Properties

Label 1300.2.bb.a.1049.1
Level $1300$
Weight $2$
Character 1300.1049
Analytic conductor $10.381$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1300.bb (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.3805522628\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 260)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1049.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1300.1049
Dual form 1300.2.bb.a.549.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{3} +(0.866025 - 0.500000i) q^{7} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{3} +(0.866025 - 0.500000i) q^{7} +(-1.00000 - 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(3.46410 + 1.00000i) q^{13} +(2.59808 - 1.50000i) q^{17} +(-3.50000 - 6.06218i) q^{19} -1.00000 q^{21} +(2.59808 + 1.50000i) q^{23} +5.00000i q^{27} +(1.50000 - 2.59808i) q^{29} -4.00000 q^{31} +(2.59808 - 1.50000i) q^{33} +(-6.06218 - 3.50000i) q^{37} +(-2.50000 - 2.59808i) q^{39} +(4.50000 - 7.79423i) q^{41} +(9.52628 - 5.50000i) q^{43} +(-3.00000 + 5.19615i) q^{49} -3.00000 q^{51} -6.00000i q^{53} +7.00000i q^{57} +(-1.50000 - 2.59808i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(-1.73205 - 1.00000i) q^{63} +(-6.06218 - 3.50000i) q^{67} +(-1.50000 - 2.59808i) q^{69} +(1.50000 + 2.59808i) q^{71} +2.00000i q^{73} +3.00000i q^{77} -8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} -12.0000i q^{83} +(-2.59808 + 1.50000i) q^{87} +(7.50000 - 12.9904i) q^{89} +(3.50000 - 0.866025i) q^{91} +(3.46410 + 2.00000i) q^{93} +(6.06218 - 3.50000i) q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{9} - 6 q^{11} - 14 q^{19} - 4 q^{21} + 6 q^{29} - 16 q^{31} - 10 q^{39} + 18 q^{41} - 12 q^{49} - 12 q^{51} - 6 q^{59} - 22 q^{61} - 6 q^{69} + 6 q^{71} - 32 q^{79} - 2 q^{81} + 30 q^{89} + 14 q^{91} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(651\) \(677\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\)

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
\(3\) −0.866025 0.500000i −0.500000 0.288675i 0.228714 0.973494i \(-0.426548\pi\)
−0.728714 + 0.684819i \(0.759881\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.866025 0.500000i 0.327327 0.188982i −0.327327 0.944911i \(-0.606148\pi\)
0.654654 + 0.755929i \(0.272814\pi\)
\(8\) 0 0
\(9\) −1.00000 1.73205i −0.333333 0.577350i
\(10\) 0 0
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) 3.46410 + 1.00000i 0.960769 + 0.277350i
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.59808 1.50000i 0.630126 0.363803i −0.150675 0.988583i \(-0.548145\pi\)
0.780801 + 0.624780i \(0.214811\pi\)
\(18\) 0 0
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 2.59808 + 1.50000i 0.541736 + 0.312772i 0.745782 0.666190i \(-0.232076\pi\)
−0.204046 + 0.978961i \(0.565409\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.00000i 0.962250i
\(28\) 0 0
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 2.59808 1.50000i 0.452267 0.261116i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6.06218 3.50000i −0.996616 0.575396i −0.0893706 0.995998i \(-0.528486\pi\)
−0.907245 + 0.420602i \(0.861819\pi\)
\(38\) 0 0
\(39\) −2.50000 2.59808i −0.400320 0.416025i
\(40\) 0 0
\(41\) 4.50000 7.79423i 0.702782 1.21725i −0.264704 0.964330i \(-0.585274\pi\)
0.967486 0.252924i \(-0.0813924\pi\)
\(42\) 0 0
\(43\) 9.52628 5.50000i 1.45274 0.838742i 0.454108 0.890947i \(-0.349958\pi\)
0.998636 + 0.0522047i \(0.0166248\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) −3.00000 + 5.19615i −0.428571 + 0.742307i
\(50\) 0 0
\(51\) −3.00000 −0.420084
\(52\) 0 0
