Properties

Label 76.3.l.a.23.2
Level $76$
Weight $3$
Character 76.23
Analytic conductor $2.071$
Analytic rank $0$
Dimension $108$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,3,Mod(23,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.23");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 76.l (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.07085000914\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(18\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 23.2
Character \(\chi\) \(=\) 76.23
Dual form 76.3.l.a.43.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.92177 + 0.553897i) q^{2} +(4.90961 - 0.865697i) q^{3} +(3.38640 - 2.12892i) q^{4} +(2.37531 - 1.99312i) q^{5} +(-8.95563 + 4.38309i) q^{6} +(-8.41114 - 4.85617i) q^{7} +(-5.32867 + 5.96702i) q^{8} +(14.8976 - 5.42229i) q^{9} +O(q^{10})\) \(q+(-1.92177 + 0.553897i) q^{2} +(4.90961 - 0.865697i) q^{3} +(3.38640 - 2.12892i) q^{4} +(2.37531 - 1.99312i) q^{5} +(-8.95563 + 4.38309i) q^{6} +(-8.41114 - 4.85617i) q^{7} +(-5.32867 + 5.96702i) q^{8} +(14.8976 - 5.42229i) q^{9} +(-3.46081 + 5.14599i) q^{10} +(7.34500 - 4.24064i) q^{11} +(14.7829 - 13.3838i) q^{12} +(-3.81970 + 21.6626i) q^{13} +(18.8541 + 4.67354i) q^{14} +(9.93640 - 11.8417i) q^{15} +(6.93536 - 14.4188i) q^{16} +(15.0608 + 5.48169i) q^{17} +(-25.6264 + 18.6721i) q^{18} +(-18.9737 + 0.998863i) q^{19} +(3.80053 - 11.8063i) q^{20} +(-45.4994 - 16.5604i) q^{21} +(-11.7665 + 12.2179i) q^{22} +(-4.86968 + 5.80346i) q^{23} +(-20.9961 + 33.9087i) q^{24} +(-2.67164 + 15.1516i) q^{25} +(-4.65827 - 43.7463i) q^{26} +(29.5904 - 17.0841i) q^{27} +(-38.8219 + 1.46176i) q^{28} +(-2.00734 + 0.730613i) q^{29} +(-12.5364 + 28.2608i) q^{30} +(6.63446 + 3.83041i) q^{31} +(-5.34165 + 31.5510i) q^{32} +(32.3900 - 27.1784i) q^{33} +(-31.9797 - 2.19240i) q^{34} +(-29.6580 + 5.22950i) q^{35} +(38.9056 - 50.0779i) q^{36} -29.7012 q^{37} +(35.9099 - 12.4291i) q^{38} +109.662i q^{39} +(-0.764244 + 24.7942i) q^{40} +(-5.39602 - 30.6024i) q^{41} +(96.6121 + 6.62334i) q^{42} +(-10.4150 - 12.4121i) q^{43} +(15.8451 - 29.9974i) q^{44} +(24.5791 - 42.5723i) q^{45} +(6.14388 - 13.8502i) q^{46} +(-17.8508 - 49.0447i) q^{47} +(21.5676 - 76.7944i) q^{48} +(22.6648 + 39.2566i) q^{49} +(-3.25817 - 30.5978i) q^{50} +(78.6883 + 13.8749i) q^{51} +(33.1830 + 81.4900i) q^{52} +(55.0654 + 46.2053i) q^{53} +(-47.4032 + 49.2217i) q^{54} +(8.99453 - 24.7123i) q^{55} +(73.7970 - 24.3125i) q^{56} +(-92.2889 + 21.3295i) q^{57} +(3.45297 - 2.51593i) q^{58} +(-18.8009 + 51.6550i) q^{59} +(8.43841 - 61.2547i) q^{60} +(-50.2381 - 42.1547i) q^{61} +(-14.8716 - 3.68635i) q^{62} +(-151.637 - 26.7378i) q^{63} +(-7.21060 - 63.5925i) q^{64} +(34.1032 + 59.0685i) q^{65} +(-47.1920 + 70.1713i) q^{66} +(-11.7982 - 32.4153i) q^{67} +(62.6720 - 13.5002i) q^{68} +(-18.8842 + 32.7084i) q^{69} +(54.0992 - 26.4774i) q^{70} +(-18.4733 - 22.0156i) q^{71} +(-47.0295 + 117.788i) q^{72} +(-7.46340 - 42.3270i) q^{73} +(57.0788 - 16.4514i) q^{74} +76.7015i q^{75} +(-62.1260 + 43.7762i) q^{76} -82.3730 q^{77} +(-60.7413 - 210.744i) q^{78} +(45.6288 - 8.04560i) q^{79} +(-12.2647 - 48.0720i) q^{80} +(21.1862 - 17.7773i) q^{81} +(27.3205 + 55.8218i) q^{82} +(123.443 + 71.2697i) q^{83} +(-189.335 + 40.7846i) q^{84} +(46.6998 - 16.9973i) q^{85} +(26.8902 + 18.0843i) q^{86} +(-9.22279 + 5.32478i) q^{87} +(-13.8351 + 66.4247i) q^{88} +(14.4005 - 81.6693i) q^{89} +(-23.6548 + 95.4285i) q^{90} +(137.325 - 163.658i) q^{91} +(-4.13554 + 30.0200i) q^{92} +(35.8886 + 13.0624i) q^{93} +(61.4708 + 84.3650i) q^{94} +(-43.0776 + 40.1895i) q^{95} +(1.08821 + 159.527i) q^{96} +(143.478 + 52.2217i) q^{97} +(-65.3007 - 62.8882i) q^{98} +(86.4289 - 103.002i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 6 q^{2} - 12 q^{5} + 12 q^{6} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 6 q^{2} - 12 q^{5} + 12 q^{6} - 3 q^{8} - 9 q^{10} - 3 q^{12} - 36 q^{13} - 63 q^{14} - 48 q^{16} - 12 q^{17} - 12 q^{18} + 18 q^{20} + 6 q^{21} - 18 q^{22} + 72 q^{24} - 12 q^{25} + 69 q^{26} - 216 q^{28} - 12 q^{29} - 270 q^{30} - 261 q^{32} - 6 q^{33} - 120 q^{34} - 165 q^{36} - 24 q^{37} + 240 q^{38} + 330 q^{40} - 168 q^{41} + 153 q^{42} + 57 q^{44} - 6 q^{45} + 132 q^{46} + 549 q^{48} + 120 q^{49} + 114 q^{50} + 249 q^{52} - 36 q^{53} + 51 q^{54} - 306 q^{56} - 12 q^{57} - 84 q^{58} + 576 q^{60} - 276 q^{61} + 432 q^{62} + 207 q^{64} - 126 q^{65} + 648 q^{66} + 234 q^{68} - 294 q^{69} + 459 q^{70} + 498 q^{72} + 276 q^{73} + 459 q^{74} - 582 q^{76} - 468 q^{77} - 903 q^{78} + 57 q^{80} - 270 q^{81} - 321 q^{82} - 621 q^{84} + 900 q^{85} - 456 q^{86} - 699 q^{88} + 348 q^{89} - 1566 q^{90} - 348 q^{92} + 366 q^{93} + 162 q^{94} - 726 q^{96} + 96 q^{97} - 1659 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.92177 + 0.553897i −0.960885 + 0.276949i
\(3\) 4.90961 0.865697i 1.63654 0.288566i 0.721645 0.692264i \(-0.243387\pi\)
0.914892 + 0.403698i \(0.132275\pi\)
\(4\) 3.38640 2.12892i 0.846599 0.532231i
\(5\) 2.37531 1.99312i 0.475062 0.398624i −0.373575 0.927600i \(-0.621868\pi\)
0.848637 + 0.528976i \(0.177424\pi\)
\(6\) −8.95563 + 4.38309i −1.49261 + 0.730515i
\(7\) −8.41114 4.85617i −1.20159 0.693739i −0.240682 0.970604i \(-0.577371\pi\)
−0.960909 + 0.276865i \(0.910705\pi\)
\(8\) −5.32867 + 5.96702i −0.666083 + 0.745877i
\(9\) 14.8976 5.42229i 1.65529 0.602476i
\(10\) −3.46081 + 5.14599i −0.346081 + 0.514599i
\(11\) 7.34500 4.24064i 0.667727 0.385512i −0.127488 0.991840i \(-0.540691\pi\)
0.795215 + 0.606328i \(0.207358\pi\)
\(12\) 14.7829 13.3838i 1.23191 1.11532i
\(13\) −3.81970 + 21.6626i −0.293823 + 1.66635i 0.378124 + 0.925755i \(0.376569\pi\)
−0.671947 + 0.740599i \(0.734542\pi\)
\(14\) 18.8541 + 4.67354i 1.34672 + 0.333824i
\(15\) 9.93640 11.8417i 0.662427 0.789449i
\(16\) 6.93536 14.4188i 0.433460 0.901173i
\(17\) 15.0608 + 5.48169i 0.885931 + 0.322453i 0.744601 0.667510i \(-0.232640\pi\)
0.141330 + 0.989963i \(0.454862\pi\)
\(18\) −25.6264 + 18.6721i −1.42369 + 1.03734i
\(19\) −18.9737 + 0.998863i −0.998617 + 0.0525717i
\(20\) 3.80053 11.8063i 0.190027 0.590317i
\(21\) −45.4994 16.5604i −2.16664 0.788592i
\(22\) −11.7665 + 12.2179i −0.534842 + 0.555359i
\(23\) −4.86968 + 5.80346i −0.211725 + 0.252324i −0.861447 0.507848i \(-0.830441\pi\)
0.649721 + 0.760172i \(0.274886\pi\)
\(24\) −20.9961 + 33.9087i −0.874836 + 1.41286i
\(25\) −2.67164 + 15.1516i −0.106866 + 0.606066i
\(26\) −4.65827 43.7463i −0.179164 1.68255i
\(27\) 29.5904 17.0841i 1.09594 0.632743i
\(28\) −38.8219 + 1.46176i −1.38650 + 0.0522056i
\(29\) −2.00734 + 0.730613i −0.0692188 + 0.0251936i −0.376397 0.926458i \(-0.622837\pi\)
0.307179 + 0.951652i \(0.400615\pi\)
\(30\) −12.5364 + 28.2608i −0.417879 + 0.942028i
\(31\) 6.63446 + 3.83041i 0.214015 + 0.123562i 0.603176 0.797608i \(-0.293902\pi\)
−0.389161 + 0.921170i \(0.627235\pi\)
\(32\) −5.34165 + 31.5510i −0.166926 + 0.985969i
\(33\) 32.3900 27.1784i 0.981514 0.823588i
\(34\) −31.9797 2.19240i −0.940580 0.0644824i
\(35\) −29.6580 + 5.22950i −0.847371 + 0.149414i
\(36\) 38.9056 50.0779i 1.08071 1.39105i
\(37\) −29.7012 −0.802735 −0.401367 0.915917i \(-0.631465\pi\)
−0.401367 + 0.915917i \(0.631465\pi\)
\(38\) 35.9099 12.4291i 0.944996 0.327081i
\(39\) 109.662i 2.81184i
\(40\) −0.764244 + 24.7942i −0.0191061 + 0.619854i
\(41\) −5.39602 30.6024i −0.131610 0.746399i −0.977160 0.212503i \(-0.931838\pi\)
0.845550 0.533896i \(-0.179273\pi\)
\(42\) 96.6121 + 6.62334i 2.30029 + 0.157699i
\(43\) −10.4150 12.4121i −0.242208 0.288653i 0.631222 0.775603i \(-0.282554\pi\)
−0.873430 + 0.486950i \(0.838109\pi\)
\(44\) 15.8451 29.9974i 0.360115 0.681759i
\(45\) 24.5791 42.5723i 0.546203 0.946052i
\(46\) 6.14388 13.8502i 0.133563 0.301092i
\(47\) −17.8508 49.0447i −0.379804 1.04350i −0.971437 0.237296i \(-0.923739\pi\)
0.591633 0.806207i \(-0.298483\pi\)
\(48\) 21.5676 76.7944i 0.449326 1.59988i
\(49\) 22.6648 + 39.2566i 0.462548 + 0.801156i
\(50\) −3.25817 30.5978i −0.0651634 0.611956i
