Properties

Label 625.2.e.a.124.1
Level $625$
Weight $2$
Character 625.124
Analytic conductor $4.991$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.e (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.99065012633\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.58140625.2
Defining polynomial: \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 124.1
Root \(1.66637 - 0.917186i\) of defining polynomial
Character \(\chi\) \(=\) 625.124
Dual form 625.2.e.a.499.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.07822 - 0.350334i) q^{2} +(-1.52988 + 2.10569i) q^{3} +(-0.578217 - 0.420099i) q^{4} +(2.38723 - 1.73443i) q^{6} -0.407162i q^{7} +(1.80902 + 2.48990i) q^{8} +(-1.16637 - 3.58973i) q^{9} +O(q^{10})\) \(q+(-1.07822 - 0.350334i) q^{2} +(-1.52988 + 2.10569i) q^{3} +(-0.578217 - 0.420099i) q^{4} +(2.38723 - 1.73443i) q^{6} -0.407162i q^{7} +(1.80902 + 2.48990i) q^{8} +(-1.16637 - 3.58973i) q^{9} +(0.618034 - 1.90211i) q^{11} +(1.76920 - 0.574848i) q^{12} +(0.666375 - 0.216518i) q^{13} +(-0.142642 + 0.439008i) q^{14} +(-0.636498 - 1.95894i) q^{16} +(0.930307 + 1.28046i) q^{17} +4.27913i q^{18} +(4.00527 - 2.91000i) q^{19} +(0.857358 + 0.622907i) q^{21} +(-1.33275 + 1.83437i) q^{22} +(1.14264 + 0.371267i) q^{23} -8.01054 q^{24} -0.794350 q^{26} +(1.91711 + 0.622907i) q^{27} +(-0.171048 + 0.235428i) q^{28} +(4.45693 + 3.23815i) q^{29} +(-6.63709 + 4.82213i) q^{31} -3.82022i q^{32} +(3.05975 + 4.21139i) q^{33} +(-0.554485 - 1.70653i) q^{34} +(-0.833625 + 2.56564i) q^{36} +(-4.88398 + 1.58690i) q^{37} +(-5.33802 + 1.73443i) q^{38} +(-0.563549 + 1.73443i) q^{39} +(2.22992 + 6.86300i) q^{41} +(-0.706192 - 0.971990i) q^{42} +9.16531i q^{43} +(-1.15643 + 0.840198i) q^{44} +(-1.10195 - 0.800613i) q^{46} +(0.748388 - 1.03007i) q^{47} +(5.09869 + 1.65667i) q^{48} +6.83422 q^{49} -4.11950 q^{51} +(-0.476268 - 0.154749i) q^{52} +(-2.98593 + 4.10978i) q^{53} +(-1.84883 - 1.34326i) q^{54} +(1.01379 - 0.736562i) q^{56} +12.8858i q^{57} +(-3.67110 - 5.05284i) q^{58} +(2.00852 + 6.18160i) q^{59} +(-2.91097 + 8.95903i) q^{61} +(8.84558 - 2.87410i) q^{62} +(-1.46160 + 0.474903i) q^{63} +(-2.61135 + 8.03690i) q^{64} +(-1.82368 - 5.61272i) q^{66} +(-1.81140 - 2.49317i) q^{67} -1.13120i q^{68} +(-2.52988 + 1.83806i) q^{69} +(-5.55503 - 4.03596i) q^{71} +(6.82808 - 9.39804i) q^{72} +(0.518464 + 0.168459i) q^{73} +5.82193 q^{74} -3.53840 q^{76} +(-0.774467 - 0.251640i) q^{77} +(1.21526 - 1.67266i) q^{78} +(4.43470 + 3.22200i) q^{79} +(4.91623 - 3.57185i) q^{81} -8.18102i q^{82} +(-0.572582 - 0.788091i) q^{83} +(-0.234056 - 0.720350i) q^{84} +(3.21092 - 9.88219i) q^{86} +(-13.6371 + 4.43096i) q^{87} +(5.85410 - 1.90211i) q^{88} +(0.700383 - 2.15556i) q^{89} +(-0.0881579 - 0.271322i) q^{91} +(-0.504726 - 0.694696i) q^{92} -21.3529i q^{93} +(-1.16779 + 0.848451i) q^{94} +(8.04421 + 5.84446i) q^{96} +(-8.94518 + 12.3120i) q^{97} +(-7.36877 - 2.39426i) q^{98} -7.54893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9} - 4 q^{11} + 10 q^{12} - 5 q^{13} - 7 q^{14} - 2 q^{16} + 15 q^{17} + 10 q^{19} + q^{21} + 10 q^{22} + 15 q^{23} - 20 q^{24} + 6 q^{26} - 5 q^{27} - 20 q^{28} + 15 q^{29} + q^{31} + 10 q^{33} - 12 q^{34} - 17 q^{36} - 5 q^{37} + 12 q^{39} - 9 q^{41} + 5 q^{42} + 8 q^{44} + 16 q^{46} - 15 q^{47} - 5 q^{48} + 14 q^{49} - 4 q^{51} - 20 q^{52} + 35 q^{53} - 10 q^{54} - 15 q^{56} - 20 q^{58} + 15 q^{59} + 6 q^{61} + 45 q^{62} - 20 q^{63} - 26 q^{64} - 18 q^{66} - 13 q^{69} - 29 q^{71} + 5 q^{72} + 10 q^{73} - 12 q^{74} - 20 q^{76} + 20 q^{77} - 25 q^{78} - 10 q^{79} - 12 q^{81} + 15 q^{83} - 27 q^{84} + 16 q^{86} - 55 q^{87} + 20 q^{88} + 40 q^{89} + q^{91} - 5 q^{92} - 7 q^{94} + 11 q^{96} - 10 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.07822 0.350334i −0.762414 0.247723i −0.0980998 0.995177i \(-0.531276\pi\)
−0.664315 + 0.747453i \(0.731276\pi\)
\(3\) −1.52988 + 2.10569i −0.883274 + 1.21572i 0.0922289 + 0.995738i \(0.470601\pi\)
−0.975503 + 0.219985i \(0.929399\pi\)
\(4\) −0.578217 0.420099i −0.289108 0.210049i
\(5\) 0 0
\(6\) 2.38723 1.73443i 0.974584 0.708077i
\(7\) 0.407162i 0.153893i −0.997035 0.0769463i \(-0.975483\pi\)
0.997035 0.0769463i \(-0.0245170\pi\)
\(8\) 1.80902 + 2.48990i 0.639584 + 0.880312i
\(9\) −1.16637 3.58973i −0.388792 1.19658i
\(10\) 0 0
\(11\) 0.618034 1.90211i 0.186344 0.573509i −0.813625 0.581390i \(-0.802509\pi\)
0.999969 + 0.00788181i \(0.00250889\pi\)
\(12\) 1.76920 0.574848i 0.510724 0.165944i
\(13\) 0.666375 0.216518i 0.184819 0.0600513i −0.215145 0.976582i \(-0.569023\pi\)
0.399964 + 0.916531i \(0.369023\pi\)
\(14\) −0.142642 + 0.439008i −0.0381228 + 0.117330i
\(15\) 0 0
\(16\) −0.636498 1.95894i −0.159125 0.489735i
\(17\) 0.930307 + 1.28046i 0.225632 + 0.310556i 0.906792 0.421579i \(-0.138524\pi\)
−0.681159 + 0.732135i \(0.738524\pi\)
\(18\) 4.27913i 1.00860i
\(19\) 4.00527 2.91000i 0.918871 0.667599i −0.0243714 0.999703i \(-0.507758\pi\)
0.943243 + 0.332104i \(0.107758\pi\)
\(20\) 0 0
\(21\) 0.857358 + 0.622907i 0.187091 + 0.135929i
\(22\) −1.33275 + 1.83437i −0.284143 + 0.391089i
\(23\) 1.14264 + 0.371267i 0.238257 + 0.0774145i 0.425712 0.904859i \(-0.360024\pi\)
−0.187454 + 0.982273i \(0.560024\pi\)
\(24\) −8.01054 −1.63514
\(25\) 0 0
\(26\) −0.794350 −0.155785
\(27\) 1.91711 + 0.622907i 0.368948 + 0.119878i
\(28\) −0.171048 + 0.235428i −0.0323251 + 0.0444916i
