Properties

Label 819.2.y.h.307.5
Level $819$
Weight $2$
Character 819.307
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.y (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \( x^{12} + 35x^{8} + 295x^{4} + 169 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 307.5
Root \(0.626770 + 0.626770i\) of defining polynomial
Character \(\chi\) \(=\) 819.307
Dual form 819.2.y.h.811.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.45161 + 1.45161i) q^{2} +2.21432i q^{4} +(-2.01464 + 2.01464i) q^{5} +(-2.38948 + 1.13594i) q^{7} +(-0.311108 + 0.311108i) q^{8} +O(q^{10})\) \(q+(1.45161 + 1.45161i) q^{2} +2.21432i q^{4} +(-2.01464 + 2.01464i) q^{5} +(-2.38948 + 1.13594i) q^{7} +(-0.311108 + 0.311108i) q^{8} -5.84892 q^{10} +(-0.451606 + 0.451606i) q^{11} +(-3.40251 + 1.19288i) q^{13} +(-5.11753 - 1.81964i) q^{14} +3.52543 q^{16} -4.32672 q^{17} +(3.40251 - 3.40251i) q^{19} +(-4.46105 - 4.46105i) q^{20} -1.31111 q^{22} +0.933323i q^{23} -3.11753i q^{25} +(-6.67068 - 3.20751i) q^{26} +(-2.51534 - 5.29108i) q^{28} -6.33185 q^{29} +(-5.47781 + 5.47781i) q^{31} +(5.73975 + 5.73975i) q^{32} +(-6.28070 - 6.28070i) q^{34} +(2.52543 - 7.10246i) q^{35} +(2.14050 - 2.14050i) q^{37} +9.87820 q^{38} -1.25354i q^{40} +(1.81964 - 1.81964i) q^{41} +10.4795i q^{43} +(-1.00000 - 1.00000i) q^{44} +(-1.35482 + 1.35482i) q^{46} +(5.90958 + 5.90958i) q^{47} +(4.41926 - 5.42864i) q^{49} +(4.52543 - 4.52543i) q^{50} +(-2.64141 - 7.53424i) q^{52} -3.36196 q^{53} -1.81964i q^{55} +(0.389986 - 1.09679i) q^{56} +(-9.19135 - 9.19135i) q^{58} +(-0.255657 - 0.255657i) q^{59} +7.78989i q^{61} -15.9032 q^{62} +9.61285i q^{64} +(4.45161 - 9.25803i) q^{65} +(7.28100 + 7.28100i) q^{67} -9.58075i q^{68} +(13.9759 - 6.64405i) q^{70} +(-5.56914 - 5.56914i) q^{71} +(8.86144 + 8.86144i) q^{73} +6.21432 q^{74} +(7.53424 + 7.53424i) q^{76} +(0.566106 - 1.59210i) q^{77} -13.7971 q^{79} +(-7.10246 + 7.10246i) q^{80} +5.28281 q^{82} +(4.30785 - 4.30785i) q^{83} +(8.71678 - 8.71678i) q^{85} +(-15.2121 + 15.2121i) q^{86} -0.280996i q^{88} +(5.61214 + 5.61214i) q^{89} +(6.77519 - 6.71541i) q^{91} -2.06668 q^{92} +17.1568i q^{94} +13.7096i q^{95} +(0.236784 - 0.236784i) q^{97} +(14.2953 - 1.46522i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8} + 8 q^{11} - 8 q^{14} + 16 q^{16} - 16 q^{22} - 20 q^{28} + 4 q^{29} + 16 q^{32} + 4 q^{35} + 12 q^{37} - 12 q^{44} + 24 q^{46} + 28 q^{50} + 12 q^{53} - 44 q^{58} + 40 q^{65} + 60 q^{67} + 4 q^{70} + 48 q^{74} - 4 q^{79} + 12 q^{85} - 36 q^{86} - 32 q^{91} - 24 q^{92} + 28 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.45161 + 1.45161i 1.02644 + 1.02644i 0.999641 + 0.0267996i \(0.00853160\pi\)
0.0267996 + 0.999641i \(0.491468\pi\)
\(3\) 0 0
\(4\) 2.21432i 1.10716i
\(5\) −2.01464 + 2.01464i −0.900973 + 0.900973i −0.995520 0.0945469i \(-0.969860\pi\)
0.0945469 + 0.995520i \(0.469860\pi\)
\(6\) 0 0
\(7\) −2.38948 + 1.13594i −0.903140 + 0.429347i
\(8\) −0.311108 + 0.311108i −0.109993 + 0.109993i
\(9\) 0 0
\(10\) −5.84892 −1.84959
\(11\) −0.451606 + 0.451606i −0.136164 + 0.136164i −0.771904 0.635739i \(-0.780695\pi\)
0.635739 + 0.771904i \(0.280695\pi\)
\(12\) 0 0
\(13\) −3.40251 + 1.19288i −0.943685 + 0.330844i
\(14\) −5.11753 1.81964i −1.36772 0.486321i
\(15\) 0 0
\(16\) 3.52543 0.881357
\(17\) −4.32672 −1.04938 −0.524692 0.851292i \(-0.675820\pi\)
−0.524692 + 0.851292i \(0.675820\pi\)
\(18\) 0 0
\(19\) 3.40251 3.40251i 0.780588 0.780588i −0.199342 0.979930i \(-0.563880\pi\)
0.979930 + 0.199342i \(0.0638803\pi\)
\(20\) −4.46105 4.46105i −0.997522 0.997522i
\(21\) 0 0
\(22\) −1.31111 −0.279529
\(23\) 0.933323i 0.194611i 0.995255 + 0.0973057i \(0.0310225\pi\)
−0.995255 + 0.0973057i \(0.968978\pi\)
\(24\) 0 0
\(25\) 3.11753i 0.623506i
\(26\) −6.67068 3.20751i −1.30823 0.629045i
\(27\) 0 0
\(28\) −2.51534 5.29108i −0.475355 0.999920i
\(29\) −6.33185 −1.17580 −0.587898 0.808935i \(-0.700044\pi\)
−0.587898 + 0.808935i \(0.700044\pi\)
\(30\) 0 0
\(31\) −5.47781 + 5.47781i −0.983843 + 0.983843i −0.999872 0.0160282i \(-0.994898\pi\)
0.0160282 + 0.999872i \(0.494898\pi\)
\(32\) 5.73975 + 5.73975i 1.01465 + 1.01465i
\(33\) 0 0
\(34\) −6.28070 6.28070i −1.07713 1.07713i
\(35\) 2.52543 7.10246i 0.426875 1.20053i
\(36\) 0 0
\(37\) 2.14050 2.14050i 0.351896 0.351896i −0.508919 0.860815i \(-0.669955\pi\)
0.860815 + 0.508919i \(0.169955\pi\)
\(38\) 9.87820 1.60246
\(39\) 0 0
\(40\) 1.25354i 0.198202i
\(41\) 1.81964 1.81964i 0.284181 0.284181i −0.550593 0.834774i \(-0.685598\pi\)
0.834774 + 0.550593i \(0.185598\pi\)
\(42\) 0 0
