Properties

Label 1148.2.k.b.729.14
Level $1148$
Weight $2$
Character 1148.729
Analytic conductor $9.167$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 729.14
Character \(\chi\) \(=\) 1148.729
Dual form 1148.2.k.b.337.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.62776 - 1.62776i) q^{3} -3.63967i q^{5} +(0.707107 - 0.707107i) q^{7} -2.29923i q^{9} +O(q^{10})\) \(q+(1.62776 - 1.62776i) q^{3} -3.63967i q^{5} +(0.707107 - 0.707107i) q^{7} -2.29923i q^{9} +(1.60909 - 1.60909i) q^{11} +(2.83000 - 2.83000i) q^{13} +(-5.92453 - 5.92453i) q^{15} +(2.68616 + 2.68616i) q^{17} +(4.94910 + 4.94910i) q^{19} -2.30201i q^{21} -4.18481 q^{23} -8.24722 q^{25} +(1.14069 + 1.14069i) q^{27} +(-1.01640 + 1.01640i) q^{29} -6.11889 q^{31} -5.23843i q^{33} +(-2.57364 - 2.57364i) q^{35} -1.89269 q^{37} -9.21314i q^{39} +(5.19627 - 3.74150i) q^{41} +6.11098i q^{43} -8.36844 q^{45} +(-1.11039 - 1.11039i) q^{47} -1.00000i q^{49} +8.74486 q^{51} +(-6.21475 + 6.21475i) q^{53} +(-5.85655 - 5.85655i) q^{55} +16.1119 q^{57} -2.32994 q^{59} +10.9365i q^{61} +(-1.62580 - 1.62580i) q^{63} +(-10.3003 - 10.3003i) q^{65} +(-3.50751 - 3.50751i) q^{67} +(-6.81188 + 6.81188i) q^{69} +(1.61276 - 1.61276i) q^{71} +3.53090i q^{73} +(-13.4245 + 13.4245i) q^{75} -2.27559i q^{77} +(-7.22498 + 7.22498i) q^{79} +10.6112 q^{81} +0.636038 q^{83} +(9.77673 - 9.77673i) q^{85} +3.30891i q^{87} +(-2.14544 + 2.14544i) q^{89} -4.00222i q^{91} +(-9.96011 + 9.96011i) q^{93} +(18.0131 - 18.0131i) q^{95} +(-11.3830 - 11.3830i) q^{97} +(-3.69966 - 3.69966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

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
\(3\) 1.62776 1.62776i 0.939790 0.939790i −0.0584977 0.998288i \(-0.518631\pi\)
0.998288 + 0.0584977i \(0.0186310\pi\)
\(4\) 0 0
\(5\) 3.63967i 1.62771i −0.581067 0.813856i \(-0.697365\pi\)
0.581067 0.813856i \(-0.302635\pi\)
\(6\) 0 0
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 0 0
\(9\) 2.29923i 0.766410i
\(10\) 0 0
\(11\) 1.60909 1.60909i 0.485158 0.485158i −0.421616 0.906774i \(-0.638537\pi\)
0.906774 + 0.421616i \(0.138537\pi\)
\(12\) 0 0
\(13\) 2.83000 2.83000i 0.784900 0.784900i −0.195753 0.980653i \(-0.562715\pi\)
0.980653 + 0.195753i \(0.0627151\pi\)
\(14\) 0 0
\(15\) −5.92453 5.92453i −1.52971 1.52971i
\(16\) 0 0
\(17\) 2.68616 + 2.68616i 0.651489 + 0.651489i 0.953351 0.301863i \(-0.0976084\pi\)
−0.301863 + 0.953351i \(0.597608\pi\)
\(18\) 0 0
\(19\) 4.94910 + 4.94910i 1.13540 + 1.13540i 0.989264 + 0.146138i \(0.0466844\pi\)
0.146138 + 0.989264i \(0.453316\pi\)
\(20\) 0 0
\(21\) 2.30201i 0.502339i
\(22\) 0 0
\(23\) −4.18481 −0.872593 −0.436297 0.899803i \(-0.643710\pi\)
−0.436297 + 0.899803i \(0.643710\pi\)
\(24\) 0 0
\(25\) −8.24722 −1.64944
\(26\) 0 0
\(27\) 1.14069 + 1.14069i 0.219526 + 0.219526i
\(28\) 0 0
\(29\) −1.01640 + 1.01640i −0.188740 + 0.188740i −0.795151 0.606411i \(-0.792609\pi\)
0.606411 + 0.795151i \(0.292609\pi\)
\(30\) 0 0
\(31\) −6.11889 −1.09899 −0.549493 0.835499i \(-0.685179\pi\)
−0.549493 + 0.835499i \(0.685179\pi\)
\(32\) 0 0
\(33\) 5.23843i 0.911893i
\(34\) 0 0
\(35\) −2.57364 2.57364i −0.435024 0.435024i
\(36\) 0 0
\(37\) −1.89269 −0.311157 −0.155578 0.987824i \(-0.549724\pi\)
−0.155578 + 0.987824i \(0.549724\pi\)
\(38\) 0 0
\(39\) 9.21314i 1.47528i
\(40\) 0 0
\(41\) 5.19627 3.74150i 0.811521 0.584323i
\(42\) 0 0
\(43\) 6.11098i 0.931916i 0.884807 + 0.465958i \(0.154290\pi\)
−0.884807 + 0.465958i \(0.845710\pi\)
\(44\) 0 0
\(45\) −8.36844 −1.24749
\(46\) 0 0
\(47\) −1.11039 1.11039i −0.161967 0.161967i 0.621470 0.783438i \(-0.286536\pi\)
−0.783438 + 0.621470i \(0.786536\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 8.74486 1.22452
\(52\) 0 0
\(53\) −6.21475 + 6.21475i −0.853661 + 0.853661i −0.990582 0.136921i \(-0.956279\pi\)
0.136921 + 0.990582i \(0.456279\pi\)
\(54\) 0 0
\(55\) −5.85655 5.85655i −0.789697 0.789697i
\(56\) 0 0
\(57\) 16.1119 2.13408
