Properties

Label 640.2.j.d.607.2
Level $640$
Weight $2$
Character 640.607
Analytic conductor $5.110$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 640.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.11042572936\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
Defining polynomial: \(x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 607.2
Root \(0.0376504 + 1.41371i\) of defining polynomial
Character \(\chi\) \(=\) 640.607
Dual form 640.2.j.d.543.8

$q$-expansion

\(f(q)\) \(=\) \(q-2.55161i q^{3} +(-1.66635 + 1.49107i) q^{5} +(2.40368 + 2.40368i) q^{7} -3.51070 q^{9} +O(q^{10})\) \(q-2.55161i q^{3} +(-1.66635 + 1.49107i) q^{5} +(2.40368 + 2.40368i) q^{7} -3.51070 q^{9} +(2.67707 + 2.67707i) q^{11} +2.40164 q^{13} +(3.80462 + 4.25187i) q^{15} +(-0.0750544 - 0.0750544i) q^{17} +(2.67236 + 2.67236i) q^{19} +(6.13324 - 6.13324i) q^{21} +(2.12375 - 2.12375i) q^{23} +(0.553442 - 4.96928i) q^{25} +1.30310i q^{27} +(-3.95795 + 3.95795i) q^{29} +1.65367i q^{31} +(6.83083 - 6.83083i) q^{33} +(-7.58941 - 0.421324i) q^{35} +2.53082 q^{37} -6.12803i q^{39} -1.70882i q^{41} +3.84601 q^{43} +(5.85005 - 5.23469i) q^{45} +(-2.15264 + 2.15264i) q^{47} +4.55532i q^{49} +(-0.191509 + 0.191509i) q^{51} -1.29475i q^{53} +(-8.45262 - 0.469246i) q^{55} +(6.81881 - 6.81881i) q^{57} +(5.29614 - 5.29614i) q^{59} +(-10.2413 - 10.2413i) q^{61} +(-8.43858 - 8.43858i) q^{63} +(-4.00197 + 3.58100i) q^{65} +10.6230 q^{67} +(-5.41898 - 5.41898i) q^{69} +2.27322 q^{71} +(9.99096 + 9.99096i) q^{73} +(-12.6796 - 1.41217i) q^{75} +12.8696i q^{77} +8.70617 q^{79} -7.20709 q^{81} +11.1310i q^{83} +(0.236978 + 0.0131558i) q^{85} +(10.0991 + 10.0991i) q^{87} -15.6390 q^{89} +(5.77276 + 5.77276i) q^{91} +4.21952 q^{93} +(-8.43775 - 0.468420i) q^{95} +(5.00672 + 5.00672i) q^{97} +(-9.39839 - 9.39839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 4 q^{5} + 2 q^{7} - 10 q^{9} + O(q^{10}) \) \( 18 q + 4 q^{5} + 2 q^{7} - 10 q^{9} + 2 q^{11} + 20 q^{15} - 6 q^{17} - 2 q^{19} + 16 q^{21} - 2 q^{23} + 6 q^{25} + 14 q^{29} - 8 q^{33} + 6 q^{35} - 8 q^{37} + 44 q^{43} + 4 q^{45} - 38 q^{47} - 8 q^{51} - 6 q^{55} + 24 q^{57} + 10 q^{59} - 14 q^{61} + 6 q^{63} - 12 q^{67} - 32 q^{69} + 24 q^{71} + 14 q^{73} - 64 q^{75} + 16 q^{79} + 2 q^{81} + 10 q^{85} + 24 q^{87} - 12 q^{89} - 16 q^{93} - 34 q^{95} + 18 q^{97} + 22 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(261\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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
\(3\) 2.55161i 1.47317i −0.676344 0.736586i \(-0.736437\pi\)
0.676344 0.736586i \(-0.263563\pi\)
\(4\) 0 0
\(5\) −1.66635 + 1.49107i −0.745214 + 0.666825i
\(6\) 0 0
\(7\) 2.40368 + 2.40368i 0.908504 + 0.908504i 0.996152 0.0876474i \(-0.0279349\pi\)
−0.0876474 + 0.996152i \(0.527935\pi\)
\(8\) 0 0
\(9\) −3.51070 −1.17023
\(10\) 0 0
\(11\) 2.67707 + 2.67707i 0.807167 + 0.807167i 0.984204 0.177037i \(-0.0566513\pi\)
−0.177037 + 0.984204i \(0.556651\pi\)
\(12\) 0 0
\(13\) 2.40164 0.666094 0.333047 0.942910i \(-0.391923\pi\)
0.333047 + 0.942910i \(0.391923\pi\)
\(14\) 0 0
\(15\) 3.80462 + 4.25187i 0.982348 + 1.09783i
\(16\) 0 0
\(17\) −0.0750544 0.0750544i −0.0182034 0.0182034i 0.697947 0.716150i \(-0.254097\pi\)
−0.716150 + 0.697947i \(0.754097\pi\)
\(18\) 0 0
\(19\) 2.67236 + 2.67236i 0.613081 + 0.613081i 0.943748 0.330666i \(-0.107274\pi\)
−0.330666 + 0.943748i \(0.607274\pi\)
\(20\) 0 0
\(21\) 6.13324 6.13324i 1.33838 1.33838i
\(22\) 0 0
\(23\) 2.12375 2.12375i 0.442833 0.442833i −0.450130 0.892963i \(-0.648622\pi\)
0.892963 + 0.450130i \(0.148622\pi\)
\(24\) 0 0
\(25\) 0.553442 4.96928i 0.110688 0.993855i
\(26\) 0 0
\(27\) 1.30310i 0.250783i
\(28\) 0 0
\(29\) −3.95795 + 3.95795i −0.734974 + 0.734974i −0.971601 0.236627i \(-0.923958\pi\)
0.236627 + 0.971601i \(0.423958\pi\)
\(30\) 0 0
\(31\) 1.65367i 0.297008i 0.988912 + 0.148504i \(0.0474458\pi\)
−0.988912 + 0.148504i \(0.952554\pi\)
\(32\) 0 0
\(33\) 6.83083 6.83083i 1.18909 1.18909i
\(34\) 0 0
\(35\) −7.58941 0.421324i −1.28284 0.0712168i
\(36\) 0 0
\(37\) 2.53082 0.416064 0.208032 0.978122i \(-0.433294\pi\)
