Properties

Label 300.2.m.b.61.1
Level $300$
Weight $2$
Character 300.61
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.m (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.26265625.1
Defining polynomial: \(x^{8} - 3 x^{7} + 2 x^{6} + x^{4} + 8 x^{2} - 24 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 61.1
Root \(1.40799 - 0.132563i\) of defining polynomial
Character \(\chi\) \(=\) 300.61
Dual form 300.2.m.b.241.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{3} +(-1.96485 + 1.06740i) q^{5} -1.74037 q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{3} +(-1.96485 + 1.06740i) q^{5} -1.74037 q^{7} +(-0.809017 - 0.587785i) q^{9} +(-1.87714 + 1.36382i) q^{11} +(-3.99517 - 2.90266i) q^{13} +(-0.407987 - 2.19853i) q^{15} +(1.15584 + 3.55730i) q^{17} +(-0.523364 - 1.61075i) q^{19} +(0.537803 - 1.65519i) q^{21} +(-7.02120 + 5.10120i) q^{23} +(2.72130 - 4.19458i) q^{25} +(0.809017 - 0.587785i) q^{27} +(0.964854 - 2.96952i) q^{29} +(2.95471 + 9.09368i) q^{31} +(-0.717004 - 2.20671i) q^{33} +(3.41957 - 1.85767i) q^{35} +(-4.34199 - 3.15464i) q^{37} +(3.99517 - 2.90266i) q^{39} +(7.05900 + 5.12866i) q^{41} +2.86270 q^{43} +(2.21700 + 0.291365i) q^{45} +(-2.61505 + 8.04830i) q^{47} -3.97112 q^{49} -3.74037 q^{51} +(-0.415470 + 1.27868i) q^{53} +(2.23256 - 4.68338i) q^{55} +1.69364 q^{57} +(-3.54991 - 2.57916i) q^{59} +(12.4035 - 9.01166i) q^{61} +(1.40799 + 1.02296i) q^{63} +(10.9482 + 1.43885i) q^{65} +(2.85246 + 8.77897i) q^{67} +(-2.68186 - 8.25391i) q^{69} +(0.00728184 - 0.0224112i) q^{71} +(0.827230 - 0.601018i) q^{73} +(3.14835 + 3.88431i) q^{75} +(3.26691 - 2.37355i) q^{77} +(-0.246835 + 0.759681i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.732396 + 2.25408i) q^{83} +(-6.06812 - 5.75583i) q^{85} +(2.52602 + 1.83526i) q^{87} +(3.93348 - 2.85784i) q^{89} +(6.95307 + 5.05170i) q^{91} -9.56166 q^{93} +(2.74765 + 2.60624i) q^{95} +(-1.06966 + 3.29209i) q^{97} +2.32027 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{3} - 5q^{5} + 8q^{7} - 2q^{9} + O(q^{10}) \) \( 8q + 2q^{3} - 5q^{5} + 8q^{7} - 2q^{9} + 8q^{11} + 5q^{15} + 3q^{17} + 5q^{19} + 7q^{21} - 7q^{23} + 5q^{25} + 2q^{27} - 3q^{29} - 3q^{31} + 7q^{33} - 10q^{35} - q^{37} + 10q^{41} - 12q^{43} + 5q^{45} - 33q^{47} - 8q^{49} - 8q^{51} - 19q^{53} - 15q^{55} + 10q^{57} - 38q^{59} + 46q^{61} + 3q^{63} + 25q^{65} - 8q^{67} + 2q^{69} - 25q^{71} - 26q^{73} - 5q^{75} + 23q^{77} - 16q^{79} - 2q^{81} + 8q^{83} - 30q^{85} + 3q^{87} - 30q^{89} + 25q^{91} - 22q^{93} - 25q^{95} - 14q^{97} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\)

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
\(3\) −0.309017 + 0.951057i −0.178411 + 0.549093i
\(4\) 0 0
\(5\) −1.96485 + 1.06740i −0.878709 + 0.477357i
\(6\) 0 0
\(7\) −1.74037 −0.657797 −0.328899 0.944365i \(-0.606677\pi\)
−0.328899 + 0.944365i \(0.606677\pi\)
\(8\) 0 0
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 0 0
\(11\) −1.87714 + 1.36382i −0.565979 + 0.411208i −0.833642 0.552305i \(-0.813749\pi\)
0.267663 + 0.963513i \(0.413749\pi\)
\(12\) 0 0
\(13\) −3.99517 2.90266i −1.10806 0.805054i −0.125705 0.992068i \(-0.540119\pi\)
−0.982357 + 0.187014i \(0.940119\pi\)
\(14\) 0 0
\(15\) −0.407987 2.19853i −0.105342 0.567659i
\(16\) 0 0
\(17\) 1.15584 + 3.55730i 0.280332 + 0.862772i 0.987759 + 0.155986i \(0.0498556\pi\)
−0.707428 + 0.706786i \(0.750144\pi\)
\(18\) 0 0
\(19\) −0.523364 1.61075i −0.120068 0.369531i 0.872902 0.487895i \(-0.162235\pi\)
−0.992970 + 0.118364i \(0.962235\pi\)
\(20\) 0 0
\(21\) 0.537803 1.65519i 0.117358 0.361192i
\(22\) 0 0
\(23\) −7.02120 + 5.10120i −1.46402 + 1.06367i −0.481728 + 0.876321i \(0.659991\pi\)
−0.982293 + 0.187352i \(0.940009\pi\)
\(24\) 0 0
\(25\) 2.72130 4.19458i 0.544261 0.838916i
\(26\) 0 0
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) 0 0
\(29\) 0.964854 2.96952i 0.179169 0.551425i −0.820630 0.571459i \(-0.806377\pi\)
0.999799 + 0.0200341i \(0.00637749\pi\)
\(30\) 0 0
\(31\) 2.95471 + 9.09368i 0.530682 + 1.63327i 0.752798 + 0.658252i \(0.228704\pi\)
−0.222115 + 0.975020i \(0.571296\pi\)
\(32\) 0 0
\(33\) −0.717004 2.20671i −0.124814 0.384139i
\(34\) 0 0
\(35\) 3.41957 1.85767i 0.578013 0.314004i
\(36\) 0 0
\(37\) −4.34199 3.15464i −0.713820 0.518620i 0.170584 0.985343i \(-0.445435\pi\)
−0.884404 + 0.466723i \(0.845435\pi\)
\(38\) 0 0
\(39\) 3.99517 2.90266i 0.639740 0.464798i
\(40\) 0 0
