Properties

Label 504.2.q.c.25.2
Level $504$
Weight $2$
Character 504.25
Analytic conductor $4.024$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 25.2
Character \(\chi\) \(=\) 504.25
Dual form 504.2.q.c.121.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.69989 - 0.332219i) q^{3} +(-1.59750 + 2.76695i) q^{5} +(-1.66645 - 2.05498i) q^{7} +(2.77926 + 1.12947i) q^{9} +O(q^{10})\) \(q+(-1.69989 - 0.332219i) q^{3} +(-1.59750 + 2.76695i) q^{5} +(-1.66645 - 2.05498i) q^{7} +(2.77926 + 1.12947i) q^{9} +(1.14139 + 1.97695i) q^{11} +(-0.675051 - 1.16922i) q^{13} +(3.63481 - 4.17279i) q^{15} +(2.21425 - 3.83519i) q^{17} +(-3.69214 - 6.39497i) q^{19} +(2.15007 + 4.04687i) q^{21} +(3.23479 - 5.60283i) q^{23} +(-2.60400 - 4.51026i) q^{25} +(-4.34921 - 2.84330i) q^{27} +(-1.06167 + 1.83887i) q^{29} -0.632308 q^{31} +(-1.28346 - 3.73979i) q^{33} +(8.34818 - 1.32814i) q^{35} +(1.92885 + 3.34087i) q^{37} +(0.759075 + 2.21182i) q^{39} +(-5.05124 - 8.74900i) q^{41} +(4.24701 - 7.35603i) q^{43} +(-7.56506 + 5.88574i) q^{45} +6.53173 q^{47} +(-1.44591 + 6.84904i) q^{49} +(-5.03810 + 5.78379i) q^{51} +(2.39950 - 4.15606i) q^{53} -7.29349 q^{55} +(4.15170 + 12.0974i) q^{57} +6.20383 q^{59} -8.91093 q^{61} +(-2.31044 - 7.59354i) q^{63} +4.31357 q^{65} -3.01570 q^{67} +(-7.36017 + 8.44954i) q^{69} -15.3791 q^{71} +(4.36577 - 7.56173i) q^{73} +(2.92813 + 8.53206i) q^{75} +(2.16053 - 5.64002i) q^{77} -1.87610 q^{79} +(6.44859 + 6.27819i) q^{81} +(-3.00140 + 5.19857i) q^{83} +(7.07451 + 12.2534i) q^{85} +(2.41563 - 2.77317i) q^{87} +(2.65390 + 4.59668i) q^{89} +(-1.27780 + 3.33566i) q^{91} +(1.07486 + 0.210065i) q^{93} +23.5927 q^{95} +(7.44539 - 12.8958i) q^{97} +(0.939319 + 6.78363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 2q^{3} + q^{5} + 5q^{7} + 6q^{9} + O(q^{10}) \) \( 22q - 2q^{3} + q^{5} + 5q^{7} + 6q^{9} + 3q^{11} + 7q^{13} - q^{15} - q^{17} + 13q^{19} - 22q^{25} - 2q^{27} - 7q^{29} - 12q^{31} - 3q^{33} + 2q^{35} + 6q^{37} - 4q^{39} + 4q^{41} + 2q^{43} - 3q^{45} - 34q^{47} - 25q^{49} + 53q^{51} + q^{53} + 2q^{55} - 21q^{57} + 42q^{59} - 62q^{61} - 22q^{63} + 6q^{65} + 52q^{67} - 40q^{69} - 32q^{71} + 17q^{73} + 53q^{75} - q^{77} + 32q^{79} - 6q^{81} - 36q^{83} + 28q^{85} - 5q^{87} - 2q^{89} + 15q^{91} - 11q^{93} + 48q^{95} + 19q^{97} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.69989 0.332219i −0.981433 0.191807i
\(4\) 0 0
\(5\) −1.59750 + 2.76695i −0.714423 + 1.23742i 0.248759 + 0.968566i \(0.419977\pi\)
−0.963182 + 0.268851i \(0.913356\pi\)
\(6\) 0 0
\(7\) −1.66645 2.05498i −0.629857 0.776711i
\(8\) 0 0
\(9\) 2.77926 + 1.12947i 0.926420 + 0.376491i
\(10\) 0 0
\(11\) 1.14139 + 1.97695i 0.344143 + 0.596073i 0.985198 0.171422i \(-0.0548362\pi\)
−0.641055 + 0.767495i \(0.721503\pi\)
\(12\) 0 0
\(13\) −0.675051 1.16922i −0.187225 0.324284i 0.757099 0.653300i \(-0.226616\pi\)
−0.944324 + 0.329017i \(0.893283\pi\)
\(14\) 0 0
\(15\) 3.63481 4.17279i 0.938503 1.07741i
\(16\) 0 0
\(17\) 2.21425 3.83519i 0.537033 0.930169i −0.462028 0.886865i \(-0.652878\pi\)
0.999062 0.0433042i \(-0.0137885\pi\)
\(18\) 0 0
\(19\) −3.69214 6.39497i −0.847034 1.46711i −0.883843 0.467784i \(-0.845052\pi\)
0.0368084 0.999322i \(-0.488281\pi\)
\(20\) 0 0
\(21\) 2.15007 + 4.04687i 0.469184 + 0.883100i
\(22\) 0 0
\(23\) 3.23479 5.60283i 0.674501 1.16827i −0.302113 0.953272i \(-0.597692\pi\)
0.976614 0.214999i \(-0.0689747\pi\)
\(24\) 0 0
\(25\) −2.60400 4.51026i −0.520800 0.902053i
\(26\) 0 0
\(27\) −4.34921 2.84330i −0.837006 0.547194i
\(28\) 0 0
\(29\) −1.06167 + 1.83887i −0.197148 + 0.341470i −0.947602 0.319452i \(-0.896501\pi\)
0.750455 + 0.660922i \(0.229834\pi\)
\(30\) 0 0
\(31\) −0.632308 −0.113566 −0.0567830 0.998387i \(-0.518084\pi\)
−0.0567830 + 0.998387i \(0.518084\pi\)
\(32\) 0 0
\(33\) −1.28346 3.73979i −0.223422 0.651014i
\(34\) 0 0
\(35\) 8.34818 1.32814i 1.41110 0.224496i
\(36\) 0 0
\(37\) 1.92885 + 3.34087i 0.317102 + 0.549236i 0.979882 0.199578i \(-0.0639570\pi\)
−0.662780 + 0.748814i \(0.730624\pi\)
\(38\) 0 0
\(39\) 0.759075 + 2.21182i 0.121549 + 0.354174i
\(40\) 0 0
\(41\) −5.05124 8.74900i −0.788871 1.36636i −0.926659 0.375903i \(-0.877333\pi\)
0.137788 0.990462i \(-0.456001\pi\)
\(42\) 0 0
\(43\) 4.24701 7.35603i 0.647663 1.12178i −0.336017 0.941856i \(-0.609080\pi\)
0.983680 0.179929i \(-0.0575867\pi\)
