Properties

Label 675.2.e.b.451.3
Level $675$
Weight $2$
Character 675.451
Analytic conductor $5.390$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.954288.1
Defining polynomial: \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.3
Root \(1.71903 + 0.211943i\) of defining polynomial
Character \(\chi\) \(=\) 675.451
Dual form 675.2.e.b.226.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.04307 - 1.80664i) q^{2} +(-1.17597 - 2.03684i) q^{4} +(2.04307 - 3.53869i) q^{7} -0.734191 q^{8} +O(q^{10})\) \(q+(1.04307 - 1.80664i) q^{2} +(-1.17597 - 2.03684i) q^{4} +(2.04307 - 3.53869i) q^{7} -0.734191 q^{8} +(-0.675970 + 1.17081i) q^{11} +(0.324030 + 0.561237i) q^{13} +(-4.26210 - 7.38217i) q^{14} +(1.58613 - 2.74726i) q^{16} -1.35194 q^{17} +0.648061 q^{19} +(1.41016 + 2.44247i) q^{22} +(-2.39500 - 4.14827i) q^{23} +1.35194 q^{26} -9.61033 q^{28} +(1.93807 - 3.35683i) q^{29} +(3.84823 + 6.66533i) q^{31} +(-4.04307 - 7.00279i) q^{32} +(-1.41016 + 2.44247i) q^{34} -7.52420 q^{37} +(0.675970 - 1.17081i) q^{38} +(-0.0898394 - 0.155606i) q^{41} +(-0.410161 + 0.710419i) q^{43} +3.17968 q^{44} -9.99258 q^{46} +(-5.45323 + 9.44526i) q^{47} +(-4.84823 - 8.39738i) q^{49} +(0.762100 - 1.32000i) q^{52} +4.17226 q^{53} +(-1.50000 + 2.59808i) q^{56} +(-4.04307 - 7.00279i) q^{58} +(2.08613 + 3.61328i) q^{59} +(1.91016 - 3.30850i) q^{61} +16.0558 q^{62} -10.5242 q^{64} +(4.07097 + 7.05113i) q^{67} +(1.58984 + 2.75368i) q^{68} +6.11644 q^{71} +12.3445 q^{73} +(-7.84823 + 13.5935i) q^{74} +(-0.762100 - 1.32000i) q^{76} +(2.76210 + 4.78410i) q^{77} +(-5.17226 + 8.95862i) q^{79} -0.374833 q^{82} +(6.12920 - 10.6161i) q^{83} +(0.855648 + 1.48203i) q^{86} +(0.496291 - 0.859601i) q^{88} +3.00000 q^{89} +2.64806 q^{91} +(-5.63290 + 9.75648i) q^{92} +(11.3761 + 19.7041i) q^{94} +(-6.79001 + 11.7606i) q^{97} -20.2281 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 5 q^{4} + 5 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 5 q^{4} + 5 q^{7} + 6 q^{8} - 2 q^{11} + 4 q^{13} - 9 q^{14} - 5 q^{16} - 4 q^{17} + 8 q^{19} - 4 q^{22} - 3 q^{23} + 4 q^{26} - 10 q^{28} - 7 q^{29} - 8 q^{31} - 17 q^{32} + 4 q^{34} - 12 q^{37} + 2 q^{38} - 13 q^{41} + 10 q^{43} + 44 q^{44} - 6 q^{46} - 13 q^{47} + 2 q^{49} - 12 q^{52} - 4 q^{53} - 9 q^{56} - 17 q^{58} - 2 q^{59} - q^{61} + 84 q^{62} - 30 q^{64} + 11 q^{67} + 22 q^{68} + 20 q^{71} + 16 q^{73} - 16 q^{74} + 12 q^{76} - 2 q^{79} + 58 q^{82} + 15 q^{83} + 28 q^{86} - 24 q^{88} + 18 q^{89} + 20 q^{91} - 39 q^{92} + 31 q^{94} - 18 q^{97} - 80 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.04307 1.80664i 0.737558 1.27749i −0.216033 0.976386i \(-0.569312\pi\)
0.953592 0.301103i \(-0.0973547\pi\)
\(3\) 0 0
\(4\) −1.17597 2.03684i −0.587985 1.01842i
\(5\) 0 0
\(6\) 0 0
\(7\) 2.04307 3.53869i 0.772206 1.33750i −0.164145 0.986436i \(-0.552487\pi\)
0.936351 0.351064i \(-0.114180\pi\)
\(8\) −0.734191 −0.259576
\(9\) 0 0
\(10\) 0 0
\(11\) −0.675970 + 1.17081i −0.203813 + 0.353014i −0.949754 0.312998i \(-0.898667\pi\)
0.745941 + 0.666012i \(0.232000\pi\)
\(12\) 0 0
\(13\) 0.324030 + 0.561237i 0.0898699 + 0.155659i 0.907456 0.420147i \(-0.138022\pi\)
−0.817586 + 0.575806i \(0.804688\pi\)
\(14\) −4.26210 7.38217i −1.13909 1.97297i
\(15\) 0 0
\(16\) 1.58613 2.74726i 0.396533 0.686815i
\(17\) −1.35194 −0.327893 −0.163947 0.986469i \(-0.552423\pi\)
−0.163947 + 0.986469i \(0.552423\pi\)
\(18\) 0 0
\(19\) 0.648061 0.148675 0.0743377 0.997233i \(-0.476316\pi\)
0.0743377 + 0.997233i \(0.476316\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.41016 + 2.44247i 0.300647 + 0.520736i
\(23\) −2.39500 4.14827i −0.499393 0.864974i 0.500607 0.865675i \(-0.333110\pi\)
−1.00000 0.000700856i \(0.999777\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 1.35194 0.265137
\(27\) 0 0
\(28\) −9.61033 −1.81618
\(29\) 1.93807 3.35683i 0.359890 0.623349i −0.628052 0.778172i \(-0.716147\pi\)
0.987942 + 0.154823i \(0.0494807\pi\)
\(30\) 0 0
\(31\) 3.84823 + 6.66533i 0.691163 + 1.19713i 0.971457 + 0.237215i \(0.0762345\pi\)
−0.280295 + 0.959914i \(0.590432\pi\)
\(32\) −4.04307 7.00279i −0.714720 1.23793i
\(33\) 0 0
\(34\) −1.41016 + 2.44247i −0.241841 + 0.418880i
\(35\) 0 0
\(36\) 0 0
\(37\) −7.52420 −1.23697 −0.618485 0.785796i \(-0.712253\pi\)
−0.618485 + 0.785796i \(0.712253\pi\)
