Properties

Label 1183.2.e.f.170.5
Level $1183$
Weight $2$
Character 1183.170
Analytic conductor $9.446$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 170.5
Root \(-0.862625 + 1.49411i\) of defining polynomial
Character \(\chi\) \(=\) 1183.170
Dual form 1183.2.e.f.508.5

$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

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

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 0.249986 0.968250i \(-0.419574\pi\)
0.713536 0.700619i \(-0.247093\pi\)
\(3\) 0.673208 + 1.16603i 0.388677 + 0.673208i 0.992272 0.124083i \(-0.0395989\pi\)
−0.603595 + 0.797291i \(0.706266\pi\)
\(4\) −2.71349 4.69991i −1.35675 2.34996i
\(5\) 1.09358 1.89414i 0.489065 0.847085i −0.510856 0.859666i \(-0.670672\pi\)
0.999921 + 0.0125813i \(0.00400485\pi\)
\(6\) 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 0.776138 0.630564i \(-0.217176\pi\)
−0.934153 + 0.356873i \(0.883843\pi\)
\(12\) 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 0.985063 + 0.172197i \(0.0550865\pi\)
−0.343404 + 0.939188i \(0.611580\pi\)
\(18\) −1.61766 2.80187i −0.381286 0.660407i
\(19\) 0.378453 0.655500i 0.0868231 0.150382i −0.819344 0.573303i \(-0.805662\pi\)
0.906167 + 0.422921i \(0.138995\pi\)
\(20\) −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 −0.898083 0.439826i \(-0.855040\pi\)
0.829942 + 0.557850i \(0.188373\pi\)
\(24\) −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 0.908482 0.417923i \(-0.137242\pi\)
−0.816173 + 0.577807i \(0.803909\pi\)
\(32\) 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 −0.0621309 + 0.998068i \(0.519790\pi\)
−0.833287 + 0.552841i \(0.813544\pi\)
\(38\) −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 −0.768108 0.640321i \(-0.778801\pi\)
0.938588 + 0.345040i \(0.112135\pi\)
\(48\) −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 0.647904 0.761722i \(-0.275646\pi\)
−0.983623 + 0.180240i \(0.942313\pi\)
\(54\) 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 0.829893 0.557923i \(-0.188402\pi\)
−0.898122 + 0.439747i \(0.855068\pi\)
\(60\) −7.99079 13.8404i −1.03161 1.78679i
\(61\) 6.24989 10.8251i 0.800217 1.38602i −0.119256 0.992864i \(-0.538051\pi\)
0.919473 0.393153i \(-0.128616\pi\)
\(62\) 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 0.969779 0.243986i \(-0.0784550\pi\)
−0.696187 + 0.717860i \(0.745122\pi\)
\(68\) 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 0.515093 0.857134i \(-0.327757\pi\)
−0.999847 + 0.0175164i \(0.994424\pi\)
\(74\) 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 −0.919922 0.392100i \(-0.871749\pi\)
0.799530 + 0.600626i \(0.205082\pi\)
\(80\) 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 −0.977415 0.211329i \(-0.932221\pi\)
0.671724 + 0.740802i \(0.265554\pi\)
\(90\) −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 0.997502 + 0.0706359i \(0.0225028\pi\)
−0.437579 + 0.899180i \(0.644164\pi\)
\(102\) 9.70764 + 16.8141i 0.961200 + 1.66485i
\(103\) −10.1167 + 17.5226i −0.996828 + 1.72656i −0.429487 + 0.903073i \(0.641306\pi\)
−0.567341 + 0.823483i \(0.692028\pi\)
\(104\) 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 −0.997512 0.0705034i \(-0.977539\pi\)
0.559813 + 0.828619i \(0.310873\pi\)
\(108\) −15.2978 26.4965i −1.47203 2.54963i
\(109\) 7.55070 + 13.0782i 0.723226 + 1.25266i 0.959700 + 0.281026i \(0.0906747\pi\)
−0.236474 + 0.971638i \(0.575992\pi\)
\(110\) −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 −0.539599 0.841922i \(-0.681424\pi\)
0.998925 + 0.0463451i \(0.0147574\pi\)
\(132\) −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 0.990025 0.140891i \(-0.0449966\pi\)
−0.617028 + 0.786942i \(0.711663\pi\)
\(138\) −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 −0.356941 0.934127i \(-0.616180\pi\)
0.987448 0.157944i \(-0.0504864\pi\)
\(150\) 0.396863 + 0.687386i 0.0324037 + 0.0561248i
\(151\) −6.83786 11.8435i −0.556457 0.963812i −0.997789 0.0664680i \(-0.978827\pi\)
0.441331 0.897344i \(-0.354506\pi\)
\(152\) −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 0.790487 0.612478i \(-0.209827\pi\)
−0.925666 + 0.378343i \(0.876494\pi\)
\(158\) 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 0.458013 + 0.888946i \(0.348561\pi\)
−0.998856 + 0.0478219i \(0.984772\pi\)
\(164\) 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 −0.933723 0.357997i \(-0.883460\pi\)
0.776896 + 0.629629i \(0.216793\pi\)
\(174\) −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 −0.998976 0.0452324i \(-0.985597\pi\)
