Properties

Label 450.2.l.c.289.1
Level $450$
Weight $2$
Character 450.289
Analytic conductor $3.593$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [450,2,Mod(19,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.l (of order \(10\), degree \(4\), 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: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + 6259 x^{8} - 11958 x^{7} - 15752 x^{6} + 14670 x^{5} + 18271 x^{4} + \cdots + 11105 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 289.1
Root \(-1.16141 - 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 450.289
Dual form 450.2.l.c.109.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-1.86682 + 1.23085i) q^{5} -2.70913i q^{7} +(0.951057 - 0.309017i) q^{8} +O(q^{10})\) \(q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-1.86682 + 1.23085i) q^{5} -2.70913i q^{7} +(0.951057 - 0.309017i) q^{8} +(2.09307 + 0.786811i) q^{10} +(4.54704 - 3.30361i) q^{11} +(-2.84536 + 3.91630i) q^{13} +(-2.19173 + 1.59239i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.994499 + 0.323132i) q^{17} +(-2.59109 - 7.97455i) q^{19} +(-0.593730 - 2.15580i) q^{20} +(-5.34536 - 1.73681i) q^{22} +(-3.11219 - 4.28357i) q^{23} +(1.97002 - 4.59555i) q^{25} +4.84082 q^{26} +(2.57654 + 0.837167i) q^{28} +(1.29490 - 3.98530i) q^{29} +(-1.72444 - 5.30729i) q^{31} +1.00000i q^{32} +(0.845972 + 0.614634i) q^{34} +(3.33453 + 5.05745i) q^{35} +(1.75853 - 2.42041i) q^{37} +(-4.92854 + 6.78356i) q^{38} +(-1.39510 + 1.74749i) q^{40} +(-1.27617 - 0.927190i) q^{41} +3.29669i q^{43} +(1.73681 + 5.34536i) q^{44} +(-1.63618 + 5.03563i) q^{46} +(-2.92330 - 0.949838i) q^{47} -0.339383 q^{49} +(-4.87582 + 1.10742i) q^{50} +(-2.84536 - 3.91630i) q^{52} +(-5.87478 - 1.90883i) q^{53} +(-4.42223 + 11.7640i) q^{55} +(-0.837167 - 2.57654i) q^{56} +(-3.98530 + 1.29490i) q^{58} +(11.4780 + 8.33925i) q^{59} +(-0.218911 + 0.159048i) q^{61} +(-3.28009 + 4.51465i) q^{62} +(0.809017 - 0.587785i) q^{64} +(0.491387 - 10.8132i) q^{65} +(6.00099 - 1.94984i) q^{67} -1.04568i q^{68} +(2.13157 - 5.67039i) q^{70} +(1.40070 - 4.31091i) q^{71} +(4.79691 + 6.60237i) q^{73} -2.99179 q^{74} +8.38494 q^{76} +(-8.94992 - 12.3185i) q^{77} +(-3.85697 + 11.8705i) q^{79} +(2.23376 + 0.101509i) q^{80} +1.57743i q^{82} +(-0.127938 + 0.0415695i) q^{83} +(1.45882 - 1.82731i) q^{85} +(2.66708 - 1.93775i) q^{86} +(3.30361 - 4.54704i) q^{88} +(-9.53844 + 6.93008i) q^{89} +(10.6098 + 7.70845i) q^{91} +(5.03563 - 1.63618i) q^{92} +(0.949838 + 2.92330i) q^{94} +(14.6526 + 11.6978i) q^{95} +(2.51108 + 0.815900i) q^{97} +(0.199485 + 0.274567i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{4} - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{4} - 4 q^{5} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 2 q^{14} - 4 q^{16} + 30 q^{17} + 4 q^{20} - 20 q^{22} + 10 q^{23} + 24 q^{25} - 4 q^{26} + 10 q^{29} - 18 q^{31} + 12 q^{34} + 34 q^{35} + 20 q^{37} - 10 q^{38} - 2 q^{40} - 22 q^{41} - 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} - 12 q^{50} + 20 q^{52} - 30 q^{53} + 18 q^{55} + 2 q^{56} - 30 q^{58} - 20 q^{59} + 12 q^{61} - 50 q^{62} + 4 q^{64} + 8 q^{65} - 50 q^{67} - 12 q^{70} + 28 q^{71} + 20 q^{73} - 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{80} + 30 q^{83} - 4 q^{85} + 6 q^{86} - 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} + 30 q^{95} - 10 q^{97} - 60 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.587785 0.809017i −0.415627 0.572061i
\(3\) 0 0
\(4\) −0.309017 + 0.951057i −0.154508 + 0.475528i
\(5\) −1.86682 + 1.23085i −0.834866 + 0.550453i
\(6\) 0 0
\(7\) 2.70913i 1.02395i −0.858999 0.511977i \(-0.828913\pi\)
0.858999 0.511977i \(-0.171087\pi\)
\(8\) 0.951057 0.309017i 0.336249 0.109254i
\(9\) 0 0
\(10\) 2.09307 + 0.786811i 0.661886 + 0.248812i
\(11\) 4.54704 3.30361i 1.37098 0.996077i 0.373323 0.927701i \(-0.378218\pi\)
0.997660 0.0683760i \(-0.0217817\pi\)
\(12\) 0 0
\(13\) −2.84536 + 3.91630i −0.789161 + 1.08619i 0.205051 + 0.978751i \(0.434264\pi\)
−0.994212 + 0.107436i \(0.965736\pi\)
\(14\) −2.19173 + 1.59239i −0.585765 + 0.425583i
\(15\) 0 0
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) −0.994499 + 0.323132i −0.241202 + 0.0783711i −0.427123 0.904193i \(-0.640473\pi\)
0.185922 + 0.982565i \(0.440473\pi\)
\(18\) 0 0
\(19\) −2.59109 7.97455i −0.594437 1.82949i −0.557510 0.830170i \(-0.688243\pi\)
−0.0369263 0.999318i \(-0.511757\pi\)
\(20\) −0.593730 2.15580i −0.132762 0.482052i
\(21\) 0 0
\(22\) −5.34536 1.73681i −1.13963 0.370290i
\(23\) −3.11219 4.28357i −0.648937 0.893185i 0.350115 0.936707i \(-0.386142\pi\)
−0.999053 + 0.0435212i \(0.986142\pi\)
\(24\) 0 0
\(25\) 1.97002 4.59555i 0.394003 0.919109i
\(26\) 4.84082 0.949362
\(27\) 0 0
\(28\) 2.57654 + 0.837167i 0.486919 + 0.158210i
\(29\) 1.29490 3.98530i 0.240457 0.740051i −0.755893 0.654695i \(-0.772797\pi\)
0.996350 0.0853563i \(-0.0272028\pi\)
\(30\) 0 0
\(31\) −1.72444 5.30729i −0.309719 0.953218i −0.977874 0.209195i \(-0.932916\pi\)
0.668155 0.744022i \(-0.267084\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 0.845972 + 0.614634i 0.145083 + 0.105409i
\(35\) 3.33453 + 5.05745i 0.563639 + 0.854865i
\(36\) 0 0
\(37\) 1.75853 2.42041i 0.289101 0.397913i −0.639621 0.768690i \(-0.720909\pi\)
0.928722 + 0.370778i \(0.120909\pi\)
\(38\) −4.92854 + 6.78356i −0.799516 + 1.10044i
\(39\) 0 0
\(40\) −1.39510 + 1.74749i −0.220584 + 0.276302i
\(41\) −1.27617 0.927190i −0.199304 0.144803i 0.483657 0.875258i \(-0.339308\pi\)
−0.682961 + 0.730455i \(0.739308\pi\)
\(42\) 0 0
\(43\) 3.29669i 0.502741i 0.967891 + 0.251370i \(0.0808812\pi\)
−0.967891 + 0.251370i \(0.919119\pi\)
\(44\) 1.73681 + 5.34536i 0.261834 + 0.805843i
\(45\) 0 0
\(46\) −1.63618 + 5.03563i −0.241241 + 0.742464i
\(47\) −2.92330 0.949838i −0.426407 0.138548i 0.0879484 0.996125i \(-0.471969\pi\)
−0.514356 + 0.857577i \(0.671969\pi\)
\(48\) 0 0
\(49\) −0.339383 −0.0484833
\(50\) −4.87582 + 1.10742i −0.689545 + 0.156613i
\(51\) 0 0
\(52\) −2.84536 3.91630i −0.394581 0.543094i
\(53\) −5.87478 1.90883i −0.806962 0.262198i −0.123652 0.992326i \(-0.539461\pi\)
−0.683311 + 0.730128i \(0.739461\pi\)
\(54\) 0 0
\(55\) −4.42223 + 11.7640i −0.596293 + 1.58625i
\(56\) −0.837167 2.57654i −0.111871 0.344304i
\(57\) 0 0
\(58\) −3.98530 + 1.29490i −0.523295 + 0.170029i
