Properties

Label 390.2.j.b.73.5
Level $390$
Weight $2$
Character 390.73
Analytic conductor $3.114$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 32x^{14} + 396x^{12} + 2412x^{10} + 7716x^{8} + 12984x^{6} + 10756x^{4} + 3648x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 73.5
Root \(-3.14581i\) of defining polynomial
Character \(\chi\) \(=\) 390.73
Dual form 390.2.j.b.187.5

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-2.22443 + 0.227886i) q^{5} +(0.707107 + 0.707107i) q^{6} +4.05336i q^{7} +1.00000 q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-2.22443 + 0.227886i) q^{5} +(0.707107 + 0.707107i) q^{6} +4.05336i q^{7} +1.00000 q^{8} +1.00000i q^{9} +(-2.22443 + 0.227886i) q^{10} +(1.63560 - 1.63560i) q^{11} +(0.707107 + 0.707107i) q^{12} +(3.18675 + 1.68659i) q^{13} +4.05336i q^{14} +(-1.73405 - 1.41177i) q^{15} +1.00000 q^{16} +(0.932546 + 0.932546i) q^{17} +1.00000i q^{18} +(-4.66558 + 4.66558i) q^{19} +(-2.22443 + 0.227886i) q^{20} +(-2.86616 + 2.86616i) q^{21} +(1.63560 - 1.63560i) q^{22} +(3.93804 - 3.93804i) q^{23} +(0.707107 + 0.707107i) q^{24} +(4.89614 - 1.01383i) q^{25} +(3.18675 + 1.68659i) q^{26} +(-0.707107 + 0.707107i) q^{27} +4.05336i q^{28} -6.86725i q^{29} +(-1.73405 - 1.41177i) q^{30} +(-6.67096 - 6.67096i) q^{31} +1.00000 q^{32} +2.31309 q^{33} +(0.932546 + 0.932546i) q^{34} +(-0.923704 - 9.01640i) q^{35} +1.00000i q^{36} -8.04614i q^{37} +(-4.66558 + 4.66558i) q^{38} +(1.06077 + 3.44598i) q^{39} +(-2.22443 + 0.227886i) q^{40} +(6.69985 + 6.69985i) q^{41} +(-2.86616 + 2.86616i) q^{42} +(-2.58651 + 2.58651i) q^{43} +(1.63560 - 1.63560i) q^{44} +(-0.227886 - 2.22443i) q^{45} +(3.93804 - 3.93804i) q^{46} +0.559306i q^{47} +(0.707107 + 0.707107i) q^{48} -9.42974 q^{49} +(4.89614 - 1.01383i) q^{50} +1.31882i q^{51} +(3.18675 + 1.68659i) q^{52} +(-6.34712 - 6.34712i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-3.26554 + 4.01100i) q^{55} +4.05336i q^{56} -6.59812 q^{57} -6.86725i q^{58} +(-2.29565 - 2.29565i) q^{59} +(-1.73405 - 1.41177i) q^{60} +6.48216 q^{61} +(-6.67096 - 6.67096i) q^{62} -4.05336 q^{63} +1.00000 q^{64} +(-7.47305 - 3.02549i) q^{65} +2.31309 q^{66} +7.13460 q^{67} +(0.932546 + 0.932546i) q^{68} +5.56923 q^{69} +(-0.923704 - 9.01640i) q^{70} +(5.56896 + 5.56896i) q^{71} +1.00000i q^{72} +7.36347 q^{73} -8.04614i q^{74} +(4.17898 + 2.74520i) q^{75} +(-4.66558 + 4.66558i) q^{76} +(6.62968 + 6.62968i) q^{77} +(1.06077 + 3.44598i) q^{78} -1.91721i q^{79} +(-2.22443 + 0.227886i) q^{80} -1.00000 q^{81} +(6.69985 + 6.69985i) q^{82} -0.718668i q^{83} +(-2.86616 + 2.86616i) q^{84} +(-2.28689 - 1.86186i) q^{85} +(-2.58651 + 2.58651i) q^{86} +(4.85588 - 4.85588i) q^{87} +(1.63560 - 1.63560i) q^{88} +(-4.02209 - 4.02209i) q^{89} +(-0.227886 - 2.22443i) q^{90} +(-6.83638 + 12.9171i) q^{91} +(3.93804 - 3.93804i) q^{92} -9.43416i q^{93} +0.559306i q^{94} +(9.31501 - 11.4414i) q^{95} +(0.707107 + 0.707107i) q^{96} -6.60149 q^{97} -9.42974 q^{98} +(1.63560 + 1.63560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} + 4 q^{11} + 4 q^{13} + 4 q^{15} + 16 q^{16} + 4 q^{17} + 4 q^{19} - 8 q^{21} + 4 q^{22} + 16 q^{23} - 16 q^{25} + 4 q^{26} + 4 q^{30} + 12 q^{31} + 16 q^{32} + 4 q^{34} - 12 q^{35} + 4 q^{38} - 4 q^{39} + 4 q^{41} - 8 q^{42} - 16 q^{43} + 4 q^{44} + 16 q^{46} - 80 q^{49} - 16 q^{50} + 4 q^{52} - 44 q^{53} - 20 q^{55} - 16 q^{57} + 12 q^{59} + 4 q^{60} - 32 q^{61} + 12 q^{62} + 16 q^{64} - 44 q^{65} - 32 q^{67} + 4 q^{68} - 16 q^{69} - 12 q^{70} + 16 q^{71} + 4 q^{76} - 32 q^{77} - 4 q^{78} - 16 q^{81} + 4 q^{82} - 8 q^{84} - 64 q^{85} - 16 q^{86} + 28 q^{87} + 4 q^{88} + 4 q^{89} + 76 q^{91} + 16 q^{92} + 40 q^{95} - 8 q^{97} - 80 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.00000 0.500000
\(5\) −2.22443 + 0.227886i −0.994793 + 0.101914i
\(6\) 0.707107 + 0.707107i 0.288675 + 0.288675i
\(7\) 4.05336i 1.53203i 0.642825 + 0.766013i \(0.277762\pi\)
−0.642825 + 0.766013i \(0.722238\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000i 0.333333i
\(10\) −2.22443 + 0.227886i −0.703425 + 0.0720639i
\(11\) 1.63560 1.63560i 0.493152 0.493152i −0.416146 0.909298i \(-0.636619\pi\)
0.909298 + 0.416146i \(0.136619\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 3.18675 + 1.68659i 0.883846 + 0.467777i
\(14\) 4.05336i 1.08331i
\(15\) −1.73405 1.41177i −0.447729 0.364517i
\(16\) 1.00000 0.250000
\(17\) 0.932546 + 0.932546i 0.226176 + 0.226176i 0.811093 0.584917i \(-0.198873\pi\)
−0.584917 + 0.811093i \(0.698873\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −4.66558 + 4.66558i −1.07036 + 1.07036i −0.0730270 + 0.997330i \(0.523266\pi\)
−0.997330 + 0.0730270i \(0.976734\pi\)
\(20\) −2.22443 + 0.227886i −0.497397 + 0.0509568i
\(21\) −2.86616 + 2.86616i −0.625447 + 0.625447i
\(22\) 1.63560 1.63560i 0.348711 0.348711i
\(23\) 3.93804 3.93804i 0.821139 0.821139i −0.165133 0.986271i \(-0.552805\pi\)
0.986271 + 0.165133i \(0.0528053\pi\)
\(24\) 0.707107 + 0.707107i 0.144338 + 0.144338i
\(25\) 4.89614 1.01383i 0.979227 0.202766i
\(26\) 3.18675 + 1.68659i 0.624974 + 0.330768i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 4.05336i 0.766013i
\(29\) 6.86725i 1.27522i −0.770361 0.637608i \(-0.779924\pi\)
0.770361 0.637608i \(-0.220076\pi\)
\(30\) −1.73405 1.41177i −0.316592 0.257752i
\(31\) −6.67096 6.67096i −1.19814 1.19814i −0.974723 0.223417i \(-0.928279\pi\)
−0.223417 0.974723i \(-0.571721\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.31309 0.402657
\(34\) 0.932546 + 0.932546i 0.159930 + 0.159930i
\(35\) −0.923704 9.01640i −0.156135 1.52405i
