Properties

Label 950.2.bb.e.143.7
Level $950$
Weight $2$
Character 950.143
Analytic conductor $7.586$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(143,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([27, 34]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.bb (of order \(36\), degree \(12\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(10\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 143.7
Character \(\chi\) \(=\) 950.143
Dual form 950.2.bb.e.857.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.573576 - 0.819152i) q^{2} +(-0.0418747 + 0.478630i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(0.368052 + 0.308832i) q^{6} +(0.971585 + 3.62600i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.72709 + 0.480860i) q^{9} +O(q^{10})\) \(q+(0.573576 - 0.819152i) q^{2} +(-0.0418747 + 0.478630i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(0.368052 + 0.308832i) q^{6} +(0.971585 + 3.62600i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.72709 + 0.480860i) q^{9} +(-2.49403 - 4.31978i) q^{11} +(0.464087 - 0.124352i) q^{12} +(-1.33531 + 0.116824i) q^{13} +(3.52753 + 1.28391i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(3.85053 + 2.69617i) q^{17} +(1.95809 - 1.95809i) q^{18} +(3.89880 + 1.94919i) q^{19} +(-1.77620 + 0.313191i) q^{21} +(-4.96907 - 0.434737i) q^{22} +(2.34802 + 1.09490i) q^{23} +(0.164326 - 0.451483i) q^{24} +(-0.670204 + 1.16083i) q^{26} +(-0.717405 + 2.67739i) q^{27} +(3.07503 - 2.15316i) q^{28} +(-0.303332 + 1.72028i) q^{29} +(1.63635 + 0.944744i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(2.17201 - 1.01283i) q^{33} +(4.41715 - 1.60771i) q^{34} +(-0.480860 - 2.72709i) q^{36} +(5.79340 + 5.79340i) q^{37} +(3.83295 - 2.07570i) q^{38} -0.644009i q^{39} +(6.01261 + 7.16555i) q^{41} +(-0.762233 + 1.63461i) q^{42} +(0.825480 + 1.77025i) q^{43} +(-3.20626 + 3.82107i) q^{44} +(2.24366 - 1.29538i) q^{46} +(-3.92548 - 5.60617i) q^{47} +(-0.275579 - 0.393568i) q^{48} +(-6.14174 + 3.54594i) q^{49} +(-1.45171 + 1.73008i) q^{51} +(0.566481 + 1.21482i) q^{52} +(4.44595 - 9.53438i) q^{53} +(1.78170 + 2.12335i) q^{54} -3.75391i q^{56} +(-1.09620 + 1.78446i) q^{57} +(1.23519 + 1.23519i) q^{58} +(-1.59029 - 9.01900i) q^{59} +(-2.01691 + 0.734095i) q^{61} +(1.71246 - 0.798532i) q^{62} +(0.906001 + 10.3556i) q^{63} +(0.866025 + 0.500000i) q^{64} +(0.416156 - 2.36014i) q^{66} +(-0.207335 + 0.145177i) q^{67} +(1.21661 - 4.54046i) q^{68} +(-0.622375 + 1.07799i) q^{69} +(4.08948 - 11.2357i) q^{71} +(-2.50971 - 1.17030i) q^{72} +(-10.4597 - 0.915101i) q^{73} +(8.06863 - 1.42272i) q^{74} +(0.498175 - 4.33034i) q^{76} +(13.2404 - 13.2404i) q^{77} +(-0.527542 - 0.369389i) q^{78} +(7.35519 - 6.17174i) q^{79} +(6.55504 + 2.38584i) q^{81} +(9.31836 - 0.815251i) q^{82} +(-14.4402 + 3.86923i) q^{83} +(0.901799 + 1.56196i) q^{84} +(1.92358 + 0.339179i) q^{86} +(-0.810675 - 0.217220i) q^{87} +(1.29100 + 4.81809i) q^{88} +(10.2071 + 8.56479i) q^{89} +(-1.72097 - 4.72832i) q^{91} +(0.225799 - 2.58090i) q^{92} +(-0.520704 + 0.743642i) q^{93} -6.84386 q^{94} -0.480458 q^{96} +(-8.07300 + 11.5294i) q^{97} +(-0.618097 + 7.06489i) q^{98} +(-4.72423 - 12.9797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.573576 0.819152i 0.405580 0.579228i