\(51\) 78.6883 + 13.8749i 1.54291 + 0.272056i
\(52\) 33.1830 + 81.4900i 0.638135 + 1.56712i
\(53\) 55.0654 + 46.2053i 1.03897 + 0.871799i 0.991891 0.127093i \(-0.0405645\pi\)
0.0470783 + 0.998891i \(0.485009\pi\)
\(54\) −47.4032 + 49.2217i −0.877837 + 0.911512i
\(55\) 8.99453 24.7123i 0.163537 0.449314i
\(56\) 73.7970 24.3125i 1.31780 0.434151i
\(57\) −92.2889 + 21.3295i −1.61910 + 0.374202i
\(58\) 3.45297 2.51593i 0.0595339 0.0433781i
\(59\) −18.8009 + 51.6550i −0.318659 + 0.875508i 0.672171 + 0.740396i \(0.265362\pi\)
−0.990830 + 0.135113i \(0.956860\pi\)
\(60\) 8.43841 61.2547i 0.140640 1.02091i
\(61\) −50.2381 42.1547i −0.823575 0.691061i 0.130232 0.991484i \(-0.458428\pi\)
−0.953806 + 0.300422i \(0.902872\pi\)
\(62\) −14.8716 3.68635i −0.239864 0.0594573i
\(63\) −151.637 26.7378i −2.40694 0.424409i
\(64\) −7.21060 63.5925i −0.112666 0.993633i
\(65\) 34.1032 + 59.0685i 0.524665 + 0.908746i
\(66\) −47.1920 + 70.1713i −0.715030 + 1.06320i
\(67\) −11.7982 32.4153i −0.176093 0.483810i 0.819976 0.572398i \(-0.193987\pi\)
−0.996068 + 0.0885878i \(0.971765\pi\)
\(68\) 62.6720 13.5002i 0.921648 0.198532i
\(69\) −18.8842 + 32.7084i −0.273684 + 0.474035i
\(70\) 54.0992 26.4774i 0.772846 0.378248i
\(71\) −18.4733 22.0156i −0.260187 0.310079i 0.620098 0.784525i \(-0.287093\pi\)
−0.880285 + 0.474446i \(0.842648\pi\)
\(72\) −47.0295 + 117.788i −0.653188 + 1.63594i
\(73\) −7.46340 42.3270i −0.102238 0.579823i −0.992287 0.123958i \(-0.960441\pi\)
0.890049 0.455865i \(-0.150670\pi\)
\(74\) 57.0788 16.4514i 0.771336 0.222316i
\(75\) 76.7015i 1.02269i
\(76\) −62.1260 + 43.7762i −0.817448 + 0.576002i
\(77\) −82.3730 −1.06978
\(78\) −60.7413 210.744i −0.778734 2.70185i
\(79\) 45.6288 8.04560i 0.577580 0.101843i 0.122776 0.992434i \(-0.460820\pi\)
0.454804 + 0.890591i \(0.349709\pi\)
\(80\) −12.2647 48.0720i −0.153309 0.600900i
\(81\) 21.1862 17.7773i 0.261558 0.219473i
\(82\) 27.3205 + 55.8218i 0.333176 + 0.680754i
\(83\) 123.443 + 71.2697i 1.48726 + 0.858672i 0.999895 0.0145248i \(-0.00462355\pi\)
0.487368 + 0.873196i \(0.337957\pi\)
\(84\) −189.335 + 40.7846i −2.25399 + 0.485531i
\(85\) 46.6998 16.9973i 0.549409 0.199969i
\(86\) 26.8902 + 18.0843i 0.312676 + 0.210283i
\(87\) −9.22279 + 5.32478i −0.106009 + 0.0612044i
\(88\) −13.8351 + 66.4247i −0.157217 + 0.754826i
\(89\) 14.4005 81.6693i 0.161803 0.917632i −0.790496 0.612467i \(-0.790177\pi\)
0.952299 0.305165i \(-0.0987117\pi\)
\(90\) −23.6548 + 95.4285i −0.262831 + 1.06032i
\(91\) 137.325 163.658i 1.50907 1.79844i
\(92\) −4.13554 + 30.0200i −0.0449515 + 0.326304i
\(93\) 35.8886 + 13.0624i 0.385899 + 0.140456i
\(94\) 61.4708 + 84.3650i 0.653945 + 0.897500i
\(95\) −43.0776 + 40.1895i −0.453448 + 0.423048i
\(96\) 1.08821 + 159.527i 0.0113355 + 1.66174i
\(97\) 143.478 + 52.2217i 1.47915 + 0.538368i 0.950569 0.310513i \(-0.100501\pi\)
0.528584 + 0.848881i \(0.322723\pi\)
\(98\) −65.3007 62.8882i −0.666334 0.641717i
\(99\) 86.4289 103.002i 0.873020 1.04042i
\(100\) 23.2095 + 56.9972i 0.232095 + 0.569972i
\(101\) 24.8471 140.915i 0.246010 1.39519i −0.572124 0.820167i \(-0.693880\pi\)
0.818134 0.575027i \(-0.195009\pi\)
\(102\) −158.906 + 16.9209i −1.55790 + 0.165891i
\(103\) −66.2327 + 38.2395i −0.643036 + 0.371257i −0.785783 0.618502i \(-0.787740\pi\)
0.142747 + 0.989759i \(0.454406\pi\)
\(104\) −108.907 138.225i −1.04718 1.32909i
\(105\) −141.082 + 51.3496i −1.34364 + 0.489044i
\(106\) −131.416 58.2954i −1.23977 0.549957i
\(107\) 67.6922 + 39.0821i 0.632637 + 0.365253i 0.781773 0.623564i \(-0.214316\pi\)
−0.149136 + 0.988817i \(0.547649\pi\)
\(108\) 63.8343 120.849i 0.591058 1.11897i
\(109\) 93.5867 78.5285i 0.858593 0.720445i −0.103071 0.994674i \(-0.532867\pi\)
0.961665 + 0.274229i \(0.0884225\pi\)
\(110\) −3.59736 + 52.4733i −0.0327033 + 0.477030i
\(111\) −145.821 + 25.7122i −1.31371 + 0.231642i
\(112\) −128.354 + 87.5989i −1.14602 + 0.782133i
\(113\) −70.8625 −0.627102 −0.313551 0.949571i \(-0.601519\pi\)
−0.313551 + 0.949571i \(0.601519\pi\)
\(114\) 165.544 92.1090i 1.45214 0.807973i
\(115\) 23.4909i 0.204268i
\(116\) −5.24224 + 6.74763i −0.0451917 + 0.0581692i
\(117\) 60.5564 + 343.433i 0.517576 + 2.93532i
\(118\) 7.51941 109.683i 0.0637238 0.929515i
\(119\) −100.059 119.245i −0.840829 1.00206i
\(120\) 17.7121 + 122.391i 0.147601 + 1.01993i
\(121\) −24.5340 + 42.4942i −0.202761 + 0.351192i
\(122\) 119.895 + 53.1850i 0.982749 + 0.435942i
\(123\) −52.9847 145.574i −0.430770 1.18353i
\(124\) 30.6216 1.15299i 0.246948 0.00929831i
\(125\) 62.6124 + 108.448i 0.500899 + 0.867583i
\(126\) 306.222 32.6077i 2.43033 0.258791i
\(127\) 33.3838 + 5.88646i 0.262864 + 0.0463501i 0.303527 0.952823i \(-0.401836\pi\)
−0.0406626 + 0.999173i \(0.512947\pi\)
\(128\) 49.0808 + 118.216i 0.383444 + 0.923564i
\(129\) −61.8785 51.9222i −0.479678 0.402498i
\(130\) −98.2564 94.6263i −0.755818 0.727895i
\(131\) 28.3793 77.9715i 0.216636 0.595202i −0.783004 0.622016i \(-0.786314\pi\)
0.999640 + 0.0268136i \(0.00853606\pi\)
\(132\) 51.8245 160.993i 0.392610 1.21964i
\(133\) 164.441 + 83.7381i 1.23640 + 0.629610i
\(134\) 40.6282 + 55.7597i 0.303195 + 0.416117i
\(135\) 36.2359 99.5572i 0.268414 0.737461i
\(136\) −112.963 + 60.6581i −0.830614 + 0.446015i
\(137\) −166.421 139.644i −1.21475 1.01930i −0.999082 0.0428309i \(-0.986362\pi\)
−0.215669 0.976467i \(-0.569193\pi\)
\(138\) 18.1740 73.3179i 0.131696 0.531289i
\(139\) −136.012 23.9827i −0.978507 0.172537i −0.338550 0.940948i \(-0.609937\pi\)
−0.639957 + 0.768411i \(0.721048\pi\)
\(140\) −89.3004 + 80.8488i −0.637860 + 0.577491i
\(141\) −130.098 225.337i −0.922683 1.59813i
\(142\) 47.6957 + 32.0766i 0.335885 + 0.225891i
\(143\) 63.8075 + 175.310i 0.446206 + 1.22594i
\(144\) 25.1376 252.411i 0.174566 1.75285i
\(145\) −3.31186 + 5.73631i −0.0228404 + 0.0395608i
\(146\) 37.7878 + 77.2089i 0.258820 + 0.528828i
\(147\) 145.260 + 173.114i 0.988162 + 1.17765i
\(148\) −100.580 + 63.2316i −0.679595 + 0.427241i
\(149\) 20.6772 + 117.266i 0.138773 + 0.787022i 0.972158 + 0.234328i \(0.0752890\pi\)
−0.833384 + 0.552694i \(0.813600\pi\)
\(150\) −42.4847 147.403i −0.283232 0.982684i
\(151\) 136.916i 0.906725i −0.891326 0.453363i \(-0.850224\pi\)
0.891326 0.453363i \(-0.149776\pi\)
\(152\) 95.1444 118.539i 0.625950 0.779863i
\(153\) 254.094 1.66074
\(154\) 158.302 45.6262i 1.02794 0.296274i
\(155\) 23.3934 4.12488i 0.150925 0.0266121i
\(156\) 233.461 + 371.358i 1.49655 + 2.38050i
\(157\) 91.4124 76.7041i 0.582244 0.488561i −0.303439 0.952851i \(-0.598135\pi\)
0.885683 + 0.464290i \(0.153690\pi\)
\(158\) −83.2317 + 40.7355i −0.526783 + 0.257819i
\(159\) 310.349 + 179.180i 1.95188 + 1.12692i
\(160\) 50.1969 + 85.5899i 0.313731 + 0.534937i
\(161\) 69.1421 25.1657i 0.429454 0.156309i
\(162\) −30.8682 + 45.8989i −0.190544 + 0.283326i
\(163\) −198.429 + 114.563i −1.21735 + 0.702840i −0.964351 0.264626i \(-0.914752\pi\)
−0.253003 + 0.967466i \(0.581418\pi\)
\(164\) −83.4232 92.1440i −0.508678 0.561854i
\(165\) 22.7663 129.114i 0.137978 0.782510i
\(166\) −276.705 68.5894i −1.66690 0.413189i
\(167\) −166.760 + 198.737i −0.998565 + 1.19004i −0.0168172 + 0.999859i \(0.505353\pi\)
−0.981748 + 0.190185i \(0.939091\pi\)
\(168\) 341.267 183.251i 2.03135 1.09078i
\(169\) −295.870 107.688i −1.75071 0.637207i
\(170\) −80.3314 + 58.5318i −0.472538 + 0.344305i
\(171\) −277.247 + 117.762i −1.62133 + 0.688665i
\(172\) −61.6935 19.8595i −0.358683 0.115462i
\(173\) −121.091 44.0735i −0.699948 0.254760i −0.0325591 0.999470i \(-0.510366\pi\)
−0.667389 + 0.744710i \(0.732588\pi\)
\(174\) 14.7747 15.3415i 0.0849120 0.0881694i
\(175\) 96.0506 114.469i 0.548861 0.654107i
\(176\) −10.2046 135.316i −0.0579804 0.768841i
\(177\) −47.5874 + 269.882i −0.268856 + 1.52476i
\(178\) 17.5619 + 164.926i 0.0986625 + 0.926550i
\(179\) 116.304 67.1482i 0.649744 0.375130i −0.138614 0.990346i \(-0.544265\pi\)
0.788358 + 0.615217i \(0.210932\pi\)
\(180\) −7.39856 196.494i −0.0411031 1.09163i