\(36\) 1.00000i 0.166667i
\(37\) 8.04614i 1.32278i −0.750043 0.661389i \(-0.769967\pi\)
0.750043 0.661389i \(-0.230033\pi\)
\(38\) −4.66558 + 4.66558i −0.756857 + 0.756857i
\(39\) 1.06077 + 3.44598i 0.169860 + 0.551798i
\(40\) −2.22443 + 0.227886i −0.351713 + 0.0360319i
\(41\) 6.69985 + 6.69985i 1.04634 + 1.04634i 0.998873 + 0.0474680i \(0.0151152\pi\)
0.0474680 + 0.998873i \(0.484885\pi\)
\(42\) −2.86616 + 2.86616i −0.442258 + 0.442258i
\(43\) −2.58651 + 2.58651i −0.394439 + 0.394439i −0.876266 0.481828i \(-0.839973\pi\)
0.481828 + 0.876266i \(0.339973\pi\)
\(44\) 1.63560 1.63560i 0.246576 0.246576i
\(45\) −0.227886 2.22443i −0.0339712 0.331598i
\(46\) 3.93804 3.93804i 0.580633 0.580633i
\(47\) 0.559306i 0.0815831i 0.999168 + 0.0407916i \(0.0129880\pi\)
−0.999168 + 0.0407916i \(0.987012\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) −9.42974 −1.34711
\(50\) 4.89614 1.01383i 0.692418 0.143377i
\(51\) 1.31882i 0.184672i
\(52\) 3.18675 + 1.68659i 0.441923 + 0.233889i
\(53\) −6.34712 6.34712i −0.871845 0.871845i 0.120829 0.992673i \(-0.461445\pi\)
−0.992673 + 0.120829i \(0.961445\pi\)
\(54\) −0.707107 + 0.707107i −0.0962250 + 0.0962250i
\(55\) −3.26554 + 4.01100i −0.440326 + 0.540844i
\(56\) 4.05336i 0.541653i
\(57\) −6.59812 −0.873943
\(58\) 6.86725i 0.901713i
\(59\) −2.29565 2.29565i −0.298868 0.298868i 0.541703 0.840570i \(-0.317780\pi\)
−0.840570 + 0.541703i \(0.817780\pi\)
\(60\) −1.73405 1.41177i −0.223864 0.182258i
\(61\) 6.48216 0.829956 0.414978 0.909832i \(-0.363789\pi\)
0.414978 + 0.909832i \(0.363789\pi\)
\(62\) −6.67096 6.67096i −0.847213 0.847213i
\(63\) −4.05336 −0.510676
\(64\) 1.00000 0.125000
\(65\) −7.47305 3.02549i −0.926917 0.375266i
\(66\) 2.31309 0.284722
\(67\) 7.13460 0.871630 0.435815 0.900036i \(-0.356460\pi\)
0.435815 + 0.900036i \(0.356460\pi\)
\(68\) 0.932546 + 0.932546i 0.113088 + 0.113088i
\(69\) 5.56923 0.670457
\(70\) −0.923704 9.01640i −0.110404 1.07767i
\(71\) 5.56896 + 5.56896i 0.660914 + 0.660914i 0.955596 0.294681i \(-0.0952135\pi\)
−0.294681 + 0.955596i \(0.595213\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 7.36347 0.861829 0.430915 0.902393i \(-0.358191\pi\)
0.430915 + 0.902393i \(0.358191\pi\)
\(74\) 8.04614i 0.935345i
\(75\) 4.17898 + 2.74520i 0.482547 + 0.316989i
\(76\) −4.66558 + 4.66558i −0.535179 + 0.535179i
\(77\) 6.62968 + 6.62968i 0.755523 + 0.755523i
\(78\) 1.06077 + 3.44598i 0.120109 + 0.390180i
\(79\) 1.91721i 0.215703i −0.994167 0.107851i \(-0.965603\pi\)
0.994167 0.107851i \(-0.0343970\pi\)
\(80\) −2.22443 + 0.227886i −0.248698 + 0.0254784i
\(81\) −1.00000 −0.111111
\(82\) 6.69985 + 6.69985i 0.739875 + 0.739875i
\(83\) 0.718668i 0.0788840i −0.999222 0.0394420i \(-0.987442\pi\)
0.999222 0.0394420i \(-0.0125580\pi\)
\(84\) −2.86616 + 2.86616i −0.312724 + 0.312724i
\(85\) −2.28689 1.86186i −0.248048 0.201948i
\(86\) −2.58651 + 2.58651i −0.278910 + 0.278910i
\(87\) 4.85588 4.85588i 0.520605 0.520605i
\(88\) 1.63560 1.63560i 0.174356 0.174356i
\(89\) −4.02209 4.02209i −0.426340 0.426340i 0.461039 0.887380i \(-0.347477\pi\)
−0.887380 + 0.461039i \(0.847477\pi\)
\(90\) −0.227886 2.22443i −0.0240213 0.234475i
\(91\) −6.83638 + 12.9171i −0.716647 + 1.35408i
\(92\) 3.93804 3.93804i 0.410569 0.410569i
\(93\) 9.43416i 0.978277i
\(94\) 0.559306i 0.0576880i
\(95\) 9.31501 11.4414i 0.955700 1.17387i
\(96\) 0.707107 + 0.707107i 0.0721688 + 0.0721688i
\(97\) −6.60149 −0.670280 −0.335140 0.942168i \(-0.608784\pi\)
−0.335140 + 0.942168i \(0.608784\pi\)
\(98\) −9.42974 −0.952548
\(99\) 1.63560 + 1.63560i 0.164384 + 0.164384i
\(100\) 4.89614 1.01383i 0.489614 0.101383i
\(101\) 14.8793i 1.48055i −0.672306 0.740273i \(-0.734696\pi\)
0.672306 0.740273i \(-0.265304\pi\)
\(102\) 1.31882i 0.130583i
\(103\) 5.70999 5.70999i 0.562622 0.562622i −0.367429 0.930051i \(-0.619762\pi\)
0.930051 + 0.367429i \(0.119762\pi\)
\(104\) 3.18675 + 1.68659i 0.312487 + 0.165384i
\(105\) 5.72240 7.02872i 0.558449 0.685932i
\(106\) −6.34712 6.34712i −0.616487 0.616487i
\(107\) −4.91690 + 4.91690i −0.475335 + 0.475335i −0.903636 0.428301i \(-0.859112\pi\)
0.428301 + 0.903636i \(0.359112\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) −12.9297 + 12.9297i −1.23844 + 1.23844i −0.277803 + 0.960638i \(0.589606\pi\)
−0.960638 + 0.277803i \(0.910394\pi\)
\(110\) −3.26554 + 4.01100i −0.311357 + 0.382434i
\(111\) 5.68948 5.68948i 0.540022 0.540022i
\(112\) 4.05336i 0.383007i
\(113\) −5.41651 5.41651i −0.509542 0.509542i 0.404844 0.914386i \(-0.367326\pi\)
−0.914386 + 0.404844i \(0.867326\pi\)
\(114\) −6.59812 −0.617971
\(115\) −7.86246 + 9.65731i −0.733178 + 0.900548i
\(116\) 6.86725i 0.637608i
\(117\) −1.68659 + 3.18675i −0.155926 + 0.294615i
\(118\) −2.29565 2.29565i −0.211331 0.211331i
\(119\) −3.77995 + 3.77995i −0.346507 + 0.346507i
\(120\) −1.73405 1.41177i −0.158296 0.128876i
\(121\) 5.64961i 0.513601i
\(122\) 6.48216 0.586867
\(123\) 9.47502i 0.854334i
\(124\) −6.67096 6.67096i −0.599070 0.599070i
\(125\) −10.6601 + 3.37095i −0.953464 + 0.301507i
\(126\) −4.05336 −0.361102
\(127\) 10.3854 + 10.3854i 0.921556 + 0.921556i 0.997139 0.0755835i \(-0.0240819\pi\)
−0.0755835 + 0.997139i \(0.524082\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.65787 −0.322058
\(130\) −7.47305 3.02549i −0.655430 0.265353i
\(131\) 11.4500 1.00039 0.500195 0.865913i \(-0.333262\pi\)
0.500195 + 0.865913i \(0.333262\pi\)
\(132\) 2.31309 0.201329
\(133\) −18.9113 18.9113i −1.63982 1.63982i
\(134\) 7.13460 0.616335
\(135\) 1.41177 1.73405i 0.121506 0.149243i
\(136\) 0.932546 + 0.932546i 0.0799651 + 0.0799651i
