Properties

Label 768.2.o.b.95.14
Level 768
Weight 2
Character 768.95
Analytic conductor 6.133
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.o (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 95.14
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.70463 - 0.306981i) q^{3} +(2.70066 - 1.11865i) q^{5} +(-3.28204 - 3.28204i) q^{7} +(2.81152 - 1.04658i) q^{9} +O(q^{10})\) \(q+(1.70463 - 0.306981i) q^{3} +(2.70066 - 1.11865i) q^{5} +(-3.28204 - 3.28204i) q^{7} +(2.81152 - 1.04658i) q^{9} +(-0.276697 + 0.114612i) q^{11} +(0.155281 - 0.374881i) q^{13} +(4.26022 - 2.73593i) q^{15} -1.41723 q^{17} +(2.51972 + 1.04370i) q^{19} +(-6.60218 - 4.58713i) q^{21} +(-3.30034 - 3.30034i) q^{23} +(2.50664 - 2.50664i) q^{25} +(4.47133 - 2.64711i) q^{27} +(0.650676 - 1.57087i) q^{29} +4.16702i q^{31} +(-0.436482 + 0.280311i) q^{33} +(-12.5351 - 5.19221i) q^{35} +(2.82757 + 6.82635i) q^{37} +(0.149615 - 0.686701i) q^{39} +(3.81949 - 3.81949i) q^{41} +(-2.07136 - 5.00071i) q^{43} +(6.42221 - 5.97156i) q^{45} +5.44085i q^{47} +14.5435i q^{49} +(-2.41585 + 0.435062i) q^{51} +(1.85159 + 4.47012i) q^{53} +(-0.619053 + 0.619053i) q^{55} +(4.61558 + 1.00562i) q^{57} +(1.37699 + 3.32434i) q^{59} +(10.9629 + 4.54098i) q^{61} +(-12.6624 - 5.79262i) q^{63} -1.18613i q^{65} +(-4.19888 + 10.1370i) q^{67} +(-6.63900 - 4.61272i) q^{69} +(3.77857 - 3.77857i) q^{71} +(-3.89137 - 3.89137i) q^{73} +(3.50340 - 5.04239i) q^{75} +(1.28429 + 0.531970i) q^{77} +4.81995 q^{79} +(6.80935 - 5.88497i) q^{81} +(3.60399 - 8.70081i) q^{83} +(-3.82744 + 1.58538i) q^{85} +(0.626933 - 2.87750i) q^{87} +(-3.69926 - 3.69926i) q^{89} +(-1.74001 + 0.720735i) q^{91} +(1.27920 + 7.10323i) q^{93} +7.97242 q^{95} +10.9958 q^{97} +(-0.657990 + 0.611818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{8}\right)\)

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
\(3\) 1.70463 0.306981i 0.984168 0.177236i
\(4\) 0 0
\(5\) 2.70066 1.11865i 1.20777 0.500275i 0.314269 0.949334i \(-0.398241\pi\)
0.893502 + 0.449059i \(0.148241\pi\)
\(6\) 0 0
\(7\) −3.28204 3.28204i −1.24049 1.24049i −0.959797 0.280697i \(-0.909435\pi\)
−0.280697 0.959797i \(-0.590565\pi\)
\(8\) 0 0
\(9\) 2.81152 1.04658i 0.937175 0.348860i
\(10\) 0 0
\(11\) −0.276697 + 0.114612i −0.0834272 + 0.0345567i −0.424007 0.905659i \(-0.639377\pi\)
0.340580 + 0.940216i \(0.389377\pi\)
\(12\) 0 0
\(13\) 0.155281 0.374881i 0.0430671 0.103973i −0.900882 0.434064i \(-0.857079\pi\)
0.943949 + 0.330091i \(0.107079\pi\)
\(14\) 0 0
\(15\) 4.26022 2.73593i 1.09998 0.706415i
\(16\) 0 0
\(17\) −1.41723 −0.343728 −0.171864 0.985121i \(-0.554979\pi\)
−0.171864 + 0.985121i \(0.554979\pi\)
\(18\) 0 0
\(19\) 2.51972 + 1.04370i 0.578062 + 0.239441i 0.652506 0.757784i \(-0.273718\pi\)
−0.0744431 + 0.997225i \(0.523718\pi\)
\(20\) 0 0
\(21\) −6.60218 4.58713i −1.44071 1.00099i
\(22\) 0 0
\(23\) −3.30034 3.30034i −0.688169 0.688169i 0.273658 0.961827i \(-0.411766\pi\)
−0.961827 + 0.273658i \(0.911766\pi\)
\(24\) 0 0
\(25\) 2.50664 2.50664i 0.501328 0.501328i
\(26\) 0 0
\(27\) 4.47133 2.64711i 0.860508 0.509438i
\(28\) 0 0
\(29\) 0.650676 1.57087i 0.120827 0.291703i −0.851880 0.523736i \(-0.824538\pi\)
0.972708 + 0.232033i \(0.0745377\pi\)
\(30\) 0 0
\(31\) 4.16702i 0.748419i 0.927344 + 0.374209i \(0.122086\pi\)
−0.927344 + 0.374209i \(0.877914\pi\)
\(32\) 0 0
\(33\) −0.436482 + 0.280311i −0.0759817 + 0.0487959i
\(34\) 0 0
\(35\) −12.5351 5.19221i −2.11882 0.877644i
\(36\) 0 0
\(37\) 2.82757 + 6.82635i 0.464849 + 1.12225i 0.966383 + 0.257107i \(0.0827693\pi\)
−0.501534 + 0.865138i \(0.667231\pi\)
\(38\) 0 0
\(39\) 0.149615 0.686701i 0.0239575 0.109960i
\(40\) 0 0
\(41\) 3.81949 3.81949i 0.596504 0.596504i −0.342877 0.939380i \(-0.611401\pi\)
0.939380 + 0.342877i \(0.111401\pi\)
\(42\) 0 0
\(43\) −2.07136 5.00071i −0.315880 0.762602i −0.999464 0.0327301i \(-0.989580\pi\)
0.683584 0.729872i \(-0.260420\pi\)
\(44\) 0 0
\(45\) 6.42221 5.97156i 0.957367 0.890188i
\(46\) 0 0
\(47\) 5.44085i 0.793629i 0.917899 + 0.396815i \(0.129884\pi\)
−0.917899 + 0.396815i \(0.870116\pi\)
\(48\) 0 0
\(49\) 14.5435i 2.07765i
\(50\) 0 0
\(51\) −2.41585 + 0.435062i −0.338286 + 0.0609209i
\(52\) 0 0
\(53\) 1.85159 + 4.47012i 0.254335 + 0.614019i 0.998545 0.0539269i \(-0.0171738\pi\)
