Properties

Label 1148.2.k.b.729.15
Level $1148$
Weight $2$
Character 1148.729
Analytic conductor $9.167$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 729.15
Character \(\chi\) \(=\) 1148.729
Dual form 1148.2.k.b.337.15

$q$-expansion

\(f(q)\) \(=\) \(q+(1.65216 - 1.65216i) q^{3} -2.95400i q^{5} +(-0.707107 + 0.707107i) q^{7} -2.45924i q^{9} +O(q^{10})\) \(q+(1.65216 - 1.65216i) q^{3} -2.95400i q^{5} +(-0.707107 + 0.707107i) q^{7} -2.45924i q^{9} +(0.583260 - 0.583260i) q^{11} +(-0.304108 + 0.304108i) q^{13} +(-4.88047 - 4.88047i) q^{15} +(-4.59921 - 4.59921i) q^{17} +(-2.24427 - 2.24427i) q^{19} +2.33650i q^{21} -2.62025 q^{23} -3.72611 q^{25} +(0.893418 + 0.893418i) q^{27} +(3.12871 - 3.12871i) q^{29} +3.25380 q^{31} -1.92727i q^{33} +(2.08879 + 2.08879i) q^{35} +9.55376 q^{37} +1.00487i q^{39} +(-6.24482 + 1.41499i) q^{41} +4.05599i q^{43} -7.26460 q^{45} +(-7.44566 - 7.44566i) q^{47} -1.00000i q^{49} -15.1972 q^{51} +(0.577050 - 0.577050i) q^{53} +(-1.72295 - 1.72295i) q^{55} -7.41578 q^{57} +5.94695 q^{59} -5.32768i q^{61} +(1.73895 + 1.73895i) q^{63} +(0.898336 + 0.898336i) q^{65} +(6.10945 + 6.10945i) q^{67} +(-4.32906 + 4.32906i) q^{69} +(-7.75761 + 7.75761i) q^{71} +5.39839i q^{73} +(-6.15612 + 6.15612i) q^{75} +0.824855i q^{77} +(3.82764 - 3.82764i) q^{79} +10.3299 q^{81} +4.27367 q^{83} +(-13.5861 + 13.5861i) q^{85} -10.3382i q^{87} +(1.40401 - 1.40401i) q^{89} -0.430074i q^{91} +(5.37579 - 5.37579i) q^{93} +(-6.62958 + 6.62958i) q^{95} +(5.46950 + 5.46950i) q^{97} +(-1.43438 - 1.43438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) 1.65216 1.65216i 0.953873 0.953873i −0.0451092 0.998982i \(-0.514364\pi\)
0.998982 + 0.0451092i \(0.0143636\pi\)
\(4\) 0 0
\(5\) 2.95400i 1.32107i −0.750796 0.660534i \(-0.770330\pi\)
0.750796 0.660534i \(-0.229670\pi\)
\(6\) 0 0
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) 0 0
\(9\) 2.45924i 0.819747i
\(10\) 0 0
\(11\) 0.583260 0.583260i 0.175860 0.175860i −0.613689 0.789548i \(-0.710315\pi\)
0.789548 + 0.613689i \(0.210315\pi\)
\(12\) 0 0
\(13\) −0.304108 + 0.304108i −0.0843445 + 0.0843445i −0.748020 0.663676i \(-0.768995\pi\)
0.663676 + 0.748020i \(0.268995\pi\)
\(14\) 0 0
\(15\) −4.88047 4.88047i −1.26013 1.26013i
\(16\) 0 0
\(17\) −4.59921 4.59921i −1.11547 1.11547i −0.992397 0.123076i \(-0.960724\pi\)
−0.123076 0.992397i \(-0.539276\pi\)
\(18\) 0 0
\(19\) −2.24427 2.24427i −0.514872 0.514872i 0.401144 0.916015i \(-0.368613\pi\)
−0.916015 + 0.401144i \(0.868613\pi\)
\(20\) 0 0
\(21\) 2.33650i 0.509867i
\(22\) 0 0
\(23\) −2.62025 −0.546359 −0.273180 0.961963i \(-0.588075\pi\)
−0.273180 + 0.961963i \(0.588075\pi\)
\(24\) 0 0
\(25\) −3.72611 −0.745223
\(26\) 0 0
\(27\) 0.893418 + 0.893418i 0.171938 + 0.171938i
\(28\) 0 0
\(29\) 3.12871 3.12871i 0.580987 0.580987i −0.354188 0.935174i \(-0.615243\pi\)
0.935174 + 0.354188i \(0.115243\pi\)
\(30\) 0 0
\(31\) 3.25380 0.584400 0.292200 0.956357i \(-0.405613\pi\)
0.292200 + 0.956357i \(0.405613\pi\)
\(32\) 0 0
\(33\) 1.92727i 0.335495i
\(34\) 0 0
\(35\) 2.08879 + 2.08879i 0.353070 + 0.353070i
\(36\) 0 0
\(37\) 9.55376 1.57063 0.785314 0.619098i \(-0.212501\pi\)
0.785314 + 0.619098i \(0.212501\pi\)
\(38\) 0 0
\(39\) 1.00487i 0.160908i
\(40\) 0 0
\(41\) −6.24482 + 1.41499i −0.975277 + 0.220984i
\(42\) 0 0
\(43\) 4.05599i 0.618533i 0.950975 + 0.309266i \(0.100083\pi\)
−0.950975 + 0.309266i \(0.899917\pi\)
\(44\) 0 0
\(45\) −7.26460 −1.08294
\(46\) 0 0
\(47\) −7.44566 7.44566i −1.08606 1.08606i −0.995930 0.0901312i \(-0.971271\pi\)
−0.0901312 0.995930i \(-0.528729\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −15.1972 −2.12804
\(52\) 0 0
\(53\) 0.577050 0.577050i 0.0792639 0.0792639i −0.666363 0.745627i \(-0.732150\pi\)
0.745627 + 0.666363i \(0.232150\pi\)
\(54\) 0 0
\(55\) −1.72295 1.72295i −0.232323 0.232323i
\(56\) 0 0
\(57\) −7.41578 −0.982244
\(58\) 0 0
\(59\) 5.94695 0.774227 0.387113 0.922032i \(-0.373472\pi\)