\(41\) 7.05900 + 5.12866i 1.10243 + 0.800963i 0.981455 0.191693i \(-0.0613978\pi\)
0.120975 + 0.992656i \(0.461398\pi\)
\(42\) 0 0
\(43\) 2.86270 0.436558 0.218279 0.975886i \(-0.429956\pi\)
0.218279 + 0.975886i \(0.429956\pi\)
\(44\) 0 0
\(45\) 2.21700 + 0.291365i 0.330491 + 0.0434342i
\(46\) 0 0
\(47\) −2.61505 + 8.04830i −0.381444 + 1.17397i 0.557582 + 0.830122i \(0.311729\pi\)
−0.939027 + 0.343844i \(0.888271\pi\)
\(48\) 0 0
\(49\) −3.97112 −0.567303
\(50\) 0 0
\(51\) −3.74037 −0.523756
\(52\) 0 0
\(53\) −0.415470 + 1.27868i −0.0570691 + 0.175641i −0.975528 0.219876i \(-0.929435\pi\)
0.918459 + 0.395517i \(0.129435\pi\)
\(54\) 0 0
\(55\) 2.23256 4.68338i 0.301038 0.631506i
\(56\) 0 0
\(57\) 1.69364 0.224328
\(58\) 0 0
\(59\) −3.54991 2.57916i −0.462159 0.335778i 0.332219 0.943202i \(-0.392203\pi\)
−0.794378 + 0.607424i \(0.792203\pi\)
\(60\) 0 0
\(61\) 12.4035 9.01166i 1.58810 1.15382i 0.681519 0.731800i \(-0.261319\pi\)
0.906584 0.422025i \(-0.138681\pi\)
\(62\) 0 0
\(63\) 1.40799 + 1.02296i 0.177390 + 0.128881i
\(64\) 0 0
\(65\) 10.9482 + 1.43885i 1.35796 + 0.178468i
\(66\) 0 0
\(67\) 2.85246 + 8.77897i 0.348483 + 1.07252i 0.959692 + 0.281052i \(0.0906835\pi\)
−0.611209 + 0.791469i \(0.709317\pi\)
\(68\) 0 0
\(69\) −2.68186 8.25391i −0.322858 0.993654i
\(70\) 0 0
\(71\) 0.00728184 0.0224112i 0.000864195 0.00265972i −0.950623 0.310347i \(-0.899555\pi\)
0.951488 + 0.307687i \(0.0995549\pi\)
\(72\) 0 0
\(73\) 0.827230 0.601018i 0.0968200 0.0703438i −0.538322 0.842739i \(-0.680942\pi\)
0.635142 + 0.772395i \(0.280942\pi\)
\(74\) 0 0
\(75\) 3.14835 + 3.88431i 0.363541 + 0.448521i
\(76\) 0 0
\(77\) 3.26691 2.37355i 0.372299 0.270491i
\(78\) 0 0
\(79\) −0.246835 + 0.759681i −0.0277711 + 0.0854708i −0.963981 0.265969i \(-0.914308\pi\)
0.936210 + 0.351440i \(0.114308\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 0 0
\(83\) 0.732396 + 2.25408i 0.0803909 + 0.247418i 0.983172 0.182683i \(-0.0584781\pi\)
−0.902781 + 0.430100i \(0.858478\pi\)
\(84\) 0 0
\(85\) −6.06812 5.75583i −0.658180 0.624308i
\(86\) 0 0
\(87\) 2.52602 + 1.83526i 0.270818 + 0.196761i
\(88\) 0 0
\(89\) 3.93348 2.85784i 0.416948 0.302931i −0.359461 0.933160i \(-0.617039\pi\)
0.776409 + 0.630230i \(0.217039\pi\)
\(90\) 0 0
\(91\) 6.95307 + 5.05170i 0.728880 + 0.529562i
\(92\) 0 0
\(93\) −9.56166 −0.991498
\(94\) 0 0
\(95\) 2.74765 + 2.60624i 0.281903 + 0.267395i
\(96\) 0 0
\(97\) −1.06966 + 3.29209i −0.108608 + 0.334261i −0.990560 0.137078i \(-0.956229\pi\)
0.881952 + 0.471339i \(0.156229\pi\)
\(98\) 0 0
\(99\) 2.32027 0.233196
\(100\) 0 0
\(101\) −7.58056 −0.754294 −0.377147 0.926154i \(-0.623095\pi\)
−0.377147 + 0.926154i \(0.623095\pi\)
\(102\) 0 0
\(103\) 3.32808 10.2428i 0.327926 1.00925i −0.642177 0.766556i \(-0.721969\pi\)
0.970103 0.242695i \(-0.0780314\pi\)
\(104\) 0 0
\(105\) 0.710047 + 3.82626i 0.0692935 + 0.373404i
\(106\) 0 0
\(107\) −4.34344 −0.419896 −0.209948 0.977713i \(-0.567329\pi\)
−0.209948 + 0.977713i \(0.567329\pi\)
\(108\) 0 0
\(109\) −0.866675 0.629677i −0.0830125 0.0603121i 0.545505 0.838108i \(-0.316338\pi\)
−0.628517 + 0.777796i \(0.716338\pi\)
\(110\) 0 0
\(111\) 4.34199 3.15464i 0.412124 0.299426i
\(112\) 0 0
\(113\) −15.0167 10.9103i −1.41265 1.02635i −0.992930 0.118699i \(-0.962128\pi\)
−0.419722 0.907653i \(-0.637872\pi\)
\(114\) 0 0
\(115\) 8.35059 17.5176i 0.778697 1.63352i
\(116\) 0 0
\(117\) 1.52602 + 4.69661i 0.141081 + 0.434202i
\(118\) 0 0
\(119\) −2.01158 6.19101i −0.184401 0.567529i
\(120\) 0 0
\(121\) −1.73554 + 5.34145i −0.157777 + 0.485586i
\(122\) 0 0
\(123\) −7.05900 + 5.12866i −0.636488 + 0.462436i
\(124\) 0 0
\(125\) −0.869658 + 11.1465i −0.0777846 + 0.996970i
\(126\) 0 0
\(127\) −15.3791 + 11.1735i −1.36467 + 0.991492i −0.366540 + 0.930402i \(0.619458\pi\)
−0.998132 + 0.0610897i \(0.980542\pi\)
\(128\) 0 0
\(129\) −0.884623 + 2.72259i −0.0778867 + 0.239711i
\(130\) 0 0
\(131\) −0.230228 0.708567i −0.0201151 0.0619078i 0.940495 0.339807i \(-0.110362\pi\)
−0.960610 + 0.277899i \(0.910362\pi\)
\(132\) 0 0
\(133\) 0.910845 + 2.80329i 0.0789803 + 0.243076i
\(134\) 0 0
\(135\) −0.962197 + 2.01846i −0.0828127 + 0.173721i
\(136\) 0 0
\(137\) 9.00643 + 6.54355i 0.769471 + 0.559054i 0.901801 0.432152i \(-0.142246\pi\)
−0.132329 + 0.991206i \(0.542246\pi\)
\(138\) 0 0
\(139\) −11.0746 + 8.04613i −0.939331 + 0.682464i −0.948260 0.317496i \(-0.897158\pi\)
