Properties

Label 1183.2.e.f.508.5
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - x^{9} + 8 x^{8} + 7 x^{7} + 41 x^{6} + 18 x^{5} + 58 x^{4} + 28 x^{3} + 64 x^{2} + 16 x + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.5
Root \(-0.862625 - 1.49411i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.f.170.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36263 + 2.36014i) q^{2} +(0.673208 - 1.16603i) q^{3} +(-2.71349 + 4.69991i) q^{4} +(1.09358 + 1.89414i) q^{5} +3.66932 q^{6} +(2.19729 + 1.47375i) q^{7} -9.33940 q^{8} +(0.593582 + 1.02811i) q^{9} +O(q^{10})\) \(q+(1.36263 + 2.36014i) q^{2} +(0.673208 - 1.16603i) q^{3} +(-2.71349 + 4.69991i) q^{4} +(1.09358 + 1.89414i) q^{5} +3.66932 q^{6} +(2.19729 + 1.47375i) q^{7} -9.33940 q^{8} +(0.593582 + 1.02811i) q^{9} +(-2.98028 + 5.16200i) q^{10} +(-0.524077 + 0.907729i) q^{11} +(3.65349 + 6.32803i) q^{12} +(-0.484172 + 7.19406i) q^{14} +2.94483 q^{15} +(-7.29912 - 12.6424i) q^{16} +(2.64562 - 4.58236i) q^{17} +(-1.61766 + 2.80187i) q^{18} +(0.378453 + 0.655500i) q^{19} -11.8697 q^{20} +(3.19767 - 1.56996i) q^{21} -2.85648 q^{22} +(-0.326792 - 0.566020i) q^{23} +(-6.28736 + 10.8900i) q^{24} +(0.108157 - 0.187333i) q^{25} +5.63766 q^{27} +(-12.8888 + 6.32803i) q^{28} -3.10408 q^{29} +(4.01270 + 6.95021i) q^{30} +(0.513956 - 0.890198i) q^{31} +(10.5525 - 18.2775i) q^{32} +(0.705626 + 1.22218i) q^{33} +14.4200 q^{34} +(-0.388575 + 5.77363i) q^{35} -6.44273 q^{36} +(-5.44661 - 9.43381i) q^{37} +(-1.03138 + 1.78640i) q^{38} +(-10.2134 - 17.6901i) q^{40} -7.32040 q^{41} +(8.06254 + 5.40766i) q^{42} +0.887771 q^{43} +(-2.84416 - 4.92623i) q^{44} +(-1.29826 + 2.24865i) q^{45} +(0.890590 - 1.54255i) q^{46} +(1.16875 + 2.02434i) q^{47} -19.6553 q^{48} +(2.65613 + 6.47650i) q^{49} +0.589510 q^{50} +(-3.56211 - 6.16976i) q^{51} +(-2.44407 + 4.23325i) q^{53} +(7.68202 + 13.3057i) q^{54} -2.29249 q^{55} +(-20.5213 - 13.7639i) q^{56} +1.01911 q^{57} +(-4.22970 - 7.32606i) q^{58} +(-0.524077 + 0.907729i) q^{59} +(-7.99079 + 13.8404i) q^{60} +(6.24989 + 10.8251i) q^{61} +2.80132 q^{62} +(-0.210913 + 3.13385i) q^{63} +28.3200 q^{64} +(-1.92301 + 3.33075i) q^{66} +(2.23944 - 3.87883i) q^{67} +(14.3578 + 24.8684i) q^{68} -0.879996 q^{69} +(-14.1560 + 6.95021i) q^{70} +6.60274 q^{71} +(-5.54370 - 9.60197i) q^{72} +(-4.14174 + 7.17370i) q^{73} +(14.8434 - 25.7095i) q^{74} +(-0.145624 - 0.252229i) q^{75} -4.10772 q^{76} +(-2.48931 + 1.22218i) q^{77} +(-1.07007 - 1.85342i) q^{79} +(15.9644 - 27.6511i) q^{80} +(2.01457 - 3.48935i) q^{81} +(-9.97496 - 17.2771i) q^{82} +6.66558 q^{83} +(-1.29817 + 19.2888i) q^{84} +11.5728 q^{85} +(1.20970 + 2.09526i) q^{86} +(-2.08969 + 3.61946i) q^{87} +(4.89457 - 8.47765i) q^{88} +(-2.88388 - 4.99503i) q^{89} -7.07617 q^{90} +3.54699 q^{92} +(-0.691998 - 1.19858i) q^{93} +(-3.18515 + 5.51684i) q^{94} +(-0.827739 + 1.43369i) q^{95} +(-14.2081 - 24.6091i) q^{96} +2.88777 q^{97} +(-11.6661 + 15.0939i) q^{98} -1.24433 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 4q^{2} - 8q^{4} + 2q^{5} + 10q^{6} - q^{7} - 18q^{8} - 3q^{9} + O(q^{10}) \) \( 10q + 4q^{2} - 8q^{4} + 2q^{5} + 10q^{6} - q^{7} - 18q^{8} - 3q^{9} + 5q^{10} + 11q^{11} - 5q^{12} + 10q^{14} - 10q^{16} + 5q^{17} + 9q^{18} + 9q^{19} - 2q^{20} - 2q^{21} + 16q^{22} - 10q^{23} - 9q^{25} - 37q^{28} - 6q^{29} + 13q^{30} - 6q^{31} + 22q^{32} + 8q^{33} + 44q^{34} - 4q^{35} + 14q^{36} + 4q^{37} + 10q^{38} - 28q^{40} - 28q^{41} + 52q^{42} + 4q^{43} - 32q^{45} + 3q^{46} + q^{47} - 46q^{48} - 11q^{49} - 18q^{50} + 8q^{51} - 17q^{53} + 23q^{54} - 21q^{56} + 32q^{57} - 27q^{58} + 11q^{59} - 29q^{60} + 11q^{61} - 46q^{62} - 5q^{63} + 18q^{64} - 21q^{66} + 13q^{67} + 32q^{68} + 36q^{69} - 49q^{70} - 30q^{71} - 19q^{72} + 33q^{74} + 20q^{75} - 16q^{76} - 46q^{77} - 2q^{79} + 55q^{80} + 19q^{81} - 34q^{82} - 12q^{83} + 23q^{84} + 44q^{85} + 28q^{86} + 8q^{87} + 3q^{88} - 4q^{89} - 68q^{90} + 42q^{92} + 18q^{93} - 20q^{94} + 12q^{95} - 37q^{96} + 24q^{97} + 7q^{98} - 22q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36263 + 2.36014i 0.963521 + 1.66887i 0.713536 + 0.700619i \(0.247093\pi\)
0.249986 + 0.968250i \(0.419574\pi\)
\(3\) 0.673208 1.16603i 0.388677 0.673208i −0.603595 0.797291i \(-0.706266\pi\)
0.992272 + 0.124083i \(0.0395989\pi\)
\(4\) −2.71349 + 4.69991i −1.35675 + 2.34996i
\(5\) 1.09358 + 1.89414i 0.489065 + 0.847085i 0.999921 0.0125813i \(-0.00400485\pi\)
−0.510856 + 0.859666i \(0.670672\pi\)
\(6\) 3.66932 1.49799
\(7\) 2.19729 + 1.47375i 0.830496 + 0.557025i
\(8\) −9.33940 −3.30198
\(9\) 0.593582 + 1.02811i 0.197861 + 0.342705i
\(10\) −2.98028 + 5.16200i −0.942449 + 1.63237i
\(11\) −0.524077 + 0.907729i −0.158015 + 0.273691i −0.934153 0.356873i \(-0.883843\pi\)
0.776138 + 0.630564i \(0.217176\pi\)
\(12\) 3.65349 + 6.32803i 1.05467 + 1.82675i
\(13\) 0 0
\(14\) −0.484172 + 7.19406i −0.129400 + 1.92269i
\(15\) 2.94483 0.760352
\(16\) −7.29912 12.6424i −1.82478 3.16061i
\(17\) 2.64562 4.58236i 0.641658 1.11138i −0.343404 0.939188i \(-0.611580\pi\)
0.985063 0.172197i \(-0.0550865\pi\)
\(18\) −1.61766 + 2.80187i −0.381286 + 0.660407i
\(19\) 0.378453 + 0.655500i 0.0868231 + 0.150382i 0.906167 0.422921i \(-0.138995\pi\)
−0.819344 + 0.573303i \(0.805662\pi\)
\(20\) −11.8697 −2.65415
\(21\) 3.19767 1.56996i 0.697788 0.342594i
\(22\) −2.85648 −0.609005
\(23\) −0.326792 0.566020i −0.0681408 0.118023i 0.829942 0.557850i \(-0.188373\pi\)
−0.898083 + 0.439826i \(0.855040\pi\)
\(24\) −6.28736 + 10.8900i −1.28340 + 2.22292i
\(25\) 0.108157 0.187333i 0.0216314 0.0374667i