0.460316 0.887755i \(-0.347736\pi\)
\(180\) −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 −0.948683 0.316229i \(-0.897583\pi\)
0.748204 + 0.663469i \(0.230917\pi\)
\(192\) 19.0653 + 33.0220i 1.37592 + 2.38316i
\(193\) −4.37044 7.56983i −0.314591 0.544888i 0.664759 0.747058i \(-0.268534\pi\)
−0.979351 + 0.202170i \(0.935201\pi\)
\(194\) 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 −0.971029 0.238963i \(-0.923192\pi\)
0.278566 0.960417i \(-0.410141\pi\)
\(200\) −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 0.978530 + 0.206104i \(0.0660786\pi\)
−0.310774 + 0.950484i \(0.600588\pi\)
\(228\) −2.76535 4.78973i −0.183140 0.317208i
\(229\) 12.6249 21.8669i 0.834275 1.44501i −0.0603445 0.998178i \(-0.519220\pi\)
0.894619 0.446829i \(-0.147447\pi\)
\(230\) 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 −0.852739 0.522337i \(-0.825060\pi\)
0.878727 + 0.477326i \(0.158394\pi\)
\(234\) 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 0.998042 0.0625446i \(-0.0199216\pi\)
−0.553186 + 0.833058i \(0.686588\pi\)
\(242\) −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 −0.982752 0.184930i \(-0.940794\pi\)
0.651530 + 0.758623i \(0.274128\pi\)
\(258\) 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 0.661008 0.750379i \(-0.270129\pi\)
−0.980351 + 0.197260i \(0.936796\pi\)
\(264\) −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 0.623849 0.781545i \(-0.285568\pi\)
−0.988762 + 0.149496i \(0.952235\pi\)
\(270\) −16.8018 29.1016i −1.02253 1.77107i
\(271\) −1.37845 + 2.38755i −0.0837351 + 0.145033i −0.904852 0.425727i \(-0.860018\pi\)
0.821116 + 0.570761i \(0.193352\pi\)
\(272\) −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 0.961463 + 0.274933i \(0.0886558\pi\)
−0.242632 + 0.970118i \(0.578011\pi\)
\(278\) −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 0.943432 0.331565i \(-0.107577\pi\)
−0.758860 + 0.651254i \(0.774243\pi\)
\(284\) −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 −0.993039 0.117785i \(-0.962420\pi\)
0.394514 0.918890i \(-0.370913\pi\)
\(312\) 0 0
\(313\) −0.990260 + 1.71518i −0.0559728 + 0.0969477i −0.892654 0.450742i \(-0.851159\pi\)
0.836681 + 0.547690i \(0.184493\pi\)
\(314\) −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 0.493189 + 0.869922i \(0.335831\pi\)
−0.999969 + 0.00784727i \(0.997502\pi\)
\(318\) −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 −0.994119 0.108296i \(-0.965460\pi\)
0.590847 + 0.806784i \(0.298794\pi\)
\(332\) −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 −0.998769 0.0496025i \(-0.984205\pi\)
0.456428 0.889761i \(-0.349129\pi\)
\(348\) −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 0.737069 0.675817i \(-0.236209\pi\)
−0.953810 + 0.300412i \(0.902876\pi\)
\(354\) −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 0.0108595 + 0.999941i \(0.496543\pi\)
−0.871404 + 0.490566i \(0.836790\pi\)
\(360\) 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 0.904314 0.426868i \(-0.140383\pi\)
−0.821835 + 0.569725i \(0.807050\pi\)
\(368\) −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 −0.846263 0.532765i \(-0.821153\pi\)
0.884520 + 0.466503i \(0.154486\pi\)
\(374\) −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 0.451454 + 0.892294i \(0.350906\pi\)
−0.998477 + 0.0551766i \(0.982428\pi\)
\(384\) 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 −0.849388 0.527769i \(-0.823029\pi\)
−0.0323675 0.999476i \(-0.510305\pi\)
\(390\) 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 −0.804742 0.593624i \(-0.797697\pi\)
0.916465 + 0.400115i \(0.131030\pi\)
\(398\) −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 −0.985064 0.172186i \(-0.944917\pi\)
0.641650 + 0.766998i \(0.278250\pi\)
\(402\) 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 0.819624 0.572902i \(-0.194182\pi\)
−0.905960 + 0.423364i \(0.860849\pi\)
\(410\) 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 0.696108 0.717937i \(-0.254913\pi\)
−0.969806 + 0.243879i \(0.921580\pi\)
\(432\) −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 −0.410239 0.911978i \(-0.634555\pi\)
0.994916 0.100711i \(-0.0321118\pi\)
\(440\) 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 −0.242288 + 0.970204i \(0.577898\pi\)
−0.719077 + 0.694930i \(0.755435\pi\)
\(444\) 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 −0.966724 0.255821i \(-0.917654\pi\)
0.704910 + 0.709297i \(0.250988\pi\)
\(458\) −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 0.484797 + 0.874626i \(0.338893\pi\)
