Properties

Label 575.2.p.a.374.1
Level $575$
Weight $2$
Character 575.374
Analytic conductor $4.591$
Analytic rank $0$
Dimension $20$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [575,2,Mod(49,575)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(575, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("575.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 575.p (of order \(22\), degree \(10\), not 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: \(4.59139811622\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{22})\)
Coefficient field: \(\Q(\zeta_{44})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 115)
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 374.1
Root \(-0.540641 + 0.841254i\) of defining polynomial
Character \(\chi\) \(=\) 575.374
Dual form 575.2.p.a.349.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.02730 - 0.925839i) q^{2} +(-0.281733 + 0.959493i) q^{3} +(1.94306 + 2.24241i) q^{4} +(1.45949 - 1.68434i) q^{6} +(0.0872586 + 0.0125459i) q^{7} +(-0.607265 - 2.06815i) q^{8} +(1.68251 + 1.08128i) q^{9} +(1.01365 + 2.21959i) q^{11} +(-2.69900 + 1.23259i) q^{12} +(-3.56484 + 0.512546i) q^{13} +(-0.165284 - 0.106222i) q^{14} +(0.160869 - 1.11887i) q^{16} +(2.55667 + 2.21537i) q^{17} +(-2.40986 - 3.74982i) q^{18} +(-1.87358 - 2.16222i) q^{19} +(-0.0366213 + 0.0801894i) q^{21} -5.43826i q^{22} +(2.15802 - 4.28287i) q^{23} +2.15546 q^{24} +(7.70154 + 2.26138i) q^{26} +(-3.77875 + 3.27430i) q^{27} +(0.141416 + 0.220047i) q^{28} +(-4.87604 + 5.62725i) q^{29} +(1.65370 - 0.485571i) q^{31} +(-3.69269 + 5.74593i) q^{32} +(-2.41526 + 0.347262i) q^{33} +(-3.13208 - 6.85830i) q^{34} +(0.844535 + 5.87387i) q^{36} +(0.382654 - 0.595421i) q^{37} +(1.79644 + 6.11811i) q^{38} +(0.512546 - 3.56484i) q^{39} +(-4.66991 + 3.00117i) q^{41} +(0.148485 - 0.128663i) q^{42} +(-0.675383 + 2.30014i) q^{43} +(-3.00764 + 6.58582i) q^{44} +(-8.34021 + 6.68469i) q^{46} +11.6146i q^{47} +(1.02822 + 0.469574i) q^{48} +(-6.70899 - 1.96994i) q^{49} +(-2.84593 + 1.82897i) q^{51} +(-8.07603 - 6.99792i) q^{52} +(10.2695 + 1.47653i) q^{53} +(10.6921 - 3.13950i) q^{54} +(-0.0270422 - 0.188083i) q^{56} +(2.60249 - 1.18852i) q^{57} +(15.0951 - 6.89372i) q^{58} +(1.64421 + 11.4357i) q^{59} +(-3.89722 + 1.14433i) q^{61} +(-3.80211 - 0.546662i) q^{62} +(0.133248 + 0.115460i) q^{63} +(10.9041 - 7.00766i) q^{64} +(5.21797 + 1.53213i) q^{66} +(11.1056 + 5.07177i) q^{67} +10.0377i q^{68} +(3.50140 + 3.27723i) q^{69} +(0.787956 - 1.72538i) q^{71} +(1.21453 - 4.13631i) q^{72} +(-4.16900 + 3.61246i) q^{73} +(-1.32702 + 0.852823i) q^{74} +(1.20812 - 8.40266i) q^{76} +(0.0606031 + 0.206395i) q^{77} +(-4.33955 + 6.75247i) q^{78} +(0.997420 + 6.93721i) q^{79} +(0.415415 + 0.909632i) q^{81} +(12.2459 - 1.76070i) q^{82} +(-2.25587 + 3.51021i) q^{83} +(-0.250975 + 0.0736930i) q^{84} +(3.49877 - 4.03779i) q^{86} +(-4.02557 - 6.26391i) q^{87} +(3.97489 - 3.44426i) q^{88} +(-15.3009 - 4.49275i) q^{89} -0.317493 q^{91} +(13.7971 - 3.48270i) q^{92} +1.72352i q^{93} +(10.7532 - 23.5463i) q^{94} +(-4.47283 - 5.16192i) q^{96} +(-7.77424 - 12.0969i) q^{97} +(11.7773 + 10.2051i) q^{98} +(-0.694523 + 4.83052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{4} + 12 q^{6} - 4 q^{9} + 16 q^{11} + 6 q^{14} + 10 q^{16} + 26 q^{19} + 12 q^{21} + 12 q^{24} + 22 q^{26} - 4 q^{29} - 40 q^{31} - 32 q^{34} + 48 q^{36} - 10 q^{41} - 38 q^{44} - 32 q^{46}+ \cdots - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/575\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(277\)
\(\chi(n)\) \(e\left(\frac{9}{11}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.02730 0.925839i −1.43352 0.654667i −0.460982 0.887410i \(-0.652503\pi\)
−0.972538 + 0.232743i \(0.925230\pi\)
\(3\) −0.281733 + 0.959493i −0.162658 + 0.553964i 0.837315 + 0.546720i \(0.184124\pi\)
−0.999974 + 0.00724338i \(0.997694\pi\)
\(4\) 1.94306 + 2.24241i 0.971531 + 1.12121i
\(5\) 0 0
\(6\) 1.45949 1.68434i 0.595836 0.687631i
\(7\) 0.0872586 + 0.0125459i 0.0329807 + 0.00474190i 0.158785 0.987313i \(-0.449242\pi\)
−0.125805 + 0.992055i \(0.540151\pi\)
\(8\) −0.607265 2.06815i −0.214700 0.731203i
\(9\) 1.68251 + 1.08128i 0.560836 + 0.360427i
\(10\) 0 0
\(11\) 1.01365 + 2.21959i 0.305628 + 0.669231i 0.998664 0.0516714i \(-0.0164549\pi\)
−0.693037 + 0.720902i \(0.743728\pi\)
\(12\) −2.69900 + 1.23259i −0.779135 + 0.355819i
\(13\) −3.56484 + 0.512546i −0.988707 + 0.142155i −0.617648 0.786455i \(-0.711914\pi\)
−0.371059 + 0.928609i \(0.621005\pi\)
\(14\) −0.165284 0.106222i −0.0441741 0.0283890i
\(15\) 0 0
\(16\) 0.160869 1.11887i 0.0402172 0.279717i
\(17\) 2.55667 + 2.21537i 0.620084 + 0.537306i 0.907259 0.420572i \(-0.138171\pi\)
−0.287175 + 0.957878i \(0.592716\pi\)
\(18\) −2.40986 3.74982i −0.568010 0.883840i
\(19\) −1.87358 2.16222i −0.429828 0.496048i 0.498978 0.866615i \(-0.333709\pi\)
−0.928806 + 0.370567i \(0.879163\pi\)
\(20\) 0 0
\(21\) −0.0366213 + 0.0801894i −0.00799142 + 0.0174988i
\(22\) 5.43826i 1.15944i
\(23\) 2.15802 4.28287i 0.449979 0.893039i
\(24\) 2.15546 0.439982
\(25\) 0 0
\(26\) 7.70154 + 2.26138i 1.51040 + 0.443492i
\(27\) −3.77875 + 3.27430i −0.727220 + 0.630140i
\(28\) 0.141416 + 0.220047i 0.0267251 + 0.0415850i
\(29\) −4.87604 + 5.62725i −0.905458 + 1.04495i 0.0933249 + 0.995636i \(0.470250\pi\)
−0.998783 + 0.0493188i \(0.984295\pi\)
\(30\) 0 0
\(31\) 1.65370 0.485571i 0.297014 0.0872110i −0.129831 0.991536i \(-0.541443\pi\)
0.426844 + 0.904325i \(0.359625\pi\)
\(32\) −3.69269 + 5.74593i −0.652781 + 1.01575i
\(33\) −2.41526 + 0.347262i −0.420442 + 0.0604505i
\(34\) −3.13208 6.85830i −0.537147 1.17619i
\(35\) 0 0
\(36\) 0.844535 + 5.87387i 0.140756 + 0.978979i
\(37\) 0.382654 0.595421i 0.0629079 0.0978866i −0.808375 0.588668i \(-0.799652\pi\)
0.871283 + 0.490782i \(0.163289\pi\)
\(38\) 1.79644 + 6.11811i 0.291421 + 0.992489i
\(39\) 0.512546 3.56484i 0.0820730 0.570830i
\(40\) 0 0
\(41\) −4.66991 + 3.00117i −0.729317 + 0.468704i −0.851867 0.523759i \(-0.824529\pi\)
0.122550 + 0.992462i \(0.460893\pi\)
\(42\) 0.148485 0.128663i 0.0229117 0.0198531i
\(43\) −0.675383 + 2.30014i −0.102995 + 0.350768i −0.994825 0.101602i \(-0.967603\pi\)
0.891830 + 0.452370i \(0.149421\pi\)
\(44\) −3.00764 + 6.58582i −0.453419 + 0.992850i
\(45\) 0 0
\(46\) −8.34021 + 6.68469i −1.22970 + 0.985604i
\(47\) 11.6146i 1.69416i 0.531466 + 0.847079i \(0.321641\pi\)
−0.531466 + 0.847079i \(0.678359\pi\)
\(48\) 1.02822 + 0.469574i 0.148411 + 0.0677772i
\(49\) −6.70899 1.96994i −0.958428 0.281420i
\(50\) 0 0
\(51\) −2.84593 + 1.82897i −0.398510 + 0.256107i
\(52\) −8.07603 6.99792i −1.11994 0.970437i
\(53\) 10.2695 + 1.47653i 1.41062 + 0.202817i 0.805160 0.593058i \(-0.202079\pi\)
0.605462 + 0.795874i \(0.292988\pi\)
\(54\) 10.6921 3.13950i 1.45502 0.427231i
\(55\) 0 0
\(56\) −0.0270422 0.188083i −0.00361367 0.0251336i
\(57\) 2.60249 1.18852i 0.344708 0.157423i
\(58\) 15.0951 6.89372i 1.98209 0.905190i
\(59\) 1.64421 + 11.4357i 0.214058 + 1.48881i 0.759417 + 0.650604i \(0.225484\pi\)