\(3\) −0.0418747 + 0.478630i −0.0241763 + 0.276337i 0.974478 + 0.224482i \(0.0720689\pi\)
−0.998655 + 0.0518551i \(0.983487\pi\)
\(4\) −0.342020 0.939693i −0.171010 0.469846i
\(5\) 0 0
\(6\) 0.368052 + 0.308832i 0.150257 + 0.126080i
\(7\) 0.971585 + 3.62600i 0.367224 + 1.37050i 0.864380 + 0.502839i \(0.167711\pi\)
−0.497156 + 0.867661i \(0.665622\pi\)
\(8\) −0.965926 0.258819i −0.341506 0.0915064i
\(9\) 2.72709 + 0.480860i 0.909030 + 0.160287i
\(10\) 0 0
\(11\) −2.49403 4.31978i −0.751977 1.30246i −0.946863 0.321637i \(-0.895767\pi\)
0.194886 0.980826i \(-0.437566\pi\)
\(12\) 0.464087 0.124352i 0.133970 0.0358972i
\(13\) −1.33531 + 0.116824i −0.370347 + 0.0324012i −0.270811 0.962633i \(-0.587292\pi\)
−0.0995369 + 0.995034i \(0.531736\pi\)
\(14\) 3.52753 + 1.28391i 0.942771 + 0.343141i
\(15\) 0 0
\(16\) −0.766044 + 0.642788i −0.191511 + 0.160697i
\(17\) 3.85053 + 2.69617i 0.933891 + 0.653917i 0.938207 0.346073i \(-0.112485\pi\)
−0.00431668 + 0.999991i \(0.501374\pi\)
\(18\) 1.95809 1.95809i 0.461527 0.461527i
\(19\) 3.89880 + 1.94919i 0.894446 + 0.447176i
\(20\) 0 0
\(21\) −1.77620 + 0.313191i −0.387598 + 0.0683440i
\(22\) −4.96907 0.434737i −1.05941 0.0926863i
\(23\) 2.34802 + 1.09490i 0.489597 + 0.228303i 0.651708 0.758470i \(-0.274053\pi\)
−0.162111 + 0.986772i \(0.551830\pi\)
\(24\) 0.164326 0.451483i 0.0335430 0.0921585i
\(25\) 0 0
\(26\) −0.670204 + 1.16083i −0.131438 + 0.227657i
\(27\) −0.717405 + 2.67739i −0.138065 + 0.515264i
\(28\) 3.07503 2.15316i 0.581125 0.406908i
\(29\) −0.303332 + 1.72028i −0.0563273 + 0.319448i −0.999932 0.0116251i \(-0.996300\pi\)
0.943605 + 0.331073i \(0.107411\pi\)
\(30\) 0 0
\(31\) 1.63635 + 0.944744i 0.293896 + 0.169681i 0.639698 0.768627i \(-0.279060\pi\)
−0.345801 + 0.938308i \(0.612393\pi\)
\(32\) 0.0871557 + 0.996195i 0.0154071 + 0.176104i
\(33\) 2.17201 1.01283i 0.378099 0.176310i
\(34\) 4.41715 1.60771i 0.757534 0.275720i
\(35\) 0 0
\(36\) −0.480860 2.72709i −0.0801433 0.454515i
\(37\) 5.79340 + 5.79340i 0.952429 + 0.952429i 0.998919 0.0464896i \(-0.0148034\pi\)
−0.0464896 + 0.998919i \(0.514803\pi\)
\(38\) 3.83295 2.07570i 0.621786 0.336723i
\(39\) 0.644009i 0.103124i
\(40\) 0 0
\(41\) 6.01261 + 7.16555i 0.939012 + 1.11907i 0.992712 + 0.120513i \(0.0384541\pi\)
−0.0537001 + 0.998557i \(0.517101\pi\)
\(42\) −0.762233 + 1.63461i −0.117615 + 0.252227i
\(43\) 0.825480 + 1.77025i 0.125885 + 0.269960i 0.959142 0.282925i \(-0.0913047\pi\)
−0.833258 + 0.552885i \(0.813527\pi\)
\(44\) −3.20626 + 3.82107i −0.483362 + 0.576048i
\(45\) 0 0
\(46\) 2.24366 1.29538i 0.330810 0.190993i
\(47\) −3.92548 5.60617i −0.572590 0.817743i 0.423518 0.905888i \(-0.360795\pi\)
−0.996108 + 0.0881446i \(0.971906\pi\)
\(48\) −0.275579 0.393568i −0.0397764 0.0568067i
\(49\) −6.14174 + 3.54594i −0.877392 + 0.506562i
\(50\) 0 0
\(51\) −1.45171 + 1.73008i −0.203280 + 0.242259i
\(52\) 0.566481 + 1.21482i 0.0785567 + 0.168465i
\(53\) 4.44595 9.53438i 0.610699 1.30965i −0.321228 0.947002i \(-0.604096\pi\)
0.931927 0.362646i \(-0.118127\pi\)
\(54\) 1.78170 + 2.12335i 0.242459 + 0.288952i
\(55\) 0 0
\(56\) 3.75391i 0.501638i
\(57\) −1.09620 + 1.78446i −0.145196 + 0.236357i
\(58\) 1.23519 + 1.23519i 0.162188 + 0.162188i
