Properties

Label 1400.2.q.j.1201.3
Level $1400$
Weight $2$
Character 1400.1201
Analytic conductor $11.179$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
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: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1201.3
Root \(0.391571i\) of defining polynomial
Character \(\chi\) \(=\) 1400.1201
Dual form 1400.2.q.j.401.3

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 −0.203724 0.979028i \(-0.565304\pi\)
0.949725 0.313084i \(-0.101362\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 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 \(-0.265387\pi\)
0.672112 + 0.740449i \(0.265387\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) 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 0.723651 0.690166i \(-0.242463\pi\)
−0.959527 + 0.281617i \(0.909129\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 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
\(35\) 0 0
\(36\) 0 0
\(37\) −1.42334 2.46529i −0.233995 0.405291i 0.724985 0.688765i \(-0.241847\pi\)
−0.958980 + 0.283473i \(0.908513\pi\)
\(38\) 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 \(-0.667418\pi\)
−0.502042 + 0.864843i \(0.667418\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.10156 10.5682i −0.890004 1.54153i −0.839869 0.542789i \(-0.817368\pi\)
−0.0501344 0.998742i \(-0.515965\pi\)
\(48\) 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 \(-0.661336\pi\)
0.999860 0.0167445i \(-0.00533020\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 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
\(65\) 0 0
\(66\) 0 0
\(67\) −2.87634 + 4.98196i −0.351401 + 0.608644i −0.986495 0.163791i \(-0.947628\pi\)
0.635094 + 0.772434i \(0.280961\pi\)
\(68\) 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 \(0.406559\pi\)
−0.973656 + 0.228022i \(0.926774\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 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 \(-0.257325\pi\)
0.690649 + 0.723190i \(0.257325\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 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
\(95\) 0 0
\(96\) 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 −0.0377483 0.999287i \(-0.512019\pi\)
0.884282 0.466953i \(-0.154648\pi\)
\(102\) 0 0
\(103\) 3.55456 + 6.15668i 0.350241 + 0.606635i 0.986292 0.165012i \(-0.0527663\pi\)
−0.636050 + 0.771648i \(0.719433\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.876338 1.51786i −0.0847188 0.146737i 0.820553 0.571571i \(-0.193666\pi\)
−0.905271 + 0.424834i \(0.860333\pi\)
\(108\) 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 \(-0.661620\pi\)
−0.486207 + 0.873844i \(0.661620\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 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
\(125\) 0 0
\(126\) 0 0
\(127\) 19.1836 1.70227 0.851133 0.524949i \(-0.175916\pi\)
0.851133 + 0.524949i \(0.175916\pi\)
\(128\) 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 0
\(136\) 0 0
\(137\) 2.00000 3.46410i 0.170872 0.295958i −0.767853 0.640626i \(-0.778675\pi\)
0.938725 + 0.344668i \(0.112008\pi\)
\(138\) 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
\(145\) 0 0
\(146\) 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
\(155\) 0 0
\(156\) 0 0
\(157\) 4.10156 7.10411i 0.327340 0.566969i −0.654643 0.755938i \(-0.727181\pi\)
0.981983 + 0.188969i \(0.0605145\pi\)
\(158\) 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 0.929240 0.369478i \(-0.120463\pi\)
−0.784597 + 0.620006i \(0.787130\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 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 −0.962400 0.271635i \(-0.912436\pi\)
0.245957 0.969281i \(-0.420898\pi\)
\(174\) 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 −0.549297 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
\(185\) 0 0
\(186\) 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 −0.532120 0.846669i \(-0.678604\pi\)
0.999297 + 0.0374948i \(0.0119378\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.84667 0.345311 0.172656 0.984982i \(-0.444765\pi\)
0.172656 + 0.984982i \(0.444765\pi\)
\(198\) 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
\(205\) 0 0
\(206\) 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
\(215\) 0 0
\(216\) 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 \(-0.356883\pi\)
0.434618 + 0.900615i \(0.356883\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.0151 + 19.0788i −0.731099 + 1.26630i 0.225314 + 0.974286i \(0.427659\pi\)
