Properties

Label 1960.2.q.w.961.3
Level $1960$
Weight $2$
Character 1960.961
Analytic conductor $15.651$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.6506787962\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.3
Root \(-0.391571i\) of defining polynomial
Character \(\chi\) \(=\) 1960.961
Dual form 1960.2.q.w.361.3

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.29211 + 2.23800i 0.746002 + 1.29211i 0.949725 + 0.313084i \(0.101362\pi\)
−0.203724 + 0.979028i \(0.565304\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −1.83911 + 3.18543i −0.613037 + 1.06181i
\(10\) 0 0
\(11\) −0.839111 1.45338i −0.253001 0.438211i 0.711349 0.702839i \(-0.248084\pi\)
−0.964351 + 0.264627i \(0.914751\pi\)
\(12\) 0 0
\(13\) 4.84667 1.34422 0.672112 0.740449i \(-0.265387\pi\)
0.672112 + 0.740449i \(0.265387\pi\)
\(14\) 0 0
\(15\) 2.58423 0.667244
\(16\) 0 0
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 0 0
\(19\) 3.42334 5.92939i 0.785367 1.36030i −0.143412 0.989663i \(-0.545808\pi\)
0.928779 0.370633i \(-0.120859\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.13122 1.95934i 0.235876 0.408550i −0.723651 0.690166i \(-0.757537\pi\)
0.959527 + 0.281617i \(0.0908706\pi\)
\(24\) 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 0.903173 + 0.429277i \(0.141232\pi\)
−0.0798217 + 0.996809i \(0.525435\pi\)
\(32\) 0 0
\(33\) 2.16845 3.75587i 0.377479 0.653813i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.42334 2.46529i 0.233995 0.405291i −0.724985 0.688765i \(-0.758153\pi\)
0.958980 + 0.283473i \(0.0914867\pi\)
\(38\) 0 0
\(39\) 6.26245 + 10.8469i 1.00279 + 1.73689i
\(40\) 0 0
\(41\) −9.52489 −1.48754 −0.743769 0.668437i \(-0.766964\pi\)
−0.743769 + 0.668437i \(0.766964\pi\)
\(42\) 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 −0.0501344 + 0.998742i \(0.515965\pi\)
−0.839869 + 0.542789i \(0.817368\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −2.58423 + 4.47601i −0.361864 + 0.626767i
\(52\) 0 0
\(53\) −3.74511 6.48673i −0.514431 0.891021i −0.999860 0.0167445i \(-0.994670\pi\)
0.485429 0.874276i \(-0.338664\pi\)
\(54\) 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 0.999709 + 0.0241347i \(0.00768307\pi\)
−0.478953 + 0.877841i \(0.658984\pi\)
\(60\) 0 0
\(61\) −3.24511 + 5.62070i −0.415494 + 0.719657i −0.995480 0.0949692i \(-0.969725\pi\)
0.579986 + 0.814627i \(0.303058\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.42334 4.19734i 0.300578 0.520616i
\(66\) 0 0
\(67\) 2.87634 + 4.98196i 0.351401 + 0.608644i 0.986495 0.163791i \(-0.0523722\pi\)
−0.635094 + 0.772434i \(0.719039\pi\)
\(68\) 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 −0.973656 0.228022i \(-0.926774\pi\)
0.289355 0.957222i \(-0.406559\pi\)
\(74\) 0 0
\(75\) 1.29211 2.23800i 0.149200 0.258423i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −2.84667 + 4.93058i −0.320276 + 0.554734i −0.980545 0.196295i \(-0.937109\pi\)
0.660269 + 0.751029i \(0.270442\pi\)
\(80\) 0 0
\(81\) 3.25268 + 5.63380i 0.361408 + 0.625978i
\(82\) 0 0
\(83\) 12.5842 1.38130 0.690649 0.723190i \(-0.257325\pi\)
0.690649 + 0.723190i \(0.257325\pi\)
\(84\) 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 \(-0.933620\pi\)