−0.744210 + 0.667946i \(0.767174\pi\)
\(54\) 0 0
\(55\) −0.619053 + 0.619053i −0.0834731 + 0.0834731i
\(56\) 0 0
\(57\) 4.61558 + 1.00562i 0.611348 + 0.133197i
\(58\) 0 0
\(59\) 1.37699 + 3.32434i 0.179268 + 0.432792i 0.987814 0.155642i \(-0.0497447\pi\)
−0.808545 + 0.588434i \(0.799745\pi\)
\(60\) 0 0
\(61\) 10.9629 + 4.54098i 1.40366 + 0.581413i 0.950698 0.310119i \(-0.100369\pi\)
0.452958 + 0.891532i \(0.350369\pi\)
\(62\) 0 0
\(63\) −12.6624 5.79262i −1.59532 0.729801i
\(64\) 0 0
\(65\) 1.18613i 0.147121i
\(66\) 0 0
\(67\) −4.19888 + 10.1370i −0.512974 + 1.23843i 0.429170 + 0.903224i \(0.358806\pi\)
−0.942145 + 0.335206i \(0.891194\pi\)
\(68\) 0 0
\(69\) −6.63900 4.61272i −0.799242 0.555306i
\(70\) 0 0
\(71\) 3.77857 3.77857i 0.448434 0.448434i −0.446400 0.894834i \(-0.647294\pi\)
0.894834 + 0.446400i \(0.147294\pi\)
\(72\) 0 0
\(73\) −3.89137 3.89137i −0.455450 0.455450i 0.441708 0.897159i \(-0.354373\pi\)
−0.897159 + 0.441708i \(0.854373\pi\)
\(74\) 0 0
\(75\) 3.50340 5.04239i 0.404538 0.582245i
\(76\) 0 0
\(77\) 1.28429 + 0.531970i 0.146358 + 0.0606236i
\(78\) 0 0
\(79\) 4.81995 0.542287 0.271143 0.962539i \(-0.412598\pi\)
0.271143 + 0.962539i \(0.412598\pi\)
\(80\) 0 0
\(81\) 6.80935 5.88497i 0.756594 0.653885i
\(82\) 0 0
\(83\) 3.60399 8.70081i 0.395590 0.955038i −0.593109 0.805122i \(-0.702100\pi\)
0.988699 0.149916i \(-0.0479003\pi\)
\(84\) 0 0
\(85\) −3.82744 + 1.58538i −0.415145 + 0.171959i
\(86\) 0 0
\(87\) 0.626933 2.87750i 0.0672143 0.308500i
\(88\) 0 0
\(89\) −3.69926 3.69926i −0.392121 0.392121i 0.483322 0.875443i \(-0.339430\pi\)
−0.875443 + 0.483322i \(0.839430\pi\)
\(90\) 0 0
\(91\) −1.74001 + 0.720735i −0.182402 + 0.0755536i
\(92\) 0 0
\(93\) 1.27920 + 7.10323i 0.132647 + 0.736570i
\(94\) 0 0
\(95\) 7.97242 0.817953
\(96\) 0 0
\(97\) 10.9958 1.11646 0.558229 0.829687i \(-0.311481\pi\)
0.558229 + 0.829687i \(0.311481\pi\)
\(98\) 0 0
\(99\) −0.657990 + 0.611818i −0.0661305 + 0.0614900i
\(100\) 0 0
\(101\) 2.51499 1.04174i 0.250251 0.103657i −0.254032 0.967196i \(-0.581757\pi\)
0.504283 + 0.863538i \(0.331757\pi\)
\(102\) 0 0
\(103\) −0.332885 0.332885i −0.0328001 0.0328001i 0.690517 0.723317i \(-0.257383\pi\)
−0.723317 + 0.690517i \(0.757383\pi\)
\(104\) 0 0
\(105\) −22.9616 5.00275i −2.24082 0.488219i
\(106\) 0 0
\(107\) −0.394269 + 0.163312i −0.0381154 + 0.0157879i −0.401660 0.915789i \(-0.631567\pi\)
0.363544 + 0.931577i \(0.381567\pi\)
\(108\) 0 0
\(109\) −1.81782 + 4.38860i −0.174115 + 0.420352i −0.986713 0.162474i \(-0.948053\pi\)
0.812598 + 0.582825i \(0.198053\pi\)
\(110\) 0 0
\(111\) 6.91552 + 10.7684i 0.656392 + 1.02209i
\(112\) 0 0
\(113\) −18.5323 −1.74337 −0.871687 0.490063i \(-0.836974\pi\)
−0.871687 + 0.490063i \(0.836974\pi\)
\(114\) 0 0
\(115\) −12.6050 5.22117i −1.17542 0.486876i
\(116\) 0 0
\(117\) 0.0442333 1.21650i 0.00408937 0.112465i
\(118\) 0 0
\(119\) 4.65139 + 4.65139i 0.426392 + 0.426392i
\(120\) 0 0
\(121\) −7.71475 + 7.71475i −0.701341 + 0.701341i
\(122\) 0 0
\(123\) 5.33830 7.68333i 0.481339 0.692782i
\(124\) 0 0
\(125\) −1.62772 + 3.92966i −0.145587 + 0.351479i
\(126\) 0 0
\(127\) 4.80013i 0.425943i 0.977058 + 0.212971i \(0.0683141\pi\)
−0.977058 + 0.212971i \(0.931686\pi\)
\(128\) 0 0
\(129\) −5.06603 7.88850i −0.446039 0.694543i
\(130\) 0 0
\(131\) 20.2118 + 8.37202i 1.76592 + 0.731467i 0.995589 + 0.0938185i \(0.0299073\pi\)
0.770328 + 0.637648i \(0.220093\pi\)
\(132\) 0 0
\(133\) −4.84434 11.6953i −0.420057 1.01411i
\(134\) 0 0
\(135\) 9.11434 12.1508i 0.784437 1.04577i
\(136\) 0 0
\(137\) 12.7302 12.7302i 1.08762 1.08762i 0.0918436 0.995773i \(-0.470724\pi\)
0.995773 0.0918436i \(-0.0292760\pi\)
\(138\) 0 0
\(139\) −0.193431 0.466984i −0.0164066 0.0396091i 0.915464 0.402400i \(-0.131824\pi\)
−0.931871 + 0.362791i \(0.881824\pi\)
\(140\) 0 0
\(141\) 1.67024 + 9.27463i 0.140660 + 0.781065i
\(142\) 0 0
\(143\) 0.121525i 0.0101624i
\(144\) 0 0
\(145\) 4.97026i 0.412758i
\(146\) 0 0
\(147\) 4.46459 + 24.7913i 0.368233 + 2.04475i
\(148\) 0 0
\(149\) −4.31949 10.4282i −0.353866 0.854308i −0.996136 0.0878294i \(-0.972007\pi\)
0.642269 0.766479i \(1.72201\pi\)
\(150\) 0 0
\(151\) −13.7687 + 13.7687i −1.12048 + 1.12048i −0.128814 + 0.991669i \(0.541117\pi\)
