Properties

Label 1323.2.g.f.361.1
Level $1323$
Weight $2$
Character 1323.361
Analytic conductor $10.564$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(1.19343 - 2.06709i\) of defining polynomial
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.f.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.19343 + 2.06709i) q^{2} +(-1.84857 - 3.20182i) q^{4} -2.92087 q^{5} +4.05086 q^{8} +O(q^{10})\) \(q+(-1.19343 + 2.06709i) q^{2} +(-1.84857 - 3.20182i) q^{4} -2.92087 q^{5} +4.05086 q^{8} +(3.48586 - 6.03769i) q^{10} +1.35371 q^{11} +(0.733001 - 1.26960i) q^{13} +(-1.13729 + 1.96984i) q^{16} +(1.65514 - 2.86678i) q^{17} +(1.10329 + 1.91096i) q^{19} +(5.39943 + 9.35209i) q^{20} +(-1.61557 + 2.79825i) q^{22} -2.62830 q^{23} +3.53146 q^{25} +(1.74958 + 3.03036i) q^{26} +(-0.521720 - 0.903646i) q^{29} +(1.63729 + 2.83587i) q^{31} +(1.33629 + 2.31453i) q^{32} +(3.95060 + 6.84263i) q^{34} +(5.43773 + 9.41842i) q^{37} -5.26683 q^{38} -11.8320 q^{40} +(-0.904289 + 1.56627i) q^{41} +(-2.17129 - 3.76078i) q^{43} +(-2.50244 - 4.33435i) q^{44} +(3.13670 - 5.43292i) q^{46} +(-1.98957 + 3.44604i) q^{47} +(-4.21456 + 7.29984i) q^{50} -5.42002 q^{52} +(3.22743 - 5.59008i) q^{53} -3.95402 q^{55} +2.49056 q^{58} +(6.10700 + 10.5776i) q^{59} +(0.279867 - 0.484744i) q^{61} -7.81600 q^{62} -10.9283 q^{64} +(-2.14100 + 3.70832i) q^{65} +(-6.40588 - 11.0953i) q^{67} -12.2386 q^{68} -12.9177 q^{71} +(-5.22772 + 9.05467i) q^{73} -25.9583 q^{74} +(4.07903 - 7.06509i) q^{76} +(-0.383838 + 0.664827i) q^{79} +(3.32187 - 5.75365i) q^{80} +(-2.15842 - 3.73849i) q^{82} +(-0.983707 - 1.70383i) q^{83} +(-4.83443 + 8.37348i) q^{85} +10.3652 q^{86} +5.48371 q^{88} +(3.20356 + 5.54872i) q^{89} +(4.85859 + 8.41533i) q^{92} +(-4.74884 - 8.22524i) q^{94} +(-3.22257 - 5.58166i) q^{95} +(4.14143 + 7.17316i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{2} - 4q^{4} - 8q^{5} + 6q^{8} + O(q^{10}) \) \( 10q - 2q^{2} - 4q^{4} - 8q^{5} + 6q^{8} + 7q^{10} + 8q^{11} + 8q^{13} + 2q^{16} + 12q^{17} - q^{19} + 5q^{20} - q^{22} + 6q^{23} + 2q^{25} + 11q^{26} - 7q^{29} + 3q^{31} + 2q^{32} - 3q^{34} - 40q^{38} - 6q^{40} + 5q^{41} - 7q^{43} + 10q^{44} + 3q^{46} + 27q^{47} - 19q^{50} - 20q^{52} + 21q^{53} - 4q^{55} + 20q^{58} + 30q^{59} + 14q^{61} - 12q^{62} - 50q^{64} + 11q^{65} - 2q^{67} - 54q^{68} + 6q^{71} - 15q^{73} - 72q^{74} - 5q^{76} - 4q^{79} + 20q^{80} + 5q^{82} + 9q^{83} - 6q^{85} - 16q^{86} + 36q^{88} + 28q^{89} - 27q^{92} + 3q^{94} + 14q^{95} + 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.19343 + 2.06709i −0.843886 + 1.46165i 0.0426999 + 0.999088i \(0.486404\pi\)
−0.886585 + 0.462565i \(0.846929\pi\)
\(3\) 0 0
\(4\) −1.84857 3.20182i −0.924286 1.60091i
\(5\) −2.92087 −1.30625 −0.653125 0.757250i \(-0.726543\pi\)
−0.653125 + 0.757250i \(0.726543\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 4.05086 1.43219
\(9\) 0 0
\(10\) 3.48586 6.03769i 1.10233 1.90929i
\(11\) 1.35371 0.408160 0.204080 0.978954i \(-0.434580\pi\)
0.204080 + 0.978954i \(0.434580\pi\)
\(12\) 0 0
\(13\) 0.733001 1.26960i 0.203298 0.352123i −0.746291 0.665620i \(-0.768167\pi\)
0.949589 + 0.313497i \(0.101501\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.13729 + 1.96984i −0.284323 + 0.492461i
\(17\) 1.65514 2.86678i 0.401430 0.695297i −0.592469 0.805593i \(-0.701847\pi\)
0.993899 + 0.110297i \(0.0351801\pi\)
\(18\) 0 0
\(19\) 1.10329 + 1.91096i 0.253113 + 0.438404i 0.964381 0.264516i \(-0.0852123\pi\)
−0.711268 + 0.702921i \(0.751879\pi\)
\(20\) 5.39943 + 9.35209i 1.20735 + 2.09119i
\(21\) 0 0
\(22\) −1.61557 + 2.79825i −0.344441 + 0.596589i
\(23\) −2.62830 −0.548038 −0.274019 0.961724i \(-0.588353\pi\)
−0.274019 + 0.961724i \(0.588353\pi\)
\(24\) 0 0
\(25\) 3.53146 0.706292
\(26\) 1.74958 + 3.03036i 0.343121 + 0.594302i
\(27\) 0 0
\(28\) 0 0
\(29\) −0.521720 0.903646i −0.0968810 0.167803i 0.813511 0.581549i \(-0.197553\pi\)
−0.910392 + 0.413747i \(0.864220\pi\)
\(30\) 0 0
\(31\) 1.63729 + 2.83587i 0.294066 + 0.509337i 0.974767 0.223224i \(-0.0716581\pi\)
−0.680701 + 0.732561i \(0.738325\pi\)
\(32\) 1.33629 + 2.31453i 0.236226 + 0.409155i
\(33\) 0 0
\(34\) 3.95060 + 6.84263i 0.677521 + 1.17350i
\(35\) 0 0
\(36\) 0 0
\(37\) 5.43773 + 9.41842i 0.893957 + 1.54838i 0.835090 + 0.550113i \(0.185415\pi\)
0.0588664 + 0.998266i \(0.481251\pi\)
\(38\) −5.26683 −0.854393
\(39\) 0 0
\(40\) −11.8320 −1.87081
\(41\) −0.904289 + 1.56627i −0.141226 + 0.244611i −0.927959 0.372683i \(-0.878438\pi\)