\(59\) 11.4780 + 8.33925i 1.49431 + 1.08568i 0.972581 + 0.232565i \(0.0747118\pi\)
0.521726 + 0.853113i \(0.325288\pi\)
\(60\) 0 0
\(61\) −0.218911 + 0.159048i −0.0280286 + 0.0203640i −0.601711 0.798714i \(-0.705514\pi\)
0.573683 + 0.819078i \(0.305514\pi\)
\(62\) −3.28009 + 4.51465i −0.416571 + 0.573361i
\(63\) 0 0
\(64\) 0.809017 0.587785i 0.101127 0.0734732i
\(65\) 0.491387 10.8132i 0.0609490 1.34122i
\(66\) 0 0
\(67\) 6.00099 1.94984i 0.733137 0.238211i 0.0814275 0.996679i \(-0.474052\pi\)
0.651710 + 0.758469i \(0.274052\pi\)
\(68\) 1.04568i 0.126807i
\(69\) 0 0
\(70\) 2.13157 5.67039i 0.254772 0.677741i
\(71\) 1.40070 4.31091i 0.166233 0.511611i −0.832892 0.553435i \(-0.813317\pi\)
0.999125 + 0.0418237i \(0.0133168\pi\)
\(72\) 0 0
\(73\) 4.79691 + 6.60237i 0.561435 + 0.772749i 0.991508 0.130045i \(-0.0415121\pi\)
−0.430073 + 0.902794i \(0.641512\pi\)
\(74\) −2.99179 −0.347788
\(75\) 0 0
\(76\) 8.38494 0.961819
\(77\) −8.94992 12.3185i −1.01994 1.40382i
\(78\) 0 0
\(79\) −3.85697 + 11.8705i −0.433943 + 1.33554i 0.460223 + 0.887804i \(0.347770\pi\)
−0.894166 + 0.447736i \(0.852230\pi\)
\(80\) 2.23376 + 0.101509i 0.249742 + 0.0113491i
\(81\) 0 0
\(82\) 1.57743i 0.174198i
\(83\) −0.127938 + 0.0415695i −0.0140430 + 0.00456285i −0.316030 0.948749i \(-0.602350\pi\)
0.301987 + 0.953312i \(0.402350\pi\)
\(84\) 0 0
\(85\) 1.45882 1.82731i 0.158231 0.198200i
\(86\) 2.66708 1.93775i 0.287599 0.208953i
\(87\) 0 0
\(88\) 3.30361 4.54704i 0.352167 0.484716i
\(89\) −9.53844 + 6.93008i −1.01107 + 0.734587i −0.964434 0.264325i \(-0.914851\pi\)
−0.0466385 + 0.998912i \(0.514851\pi\)
\(90\) 0 0
\(91\) 10.6098 + 7.70845i 1.11221 + 0.808065i
\(92\) 5.03563 1.63618i 0.525001 0.170583i
\(93\) 0 0
\(94\) 0.949838 + 2.92330i 0.0979683 + 0.301516i
\(95\) 14.6526 + 11.6978i 1.50332 + 1.20017i
\(96\) 0 0
\(97\) 2.51108 + 0.815900i 0.254962 + 0.0828421i 0.433709 0.901053i \(-0.357205\pi\)
−0.178748 + 0.983895i \(0.557205\pi\)
\(98\) 0.199485 + 0.274567i 0.0201510 + 0.0277354i
\(99\) 0 0
\(100\) 3.76186 + 3.29370i 0.376186 + 0.329370i
\(101\) 3.82844 0.380944 0.190472 0.981693i \(-0.438998\pi\)
0.190472 + 0.981693i \(0.438998\pi\)
\(102\) 0 0
\(103\) −5.60479 1.82111i −0.552256 0.179439i 0.0195778 0.999808i \(-0.493768\pi\)
−0.571834 + 0.820369i \(0.693768\pi\)
\(104\) −1.49589 + 4.60389i −0.146685 + 0.451449i
\(105\) 0 0
\(106\) 1.90883 + 5.87478i 0.185402 + 0.570609i
\(107\) 5.90758i 0.571108i −0.958363 0.285554i \(-0.907822\pi\)
0.958363 0.285554i \(-0.0921775\pi\)
\(108\) 0 0
\(109\) 4.56128 + 3.31397i 0.436892 + 0.317420i 0.784399 0.620257i \(-0.212972\pi\)
−0.347507 + 0.937677i \(0.612972\pi\)
\(110\) 12.1166 3.33703i 1.15527 0.318173i
\(111\) 0 0
\(112\) −1.59239 + 2.19173i −0.150466 + 0.207099i
\(113\) −2.97826 + 4.09923i −0.280171 + 0.385623i −0.925791 0.378037i \(-0.876599\pi\)
0.645619 + 0.763659i \(0.276599\pi\)
\(114\) 0 0
\(115\) 11.0823 + 4.16599i 1.03343 + 0.388481i
\(116\) 3.39010 + 2.46305i 0.314763 + 0.228688i
\(117\) 0 0
\(118\) 14.1876i 1.30607i
\(119\) 0.875408 + 2.69423i 0.0802485 + 0.246979i
\(120\) 0 0
\(121\) 6.36248 19.5817i 0.578407 1.78015i
\(122\) 0.257345 + 0.0836164i 0.0232989 + 0.00757027i
\(123\) 0 0
\(124\) 5.58042 0.501136
\(125\) 1.97877 + 11.0038i 0.176987 + 0.984213i
\(126\) 0 0
\(127\) −5.60106 7.70919i −0.497013 0.684080i 0.484649 0.874709i \(-0.338947\pi\)
−0.981662 + 0.190628i \(0.938947\pi\)
\(128\) −0.951057 0.309017i −0.0840623 0.0273135i
\(129\) 0 0
\(130\) −9.03692 + 5.95832i −0.792591 + 0.522579i
\(131\) −0.0460083 0.141599i −0.00401976 0.0123716i 0.949027 0.315196i \(-0.102070\pi\)
−0.953046 + 0.302825i \(0.902070\pi\)
\(132\) 0 0
\(133\) −21.6041 + 7.01960i −1.87331 + 0.608676i
\(134\) −5.10474 3.70881i −0.440983 0.320393i
\(135\) 0 0
\(136\) −0.845972 + 0.614634i −0.0725415 + 0.0527045i
\(137\) 5.30429 7.30072i 0.453176 0.623743i −0.519900 0.854227i \(-0.674031\pi\)
0.973076 + 0.230484i \(0.0740309\pi\)
\(138\) 0 0
\(139\) 5.75420 4.18067i 0.488065 0.354600i −0.316375 0.948634i \(-0.602466\pi\)
0.804440 + 0.594034i \(0.202466\pi\)
\(140\) −5.84035 + 1.60849i −0.493600 + 0.135942i
\(141\) 0 0
\(142\) −4.31091 + 1.40070i −0.361764 + 0.117544i
\(143\) 27.2075i 2.27521i
\(144\) 0 0
\(145\) 2.48796 + 9.03365i 0.206614 + 0.750204i
\(146\) 2.52188 7.76156i 0.208712 0.642351i
\(147\) 0 0
\(148\) 1.75853 + 2.42041i 0.144550 + 0.198956i
\(149\) 15.4351 1.26449 0.632246 0.774768i \(-0.282133\pi\)
0.632246 + 0.774768i \(0.282133\pi\)
\(150\) 0 0
\(151\) −7.99801 −0.650868 −0.325434 0.945565i \(-0.605510\pi\)
−0.325434 + 0.945565i \(0.605510\pi\)
\(152\) −4.92854 6.78356i −0.399758 0.550219i
\(153\) 0 0
\(154\) −4.70525 + 14.4813i −0.379160 + 1.16693i
\(155\) 9.75170 + 7.78521i 0.783276 + 0.625323i
\(156\) 0 0
\(157\) 15.6147i 1.24619i 0.782146 + 0.623095i \(0.214125\pi\)
−0.782146 + 0.623095i \(0.785875\pi\)
\(158\) 11.8705 3.85697i 0.944369 0.306844i
\(159\) 0 0
\(160\) −1.23085 1.86682i −0.0973073 0.147585i
\(161\) −11.6047 + 8.43133i −0.914581 + 0.664482i
\(162\) 0 0
\(163\) 2.14970 2.95881i 0.168378 0.231752i −0.716487 0.697601i \(-0.754251\pi\)
0.884864 + 0.465849i \(0.154251\pi\)
\(164\) 1.27617 0.927190i 0.0996519 0.0724014i
\(165\) 0 0
\(166\) 0.108830 + 0.0790699i 0.00844688 + 0.00613702i
\(167\) −5.99458 + 1.94776i −0.463874 + 0.150722i −0.531624 0.846980i \(-0.678418\pi\)
0.0677496 + 0.997702i \(0.478418\pi\)
\(168\) 0 0
\(169\) −3.22413 9.92286i −0.248010 0.763297i
\(170\) −2.33580 0.106146i −0.179148 0.00814101i
\(171\) 0 0
\(172\) −3.13534 1.01873i −0.239068 0.0776777i
\(173\) −6.25725 8.61237i −0.475730 0.654786i 0.501947 0.864898i \(-0.332617\pi\)
−0.977677 + 0.210112i \(0.932617\pi\)
\(174\) 0 0
\(175\) −12.4499 5.33703i −0.941126 0.403441i
\(176\) −5.62045 −0.423657
\(177\) 0 0
\(178\) 11.2131 + 3.64336i 0.840458 + 0.273081i
\(179\) −0.246999 + 0.760184i −0.0184615 + 0.0568188i −0.959863 0.280470i \(-0.909510\pi\)
0.941401 + 0.337288i \(0.109510\pi\)
\(180\) 0 0
\(181\) −5.04439 15.5250i −0.374946 1.15397i −0.943515 0.331330i \(-0.892503\pi\)
0.568568 0.822636i \(-0.307497\pi\)
\(182\) 13.1144i 0.972104i
\(183\) 0 0
\(184\) −4.28357 3.11219i −0.315789 0.229434i
\(185\) −0.303694 + 6.68295i −0.0223280 + 0.491340i
\(186\) 0 0
\(187\) −3.45452 + 4.75474i −0.252619 + 0.347701i
\(188\) 1.80670 2.48671i 0.131767 0.181362i