0.668461 + 0.743747i \(0.266953\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 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 \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) 6.17287 0.620397
\(100\) 0 0
\(101\) −8.50756 14.7355i −0.846534 1.46624i −0.884282 0.466953i \(-0.845352\pi\)
0.0377483 0.999287i \(-0.487981\pi\)
\(102\) 0 0
\(103\) 3.55456 6.15668i 0.350241 0.606635i −0.636050 0.771648i \(-0.719433\pi\)
0.986292 + 0.165012i \(0.0527663\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.876338 1.51786i 0.0847188 0.146737i −0.820553 0.571571i \(-0.806334\pi\)
0.905271 + 0.424834i \(0.139667\pi\)
\(108\) 0 0
\(109\) −9.77001 16.9222i −0.935797 1.62085i −0.773206 0.634154i \(-0.781348\pi\)
−0.162591 0.986694i \(-0.551985\pi\)
\(110\) 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
\(119\) 0 0
\(120\) 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 0.153862 + 0.988092i \(0.450829\pi\)
−0.932644 + 0.360797i \(0.882505\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.876338 + 1.51786i −0.0754232 + 0.130637i
\(136\) 0 0
\(137\) −2.00000 3.46410i −0.170872 0.295958i 0.767853 0.640626i \(-0.221325\pi\)
−0.938725 + 0.344668i \(0.887992\pi\)
\(138\) 0 0
\(139\) 5.16845 0.438382 0.219191 0.975682i \(-0.429658\pi\)
0.219191 + 0.975682i \(0.429658\pi\)
\(140\) 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
\(147\) 0 0
\(148\) 0 0
\(149\) −0.398443 + 0.690123i −0.0326417 + 0.0565371i −0.881885 0.471465i \(-0.843725\pi\)
0.849243 + 0.528002i \(0.177059\pi\)
\(150\) 0 0
\(151\) 8.26245 + 14.3110i 0.672388 + 1.16461i 0.977225 + 0.212206i \(0.0680648\pi\)
−0.304837 + 0.952405i \(0.598602\pi\)
\(152\) 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 \(-0.0605145\pi\)
−0.654643 + 0.755938i \(0.727181\pi\)
\(158\) 0 0
\(159\) 9.67822 16.7632i 0.767533 1.32941i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.84667 + 3.19853i −0.144643 + 0.250528i −0.929240 0.369478i \(-0.879537\pi\)
0.784597 + 0.620006i \(0.212870\pi\)
\(164\) 0 0
\(165\) −2.16845 3.75587i −0.168814 0.292394i
\(166\) 0 0
\(167\) 0.262447 0.0203087 0.0101544 0.999948i \(-0.496768\pi\)
0.0101544 + 0.999948i \(0.496768\pi\)
\(168\) 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 0.245957 + 0.969281i \(0.420898\pi\)
−0.962400 + 0.271635i \(0.912436\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −10.3369 + 17.9040i −0.776969 + 1.34575i
\(178\) 0 0
\(179\) 6.00756 + 10.4054i 0.449026 + 0.777736i 0.998323 0.0578912i \(-0.0184376\pi\)
−0.549297 + 0.835627i \(0.685104\pi\)
\(180\) 0 0
\(181\) 6.03466 0.448553 0.224276 0.974526i \(-0.427998\pi\)
0.224276 + 0.974526i \(0.427998\pi\)
\(182\) 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 0
\(190\) 0 0
\(191\) −1.41577 + 2.45219i −0.102442 + 0.177434i −0.912690 0.408652i \(-0.865999\pi\)
0.810248 + 0.586087i \(0.199332\pi\)
\(192\) 0 0
\(193\) −6.49023 11.2414i −0.467177 0.809174i 0.532120 0.846669i \(-0.321396\pi\)
−0.999297 + 0.0374948i \(0.988062\pi\)
\(194\) 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 −0.998584 0.0532026i \(-0.983057\pi\)
0.453217 0.891400i \(-0.350276\pi\)
\(200\) 0 0
\(201\) −7.43311 + 12.8745i −0.524291 + 0.908098i
\(202\) 0 0
\(203\) 0 0
\(204\) 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
\(217\) 0 0