0.786732 + 0.617294i \(0.211771\pi\)
\(42\) 0 0
\(43\) −2.17129 3.76078i −0.331118 0.573514i 0.651613 0.758551i \(-0.274093\pi\)
−0.982731 + 0.185038i \(0.940759\pi\)
\(44\) −2.50244 4.33435i −0.377257 0.653428i
\(45\) 0 0
\(46\) 3.13670 5.43292i 0.462481 0.801041i
\(47\) −1.98957 + 3.44604i −0.290209 + 0.502656i −0.973859 0.227154i \(-0.927058\pi\)
0.683650 + 0.729810i \(0.260391\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −4.21456 + 7.29984i −0.596029 + 1.03235i
\(51\) 0 0
\(52\) −5.42002 −0.751622
\(53\) 3.22743 5.59008i 0.443322 0.767856i −0.554612 0.832109i \(-0.687133\pi\)
0.997934 + 0.0642533i \(0.0204666\pi\)
\(54\) 0 0
\(55\) −3.95402 −0.533160
\(56\) 0 0
\(57\) 0 0
\(58\) 2.49056 0.327026
\(59\) 6.10700 + 10.5776i 0.795064 + 1.37709i 0.922799 + 0.385283i \(0.125896\pi\)
−0.127735 + 0.991808i \(0.540771\pi\)
\(60\) 0 0
\(61\) 0.279867 0.484744i 0.0358333 0.0620651i −0.847553 0.530711i \(-0.821925\pi\)
0.883386 + 0.468646i \(0.155258\pi\)
\(62\) −7.81600 −0.992632
\(63\) 0 0
\(64\) −10.9283 −1.36604
\(65\) −2.14100 + 3.70832i −0.265558 + 0.459960i
\(66\) 0 0
\(67\) −6.40588 11.0953i −0.782603 1.35551i −0.930420 0.366494i \(-0.880558\pi\)
0.147817 0.989015i \(-0.452775\pi\)
\(68\) −12.2386 −1.48414
\(69\) 0 0
\(70\) 0 0
\(71\) −12.9177 −1.53305 −0.766525 0.642214i \(-0.778016\pi\)
−0.766525 + 0.642214i \(0.778016\pi\)
\(72\) 0 0
\(73\) −5.22772 + 9.05467i −0.611858 + 1.05977i 0.379069 + 0.925368i \(0.376244\pi\)
−0.990927 + 0.134401i \(0.957089\pi\)
\(74\) −25.9583 −3.01759
\(75\) 0 0
\(76\) 4.07903 7.06509i 0.467897 0.810422i
\(77\) 0 0
\(78\) 0 0
\(79\) −0.383838 + 0.664827i −0.0431852 + 0.0747989i −0.886810 0.462134i \(-0.847084\pi\)
0.843625 + 0.536933i \(0.180417\pi\)
\(80\) 3.32187 5.75365i 0.371397 0.643278i
\(81\) 0 0
\(82\) −2.15842 3.73849i −0.238358 0.412847i
\(83\) −0.983707 1.70383i −0.107976 0.187020i 0.806974 0.590587i \(-0.201104\pi\)
−0.914950 + 0.403567i \(0.867770\pi\)
\(84\) 0 0
\(85\) −4.83443 + 8.37348i −0.524368 + 0.908232i
\(86\) 10.3652 1.11770
\(87\) 0 0
\(88\) 5.48371 0.584565
\(89\) 3.20356 + 5.54872i 0.339576 + 0.588163i 0.984353 0.176208i \(-0.0563830\pi\)
−0.644777 + 0.764371i \(0.723050\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 4.85859 + 8.41533i 0.506543 + 0.877359i
\(93\) 0 0
\(94\) −4.74884 8.22524i −0.489806 0.848369i
\(95\) −3.22257 5.58166i −0.330629 0.572666i
\(96\) 0 0
\(97\) 4.14143 + 7.17316i 0.420498 + 0.728324i 0.995988 0.0894847i \(-0.0285220\pi\)
−0.575490 + 0.817809i \(0.695189\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −6.52815 11.3071i −0.652815 1.13071i
\(101\) −16.2266 −1.61461 −0.807305 0.590134i \(-0.799075\pi\)
−0.807305 + 0.590134i \(0.799075\pi\)
\(102\) 0 0
\(103\) 2.22683 0.219416 0.109708 0.993964i \(-0.465008\pi\)
0.109708 + 0.993964i \(0.465008\pi\)
\(104\) 2.96929 5.14295i 0.291162 0.504308i
\(105\) 0 0
\(106\) 7.70346 + 13.3428i 0.748226 + 1.29597i
\(107\) 8.75403 + 15.1624i 0.846284 + 1.46581i 0.884501 + 0.466537i \(0.154499\pi\)
−0.0382175 + 0.999269i \(0.512168\pi\)
\(108\) 0 0
\(109\) −7.79917 + 13.5086i −0.747025 + 1.29388i 0.202218 + 0.979341i \(0.435185\pi\)
−0.949243 + 0.314544i \(0.898148\pi\)
\(110\) 4.71886 8.17331i 0.449926 0.779295i
\(111\) 0 0
\(112\) 0 0
\(113\) 0.844555 1.46281i 0.0794491 0.137610i −0.823563 0.567224i \(-0.808017\pi\)
0.903012 + 0.429615i \(0.141351\pi\)
\(114\) 0 0
\(115\) 7.67690 0.715875
\(116\) −1.92887 + 3.34091i −0.179092 + 0.310196i
\(117\) 0 0
\(118\) −29.1532 −2.68377
\(119\) 0 0
\(120\) 0 0
\(121\) −9.16746 −0.833405
\(122\) 0.668005 + 1.15702i 0.0604784 + 0.104752i
\(123\) 0 0
\(124\) 6.05330 10.4846i 0.543602 0.941546i
\(125\) 4.28942 0.383657
\(126\) 0 0
\(127\) −3.96918 −0.352208 −0.176104 0.984372i \(-0.556350\pi\)
−0.176104 + 0.984372i \(0.556350\pi\)
\(128\) 10.3696 17.9607i 0.916552 1.58751i
\(129\) 0 0
\(130\) −5.11028 8.85127i −0.448202 0.776308i
\(131\) 5.32863 0.465565 0.232782 0.972529i \(-0.425217\pi\)
0.232782 + 0.972529i \(0.425217\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 30.5800 2.64171
\(135\) 0 0
\(136\) 6.70473 11.6129i 0.574925 0.995800i
\(137\) 7.49543 0.640378 0.320189 0.947354i \(-0.396254\pi\)
0.320189 + 0.947354i \(0.396254\pi\)
\(138\) 0 0
\(139\) −7.03285 + 12.1812i −0.596518 + 1.03320i 0.396812 + 0.917900i \(0.370116\pi\)
−0.993331 + 0.115300i \(0.963217\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 15.4164 26.7021i 1.29372 2.24079i