−0.545359 + 0.838203i \(0.683607\pi\)
\(60\) 0 0
\(61\) −3.89722 + 1.14433i −0.498988 + 0.146516i −0.521535 0.853230i \(-0.674641\pi\)
0.0225474 + 0.999746i \(0.492822\pi\)
\(62\) −3.80211 0.546662i −0.482869 0.0694261i
\(63\) 0.133248 + 0.115460i 0.0167876 + 0.0145466i
\(64\) 10.9041 7.00766i 1.36302 0.875958i
\(65\) 0 0
\(66\) 5.21797 + 1.53213i 0.642288 + 0.188593i
\(67\) 11.1056 + 5.07177i 1.35677 + 0.619615i 0.955131 0.296184i \(-0.0957141\pi\)
0.401637 + 0.915799i \(0.368441\pi\)
\(68\) 10.0377i 1.21725i
\(69\) 3.50140 + 3.27723i 0.421518 + 0.394532i
\(70\) 0 0
\(71\) 0.787956 1.72538i 0.0935131 0.204765i −0.857095 0.515158i \(-0.827733\pi\)
0.950608 + 0.310393i \(0.100461\pi\)
\(72\) 1.21453 4.13631i 0.143134 0.487468i
\(73\) −4.16900 + 3.61246i −0.487944 + 0.422806i −0.863772 0.503884i \(-0.831904\pi\)
0.375827 + 0.926690i \(0.377359\pi\)
\(74\) −1.32702 + 0.852823i −0.154263 + 0.0991387i
\(75\) 0 0
\(76\) 1.20812 8.40266i 0.138581 0.963852i
\(77\) 0.0606031 + 0.206395i 0.00690637 + 0.0235209i
\(78\) −4.33955 + 6.75247i −0.491357 + 0.764566i
\(79\) 0.997420 + 6.93721i 0.112219 + 0.780497i 0.965753 + 0.259461i \(0.0835450\pi\)
−0.853535 + 0.521036i \(0.825546\pi\)
\(80\) 0 0
\(81\) 0.415415 + 0.909632i 0.0461572 + 0.101070i
\(82\) 12.2459 1.76070i 1.35234 0.194436i
\(83\) −2.25587 + 3.51021i −0.247614 + 0.385295i −0.942705 0.333626i \(-0.891728\pi\)
0.695091 + 0.718922i \(0.255364\pi\)
\(84\) −0.250975 + 0.0736930i −0.0273836 + 0.00804056i
\(85\) 0 0
\(86\) 3.49877 4.03779i 0.377282 0.435406i
\(87\) −4.02557 6.26391i −0.431586 0.671561i
\(88\) 3.97489 3.44426i 0.423725 0.367160i
\(89\) −15.3009 4.49275i −1.62189 0.476231i −0.660367 0.750943i \(-0.729599\pi\)
−0.961526 + 0.274713i \(0.911417\pi\)
\(90\) 0 0
\(91\) −0.317493 −0.0332823
\(92\) 13.7971 3.48270i 1.43845 0.363096i
\(93\) 1.72352i 0.178720i
\(94\) 10.7532 23.5463i 1.10911 2.42861i
\(95\) 0 0
\(96\) −4.47283 5.16192i −0.456506 0.526836i
\(97\) −7.77424 12.0969i −0.789354 1.22826i −0.969614 0.244640i \(-0.921330\pi\)
0.180260 0.983619i \(-0.442306\pi\)
\(98\) 11.7773 + 10.2051i 1.18969 + 1.03087i
\(99\) −0.694523 + 4.83052i −0.0698022 + 0.485485i
\(100\) 0 0
\(101\) 14.6237 + 9.39808i 1.45511 + 0.935144i 0.998976 + 0.0452346i \(0.0144035\pi\)
0.456137 + 0.889910i \(0.349233\pi\)
\(102\) 7.46289 1.07300i 0.738937 0.106243i
\(103\) −1.05821 + 0.483270i −0.104269 + 0.0476180i −0.466867 0.884328i \(-0.654617\pi\)
0.362598 + 0.931946i \(0.381890\pi\)
\(104\) 3.22482 + 7.06137i 0.316220 + 0.692425i
\(105\) 0 0
\(106\) −19.4523 12.5013i −1.88938 1.21423i
\(107\) 4.83181 + 16.4556i 0.467108 + 1.59083i 0.770160 + 0.637851i \(0.220176\pi\)
−0.303051 + 0.952974i \(0.598005\pi\)
\(108\) −14.6847 2.11134i −1.41303 0.203164i
\(109\) 1.71227 1.97606i 0.164006 0.189273i −0.667798 0.744343i \(-0.732763\pi\)
0.831804 + 0.555070i \(0.187308\pi\)
\(110\) 0 0
\(111\) 0.463496 + 0.534903i 0.0439931 + 0.0507707i
\(112\) 0.0280744 0.0956126i 0.00265278 0.00903454i
\(113\) −16.2969 7.44256i −1.53309 0.700137i −0.542888 0.839805i \(-0.682669\pi\)
−0.990198 + 0.139668i \(0.955396\pi\)
\(114\) −6.37640 −0.597205
\(115\) 0 0
\(116\) −22.0931 −2.05129
\(117\) −6.55207 2.99223i −0.605739 0.276632i
\(118\) 7.25434 24.7060i 0.667816 2.27437i
\(119\) 0.195298 + 0.225386i 0.0179029 + 0.0206611i
\(120\) 0 0
\(121\) 3.30439 3.81347i 0.300399 0.346679i
\(122\) 8.96031 + 1.28830i 0.811228 + 0.116637i
\(123\) −1.56393 5.32627i −0.141015 0.480254i
\(124\) 4.30209 + 2.76479i 0.386339 + 0.248285i
\(125\) 0 0
\(126\) −0.163236 0.357438i −0.0145422 0.0318431i
\(127\) 2.72142 1.24283i 0.241487 0.110283i −0.290996 0.956724i \(-0.593987\pi\)
0.532482 + 0.846441i \(0.321259\pi\)
\(128\) −15.0726 + 2.16711i −1.33224 + 0.191548i
\(129\) −2.01669 1.29605i −0.177560 0.114111i
\(130\) 0 0
\(131\) 1.91036 13.2869i 0.166909 1.16088i −0.718316 0.695716i \(-0.755087\pi\)
0.885226 0.465162i \(-0.154004\pi\)
\(132\) −5.47170 4.74125i −0.476250 0.412673i
\(133\) −0.136359 0.212178i −0.0118238 0.0183982i
\(134\) −17.8188 20.5640i −1.53931 1.77646i
\(135\) 0 0
\(136\) 3.02915 6.63291i 0.259747 0.568767i
\(137\) 19.2932i 1.64833i −0.566350 0.824165i \(-0.691645\pi\)
0.566350 0.824165i \(-0.308355\pi\)
\(138\) −4.06421 9.88567i −0.345968 0.841524i
\(139\) −15.4962 −1.31437 −0.657185 0.753729i \(-0.728253\pi\)
−0.657185 + 0.753729i \(0.728253\pi\)
\(140\) 0 0
\(141\) −11.1441 3.27220i −0.938502 0.275569i
\(142\) −3.19485 + 2.76835i −0.268106 + 0.232315i
\(143\) −4.75114 7.39292i −0.397310 0.618227i
\(144\) 1.48047 1.70856i 0.123373 0.142380i
\(145\) 0 0
\(146\) 11.7964 3.46373i 0.976275 0.286660i
\(147\) 3.78028 5.88224i 0.311793 0.485159i
\(148\) 2.07870 0.298872i 0.170868 0.0245671i
\(149\) 6.62691 + 14.5109i 0.542898 + 1.18878i 0.960020 + 0.279930i \(0.0903114\pi\)
−0.417122 + 0.908850i \(0.636961\pi\)
\(150\) 0 0
\(151\) −0.0629411 0.437765i −0.00512208 0.0356248i 0.987100 0.160104i \(-0.0511830\pi\)
−0.992222 + 0.124479i \(0.960274\pi\)
\(152\) −3.33405 + 5.18789i −0.270427 + 0.420793i
\(153\) 1.90618 + 6.49186i 0.154106 + 0.524836i
\(154\) 0.0682278 0.474535i 0.00549795 0.0382391i
\(155\) 0 0
\(156\) 8.98974 5.77735i 0.719755 0.462559i
\(157\) −5.37996 + 4.66176i −0.429367 + 0.372049i −0.842567 0.538592i \(-0.818957\pi\)
0.413200 + 0.910640i \(0.364411\pi\)
\(158\) 4.40066 14.9873i 0.350098 1.19232i
\(159\) −4.30997 + 9.43751i −0.341803 + 0.748443i
\(160\) 0 0
\(161\) 0.242038 0.346643i 0.0190753 0.0273193i
\(162\) 2.22871i 0.175104i
\(163\) −6.50054 2.96870i −0.509162 0.232526i 0.144233 0.989544i \(-0.453929\pi\)
−0.653395 + 0.757017i \(0.726656\pi\)
\(164\) −15.8038 4.64041i −1.23407 0.362355i
\(165\) 0 0
\(166\) 7.82322 5.02768i 0.607200 0.390224i
\(167\) 1.00714 + 0.872694i 0.0779351 + 0.0675311i 0.692957 0.720979i \(-0.256307\pi\)
−0.615022 + 0.788510i \(0.710853\pi\)
\(168\) 0.188083 + 0.0270422i 0.0145109 + 0.00208635i
\(169\) −0.0280633 + 0.00824014i −0.00215872 + 0.000633857i
\(170\) 0 0
\(171\) −0.814334 5.66382i −0.0622737 0.433123i
\(172\) −6.47018 + 2.95483i −0.493346 + 0.225304i
\(173\) −2.45670 + 1.12194i −0.186779 + 0.0852992i −0.506609 0.862176i \(-0.669101\pi\)
0.319830 + 0.947475i \(0.396374\pi\)
\(174\) 2.36168 + 16.4259i 0.179039 + 1.24524i
\(175\) 0 0
\(176\) 2.64649 0.777080i 0.199487 0.0585746i
\(177\) −11.4357 1.64421i −0.859563 0.123587i
\(178\) 26.8600 + 23.2743i 2.01324 + 1.74449i
\(179\) 16.6467 10.6982i 1.24423 0.799620i 0.258188 0.966095i \(-0.416875\pi\)
0.986046 + 0.166474i \(0.0532383\pi\)
\(180\) 0 0
\(181\) −3.82402 1.12283i −0.284237 0.0834596i 0.136506 0.990639i \(-0.456413\pi\)
−0.420744 + 0.907180i \(0.638231\pi\)
\(182\) 0.643655 + 0.293947i 0.0477109 + 0.0217888i
\(183\) 4.06175i 0.300253i
\(184\) −10.1681 1.86229i −0.749603 0.137290i
\(185\) 0 0
\(186\) 1.59570 3.49409i 0.117002 0.256199i
\(187\) −2.32563 + 7.92038i −0.170067 + 0.579195i
\(188\) −26.0447 + 22.5678i −1.89950 + 1.64593i
\(189\) −0.370807 + 0.238303i −0.0269723 + 0.0173340i
\(190\) 0 0