0.208032 + 0.978122i \(0.433294\pi\)
\(38\) 0 0
\(39\) 6.12803i 0.981271i
\(40\) 0 0
\(41\) 1.70882i 0.266873i −0.991057 0.133436i \(-0.957399\pi\)
0.991057 0.133436i \(-0.0426012\pi\)
\(42\) 0 0
\(43\) 3.84601 0.586510 0.293255 0.956034i \(-0.405261\pi\)
0.293255 + 0.956034i \(0.405261\pi\)
\(44\) 0 0
\(45\) 5.85005 5.23469i 0.872074 0.780341i
\(46\) 0 0
\(47\) −2.15264 + 2.15264i −0.313995 + 0.313995i −0.846455 0.532460i \(-0.821268\pi\)
0.532460 + 0.846455i \(0.321268\pi\)
\(48\) 0 0
\(49\) 4.55532i 0.650760i
\(50\) 0 0
\(51\) −0.191509 + 0.191509i −0.0268167 + 0.0268167i
\(52\) 0 0
\(53\) 1.29475i 0.177848i −0.996038 0.0889239i \(-0.971657\pi\)
0.996038 0.0889239i \(-0.0283428\pi\)
\(54\) 0 0
\(55\) −8.45262 0.469246i −1.13975 0.0632731i
\(56\) 0 0
\(57\) 6.81881 6.81881i 0.903174 0.903174i
\(58\) 0 0
\(59\) 5.29614 5.29614i 0.689499 0.689499i −0.272622 0.962121i \(-0.587891\pi\)
0.962121 + 0.272622i \(0.0878908\pi\)
\(60\) 0 0
\(61\) −10.2413 10.2413i −1.31126 1.31126i −0.920484 0.390780i \(-0.872205\pi\)
−0.390780 0.920484i \(-0.627795\pi\)
\(62\) 0 0
\(63\) −8.43858 8.43858i −1.06316 1.06316i
\(64\) 0 0
\(65\) −4.00197 + 3.58100i −0.496383 + 0.444168i
\(66\) 0 0
\(67\) 10.6230 1.29780 0.648901 0.760873i \(-0.275229\pi\)
0.648901 + 0.760873i \(0.275229\pi\)
\(68\) 0 0
\(69\) −5.41898 5.41898i −0.652369 0.652369i
\(70\) 0 0
\(71\) 2.27322 0.269781 0.134891 0.990860i \(-0.456932\pi\)
0.134891 + 0.990860i \(0.456932\pi\)
\(72\) 0 0
\(73\) 9.99096 + 9.99096i 1.16935 + 1.16935i 0.982361 + 0.186992i \(0.0598739\pi\)
0.186992 + 0.982361i \(0.440126\pi\)
\(74\) 0 0
\(75\) −12.6796 1.41217i −1.46412 0.163063i
\(76\) 0 0
\(77\) 12.8696i 1.46663i
\(78\) 0 0
\(79\) 8.70617 0.979520 0.489760 0.871857i \(-0.337084\pi\)
0.489760 + 0.871857i \(0.337084\pi\)
\(80\) 0 0
\(81\) −7.20709 −0.800787
\(82\) 0 0
\(83\) 11.1310i 1.22178i 0.791715 + 0.610890i \(0.209188\pi\)
−0.791715 + 0.610890i \(0.790812\pi\)
\(84\) 0 0
\(85\) 0.236978 + 0.0131558i 0.0257039 + 0.00142695i
\(86\) 0 0
\(87\) 10.0991 + 10.0991i 1.08274 + 1.08274i
\(88\) 0 0
\(89\) −15.6390 −1.65773 −0.828866 0.559447i \(-0.811014\pi\)
−0.828866 + 0.559447i \(0.811014\pi\)
\(90\) 0 0
\(91\) 5.77276 + 5.77276i 0.605149 + 0.605149i
\(92\) 0 0
\(93\) 4.21952 0.437544
\(94\) 0 0
\(95\) −8.43775 0.468420i −0.865695 0.0480589i
\(96\) 0 0
\(97\) 5.00672 + 5.00672i 0.508355 + 0.508355i 0.914021 0.405666i \(-0.132960\pi\)
−0.405666 + 0.914021i \(0.632960\pi\)
\(98\) 0 0
\(99\) −9.39839 9.39839i −0.944573 0.944573i
\(100\) 0 0
\(101\) −6.37101 + 6.37101i −0.633939 + 0.633939i −0.949054 0.315115i \(-0.897957\pi\)
0.315115 + 0.949054i \(0.397957\pi\)
\(102\) 0 0
\(103\) −1.93695 + 1.93695i −0.190854 + 0.190854i −0.796065 0.605211i \(-0.793089\pi\)
0.605211 + 0.796065i \(0.293089\pi\)
\(104\) 0 0
\(105\) −1.07505 + 19.3652i −0.104915 + 1.88985i
\(106\) 0 0
\(107\) 6.97778i 0.674568i −0.941403 0.337284i \(-0.890492\pi\)
0.941403 0.337284i \(-0.109508\pi\)
\(108\) 0 0
\(109\) 0.277748 0.277748i 0.0266034 0.0266034i −0.693680 0.720283i \(-0.744012\pi\)
0.720283 + 0.693680i \(0.244012\pi\)
\(110\) 0 0
\(111\) 6.45766i 0.612934i
\(112\) 0 0
\(113\) −8.75577 + 8.75577i −0.823674 + 0.823674i −0.986633 0.162959i \(-0.947896\pi\)
0.162959 + 0.986633i \(0.447896\pi\)
\(114\) 0 0
\(115\) −0.372258 + 6.70557i −0.0347133 + 0.625298i
\(116\) 0 0
\(117\) −8.43142 −0.779485
\(118\) 0 0
\(119\) 0.360813i 0.0330757i
\(120\) 0 0
\(121\) 3.33340i 0.303036i
\(122\) 0 0
\(123\) −4.36024 −0.393149
\(124\) 0 0
\(125\) 6.48729 + 9.10577i 0.580241 + 0.814445i
\(126\) 0 0
\(127\) 0.679502 0.679502i 0.0602961 0.0602961i −0.676316 0.736612i \(-0.736424\pi\)
0.736612 + 0.676316i \(0.236424\pi\)
\(128\) 0 0
\(129\) 9.81350i 0.864030i
\(130\) 0 0
\(131\) 5.43859 5.43859i 0.475172 0.475172i −0.428412 0.903584i \(-0.640927\pi\)
0.903584 + 0.428412i \(0.140927\pi\)
\(132\) 0 0
\(133\) 12.8470i 1.11397i
\(134\) 0 0
\(135\) −1.94302 2.17143i −0.167228 0.186887i
\(136\) 0 0
\(137\) 7.47496 7.47496i 0.638629 0.638629i −0.311588 0.950217i \(-0.600861\pi\)
0.950217 + 0.311588i \(0.100861\pi\)
\(138\) 0 0
\(139\) −11.5307 + 11.5307i −0.978023 + 0.978023i −0.999764 0.0217404i \(-0.993079\pi\)