\(189\) 0 0
\(190\) 0.851147 18.7300i 0.0617487 1.35881i
\(191\) −12.5641 9.12835i −0.909106 0.660504i 0.0316826 0.999498i \(-0.489913\pi\)
−0.940789 + 0.338994i \(0.889913\pi\)
\(192\) 0 0
\(193\) 21.0202i 1.51307i −0.653956 0.756533i \(-0.726892\pi\)
0.653956 0.756533i \(-0.273108\pi\)
\(194\) −0.815900 2.51108i −0.0585782 0.180285i
\(195\) 0 0
\(196\) 0.104875 0.322773i 0.00749109 0.0230552i
\(197\) 22.9751 + 7.46505i 1.63691 + 0.531863i 0.975844 0.218468i \(-0.0701061\pi\)
0.661062 + 0.750331i \(0.270106\pi\)
\(198\) 0 0
\(199\) 25.4930 1.80715 0.903574 0.428432i \(-0.140934\pi\)
0.903574 + 0.428432i \(0.140934\pi\)
\(200\) 0.453494 4.97939i 0.0320669 0.352096i
\(201\) 0 0
\(202\) −2.25030 3.09727i −0.158331 0.217923i
\(203\) −10.7967 3.50806i −0.757779 0.246217i
\(204\) 0 0
\(205\) 3.52360 + 0.160123i 0.246099 + 0.0111835i
\(206\) 1.82111 + 5.60479i 0.126882 + 0.390504i
\(207\) 0 0
\(208\) 4.60389 1.49589i 0.319222 0.103722i
\(209\) −38.1266 27.7006i −2.63727 1.91609i
\(210\) 0 0
\(211\) −4.24669 + 3.08540i −0.292354 + 0.212408i −0.724288 0.689498i \(-0.757831\pi\)
0.431934 + 0.901905i \(0.357831\pi\)
\(212\) 3.63081 4.99738i 0.249365 0.343222i
\(213\) 0 0
\(214\) −4.77934 + 3.47239i −0.326709 + 0.237368i
\(215\) −4.05774 6.15432i −0.276735 0.419721i
\(216\) 0 0
\(217\) −14.3781 + 4.67174i −0.976052 + 0.317139i
\(218\) 5.63805i 0.381857i
\(219\) 0 0
\(220\) −9.82165 7.84106i −0.662176 0.528644i
\(221\) 1.56423 4.81419i 0.105221 0.323837i
\(222\) 0 0
\(223\) 8.69743 + 11.9710i 0.582423 + 0.801637i 0.993958 0.109757i \(-0.0350073\pi\)
−0.411535 + 0.911394i \(0.635007\pi\)
\(224\) 2.70913 0.181011
\(225\) 0 0
\(226\) 5.06692 0.337047
\(227\) −6.98197 9.60986i −0.463410 0.637829i 0.511802 0.859104i \(-0.328978\pi\)
−0.975211 + 0.221275i \(0.928978\pi\)
\(228\) 0 0
\(229\) −5.64177 + 17.3636i −0.372819 + 1.14742i 0.572119 + 0.820170i \(0.306121\pi\)
−0.944938 + 0.327248i \(0.893879\pi\)
\(230\) −3.14367 11.4145i −0.207287 0.752650i
\(231\) 0 0
\(232\) 4.19039i 0.275113i
\(233\) −2.71852 + 0.883301i −0.178096 + 0.0578669i −0.396708 0.917945i \(-0.629847\pi\)
0.218611 + 0.975812i \(0.429847\pi\)
\(234\) 0 0
\(235\) 6.62638 1.82497i 0.432257 0.119048i
\(236\) −11.4780 + 8.33925i −0.747154 + 0.542839i
\(237\) 0 0
\(238\) 1.66512 2.29185i 0.107934 0.148558i
\(239\) −13.2548 + 9.63014i −0.857379 + 0.622922i −0.927171 0.374640i \(-0.877766\pi\)
0.0697919 + 0.997562i \(0.477766\pi\)
\(240\) 0 0
\(241\) −21.2995 15.4750i −1.37202 0.996831i −0.997576 0.0695808i \(-0.977834\pi\)
−0.374443 0.927250i \(-0.622166\pi\)
\(242\) −19.5817 + 6.36248i −1.25876 + 0.408995i
\(243\) 0 0
\(244\) −0.0836164 0.257345i −0.00535299 0.0164748i
\(245\) 0.633567 0.417730i 0.0404771 0.0266878i
\(246\) 0 0
\(247\) 38.6034 + 12.5430i 2.45627 + 0.798091i
\(248\) −3.28009 4.51465i −0.208286 0.286681i
\(249\) 0 0
\(250\) 7.73920 8.06875i 0.489470 0.510313i
\(251\) 13.8356 0.873295 0.436647 0.899633i \(-0.356166\pi\)
0.436647 + 0.899633i \(0.356166\pi\)
\(252\) 0 0
\(253\) −28.3025 9.19604i −1.77936 0.578150i
\(254\) −2.94465 + 9.06270i −0.184764 + 0.568644i
\(255\) 0 0
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) 28.6204i 1.78529i 0.450756 + 0.892647i \(0.351154\pi\)
−0.450756 + 0.892647i \(0.648846\pi\)
\(258\) 0 0
\(259\) −6.55720 4.76409i −0.407445 0.296026i
\(260\) 10.1322 + 3.80881i 0.628369 + 0.236212i
\(261\) 0 0
\(262\) −0.0875130 + 0.120451i −0.00540657 + 0.00744150i
\(263\) −1.83569 + 2.52661i −0.113194 + 0.155798i −0.861855 0.507155i \(-0.830697\pi\)
0.748661 + 0.662953i \(0.230697\pi\)
\(264\) 0 0
\(265\) 13.3166 3.66753i 0.818033 0.225295i
\(266\) 18.3775 + 13.3521i 1.12680 + 0.818668i
\(267\) 0 0
\(268\) 6.30981i 0.385433i
\(269\) 2.85284 + 8.78015i 0.173941 + 0.535335i 0.999584 0.0288583i \(-0.00918715\pi\)
−0.825643 + 0.564194i \(0.809187\pi\)
\(270\) 0 0
\(271\) −6.70088 + 20.6232i −0.407050 + 1.25277i 0.512122 + 0.858913i \(0.328860\pi\)
−0.919172 + 0.393857i \(0.871140\pi\)
\(272\) 0.994499 + 0.323132i 0.0603004 + 0.0195928i
\(273\) 0 0
\(274\) −9.02419 −0.545171
\(275\) −6.22418 27.4043i −0.375332 1.65254i
\(276\) 0 0
\(277\) −6.05129 8.32889i −0.363587 0.500434i 0.587557 0.809183i \(-0.300090\pi\)
−0.951144 + 0.308749i \(0.900090\pi\)
\(278\) −6.76447 2.19791i −0.405706 0.131822i
\(279\) 0 0
\(280\) 4.73417 + 3.77949i 0.282921 + 0.225868i
\(281\) 0.246763 + 0.759459i 0.0147207 + 0.0453055i 0.958147 0.286277i \(-0.0924176\pi\)
−0.943426 + 0.331582i \(0.892418\pi\)
\(282\) 0 0
\(283\) −0.694882 + 0.225781i −0.0413064 + 0.0134213i −0.329597 0.944122i \(-0.606913\pi\)
0.288291 + 0.957543i \(0.406913\pi\)
\(284\) 3.66708 + 2.66429i 0.217601 + 0.158097i
\(285\) 0 0
\(286\) 22.0114 15.9922i 1.30156 0.945638i
\(287\) −2.51188 + 3.45730i −0.148271 + 0.204078i
\(288\) 0 0
\(289\) −12.8687 + 9.34964i −0.756981 + 0.549979i
\(290\) 5.84599 7.32265i 0.343289 0.430001i
\(291\) 0 0
\(292\) −7.76156 + 2.52188i −0.454211 + 0.147582i
\(293\) 18.4842i 1.07986i −0.841711 0.539929i \(-0.818451\pi\)
0.841711 0.539929i \(-0.181549\pi\)
\(294\) 0 0
\(295\) −31.6917 1.44017i −1.84516 0.0838498i
\(296\) 0.924514 2.84536i 0.0537363 0.165383i
\(297\) 0 0
\(298\) −9.07251 12.4872i −0.525557 0.723367i
\(299\) 25.6311 1.48228
\(300\) 0 0
\(301\) 8.93117 0.514784
\(302\) 4.70111 + 6.47052i 0.270518 + 0.372337i
\(303\) 0 0
\(304\) −2.59109 + 7.97455i −0.148609 + 0.457372i
\(305\) 0.212902 0.566359i 0.0121907 0.0324296i
\(306\) 0 0
\(307\) 14.1923i 0.809998i −0.914317 0.404999i \(-0.867272\pi\)
0.914317 0.404999i \(-0.132728\pi\)
\(308\) 14.4813 4.70525i 0.825147 0.268107i
\(309\) 0 0
\(310\) 0.566463 12.4653i 0.0321729 0.707983i
\(311\) 8.18254 5.94496i 0.463989 0.337108i −0.331105 0.943594i \(-0.607421\pi\)
0.795094 + 0.606486i \(0.207421\pi\)
\(312\) 0 0
\(313\) 4.11476 5.66348i 0.232580 0.320119i −0.676735 0.736226i \(-0.736606\pi\)
0.909316 + 0.416107i \(0.136606\pi\)
\(314\) 12.6326 9.17810i 0.712898 0.517950i
\(315\) 0 0
\(316\) −10.0977 7.33640i −0.568039 0.412704i
\(317\) 14.5878 4.73987i 0.819333 0.266218i 0.130788 0.991410i \(-0.458249\pi\)
0.688546 + 0.725193i \(0.258249\pi\)
\(318\) 0 0
\(319\) −7.27792 22.3991i −0.407485 1.25411i
\(320\) −0.786811 + 2.09307i −0.0439841 + 0.117006i
\(321\) 0 0
\(322\) 13.6422 + 4.43261i 0.760249 + 0.247020i