\(58\) 0 0
\(59\) −2.32994 −0.303332 −0.151666 0.988432i \(-0.548464\pi\)
−0.151666 + 0.988432i \(0.548464\pi\)
\(60\) 0 0
\(61\) 10.9365i 1.40027i 0.714009 + 0.700136i \(0.246877\pi\)
−0.714009 + 0.700136i \(0.753123\pi\)
\(62\) 0 0
\(63\) −1.62580 1.62580i −0.204832 0.204832i
\(64\) 0 0
\(65\) −10.3003 10.3003i −1.27759 1.27759i
\(66\) 0 0
\(67\) −3.50751 3.50751i −0.428511 0.428511i 0.459610 0.888121i \(-0.347989\pi\)
−0.888121 + 0.459610i \(0.847989\pi\)
\(68\) 0 0
\(69\) −6.81188 + 6.81188i −0.820054 + 0.820054i
\(70\) 0 0
\(71\) 1.61276 1.61276i 0.191399 0.191399i −0.604901 0.796301i \(-0.706787\pi\)
0.796301 + 0.604901i \(0.206787\pi\)
\(72\) 0 0
\(73\) 3.53090i 0.413260i 0.978419 + 0.206630i \(0.0662497\pi\)
−0.978419 + 0.206630i \(0.933750\pi\)
\(74\) 0 0
\(75\) −13.4245 + 13.4245i −1.55013 + 1.55013i
\(76\) 0 0
\(77\) 2.27559i 0.259328i
\(78\) 0 0
\(79\) −7.22498 + 7.22498i −0.812874 + 0.812874i −0.985064 0.172190i \(-0.944916\pi\)
0.172190 + 0.985064i \(0.444916\pi\)
\(80\) 0 0
\(81\) 10.6112 1.17903
\(82\) 0 0
\(83\) 0.636038 0.0698142 0.0349071 0.999391i \(-0.488886\pi\)
0.0349071 + 0.999391i \(0.488886\pi\)
\(84\) 0 0
\(85\) 9.77673 9.77673i 1.06044 1.06044i
\(86\) 0 0
\(87\) 3.30891i 0.354752i
\(88\) 0 0
\(89\) −2.14544 + 2.14544i −0.227417 + 0.227417i −0.811613 0.584196i \(-0.801410\pi\)
0.584196 + 0.811613i \(0.301410\pi\)
\(90\) 0 0
\(91\) 4.00222i 0.419547i
\(92\) 0 0
\(93\) −9.96011 + 9.96011i −1.03282 + 1.03282i
\(94\) 0 0
\(95\) 18.0131 18.0131i 1.84811 1.84811i
\(96\) 0 0
\(97\) −11.3830 11.3830i −1.15577 1.15577i −0.985375 0.170397i \(-0.945495\pi\)
−0.170397 0.985375i \(-0.554505\pi\)
\(98\) 0 0
\(99\) −3.69966 3.69966i −0.371830 0.371830i
\(100\) 0 0
\(101\) −2.60851 2.60851i −0.259556 0.259556i 0.565317 0.824873i \(-0.308754\pi\)
−0.824873 + 0.565317i \(0.808754\pi\)
\(102\) 0 0
\(103\) 13.7456i 1.35439i 0.735803 + 0.677196i \(0.236805\pi\)
−0.735803 + 0.677196i \(0.763195\pi\)
\(104\) 0 0
\(105\) −8.37855 −0.817662
\(106\) 0 0
\(107\) 9.85969 0.953172 0.476586 0.879128i \(-0.341874\pi\)
0.476586 + 0.879128i \(0.341874\pi\)
\(108\) 0 0
\(109\) 2.42649 + 2.42649i 0.232415 + 0.232415i 0.813700 0.581285i \(-0.197450\pi\)
−0.581285 + 0.813700i \(0.697450\pi\)
\(110\) 0 0
\(111\) −3.08085 + 3.08085i −0.292422 + 0.292422i
\(112\) 0 0
\(113\) 16.3563 1.53867 0.769334 0.638846i \(-0.220588\pi\)
0.769334 + 0.638846i \(0.220588\pi\)
\(114\) 0 0
\(115\) 15.2313i 1.42033i
\(116\) 0 0
\(117\) −6.50681 6.50681i −0.601555 0.601555i
\(118\) 0 0
\(119\) 3.79880 0.348235
\(120\) 0 0
\(121\) 5.82168i 0.529243i
\(122\) 0 0
\(123\) 2.36803 14.5486i 0.213518 1.31180i
\(124\) 0 0
\(125\) 11.8188i 1.05711i
\(126\) 0 0
\(127\) 21.0335 1.86642 0.933212 0.359326i \(-0.116993\pi\)
0.933212 + 0.359326i \(0.116993\pi\)
\(128\) 0 0
\(129\) 9.94723 + 9.94723i 0.875805 + 0.875805i
\(130\) 0 0
\(131\) 2.42453i 0.211832i 0.994375 + 0.105916i \(0.0337774\pi\)
−0.994375 + 0.105916i \(0.966223\pi\)
\(132\) 0 0
\(133\) 6.99909 0.606898
\(134\) 0 0
\(135\) 4.15174 4.15174i 0.357325 0.357325i
\(136\) 0 0
\(137\) −9.63456 9.63456i −0.823136 0.823136i 0.163420 0.986557i \(-0.447747\pi\)
−0.986557 + 0.163420i \(0.947747\pi\)
\(138\) 0 0
\(139\) 6.81013 0.577628 0.288814 0.957385i \(-0.406739\pi\)
0.288814 + 0.957385i \(0.406739\pi\)
\(140\) 0 0
\(141\) −3.61491 −0.304431
\(142\) 0 0
\(143\) 9.10743i 0.761601i
\(144\) 0 0
\(145\) 3.69935 + 3.69935i 0.307215 + 0.307215i
\(146\) 0 0
\(147\) −1.62776 1.62776i −0.134256 0.134256i
\(148\) 0 0
\(149\) −16.7060 16.7060i −1.36861 1.36861i −0.862426 0.506183i \(-0.831056\pi\)
−0.506183 0.862426i \(-0.668944\pi\)
\(150\) 0 0
\(151\) 11.6674 11.6674i 0.949483 0.949483i −0.0493013 0.998784i \(-0.515699\pi\)
0.998784 + 0.0493013i \(0.0156995\pi\)
\(152\) 0 0
\(153\) 6.17609 6.17609i 0.499307 0.499307i
\(154\) 0 0
\(155\) 22.2708i 1.78883i
\(156\) 0 0
\(157\) 10.7274 10.7274i 0.856137 0.856137i −0.134744 0.990880i \(-0.543021\pi\)
