(8\) 0 0
\(9\) −1.83911 3.18543i −0.613037 1.06181i
\(10\) 0 0
\(11\) −0.839111 + 1.45338i −0.253001 + 0.438211i −0.964351 0.264627i \(-0.914751\pi\)
0.711349 + 0.702839i \(0.248084\pi\)
\(12\) 0 0
\(13\) −4.84667 −1.34422 −0.672112 0.740449i \(-0.734613\pi\)
−0.672112 + 0.740449i \(0.734613\pi\)
\(14\) 0 0
\(15\) 2.58423 0.667244
\(16\) 0 0
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 0 0
\(19\) −3.42334 5.92939i −0.785367 1.36030i −0.928779 0.370633i \(-0.879141\pi\)
0.143412 0.989663i \(-0.454192\pi\)
\(20\) 0 0
\(21\) −5.50756 4.05146i −1.20185 0.884101i
\(22\) 0 0
\(23\) 1.13122 + 1.95934i 0.235876 + 0.408550i 0.959527 0.281617i \(-0.0908706\pi\)
−0.723651 + 0.690166i \(0.757537\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 1.75268 0.337303
\(28\) 0 0
\(29\) 3.32178 0.616839 0.308419 0.951250i \(-0.400200\pi\)
0.308419 + 0.951250i \(0.400200\pi\)
\(30\) 0 0
\(31\) −4.58423 + 7.94011i −0.823351 + 1.42609i 0.0798217 + 0.996809i \(0.474565\pi\)
−0.903173 + 0.429277i \(0.858768\pi\)
\(32\) 0 0
\(33\) −2.16845 3.75587i −0.377479 0.653813i
\(34\) 0 0
\(35\) 2.42334 1.06181i 0.409619 0.179479i
\(36\) 0 0
\(37\) 1.42334 + 2.46529i 0.233995 + 0.405291i 0.958980 0.283473i \(-0.0914867\pi\)
−0.724985 + 0.688765i \(0.758153\pi\)
\(38\) 0 0
\(39\) 6.26245 10.8469i 1.00279 1.73689i
\(40\) 0 0
\(41\) 9.52489 1.48754 0.743769 0.668437i \(-0.233036\pi\)
0.743769 + 0.668437i \(0.233036\pi\)
\(42\) 0 0
\(43\) 6.58423 1.00408 0.502042 0.864843i \(-0.332582\pi\)
0.502042 + 0.864843i \(0.332582\pi\)
\(44\) 0 0
\(45\) −1.83911 + 3.18543i −0.274158 + 0.474856i
\(46\) 0 0
\(47\) 6.10156 + 10.5682i 0.890004 + 1.54153i 0.839869 + 0.542789i \(0.182632\pi\)
0.0501344 + 0.998742i \(0.484035\pi\)
\(48\) 0 0
\(49\) −6.82934 1.53627i −0.975620 0.219466i
\(50\) 0 0
\(51\) −2.58423 4.47601i −0.361864 0.626767i
\(52\) 0 0
\(53\) −3.74511 + 6.48673i −0.514431 + 0.891021i 0.485429 + 0.874276i \(0.338664\pi\)
−0.999860 + 0.0167445i \(0.994670\pi\)
\(54\) 0 0
\(55\) 1.67822 0.226291
\(56\) 0 0
\(57\) 17.6933 2.34354
\(58\) 0 0
\(59\) −4.00000 + 6.92820i −0.520756 + 0.901975i 0.478953 + 0.877841i \(0.341016\pi\)
−0.999709 + 0.0241347i \(0.992317\pi\)
\(60\) 0 0
\(61\) 3.24511 + 5.62070i 0.415494 + 0.719657i 0.995480 0.0949692i \(-0.0302753\pi\)
−0.579986 + 0.814627i \(0.696942\pi\)
\(62\) 0 0
\(63\) 8.91357 3.90558i 1.12300 0.492056i
\(64\) 0 0
\(65\) 2.42334 + 4.19734i 0.300578 + 0.520616i
\(66\) 0 0
\(67\) 2.87634 4.98196i 0.351401 0.608644i −0.635094 0.772434i \(-0.719039\pi\)
0.986495 + 0.163791i \(0.0523722\pi\)
\(68\) 0 0
\(69\) −5.84667 −0.703857
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 5.84667 10.1267i 0.684301 1.18524i −0.289355 0.957222i \(-0.593441\pi\)
0.973656 0.228022i \(-0.0732260\pi\)
\(74\) 0 0
\(75\) −1.29211 2.23800i −0.149200 0.258423i
\(76\) 0 0
\(77\) −3.57666 2.63106i −0.407599 0.299837i
\(78\) 0 0
\(79\) −2.84667 4.93058i −0.320276 0.554734i 0.660269 0.751029i \(-0.270442\pi\)
−0.980545 + 0.196295i \(0.937109\pi\)
\(80\) 0 0
\(81\) 3.25268 5.63380i 0.361408 0.625978i
\(82\) 0 0
\(83\) −12.5842 −1.38130 −0.690649 0.723190i \(-0.742675\pi\)
−0.690649 + 0.723190i \(0.742675\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 0 0
\(87\) −4.29211 + 7.43416i −0.460163 + 0.797025i
\(88\) 0 0
\(89\) 2.92334 + 5.06337i 0.309873 + 0.536716i 0.978334 0.207031i \(-0.0663801\pi\)
−0.668461 + 0.743747i \(0.733047\pi\)
\(90\) 0 0
\(91\) 1.41577 12.7447i 0.148414 1.33601i
\(92\) 0 0
\(93\) −11.8467 20.5190i −1.22844 2.12773i
\(94\) 0 0
\(95\) −3.42334 + 5.92939i −0.351227 + 0.608343i
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 6.17287 0.620397
\(100\) 0 0
\(101\) 8.50756 14.7355i 0.846534 1.46624i −0.0377483 0.999287i \(-0.512019\pi\)
0.884282 0.466953i \(-0.154648\pi\)
\(102\) 0 0