0.387113 + 0.922032i \(0.373472\pi\)
\(60\) 0 0
\(61\) 5.32768i 0.682140i −0.940038 0.341070i \(-0.889211\pi\)
0.940038 0.341070i \(-0.110789\pi\)
\(62\) 0 0
\(63\) 1.73895 + 1.73895i 0.219087 + 0.219087i
\(64\) 0 0
\(65\) 0.898336 + 0.898336i 0.111425 + 0.111425i
\(66\) 0 0
\(67\) 6.10945 + 6.10945i 0.746388 + 0.746388i 0.973799 0.227411i \(-0.0730260\pi\)
−0.227411 + 0.973799i \(0.573026\pi\)
\(68\) 0 0
\(69\) −4.32906 + 4.32906i −0.521157 + 0.521157i
\(70\) 0 0
\(71\) −7.75761 + 7.75761i −0.920658 + 0.920658i −0.997076 0.0764175i \(-0.975652\pi\)
0.0764175 + 0.997076i \(0.475652\pi\)
\(72\) 0 0
\(73\) 5.39839i 0.631834i 0.948787 + 0.315917i \(0.102312\pi\)
−0.948787 + 0.315917i \(0.897688\pi\)
\(74\) 0 0
\(75\) −6.15612 + 6.15612i −0.710848 + 0.710848i
\(76\) 0 0
\(77\) 0.824855i 0.0940009i
\(78\) 0 0
\(79\) 3.82764 3.82764i 0.430643 0.430643i −0.458204 0.888847i \(-0.651507\pi\)
0.888847 + 0.458204i \(0.151507\pi\)
\(80\) 0 0
\(81\) 10.3299 1.14776
\(82\) 0 0
\(83\) 4.27367 0.469097 0.234548 0.972104i \(-0.424639\pi\)
0.234548 + 0.972104i \(0.424639\pi\)
\(84\) 0 0
\(85\) −13.5861 + 13.5861i −1.47362 + 1.47362i
\(86\) 0 0
\(87\) 10.3382i 1.10837i
\(88\) 0 0
\(89\) 1.40401 1.40401i 0.148825 0.148825i −0.628768 0.777593i \(-0.716441\pi\)
0.777593 + 0.628768i \(0.216441\pi\)
\(90\) 0 0
\(91\) 0.430074i 0.0450840i
\(92\) 0 0
\(93\) 5.37579 5.37579i 0.557443 0.557443i
\(94\) 0 0
\(95\) −6.62958 + 6.62958i −0.680181 + 0.680181i
\(96\) 0 0
\(97\) 5.46950 + 5.46950i 0.555343 + 0.555343i 0.927978 0.372635i \(-0.121546\pi\)
−0.372635 + 0.927978i \(0.621546\pi\)
\(98\) 0 0
\(99\) −1.43438 1.43438i −0.144160 0.144160i
\(100\) 0 0
\(101\) −10.8247 10.8247i −1.07710 1.07710i −0.996768 0.0803306i \(-0.974402\pi\)
−0.0803306 0.996768i \(-0.525598\pi\)
\(102\) 0 0
\(103\) 5.20778i 0.513138i −0.966526 0.256569i \(-0.917408\pi\)
0.966526 0.256569i \(-0.0825921\pi\)
\(104\) 0 0
\(105\) 6.90203 0.673569
\(106\) 0 0
\(107\) 19.6992 1.90440 0.952199 0.305478i \(-0.0988164\pi\)
0.952199 + 0.305478i \(0.0988164\pi\)
\(108\) 0 0
\(109\) −0.590425 0.590425i −0.0565525 0.0565525i 0.678265 0.734817i \(-0.262732\pi\)
−0.734817 + 0.678265i \(0.762732\pi\)
\(110\) 0 0
\(111\) 15.7843 15.7843i 1.49818 1.49818i
\(112\) 0 0
\(113\) −0.357625 −0.0336425 −0.0168213 0.999859i \(-0.505355\pi\)
−0.0168213 + 0.999859i \(0.505355\pi\)
\(114\) 0 0
\(115\) 7.74021i 0.721778i
\(116\) 0 0
\(117\) 0.747876 + 0.747876i 0.0691412 + 0.0691412i
\(118\) 0 0
\(119\) 6.50427 0.596246
\(120\) 0 0
\(121\) 10.3196i 0.938147i
\(122\) 0 0
\(123\) −7.97964 + 12.6552i −0.719500 + 1.14108i
\(124\) 0 0
\(125\) 3.76306i 0.336578i
\(126\) 0 0
\(127\) −2.66971 −0.236899 −0.118449 0.992960i \(-0.537792\pi\)
−0.118449 + 0.992960i \(0.537792\pi\)
\(128\) 0 0
\(129\) 6.70113 + 6.70113i 0.590001 + 0.590001i
\(130\) 0 0
\(131\) 10.8716i 0.949855i −0.880025 0.474928i \(-0.842474\pi\)
0.880025 0.474928i \(-0.157526\pi\)
\(132\) 0 0
\(133\) 3.17388 0.275210
\(134\) 0 0
\(135\) 2.63916 2.63916i 0.227142 0.227142i
\(136\) 0 0
\(137\) −1.62969 1.62969i −0.139234 0.139234i 0.634054 0.773288i \(-0.281389\pi\)
−0.773288 + 0.634054i \(0.781389\pi\)
\(138\) 0 0
\(139\) 11.1845 0.948655 0.474328 0.880348i \(-0.342691\pi\)
0.474328 + 0.880348i \(0.342691\pi\)
\(140\) 0 0
\(141\) −24.6028 −2.07193
\(142\) 0 0
\(143\) 0.354749i 0.0296656i
\(144\) 0 0
\(145\) −9.24220 9.24220i −0.767523 0.767523i
\(146\) 0 0
\(147\) −1.65216 1.65216i −0.136268 0.136268i
\(148\) 0 0
\(149\) −3.73283 3.73283i −0.305805 0.305805i 0.537475 0.843280i \(-0.319378\pi\)
−0.843280 + 0.537475i \(0.819378\pi\)
\(150\) 0 0
\(151\) 5.68611 5.68611i 0.462729 0.462729i −0.436820 0.899549i \(-0.643895\pi\)
0.899549 + 0.436820i \(0.143895\pi\)
\(152\) 0 0
\(153\) −11.3106 + 11.3106i −0.914406 + 0.914406i
\(154\) 0 0
\(155\) 9.61172i 0.772032i
\(156\) 0 0
\(157\) −4.12315 + 4.12315i −0.329064 + 0.329064i −0.852230 0.523167i \(-0.824750\pi\)