\(143\) 0.992275 1.71867i 0.0829782 0.143722i
\(144\) 0 0
\(145\) 1.52388 + 2.63943i 0.126551 + 0.219193i
\(146\) −12.4779 21.6123i −1.03268 1.78865i
\(147\) 0 0
\(148\) 20.1041 34.8212i 1.65254 2.86229i
\(149\) −2.17971 −0.178569 −0.0892846 0.996006i \(-0.528458\pi\)
−0.0892846 + 0.996006i \(0.528458\pi\)
\(150\) 0 0
\(151\) 14.0277 1.14156 0.570781 0.821102i \(-0.306641\pi\)
0.570781 + 0.821102i \(0.306641\pi\)
\(152\) 4.46929 + 7.74103i 0.362507 + 0.627880i
\(153\) 0 0
\(154\) 0 0
\(155\) −4.78231 8.28320i −0.384124 0.665322i
\(156\) 0 0
\(157\) 1.48312 + 2.56883i 0.118365 + 0.205015i 0.919120 0.393978i \(-0.128901\pi\)
−0.800755 + 0.598993i \(0.795568\pi\)
\(158\) −0.916172 1.58686i −0.0728867 0.126243i
\(159\) 0 0
\(160\) −3.90314 6.76043i −0.308570 0.534459i
\(161\) 0 0
\(162\) 0 0
\(163\) −0.194278 0.336499i −0.0152170 0.0263566i 0.858317 0.513120i \(-0.171511\pi\)
−0.873534 + 0.486764i \(0.838177\pi\)
\(164\) 6.68657 0.522133
\(165\) 0 0
\(166\) 4.69596 0.364477
\(167\) 3.64889 6.32006i 0.282360 0.489061i −0.689606 0.724185i \(-0.742216\pi\)
0.971965 + 0.235124i \(0.0755496\pi\)
\(168\) 0 0
\(169\) 5.42542 + 9.39710i 0.417340 + 0.722854i
\(170\) −11.5392 19.9864i −0.885013 1.53289i
\(171\) 0 0
\(172\) −8.02756 + 13.9041i −0.612096 + 1.06018i
\(173\) 2.02754 3.51181i 0.154151 0.266998i −0.778598 0.627522i \(-0.784069\pi\)
0.932750 + 0.360525i \(0.117402\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.53957 + 2.66661i −0.116049 + 0.201003i
\(177\) 0 0
\(178\) −15.2929 −1.14625
\(179\) −5.29243 + 9.16675i −0.395575 + 0.685155i −0.993174 0.116639i \(-0.962788\pi\)
0.597600 + 0.801795i \(0.296121\pi\)
\(180\) 0 0
\(181\) 19.6312 1.45917 0.729586 0.683889i \(-0.239713\pi\)
0.729586 + 0.683889i \(0.239713\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −10.6469 −0.784896
\(185\) −15.8829 27.5099i −1.16773 2.02257i
\(186\) 0 0
\(187\) 2.24058 3.88081i 0.163848 0.283793i
\(188\) 14.7115 1.07294
\(189\) 0 0
\(190\) 15.3837 1.11605
\(191\) 4.14357 7.17688i 0.299818 0.519301i −0.676276 0.736648i \(-0.736407\pi\)
0.976094 + 0.217348i \(0.0697406\pi\)
\(192\) 0 0
\(193\) 9.39242 + 16.2682i 0.676082 + 1.17101i 0.976152 + 0.217090i \(0.0696566\pi\)
−0.300070 + 0.953917i \(0.597010\pi\)
\(194\) −19.7701 −1.41941
\(195\) 0 0
\(196\) 0 0
\(197\) −5.99634 −0.427222 −0.213611 0.976919i \(-0.568522\pi\)
−0.213611 + 0.976919i \(0.568522\pi\)
\(198\) 0 0
\(199\) −7.20434 + 12.4783i −0.510702 + 0.884562i 0.489221 + 0.872160i \(0.337281\pi\)
−0.999923 + 0.0124022i \(0.996052\pi\)
\(200\) 14.3054 1.01155
\(201\) 0 0
\(202\) 19.3654 33.5419i 1.36255 2.36000i
\(203\) 0 0
\(204\) 0 0
\(205\) 2.64131 4.57488i 0.184477 0.319523i
\(206\) −2.65758 + 4.60306i −0.185162 + 0.320710i
\(207\) 0 0
\(208\) 1.66727 + 2.88780i 0.115604 + 0.200233i
\(209\) 1.49354 + 2.58690i 0.103311 + 0.178939i
\(210\) 0 0
\(211\) −6.92418 + 11.9930i −0.476680 + 0.825634i −0.999643 0.0267212i \(-0.991493\pi\)
0.522963 + 0.852356i \(0.324827\pi\)
\(212\) −23.8646 −1.63902
\(213\) 0 0
\(214\) −41.7894 −2.85667
\(215\) 6.34204 + 10.9847i 0.432523 + 0.749153i
\(216\) 0 0
\(217\) 0 0
\(218\) −18.6156 32.2431i −1.26081 2.18378i
\(219\) 0 0
\(220\) 7.30929 + 12.6601i 0.492792 + 0.853541i
\(221\) −2.42644 4.20271i −0.163220 0.282705i
\(222\) 0 0
\(223\) −2.33756 4.04878i −0.156535 0.271126i 0.777082 0.629399i \(-0.216699\pi\)
−0.933617 + 0.358273i \(0.883366\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 2.01584 + 3.49154i 0.134092 + 0.232254i
\(227\) 19.7126 1.30837 0.654187 0.756333i \(-0.273011\pi\)
0.654187 + 0.756333i \(0.273011\pi\)
\(228\) 0 0
\(229\) −28.0728 −1.85510 −0.927552 0.373694i \(-0.878091\pi\)
−0.927552 + 0.373694i \(0.878091\pi\)
\(230\) −9.16188 + 15.8688i −0.604116 + 1.04636i
\(231\) 0 0
\(232\) −2.11342 3.66054i −0.138753 0.240326i
\(233\) 6.90113 + 11.9531i 0.452108 + 0.783074i 0.998517 0.0544448i \(-0.0173389\pi\)
−0.546409 + 0.837518i \(0.684006\pi\)
\(234\) 0 0
\(235\) 5.81127 10.0654i 0.379085 0.656595i
\(236\) 22.5785 39.1070i 1.46973 2.54565i
\(237\) 0 0
\(238\) 0 0
\(239\) −5.53069 + 9.57944i −0.357751 + 0.619642i −0.987585 0.157087i \(-0.949790\pi\)
0.629834 + 0.776730i \(0.283123\pi\)
\(240\) 0 0
\(241\) 23.1697 1.49249 0.746247 0.665669i \(-0.231854\pi\)
0.746247 + 0.665669i \(0.231854\pi\)
\(242\) 10.9408 18.9499i 0.703299 1.21815i
\(243\) 0 0
\(244\) −2.06942 −0.132481
\(245\) 0 0
\(246\) 0 0
