Properties

Label 300.2.j.d.7.1
Level $300$
Weight $2$
Character 300.7
Analytic conductor $2.396$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.426337261060096.1
Defining polynomial: \(x^{12} - 4 x^{9} - 3 x^{8} + 4 x^{7} + 8 x^{6} + 8 x^{5} - 12 x^{4} - 32 x^{3} + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.1
Root \(-1.35818 - 0.394157i\) of defining polynomial
Character \(\chi\) \(=\) 300.7
Dual form 300.2.j.d.43.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.35818 - 0.394157i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.68928 + 1.07067i) q^{4} +(-0.681664 - 1.23909i) q^{6} +(2.47817 - 2.47817i) q^{7} +(-1.87233 - 2.12000i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-1.35818 - 0.394157i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.68928 + 1.07067i) q^{4} +(-0.681664 - 1.23909i) q^{6} +(2.47817 - 2.47817i) q^{7} +(-1.87233 - 2.12000i) q^{8} +1.00000i q^{9} -3.02831i q^{11} +(0.437425 + 1.95158i) q^{12} +(-0.363328 + 0.363328i) q^{13} +(-4.34258 + 2.38900i) q^{14} +(1.70734 + 3.61732i) q^{16} +(2.36333 + 2.36333i) q^{17} +(0.394157 - 1.35818i) q^{18} +4.95634 q^{19} +3.50466 q^{21} +(-1.19363 + 4.11297i) q^{22} +(-0.900390 - 0.900390i) q^{23} +(0.175128 - 2.82300i) q^{24} +(0.636672 - 0.350255i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(6.83963 - 1.53303i) q^{28} +3.50466i q^{29} -3.85607i q^{31} +(-0.893077 - 5.58591i) q^{32} +(2.14134 - 2.14134i) q^{33} +(-2.27829 - 4.14134i) q^{34} +(-1.07067 + 1.68928i) q^{36} +(0.363328 + 0.363328i) q^{37} +(-6.73158 - 1.95358i) q^{38} -0.513824 q^{39} +2.72666 q^{41} +(-4.75995 - 1.38139i) q^{42} +(3.92870 + 3.92870i) q^{43} +(3.24231 - 5.11566i) q^{44} +(0.867993 + 1.57778i) q^{46} +(5.85673 - 5.85673i) q^{47} +(-1.35056 + 3.76510i) q^{48} -5.28267i q^{49} +3.34225i q^{51} +(-1.00277 + 0.224760i) q^{52} +(-3.14134 + 3.14134i) q^{53} +(1.23909 - 0.681664i) q^{54} +(-9.89367 - 0.613763i) q^{56} +(3.50466 + 3.50466i) q^{57} +(1.38139 - 4.75995i) q^{58} -8.68516 q^{59} -15.2920 q^{61} +(-1.51990 + 5.23723i) q^{62} +(2.47817 + 2.47817i) q^{63} +(-0.988770 + 7.93866i) q^{64} +(-3.75233 + 2.06429i) q^{66} +(-3.92870 + 3.92870i) q^{67} +(1.46199 + 6.52267i) q^{68} -1.27334i q^{69} +4.25583i q^{71} +(2.12000 - 1.87233i) q^{72} +(-9.28267 + 9.28267i) q^{73} +(-0.350255 - 0.636672i) q^{74} +(8.37266 + 5.30660i) q^{76} +(-7.50466 - 7.50466i) q^{77} +(0.697863 + 0.202527i) q^{78} -0.399759 q^{79} -1.00000 q^{81} +(-3.70328 - 1.07473i) q^{82} +(-0.199879 - 0.199879i) q^{83} +(5.92036 + 3.75233i) q^{84} +(-3.78734 - 6.88438i) q^{86} +(-2.47817 + 2.47817i) q^{87} +(-6.42000 + 5.66999i) q^{88} +4.28267i q^{89} +1.80078i q^{91} +(-0.556993 - 2.48503i) q^{92} +(2.72666 - 2.72666i) q^{93} +(-10.2629 + 5.64600i) q^{94} +(3.31834 - 4.58134i) q^{96} +(-6.73599 - 6.73599i) q^{97} +(-2.08220 + 7.17480i) q^{98} +3.02831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{6} + 12q^{8} + O(q^{10}) \) \( 12q - 4q^{6} + 12q^{8} + 8q^{12} + 4q^{13} + 12q^{16} + 20q^{17} - 12q^{22} + 16q^{26} + 4q^{28} - 20q^{32} - 8q^{33} + 4q^{36} - 4q^{37} - 16q^{38} + 16q^{41} - 20q^{42} - 40q^{46} - 16q^{48} + 8q^{52} - 4q^{53} - 64q^{56} + 20q^{58} - 32q^{61} + 56q^{62} - 24q^{66} + 16q^{68} + 12q^{72} - 44q^{73} + 8q^{76} - 48q^{77} + 24q^{78} - 12q^{81} - 16q^{82} + 64q^{86} - 60q^{88} - 56q^{92} + 16q^{93} + 44q^{96} + 20q^{97} - 24q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35818 0.394157i −0.960375 0.278711i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.68928 + 1.07067i 0.844640 + 0.535334i
\(5\) 0 0
\(6\) −0.681664 1.23909i −0.278288 0.505855i
\(7\) 2.47817 2.47817i 0.936661 0.936661i −0.0614493 0.998110i \(-0.519572\pi\)
0.998110 + 0.0614493i \(0.0195722\pi\)
\(8\) −1.87233 2.12000i −0.661968 0.749532i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 3.02831i 0.913069i −0.889706 0.456534i \(-0.849091\pi\)
0.889706 0.456534i \(-0.150909\pi\)
\(12\) 0.437425 + 1.95158i 0.126274 + 0.563372i
\(13\) −0.363328 + 0.363328i −0.100769 + 0.100769i −0.755694 0.654925i \(-0.772700\pi\)
0.654925 + 0.755694i \(0.272700\pi\)
\(14\) −4.34258 + 2.38900i −1.16060 + 0.638488i
\(15\) 0 0
\(16\) 1.70734 + 3.61732i 0.426835 + 0.904330i
\(17\) 2.36333 + 2.36333i 0.573191 + 0.573191i 0.933019 0.359828i \(-0.117164\pi\)
−0.359828 + 0.933019i \(0.617164\pi\)
\(18\) 0.394157 1.35818i 0.0929036 0.320125i
\(19\) 4.95634 1.13706 0.568532 0.822661i \(-0.307512\pi\)
0.568532 + 0.822661i \(0.307512\pi\)
\(20\) 0 0
\(21\) 3.50466 0.764780
\(22\) −1.19363 + 4.11297i −0.254482 + 0.876888i
\(23\) −0.900390 0.900390i −0.187744 0.187744i 0.606976 0.794720i \(-0.292382\pi\)
−0.794720 + 0.606976i \(0.792382\pi\)
\(24\) 0.175128 2.82300i 0.0357478 0.576243i
\(25\) 0 0
\(26\) 0.636672 0.350255i 0.124862 0.0686907i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 6.83963 1.53303i 1.29257 0.289715i
\(29\) 3.50466i 0.650800i 0.945576 + 0.325400i \(0.105499\pi\)
−0.945576 + 0.325400i \(0.894501\pi\)
\(30\) 0 0
\(31\) 3.85607i 0.692571i −0.938129 0.346286i \(-0.887443\pi\)
0.938129 0.346286i \(-0.112557\pi\)
\(32\) −0.893077 5.58591i −0.157875 0.987459i
\(33\) 2.14134 2.14134i 0.372759 0.372759i
\(34\) −2.27829 4.14134i −0.390724 0.710233i
\(35\) 0 0