\(181\) 246.720 89.7988i 1.36310 0.496126i 0.446085 0.894991i \(-0.352818\pi\)
0.917010 + 0.398864i \(0.130596\pi\)
\(182\) −173.258 + 390.577i −0.951967 + 2.14603i
\(183\) −283.142 163.472i −1.54723 0.893292i
\(184\) −8.68043 59.9822i −0.0471763 0.325990i
\(185\) −70.5495 + 59.1980i −0.381348 + 0.319989i
\(186\) −76.2048 5.22430i −0.409703 0.0280876i
\(187\) 133.868 23.6045i 0.715869 0.126227i
\(188\) −164.862 128.082i −0.876927 0.681285i
\(189\) −331.852 −1.75583
\(190\) 60.5243 101.096i 0.318549 0.532082i
\(191\) 112.860i 0.590890i 0.955360 + 0.295445i \(0.0954679\pi\)
−0.955360 + 0.295445i \(0.904532\pi\)
\(192\) −90.4531 305.972i −0.471110 1.59361i
\(193\) −8.66327 49.1319i −0.0448874 0.254569i 0.954104 0.299476i \(-0.0968119\pi\)
−0.998991 + 0.0449071i \(0.985701\pi\)
\(194\) −304.657 20.8861i −1.57040 0.107660i
\(195\) 218.569 + 260.480i 1.12087 + 1.33580i
\(196\) 160.327 + 84.6868i 0.817993 + 0.432076i
\(197\) 7.51225 13.0116i 0.0381333 0.0660488i −0.846329 0.532661i \(-0.821192\pi\)
0.884462 + 0.466612i \(0.154526\pi\)
\(198\) −109.044 + 245.819i −0.550727 + 1.24151i
\(199\) 57.1343 + 156.975i 0.287107 + 0.788820i 0.996468 + 0.0839746i \(0.0267615\pi\)
−0.709361 + 0.704846i \(0.751016\pi\)
\(200\) −76.1738 96.6798i −0.380869 0.483399i
\(201\) −85.9864 148.933i −0.427793 0.740959i
\(202\) 30.3019 + 284.568i 0.150009 + 1.40875i
\(203\) 20.4320 + 3.60272i 0.100650 + 0.0177474i
\(204\) 296.008 120.536i 1.45102 0.590861i
\(205\) −73.8114 61.9351i −0.360056 0.302122i
\(206\) 106.103 110.174i 0.515065 0.534823i
\(207\) −41.0786 + 112.862i −0.198447 + 0.545229i
\(208\) 285.857 + 205.313i 1.37431 + 0.987083i
\(209\) −135.126 + 87.7973i −0.646536 + 0.420083i
\(210\) 242.685 176.827i 1.15564 0.842034i
\(211\) 46.4753 127.690i 0.220262 0.605165i −0.779513 0.626386i \(-0.784533\pi\)
0.999775 + 0.0212215i \(0.00675554\pi\)
\(212\) 284.841 + 39.2395i 1.34359 + 0.185092i
\(213\) −109.755 92.0957i −0.515283 0.432374i
\(214\) −151.736 37.6123i −0.709048 0.175758i
\(215\) −49.4775 8.72421i −0.230128 0.0405777i
\(216\) −55.7368 + 267.602i −0.258041 + 1.23890i
\(217\) −37.2023 64.4362i −0.171439 0.296941i
\(218\) −136.355 + 202.751i −0.625483 + 0.930051i
\(219\) −73.2848 201.348i −0.334634 0.919398i
\(220\) −22.1515 102.834i −0.100689 0.467428i
\(221\) −176.276 + 305.318i −0.797627 + 1.38153i
\(222\) 265.993 130.183i 1.19817 0.586410i
\(223\) −23.8995 28.4823i −0.107173 0.127723i 0.709792 0.704412i \(-0.248789\pi\)
−0.816964 + 0.576688i \(0.804345\pi\)
\(224\) 198.147 239.440i 0.884583 1.06893i
\(225\) 42.3555 + 240.210i 0.188246 + 1.06760i
\(226\) 136.181 39.2506i 0.602573 0.173675i
\(227\) 163.724i 0.721250i −0.932711 0.360625i \(-0.882563\pi\)
0.932711 0.360625i \(-0.117437\pi\)
\(228\) −267.118 + 268.706i −1.17157 + 1.17854i
\(229\) 41.4636 0.181064 0.0905318 0.995894i \(-0.471143\pi\)
0.0905318 + 0.995894i \(0.471143\pi\)
\(230\) −13.0115 45.1440i −0.0565718 0.196278i
\(231\) −404.420 + 71.3101i −1.75073 + 0.308702i
\(232\) 6.33689 15.8711i 0.0273142 0.0684097i
\(233\) 165.745 139.076i 0.711351 0.596894i −0.213627 0.976915i \(-0.568528\pi\)
0.924978 + 0.380021i \(0.124083\pi\)
\(234\) −306.602 626.456i −1.31026 2.67716i
\(235\) −140.153 80.9174i −0.596396 0.344329i
\(236\) 46.3024 + 214.950i 0.196196 + 0.910805i
\(237\) 217.055 79.0015i 0.915843 0.333340i
\(238\) 258.339 + 173.740i 1.08546 + 0.729999i
\(239\) 158.015 91.2300i 0.661151 0.381715i −0.131565 0.991308i \(-0.542000\pi\)
0.792715 + 0.609592i \(0.208667\pi\)
\(240\) −101.831 225.397i −0.424295 0.939155i
\(241\) −61.6041 + 349.374i −0.255619 + 1.44969i 0.538860 + 0.842395i \(0.318855\pi\)
−0.794479 + 0.607291i \(0.792256\pi\)
\(242\) 23.6113 95.2533i 0.0975675 0.393609i
\(243\) −109.039 + 129.948i −0.448722 + 0.534766i
\(244\) −259.870 35.7996i −1.06504 0.146720i
\(245\) 132.079 + 48.0729i 0.539099 + 0.196216i
\(246\) 182.458 + 250.412i 0.741698 + 1.01794i
\(247\) 50.8360 414.836i 0.205814 1.67950i
\(248\) −58.2090 + 19.1770i −0.234714 + 0.0773265i
\(249\) 667.754 + 243.043i 2.68174 + 0.976075i
\(250\) −180.395 173.731i −0.721582 0.694924i
\(251\) −23.5121 + 28.0207i −0.0936738 + 0.111636i −0.810845 0.585261i \(-0.800992\pi\)
0.717171 + 0.696897i \(0.245437\pi\)
\(252\) −570.427 + 232.280i −2.26360 + 0.921746i
\(253\) −11.1574 + 63.2769i −0.0441005 + 0.250106i
\(254\) −67.4164 + 7.17875i −0.265419 + 0.0282628i
\(255\) 214.563 123.878i 0.841424 0.485796i
\(256\) −159.802 199.999i −0.624225 0.781245i
\(257\) 1.80290 0.656204i 0.00701519 0.00255332i −0.338510 0.940963i \(-0.609923\pi\)
0.345525 + 0.938409i \(0.387701\pi\)
\(258\) 147.676 + 65.5082i 0.572387 + 0.253908i
\(259\) 249.821 + 144.234i 0.964559 + 0.556888i
\(260\) 241.239 + 127.426i 0.927844 + 0.490100i
\(261\) −25.9430 + 21.7688i −0.0993986 + 0.0834053i
\(262\) −11.3503 + 165.563i −0.0433218 + 0.631918i
\(263\) 150.893 26.6066i 0.573739 0.101166i 0.120752 0.992683i \(-0.461469\pi\)
0.452987 + 0.891517i \(0.350358\pi\)
\(264\) −10.4213 + 338.096i −0.0394747 + 1.28067i
\(265\) 222.890 0.841094
\(266\) −362.401 69.8418i −1.36241 0.262563i
\(267\) 413.431i 1.54843i
\(268\) −108.963 84.6535i −0.406579 0.315871i
\(269\) −76.1222 431.710i −0.282982 1.60487i −0.712405 0.701768i \(-0.752394\pi\)
0.429423 0.903103i \(-0.358717\pi\)
\(270\) −14.4925 + 211.397i −0.0536760 + 0.782952i
\(271\) 71.9024 + 85.6899i 0.265322 + 0.316199i 0.882214 0.470850i \(-0.156053\pi\)
−0.616891 + 0.787049i \(0.711608\pi\)
\(272\) 183.491 179.141i 0.674601 0.658607i
\(273\) 532.536 922.379i 1.95068 3.37868i
\(274\) 397.171 + 176.183i 1.44953 + 0.643004i
\(275\) 44.6294 + 122.618i 0.162289 + 0.445885i
\(276\) 5.68433 + 150.967i 0.0205954 + 0.546980i
\(277\) 33.9635 + 58.8265i 0.122612 + 0.212370i 0.920797 0.390042i \(-0.127540\pi\)
−0.798185 + 0.602412i \(0.794206\pi\)
\(278\) 274.669 29.2477i 0.988016 0.105208i
\(279\) 119.607 + 21.0900i 0.428700 + 0.0755913i
\(280\) 126.833 204.836i 0.452975 0.731557i
\(281\) −18.9983 15.9415i −0.0676097 0.0567313i 0.608357 0.793664i \(-0.291829\pi\)
−0.675966 + 0.736933i \(0.736274\pi\)
\(282\) 374.832 + 360.984i 1.32919 + 1.28009i
\(283\) −5.85053 + 16.0742i −0.0206732 + 0.0567993i −0.949600 0.313464i \(-0.898510\pi\)
0.928927 + 0.370264i \(0.120733\pi\)
\(284\) −109.427 35.2253i −0.385307 0.124033i
\(285\) −176.702 + 234.607i −0.620008 + 0.823182i
\(286\) −219.727 301.562i −0.768276 1.05441i
\(287\) −103.224 + 283.605i −0.359664 + 0.988170i
\(288\) 91.5009 + 498.999i 0.317711 + 1.73263i
\(289\) −24.6073 20.6480i −0.0851464 0.0714463i
\(290\) 3.18731 12.8583i 0.0109907 0.0443389i
\(291\) 749.628 + 132.180i 2.57604 + 0.454226i
\(292\) −115.385 127.447i −0.395155 0.436463i
\(293\) 36.6813 + 63.5338i 0.125192 + 0.216839i 0.921808 0.387647i \(-0.126712\pi\)
−0.796616 + 0.604486i \(0.793379\pi\)
\(294\) −375.043 252.226i −1.27566 0.857912i
\(295\) 58.2967 + 160.169i 0.197616 + 0.542945i
\(296\) 158.268 177.228i 0.534688 0.598742i
\(297\) 144.894 250.965i 0.487860 0.844999i
\(298\) −104.690 213.906i −0.351310 0.717804i
\(299\) −107.117 127.657i −0.358252 0.426948i
\(300\) 163.292 + 259.742i 0.544306 + 0.865806i
\(301\) 27.3265 + 154.976i 0.0907858 + 0.514872i
\(302\) 75.8371 + 263.120i 0.251116 + 0.871259i
\(303\) 713.346i 2.35428i
\(304\) −117.187 + 280.505i −0.385484 + 0.922714i
\(305\) −203.350 −0.666722
\(306\) −488.309 + 140.742i −1.59578 + 0.459940i
\(307\) −528.495 + 93.1880i −1.72148 + 0.303544i −0.945115 0.326737i \(-0.894051\pi\)
−0.776368 + 0.630280i \(0.782940\pi\)
\(308\) −278.948 + 175.366i −0.905674 + 0.569370i
\(309\) −292.073 + 245.078i −0.945220 + 0.793134i
\(310\) −42.6719 + 20.8846i −0.137651 + 0.0673696i
\(311\) −50.3529 29.0713i −0.161906 0.0934767i 0.416858 0.908972i \(-0.363131\pi\)
−0.578764 + 0.815495i \(0.696465\pi\)
\(312\) −654.353 584.351i −2.09729 1.87292i
\(313\) −522.107 + 190.031i −1.66807 + 0.607129i −0.991601 0.129338i \(-0.958715\pi\)
−0.676473 + 0.736467i \(0.736493\pi\)
\(314\) −133.187 + 198.041i −0.424164 + 0.630703i