\(103\) −3.55456 6.15668i −0.350241 0.606635i 0.636050 0.771648i \(-0.280567\pi\)
−0.986292 + 0.165012i \(0.947234\pi\)
\(104\) 0 0
\(105\) −0.754885 + 6.79542i −0.0736692 + 0.663165i
\(106\) 0 0
\(107\) 0.876338 + 1.51786i 0.0847188 + 0.146737i 0.905271 0.424834i \(-0.139667\pi\)
−0.820553 + 0.571571i \(0.806334\pi\)
\(108\) 0 0
\(109\) −9.77001 + 16.9222i −0.935797 + 1.62085i −0.162591 + 0.986694i \(0.551985\pi\)
−0.773206 + 0.634154i \(0.781348\pi\)
\(110\) 0 0
\(111\) −7.35644 −0.698243
\(112\) 0 0
\(113\) 10.3369 0.972414 0.486207 0.873844i \(-0.338380\pi\)
0.486207 + 0.873844i \(0.338380\pi\)
\(114\) 0 0
\(115\) 1.13122 1.95934i 0.105487 0.182709i
\(116\) 0 0
\(117\) 8.91357 + 15.4387i 0.824059 + 1.42731i
\(118\) 0 0
\(119\) −4.26245 3.13553i −0.390738 0.287434i
\(120\) 0 0
\(121\) 4.09179 + 7.08718i 0.371981 + 0.644289i
\(122\) 0 0
\(123\) −12.3072 + 21.3168i −1.10971 + 1.92207i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −19.1836 −1.70227 −0.851133 0.524949i \(-0.824084\pi\)
−0.851133 + 0.524949i \(0.824084\pi\)
\(128\) 0 0
\(129\) −8.50756 + 14.7355i −0.749049 + 1.29739i
\(130\) 0 0
\(131\) 8.91357 + 15.4387i 0.778782 + 1.34889i 0.932644 + 0.360797i \(0.117495\pi\)
−0.153862 + 0.988092i \(0.549171\pi\)
\(132\) 0 0
\(133\) 16.5918 7.26987i 1.43869 0.630378i
\(134\) 0 0
\(135\) −0.876338 1.51786i −0.0754232 0.130637i
\(136\) 0 0
\(137\) −2.00000 + 3.46410i −0.170872 + 0.295958i −0.938725 0.344668i \(-0.887992\pi\)
0.767853 + 0.640626i \(0.221325\pi\)
\(138\) 0 0
\(139\) −5.16845 −0.438382 −0.219191 0.975682i \(-0.570342\pi\)
−0.219191 + 0.975682i \(0.570342\pi\)
\(140\) 0 0
\(141\) −31.5356 −2.65578
\(142\) 0 0
\(143\) 4.06689 7.04407i 0.340091 0.589054i
\(144\) 0 0
\(145\) −1.66089 2.87674i −0.137929 0.238901i
\(146\) 0 0
\(147\) 12.2624 13.2991i 1.01139 1.09689i
\(148\) 0 0
\(149\) −0.398443 0.690123i −0.0326417 0.0565371i 0.849243 0.528002i \(-0.177059\pi\)
−0.881885 + 0.471465i \(0.843725\pi\)
\(150\) 0 0
\(151\) 8.26245 14.3110i 0.672388 1.16461i −0.304837 0.952405i \(-0.598602\pi\)
0.977225 0.212206i \(-0.0680648\pi\)
\(152\) 0 0
\(153\) 7.35644 0.594733
\(154\) 0 0
\(155\) 9.16845 0.736428
\(156\) 0 0
\(157\) −4.10156 + 7.10411i −0.327340 + 0.566969i −0.981983 0.188969i \(-0.939486\pi\)
0.654643 + 0.755938i \(0.272819\pi\)
\(158\) 0 0
\(159\) −9.67822 16.7632i −0.767533 1.32941i
\(160\) 0 0
\(161\) −5.48267 + 2.40229i −0.432095 + 0.189327i
\(162\) 0 0
\(163\) −1.84667 3.19853i −0.144643 0.250528i 0.784597 0.620006i \(-0.212870\pi\)
−0.929240 + 0.369478i \(0.879537\pi\)
\(164\) 0 0
\(165\) −2.16845 + 3.75587i −0.168814 + 0.292394i
\(166\) 0 0
\(167\) −0.262447 −0.0203087 −0.0101544 0.999948i \(-0.503232\pi\)
−0.0101544 + 0.999948i \(0.503232\pi\)
\(168\) 0 0
\(169\) 10.4902 0.806941
\(170\) 0 0
\(171\) −12.5918 + 21.8096i −0.962918 + 1.66782i
\(172\) 0 0
\(173\) 9.42334 + 16.3217i 0.716443 + 1.24092i 0.962400 + 0.271635i \(0.0875643\pi\)
−0.245957 + 0.969281i \(0.579102\pi\)
\(174\) 0 0
\(175\) −2.13122 1.56777i −0.161105 0.118512i
\(176\) 0 0
\(177\) −10.3369 17.9040i −0.776969 1.34575i
\(178\) 0 0
\(179\) 6.00756 10.4054i 0.449026 0.777736i −0.549297 0.835627i \(-0.685104\pi\)
0.998323 + 0.0578912i \(0.0184376\pi\)
\(180\) 0 0
\(181\) −6.03466 −0.448553 −0.224276 0.974526i \(-0.572002\pi\)
−0.224276 + 0.974526i \(0.572002\pi\)
\(182\) 0 0
\(183\) −16.7722 −1.23984
\(184\) 0 0
\(185\) 1.42334 2.46529i 0.104646 0.181252i
\(186\) 0 0
\(187\) −1.67822 2.90676i −0.122724 0.212564i
\(188\) 0 0
\(189\) −0.511979 + 4.60880i −0.0372410 + 0.335241i
\(190\) 0 0
\(191\) −1.41577 2.45219i −0.102442 0.177434i 0.810248 0.586087i \(-0.199332\pi\)
−0.912690 + 0.408652i \(0.865999\pi\)
\(192\) 0 0
\(193\) −6.49023 + 11.2414i −0.467177 + 0.809174i −0.999297 0.0374948i \(-0.988062\pi\)
0.532120 + 0.846669i \(0.321396\pi\)
\(194\) 0 0
\(195\) −12.5249 −0.896926