\(323\) 5.15367 + 7.09342i 0.286758 + 0.394689i
\(324\) 0 0
\(325\) 12.3921 + 20.7912i 0.687393 + 1.15329i
\(326\) −3.65730 −0.202559
\(327\) 0 0
\(328\) −1.50022 0.487453i −0.0828361 0.0269151i
\(329\) −2.57324 + 7.91960i −0.141867 + 0.436622i
\(330\) 0 0
\(331\) 7.30737 + 22.4898i 0.401650 + 1.23615i 0.923661 + 0.383212i \(0.125182\pi\)
−0.522011 + 0.852939i \(0.674818\pi\)
\(332\) 0.134522i 0.00738284i
\(333\) 0 0
\(334\) 5.09929 + 3.70485i 0.279021 + 0.202721i
\(335\) −8.80279 + 11.0263i −0.480948 + 0.602431i
\(336\) 0 0
\(337\) 16.2888 22.4196i 0.887306 1.22127i −0.0870374 0.996205i \(-0.527740\pi\)
0.974343 0.225067i \(-0.0722600\pi\)
\(338\) −6.13266 + 8.44089i −0.333573 + 0.459124i
\(339\) 0 0
\(340\) 1.28707 + 1.95209i 0.0698014 + 0.105867i
\(341\) −25.3744 18.4355i −1.37410 0.998341i
\(342\) 0 0
\(343\) 18.0445i 0.974310i
\(344\) 1.01873 + 3.13534i 0.0549265 + 0.169046i
\(345\) 0 0
\(346\) −3.28963 + 10.1244i −0.176852 + 0.544294i
\(347\) 25.3799 + 8.24643i 1.36246 + 0.442692i 0.896865 0.442304i \(-0.145839\pi\)
0.465600 + 0.884996i \(0.345839\pi\)
\(348\) 0 0
\(349\) 5.73576 0.307028 0.153514 0.988146i \(-0.450941\pi\)
0.153514 + 0.988146i \(0.450941\pi\)
\(350\) 3.00014 + 13.2092i 0.160364 + 0.706063i
\(351\) 0 0
\(352\) 3.30361 + 4.54704i 0.176083 + 0.242358i
\(353\) 27.6785 + 8.99327i 1.47318 + 0.478664i 0.932066 0.362288i \(-0.118004\pi\)
0.541109 + 0.840952i \(0.318004\pi\)
\(354\) 0 0
\(355\) 2.69124 + 9.77174i 0.142836 + 0.518630i
\(356\) −3.64336 11.2131i −0.193098 0.594293i
\(357\) 0 0
\(358\) 0.760184 0.246999i 0.0401770 0.0130543i
\(359\) 10.5088 + 7.63506i 0.554631 + 0.402963i 0.829490 0.558521i \(-0.188631\pi\)
−0.274859 + 0.961485i \(0.588631\pi\)
\(360\) 0 0
\(361\) −41.5084 + 30.1576i −2.18465 + 1.58724i
\(362\) −9.59500 + 13.2064i −0.504302 + 0.694112i
\(363\) 0 0
\(364\) −10.6098 + 7.70845i −0.556103 + 0.404033i
\(365\) −17.0815 6.42116i −0.894086 0.336099i
\(366\) 0 0
\(367\) −3.50756 + 1.13968i −0.183093 + 0.0594906i −0.399129 0.916895i \(-0.630687\pi\)
0.216035 + 0.976386i \(0.430687\pi\)
\(368\) 5.29478i 0.276009i
\(369\) 0 0
\(370\) 5.58513 3.68244i 0.290357 0.191441i
\(371\) −5.17127 + 15.9155i −0.268479 + 0.826293i
\(372\) 0 0
\(373\) 15.2853 + 21.0383i 0.791440 + 1.08932i 0.993927 + 0.110039i \(0.0350976\pi\)
−0.202487 + 0.979285i \(0.564902\pi\)
\(374\) 5.87718 0.303902
\(375\) 0 0
\(376\) −3.07374 −0.158516
\(377\) 11.9232 + 16.4108i 0.614074 + 0.845201i
\(378\) 0 0
\(379\) 9.32153 28.6887i 0.478815 1.47364i −0.361929 0.932206i \(-0.617882\pi\)
0.840743 0.541434i \(-0.182118\pi\)
\(380\) −15.6532 + 10.3206i −0.802990 + 0.529436i
\(381\) 0 0
\(382\) 15.5301i 0.794588i
\(383\) −12.7109 + 4.13001i −0.649495 + 0.211034i −0.615191 0.788378i \(-0.710921\pi\)
−0.0343033 + 0.999411i \(0.510921\pi\)
\(384\) 0 0
\(385\) 31.8701 + 11.9804i 1.62425 + 0.610578i
\(386\) −17.0057 + 12.3554i −0.865567 + 0.628871i
\(387\) 0 0
\(388\) −1.55193 + 2.13605i −0.0787875 + 0.108442i
\(389\) 7.84772 5.70170i 0.397895 0.289088i −0.370788 0.928718i \(-0.620912\pi\)
0.768683 + 0.639630i \(0.220912\pi\)
\(390\) 0 0
\(391\) 4.47923 + 3.25435i 0.226525 + 0.164580i
\(392\) −0.322773 + 0.104875i −0.0163025 + 0.00529700i
\(393\) 0 0
\(394\) −7.46505 22.9751i −0.376084 1.15747i
\(395\) −7.41059 26.9075i −0.372867 1.35386i
\(396\) 0 0
\(397\) 7.52519 + 2.44508i 0.377679 + 0.122715i 0.491704 0.870763i \(-0.336374\pi\)
−0.114025 + 0.993478i \(0.536374\pi\)
\(398\) −14.9844 20.6242i −0.751100 1.03380i
\(399\) 0 0
\(400\) −4.29497 + 2.55993i −0.214748 + 0.127996i
\(401\) 20.1362 1.00555 0.502777 0.864416i \(-0.332312\pi\)
0.502777 + 0.864416i \(0.332312\pi\)
\(402\) 0 0
\(403\) 25.6916 + 8.34772i 1.27979 + 0.415829i
\(404\) −1.18305 + 3.64106i −0.0588591 + 0.181150i
\(405\) 0 0
\(406\) 3.50806 + 10.7967i 0.174102 + 0.535831i
\(407\) 16.8152i 0.833498i
\(408\) 0 0
\(409\) −2.27125 1.65016i −0.112306 0.0815951i 0.530215 0.847863i \(-0.322111\pi\)
−0.642521 + 0.766268i \(0.722111\pi\)
\(410\) −1.94158 2.94477i −0.0958878 0.145432i
\(411\) 0 0
\(412\) 3.46395 4.76772i 0.170657 0.234889i
\(413\) 22.5921 31.0954i 1.11168 1.53010i
\(414\) 0 0
\(415\) 0.187671 0.235075i 0.00921240 0.0115394i
\(416\) −3.91630 2.84536i −0.192013 0.139505i
\(417\) 0 0
\(418\) 47.1271i 2.30506i
\(419\) −10.2582 31.5714i −0.501144 1.54236i −0.807157 0.590337i \(-0.798995\pi\)
0.306013 0.952027i \(-0.401005\pi\)
\(420\) 0 0
\(421\) 5.91384 18.2009i 0.288223 0.887059i −0.697191 0.716885i \(-0.745567\pi\)
0.985414 0.170174i \(-0.0544329\pi\)
\(422\) 4.99228 + 1.62209i 0.243021 + 0.0789622i
\(423\) 0 0
\(424\) −6.17710 −0.299987
\(425\) −0.474209 + 5.20684i −0.0230025 + 0.252569i
\(426\) 0 0
\(427\) 0.430881 + 0.593057i 0.0208518 + 0.0287000i
\(428\) 5.61845 + 1.82554i 0.271578 + 0.0882410i
\(429\) 0 0
\(430\) −2.59388 + 6.90020i −0.125088 + 0.332757i
\(431\) 6.19003 + 19.0510i 0.298163 + 0.917652i 0.982141 + 0.188149i \(0.0602487\pi\)
−0.683977 + 0.729503i \(0.739751\pi\)
\(432\) 0 0
\(433\) 30.7778 10.0003i 1.47909 0.480585i 0.545247 0.838275i \(-0.316436\pi\)
0.933840 + 0.357691i \(0.116436\pi\)
\(434\) 12.2308 + 8.88618i 0.587096 + 0.426550i
\(435\) 0 0
\(436\) −4.56128 + 3.31397i −0.218446 + 0.158710i
\(437\) −26.0956 + 35.9175i −1.24832 + 1.71816i
\(438\) 0 0
\(439\) 14.0178 10.1846i 0.669035 0.486083i −0.200667 0.979660i \(-0.564311\pi\)
0.869702 + 0.493577i \(0.164311\pi\)
\(440\) −0.570526 + 12.5547i −0.0271988 + 0.598524i
\(441\) 0 0
\(442\) −4.81419 + 1.56423i −0.228988 + 0.0744026i
\(443\) 16.5326i 0.785489i 0.919648 + 0.392745i \(0.128474\pi\)
−0.919648 + 0.392745i \(0.871526\pi\)
\(444\) 0 0
\(445\) 9.27663 24.6776i 0.439754 1.16983i
\(446\) 4.57251 14.0727i 0.216515 0.666364i
\(447\) 0 0
\(448\) −1.59239 2.19173i −0.0752332 0.103550i
\(449\) 2.51289 0.118591 0.0592954 0.998240i \(-0.481115\pi\)
0.0592954 + 0.998240i \(0.481115\pi\)
\(450\) 0 0
\(451\) −8.86586 −0.417477
\(452\) −2.97826 4.09923i −0.140086 0.192811i
\(453\) 0 0
\(454\) −3.67064 + 11.2971i −0.172272 + 0.530198i
\(455\) −29.2945 1.33123i −1.37335 0.0624090i
\(456\) 0 0
\(457\) 36.7686i 1.71996i 0.510324 + 0.859982i \(0.329525\pi\)
−0.510324 + 0.859982i \(0.670475\pi\)
\(458\) 17.3636 5.64177i 0.811347 0.263623i
\(459\) 0 0
\(460\) −7.38672 + 9.25256i −0.344408 + 0.431403i