0.00892821 + 0.999960i \(0.497158\pi\)
\(140\) 0 0
\(141\) −6.84629 4.97412i −0.576562 0.418897i
\(142\) 0 0
\(143\) 11.4582 0.958185
\(144\) 0 0
\(145\) 1.27387 + 6.86455i 0.105789 + 0.570070i
\(146\) 0 0
\(147\) 1.22714 3.77676i 0.101213 0.311502i
\(148\) 0 0
\(149\) −10.6283 −0.870701 −0.435351 0.900261i \(-0.643376\pi\)
−0.435351 + 0.900261i \(0.643376\pi\)
\(150\) 0 0
\(151\) −10.4689 −0.851943 −0.425972 0.904737i \(-0.640068\pi\)
−0.425972 + 0.904737i \(0.640068\pi\)
\(152\) 0 0
\(153\) 1.15584 3.55730i 0.0934439 0.287591i
\(154\) 0 0
\(155\) −15.5122 14.7139i −1.24597 1.18185i
\(156\) 0 0
\(157\) −17.2987 −1.38059 −0.690295 0.723528i \(-0.742519\pi\)
−0.690295 + 0.723528i \(0.742519\pi\)
\(158\) 0 0
\(159\) −1.08771 0.790270i −0.0862613 0.0626725i
\(160\) 0 0
\(161\) 12.2195 8.87796i 0.963028 0.699681i
\(162\) 0 0
\(163\) 4.97293 + 3.61304i 0.389510 + 0.282995i 0.765255 0.643728i \(-0.222613\pi\)
−0.375745 + 0.926723i \(0.622613\pi\)
\(164\) 0 0
\(165\) 3.76426 + 3.57053i 0.293047 + 0.277966i
\(166\) 0 0
\(167\) −0.587188 1.80718i −0.0454379 0.139844i 0.925764 0.378103i \(-0.123423\pi\)
−0.971202 + 0.238259i \(0.923423\pi\)
\(168\) 0 0
\(169\) 3.51874 + 10.8296i 0.270672 + 0.833043i
\(170\) 0 0
\(171\) −0.523364 + 1.61075i −0.0400226 + 0.123177i
\(172\) 0 0
\(173\) −9.37317 + 6.81000i −0.712629 + 0.517755i −0.884021 0.467448i \(-0.845174\pi\)
0.171392 + 0.985203i \(0.445174\pi\)
\(174\) 0 0
\(175\) −4.73607 + 7.30011i −0.358013 + 0.551837i
\(176\) 0 0
\(177\) 3.54991 2.57916i 0.266828 0.193862i
\(178\) 0 0
\(179\) 6.81312 20.9686i 0.509236 1.56727i −0.284294 0.958737i \(-0.591759\pi\)
0.793530 0.608531i \(-0.208241\pi\)
\(180\) 0 0
\(181\) 6.38341 + 19.6461i 0.474475 + 1.46028i 0.846665 + 0.532127i \(0.178607\pi\)
−0.372190 + 0.928157i \(0.621393\pi\)
\(182\) 0 0
\(183\) 4.73771 + 14.5812i 0.350222 + 1.07787i
\(184\) 0 0
\(185\) 11.8987 + 1.56376i 0.874807 + 0.114970i
\(186\) 0 0
\(187\) −7.02120 5.10120i −0.513441 0.373036i
\(188\) 0 0
\(189\) −1.40799 + 1.02296i −0.102416 + 0.0744096i
\(190\) 0 0
\(191\) −16.8535 12.2448i −1.21948 0.886004i −0.223423 0.974722i \(-0.571723\pi\)
−0.996057 + 0.0887181i \(0.971723\pi\)
\(192\) 0 0
\(193\) 4.78053 0.344110 0.172055 0.985087i \(-0.444959\pi\)
0.172055 + 0.985087i \(0.444959\pi\)
\(194\) 0 0
\(195\) −4.75162 + 9.96777i −0.340271 + 0.713807i
\(196\) 0 0
\(197\) 5.36207 16.5028i 0.382032 1.17577i −0.556579 0.830795i \(-0.687886\pi\)
0.938611 0.344978i \(-0.112114\pi\)
\(198\) 0 0
\(199\) 11.0756 0.785129 0.392564 0.919724i \(-0.371588\pi\)
0.392564 + 0.919724i \(0.371588\pi\)
\(200\) 0 0
\(201\) −9.23075 −0.651087
\(202\) 0 0
\(203\) −1.67920 + 5.16805i −0.117857 + 0.362726i
\(204\) 0 0
\(205\) −19.3443 2.54228i −1.35106 0.177561i
\(206\) 0 0
\(207\) 8.67867 0.603210
\(208\) 0 0
\(209\) 3.17920 + 2.30982i 0.219910 + 0.159774i
\(210\) 0 0
\(211\) −4.58634 + 3.33217i −0.315736 + 0.229396i −0.734354 0.678767i \(-0.762515\pi\)
0.418618 + 0.908163i \(0.362515\pi\)
\(212\) 0 0
\(213\) 0.0190641 + 0.0138509i 0.00130625 + 0.000949047i
\(214\) 0 0
\(215\) −5.62479 + 3.05565i −0.383607 + 0.208394i
\(216\) 0 0
\(217\) −5.14229 15.8263i −0.349081 1.07436i
\(218\) 0 0
\(219\) 0.315974 + 0.972467i 0.0213515 + 0.0657132i
\(220\) 0 0
\(221\) 5.70788 17.5670i 0.383953 1.18169i
\(222\) 0 0
\(223\) 17.2972 12.5671i 1.15831 0.841559i 0.168743 0.985660i \(-0.446029\pi\)
0.989563 + 0.144101i \(0.0460292\pi\)
\(224\) 0 0
\(225\) −4.66709 + 1.79395i −0.311140 + 0.119596i
\(226\) 0 0
\(227\) 18.5770 13.4970i 1.23300 0.895827i 0.235888 0.971780i \(-0.424200\pi\)
0.997111 + 0.0759536i \(0.0242001\pi\)
\(228\) 0 0
\(229\) −8.68482 + 26.7291i −0.573909 + 1.76631i 0.0659560 + 0.997823i \(0.478990\pi\)
−0.639865 + 0.768487i \(0.721010\pi\)
\(230\) 0 0
\(231\) 1.24785 + 3.84049i 0.0821025 + 0.252686i
\(232\) 0 0
\(233\) −0.411596 1.26676i −0.0269646 0.0829885i 0.936669 0.350217i \(-0.113892\pi\)
−0.963633 + 0.267229i \(0.913892\pi\)
\(234\) 0 0
\(235\) −3.45258 18.6051i −0.225222 1.21366i
\(236\) 0 0
\(237\) −0.646223 0.469509i −0.0419767 0.0304979i
\(238\) 0 0
\(239\) −2.78730 + 2.02509i −0.180295 + 0.130992i −0.674272 0.738483i \(-0.735543\pi\)
0.493977 + 0.869475i \(0.335543\pi\)
\(240\) 0 0
\(241\) 19.4923 + 14.1620i 1.25561 + 0.912253i 0.998533 0.0541389i \(-0.0172414\pi\)
0.257075 + 0.966392i \(0.417241\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 7.80267 4.23878i 0.498495 0.270806i
