Properties

Label 324.3.o.a.5.8
Level $324$
Weight $3$
Character 324.5
Analytic conductor $8.828$
Analytic rank $0$
Dimension $324$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.o (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(324\)
Relative dimension: \(18\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 5.8
Character \(\chi\) \(=\) 324.5
Dual form 324.3.o.a.65.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.763445 + 2.90123i) q^{3} +(3.55757 - 2.64851i) q^{5} +(5.32637 - 3.50321i) q^{7} +(-7.83430 - 4.42986i) q^{9} +O(q^{10})\) \(q+(-0.763445 + 2.90123i) q^{3} +(3.55757 - 2.64851i) q^{5} +(5.32637 - 3.50321i) q^{7} +(-7.83430 - 4.42986i) q^{9} +(1.41760 - 12.1283i) q^{11} +(-6.32933 - 21.1414i) q^{13} +(4.96794 + 12.3433i) q^{15} +(2.26759 + 0.399837i) q^{17} +(3.02250 + 17.1415i) q^{19} +(6.09723 + 18.1276i) q^{21} +(11.2770 - 17.1459i) q^{23} +(-1.52839 + 5.10518i) q^{25} +(18.8331 - 19.3472i) q^{27} +(2.31814 - 2.18705i) q^{29} +(1.37307 - 23.5747i) q^{31} +(34.1048 + 13.3721i) q^{33} +(9.67065 - 26.5699i) q^{35} +(8.10013 - 2.94820i) q^{37} +(66.1683 - 2.22253i) q^{39} +(-4.01514 + 16.9412i) q^{41} +(12.5349 + 29.0591i) q^{43} +(-39.6036 + 4.98970i) q^{45} +(85.4564 - 4.97727i) q^{47} +(-3.31015 + 7.67379i) q^{49} +(-2.89120 + 6.27355i) q^{51} +(27.5474 + 15.9045i) q^{53} +(-27.0788 - 46.9018i) q^{55} +(-52.0389 - 4.31759i) q^{57} +(5.47823 + 46.8693i) q^{59} +(-65.8002 - 33.0461i) q^{61} +(-57.2472 + 3.85010i) q^{63} +(-78.5105 - 58.4489i) q^{65} +(21.2962 - 22.5727i) q^{67} +(41.1348 + 45.8072i) q^{69} +(59.2886 - 70.6574i) q^{71} +(-89.1818 + 74.8324i) q^{73} +(-13.6445 - 8.33175i) q^{75} +(-34.9374 - 69.5660i) q^{77} +(-136.788 + 32.4195i) q^{79} +(41.7526 + 69.4098i) q^{81} +(-7.83827 - 33.0723i) q^{83} +(9.12609 - 4.58329i) q^{85} +(4.57537 + 8.39515i) q^{87} +(33.4672 + 39.8846i) q^{89} +(-107.775 - 90.4342i) q^{91} +(67.3475 + 21.9816i) q^{93} +(56.1522 + 52.9769i) q^{95} +(-57.7011 + 77.5061i) q^{97} +(-64.8326 + 88.7370i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q + O(q^{10}) \) \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{54}\right)\)

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
\(3\) −0.763445 + 2.90123i −0.254482 + 0.967078i
\(4\) 0 0
\(5\) 3.55757 2.64851i 0.711514 0.529703i −0.179455 0.983766i \(-0.557433\pi\)
0.890969 + 0.454063i \(0.150026\pi\)
\(6\) 0 0
\(7\) 5.32637 3.50321i 0.760910 0.500459i −0.108774 0.994066i \(-0.534693\pi\)
0.869685 + 0.493608i \(0.164322\pi\)
\(8\) 0 0
\(9\) −7.83430 4.42986i −0.870478 0.492207i
\(10\) 0 0
\(11\) 1.41760 12.1283i 0.128872 1.10257i −0.761763 0.647855i \(-0.775666\pi\)
0.890636 0.454718i \(-0.150260\pi\)
\(12\) 0 0
\(13\) −6.32933 21.1414i −0.486872 1.62626i −0.749953 0.661491i \(-0.769924\pi\)
0.263081 0.964774i \(-0.415261\pi\)
\(14\) 0 0
\(15\) 4.96794 + 12.3433i 0.331196 + 0.822889i
\(16\) 0 0
\(17\) 2.26759 + 0.399837i 0.133388 + 0.0235198i 0.239943 0.970787i \(-0.422871\pi\)
−0.106556 + 0.994307i \(0.533982\pi\)
\(18\) 0 0
\(19\) 3.02250 + 17.1415i 0.159079 + 0.902183i 0.954961 + 0.296731i \(0.0958964\pi\)
−0.795882 + 0.605452i \(0.792992\pi\)
\(20\) 0 0
\(21\) 6.09723 + 18.1276i 0.290344 + 0.863217i
\(22\) 0 0
\(23\) 11.2770 17.1459i 0.490306 0.745473i −0.502582 0.864530i \(-0.667616\pi\)
0.992888 + 0.119056i \(0.0379869\pi\)
\(24\) 0 0
\(25\) −1.52839 + 5.10518i −0.0611357 + 0.204207i
\(26\) 0 0
\(27\) 18.8331 19.3472i 0.697523 0.716562i
\(28\) 0 0
\(29\) 2.31814 2.18705i 0.0799358 0.0754155i −0.645237 0.763982i \(-0.723241\pi\)
0.725173 + 0.688567i \(0.241760\pi\)
\(30\) 0 0
\(31\) 1.37307 23.5747i 0.0442927 0.760476i −0.900913 0.434000i \(-0.857102\pi\)
0.945206 0.326476i \(-0.105861\pi\)
\(32\) 0 0
\(33\) 34.1048 + 13.3721i 1.03348 + 0.405214i
\(34\) 0 0
\(35\) 9.67065 26.5699i 0.276304 0.759140i
\(36\) 0 0
\(37\) 8.10013 2.94820i 0.218922 0.0796812i −0.230231 0.973136i \(-0.573948\pi\)
0.449153 + 0.893455i \(0.351726\pi\)
\(38\) 0 0
\(39\) 66.1683 2.22253i 1.69662 0.0569880i
\(40\) 0 0
\(41\) −4.01514 + 16.9412i −0.0979303 + 0.413200i −0.999824 0.0187575i \(-0.994029\pi\)
0.901894 + 0.431958i \(0.142177\pi\)
\(42\) 0 0
\(43\) 12.5349 + 29.0591i 0.291509 + 0.675794i 0.999538 0.0303894i \(-0.00967472\pi\)
−0.708029 + 0.706183i \(0.750415\pi\)
\(44\) 0 0
\(45\) −39.6036 + 4.98970i −0.880081 + 0.110882i
\(46\) 0 0
\(47\) 85.4564 4.97727i 1.81822 0.105899i 0.885086 0.465427i \(-0.154099\pi\)
0.933134 + 0.359528i \(0.117062\pi\)