\(53\) 6.00000i 0.824163i −0.911147 0.412082i \(-0.864802\pi\)
0.911147 0.412082i \(-0.135198\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 7.00000i 0.927173i
\(58\) 0 0
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0 0
\(61\) −5.50000 9.52628i −0.704203 1.21972i −0.966978 0.254858i \(-0.917971\pi\)
0.262776 0.964857i \(-0.415362\pi\)
\(62\) 0 0
\(63\) −1.73205 1.00000i −0.218218 0.125988i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −6.06218 3.50000i −0.740613 0.427593i 0.0816792 0.996659i \(-0.473972\pi\)
−0.822292 + 0.569066i \(0.807305\pi\)
\(68\) 0 0
\(69\) −1.50000 2.59808i −0.180579 0.312772i
\(70\) 0 0
\(71\) 1.50000 + 2.59808i 0.178017 + 0.308335i 0.941201 0.337846i \(-0.109698\pi\)
−0.763184 + 0.646181i \(0.776365\pi\)
\(72\) 0 0
\(73\) 2.00000i 0.234082i 0.993127 + 0.117041i \(0.0373409\pi\)
−0.993127 + 0.117041i \(0.962659\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.00000i 0.341882i
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.59808 + 1.50000i −0.278543 + 0.160817i
\(88\) 0 0
\(89\) 7.50000 12.9904i 0.794998 1.37698i −0.127842 0.991795i \(-0.540805\pi\)
0.922840 0.385183i \(-0.125862\pi\)
\(90\) 0 0
\(91\) 3.50000 0.866025i 0.366900 0.0907841i
\(92\) 0 0
\(93\) 3.46410 + 2.00000i 0.359211 + 0.207390i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.06218 3.50000i 0.615521 0.355371i −0.159602 0.987181i \(-0.551021\pi\)
0.775123 + 0.631810i \(0.217688\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i \(-0.685553\pi\)
0.998240 + 0.0592978i \(0.0188862\pi\)
\(102\) 0 0
\(103\) 8.00000i 0.788263i 0.919054 + 0.394132i \(0.128955\pi\)
−0.919054 + 0.394132i \(0.871045\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.79423 + 4.50000i 0.753497 + 0.435031i 0.826956 0.562267i \(-0.190071\pi\)
−0.0734594 + 0.997298i \(0.523404\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 0 0
\(111\) 3.50000 + 6.06218i 0.332205 + 0.575396i
\(112\) 0 0
\(113\) 7.79423 4.50000i 0.733219 0.423324i −0.0863794 0.996262i \(-0.527530\pi\)
0.819599 + 0.572938i \(0.194196\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.73205 7.00000i −0.160128 0.647150i
\(118\) 0 0
\(119\) 1.50000 2.59808i 0.137505 0.238165i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) −7.79423 + 4.50000i −0.702782 + 0.405751i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −16.4545 9.50000i −1.46010 0.842989i −0.461084 0.887357i \(-0.652539\pi\)
−0.999015 + 0.0443678i \(0.985873\pi\)
\(128\) 0 0
\(129\) −11.0000 −0.968496
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) −6.06218 3.50000i −0.525657 0.303488i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 12.9904 7.50000i 1.10984 0.640768i 0.171054 0.985262i \(-0.445283\pi\)
0.938789 + 0.344493i \(0.111949\pi\)
\(138\) 0 0
\(139\) 2.50000 + 4.33013i 0.212047 + 0.367277i 0.952355 0.304991i \(-0.0986536\pi\)
−0.740308 + 0.672268i \(0.765320\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −7.79423 + 7.50000i −0.651786 + 0.627182i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 5.19615 3.00000i 0.428571 0.247436i
\(148\) 0 0
\(149\) −10.5000 18.1865i −0.860194 1.48990i −0.871742 0.489966i \(-0.837009\pi\)
0.0115483 0.999933i \(-0.496324\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 0 0
\(153\) −5.19615 3.00000i −0.420084 0.242536i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 10.0000i 0.798087i 0.916932 + 0.399043i \(0.130658\pi\)
−0.916932 + 0.399043i \(0.869342\pi\)
\(158\) 0 0
\(159\) −3.00000 + 5.19615i −0.237915 + 0.412082i
\(160\) 0 0
\(161\) 3.00000 0.236433
\(162\) 0 0
