Properties

Label 4020.2.g.c.1609.8
Level 4020
Weight 2
Character 4020.1609
Analytic conductor 32.100
Analytic rank 0
Dimension 38
CM No

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.g (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(38\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1609.8
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.27

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(-0.676225 - 2.13137i) q^{5}\) \(-4.23231i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(-0.676225 - 2.13137i) q^{5}\) \(-4.23231i q^{7}\) \(-1.00000 q^{9}\) \(-1.39022 q^{11}\) \(-6.36038i q^{13}\) \(+(-2.13137 + 0.676225i) q^{15}\) \(+4.10855i q^{17}\) \(-5.15323 q^{19}\) \(-4.23231 q^{21}\) \(+1.91335i q^{23}\) \(+(-4.08544 + 2.88257i) q^{25}\) \(+1.00000i q^{27}\) \(-5.40553 q^{29}\) \(+0.479723 q^{31}\) \(+1.39022i q^{33}\) \(+(-9.02060 + 2.86199i) q^{35}\) \(-2.52485i q^{37}\) \(-6.36038 q^{39}\) \(+4.14785 q^{41}\) \(-0.604550i q^{43}\) \(+(0.676225 + 2.13137i) q^{45}\) \(+0.216591i q^{47}\) \(-10.9124 q^{49}\) \(+4.10855 q^{51}\) \(-2.89586i q^{53}\) \(+(0.940102 + 2.96307i) q^{55}\) \(+5.15323i q^{57}\) \(-0.893364 q^{59}\) \(+2.90540 q^{61}\) \(+4.23231i q^{63}\) \(+(-13.5563 + 4.30105i) q^{65}\) \(-1.00000i q^{67}\) \(+1.91335 q^{69}\) \(+8.26764 q^{71}\) \(-12.6582i q^{73}\) \(+(2.88257 + 4.08544i) q^{75}\) \(+5.88384i q^{77}\) \(+13.7111 q^{79}\) \(+1.00000 q^{81}\) \(+12.0898i q^{83}\) \(+(8.75681 - 2.77830i) q^{85}\) \(+5.40553i q^{87}\) \(+17.0123 q^{89}\) \(-26.9191 q^{91}\) \(-0.479723i q^{93}\) \(+(3.48474 + 10.9834i) q^{95}\) \(+0.636187i q^{97}\) \(+1.39022 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) −0.676225 2.13137i −0.302417 0.953176i
\(6\) 0 0
\(7\) 4.23231i 1.59966i −0.600225 0.799831i \(-0.704922\pi\)
0.600225 0.799831i \(-0.295078\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) −1.39022 −0.419167 −0.209584 0.977791i \(-0.567211\pi\)
−0.209584 + 0.977791i \(0.567211\pi\)
\(12\) 0 0
\(13\) 6.36038i 1.76405i −0.471201 0.882026i \(-0.656179\pi\)
0.471201 0.882026i \(-0.343821\pi\)
\(14\) 0 0
\(15\) −2.13137 + 0.676225i −0.550316 + 0.174601i
\(16\) 0 0
\(17\) 4.10855i 0.996469i 0.867042 + 0.498234i \(0.166018\pi\)
−0.867042 + 0.498234i \(0.833982\pi\)
\(18\) 0 0
\(19\) −5.15323 −1.18223 −0.591116 0.806587i \(-0.701312\pi\)
−0.591116 + 0.806587i \(0.701312\pi\)
\(20\) 0 0
\(21\) −4.23231 −0.923566
\(22\) 0 0
\(23\) 1.91335i 0.398962i 0.979902 + 0.199481i \(0.0639256\pi\)
−0.979902 + 0.199481i \(0.936074\pi\)
\(24\) 0 0
\(25\) −4.08544 + 2.88257i −0.817088 + 0.576513i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −5.40553 −1.00378 −0.501891 0.864931i \(-0.667362\pi\)
−0.501891 + 0.864931i \(0.667362\pi\)
\(30\) 0 0
\(31\) 0.479723 0.0861608 0.0430804 0.999072i \(-0.486283\pi\)
0.0430804 + 0.999072i \(0.486283\pi\)
\(32\) 0 0
\(33\) 1.39022i 0.242006i
\(34\) 0 0
\(35\) −9.02060 + 2.86199i −1.52476 + 0.483765i
\(36\) 0 0
\(37\) 2.52485i 0.415083i −0.978226 0.207541i \(-0.933454\pi\)
0.978226 0.207541i \(-0.0665462\pi\)
\(38\) 0 0
\(39\) −6.36038 −1.01848
\(40\) 0 0
\(41\) 4.14785 0.647785 0.323893 0.946094i \(-0.395008\pi\)
0.323893 + 0.946094i \(0.395008\pi\)
\(42\) 0 0
\(43\) 0.604550i 0.0921930i −0.998937 0.0460965i \(-0.985322\pi\)
0.998937 0.0460965i \(-0.0146782\pi\)
\(44\) 0 0
\(45\) 0.676225 + 2.13137i 0.100806 + 0.317725i
\(46\) 0 0
\(47\) 0.216591i 0.0315931i 0.999875 + 0.0157965i \(0.00502841\pi\)
−0.999875 + 0.0157965i \(0.994972\pi\)
\(48\) 0 0
\(49\) −10.9124 −1.55892
\(50\) 0 0
\(51\) 4.10855 0.575312
