Properties

Label 1078.2.c.c.1077.3
Level $1078$
Weight $2$
Character 1078.1077
Analytic conductor $8.608$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 32x^{14} + 512x^{12} - 2272x^{10} - 1087x^{8} + 72448x^{6} + 819200x^{4} + 1310720x^{2} + 1048576 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1077.3
Root \(-0.807586 - 1.94969i\) of defining polynomial
Character \(\chi\) \(=\) 1078.1077
Dual form 1078.2.c.c.1077.14

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -0.765367i q^{3} -1.00000 q^{4} -2.05161i q^{5} -0.765367 q^{6} +1.00000i q^{8} +2.41421 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -0.765367i q^{3} -1.00000 q^{4} -2.05161i q^{5} -0.765367 q^{6} +1.00000i q^{8} +2.41421 q^{9} -2.05161 q^{10} +(2.49222 - 2.18834i) q^{11} +0.765367i q^{12} +6.59694 q^{13} -1.57024 q^{15} +1.00000 q^{16} -3.61108 q^{17} -2.41421i q^{18} -0.878539 q^{19} +2.05161i q^{20} +(-2.18834 - 2.49222i) q^{22} +6.61931 q^{23} +0.765367 q^{24} +0.790886 q^{25} -6.59694i q^{26} -4.14386i q^{27} +6.18955i q^{29} +1.57024i q^{30} -6.48376i q^{31} -1.00000i q^{32} +(-1.67488 - 1.90747i) q^{33} +3.61108i q^{34} -2.41421 q^{36} -11.0491 q^{37} +0.878539i q^{38} -5.04908i q^{39} +2.05161 q^{40} -2.36864 q^{41} +7.81288i q^{43} +(-2.49222 + 2.18834i) q^{44} -4.95303i q^{45} -6.61931i q^{46} -5.74713i q^{47} -0.765367i q^{48} -0.790886i q^{50} +2.76380i q^{51} -6.59694 q^{52} +0.429764 q^{53} -4.14386 q^{54} +(-4.48962 - 5.11308i) q^{55} +0.672404i q^{57} +6.18955 q^{58} -3.21844i q^{59} +1.57024 q^{60} -11.3342 q^{61} -6.48376 q^{62} -1.00000 q^{64} -13.5344i q^{65} +(-1.90747 + 1.67488i) q^{66} +2.96246 q^{67} +3.61108 q^{68} -5.06620i q^{69} -2.13403 q^{71} +2.41421i q^{72} -10.8252 q^{73} +11.0491i q^{74} -0.605318i q^{75} +0.878539 q^{76} -5.04908 q^{78} +8.48528i q^{79} -2.05161i q^{80} +4.07107 q^{81} +2.36864i q^{82} +12.3153 q^{83} +7.40854i q^{85} +7.81288 q^{86} +4.73728 q^{87} +(2.18834 + 2.49222i) q^{88} +6.72825i q^{89} -4.95303 q^{90} -6.61931 q^{92} -4.96246 q^{93} -5.74713 q^{94} +1.80242i q^{95} -0.765367 q^{96} +9.23880i q^{97} +(6.01676 - 5.28311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} + 16 q^{9} + 16 q^{11} + 16 q^{16} - 8 q^{22} - 16 q^{23} - 64 q^{25} - 16 q^{36} - 80 q^{37} - 16 q^{44} + 32 q^{53} - 48 q^{58} - 16 q^{64} + 16 q^{67} - 48 q^{71} + 16 q^{78} - 48 q^{81} + 32 q^{86} + 8 q^{88} + 16 q^{92} - 48 q^{93} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.765367i 0.441885i −0.975287 0.220942i \(-0.929087\pi\)
0.975287 0.220942i \(-0.0709133\pi\)
\(4\) −1.00000 −0.500000
\(5\) 2.05161i 0.917509i −0.888563 0.458755i \(-0.848296\pi\)
0.888563 0.458755i \(-0.151704\pi\)
\(6\) −0.765367 −0.312460
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 2.41421 0.804738
\(10\) −2.05161 −0.648777
\(11\) 2.49222 2.18834i 0.751434 0.659808i
\(12\) 0.765367i 0.220942i
\(13\) 6.59694 1.82966 0.914830 0.403838i \(-0.132324\pi\)
0.914830 + 0.403838i \(0.132324\pi\)
\(14\) 0 0
\(15\) −1.57024 −0.405433
\(16\) 1.00000 0.250000
\(17\) −3.61108 −0.875815 −0.437908 0.899020i \(-0.644280\pi\)
−0.437908 + 0.899020i \(0.644280\pi\)
\(18\) 2.41421i 0.569036i
\(19\) −0.878539 −0.201551 −0.100775 0.994909i \(-0.532132\pi\)
−0.100775 + 0.994909i \(0.532132\pi\)
\(20\) 2.05161i 0.458755i
\(21\) 0 0
\(22\) −2.18834 2.49222i −0.466555 0.531344i
\(23\) 6.61931 1.38022 0.690111 0.723703i \(-0.257562\pi\)
0.690111 + 0.723703i \(0.257562\pi\)
\(24\) 0.765367 0.156230
\(25\) 0.790886 0.158177
\(26\) 6.59694i 1.29377i
\(27\) 4.14386i 0.797486i
\(28\) 0 0
\(29\) 6.18955i 1.14937i 0.818375 + 0.574685i \(0.194876\pi\)
−0.818375 + 0.574685i \(0.805124\pi\)
\(30\) 1.57024i 0.286685i
\(31\) 6.48376i 1.16452i −0.813003 0.582259i \(-0.802169\pi\)
0.813003 0.582259i \(-0.197831\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −1.67488 1.90747i −0.291559 0.332047i
\(34\) 3.61108i 0.619295i
\(35\) 0 0
\(36\) −2.41421 −0.402369
\(37\) −11.0491 −1.81646 −0.908229 0.418475i \(-0.862565\pi\)
−0.908229 + 0.418475i \(0.862565\pi\)
\(38\) 0.878539i 0.142518i
\(39\) 5.04908i 0.808499i
\(40\) 2.05161 0.324388
\(41\) −2.36864 −0.369919 −0.184960 0.982746i \(-0.559215\pi\)