0.523167 + 0.852230i \(0.324750\pi\)
\(158\) 0 0
\(159\) 1.90675i 0.151215i
\(160\) 0 0
\(161\) 1.85279 1.85279i 0.146021 0.146021i
\(162\) 0 0
\(163\) 11.8690 0.929651 0.464826 0.885402i \(-0.346117\pi\)
0.464826 + 0.885402i \(0.346117\pi\)
\(164\) 0 0
\(165\) −5.69317 −0.443213
\(166\) 0 0
\(167\) 6.18373 6.18373i 0.478512 0.478512i −0.426144 0.904655i \(-0.640128\pi\)
0.904655 + 0.426144i \(0.140128\pi\)
\(168\) 0 0
\(169\) 12.8150i 0.985772i
\(170\) 0 0
\(171\) −5.51921 + 5.51921i −0.422064 + 0.422064i
\(172\) 0 0
\(173\) 9.85989i 0.749634i 0.927099 + 0.374817i \(0.122294\pi\)
−0.927099 + 0.374817i \(0.877706\pi\)
\(174\) 0 0
\(175\) 2.63476 2.63476i 0.199169 0.199169i
\(176\) 0 0
\(177\) 9.82529 9.82529i 0.738514 0.738514i
\(178\) 0 0
\(179\) 17.7789 + 17.7789i 1.32885 + 1.32885i 0.906371 + 0.422483i \(0.138841\pi\)
0.422483 + 0.906371i \(0.361159\pi\)
\(180\) 0 0
\(181\) −12.3686 12.3686i −0.919351 0.919351i 0.0776310 0.996982i \(-0.475264\pi\)
−0.996982 + 0.0776310i \(0.975264\pi\)
\(182\) 0 0
\(183\) −8.80216 8.80216i −0.650674 0.650674i
\(184\) 0 0
\(185\) 28.2218i 2.07491i
\(186\) 0 0
\(187\) −5.36508 −0.392333
\(188\) 0 0
\(189\) −1.26348 −0.0919049
\(190\) 0 0
\(191\) 9.54514 + 9.54514i 0.690662 + 0.690662i 0.962378 0.271716i \(-0.0875910\pi\)
−0.271716 + 0.962378i \(0.587591\pi\)
\(192\) 0 0
\(193\) 12.5298 12.5298i 0.901917 0.901917i −0.0936851 0.995602i \(-0.529865\pi\)
0.995602 + 0.0936851i \(0.0298647\pi\)
\(194\) 0 0
\(195\) 2.96838 0.212570
\(196\) 0 0
\(197\) 15.5518i 1.10802i −0.832510 0.554010i \(-0.813097\pi\)
0.832510 0.554010i \(-0.186903\pi\)
\(198\) 0 0
\(199\) −3.71168 3.71168i −0.263114 0.263114i 0.563204 0.826318i \(-0.309569\pi\)
−0.826318 + 0.563204i \(0.809569\pi\)
\(200\) 0 0
\(201\) 20.1875 1.42392
\(202\) 0 0
\(203\) 4.42466i 0.310550i
\(204\) 0 0
\(205\) 4.17987 + 18.4472i 0.291935 + 1.28841i
\(206\) 0 0
\(207\) 6.44382i 0.447876i
\(208\) 0 0
\(209\) −2.61799 −0.181090
\(210\) 0 0
\(211\) −8.78315 8.78315i −0.604657 0.604657i 0.336888 0.941545i \(-0.390626\pi\)
−0.941545 + 0.336888i \(0.890626\pi\)
\(212\) 0 0
\(213\) 25.6336i 1.75638i
\(214\) 0 0
\(215\) 11.9814 0.817124
\(216\) 0 0
\(217\) −2.30078 + 2.30078i −0.156187 + 0.156187i
\(218\) 0 0
\(219\) 8.91899 + 8.91899i 0.602690 + 0.602690i
\(220\) 0 0
\(221\) 2.79732 0.188168
\(222\) 0 0
\(223\) 14.9853 1.00349 0.501743 0.865016i \(-0.332692\pi\)
0.501743 + 0.865016i \(0.332692\pi\)
\(224\) 0 0
\(225\) 9.16341i 0.610894i
\(226\) 0 0
\(227\) −4.68712 4.68712i −0.311095 0.311095i 0.534239 0.845334i \(-0.320598\pi\)
−0.845334 + 0.534239i \(0.820598\pi\)
\(228\) 0 0
\(229\) 4.91562 + 4.91562i 0.324833 + 0.324833i 0.850618 0.525785i \(-0.176228\pi\)
−0.525785 + 0.850618i \(0.676228\pi\)
\(230\) 0 0
\(231\) 1.36279 + 1.36279i 0.0896649 + 0.0896649i
\(232\) 0 0
\(233\) −5.61073 + 5.61073i −0.367571 + 0.367571i −0.866591 0.499020i \(-0.833694\pi\)
0.499020 + 0.866591i \(0.333694\pi\)
\(234\) 0 0
\(235\) −21.9945 + 21.9945i −1.43476 + 1.43476i
\(236\) 0 0
\(237\) 12.6477i 0.821557i
\(238\) 0 0
\(239\) 2.26725 2.26725i 0.146656 0.146656i −0.629966 0.776622i \(-0.716931\pi\)
0.776622 + 0.629966i \(0.216931\pi\)
\(240\) 0 0
\(241\) 15.7463i 1.01431i −0.861855 0.507155i \(-0.830697\pi\)
0.861855 0.507155i \(-0.169303\pi\)
\(242\) 0 0
\(243\) 14.3863 14.3863i 0.922880 0.922880i
\(244\) 0 0
\(245\) −2.95400 −0.188724
\(246\) 0 0
\(247\) 1.36500 0.0868532
\(248\) 0 0
\(249\) 7.06078 7.06078i 0.447459 0.447459i
\(250\) 0 0
\(251\) 24.9768i 1.57652i 0.615340 + 0.788262i \(0.289019\pi\)
−0.615340 + 0.788262i \(0.710981\pi\)
\(252\) 0 0
\(253\) −1.52829 + 1.52829i −0.0960825 + 0.0960825i
\(254\) 0 0
\(255\) 44.8926i 2.81129i
\(256\) 0 0
\(257\) 7.98241 7.98241i 0.497929 0.497929i −0.412864 0.910793i \(-0.635471\pi\)
0.910793 + 0.412864i \(0.135471\pi\)
\(258\) 0 0
\(259\) −6.75553 + 6.75553i −0.419768 + 0.419768i
\(260\) 0 0