\(163\) −0.866025 + 0.500000i −0.0678323 + 0.0391630i −0.533533 0.845780i \(-0.679136\pi\)
0.465700 + 0.884943i \(0.345802\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.59808 1.50000i −0.201045 0.116073i 0.396098 0.918208i \(-0.370364\pi\)
−0.597143 + 0.802135i \(0.703697\pi\)
\(168\) 0 0
\(169\) 11.0000 + 6.92820i 0.846154 + 0.532939i
\(170\) 0 0
\(171\) −7.00000 + 12.1244i −0.535303 + 0.927173i
\(172\) 0 0
\(173\) −2.59808 + 1.50000i −0.197528 + 0.114043i −0.595502 0.803354i \(-0.703047\pi\)
0.397974 + 0.917397i \(0.369713\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 3.00000i 0.225494i
\(178\) 0 0
\(179\) −10.5000 + 18.1865i −0.784807 + 1.35933i 0.144308 + 0.989533i \(0.453905\pi\)
−0.929114 + 0.369792i \(0.879429\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 11.0000i 0.813143i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 9.00000i 0.658145i
\(188\) 0 0
\(189\) 2.50000 + 4.33013i 0.181848 + 0.314970i
\(190\) 0 0
\(191\) 1.50000 + 2.59808i 0.108536 + 0.187990i 0.915177 0.403051i \(-0.132050\pi\)
−0.806641 + 0.591041i \(0.798717\pi\)
\(192\) 0 0
\(193\) −4.33013 2.50000i −0.311689 0.179954i 0.335993 0.941865i \(-0.390928\pi\)
−0.647682 + 0.761911i \(0.724262\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.1865 + 10.5000i 1.29574 + 0.748094i 0.979665 0.200641i \(-0.0643025\pi\)
0.316072 + 0.948735i \(0.397636\pi\)
\(198\) 0 0
\(199\) 8.50000 + 14.7224i 0.602549 + 1.04365i 0.992434 + 0.122782i \(0.0391815\pi\)
−0.389885 + 0.920864i \(0.627485\pi\)
\(200\) 0 0
\(201\) 3.50000 + 6.06218i 0.246871 + 0.427593i
\(202\) 0 0
\(203\) 3.00000i 0.210559i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.00000i 0.417029i
\(208\) 0 0
\(209\) 21.0000 1.45260
\(210\) 0 0
\(211\) −5.50000 + 9.52628i −0.378636 + 0.655816i −0.990864 0.134865i \(-0.956940\pi\)
0.612228 + 0.790681i \(0.290273\pi\)
\(212\) 0 0
\(213\) 3.00000i 0.205557i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −3.46410 + 2.00000i −0.235159 + 0.135769i
\(218\) 0 0
\(219\) 1.00000 1.73205i 0.0675737 0.117041i
\(220\) 0 0
\(221\) 10.5000 2.59808i 0.706306 0.174766i
\(222\) 0 0
\(223\) 16.4545 + 9.50000i 1.10187 + 0.636167i 0.936713 0.350100i \(-0.113852\pi\)
0.165161 + 0.986267i \(0.447186\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −23.3827 + 13.5000i −1.55196 + 0.896026i −0.553981 + 0.832529i \(0.686892\pi\)
−0.997982 + 0.0634974i \(0.979775\pi\)
\(228\) 0 0
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 1.50000 2.59808i 0.0986928 0.170941i
\(232\) 0 0
\(233\) 18.0000i 1.17922i 0.807688 + 0.589610i \(0.200718\pi\)
−0.807688 + 0.589610i \(0.799282\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 6.92820 + 4.00000i 0.450035 + 0.259828i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 0 0
\(243\) 13.8564 8.00000i 0.888889 0.513200i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.06218 24.5000i −0.385727 1.55890i
\(248\) 0 0
\(249\) −6.00000 + 10.3923i −0.380235 + 0.658586i
\(250\) 0 0
\(251\) −10.5000 18.1865i −0.662754 1.14792i −0.979889 0.199543i \(-0.936054\pi\)
0.317135 0.948380i \(-0.397279\pi\)
\(252\) 0 0
\(253\) −7.79423 + 4.50000i −0.490019 + 0.282913i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.79423 + 4.50000i 0.486191 + 0.280702i 0.722993 0.690856i \(-0.242766\pi\)
−0.236802 + 0.971558i \(0.576099\pi\)
\(258\) 0 0
\(259\) −7.00000 −0.434959
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 0 0
\(263\) 2.59808 + 1.50000i 0.160204 + 0.0924940i 0.577959 0.816066i \(-0.303849\pi\)
