Properties

Label 1900.2.s.c.49.3
Level $1900$
Weight $2$
Character 1900.49
Analytic conductor $15.172$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 9 x^{10} + 59 x^{8} - 180 x^{6} + 403 x^{4} - 198 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.3
Root \(-1.90412 + 1.09935i\) of defining polynomial
Character \(\chi\) \(=\) 1900.49
Dual form 1900.2.s.c.349.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.315621 - 0.182224i) q^{3} +0.635552i q^{7} +(-1.43359 - 2.48305i) q^{9} +O(q^{10})\) \(q+(-0.315621 - 0.182224i) q^{3} +0.635552i q^{7} +(-1.43359 - 2.48305i) q^{9} +1.63555 q^{11} +(0.866025 - 0.500000i) q^{13} +(5.71237 + 3.29804i) q^{17} +(-0.0466721 + 4.35865i) q^{19} +(0.115813 - 0.200594i) q^{21} +(-0.750998 + 0.433589i) q^{23} +2.13828i q^{27} +(-4.54940 - 7.87979i) q^{29} -1.86718 q^{31} +(-0.516215 - 0.298037i) q^{33} +0.635552i q^{37} -0.364448 q^{39} +(-0.953328 + 1.65121i) q^{41} +(3.42991 + 1.98026i) q^{43} +(7.87979 - 4.54940i) q^{47} +6.59607 q^{49} +(-1.20196 - 2.08186i) q^{51} +(8.54523 - 4.93359i) q^{53} +(0.808981 - 1.36718i) q^{57} +(4.54940 - 7.87979i) q^{59} +(-1.13555 - 1.96683i) q^{61} +(1.57811 - 0.911120i) q^{63} +(10.7935 - 6.23163i) q^{67} +0.316041 q^{69} +(-1.25136 + 2.16743i) q^{71} +(-0.349810 - 0.201963i) q^{73} +1.03948i q^{77} +(5.36445 - 9.29150i) q^{79} +(-3.91112 + 6.77426i) q^{81} +15.8672i q^{83} +3.31604i q^{87} +(0.271104 + 0.469566i) q^{89} +(0.317776 + 0.550404i) q^{91} +(0.589321 + 0.340245i) q^{93} +(6.38253 + 3.68495i) q^{97} +(-2.34471 - 4.06116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 16q^{9} + O(q^{10}) \) \( 12q + 16q^{9} + 20q^{11} - 32q^{21} + 12q^{29} + 44q^{31} - 4q^{39} - 12q^{41} + 12q^{49} - 48q^{51} - 12q^{59} - 14q^{61} - 60q^{69} + 18q^{71} + 64q^{79} - 46q^{81} + 4q^{89} + 4q^{91} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −0.315621 0.182224i −0.182224 0.105207i 0.406113 0.913823i \(-0.366884\pi\)
−0.588337 + 0.808616i \(0.700217\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.635552i 0.240216i 0.992761 + 0.120108i \(0.0383241\pi\)
−0.992761 + 0.120108i \(0.961676\pi\)
\(8\) 0 0
\(9\) −1.43359 2.48305i −0.477863 0.827683i
\(10\) 0 0
\(11\) 1.63555 0.493137 0.246569 0.969125i \(-0.420697\pi\)
0.246569 + 0.969125i \(0.420697\pi\)
\(12\) 0 0
\(13\) 0.866025 0.500000i 0.240192 0.138675i −0.375073 0.926995i \(-0.622382\pi\)
0.615265 + 0.788320i \(0.289049\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.71237 + 3.29804i 1.38545 + 0.799891i 0.992799 0.119795i \(-0.0382237\pi\)
0.392654 + 0.919686i \(0.371557\pi\)
\(18\) 0 0
\(19\) −0.0466721 + 4.35865i −0.0107073 + 0.999943i
\(20\) 0 0
\(21\) 0.115813 0.200594i 0.0252724 0.0437731i
\(22\) 0 0
\(23\) −0.750998 + 0.433589i −0.156594 + 0.0904095i −0.576249 0.817274i \(-0.695484\pi\)
0.419655 + 0.907684i \(0.362151\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2.13828i 0.411512i
\(28\) 0 0
\(29\) −4.54940 7.87979i −0.844803 1.46324i −0.885792 0.464082i \(-0.846384\pi\)
0.0409898 0.999160i \(-0.486949\pi\)
\(30\) 0 0
\(31\) −1.86718 −0.335355 −0.167677 0.985842i \(-0.553627\pi\)
−0.167677 + 0.985842i \(0.553627\pi\)
\(32\) 0 0
\(33\) −0.516215 0.298037i −0.0898615 0.0518816i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.635552i 0.104484i 0.998634 + 0.0522420i \(0.0166367\pi\)
−0.998634 + 0.0522420i \(0.983363\pi\)
\(38\) 0 0
\(39\) −0.364448 −0.0583584
\(40\) 0 0
\(41\) −0.953328 + 1.65121i −0.148885 + 0.257876i −0.930816 0.365489i \(-0.880902\pi\)
0.781931 + 0.623365i \(0.214235\pi\)
\(42\) 0 0
\(43\) 3.42991 + 1.98026i 0.523057 + 0.301987i 0.738184 0.674599i \(-0.235683\pi\)
−0.215128 + 0.976586i \(0.569017\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7.87979 4.54940i 1.14939 0.663598i 0.200649 0.979663i \(-0.435695\pi\)
0.948738 + 0.316065i \(0.102362\pi\)
\(48\) 0 0
\(49\) 6.59607 0.942296
\(50\) 0 0
\(51\) −1.20196 2.08186i −0.168309 0.291519i
\(52\) 0 0