\(29\) 4.45693 + 3.23815i 0.827631 + 0.601309i 0.918888 0.394519i \(-0.129089\pi\)
−0.0912574 + 0.995827i \(0.529089\pi\)
\(30\) 0 0
\(31\) −6.63709 + 4.82213i −1.19206 + 0.866080i −0.993480 0.114005i \(-0.963632\pi\)
−0.198577 + 0.980085i \(0.563632\pi\)
\(32\) 3.82022i 0.675325i
\(33\) 3.05975 + 4.21139i 0.532634 + 0.733108i
\(34\) −0.554485 1.70653i −0.0950933 0.292667i
\(35\) 0 0
\(36\) −0.833625 + 2.56564i −0.138938 + 0.427606i
\(37\) −4.88398 + 1.58690i −0.802921 + 0.260885i −0.681597 0.731728i \(-0.738714\pi\)
−0.121324 + 0.992613i \(0.538714\pi\)
\(38\) −5.33802 + 1.73443i −0.865941 + 0.281361i
\(39\) −0.563549 + 1.73443i −0.0902401 + 0.277731i
\(40\) 0 0
\(41\) 2.22992 + 6.86300i 0.348256 + 1.07182i 0.959818 + 0.280624i \(0.0905414\pi\)
−0.611562 + 0.791196i \(0.709459\pi\)
\(42\) −0.706192 0.971990i −0.108968 0.149981i
\(43\) 9.16531i 1.39770i 0.715270 + 0.698848i \(0.246304\pi\)
−0.715270 + 0.698848i \(0.753696\pi\)
\(44\) −1.15643 + 0.840198i −0.174339 + 0.126665i
\(45\) 0 0
\(46\) −1.10195 0.800613i −0.162473 0.118044i
\(47\) 0.748388 1.03007i 0.109164 0.150251i −0.750940 0.660371i \(-0.770399\pi\)
0.860103 + 0.510120i \(0.170399\pi\)
\(48\) 5.09869 + 1.65667i 0.735933 + 0.239119i
\(49\) 6.83422 0.976317
\(50\) 0 0
\(51\) −4.11950 −0.576846
\(52\) −0.476268 0.154749i −0.0660465 0.0214598i
\(53\) −2.98593 + 4.10978i −0.410149 + 0.564521i −0.963255 0.268590i \(-0.913442\pi\)
0.553106 + 0.833111i \(0.313442\pi\)
\(54\) −1.84883 1.34326i −0.251594 0.182794i
\(55\) 0 0
\(56\) 1.01379 0.736562i 0.135473 0.0984273i
\(57\) 12.8858i 1.70677i
\(58\) −3.67110 5.05284i −0.482039 0.663470i
\(59\) 2.00852 + 6.18160i 0.261487 + 0.804776i 0.992482 + 0.122392i \(0.0390566\pi\)
−0.730994 + 0.682383i \(0.760943\pi\)
\(60\) 0 0
\(61\) −2.91097 + 8.95903i −0.372711 + 1.14709i 0.572299 + 0.820045i \(0.306052\pi\)
−0.945010 + 0.327041i \(0.893948\pi\)
\(62\) 8.84558 2.87410i 1.12339 0.365011i
\(63\) −1.46160 + 0.474903i −0.184144 + 0.0598321i
\(64\) −2.61135 + 8.03690i −0.326419 + 1.00461i
\(65\) 0 0
\(66\) −1.82368 5.61272i −0.224480 0.690878i
\(67\) −1.81140 2.49317i −0.221297 0.304590i 0.683905 0.729571i \(-0.260280\pi\)
−0.905202 + 0.424982i \(0.860280\pi\)
\(68\) 1.13120i 0.137178i
\(69\) −2.52988 + 1.83806i −0.304561 + 0.221277i
\(70\) 0 0
\(71\) −5.55503 4.03596i −0.659260 0.478981i 0.207153 0.978309i \(-0.433580\pi\)
−0.866413 + 0.499328i \(0.833580\pi\)
\(72\) 6.82808 9.39804i 0.804696 1.10757i
\(73\) 0.518464 + 0.168459i 0.0606817 + 0.0197167i 0.339201 0.940714i \(-0.389843\pi\)
−0.278519 + 0.960431i \(0.589843\pi\)
\(74\) 5.82193 0.676786
\(75\) 0 0
\(76\) −3.53840 −0.405882
\(77\) −0.774467 0.251640i −0.0882587 0.0286770i
\(78\) 1.21526 1.67266i 0.137601 0.189391i
\(79\) 4.43470 + 3.22200i 0.498942 + 0.362503i 0.808613 0.588341i \(-0.200219\pi\)
−0.309670 + 0.950844i \(0.600219\pi\)
\(80\) 0 0
\(81\) 4.91623 3.57185i 0.546248 0.396873i
\(82\) 8.18102i 0.903442i
\(83\) −0.572582 0.788091i −0.0628490 0.0865043i 0.776435 0.630197i \(-0.217026\pi\)
−0.839284 + 0.543693i \(0.817026\pi\)
\(84\) −0.234056 0.720350i −0.0255376 0.0785966i
\(85\) 0 0
\(86\) 3.21092 9.88219i 0.346242 1.06562i
\(87\) −13.6371 + 4.43096i −1.46205 + 0.475049i
\(88\) 5.85410 1.90211i 0.624049 0.202766i
\(89\) 0.700383 2.15556i 0.0742404 0.228488i −0.907050 0.421024i \(-0.861671\pi\)
0.981290 + 0.192535i \(0.0616709\pi\)
\(90\) 0 0
\(91\) −0.0881579 0.271322i −0.00924146 0.0284423i
\(92\) −0.504726 0.694696i −0.0526213 0.0724270i
\(93\) 21.3529i 2.21420i
\(94\) −1.16779 + 0.848451i −0.120449 + 0.0875110i
\(95\) 0 0
\(96\) 8.04421 + 5.84446i 0.821009 + 0.596498i
\(97\) −8.94518 + 12.3120i −0.908245 + 1.25009i 0.0595168 + 0.998227i \(0.481044\pi\)
−0.967762 + 0.251865i \(0.918956\pi\)
\(98\) −7.36877 2.39426i −0.744358 0.241857i
\(99\) −7.54893 −0.758696
\(100\) 0 0
\(101\) 18.3965 1.83052 0.915261 0.402861i \(-0.131984\pi\)
0.915261 + 0.402861i \(0.131984\pi\)
\(102\) 4.44172 + 1.44320i 0.439796 + 0.142898i
\(103\) 6.98539 9.61456i 0.688290 0.947351i −0.311706 0.950179i \(-0.600900\pi\)
0.999996 + 0.00282822i \(0.000900250\pi\)
\(104\) 1.74459 + 1.26752i 0.171071 + 0.124291i
\(105\) 0 0
\(106\) 4.65927 3.38516i 0.452548 0.328796i
\(107\) 0.754919i 0.0729808i −0.999334 0.0364904i \(-0.988382\pi\)
0.999334 0.0364904i \(-0.0116178\pi\)
\(108\) −0.846822 1.16555i −0.0814855 0.112155i
\(109\) 2.82983 + 8.70932i 0.271048 + 0.834201i 0.990238 + 0.139387i \(0.0445133\pi\)
−0.719190 + 0.694814i \(0.755487\pi\)
\(110\) 0 0
\(111\) 4.13035 12.7119i 0.392036 1.20656i
\(112\) −0.797605 + 0.259158i −0.0753666 + 0.0244881i
\(113\) 12.2115 3.96774i 1.14876 0.373254i 0.328082 0.944649i \(-0.393598\pi\)
0.820675 + 0.571395i \(0.193598\pi\)
\(114\) 4.51433 13.8937i 0.422806 1.30126i
\(115\) 0 0
\(116\) −1.21673 3.74470i −0.112970 0.347687i
\(117\) −1.55448 2.13956i −0.143712 0.197803i
\(118\) 7.36876i 0.678349i
\(119\) 0.521353 0.378785i 0.0477923 0.0347232i
\(120\) 0 0
\(121\) 5.66312 + 4.11450i 0.514829 + 0.374045i
\(122\) 6.27730 8.63997i 0.568320 0.782226i
\(123\) −17.8629 5.80400i −1.61064 0.523329i
\(124\) 5.86345 0.526553
\(125\) 0 0
\(126\) 1.74230 0.155216
\(127\) −6.75742 2.19562i −0.599624 0.194830i −0.00655135 0.999979i \(-0.502085\pi\)
−0.593073 + 0.805149i \(0.702085\pi\)
\(128\) 1.14026 1.56944i 0.100786 0.138720i
\(129\) −19.2993 14.0218i −1.69921 1.23455i
\(130\) 0 0