−0.184960 + 0.982746i \(0.559215\pi\)
\(42\) 0 0
\(43\) 7.81288i 1.19145i 0.803188 + 0.595726i \(0.203136\pi\)
−0.803188 + 0.595726i \(0.796864\pi\)
\(44\) −2.49222 + 2.18834i −0.375717 + 0.329904i
\(45\) 4.95303i 0.738354i
\(46\) 6.61931i 0.975964i
\(47\) 5.74713i 0.838305i −0.907916 0.419153i \(-0.862327\pi\)
0.907916 0.419153i \(-0.137673\pi\)
\(48\) 0.765367i 0.110471i
\(49\) 0 0
\(50\) 0.790886i 0.111848i
\(51\) 2.76380i 0.387009i
\(52\) −6.59694 −0.914830
\(53\) 0.429764 0.0590326 0.0295163 0.999564i \(-0.490603\pi\)
0.0295163 + 0.999564i \(0.490603\pi\)
\(54\) −4.14386 −0.563908
\(55\) −4.48962 5.11308i −0.605380 0.689448i
\(56\) 0 0
\(57\) 0.672404i 0.0890621i
\(58\) 6.18955 0.812728
\(59\) 3.21844i 0.419006i −0.977808 0.209503i \(-0.932815\pi\)
0.977808 0.209503i \(-0.0671845\pi\)
\(60\) 1.57024 0.202717
\(61\) −11.3342 −1.45120 −0.725599 0.688118i \(-0.758437\pi\)
−0.725599 + 0.688118i \(0.758437\pi\)
\(62\) −6.48376 −0.823439
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 13.5344i 1.67873i
\(66\) −1.90747 + 1.67488i −0.234793 + 0.206163i
\(67\) 2.96246 0.361922 0.180961 0.983490i \(-0.442079\pi\)
0.180961 + 0.983490i \(0.442079\pi\)
\(68\) 3.61108 0.437908
\(69\) 5.06620i 0.609899i
\(70\) 0 0
\(71\) −2.13403 −0.253263 −0.126631 0.991950i \(-0.540417\pi\)
−0.126631 + 0.991950i \(0.540417\pi\)
\(72\) 2.41421i 0.284518i
\(73\) −10.8252 −1.26700 −0.633499 0.773744i \(-0.718382\pi\)
−0.633499 + 0.773744i \(0.718382\pi\)
\(74\) 11.0491i 1.28443i
\(75\) 0.605318i 0.0698961i
\(76\) 0.878539 0.100775
\(77\) 0 0
\(78\) −5.04908 −0.571695
\(79\) 8.48528i 0.954669i 0.878722 + 0.477334i \(0.158397\pi\)
−0.878722 + 0.477334i \(0.841603\pi\)
\(80\) 2.05161i 0.229377i
\(81\) 4.07107 0.452341
\(82\) 2.36864i 0.261572i
\(83\) 12.3153 1.35178 0.675892 0.737001i \(-0.263759\pi\)
0.675892 + 0.737001i \(0.263759\pi\)
\(84\) 0 0
\(85\) 7.40854i 0.803569i
\(86\) 7.81288 0.842484
\(87\) 4.73728 0.507889
\(88\) 2.18834 + 2.49222i 0.233277 + 0.265672i
\(89\) 6.72825i 0.713193i 0.934258 + 0.356597i \(0.116063\pi\)
−0.934258 + 0.356597i \(0.883937\pi\)
\(90\) −4.95303 −0.522095
\(91\) 0 0
\(92\) −6.61931 −0.690111
\(93\) −4.96246 −0.514583
\(94\) −5.74713 −0.592771
\(95\) 1.80242i 0.184924i
\(96\) −0.765367 −0.0781149
\(97\) 9.23880i 0.938058i 0.883183 + 0.469029i \(0.155396\pi\)
−0.883183 + 0.469029i \(0.844604\pi\)
\(98\) 0 0
\(99\) 6.01676 5.28311i 0.604707 0.530973i
\(100\) −0.790886 −0.0790886
\(101\) 1.85966 0.185043 0.0925216 0.995711i \(-0.470507\pi\)
0.0925216 + 0.995711i \(0.470507\pi\)
\(102\) 2.76380 0.273657
\(103\) 6.71011i 0.661167i 0.943777 + 0.330583i \(0.107245\pi\)
−0.943777 + 0.330583i \(0.892755\pi\)
\(104\) 6.59694i 0.646883i
\(105\) 0 0
\(106\) 0.429764i 0.0417423i
\(107\) 14.7533i 1.42626i −0.701032 0.713130i \(-0.747277\pi\)
0.701032 0.713130i \(-0.252723\pi\)
\(108\) 4.14386i 0.398743i
\(109\) 6.00000i 0.574696i −0.957826 0.287348i \(-0.907226\pi\)
0.957826 0.287348i \(-0.0927736\pi\)
\(110\) −5.11308 + 4.48962i −0.487513 + 0.428068i
\(111\) 8.45660i 0.802665i
\(112\) 0 0
\(113\) −0.597322 −0.0561913 −0.0280956 0.999605i \(-0.508944\pi\)
−0.0280956 + 0.999605i \(0.508944\pi\)
\(114\) 0.672404 0.0629764
\(115\) 13.5803i 1.26637i
\(116\) 6.18955i 0.574685i
\(117\) 15.9264 1.47240
\(118\) −3.21844 −0.296282
\(119\) 0 0
\(120\) 1.57024i 0.143342i
\(121\) 1.42237 10.9077i 0.129306 0.991605i
\(122\) 11.3342i 1.02615i
\(123\) 1.81288i 0.163462i
\(124\) 6.48376i 0.582259i
\(125\) 11.8807i 1.06264i
\(126\) 0 0
\(127\) 7.33002i 0.650434i −0.945639 0.325217i \(-0.894563\pi\)
0.945639 0.325217i \(-0.105437\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 5.97972 0.526485
\(130\) −13.5344 −1.18704
\(131\) −8.82050 −0.770651 −0.385325 0.922781i \(-0.625911\pi\)
−0.385325 + 0.922781i \(0.625911\pi\)
\(132\) 1.67488 + 1.90747i 0.145780 + 0.166024i
\(133\) 0 0
\(134\) 2.96246i 0.255917i
\(135\) −8.50159 −0.731701
\(136\) 3.61108i 0.309647i
\(137\) 3.23620 0.276487 0.138244 0.990398i \(-0.455854\pi\)
0.138244 + 0.990398i \(0.455854\pi\)
\(138\) −5.06620 −0.431264
\(139\) −2.47122 −0.209606 −0.104803 0.994493i \(-0.533421\pi\)