\(52\) 0 0
\(53\) 2.89586i 0.397777i −0.980022 0.198889i \(-0.936267\pi\)
0.980022 0.198889i \(-0.0637332\pi\)
\(54\) 0 0
\(55\) 0.940102 + 2.96307i 0.126763 + 0.399540i
\(56\) 0 0
\(57\) 5.15323i 0.682562i
\(58\) 0 0
\(59\) −0.893364 −0.116306 −0.0581530 0.998308i \(-0.518521\pi\)
−0.0581530 + 0.998308i \(0.518521\pi\)
\(60\) 0 0
\(61\) 2.90540 0.371998 0.185999 0.982550i \(-0.440448\pi\)
0.185999 + 0.982550i \(0.440448\pi\)
\(62\) 0 0
\(63\) 4.23231i 0.533221i
\(64\) 0 0
\(65\) −13.5563 + 4.30105i −1.68145 + 0.533479i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) 1.91335 0.230341
\(70\) 0 0
\(71\) 8.26764 0.981188 0.490594 0.871388i \(-0.336780\pi\)
0.490594 + 0.871388i \(0.336780\pi\)
\(72\) 0 0
\(73\) 12.6582i 1.48153i −0.671764 0.740765i \(-0.734463\pi\)
0.671764 0.740765i \(-0.265537\pi\)
\(74\) 0 0
\(75\) 2.88257 + 4.08544i 0.332850 + 0.471746i
\(76\) 0 0
\(77\) 5.88384i 0.670526i
\(78\) 0 0
\(79\) 13.7111 1.54262 0.771308 0.636462i \(-0.219603\pi\)
0.771308 + 0.636462i \(0.219603\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 12.0898i 1.32703i 0.748163 + 0.663514i \(0.230936\pi\)
−0.748163 + 0.663514i \(0.769064\pi\)
\(84\) 0 0
\(85\) 8.75681 2.77830i 0.949810 0.301349i
\(86\) 0 0
\(87\) 5.40553i 0.579534i
\(88\) 0 0
\(89\) 17.0123 1.80330 0.901648 0.432471i \(-0.142358\pi\)
0.901648 + 0.432471i \(0.142358\pi\)
\(90\) 0 0
\(91\) −26.9191 −2.82189
\(92\) 0 0
\(93\) 0.479723i 0.0497449i
\(94\) 0 0
\(95\) 3.48474 + 10.9834i 0.357527 + 1.12687i
\(96\) 0 0
\(97\) 0.636187i 0.0645950i 0.999478 + 0.0322975i \(0.0102824\pi\)
−0.999478 + 0.0322975i \(0.989718\pi\)
\(98\) 0 0
\(99\) 1.39022 0.139722
\(100\) 0 0
\(101\) −1.71282 −0.170432 −0.0852162 0.996362i \(-0.527158\pi\)
−0.0852162 + 0.996362i \(0.527158\pi\)
\(102\) 0 0
\(103\) 6.41050i 0.631645i 0.948818 + 0.315823i \(0.102280\pi\)
−0.948818 + 0.315823i \(0.897720\pi\)
\(104\) 0 0
\(105\) 2.86199 + 9.02060i 0.279302 + 0.880320i
\(106\) 0 0
\(107\) 18.9246i 1.82951i −0.404008 0.914755i \(-0.632383\pi\)
0.404008 0.914755i \(-0.367617\pi\)
\(108\) 0 0
\(109\) 4.89694 0.469042 0.234521 0.972111i \(-0.424648\pi\)
0.234521 + 0.972111i \(0.424648\pi\)
\(110\) 0 0
\(111\) −2.52485 −0.239648
\(112\) 0 0
\(113\) 2.88818i 0.271697i −0.990730 0.135848i \(-0.956624\pi\)
0.990730 0.135848i \(-0.0433760\pi\)
\(114\) 0 0
\(115\) 4.07806 1.29386i 0.380281 0.120653i
\(116\) 0 0
\(117\) 6.36038i 0.588017i
\(118\) 0 0
\(119\) 17.3886 1.59401
\(120\) 0 0
\(121\) −9.06729 −0.824299
\(122\) 0 0
\(123\) 4.14785i 0.373999i
\(124\) 0 0
\(125\) 8.90648 + 6.75830i 0.796620 + 0.604481i
\(126\) 0 0
\(127\) 3.09910i 0.275001i 0.990502 + 0.137500i \(0.0439068\pi\)
−0.990502 + 0.137500i \(0.956093\pi\)
\(128\) 0 0
\(129\) −0.604550 −0.0532276
\(130\) 0 0
\(131\) 2.52174 0.220326 0.110163 0.993914i \(-0.464863\pi\)
0.110163 + 0.993914i \(0.464863\pi\)
\(132\) 0 0
\(133\) 21.8101i 1.89117i
\(134\) 0 0
\(135\) 2.13137 0.676225i 0.183439 0.0582002i
\(136\) 0 0
\(137\) 10.3830i 0.887077i −0.896255 0.443538i \(-0.853723\pi\)
0.896255 0.443538i \(-0.146277\pi\)
\(138\) 0 0
\(139\) −14.7427 −1.25046 −0.625230 0.780440i \(-0.714995\pi\)
−0.625230 + 0.780440i \(0.714995\pi\)
\(140\) 0 0
\(141\) 0.216591 0.0182403
\(142\) 0 0
\(143\) 8.84233i 0.739433i
\(144\) 0 0
\(145\) 3.65536 + 11.5212i 0.303561 + 0.956781i
\(146\) 0 0
\(147\) 10.9124i 0.900044i
\(148\) 0 0
\(149\) −8.09056 −0.662804 −0.331402 0.943490i \(-0.607522\pi\)
−0.331402 + 0.943490i \(0.607522\pi\)
\(150\) 0 0
\(151\) 7.26776 0.591442 0.295721 0.955274i \(-0.404440\pi\)