−0.991669 + 0.128814i \(0.958883\pi\)
\(152\) 0 0
\(153\) −3.98457 + 1.48324i −0.322133 + 0.119913i
\(154\) 0 0
\(155\) 4.66143 + 11.2537i 0.374415 + 0.903918i
\(156\) 0 0
\(157\) −7.94660 3.29159i −0.634208 0.262697i 0.0423321 0.999104i \(-0.486521\pi\)
−0.676540 + 0.736406i \(0.736521\pi\)
\(158\) 0 0
\(159\) 4.52851 + 7.05151i 0.359135 + 0.559221i
\(160\) 0 0
\(161\) 21.6637i 1.70734i
\(162\) 0 0
\(163\) −4.77631 + 11.5310i −0.374110 + 0.903181i 0.618935 + 0.785442i \(0.287565\pi\)
−0.993045 + 0.117739i \(0.962435\pi\)
\(164\) 0 0
\(165\) −0.865219 + 1.24529i −0.0673572 + 0.0969460i
\(166\) 0 0
\(167\) −14.7585 + 14.7585i −1.14205 + 1.14205i −0.153970 + 0.988076i \(0.549206\pi\)
−0.988076 + 0.153970i \(0.950794\pi\)
\(168\) 0 0
\(169\) 9.07596 + 9.07596i 0.698151 + 0.698151i
\(170\) 0 0
\(171\) 8.17656 + 0.297309i 0.625277 + 0.0227358i
\(172\) 0 0
\(173\) −7.60827 3.15145i −0.578446 0.239600i 0.0742253 0.997241i \(-0.476352\pi\)
−0.652671 + 0.757641i \(0.726352\pi\)
\(174\) 0 0
\(175\) −16.4538 −1.24379
\(176\) 0 0
\(177\) 3.36776 + 5.24406i 0.253136 + 0.394167i
\(178\) 0 0
\(179\) 1.38731 3.34926i 0.103692 0.250335i −0.863515 0.504323i \(-0.831742\pi\)
0.967208 + 0.253987i \(0.0817422\pi\)
\(180\) 0 0
\(181\) −6.51464 + 2.69845i −0.484229 + 0.200574i −0.611424 0.791303i \(-0.709403\pi\)
0.127194 + 0.991878i \(0.459403\pi\)
\(182\) 0 0
\(183\) 20.0817 + 4.37529i 1.48448 + 0.323431i
\(184\) 0 0
\(185\) 15.2726 + 15.2726i 1.12286 + 1.12286i
\(186\) 0 0
\(187\) 0.392142 0.162431i 0.0286763 0.0118781i
\(188\) 0 0
\(189\) −23.3630 5.98714i −1.69941 0.435500i
\(190\) 0 0
\(191\) 18.8097 1.36102 0.680511 0.732737i \(-0.261758\pi\)
0.680511 + 0.732737i \(0.261758\pi\)
\(192\) 0 0
\(193\) −11.1498 −0.802582 −0.401291 0.915951i \(-0.631438\pi\)
−0.401291 + 0.915951i \(0.631438\pi\)
\(194\) 0 0
\(195\) −0.364119 2.02191i −0.0260751 0.144792i
\(196\) 0 0
\(197\) −14.7643 + 6.11558i −1.05191 + 0.435717i −0.840575 0.541696i \(-0.817783\pi\)
−0.211340 + 0.977413i \(0.567783\pi\)
\(198\) 0 0
\(199\) 0.686194 + 0.686194i 0.0486430 + 0.0486430i 0.731010 0.682367i \(-0.239049\pi\)
−0.682367 + 0.731010i \(0.739049\pi\)
\(200\) 0 0
\(201\) −4.04566 + 18.5688i −0.285359 + 1.30974i
\(202\) 0 0
\(203\) −7.29119 + 3.02011i −0.511742 + 0.211970i
\(204\) 0 0
\(205\) 6.04246 14.5878i 0.422024 1.01886i
\(206\) 0 0
\(207\) −12.7331 5.82492i −0.885009 0.404860i
\(208\) 0 0
\(209\) −0.816817 −0.0565004
\(210\) 0 0
\(211\) −2.25868 0.935575i −0.155494 0.0644076i 0.303579 0.952806i \(-0.401818\pi\)
−0.459073 + 0.888399i \(0.651818\pi\)
\(212\) 0 0
\(213\) 5.28111 7.60101i 0.361856 0.520813i
\(214\) 0 0
\(215\) −11.1881 11.1881i −0.763021 0.763021i
\(216\) 0 0
\(217\) 13.6763 13.6763i 0.928409 0.928409i
\(218\) 0 0
\(219\) −7.82792 5.43876i −0.528962 0.367518i
\(220\) 0 0
\(221\) −0.220068 + 0.531291i −0.0148034 + 0.0357385i
\(222\) 0 0
\(223\) 10.3472i 0.692900i −0.938068 0.346450i \(-0.887387\pi\)
0.938068 0.346450i \(-0.112613\pi\)
\(224\) 0 0
\(225\) 4.42409 9.67088i 0.294939 0.644725i
\(226\) 0 0
\(227\) −10.4804 4.34114i −0.695611 0.288131i 0.00672494 0.999977i \(-0.497859\pi\)
−0.702336 + 0.711846i \(0.747859\pi\)
\(228\) 0 0
\(229\) 7.39471 + 17.8524i 0.488656 + 1.17972i 0.955396 + 0.295326i \(0.0954284\pi\)
−0.466740 + 0.884395i \(0.654572\pi\)
\(230\) 0 0
\(231\) 2.35254 + 0.512559i 0.154786 + 0.0337239i
\(232\) 0 0
\(233\) −15.9703 + 15.9703i −1.04625 + 1.04625i −0.0473714 + 0.998877i \(0.515084\pi\)
−0.998877 + 0.0473714i \(0.984916\pi\)
\(234\) 0 0
\(235\) 6.08640 + 14.6939i 0.397033 + 0.958522i
\(236\) 0 0
\(237\) 8.21623 1.47963i 0.533702 0.0961126i
\(238\) 0 0
\(239\) 22.5155i 1.45641i −0.685361 0.728204i \(-0.740355\pi\)
0.685361 0.728204i \(-0.259645\pi\)
\(240\) 0 0
\(241\) 21.7886i 1.40353i −0.712409 0.701765i \(-0.752396\pi\)
0.712409 0.701765i \(-0.247604\pi\)
\(242\) 0 0
\(243\) 9.80084 12.1220i 0.628724 0.777628i
\(244\) 0 0
\(245\) 16.2691 + 39.2771i 1.03939 + 2.50932i
\(246\) 0 0
\(247\) 0.782526 0.782526i 0.0497909 0.0497909i
\(248\) 0 0
\(249\) 3.47249 15.9380i 0.220060 1.01003i
\(250\) 0 0
\(251\) 5.96821 + 14.4085i 0.376710 + 0.909458i 0.992578 + 0.121609i \(0.0388054\pi\)
−0.615868 + 0.787849i \(0.711195\pi\)
\(252\) 0 0