\(38\) 0.675970 1.17081i 0.109657 0.189931i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.0898394 0.155606i −0.0140306 0.0243016i 0.858925 0.512102i \(-0.171133\pi\)
−0.872955 + 0.487800i \(0.837800\pi\)
\(42\) 0 0
\(43\) −0.410161 + 0.710419i −0.0625489 + 0.108338i −0.895604 0.444852i \(-0.853256\pi\)
0.833055 + 0.553190i \(0.186590\pi\)
\(44\) 3.17968 0.479355
\(45\) 0 0
\(46\) −9.99258 −1.47333
\(47\) −5.45323 + 9.44526i −0.795435 + 1.37773i 0.127128 + 0.991886i \(0.459424\pi\)
−0.922563 + 0.385847i \(0.873909\pi\)
\(48\) 0 0
\(49\) −4.84823 8.39738i −0.692604 1.19963i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.762100 1.32000i 0.105684 0.183050i
\(53\) 4.17226 0.573104 0.286552 0.958065i \(-0.407491\pi\)
0.286552 + 0.958065i \(0.407491\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.50000 + 2.59808i −0.200446 + 0.347183i
\(57\) 0 0
\(58\) −4.04307 7.00279i −0.530880 0.919512i
\(59\) 2.08613 + 3.61328i 0.271591 + 0.470409i 0.969269 0.246002i \(-0.0791169\pi\)
−0.697678 + 0.716411i \(0.745784\pi\)
\(60\) 0 0
\(61\) 1.91016 3.30850i 0.244571 0.423609i −0.717440 0.696620i \(-0.754686\pi\)
0.962011 + 0.273011i \(0.0880195\pi\)
\(62\) 16.0558 2.03909
\(63\) 0 0
\(64\) −10.5242 −1.31552
\(65\) 0 0
\(66\) 0 0
\(67\) 4.07097 + 7.05113i 0.497349 + 0.861433i 0.999995 0.00305885i \(-0.000973664\pi\)
−0.502647 + 0.864492i \(0.667640\pi\)
\(68\) 1.58984 + 2.75368i 0.192796 + 0.333933i
\(69\) 0 0
\(70\) 0 0
\(71\) 6.11644 0.725888 0.362944 0.931811i \(-0.381772\pi\)
0.362944 + 0.931811i \(0.381772\pi\)
\(72\) 0 0
\(73\) 12.3445 1.44482 0.722408 0.691467i \(-0.243035\pi\)
0.722408 + 0.691467i \(0.243035\pi\)
\(74\) −7.84823 + 13.5935i −0.912338 + 1.58022i
\(75\) 0 0
\(76\) −0.762100 1.32000i −0.0874188 0.151414i
\(77\) 2.76210 + 4.78410i 0.314770 + 0.545198i
\(78\) 0 0
\(79\) −5.17226 + 8.95862i −0.581925 + 1.00792i 0.413326 + 0.910583i \(0.364367\pi\)
−0.995251 + 0.0973403i \(0.968966\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −0.374833 −0.0413934
\(83\) 6.12920 10.6161i 0.672767 1.16527i −0.304350 0.952560i \(-0.598439\pi\)
0.977116 0.212706i \(-0.0682275\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.855648 + 1.48203i 0.0922669 + 0.159811i
\(87\) 0 0
\(88\) 0.496291 0.859601i 0.0529048 0.0916338i
\(89\) 3.00000 0.317999 0.159000 0.987279i \(-0.449173\pi\)
0.159000 + 0.987279i \(0.449173\pi\)
\(90\) 0 0
\(91\) 2.64806 0.277592
\(92\) −5.63290 + 9.75648i −0.587271 + 1.01718i
\(93\) 0 0
\(94\) 11.3761 + 19.7041i 1.17336 + 2.03232i
\(95\) 0 0
\(96\) 0 0
\(97\) −6.79001 + 11.7606i −0.689421 + 1.19411i 0.282605 + 0.959237i \(0.408802\pi\)
−0.972025 + 0.234876i \(0.924532\pi\)
\(98\) −20.2281 −2.04334
\(99\) 0 0
\(100\) 0 0
\(101\) −0.734191 + 1.27166i −0.0730547 + 0.126535i −0.900239 0.435397i \(-0.856608\pi\)
0.827184 + 0.561931i \(0.189941\pi\)
\(102\) 0 0
\(103\) 3.76210 + 6.51615i 0.370691 + 0.642055i 0.989672 0.143351i \(-0.0457877\pi\)
−0.618981 + 0.785406i \(0.712454\pi\)
\(104\) −0.237900 0.412055i −0.0233280 0.0404053i
\(105\) 0 0
\(106\) 4.35194 7.53778i 0.422698 0.732134i
\(107\) 1.20999 0.116974 0.0584871 0.998288i \(-0.481372\pi\)
0.0584871 + 0.998288i \(0.481372\pi\)
\(108\) 0 0
\(109\) 14.1042 1.35094 0.675469 0.737388i \(-0.263941\pi\)
0.675469 + 0.737388i \(0.263941\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −6.48113 11.2257i −0.612410 1.06072i
\(113\) 5.96227 + 10.3270i 0.560883 + 0.971478i 0.997420 + 0.0717915i \(0.0228716\pi\)
−0.436537 + 0.899687i \(0.643795\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −9.11644 −0.846440
\(117\) 0 0
\(118\) 8.70388 0.801257
\(119\) −2.76210 + 4.78410i −0.253201 + 0.438557i
\(120\) 0 0
\(121\) 4.58613 + 7.94341i 0.416921 + 0.722128i
\(122\) −3.98484 6.90195i −0.360771 0.624873i
\(123\) 0 0
\(124\) 9.05080 15.6765i 0.812786 1.40779i
\(125\) 0 0
\(126\) 0 0
\(127\) 7.07871 0.628134 0.314067 0.949401i \(-0.398308\pi\)
0.314067 + 0.949401i \(0.398308\pi\)
\(128\) −2.89130 + 5.00787i −0.255557 + 0.442637i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 0 0
\(133\) 1.32403 2.29329i 0.114808 0.198853i
\(134\) 16.9852 1.46729
\(135\) 0 0
\(136\) 0.992582 0.0851132
\(137\) 3.73419 6.46781i 0.319033 0.552582i −0.661253 0.750163i \(-0.729975\pi\)
0.980287 + 0.197581i \(0.0633084\pi\)
\(138\) 0 0
\(139\) −4.00000 6.92820i −0.339276 0.587643i 0.645021 0.764165i \(-0.276849\pi\)