\(246\) 0 0
\(247\) −2.58453 + 7.95437i −0.164450 + 0.506124i
\(248\) 0 0
\(249\) −2.37008 −0.150198
\(250\) 0 0
\(251\) −30.1621 −1.90381 −0.951907 0.306387i \(-0.900880\pi\)
−0.951907 + 0.306387i \(0.900880\pi\)
\(252\) 0 0
\(253\) 6.22264 19.1513i 0.391214 1.20403i
\(254\) 0 0
\(255\) 7.34928 3.99248i 0.460230 0.250019i
\(256\) 0 0
\(257\) 10.6862 0.666588 0.333294 0.942823i \(-0.391840\pi\)
0.333294 + 0.942823i \(0.391840\pi\)
\(258\) 0 0
\(259\) 7.55667 + 5.49024i 0.469548 + 0.341147i
\(260\) 0 0
\(261\) −2.52602 + 1.83526i −0.156357 + 0.113600i
\(262\) 0 0
\(263\) −7.46948 5.42689i −0.460588 0.334637i 0.333174 0.942865i \(-0.391880\pi\)
−0.793762 + 0.608229i \(0.791880\pi\)
\(264\) 0 0
\(265\) −0.548533 2.95590i −0.0336961 0.181580i
\(266\) 0 0
\(267\) 1.50246 + 4.62409i 0.0919488 + 0.282989i
\(268\) 0 0
\(269\) 8.26252 + 25.4294i 0.503774 + 1.55046i 0.802821 + 0.596220i \(0.203331\pi\)
−0.299047 + 0.954238i \(0.596669\pi\)
\(270\) 0 0
\(271\) 7.47325 23.0003i 0.453968 1.39717i −0.418375 0.908274i \(-0.637400\pi\)
0.872343 0.488895i \(-0.162600\pi\)
\(272\) 0 0
\(273\) −6.95307 + 5.05170i −0.420819 + 0.305743i
\(274\) 0 0
\(275\) 0.612394 + 11.5852i 0.0369288 + 0.698613i
\(276\) 0 0
\(277\) 25.5713 18.5787i 1.53643 1.11628i 0.583909 0.811819i \(-0.301523\pi\)
0.952524 0.304464i \(-0.0984775\pi\)
\(278\) 0 0
\(279\) 2.95471 9.09368i 0.176894 0.544424i
\(280\) 0 0
\(281\) 7.18851 + 22.1240i 0.428831 + 1.31981i 0.899278 + 0.437377i \(0.144093\pi\)
−0.470447 + 0.882428i \(0.655907\pi\)
\(282\) 0 0
\(283\) 7.67355 + 23.6167i 0.456145 + 1.40387i 0.869786 + 0.493430i \(0.164257\pi\)
−0.413641 + 0.910440i \(0.635743\pi\)
\(284\) 0 0
\(285\) −3.32776 + 1.80780i −0.197119 + 0.107085i
\(286\) 0 0
\(287\) −12.2853 8.92576i −0.725175 0.526871i
\(288\) 0 0
\(289\) 2.43486 1.76903i 0.143227 0.104060i
\(290\) 0 0
\(291\) −2.80042 2.03462i −0.164163 0.119272i
\(292\) 0 0
\(293\) 29.2758 1.71031 0.855156 0.518371i \(-0.173461\pi\)
0.855156 + 0.518371i \(0.173461\pi\)
\(294\) 0 0
\(295\) 9.72806 + 1.27849i 0.566390 + 0.0744366i
\(296\) 0 0
\(297\) −0.717004 + 2.20671i −0.0416048 + 0.128046i
\(298\) 0 0
\(299\) 42.8580 2.47854
\(300\) 0 0
\(301\) −4.98215 −0.287166
\(302\) 0 0
\(303\) 2.34252 7.20954i 0.134574 0.414177i
\(304\) 0 0
\(305\) −14.7520 + 30.9461i −0.844695 + 1.77197i
\(306\) 0 0
\(307\) 8.73972 0.498802 0.249401 0.968400i \(-0.419766\pi\)
0.249401 + 0.968400i \(0.419766\pi\)
\(308\) 0 0
\(309\) 8.71303 + 6.33039i 0.495667 + 0.360123i
\(310\) 0 0
\(311\) 12.5043 9.08488i 0.709052 0.515156i −0.173816 0.984778i \(-0.555610\pi\)
0.882868 + 0.469622i \(0.155610\pi\)
\(312\) 0 0
\(313\) 1.26124 + 0.916343i 0.0712894 + 0.0517948i 0.622859 0.782334i \(-0.285971\pi\)
−0.551570 + 0.834129i \(0.685971\pi\)
\(314\) 0 0
\(315\) −3.85840 0.507083i −0.217396 0.0285709i
\(316\) 0 0
\(317\) −1.68802 5.19520i −0.0948088 0.291792i 0.892395 0.451255i \(-0.149024\pi\)
−0.987204 + 0.159464i \(0.949024\pi\)
\(318\) 0 0
\(319\) 2.23873 + 6.89009i 0.125345 + 0.385771i
\(320\) 0 0
\(321\) 1.34220 4.13085i 0.0749140 0.230562i
\(322\) 0 0
\(323\) 5.12499 3.72352i 0.285162 0.207182i
\(324\) 0 0
\(325\) −23.0475 + 8.85905i −1.27845 + 0.491412i
\(326\) 0 0
\(327\) 0.866675 0.629677i 0.0479273 0.0348212i
\(328\) 0 0
\(329\) 4.55115 14.0070i 0.250913 0.772231i
\(330\) 0 0
\(331\) 0.264458 + 0.813918i 0.0145359 + 0.0447370i 0.958061 0.286563i \(-0.0925128\pi\)
−0.943525 + 0.331300i \(0.892513\pi\)
\(332\) 0 0
\(333\) 1.65849 + 5.10432i 0.0908849 + 0.279715i
\(334\) 0 0
\(335\) −14.9754 14.2047i −0.818191 0.776084i
\(336\) 0 0
\(337\) −11.9933 8.71367i −0.653318 0.474664i 0.211082 0.977468i \(-0.432301\pi\)
−0.864400 + 0.502805i \(0.832301\pi\)
\(338\) 0 0
\(339\) 15.0167 10.9103i 0.815595 0.592564i
\(340\) 0 0
\(341\) −17.9486 13.0404i −0.971970 0.706177i
\(342\) 0 0
\(343\) 19.0938 1.03097
\(344\) 0 0
\(345\) 14.0797 + 13.3551i 0.758026 + 0.719015i
\(346\) 0 0
\(347\) −0.361763 + 1.11339i −0.0194204 + 0.0597700i −0.960297 0.278979i \(-0.910004\pi\)
0.940877 + 0.338749i \(0.110004\pi\)
\(348\) 0 0
\(349\) −21.4346 −1.14737 −0.573683 0.819077i \(-0.694486\pi\)
−0.573683 + 0.819077i \(0.694486\pi\)
\(350\) 0 0
\(351\) −4.93831 −0.263587
\(352\) 0 0
\(353\) −1.10094 + 3.38834i −0.0585970 + 0.180343i −0.976071 0.217453i \(-0.930225\pi\)
0.917474 + 0.397796i \(0.130225\pi\)