\(461\) 4.91129 3.56826i 0.228741 0.166190i −0.467511 0.883987i \(-0.654849\pi\)
0.696253 + 0.717797i \(0.254849\pi\)
\(462\) 0 0
\(463\) −19.5805 + 26.9502i −0.909982 + 1.25248i 0.0571903 + 0.998363i \(0.481786\pi\)
−0.967173 + 0.254120i \(0.918214\pi\)
\(464\) −3.39010 + 2.46305i −0.157381 + 0.114344i
\(465\) 0 0
\(466\) 2.31251 + 1.68014i 0.107125 + 0.0778309i
\(467\) −8.68934 + 2.82334i −0.402094 + 0.130648i −0.503081 0.864239i \(-0.667800\pi\)
0.100986 + 0.994888i \(0.467800\pi\)
\(468\) 0 0
\(469\) −5.28236 16.2574i −0.243917 0.750699i
\(470\) −5.37132 4.28816i −0.247761 0.197798i
\(471\) 0 0
\(472\) 13.4932 + 4.38420i 0.621074 + 0.201799i
\(473\) 10.8910 + 14.9902i 0.500769 + 0.689249i
\(474\) 0 0
\(475\) −41.7519 3.80252i −1.91571 0.174472i
\(476\) −2.83288 −0.129845
\(477\) 0 0
\(478\) 15.5819 + 5.06286i 0.712699 + 0.231570i
\(479\) 6.44637 19.8399i 0.294542 0.906507i −0.688833 0.724920i \(-0.741877\pi\)
0.983375 0.181587i \(-0.0581233\pi\)
\(480\) 0 0
\(481\) 4.47540 + 13.7739i 0.204061 + 0.628034i
\(482\) 26.3276i 1.19919i
\(483\) 0 0
\(484\) 16.6572 + 12.1021i 0.757144 + 0.550098i
\(485\) −5.69198 + 1.56763i −0.258460 + 0.0711824i
\(486\) 0 0
\(487\) −0.748202 + 1.02981i −0.0339043 + 0.0466652i −0.825633 0.564208i \(-0.809182\pi\)
0.791728 + 0.610873i \(0.209182\pi\)
\(488\) −0.159048 + 0.218911i −0.00719976 + 0.00990961i
\(489\) 0 0
\(490\) −0.710352 0.267031i −0.0320904 0.0120632i
\(491\) 8.65507 + 6.28827i 0.390598 + 0.283786i 0.765700 0.643197i \(-0.222393\pi\)
−0.375103 + 0.926983i \(0.622393\pi\)
\(492\) 0 0
\(493\) 4.38180i 0.197346i
\(494\) −12.5430 38.6034i −0.564336 1.73685i
\(495\) 0 0
\(496\) −1.72444 + 5.30729i −0.0774298 + 0.238304i
\(497\) −11.6788 3.79468i −0.523867 0.170215i
\(498\) 0 0
\(499\) 7.08035 0.316960 0.158480 0.987362i \(-0.449341\pi\)
0.158480 + 0.987362i \(0.449341\pi\)
\(500\) −11.0767 1.51845i −0.495367 0.0679072i
\(501\) 0 0
\(502\) −8.13236 11.1932i −0.362965 0.499578i
\(503\) −5.26012 1.70912i −0.234537 0.0762058i 0.189390 0.981902i \(-0.439349\pi\)
−0.423928 + 0.905696i \(0.639349\pi\)
\(504\) 0 0
\(505\) −7.14700 + 4.71223i −0.318037 + 0.209692i
\(506\) 9.19604 + 28.3025i 0.408814 + 1.25820i
\(507\) 0 0
\(508\) 9.06270 2.94465i 0.402092 0.130648i
\(509\) −7.79724 5.66503i −0.345607 0.251098i 0.401417 0.915895i \(-0.368518\pi\)
−0.747024 + 0.664798i \(0.768518\pi\)
\(510\) 0 0
\(511\) 17.8867 12.9954i 0.791260 0.574884i
\(512\) 0.587785 0.809017i 0.0259767 0.0357538i
\(513\) 0 0
\(514\) 23.1544 16.8227i 1.02130 0.742016i
\(515\) 12.7046 3.49898i 0.559833 0.154184i
\(516\) 0 0
\(517\) −16.4303 + 5.33851i −0.722602 + 0.234788i
\(518\) 8.10515i 0.356120i
\(519\) 0 0
\(520\) −2.87414 10.4358i −0.126039 0.457642i
\(521\) −6.26109 + 19.2697i −0.274304 + 0.844219i 0.715099 + 0.699023i \(0.246381\pi\)
−0.989403 + 0.145197i \(0.953619\pi\)
\(522\) 0 0
\(523\) −15.0873 20.7659i −0.659722 0.908030i 0.339750 0.940516i \(-0.389658\pi\)
−0.999472 + 0.0324859i \(0.989658\pi\)
\(524\) 0.148886 0.00650411
\(525\) 0 0
\(526\) 3.12306 0.136172
\(527\) 3.42992 + 4.72088i 0.149410 + 0.205645i
\(528\) 0 0
\(529\) −1.55580 + 4.78827i −0.0676436 + 0.208186i
\(530\) −10.7944 8.61765i −0.468879 0.374327i
\(531\) 0 0
\(532\) 22.7159i 0.984859i
\(533\) 7.26231 2.35967i 0.314566 0.102209i
\(534\) 0 0
\(535\) 7.27135 + 11.0284i 0.314368 + 0.476798i
\(536\) 5.10474 3.70881i 0.220491 0.160196i
\(537\) 0 0
\(538\) 5.42643 7.46884i 0.233950 0.322005i
\(539\) −1.54319 + 1.12119i −0.0664698 + 0.0482932i
\(540\) 0 0
\(541\) 3.20447 + 2.32818i 0.137771 + 0.100096i 0.654536 0.756031i \(-0.272864\pi\)
−0.516765 + 0.856127i \(0.672864\pi\)
\(542\) 20.6232 6.70088i 0.885842 0.287828i
\(543\) 0 0
\(544\) −0.323132 0.994499i −0.0138542 0.0426388i
\(545\) −12.5941 0.572313i −0.539471 0.0245152i
\(546\) 0 0
\(547\) −9.46392 3.07502i −0.404648 0.131478i 0.0996194 0.995026i \(-0.468237\pi\)
−0.504268 + 0.863547i \(0.668237\pi\)
\(548\) 5.30429 + 7.30072i 0.226588 + 0.311871i
\(549\) 0 0
\(550\) −18.5120 + 21.1433i −0.789356 + 0.901553i
\(551\) −35.1362 −1.49685
\(552\) 0 0
\(553\) 32.1588 + 10.4490i 1.36753 + 0.444338i
\(554\) −3.18135 + 9.79119i −0.135163 + 0.415988i
\(555\) 0 0
\(556\) 2.19791 + 6.76447i 0.0932122 + 0.286878i
\(557\) 18.7017i 0.792415i −0.918161 0.396207i \(-0.870326\pi\)
0.918161 0.396207i \(-0.129674\pi\)
\(558\) 0 0
\(559\) −12.9108 9.38028i −0.546071 0.396744i
\(560\) 0.275001 6.05155i 0.0116209 0.255725i
\(561\) 0 0
\(562\) 0.469371 0.646034i 0.0197992 0.0272513i
\(563\) 22.5630 31.0553i 0.950917 1.30882i −0.000202039 1.00000i \(-0.500064\pi\)
0.951119 0.308825i \(-0.0999357\pi\)
\(564\) 0 0
\(565\) 0.514338 11.3183i 0.0216384 0.476165i
\(566\) 0.591102 + 0.429461i 0.0248459 + 0.0180516i
\(567\) 0 0
\(568\) 4.53276i 0.190190i
\(569\) −4.90344 15.0913i −0.205563 0.632658i −0.999690 0.0249059i \(-0.992071\pi\)
0.794127 0.607752i \(-0.207929\pi\)
\(570\) 0 0
\(571\) 9.96877 30.6807i 0.417180 1.28395i −0.493106 0.869969i \(-0.664139\pi\)
0.910286 0.413979i \(-0.135861\pi\)
\(572\) −25.8759 8.40759i −1.08193 0.351539i
\(573\) 0 0
\(574\) 4.27346 0.178371
\(575\) −25.8164 + 5.86353i −1.07662 + 0.244526i
\(576\) 0 0
\(577\) −16.4815 22.6848i −0.686132 0.944379i 0.313855 0.949471i \(-0.398379\pi\)
−0.999987 + 0.00509145i \(0.998379\pi\)
\(578\) 15.1280 + 4.91540i 0.629243 + 0.204454i
\(579\) 0 0
\(580\) −9.36034 0.425362i −0.388667 0.0176622i
\(581\) 0.112617 + 0.346600i 0.00467215 + 0.0143794i
\(582\) 0 0
\(583\) −33.0189 + 10.7285i −1.36750 + 0.444328i
\(584\) 6.60237 + 4.79691i 0.273208 + 0.198497i
\(585\) 0 0
\(586\) −14.9540 + 10.8647i −0.617745 + 0.448818i
\(587\) 6.69311 9.21228i 0.276254 0.380231i −0.648234 0.761441i \(-0.724492\pi\)
0.924489 + 0.381209i \(0.124492\pi\)
\(588\) 0 0
\(589\) −37.8551 + 27.5033i −1.55979 + 1.13326i
\(590\) 17.4628 + 26.4856i 0.718931 + 1.09040i
\(591\) 0 0
\(592\) −2.84536 + 0.924514i −0.116944 + 0.0379973i
\(593\) 34.9063i 1.43343i −0.697366 0.716715i \(-0.745645\pi\)
0.697366 0.716715i \(-0.254355\pi\)
\(594\) 0 0
\(595\) −4.95042 3.95214i −0.202947 0.162022i
\(596\) −4.76970 + 14.6796i −0.195375 + 0.601301i
\(597\) 0 0
\(598\) −15.0656 20.7360i −0.616076 0.847957i
\(599\) 21.2325 0.867535 0.433768 0.901025i \(-0.357184\pi\)
0.433768 + 0.901025i \(0.357184\pi\)
\(600\) 0 0