\(131\) −1.93699 + 1.40731i −0.169236 + 0.122957i −0.669179 0.743101i \(-0.733354\pi\)
0.499943 + 0.866058i \(0.333354\pi\)
\(132\) 3.72049i 0.323827i
\(133\) −1.18484 1.63079i −0.102739 0.141408i
\(134\) 1.07963 + 3.32277i 0.0932662 + 0.287044i
\(135\) 0 0
\(136\) −1.50527 + 4.63274i −0.129076 + 0.397254i
\(137\) 18.0885 5.87730i 1.54540 0.502132i 0.592542 0.805540i \(-0.298125\pi\)
0.952861 + 0.303408i \(0.0981246\pi\)
\(138\) 3.37169 1.09553i 0.287017 0.0932576i
\(139\) 2.08114 6.40508i 0.176520 0.543272i −0.823180 0.567781i \(-0.807802\pi\)
0.999700 + 0.0245087i \(0.00780215\pi\)
\(140\) 0 0
\(141\) 1.02407 + 3.15175i 0.0862420 + 0.265426i
\(142\) 4.57559 + 6.29776i 0.383975 + 0.528496i
\(143\) 1.40134i 0.117186i
\(144\) −6.28968 + 4.56972i −0.524140 + 0.380810i
\(145\) 0 0
\(146\) −0.500000 0.363271i −0.0413803 0.0300645i
\(147\) −10.4555 + 14.3908i −0.862356 + 1.18693i
\(148\) 3.49065 + 1.13418i 0.286930 + 0.0932292i
\(149\) 0.720492 0.0590250 0.0295125 0.999564i \(-0.490605\pi\)
0.0295125 + 0.999564i \(0.490605\pi\)
\(150\) 0 0
\(151\) −15.5178 −1.26282 −0.631412 0.775447i \(-0.717524\pi\)
−0.631412 + 0.775447i \(0.717524\pi\)
\(152\) 14.4912 + 4.70847i 1.17539 + 0.381908i
\(153\) 3.51141 4.83304i 0.283881 0.390728i
\(154\) 0.746886 + 0.542644i 0.0601858 + 0.0437275i
\(155\) 0 0
\(156\) 1.05448 0.766128i 0.0844263 0.0613393i
\(157\) 2.78418i 0.222202i 0.993809 + 0.111101i \(0.0354376\pi\)
−0.993809 + 0.111101i \(0.964562\pi\)
\(158\) −3.65279 5.02763i −0.290600 0.399977i
\(159\) −4.08583 12.5749i −0.324027 0.997254i
\(160\) 0 0
\(161\) 0.151166 0.465240i 0.0119135 0.0366661i
\(162\) −6.55211 + 2.12891i −0.514782 + 0.167263i
\(163\) −23.0226 + 7.48049i −1.80327 + 0.585917i −0.999954 0.00963930i \(-0.996932\pi\)
−0.803314 + 0.595556i \(0.796932\pi\)
\(164\) 1.59376 4.90509i 0.124452 0.383023i
\(165\) 0 0
\(166\) 0.341272 + 1.05033i 0.0264879 + 0.0815213i
\(167\) 11.1951 + 15.4087i 0.866300 + 1.19236i 0.980030 + 0.198848i \(0.0637199\pi\)
−0.113731 + 0.993512i \(0.536280\pi\)
\(168\) 3.26158i 0.251637i
\(169\) −10.1200 + 7.35264i −0.778465 + 0.565588i
\(170\) 0 0
\(171\) −15.1178 10.9837i −1.15608 0.839944i
\(172\) 3.85034 5.29953i 0.293585 0.404086i
\(173\) 12.5987 + 4.09356i 0.957861 + 0.311228i 0.745906 0.666052i \(-0.232017\pi\)
0.211955 + 0.977279i \(0.432017\pi\)
\(174\) 16.2561 1.23237
\(175\) 0 0
\(176\) −4.11950 −0.310519
\(177\) −16.0893 5.22775i −1.20935 0.392941i
\(178\) −1.51033 + 2.07879i −0.113204 + 0.155812i
\(179\) −9.89021 7.18566i −0.739229 0.537081i 0.153241 0.988189i \(-0.451029\pi\)
−0.892469 + 0.451108i \(0.851029\pi\)
\(180\) 0 0
\(181\) −8.83187 + 6.41673i −0.656468 + 0.476952i −0.865468 0.500964i \(-0.832979\pi\)
0.209000 + 0.977916i \(0.432979\pi\)
\(182\) 0.323429i 0.0239741i
\(183\) −14.4116 19.8358i −1.06533 1.46631i
\(184\) 1.14264 + 3.51669i 0.0842367 + 0.259254i
\(185\) 0 0
\(186\) −7.48066 + 23.0231i −0.548509 + 1.68814i
\(187\) 3.01054 0.978182i 0.220152 0.0715318i
\(188\) −0.865461 + 0.281205i −0.0631202 + 0.0205090i
\(189\) 0.253624 0.780573i 0.0184484 0.0567784i
\(190\) 0 0
\(191\) 0.484424 + 1.49090i 0.0350517 + 0.107878i 0.967052 0.254581i \(-0.0819374\pi\)
−0.932000 + 0.362459i \(0.881937\pi\)
\(192\) −12.9282 17.7942i −0.933014 1.28418i
\(193\) 1.65786i 0.119335i −0.998218 0.0596675i \(-0.980996\pi\)
0.998218 0.0596675i \(-0.0190040\pi\)
\(194\) 13.9581 10.1412i 1.00214 0.728095i
\(195\) 0 0
\(196\) −3.95166 2.87105i −0.282261 0.205075i
\(197\) 7.80760 10.7462i 0.556268 0.765638i −0.434578 0.900634i \(-0.643102\pi\)
0.990846 + 0.134997i \(0.0431024\pi\)
\(198\) 8.13939 + 2.64465i 0.578441 + 0.187947i
\(199\) −12.1025 −0.857921 −0.428960 0.903323i \(-0.641120\pi\)
−0.428960 + 0.903323i \(0.641120\pi\)
\(200\) 0 0
\(201\) 8.02107 0.565763
\(202\) −19.8354 6.44493i −1.39562 0.453463i
\(203\) 1.31845 1.81469i 0.0925370 0.127366i
\(204\) 2.38197 + 1.73060i 0.166771 + 0.121166i
\(205\) 0 0
\(206\) −10.9001 + 7.91936i −0.759443 + 0.551768i
\(207\) 4.53482i 0.315192i
\(208\) −0.848293 1.16757i −0.0588185 0.0809567i
\(209\) −3.05975 9.41695i −0.211647 0.651384i
\(210\) 0 0
\(211\) −2.07060 + 6.37266i −0.142546 + 0.438712i −0.996687 0.0813294i \(-0.974083\pi\)
0.854141 + 0.520041i \(0.174083\pi\)
\(212\) 3.45303 1.12196i 0.237155 0.0770562i
\(213\) 16.9970 5.52266i 1.16462 0.378407i
\(214\) −0.264474 + 0.813966i −0.0180790 + 0.0556416i
\(215\) 0 0
\(216\) 1.91711 + 5.90026i 0.130443 + 0.401462i
\(217\) 1.96339 + 2.70237i 0.133283 + 0.183449i
\(218\) 10.3819i 0.703152i
\(219\) −1.14791 + 0.834005i −0.0775686 + 0.0563569i
\(220\) 0 0
\(221\) 0.897175 + 0.651836i 0.0603505 + 0.0438472i
\(222\) −8.90683 + 12.2592i −0.597788 + 0.822784i
\(223\) 10.0733 + 3.27301i 0.674558 + 0.219177i 0.626211 0.779654i \(-0.284605\pi\)
0.0483465 + 0.998831i \(0.484605\pi\)
\(224\) −1.55545 −0.103928
\(225\) 0 0
\(226\) −14.5566 −0.968293
\(227\) 18.6514 + 6.06020i 1.23794 + 0.402230i 0.853583 0.520956i \(-0.174425\pi\)
0.384353 + 0.923186i \(0.374425\pi\)
\(228\) 5.41331 7.45079i 0.358505 0.493440i
\(229\) 7.15088 + 5.19542i 0.472544 + 0.343323i 0.798432 0.602085i \(-0.205663\pi\)
−0.325888 + 0.945408i \(0.605663\pi\)
\(230\) 0 0
\(231\) 1.71472 1.24581i 0.112820 0.0819685i
\(232\) 16.9552i 1.11316i
\(233\) 6.50233 + 8.94969i 0.425982 + 0.586313i 0.967025 0.254681i \(-0.0819706\pi\)
−0.541043 + 0.840995i \(0.681971\pi\)