−0.104803 + 0.994493i \(0.533421\pi\)
\(140\) 0 0
\(141\) −4.39866 −0.370434
\(142\) 2.13403i 0.179084i
\(143\) 16.4410 14.4363i 1.37487 1.20723i
\(144\) 2.41421 0.201184
\(145\) 12.6986 1.05456
\(146\) 10.8252i 0.895903i
\(147\) 0 0
\(148\) 11.0491 0.908229
\(149\) 3.90860i 0.320205i 0.987100 + 0.160103i \(0.0511825\pi\)
−0.987100 + 0.160103i \(0.948817\pi\)
\(150\) −0.605318 −0.0494240
\(151\) 24.1895i 1.96852i 0.176733 + 0.984259i \(0.443447\pi\)
−0.176733 + 0.984259i \(0.556553\pi\)
\(152\) 0.878539i 0.0712589i
\(153\) −8.71792 −0.704802
\(154\) 0 0
\(155\) −13.3022 −1.06846
\(156\) 5.04908i 0.404250i
\(157\) 20.3029i 1.62034i 0.586192 + 0.810172i \(0.300626\pi\)
−0.586192 + 0.810172i \(0.699374\pi\)
\(158\) 8.48528 0.675053
\(159\) 0.328927i 0.0260856i
\(160\) −2.05161 −0.162194
\(161\) 0 0
\(162\) 4.07107i 0.319853i
\(163\) −13.2606 −1.03865 −0.519326 0.854576i \(-0.673817\pi\)
−0.519326 + 0.854576i \(0.673817\pi\)
\(164\) 2.36864 0.184960
\(165\) −3.91338 + 3.43620i −0.304656 + 0.267508i
\(166\) 12.3153i 0.955855i
\(167\) 20.4160 1.57984 0.789920 0.613210i \(-0.210122\pi\)
0.789920 + 0.613210i \(0.210122\pi\)
\(168\) 0 0
\(169\) 30.5196 2.34766
\(170\) 7.40854 0.568209
\(171\) −2.12098 −0.162195
\(172\) 7.81288i 0.595726i
\(173\) −15.5762 −1.18423 −0.592117 0.805852i \(-0.701708\pi\)
−0.592117 + 0.805852i \(0.701708\pi\)
\(174\) 4.73728i 0.359132i
\(175\) 0 0
\(176\) 2.49222 2.18834i 0.187859 0.164952i
\(177\) −2.46329 −0.185152
\(178\) 6.72825 0.504304
\(179\) −4.50159 −0.336465 −0.168232 0.985747i \(-0.553806\pi\)
−0.168232 + 0.985747i \(0.553806\pi\)
\(180\) 4.95303i 0.369177i
\(181\) 8.18338i 0.608266i −0.952630 0.304133i \(-0.901633\pi\)
0.952630 0.304133i \(-0.0983667\pi\)
\(182\) 0 0
\(183\) 8.67483i 0.641262i
\(184\) 6.61931i 0.487982i
\(185\) 22.6684i 1.66662i
\(186\) 4.96246i 0.363865i
\(187\) −8.99962 + 7.90226i −0.658118 + 0.577870i
\(188\) 5.74713i 0.419153i
\(189\) 0 0
\(190\) 1.80242 0.130761
\(191\) 10.3662 0.750073 0.375037 0.927010i \(-0.377630\pi\)
0.375037 + 0.927010i \(0.377630\pi\)
\(192\) 0.765367i 0.0552356i
\(193\) 1.62333i 0.116850i 0.998292 + 0.0584248i \(0.0186078\pi\)
−0.998292 + 0.0584248i \(0.981392\pi\)
\(194\) 9.23880 0.663307
\(195\) −10.3587 −0.741805
\(196\) 0 0
\(197\) 4.38713i 0.312570i −0.987712 0.156285i \(-0.950048\pi\)
0.987712 0.156285i \(-0.0499518\pi\)
\(198\) −5.28311 6.01676i −0.375454 0.427593i
\(199\) 20.0640i 1.42230i 0.703040 + 0.711151i \(0.251826\pi\)
−0.703040 + 0.711151i \(0.748174\pi\)
\(200\) 0.790886i 0.0559241i
\(201\) 2.26737i 0.159928i
\(202\) 1.85966i 0.130845i
\(203\) 0 0
\(204\) 2.76380i 0.193505i
\(205\) 4.85953i 0.339404i
\(206\) 6.71011 0.467515
\(207\) 15.9804 1.11072
\(208\) 6.59694 0.457415
\(209\) −2.18952 + 1.92254i −0.151452 + 0.132985i
\(210\) 0 0
\(211\) 8.56380i 0.589556i −0.955566 0.294778i \(-0.904754\pi\)
0.955566 0.294778i \(-0.0952457\pi\)
\(212\) −0.429764 −0.0295163
\(213\) 1.63332i 0.111913i
\(214\) −14.7533 −1.00852
\(215\) 16.0290 1.09317
\(216\) 4.14386 0.281954
\(217\) 0 0
\(218\) −6.00000 −0.406371
\(219\) 8.28528i 0.559867i
\(220\) 4.48962 + 5.11308i 0.302690 + 0.344724i
\(221\) −23.8221 −1.60245
\(222\) 8.45660 0.567570
\(223\) 8.24084i 0.551848i −0.961180 0.275924i \(-0.911016\pi\)
0.961180 0.275924i \(-0.0889837\pi\)
\(224\) 0 0
\(225\) 1.90937 0.127291
\(226\) 0.597322i 0.0397332i
\(227\) 27.4795 1.82388 0.911938 0.410329i \(-0.134586\pi\)
0.911938 + 0.410329i \(0.134586\pi\)
\(228\) 0.672404i 0.0445311i
\(229\) 0.104343i 0.00689519i −0.999994 0.00344759i \(-0.998903\pi\)
0.999994 0.00344759i \(-0.00109741\pi\)
\(230\) −13.5803 −0.895456
\(231\) 0 0
\(232\) −6.18955 −0.406364
\(233\) 15.1577i 0.993013i 0.868033 + 0.496507i \(0.165384\pi\)
−0.868033 + 0.496507i \(0.834616\pi\)
\(234\) 15.9264i 1.04114i
\(235\) −11.7909 −0.769153
\(236\) 3.21844i 0.209503i
\(237\) 6.49435 0.421854
\(238\) 0 0
\(239\) 25.9135i 1.67620i −0.545515 0.838101i \(-0.683666\pi\)
0.545515 0.838101i \(-0.316334\pi\)
\(240\) −1.57024 −0.101358
\(241\) −7.31108 −0.470948 −0.235474 0.971881i \(-0.575664\pi\)
−0.235474 + 0.971881i \(0.575664\pi\)
\(242\) −10.9077 1.42237i −0.701170 0.0914334i