\(26\) 0 0
\(27\) 5.63766 1.08497
\(28\) −12.8888 + 6.32803i −2.43576 + 1.19589i
\(29\) −3.10408 −0.576414 −0.288207 0.957568i \(-0.593059\pi\)
−0.288207 + 0.957568i \(0.593059\pi\)
\(30\) 4.01270 + 6.95021i 0.732616 + 1.26893i
\(31\) 0.513956 0.890198i 0.0923092 0.159884i −0.816173 0.577807i \(-0.803909\pi\)
0.908482 + 0.417923i \(0.137242\pi\)
\(32\) 10.5525 18.2775i 1.86544 3.23104i
\(33\) 0.705626 + 1.22218i 0.122834 + 0.212754i
\(34\) 14.4200 2.47301
\(35\) −0.388575 + 5.77363i −0.0656811 + 0.975922i
\(36\) −6.44273 −1.07379
\(37\) −5.44661 9.43381i −0.895418 1.55091i −0.833287 0.552841i \(-0.813544\pi\)
−0.0621309 0.998068i \(-0.519790\pi\)
\(38\) −1.03138 + 1.78640i −0.167312 + 0.289793i
\(39\) 0 0
\(40\) −10.2134 17.6901i −1.61488 2.79706i
\(41\) −7.32040 −1.14325 −0.571627 0.820514i \(-0.693688\pi\)
−0.571627 + 0.820514i \(0.693688\pi\)
\(42\) 8.06254 + 5.40766i 1.24408 + 0.834420i
\(43\) 0.887771 0.135384 0.0676919 0.997706i \(-0.478437\pi\)
0.0676919 + 0.997706i \(0.478437\pi\)
\(44\) −2.84416 4.92623i −0.428774 0.742658i
\(45\) −1.29826 + 2.24865i −0.193533 + 0.335210i
\(46\) 0.890590 1.54255i 0.131310 0.227436i
\(47\) 1.16875 + 2.02434i 0.170480 + 0.295281i 0.938588 0.345040i \(-0.112135\pi\)
−0.768108 + 0.640321i \(0.778801\pi\)
\(48\) −19.6553 −2.83700
\(49\) 2.65613 + 6.47650i 0.379447 + 0.925214i
\(50\) 0.589510 0.0833692
\(51\) −3.56211 6.16976i −0.498795 0.863939i
\(52\) 0 0
\(53\) −2.44407 + 4.23325i −0.335719 + 0.581482i −0.983623 0.180240i \(-0.942313\pi\)
0.647904 + 0.761722i \(0.275646\pi\)
\(54\) 7.68202 + 13.3057i 1.04539 + 1.81067i
\(55\) −2.29249 −0.309119
\(56\) −20.5213 13.7639i −2.74228 1.83928i
\(57\) 1.01911 0.134985
\(58\) −4.22970 7.32606i −0.555387 0.961959i
\(59\) −0.524077 + 0.907729i −0.0682291 + 0.118176i −0.898122 0.439747i \(-0.855068\pi\)
0.829893 + 0.557923i \(0.188402\pi\)
\(60\) −7.99079 + 13.8404i −1.03161 + 1.78679i
\(61\) 6.24989 + 10.8251i 0.800217 + 1.38602i 0.919473 + 0.393153i \(0.128616\pi\)
−0.119256 + 0.992864i \(0.538051\pi\)
\(62\) 2.80132 0.355768
\(63\) −0.210913 + 3.13385i −0.0265726 + 0.394828i
\(64\) 28.3200 3.54000
\(65\) 0 0
\(66\) −1.92301 + 3.33075i −0.236706 + 0.409987i
\(67\) 2.23944 3.87883i 0.273592 0.473875i −0.696187 0.717860i \(-0.745122\pi\)
0.969779 + 0.243986i \(0.0784550\pi\)
\(68\) 14.3578 + 24.8684i 1.74114 + 3.01574i
\(69\) −0.879996 −0.105939
\(70\) −14.1560 + 6.95021i −1.69197 + 0.830708i
\(71\) 6.60274 0.783601 0.391801 0.920050i \(-0.371852\pi\)
0.391801 + 0.920050i \(0.371852\pi\)
\(72\) −5.54370 9.60197i −0.653331 1.13160i
\(73\) −4.14174 + 7.17370i −0.484754 + 0.839618i −0.999847 0.0175164i \(-0.994424\pi\)
0.515093 + 0.857134i \(0.327757\pi\)
\(74\) 14.8434 25.7095i 1.72551 2.98867i
\(75\) −0.145624 0.252229i −0.0168152 0.0291249i
\(76\) −4.10772 −0.471188
\(77\) −2.48931 + 1.22218i −0.283683 + 0.139280i
\(78\) 0 0
\(79\) −1.07007 1.85342i −0.120392 0.208526i 0.799530 0.600626i \(-0.205082\pi\)
−0.919922 + 0.392100i \(0.871749\pi\)
\(80\) 15.9644 27.6511i 1.78487 3.09149i
\(81\) 2.01457 3.48935i 0.223842 0.387705i
\(82\) −9.97496 17.2771i −1.10155 1.90794i
\(83\) 6.66558 0.731642 0.365821 0.930685i \(-0.380788\pi\)
0.365821 + 0.930685i \(0.380788\pi\)
\(84\) −1.29817 + 19.2888i −0.141642 + 2.10458i
\(85\) 11.5728 1.25525
\(86\) 1.20970 + 2.09526i 0.130445 + 0.225938i
\(87\) −2.08969 + 3.61946i −0.224039 + 0.388047i
\(88\) 4.89457 8.47765i 0.521763 0.903720i
\(89\) −2.88388 4.99503i −0.305691 0.529472i 0.671724 0.740802i \(-0.265554\pi\)
−0.977415 + 0.211329i \(0.932221\pi\)
\(90\) −7.07617 −0.745894
\(91\) 0 0
\(92\) 3.54699 0.369800
\(93\) −0.691998 1.19858i −0.0717569 0.124287i
\(94\) −3.18515 + 5.51684i −0.328523 + 0.569019i
\(95\) −0.827739 + 1.43369i −0.0849242 + 0.147093i
\(96\) −14.2081 24.6091i −1.45011 2.51166i
\(97\) 2.88777 0.293209 0.146604 0.989195i \(-0.453166\pi\)
0.146604 + 0.989195i \(0.453166\pi\)
\(98\) −11.6661 + 15.0939i −1.17845 + 1.52471i
\(99\) −1.24433 −0.125060
\(100\) 0.586967 + 1.01666i 0.0586967 + 0.101666i
\(101\) 5.62716 9.74653i 0.559924 0.969816i −0.437579 0.899180i \(-0.644164\pi\)
0.997502 0.0706359i \(-0.0225028\pi\)
\(102\) 9.70764 16.8141i 0.961200 1.66485i
\(103\) −10.1167 17.5226i −0.996828 1.72656i −0.567341 0.823483i \(-0.692028\pi\)
−0.429487 0.903073i \(-0.641306\pi\)
\(104\) 0 0
\(105\) 6.47064 + 4.33994i 0.631470 + 0.423535i
\(106\) −13.3214 −1.29389
\(107\) −4.52758 7.84201i −0.437698 0.758115i 0.559813 0.828619i \(-0.310873\pi\)
−0.997512 + 0.0705034i \(0.977539\pi\)
\(108\) −15.2978 + 26.4965i −1.47203 + 2.54963i
\(109\) 7.55070 13.0782i 0.723226 1.25266i −0.236474 0.971638i \(-0.575992\pi\)
0.959700 0.281026i \(-0.0906747\pi\)
\(110\) −3.12380 5.41058i −0.297843 0.515879i
\(111\) −14.6668 −1.39211
\(112\) 2.59354 38.5361i 0.245067 3.64132i
\(113\) 3.10408 0.292008 0.146004 0.989284i \(-0.453359\pi\)
0.146004 + 0.989284i \(0.453359\pi\)
\(114\) 1.38867 + 2.40524i 0.130061 + 0.225271i
\(115\) 0.714748 1.23798i 0.0666506 0.115442i
\(116\) 8.42292 14.5889i 0.782048 1.35455i
\(117\) 0 0
\(118\) −2.85648 −0.262961
\(119\) 12.5664 6.16976i 1.15196 0.565581i
\(120\) −27.5030 −2.51067
\(121\) 4.95069 + 8.57484i 0.450062 + 0.779531i
\(122\) −17.0325 + 29.5012i −1.54205 + 2.67091i
\(123\) −4.92815 + 8.53581i −0.444356 + 0.769648i
\(124\) 2.78923 + 4.83109i 0.250481 + 0.433845i
\(125\) 11.4089 1.02045
\(126\) −7.68371 + 3.77248i −0.684519 + 0.336079i
\(127\) 8.78914 0.779910 0.389955 0.920834i \(-0.372491\pi\)
0.389955 + 0.920834i \(0.372491\pi\)