\(253\) 1.29145 + 0.534937i 0.0811928 + 0.0336312i
\(254\) 0 0
\(255\) −6.03769 + 3.87744i −0.378095 + 0.242815i
\(256\) 0 0
\(257\) 11.8781i 0.740934i 0.928846 + 0.370467i \(0.120802\pi\)
−0.928846 + 0.370467i \(0.879198\pi\)
\(258\) 0 0
\(259\) 13.1242 31.6845i 0.815495 1.96878i
\(260\) 0 0
\(261\) 0.185352 5.09752i 0.0114730 0.315529i
\(262\) 0 0
\(263\) −3.29543 + 3.29543i −0.203205 + 0.203205i −0.801372 0.598167i \(-0.795896\pi\)
0.598167 + 0.801372i \(0.295896\pi\)
\(264\) 0 0
\(265\) 10.0010 + 10.0010i 0.614357 + 0.614357i
\(266\) 0 0
\(267\) −7.44148 5.17027i −0.455411 0.316415i
\(268\) 0 0
\(269\) −26.9975 11.1827i −1.64607 0.681824i −0.649180 0.760635i \(-0.724888\pi\)
−0.996890 + 0.0788107i \(0.974888\pi\)
\(270\) 0 0
\(271\) 3.49827 0.212505 0.106252 0.994339i \(-0.466115\pi\)
0.106252 + 0.994339i \(0.466115\pi\)
\(272\) 0 0
\(273\) −2.74482 + 1.76274i −0.166124 + 0.106686i
\(274\) 0 0
\(275\) −0.406289 + 0.980869i −0.0245002 + 0.0591486i
\(276\) 0 0
\(277\) 10.1905 4.22105i 0.612289 0.253619i −0.0549177 0.998491i \(-0.517490\pi\)
0.667207 + 0.744872i \(0.267490\pi\)
\(278\) 0 0
\(279\) 4.36112 + 11.7157i 0.261093 + 0.701399i
\(280\) 0 0
\(281\) −14.1081 14.1081i −0.841616 0.841616i 0.147453 0.989069i \(-0.452893\pi\)
−0.989069 + 0.147453i \(0.952893\pi\)
\(282\) 0 0
\(283\) −17.2200 + 7.13275i −1.02362 + 0.423998i −0.830406 0.557159i \(-0.811892\pi\)
−0.193215 + 0.981156i \(0.561892\pi\)
\(284\) 0 0
\(285\) 13.5900 2.44738i 0.805004 0.144971i
\(286\) 0 0
\(287\) −25.0714 −1.47992
\(288\) 0 0
\(289\) −14.9915 −0.881851
\(290\) 0 0
\(291\) 18.7438 3.37552i 1.09878 0.197876i
\(292\) 0 0
\(293\) 21.6538 8.96928i 1.26503 0.523991i 0.353577 0.935405i \(-0.384965\pi\)
0.911448 + 0.411414i \(0.134965\pi\)
\(294\) 0 0
\(295\) 7.43753 + 7.43753i 0.433030 + 0.433030i
\(296\) 0 0
\(297\) −0.933812 + 1.24491i −0.0541853 + 0.0722372i
\(298\) 0 0
\(299\) −1.74971 + 0.724755i −0.101189 + 0.0419137i
\(300\) 0 0
\(301\) −9.61423 + 23.2108i −0.554155 + 1.33785i
\(302\) 0 0
\(303\) 3.96733 2.54784i 0.227917 0.146370i
\(304\) 0 0
\(305\) 34.6868 1.98616
\(306\) 0 0
\(307\) 19.7154 + 8.16639i 1.12522 + 0.466081i 0.866153 0.499779i \(-0.166585\pi\)
0.259065 + 0.965860i \(0.416585\pi\)
\(308\) 0 0
\(309\) −0.669635 0.465256i −0.0380942 0.0264675i
\(310\) 0 0
\(311\) −10.5699 10.5699i −0.599365 0.599365i 0.340779 0.940144i \(-0.389309\pi\)
−0.940144 + 0.340779i \(0.889309\pi\)
\(312\) 0 0
\(313\) −24.0589 + 24.0589i −1.35989 + 1.35989i −0.485846 + 0.874044i \(0.661489\pi\)
−0.874044 + 0.485846i \(0.838511\pi\)
\(314\) 0 0
\(315\) −40.6768 1.47905i −2.29188 0.0833352i
\(316\) 0 0
\(317\) 8.93517 21.5714i 0.501849 1.21157i −0.446626 0.894721i \(-0.647375\pi\)
0.948475 0.316851i \(-0.102625\pi\)
\(318\) 0 0
\(319\) 0.509230i 0.0285114i
\(320\) 0 0
\(321\) −0.621949 + 0.399419i −0.0347138 + 0.0222934i
\(322\) 0 0
\(323\) −3.57101 1.47916i −0.198696 0.0823027i
\(324\) 0 0
\(325\) −0.550458 1.32892i −0.0305339 0.0737154i
\(326\) 0 0
\(327\) −1.75149 + 8.03897i −0.0968575 + 0.444556i
\(328\) 0 0
\(329\) 17.8571 17.8571i 0.984492 0.984492i
\(330\) 0 0
\(331\) 10.6785 + 25.7802i 0.586943 + 1.41701i 0.886411 + 0.462900i \(0.153191\pi\)
−0.299467 + 0.954107i \(0.596809\pi\)
\(332\) 0 0
\(333\) 15.0941 + 16.2332i 0.827151 + 0.889573i
\(334\) 0 0
\(335\) 32.0736i 1.75237i
\(336\) 0 0
\(337\) 7.72298i 0.420698i 0.977626 + 0.210349i \(0.0674600\pi\)
−0.977626 + 0.210349i \(0.932540\pi\)
\(338\) 0 0
\(339\) −31.5907 + 5.68907i −1.71577 + 0.308988i
\(340\) 0 0
\(341\) −0.477589 1.15300i −0.0258629 0.0624385i
\(342\) 0 0
\(343\) 24.7581 24.7581i 1.33681 1.33681i
\(344\) 0 0
\(345\) −23.0897 5.03065i −1.24311 0.270841i
\(346\) 0 0
\(347\) −2.88801 6.97227i −0.155037 0.374291i 0.827208 0.561896i \(-0.189928\pi\)
−0.982245 + 0.187604i \(0.939928\pi\)
\(348\) 0 0
\(349\) −3.70439 1.53441i −0.198292 0.0821351i 0.281328 0.959612i \(-0.409225\pi\)
−0.479619 + 0.877477i \(0.659225\pi\)
\(350\) 0 0
\(351\) −0.298041 2.08726i −0.0159083 0.111410i
\(352\) 0 0
\(353\) 33.0427i 1.75869i −0.476189 0.879343i \(-0.657982\pi\)
0.476189 0.879343i \(-0.342018\pi\)
\(354\) 0 0
\(355\) 5.97773 14.4315i 0.317265 0.765945i
\(356\) 0 0
\(357\) 9.35679 + 6.50101i 0.495214 + 0.344070i