\(234\) 0.926509 + 2.85150i 0.0605678 + 0.186409i
\(235\) 0 0
\(236\) 1.43552 4.41808i 0.0934445 0.287593i
\(237\) −13.5691 + 4.40886i −0.881406 + 0.286386i
\(238\) −0.694833 + 0.225765i −0.0450393 + 0.0146342i
\(239\) −4.97686 + 15.3172i −0.321926 + 0.990788i 0.650882 + 0.759179i \(0.274399\pi\)
−0.972809 + 0.231609i \(0.925601\pi\)
\(240\) 0 0
\(241\) 1.85062 + 5.69562i 0.119209 + 0.366887i 0.992802 0.119771i \(-0.0382159\pi\)
−0.873593 + 0.486658i \(0.838216\pi\)
\(242\) −4.66462 6.42030i −0.299853 0.412713i
\(243\) 21.8639i 1.40257i
\(244\) 5.44685 3.95737i 0.348699 0.253344i
\(245\) 0 0
\(246\) 17.2267 + 12.5159i 1.09834 + 0.797988i
\(247\) 2.03894 2.80636i 0.129735 0.178565i
\(248\) −24.0132 7.80237i −1.52484 0.495451i
\(249\) 2.53546 0.160678
\(250\) 0 0
\(251\) 3.73176 0.235547 0.117773 0.993041i \(-0.462424\pi\)
0.117773 + 0.993041i \(0.462424\pi\)
\(252\) 1.04463 + 0.339420i 0.0658054 + 0.0213815i
\(253\) 1.41238 1.94398i 0.0887958 0.122217i
\(254\) 6.51676 + 4.73471i 0.408898 + 0.297082i
\(255\) 0 0
\(256\) 11.8939 8.64144i 0.743370 0.540090i
\(257\) 23.5935i 1.47172i −0.677132 0.735862i \(-0.736777\pi\)
0.677132 0.735862i \(-0.263223\pi\)
\(258\) 15.8966 + 21.8797i 0.989676 + 1.36217i
\(259\) 0.646125 + 1.98857i 0.0401482 + 0.123564i
\(260\) 0 0
\(261\) 6.42563 19.7761i 0.397737 1.22411i
\(262\) 2.58152 0.838788i 0.159487 0.0518205i
\(263\) −6.31621 + 2.05226i −0.389474 + 0.126548i −0.497207 0.867632i \(-0.665641\pi\)
0.107733 + 0.994180i \(0.465641\pi\)
\(264\) −4.95078 + 15.2369i −0.304700 + 0.937769i
\(265\) 0 0
\(266\) 0.706192 + 2.17344i 0.0432994 + 0.133262i
\(267\) 3.46744 + 4.77252i 0.212204 + 0.292074i
\(268\) 2.20256i 0.134543i
\(269\) −10.5527 + 7.66701i −0.643411 + 0.467466i −0.861020 0.508570i \(-0.830174\pi\)
0.217609 + 0.976036i \(0.430174\pi\)
\(270\) 0 0
\(271\) 9.58586 + 6.96454i 0.582300 + 0.423066i 0.839552 0.543279i \(-0.182817\pi\)
−0.257253 + 0.966344i \(0.582817\pi\)
\(272\) 1.91620 2.63742i 0.116187 0.159917i
\(273\) 0.706192 + 0.229456i 0.0427407 + 0.0138873i
\(274\) −21.5623 −1.30263
\(275\) 0 0
\(276\) 2.23498 0.134530
\(277\) 16.1260 + 5.23965i 0.968917 + 0.314820i 0.750379 0.661008i \(-0.229871\pi\)
0.218538 + 0.975828i \(0.429871\pi\)
\(278\) −4.48783 + 6.17697i −0.269162 + 0.370470i
\(279\) 25.0515 + 18.2010i 1.49979 + 1.08966i
\(280\) 0 0
\(281\) 4.10575 2.98300i 0.244928 0.177951i −0.458548 0.888670i \(-0.651630\pi\)
0.703476 + 0.710719i \(0.251630\pi\)
\(282\) 3.75704i 0.223728i
\(283\) 6.95047 + 9.56650i 0.413162 + 0.568669i 0.963986 0.265952i \(-0.0856864\pi\)
−0.550824 + 0.834622i \(0.685686\pi\)
\(284\) 1.51650 + 4.66732i 0.0899880 + 0.276955i
\(285\) 0 0
\(286\) −0.490935 + 1.51094i −0.0290296 + 0.0893439i
\(287\) 2.79435 0.907939i 0.164945 0.0535940i
\(288\) −13.7136 + 4.45580i −0.808079 + 0.262561i
\(289\) 4.47919 13.7855i 0.263482 0.810913i
\(290\) 0 0
\(291\) −12.2403 37.6716i −0.717536 2.20835i
\(292\) −0.229015 0.315212i −0.0134021 0.0184464i
\(293\) 19.4348i 1.13540i 0.823237 + 0.567698i \(0.192166\pi\)
−0.823237 + 0.567698i \(0.807834\pi\)
\(294\) 16.3149 11.8535i 0.951503 0.691307i
\(295\) 0 0
\(296\) −12.7864 9.28988i −0.743196 0.539963i
\(297\) 2.36968 3.26158i 0.137503 0.189256i
\(298\) −0.776846 0.252413i −0.0450015 0.0146219i
\(299\) 0.841814 0.0486834
\(300\) 0 0
\(301\) 3.73176 0.215095
\(302\) 16.7316 + 5.43643i 0.962795 + 0.312831i
\(303\) −28.1444 + 38.7374i −1.61685 + 2.22541i
\(304\) −8.24986 5.99387i −0.473162 0.343772i
\(305\) 0 0
\(306\) −5.47924 + 3.98090i −0.313227 + 0.227573i
\(307\) 25.4169i 1.45062i 0.688423 + 0.725310i \(0.258303\pi\)
−0.688423 + 0.725310i \(0.741697\pi\)
\(308\) 0.342096 + 0.470855i 0.0194927 + 0.0268295i
\(309\) 9.55854 + 29.4182i 0.543766 + 1.67354i
\(310\) 0 0
\(311\) 4.90032 15.0816i 0.277872 0.855201i −0.710573 0.703623i \(-0.751564\pi\)
0.988445 0.151578i \(-0.0484356\pi\)
\(312\) −5.33802 + 1.73443i −0.302206 + 0.0981926i
\(313\) 6.67303 2.16820i 0.377182 0.122554i −0.114290 0.993447i \(-0.536459\pi\)
0.491471 + 0.870894i \(0.336459\pi\)
\(314\) 0.975392 3.00195i 0.0550445 0.169410i
\(315\) 0 0
\(316\) −1.21066 3.72602i −0.0681049 0.209605i
\(317\) −7.66100 10.5445i −0.430285 0.592236i 0.537734 0.843115i \(-0.319280\pi\)
−0.968019 + 0.250879i \(0.919280\pi\)
\(318\) 14.9899i 0.840590i
\(319\) 8.91385 6.47629i 0.499080 0.362603i
\(320\) 0 0
\(321\) 1.58963 + 1.15493i 0.0887244 + 0.0644620i
\(322\) −0.325979 + 0.448671i −0.0181661 + 0.0250035i
\(323\) 7.45225 + 2.42138i 0.414654 + 0.134729i
\(324\) −4.34318 −0.241288
\(325\) 0 0
\(326\) 27.4440 1.51998
\(327\) −22.6684 7.36542i −1.25357 0.407309i
\(328\) −13.0542 + 17.9676i −0.720798 + 0.992093i
\(329\) −0.419404 0.304715i −0.0231225 0.0167995i
\(330\) 0 0
\(331\) 14.2742 10.3708i 0.784580 0.570031i −0.121770 0.992558i \(-0.538857\pi\)
0.906350 + 0.422527i \(0.138857\pi\)
\(332\) 0.696229i 0.0382105i
\(333\) 11.3931 + 15.6813i 0.624338 + 0.859327i
\(334\) −6.67252 20.5359i −0.365104 1.12367i
\(335\) 0 0
\(336\) 0.674531 2.07599i 0.0367987 0.113255i
\(337\) −23.6333 + 7.67892i −1.28739 + 0.418297i −0.871176 0.490971i \(-0.836642\pi\)
−0.416211 + 0.909268i \(0.636642\pi\)
\(338\) 13.4875 4.38235i 0.733622 0.238368i
\(339\) −10.3272 + 31.7838i −0.560895 + 1.72626i
\(340\) 0 0
\(341\) 5.07029 + 15.6047i 0.274571 + 0.845044i
\(342\) 12.4523 + 17.1391i 0.673341 + 0.926774i