0.990880 + 0.134744i \(0.0430211\pi\)
\(158\) 0 0
\(159\) 20.2323i 1.60452i
\(160\) 0 0
\(161\) −2.95911 + 2.95911i −0.233210 + 0.233210i
\(162\) 0 0
\(163\) −7.02604 −0.550322 −0.275161 0.961398i \(-0.588731\pi\)
−0.275161 + 0.961398i \(0.588731\pi\)
\(164\) 0 0
\(165\) −19.0662 −1.48430
\(166\) 0 0
\(167\) 4.17785 4.17785i 0.323292 0.323292i −0.526737 0.850028i \(-0.676585\pi\)
0.850028 + 0.526737i \(0.176585\pi\)
\(168\) 0 0
\(169\) 3.01778i 0.232137i
\(170\) 0 0
\(171\) 11.3791 11.3791i 0.870183 0.870183i
\(172\) 0 0
\(173\) 11.6029i 0.882151i −0.897470 0.441075i \(-0.854597\pi\)
0.897470 0.441075i \(-0.145403\pi\)
\(174\) 0 0
\(175\) −5.83166 + 5.83166i −0.440832 + 0.440832i
\(176\) 0 0
\(177\) −3.79258 + 3.79258i −0.285068 + 0.285068i
\(178\) 0 0
\(179\) 5.87965 + 5.87965i 0.439465 + 0.439465i 0.891832 0.452367i \(-0.149420\pi\)
−0.452367 + 0.891832i \(0.649420\pi\)
\(180\) 0 0
\(181\) −16.7368 16.7368i −1.24404 1.24404i −0.958312 0.285723i \(-0.907766\pi\)
−0.285723 0.958312i \(-0.592234\pi\)
\(182\) 0 0
\(183\) 17.8020 + 17.8020i 1.31596 + 1.31596i
\(184\) 0 0
\(185\) 6.88878i 0.506473i
\(186\) 0 0
\(187\) 8.64452 0.632150
\(188\) 0 0
\(189\) 1.61318 0.117341
\(190\) 0 0
\(191\) −12.0435 12.0435i −0.871436 0.871436i 0.121193 0.992629i \(-0.461328\pi\)
−0.992629 + 0.121193i \(0.961328\pi\)
\(192\) 0 0
\(193\) −17.3747 + 17.3747i −1.25066 + 1.25066i −0.295236 + 0.955424i \(0.595398\pi\)
−0.955424 + 0.295236i \(0.904602\pi\)
\(194\) 0 0
\(195\) −33.5328 −2.40133
\(196\) 0 0
\(197\) 8.37995i 0.597047i −0.954402 0.298523i \(-0.903506\pi\)
0.954402 0.298523i \(-0.0964941\pi\)
\(198\) 0 0
\(199\) 13.2564 + 13.2564i 0.939721 + 0.939721i 0.998284 0.0585626i \(-0.0186517\pi\)
−0.0585626 + 0.998284i \(0.518652\pi\)
\(200\) 0 0
\(201\) −11.4188 −0.805421
\(202\) 0 0
\(203\) 1.43740i 0.100886i
\(204\) 0 0
\(205\) −13.6178 18.9127i −0.951110 1.32092i
\(206\) 0 0
\(207\) 9.62184i 0.668764i
\(208\) 0 0
\(209\) 15.9271 1.10170
\(210\) 0 0
\(211\) 12.1193 + 12.1193i 0.834330 + 0.834330i 0.988106 0.153776i \(-0.0491434\pi\)
−0.153776 + 0.988106i \(0.549143\pi\)
\(212\) 0 0
\(213\) 5.25038i 0.359750i
\(214\) 0 0
\(215\) 22.2420 1.51689
\(216\) 0 0
\(217\) −4.32671 + 4.32671i −0.293716 + 0.293716i
\(218\) 0 0
\(219\) 5.74747 + 5.74747i 0.388378 + 0.388378i
\(220\) 0 0
\(221\) 15.2036 1.02271
\(222\) 0 0
\(223\) −14.5490 −0.974274 −0.487137 0.873326i \(-0.661959\pi\)
−0.487137 + 0.873326i \(0.661959\pi\)
\(224\) 0 0
\(225\) 18.9622i 1.26415i
\(226\) 0 0
\(227\) 7.25739 + 7.25739i 0.481690 + 0.481690i 0.905671 0.423981i \(-0.139368\pi\)
−0.423981 + 0.905671i \(0.639368\pi\)
\(228\) 0 0
\(229\) 6.97691 + 6.97691i 0.461047 + 0.461047i 0.898999 0.437952i \(-0.144296\pi\)
−0.437952 + 0.898999i \(0.644296\pi\)
\(230\) 0 0
\(231\) −3.70413 3.70413i −0.243714 0.243714i
\(232\) 0 0
\(233\) 21.2203 21.2203i 1.39018 1.39018i 0.565298 0.824887i \(-0.308761\pi\)
0.824887 0.565298i \(-0.191239\pi\)
\(234\) 0 0
\(235\) −4.04146 + 4.04146i −0.263636 + 0.263636i
\(236\) 0 0
\(237\) 23.5211i 1.52786i
\(238\) 0 0
\(239\) −5.63864 + 5.63864i −0.364733 + 0.364733i −0.865552 0.500819i \(-0.833032\pi\)
0.500819 + 0.865552i \(0.333032\pi\)
\(240\) 0 0
\(241\) 6.54156i 0.421379i 0.977553 + 0.210690i \(0.0675709\pi\)
−0.977553 + 0.210690i \(0.932429\pi\)
\(242\) 0 0
\(243\) 13.8505 13.8505i 0.888511 0.888511i
\(244\) 0 0
\(245\) −3.63967 −0.232530
\(246\) 0 0
\(247\) 28.0119 1.78236
\(248\) 0 0
\(249\) 1.03532 1.03532i 0.0656107 0.0656107i
\(250\) 0 0
\(251\) 11.2434i 0.709675i 0.934928 + 0.354837i \(0.115464\pi\)
−0.934928 + 0.354837i \(0.884536\pi\)
\(252\) 0 0
\(253\) −6.73372 + 6.73372i −0.423346 + 0.423346i
\(254\) 0 0
\(255\) 31.8284i 1.99317i
\(256\) 0 0
\(257\) −7.84302 + 7.84302i −0.489234 + 0.489234i −0.908064 0.418830i \(-0.862440\pi\)
0.418830 + 0.908064i \(0.362440\pi\)
\(258\) 0 0
\(259\) −1.33833 + 1.33833i −0.0831601 + 0.0831601i