−0.417755 + 0.908560i \(0.637183\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −12.9904 + 7.50000i −0.794998 + 0.458993i
\(268\) 0 0
\(269\) 13.5000 + 23.3827i 0.823110 + 1.42567i 0.903356 + 0.428892i \(0.141096\pi\)
−0.0802460 + 0.996775i \(0.525571\pi\)
\(270\) 0 0
\(271\) −11.5000 + 19.9186i −0.698575 + 1.20997i 0.270385 + 0.962752i \(0.412849\pi\)
−0.968960 + 0.247216i \(0.920484\pi\)
\(272\) 0 0
\(273\) −3.46410 1.00000i −0.209657 0.0605228i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 16.4545 9.50000i 0.988654 0.570800i 0.0837823 0.996484i \(-0.473300\pi\)
0.904872 + 0.425684i \(0.139967\pi\)
\(278\) 0 0
\(279\) 4.00000 + 6.92820i 0.239474 + 0.414781i
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −4.33013 2.50000i −0.257399 0.148610i 0.365748 0.930714i \(-0.380813\pi\)
−0.623148 + 0.782104i \(0.714146\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 9.00000i 0.531253i
\(288\) 0 0
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) 0 0
\(291\) −7.00000 −0.410347
\(292\) 0 0
\(293\) −23.3827 + 13.5000i −1.36603 + 0.788678i −0.990419 0.138098i \(-0.955901\pi\)
−0.375613 + 0.926777i \(0.622568\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −12.9904 7.50000i −0.753778 0.435194i
\(298\) 0 0
\(299\) 7.50000 + 7.79423i 0.433736 + 0.450752i
\(300\) 0 0
\(301\) 5.50000 9.52628i 0.317015 0.549086i
\(302\) 0 0
\(303\) −7.79423 + 4.50000i −0.447767 + 0.258518i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 20.0000i 1.14146i −0.821138 0.570730i \(-0.806660\pi\)
0.821138 0.570730i \(-0.193340\pi\)
\(308\) 0 0
\(309\) 4.00000 6.92820i 0.227552 0.394132i
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 22.0000i 1.24351i −0.783210 0.621757i \(-0.786419\pi\)
0.783210 0.621757i \(-0.213581\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 0 0
\(321\) −4.50000 7.79423i −0.251166 0.435031i
\(322\) 0 0
\(323\) −18.1865 10.5000i −1.01193 0.584236i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.73205 + 1.00000i 0.0957826 + 0.0553001i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 9.50000 + 16.4545i 0.522167 + 0.904420i 0.999667 + 0.0257885i \(0.00820965\pi\)
−0.477500 + 0.878632i \(0.658457\pi\)
\(332\) 0 0
\(333\) 14.0000i 0.767195i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 34.0000i 1.85210i 0.377403 + 0.926049i \(0.376817\pi\)
−0.377403 + 0.926049i \(0.623183\pi\)
\(338\) 0 0
\(339\) −9.00000 −0.488813
\(340\) 0 0
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) 0 0
\(343\) 13.0000i 0.701934i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 28.5788 16.5000i 1.53419 0.885766i 0.535031 0.844833i \(-0.320300\pi\)
0.999162 0.0409337i \(-0.0130332\pi\)
\(348\) 0 0
\(349\) −0.500000 + 0.866025i −0.0267644 + 0.0463573i −0.879097 0.476642i \(-0.841854\pi\)
0.852333 + 0.523000i \(0.175187\pi\)
\(350\) 0 0
\(351\) −5.00000 + 17.3205i −0.266880 + 0.924500i
\(352\) 0 0
\(353\) −7.79423 4.50000i −0.414845 0.239511i 0.278024 0.960574i \(-0.410320\pi\)
−0.692869 + 0.721063i \(0.743654\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −2.59808 + 1.50000i −0.137505 + 0.0793884i
\(358\) 0 0
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 0 0
\(363\) 2.00000i 0.104973i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 4.33013 + 2.50000i 0.226031 + 0.130499i 0.608740 0.793370i \(-0.291675\pi\)
−0.382709 + 0.923869i \(0.625009\pi\)
\(368\) 0 0
\(369\) −18.0000 −0.937043
\(370\) 0 0
\(371\) −3.00000 5.19615i −0.155752 0.269771i
\(372\) 0 0
\(373\) −26.8468 + 15.5000i −1.39007 + 0.802560i −0.993323 0.115367i \(-0.963196\pi\)