\(354\) 0 0
\(355\) 0.00961402 + 0.0518074i 0.000510259 + 0.00274965i
\(356\) 0 0
\(357\) 6.50961 0.344525
\(358\) 0 0
\(359\) −10.8337 7.87116i −0.571782 0.415424i 0.263970 0.964531i \(-0.414968\pi\)
−0.835752 + 0.549107i \(0.814968\pi\)
\(360\) 0 0
\(361\) 13.0507 9.48191i 0.686880 0.499048i
\(362\) 0 0
\(363\) −4.54371 3.30120i −0.238483 0.173268i
\(364\) 0 0
\(365\) −0.983858 + 2.06390i −0.0514975 + 0.108029i
\(366\) 0 0
\(367\) −0.440150 1.35464i −0.0229757 0.0707118i 0.938911 0.344159i \(-0.111836\pi\)
−0.961887 + 0.273447i \(0.911836\pi\)
\(368\) 0 0
\(369\) −2.69630 8.29835i −0.140364 0.431995i
\(370\) 0 0
\(371\) 0.723070 2.22538i 0.0375399 0.115536i
\(372\) 0 0
\(373\) −20.6564 + 15.0077i −1.06955 + 0.777072i −0.975831 0.218527i \(-0.929875\pi\)
−0.0937165 + 0.995599i \(0.529875\pi\)
\(374\) 0 0
\(375\) −10.3322 4.27154i −0.533551 0.220581i
\(376\) 0 0
\(377\) −12.4743 + 9.06309i −0.642457 + 0.466773i
\(378\) 0 0
\(379\) −11.7671 + 36.2153i −0.604434 + 1.86026i −0.103800 + 0.994598i \(0.533100\pi\)
−0.500634 + 0.865659i \(0.666900\pi\)
\(380\) 0 0
\(381\) −5.87428 18.0792i −0.300949 0.926225i
\(382\) 0 0
\(383\) 4.21946 + 12.9862i 0.215604 + 0.663562i 0.999110 + 0.0421775i \(0.0134295\pi\)
−0.783506 + 0.621384i \(0.786571\pi\)
\(384\) 0 0
\(385\) −3.88547 + 8.15080i −0.198022 + 0.415403i
\(386\) 0 0
\(387\) −2.31597 1.68265i −0.117728 0.0855341i
\(388\) 0 0
\(389\) −28.9546 + 21.0368i −1.46806 + 1.06661i −0.486888 + 0.873465i \(0.661868\pi\)
−0.981171 + 0.193142i \(0.938132\pi\)
\(390\) 0 0
\(391\) −26.2619 19.0804i −1.32812 0.964935i
\(392\) 0 0
\(393\) 0.745032 0.0375819
\(394\) 0 0
\(395\) −0.325890 1.75613i −0.0163973 0.0883607i
\(396\) 0 0
\(397\) 7.58400 23.3412i 0.380630 1.17146i −0.558971 0.829187i \(-0.688804\pi\)
0.939601 0.342272i \(-0.111196\pi\)
\(398\) 0 0
\(399\) −2.94756 −0.147562
\(400\) 0 0
\(401\) −25.7068 −1.28373 −0.641867 0.766816i \(-0.721840\pi\)
−0.641867 + 0.766816i \(0.721840\pi\)
\(402\) 0 0
\(403\) 14.5913 44.9074i 0.726844 2.23700i
\(404\) 0 0
\(405\) −1.62233 1.53884i −0.0806144 0.0764657i
\(406\) 0 0
\(407\) 12.4529 0.617268
\(408\) 0 0
\(409\) 15.0121 + 10.9069i 0.742299 + 0.539312i 0.893430 0.449202i \(-0.148292\pi\)
−0.151131 + 0.988514i \(0.548292\pi\)
\(410\) 0 0
\(411\) −9.00643 + 6.54355i −0.444254 + 0.322770i
\(412\) 0 0
\(413\) 6.17815 + 4.48869i 0.304007 + 0.220874i
\(414\) 0 0
\(415\) −3.84506 3.64718i −0.188747 0.179033i
\(416\) 0 0
\(417\) −4.23010 13.0189i −0.207149 0.637539i
\(418\) 0 0
\(419\) 1.45029 + 4.46354i 0.0708513 + 0.218058i 0.980212 0.197951i \(-0.0634286\pi\)
−0.909361 + 0.416009i \(0.863429\pi\)
\(420\) 0 0
\(421\) 2.84929 8.76921i 0.138866 0.427385i −0.857305 0.514808i \(-0.827863\pi\)
0.996171 + 0.0874228i \(0.0278631\pi\)
\(422\) 0 0
\(423\) 6.84629 4.97412i 0.332878 0.241850i
\(424\) 0 0
\(425\) 18.0668 + 4.83224i 0.876367 + 0.234398i
\(426\) 0 0
\(427\) −21.5866 + 15.6836i −1.04465 + 0.758983i
\(428\) 0 0
\(429\) −3.54079 + 10.8974i −0.170951 + 0.526132i
\(430\) 0 0
\(431\) 8.83198 + 27.1820i 0.425421 + 1.30931i 0.902590 + 0.430501i \(0.141663\pi\)
−0.477169 + 0.878812i \(0.658337\pi\)
\(432\) 0 0
\(433\) 1.12286 + 3.45581i 0.0539612 + 0.166075i 0.974405 0.224799i \(-0.0721726\pi\)
−0.920444 + 0.390875i \(0.872173\pi\)
\(434\) 0 0
\(435\) −6.92223 0.909740i −0.331895 0.0436187i
\(436\) 0 0
\(437\) 11.8914 + 8.63959i 0.568842 + 0.413288i
\(438\) 0 0
\(439\) 14.2446 10.3493i 0.679859 0.493947i −0.193452 0.981110i \(-0.561968\pi\)
0.873311 + 0.487163i \(0.161968\pi\)
\(440\) 0 0
\(441\) 3.21270 + 2.33417i 0.152986 + 0.111151i
\(442\) 0 0
\(443\) 7.11807 0.338190 0.169095 0.985600i \(-0.445916\pi\)
0.169095 + 0.985600i \(0.445916\pi\)
\(444\) 0 0
\(445\) −4.67825 + 9.81385i −0.221770 + 0.465221i
\(446\) 0 0
\(447\) 3.28431 10.1081i 0.155343 0.478096i
\(448\) 0 0
\(449\) −20.4121 −0.963305 −0.481653 0.876362i \(-0.659963\pi\)
−0.481653 + 0.876362i \(0.659963\pi\)
\(450\) 0 0
\(451\) −20.2453 −0.953315
\(452\) 0 0
\(453\) 3.23505 9.95647i 0.151996 0.467796i
\(454\) 0 0
\(455\) −19.0540 2.50413i −0.893264 0.117395i
\(456\) 0 0
\(457\) −16.8375 −0.787624 −0.393812 0.919191i \(-0.628844\pi\)
−0.393812 + 0.919191i \(0.628844\pi\)
\(458\) 0 0
\(459\) 3.02602 + 2.19853i 0.141243 + 0.102619i
\(460\) 0 0
\(461\) −14.0162 + 10.1833i −0.652798 + 0.474286i −0.864223 0.503109i \(-0.832190\pi\)