\(44\) 0 0
\(45\) −7.56506 + 5.88574i −1.12773 + 0.877395i
\(46\) 0 0
\(47\) 6.53173 0.952751 0.476375 0.879242i \(-0.341950\pi\)
0.476375 + 0.879242i \(0.341950\pi\)
\(48\) 0 0
\(49\) −1.44591 + 6.84904i −0.206559 + 0.978434i
\(50\) 0 0
\(51\) −5.03810 + 5.78379i −0.705475 + 0.809892i
\(52\) 0 0
\(53\) 2.39950 4.15606i 0.329597 0.570879i −0.652835 0.757500i \(-0.726420\pi\)
0.982432 + 0.186621i \(0.0597538\pi\)
\(54\) 0 0
\(55\) −7.29349 −0.983454
\(56\) 0 0
\(57\) 4.15170 + 12.0974i 0.549906 + 1.60233i
\(58\) 0 0
\(59\) 6.20383 0.807670 0.403835 0.914832i \(-0.367677\pi\)
0.403835 + 0.914832i \(0.367677\pi\)
\(60\) 0 0
\(61\) −8.91093 −1.14093 −0.570464 0.821323i \(-0.693236\pi\)
−0.570464 + 0.821323i \(0.693236\pi\)
\(62\) 0 0
\(63\) −2.31044 7.59354i −0.291088 0.956696i
\(64\) 0 0
\(65\) 4.31357 0.535033
\(66\) 0 0
\(67\) −3.01570 −0.368426 −0.184213 0.982886i \(-0.558974\pi\)
−0.184213 + 0.982886i \(0.558974\pi\)
\(68\) 0 0
\(69\) −7.36017 + 8.44954i −0.886060 + 1.01721i
\(70\) 0 0
\(71\) −15.3791 −1.82516 −0.912580 0.408899i \(-0.865913\pi\)
−0.912580 + 0.408899i \(0.865913\pi\)
\(72\) 0 0
\(73\) 4.36577 7.56173i 0.510974 0.885033i −0.488945 0.872315i \(-0.662618\pi\)
0.999919 0.0127186i \(-0.00404857\pi\)
\(74\) 0 0
\(75\) 2.92813 + 8.53206i 0.338111 + 0.985197i
\(76\) 0 0
\(77\) 2.16053 5.64002i 0.246215 0.642740i
\(78\) 0 0
\(79\) −1.87610 −0.211078 −0.105539 0.994415i \(-0.533657\pi\)
−0.105539 + 0.994415i \(0.533657\pi\)
\(80\) 0 0
\(81\) 6.44859 + 6.27819i 0.716510 + 0.697577i
\(82\) 0 0
\(83\) −3.00140 + 5.19857i −0.329446 + 0.570617i −0.982402 0.186779i \(-0.940195\pi\)
0.652956 + 0.757396i \(0.273529\pi\)
\(84\) 0 0
\(85\) 7.07451 + 12.2534i 0.767338 + 1.32907i
\(86\) 0 0
\(87\) 2.41563 2.77317i 0.258983 0.297315i
\(88\) 0 0
\(89\) 2.65390 + 4.59668i 0.281313 + 0.487248i 0.971708 0.236184i \(-0.0758969\pi\)
−0.690396 + 0.723432i \(0.742564\pi\)
\(90\) 0 0
\(91\) −1.27780 + 3.33566i −0.133949 + 0.349673i
\(92\) 0 0
\(93\) 1.07486 + 0.210065i 0.111457 + 0.0217827i
\(94\) 0 0
\(95\) 23.5927 2.42056
\(96\) 0 0
\(97\) 7.44539 12.8958i 0.755965 1.30937i −0.188929 0.981991i \(-0.560502\pi\)
0.944893 0.327378i \(-0.106165\pi\)
\(98\) 0 0
\(99\) 0.939319 + 6.78363i 0.0944051 + 0.681781i
\(100\) 0 0
\(101\) 7.00299 + 12.1295i 0.696824 + 1.20693i 0.969562 + 0.244846i \(0.0787374\pi\)
−0.272738 + 0.962088i \(0.587929\pi\)
\(102\) 0 0
\(103\) −8.03055 + 13.9093i −0.791274 + 1.37053i 0.133905 + 0.990994i \(0.457248\pi\)
−0.925179 + 0.379532i \(0.876085\pi\)
\(104\) 0 0
\(105\) −14.6322 0.515732i −1.42796 0.0503303i
\(106\) 0 0
\(107\) 1.26820 + 2.19658i 0.122601 + 0.212352i 0.920793 0.390052i \(-0.127543\pi\)
−0.798191 + 0.602404i \(0.794210\pi\)
\(108\) 0 0
\(109\) 8.10946 14.0460i 0.776746 1.34536i −0.157062 0.987589i \(-0.550202\pi\)
0.933808 0.357775i \(-0.116464\pi\)
\(110\) 0 0
\(111\) −2.16894 6.31992i −0.205867 0.599860i
\(112\) 0 0
\(113\) 1.61499 + 2.79725i 0.151926 + 0.263143i 0.931935 0.362625i \(-0.118119\pi\)
−0.780010 + 0.625767i \(0.784786\pi\)
\(114\) 0 0
\(115\) 10.3352 + 17.9010i 0.963759 + 1.66928i
\(116\) 0 0
\(117\) −0.555539 4.01203i −0.0513596 0.370912i
\(118\) 0 0
\(119\) −11.5712 + 1.84089i −1.06073 + 0.168754i
\(120\) 0 0
\(121\) 2.89445 5.01333i 0.263131 0.455757i
\(122\) 0 0
\(123\) 5.67997 + 16.5505i 0.512146 + 1.49231i
\(124\) 0 0
\(125\) 0.664575 0.0594414
\(126\) 0 0
\(127\) −12.6429 −1.12187 −0.560936 0.827859i \(-0.689559\pi\)
−0.560936 + 0.827859i \(0.689559\pi\)
\(128\) 0 0
\(129\) −9.66326 + 11.0935i −0.850803 + 0.976730i
\(130\) 0 0
\(131\) −9.53430 + 16.5139i −0.833015 + 1.44282i 0.0626210 + 0.998037i \(0.480054\pi\)
−0.895636 + 0.444787i \(0.853279\pi\)
\(132\) 0 0
\(133\) −6.98881 + 18.2442i −0.606007 + 1.58197i
\(134\) 0 0
\(135\) 14.8151 7.49187i 1.27508 0.644797i
\(136\) 0 0
\(137\) −3.38236 5.85842i −0.288975 0.500519i 0.684591 0.728928i \(-0.259981\pi\)
−0.973565 + 0.228409i \(0.926648\pi\)
\(138\) 0 0
\(139\) −6.57218 11.3834i −0.557445 0.965524i −0.997709 0.0676550i \(-0.978448\pi\)
0.440263 0.897869i \(-0.354885\pi\)
\(140\) 0 0
\(141\) −11.1032 2.16996i −0.935061 0.182744i
\(142\) 0 0
\(143\) 1.54100 2.66908i 0.128865 0.223200i
\(144\) 0 0
\(145\) −3.39204 5.87518i −0.281693 0.487907i
\(146\) 0 0
\(147\) 4.73328 11.1623i 0.390394 0.920648i