\(191\) 0.850935 5.91838i 0.0615715 0.428239i −0.935599 0.353065i \(-0.885140\pi\)
0.997170 0.0751744i \(-0.0239513\pi\)
\(192\) 3.65175 + 12.4367i 0.263543 + 0.897544i
\(193\) −5.45312 + 8.48523i −0.392524 + 0.610780i −0.980127 0.198370i \(-0.936435\pi\)
0.587603 + 0.809149i \(0.300072\pi\)
\(194\) 4.56092 + 31.7219i 0.327455 + 2.27750i
\(195\) 0 0
\(196\) −8.61857 18.8720i −0.615612 1.34800i
\(197\) 5.06355 0.728029i 0.360763 0.0518699i 0.0404498 0.999182i \(-0.487121\pi\)
0.320313 + 0.947312i \(0.396212\pi\)
\(198\) 5.88029 9.14991i 0.417894 0.650255i
\(199\) 25.5033 7.48844i 1.80788 0.530842i 0.809468 0.587164i \(-0.199756\pi\)
0.998413 + 0.0563229i \(0.0179376\pi\)
\(200\) 0 0
\(201\) −7.99514 + 9.22689i −0.563934 + 0.650814i
\(202\) −20.9456 32.5920i −1.47373 2.29316i
\(203\) −0.496076 + 0.429852i −0.0348177 + 0.0301697i
\(204\) −9.63112 2.82795i −0.674313 0.197996i
\(205\) 0 0
\(206\) 2.59275 0.180646
\(207\) 8.26187 4.87252i 0.574240 0.338664i
\(208\) 4.07103i 0.282275i
\(209\) 2.90009 6.35031i 0.200603 0.439260i
\(210\) 0 0
\(211\) 9.65433 + 11.1417i 0.664631 + 0.767026i 0.983526 0.180765i \(-0.0578572\pi\)
−0.318895 + 0.947790i \(0.603312\pi\)
\(212\) 16.6432 + 25.8974i 1.14306 + 1.77864i
\(213\) 1.43350 + 1.24213i 0.0982217 + 0.0851096i
\(214\) 5.43971 37.8340i 0.371851 2.58628i
\(215\) 0 0
\(216\) 9.06646 + 5.82666i 0.616895 + 0.396454i
\(217\) 0.150392 0.0216231i 0.0102092 0.00146787i
\(218\) −5.30081 + 2.42080i −0.359016 + 0.163957i
\(219\) −2.29158 5.01787i −0.154851 0.339076i
\(220\) 0 0
\(221\) −10.2496 6.58702i −0.689463 0.443091i
\(222\) −0.444413 1.51353i −0.0298271 0.101582i
\(223\) 1.00163 + 0.144012i 0.0670740 + 0.00964378i 0.175770 0.984431i \(-0.443758\pi\)
−0.108696 + 0.994075i \(0.534668\pi\)
\(224\) −0.394306 + 0.455054i −0.0263457 + 0.0304046i
\(225\) 0 0
\(226\) 26.1482 + 30.1767i 1.73935 + 2.00732i
\(227\) −1.42057 + 4.83803i −0.0942867 + 0.321111i −0.993108 0.117205i \(-0.962607\pi\)
0.898821 + 0.438316i \(0.144425\pi\)
\(228\) 7.72193 + 3.52649i 0.511397 + 0.233547i
\(229\) 22.9504 1.51661 0.758304 0.651901i \(-0.226028\pi\)
0.758304 + 0.651901i \(0.226028\pi\)
\(230\) 0 0
\(231\) −0.215109 −0.0141531
\(232\) 14.5991 + 6.66717i 0.958476 + 0.437721i
\(233\) 6.06370 20.6511i 0.397246 1.35290i −0.481850 0.876254i \(-0.660035\pi\)
0.879097 0.476644i \(-0.158147\pi\)
\(234\) 10.5127 + 12.1323i 0.687237 + 0.793114i
\(235\) 0 0
\(236\) −22.4489 + 25.9074i −1.46130 + 1.68643i
\(237\) −6.93721 0.997420i −0.450620 0.0647894i
\(238\) −0.187257 0.637740i −0.0121381 0.0413386i
\(239\) 7.37760 + 4.74129i 0.477217 + 0.306689i 0.757047 0.653361i \(-0.226642\pi\)
−0.279830 + 0.960050i \(0.590278\pi\)
\(240\) 0 0
\(241\) 3.66317 + 8.02123i 0.235966 + 0.516693i 0.990157 0.139962i \(-0.0446980\pi\)
−0.754191 + 0.656655i \(0.771971\pi\)
\(242\) −10.2296 + 4.67172i −0.657587 + 0.300310i
\(243\) −15.8371 + 2.27704i −1.01595 + 0.146072i
\(244\) −10.1386 6.51568i −0.649057 0.417123i
\(245\) 0 0
\(246\) −1.76070 + 12.2459i −0.112258 + 0.780771i
\(247\) 7.78723 + 6.74767i 0.495490 + 0.429344i
\(248\) −2.00847 3.12524i −0.127538 0.198453i
\(249\) −2.73247 3.15343i −0.173163 0.199841i
\(250\) 0 0
\(251\) −2.44763 + 5.35957i −0.154493 + 0.338293i −0.971014 0.239023i \(-0.923173\pi\)
0.816521 + 0.577316i \(0.195900\pi\)
\(252\) 0.523141i 0.0329548i
\(253\) 11.6937 + 0.448583i 0.735175 + 0.0282022i
\(254\) −6.66780 −0.418375
\(255\) 0 0
\(256\) 7.68968 + 2.25789i 0.480605 + 0.141118i
\(257\) 5.82941 5.05121i 0.363628 0.315086i −0.453814 0.891097i \(-0.649937\pi\)
0.817442 + 0.576011i \(0.195391\pi\)
\(258\) 2.88852 + 4.49462i 0.179831 + 0.279823i
\(259\) 0.0408599 0.0471549i 0.00253891 0.00293006i
\(260\) 0 0
\(261\) −14.2886 + 4.19552i −0.884443 + 0.259696i
\(262\) −16.1744 + 25.1678i −0.999256 + 1.55487i
\(263\) 22.1627 3.18652i 1.36661 0.196489i 0.580343 0.814372i \(-0.302919\pi\)
0.786270 + 0.617883i \(0.212009\pi\)
\(264\) 2.18489 + 4.78424i 0.134471 + 0.294450i
\(265\) 0 0
\(266\) 0.0799977 + 0.556396i 0.00490497 + 0.0341148i
\(267\) 8.62153 13.4154i 0.527629 0.821007i
\(268\) 10.2059 + 34.7581i 0.623425 + 2.12319i
\(269\) 1.31816 9.16802i 0.0803698 0.558984i −0.909357 0.416016i \(-0.863426\pi\)
0.989727 0.142968i \(-0.0456648\pi\)
\(270\) 0 0
\(271\) 18.4727 11.8717i 1.12214 0.721154i 0.158233 0.987402i \(-0.449420\pi\)
0.963905 + 0.266247i \(0.0857838\pi\)
\(272\) 2.88999 2.50419i 0.175232 0.151839i
\(273\) 0.0894481 0.304632i 0.00541365 0.0184372i
\(274\) −17.8624 + 39.1132i −1.07911 + 2.36291i
\(275\) 0 0
\(276\) −0.545473 + 14.2194i −0.0328336 + 0.855909i
\(277\) 12.5089i 0.751589i −0.926703 0.375795i \(-0.877370\pi\)
0.926703 0.375795i \(-0.122630\pi\)
\(278\) 31.4155 + 14.3470i 1.88418 + 0.860474i
\(279\) 3.30740 + 0.971141i 0.198009 + 0.0581407i
\(280\) 0 0
\(281\) −20.6303 + 13.2583i −1.23070 + 0.790922i −0.984000 0.178171i \(-0.942982\pi\)
−0.246699 + 0.969092i \(0.579346\pi\)
\(282\) 19.5629 + 16.9514i 1.16496 + 1.00944i
\(283\) 17.4860 + 2.51410i 1.03943 + 0.149448i 0.640836 0.767678i \(-0.278588\pi\)
0.398597 + 0.917126i \(0.369497\pi\)
\(284\) 5.40006 1.58560i 0.320435 0.0940882i
\(285\) 0 0
\(286\) 2.78736 + 19.3865i 0.164820 + 1.14635i
\(287\) −0.445142 + 0.203290i −0.0262759 + 0.0119998i
\(288\) −12.4259 + 5.67474i −0.732205 + 0.334387i
\(289\) −0.790638 5.49901i −0.0465081 0.323471i
\(290\) 0 0
\(291\) 13.7972 4.05122i 0.808806 0.237487i
\(292\) −16.2012 2.32939i −0.948106 0.136317i
\(293\) −6.41653 5.55996i −0.374858 0.324816i 0.446973 0.894547i \(-0.352502\pi\)
−0.821831 + 0.569731i \(0.807047\pi\)
\(294\) −13.1098 + 8.42515i −0.764578 + 0.491365i
\(295\) 0 0
\(296\) −1.46379 0.429809i −0.0850813 0.0249821i
\(297\) −11.0979 5.06826i −0.643968 0.294090i
\(298\) 35.5535i 2.05956i
\(299\) −5.49782 + 16.3738i −0.317947 + 0.946921i
\(300\) 0 0
\(301\) −0.0877903 + 0.192234i −0.00506015 + 0.0110802i
\(302\) −0.277699 + 0.945756i −0.0159798 + 0.0544222i
\(303\) −13.1374 + 11.3836i −0.754722 + 0.653970i
\(304\) −2.72064 + 1.74845i −0.156039 + 0.100280i
\(305\) 0 0
\(306\) 2.14600 14.9258i 0.122679 0.853251i
\(307\) −4.13574 14.0850i −0.236039 0.803875i −0.989267 0.146116i \(-0.953323\pi\)
0.753228 0.657759i \(-0.228496\pi\)
\(308\) −0.345068 + 0.536936i −0.0196621 + 0.0305948i
\(309\) −0.165561 1.15150i −0.00941843 0.0655066i
\(310\) 0 0
\(311\) 12.5355 + 27.4490i 0.710826 + 1.55649i 0.826332 + 0.563184i \(0.190424\pi\)
−0.115506 + 0.993307i \(0.536849\pi\)
\(312\) −7.68388 + 1.10477i −0.435014 + 0.0625455i
\(313\) 3.00922 4.68243i 0.170091 0.264667i −0.745734 0.666243i \(-0.767901\pi\)
0.915826 + 0.401576i \(0.131538\pi\)
\(314\) 15.2228 4.46983i 0.859074 0.252247i
\(315\) 0 0
\(316\) −13.6180 + 15.7160i −0.766074 + 0.884097i
\(317\) −1.51979 2.36484i −0.0853600 0.132823i 0.795948 0.605365i \(-0.206973\pi\)
−0.881308 + 0.472542i \(0.843336\pi\)
\(318\) 17.4752 15.1424i 0.979962 0.849142i
\(319\) −17.4328 5.11873i −0.976049 0.286594i
\(320\) 0 0
\(321\) −17.1503 −0.957238
\(322\) −0.811620 + 0.478662i −0.0452298 + 0.0266748i
\(323\) 9.67876i 0.538541i