\(128\) 17.4846 + 30.2841i 1.54543 + 2.67676i
\(129\) 0.597654 1.03517i 0.0526205 0.0911414i
\(130\) 0 0
\(131\) 5.25723 + 9.10580i 0.459327 + 0.795577i 0.998925 0.0463451i \(-0.0147574\pi\)
−0.539599 + 0.841922i \(0.681424\pi\)
\(132\) −7.65885 −0.666618
\(133\) −0.134473 + 1.99807i −0.0116603 + 0.173254i
\(134\) 12.2061 1.05445
\(135\) 6.16525 + 10.6785i 0.530620 + 0.919061i
\(136\) −24.7086 + 42.7965i −2.11874 + 3.66977i
\(137\) 4.36583 7.56183i 0.372998 0.646051i −0.617028 0.786942i \(-0.711663\pi\)
0.990025 + 0.140891i \(0.0449966\pi\)
\(138\) −1.19910 2.07691i −0.102075 0.176798i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −26.0812 17.4930i −2.20426 1.47843i
\(141\) 3.14726 0.265047
\(142\) 8.99706 + 15.5834i 0.755016 + 1.30773i
\(143\) 0 0
\(144\) 8.66525 15.0087i 0.722104 1.25072i
\(145\) −3.39457 5.87957i −0.281904 0.488272i
\(146\) −22.5745 −1.86828
\(147\) 9.33992 + 1.26290i 0.770343 + 0.104163i
\(148\) 59.1174 4.85942
\(149\) 7.69632 + 13.3304i 0.630507 + 1.09207i 0.987448 + 0.157944i \(0.0504864\pi\)
−0.356941 + 0.934127i \(0.616180\pi\)
\(150\) 0.396863 0.687386i 0.0324037 0.0561248i
\(151\) −6.83786 + 11.8435i −0.556457 + 0.963812i 0.441331 + 0.897344i \(0.354506\pi\)
−0.997789 + 0.0664680i \(0.978827\pi\)
\(152\) −3.53453 6.12198i −0.286688 0.496558i
\(153\) 6.28158 0.507836
\(154\) −6.27651 4.20974i −0.505776 0.339231i
\(155\) 2.24821 0.180581
\(156\) 0 0
\(157\) −1.69378 + 2.93371i −0.135178 + 0.234136i −0.925666 0.378343i \(-0.876494\pi\)
0.790487 + 0.612478i \(0.209827\pi\)
\(158\) 2.91621 5.05102i 0.232001 0.401838i
\(159\) 3.29074 + 5.69972i 0.260972 + 0.452017i
\(160\) 46.1602 3.64928
\(161\) 0.116117 1.72532i 0.00915128 0.135974i
\(162\) 10.9804 0.862705
\(163\) −6.90502 11.9598i −0.540843 0.936767i −0.998856 0.0478219i \(-0.984772\pi\)
0.458013 0.888946i \(-0.348561\pi\)
\(164\) 19.8639 34.4052i 1.55111 2.68660i
\(165\) −1.54332 + 2.67311i −0.120147 + 0.208101i
\(166\) 9.08268 + 15.7317i 0.704953 + 1.22101i
\(167\) −16.3783 −1.26739 −0.633695 0.773583i \(-0.718462\pi\)
−0.633695 + 0.773583i \(0.718462\pi\)
\(168\) −29.8643 + 14.6625i −2.30408 + 1.13124i
\(169\) 0 0
\(170\) 15.7694 + 27.3134i 1.20946 + 2.09485i
\(171\) −0.449286 + 0.778186i −0.0343578 + 0.0595094i
\(172\) −2.40896 + 4.17244i −0.183682 + 0.318146i
\(173\) −2.06273 3.57275i −0.156826 0.271631i 0.776896 0.629629i \(-0.216793\pi\)
−0.933723 + 0.357997i \(0.883460\pi\)
\(174\) −11.3899 −0.863465
\(175\) 0.513734 0.252229i 0.0388346 0.0190667i
\(176\) 15.3012 1.15337
\(177\) 0.705626 + 1.22218i 0.0530381 + 0.0918647i
\(178\) 7.85930 13.6127i 0.589080 1.02032i
\(179\) −7.20679 + 12.4825i −0.538661 + 0.932988i 0.460316 + 0.887755i \(0.347736\pi\)
−0.998976 + 0.0452324i \(0.985597\pi\)
\(180\) −7.04565 12.2034i −0.525152 0.909589i
\(181\) 18.1014 1.34547 0.672733 0.739885i \(-0.265120\pi\)
0.672733 + 0.739885i \(0.265120\pi\)
\(182\) 0 0
\(183\) 16.8299 1.24410
\(184\) 3.05204 + 5.28629i 0.225000 + 0.389711i
\(185\) 11.9126 20.6333i 0.875834 1.51699i
\(186\) 1.88587 3.26642i 0.138279 0.239506i
\(187\) 2.77302 + 4.80302i 0.202784 + 0.351232i
\(188\) −12.6856 −0.925195
\(189\) 12.3876 + 8.30850i 0.901062 + 0.604355i
\(190\) −4.51159 −0.327305
\(191\) −2.77068 4.79895i −0.200479 0.347240i 0.748204 0.663469i \(-0.230917\pi\)
−0.948683 + 0.316229i \(0.897583\pi\)
\(192\) 19.0653 33.0220i 1.37592 2.38316i
\(193\) −4.37044 + 7.56983i −0.314591 + 0.544888i −0.979351 0.202170i \(-0.935201\pi\)
0.664759 + 0.747058i \(0.268534\pi\)
\(194\) 3.93495 + 6.81553i 0.282513 + 0.489327i
\(195\) 0 0
\(196\) −37.6463 5.09038i −2.68902 0.363598i
\(197\) 5.46874 0.389632 0.194816 0.980840i \(-0.437589\pi\)
0.194816 + 0.980840i \(0.437589\pi\)
\(198\) −1.69556 2.93679i −0.120498 0.208709i
\(199\) −9.76839 + 16.9193i −0.692463 + 1.19938i 0.278566 + 0.960417i \(0.410141\pi\)
−0.971029 + 0.238963i \(0.923192\pi\)
\(200\) −1.01012 + 1.74958i −0.0714264 + 0.123714i
\(201\) −3.01522 5.22252i −0.212677 0.368368i
\(202\) 30.6708 2.15799
\(203\) −6.82056 4.57464i −0.478709 0.321077i
\(204\) 38.6631 2.70696
\(205\) −8.00546 13.8659i −0.559125 0.968433i
\(206\) 27.5705 47.7536i 1.92093 3.32715i
\(207\) 0.387956 0.671959i 0.0269648 0.0467044i
\(208\) 0 0
\(209\) −0.793355 −0.0548775
\(210\) −1.42581 + 21.1853i −0.0983899 + 1.46192i
\(211\) 16.6905 1.14902 0.574511 0.818497i \(-0.305192\pi\)
0.574511 + 0.818497i \(0.305192\pi\)
\(212\) −13.2639 22.9738i −0.910971 1.57785i
\(213\) 4.44502 7.69900i 0.304568 0.527527i
\(214\) 12.3388 21.3714i 0.843463 1.46092i
\(215\) 0.970850 + 1.68156i 0.0662114 + 0.114682i
\(216\) −52.6524 −3.58254
\(217\) 2.44124 1.19858i 0.165722 0.0813647i
\(218\) 41.1551 2.78737
\(219\) 5.57650 + 9.65878i 0.376825 + 0.652680i
\(220\) 6.22065 10.7745i 0.419396 0.726415i
\(221\) 0 0
\(222\) −19.9854 34.6157i −1.34133 2.32325i
\(223\) 5.34217 0.357738 0.178869 0.983873i \(-0.442756\pi\)
0.178869 + 0.983873i \(0.442756\pi\)
\(224\) 50.1233 24.6091i 3.34901 1.64427i
\(225\) 0.256800 0.0171200
\(226\) 4.22970 + 7.32606i 0.281356 + 0.487322i
\(227\) 10.0608 17.4258i 0.667757 1.15659i −0.310774 0.950484i \(-0.600588\pi\)
0.978530 0.206104i \(-0.0660786\pi\)
\(228\) −2.76535 + 4.78973i −0.183140 + 0.317208i
\(229\) 12.6249 + 21.8669i 0.834275 + 1.44501i 0.894619 + 0.446829i \(0.147447\pi\)
−0.0603445 + 0.998178i \(0.519220\pi\)
\(230\) 3.89573 0.256877
\(231\) −0.250725 + 3.72540i −0.0164965 + 0.245113i
\(232\) 28.9903 1.90331
\(233\) 0.396678 + 0.687066i 0.0259872 + 0.0450112i 0.878727 0.477326i \(-0.158394\pi\)
