Properties

Label 2352.2.bl.o.607.4
Level $2352$
Weight $2$
Character 2352.607
Analytic conductor $18.781$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.bl (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.7808145554\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.339738624.1
Defining polynomial: \(x^{8} - 4 x^{6} + 14 x^{4} - 8 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 607.4
Root \(-0.662827 - 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 2352.607
Dual form 2352.2.bl.o.31.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(3.72153 + 2.14862i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(3.72153 + 2.14862i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(-4.38435 + 2.53131i) q^{11} -3.37849i q^{13} -4.29725i q^{15} +(-2.39587 + 1.38326i) q^{17} +(-2.35159 + 4.07308i) q^{19} +(-4.18394 - 2.41560i) q^{23} +(6.73317 + 11.6622i) q^{25} +1.00000 q^{27} +2.46054 q^{29} +(2.84882 + 4.93430i) q^{31} +(4.38435 + 2.53131i) q^{33} +(1.16765 - 2.02243i) q^{37} +(-2.92586 + 1.68925i) q^{39} +5.14822i q^{41} +13.0199i q^{43} +(-3.72153 + 2.14862i) q^{45} +(-2.67725 + 4.63713i) q^{47} +(2.39587 + 1.38326i) q^{51} +(2.11185 + 3.65784i) q^{53} -21.7553 q^{55} +4.70319 q^{57} +(-4.80249 - 8.31815i) q^{59} +(-3.35757 - 1.93849i) q^{61} +(7.25911 - 12.5732i) q^{65} +(4.12524 - 2.38171i) q^{67} +4.83120i q^{69} -12.3181i q^{71} +(-9.96809 + 5.75508i) q^{73} +(6.73317 - 11.6622i) q^{75} +(12.0521 + 6.95830i) q^{79} +(-0.500000 - 0.866025i) q^{81} +7.32191 q^{83} -11.8884 q^{85} +(-1.23027 - 2.13089i) q^{87} +(-12.1631 - 7.02239i) q^{89} +(2.84882 - 4.93430i) q^{93} +(-17.5030 + 10.1054i) q^{95} +14.5716i q^{97} -5.06262i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{3} - 4q^{9} + O(q^{10}) \) \( 8q - 4q^{3} - 4q^{9} - 24q^{23} + 12q^{25} + 8q^{27} + 16q^{29} + 16q^{31} + 8q^{47} - 8q^{53} - 64q^{55} - 24q^{59} - 48q^{61} + 8q^{65} + 48q^{67} - 48q^{73} + 12q^{75} + 24q^{79} - 4q^{81} - 64q^{85} - 8q^{87} - 48q^{89} + 16q^{93} - 72q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0 0
\(5\) 3.72153 + 2.14862i 1.66432 + 0.960894i 0.970617 + 0.240630i \(0.0773542\pi\)
0.693701 + 0.720264i \(0.255979\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −4.38435 + 2.53131i −1.32193 + 0.763218i −0.984037 0.177966i \(-0.943048\pi\)
−0.337896 + 0.941184i \(0.609715\pi\)
\(12\) 0 0
\(13\) 3.37849i 0.937025i −0.883457 0.468513i \(-0.844790\pi\)
0.883457 0.468513i \(-0.155210\pi\)
\(14\) 0 0
\(15\) 4.29725i 1.10954i
\(16\) 0 0
\(17\) −2.39587 + 1.38326i −0.581084 + 0.335489i −0.761564 0.648089i \(-0.775568\pi\)
0.180480 + 0.983579i \(0.442235\pi\)
\(18\) 0 0
\(19\) −2.35159 + 4.07308i −0.539492 + 0.934428i 0.459439 + 0.888209i \(0.348050\pi\)
−0.998931 + 0.0462188i \(0.985283\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.18394 2.41560i −0.872412 0.503687i −0.00426301 0.999991i \(-0.501357\pi\)
−0.868149 + 0.496304i \(0.834690\pi\)
\(24\) 0 0
\(25\) 6.73317 + 11.6622i 1.34663 + 2.33244i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 2.46054 0.456912 0.228456 0.973554i \(-0.426632\pi\)
0.228456 + 0.973554i \(0.426632\pi\)
\(30\) 0 0
\(31\) 2.84882 + 4.93430i 0.511663 + 0.886227i 0.999909 + 0.0135202i \(0.00430375\pi\)
−0.488245 + 0.872706i \(0.662363\pi\)
\(32\) 0 0
\(33\) 4.38435 + 2.53131i 0.763218 + 0.440644i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.16765 2.02243i 0.191961 0.332486i −0.753939 0.656944i \(-0.771849\pi\)
0.945900 + 0.324458i \(0.105182\pi\)
\(38\) 0 0
\(39\) −2.92586 + 1.68925i −0.468513 + 0.270496i
\(40\) 0 0
\(41\) 5.14822i 0.804018i 0.915636 + 0.402009i \(0.131688\pi\)
−0.915636 + 0.402009i \(0.868312\pi\)
\(42\) 0 0
\(43\) 13.0199i 1.98552i 0.120117 + 0.992760i \(0.461673\pi\)
−0.120117 + 0.992760i \(0.538327\pi\)
\(44\) 0 0
\(45\) −3.72153 + 2.14862i −0.554772 + 0.320298i
\(46\) 0 0
\(47\) −2.67725 + 4.63713i −0.390517 + 0.676395i −0.992518 0.122101i \(-0.961037\pi\)