\(324\) −1.23259 + 2.69900i −0.0684774 + 0.149945i
\(325\) 0 0
\(326\) 10.4300 + 12.0369i 0.577667 + 0.666663i
\(327\) 1.41362 + 2.19963i 0.0781732 + 0.121640i
\(328\) 9.04274 + 7.83558i 0.499302 + 0.432648i
\(329\) −0.145715 + 1.01347i −0.00803354 + 0.0558745i
\(330\) 0 0
\(331\) −11.6540 7.48954i −0.640560 0.411663i 0.179646 0.983731i \(-0.442505\pi\)
−0.820206 + 0.572069i \(0.806141\pi\)
\(332\) −12.2546 + 1.76195i −0.672560 + 0.0966995i
\(333\) 1.28764 0.588043i 0.0705620 0.0322246i
\(334\) −1.23381 2.70167i −0.0675111 0.147829i
\(335\) 0 0
\(336\) 0.0838301 + 0.0538744i 0.00457331 + 0.00293909i
\(337\) 6.07980 + 20.7059i 0.331188 + 1.12792i 0.941851 + 0.336031i \(0.109085\pi\)
−0.610663 + 0.791890i \(0.709097\pi\)
\(338\) 0.0645219 + 0.00927685i 0.00350953 + 0.000504594i
\(339\) 11.7325 13.5400i 0.637220 0.735391i
\(340\) 0 0
\(341\) 2.75404 + 3.17834i 0.149140 + 0.172117i
\(342\) −3.59288 + 12.2362i −0.194281 + 0.661659i
\(343\) −1.12203 0.512414i −0.0605839 0.0276677i
\(344\) 5.16718 0.278596
\(345\) 0 0
\(346\) 6.01920 0.323594
\(347\) −17.1989 7.85449i −0.923288 0.421651i −0.103702 0.994608i \(-0.533069\pi\)
−0.819585 + 0.572957i \(0.805796\pi\)
\(348\) 6.22434 21.1981i 0.333659 1.13634i
\(349\) 13.7056 + 15.8171i 0.733643 + 0.846669i 0.992877 0.119146i \(-0.0380155\pi\)
−0.259234 + 0.965815i \(0.583470\pi\)
\(350\) 0 0
\(351\) 11.7924 13.6091i 0.629431 0.726402i
\(352\) −16.4967 2.37187i −0.879277 0.126421i
\(353\) −0.454159 1.54672i −0.0241724 0.0823238i 0.946523 0.322635i \(-0.104569\pi\)
−0.970696 + 0.240311i \(0.922750\pi\)
\(354\) 21.6615 + 13.9210i 1.15129 + 0.739891i
\(355\) 0 0
\(356\) −19.6560 43.0406i −1.04177 2.28115i
\(357\) −0.271278 + 0.123889i −0.0143576 + 0.00655688i
\(358\) −43.6527 + 6.27632i −2.30712 + 0.331714i
\(359\) −29.2892 18.8230i −1.54583 0.993442i −0.986362 0.164588i \(-0.947371\pi\)
−0.559464 0.828854i \(-0.688993\pi\)
\(360\) 0 0
\(361\) 1.53906 10.7044i 0.0810034 0.563391i
\(362\) 6.71289 + 5.81675i 0.352822 + 0.305722i
\(363\) 2.72804 + 4.24491i 0.143185 + 0.222800i
\(364\) −0.616908 0.711950i −0.0323348 0.0373163i
\(365\) 0 0
\(366\) −3.76052 + 8.23440i −0.196566 + 0.430419i
\(367\) 22.6244i 1.18098i 0.807044 + 0.590491i \(0.201066\pi\)
−0.807044 + 0.590491i \(0.798934\pi\)
\(368\) −4.44480 3.10352i −0.231701 0.161782i
\(369\) −11.1023 −0.577961
\(370\) 0 0
\(371\) 0.877577 + 0.257680i 0.0455615 + 0.0133781i
\(372\) −3.86483 + 3.34890i −0.200382 + 0.173632i
\(373\) 5.83633 + 9.08151i 0.302194 + 0.470223i 0.958828 0.283986i \(-0.0916570\pi\)
−0.656635 + 0.754209i \(0.728021\pi\)
\(374\) 12.0478 13.9038i 0.622974 0.718951i
\(375\) 0 0
\(376\) 24.0207 7.05312i 1.23877 0.363737i
\(377\) 14.4981 22.5594i 0.746688 1.16187i
\(378\) 0.972370 0.139806i 0.0500133 0.00719083i
\(379\) 1.53173 + 3.35401i 0.0786795 + 0.172284i 0.944884 0.327406i \(-0.106174\pi\)
−0.866204 + 0.499690i \(0.833447\pi\)
\(380\) 0 0
\(381\) 0.425774 + 2.96133i 0.0218131 + 0.151713i
\(382\) −7.20457 + 11.2105i −0.368618 + 0.573580i
\(383\) 1.67426 + 5.70202i 0.0855509 + 0.291360i 0.991145 0.132787i \(-0.0423925\pi\)
−0.905594 + 0.424146i \(0.860574\pi\)
\(384\) 2.16711 15.0726i 0.110590 0.769171i
\(385\) 0 0
\(386\) 18.9111 12.1534i 0.962549 0.618593i
\(387\) −3.62344 + 3.13973i −0.184190 + 0.159601i
\(388\) 12.0205 40.9382i 0.610250 2.07832i
\(389\) −2.75929 + 6.04199i −0.139901 + 0.306341i −0.966594 0.256313i \(-0.917492\pi\)
0.826693 + 0.562654i \(0.190220\pi\)
\(390\) 0 0
\(391\) 15.0055 6.16908i 0.758860 0.311984i
\(392\) 15.0715i 0.761226i
\(393\) 12.2104 + 5.57632i 0.615935 + 0.281288i
\(394\) −10.9394 3.21210i −0.551119 0.161823i
\(395\) 0 0
\(396\) −12.1815 + 7.82858i −0.612144 + 0.393401i
\(397\) −3.44429 2.98449i −0.172864 0.149787i 0.564132 0.825685i \(-0.309211\pi\)
−0.736996 + 0.675897i \(0.763756\pi\)
\(398\) −58.6360 8.43058i −2.93916 0.422587i
\(399\) 0.242000 0.0710577i 0.0121152 0.00355733i
\(400\) 0 0
\(401\) 3.97219 + 27.6272i 0.198362 + 1.37964i 0.809038 + 0.587756i \(0.199989\pi\)
−0.610676 + 0.791880i \(0.709102\pi\)
\(402\) 24.7512 11.3035i 1.23448 0.563767i
\(403\) −5.64630 + 2.57858i −0.281262 + 0.128448i
\(404\) 7.34038 + 51.0534i 0.365197 + 2.54000i
\(405\) 0 0
\(406\) 1.40367 0.412155i 0.0696629 0.0204549i
\(407\) 1.70947 + 0.245784i 0.0847351 + 0.0121831i
\(408\) 5.51082 + 4.77515i 0.272826 + 0.236405i
\(409\) −6.83017 + 4.38949i −0.337730 + 0.217046i −0.698502 0.715608i \(-0.746150\pi\)
0.360772 + 0.932654i \(0.382513\pi\)
\(410\) 0 0
\(411\) 18.5117 + 5.43552i 0.913115 + 0.268115i
\(412\) −3.13987 1.43393i −0.154690 0.0706446i
\(413\) 1.01850i 0.0501169i
\(414\) −21.2605 + 2.22893i −1.04490 + 0.109546i
\(415\) 0 0
\(416\) 10.2188 22.3760i 0.501016 1.09707i
\(417\) 4.36578 14.8685i 0.213793 0.728113i
\(418\) −11.7587 + 10.1890i −0.575138 + 0.498360i
\(419\) 23.3315 14.9942i 1.13982 0.732517i 0.172232 0.985056i \(-0.444902\pi\)
0.967587 + 0.252539i \(0.0812658\pi\)
\(420\) 0 0
\(421\) 4.97445 34.5981i 0.242440 1.68621i −0.397359 0.917663i \(-0.630073\pi\)
0.639799 0.768543i \(-0.279018\pi\)
\(422\) −9.25685 31.5259i −0.450616 1.53466i
\(423\) −12.5586 + 19.5416i −0.610621 + 0.950145i
\(424\) −3.18261 22.1355i −0.154561 1.07500i
\(425\) 0 0
\(426\) −1.75612 3.84537i −0.0850844 0.186309i
\(427\) −0.354423 + 0.0509583i −0.0171517 + 0.00246604i
\(428\) −27.5118 + 42.8092i −1.32983 + 2.06926i
\(429\) 8.43201 2.47586i 0.407101 0.119536i
\(430\) 0 0
\(431\) 6.06858 7.00351i 0.292313 0.337347i −0.590530 0.807016i \(-0.701081\pi\)
0.882843 + 0.469669i \(0.155627\pi\)
\(432\) 3.05563 + 4.75465i 0.147014 + 0.228758i
\(433\) 17.1014 14.8185i 0.821841 0.712129i −0.138680 0.990337i \(-0.544286\pi\)
0.960521 + 0.278208i \(0.0897404\pi\)
\(434\) −0.324909 0.0954019i −0.0155961 0.00457944i
\(435\) 0 0
\(436\) 7.75820 0.371550
\(437\) −13.3037 + 3.35816i −0.636404 + 0.160642i
\(438\) 12.2944i 0.587448i
\(439\) 7.68428 16.8262i 0.366751 0.803072i −0.632835 0.774287i \(-0.718109\pi\)
0.999586 0.0287853i \(-0.00916393\pi\)
\(440\) 0 0
\(441\) −9.15787 10.5687i −0.436089 0.503274i
\(442\) 14.6805 + 22.8434i 0.698282 + 1.08655i
\(443\) 16.9129 + 14.6551i 0.803554 + 0.696284i 0.956430 0.291962i \(-0.0943080\pi\)
−0.152876 + 0.988245i \(0.548853\pi\)
\(444\) −0.298872 + 2.07870i −0.0141838 + 0.0986507i
\(445\) 0 0
\(446\) −1.89727 1.21930i −0.0898384 0.0577356i
\(447\) −15.7901 + 2.27028i −0.746848 + 0.107381i
\(448\) 1.03940 0.474677i 0.0491069 0.0224264i
\(449\) −2.04143 4.47012i −0.0963412 0.210958i 0.855325 0.518092i \(-0.173357\pi\)
−0.951666 + 0.307134i \(0.900630\pi\)
\(450\) 0 0
\(451\) −11.3950 7.32313i −0.536570 0.344833i
\(452\) −14.9767 51.0058i −0.704442 2.39911i
\(453\) 0.437765 + 0.0629411i 0.0205680 + 0.00295723i
\(454\) 7.35916 8.49293i 0.345383 0.398593i
\(455\) 0 0
\(456\) −4.03843 4.66060i −0.189117 0.218252i
\(457\) −3.26318 + 11.1134i −0.152645 + 0.519861i −0.999937 0.0112669i \(-0.996414\pi\)
0.847291 + 0.531128i \(0.178232\pi\)
\(458\) −46.5275 21.2484i −2.17409 0.992873i