\(218\) 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 \(-0.356883\pi\)
0.434618 + 0.900615i \(0.356883\pi\)
\(224\) 0 0
\(225\) 3.67822 0.245215
\(226\) 0 0
\(227\) −11.0151 19.0788i −0.731099 1.26630i −0.956414 0.292015i \(-0.905674\pi\)
0.225314 0.974286i \(-0.427659\pi\)
\(228\) 0 0
\(229\) 2.15333 3.72967i 0.142296 0.246464i −0.786065 0.618144i \(-0.787885\pi\)
0.928361 + 0.371680i \(0.121218\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i \(0.367385\pi\)
−0.994283 + 0.106773i \(0.965948\pi\)
\(234\) 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 \(-0.164584\pi\)
−0.862736 + 0.505655i \(0.831251\pi\)
\(242\) 0 0
\(243\) −11.0347 + 19.1126i −0.707874 + 1.22607i
\(244\) 0 0
\(245\) 0 0
\(246\) 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 \(-0.550792\pi\)
−0.158893 + 0.987296i \(0.550792\pi\)
\(252\) 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 −0.227722 0.973726i \(-0.573128\pi\)
0.957133 0.289650i \(-0.0935390\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −6.10912 + 10.5813i −0.378145 + 0.654966i
\(262\) 0 0
\(263\) −13.5546 23.4772i −0.835810 1.44767i −0.893369 0.449323i \(-0.851665\pi\)
0.0575594 0.998342i \(-0.481668\pi\)
\(264\) 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 \(-0.103268\pi\)
−0.749976 + 0.661466i \(0.769935\pi\)
\(270\) 0 0
\(271\) −11.6933 + 20.2535i −0.710320 + 1.23031i 0.254417 + 0.967095i \(0.418116\pi\)
−0.964737 + 0.263216i \(0.915217\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.839111 + 1.45338i −0.0506003 + 0.0876422i
\(276\) 0 0
\(277\) −1.83155 3.17234i −0.110047 0.190607i 0.805742 0.592267i \(-0.201767\pi\)
−0.915789 + 0.401660i \(0.868434\pi\)
\(278\) 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 −0.992138 0.125150i \(-0.960059\pi\)
0.387686 0.921791i \(-0.373274\pi\)
\(284\) 0 0
\(285\) 8.84667 15.3229i 0.524032 0.907649i
\(286\) 0 0
\(287\) 0 0
\(288\) 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 \(-0.685569\pi\)
−0.550517 + 0.834824i \(0.685569\pi\)
\(294\) 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
\(301\) 0 0
\(302\) 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 \(-0.478217\pi\)
0.0683802 + 0.997659i \(0.478217\pi\)
\(308\) 0 0
\(309\) 18.3716 1.04512
\(310\) 0 0
\(311\) −2.83155 4.90439i −0.160562 0.278102i 0.774508 0.632564i \(-0.217997\pi\)
−0.935071 + 0.354462i \(0.884664\pi\)
\(312\) 0 0
\(313\) 14.8618 25.7414i 0.840038 1.45499i −0.0498231 0.998758i \(-0.515866\pi\)
0.889861 0.456231i \(-0.150801\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −9.52489 + 16.4976i −0.534971 + 0.926597i 0.464193 + 0.885734i \(0.346344\pi\)
−0.999165 + 0.0408636i \(0.986989\pi\)
\(318\) 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
\(329\) 0 0
\(330\) 0 0
\(331\) −1.16089 + 2.01072i −0.0638083 + 0.110519i −0.896165 0.443722i \(-0.853658\pi\)
0.832356 + 0.554241i \(0.186991\pi\)
\(332\) 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
\(343\) 0 0
\(344\) 0 0
\(345\) 2.92334 5.06337i 0.157387 0.272602i
\(346\) 0 0
\(347\) −2.29211 3.97006i −0.123047 0.213124i 0.797921 0.602762i \(-0.205933\pi\)
−0.920968 + 0.389639i \(0.872600\pi\)
\(348\) 0 0
\(349\) −12.3716 −0.662235 −0.331117 0.943590i \(-0.607426\pi\)
−0.331117 + 0.943590i \(0.607426\pi\)
\(350\) 0 0