\(53\) 8.54523 4.93359i 1.17378 0.677681i 0.219210 0.975678i \(-0.429652\pi\)
0.954567 + 0.297997i \(0.0963186\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.808981 1.36718i 0.107152 0.181087i
\(58\) 0 0
\(59\) 4.54940 7.87979i 0.592282 1.02586i −0.401643 0.915796i \(-0.631561\pi\)
0.993924 0.110065i \(-0.0351060\pi\)
\(60\) 0 0
\(61\) −1.13555 1.96683i −0.145393 0.251827i 0.784127 0.620601i \(-0.213111\pi\)
−0.929519 + 0.368773i \(0.879778\pi\)
\(62\) 0 0
\(63\) 1.57811 0.911120i 0.198823 0.114790i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 10.7935 6.23163i 1.31863 0.761314i 0.335126 0.942173i \(-0.391221\pi\)
0.983509 + 0.180859i \(0.0578878\pi\)
\(68\) 0 0
\(69\) 0.316041 0.0380469
\(70\) 0 0
\(71\) −1.25136 + 2.16743i −0.148510 + 0.257226i −0.930677 0.365842i \(-0.880781\pi\)
0.782167 + 0.623069i \(0.214114\pi\)
\(72\) 0 0
\(73\) −0.349810 0.201963i −0.0409422 0.0236380i 0.479389 0.877602i \(-0.340858\pi\)
−0.520331 + 0.853964i \(0.674192\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.03948i 0.118460i
\(78\) 0 0
\(79\) 5.36445 9.29150i 0.603548 1.04538i −0.388732 0.921351i \(-0.627087\pi\)
0.992279 0.124024i \(-0.0395800\pi\)
\(80\) 0 0
\(81\) −3.91112 + 6.77426i −0.434569 + 0.752695i
\(82\) 0 0
\(83\) 15.8672i 1.74165i 0.491594 + 0.870825i \(0.336414\pi\)
−0.491594 + 0.870825i \(0.663586\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 3.31604i 0.355517i
\(88\) 0 0
\(89\) 0.271104 + 0.469566i 0.0287370 + 0.0497739i 0.880036 0.474907i \(-0.157518\pi\)
−0.851299 + 0.524680i \(0.824185\pi\)
\(90\) 0 0
\(91\) 0.317776 + 0.550404i 0.0333120 + 0.0576980i
\(92\) 0 0
\(93\) 0.589321 + 0.340245i 0.0611097 + 0.0352817i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.38253 + 3.68495i 0.648047 + 0.374150i 0.787708 0.616049i \(-0.211268\pi\)
−0.139660 + 0.990199i \(0.544601\pi\)
\(98\) 0 0
\(99\) −2.34471 4.06116i −0.235652 0.408161i
\(100\) 0 0
\(101\) 4.66248 + 8.07566i 0.463935 + 0.803558i 0.999153 0.0411556i \(-0.0131039\pi\)
−0.535218 + 0.844714i \(0.679771\pi\)
\(102\) 0 0
\(103\) 10.8672i 1.07077i 0.844607 + 0.535387i \(0.179834\pi\)
−0.844607 + 0.535387i \(0.820166\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.3304i 1.09535i 0.836690 + 0.547677i \(0.184488\pi\)
−0.836690 + 0.547677i \(0.815512\pi\)
\(108\) 0 0
\(109\) 6.61581 11.4589i 0.633680 1.09757i −0.353113 0.935581i \(-0.614877\pi\)
0.986793 0.161985i \(-0.0517897\pi\)
\(110\) 0 0
\(111\) 0.115813 0.200594i 0.0109925 0.0190395i
\(112\) 0 0
\(113\) 7.09334i 0.667286i −0.942700 0.333643i \(-0.891722\pi\)
0.942700 0.333643i \(-0.108278\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −2.48305 1.43359i −0.229558 0.132535i
\(118\) 0 0
\(119\) −2.09607 + 3.63051i −0.192147 + 0.332808i
\(120\) 0 0
\(121\) −8.32497 −0.756815
\(122\) 0 0
\(123\) 0.601781 0.347439i 0.0542608 0.0313275i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 14.0959 8.13828i 1.25081 0.722156i 0.279540 0.960134i \(-0.409818\pi\)
0.971270 + 0.237978i \(0.0764847\pi\)
\(128\) 0 0
\(129\) −0.721702 1.25002i −0.0635423 0.110059i
\(130\) 0 0
\(131\) 5.31778 9.21066i 0.464616 0.804739i −0.534568 0.845126i \(-0.679526\pi\)
0.999184 + 0.0403866i \(0.0128590\pi\)
\(132\) 0 0
\(133\) −2.77015 0.0296625i −0.240202 0.00257207i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.02873 1.74864i 0.258761 0.149396i −0.365008 0.931004i \(-0.618934\pi\)
0.623769 + 0.781608i \(0.285600\pi\)
\(138\) 0 0
\(139\) 0.367178 + 0.635970i 0.0311436 + 0.0539423i 0.881177 0.472786i \(-0.156752\pi\)
−0.850034 + 0.526729i \(0.823418\pi\)
\(140\) 0 0
\(141\) −3.31604 −0.279261
\(142\) 0 0
\(143\) 1.41643 0.817776i 0.118448 0.0683859i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −2.08186 1.20196i −0.171709 0.0991362i
\(148\) 0 0
\(149\) 5.06914 8.78001i 0.415280 0.719286i −0.580178 0.814490i \(-0.697017\pi\)
0.995458 + 0.0952036i \(0.0303502\pi\)
\(150\) 0 0