\(36\) −1.07067 + 1.68928i −0.178445 + 0.281547i
\(37\) 0.363328 + 0.363328i 0.0597308 + 0.0597308i 0.736341 0.676610i \(-0.236552\pi\)
−0.676610 + 0.736341i \(0.736552\pi\)
\(38\) −6.73158 1.95358i −1.09201 0.316912i
\(39\) −0.513824 −0.0822776
\(40\) 0 0
\(41\) 2.72666 0.425832 0.212916 0.977070i \(-0.431704\pi\)
0.212916 + 0.977070i \(0.431704\pi\)
\(42\) −4.75995 1.38139i −0.734476 0.213153i
\(43\) 3.92870 + 3.92870i 0.599121 + 0.599121i 0.940079 0.340958i \(-0.110751\pi\)
−0.340958 + 0.940079i \(0.610751\pi\)
\(44\) 3.24231 5.11566i 0.488797 0.771215i
\(45\) 0 0
\(46\) 0.867993 + 1.57778i 0.127979 + 0.232631i
\(47\) 5.85673 5.85673i 0.854292 0.854292i −0.136366 0.990659i \(-0.543542\pi\)
0.990659 + 0.136366i \(0.0435423\pi\)
\(48\) −1.35056 + 3.76510i −0.194936 + 0.543446i
\(49\) 5.28267i 0.754667i
\(50\) 0 0
\(51\) 3.34225i 0.468009i
\(52\) −1.00277 + 0.224760i −0.139059 + 0.0311685i
\(53\) −3.14134 + 3.14134i −0.431496 + 0.431496i −0.889137 0.457641i \(-0.848694\pi\)
0.457641 + 0.889137i \(0.348694\pi\)
\(54\) 1.23909 0.681664i 0.168618 0.0927627i
\(55\) 0 0
\(56\) −9.89367 0.613763i −1.32210 0.0820176i
\(57\) 3.50466 + 3.50466i 0.464204 + 0.464204i
\(58\) 1.38139 4.75995i 0.181385 0.625012i
\(59\) −8.68516 −1.13071 −0.565356 0.824847i \(-0.691261\pi\)
−0.565356 + 0.824847i \(0.691261\pi\)
\(60\) 0 0
\(61\) −15.2920 −1.95794 −0.978970 0.204004i \(-0.934604\pi\)
−0.978970 + 0.204004i \(0.934604\pi\)
\(62\) −1.51990 + 5.23723i −0.193027 + 0.665128i
\(63\) 2.47817 + 2.47817i 0.312220 + 0.312220i
\(64\) −0.988770 + 7.93866i −0.123596 + 0.992333i
\(65\) 0 0
\(66\) −3.75233 + 2.06429i −0.461880 + 0.254096i
\(67\) −3.92870 + 3.92870i −0.479967 + 0.479967i −0.905121 0.425154i \(-0.860220\pi\)
0.425154 + 0.905121i \(0.360220\pi\)
\(68\) 1.46199 + 6.52267i 0.177292 + 0.790989i
\(69\) 1.27334i 0.153293i
\(70\) 0 0
\(71\) 4.25583i 0.505075i 0.967587 + 0.252537i \(0.0812650\pi\)
−0.967587 + 0.252537i \(0.918735\pi\)
\(72\) 2.12000 1.87233i 0.249844 0.220656i
\(73\) −9.28267 + 9.28267i −1.08645 + 1.08645i −0.0905640 + 0.995891i \(0.528867\pi\)
−0.995891 + 0.0905640i \(0.971133\pi\)
\(74\) −0.350255 0.636672i −0.0407163 0.0740116i
\(75\) 0 0
\(76\) 8.37266 + 5.30660i 0.960410 + 0.608709i
\(77\) −7.50466 7.50466i −0.855236 0.855236i
\(78\) 0.697863 + 0.202527i 0.0790174 + 0.0229317i
\(79\) −0.399759 −0.0449764 −0.0224882 0.999747i \(-0.507159\pi\)
−0.0224882 + 0.999747i \(0.507159\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) −3.70328 1.07473i −0.408959 0.118684i
\(83\) −0.199879 0.199879i −0.0219396 0.0219396i 0.696052 0.717991i \(-0.254938\pi\)
−0.717991 + 0.696052i \(0.754938\pi\)
\(84\) 5.92036 + 3.75233i 0.645965 + 0.409413i
\(85\) 0 0
\(86\) −3.78734 6.88438i −0.408399 0.742362i
\(87\) −2.47817 + 2.47817i −0.265688 + 0.265688i
\(88\) −6.42000 + 5.66999i −0.684374 + 0.604422i
\(89\) 4.28267i 0.453962i 0.973899 + 0.226981i \(0.0728856\pi\)
−0.973899 + 0.226981i \(0.927114\pi\)
\(90\) 0 0
\(91\) 1.80078i 0.188773i
\(92\) −0.556993 2.48503i −0.0580705 0.259082i
\(93\) 2.72666 2.72666i 0.282741 0.282741i
\(94\) −10.2629 + 5.64600i −1.05854 + 0.582340i
\(95\) 0 0
\(96\) 3.31834 4.58134i 0.338676 0.467581i
\(97\) −6.73599 6.73599i −0.683936 0.683936i 0.276949 0.960885i \(-0.410677\pi\)
−0.960885 + 0.276949i \(0.910677\pi\)
\(98\) −2.08220 + 7.17480i −0.210334 + 0.724764i
\(99\) 3.02831 0.304356
\(100\) 0 0
\(101\) 5.78734 0.575862 0.287931 0.957651i \(-0.407033\pi\)
0.287931 + 0.957651i \(0.407033\pi\)
\(102\) 1.31737 4.53936i 0.130439 0.449464i
\(103\) −13.0914 13.0914i −1.28993 1.28993i −0.934827 0.355104i \(-0.884445\pi\)
−0.355104 0.934827i \(-0.615555\pi\)
\(104\) 1.45052 + 0.0899847i 0.142236 + 0.00882373i
\(105\) 0 0
\(106\) 5.50466 3.02831i 0.534660 0.294135i
\(107\) −9.71281 + 9.71281i −0.938973 + 0.938973i −0.998242 0.0592694i \(-0.981123\pi\)
0.0592694 + 0.998242i \(0.481123\pi\)
\(108\) −1.95158 + 0.437425i −0.187791 + 0.0420913i
\(109\) 10.4626i 1.00214i −0.865407 0.501070i \(-0.832940\pi\)
0.865407 0.501070i \(-0.167060\pi\)
\(110\) 0 0
\(111\) 0.513824i 0.0487700i
\(112\) 13.1954 + 4.73325i 1.24685 + 0.447251i
\(113\) 10.6460 10.6460i 1.00149 1.00149i 0.00149259 0.999999i \(-0.499525\pi\)
0.999999 0.00149259i \(-0.000475108\pi\)
\(114\) −3.37856 6.14134i −0.316431 0.575189i
\(115\) 0 0
\(116\) −3.75233 + 5.92036i −0.348395 + 0.549692i
\(117\) −0.363328 0.363328i −0.0335897 0.0335897i
\(118\) 11.7960 + 3.42331i 1.08591 + 0.315142i
\(119\) 11.7135 1.07377
\(120\) 0 0
\(121\) 1.82936 0.166305
\(122\) 20.7692 + 6.02745i 1.88036 + 0.545699i
\(123\) 1.92804 + 1.92804i 0.173845 + 0.173845i
\(124\) 4.12858 6.51399i 0.370757 0.584974i
\(125\) 0 0
\(126\) −2.38900 4.34258i −0.212829 0.386868i
\(127\) −1.77766 + 1.77766i −0.157742 + 0.157742i −0.781565 0.623823i \(-0.785578\pi\)
0.623823 + 0.781565i \(0.285578\pi\)
\(128\) 4.47200 10.3924i 0.395273 0.918564i
\(129\) 5.55602i 0.489180i
\(130\) 0 0
\(131\) 18.1981i 1.58997i 0.606626 + 0.794987i \(0.292523\pi\)
−0.606626 + 0.794987i \(0.707477\pi\)
\(132\) 5.90998 1.32466i 0.514398 0.115297i
\(133\) 12.2827 12.2827i 1.06504 1.06504i
\(134\) 6.88438 3.78734i 0.594720 0.327176i
\(135\) 0 0
\(136\) 0.585320 9.43517i 0.0501908 0.809060i
\(137\) 5.91934 + 5.91934i 0.505724 + 0.505724i 0.913211 0.407487i \(-0.133595\pi\)