\(48\) 0 0
\(49\) −3.31015 + 7.67379i −0.0675541 + 0.156608i
\(50\) 0 0
\(51\) −2.89120 + 6.27355i −0.0566902 + 0.123011i
\(52\) 0 0
\(53\) 27.5474 + 15.9045i 0.519763 + 0.300085i 0.736838 0.676070i \(-0.236318\pi\)
−0.217075 + 0.976155i \(0.569651\pi\)
\(54\) 0 0
\(55\) −27.0788 46.9018i −0.492341 0.852760i
\(56\) 0 0
\(57\) −52.0389 4.31759i −0.912963 0.0757472i
\(58\) 0 0
\(59\) 5.47823 + 46.8693i 0.0928514 + 0.794394i 0.956787 + 0.290791i \(0.0939185\pi\)
−0.863935 + 0.503603i \(0.832007\pi\)
\(60\) 0 0
\(61\) −65.8002 33.0461i −1.07869 0.541740i −0.181505 0.983390i \(-0.558097\pi\)
−0.897187 + 0.441650i \(0.854393\pi\)
\(62\) 0 0
\(63\) −57.2472 + 3.85010i −0.908685 + 0.0611127i
\(64\) 0 0
\(65\) −78.5105 58.4489i −1.20785 0.899213i
\(66\) 0 0
\(67\) 21.2962 22.5727i 0.317854 0.336906i −0.548672 0.836038i \(-0.684866\pi\)
0.866526 + 0.499132i \(0.166348\pi\)
\(68\) 0 0
\(69\) 41.1348 + 45.8072i 0.596157 + 0.663873i
\(70\) 0 0
\(71\) 59.2886 70.6574i 0.835051 0.995175i −0.164910 0.986309i \(-0.552733\pi\)
0.999961 0.00886648i \(-0.00282233\pi\)
\(72\) 0 0
\(73\) −89.1818 + 74.8324i −1.22167 + 1.02510i −0.222932 + 0.974834i \(0.571563\pi\)
−0.998736 + 0.0502673i \(0.983993\pi\)
\(74\) 0 0
\(75\) −13.6445 8.33175i −0.181926 0.111090i
\(76\) 0 0
\(77\) −34.9374 69.5660i −0.453732 0.903454i
\(78\) 0 0
\(79\) −136.788 + 32.4195i −1.73150 + 0.410373i −0.971022 0.238991i \(-0.923183\pi\)
−0.760478 + 0.649364i \(0.775035\pi\)
\(80\) 0 0
\(81\) 41.7526 + 69.4098i 0.515464 + 0.856911i
\(82\) 0 0
\(83\) −7.83827 33.0723i −0.0944370 0.398461i 0.905212 0.424961i \(-0.139712\pi\)
−0.999649 + 0.0264997i \(0.991564\pi\)
\(84\) 0 0
\(85\) 9.12609 4.58329i 0.107366 0.0539211i
\(86\) 0 0
\(87\) 4.57537 + 8.39515i 0.0525905 + 0.0964960i
\(88\) 0 0
\(89\) 33.4672 + 39.8846i 0.376036 + 0.448142i 0.920559 0.390604i \(-0.127734\pi\)
−0.544523 + 0.838746i \(0.683289\pi\)
\(90\) 0 0
\(91\) −107.775 90.4342i −1.18434 0.993783i
\(92\) 0 0
\(93\) 67.3475 + 21.9816i 0.724167 + 0.236362i
\(94\) 0 0
\(95\) 56.1522 + 52.9769i 0.591076 + 0.557651i
\(96\) 0 0
\(97\) −57.7011 + 77.5061i −0.594857 + 0.799031i −0.992978 0.118302i \(-0.962255\pi\)
0.398121 + 0.917333i \(0.369662\pi\)
\(98\) 0 0
\(99\) −64.8326 + 88.7370i −0.654875 + 0.896334i
\(100\) 0 0
\(101\) 52.0604 103.661i 0.515449 1.02634i −0.473872 0.880594i \(-0.657144\pi\)
0.989321 0.145750i \(-0.0465597\pi\)
\(102\) 0 0
\(103\) −19.1924 + 2.24327i −0.186334 + 0.0217793i −0.208748 0.977969i \(-0.566939\pi\)
0.0224140 + 0.999749i \(0.492865\pi\)
\(104\) 0 0
\(105\) 69.7024 + 48.3415i 0.663833 + 0.460395i
\(106\) 0 0
\(107\) −92.4687 + 53.3868i −0.864194 + 0.498942i −0.865414 0.501057i \(-0.832945\pi\)
0.00122076 + 0.999999i \(0.499611\pi\)
\(108\) 0 0
\(109\) 11.0928 19.2133i 0.101769 0.176269i −0.810645 0.585538i \(-0.800883\pi\)
0.912414 + 0.409270i \(0.134216\pi\)
\(110\) 0 0
\(111\) 2.36943 + 25.7511i 0.0213462 + 0.231992i
\(112\) 0 0
\(113\) −33.9560 14.6472i −0.300496 0.129621i 0.240493 0.970651i \(-0.422691\pi\)
−0.540989 + 0.841030i \(0.681950\pi\)
\(114\) 0 0
\(115\) −5.29229 90.8651i −0.0460199 0.790131i
\(116\) 0 0
\(117\) −44.0678 + 193.667i −0.376648 + 1.65527i
\(118\) 0 0
\(119\) 13.4787 5.81416i 0.113267 0.0488585i
\(120\) 0 0
\(121\) −27.3477 6.48153i −0.226014 0.0535663i
\(122\) 0 0
\(123\) −46.0851 24.5826i −0.374675 0.199858i
\(124\) 0 0
\(125\) 46.0069 + 126.403i 0.368055 + 1.01122i
\(126\) 0 0
\(127\) −106.400 38.7263i −0.837791 0.304931i −0.112739 0.993625i \(-0.535962\pi\)
−0.725053 + 0.688694i \(0.758185\pi\)
\(128\) 0 0
\(129\) −93.8770 + 14.1816i −0.727729 + 0.109935i
\(130\) 0 0
\(131\) 234.207 + 13.6410i 1.78784 + 0.104130i 0.919807 0.392371i \(-0.128345\pi\)
0.868036 + 0.496501i \(0.165382\pi\)
\(132\) 0 0
\(133\) 76.1491 + 80.7134i 0.572550 + 0.606868i
\(134\) 0 0
\(135\) 15.7589 118.709i 0.116733 0.879324i
\(136\) 0 0
\(137\) −155.174 46.4562i −1.13266 0.339096i −0.335009 0.942215i \(-0.608739\pi\)
−0.797651 + 0.603119i \(0.793924\pi\)
\(138\) 0 0
\(139\) 133.604 + 87.8725i 0.961177 + 0.632176i 0.930087 0.367340i \(-0.119732\pi\)
0.0310906 + 0.999517i \(0.490102\pi\)
\(140\) 0 0
\(141\) −50.8010 + 251.729i −0.360291 + 1.78531i
\(142\) 0 0
\(143\) −265.382 + 46.7941i −1.85582 + 0.327231i
\(144\) 0 0
\(145\) 2.45451 13.9202i 0.0169276 0.0960014i
\(146\) 0 0
\(147\) −19.7363 15.4620i −0.134261 0.105184i
\(148\) 0 0
\(149\) 246.068 73.6680i 1.65147 0.494416i 0.680322 0.732913i \(-0.261840\pi\)