−0.852739 + 0.522337i \(0.825060\pi\)
\(234\) 0 0
\(235\) −2.55626 + 4.42757i −0.166752 + 0.288823i
\(236\) −2.84416 4.92623i −0.185139 0.320671i
\(237\) −2.88152 −0.187175
\(238\) 31.6848 + 21.2514i 2.05382 + 1.37753i
\(239\) −20.0488 −1.29685 −0.648425 0.761279i \(-0.724572\pi\)
−0.648425 + 0.761279i \(0.724572\pi\)
\(240\) −21.4947 37.2299i −1.38748 2.40318i
\(241\) 6.90602 11.9616i 0.444856 0.770513i −0.553186 0.833058i \(-0.686588\pi\)
0.998042 + 0.0625446i \(0.0199216\pi\)
\(242\) −13.4919 + 23.3686i −0.867289 + 1.50219i
\(243\) 5.74404 + 9.94897i 0.368480 + 0.638227i
\(244\) −67.8362 −4.34277
\(245\) −9.36269 + 12.1137i −0.598161 + 0.773913i
\(246\) −26.8609 −1.71259
\(247\) 0 0
\(248\) −4.80004 + 8.31392i −0.304803 + 0.527934i
\(249\) 4.48732 7.77227i 0.284372 0.492547i
\(250\) 15.5461 + 26.9266i 0.983222 + 1.70299i
\(251\) −26.1095 −1.64802 −0.824010 0.566576i \(-0.808268\pi\)
−0.824010 + 0.566576i \(0.808268\pi\)
\(252\) −14.1565 9.49496i −0.891776 0.598126i
\(253\) 0.685057 0.0430692
\(254\) 11.9763 + 20.7436i 0.751460 + 1.30157i
\(255\) 7.79092 13.4943i 0.487886 0.845044i
\(256\) −19.3298 + 33.4801i −1.20811 + 2.09251i
\(257\) −5.30990 9.19701i −0.331222 0.573694i 0.651530 0.758623i \(-0.274128\pi\)
−0.982752 + 0.184930i \(0.940794\pi\)
\(258\) 3.25752 0.202804
\(259\) 1.93531 28.7557i 0.120254 1.78679i
\(260\) 0 0
\(261\) −1.84253 3.19135i −0.114050 0.197540i
\(262\) −14.3273 + 24.8156i −0.885142 + 1.53311i
\(263\) −5.17888 + 8.97008i −0.319343 + 0.553119i −0.980351 0.197260i \(-0.936796\pi\)
0.661008 + 0.750379i \(0.270129\pi\)
\(264\) −6.59013 11.4144i −0.405594 0.702510i
\(265\) −10.6912 −0.656753
\(266\) −4.89894 + 2.40524i −0.300374 + 0.147475i
\(267\) −7.76581 −0.475260
\(268\) 12.1534 + 21.0504i 0.742389 + 1.28586i
\(269\) −5.98503 + 10.3664i −0.364914 + 0.632049i −0.988762 0.149496i \(-0.952235\pi\)
0.623849 + 0.781545i \(0.285568\pi\)
\(270\) −16.8018 + 29.1016i −1.02253 + 1.77107i
\(271\) −1.37845 2.38755i −0.0837351 0.145033i 0.821116 0.570761i \(-0.193352\pi\)
−0.904852 + 0.425727i \(0.860018\pi\)
\(272\) −77.2429 −4.68354
\(273\) 0 0
\(274\) 23.7959 1.43757
\(275\) 0.113365 + 0.196354i 0.00683618 + 0.0118406i
\(276\) 2.38786 4.13590i 0.143733 0.248952i
\(277\) 11.9637 20.7218i 0.718831 1.24505i −0.242632 0.970118i \(-0.578011\pi\)
0.961463 0.274933i \(-0.0886558\pi\)
\(278\) −5.45050 9.44054i −0.326899 0.566206i
\(279\) 1.22030 0.0730574
\(280\) 3.62906 53.9223i 0.216878 3.22247i
\(281\) 3.87870 0.231384 0.115692 0.993285i \(-0.463091\pi\)
0.115692 + 0.993285i \(0.463091\pi\)
\(282\) 4.28854 + 7.42796i 0.255379 + 0.442329i
\(283\) 3.10499 5.37801i 0.184573 0.319689i −0.758860 0.651254i \(-0.774243\pi\)
0.943432 + 0.331565i \(0.107577\pi\)
\(284\) −17.9165 + 31.0323i −1.06315 + 1.84143i
\(285\) 1.11448 + 1.93034i 0.0660162 + 0.114343i
\(286\) 0 0
\(287\) −16.0850 10.7884i −0.949468 0.636821i
\(288\) 25.0551 1.47639
\(289\) −5.49866 9.52395i −0.323450 0.560232i
\(290\) 9.25106 16.0233i 0.543241 0.940920i
\(291\) 1.94407 3.36723i 0.113963 0.197390i
\(292\) −22.4772 38.9316i −1.31538 2.27830i
\(293\) −16.5754 −0.968347 −0.484174 0.874972i \(-0.660880\pi\)
−0.484174 + 0.874972i \(0.660880\pi\)
\(294\) 9.74618 + 23.7643i 0.568409 + 1.38596i
\(295\) −2.29249 −0.133474
\(296\) 50.8681 + 88.1062i 2.95665 + 5.12107i
\(297\) −2.95457 + 5.11747i −0.171442 + 0.296946i
\(298\) −20.9744 + 36.3287i −1.21501 + 2.10447i
\(299\) 0 0
\(300\) 1.58060 0.0912561
\(301\) 1.95069 + 1.30835i 0.112436 + 0.0754121i
\(302\) −37.2698 −2.14463
\(303\) −7.57650 13.1229i −0.435259 0.753890i
\(304\) 5.52475 9.56914i 0.316866 0.548828i
\(305\) −13.6695 + 23.6763i −0.782716 + 1.35570i
\(306\) 8.55944 + 14.8254i 0.489311 + 0.847511i
\(307\) 7.05788 0.402815 0.201407 0.979508i \(-0.435449\pi\)
0.201407 + 0.979508i \(0.435449\pi\)
\(308\) 1.01060 15.0159i 0.0575841 0.855612i
\(309\) −27.2426 −1.54978
\(310\) 3.06347 + 5.30609i 0.173993 + 0.301365i
\(311\) −10.5551 + 18.2820i −0.598525 + 1.03668i 0.394514 + 0.918890i \(0.370913\pi\)
−0.993039 + 0.117785i \(0.962420\pi\)
\(312\) 0 0
\(313\) −0.990260 1.71518i −0.0559728 0.0969477i 0.836681 0.547690i \(-0.184493\pi\)
−0.892654 + 0.450742i \(0.851159\pi\)
\(314\) −9.23194 −0.520989
\(315\) −6.16660 + 3.02762i −0.347449 + 0.170587i
\(316\) 11.6145 0.653368
\(317\) −9.02297 15.6282i −0.506781 0.877770i −0.999969 0.00784727i \(-0.997502\pi\)
0.493189 0.869922i \(-0.335831\pi\)
\(318\) −8.96808 + 15.5332i −0.502905 + 0.871057i
\(319\) 1.62678 2.81767i 0.0910822 0.157759i
\(320\) 30.9703 + 53.6421i 1.73129 + 2.99868i
\(321\) −12.1920 −0.680492
\(322\) 4.23021 2.07691i 0.235740 0.115742i
\(323\) 4.00498 0.222843
\(324\) 10.9331 + 18.9366i 0.607393 + 1.05204i
\(325\) 0 0
\(326\) 18.8179 32.5936i 1.04223 1.80519i
\(327\) −10.1664 17.6087i −0.562202 0.973763i
\(328\) 68.3682 3.77500
\(329\) −0.415285 + 6.17051i −0.0228954 + 0.340191i
\(330\) −8.41187 −0.463058
\(331\) −7.33689 12.7079i −0.403272 0.698488i 0.590847 0.806784i \(-0.298794\pi\)
−0.994119 + 0.108296i \(0.965460\pi\)
\(332\) −18.0870 + 31.3276i −0.992653 + 1.71933i
\(333\) 6.46602 11.1995i 0.354336 0.613728i
\(334\) −22.3175 38.6550i −1.22116 2.11511i
\(335\) 9.79606 0.535216
\(336\) −43.1883 28.9670i −2.35611 1.58028i
\(337\) 12.8080 0.697698 0.348849 0.937179i \(-0.386573\pi\)
0.348849 + 0.937179i \(0.386573\pi\)
\(338\) 0 0
\(339\) 2.08969 3.61946i 0.113497 0.196582i
\(340\) −31.4028 + 54.3913i −1.70306 + 2.94978i
\(341\) 0.538705 + 0.933065i 0.0291725 + 0.0505283i
\(342\) −2.44883 −0.132418