\(243\) 15.5474i 0.997369i
\(244\) 11.3342 0.725599
\(245\) 0 0
\(246\) 1.81288 0.115585
\(247\) −5.79566 −0.368769
\(248\) 6.48376 0.411719
\(249\) 9.42575i 0.597333i
\(250\) −11.8807 −0.751399
\(251\) 10.0161i 0.632208i 0.948724 + 0.316104i \(0.102375\pi\)
−0.948724 + 0.316104i \(0.897625\pi\)
\(252\) 0 0
\(253\) 16.4968 14.4853i 1.03715 0.910682i
\(254\) −7.33002 −0.459926
\(255\) 5.67025 0.355085
\(256\) 1.00000 0.0625000
\(257\) 17.5115i 1.09234i 0.837674 + 0.546170i \(0.183915\pi\)
−0.837674 + 0.546170i \(0.816085\pi\)
\(258\) 5.97972i 0.372281i
\(259\) 0 0
\(260\) 13.5344i 0.839365i
\(261\) 14.9429i 0.924942i
\(262\) 8.82050i 0.544932i
\(263\) 8.48528i 0.523225i 0.965173 + 0.261612i \(0.0842542\pi\)
−0.965173 + 0.261612i \(0.915746\pi\)
\(264\) 1.90747 1.67488i 0.117396 0.103082i
\(265\) 0.881709i 0.0541629i
\(266\) 0 0
\(267\) 5.14958 0.315149
\(268\) −2.96246 −0.180961
\(269\) 6.75523i 0.411873i 0.978565 + 0.205937i \(0.0660241\pi\)
−0.978565 + 0.205937i \(0.933976\pi\)
\(270\) 8.50159i 0.517391i
\(271\) 19.5432 1.18716 0.593581 0.804774i \(-0.297714\pi\)
0.593581 + 0.804774i \(0.297714\pi\)
\(272\) −3.61108 −0.218954
\(273\) 0 0
\(274\) 3.23620i 0.195506i
\(275\) 1.97107 1.73072i 0.118860 0.104367i
\(276\) 5.06620i 0.304950i
\(277\) 26.6748i 1.60274i −0.598172 0.801368i \(-0.704106\pi\)
0.598172 0.801368i \(-0.295894\pi\)
\(278\) 2.47122i 0.148214i
\(279\) 15.6532i 0.937132i
\(280\) 0 0
\(281\) 20.9533i 1.24997i 0.780636 + 0.624986i \(0.214895\pi\)
−0.780636 + 0.624986i \(0.785105\pi\)
\(282\) 4.39866i 0.261937i
\(283\) −10.0629 −0.598180 −0.299090 0.954225i \(-0.596683\pi\)
−0.299090 + 0.954225i \(0.596683\pi\)
\(284\) 2.13403 0.126631
\(285\) 1.37951 0.0817153
\(286\) −14.4363 16.4410i −0.853637 0.972180i
\(287\) 0 0
\(288\) 2.41421i 0.142259i
\(289\) −3.96011 −0.232947
\(290\) 12.6986i 0.745685i
\(291\) 7.07107 0.414513
\(292\) 10.8252 0.633499
\(293\) 29.6429 1.73176 0.865879 0.500253i \(-0.166760\pi\)
0.865879 + 0.500253i \(0.166760\pi\)
\(294\) 0 0
\(295\) −6.60300 −0.384442
\(296\) 11.0491i 0.642215i
\(297\) −9.06816 10.3274i −0.526188 0.599258i
\(298\) 3.90860 0.226419
\(299\) 43.6672 2.52534
\(300\) 0.605318i 0.0349480i
\(301\) 0 0
\(302\) 24.1895 1.39195
\(303\) 1.42332i 0.0817677i
\(304\) −0.878539 −0.0503876
\(305\) 23.2534i 1.33149i
\(306\) 8.71792i 0.498370i
\(307\) −16.1877 −0.923883 −0.461941 0.886910i \(-0.652847\pi\)
−0.461941 + 0.886910i \(0.652847\pi\)
\(308\) 0 0
\(309\) 5.13569 0.292159
\(310\) 13.3022i 0.755513i
\(311\) 1.42639i 0.0808832i 0.999182 + 0.0404416i \(0.0128765\pi\)
−0.999182 + 0.0404416i \(0.987124\pi\)
\(312\) 5.04908 0.285848
\(313\) 11.5468i 0.652664i 0.945255 + 0.326332i \(0.105813\pi\)
−0.945255 + 0.326332i \(0.894187\pi\)
\(314\) 20.3029 1.14576
\(315\) 0 0
\(316\) 8.48528i 0.477334i
\(317\) 31.7239 1.78179 0.890896 0.454207i \(-0.150077\pi\)
0.890896 + 0.454207i \(0.150077\pi\)
\(318\) −0.328927 −0.0184453
\(319\) 13.5448 + 15.4257i 0.758364 + 0.863676i
\(320\) 2.05161i 0.114689i
\(321\) −11.2917 −0.630242
\(322\) 0 0
\(323\) 3.17247 0.176521
\(324\) −4.07107 −0.226170
\(325\) 5.21742 0.289411
\(326\) 13.2606i 0.734438i
\(327\) −4.59220 −0.253949
\(328\) 2.36864i 0.130786i
\(329\) 0 0
\(330\) 3.43620 + 3.91338i 0.189157 + 0.215425i
\(331\) 31.9239 1.75470 0.877348 0.479854i \(-0.159310\pi\)
0.877348 + 0.479854i \(0.159310\pi\)
\(332\) −12.3153 −0.675892
\(333\) −26.6748 −1.46177
\(334\) 20.4160i 1.11712i
\(335\) 6.07782i 0.332067i
\(336\) 0 0
\(337\) 1.40854i 0.0767278i −0.999264 0.0383639i \(-0.987785\pi\)
0.999264 0.0383639i \(-0.0122146\pi\)
\(338\) 30.5196i 1.66005i
\(339\) 0.457170i 0.0248301i
\(340\) 7.40854i 0.401784i
\(341\) −14.1887 16.1590i −0.768359 0.875059i
\(342\) 2.12098i 0.114689i
\(343\) 0 0
\(344\) −7.81288 −0.421242
\(345\) −10.3939 −0.559588
\(346\) 15.5762i 0.837380i
\(347\) 11.0386i 0.592584i 0.955097 + 0.296292i \(0.0957502\pi\)
−0.955097 + 0.296292i \(0.904250\pi\)
\(348\) −4.73728 −0.253945
\(349\) −15.5762 −0.833773 −0.416887 0.908958i \(-0.636879\pi\)
−0.416887 + 0.908958i \(0.636879\pi\)
\(350\) 0 0
\(351\) 27.3368i 1.45913i
\(352\) −2.18834 2.49222i −0.116639 0.132836i