\(358\) 0 0
\(359\) −1.02805 + 1.02805i −0.0542584 + 0.0542584i −0.733715 0.679457i \(-0.762215\pi\)
0.679457 + 0.733715i \(0.262215\pi\)
\(360\) 0 0
\(361\) −8.17537 8.17537i −0.430283 0.430283i
\(362\) 0 0
\(363\) −10.7825 + 15.5191i −0.565935 + 0.814540i
\(364\) 0 0
\(365\) −14.8623 6.15618i −0.777930 0.322229i
\(366\) 0 0
\(367\) 11.6801 0.609694 0.304847 0.952401i \(-0.401395\pi\)
0.304847 + 0.952401i \(0.401395\pi\)
\(368\) 0 0
\(369\) 6.74119 14.7360i 0.350932 0.767125i
\(370\) 0 0
\(371\) 8.59414 20.7481i 0.446185 1.07719i
\(372\) 0 0
\(373\) 11.6155 4.81129i 0.601427 0.249119i −0.0611312 0.998130i \(-0.519471\pi\)
0.662558 + 0.749011i \(0.269471\pi\)
\(374\) 0 0
\(375\) −1.56832 + 7.19829i −0.0809879 + 0.371718i
\(376\) 0 0
\(377\) −0.487851 0.487851i −0.0251256 0.0251256i
\(378\) 0 0
\(379\) 15.2623 6.32186i 0.783972 0.324732i 0.0454550 0.998966i \(-0.485526\pi\)
0.738517 + 0.674234i \(0.235526\pi\)
\(380\) 0 0
\(381\) 1.47355 + 8.18244i 0.0754923 + 0.419199i
\(382\) 0 0
\(383\) 28.9536 1.47946 0.739729 0.672905i \(-0.234954\pi\)
0.739729 + 0.672905i \(0.234954\pi\)
\(384\) 0 0
\(385\) 4.06351 0.207096
\(386\) 0 0
\(387\) −11.0573 11.8918i −0.562076 0.604493i
\(388\) 0 0
\(389\) −6.31149 + 2.61431i −0.320005 + 0.132551i −0.536903 0.843644i \(-0.680406\pi\)
0.216898 + 0.976194i \(0.430406\pi\)
\(390\) 0 0
\(391\) 4.67733 + 4.67733i 0.236543 + 0.236543i
\(392\) 0 0
\(393\) 37.0238 + 8.06654i 1.86760 + 0.406903i
\(394\) 0 0
\(395\) 13.0170 5.39183i 0.654958 0.271293i
\(396\) 0 0
\(397\) 1.66407 4.01741i 0.0835171 0.201628i −0.876604 0.481212i \(-0.840197\pi\)
0.960121 + 0.279584i \(0.0901966\pi\)
\(398\) 0 0
\(399\) −11.8480 18.4490i −0.593143 0.923604i
\(400\) 0 0
\(401\) −3.93840 −0.196674 −0.0983371 0.995153i \(-0.531352\pi\)
−0.0983371 + 0.995153i \(0.531352\pi\)
\(402\) 0 0
\(403\) 1.56214 + 0.647058i 0.0778155 + 0.0322322i
\(404\) 0 0
\(405\) 11.8065 23.5105i 0.586670 1.16825i
\(406\) 0 0
\(407\) −1.56476 1.56476i −0.0775621 0.0775621i
\(408\) 0 0
\(409\) 12.8960 12.8960i 0.637664 0.637664i −0.312314 0.949979i \(-0.601104\pi\)
0.949979 + 0.312314i \(0.101104\pi\)
\(410\) 0 0
\(411\) 17.7924 25.6083i 0.877634 1.26316i
\(412\) 0 0
\(413\) 6.39128 15.4299i 0.314494 0.759256i
\(414\) 0 0
\(415\) 27.5295i 1.35137i
\(416\) 0 0
\(417\) −0.473084 0.736656i −0.0231670 0.0360742i
\(418\) 0 0
\(419\) 5.81232 + 2.40754i 0.283951 + 0.117616i 0.520113 0.854097i \(-0.325890\pi\)
−0.236163 + 0.971714i \(0.575890\pi\)
\(420\) 0 0
\(421\) −7.88620 19.0390i −0.384350 0.927903i −0.991113 0.133020i \(-0.957532\pi\)
0.606763 0.794883i \(-0.292468\pi\)
\(422\) 0 0
\(423\) 5.69428 + 15.2971i 0.276865 + 0.743770i
\(424\) 0 0
\(425\) −3.55248 + 3.55248i −0.172321 + 0.172321i
\(426\) 0 0
\(427\) −21.0770 50.8843i −1.01999 2.46246i
\(428\) 0 0
\(429\) 0.0373060 + 0.207155i 0.00180115 + 0.0100016i
\(430\) 0 0
\(431\) 33.6809i 1.62235i −0.584801 0.811177i \(-0.698827\pi\)
0.584801 0.811177i \(-0.301173\pi\)
\(432\) 0 0
\(433\) 20.3471i 0.977819i −0.872335 0.488909i \(-0.837395\pi\)
0.872335 0.488909i \(-0.162605\pi\)
\(434\) 0 0
\(435\) −1.52578 8.47245i −0.0731554 0.406223i
\(436\) 0 0
\(437\) −4.87135 11.7605i −0.233028 0.562580i
\(438\) 0 0
\(439\) 12.4753 12.4753i 0.595414 0.595414i −0.343675 0.939089i \(-0.611672\pi\)
0.939089 + 0.343675i \(0.111672\pi\)
\(440\) 0 0
\(441\) 15.2209 + 40.8895i 0.724807 + 1.94712i
\(442\) 0 0
\(443\) −10.7190 25.8778i −0.509273 1.22949i −0.944303 0.329077i \(-0.893262\pi\)
0.435030 0.900416i \(1.64326\pi\)
\(444\) 0 0
\(445\) −14.1286 5.85227i −0.669761 0.277424i
\(446\) 0 0
\(447\) −10.5644 16.4502i −0.499678 0.778066i
\(448\) 0 0
\(449\) 16.2439i 0.766596i −0.923625 0.383298i \(-0.874788\pi\)
0.923625 0.383298i \(-0.125212\pi\)
\(450\) 0 0
\(451\) −0.619083 + 1.49460i −0.0291515 + 0.0703779i
\(452\) 0 0
\(453\) −19.2438 + 27.6973i −0.904154 + 1.30133i
\(454\) 0 0
\(455\) −3.89292 + 3.89292i −0.182503 + 0.182503i
\(456\) 0 0
\(457\) −2.84177 2.84177i −0.132932 0.132932i 0.637510 0.770442i \(-0.279965\pi\)
−0.770442 + 0.637510i \(0.779965\pi\)
\(458\) 0 0
\(459\) −6.33689 + 3.75156i −0.295781 + 0.175108i
\(460\) 0 0
\(461\) 20.8642 + 8.64224i 0.971743 + 0.402509i 0.811361 0.584546i \(-0.198727\pi\)