−0.407487 + 0.913211i \(0.633595\pi\)
\(138\) −0.501897 + 1.72942i −0.0427243 + 0.147218i
\(139\) −12.4140 −1.05294 −0.526470 0.850194i \(-0.676485\pi\)
−0.526470 + 0.850194i \(0.676485\pi\)
\(140\) 0 0
\(141\) 8.28267 0.697527
\(142\) 1.67747 5.78017i 0.140770 0.485061i
\(143\) 1.10027 + 1.10027i 0.0920091 + 0.0920091i
\(144\) −3.61732 + 1.70734i −0.301443 + 0.142278i
\(145\) 0 0
\(146\) 16.2663 8.94867i 1.34621 0.740597i
\(147\) 3.73541 3.73541i 0.308092 0.308092i
\(148\) 0.224760 + 1.00277i 0.0184751 + 0.0824270i
\(149\) 5.78734i 0.474117i −0.971495 0.237059i \(-0.923817\pi\)
0.971495 0.237059i \(-0.0761833\pi\)
\(150\) 0 0
\(151\) 18.0708i 1.47058i −0.677751 0.735292i \(-0.737045\pi\)
0.677751 0.735292i \(-0.262955\pi\)
\(152\) −9.27990 10.5074i −0.752700 0.852265i
\(153\) −2.36333 + 2.36333i −0.191064 + 0.191064i
\(154\) 7.23464 + 13.1507i 0.582984 + 1.05971i
\(155\) 0 0
\(156\) −0.867993 0.550135i −0.0694950 0.0440460i
\(157\) 3.91934 + 3.91934i 0.312798 + 0.312798i 0.845992 0.533195i \(-0.179009\pi\)
−0.533195 + 0.845992i \(0.679009\pi\)
\(158\) 0.542943 + 0.157568i 0.0431942 + 0.0125354i
\(159\) −4.44252 −0.352315
\(160\) 0 0
\(161\) −4.46264 −0.351705
\(162\) 1.35818 + 0.394157i 0.106708 + 0.0309679i
\(163\) −3.22819 3.22819i −0.252851 0.252851i 0.569287 0.822139i \(-0.307219\pi\)
−0.822139 + 0.569287i \(0.807219\pi\)
\(164\) 4.60609 + 2.91934i 0.359675 + 0.227962i
\(165\) 0 0
\(166\) 0.192688 + 0.350255i 0.0149555 + 0.0271851i
\(167\) −6.95700 + 6.95700i −0.538349 + 0.538349i −0.923044 0.384695i \(-0.874307\pi\)
0.384695 + 0.923044i \(0.374307\pi\)
\(168\) −6.56188 7.42988i −0.506260 0.573227i
\(169\) 12.7360i 0.979691i
\(170\) 0 0
\(171\) 4.95634i 0.379021i
\(172\) 2.43034 + 10.8430i 0.185312 + 0.826771i
\(173\) −0.627343 + 0.627343i −0.0476960 + 0.0476960i −0.730553 0.682857i \(-0.760737\pi\)
0.682857 + 0.730553i \(0.260737\pi\)
\(174\) 4.34258 2.38900i 0.329210 0.181110i
\(175\) 0 0
\(176\) 10.9543 5.17035i 0.825715 0.389730i
\(177\) −6.14134 6.14134i −0.461611 0.461611i
\(178\) 1.68804 5.81662i 0.126524 0.435974i
\(179\) −8.93968 −0.668183 −0.334091 0.942541i \(-0.608429\pi\)
−0.334091 + 0.942541i \(0.608429\pi\)
\(180\) 0 0
\(181\) −1.00933 −0.0750228 −0.0375114 0.999296i \(-0.511943\pi\)
−0.0375114 + 0.999296i \(0.511943\pi\)
\(182\) 0.709789 2.44577i 0.0526131 0.181293i
\(183\) −10.8131 10.8131i −0.799326 0.799326i
\(184\) −0.222998 + 3.59465i −0.0164396 + 0.265001i
\(185\) 0 0
\(186\) −4.77801 + 2.62855i −0.350341 + 0.192734i
\(187\) 7.15688 7.15688i 0.523363 0.523363i
\(188\) 16.1643 3.62305i 1.17890 0.264238i
\(189\) 3.50466i 0.254927i
\(190\) 0 0
\(191\) 21.6262i 1.56481i −0.622768 0.782407i \(-0.713992\pi\)
0.622768 0.782407i \(-0.286008\pi\)
\(192\) −6.31265 + 4.91431i −0.455576 + 0.354660i
\(193\) −11.5653 + 11.5653i −0.832492 + 0.832492i −0.987857 0.155365i \(-0.950345\pi\)
0.155365 + 0.987857i \(0.450345\pi\)
\(194\) 6.49362 + 11.8037i 0.466214 + 0.847455i
\(195\) 0 0
\(196\) 5.65599 8.92392i 0.403999 0.637423i
\(197\) 9.42401 + 9.42401i 0.671433 + 0.671433i 0.958046 0.286614i \(-0.0925296\pi\)
−0.286614 + 0.958046i \(0.592530\pi\)
\(198\) −4.11297 1.19363i −0.292296 0.0848274i
\(199\) 11.0130 0.780688 0.390344 0.920669i \(-0.372356\pi\)
0.390344 + 0.920669i \(0.372356\pi\)
\(200\) 0 0
\(201\) −5.55602 −0.391891
\(202\) −7.86022 2.28112i −0.553043 0.160499i
\(203\) 8.68516 + 8.68516i 0.609579 + 0.609579i
\(204\) −3.57844 + 5.64600i −0.250541 + 0.395299i
\(205\) 0 0
\(206\) 12.6203 + 22.9404i 0.879300 + 1.59834i
\(207\) 0.900390 0.900390i 0.0625814 0.0625814i
\(208\) −1.93460 0.693949i −0.134140 0.0481167i
\(209\) 15.0093i 1.03822i
\(210\) 0 0
\(211\) 27.9835i 1.92646i 0.268669 + 0.963232i \(0.413416\pi\)
−0.268669 + 0.963232i \(0.586584\pi\)
\(212\) −8.66993 + 1.94327i −0.595453 + 0.133464i
\(213\) −3.00933 + 3.00933i −0.206196 + 0.206196i
\(214\) 17.0201 9.36333i 1.16347 0.640064i
\(215\) 0 0
\(216\) 2.82300 + 0.175128i 0.192081 + 0.0119159i
\(217\) −9.55602 9.55602i −0.648705 0.648705i
\(218\) −4.12392 + 14.2101i −0.279307 + 0.962430i
\(219\) −13.1277 −0.887086
\(220\) 0 0
\(221\) −1.71733 −0.115520
\(222\) 0.202527 0.697863i 0.0135927 0.0468375i
\(223\) 8.53479 + 8.53479i 0.571531 + 0.571531i 0.932556 0.361025i \(-0.117573\pi\)
−0.361025 + 0.932556i \(0.617573\pi\)
\(224\) −16.0560 11.6297i −1.07279 0.777039i
\(225\) 0 0
\(226\) −18.6553 + 10.2629i −1.24093 + 0.682681i
\(227\) 1.02765 1.02765i 0.0682074 0.0682074i −0.672180 0.740388i \(-0.734642\pi\)
0.740388 + 0.672180i \(0.234642\pi\)
\(228\) 2.16803 + 9.67269i 0.143581 + 0.640590i
\(229\) 8.84802i 0.584693i 0.956312 + 0.292347i \(0.0944361\pi\)
−0.956312 + 0.292347i \(0.905564\pi\)
\(230\) 0 0
\(231\) 10.6132i 0.698297i
\(232\) 7.42988 6.56188i 0.487795 0.430809i
\(233\) 4.91002 4.91002i 0.321666 0.321666i −0.527740 0.849406i \(-0.676960\pi\)
0.849406 + 0.527740i \(0.176960\pi\)
\(234\) 0.350255 + 0.636672i 0.0228969 + 0.0416205i
\(235\) 0 0
\(236\) −14.6717 9.29892i −0.955045 0.605308i
\(237\) −0.282672 0.282672i −0.0183615 0.0183615i
\(238\) −15.9089 4.61694i −1.03122 0.299272i
\(239\) 19.0259 1.23068 0.615340 0.788262i \(-0.289019\pi\)
0.615340 + 0.788262i \(0.289019\pi\)
\(240\) 0 0