0.0217404 + 0.999764i \(0.493079\pi\)
\(140\) 0 0
\(141\) 5.49270 + 5.49270i 0.462568 + 0.462568i
\(142\) 0 0
\(143\) 6.42935 + 6.42935i 0.537649 + 0.537649i
\(144\) 0 0
\(145\) 0.693763 12.4969i 0.0576139 1.03781i
\(146\) 0 0
\(147\) 11.6234 0.958680
\(148\) 0 0
\(149\) 5.51174 + 5.51174i 0.451539 + 0.451539i 0.895865 0.444326i \(-0.146557\pi\)
−0.444326 + 0.895865i \(0.646557\pi\)
\(150\) 0 0
\(151\) −4.13617 −0.336597 −0.168299 0.985736i \(-0.553827\pi\)
−0.168299 + 0.985736i \(0.553827\pi\)
\(152\) 0 0
\(153\) 0.263494 + 0.263494i 0.0213022 + 0.0213022i
\(154\) 0 0
\(155\) −2.46573 2.75559i −0.198052 0.221335i
\(156\) 0 0
\(157\) 20.2700i 1.61772i −0.587999 0.808861i \(-0.700084\pi\)
0.587999 0.808861i \(-0.299916\pi\)
\(158\) 0 0
\(159\) −3.30370 −0.262000
\(160\) 0 0
\(161\) 10.2096 0.804631
\(162\) 0 0
\(163\) 13.1835i 1.03262i −0.856403 0.516308i \(-0.827306\pi\)
0.856403 0.516308i \(-0.172694\pi\)
\(164\) 0 0
\(165\) −1.19733 + 21.5678i −0.0932121 + 1.67905i
\(166\) 0 0
\(167\) −11.8190 11.8190i −0.914585 0.914585i 0.0820441 0.996629i \(-0.473855\pi\)
−0.996629 + 0.0820441i \(0.973855\pi\)
\(168\) 0 0
\(169\) −7.23214 −0.556319
\(170\) 0 0
\(171\) −9.38185 9.38185i −0.717448 0.717448i
\(172\) 0 0
\(173\) −15.5763 −1.18424 −0.592120 0.805849i \(-0.701709\pi\)
−0.592120 + 0.805849i \(0.701709\pi\)
\(174\) 0 0
\(175\) 13.2748 10.6142i 1.00348 0.802361i
\(176\) 0 0
\(177\) −13.5137 13.5137i −1.01575 1.01575i
\(178\) 0 0
\(179\) −15.5963 15.5963i −1.16572 1.16572i −0.983202 0.182523i \(-0.941574\pi\)
−0.182523 0.983202i \(-0.558426\pi\)
\(180\) 0 0
\(181\) −2.98705 + 2.98705i −0.222026 + 0.222026i −0.809351 0.587325i \(-0.800181\pi\)
0.587325 + 0.809351i \(0.300181\pi\)
\(182\) 0 0
\(183\) −26.1318 + 26.1318i −1.93172 + 1.93172i
\(184\) 0 0
\(185\) −4.21723 + 3.77362i −0.310057 + 0.277442i
\(186\) 0 0
\(187\) 0.401852i 0.0293863i
\(188\) 0 0
\(189\) −3.13224 + 3.13224i −0.227837 + 0.227837i
\(190\) 0 0
\(191\) 6.47168i 0.468274i −0.972204 0.234137i \(-0.924774\pi\)
0.972204 0.234137i \(-0.0752264\pi\)
\(192\) 0 0
\(193\) −11.1131 + 11.1131i −0.799936 + 0.799936i −0.983085 0.183149i \(-0.941371\pi\)
0.183149 + 0.983085i \(0.441371\pi\)
\(194\) 0 0
\(195\) 9.13730 + 10.2114i 0.654336 + 0.731257i
\(196\) 0 0
\(197\) 25.0927 1.78778 0.893889 0.448288i \(-0.147966\pi\)
0.893889 + 0.448288i \(0.147966\pi\)
\(198\) 0 0
\(199\) 18.7579i 1.32972i −0.746970 0.664858i \(-0.768492\pi\)
0.746970 0.664858i \(-0.231508\pi\)
\(200\) 0 0
\(201\) 27.1056i 1.91188i
\(202\) 0 0
\(203\) −19.0273 −1.33545
\(204\) 0 0
\(205\) 2.54796 + 2.84749i 0.177958 + 0.198877i
\(206\) 0 0
\(207\) −7.45586 + 7.45586i −0.518218 + 0.518218i
\(208\) 0 0
\(209\) 14.3082i 0.989718i
\(210\) 0 0
\(211\) −6.38863 + 6.38863i −0.439811 + 0.439811i −0.891948 0.452137i \(-0.850662\pi\)
0.452137 + 0.891948i \(0.350662\pi\)
\(212\) 0 0
\(213\) 5.80036i 0.397434i
\(214\) 0 0
\(215\) −6.40879 + 5.73465i −0.437076 + 0.391100i
\(216\) 0 0
\(217\) −3.97489 + 3.97489i −0.269833 + 0.269833i
\(218\) 0 0
\(219\) 25.4930 25.4930i 1.72266 1.72266i
\(220\) 0 0
\(221\) −0.180253 0.180253i −0.0121252 0.0121252i
\(222\) 0 0
\(223\) 4.29779 + 4.29779i 0.287801 + 0.287801i 0.836210 0.548409i \(-0.184766\pi\)
−0.548409 + 0.836210i \(0.684766\pi\)
\(224\) 0 0
\(225\) −1.94297 + 17.4456i −0.129531 + 1.16304i
\(226\) 0 0
\(227\) −29.1029 −1.93163 −0.965813 0.259241i \(-0.916528\pi\)
−0.965813 + 0.259241i \(0.916528\pi\)
\(228\) 0 0
\(229\) −18.3405 18.3405i −1.21198 1.21198i −0.970376 0.241600i \(-0.922328\pi\)
−0.241600 0.970376i \(-0.577672\pi\)
\(230\) 0 0
\(231\) 32.8382 2.16060
\(232\) 0 0
\(233\) −1.46663 1.46663i −0.0960824 0.0960824i 0.657432 0.753514i \(-0.271643\pi\)
−0.753514 + 0.657432i \(0.771643\pi\)
\(234\) 0 0
\(235\) 0.377322 6.79678i 0.0246138 0.443373i
\(236\) 0 0
\(237\) 22.2147i 1.44300i
\(238\) 0 0
\(239\) −12.5432 −0.811352 −0.405676 0.914017i \(-0.632964\pi\)
−0.405676 + 0.914017i \(0.632964\pi\)
\(240\) 0 0
\(241\) 14.8870 0.958954 0.479477 0.877554i \(-0.340826\pi\)
0.479477 + 0.877554i \(0.340826\pi\)
\(242\) 0 0