−0.999847 + 0.0174663i \(0.994440\pi\)
\(468\) 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 −0.947299 0.320350i \(-0.896200\pi\)
0.196219 0.980560i \(-0.437134\pi\)
\(480\) 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 −0.987150 0.159796i \(-0.948916\pi\)
0.355188 0.934795i \(-0.384417\pi\)
\(488\) −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 0.449727 + 0.893166i \(0.351521\pi\)
−0.998368 + 0.0571077i \(0.981812\pi\)
\(500\) −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 0.0353545 0.999375i \(-0.488744\pi\)
0.847807 0.530305i \(-0.177923\pi\)
\(510\) 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 0.996880 0.0789382i \(-0.0251530\pi\)
−0.566802 + 0.823854i \(0.691820\pi\)
\(522\) 5.02135 + 8.69724i 0.219779 + 0.380668i
\(523\) −11.4162 + 19.7734i −0.499195 + 0.864632i −1.00000 0.000928862i \(-0.999704\pi\)
0.500804 + 0.865561i \(0.333038\pi\)
\(524\) −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 −0.950886 0.309542i \(-0.899824\pi\)
0.743514 + 0.668720i \(0.233158\pi\)
\(542\) 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 0.979667 0.200633i \(-0.0642997\pi\)
−0.663586 + 0.748100i \(0.730966\pi\)
\(558\) 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 0.988602 0.150555i \(-0.0481062\pi\)
−0.624686 + 0.780876i \(0.714773\pi\)
\(564\) −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 0.441665 + 0.897180i \(0.354388\pi\)
−0.997813 + 0.0660972i \(0.978945\pi\)
\(570\) −3.03724 5.26065i −0.127216 0.220345i
\(571\) 0.992844 + 1.71966i 0.0415492 + 0.0719654i 0.886052 0.463586i \(-0.153437\pi\)
−0.844503 + 0.535551i \(0.820104\pi\)
\(572\) 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 0.962878 0.269937i \(-0.0870030\pi\)
−0.715212 + 0.698908i \(0.753670\pi\)
\(578\) 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 −0.234793 0.972045i \(-0.575441\pi\)
0.959213 0.282686i \(-0.0912253\pi\)
\(594\) −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 0.999921 + 0.0126040i \(0.00401207\pi\)
−0.489045 + 0.872259i \(0.662655\pi\)
\(600\) 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 0.224672 + 0.974434i \(0.427869\pi\)
−0.956221 + 0.292646i \(0.905464\pi\)
\(608\) 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 0.989577 0.144006i \(-0.0459985\pi\)
−0.619501 + 0.784996i \(0.712665\pi\)
\(614\) 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 −0.999996 0.00299144i \(-0.999048\pi\)
0.497407 0.867517i \(-0.334286\pi\)
\(620\) −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 0.995919 0.0902567i \(-0.0287687\pi\)
−0.576124 + 0.817362i \(0.695435\pi\)
\(642\) −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 −0.930299 0.366802i \(-0.880453\pi\)
0.147490 0.989064i \(-0.452881\pi\)
\(648\) −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 −0.351195 0.936303i \(-0.614224\pi\)
0.986459 0.164008i \(-0.0524423\pi\)
\(654\) 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 0.969635 0.244557i \(-0.0786426\pi\)
−0.696610 + 0.717450i \(0.745309\pi\)
\(662\) 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 −0.759065 0.651015i \(-0.774344\pi\)
0.943328 + 0.331862i \(0.107677\pi\)
\(678\) 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 0.820581 + 0.571530i \(0.193650\pi\)
0.0846691 + 0.996409i \(0.473017\pi\)
\(684\) −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 0.484142 + 0.874990i \(0.339132\pi\)
−0.999834 + 0.0182158i \(0.994201\pi\)
\(692\) 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 0.467462 + 0.884013i \(0.345168\pi\)
−0.999309 + 0.0371721i \(0.988165\pi\)
\(710\) −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 −0.149966 0.988691i \(-0.547916\pi\)
0.931215 0.364471i \(-0.118750\pi\)
\(720\) 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 −0.654212 0.756311i \(-0.727000\pi\)
0.982091 + 0.188409i \(0.0603330\pi\)
\(734\) 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 0.909284 + 0.416176i \(0.136630\pi\)
−0.0942227 + 0.995551i \(0.530037\pi\)
\(740\) 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 −0.371103 0.928592i \(-0.621020\pi\)
0.989736 0.142911i \(-0.0456462\pi\)
\(752\) 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 −0.622079 0.782955i \(-0.713712\pi\)
0.989098 + 0.147258i \(0.0470449\pi\)
\(762\) 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 0.763402 0.645924i \(-0.223528\pi\)
−0.941088 + 0.338163i \(0.890194\pi\)
\(774\) −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