\(151\) 2.81331 0.228944 0.114472 0.993426i \(-0.463482\pi\)
0.114472 + 0.993426i \(0.463482\pi\)
\(152\) 0 0
\(153\) 18.9121i 1.52895i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.831836 0.480261i −0.0663878 0.0383290i 0.466439 0.884554i \(-0.345537\pi\)
−0.532826 + 0.846225i \(0.678870\pi\)
\(158\) 0 0
\(159\) −3.59607 −0.285187
\(160\) 0 0
\(161\) −0.275568 0.477298i −0.0217178 0.0376164i
\(162\) 0 0
\(163\) 3.13828i 0.245809i −0.992418 0.122905i \(-0.960779\pi\)
0.992418 0.122905i \(-0.0392209\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −9.21066 + 5.31778i −0.712742 + 0.411502i −0.812076 0.583552i \(-0.801662\pi\)
0.0993334 + 0.995054i \(0.468329\pi\)
\(168\) 0 0
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) 0 0
\(171\) 10.8896 6.13262i 0.832752 0.468973i
\(172\) 0 0
\(173\) 10.7127 + 6.18495i 0.814468 + 0.470233i 0.848505 0.529187i \(-0.177503\pi\)
−0.0340371 + 0.999421i \(0.510836\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −2.87178 + 1.65802i −0.215856 + 0.124624i
\(178\) 0 0
\(179\) 0.324970 0.0242894 0.0121447 0.999926i \(-0.496134\pi\)
0.0121447 + 0.999926i \(0.496134\pi\)
\(180\) 0 0
\(181\) −4.40666 7.63255i −0.327544 0.567323i 0.654480 0.756079i \(-0.272888\pi\)
−0.982024 + 0.188756i \(0.939554\pi\)
\(182\) 0 0
\(183\) 0.827699i 0.0611853i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 9.34287 + 5.39411i 0.683219 + 0.394456i
\(188\) 0 0
\(189\) −1.35899 −0.0988519
\(190\) 0 0
\(191\) 25.1921 1.82284 0.911420 0.411478i \(-0.134987\pi\)
0.911420 + 0.411478i \(0.134987\pi\)
\(192\) 0 0
\(193\) −16.3442 9.43632i −1.17648 0.679241i −0.221282 0.975210i \(-0.571024\pi\)
−0.955198 + 0.295969i \(0.904358\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 7.36445i 0.524695i −0.964973 0.262348i \(-0.915503\pi\)
0.964973 0.262348i \(-0.0844967\pi\)
\(198\) 0 0
\(199\) 1.38419 + 2.39748i 0.0981224 + 0.169953i 0.910907 0.412611i \(-0.135383\pi\)
−0.812785 + 0.582564i \(0.802050\pi\)
\(200\) 0 0
\(201\) −4.54221 −0.320383
\(202\) 0 0
\(203\) 5.00802 2.89138i 0.351494 0.202935i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 2.15324 + 1.24318i 0.149661 + 0.0864067i
\(208\) 0 0
\(209\) −0.0763346 + 7.12880i −0.00528018 + 0.493109i
\(210\) 0 0
\(211\) −8.46325 + 14.6588i −0.582634 + 1.00915i 0.412532 + 0.910943i \(0.364645\pi\)
−0.995166 + 0.0982088i \(0.968689\pi\)
\(212\) 0 0
\(213\) 0.789915 0.456057i 0.0541241 0.0312485i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 1.18669i 0.0805577i
\(218\) 0 0
\(219\) 0.0736051 + 0.127488i 0.00497377 + 0.00861482i
\(220\) 0 0
\(221\) 6.59607 0.443700
\(222\) 0 0
\(223\) 7.48334 + 4.32051i 0.501121 + 0.289322i 0.729176 0.684326i \(-0.239903\pi\)
−0.228055 + 0.973648i \(0.573237\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 20.9265i 1.38894i 0.719521 + 0.694470i \(0.244361\pi\)
−0.719521 + 0.694470i \(0.755639\pi\)
\(228\) 0 0
\(229\) −22.3754 −1.47861 −0.739303 0.673373i \(-0.764845\pi\)
−0.739303 + 0.673373i \(0.764845\pi\)
\(230\) 0 0
\(231\) 0.189418 0.328081i 0.0124628 0.0215862i
\(232\) 0 0
\(233\) −16.6598 9.61854i −1.09142 0.630132i −0.157466 0.987524i \(-0.550332\pi\)
−0.933954 + 0.357393i \(0.883666\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −3.38627 + 1.95506i −0.219962 + 0.126995i
\(238\) 0 0
\(239\) 2.13282 0.137961 0.0689804 0.997618i \(-0.478025\pi\)
0.0689804 + 0.997618i \(0.478025\pi\)
\(240\) 0 0
\(241\) −12.2316 21.1858i −0.787908 1.36470i −0.927246 0.374452i \(-0.877831\pi\)
0.139338 0.990245i \(-0.455503\pi\)
\(242\) 0 0
\(243\) 8.02428 4.63282i 0.514758 0.297196i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.13891 + 3.79804i 0.136095 + 0.241663i
\(248\) 0 0
\(249\) 2.89138 5.00802i 0.183234 0.317370i
\(250\) 0 0
\(251\) −1.64002 2.84059i −0.103517 0.179297i 0.809614 0.586962i \(-0.199676\pi\)
−0.913131 + 0.407666i \(0.866343\pi\)
\(252\) 0 0