\(343\) 5.63276i 0.304141i
\(344\) −22.8207 + 16.5802i −1.23041 + 0.893944i
\(345\) 0 0
\(346\) −12.1500 8.82750i −0.653188 0.474569i
\(347\) 7.80431 10.7417i 0.418957 0.576645i −0.546417 0.837513i \(-0.684009\pi\)
0.965375 + 0.260868i \(0.0840087\pi\)
\(348\) 9.74664 + 3.16687i 0.522475 + 0.169762i
\(349\) 18.1283 0.970385 0.485192 0.874407i \(-0.338750\pi\)
0.485192 + 0.874407i \(0.338750\pi\)
\(350\) 0 0
\(351\) 1.41238 0.0753875
\(352\) −7.26649 2.36102i −0.387305 0.125843i
\(353\) 10.4063 14.3230i 0.553871 0.762338i −0.436660 0.899627i \(-0.643839\pi\)
0.990531 + 0.137288i \(0.0438387\pi\)
\(354\) 15.5163 + 11.2733i 0.824684 + 0.599168i
\(355\) 0 0
\(356\) −1.31052 + 0.952148i −0.0694574 + 0.0504638i
\(357\) 1.67730i 0.0887723i
\(358\) 8.14641 + 11.2126i 0.430551 + 0.592603i
\(359\) −10.0568 30.9515i −0.530775 1.63356i −0.752605 0.658473i \(-0.771203\pi\)
0.221829 0.975086i \(-0.428797\pi\)
\(360\) 0 0
\(361\) 1.70276 5.24056i 0.0896190 0.275819i
\(362\) 11.7707 3.82452i 0.618653 0.201012i
\(363\) −17.3277 + 5.63012i −0.909471 + 0.295505i
\(364\) −0.0630078 + 0.193918i −0.00330250 + 0.0101641i
\(365\) 0 0
\(366\) 8.58963 + 26.4362i 0.448987 + 1.38184i
\(367\) −19.3664 26.6556i −1.01092 1.39141i −0.918379 0.395702i \(-0.870501\pi\)
−0.0925399 0.995709i \(-0.529499\pi\)
\(368\) 2.47468i 0.129002i
\(369\) 22.0354 16.0097i 1.14712 0.833429i
\(370\) 0 0
\(371\) 1.67334 + 1.21575i 0.0868756 + 0.0631188i
\(372\) −8.97035 + 12.3466i −0.465091 + 0.640143i
\(373\) −3.29681 1.07120i −0.170703 0.0554646i 0.222419 0.974951i \(-0.428605\pi\)
−0.393121 + 0.919487i \(0.628605\pi\)
\(374\) −3.58870 −0.185567
\(375\) 0 0
\(376\) 3.91861 0.202087
\(377\) 3.67110 + 1.19281i 0.189071 + 0.0614330i
\(378\) −0.546923 + 0.752774i −0.0281307 + 0.0387185i
\(379\) −1.56029 1.13362i −0.0801469 0.0582301i 0.546990 0.837139i \(-0.315773\pi\)
−0.627137 + 0.778909i \(0.715773\pi\)
\(380\) 0 0
\(381\) 14.9613 10.8700i 0.766492 0.556889i
\(382\) 1.77723i 0.0909309i
\(383\) −2.89780 3.98848i −0.148071 0.203802i 0.728538 0.685005i \(-0.240200\pi\)
−0.876609 + 0.481203i \(0.840200\pi\)
\(384\) 1.56029 + 4.80209i 0.0796234 + 0.245056i
\(385\) 0 0
\(386\) −0.580803 + 1.78753i −0.0295621 + 0.0909827i
\(387\) 32.9010 10.6902i 1.67245 0.543413i
\(388\) 10.3445 3.36113i 0.525163 0.170636i
\(389\) −4.13650 + 12.7308i −0.209729 + 0.645479i 0.789757 + 0.613420i \(0.210207\pi\)
−0.999486 + 0.0320593i \(0.989793\pi\)
\(390\) 0 0
\(391\) 0.587616 + 1.80850i 0.0297170 + 0.0914596i
\(392\) 12.3632 + 17.0165i 0.624437 + 0.859464i
\(393\) 6.23172i 0.314349i
\(394\) −12.1831 + 8.85151i −0.613773 + 0.445932i
\(395\) 0 0
\(396\) 4.36492 + 3.17130i 0.219345 + 0.159364i
\(397\) 1.25719 1.73038i 0.0630968 0.0868452i −0.776302 0.630361i \(-0.782907\pi\)
0.839399 + 0.543515i \(0.182907\pi\)
\(398\) 13.0491 + 4.23990i 0.654091 + 0.212527i
\(399\) 5.24660 0.262659
\(400\) 0 0
\(401\) −26.8213 −1.33939 −0.669696 0.742635i \(-0.733576\pi\)
−0.669696 + 0.742635i \(0.733576\pi\)
\(402\) −8.64845 2.81005i −0.431346 0.140153i
\(403\) −3.37871 + 4.65040i −0.168306 + 0.231653i
\(404\) −10.6372 7.72836i −0.529219 0.384500i
\(405\) 0 0
\(406\) −2.05732 + 1.49473i −0.102103 + 0.0741823i
\(407\) 10.2706i 0.509097i
\(408\) −7.45225 10.2571i −0.368942 0.507804i
\(409\) −4.32570 13.3131i −0.213892 0.658292i −0.999230 0.0392250i \(-0.987511\pi\)
0.785338 0.619067i \(-0.212489\pi\)
\(410\) 0 0
\(411\) −15.2973 + 47.0803i −0.754561 + 2.32230i
\(412\) −8.07813 + 2.62474i −0.397981 + 0.129312i
\(413\) 2.51691 0.817793i 0.123849 0.0402410i
\(414\) −1.58870 + 4.88951i −0.0780803 + 0.240307i
\(415\) 0 0
\(416\) −0.827147 2.54570i −0.0405542 0.124813i
\(417\) 10.3033 + 14.1812i 0.504553 + 0.694457i
\(418\) 11.2254i 0.549055i
\(419\) 25.0003 18.1638i 1.22134 0.887357i 0.225132 0.974328i \(-0.427719\pi\)
0.996211 + 0.0869710i \(0.0277187\pi\)
\(420\) 0 0
\(421\) 6.66609 + 4.84320i 0.324885 + 0.236043i 0.738257 0.674519i \(-0.235649\pi\)
−0.413372 + 0.910562i \(0.635649\pi\)
\(422\) 4.46512 6.14570i 0.217358 0.299168i
\(423\) −4.57057 1.48507i −0.222229 0.0722065i
\(424\) −15.6345 −0.759279
\(425\) 0 0
\(426\) −20.2612 −0.981660
\(427\) 3.64777 + 1.18523i 0.176528 + 0.0573575i
\(428\) −0.317141 + 0.436507i −0.0153296 + 0.0210993i
\(429\) 2.95078 + 2.14387i 0.142465 + 0.103507i
\(430\) 0 0
\(431\) −21.9633 + 15.9573i −1.05794 + 0.768636i −0.973705 0.227810i \(-0.926843\pi\)
−0.0842309 + 0.996446i \(0.526843\pi\)
\(432\) 4.15198i 0.199762i
\(433\) −12.6318 17.3862i −0.607045 0.835526i 0.389285 0.921117i \(-0.372722\pi\)
−0.996330 + 0.0855913i \(0.972722\pi\)
\(434\) −1.17022 3.60158i −0.0561726 0.172881i
\(435\) 0 0
\(436\) 2.02252 6.22468i 0.0968612 0.298108i
\(437\) 5.65697 1.83806i 0.270610 0.0879265i
\(438\) 1.52988 0.497087i 0.0731003 0.0237517i
\(439\) 7.97128 24.5331i 0.380448 1.17090i −0.559280 0.828979i \(-0.688922\pi\)
0.939729 0.341921i \(-0.111078\pi\)
\(440\) 0 0
\(441\) −7.97126 24.5330i −0.379584 1.16824i
\(442\) −0.738989 1.01713i −0.0351501 0.0483800i
\(443\) 3.18479i 0.151314i 0.997134 + 0.0756570i \(0.0241054\pi\)
−0.997134 + 0.0756570i \(0.975895\pi\)
\(444\) −7.72851 + 5.61509i −0.366779 + 0.266480i
\(445\) 0 0
\(446\) −9.71455 7.05803i −0.459997 0.334207i
\(447\) −1.10226 + 1.51714i −0.0521353 + 0.0717580i
\(448\) 3.27232 + 1.06324i 0.154602 + 0.0502334i
\(449\) −36.0785 −1.70265 −0.851325 0.524639i \(-0.824200\pi\)