\(43\) 10.4795i 1.59811i 0.601259 + 0.799054i \(0.294666\pi\)
−0.601259 + 0.799054i \(0.705334\pi\)
\(44\) −1.00000 1.00000i −0.150756 0.150756i
\(45\) 0 0
\(46\) −1.35482 + 1.35482i −0.199757 + 0.199757i
\(47\) 5.90958 + 5.90958i 0.862002 + 0.862002i 0.991570 0.129569i \(-0.0413593\pi\)
−0.129569 + 0.991570i \(0.541359\pi\)
\(48\) 0 0
\(49\) 4.41926 5.42864i 0.631323 0.775520i
\(50\) 4.52543 4.52543i 0.639992 0.639992i
\(51\) 0 0
\(52\) −2.64141 7.53424i −0.366297 1.04481i
\(53\) −3.36196 −0.461801 −0.230901 0.972977i \(-0.574167\pi\)
−0.230901 + 0.972977i \(0.574167\pi\)
\(54\) 0 0
\(55\) 1.81964i 0.245361i
\(56\) 0.389986 1.09679i 0.0521141 0.146564i
\(57\) 0 0
\(58\) −9.19135 9.19135i −1.20688 1.20688i
\(59\) −0.255657 0.255657i −0.0332837 0.0332837i 0.690269 0.723553i \(-0.257492\pi\)
−0.723553 + 0.690269i \(0.757492\pi\)
\(60\) 0 0
\(61\) 7.78989i 0.997394i 0.866776 + 0.498697i \(0.166188\pi\)
−0.866776 + 0.498697i \(0.833812\pi\)
\(62\) −15.9032 −2.01971
\(63\) 0 0
\(64\) 9.61285i 1.20161i
\(65\) 4.45161 9.25803i 0.552154 1.14832i
\(66\) 0 0
\(67\) 7.28100 + 7.28100i 0.889515 + 0.889515i 0.994476 0.104961i \(-0.0334718\pi\)
−0.104961 + 0.994476i \(0.533472\pi\)
\(68\) 9.58075i 1.16184i
\(69\) 0 0
\(70\) 13.9759 6.64405i 1.67044 0.794116i
\(71\) −5.56914 5.56914i −0.660935 0.660935i 0.294665 0.955600i \(-0.404792\pi\)
−0.955600 + 0.294665i \(0.904792\pi\)
\(72\) 0 0
\(73\) 8.86144 + 8.86144i 1.03715 + 1.03715i 0.999283 + 0.0378706i \(0.0120575\pi\)
0.0378706 + 0.999283i \(0.487943\pi\)
\(74\) 6.21432 0.722400
\(75\) 0 0
\(76\) 7.53424 + 7.53424i 0.864236 + 0.864236i
\(77\) 0.566106 1.59210i 0.0645137 0.181437i
\(78\) 0 0
\(79\) −13.7971 −1.55229 −0.776145 0.630554i \(-0.782828\pi\)
−0.776145 + 0.630554i \(0.782828\pi\)
\(80\) −7.10246 + 7.10246i −0.794079 + 0.794079i
\(81\) 0 0
\(82\) 5.28281 0.583389
\(83\) 4.30785 4.30785i 0.472848 0.472848i −0.429987 0.902835i \(-0.641482\pi\)
0.902835 + 0.429987i \(0.141482\pi\)
\(84\) 0 0
\(85\) 8.71678 8.71678i 0.945468 0.945468i
\(86\) −15.2121 + 15.2121i −1.64036 + 1.64036i
\(87\) 0 0
\(88\) 0.280996i 0.0299543i
\(89\) 5.61214 + 5.61214i 0.594885 + 0.594885i 0.938947 0.344062i \(-0.111803\pi\)
−0.344062 + 0.938947i \(0.611803\pi\)
\(90\) 0 0
\(91\) 6.77519 6.71541i 0.710233 0.703967i
\(92\) −2.06668 −0.215466
\(93\) 0 0
\(94\) 17.1568i 1.76959i
\(95\) 13.7096i 1.40658i
\(96\) 0 0
\(97\) 0.236784 0.236784i 0.0240417 0.0240417i −0.694984 0.719025i \(-0.744588\pi\)
0.719025 + 0.694984i \(0.244588\pi\)
\(98\) 14.2953 1.46522i 1.44404 0.148009i
\(99\) 0 0
\(100\) 6.90321 0.690321
\(101\) 9.21955 0.917380 0.458690 0.888596i \(-0.348319\pi\)
0.458690 + 0.888596i \(0.348319\pi\)
\(102\) 0 0
\(103\) 2.50708 0.247030 0.123515 0.992343i \(-0.460583\pi\)
0.123515 + 0.992343i \(0.460583\pi\)
\(104\) 0.687433 1.42966i 0.0674084 0.140190i
\(105\) 0 0
\(106\) −4.88025 4.88025i −0.474011 0.474011i
\(107\) −2.88247 −0.278659 −0.139329 0.990246i \(-0.544495\pi\)
−0.139329 + 0.990246i \(0.544495\pi\)
\(108\) 0 0
\(109\) −3.54839 3.54839i −0.339875 0.339875i 0.516446 0.856320i \(-0.327255\pi\)
−0.856320 + 0.516446i \(0.827255\pi\)
\(110\) 2.64141 2.64141i 0.251848 0.251848i
\(111\) 0 0
\(112\) −8.42395 + 4.00469i −0.795989 + 0.378408i
\(113\) 16.3526 1.53832 0.769161 0.639055i \(-0.220674\pi\)
0.769161 + 0.639055i \(0.220674\pi\)
\(114\) 0 0
\(115\) −1.88031 1.88031i −0.175340 0.175340i
\(116\) 14.0207i 1.30179i
\(117\) 0 0
\(118\) 0.742226i 0.0683274i
\(119\) 10.3386 4.91492i 0.947741 0.450550i
\(120\) 0 0
\(121\) 10.5921i 0.962919i
\(122\) −11.3079 + 11.3079i −1.02377 + 1.02377i
\(123\) 0 0
\(124\) −12.1296 12.1296i −1.08927 1.08927i
\(125\) −3.79249 3.79249i −0.339211 0.339211i
\(126\) 0 0
\(127\) 13.8272i 1.22696i −0.789709 0.613481i \(-0.789769\pi\)
0.789709 0.613481i \(-0.210231\pi\)
\(128\) −2.47457 + 2.47457i −0.218723 + 0.218723i
\(129\) 0 0
\(130\) 19.9010 6.97703i 1.74543 0.611926i
\(131\) 12.8301i 1.12097i 0.828166 + 0.560483i \(0.189385\pi\)
−0.828166 + 0.560483i \(0.810615\pi\)
\(132\) 0 0
\(133\) −4.26517 + 11.9953i −0.369838 + 1.04012i
\(134\) 21.1383i 1.82607i
\(135\) 0 0
\(136\) 1.34608 1.34608i 0.115425 0.115425i
\(137\) −2.40075 + 2.40075i −0.205110 + 0.205110i −0.802185 0.597075i \(-0.796329\pi\)
0.597075 + 0.802185i \(0.296329\pi\)
\(138\) 0 0
\(139\) 3.34184i 0.283451i 0.989906 + 0.141726i \(0.0452651\pi\)
−0.989906 + 0.141726i \(0.954735\pi\)
\(140\) 15.7271 + 5.59210i 1.32918 + 0.472619i
\(141\) 0 0
\(142\) 16.1684i 1.35682i
\(143\) 0.997882 2.07530i 0.0834471 0.173545i