\(253\) −1.22830 + 0.709157i −0.0772223 + 0.0445843i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.61258 + 3.81778i −0.412482 + 0.238146i −0.691855 0.722036i \(-0.743206\pi\)
0.279374 + 0.960182i \(0.409873\pi\)
\(258\) 0 0
\(259\) −0.403926 −0.0250988
\(260\) 0 0
\(261\) −13.0439 + 22.5928i −0.807400 + 1.39846i
\(262\) 0 0
\(263\) 12.7556 + 7.36445i 0.786544 + 0.454111i 0.838744 0.544525i \(-0.183290\pi\)
−0.0522005 + 0.998637i \(0.516624\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.197607i 0.0120933i
\(268\) 0 0
\(269\) −6.73163 + 11.6595i −0.410434 + 0.710893i −0.994937 0.100498i \(-0.967956\pi\)
0.584503 + 0.811392i \(0.301290\pi\)
\(270\) 0 0
\(271\) −1.93086 + 3.34435i −0.117291 + 0.203155i −0.918693 0.394971i \(-0.870754\pi\)
0.801402 + 0.598126i \(0.204088\pi\)
\(272\) 0 0
\(273\) 0.231626i 0.0140186i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 24.2766i 1.45864i −0.684174 0.729319i \(-0.739837\pi\)
0.684174 0.729319i \(-0.260163\pi\)
\(278\) 0 0
\(279\) 2.67676 + 4.63629i 0.160254 + 0.277568i
\(280\) 0 0
\(281\) −0.248635 0.430649i −0.0148323 0.0256904i 0.858514 0.512790i \(-0.171388\pi\)
−0.873346 + 0.487100i \(0.838055\pi\)
\(282\) 0 0
\(283\) −13.1273 7.57906i −0.780338 0.450529i 0.0562118 0.998419i \(-0.482098\pi\)
−0.836550 + 0.547890i \(0.815431\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.04943 0.605889i −0.0619460 0.0357645i
\(288\) 0 0
\(289\) 13.2541 + 22.9568i 0.779653 + 1.35040i
\(290\) 0 0
\(291\) −1.34297 2.32610i −0.0787265 0.136358i
\(292\) 0 0
\(293\) 13.4094i 0.783385i 0.920096 + 0.391692i \(0.128110\pi\)
−0.920096 + 0.391692i \(0.871890\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 3.49727i 0.202932i
\(298\) 0 0
\(299\) −0.433589 + 0.750998i −0.0250751 + 0.0434313i
\(300\) 0 0
\(301\) −1.25856 + 2.17989i −0.0725421 + 0.125647i
\(302\) 0 0
\(303\) 3.39847i 0.195237i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −27.8917 16.1033i −1.59186 0.919062i −0.992988 0.118219i \(-0.962281\pi\)
−0.598875 0.800843i \(-0.704385\pi\)
\(308\) 0 0
\(309\) 1.98026 3.42991i 0.112653 0.195121i
\(310\) 0 0
\(311\) 12.3699 0.701433 0.350717 0.936482i \(-0.385938\pi\)
0.350717 + 0.936482i \(0.385938\pi\)
\(312\) 0 0
\(313\) −21.4672 + 12.3941i −1.21340 + 0.700557i −0.963498 0.267715i \(-0.913732\pi\)
−0.249901 + 0.968271i \(0.580398\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.33115 3.65529i 0.355593 0.205302i −0.311553 0.950229i \(-0.600849\pi\)
0.667146 + 0.744927i \(0.267516\pi\)
\(318\) 0 0
\(319\) −7.44078 12.8878i −0.416604 0.721579i
\(320\) 0 0
\(321\) 2.06468 3.57612i 0.115239 0.199600i
\(322\) 0 0
\(323\) −14.6416 + 24.7443i −0.814680 + 1.37681i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −4.17618 + 2.41112i −0.230943 + 0.133335i
\(328\) 0 0
\(329\) 2.89138 + 5.00802i 0.159407 + 0.276101i
\(330\) 0 0
\(331\) 18.4722 1.01532 0.507661 0.861557i \(-0.330510\pi\)
0.507661 + 0.861557i \(0.330510\pi\)
\(332\) 0 0
\(333\) 1.57811 0.911120i 0.0864797 0.0499291i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −26.3819 15.2316i −1.43712 0.829720i −0.439468 0.898258i \(-0.644833\pi\)
−0.997648 + 0.0685388i \(0.978166\pi\)
\(338\) 0 0
\(339\) −1.29258 + 2.23881i −0.0702032 + 0.121595i
\(340\) 0 0
\(341\) −3.05387 −0.165376
\(342\) 0 0
\(343\) 8.64101i 0.466571i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −20.1970 11.6608i −1.08423 0.625982i −0.152197 0.988350i \(-0.548635\pi\)
−0.932035 + 0.362368i \(0.881968\pi\)
\(348\) 0 0
\(349\) 17.6894 0.946893 0.473446 0.880823i \(-0.343010\pi\)
0.473446 + 0.880823i \(0.343010\pi\)
\(350\) 0 0
\(351\) 1.06914 + 1.85181i 0.0570665 + 0.0988421i
\(352\) 0 0
\(353\) 7.13828i 0.379932i 0.981791 + 0.189966i \(0.0608378\pi\)
−0.981791 + 0.189966i \(0.939162\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 1.32313 0.763910i 0.0700275 0.0404304i
\(358\) 0 0
\(359\) −15.0719 + 26.1052i −0.795463 + 1.37778i 0.127082 + 0.991892i \(0.459439\pi\)
−0.922545 + 0.385890i \(0.873894\pi\)
\(360\) 0 0