\(137\) 20.7669i 1.77423i −0.461546 0.887116i \(-0.652705\pi\)
0.461546 0.887116i \(-0.347295\pi\)
\(138\) 5.56923 0.474085
\(139\) 13.0183i 1.10420i 0.833780 + 0.552098i \(0.186172\pi\)
−0.833780 + 0.552098i \(0.813828\pi\)
\(140\) −0.923704 9.01640i −0.0780673 0.762025i
\(141\) −0.395489 + 0.395489i −0.0333062 + 0.0333062i
\(142\) 5.56896 + 5.56896i 0.467337 + 0.467337i
\(143\) 7.97086 2.45366i 0.666556 0.205186i
\(144\) 1.00000i 0.0833333i
\(145\) 1.56495 + 15.2757i 0.129962 + 1.26858i
\(146\) 7.36347 0.609405
\(147\) −6.66783 6.66783i −0.549954 0.549954i
\(148\) 8.04614i 0.661389i
\(149\) −4.39862 + 4.39862i −0.360349 + 0.360349i −0.863941 0.503592i \(-0.832011\pi\)
0.503592 + 0.863941i \(0.332011\pi\)
\(150\) 4.17898 + 2.74520i 0.341212 + 0.224145i
\(151\) −3.77985 + 3.77985i −0.307600 + 0.307600i −0.843978 0.536378i \(-0.819792\pi\)
0.536378 + 0.843978i \(0.319792\pi\)
\(152\) −4.66558 + 4.66558i −0.378428 + 0.378428i
\(153\) −0.932546 + 0.932546i −0.0753919 + 0.0753919i
\(154\) 6.62968 + 6.62968i 0.534235 + 0.534235i
\(155\) 16.3593 + 13.3188i 1.31401 + 1.06979i
\(156\) 1.06077 + 3.44598i 0.0849298 + 0.275899i
\(157\) 13.1242 13.1242i 1.04743 1.04743i 0.0486112 0.998818i \(-0.484520\pi\)
0.998818 0.0486112i \(-0.0154795\pi\)
\(158\) 1.91721i 0.152525i
\(159\) 8.97619i 0.711858i
\(160\) −2.22443 + 0.227886i −0.175856 + 0.0180160i
\(161\) 15.9623 + 15.9623i 1.25801 + 1.25801i
\(162\) −1.00000 −0.0785674
\(163\) 9.96010 0.780135 0.390068 0.920786i \(-0.372452\pi\)
0.390068 + 0.920786i \(0.372452\pi\)
\(164\) 6.69985 + 6.69985i 0.523170 + 0.523170i
\(165\) −5.14530 + 0.527121i −0.400561 + 0.0410363i
\(166\) 0.718668i 0.0557794i
\(167\) 10.9823i 0.849833i 0.905233 + 0.424916i \(0.139696\pi\)
−0.905233 + 0.424916i \(0.860304\pi\)
\(168\) −2.86616 + 2.86616i −0.221129 + 0.221129i
\(169\) 7.31080 + 10.7495i 0.562369 + 0.826886i
\(170\) −2.28689 1.86186i −0.175397 0.142798i
\(171\) −4.66558 4.66558i −0.356786 0.356786i
\(172\) −2.58651 + 2.58651i −0.197219 + 0.197219i
\(173\) −5.50754 + 5.50754i −0.418730 + 0.418730i −0.884766 0.466036i \(-0.845682\pi\)
0.466036 + 0.884766i \(0.345682\pi\)
\(174\) 4.85588 4.85588i 0.368123 0.368123i
\(175\) 4.10942 + 19.8458i 0.310643 + 1.50020i
\(176\) 1.63560 1.63560i 0.123288 0.123288i
\(177\) 3.24653i 0.244024i
\(178\) −4.02209 4.02209i −0.301468 0.301468i
\(179\) −23.3767 −1.74726 −0.873628 0.486594i \(-0.838239\pi\)
−0.873628 + 0.486594i \(0.838239\pi\)
\(180\) −0.227886 2.22443i −0.0169856 0.165799i
\(181\) 15.3920i 1.14408i −0.820226 0.572039i \(-0.806153\pi\)
0.820226 0.572039i \(-0.193847\pi\)
\(182\) −6.83638 + 12.9171i −0.506746 + 0.957477i
\(183\) 4.58358 + 4.58358i 0.338828 + 0.338828i
\(184\) 3.93804 3.93804i 0.290316 0.290316i
\(185\) 1.83360 + 17.8980i 0.134809 + 1.31589i
\(186\) 9.43416i 0.691746i
\(187\) 3.05055 0.223078
\(188\) 0.559306i 0.0407916i
\(189\) −2.86616 2.86616i −0.208482 0.208482i
\(190\) 9.31501 11.4414i 0.675782 0.830050i
\(191\) −18.3221 −1.32574 −0.662870 0.748734i \(-0.730662\pi\)
−0.662870 + 0.748734i \(0.730662\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) 10.6298 0.765149 0.382575 0.923925i \(-0.375038\pi\)
0.382575 + 0.923925i \(0.375038\pi\)
\(194\) −6.60149 −0.473960
\(195\) −3.14490 7.42358i −0.225211 0.531614i
\(196\) −9.42974 −0.673553
\(197\) −0.621588 −0.0442863 −0.0221432 0.999755i \(-0.507049\pi\)
−0.0221432 + 0.999755i \(0.507049\pi\)
\(198\) 1.63560 + 1.63560i 0.116237 + 0.116237i
\(199\) −5.48672 −0.388943 −0.194472 0.980908i \(-0.562299\pi\)
−0.194472 + 0.980908i \(0.562299\pi\)
\(200\) 4.89614 1.01383i 0.346209 0.0716886i
\(201\) 5.04492 + 5.04492i 0.355841 + 0.355841i
\(202\) 14.8793i 1.04690i
\(203\) 27.8354 1.95366
\(204\) 1.31882i 0.0923358i
\(205\) −16.4301 13.3765i −1.14753 0.934256i
\(206\) 5.70999 5.70999i 0.397834 0.397834i
\(207\) 3.93804 + 3.93804i 0.273713 + 0.273713i
\(208\) 3.18675 + 1.68659i 0.220962 + 0.116944i
\(209\) 15.2621i 1.05570i
\(210\) 5.72240 7.02872i 0.394883 0.485027i
\(211\) 12.2985 0.846666 0.423333 0.905974i \(-0.360860\pi\)
0.423333 + 0.905974i \(0.360860\pi\)
\(212\) −6.34712 6.34712i −0.435922 0.435922i
\(213\) 7.87570i 0.539634i
\(214\) −4.91690 + 4.91690i −0.336112 + 0.336112i
\(215\) 5.16406 6.34292i 0.352186 0.432584i
\(216\) −0.707107 + 0.707107i −0.0481125 + 0.0481125i
\(217\) 27.0398 27.0398i 1.83558 1.83558i
\(218\) −12.9297 + 12.9297i −0.875710 + 0.875710i
\(219\) 5.20676 + 5.20676i 0.351840 + 0.351840i
\(220\) −3.26554 + 4.01100i −0.220163 + 0.270422i
\(221\) 1.39897 + 4.54462i 0.0941047 + 0.305704i
\(222\) 5.68948 5.68948i 0.381853 0.381853i
\(223\) 10.5250i 0.704806i 0.935848 + 0.352403i \(0.114635\pi\)
−0.935848 + 0.352403i \(0.885365\pi\)
\(224\) 4.05336i 0.270827i
\(225\) 1.01383 + 4.89614i 0.0675887 + 0.326409i
\(226\) −5.41651 5.41651i −0.360301 0.360301i
\(227\) −17.9899 −1.19403 −0.597015 0.802230i \(-0.703647\pi\)
−0.597015 + 0.802230i \(0.703647\pi\)
\(228\) −6.59812 −0.436971
\(229\) 1.48156 + 1.48156i 0.0979041 + 0.0979041i 0.754362 0.656458i \(-0.227946\pi\)
−0.656458 + 0.754362i \(0.727946\pi\)
\(230\) −7.86246 + 9.65731i −0.518435 + 0.636784i
\(231\) 9.37579i 0.616882i
\(232\) 6.86725i 0.450857i
\(233\) 2.70461 2.70461i 0.177185 0.177185i −0.612943 0.790127i \(-0.710014\pi\)
0.790127 + 0.612943i \(0.210014\pi\)
\(234\) −1.68659 + 3.18675i −0.110256 + 0.208325i
\(235\) −0.127458 1.24413i −0.00831444 0.0811584i
\(236\) −2.29565 2.29565i −0.149434 0.149434i
\(237\) 1.35567 1.35567i 0.0880602 0.0880602i
\(238\) −3.77995 + 3.77995i −0.245017 + 0.245017i
\(239\) −3.98109 + 3.98109i −0.257515 + 0.257515i −0.824043 0.566528i \(-0.808286\pi\)