0.602001 + 0.798495i \(0.294370\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 2.39587 + 1.38326i 0.335489 + 0.193695i
\(52\) 0 0
\(53\) 2.11185 + 3.65784i 0.290085 + 0.502443i 0.973830 0.227279i \(-0.0729830\pi\)
−0.683744 + 0.729722i \(0.739650\pi\)
\(54\) 0 0
\(55\) −21.7553 −2.93349
\(56\) 0 0
\(57\) 4.70319 0.622952
\(58\) 0 0
\(59\) −4.80249 8.31815i −0.625231 1.08293i −0.988496 0.151246i \(-0.951672\pi\)
0.363265 0.931686i \(-0.381662\pi\)
\(60\) 0 0
\(61\) −3.35757 1.93849i −0.429892 0.248198i 0.269408 0.963026i \(-0.413172\pi\)
−0.699301 + 0.714828i \(0.746505\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 7.25911 12.5732i 0.900382 1.55951i
\(66\) 0 0
\(67\) 4.12524 2.38171i 0.503978 0.290972i −0.226377 0.974040i \(-0.572688\pi\)
0.730355 + 0.683068i \(0.239355\pi\)
\(68\) 0 0
\(69\) 4.83120i 0.581608i
\(70\) 0 0
\(71\) 12.3181i 1.46189i −0.682437 0.730944i \(-0.739080\pi\)
0.682437 0.730944i \(-0.260920\pi\)
\(72\) 0 0
\(73\) −9.96809 + 5.75508i −1.16668 + 0.673581i −0.952895 0.303300i \(-0.901911\pi\)
−0.213782 + 0.976881i \(0.568578\pi\)
\(74\) 0 0
\(75\) 6.73317 11.6622i 0.777480 1.34663i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 12.0521 + 6.95830i 1.35597 + 0.782870i 0.989078 0.147393i \(-0.0470882\pi\)
0.366893 + 0.930263i \(0.380422\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 7.32191 0.803685 0.401842 0.915709i \(-0.368370\pi\)
0.401842 + 0.915709i \(0.368370\pi\)
\(84\) 0 0
\(85\) −11.8884 −1.28948
\(86\) 0 0
\(87\) −1.23027 2.13089i −0.131899 0.228456i
\(88\) 0 0
\(89\) −12.1631 7.02239i −1.28929 0.744372i −0.310762 0.950488i \(-0.600584\pi\)
−0.978528 + 0.206116i \(0.933918\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 2.84882 4.93430i 0.295409 0.511663i
\(94\) 0 0
\(95\) −17.5030 + 10.1054i −1.79577 + 1.03679i
\(96\) 0 0
\(97\) 14.5716i 1.47952i 0.672868 + 0.739762i \(0.265062\pi\)
−0.672868 + 0.739762i \(0.734938\pi\)
\(98\) 0 0
\(99\) 5.06262i 0.508812i
\(100\) 0 0
\(101\) −11.3524 + 6.55434i −1.12961 + 0.652181i −0.943837 0.330412i \(-0.892812\pi\)
−0.185773 + 0.982593i \(0.559479\pi\)
\(102\) 0 0
\(103\) −0.104849 + 0.181604i −0.0103311 + 0.0178939i −0.871145 0.491026i \(-0.836622\pi\)
0.860814 + 0.508920i \(0.169955\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.56558 + 3.21329i 0.538044 + 0.310640i 0.744286 0.667861i \(-0.232790\pi\)
−0.206242 + 0.978501i \(0.566123\pi\)
\(108\) 0 0
\(109\) −0.470012 0.814084i −0.0450190 0.0779751i 0.842638 0.538481i \(-0.181001\pi\)
−0.887657 + 0.460506i \(0.847668\pi\)
\(110\) 0 0
\(111\) −2.33530 −0.221657
\(112\) 0 0
\(113\) 1.09821 0.103311 0.0516554 0.998665i \(-0.483550\pi\)
0.0516554 + 0.998665i \(0.483550\pi\)
\(114\) 0 0
\(115\) −10.3804 17.9794i −0.967980 1.67659i
\(116\) 0 0
\(117\) 2.92586 + 1.68925i 0.270496 + 0.156171i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 7.31504 12.6700i 0.665004 1.15182i
\(122\) 0 0
\(123\) 4.45849 2.57411i 0.402009 0.232100i
\(124\) 0 0
\(125\) 36.3820i 3.25411i
\(126\) 0 0
\(127\) 5.22625i 0.463755i −0.972745 0.231877i \(-0.925513\pi\)
0.972745 0.231877i \(-0.0744868\pi\)
\(128\) 0 0
\(129\) 11.2756 6.50996i 0.992760 0.573170i
\(130\) 0 0
\(131\) −0.437508 + 0.757785i −0.0382252 + 0.0662080i −0.884505 0.466531i \(-0.845504\pi\)
0.846280 + 0.532739i \(0.178837\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 3.72153 + 2.14862i 0.320298 + 0.184924i
\(136\) 0 0
\(137\) −0.118419 0.205108i −0.0101172 0.0175235i 0.860922 0.508736i \(-0.169887\pi\)
−0.871040 + 0.491213i \(0.836554\pi\)
\(138\) 0 0
\(139\) −3.00555 −0.254927 −0.127464 0.991843i \(-0.540684\pi\)
−0.127464 + 0.991843i \(0.540684\pi\)
\(140\) 0 0
\(141\) 5.35449 0.450930
\(142\) 0 0
\(143\) 8.55201 + 14.8125i 0.715155 + 1.23868i
\(144\) 0 0
\(145\) 9.15698 + 5.28679i 0.760446 + 0.439044i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.40083 12.8186i 0.606299 1.05014i −0.385545 0.922689i \(-0.625987\pi\)
0.991845 0.127452i \(-0.0406799\pi\)
\(150\) 0 0