\(361\) −18.9956 0.406855i −0.999771 0.0214134i
\(362\) 0 0
\(363\) 2.62754 + 1.51701i 0.137910 + 0.0796224i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −26.1566 + 15.1015i −1.36536 + 0.788294i −0.990332 0.138718i \(-0.955702\pi\)
−0.375033 + 0.927012i \(0.622369\pi\)
\(368\) 0 0
\(369\) 5.46672 0.284586
\(370\) 0 0
\(371\) 3.13555 + 5.43094i 0.162790 + 0.281960i
\(372\) 0 0
\(373\) 29.0449i 1.50389i −0.659226 0.751945i \(-0.729116\pi\)
0.659226 0.751945i \(-0.270884\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −7.87979 4.54940i −0.405830 0.234306i
\(378\) 0 0
\(379\) −2.76837 −0.142202 −0.0711009 0.997469i \(-0.522651\pi\)
−0.0711009 + 0.997469i \(0.522651\pi\)
\(380\) 0 0
\(381\) −5.93196 −0.303904
\(382\) 0 0
\(383\) 23.0453 + 13.3052i 1.17756 + 0.679866i 0.955449 0.295156i \(-0.0953715\pi\)
0.222112 + 0.975021i \(0.428705\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 11.3555i 0.577233i
\(388\) 0 0
\(389\) −2.77830 4.81215i −0.140865 0.243986i 0.786957 0.617007i \(-0.211655\pi\)
−0.927823 + 0.373021i \(0.878322\pi\)
\(390\) 0 0
\(391\) −5.71997 −0.289271
\(392\) 0 0
\(393\) −3.35681 + 1.93805i −0.169328 + 0.0977618i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −2.35083 1.35725i −0.117985 0.0681186i 0.439846 0.898073i \(-0.355033\pi\)
−0.557831 + 0.829955i \(0.688366\pi\)
\(398\) 0 0
\(399\) 0.868912 + 0.514150i 0.0435000 + 0.0257397i
\(400\) 0 0
\(401\) 8.94078 15.4859i 0.446481 0.773328i −0.551673 0.834061i \(-0.686010\pi\)
0.998154 + 0.0607322i \(0.0193436\pi\)
\(402\) 0 0
\(403\) −1.61702 + 0.933589i −0.0805497 + 0.0465054i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.03948i 0.0515250i
\(408\) 0 0
\(409\) 13.1625 + 22.7981i 0.650843 + 1.12729i 0.982919 + 0.184040i \(0.0589177\pi\)
−0.332076 + 0.943253i \(0.607749\pi\)
\(410\) 0 0
\(411\) −1.27457 −0.0628701
\(412\) 0 0
\(413\) 5.00802 + 2.89138i 0.246428 + 0.142276i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.267634i 0.0131061i
\(418\) 0 0
\(419\) −15.3250 −0.748674 −0.374337 0.927293i \(-0.622130\pi\)
−0.374337 + 0.927293i \(0.622130\pi\)
\(420\) 0 0
\(421\) −10.9166 + 18.9081i −0.532042 + 0.921523i 0.467259 + 0.884121i \(0.345242\pi\)
−0.999300 + 0.0374023i \(0.988092\pi\)
\(422\) 0 0
\(423\) −22.5928 13.0439i −1.09850 0.634218i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.25002 0.721702i 0.0604929 0.0349256i
\(428\) 0 0
\(429\) −0.596074 −0.0287787
\(430\) 0 0
\(431\) −11.6427 20.1658i −0.560811 0.971354i −0.997426 0.0717050i \(-0.977156\pi\)
0.436615 0.899649i \(-0.356177\pi\)
\(432\) 0 0
\(433\) 3.37854 1.95060i 0.162362 0.0937398i −0.416617 0.909082i \(-0.636784\pi\)
0.578979 + 0.815342i \(0.303451\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.85481 3.29357i −0.0887276 0.157553i
\(438\) 0 0
\(439\) −9.73882 + 16.8681i −0.464808 + 0.805072i −0.999193 0.0401697i \(-0.987210\pi\)
0.534384 + 0.845242i \(0.320543\pi\)
\(440\) 0 0
\(441\) −9.45606 16.3784i −0.450288 0.779922i
\(442\) 0 0
\(443\) −1.65121 + 0.953328i −0.0784515 + 0.0452940i −0.538713 0.842490i \(-0.681089\pi\)
0.460261 + 0.887784i \(0.347756\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −3.19986 + 1.84744i −0.151348 + 0.0873808i
\(448\) 0 0
\(449\) 8.05933 0.380343 0.190172 0.981751i \(-0.439096\pi\)
0.190172 + 0.981751i \(0.439096\pi\)
\(450\) 0 0
\(451\) −1.55922 + 2.70064i −0.0734207 + 0.127168i
\(452\) 0 0
\(453\) −0.887941 0.512653i −0.0417191 0.0240865i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 11.3250i 0.529760i 0.964281 + 0.264880i \(0.0853323\pi\)
−0.964281 + 0.264880i \(0.914668\pi\)
\(458\) 0 0
\(459\) −7.05213 + 12.2146i −0.329165 + 0.570131i
\(460\) 0 0
\(461\) −10.0521 + 17.4108i −0.468174 + 0.810902i −0.999338 0.0363671i \(-0.988421\pi\)
0.531164 + 0.847269i \(0.321755\pi\)
\(462\) 0 0
\(463\) 1.33043i 0.0618303i −0.999522 0.0309151i \(-0.990158\pi\)
0.999522 0.0309151i \(-0.00984216\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 10.0844i 0.466651i 0.972399 + 0.233326i \(0.0749608\pi\)