\(241\) 2.90663 0.187232 0.0936161 0.995608i \(-0.470157\pi\)
0.0936161 + 0.995608i \(0.470157\pi\)
\(242\) −2.48459 0.721054i −0.159716 0.0463511i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) −25.8325 16.3727i −1.65376 1.04815i
\(245\) 0 0
\(246\) −1.85866 3.37856i −0.118504 0.215409i
\(247\) −1.80078 + 1.80078i −0.114581 + 0.114581i
\(248\) −8.17486 + 7.21984i −0.519104 + 0.458460i
\(249\) 0.282672i 0.0179136i
\(250\) 0 0
\(251\) 2.77379i 0.175080i 0.996161 + 0.0875401i \(0.0279006\pi\)
−0.996161 + 0.0875401i \(0.972099\pi\)
\(252\) 1.53303 + 6.83963i 0.0965717 + 0.430856i
\(253\) −2.72666 + 2.72666i −0.171423 + 0.171423i
\(254\) 3.11505 1.71370i 0.195456 0.107527i
\(255\) 0 0
\(256\) −10.1700 + 12.3520i −0.635624 + 0.771999i
\(257\) 2.08066 + 2.08066i 0.129788 + 0.129788i 0.769017 0.639229i \(-0.220746\pi\)
−0.639229 + 0.769017i \(0.720746\pi\)
\(258\) 2.18994 7.54604i 0.136340 0.469796i
\(259\) 1.80078 0.111895
\(260\) 0 0
\(261\) −3.50466 −0.216933
\(262\) 7.17290 24.7162i 0.443143 1.52697i
\(263\) −4.75646 4.75646i −0.293296 0.293296i 0.545085 0.838381i \(-0.316497\pi\)
−0.838381 + 0.545085i \(0.816497\pi\)
\(264\) −8.54891 0.530340i −0.526149 0.0326402i
\(265\) 0 0
\(266\) −21.5233 + 11.8407i −1.31968 + 0.726001i
\(267\) −3.02831 + 3.02831i −0.185329 + 0.185329i
\(268\) −10.8430 + 2.43034i −0.662342 + 0.148457i
\(269\) 21.6846i 1.32214i 0.750326 + 0.661068i \(0.229896\pi\)
−0.750326 + 0.661068i \(0.770104\pi\)
\(270\) 0 0
\(271\) 3.15556i 0.191687i 0.995396 + 0.0958434i \(0.0305548\pi\)
−0.995396 + 0.0958434i \(0.969445\pi\)
\(272\) −4.51391 + 12.5839i −0.273696 + 0.763012i
\(273\) −1.27334 + 1.27334i −0.0770663 + 0.0770663i
\(274\) −5.70636 10.3727i −0.344734 0.626635i
\(275\) 0 0
\(276\) 1.36333 2.15103i 0.0820627 0.129477i
\(277\) 3.53397 + 3.53397i 0.212336 + 0.212336i 0.805259 0.592923i \(-0.202026\pi\)
−0.592923 + 0.805259i \(0.702026\pi\)
\(278\) 16.8604 + 4.89305i 1.01122 + 0.293466i
\(279\) 3.85607 0.230857
\(280\) 0 0
\(281\) 0.179969 0.0107361 0.00536804 0.999986i \(-0.498291\pi\)
0.00536804 + 0.999986i \(0.498291\pi\)
\(282\) −11.2493 3.26467i −0.669887 0.194408i
\(283\) 9.84007 + 9.84007i 0.584931 + 0.584931i 0.936254 0.351323i \(-0.114268\pi\)
−0.351323 + 0.936254i \(0.614268\pi\)
\(284\) −4.55658 + 7.18930i −0.270384 + 0.426606i
\(285\) 0 0
\(286\) −1.06068 1.92804i −0.0627193 0.114007i
\(287\) 6.75712 6.75712i 0.398860 0.398860i
\(288\) 5.58591 0.893077i 0.329153 0.0526250i
\(289\) 5.82936i 0.342903i
\(290\) 0 0
\(291\) 9.52612i 0.558431i
\(292\) −25.6197 + 5.74238i −1.49928 + 0.336047i
\(293\) −15.8680 + 15.8680i −0.927018 + 0.927018i −0.997512 0.0704942i \(-0.977542\pi\)
0.0704942 + 0.997512i \(0.477542\pi\)
\(294\) −6.54569 + 3.60101i −0.381752 + 0.210015i
\(295\) 0 0
\(296\) 0.0899847 1.45052i 0.00523026 0.0843100i
\(297\) 2.14134 + 2.14134i 0.124253 + 0.124253i
\(298\) −2.28112 + 7.86022i −0.132142 + 0.455330i
\(299\) 0.654274 0.0378376
\(300\) 0 0
\(301\) 19.4720 1.12235
\(302\) −7.12274 + 24.5434i −0.409868 + 1.41231i
\(303\) 4.09226 + 4.09226i 0.235094 + 0.235094i
\(304\) 8.46216 + 17.9287i 0.485338 + 1.02828i
\(305\) 0 0
\(306\) 4.14134 2.27829i 0.236744 0.130241i
\(307\) 7.78477 7.78477i 0.444300 0.444300i −0.449154 0.893454i \(-0.648275\pi\)
0.893454 + 0.449154i \(0.148275\pi\)
\(308\) −4.64248 20.7125i −0.264530 1.18020i
\(309\) 18.5140i 1.05322i
\(310\) 0 0
\(311\) 7.05788i 0.400215i −0.979774 0.200108i \(-0.935871\pi\)
0.979774 0.200108i \(-0.0641292\pi\)
\(312\) 0.962047 + 1.08930i 0.0544652 + 0.0616697i
\(313\) 11.3013 11.3013i 0.638789 0.638789i −0.311468 0.950257i \(-0.600821\pi\)
0.950257 + 0.311468i \(0.100821\pi\)
\(314\) −3.77832 6.86799i −0.213223 0.387583i
\(315\) 0 0
\(316\) −0.675305 0.428009i −0.0379889 0.0240774i
\(317\) −19.4754 19.4754i −1.09385 1.09385i −0.995114 0.0987310i \(-0.968522\pi\)
−0.0987310 0.995114i \(-0.531478\pi\)
\(318\) 6.03372 + 1.75105i 0.338354 + 0.0981940i
\(319\) 10.6132 0.594225
\(320\) 0 0
\(321\) −13.7360 −0.766668
\(322\) 6.06105 + 1.75898i 0.337769 + 0.0980241i
\(323\) 11.7135 + 11.7135i 0.651755 + 0.651755i
\(324\) −1.68928 1.07067i −0.0938489 0.0594816i
\(325\) 0 0
\(326\) 3.11203 + 5.65685i 0.172359 + 0.313304i
\(327\) 7.39820 7.39820i 0.409122 0.409122i
\(328\) −5.10520 5.78050i −0.281887 0.319175i
\(329\) 29.0280i 1.60036i
\(330\) 0 0
\(331\) 15.0143i 0.825259i −0.910899 0.412630i \(-0.864610\pi\)
0.910899 0.412630i \(-0.135390\pi\)
\(332\) −0.123648 0.551657i −0.00678607 0.0302761i
\(333\) −0.363328 + 0.363328i −0.0199103 + 0.0199103i
\(334\) 12.1910 6.70668i 0.667061 0.366973i
\(335\) 0 0
\(336\) 5.98365 + 12.6775i 0.326435 + 0.691614i
\(337\) 21.5840 + 21.5840i 1.17576 + 1.17576i 0.980815 + 0.194940i \(0.0624513\pi\)
0.194940 + 0.980815i \(0.437549\pi\)
\(338\) 5.01997 17.2977i 0.273051 0.940871i
\(339\) 15.0557 0.817714
\(340\) 0 0
\(341\) −11.6774 −0.632365
\(342\) 1.95358 6.73158i 0.105637 0.364002i
\(343\) 4.25583 + 4.25583i 0.229793 + 0.229793i
\(344\) 0.973012 15.6846i 0.0524613 0.845659i
\(345\) 0 0
\(346\) 1.09931 0.604770i 0.0590995 0.0325127i
\(347\) 16.9969 16.9969i 0.912444 0.912444i −0.0840201 0.996464i \(-0.526776\pi\)
0.996464 + 0.0840201i \(0.0267760\pi\)
\(348\) −6.83963 + 1.53303i −0.366643 + 0.0821790i