−0.396751 + 0.917926i \(0.629862\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 7.79423 7.50000i 0.401423 0.386270i
\(378\) 0 0
\(379\) −0.500000 + 0.866025i −0.0256833 + 0.0444847i −0.878581 0.477593i \(-0.841509\pi\)
0.852898 + 0.522077i \(0.174843\pi\)
\(380\) 0 0
\(381\) 9.50000 + 16.4545i 0.486700 + 0.842989i
\(382\) 0 0
\(383\) −7.79423 + 4.50000i −0.398266 + 0.229939i −0.685736 0.727851i \(-0.740519\pi\)
0.287469 + 0.957790i \(0.407186\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −19.0526 11.0000i −0.968496 0.559161i
\(388\) 0 0
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) 0 0
\(391\) 9.00000 0.455150
\(392\) 0 0
\(393\) 10.3923 + 6.00000i 0.524222 + 0.302660i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −4.33013 + 2.50000i −0.217323 + 0.125471i −0.604710 0.796446i \(-0.706711\pi\)
0.387387 + 0.921917i \(0.373378\pi\)
\(398\) 0 0
\(399\) 3.50000 + 6.06218i 0.175219 + 0.303488i
\(400\) 0 0
\(401\) 16.5000 28.5788i 0.823971 1.42716i −0.0787327 0.996896i \(-0.525087\pi\)
0.902703 0.430263i \(-0.141579\pi\)
\(402\) 0 0
\(403\) −13.8564 4.00000i −0.690237 0.199254i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 18.1865 10.5000i 0.901473 0.520466i
\(408\) 0 0
\(409\) −12.5000 21.6506i −0.618085 1.07056i −0.989835 0.142222i \(-0.954575\pi\)
0.371750 0.928333i \(-0.378758\pi\)
\(410\) 0 0
\(411\) −15.0000 −0.739895
\(412\) 0 0
\(413\) −2.59808 1.50000i −0.127843 0.0738102i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 5.00000i 0.244851i
\(418\) 0 0
\(419\) −4.50000 + 7.79423i −0.219839 + 0.380773i −0.954759 0.297382i \(-0.903887\pi\)
0.734919 + 0.678155i \(0.237220\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −9.52628 5.50000i −0.461009 0.266164i
\(428\) 0 0
\(429\) 10.5000 2.59808i 0.506945 0.125436i
\(430\) 0 0
\(431\) 4.50000 7.79423i 0.216757 0.375435i −0.737057 0.675830i \(-0.763785\pi\)
0.953815 + 0.300395i \(0.0971186\pi\)
\(432\) 0 0
\(433\) 25.1147 14.5000i 1.20694 0.696826i 0.244848 0.969561i \(-0.421262\pi\)
0.962089 + 0.272736i \(0.0879285\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 21.0000i 1.00457i
\(438\) 0 0
\(439\) 5.50000 9.52628i 0.262501 0.454665i −0.704405 0.709798i \(-0.748786\pi\)
0.966906 + 0.255134i \(0.0821195\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 21.0000i 0.993266i
\(448\) 0 0
\(449\) 1.50000 + 2.59808i 0.0707894 + 0.122611i 0.899247 0.437440i \(-0.144115\pi\)
−0.828458 + 0.560051i \(0.810782\pi\)
\(450\) 0 0
\(451\) 13.5000 + 23.3827i 0.635690 + 1.10105i
\(452\) 0 0
\(453\) −6.92820 4.00000i −0.325515 0.187936i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 4.33013 + 2.50000i 0.202555 + 0.116945i 0.597847 0.801611i \(-0.296023\pi\)
−0.395292 + 0.918556i \(0.629357\pi\)
\(458\) 0 0
\(459\) 7.50000 + 12.9904i 0.350070 + 0.606339i
\(460\) 0 0
\(461\) −13.5000 23.3827i −0.628758 1.08904i −0.987801 0.155719i \(-0.950230\pi\)
0.359044 0.933321i \(-0.383103\pi\)
\(462\) 0 0
\(463\) 4.00000i 0.185896i −0.995671 0.0929479i \(-0.970371\pi\)
0.995671 0.0929479i \(-0.0296290\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 36.0000i 1.66588i 0.553362 + 0.832941i \(0.313345\pi\)
−0.553362 + 0.832941i \(0.686655\pi\)
\(468\) 0 0
\(469\) −7.00000 −0.323230
\(470\) 0 0
\(471\) 5.00000 8.66025i 0.230388 0.399043i
\(472\) 0 0
\(473\) 33.0000i 1.51734i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −10.3923 + 6.00000i −0.475831 + 0.274721i
\(478\) 0 0
\(479\) 19.5000 33.7750i 0.890978 1.54322i 0.0522726 0.998633i \(-0.483354\pi\)
0.838705 0.544586i \(-0.183313\pi\)
\(480\) 0 0
\(481\) −17.5000 18.1865i −0.797931 0.829235i