−0.972399 + 0.233326i \(0.925039\pi\)
\(468\) 0 0
\(469\) 3.96052 + 6.85982i 0.182880 + 0.316757i
\(470\) 0 0
\(471\) 0.175030 + 0.303161i 0.00806496 + 0.0139689i
\(472\) 0 0
\(473\) 5.60980 + 3.23882i 0.257939 + 0.148921i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −24.5007 14.1455i −1.12181 0.647677i
\(478\) 0 0
\(479\) 4.44078 + 7.69166i 0.202905 + 0.351441i 0.949463 0.313879i \(-0.101629\pi\)
−0.746559 + 0.665320i \(0.768295\pi\)
\(480\) 0 0
\(481\) 0.317776 + 0.550404i 0.0144893 + 0.0250963i
\(482\) 0 0
\(483\) 0.200861i 0.00913947i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 5.32497i 0.241297i 0.992695 + 0.120649i \(0.0384975\pi\)
−0.992695 + 0.120649i \(0.961503\pi\)
\(488\) 0 0
\(489\) −0.571870 + 0.990508i −0.0258609 + 0.0447923i
\(490\) 0 0
\(491\) 9.70469 16.8090i 0.437967 0.758580i −0.559566 0.828786i \(-0.689032\pi\)
0.997533 + 0.0702054i \(0.0223655\pi\)
\(492\) 0 0
\(493\) 60.0164i 2.70300i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.37751 0.795307i −0.0617899 0.0356744i
\(498\) 0 0
\(499\) 5.79357 10.0348i 0.259356 0.449218i −0.706714 0.707500i \(-0.749823\pi\)
0.966070 + 0.258282i \(0.0831564\pi\)
\(500\) 0 0
\(501\) 3.87611 0.173172
\(502\) 0 0
\(503\) −30.4012 + 17.5521i −1.35552 + 0.782611i −0.989017 0.147805i \(-0.952779\pi\)
−0.366505 + 0.930416i \(0.619446\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3.78746 2.18669i 0.168207 0.0971142i
\(508\) 0 0
\(509\) −7.93359 13.7414i −0.351650 0.609076i 0.634889 0.772604i \(-0.281046\pi\)
−0.986539 + 0.163528i \(0.947713\pi\)
\(510\) 0 0
\(511\) 0.128358 0.222323i 0.00567823 0.00983498i
\(512\) 0 0
\(513\) −9.32002 0.0997981i −0.411489 0.00440619i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 12.8878 7.44078i 0.566805 0.327245i
\(518\) 0 0
\(519\) −2.25409 3.90421i −0.0989438 0.171376i
\(520\) 0 0
\(521\) 36.6949 1.60763 0.803816 0.594878i \(-0.202800\pi\)
0.803816 + 0.594878i \(0.202800\pi\)
\(522\) 0 0
\(523\) 26.8687 15.5127i 1.17489 0.678321i 0.220060 0.975486i \(-0.429375\pi\)
0.954826 + 0.297165i \(0.0960412\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10.6660 6.15802i −0.464618 0.268248i
\(528\) 0 0
\(529\) −11.1240 + 19.2673i −0.483652 + 0.837710i
\(530\) 0 0
\(531\) −26.0879 −1.13212
\(532\) 0 0
\(533\) 1.90666i 0.0825864i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −0.102567 0.0592173i −0.00442611 0.00255542i
\(538\) 0 0
\(539\) 10.7882 0.464682
\(540\) 0 0
\(541\) 3.79357 + 6.57066i 0.163098 + 0.282495i 0.935978 0.352058i \(-0.114518\pi\)
−0.772880 + 0.634552i \(0.781185\pi\)
\(542\) 0 0
\(543\) 3.21199i 0.137840i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −26.6587 + 15.3914i −1.13984 + 0.658088i −0.946391 0.323022i \(-0.895301\pi\)
−0.193450 + 0.981110i \(0.561968\pi\)
\(548\) 0 0
\(549\) −3.25583 + 5.63926i −0.138955 + 0.240678i
\(550\) 0 0
\(551\) 34.5576 19.4615i 1.47220 0.829087i
\(552\) 0 0
\(553\) 5.90523 + 3.40939i 0.251116 + 0.144982i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 26.9106 15.5369i 1.14024 0.658318i 0.193750 0.981051i \(-0.437935\pi\)
0.946490 + 0.322733i \(0.104602\pi\)
\(558\) 0 0
\(559\) 3.96052 0.167512
\(560\) 0 0
\(561\) −1.96587 3.40499i −0.0829992 0.143759i
\(562\) 0 0
\(563\) 23.2766i 0.980990i 0.871444 + 0.490495i \(0.163184\pi\)
−0.871444 + 0.490495i \(0.836816\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −4.30539 2.48572i −0.180810 0.104390i
\(568\) 0 0
\(569\) −24.1976 −1.01442 −0.507208 0.861824i \(-0.669322\pi\)
−0.507208 + 0.861824i \(0.669322\pi\)
\(570\) 0 0
\(571\) 29.8475 1.24908 0.624540 0.780992i \(-0.285286\pi\)
0.624540 + 0.780992i \(0.285286\pi\)
\(572\) 0 0
\(573\) −7.95118 4.59061i −0.332165 0.191776i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 33.7882i 1.40662i 0.710882 + 0.703311i \(0.248296\pi\)
−0.710882 + 0.703311i \(0.751704\pi\)
\(578\) 0 0