0.566528 + 0.824043i \(0.308286\pi\)
\(240\) −1.73405 1.41177i −0.111932 0.0911291i
\(241\) −15.4622 + 15.4622i −0.996011 + 0.996011i −0.999992 0.00398120i \(-0.998733\pi\)
0.00398120 + 0.999992i \(0.498733\pi\)
\(242\) 5.64961i 0.363171i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 6.48216 0.414978
\(245\) 20.9758 2.14891i 1.34009 0.137289i
\(246\) 9.47502i 0.604105i
\(247\) −22.7370 + 6.99911i −1.44672 + 0.445343i
\(248\) −6.67096 6.67096i −0.423606 0.423606i
\(249\) 0.508175 0.508175i 0.0322043 0.0322043i
\(250\) −10.6601 + 3.37095i −0.674201 + 0.213198i
\(251\) 17.9961i 1.13590i 0.823062 + 0.567951i \(0.192264\pi\)
−0.823062 + 0.567951i \(0.807736\pi\)
\(252\) −4.05336 −0.255338
\(253\) 12.8821i 0.809893i
\(254\) 10.3854 + 10.3854i 0.651638 + 0.651638i
\(255\) −0.300540 2.93361i −0.0188206 0.183710i
\(256\) 1.00000 0.0625000
\(257\) 1.36406 + 1.36406i 0.0850880 + 0.0850880i 0.748370 0.663282i \(-0.230837\pi\)
−0.663282 + 0.748370i \(0.730837\pi\)
\(258\) −3.65787 −0.227729
\(259\) 32.6139 2.02653
\(260\) −7.47305 3.02549i −0.463459 0.187633i
\(261\) 6.86725 0.425072
\(262\) 11.4500 0.707382
\(263\) −2.33074 2.33074i −0.143719 0.143719i 0.631586 0.775306i \(-0.282404\pi\)
−0.775306 + 0.631586i \(0.782404\pi\)
\(264\) 2.31309 0.142361
\(265\) 15.5651 + 12.6723i 0.956158 + 0.778452i
\(266\) −18.9113 18.9113i −1.15952 1.15952i
\(267\) 5.68809i 0.348105i
\(268\) 7.13460 0.435815
\(269\) 12.4274i 0.757711i −0.925456 0.378855i \(-0.876318\pi\)
0.925456 0.378855i \(-0.123682\pi\)
\(270\) 1.41177 1.73405i 0.0859174 0.105531i
\(271\) 3.48130 3.48130i 0.211474 0.211474i −0.593419 0.804893i \(-0.702222\pi\)
0.804893 + 0.593419i \(0.202222\pi\)
\(272\) 0.932546 + 0.932546i 0.0565439 + 0.0565439i
\(273\) −13.9678 + 4.29970i −0.845369 + 0.260229i
\(274\) 20.7669i 1.25457i
\(275\) 6.34990 9.66635i 0.382914 0.582903i
\(276\) 5.56923 0.335228
\(277\) −12.9182 12.9182i −0.776178 0.776178i 0.203001 0.979179i \(-0.434931\pi\)
−0.979179 + 0.203001i \(0.934931\pi\)
\(278\) 13.0183i 0.780784i
\(279\) 6.67096 6.67096i 0.399380 0.399380i
\(280\) −0.923704 9.01640i −0.0552019 0.538833i
\(281\) −17.4567 + 17.4567i −1.04138 + 1.04138i −0.0422717 + 0.999106i \(0.513460\pi\)
−0.999106 + 0.0422717i \(0.986540\pi\)
\(282\) −0.395489 + 0.395489i −0.0235510 + 0.0235510i
\(283\) −7.63296 + 7.63296i −0.453733 + 0.453733i −0.896591 0.442859i \(-0.853964\pi\)
0.442859 + 0.896591i \(0.353964\pi\)
\(284\) 5.56896 + 5.56896i 0.330457 + 0.330457i
\(285\) 14.6770 1.50362i 0.869392 0.0890667i
\(286\) 7.97086 2.45366i 0.471327 0.145088i
\(287\) −27.1569 + 27.1569i −1.60302 + 1.60302i
\(288\) 1.00000i 0.0589256i
\(289\) 15.2607i 0.897689i
\(290\) 1.56495 + 15.2757i 0.0918970 + 0.897018i
\(291\) −4.66796 4.66796i −0.273641 0.273641i
\(292\) 7.36347 0.430915
\(293\) 0.359058 0.0209764 0.0104882 0.999945i \(-0.496661\pi\)
0.0104882 + 0.999945i \(0.496661\pi\)
\(294\) −6.66783 6.66783i −0.388876 0.388876i
\(295\) 5.62964 + 4.58335i 0.327770 + 0.266853i
\(296\) 8.04614i 0.467672i
\(297\) 2.31309i 0.134219i
\(298\) −4.39862 + 4.39862i −0.254805 + 0.254805i
\(299\) 19.1915 5.90769i 1.10987 0.341651i
\(300\) 4.17898 + 2.74520i 0.241273 + 0.158494i
\(301\) −10.4840 10.4840i −0.604290 0.604290i
\(302\) −3.77985 + 3.77985i −0.217506 + 0.217506i
\(303\) 10.5213 10.5213i 0.604430 0.604430i
\(304\) −4.66558 + 4.66558i −0.267589 + 0.267589i
\(305\) −14.4191 + 1.47719i −0.825634 + 0.0845838i
\(306\) −0.932546 + 0.932546i −0.0533101 + 0.0533101i
\(307\) 4.45946i 0.254515i 0.991870 + 0.127257i \(0.0406174\pi\)
−0.991870 + 0.127257i \(0.959383\pi\)
\(308\) 6.62968 + 6.62968i 0.377761 + 0.377761i
\(309\) 8.07515 0.459379
\(310\) 16.3593 + 13.3188i 0.929144 + 0.756459i
\(311\) 17.3852i 0.985824i 0.870079 + 0.492912i \(0.164068\pi\)
−0.870079 + 0.492912i \(0.835932\pi\)
\(312\) 1.06077 + 3.44598i 0.0600544 + 0.195090i
\(313\) 4.06946 + 4.06946i 0.230019 + 0.230019i 0.812701 0.582681i \(-0.197996\pi\)
−0.582681 + 0.812701i \(0.697996\pi\)
\(314\) 13.1242 13.1242i 0.740644 0.740644i
\(315\) 9.01640 0.923704i 0.508017 0.0520448i
\(316\) 1.91721i 0.107851i
\(317\) 5.85556 0.328881 0.164440 0.986387i \(-0.447418\pi\)
0.164440 + 0.986387i \(0.447418\pi\)
\(318\) 8.97619i 0.503360i
\(319\) −11.2321 11.2321i −0.628876 0.628876i
\(320\) −2.22443 + 0.227886i −0.124349 + 0.0127392i
\(321\) −6.95355 −0.388109
\(322\) 15.9623 + 15.9623i 0.889545 + 0.889545i
\(323\) −8.70173 −0.484177
\(324\) −1.00000 −0.0555556
\(325\) 17.3127 + 5.02697i 0.960336 + 0.278846i
\(326\) 9.96010 0.551639
\(327\) −18.2854 −1.01118
\(328\) 6.69985 + 6.69985i 0.369937 + 0.369937i
\(329\) −2.26707 −0.124988
\(330\) −5.14530 + 0.527121i −0.283239 + 0.0290170i
\(331\) −22.6533 22.6533i −1.24514 1.24514i −0.957842 0.287294i \(-0.907244\pi\)
−0.287294 0.957842i \(-0.592756\pi\)
\(332\) 0.718668i 0.0394420i
\(333\) 8.04614 0.440926
\(334\) 10.9823i 0.600922i
\(335\) −15.8704 + 1.62587i −0.867091 + 0.0888310i
\(336\) −2.86616 + 2.86616i −0.156362 + 0.156362i
\(337\) 7.97905 + 7.97905i 0.434647 + 0.434647i 0.890206 0.455559i \(-0.150561\pi\)
−0.455559 + 0.890206i \(0.650561\pi\)
\(338\) 7.31080 + 10.7495i 0.397655 + 0.584697i
\(339\) 7.66010i 0.416039i
\(340\) −2.28689 1.86186i −0.124024 0.100974i
\(341\) −21.8221 −1.18173
\(342\) −4.66558 4.66558i −0.252286 0.252286i
\(343\) 9.84862i 0.531775i
\(344\) −2.58651 + 2.58651i −0.139455 + 0.139455i
\(345\) −12.3883 + 1.26915i −0.666966 + 0.0683287i
\(346\) −5.50754 + 5.50754i −0.296087 + 0.296087i
\(347\) 13.0579 13.0579i 0.700985 0.700985i −0.263637 0.964622i \(-0.584922\pi\)