\(148\) 0 0
\(149\) −0.140257 + 0.242932i −0.0114903 + 0.0199018i −0.871713 0.490016i \(-0.836991\pi\)
0.860223 + 0.509918i \(0.170324\pi\)
\(150\) 0 0
\(151\) −4.42899 7.67123i −0.360426 0.624276i 0.627605 0.778532i \(-0.284035\pi\)
−0.988031 + 0.154256i \(0.950702\pi\)
\(152\) 0 0
\(153\) 10.4857 8.15806i 0.847719 0.659540i
\(154\) 0 0
\(155\) 1.01011 1.74956i 0.0811341 0.140528i
\(156\) 0 0
\(157\) −1.92894 −0.153946 −0.0769731 0.997033i \(-0.524526\pi\)
−0.0769731 + 0.997033i \(0.524526\pi\)
\(158\) 0 0
\(159\) −5.45962 + 6.26769i −0.432976 + 0.497060i
\(160\) 0 0
\(161\) −16.9043 + 2.68936i −1.33225 + 0.211952i
\(162\) 0 0
\(163\) −12.1983 21.1281i −0.955446 1.65488i −0.733345 0.679856i \(-0.762042\pi\)
−0.222100 0.975024i \(-0.571291\pi\)
\(164\) 0 0
\(165\) 12.3981 + 2.42304i 0.965194 + 0.188633i
\(166\) 0 0
\(167\) 2.75658 + 4.77453i 0.213310 + 0.369464i 0.952749 0.303760i \(-0.0982421\pi\)
−0.739438 + 0.673224i \(0.764909\pi\)
\(168\) 0 0
\(169\) 5.58861 9.67976i 0.429893 0.744597i
\(170\) 0 0
\(171\) −3.03848 21.9435i −0.232358 1.67806i
\(172\) 0 0
\(173\) 12.6052 0.958355 0.479178 0.877718i \(-0.340935\pi\)
0.479178 + 0.877718i \(0.340935\pi\)
\(174\) 0 0
\(175\) −4.92909 + 12.8673i −0.372604 + 0.972676i
\(176\) 0 0
\(177\) −10.5458 2.06103i −0.792674 0.154916i
\(178\) 0 0
\(179\) 5.10472 8.84164i 0.381545 0.660855i −0.609738 0.792603i \(-0.708725\pi\)
0.991283 + 0.131747i \(0.0420588\pi\)
\(180\) 0 0
\(181\) −16.2398 −1.20710 −0.603548 0.797327i \(-0.706247\pi\)
−0.603548 + 0.797327i \(0.706247\pi\)
\(182\) 0 0
\(183\) 15.1476 + 2.96038i 1.11974 + 0.218837i
\(184\) 0 0
\(185\) −12.3254 −0.906179
\(186\) 0 0
\(187\) 10.1093 0.739265
\(188\) 0 0
\(189\) 1.40479 + 13.6758i 0.102183 + 0.994766i
\(190\) 0 0
\(191\) −3.94120 −0.285175 −0.142587 0.989782i \(-0.545542\pi\)
−0.142587 + 0.989782i \(0.545542\pi\)
\(192\) 0 0
\(193\) −5.74112 −0.413255 −0.206627 0.978420i \(-0.566249\pi\)
−0.206627 + 0.978420i \(0.566249\pi\)
\(194\) 0 0
\(195\) −7.33260 1.43305i −0.525098 0.102623i
\(196\) 0 0
\(197\) −7.67480 −0.546807 −0.273403 0.961899i \(-0.588149\pi\)
−0.273403 + 0.961899i \(0.588149\pi\)
\(198\) 0 0
\(199\) −2.26928 + 3.93050i −0.160865 + 0.278626i −0.935179 0.354175i \(-0.884762\pi\)
0.774314 + 0.632801i \(0.218095\pi\)
\(200\) 0 0
\(201\) 5.12636 + 1.00187i 0.361586 + 0.0706666i
\(202\) 0 0
\(203\) 5.54807 0.882659i 0.389398 0.0619505i
\(204\) 0 0
\(205\) 32.2774 2.25435
\(206\) 0 0
\(207\) 15.3186 11.9181i 1.06471 0.828366i
\(208\) 0 0
\(209\) 8.42836 14.5983i 0.583002 1.00979i
\(210\) 0 0
\(211\) 9.84097 + 17.0451i 0.677480 + 1.17343i 0.975737 + 0.218944i \(0.0702613\pi\)
−0.298257 + 0.954486i \(0.596405\pi\)
\(212\) 0 0
\(213\) 26.1427 + 5.10922i 1.79127 + 0.350078i
\(214\) 0 0
\(215\) 13.5692 + 23.5025i 0.925410 + 1.60286i
\(216\) 0 0
\(217\) 1.05371 + 1.29938i 0.0715304 + 0.0882079i
\(218\) 0 0
\(219\) −9.93348 + 11.4037i −0.671242 + 0.770592i
\(220\) 0 0
\(221\) −5.97891 −0.402185
\(222\) 0 0
\(223\) 6.63518 11.4925i 0.444324 0.769592i −0.553681 0.832729i \(-0.686777\pi\)
0.998005 + 0.0631368i \(0.0201105\pi\)
\(224\) 0 0
\(225\) −2.14299 15.4764i −0.142866 1.03176i
\(226\) 0 0
\(227\) −11.0305 19.1053i −0.732118 1.26807i −0.955976 0.293445i \(-0.905198\pi\)
0.223858 0.974622i \(-0.428135\pi\)
\(228\) 0 0
\(229\) 8.92359 15.4561i 0.589688 1.02137i −0.404585 0.914500i \(-0.632584\pi\)
0.994273 0.106869i \(-0.0340825\pi\)
\(230\) 0 0
\(231\) −5.54639 + 8.86966i −0.364926 + 0.583581i
\(232\) 0 0
\(233\) −7.84409 13.5864i −0.513883 0.890072i −0.999870 0.0161061i \(-0.994873\pi\)
0.485987 0.873966i \(-0.338460\pi\)
\(234\) 0 0
\(235\) −10.4344 + 18.0730i −0.680667 + 1.17895i
\(236\) 0 0
\(237\) 3.18917 + 0.623276i 0.207159 + 0.0404861i
\(238\) 0 0
\(239\) −0.0639656 0.110792i −0.00413759 0.00716652i 0.863949 0.503579i \(-0.167984\pi\)
−0.868087 + 0.496412i \(0.834650\pi\)
\(240\) 0 0
\(241\) −7.54343 13.0656i −0.485915 0.841630i 0.513954 0.857818i \(-0.328180\pi\)
−0.999869 + 0.0161883i \(0.994847\pi\)
\(242\) 0 0
\(243\) −8.87616 12.8146i −0.569406 0.822056i
\(244\) 0 0
\(245\) −16.6411 14.9421i −1.06316 0.954616i
\(246\) 0 0
\(247\) −4.98476 + 8.63386i −0.317173 + 0.549359i
\(248\) 0 0
\(249\) 6.82911 7.83989i 0.432777 0.496833i
\(250\) 0 0
\(251\) 12.3738 0.781030 0.390515 0.920596i \(-0.372297\pi\)