\(315\) −413.477 + 238.721i −1.31263 + 0.757845i
\(316\) 137.389 124.386i 0.434775 0.393626i
\(317\) −30.8285 + 174.837i −0.0972507 + 0.551536i 0.896784 + 0.442469i \(0.145897\pi\)
−0.994034 + 0.109067i \(0.965214\pi\)
\(318\) −695.667 172.442i −2.18763 0.542269i
\(319\) −11.6457 + 13.8788i −0.0365068 + 0.0435071i
\(320\) −143.875 136.680i −0.449609 0.427126i
\(321\) 366.175 + 133.277i 1.14073 + 0.415193i
\(322\) −118.936 + 86.6603i −0.369367 + 0.269131i
\(323\) −291.235 88.9644i −0.901658 0.275432i
\(324\) 33.8982 105.305i 0.104624 0.325015i
\(325\) −318.019 115.750i −0.978521 0.356152i
\(326\) 317.878 330.073i 0.975087 1.01249i
\(327\) 391.492 466.562i 1.19722 1.42680i
\(328\) 211.358 + 130.872i 0.644385 + 0.398999i
\(329\) −88.0238 + 499.208i −0.267550 + 1.51735i
\(330\) 27.7643 + 260.738i 0.0841344 + 0.790115i
\(331\) −138.083 + 79.7223i −0.417169 + 0.240853i −0.693865 0.720105i \(-0.744094\pi\)
0.276696 + 0.960957i \(0.410760\pi\)
\(332\) 569.754 21.4529i 1.71613 0.0646172i
\(333\) −442.477 + 161.048i −1.32876 + 0.483629i
\(334\) 210.395 474.295i 0.629925 1.42005i
\(335\) −92.6319 53.4811i −0.276513 0.159645i
\(336\) −554.335 + 541.193i −1.64981 + 1.61069i
\(337\) 44.1059 37.0092i 0.130878 0.109820i −0.574999 0.818154i \(-0.694998\pi\)
0.705877 + 0.708334i \(0.250553\pi\)
\(338\) 628.243 + 43.0698i 1.85871 + 0.127425i
\(339\) −347.907 + 61.3455i −1.02628 + 0.180960i
\(340\) 121.958 156.980i 0.358700 0.461706i
\(341\) 64.9735 0.190538
\(342\) 467.577 379.877i 1.36718 1.11075i
\(343\) 35.6475i 0.103929i
\(344\) 129.561 + 3.99352i 0.376630 + 0.0116091i
\(345\) 20.3360 + 115.331i 0.0589448 + 0.334293i
\(346\) 257.121 + 17.6272i 0.743124 + 0.0509456i
\(347\) 217.954 + 259.747i 0.628109 + 0.748551i 0.982442 0.186568i \(-0.0597365\pi\)
−0.354333 + 0.935119i \(0.615292\pi\)
\(348\) −19.8960 + 37.6664i −0.0571723 + 0.108237i
\(349\) 174.648 302.498i 0.500423 0.866758i −0.499577 0.866269i \(-0.666511\pi\)
1.00000 0.000488300i \(-0.000155431\pi\)
\(350\) −121.183 + 273.184i −0.346238 + 0.780527i
\(351\) 257.058 + 706.262i 0.732360 + 2.01214i
\(352\) 94.5620 + 254.394i 0.268642 + 0.722710i
\(353\) 54.8594 + 95.0193i 0.155409 + 0.269177i 0.933208 0.359337i \(-0.116997\pi\)
−0.777799 + 0.628513i \(0.783664\pi\)
\(354\) −58.0346 545.009i −0.163940 1.53957i
\(355\) −87.7594 15.4743i −0.247210 0.0435897i
\(356\) −125.102 307.222i −0.351410 0.862983i
\(357\) −594.479 498.827i −1.66521 1.39728i
\(358\) −186.316 + 193.464i −0.520437 + 0.540402i
\(359\) −8.69046 + 23.8768i −0.0242074 + 0.0665093i −0.951208 0.308551i \(-0.900156\pi\)
0.927000 + 0.375061i \(0.122378\pi\)
\(360\) 123.056 + 373.518i 0.341821 + 1.03755i
\(361\) 359.005 37.9043i 0.994472 0.104998i
\(362\) −424.400 + 309.230i −1.17238 + 0.854227i
\(363\) −83.6654 + 229.869i −0.230483 + 0.633248i
\(364\) 116.623 846.566i 0.320392 2.32573i
\(365\) −102.091 85.6643i −0.279701 0.234697i
\(366\) 634.681 + 157.324i 1.73410 + 0.429848i
\(367\) −39.9442 7.04324i −0.108840 0.0191914i 0.118963 0.992899i \(-0.462043\pi\)
−0.227803 + 0.973707i \(0.573154\pi\)
\(368\) 49.9057 + 110.464i 0.135613 + 0.300173i
\(369\) −246.323 426.643i −0.667541 1.15621i
\(370\) 102.790 152.842i 0.277811 0.413087i
\(371\) −238.781 656.046i −0.643615 1.76832i
\(372\) 149.342 32.1697i 0.401457 0.0864778i
\(373\) −187.994 + 325.615i −0.504005 + 0.872962i 0.495985 + 0.868331i \(0.334807\pi\)
−0.999989 + 0.00463050i \(0.998526\pi\)
\(374\) −244.188 + 119.511i −0.652910 + 0.319549i
\(375\) 401.285 + 478.233i 1.07009 + 1.27529i
\(376\) 387.771 + 154.827i 1.03131 + 0.411773i
\(377\) −8.15954 46.2750i −0.0216433 0.122745i
\(378\) 637.744 183.812i 1.68715 0.486275i
\(379\) 587.058i 1.54897i 0.632595 + 0.774483i \(0.281990\pi\)
−0.632595 + 0.774483i \(0.718010\pi\)
\(380\) −60.3173 + 227.807i −0.158730 + 0.599491i
\(381\) 168.997 0.443562
\(382\) −62.5128 216.891i −0.163646 0.567777i
\(383\) 272.406 48.0325i 0.711242 0.125411i 0.193690 0.981063i \(-0.437954\pi\)
0.517552 + 0.855652i \(0.326843\pi\)
\(384\) 343.307 + 537.906i 0.894029 + 1.40080i
\(385\) −195.661 + 164.179i −0.508211 + 0.426440i
\(386\) 43.8628 + 89.6216i 0.113634 + 0.232180i
\(387\) −222.460 128.437i −0.574832 0.331879i
\(388\) 597.049 128.610i 1.53879 0.331470i
\(389\) 610.779 222.305i 1.57013 0.571479i 0.597098 0.802168i \(-0.296320\pi\)
0.973027 + 0.230690i \(0.0740982\pi\)
\(390\) −564.318 379.518i −1.44697 0.973124i
\(391\) −105.154 + 60.7108i −0.268937 + 0.155271i
\(392\) −355.019 73.9442i −0.905659 0.188633i
\(393\) 71.8317 407.378i 0.182778 1.03658i
\(394\) −7.22973 + 29.1663i −0.0183496 + 0.0740262i
\(395\) 92.3467 110.055i 0.233789 0.278619i
\(396\) 73.3991 532.806i 0.185351 1.34547i
\(397\) 439.562 + 159.988i 1.10721 + 0.402992i 0.829969 0.557809i \(-0.188358\pi\)
0.277241 + 0.960800i \(0.410580\pi\)
\(398\) −196.747 270.024i −0.494339 0.678451i
\(399\) 879.834 + 268.765i 2.20510 + 0.673597i
\(400\) 199.939 + 143.604i 0.499848 + 0.359010i
\(401\) −68.3783 24.8877i −0.170520 0.0620640i 0.255350 0.966849i \(-0.417809\pi\)
−0.425869 + 0.904785i \(0.640032\pi\)
\(402\) 247.739 + 238.587i 0.616267 + 0.593500i
\(403\) −108.318 + 129.089i −0.268780 + 0.320319i
\(404\) −215.855 530.090i −0.534294 1.31210i
\(405\) 14.8914 84.4532i 0.0367688 0.208526i
\(406\) −41.2612 + 4.39365i −0.101629 + 0.0108218i
\(407\) −218.155 + 125.952i −0.536008 + 0.309464i
\(408\) −502.095 + 395.600i −1.23063 + 0.969607i
\(409\) −112.901 + 41.0926i −0.276042 + 0.100471i −0.476332 0.879266i \(-0.658034\pi\)
0.200290 + 0.979737i \(0.435812\pi\)
\(410\) 176.154 + 78.1411i 0.429644 + 0.190588i
\(411\) −937.951 541.526i −2.28212 1.31758i
\(412\) −142.881 + 270.499i −0.346799 + 0.656550i
\(413\) 408.982 343.177i 0.990272 0.830937i
\(414\) 16.4294 239.649i 0.0396845 0.578862i
\(415\) 435.264 76.7488i 1.04883 0.184937i
\(416\) −663.074 236.229i −1.59393 0.567859i
\(417\) −688.530 −1.65115
\(418\) 211.051 243.572i 0.504906 0.582708i
\(419\) 49.9892i 0.119306i 0.998219 + 0.0596530i \(0.0189994\pi\)
−0.998219 + 0.0596530i \(0.981001\pi\)
\(420\) −368.440 + 474.243i −0.877238 + 1.12915i
\(421\) −19.7726 112.136i −0.0469659 0.266357i 0.952278 0.305231i \(-0.0987338\pi\)
−0.999244 + 0.0388747i \(0.987623\pi\)
\(422\) −18.5878 + 271.133i −0.0440469 + 0.642495i
\(423\) −531.868 633.856i −1.25737 1.49848i
\(424\) −569.133 + 82.3632i −1.34229 + 0.194253i
\(425\) −123.294 + 213.551i −0.290103 + 0.502473i
\(426\) 261.936 + 116.194i 0.614873 + 0.272755i
\(427\) 217.849 + 598.534i 0.510184 + 1.40172i
\(428\) 312.435 11.7641i 0.729989 0.0274862i
\(429\) 465.035 + 805.464i 1.08400 + 1.87754i
\(430\) 99.9166 10.6395i 0.232364 0.0247430i
\(431\) −395.778 69.7863i −0.918277 0.161917i −0.305518 0.952186i \(-0.598830\pi\)
−0.612760 + 0.790269i \(0.709941\pi\)
\(432\) −41.1106 545.142i −0.0951635 1.26190i
\(433\) −297.592 249.710i −0.687281 0.576697i 0.230843 0.972991i \(-0.425852\pi\)
−0.918124 + 0.396294i \(0.870296\pi\)
\(434\) 107.185 + 103.225i 0.246970 + 0.237846i
\(435\) −11.2940 + 31.0301i −0.0259633 + 0.0713336i
\(436\) 149.740 465.168i 0.343441 1.06690i
\(437\) 86.5991 114.977i 0.198167 0.263106i
\(438\) 252.363 + 346.353i 0.576170 + 0.790760i
\(439\) −173.043 + 475.432i −0.394175 + 1.08299i 0.570901 + 0.821019i \(0.306594\pi\)
−0.965076 + 0.261969i \(0.915628\pi\)
\(440\) 99.5297 + 185.354i 0.226204 + 0.421259i
\(441\) 550.513 + 461.935i 1.24833 + 1.04747i
\(442\) 169.646 684.390i 0.383815 1.54839i
\(443\) 156.090 + 27.5228i 0.352347 + 0.0621283i 0.347020 0.937858i \(-0.387193\pi\)
0.00532640 + 0.999986i \(0.498305\pi\)
\(444\) −439.069 + 397.514i −0.988895 + 0.895302i
\(445\) −128.571 222.692i −0.288924 0.500430i
\(446\) 61.7056 + 41.4986i 0.138353 + 0.0930461i
\(447\) 203.034 + 557.832i 0.454215 + 1.24795i
\(448\) −248.167 + 569.901i −0.553944 + 1.27210i
\(449\) −126.598 + 219.274i −0.281956 + 0.488361i −0.971866 0.235533i \(-0.924316\pi\)
0.689911 + 0.723894i \(0.257650\pi\)