\(459\) −16.9148 −0.789516
\(460\) 0 0
\(461\) −15.5495 −0.724210 −0.362105 0.932137i \(-0.617942\pi\)
−0.362105 + 0.932137i \(0.617942\pi\)
\(462\) 0.436091 + 0.199156i 0.0202888 + 0.00926558i
\(463\) 2.85313 9.71687i 0.132596 0.451581i −0.866250 0.499611i \(-0.833476\pi\)
0.998846 + 0.0480300i \(0.0152943\pi\)
\(464\) 5.51175 + 6.36089i 0.255876 + 0.295297i
\(465\) 0 0
\(466\) −31.4125 + 36.2520i −1.45516 + 1.67934i
\(467\) 0.158222 + 0.0227489i 0.00732164 + 0.00105269i 0.145975 0.989288i \(-0.453368\pi\)
−0.138653 + 0.990341i \(0.544277\pi\)
\(468\) −6.02126 20.5065i −0.278333 0.947914i
\(469\) 0.905432 + 0.581886i 0.0418089 + 0.0268690i
\(470\) 0 0
\(471\) −2.95722 6.47540i −0.136261 0.298371i
\(472\) 22.6524 10.3450i 1.04266 0.476168i
\(473\) −5.78997 + 0.832472i −0.266223 + 0.0382771i
\(474\) 13.1404 + 8.44481i 0.603558 + 0.387883i
\(475\) 0 0
\(476\) −0.125932 + 0.875877i −0.00577209 + 0.0401458i
\(477\) 15.6819 + 13.5885i 0.718026 + 0.622173i
\(478\) −10.5670 16.4425i −0.483321 0.752063i
\(479\) 3.84712 + 4.43982i 0.175779 + 0.202860i 0.836802 0.547506i \(-0.184423\pi\)
−0.661022 + 0.750366i \(0.729877\pi\)
\(480\) 0 0
\(481\) −1.05892 + 2.31870i −0.0482825 + 0.105724i
\(482\) 19.6530i 0.895169i
\(483\) 0.264411 + 0.329895i 0.0120311 + 0.0150107i
\(484\) 14.9720 0.680545
\(485\) 0 0
\(486\) 34.2149 + 10.0464i 1.55202 + 0.455714i
\(487\) 5.24040 4.54083i 0.237465 0.205765i −0.527996 0.849247i \(-0.677056\pi\)
0.765461 + 0.643482i \(0.222511\pi\)
\(488\) 4.73329 + 7.36514i 0.214266 + 0.333404i
\(489\) 4.67986 5.40085i 0.211631 0.244235i
\(490\) 0 0
\(491\) 21.0671 6.18586i 0.950745 0.279164i 0.230648 0.973037i \(-0.425915\pi\)
0.720097 + 0.693873i \(0.244097\pi\)
\(492\) 8.90487 13.8563i 0.401463 0.624688i
\(493\) −24.9329 + 3.58481i −1.12292 + 0.161452i
\(494\) −9.53982 20.8893i −0.429217 0.939854i
\(495\) 0 0
\(496\) −0.277260 1.92839i −0.0124493 0.0865871i
\(497\) 0.0904024 0.140669i 0.00405510 0.00630986i
\(498\) 2.61997 + 8.92279i 0.117404 + 0.399840i
\(499\) −4.04910 + 28.1621i −0.181263 + 1.26071i 0.672520 + 0.740079i \(0.265212\pi\)
−0.853783 + 0.520630i \(0.825697\pi\)
\(500\) 0 0
\(501\) −1.12109 + 0.720480i −0.0500866 + 0.0321887i
\(502\) 9.92419 8.59936i 0.442938 0.383808i
\(503\) 9.67821 32.9609i 0.431530 1.46966i −0.401207 0.915987i \(-0.631409\pi\)
0.832737 0.553668i \(-0.186773\pi\)
\(504\) 0.157872 0.345691i 0.00703217 0.0153983i
\(505\) 0 0
\(506\) −23.2913 11.7359i −1.03543 0.521723i
\(507\) 0.0292481i 0.00129895i
\(508\) 8.07482 + 3.68765i 0.358262 + 0.163613i
\(509\) −6.60273 1.93874i −0.292661 0.0859329i 0.132107 0.991236i \(-0.457826\pi\)
−0.424767 + 0.905303i \(0.639644\pi\)
\(510\) 0 0
\(511\) −0.409102 + 0.262914i −0.0180976 + 0.0116306i
\(512\) 9.51763 + 8.24708i 0.420624 + 0.364473i
\(513\) 14.1595 + 2.03584i 0.625159 + 0.0898843i
\(514\) −16.4946 + 4.84325i −0.727545 + 0.213626i
\(515\) 0 0
\(516\) −1.01228 7.04056i −0.0445631 0.309943i
\(517\) −25.7796 + 11.7731i −1.13378 + 0.517782i
\(518\) −0.126493 + 0.0577675i −0.00555779 + 0.00253816i
\(519\) −0.384358 2.67327i −0.0168714 0.117343i
\(520\) 0 0
\(521\) 5.29187 1.55383i 0.231841 0.0680747i −0.163748 0.986502i \(-0.552358\pi\)
0.395589 + 0.918427i \(0.370540\pi\)
\(522\) 32.8517 + 4.72337i 1.43788 + 0.206736i
\(523\) 3.59678 + 3.11663i 0.157276 + 0.136281i 0.729944 0.683507i \(-0.239546\pi\)
−0.572668 + 0.819787i \(0.694092\pi\)
\(524\) 33.5066 21.5334i 1.46374 0.940689i
\(525\) 0 0
\(526\) −47.8808 14.0591i −2.08770 0.613005i
\(527\) 5.30369 + 2.42212i 0.231033 + 0.105509i
\(528\) 2.75822i 0.120036i
\(529\) −13.6859 18.4850i −0.595039 0.803697i
\(530\) 0 0
\(531\) −9.59886 + 21.0186i −0.416555 + 0.912129i
\(532\) 0.210838 0.718048i 0.00914098 0.0311313i
\(533\) 15.1092 13.0922i 0.654453 0.567087i
\(534\) −29.8989 + 19.2149i −1.29385 + 0.831508i
\(535\) 0 0
\(536\) 3.74514 26.0480i 0.161766 1.12510i
\(537\) 5.57492 + 18.9864i 0.240576 + 0.819325i
\(538\) −11.1604 + 17.3660i −0.481160 + 0.748700i
\(539\) −2.42813 16.8880i −0.104587 0.727419i
\(540\) 0 0
\(541\) −7.02447 15.3814i −0.302006 0.661300i 0.696406 0.717648i \(-0.254782\pi\)
−0.998411 + 0.0563484i \(0.982054\pi\)
\(542\) −48.4411 + 6.96478i −2.08072 + 0.299163i
\(543\) 2.15470 3.35278i 0.0924671 0.143882i
\(544\) −22.1704 + 6.50980i −0.950546 + 0.279106i
\(545\) 0 0
\(546\) −0.463379 + 0.534768i −0.0198308 + 0.0228859i
\(547\) 20.8518 + 32.4460i 0.891557 + 1.38729i 0.921766 + 0.387746i \(0.126746\pi\)
−0.0302093 + 0.999544i \(0.509617\pi\)
\(548\) 43.2633 37.4879i 1.84812 1.60140i
\(549\) −7.79444 2.28865i −0.332659 0.0976774i
\(550\) 0 0
\(551\) 21.3030 0.907539
\(552\) 4.65154 9.23157i 0.197983 0.392922i
\(553\) 0.617845i 0.0262734i
\(554\) −11.5813 + 25.3594i −0.492040 + 1.07742i
\(555\) 0 0
\(556\) −30.1100 34.7488i −1.27695 1.47368i
\(557\) −22.7805 35.4471i −0.965239 1.50194i −0.861764 0.507309i \(-0.830640\pi\)
−0.103475 0.994632i \(-0.532996\pi\)
\(558\) −5.80599 5.03092i −0.245787 0.212976i
\(559\) 1.22870 8.54579i 0.0519685 0.361449i
\(560\) 0 0
\(561\) −6.94434 4.46286i −0.293190 0.188422i
\(562\) 54.0988 7.77824i 2.28202 0.328105i
\(563\) 5.47564 2.50064i 0.230771 0.105389i −0.296674 0.954979i \(-0.595877\pi\)
0.527445 + 0.849589i \(0.323150\pi\)
\(564\) −14.3160 31.3477i −0.602814 1.31998i
\(565\) 0 0
\(566\) −33.1217 21.2860i −1.39221 0.894719i
\(567\) 0.0248364 + 0.0845850i 0.00104303 + 0.00355224i
\(568\) −4.04685 0.581849i −0.169802 0.0244139i
\(569\) −11.4512 + 13.2154i −0.480061 + 0.554020i −0.943183 0.332275i \(-0.892184\pi\)
0.463121 + 0.886295i \(0.346729\pi\)
\(570\) 0 0
\(571\) −8.64327 9.97487i −0.361710 0.417435i 0.545502 0.838109i \(-0.316339\pi\)
−0.907212 + 0.420674i \(0.861794\pi\)
\(572\) 7.34622 25.0189i 0.307161 1.04609i
\(573\) 5.43891 + 2.48387i 0.227214 + 0.103765i
\(574\) 1.09065 0.0455229
\(575\) 0 0
\(576\) 25.9235 1.08015
\(577\) 29.5506 + 13.4953i 1.23021 + 0.561818i 0.921143 0.389223i \(-0.127257\pi\)
0.309065 + 0.951041i \(0.399984\pi\)
\(578\) −3.48833 + 11.8802i −0.145095 + 0.494149i
\(579\) −6.60519 7.62280i −0.274502 0.316793i
\(580\) 0 0
\(581\) −0.240883 + 0.277994i −0.00999351 + 0.0115331i
\(582\) −31.7219 4.56092i −1.31491 0.189056i
\(583\) 7.13240 + 24.2907i 0.295394 + 1.00602i
\(584\) 10.0028 + 6.42841i 0.413919 + 0.266009i
\(585\) 0 0
\(586\) 7.86064 + 17.2124i 0.324720 + 0.711037i
\(587\) −11.9812 + 5.47162i −0.494516 + 0.225838i −0.647032 0.762463i \(-0.723990\pi\)
0.152515 + 0.988301i \(0.451263\pi\)
\(588\) 20.5357 2.95259i 0.846879 0.121763i
\(589\) −4.14825 2.66592i −0.170926 0.109847i
\(590\) 0 0
\(591\) −0.728029 + 5.06355i −0.0299471 + 0.208287i
\(592\) −0.604640 0.523923i −0.0248505 0.0215331i
\(593\) 17.0754 + 26.5698i 0.701202 + 1.09109i 0.990982 + 0.133999i \(0.0427818\pi\)
−0.289779 + 0.957094i \(0.593582\pi\)
\(594\) 17.8065 + 20.5498i 0.730610 + 0.843169i
\(595\) 0 0
\(596\) −19.6630 + 43.0559i −0.805426 + 1.76364i
\(597\) 26.5800i 1.08785i
\(598\) 26.3053 28.1046i 1.07570 1.14928i
\(599\) 5.38162 0.219887 0.109943 0.993938i \(-0.464933\pi\)