\(261\) −7.69425 7.69425i −0.476262 0.476262i
\(262\) 0 0
\(263\) 8.44004 + 8.44004i 0.520435 + 0.520435i 0.917703 0.397268i \(-0.130042\pi\)
−0.397268 + 0.917703i \(0.630042\pi\)
\(264\) 0 0
\(265\) −1.70460 1.70460i −0.104713 0.104713i
\(266\) 0 0
\(267\) 4.63928i 0.283920i
\(268\) 0 0
\(269\) −12.1960 −0.743603 −0.371802 0.928312i \(-0.621260\pi\)
−0.371802 + 0.928312i \(0.621260\pi\)
\(270\) 0 0
\(271\) 0.702973 0.0427025 0.0213513 0.999772i \(-0.493203\pi\)
0.0213513 + 0.999772i \(0.493203\pi\)
\(272\) 0 0
\(273\) −0.710550 0.710550i −0.0430044 0.0430044i
\(274\) 0 0
\(275\) −2.17329 + 2.17329i −0.131055 + 0.131055i
\(276\) 0 0
\(277\) −27.0584 −1.62578 −0.812891 0.582416i \(-0.802107\pi\)
−0.812891 + 0.582416i \(0.802107\pi\)
\(278\) 0 0
\(279\) 8.00188i 0.479060i
\(280\) 0 0
\(281\) 2.09997 + 2.09997i 0.125274 + 0.125274i 0.766964 0.641690i \(-0.221766\pi\)
−0.641690 + 0.766964i \(0.721766\pi\)
\(282\) 0 0
\(283\) 21.9796 1.30655 0.653275 0.757120i \(-0.273394\pi\)
0.653275 + 0.757120i \(0.273394\pi\)
\(284\) 0 0
\(285\) 21.9062i 1.29761i
\(286\) 0 0
\(287\) 3.41521 5.41630i 0.201593 0.319714i
\(288\) 0 0
\(289\) 25.3055i 1.48856i
\(290\) 0 0
\(291\) 18.0729 1.05945
\(292\) 0 0
\(293\) 2.14640 + 2.14640i 0.125394 + 0.125394i 0.767019 0.641625i \(-0.221739\pi\)
−0.641625 + 0.767019i \(0.721739\pi\)
\(294\) 0 0
\(295\) 17.5673i 1.02281i
\(296\) 0 0
\(297\) 1.04219 0.0604740
\(298\) 0 0
\(299\) 0.796839 0.796839i 0.0460824 0.0460824i
\(300\) 0 0
\(301\) −2.86802 2.86802i −0.165310 0.165310i
\(302\) 0 0
\(303\) −35.7682 −2.05483
\(304\) 0 0
\(305\) −15.7380 −0.901153
\(306\) 0 0
\(307\) 25.7136i 1.46755i 0.679392 + 0.733776i \(0.262244\pi\)
−0.679392 + 0.733776i \(0.737756\pi\)
\(308\) 0 0
\(309\) −8.60407 8.60407i −0.489469 0.489469i
\(310\) 0 0
\(311\) 18.5145 + 18.5145i 1.04986 + 1.04986i 0.998690 + 0.0511688i \(0.0162947\pi\)
0.0511688 + 0.998690i \(0.483705\pi\)
\(312\) 0 0
\(313\) 7.51282 + 7.51282i 0.424650 + 0.424650i 0.886801 0.462151i \(-0.152922\pi\)
−0.462151 + 0.886801i \(0.652922\pi\)
\(314\) 0 0
\(315\) 5.13685 5.13685i 0.289428 0.289428i
\(316\) 0 0
\(317\) 23.3975 23.3975i 1.31414 1.31414i 0.395798 0.918338i \(-0.370468\pi\)
0.918338 0.395798i \(-0.129532\pi\)
\(318\) 0 0
\(319\) 3.64970i 0.204344i
\(320\) 0 0
\(321\) 32.5462 32.5462i 1.81655 1.81655i
\(322\) 0 0
\(323\) 20.6438i 1.14865i
\(324\) 0 0
\(325\) 1.13314 1.13314i 0.0628554 0.0628554i
\(326\) 0 0
\(327\) −1.95095 −0.107888
\(328\) 0 0
\(329\) 10.5298 0.580524
\(330\) 0 0
\(331\) −19.8680 + 19.8680i −1.09204 + 1.09204i −0.0967336 + 0.995310i \(0.530839\pi\)
−0.995310 + 0.0967336i \(0.969161\pi\)
\(332\) 0 0
\(333\) 23.4950i 1.28752i
\(334\) 0 0
\(335\) 18.0473 18.0473i 0.986030 0.986030i
\(336\) 0 0
\(337\) 5.40369i 0.294358i −0.989110 0.147179i \(-0.952981\pi\)
0.989110 0.147179i \(-0.0470193\pi\)
\(338\) 0 0
\(339\) −0.590852 + 0.590852i −0.0320907 + 0.0320907i
\(340\) 0 0
\(341\) 1.89781 1.89781i 0.102772 0.102772i
\(342\) 0 0
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) 0 0
\(345\) 12.7880 + 12.7880i 0.688485 + 0.688485i
\(346\) 0 0
\(347\) −15.3749 15.3749i −0.825368 0.825368i 0.161504 0.986872i \(-0.448366\pi\)
−0.986872 + 0.161504i \(0.948366\pi\)
\(348\) 0 0
\(349\) 10.6437i 0.569743i 0.958566 + 0.284872i \(0.0919509\pi\)
−0.958566 + 0.284872i \(0.908049\pi\)
\(350\) 0 0
\(351\) −0.543392 −0.0290041
\(352\) 0 0
\(353\) 6.85305 0.364751 0.182375 0.983229i \(-0.441621\pi\)
0.182375 + 0.983229i \(0.441621\pi\)
\(354\) 0 0
\(355\) 22.9160 + 22.9160i 1.21625 + 1.21625i
\(356\) 0 0
\(357\) 10.7461 10.7461i 0.568742 0.568742i
\(358\) 0 0
\(359\) 27.9264 1.47390 0.736948 0.675949i \(-0.236266\pi\)
0.736948 + 0.675949i \(0.236266\pi\)
\(360\) 0 0
\(361\) 8.92648i 0.469815i
\(362\) 0 0
\(363\) 17.0496 + 17.0496i 0.894873 + 0.894873i
\(364\) 0 0
\(365\) 15.9469 0.834697
\(366\) 0 0
\(367\) 22.4127i 1.16993i 0.811057 + 0.584966i \(0.198892\pi\)