\(349\) 4.38538i 0.234744i −0.993088 0.117372i \(-0.962553\pi\)
0.993088 0.117372i \(-0.0374469\pi\)
\(350\) 0 0
\(351\) 0.513824i 0.0274259i
\(352\) −16.9159 + 2.70451i −0.901618 + 0.144151i
\(353\) 2.62734 2.62734i 0.139839 0.139839i −0.633722 0.773561i \(-0.718474\pi\)
0.773561 + 0.633722i \(0.218474\pi\)
\(354\) 5.92036 + 10.7617i 0.314664 + 0.571976i
\(355\) 0 0
\(356\) −4.58532 + 7.23464i −0.243021 + 0.383435i
\(357\) 8.28267 + 8.28267i 0.438366 + 0.438366i
\(358\) 12.1416 + 3.52363i 0.641706 + 0.186230i
\(359\) −34.9952 −1.84697 −0.923487 0.383630i \(-0.874674\pi\)
−0.923487 + 0.383630i \(0.874674\pi\)
\(360\) 0 0
\(361\) 5.56534 0.292913
\(362\) 1.37085 + 0.397834i 0.0720500 + 0.0209097i
\(363\) 1.29355 + 1.29355i 0.0678939 + 0.0678939i
\(364\) −1.92804 + 3.04202i −0.101057 + 0.159445i
\(365\) 0 0
\(366\) 10.4240 + 18.9481i 0.544872 + 0.990433i
\(367\) 9.93581 9.93581i 0.518645 0.518645i −0.398516 0.917161i \(-0.630475\pi\)
0.917161 + 0.398516i \(0.130475\pi\)
\(368\) 1.71973 4.79427i 0.0896469 0.249918i
\(369\) 2.72666i 0.141944i
\(370\) 0 0
\(371\) 15.5695i 0.808330i
\(372\) 7.52543 1.68674i 0.390176 0.0874536i
\(373\) 7.08998 7.08998i 0.367105 0.367105i −0.499315 0.866421i \(-0.666415\pi\)
0.866421 + 0.499315i \(0.166415\pi\)
\(374\) −12.5412 + 6.89937i −0.648492 + 0.356758i
\(375\) 0 0
\(376\) −23.3820 1.45052i −1.20583 0.0748051i
\(377\) −1.27334 1.27334i −0.0655805 0.0655805i
\(378\) 1.38139 4.75995i 0.0710509 0.244825i
\(379\) −30.0388 −1.54299 −0.771495 0.636235i \(-0.780491\pi\)
−0.771495 + 0.636235i \(0.780491\pi\)
\(380\) 0 0
\(381\) −2.51399 −0.128796
\(382\) −8.52410 + 29.3721i −0.436131 + 1.50281i
\(383\) −11.9133 11.9133i −0.608744 0.608744i 0.333874 0.942618i \(-0.391644\pi\)
−0.942618 + 0.333874i \(0.891644\pi\)
\(384\) 10.5107 4.18633i 0.536372 0.213633i
\(385\) 0 0
\(386\) 20.2663 11.1492i 1.03153 0.567480i
\(387\) −3.92870 + 3.92870i −0.199707 + 0.199707i
\(388\) −4.16697 18.5910i −0.211546 0.943814i
\(389\) 16.3340i 0.828168i 0.910239 + 0.414084i \(0.135898\pi\)
−0.910239 + 0.414084i \(0.864102\pi\)
\(390\) 0 0
\(391\) 4.25583i 0.215227i
\(392\) −11.1992 + 9.89090i −0.565647 + 0.499566i
\(393\) −12.8680 + 12.8680i −0.649104 + 0.649104i
\(394\) −9.08492 16.5140i −0.457692 0.831963i
\(395\) 0 0
\(396\) 5.11566 + 3.24231i 0.257072 + 0.162932i
\(397\) 19.1927 + 19.1927i 0.963253 + 0.963253i 0.999348 0.0360950i \(-0.0114919\pi\)
−0.0360950 + 0.999348i \(0.511492\pi\)
\(398\) −14.9575 4.34083i −0.749753 0.217586i
\(399\) 17.3703 0.869604
\(400\) 0 0
\(401\) 26.5653 1.32661 0.663305 0.748349i \(-0.269153\pi\)
0.663305 + 0.748349i \(0.269153\pi\)
\(402\) 7.54604 + 2.18994i 0.376362 + 0.109224i
\(403\) 1.40102 + 1.40102i 0.0697898 + 0.0697898i
\(404\) 9.77644 + 6.19632i 0.486396 + 0.308278i
\(405\) 0 0
\(406\) −8.37266 15.2193i −0.415528 0.755321i
\(407\) 1.10027 1.10027i 0.0545383 0.0545383i
\(408\) 7.08556 6.25779i 0.350787 0.309807i
\(409\) 25.3947i 1.25569i 0.778339 + 0.627844i \(0.216062\pi\)
−0.778339 + 0.627844i \(0.783938\pi\)
\(410\) 0 0
\(411\) 8.37122i 0.412922i
\(412\) −8.09849 36.1315i −0.398984 1.78007i
\(413\) −21.5233 + 21.5233i −1.05909 + 1.05909i
\(414\) −1.57778 + 0.867993i −0.0775438 + 0.0426595i
\(415\) 0 0
\(416\) 2.35400 + 1.70504i 0.115414 + 0.0835964i
\(417\) −8.77801 8.77801i −0.429861 0.429861i
\(418\) −5.91603 + 20.3853i −0.289362 + 0.997078i
\(419\) 40.0788 1.95798 0.978988 0.203919i \(-0.0653679\pi\)
0.978988 + 0.203919i \(0.0653679\pi\)
\(420\) 0 0
\(421\) 19.3947 0.945240 0.472620 0.881266i \(-0.343308\pi\)
0.472620 + 0.881266i \(0.343308\pi\)
\(422\) 11.0299 38.0065i 0.536927 1.85013i
\(423\) 5.85673 + 5.85673i 0.284764 + 0.284764i
\(424\) 12.5412 + 0.778008i 0.609056 + 0.0377834i
\(425\) 0 0
\(426\) 5.27334 2.90105i 0.255494 0.140556i
\(427\) −37.8962 + 37.8962i −1.83393 + 1.83393i
\(428\) −26.8069 + 6.00847i −1.29576 + 0.290430i
\(429\) 1.55602i 0.0751251i
\(430\) 0 0
\(431\) 15.8241i 0.762218i −0.924530 0.381109i \(-0.875542\pi\)
0.924530 0.381109i \(-0.124458\pi\)
\(432\) −3.76510 1.35056i −0.181149 0.0649788i
\(433\) 21.1214 21.1214i 1.01503 1.01503i 0.0151424 0.999885i \(-0.495180\pi\)
0.999885 0.0151424i \(-0.00482018\pi\)
\(434\) 9.21218 + 16.7453i 0.442199 + 0.803801i
\(435\) 0 0
\(436\) 11.2020 17.6743i 0.536479 0.846447i
\(437\) −4.46264 4.46264i −0.213477 0.213477i
\(438\) 17.8297 + 5.17436i 0.851936 + 0.247241i
\(439\) −6.61188 −0.315568 −0.157784 0.987474i \(-0.550435\pi\)
−0.157784 + 0.987474i \(0.550435\pi\)
\(440\) 0 0
\(441\) 5.28267 0.251556
\(442\) 2.33243 + 0.676896i 0.110942 + 0.0321967i
\(443\) −14.5419 14.5419i −0.690906 0.690906i 0.271525 0.962431i \(-0.412472\pi\)
−0.962431 + 0.271525i \(0.912472\pi\)
\(444\) −0.550135 + 0.867993i −0.0261082 + 0.0411931i
\(445\) 0 0
\(446\) −8.22769 14.9558i −0.389593 0.708177i
\(447\) 4.09226 4.09226i 0.193557 0.193557i
\(448\) 17.2230 + 22.1237i 0.813711 + 1.04525i
\(449\) 33.6120i 1.58625i 0.609060 + 0.793124i \(0.291547\pi\)
−0.609060 + 0.793124i \(0.708453\pi\)
\(450\) 0 0
\(451\) 8.25715i 0.388814i
\(452\) 29.3824 6.58575i 1.38203 0.309768i
\(453\) 12.7780 12.7780i 0.600363 0.600363i
\(454\) −1.80078 + 0.990671i −0.0845148 + 0.0464945i
\(455\) 0 0
\(456\) 0.867993 13.9918i 0.0406475 0.655224i