\(196\) 0 0
\(197\) −4.84667 −0.345311 −0.172656 0.984982i \(-0.555235\pi\)
−0.172656 + 0.984982i \(0.555235\pi\)
\(198\) 0 0
\(199\) 7.69334 13.3253i 0.545367 0.944603i −0.453217 0.891400i \(-0.649724\pi\)
0.998584 0.0532026i \(-0.0169429\pi\)
\(200\) 0 0
\(201\) 7.43311 + 12.8745i 0.524291 + 0.908098i
\(202\) 0 0
\(203\) −0.970334 + 8.73487i −0.0681041 + 0.613068i
\(204\) 0 0
\(205\) −4.76245 8.24880i −0.332624 0.576121i
\(206\) 0 0
\(207\) 4.16089 7.20687i 0.289202 0.500912i
\(208\) 0 0
\(209\) 11.4902 0.794796
\(210\) 0 0
\(211\) 9.18357 0.632223 0.316112 0.948722i \(-0.397623\pi\)
0.316112 + 0.948722i \(0.397623\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3.29211 5.70211i −0.224520 0.388880i
\(216\) 0 0
\(217\) −19.5400 14.3740i −1.32646 0.975769i
\(218\) 0 0
\(219\) 15.1091 + 26.1698i 1.02098 + 1.76839i
\(220\) 0 0
\(221\) 4.84667 8.39468i 0.326022 0.564687i
\(222\) 0 0
\(223\) −12.9805 −0.869236 −0.434618 0.900615i \(-0.643117\pi\)
−0.434618 + 0.900615i \(0.643117\pi\)
\(224\) 0 0
\(225\) 3.67822 0.245215
\(226\) 0 0
\(227\) 11.0151 19.0788i 0.731099 1.26630i −0.225314 0.974286i \(-0.572341\pi\)
0.956414 0.292015i \(-0.0943258\pi\)
\(228\) 0 0
\(229\) −2.15333 3.72967i −0.142296 0.246464i 0.786065 0.618144i \(-0.212115\pi\)
−0.928361 + 0.371680i \(0.878782\pi\)
\(230\) 0 0
\(231\) 10.5098 4.60497i 0.691492 0.302985i
\(232\) 0 0
\(233\) −9.00000 15.5885i −0.589610 1.02123i −0.994283 0.106773i \(-0.965948\pi\)
0.404674 0.914461i \(-0.367385\pi\)
\(234\) 0 0
\(235\) 6.10156 10.5682i 0.398022 0.689394i
\(236\) 0 0
\(237\) 14.7129 0.955705
\(238\) 0 0
\(239\) 10.8618 0.702591 0.351296 0.936265i \(-0.385741\pi\)
0.351296 + 0.936265i \(0.385741\pi\)
\(240\) 0 0
\(241\) −0.101557 + 0.175902i −0.00654187 + 0.0113309i −0.869278 0.494324i \(-0.835416\pi\)
0.862736 + 0.505655i \(0.168749\pi\)
\(242\) 0 0
\(243\) 11.0347 + 19.1126i 0.707874 + 1.22607i
\(244\) 0 0
\(245\) 2.08423 + 6.68251i 0.133156 + 0.426930i
\(246\) 0 0
\(247\) 16.5918 + 28.7378i 1.05571 + 1.82854i
\(248\) 0 0
\(249\) 16.2602 28.1636i 1.03045 1.78479i
\(250\) 0 0
\(251\) 5.03466 0.317785 0.158893 0.987296i \(-0.449208\pi\)
0.158893 + 0.987296i \(0.449208\pi\)
\(252\) 0 0
\(253\) −3.79689 −0.238708
\(254\) 0 0
\(255\) −2.58423 + 4.47601i −0.161830 + 0.280299i
\(256\) 0 0
\(257\) −11.6933 20.2535i −0.729411 1.26338i −0.957133 0.289650i \(-0.906461\pi\)
0.227722 0.973726i \(-0.426872\pi\)
\(258\) 0 0
\(259\) −6.89844 + 3.02263i −0.428648 + 0.187817i
\(260\) 0 0
\(261\) −6.10912 10.5813i −0.378145 0.654966i
\(262\) 0 0
\(263\) −13.5546 + 23.4772i −0.835810 + 1.44767i 0.0575594 + 0.998342i \(0.481668\pi\)
−0.893369 + 0.449323i \(0.851665\pi\)
\(264\) 0 0
\(265\) 7.49023 0.460121
\(266\) 0 0
\(267\) −15.1091 −0.924663
\(268\) 0 0
\(269\) −3.24511 + 5.62070i −0.197858 + 0.342700i −0.947834 0.318765i \(-0.896732\pi\)
0.749976 + 0.661466i \(0.230065\pi\)
\(270\) 0 0
\(271\) 11.6933 + 20.2535i 0.710320 + 1.23031i 0.964737 + 0.263216i \(0.0847831\pi\)
−0.254417 + 0.967095i \(0.581884\pi\)
\(272\) 0 0
\(273\) 26.6933 + 19.6361i 1.61555 + 1.18843i
\(274\) 0 0
\(275\) −0.839111 1.45338i −0.0506003 0.0876422i
\(276\) 0 0
\(277\) −1.83155 + 3.17234i −0.110047 + 0.190607i −0.915789 0.401660i \(-0.868434\pi\)
0.805742 + 0.592267i \(0.201767\pi\)
\(278\) 0 0
\(279\) 33.7236 2.01898
\(280\) 0 0
\(281\) 13.8965 0.828993 0.414497 0.910051i \(-0.363958\pi\)
0.414497 + 0.910051i \(0.363958\pi\)
\(282\) 0 0
\(283\) 10.1685 17.6123i 0.604452 1.04694i −0.387686 0.921791i \(-0.626726\pi\)
0.992138 0.125150i \(-0.0399411\pi\)
\(284\) 0 0
\(285\) −8.84667 15.3229i −0.524032 0.907649i
\(286\) 0 0
\(287\) −2.78234 + 25.0464i −0.164236 + 1.47844i
\(288\) 0 0
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 0 0
\(291\) 2.58423 4.47601i 0.151490 0.262388i
\(292\) 0 0