\(351\) −8.49465 −0.453411
\(352\) 0 0
\(353\) 9.69334 + 16.7894i 0.515925 + 0.893608i 0.999829 + 0.0184869i \(0.00588489\pi\)
−0.483904 + 0.875121i \(0.660782\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.90600 8.49745i 0.258929 0.448478i −0.707026 0.707187i \(-0.749964\pi\)
0.965955 + 0.258709i \(0.0832971\pi\)
\(360\) 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 \(-0.274369\pi\)
−0.982892 + 0.184184i \(0.941036\pi\)
\(368\) 0 0
\(369\) 17.5173 30.3409i 0.911916 1.57948i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 8.20311 14.2082i 0.424741 0.735673i −0.571655 0.820494i \(-0.693698\pi\)
0.996396 + 0.0848208i \(0.0270318\pi\)
\(374\) 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 \(-0.862240\pi\)
0.817113 + 0.576477i \(0.195573\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −12.1091 + 20.9736i −0.615541 + 1.06615i
\(388\) 0 0
\(389\) −4.49023 7.77731i −0.227664 0.394325i 0.729452 0.684032i \(-0.239775\pi\)
−0.957115 + 0.289707i \(0.906442\pi\)
\(390\) 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 0.261503 + 0.965203i \(0.415782\pi\)
−0.966642 + 0.256133i \(0.917551\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 13.3467 23.1171i 0.666501 1.15441i −0.312375 0.949959i \(-0.601125\pi\)
0.978876 0.204455i \(-0.0655421\pi\)
\(402\) 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 0.970563 + 0.240846i \(0.0774248\pi\)
−0.276703 + 0.960955i \(0.589242\pi\)
\(410\) 0 0
\(411\) 5.16845 8.95202i 0.254941 0.441571i
\(412\) 0 0
\(413\) 0 0
\(414\) 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 \(-0.347455\pi\)
0.461099 + 0.887349i \(0.347455\pi\)
\(420\) 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
\(427\) 0 0
\(428\) 0 0
\(429\) 10.5098 18.2035i 0.507416 0.878871i
\(430\) 0 0
\(431\) −1.41577 2.45219i −0.0681955 0.118118i 0.829912 0.557895i \(-0.188391\pi\)
−0.898107 + 0.439777i \(0.855057\pi\)
\(432\) 0 0
\(433\) 2.33690 0.112304 0.0561522 0.998422i \(-0.482117\pi\)
0.0561522 + 0.998422i \(0.482117\pi\)
\(434\) 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 \(-0.879599\pi\)
0.784475 + 0.620160i \(0.212932\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5.80188 + 10.0492i −0.275656 + 0.477450i −0.970300 0.241903i \(-0.922228\pi\)
0.694645 + 0.719353i \(0.255562\pi\)
\(444\) 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
\(455\) 0 0
\(456\) 0 0
\(457\) 6.32178 10.9496i 0.295720 0.512203i −0.679432 0.733739i \(-0.737774\pi\)
0.975152 + 0.221536i \(0.0711070\pi\)
\(458\) 0 0
\(459\) −1.75268 3.03572i −0.0818079 0.141695i
\(460\) 0 0
\(461\) −20.7129 −0.964695 −0.482348 0.875980i \(-0.660216\pi\)
−0.482348 + 0.875980i \(0.660216\pi\)
\(462\) 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 \(-0.846022\pi\)
0.845411 + 0.534116i \(0.179355\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 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 \(-0.179627\pi\)
−0.885660 + 0.464334i \(0.846294\pi\)
\(480\) 0 0
\(481\) 6.89844 11.9485i 0.314542 0.544803i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 0 0
\(487\) 5.50977 + 9.54320i 0.249672 + 0.432444i 0.963435 0.267943i \(-0.0863440\pi\)
−0.713763 + 0.700387i \(0.753011\pi\)
\(488\) 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 −0.769721 0.638380i \(-0.779605\pi\)