\(482\) 0 0
\(483\) −2.59808 1.50000i −0.118217 0.0682524i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −9.52628 + 5.50000i −0.431677 + 0.249229i −0.700061 0.714083i \(-0.746844\pi\)
0.268384 + 0.963312i \(0.413510\pi\)
\(488\) 0 0
\(489\) 1.00000 0.0452216
\(490\) 0 0
\(491\) 4.50000 7.79423i 0.203082 0.351749i −0.746438 0.665455i \(-0.768237\pi\)
0.949520 + 0.313707i \(0.101571\pi\)
\(492\) 0 0
\(493\) 9.00000i 0.405340i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.59808 + 1.50000i 0.116540 + 0.0672842i
\(498\) 0 0
\(499\) −32.0000 −1.43252 −0.716258 0.697835i \(-0.754147\pi\)
−0.716258 + 0.697835i \(0.754147\pi\)
\(500\) 0 0
\(501\) 1.50000 + 2.59808i 0.0670151 + 0.116073i
\(502\) 0 0
\(503\) 12.9904 7.50000i 0.579212 0.334408i −0.181608 0.983371i \(-0.558130\pi\)
0.760820 + 0.648963i \(0.224797\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −6.06218 11.5000i −0.269231 0.510733i
\(508\) 0 0
\(509\) −4.50000 + 7.79423i −0.199459 + 0.345473i −0.948353 0.317217i \(-0.897252\pi\)
0.748894 + 0.662690i \(0.230585\pi\)
\(510\) 0 0
\(511\) 1.00000 + 1.73205i 0.0442374 + 0.0766214i
\(512\) 0 0
\(513\) 30.3109 17.5000i 1.33826 0.772644i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 3.00000 0.131685
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) −25.1147 14.5000i −1.09819 0.634041i −0.162446 0.986718i \(-0.551938\pi\)
−0.935745 + 0.352677i \(0.885272\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10.3923 + 6.00000i −0.452696 + 0.261364i
\(528\) 0 0
\(529\) −7.00000 12.1244i −0.304348 0.527146i
\(530\) 0 0
\(531\) −3.00000 + 5.19615i −0.130189 + 0.225494i
\(532\) 0 0
\(533\) 23.3827 22.5000i 1.01282 0.974583i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 18.1865 10.5000i 0.784807 0.453108i
\(538\) 0 0
\(539\) −9.00000 15.5885i −0.387657 0.671442i
\(540\) 0 0
\(541\) −22.0000 −0.945854 −0.472927 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 0 0
\(543\) −1.73205 1.00000i −0.0743294 0.0429141i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 8.00000i 0.342055i −0.985266 0.171028i \(-0.945291\pi\)
0.985266 0.171028i \(-0.0547087\pi\)
\(548\) 0 0
\(549\) −11.0000 + 19.0526i −0.469469 + 0.813143i
\(550\) 0 0
\(551\) −21.0000 −0.894630
\(552\) 0 0
\(553\) −6.92820 + 4.00000i −0.294617 + 0.170097i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −33.7750 19.5000i −1.43109 0.826242i −0.433888 0.900967i \(-0.642859\pi\)
−0.997204 + 0.0747252i \(0.976192\pi\)
\(558\) 0 0
\(559\) 38.5000 9.52628i 1.62838 0.402919i
\(560\) 0 0
\(561\) 4.50000 7.79423i 0.189990 0.329073i
\(562\) 0 0
\(563\) 33.7750 19.5000i 1.42345 0.821827i 0.426855 0.904320i \(-0.359622\pi\)
0.996592 + 0.0824933i \(0.0262883\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.00000i 0.0419961i
\(568\) 0 0
\(569\) 13.5000 23.3827i 0.565949 0.980253i −0.431011 0.902347i \(-0.641843\pi\)
0.996961 0.0779066i \(-0.0248236\pi\)
\(570\) 0 0
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) 0 0
\(573\) 3.00000i 0.125327i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 2.00000i 0.0832611i −0.999133 0.0416305i \(-0.986745\pi\)
0.999133 0.0416305i \(-0.0132552\pi\)
\(578\) 0 0
\(579\) 2.50000 + 4.33013i 0.103896 + 0.179954i
\(580\) 0 0
\(581\) −6.00000 10.3923i −0.248922 0.431145i
\(582\) 0 0
\(583\) 15.5885 + 9.00000i 0.645608 + 0.372742i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 28.5788 + 16.5000i 1.17957 + 0.681028i 0.955916 0.293640i \(-0.0948666\pi\)
0.223659 + 0.974668i \(0.428200\pi\)
\(588\) 0 0
\(589\) 14.0000 + 24.2487i 0.576860 + 0.999151i