\(343\) −3.70846 + 18.1452i −0.200238 + 0.979747i
\(344\) −8.29125 −0.447034
\(345\) −0.962348 1.66684i −0.0518111 0.0897394i
\(346\) 5.62146 9.73665i 0.302211 0.523445i
\(347\) −10.1027 + 17.4984i −0.542342 + 0.939363i 0.456428 + 0.889761i \(0.349129\pi\)
−0.998769 + 0.0496025i \(0.984205\pi\)
\(348\) −11.3408 19.6428i −0.607928 1.05296i
\(349\) 18.4434 0.987252 0.493626 0.869674i \(-0.335671\pi\)
0.493626 + 0.869674i \(0.335671\pi\)
\(350\) 1.29532 + 0.868789i 0.0692378 + 0.0464387i
\(351\) 0 0
\(352\) 11.0607 + 19.1576i 0.589536 + 1.02111i
\(353\) −4.07218 + 7.05322i −0.216740 + 0.375405i −0.953810 0.300412i \(-0.902876\pi\)
0.737069 + 0.675817i \(0.236209\pi\)
\(354\) −1.92301 + 3.33075i −0.102207 + 0.177027i
\(355\) 7.22064 + 12.5065i 0.383232 + 0.663777i
\(356\) 31.3016 1.65898
\(357\) 1.26570 18.8064i 0.0669879 0.995339i
\(358\) −39.2806 −2.07604
\(359\) −16.3050 28.2411i −0.860545 1.49051i −0.871404 0.490566i \(-0.836790\pi\)
0.0108595 0.999941i \(-0.496543\pi\)
\(360\) 12.1250 21.0011i 0.639043 1.10685i
\(361\) 9.21355 15.9583i 0.484923 0.839912i
\(362\) 24.6654 + 42.7218i 1.29639 + 2.24541i
\(363\) 13.3314 0.699715
\(364\) 0 0
\(365\) −18.1173 −0.948304
\(366\) 22.9329 + 39.7209i 1.19872 + 2.07624i
\(367\) 1.58006 2.73675i 0.0824786 0.142857i −0.821835 0.569725i \(-0.807050\pi\)
0.904314 + 0.426868i \(0.140383\pi\)
\(368\) −4.77059 + 8.26290i −0.248684 + 0.430733i
\(369\) −4.34526 7.52621i −0.226205 0.391799i
\(370\) 64.9298 3.37554
\(371\) −11.6091 + 5.69972i −0.602713 + 0.295915i
\(372\) 7.51094 0.389424
\(373\) 0.738849 + 1.27972i 0.0382561 + 0.0662616i 0.884520 0.466503i \(-0.154486\pi\)
−0.846263 + 0.532765i \(0.821153\pi\)
\(374\) −7.55718 + 13.0894i −0.390773 + 0.676838i
\(375\) 7.68059 13.3032i 0.396624 0.686972i
\(376\) −10.9155 18.9061i −0.562922 0.975010i
\(377\) 0 0
\(378\) −2.72960 + 40.5577i −0.140395 + 2.08606i
\(379\) −10.7254 −0.550927 −0.275463 0.961312i \(-0.588831\pi\)
−0.275463 + 0.961312i \(0.588831\pi\)
\(380\) −4.49213 7.78060i −0.230441 0.399136i
\(381\) 5.91692 10.2484i 0.303133 0.525042i
\(382\) 7.55079 13.0784i 0.386332 0.669147i
\(383\) −10.7054 18.5424i −0.547023 0.947471i −0.998477 0.0551766i \(-0.982428\pi\)
0.451454 0.892294i \(-0.350906\pi\)
\(384\) 47.0830 2.40269
\(385\) −5.03725 3.37855i −0.256722 0.172187i
\(386\) −23.8211 −1.21246
\(387\) 0.526965 + 0.912730i 0.0267871 + 0.0463967i
\(388\) −7.83595 + 13.5723i −0.397810 + 0.689027i
\(389\) −17.3909 + 30.1220i −0.881755 + 1.52725i −0.0323675 + 0.999476i \(0.510305\pi\)
−0.849388 + 0.527769i \(0.823029\pi\)
\(390\) 0 0
\(391\) −3.45828 −0.174893
\(392\) −24.8066 60.4866i −1.25292 3.05503i
\(393\) 14.1568 0.714119
\(394\) 7.45185 + 12.9070i 0.375419 + 0.650244i
\(395\) 2.34042 4.05373i 0.117759 0.203965i
\(396\) 3.37649 5.84825i 0.169675 0.293886i
\(397\) 2.22605 + 3.85564i 0.111722 + 0.193509i 0.916465 0.400115i \(-0.131030\pi\)
−0.804742 + 0.593624i \(0.797697\pi\)
\(398\) −53.2426 −2.66881
\(399\) 2.23928 + 1.50191i 0.112104 + 0.0751897i
\(400\) −3.15780 −0.157890
\(401\) −6.87687 11.9111i −0.343415 0.594811i 0.641650 0.766998i \(-0.278250\pi\)
−0.985064 + 0.172186i \(0.944917\pi\)
\(402\) 8.21724 14.2327i 0.409839 0.709861i
\(403\) 0 0
\(404\) 30.5385 + 52.8943i 1.51935 + 2.63159i
\(405\) 8.81241 0.437892
\(406\) 1.50291 22.3310i 0.0745882 1.10827i
\(407\) 11.4178 0.565959
\(408\) 33.2680 + 57.6219i 1.64701 + 2.85271i
\(409\) −1.74603 + 3.02422i −0.0863358 + 0.149538i −0.905960 0.423364i \(-0.860849\pi\)
0.819624 + 0.572902i \(0.194182\pi\)
\(410\) 21.8169 37.7879i 1.07746 1.86621i
\(411\) −5.87822 10.1814i −0.289951 0.502210i
\(412\) 109.806 5.40977
\(413\) −2.48931 + 1.22218i −0.122491 + 0.0601396i
\(414\) 2.11455 0.103925
\(415\) 7.28935 + 12.6255i 0.357820 + 0.619763i
\(416\) 0 0
\(417\) −2.69283 + 4.66412i −0.131869 + 0.228403i
\(418\) −1.08105 1.87243i −0.0528757 0.0915834i
\(419\) −3.56737 −0.174278 −0.0871388 0.996196i \(-0.527772\pi\)
−0.0871388 + 0.996196i \(0.527772\pi\)
\(420\) −37.9554 + 18.6350i −1.85203 + 0.909295i
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 22.7429 + 39.3919i 1.10711 + 1.91757i
\(423\) −1.38750 + 2.40323i −0.0674627 + 0.116849i
\(424\) 22.8262 39.5361i 1.10854 1.92004i
\(425\) −0.572285 0.991227i −0.0277599 0.0480816i
\(426\) 24.2276 1.17383
\(427\) −2.22073 + 32.9967i −0.107469 + 1.59682i
\(428\) 49.1423 2.37538
\(429\) 0 0
\(430\) −2.64581 + 4.58268i −0.127592 + 0.220996i
\(431\) −5.68211 + 9.84171i −0.273698 + 0.474059i −0.969806 0.243879i \(-0.921580\pi\)
0.696108 + 0.717937i \(0.254913\pi\)
\(432\) −41.1500 71.2738i −1.97983 3.42916i
\(433\) −21.2136 −1.01946 −0.509731 0.860334i \(-0.670255\pi\)
−0.509731 + 0.860334i \(0.670255\pi\)
\(434\) 6.15529 + 4.12844i 0.295464 + 0.198171i
\(435\) −9.14101 −0.438278
\(436\) 40.9776 + 70.9752i 1.96247 + 3.39910i
\(437\) 0.247351 0.428424i 0.0118324 0.0204943i
\(438\) −15.1974 + 26.3226i −0.726158 + 1.25774i
\(439\) 12.2503 + 21.2182i 0.584676 + 1.01269i 0.994916 + 0.100711i \(0.0321118\pi\)
−0.410239 + 0.911978i \(0.634555\pi\)
\(440\) 21.4105 1.02070
\(441\) −5.08195 + 6.57513i −0.241997 + 0.313102i
\(442\) 0 0
\(443\) −20.2344 35.0470i −0.961366 1.66513i −0.719077 0.694930i \(-0.755435\pi\)
−0.242288 0.970204i \(-0.577898\pi\)
\(444\) 39.7983 68.9327i 1.88874 3.27140i
\(445\) 6.30753 10.9250i 0.299005 0.517893i
\(446\) 7.27937 + 12.6082i 0.344688 + 0.597017i
\(447\) 20.7249 0.980254
\(448\) 62.2272 + 41.7366i 2.93996 + 1.97187i
\(449\) 27.7638 1.31025 0.655127 0.755519i \(-0.272615\pi\)
0.655127 + 0.755519i \(0.272615\pi\)