\(144\) 0 0
\(145\) 12.7564 12.7564i 1.05936 1.05936i
\(146\) 25.7266i 2.12915i
\(147\) 0 0
\(148\) 4.73975 + 4.73975i 0.389605 + 0.389605i
\(149\) −2.62936 2.62936i −0.215406 0.215406i 0.591153 0.806559i \(-0.298673\pi\)
−0.806559 + 0.591153i \(0.798673\pi\)
\(150\) 0 0
\(151\) −4.78346 + 4.78346i −0.389272 + 0.389272i −0.874428 0.485156i \(-0.838763\pi\)
0.485156 + 0.874428i \(0.338763\pi\)
\(152\) 2.11709i 0.171719i
\(153\) 0 0
\(154\) 3.13287 1.48935i 0.252454 0.120015i
\(155\) 22.0716i 1.77283i
\(156\) 0 0
\(157\) 3.42542i 0.273379i 0.990614 + 0.136689i \(0.0436462\pi\)
−0.990614 + 0.136689i \(0.956354\pi\)
\(158\) −20.0279 20.0279i −1.59333 1.59333i
\(159\) 0 0
\(160\) −23.1270 −1.82835
\(161\) −1.06020 2.23016i −0.0835557 0.175761i
\(162\) 0 0
\(163\) 10.4494 10.4494i 0.818459 0.818459i −0.167426 0.985885i \(-0.553545\pi\)
0.985885 + 0.167426i \(0.0535455\pi\)
\(164\) 4.02928 + 4.02928i 0.314634 + 0.314634i
\(165\) 0 0
\(166\) 12.5066 0.970701
\(167\) −16.2326 16.2326i −1.25611 1.25611i −0.952933 0.303180i \(-0.901952\pi\)
−0.303180 0.952933i \(-0.598048\pi\)
\(168\) 0 0
\(169\) 10.1541 8.11753i 0.781084 0.624426i
\(170\) 25.3067 1.94093
\(171\) 0 0
\(172\) −23.2050 −1.76936
\(173\) 14.3810 1.09337 0.546685 0.837338i \(-0.315889\pi\)
0.546685 + 0.837338i \(0.315889\pi\)
\(174\) 0 0
\(175\) 3.54134 + 7.44929i 0.267700 + 0.563113i
\(176\) −1.59210 + 1.59210i −0.120009 + 0.120009i
\(177\) 0 0
\(178\) 16.2932i 1.22123i
\(179\) 4.11108i 0.307276i 0.988127 + 0.153638i \(0.0490990\pi\)
−0.988127 + 0.153638i \(0.950901\pi\)
\(180\) 0 0
\(181\) −21.5760 −1.60373 −0.801867 0.597502i \(-0.796160\pi\)
−0.801867 + 0.597502i \(0.796160\pi\)
\(182\) 19.5830 + 0.0867758i 1.45159 + 0.00643225i
\(183\) 0 0
\(184\) −0.290364 0.290364i −0.0214059 0.0214059i
\(185\) 8.62466i 0.634097i
\(186\) 0 0
\(187\) 1.95397 1.95397i 0.142889 0.142889i
\(188\) −13.0857 + 13.0857i −0.954373 + 0.954373i
\(189\) 0 0
\(190\) −19.9010 + 19.9010i −1.44377 + 1.44377i
\(191\) −10.3017 −0.745408 −0.372704 0.927950i \(-0.621569\pi\)
−0.372704 + 0.927950i \(0.621569\pi\)
\(192\) 0 0
\(193\) 6.28592 6.28592i 0.452470 0.452470i −0.443703 0.896174i \(-0.646336\pi\)
0.896174 + 0.443703i \(0.146336\pi\)
\(194\) 0.687433 0.0493548
\(195\) 0 0
\(196\) 12.0207 + 9.78566i 0.858625 + 0.698976i
\(197\) 3.25088 + 3.25088i 0.231616 + 0.231616i 0.813367 0.581751i \(-0.197632\pi\)
−0.581751 + 0.813367i \(0.697632\pi\)
\(198\) 0 0
\(199\) 6.20116 0.439589 0.219794 0.975546i \(-0.429461\pi\)
0.219794 + 0.975546i \(0.429461\pi\)
\(200\) 0.969888 + 0.969888i 0.0685815 + 0.0685815i
\(201\) 0 0
\(202\) 13.3832 + 13.3832i 0.941636 + 0.941636i
\(203\) 15.1299 7.19263i 1.06191 0.504824i
\(204\) 0 0
\(205\) 7.33185i 0.512079i
\(206\) 3.63929 + 3.63929i 0.253561 + 0.253561i
\(207\) 0 0
\(208\) −11.9953 + 4.20540i −0.831724 + 0.291592i
\(209\) 3.07318i 0.212577i
\(210\) 0 0
\(211\) −9.55554 −0.657830 −0.328915 0.944359i \(-0.606683\pi\)
−0.328915 + 0.944359i \(0.606683\pi\)
\(212\) 7.44446i 0.511288i
\(213\) 0 0
\(214\) −4.18421 4.18421i −0.286027 0.286027i
\(215\) −21.1124 21.1124i −1.43985 1.43985i
\(216\) 0 0
\(217\) 6.86665 19.3116i 0.466138 1.31096i
\(218\) 10.3017i 0.697722i
\(219\) 0 0
\(220\) 4.02928 0.271654
\(221\) 14.7217 5.16124i 0.990289 0.347183i
\(222\) 0 0
\(223\) 2.58074 2.58074i 0.172819 0.172819i −0.615398 0.788217i \(-0.711005\pi\)
0.788217 + 0.615398i \(0.211005\pi\)
\(224\) −20.2351 7.19500i −1.35201 0.480736i
\(225\) 0 0
\(226\) 23.7375 + 23.7375i 1.57900 + 1.57900i
\(227\) 5.25403 5.25403i 0.348722 0.348722i −0.510911 0.859633i \(-0.670692\pi\)
0.859633 + 0.510911i \(0.170692\pi\)
\(228\) 0 0
\(229\) 0.729224 + 0.729224i 0.0481885 + 0.0481885i 0.730790 0.682602i \(-0.239152\pi\)
−0.682602 + 0.730790i \(0.739152\pi\)
\(230\) 5.45893i 0.359952i
\(231\) 0 0
\(232\) 1.96989 1.96989i 0.129330 0.129330i
\(233\) 24.6128i 1.61244i 0.591615 + 0.806221i \(0.298491\pi\)
−0.591615 + 0.806221i \(0.701509\pi\)
\(234\) 0 0
\(235\) −23.8113 −1.55328
\(236\) 0.566106 0.566106i 0.0368503 0.0368503i
\(237\) 0 0
\(238\) 22.1421 + 7.87310i 1.43526 + 0.510337i
\(239\) 6.52543 + 6.52543i 0.422095 + 0.422095i 0.885924 0.463830i \(-0.153525\pi\)
−0.463830 + 0.885924i \(0.653525\pi\)
\(240\) 0 0
\(241\) −20.1563 20.1563i −1.29838 1.29838i −0.929461 0.368920i \(-0.879728\pi\)
−0.368920 0.929461i \(-0.620272\pi\)
\(242\) −15.3756 + 15.3756i −0.988379 + 0.988379i
\(243\) 0 0
\(244\) −17.2493 −1.10427
\(245\) 2.03353 + 19.8400i 0.129918 + 1.26753i
\(246\) 0 0
\(247\) −7.51828 + 15.6358i −0.478377 + 0.994883i