0.964622 + 0.263637i \(0.0849221\pi\)
\(348\) 4.85588 4.85588i 0.260302 0.260302i
\(349\) −21.5924 21.5924i −1.15581 1.15581i −0.985367 0.170447i \(-0.945479\pi\)
−0.170447 0.985367i \(-0.554521\pi\)
\(350\) 4.10942 + 19.8458i 0.219658 + 1.06080i
\(351\) −3.44598 + 1.06077i −0.183933 + 0.0566199i
\(352\) 1.63560 1.63560i 0.0871779 0.0871779i
\(353\) 0.516800i 0.0275065i −0.999905 0.0137533i \(-0.995622\pi\)
0.999905 0.0137533i \(-0.00437794\pi\)
\(354\) 3.24653i 0.172551i
\(355\) −13.6568 11.1187i −0.724829 0.590117i
\(356\) −4.02209 4.02209i −0.213170 0.213170i
\(357\) −5.34565 −0.282922
\(358\) −23.3767 −1.23550
\(359\) 0.362077 + 0.362077i 0.0191097 + 0.0191097i 0.716597 0.697487i \(-0.245699\pi\)
−0.697487 + 0.716597i \(0.745699\pi\)
\(360\) −0.227886 2.22443i −0.0120106 0.117238i
\(361\) 24.5352i 1.29133i
\(362\) 15.3920i 0.808985i
\(363\) −3.99488 + 3.99488i −0.209677 + 0.209677i
\(364\) −6.83638 + 12.9171i −0.358324 + 0.677038i
\(365\) −16.3795 + 1.67803i −0.857342 + 0.0878322i
\(366\) 4.58358 + 4.58358i 0.239588 + 0.239588i
\(367\) 5.81538 5.81538i 0.303560 0.303560i −0.538845 0.842405i \(-0.681139\pi\)
0.842405 + 0.538845i \(0.181139\pi\)
\(368\) 3.93804 3.93804i 0.205285 0.205285i
\(369\) −6.69985 + 6.69985i −0.348780 + 0.348780i
\(370\) 1.83360 + 17.8980i 0.0953244 + 0.930475i
\(371\) 25.7272 25.7272i 1.33569 1.33569i
\(372\) 9.43416i 0.489138i
\(373\) −10.4146 10.4146i −0.539248 0.539248i 0.384060 0.923308i \(-0.374525\pi\)
−0.923308 + 0.384060i \(0.874525\pi\)
\(374\) 3.05055 0.157740
\(375\) −9.92142 5.15417i −0.512340 0.266160i
\(376\) 0.559306i 0.0288440i
\(377\) 11.5823 21.8842i 0.596517 1.12709i
\(378\) −2.86616 2.86616i −0.147419 0.147419i
\(379\) 23.6838 23.6838i 1.21656 1.21656i 0.247726 0.968830i \(-0.420317\pi\)
0.968830 0.247726i \(-0.0796832\pi\)
\(380\) 9.31501 11.4414i 0.477850 0.586934i
\(381\) 14.6872i 0.752447i
\(382\) −18.3221 −0.937440
\(383\) 25.2587i 1.29066i 0.763904 + 0.645330i \(0.223280\pi\)
−0.763904 + 0.645330i \(0.776720\pi\)
\(384\) 0.707107 + 0.707107i 0.0360844 + 0.0360844i
\(385\) −16.2581 13.2364i −0.828587 0.674591i
\(386\) 10.6298 0.541042
\(387\) −2.58651 2.58651i −0.131480 0.131480i
\(388\) −6.60149 −0.335140
\(389\) 19.0841 0.967604 0.483802 0.875177i \(-0.339255\pi\)
0.483802 + 0.875177i \(0.339255\pi\)
\(390\) −3.14490 7.42358i −0.159248 0.375908i
\(391\) 7.34481 0.371443
\(392\) −9.42974 −0.476274
\(393\) 8.09636 + 8.09636i 0.408407 + 0.408407i
\(394\) −0.621588 −0.0313152
\(395\) 0.436904 + 4.26468i 0.0219830 + 0.214579i
\(396\) 1.63560 + 1.63560i 0.0821921 + 0.0821921i
\(397\) 13.5313i 0.679118i 0.940585 + 0.339559i \(0.110278\pi\)
−0.940585 + 0.339559i \(0.889722\pi\)
\(398\) −5.48672 −0.275024
\(399\) 26.7446i 1.33890i
\(400\) 4.89614 1.01383i 0.244807 0.0506915i
\(401\) −2.75570 + 2.75570i −0.137613 + 0.137613i −0.772558 0.634945i \(-0.781023\pi\)
0.634945 + 0.772558i \(0.281023\pi\)
\(402\) 5.04492 + 5.04492i 0.251618 + 0.251618i
\(403\) −10.0075 32.5099i −0.498509 1.61943i
\(404\) 14.8793i 0.740273i
\(405\) 2.22443 0.227886i 0.110533 0.0113237i
\(406\) 27.8354 1.38145
\(407\) −13.1603 13.1603i −0.652331 0.652331i
\(408\) 1.31882i 0.0652913i
\(409\) −3.99155 + 3.99155i −0.197369 + 0.197369i −0.798871 0.601502i \(-0.794569\pi\)
0.601502 + 0.798871i \(0.294569\pi\)
\(410\) −16.4301 13.3765i −0.811426 0.660619i
\(411\) 14.6844 14.6844i 0.724328 0.724328i
\(412\) 5.70999 5.70999i 0.281311 0.281311i
\(413\) 9.30508 9.30508i 0.457873 0.457873i
\(414\) 3.93804 + 3.93804i 0.193544 + 0.193544i
\(415\) 0.163774 + 1.59862i 0.00803936 + 0.0784733i
\(416\) 3.18675 + 1.68659i 0.156243 + 0.0826921i
\(417\) −9.20531 + 9.20531i −0.450786 + 0.450786i
\(418\) 15.2621i 0.746491i
\(419\) 36.0580i 1.76155i −0.473538 0.880773i \(-0.657023\pi\)
0.473538 0.880773i \(-0.342977\pi\)
\(420\) 5.72240 7.02872i 0.279225 0.342966i
\(421\) −25.5839 25.5839i −1.24688 1.24688i −0.957090 0.289791i \(-0.906414\pi\)
−0.289791 0.957090i \(-0.593586\pi\)
\(422\) 12.2985 0.598683
\(423\) −0.559306 −0.0271944
\(424\) −6.34712 6.34712i −0.308244 0.308244i
\(425\) 5.51131 + 3.62043i 0.267338 + 0.175617i
\(426\) 7.87570i 0.381579i
\(427\) 26.2745i 1.27151i
\(428\) −4.91690 + 4.91690i −0.237667 + 0.237667i
\(429\) 7.37125 + 3.90124i 0.355887 + 0.188354i
\(430\) 5.16406 6.34292i 0.249033 0.305883i
\(431\) −19.5932 19.5932i −0.943773 0.943773i 0.0547284 0.998501i \(-0.482571\pi\)
−0.998501 + 0.0547284i \(0.982571\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) −6.55103 + 6.55103i −0.314823 + 0.314823i −0.846775 0.531952i \(-0.821459\pi\)
0.531952 + 0.846775i \(0.321459\pi\)
\(434\) 27.0398 27.0398i 1.29795 1.29795i
\(435\) −9.69495 + 11.9081i −0.464837 + 0.570951i
\(436\) −12.9297 + 12.9297i −0.619221 + 0.619221i
\(437\) 36.7465i 1.75782i
\(438\) 5.20676 + 5.20676i 0.248789 + 0.248789i
\(439\) 1.85121 0.0883534 0.0441767 0.999024i \(-0.485934\pi\)
0.0441767 + 0.999024i \(0.485934\pi\)
\(440\) −3.26554 + 4.01100i −0.155679 + 0.191217i
\(441\) 9.42974i 0.449035i
\(442\) 1.39897 + 4.54462i 0.0665421 + 0.216166i
\(443\) −2.16126 2.16126i −0.102685 0.102685i 0.653898 0.756583i \(-0.273133\pi\)
−0.756583 + 0.653898i \(0.773133\pi\)
\(444\) 5.68948 5.68948i 0.270011 0.270011i
\(445\) 9.86341 + 8.03026i 0.467570 + 0.380671i
\(446\) 10.5250i 0.498373i
\(447\) −6.22059 −0.294224
\(448\) 4.05336i 0.191503i
\(449\) 8.96066 + 8.96066i 0.422880 + 0.422880i 0.886194 0.463314i \(-0.153340\pi\)
−0.463314 + 0.886194i \(0.653340\pi\)
\(450\) 1.01383 + 4.89614i 0.0477924 + 0.230806i
\(451\) 21.9166 1.03201