\(151\) 10.7087 6.18269i 0.871464 0.503140i 0.00362965 0.999993i \(-0.498845\pi\)
0.867835 + 0.496853i \(0.165511\pi\)
\(152\) 0 0
\(153\) 2.76652i 0.223659i
\(154\) 0 0
\(155\) 24.4842i 1.96662i
\(156\) 0 0
\(157\) −9.43153 + 5.44530i −0.752718 + 0.434582i −0.826675 0.562679i \(-0.809771\pi\)
0.0739569 + 0.997261i \(0.476437\pi\)
\(158\) 0 0
\(159\) 2.11185 3.65784i 0.167481 0.290085i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1.30791 + 0.755120i 0.102443 + 0.0591455i 0.550346 0.834937i \(-0.314496\pi\)
−0.447903 + 0.894082i \(0.647829\pi\)
\(164\) 0 0
\(165\) 10.8777 + 18.8407i 0.846825 + 1.46674i
\(166\) 0 0
\(167\) 10.3333 0.799612 0.399806 0.916600i \(-0.369078\pi\)
0.399806 + 0.916600i \(0.369078\pi\)
\(168\) 0 0
\(169\) 1.58579 0.121984
\(170\) 0 0
\(171\) −2.35159 4.07308i −0.179831 0.311476i
\(172\) 0 0
\(173\) −2.90674 1.67821i −0.220996 0.127592i 0.385416 0.922743i \(-0.374058\pi\)
−0.606411 + 0.795151i \(0.707391\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.80249 + 8.31815i −0.360977 + 0.625231i
\(178\) 0 0
\(179\) −11.4826 + 6.62946i −0.858247 + 0.495509i −0.863425 0.504477i \(-0.831685\pi\)
0.00517789 + 0.999987i \(0.498352\pi\)
\(180\) 0 0
\(181\) 11.8519i 0.880946i −0.897766 0.440473i \(-0.854811\pi\)
0.897766 0.440473i \(-0.145189\pi\)
\(182\) 0 0
\(183\) 3.87698i 0.286595i
\(184\) 0 0
\(185\) 8.69089 5.01769i 0.638967 0.368908i
\(186\) 0 0
\(187\) 7.00290 12.1294i 0.512103 0.886988i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.16619 0.673302i −0.0843828 0.0487184i 0.457215 0.889356i \(-0.348847\pi\)
−0.541598 + 0.840638i \(0.682180\pi\)
\(192\) 0 0
\(193\) 13.0577 + 22.6166i 0.939912 + 1.62798i 0.765631 + 0.643280i \(0.222427\pi\)
0.174281 + 0.984696i \(0.444240\pi\)
\(194\) 0 0
\(195\) −14.5182 −1.03967
\(196\) 0 0
\(197\) −7.49083 −0.533699 −0.266850 0.963738i \(-0.585983\pi\)
−0.266850 + 0.963738i \(0.585983\pi\)
\(198\) 0 0
\(199\) −2.24674 3.89147i −0.159267 0.275859i 0.775337 0.631547i \(-0.217580\pi\)
−0.934605 + 0.355688i \(0.884247\pi\)
\(200\) 0 0
\(201\) −4.12524 2.38171i −0.290972 0.167993i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −11.0616 + 19.1593i −0.772576 + 1.33814i
\(206\) 0 0
\(207\) 4.18394 2.41560i 0.290804 0.167896i
\(208\) 0 0
\(209\) 23.8104i 1.64700i
\(210\) 0 0
\(211\) 5.93122i 0.408322i −0.978937 0.204161i \(-0.934553\pi\)
0.978937 0.204161i \(-0.0654466\pi\)
\(212\) 0 0
\(213\) −10.6678 + 6.15905i −0.730944 + 0.422011i
\(214\) 0 0
\(215\) −27.9749 + 48.4540i −1.90787 + 3.30453i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 9.96809 + 5.75508i 0.673581 + 0.388892i
\(220\) 0 0
\(221\) 4.67333 + 8.09444i 0.314362 + 0.544491i
\(222\) 0 0
\(223\) 20.6163 1.38057 0.690286 0.723537i \(-0.257485\pi\)
0.690286 + 0.723537i \(0.257485\pi\)
\(224\) 0 0
\(225\) −13.4663 −0.897756
\(226\) 0 0
\(227\) −10.2455 17.7458i −0.680021 1.17783i −0.974974 0.222318i \(-0.928638\pi\)
0.294954 0.955512i \(-0.404696\pi\)
\(228\) 0 0
\(229\) 25.1502 + 14.5205i 1.66197 + 0.959539i 0.971773 + 0.235917i \(0.0758095\pi\)
0.690197 + 0.723622i \(0.257524\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.86819 + 15.3602i −0.580975 + 1.00628i 0.414390 + 0.910100i \(0.363995\pi\)
−0.995364 + 0.0961779i \(0.969338\pi\)
\(234\) 0 0
\(235\) −19.9269 + 11.5048i −1.29989 + 0.750490i
\(236\) 0 0
\(237\) 13.9166i 0.903981i
\(238\) 0 0
\(239\) 20.4248i 1.32117i 0.750750 + 0.660586i \(0.229692\pi\)
−0.750750 + 0.660586i \(0.770308\pi\)
\(240\) 0 0
\(241\) 2.82101 1.62871i 0.181717 0.104915i −0.406382 0.913703i \(-0.633210\pi\)
0.588099 + 0.808789i \(0.299876\pi\)
\(242\) 0 0
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 13.7609 + 7.94484i 0.875583 + 0.505518i
\(248\) 0 0
\(249\) −3.66096 6.34096i −0.232004 0.401842i
\(250\) 0 0
\(251\) 3.95633 0.249721 0.124861 0.992174i \(-0.460152\pi\)
0.124861 + 0.992174i \(0.460152\pi\)
\(252\) 0 0
\(253\) 24.4585 1.53769
\(254\) 0 0
\(255\) 5.94420 + 10.2957i 0.372240 + 0.644739i