−0.811057 + 0.584966i \(0.801108\pi\)
\(368\) 0 0
\(369\) 3.47980 + 15.3575i 0.181151 + 0.799481i
\(370\) 0 0
\(371\) 0.816072i 0.0423683i
\(372\) 0 0
\(373\) −8.45165 −0.437610 −0.218805 0.975769i \(-0.570216\pi\)
−0.218805 + 0.975769i \(0.570216\pi\)
\(374\) 0 0
\(375\) −6.21716 6.21716i −0.321053 0.321053i
\(376\) 0 0
\(377\) 1.90293i 0.0980060i
\(378\) 0 0
\(379\) −20.7183 −1.06423 −0.532113 0.846673i \(-0.678602\pi\)
−0.532113 + 0.846673i \(0.678602\pi\)
\(380\) 0 0
\(381\) −4.41078 + 4.41078i −0.225971 + 0.225971i
\(382\) 0 0
\(383\) −1.22706 1.22706i −0.0626996 0.0626996i 0.675062 0.737761i \(-0.264117\pi\)
−0.737761 + 0.675062i \(0.764117\pi\)
\(384\) 0 0
\(385\) 2.43662 0.124182
\(386\) 0 0
\(387\) 9.97465 0.507040
\(388\) 0 0
\(389\) 7.77430i 0.394172i 0.980386 + 0.197086i \(0.0631479\pi\)
−0.980386 + 0.197086i \(0.936852\pi\)
\(390\) 0 0
\(391\) 12.0511 + 12.0511i 0.609449 + 0.609449i
\(392\) 0 0
\(393\) −17.9616 17.9616i −0.906041 0.906041i
\(394\) 0 0
\(395\) −11.3068 11.3068i −0.568909 0.568909i
\(396\) 0 0
\(397\) −13.3035 + 13.3035i −0.667681 + 0.667681i −0.957179 0.289498i \(-0.906512\pi\)
0.289498 + 0.957179i \(0.406512\pi\)
\(398\) 0 0
\(399\) 5.24375 5.24375i 0.262516 0.262516i
\(400\) 0 0
\(401\) 19.7275i 0.985144i −0.870272 0.492572i \(-0.836057\pi\)
0.870272 0.492572i \(-0.163943\pi\)
\(402\) 0 0
\(403\) −0.989508 + 0.989508i −0.0492909 + 0.0492909i
\(404\) 0 0
\(405\) 30.5144i 1.51627i
\(406\) 0 0
\(407\) 5.57233 5.57233i 0.276210 0.276210i
\(408\) 0 0
\(409\) −30.4183 −1.50409 −0.752044 0.659113i \(-0.770932\pi\)
−0.752044 + 0.659113i \(0.770932\pi\)
\(410\) 0 0
\(411\) −5.38501 −0.265623
\(412\) 0 0
\(413\) −4.20513 + 4.20513i −0.206921 + 0.206921i
\(414\) 0 0
\(415\) 12.6244i 0.619709i
\(416\) 0 0
\(417\) 18.4785 18.4785i 0.904896 0.904896i
\(418\) 0 0
\(419\) 33.8189i 1.65216i 0.563553 + 0.826080i \(0.309434\pi\)
−0.563553 + 0.826080i \(0.690566\pi\)
\(420\) 0 0
\(421\) −2.40237 + 2.40237i −0.117084 + 0.117084i −0.763221 0.646137i \(-0.776383\pi\)
0.646137 + 0.763221i \(0.276383\pi\)
\(422\) 0 0
\(423\) −18.3107 + 18.3107i −0.890295 + 0.890295i
\(424\) 0 0
\(425\) 17.1372 + 17.1372i 0.831276 + 0.831276i
\(426\) 0 0
\(427\) 3.76724 + 3.76724i 0.182309 + 0.182309i
\(428\) 0 0
\(429\) 0.586100 + 0.586100i 0.0282972 + 0.0282972i
\(430\) 0 0
\(431\) 8.60222i 0.414354i −0.978303 0.207177i \(-0.933572\pi\)
0.978303 0.207177i \(-0.0664277\pi\)
\(432\) 0 0
\(433\) −22.6257 −1.08732 −0.543661 0.839305i \(-0.682962\pi\)
−0.543661 + 0.839305i \(0.682962\pi\)
\(434\) 0 0
\(435\) −30.5391 −1.46424
\(436\) 0 0
\(437\) 5.88055 + 5.88055i 0.281305 + 0.281305i
\(438\) 0 0
\(439\) 7.12568 7.12568i 0.340090 0.340090i −0.516311 0.856401i \(-0.672695\pi\)
0.856401 + 0.516311i \(0.172695\pi\)
\(440\) 0 0
\(441\) −2.45924 −0.117107
\(442\) 0 0
\(443\) 13.4557i 0.639298i −0.947536 0.319649i \(-0.896435\pi\)
0.947536 0.319649i \(-0.103565\pi\)
\(444\) 0 0
\(445\) −4.14744 4.14744i −0.196608 0.196608i
\(446\) 0 0
\(447\) −12.3344 −0.583398
\(448\) 0 0
\(449\) 31.9547i 1.50803i 0.656855 + 0.754017i \(0.271887\pi\)
−0.656855 + 0.754017i \(0.728113\pi\)
\(450\) 0 0
\(451\) −2.81705 + 4.46766i −0.132650 + 0.210374i
\(452\) 0 0
\(453\) 18.7887i 0.882769i
\(454\) 0 0
\(455\) −1.27044 −0.0595591
\(456\) 0 0
\(457\) 8.80331 + 8.80331i 0.411801 + 0.411801i 0.882366 0.470564i \(-0.155950\pi\)
−0.470564 + 0.882366i \(0.655950\pi\)
\(458\) 0 0
\(459\) 8.21804i 0.383585i
\(460\) 0 0
\(461\) −32.9461 −1.53445 −0.767226 0.641377i \(-0.778364\pi\)
−0.767226 + 0.641377i \(0.778364\pi\)
\(462\) 0 0
\(463\) −22.6636 + 22.6636i −1.05327 + 1.05327i −0.0547672 + 0.998499i \(0.517442\pi\)
−0.998499 + 0.0547672i \(0.982558\pi\)
\(464\) 0 0
\(465\) −15.8801 15.8801i −0.736421 0.736421i
\(466\) 0 0
\(467\) 22.5274 1.04244 0.521221 0.853422i \(-0.325477\pi\)
0.521221 + 0.853422i \(0.325477\pi\)
\(468\) 0 0
\(469\) −8.64007 −0.398961
\(470\) 0 0