−0.984297 + 0.176522i \(0.943515\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.37985 11.0502i 0.535385 0.927314i
\(143\) −0.876139 −0.0732664
\(144\) 0 0
\(145\) 0 0
\(146\) 12.8761 22.3021i 1.06564 1.84574i
\(147\) 0 0
\(148\) 8.84823 + 15.3256i 0.727320 + 1.25976i
\(149\) −5.29241 9.16673i −0.433571 0.750968i 0.563607 0.826043i \(-0.309413\pi\)
−0.997178 + 0.0750759i \(0.976080\pi\)
\(150\) 0 0
\(151\) −8.84823 + 15.3256i −0.720059 + 1.24718i 0.240917 + 0.970546i \(0.422552\pi\)
−0.960976 + 0.276633i \(0.910781\pi\)
\(152\) −0.475800 −0.0385925
\(153\) 0 0
\(154\) 11.5242 0.928646
\(155\) 0 0
\(156\) 0 0
\(157\) −1.26581 2.19245i −0.101023 0.174976i 0.811084 0.584930i \(-0.198878\pi\)
−0.912106 + 0.409954i \(0.865545\pi\)
\(158\) 10.7900 + 18.6888i 0.858407 + 1.48680i
\(159\) 0 0
\(160\) 0 0
\(161\) −19.5726 −1.54254
\(162\) 0 0
\(163\) −8.47580 −0.663876 −0.331938 0.943301i \(-0.607702\pi\)
−0.331938 + 0.943301i \(0.607702\pi\)
\(164\) −0.211297 + 0.365977i −0.0164995 + 0.0285780i
\(165\) 0 0
\(166\) −12.7863 22.1465i −0.992409 1.71890i
\(167\) −6.36710 11.0281i −0.492701 0.853383i 0.507264 0.861791i \(-0.330657\pi\)
−0.999965 + 0.00840816i \(0.997324\pi\)
\(168\) 0 0
\(169\) 6.29001 10.8946i 0.483847 0.838047i
\(170\) 0 0
\(171\) 0 0
\(172\) 1.92935 0.147111
\(173\) −11.5242 + 19.9605i −0.876169 + 1.51757i −0.0206561 + 0.999787i \(0.506576\pi\)
−0.855513 + 0.517782i \(0.826758\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.14435 + 3.71413i 0.161637 + 0.279963i
\(177\) 0 0
\(178\) 3.12920 5.41993i 0.234543 0.406241i
\(179\) −2.22808 −0.166534 −0.0832672 0.996527i \(-0.526535\pi\)
−0.0832672 + 0.996527i \(0.526535\pi\)
\(180\) 0 0
\(181\) 0.468382 0.0348146 0.0174073 0.999848i \(-0.494459\pi\)
0.0174073 + 0.999848i \(0.494459\pi\)
\(182\) 2.76210 4.78410i 0.204740 0.354621i
\(183\) 0 0
\(184\) 1.75839 + 3.04562i 0.129630 + 0.224526i
\(185\) 0 0
\(186\) 0 0
\(187\) 0.913870 1.58287i 0.0668288 0.115751i
\(188\) 25.6513 1.87081
\(189\) 0 0
\(190\) 0 0
\(191\) −10.1140 + 17.5180i −0.731826 + 1.26756i 0.224276 + 0.974526i \(0.427998\pi\)
−0.956102 + 0.293034i \(0.905335\pi\)
\(192\) 0 0
\(193\) −9.96467 17.2593i −0.717273 1.24235i −0.962076 0.272780i \(-0.912057\pi\)
0.244804 0.969573i \(-0.421277\pi\)
\(194\) 14.1648 + 24.5342i 1.01698 + 1.76145i
\(195\) 0 0
\(196\) −11.4027 + 19.7501i −0.814482 + 1.41072i
\(197\) −15.5800 −1.11003 −0.555015 0.831840i \(-0.687288\pi\)
−0.555015 + 0.831840i \(0.687288\pi\)
\(198\) 0 0
\(199\) 3.58482 0.254121 0.127061 0.991895i \(-0.459446\pi\)
0.127061 + 0.991895i \(0.459446\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 1.53162 + 2.65284i 0.107764 + 0.186653i
\(203\) −7.91920 13.7165i −0.555819 0.962707i
\(204\) 0 0
\(205\) 0 0
\(206\) 15.6965 1.09362
\(207\) 0 0
\(208\) 2.05582 0.142545
\(209\) −0.438069 + 0.758758i −0.0303019 + 0.0524844i
\(210\) 0 0
\(211\) −7.49629 12.9840i −0.516066 0.893852i −0.999826 0.0186518i \(-0.994063\pi\)
0.483760 0.875201i \(-0.339271\pi\)
\(212\) −4.90645 8.49822i −0.336976 0.583660i
\(213\) 0 0
\(214\) 1.26210 2.18602i 0.0862754 0.149433i
\(215\) 0 0
\(216\) 0 0
\(217\) 31.4487 2.13488
\(218\) 14.7116 25.4813i 0.996396 1.72581i
\(219\) 0 0
\(220\) 0 0
\(221\) −0.438069 0.758758i −0.0294677 0.0510396i
\(222\) 0 0
\(223\) −13.4155 + 23.2363i −0.898368 + 1.55602i −0.0687878 + 0.997631i \(0.521913\pi\)
−0.829580 + 0.558388i \(0.811420\pi\)
\(224\) −33.0410 −2.20764
\(225\) 0 0
\(226\) 24.8761 1.65474
\(227\) −0.675970 + 1.17081i −0.0448657 + 0.0777096i −0.887586 0.460642i \(-0.847619\pi\)
0.842721 + 0.538351i \(0.180953\pi\)
\(228\) 0 0
\(229\) 4.11775 + 7.13215i 0.272108 + 0.471306i 0.969402 0.245480i \(-0.0789457\pi\)
−0.697293 + 0.716786i \(0.745612\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1.42291 + 2.46456i −0.0934188 + 0.161806i
\(233\) 8.58744 0.562582 0.281291 0.959623i \(-0.409237\pi\)
0.281291 + 0.959623i \(0.409237\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 4.90645 8.49822i 0.319383 0.553187i
\(237\) 0 0
\(238\) 5.76210 + 9.98025i 0.373501 + 0.646923i
\(239\) −11.9623 20.7193i −0.773775 1.34022i −0.935480 0.353378i \(-0.885033\pi\)
0.161706 0.986839i \(-0.448300\pi\)
\(240\) 0 0
\(241\) 3.12015 5.40426i 0.200987 0.348119i −0.747860 0.663857i \(-0.768919\pi\)