\(457\) −15.5653 15.5653i −0.728116 0.728116i 0.242128 0.970244i \(-0.422155\pi\)
−0.970244 + 0.242128i \(0.922155\pi\)
\(458\) 3.48751 12.0172i 0.162960 0.561525i
\(459\) −3.34225 −0.156003
\(460\) 0 0
\(461\) −26.1473 −1.21780 −0.608900 0.793247i \(-0.708389\pi\)
−0.608900 + 0.793247i \(0.708389\pi\)
\(462\) −4.18326 + 14.4146i −0.194623 + 0.670627i
\(463\) −5.77898 5.77898i −0.268572 0.268572i 0.559953 0.828525i \(-0.310819\pi\)
−0.828525 + 0.559953i \(0.810819\pi\)
\(464\) −12.6775 + 5.98365i −0.588538 + 0.277784i
\(465\) 0 0
\(466\) −8.60398 + 4.73335i −0.398572 + 0.219268i
\(467\) −2.25517 + 2.25517i −0.104357 + 0.104357i −0.757357 0.653000i \(-0.773510\pi\)
0.653000 + 0.757357i \(0.273510\pi\)
\(468\) −0.224760 1.00277i −0.0103895 0.0463529i
\(469\) 19.4720i 0.899132i
\(470\) 0 0
\(471\) 5.54279i 0.255398i
\(472\) 16.2615 + 18.4125i 0.748495 + 0.847505i
\(473\) 11.8973 11.8973i 0.547038 0.547038i
\(474\) 0.272501 + 0.495336i 0.0125164 + 0.0227515i
\(475\) 0 0
\(476\) 19.7873 + 12.5412i 0.906951 + 0.574827i
\(477\) −3.14134 3.14134i −0.143832 0.143832i
\(478\) −25.8405 7.49917i −1.18191 0.343004i
\(479\) 1.40102 0.0640143 0.0320071 0.999488i \(-0.489810\pi\)
0.0320071 + 0.999488i \(0.489810\pi\)
\(480\) 0 0
\(481\) −0.264015 −0.0120380
\(482\) −3.94771 1.14567i −0.179813 0.0521837i
\(483\) −3.15556 3.15556i −0.143583 0.143583i
\(484\) 3.09030 + 1.95864i 0.140468 + 0.0890289i
\(485\) 0 0
\(486\) 0.681664 + 1.23909i 0.0309209 + 0.0562061i
\(487\) −0.978144 + 0.978144i −0.0443239 + 0.0443239i −0.728921 0.684597i \(-0.759978\pi\)
0.684597 + 0.728921i \(0.259978\pi\)
\(488\) 28.6317 + 32.4190i 1.29609 + 1.46754i
\(489\) 4.56534i 0.206452i
\(490\) 0 0
\(491\) 36.1134i 1.62978i −0.579619 0.814888i \(-0.696799\pi\)
0.579619 0.814888i \(-0.303201\pi\)
\(492\) 1.19271 + 5.32128i 0.0537715 + 0.239902i
\(493\) −8.28267 + 8.28267i −0.373033 + 0.373033i
\(494\) 3.15556 1.73599i 0.141976 0.0781057i
\(495\) 0 0
\(496\) 13.9486 6.58363i 0.626313 0.295614i
\(497\) 10.5467 + 10.5467i 0.473084 + 0.473084i
\(498\) −0.111417 + 0.383918i −0.00499272 + 0.0172038i
\(499\) 6.35736 0.284595 0.142297 0.989824i \(-0.454551\pi\)
0.142297 + 0.989824i \(0.454551\pi\)
\(500\) 0 0
\(501\) −9.83869 −0.439560
\(502\) 1.09331 3.76730i 0.0487968 0.168143i
\(503\) −17.1704 17.1704i −0.765592 0.765592i 0.211735 0.977327i \(-0.432089\pi\)
−0.977327 + 0.211735i \(0.932089\pi\)
\(504\) 0.613763 9.89367i 0.0273392 0.440699i
\(505\) 0 0
\(506\) 4.77801 2.62855i 0.212408 0.116853i
\(507\) −9.00570 + 9.00570i −0.399957 + 0.399957i
\(508\) −4.90626 + 1.09968i −0.217680 + 0.0487906i
\(509\) 18.8739i 0.836572i −0.908315 0.418286i \(-0.862631\pi\)
0.908315 0.418286i \(-0.137369\pi\)
\(510\) 0 0
\(511\) 46.0081i 2.03528i
\(512\) 18.6812 12.7676i 0.825602 0.564253i
\(513\) −3.50466 + 3.50466i −0.154735 + 0.154735i
\(514\) −2.00579 3.64600i −0.0884717 0.160818i
\(515\) 0 0
\(516\) −5.94865 + 9.38567i −0.261875 + 0.413181i
\(517\) −17.7360 17.7360i −0.780028 0.780028i
\(518\) −2.44577 0.709789i −0.107461 0.0311864i
\(519\) −0.887197 −0.0389436
\(520\) 0 0
\(521\) −33.9346 −1.48670 −0.743351 0.668901i \(-0.766765\pi\)
−0.743351 + 0.668901i \(0.766765\pi\)
\(522\) 4.75995 + 1.38139i 0.208337 + 0.0604617i
\(523\) −3.78345 3.78345i −0.165439 0.165439i 0.619532 0.784971i \(-0.287322\pi\)
−0.784971 + 0.619532i \(0.787322\pi\)
\(524\) −19.4841 + 30.7417i −0.851167 + 1.34296i
\(525\) 0 0
\(526\) 4.58532 + 8.33491i 0.199929 + 0.363419i
\(527\) 9.11317 9.11317i 0.396976 0.396976i
\(528\) 11.4019 + 4.08991i 0.496203 + 0.177990i
\(529\) 21.3786i 0.929504i
\(530\) 0 0
\(531\) 8.68516i 0.376904i
\(532\) 33.8995 7.59822i 1.46973 0.329425i
\(533\) −0.990671 + 0.990671i −0.0429107 + 0.0429107i
\(534\) 5.30660 2.91934i 0.229639 0.126332i
\(535\) 0 0
\(536\) 15.6846 + 0.973012i 0.677473 + 0.0420277i
\(537\) −6.32131 6.32131i −0.272784 0.272784i
\(538\) 8.54715 29.4515i 0.368494 1.26975i
\(539\) −15.9976 −0.689063
\(540\) 0 0
\(541\) 28.4813 1.22451 0.612253 0.790662i \(-0.290263\pi\)
0.612253 + 0.790662i \(0.290263\pi\)
\(542\) 1.24379 4.28581i 0.0534252 0.184091i
\(543\) −0.713703 0.713703i −0.0306279 0.0306279i
\(544\) 11.0907 15.3120i 0.475510 0.656496i
\(545\) 0 0
\(546\) 2.23132 1.22753i 0.0954917 0.0525333i
\(547\) −0.726896 + 0.726896i −0.0310798 + 0.0310798i −0.722476 0.691396i \(-0.756996\pi\)
0.691396 + 0.722476i \(0.256996\pi\)
\(548\) 3.66178 + 16.3371i 0.156424 + 0.697886i
\(549\) 15.2920i 0.652647i
\(550\) 0 0
\(551\) 17.3703i 0.740001i
\(552\) −2.69948 + 2.38412i −0.114898 + 0.101475i
\(553\) −0.990671 + 0.990671i −0.0421276 + 0.0421276i
\(554\) −3.40681 6.19269i −0.144742 0.263102i
\(555\) 0 0
\(556\) −20.9707 13.2912i −0.889356 0.563675i
\(557\) 11.4427 + 11.4427i 0.484841 + 0.484841i 0.906674 0.421832i \(-0.138613\pi\)
−0.421832 + 0.906674i \(0.638613\pi\)
\(558\) −5.23723 1.51990i −0.221709 0.0643424i
\(559\) −2.85481 −0.120746
\(560\) 0 0
\(561\) 10.1214 0.427324
\(562\) −0.244430 0.0709362i −0.0103107 0.00299226i
\(563\) 7.08426 + 7.08426i 0.298566 + 0.298566i 0.840452 0.541886i \(-0.182290\pi\)
−0.541886 + 0.840452i \(0.682290\pi\)
\(564\) 13.9918 + 8.86799i 0.589159 + 0.373410i
\(565\) 0 0
\(566\) −9.48601 17.2431i −0.398727 0.724780i
\(567\) −2.47817 + 2.47817i −0.104073 + 0.104073i