\(471\) 13.6242i 0.627770i
\(472\) 0 0
\(473\) 2.36570 + 2.36570i 0.108775 + 0.108775i
\(474\) 0 0
\(475\) 8.36242 + 8.36242i 0.383694 + 0.383694i
\(476\) 0 0
\(477\) −1.41910 1.41910i −0.0649763 0.0649763i
\(478\) 0 0
\(479\) −24.9383 + 24.9383i −1.13946 + 1.13946i −0.150915 + 0.988547i \(0.548222\pi\)
−0.988547 + 0.150915i \(0.951778\pi\)
\(480\) 0 0
\(481\) −2.90538 + 2.90538i −0.132474 + 0.132474i
\(482\) 0 0
\(483\) 6.12221i 0.278570i
\(484\) 0 0
\(485\) 16.1569 16.1569i 0.733647 0.733647i
\(486\) 0 0
\(487\) 14.7261i 0.667302i −0.942697 0.333651i \(-0.891719\pi\)
0.942697 0.333651i \(-0.108281\pi\)
\(488\) 0 0
\(489\) 19.6094 19.6094i 0.886769 0.886769i
\(490\) 0 0
\(491\) −18.4511 −0.832687 −0.416344 0.909207i \(-0.636689\pi\)
−0.416344 + 0.909207i \(0.636689\pi\)
\(492\) 0 0
\(493\) −28.7792 −1.29615
\(494\) 0 0
\(495\) −4.23715 + 4.23715i −0.190446 + 0.190446i
\(496\) 0 0
\(497\) 10.9709i 0.492113i
\(498\) 0 0
\(499\) 3.86414 3.86414i 0.172982 0.172982i −0.615306 0.788288i \(-0.710968\pi\)
0.788288 + 0.615306i \(0.210968\pi\)
\(500\) 0 0
\(501\) 20.4330i 0.912879i
\(502\) 0 0
\(503\) 14.9077 14.9077i 0.664701 0.664701i −0.291784 0.956484i \(-0.594249\pi\)
0.956484 + 0.291784i \(0.0942487\pi\)
\(504\) 0 0
\(505\) −31.9762 + 31.9762i −1.42292 + 1.42292i
\(506\) 0 0
\(507\) 21.1724 + 21.1724i 0.940301 + 0.940301i
\(508\) 0 0
\(509\) 26.8720 + 26.8720i 1.19108 + 1.19108i 0.976764 + 0.214318i \(0.0687530\pi\)
0.214318 + 0.976764i \(0.431247\pi\)
\(510\) 0 0
\(511\) −3.81724 3.81724i −0.168865 0.168865i
\(512\) 0 0
\(513\) 4.01015i 0.177052i
\(514\) 0 0
\(515\) −15.3838 −0.677891
\(516\) 0 0
\(517\) −8.68552 −0.381989
\(518\) 0 0
\(519\) 16.2901 + 16.2901i 0.715055 + 0.715055i
\(520\) 0 0
\(521\) −11.7175 + 11.7175i −0.513354 + 0.513354i −0.915552 0.402199i \(-0.868246\pi\)
0.402199 + 0.915552i \(0.368246\pi\)
\(522\) 0 0
\(523\) 15.1470 0.662331 0.331166 0.943573i \(-0.392558\pi\)
0.331166 + 0.943573i \(0.392558\pi\)
\(524\) 0 0
\(525\) 8.70607i 0.379964i
\(526\) 0 0
\(527\) −14.9649 14.9649i −0.651882 0.651882i
\(528\) 0 0
\(529\) −16.1343 −0.701492
\(530\) 0 0
\(531\) 14.6250i 0.634670i
\(532\) 0 0
\(533\) 1.46879 2.32941i 0.0636205 0.100898i
\(534\) 0 0
\(535\) 58.1916i 2.51584i
\(536\) 0 0
\(537\) 58.7469 2.53512
\(538\) 0 0
\(539\) −0.583260 0.583260i −0.0251228 0.0251228i
\(540\) 0 0
\(541\) 22.3169i 0.959481i −0.877411 0.479740i \(-0.840731\pi\)
0.877411 0.479740i \(-0.159269\pi\)
\(542\) 0 0
\(543\) −40.8697 −1.75389
\(544\) 0 0
\(545\) −1.74412 + 1.74412i −0.0747097 + 0.0747097i
\(546\) 0 0
\(547\) −16.8083 16.8083i −0.718673 0.718673i 0.249660 0.968333i \(-0.419681\pi\)
−0.968333 + 0.249660i \(0.919681\pi\)
\(548\) 0 0
\(549\) −13.1020 −0.559182
\(550\) 0 0
\(551\) −14.0434 −0.598267
\(552\) 0 0
\(553\) 5.41310i 0.230188i
\(554\) 0 0
\(555\) −46.6268 46.6268i −1.97920 1.97920i
\(556\) 0 0
\(557\) −22.3758 22.3758i −0.948091 0.948091i 0.0506266 0.998718i \(-0.483878\pi\)
−0.998718 + 0.0506266i \(0.983878\pi\)
\(558\) 0 0
\(559\) −1.23346 1.23346i −0.0521698 0.0521698i
\(560\) 0 0
\(561\) −8.86395 + 8.86395i −0.374236 + 0.374236i
\(562\) 0 0
\(563\) −5.34204 + 5.34204i −0.225140 + 0.225140i −0.810659 0.585519i \(-0.800891\pi\)
0.585519 + 0.810659i \(0.300891\pi\)
\(564\) 0 0
\(565\) 1.05642i 0.0444441i
\(566\) 0 0
\(567\) −7.30431 + 7.30431i −0.306752 + 0.306752i
\(568\) 0 0
\(569\) 12.2047i 0.511650i 0.966723 + 0.255825i \(0.0823470\pi\)
−0.966723 + 0.255825i \(0.917653\pi\)
\(570\) 0 0
\(571\) −0.427220 + 0.427220i −0.0178786 + 0.0178786i −0.715990 0.698111i \(-0.754024\pi\)
0.698111 + 0.715990i \(0.254024\pi\)
\(572\) 0 0
\(573\) 31.5401 1.31761
\(574\) 0 0
\(575\) 9.76334 0.407159
\(576\) 0 0
\(577\) 13.5326 13.5326i 0.563371 0.563371i −0.366893 0.930263i \(-0.619578\pi\)
0.930263 + 0.366893i \(0.119578\pi\)
\(578\) 0 0
\(579\) 41.4025i 1.72063i
\(580\) 0 0
\(581\) −3.02194 + 3.02194i −0.125371 + 0.125371i