\(353\) 6.28791i 0.334672i 0.985900 + 0.167336i \(0.0535165\pi\)
−0.985900 + 0.167336i \(0.946484\pi\)
\(354\) 2.46329i 0.130922i
\(355\) 4.37821i 0.232371i
\(356\) 6.72825i 0.356597i
\(357\) 0 0
\(358\) 4.50159i 0.237917i
\(359\) 10.2877i 0.542964i 0.962443 + 0.271482i \(0.0875138\pi\)
−0.962443 + 0.271482i \(0.912486\pi\)
\(360\) 4.95303 0.261048
\(361\) −18.2282 −0.959377
\(362\) −8.18338 −0.430109
\(363\) −8.34836 1.08864i −0.438175 0.0571385i
\(364\) 0 0
\(365\) 22.2092i 1.16248i
\(366\) 8.67483 0.453441
\(367\) 4.52152i 0.236021i −0.993012 0.118011i \(-0.962348\pi\)
0.993012 0.118011i \(-0.0376517\pi\)
\(368\) 6.61931 0.345056
\(369\) −5.71840 −0.297688
\(370\) 22.6684 1.17848
\(371\) 0 0
\(372\) 4.96246 0.257291
\(373\) 19.7239i 1.02127i −0.859799 0.510633i \(-0.829411\pi\)
0.859799 0.510633i \(-0.170589\pi\)
\(374\) 7.90226 + 8.99962i 0.408616 + 0.465359i
\(375\) −9.09306 −0.469564
\(376\) 5.74713 0.296386
\(377\) 40.8321i 2.10296i
\(378\) 0 0
\(379\) −35.6268 −1.83003 −0.915014 0.403423i \(-0.867820\pi\)
−0.915014 + 0.403423i \(0.867820\pi\)
\(380\) 1.80242i 0.0924622i
\(381\) −5.61016 −0.287417
\(382\) 10.3662i 0.530382i
\(383\) 21.6373i 1.10561i −0.833310 0.552806i \(-0.813557\pi\)
0.833310 0.552806i \(-0.186443\pi\)
\(384\) 0.765367 0.0390575
\(385\) 0 0
\(386\) 1.62333 0.0826252
\(387\) 18.8620i 0.958807i
\(388\) 9.23880i 0.469029i
\(389\) −8.64698 −0.438419 −0.219210 0.975678i \(-0.570348\pi\)
−0.219210 + 0.975678i \(0.570348\pi\)
\(390\) 10.3587i 0.524536i
\(391\) −23.9029 −1.20882
\(392\) 0 0
\(393\) 6.75092i 0.340539i
\(394\) −4.38713 −0.221020
\(395\) 17.4085 0.875917
\(396\) −6.01676 + 5.28311i −0.302354 + 0.265486i
\(397\) 36.1718i 1.81541i 0.419608 + 0.907705i \(0.362168\pi\)
−0.419608 + 0.907705i \(0.637832\pi\)
\(398\) 20.0640 1.00572
\(399\) 0 0
\(400\) 0.790886 0.0395443
\(401\) −8.99356 −0.449117 −0.224558 0.974461i \(-0.572094\pi\)
−0.224558 + 0.974461i \(0.572094\pi\)
\(402\) −2.26737 −0.113086
\(403\) 42.7730i 2.13067i
\(404\) −1.85966 −0.0925216
\(405\) 8.35225i 0.415027i
\(406\) 0 0
\(407\) −27.5368 + 24.1791i −1.36495 + 1.19851i
\(408\) −2.76380 −0.136829
\(409\) −9.58279 −0.473839 −0.236919 0.971529i \(-0.576138\pi\)
−0.236919 + 0.971529i \(0.576138\pi\)
\(410\) 4.85953 0.239995
\(411\) 2.47688i 0.122175i
\(412\) 6.71011i 0.330583i
\(413\) 0 0
\(414\) 15.9804i 0.785396i
\(415\) 25.2663i 1.24027i
\(416\) 6.59694i 0.323441i
\(417\) 1.89139i 0.0926218i
\(418\) 1.92254 + 2.18952i 0.0940344 + 0.107093i
\(419\) 37.9064i 1.85185i 0.377709 + 0.925924i \(0.376712\pi\)
−0.377709 + 0.925924i \(0.623288\pi\)
\(420\) 0 0
\(421\) 2.88394 0.140555 0.0702774 0.997527i \(-0.477612\pi\)
0.0702774 + 0.997527i \(0.477612\pi\)
\(422\) −8.56380 −0.416879
\(423\) 13.8748i 0.674616i
\(424\) 0.429764i 0.0208712i
\(425\) −2.85595 −0.138534
\(426\) 1.63332 0.0791345
\(427\) 0 0
\(428\) 14.7533i 0.713130i
\(429\) −11.0491 12.5834i −0.533454 0.607534i
\(430\) 16.0290i 0.772987i
\(431\) 32.4068i 1.56098i −0.625169 0.780490i \(-0.714970\pi\)
0.625169 0.780490i \(-0.285030\pi\)
\(432\) 4.14386i 0.199372i
\(433\) 10.2319i 0.491714i 0.969306 + 0.245857i \(0.0790694\pi\)
−0.969306 + 0.245857i \(0.920931\pi\)
\(434\) 0 0
\(435\) 9.71905i 0.465993i
\(436\) 6.00000i 0.287348i
\(437\) −5.81532 −0.278185
\(438\) 8.28528 0.395886
\(439\) −28.8726 −1.37802 −0.689008 0.724754i \(-0.741953\pi\)
−0.689008 + 0.724754i \(0.741953\pi\)
\(440\) 5.11308 4.48962i 0.243757 0.214034i
\(441\) 0 0
\(442\) 23.8221i 1.13310i
\(443\) −8.56036 −0.406715 −0.203358 0.979105i \(-0.565185\pi\)
−0.203358 + 0.979105i \(0.565185\pi\)
\(444\) 8.45660i 0.401332i
\(445\) 13.8038 0.654361
\(446\) −8.24084 −0.390215
\(447\) 2.99152 0.141494
\(448\) 0 0
\(449\) −10.8089 −0.510102 −0.255051 0.966928i \(-0.582092\pi\)
−0.255051 + 0.966928i \(0.582092\pi\)
\(450\) 1.90937i 0.0900084i
\(451\) −5.90318 + 5.18338i −0.277970 + 0.244076i
\(452\) 0.597322 0.0280956
\(453\) 18.5139 0.869858
\(454\) 27.4795i 1.28967i
\(455\) 0 0
\(456\) −0.672404 −0.0314882
\(457\) 24.3896i 1.14090i 0.821334 + 0.570448i \(0.193230\pi\)
−0.821334 + 0.570448i \(0.806770\pi\)
\(458\) −0.104343 −0.00487563
\(459\) 14.9638i 0.698451i