0.109943 + 0.993938i \(0.464933\pi\)
\(600\) 0 0
\(601\) −32.4793 9.53678i −1.32486 0.389013i −0.458614 0.888636i \(-0.651654\pi\)
−0.866243 + 0.499622i \(0.833472\pi\)
\(602\) 0.355955 0.308437i 0.0145077 0.0125710i
\(603\) 13.2013 + 20.5416i 0.537598 + 0.836518i
\(604\) 0.859352 0.991745i 0.0349665 0.0403535i
\(605\) 0 0
\(606\) 37.1728 10.9149i 1.51004 0.443388i
\(607\) 11.7812 18.3320i 0.478186 0.744072i −0.515424 0.856935i \(-0.672366\pi\)
0.993611 + 0.112863i \(0.0360021\pi\)
\(608\) 19.3425 2.78103i 0.784442 0.112786i
\(609\) −0.272679 0.597084i −0.0110495 0.0241951i
\(610\) 0 0
\(611\) −5.95300 41.4040i −0.240833 1.67503i
\(612\) −10.8536 + 16.8885i −0.438731 + 0.682678i
\(613\) 1.91064 + 6.50705i 0.0771701 + 0.262817i 0.989037 0.147669i \(-0.0471771\pi\)
−0.911867 + 0.410486i \(0.865359\pi\)
\(614\) −4.65607 + 32.3837i −0.187904 + 1.30690i
\(615\) 0 0
\(616\) 0.390055 0.250673i 0.0157158 0.0100999i
\(617\) 24.3863 21.1308i 0.981755 0.850695i −0.00704038 0.999975i \(-0.502241\pi\)
0.988795 + 0.149280i \(0.0476956\pi\)
\(618\) −0.730462 + 2.48773i −0.0293835 + 0.100071i
\(619\) 14.5801 31.9260i 0.586024 1.28321i −0.351792 0.936078i \(-0.614427\pi\)
0.937815 0.347134i \(-0.112845\pi\)
\(620\) 0 0
\(621\) 5.86879 + 23.2499i 0.235506 + 0.932986i
\(622\) 67.2534i 2.69661i
\(623\) −1.27877 0.583995i −0.0512329 0.0233973i
\(624\) −3.90613 1.14694i −0.156370 0.0459144i
\(625\) 0 0
\(626\) −10.4358 + 6.70667i −0.417098 + 0.268052i
\(627\) 5.27603 + 4.57170i 0.210704 + 0.182576i
\(628\) −20.9072 3.00600i −0.834287 0.119952i
\(629\) 2.29740 0.674577i 0.0916033 0.0268971i
\(630\) 0 0
\(631\) 1.85675 + 12.9139i 0.0739159 + 0.514096i 0.992820 + 0.119616i \(0.0381663\pi\)
−0.918904 + 0.394480i \(0.870925\pi\)
\(632\) 13.7415 6.27554i 0.546608 0.249628i
\(633\) −13.4103 + 6.12428i −0.533012 + 0.243418i
\(634\) 0.891617 + 6.20133i 0.0354106 + 0.246286i
\(635\) 0 0
\(636\) −29.5373 + 8.67294i −1.17123 + 0.343904i
\(637\) 24.9261 + 3.58384i 0.987610 + 0.141997i
\(638\) 30.6024 + 26.5172i 1.21156 + 1.04982i
\(639\) 3.19136 2.05097i 0.126248 0.0811349i
\(640\) 0 0
\(641\) 34.6688 + 10.1797i 1.36934 + 0.402073i 0.882044 0.471166i \(-0.156167\pi\)
0.487291 + 0.873239i \(0.337985\pi\)
\(642\) 34.7689 + 15.8784i 1.37222 + 0.626672i
\(643\) 31.5510i 1.24425i 0.782917 + 0.622126i \(0.213731\pi\)
−0.782917 + 0.622126i \(0.786269\pi\)
\(644\) 1.24761 0.130798i 0.0491628 0.00515417i
\(645\) 0 0
\(646\) −8.96097 + 19.6218i −0.352565 + 0.772009i
\(647\) 3.90562 13.3013i 0.153546 0.522929i −0.846408 0.532535i \(-0.821239\pi\)
0.999954 + 0.00960580i \(0.00305767\pi\)
\(648\) 1.62899 1.41153i 0.0639928 0.0554501i
\(649\) −23.7160 + 15.2413i −0.930934 + 0.598275i
\(650\) 0 0
\(651\) −0.0216231 + 0.150392i −0.000847474 + 0.00589431i
\(652\) −5.97391 20.3453i −0.233956 0.796782i
\(653\) 3.05729 4.75724i 0.119641 0.186165i −0.776267 0.630404i \(-0.782889\pi\)
0.895909 + 0.444239i \(0.146526\pi\)
\(654\) −0.829328 5.76810i −0.0324293 0.225551i
\(655\) 0 0
\(656\) 2.60667 + 5.70780i 0.101773 + 0.222852i
\(657\) −10.9204 + 1.57012i −0.426047 + 0.0612564i
\(658\) 1.23372 1.91971i 0.0480954 0.0748379i
\(659\) 28.0838 8.24614i 1.09399 0.321224i 0.315527 0.948917i \(-0.397819\pi\)
0.778461 + 0.627692i \(0.216000\pi\)
\(660\) 0 0
\(661\) −10.5207 + 12.1415i −0.409207 + 0.472250i −0.922519 0.385952i \(-0.873873\pi\)
0.513312 + 0.858202i \(0.328418\pi\)
\(662\) 16.6920 + 25.9733i 0.648753 + 1.00948i
\(663\) 9.20784 7.97864i 0.357603 0.309865i
\(664\) 8.62956 + 2.53387i 0.334892 + 0.0983331i
\(665\) 0 0
\(666\) −3.15486 −0.122248
\(667\) 13.5782 + 33.0272i 0.525749 + 1.27882i
\(668\) 3.95413i 0.152990i
\(669\) −0.420370 + 0.920482i −0.0162524 + 0.0355879i
\(670\) 0 0
\(671\) −6.49036 7.49027i −0.250558 0.289159i
\(672\) −0.325532 0.506538i −0.0125577 0.0195401i
\(673\) −2.88949 2.50376i −0.111382 0.0965128i 0.597389 0.801951i \(-0.296205\pi\)
−0.708771 + 0.705438i \(0.750750\pi\)
\(674\) 6.84471 47.6060i 0.263649 1.83372i
\(675\) 0 0
\(676\) −0.0730065 0.0469185i −0.00280794 0.00180456i
\(677\) −16.2586 + 2.33764i −0.624870 + 0.0898428i −0.447474 0.894297i \(-0.647676\pi\)
−0.177396 + 0.984140i \(0.556767\pi\)
\(678\) −36.3211 + 16.5873i −1.39490 + 0.637031i
\(679\) −0.526602 1.15310i −0.0202091 0.0442518i
\(680\) 0 0
\(681\) −4.24183 2.72606i −0.162547 0.104463i
\(682\) −2.64066 8.99325i −0.101116 0.344369i
\(683\) −7.28651 1.04764i −0.278811 0.0400869i 0.00149105 0.999999i \(-0.499525\pi\)
−0.280302 + 0.959912i \(0.590434\pi\)
\(684\) 11.1183 12.8312i 0.425119 0.490614i
\(685\) 0 0
\(686\) 1.80028 + 2.07764i 0.0687351 + 0.0793245i
\(687\) −6.46589 + 22.0208i −0.246689 + 0.840145i
\(688\) 2.46491 + 1.12569i 0.0939737 + 0.0429163i
\(689\) −37.3658 −1.42352
\(690\) 0 0
\(691\) −9.67502 −0.368055 −0.184028 0.982921i \(-0.558914\pi\)
−0.184028 + 0.982921i \(0.558914\pi\)
\(692\) −7.28935 3.32894i −0.277100 0.126547i
\(693\) −0.121206 + 0.412791i −0.00460425 + 0.0156806i
\(694\) 27.5955 + 31.8469i 1.04751 + 1.20889i
\(695\) 0 0
\(696\) −10.5101 + 12.1293i −0.398386 + 0.459762i
\(697\) −18.5881 2.67257i −0.704076 0.101231i
\(698\) −13.1413 44.7552i −0.497406 1.69401i
\(699\) 18.1062 + 11.6362i 0.684840 + 0.440120i
\(700\) 0 0
\(701\) 17.6838 + 38.7221i 0.667908 + 1.46252i 0.874965 + 0.484186i \(0.160884\pi\)
−0.207057 + 0.978329i \(0.566388\pi\)
\(702\) −36.5066 + 16.6720i −1.37785 + 0.629244i
\(703\) −2.00436 + 0.288184i −0.0755960 + 0.0108691i
\(704\) 26.6071 + 17.0994i 1.00279 + 0.644456i
\(705\) 0 0
\(706\) −0.511298 + 3.55616i −0.0192430 + 0.133838i
\(707\) 1.15814 + 1.00353i 0.0435562 + 0.0377417i
\(708\) −18.5334 28.8385i −0.696526 1.08382i
\(709\) 22.9666 + 26.5049i 0.862529 + 0.995411i 0.999988 + 0.00490358i \(0.00156086\pi\)
−0.137459 + 0.990507i \(0.543894\pi\)
\(710\) 0 0
\(711\) −5.82291 + 12.7504i −0.218376 + 0.478177i
\(712\) 34.3729i 1.28818i
\(713\) 1.48909 8.13045i 0.0557668 0.304488i
\(714\) 0.664664 0.0248744
\(715\) 0 0
\(716\) 56.3353 + 16.5415i 2.10535 + 0.618187i
\(717\) −6.62775 + 5.74298i −0.247518 + 0.214475i
\(718\) 41.9511 + 65.2771i 1.56560 + 2.43612i
\(719\) 14.5394 16.7793i 0.542226 0.625763i −0.416828 0.908986i \(-0.636858\pi\)
0.959054 + 0.283223i \(0.0914036\pi\)
\(720\) 0 0
\(721\) −0.0984013 + 0.0288932i −0.00366466 + 0.00107604i
\(722\) −13.0307 + 20.2762i −0.484953 + 0.754602i
\(723\) −8.72835 + 1.25495i −0.324611 + 0.0466720i
\(724\) −4.91245 10.7568i −0.182570 0.399772i
\(725\) 0 0
\(726\) −1.60046 11.1315i −0.0593987 0.413127i
\(727\) 0.377738 0.587772i 0.0140095 0.0217993i −0.834178 0.551495i \(-0.814058\pi\)
0.848188 + 0.529696i \(0.177694\pi\)
\(728\) 0.192802 + 0.656624i 0.00714573 + 0.0243361i
\(729\) 1.85009 12.8677i 0.0685220 0.476581i
\(730\) 0 0
\(731\) −6.82240 + 4.38449i −0.252336 + 0.162166i
\(732\) 9.10812 7.89223i 0.336646 0.291705i
\(733\) −10.5094 + 35.7918i −0.388174 + 1.32200i 0.501403 + 0.865214i \(0.332817\pi\)
−0.889577 + 0.456785i \(0.849001\pi\)
\(734\) 20.9465 45.8664i 0.773149 1.69296i