0.211425 + 0.977394i \(0.432190\pi\)
\(462\) 0 0
\(463\) −6.96088 5.05738i −0.323500 0.235036i 0.414168 0.910201i \(-0.364073\pi\)
−0.737667 + 0.675164i \(0.764073\pi\)
\(464\) 0 0
\(465\) 18.7873 10.2061i 0.871238 0.473298i
\(466\) 0 0
\(467\) 0.258292 + 0.794942i 0.0119523 + 0.0367855i 0.956855 0.290566i \(-0.0938437\pi\)
−0.944902 + 0.327352i \(0.893844\pi\)
\(468\) 0 0
\(469\) −4.96433 15.2786i −0.229231 0.705502i
\(470\) 0 0
\(471\) 5.34560 16.4521i 0.246312 0.758072i
\(472\) 0 0
\(473\) −5.37369 + 3.90422i −0.247083 + 0.179516i
\(474\) 0 0
\(475\) −8.18064 2.18804i −0.375354 0.100394i
\(476\) 0 0
\(477\) 1.08771 0.790270i 0.0498030 0.0361840i
\(478\) 0 0
\(479\) −10.3365 + 31.8123i −0.472285 + 1.45354i 0.377300 + 0.926091i \(0.376853\pi\)
−0.849585 + 0.527452i \(0.823147\pi\)
\(480\) 0 0
\(481\) 8.19015 + 25.2067i 0.373439 + 1.14933i
\(482\) 0 0
\(483\) 4.66742 + 14.3648i 0.212375 + 0.653623i
\(484\) 0 0
\(485\) −1.41225 7.61024i −0.0641269 0.345563i
\(486\) 0 0
\(487\) 19.7528 + 14.3512i 0.895083 + 0.650316i 0.937198 0.348797i \(-0.113410\pi\)
−0.0421152 + 0.999113i \(0.513410\pi\)
\(488\) 0 0
\(489\) −4.97293 + 3.61304i −0.224884 + 0.163387i
\(490\) 0 0
\(491\) 11.8501 + 8.60958i 0.534786 + 0.388545i 0.822145 0.569278i \(-0.192777\pi\)
−0.287359 + 0.957823i \(0.592777\pi\)
\(492\) 0 0
\(493\) 11.6787 0.525981
\(494\) 0 0
\(495\) −4.55900 + 2.47667i −0.204912 + 0.111318i
\(496\) 0 0
\(497\) −0.0126731 + 0.0390037i −0.000568465 + 0.00174956i
\(498\) 0 0
\(499\) −13.5655 −0.607276 −0.303638 0.952787i \(-0.598201\pi\)
−0.303638 + 0.952787i \(0.598201\pi\)
\(500\) 0 0
\(501\) 1.90018 0.0848937
\(502\) 0 0
\(503\) −12.6475 + 38.9250i −0.563924 + 1.73558i 0.107202 + 0.994237i \(0.465811\pi\)
−0.671126 + 0.741343i \(0.734189\pi\)
\(504\) 0 0
\(505\) 14.8947 8.09151i 0.662805 0.360067i
\(506\) 0 0
\(507\) −11.3869 −0.505709
\(508\) 0 0
\(509\) −9.82240 7.13639i −0.435370 0.316315i 0.348422 0.937338i \(-0.386718\pi\)
−0.783793 + 0.621023i \(0.786718\pi\)
\(510\) 0 0
\(511\) −1.43968 + 1.04599i −0.0636879 + 0.0462720i
\(512\) 0 0
\(513\) −1.37018 0.995497i −0.0604951 0.0439523i
\(514\) 0 0
\(515\) 4.39398 + 23.6780i 0.193622 + 1.04338i
\(516\) 0 0
\(517\) −6.06763 18.6743i −0.266854 0.821293i
\(518\) 0 0
\(519\) −3.58023 11.0188i −0.157155 0.483672i
\(520\) 0 0
\(521\) 8.10398 24.9415i 0.355042 1.09271i −0.600943 0.799292i \(-0.705208\pi\)
0.955985 0.293415i \(-0.0947918\pi\)
\(522\) 0 0
\(523\) −12.3978 + 9.00754i −0.542118 + 0.393872i −0.824871 0.565321i \(-0.808752\pi\)
0.282753 + 0.959193i \(0.408752\pi\)
\(524\) 0 0
\(525\) −5.47929 6.76013i −0.239136 0.295036i
\(526\) 0 0
\(527\) −28.9338 + 21.0216i −1.26037 + 0.915716i
\(528\) 0 0
\(529\) 16.1676 49.7587i 0.702938 2.16342i
\(530\) 0 0
\(531\) 1.35595 + 4.17317i 0.0588430 + 0.181100i
\(532\) 0 0
\(533\) −13.3151 40.9798i −0.576743 1.77503i
\(534\) 0 0
\(535\) 8.53422 4.63619i 0.368966 0.200440i
\(536\) 0 0
\(537\) 17.8370 + 12.9593i 0.769722 + 0.559236i
\(538\) 0 0
\(539\) 7.45435 5.41590i 0.321082 0.233279i
\(540\) 0 0
\(541\) −7.66742 5.57071i −0.329648 0.239503i 0.410633 0.911801i \(-0.365308\pi\)
−0.740281 + 0.672297i \(0.765308\pi\)
\(542\) 0 0
\(543\) −20.6571 −0.886483
\(544\) 0 0
\(545\) 2.37501 + 0.312131i 0.101734 + 0.0133702i
\(546\) 0 0
\(547\) 0.199605 0.614321i 0.00853449 0.0262665i −0.946699 0.322121i \(-0.895604\pi\)
0.955233 + 0.295854i \(0.0956043\pi\)
\(548\) 0 0
\(549\) −15.3316 −0.654335
\(550\) 0 0
\(551\) −5.28811 −0.225281
\(552\) 0 0
\(553\) 0.429584 1.32212i 0.0182678 0.0562224i
\(554\) 0 0
\(555\) −5.16411 + 10.8331i −0.219204 + 0.459838i
\(556\) 0 0
\(557\) −12.0297 −0.509716 −0.254858 0.966978i \(-0.582029\pi\)
−0.254858 + 0.966978i \(0.582029\pi\)
\(558\) 0 0
\(559\) −11.4370 8.30946i −0.483733 0.351453i
\(560\) 0 0
\(561\) 7.02120 5.10120i 0.296435 0.215373i
\(562\) 0 0
\(563\) −12.8498 9.33593i −0.541555 0.393462i 0.283107 0.959088i \(-0.408635\pi\)
−0.824662 + 0.565626i \(0.808635\pi\)
\(564\) 0 0
\(565\) 41.1513 + 5.40822i 1.73125 + 0.227526i
\(566\) 0 0
\(567\) −0.537803 1.65519i −0.0225856 0.0695114i
\(568\) 0 0
\(569\) 6.77685 + 20.8570i 0.284100 + 0.874371i 0.986667 + 0.162753i \(0.0520374\pi\)
−0.702566 + 0.711618i \(0.747963\pi\)
\(570\) 0 0
\(571\) −2.10390 + 6.47513i −0.0880453 + 0.270976i −0.985379 0.170377i \(-0.945501\pi\)
0.897334 + 0.441353i \(0.145501\pi\)
\(572\) 0 0