\(452\) −5.41651 5.41651i −0.254771 0.254771i
\(453\) −5.34551 −0.251154
\(454\) −17.9899 −0.844306
\(455\) 12.2634 30.2910i 0.574917 1.42006i
\(456\) −6.59812 −0.308985
\(457\) 19.1156 0.894189 0.447094 0.894487i \(-0.352459\pi\)
0.447094 + 0.894487i \(0.352459\pi\)
\(458\) 1.48156 + 1.48156i 0.0692286 + 0.0692286i
\(459\) −1.31882 −0.0615572
\(460\) −7.86246 + 9.65731i −0.366589 + 0.450274i
\(461\) −23.8829 23.8829i −1.11234 1.11234i −0.992834 0.119506i \(-0.961869\pi\)
−0.119506 0.992834i \(-0.538131\pi\)
\(462\) 9.37579i 0.436201i
\(463\) −0.610648 −0.0283792 −0.0141896 0.999899i \(-0.504517\pi\)
−0.0141896 + 0.999899i \(0.504517\pi\)
\(464\) 6.86725i 0.318804i
\(465\) 2.14991 + 20.9856i 0.0996998 + 0.973183i
\(466\) 2.70461 2.70461i 0.125289 0.125289i
\(467\) −24.0091 24.0091i −1.11101 1.11101i −0.993015 0.117992i \(-0.962354\pi\)
−0.117992 0.993015i \(-0.537646\pi\)
\(468\) −1.68659 + 3.18675i −0.0779629 + 0.147308i
\(469\) 28.9191i 1.33536i
\(470\) −0.127458 1.24413i −0.00587920 0.0573876i
\(471\) 18.5605 0.855222
\(472\) −2.29565 2.29565i −0.105666 0.105666i
\(473\) 8.46099i 0.389037i
\(474\) 1.35567 1.35567i 0.0622680 0.0622680i
\(475\) −18.1132 + 27.5734i −0.831091 + 1.26515i
\(476\) −3.77995 + 3.77995i −0.173253 + 0.173253i
\(477\) 6.34712 6.34712i 0.290615 0.290615i
\(478\) −3.98109 + 3.98109i −0.182091 + 0.182091i
\(479\) 0.400346 + 0.400346i 0.0182923 + 0.0182923i 0.716194 0.697901i \(-0.245883\pi\)
−0.697901 + 0.716194i \(0.745883\pi\)
\(480\) −1.73405 1.41177i −0.0791480 0.0644380i
\(481\) 13.5706 25.6411i 0.618765 1.16913i
\(482\) −15.4622 + 15.4622i −0.704286 + 0.704286i
\(483\) 22.5741i 1.02716i
\(484\) 5.64961i 0.256801i
\(485\) 14.6845 1.50439i 0.666790 0.0683107i
\(486\) −0.707107 0.707107i −0.0320750 0.0320750i
\(487\) 4.51084 0.204406 0.102203 0.994764i \(-0.467411\pi\)
0.102203 + 0.994764i \(0.467411\pi\)
\(488\) 6.48216 0.293434
\(489\) 7.04286 + 7.04286i 0.318489 + 0.318489i
\(490\) 20.9758 2.14891i 0.947588 0.0970777i
\(491\) 13.4933i 0.608944i 0.952521 + 0.304472i \(0.0984800\pi\)
−0.952521 + 0.304472i \(0.901520\pi\)
\(492\) 9.47502i 0.427167i
\(493\) 6.40402 6.40402i 0.288423 0.288423i
\(494\) −22.7370 + 6.99911i −1.02299 + 0.314905i
\(495\) −4.01100 3.26554i −0.180281 0.146775i
\(496\) −6.67096 6.67096i −0.299535 0.299535i
\(497\) −22.5730 + 22.5730i −1.01254 + 1.01254i
\(498\) 0.508175 0.508175i 0.0227719 0.0227719i
\(499\) 8.38741 8.38741i 0.375472 0.375472i −0.493993 0.869466i \(-0.664463\pi\)
0.869466 + 0.493993i \(0.164463\pi\)
\(500\) −10.6601 + 3.37095i −0.476732 + 0.150754i
\(501\) −7.76563 + 7.76563i −0.346943 + 0.346943i
\(502\) 17.9961i 0.803204i
\(503\) −9.71446 9.71446i −0.433146 0.433146i 0.456551 0.889697i \(-0.349085\pi\)
−0.889697 + 0.456551i \(0.849085\pi\)
\(504\) −4.05336 −0.180551
\(505\) 3.39078 + 33.0979i 0.150888 + 1.47284i
\(506\) 12.8821i 0.572681i
\(507\) −2.43155 + 12.7706i −0.107989 + 0.567161i
\(508\) 10.3854 + 10.3854i 0.460778 + 0.460778i
\(509\) −4.00130 + 4.00130i −0.177354 + 0.177354i −0.790202 0.612847i \(-0.790024\pi\)
0.612847 + 0.790202i \(0.290024\pi\)
\(510\) −0.300540 2.93361i −0.0133081 0.129903i
\(511\) 29.8468i 1.32035i
\(512\) 1.00000 0.0441942
\(513\) 6.59812i 0.291314i
\(514\) 1.36406 + 1.36406i 0.0601663 + 0.0601663i
\(515\) −11.4002 + 14.0027i −0.502354 + 0.617032i
\(516\) −3.65787 −0.161029
\(517\) 0.914801 + 0.914801i 0.0402329 + 0.0402329i
\(518\) 32.6139 1.43297
\(519\) −7.78883 −0.341892
\(520\) −7.47305 3.02549i −0.327715 0.132676i
\(521\) 11.8398 0.518712 0.259356 0.965782i \(-0.416490\pi\)
0.259356 + 0.965782i \(0.416490\pi\)
\(522\) 6.86725 0.300571
\(523\) 11.9564 + 11.9564i 0.522816 + 0.522816i 0.918421 0.395605i \(-0.129465\pi\)
−0.395605 + 0.918421i \(0.629465\pi\)
\(524\) 11.4500 0.500195
\(525\) −11.1273 + 16.9389i −0.485635 + 0.739275i
\(526\) −2.33074 2.33074i −0.101625 0.101625i
\(527\) 12.4419i 0.541980i
\(528\) 2.31309 0.100664
\(529\) 8.01635i 0.348537i
\(530\) 15.5651 + 12.6723i 0.676106 + 0.550449i
\(531\) 2.29565 2.29565i 0.0996226 0.0996226i
\(532\) −18.9113 18.9113i −0.819908 0.819908i
\(533\) 10.0508 + 32.6507i 0.435350 + 1.41426i
\(534\) 5.68809i 0.246148i
\(535\) 9.81679 12.0578i 0.424417 0.521303i
\(536\) 7.13460 0.308168
\(537\) −16.5298 16.5298i −0.713315 0.713315i
\(538\) 12.4274i 0.535782i
\(539\) −15.4233 + 15.4233i −0.664329 + 0.664329i
\(540\) 1.41177 1.73405i 0.0607528 0.0746215i
\(541\) 17.5003 17.5003i 0.752395 0.752395i −0.222530 0.974926i \(-0.571432\pi\)
0.974926 + 0.222530i \(0.0714316\pi\)
\(542\) 3.48130 3.48130i 0.149535 0.149535i
\(543\) 10.8838 10.8838i 0.467068 0.467068i
\(544\) 0.932546 + 0.932546i 0.0399826 + 0.0399826i
\(545\) 25.8147 31.7077i 1.10578 1.35821i
\(546\) −13.9678 + 4.29970i −0.597766 + 0.184010i
\(547\) −15.1432 + 15.1432i −0.647478 + 0.647478i −0.952383 0.304905i \(-0.901375\pi\)
0.304905 + 0.952383i \(0.401375\pi\)
\(548\) 20.7669i 0.887116i
\(549\) 6.48216i 0.276652i
\(550\) 6.34990 9.66635i 0.270761 0.412175i
\(551\) 32.0397 + 32.0397i 1.36494 + 1.36494i
\(552\) 5.56923 0.237042
\(553\) 7.77113 0.330462
\(554\) −12.9182 12.9182i −0.548841 0.548841i
\(555\) −11.3593 + 13.9524i −0.482174 + 0.592245i
\(556\) 13.0183i 0.552098i
\(557\) 21.9240i 0.928952i −0.885586 0.464476i \(-0.846243\pi\)
0.885586 0.464476i \(-0.153757\pi\)
\(558\) 6.67096 6.67096i 0.282404 0.282404i
\(559\) −12.6049 + 3.88017i −0.533132 + 0.164114i
\(560\) −0.923704 9.01640i −0.0390336 0.381012i
\(561\) 2.15706 + 2.15706i 0.0910712 + 0.0910712i
\(562\) −17.4567 + 17.4567i −0.736365 + 0.736365i