−0.851325 + 0.524639i \(0.824200\pi\)
\(450\) 0 0
\(451\) 14.4324 0.679594
\(452\) −8.72771 2.83581i −0.410517 0.133385i
\(453\) 23.7404 32.6758i 1.11542 1.53524i
\(454\) −17.9871 13.0684i −0.844179 0.613332i
\(455\) 0 0
\(456\) −32.0843 + 23.3106i −1.50249 + 1.09162i
\(457\) 25.5245i 1.19399i −0.802246 0.596994i \(-0.796362\pi\)
0.802246 0.596994i \(-0.203638\pi\)
\(458\) −5.89007 8.10699i −0.275225 0.378815i
\(459\) 0.985894 + 3.03427i 0.0460176 + 0.141628i
\(460\) 0 0
\(461\) −5.14179 + 15.8248i −0.239477 + 0.737034i 0.757019 + 0.653393i \(0.226655\pi\)
−0.996496 + 0.0836412i \(0.973345\pi\)
\(462\) −2.28528 + 0.742534i −0.106321 + 0.0345458i
\(463\) −16.9457 + 5.50599i −0.787534 + 0.255885i −0.675054 0.737769i \(-0.735880\pi\)
−0.112480 + 0.993654i \(0.535880\pi\)
\(464\) 3.50651 10.7919i 0.162786 0.501003i
\(465\) 0 0
\(466\) −3.87554 11.9277i −0.179531 0.552539i
\(467\) −8.37479 11.5269i −0.387539 0.533402i 0.570023 0.821629i \(-0.306934\pi\)
−0.957562 + 0.288227i \(0.906934\pi\)
\(468\) 1.89017i 0.0873731i
\(469\) −1.01512 + 0.737531i −0.0468741 + 0.0340560i
\(470\) 0 0
\(471\) −5.86263 4.25945i −0.270136 0.196265i
\(472\) −11.7581 + 16.1836i −0.541210 + 0.744912i
\(473\) 17.4335 + 5.66447i 0.801591 + 0.260453i
\(474\) 16.1750 0.742941
\(475\) 0 0
\(476\) −0.460582 −0.0211107
\(477\) 18.2357 + 5.92514i 0.834955 + 0.271293i
\(478\) 10.7323 14.7717i 0.490883 0.675642i
\(479\) 2.35314 + 1.70966i 0.107518 + 0.0781162i 0.640245 0.768171i \(-0.278833\pi\)
−0.532727 + 0.846287i \(0.678833\pi\)
\(480\) 0 0
\(481\) −2.91097 + 2.11494i −0.132729 + 0.0964330i
\(482\) 6.78945i 0.309251i
\(483\) 0.748388 + 1.03007i 0.0340529 + 0.0468697i
\(484\) −1.54601 4.75814i −0.0702734 0.216279i
\(485\) 0 0
\(486\) 7.65966 23.5740i 0.347449 1.06934i
\(487\) −16.2300 + 5.27344i −0.735450 + 0.238962i −0.652709 0.757609i \(-0.726368\pi\)
−0.0827414 + 0.996571i \(0.526368\pi\)
\(488\) −27.5731 + 8.95903i −1.24817 + 0.405556i
\(489\) 19.4701 59.9227i 0.880467 2.70980i
\(490\) 0 0
\(491\) 9.51057 + 29.2705i 0.429206 + 1.32096i 0.898909 + 0.438135i \(0.144361\pi\)
−0.469703 + 0.882824i \(0.655639\pi\)
\(492\) 7.89036 + 10.8602i 0.355725 + 0.489613i
\(493\) 8.71937i 0.392701i
\(494\) −3.18158 + 2.31156i −0.143146 + 0.104002i
\(495\) 0 0
\(496\) 13.6708 + 9.93239i 0.613836 + 0.445978i
\(497\) −1.64329 + 2.26179i −0.0737116 + 0.101455i
\(498\) −2.73377 0.888257i −0.122503 0.0398037i
\(499\) 11.8824 0.531927 0.265964 0.963983i \(-0.414310\pi\)
0.265964 + 0.963983i \(0.414310\pi\)
\(500\) 0 0
\(501\) −49.5730 −2.21476
\(502\) −4.02365 1.30736i −0.179584 0.0583504i
\(503\) −1.75056 + 2.40944i −0.0780536 + 0.107432i −0.846259 0.532772i \(-0.821150\pi\)
0.768205 + 0.640204i \(0.221150\pi\)
\(504\) −3.82652 2.78013i −0.170447 0.123837i
\(505\) 0 0
\(506\) −2.20390 + 1.60123i −0.0979752 + 0.0711831i
\(507\) 32.5584i 1.44597i
\(508\) 2.98488 + 4.10833i 0.132432 + 0.182278i
\(509\) 11.3458 + 34.9189i 0.502895 + 1.54775i 0.804280 + 0.594250i \(0.202551\pi\)
−0.301385 + 0.953503i \(0.597449\pi\)
\(510\) 0 0
\(511\) 0.0685902 0.211099i 0.00303425 0.00933846i
\(512\) −19.5416 + 6.34944i −0.863624 + 0.280608i
\(513\) 9.49119 3.08388i 0.419046 0.136156i
\(514\) −8.26561 + 25.4389i −0.364580 + 1.12206i
\(515\) 0 0
\(516\) 5.26866 + 16.2153i 0.231940 + 0.713837i
\(517\) −1.49678 2.06014i −0.0658282 0.0906047i
\(518\) 2.37047i 0.104152i
\(519\) −27.8942 + 20.2663i −1.22442 + 0.889594i
\(520\) 0 0
\(521\) −2.02286 1.46969i −0.0886229 0.0643883i 0.542591 0.839997i \(-0.317443\pi\)
−0.631214 + 0.775608i \(0.717443\pi\)
\(522\) −13.8564 + 19.0718i −0.606480 + 0.834749i
\(523\) −40.0640 13.0176i −1.75188 0.569220i −0.755570 0.655068i \(-0.772640\pi\)
−0.996308 + 0.0858485i \(0.972640\pi\)
\(524\) 1.71121 0.0747545
\(525\) 0 0
\(526\) 7.52922 0.328290
\(527\) −12.3491 4.01245i −0.537934 0.174785i
\(528\) 6.30233 8.67441i 0.274274 0.377505i
\(529\) −17.4396 12.6706i −0.758243 0.550896i
\(530\) 0 0
\(531\) 19.8476 14.4201i 0.861312 0.625780i
\(532\) 1.44070i 0.0624623i
\(533\) 2.97193 + 4.09051i 0.128729 + 0.177180i
\(534\) −2.06668 6.36058i −0.0894339 0.275249i
\(535\) 0 0
\(536\) 2.93090 9.02038i 0.126596 0.389621i
\(537\) 30.2616 9.83258i 1.30588 0.424307i
\(538\) 14.0641 4.56972i 0.606348 0.197014i
\(539\) 4.22378 12.9995i 0.181931 0.559926i
\(540\) 0 0
\(541\) −8.45136 26.0106i −0.363352 1.11828i −0.951006 0.309171i \(-0.899948\pi\)
0.587654 0.809112i \(-0.300052\pi\)
\(542\) −7.89572 10.8675i −0.339150 0.466800i
\(543\) 28.4140i 1.21936i
\(544\) 4.89162 3.55397i 0.209727 0.152375i
\(545\) 0 0
\(546\) −0.681042 0.494806i −0.0291459 0.0211757i
\(547\) 11.9551 16.4547i 0.511162 0.703554i −0.472953 0.881088i \(-0.656812\pi\)
0.984115 + 0.177534i \(0.0568119\pi\)
\(548\) −12.9281 4.20059i −0.552261 0.179441i
\(549\) 35.5558 1.51748
\(550\) 0 0
\(551\) 27.2742 1.16192
\(552\) −9.15318 2.97405i −0.389585 0.126584i
\(553\) 1.31187 1.80564i 0.0557865 0.0767836i
\(554\) −15.5517 11.2990i −0.660728 0.480047i
\(555\) 0 0
\(556\) −3.89412 + 2.82924i −0.165147 + 0.119987i
\(557\) 28.2605i 1.19744i 0.800960 + 0.598718i \(0.204323\pi\)
−0.800960 + 0.598718i \(0.795677\pi\)
\(558\) −20.6345 28.4010i −0.873529 1.20231i
\(559\) 1.98446 + 6.10753i 0.0839336 + 0.258321i
\(560\) 0 0
\(561\) −2.54599 + 7.83576i −0.107492 + 0.330826i
\(562\) −5.47193 + 1.77794i −0.230819 + 0.0749978i