0.295721 + 0.955274i \(0.404440\pi\)
\(152\) 0 0
\(153\) 4.10855i 0.332156i
\(154\) 0 0
\(155\) −0.324401 1.02246i −0.0260565 0.0821263i
\(156\) 0 0
\(157\) 19.9836i 1.59486i 0.603410 + 0.797431i \(0.293808\pi\)
−0.603410 + 0.797431i \(0.706192\pi\)
\(158\) 0 0
\(159\) −2.89586 −0.229657
\(160\) 0 0
\(161\) 8.09791 0.638205
\(162\) 0 0
\(163\) 13.3663i 1.04693i −0.852048 0.523464i \(-0.824639\pi\)
0.852048 0.523464i \(-0.175361\pi\)
\(164\) 0 0
\(165\) 2.96307 0.940102i 0.230674 0.0731868i
\(166\) 0 0
\(167\) 10.4531i 0.808886i 0.914563 + 0.404443i \(0.132535\pi\)
−0.914563 + 0.404443i \(0.867465\pi\)
\(168\) 0 0
\(169\) −27.4544 −2.11188
\(170\) 0 0
\(171\) 5.15323 0.394077
\(172\) 0 0
\(173\) 17.7535i 1.34977i −0.737922 0.674886i \(-0.764193\pi\)
0.737922 0.674886i \(-0.235807\pi\)
\(174\) 0 0
\(175\) 12.1999 + 17.2908i 0.922227 + 1.30707i
\(176\) 0 0
\(177\) 0.893364i 0.0671493i
\(178\) 0 0
\(179\) −16.2777 −1.21665 −0.608327 0.793687i \(-0.708159\pi\)
−0.608327 + 0.793687i \(0.708159\pi\)
\(180\) 0 0
\(181\) −17.6664 −1.31314 −0.656568 0.754267i \(-0.727993\pi\)
−0.656568 + 0.754267i \(0.727993\pi\)
\(182\) 0 0
\(183\) 2.90540i 0.214773i
\(184\) 0 0
\(185\) −5.38138 + 1.70737i −0.395647 + 0.125528i
\(186\) 0 0
\(187\) 5.71178i 0.417687i
\(188\) 0 0
\(189\) 4.23231 0.307855
\(190\) 0 0
\(191\) 20.0200 1.44859 0.724297 0.689488i \(-0.242164\pi\)
0.724297 + 0.689488i \(0.242164\pi\)
\(192\) 0 0
\(193\) 1.15297i 0.0829923i 0.999139 + 0.0414962i \(0.0132124\pi\)
−0.999139 + 0.0414962i \(0.986788\pi\)
\(194\) 0 0
\(195\) 4.30105 + 13.5563i 0.308004 + 0.970786i
\(196\) 0 0
\(197\) 3.53115i 0.251584i −0.992057 0.125792i \(-0.959853\pi\)
0.992057 0.125792i \(-0.0401472\pi\)
\(198\) 0 0
\(199\) −3.63461 −0.257651 −0.128825 0.991667i \(-0.541121\pi\)
−0.128825 + 0.991667i \(0.541121\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 22.8779i 1.60571i
\(204\) 0 0
\(205\) −2.80488 8.84058i −0.195901 0.617453i
\(206\) 0 0
\(207\) 1.91335i 0.132987i
\(208\) 0 0
\(209\) 7.16412 0.495553
\(210\) 0 0
\(211\) 19.9563 1.37385 0.686925 0.726728i \(-0.258960\pi\)
0.686925 + 0.726728i \(0.258960\pi\)
\(212\) 0 0
\(213\) 8.26764i 0.566489i
\(214\) 0 0
\(215\) −1.28852 + 0.408812i −0.0878761 + 0.0278807i
\(216\) 0 0
\(217\) 2.03034i 0.137828i
\(218\) 0 0
\(219\) −12.6582 −0.855361
\(220\) 0 0
\(221\) 26.1319 1.75782
\(222\) 0 0
\(223\) 21.2283i 1.42155i 0.703417 + 0.710777i \(0.251657\pi\)
−0.703417 + 0.710777i \(0.748343\pi\)
\(224\) 0 0
\(225\) 4.08544 2.88257i 0.272363 0.192171i
\(226\) 0 0
\(227\) 11.5637i 0.767507i −0.923436 0.383754i \(-0.874631\pi\)
0.923436 0.383754i \(-0.125369\pi\)
\(228\) 0 0
\(229\) −12.9167 −0.853560 −0.426780 0.904355i \(-0.640352\pi\)
−0.426780 + 0.904355i \(0.640352\pi\)
\(230\) 0 0
\(231\) 5.88384 0.387128
\(232\) 0 0
\(233\) 15.9294i 1.04357i 0.853078 + 0.521784i \(0.174733\pi\)
−0.853078 + 0.521784i \(0.825267\pi\)
\(234\) 0 0
\(235\) 0.461635 0.146464i 0.0301138 0.00955429i
\(236\) 0 0
\(237\) 13.7111i 0.890629i
\(238\) 0 0
\(239\) −9.80764 −0.634403 −0.317202 0.948358i \(-0.602743\pi\)
−0.317202 + 0.948358i \(0.602743\pi\)
\(240\) 0 0
\(241\) −18.9392 −1.21998 −0.609989 0.792410i \(-0.708826\pi\)
−0.609989 + 0.792410i \(0.708826\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 7.37927 + 23.2584i 0.471444 + 1.48593i
\(246\) 0 0
\(247\) 32.7765i 2.08552i
\(248\) 0 0
\(249\) 12.0898 0.766160
\(250\) 0 0
\(251\) −13.4401 −0.848334 −0.424167 0.905584i \(-0.639433\pi\)
−0.424167 + 0.905584i \(0.639433\pi\)
\(252\) 0 0
\(253\) 2.65998i 0.167232i
\(254\) 0 0