\(601\) −22.6617 −0.924389 −0.462195 0.886779i \(-0.652938\pi\)
−0.462195 + 0.886779i \(0.652938\pi\)
\(602\) −5.24961 7.22547i −0.213958 0.294488i
\(603\) 0 0
\(604\) 2.47152 7.60655i 0.100565 0.309506i
\(605\) 12.2245 + 44.3867i 0.496998 + 1.80458i
\(606\) 0 0
\(607\) 21.3752i 0.867591i −0.901011 0.433796i \(-0.857174\pi\)
0.901011 0.433796i \(-0.142826\pi\)
\(608\) 7.97455 2.59109i 0.323411 0.105083i
\(609\) 0 0
\(610\) −0.583335 + 0.160656i −0.0236185 + 0.00650479i
\(611\) 12.0377 8.74590i 0.486993 0.353821i
\(612\) 0 0
\(613\) 19.9898 27.5136i 0.807380 1.11126i −0.184342 0.982862i \(-0.559015\pi\)
0.991722 0.128401i \(-0.0409845\pi\)
\(614\) −11.4818 + 8.34203i −0.463368 + 0.336657i
\(615\) 0 0
\(616\) −12.3185 8.94992i −0.496327 0.360603i
\(617\) 23.1992 7.53787i 0.933963 0.303463i 0.197781 0.980246i \(-0.436627\pi\)
0.736182 + 0.676783i \(0.236627\pi\)
\(618\) 0 0
\(619\) 7.50529 + 23.0989i 0.301663 + 0.928423i 0.980901 + 0.194505i \(0.0623102\pi\)
−0.679239 + 0.733918i \(0.737690\pi\)
\(620\) −10.4176 + 6.86866i −0.418382 + 0.275852i
\(621\) 0 0
\(622\) −9.61915 3.12545i −0.385693 0.125319i
\(623\) 18.7745 + 25.8409i 0.752184 + 1.03529i
\(624\) 0 0
\(625\) −17.2381 18.1066i −0.689523 0.724264i
\(626\) −7.00045 −0.279794
\(627\) 0 0
\(628\) −14.8505 4.82522i −0.592599 0.192547i
\(629\) −0.966744 + 2.97533i −0.0385466 + 0.118634i
\(630\) 0 0
\(631\) 0.319506 + 0.983337i 0.0127193 + 0.0391460i 0.957215 0.289379i \(-0.0934486\pi\)
−0.944495 + 0.328525i \(0.893449\pi\)
\(632\) 12.4814i 0.496484i
\(633\) 0 0
\(634\) −12.4091 9.01577i −0.492830 0.358062i
\(635\) 19.9450 + 7.49760i 0.791494 + 0.297533i
\(636\) 0 0
\(637\) 0.965668 1.32913i 0.0382612 0.0526620i
\(638\) −13.8434 + 19.0538i −0.548067 + 0.754349i
\(639\) 0 0
\(640\) 2.15580 0.593730i 0.0852156 0.0234692i
\(641\) 3.99638 + 2.90354i 0.157847 + 0.114683i 0.663905 0.747817i \(-0.268898\pi\)
−0.506058 + 0.862499i \(0.668898\pi\)
\(642\) 0 0
\(643\) 36.3220i 1.43240i 0.697896 + 0.716199i \(0.254120\pi\)
−0.697896 + 0.716199i \(0.745880\pi\)
\(644\) −4.43261 13.6422i −0.174669 0.537577i
\(645\) 0 0
\(646\) 2.70945 8.33882i 0.106602 0.328086i
\(647\) 13.5750 + 4.41077i 0.533687 + 0.173405i 0.563448 0.826152i \(-0.309475\pi\)
−0.0297610 + 0.999557i \(0.509475\pi\)
\(648\) 0 0
\(649\) 79.7405 3.13009
\(650\) 9.53648 22.2462i 0.374052 0.872568i
\(651\) 0 0
\(652\) 2.14970 + 2.95881i 0.0841889 + 0.115876i
\(653\) −5.48428 1.78195i −0.214616 0.0697331i 0.199736 0.979850i \(-0.435992\pi\)
−0.414352 + 0.910117i \(0.635992\pi\)
\(654\) 0 0
\(655\) 0.260176 + 0.207710i 0.0101659 + 0.00811591i
\(656\) 0.487453 + 1.50022i 0.0190318 + 0.0585739i
\(657\) 0 0
\(658\) 7.91960 2.57324i 0.308738 0.100315i
\(659\) −8.14688 5.91906i −0.317357 0.230574i 0.417690 0.908590i \(-0.362840\pi\)
−0.735047 + 0.678016i \(0.762840\pi\)
\(660\) 0 0
\(661\) 29.8762 21.7064i 1.16205 0.844279i 0.172015 0.985094i \(-0.444972\pi\)
0.990036 + 0.140815i \(0.0449723\pi\)
\(662\) 13.8995 19.1310i 0.540218 0.743546i
\(663\) 0 0
\(664\) −0.108830 + 0.0790699i −0.00422344 + 0.00306851i
\(665\) 31.6908 39.6957i 1.22892 1.53933i
\(666\) 0 0
\(667\) −21.1013 + 6.85622i −0.817044 + 0.265474i
\(668\) 6.30307i 0.243873i
\(669\) 0 0
\(670\) 14.0946 + 0.640503i 0.544523 + 0.0247448i
\(671\) −0.469961 + 1.44639i −0.0181427 + 0.0558373i
\(672\) 0 0
\(673\) −15.8901 21.8708i −0.612518 0.843059i 0.384263 0.923223i \(-0.374455\pi\)
−0.996782 + 0.0801645i \(0.974455\pi\)
\(674\) −27.7121 −1.06743
\(675\) 0 0
\(676\) 10.4335 0.401289
\(677\) 5.08479 + 6.99862i 0.195425 + 0.268979i 0.895472 0.445117i \(-0.146838\pi\)
−0.700048 + 0.714096i \(0.746838\pi\)
\(678\) 0 0
\(679\) 2.21038 6.80284i 0.0848265 0.261069i
\(680\) 0.822752 2.18868i 0.0315511 0.0839319i
\(681\) 0 0
\(682\) 31.3644i 1.20101i
\(683\) −44.1971 + 14.3605i −1.69115 + 0.549489i −0.987023 0.160580i \(-0.948664\pi\)
−0.704132 + 0.710069i \(0.748664\pi\)
\(684\) 0 0
\(685\) −0.916037 + 20.1579i −0.0350000 + 0.770194i
\(686\) −14.5983 + 10.6063i −0.557365 + 0.404949i
\(687\) 0 0
\(688\) 1.93775 2.66708i 0.0738759 0.101681i
\(689\) 24.1914 17.5761i 0.921619 0.669596i
\(690\) 0 0
\(691\) 38.2570 + 27.7954i 1.45537 + 1.05739i 0.984540 + 0.175159i \(0.0560440\pi\)
0.470826 + 0.882226i \(0.343956\pi\)
\(692\) 10.1244 3.28963i 0.384874 0.125053i
\(693\) 0 0
\(694\) −8.24643 25.3799i −0.313030 0.963408i
\(695\) −5.59627 + 14.8871i −0.212278 + 0.564701i
\(696\) 0 0
\(697\) 1.56875 + 0.509719i 0.0594208 + 0.0193070i
\(698\) −3.37139 4.64032i −0.127609 0.175639i
\(699\) 0 0
\(700\) 8.92305 10.1914i 0.337260 0.385197i
\(701\) −30.1858 −1.14010 −0.570052 0.821609i \(-0.693077\pi\)
−0.570052 + 0.821609i \(0.693077\pi\)
\(702\) 0 0
\(703\) −23.8582 7.75199i −0.899828 0.292372i
\(704\) 1.73681 5.34536i 0.0654586 0.201461i
\(705\) 0 0
\(706\) −8.99327 27.6785i −0.338466 1.04169i
\(707\) 10.3717i 0.390069i
\(708\) 0 0
\(709\) −14.0202 10.1862i −0.526538 0.382553i 0.292523 0.956259i \(-0.405505\pi\)
−0.819061 + 0.573706i \(0.805505\pi\)
\(710\) 6.32363 7.92094i 0.237322 0.297268i
\(711\) 0 0
\(712\) −6.93008 + 9.53844i −0.259716 + 0.357468i
\(713\) −17.3673 + 23.9041i −0.650412 + 0.895215i
\(714\) 0 0
\(715\) −33.4884 50.7915i −1.25240 1.89950i
\(716\) −0.646651 0.469819i −0.0241665 0.0175580i
\(717\) 0 0
\(718\) 12.9895i 0.484765i
\(719\) −5.82077 17.9145i −0.217078 0.668098i −0.999000 0.0447207i \(-0.985760\pi\)
0.781921 0.623377i \(-0.214240\pi\)
\(720\) 0 0
\(721\) −4.93361 + 15.1841i −0.183737 + 0.565485i
\(722\) 48.7961 + 15.8548i 1.81600 + 0.590055i
\(723\) 0 0
\(724\) 16.3240 0.606676
\(725\) −15.7636 13.8019i −0.585447 0.512589i
\(726\) 0 0
\(727\) 12.5396 + 17.2593i 0.465068 + 0.640111i 0.975550 0.219777i \(-0.0705331\pi\)
−0.510482 + 0.859888i \(0.670533\pi\)
\(728\) 12.4725 + 4.05257i 0.462263 + 0.150198i
\(729\) 0 0
\(730\) 4.84542 + 17.5935i 0.179337 + 0.651164i
\(731\) −1.06527 3.27856i −0.0394004 0.121262i
\(732\) 0 0
\(733\) 19.8497 6.44956i 0.733165 0.238220i 0.0814434 0.996678i \(-0.474047\pi\)
0.651722 + 0.758458i \(0.274047\pi\)
\(734\) 2.98371 + 2.16779i 0.110131 + 0.0800147i
\(735\) 0 0
\(736\) 4.28357 3.11219i 0.157894 0.114717i
\(737\) 20.8452 28.6909i 0.767842 1.05684i
\(738\) 0 0
\(739\) −13.1129 + 9.52707i −0.482365 + 0.350459i −0.802241 0.597001i \(-0.796359\pi\)