\(260\) 0 0
\(261\) 2.33693 + 2.33693i 0.144652 + 0.144652i
\(262\) 0 0
\(263\) 16.0480 + 16.0480i 0.989564 + 0.989564i 0.999946 0.0103825i \(-0.00330491\pi\)
−0.0103825 + 0.999946i \(0.503305\pi\)
\(264\) 0 0
\(265\) 22.6197 + 22.6197i 1.38951 + 1.38951i
\(266\) 0 0
\(267\) 6.98455i 0.427448i
\(268\) 0 0
\(269\) 10.8937 0.664201 0.332100 0.943244i \(-0.392243\pi\)
0.332100 + 0.943244i \(0.392243\pi\)
\(270\) 0 0
\(271\) −10.1897 −0.618982 −0.309491 0.950902i \(-0.600159\pi\)
−0.309491 + 0.950902i \(0.600159\pi\)
\(272\) 0 0
\(273\) −6.51467 6.51467i −0.394286 0.394286i
\(274\) 0 0
\(275\) −13.2705 + 13.2705i −0.800241 + 0.800241i
\(276\) 0 0
\(277\) −16.1367 −0.969562 −0.484781 0.874636i \(-0.661101\pi\)
−0.484781 + 0.874636i \(0.661101\pi\)
\(278\) 0 0
\(279\) 14.0687i 0.842273i
\(280\) 0 0
\(281\) −17.6513 17.6513i −1.05299 1.05299i −0.998515 0.0544708i \(-0.982653\pi\)
−0.0544708 0.998515i \(-0.517347\pi\)
\(282\) 0 0
\(283\) −24.0875 −1.43185 −0.715925 0.698177i \(-0.753995\pi\)
−0.715925 + 0.698177i \(0.753995\pi\)
\(284\) 0 0
\(285\) 58.6422i 3.47366i
\(286\) 0 0
\(287\) 1.02868 6.31995i 0.0607211 0.373055i
\(288\) 0 0
\(289\) 2.56913i 0.151125i
\(290\) 0 0
\(291\) −37.0578 −2.17237
\(292\) 0 0
\(293\) 8.67027 + 8.67027i 0.506523 + 0.506523i 0.913457 0.406935i \(-0.133402\pi\)
−0.406935 + 0.913457i \(0.633402\pi\)
\(294\) 0 0
\(295\) 8.48020i 0.493737i
\(296\) 0 0
\(297\) 3.67094 0.213009
\(298\) 0 0
\(299\) −11.8430 + 11.8430i −0.684899 + 0.684899i
\(300\) 0 0
\(301\) 4.32112 + 4.32112i 0.249065 + 0.249065i
\(302\) 0 0
\(303\) −8.49206 −0.487856
\(304\) 0 0
\(305\) 39.8052 2.27924
\(306\) 0 0
\(307\) 32.9525i 1.88070i −0.340211 0.940349i \(-0.610499\pi\)
0.340211 0.940349i \(-0.389501\pi\)
\(308\) 0 0
\(309\) 22.3745 + 22.3745i 1.27284 + 1.27284i
\(310\) 0 0
\(311\) −1.89889 1.89889i −0.107676 0.107676i 0.651216 0.758892i \(-0.274259\pi\)
−0.758892 + 0.651216i \(0.774259\pi\)
\(312\) 0 0
\(313\) −10.6576 10.6576i −0.602403 0.602403i 0.338547 0.940950i \(-0.390065\pi\)
−0.940950 + 0.338547i \(0.890065\pi\)
\(314\) 0 0
\(315\) −5.91738 + 5.91738i −0.333407 + 0.333407i
\(316\) 0 0
\(317\) 3.86773 3.86773i 0.217233 0.217233i −0.590098 0.807332i \(-0.700911\pi\)
0.807332 + 0.590098i \(0.200911\pi\)
\(318\) 0 0
\(319\) 3.27094i 0.183138i
\(320\) 0 0
\(321\) 16.0492 16.0492i 0.895782 0.895782i
\(322\) 0 0
\(323\) 26.5881i 1.47940i
\(324\) 0 0
\(325\) −23.3396 + 23.3396i −1.29465 + 1.29465i
\(326\) 0 0
\(327\) 7.89950 0.436843
\(328\) 0 0
\(329\) −1.57033 −0.0865752
\(330\) 0 0
\(331\) −17.7620 + 17.7620i −0.976289 + 0.976289i −0.999725 0.0234362i \(-0.992539\pi\)
0.0234362 + 0.999725i \(0.492539\pi\)
\(332\) 0 0
\(333\) 4.35173i 0.238473i
\(334\) 0 0
\(335\) −12.7662 + 12.7662i −0.697492 + 0.697492i
\(336\) 0 0
\(337\) 14.8935i 0.811302i −0.914028 0.405651i \(-0.867045\pi\)
0.914028 0.405651i \(-0.132955\pi\)
\(338\) 0 0
\(339\) 26.6242 26.6242i 1.44603 1.44603i
\(340\) 0 0
\(341\) −9.84583 + 9.84583i −0.533181 + 0.533181i
\(342\) 0 0
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 0 0
\(345\) 24.7930 + 24.7930i 1.33481 + 1.33481i
\(346\) 0 0
\(347\) 16.3099 + 16.3099i 0.875563 + 0.875563i 0.993072 0.117508i \(-0.0374907\pi\)
−0.117508 + 0.993072i \(0.537491\pi\)
\(348\) 0 0
\(349\) 30.6680i 1.64162i 0.571203 + 0.820809i \(0.306477\pi\)
−0.571203 + 0.820809i \(0.693523\pi\)
\(350\) 0 0
\(351\) 6.45630 0.344612
\(352\) 0 0
\(353\) −1.68699 −0.0897895 −0.0448948 0.998992i \(-0.514295\pi\)
−0.0448948 + 0.998992i \(0.514295\pi\)
\(354\) 0 0
\(355\) −5.86992 5.86992i −0.311543 0.311543i
\(356\) 0 0
\(357\) 6.18355 6.18355i 0.327268 0.327268i
\(358\) 0 0
\(359\) 6.47232 0.341596 0.170798 0.985306i \(-0.445365\pi\)
0.170798 + 0.985306i \(0.445365\pi\)
\(360\) 0 0
\(361\) 29.9873i 1.57828i
\(362\) 0 0
\(363\) 9.47632 + 9.47632i 0.497378 + 0.497378i
\(364\) 0 0
\(365\) 12.8513 0.672669
\(366\) 0 0