0.948847 + 0.315737i \(0.102252\pi\)
\(242\) 19.1345 1.23001
\(243\) 0 0
\(244\) −8.98516 −0.575216
\(245\) 0 0
\(246\) 0 0
\(247\) 0.209991 + 0.363716i 0.0133614 + 0.0231427i
\(248\) −2.82534 4.89363i −0.179409 0.310746i
\(249\) 0 0
\(250\) 0 0
\(251\) 28.5726 1.80349 0.901743 0.432272i \(-0.142288\pi\)
0.901743 + 0.432272i \(0.142288\pi\)
\(252\) 0 0
\(253\) 6.47580 0.407130
\(254\) 7.38356 12.7887i 0.463286 0.802434i
\(255\) 0 0
\(256\) −4.49258 7.78138i −0.280786 0.486336i
\(257\) 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) 0 0
\(259\) −15.3724 + 26.6258i −0.955196 + 1.65445i
\(260\) 0 0
\(261\) 0 0
\(262\) −12.5168 −0.773289
\(263\) −15.9344 + 27.5991i −0.982555 + 1.70183i −0.330220 + 0.943904i \(0.607123\pi\)
−0.652335 + 0.757931i \(0.726211\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −2.76210 4.78410i −0.169355 0.293332i
\(267\) 0 0
\(268\) 9.57468 16.5838i 0.584867 1.01302i
\(269\) 31.4971 1.92041 0.960207 0.279289i \(-0.0900987\pi\)
0.960207 + 0.279289i \(0.0900987\pi\)
\(270\) 0 0
\(271\) −3.24030 −0.196834 −0.0984172 0.995145i \(-0.531378\pi\)
−0.0984172 + 0.995145i \(0.531378\pi\)
\(272\) −2.14435 + 3.71413i −0.130020 + 0.225202i
\(273\) 0 0
\(274\) −7.79001 13.4927i −0.470612 0.815123i
\(275\) 0 0
\(276\) 0 0
\(277\) −2.79241 + 4.83660i −0.167780 + 0.290603i −0.937639 0.347611i \(-0.886993\pi\)
0.769859 + 0.638214i \(0.220326\pi\)
\(278\) −16.6890 −1.00094
\(279\) 0 0
\(280\) 0 0
\(281\) −12.0521 + 20.8749i −0.718969 + 1.24529i 0.242440 + 0.970166i \(0.422052\pi\)
−0.961409 + 0.275124i \(0.911281\pi\)
\(282\) 0 0
\(283\) −5.27114 9.12989i −0.313337 0.542715i 0.665746 0.746179i \(-0.268114\pi\)
−0.979083 + 0.203463i \(0.934780\pi\)
\(284\) −7.19275 12.4582i −0.426811 0.739259i
\(285\) 0 0
\(286\) −0.913870 + 1.58287i −0.0540383 + 0.0935970i
\(287\) −0.734191 −0.0433379
\(288\) 0 0
\(289\) −15.1723 −0.892486
\(290\) 0 0
\(291\) 0 0
\(292\) −14.5168 25.1438i −0.849530 1.47143i
\(293\) −9.49629 16.4481i −0.554779 0.960906i −0.997921 0.0644541i \(-0.979469\pi\)
0.443141 0.896452i \(-0.353864\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 5.52420 0.321088
\(297\) 0 0
\(298\) −22.0813 −1.27914
\(299\) 1.55211 2.68833i 0.0897607 0.155470i
\(300\) 0 0
\(301\) 1.67597 + 2.90286i 0.0966013 + 0.167318i
\(302\) 18.4586 + 31.9712i 1.06217 + 1.83973i
\(303\) 0 0
\(304\) 1.02791 1.78039i 0.0589546 0.102112i
\(305\) 0 0
\(306\) 0 0
\(307\) −29.4791 −1.68246 −0.841229 0.540679i \(-0.818167\pi\)
−0.841229 + 0.540679i \(0.818167\pi\)
\(308\) 6.49629 11.2519i 0.370161 0.641137i
\(309\) 0 0
\(310\) 0 0
\(311\) −4.70628 8.15152i −0.266869 0.462230i 0.701183 0.712982i \(-0.252656\pi\)
−0.968052 + 0.250751i \(0.919322\pi\)
\(312\) 0 0
\(313\) 5.81050 10.0641i 0.328429 0.568855i −0.653771 0.756692i \(-0.726814\pi\)
0.982200 + 0.187837i \(0.0601476\pi\)
\(314\) −5.28128 −0.298040
\(315\) 0 0
\(316\) 24.3297 1.36865
\(317\) 4.58984 7.94984i 0.257791 0.446507i −0.707859 0.706354i \(-0.750339\pi\)
0.965650 + 0.259847i \(0.0836720\pi\)
\(318\) 0 0
\(319\) 2.62015 + 4.53824i 0.146700 + 0.254092i
\(320\) 0 0
\(321\) 0 0
\(322\) −20.4155 + 35.3607i −1.13771 + 1.97057i
\(323\) −0.876139 −0.0487497
\(324\) 0 0
\(325\) 0 0
\(326\) −8.84081 + 15.3127i −0.489647 + 0.848094i
\(327\) 0 0
\(328\) 0.0659593 + 0.114245i 0.00364199 + 0.00630812i
\(329\) 22.2826 + 38.5946i 1.22848 + 2.12779i
\(330\) 0 0
\(331\) 3.61033 6.25327i 0.198442 0.343711i −0.749582 0.661912i \(-0.769745\pi\)
0.948023 + 0.318201i \(0.103079\pi\)
\(332\) −28.8310 −1.58231
\(333\) 0 0
\(334\) −26.5652 −1.45358
\(335\) 0 0
\(336\) 0 0
\(337\) 1.14195 + 1.97791i 0.0622059 + 0.107744i 0.895451 0.445160i \(-0.146853\pi\)
−0.833245 + 0.552904i \(0.813520\pi\)
\(338\) −13.1218 22.7276i −0.713731 1.23622i
\(339\) 0 0
\(340\) 0 0
\(341\) −10.4051 −0.563470
\(342\) 0 0
\(343\) −11.0181 −0.594921
\(344\) 0.301136 0.521583i 0.0162362 0.0281219i
\(345\) 0 0
\(346\) 24.0410 + 41.6402i 1.29245 + 2.23859i
\(347\) 0.354343 + 0.613740i 0.0190221 + 0.0329473i 0.875380 0.483436i \(-0.160611\pi\)
−0.856358 + 0.516383i \(0.827278\pi\)
\(348\) 0 0
\(349\) 10.6723 18.4849i 0.571273 0.989474i −0.425163 0.905117i \(-0.639783\pi\)
0.996436 0.0843569i \(-0.0268836\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.9320 0.582675
\(353\) 5.04840 8.74408i 0.268699 0.465401i −0.699827 0.714312i \(-0.746740\pi\)