\(256\) 0 0
\(257\) 4.45849 + 2.57411i 0.278113 + 0.160569i 0.632569 0.774504i \(-0.282001\pi\)
−0.354456 + 0.935073i \(0.615334\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1.23027 + 2.13089i −0.0761519 + 0.131899i
\(262\) 0 0
\(263\) −0.0679848 + 0.0392511i −0.00419212 + 0.00242032i −0.502095 0.864813i \(-0.667437\pi\)
0.497902 + 0.867233i \(0.334104\pi\)
\(264\) 0 0
\(265\) 18.1503i 1.11497i
\(266\) 0 0
\(267\) 14.0448i 0.859527i
\(268\) 0 0
\(269\) −0.764956 + 0.441648i −0.0466402 + 0.0269277i −0.523139 0.852247i \(-0.675239\pi\)
0.476499 + 0.879175i \(0.341906\pi\)
\(270\) 0 0
\(271\) 9.65421 16.7216i 0.586451 1.01576i −0.408241 0.912874i \(-0.633858\pi\)
0.994693 0.102890i \(-0.0328089\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −59.0412 34.0875i −3.56032 2.05555i
\(276\) 0 0
\(277\) −8.46635 14.6641i −0.508694 0.881083i −0.999949 0.0100677i \(-0.996795\pi\)
0.491256 0.871015i \(-0.336538\pi\)
\(278\) 0 0
\(279\) −5.69764 −0.341109
\(280\) 0 0
\(281\) 5.05417 0.301507 0.150753 0.988571i \(-0.451830\pi\)
0.150753 + 0.988571i \(0.451830\pi\)
\(282\) 0 0
\(283\) 9.55781 + 16.5546i 0.568153 + 0.984069i 0.996749 + 0.0805731i \(0.0256750\pi\)
−0.428596 + 0.903496i \(0.640992\pi\)
\(284\) 0 0
\(285\) 17.5030 + 10.1054i 1.03679 + 0.598591i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −4.67320 + 8.09421i −0.274894 + 0.476130i
\(290\) 0 0
\(291\) 12.6194 7.28581i 0.739762 0.427102i
\(292\) 0 0
\(293\) 2.37837i 0.138946i 0.997584 + 0.0694730i \(0.0221318\pi\)
−0.997584 + 0.0694730i \(0.977868\pi\)
\(294\) 0 0
\(295\) 41.2750i 2.40312i
\(296\) 0 0
\(297\) −4.38435 + 2.53131i −0.254406 + 0.146881i
\(298\) 0 0
\(299\) −8.16109 + 14.1354i −0.471968 + 0.817472i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 11.3524 + 6.55434i 0.652181 + 0.376537i
\(304\) 0 0
\(305\) −8.33018 14.4283i −0.476985 0.826162i
\(306\) 0 0
\(307\) 4.89599 0.279429 0.139714 0.990192i \(-0.455382\pi\)
0.139714 + 0.990192i \(0.455382\pi\)
\(308\) 0 0
\(309\) 0.209698 0.0119293
\(310\) 0 0
\(311\) −5.24000 9.07594i −0.297133 0.514649i 0.678346 0.734743i \(-0.262697\pi\)
−0.975479 + 0.220093i \(0.929364\pi\)
\(312\) 0 0
\(313\) 8.31534 + 4.80086i 0.470011 + 0.271361i 0.716244 0.697850i \(-0.245860\pi\)
−0.246234 + 0.969211i \(0.579193\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8.39672 14.5435i 0.471607 0.816847i −0.527865 0.849328i \(-0.677007\pi\)
0.999472 + 0.0324809i \(0.0103408\pi\)
\(318\) 0 0
\(319\) −10.7879 + 6.22840i −0.604006 + 0.348723i
\(320\) 0 0
\(321\) 6.42657i 0.358696i
\(322\) 0 0
\(323\) 13.0114i 0.723976i
\(324\) 0 0
\(325\) 39.4007 22.7480i 2.18556 1.26183i
\(326\) 0 0
\(327\) −0.470012 + 0.814084i −0.0259917 + 0.0450190i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −23.2409 13.4181i −1.27743 0.737526i −0.301057 0.953606i \(-0.597340\pi\)
−0.976376 + 0.216080i \(0.930673\pi\)
\(332\) 0 0
\(333\) 1.16765 + 2.02243i 0.0639869 + 0.110829i
\(334\) 0 0
\(335\) 20.4696 1.11837
\(336\) 0 0
\(337\) 23.0827 1.25739 0.628697 0.777651i \(-0.283589\pi\)
0.628697 + 0.777651i \(0.283589\pi\)
\(338\) 0 0
\(339\) −0.549104 0.951076i −0.0298232 0.0516554i
\(340\) 0 0
\(341\) −24.9805 14.4225i −1.35277 0.781021i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −10.3804 + 17.9794i −0.558864 + 0.967980i
\(346\) 0 0
\(347\) −1.13181 + 0.653449i −0.0607586 + 0.0350790i −0.530072 0.847953i \(-0.677835\pi\)
0.469313 + 0.883032i \(0.344502\pi\)
\(348\) 0 0
\(349\) 26.5489i 1.42113i −0.703633 0.710564i \(-0.748440\pi\)
0.703633 0.710564i \(-0.251560\pi\)
\(350\) 0 0
\(351\) 3.37849i 0.180331i
\(352\) 0 0
\(353\) −14.6266 + 8.44466i −0.778494 + 0.449464i −0.835896 0.548887i \(-0.815052\pi\)
0.0574020 + 0.998351i \(0.481718\pi\)
\(354\) 0 0
\(355\) 26.4670 45.8421i 1.40472 2.43305i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 29.0899 + 16.7950i 1.53530 + 0.886408i 0.999104 + 0.0423171i \(0.0134740\pi\)
0.536200 + 0.844091i \(0.319859\pi\)
\(360\) 0 0