\(247\) 3.23486 0.205829
\(248\) 6.63243 + 11.4877i 0.421160 + 0.729470i
\(249\) 0 0
\(250\) −5.11914 + 8.86660i −0.323763 + 0.560773i
\(251\) −7.78402 −0.491323 −0.245662 0.969356i \(-0.579005\pi\)
−0.245662 + 0.969356i \(0.579005\pi\)
\(252\) 0 0
\(253\) −3.55796 −0.223687
\(254\) 4.73696 8.20466i 0.297223 0.514806i
\(255\) 0 0
\(256\) 13.8226 + 23.9414i 0.863912 + 1.49634i
\(257\) 10.3760 0.647235 0.323618 0.946188i \(-0.395101\pi\)
0.323618 + 0.946188i \(0.395101\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 15.8312 0.981807
\(261\) 0 0
\(262\) −6.35937 + 11.0148i −0.392883 + 0.680494i
\(263\) 19.1331 1.17980 0.589898 0.807478i \(-0.299168\pi\)
0.589898 + 0.807478i \(0.299168\pi\)
\(264\) 0 0
\(265\) −9.42689 + 16.3279i −0.579090 + 1.00301i
\(266\) 0 0
\(267\) 0 0
\(268\) −23.6835 + 41.0210i −1.44670 + 2.50576i
\(269\) −4.41840 + 7.65290i −0.269395 + 0.466605i −0.968706 0.248212i \(-0.920157\pi\)
0.699311 + 0.714818i \(0.253490\pi\)
\(270\) 0 0
\(271\) 9.16955 + 15.8821i 0.557010 + 0.964770i 0.997744 + 0.0671321i \(0.0213849\pi\)
−0.440734 + 0.897638i \(0.645282\pi\)
\(272\) 3.76474 + 6.52073i 0.228271 + 0.395377i
\(273\) 0 0
\(274\) −8.94531 + 15.4937i −0.540406 + 0.936010i
\(275\) 4.78059 0.288280
\(276\) 0 0
\(277\) 5.10482 0.306719 0.153360 0.988170i \(-0.450991\pi\)
0.153360 + 0.988170i \(0.450991\pi\)
\(278\) −16.7865 29.0750i −1.00679 1.74381i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.853180 + 1.47775i 0.0508964 + 0.0881552i 0.890351 0.455274i \(-0.150459\pi\)
−0.839455 + 0.543430i \(0.817125\pi\)
\(282\) 0 0
\(283\) −6.24415 10.8152i −0.371176 0.642896i 0.618571 0.785729i \(-0.287712\pi\)
−0.989747 + 0.142833i \(0.954379\pi\)
\(284\) 23.8793 + 41.3602i 1.41698 + 2.45428i
\(285\) 0 0
\(286\) 2.36843 + 4.10224i 0.140048 + 0.242571i
\(287\) 0 0
\(288\) 0 0
\(289\) 3.02104 + 5.23260i 0.177708 + 0.307800i
\(290\) −7.27458 −0.427178
\(291\) 0 0
\(292\) 38.6552 2.26213
\(293\) −2.60202 + 4.50684i −0.152012 + 0.263292i −0.931967 0.362543i \(-0.881909\pi\)
0.779955 + 0.625835i \(0.215242\pi\)
\(294\) 0 0
\(295\) −17.8377 30.8959i −1.03855 1.79883i
\(296\) 22.0275 + 38.1527i 1.28032 + 2.21758i
\(297\) 0 0
\(298\) 2.60135 4.50566i 0.150692 0.261006i
\(299\) −1.92654 + 3.33687i −0.111415 + 0.192976i
\(300\) 0 0
\(301\) 0 0
\(302\) −16.7412 + 28.9966i −0.963347 + 1.66857i
\(303\) 0 0
\(304\) −5.01906 −0.287863
\(305\) −0.817453 + 1.41587i −0.0468072 + 0.0810725i
\(306\) 0 0
\(307\) −5.00136 −0.285442 −0.142721 0.989763i \(-0.545585\pi\)
−0.142721 + 0.989763i \(0.545585\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 22.8295 1.29663
\(311\) 16.1984 + 28.0565i 0.918528 + 1.59094i 0.801652 + 0.597791i \(0.203955\pi\)
0.116876 + 0.993146i \(0.462712\pi\)
\(312\) 0 0
\(313\) 0.759535 1.31555i 0.0429315 0.0743595i −0.843761 0.536719i \(-0.819664\pi\)
0.886693 + 0.462359i \(0.152997\pi\)
\(314\) −7.08000 −0.399548
\(315\) 0 0
\(316\) 2.83821 0.159662
\(317\) −10.7544 + 18.6272i −0.604029 + 1.04621i 0.388175 + 0.921586i \(0.373106\pi\)
−0.992204 + 0.124623i \(0.960228\pi\)
\(318\) 0 0
\(319\) −0.706261 1.22328i −0.0395430 0.0684905i
\(320\) 31.9200 1.78439
\(321\) 0 0
\(322\) 0 0
\(323\) 7.30441 0.406428
\(324\) 0 0
\(325\) 2.58856 4.48352i 0.143588 0.248701i
\(326\) 0.927430 0.0513656
\(327\) 0 0
\(328\) −3.66315 + 6.34476i −0.202263 + 0.350330i
\(329\) 0 0
\(330\) 0 0
\(331\) −9.73902 + 16.8685i −0.535305 + 0.927175i 0.463844 + 0.885917i \(0.346470\pi\)
−0.999149 + 0.0412580i \(0.986863\pi\)
\(332\) −3.63691 + 6.29931i −0.199601 + 0.345719i
\(333\) 0 0
\(334\) 8.70942 + 15.0852i 0.476558 + 0.825423i
\(335\) 18.7107 + 32.4079i 1.02228 + 1.77063i
\(336\) 0 0
\(337\) 4.84742 8.39598i 0.264056 0.457358i −0.703260 0.710933i \(-0.748273\pi\)
0.967316 + 0.253575i \(0.0816063\pi\)
\(338\) −25.8995 −1.40875
\(339\) 0 0
\(340\) 35.7472 1.93866
\(341\) 2.21642 + 3.83896i 0.120026 + 0.207891i
\(342\) 0 0
\(343\) 0 0
\(344\) −8.79558 15.2344i −0.474226 0.821383i
\(345\) 0 0
\(346\) 4.83948 + 8.38222i 0.260172 + 0.450631i
\(347\) 1.01302 + 1.75460i 0.0543817 + 0.0941919i 0.891935 0.452164i \(-0.149348\pi\)
−0.837553 + 0.546356i \(0.816015\pi\)
\(348\) 0 0
\(349\) −8.14577 14.1089i −0.436033 0.755231i 0.561346 0.827581i \(-0.310284\pi\)
−0.997379 + 0.0723497i \(0.976950\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.80896 + 3.13321i 0.0964180 + 0.167001i
\(353\) 17.0614 0.908089 0.454045 0.890979i \(-0.349981\pi\)