\(563\) 12.2928 3.99418i 0.518081 0.168335i −0.0382934 0.999267i \(-0.512192\pi\)
0.556374 + 0.830932i \(0.312192\pi\)
\(564\) 0.731916 2.25261i 0.0308192 0.0948518i
\(565\) 0 0
\(566\) −4.14264 12.7497i −0.174128 0.535912i
\(567\) −1.45432 2.00170i −0.0610757 0.0840635i
\(568\) 21.1326i 0.886703i
\(569\) −2.49536 + 1.81298i −0.104611 + 0.0760043i −0.638861 0.769322i \(-0.720594\pi\)
0.534250 + 0.845326i \(0.320594\pi\)
\(570\) 0 0
\(571\) 3.33935 + 2.42618i 0.139747 + 0.101532i 0.655463 0.755228i \(-0.272474\pi\)
−0.515715 + 0.856760i \(0.672474\pi\)
\(572\) −0.588700 + 0.810275i −0.0246148 + 0.0338793i
\(573\) −3.88050 1.26085i −0.162110 0.0526727i
\(574\) −3.33100 −0.139033
\(575\) 0 0
\(576\) 31.8961 1.32901
\(577\) 6.04463 + 1.96402i 0.251641 + 0.0817632i 0.432121 0.901815i \(-0.357765\pi\)
−0.180480 + 0.983579i \(0.557765\pi\)
\(578\) −9.65907 + 13.2946i −0.401764 + 0.552981i
\(579\) 3.49094 + 2.53631i 0.145078 + 0.105406i
\(580\) 0 0
\(581\) −0.320880 + 0.233133i −0.0133124 + 0.00967200i
\(582\) 44.9063i 1.86143i
\(583\) 5.97185 + 8.21955i 0.247329 + 0.340419i
\(584\) 0.518464 + 1.59567i 0.0214542 + 0.0660293i
\(585\) 0 0
\(586\) 6.80868 20.9550i 0.281264 0.865642i
\(587\) 20.0711 6.52148i 0.828421 0.269170i 0.136041 0.990703i \(-0.456562\pi\)
0.692380 + 0.721533i \(0.256562\pi\)
\(588\) 12.0911 3.92864i 0.498629 0.162014i
\(589\) −12.5509 + 38.6278i −0.517153 + 1.59163i
\(590\) 0 0
\(591\) 10.6836 + 32.8808i 0.439466 + 1.35254i
\(592\) 6.21729 + 8.55736i 0.255529 + 0.351705i
\(593\) 21.6529i 0.889177i −0.895735 0.444589i \(-0.853350\pi\)
0.895735 0.444589i \(-0.146650\pi\)
\(594\) −3.69767 + 2.68651i −0.151717 + 0.110229i
\(595\) 0 0
\(596\) −0.416600 0.302678i −0.0170646 0.0123982i
\(597\) 18.5153 25.4841i 0.757779 1.04299i
\(598\) −0.907658 0.294916i −0.0371169 0.0120600i
\(599\) 3.38501 0.138308 0.0691539 0.997606i \(-0.477970\pi\)
0.0691539 + 0.997606i \(0.477970\pi\)
\(600\) 0 0
\(601\) 28.8265 1.17586 0.587928 0.808913i \(-0.299944\pi\)
0.587928 + 0.808913i \(0.299944\pi\)
\(602\) −4.02365 1.30736i −0.163992 0.0532841i
\(603\) −6.83706 + 9.41040i −0.278426 + 0.383221i
\(604\) 8.97268 + 6.51903i 0.365093 + 0.265256i
\(605\) 0 0
\(606\) 43.9168 31.9074i 1.78400 1.29615i
\(607\) 15.6708i 0.636059i −0.948081 0.318029i \(-0.896979\pi\)
0.948081 0.318029i \(-0.103021\pi\)
\(608\) −11.1168 15.3010i −0.450847 0.620537i
\(609\) 1.80412 + 5.55250i 0.0731065 + 0.224999i
\(610\) 0 0
\(611\) 0.275678 0.848451i 0.0111528 0.0343247i
\(612\) −4.06071 + 1.31941i −0.164145 + 0.0533338i
\(613\) 36.3308 11.8046i 1.46739 0.476783i 0.537070 0.843538i \(-0.319531\pi\)
0.930318 + 0.366754i \(0.119531\pi\)
\(614\) 8.90440 27.4049i 0.359352 1.10597i
\(615\) 0 0
\(616\) −0.774467 2.38357i −0.0312042 0.0960366i
\(617\) 7.77744 + 10.7047i 0.313108 + 0.430956i 0.936347 0.351075i \(-0.114184\pi\)
−0.623239 + 0.782031i \(0.714184\pi\)
\(618\) 35.0678i 1.41064i
\(619\) 4.89021 3.55294i 0.196554 0.142805i −0.485155 0.874428i \(-0.661237\pi\)
0.681709 + 0.731623i \(0.261237\pi\)
\(620\) 0 0
\(621\) 1.95931 + 1.42352i 0.0786243 + 0.0571239i
\(622\) −10.5672 + 14.5445i −0.423707 + 0.583182i
\(623\) −0.877660 0.285169i −0.0351627 0.0114250i
\(624\) 3.75634 0.150374
\(625\) 0 0
\(626\) −7.95456 −0.317928
\(627\) 24.5103 + 7.96386i 0.978845 + 0.318046i
\(628\) 1.16963 1.60986i 0.0466733 0.0642403i
\(629\) −6.57556 4.77742i −0.262185 0.190488i
\(630\) 0 0
\(631\) 30.5691 22.2097i 1.21694 0.884156i 0.221094 0.975253i \(-0.429037\pi\)
0.995842 + 0.0910970i \(0.0290373\pi\)
\(632\) 16.8706i 0.671076i
\(633\) −10.2511 14.1094i −0.407445 0.560800i
\(634\) 4.56614 + 14.0531i 0.181344 + 0.558121i
\(635\) 0 0
\(636\) −2.92021 + 8.98747i −0.115794 + 0.356376i
\(637\) 4.55415 1.47973i 0.180442 0.0586292i
\(638\) −11.8799 + 3.86002i −0.470331 + 0.152820i
\(639\) −8.00878 + 24.6485i −0.316823 + 0.975080i
\(640\) 0 0
\(641\) −6.44517 19.8362i −0.254569 0.783482i −0.993914 0.110156i \(-0.964865\pi\)
0.739345 0.673326i \(-0.235135\pi\)
\(642\) −1.30935 1.80217i −0.0516760 0.0711259i
\(643\) 37.5552i 1.48103i −0.672039 0.740516i \(-0.734581\pi\)
0.672039 0.740516i \(-0.265419\pi\)
\(644\) −0.282853 + 0.205505i −0.0111460 + 0.00809803i
\(645\) 0 0
\(646\) −7.18685 5.22155i −0.282763 0.205439i
\(647\) 16.1055 22.1673i 0.633171 0.871485i −0.365057 0.930985i \(-0.618951\pi\)
0.998228 + 0.0594998i \(0.0189506\pi\)
\(648\) 17.7871 + 5.77938i 0.698743 + 0.227035i
\(649\) 12.9994 0.510272
\(650\) 0 0
\(651\) −8.69410 −0.340749
\(652\) 16.4546 + 5.34642i 0.644411 + 0.209382i
\(653\) 13.5462 18.6447i 0.530103 0.729624i −0.457044 0.889444i \(-0.651092\pi\)
0.987146 + 0.159821i \(0.0510916\pi\)
\(654\) 21.8611 + 15.8830i 0.854838 + 0.621076i
\(655\) 0 0
\(656\) 12.0249 8.73658i 0.469492 0.341106i
\(657\) 2.05763i 0.0802760i
\(658\) 0.345457 + 0.475480i 0.0134673 + 0.0185361i
\(659\) −6.32981 19.4811i −0.246574 0.758878i −0.995374 0.0960808i \(-0.969369\pi\)
0.748799 0.662797i \(-0.230631\pi\)
\(660\) 0 0
\(661\) 4.32314 13.3053i 0.168151 0.517515i −0.831104 0.556117i \(-0.812291\pi\)
0.999255 + 0.0386024i \(0.0122906\pi\)
\(662\) −19.0239 + 6.18124i −0.739385 + 0.240241i
\(663\) −2.74513 + 0.891948i −0.106612 + 0.0346404i
\(664\) 0.926457 2.85134i 0.0359535 0.110654i
\(665\) 0 0
\(666\) −6.79055 20.8992i −0.263129 0.809826i
\(667\) 3.89046 + 5.35475i 0.150639 + 0.207337i