0.971143 + 0.238497i \(0.0766546\pi\)
\(150\) 0 0
\(151\) 256.212 + 29.9468i 1.69677 + 0.198323i 0.908753 0.417335i \(-0.137036\pi\)
0.788013 + 0.615659i \(0.211110\pi\)
\(152\) 0 0
\(153\) −15.9938 13.1776i −0.104534 0.0861279i
\(154\) 0 0
\(155\) −57.5532 87.5054i −0.371311 0.564551i
\(156\) 0 0
\(157\) −68.5027 92.0151i −0.436323 0.586083i 0.528517 0.848923i \(-0.322748\pi\)
−0.964840 + 0.262840i \(0.915341\pi\)
\(158\) 0 0
\(159\) −67.1737 + 67.7793i −0.422476 + 0.426285i
\(160\) 0 0
\(161\) 130.831i 0.812616i
\(162\) 0 0
\(163\) 182.315 1.11849 0.559247 0.829001i \(-0.311090\pi\)
0.559247 + 0.829001i \(0.311090\pi\)
\(164\) 0 0
\(165\) 156.746 42.7549i 0.949977 0.259120i
\(166\) 0 0
\(167\) 51.3118 38.2002i 0.307256 0.228744i −0.432475 0.901646i \(-0.642360\pi\)
0.739732 + 0.672902i \(0.234952\pi\)
\(168\) 0 0
\(169\) −265.703 + 174.755i −1.57221 + 1.03406i
\(170\) 0 0
\(171\) 52.2552 147.681i 0.305586 0.863630i
\(172\) 0 0
\(173\) 7.67686 65.6797i 0.0443749 0.379651i −0.952743 0.303779i \(-0.901752\pi\)
0.997118 0.0758727i \(-0.0241743\pi\)
\(174\) 0 0
\(175\) 9.74375 + 32.5464i 0.0556786 + 0.185979i
\(176\) 0 0
\(177\) −140.161 19.8885i −0.791870 0.112364i
\(178\) 0 0
\(179\) −323.965 57.1238i −1.80986 0.319128i −0.836425 0.548081i \(-0.815358\pi\)
−0.973437 + 0.228954i \(0.926470\pi\)
\(180\) 0 0
\(181\) −39.5977 224.569i −0.218772 1.24072i −0.874240 0.485493i \(-0.838640\pi\)
0.655469 0.755222i \(-0.272471\pi\)
\(182\) 0 0
\(183\) 146.109 165.673i 0.798412 0.905316i
\(184\) 0 0
\(185\) 21.0084 31.9417i 0.113559 0.172658i
\(186\) 0 0
\(187\) 8.06387 26.9352i 0.0431223 0.144039i
\(188\) 0 0
\(189\) 32.5350 169.027i 0.172143 0.894321i
\(190\) 0 0
\(191\) 46.4637 43.8363i 0.243266 0.229509i −0.554946 0.831886i \(-0.687261\pi\)
0.798212 + 0.602377i \(0.205780\pi\)
\(192\) 0 0
\(193\) −10.6332 + 182.565i −0.0550943 + 0.945933i 0.851613 + 0.524172i \(0.175625\pi\)
−0.906707 + 0.421761i \(0.861412\pi\)
\(194\) 0 0
\(195\) 229.512 183.155i 1.17699 0.939254i
\(196\) 0 0
\(197\) −122.870 + 337.582i −0.623705 + 1.71361i 0.0740282 + 0.997256i \(0.476415\pi\)
−0.697733 + 0.716358i \(0.745808\pi\)
\(198\) 0 0
\(199\) −235.519 + 85.7219i −1.18351 + 0.430763i −0.857441 0.514582i \(-0.827947\pi\)
−0.326072 + 0.945345i \(0.605725\pi\)
\(200\) 0 0
\(201\) 49.2301 + 79.0183i 0.244926 + 0.393126i
\(202\) 0 0
\(203\) 4.68557 19.7700i 0.0230816 0.0973890i
\(204\) 0 0
\(205\) 30.5849 + 70.9037i 0.149195 + 0.345872i
\(206\) 0 0
\(207\) −164.302 + 84.3704i −0.793728 + 0.407586i
\(208\) 0 0
\(209\) 212.182 12.3582i 1.01522 0.0591300i
\(210\) 0 0
\(211\) 98.8941 229.262i 0.468692 1.08655i −0.505905 0.862589i \(-0.668842\pi\)
0.974598 0.223962i \(-0.0718992\pi\)
\(212\) 0 0
\(213\) 159.730 + 225.953i 0.749906 + 1.06081i
\(214\) 0 0
\(215\) 121.557 + 70.1811i 0.565383 + 0.326424i
\(216\) 0 0
\(217\) −75.2738 130.378i −0.346884 0.600820i
\(218\) 0 0
\(219\) −149.021 315.867i −0.680460 1.44232i
\(220\) 0 0
\(221\) −5.89919 50.4708i −0.0266932 0.228375i
\(222\) 0 0
\(223\) 242.003 + 121.539i 1.08522 + 0.545016i 0.899203 0.437532i \(-0.144147\pi\)
0.186013 + 0.982547i \(0.440443\pi\)
\(224\) 0 0
\(225\) 34.5892 33.2250i 0.153730 0.147667i
\(226\) 0 0
\(227\) 70.9790 + 52.8419i 0.312683 + 0.232784i 0.742047 0.670348i \(-0.233855\pi\)
−0.429365 + 0.903131i \(0.641262\pi\)
\(228\) 0 0
\(229\) 69.4027 73.5625i 0.303068 0.321234i −0.557884 0.829919i \(-0.688387\pi\)
0.860953 + 0.508685i \(0.169868\pi\)
\(230\) 0 0
\(231\) 228.500 48.2516i 0.989177 0.208881i
\(232\) 0 0
\(233\) 104.017 123.963i 0.446427 0.532031i −0.495160 0.868802i \(-0.664890\pi\)
0.941586 + 0.336771i \(0.109335\pi\)
\(234\) 0 0
\(235\) 290.835 244.039i 1.23759 1.03847i
\(236\) 0 0
\(237\) 10.3741 421.606i 0.0437726 1.77893i
\(238\) 0 0
\(239\) 124.836 + 248.569i 0.522327 + 1.04004i 0.987909 + 0.155034i \(0.0495488\pi\)
−0.465582 + 0.885005i \(0.654155\pi\)
\(240\) 0 0
\(241\) −101.980 + 24.1698i −0.423155 + 0.100290i −0.436676 0.899619i \(-0.643844\pi\)
0.0135207 + 0.999909i \(0.495696\pi\)
\(242\) 0 0
\(243\) −233.250 + 68.1434i −0.959876 + 0.280426i
\(244\) 0 0
\(245\) 8.54804 + 36.0670i 0.0348900 + 0.147212i
\(246\) 0 0
\(247\) 343.265 172.394i 1.38974 0.697952i
\(248\) 0 0
\(249\) 101.934 + 2.50822i 0.409375 + 0.0100732i
\(250\) 0 0
\(251\) 27.4922 + 32.7639i 0.109531 + 0.130534i 0.818024 0.575184i \(-0.195069\pi\)
−0.708494 + 0.705717i \(0.750625\pi\)
\(252\) 0 0
\(253\) −191.964 161.077i −0.758752 0.636668i