0.454045 + 0.890979i \(0.349981\pi\)
\(354\) 0 0
\(355\) 37.7309 2.00255
\(356\) 11.8440 20.5144i 0.627731 1.08726i
\(357\) 0 0
\(358\) −12.6323 21.8798i −0.667639 1.15639i
\(359\) −1.48363 2.56972i −0.0783030 0.135625i 0.824215 0.566277i \(-0.191617\pi\)
−0.902518 + 0.430652i \(0.858283\pi\)
\(360\) 0 0
\(361\) 7.06549 12.2378i 0.371868 0.644094i
\(362\) −23.4285 + 40.5794i −1.23137 + 2.13280i
\(363\) 0 0
\(364\) 0 0
\(365\) 15.2695 26.4475i 0.799240 1.38432i
\(366\) 0 0
\(367\) 10.1575 0.530216 0.265108 0.964219i \(-0.414592\pi\)
0.265108 + 0.964219i \(0.414592\pi\)
\(368\) 2.98914 5.17733i 0.155819 0.269887i
\(369\) 0 0
\(370\) 75.8207 3.94173
\(371\) 0 0
\(372\) 0 0
\(373\) −25.4846 −1.31954 −0.659771 0.751467i \(-0.729347\pi\)
−0.659771 + 0.751467i \(0.729347\pi\)
\(374\) 5.34798 + 9.26297i 0.276537 + 0.478977i
\(375\) 0 0
\(376\) −8.05947 + 13.9594i −0.415635 + 0.719902i
\(377\) −1.52969 −0.0787829
\(378\) 0 0
\(379\) 9.85497 0.506216 0.253108 0.967438i \(-0.418547\pi\)
0.253108 + 0.967438i \(0.418547\pi\)
\(380\) −11.9143 + 20.6362i −0.611191 + 1.05861i
\(381\) 0 0
\(382\) 9.89016 + 17.1303i 0.506025 + 0.876460i
\(383\) −27.3127 −1.39561 −0.697806 0.716286i \(-0.745840\pi\)
−0.697806 + 0.716286i \(0.745840\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −44.8370 −2.28214
\(387\) 0 0
\(388\) 15.3114 26.5202i 0.777321 1.34636i
\(389\) −4.18446 −0.212161 −0.106080 0.994358i \(-0.533830\pi\)
−0.106080 + 0.994358i \(0.533830\pi\)
\(390\) 0 0
\(391\) −4.35019 + 7.53475i −0.219999 + 0.381049i
\(392\) 0 0
\(393\) 0 0
\(394\) 7.15624 12.3950i 0.360526 0.624450i
\(395\) 1.12114 1.94187i 0.0564107 0.0977062i
\(396\) 0 0
\(397\) −15.3354 26.5618i −0.769664 1.33310i −0.937745 0.347323i \(-0.887091\pi\)
0.168082 0.985773i \(-0.446243\pi\)
\(398\) −17.1958 29.7840i −0.861948 1.49294i
\(399\) 0 0
\(400\) −4.01629 + 6.95642i −0.200815 + 0.347821i
\(401\) 6.84803 0.341974 0.170987 0.985273i \(-0.445304\pi\)
0.170987 + 0.985273i \(0.445304\pi\)
\(402\) 0 0
\(403\) 4.80055 0.239132
\(404\) 29.9961 + 51.9547i 1.49236 + 2.58485i
\(405\) 0 0
\(406\) 0 0
\(407\) 7.36113 + 12.7499i 0.364878 + 0.631987i
\(408\) 0 0
\(409\) −9.13490 15.8221i −0.451692 0.782353i 0.546799 0.837264i \(-0.315846\pi\)
−0.998491 + 0.0549104i \(0.982513\pi\)
\(410\) 6.30445 + 10.9196i 0.311355 + 0.539282i
\(411\) 0 0
\(412\) −4.11646 7.12991i −0.202803 0.351265i
\(413\) 0 0
\(414\) 0 0
\(415\) 2.87328 + 4.97666i 0.141044 + 0.244295i
\(416\) 3.91802 0.192097
\(417\) 0 0
\(418\) −7.12979 −0.348729
\(419\) 11.2310 19.4526i 0.548669 0.950322i −0.449698 0.893181i \(-0.648468\pi\)
0.998366 0.0571410i \(-0.0181984\pi\)
\(420\) 0 0
\(421\) 10.4177 + 18.0440i 0.507728 + 0.879411i 0.999960 + 0.00894684i \(0.00284791\pi\)
−0.492232 + 0.870464i \(0.663819\pi\)
\(422\) −16.5271 28.6258i −0.804527 1.39348i
\(423\) 0 0
\(424\) 13.0739 22.6446i 0.634923 1.09972i
\(425\) 5.84505 10.1239i 0.283526 0.491082i
\(426\) 0 0
\(427\) 0 0
\(428\) 32.3649 56.0577i 1.56442 2.70965i
\(429\) 0 0
\(430\) −30.2752 −1.46000
\(431\) 10.1213 17.5307i 0.487527 0.844422i −0.512370 0.858765i \(-0.671232\pi\)
0.999897 + 0.0143427i \(0.00456557\pi\)
\(432\) 0 0
\(433\) 21.6764 1.04170 0.520851 0.853648i \(-0.325615\pi\)
0.520851 + 0.853648i \(0.325615\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 57.6693 2.76186
\(437\) −2.89978 5.02257i −0.138715 0.240262i
\(438\) 0 0
\(439\) −17.7390 + 30.7249i −0.846639 + 1.46642i 0.0375520 + 0.999295i \(0.488044\pi\)
−0.884191 + 0.467126i \(0.845289\pi\)
\(440\) −16.0172 −0.763589
\(441\) 0 0
\(442\) 11.5832 0.550955
\(443\) −9.60313 + 16.6331i −0.456258 + 0.790263i −0.998760 0.0497923i \(-0.984144\pi\)
0.542501 + 0.840055i \(0.317477\pi\)
\(444\) 0 0
\(445\) −9.35716 16.2071i −0.443572 0.768289i
\(446\) 11.1589 0.528390
\(447\) 0 0
\(448\) 0 0
\(449\) 29.6082 1.39730 0.698648 0.715465i \(-0.253785\pi\)
0.698648 + 0.715465i \(0.253785\pi\)
\(450\) 0 0
\(451\) −1.22415 + 2.12029i −0.0576429 + 0.0998405i
\(452\) −6.24488 −0.293735
\(453\) 0 0
\(454\) −23.5257 + 40.7478i −1.10412 + 1.91239i
\(455\) 0 0
\(456\) 0 0
\(457\) 4.78098 8.28090i 0.223645 0.387364i −0.732267 0.681017i \(-0.761538\pi\)
0.955912 + 0.293653i \(0.0948711\pi\)
\(458\) 33.5031 58.0290i 1.56550 2.71152i
\(459\) 0 0
\(460\) −14.1913 24.5800i −0.661673 1.14605i
\(461\) 10.9187 + 18.9118i 0.508536 + 0.880809i 0.999951 + 0.00988416i \(0.00314628\pi\)
−0.491416 + 0.870925i \(0.663520\pi\)