\(243\) 22.2990i 1.43048i
\(244\) 0 0
\(245\) −6.79228 7.59075i −0.433943 0.484955i
\(246\) 0 0
\(247\) 6.41803 + 6.41803i 0.408370 + 0.408370i
\(248\) 0 0
\(249\) 28.4018 1.79989
\(250\) 0 0
\(251\) 5.38459 + 5.38459i 0.339872 + 0.339872i 0.856319 0.516447i \(-0.172746\pi\)
−0.516447 + 0.856319i \(0.672746\pi\)
\(252\) 0 0
\(253\) 11.3709 0.714880
\(254\) 0 0
\(255\) 0.0335684 0.604675i 0.00210214 0.0378662i
\(256\) 0 0
\(257\) −3.88657 3.88657i −0.242437 0.242437i 0.575420 0.817858i \(-0.304838\pi\)
−0.817858 + 0.575420i \(0.804838\pi\)
\(258\) 0 0
\(259\) 6.08327 + 6.08327i 0.377996 + 0.377996i
\(260\) 0 0
\(261\) 13.8952 13.8952i 0.860090 0.860090i
\(262\) 0 0
\(263\) 16.9658 16.9658i 1.04615 1.04615i 0.0472716 0.998882i \(-0.484947\pi\)
0.998882 0.0472716i \(-0.0150526\pi\)
\(264\) 0 0
\(265\) 1.93056 + 2.15751i 0.118593 + 0.132535i
\(266\) 0 0
\(267\) 39.9046i 2.44212i
\(268\) 0 0
\(269\) 2.55482 2.55482i 0.155770 0.155770i −0.624919 0.780689i \(-0.714868\pi\)
0.780689 + 0.624919i \(0.214868\pi\)
\(270\) 0 0
\(271\) 3.33684i 0.202698i 0.994851 + 0.101349i \(0.0323159\pi\)
−0.994851 + 0.101349i \(0.967684\pi\)
\(272\) 0 0
\(273\) 14.7298 14.7298i 0.891488 0.891488i
\(274\) 0 0
\(275\) 14.7847 11.8215i 0.891551 0.712863i
\(276\) 0 0
\(277\) −4.60736 −0.276830 −0.138415 0.990374i \(-0.544201\pi\)
−0.138415 + 0.990374i \(0.544201\pi\)
\(278\) 0 0
\(279\) 5.80554i 0.347569i
\(280\) 0 0
\(281\) 22.1178i 1.31944i 0.751513 + 0.659718i \(0.229324\pi\)
−0.751513 + 0.659718i \(0.770676\pi\)
\(282\) 0 0
\(283\) 10.8629 0.645734 0.322867 0.946444i \(-0.395353\pi\)
0.322867 + 0.946444i \(0.395353\pi\)
\(284\) 0 0
\(285\) −1.19522 + 21.5298i −0.0707990 + 1.27532i
\(286\) 0 0
\(287\) 4.10745 4.10745i 0.242455 0.242455i
\(288\) 0 0
\(289\) 16.9887i 0.999337i
\(290\) 0 0
\(291\) 12.7752 12.7752i 0.748895 0.748895i
\(292\) 0 0
\(293\) 18.4067i 1.07533i −0.843159 0.537665i \(-0.819307\pi\)
0.843159 0.537665i \(-0.180693\pi\)
\(294\) 0 0
\(295\) −0.928326 + 16.7221i −0.0540492 + 0.973600i
\(296\) 0 0
\(297\) −3.48850 + 3.48850i −0.202423 + 0.202423i
\(298\) 0 0
\(299\) 5.10048 5.10048i 0.294968 0.294968i
\(300\) 0 0
\(301\) 9.24455 + 9.24455i 0.532847 + 0.532847i
\(302\) 0 0
\(303\) 16.2563 + 16.2563i 0.933900 + 0.933900i
\(304\) 0 0
\(305\) 32.3360 + 1.79513i 1.85156 + 0.102789i
\(306\) 0 0
\(307\) 6.60872 0.377180 0.188590 0.982056i \(-0.439608\pi\)
0.188590 + 0.982056i \(0.439608\pi\)
\(308\) 0 0
\(309\) 4.94234 + 4.94234i 0.281160 + 0.281160i
\(310\) 0 0
\(311\) −0.606102 −0.0343689 −0.0171845 0.999852i \(-0.505470\pi\)
−0.0171845 + 0.999852i \(0.505470\pi\)
\(312\) 0 0
\(313\) −19.3708 19.3708i −1.09490 1.09490i −0.994997 0.0999032i \(-0.968147\pi\)
−0.0999032 0.994997i \(-0.531853\pi\)
\(314\) 0 0
\(315\) 26.6441 + 1.47914i 1.50123 + 0.0833403i
\(316\) 0 0
\(317\) 7.04328i 0.395590i 0.980243 + 0.197795i \(0.0633780\pi\)
−0.980243 + 0.197795i \(0.936622\pi\)
\(318\) 0 0
\(319\) −21.1914 −1.18649
\(320\) 0 0
\(321\) −17.8046 −0.993753
\(322\) 0 0
\(323\) 0.401145i 0.0223203i
\(324\) 0 0
\(325\) 1.32917 11.9344i 0.0737290 0.662001i
\(326\) 0 0
\(327\) −0.708703 0.708703i −0.0391914 0.0391914i
\(328\) 0 0
\(329\) −10.3485 −0.570532
\(330\) 0 0
\(331\) 13.2275 + 13.2275i 0.727047 + 0.727047i 0.970031 0.242983i \(-0.0781260\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(332\) 0 0
\(333\) −8.88495 −0.486892
\(334\) 0 0
\(335\) −17.7016 + 15.8395i −0.967140 + 0.865407i
\(336\) 0 0
\(337\) 7.73287 + 7.73287i 0.421236 + 0.421236i 0.885629 0.464393i \(-0.153727\pi\)
−0.464393 + 0.885629i \(0.653727\pi\)
\(338\) 0 0
\(339\) 22.3413 + 22.3413i 1.21341 + 1.21341i
\(340\) 0 0
\(341\) −4.42699 + 4.42699i −0.239735 + 0.239735i
\(342\) 0 0
\(343\) 5.87623 5.87623i 0.317286 0.317286i
\(344\) 0 0
\(345\) 17.1100 + 0.949857i 0.921170 + 0.0511386i
\(346\) 0 0
\(347\) 11.3945i 0.611691i 0.952081 + 0.305845i \(0.0989391\pi\)
−0.952081 + 0.305845i \(0.901061\pi\)
\(348\) 0 0
\(349\) −12.0508 + 12.0508i −0.645066 + 0.645066i −0.951796 0.306730i \(-0.900765\pi\)
0.306730 + 0.951796i \(0.400765\pi\)
\(350\) 0 0
\(351\) 3.12958i 0.167045i
\(352\) 0 0