−0.956414 + 0.292015i \(0.905674\pi\)
\(228\) 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 \(0.0340517\pi\)
−0.404674 + 0.914461i \(0.632615\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 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
\(245\) 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 \(-0.449208\pi\)
0.158893 + 0.987296i \(0.449208\pi\)
\(252\) 0 0
\(253\) 3.79689 0.238708
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.6933 + 20.2535i 0.729411 + 1.26338i 0.957133 + 0.289650i \(0.0935390\pi\)
−0.227722 + 0.973726i \(0.573128\pi\)
\(258\) 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 \(-0.518332\pi\)
0.893369 0.449323i \(-0.148335\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 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 0
\(276\) 0 0
\(277\) 1.83155 3.17234i 0.110047 0.190607i −0.805742 0.592267i \(-0.798233\pi\)
0.915789 + 0.401660i \(0.131566\pi\)
\(278\) 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 \(0.373274\pi\)
−0.992138 + 0.125150i \(0.960059\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 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 \(-0.685569\pi\)
−0.550517 + 0.834824i \(0.685569\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 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
\(305\) 0 0
\(306\) 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 \(-0.782003\pi\)
0.935071 + 0.354462i \(0.115336\pi\)
\(312\) 0 0
\(313\) 14.8618 + 25.7414i 0.840038 + 1.45499i 0.889861 + 0.456231i \(0.150801\pi\)
−0.0498231 + 0.998758i \(0.515866\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.52489 + 16.4976i 0.534971 + 0.926597i 0.999165 + 0.0408636i \(0.0130109\pi\)
−0.464193 + 0.885734i \(0.653656\pi\)
\(318\) 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
\(325\) 0 0
\(326\) 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
\(335\) 0 0
\(336\) 0 0
\(337\) 16.4062 0.893704 0.446852 0.894608i \(-0.352545\pi\)
0.446852 + 0.894608i \(0.352545\pi\)
\(338\) 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
\(345\) 0 0
\(346\) 0 0
\(347\) 2.29211 3.97006i 0.123047 0.213124i −0.797921 0.602762i \(-0.794067\pi\)
0.920968 + 0.389639i \(0.127400\pi\)
\(348\) 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 \(-0.660782\pi\)
0.999829 0.0184869i \(-0.00588489\pi\)
\(354\) 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
\(365\) 0 0
\(366\) 0 0
\(367\) −6.35901 + 11.0141i −0.331937 + 0.574933i −0.982892 0.184184i \(-0.941036\pi\)
0.650954 + 0.759117i \(0.274369\pi\)
\(368\) 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 0.571655 0.820494i \(-0.306302\pi\)
−0.996396 + 0.0848208i \(0.972968\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 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 0.817113 0.576477i \(-0.195573\pi\)
−0.907800 + 0.419402i \(0.862240\pi\)
\(384\) 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 −0.957115 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
\(395\) 0 0
\(396\) 0 0
\(397\) −14.0498 24.3349i −0.705139 1.22134i −0.966642 0.256133i \(-0.917551\pi\)
0.261503 0.965203i \(-0.415782\pi\)
\(398\) 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
\(405\) 0 0
\(406\) 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
\(415\) 0 0
\(416\) 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
\(425\) 0 0
\(426\) 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 \(-0.482117\pi\)
0.0561522 + 0.998422i \(0.482117\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 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 0.970300 0.241903i \(-0.0777717\pi\)
−0.694645 + 0.719353i \(0.744438\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 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 \(-0.262226\pi\)
−0.975152 + 0.221536i \(0.928893\pi\)
\(458\) 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 \(-0.375701\pi\)
0.380647 + 0.924720i \(0.375701\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −0.861215 1.49167i −0.0398523 0.0690262i 0.845411 0.534116i \(-0.179355\pi\)
−0.885264 + 0.465090i \(0.846022\pi\)
\(468\) 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
\(475\) 0 0
\(476\) 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
\(485\) 0 0
\(486\) 0 0
\(487\) −5.50977 + 9.54320i −0.249672 + 0.432444i −0.963435 0.267943i \(-0.913656\pi\)
0.713763 + 0.700387i \(0.246989\pi\)
\(488\) 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
\(495\) 0 0