\(460\) 13.5803i 0.633183i
\(461\) −1.13186 −0.0527158 −0.0263579 0.999653i \(-0.508391\pi\)
−0.0263579 + 0.999653i \(0.508391\pi\)
\(462\) 0 0
\(463\) 6.38388 0.296684 0.148342 0.988936i \(-0.452606\pi\)
0.148342 + 0.988936i \(0.452606\pi\)
\(464\) 6.18955i 0.287343i
\(465\) 10.1810i 0.472135i
\(466\) 15.1577 0.702166
\(467\) 35.6840i 1.65126i −0.564213 0.825629i \(-0.690820\pi\)
0.564213 0.825629i \(-0.309180\pi\)
\(468\) −15.9264 −0.736199
\(469\) 0 0
\(470\) 11.7909i 0.543873i
\(471\) 15.5391 0.716006
\(472\) 3.21844 0.148141
\(473\) 17.0972 + 19.4714i 0.786130 + 0.895298i
\(474\) 6.49435i 0.298296i
\(475\) −0.694824 −0.0318807
\(476\) 0 0
\(477\) 1.03754 0.0475058
\(478\) −25.9135 −1.18525
\(479\) −11.5819 −0.529189 −0.264595 0.964360i \(-0.585238\pi\)
−0.264595 + 0.964360i \(0.585238\pi\)
\(480\) 1.57024i 0.0716712i
\(481\) −72.8901 −3.32350
\(482\) 7.31108i 0.333011i
\(483\) 0 0
\(484\) −1.42237 + 10.9077i −0.0646532 + 0.495802i
\(485\) 18.9544 0.860676
\(486\) −15.5474 −0.705246
\(487\) 40.0638 1.81546 0.907732 0.419550i \(-0.137812\pi\)
0.907732 + 0.419550i \(0.137812\pi\)
\(488\) 11.3342i 0.513076i
\(489\) 10.1492i 0.458964i
\(490\) 0 0
\(491\) 19.7876i 0.893003i −0.894783 0.446502i \(-0.852670\pi\)
0.894783 0.446502i \(-0.147330\pi\)
\(492\) 1.81288i 0.0817308i
\(493\) 22.3510i 1.00664i
\(494\) 5.79566i 0.260759i
\(495\) −10.8389 12.3441i −0.487172 0.554825i
\(496\) 6.48376i 0.291130i
\(497\) 0 0
\(498\) −9.42575 −0.422378
\(499\) −26.6553 −1.19325 −0.596627 0.802519i \(-0.703493\pi\)
−0.596627 + 0.802519i \(0.703493\pi\)
\(500\) 11.8807i 0.531319i
\(501\) 15.6258i 0.698107i
\(502\) 10.0161 0.447039
\(503\) 10.9142 0.486638 0.243319 0.969946i \(-0.421764\pi\)
0.243319 + 0.969946i \(0.421764\pi\)
\(504\) 0 0
\(505\) 3.81530i 0.169779i
\(506\) −14.4853 16.4968i −0.643949 0.733373i
\(507\) 23.3587i 1.03739i
\(508\) 7.33002i 0.325217i
\(509\) 22.4340i 0.994369i 0.867645 + 0.497184i \(0.165633\pi\)
−0.867645 + 0.497184i \(0.834367\pi\)
\(510\) 5.67025i 0.251083i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 3.64054i 0.160734i
\(514\) 17.5115 0.772401
\(515\) 13.7665 0.606626
\(516\) −5.97972 −0.263242
\(517\) −12.5767 14.3231i −0.553121 0.629931i
\(518\) 0 0
\(519\) 11.9215i 0.523295i
\(520\) 13.5344 0.593521
\(521\) 39.2106i 1.71785i 0.512102 + 0.858925i \(0.328867\pi\)
−0.512102 + 0.858925i \(0.671133\pi\)
\(522\) 14.9429 0.654033
\(523\) 18.0899 0.791015 0.395508 0.918463i \(-0.370569\pi\)
0.395508 + 0.918463i \(0.370569\pi\)
\(524\) 8.82050 0.385325
\(525\) 0 0
\(526\) 8.48528 0.369976
\(527\) 23.4134i 1.01990i
\(528\) −1.67488 1.90747i −0.0728898 0.0830118i
\(529\) 20.8153 0.905013
\(530\) −0.881709 −0.0382990
\(531\) 7.77001i 0.337190i
\(532\) 0 0
\(533\) −15.6258 −0.676827
\(534\) 5.14958i 0.222844i
\(535\) −30.2681 −1.30861
\(536\) 2.96246i 0.127959i
\(537\) 3.44537i 0.148679i
\(538\) 6.75523 0.291238
\(539\) 0 0
\(540\) 8.50159 0.365850
\(541\) 9.62575i 0.413843i 0.978357 + 0.206922i \(0.0663446\pi\)
−0.978357 + 0.206922i \(0.933655\pi\)
\(542\) 19.5432i 0.839450i
\(543\) −6.26328 −0.268783
\(544\) 3.61108i 0.154824i
\(545\) −12.3097 −0.527289
\(546\) 0 0
\(547\) 10.2834i 0.439685i −0.975535 0.219843i \(-0.929446\pi\)
0.975535 0.219843i \(-0.0705544\pi\)
\(548\) −3.23620 −0.138244
\(549\) −27.3632 −1.16783
\(550\) −1.73072 1.97107i −0.0737983 0.0840465i
\(551\) 5.43776i 0.231656i
\(552\) 5.06620 0.215632
\(553\) 0 0
\(554\) −26.6748 −1.13330
\(555\) 17.3497 0.736452
\(556\) 2.47122 0.104803
\(557\) 37.2306i 1.57751i −0.614707 0.788755i \(-0.710726\pi\)
0.614707 0.788755i \(-0.289274\pi\)
\(558\) −15.6532 −0.662652
\(559\) 51.5411i 2.17995i
\(560\) 0 0
\(561\) 6.04812 + 6.88801i 0.255352 + 0.290812i
\(562\) 20.9533 0.883864
\(563\) −16.1877 −0.682232 −0.341116 0.940021i \(-0.610805\pi\)
−0.341116 + 0.940021i \(0.610805\pi\)
\(564\) 4.39866 0.185217
\(565\) 1.22547i 0.0515560i
\(566\) 10.0629i 0.422977i
\(567\) 0 0
\(568\) 2.13403i 0.0895420i
\(569\) 30.4901i 1.27821i −0.769118 0.639106i \(-0.779304\pi\)
0.769118 0.639106i \(-0.220696\pi\)
\(570\) 1.37951i 0.0577815i
\(571\) 40.4877i 1.69436i 0.531308 + 0.847179i \(0.321701\pi\)