0.160382 + 0.987055i \(0.448727\pi\)
\(462\) 0 0
\(463\) −22.3599 −1.03915 −0.519576 0.854424i \(-0.673910\pi\)
−0.519576 + 0.854424i \(0.673910\pi\)
\(464\) 0 0
\(465\) 11.4007 + 17.7524i 0.528694 + 0.823248i
\(466\) 0 0
\(467\) −3.58346 + 8.65124i −0.165823 + 0.400332i −0.984847 0.173428i \(-0.944516\pi\)
0.819024 + 0.573760i \(0.194516\pi\)
\(468\) 0 0
\(469\) 47.0508 19.4891i 2.17260 0.899922i
\(470\) 0 0
\(471\) −14.5565 3.17148i −0.670726 0.146134i
\(472\) 0 0
\(473\) 1.14628 + 1.14628i 0.0527060 + 0.0527060i
\(474\) 0 0
\(475\) 8.93220 3.69984i 0.409838 0.169760i
\(476\) 0 0
\(477\) 9.88412 + 10.6300i 0.452563 + 0.486716i
\(478\) 0 0
\(479\) −1.51545 −0.0692426 −0.0346213 0.999401i \(-0.511023\pi\)
−0.0346213 + 0.999401i \(0.511023\pi\)
\(480\) 0 0
\(481\) 2.99813 0.136703
\(482\) 0 0
\(483\) 6.65035 + 36.9286i 0.302601 + 1.68031i
\(484\) 0 0
\(485\) 29.6960 12.3005i 1.34843 0.558536i
\(486\) 0 0
\(487\) 10.7114 + 10.7114i 0.485378 + 0.485378i 0.906844 0.421466i \(-0.138484\pi\)
−0.421466 + 0.906844i \(0.638484\pi\)
\(488\) 0 0
\(489\) −4.60203 + 21.1224i −0.208111 + 0.955188i
\(490\) 0 0
\(491\) −20.2550 + 8.38989i −0.914095 + 0.378630i −0.789623 0.613593i \(-0.789724\pi\)
−0.124472 + 0.992223i \(0.539724\pi\)
\(492\) 0 0
\(493\) −0.922155 + 2.22628i −0.0415318 + 0.100267i
\(494\) 0 0
\(495\) −1.09260 + 2.38837i −0.0491085 + 0.107349i
\(496\) 0 0
\(497\) −24.8028 −1.11256
\(498\) 0 0
\(499\) −10.2527 4.24681i −0.458974 0.190113i 0.141203 0.989981i \(-0.454903\pi\)
−0.600177 + 0.799867i \(0.704903\pi\)
\(500\) 0 0
\(501\) −20.6272 + 29.6883i −0.921554 + 1.32638i
\(502\) 0 0
\(503\) 14.9291 + 14.9291i 0.665655 + 0.665655i 0.956707 0.291052i \(-0.0940054\pi\)
−0.291052 + 0.956707i \(0.594005\pi\)
\(504\) 0 0
\(505\) 5.62678 5.62678i 0.250389 0.250389i
\(506\) 0 0
\(507\) 18.2573 + 12.6850i 0.810836 + 0.563361i
\(508\) 0 0
\(509\) −0.540947 + 1.30596i −0.0239770 + 0.0578857i −0.935415 0.353553i \(-0.884973\pi\)
0.911438 + 0.411438i \(0.134973\pi\)
\(510\) 0 0
\(511\) 25.5432i 1.12997i
\(512\) 0 0
\(513\) 14.0293 2.00325i 0.619407 0.0884456i
\(514\) 0 0
\(515\) −1.27139 0.526627i −0.0560241 0.0232059i
\(516\) 0 0
\(517\) −0.623584 1.50547i −0.0274252 0.0662103i
\(518\) 0 0
\(519\) −13.9367 3.03645i −0.611754 0.133286i
\(520\) 0 0
\(521\) −4.02013 + 4.02013i −0.176125 + 0.176125i −0.789664 0.613539i \(-0.789745\pi\)
0.613539 + 0.789664i \(0.289745\pi\)
\(522\) 0 0
\(523\) −2.35502 5.68552i −0.102978 0.248610i 0.863990 0.503509i \(-0.167958\pi\)
−0.966968 + 0.254899i \(0.917958\pi\)
\(524\) 0 0
\(525\) −28.0476 + 5.05100i −1.22410 + 0.220444i
\(526\) 0 0
\(527\) 5.90561i 0.257253i
\(528\) 0 0
\(529\) 1.21549i 0.0528475i
\(530\) 0 0
\(531\) 7.35061 + 7.90533i 0.318989 + 0.343062i
\(532\) 0 0
\(533\) −0.838760 2.02495i −0.0363307 0.0877101i
\(534\) 0 0
\(535\) −0.882097 + 0.882097i −0.0381364 + 0.0381364i
\(536\) 0 0
\(537\) 1.33669 6.13513i 0.0576823 0.264750i
\(538\) 0 0
\(539\) −1.66686 4.02415i −0.0717966 0.173332i
\(540\) 0 0
\(541\) −27.0891 11.2207i −1.16465 0.482414i −0.285230 0.958459i \(-0.592070\pi\)
−0.879421 + 0.476045i \(0.842070\pi\)
\(542\) 0 0
\(543\) −10.2767 + 6.59973i −0.441014 + 0.283222i
\(544\) 0 0
\(545\) 13.8856i 0.594794i
\(546\) 0 0
\(547\) −2.18960 + 5.28616i −0.0936205 + 0.226020i −0.963752 0.266800i \(-0.914034\pi\)
0.870132 + 0.492820i \(0.164034\pi\)
\(548\) 0 0
\(549\) 35.5750 + 1.29354i 1.51830 + 0.0552071i
\(550\) 0 0
\(551\) 3.27904 3.27904i 0.139692 0.139692i
\(552\) 0 0
\(553\) −15.8193 15.8193i −0.672703 0.672703i
\(554\) 0 0
\(555\) 30.7225 + 21.3457i 1.30410 + 0.906074i
\(556\) 0 0
\(557\) 33.6235 + 13.9273i 1.42467 + 0.590119i 0.956030 0.293268i \(-0.0947428\pi\)
0.468644 + 0.883387i \(0.344743\pi\)
\(558\) 0 0
\(559\) −2.19631 −0.0928941
\(560\) 0 0
\(561\) 0.618594 0.397264i 0.0261171 0.0167725i
\(562\) 0 0
\(563\) −10.2970 + 24.8591i −0.433965 + 1.04768i 0.544031 + 0.839065i \(0.316897\pi\)
−0.977997 + 0.208620i \(0.933103\pi\)
\(564\) 0 0
\(565\) −50.0494 + 20.7312i −2.10560 + 0.872166i
\(566\) 0 0
\(567\) −41.6632 3.03385i −1.74969 0.127410i
\(568\) 0 0
\(569\) 5.01618 + 5.01618i 0.210289 + 0.210289i 0.804390 0.594101i \(-0.202492\pi\)
−0.594101 + 0.804390i \(0.702492\pi\)