\(59\) −1.59029 9.01900i −0.207039 1.17417i −0.894199 0.447669i \(-0.852254\pi\)
0.687161 0.726505i \(-0.258857\pi\)
\(60\) 0 0
\(61\) −2.01691 + 0.734095i −0.258239 + 0.0939912i −0.467895 0.883784i \(-0.654988\pi\)
0.209657 + 0.977775i \(0.432765\pi\)
\(62\) 1.71246 0.798532i 0.217482 0.101414i
\(63\) 0.906001 + 10.3556i 0.114145 + 1.30469i
\(64\) 0.866025 + 0.500000i 0.108253 + 0.0625000i
\(65\) 0 0
\(66\) 0.416156 2.36014i 0.0512253 0.290513i
\(67\) −0.207335 + 0.145177i −0.0253300 + 0.0177363i −0.586173 0.810186i \(-0.699366\pi\)
0.560843 + 0.827922i \(0.310477\pi\)
\(68\) 1.21661 4.54046i 0.147536 0.550612i
\(69\) −0.622375 + 1.07799i −0.0749252 + 0.129774i
\(70\) 0 0
\(71\) 4.08948 11.2357i 0.485332 1.33344i −0.419534 0.907740i \(-0.637806\pi\)
0.904865 0.425698i \(-0.139971\pi\)
\(72\) −2.50971 1.17030i −0.295772 0.137921i
\(73\) −10.4597 0.915101i −1.22421 0.107104i −0.543343 0.839511i \(-0.682841\pi\)
−0.680867 + 0.732407i \(0.738397\pi\)
\(74\) 8.06863 1.42272i 0.937960 0.165388i
\(75\) 0 0
\(76\) 0.498175 4.33034i 0.0571446 0.496724i
\(77\) 13.2404 13.2404i 1.50888 1.50888i
\(78\) −0.527542 0.369389i −0.0597323 0.0418250i
\(79\) 7.35519 6.17174i 0.827523 0.694375i −0.127197 0.991877i \(-0.540598\pi\)
0.954721 + 0.297503i \(0.0961537\pi\)
\(80\) 0 0
\(81\) 6.55504 + 2.38584i 0.728338 + 0.265093i
\(82\) 9.31836 0.815251i 1.02904 0.0900294i
\(83\) −14.4402 + 3.86923i −1.58501 + 0.424703i −0.940473 0.339868i \(-0.889618\pi\)
−0.644539 + 0.764571i \(0.722951\pi\)
\(84\) 0.901799 + 1.56196i 0.0983943 + 0.170424i
\(85\) 0 0
\(86\) 1.92358 + 0.339179i 0.207425 + 0.0365746i
\(87\) −0.810675 0.217220i −0.0869134 0.0232884i
\(88\) 1.29100 + 4.81809i 0.137621 + 0.513610i
\(89\) 10.2071 + 8.56479i 1.08195 + 0.907866i 0.996081 0.0884402i \(-0.0281882\pi\)
0.0858712 + 0.996306i \(0.472633\pi\)
\(90\) 0 0
\(91\) −1.72097 4.72832i −0.180406 0.495663i
\(92\) 0.225799 2.58090i 0.0235412 0.269077i
\(93\) −0.520704 + 0.743642i −0.0539945 + 0.0771121i
\(94\) −6.84386 −0.705891
\(95\) 0 0
\(96\) −0.480458 −0.0490365
\(97\) −8.07300 + 11.5294i −0.819689 + 1.17064i 0.163229 + 0.986588i \(0.447809\pi\)
−0.982917 + 0.184048i \(0.941080\pi\)
\(98\) −0.618097 + 7.06489i −0.0624373 + 0.713661i
\(99\) −4.72423 12.9797i −0.474803 1.30451i
\(100\) 0 0
\(101\) −8.61490 7.22876i −0.857214 0.719288i 0.104152 0.994561i \(-0.466787\pi\)
−0.961366 + 0.275273i \(0.911232\pi\)
\(102\) 0.584531 + 2.18150i 0.0578772 + 0.216001i
\(103\) −2.30555 0.617770i −0.227173 0.0608707i 0.143437 0.989659i \(-0.454185\pi\)
−0.370610 + 0.928789i \(0.620851\pi\)
\(104\) 1.32004 + 0.232759i 0.129441 + 0.0228239i
\(105\) 0 0
\(106\) −5.26001 9.11061i −0.510898 0.884901i
\(107\) −6.81684 + 1.82657i −0.659009 + 0.176581i −0.572799 0.819696i \(-0.694142\pi\)
−0.0862101 + 0.996277i \(0.527476\pi\)
\(108\) 2.76129 0.241582i 0.265705 0.0232462i
\(109\) −2.80009 1.01915i −0.268200 0.0976167i 0.204420 0.978883i \(-0.434469\pi\)
−0.472620 + 0.881267i \(0.656691\pi\)
\(110\) 0 0
\(111\) −3.01549 + 2.53030i −0.286218 + 0.240165i
\(112\) −3.07503 2.15316i −0.290563 0.203454i
\(113\) 6.03088 6.03088i 0.567338 0.567338i −0.364044 0.931382i \(-0.618604\pi\)
0.931382 + 0.364044i \(0.118604\pi\)