0.390515 + 0.920596i \(0.372297\pi\)
\(252\) 0 0
\(253\) 14.7687 0.928499
\(254\) 0 0
\(255\) −7.95508 23.1797i −0.498167 1.45157i
\(256\) 0 0
\(257\) −11.0433 + 19.1276i −0.688865 + 1.19315i 0.283340 + 0.959019i \(0.408557\pi\)
−0.972205 + 0.234130i \(0.924776\pi\)
\(258\) 0 0
\(259\) 3.65111 9.53115i 0.226869 0.592237i
\(260\) 0 0
\(261\) −5.02762 + 3.91157i −0.311202 + 0.242120i
\(262\) 0 0
\(263\) 3.89678 + 6.74943i 0.240286 + 0.416187i 0.960796 0.277257i \(-0.0894255\pi\)
−0.720510 + 0.693445i \(0.756092\pi\)
\(264\) 0 0
\(265\) 7.66641 + 13.2786i 0.470944 + 0.815698i
\(266\) 0 0
\(267\) −2.98423 8.69554i −0.182632 0.532158i
\(268\) 0 0
\(269\) −3.85738 + 6.68119i −0.235189 + 0.407359i −0.959328 0.282295i \(-0.908904\pi\)
0.724139 + 0.689654i \(0.242238\pi\)
\(270\) 0 0
\(271\) 12.5744 + 21.7795i 0.763839 + 1.32301i 0.940858 + 0.338801i \(0.110021\pi\)
−0.177019 + 0.984207i \(0.556645\pi\)
\(272\) 0 0
\(273\) 3.28029 5.24576i 0.198532 0.317488i
\(274\) 0 0
\(275\) 5.94438 10.2960i 0.358460 0.620870i
\(276\) 0 0
\(277\) 3.98137 + 6.89593i 0.239217 + 0.414336i 0.960490 0.278315i \(-0.0897759\pi\)
−0.721273 + 0.692651i \(0.756443\pi\)
\(278\) 0 0
\(279\) −1.75735 0.714175i −0.105210 0.0427565i
\(280\) 0 0
\(281\) 13.3385 23.1030i 0.795710 1.37821i −0.126678 0.991944i \(-0.540431\pi\)
0.922388 0.386266i \(-0.126235\pi\)
\(282\) 0 0
\(283\) 14.4399 0.858364 0.429182 0.903218i \(-0.358802\pi\)
0.429182 + 0.903218i \(0.358802\pi\)
\(284\) 0 0
\(285\) −40.1051 7.83795i −2.37562 0.464280i
\(286\) 0 0
\(287\) −9.56144 + 24.9600i −0.564394 + 1.47334i
\(288\) 0 0
\(289\) −1.30577 2.26166i −0.0768099 0.133039i
\(290\) 0 0
\(291\) −16.9406 + 19.4479i −0.993074 + 1.14006i
\(292\) 0 0
\(293\) −8.27703 14.3362i −0.483549 0.837532i 0.516272 0.856424i \(-0.327319\pi\)
−0.999822 + 0.0188927i \(0.993986\pi\)
\(294\) 0 0
\(295\) −9.91061 + 17.1657i −0.577018 + 0.999424i
\(296\) 0 0
\(297\) 0.656910 11.8435i 0.0381178 0.687229i
\(298\) 0 0
\(299\) −8.73460 −0.505135
\(300\) 0 0
\(301\) −22.1939 + 3.53090i −1.27924 + 0.203518i
\(302\) 0 0
\(303\) −7.87467 22.9454i −0.452388 1.31818i
\(304\) 0 0
\(305\) 14.2352 24.6561i 0.815105 1.41180i
\(306\) 0 0
\(307\) 10.9233 0.623425 0.311713 0.950176i \(-0.399097\pi\)
0.311713 + 0.950176i \(0.399097\pi\)
\(308\) 0 0
\(309\) 18.2720 20.9764i 1.03946 1.19331i
\(310\) 0 0
\(311\) −5.25360 −0.297904 −0.148952 0.988844i \(-0.547590\pi\)
−0.148952 + 0.988844i \(0.547590\pi\)
\(312\) 0 0
\(313\) 21.5184 1.21629 0.608145 0.793826i \(-0.291914\pi\)
0.608145 + 0.793826i \(0.291914\pi\)
\(314\) 0 0
\(315\) 24.7019 + 5.73779i 1.39179 + 0.323288i
\(316\) 0 0
\(317\) −17.5323 −0.984710 −0.492355 0.870394i \(-0.663864\pi\)
−0.492355 + 0.870394i \(0.663864\pi\)
\(318\) 0 0
\(319\) −4.84714 −0.271388
\(320\) 0 0
\(321\) −1.42605 4.15527i −0.0795945 0.231925i
\(322\) 0 0
\(323\) −32.7012 −1.81954
\(324\) 0 0
\(325\) −3.51567 + 6.08932i −0.195014 + 0.337774i
\(326\) 0 0
\(327\) −18.4516 + 21.1826i −1.02037 + 1.17140i
\(328\) 0 0
\(329\) −10.8848 13.4226i −0.600097 0.740012i
\(330\) 0 0
\(331\) 6.27589 0.344954 0.172477 0.985014i \(-0.444823\pi\)
0.172477 + 0.985014i \(0.444823\pi\)
\(332\) 0 0
\(333\) 1.58737 + 11.4637i 0.0869872 + 0.628209i
\(334\) 0 0
\(335\) 4.81757 8.34428i 0.263212 0.455897i
\(336\) 0 0
\(337\) 13.5924 + 23.5427i 0.740426 + 1.28246i 0.952302 + 0.305159i \(0.0987095\pi\)
−0.211876 + 0.977297i \(0.567957\pi\)
\(338\) 0 0
\(339\) −1.81601 5.29155i −0.0986322 0.287397i
\(340\) 0 0
\(341\) −0.721712 1.25004i −0.0390829 0.0676936i
\(342\) 0 0
\(343\) 16.4842 8.44222i 0.890063 0.455837i
\(344\) 0 0
\(345\) −11.6216 33.8633i −0.625685 1.82314i
\(346\) 0 0
\(347\) −19.1808 −1.02968 −0.514840 0.857286i \(-0.672149\pi\)
−0.514840 + 0.857286i \(0.672149\pi\)
\(348\) 0 0
\(349\) 10.1028 17.4985i 0.540789 0.936675i −0.458069 0.888916i \(-0.651459\pi\)
0.998859 0.0477584i \(-0.0152078\pi\)
\(350\) 0 0
\(351\) −0.388515 + 7.00457i −0.0207374 + 0.373876i
\(352\) 0 0
\(353\) 14.2499 + 24.6816i 0.758448 + 1.31367i 0.943642 + 0.330969i \(0.107376\pi\)
−0.185193 + 0.982702i \(0.559291\pi\)
\(354\) 0 0
\(355\) 24.5680 42.5531i 1.30394 2.25848i
\(356\) 0 0
\(357\) 20.2813 + 0.714841i 1.07340 + 0.0378334i
\(358\) 0 0
\(359\) 15.4572 + 26.7727i 0.815802 + 1.41301i 0.908751 + 0.417339i \(0.137037\pi\)