\(255\) −2.77830 8.75681i −0.173984 0.548373i
\(256\) 0 0
\(257\) 6.47817i 0.404097i −0.979376 0.202049i \(-0.935240\pi\)
0.979376 0.202049i \(-0.0647599\pi\)
\(258\) 0 0
\(259\) −10.6860 −0.663993
\(260\) 0 0
\(261\) 5.40553 0.334594
\(262\) 0 0
\(263\) 21.0096i 1.29551i 0.761850 + 0.647753i \(0.224291\pi\)
−0.761850 + 0.647753i \(0.775709\pi\)
\(264\) 0 0
\(265\) −6.17214 + 1.95825i −0.379151 + 0.120295i
\(266\) 0 0
\(267\) 17.0123i 1.04113i
\(268\) 0 0
\(269\) −14.6527 −0.893393 −0.446697 0.894686i \(-0.647400\pi\)
−0.446697 + 0.894686i \(0.647400\pi\)
\(270\) 0 0
\(271\) −15.3153 −0.930337 −0.465169 0.885222i \(-0.654006\pi\)
−0.465169 + 0.885222i \(0.654006\pi\)
\(272\) 0 0
\(273\) 26.9191i 1.62922i
\(274\) 0 0
\(275\) 5.67966 4.00740i 0.342496 0.241655i
\(276\) 0 0
\(277\) 14.6763i 0.881815i −0.897553 0.440907i \(-0.854657\pi\)
0.897553 0.440907i \(-0.145343\pi\)
\(278\) 0 0
\(279\) −0.479723 −0.0287203
\(280\) 0 0
\(281\) 16.9400 1.01056 0.505278 0.862957i \(-0.331390\pi\)
0.505278 + 0.862957i \(0.331390\pi\)
\(282\) 0 0
\(283\) 17.7694i 1.05628i 0.849158 + 0.528139i \(0.177110\pi\)
−0.849158 + 0.528139i \(0.822890\pi\)
\(284\) 0 0
\(285\) 10.9834 3.48474i 0.650602 0.206418i
\(286\) 0 0
\(287\) 17.5550i 1.03624i
\(288\) 0 0
\(289\) 0.119848 0.00704986
\(290\) 0 0
\(291\) 0.636187 0.0372939
\(292\) 0 0
\(293\) 12.4037i 0.724630i −0.932056 0.362315i \(-0.881986\pi\)
0.932056 0.362315i \(-0.118014\pi\)
\(294\) 0 0
\(295\) 0.604115 + 1.90408i 0.0351729 + 0.110860i
\(296\) 0 0
\(297\) 1.39022i 0.0806687i
\(298\) 0 0
\(299\) 12.1697 0.703790
\(300\) 0 0
\(301\) −2.55864 −0.147478
\(302\) 0 0
\(303\) 1.71282i 0.0983992i
\(304\) 0 0
\(305\) −1.96470 6.19246i −0.112499 0.354579i
\(306\) 0 0
\(307\) 2.43370i 0.138899i 0.997585 + 0.0694494i \(0.0221242\pi\)
−0.997585 + 0.0694494i \(0.977876\pi\)
\(308\) 0 0
\(309\) 6.41050 0.364681
\(310\) 0 0
\(311\) −15.6408 −0.886909 −0.443455 0.896297i \(-0.646247\pi\)
−0.443455 + 0.896297i \(0.646247\pi\)
\(312\) 0 0
\(313\) 34.9072i 1.97307i −0.163538 0.986537i \(-0.552290\pi\)
0.163538 0.986537i \(-0.447710\pi\)
\(314\) 0 0
\(315\) 9.02060 2.86199i 0.508253 0.161255i
\(316\) 0 0
\(317\) 9.84170i 0.552765i −0.961048 0.276382i \(-0.910864\pi\)
0.961048 0.276382i \(-0.0891356\pi\)
\(318\) 0 0
\(319\) 7.51488 0.420752
\(320\) 0 0
\(321\) −18.9246 −1.05627
\(322\) 0 0
\(323\) 21.1723i 1.17806i
\(324\) 0 0
\(325\) 18.3342 + 25.9849i 1.01700 + 1.44139i
\(326\) 0 0
\(327\) 4.89694i 0.270802i
\(328\) 0 0
\(329\) 0.916682 0.0505383
\(330\) 0 0
\(331\) 16.9414 0.931182 0.465591 0.885000i \(-0.345842\pi\)
0.465591 + 0.885000i \(0.345842\pi\)
\(332\) 0 0
\(333\) 2.52485i 0.138361i
\(334\) 0 0
\(335\) −2.13137 + 0.676225i −0.116449 + 0.0369461i
\(336\) 0 0
\(337\) 27.6820i 1.50793i 0.656913 + 0.753966i \(0.271862\pi\)
−0.656913 + 0.753966i \(0.728138\pi\)
\(338\) 0 0
\(339\) −2.88818 −0.156864
\(340\) 0 0
\(341\) −0.666920 −0.0361158
\(342\) 0 0
\(343\) 16.5587i 0.894086i
\(344\) 0 0
\(345\) −1.29386 4.07806i −0.0696590 0.219555i
\(346\) 0 0
\(347\) 30.2355i 1.62312i 0.584266 + 0.811562i \(0.301382\pi\)
−0.584266 + 0.811562i \(0.698618\pi\)
\(348\) 0 0
\(349\) −15.3093 −0.819486 −0.409743 0.912201i \(-0.634382\pi\)
−0.409743 + 0.912201i \(0.634382\pi\)
\(350\) 0 0
\(351\) 6.36038 0.339492
\(352\) 0 0
\(353\) 15.8352i 0.842824i −0.906869 0.421412i \(-0.861535\pi\)
0.906869 0.421412i \(-0.138465\pi\)
\(354\) 0 0
\(355\) −5.59079 17.6214i −0.296728 0.935245i
\(356\) 0 0
\(357\) 17.3886i 0.920305i
\(358\) 0 0
\(359\) 10.6388 0.561496 0.280748 0.959782i \(-0.409417\pi\)