\(462\) 0 0
\(463\) 13.0744 22.6456i 0.607621 1.05243i −0.384010 0.923329i \(-0.625457\pi\)
0.991631 0.129102i \(-0.0412094\pi\)
\(464\) 2.37339 0.110182
\(465\) 0 0
\(466\) −32.9442 −1.52611
\(467\) −17.4764 30.2699i −0.808709 1.40073i −0.913758 0.406258i \(-0.866833\pi\)
0.105049 0.994467i \(-0.466500\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 13.8707 + 24.0248i 0.639809 + 1.10818i
\(471\) 0 0
\(472\) 24.7386 + 42.8485i 1.13869 + 1.97226i
\(473\) −2.93930 5.09102i −0.135149 0.234086i
\(474\) 0 0
\(475\) 3.89623 + 6.74848i 0.178771 + 0.309641i
\(476\) 0 0
\(477\) 0 0
\(478\) −13.2010 22.8649i −0.603801 1.04581i
\(479\) −29.8109 −1.36209 −0.681047 0.732240i \(-0.738475\pi\)
−0.681047 + 0.732240i \(0.738475\pi\)
\(480\) 0 0
\(481\) 15.9434 0.726959
\(482\) −27.6516 + 47.8939i −1.25949 + 2.18151i
\(483\) 0 0
\(484\) 16.9467 + 29.3525i 0.770304 + 1.33421i
\(485\) −12.0965 20.9518i −0.549276 0.951374i
\(486\) 0 0
\(487\) −11.2253 + 19.4428i −0.508667 + 0.881037i 0.491283 + 0.871000i \(0.336528\pi\)
−0.999950 + 0.0100365i \(0.996805\pi\)
\(488\) 1.13370 1.96363i 0.0513202 0.0888892i
\(489\) 0 0
\(490\) 0 0
\(491\) −17.5222 + 30.3494i −0.790767 + 1.36965i 0.134726 + 0.990883i \(0.456984\pi\)
−0.925493 + 0.378765i \(0.876349\pi\)
\(492\) 0 0
\(493\) −3.45407 −0.155564
\(494\) −3.86060 + 6.68675i −0.173696 + 0.300851i
\(495\) 0 0
\(496\) −7.44830 −0.334438
\(497\) 0 0
\(498\) 0 0
\(499\) −8.93520 −0.399994 −0.199997 0.979796i \(-0.564093\pi\)
−0.199997 + 0.979796i \(0.564093\pi\)
\(500\) −7.92929 13.7339i −0.354609 0.614200i
\(501\) 0 0
\(502\) 9.28972 16.0903i 0.414621 0.718144i
\(503\) −12.6403 −0.563603 −0.281802 0.959473i \(-0.590932\pi\)
−0.281802 + 0.959473i \(0.590932\pi\)
\(504\) 0 0
\(505\) 47.3958 2.10909
\(506\) 4.24620 7.35463i 0.188766 0.326953i
\(507\) 0 0
\(508\) 7.33732 + 12.7086i 0.325541 + 0.563854i
\(509\) −28.1110 −1.24600 −0.623000 0.782222i \(-0.714086\pi\)
−0.623000 + 0.782222i \(0.714086\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −24.5070 −1.08307
\(513\) 0 0
\(514\) −12.3830 + 21.4480i −0.546192 + 0.946033i
\(515\) −6.50427 −0.286613
\(516\) 0 0
\(517\) −2.69331 + 4.66495i −0.118452 + 0.205164i
\(518\) 0 0
\(519\) 0 0
\(520\) −8.67288 + 15.0219i −0.380331 + 0.658753i
\(521\) 4.23768 7.33988i 0.185656 0.321566i −0.758141 0.652090i \(-0.773892\pi\)
0.943797 + 0.330524i \(0.107226\pi\)
\(522\) 0 0
\(523\) −16.7236 28.9662i −0.731273 1.26660i −0.956339 0.292259i \(-0.905593\pi\)
0.225066 0.974344i \(-0.427740\pi\)
\(524\) −9.85035 17.0613i −0.430315 0.745327i
\(525\) 0 0
\(526\) −22.8341 + 39.5498i −0.995613 + 1.72445i
\(527\) 10.8398 0.472187
\(528\) 0 0
\(529\) −16.0921 −0.699655
\(530\) −22.5008 38.9725i −0.977371 1.69286i
\(531\) 0 0
\(532\) 0 0
\(533\) 1.32569 + 2.29616i 0.0574220 + 0.0994579i
\(534\) 0 0
\(535\) −25.5693 44.2874i −1.10546 1.91471i
\(536\) −25.9493 44.9456i −1.12084 1.94135i
\(537\) 0 0
\(538\) −10.5461 18.2665i −0.454677 0.787523i
\(539\) 0 0
\(540\) 0 0
\(541\) −9.12929 15.8124i −0.392499 0.679828i 0.600280 0.799790i \(-0.295056\pi\)
−0.992778 + 0.119962i \(0.961723\pi\)
\(542\) −43.7730 −1.88021
\(543\) 0 0
\(544\) 8.84701 0.379312
\(545\) 22.7803 39.4567i 0.975802 1.69014i
\(546\) 0 0
\(547\) −2.88599 4.99869i −0.123396 0.213728i 0.797709 0.603043i \(-0.206045\pi\)
−0.921105 + 0.389315i \(0.872712\pi\)
\(548\) −13.8558 23.9990i −0.591892 1.02519i
\(549\) 0 0
\(550\) −5.70532 + 9.88190i −0.243276 + 0.421366i
\(551\) 1.15122 1.99397i 0.0490437 0.0849461i
\(552\) 0 0
\(553\) 0 0
\(554\) −6.09227 + 10.5521i −0.258836 + 0.448317i
\(555\) 0 0
\(556\) 52.0029 2.20541
\(557\) −16.6911 + 28.9098i −0.707223 + 1.22495i 0.258661 + 0.965968i \(0.416719\pi\)
−0.965883 + 0.258977i \(0.916614\pi\)
\(558\) 0 0
\(559\) −6.36623 −0.269263
\(560\) 0 0
\(561\) 0 0
\(562\) −4.07286 −0.171803
\(563\) −1.09566 1.89773i −0.0461764 0.0799799i 0.842013 0.539457i \(-0.181370\pi\)
−0.888190 + 0.459477i \(0.848037\pi\)
\(564\) 0 0
\(565\) −2.46683 + 4.27268i −0.103780 + 0.179753i
\(566\) 29.8079 1.25292
\(567\) 0 0
\(568\) −52.3278 −2.19563
\(569\) 9.49302 16.4424i 0.397968 0.689301i −0.595507 0.803350i \(-0.703049\pi\)
0.993475 + 0.114049i \(0.0363822\pi\)
\(570\) 0 0
\(571\) 10.8690 + 18.8257i 0.454854 + 0.787831i 0.998680 0.0513674i \(-0.0163580\pi\)
−0.543825 + 0.839198i \(0.683025\pi\)
\(572\) −7.33717 −0.306782
\(573\) 0 0
\(574\) 0 0
\(575\) −9.28172 −0.387074