0.968526 + 0.248912i \(0.0800729\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −3.52791 6.11052i −0.186979 0.323857i
\(357\) 0 0
\(358\) −2.32403 + 4.02534i −0.122829 + 0.212746i
\(359\) −30.5578 −1.61278 −0.806388 0.591386i \(-0.798581\pi\)
−0.806388 + 0.591386i \(0.798581\pi\)
\(360\) 0 0
\(361\) −18.5800 −0.977896
\(362\) 0.488553 0.846198i 0.0256778 0.0444752i
\(363\) 0 0
\(364\) −3.11404 5.39367i −0.163220 0.282705i
\(365\) 0 0
\(366\) 0 0
\(367\) −3.58984 + 6.21778i −0.187388 + 0.324566i −0.944379 0.328860i \(-0.893336\pi\)
0.756991 + 0.653426i \(0.226669\pi\)
\(368\) −15.1952 −0.792102
\(369\) 0 0
\(370\) 0 0
\(371\) 8.52420 14.7643i 0.442554 0.766527i
\(372\) 0 0
\(373\) −10.9623 18.9872i −0.567605 0.983120i −0.996802 0.0799096i \(-0.974537\pi\)
0.429197 0.903211i \(-0.358796\pi\)
\(374\) −1.90645 3.30207i −0.0985803 0.170746i
\(375\) 0 0
\(376\) 4.00371 6.93463i 0.206476 0.357626i
\(377\) 2.51197 0.129373
\(378\) 0 0
\(379\) −17.3929 −0.893414 −0.446707 0.894680i \(-0.647403\pi\)
−0.446707 + 0.894680i \(0.647403\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 21.0992 + 36.5449i 1.07953 + 1.86980i
\(383\) −0.237900 0.412055i −0.0121561 0.0210550i 0.859883 0.510491i \(-0.170536\pi\)
−0.872039 + 0.489436i \(0.837203\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −41.5752 −2.11612
\(387\) 0 0
\(388\) 31.9394 1.62148
\(389\) −2.79372 + 4.83886i −0.141647 + 0.245340i −0.928117 0.372289i \(-0.878573\pi\)
0.786470 + 0.617629i \(0.211906\pi\)
\(390\) 0 0
\(391\) 3.23790 + 5.60821i 0.163748 + 0.283619i
\(392\) 3.55953 + 6.16528i 0.179783 + 0.311394i
\(393\) 0 0
\(394\) −16.2510 + 28.1475i −0.818712 + 1.41805i
\(395\) 0 0
\(396\) 0 0
\(397\) −3.75228 −0.188321 −0.0941607 0.995557i \(-0.530017\pi\)
−0.0941607 + 0.995557i \(0.530017\pi\)
\(398\) 3.73921 6.47649i 0.187429 0.324637i
\(399\) 0 0
\(400\) 0 0
\(401\) 11.7826 + 20.4080i 0.588394 + 1.01913i 0.994443 + 0.105278i \(0.0335731\pi\)
−0.406048 + 0.913852i \(0.633094\pi\)
\(402\) 0 0
\(403\) −2.49389 + 4.31954i −0.124229 + 0.215172i
\(404\) 3.45355 0.171820
\(405\) 0 0
\(406\) −33.0410 −1.63980
\(407\) 5.08613 8.80944i 0.252110 0.436668i
\(408\) 0 0
\(409\) −0.524200 0.907940i −0.0259200 0.0448948i 0.852774 0.522279i \(-0.174918\pi\)
−0.878694 + 0.477385i \(0.841585\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 8.84823 15.3256i 0.435921 0.755037i
\(413\) 17.0484 0.838897
\(414\) 0 0
\(415\) 0 0
\(416\) 2.62015 4.53824i 0.128464 0.222505i
\(417\) 0 0
\(418\) 0.913870 + 1.58287i 0.0446988 + 0.0774207i
\(419\) −12.9599 22.4471i −0.633131 1.09661i −0.986908 0.161285i \(-0.948436\pi\)
0.353777 0.935330i \(-0.384897\pi\)
\(420\) 0 0
\(421\) −3.82032 + 6.61699i −0.186191 + 0.322492i −0.943977 0.330011i \(-0.892948\pi\)
0.757786 + 0.652503i \(0.226281\pi\)
\(422\) −31.2765 −1.52252
\(423\) 0 0
\(424\) −3.06324 −0.148764
\(425\) 0 0
\(426\) 0 0
\(427\) −7.80516 13.5189i −0.377718 0.654227i
\(428\) −1.42291 2.46456i −0.0687791 0.119129i
\(429\) 0 0
\(430\) 0 0
\(431\) −7.98516 −0.384632 −0.192316 0.981333i \(-0.561600\pi\)
−0.192316 + 0.981333i \(0.561600\pi\)
\(432\) 0 0
\(433\) 12.5120 0.601287 0.300644 0.953737i \(-0.402799\pi\)
0.300644 + 0.953737i \(0.402799\pi\)
\(434\) 32.8031 56.8166i 1.57460 2.72728i
\(435\) 0 0
\(436\) −16.5861 28.7280i −0.794332 1.37582i
\(437\) −1.55211 2.68833i −0.0742474 0.128600i
\(438\) 0 0
\(439\) 4.38225 7.59028i 0.209153 0.362264i −0.742295 0.670074i \(-0.766263\pi\)
0.951448 + 0.307809i \(0.0995958\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −1.82774 −0.0869367
\(443\) −1.83548 + 3.17914i −0.0872062 + 0.151046i −0.906329 0.422572i \(-0.861127\pi\)
0.819123 + 0.573618i \(0.194461\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 27.9865 + 48.4740i 1.32520 + 2.29531i
\(447\) 0 0
\(448\) −21.5016 + 37.2419i −1.01586 + 1.75951i
\(449\) −28.1723 −1.32953 −0.664766 0.747052i \(-0.731469\pi\)
−0.664766 + 0.747052i \(0.731469\pi\)
\(450\) 0 0
\(451\) 0.242915 0.0114384
\(452\) 14.0229 24.2884i 0.659581 1.14243i
\(453\) 0 0
\(454\) 1.41016 + 2.44247i 0.0661821 + 0.114631i
\(455\) 0 0
\(456\) 0 0
\(457\) 17.6308 30.5375i 0.824735 1.42848i −0.0773867 0.997001i \(-0.524658\pi\)
0.902122 0.431482i \(-0.142009\pi\)
\(458\) 17.1803 0.802784
\(459\) 0 0
\(460\) 0 0