\(114\) 0.832987 + 1.92148i 0.0780164 + 0.179963i
\(115\) 0 0
\(116\) 1.72028 0.303332i 0.159724 0.0281636i
\(117\) −3.69768 0.323505i −0.341850 0.0299080i
\(118\) −8.30009 3.87040i −0.764085 0.356299i
\(119\) −6.03521 + 16.5816i −0.553246 + 1.52003i
\(120\) 0 0
\(121\) −6.94033 + 12.0210i −0.630939 + 1.09282i
\(122\) −0.555516 + 2.07321i −0.0502941 + 0.187700i
\(123\) −3.68142 + 2.57776i −0.331942 + 0.232429i
\(124\) 0.328106 1.86078i 0.0294648 0.167103i
\(125\) 0 0
\(126\) 9.00250 + 5.19760i 0.802006 + 0.463039i
\(127\) −0.663010 7.57824i −0.0588326 0.672460i −0.967155 0.254188i \(-0.918192\pi\)
0.908322 0.418271i \(-0.137364\pi\)
\(128\) 0.906308 0.422618i 0.0801070 0.0373545i
\(129\) −0.881860 + 0.320971i −0.0776434 + 0.0282599i
\(130\) 0 0
\(131\) 1.78830 + 10.1420i 0.156245 + 0.886107i 0.957639 + 0.287971i \(0.0929807\pi\)
−0.801394 + 0.598136i \(0.795908\pi\)
\(132\) −1.69462 1.69462i −0.147497 0.147497i
\(133\) −3.27977 + 16.0309i −0.284392 + 1.39005i
\(134\) 0.253109i 0.0218653i
\(135\) 0 0
\(136\) −3.02151 3.60089i −0.259092 0.308774i
\(137\) −5.94775 + 12.7550i −0.508150 + 1.08973i 0.470159 + 0.882582i \(0.344197\pi\)
−0.978309 + 0.207150i \(0.933581\pi\)
\(138\) 0.526054 + 1.12813i 0.0447807 + 0.0960325i
\(139\) −11.9222 + 14.2084i −1.01123 + 1.20514i −0.0326101 + 0.999468i \(0.510382\pi\)
−0.978621 + 0.205670i \(0.934062\pi\)
\(140\) 0 0
\(141\) 2.84765 1.64409i 0.239816 0.138458i
\(142\) −6.85816 9.79446i −0.575524 0.821933i
\(143\) 3.83494 + 5.47687i 0.320694 + 0.457999i
\(144\) −2.39816 + 1.38458i −0.199847 + 0.115382i
\(145\) 0 0
\(146\) −6.74902 + 8.04317i −0.558553 + 0.665657i
\(147\) −1.44001 3.08810i −0.118770 0.254703i
\(148\) 3.46256 7.42548i 0.284620 0.610370i
\(149\) −5.19534 6.19156i −0.425618 0.507232i 0.510034 0.860154i \(-0.329633\pi\)
−0.935653 + 0.352922i \(0.885188\pi\)
\(150\) 0 0
\(151\) 11.3814i 0.926208i −0.886304 0.463104i \(-0.846736\pi\)
0.886304 0.463104i \(-0.153264\pi\)
\(152\) −3.26146 2.89186i −0.264540 0.234561i
\(153\) 9.20427 + 9.20427i 0.744121 + 0.744121i
\(154\) −3.25151 18.4402i −0.262014 1.48596i
\(155\) 0 0
\(156\) −0.605171 + 0.220264i −0.0484524 + 0.0176352i
\(157\) 2.27098 1.05898i 0.181244 0.0845154i −0.329878 0.944023i \(-0.607008\pi\)
0.511122 + 0.859508i \(0.329230\pi\)
\(158\) −0.836827 9.56498i −0.0665744 0.760949i
\(159\) 4.37726 + 2.52721i 0.347140 + 0.200421i
\(160\) 0 0
\(161\) −1.68881 + 9.57773i −0.133097 + 0.754831i
\(162\) 5.71418 4.00111i 0.448949 0.314357i
\(163\) 3.42920 12.7979i 0.268596 1.00241i −0.691417 0.722456i \(-0.743013\pi\)
0.960013 0.279956i \(-0.0903200\pi\)
\(164\) 4.67698 8.10076i 0.365211 0.632563i
\(165\) 0 0
\(166\) −5.11305 + 14.0480i −0.396849 + 1.09033i
\(167\) 9.96206 + 4.64539i 0.770888 + 0.359471i 0.767937 0.640525i \(-0.221283\pi\)
0.00295017 + 0.999996i \(0.499061\pi\)
\(168\) 1.79673 + 0.157194i 0.138621 + 0.0121278i
\(169\) −11.0331 + 1.94543i −0.848700 + 0.149649i
\(170\) 0 0
\(171\) 9.69509 + 7.19040i 0.741402 + 0.549864i
\(172\) 1.38116 1.38116i 0.105312 0.105312i
\(173\) −14.4251 10.1006i −1.09672 0.767934i −0.122264 0.992498i \(-0.539015\pi\)
−0.974459 + 0.224563i \(0.927904\pi\)
\(174\) −0.642920 + 0.539474i −0.0487396 + 0.0408974i
\(175\) 0 0