\(293\) 18.8467 1.10103 0.550517 0.834824i \(-0.314431\pi\)
0.550517 + 0.834824i \(0.314431\pi\)
\(294\) 0 0
\(295\) 8.00000 0.465778
\(296\) 0 0
\(297\) −1.47069 + 2.54731i −0.0853380 + 0.147810i
\(298\) 0 0
\(299\) −5.48267 9.49626i −0.317071 0.549183i
\(300\) 0 0
\(301\) −1.92334 + 17.3137i −0.110859 + 0.997946i
\(302\) 0 0
\(303\) 21.9855 + 38.0799i 1.26303 + 2.18763i
\(304\) 0 0
\(305\) 3.24511 5.62070i 0.185815 0.321841i
\(306\) 0 0
\(307\) −2.39623 −0.136760 −0.0683802 0.997659i \(-0.521783\pi\)
−0.0683802 + 0.997659i \(0.521783\pi\)
\(308\) 0 0
\(309\) 18.3716 1.04512
\(310\) 0 0
\(311\) 2.83155 4.90439i 0.160562 0.278102i −0.774508 0.632564i \(-0.782003\pi\)
0.935071 + 0.354462i \(0.115336\pi\)
\(312\) 0 0
\(313\) −14.8618 25.7414i −0.840038 1.45499i −0.889861 0.456231i \(-0.849199\pi\)
0.0498231 0.998758i \(-0.484134\pi\)
\(314\) 0 0
\(315\) −7.83911 5.76659i −0.441684 0.324910i
\(316\) 0 0
\(317\) −9.52489 16.4976i −0.534971 0.926597i −0.999165 0.0408636i \(-0.986989\pi\)
0.464193 0.885734i \(-0.346344\pi\)
\(318\) 0 0
\(319\) −2.78734 + 4.82781i −0.156061 + 0.270306i
\(320\) 0 0
\(321\) −4.52931 −0.252801
\(322\) 0 0
\(323\) 13.6933 0.761918
\(324\) 0 0
\(325\) 2.42334 4.19734i 0.134422 0.232827i
\(326\) 0 0
\(327\) −25.2479 43.7307i −1.39621 2.41831i
\(328\) 0 0
\(329\) −29.5722 + 12.9574i −1.63037 + 0.714365i
\(330\) 0 0
\(331\) −1.16089 2.01072i −0.0638083 0.110519i 0.832356 0.554241i \(-0.186991\pi\)
−0.896165 + 0.443722i \(0.853658\pi\)
\(332\) 0 0
\(333\) 5.23534 9.06788i 0.286895 0.496917i
\(334\) 0 0
\(335\) −5.75268 −0.314302
\(336\) 0 0
\(337\) −16.4062 −0.893704 −0.446852 0.894608i \(-0.647455\pi\)
−0.446852 + 0.894608i \(0.647455\pi\)
\(338\) 0 0
\(339\) −13.3564 + 23.1340i −0.725422 + 1.25647i
\(340\) 0 0
\(341\) −7.69334 13.3253i −0.416618 0.721603i
\(342\) 0 0
\(343\) 6.03466 17.5095i 0.325841 0.945425i
\(344\) 0 0
\(345\) 2.92334 + 5.06337i 0.157387 + 0.272602i
\(346\) 0 0
\(347\) −2.29211 + 3.97006i −0.123047 + 0.213124i −0.920968 0.389639i \(-0.872600\pi\)
0.797921 + 0.602762i \(0.205933\pi\)
\(348\) 0 0
\(349\) 12.3716 0.662235 0.331117 0.943590i \(-0.392574\pi\)
0.331117 + 0.943590i \(0.392574\pi\)
\(350\) 0 0
\(351\) −8.49465 −0.453411
\(352\) 0 0
\(353\) −9.69334 + 16.7894i −0.515925 + 0.893608i 0.483904 + 0.875121i \(0.339218\pi\)
−0.999829 + 0.0184869i \(0.994115\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 12.5249 5.48792i 0.662888 0.290451i
\(358\) 0 0
\(359\) 4.90600 + 8.49745i 0.258929 + 0.448478i 0.965955 0.258709i \(-0.0832971\pi\)
−0.707026 + 0.707187i \(0.749964\pi\)
\(360\) 0 0
\(361\) −13.9385 + 24.1421i −0.733603 + 1.27064i
\(362\) 0 0
\(363\) −21.1482 −1.10999
\(364\) 0 0
\(365\) −11.6933 −0.612058
\(366\) 0 0
\(367\) 6.35901 11.0141i 0.331937 0.574933i −0.650954 0.759117i \(-0.725631\pi\)
0.982892 + 0.184184i \(0.0589644\pi\)
\(368\) 0 0
\(369\) −17.5173 30.3409i −0.911916 1.57948i
\(370\) 0 0
\(371\) −15.9634 11.7429i −0.828776 0.609662i
\(372\) 0 0
\(373\) 8.20311 + 14.2082i 0.424741 + 0.735673i 0.996396 0.0848208i \(-0.0270318\pi\)
−0.571655 + 0.820494i \(0.693698\pi\)
\(374\) 0 0
\(375\) −1.29211 + 2.23800i −0.0667244 + 0.115570i
\(376\) 0 0
\(377\) −16.0996 −0.829170
\(378\) 0 0
\(379\) 14.4707 0.743309 0.371655 0.928371i \(-0.378791\pi\)
0.371655 + 0.928371i \(0.378791\pi\)
\(380\) 0 0
\(381\) 24.7873 42.9329i 1.26989 2.19952i
\(382\) 0 0
\(383\) 1.77478 + 3.07401i 0.0906871 + 0.157075i 0.907800 0.419402i \(-0.137760\pi\)
−0.817113 + 0.576477i \(0.804427\pi\)
\(384\) 0 0
\(385\) −0.490230 + 4.41301i −0.0249844 + 0.224908i
\(386\) 0 0
\(387\) −12.1091 20.9736i −0.615541 1.06615i
\(388\) 0 0
\(389\) −4.49023 + 7.77731i −0.227664 + 0.394325i −0.957115 0.289707i \(-0.906442\pi\)
0.729452 + 0.684032i \(0.239775\pi\)
\(390\) 0 0
\(391\) −4.52489 −0.228834
\(392\) 0 0