\(461\) 17.3384 30.0310i 0.807530 1.39868i −0.107039 0.994255i \(-0.534137\pi\)
0.914570 0.404428i \(-0.132530\pi\)
\(462\) 0 0
\(463\) 3.72437 + 6.45080i 0.173086 + 0.299794i 0.939497 0.342556i \(-0.111293\pi\)
−0.766411 + 0.642350i \(0.777959\pi\)
\(464\) −6.14806 10.6488i −0.285417 0.494356i
\(465\) 0 0
\(466\) 8.95725 15.5144i 0.414937 0.718692i
\(467\) 29.9655 1.38664 0.693319 0.720630i \(-0.256148\pi\)
0.693319 + 0.720630i \(0.256148\pi\)
\(468\) 0 0
\(469\) 33.2691 1.53622
\(470\) 0 0
\(471\) 0 0
\(472\) −1.53162 2.65284i −0.0704984 0.122107i
\(473\) −0.554512 0.960443i −0.0254965 0.0441612i
\(474\) 0 0
\(475\) 0 0
\(476\) 12.9926 0.595514
\(477\) 0 0
\(478\) −49.9097 −2.28282
\(479\) −3.99258 + 6.91535i −0.182426 + 0.315971i −0.942706 0.333625i \(-0.891728\pi\)
0.760280 + 0.649595i \(0.225062\pi\)
\(480\) 0 0
\(481\) −2.43807 4.22286i −0.111166 0.192546i
\(482\) −6.50904 11.2740i −0.296479 0.513516i
\(483\) 0 0
\(484\) 10.7863 18.6824i 0.490286 0.849201i
\(485\) 0 0
\(486\) 0 0
\(487\) 11.9442 0.541243 0.270621 0.962686i \(-0.412771\pi\)
0.270621 + 0.962686i \(0.412771\pi\)
\(488\) −1.40242 + 2.42907i −0.0634847 + 0.109959i
\(489\) 0 0
\(490\) 0 0
\(491\) −4.61033 7.98533i −0.208061 0.360373i 0.743042 0.669244i \(-0.233382\pi\)
−0.951104 + 0.308872i \(0.900049\pi\)
\(492\) 0 0
\(493\) −2.62015 + 4.53824i −0.118006 + 0.204392i
\(494\) 0.876139 0.0394193
\(495\) 0 0
\(496\) 24.4152 1.09627
\(497\) 12.4963 21.6442i 0.560535 0.970876i
\(498\) 0 0
\(499\) −15.0861 26.1299i −0.675348 1.16974i −0.976367 0.216119i \(-0.930660\pi\)
0.301019 0.953618i \(-0.402673\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 29.8031 51.6204i 1.33018 2.30393i
\(503\) −10.5981 −0.472546 −0.236273 0.971687i \(-0.575926\pi\)
−0.236273 + 0.971687i \(0.575926\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 6.75468 11.6995i 0.300282 0.520104i
\(507\) 0 0
\(508\) −8.32435 14.4182i −0.369333 0.639704i
\(509\) 14.3761 + 24.9002i 0.637211 + 1.10368i 0.986042 + 0.166496i \(0.0532454\pi\)
−0.348831 + 0.937186i \(0.613421\pi\)
\(510\) 0 0
\(511\) 25.2207 43.6835i 1.11570 1.93244i
\(512\) −30.3094 −1.33950
\(513\) 0 0
\(514\) 37.5503 1.65627
\(515\) 0 0
\(516\) 0 0
\(517\) −7.37243 12.7694i −0.324239 0.561599i
\(518\) 32.0689 + 55.5449i 1.40903 + 2.44050i
\(519\) 0 0
\(520\) 0 0
\(521\) 36.0942 1.58132 0.790658 0.612259i \(-0.209739\pi\)
0.790658 + 0.612259i \(0.209739\pi\)
\(522\) 0 0
\(523\) −11.1297 −0.486669 −0.243334 0.969942i \(-0.578241\pi\)
−0.243334 + 0.969942i \(0.578241\pi\)
\(524\) −7.05582 + 12.2210i −0.308235 + 0.533878i
\(525\) 0 0
\(526\) 33.2411 + 57.5754i 1.44938 + 2.51041i
\(527\) −5.20257 9.01112i −0.226628 0.392531i
\(528\) 0 0
\(529\) 0.0279088 0.0483395i 0.00121343 0.00210172i
\(530\) 0 0
\(531\) 0 0
\(532\) −6.22808 −0.270021
\(533\) 0.0582214 0.100842i 0.00252185 0.00436797i
\(534\) 0 0
\(535\) 0 0
\(536\) −2.98887 5.17688i −0.129100 0.223607i
\(537\) 0 0
\(538\) 32.8536 56.9040i 1.41642 2.45331i
\(539\) 13.1090 0.564646
\(540\) 0 0
\(541\) −34.7374 −1.49348 −0.746740 0.665116i \(-0.768382\pi\)
−0.746740 + 0.665116i \(0.768382\pi\)
\(542\) −3.37985 + 5.85407i −0.145177 + 0.251454i
\(543\) 0 0
\(544\) 5.46598 + 9.46735i 0.234352 + 0.405909i
\(545\) 0 0
\(546\) 0 0
\(547\) −1.35727 + 2.35087i −0.0580328 + 0.100516i −0.893582 0.448899i \(-0.851816\pi\)
0.835549 + 0.549415i \(0.185149\pi\)
\(548\) −17.5652 −0.750347
\(549\) 0 0
\(550\) 0 0
\(551\) 1.25599 2.17543i 0.0535068 0.0926766i
\(552\) 0 0
\(553\) 21.1345 + 36.6061i 0.898732 + 1.55665i
\(554\) 5.82534 + 10.0898i 0.247495 + 0.428674i
\(555\) 0 0
\(556\) −9.40776 + 16.2947i −0.398978 + 0.691050i
\(557\) −8.93676 −0.378663 −0.189331 0.981913i \(-0.560632\pi\)
−0.189331 + 0.981913i \(0.560632\pi\)
\(558\) 0 0
\(559\) −0.531618 −0.0224850
\(560\) 0 0
\(561\) 0 0
\(562\) 25.1423 + 43.5477i 1.06056 + 1.83695i
\(563\) 4.68130 + 8.10826i 0.197293 + 0.341722i 0.947650 0.319311i \(-0.103451\pi\)
−0.750357 + 0.661033i \(0.770118\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −21.9926 −0.924417
\(567\) 0 0
\(568\) −4.49064 −0.188423
\(569\) 17.9368 31.0674i 0.751948 1.30241i −0.194929 0.980817i \(-0.562448\pi\)
0.946877 0.321595i \(-0.104219\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) 1.03031 + 1.78455i 0.0430795 + 0.0746159i
\(573\) 0 0