\(450\) 0.349922 + 0.606083i 0.0164955 + 0.0285710i
\(451\) 3.83646 6.64494i 0.180652 0.312898i
\(452\) −8.42292 + 14.5889i −0.396181 + 0.686205i
\(453\) 9.20661 + 15.9463i 0.432564 + 0.749223i
\(454\) 54.8362 2.57359
\(455\) 0 0
\(456\) −9.51789 −0.445716
\(457\) −5.59696 9.69422i −0.261815 0.453476i 0.704910 0.709297i \(-0.250988\pi\)
−0.966724 + 0.255821i \(0.917654\pi\)
\(458\) −34.4059 + 59.5928i −1.60768 + 2.78459i
\(459\) 14.9151 25.8338i 0.696179 1.20582i
\(460\) 3.87893 + 6.71850i 0.180856 + 0.313252i
\(461\) 9.29773 0.433038 0.216519 0.976278i \(-0.430530\pi\)
0.216519 + 0.976278i \(0.430530\pi\)
\(462\) −9.13409 + 4.48457i −0.424956 + 0.208641i
\(463\) −28.2439 −1.31260 −0.656302 0.754499i \(-0.727880\pi\)
−0.656302 + 0.754499i \(0.727880\pi\)
\(464\) 22.6571 + 39.2432i 1.05183 + 1.82182i
\(465\) 1.51351 2.62148i 0.0701875 0.121568i
\(466\) −1.08105 + 1.87243i −0.0500785 + 0.0867385i
\(467\) −11.1303 19.2783i −0.515050 0.892093i −0.999847 0.0174663i \(-0.994440\pi\)
0.484797 0.874626i \(-0.338893\pi\)
\(468\) 0 0
\(469\) 10.6371 5.22252i 0.491177 0.241154i
\(470\) −13.9329 −0.642676
\(471\) 2.28053 + 3.95000i 0.105081 + 0.182006i
\(472\) 4.89457 8.47765i 0.225291 0.390215i
\(473\) −0.465261 + 0.805855i −0.0213927 + 0.0370533i
\(474\) −3.92643 6.80078i −0.180347 0.312370i
\(475\) 0.163729 0.00751242
\(476\) −5.10165 + 75.8027i −0.233834 + 3.47441i
\(477\) −5.80302 −0.265702
\(478\) −27.3190 47.3179i −1.24954 2.16427i
\(479\) −16.4382 + 28.4718i −0.751081 + 1.30091i 0.196219 + 0.980560i \(0.437134\pi\)
−0.947299 + 0.320350i \(0.896200\pi\)
\(480\) 31.0754 53.8242i 1.41839 2.45673i
\(481\) 0 0
\(482\) 37.6413 1.71451
\(483\) −1.93360 1.29689i −0.0879820 0.0590107i
\(484\) −53.7346 −2.44248
\(485\) 3.15801 + 5.46984i 0.143398 + 0.248373i
\(486\) −15.6539 + 27.1134i −0.710078 + 1.22989i
\(487\) −13.9462 + 24.1555i −0.631962 + 1.09459i 0.355188 + 0.934795i \(0.384417\pi\)
−0.987150 + 0.159796i \(0.948916\pi\)
\(488\) −58.3703 101.100i −2.64230 4.57660i
\(489\) −18.5941 −0.840852
\(490\) −41.3477 5.59086i −1.86790 0.252569i
\(491\) 10.6571 0.480948 0.240474 0.970656i \(-0.422697\pi\)
0.240474 + 0.970656i \(0.422697\pi\)
\(492\) −26.7450 46.3237i −1.20576 2.08844i
\(493\) −8.21224 + 14.2240i −0.369861 + 0.640618i
\(494\) 0 0
\(495\) −1.36078 2.35694i −0.0611625 0.105936i
\(496\) −15.0057 −0.673776
\(497\) 14.5081 + 9.73078i 0.650777 + 0.436485i
\(498\) 24.4581 1.09600
\(499\) −12.2557 21.2275i −0.548641 0.950274i −0.998368 0.0571077i \(-0.981812\pi\)
0.449727 0.893166i \(-0.351521\pi\)
\(500\) −30.9581 + 53.6210i −1.38449 + 2.39800i
\(501\) −11.0260 + 19.0976i −0.492605 + 0.853217i
\(502\) −35.5775 61.6221i −1.58790 2.75033i
\(503\) −38.0054 −1.69458 −0.847288 0.531134i \(-0.821766\pi\)
−0.847288 + 0.531134i \(0.821766\pi\)
\(504\) 1.96980 29.2683i 0.0877421 1.30371i
\(505\) 24.6151 1.09536
\(506\) 0.933476 + 1.61683i 0.0414981 + 0.0718768i
\(507\) 0 0
\(508\) −23.8493 + 41.3082i −1.05814 + 1.83275i
\(509\) 19.9250 + 34.5112i 0.883161 + 1.52968i 0.847807 + 0.530305i \(0.177923\pi\)
0.0353545 + 0.999375i \(0.488744\pi\)
\(510\) 42.4644 1.88036
\(511\) −19.6728 + 9.65878i −0.870274 + 0.427279i
\(512\) −35.4186 −1.56530
\(513\) 2.13359 + 3.69549i 0.0942004 + 0.163160i
\(514\) 14.4708 25.0642i 0.638279 1.10553i
\(515\) 22.1269 38.3249i 0.975027 1.68880i
\(516\) 3.24346 + 5.61784i 0.142786 + 0.247312i
\(517\) −2.45007 −0.107754
\(518\) 70.5045 34.6157i 3.09779 1.52093i
\(519\) −5.55459 −0.243819
\(520\) 0 0
\(521\) 9.81670 17.0030i 0.430077 0.744916i −0.566802 0.823854i \(-0.691820\pi\)
0.996880 + 0.0789382i \(0.0251530\pi\)
\(522\) 5.02135 8.69724i 0.219779 0.380668i
\(523\) −11.4162 19.7734i −0.499195 0.864632i 0.500804 0.865561i \(-0.333038\pi\)
−1.00000 0.000928862i \(0.999704\pi\)
\(524\) −57.0619 −2.49276
\(525\) 0.0517436 0.768832i 0.00225828 0.0335546i
\(526\) −28.2275 −1.23078
\(527\) −2.71947 4.71026i −0.118462 0.205182i
\(528\) 10.3009 17.8417i 0.448289 0.776459i
\(529\) 11.2864 19.5486i 0.490714 0.849941i
\(530\) −14.5681 25.2326i −0.632796 1.09603i
\(531\) −1.24433 −0.0539994
\(532\) −9.02584 6.05375i −0.391320 0.262463i
\(533\) 0 0
\(534\) −10.5819 18.3284i −0.457923 0.793146i
\(535\) 9.90257 17.1518i 0.428125 0.741535i
\(536\) −20.9151 + 36.2260i −0.903394 + 1.56472i
\(537\) 9.70333 + 16.8067i 0.418730 + 0.725261i
\(538\) −32.6214 −1.40641
\(539\) −7.27092 0.983142i −0.313181 0.0423469i
\(540\) −66.9175 −2.87967
\(541\) −4.82334 8.35427i −0.207372 0.359178i 0.743514 0.668720i \(-0.233158\pi\)
−0.950886 + 0.309542i \(0.899824\pi\)
\(542\) 3.75663 6.50667i 0.161361 0.279486i
\(543\) 12.1860 21.1068i 0.522952 0.905779i
\(544\) −55.8360 96.7108i −2.39395 4.14644i
\(545\) 33.0292 1.41482
\(546\) 0 0
\(547\) −43.8570 −1.87519 −0.937596 0.347728i \(-0.886953\pi\)
−0.937596 + 0.347728i \(0.886953\pi\)
\(548\) 23.6933 + 41.0380i 1.01213 + 1.75306i
\(549\) −7.41965 + 12.8512i −0.316663 + 0.548476i
\(550\) −0.308949 + 0.535115i −0.0131736 + 0.0228174i
\(551\) −1.17475 2.03473i −0.0500461 0.0866823i
\(552\) 8.21864 0.349808
\(553\) 0.380221 5.64950i 0.0161686 0.240241i
\(554\) 65.2083 2.77044
\(555\) −16.0394 27.7810i −0.680833 1.17924i
\(556\) 10.8540 18.7996i 0.460311 0.797282i
\(557\) 7.45977 12.9207i 0.316080 0.547467i −0.663586 0.748100i \(-0.730966\pi\)
0.979667 + 0.200633i \(0.0642997\pi\)
\(558\) 1.66281 + 2.88007i 0.0703924 + 0.121923i
\(559\) 0 0
\(560\) 75.8290 37.2299i 3.20436 1.57325i
\(561\) 7.46729 0.315269
\(562\) 5.28521 + 9.15426i 0.222943 + 0.386149i