\(393\) −46.0693 −2.32389
\(394\) 0 0
\(395\) −2.84667 + 4.93058i −0.143232 + 0.248084i
\(396\) 0 0
\(397\) 14.0498 + 24.3349i 0.705139 + 1.22134i 0.966642 + 0.256133i \(0.0824486\pi\)
−0.261503 + 0.965203i \(0.584218\pi\)
\(398\) 0 0
\(399\) −5.16845 + 46.5260i −0.258746 + 2.32921i
\(400\) 0 0
\(401\) 13.3467 + 23.1171i 0.666501 + 1.15441i 0.978876 + 0.204455i \(0.0655421\pi\)
−0.312375 + 0.949959i \(0.601125\pi\)
\(402\) 0 0
\(403\) 22.2182 38.4831i 1.10677 1.91698i
\(404\) 0 0
\(405\) −6.50535 −0.323254
\(406\) 0 0
\(407\) −4.77735 −0.236804
\(408\) 0 0
\(409\) −14.0325 + 24.3049i −0.693860 + 1.20180i 0.276703 + 0.960955i \(0.410758\pi\)
−0.970563 + 0.240846i \(0.922575\pi\)
\(410\) 0 0
\(411\) −5.16845 8.95202i −0.254941 0.441571i
\(412\) 0 0
\(413\) −17.0498 12.5421i −0.838965 0.617157i
\(414\) 0 0
\(415\) 6.29211 + 10.8983i 0.308868 + 0.534974i
\(416\) 0 0
\(417\) 6.67822 11.5670i 0.327034 0.566439i
\(418\) 0 0
\(419\) −18.8769 −0.922198 −0.461099 0.887349i \(-0.652545\pi\)
−0.461099 + 0.887349i \(0.652545\pi\)
\(420\) 0 0
\(421\) −28.1836 −1.37358 −0.686792 0.726854i \(-0.740982\pi\)
−0.686792 + 0.726854i \(0.740982\pi\)
\(422\) 0 0
\(423\) 22.4429 38.8722i 1.09121 1.89003i
\(424\) 0 0
\(425\) −1.00000 1.73205i −0.0485071 0.0840168i
\(426\) 0 0
\(427\) −15.7280 + 6.89140i −0.761132 + 0.333498i
\(428\) 0 0
\(429\) 10.5098 + 18.2035i 0.507416 + 0.878871i
\(430\) 0 0
\(431\) −1.41577 + 2.45219i −0.0681955 + 0.118118i −0.898107 0.439777i \(-0.855057\pi\)
0.829912 + 0.557895i \(0.188391\pi\)
\(432\) 0 0
\(433\) −2.33690 −0.112304 −0.0561522 0.998422i \(-0.517883\pi\)
−0.0561522 + 0.998422i \(0.517883\pi\)
\(434\) 0 0
\(435\) 8.58423 0.411582
\(436\) 0 0
\(437\) 7.74511 13.4149i 0.370499 0.641723i
\(438\) 0 0
\(439\) 3.03466 + 5.25619i 0.144837 + 0.250864i 0.929312 0.369296i \(-0.120401\pi\)
−0.784475 + 0.620160i \(0.787068\pi\)
\(440\) 0 0
\(441\) 7.66624 + 24.5798i 0.365059 + 1.17047i
\(442\) 0 0
\(443\) −5.80188 10.0492i −0.275656 0.477450i 0.694645 0.719353i \(-0.255562\pi\)
−0.970300 + 0.241903i \(0.922228\pi\)
\(444\) 0 0
\(445\) 2.92334 5.06337i 0.138579 0.240027i
\(446\) 0 0
\(447\) 2.05933 0.0974031
\(448\) 0 0
\(449\) 4.13821 0.195294 0.0976470 0.995221i \(-0.468868\pi\)
0.0976470 + 0.995221i \(0.468868\pi\)
\(450\) 0 0
\(451\) −7.99244 + 13.8433i −0.376349 + 0.651856i
\(452\) 0 0
\(453\) 21.3520 + 36.9828i 1.00321 + 1.73760i
\(454\) 0 0
\(455\) −11.7451 + 5.14625i −0.550619 + 0.241260i
\(456\) 0 0
\(457\) 6.32178 + 10.9496i 0.295720 + 0.512203i 0.975152 0.221536i \(-0.0711070\pi\)
−0.679432 + 0.733739i \(0.737774\pi\)
\(458\) 0 0
\(459\) −1.75268 + 3.03572i −0.0818079 + 0.141695i
\(460\) 0 0
\(461\) 20.7129 0.964695 0.482348 0.875980i \(-0.339784\pi\)
0.482348 + 0.875980i \(0.339784\pi\)
\(462\) 0 0
\(463\) −16.3811 −0.761295 −0.380647 0.924720i \(-0.624299\pi\)
−0.380647 + 0.924720i \(0.624299\pi\)
\(464\) 0 0
\(465\) −11.8467 + 20.5190i −0.549376 + 0.951548i
\(466\) 0 0
\(467\) 0.861215 + 1.49167i 0.0398523 + 0.0690262i 0.885264 0.465090i \(-0.153978\pi\)
−0.845411 + 0.534116i \(0.820645\pi\)
\(468\) 0 0
\(469\) 12.2602 + 9.01884i 0.566125 + 0.416452i
\(470\) 0 0
\(471\) −10.5993 18.3586i −0.488392 0.845920i
\(472\) 0 0
\(473\) −5.52489 + 9.56940i −0.254035 + 0.440001i
\(474\) 0 0
\(475\) 6.84667 0.314147
\(476\) 0 0
\(477\) 27.5507 1.26146
\(478\) 0 0
\(479\) 0.890881 1.54305i 0.0407054 0.0705038i −0.844955 0.534838i \(-0.820373\pi\)
0.885660 + 0.464334i \(0.153706\pi\)
\(480\) 0 0
\(481\) −6.89844 11.9485i −0.314542 0.544803i
\(482\) 0 0
\(483\) 1.70789 15.3743i 0.0777116 0.699553i
\(484\) 0 0
\(485\) 1.00000 + 1.73205i 0.0454077 + 0.0786484i
\(486\) 0 0
\(487\) 5.50977 9.54320i 0.249672 0.432444i −0.713763 0.700387i \(-0.753011\pi\)
0.963435 + 0.267943i \(0.0863440\pi\)
\(488\) 0 0
\(489\) 9.54443 0.431614
\(490\) 0 0