−0.531308 + 0.847179i \(0.678299\pi\)
\(572\) −16.4410 + 14.4363i −0.687435 + 0.603613i
\(573\) 7.93396i 0.331446i
\(574\) 0 0
\(575\) 5.23512 0.218320
\(576\) −2.41421 −0.100592
\(577\) 25.5604i 1.06409i −0.846715 0.532047i \(-0.821423\pi\)
0.846715 0.532047i \(-0.178577\pi\)
\(578\) 3.96011i 0.164719i
\(579\) 1.24244 0.0516341
\(580\) −12.6986 −0.527279
\(581\) 0 0
\(582\) 7.07107i 0.293105i
\(583\) 1.07107 0.940467i 0.0443591 0.0389502i
\(584\) 10.8252i 0.447951i
\(585\) 32.6748i 1.35094i
\(586\) 29.6429i 1.22454i
\(587\) 7.18094i 0.296389i −0.988958 0.148195i \(-0.952654\pi\)
0.988958 0.148195i \(-0.0473462\pi\)
\(588\) 0 0
\(589\) 5.69624i 0.234709i
\(590\) 6.60300i 0.271841i
\(591\) −3.35776 −0.138120
\(592\) −11.0491 −0.454114
\(593\) −19.7771 −0.812150 −0.406075 0.913840i \(-0.633103\pi\)
−0.406075 + 0.913840i \(0.633103\pi\)
\(594\) −10.3274 + 9.06816i −0.423740 + 0.372071i
\(595\) 0 0
\(596\) 3.90860i 0.160103i
\(597\) 15.3563 0.628493
\(598\) 43.6672i 1.78568i
\(599\) −13.7598 −0.562210 −0.281105 0.959677i \(-0.590701\pi\)
−0.281105 + 0.959677i \(0.590701\pi\)
\(600\) 0.605318 0.0247120
\(601\) −11.0384 −0.450266 −0.225133 0.974328i \(-0.572282\pi\)
−0.225133 + 0.974328i \(0.572282\pi\)
\(602\) 0 0
\(603\) 7.15201 0.291252
\(604\) 24.1895i 0.984259i
\(605\) −22.3783 2.91815i −0.909806 0.118640i
\(606\) −1.42332 −0.0578185
\(607\) 11.8144 0.479530 0.239765 0.970831i \(-0.422930\pi\)
0.239765 + 0.970831i \(0.422930\pi\)
\(608\) 0.878539i 0.0356294i
\(609\) 0 0
\(610\) 23.2534 0.941503
\(611\) 37.9135i 1.53381i
\(612\) 8.71792 0.352401
\(613\) 21.1472i 0.854129i −0.904221 0.427064i \(-0.859548\pi\)
0.904221 0.427064i \(-0.140452\pi\)
\(614\) 16.1877i 0.653284i
\(615\) 3.71932 0.149978
\(616\) 0 0
\(617\) −43.8743 −1.76631 −0.883157 0.469078i \(-0.844586\pi\)
−0.883157 + 0.469078i \(0.844586\pi\)
\(618\) 5.13569i 0.206588i
\(619\) 4.76850i 0.191662i 0.995398 + 0.0958310i \(0.0305509\pi\)
−0.995398 + 0.0958310i \(0.969449\pi\)
\(620\) 13.3022 0.534228
\(621\) 27.4295i 1.10071i
\(622\) 1.42639 0.0571931
\(623\) 0 0
\(624\) 5.04908i 0.202125i
\(625\) −20.4201 −0.816803
\(626\) 11.5468 0.461503
\(627\) 1.47145 + 1.67578i 0.0587639 + 0.0669243i
\(628\) 20.3029i 0.810172i
\(629\) 39.8991 1.59088
\(630\) 0 0
\(631\) −6.66195 −0.265208 −0.132604 0.991169i \(-0.542334\pi\)
−0.132604 + 0.991169i \(0.542334\pi\)
\(632\) −8.48528 −0.337526
\(633\) −6.55445 −0.260516
\(634\) 31.7239i 1.25992i
\(635\) −15.0384 −0.596779
\(636\) 0.328927i 0.0130428i
\(637\) 0 0
\(638\) 15.4257 13.5448i 0.610711 0.536244i
\(639\) −5.15201 −0.203810
\(640\) 2.05161 0.0810971
\(641\) −11.5215 −0.455071 −0.227535 0.973770i \(-0.573067\pi\)
−0.227535 + 0.973770i \(0.573067\pi\)
\(642\) 11.2917i 0.445649i
\(643\) 21.7793i 0.858892i −0.903093 0.429446i \(-0.858709\pi\)
0.903093 0.429446i \(-0.141291\pi\)
\(644\) 0 0
\(645\) 12.2681i 0.483055i
\(646\) 3.17247i 0.124819i
\(647\) 17.5615i 0.690413i −0.938527 0.345207i \(-0.887809\pi\)
0.938527 0.345207i \(-0.112191\pi\)
\(648\) 4.07107i 0.159927i
\(649\) −7.04304 8.02109i −0.276463 0.314855i
\(650\) 5.21742i 0.204644i
\(651\) 0 0
\(652\) 13.2606 0.519326
\(653\) 26.4426 1.03478 0.517390 0.855750i \(-0.326904\pi\)
0.517390 + 0.855750i \(0.326904\pi\)
\(654\) 4.59220i 0.179569i
\(655\) 18.0962i 0.707079i
\(656\) −2.36864 −0.0924798
\(657\) −26.1344 −1.01960
\(658\) 0 0
\(659\) 38.9324i 1.51659i 0.651910 + 0.758296i \(0.273968\pi\)
−0.651910 + 0.758296i \(0.726032\pi\)
\(660\) 3.91338 3.43620i 0.152328 0.133754i
\(661\) 11.8914i 0.462521i 0.972892 + 0.231261i \(0.0742850\pi\)
−0.972892 + 0.231261i \(0.925715\pi\)
\(662\) 31.9239i 1.24076i
\(663\) 18.2326i 0.708096i
\(664\) 12.3153i 0.477928i
\(665\) 0 0
\(666\) 26.6748i 1.03363i
\(667\) 40.9706i 1.58639i
\(668\) −20.4160 −0.789920
\(669\) −6.30727 −0.243853
\(670\) −6.07782 −0.234807
\(671\) −28.2474 + 24.8031i −1.09048 + 0.957512i
\(672\) 0 0
\(673\) 17.4386i 0.672210i 0.941825 + 0.336105i \(0.109110\pi\)
−0.941825 + 0.336105i \(0.890890\pi\)
\(674\) −1.40854 −0.0542548
\(675\) 3.27732i 0.126144i
\(676\) −30.5196 −1.17383
\(677\) 41.4300 1.59228 0.796141 0.605111i \(-0.206871\pi\)