\(361\) −1.55998 2.70196i −0.0821040 0.142208i
\(362\) 0 0
\(363\) −14.6301 −0.767880
\(364\) 0 0
\(365\) −49.4620 −2.58896
\(366\) 0 0
\(367\) 3.67989 + 6.37376i 0.192089 + 0.332708i 0.945942 0.324335i \(-0.105141\pi\)
−0.753854 + 0.657043i \(0.771807\pi\)
\(368\) 0 0
\(369\) −4.45849 2.57411i −0.232100 0.134003i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −1.81504 + 3.14374i −0.0939791 + 0.162777i −0.909182 0.416399i \(-0.863292\pi\)
0.815203 + 0.579175i \(0.196625\pi\)
\(374\) 0 0
\(375\) 31.5077 18.1910i 1.62705 0.939379i
\(376\) 0 0
\(377\) 8.31293i 0.428138i
\(378\) 0 0
\(379\) 13.6647i 0.701908i −0.936393 0.350954i \(-0.885857\pi\)
0.936393 0.350954i \(-0.114143\pi\)
\(380\) 0 0
\(381\) −4.52607 + 2.61313i −0.231877 + 0.133874i
\(382\) 0 0
\(383\) 6.82843 11.8272i 0.348916 0.604341i −0.637141 0.770747i \(-0.719883\pi\)
0.986057 + 0.166407i \(0.0532164\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −11.2756 6.50996i −0.573170 0.330920i
\(388\) 0 0
\(389\) −13.4540 23.3030i −0.682144 1.18151i −0.974325 0.225145i \(-0.927714\pi\)
0.292181 0.956363i \(-0.405619\pi\)
\(390\) 0 0
\(391\) 13.3656 0.675927
\(392\) 0 0
\(393\) 0.875015 0.0441387
\(394\) 0 0
\(395\) 29.9016 + 51.7910i 1.50451 + 2.60589i
\(396\) 0 0
\(397\) −31.8041 18.3621i −1.59620 0.921568i −0.992210 0.124579i \(-0.960242\pi\)
−0.603994 0.796989i \(-0.706425\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 13.8408 23.9730i 0.691176 1.19715i −0.280276 0.959919i \(-0.590426\pi\)
0.971453 0.237233i \(-0.0762405\pi\)
\(402\) 0 0
\(403\) 16.6705 9.62472i 0.830417 0.479441i
\(404\) 0 0
\(405\) 4.29725i 0.213532i
\(406\) 0 0
\(407\) 11.8227i 0.586032i
\(408\) 0 0
\(409\) 7.29903 4.21410i 0.360914 0.208374i −0.308568 0.951202i \(-0.599850\pi\)
0.669482 + 0.742829i \(0.266516\pi\)
\(410\) 0 0
\(411\) −0.118419 + 0.205108i −0.00584118 + 0.0101172i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 27.2487 + 15.7320i 1.33759 + 0.772256i
\(416\) 0 0
\(417\) 1.50277 + 2.60288i 0.0735911 + 0.127464i
\(418\) 0 0
\(419\) −18.3029 −0.894154 −0.447077 0.894495i \(-0.647535\pi\)
−0.447077 + 0.894495i \(0.647535\pi\)
\(420\) 0 0
\(421\) 22.6274 1.10279 0.551396 0.834243i \(-0.314095\pi\)
0.551396 + 0.834243i \(0.314095\pi\)
\(422\) 0 0
\(423\) −2.67725 4.63713i −0.130172 0.225465i
\(424\) 0 0
\(425\) −32.2636 18.6274i −1.56502 0.903563i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 8.55201 14.8125i 0.412895 0.715155i
\(430\) 0 0
\(431\) 3.85300 2.22453i 0.185592 0.107152i −0.404325 0.914615i \(-0.632494\pi\)
0.589918 + 0.807464i \(0.299160\pi\)
\(432\) 0 0
\(433\) 1.66205i 0.0798730i 0.999202 + 0.0399365i \(0.0127156\pi\)
−0.999202 + 0.0399365i \(0.987284\pi\)
\(434\) 0 0
\(435\) 10.5736i 0.506964i
\(436\) 0 0
\(437\) 19.6779 11.3610i 0.941319 0.543471i
\(438\) 0 0
\(439\) −9.37753 + 16.2424i −0.447565 + 0.775206i −0.998227 0.0595229i \(-0.981042\pi\)
0.550662 + 0.834728i \(0.314375\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −28.6060 16.5157i −1.35911 0.784684i −0.369609 0.929187i \(-0.620508\pi\)
−0.989504 + 0.144503i \(0.953842\pi\)
\(444\) 0 0
\(445\) −30.1770 52.2680i −1.43053 2.47774i
\(446\) 0 0
\(447\) −14.8017 −0.700094
\(448\) 0 0
\(449\) 9.29441 0.438630 0.219315 0.975654i \(-0.429618\pi\)
0.219315 + 0.975654i \(0.429618\pi\)
\(450\) 0 0
\(451\) −13.0317 22.5716i −0.613641 1.06286i
\(452\) 0 0
\(453\) −10.7087 6.18269i −0.503140 0.290488i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 13.7224 23.7679i 0.641906 1.11181i −0.343101 0.939298i \(-0.611477\pi\)
0.985007 0.172515i \(-0.0551893\pi\)
\(458\) 0 0
\(459\) −2.39587 + 1.38326i −0.111830 + 0.0645649i
\(460\) 0 0
\(461\) 4.28209i 0.199437i 0.995016 + 0.0997183i \(0.0317942\pi\)
−0.995016 + 0.0997183i \(0.968206\pi\)
\(462\) 0 0
\(463\) 16.1278i 0.749521i 0.927122 + 0.374760i \(0.122275\pi\)
−0.927122 + 0.374760i \(0.877725\pi\)
\(464\) 0 0
\(465\) 21.2039 12.2421i 0.983308 0.567713i
\(466\) 0 0