\(576\) 0 0
\(577\) 15.4516 26.7629i 0.643258 1.11416i −0.341443 0.939903i \(-0.610916\pi\)
0.984701 0.174253i \(-0.0557511\pi\)
\(578\) −14.4217 −0.599862
\(579\) 0 0
\(580\) 5.63398 9.75835i 0.233938 0.405193i
\(581\) 0 0
\(582\) 0 0
\(583\) 4.36902 7.56737i 0.180946 0.313408i
\(584\) −21.1767 + 36.6792i −0.876299 + 1.51780i
\(585\) 0 0
\(586\) −6.21069 10.7572i −0.256561 0.444377i
\(587\) −9.18332 15.9060i −0.379036 0.656510i 0.611886 0.790946i \(-0.290411\pi\)
−0.990922 + 0.134436i \(0.957078\pi\)
\(588\) 0 0
\(589\) −3.61282 + 6.25759i −0.148864 + 0.257840i
\(590\) 85.1527 3.50568
\(591\) 0 0
\(592\) −24.7371 −1.01669
\(593\) 13.8775 + 24.0365i 0.569880 + 0.987061i 0.996577 + 0.0826662i \(0.0263435\pi\)
−0.426698 + 0.904394i \(0.640323\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4.02936 + 6.97905i 0.165049 + 0.285873i
\(597\) 0 0
\(598\) −4.59841 7.96468i −0.188043 0.325700i
\(599\) 0.201412 + 0.348855i 0.00822945 + 0.0142538i 0.870111 0.492856i \(-0.164047\pi\)
−0.861881 + 0.507110i \(0.830714\pi\)
\(600\) 0 0
\(601\) −12.3733 21.4312i −0.504717 0.874196i −0.999985 0.00545577i \(-0.998263\pi\)
0.495268 0.868740i \(-0.335070\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −25.9313 44.9143i −1.05513 1.82754i
\(605\) 26.7769 1.08864
\(606\) 0 0
\(607\) −24.0697 −0.976957 −0.488479 0.872576i \(-0.662448\pi\)
−0.488479 + 0.872576i \(0.662448\pi\)
\(608\) −2.94865 + 5.10721i −0.119584 + 0.207125i
\(609\) 0 0
\(610\) −1.95115 3.37950i −0.0789999 0.136832i
\(611\) 2.91672 + 5.05190i 0.117998 + 0.204378i
\(612\) 0 0
\(613\) 10.1907 17.6509i 0.411600 0.712912i −0.583465 0.812138i \(-0.698303\pi\)
0.995065 + 0.0992261i \(0.0316367\pi\)
\(614\) 5.96879 10.3382i 0.240881 0.417218i
\(615\) 0 0
\(616\) 0 0
\(617\) 20.9315 36.2544i 0.842669 1.45955i −0.0449604 0.998989i \(-0.514316\pi\)
0.887630 0.460558i \(-0.152350\pi\)
\(618\) 0 0
\(619\) −14.8219 −0.595743 −0.297871 0.954606i \(-0.596277\pi\)
−0.297871 + 0.954606i \(0.596277\pi\)
\(620\) −17.6809 + 30.6242i −0.710081 + 1.22990i
\(621\) 0 0
\(622\) −77.3270 −3.10053
\(623\) 0 0
\(624\) 0 0
\(625\) −30.1861 −1.20744
\(626\) 1.81291 + 3.14005i 0.0724585 + 0.125502i
\(627\) 0 0
\(628\) 5.48329 9.49734i 0.218807 0.378985i
\(629\) 36.0007 1.43544
\(630\) 0 0
\(631\) −21.0294 −0.837169 −0.418585 0.908178i \(-0.637474\pi\)
−0.418585 + 0.908178i \(0.637474\pi\)
\(632\) −1.55487 + 2.69312i −0.0618496 + 0.107127i
\(633\) 0 0
\(634\) −25.6694 44.4607i −1.01946 1.76576i
\(635\) 11.5935 0.460072
\(636\) 0 0
\(637\) 0 0
\(638\) 3.37150 0.133479
\(639\) 0 0
\(640\) −30.2882 + 52.4607i −1.19725 + 2.07369i
\(641\) −11.9318 −0.471279 −0.235640 0.971840i \(-0.575719\pi\)
−0.235640 + 0.971840i \(0.575719\pi\)
\(642\) 0 0
\(643\) 19.9678 34.5852i 0.787452 1.36391i −0.140072 0.990141i \(-0.544733\pi\)
0.927524 0.373765i \(-0.121933\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −8.71733 + 15.0989i −0.342979 + 0.594057i
\(647\) 0.494477 0.856459i 0.0194399 0.0336709i −0.856142 0.516741i \(-0.827145\pi\)
0.875582 + 0.483070i \(0.160478\pi\)
\(648\) 0 0
\(649\) 8.26714 + 14.3191i 0.324514 + 0.562074i
\(650\) 6.17856 + 10.7016i 0.242343 + 0.419751i
\(651\) 0 0
\(652\) −0.718272 + 1.24408i −0.0281297 + 0.0487221i
\(653\) −22.7147 −0.888894 −0.444447 0.895805i \(-0.646600\pi\)
−0.444447 + 0.895805i \(0.646600\pi\)
\(654\) 0 0
\(655\) −15.5642 −0.608144
\(656\) −2.05688 3.56262i −0.0803076 0.139097i
\(657\) 0 0
\(658\) 0 0
\(659\) 19.1943 + 33.2454i 0.747702 + 1.29506i 0.948922 + 0.315512i \(0.102176\pi\)
−0.201220 + 0.979546i \(0.564491\pi\)
\(660\) 0 0
\(661\) 16.9629 + 29.3806i 0.659780 + 1.14277i 0.980672 + 0.195657i \(0.0626839\pi\)
−0.320892 + 0.947116i \(0.603983\pi\)
\(662\) −23.2458 40.2628i −0.903472 1.56486i
\(663\) 0 0
\(664\) −3.98486 6.90198i −0.154642 0.267849i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.37124 + 2.37505i 0.0530944 + 0.0919623i
\(668\) −26.9809 −1.04392
\(669\) 0 0
\(670\) −89.3201 −3.45074
\(671\) 0.378860 0.656205i 0.0146257 0.0253325i
\(672\) 0 0
\(673\) −16.1030 27.8912i −0.620725 1.07513i −0.989351 0.145549i \(-0.953505\pi\)
0.368626 0.929578i \(-0.379828\pi\)
\(674\) 11.5702 + 20.0401i 0.445666 + 0.771916i
\(675\) 0 0
\(676\) 20.0585 34.7424i 0.771483 1.33625i
\(677\) 18.9842 32.8816i 0.729622 1.26374i −0.227421 0.973797i \(-0.573029\pi\)
0.957043 0.289946i \(-0.0936375\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −19.5836 + 33.9198i −0.750997 + 1.30076i