0.796141 + 0.605111i \(0.206871\pi\)
\(678\) 0.457170 0.0175575
\(679\) 0 0
\(680\) −7.40854 −0.284104
\(681\) 21.0319i 0.805943i
\(682\) −16.1590 + 14.1887i −0.618760 + 0.543312i
\(683\) 21.4153 0.819433 0.409717 0.912213i \(-0.365628\pi\)
0.409717 + 0.912213i \(0.365628\pi\)
\(684\) 2.12098 0.0810977
\(685\) 6.63943i 0.253679i
\(686\) 0 0
\(687\) −0.0798608 −0.00304688
\(688\) 7.81288i 0.297863i
\(689\) 2.83512 0.108010
\(690\) 10.3939i 0.395688i
\(691\) 13.4791i 0.512769i −0.966575 0.256384i \(-0.917469\pi\)
0.966575 0.256384i \(-0.0825313\pi\)
\(692\) 15.5762 0.592117
\(693\) 0 0
\(694\) 11.0386 0.419020
\(695\) 5.06999i 0.192316i
\(696\) 4.73728i 0.179566i
\(697\) 8.55334 0.323981
\(698\) 15.5762i 0.589567i
\(699\) 11.6012 0.438797
\(700\) 0 0
\(701\) 26.4644i 0.999545i −0.866157 0.499773i \(-0.833417\pi\)
0.866157 0.499773i \(-0.166583\pi\)
\(702\) −27.3368 −1.03176
\(703\) 9.70704 0.366108
\(704\) −2.49222 + 2.18834i −0.0939293 + 0.0824760i
\(705\) 9.02435i 0.339877i
\(706\) 6.28791 0.236649
\(707\) 0 0
\(708\) 2.46329 0.0925761
\(709\) 18.7778 0.705214 0.352607 0.935772i \(-0.385295\pi\)
0.352607 + 0.935772i \(0.385295\pi\)
\(710\) 4.37821 0.164311
\(711\) 20.4853i 0.768258i
\(712\) −6.72825 −0.252152
\(713\) 42.9181i 1.60729i
\(714\) 0 0
\(715\) −29.6177 33.7307i −1.10764 1.26146i
\(716\) 4.50159 0.168232
\(717\) −19.8333 −0.740688
\(718\) 10.2877 0.383934
\(719\) 3.46741i 0.129313i 0.997908 + 0.0646564i \(0.0205951\pi\)
−0.997908 + 0.0646564i \(0.979405\pi\)
\(720\) 4.95303i 0.184589i
\(721\) 0 0
\(722\) 18.2282i 0.678382i
\(723\) 5.59566i 0.208105i
\(724\) 8.18338i 0.304133i
\(725\) 4.89523i 0.181804i
\(726\) −1.08864 + 8.34836i −0.0404030 + 0.309837i
\(727\) 21.6647i 0.803500i −0.915749 0.401750i \(-0.868402\pi\)
0.915749 0.401750i \(-0.131598\pi\)
\(728\) 0 0
\(729\) 0.313708 0.0116188
\(730\) 22.2092 0.821999
\(731\) 28.2129i 1.04349i
\(732\) 8.67483i 0.320631i
\(733\) 14.9085 0.550656 0.275328 0.961350i \(-0.411213\pi\)
0.275328 + 0.961350i \(0.411213\pi\)
\(734\) −4.52152 −0.166892
\(735\) 0 0
\(736\) 6.61931i 0.243991i
\(737\) 7.38311 6.48286i 0.271960 0.238799i
\(738\) 5.71840i 0.210497i
\(739\) 4.75577i 0.174944i 0.996167 + 0.0874719i \(0.0278788\pi\)
−0.996167 + 0.0874719i \(0.972121\pi\)
\(740\) 22.6684i 0.833308i
\(741\) 4.43581i 0.162954i
\(742\) 0 0
\(743\) 14.8792i 0.545864i 0.962033 + 0.272932i \(0.0879934\pi\)
−0.962033 + 0.272932i \(0.912007\pi\)
\(744\) 4.96246i 0.181933i
\(745\) 8.01894 0.293791
\(746\) −19.7239 −0.722144
\(747\) 29.7318 1.08783
\(748\) 8.99962 7.90226i 0.329059 0.288935i
\(749\) 0 0
\(750\) 9.09306i 0.332032i
\(751\) 16.4820 0.601438 0.300719 0.953713i \(-0.402773\pi\)
0.300719 + 0.953713i \(0.402773\pi\)
\(752\) 5.74713i 0.209576i
\(753\) 7.66596 0.279363
\(754\) 40.8321 1.48702
\(755\) 49.6276 1.80613
\(756\) 0 0
\(757\) −3.82008 −0.138843 −0.0694216 0.997587i \(-0.522115\pi\)
−0.0694216 + 0.997587i \(0.522115\pi\)
\(758\) 35.6268i 1.29402i
\(759\) −11.0866 12.6261i −0.402416 0.458299i
\(760\) −1.80242 −0.0653807
\(761\) −1.85400 −0.0672075 −0.0336038 0.999435i \(-0.510698\pi\)
−0.0336038 + 0.999435i \(0.510698\pi\)
\(762\) 5.61016i 0.203235i
\(763\) 0 0
\(764\) −10.3662 −0.375037
\(765\) 17.8858i 0.646662i
\(766\) −21.6373 −0.781786
\(767\) 21.2319i 0.766638i
\(768\) 0.765367i 0.0276178i
\(769\) 8.92308 0.321775 0.160887 0.986973i \(-0.448564\pi\)
0.160887 + 0.986973i \(0.448564\pi\)
\(770\) 0 0
\(771\) 13.4028 0.482688
\(772\) 1.62333i 0.0584248i
\(773\) 20.3267i 0.731099i 0.930792 + 0.365550i \(0.119119\pi\)
−0.930792 + 0.365550i \(0.880881\pi\)
\(774\) 18.8620 0.677979
\(775\) 5.12792i 0.184200i
\(776\) −9.23880 −0.331653
\(777\) 0 0
\(778\) 8.64698i 0.310009i
\(779\) 2.08094 0.0745574
\(780\) 10.3587 0.370903
\(781\) −5.31849 + 4.66998i −0.190310 + 0.167105i
\(782\) 23.9029i 0.854765i
\(783\) 25.6486 0.916607
\(784\) 0 0
\(785\) 41.6536 1.48668
\(786\) 6.75092 0.240797
\(787\) 38.4016 1.36887 0.684435 0.729074i \(-0.260049\pi\)
0.684435 + 0.729074i \(0.260049\pi\)
\(788\) 4.38713i 0.156285i
\(789\) 6.49435 0.231205
\(790\) 17.4085i 0.619367i
\(791\) 0 0
\(792\) 5.28311 + 6.01676i 0.187727 + 0.213796i
\(793\)