\(563\) 8.63486 14.9560i 0.363916 0.630321i −0.624686 0.780876i \(-0.714773\pi\)
0.988602 + 0.150555i \(0.0481062\pi\)
\(564\) −8.54007 + 14.7918i −0.359602 + 0.622849i
\(565\) 3.39457 + 5.87957i 0.142811 + 0.247355i
\(566\) 16.9238 0.711359
\(567\) 9.56902 4.69811i 0.401861 0.197302i
\(568\) −61.6657 −2.58743
\(569\) −13.2662 22.9777i −0.556148 0.963277i −0.997813 0.0660972i \(-0.978945\pi\)
0.441665 0.897180i \(-0.354388\pi\)
\(570\) −3.03724 + 5.26065i −0.127216 + 0.220345i
\(571\) 0.992844 1.71966i 0.0415492 0.0719654i −0.844503 0.535551i \(-0.820104\pi\)
0.886052 + 0.463586i \(0.153437\pi\)
\(572\) 0 0
\(573\) −7.46097 −0.311686
\(574\) 3.54433 52.6634i 0.147938 2.19813i
\(575\) −0.141379 −0.00589593
\(576\) 16.8103 + 29.1162i 0.700428 + 1.21318i
\(577\) 5.94915 10.3042i 0.247666 0.428971i −0.715212 0.698908i \(-0.753670\pi\)
0.962878 + 0.269937i \(0.0870030\pi\)
\(578\) 14.9852 25.9551i 0.623303 1.07959i
\(579\) 5.88443 + 10.1921i 0.244549 + 0.423571i
\(580\) 36.8446 1.52989
\(581\) 14.6462 + 9.82339i 0.607626 + 0.407543i
\(582\) 10.5962 0.439225
\(583\) −2.56176 4.43711i −0.106097 0.183766i
\(584\) 38.6814 66.9981i 1.60065 2.77240i
\(585\) 0 0
\(586\) −22.5861 39.1203i −0.933024 1.61604i
\(587\) −33.5122 −1.38320 −0.691598 0.722283i \(-0.743093\pi\)
−0.691598 + 0.722283i \(0.743093\pi\)
\(588\) −31.2793 + 40.4699i −1.28994 + 1.66895i
\(589\) 0.778033 0.0320583
\(590\) −3.12380 5.41058i −0.128605 0.222750i
\(591\) 3.68160 6.37672i 0.151441 0.262303i
\(592\) −79.5109 + 137.717i −3.26788 + 5.66013i
\(593\) 17.6408 + 30.5547i 0.724419 + 1.25473i 0.959213 + 0.282686i \(0.0912253\pi\)
−0.234793 + 0.972045i \(0.575441\pi\)
\(594\) −16.1039 −0.660751
\(595\) 25.4288 + 17.0554i 1.04248 + 0.699205i
\(596\) −83.5357 −3.42176
\(597\) 13.1523 + 22.7805i 0.538288 + 0.932343i
\(598\) 0 0
\(599\) 12.5034 21.6565i 0.510876 0.884863i −0.489045 0.872259i \(-0.662655\pi\)
0.999921 0.0126040i \(-0.00401207\pi\)
\(600\) 1.36004 + 2.35566i 0.0555236 + 0.0961696i
\(601\) −28.4688 −1.16127 −0.580634 0.814165i \(-0.697195\pi\)
−0.580634 + 0.814165i \(0.697195\pi\)
\(602\) −0.429834 + 6.38668i −0.0175187 + 0.260301i
\(603\) 5.31717 0.216532
\(604\) −37.1090 64.2747i −1.50994 2.61530i
\(605\) −10.8280 + 18.7546i −0.440219 + 0.762482i
\(606\) 20.6479 35.7631i 0.838762 1.45278i
\(607\) −18.0234 31.2175i −0.731549 1.26708i −0.956221 0.292646i \(-0.905464\pi\)
0.224672 0.974434i \(-0.427869\pi\)
\(608\) 15.9745 0.647853
\(609\) −9.92583 + 4.87330i −0.402215 + 0.197476i
\(610\) −74.5058 −3.01665
\(611\) 0 0
\(612\) −17.0450 + 29.5229i −0.689005 + 1.19339i
\(613\) 9.16264 15.8702i 0.370075 0.640989i −0.619501 0.784996i \(-0.712665\pi\)
0.989577 + 0.144006i \(0.0459985\pi\)
\(614\) 9.61725 + 16.6576i 0.388121 + 0.672245i
\(615\) −21.5573 −0.869276
\(616\) 23.2487 11.4144i 0.936717 0.459901i
\(617\) −44.3782 −1.78660 −0.893299 0.449463i \(-0.851615\pi\)
−0.893299 + 0.449463i \(0.851615\pi\)
\(618\) −37.1214 64.2962i −1.49324 2.58637i
\(619\) −12.5043 + 21.6580i −0.502588 + 0.870509i 0.497407 + 0.867517i \(0.334286\pi\)
−0.999996 + 0.00299144i \(0.999048\pi\)
\(620\) −6.10051 + 10.5664i −0.245002 + 0.424357i
\(621\) −1.84234 3.19103i −0.0739307 0.128052i
\(622\) −57.5306 −2.30677
\(623\) 1.02471 15.2256i 0.0410541 0.610002i
\(624\) 0 0
\(625\) 11.9358 + 20.6734i 0.477433 + 0.826938i
\(626\) 2.69871 4.67429i 0.107862 0.186822i
\(627\) −0.534093 + 0.925076i −0.0213296 + 0.0369440i
\(628\) −9.19212 15.9212i −0.366806 0.635326i
\(629\) −57.6388 −2.29821
\(630\) −15.5484 10.4285i −0.619462 0.415482i
\(631\) 18.4638 0.735032 0.367516 0.930017i \(-0.380208\pi\)
0.367516 + 0.930017i \(0.380208\pi\)
\(632\) 9.99382 + 17.3098i 0.397533 + 0.688547i
\(633\) 11.2362 19.4616i 0.446598 0.773531i
\(634\) 24.5899 42.5909i 0.976588 1.69150i
\(635\) 9.61165 + 16.6479i 0.381427 + 0.660650i
\(636\) −35.7176 −1.41629
\(637\) 0 0
\(638\) 8.86677 0.351039
\(639\) 3.91927 + 6.78837i 0.155044 + 0.268544i
\(640\) −38.2416 + 66.2364i −1.51163 + 2.61822i
\(641\) 10.6284 18.4088i 0.419795 0.727106i −0.576124 0.817362i \(-0.695435\pi\)
0.995919 + 0.0902567i \(0.0287687\pi\)
\(642\) −16.6132 28.7748i −0.655669 1.13565i
\(643\) 36.0554 1.42188 0.710942 0.703251i \(-0.248269\pi\)
0.710942 + 0.703251i \(0.248269\pi\)
\(644\) 7.79376 + 5.22738i 0.307117 + 0.205988i
\(645\) 2.61434 0.102939
\(646\) 5.45729 + 9.45230i 0.214714 + 0.371896i
\(647\) −19.9117 + 34.4881i −0.782809 + 1.35587i 0.147490 + 0.989064i \(0.452881\pi\)
−0.930299 + 0.366802i \(0.880453\pi\)
\(648\) −18.8149 + 32.5884i −0.739120 + 1.28019i
\(649\) −0.549314 0.951440i −0.0215625 0.0373473i
\(650\) 0 0
\(651\) 0.245883 3.65345i 0.00963691 0.143190i
\(652\) 74.9469 2.93515
\(653\) 16.2335 + 28.1172i 0.635265 + 1.10031i 0.986459 + 0.164008i \(0.0524423\pi\)
−0.351195 + 0.936303i \(0.614224\pi\)
\(654\) 27.7059 47.9881i 1.08339 1.87648i
\(655\) −11.4984 + 19.9159i −0.449281 + 0.778177i
\(656\) 53.4324 + 92.5477i 2.08619 + 3.61338i
\(657\) −9.83384 −0.383655
\(658\) −15.1291 + 7.42796i −0.589794 + 0.289572i
\(659\) 23.5230 0.916327 0.458164 0.888868i \(-0.348507\pi\)
0.458164 + 0.888868i \(0.348507\pi\)
\(660\) −8.37558 14.5069i −0.326019 0.564682i
\(661\) 7.01944 12.1580i 0.273025 0.472893i −0.696610 0.717450i \(-0.745309\pi\)
0.969635 + 0.244557i \(0.0786426\pi\)
\(662\) 19.9949 34.6321i 0.777122 1.34602i
\(663\) 0 0
\(664\) −62.2525 −2.41587
\(665\) −3.93167 + 1.93034i −0.152464 + 0.0748553i
\(666\) 35.2431 1.36564
\(667\) 1.01439 + 1.75698i 0.0392773 + 0.0680303i
\(668\) 44.4424 76.9765i 1.71953 2.97831i