\(353\) −6.47876 + 6.47876i −0.344830 + 0.344830i −0.858179 0.513350i \(-0.828404\pi\)
0.513350 + 0.858179i \(0.328404\pi\)
\(354\) 0 0
\(355\) −3.78798 + 3.38952i −0.201045 + 0.179897i
\(356\) 0 0
\(357\) −0.920653 −0.0487261
\(358\) 0 0
\(359\) 3.25098i 0.171580i −0.996313 0.0857902i \(-0.972659\pi\)
0.996313 0.0857902i \(-0.0273415\pi\)
\(360\) 0 0
\(361\) 4.71699i 0.248263i
\(362\) 0 0
\(363\) 8.50553 0.446424
\(364\) 0 0
\(365\) −31.5456 1.75125i −1.65117 0.0916646i
\(366\) 0 0
\(367\) 12.7038 12.7038i 0.663132 0.663132i −0.292985 0.956117i \(-0.594649\pi\)
0.956117 + 0.292985i \(0.0946487\pi\)
\(368\) 0 0
\(369\) 5.99916i 0.312304i
\(370\) 0 0
\(371\) 3.11216 3.11216i 0.161575 0.161575i
\(372\) 0 0
\(373\) 21.9761i 1.13788i 0.822379 + 0.568939i \(0.192646\pi\)
−0.822379 + 0.568939i \(0.807354\pi\)
\(374\) 0 0
\(375\) 23.2343 16.5530i 1.19982 0.854794i
\(376\) 0 0
\(377\) −9.50557 + 9.50557i −0.489562 + 0.489562i
\(378\) 0 0
\(379\) −17.0642 + 17.0642i −0.876527 + 0.876527i −0.993174 0.116646i \(-0.962786\pi\)
0.116646 + 0.993174i \(0.462786\pi\)
\(380\) 0 0
\(381\) −1.73382 1.73382i −0.0888264 0.0888264i
\(382\) 0 0
\(383\) 0.228058 + 0.228058i 0.0116532 + 0.0116532i 0.712909 0.701256i \(-0.247377\pi\)
−0.701256 + 0.712909i \(0.747377\pi\)
\(384\) 0 0
\(385\) −19.1894 21.4453i −0.977985 1.09295i
\(386\) 0 0
\(387\) −13.5022 −0.686354
\(388\) 0 0
\(389\) −14.3036 14.3036i −0.725221 0.725221i 0.244443 0.969664i \(-0.421395\pi\)
−0.969664 + 0.244443i \(0.921395\pi\)
\(390\) 0 0
\(391\) −0.318794 −0.0161221
\(392\) 0 0
\(393\) −13.8771 13.8771i −0.700009 0.700009i
\(394\) 0 0
\(395\) −14.5075 + 12.9815i −0.729953 + 0.653169i
\(396\) 0 0
\(397\) 5.11618i 0.256774i −0.991724 0.128387i \(-0.959020\pi\)
0.991724 0.128387i \(-0.0409799\pi\)
\(398\) 0 0
\(399\) 32.7804 1.64107
\(400\) 0 0
\(401\) −16.2837 −0.813170 −0.406585 0.913613i \(-0.633281\pi\)
−0.406585 + 0.913613i \(0.633281\pi\)
\(402\) 0 0
\(403\) 3.97152i 0.197835i
\(404\) 0 0
\(405\) 12.0095 10.7462i 0.596758 0.533985i
\(406\) 0 0
\(407\) 6.77518 + 6.77518i 0.335833 + 0.335833i
\(408\) 0 0
\(409\) 17.4256 0.861640 0.430820 0.902438i \(-0.358224\pi\)
0.430820 + 0.902438i \(0.358224\pi\)
\(410\) 0 0
\(411\) −19.0732 19.0732i −0.940810 0.940810i
\(412\) 0 0
\(413\) 25.4604 1.25283
\(414\) 0 0
\(415\) −16.5970 18.5481i −0.814714 0.910488i
\(416\) 0 0
\(417\) 29.4219 + 29.4219i 1.44080 + 1.44080i
\(418\) 0 0
\(419\) −11.7257 11.7257i −0.572837 0.572837i 0.360083 0.932920i \(-0.382748\pi\)
−0.932920 + 0.360083i \(0.882748\pi\)
\(420\) 0 0
\(421\) 23.5406 23.5406i 1.14730 1.14730i 0.160216 0.987082i \(-0.448781\pi\)
0.987082 0.160216i \(-0.0512191\pi\)
\(422\) 0 0
\(423\) 7.55728 7.55728i 0.367447 0.367447i
\(424\) 0 0
\(425\) −0.414505 + 0.331428i −0.0201064 + 0.0160766i
\(426\) 0 0
\(427\) 49.2335i 2.38258i
\(428\) 0 0
\(429\) 16.4052 16.4052i 0.792049 0.792049i
\(430\) 0 0
\(431\) 35.0243i 1.68706i 0.537079 + 0.843532i \(0.319528\pi\)
−0.537079 + 0.843532i \(0.680472\pi\)
\(432\) 0 0
\(433\) 10.1094 10.1094i 0.485828 0.485828i −0.421159 0.906987i \(-0.638376\pi\)
0.906987 + 0.421159i \(0.138376\pi\)
\(434\) 0 0
\(435\) −31.8872 1.77021i −1.52887 0.0848752i
\(436\) 0 0
\(437\) 11.3509 0.542985
\(438\) 0 0
\(439\) 22.6071i 1.07898i 0.841993 + 0.539488i \(0.181382\pi\)
−0.841993 + 0.539488i \(0.818618\pi\)
\(440\) 0 0
\(441\) 15.9923i 0.761540i
\(442\) 0 0
\(443\) 10.9178 0.518721 0.259360 0.965781i \(-0.416488\pi\)
0.259360 + 0.965781i \(0.416488\pi\)
\(444\) 0 0
\(445\) 26.0601 23.3188i 1.23537 1.10542i
\(446\) 0 0
\(447\) 14.0638 14.0638i 0.665195 0.665195i
\(448\) 0 0
\(449\) 28.8112i 1.35969i −0.733358 0.679843i \(-0.762048\pi\)
0.733358 0.679843i \(-0.237952\pi\)
\(450\) 0 0
\(451\) 4.57463 4.57463i 0.215411 0.215411i
\(452\) 0 0
\(453\) 10.5539i 0.495865i
\(454\) 0 0
\(455\) −18.2270 1.01187i −0.854495 0.0474371i
\(456\) 0 0
\(457\) 19.1653 19.1653i 0.896513 0.896513i −0.0986128 0.995126i \(-0.531441\pi\)
0.995126 + 0.0986128i \(0.0314405\pi\)
\(458\) 0 0
\(459\) 0.0978038 0.0978038i 0.00456509 0.00456509i
\(460\) 0 0
\(461\) −4.43227 4.43227i −0.206431 0.206431i 0.596317 0.802749i \(-0.296630\pi\)