\(467\) −13.7702 + 23.8506i −0.637207 + 1.10368i 0.348836 + 0.937184i \(0.386577\pi\)
−0.986043 + 0.166491i \(0.946756\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 9.43153 + 5.44530i 0.434582 + 0.250906i
\(472\) 0 0
\(473\) −32.9574 57.0839i −1.51538 2.62472i
\(474\) 0 0
\(475\) −63.3347 −2.90600
\(476\) 0 0
\(477\) −4.22371 −0.193390
\(478\) 0 0
\(479\) 9.77545 + 16.9316i 0.446652 + 0.773624i 0.998166 0.0605420i \(-0.0192829\pi\)
−0.551514 + 0.834166i \(0.685950\pi\)
\(480\) 0 0
\(481\) −6.83277 3.94490i −0.311548 0.179872i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −31.3089 + 54.2287i −1.42167 + 2.46240i
\(486\) 0 0
\(487\) 32.7285 18.8958i 1.48307 0.856252i 0.483257 0.875479i \(-0.339454\pi\)
0.999815 + 0.0192268i \(0.00612046\pi\)
\(488\) 0 0
\(489\) 1.51024i 0.0682954i
\(490\) 0 0
\(491\) 29.2605i 1.32051i 0.751042 + 0.660254i \(0.229551\pi\)
−0.751042 + 0.660254i \(0.770449\pi\)
\(492\) 0 0
\(493\) −5.89515 + 3.40357i −0.265504 + 0.153289i
\(494\) 0 0
\(495\) 10.8777 18.8407i 0.488914 0.846825i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −10.9485 6.32111i −0.490122 0.282972i 0.234503 0.972115i \(-0.424654\pi\)
−0.724625 + 0.689143i \(0.757987\pi\)
\(500\) 0 0
\(501\) −5.16663 8.94887i −0.230828 0.399806i
\(502\) 0 0
\(503\) 27.0714 1.20706 0.603528 0.797342i \(-0.293761\pi\)
0.603528 + 0.797342i \(0.293761\pi\)
\(504\) 0 0
\(505\) −56.3312 −2.50671
\(506\) 0 0
\(507\) −0.792893 1.37333i −0.0352136 0.0609918i
\(508\) 0 0
\(509\) −10.1311 5.84917i −0.449051 0.259260i 0.258378 0.966044i \(-0.416812\pi\)
−0.707429 + 0.706784i \(0.750145\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2.35159 + 4.07308i −0.103825 + 0.179831i
\(514\) 0 0
\(515\) −0.780396 + 0.450562i −0.0343884 + 0.0198541i
\(516\) 0 0
\(517\) 27.1077i 1.19220i
\(518\) 0 0
\(519\) 3.35642i 0.147330i
\(520\) 0 0
\(521\) −6.24095 + 3.60322i −0.273421 + 0.157860i −0.630441 0.776237i \(-0.717126\pi\)
0.357020 + 0.934097i \(0.383793\pi\)
\(522\) 0 0
\(523\) 8.85727 15.3412i 0.387301 0.670825i −0.604784 0.796389i \(-0.706741\pi\)
0.992086 + 0.125564i \(0.0400740\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −13.6508 7.88130i −0.594639 0.343315i
\(528\) 0 0
\(529\) 0.170243 + 0.294869i 0.00740185 + 0.0128204i
\(530\) 0 0
\(531\) 9.60498 0.416821
\(532\) 0 0
\(533\) 17.3932 0.753385
\(534\) 0 0
\(535\) 13.8083 + 23.9167i 0.596984 + 1.03401i
\(536\) 0 0
\(537\) 11.4826 + 6.62946i 0.495509 + 0.286082i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −11.5590 + 20.0208i −0.496961 + 0.860761i −0.999994 0.00350600i \(-0.998884\pi\)
0.503033 + 0.864267i \(0.332217\pi\)
\(542\) 0 0
\(543\) −10.2641 + 5.92596i −0.440473 + 0.254307i
\(544\) 0 0
\(545\) 4.03951i 0.173034i
\(546\) 0 0
\(547\) 16.0524i 0.686351i −0.939271 0.343176i \(-0.888497\pi\)
0.939271 0.343176i \(-0.111503\pi\)
\(548\) 0 0
\(549\) 3.35757 1.93849i 0.143297 0.0827328i
\(550\) 0 0
\(551\) −5.78620 + 10.0220i −0.246500 + 0.426951i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −8.69089 5.01769i −0.368908 0.212989i
\(556\) 0 0
\(557\) 6.29041 + 10.8953i 0.266533 + 0.461649i 0.967964 0.251088i \(-0.0807884\pi\)
−0.701431 + 0.712738i \(0.747455\pi\)
\(558\) 0 0
\(559\) 43.9877 1.86048
\(560\) 0 0
\(561\) −14.0058 −0.591325
\(562\) 0 0
\(563\) −18.2974 31.6921i −0.771144 1.33566i −0.936936 0.349500i \(-0.886351\pi\)
0.165792 0.986161i \(-0.446982\pi\)
\(564\) 0 0
\(565\) 4.08701 + 2.35964i 0.171942 + 0.0992707i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 12.2495 21.2167i 0.513524 0.889450i −0.486353 0.873763i \(-0.661673\pi\)
0.999877 0.0156875i \(-0.00499368\pi\)
\(570\) 0 0
\(571\) 28.3990 16.3962i 1.18846 0.686159i 0.230506 0.973071i \(-0.425962\pi\)
0.957957 + 0.286912i \(0.0926286\pi\)
\(572\) 0 0
\(573\) 1.34660i 0.0562552i
\(574\) 0 0
\(575\) 65.0586i 2.71313i
\(576\) 0 0
\(577\) −16.6398 + 9.60699i −0.692724 + 0.399944i −0.804632 0.593774i \(-0.797637\pi\)
0.111908 + 0.993719i \(0.464304\pi\)
\(578\) 0 0