\(574\) −0.765809 + 1.32642i −0.0319643 + 0.0553637i
\(575\) 0 0
\(576\) 0 0
\(577\) −1.35675 −0.0564821 −0.0282411 0.999601i \(-0.508991\pi\)
−0.0282411 + 0.999601i \(0.508991\pi\)
\(578\) −15.8257 + 27.4108i −0.658260 + 1.14014i
\(579\) 0 0
\(580\) 0 0
\(581\) −25.0447 43.3787i −1.03903 1.79965i
\(582\) 0 0
\(583\) −2.82032 + 4.88494i −0.116806 + 0.202314i
\(584\) −9.06324 −0.375039
\(585\) 0 0
\(586\) −39.6210 −1.63673
\(587\) −14.3950 + 24.9329i −0.594145 + 1.02909i 0.399521 + 0.916724i \(0.369176\pi\)
−0.993667 + 0.112366i \(0.964157\pi\)
\(588\) 0 0
\(589\) 2.49389 + 4.31954i 0.102759 + 0.177984i
\(590\) 0 0
\(591\) 0 0
\(592\) −11.9344 + 20.6709i −0.490499 + 0.849570i
\(593\) 30.9171 1.26961 0.634807 0.772671i \(-0.281080\pi\)
0.634807 + 0.772671i \(0.281080\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −12.4474 + 21.5596i −0.509867 + 0.883115i
\(597\) 0 0
\(598\) −3.23790 5.60821i −0.132408 0.229337i
\(599\) 0.696460 + 1.20630i 0.0284566 + 0.0492882i 0.879903 0.475153i \(-0.157607\pi\)
−0.851446 + 0.524442i \(0.824274\pi\)
\(600\) 0 0
\(601\) −4.41256 + 7.64279i −0.179992 + 0.311756i −0.941878 0.335956i \(-0.890941\pi\)
0.761885 + 0.647712i \(0.224274\pi\)
\(602\) 6.99258 0.284996
\(603\) 0 0
\(604\) 41.6210 1.69353
\(605\) 0 0
\(606\) 0 0
\(607\) −1.07839 1.86783i −0.0437706 0.0758129i 0.843310 0.537427i \(-0.180604\pi\)
−0.887081 + 0.461614i \(0.847270\pi\)
\(608\) −2.62015 4.53824i −0.106261 0.184050i
\(609\) 0 0
\(610\) 0 0
\(611\) −7.06804 −0.285942
\(612\) 0 0
\(613\) 9.57521 0.386739 0.193370 0.981126i \(-0.438058\pi\)
0.193370 + 0.981126i \(0.438058\pi\)
\(614\) −30.7486 + 53.2581i −1.24091 + 2.14932i
\(615\) 0 0
\(616\) −2.02791 3.51244i −0.0817068 0.141520i
\(617\) 18.8384 + 32.6291i 0.758406 + 1.31360i 0.943663 + 0.330907i \(0.107355\pi\)
−0.185258 + 0.982690i \(0.559312\pi\)
\(618\) 0 0
\(619\) −8.55211 + 14.8127i −0.343738 + 0.595372i −0.985124 0.171847i \(-0.945027\pi\)
0.641385 + 0.767219i \(0.278360\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −19.6358 −0.787325
\(623\) 6.12920 10.6161i 0.245561 0.425324i
\(624\) 0 0
\(625\) 0 0
\(626\) −12.1215 20.9950i −0.484471 0.839128i
\(627\) 0 0
\(628\) −2.97711 + 5.15650i −0.118799 + 0.205767i
\(629\) 10.1723 0.405595
\(630\) 0 0
\(631\) 33.1090 1.31805 0.659025 0.752121i \(-0.270969\pi\)
0.659025 + 0.752121i \(0.270969\pi\)
\(632\) 3.79743 6.57734i 0.151054 0.261632i
\(633\) 0 0
\(634\) −9.57500 16.5844i −0.380272 0.658650i
\(635\) 0 0
\(636\) 0 0
\(637\) 3.14195 5.44201i 0.124489 0.215620i
\(638\) 10.9320 0.432800
\(639\) 0 0
\(640\) 0 0
\(641\) −11.5763 + 20.0508i −0.457237 + 0.791957i −0.998814 0.0486939i \(-0.984494\pi\)
0.541577 + 0.840651i \(0.317827\pi\)
\(642\) 0 0
\(643\) 21.5319 + 37.2944i 0.849137 + 1.47075i 0.881980 + 0.471287i \(0.156211\pi\)
−0.0328430 + 0.999461i \(0.510456\pi\)
\(644\) 23.0168 + 39.8662i 0.906988 + 1.57095i
\(645\) 0 0
\(646\) −0.913870 + 1.58287i −0.0359557 + 0.0622771i
\(647\) −20.6439 −0.811595 −0.405798 0.913963i \(-0.633006\pi\)
−0.405798 + 0.913963i \(0.633006\pi\)
\(648\) 0 0
\(649\) −5.64064 −0.221415
\(650\) 0 0
\(651\) 0 0
\(652\) 9.96728 + 17.2638i 0.390349 + 0.676104i
\(653\) −3.41758 5.91942i −0.133740 0.231645i 0.791375 0.611331i \(-0.209365\pi\)
−0.925116 + 0.379686i \(0.876032\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.569988 −0.0222543
\(657\) 0 0
\(658\) 92.9688 3.62430
\(659\) −13.4307 + 23.2626i −0.523184 + 0.906181i 0.476452 + 0.879200i \(0.341923\pi\)
−0.999636 + 0.0269806i \(0.991411\pi\)
\(660\) 0 0
\(661\) 1.06063 + 1.83706i 0.0412535 + 0.0714532i 0.885915 0.463848i \(-0.153532\pi\)
−0.844661 + 0.535301i \(0.820198\pi\)
\(662\) −7.53162 13.0451i −0.292725 0.507014i
\(663\) 0 0
\(664\) −4.50000 + 7.79423i −0.174634 + 0.302475i
\(665\) 0 0
\(666\) 0 0
\(667\) −18.5667 −0.718907
\(668\) −14.9750 + 25.9375i −0.579401 + 1.00355i
\(669\) 0 0
\(670\) 0 0
\(671\) 2.58242 + 4.47288i 0.0996933 + 0.172674i
\(672\) 0 0
\(673\) 17.4102 30.1553i 0.671112 1.16240i −0.306477 0.951878i \(-0.599150\pi\)
0.977589 0.210523i \(-0.0675165\pi\)
\(674\) 4.76450 0.183522
\(675\) 0 0
\(676\) −29.5874 −1.13798
\(677\) 12.3421 21.3772i 0.474346 0.821592i −0.525222 0.850965i \(-0.676018\pi\)
0.999569 + 0.0293735i \(0.00935121\pi\)
\(678\) 0 0
\(679\) 27.7449 + 48.0555i 1.06475 + 1.84420i
\(680\) 0 0
\(681\) 0 0