0.319875 + 0.947460i \(0.396359\pi\)
\(740\) −6.26201 2.35397i −0.230196 0.0865338i
\(741\) 0 0
\(742\) 15.9155 5.17127i 0.584277 0.189843i
\(743\) 34.7758i 1.27580i −0.770120 0.637900i \(-0.779803\pi\)
0.770120 0.637900i \(-0.220197\pi\)
\(744\) 0 0
\(745\) −28.8145 + 18.9983i −1.05568 + 0.696043i
\(746\) 8.03593 24.7321i 0.294216 0.905505i
\(747\) 0 0
\(748\) −3.45452 4.75474i −0.126310 0.173850i
\(749\) −16.0044 −0.584788
\(750\) 0 0
\(751\) 21.2393 0.775034 0.387517 0.921863i \(-0.373333\pi\)
0.387517 + 0.921863i \(0.373333\pi\)
\(752\) 1.80670 + 2.48671i 0.0658836 + 0.0906809i
\(753\) 0 0
\(754\) 6.26838 19.2921i 0.228281 0.702577i
\(755\) 14.9308 9.84435i 0.543388 0.358272i
\(756\) 0 0
\(757\) 53.9563i 1.96107i 0.196335 + 0.980537i \(0.437096\pi\)
−0.196335 + 0.980537i \(0.562904\pi\)
\(758\) −28.6887 + 9.32153i −1.04202 + 0.338573i
\(759\) 0 0
\(760\) 17.5502 + 6.59737i 0.636614 + 0.239312i
\(761\) −34.2990 + 24.9197i −1.24334 + 0.903339i −0.997816 0.0660520i \(-0.978960\pi\)
−0.245523 + 0.969391i \(0.578960\pi\)
\(762\) 0 0
\(763\) 8.97796 12.3571i 0.325024 0.447357i
\(764\) 12.5641 9.12835i 0.454553 0.330252i
\(765\) 0 0
\(766\) 10.8125 + 7.85574i 0.390672 + 0.283840i
\(767\) −65.3181 + 21.2231i −2.35850 + 0.766323i
\(768\) 0 0
\(769\) −1.55943 4.79943i −0.0562345 0.173072i 0.918994 0.394271i \(-0.129003\pi\)
−0.975229 + 0.221199i \(0.929003\pi\)
\(770\) −9.04044 32.8254i −0.325795 1.18294i
\(771\) 0 0
\(772\) 19.9914 + 6.49559i 0.719506 + 0.233782i
\(773\) 20.4840 + 28.1938i 0.736758 + 1.01406i 0.998799 + 0.0490036i \(0.0156046\pi\)
−0.262041 + 0.965057i \(0.584395\pi\)
\(774\) 0 0
\(775\) −27.7871 2.53069i −0.998142 0.0909050i
\(776\) 2.64031 0.0947815
\(777\) 0 0
\(778\) −9.22554 2.99756i −0.330752 0.107468i
\(779\) −4.08726 + 12.5793i −0.146441 + 0.450700i
\(780\) 0 0
\(781\) −7.87256 24.2292i −0.281702 0.866990i
\(782\) 5.53664i 0.197990i
\(783\) 0 0
\(784\) 0.274567 + 0.199485i 0.00980596 + 0.00712445i
\(785\) −19.2194 29.1498i −0.685969 1.04040i
\(786\) 0 0
\(787\) 9.42980 12.9790i 0.336136 0.462652i −0.607172 0.794571i \(-0.707696\pi\)
0.943308 + 0.331919i \(0.107696\pi\)
\(788\) −14.1994 + 19.5438i −0.505832 + 0.696218i
\(789\) 0 0
\(790\) −17.4128 + 21.8111i −0.619519 + 0.776005i
\(791\) 11.1053 + 8.06850i 0.394860 + 0.286883i
\(792\) 0 0
\(793\) 1.30987i 0.0465148i
\(794\) −2.44508 7.52519i −0.0867728 0.267059i
\(795\) 0 0
\(796\) −7.87776 + 24.2453i −0.279220 + 0.859350i
\(797\) −35.4218 11.5093i −1.25471 0.407679i −0.395101 0.918638i \(-0.629290\pi\)
−0.859605 + 0.510959i \(0.829290\pi\)
\(798\) 0 0
\(799\) 3.21415 0.113708
\(800\) 4.59555 + 1.97002i 0.162477 + 0.0696506i
\(801\) 0 0
\(802\) −11.8358 16.2905i −0.417935 0.575239i
\(803\) 43.6234 + 14.1741i 1.53944 + 0.500193i
\(804\) 0 0
\(805\) 11.2862 30.0235i 0.397787 1.05819i
\(806\) −8.34772 25.6916i −0.294036 0.904949i
\(807\) 0 0
\(808\) 3.64106 1.18305i 0.128092 0.0416196i
\(809\) 6.97671 + 5.06888i 0.245288 + 0.178212i 0.703636 0.710561i \(-0.251559\pi\)
−0.458348 + 0.888773i \(0.651559\pi\)
\(810\) 0 0
\(811\) −0.148704 + 0.108040i −0.00522171 + 0.00379379i −0.590393 0.807116i \(-0.701027\pi\)
0.585171 + 0.810910i \(0.301027\pi\)
\(812\) 6.67272 9.18421i 0.234167 0.322303i
\(813\) 0 0
\(814\) −13.6038 + 9.88372i −0.476812 + 0.346424i
\(815\) −0.371248 + 8.16953i −0.0130043 + 0.286166i
\(816\) 0 0
\(817\) 26.2897 8.54203i 0.919758 0.298848i
\(818\) 2.80742i 0.0981591i
\(819\) 0 0
\(820\) −1.24114 + 3.30167i −0.0433425 + 0.115299i
\(821\) −8.46892 + 26.0647i −0.295567 + 0.909663i 0.687463 + 0.726220i \(0.258724\pi\)
−0.983030 + 0.183443i \(0.941276\pi\)
\(822\) 0 0
\(823\) 19.1609 + 26.3728i 0.667908 + 0.919296i 0.999711 0.0240525i \(-0.00765687\pi\)
−0.331803 + 0.943349i \(0.607657\pi\)
\(824\) −5.89322 −0.205300
\(825\) 0 0
\(826\) −38.4360 −1.33736
\(827\) −22.6934 31.2347i −0.789125 1.08614i −0.994216 0.107395i \(-0.965749\pi\)
0.205091 0.978743i \(-0.434251\pi\)
\(828\) 0 0
\(829\) −11.1557 + 34.3338i −0.387455 + 1.19246i 0.547229 + 0.836983i \(0.315683\pi\)
−0.934684 + 0.355480i \(0.884317\pi\)
\(830\) −0.300490 0.0136552i −0.0104302 0.000473978i
\(831\) 0 0
\(832\) 4.84082i 0.167825i
\(833\) 0.337517 0.109666i 0.0116943 0.00379969i
\(834\) 0 0
\(835\) 8.79339 11.0145i 0.304308 0.381174i
\(836\) 38.1266 27.7006i 1.31864 0.958046i
\(837\) 0 0
\(838\) −19.5122 + 26.8562i −0.674038 + 0.927733i
\(839\) −26.7665 + 19.4470i −0.924081 + 0.671384i −0.944536 0.328407i \(-0.893488\pi\)
0.0204558 + 0.999791i \(0.493488\pi\)
\(840\) 0 0
\(841\) 9.25567 + 6.72464i 0.319161 + 0.231884i
\(842\) −18.2009 + 5.91384i −0.627246 + 0.203804i
\(843\) 0 0
\(844\) −1.62209 4.99228i −0.0558347 0.171841i
\(845\) 18.2324 + 14.5557i 0.627214 + 0.500733i
\(846\) 0 0
\(847\) −53.0493 17.2368i −1.82280 0.592262i
\(848\) 3.63081 + 4.99738i 0.124683 + 0.171611i
\(849\) 0 0
\(850\) 4.49116 2.67686i 0.154045 0.0918156i
\(851\) −15.8409 −0.543018
\(852\) 0 0
\(853\) −19.1614 6.22591i −0.656073 0.213171i −0.0379832 0.999278i \(-0.512093\pi\)
−0.618090 + 0.786107i \(0.712093\pi\)
\(854\) 0.226528 0.697180i 0.00775162 0.0238570i
\(855\) 0 0
\(856\) −1.82554 5.61845i −0.0623958 0.192035i
\(857\) 55.8400i 1.90746i 0.300668 + 0.953729i \(0.402790\pi\)
−0.300668 + 0.953729i \(0.597210\pi\)
\(858\) 0 0
\(859\) −41.2044 29.9368i −1.40588 1.02143i −0.993906 0.110232i \(-0.964841\pi\)
−0.411971 0.911197i \(-0.635159\pi\)
\(860\) 7.10702 1.95734i 0.242347 0.0667449i
\(861\) 0 0
\(862\) 11.7741 16.2057i 0.401029 0.551969i
\(863\) 16.2660 22.3882i 0.553701 0.762104i −0.436808 0.899555i \(-0.643891\pi\)
0.990509 + 0.137451i \(0.0438910\pi\)
\(864\) 0 0
\(865\) 22.2817 + 8.37598i 0.757600 + 0.284792i
\(866\) −26.1812 19.0217i −0.889672 0.646385i
\(867\) 0 0
\(868\) 15.1181i 0.513141i
\(869\) 21.6779 + 66.7177i 0.735372 + 2.26324i
\(870\) 0 0
\(871\) −9.43881 + 29.0497i −0.319822 + 0.984311i
\(872\) 5.36211 + 1.74225i 0.181584 + 0.0590002i
\(873\) 0 0
\(874\) 44.3964 1.50173
\(875\) 29.8108 5.36074i 1.00779 0.181226i
\(876\) 0 0
\(877\) 19.7507 + 27.1845i 0.666934 + 0.917956i 0.999686 0.0250581i \(-0.00797707\pi\)
−0.332752 + 0.943015i \(0.607977\pi\)
\(878\) −16.4790 5.35434i −0.556138 0.180700i
\(879\) 0 0
\(880\) 10.4923 6.91793i 0.353697 0.233203i