\(573\) 16.8535 12.2448i 0.704067 0.511534i
\(574\) 0 0
\(575\) 2.29058 + 43.3329i 0.0955238 + 1.80711i
\(576\) 0 0
\(577\) −15.0698 + 10.9488i −0.627364 + 0.455806i −0.855486 0.517826i \(-0.826741\pi\)
0.228122 + 0.973632i \(0.426741\pi\)
\(578\) 0 0
\(579\) −1.47726 + 4.54655i −0.0613930 + 0.188948i
\(580\) 0 0
\(581\) −1.27464 3.92293i −0.0528809 0.162751i
\(582\) 0 0
\(583\) −0.964003 2.96690i −0.0399249 0.122876i
\(584\) 0 0
\(585\) −8.01158 7.59927i −0.331238 0.314191i
\(586\) 0 0
\(587\) 11.4963 + 8.35254i 0.474503 + 0.344746i 0.799194 0.601074i \(-0.205260\pi\)
−0.324691 + 0.945820i \(0.605260\pi\)
\(588\) 0 0
\(589\) 13.1012 9.51860i 0.539827 0.392207i
\(590\) 0 0
\(591\) 14.0381 + 10.1993i 0.577450 + 0.419542i
\(592\) 0 0
\(593\) 40.7850 1.67484 0.837420 0.546559i \(-0.184063\pi\)
0.837420 + 0.546559i \(0.184063\pi\)
\(594\) 0 0
\(595\) 10.5608 + 10.0173i 0.432949 + 0.410668i
\(596\) 0 0
\(597\) −3.42255 + 10.5335i −0.140076 + 0.431109i
\(598\) 0 0
\(599\) 34.8928 1.42568 0.712841 0.701326i \(-0.247408\pi\)
0.712841 + 0.701326i \(0.247408\pi\)
\(600\) 0 0
\(601\) 10.6287 0.433552 0.216776 0.976221i \(-0.430446\pi\)
0.216776 + 0.976221i \(0.430446\pi\)
\(602\) 0 0
\(603\) 2.85246 8.77897i 0.116161 0.357507i
\(604\) 0 0
\(605\) −2.29139 12.3477i −0.0931582 0.502005i
\(606\) 0 0
\(607\) 30.5033 1.23809 0.619045 0.785355i \(-0.287520\pi\)
0.619045 + 0.785355i \(0.287520\pi\)
\(608\) 0 0
\(609\) −4.39620 3.19403i −0.178143 0.129429i
\(610\) 0 0
\(611\) 33.8091 24.5638i 1.36777 0.993743i
\(612\) 0 0
\(613\) 10.3337 + 7.50789i 0.417375 + 0.303241i 0.776581 0.630018i \(-0.216952\pi\)
−0.359206 + 0.933258i \(0.616952\pi\)
\(614\) 0 0
\(615\) 8.39555 17.6119i 0.338541 0.710179i
\(616\) 0 0
\(617\) −3.68740 11.3486i −0.148449 0.456879i 0.848989 0.528410i \(-0.177212\pi\)
−0.997438 + 0.0715308i \(0.977212\pi\)
\(618\) 0 0
\(619\) −4.48215 13.7946i −0.180153 0.554454i 0.819678 0.572824i \(-0.194152\pi\)
−0.999831 + 0.0183705i \(0.994152\pi\)
\(620\) 0 0
\(621\) −2.68186 + 8.25391i −0.107619 + 0.331218i
\(622\) 0 0
\(623\) −6.84570 + 4.97369i −0.274267 + 0.199267i
\(624\) 0 0
\(625\) −10.1890 22.8295i −0.407561 0.913178i
\(626\) 0 0
\(627\) −3.17920 + 2.30982i −0.126965 + 0.0922455i
\(628\) 0 0
\(629\) 6.20338 19.0920i 0.247345 0.761249i
\(630\) 0 0
\(631\) −1.13341 3.48828i −0.0451204 0.138866i 0.925958 0.377626i \(-0.123259\pi\)
−0.971079 + 0.238759i \(0.923259\pi\)
\(632\) 0 0
\(633\) −1.75182 5.39156i −0.0696288 0.214295i
\(634\) 0 0
\(635\) 18.2910 38.3701i 0.725854 1.52267i
\(636\) 0 0
\(637\) 15.8653 + 11.5268i 0.628607 + 0.456710i
\(638\) 0 0
\(639\) −0.0190641 + 0.0138509i −0.000754164 + 0.000547932i
\(640\) 0 0
\(641\) 11.2064 + 8.14192i 0.442626 + 0.321587i 0.786678 0.617364i \(-0.211799\pi\)
−0.344051 + 0.938951i \(0.611799\pi\)
\(642\) 0 0
\(643\) −27.1641 −1.07125 −0.535624 0.844456i \(-0.679924\pi\)
−0.535624 + 0.844456i \(0.679924\pi\)
\(644\) 0 0
\(645\) −1.16794 6.29374i −0.0459878 0.247816i
\(646\) 0 0
\(647\) −1.59140 + 4.89783i −0.0625644 + 0.192553i −0.977453 0.211153i \(-0.932278\pi\)
0.914889 + 0.403706i \(0.132278\pi\)
\(648\) 0 0
\(649\) 10.1812 0.399647
\(650\) 0 0
\(651\) 16.6408 0.652204
\(652\) 0 0
\(653\) −9.16957 + 28.2210i −0.358833 + 1.10437i 0.594920 + 0.803785i \(0.297184\pi\)
−0.953753 + 0.300590i \(0.902816\pi\)
\(654\) 0 0
\(655\) 1.20869 + 1.14649i 0.0472274 + 0.0447969i
\(656\) 0 0
\(657\) −1.02251 −0.0398920
\(658\) 0 0
\(659\) −12.7614 9.27170i −0.497114 0.361174i 0.310800 0.950475i \(-0.399403\pi\)
−0.807913 + 0.589301i \(0.799403\pi\)
\(660\) 0 0
\(661\) 19.4614 14.1396i 0.756962 0.549965i −0.141015 0.990007i \(-0.545037\pi\)
0.897977 + 0.440042i \(0.145037\pi\)
\(662\) 0 0
\(663\) 14.9434 + 10.8570i 0.580354 + 0.421652i
\(664\) 0 0
\(665\) −4.78192 4.53582i −0.185435 0.175892i
\(666\) 0 0
\(667\) 8.37366 + 25.7715i 0.324229 + 0.997875i
\(668\) 0 0
\(669\) 6.60694 + 20.3341i 0.255439 + 0.786161i
\(670\) 0 0
\(671\) −10.9928 + 33.8323i −0.424372 + 1.30608i
\(672\) 0 0
\(673\) −25.8914 + 18.8112i −0.998040 + 0.725119i −0.961667 0.274220i \(-0.911580\pi\)
−0.0363731 + 0.999338i \(0.511580\pi\)
\(674\) 0 0
\(675\) −0.263932 4.99303i −0.0101587 0.192182i
\(676\) 0 0
\(677\) 19.7246 14.3307i 0.758077 0.550775i −0.140243 0.990117i \(-0.544788\pi\)
0.898320 + 0.439342i \(0.144788\pi\)
\(678\) 0 0
\(679\) 1.86161 5.72944i 0.0714420 0.219876i