\(254\) 0 0
\(255\) 6.32993 + 29.9760i 0.0248233 + 0.117553i
\(256\) 0 0
\(257\) 222.109 + 209.549i 0.864238 + 0.815367i 0.984135 0.177420i \(-0.0567750\pi\)
−0.119897 + 0.992786i \(0.538256\pi\)
\(258\) 0 0
\(259\) 32.8161 44.0797i 0.126703 0.170192i
\(260\) 0 0
\(261\) −27.8493 + 6.86498i −0.106702 + 0.0263026i
\(262\) 0 0
\(263\) −166.435 + 331.399i −0.632831 + 1.26007i 0.317331 + 0.948315i \(0.397213\pi\)
−0.950162 + 0.311756i \(0.899083\pi\)
\(264\) 0 0
\(265\) 140.125 16.3783i 0.528775 0.0618049i
\(266\) 0 0
\(267\) −141.265 + 66.6463i −0.529082 + 0.249612i
\(268\) 0 0
\(269\) 89.3054 51.5605i 0.331990 0.191675i −0.324734 0.945805i \(-0.605275\pi\)
0.656724 + 0.754131i \(0.271941\pi\)
\(270\) 0 0
\(271\) −144.975 + 251.105i −0.534964 + 0.926586i 0.464201 + 0.885730i \(0.346342\pi\)
−0.999165 + 0.0408556i \(0.986992\pi\)
\(272\) 0 0
\(273\) 344.651 243.640i 1.26246 0.892453i
\(274\) 0 0
\(275\) 59.7506 + 25.7739i 0.217275 + 0.0937232i
\(276\) 0 0
\(277\) 21.8059 + 374.393i 0.0787216 + 1.35160i 0.774150 + 0.633002i \(0.218178\pi\)
−0.695428 + 0.718596i \(0.744785\pi\)
\(278\) 0 0
\(279\) −115.190 + 178.609i −0.412867 + 0.640176i
\(280\) 0 0
\(281\) 206.288 88.9838i 0.734120 0.316668i 0.00400426 0.999992i \(-0.498725\pi\)
0.730116 + 0.683324i \(0.239466\pi\)
\(282\) 0 0
\(283\) 374.890 + 88.8506i 1.32470 + 0.313960i 0.831291 0.555838i \(-0.187602\pi\)
0.493409 + 0.869797i \(0.335750\pi\)
\(284\) 0 0
\(285\) −196.567 + 122.466i −0.689710 + 0.429704i
\(286\) 0 0
\(287\) 37.9625 + 104.301i 0.132274 + 0.363418i
\(288\) 0 0
\(289\) −266.589 97.0305i −0.922454 0.335746i
\(290\) 0 0
\(291\) −180.811 226.576i −0.621345 0.778612i
\(292\) 0 0
\(293\) −406.158 23.6560i −1.38621 0.0807373i −0.651255 0.758859i \(-0.725757\pi\)
−0.734950 + 0.678121i \(0.762794\pi\)
\(294\) 0 0
\(295\) 143.623 + 152.232i 0.486858 + 0.516039i
\(296\) 0 0
\(297\) −207.951 255.840i −0.700171 0.861415i
\(298\) 0 0
\(299\) −433.865 129.891i −1.45105 0.434417i
\(300\) 0 0
\(301\) 168.566 + 110.867i 0.560019 + 0.368330i
\(302\) 0 0
\(303\) 260.999 + 230.179i 0.861382 + 0.759665i
\(304\) 0 0
\(305\) −321.612 + 56.7089i −1.05447 + 0.185931i
\(306\) 0 0
\(307\) −21.5340 + 122.126i −0.0701435 + 0.397803i 0.929441 + 0.368971i \(0.120290\pi\)
−0.999584 + 0.0288321i \(0.990821\pi\)
\(308\) 0 0
\(309\) 8.14410 57.3942i 0.0263563 0.185742i
\(310\) 0 0
\(311\) −480.631 + 143.891i −1.54544 + 0.462673i −0.942245 0.334924i \(-0.891289\pi\)
−0.603191 + 0.797597i \(0.706104\pi\)
\(312\) 0 0
\(313\) 172.483 + 20.1603i 0.551063 + 0.0644100i 0.387068 0.922051i \(-0.373488\pi\)
0.163995 + 0.986461i \(0.447562\pi\)
\(314\) 0 0
\(315\) −193.464 + 165.317i −0.614171 + 0.524816i
\(316\) 0 0
\(317\) −222.429 338.187i −0.701669 1.06684i −0.993878 0.110481i \(-0.964761\pi\)
0.292210 0.956354i \(-0.405610\pi\)
\(318\) 0 0
\(319\) −23.2390 31.2154i −0.0728496 0.0978540i
\(320\) 0 0
\(321\) −84.2928 309.031i −0.262595 0.962714i
\(322\) 0 0
\(323\) 40.0783i 0.124082i
\(324\) 0 0
\(325\) 117.605 0.361860
\(326\) 0 0
\(327\) 47.2735 + 46.8511i 0.144567 + 0.143276i
\(328\) 0 0
\(329\) 437.736 325.882i 1.33050 0.990524i
\(330\) 0 0
\(331\) 260.204 171.139i 0.786115 0.517036i −0.0918432 0.995773i \(-0.529276\pi\)
0.877958 + 0.478738i \(0.158905\pi\)
\(332\) 0 0
\(333\) −76.5190 12.7853i −0.229787 0.0383944i
\(334\) 0 0
\(335\) 15.9788 136.707i 0.0476979 0.408081i
\(336\) 0 0
\(337\) 65.8240 + 219.868i 0.195324 + 0.652426i 0.998400 + 0.0565498i \(0.0180100\pi\)
−0.803076 + 0.595876i \(0.796805\pi\)
\(338\) 0 0
\(339\) 68.4185 87.3320i 0.201824 0.257616i
\(340\) 0 0
\(341\) −283.975 50.0725i −0.832772 0.146840i
\(342\) 0 0
\(343\) 63.4966 + 360.107i 0.185121 + 1.04987i
\(344\) 0 0
\(345\) 267.661 + 54.0164i 0.775829 + 0.156569i
\(346\) 0 0
\(347\) −190.634 + 289.845i −0.549379 + 0.835290i −0.998300 0.0582816i \(-0.981438\pi\)
0.448922 + 0.893571i \(0.351808\pi\)
\(348\) 0 0
\(349\) −23.2040 + 77.5066i −0.0664870 + 0.222082i −0.984776 0.173829i \(-0.944386\pi\)
0.918289 + 0.395911i \(0.129571\pi\)
\(350\) 0 0
\(351\) −528.228 275.705i −1.50492 0.785484i
\(352\) 0 0
\(353\) −135.851 + 128.169i −0.384846 + 0.363084i −0.854216 0.519918i \(-0.825963\pi\)
0.469370 + 0.883002i \(0.344481\pi\)
\(354\) 0 0
\(355\) 23.7863 408.396i 0.0670038 1.15041i
\(356\) 0 0
\(357\) 6.57795 + 43.5438i 0.0184256 + 0.121971i
\(358\) 0 0
\(359\) −136.467 + 374.941i −0.380132 + 1.04440i 0.591168 + 0.806548i \(0.298667\pi\)
−0.971300 + 0.237856i \(0.923555\pi\)