\(881\) −0.801894 2.46798i −0.0270165 0.0831482i 0.936639 0.350296i \(-0.113919\pi\)
−0.963656 + 0.267147i \(0.913919\pi\)
\(882\) 0 0
\(883\) 38.0222 12.3541i 1.27955 0.415750i 0.411127 0.911578i \(-0.365135\pi\)
0.868421 + 0.495828i \(0.165135\pi\)
\(884\) 4.09519 + 2.97533i 0.137736 + 0.100071i
\(885\) 0 0
\(886\) 13.3752 9.71764i 0.449348 0.326470i
\(887\) 12.8634 17.7050i 0.431911 0.594475i −0.536480 0.843913i \(-0.680246\pi\)
0.968391 + 0.249439i \(0.0802461\pi\)
\(888\) 0 0
\(889\) −20.8852 + 15.1740i −0.700467 + 0.508919i
\(890\) −25.4172 + 7.00017i −0.851988 + 0.234646i
\(891\) 0 0
\(892\) −14.0727 + 4.57251i −0.471190 + 0.153099i
\(893\) 25.7731i 0.862465i
\(894\) 0 0
\(895\) −0.474571 1.72314i −0.0158632 0.0575983i
\(896\) −0.837167 + 2.57654i −0.0279678 + 0.0860760i
\(897\) 0 0
\(898\) −1.47704 2.03297i −0.0492895 0.0678412i
\(899\) −23.3841 −0.779904
\(900\) 0 0
\(901\) 6.45927 0.215189
\(902\) 5.21122 + 7.17263i 0.173515 + 0.238822i
\(903\) 0 0
\(904\) −1.56576 + 4.81893i −0.0520766 + 0.160275i
\(905\) 28.5259 + 22.7735i 0.948234 + 0.757017i
\(906\) 0 0
\(907\) 22.6784i 0.753025i −0.926412 0.376512i \(-0.877123\pi\)
0.926412 0.376512i \(-0.122877\pi\)
\(908\) 11.2971 3.67064i 0.374906 0.121814i
\(909\) 0 0
\(910\) 16.1419 + 24.4822i 0.535098 + 0.811577i
\(911\) 39.1006 28.4082i 1.29546 0.941207i 0.295560 0.955324i \(-0.404494\pi\)
0.999900 + 0.0141173i \(0.00449382\pi\)
\(912\) 0 0
\(913\) −0.444408 + 0.611676i −0.0147078 + 0.0202435i
\(914\) 29.7465 21.6121i 0.983925 0.714863i
\(915\) 0 0
\(916\) −14.7704 10.7313i −0.488026 0.354572i
\(917\) −0.383610 + 0.124642i −0.0126679 + 0.00411606i
\(918\) 0 0
\(919\) 13.3112 + 40.9678i 0.439097 + 1.35140i 0.888829 + 0.458239i \(0.151519\pi\)
−0.449732 + 0.893164i \(0.648481\pi\)
\(920\) 11.8273 + 0.537468i 0.389934 + 0.0177198i
\(921\) 0 0
\(922\) −5.77356 1.87594i −0.190142 0.0617809i
\(923\) 12.8973 + 17.7517i 0.424521 + 0.584303i
\(924\) 0 0
\(925\) −7.65877 12.8496i −0.251819 0.422494i
\(926\) 33.3123 1.09471
\(927\) 0 0
\(928\) 3.98530 + 1.29490i 0.130824 + 0.0425072i
\(929\) −11.7192 + 36.0680i −0.384495 + 1.18335i 0.552351 + 0.833612i \(0.313731\pi\)
−0.936846 + 0.349742i \(0.886269\pi\)
\(930\) 0 0
\(931\) 0.879373 + 2.70643i 0.0288203 + 0.0886997i
\(932\) 2.85842i 0.0936307i
\(933\) 0 0
\(934\) 7.39159 + 5.37030i 0.241860 + 0.175722i
\(935\) 0.596587 13.1282i 0.0195105 0.429339i
\(936\) 0 0
\(937\) −9.74401 + 13.4115i −0.318323 + 0.438134i −0.937954 0.346759i \(-0.887282\pi\)
0.619631 + 0.784893i \(0.287282\pi\)
\(938\) −10.0477 + 13.8294i −0.328068 + 0.451546i
\(939\) 0 0
\(940\) −0.312012 + 6.86601i −0.0101767 + 0.223945i
\(941\) 20.7160 + 15.0510i 0.675321 + 0.490650i 0.871802 0.489858i \(-0.162951\pi\)
−0.196481 + 0.980508i \(0.562951\pi\)
\(942\) 0 0
\(943\) 8.35214i 0.271983i
\(944\) −4.38420 13.4932i −0.142694 0.439166i
\(945\) 0 0
\(946\) 5.72574 17.6220i 0.186160 0.572941i
\(947\) −18.9867 6.16914i −0.616984 0.200470i −0.0161830 0.999869i \(-0.505151\pi\)
−0.600801 + 0.799399i \(0.705151\pi\)
\(948\) 0 0
\(949\) −39.5058 −1.28241
\(950\) 21.4649 + 36.0131i 0.696412 + 1.16842i
\(951\) 0 0
\(952\) 1.66512 + 2.29185i 0.0539670 + 0.0742792i
\(953\) −42.9246 13.9470i −1.39046 0.451789i −0.484368 0.874864i \(-0.660951\pi\)
−0.906094 + 0.423075i \(0.860951\pi\)
\(954\) 0 0
\(955\) 34.6905 + 1.57644i 1.12256 + 0.0510125i
\(956\) −5.06286 15.5819i −0.163745 0.503955i
\(957\) 0 0
\(958\) −19.8399 + 6.44637i −0.640997 + 0.208273i
\(959\) −19.7786 14.3700i −0.638685 0.464031i
\(960\) 0 0
\(961\) −0.114121 + 0.0829138i −0.00368132 + 0.00267464i
\(962\) 8.51272 11.7168i 0.274461 0.377763i
\(963\) 0 0
\(964\) 21.2995 15.4750i 0.686010 0.498415i
\(965\) 25.8727 + 39.2408i 0.832872 + 1.26321i
\(966\) 0 0
\(967\) 7.46499 2.42552i 0.240058 0.0779995i −0.186517 0.982452i \(-0.559720\pi\)
0.426575 + 0.904452i \(0.359720\pi\)
\(968\) 20.5894i 0.661768i
\(969\) 0 0
\(970\) 4.61390 + 3.68348i 0.148143 + 0.118269i
\(971\) −1.32948 + 4.09171i −0.0426649 + 0.131309i −0.970120 0.242625i \(-0.921991\pi\)
0.927455 + 0.373934i \(0.121991\pi\)
\(972\) 0 0
\(973\) −11.3260 15.5889i −0.363095 0.499757i
\(974\) 1.27292 0.0407869
\(975\) 0 0
\(976\) 0.270588 0.00866132
\(977\) −0.250593 0.344912i −0.00801720 0.0110347i 0.804990 0.593289i \(-0.202171\pi\)
−0.813007 + 0.582254i \(0.802171\pi\)
\(978\) 0 0
\(979\) −20.4773 + 63.0226i −0.654457 + 2.01421i
\(980\) 0.201502 + 0.731644i 0.00643675 + 0.0233715i
\(981\) 0 0
\(982\) 10.6983i 0.341395i
\(983\) −56.6743 + 18.4146i −1.80763 + 0.587335i −0.999997 0.00234965i \(-0.999252\pi\)
−0.807634 + 0.589685i \(0.799252\pi\)
\(984\) 0 0
\(985\) −52.0786 + 14.3430i −1.65936 + 0.457005i
\(986\) 3.54495 2.57556i 0.112894 0.0820225i
\(987\) 0 0
\(988\) −23.8582 + 32.8380i −0.759030 + 1.04472i
\(989\) 14.1216 10.2599i 0.449041 0.326247i
\(990\) 0 0
\(991\) −17.7809 12.9186i −0.564830 0.410373i 0.268393 0.963309i \(-0.413507\pi\)
−0.833224 + 0.552936i \(0.813507\pi\)
\(992\) 5.30729 1.72444i 0.168507 0.0547511i
\(993\) 0 0
\(994\) 3.79468 + 11.6788i 0.120360 + 0.370430i
\(995\) −47.5907 + 31.3780i −1.50873 + 0.994750i
\(996\) 0 0
\(997\) 42.6506 + 13.8580i 1.35076 + 0.438887i 0.892947 0.450163i \(-0.148634\pi\)
0.457810 + 0.889050i \(0.348634\pi\)
\(998\) −4.16172 5.72812i −0.131737 0.181320i
\(999\) 0 0
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 450.2.l.c.289.1 16
3.2 odd 2 150.2.h.b.139.4 yes 16
15.2 even 4 750.2.g.f.301.3 16
15.8 even 4 750.2.g.g.301.2 16
15.14 odd 2 750.2.h.d.199.2 16
25.9 even 10 inner 450.2.l.c.109.1 16
75.29 odd 10 3750.2.c.k.1249.14 16
75.38 even 20 750.2.g.g.451.2 16
75.41 odd 10 750.2.h.d.49.1 16
75.47 even 20 3750.2.a.v.1.6 8
75.53 even 20 3750.2.a.u.1.3 8
75.59 odd 10 150.2.h.b.109.4 16
75.62 even 20 750.2.g.f.451.3 16
75.71 odd 10 3750.2.c.k.1249.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.h.b.109.4 16 75.59 odd 10
150.2.h.b.139.4 yes 16 3.2 odd 2
450.2.l.c.109.1 16 25.9 even 10 inner
450.2.l.c.289.1 16 1.1 even 1 trivial
750.2.g.f.301.3 16 15.2 even 4
750.2.g.f.451.3 16 75.62 even 20
750.2.g.g.301.2 16 15.8 even 4
750.2.g.g.451.2 16 75.38 even 20
750.2.h.d.49.1 16 75.41 odd 10
750.2.h.d.199.2 16 15.14 odd 2
3750.2.a.u.1.3 8 75.53 even 20
3750.2.a.v.1.6 8 75.47 even 20
3750.2.c.k.1249.3 16 75.71 odd 10
3750.2.c.k.1249.14 16 75.29 odd 10