\(367\) 0.243504i 0.0127108i 0.999980 + 0.00635539i \(0.00202300\pi\)
−0.999980 + 0.00635539i \(0.997977\pi\)
\(368\) 0 0
\(369\) −8.60256 11.9474i −0.447831 0.621958i
\(370\) 0 0
\(371\) 8.78898i 0.456301i
\(372\) 0 0
\(373\) −5.21111 −0.269821 −0.134910 0.990858i \(-0.543075\pi\)
−0.134910 + 0.990858i \(0.543075\pi\)
\(374\) 0 0
\(375\) 19.2382 + 19.2382i 0.993459 + 0.993459i
\(376\) 0 0
\(377\) 5.75280i 0.296284i
\(378\) 0 0
\(379\) 24.5983 1.26353 0.631764 0.775161i \(-0.282331\pi\)
0.631764 + 0.775161i \(0.282331\pi\)
\(380\) 0 0
\(381\) 34.2376 34.2376i 1.75405 1.75405i
\(382\) 0 0
\(383\) 13.9311 + 13.9311i 0.711845 + 0.711845i 0.966921 0.255076i \(-0.0821005\pi\)
−0.255076 + 0.966921i \(0.582101\pi\)
\(384\) 0 0
\(385\) −8.28241 −0.422111
\(386\) 0 0
\(387\) 14.0505 0.714230
\(388\) 0 0
\(389\) 16.3575i 0.829360i −0.909967 0.414680i \(-0.863894\pi\)
0.909967 0.414680i \(-0.136106\pi\)
\(390\) 0 0
\(391\) −11.2411 11.2411i −0.568485 0.568485i
\(392\) 0 0
\(393\) 3.94655 + 3.94655i 0.199077 + 0.199077i
\(394\) 0 0
\(395\) 26.2966 + 26.2966i 1.32312 + 1.32312i
\(396\) 0 0
\(397\) −11.1771 + 11.1771i −0.560963 + 0.560963i −0.929581 0.368618i \(-0.879831\pi\)
0.368618 + 0.929581i \(0.379831\pi\)
\(398\) 0 0
\(399\) 11.3929 11.3929i 0.570357 0.570357i
\(400\) 0 0
\(401\) 13.6373i 0.681013i −0.940242 0.340507i \(-0.889401\pi\)
0.940242 0.340507i \(-0.110599\pi\)
\(402\) 0 0
\(403\) −17.3164 + 17.3164i −0.862594 + 0.862594i
\(404\) 0 0
\(405\) 38.6214i 1.91911i
\(406\) 0 0
\(407\) −3.04551 + 3.04551i −0.150960 + 0.150960i
\(408\) 0 0
\(409\) −8.52231 −0.421401 −0.210701 0.977551i \(-0.567575\pi\)
−0.210701 + 0.977551i \(0.567575\pi\)
\(410\) 0 0
\(411\) −31.3656 −1.54715
\(412\) 0 0
\(413\) −1.64751 + 1.64751i −0.0810688 + 0.0810688i
\(414\) 0 0
\(415\) 2.31497i 0.113637i
\(416\) 0 0
\(417\) 11.0853 11.0853i 0.542849 0.542849i
\(418\) 0 0
\(419\) 16.8391i 0.822642i 0.911491 + 0.411321i \(0.134933\pi\)
−0.911491 + 0.411321i \(0.865067\pi\)
\(420\) 0 0
\(421\) −7.80018 + 7.80018i −0.380157 + 0.380157i −0.871159 0.491001i \(-0.836631\pi\)
0.491001 + 0.871159i \(0.336631\pi\)
\(422\) 0 0
\(423\) −2.55305 + 2.55305i −0.124133 + 0.124133i
\(424\) 0 0
\(425\) −22.1533 22.1533i −1.07459 1.07459i
\(426\) 0 0
\(427\) 7.73326 + 7.73326i 0.374239 + 0.374239i
\(428\) 0 0
\(429\) −14.8247 14.8247i −0.715745 0.715745i
\(430\) 0 0
\(431\) 5.40983i 0.260582i 0.991476 + 0.130291i \(0.0415912\pi\)
−0.991476 + 0.130291i \(0.958409\pi\)
\(432\) 0 0
\(433\) −15.6205 −0.750671 −0.375336 0.926889i \(-0.622473\pi\)
−0.375336 + 0.926889i \(0.622473\pi\)
\(434\) 0 0
\(435\) 12.0433 0.577434
\(436\) 0 0
\(437\) −20.7111 20.7111i −0.990745 0.990745i
\(438\) 0 0
\(439\) −10.4882 + 10.4882i −0.500575 + 0.500575i −0.911617 0.411041i \(-0.865165\pi\)
0.411041 + 0.911617i \(0.365165\pi\)
\(440\) 0 0
\(441\) −2.29923 −0.109487
\(442\) 0 0
\(443\) 22.0107i 1.04576i 0.852406 + 0.522880i \(0.175142\pi\)
−0.852406 + 0.522880i \(0.824858\pi\)
\(444\) 0 0
\(445\) 7.80872 + 7.80872i 0.370169 + 0.370169i
\(446\) 0 0
\(447\) −54.3869 −2.57241
\(448\) 0 0
\(449\) 27.4642i 1.29611i −0.761591 0.648057i \(-0.775582\pi\)
0.761591 0.648057i \(-0.224418\pi\)
\(450\) 0 0
\(451\) 2.34086 14.3816i 0.110227 0.677205i
\(452\) 0 0
\(453\) 37.9837i 1.78463i
\(454\) 0 0
\(455\) −14.5668 −0.682901
\(456\) 0 0
\(457\) −15.3741 15.3741i −0.719172 0.719172i 0.249264 0.968436i \(-0.419811\pi\)
−0.968436 + 0.249264i \(0.919811\pi\)
\(458\) 0 0
\(459\) 6.12814i 0.286037i
\(460\) 0 0
\(461\) −7.51081 −0.349814 −0.174907 0.984585i \(-0.555962\pi\)
−0.174907 + 0.984585i \(0.555962\pi\)
\(462\) 0 0
\(463\) 26.1709 26.1709i 1.21627 1.21627i 0.247336 0.968930i \(-0.420445\pi\)
0.968930 0.247336i \(-0.0795550\pi\)
\(464\) 0 0
\(465\) 36.2515 + 36.2515i 1.68112 + 1.68112i
\(466\) 0 0
\(467\) −25.7958 −1.19369 −0.596844 0.802358i \(-0.703579\pi\)
−0.596844 + 0.802358i \(0.703579\pi\)