\(360\) 0 0
\(361\) 54.5346 19.8490i 0.151065 0.0549833i
\(362\) 0 0
\(363\) 39.6829 74.3938i 0.109319 0.204942i
\(364\) 0 0
\(365\) −119.076 + 502.421i −0.326235 + 1.37650i
\(366\) 0 0
\(367\) 125.584 + 291.136i 0.342190 + 0.793286i 0.999223 + 0.0394239i \(0.0125523\pi\)
−0.657032 + 0.753863i \(0.728188\pi\)
\(368\) 0 0
\(369\) 106.503 114.936i 0.288626 0.311480i
\(370\) 0 0
\(371\) 202.445 11.7911i 0.545673 0.0317819i
\(372\) 0 0
\(373\) 25.6236 59.4021i 0.0686959 0.159255i −0.880409 0.474215i \(-0.842732\pi\)
0.949105 + 0.314960i \(0.101991\pi\)
\(374\) 0 0
\(375\) −401.848 + 36.9750i −1.07160 + 0.0986001i
\(376\) 0 0
\(377\) −60.9097 35.1662i −0.161564 0.0932791i
\(378\) 0 0
\(379\) 14.8684 + 25.7529i 0.0392307 + 0.0679496i 0.884974 0.465640i \(-0.154176\pi\)
−0.845743 + 0.533590i \(0.820843\pi\)
\(380\) 0 0
\(381\) 193.584 279.124i 0.508095 0.732610i
\(382\) 0 0
\(383\) 19.8192 + 169.564i 0.0517473 + 0.442726i 0.994130 + 0.108190i \(0.0345055\pi\)
−0.942383 + 0.334536i \(0.891420\pi\)
\(384\) 0 0
\(385\) −308.539 154.954i −0.801399 0.402478i
\(386\) 0 0
\(387\) 30.5259 283.186i 0.0788784 0.731747i
\(388\) 0 0
\(389\) −621.776 462.895i −1.59840 1.18996i −0.850151 0.526540i \(-0.823489\pi\)
−0.748245 0.663422i \(-0.769103\pi\)
\(390\) 0 0
\(391\) 32.4272 34.3709i 0.0829341 0.0879050i
\(392\) 0 0
\(393\) −218.380 + 669.076i −0.555675 + 1.70248i
\(394\) 0 0
\(395\) −400.771 + 477.621i −1.01461 + 1.20917i
\(396\) 0 0
\(397\) 391.914 328.855i 0.987188 0.828349i 0.00203021 0.999998i \(-0.499354\pi\)
0.985158 + 0.171648i \(0.0549093\pi\)
\(398\) 0 0
\(399\) −292.304 + 159.306i −0.732591 + 0.399264i
\(400\) 0 0
\(401\) −129.946 258.744i −0.324055 0.645246i 0.671335 0.741154i \(-0.265721\pi\)
−0.995390 + 0.0959075i \(0.969425\pi\)
\(402\) 0 0
\(403\) −507.095 + 120.184i −1.25830 + 0.298222i
\(404\) 0 0
\(405\) 332.371 + 136.348i 0.820668 + 0.336662i
\(406\) 0 0
\(407\) −24.2740 102.420i −0.0596413 0.251647i
\(408\) 0 0
\(409\) 323.650 162.543i 0.791319 0.397415i −0.00675308 0.999977i \(-0.502150\pi\)
0.798072 + 0.602562i \(0.205853\pi\)
\(410\) 0 0
\(411\) 253.247 414.730i 0.616174 1.00908i
\(412\) 0 0
\(413\) 193.372 + 230.452i 0.468213 + 0.557995i
\(414\) 0 0
\(415\) −115.478 96.8972i −0.278259 0.233487i
\(416\) 0 0
\(417\) −356.938 + 320.529i −0.855965 + 0.768656i
\(418\) 0 0
\(419\) 496.679 + 468.592i 1.18539 + 1.11836i 0.990497 + 0.137534i \(0.0439177\pi\)
0.194894 + 0.980824i \(0.437564\pi\)
\(420\) 0 0
\(421\) −238.221 + 319.987i −0.565846 + 0.760063i −0.989307 0.145851i \(-0.953408\pi\)
0.423460 + 0.905915i \(0.360815\pi\)
\(422\) 0 0
\(423\) −691.540 339.567i −1.63485 0.802758i
\(424\) 0 0
\(425\) −5.50701 + 10.9654i −0.0129577 + 0.0258008i
\(426\) 0 0
\(427\) −466.244 + 54.4961i −1.09191 + 0.127626i
\(428\) 0 0
\(429\) 66.8444 805.660i 0.155814 1.87800i
\(430\) 0 0
\(431\) −207.851 + 120.003i −0.482254 + 0.278429i −0.721355 0.692565i \(-0.756480\pi\)
0.239102 + 0.970995i \(0.423147\pi\)
\(432\) 0 0
\(433\) −363.924 + 630.335i −0.840472 + 1.45574i 0.0490248 + 0.998798i \(0.484389\pi\)
−0.889496 + 0.456942i \(0.848945\pi\)
\(434\) 0 0
\(435\) 38.5119 + 17.7484i 0.0885330 + 0.0408010i
\(436\) 0 0
\(437\) 327.991 + 141.481i 0.750550 + 0.323756i
\(438\) 0 0
\(439\) −31.7534 545.184i −0.0723311 1.24188i −0.817865 0.575410i \(-0.804843\pi\)
0.745534 0.666467i \(-0.232194\pi\)
\(440\) 0 0
\(441\) 59.9266 45.4553i 0.135888 0.103073i
\(442\) 0 0
\(443\) 153.267 66.1131i 0.345976 0.149240i −0.215999 0.976394i \(-0.569301\pi\)
0.561975 + 0.827154i \(0.310042\pi\)
\(444\) 0 0
\(445\) 224.697 + 53.2541i 0.504937 + 0.119672i
\(446\) 0 0
\(447\) 25.8684 + 770.143i 0.0578711 + 1.72292i
\(448\) 0 0
\(449\) −73.0080 200.588i −0.162601 0.446743i 0.831457 0.555588i \(-0.187507\pi\)
−0.994059 + 0.108845i \(0.965285\pi\)
\(450\) 0 0
\(451\) 199.776 + 72.7126i 0.442963 + 0.161225i
\(452\) 0 0
\(453\) −282.486 + 720.467i −0.623590 + 1.59043i
\(454\) 0 0
\(455\) −622.935 36.2818i −1.36909 0.0797402i
\(456\) 0 0
\(457\) 196.641 + 208.427i 0.430286 + 0.456077i 0.905846 0.423606i \(-0.139236\pi\)
−0.475560 + 0.879683i \(0.657755\pi\)
\(458\) 0 0
\(459\) 50.4415 36.3413i 0.109894 0.0791749i
\(460\) 0 0
\(461\) −23.0352 6.89629i −0.0499679 0.0149594i 0.261722 0.965143i \(-0.415710\pi\)
−0.311690 + 0.950184i \(0.600895\pi\)
\(462\) 0 0
\(463\) −168.627 110.908i −0.364205 0.239542i 0.354195 0.935172i \(-0.384755\pi\)
−0.718400 + 0.695630i \(0.755125\pi\)
\(464\) 0 0