\(590\) 0 0
\(591\) −10.5000 18.1865i −0.431912 0.748094i
\(592\) 0 0
\(593\) 6.00000i 0.246390i −0.992382 0.123195i \(-0.960686\pi\)
0.992382 0.123195i \(-0.0393141\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 17.0000i 0.695764i
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i \(0.419712\pi\)
−0.963405 + 0.268049i \(0.913621\pi\)
\(602\) 0 0
\(603\) 14.0000i 0.570124i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 11.2583 6.50000i 0.456962 0.263827i −0.253804 0.967256i \(-0.581682\pi\)
0.710766 + 0.703429i \(0.248349\pi\)
\(608\) 0 0
\(609\) −1.50000 + 2.59808i −0.0607831 + 0.105279i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 37.2391 + 21.5000i 1.50407 + 0.868377i 0.999989 + 0.00472215i \(0.00150311\pi\)
0.504084 + 0.863655i \(0.331830\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −28.5788 + 16.5000i −1.15054 + 0.664265i −0.949019 0.315219i \(-0.897922\pi\)
−0.201522 + 0.979484i \(0.564589\pi\)
\(618\) 0 0
\(619\) −44.0000 −1.76851 −0.884255 0.467005i \(-0.845333\pi\)
−0.884255 + 0.467005i \(0.845333\pi\)
\(620\) 0 0
\(621\) −7.50000 + 12.9904i −0.300965 + 0.521286i
\(622\) 0 0
\(623\) 15.0000i 0.600962i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −18.1865 10.5000i −0.726300 0.419330i
\(628\) 0 0
\(629\) −21.0000 −0.837325
\(630\) 0 0
\(631\) −8.50000 14.7224i −0.338380 0.586091i 0.645748 0.763550i \(-0.276545\pi\)
−0.984128 + 0.177459i \(0.943212\pi\)
\(632\) 0 0
\(633\) 9.52628 5.50000i 0.378636 0.218605i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −15.5885 + 15.0000i −0.617637 + 0.594322i
\(638\) 0 0
\(639\) 3.00000 5.19615i 0.118678 0.205557i
\(640\) 0 0
\(641\) −13.5000 23.3827i −0.533218 0.923561i −0.999247 0.0387913i \(-0.987649\pi\)
0.466029 0.884769i \(-0.345684\pi\)
\(642\) 0 0
\(643\) 9.52628 5.50000i 0.375680 0.216899i −0.300257 0.953858i \(-0.597072\pi\)
0.675937 + 0.736959i \(0.263739\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 38.9711 + 22.5000i 1.53211 + 0.884566i 0.999264 + 0.0383563i \(0.0122122\pi\)
0.532850 + 0.846210i \(0.321121\pi\)
\(648\) 0 0
\(649\) 9.00000 0.353281
\(650\) 0 0
\(651\) 4.00000 0.156772
\(652\) 0 0
\(653\) 33.7750 + 19.5000i 1.32172 + 0.763094i 0.984003 0.178154i \(-0.0570127\pi\)
0.337715 + 0.941248i \(0.390346\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 3.46410 2.00000i 0.135147 0.0780274i
\(658\) 0 0
\(659\) −19.5000 33.7750i −0.759612 1.31569i −0.943049 0.332655i \(-0.892055\pi\)
0.183436 0.983032i \(-0.441278\pi\)
\(660\) 0 0
\(661\) 0.500000 0.866025i 0.0194477 0.0336845i −0.856138 0.516748i \(-0.827143\pi\)
0.875585 + 0.483063i \(0.160476\pi\)
\(662\) 0 0
\(663\) −10.3923 3.00000i −0.403604 0.116510i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 7.79423 4.50000i 0.301794 0.174241i
\(668\) 0 0
\(669\) −9.50000 16.4545i −0.367291 0.636167i
\(670\) 0 0
\(671\) 33.0000 1.27395
\(672\) 0 0
\(673\) −14.7224 8.50000i −0.567508 0.327651i 0.188645 0.982045i \(-0.439590\pi\)
−0.756153 + 0.654394i \(0.772924\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 42.0000i 1.61419i 0.590421 + 0.807096i \(0.298962\pi\)
−0.590421 + 0.807096i \(0.701038\pi\)
\(678\) 0 0
\(679\) 3.50000 6.06218i 0.134318 0.232645i
\(680\) 0 0
\(681\) 27.0000 1.03464
\(682\) 0 0
\(683\) 44.1673 25.5000i 1.69001 0.975730i 0.735520 0.677503i \(-0.236938\pi\)
0.954495 0.298227i \(-0.0963952\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −19.0526 11.0000i −0.726900 0.419676i
\(688\) 0 0
\(689\) 6.00000 20.7846i 0.228582 0.791831i
\(690\) 0 0