\(570\) 0 0
\(571\) 8.20928 3.40040i 0.343548 0.142302i −0.204237 0.978921i \(-0.565471\pi\)
0.547785 + 0.836619i \(0.315471\pi\)
\(572\) 0 0
\(573\) 32.0636 5.77423i 1.33948 0.241222i
\(574\) 0 0
\(575\) −16.5455 −0.689997
\(576\) 0 0
\(577\) 36.7704 1.53077 0.765386 0.643571i \(-0.222548\pi\)
0.765386 + 0.643571i \(0.222548\pi\)
\(578\) 0 0
\(579\) −19.0063 + 3.42279i −0.789875 + 0.142246i
\(580\) 0 0
\(581\) −40.3848 + 16.7279i −1.67544 + 0.693992i
\(582\) 0 0
\(583\) −1.02466 1.02466i −0.0424369 0.0424369i
\(584\) 0 0
\(585\) −1.24138 3.33483i −0.0513246 0.137878i
\(586\) 0 0
\(587\) −22.3129 + 9.24233i −0.920954 + 0.381472i −0.792240 0.610210i \(-0.791085\pi\)
−0.128714 + 0.991682i \(0.541085\pi\)
\(588\) 0 0
\(589\) −4.34912 + 10.4997i −0.179202 + 0.432633i
\(590\) 0 0
\(591\) −23.2903 + 14.9572i −0.958036 + 0.615256i
\(592\) 0 0
\(593\) −2.15691 −0.0885737 −0.0442868 0.999019i \(-0.514102\pi\)
−0.0442868 + 0.999019i \(0.514102\pi\)
\(594\) 0 0
\(595\) 17.7651 + 7.35854i 0.728297 + 0.301671i
\(596\) 0 0
\(597\) 1.38035 + 0.959057i 0.0564942 + 0.0392516i
\(598\) 0 0
\(599\) 4.80949 + 4.80949i 0.196511 + 0.196511i 0.798502 0.601992i \(-0.205626\pi\)
−0.601992 + 0.798502i \(0.705626\pi\)
\(600\) 0 0
\(601\) 5.18282 5.18282i 0.211411 0.211411i −0.593455 0.804867i \(-0.702237\pi\)
0.804867 + 0.593455i \(0.202237\pi\)
\(602\) 0 0
\(603\) −1.19609 + 32.8948i −0.0487086 + 1.33958i
\(604\) 0 0
\(605\) −12.2048 + 29.4650i −0.496196 + 1.19792i
\(606\) 0 0
\(607\) 5.19779i 0.210972i −0.994421 0.105486i \(-0.966360\pi\)
0.994421 0.105486i \(-0.0336398\pi\)
\(608\) 0 0
\(609\) −11.5017 + 7.38643i −0.466071 + 0.299313i
\(610\) 0 0
\(611\) 2.03967 + 0.844859i 0.0825162 + 0.0341793i
\(612\) 0 0
\(613\) −12.1586 29.3536i −0.491083 1.18558i −0.954170 0.299266i \(-0.903258\pi\)
0.463087 0.886313i \(-0.346742\pi\)
\(614\) 0 0
\(615\) 5.82198 26.7217i 0.234765 1.07752i
\(616\) 0 0
\(617\) −10.7968 + 10.7968i −0.434663 + 0.434663i −0.890211 0.455548i \(-0.849443\pi\)
0.455548 + 0.890211i \(0.349443\pi\)
\(618\) 0 0
\(619\) 11.7667 + 28.4074i 0.472944 + 1.14179i 0.962856 + 0.270016i \(0.0870290\pi\)
−0.489912 + 0.871772i \(0.662971\pi\)
\(620\) 0 0
\(621\) −23.4933 6.02053i −0.942753 0.241595i
\(622\) 0 0
\(623\) 24.2822i 0.972848i
\(624\) 0 0
\(625\) 30.1581i 1.20633i
\(626\) 0 0
\(627\) −1.39237 + 0.250748i −0.0556059 + 0.0100139i
\(628\) 0 0
\(629\) −4.00730 9.67449i −0.159782 0.385747i
\(630\) 0 0
\(631\) −5.17311 + 5.17311i −0.205938 + 0.205938i −0.802539 0.596600i \(-0.796518\pi\)
0.596600 + 0.802539i \(0.296518\pi\)
\(632\) 0 0
\(633\) −4.13741 0.901437i −0.164447 0.0358289i
\(634\) 0 0
\(635\) 5.36966 + 12.9635i 0.213088 + 0.514441i
\(636\) 0 0
\(637\) 5.45209 + 2.25833i 0.216020 + 0.0894782i
\(638\) 0 0
\(639\) 6.66897 14.5781i 0.263820 0.576701i
\(640\) 0 0
\(641\) 35.5298i 1.40334i 0.712500 + 0.701672i \(0.247563\pi\)
−0.712500 + 0.701672i \(0.752437\pi\)
\(642\) 0 0
\(643\) −3.04889 + 7.36067i −0.120237 + 0.290277i −0.972526 0.232793i \(-0.925213\pi\)
0.852290 + 0.523070i \(0.175213\pi\)
\(644\) 0 0
\(645\) −22.5061 15.6370i −0.886176 0.615707i
\(646\) 0 0
\(647\) 9.34579 9.34579i 0.367421 0.367421i −0.499115 0.866536i \(-0.666341\pi\)
0.866536 + 0.499115i \(0.166341\pi\)
\(648\) 0 0
\(649\) −0.762015 0.762015i −0.0299117 0.0299117i
\(650\) 0 0
\(651\) 19.1147 27.5114i 0.749163 1.07826i
\(652\) 0 0
\(653\) 3.13779 + 1.29972i 0.122791 + 0.0508618i 0.443233 0.896406i \(-0.353831\pi\)
−0.320442 + 0.947268i \(0.603831\pi\)
\(654\) 0 0
\(655\) 63.9506 2.49876
\(656\) 0 0
\(657\) −15.0133 6.86805i −0.585725 0.267948i
\(658\) 0 0
\(659\) 12.0747 29.1508i 0.470362 1.13555i −0.493642 0.869665i \(-0.664335\pi\)
0.964004 0.265889i \(-0.0856653\pi\)
\(660\) 0 0
\(661\) −21.5134 + 8.91114i −0.836774 + 0.346603i −0.759581 0.650413i \(-0.774596\pi\)
−0.0771932 + 0.997016i \(0.524596\pi\)
\(662\) 0 0
\(663\) −0.212038 + 0.973211i −0.00823487 + 0.0377964i
\(664\) 0 0
\(665\) −26.1658 26.1658i −1.01467 1.01467i
\(666\) 0 0
\(667\) −7.33186 + 3.03696i −0.283891 + 0.117591i
\(668\) 0 0
\(669\) −3.17640 17.6382i −0.122807 0.681931i
\(670\) 0 0
\(671\) −3.55385 −0.137195
\(672\) 0 0
\(673\) −27.9251 −1.07643 −0.538216 0.842807i \(-0.680902\pi\)