\(468\) 0 0
\(469\) −4.96037 −0.229049
\(470\) 0 0
\(471\) 34.9232i 1.60918i
\(472\) 0 0
\(473\) 9.83310 + 9.83310i 0.452126 + 0.452126i
\(474\) 0 0
\(475\) −40.8164 40.8164i −1.87278 1.87278i
\(476\) 0 0
\(477\) 14.2891 + 14.2891i 0.654254 + 0.654254i
\(478\) 0 0
\(479\) −20.7038 + 20.7038i −0.945981 + 0.945981i −0.998614 0.0526329i \(-0.983239\pi\)
0.0526329 + 0.998614i \(0.483239\pi\)
\(480\) 0 0
\(481\) −5.35631 + 5.35631i −0.244227 + 0.244227i
\(482\) 0 0
\(483\) 9.63346i 0.438338i
\(484\) 0 0
\(485\) −41.4305 + 41.4305i −1.88126 + 1.88126i
\(486\) 0 0
\(487\) 14.0123i 0.634957i −0.948265 0.317479i \(-0.897164\pi\)
0.948265 0.317479i \(-0.102836\pi\)
\(488\) 0 0
\(489\) −11.4367 + 11.4367i −0.517187 + 0.517187i
\(490\) 0 0
\(491\) 0.776362 0.0350367 0.0175184 0.999847i \(-0.494423\pi\)
0.0175184 + 0.999847i \(0.494423\pi\)
\(492\) 0 0
\(493\) −5.46040 −0.245924
\(494\) 0 0
\(495\) −13.4656 + 13.4656i −0.605232 + 0.605232i
\(496\) 0 0
\(497\) 2.28079i 0.102307i
\(498\) 0 0
\(499\) −1.01843 + 1.01843i −0.0455911 + 0.0455911i −0.729535 0.683944i \(-0.760263\pi\)
0.683944 + 0.729535i \(0.260263\pi\)
\(500\) 0 0
\(501\) 13.6011i 0.607653i
\(502\) 0 0
\(503\) 29.3217 29.3217i 1.30739 1.30739i 0.384094 0.923294i \(-0.374514\pi\)
0.923294 0.384094i \(-0.125486\pi\)
\(504\) 0 0
\(505\) −9.49411 + 9.49411i −0.422482 + 0.422482i
\(506\) 0 0
\(507\) −4.91223 4.91223i −0.218160 0.218160i
\(508\) 0 0
\(509\) −21.7571 21.7571i −0.964366 0.964366i 0.0350207 0.999387i \(-0.488850\pi\)
−0.999387 + 0.0350207i \(0.988850\pi\)
\(510\) 0 0
\(511\) 2.49672 + 2.49672i 0.110448 + 0.110448i
\(512\) 0 0
\(513\) 11.2908i 0.498500i
\(514\) 0 0
\(515\) 50.0294 2.20456
\(516\) 0 0
\(517\) −3.57344 −0.157159
\(518\) 0 0
\(519\) −18.8867 18.8867i −0.829036 0.829036i
\(520\) 0 0
\(521\) 17.2837 17.2837i 0.757211 0.757211i −0.218603 0.975814i \(-0.570150\pi\)
0.975814 + 0.218603i \(0.0701500\pi\)
\(522\) 0 0
\(523\) −16.1813 −0.707558 −0.353779 0.935329i \(-0.615103\pi\)
−0.353779 + 0.935329i \(0.615103\pi\)
\(524\) 0 0
\(525\) 18.9851i 0.828580i
\(526\) 0 0
\(527\) −16.4363 16.4363i −0.715976 0.715976i
\(528\) 0 0
\(529\) −5.48736 −0.238581
\(530\) 0 0
\(531\) 5.35706i 0.232476i
\(532\) 0 0
\(533\) 4.11701 25.2939i 0.178327 1.09560i
\(534\) 0 0
\(535\) 35.8861i 1.55149i
\(536\) 0 0
\(537\) 19.1414 0.826010
\(538\) 0 0
\(539\) −1.60909 1.60909i −0.0693083 0.0693083i
\(540\) 0 0
\(541\) 32.8080i 1.41053i −0.708945 0.705263i \(-0.750829\pi\)
0.708945 0.705263i \(-0.249171\pi\)
\(542\) 0 0
\(543\) −54.4870 −2.33826
\(544\) 0 0
\(545\) 8.83162 8.83162i 0.378305 0.378305i
\(546\) 0 0
\(547\) 12.0579 + 12.0579i 0.515559 + 0.515559i 0.916224 0.400666i \(-0.131221\pi\)
−0.400666 + 0.916224i \(0.631221\pi\)
\(548\) 0 0
\(549\) 25.1455 1.07318
\(550\) 0 0
\(551\) −10.0605 −0.428592
\(552\) 0 0
\(553\) 10.2177i 0.434499i
\(554\) 0 0
\(555\) 11.2133 + 11.2133i 0.475978 + 0.475978i
\(556\) 0 0
\(557\) 21.9362 + 21.9362i 0.929467 + 0.929467i 0.997671 0.0682046i \(-0.0217271\pi\)
−0.0682046 + 0.997671i \(0.521727\pi\)
\(558\) 0 0
\(559\) 17.2941 + 17.2941i 0.731461 + 0.731461i
\(560\) 0 0
\(561\) 14.0712 14.0712i 0.594088 0.594088i
\(562\) 0 0
\(563\) 23.4245 23.4245i 0.987226 0.987226i −0.0126939 0.999919i \(-0.504041\pi\)
0.999919 + 0.0126939i \(0.00404070\pi\)
\(564\) 0 0
\(565\) 59.5315i 2.50451i
\(566\) 0 0
\(567\) 7.50327 7.50327i 0.315108 0.315108i
\(568\) 0 0
\(569\) 28.7285i 1.20436i 0.798359 + 0.602181i \(0.205702\pi\)
−0.798359 + 0.602181i \(0.794298\pi\)
\(570\) 0 0
\(571\) −1.55817 + 1.55817i −0.0652073 + 0.0652073i −0.738958 0.673751i \(-0.764682\pi\)
0.673751 + 0.738958i \(0.264682\pi\)
\(572\) 0 0
\(573\) −39.2079 −1.63793
\(574\) 0 0
\(575\) 34.5131 1.43929
\(576\) 0 0
\(577\) 8.67296 8.67296i 0.361060 0.361060i −0.503143 0.864203i \(-0.667823\pi\)
0.864203 + 0.503143i \(0.167823\pi\)
\(578\) 0 0
\(579\) 56.5639i 2.35072i
\(580\) 0 0