−0.802749 + 0.596317i \(0.796630\pi\)
\(462\) 0 0
\(463\) −20.1518 20.1518i −0.936534 0.936534i 0.0615691 0.998103i \(-0.480390\pi\)
−0.998103 + 0.0615691i \(0.980390\pi\)
\(464\) 0 0
\(465\) −7.03120 + 6.29158i −0.326064 + 0.291765i
\(466\) 0 0
\(467\) 3.89858 0.180405 0.0902025 0.995923i \(-0.471249\pi\)
0.0902025 + 0.995923i \(0.471249\pi\)
\(468\) 0 0
\(469\) 25.5342 + 25.5342i 1.17906 + 1.17906i
\(470\) 0 0
\(471\) −51.7211 −2.38318
\(472\) 0 0
\(473\) 10.2960 + 10.2960i 0.473412 + 0.473412i
\(474\) 0 0
\(475\) 14.7587 11.8007i 0.677175 0.541453i
\(476\) 0 0
\(477\) 4.54548i 0.208123i
\(478\) 0 0
\(479\) −9.85299 −0.450194 −0.225097 0.974336i \(-0.572270\pi\)
−0.225097 + 0.974336i \(0.572270\pi\)
\(480\) 0 0
\(481\) 6.07811 0.277138
\(482\) 0 0
\(483\) 26.0510i 1.18536i
\(484\) 0 0
\(485\) −15.8083 0.877595i −0.717818 0.0398495i
\(486\) 0 0
\(487\) −13.9164 13.9164i −0.630611 0.630611i 0.317610 0.948221i \(-0.397120\pi\)
−0.948221 + 0.317610i \(0.897120\pi\)
\(488\) 0 0
\(489\) −33.6392 −1.52122
\(490\) 0 0
\(491\) −2.39213 2.39213i −0.107955 0.107955i 0.651066 0.759021i \(-0.274322\pi\)
−0.759021 + 0.651066i \(0.774322\pi\)
\(492\) 0 0
\(493\) 0.594124 0.0267580
\(494\) 0 0
\(495\) 29.6746 + 1.64738i 1.33377 + 0.0740443i
\(496\) 0 0
\(497\) 5.46408 + 5.46408i 0.245098 + 0.245098i
\(498\) 0 0
\(499\) −9.87034 9.87034i −0.441857 0.441857i 0.450779 0.892636i \(-0.351146\pi\)
−0.892636 + 0.450779i \(0.851146\pi\)
\(500\) 0 0
\(501\) −30.1575 + 30.1575i −1.34734 + 1.34734i
\(502\) 0 0
\(503\) 9.29035 9.29035i 0.414236 0.414236i −0.468975 0.883211i \(-0.655377\pi\)
0.883211 + 0.468975i \(0.155377\pi\)
\(504\) 0 0
\(505\) 1.11673 20.1159i 0.0496939 0.895146i
\(506\) 0 0
\(507\) 18.4536i 0.819553i
\(508\) 0 0
\(509\) −6.53818 + 6.53818i −0.289800 + 0.289800i −0.837001 0.547201i \(-0.815693\pi\)
0.547201 + 0.837001i \(0.315693\pi\)
\(510\) 0 0
\(511\) 48.0301i 2.12473i
\(512\) 0 0
\(513\) −3.48236 + 3.48236i −0.153750 + 0.153750i
\(514\) 0 0
\(515\) 0.339516 6.11577i 0.0149608 0.269493i
\(516\) 0 0
\(517\) −11.5255 −0.506893
\(518\) 0 0
\(519\) 39.7445i 1.74459i
\(520\) 0 0
\(521\) 14.2961i 0.626324i −0.949700 0.313162i \(-0.898612\pi\)
0.949700 0.313162i \(-0.101388\pi\)
\(522\) 0 0
\(523\) −16.0319 −0.701027 −0.350513 0.936558i \(-0.613993\pi\)
−0.350513 + 0.936558i \(0.613993\pi\)
\(524\) 0 0
\(525\) −27.0834 33.8721i −1.18201 1.47830i
\(526\) 0 0
\(527\) 0.124115 0.124115i 0.00540655 0.00540655i
\(528\) 0 0
\(529\) 13.9794i 0.607798i
\(530\) 0 0
\(531\) −18.5932 + 18.5932i −0.806875 + 0.806875i
\(532\) 0 0
\(533\) 4.10397i 0.177762i
\(534\) 0 0
\(535\) 10.4043 + 11.6274i 0.449819 + 0.502697i
\(536\) 0 0
\(537\) −39.7957 + 39.7957i −1.71731 + 1.71731i
\(538\) 0 0
\(539\) −12.1949 + 12.1949i −0.525271 + 0.525271i
\(540\) 0 0
\(541\) 14.3926 + 14.3926i 0.618785 + 0.618785i 0.945220 0.326435i \(-0.105847\pi\)
−0.326435 + 0.945220i \(0.605847\pi\)
\(542\) 0 0
\(543\) 7.62178 + 7.62178i 0.327082 + 0.327082i
\(544\) 0 0
\(545\) −0.0486846 + 0.876965i −0.00208542 + 0.0375651i
\(546\) 0 0
\(547\) 11.6741 0.499148 0.249574 0.968356i \(-0.419709\pi\)
0.249574 + 0.968356i \(0.419709\pi\)
\(548\) 0 0
\(549\) 35.9541 + 35.9541i 1.53448 + 1.53448i
\(550\) 0 0
\(551\) −21.1541 −0.901197
\(552\) 0 0
\(553\) 20.9268 + 20.9268i 0.889898 + 0.889898i
\(554\) 0 0
\(555\) 9.62880 + 10.7607i 0.408720 + 0.456767i
\(556\) 0 0
\(557\) 39.6712i 1.68092i 0.541873 + 0.840460i \(0.317715\pi\)
−0.541873 + 0.840460i \(0.682285\pi\)
\(558\) 0 0
\(559\) 9.23671 0.390671
\(560\) 0 0
\(561\) −1.02537 −0.0432911
\(562\) 0 0
\(563\) 12.4534i 0.524850i −0.964952 0.262425i \(-0.915478\pi\)
0.964952 0.262425i \(-0.0845222\pi\)
\(564\) 0 0
\(565\) 1.53474 27.6456i 0.0645671 1.16306i
\(566\) 0 0
\(567\) −17.3235 17.3235i −0.727519 0.727519i
\(568\) 0 0
\(569\) 5.62622 0.235863 0.117932 0.993022i \(-0.462374\pi\)
0.117932 + 0.993022i \(0.462374\pi\)
\(570\) 0 0
\(571\) −23.1808 23.1808i −0.970086 0.970086i 0.0294797 0.999565i \(-0.490615\pi\)
−0.999565 + 0.0294797i \(0.990615\pi\)
\(572\) 0 0
\(573\) −16.5132 −0.689848
\(574\) 0 0
\(575\) −9.37814 11.7289i −0.391095 0.489128i