\(465\) 297.812 100.170i 0.640457 0.215419i
\(466\) 0 0
\(467\) 630.376 111.152i 1.34984 0.238014i 0.548465 0.836173i \(-0.315212\pi\)
0.801377 + 0.598160i \(0.204101\pi\)
\(468\) 0 0
\(469\) 34.3548 194.836i 0.0732511 0.415428i
\(470\) 0 0
\(471\) 319.255 128.494i 0.677824 0.272811i
\(472\) 0 0
\(473\) 370.207 110.833i 0.782679 0.234319i
\(474\) 0 0
\(475\) −92.1299 10.7684i −0.193958 0.0226704i
\(476\) 0 0
\(477\) −145.360 246.632i −0.304738 0.517049i
\(478\) 0 0
\(479\) 219.903 + 334.346i 0.459087 + 0.698008i 0.988646 0.150265i \(-0.0480128\pi\)
−0.529559 + 0.848273i \(0.677642\pi\)
\(480\) 0 0
\(481\) −113.598 152.588i −0.236170 0.317231i
\(482\) 0 0
\(483\) 379.572 + 99.8824i 0.785863 + 0.206796i
\(484\) 0 0
\(485\) 428.556i 0.883620i
\(486\) 0 0
\(487\) 248.564 0.510398 0.255199 0.966889i \(-0.417859\pi\)
0.255199 + 0.966889i \(0.417859\pi\)
\(488\) 0 0
\(489\) −139.187 + 528.937i −0.284636 + 1.08167i
\(490\) 0 0
\(491\) 407.235 303.175i 0.829400 0.617465i −0.0964582 0.995337i \(-0.530751\pi\)
0.925858 + 0.377872i \(0.123344\pi\)
\(492\) 0 0
\(493\) 6.13105 4.03245i 0.0124362 0.00817942i
\(494\) 0 0
\(495\) 4.37462 + 487.398i 0.00883762 + 0.984643i
\(496\) 0 0
\(497\) 68.2655 584.048i 0.137355 1.17515i
\(498\) 0 0
\(499\) 196.196 + 655.339i 0.393178 + 1.31331i 0.894121 + 0.447825i \(0.147801\pi\)
−0.500943 + 0.865480i \(0.667014\pi\)
\(500\) 0 0
\(501\) 71.6540 + 178.031i 0.143022 + 0.355352i
\(502\) 0 0
\(503\) −33.1347 5.84255i −0.0658743 0.0116154i 0.140614 0.990065i \(-0.455092\pi\)
−0.206488 + 0.978449i \(0.566203\pi\)
\(504\) 0 0
\(505\) −89.3384 506.663i −0.176908 1.00329i
\(506\) 0 0
\(507\) −304.157 904.282i −0.599915 1.78359i
\(508\) 0 0
\(509\) 486.078 739.046i 0.954967 1.45196i 0.0639684 0.997952i \(-0.479624\pi\)
0.890999 0.454005i \(-0.150005\pi\)
\(510\) 0 0
\(511\) −212.862 + 711.008i −0.416559 + 1.39140i
\(512\) 0 0
\(513\) 388.562 + 264.351i 0.757431 + 0.515303i
\(514\) 0 0
\(515\) −62.3370 + 58.8119i −0.121043 + 0.114198i
\(516\) 0 0
\(517\) 60.7767 1043.50i 0.117557 2.01837i
\(518\) 0 0
\(519\) 184.691 + 72.4152i 0.355860 + 0.139528i
\(520\) 0 0
\(521\) 149.208 409.945i 0.286387 0.786842i −0.710177 0.704023i \(-0.751385\pi\)
0.996565 0.0828196i \(-0.0263925\pi\)
\(522\) 0 0
\(523\) −173.509 + 63.1521i −0.331757 + 0.120750i −0.502528 0.864561i \(-0.667597\pi\)
0.170771 + 0.985311i \(0.445374\pi\)
\(524\) 0 0
\(525\) −101.863 + 3.42150i −0.194026 + 0.00651714i
\(526\) 0 0
\(527\) 12.5396 52.9088i 0.0237944 0.100396i
\(528\) 0 0
\(529\) 42.7161 + 99.0270i 0.0807488 + 0.187197i
\(530\) 0 0
\(531\) 164.706 391.456i 0.310182 0.737205i
\(532\) 0 0
\(533\) 383.575 22.3407i 0.719653 0.0419150i
\(534\) 0 0
\(535\) −187.568 + 434.832i −0.350595 + 0.812770i
\(536\) 0 0
\(537\) 413.059 896.288i 0.769198 1.66907i
\(538\) 0 0
\(539\) 88.3776 + 51.0248i 0.163966 + 0.0946657i
\(540\) 0 0
\(541\) 48.1113 + 83.3312i 0.0889302 + 0.154032i 0.907059 0.421003i \(-0.138322\pi\)
−0.818129 + 0.575035i \(0.804989\pi\)
\(542\) 0 0
\(543\) 681.759 + 56.5645i 1.25554 + 0.104170i
\(544\) 0 0
\(545\) −11.4233 97.7322i −0.0209601 0.179325i
\(546\) 0 0
\(547\) −208.757 104.842i −0.381639 0.191666i 0.247628 0.968855i \(-0.420349\pi\)
−0.629268 + 0.777189i \(0.716645\pi\)
\(548\) 0 0
\(549\) 369.109 + 550.379i 0.672330 + 1.00251i
\(550\) 0 0
\(551\) 44.4958 + 33.1259i 0.0807547 + 0.0601196i
\(552\) 0 0
\(553\) −615.014 + 651.877i −1.11214 + 1.17880i
\(554\) 0 0
\(555\) 76.6317 + 85.3361i 0.138075 + 0.153759i
\(556\) 0 0
\(557\) −219.828 + 261.980i −0.394664 + 0.470342i −0.926385 0.376577i \(-0.877101\pi\)
0.531721 + 0.846919i \(0.321545\pi\)
\(558\) 0 0
\(559\) 535.015 448.931i 0.957092 0.803096i
\(560\) 0 0
\(561\) 71.9890 + 43.9587i 0.128323 + 0.0783578i
\(562\) 0 0
\(563\) 36.1500 + 71.9805i 0.0642095 + 0.127852i 0.923448 0.383724i \(-0.125358\pi\)
−0.859238 + 0.511575i \(0.829062\pi\)
\(564\) 0 0
\(565\) −159.594 + 37.8245i −0.282468 + 0.0669461i
\(566\) 0 0
\(567\) 465.547 + 223.434i 0.821070 + 0.394064i
\(568\) 0 0
\(569\) 136.622 + 576.455i 0.240109 + 1.01310i 0.950851 + 0.309648i \(0.100211\pi\)
−0.710742 + 0.703453i \(0.751641\pi\)
\(570\) 0 0
\(571\) 266.527 133.855i 0.466772 0.234422i −0.199837 0.979829i \(-0.564041\pi\)
0.666609 + 0.745407i \(0.267745\pi\)
\(572\) 0 0
\(573\) 91.7067 + 168.269i 0.160047 + 0.293663i
\(574\) 0 0
\(575\) 70.2972 + 83.7769i 0.122256 + 0.145699i
\(576\) 0 0
\(577\) −614.163 515.344i −1.06441 0.893144i −0.0698738 0.997556i \(-0.522260\pi\)