\(680\) 0 0
\(681\) 7.09579 + 21.8386i 0.271911 + 0.836856i
\(682\) 0 0
\(683\) −3.44642 10.6070i −0.131873 0.405865i 0.863217 0.504833i \(-0.168446\pi\)
−0.995091 + 0.0989680i \(0.968446\pi\)
\(684\) 0 0
\(685\) −24.6809 3.24364i −0.943010 0.123933i
\(686\) 0 0
\(687\) −22.7371 16.5195i −0.867476 0.630258i
\(688\) 0 0
\(689\) 5.37146 3.90260i 0.204636 0.148677i
\(690\) 0 0
\(691\) −8.76055 6.36491i −0.333267 0.242133i 0.408549 0.912737i \(-0.366035\pi\)
−0.741816 + 0.670604i \(0.766035\pi\)
\(692\) 0 0
\(693\) −4.03813 −0.153396
\(694\) 0 0
\(695\) 13.1714 27.6305i 0.499620 1.04808i
\(696\) 0 0
\(697\) −10.0851 + 31.0389i −0.382002 + 1.17568i
\(698\) 0 0
\(699\) 1.33195 0.0503791
\(700\) 0 0
\(701\) 43.2512 1.63357 0.816787 0.576939i \(-0.195753\pi\)
0.816787 + 0.576939i \(0.195753\pi\)
\(702\) 0 0
\(703\) −2.80889 + 8.64488i −0.105939 + 0.326048i
\(704\) 0 0
\(705\) 18.7614 + 2.46568i 0.706594 + 0.0928627i
\(706\) 0 0
\(707\) 13.1930 0.496172
\(708\) 0 0
\(709\) 36.0864 + 26.2183i 1.35525 + 0.984649i 0.998731 + 0.0503617i \(0.0160374\pi\)
0.356522 + 0.934287i \(0.383963\pi\)
\(710\) 0 0
\(711\) 0.646223 0.469509i 0.0242353 0.0176079i
\(712\) 0 0
\(713\) −67.1343 48.7759i −2.51420 1.82667i
\(714\) 0 0
\(715\) −22.5137 + 12.2305i −0.841966 + 0.457396i
\(716\) 0 0
\(717\) −1.06465 3.27666i −0.0397602 0.122369i
\(718\) 0 0
\(719\) −9.91537 30.5164i −0.369781 1.13807i −0.946933 0.321432i \(-0.895836\pi\)
0.577152 0.816637i \(-0.304164\pi\)
\(720\) 0 0
\(721\) −5.79208 + 17.8262i −0.215708 + 0.663882i
\(722\) 0 0
\(723\) −19.4923 + 14.1620i −0.724926 + 0.526689i
\(724\) 0 0
\(725\) −9.83021 12.1281i −0.365085 0.450427i
\(726\) 0 0
\(727\) 11.0201 8.00656i 0.408712 0.296947i −0.364368 0.931255i \(-0.618715\pi\)
0.773080 + 0.634308i \(0.218715\pi\)
\(728\) 0 0
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 0 0
\(731\) 3.30882 + 10.1835i 0.122381 + 0.376650i
\(732\) 0 0
\(733\) 8.78355 + 27.0330i 0.324428 + 0.998486i 0.971698 + 0.236225i \(0.0759104\pi\)
−0.647271 + 0.762260i \(0.724090\pi\)
\(734\) 0 0
\(735\) 1.62017 + 8.73064i 0.0597607 + 0.322035i
\(736\) 0 0
\(737\) −17.3274 12.5891i −0.638264 0.463726i
\(738\) 0 0
\(739\) −7.85925 + 5.71008i −0.289107 + 0.210049i −0.722880 0.690974i \(-0.757182\pi\)
0.433773 + 0.901022i \(0.357182\pi\)
\(740\) 0 0
\(741\) −6.76639 4.91607i −0.248569 0.180596i
\(742\) 0 0
\(743\) 34.2029 1.25478 0.627390 0.778705i \(-0.284123\pi\)
0.627390 + 0.778705i \(0.284123\pi\)
\(744\) 0 0
\(745\) 20.8830 11.3446i 0.765093 0.415635i
\(746\) 0 0
\(747\) 0.732396 2.25408i 0.0267970 0.0824726i
\(748\) 0 0
\(749\) 7.55917 0.276206
\(750\) 0 0
\(751\) −12.7840 −0.466495 −0.233248 0.972417i \(-0.574935\pi\)
−0.233248 + 0.972417i \(0.574935\pi\)
\(752\) 0 0
\(753\) 9.32060 28.6859i 0.339661 1.04537i
\(754\) 0 0
\(755\) 20.5698 11.1745i 0.748610 0.406681i
\(756\) 0 0
\(757\) 26.6200 0.967520 0.483760 0.875201i \(-0.339271\pi\)
0.483760 + 0.875201i \(0.339271\pi\)
\(758\) 0 0
\(759\) 16.2911 + 11.8362i 0.591329 + 0.429626i
\(760\) 0 0
\(761\) −20.8028 + 15.1141i −0.754102 + 0.547887i −0.897096 0.441836i \(-0.854327\pi\)
0.142993 + 0.989724i \(0.454327\pi\)
\(762\) 0 0
\(763\) 1.50833 + 1.09587i 0.0546053 + 0.0396731i
\(764\) 0 0
\(765\) 1.52602 + 8.22332i 0.0551734 + 0.297315i
\(766\) 0 0
\(767\) 6.69607 + 20.6084i 0.241781 + 0.744126i
\(768\) 0 0
\(769\) −11.8575 36.4937i −0.427593 1.31600i −0.900490 0.434877i \(-0.856792\pi\)
0.472897 0.881118i \(-0.343208\pi\)
\(770\) 0 0
\(771\) −3.30222 + 10.1632i −0.118927 + 0.366019i
\(772\) 0 0
\(773\) 1.13168 0.822215i 0.0407038 0.0295730i −0.567247 0.823547i \(-0.691992\pi\)
0.607951 + 0.793974i \(0.291992\pi\)
\(774\) 0 0
\(775\) 46.1848 + 12.3529i 1.65901 + 0.443728i
\(776\) 0 0
\(777\) −7.55667 + 5.49024i −0.271094 + 0.196961i
\(778\) 0 0
\(779\) 4.56656 14.0544i 0.163614 0.503552i
\(780\) 0 0
\(781\) 0.0168959 + 0.0520001i 0.000604581 + 0.00186071i
\(782\) 0 0
\(783\) −0.964854 2.96952i −0.0344811 0.106122i
\(784\) 0 0
\(785\) 33.9895 18.4647i 1.21314 0.659034i
\(786\) 0 0
\(787\) 3.40614 + 2.47471i 0.121416 + 0.0882138i 0.646836 0.762629i \(-0.276092\pi\)
−0.525420 + 0.850843i \(0.676092\pi\)
\(788\) 0 0
\(789\) 7.46948 5.42689i 0.265920 0.193203i
\(790\) 0 0
\(791\) 26.1346 + 18.9879i 0.929238 + 0.675131i
\(792\) 0 0
\(793\) −75.7119 −2.68861
\(794\) 0 0
\(795\) 2.98073 + 0.391737i 0.105716 + 0.0138935i