\(563\) −22.7318 + 22.7318i −0.958032 + 0.958032i −0.999154 0.0411219i \(-0.986907\pi\)
0.0411219 + 0.999154i \(0.486907\pi\)
\(564\) −0.395489 + 0.395489i −0.0166531 + 0.0166531i
\(565\) 13.2830 + 10.8143i 0.558818 + 0.454960i
\(566\) −7.63296 + 7.63296i −0.320837 + 0.320837i
\(567\) 4.05336i 0.170225i
\(568\) 5.56896 + 5.56896i 0.233668 + 0.233668i
\(569\) −14.5679 −0.610717 −0.305358 0.952238i \(-0.598776\pi\)
−0.305358 + 0.952238i \(0.598776\pi\)
\(570\) 14.6770 1.50362i 0.614753 0.0629797i
\(571\) 7.78560i 0.325817i −0.986641 0.162909i \(-0.947912\pi\)
0.986641 0.162909i \(-0.0520876\pi\)
\(572\) 7.97086 2.45366i 0.333278 0.102593i
\(573\) −12.9557 12.9557i −0.541231 0.541231i
\(574\) −27.1569 + 27.1569i −1.13351 + 1.13351i
\(575\) 15.2887 23.2737i 0.637582 0.970580i
\(576\) 1.00000i 0.0416667i
\(577\) −2.68505 −0.111780 −0.0558901 0.998437i \(-0.517800\pi\)
−0.0558901 + 0.998437i \(0.517800\pi\)
\(578\) 15.2607i 0.634762i
\(579\) 7.51640 + 7.51640i 0.312371 + 0.312371i
\(580\) 1.56495 + 15.2757i 0.0649810 + 0.634288i
\(581\) 2.91302 0.120852
\(582\) −4.66796 4.66796i −0.193493 0.193493i
\(583\) −20.7627 −0.859905
\(584\) 7.36347 0.304703
\(585\) 3.02549 7.47305i 0.125089 0.308972i
\(586\) 0.359058 0.0148325
\(587\) 20.4677 0.844792 0.422396 0.906411i \(-0.361189\pi\)
0.422396 + 0.906411i \(0.361189\pi\)
\(588\) −6.66783 6.66783i −0.274977 0.274977i
\(589\) 62.2478 2.56487
\(590\) 5.62964 + 4.58335i 0.231769 + 0.188693i
\(591\) −0.439529 0.439529i −0.0180798 0.0180798i
\(592\) 8.04614i 0.330694i
\(593\) −1.45240 −0.0596428 −0.0298214 0.999555i \(-0.509494\pi\)
−0.0298214 + 0.999555i \(0.509494\pi\)
\(594\) 2.31309i 0.0949072i
\(595\) 7.54681 9.26960i 0.309389 0.380017i
\(596\) −4.39862 + 4.39862i −0.180174 + 0.180174i
\(597\) −3.87970 3.87970i −0.158785 0.158785i
\(598\) 19.1915 5.90769i 0.784797 0.241583i
\(599\) 9.73974i 0.397955i −0.980004 0.198978i \(-0.936238\pi\)
0.980004 0.198978i \(-0.0637621\pi\)
\(600\) 4.17898 + 2.74520i 0.170606 + 0.112073i
\(601\) −5.83608 −0.238059 −0.119029 0.992891i \(-0.537978\pi\)
−0.119029 + 0.992891i \(0.537978\pi\)
\(602\) −10.4840 10.4840i −0.427298 0.427298i
\(603\) 7.13460i 0.290543i
\(604\) −3.77985 + 3.77985i −0.153800 + 0.153800i
\(605\) −1.28747 12.5671i −0.0523430 0.510927i
\(606\) 10.5213 10.5213i 0.427397 0.427397i
\(607\) −25.1205 + 25.1205i −1.01961 + 1.01961i −0.0198060 + 0.999804i \(0.506305\pi\)
−0.999804 + 0.0198060i \(0.993695\pi\)
\(608\) −4.66558 + 4.66558i −0.189214 + 0.189214i
\(609\) 19.6826 + 19.6826i 0.797580 + 0.797580i
\(610\) −14.4191 + 1.47719i −0.583812 + 0.0598098i
\(611\) −0.943322 + 1.78237i −0.0381627 + 0.0721070i
\(612\) −0.932546 + 0.932546i −0.0376959 + 0.0376959i
\(613\) 46.0466i 1.85980i 0.367808 + 0.929902i \(0.380108\pi\)
−0.367808 + 0.929902i \(0.619892\pi\)
\(614\) 4.45946i 0.179969i
\(615\) −2.15922 21.0765i −0.0870683 0.849885i
\(616\) 6.62968 + 6.62968i 0.267118 + 0.267118i
\(617\) 25.5757 1.02964 0.514819 0.857299i \(-0.327859\pi\)
0.514819 + 0.857299i \(0.327859\pi\)
\(618\) 8.07515 0.324830
\(619\) 2.22356 + 2.22356i 0.0893725 + 0.0893725i 0.750380 0.661007i \(-0.229871\pi\)
−0.661007 + 0.750380i \(0.729871\pi\)
\(620\) 16.3593 + 13.3188i 0.657004 + 0.534897i
\(621\) 5.56923i 0.223486i
\(622\) 17.3852i 0.697083i
\(623\) 16.3030 16.3030i 0.653165 0.653165i
\(624\) 1.06077 + 3.44598i 0.0424649 + 0.137950i
\(625\) 22.9443 9.92770i 0.917772 0.397108i
\(626\) 4.06946 + 4.06946i 0.162648 + 0.162648i
\(627\) −10.7919 + 10.7919i −0.430987 + 0.430987i
\(628\) 13.1242 13.1242i 0.523714 0.523714i
\(629\) 7.50339 7.50339i 0.299180 0.299180i
\(630\) 9.01640 0.923704i 0.359222 0.0368013i
\(631\) −11.3678 + 11.3678i −0.452546 + 0.452546i −0.896199 0.443653i \(-0.853682\pi\)
0.443653 + 0.896199i \(0.353682\pi\)
\(632\) 1.91721i 0.0762624i
\(633\) 8.69637 + 8.69637i 0.345650 + 0.345650i
\(634\) 5.85556 0.232554
\(635\) −25.4683 20.7349i −1.01068 0.822838i
\(636\) 8.97619i 0.355929i
\(637\) −30.0503 15.9042i −1.19063 0.630145i
\(638\) −11.2321 11.2321i −0.444682 0.444682i
\(639\) −5.56896 + 5.56896i −0.220305 + 0.220305i
\(640\) −2.22443 + 0.227886i −0.0879281 + 0.00900798i
\(641\) 27.2559i 1.07654i 0.842772 + 0.538271i \(0.180922\pi\)
−0.842772 + 0.538271i \(0.819078\pi\)
\(642\) −6.95355 −0.274435
\(643\) 12.3529i 0.487153i 0.969882 + 0.243576i \(0.0783207\pi\)
−0.969882 + 0.243576i \(0.921679\pi\)
\(644\) 15.9623 + 15.9623i 0.629003 + 0.629003i
\(645\) 8.13666 0.833578i 0.320381 0.0328221i
\(646\) −8.70173 −0.342365
\(647\) 6.52838 + 6.52838i 0.256657 + 0.256657i 0.823693 0.567036i \(-0.191910\pi\)
−0.567036 + 0.823693i \(0.691910\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −7.50953 −0.294775
\(650\) 17.3127 + 5.02697i 0.679060 + 0.197174i
\(651\) 38.2401 1.49875
\(652\) 9.96010 0.390068
\(653\) 13.6586 + 13.6586i 0.534500 + 0.534500i 0.921908 0.387408i \(-0.126630\pi\)
−0.387408 + 0.921908i \(0.626630\pi\)
\(654\) −18.2854 −0.715014
\(655\) −25.4696 + 2.60929i −0.995181 + 0.101953i
\(656\) 6.69985 + 6.69985i 0.261585 + 0.261585i
\(657\) 7.36347i 0.287276i
\(658\) −2.26707 −0.0883795
\(659\) 49.7146i 1.93661i 0.249776 + 0.968304i \(0.419643\pi\)
−0.249776 + 0.968304i \(0.580357\pi\)
\(660\) −5.14530 + 0.527121i −0.200280 + 0.0205181i
\(661\) −24.9427 + 24.9427i −0.970157 + 0.970157i −0.999567 0.0294100i \(-0.990637\pi\)
0.0294100 + 0.999567i \(0.490637\pi\)
\(662\) −22.6533 22.6533i −0.880444 0.880444i
\(663\) −2.22431 + 4.20275i −0.0863851 + 0.163221i
\(664\) 0.718668i 0.0278897i
\(665\) 46.3763 + 37.7571i 1.79840 + 1.46416i
\(666\) 8.04614 0.311782