\(669\) 3.59639 6.22913i 0.139044 0.240832i
\(670\) 13.3484 + 23.1200i 0.515692 + 0.893205i
\(671\) −13.1017 −0.505786
\(672\) 5.04846 75.0124i 0.194748 2.89367i
\(673\) −47.1937 −1.81918 −0.909592 0.415502i \(-0.863606\pi\)
−0.909592 + 0.415502i \(0.863606\pi\)
\(674\) 17.4526 + 30.2287i 0.672247 + 1.16437i
\(675\) 0.609753 1.05612i 0.0234694 0.0406502i
\(676\) 0 0
\(677\) 4.79438 + 8.30411i 0.184263 + 0.319153i 0.943328 0.331862i \(-0.107677\pi\)
−0.759065 + 0.651015i \(0.774344\pi\)
\(678\) 11.3899 0.437426
\(679\) 6.34526 + 4.25585i 0.243509 + 0.163325i
\(680\) −108.083 −4.14481
\(681\) −13.5460 23.4623i −0.519083 0.899078i
\(682\) −1.46811 + 2.54284i −0.0562167 + 0.0973702i
\(683\) 23.6581 40.9769i 0.905250 1.56794i 0.0846691 0.996409i \(-0.473017\pi\)
0.820581 0.571530i \(-0.193650\pi\)
\(684\) −2.43827 4.22321i −0.0932296 0.161478i
\(685\) 19.0976 0.729680
\(686\) −47.8783 + 15.9726i −1.82800 + 0.609837i
\(687\) 33.9967 1.29705
\(688\) −6.47994 11.2236i −0.247045 0.427895i
\(689\) 0 0
\(690\) 2.62264 4.54254i 0.0998421 0.172932i
\(691\) −13.5559 23.4796i −0.515692 0.893205i −0.999834 0.0182158i \(-0.994201\pi\)
0.484142 0.874990i \(-0.339132\pi\)
\(692\) 22.3888 0.851095
\(693\) −2.73415 1.83383i −0.103862 0.0696615i
\(694\) −55.0648 −2.09023
\(695\) −4.37433 7.57656i −0.165928 0.287395i
\(696\) 19.5165 33.8036i 0.739771 1.28132i
\(697\) −19.3670 + 33.5447i −0.733578 + 1.27059i
\(698\) 25.1314 + 43.5289i 0.951238 + 1.64759i
\(699\) 1.06819 0.0404025
\(700\) −0.208563 + 3.09893i −0.00788293 + 0.117128i
\(701\) −1.79821 −0.0679176 −0.0339588 0.999423i \(-0.510811\pi\)
−0.0339588 + 0.999423i \(0.510811\pi\)
\(702\) 0 0
\(703\) 4.12258 7.14051i 0.155486 0.269310i
\(704\) −14.8419 + 25.7069i −0.559375 + 0.968866i
\(705\) 3.44179 + 5.96135i 0.129625 + 0.224517i
\(706\) −22.1954 −0.835336
\(707\) 26.7284 13.1229i 1.00523 0.493537i
\(708\) −7.65885 −0.287837
\(709\) −14.1615 24.5284i −0.531846 0.921185i −0.999309 0.0371721i \(-0.988165\pi\)
0.467462 0.884013i \(-0.345168\pi\)
\(710\) −19.6780 + 34.0834i −0.738504 + 1.27913i
\(711\) 1.27035 2.20031i 0.0476418 0.0825180i
\(712\) 26.9337 + 46.6506i 1.00938 + 1.74831i
\(713\) −0.671827 −0.0251601
\(714\) 46.1103 22.6388i 1.72563 0.847236i
\(715\) 0 0
\(716\) −39.1112 67.7425i −1.46165 2.53166i
\(717\) −13.4970 + 23.3775i −0.504055 + 0.873050i
\(718\) 44.4352 76.9640i 1.65831 2.87227i
\(719\) 20.9485 + 36.2839i 0.781249 + 1.35316i 0.931215 + 0.364471i \(0.118750\pi\)
−0.149966 + 0.988691i \(0.547916\pi\)
\(720\) 37.9046 1.41262
\(721\) 3.59469 53.4117i 0.133873 1.98916i
\(722\) 50.2184 1.86894
\(723\) −9.29838 16.1053i −0.345810 0.598961i
\(724\) −49.1180 + 85.0749i −1.82546 + 3.16179i
\(725\) −0.335728 + 0.581499i −0.0124686 + 0.0215963i
\(726\) 18.1657 + 31.4638i 0.674191 + 1.16773i
\(727\) 19.5123 0.723670 0.361835 0.932242i \(-0.382150\pi\)
0.361835 + 0.932242i \(0.382150\pi\)
\(728\) 0 0
\(729\) 27.5552 1.02056
\(730\) −24.6871 42.7593i −0.913711 1.58259i
\(731\) 2.34871 4.06808i 0.0868701 0.150463i
\(732\) −45.6679 + 79.0991i −1.68793 + 2.92359i
\(733\) 8.87698 + 15.3754i 0.327879 + 0.567902i 0.982091 0.188409i \(-0.0603330\pi\)
−0.654212 + 0.756311i \(0.727000\pi\)
\(734\) 8.61213 0.317880
\(735\) 7.82185 + 19.0722i 0.288513 + 0.703488i
\(736\) −13.7939 −0.508450
\(737\) 2.34728 + 4.06562i 0.0864633 + 0.149759i
\(738\) 11.8419 20.5108i 0.435907 0.755013i
\(739\) 22.1571 38.3772i 0.815061 1.41173i −0.0942227 0.995551i \(-0.530037\pi\)
0.909284 0.416176i \(-0.136630\pi\)
\(740\) 64.6497 + 111.977i 2.37657 + 4.11634i
\(741\) 0 0
\(742\) −29.2709 19.6324i −1.07457 0.720729i
\(743\) 7.16727 0.262941 0.131471 0.991320i \(-0.458030\pi\)
0.131471 + 0.991320i \(0.458030\pi\)
\(744\) 6.46285 + 11.1940i 0.236940 + 0.410392i
\(745\) −16.8331 + 29.1558i −0.616718 + 1.06819i
\(746\) −2.01355 + 3.48757i −0.0737212 + 0.127689i
\(747\) 3.95657 + 6.85297i 0.144763 + 0.250737i
\(748\) −30.0983 −1.10050
\(749\) 1.60875 23.9036i 0.0587826 0.873420i
\(750\) 41.8630 1.52862
\(751\) 16.9532 + 29.3639i 0.618632 + 1.07150i 0.989736 + 0.142911i \(0.0456462\pi\)
−0.371103 + 0.928592i \(0.621020\pi\)
\(752\) 17.0618 29.5518i 0.622178 1.07764i
\(753\) −17.5772 + 30.4445i −0.640547 + 1.10946i
\(754\) 0 0
\(755\) −29.9110 −1.08857
\(756\) −72.6628 + 35.6753i −2.64272 + 1.29750i
\(757\) −0.906670 −0.0329535 −0.0164767 0.999864i \(-0.505245\pi\)
−0.0164767 + 0.999864i \(0.505245\pi\)
\(758\) −14.6147 25.3134i −0.530830 0.919424i
\(759\) 0.461186 0.798798i 0.0167400 0.0289945i
\(760\) 7.73059 13.3898i 0.280418 0.485698i
\(761\) 10.1247 + 17.5365i 0.367020 + 0.635697i 0.989098 0.147258i \(-0.0470449\pi\)
−0.622079 + 0.782955i \(0.713712\pi\)
\(762\) 32.2502 1.16830
\(763\) 35.8650 17.6087i 1.29840 0.637477i
\(764\) 30.0729 1.08800
\(765\) 6.86942 + 11.8982i 0.248364 + 0.430180i
\(766\) 29.1750 50.5326i 1.05414 1.82582i
\(767\) 0 0
\(768\) 26.0259 + 45.0782i 0.939129 + 1.62662i
\(769\) 36.9094 1.33099 0.665494 0.746403i \(-0.268221\pi\)
0.665494 + 0.746403i \(0.268221\pi\)
\(770\) 1.10996 16.4923i 0.0400001 0.594341i
\(771\) −14.2987 −0.514954
\(772\) −23.7183 41.0814i −0.853642 1.47855i
\(773\) −4.94018 + 8.55665i −0.177686 + 0.307761i −0.941088 0.338163i \(-0.890194\pi\)
0.763402 + 0.645924i \(0.223528\pi\)
\(774\) −1.43611 + 2.48742i −0.0516199 + 0.0894083i
\(775\) −0.111176 0.192562i −0.00399355 0.00691704i
\(776\) −26.9701 −0.968169
\(777\) −32.2272 21.6152i −1.15614 0.775441i
\(778\) −94.7893 −3.39836
\(779\) −2.77043 4.79852i −0.0992609 0.171925i
\(780\) 0 0