−0.0929489 + 0.995671i \(0.529629\pi\)
\(360\) 0 0
\(361\) −17.7638 + 30.7677i −0.934934 + 1.61935i
\(362\) 0 0
\(363\) −6.58576 + 7.56052i −0.345663 + 0.396824i
\(364\) 0 0
\(365\) 13.9486 + 24.1597i 0.730103 + 1.26458i
\(366\) 0 0
\(367\) 3.41547 + 5.91577i 0.178286 + 0.308801i 0.941294 0.337589i \(-0.109611\pi\)
−0.763007 + 0.646390i \(0.776278\pi\)
\(368\) 0 0
\(369\) −4.15696 30.0210i −0.216403 1.56283i
\(370\) 0 0
\(371\) −12.5393 + 1.99491i −0.651007 + 0.103571i
\(372\) 0 0
\(373\) −3.38245 + 5.85858i −0.175137 + 0.303346i −0.940209 0.340599i \(-0.889370\pi\)
0.765072 + 0.643945i \(0.222703\pi\)
\(374\) 0 0
\(375\) −1.12970 0.220784i −0.0583377 0.0114012i
\(376\) 0 0
\(377\) 2.86673 0.147644
\(378\) 0 0
\(379\) −7.62967 −0.391910 −0.195955 0.980613i \(-0.562781\pi\)
−0.195955 + 0.980613i \(0.562781\pi\)
\(380\) 0 0
\(381\) 21.4915 + 4.20019i 1.10104 + 0.215182i
\(382\) 0 0
\(383\) 3.21132 5.56217i 0.164091 0.284214i −0.772241 0.635329i \(-0.780864\pi\)
0.936332 + 0.351116i \(0.114198\pi\)
\(384\) 0 0
\(385\) 12.1542 + 14.9880i 0.619436 + 0.763860i
\(386\) 0 0
\(387\) 20.1120 15.6475i 1.02235 0.795405i
\(388\) 0 0
\(389\) 7.92675 + 13.7295i 0.401902 + 0.696115i 0.993955 0.109784i \(-0.0350159\pi\)
−0.592053 + 0.805899i \(0.701683\pi\)
\(390\) 0 0
\(391\) −14.3253 24.8121i −0.724460 1.25480i
\(392\) 0 0
\(393\) 21.6935 24.9043i 1.09429 1.25626i
\(394\) 0 0
\(395\) 2.99707 5.19107i 0.150799 0.261191i
\(396\) 0 0
\(397\) −8.56287 14.8313i −0.429758 0.744363i 0.567093 0.823654i \(-0.308068\pi\)
−0.996852 + 0.0792903i \(0.974735\pi\)
\(398\) 0 0
\(399\) 17.9413 28.6913i 0.898187 1.43636i
\(400\) 0 0
\(401\) −11.8845 + 20.5846i −0.593486 + 1.02795i 0.400273 + 0.916396i \(0.368915\pi\)
−0.993759 + 0.111552i \(0.964418\pi\)
\(402\) 0 0
\(403\) 0.426840 + 0.739309i 0.0212624 + 0.0368276i
\(404\) 0 0
\(405\) −27.6730 + 7.81350i −1.37508 + 0.388256i
\(406\) 0 0
\(407\) −4.40316 + 7.62649i −0.218256 + 0.378031i
\(408\) 0 0
\(409\) 15.1189 0.747582 0.373791 0.927513i \(-0.378058\pi\)
0.373791 + 0.927513i \(0.378058\pi\)
\(410\) 0 0
\(411\) 3.80337 + 11.0824i 0.187606 + 0.546653i
\(412\) 0 0
\(413\) −10.3383 12.7488i −0.508717 0.627326i
\(414\) 0 0
\(415\) −9.58945 16.6094i −0.470728 0.815324i
\(416\) 0 0
\(417\) 7.39023 + 21.5339i 0.361901 + 1.05452i
\(418\) 0 0
\(419\) 2.82673 + 4.89604i 0.138095 + 0.239187i 0.926775 0.375616i \(-0.122569\pi\)
−0.788681 + 0.614803i \(0.789236\pi\)
\(420\) 0 0
\(421\) −12.5088 + 21.6658i −0.609640 + 1.05593i 0.381660 + 0.924303i \(0.375353\pi\)
−0.991300 + 0.131625i \(0.957981\pi\)
\(422\) 0 0
\(423\) 18.1534 + 7.37741i 0.882648 + 0.358702i
\(424\) 0 0
\(425\) −23.0636 −1.11875
\(426\) 0 0
\(427\) 14.8496 + 18.3118i 0.718622 + 0.886171i
\(428\) 0 0
\(429\) −3.50625 + 4.02520i −0.169283 + 0.194339i
\(430\) 0 0
\(431\) 10.4514 18.1024i 0.503428 0.871962i −0.496564 0.868000i \(-0.665405\pi\)
0.999992 0.00396247i \(-0.00126130\pi\)
\(432\) 0 0
\(433\) −21.2708 −1.02221 −0.511104 0.859519i \(-0.670763\pi\)
−0.511104 + 0.859519i \(0.670763\pi\)
\(434\) 0 0
\(435\) 3.81425 + 11.1141i 0.182879 + 0.532879i
\(436\) 0 0
\(437\) −47.7732 −2.28530
\(438\) 0 0
\(439\) 17.1817 0.820040 0.410020 0.912077i \(-0.365522\pi\)
0.410020 + 0.912077i \(0.365522\pi\)
\(440\) 0 0
\(441\) −11.7544 + 17.4021i −0.559732 + 0.828674i
\(442\) 0 0
\(443\) −12.7436 −0.605467 −0.302734 0.953075i \(-0.597899\pi\)
−0.302734 + 0.953075i \(0.597899\pi\)
\(444\) 0 0
\(445\) −16.9584 −0.803905
\(446\) 0 0
\(447\) 0.319128 0.366362i 0.0150942 0.0173283i
\(448\) 0 0
\(449\) 31.5913 1.49088 0.745442 0.666570i \(-0.232238\pi\)
0.745442 + 0.666570i \(0.232238\pi\)
\(450\) 0 0
\(451\) 11.5309 19.9721i 0.542969 0.940449i
\(452\) 0 0
\(453\) 4.98027 + 14.5117i 0.233994 + 0.681817i
\(454\) 0 0
\(455\) −7.18833 8.86432i −0.336994 0.415566i
\(456\) 0 0
\(457\) −7.30486 −0.341707 −0.170853 0.985296i \(-0.554652\pi\)
−0.170853 + 0.985296i \(0.554652\pi\)
\(458\) 0 0
\(459\) −20.5348 + 10.3843i −0.958483 + 0.484696i
\(460\) 0 0
\(461\) −13.3651 + 23.1491i −0.622477 + 1.07816i 0.366546 + 0.930400i \(0.380540\pi\)
−0.989023 + 0.147761i \(0.952793\pi\)
\(462\) 0 0
\(463\) −1.75608 3.04161i −0.0816117 0.141356i 0.822331 0.569010i \(-0.192673\pi\)
−0.903942 + 0.427654i \(0.859340\pi\)
\(464\) 0 0