−0.994534 + 0.104412i \(0.966704\pi\)
\(578\) 0 0
\(579\) −521.546 170.228i −0.900770 0.294003i
\(580\) 0 0
\(581\) −157.609 148.696i −0.271271 0.255931i
\(582\) 0 0
\(583\) 231.946 311.558i 0.397849 0.534404i
\(584\) 0 0
\(585\) 356.154 + 805.697i 0.608810 + 1.37726i
\(586\) 0 0
\(587\) −105.169 + 209.408i −0.179163 + 0.356742i −0.965231 0.261397i \(-0.915817\pi\)
0.786069 + 0.618139i \(0.212113\pi\)
\(588\) 0 0
\(589\) 408.256 47.7183i 0.693134 0.0810157i
\(590\) 0 0
\(591\) −885.600 614.199i −1.49848 1.03925i
\(592\) 0 0
\(593\) 973.051 561.791i 1.64090 0.947372i 0.660380 0.750932i \(-0.270395\pi\)
0.980516 0.196440i \(-0.0629381\pi\)
\(594\) 0 0
\(595\) 32.5527 56.3829i 0.0547104 0.0947612i
\(596\) 0 0
\(597\) −68.8934 748.740i −0.115399 1.25417i
\(598\) 0 0
\(599\) −35.4481 15.2908i −0.0591788 0.0255273i 0.366285 0.930503i \(-0.380630\pi\)
−0.425463 + 0.904976i \(0.639889\pi\)
\(600\) 0 0
\(601\) −62.0601 1065.53i −0.103261 1.77293i −0.510759 0.859724i \(-0.670635\pi\)
0.407497 0.913206i \(-0.366402\pi\)
\(602\) 0 0
\(603\) −266.835 + 82.5018i −0.442513 + 0.136819i
\(604\) 0 0
\(605\) −114.458 + 49.3723i −0.189187 + 0.0816071i
\(606\) 0 0
\(607\) −306.367 72.6103i −0.504723 0.119622i −0.0296368 0.999561i \(-0.509435\pi\)
−0.475086 + 0.879939i \(0.657583\pi\)
\(608\) 0 0
\(609\) 53.7801 + 28.6872i 0.0883089 + 0.0471054i
\(610\) 0 0
\(611\) −646.108 1775.17i −1.05746 2.90535i
\(612\) 0 0
\(613\) −526.129 191.495i −0.858286 0.312391i −0.124872 0.992173i \(-0.539852\pi\)
−0.733414 + 0.679782i \(0.762074\pi\)
\(614\) 0 0
\(615\) −229.058 + 34.6028i −0.372452 + 0.0562646i
\(616\) 0 0
\(617\) −634.477 36.9541i −1.02833 0.0598931i −0.464323 0.885666i \(-0.653702\pi\)
−0.564003 + 0.825773i \(0.690739\pi\)
\(618\) 0 0
\(619\) −416.146 441.089i −0.672287 0.712583i 0.297993 0.954568i \(-0.403683\pi\)
−0.970280 + 0.241986i \(0.922201\pi\)
\(620\) 0 0
\(621\) −119.343 541.089i −0.192178 0.871319i
\(622\) 0 0
\(623\) 317.983 + 95.1978i 0.510406 + 0.152805i
\(624\) 0 0
\(625\) 387.144 + 254.629i 0.619430 + 0.407406i
\(626\) 0 0
\(627\) −126.135 + 625.023i −0.201172 + 0.996847i
\(628\) 0 0
\(629\) 19.5466 3.44659i 0.0310756 0.00547947i
\(630\) 0 0
\(631\) −59.4245 + 337.013i −0.0941752 + 0.534094i 0.900822 + 0.434189i \(0.142965\pi\)
−0.994997 + 0.0999050i \(0.968146\pi\)
\(632\) 0 0
\(633\) 589.643 + 461.944i 0.931506 + 0.729769i
\(634\) 0 0
\(635\) −481.091 + 144.029i −0.757623 + 0.226818i
\(636\) 0 0
\(637\) 183.186 + 21.4114i 0.287576 + 0.0336128i
\(638\) 0 0
\(639\) −777.488 + 290.911i −1.21673 + 0.455260i
\(640\) 0 0
\(641\) 197.292 + 299.968i 0.307788 + 0.467968i 0.955948 0.293535i \(-0.0948318\pi\)
−0.648161 + 0.761504i \(0.724461\pi\)
\(642\) 0 0
\(643\) −305.506 410.366i −0.475126 0.638205i 0.498355 0.866973i \(-0.333938\pi\)
−0.973481 + 0.228768i \(0.926530\pi\)
\(644\) 0 0
\(645\) −296.414 + 299.087i −0.459557 + 0.463700i
\(646\) 0 0
\(647\) 258.228i 0.399116i −0.979886 0.199558i \(-0.936049\pi\)
0.979886 0.199558i \(-0.0639506\pi\)
\(648\) 0 0
\(649\) 576.211 0.887844
\(650\) 0 0
\(651\) 435.724 118.850i 0.669315 0.182566i
\(652\) 0 0
\(653\) 766.737 570.815i 1.17418 0.874142i 0.180189 0.983632i \(-0.442329\pi\)
0.993988 + 0.109490i \(0.0349217\pi\)
\(654\) 0 0
\(655\) 869.338 571.773i 1.32723 0.872935i
\(656\) 0 0
\(657\) 1030.17 191.196i 1.56800 0.291014i
\(658\) 0 0
\(659\) 87.7427 750.687i 0.133145 1.13913i −0.747134 0.664674i \(-0.768570\pi\)
0.880279 0.474457i \(-0.157355\pi\)
\(660\) 0 0
\(661\) −7.66100 25.5895i −0.0115900 0.0387133i 0.951999 0.306101i \(-0.0990246\pi\)
−0.963589 + 0.267388i \(0.913839\pi\)
\(662\) 0 0
\(663\) 150.931 + 21.4168i 0.227649 + 0.0323028i
\(664\) 0 0
\(665\) 484.677 + 85.4615i 0.728837 + 0.128514i
\(666\) 0 0
\(667\) −11.3572 64.4099i −0.0170273 0.0965666i
\(668\) 0 0
\(669\) −537.368 + 609.319i −0.803240 + 0.910791i
\(670\) 0 0
\(671\) −494.071 + 751.199i −0.736321 + 1.11952i
\(672\) 0 0
\(673\) −348.955 + 1165.59i −0.518507 + 1.73193i 0.150434 + 0.988620i \(0.451933\pi\)
−0.668942 + 0.743315i \(0.733252\pi\)
\(674\) 0 0
\(675\) 69.9865 + 125.717i 0.103684 + 0.186247i
\(676\) 0 0
\(677\) 77.3830 73.0071i 0.114303 0.107839i −0.626969 0.779045i \(-0.715705\pi\)
0.741272 + 0.671205i \(0.234223\pi\)
\(678\) 0 0
\(679\) −35.8176 + 614.965i −0.0527506 + 0.905693i
\(680\) 0 0
\(681\) −207.495 + 165.585i −0.304692 + 0.243149i
\(682\) 0 0
\(683\) −87.4529 + 240.275i −0.128042 + 0.351794i −0.987104 0.160078i \(-0.948825\pi\)