\(176\) 4.68724 + 1.70601i 0.353314 + 0.128596i
\(177\) 4.38336 0.383494i 0.329473 0.0288252i
\(178\) 12.8704 3.44862i 0.964680 0.258485i
\(179\) −9.94971 17.2334i −0.743676 1.28808i −0.950811 0.309772i \(-0.899747\pi\)
0.207135 0.978312i \(-0.433586\pi\)
\(180\) 0 0
\(181\) 7.23169 + 1.27514i 0.537527 + 0.0947805i 0.435820 0.900034i \(-0.356458\pi\)
0.101707 + 0.994814i \(0.467570\pi\)
\(182\) −4.86032 1.30232i −0.360271 0.0965343i
\(183\) −0.266902 0.996092i −0.0197300 0.0736333i
\(184\) −1.98464 1.66531i −0.146309 0.122768i
\(185\) 0 0
\(186\) 0.310493 + 0.853071i 0.0227664 + 0.0625502i
\(187\) 2.04354 23.3578i 0.149438 1.70809i
\(188\) −3.92548 + 5.60617i −0.286295 + 0.408872i
\(189\) −10.4052 −0.756870
\(190\) 0 0
\(191\) 2.96590 0.214605 0.107303 0.994226i \(-0.465779\pi\)
0.107303 + 0.994226i \(0.465779\pi\)
\(192\) −0.275579 + 0.393568i −0.0198882 + 0.0284033i
\(193\) 0.855286 9.77596i 0.0615648 0.703689i −0.901210 0.433383i \(-0.857320\pi\)
0.962774 0.270306i \(-0.0871248\pi\)
\(194\) 4.81388 + 13.2260i 0.345616 + 0.949573i
\(195\) 0 0
\(196\) 5.43269 + 4.55857i 0.388049 + 0.325612i
\(197\) −2.39954 8.95519i −0.170960 0.638031i −0.997205 0.0747197i \(-0.976194\pi\)
0.826245 0.563311i \(-0.190473\pi\)
\(198\) −13.3421 3.57499i −0.948179 0.254064i
\(199\) 9.86381 + 1.73926i 0.699227 + 0.123293i 0.511951 0.859015i \(-0.328923\pi\)
0.187276 + 0.982307i \(0.440034\pi\)
\(200\) 0 0
\(201\) −0.0608042 0.105316i −0.00428879 0.00742841i
\(202\) −10.8628 + 2.91067i −0.764301 + 0.204794i
\(203\) −6.53245 + 0.571515i −0.458488 + 0.0401125i
\(204\) 2.12225 + 0.772437i 0.148587 + 0.0540814i
\(205\) 0 0
\(206\) −1.82846 + 1.53426i −0.127395 + 0.106897i
\(207\) 5.87678 + 4.11497i 0.408465 + 0.286010i
\(208\) 0.947811 0.947811i 0.0657189 0.0657189i
\(209\) −1.30362 21.7033i −0.0901732 1.50125i
\(210\) 0 0
\(211\) −23.8211 + 4.20030i −1.63991 + 0.289160i −0.916133 0.400874i \(-0.868706\pi\)
−0.723776 + 0.690035i \(0.757595\pi\)
\(212\) −10.4800 0.916881i −0.719769 0.0629716i
\(213\) 5.20651 + 2.42784i 0.356744 + 0.166353i
\(214\) −2.41374 + 6.63170i −0.165000 + 0.453334i
\(215\) 0 0
\(216\) 1.38592 2.40048i 0.0942999 0.163332i
\(217\) −1.83580 + 6.85129i −0.124622 + 0.465096i
\(218\) −2.44090 + 1.70914i −0.165319 + 0.115757i
\(219\) 0.875989 4.96798i 0.0591939 0.335705i
\(220\) 0 0
\(221\) −5.45662 3.15038i −0.367052 0.211917i
\(222\) 0.343084 + 3.92146i 0.0230263 + 0.263191i
\(223\) −1.50444 + 0.701532i −0.100745 + 0.0469780i −0.472337 0.881418i \(-0.656590\pi\)
0.371593 + 0.928396i \(0.378812\pi\)
\(224\) −3.52753 + 1.28391i −0.235693 + 0.0857851i
\(225\) 0 0
\(226\) −1.48104 8.39938i −0.0985171 0.558719i
\(227\) −11.1061 11.1061i −0.737139 0.737139i 0.234885 0.972023i \(-0.424529\pi\)
−0.972023 + 0.234885i \(0.924529\pi\)
\(228\) 2.05177 + 0.419773i 0.135882 + 0.0278001i
\(229\) 3.84236i 0.253911i 0.991908 + 0.126955i \(0.0405205\pi\)
−0.991908 + 0.126955i \(0.959480\pi\)
\(230\) 0 0
\(231\) 5.78280 + 6.89167i 0.380480 + 0.453439i
\(232\) 0.738237 1.58315i 0.0484676 0.103939i
\(233\) 2.99274 + 6.41796i 0.196061 + 0.420454i 0.979619 0.200864i \(-0.0643750\pi\)
−0.783558 + 0.621319i \(0.786597\pi\)
\(234\) −2.38590 + 2.84341i −0.155971 + 0.185879i
\(235\) 0 0