\(681\) 0 0
\(682\) −10.5806 −0.405153
\(683\) −7.59357 + 13.1525i −0.290560 + 0.503265i −0.973942 0.226796i \(-0.927175\pi\)
0.683382 + 0.730061i \(0.260508\pi\)
\(684\) 0 0
\(685\) −21.8932 −0.836495
\(686\) 0 0
\(687\) 0 0
\(688\) 9.87754 0.376578
\(689\) −4.73142 8.19507i −0.180253 0.312207i
\(690\) 0 0
\(691\) 1.34574 2.33089i 0.0511943 0.0886711i −0.839293 0.543680i \(-0.817031\pi\)
0.890487 + 0.455009i \(0.150364\pi\)
\(692\) −14.9922 −0.569919
\(693\) 0 0
\(694\) −4.83589 −0.183568
\(695\) 20.5420 35.5798i 0.779203 1.34962i
\(696\) 0 0
\(697\) 2.99344 + 5.18480i 0.113385 + 0.196388i
\(698\) 38.8858 1.47185
\(699\) 0 0
\(700\) 0 0
\(701\) 11.8515 0.447625 0.223813 0.974632i \(-0.428150\pi\)
0.223813 + 0.974632i \(0.428150\pi\)
\(702\) 0 0
\(703\) −11.9988 + 20.7826i −0.452544 + 0.783829i
\(704\) −14.7938 −0.557562
\(705\) 0 0
\(706\) −20.3617 + 35.2675i −0.766323 + 1.32731i
\(707\) 0 0
\(708\) 0 0
\(709\) 20.5167 35.5359i 0.770520 1.33458i −0.166759 0.985998i \(-0.553330\pi\)
0.937278 0.348582i \(-0.113337\pi\)
\(710\) −45.0294 + 77.9931i −1.68992 + 2.92703i
\(711\) 0 0
\(712\) 12.9772 + 22.4771i 0.486339 + 0.842364i
\(713\) −4.30328 7.45351i −0.161159 0.279136i
\(714\) 0 0
\(715\) −2.89830 + 5.02001i −0.108390 + 0.187738i
\(716\) 39.1337 1.46250
\(717\) 0 0
\(718\) 7.08246 0.264315
\(719\) 10.4555 + 18.1094i 0.389923 + 0.675366i 0.992439 0.122741i \(-0.0391685\pi\)
−0.602516 + 0.798107i \(0.705835\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 16.8644 + 29.2100i 0.627628 + 1.08708i
\(723\) 0 0
\(724\) −36.2896 62.8554i −1.34869 2.33600i
\(725\) −1.84243 3.19119i −0.0684263 0.118518i
\(726\) 0 0
\(727\) −1.32165 2.28917i −0.0490173 0.0849005i 0.840476 0.541849i \(-0.182276\pi\)
−0.889493 + 0.456949i \(0.848942\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 36.4462 + 63.1267i 1.34893 + 2.33642i
\(731\) −14.3751 −0.531683
\(732\) 0 0
\(733\) −14.1489 −0.522602 −0.261301 0.965257i \(-0.584152\pi\)
−0.261301 + 0.965257i \(0.584152\pi\)
\(734\) −12.1223 + 20.9964i −0.447442 + 0.774992i
\(735\) 0 0
\(736\) −3.51218 6.08327i −0.129461 0.224232i
\(737\) −8.67174 15.0199i −0.319428 0.553265i
\(738\) 0 0
\(739\) −7.85905 + 13.6123i −0.289100 + 0.500736i −0.973595 0.228282i \(-0.926689\pi\)
0.684495 + 0.729017i \(0.260023\pi\)
\(740\) −58.7212 + 101.708i −2.15864 + 3.73887i
\(741\) 0 0
\(742\) 0 0
\(743\) −10.5496 + 18.2724i −0.387026 + 0.670348i −0.992048 0.125861i \(-0.959831\pi\)
0.605022 + 0.796208i \(0.293164\pi\)
\(744\) 0 0
\(745\) 6.36665 0.233256
\(746\) 30.4142 52.6789i 1.11354 1.92871i
\(747\) 0 0
\(748\) −16.5675 −0.605768
\(749\) 0 0
\(750\) 0 0
\(751\) 13.0370 0.475725 0.237863 0.971299i \(-0.423553\pi\)
0.237863 + 0.971299i \(0.423553\pi\)
\(752\) −4.52544 7.83829i −0.165026 0.285833i
\(753\) 0 0
\(754\) 1.82558 3.16200i 0.0664838 0.115153i
\(755\) −40.9732 −1.49117
\(756\) 0 0
\(757\) −12.6856 −0.461065 −0.230532 0.973065i \(-0.574047\pi\)
−0.230532 + 0.973065i \(0.574047\pi\)
\(758\) −11.7613 + 20.3711i −0.427188 + 0.739912i
\(759\) 0 0
\(760\) −13.0542 22.6105i −0.473525 0.820169i
\(761\) −6.04077 −0.218978 −0.109489 0.993988i \(-0.534921\pi\)
−0.109489 + 0.993988i \(0.534921\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −30.6388 −1.10847
\(765\) 0 0
\(766\) 32.5959 56.4577i 1.17774 2.03990i
\(767\) 17.9058 0.646540
\(768\) 0 0
\(769\) −0.108129 + 0.187285i −0.00389924 + 0.00675368i −0.867968 0.496619i \(-0.834575\pi\)
0.864069 + 0.503373i \(0.167908\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 34.7251 60.1457i 1.24979 2.16469i
\(773\) 18.8132 32.5854i 0.676663 1.17202i −0.299316 0.954154i \(-0.596759\pi\)
0.975980 0.217861i \(-0.0699081\pi\)
\(774\) 0 0
\(775\) 5.78202 + 10.0148i 0.207696 + 0.359741i
\(776\) 16.7763 + 29.0575i 0.602235 + 1.04310i
\(777\) 0 0
\(778\) 4.99388 8.64965i 0.179039 0.310105i
\(779\) −3.99078 −0.142985
\(780\) 0 0
\(781\) −17.4869 −0.625730
\(782\) −10.3833 17.9845i −0.371307 0.643123i
\(783\) 0 0
\(784\) 0 0
\(785\) −4.33198 7.50321i −0.154615 0.267801i
\(786\) 0 0
\(787\) 15.4067 + 26.6853i 0.549191 + 0.951226i 0.998330 + 0.0577648i \(0.0183973\pi\)
−0.449139 + 0.893462i \(0.648269\pi\)
\(788\) 11.0847 + 19.1992i 0.394875 + 0.683943i
\(789\) 0 0
\(790\) 2.67601 + 4.63499i 0.0952083 + 0.164906i
\(791\) 0 0
\(792\) 0 0
\(793\) −0.410286 0.710636i −0.0145697 0.0252354i
\(794\) 73.2074 2.59803
\(795\) 0 0
\(796\) 53.2