\(667\) −27.0435 27.0435i −1.04713 1.04713i
\(668\) 10.9823i 0.424916i
\(669\) −7.44230 + 7.44230i −0.287736 + 0.287736i
\(670\) −15.8704 + 1.62587i −0.613126 + 0.0628130i
\(671\) 10.6022 10.6022i 0.409295 0.409295i
\(672\) −2.86616 + 2.86616i −0.110565 + 0.110565i
\(673\) 5.37765 5.37765i 0.207293 0.207293i −0.595823 0.803116i \(-0.703174\pi\)
0.803116 + 0.595823i \(0.203174\pi\)
\(674\) 7.97905 + 7.97905i 0.307342 + 0.307342i
\(675\) −2.74520 + 4.17898i −0.105663 + 0.160849i
\(676\) 7.31080 + 10.7495i 0.281185 + 0.413443i
\(677\) −10.8097 + 10.8097i −0.415449 + 0.415449i −0.883632 0.468183i \(-0.844909\pi\)
0.468183 + 0.883632i \(0.344909\pi\)
\(678\) 7.66010i 0.294184i
\(679\) 26.7582i 1.02689i
\(680\) −2.28689 1.86186i −0.0876983 0.0713992i
\(681\) −12.7208 12.7208i −0.487461 0.487461i
\(682\) −21.8221 −0.835610
\(683\) 29.1338 1.11477 0.557386 0.830253i \(-0.311804\pi\)
0.557386 + 0.830253i \(0.311804\pi\)
\(684\) −4.66558 4.66558i −0.178393 0.178393i
\(685\) 4.73248 + 46.1943i 0.180819 + 1.76499i
\(686\) 9.84862i 0.376022i
\(687\) 2.09524i 0.0799383i
\(688\) −2.58651 + 2.58651i −0.0986096 + 0.0986096i
\(689\) −9.52170 30.9317i −0.362748 1.17841i
\(690\) −12.3883 + 1.26915i −0.471616 + 0.0483157i
\(691\) −23.8730 23.8730i −0.908172 0.908172i 0.0879526 0.996125i \(-0.471968\pi\)
−0.996125 + 0.0879526i \(0.971968\pi\)
\(692\) −5.50754 + 5.50754i −0.209365 + 0.209365i
\(693\) −6.62968 + 6.62968i −0.251841 + 0.251841i
\(694\) 13.0579 13.0579i 0.495671 0.495671i
\(695\) −2.96668 28.9582i −0.112533 1.09845i
\(696\) 4.85588 4.85588i 0.184061 0.184061i
\(697\) 12.4958i 0.473313i
\(698\) −21.5924 21.5924i −0.817284 0.817284i
\(699\) 3.82490 0.144671
\(700\) 4.10942 + 19.8458i 0.155322 + 0.750101i
\(701\) 13.7155i 0.518027i −0.965874 0.259013i \(-0.916603\pi\)
0.965874 0.259013i \(-0.0833974\pi\)
\(702\) −3.44598 + 1.06077i −0.130060 + 0.0400363i
\(703\) 37.5399 + 37.5399i 1.41584 + 1.41584i
\(704\) 1.63560 1.63560i 0.0616441 0.0616441i
\(705\) 0.789609 0.969862i 0.0297384 0.0365271i
\(706\) 0.516800i 0.0194500i
\(707\) 60.3112 2.26824
\(708\) 3.24653i 0.122012i
\(709\) 36.2581 + 36.2581i 1.36170 + 1.36170i 0.871751 + 0.489949i \(0.162985\pi\)
0.489949 + 0.871751i \(0.337015\pi\)
\(710\) −13.6568 11.1187i −0.512532 0.417276i
\(711\) 1.91721 0.0719008
\(712\) −4.02209 4.02209i −0.150734 0.150734i
\(713\) −52.5410 −1.96768
\(714\) −5.34565 −0.200056
\(715\) −17.1714 + 7.27444i −0.642175 + 0.272048i
\(716\) −23.3767 −0.873628
\(717\) −5.63011 −0.210260
\(718\) 0.362077 + 0.362077i 0.0135126 + 0.0135126i
\(719\) 23.5875 0.879666 0.439833 0.898080i \(-0.355038\pi\)
0.439833 + 0.898080i \(0.355038\pi\)
\(720\) −0.227886 2.22443i −0.00849281 0.0828994i
\(721\) 23.1447 + 23.1447i 0.861952 + 0.861952i
\(722\) 24.5352i 0.913107i
\(723\) −21.8669 −0.813239
\(724\) 15.3920i 0.572039i
\(725\) −6.96222 33.6230i −0.258570 1.24873i
\(726\) −3.99488 + 3.99488i −0.148264 + 0.148264i
\(727\) 16.9055 + 16.9055i 0.626991 + 0.626991i 0.947310 0.320319i \(-0.103790\pi\)
−0.320319 + 0.947310i \(0.603790\pi\)
\(728\) −6.83638 + 12.9171i −0.253373 + 0.478738i
\(729\) 1.00000i 0.0370370i
\(730\) −16.3795 + 1.67803i −0.606232 + 0.0621068i
\(731\) −4.82407 −0.178425
\(732\) 4.58358 + 4.58358i 0.169414 + 0.169414i
\(733\) 41.5404i 1.53433i −0.641449 0.767165i \(-0.721667\pi\)
0.641449 0.767165i \(-0.278333\pi\)
\(734\) 5.81538 5.81538i 0.214650 0.214650i
\(735\) 16.3516 + 13.3126i 0.603138 + 0.491042i
\(736\) 3.93804 3.93804i 0.145158 0.145158i
\(737\) 11.6694 11.6694i 0.429846 0.429846i
\(738\) −6.69985 + 6.69985i −0.246625 + 0.246625i
\(739\) −16.5636 16.5636i −0.609303 0.609303i 0.333461 0.942764i \(-0.391783\pi\)
−0.942764 + 0.333461i \(0.891783\pi\)
\(740\) 1.83360 + 17.8980i 0.0674046 + 0.657945i
\(741\) −21.0266 11.1284i −0.772431 0.408811i
\(742\) 25.7272 25.7272i 0.944475 0.944475i
\(743\) 8.59040i 0.315151i 0.987507 + 0.157576i \(0.0503678\pi\)
−0.987507 + 0.157576i \(0.949632\pi\)
\(744\) 9.43416i 0.345873i
\(745\) 8.78202 10.7868i 0.321748 0.395197i
\(746\) −10.4146 10.4146i −0.381306 0.381306i
\(747\) 0.718668 0.0262947
\(748\) 3.05055 0.111539
\(749\) −19.9300 19.9300i −0.728226 0.728226i
\(750\) −9.92142 5.15417i −0.362279 0.188204i
\(751\) 28.0811i 1.02469i 0.858779 + 0.512347i \(0.171224\pi\)
−0.858779 + 0.512347i \(0.828776\pi\)
\(752\) 0.559306i 0.0203958i
\(753\) −12.7251 + 12.7251i −0.463730 + 0.463730i
\(754\) 11.5823 21.8842i 0.421801 0.796976i
\(755\) 7.54662 9.26937i 0.274650 0.337347i
\(756\) −2.86616 2.86616i −0.104241 0.104241i
\(757\) 28.5156 28.5156i 1.03642 1.03642i 0.0371063 0.999311i \(-0.488186\pi\)
0.999311 0.0371063i \(-0.0118140\pi\)
\(758\) 23.6838 23.6838i 0.860235 0.860235i
\(759\) 9.10905 9.10905i 0.330637 0.330637i
\(760\) 9.31501 11.4414i 0.337891 0.415025i
\(761\) −6.51275 + 6.51275i −0.236087 + 0.236087i −0.815228 0.579141i \(-0.803388\pi\)
0.579141 + 0.815228i \(0.303388\pi\)
\(762\) 14.6872i 0.532061i
\(763\) −52.4088 52.4088i −1.89733 1.89733i
\(764\) −18.3221 −0.662870
\(765\) 1.86186 2.28689i 0.0673158 0.0826828i
\(766\) 25.2587i 0.912635i
\(767\) −3.44383 11.1875i −0.124350 0.403957i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) 1.48463 1.48463i 0.0535371 0.0535371i −0.679831 0.733368i \(-0.737947\pi\)
0.733368 + 0.679831i \(0.237947\pi\)
\(770\) −16.2581 13.2364i −0.585899 0.477008i
\(771\) 1.92908i 0.0694741i
\(772\) 10.6298 0.382575
\(773\) 31.8123i 1.14421i −0.820181 0.572104i \(-0.806128\pi\)
0.820181 0.572104i \(-0.193872\pi\)
\(774\) −2.58651 2.58651i −0.0929701 0.0929701i
\(775\) −39.4251 25.8987i −1.41619