\(579\) 3.43905 + 5.95661i 0.142922 + 0.247548i
\(580\) 0 0
\(581\) −10.0844 −0.418372
\(582\) 0 0
\(583\) 13.9762 8.06914i 0.578833 0.334190i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 26.5825 + 15.3474i 1.09718 + 0.633457i 0.935479 0.353383i \(-0.114969\pi\)
0.161700 + 0.986840i \(0.448302\pi\)
\(588\) 0 0
\(589\) 0.0871451 8.13837i 0.00359075 0.335336i
\(590\) 0 0
\(591\) −1.34198 + 2.32438i −0.0552017 + 0.0956121i
\(592\) 0 0
\(593\) −6.05745 + 3.49727i −0.248750 + 0.143616i −0.619192 0.785240i \(-0.712540\pi\)
0.370442 + 0.928856i \(0.379206\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.00893i 0.0412927i
\(598\) 0 0
\(599\) −2.26837 3.92894i −0.0926833 0.160532i 0.815956 0.578114i \(-0.196211\pi\)
−0.908639 + 0.417582i \(0.862878\pi\)
\(600\) 0 0
\(601\) 16.0790 0.655874 0.327937 0.944700i \(-0.393647\pi\)
0.327937 + 0.944700i \(0.393647\pi\)
\(602\) 0 0
\(603\) −30.9469 17.8672i −1.26025 0.727608i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 34.0702i 1.38287i −0.722439 0.691434i \(-0.756979\pi\)
0.722439 0.691434i \(-0.243021\pi\)
\(608\) 0 0
\(609\) −2.10752 −0.0854009
\(610\) 0 0
\(611\) 4.54940 7.87979i 0.184049 0.318782i
\(612\) 0 0
\(613\) −34.1544 19.7191i −1.37949 0.796446i −0.387388 0.921917i \(-0.626623\pi\)
−0.992097 + 0.125471i \(0.959956\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −33.9928 + 19.6257i −1.36850 + 0.790102i −0.990736 0.135801i \(-0.956639\pi\)
−0.377761 + 0.925903i \(0.623306\pi\)
\(618\) 0 0
\(619\) −24.3644 −0.979290 −0.489645 0.871922i \(-0.662874\pi\)
−0.489645 + 0.871922i \(0.662874\pi\)
\(620\) 0 0
\(621\) −0.927135 1.60584i −0.0372046 0.0644403i
\(622\) 0 0
\(623\) −0.298433 + 0.172301i −0.0119565 + 0.00690308i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 1.32313 2.23609i 0.0528408 0.0893008i
\(628\) 0 0
\(629\) −2.09607 + 3.63051i −0.0835759 + 0.144758i
\(630\) 0 0
\(631\) 17.6949 + 30.6484i 0.704422 + 1.22009i 0.966900 + 0.255157i \(0.0821270\pi\)
−0.262478 + 0.964938i \(0.584540\pi\)
\(632\) 0 0
\(633\) 5.34236 3.08442i 0.212340 0.122595i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 5.71237 3.29804i 0.226332 0.130673i
\(638\) 0 0
\(639\) 7.17577 0.283869
\(640\) 0 0
\(641\) −17.8546 + 30.9251i −0.705216 + 1.22147i 0.261398 + 0.965231i \(0.415816\pi\)
−0.966614 + 0.256238i \(0.917517\pi\)
\(642\) 0 0
\(643\) 18.2816 + 10.5549i 0.720954 + 0.416243i 0.815104 0.579315i \(-0.196680\pi\)
−0.0941496 + 0.995558i \(0.530013\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 43.7058i 1.71825i 0.511764 + 0.859126i \(0.328992\pi\)
−0.511764 + 0.859126i \(0.671008\pi\)
\(648\) 0 0
\(649\) 7.44078 12.8878i 0.292076 0.505891i
\(650\) 0 0
\(651\) −0.216243 + 0.374544i −0.00847524 + 0.0146795i
\(652\) 0 0
\(653\) 24.1887i 0.946576i 0.880908 + 0.473288i \(0.156933\pi\)
−0.880908 + 0.473288i \(0.843067\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1.15813i 0.0451829i
\(658\) 0 0
\(659\) 16.9956 + 29.4373i 0.662056 + 1.14672i 0.980074 + 0.198630i \(0.0636494\pi\)
−0.318018 + 0.948085i \(0.603017\pi\)
\(660\) 0 0
\(661\) −2.27830 3.94613i −0.0886155 0.153487i 0.818311 0.574776i \(-0.194911\pi\)
−0.906926 + 0.421290i \(0.861578\pi\)
\(662\) 0 0
\(663\) −2.08186 1.20196i −0.0808528 0.0466804i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6.83318 + 3.94514i 0.264582 + 0.152756i
\(668\) 0 0
\(669\) −1.57460 2.72729i −0.0608775 0.105443i
\(670\) 0 0
\(671\) −1.85725 3.21686i −0.0716985 0.124185i
\(672\) 0 0
\(673\) 22.7487i 0.876900i 0.898756 + 0.438450i \(0.144472\pi\)
−0.898756 + 0.438450i \(0.855528\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15.6949i 0.603203i −0.953434 0.301602i \(-0.902479\pi\)
0.953434 0.301602i \(-0.0975212\pi\)
\(678\) 0 0
\(679\) −2.34198 + 4.05643i −0.0898769 + 0.155671i
\(680\) 0 0
\(681\) 3.81331 6.60485i 0.146126 0.253098i
\(682\) 0 0
\(683\) 8.82770i 0.337783i 0.985635 + 0.168891i \(0.0540187\pi\)