\(248\) 3.40838i 0.216432i
\(249\) 0 0
\(250\) 11.0104i 0.696359i
\(251\) −14.4448 −0.911747 −0.455873 0.890045i \(-0.650673\pi\)
−0.455873 + 0.890045i \(0.650673\pi\)
\(252\) 0 0
\(253\) −0.421494 0.421494i −0.0264991 0.0264991i
\(254\) 20.0716 20.0716i 1.25940 1.25940i
\(255\) 0 0
\(256\) 12.0415 0.752593
\(257\) 14.6237 0.912201 0.456101 0.889928i \(-0.349246\pi\)
0.456101 + 0.889928i \(0.349246\pi\)
\(258\) 0 0
\(259\) −2.68320 + 7.54617i −0.166726 + 0.468896i
\(260\) 20.5002 + 9.85728i 1.27137 + 0.611322i
\(261\) 0 0
\(262\) −18.6242 + 18.6242i −1.15061 + 1.15061i
\(263\) 2.61729 0.161389 0.0806946 0.996739i \(-0.474286\pi\)
0.0806946 + 0.996739i \(0.474286\pi\)
\(264\) 0 0
\(265\) 6.77314 6.77314i 0.416071 0.416071i
\(266\) −23.6038 + 11.2211i −1.44724 + 0.688009i
\(267\) 0 0
\(268\) −16.1225 + 16.1225i −0.984836 + 0.984836i
\(269\) 9.82340i 0.598944i −0.954105 0.299472i \(-0.903190\pi\)
0.954105 0.299472i \(-0.0968104\pi\)
\(270\) 0 0
\(271\) 3.43438 + 3.43438i 0.208624 + 0.208624i 0.803682 0.595059i \(-0.202871\pi\)
−0.595059 + 0.803682i \(0.702871\pi\)
\(272\) −15.2535 −0.924882
\(273\) 0 0
\(274\) −6.96989 −0.421066
\(275\) 1.40790 + 1.40790i 0.0848993 + 0.0848993i
\(276\) 0 0
\(277\) 5.89877i 0.354423i 0.984173 + 0.177211i \(0.0567076\pi\)
−0.984173 + 0.177211i \(0.943292\pi\)
\(278\) −4.85104 + 4.85104i −0.290946 + 0.290946i
\(279\) 0 0
\(280\) 1.42395 + 2.99531i 0.0850973 + 0.179004i
\(281\) −9.23729 + 9.23729i −0.551050 + 0.551050i −0.926744 0.375694i \(-0.877405\pi\)
0.375694 + 0.926744i \(0.377405\pi\)
\(282\) 0 0
\(283\) −8.32721 −0.495001 −0.247501 0.968888i \(-0.579609\pi\)
−0.247501 + 0.968888i \(0.579609\pi\)
\(284\) 12.3319 12.3319i 0.731761 0.731761i
\(285\) 0 0
\(286\) 4.46105 1.56399i 0.263788 0.0924806i
\(287\) −2.28100 + 6.41503i −0.134643 + 0.378667i
\(288\) 0 0
\(289\) 1.72054 0.101208
\(290\) 37.0345 2.17474
\(291\) 0 0
\(292\) −19.6221 + 19.6221i −1.14829 + 1.14829i
\(293\) 15.4903 + 15.4903i 0.904955 + 0.904955i 0.995860 0.0909047i \(-0.0289759\pi\)
−0.0909047 + 0.995860i \(0.528976\pi\)
\(294\) 0 0
\(295\) 1.03011 0.0599754
\(296\) 1.33185i 0.0774123i
\(297\) 0 0
\(298\) 7.63359i 0.442202i
\(299\) −1.11334 3.17564i −0.0643860 0.183652i
\(300\) 0 0
\(301\) −11.9041 25.0406i −0.686142 1.44331i
\(302\) −13.8874 −0.799130
\(303\) 0 0
\(304\) 11.9953 11.9953i 0.687977 0.687977i
\(305\) −15.6938 15.6938i −0.898625 0.898625i
\(306\) 0 0
\(307\) 5.77526 + 5.77526i 0.329611 + 0.329611i 0.852439 0.522827i \(-0.175123\pi\)
−0.522827 + 0.852439i \(0.675123\pi\)
\(308\) 3.52543 + 1.25354i 0.200880 + 0.0714270i
\(309\) 0 0
\(310\) 32.0393 32.0393i 1.81971 1.81971i
\(311\) 2.62562 0.148885 0.0744426 0.997225i \(-0.476282\pi\)
0.0744426 + 0.997225i \(0.476282\pi\)
\(312\) 0 0
\(313\) 19.8489i 1.12193i 0.827840 + 0.560964i \(0.189569\pi\)
−0.827840 + 0.560964i \(0.810431\pi\)
\(314\) −4.97237 + 4.97237i −0.280607 + 0.280607i
\(315\) 0 0
\(316\) 30.5511i 1.71863i
\(317\) −1.14764 1.14764i −0.0644581 0.0644581i 0.674143 0.738601i \(-0.264513\pi\)
−0.738601 + 0.674143i \(0.764513\pi\)
\(318\) 0 0
\(319\) 2.85950 2.85950i 0.160101 0.160101i
\(320\) −19.3664 19.3664i −1.08262 1.08262i
\(321\) 0 0
\(322\) 1.69832 4.77631i 0.0946435 0.266173i
\(323\) −14.7217 + 14.7217i −0.819137 + 0.819137i
\(324\) 0 0
\(325\) 3.71883 + 10.6074i 0.206283 + 0.588394i
\(326\) 30.3368 1.68020
\(327\) 0 0
\(328\) 1.13221i 0.0625159i
\(329\) −20.8338 7.40790i −1.14861 0.408411i
\(330\) 0 0
\(331\) −2.90321 2.90321i −0.159575 0.159575i 0.622803 0.782378i \(-0.285994\pi\)
−0.782378 + 0.622803i \(0.785994\pi\)
\(332\) 9.53896 + 9.53896i 0.523518 + 0.523518i
\(333\) 0 0
\(334\) 47.1266i 2.57865i
\(335\) −29.3371 −1.60286
\(336\) 0 0
\(337\) 4.47304i 0.243662i −0.992551 0.121831i \(-0.961123\pi\)
0.992551 0.121831i \(-0.0388766\pi\)
\(338\) 26.5232 + 2.95629i 1.44267 + 0.160801i
\(339\) 0 0
\(340\) 19.3017 + 19.3017i 1.04678 + 1.04678i
\(341\) 4.94762i 0.267929i
\(342\) 0 0
\(343\) −4.39312 + 17.9917i −0.237206 + 0.971459i
\(344\) −3.26025 3.26025i −0.175781 0.175781i
\(345\) 0 0
\(346\) 20.8756 + 20.8756i 1.12228 + 1.12228i
\(347\) −8.81135 −0.473018 −0.236509 0.971629i \(-0.576003\pi\)
−0.236509 + 0.971629i \(0.576003\pi\)
\(348\) 0 0
\(349\) −11.8133 11.8133i −0.632351 0.632351i 0.316306 0.948657i \(-0.397557\pi\)
−0.948657 + 0.316306i \(0.897557\pi\)
\(350\) −5.67280 + 15.9541i −0.303224 + 0.852781i
\(351\) 0 0
\(352\) −5.18421 −0.276319
\(353\) 2.91007 2.91007i 0.154887 0.154887i −0.625410 0.780297i \(-0.715068\pi\)