\(735\) 0 0
\(736\) 16.6402 + 28.2151i 0.613364 + 1.04002i
\(737\) 29.7909i 1.09736i
\(738\) 22.5077 + 10.2789i 0.828518 + 0.378372i
\(739\) −23.5752 6.92231i −0.867229 0.254641i −0.182293 0.983244i \(-0.558352\pi\)
−0.684936 + 0.728603i \(0.740170\pi\)
\(740\) 0 0
\(741\) −8.66826 + 5.57075i −0.318437 + 0.204647i
\(742\) −1.54054 1.33489i −0.0565552 0.0490053i
\(743\) −40.9388 5.88612i −1.50190 0.215941i −0.658236 0.752811i \(-0.728697\pi\)
−0.843665 + 0.536871i \(0.819606\pi\)
\(744\) 3.56450 1.04663i 0.130681 0.0383713i
\(745\) 0 0
\(746\) −3.42400 23.8145i −0.125362 0.871910i
\(747\) −7.59104 + 3.46671i −0.277742 + 0.126840i
\(748\) −22.2796 + 10.1748i −0.814623 + 0.372026i
\(749\) 0.215166 + 1.49651i 0.00786201 + 0.0546815i
\(750\) 0 0
\(751\) 39.3106 11.5426i 1.43446 0.421197i 0.530091 0.847941i \(-0.322158\pi\)
0.904372 + 0.426744i \(0.140339\pi\)
\(752\) 12.9952 + 1.86842i 0.473885 + 0.0681344i
\(753\) −4.45289 3.85845i −0.162272 0.140610i
\(754\) −50.2783 + 32.3119i −1.83103 + 1.17673i
\(755\) 0 0
\(756\) −1.25488 0.368465i −0.0456394 0.0134009i
\(757\) −9.08592 4.14940i −0.330233 0.150812i 0.243397 0.969927i \(-0.421738\pi\)
−0.573630 + 0.819114i \(0.694465\pi\)
\(758\) 8.21774i 0.298482i
\(759\) −3.72490 + 11.0936i −0.135205 + 0.402673i
\(760\) 0 0
\(761\) −7.00401 + 15.3366i −0.253895 + 0.555953i −0.993065 0.117566i \(-0.962491\pi\)
0.739170 + 0.673519i \(0.235218\pi\)
\(762\) 1.87854 6.39771i 0.0680522 0.231764i
\(763\) 0.174202 0.150947i 0.00630653 0.00546464i
\(764\) 14.9249 9.59163i 0.539963 0.347013i
\(765\) 0 0
\(766\) 1.88491 13.1098i 0.0681045 0.473677i
\(767\) −11.7227 39.9238i −0.423282 1.44157i
\(768\) −4.33287 + 6.74207i −0.156349 + 0.243283i
\(769\) −6.22901 43.3237i −0.224624 1.56229i −0.720223 0.693743i \(-0.755961\pi\)
0.495599 0.868551i \(-0.334949\pi\)
\(770\) 0 0
\(771\) 3.20427 + 7.01636i 0.115399 + 0.252688i
\(772\) −29.6231 + 4.25916i −1.06616 + 0.153291i
\(773\) −18.1814 + 28.2907i −0.653938 + 1.01755i 0.342999 + 0.939336i \(0.388557\pi\)
−0.996937 + 0.0782114i \(0.975079\pi\)
\(774\) 10.2527 3.01046i 0.368525 0.108209i
\(775\) 0 0
\(776\) −20.2973 + 23.4244i −0.728632 + 0.840886i
\(777\) 0.0337332 + 0.0524899i 0.00121017 + 0.00188306i
\(778\) 11.1878 9.69430i 0.401103 0.347558i
\(779\) 15.2386 + 4.47446i 0.545980 + 0.160314i
\(780\) 0 0
\(781\) 4.62835 0.165615
\(782\) −36.1323 1.38607i −1.29209 0.0495659i
\(783\) 37.2296i 1.33048i
\(784\) −3.28337 + 7.18957i −0.117263 + 0.256770i
\(785\) 0 0
\(786\) −19.5915 22.6098i −0.698805 0.806464i
\(787\) −0.676215 1.05221i −0.0241045 0.0375073i 0.828992 0.559260i \(-0.188915\pi\)
−0.853097 + 0.521753i \(0.825278\pi\)
\(788\) 11.4713 + 9.93997i 0.408649 + 0.354097i
\(789\) −3.18652 + 22.1627i −0.113443 + 0.789014i
\(790\) 0 0
\(791\) −1.32867 0.853887i −0.0472422 0.0303607i
\(792\) 10.4120 1.49702i 0.369975 0.0531943i
\(793\) 13.3064 6.07684i 0.472525 0.215795i
\(794\) 4.21946 + 9.23933i 0.149743 + 0.327892i
\(795\) 0 0
\(796\) 66.3466 + 42.6384i 2.35159 + 1.51128i
\(797\) −3.44308 11.7261i −0.121960 0.415358i 0.875768 0.482733i \(-0.160356\pi\)
−0.997728 + 0.0673749i \(0.978538\pi\)
\(798\) −0.556396 0.0799977i −0.0196962 0.00283189i
\(799\) −25.7306 + 29.6947i −0.910282 + 1.05052i
\(800\) 0 0
\(801\) −20.8860 24.1037i −0.737969 0.851662i
\(802\) 17.5255 59.6863i 0.618846 2.10760i
\(803\) −12.2441 5.59168i −0.432084 0.197326i
\(804\) −36.2255 −1.27758
\(805\) 0 0
\(806\) 13.8341 0.487285
\(807\) 8.42528 + 3.84770i 0.296584 + 0.135445i
\(808\) 10.5562 35.9512i 0.371367 1.26476i
\(809\) −17.5520 20.2561i −0.617097 0.712167i 0.358056 0.933700i \(-0.383440\pi\)
−0.975153 + 0.221533i \(0.928894\pi\)
\(810\) 0 0
\(811\) 25.9259 29.9201i 0.910381 1.05064i −0.0881316 0.996109i \(-0.528090\pi\)
0.998512 0.0545266i \(-0.0173650\pi\)
\(812\) −1.92781 0.277177i −0.0676529 0.00972702i
\(813\) 6.18644 + 21.0691i 0.216968 + 0.738925i
\(814\) −3.23805 2.08097i −0.113494 0.0729379i
\(815\) 0 0
\(816\) 1.58855 + 3.47844i 0.0556104 + 0.121770i
\(817\) 6.23880 2.84917i 0.218268 0.0996797i
\(818\) 17.9108 2.57518i 0.626236 0.0900392i
\(819\) −0.534184 0.343299i −0.0186659 0.0119958i
\(820\) 0 0
\(821\) 4.50608 31.3404i 0.157263 1.09379i −0.746385 0.665514i \(-0.768212\pi\)
0.903648 0.428275i \(-0.140879\pi\)
\(822\) −32.4964 28.1583i −1.13344 0.982134i
\(823\) −25.3640 39.4672i −0.884134 1.37574i −0.926363 0.376632i \(-0.877082\pi\)
0.0422285 0.999108i \(-0.486554\pi\)
\(824\) 1.64209 + 1.89508i 0.0572050 + 0.0660181i
\(825\) 0 0
\(826\) 0.942962 2.06480i 0.0328099 0.0718436i
\(827\) 24.2676i 0.843869i 0.906626 + 0.421934i \(0.138649\pi\)
−0.906626 + 0.421934i \(0.861351\pi\)
\(828\) 26.9795 + 9.05891i 0.937603 + 0.314819i
\(829\) 21.8597 0.759220 0.379610 0.925147i \(-0.376058\pi\)
0.379610 + 0.925147i \(0.376058\pi\)
\(830\) 0 0
\(831\) 12.0022 + 3.52417i 0.416353 + 0.122252i
\(832\) −35.2797 + 30.5700i −1.22310 + 1.05983i
\(833\) −12.7886 19.8994i −0.443098 0.689473i
\(834\) −22.6166 + 26.1009i −0.783148 + 0.903801i
\(835\) 0 0
\(836\) 19.8751 5.83585i 0.687393 0.201837i
\(837\) −4.65902 + 7.24957i −0.161039 + 0.250582i
\(838\) −61.1823 + 8.79669i −2.11351 + 0.303876i
\(839\) 11.3411 + 24.8335i 0.391538 + 0.857348i 0.998059 + 0.0622806i \(0.0198374\pi\)
−0.606521 + 0.795068i \(0.707435\pi\)
\(840\) 0 0
\(841\) −3.76305 26.1726i −0.129760 0.902504i
\(842\) −42.1169 + 65.5352i −1.45145 + 2.25849i
\(843\) −6.90899 23.5299i −0.237958 0.810412i
\(844\) −6.22531 + 43.2980i −0.214284 + 1.49038i
\(845\) 0 0
\(846\) 43.5525 27.9895i 1.49737 0.962298i
\(847\) 0.336180 0.291301i 0.0115513 0.0100092i
\(848\) 3.30408 11.2527i 0.113463 0.386418i
\(849\) −7.33863 + 16.0694i −0.251861 + 0.551499i
\(850\) 0 0
\(851\) −1.72433 2.92379i −0.0591094 0.100226i
\(852\) 5.62804i 0.192813i
\(853\) −25.6230 11.7016i −0.877316 0.400657i −0.0747372 0.997203i \(-0.523812\pi\)
−0.802578 + 0.596547i \(0.796539\pi\)
\(854\) 0.765701 + 0.224830i 0.0262018 + 0.00769353i
\(855\) 0 0
\(856\) 31.0986 19.9858i 1.06293 0.683102i
\(857\) −8.49369 7.35982i −0.290139 0.251407i 0.497613 0.867399i \(-0.334210\pi\)
−0.787752 + 0.615992i \(0.788755\pi\)
\(858\) −19.3865 2.78736i −0.661844 0.0951588i
\(859\) −8.44772 + 2.48047i −0.288233 + 0.0846327i −0.422653 0.906292i \(-0.638901\pi\)
0.134420 + 0.990924i \(0.457083\pi\)
\(860\) 0 0
\(861\) −0.0696439 0.484384i −0.00237346 0.0165078i
\(862\) −18.7870 + 8.57972i −0.639887 + 0.292226i
\(863\) 43.5371 19.8827i 1.48202 0.676816i 0.500075 0.865982i \(-0.333306\pi\)
0.981945 + 0.189166i \(0.0605786\pi\)
\(864\) −4.86019 33.8034i −0.165347 1.15001i
\(865\) 0 0
\(866\) −48.3892 + 14.2084i −1.64433 + 0.482820i
\(867\) 5.49901 + 0.790638i 0.186756 + 0.0268515i
\(868\) 0.340708 + 0.295225i 0.0115644 + 0.0100206i
\(869\) −14.3867 + 9.24578i −0.488036 + 0.313641i
\(870\) 0 0
\(871\) −42.1892 12.3879i −1.42953 0.419747i
\(872\) −5.12661 2.34124i −0.173609 0.0792845i
\(873\) 28.7593i 0.973356i
\(874\) 30.0798 + 5.50910i 1.01746 + 0.186348i
\(875\) 0 0