\(491\) −20.9311 −0.944608 −0.472304 0.881436i \(-0.656578\pi\)
−0.472304 + 0.881436i \(0.656578\pi\)
\(492\) 0 0
\(493\) −3.32178 + 5.75349i −0.149605 + 0.259124i
\(494\) 0 0
\(495\) −3.08643 5.34586i −0.138725 0.240279i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3.75268 + 6.49983i 0.167993 + 0.290972i 0.937714 0.347408i \(-0.112938\pi\)
−0.769721 + 0.638380i \(0.779605\pi\)
\(500\) 0 0
\(501\) 0.339111 0.587357i 0.0151503 0.0262412i
\(502\) 0 0
\(503\) 20.5842 0.917805 0.458903 0.888487i \(-0.348243\pi\)
0.458903 + 0.888487i \(0.348243\pi\)
\(504\) 0 0
\(505\) −17.0151 −0.757163
\(506\) 0 0
\(507\) −13.5546 + 23.4772i −0.601979 + 1.04266i
\(508\) 0 0
\(509\) −6.82934 11.8288i −0.302705 0.524301i 0.674043 0.738693i \(-0.264556\pi\)
−0.976748 + 0.214392i \(0.931223\pi\)
\(510\) 0 0
\(511\) 24.9211 + 18.3324i 1.10245 + 0.810978i
\(512\) 0 0
\(513\) −6.00000 10.3923i −0.264906 0.458831i
\(514\) 0 0
\(515\) −3.55456 + 6.15668i −0.156633 + 0.271296i
\(516\) 0 0
\(517\) −20.4795 −0.900688
\(518\) 0 0
\(519\) −48.7040 −2.13787
\(520\) 0 0
\(521\) 21.0820 36.5151i 0.923620 1.59976i 0.129854 0.991533i \(-0.458549\pi\)
0.793766 0.608224i \(-0.208118\pi\)
\(522\) 0 0
\(523\) 15.3218 + 26.5381i 0.669975 + 1.16043i 0.977911 + 0.209023i \(0.0670284\pi\)
−0.307936 + 0.951407i \(0.599638\pi\)
\(524\) 0 0
\(525\) 6.26245 2.74396i 0.273316 0.119756i
\(526\) 0 0
\(527\) −9.16845 15.8802i −0.399384 0.691753i
\(528\) 0 0
\(529\) 8.94067 15.4857i 0.388725 0.673291i
\(530\) 0 0
\(531\) 29.4258 1.27697
\(532\) 0 0
\(533\) −46.1640 −1.99959
\(534\) 0 0
\(535\) 0.876338 1.51786i 0.0378874 0.0656229i
\(536\) 0 0
\(537\) 15.5249 + 26.8899i 0.669949 + 1.16038i
\(538\) 0 0
\(539\) 7.96335 8.63654i 0.343006 0.372002i
\(540\) 0 0
\(541\) 16.8445 + 29.1755i 0.724200 + 1.25435i 0.959302 + 0.282381i \(0.0911241\pi\)
−0.235102 + 0.971971i \(0.575543\pi\)
\(542\) 0 0
\(543\) 7.79747 13.5056i 0.334621 0.579581i
\(544\) 0 0
\(545\) 19.5400 0.837002
\(546\) 0 0
\(547\) −3.03979 −0.129972 −0.0649861 0.997886i \(-0.520700\pi\)
−0.0649861 + 0.997886i \(0.520700\pi\)
\(548\) 0 0
\(549\) 11.9363 20.6742i 0.509427 0.882353i
\(550\) 0 0
\(551\) −11.3716 19.6961i −0.484445 0.839083i
\(552\) 0 0
\(553\) 13.7969 6.04526i 0.586703 0.257070i
\(554\) 0 0
\(555\) 3.67822 + 6.37087i 0.156132 + 0.270428i
\(556\) 0 0
\(557\) −9.08202 + 15.7305i −0.384817 + 0.666523i −0.991744 0.128235i \(-0.959069\pi\)
0.606926 + 0.794758i \(0.292402\pi\)
\(558\) 0 0
\(559\) −31.9116 −1.34972
\(560\) 0 0
\(561\) 8.67380 0.366208
\(562\) 0 0
\(563\) 18.4952 32.0347i 0.779481 1.35010i −0.152760 0.988263i \(-0.548816\pi\)
0.932241 0.361837i \(-0.117850\pi\)
\(564\) 0 0
\(565\) −5.16845 8.95202i −0.217438 0.376614i
\(566\) 0 0
\(567\) 13.8644 + 10.1989i 0.582248 + 0.428312i
\(568\) 0 0
\(569\) −16.3047 28.2405i −0.683527 1.18390i −0.973897 0.226990i \(-0.927112\pi\)
0.290370 0.956915i \(-0.406222\pi\)
\(570\) 0 0
\(571\) −20.2182 + 35.0190i −0.846107 + 1.46550i 0.0385496 + 0.999257i \(0.487726\pi\)
−0.884656 + 0.466243i \(0.845607\pi\)
\(572\) 0 0
\(573\) 7.31736 0.305687
\(574\) 0 0
\(575\) −2.26245 −0.0943505
\(576\) 0 0
\(577\) 19.0151 32.9352i 0.791610 1.37111i −0.133360 0.991068i \(-0.542577\pi\)
0.924970 0.380041i \(-0.124090\pi\)
\(578\) 0 0
\(579\) −16.7722 29.0503i −0.697030 1.20729i
\(580\) 0 0
\(581\) 3.67601 33.0912i 0.152507 1.37285i
\(582\) 0 0
\(583\) −6.28513 10.8862i −0.260304 0.450859i
\(584\) 0 0
\(585\) 8.91357 15.4387i 0.368531 0.638314i
\(586\) 0 0
\(587\) 34.0302 1.40458 0.702289 0.711892i \(-0.252161\pi\)
0.702289 + 0.711892i \(0.252161\pi\)
\(588\) 0 0
\(589\) 62.7734 2.58653
\(590\) 0 0
\(591\) 6.26245 10.8469i 0.257603 0.446181i
\(592\) 0 0
\(593\) 16.8618 + 29.2055i 0.692431 + 1.19933i 0.971039 + 0.238921i \(0.0767936\pi\)
−0.278608 + 0.960405i \(0.589873\pi\)