\(450\) −214.449 438.167i −0.476553 0.973705i
\(451\) −169.407 201.892i −0.375626 0.447653i
\(452\) −239.969 + 150.861i −0.530904 + 0.333763i
\(453\) −118.527 672.202i −0.261650 1.48389i
\(454\) 90.6861 + 314.639i 0.199749 + 0.693038i
\(455\) 662.444i 1.45592i
\(456\) 364.503 664.347i 0.799349 1.45690i
\(457\) −536.519 −1.17400 −0.587001 0.809586i \(-0.699691\pi\)
−0.587001 + 0.809586i \(0.699691\pi\)
\(458\) −79.6834 + 22.9665i −0.173981 + 0.0501453i
\(459\) 539.306 95.0942i 1.17496 0.207177i
\(460\) 50.0103 + 79.5493i 0.108718 + 0.172933i
\(461\) 237.716 199.467i 0.515653 0.432684i −0.347461 0.937695i \(-0.612956\pi\)
0.863113 + 0.505011i \(0.168511\pi\)
\(462\) 737.703 361.048i 1.59676 0.781490i
\(463\) 18.7328 + 10.8154i 0.0404597 + 0.0233594i 0.520093 0.854109i \(-0.325897\pi\)
−0.479634 + 0.877469i \(0.659230\pi\)
\(464\) −3.38710 + 34.0105i −0.00729979 + 0.0732985i
\(465\) 111.281 40.5031i 0.239315 0.0871034i
\(466\) −241.489 + 359.078i −0.518217 + 0.770554i
\(467\) 469.726 271.197i 1.00584 0.580721i 0.0958677 0.995394i \(-0.469437\pi\)
0.909970 + 0.414673i \(0.136104\pi\)
\(468\) 936.210 + 1034.08i 2.00045 + 2.20957i
\(469\) −58.1780 + 329.944i −0.124047 + 0.703505i
\(470\) 314.162 + 77.8742i 0.668429 + 0.165690i
\(471\) 382.397 455.723i 0.811883 0.967564i
\(472\) −208.043 387.437i −0.440768 0.820842i
\(473\) −129.133 47.0005i −0.273008 0.0993669i
\(474\) −373.371 + 272.049i −0.787702 + 0.573942i
\(475\) 35.5566 290.152i 0.0748561 0.610846i
\(476\) −592.702 190.794i −1.24517 0.400828i
\(477\) 1070.88 + 389.769i 2.24503 + 0.817125i
\(478\) −253.136 + 262.847i −0.529574 + 0.549889i
\(479\) −100.003 + 119.179i −0.208775 + 0.248809i −0.860263 0.509850i \(-0.829701\pi\)
0.651488 + 0.758659i \(0.274145\pi\)
\(480\) 320.542 + 376.758i 0.667796 + 0.784912i
\(481\) 113.450 643.405i 0.235862 1.33764i
\(482\) −75.1285 705.539i −0.155868 1.46377i
\(483\) 317.675 183.410i 0.657713 0.379731i
\(484\) 7.38498 + 196.133i 0.0152582 + 0.405234i
\(485\) 444.888 161.926i 0.917295 0.333868i
\(486\) 137.571 310.127i 0.283067 0.638121i
\(487\) 174.976 + 101.023i 0.359294 + 0.207439i 0.668771 0.743468i \(-0.266821\pi\)
−0.309477 + 0.950907i \(0.600154\pi\)
\(488\) 519.240 75.1428i 1.06402 0.153981i
\(489\) −875.031 + 734.238i −1.78943 + 1.50151i
\(490\) −280.453 19.2267i −0.572353 0.0392383i
\(491\) −479.984 + 84.6341i −0.977564 + 0.172371i −0.639533 0.768764i \(-0.720872\pi\)
−0.338031 + 0.941135i \(0.609761\pi\)
\(492\) −489.344 380.172i −0.994602 0.772707i
\(493\) −34.2373 −0.0694468
\(494\) 132.081 + 825.377i 0.267371 + 1.67080i
\(495\) 416.925i 0.842272i
\(496\) 101.242 69.0955i 0.204117 0.139305i
\(497\) 48.4697 + 274.885i 0.0975246 + 0.553090i
\(498\) −1417.89 97.2049i −2.84717 0.195191i
\(499\) 630.877 + 751.849i 1.26428 + 1.50671i 0.770988 + 0.636849i \(0.219763\pi\)
0.493294 + 0.869863i \(0.335793\pi\)
\(500\) 442.908 + 233.950i 0.885815 + 0.467900i
\(501\) −646.682 + 1120.09i −1.29078 + 2.23570i
\(502\) 29.6643 66.8725i 0.0590923 0.133212i
\(503\) −203.242 558.403i −0.404060 1.11015i −0.960262 0.279098i \(-0.909964\pi\)
0.556203 0.831047i \(-0.312258\pi\)
\(504\) 967.570 762.346i 1.91978 1.51259i
\(505\) −221.840 384.239i −0.439288 0.760869i
\(506\) −13.6069 127.784i −0.0268911 0.252537i
\(507\) −1545.83 272.572i −3.04898 0.537618i
\(508\) 125.582 51.1376i 0.247210 0.100665i
\(509\) 419.206 + 351.756i 0.823588 + 0.691072i 0.953809 0.300413i \(-0.0971244\pi\)
−0.130221 + 0.991485i \(0.541569\pi\)
\(510\) −343.725 + 356.911i −0.673971 + 0.699826i
\(511\) −142.772 + 392.262i −0.279397 + 0.767636i
\(512\) 417.881 + 295.838i 0.816173 + 0.577808i
\(513\) −544.376 + 353.705i −1.06116 + 0.689483i
\(514\) −3.10130 + 2.25970i −0.00603365 + 0.00439629i
\(515\) −81.1072 + 222.840i −0.157490 + 0.432700i
\(516\) −320.084 44.0945i −0.620317 0.0854545i
\(517\) −339.095 284.534i −0.655889 0.550356i
\(518\) −559.989 138.810i −1.08106 0.267972i
\(519\) −632.664 111.556i −1.21900 0.214943i
\(520\) −534.187 111.262i −1.02728 0.213965i
\(521\) −41.1913 71.3454i −0.0790620 0.136939i 0.823783 0.566905i \(-0.191859\pi\)
−0.902845 + 0.429965i \(0.858526\pi\)
\(522\) 37.7989 56.2044i 0.0724116 0.107671i
\(523\) −327.489 899.769i −0.626174 1.72040i −0.691344 0.722526i \(-0.742981\pi\)
0.0651695 0.997874i \(-0.479241\pi\)
\(524\) −69.8919 324.460i −0.133382 0.619198i
\(525\) 372.476 645.147i 0.709478 1.22885i
\(526\) −275.245 + 134.711i −0.523280 + 0.256105i
\(527\) 78.9234 + 94.0572i 0.149760 + 0.178477i
\(528\) −167.243 655.515i −0.316748 1.24151i
\(529\) 81.8935 + 464.441i 0.154808 + 0.877961i
\(530\) −428.343 + 123.458i −0.808195 + 0.232940i
\(531\) 871.480i 1.64120i
\(532\) 735.136 66.5127i 1.38183 0.125024i
\(533\) 683.538 1.28244
\(534\) 228.998 + 794.519i 0.428835 + 1.48786i
\(535\) 238.685 42.0866i 0.446140 0.0786666i
\(536\) 256.291 + 102.330i 0.478156 + 0.190915i
\(537\) 512.878 430.356i 0.955080 0.801407i
\(538\) 385.412 + 787.484i 0.716380 + 1.46372i
\(539\) 332.946 + 192.227i 0.617711 + 0.356636i
\(540\) −89.2408 414.284i −0.165261 0.767192i
\(541\) 3.85360 1.40259i 0.00712310 0.00259260i −0.338456 0.940982i \(-0.609905\pi\)
0.345579 + 0.938390i \(0.387682\pi\)
\(542\) −185.643 124.850i −0.342515 0.230350i
\(543\) 1133.56 654.462i 2.08759 1.20527i
\(544\) −253.403 + 445.903i −0.465814 + 0.819675i
\(545\) 65.7803 373.059i 0.120698 0.684512i
\(546\) −512.508 + 2067.57i −0.938660 + 3.78676i
\(547\) 291.437 347.321i 0.532792 0.634956i −0.430764 0.902465i \(-0.641756\pi\)
0.963556 + 0.267508i \(0.0862003\pi\)
\(548\) −860.858 118.591i −1.57091 0.216408i
\(549\) −977.002 355.600i −1.77960 0.647722i
\(550\) −153.685 210.924i −0.279428 0.383498i
\(551\) 37.3570 15.8675i 0.0677986 0.0287977i
\(552\) −94.5439 286.974i −0.171275 0.519881i
\(553\) −422.861 153.909i −0.764668 0.278316i
\(554\) −97.8539 94.2387i −0.176632 0.170106i
\(555\) −295.123 + 351.714i −0.531753 + 0.633718i
\(556\) −511.649 + 208.346i −0.920233 + 0.374722i
\(557\) −23.1565 + 131.327i −0.0415736 + 0.235776i −0.998513 0.0545117i \(-0.982640\pi\)
0.956940 + 0.290287i \(0.0937509\pi\)
\(558\) −241.539 + 25.7200i −0.432866 + 0.0460932i
\(559\) 308.660 178.205i 0.552164 0.318792i
\(560\) −130.286 + 463.900i −0.232653 + 0.828393i
\(561\) 636.803 231.777i 1.13512 0.413151i
\(562\) 45.3404 + 20.1128i 0.0806768 + 0.0357878i
\(563\) 774.796 + 447.329i 1.37619 + 0.794545i 0.991699 0.128583i \(-0.0410427\pi\)
0.384494 + 0.923128i \(0.374376\pi\)
\(564\) −920.289 486.110i −1.63172 0.861897i
\(565\) −168.320 + 141.238i −0.297912 + 0.249978i
\(566\) 2.33992 34.1315i 0.00413413 0.0603030i
\(567\) −264.530 + 46.6437i −0.466543 + 0.0822640i
\(568\) 229.805 + 7.08341i 0.404587 + 0.0124708i
\(569\) 560.293 0.984697 0.492349 0.870398i \(-0.336139\pi\)
0.492349 + 0.870398i \(0.336139\pi\)
\(570\) 209.633 548.735i 0.367777 0.962694i
\(571\) 3.09674i 0.00542337i 0.999996 + 0.00271168i \(0.000863156\pi\)
−0.999996 + 0.00271168i \(0.999137\pi\)
\(572\) 589.299 + 457.827i 1.03024 + 0.800396i
\(573\) 97.7025 + 554.098i 0.170510 + 0.967013i
\(574\) 41.2843 602.198i 0.0719239 1.04913i
\(575\) −74.9219 89.2884i −0.130299 0.155284i
\(576\) −452.237 908.278i −0.785135 1.57687i
\(577\) 339.962 588.832i 0.589189 1.02051i −0.405149 0.914250i \(-0.632781\pi\)
0.994339 0.106256i \(-0.0338862\pi\)
\(578\) 58.7264 + 26.0507i 0.101603 + 0.0450705i
\(579\) −85.0666 233.719i −0.146920 0.403659i
\(580\) 0.996903 + 26.4761i 0.00171880 + 0.0456485i
\(581\) −692.196 1198.92i −1.19139 2.06354i
\(582\) −1513.83 + 161.198i −2.60108 + 0.276973i
\(583\) 600.395 + 105.866i 1.02984 + 0.181588i
\(584\) 292.336 + 181.013i 0.500576 + 0.309953i
\(585\) 828.342 + 695.062i 1.41597 + 1.18814i
\(586\) −105.684 101.780i −0.180348 0.173686i
\(587\) 336.045 923.275i 0.572478 1.57287i −0.228097 0.973638i \(-0.573250\pi\)
0.800575 0.599233i \(-0.204528\pi\)
\(588\) 860.454 + 276.985i 1.46336 + 0.471063i
\(589\) −129.707 66.0502i −0.220215 0.112140i