\(682\) −10.8532 + 18.7984i −0.415592 + 0.719827i
\(683\) −38.4610 −1.47167 −0.735834 0.677162i \(-0.763210\pi\)
−0.735834 + 0.677162i \(0.763210\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −11.4926 + 19.9057i −0.438789 + 0.760005i
\(687\) 0 0
\(688\) 1.30114 + 2.25363i 0.0496054 + 0.0859190i
\(689\) 1.35194 + 2.34163i 0.0515048 + 0.0892089i
\(690\) 0 0
\(691\) −0.240304 + 0.416219i −0.00914159 + 0.0158337i −0.870560 0.492062i \(-0.836243\pi\)
0.861418 + 0.507896i \(0.169577\pi\)
\(692\) 54.2084 2.06070
\(693\) 0 0
\(694\) 1.47841 0.0561197
\(695\) 0 0
\(696\) 0 0
\(697\) 0.121457 + 0.210370i 0.00460053 + 0.00796835i
\(698\) −22.2637 38.5619i −0.842694 1.45959i
\(699\) 0 0
\(700\) 0 0
\(701\) 18.1797 0.686637 0.343318 0.939219i \(-0.388449\pi\)
0.343318 + 0.939219i \(0.388449\pi\)
\(702\) 0 0
\(703\) −4.87614 −0.183907
\(704\) 7.11404 12.3219i 0.268120 0.464398i
\(705\) 0 0
\(706\) −10.5316 18.2413i −0.396363 0.686520i
\(707\) 3.00000 + 5.19615i 0.112827 + 0.195421i
\(708\) 0 0
\(709\) −3.59355 + 6.22421i −0.134959 + 0.233755i −0.925582 0.378548i \(-0.876423\pi\)
0.790623 + 0.612303i \(0.209757\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −2.20257 −0.0825449
\(713\) 18.4331 31.9270i 0.690323 1.19568i
\(714\) 0 0
\(715\) 0 0
\(716\) 2.62015 + 4.53824i 0.0979197 + 0.169602i
\(717\) 0 0
\(718\) −31.8737 + 55.2069i −1.18952 + 2.06030i
\(719\) −12.5168 −0.466797 −0.233399 0.972381i \(-0.574985\pi\)
−0.233399 + 0.972381i \(0.574985\pi\)
\(720\) 0 0
\(721\) 30.7449 1.14500
\(722\) −19.3802 + 33.5674i −0.721255 + 1.24925i
\(723\) 0 0
\(724\) −0.550803 0.954019i −0.0204704 0.0354558i
\(725\) 0 0
\(726\) 0 0
\(727\) 4.21292 7.29699i 0.156249 0.270631i −0.777264 0.629174i \(-0.783393\pi\)
0.933513 + 0.358544i \(0.116727\pi\)
\(728\) −1.94418 −0.0720562
\(729\) 0 0
\(730\) 0 0
\(731\) 0.554512 0.960443i 0.0205094 0.0355233i
\(732\) 0 0
\(733\) −11.0000 19.0526i −0.406294 0.703722i 0.588177 0.808732i \(-0.299846\pi\)
−0.994471 + 0.105010i \(0.966513\pi\)
\(734\) 7.48887 + 12.9711i 0.276419 + 0.478772i
\(735\) 0 0
\(736\) −19.3663 + 33.5434i −0.713852 + 1.23643i
\(737\) −11.0074 −0.405463
\(738\) 0 0
\(739\) −1.81290 −0.0666887 −0.0333444 0.999444i \(-0.510616\pi\)
−0.0333444 + 0.999444i \(0.510616\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −17.7826 30.8003i −0.652819 1.13072i
\(743\) −10.0686 17.4393i −0.369380 0.639785i 0.620089 0.784532i \(-0.287097\pi\)
−0.989469 + 0.144747i \(0.953763\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −45.7374 −1.67457
\(747\) 0 0
\(748\) −4.29873 −0.157177
\(749\) 2.47209 4.28179i 0.0903282 0.156453i
\(750\) 0 0
\(751\) −6.10662 10.5770i −0.222834 0.385959i 0.732834 0.680408i \(-0.238197\pi\)
−0.955667 + 0.294449i \(0.904864\pi\)
\(752\) 17.2991 + 29.9628i 0.630832 + 1.09263i
\(753\) 0 0
\(754\) 2.62015 4.53824i 0.0954203 0.165273i
\(755\) 0 0
\(756\) 0 0
\(757\) −52.9533 −1.92462 −0.962310 0.271955i \(-0.912330\pi\)
−0.962310 + 0.271955i \(0.912330\pi\)
\(758\) −18.1419 + 31.4228i −0.658945 + 1.14133i
\(759\) 0 0
\(760\) 0 0
\(761\) −9.22677 15.9812i −0.334470 0.579319i 0.648913 0.760863i \(-0.275224\pi\)
−0.983383 + 0.181543i \(0.941891\pi\)
\(762\) 0 0
\(763\) 28.8158 49.9105i 1.04320 1.80688i
\(764\) 47.5752 1.72121
\(765\) 0 0
\(766\) −0.992582 −0.0358634
\(767\) −1.35194 + 2.34163i −0.0488157 + 0.0845513i
\(768\) 0 0
\(769\) 2.22677 + 3.85688i 0.0802995 + 0.139083i 0.903379 0.428844i \(-0.141079\pi\)
−0.823079 + 0.567927i \(0.807746\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −23.4363 + 40.5929i −0.843491 + 1.46097i
\(773\) 38.9368 1.40046 0.700229 0.713918i \(-0.253081\pi\)
0.700229 + 0.713918i \(0.253081\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 4.98516 8.63456i 0.178957 0.309962i
\(777\) 0 0
\(778\) 5.82806 + 10.0945i 0.208946 + 0.361905i
\(779\) −0.0582214 0.100842i −0.00208600 0.00361305i
\(780\) 0 0
\(781\) −4.13453 + 7.16121i −0.147945 + 0.256248i
\(782\) 13.5094 0.483094
\(783\) 0 0
\(784\) −30.7597 −1.09856
\(785\) 0 0
\(786\) 0 0
\(787\) 17.1140 + 29.6424i 0.610050 + 1.05664i 0.991231 + 0.132137i \(0.0421838\pi\)
−0.381182 + 0.924500i \(0.624483\pi\)
\(788\) 18.3216 + 31.7340i 0.652681 + 1.13048i
\(789\) 0 0
\(790\) 0 0
\(791\) 48.7252 1.73247
\(792\) 0 0
\(793\) 2.47580 0.0879183
\(794\) −3.91387 + 6.77902i −0.138898 +