0.937714 + 0.347408i \(0.112938\pi\)
\(500\) 0 0
\(501\) 0.339111 + 0.587357i 0.0151503 + 0.0262412i
\(502\) 0 0
\(503\) −20.5842 −0.917805 −0.458903 0.888487i \(-0.651757\pi\)
−0.458903 + 0.888487i \(0.651757\pi\)
\(504\) 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 \(-0.735444\pi\)
0.976748 + 0.214392i \(0.0687769\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 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 −0.793766 0.608224i \(-0.791882\pi\)
−0.129854 0.991533i \(-0.541451\pi\)
\(522\) 0 0
\(523\) −15.3218 + 26.5381i −0.669975 + 1.16043i 0.307936 + 0.951407i \(0.400362\pi\)
−0.977911 + 0.209023i \(0.932972\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 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
\(539\) 0 0
\(540\) 0 0
\(541\) 16.8445 29.1755i 0.724200 1.25435i −0.235102 0.971971i \(-0.575543\pi\)
0.959302 0.282381i \(-0.0911241\pi\)
\(542\) 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
\(553\) 0 0
\(554\) 0 0
\(555\) 3.67822 6.37087i 0.156132 0.270428i
\(556\) 0 0
\(557\) −9.08202 15.7305i −0.384817 0.666523i 0.606926 0.794758i \(-0.292402\pi\)
−0.991744 + 0.128235i \(0.959069\pi\)
\(558\) 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 −0.932241 0.361837i \(-0.882150\pi\)
0.152760 0.988263i \(-0.451184\pi\)
\(564\) 0 0
\(565\) 5.16845 8.95202i 0.217438 0.376614i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −16.3047 + 28.2405i −0.683527 + 1.18390i 0.290370 + 0.956915i \(0.406222\pi\)
−0.973897 + 0.226990i \(0.927112\pi\)
\(570\) 0 0
\(571\) −20.2182 35.0190i −0.846107 1.46550i −0.884656 0.466243i \(-0.845607\pi\)
0.0385496 0.999257i \(-0.487726\pi\)
\(572\) 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 −0.924970 0.380041i \(-0.875910\pi\)
0.133360 0.991068i \(-0.457423\pi\)
\(578\) 0 0
\(579\) 16.7722 29.0503i 0.697030 1.20729i
\(580\) 0 0
\(581\) 0 0
\(582\) 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 \(-0.747839\pi\)
−0.702289 + 0.711892i \(0.747839\pi\)
\(588\) 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 0.278608 + 0.960405i \(0.410127\pi\)
−0.971039 + 0.238921i \(0.923206\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 19.8813 34.4355i 0.813689 1.40935i
\(598\) 0 0
\(599\) −3.15333 5.46172i −0.128841 0.223160i 0.794387 0.607413i \(-0.207793\pi\)
−0.923228 + 0.384253i \(0.874459\pi\)
\(600\) 0 0
\(601\) 11.2871 0.460411 0.230206 0.973142i \(-0.426060\pi\)
0.230206 + 0.973142i \(0.426060\pi\)
\(602\) 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 \(-0.934927\pi\)
0.665402 + 0.746485i \(0.268260\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −29.5722 + 51.2206i −1.19637 + 2.07217i
\(612\) 0 0
\(613\) 11.0820 + 19.1946i 0.447598 + 0.775263i 0.998229 0.0594857i \(-0.0189461\pi\)
−0.550631 + 0.834749i \(0.685613\pi\)
\(614\) 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 \(-0.00908990\pi\)
−0.524524 + 0.851396i \(0.675757\pi\)
\(620\) 0 0
\(621\) −1.98267 + 3.43408i −0.0795617 + 0.137805i
\(622\) 0 0
\(623\) 0 0
\(624\) 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
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −21.9309 37.9854i −0.866218 1.50033i −0.865832 0.500334i \(-0.833210\pi\)