\(496\) 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 \(-0.651757\pi\)
−0.458903 + 0.888487i \(0.651757\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 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
\(515\) 0 0
\(516\) 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 \(-0.932972\pi\)
0.307936 0.951407i \(-0.400362\pi\)
\(524\) 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 0
\(536\) 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
\(545\) 0 0
\(546\) 0 0
\(547\) 3.03979 0.129972 0.0649861 0.997886i \(-0.479300\pi\)
0.0649861 + 0.997886i \(0.479300\pi\)
\(548\) 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
\(555\) 0 0
\(556\) 0 0
\(557\) 9.08202 15.7305i 0.384817 0.666523i −0.606926 0.794758i \(-0.707598\pi\)
0.991744 + 0.128235i \(0.0409311\pi\)
\(558\) 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 \(0.451184\pi\)
−0.932241 + 0.361837i \(0.882150\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 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
\(575\) 0 0
\(576\) 0 0
\(577\) −19.0151 + 32.9352i −0.791610 + 1.37111i 0.133360 + 0.991068i \(0.457423\pi\)
−0.924970 + 0.380041i \(0.875910\pi\)
\(578\) 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
\(585\) 0 0
\(586\) 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 −0.971039 0.238921i \(-0.923206\pi\)
0.278608 0.960405i \(-0.410127\pi\)
\(594\) 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 −0.923228 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
\(605\) 0 0
\(606\) 0 0
\(607\) −7.73057 13.3897i −0.313774 0.543473i 0.665402 0.746485i \(-0.268260\pi\)
−0.979176 + 0.203012i \(0.934927\pi\)
\(608\) 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 −0.998229 0.0594857i \(-0.981054\pi\)
0.550631 + 0.834749i \(0.314387\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 14.9805 0.603091 0.301545 0.953452i \(-0.402498\pi\)
0.301545 + 0.953452i \(0.402498\pi\)
\(618\) 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 0
\(626\) 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
\(635\) 0 0
\(636\) 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 \(-0.544391\pi\)
−0.139008 + 0.990291i \(0.544391\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −12.2403 + 21.2009i −0.481217 + 0.833493i −0.999768 0.0215540i \(-0.993139\pi\)
0.518550 + 0.855047i \(0.326472\pi\)
\(648\) 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 0.873902 0.486102i \(-0.161582\pi\)
−0.857928 + 0.513771i \(0.828248\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 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
\(665\) 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 \(-0.639851\pi\)
−0.425355 + 0.905027i \(0.639851\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.74511 + 4.75468i 0.105503 + 0.182737i 0.913944 0.405841i \(-0.133021\pi\)
−0.808440 + 0.588578i \(0.799688\pi\)
\(678\) 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 −0.621366 0.783520i \(-0.713422\pi\)
0.989232 + 0.146359i \(0.0467554\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 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
\(695\) 0 0
\(696\) 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
\(705\) 0 0
\(706\) 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
\(715\) 0 0
\(716\) 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
\(725\) 0 0
\(726\) 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 0.769509 0.638637i \(-0.220501\pi\)
−0.937830 + 0.347096i \(0.887168\pi\)
\(734\) 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 −0.340941 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 \(-0.205633\pi\)
0.798489 + 0.602009i \(0.205633\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 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
\(755\) 0 0
\(756\) 0 0
\(757\) −24.3369 −0.884540 −0.442270 0.896882i \(-0.645827\pi\)
−0.442270 + 0.896882i \(0.645827\pi\)
\(758\) 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
\(765\) 0 0
\(766\) 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 \(-0.578946\pi\)
0.962267 0.272107i \(-0.0877205\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 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
\(785\) 0 0
\(786\) 0 0
\(787\) 17.6637 30.5944i 0.629642 1.09057i −0.357981 0.933729i \(-0.616535\pi\)
0.987623 0.156843i \(-0.0501318\pi\)
\(788\) 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
\(795\) 0 0
\(796\) 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