\(576\) 0 0
\(577\) −25.6307 25.6307i −1.06702 1.06702i −0.997587 0.0694322i \(-0.977881\pi\)
−0.0694322 0.997587i \(-0.522119\pi\)
\(578\) 0 0
\(579\) 28.3562 + 28.3562i 1.17844 + 1.17844i
\(580\) 0 0
\(581\) −26.7552 + 26.7552i −1.10999 + 1.10999i
\(582\) 0 0
\(583\) 3.46614 3.46614i 0.143553 0.143553i
\(584\) 0 0
\(585\) 14.0497 12.5718i 0.580884 0.519780i
\(586\) 0 0
\(587\) 25.5579i 1.05489i −0.849590 0.527444i \(-0.823151\pi\)
0.849590 0.527444i \(-0.176849\pi\)
\(588\) 0 0
\(589\) −4.41920 + 4.41920i −0.182090 + 0.182090i
\(590\) 0 0
\(591\) 64.0266i 2.63370i
\(592\) 0 0
\(593\) 2.96607 2.96607i 0.121802 0.121802i −0.643578 0.765380i \(-0.722551\pi\)
0.765380 + 0.643578i \(0.222551\pi\)
\(594\) 0 0
\(595\) 0.537996 + 0.601241i 0.0220557 + 0.0246485i
\(596\) 0 0
\(597\) −47.8629 −1.95890
\(598\) 0 0
\(599\) 5.14724i 0.210311i 0.994456 + 0.105155i \(0.0335340\pi\)
−0.994456 + 0.105155i \(0.966466\pi\)
\(600\) 0 0
\(601\) 33.5619i 1.36902i 0.729005 + 0.684509i \(0.239983\pi\)
−0.729005 + 0.684509i \(0.760017\pi\)
\(602\) 0 0
\(603\) −37.2940 −1.51873
\(604\) 0 0
\(605\) −4.97032 5.55461i −0.202072 0.225827i
\(606\) 0 0
\(607\) 3.29572 3.29572i 0.133769 0.133769i −0.637052 0.770821i \(-0.719846\pi\)
0.770821 + 0.637052i \(0.219846\pi\)
\(608\) 0 0
\(609\) 48.5501i 1.96735i
\(610\) 0 0
\(611\) −5.16986 + 5.16986i −0.209150 + 0.209150i
\(612\) 0 0
\(613\) 0.261903i 0.0105781i 0.999986 + 0.00528907i \(0.00168357\pi\)
−0.999986 + 0.00528907i \(0.998316\pi\)
\(614\) 0 0
\(615\) 7.26568 6.50140i 0.292981 0.262162i
\(616\) 0 0
\(617\) −12.1529 + 12.1529i −0.489259 + 0.489259i −0.908072 0.418813i \(-0.862446\pi\)
0.418813 + 0.908072i \(0.362446\pi\)
\(618\) 0 0
\(619\) −12.1134 + 12.1134i −0.486877 + 0.486877i −0.907319 0.420442i \(-0.861875\pi\)
0.420442 + 0.907319i \(0.361875\pi\)
\(620\) 0 0
\(621\) 2.76747 + 2.76747i 0.111055 + 0.111055i
\(622\) 0 0
\(623\) −37.5911 37.5911i −1.50606 1.50606i
\(624\) 0 0
\(625\) −24.3874 5.50042i −0.975496 0.220017i
\(626\) 0 0
\(627\) 36.5089 1.45802
\(628\) 0 0
\(629\) −0.189949 0.189949i −0.00757377 0.00757377i
\(630\) 0 0
\(631\) 49.8568 1.98477 0.992384 0.123179i \(-0.0393090\pi\)
0.992384 + 0.123179i \(0.0393090\pi\)
\(632\) 0 0
\(633\) 16.3013 + 16.3013i 0.647917 + 0.647917i
\(634\) 0 0
\(635\) −0.119105 + 2.14547i −0.00472656 + 0.0851404i
\(636\) 0 0
\(637\) 10.9402i 0.433467i
\(638\) 0 0
\(639\) −7.98059 −0.315707
\(640\) 0 0
\(641\) −4.10036 −0.161954 −0.0809772 0.996716i \(-0.525804\pi\)
−0.0809772 + 0.996716i \(0.525804\pi\)
\(642\) 0 0
\(643\) 18.7451i 0.739233i −0.929184 0.369617i \(-0.879489\pi\)
0.929184 0.369617i \(-0.120511\pi\)
\(644\) 0 0
\(645\) 14.6326 + 16.3527i 0.576157 + 0.643888i
\(646\) 0 0
\(647\) 5.46529 + 5.46529i 0.214863 + 0.214863i 0.806330 0.591467i \(-0.201451\pi\)
−0.591467 + 0.806330i \(0.701451\pi\)
\(648\) 0 0
\(649\) 28.3563 1.11308
\(650\) 0 0
\(651\) 10.1424 + 10.1424i 0.397510 + 0.397510i
\(652\) 0 0
\(653\) 33.9219 1.32747 0.663733 0.747970i \(-0.268971\pi\)
0.663733 + 0.747970i \(0.268971\pi\)
\(654\) 0 0
\(655\) −0.953294 + 17.1719i −0.0372483 + 0.670961i
\(656\) 0 0
\(657\) −35.0753 35.0753i −1.36842 1.36842i
\(658\) 0 0
\(659\) 26.4961 + 26.4961i 1.03214 + 1.03214i 0.999466 + 0.0326746i \(0.0104025\pi\)
0.0326746 + 0.999466i \(0.489598\pi\)
\(660\) 0 0
\(661\) −10.6974 + 10.6974i −0.416081 + 0.416081i −0.883851 0.467769i \(-0.845058\pi\)
0.467769 + 0.883851i \(0.345058\pi\)
\(662\) 0 0
\(663\) −0.459936 + 0.459936i −0.0178624 + 0.0178624i
\(664\) 0 0
\(665\) −19.1557 21.4075i −0.742826 0.830149i
\(666\) 0 0
\(667\) 16.8114i 0.650941i
\(668\) 0 0
\(669\) 10.9663 10.9663i 0.423980 0.423980i
\(670\) 0 0
\(671\) 54.8333i 2.11682i
\(672\) 0 0
\(673\) −6.70854 + 6.70854i −0.258595 + 0.258595i −0.824483 0.565887i \(-0.808534\pi\)
0.565887 + 0.824483i \(0.308534\pi\)
\(674\) 0 0
\(675\) 6.47549 + 0.721194i 0.249242 + 0.0277588i
\(676\) 0 0
\(677\) −13.1970 −0.507200 −0.253600 0.967309i \(-0.581615\pi\)
−0.253600 + 0.967309i \(0.581615\pi\)
\(678\) 0 0
\(679\) 24.0691i 0.923686i
\(680\) 0 0
\(681\) 74.2591i 2.84561i
\(682\) 0 0