−0.000386062 1.00000i \(-0.500123\pi\)
\(642\) 0 0
\(643\) −7.04979 −0.278016 −0.139008 0.990291i \(-0.544391\pi\)
−0.139008 + 0.990291i \(0.544391\pi\)
\(644\) 0 0
\(645\) 17.0151 0.669970
\(646\) 0 0
\(647\) −12.2403 21.2009i −0.481217 0.833493i 0.518550 0.855047i \(-0.326472\pi\)
−0.999768 + 0.0215540i \(0.993139\pi\)
\(648\) 0 0
\(649\) 6.71288 11.6271i 0.263504 0.456402i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −0.408213 + 0.707046i −0.0159746 + 0.0276688i −0.873902 0.486102i \(-0.838418\pi\)
0.857928 + 0.513771i \(0.171752\pi\)
\(654\) 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 0.999986 + 0.00531513i \(0.00169187\pi\)
−0.495390 + 0.868671i \(0.664975\pi\)
\(662\) 0 0
\(663\) −12.5249 + 21.6938i −0.486427 + 0.842515i
\(664\) 0 0
\(665\) 0 0
\(666\) 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 \(-0.799688\pi\)
0.913944 + 0.405841i \(0.133021\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 28.4656 49.3038i 1.09080 1.88933i
\(682\) 0 0
\(683\) −9.61389 16.6517i −0.367865 0.637161i 0.621366 0.783520i \(-0.286578\pi\)
−0.989232 + 0.146359i \(0.953245\pi\)
\(684\) 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 \(-0.746163\pi\)
0.968975 + 0.247157i \(0.0794963\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 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
\(707\) 0 0
\(708\) 0 0
\(709\) −8.52268 + 14.7617i −0.320076 + 0.554388i −0.980503 0.196502i \(-0.937042\pi\)
0.660427 + 0.750890i \(0.270375\pi\)
\(710\) 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 \(-0.902158\pi\)
0.738591 + 0.674154i \(0.235491\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 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 \(-0.598433\pi\)
−0.304332 + 0.952566i \(0.598433\pi\)
\(728\) 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 \(-0.887168\pi\)
0.769509 + 0.638637i \(0.220501\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.82713 8.36084i 0.177810 0.307975i
\(738\) 0 0
\(739\) 17.4978 + 30.3071i 0.643667 + 1.11486i 0.984608 + 0.174779i \(0.0559210\pi\)
−0.340941 + 0.940085i \(0.610746\pi\)
\(740\) 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
\(749\) 0 0
\(750\) 0 0
\(751\) −3.15333 + 5.46172i −0.115067 + 0.199301i −0.917806 0.397028i \(-0.870041\pi\)
0.802740 + 0.596329i \(0.203375\pi\)
\(752\) 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 0.488735 + 0.872432i \(0.337459\pi\)
−0.999916 + 0.0129592i \(0.995875\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 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 \(-0.227437\pi\)
0.755412 + 0.655250i \(0.227437\pi\)
\(770\) 0 0
\(771\) 60.4365 2.17657
\(772\) 0 0
\(773\) 19.9287 + 34.5175i 0.716785 + 1.24151i 0.962267 + 0.272107i \(0.0877205\pi\)
−0.245482 + 0.969401i \(0.578946\pi\)
\(774\) 0 0
\(775\) 4.58423 7.94011i 0.164670 0.285217i
\(776\) 0 0
\(777\) 0 0
\(778\) 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 0.987623 + 0.156843i \(0.0501318\pi\)
−0.357981 + 0.933729i \(0.616535\pi\)
\(788\) 0 0
\(789\) 35.0280 60.6703i 1.24703 2.15992i
\(790\) 0 0
\(791\) 0 0
\(792\) 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 −0.525896 0.850549i \(-0.676270\pi\)
−0.525896 + 0.850549i \(0.676270\pi\)
\(798\) 0 0
\(799\) −24.4062 −0.863430
\(800\) 0 0