0.280748 + 0.959782i \(0.409417\pi\)
\(360\) 0 0
\(361\) 7.55578 0.397673
\(362\) 0 0
\(363\) 9.06729i 0.475909i
\(364\) 0 0
\(365\) −26.9792 + 8.55979i −1.41216 + 0.448040i
\(366\) 0 0
\(367\) 21.5187i 1.12327i −0.827386 0.561633i \(-0.810173\pi\)
0.827386 0.561633i \(-0.189827\pi\)
\(368\) 0 0
\(369\) −4.14785 −0.215928
\(370\) 0 0
\(371\) −12.2562 −0.636309
\(372\) 0 0
\(373\) 28.9322i 1.49805i 0.662540 + 0.749027i \(0.269479\pi\)
−0.662540 + 0.749027i \(0.730521\pi\)
\(374\) 0 0
\(375\) 6.75830 8.90648i 0.348997 0.459929i
\(376\) 0 0
\(377\) 34.3812i 1.77072i
\(378\) 0 0
\(379\) −18.3578 −0.942976 −0.471488 0.881873i \(-0.656283\pi\)
−0.471488 + 0.881873i \(0.656283\pi\)
\(380\) 0 0
\(381\) 3.09910 0.158772
\(382\) 0 0
\(383\) 6.14772i 0.314134i 0.987588 + 0.157067i \(0.0502039\pi\)
−0.987588 + 0.157067i \(0.949796\pi\)
\(384\) 0 0
\(385\) 12.5406 3.97880i 0.639129 0.202778i
\(386\) 0 0
\(387\) 0.604550i 0.0307310i
\(388\) 0 0
\(389\) −10.1069 −0.512439 −0.256219 0.966619i \(-0.582477\pi\)
−0.256219 + 0.966619i \(0.582477\pi\)
\(390\) 0 0
\(391\) −7.86111 −0.397553
\(392\) 0 0
\(393\) 2.52174i 0.127205i
\(394\) 0 0
\(395\) −9.27177 29.2233i −0.466513 1.47038i
\(396\) 0 0
\(397\) 7.09727i 0.356202i 0.984012 + 0.178101i \(0.0569953\pi\)
−0.984012 + 0.178101i \(0.943005\pi\)
\(398\) 0 0
\(399\) 21.8101 1.09187
\(400\) 0 0
\(401\) 4.82791 0.241094 0.120547 0.992708i \(-0.461535\pi\)
0.120547 + 0.992708i \(0.461535\pi\)
\(402\) 0 0
\(403\) 3.05122i 0.151992i
\(404\) 0 0
\(405\) −0.676225 2.13137i −0.0336019 0.105908i
\(406\) 0 0
\(407\) 3.51010i 0.173989i
\(408\) 0 0
\(409\) −34.0608 −1.68420 −0.842098 0.539324i \(-0.818680\pi\)
−0.842098 + 0.539324i \(0.818680\pi\)
\(410\) 0 0
\(411\) −10.3830 −0.512154
\(412\) 0 0
\(413\) 3.78099i 0.186050i
\(414\) 0 0
\(415\) 25.7678 8.17543i 1.26489 0.401316i
\(416\) 0 0
\(417\) 14.7427i 0.721954i
\(418\) 0 0
\(419\) −30.2974 −1.48013 −0.740063 0.672538i \(-0.765204\pi\)
−0.740063 + 0.672538i \(0.765204\pi\)
\(420\) 0 0
\(421\) −13.6514 −0.665327 −0.332663 0.943046i \(-0.607947\pi\)
−0.332663 + 0.943046i \(0.607947\pi\)
\(422\) 0 0
\(423\) 0.216591i 0.0105310i
\(424\) 0 0
\(425\) −11.8432 16.7852i −0.574477 0.814203i
\(426\) 0 0
\(427\) 12.2965i 0.595071i
\(428\) 0 0
\(429\) 8.84233 0.426912
\(430\) 0 0
\(431\) −4.97781 −0.239773 −0.119886 0.992788i \(-0.538253\pi\)
−0.119886 + 0.992788i \(0.538253\pi\)
\(432\) 0 0
\(433\) 29.9998i 1.44170i −0.693093 0.720848i \(-0.743752\pi\)
0.693093 0.720848i \(-0.256248\pi\)
\(434\) 0 0
\(435\) 11.5212 3.65536i 0.552398 0.175261i
\(436\) 0 0
\(437\) 9.85996i 0.471666i
\(438\) 0 0
\(439\) −4.68934 −0.223810 −0.111905 0.993719i \(-0.535695\pi\)
−0.111905 + 0.993719i \(0.535695\pi\)
\(440\) 0 0
\(441\) 10.9124 0.519640
\(442\) 0 0
\(443\) 24.5335i 1.16562i 0.812608 + 0.582811i \(0.198047\pi\)
−0.812608 + 0.582811i \(0.801953\pi\)
\(444\) 0 0
\(445\) −11.5041 36.2594i −0.545347 1.71886i
\(446\) 0 0
\(447\) 8.09056i 0.382670i
\(448\) 0 0
\(449\) −16.8758 −0.796417 −0.398208 0.917295i \(-0.630368\pi\)
−0.398208 + 0.917295i \(0.630368\pi\)
\(450\) 0 0
\(451\) −5.76642 −0.271530
\(452\) 0 0
\(453\) 7.26776i 0.341469i
\(454\) 0 0
\(455\) 18.2034 + 57.3744i 0.853387 + 2.68976i
\(456\) 0 0
\(457\) 31.4653i 1.47188i 0.677045 + 0.735942i \(0.263260\pi\)
−0.677045 + 0.735942i \(0.736740\pi\)
\(458\) 0 0
\(459\) −4.10855 −0.191771
\(460\) 0 0
\(461\) 33.7846 1.57350 0.786752 0.617270i \(-0.211761\pi\)
0.786752 + 0.617270i \(0.211761\pi\)
\(462\) 0 0
\(463\) 21.4179i 0.995373i −0.867357 0.497687i \(-0.834183\pi\)