\(568\) 9.02235 7.96832i 0.378569 0.334343i
\(569\) 46.2427i 1.93860i −0.245890 0.969298i \(-0.579080\pi\)
0.245890 0.969298i \(-0.420920\pi\)
\(570\) 0 0
\(571\) 31.2381i 1.30727i 0.756808 + 0.653637i \(0.226758\pi\)
−0.756808 + 0.653637i \(0.773242\pi\)
\(572\) 0.680641 + 3.03669i 0.0284590 + 0.126970i
\(573\) 15.2920 15.2920i 0.638833 0.638833i
\(574\) −11.8407 + 6.51399i −0.494222 + 0.271889i
\(575\) 0 0
\(576\) −7.93866 0.988770i −0.330778 0.0411988i
\(577\) −1.16131 1.16131i −0.0483461 0.0483461i 0.682520 0.730866i \(-0.260884\pi\)
−0.730866 + 0.682520i \(0.760884\pi\)
\(578\) −2.29768 + 7.91729i −0.0955709 + 0.329316i
\(579\) −16.3559 −0.679727
\(580\) 0 0
\(581\) −0.990671 −0.0411000
\(582\) −3.75479 + 12.9381i −0.155641 + 0.536303i
\(583\) 9.51293 + 9.51293i 0.393985 + 0.393985i
\(584\) 37.0594 + 2.29902i 1.53353 + 0.0951341i
\(585\) 0 0
\(586\) 27.8060 15.2970i 1.14866 0.631915i
\(587\) −23.6268 + 23.6268i −0.975183 + 0.975183i −0.999699 0.0245164i \(-0.992195\pi\)
0.0245164 + 0.999699i \(0.492195\pi\)
\(588\) 10.3096 2.31077i 0.425159 0.0952947i
\(589\) 19.1120i 0.787498i
\(590\) 0 0
\(591\) 13.3276i 0.548223i
\(592\) −0.693949 + 1.93460i −0.0285211 + 0.0795115i
\(593\) 0.260625 0.260625i 0.0107026 0.0107026i −0.701735 0.712438i \(-0.747591\pi\)
0.712438 + 0.701735i \(0.247591\pi\)
\(594\) −2.06429 3.75233i −0.0846988 0.153960i
\(595\) 0 0
\(596\) 6.19632 9.77644i 0.253811 0.400458i
\(597\) 7.78734 + 7.78734i 0.318714 + 0.318714i
\(598\) −0.888619 0.257887i −0.0363383 0.0105458i
\(599\) −33.0851 −1.35182 −0.675910 0.736984i \(-0.736249\pi\)
−0.675910 + 0.736984i \(0.736249\pi\)
\(600\) 0 0
\(601\) −24.3200 −0.992033 −0.496016 0.868313i \(-0.665204\pi\)
−0.496016 + 0.868313i \(0.665204\pi\)
\(602\) −26.4464 7.67501i −1.07787 0.312810i
\(603\) −3.92870 3.92870i −0.159989 0.159989i
\(604\) 19.3479 30.5267i 0.787253 1.24211i
\(605\) 0 0
\(606\) −3.94502 7.17101i −0.160255 0.291302i
\(607\) 4.53347 4.53347i 0.184008 0.184008i −0.609092 0.793100i \(-0.708466\pi\)
0.793100 + 0.609092i \(0.208466\pi\)
\(608\) −4.42639 27.6857i −0.179514 1.12280i
\(609\) 12.2827i 0.497719i
\(610\) 0 0
\(611\) 4.25583i 0.172173i
\(612\) −6.52267 + 1.46199i −0.263663 + 0.0590972i
\(613\) 20.2793 20.2793i 0.819073 0.819073i −0.166901 0.985974i \(-0.553376\pi\)
0.985974 + 0.166901i \(0.0533761\pi\)
\(614\) −13.6415 + 7.50466i −0.550526 + 0.302864i
\(615\) 0 0
\(616\) −1.85866 + 29.9611i −0.0748877 + 1.20717i
\(617\) −17.1086 17.1086i −0.688768 0.688768i 0.273192 0.961960i \(-0.411921\pi\)
−0.961960 + 0.273192i \(0.911921\pi\)
\(618\) −7.29742 + 25.1453i −0.293545 + 1.01149i
\(619\) 29.4373 1.18319 0.591593 0.806237i \(-0.298499\pi\)
0.591593 + 0.806237i \(0.298499\pi\)
\(620\) 0 0
\(621\) 1.27334 0.0510975
\(622\) −2.78191 + 9.58583i −0.111544 + 0.384357i
\(623\) 10.6132 + 10.6132i 0.425209 + 0.425209i
\(624\) −0.877272 1.85866i −0.0351190 0.0744061i
\(625\) 0 0
\(626\) −19.8037 + 10.8947i −0.791514 + 0.435439i
\(627\) 10.6132 10.6132i 0.423850 0.423850i
\(628\) 2.42456 + 10.8172i 0.0967503 + 0.431653i
\(629\) 1.71733i 0.0684743i
\(630\) 0 0
\(631\) 5.25710i 0.209282i −0.994510 0.104641i \(-0.966631\pi\)
0.994510 0.104641i \(-0.0333693\pi\)
\(632\) 0.748480 + 0.847487i 0.0297729 + 0.0337112i
\(633\) −19.7873 + 19.7873i −0.786476 + 0.786476i
\(634\) 18.7746 + 34.1273i 0.745635 + 1.35537i
\(635\) 0 0
\(636\) −7.50466 4.75646i −0.297579 0.188606i
\(637\) 1.91934 + 1.91934i 0.0760472 + 0.0760472i
\(638\) −14.4146 4.18326i −0.570679 0.165617i
\(639\) −4.25583 −0.168358
\(640\) 0 0
\(641\) 20.0773 0.793004 0.396502 0.918034i \(-0.370224\pi\)
0.396502 + 0.918034i \(0.370224\pi\)
\(642\) 18.6559 + 5.41413i 0.736289 + 0.213679i
\(643\) 9.28480 + 9.28480i 0.366157 + 0.366157i 0.866073 0.499917i \(-0.166636\pi\)
−0.499917 + 0.866073i \(0.666636\pi\)
\(644\) −7.53866 4.77801i −0.297065 0.188280i
\(645\) 0 0
\(646\) −11.2920 20.5259i −0.444278 0.807580i
\(647\) −28.7387 + 28.7387i −1.12983 + 1.12983i −0.139630 + 0.990204i \(0.544591\pi\)
−0.990204 + 0.139630i \(0.955409\pi\)
\(648\) 1.87233 + 2.12000i 0.0735520 + 0.0832813i
\(649\) 26.3013i 1.03242i
\(650\) 0 0
\(651\) 13.5142i 0.529665i
\(652\) −1.99700 8.90963i −0.0782084 0.348928i
\(653\) 11.9380 11.9380i 0.467170 0.467170i −0.433826 0.900996i \(-0.642837\pi\)
0.900996 + 0.433826i \(0.142837\pi\)
\(654\) −12.9641 + 7.13201i −0.506937 + 0.278884i
\(655\) 0 0
\(656\) 4.65533 + 9.86318i 0.181760 + 0.385093i
\(657\) −9.28267 9.28267i −0.362152 0.362152i
\(658\) −11.4416 + 39.4251i −0.446039 + 1.53695i
\(659\) −17.9963 −0.701038 −0.350519 0.936556i \(-0.613995\pi\)
−0.350519 + 0.936556i \(0.613995\pi\)
\(660\) 0 0
\(661\) −9.06794 −0.352702 −0.176351 0.984327i \(-0.556429\pi\)
−0.176351 + 0.984327i \(0.556429\pi\)
\(662\) −5.91798 + 20.3920i −0.230009 + 0.792558i
\(663\) −1.21433 1.21433i −0.0471608 0.0471608i
\(664\) −0.0495037 + 0.797984i −0.00192112 + 0.0309678i
\(665\) 0 0
\(666\) 0.636672 0.350255i 0.0246705 0.0135721i
\(667\) 3.15556 3.15556i 0.122184 0.122184i
\(668\) −19.2010 + 4.30369i −0.742908 + 0.166515i
\(669\) 12.0700i 0.466654i
\(670\) 0 0
\(671\) 46.3089i 1.78773i
\(672\) −3.12993 19.5767i −0.120740 0.755189i
\(673\) −35.7640 + 35.7640i −1.37860 + 1.37860i −0.531611 + 0.846988i \(0.678413\pi\)