\(691\) −11.5000 + 19.9186i −0.437481 + 0.757739i −0.997494 0.0707446i \(-0.977462\pi\)
0.560014 + 0.828483i \(0.310796\pi\)
\(692\) 0 0
\(693\) 5.19615 3.00000i 0.197386 0.113961i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 27.0000i 1.02270i
\(698\) 0 0
\(699\) 9.00000 15.5885i 0.340411 0.589610i
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 49.0000i 1.84807i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9.00000i 0.338480i
\(708\) 0 0
\(709\) −18.5000 32.0429i −0.694782 1.20340i −0.970254 0.242089i \(-0.922167\pi\)
0.275472 0.961309i \(-0.411166\pi\)
\(710\) 0 0
\(711\) 8.00000 + 13.8564i 0.300023 + 0.519656i
\(712\) 0 0
\(713\) −10.3923 6.00000i −0.389195 0.224702i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4.50000 + 7.79423i 0.167822 + 0.290676i 0.937654 0.347571i \(-0.112993\pi\)
−0.769832 + 0.638247i \(0.779660\pi\)
\(720\) 0 0
\(721\) 4.00000 + 6.92820i 0.148968 + 0.258020i
\(722\) 0 0
\(723\) 1.00000i 0.0371904i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 52.0000i 1.92857i 0.264861 + 0.964287i \(0.414674\pi\)
−0.264861 + 0.964287i \(0.585326\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 16.5000 28.5788i 0.610275 1.05703i
\(732\) 0 0
\(733\) 34.0000i 1.25582i −0.778287 0.627909i \(-0.783911\pi\)
0.778287 0.627909i \(-0.216089\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 18.1865 10.5000i 0.669910 0.386772i
\(738\) 0 0
\(739\) 23.5000 40.7032i 0.864461 1.49729i −0.00311943 0.999995i \(-0.500993\pi\)
0.867581 0.497296i \(-0.165674\pi\)
\(740\) 0 0
\(741\) −7.00000 + 24.2487i −0.257151 + 0.890799i
\(742\) 0 0
\(743\) −18.1865 10.5000i −0.667199 0.385208i 0.127815 0.991798i \(-0.459204\pi\)
−0.795015 + 0.606590i \(0.792537\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −20.7846 + 12.0000i −0.760469 + 0.439057i
\(748\) 0 0
\(749\) 9.00000 0.328853
\(750\) 0 0
\(751\) 6.50000 11.2583i 0.237188 0.410822i −0.722718 0.691143i \(-0.757107\pi\)
0.959906 + 0.280321i \(0.0904408\pi\)
\(752\) 0 0
\(753\) 21.0000i 0.765283i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 25.1147 + 14.5000i 0.912811 + 0.527011i 0.881334 0.472493i \(-0.156646\pi\)
0.0314762 + 0.999505i \(0.489979\pi\)
\(758\) 0 0
\(759\) 9.00000 0.326679
\(760\) 0 0
\(761\) −1.50000 2.59808i −0.0543750 0.0941802i 0.837557 0.546350i \(-0.183983\pi\)
−0.891932 + 0.452170i \(0.850650\pi\)
\(762\) 0 0
\(763\) −1.73205 + 1.00000i −0.0627044 + 0.0362024i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.59808 10.5000i −0.0938111 0.379133i
\(768\) 0 0
\(769\) −6.50000 + 11.2583i −0.234396 + 0.405986i −0.959097 0.283078i \(-0.908645\pi\)
0.724701 + 0.689063i \(0.241978\pi\)
\(770\) 0 0
\(771\) −4.50000 7.79423i −0.162064 0.280702i
\(772\) 0 0
\(773\) −23.3827 + 13.5000i −0.841017 + 0.485561i −0.857610 0.514301i \(-0.828051\pi\)
0.0165929 + 0.999862i \(0.494718\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 6.06218 + 3.50000i 0.217479 + 0.125562i
\(778\) 0 0
\(779\) −63.0000 −2.25721
\(780\) 0 0
\(781\) −9.00000 −0.322045
\(782\) 0 0
\(783\) 12.9904 + 7.50000i 0.464238 + 0.268028i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 32.0429 18.5000i 1.14221 0.659454i 0.195231 0.980757i \(-0.437454\pi\)
0.946976 + 0.321303i \(0.104121\pi\)
\(788\) 0 0
\(789\) −1.50000 2.59808i −0.0534014 0.0924940i
\(790\) 0 0
\(791\) 4.50000 7.79423i 0.160002 0.277131i
\(792\) 0 0
\(793\) −9.52628 38.5000i −0.338288 1.36718i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 44.1673 25.5000i 1.56449 0.903256i 0.567692 0.823241i \(-0.307836\pi\)
0.996794 0.0800155i \(-0.0254970\pi\)
\(798\) 0 0
\(799\)