0.867357 0.497687i \(-0.165817\pi\)
\(464\) 0 0
\(465\) −1.02246 + 0.324401i −0.0474157 + 0.0150437i
\(466\) 0 0
\(467\) 26.8173i 1.24096i 0.784224 + 0.620478i \(0.213062\pi\)
−0.784224 + 0.620478i \(0.786938\pi\)
\(468\) 0 0
\(469\) −4.23231 −0.195430
\(470\) 0 0
\(471\) 19.9836 0.920794
\(472\) 0 0
\(473\) 0.840457i 0.0386443i
\(474\) 0 0
\(475\) 21.0532 14.8545i 0.965988 0.681572i
\(476\) 0 0
\(477\) 2.89586i 0.132592i
\(478\) 0 0
\(479\) −16.9878 −0.776194 −0.388097 0.921619i \(-0.626867\pi\)
−0.388097 + 0.921619i \(0.626867\pi\)
\(480\) 0 0
\(481\) −16.0590 −0.732228
\(482\) 0 0
\(483\) 8.09791i 0.368468i
\(484\) 0 0
\(485\) 1.35595 0.430205i 0.0615704 0.0195346i
\(486\) 0 0
\(487\) 39.5253i 1.79106i −0.444999 0.895531i \(-0.646796\pi\)
0.444999 0.895531i \(-0.353204\pi\)
\(488\) 0 0
\(489\) −13.3663 −0.604445
\(490\) 0 0
\(491\) −19.0417 −0.859339 −0.429669 0.902986i \(-0.641370\pi\)
−0.429669 + 0.902986i \(0.641370\pi\)
\(492\) 0 0
\(493\) 22.2089i 1.00024i
\(494\) 0 0
\(495\) −0.940102 2.96307i −0.0422544 0.133180i
\(496\) 0 0
\(497\) 34.9912i 1.56957i
\(498\) 0 0
\(499\) −20.3317 −0.910170 −0.455085 0.890448i \(-0.650391\pi\)
−0.455085 + 0.890448i \(0.650391\pi\)
\(500\) 0 0
\(501\) 10.4531 0.467011
\(502\) 0 0
\(503\) 32.9475i 1.46906i 0.678578 + 0.734528i \(0.262596\pi\)
−0.678578 + 0.734528i \(0.737404\pi\)
\(504\) 0 0
\(505\) 1.15825 + 3.65065i 0.0515416 + 0.162452i
\(506\) 0 0
\(507\) 27.4544i 1.21929i
\(508\) 0 0
\(509\) 35.7348 1.58392 0.791959 0.610574i \(-0.209061\pi\)
0.791959 + 0.610574i \(0.209061\pi\)
\(510\) 0 0
\(511\) −53.5734 −2.36995
\(512\) 0 0
\(513\) 5.15323i 0.227521i
\(514\) 0 0
\(515\) 13.6631 4.33494i 0.602069 0.191020i
\(516\) 0 0
\(517\) 0.301110i 0.0132428i
\(518\) 0 0
\(519\) −17.7535 −0.779292
\(520\) 0 0
\(521\) 44.8076 1.96305 0.981527 0.191322i \(-0.0612774\pi\)
0.981527 + 0.191322i \(0.0612774\pi\)
\(522\) 0 0
\(523\) 13.8543i 0.605806i 0.953021 + 0.302903i \(0.0979558\pi\)
−0.953021 + 0.302903i \(0.902044\pi\)
\(524\) 0 0
\(525\) 17.2908 12.1999i 0.754634 0.532448i
\(526\) 0 0
\(527\) 1.97096i 0.0858565i
\(528\) 0 0
\(529\) 19.3391 0.840829
\(530\) 0 0
\(531\) 0.893364 0.0387687
\(532\) 0 0
\(533\) 26.3819i 1.14273i
\(534\) 0 0
\(535\) −40.3353 + 12.7973i −1.74385 + 0.553275i
\(536\) 0 0
\(537\) 16.2777i 0.702435i
\(538\) 0 0
\(539\) 15.1707 0.653449
\(540\) 0 0
\(541\) 3.29139 0.141508 0.0707540 0.997494i \(-0.477459\pi\)
0.0707540 + 0.997494i \(0.477459\pi\)
\(542\) 0 0
\(543\) 17.6664i 0.758140i
\(544\) 0 0
\(545\) −3.31143 10.4372i −0.141846 0.447079i
\(546\) 0 0
\(547\) 7.38046i 0.315566i 0.987474 + 0.157783i \(0.0504346\pi\)
−0.987474 + 0.157783i \(0.949565\pi\)
\(548\) 0 0
\(549\) −2.90540 −0.123999
\(550\) 0 0
\(551\) 27.8559 1.18670
\(552\) 0 0
\(553\) 58.0295i 2.46766i
\(554\) 0 0
\(555\) 1.70737 + 5.38138i 0.0724737 + 0.228427i
\(556\) 0 0
\(557\) 1.83073i 0.0775705i 0.999248 + 0.0387852i \(0.0123488\pi\)
−0.999248 + 0.0387852i \(0.987651\pi\)
\(558\) 0 0
\(559\) −3.84517 −0.162633
\(560\) 0 0
\(561\) −5.71178 −0.241152
\(562\) 0 0
\(563\) 19.4344i 0.819063i 0.912296 + 0.409532i \(0.134308\pi\)
−0.912296 + 0.409532i \(0.865692\pi\)
\(564\) 0 0
\(565\) −6.15576 + 1.95306i −0.258975 + 0.0821657i
\(566\) 0 0
\(567\) 4.23231i 0.177740i
\(568\) 0 0
\(569\) −14.5151 −0.608506 −0.304253 0.952591i \(-0.598407\pi\)
−0.304253 + 0.952591i \(0.598407\pi\)
\(570\) 0 0
\(571\) −12.3594 −0.517225 −0.258613 0.965981i \(-0.583265\pi\)
−0.258613 + 0.965981i \(0.583265\pi\)
\(572\) 0 0
\(573\) 20.0200i 0.836346i