−0.538216 + 0.842807i \(0.680902\pi\)
\(674\) 0 0
\(675\) 4.57265 17.8434i 0.176001 0.686792i
\(676\) 0 0
\(677\) −6.25960 + 2.59281i −0.240576 + 0.0996498i −0.499714 0.866191i \(-0.666562\pi\)
0.259138 + 0.965840i \(0.416562\pi\)
\(678\) 0 0
\(679\) −36.0887 36.0887i −1.38496 1.38496i
\(680\) 0 0
\(681\) −19.1979 4.18273i −0.735665 0.160283i
\(682\) 0 0
\(683\) 26.2767 10.8842i 1.00545 0.416471i 0.181657 0.983362i \(-0.441854\pi\)
0.823793 + 0.566891i \(0.191854\pi\)
\(684\) 0 0
\(685\) 20.1393 48.6207i 0.769484 1.85770i
\(686\) 0 0
\(687\) 18.0856 + 28.1617i 0.690009 + 1.07444i
\(688\) 0 0
\(689\) 1.96328 0.0747950
\(690\) 0 0
\(691\) 26.2910 + 10.8901i 1.00016 + 0.414279i 0.821855 0.569697i \(-0.192939\pi\)
0.178303 + 0.983976i \(0.442939\pi\)
\(692\) 0 0
\(693\) 4.16756 + 0.151537i 0.158312 + 0.00575641i
\(694\) 0 0
\(695\) −1.04478 1.04478i −0.0396309 0.0396309i
\(696\) 0 0
\(697\) −5.41308 + 5.41308i −0.205035 + 0.205035i
\(698\) 0 0
\(699\) −22.3209 + 32.1260i −0.844252 + 1.21512i
\(700\) 0 0
\(701\) −15.7331 + 37.9830i −0.594230 + 1.43460i 0.285153 + 0.958482i \(0.407956\pi\)
−0.879383 + 0.476116i \(0.842044\pi\)
\(702\) 0 0
\(703\) 20.1516i 0.760032i
\(704\) 0 0
\(705\) 14.8858 + 23.1792i 0.560632 + 0.872979i
\(706\) 0 0
\(707\) −11.6733 4.83525i −0.439021 0.181848i
\(708\) 0 0
\(709\) −3.26185 7.87481i −0.122501 0.295745i 0.850718 0.525622i \(-0.176167\pi\)
−0.973220 + 0.229877i \(0.926167\pi\)
\(710\) 0 0
\(711\) 13.5514 5.04446i 0.508218 0.189182i
\(712\) 0 0
\(713\) 13.7526 13.7526i 0.515039 0.515039i
\(714\) 0 0
\(715\) 0.135944 + 0.328198i 0.00508402 + 0.0122739i
\(716\) 0 0
\(717\) −6.91184 38.3806i −0.258127 1.43335i
\(718\) 0 0
\(719\) 6.72495i 0.250798i 0.992106 + 0.125399i \(0.0400211\pi\)
−0.992106 + 0.125399i \(0.959979\pi\)
\(720\) 0 0
\(721\) 2.18508i 0.0813766i
\(722\) 0 0
\(723\) −6.68870 37.1415i −0.248756 1.38131i
\(724\) 0 0
\(725\) −2.30660 5.56862i −0.0856649 0.206813i
\(726\) 0 0
\(727\) −11.8994 + 11.8994i −0.441326 + 0.441326i −0.892457 0.451132i \(-0.851021\pi\)
0.451132 + 0.892457i \(0.351021\pi\)
\(728\) 0 0
\(729\) 12.9856 23.6722i 0.480947 0.876750i
\(730\) 0 0
\(731\) 2.93559 + 7.08715i 0.108577 + 0.262128i
\(732\) 0 0
\(733\) 27.8224 + 11.5244i 1.02764 + 0.425664i 0.831861 0.554984i \(-0.187276\pi\)
0.195782 + 0.980647i \(0.437276\pi\)
\(734\) 0 0
\(735\) 39.7901 + 61.9586i 1.46768 + 2.28538i
\(736\) 0 0
\(737\) 3.28611i 0.121045i
\(738\) 0 0
\(739\) 9.46555 22.8519i 0.348196 0.840619i −0.648637 0.761098i \(-0.724661\pi\)
0.996833 0.0795214i \(-0.0253392\pi\)
\(740\) 0 0
\(741\) 1.09370 1.57414i 0.0401779 0.0578274i
\(742\) 0 0
\(743\) 34.0574 34.0574i 1.24944 1.24944i 0.293479 0.955966i \(-0.405187\pi\)
0.955966 0.293479i \(-0.0948130\pi\)
\(744\) 0 0
\(745\) −23.3309 23.3309i −0.854778 0.854778i
\(746\) 0 0
\(747\) 1.02663 28.2344i 0.0375626 1.03304i
\(748\) 0 0
\(749\) 1.83000 + 0.758011i 0.0668667 + 0.0276971i
\(750\) 0 0
\(751\) −28.4849 −1.03943 −0.519714 0.854341i \(-0.673961\pi\)
−0.519714 + 0.854341i \(0.673961\pi\)
\(752\) 0 0
\(753\) 14.5967 + 22.7291i 0.531935 + 0.828294i
\(754\) 0 0
\(755\) −21.7822 + 52.5870i −0.792737 + 1.91384i
\(756\) 0 0
\(757\) −25.6728 + 10.6340i −0.933093 + 0.386500i −0.796851 0.604176i \(-0.793502\pi\)
−0.136242 + 0.990676i \(0.543502\pi\)
\(758\) 0 0
\(759\) 2.36566 + 0.515417i 0.0858681 + 0.0187085i
\(760\) 0 0
\(761\) 29.3477 + 29.3477i 1.06385 + 1.06385i 0.997817 + 0.0660371i \(0.0210356\pi\)
0.0660371 + 0.997817i \(0.478964\pi\)
\(762\) 0 0
\(763\) 20.3697 8.43740i 0.737432 0.305454i
\(764\) 0 0
\(765\) −9.10173 + 8.46306i −0.329074 + 0.305982i
\(766\) 0 0
\(767\) 1.46005 0.0527193
\(768\) 0 0
\(769\) −32.2426 −1.16270 −0.581349 0.813654i \(-0.697475\pi\)
−0.581349 + 0.813654i \(0.697475\pi\)
\(770\) 0 0
\(771\) 3.64635 + 20.2477i 0.131320 + 0.729204i
\(772\) 0 0
\(773\) 12.3588 5.11920i 0.444517 0.184125i −0.149186 0.988809i \(-0.547665\pi\)
0.593703 + 0.804684i \(0.297665\pi\)
\(774\) 0 0
\(775\) 10.4452 + 10.4452i 0.375203 + 0.375203i
\(776\) 0 0
\(777\) 12.6453 58.0392i 0.453647 2.08215i
\(778\) 0 0
\(779\) 13.6104 5.63762i 0.487644 0.201989i
\(780\) 0 0
\(781\) −0.612450 + 1.47859i −0.0219152 + 0.0529079i
\(782\) 0 0
\(783\) −1.24889