\(579\) 13.0577 22.6166i 0.542659 0.939912i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −18.5182 10.6915i −0.766946 0.442797i
\(584\) 0 0
\(585\) 7.25911 + 12.5732i 0.300127 + 0.519836i
\(586\) 0 0
\(587\) 24.1451 0.996573 0.498286 0.867012i \(-0.333963\pi\)
0.498286 + 0.867012i \(0.333963\pi\)
\(588\) 0 0
\(589\) −26.7971 −1.10415
\(590\) 0 0
\(591\) 3.74541 + 6.48725i 0.154066 + 0.266850i
\(592\) 0 0
\(593\) −2.20475 1.27291i −0.0905380 0.0522722i 0.454047 0.890978i \(-0.349980\pi\)
−0.544585 + 0.838705i \(0.683313\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.24674 + 3.89147i −0.0919531 + 0.159267i
\(598\) 0 0
\(599\) 12.9816 7.49493i 0.530414 0.306234i −0.210771 0.977535i \(-0.567598\pi\)
0.741185 + 0.671301i \(0.234264\pi\)
\(600\) 0 0
\(601\) 24.3343i 0.992618i −0.868146 0.496309i \(-0.834688\pi\)
0.868146 0.496309i \(-0.165312\pi\)
\(602\) 0 0
\(603\) 4.76342i 0.193981i
\(604\) 0 0
\(605\) 54.4462 31.4345i 2.21355 1.27800i
\(606\) 0 0
\(607\) −4.45644 + 7.71878i −0.180881 + 0.313296i −0.942181 0.335105i \(-0.891228\pi\)
0.761300 + 0.648400i \(0.224562\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 15.6665 + 9.04506i 0.633799 + 0.365924i
\(612\) 0 0
\(613\) 8.58741 + 14.8738i 0.346842 + 0.600748i 0.985687 0.168588i \(-0.0539206\pi\)
−0.638844 + 0.769336i \(0.720587\pi\)
\(614\) 0 0
\(615\) 22.1232 0.892094
\(616\) 0 0
\(617\) 35.9980 1.44922 0.724612 0.689157i \(-0.242019\pi\)
0.724612 + 0.689157i \(0.242019\pi\)
\(618\) 0 0
\(619\) 2.05562 + 3.56043i 0.0826222 + 0.143106i 0.904376 0.426738i \(-0.140337\pi\)
−0.821753 + 0.569843i \(0.807004\pi\)
\(620\) 0 0
\(621\) −4.18394 2.41560i −0.167896 0.0969347i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −44.5054 + 77.0856i −1.78022 + 3.08342i
\(626\) 0 0
\(627\) −20.6204 + 11.9052i −0.823501 + 0.475448i
\(628\) 0 0
\(629\) 6.46065i 0.257603i
\(630\) 0 0
\(631\) 34.8970i 1.38923i 0.719383 + 0.694613i \(0.244425\pi\)
−0.719383 + 0.694613i \(0.755575\pi\)
\(632\) 0 0
\(633\) −5.13659 + 2.96561i −0.204161 + 0.117872i
\(634\) 0 0
\(635\) 11.2293 19.4496i 0.445619 0.771835i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 10.6678 + 6.15905i 0.422011 + 0.243648i
\(640\) 0 0
\(641\) −3.66368 6.34567i −0.144707 0.250639i 0.784557 0.620057i \(-0.212890\pi\)
−0.929263 + 0.369418i \(0.879557\pi\)
\(642\) 0 0
\(643\) 9.24275 0.364498 0.182249 0.983252i \(-0.441662\pi\)
0.182249 + 0.983252i \(0.441662\pi\)
\(644\) 0 0
\(645\) 55.9498 2.20302
\(646\) 0 0
\(647\) 7.59013 + 13.1465i 0.298399 + 0.516842i 0.975770 0.218800i \(-0.0702141\pi\)
−0.677371 + 0.735642i \(0.736881\pi\)
\(648\) 0 0
\(649\) 42.1116 + 24.3132i 1.65303 + 0.954375i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.06425 1.84333i 0.0416471 0.0721349i −0.844450 0.535634i \(-0.820073\pi\)
0.886098 + 0.463499i \(0.153406\pi\)
\(654\) 0 0
\(655\) −3.25639 + 1.88008i −0.127238 + 0.0734608i
\(656\) 0 0
\(657\) 11.5102i 0.449054i
\(658\) 0 0
\(659\) 13.0520i 0.508436i −0.967147 0.254218i \(-0.918182\pi\)
0.967147 0.254218i \(-0.0818180\pi\)
\(660\) 0 0
\(661\) −16.6958 + 9.63931i −0.649390 + 0.374926i −0.788223 0.615390i \(-0.788998\pi\)
0.138832 + 0.990316i \(0.455665\pi\)
\(662\) 0 0
\(663\) 4.67333 8.09444i 0.181497 0.314362i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −10.2948 5.94369i −0.398615 0.230141i
\(668\) 0 0
\(669\) −10.3082 17.8543i −0.398537 0.690286i
\(670\) 0 0
\(671\) 19.6277 0.757718
\(672\) 0 0
\(673\) −7.08216 −0.272997 −0.136499 0.990640i \(-0.543585\pi\)
−0.136499 + 0.990640i \(0.543585\pi\)
\(674\) 0 0
\(675\) 6.73317 + 11.6622i 0.259160 + 0.448878i
\(676\) 0 0
\(677\) 31.6135 + 18.2521i 1.21501 + 0.701485i 0.963846 0.266461i \(-0.0858542\pi\)
0.251161 + 0.967945i \(0.419188\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −10.2455 + 17.7458i −0.392610 + 0.680021i
\(682\) 0 0
\(683\) −26.0852 + 15.0603i −0.998124 + 0.576267i −0.907693 0.419636i \(-0.862158\pi\)
−0.0904313 + 0.995903i \(0.528825\pi\)