\(581\) 0.449747 0.449747i 0.0186586 0.0186586i
\(582\) 0 0
\(583\) 20.0001i 0.828321i
\(584\) 0 0
\(585\) −23.6827 + 23.6827i −0.979158 + 0.979158i
\(586\) 0 0
\(587\) 31.3864 31.3864i 1.29545 1.29545i 0.364091 0.931363i \(-0.381380\pi\)
0.931363 0.364091i \(-0.118620\pi\)
\(588\) 0 0
\(589\) −30.2830 30.2830i −1.24779 1.24779i
\(590\) 0 0
\(591\) −13.6406 13.6406i −0.561099 0.561099i
\(592\) 0 0
\(593\) 8.43599 + 8.43599i 0.346424 + 0.346424i 0.858776 0.512351i \(-0.171225\pi\)
−0.512351 + 0.858776i \(0.671225\pi\)
\(594\) 0 0
\(595\) 13.8264i 0.566827i
\(596\) 0 0
\(597\) 43.1566 1.76628
\(598\) 0 0
\(599\) −21.7287 −0.887811 −0.443905 0.896074i \(-0.646407\pi\)
−0.443905 + 0.896074i \(0.646407\pi\)
\(600\) 0 0
\(601\) −2.87854 2.87854i −0.117418 0.117418i 0.645956 0.763374i \(-0.276459\pi\)
−0.763374 + 0.645956i \(0.776459\pi\)
\(602\) 0 0
\(603\) −8.06458 + 8.06458i −0.328415 + 0.328415i
\(604\) 0 0
\(605\) 21.1890 0.861456
\(606\) 0 0
\(607\) 34.7827i 1.41179i −0.708319 0.705893i \(-0.750546\pi\)
0.708319 0.705893i \(-0.249454\pi\)
\(608\) 0 0
\(609\) 2.33975 + 2.33975i 0.0948115 + 0.0948115i
\(610\) 0 0
\(611\) −6.28482 −0.254256
\(612\) 0 0
\(613\) 38.3345i 1.54832i −0.632992 0.774158i \(-0.718174\pi\)
0.632992 0.774158i \(-0.281826\pi\)
\(614\) 0 0
\(615\) −52.9520 8.61885i −2.13523 0.347546i
\(616\) 0 0
\(617\) 2.75803i 0.111034i −0.998458 0.0555171i \(-0.982319\pi\)
0.998458 0.0555171i \(-0.0176807\pi\)
\(618\) 0 0
\(619\) −16.4276 −0.660282 −0.330141 0.943932i \(-0.607096\pi\)
−0.330141 + 0.943932i \(0.607096\pi\)
\(620\) 0 0
\(621\) −4.77357 4.77357i −0.191557 0.191557i
\(622\) 0 0
\(623\) 3.03412i 0.121559i
\(624\) 0 0
\(625\) 1.78053 0.0712213
\(626\) 0 0
\(627\) 25.9255 25.9255i 1.03537 1.03537i
\(628\) 0 0
\(629\) −5.08407 5.08407i −0.202715 0.202715i
\(630\) 0 0
\(631\) −17.8966 −0.712451 −0.356225 0.934400i \(-0.615936\pi\)
−0.356225 + 0.934400i \(0.615936\pi\)
\(632\) 0 0
\(633\) 39.4548 1.56819
\(634\) 0 0
\(635\) 76.5552i 3.03800i
\(636\) 0 0
\(637\) −2.83000 2.83000i −0.112129 0.112129i
\(638\) 0 0
\(639\) −3.70811 3.70811i −0.146690 0.146690i
\(640\) 0 0
\(641\) −25.2395 25.2395i −0.996902 0.996902i 0.00309336 0.999995i \(-0.499015\pi\)
−0.999995 + 0.00309336i \(0.999015\pi\)
\(642\) 0 0
\(643\) 29.6138 29.6138i 1.16785 1.16785i 0.185143 0.982712i \(-0.440725\pi\)
0.982712 0.185143i \(-0.0592749\pi\)
\(644\) 0 0
\(645\) 36.2047 36.2047i 1.42556 1.42556i
\(646\) 0 0
\(647\) 12.6871i 0.498781i 0.968403 + 0.249390i \(0.0802302\pi\)
−0.968403 + 0.249390i \(0.919770\pi\)
\(648\) 0 0
\(649\) −3.74907 + 3.74907i −0.147164 + 0.147164i
\(650\) 0 0
\(651\) 14.0857i 0.552063i
\(652\) 0 0
\(653\) −28.0097 + 28.0097i −1.09610 + 1.09610i −0.101242 + 0.994862i \(0.532282\pi\)
−0.994862 + 0.101242i \(0.967718\pi\)
\(654\) 0 0
\(655\) 8.82448 0.344801
\(656\) 0 0
\(657\) 8.11835 0.316727
\(658\) 0 0
\(659\) −15.5178 + 15.5178i −0.604489 + 0.604489i −0.941501 0.337011i \(-0.890584\pi\)
0.337011 + 0.941501i \(0.390584\pi\)
\(660\) 0 0
\(661\) 41.7422i 1.62358i 0.583947 + 0.811792i \(0.301508\pi\)
−0.583947 + 0.811792i \(0.698492\pi\)
\(662\) 0 0
\(663\) 24.7479 24.7479i 0.961130 0.961130i
\(664\) 0 0
\(665\) 25.4744i 0.987855i
\(666\) 0 0
\(667\) 4.25343 4.25343i 0.164693 0.164693i
\(668\) 0 0
\(669\) −23.6824 + 23.6824i −0.915613 + 0.915613i
\(670\) 0 0
\(671\) 17.5977 + 17.5977i 0.679353 + 0.679353i
\(672\) 0 0
\(673\) 25.9004 + 25.9004i 0.998388 + 0.998388i 0.999999 0.00161040i \(-0.000512606\pi\)
−0.00161040 + 0.999999i \(0.500513\pi\)
\(674\) 0 0
\(675\) −9.40751 9.40751i −0.362095 0.362095i
\(676\) 0 0
\(677\) 19.8641i 0.763438i 0.924278 + 0.381719i \(0.124668\pi\)
−0.924278 + 0.381719i \(0.875332\pi\)
\(678\) 0 0
\(679\) −16.0980 −0.617786
\(680\) 0 0
\(681\) 23.6266 0.905374
\(682\) 0 0
\(683\) −21.5579 21.5579i −0.824890 0.824890i 0.161915 0.986805i \(-0.448233\pi\)
−0.986805 + 0.161915i \(0.948233\pi\)
\(684\) 0 0