\(594\) 0 0
\(595\) −0.584225 + 5.25915i −0.0239509 + 0.215604i
\(596\) 0 0
\(597\) 19.8813 + 34.4355i 0.813689 + 1.40935i
\(598\) 0 0
\(599\) −3.15333 + 5.46172i −0.128841 + 0.223160i −0.923228 0.384253i \(-0.874459\pi\)
0.794387 + 0.607413i \(0.207793\pi\)
\(600\) 0 0
\(601\) −11.2871 −0.460411 −0.230206 0.973142i \(-0.573940\pi\)
−0.230206 + 0.973142i \(0.573940\pi\)
\(602\) 0 0
\(603\) −21.1596 −0.861686
\(604\) 0 0
\(605\) 4.09179 7.08718i 0.166355 0.288135i
\(606\) 0 0
\(607\) 7.73057 + 13.3897i 0.313774 + 0.543473i 0.979176 0.203012i \(-0.0650732\pi\)
−0.665402 + 0.746485i \(0.731740\pi\)
\(608\) 0 0
\(609\) −18.2949 13.4580i −0.741347 0.545348i
\(610\) 0 0
\(611\) −29.5722 51.2206i −1.19637 2.07217i
\(612\) 0 0
\(613\) 11.0820 19.1946i 0.447598 0.775263i −0.550631 0.834749i \(-0.685613\pi\)
0.998229 + 0.0594857i \(0.0189461\pi\)
\(614\) 0 0
\(615\) 24.6145 0.992551
\(616\) 0 0
\(617\) −14.9805 −0.603091 −0.301545 0.953452i \(-0.597502\pi\)
−0.301545 + 0.953452i \(0.597502\pi\)
\(618\) 0 0
\(619\) −11.8196 + 20.4721i −0.475069 + 0.822843i −0.999592 0.0285529i \(-0.990910\pi\)
0.524524 + 0.851396i \(0.324243\pi\)
\(620\) 0 0
\(621\) 1.98267 + 3.43408i 0.0795617 + 0.137805i
\(622\) 0 0
\(623\) −14.1685 + 6.20806i −0.567647 + 0.248721i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) −14.8467 + 25.7152i −0.592919 + 1.02697i
\(628\) 0 0
\(629\) −5.69334 −0.227008
\(630\) 0 0
\(631\) −13.7818 −0.548643 −0.274322 0.961638i \(-0.588453\pi\)
−0.274322 + 0.961638i \(0.588453\pi\)
\(632\) 0 0
\(633\) −11.8662 + 20.5529i −0.471640 + 0.816904i
\(634\) 0 0
\(635\) 9.59179 + 16.6135i 0.380638 + 0.659285i
\(636\) 0 0
\(637\) 33.0996 + 7.44577i 1.31145 + 0.295012i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −21.9309 + 37.9854i −0.866218 + 1.50033i −0.000386062 1.00000i \(0.500123\pi\)
−0.865832 + 0.500334i \(0.833210\pi\)
\(642\) 0 0
\(643\) 7.04979 0.278016 0.139008 0.990291i \(-0.455609\pi\)
0.139008 + 0.990291i \(0.455609\pi\)
\(644\) 0 0
\(645\) 17.0151 0.669970
\(646\) 0 0
\(647\) 12.2403 21.2009i 0.481217 0.833493i −0.518550 0.855047i \(-0.673528\pi\)
0.999768 + 0.0215540i \(0.00686140\pi\)
\(648\) 0 0
\(649\) −6.71288 11.6271i −0.263504 0.456402i
\(650\) 0 0
\(651\) 57.4169 25.1579i 2.25035 0.986014i
\(652\) 0 0
\(653\) −0.408213 0.707046i −0.0159746 0.0276688i 0.857928 0.513771i \(-0.171752\pi\)
−0.873902 + 0.486102i \(0.838418\pi\)
\(654\) 0 0
\(655\) 8.91357 15.4387i 0.348282 0.603242i
\(656\) 0 0
\(657\) −43.0107 −1.67801
\(658\) 0 0
\(659\) 21.2871 0.829228 0.414614 0.909997i \(-0.363917\pi\)
0.414614 + 0.909997i \(0.363917\pi\)
\(660\) 0 0
\(661\) −12.9731 + 22.4701i −0.504596 + 0.873986i 0.495390 + 0.868671i \(0.335025\pi\)
−0.999986 + 0.00531513i \(0.998308\pi\)
\(662\) 0 0
\(663\) 12.5249 + 21.6938i 0.486427 + 0.842515i
\(664\) 0 0
\(665\) −14.5918 10.7340i −0.565845 0.416246i
\(666\) 0 0
\(667\) 3.75767 + 6.50848i 0.145498 + 0.252009i
\(668\) 0 0
\(669\) 16.7722 29.0503i 0.648451 1.12315i
\(670\) 0 0
\(671\) −10.8920 −0.420483
\(672\) 0 0
\(673\) 22.0693 0.850710 0.425355 0.905027i \(-0.360149\pi\)
0.425355 + 0.905027i \(0.360149\pi\)
\(674\) 0 0
\(675\) −0.876338 + 1.51786i −0.0337303 + 0.0584225i
\(676\) 0 0
\(677\) −2.74511 4.75468i −0.105503 0.182737i 0.808440 0.588578i \(-0.200312\pi\)
−0.913944 + 0.405841i \(0.866979\pi\)
\(678\) 0 0
\(679\) 0.584225 5.25915i 0.0224205 0.201828i
\(680\) 0 0
\(681\) 28.4656 + 49.3038i 1.09080 + 1.88933i
\(682\) 0 0
\(683\) −9.61389 + 16.6517i −0.367865 + 0.637161i −0.989232 0.146359i \(-0.953245\pi\)
0.621366 + 0.783520i \(0.286578\pi\)
\(684\) 0 0
\(685\) 4.00000 0.152832
\(686\) 0 0
\(687\) 11.1294 0.424612
\(688\) 0 0
\(689\) 18.1513 31.4390i 0.691511 1.19773i
\(690\) 0 0
\(691\) −7.10912 12.3134i −0.270444 0.468422i 0.698532 0.715579i \(-0.253837\pi\)