0.780297 + 0.625410i \(0.215068\pi\)
\(354\) 0 0
\(355\) 22.4396 1.19097
\(356\) −12.4271 + 12.4271i −0.658633 + 0.658633i
\(357\) 0 0
\(358\) −5.96767 + 5.96767i −0.315401 + 0.315401i
\(359\) −3.52320 + 3.52320i −0.185948 + 0.185948i −0.793942 0.607994i \(-0.791974\pi\)
0.607994 + 0.793942i \(0.291974\pi\)
\(360\) 0 0
\(361\) 4.15410i 0.218637i
\(362\) −31.3199 31.3199i −1.64614 1.64614i
\(363\) 0 0
\(364\) 14.8701 + 15.0024i 0.779404 + 0.786342i
\(365\) −35.7052 −1.86890
\(366\) 0 0
\(367\) 19.8112i 1.03414i −0.855944 0.517068i \(-0.827024\pi\)
0.855944 0.517068i \(-0.172976\pi\)
\(368\) 3.29036i 0.171522i
\(369\) 0 0
\(370\) −12.5196 + 12.5196i −0.650863 + 0.650863i
\(371\) 8.03335 3.81900i 0.417071 0.198273i
\(372\) 0 0
\(373\) −24.5368 −1.27047 −0.635234 0.772320i \(-0.719096\pi\)
−0.635234 + 0.772320i \(0.719096\pi\)
\(374\) 5.67280 0.293334
\(375\) 0 0
\(376\) −3.67704 −0.189629
\(377\) 21.5442 7.55311i 1.10958 0.389005i
\(378\) 0 0
\(379\) −8.78346 8.78346i −0.451176 0.451176i 0.444569 0.895745i \(-0.353357\pi\)
−0.895745 + 0.444569i \(0.853357\pi\)
\(380\) −30.3575 −1.55731
\(381\) 0 0
\(382\) −14.9541 14.9541i −0.765117 0.765117i
\(383\) 17.8990 17.8990i 0.914596 0.914596i −0.0820333 0.996630i \(-0.526141\pi\)
0.996630 + 0.0820333i \(0.0261414\pi\)
\(384\) 0 0
\(385\) 2.06702 + 4.34801i 0.105345 + 0.221595i
\(386\) 18.2494 0.928868
\(387\) 0 0
\(388\) 0.524315 + 0.524315i 0.0266181 + 0.0266181i
\(389\) 12.0667i 0.611805i −0.952063 0.305902i \(-0.901042\pi\)
0.952063 0.305902i \(-0.0989581\pi\)
\(390\) 0 0
\(391\) 4.03823i 0.204222i
\(392\) 0.314025 + 3.06376i 0.0158607 + 0.154743i
\(393\) 0 0
\(394\) 9.43801i 0.475480i
\(395\) 27.7961 27.7961i 1.39857 1.39857i
\(396\) 0 0
\(397\) 7.82177 + 7.82177i 0.392563 + 0.392563i 0.875600 0.483037i \(-0.160466\pi\)
−0.483037 + 0.875600i \(0.660466\pi\)
\(398\) 9.00164 + 9.00164i 0.451212 + 0.451212i
\(399\) 0 0
\(400\) 10.9906i 0.549532i
\(401\) 17.6178 17.6178i 0.879789 0.879789i −0.113723 0.993512i \(-0.536278\pi\)
0.993512 + 0.113723i \(0.0362777\pi\)
\(402\) 0 0
\(403\) 12.1039 25.1726i 0.602940 1.25394i
\(404\) 20.4150i 1.01569i
\(405\) 0 0
\(406\) 32.4035 + 11.5217i 1.60816 + 0.571813i
\(407\) 1.93332i 0.0958313i
\(408\) 0 0
\(409\) 24.0225 24.0225i 1.18783 1.18783i 0.210169 0.977665i \(-0.432599\pi\)
0.977665 0.210169i \(-0.0674013\pi\)
\(410\) −10.6430 + 10.6430i −0.525618 + 0.525618i
\(411\) 0 0
\(412\) 5.55147i 0.273501i
\(413\) 0.901299 + 0.320476i 0.0443500 + 0.0157696i
\(414\) 0 0
\(415\) 17.3575i 0.852047i
\(416\) −26.3763 12.6827i −1.29321 0.621822i
\(417\) 0 0
\(418\) −4.46105 + 4.46105i −0.218197 + 0.218197i
\(419\) 19.6899i 0.961912i −0.876745 0.480956i \(-0.840290\pi\)
0.876745 0.480956i \(-0.159710\pi\)
\(420\) 0 0
\(421\) 26.6042 + 26.6042i 1.29661 + 1.29661i 0.930619 + 0.365989i \(0.119269\pi\)
0.365989 + 0.930619i \(0.380731\pi\)
\(422\) −13.8709 13.8709i −0.675224 0.675224i
\(423\) 0 0
\(424\) 1.04593 1.04593i 0.0507950 0.0507950i
\(425\) 13.4887i 0.654298i
\(426\) 0 0
\(427\) −8.84888 18.6138i −0.428228 0.900786i
\(428\) 6.38271i 0.308520i
\(429\) 0 0
\(430\) 61.2937i 2.95585i
\(431\) 4.81135 + 4.81135i 0.231754 + 0.231754i 0.813425 0.581670i \(-0.197601\pi\)
−0.581670 + 0.813425i \(0.697601\pi\)
\(432\) 0 0
\(433\) 8.34704 0.401133 0.200567 0.979680i \(-0.435722\pi\)
0.200567 + 0.979680i \(0.435722\pi\)
\(434\) 38.0005 18.0652i 1.82408 0.867157i
\(435\) 0 0
\(436\) 7.85728 7.85728i 0.376295 0.376295i
\(437\) 3.17564 + 3.17564i 0.151911 + 0.151911i
\(438\) 0 0
\(439\) 2.42350 0.115667 0.0578336 0.998326i \(-0.481581\pi\)
0.0578336 + 0.998326i \(0.481581\pi\)
\(440\) 0.566106 + 0.566106i 0.0269880 + 0.0269880i
\(441\) 0 0
\(442\) 28.8622 + 13.8780i 1.37283 + 0.660110i
\(443\) −13.7763 −0.654532 −0.327266 0.944932i \(-0.606127\pi\)
−0.327266 + 0.944932i \(0.606127\pi\)
\(444\) 0 0
\(445\) −22.6128 −1.07195
\(446\) 7.49245 0.354778
\(447\) 0 0
\(448\) −10.9197 22.9697i −0.515905 1.08522i
\(449\) 24.7447 24.7447i 1.16777 1.16777i 0.185043 0.982730i \(-0.440758\pi\)
0.982730 0.185043i \(-0.0592423\pi\)
\(450\) 0 0
\(451\) 1.64353i 0.0773906i
\(452\) 36.2099i 1.70317i
\(453\) 0 0
\(454\) 15.2535 0.715885
\(455\) −0.120433 + 27.1787i −0.00564600 + 1.27416i
\(456\) 0 0
\(457\) −2.84521 2.84521i −0.133093 0.133093i 0.637422 0.770515i \(-0.280001\pi\)
−0.770515 + 0.637422i \(0.780001\pi\)
\(458\) 2.11709i 0.0989252i
\(459\) 0 0
\(460\) 4.16360 4.16360i 0.194129 0.194129i
\(461\) −2.38575 + 2.38575i −0.111115 + 0.111115i −0.760479 0.649363i \(-0.775036\pi\)