0.859062 + 0.511872i \(0.171048\pi\)
\(684\) 0 0
\(685\) −675.084 + 245.710i −0.985524 + 0.358701i
\(686\) 0 0
\(687\) 160.437 + 257.514i 0.233533 + 0.374839i
\(688\) 0 0
\(689\) 161.888 683.058i 0.234960 0.991376i
\(690\) 0 0
\(691\) −108.629 251.829i −0.157205 0.364442i 0.821351 0.570423i \(-0.193221\pi\)
−0.978556 + 0.205981i \(0.933961\pi\)
\(692\) 0 0
\(693\) −34.4581 + 699.769i −0.0497231 + 1.00977i
\(694\) 0 0
\(695\) 708.036 41.2384i 1.01876 0.0593358i
\(696\) 0 0
\(697\) −15.8784 + 36.8103i −0.0227811 + 0.0528125i
\(698\) 0 0
\(699\) 280.234 + 396.418i 0.400907 + 0.567121i
\(700\) 0 0
\(701\) 690.852 + 398.863i 0.985523 + 0.568992i 0.903933 0.427674i \(-0.140667\pi\)
0.0815900 + 0.996666i \(0.474000\pi\)
\(702\) 0 0
\(703\) 75.0192 + 129.937i 0.106713 + 0.184832i
\(704\) 0 0
\(705\) 485.978 + 1030.09i 0.689331 + 1.46112i
\(706\) 0 0
\(707\) −85.8524 734.514i −0.121432 1.03892i
\(708\) 0 0
\(709\) −175.555 88.1668i −0.247609 0.124354i 0.320667 0.947192i \(-0.396093\pi\)
−0.568276 + 0.822838i \(0.692389\pi\)
\(710\) 0 0
\(711\) 1215.26 + 351.970i 1.70922 + 0.495036i
\(712\) 0 0
\(713\) −388.726 289.396i −0.545197 0.405884i
\(714\) 0 0
\(715\) −820.182 + 869.342i −1.14711 + 1.21586i
\(716\) 0 0
\(717\) −816.463 + 172.410i −1.13872 + 0.240460i
\(718\) 0 0
\(719\) 101.585 121.064i 0.141286 0.168378i −0.690761 0.723083i \(-0.742724\pi\)
0.832047 + 0.554705i \(0.187169\pi\)
\(720\) 0 0
\(721\) −94.3672 + 79.1835i −0.130884 + 0.109825i
\(722\) 0 0
\(723\) 7.73424 314.321i 0.0106974 0.434745i
\(724\) 0 0
\(725\) 7.62227 + 15.1772i 0.0105135 + 0.0209341i
\(726\) 0 0
\(727\) 1039.49 246.363i 1.42983 0.338877i 0.558473 0.829522i \(-0.311387\pi\)
0.871359 + 0.490646i \(0.163239\pi\)
\(728\) 0 0
\(729\) −19.6264 728.736i −0.0269224 0.999638i
\(730\) 0 0
\(731\) 16.8051 + 70.9061i 0.0229891 + 0.0969988i
\(732\) 0 0
\(733\) 316.933 159.170i 0.432378 0.217149i −0.219279 0.975662i \(-0.570370\pi\)
0.651657 + 0.758514i \(0.274074\pi\)
\(734\) 0 0
\(735\) −111.165 2.73534i −0.151245 0.00372155i
\(736\) 0 0
\(737\) −243.579 290.286i −0.330501 0.393875i
\(738\) 0 0
\(739\) 263.955 + 221.485i 0.357179 + 0.299709i 0.803665 0.595082i \(-0.202880\pi\)
−0.446486 + 0.894791i \(0.647325\pi\)
\(740\) 0 0
\(741\) 238.092 + 1127.51i 0.321311 + 1.52160i
\(742\) 0 0
\(743\) 786.016 + 741.567i 1.05789 + 0.998072i 1.00000 0.000250823i \(-7.98395e-5\pi\)
0.0578944 + 0.998323i \(0.481561\pi\)
\(744\) 0 0
\(745\) 680.295 913.795i 0.913148 1.22657i
\(746\) 0 0
\(747\) −85.0983 + 293.821i −0.113920 + 0.393334i
\(748\) 0 0
\(749\) −305.497 + 608.296i −0.407874 + 0.812144i
\(750\) 0 0
\(751\) −1251.79 + 146.314i −1.66684 + 0.194825i −0.896571 0.442900i \(-0.853950\pi\)
−0.770264 + 0.637725i \(0.779876\pi\)
\(752\) 0 0
\(753\) −116.045 + 54.7478i −0.154110 + 0.0727063i
\(754\) 0 0
\(755\) 990.806 572.042i 1.31233 0.757671i
\(756\) 0 0
\(757\) −645.604 + 1118.22i −0.852846 + 1.47717i 0.0257829 + 0.999668i \(0.491792\pi\)
−0.878629 + 0.477505i \(0.841541\pi\)
\(758\) 0 0
\(759\) 613.876 433.959i 0.808796 0.571751i
\(760\) 0 0
\(761\) −1091.01 470.617i −1.43366 0.618419i −0.469303 0.883037i \(-0.655495\pi\)
−0.964353 + 0.264618i \(0.914754\pi\)
\(762\) 0 0
\(763\) −8.22383 141.198i −0.0107783 0.185056i
\(764\) 0 0
\(765\) −91.7999 4.52043i −0.120000 0.00590905i
\(766\) 0 0
\(767\) 956.210 412.469i 1.24669 0.537769i
\(768\) 0 0
\(769\) −1274.78 302.129i −1.65772 0.392886i −0.708053 0.706159i \(-0.750426\pi\)
−0.949663 + 0.313274i \(0.898574\pi\)
\(770\) 0 0
\(771\) −777.519 + 484.411i −1.00846 + 0.628290i
\(772\) 0 0
\(773\) −440.248 1209.57i −0.569531 1.56477i −0.805239 0.592950i \(-0.797963\pi\)
0.235708 0.971824i \(-0.424259\pi\)
\(774\) 0 0
\(775\) 118.255 + 43.0412i 0.152587 + 0.0555371i
\(776\) 0 0
\(777\) 102.832 + 128.860i 0.132345 + 0.165842i
\(778\) 0 0
\(779\) −302.533 17.6205i −0.388361 0.0226194i
\(780\) 0 0
\(781\) −772.907 819.234i −0.989638 1.04896i
\(782\) 0 0
\(783\) 1.34455 86.0384i 0.00171717 0.109883i
\(784\) 0 0
\(785\) −487.406 145.920i −0.620900 0.185885i
\(786\) 0 0
\(787\) −1014.58 667.299i −1.28917 0.847902i −0.294979 0.955504i \(-0.595312\pi\)
−0.994194 + 0.107602i \(0.965683\pi\)
\(788\) 0 0
\(789\) −834.401 735.870i −1.05754 0.932662i
\(790\) 0 0
\(791\) −232.175 + 40.9386i −0.293520 + 0.0517555i
\(792\) 0 0
\(793\) −282.171 + 1600.27i −0.355827 + 2.01800i
\(794\) 0 0
\(795\) −59.4608 + 419.040i −0.0747934 + 0.527095i
\(796\) 0