\(574\) 0 0
\(575\) −5.51537 7.81690i −0.230007 0.325987i
\(576\) 0 0
\(577\) 32.1837i 1.33983i −0.742439 0.669913i \(-0.766331\pi\)
0.742439 0.669913i \(-0.233669\pi\)
\(578\) 0 0
\(579\) 1.15297 0.0479157
\(580\) 0 0
\(581\) 51.1678 2.12280
\(582\) 0 0
\(583\) 4.02588i 0.166735i
\(584\) 0 0
\(585\) 13.5563 4.30105i 0.560484 0.177826i
\(586\) 0 0
\(587\) 36.8765i 1.52206i 0.648718 + 0.761029i \(0.275305\pi\)
−0.648718 + 0.761029i \(0.724695\pi\)
\(588\) 0 0
\(589\) −2.47212 −0.101862
\(590\) 0 0
\(591\) −3.53115 −0.145252
\(592\) 0 0
\(593\) 31.4549i 1.29170i −0.763465 0.645849i \(-0.776504\pi\)
0.763465 0.645849i \(-0.223496\pi\)
\(594\) 0 0
\(595\) −11.7586 37.0616i −0.482057 1.51938i
\(596\) 0 0
\(597\) 3.63461i 0.148755i
\(598\) 0 0
\(599\) 8.68221 0.354746 0.177373 0.984144i \(-0.443240\pi\)
0.177373 + 0.984144i \(0.443240\pi\)
\(600\) 0 0
\(601\) 11.1262 0.453848 0.226924 0.973913i \(-0.427133\pi\)
0.226924 + 0.973913i \(0.427133\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) 6.13153 + 19.3257i 0.249282 + 0.785702i
\(606\) 0 0
\(607\) 27.8119i 1.12885i 0.825485 + 0.564424i \(0.190902\pi\)
−0.825485 + 0.564424i \(0.809098\pi\)
\(608\) 0 0
\(609\) 22.8779 0.927059
\(610\) 0 0
\(611\) 1.37760 0.0557319
\(612\) 0 0
\(613\) 27.6331i 1.11609i −0.829811 0.558045i \(-0.811552\pi\)
0.829811 0.558045i \(-0.188448\pi\)
\(614\) 0 0
\(615\) −8.84058 + 2.80488i −0.356487 + 0.113104i
\(616\) 0 0
\(617\) 17.6017i 0.708618i −0.935128 0.354309i \(-0.884716\pi\)
0.935128 0.354309i \(-0.115284\pi\)
\(618\) 0 0
\(619\) −16.8586 −0.677604 −0.338802 0.940858i \(-0.610022\pi\)
−0.338802 + 0.940858i \(0.610022\pi\)
\(620\) 0 0
\(621\) −1.91335 −0.0767803
\(622\) 0 0
\(623\) 72.0012i 2.88467i
\(624\) 0 0
\(625\) 8.38163 23.5531i 0.335265 0.942124i
\(626\) 0 0
\(627\) 7.16412i 0.286108i
\(628\) 0 0
\(629\) 10.3735 0.413617
\(630\) 0 0
\(631\) 41.7361 1.66149 0.830744 0.556654i \(-0.187915\pi\)
0.830744 + 0.556654i \(0.187915\pi\)
\(632\) 0 0
\(633\) 19.9563i 0.793192i
\(634\) 0 0
\(635\) 6.60532 2.09569i 0.262124 0.0831649i
\(636\) 0 0
\(637\) 69.4073i 2.75002i
\(638\) 0 0
\(639\) −8.26764 −0.327063
\(640\) 0 0
\(641\) 12.2358 0.483286 0.241643 0.970365i \(-0.422314\pi\)
0.241643 + 0.970365i \(0.422314\pi\)
\(642\) 0 0
\(643\) 0.694878i 0.0274033i −0.999906 0.0137017i \(-0.995638\pi\)
0.999906 0.0137017i \(-0.00436151\pi\)
\(644\) 0 0
\(645\) 0.408812 + 1.28852i 0.0160969 + 0.0507353i
\(646\) 0 0
\(647\) 2.15047i 0.0845437i 0.999106 + 0.0422719i \(0.0134596\pi\)
−0.999106 + 0.0422719i \(0.986540\pi\)
\(648\) 0 0
\(649\) 1.24197 0.0487517
\(650\) 0 0
\(651\) −2.03034 −0.0795751
\(652\) 0 0
\(653\) 35.3611i 1.38379i 0.722000 + 0.691893i \(0.243223\pi\)
−0.722000 + 0.691893i \(0.756777\pi\)
\(654\) 0 0
\(655\) −1.70526 5.37475i −0.0666302 0.210009i
\(656\) 0 0
\(657\) 12.6582i 0.493843i
\(658\) 0 0
\(659\) −5.37707 −0.209461 −0.104730 0.994501i \(-0.533398\pi\)
−0.104730 + 0.994501i \(0.533398\pi\)
\(660\) 0 0
\(661\) 11.5561 0.449481 0.224741 0.974419i \(-0.427846\pi\)
0.224741 + 0.974419i \(0.427846\pi\)
\(662\) 0 0
\(663\) 26.1319i 1.01488i
\(664\) 0 0
\(665\) 46.4852 14.7485i 1.80262 0.571923i
\(666\) 0 0
\(667\) 10.3427i 0.400471i
\(668\) 0 0
\(669\) 21.2283 0.820735
\(670\) 0 0
\(671\) −4.03914 −0.155929
\(672\) 0 0
\(673\) 15.1408i 0.583634i −0.956474 0.291817i \(-0.905740\pi\)
0.956474 0.291817i \(-0.0942598\pi\)
\(674\) 0 0
\(675\) −2.88257 4.08544i −0.110950 0.157249i
\(676\) 0 0
\(677\) 40.1536i 1.54323i −0.636092 0.771613i \(-0.719450\pi\)
0.636092 0.771613i \(-0.280550\pi\)