\(236\) −7.93118 + 4.57907i −0.516276 + 0.298072i
\(237\) 2.64598 + 3.77885i 0.171875 + 0.245463i
\(238\) 10.1212 + 14.4546i 0.656059 + 0.936950i
\(239\) −7.49094 + 4.32489i −0.484548 + 0.279754i −0.722310 0.691569i \(-0.756920\pi\)
0.237762 + 0.971324i \(0.423586\pi\)
\(240\) 0 0
\(241\) 13.2053 15.7374i 0.850625 1.01374i −0.149064 0.988828i \(-0.547626\pi\)
0.999690 0.0249084i \(-0.00792942\pi\)
\(242\) 5.86622 + 12.5801i 0.377095 + 0.808683i
\(243\) −4.93071 + 10.5739i −0.316305 + 0.678319i
\(244\) 1.37965 + 1.64420i 0.0883229 + 0.105259i
\(245\) 0 0
\(246\) 4.49418i 0.286539i
\(247\) −5.43381 2.14730i −0.345745 0.136629i
\(248\) −1.33607 1.33607i −0.0848405 0.0848405i
\(249\) −1.24725 7.07351i −0.0790413 0.448265i
\(250\) 0 0
\(251\) −1.95128 + 0.710207i −0.123163 + 0.0448278i −0.402867 0.915259i \(-0.631986\pi\)
0.279703 + 0.960087i \(0.409764\pi\)
\(252\) 9.42124 4.39320i 0.593482 0.276745i
\(253\) −1.12630 12.8737i −0.0708098 0.809360i
\(254\) −6.58801 3.80359i −0.413369 0.238659i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) 13.0723 9.15332i 0.815427 0.570968i −0.0897689 0.995963i \(-0.528613\pi\)
0.905196 + 0.424994i \(0.139724\pi\)
\(258\) −0.242890 + 0.906478i −0.0151217 + 0.0564349i
\(259\) −15.3781 + 26.6357i −0.955549 + 1.65506i
\(260\) 0 0
\(261\) −1.65443 + 4.54550i −0.102406 + 0.281359i
\(262\) 9.33354 + 4.35230i 0.576628 + 0.268886i
\(263\) −6.43268 0.562787i −0.396656 0.0347029i −0.112917 0.993604i \(-0.536019\pi\)
−0.283739 + 0.958901i \(0.591575\pi\)
\(264\) −2.36014 + 0.416156i −0.145257 + 0.0256126i
\(265\) 0 0
\(266\) 11.2505 + 11.8816i 0.689814 + 0.728505i
\(267\) −4.52678 + 4.52678i −0.277035 + 0.277035i
\(268\) 0.207335 + 0.145177i 0.0126650 + 0.00886813i
\(269\) 16.5823 13.9142i 1.01104 0.848366i 0.0225671 0.999745i \(-0.492816\pi\)
0.988476 + 0.151380i \(0.0483716\pi\)
\(270\) 0 0
\(271\) −24.3332 8.85654i −1.47813 0.537997i −0.527838 0.849345i \(-0.676997\pi\)
−0.950296 + 0.311348i \(0.899219\pi\)
\(272\) −4.68274 + 0.409687i −0.283933 + 0.0248409i
\(273\) 2.33518 0.625709i 0.141331 0.0378697i
\(274\) 7.03679 + 12.1881i 0.425108 + 0.736308i
\(275\) 0 0
\(276\) 1.22584 + 0.216149i 0.0737869 + 0.0130106i
\(277\) 8.01321 + 2.14713i 0.481467 + 0.129009i 0.491386 0.870942i \(-0.336491\pi\)
−0.00991869 + 0.999951i \(0.503157\pi\)
\(278\) 4.80050 + 17.9157i 0.287915 + 1.07451i
\(279\) 4.00817 + 3.36326i 0.239963 + 0.201353i
\(280\) 0 0
\(281\) 8.25824 + 22.6893i 0.492645 + 1.35353i 0.898251 + 0.439484i \(0.144839\pi\)
−0.405605 + 0.914048i \(0.632939\pi\)
\(282\) 0.286584 3.27568i 0.0170659 0.195064i
\(283\) 5.09656 7.27864i 0.302959 0.432670i −0.638590 0.769547i \(-0.720482\pi\)
0.941549 + 0.336877i \(0.109371\pi\)
\(284\) −11.9568 −0.709507
\(285\) 0 0
\(286\) 6.68602 0.395353
\(287\) −20.1405 + 28.7637i −1.18886 + 1.69787i
\(288\) −0.241348 + 2.75862i −0.0142216 + 0.162553i
\(289\) 1.74291 + 4.78860i 0.102524 + 0.281682i
\(290\) 0 0
\(291\) −5.18027 4.34677i −0.303673 0.254812i
\(292\) 2.71750 + 10.1418i 0.159030 + 0.593507i
\(293\) 13.2971 + 3.56296i 0.776827 + 0.208150i 0.625385 0.780316i \(-0.284942\pi\)
0.151441 + 0.988466i \(0.451608\pi\)
\(294\) −3.35558 0.591679i −0.195701 0.0345074i
\(295\) 0 0
\(296\) −4.09655 7.09544i −0.238107 0.412414i