0.649363 + 0.760479i \(0.275036\pi\)
\(462\) 0 0
\(463\) 17.5899 17.5899i 0.817471 0.817471i −0.168270 0.985741i \(-0.553818\pi\)
0.985741 + 0.168270i \(0.0538180\pi\)
\(464\) −22.3225 −1.03630
\(465\) 0 0
\(466\) −35.7282 + 35.7282i −1.65507 + 1.65507i
\(467\) −21.4287 −0.991602 −0.495801 0.868436i \(-0.665126\pi\)
−0.495801 + 0.868436i \(0.665126\pi\)
\(468\) 0 0
\(469\) −25.6686 9.12701i −1.18527 0.421446i
\(470\) −34.5647 34.5647i −1.59435 1.59435i
\(471\) 0 0
\(472\) 0.159074 0.00732196
\(473\) −4.73260 4.73260i −0.217605 0.217605i
\(474\) 0 0
\(475\) −10.6074 10.6074i −0.486702 0.486702i
\(476\) 10.8832 + 22.8930i 0.498830 + 1.04930i
\(477\) 0 0
\(478\) 18.9447i 0.866510i
\(479\) 4.61425 + 4.61425i 0.210831 + 0.210831i 0.804620 0.593790i \(-0.202369\pi\)
−0.593790 + 0.804620i \(0.702369\pi\)
\(480\) 0 0
\(481\) −4.72971 + 9.83641i −0.215656 + 0.448501i
\(482\) 58.5180i 2.66542i
\(483\) 0 0
\(484\) −23.4543 −1.06610
\(485\) 0.954067i 0.0433220i
\(486\) 0 0
\(487\) 9.62867 + 9.62867i 0.436317 + 0.436317i 0.890770 0.454454i \(-0.150166\pi\)
−0.454454 + 0.890770i \(0.650166\pi\)
\(488\) −2.42350 2.42350i −0.109707 0.109707i
\(489\) 0 0
\(490\) −25.8479 + 31.7517i −1.16769 + 1.43439i
\(491\) 9.21924i 0.416059i 0.978123 + 0.208029i \(0.0667049\pi\)
−0.978123 + 0.208029i \(0.933295\pi\)
\(492\) 0 0
\(493\) 27.3962 1.23386
\(494\) −33.6106 + 11.7835i −1.51221 + 0.530163i
\(495\) 0 0
\(496\) −19.3116 + 19.3116i −0.867117 + 0.867117i
\(497\) 19.6336 + 6.98113i 0.880687 + 0.313147i
\(498\) 0 0
\(499\) −6.65947 6.65947i −0.298119 0.298119i 0.542158 0.840277i \(-0.317608\pi\)
−0.840277 + 0.542158i \(0.817608\pi\)
\(500\) 8.39779 8.39779i 0.375561 0.375561i
\(501\) 0 0
\(502\) −20.9681 20.9681i −0.935854 0.935854i
\(503\) 1.81069i 0.0807346i −0.999185 0.0403673i \(-0.987147\pi\)
0.999185 0.0403673i \(-0.0128528\pi\)
\(504\) 0 0
\(505\) −18.5741 + 18.5741i −0.826535 + 0.826535i
\(506\) 1.22369i 0.0543996i
\(507\) 0 0
\(508\) 30.6178 1.35844
\(509\) −22.2864 + 22.2864i −0.987827 + 0.987827i −0.999927 0.0121000i \(-0.996148\pi\)
0.0121000 + 0.999927i \(0.496148\pi\)
\(510\) 0 0
\(511\) −31.2404 11.1082i −1.38199 0.491396i
\(512\) 22.4286 + 22.4286i 0.991215 + 0.991215i
\(513\) 0 0
\(514\) 21.2278 + 21.2278i 0.936320 + 0.936320i
\(515\) −5.05086 + 5.05086i −0.222567 + 0.222567i
\(516\) 0 0
\(517\) −5.33761 −0.234748
\(518\) −14.8490 + 7.05912i −0.652428 + 0.310160i
\(519\) 0 0
\(520\) 1.49532 + 4.26517i 0.0655739 + 0.187040i
\(521\) 15.8744i 0.695472i −0.937592 0.347736i \(-0.886951\pi\)
0.937592 0.347736i \(-0.113049\pi\)
\(522\) 0 0
\(523\) 3.90795i 0.170883i 0.996343 + 0.0854413i \(0.0272300\pi\)
−0.996343 + 0.0854413i \(0.972770\pi\)
\(524\) −28.4098 −1.24109
\(525\) 0 0
\(526\) 3.79928 + 3.79928i 0.165656 + 0.165656i
\(527\) 23.7010 23.7010i 1.03243 1.03243i
\(528\) 0 0
\(529\) 22.1289 0.962126
\(530\) 19.6639 0.854143
\(531\) 0 0
\(532\) −26.5614 9.44446i −1.15158 0.409469i
\(533\) −4.02074 + 8.36196i −0.174158 + 0.362197i
\(534\) 0 0
\(535\) 5.80713 5.80713i 0.251064 0.251064i
\(536\) −4.53035 −0.195681
\(537\) 0 0
\(538\) 14.2597 14.2597i 0.614780 0.614780i
\(539\) 0.455841 + 4.44737i 0.0196345 + 0.191562i
\(540\) 0 0
\(541\) 8.57406 8.57406i 0.368628 0.368628i −0.498349 0.866977i \(-0.666060\pi\)
0.866977 + 0.498349i \(0.166060\pi\)
\(542\) 9.97073i 0.428280i
\(543\) 0 0
\(544\) −24.8343 24.8343i −1.06476 1.06476i
\(545\) 14.2975 0.612436
\(546\) 0 0
\(547\) −4.72546 −0.202046 −0.101023 0.994884i \(-0.532212\pi\)
−0.101023 + 0.994884i \(0.532212\pi\)
\(548\) −5.31603 5.31603i −0.227090 0.227090i
\(549\) 0 0
\(550\) 4.08742i 0.174288i
\(551\) −21.5442 + 21.5442i −0.917812 + 0.917812i
\(552\) 0 0
\(553\) 32.9678 15.6727i 1.40193 0.666470i
\(554\) −8.56268 + 8.56268i −0.363794 + 0.363794i
\(555\) 0 0
\(556\) −7.39991 −0.313826
\(557\) 23.8415 23.8415i 1.01019 1.01019i 0.0102475 0.999947i \(-0.496738\pi\)
0.999947 0.0102475i \(-0.00326193\pi\)
\(558\) 0 0
\(559\) −12.5007 35.6565i −0.528725 1.50811i
\(560\) 8.90321 25.0392i 0.376229 1.05810i
\(561\) 0 0
\(562\) −26.8178 −1.13124
\(563\) −41.2776 −1.73965 −0.869823 0.493365i \(-0.835767\pi\)
−0.869823 + 0.493365i \(0.835767\pi\)
\(564\) 0 0
\(565\) −32.9446 + 32.9446i −1.38599 + 1.38599i
\(566\) −12.0878 12.0878i −0.508089 0.508089i
\(567\) 0 0
\(568\) 3.46520 0.145397
\(569\) 43.5402i 1.82530i 0.408742 + 0.912650i \(0.365968\pi\)
−0.408742 + 0.912650i \(0.634032\pi\)
\(570\) 0 0
\(571\) 21.2701i 0.890126i 0.895499 + 0.445063i \(0.146819\pi\)
−0.895499 + 0.445063i \(0.853181\pi\)