\(685\) −35.0667 + 35.0667i −1.33983 + 1.33983i
\(686\) 0 0
\(687\) 22.7135 0.866575
\(688\) 0 0
\(689\) 35.1755i 1.34008i
\(690\) 0 0
\(691\) −10.1740 10.1740i −0.387036 0.387036i 0.486593 0.873629i \(-0.338240\pi\)
−0.873629 + 0.486593i \(0.838240\pi\)
\(692\) 0 0
\(693\) −5.23211 −0.198751
\(694\) 0 0
\(695\) 24.7867i 0.940212i
\(696\) 0 0
\(697\) 24.0082 + 3.90775i 0.909377 + 0.148017i
\(698\) 0 0
\(699\) 69.0831i 2.61296i
\(700\) 0 0
\(701\) 8.57891 0.324021 0.162010 0.986789i \(-0.448202\pi\)
0.162010 + 0.986789i \(0.448202\pi\)
\(702\) 0 0
\(703\) −9.36713 9.36713i −0.353288 0.353288i
\(704\) 0 0
\(705\) 13.1571i 0.495525i
\(706\) 0 0
\(707\) −3.68899 −0.138739
\(708\) 0 0
\(709\) 12.4042 12.4042i 0.465848 0.465848i −0.434718 0.900566i \(-0.643152\pi\)
0.900566 + 0.434718i \(0.143152\pi\)
\(710\) 0 0
\(711\) 16.6119 + 16.6119i 0.622994 + 0.622994i
\(712\) 0 0
\(713\) 25.6064 0.958967
\(714\) 0 0
\(715\) −33.1481 −1.23967
\(716\) 0 0
\(717\) 18.3567i 0.685545i
\(718\) 0 0
\(719\) −34.7937 34.7937i −1.29759 1.29759i −0.929982 0.367606i \(-0.880178\pi\)
−0.367606 0.929982i \(-0.619822\pi\)
\(720\) 0 0
\(721\) 9.71958 + 9.71958i 0.361976 + 0.361976i
\(722\) 0 0
\(723\) 10.6481 + 10.6481i 0.396008 + 0.396008i
\(724\) 0 0
\(725\) 8.38245 8.38245i 0.311316 0.311316i
\(726\) 0 0
\(727\) −26.7208 + 26.7208i −0.991021 + 0.991021i −0.999960 0.00893861i \(-0.997155\pi\)
0.00893861 + 0.999960i \(0.497155\pi\)
\(728\) 0 0
\(729\) 13.2570i 0.491001i
\(730\) 0 0
\(731\) −16.4151 + 16.4151i −0.607133 + 0.607133i
\(732\) 0 0
\(733\) 14.6974i 0.542862i 0.962458 + 0.271431i \(0.0874969\pi\)
−0.962458 + 0.271431i \(0.912503\pi\)
\(734\) 0 0
\(735\) −5.92453 + 5.92453i −0.218529 + 0.218529i
\(736\) 0 0
\(737\) −11.2878 −0.415791
\(738\) 0 0
\(739\) 9.00515 0.331260 0.165630 0.986188i \(-0.447034\pi\)
0.165630 + 0.986188i \(0.447034\pi\)
\(740\) 0 0
\(741\) 45.5968 45.5968i 1.67504 1.67504i
\(742\) 0 0
\(743\) 27.0326i 0.991731i −0.868399 0.495865i \(-0.834851\pi\)
0.868399 0.495865i \(-0.165149\pi\)
\(744\) 0 0
\(745\) −60.8044 + 60.8044i −2.22770 + 2.22770i
\(746\) 0 0
\(747\) 1.46240i 0.0535063i
\(748\) 0 0
\(749\) 6.97186 6.97186i 0.254746 0.254746i
\(750\) 0 0
\(751\) 2.38522 2.38522i 0.0870379 0.0870379i −0.662247 0.749285i \(-0.730397\pi\)
0.749285 + 0.662247i \(0.230397\pi\)
\(752\) 0 0
\(753\) 18.3015 + 18.3015i 0.666945 + 0.666945i
\(754\) 0 0
\(755\) −42.4657 42.4657i −1.54548 1.54548i
\(756\) 0 0
\(757\) −7.65379 7.65379i −0.278182 0.278182i 0.554201 0.832383i \(-0.313024\pi\)
−0.832383 + 0.554201i \(0.813024\pi\)
\(758\) 0 0
\(759\) 21.9218i 0.795712i
\(760\) 0 0
\(761\) 2.85100 0.103349 0.0516743 0.998664i \(-0.483544\pi\)
0.0516743 + 0.998664i \(0.483544\pi\)
\(762\) 0 0
\(763\) 3.43157 0.124231
\(764\) 0 0
\(765\) −22.4789 22.4789i −0.812728 0.812728i
\(766\) 0 0
\(767\) −6.59371 + 6.59371i −0.238085 + 0.238085i
\(768\) 0 0
\(769\) −26.4780 −0.954820 −0.477410 0.878681i \(-0.658424\pi\)
−0.477410 + 0.878681i \(0.658424\pi\)
\(770\) 0 0
\(771\) 25.5332i 0.919554i
\(772\) 0 0
\(773\) −19.9132 19.9132i −0.716229 0.716229i 0.251602 0.967831i \(-0.419043\pi\)
−0.967831 + 0.251602i \(0.919043\pi\)
\(774\) 0 0
\(775\) 50.4638 1.81271
\(776\) 0 0
\(777\) 4.35699i 0.156306i
\(778\) 0 0
\(779\) 44.2339 + 7.19983i 1.58485 + 0.257961i
\(780\) 0 0
\(781\) 5.19014i 0.185718i
\(782\) 0 0
\(783\) −2.31879 −0.0828667
\(784\) 0 0
\(785\) −39.0441 39.0441i −1.39354 1.39354i
\(786\) 0 0
\(787\) 44.3469i 1.58080i 0.612593 + 0.790399i \(0.290127\pi\)
−0.612593 + 0.790399i \(0.709873\pi\)
\(788\) 0 0
\(789\) 52.2448 1.85996
\(790\) 0 0
\(791\) 11.5656 11.5656i 0.411227 0.411227i
\(792\) 0 0
\(793\) 30.9502 + 30.9502i 1.09907 + 1.09907i
\(794\) 0 0
\(795\) 73.6389 2.61170
\(796\) 0 0
\(797\) 39.4176 1.39624 0.698122 0.715979i \(-0.254019\pi\)
0.698122 + 0.715979i \(0.254019\pi\)
\(798\) 0 0
\(799\) 5.96537i 0.211040i
\(800\) 0 0
\(801\)