\(297\) 13.3550 3.57845i 0.774933 0.207643i
\(298\) −8.05175 + 0.704437i −0.466425 + 0.0408069i
\(299\) −3.26324 1.18772i −0.188718 0.0686878i
\(300\) 0 0
\(301\) −5.61690 + 4.71314i −0.323753 + 0.271661i
\(302\) −9.32312 6.52812i −0.536486 0.375651i
\(303\) 3.82064 3.82064i 0.219490 0.219490i
\(304\) −4.23957 + 1.01293i −0.243156 + 0.0580956i
\(305\) 0 0
\(306\) 12.8190 2.26034i 0.732816 0.129215i
\(307\) −5.34855 0.467937i −0.305258 0.0267066i −0.0665022 0.997786i \(-0.521184\pi\)
−0.238756 + 0.971080i \(0.576739\pi\)
\(308\) −16.9704 7.91341i −0.966976 0.450908i
\(309\) 0.392227 1.07764i 0.0223130 0.0613045i
\(310\) 0 0
\(311\) 5.24325 9.08157i 0.297317 0.514969i −0.678204 0.734874i \(-0.737241\pi\)
0.975521 + 0.219905i \(0.0705748\pi\)
\(312\) −0.166682 + 0.622065i −0.00943650 + 0.0352175i
\(313\) −5.10972 + 3.57786i −0.288818 + 0.202233i −0.709002 0.705206i \(-0.750854\pi\)
0.420184 + 0.907439i \(0.361966\pi\)
\(314\) 0.435119 2.46768i 0.0245552 0.139259i
\(315\) 0 0
\(316\) −8.31516 4.80076i −0.467764 0.270064i
\(317\) 1.13557 + 12.9797i 0.0637802 + 0.729012i 0.959004 + 0.283394i \(0.0914604\pi\)
−0.895223 + 0.445618i \(0.852984\pi\)
\(318\) 4.58087 2.13609i 0.256882 0.119786i
\(319\) 8.18774 2.98010i 0.458426 0.166853i
\(320\) 0 0
\(321\) −0.588796 3.33923i −0.0328634 0.186378i
\(322\) 6.87696 + 6.87696i 0.383238 + 0.383238i
\(323\) 9.75709 + 18.0173i 0.542899 + 1.00251i
\(324\) 6.97573i 0.387541i
\(325\) 0 0
\(326\) −8.51655 10.1496i −0.471688 0.562136i
\(327\) 0.605047 1.29753i 0.0334592 0.0717535i
\(328\) −3.95315 8.47756i −0.218276 0.468095i
\(329\) 16.5140 19.6807i 0.910448 1.08503i
\(330\) 0 0
\(331\) −13.6536 + 7.88293i −0.750471 + 0.433285i −0.825864 0.563869i \(-0.809312\pi\)
0.0753928 + 0.997154i \(0.475979\pi\)
\(332\) 8.57471 + 12.2460i 0.470598 + 0.672084i
\(333\) 13.0133 + 18.5849i 0.713125 + 1.01845i
\(334\) 9.51928 5.49596i 0.520872 0.300726i
\(335\) 0 0
\(336\) 1.15933 1.38164i 0.0632466 0.0753744i
\(337\) −11.8506 25.4137i −0.645544 1.38437i −0.907812 0.419378i \(-0.862248\pi\)
0.262268 0.964995i \(-0.415530\pi\)
\(338\) −4.73472 + 10.1536i −0.257535 + 0.552285i
\(339\) 2.63402 + 3.13910i 0.143060 + 0.170492i
\(340\) 0 0
\(341\) 9.42487i 0.510385i
\(342\) 11.4509 3.81751i 0.619194 0.206427i
\(343\) −0.243870 0.243870i −0.0131678 0.0131678i
\(344\) −0.339179 1.92358i −0.0182873 0.103712i
\(345\) 0 0
\(346\) −16.5478 + 6.02292i −0.889618 + 0.323794i
\(347\) −1.77554 + 0.827948i −0.0953160 + 0.0444466i −0.469692 0.882831i \(-0.655635\pi\)
0.374376 + 0.927277i \(0.377857\pi\)
\(348\) 0.0731474 + 0.836078i 0.00392111 + 0.0448185i
\(349\) 15.6149 + 9.01529i 0.835848 + 0.482577i 0.855851 0.517223i \(-0.173034\pi\)
−0.0200025 + 0.999800i \(0.506367\pi\)
\(350\) 0 0
\(351\) 0.645171 3.65895i 0.0344367 0.195300i
\(352\) 4.08597 2.86103i 0.217783 0.152493i
\(353\) −1.67238 + 6.24143i −0.0890121 + 0.332198i −0.996044 0.0888650i \(-0.971676\pi\)
0.907032 + 0.421063i \(0.138343\pi\)
\(354\) 2.20005 3.81060i 0.116931 0.202531i
\(355\) 0 0
\(356\) 4.55723 12.5209i 0.241533 0.663606i
\(357\) −7.68372 3.58298i −0.406665 0.189631i
\(358\) −19.8237 1.73435i −1.04771 0.0916632i
\(359\) −19.3534 + 3.41253i −1.02143 + 0.180106i −0.659190 0.751977i \(-0.729101\pi\)