\(678\) 0 0
\(679\) 2.69254 0.103330
\(680\) 0 0
\(681\) −11.5637 −0.443121
\(682\) 0 0
\(683\) 39.1608i 1.49844i 0.662319 + 0.749222i \(0.269573\pi\)
−0.662319 + 0.749222i \(0.730427\pi\)
\(684\) 0 0
\(685\) −22.1299 + 7.02122i −0.845540 + 0.268267i
\(686\) 0 0
\(687\) 12.9167i 0.492803i
\(688\) 0 0
\(689\) −18.4188 −0.701699
\(690\) 0 0
\(691\) 36.7016 1.39620 0.698098 0.716002i \(-0.254030\pi\)
0.698098 + 0.716002i \(0.254030\pi\)
\(692\) 0 0
\(693\) 5.88384i 0.223509i
\(694\) 0 0
\(695\) 9.96939 + 31.4221i 0.378161 + 1.19191i
\(696\) 0 0
\(697\) 17.0416i 0.645498i
\(698\) 0 0
\(699\) 15.9294 0.602504
\(700\) 0 0
\(701\) −39.1254 −1.47775 −0.738873 0.673844i \(-0.764642\pi\)
−0.738873 + 0.673844i \(0.764642\pi\)
\(702\) 0 0
\(703\) 13.0111i 0.490724i
\(704\) 0 0
\(705\) −0.146464 0.461635i −0.00551617 0.0173862i
\(706\) 0 0
\(707\) 7.24920i 0.272634i
\(708\) 0 0
\(709\) 5.88538 0.221030 0.110515 0.993874i \(-0.464750\pi\)
0.110515 + 0.993874i \(0.464750\pi\)
\(710\) 0 0
\(711\) −13.7111 −0.514205
\(712\) 0 0
\(713\) 0.917880i 0.0343749i
\(714\) 0 0
\(715\) 18.8462 5.97940i 0.704809 0.223617i
\(716\) 0 0
\(717\) 9.80764i 0.366273i
\(718\) 0 0
\(719\) −8.40620 −0.313498 −0.156749 0.987638i \(-0.550101\pi\)
−0.156749 + 0.987638i \(0.550101\pi\)
\(720\) 0 0
\(721\) 27.1312 1.01042
\(722\) 0 0
\(723\) 18.9392i 0.704355i
\(724\) 0 0
\(725\) 22.0840 15.5818i 0.820178 0.578694i
\(726\) 0 0
\(727\) 17.9152i 0.664439i 0.943202 + 0.332220i \(0.107797\pi\)
−0.943202 + 0.332220i \(0.892203\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 2.48382 0.0918674
\(732\) 0 0
\(733\) 22.1553i 0.818325i 0.912462 + 0.409162i \(0.134179\pi\)
−0.912462 + 0.409162i \(0.865821\pi\)
\(734\) 0 0
\(735\) 23.2584 7.37927i 0.857900 0.272189i
\(736\) 0 0
\(737\) 1.39022i 0.0512094i
\(738\) 0 0
\(739\) 23.3616 0.859371 0.429686 0.902979i \(-0.358624\pi\)
0.429686 + 0.902979i \(0.358624\pi\)
\(740\) 0 0
\(741\) 32.7765 1.20407
\(742\) 0 0
\(743\) 13.2885i 0.487508i −0.969837 0.243754i \(-0.921621\pi\)
0.969837 0.243754i \(-0.0783789\pi\)
\(744\) 0 0
\(745\) 5.47104 + 17.2439i 0.200443 + 0.631769i
\(746\) 0 0
\(747\) 12.0898i 0.442343i
\(748\) 0 0
\(749\) −80.0948 −2.92660
\(750\) 0 0
\(751\) −35.4870 −1.29494 −0.647470 0.762091i \(-0.724173\pi\)
−0.647470 + 0.762091i \(0.724173\pi\)
\(752\) 0 0
\(753\) 13.4401i 0.489786i
\(754\) 0 0
\(755\) −4.91464 15.4903i −0.178862 0.563748i
\(756\) 0 0
\(757\) 37.0646i 1.34714i −0.739125 0.673568i \(-0.764761\pi\)
0.739125 0.673568i \(-0.235239\pi\)
\(758\) 0 0
\(759\) −2.65998 −0.0965513
\(760\) 0 0
\(761\) 18.9718 0.687726 0.343863 0.939020i \(-0.388264\pi\)
0.343863 + 0.939020i \(0.388264\pi\)
\(762\) 0 0
\(763\) 20.7254i 0.750309i
\(764\) 0 0
\(765\) −8.75681 + 2.77830i −0.316603 + 0.100450i
\(766\) 0 0
\(767\) 5.68213i 0.205170i
\(768\) 0 0
\(769\) −17.7057 −0.638483 −0.319241 0.947673i \(-0.603428\pi\)
−0.319241 + 0.947673i \(0.603428\pi\)
\(770\) 0 0
\(771\) −6.47817 −0.233306
\(772\) 0 0
\(773\) 28.7012i 1.03231i −0.856495 0.516155i \(-0.827363\pi\)
0.856495 0.516155i \(-0.172637\pi\)
\(774\) 0 0
\(775\) −1.95988 + 1.38283i −0.0704009 + 0.0496728i
\(776\) 0 0
\(777\) 10.6860i 0.383356i
\(778\) 0 0
\(779\) −21.3748 −0.765832
\(780\) 0 0
\(781\) −11.4938 −0.411282
\(782\) 0 0
\(783\) 5.40553i 0.193178i
\(784\) 0 0
\(785\) 42.5923 13.5134i 1.52018 0.482313i
\(786\) 0 0
\(787\) 29.9880i 1.06896i −0.845182 0.534478i \(-0.820508\pi\)
0.845182 0.534478i \(-0.179492\pi\)
\(788\) 0 0
\(789\) 21.0096 0.747961
\(790\) 0 0
\(791\) −12.2237 −0.434623
\(792\) 0