\(582\) 0 0
\(583\) 0.673140i 0.0278786i
\(584\) 0 0
\(585\) 2.20923 2.20923i 0.0913402 0.0913402i
\(586\) 0 0
\(587\) −4.29502 + 4.29502i −0.177275 + 0.177275i −0.790167 0.612892i \(-0.790006\pi\)
0.612892 + 0.790167i \(0.290006\pi\)
\(588\) 0 0
\(589\) −7.30242 7.30242i −0.300891 0.300891i
\(590\) 0 0
\(591\) −25.6940 25.6940i −1.05691 1.05691i
\(592\) 0 0
\(593\) −7.52938 7.52938i −0.309194 0.309194i 0.535403 0.844597i \(-0.320160\pi\)
−0.844597 + 0.535403i \(0.820160\pi\)
\(594\) 0 0
\(595\) 19.2136i 0.787681i
\(596\) 0 0
\(597\) −12.2646 −0.501955
\(598\) 0 0
\(599\) −12.9937 −0.530908 −0.265454 0.964123i \(-0.585522\pi\)
−0.265454 + 0.964123i \(0.585522\pi\)
\(600\) 0 0
\(601\) 17.3582 + 17.3582i 0.708056 + 0.708056i 0.966126 0.258070i \(-0.0830866\pi\)
−0.258070 + 0.966126i \(0.583087\pi\)
\(602\) 0 0
\(603\) 15.0246 15.0246i 0.611850 0.611850i
\(604\) 0 0
\(605\) 30.4841 1.23936
\(606\) 0 0
\(607\) 35.1559i 1.42693i −0.700689 0.713467i \(-0.747124\pi\)
0.700689 0.713467i \(-0.252876\pi\)
\(608\) 0 0
\(609\) 7.31023 + 7.31023i 0.296226 + 0.296226i
\(610\) 0 0
\(611\) 4.52858 0.183207
\(612\) 0 0
\(613\) 39.5795i 1.59860i 0.600933 + 0.799300i \(0.294796\pi\)
−0.600933 + 0.799300i \(0.705204\pi\)
\(614\) 0 0
\(615\) 37.3835 + 23.5719i 1.50745 + 0.950509i
\(616\) 0 0
\(617\) 21.9755i 0.884701i 0.896842 + 0.442351i \(0.145855\pi\)
−0.896842 + 0.442351i \(0.854145\pi\)
\(618\) 0 0
\(619\) 17.1165 0.687970 0.343985 0.938975i \(-0.388223\pi\)
0.343985 + 0.938975i \(0.388223\pi\)
\(620\) 0 0
\(621\) −2.34098 2.34098i −0.0939401 0.0939401i
\(622\) 0 0
\(623\) 1.98557i 0.0795501i
\(624\) 0 0
\(625\) −29.7466 −1.18987
\(626\) 0 0
\(627\) −4.32533 + 4.32533i −0.172737 + 0.172737i
\(628\) 0 0
\(629\) −43.9398 43.9398i −1.75199 1.75199i
\(630\) 0 0
\(631\) −1.15821 −0.0461075 −0.0230537 0.999734i \(-0.507339\pi\)
−0.0230537 + 0.999734i \(0.507339\pi\)
\(632\) 0 0
\(633\) −29.0223 −1.15353
\(634\) 0 0
\(635\) 7.88633i 0.312959i
\(636\) 0 0
\(637\) 0.304108 + 0.304108i 0.0120492 + 0.0120492i
\(638\) 0 0
\(639\) 19.0778 + 19.0778i 0.754707 + 0.754707i
\(640\) 0 0
\(641\) −31.2194 31.2194i −1.23309 1.23309i −0.962771 0.270320i \(-0.912871\pi\)
−0.270320 0.962771i \(-0.587129\pi\)
\(642\) 0 0
\(643\) 27.6878 27.6878i 1.09190 1.09190i 0.0965746 0.995326i \(-0.469211\pi\)
0.995326 0.0965746i \(-0.0307886\pi\)
\(644\) 0 0
\(645\) 19.7951 19.7951i 0.779432 0.779432i
\(646\) 0 0
\(647\) 19.4427i 0.764371i −0.924086 0.382185i \(-0.875172\pi\)
0.924086 0.382185i \(-0.124828\pi\)
\(648\) 0 0
\(649\) 3.46862 3.46862i 0.136155 0.136155i
\(650\) 0 0
\(651\) 7.60251i 0.297966i
\(652\) 0 0
\(653\) 17.3031 17.3031i 0.677122 0.677122i −0.282226 0.959348i \(-0.591073\pi\)
0.959348 + 0.282226i \(0.0910728\pi\)
\(654\) 0 0
\(655\) −32.1147 −1.25482
\(656\) 0 0
\(657\) 13.2760 0.517944
\(658\) 0 0
\(659\) 2.94442 2.94442i 0.114698 0.114698i −0.647428 0.762126i \(-0.724155\pi\)
0.762126 + 0.647428i \(0.224155\pi\)
\(660\) 0 0
\(661\) 48.4460i 1.88433i −0.335150 0.942165i \(-0.608787\pi\)
0.335150 0.942165i \(-0.391213\pi\)
\(662\) 0 0
\(663\) 4.62161 4.62161i 0.179488 0.179488i
\(664\) 0 0
\(665\) 9.37565i 0.363572i
\(666\) 0 0
\(667\) −8.19799 + 8.19799i −0.317427 + 0.317427i
\(668\) 0 0
\(669\) 24.7580 24.7580i 0.957199 0.957199i
\(670\) 0 0
\(671\) −3.10742 3.10742i −0.119961 0.119961i
\(672\) 0 0
\(673\) 22.1467 + 22.1467i 0.853691 + 0.853691i 0.990586 0.136894i \(-0.0437120\pi\)
−0.136894 + 0.990586i \(0.543712\pi\)
\(674\) 0 0
\(675\) −3.32898 3.32898i −0.128132 0.128132i
\(676\) 0 0
\(677\) 15.2820i 0.587333i −0.955908 0.293667i \(-0.905124\pi\)
0.955908 0.293667i \(-0.0948755\pi\)
\(678\) 0 0
\(679\) −7.73504 −0.296844
\(680\) 0 0
\(681\) −15.4877 −0.593490
\(682\) 0 0
\(683\) 9.64237 + 9.64237i 0.368955 + 0.368955i 0.867096 0.498141i \(-0.165984\pi\)
−0.498141 + 0.867096i \(0.665984\pi\)
\(684\) 0 0
\(685\) −4.81411 + 4.81411i −0.183938 + 0.183938i