\(590\) −200.750 275.517i −0.340254 0.466979i
\(591\) 25.6181 70.3852i 0.0433471 0.119095i
\(592\) −205.988 + 428.254i −0.347953 + 0.723403i
\(593\) −303.538 254.698i −0.511868 0.429508i 0.349918 0.936780i \(-0.386209\pi\)
−0.861786 + 0.507272i \(0.830654\pi\)
\(594\) −139.445 + 562.553i −0.234756 + 0.947058i
\(595\) −475.340 83.8153i −0.798891 0.140866i
\(596\) 319.672 + 353.090i 0.536363 + 0.592433i
\(597\) 416.400 + 721.226i 0.697488 + 1.20808i
\(598\) 276.564 + 185.996i 0.462481 + 0.311030i
\(599\) 192.043 + 527.634i 0.320606 + 0.880858i 0.990390 + 0.138302i \(0.0441645\pi\)
−0.669784 + 0.742556i \(0.733613\pi\)
\(600\) −457.679 408.717i −0.762799 0.681195i
\(601\) −422.927 + 732.532i −0.703706 + 1.21885i 0.263451 + 0.964673i \(0.415139\pi\)
−0.967157 + 0.254182i \(0.918194\pi\)
\(602\) −138.356 282.693i −0.229828 0.469590i
\(603\) −351.530 418.937i −0.582969 0.694755i
\(604\) −291.483 463.650i −0.482588 0.767633i
\(605\) 26.4201 + 149.836i 0.0436696 + 0.247663i
\(606\) 395.120 + 1370.89i 0.652014 + 2.26219i
\(607\) 846.188i 1.39405i 0.717047 + 0.697024i \(0.245493\pi\)
−0.717047 + 0.697024i \(0.754507\pi\)
\(608\) 69.8358 603.976i 0.114862 0.993382i
\(609\) 103.432 0.169839
\(610\) 390.792 112.635i 0.640643 0.184648i
\(611\) 1130.62 199.359i 1.85044 0.326283i
\(612\) 860.462 540.946i 1.40598 0.883899i
\(613\) 524.606 440.197i 0.855801 0.718102i −0.105258 0.994445i \(-0.533567\pi\)
0.961059 + 0.276343i \(0.0891224\pi\)
\(614\) 964.030 471.818i 1.57008 0.768433i
\(615\) −416.002 240.179i −0.676426 0.390535i
\(616\) 438.939 491.521i 0.712563 0.797924i
\(617\) 809.257 294.545i 1.31160 0.477383i 0.410842 0.911707i \(-0.365235\pi\)
0.900757 + 0.434324i \(0.143013\pi\)
\(618\) 425.549 632.763i 0.688591 1.02389i
\(619\) −747.857 + 431.776i −1.20817 + 0.697537i −0.962359 0.271781i \(-0.912387\pi\)
−0.245811 + 0.969318i \(0.579054\pi\)
\(620\) 70.4376 63.7712i 0.113609 0.102857i
\(621\) −44.9494 + 254.921i −0.0723823 + 0.410500i
\(622\) 112.869 + 27.9779i 0.181462 + 0.0449806i
\(623\) −517.725 + 617.000i −0.831019 + 0.990370i
\(624\) 1581.19 + 760.543i 2.53395 + 1.21882i
\(625\) 3.43481 + 1.25017i 0.00549569 + 0.00200027i
\(626\) 898.112 654.390i 1.43468 1.04535i
\(627\) −587.411 + 548.029i −0.936859 + 0.874049i
\(628\) 146.261 454.361i 0.232900 0.723504i
\(629\) −447.324 162.813i −0.711168 0.258844i
\(630\) 662.381 687.791i 1.05140 1.09173i
\(631\) −189.752 + 226.137i −0.300716 + 0.358380i −0.895150 0.445765i \(-0.852932\pi\)
0.594434 + 0.804144i \(0.297376\pi\)
\(632\) −195.133 + 315.140i −0.308754 + 0.498640i
\(633\) 117.635 667.140i 0.185837 1.05393i
\(634\) −37.5965 353.072i −0.0593004 0.556896i
\(635\) 91.0291 52.5557i 0.143353 0.0827649i
\(636\) 1432.43 53.9350i 2.25224 0.0848035i
\(637\) −936.974 + 341.031i −1.47092 + 0.535370i
\(638\) 14.6929 33.1223i 0.0230296 0.0519158i
\(639\) −394.582 227.812i −0.617500 0.356514i
\(640\) 352.201 + 182.976i 0.550314 + 0.285900i
\(641\) 58.4834 49.0734i 0.0912378 0.0765576i −0.596028 0.802964i \(-0.703255\pi\)
0.687266 + 0.726406i \(0.258811\pi\)
\(642\) −777.527 53.3041i −1.21110 0.0830282i
\(643\) −197.912 + 34.8973i −0.307795 + 0.0542726i −0.325412 0.945572i \(-0.605503\pi\)
0.0176170 + 0.999845i \(0.494392\pi\)
\(644\) 180.567 232.419i 0.280383 0.360900i
\(645\) −250.468 −0.388322
\(646\) 608.965 + 9.65468i 0.942670 + 0.0149453i
\(647\) 105.835i 0.163578i −0.996650 0.0817891i \(-0.973937\pi\)
0.996650 0.0817891i \(-0.0260634\pi\)
\(648\) −6.81656 + 221.148i −0.0105194 + 0.341277i
\(649\) 80.9576 + 459.133i 0.124742 + 0.707447i
\(650\) 675.273 + 46.2940i 1.03888 + 0.0712216i
\(651\) −238.431 284.151i −0.366253 0.436483i
\(652\) −428.063 + 810.395i −0.656538 + 1.24294i
\(653\) −287.146 + 497.352i −0.439734 + 0.761641i −0.997669 0.0682433i \(-0.978261\pi\)
0.557935 + 0.829885i \(0.311594\pi\)
\(654\) −493.930 + 1113.47i −0.755245 + 1.70256i
\(655\) −87.9970 241.770i −0.134347 0.369114i
\(656\) −478.672 134.434i −0.729682 0.204930i
\(657\) −340.696 590.103i −0.518563 0.898178i
\(658\) −107.348 1008.12i −0.163143 1.53210i
\(659\) 497.889 + 87.7912i 0.755522 + 0.133219i 0.538126 0.842865i \(-0.319133\pi\)
0.217396 + 0.976083i \(0.430244\pi\)
\(660\) −197.779 485.699i −0.299665 0.735908i
\(661\) 422.830 + 354.796i 0.639682 + 0.536757i 0.903920 0.427701i \(-0.140676\pi\)
−0.264239 + 0.964457i \(0.585121\pi\)
\(662\) 221.206 229.692i 0.334148 0.346966i
\(663\) −601.131 + 1651.60i −0.906684 + 2.49109i
\(664\) −1083.05 + 356.813i −1.63110 + 0.537369i
\(665\) 557.499 128.847i 0.838344 0.193755i
\(666\) 761.134 554.584i 1.14284 0.832709i
\(667\) 5.53504 15.2074i 0.00829841 0.0227997i
\(668\) −141.620 + 1028.02i −0.212006 + 1.53896i
\(669\) −141.994 119.147i −0.212248 0.178098i
\(670\) 207.640 + 51.4697i 0.309911 + 0.0768205i
\(671\) −547.761 96.5851i −0.816336 0.143942i
\(672\) 765.540 1347.09i 1.13920 2.00460i
\(673\) 487.962 + 845.175i 0.725055 + 1.25583i 0.958952 + 0.283570i \(0.0915188\pi\)
−0.233897 + 0.972261i \(0.575148\pi\)
\(674\) −64.2621 + 95.5534i −0.0953443 + 0.141771i
\(675\) 179.796 + 493.987i 0.266365 + 0.731832i
\(676\) −1231.19 + 265.211i −1.82129 + 0.392325i
\(677\) 115.366 199.819i 0.170407 0.295154i −0.768155 0.640264i \(-0.778825\pi\)
0.938562 + 0.345110i \(0.112158\pi\)
\(678\) 634.619 310.597i 0.936016 0.458107i
\(679\) −953.215 1136.00i −1.40385 1.67304i
\(680\) −147.424 + 369.231i −0.216800 + 0.542987i
\(681\) −141.735 803.820i −0.208128 1.18035i
\(682\) −124.864 + 35.9886i −0.183085 + 0.0527692i
\(683\) 847.020i 1.24015i −0.784544 0.620073i \(-0.787103\pi\)
0.784544 0.620073i \(-0.212897\pi\)
\(684\) −688.163 + 989.026i −1.00609 + 1.44594i
\(685\) −673.628 −0.983398
\(686\) −19.7450 68.5062i −0.0287828 0.0998633i
\(687\) 203.570 35.8949i 0.296317 0.0522487i
\(688\) −251.198 + 64.0888i −0.365114 + 0.0931523i
\(689\) −1211.26 + 1016.37i −1.75800 + 1.47514i
\(690\) −102.962 210.375i −0.149221 0.304892i
\(691\) 1066.93 + 615.993i 1.54404 + 0.891451i 0.998578 + 0.0533155i \(0.0169789\pi\)
0.545461 + 0.838136i \(0.316354\pi\)
\(692\) −503.891 + 108.543i −0.728166 + 0.156854i
\(693\) −1227.16 + 446.650i −1.77080 + 0.644517i
\(694\) −562.730 378.450i −0.810851 0.545318i
\(695\) −370.872 + 214.123i −0.533629 + 0.308091i
\(696\) 17.3721 83.4065i 0.0249599 0.119837i
\(697\) 86.4842 490.476i 0.124081 0.703696i
\(698\) −168.079 + 678.069i −0.240801 + 0.971446i
\(699\) 693.344 826.295i 0.991909 1.18211i
\(700\) 81.5702 592.121i 0.116529 0.845887i
\(701\) −421.313 153.346i −0.601018 0.218753i 0.0235508 0.999723i \(-0.492503\pi\)
−0.624568 + 0.780970i \(0.714725\pi\)
\(702\) −885.204 1214.89i −1.26097 1.73061i
\(703\) 563.542 29.6674i 0.801625 0.0422012i
\(704\) −322.634 436.509i −0.458288 0.620041i
\(705\) −758.147 275.943i −1.07539 0.391408i
\(706\) −158.058 152.219i −0.223878 0.215607i
\(707\) −893.298 + 1064.59i −1.26350 + 1.50579i
\(708\) 413.408 + 1015.24i 0.583910 + 1.43395i
\(709\) 65.0481 368.906i 0.0917462 0.520319i −0.903950 0.427639i \(-0.859346\pi\)
0.995696 0.0926800i \(-0.0295434\pi\)
\(710\) 177.225 18.8715i 0.249612 0.0265796i
\(711\) 636.135 367.273i 0.894705 0.516558i
\(712\) 410.587 + 521.116i 0.576666 + 0.731905i
\(713\) −54.5373 + 19.8500i −0.0764899 + 0.0278401i
\(714\) 1418.75 + 629.351i 1.98705 + 0.881444i
\(715\) 500.976 + 289.238i 0.700665 + 0.404529i
\(716\) 250.898 474.993i 0.350417 0.663398i
\(717\) 696.814 584.697i 0.971847 0.815477i
\(718\) 3.47575 50.6994i 0.00484088 0.0706120i
\(719\) −148.394 + 26.1659i −0.206390 + 0.0363921i −0.275887 0.961190i \(-0.588972\pi\)
0.0694974 + 0.997582i \(0.477860\pi\)
\(720\) −443.375 649.655i −0.615799 0.902299i
\(721\) 742.790 1.03022
\(722\) −668.929 + 271.695i −0.926494 + 0.376309i
\(723\) 1768.62i 2.44623i
\(724\) 644.317 829.343i 0.889941 1.14550i
\(725\) −5.70709 32.3665i −0.00787185 0.0446435i
\(726\) 33.4620 488.097i 0.0460909 0.672310i
\(727\) −754.323 898.967i −1.03758 1.23654i −0.971079 0.238758i \(-0.923260\pi\)