\(465\) −2.29832 + 2.63849i −0.106582 + 0.122357i
\(466\) 0 0
\(467\) −7.80239 13.5141i −0.361052 0.625360i 0.627083 0.778953i \(-0.284249\pi\)
−0.988134 + 0.153593i \(0.950915\pi\)
\(468\) 0 0
\(469\) 5.02550 + 6.19721i 0.232056 + 0.286161i
\(470\) 0 0
\(471\) 3.27899 + 0.640831i 0.151088 + 0.0295279i
\(472\) 0 0
\(473\) 19.3900 0.891554
\(474\) 0 0
\(475\) −19.2287 + 33.3050i −0.882272 + 1.52814i
\(476\) 0 0
\(477\) 11.3630 8.84061i 0.520276 0.404784i
\(478\) 0 0
\(479\) 8.54444 + 14.7994i 0.390405 + 0.676202i 0.992503 0.122221i \(-0.0390015\pi\)
−0.602098 + 0.798422i \(0.705668\pi\)
\(480\) 0 0
\(481\) 2.60415 4.51052i 0.118739 0.205662i
\(482\) 0 0
\(483\) 29.6290 + 1.04431i 1.34817 + 0.0475179i
\(484\) 0 0
\(485\) 23.7880 + 41.2020i 1.08016 + 1.87089i
\(486\) 0 0
\(487\) −12.9335 + 22.4014i −0.586072 + 1.01511i 0.408669 + 0.912683i \(0.365993\pi\)
−0.994741 + 0.102423i \(0.967340\pi\)
\(488\) 0 0
\(489\) 13.7167 + 39.9680i 0.620289 + 1.80741i
\(490\) 0 0
\(491\) −7.51452 13.0155i −0.339126 0.587383i 0.645143 0.764062i \(-0.276798\pi\)
−0.984269 + 0.176679i \(0.943465\pi\)
\(492\) 0 0
\(493\) 4.70160 + 8.14342i 0.211750 + 0.366761i
\(494\) 0 0
\(495\) −20.2705 8.23779i −0.911092 0.370261i
\(496\) 0 0
\(497\) 25.6284 + 31.6037i 1.14959 + 1.41762i
\(498\) 0 0
\(499\) −7.62094 + 13.1999i −0.341160 + 0.590907i −0.984648 0.174549i \(-0.944153\pi\)
0.643488 + 0.765456i \(0.277487\pi\)
\(500\) 0 0
\(501\) −3.09969 9.03197i −0.138484 0.403519i
\(502\) 0 0
\(503\) 18.6284 0.830599 0.415299 0.909685i \(-0.363677\pi\)
0.415299 + 0.909685i \(0.363677\pi\)
\(504\) 0 0
\(505\) −44.7491 −1.99131
\(506\) 0 0
\(507\) −12.7158 + 14.5979i −0.564730 + 0.648316i
\(508\) 0 0
\(509\) 3.72333 6.44899i 0.165034 0.285847i −0.771634 0.636067i \(-0.780560\pi\)
0.936667 + 0.350221i \(0.113893\pi\)
\(510\) 0 0
\(511\) −22.8145 + 3.62964i −1.00926 + 0.160566i
\(512\) 0 0
\(513\) −2.12495 + 38.3109i −0.0938188 + 1.69147i
\(514\) 0 0
\(515\) −25.6576 44.4402i −1.13061 1.95827i
\(516\) 0 0
\(517\) 7.45527 + 12.9129i 0.327882 + 0.567909i
\(518\) 0 0
\(519\) −21.4275 4.18768i −0.940561 0.183819i
\(520\) 0 0
\(521\) −11.3853 + 19.7200i −0.498800 + 0.863947i −0.999999 0.00138491i \(-0.999559\pi\)
0.501199 + 0.865332i \(0.332893\pi\)
\(522\) 0 0
\(523\) 16.5092 + 28.5949i 0.721899 + 1.25037i 0.960238 + 0.279184i \(0.0900639\pi\)
−0.238339 + 0.971182i \(0.576603\pi\)
\(524\) 0 0
\(525\) 12.6537 20.2355i 0.552252 0.883148i
\(526\) 0 0
\(527\) −1.40009 + 2.42502i −0.0609887 + 0.105636i
\(528\) 0 0
\(529\) −9.42780 16.3294i −0.409904 0.709975i
\(530\) 0 0
\(531\) 17.2421 + 7.00705i 0.748242 + 0.304080i
\(532\) 0 0
\(533\) −6.81969 + 11.8120i −0.295393 + 0.511636i
\(534\) 0 0
\(535\) −8.10378 −0.350357
\(536\) 0 0
\(537\) −11.6148 + 13.3339i −0.501217 + 0.575402i
\(538\) 0 0
\(539\) −15.1906 + 4.95894i −0.654304 + 0.213597i
\(540\) 0 0
\(541\) 8.53464 + 14.7824i 0.366933 + 0.635546i 0.989084 0.147351i \(-0.0470745\pi\)
−0.622151 + 0.782897i \(0.713741\pi\)
\(542\) 0 0
\(543\) 27.6059 + 5.39517i 1.18468 + 0.231529i
\(544\) 0 0
\(545\) 25.9097 + 44.8769i 1.10985 + 1.92232i
\(546\) 0 0
\(547\) 16.3574 28.3318i 0.699390 1.21138i −0.269288 0.963060i \(-0.586788\pi\)
0.968678 0.248319i \(-0.0798782\pi\)
\(548\) 0 0
\(549\) −24.7658 10.0646i −1.05698 0.429548i
\(550\) 0 0
\(551\) 15.6794 0.667963
\(552\) 0 0
\(553\) 3.12642 + 3.85536i 0.132949 + 0.163946i
\(554\) 0 0
\(555\) 20.9518 + 4.09472i 0.889353 + 0.173811i
\(556\) 0 0
\(557\) 17.0783 29.5806i 0.723633 1.25337i −0.235902 0.971777i \(-0.575804\pi\)
0.959534 0.281592i \(-0.0908623\pi\)
\(558\) 0 0
\(559\) −11.4678 −0.485036
\(560\) 0 0
\(561\) −17.1847 3.35850i −0.725539 0.141796i
\(562\) 0 0
\(563\) −9.67074 −0.407573 −0.203786 0.979015i \(-0.565325\pi\)
−0.203786 + 0.979015i \(0.565325\pi\)
\(564\) 0 0
\(565\) −10.3198 −0.434157
\(566\) 0 0
\(567\) 2.15536 23.7140i 0.0905168 0.995895i
\(568\) 0 0
\(569\) 11.1274 0.466484 0.233242 0.972419i \(-0.425067\pi\)
0.233242 + 0.972419i \(0.425067\pi\)
\(570\) 0 0
\(571\) 0.729305 0.0305205 0.0152602 0.999884i \(-0.495142\pi\)
0.0152602 + 0.999884i \(0.495142\pi\)
\(572\) 0 0
\(573\) 6.69960 + 1.30934i 0.279880 + 0.0546984i
\(574\) 0 0
\(575\) −33.6937 −1.40512
\(576\) 0 0
\(577\) 9.49359 16.4434i 0.395223 0.684547i −0.597906 0.801566i \(-0.704001\pi\)
0.993130 + 0.117019i \(0.0373338\pi\)