\(668\) 13.6126i 0.526687i
\(669\) −22.3028 + 16.2040i −0.862278 + 0.626482i
\(670\) 0 0
\(671\) 15.2420 + 11.0740i 0.588411 + 0.427506i
\(672\) 2.37964 3.27529i 0.0917966 0.126347i
\(673\) 7.46172 + 2.42446i 0.287628 + 0.0934561i 0.449278 0.893392i \(-0.351681\pi\)
−0.161649 + 0.986848i \(0.551681\pi\)
\(674\) 28.1720 1.08514
\(675\) 0 0
\(676\) 8.94042 0.343862
\(677\) −13.6936 4.44932i −0.526287 0.171001i 0.0338094 0.999428i \(-0.489236\pi\)
−0.560097 + 0.828427i \(0.689236\pi\)
\(678\) 22.2698 30.6518i 0.855268 1.17718i
\(679\) 5.01297 + 3.64213i 0.192380 + 0.139772i
\(680\) 0 0
\(681\) −41.2953 + 30.0028i −1.58244 + 1.14971i
\(682\) 18.6016i 0.712291i
\(683\) 7.44957 + 10.2535i 0.285050 + 0.392338i 0.927398 0.374075i \(-0.122040\pi\)
−0.642348 + 0.766413i \(0.722040\pi\)
\(684\) 4.12710 + 12.7019i 0.157804 + 0.485669i
\(685\) 0 0
\(686\) −1.97335 + 6.07334i −0.0753427 + 0.231881i
\(687\) −21.8799 + 7.10922i −0.834771 + 0.271234i
\(688\) 17.9543 5.83371i 0.684501 0.222408i
\(689\) −1.09990 + 3.38516i −0.0419030 + 0.128964i
\(690\) 0 0
\(691\) 1.77540 + 5.46411i 0.0675392 + 0.207864i 0.979130 0.203234i \(-0.0651452\pi\)
−0.911591 + 0.411098i \(0.865145\pi\)
\(692\) −5.56507 7.65966i −0.211552 0.291177i
\(693\) 3.07364i 0.116758i
\(694\) −12.1779 + 8.84778i −0.462268 + 0.335857i
\(695\) 0 0
\(696\) −35.7024 25.9393i −1.35329 0.983226i
\(697\) −6.71326 + 9.24002i −0.254283 + 0.349991i
\(698\) −19.5462 6.35095i −0.739835 0.240387i
\(699\) −28.7931 −1.08905
\(700\) 0 0
\(701\) −30.5834 −1.15512 −0.577560 0.816348i \(-0.695995\pi\)
−0.577560 + 0.816348i \(0.695995\pi\)
\(702\) −1.52286 0.494806i −0.0574765 0.0186752i
\(703\) −14.9438 + 20.5683i −0.563615 + 0.775749i
\(704\) 13.6732 + 9.93416i 0.515328 + 0.374408i
\(705\) 0 0
\(706\) −16.2381 + 11.7977i −0.611128 + 0.444011i
\(707\) 7.49036i 0.281704i
\(708\) 7.10696 + 9.78189i 0.267096 + 0.367626i
\(709\) 8.36497 + 25.7447i 0.314153 + 0.966864i 0.976102 + 0.217315i \(0.0697297\pi\)
−0.661949 + 0.749549i \(0.730270\pi\)
\(710\) 0 0
\(711\) 6.39358 19.6774i 0.239778 0.737961i
\(712\) 6.63412 2.15556i 0.248624 0.0807829i
\(713\) −9.37412 + 3.04584i −0.351064 + 0.114067i
\(714\) 0.587616 1.80850i 0.0219910 0.0676813i
\(715\) 0 0
\(716\) 2.70000 + 8.30973i 0.100904 + 0.310549i
\(717\) −24.6394 33.9132i −0.920174 1.26651i
\(718\) 36.8957i 1.37693i
\(719\) −13.5159 + 9.81991i −0.504060 + 0.366221i −0.810565 0.585648i \(-0.800840\pi\)
0.306506 + 0.951869i \(0.400840\pi\)
\(720\) 0 0
\(721\) −3.91468 2.84418i −0.145790 0.105923i
\(722\) −3.67189 + 5.05393i −0.136654 + 0.188088i
\(723\) −14.8245 4.81676i −0.551327 0.179137i
\(724\) 7.80240 0.289974
\(725\) 0 0
\(726\) 20.6555 0.766597
\(727\) −11.1279 3.61568i −0.412712 0.134098i 0.0952994 0.995449i \(-0.469619\pi\)
−0.508011 + 0.861350i \(0.669619\pi\)
\(728\) 0.516085 0.710330i 0.0191274 0.0263266i
\(729\) −31.2899 22.7335i −1.15889 0.841980i
\(730\) 0 0
\(731\) −11.7358 + 8.52655i −0.434064 + 0.315366i
\(732\) 17.5237i 0.647694i
\(733\) −20.0481 27.5938i −0.740493 1.01920i −0.998590 0.0530818i \(-0.983096\pi\)
0.258098 0.966119i \(-0.416904\pi\)
\(734\) 11.5428 + 35.5252i 0.426054 + 1.31126i
\(735\) 0 0
\(736\) 1.41832 4.36514i 0.0522800 0.160901i
\(737\) −5.86180 + 1.90461i −0.215922 + 0.0701574i
\(738\) −29.3677 + 9.54213i −1.08104 + 0.351251i
\(739\) −1.77536 + 5.46398i −0.0653075 + 0.200996i −0.978386 0.206789i \(-0.933699\pi\)
0.913078 + 0.407785i \(0.133699\pi\)
\(740\) 0 0
\(741\) 2.79001 + 8.58677i 0.102494 + 0.315443i
\(742\) −1.37831 1.89708i −0.0505992 0.0696438i
\(743\) 36.4348i 1.33666i 0.743863 + 0.668332i \(0.232991\pi\)
−0.743863 + 0.668332i \(0.767009\pi\)
\(744\) 53.1667 38.6278i 1.94918 1.41617i
\(745\) 0 0
\(746\) 3.17940 + 2.30997i 0.116406 + 0.0845740i
\(747\) −2.16119 + 2.97463i −0.0790739 + 0.108836i
\(748\) −2.15167 0.699122i −0.0786730 0.0255624i
\(749\) −0.307374 −0.0112312
\(750\) 0 0
\(751\) 1.48912 0.0543387 0.0271693 0.999631i \(-0.491351\pi\)
0.0271693 + 0.999631i \(0.491351\pi\)
\(752\) −2.49419 0.810412i −0.0909538 0.0295527i
\(753\) −5.70913 + 7.85795i −0.208052 + 0.286360i
\(754\) −3.54036 2.57222i −0.128932 0.0936748i
\(755\) 0 0
\(756\) −0.474567 + 0.344793i −0.0172599 + 0.0125400i
\(757\) 5.53316i 0.201106i 0.994932 + 0.100553i \(0.0320612\pi\)
−0.994932 + 0.100553i \(0.967939\pi\)
\(758\) 1.28519 + 1.76891i 0.0466802 + 0.0642498i
\(759\) 1.93265 + 5.94810i 0.0701509 + 0.215902i
\(760\) 0 0
\(761\) −5.76925 + 17.7559i −0.209135 + 0.643652i 0.790383 + 0.612613i \(0.209882\pi\)
−0.999518 + 0.0310389i \(0.990118\pi\)
\(762\) −19.9397 + 6.47880i −0.722339 + 0.234702i
\(763\) 3.54610 1.15220i 0.128377 0.0417123i
\(764\) 0.346225 1.06557i 0.0125260 0.0385510i
\(765\) 0 0
\(766\) 1.72716 + 5.31564i 0.0624047 + 0.192062i
\(767\) 2.67686 + 3.68438i 0.0966557 + 0.133035i
\(768\) 38.2653i 1.38078i
\(769\) −10.6332 + 7.72544i −0.383441 + 0.278587i −0.762763 0.646679i \(-0.776158\pi\)
0.379321 + 0.925265i \(0.376158\pi\)
\(770\) 0 0
\(771\) 49.6807 + 36.0952i 1.78921 + 1.29994i
\(772\) −0.696463 + 0.958599i −0.0250663 + 0.0345007i
\(773\) 26.6045 + 8.64431i 0.956896 + 0.310914i 0.745514 0.666489i \(-0.232204\pi\)
0.211381 + 0.977404i \(0.432204\pi\)
\(774\) −39.2195 −1.40972
\(775\) 0 0
\(776\) −46.8376 −1.68137
\(777\) −5.17581 1.68172i −0.185681 0.0603314i
\(778\) 8.92008 12.2774i 0.319800 0.440168i
\(779\)