−0.968975 + 0.247157i \(0.920504\pi\)
\(692\) 0 0
\(693\) −1.80317 + 16.2320i −0.0684969 + 0.616604i
\(694\) 0 0
\(695\) 2.58423 + 4.47601i 0.0980253 + 0.169785i
\(696\) 0 0
\(697\) −9.52489 + 16.4976i −0.360781 + 0.624891i
\(698\) 0 0
\(699\) 46.5161 1.75940
\(700\) 0 0
\(701\) 14.1533 0.534564 0.267282 0.963618i \(-0.413875\pi\)
0.267282 + 0.963618i \(0.413875\pi\)
\(702\) 0 0
\(703\) 9.74511 16.8790i 0.367544 0.636605i
\(704\) 0 0
\(705\) 15.7678 + 27.3106i 0.593850 + 1.02858i
\(706\) 0 0
\(707\) 36.2630 + 26.6757i 1.36381 + 1.00324i
\(708\) 0 0
\(709\) −8.52268 14.7617i −0.320076 0.554388i 0.660427 0.750890i \(-0.270375\pi\)
−0.980503 + 0.196502i \(0.937042\pi\)
\(710\) 0 0
\(711\) −10.4707 + 18.1358i −0.392682 + 0.680144i
\(712\) 0 0
\(713\) −20.7431 −0.776836
\(714\) 0 0
\(715\) −8.13379 −0.304186
\(716\) 0 0
\(717\) −14.0347 + 24.3088i −0.524134 + 0.907827i
\(718\) 0 0
\(719\) 5.75268 + 9.96393i 0.214539 + 0.371592i 0.953130 0.302562i \(-0.0978419\pi\)
−0.738591 + 0.674154i \(0.764509\pi\)
\(720\) 0 0
\(721\) 17.2278 7.54854i 0.641596 0.281122i
\(722\) 0 0
\(723\) −0.262447 0.454571i −0.00976049 0.0169057i
\(724\) 0 0
\(725\) −1.66089 + 2.87674i −0.0616839 + 0.106840i
\(726\) 0 0
\(727\) 16.4114 0.608664 0.304332 0.952566i \(-0.401567\pi\)
0.304332 + 0.952566i \(0.401567\pi\)
\(728\) 0 0
\(729\) −37.5161 −1.38948
\(730\) 0 0
\(731\) −6.58423 + 11.4042i −0.243526 + 0.421800i
\(732\) 0 0
\(733\) 4.55712 + 7.89317i 0.168321 + 0.291541i 0.937830 0.347096i \(-0.112832\pi\)
−0.769509 + 0.638637i \(0.779499\pi\)
\(734\) 0 0
\(735\) −17.6486 3.97006i −0.650977 0.146438i
\(736\) 0 0
\(737\) 4.82713 + 8.36084i 0.177810 + 0.307975i
\(738\) 0 0
\(739\) 17.4978 30.3071i 0.643667 1.11486i −0.340941 0.940085i \(-0.610746\pi\)
0.984608 0.174779i \(-0.0559210\pi\)
\(740\) 0 0
\(741\) −85.7538 −3.15025
\(742\) 0 0
\(743\) −43.5305 −1.59698 −0.798489 0.602009i \(-0.794367\pi\)
−0.798489 + 0.602009i \(0.794367\pi\)
\(744\) 0 0
\(745\) −0.398443 + 0.690123i −0.0145978 + 0.0252842i
\(746\) 0 0
\(747\) 23.1438 + 40.0862i 0.846787 + 1.46668i
\(748\) 0 0
\(749\) −4.24732 + 1.86101i −0.155194 + 0.0679999i
\(750\) 0 0
\(751\) −3.15333 5.46172i −0.115067 0.199301i 0.802740 0.596329i \(-0.203375\pi\)
−0.917806 + 0.397028i \(0.870041\pi\)
\(752\) 0 0
\(753\) −6.50535 + 11.2676i −0.237068 + 0.410614i
\(754\) 0 0
\(755\) −16.5249 −0.601402
\(756\) 0 0
\(757\) 24.3369 0.884540 0.442270 0.896882i \(-0.354173\pi\)
0.442270 + 0.896882i \(0.354173\pi\)
\(758\) 0 0
\(759\) 4.90600 8.49745i 0.178077 0.308438i
\(760\) 0 0
\(761\) 14.1016 + 24.4246i 0.511181 + 0.885392i 0.999916 + 0.0129592i \(0.00412517\pi\)
−0.488735 + 0.872432i \(0.662541\pi\)
\(762\) 0 0
\(763\) −41.6441 30.6342i −1.50762 1.10903i
\(764\) 0 0
\(765\) −3.67822 6.37087i −0.132986 0.230339i
\(766\) 0 0
\(767\) 19.3867 33.5787i 0.700013 1.21246i
\(768\) 0 0
\(769\) −41.8965 −1.51082 −0.755412 0.655250i \(-0.772563\pi\)
−0.755412 + 0.655250i \(0.772563\pi\)
\(770\) 0 0
\(771\) 60.4365 2.17657
\(772\) 0 0
\(773\) −19.9287 + 34.5175i −0.716785 + 1.24151i 0.245482 + 0.969401i \(0.421054\pi\)
−0.962267 + 0.272107i \(0.912280\pi\)
\(774\) 0 0
\(775\) −4.58423 7.94011i −0.164670 0.285217i
\(776\) 0 0
\(777\) 2.14891 19.3443i 0.0770917 0.693974i
\(778\) 0 0
\(779\) −32.6069 56.4768i −1.16826 2.02349i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 5.82200 0.208061
\(784\) 0 0
\(785\) 8.20311 0.292782
\(786\) 0 0
\(787\) −17.6637 + 30.5944i −0.629642 + 1.09057i 0.357981 + 0.933729i \(0.383465\pi\)
−0.987623 + 0.156843i \(0.949868\pi\)
\(788\) 0 0
\(789\) −35.0280 60.6703i −1.24703 2.15992i
\(790\) 0 0
\(791\) −3.01954 + 27.1817i −0.107363 + 0.966469i
\(792\) 0 0
\(793\) −15.7280 27.2417i −0.558518 0.967381i
\(794\) 0 0
\(795\) −9.67822 + 16.7632i −0.343251 + 0.594528i
\(796\) 0 0
\(797\) 29.6933 1.05179