\(683\) 37.9089 1.45054 0.725272 0.688462i \(-0.241714\pi\)
0.725272 + 0.688462i \(0.241714\pi\)
\(684\) 0 0
\(685\) −1.31024 + 23.6016i −0.0500616 + 0.901770i
\(686\) 0 0
\(687\) −46.7978 + 46.7978i −1.78545 + 1.78545i
\(688\) 0 0
\(689\) 3.10952i 0.118463i
\(690\) 0 0
\(691\) −20.8280 + 20.8280i −0.792335 + 0.792335i −0.981873 0.189538i \(-0.939301\pi\)
0.189538 + 0.981873i \(0.439301\pi\)
\(692\) 0 0
\(693\) 45.1813i 1.71630i
\(694\) 0 0
\(695\) 2.02114 36.4073i 0.0766664 1.38101i
\(696\) 0 0
\(697\) −0.128255 + 0.128255i −0.00485799 + 0.00485799i
\(698\) 0 0
\(699\) −3.74227 + 3.74227i −0.141546 + 0.141546i
\(700\) 0 0
\(701\) −19.9053 19.9053i −0.751812 0.751812i 0.223005 0.974817i \(-0.428413\pi\)
−0.974817 + 0.223005i \(0.928413\pi\)
\(702\) 0 0
\(703\) 6.76326 + 6.76326i 0.255081 + 0.255081i
\(704\) 0 0
\(705\) −17.3427 0.962778i −0.653165 0.0362603i
\(706\) 0 0
\(707\) −30.6277 −1.15187
\(708\) 0 0
\(709\) −8.57112 8.57112i −0.321895 0.321895i 0.527599 0.849494i \(-0.323092\pi\)
−0.849494 + 0.527599i \(0.823092\pi\)
\(710\) 0 0
\(711\) −30.5647 −1.14627
\(712\) 0 0
\(713\) 3.51199 + 3.51199i 0.131525 + 0.131525i
\(714\) 0 0
\(715\) −20.3001 1.12696i −0.759182 0.0421458i
\(716\) 0 0
\(717\) 32.0053i 1.19526i
\(718\) 0 0
\(719\) 33.1900 1.23778 0.618889 0.785478i \(-0.287583\pi\)
0.618889 + 0.785478i \(0.287583\pi\)
\(720\) 0 0
\(721\) −9.31162 −0.346783
\(722\) 0 0
\(723\) 37.9857i 1.41270i
\(724\) 0 0
\(725\) 17.4777 + 21.8587i 0.649104 + 0.811810i
\(726\) 0 0
\(727\) 5.06503 + 5.06503i 0.187852 + 0.187852i 0.794767 0.606915i \(-0.207593\pi\)
−0.606915 + 0.794767i \(0.707593\pi\)
\(728\) 0 0
\(729\) 35.2770 1.30655
\(730\) 0 0
\(731\) −0.288660 0.288660i −0.0106765 0.0106765i
\(732\) 0 0
\(733\) −43.0744 −1.59099 −0.795494 0.605961i \(-0.792789\pi\)
−0.795494 + 0.605961i \(0.792789\pi\)
\(734\) 0 0
\(735\) −19.3686 + 17.3312i −0.714422 + 0.639272i
\(736\) 0 0
\(737\) 28.4384 + 28.4384i 1.04754 + 1.04754i
\(738\) 0 0
\(739\) 11.3838 + 11.3838i 0.418762 + 0.418762i 0.884777 0.466015i \(-0.154311\pi\)
−0.466015 + 0.884777i \(0.654311\pi\)
\(740\) 0 0
\(741\) 16.3763 16.3763i 0.601599 0.601599i
\(742\) 0 0
\(743\) 1.54795 1.54795i 0.0567888 0.0567888i −0.678142 0.734931i \(-0.737215\pi\)
0.734931 + 0.678142i \(0.237215\pi\)
\(744\) 0 0
\(745\) −17.4029 0.966116i −0.637591 0.0353958i
\(746\) 0 0
\(747\) 39.0774i 1.42977i
\(748\) 0 0
\(749\) 16.7723 16.7723i 0.612847 0.612847i
\(750\) 0 0
\(751\) 1.49244i 0.0544600i −0.999629 0.0272300i \(-0.991331\pi\)
0.999629 0.0272300i \(-0.00866865\pi\)
\(752\) 0 0
\(753\) 13.7394 13.7394i 0.500690 0.500690i
\(754\) 0 0
\(755\) 6.89231 6.16731i 0.250837 0.224451i
\(756\) 0 0
\(757\) 22.7030 0.825154 0.412577 0.910923i \(-0.364629\pi\)
0.412577 + 0.910923i \(0.364629\pi\)
\(758\) 0 0
\(759\) 29.0140i 1.05314i
\(760\) 0 0
\(761\) 33.6599i 1.22017i −0.792335 0.610086i \(-0.791135\pi\)
0.792335 0.610086i \(-0.208865\pi\)
\(762\) 0 0
\(763\) 1.33523 0.0483386
\(764\) 0 0
\(765\) −0.831959 0.0461860i −0.0300795 0.00166986i
\(766\) 0 0
\(767\) 12.7194 12.7194i 0.459271 0.459271i
\(768\) 0 0
\(769\) 10.1943i 0.367615i 0.982962 + 0.183808i \(0.0588423\pi\)
−0.982962 + 0.183808i \(0.941158\pi\)
\(770\) 0 0
\(771\) −9.91699 + 9.91699i −0.357152 + 0.357152i
\(772\) 0 0
\(773\) 7.34419i 0.264152i 0.991240 + 0.132076i \(0.0421643\pi\)
−0.991240 + 0.132076i \(0.957836\pi\)
\(774\) 0 0
\(775\) 8.21755 + 0.915212i 0.295183 + 0.0328754i
\(776\) 0 0
\(777\) 15.5221 15.5221i 0.556853 0.556853i
\(778\) 0 0
\(779\) 4.56658 4.56658i 0.163615 0.163615i
\(780\) 0 0
\(781\) 6.08556 + 6.08556i 0.217759 + 0.217759i
\(782\) 0 0
\(783\) −5.15763 5.15763i −0.184319 0.184319i
\(784\) 0 0
\(785\) 30.2239 + 33.7769i 1.07874 + 1.20555i
\(786\) 0 0
\(787\) −29.4359 −1.04928 −0.524638 0.851326i \(-0.675799\pi\)
−0.524638 + 0.851326i \(0.675799\pi\)
\(788\) 0 0
\(789\) −43.2900 43.2900i −1.54116 1.54116i
\(790\) 0 0
\(791\) −42.0921 −1.49662
\(792\) 0 0
\(793\) −24.5959 24.5959i −0.873425 0.873425i
\(794\) 0 0
\(795\) 5.50511 4.92603i 0.195246 0.174708i
\(796\) 0 0
\(797\) 50.3934i 1.78503i −0.451022 0.892513i \(-0.648940\pi\)
0.451022