\(876\) 6.79944 14.8887i 0.229732 0.503043i
\(877\) 13.2847 45.2435i 0.448592 1.52776i −0.356317 0.934365i \(-0.615968\pi\)
0.804909 0.593398i \(-0.202214\pi\)
\(878\) −31.1567 + 26.9975i −1.05149 + 0.911121i
\(879\) 7.14248 4.59020i 0.240910 0.154823i
\(880\) 0 0
\(881\) −5.26169 + 36.5959i −0.177271 + 1.23295i 0.685773 + 0.727816i \(0.259464\pi\)
−0.863043 + 0.505130i \(0.831445\pi\)
\(882\) 8.78083 + 29.9048i 0.295666 + 1.00695i
\(883\) 29.4975 45.8990i 0.992670 1.54462i 0.162807 0.986658i \(-0.447945\pi\)
0.829863 0.557967i \(-0.188418\pi\)
\(884\) −5.14479 35.7828i −0.173038 1.20351i
\(885\) 0 0
\(886\) −20.7193 45.3689i −0.696077 1.52420i
\(887\) 14.0346 2.01788i 0.471237 0.0677537i 0.0973946 0.995246i \(-0.468949\pi\)
0.373843 + 0.927492i \(0.378040\pi\)
\(888\) 0.824797 1.28341i 0.0276784 0.0430684i
\(889\) 0.253060 0.0743050i 0.00848734 0.00249211i
\(890\) 0 0
\(891\) −1.59792 + 1.84410i −0.0535324 + 0.0617797i
\(892\) 1.62329 + 2.52589i 0.0543517 + 0.0845730i
\(893\) 25.1133 21.7608i 0.840384 0.728197i
\(894\) 34.1133 + 10.0166i 1.14092 + 0.335004i
\(895\) 0 0
\(896\) −1.34240 −0.0448465
\(897\) −14.1616 9.88816i −0.472843 0.330156i
\(898\) 10.9523i 0.365484i
\(899\) −5.33109 + 11.6735i −0.177802 + 0.389332i
\(900\) 0 0
\(901\) 22.9847 + 26.5257i 0.765730 + 0.883699i
\(902\) 16.3211 + 25.3962i 0.543434 + 0.845600i
\(903\) −0.159714 0.138393i −0.00531494 0.00460542i
\(904\) −5.49580 + 38.2242i −0.182788 + 1.27132i
\(905\) 0 0
\(906\) −0.829210 0.532901i −0.0275486 0.0177044i
\(907\) −49.3023 + 7.08860i −1.63706 + 0.235373i −0.898549 0.438873i \(-0.855378\pi\)
−0.738506 + 0.674246i \(0.764469\pi\)
\(908\) −13.6091 + 6.21507i −0.451634 + 0.206254i
\(909\) 14.4425 + 31.6247i 0.479028 + 1.04892i
\(910\) 0 0
\(911\) −17.7763 11.4241i −0.588955 0.378498i 0.211959 0.977279i \(-0.432016\pi\)
−0.800913 + 0.598781i \(0.795652\pi\)
\(912\) −0.911132 3.10303i −0.0301706 0.102752i
\(913\) −10.0779 1.44898i −0.333529 0.0479543i
\(914\) 16.9046 19.5090i 0.559156 0.645300i
\(915\) 0 0
\(916\) 44.5941 + 51.4644i 1.47343 + 1.70043i
\(917\) 0.333391 1.13543i 0.0110095 0.0374951i
\(918\) 34.2915 + 15.6604i 1.13179 + 0.516870i
\(919\) 1.66022 0.0547657 0.0273829 0.999625i \(-0.491283\pi\)
0.0273829 + 0.999625i \(0.491283\pi\)
\(920\) 0 0
\(921\) 14.6797 0.483711
\(922\) 31.5235 + 14.3963i 1.03817 + 0.474116i
\(923\) −1.92459 + 6.55457i −0.0633488 + 0.215746i
\(924\) −0.417970 0.482363i −0.0137502 0.0158686i
\(925\) 0 0
\(926\) −14.7804 + 17.0575i −0.485715 + 0.560545i
\(927\) −2.30300 0.331122i −0.0756406 0.0108755i
\(928\) −14.3281 48.7971i −0.470343 1.60184i
\(929\) −24.5455 15.7744i −0.805311 0.517542i 0.0720340 0.997402i \(-0.477051\pi\)
−0.877345 + 0.479860i \(0.840687\pi\)
\(930\) 0 0
\(931\) 8.31037 + 18.1972i 0.272361 + 0.596388i
\(932\) 58.0904 26.5290i 1.90281 0.868986i
\(933\) −29.8688 + 4.29449i −0.977861 + 0.140595i
\(934\) −0.299702 0.192607i −0.00980656 0.00630229i
\(935\) 0 0
\(936\) −2.20955 + 15.3678i −0.0722214 + 0.502311i
\(937\) 13.9149 + 12.0573i 0.454580 + 0.393895i 0.851833 0.523813i \(-0.175491\pi\)
−0.397253 + 0.917709i \(0.630037\pi\)
\(938\) −1.29685 2.01794i −0.0423437 0.0658881i
\(939\) 3.64497 + 4.20652i 0.118949 + 0.137275i
\(940\) 0 0
\(941\) 17.9910 39.3947i 0.586489 1.28423i −0.351052 0.936356i \(-0.614176\pi\)
0.937541 0.347876i \(-0.113097\pi\)
\(942\) 15.8655i 0.516926i
\(943\) 2.77584 + 26.4772i 0.0903937 + 0.862215i
\(944\) 13.0596 0.425053
\(945\) 0 0
\(946\) 12.5088 + 3.67290i 0.406695 + 0.119416i
\(947\) 15.9299 13.8033i 0.517652 0.448548i −0.356433 0.934321i \(-0.616007\pi\)
0.874085 + 0.485773i \(0.161462\pi\)
\(948\) −11.2428 17.4941i −0.365149 0.568183i
\(949\) 13.0102 15.0146i 0.422330 0.487395i
\(950\) 0 0
\(951\) 2.69722 0.791977i 0.0874635 0.0256816i
\(952\) 0.347535 0.540775i 0.0112637 0.0175266i
\(953\) 14.5941 2.09831i 0.472749 0.0679710i 0.0981772 0.995169i \(-0.468699\pi\)
0.374572 + 0.927198i \(0.377790\pi\)
\(954\) −19.2113 42.0669i −0.621989 1.36197i
\(955\) 0 0
\(956\) 3.70319 + 25.7562i 0.119770 + 0.833016i
\(957\) 9.82277 15.2845i 0.317525 0.494079i
\(958\) −3.68873 12.5627i −0.119178 0.405881i
\(959\) 0.242051 1.68350i 0.00781622 0.0543630i
\(960\) 0 0
\(961\) −23.5799 + 15.1539i −0.760642 + 0.488835i
\(962\) 4.29349 3.72033i 0.138428 0.119948i
\(963\) −9.66362 + 32.9113i −0.311406 + 1.06055i
\(964\) −10.8691 + 23.8001i −0.350071 + 0.766549i
\(965\) 0 0
\(966\) −0.230613 0.913599i −0.00741984 0.0293946i
\(967\) 25.3720i 0.815909i 0.913002 + 0.407955i \(0.133758\pi\)
−0.913002 + 0.407955i \(0.866242\pi\)
\(968\) −9.89347 4.51820i −0.317988 0.145220i
\(969\) 9.28671 + 2.72682i 0.298332 + 0.0875982i
\(970\) 0 0
\(971\) −32.9014 + 21.1444i −1.05586 + 0.678557i −0.948858 0.315702i \(-0.897760\pi\)
−0.106997 + 0.994259i \(0.534124\pi\)
\(972\) −35.8786 31.0890i −1.15081 0.997180i
\(973\) −1.35218 0.194414i −0.0433488 0.00623261i
\(974\) −14.8280 + 4.35388i −0.475118 + 0.139507i
\(975\) 0 0
\(976\) 0.653409 + 4.54456i 0.0209151 + 0.145468i
\(977\) −21.1528 + 9.66014i −0.676736 + 0.309055i −0.723973 0.689829i \(-0.757686\pi\)
0.0472363 + 0.998884i \(0.484959\pi\)
\(978\) −14.4878 + 6.61636i −0.463269 + 0.211568i
\(979\) −5.53774 38.5158i −0.176987 1.23097i
\(980\) 0 0
\(981\) 5.01759 1.47330i 0.160199 0.0470387i
\(982\) −48.4365 6.96412i −1.54567 0.222234i
\(983\) −0.497051 0.430697i −0.0158535 0.0137371i 0.646898 0.762577i \(-0.276066\pi\)
−0.662751 + 0.748839i \(0.730611\pi\)
\(984\) −10.0658 + 6.46891i −0.320887 + 0.206221i
\(985\) 0 0
\(986\) 53.8655 + 15.8163i 1.71543 + 0.503695i
\(987\) −0.931366 0.425341i −0.0296457 0.0135387i
\(988\) 30.5733i 0.972667i
\(989\) 8.39371 + 7.85633i 0.266905 + 0.249817i
\(990\) 0 0
\(991\) 1.31140 2.87157i 0.0416581 0.0912185i −0.887659 0.460502i \(-0.847670\pi\)
0.929317 + 0.369283i \(0.120397\pi\)
\(992\) −3.31654 + 11.2951i −0.105300 + 0.358620i
\(993\) 10.4695 9.07184i 0.332238 0.287886i
\(994\) −0.313510 + 0.201480i −0.00994392 + 0.00639057i
\(995\) 0 0
\(996\) 1.76195 12.2546i 0.0558295 0.388303i
\(997\) −2.48154 8.45136i −0.0785913 0.267657i 0.910818 0.412807i \(-0.135452\pi\)
−0.989410 + 0.145150i \(0.953634\pi\)
\(998\) 34.2823 53.3443i 1.08519 1.68858i
\(999\) 0.503637 + 3.50287i 0.0159344 + 0.110826i
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 575.2.p.a.374.1 20
5.2 odd 4 115.2.g.a.6.1 10
5.3 odd 4 575.2.k.a.351.1 10
5.4 even 2 inner 575.2.p.a.374.2 20
23.4 even 11 inner 575.2.p.a.349.2 20
115.2 odd 44 2645.2.a.n.1.5 5
115.4 even 22 inner 575.2.p.a.349.1 20
115.27 odd 44 115.2.g.a.96.1 yes 10
115.67 even 44 2645.2.a.o.1.5 5
115.73 odd 44 575.2.k.a.326.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.2.g.a.6.1 10 5.2 odd 4
115.2.g.a.96.1 yes 10 115.27 odd 44
575.2.k.a.326.1 10 115.73 odd 44
575.2.k.a.351.1 10 5.3 odd 4
575.2.p.a.349.1 20 115.4 even 22 inner
575.2.p.a.349.2 20 23.4 even 11 inner
575.2.p.a.374.1 20 1.1 even 1 trivial
575.2.p.a.374.2 20 5.4 even 2 inner
2645.2.a.n.1.5 5 115.2 odd 44
2645.2.a.o.1.5 5 115.67 even 44