\(686\) 0 0
\(687\) 16.2427 0.619699
\(688\) 0 0
\(689\) 0.350971i 0.0133709i
\(690\) 0 0
\(691\) −25.9580 25.9580i −0.987489 0.987489i 0.0124342 0.999923i \(-0.496042\pi\)
−0.999923 + 0.0124342i \(0.996042\pi\)
\(692\) 0 0
\(693\) 2.02852 0.0770570
\(694\) 0 0
\(695\) 33.0389i 1.25324i
\(696\) 0 0
\(697\) 35.2291 + 22.2134i 1.33440 + 0.841394i
\(698\) 0 0
\(699\) 18.5396i 0.701232i
\(700\) 0 0
\(701\) −22.5048 −0.849993 −0.424996 0.905195i \(-0.639725\pi\)
−0.424996 + 0.905195i \(0.639725\pi\)
\(702\) 0 0
\(703\) −21.4412 21.4412i −0.808672 0.808672i
\(704\) 0 0
\(705\) 72.6766i 2.73716i
\(706\) 0 0
\(707\) 15.3085 0.575734
\(708\) 0 0
\(709\) −5.36395 + 5.36395i −0.201447 + 0.201447i −0.800620 0.599173i \(-0.795496\pi\)
0.599173 + 0.800620i \(0.295496\pi\)
\(710\) 0 0
\(711\) −9.41309 9.41309i −0.353018 0.353018i
\(712\) 0 0
\(713\) −8.52576 −0.319292
\(714\) 0 0
\(715\) 1.04793 0.0391903
\(716\) 0 0
\(717\) 7.49169i 0.279782i
\(718\) 0 0
\(719\) 17.1389 + 17.1389i 0.639174 + 0.639174i 0.950352 0.311178i \(-0.100723\pi\)
−0.311178 + 0.950352i \(0.600723\pi\)
\(720\) 0 0
\(721\) 3.68246 + 3.68246i 0.137142 + 0.137142i
\(722\) 0 0
\(723\) −26.0154 26.0154i −0.967523 0.967523i
\(724\) 0 0
\(725\) −11.6579 + 11.6579i −0.432964 + 0.432964i
\(726\) 0 0
\(727\) −22.6030 + 22.6030i −0.838298 + 0.838298i −0.988635 0.150337i \(-0.951964\pi\)
0.150337 + 0.988635i \(0.451964\pi\)
\(728\) 0 0
\(729\) 16.5472i 0.612860i
\(730\) 0 0
\(731\) 18.6544 18.6544i 0.689956 0.689956i
\(732\) 0 0
\(733\) 12.9847i 0.479600i 0.970822 + 0.239800i \(0.0770818\pi\)
−0.970822 + 0.239800i \(0.922918\pi\)
\(734\) 0 0
\(735\) −4.88047 + 4.88047i −0.180019 + 0.180019i
\(736\) 0 0
\(737\) 7.12680 0.262519
\(738\) 0 0
\(739\) −20.7989 −0.765099 −0.382550 0.923935i \(-0.624954\pi\)
−0.382550 + 0.923935i \(0.624954\pi\)
\(740\) 0 0
\(741\) 2.25520 2.25520i 0.0828469 0.0828469i
\(742\) 0 0
\(743\) 42.9275i 1.57486i −0.616406 0.787429i \(-0.711412\pi\)
0.616406 0.787429i \(-0.288588\pi\)
\(744\) 0 0
\(745\) −11.0268 + 11.0268i −0.403990 + 0.403990i
\(746\) 0 0
\(747\) 10.5100i 0.384541i
\(748\) 0 0
\(749\) −13.9295 + 13.9295i −0.508972 + 0.508972i
\(750\) 0 0
\(751\) −27.1730 + 27.1730i −0.991555 + 0.991555i −0.999965 0.00840929i \(-0.997323\pi\)
0.00840929 + 0.999965i \(0.497323\pi\)
\(752\) 0 0
\(753\) 41.2656 + 41.2656i 1.50380 + 1.50380i
\(754\) 0 0
\(755\) −16.7968 16.7968i −0.611297 0.611297i
\(756\) 0 0
\(757\) 8.44327 + 8.44327i 0.306876 + 0.306876i 0.843696 0.536821i \(-0.180375\pi\)
−0.536821 + 0.843696i \(0.680375\pi\)
\(758\) 0 0
\(759\) 5.04994i 0.183301i
\(760\) 0 0
\(761\) 39.3579 1.42672 0.713361 0.700796i \(-0.247172\pi\)
0.713361 + 0.700796i \(0.247172\pi\)
\(762\) 0 0
\(763\) 0.834987 0.0302286
\(764\) 0 0
\(765\) 33.4114 + 33.4114i 1.20799 + 1.20799i
\(766\) 0 0
\(767\) −1.80852 + 1.80852i −0.0653018 + 0.0653018i
\(768\) 0 0
\(769\) −17.0701 −0.615563 −0.307781 0.951457i \(-0.599587\pi\)
−0.307781 + 0.951457i \(0.599587\pi\)
\(770\) 0 0
\(771\) 26.3764i 0.949922i
\(772\) 0 0
\(773\) 28.6315 + 28.6315i 1.02980 + 1.02980i 0.999542 + 0.0302606i \(0.00963372\pi\)
0.0302606 + 0.999542i \(0.490366\pi\)
\(774\) 0 0
\(775\) −12.1240 −0.435508
\(776\) 0 0
\(777\) 22.3224i 0.800811i
\(778\) 0 0
\(779\) 17.1907 + 10.8395i 0.615921 + 0.388364i
\(780\) 0 0
\(781\) 9.04941i 0.323813i
\(782\) 0 0
\(783\) 5.59049 0.199788
\(784\) 0 0
\(785\) 12.1798 + 12.1798i 0.434716 + 0.434716i
\(786\) 0 0
\(787\) 34.1654i 1.21786i −0.793222 0.608932i \(-0.791598\pi\)
0.793222 0.608932i \(-0.208402\pi\)
\(788\) 0 0
\(789\) 27.8885 0.992858
\(790\) 0 0
\(791\) 0.252879 0.252879i 0.00899134 0.00899134i
\(792\) 0 0
\(793\) 1.62019 + 1.62019i 0.0575347 + 0.0575347i
\(794\) 0 0
\(795\) −5.63255 −0.199766
\(796\) 0 0
\(797\) −22.8507 −0.809412 −0.404706 0.914447i \(-0.632626\pi\)
−0.404706 + 0.914447i \(0.632626\pi\)
\(798\) 0 0
\(799\) 68.4884i 2.42294i
\(800\) 0 0