−0.0665043 0.997786i \(-0.521185\pi\)
\(728\) 244.789 + 1691.50i 0.336249 + 2.32349i
\(729\) −547.300 + 947.951i −0.750754 + 1.30034i
\(730\) 243.644 + 108.079i 0.333759 + 0.148054i
\(731\) −88.8188 244.028i −0.121503 0.333827i
\(732\) −1306.85 + 49.2068i −1.78532 + 0.0672224i
\(733\) 427.264 + 740.043i 0.582897 + 1.00961i 0.995134 + 0.0985311i \(0.0314144\pi\)
−0.412237 + 0.911077i \(0.635252\pi\)
\(734\) 80.6648 8.58949i 0.109898 0.0117023i
\(735\) 690.074 + 121.679i 0.938876 + 0.165549i
\(736\) −157.093 184.643i −0.213441 0.250874i
\(737\) −224.119 188.058i −0.304097 0.255167i
\(738\) 709.692 + 683.473i 0.961642 + 0.926115i
\(739\) 428.837 1178.22i 0.580294 1.59434i −0.207386 0.978259i \(-0.566496\pi\)
0.787680 0.616085i \(-0.211282\pi\)
\(740\) −112.880 + 350.662i −0.152541 + 0.473868i
\(741\) −109.537 2080.69i −0.147823 2.80795i
\(742\) 822.265 + 1128.51i 1.10817 + 1.52090i
\(743\) −414.918 + 1139.98i −0.558436 + 1.53429i 0.263471 + 0.964667i \(0.415133\pi\)
−0.821907 + 0.569622i \(0.807090\pi\)
\(744\) −269.182 + 144.543i −0.361804 + 0.194278i
\(745\) 282.841 + 237.331i 0.379652 + 0.318566i
\(746\) 180.924 729.886i 0.242525 0.978399i
\(747\) 2225.45 + 392.406i 2.97918 + 0.525310i
\(748\) 403.076 364.928i 0.538872 0.487872i
\(749\) −379.579 657.450i −0.506781 0.877770i
\(750\) −1036.07 696.783i −1.38143 0.929044i
\(751\) 91.2358 + 250.668i 0.121486 + 0.333779i 0.985497 0.169693i \(-0.0542777\pi\)
−0.864011 + 0.503473i \(0.832055\pi\)
\(752\) −830.965 82.7558i −1.10501 0.110048i
\(753\) −91.1780 + 157.925i −0.121086 + 0.209728i
\(754\) 41.3123 + 84.4104i 0.0547909 + 0.111950i
\(755\) −272.889 325.216i −0.361442 0.430750i
\(756\) −1123.78 + 706.489i −1.48649 + 0.934509i
\(757\) 102.793 + 582.968i 0.135790 + 0.770104i 0.974306 + 0.225227i \(0.0723124\pi\)
−0.838516 + 0.544877i \(0.816577\pi\)
\(758\) −325.170 1128.19i −0.428984 1.48838i
\(759\) 320.324i 0.422034i
\(760\) −10.2654 471.201i −0.0135071 0.620002i
\(761\) −1237.85 −1.62661 −0.813307 0.581835i \(-0.802335\pi\)
−0.813307 + 0.581835i \(0.802335\pi\)
\(762\) −324.774 + 93.6070i −0.426212 + 0.122844i
\(763\) −1168.52 + 206.041i −1.53148 + 0.270041i
\(764\) 240.270 + 382.189i 0.314490 + 0.500247i
\(765\) 603.551 506.439i 0.788955 0.662012i
\(766\) −496.896 + 243.192i −0.648689 + 0.317483i
\(767\) −1047.17 604.583i −1.36528 0.788243i
\(768\) −957.702 843.575i −1.24701 1.09841i
\(769\) 810.974 295.170i 1.05458 0.383837i 0.244192 0.969727i \(-0.421477\pi\)
0.810390 + 0.585890i \(0.199255\pi\)
\(770\) 285.078 423.891i 0.370231 0.550508i
\(771\) 8.28349 4.78247i 0.0107438 0.00620295i
\(772\) −133.935 147.936i −0.173491 0.191628i
\(773\) −233.980 + 1326.96i −0.302690 + 1.71664i 0.331491 + 0.943458i \(0.392448\pi\)
−0.634181 + 0.773184i \(0.718663\pi\)
\(774\) 498.657 + 123.607i 0.644260 + 0.159699i
\(775\) −75.7619 + 90.2895i −0.0977573 + 0.116503i
\(776\) −1076.15 + 577.863i −1.38680 + 0.744669i
\(777\) 1351.39 + 491.864i 1.73924 + 0.633030i
\(778\) −1050.64 + 765.528i −1.35044 + 0.983969i
\(779\) 132.950 + 575.251i 0.170668 + 0.738448i
\(780\) 1294.70 + 416.772i 1.65988 + 0.534324i
\(781\) −229.046 83.3660i −0.293273 0.106743i
\(782\) 168.455 174.917i 0.215415 0.223679i
\(783\) −46.9164 + 55.9128i −0.0599187 + 0.0714084i
\(784\) 723.221 54.5401i 0.922476 0.0695664i
\(785\) 64.2521 364.392i 0.0818498 0.464193i
\(786\) 87.6014 + 822.673i 0.111452 + 1.04666i
\(787\) −107.996 + 62.3514i −0.137225 + 0.0792266i −0.567041 0.823690i \(-0.691912\pi\)
0.429816 + 0.902916i \(0.358578\pi\)
\(788\) −2.26126 60.0555i −0.00286962 0.0762125i
\(789\) 717.795 261.256i 0.909753 0.331123i
\(790\) −116.510 + 262.650i −0.147481 + 0.332468i
\(791\) 596.035 + 344.121i 0.753520 + 0.435045i
\(792\) 154.064 + 1064.59i 0.194525 + 1.34417i
\(793\) 1105.08 927.269i 1.39354 1.16932i
\(794\) −933.354 63.9871i −1.17551 0.0805882i
\(795\) 1094.30 192.955i 1.37648 0.242711i
\(796\) 527.668 + 409.946i 0.662899 + 0.515007i
\(797\) −1489.07 −1.86834 −0.934170 0.356829i \(-0.883858\pi\)
−0.934170 + 0.356829i \(0.883858\pi\)
\(798\) −1839.71 29.1672i −2.30540 0.0365504i
\(799\) 836.506i 1.04694i
\(800\) −463.779 165.228i −0.579724 0.206535i
\(801\) −228.301 1294.76i −0.285020 1.61643i
\(802\) 145.193 + 9.95382i 0.181038 + 0.0124113i
\(803\) −234.312 279.242i −0.291796 0.347749i
\(804\) −608.251 321.287i −0.756531 0.399611i
\(805\) 114.076 197.585i 0.141709 0.245447i
\(806\) 136.661 308.076i 0.169555 0.382228i
\(807\) −747.461 2053.63i −0.926221 2.54477i
\(808\) 708.439 + 899.150i 0.876780 + 1.11281i
\(809\) 753.331 + 1304.81i 0.931187 + 1.61286i 0.781295 + 0.624161i \(0.214559\pi\)
0.149892 + 0.988702i \(0.452107\pi\)
\(810\) 18.1606 + 170.548i 0.0224205 + 0.210553i
\(811\) −303.492 53.5138i −0.374219 0.0659849i −0.0166245 0.999862i \(-0.505292\pi\)
−0.357595 + 0.933877i \(0.616403\pi\)
\(812\) 76.8609 31.2980i 0.0946563 0.0385444i
\(813\) 427.194 + 358.458i 0.525454 + 0.440908i
\(814\) 349.479 362.886i 0.429336 0.445806i
\(815\) −242.992 + 667.614i −0.298149 + 0.819159i
\(816\) 745.790 1038.36i 0.913958 1.27250i
\(817\) 210.009 + 225.100i 0.257048 + 0.275520i
\(818\) 194.209 141.506i 0.237419 0.172990i
\(819\) 1158.42 3182.73i 1.41443 3.88612i
\(820\) −381.810 52.5979i −0.465622 0.0641438i
\(821\) 1162.88 + 975.776i 1.41642 + 1.18852i 0.953223 + 0.302269i \(0.0977439\pi\)
0.463202 + 0.886253i \(0.346701\pi\)
\(822\) 2102.48 + 521.160i 2.55776 + 0.634015i
\(823\) −869.877 153.383i −1.05696 0.186370i −0.381952 0.924182i \(-0.624748\pi\)
−0.675007 + 0.737812i \(0.735859\pi\)
\(824\) 124.757 598.977i 0.151404 0.726914i
\(825\) 325.263 + 563.372i 0.394258 + 0.682876i
\(826\) −595.885 + 886.041i −0.721411 + 1.07269i
\(827\) 185.713 + 510.242i 0.224562 + 0.616980i 0.999894 0.0145747i \(-0.00463945\pi\)
−0.775332 + 0.631554i \(0.782417\pi\)
\(828\) 101.167 + 469.650i 0.122183 + 0.567210i
\(829\) 706.291 1223.33i 0.851979 1.47567i −0.0274400 0.999623i \(-0.508736\pi\)
0.879419 0.476048i \(-0.157931\pi\)
\(830\) −793.966 + 388.585i −0.956585 + 0.468174i
\(831\) 217.674 + 259.413i 0.261942 + 0.312170i
\(832\) 1405.12 + 86.7040i 1.68885 + 0.104212i
\(833\) 126.158 + 715.479i 0.151451 + 0.858919i
\(834\) 1323.20 381.375i 1.58657 0.457284i
\(835\) 804.436i 0.963396i
\(836\) −270.677 + 584.990i −0.323776 + 0.699749i
\(837\) 261.756 0.312731
\(838\) −27.6889 96.0678i −0.0330416 0.114639i
\(839\) −462.957 + 81.6318i −0.551796 + 0.0972965i −0.442592 0.896723i \(-0.645941\pi\)
−0.109203 + 0.994019i \(0.534830\pi\)
\(840\) 445.375 1115.46i 0.530208 1.32793i
\(841\) −640.748 + 537.651i −0.761888 + 0.639300i
\(842\) 100.110 + 204.548i 0.118896 + 0.242931i
\(843\) −107.075 61.8197i −0.127016 0.0733330i
\(844\) −114.458 531.350i −0.135614 0.629562i
\(845\) −917.418 + 333.913i −1.08570 + 0.395163i
\(846\) 1373.22 + 923.525i 1.62319 + 1.09164i
\(847\) 412.718 238.283i 0.487271 0.281326i
\(848\) 1048.12 473.524i 1.23599 0.558401i
\(849\) −14.8084 + 83.9828i −0.0174422 + 0.0989197i
\(850\) 118.657 478.688i 0.139596 0.563163i
\(851\) 144.635 172.370i 0.169959 0.202549i
\(852\) −567.740 78.2115i −0.666361 0.0917976i
\(853\) −686.353 249.812i −0.804634 0.292863i −0.0932287 0.995645i \(-0.529719\pi\)
−0.711405 + 0.702782i \(0.751941\pi\)
\(854\) −750.181 1029.58i −0.878432 1.20560i
\(855\) −423.834 + 832.307i −0.495712 + 0.973458i
\(856\) −593.913 + 195.665i −0.693823 + 0.228580i
\(857\) −659.316 239.971i −0.769330 0.280013i −0.0726141 0.997360i \(-0.523134\pi\)
−0.696716 + 0.717347i \(0.745356\pi\)
\(858\) −1339.83 1290.34i −1.56158 1.50389i
\(859\) 310.044 369.496i 0.360936 0.430147i −0.554765 0.832007i \(-0.687192\pi\)
0.915701 + 0.401860i \(0.131636\pi\)
\(860\) −186.124 + 75.7902i −0.216423 + 0.0881281i
\(861\) −261.272 + 1481.75i −0.303452 + 1.72096i
\(862\) 799.248 85.1069i 0.927201 0.0987319i
\(863\) −995.383 + 574.685i −1.15340 + 0.665915i −0.949713 0.313121i \(-0.898625\pi\)
−0.203685 + 0.979036i \(0.565292\pi\)
\(864\) 380.958 + 1024.87i 0.440923 + 1.18619i