\(572\) 4.59538 + 2.20963i 0.192143 + 0.0923893i
\(573\) 0 0
\(574\) −12.6232 + 6.00098i −0.526882 + 0.250476i
\(575\) 2.90967 0.121341
\(576\) 0 0
\(577\) −8.73703 + 8.73703i −0.363727 + 0.363727i −0.865183 0.501456i \(-0.832798\pi\)
0.501456 + 0.865183i \(0.332798\pi\)
\(578\) 2.49754 + 2.49754i 0.103884 + 0.103884i
\(579\) 0 0
\(580\) 28.2467 + 28.2467i 1.17288 + 1.17288i
\(581\) −5.40006 + 15.1870i −0.224032 + 0.630064i
\(582\) 0 0
\(583\) 1.51828 1.51828i 0.0628808 0.0628808i
\(584\) −5.51373 −0.228160
\(585\) 0 0
\(586\) 44.9717i 1.85776i
\(587\) −30.6931 + 30.6931i −1.26684 + 1.26684i −0.319131 + 0.947711i \(0.603391\pi\)
−0.947711 + 0.319131i \(0.896609\pi\)
\(588\) 0 0
\(589\) 37.2766i 1.53595i
\(590\) 1.49532 + 1.49532i 0.0615612 + 0.0615612i
\(591\) 0 0
\(592\) 7.54617 7.54617i 0.310146 0.310146i
\(593\) −5.18036 5.18036i −0.212732 0.212732i 0.592695 0.805427i \(-0.298064\pi\)
−0.805427 + 0.592695i \(0.798064\pi\)
\(594\) 0 0
\(595\) −10.9268 + 30.7304i −0.447956 + 1.25982i
\(596\) 5.82225 5.82225i 0.238488 0.238488i
\(597\) 0 0
\(598\) 2.99365 6.22591i 0.122419 0.254596i
\(599\) 18.5254 0.756928 0.378464 0.925616i \(-0.376452\pi\)
0.378464 + 0.925616i \(0.376452\pi\)
\(600\) 0 0
\(601\) 30.9807i 1.26373i −0.775079 0.631864i \(-0.782290\pi\)
0.775079 0.631864i \(-0.217710\pi\)
\(602\) 19.0690 53.6291i 0.777193 2.18576i
\(603\) 0 0
\(604\) −10.5921 10.5921i −0.430987 0.430987i
\(605\) −21.3393 21.3393i −0.867564 0.867564i
\(606\) 0 0
\(607\) 29.4674i 1.19605i 0.801479 + 0.598023i \(0.204047\pi\)
−0.801479 + 0.598023i \(0.795953\pi\)
\(608\) 39.0591 1.58405
\(609\) 0 0
\(610\) 45.5625i 1.84477i
\(611\) −27.1568 13.0580i −1.09865 0.528270i
\(612\) 0 0
\(613\) 13.9398 + 13.9398i 0.563022 + 0.563022i 0.930165 0.367142i \(-0.119664\pi\)
−0.367142 + 0.930165i \(0.619664\pi\)
\(614\) 16.7668i 0.676653i
\(615\) 0 0
\(616\) 0.319196 + 0.671436i 0.0128608 + 0.0270529i
\(617\) 27.7052 + 27.7052i 1.11537 + 1.11537i 0.992412 + 0.122957i \(0.0392377\pi\)
0.122957 + 0.992412i \(0.460762\pi\)
\(618\) 0 0
\(619\) −4.58642 4.58642i −0.184344 0.184344i 0.608902 0.793246i \(-0.291610\pi\)
−0.793246 + 0.608902i \(0.791610\pi\)
\(620\) 48.8736 1.96281
\(621\) 0 0
\(622\) 3.81137 + 3.81137i 0.152822 + 0.152822i
\(623\) −19.7852 7.03503i −0.792677 0.281853i
\(624\) 0 0
\(625\) 30.8687 1.23475
\(626\) −28.8128 + 28.8128i −1.15159 + 1.15159i
\(627\) 0 0
\(628\) −7.58498 −0.302674
\(629\) −9.26134 + 9.26134i −0.369274 + 0.369274i
\(630\) 0 0
\(631\) 11.1175 11.1175i 0.442582 0.442582i −0.450297 0.892879i \(-0.648682\pi\)
0.892879 + 0.450297i \(0.148682\pi\)
\(632\) 4.29237 4.29237i 0.170741 0.170741i
\(633\) 0 0
\(634\) 3.33185i 0.132325i
\(635\) 27.8567 + 27.8567i 1.10546 + 1.10546i
\(636\) 0 0
\(637\) −8.56087 + 23.7426i −0.339194 + 0.940716i
\(638\) 8.30174 0.328669
\(639\) 0 0
\(640\) 9.97073i 0.394128i
\(641\) 22.3590i 0.883129i 0.897229 + 0.441565i \(0.145576\pi\)
−0.897229 + 0.441565i \(0.854424\pi\)
\(642\) 0 0
\(643\) 5.69880 5.69880i 0.224739 0.224739i −0.585752 0.810491i \(-0.699201\pi\)
0.810491 + 0.585752i \(0.199201\pi\)
\(644\) 4.93829 2.34763i 0.194596 0.0925096i
\(645\) 0 0
\(646\) −42.7402 −1.68159
\(647\) 7.73510 0.304098 0.152049 0.988373i \(-0.451413\pi\)
0.152049 + 0.988373i \(0.451413\pi\)
\(648\) 0 0
\(649\) 0.230912 0.00906410
\(650\) −9.99952 + 20.7961i −0.392214 + 0.815689i
\(651\) 0 0
\(652\) 23.1383 + 23.1383i 0.906165 + 0.906165i
\(653\) −21.3921 −0.837137 −0.418568 0.908185i \(-0.637468\pi\)
−0.418568 + 0.908185i \(0.637468\pi\)
\(654\) 0 0
\(655\) −25.8479 25.8479i −1.00996 1.00996i
\(656\) 6.41503 6.41503i 0.250465 0.250465i
\(657\) 0 0
\(658\) −19.4891 40.9958i −0.759766 1.59818i
\(659\) 1.68445 0.0656167 0.0328084 0.999462i \(-0.489555\pi\)
0.0328084 + 0.999462i \(0.489555\pi\)
\(660\) 0 0
\(661\) 23.4056 + 23.4056i 0.910372 + 0.910372i 0.996301 0.0859290i \(-0.0273858\pi\)
−0.0859290 + 0.996301i \(0.527386\pi\)
\(662\) 8.42864i 0.327588i
\(663\) 0 0
\(664\) 2.68041i 0.104020i
\(665\) −15.5734 32.7589i −0.603910 1.27034i
\(666\) 0 0
\(667\) 5.90967i 0.228823i
\(668\) 35.9441 35.9441i 1.39072 1.39072i
\(669\) 0 0
\(670\) −42.5860 42.5860i −1.64524 1.64524i
\(671\) −3.51796 3.51796i −0.135809 0.135809i
\(672\) 0 0
\(673\) 26.2464i 1.01173i 0.862614 + 0.505863i \(0.168826\pi\)
−0.862614 + 0.505863i \(0.831174\pi\)
\(674\) 6.49309 6.49309i 0.250105 0.250105i
\(675\) 0 0
\(676\) 17.9748 + 22.4844i 0.691339 + 0.864785i
\(677\) 36.7658i 1.41303i 0.707700 + 0.706513i \(0.249733\pi\)
−0.707700 + 0.706513i \(0.750267\pi\)