\(578\) 0 0
\(579\) 9.75928 + 1.90731i 0.405582 + 0.0792650i
\(580\) 0 0
\(581\) 15.6846 2.49532i 0.650709 0.103523i
\(582\) 0 0
\(583\) 10.9551 0.453714
\(584\) 0 0
\(585\) 11.9885 + 4.87206i 0.495665 + 0.201435i
\(586\) 0 0
\(587\) −1.30535 + 2.26093i −0.0538775 + 0.0933185i −0.891706 0.452615i \(-0.850491\pi\)
0.837829 + 0.545933i \(0.183825\pi\)
\(588\) 0 0
\(589\) 2.33457 + 4.04359i 0.0961942 + 0.166613i
\(590\) 0 0
\(591\) 13.0463 + 2.54971i 0.536654 + 0.104881i
\(592\) 0 0
\(593\) −7.92622 13.7286i −0.325491 0.563767i 0.656121 0.754656i \(-0.272196\pi\)
−0.981612 + 0.190889i \(0.938863\pi\)
\(594\) 0 0
\(595\) 13.3913 34.9576i 0.548988 1.43312i
\(596\) 0 0
\(597\) 5.16331 5.92753i 0.211320 0.242598i
\(598\) 0 0
\(599\) 15.8610 0.648063 0.324032 0.946046i \(-0.394962\pi\)
0.324032 + 0.946046i \(0.394962\pi\)
\(600\) 0 0
\(601\) 0.834141 1.44477i 0.0340253 0.0589336i −0.848511 0.529177i \(-0.822501\pi\)
0.882537 + 0.470244i \(0.155834\pi\)
\(602\) 0 0
\(603\) −8.38142 3.40615i −0.341318 0.138709i
\(604\) 0 0
\(605\) 9.24774 + 16.0176i 0.375974 + 0.651207i
\(606\) 0 0
\(607\) 18.2555 31.6194i 0.740968 1.28339i −0.211088 0.977467i \(-0.567701\pi\)
0.952055 0.305926i \(-0.0989661\pi\)
\(608\) 0 0
\(609\) −9.72435 0.342747i −0.394050 0.0138888i
\(610\) 0 0
\(611\) −4.40925 7.63705i −0.178379 0.308962i
\(612\) 0 0
\(613\) 18.2957 31.6891i 0.738958 1.27991i −0.214007 0.976832i \(-0.568652\pi\)
0.952965 0.303080i \(-0.0980150\pi\)
\(614\) 0 0
\(615\) −54.8680 10.7232i −2.21249 0.432399i
\(616\) 0 0
\(617\) −5.10936 8.84967i −0.205695 0.356274i 0.744659 0.667445i \(-0.232612\pi\)
−0.950354 + 0.311171i \(0.899279\pi\)
\(618\) 0 0
\(619\) 12.3664 + 21.4193i 0.497049 + 0.860914i 0.999994 0.00340432i \(-0.00108363\pi\)
−0.502945 + 0.864318i \(0.667750\pi\)
\(620\) 0 0
\(621\) −29.9993 + 15.1704i −1.20383 + 0.608767i
\(622\) 0 0
\(623\) 5.02353 13.1138i 0.201264 0.525395i
\(624\) 0 0
\(625\) 11.9584 20.7125i 0.478334 0.828499i
\(626\) 0 0
\(627\) −19.1771 + 22.0155i −0.765861 + 0.879216i
\(628\) 0 0
\(629\) 17.0838 0.681177
\(630\) 0 0
\(631\) 42.1420 1.67765 0.838823 0.544404i \(-0.183244\pi\)
0.838823 + 0.544404i \(0.183244\pi\)
\(632\) 0 0
\(633\) −11.0659 32.2441i −0.439829 1.28159i
\(634\) 0 0
\(635\) 20.1969 34.9821i 0.801491 1.38822i
\(636\) 0 0
\(637\) 8.98411 2.93285i 0.355964 0.116204i
\(638\) 0 0
\(639\) −42.7424 17.3702i −1.69086 0.687155i
\(640\) 0 0
\(641\) 1.16519 + 2.01817i 0.0460222 + 0.0797128i 0.888119 0.459614i \(-0.152012\pi\)
−0.842097 + 0.539327i \(0.818679\pi\)
\(642\) 0 0
\(643\) 16.5035 + 28.5850i 0.650836 + 1.12728i 0.982920 + 0.184031i \(0.0589147\pi\)
−0.332085 + 0.943250i \(0.607752\pi\)
\(644\) 0 0
\(645\) −15.2582 44.4596i −0.600789 1.75060i
\(646\) 0 0
\(647\) −10.4187 + 18.0458i −0.409603 + 0.709452i −0.994845 0.101406i \(-0.967666\pi\)
0.585243 + 0.810858i \(0.300999\pi\)
\(648\) 0 0
\(649\) 7.08101 + 12.2647i 0.277954 + 0.481430i
\(650\) 0 0
\(651\) −1.35951 2.55887i −0.0532834 0.100290i
\(652\) 0 0
\(653\) 24.4176 42.2925i 0.955534 1.65503i 0.222391 0.974958i \(-0.428614\pi\)
0.733142 0.680075i \(-0.238053\pi\)
\(654\) 0 0
\(655\) −30.4620 52.7618i −1.19025 2.06157i
\(656\) 0 0
\(657\) 20.6744 16.0850i 0.806584 0.627536i
\(658\) 0 0
\(659\) 0.272662 0.472265i 0.0106214 0.0183968i −0.860666 0.509170i \(-0.829952\pi\)
0.871287 + 0.490773i \(0.163286\pi\)
\(660\) 0 0
\(661\) −46.4250 −1.80572 −0.902861 0.429933i \(-0.858537\pi\)
−0.902861 + 0.429933i \(0.858537\pi\)
\(662\) 0 0
\(663\) 10.1635 + 1.98631i 0.394718 + 0.0771418i
\(664\) 0 0
\(665\) −39.3160 48.4827i −1.52461 1.88008i
\(666\) 0 0
\(667\) 6.86858 + 11.8967i 0.265953 + 0.460643i
\(668\) 0 0
\(669\) −15.0971 + 17.3316i −0.583687 + 0.670079i
\(670\) 0 0
\(671\) −10.1709 17.6165i −0.392642 0.680076i
\(672\) 0 0
\(673\) −16.9838 + 29.4168i −0.654677 + 1.13393i 0.327298 + 0.944921i \(0.393862\pi\)
−0.981975 + 0.189013i \(0.939471\pi\)
\(674\) 0 0
\(675\) −1.49869 + 27.0201i −0.0576847 + 1.04000i
\(676\) 0 0
\(677\) 31.2851 1.20238 0.601191 0.799105i \(-0.294693\pi\)
0.601191 + 0.799105i \(0.294693\pi\)
\(678\) 0 0
\(679\) −38.9080 + 6.18999i −1.49315 + 0.237550i
\(680\) 0 0
\(681\) 12.4035 + 36.1415i 0.475301 + 1.38495i
\(682\) 0 0
\(683\) 0.289712 0.501795i 0.0110855 0.0192007i −0.860429 0.509570i \(-0.829805\pi\)