\(865\) −375.472 + 136.661i −0.434072 + 0.157989i
\(866\) 710.218 + 315.049i 0.820113 + 0.363798i
\(867\) −138.687 80.0711i −0.159962 0.0923542i
\(868\) −263.161 139.006i −0.303181 0.160145i
\(869\) 301.025 252.590i 0.346404 0.290668i
\(870\) 4.51705 65.8884i 0.00519201 0.0757338i
\(871\) 747.265 131.763i 0.857940 0.151278i
\(872\) −30.1111 + 976.886i −0.0345310 + 1.12028i
\(873\) 2420.64 2.77278
\(874\) −102.738 + 268.927i −0.117549 + 0.307697i
\(875\) 1216.23i 1.38997i
\(876\) −676.827 525.827i −0.772633 0.600259i
\(877\) −91.0571 516.410i −0.103828 0.588838i −0.991682 0.128712i \(-0.958916\pi\)
0.887854 0.460125i \(-0.152195\pi\)
\(878\) 69.2085 1009.52i 0.0788252 1.14979i
\(879\) 235.092 + 280.172i 0.267454 + 0.318739i
\(880\) −293.940 301.078i −0.334023 0.342135i
\(881\) −179.286 + 310.533i −0.203503 + 0.352478i −0.949655 0.313298i \(-0.898566\pi\)
0.746152 + 0.665776i \(0.231899\pi\)
\(882\) −1313.82 582.805i −1.48960 0.660777i
\(883\) −273.948 752.665i −0.310246 0.852395i −0.992606 0.121379i \(-0.961269\pi\)
0.682360 0.731016i \(-0.260954\pi\)
\(884\) 53.0607 + 1409.21i 0.0600234 + 1.59412i
\(885\) 424.872 + 735.900i 0.480081 + 0.831525i
\(886\) −315.213 + 33.5651i −0.355771 + 0.0378838i
\(887\) 1396.10 + 246.171i 1.57396 + 0.277532i 0.891373 0.453270i \(-0.149743\pi\)
0.682589 + 0.730802i \(0.260854\pi\)
\(888\) 623.608 1007.13i 0.702261 1.13416i
\(889\) −252.210 211.629i −0.283701 0.238053i
\(890\) 370.432 + 356.747i 0.416216 + 0.400839i
\(891\) 80.2253 220.417i 0.0900396 0.247382i
\(892\) −141.570 45.5721i −0.158711 0.0510898i
\(893\) 387.685 + 912.729i 0.434138 + 1.02209i
\(894\) −699.166 959.564i −0.782065 1.07334i
\(895\) 142.424 391.306i 0.159133 0.437213i
\(896\) 161.253 1232.68i 0.179970 1.37576i
\(897\) −636.417 534.017i −0.709495 0.595337i
\(898\) 121.837 491.517i 0.135676 0.547346i
\(899\) −16.1162 2.84172i −0.0179268 0.00316098i
\(900\) 654.821 + 723.274i 0.727579 + 0.803637i
\(901\) 576.047 + 997.742i 0.639341 + 1.10737i
\(902\) 437.389 + 294.155i 0.484910 + 0.326114i
\(903\) 268.325 + 737.218i 0.297149 + 0.816409i
\(904\) 377.603 422.838i 0.417702 0.467741i
\(905\) 407.057 705.043i 0.449786 0.779053i
\(906\) 600.113 + 1226.17i 0.662376 + 1.35338i
\(907\) 268.134 + 319.549i 0.295627 + 0.352314i 0.893329 0.449404i \(-0.148364\pi\)
−0.597702 + 0.801719i \(0.703919\pi\)
\(908\) −348.555 554.433i −0.383872 0.610609i
\(909\) −393.918 2234.02i −0.433353 2.45767i
\(910\) 366.926 + 1273.07i 0.403215 + 1.39897i
\(911\) 1616.96i 1.77493i −0.460874 0.887465i \(-0.652464\pi\)
0.460874 0.887465i \(-0.347536\pi\)
\(912\) −332.511 + 1478.62i −0.364595 + 1.62129i
\(913\) 1208.92 1.32411
\(914\) 1031.07 297.176i 1.12808 0.325138i
\(915\) −998.371 + 176.040i −1.09112 + 0.192393i
\(916\) 140.412 88.2728i 0.153288 0.0963677i
\(917\) −617.346 + 518.014i −0.673223 + 0.564901i
\(918\) −983.750 + 481.469i −1.07162 + 0.524476i
\(919\) 186.867 + 107.888i 0.203338 + 0.117397i 0.598211 0.801338i \(-0.295878\pi\)
−0.394874 + 0.918735i \(0.629212\pi\)
\(920\) −140.170 125.175i −0.152359 0.136060i
\(921\) −2514.03 + 915.033i −2.72968 + 0.993522i
\(922\) −346.351 + 515.000i −0.375652 + 0.558569i
\(923\) 547.477 316.086i 0.593150 0.342455i
\(924\) −1217.71 + 1102.46i −1.31787 + 1.19314i
\(925\) 79.3510 450.022i 0.0857849 0.486510i
\(926\) −41.9908 10.4087i −0.0453465 0.0112405i
\(927\) −779.364 + 928.810i −0.840738 + 1.00195i
\(928\) −12.3291 67.2364i −0.0132856 0.0724530i
\(929\) 492.556 + 179.276i 0.530200 + 0.192977i 0.593228 0.805035i \(-0.297853\pi\)
−0.0630277 + 0.998012i \(0.520076\pi\)
\(930\) −191.423 + 139.476i −0.205831 + 0.149974i
\(931\) −469.248 722.206i −0.504026 0.775731i
\(932\) 265.194 823.826i 0.284543 0.883933i
\(933\) −272.380 99.1382i −0.291940 0.106257i
\(934\) −752.491 + 781.358i −0.805665 + 0.836571i
\(935\) 270.930 322.882i 0.289765 0.345328i
\(936\) −2371.95 1468.70i −2.53414 1.56912i
\(937\) 201.001 1139.93i 0.214516 1.21658i −0.667230 0.744852i \(-0.732520\pi\)
0.881745 0.471726i \(-0.156369\pi\)
\(938\) −70.9502 666.300i −0.0756398 0.710341i
\(939\) −2398.83 + 1384.97i −2.55467 + 1.47494i
\(940\) −646.881 + 24.3569i −0.688171 + 0.0259116i
\(941\) −153.395 + 55.8313i −0.163013 + 0.0593319i −0.422238 0.906485i \(-0.638755\pi\)
0.259225 + 0.965817i \(0.416533\pi\)
\(942\) −482.455 + 1087.60i −0.512160 + 1.15457i
\(943\) 203.876 + 117.708i 0.216200 + 0.124823i
\(944\) 614.410 + 629.331i 0.650858 + 0.666665i
\(945\) −788.252 + 661.422i −0.834129 + 0.699917i
\(946\) 274.197 + 18.7979i 0.289849 + 0.0198709i
\(947\) 722.990 127.483i 0.763453 0.134617i 0.221654 0.975125i \(-0.428855\pi\)
0.541799 + 0.840508i \(0.317743\pi\)
\(948\) 566.845 729.624i 0.597938 0.769645i
\(949\) 945.422 0.996230
\(950\) 92.3826 + 577.300i 0.0972448 + 0.607684i
\(951\) 885.070i 0.930673i
\(952\) 1244.72 + 38.3666i 1.30748 + 0.0403011i
\(953\) −216.769 1229.36i −0.227459 1.28998i −0.857928 0.513770i \(-0.828248\pi\)
0.630469 0.776215i \(-0.282863\pi\)
\(954\) −2273.88 155.888i −2.38352 0.163405i
\(955\) 224.943 + 268.077i 0.235543 + 0.280709i
\(956\) 340.880 645.343i 0.356569 0.675045i
\(957\) −45.1609 + 78.2210i −0.0471901 + 0.0817356i
\(958\) 126.170 284.427i 0.131702 0.296896i
\(959\) 721.655 + 1982.73i 0.752508 + 2.06750i
\(960\) −824.693 546.494i −0.859055 0.569265i
\(961\) −451.156 781.425i −0.469465 0.813137i
\(962\) 138.356 + 1299.32i 0.143821 + 1.35064i
\(963\) 1220.37 + 215.183i 1.26725 + 0.223451i
\(964\) 535.176 + 1314.27i 0.555162 + 1.36335i
\(965\) −118.504 99.4364i −0.122802 0.103043i
\(966\) −508.908 + 528.431i −0.526820 + 0.547030i
\(967\) 566.709 1557.02i 0.586049 1.61016i −0.191612 0.981471i \(-0.561371\pi\)
0.777660 0.628685i \(-0.216406\pi\)
\(968\) −122.830 372.832i −0.126890 0.385157i
\(969\) −1506.87 184.659i −1.55508 0.190567i
\(970\) −765.282 + 557.607i −0.788951 + 0.574852i
\(971\) −144.176 + 396.121i −0.148482 + 0.407951i −0.991528 0.129890i \(-0.958538\pi\)
0.843046 + 0.537841i \(0.180760\pi\)
\(972\) −92.6009 + 672.192i −0.0952684 + 0.691556i
\(973\) 1027.56 + 862.222i 1.05607 + 0.886148i
\(974\) −392.220 97.2233i −0.402690 0.0998186i
\(975\) −1661.55 292.977i −1.70416 0.300489i
\(976\) −956.238 + 432.013i −0.979752 + 0.442636i
\(977\) −437.363 757.536i −0.447660 0.775369i 0.550574 0.834787i \(-0.314409\pi\)
−0.998233 + 0.0594174i \(0.981076\pi\)
\(978\) 1274.92 1895.71i 1.30359 1.93836i
\(979\) −240.558 660.928i −0.245718 0.675105i
\(980\) 549.616 118.393i 0.560833 0.120809i
\(981\) 968.413 1677.34i 0.987170 1.70983i
\(982\) 875.540 428.509i 0.891589 0.436364i
\(983\) 1009.13 + 1202.64i 1.02659 + 1.22344i 0.974405 + 0.224800i \(0.0721730\pi\)
0.0521815 + 0.998638i \(0.483383\pi\)
\(984\) 1150.98 + 459.556i 1.16970 + 0.467029i
\(985\) −8.08977 45.8794i −0.00821297 0.0465781i
\(986\) 65.7961 18.9639i 0.0667303 0.0192332i
\(987\) 2527.12i 2.56040i
\(988\) −711.003 1513.02i −0.719639 1.53140i
\(989\) 122.750 0.124116
\(990\) 230.933 + 801.233i 0.233266 + 0.809326i
\(991\) 195.901 34.5426i 0.197680 0.0348564i −0.0739313 0.997263i \(-0.523555\pi\)
0.271611 + 0.962407i \(0.412443\pi\)
\(992\) −156.292 + 188.863i −0.157553 + 0.190386i
\(993\) −608.919 + 510.943i −0.613211 + 0.514545i
\(994\) −245.406 501.419i −0.246887 0.504446i
\(995\) 448.582 + 258.989i 0.450836 + 0.260290i
\(996\) 2778.70 598.560i 2.78986 0.600964i
\(997\) 132.207 48.1195i 0.132605 0.0482643i −0.274865 0.961483i \(-0.588633\pi\)
0.407470 + 0.913218i \(0.366411\pi\)
\(998\) −1628.85 1095.44i −1.63211 1.09764i
\(999\) −878.871 + 507.417i −0.879751 + 0.507925i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 76.3.l.a.23.2 108
4.3 odd 2 inner 76.3.l.a.23.6 yes 108
19.5 even 9 inner 76.3.l.a.43.6 yes 108
76.43 odd 18 inner 76.3.l.a.43.2 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.3.l.a.23.2 108 1.1 even 1 trivial
76.3.l.a.23.6 yes 108 4.3 odd 2 inner
76.3.l.a.43.2 yes 108 76.43 odd 18 inner
76.3.l.a.43.6 yes 108 19.5 even 9 inner