−0.846988 + 0.531611i \(0.821587\pi\)
\(674\) −20.8074 37.8223i −0.801470 1.45686i
\(675\) 0 0
\(676\) −13.6360 + 21.5147i −0.524462 + 0.827487i
\(677\) −16.2020 16.2020i −0.622694 0.622694i 0.323525 0.946219i \(-0.395132\pi\)
−0.946219 + 0.323525i \(0.895132\pi\)
\(678\) −20.4483 5.93431i −0.785312 0.227906i
\(679\) −33.3859 −1.28123
\(680\) 0 0
\(681\) 1.45331 0.0556911
\(682\) 15.8599 + 4.60272i 0.607308 + 0.176247i
\(683\) −33.3943 33.3943i −1.27780 1.27780i −0.941899 0.335897i \(-0.890961\pi\)
−0.335897 0.941899i \(-0.609039\pi\)
\(684\) −5.30660 + 8.37266i −0.202903 + 0.320137i
\(685\) 0 0
\(686\) −4.10270 7.45763i −0.156642 0.284734i
\(687\) −6.25649 + 6.25649i −0.238700 + 0.238700i
\(688\) −7.50373 + 20.9190i −0.286077 + 0.797528i
\(689\) 2.28267i 0.0869629i
\(690\) 0 0
\(691\) 24.6365i 0.937216i −0.883406 0.468608i \(-0.844756\pi\)
0.883406 0.468608i \(-0.155244\pi\)
\(692\) −1.73143 + 0.388082i −0.0658193 + 0.0147527i
\(693\) 7.50466 7.50466i 0.285079 0.285079i
\(694\) −29.7843 + 16.3854i −1.13060 + 0.621980i
\(695\) 0 0
\(696\) 9.89367 + 0.613763i 0.375019 + 0.0232646i
\(697\) 6.44398 + 6.44398i 0.244083 + 0.244083i
\(698\) −1.72853 + 5.95611i −0.0654256 + 0.225442i
\(699\) 6.94381 0.262639
\(700\) 0 0
\(701\) −23.0420 −0.870285 −0.435143 0.900362i \(-0.643302\pi\)
−0.435143 + 0.900362i \(0.643302\pi\)
\(702\) −0.202527 + 0.697863i −0.00764389 + 0.0263391i
\(703\) 1.80078 + 1.80078i 0.0679177 + 0.0679177i
\(704\) 24.0407 + 2.99430i 0.906068 + 0.112852i
\(705\) 0 0
\(706\) −4.60398 + 2.53281i −0.173273 + 0.0953235i
\(707\) 14.3420 14.3420i 0.539387 0.539387i
\(708\) −3.79911 16.9498i −0.142779 0.637012i
\(709\) 37.7360i 1.41720i −0.705608 0.708602i \(-0.749326\pi\)
0.705608 0.708602i \(-0.250674\pi\)
\(710\) 0 0
\(711\) 0.399759i 0.0149921i
\(712\) 9.07925 8.01857i 0.340259 0.300509i
\(713\) −3.47197 + 3.47197i −0.130026 + 0.130026i
\(714\) −7.98465 14.5140i −0.298818 0.543173i
\(715\) 0 0
\(716\) −15.1016 9.57143i −0.564374 0.357701i
\(717\) 13.4533 + 13.4533i 0.502423 + 0.502423i
\(718\) 47.5296 + 13.7936i 1.77379 + 0.514772i
\(719\) 41.3423 1.54181 0.770903 0.636953i \(-0.219805\pi\)
0.770903 + 0.636953i \(0.219805\pi\)
\(720\) 0 0
\(721\) −64.8853 −2.41646
\(722\) −7.55871 2.19362i −0.281306 0.0816380i
\(723\) 2.05529 + 2.05529i 0.0764372 + 0.0764372i
\(724\) −1.70504 1.08066i −0.0633673 0.0401623i
\(725\) 0 0
\(726\) −1.24701 2.26673i −0.0462808 0.0841264i
\(727\) −9.48981 + 9.48981i −0.351958 + 0.351958i −0.860838 0.508880i \(-0.830060\pi\)
0.508880 + 0.860838i \(0.330060\pi\)
\(728\) 3.81765 3.37165i 0.141491 0.124962i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 18.5696i 0.686821i
\(732\) −6.68911 29.8435i −0.247237 1.10305i
\(733\) −3.21134 + 3.21134i −0.118614 + 0.118614i −0.763922 0.645308i \(-0.776729\pi\)
0.645308 + 0.763922i \(0.276729\pi\)
\(734\) −17.4108 + 9.57830i −0.642646 + 0.353542i
\(735\) 0 0
\(736\) −4.22538 + 5.83362i −0.155750 + 0.215030i
\(737\) 11.8973 + 11.8973i 0.438243 + 0.438243i
\(738\) 1.07473 3.70328i 0.0395614 0.136320i
\(739\) 25.3832 0.933737 0.466868 0.884327i \(-0.345382\pi\)
0.466868 + 0.884327i \(0.345382\pi\)
\(740\) 0 0
\(741\) −2.54669 −0.0935549
\(742\) 6.13684 21.1462i 0.225290 0.776300i
\(743\) 32.7400 + 32.7400i 1.20111 + 1.20111i 0.973828 + 0.227285i \(0.0729850\pi\)
0.227285 + 0.973828i \(0.427015\pi\)
\(744\) −10.8857 0.675305i −0.399089 0.0247579i
\(745\) 0 0
\(746\) −12.4240 + 6.83488i −0.454875 + 0.250243i
\(747\) 0.199879 0.199879i 0.00731321 0.00731321i
\(748\) 19.7526 4.42734i 0.722228 0.161880i
\(749\) 48.1400i 1.75900i
\(750\) 0 0
\(751\) 24.4810i 0.893323i −0.894703 0.446662i \(-0.852613\pi\)
0.894703 0.446662i \(-0.147387\pi\)
\(752\) 31.1851 + 11.1862i 1.13720 + 0.407920i
\(753\) −1.96137 + 1.96137i −0.0714762 + 0.0714762i
\(754\) 1.22753 + 2.23132i 0.0447039 + 0.0812599i
\(755\) 0 0
\(756\) −3.75233 + 5.92036i −0.136471 + 0.215322i
\(757\) −22.9473 22.9473i −0.834035 0.834035i 0.154031 0.988066i \(-0.450774\pi\)
−0.988066 + 0.154031i \(0.950774\pi\)
\(758\) 40.7980 + 11.8400i 1.48185 + 0.430048i
\(759\) −3.85607 −0.139967
\(760\) 0 0
\(761\) 37.0466 1.34294 0.671470 0.741032i \(-0.265663\pi\)
0.671470 + 0.741032i \(0.265663\pi\)
\(762\) 3.41444 + 0.990907i 0.123692 + 0.0358968i
\(763\) −25.9282 25.9282i −0.938665 0.938665i
\(764\) 23.1544 36.5327i 0.837698 1.32170i
\(765\) 0 0
\(766\) 11.4847 + 20.8761i 0.414959 + 0.754286i
\(767\) 3.15556 3.15556i 0.113941 0.113941i
\(768\) −15.9254 + 1.54291i −0.574660 + 0.0556749i
\(769\) 6.62395i 0.238866i 0.992842 + 0.119433i \(0.0381077\pi\)
−0.992842 + 0.119433i \(0.961892\pi\)
\(770\) 0 0
\(771\) 2.94249i 0.105971i
\(772\) −31.9198 + 7.15447i −1.14882 + 0.257495i
\(773\) −16.2606 + 16.2606i −0.584854 + 0.584854i −0.936233 0.351379i \(-0.885713\pi\)
0.351379 + 0.936233i \(0.385713\pi\)
\(774\) 6.88438 3.78734i 0.247454 0.136133i
\(775\) 0 0
\(776\) −1.66829 + 26.8922i −0.0598880 + 0.965375i
\(777\) 1.27334 + 1.27334i 0.0456809 + 0.0456809i
\(778\) 6.43817 22.1845i 0.230819 0.795352i
\(779\) 13.5142 0.484198
\(780\) 0 0
\(781\) 12.8880 0.461168
\(782\) −1.67747 + 5.78017i −0.0599860 + 0.206698i
\(783\) −2.47817 2.47817i −0.0885626 0.0885626i
\(784\) 19.1091 9.01932i 0.682468