\(684\) 0 0
\(685\) 1.01775i 0.0388863i
\(686\) 0 0
\(687\) 29.0409i 1.10798i
\(688\) 0 0
\(689\) 12.3580 7.13488i 0.470801 0.271817i
\(690\) 0 0
\(691\) −19.9057 + 34.4776i −0.757247 + 1.31159i 0.187002 + 0.982359i \(0.440123\pi\)
−0.944249 + 0.329231i \(0.893211\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −11.1852 6.45779i −0.424280 0.244958i
\(696\) 0 0
\(697\) −7.12132 12.3345i −0.269739 0.467202i
\(698\) 0 0
\(699\) 17.7364 0.670852
\(700\) 0 0
\(701\) 28.0795 1.06055 0.530275 0.847826i \(-0.322089\pi\)
0.530275 + 0.847826i \(0.322089\pi\)
\(702\) 0 0
\(703\) 5.49168 + 9.51187i 0.207123 + 0.358747i
\(704\) 0 0
\(705\) 19.9269 + 11.5048i 0.750490 + 0.433296i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 18.4738 31.9975i 0.693797 1.20169i −0.276787 0.960931i \(-0.589270\pi\)
0.970585 0.240761i \(-0.0773969\pi\)
\(710\) 0 0
\(711\) −12.0521 + 6.95830i −0.451990 + 0.260957i
\(712\) 0 0
\(713\) 27.5264i 1.03087i
\(714\) 0 0
\(715\) 73.5002i 2.74875i
\(716\) 0 0
\(717\) 17.6884 10.2124i 0.660586 0.381389i
\(718\) 0 0
\(719\) −9.35449 + 16.2025i −0.348864 + 0.604250i −0.986048 0.166462i \(-0.946766\pi\)
0.637184 + 0.770712i \(0.280099\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −2.82101 1.62871i −0.104915 0.0605724i
\(724\) 0 0
\(725\) 16.5673 + 28.6954i 0.615293 + 1.06572i
\(726\) 0 0
\(727\) −31.2078 −1.15743 −0.578716 0.815529i \(-0.696446\pi\)
−0.578716 + 0.815529i \(0.696446\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −18.0099 31.1941i −0.666120 1.15375i
\(732\) 0 0
\(733\) −3.52383 2.03449i −0.130156 0.0751455i 0.433508 0.901150i \(-0.357275\pi\)
−0.563664 + 0.826004i \(0.690609\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −12.0577 + 20.8845i −0.444150 + 0.769291i
\(738\) 0 0
\(739\) 34.5566 19.9513i 1.27119 0.733919i 0.295974 0.955196i \(-0.404356\pi\)
0.975211 + 0.221277i \(0.0710224\pi\)
\(740\) 0 0
\(741\) 15.8897i 0.583722i
\(742\) 0 0
\(743\) 41.7530i 1.53177i 0.642979 + 0.765884i \(0.277698\pi\)
−0.642979 + 0.765884i \(0.722302\pi\)
\(744\) 0 0
\(745\) 55.0847 31.8032i 2.01815 1.16518i
\(746\) 0 0
\(747\) −3.66096 + 6.34096i −0.133947 + 0.232004i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 7.88020 + 4.54963i 0.287552 + 0.166019i 0.636838 0.770998i \(-0.280242\pi\)
−0.349285 + 0.937017i \(0.613576\pi\)
\(752\) 0 0
\(753\) −1.97816 3.42628i −0.0720883 0.124861i
\(754\) 0 0
\(755\) 53.1371 1.93386
\(756\) 0 0
\(757\) −0.902155 −0.0327894 −0.0163947 0.999866i \(-0.505219\pi\)
−0.0163947 + 0.999866i \(0.505219\pi\)
\(758\) 0 0
\(759\) −12.2293 21.1817i −0.443894 0.768847i
\(760\) 0 0
\(761\) 20.5924 + 11.8891i 0.746475 + 0.430978i 0.824419 0.565980i \(-0.191502\pi\)
−0.0779436 + 0.996958i \(0.524835\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 5.94420 10.2957i 0.214913 0.372240i
\(766\) 0 0
\(767\) −28.1028 + 16.2252i −1.01473 + 0.585857i
\(768\) 0 0
\(769\) 16.3028i 0.587895i −0.955822 0.293948i \(-0.905031\pi\)
0.955822 0.293948i \(-0.0949691\pi\)
\(770\) 0 0
\(771\) 5.14822i 0.185409i
\(772\) 0 0
\(773\) −21.7270 + 12.5441i −0.781465 + 0.451179i −0.836949 0.547281i \(-0.815663\pi\)
0.0554845 + 0.998460i \(0.482330\pi\)
\(774\) 0 0
\(775\) −38.3632 + 66.4470i −1.37805 + 2.38685i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −20.9691 12.1065i −0.751297 0.433761i
\(780\) 0 0
\(781\) 31.1809 + 54.0069i 1.11574 + 1.93252i
\(782\) 0 0
\(783\) 2.46054 0.0879327
\(784\) 0 0
\(785\) −46.7996 −1.67035
\(786\) 0 0
\(787\) 2.23565 + 3.87226i 0.0796924 + 0.138031i 0.903117 0.429394i \(-0.141273\pi\)
−0.823425 + 0.567425i \(0.807940\pi\)
\(788\) 0 0
\(789\) 0.0679848 + 0.0392511i 0.00242032 + 0.00139737i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −6.54918 + 11.3435i −0.232568 + 0.402820i
\(794\) 0 0
\(795\) 15.7186 9.07516i 0.557483 0.321863i
\(796\) 0 0
\(797\) 6.62320i 0.234606i −0.993096 0.117303i \(-0.962575\pi\)
0.993096 0.117303i \(-0.0374248\pi\)
\(798\) 0 0
\(799\) 14.8133i 0.524056i