−0.985635 + 0.168891i \(0.945981\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 7.06214 + 4.07733i 0.269438 + 0.155560i
\(688\) 0 0
\(689\) 4.93359 8.54523i 0.187955 0.325547i
\(690\) 0 0
\(691\) −23.0198 −0.875716 −0.437858 0.899044i \(-0.644263\pi\)
−0.437858 + 0.899044i \(0.644263\pi\)
\(692\) 0 0
\(693\) 2.58107 1.49018i 0.0980469 0.0566074i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −10.8915 + 6.28822i −0.412546 + 0.238183i
\(698\) 0 0
\(699\) 3.50546 + 6.07163i 0.132589 + 0.229650i
\(700\) 0 0
\(701\) 4.95606 8.58414i 0.187188 0.324219i −0.757124 0.653271i \(-0.773396\pi\)
0.944312 + 0.329053i \(0.106729\pi\)
\(702\) 0 0
\(703\) −2.77015 0.0296625i −0.104478 0.00111874i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.13250 + 2.96325i −0.193028 + 0.111445i
\(708\) 0 0
\(709\) −18.0521 31.2672i −0.677962 1.17426i −0.975594 0.219584i \(-0.929530\pi\)
0.297632 0.954681i \(-0.403803\pi\)
\(710\) 0 0
\(711\) −30.7617 −1.15365
\(712\) 0 0
\(713\) 1.40225 0.809587i 0.0525145 0.0303193i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −0.673164 0.388651i −0.0251398 0.0145145i
\(718\) 0 0
\(719\) −9.50546 + 16.4639i −0.354494 + 0.614001i −0.987031 0.160529i \(-0.948680\pi\)
0.632537 + 0.774530i \(0.282013\pi\)
\(720\) 0 0
\(721\) −6.90666 −0.257217
\(722\) 0 0
\(723\) 8.91558i 0.331574i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.50024 + 1.44351i 0.0927286 + 0.0535369i 0.545647 0.838015i \(-0.316284\pi\)
−0.452919 + 0.891552i \(0.649617\pi\)
\(728\) 0 0
\(729\) 20.0899 0.744069
\(730\) 0 0
\(731\) 13.0619 + 22.6240i 0.483114 + 0.836777i
\(732\) 0 0
\(733\) 44.9463i 1.66013i −0.557666 0.830066i \(-0.688303\pi\)
0.557666 0.830066i \(-0.311697\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 17.6533 10.1921i 0.650268 0.375433i
\(738\) 0 0
\(739\) 25.4956 44.1597i 0.937872 1.62444i 0.168442 0.985711i \(-0.446126\pi\)
0.769430 0.638731i \(-0.220540\pi\)
\(740\) 0 0
\(741\) 0.0170096 1.58850i 0.000624862 0.0583550i
\(742\) 0 0
\(743\) 16.3472 + 9.43805i 0.599720 + 0.346249i 0.768931 0.639331i \(-0.220789\pi\)
−0.169211 + 0.985580i \(0.554122\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 39.3990 22.7470i 1.44153 0.832270i
\(748\) 0 0
\(749\) −7.20108 −0.263122
\(750\) 0 0
\(751\) −13.0127 22.5386i −0.474838 0.822444i 0.524746 0.851259i \(-0.324160\pi\)
−0.999585 + 0.0288143i \(0.990827\pi\)
\(752\) 0 0
\(753\) 1.19540i 0.0435629i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 10.3192 + 5.95779i 0.375058 + 0.216540i 0.675666 0.737208i \(-0.263856\pi\)
−0.300608 + 0.953748i \(0.597190\pi\)
\(758\) 0 0
\(759\) 0.516902 0.0187623
\(760\) 0 0
\(761\) −2.39500 −0.0868186 −0.0434093 0.999057i \(-0.513822\pi\)
−0.0434093 + 0.999057i \(0.513822\pi\)
\(762\) 0 0
\(763\) 7.28274 + 4.20469i 0.263653 + 0.152220i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.09880i 0.328539i
\(768\) 0 0
\(769\) 2.66248 + 4.61156i 0.0960117 + 0.166297i 0.910030 0.414542i \(-0.136058\pi\)
−0.814019 + 0.580839i \(0.802725\pi\)
\(770\) 0 0
\(771\) 2.78276 0.100219
\(772\) 0 0
\(773\) 21.2153 12.2486i 0.763060 0.440553i −0.0673334 0.997731i \(-0.521449\pi\)
0.830393 + 0.557178i \(0.188116\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0.127488 + 0.0736051i 0.00457360 + 0.00264057i
\(778\) 0 0
\(779\) −7.15256 4.23229i −0.256267 0.151637i
\(780\) 0 0
\(781\) −2.04667 + 3.54494i −0.0732357 + 0.126848i
\(782\) 0 0
\(783\) 16.8492 9.72790i 0.602142 0.347647i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 20.5171i 0.731356i −0.930741 0.365678i \(-0.880837\pi\)
0.930741 0.365678i \(-0.119163\pi\)
\(788\) 0 0
\(789\) −2.68396 4.64875i −0.0955515 0.165500i
\(790\) 0 0
\(791\) 4.50819 0.160293
\(792\) 0 0
\(793\) −1.96683 1.13555i −0.0698443 0.0403246i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 23.0144i 0.815211i −0.913158 0.407606i \(-0.866364\pi\)
0.913158 0.407606i \(-0.133636\pi\)
\(798\) 0 0
\(799\) 60.0164 2.12323
\(800\) 0