0.871515 + 0.490369i \(0.163138\pi\)
\(684\) 0 0
\(685\) 21.6133 0.825801
\(686\) 0 0
\(687\) −20.3040 + 23.3091i −0.774644 + 0.889299i
\(688\) 0 0
\(689\) −6.47915 −0.246836
\(690\) 0 0
\(691\) 2.21565 0.0842872 0.0421436 0.999112i \(-0.486581\pi\)
0.0421436 + 0.999112i \(0.486581\pi\)
\(692\) 0 0
\(693\) 12.3749 13.2348i 0.470085 0.502750i
\(694\) 0 0
\(695\) 41.9962 1.59301
\(696\) 0 0
\(697\) −44.7387 −1.69460
\(698\) 0 0
\(699\) 8.82046 + 25.7013i 0.333620 + 0.972112i
\(700\) 0 0
\(701\) 4.74299 0.179140 0.0895702 0.995981i \(-0.471451\pi\)
0.0895702 + 0.995981i \(0.471451\pi\)
\(702\) 0 0
\(703\) 14.2432 24.6699i 0.537192 0.930444i
\(704\) 0 0
\(705\) 23.7416 27.2556i 0.894159 1.02650i
\(706\) 0 0
\(707\) 13.2559 34.6043i 0.498539 1.30143i
\(708\) 0 0
\(709\) −23.3765 −0.877923 −0.438962 0.898506i \(-0.644654\pi\)
−0.438962 + 0.898506i \(0.644654\pi\)
\(710\) 0 0
\(711\) −5.21417 2.11900i −0.195547 0.0794688i
\(712\) 0 0
\(713\) −2.04539 + 3.54272i −0.0766004 + 0.132676i
\(714\) 0 0
\(715\) 4.92348 + 8.52771i 0.184128 + 0.318918i
\(716\) 0 0
\(717\) 0.0719275 + 0.209584i 0.00268618 + 0.00782707i
\(718\) 0 0
\(719\) 13.0256 + 22.5610i 0.485772 + 0.841382i 0.999866 0.0163516i \(-0.00520511\pi\)
−0.514094 + 0.857734i \(0.671872\pi\)
\(720\) 0 0
\(721\) 41.9659 6.67649i 1.56289 0.248645i
\(722\) 0 0
\(723\) 8.48237 + 24.7162i 0.315463 + 0.919205i
\(724\) 0 0
\(725\) 11.0584 0.410698
\(726\) 0 0
\(727\) 5.79712 10.0409i 0.215003 0.372396i −0.738270 0.674505i \(-0.764357\pi\)
0.953274 + 0.302108i \(0.0976905\pi\)
\(728\) 0 0
\(729\) 10.8313 + 24.7322i 0.401158 + 0.916009i
\(730\) 0 0
\(731\) −18.8078 32.5761i −0.695633 1.20487i
\(732\) 0 0
\(733\) 17.6743 30.6128i 0.652816 1.13071i −0.329620 0.944114i \(-0.606921\pi\)
0.982436 0.186597i \(-0.0597459\pi\)
\(734\) 0 0
\(735\) 23.3240 + 30.9284i 0.860319 + 1.14081i
\(736\) 0 0
\(737\) −3.44210 5.96189i −0.126791 0.219609i
\(738\) 0 0
\(739\) 4.66968 8.08812i 0.171777 0.297526i −0.767264 0.641331i \(-0.778383\pi\)
0.939041 + 0.343805i \(0.111716\pi\)
\(740\) 0 0
\(741\) 11.3419 13.0206i 0.416654 0.478323i
\(742\) 0 0
\(743\) −14.6308 25.3412i −0.536750 0.929679i −0.999076 0.0429687i \(-0.986318\pi\)
0.462326 0.886710i \(-0.347015\pi\)
\(744\) 0 0
\(745\) −0.448120 0.776167i −0.0164179 0.0284366i
\(746\) 0 0
\(747\) −14.2133 + 11.0582i −0.520038 + 0.404598i
\(748\) 0 0
\(749\) 2.40056 6.26662i 0.0877146 0.228977i
\(750\) 0 0
\(751\) −13.3106 + 23.0547i −0.485712 + 0.841278i −0.999865 0.0164202i \(-0.994773\pi\)
0.514153 + 0.857699i \(0.328106\pi\)
\(752\) 0 0
\(753\) −21.0342 4.11083i −0.766529 0.149807i
\(754\) 0 0
\(755\) 28.3012 1.02999
\(756\) 0 0
\(757\) −35.3183 −1.28367 −0.641833 0.766845i \(-0.721826\pi\)
−0.641833 + 0.766845i \(0.721826\pi\)
\(758\) 0 0
\(759\) −25.1052 4.90644i −0.911260 0.178092i
\(760\) 0 0
\(761\) −15.7824 + 27.3359i −0.572112 + 0.990927i 0.424237 + 0.905551i \(0.360542\pi\)
−0.996349 + 0.0853760i \(0.972791\pi\)
\(762\) 0 0
\(763\) −42.3783 + 6.74210i −1.53420 + 0.244080i
\(764\) 0 0
\(765\) 5.82203 + 42.0459i 0.210496 + 1.52017i
\(766\) 0 0
\(767\) −4.18790 7.25366i −0.151216 0.261914i
\(768\) 0 0
\(769\) −23.8477 41.3055i −0.859972 1.48951i −0.871955 0.489587i \(-0.837148\pi\)
0.0119829 0.999928i \(-0.496186\pi\)
\(770\) 0 0
\(771\) 25.1270 28.8461i 0.904928 1.03887i
\(772\) 0 0
\(773\) 20.7219 35.8914i 0.745314 1.29092i −0.204733 0.978818i \(-0.565633\pi\)
0.950048 0.312105i \(-0.101034\pi\)
\(774\) 0 0
\(775\) 1.64653 + 2.85188i 0.0591452 + 0.102442i
\(776\) 0 0
\(777\) −9.37291 + 14.9889i −0.336251 + 0.537725i
\(778\) 0 0
\(779\) −37.2997 + 64.6050i −1.33640 + 2.31472i
\(780\) 0 0
\(781\) −17.5536 30.4036i −0.628116 1.08793i
\(782\) 0 0
\(783\) 9.84590 4.97898i 0.351864 0.177934i
\(784\) 0 0
\(785\) 3.08148 5.33728i 0.109983 0.190496i
\(786\) 0 0
\(787\) −26.3177 −0.938125 −0.469063 0.883165i \(-0.655408\pi\)
−0.469063 + 0.883165i \(0.655408\pi\)
\(788\) 0 0
\(789\) −4.38182 12.7679i −0.155997 0.454548i
\(790\) 0 0
\(791\) 3.05700 7.98024i 0.108694 0.283745i
\(792\) 0 0
\(793\) 6.01533 + 10.4189i 0.213611 + 0.369984i
\(794\) 0 0
\(795\) −8.62065 25.1191i −0.305743 0.890883i
\(796\) 0 0
\(797\) 8.42109 + 14.5858i 0.298290 + 0.516654i 0.975745 0.218911i \(-0.0702503\pi\)
−0.677455 + 0.735565i \(0.736917\pi\)