\(678\) 0 0
\(679\) −0.296818 + 0.834764i −0.0113908 + 0.0320353i
\(680\) 5.42372i 0.207990i
\(681\) 0 0
\(682\) 7.18200 7.18200i 0.275013 0.275013i
\(683\) 14.5812 14.5812i 0.557934 0.557934i −0.370785 0.928719i \(-0.620911\pi\)
0.928719 + 0.370785i \(0.120911\pi\)
\(684\) 0 0
\(685\) 9.67329i 0.369597i
\(686\) −32.4939 + 19.7397i −1.24062 + 0.753667i
\(687\) 0 0
\(688\) 36.9447i 1.40850i
\(689\) 11.4391 4.01040i 0.435795 0.152784i
\(690\) 0 0
\(691\) −30.4663 + 30.4663i −1.15899 + 1.15899i −0.174299 + 0.984693i \(0.555766\pi\)
−0.984693 + 0.174299i \(0.944234\pi\)
\(692\) 31.8442i 1.21054i
\(693\) 0 0
\(694\) −12.7906 12.7906i −0.485525 0.485525i
\(695\) −6.73260 6.73260i −0.255382 0.255382i
\(696\) 0 0
\(697\) −7.87310 + 7.87310i −0.298215 + 0.298215i
\(698\) 34.2965i 1.29814i
\(699\) 0 0
\(700\) −16.4951 + 7.84166i −0.623457 + 0.296387i
\(701\) 17.7368i 0.669911i 0.942234 + 0.334955i \(0.108721\pi\)
−0.942234 + 0.334955i \(0.891279\pi\)
\(702\) 0 0
\(703\) 14.5661i 0.549371i
\(704\) −4.34122 4.34122i −0.163616 0.163616i
\(705\) 0 0
\(706\) 8.44854 0.317965
\(707\) −22.0300 + 10.4729i −0.828522 + 0.393874i
\(708\) 0 0
\(709\) 19.2422 19.2422i 0.722656 0.722656i −0.246489 0.969146i \(-0.579277\pi\)
0.969146 + 0.246489i \(0.0792770\pi\)
\(710\) 32.5734 + 32.5734i 1.22246 + 1.22246i
\(711\) 0 0
\(712\) −3.49196 −0.130867
\(713\) −5.11257 5.11257i −0.191467 0.191467i
\(714\) 0 0
\(715\) 2.17061 + 6.19135i 0.0811762 + 0.231543i
\(716\) −9.10324 −0.340204
\(717\) 0 0
\(718\) −10.2286 −0.381728
\(719\) 42.3551 1.57958 0.789789 0.613379i \(-0.210190\pi\)
0.789789 + 0.613379i \(0.210190\pi\)
\(720\) 0 0
\(721\) −5.99062 + 2.84790i −0.223102 + 0.106061i
\(722\) 6.03011 6.03011i 0.224418 0.224418i
\(723\) 0 0
\(724\) 47.7762i 1.77559i
\(725\) 19.7397i 0.733116i
\(726\) 0 0
\(727\) −23.2484 −0.862234 −0.431117 0.902296i \(-0.641880\pi\)
−0.431117 + 0.902296i \(0.641880\pi\)
\(728\) −0.0185978 + 4.19703i −0.000689279 + 0.155552i
\(729\) 0 0
\(730\) −51.8299 51.8299i −1.91831 1.91831i
\(731\) 45.3419i 1.67703i
\(732\) 0 0
\(733\) −24.1280 + 24.1280i −0.891188 + 0.891188i −0.994635 0.103447i \(-0.967013\pi\)
0.103447 + 0.994635i \(0.467013\pi\)
\(734\) 28.7580 28.7580i 1.06148 1.06148i
\(735\) 0 0
\(736\) −5.35704 + 5.35704i −0.197463 + 0.197463i
\(737\) −6.57628 −0.242240
\(738\) 0 0
\(739\) 4.46590 4.46590i 0.164281 0.164281i −0.620179 0.784460i \(-0.712940\pi\)
0.784460 + 0.620179i \(0.212940\pi\)
\(740\) −19.0977 −0.702047
\(741\) 0 0
\(742\) 17.2050 + 6.11758i 0.631614 + 0.224583i
\(743\) −10.0114 10.0114i −0.367282 0.367282i 0.499203 0.866485i \(-0.333626\pi\)
−0.866485 + 0.499203i \(0.833626\pi\)
\(744\) 0 0
\(745\) 10.5944 0.388149
\(746\) −35.6178 35.6178i −1.30406 1.30406i
\(747\) 0 0
\(748\) 4.32672 + 4.32672i 0.158201 + 0.158201i
\(749\) 6.88761 3.27432i 0.251668 0.119641i
\(750\) 0 0
\(751\) 8.16686i 0.298013i 0.988836 + 0.149006i \(0.0476075\pi\)
−0.988836 + 0.149006i \(0.952392\pi\)
\(752\) 20.8338 + 20.8338i 0.759731 + 0.759731i
\(753\) 0 0
\(754\) 42.2378 + 20.3095i 1.53821 + 0.739628i
\(755\) 19.2739i 0.701448i
\(756\) 0 0
\(757\) 10.5210 0.382392 0.191196 0.981552i \(-0.438763\pi\)
0.191196 + 0.981552i \(0.438763\pi\)
\(758\) 25.5002i 0.926210i
\(759\) 0 0
\(760\) −4.26517 4.26517i −0.154714 0.154714i
\(761\) 5.95138 + 5.95138i 0.215737 + 0.215737i 0.806699 0.590962i \(-0.201252\pi\)
−0.590962 + 0.806699i \(0.701252\pi\)
\(762\) 0 0
\(763\) 12.5096 + 4.44805i 0.452878 + 0.161030i
\(764\) 22.8113i 0.825286i
\(765\) 0 0
\(766\) 51.9646 1.87756
\(767\) 1.17484 + 0.564907i 0.0424210 + 0.0203976i
\(768\) 0 0
\(769\) −9.73800 + 9.73800i −0.351161 + 0.351161i −0.860541 0.509380i \(-0.829875\pi\)
0.509380 + 0.860541i \(0.329875\pi\)
\(770\) −3.31111 + 9.31209i −0.119324 + 0.335584i
\(771\) 0 0
\(772\) 13.9190 + 13.9190i 0.500957 + 0.500957i
\(773\) −16.0246 + 16.0246i −0.576364 + 0.576364i −0.933899 0.357536i \(-0.883617\pi\)
0.357536 + 0.933899i \(0.383617\pi\)
\(774\) 0 0
\(775\) 17.0772 + 17.0772i 0.613433 + 0.613433i
\(776\) 0.147331i 0.00528886i
\(777\) 0 0
\(778\) 17.5161 17.5161i 0.627981 0.627981i
\(779\) 12.3827i 0.443657i
\(780\) 0 0
\(781\) 5.03011 0.179992
\(782\) 5.86192 5.86192i 0.209622 0.209622i
\(783\) 0 0
\(784\) 15.5798 19.1383i 0.556421 0.683510i
\(785\) −6.90099 6.90099i −0.246307 0.246307i
\(786\) 0 0
\(787\) 17.9844 + 17.9844i 0.641075 + 0.641075i 0.950820 0.309745i \(-0.100244\pi\)
−0.309745 + 0.950820i \(0.600244\pi\)
\(788\) −7.19850 + 7.19850i −0.256436 + 0.256436i
\(789\) 0 0