−0.362244 + 0.932083i \(0.617989\pi\)
\(360\) 0 0
\(361\) 11.4013 + 15.1990i 0.600068 + 0.799949i
\(362\) 5.19246 5.19246i 0.272910 0.272910i
\(363\) −5.46298 3.82522i −0.286732 0.200772i
\(364\) −3.85456 + 3.23436i −0.202034 + 0.169527i
\(365\) 0 0
\(366\) −0.969040 0.352702i −0.0506525 0.0184360i
\(367\) −14.0514 + 1.22934i −0.733479 + 0.0641711i −0.447774 0.894147i \(-0.647783\pi\)
−0.285704 + 0.958318i \(0.592228\pi\)
\(368\) −2.50248 + 0.670538i −0.130451 + 0.0349542i
\(369\) 12.9513 + 22.4323i 0.674218 + 1.16778i
\(370\) 0 0
\(371\) 38.8913 + 6.85759i 2.01914 + 0.356028i
\(372\) 0.876887 + 0.234961i 0.0454644 + 0.0121822i
\(373\) −9.39261 35.0537i −0.486331 1.81501i −0.573993 0.818861i \(-0.694606\pi\)
0.0876618 0.996150i \(-0.472061\pi\)
\(374\) −17.9614 15.0714i −0.928763 0.779325i
\(375\) 0 0
\(376\) 2.34074 + 6.43113i 0.120714 + 0.331660i
\(377\) 0.204071 2.33254i 0.0105102 0.120132i
\(378\) −5.96820 + 8.52348i −0.306971 + 0.438400i
\(379\) 8.38366 0.430640 0.215320 0.976544i \(-0.430921\pi\)
0.215320 + 0.976544i \(0.430921\pi\)
\(380\) 0 0
\(381\) 3.65493 0.187248
\(382\) 1.70117 2.42952i 0.0870395 0.124305i
\(383\) 1.39172 15.9074i 0.0711136 0.812832i −0.873965 0.485989i \(-0.838460\pi\)
0.945079 0.326843i \(-0.105985\pi\)
\(384\) 0.164326 + 0.451483i 0.00838574 + 0.0230396i
\(385\) 0 0
\(386\) −7.51743 6.30787i −0.382627 0.321062i
\(387\) 1.39992 + 5.22457i 0.0711618 + 0.265580i
\(388\) 13.5953 + 3.64284i 0.690194 + 0.184937i
\(389\) 27.1705 + 4.79090i 1.37760 + 0.242908i 0.812908 0.582392i \(-0.197883\pi\)
0.564693 + 0.825301i \(0.308994\pi\)
\(390\) 0 0
\(391\) 6.08910 + 10.5466i 0.307939 + 0.533366i
\(392\) 6.85022 1.83551i 0.345989 0.0927074i
\(393\) −4.92913 + 0.431243i −0.248642 + 0.0217533i
\(394\) −8.71198 3.17090i −0.438903 0.159748i
\(395\) 0 0
\(396\) −10.5812 + 8.87864i −0.531723 + 0.446169i
\(397\) 11.1433 + 7.80262i 0.559266 + 0.391602i 0.818754 0.574144i \(-0.194665\pi\)
−0.259489 + 0.965746i \(0.583554\pi\)
\(398\) 7.08236 7.08236i 0.355007 0.355007i
\(399\) −7.53551 2.24108i −0.377247 0.112194i
\(400\) 0 0
\(401\) 23.9183 4.21744i 1.19442 0.210609i 0.459136 0.888366i \(-0.348159\pi\)
0.735286 + 0.677757i \(0.237048\pi\)
\(402\) −0.121146 0.0105989i −0.00604219 0.000528623i
\(403\) −2.29539 1.07036i −0.114342 0.0533184i
\(404\) −3.84634 + 10.5677i −0.191363 + 0.525764i
\(405\) 0 0
\(406\) −3.27870 + 5.67888i −0.162719 + 0.281838i
\(407\) 10.5773 39.4751i 0.524298 1.95671i
\(408\) 1.85002 1.29540i 0.0915895 0.0641317i
\(409\) −1.91034 + 10.8341i −0.0944600 + 0.535709i 0.900451 + 0.434956i \(0.143236\pi\)
−0.994911 + 0.100753i \(0.967875\pi\)
\(410\) 0 0
\(411\) −5.85585 3.38088i −0.288848 0.166766i
\(412\) 0.208030 + 2.37780i 0.0102489 + 0.117146i
\(413\) 31.1578 14.5291i 1.53318 0.714932i
\(414\) 6.74157 2.45373i 0.331330 0.120594i
\(415\) 0 0
\(416\) −0.232759 1.32004i −0.0114120 0.0647205i
\(417\) −6.30131 6.30131i −0.308576 0.308576i
\(418\) −18.5260 11.3806i −0.906138 0.556645i
\(419\) 20.2401i 0.988793i −0.869237 0.494396i \(-0.835389\pi\)
0.869237 0.494396i \(-0.164611\pi\)
\(420\) 0 0
\(421\) −18.3645 21.8860i −0.895032 1.06666i −0.997411 0.0719127i \(-0.977090\pi\)
0.102378 0.994746i \(-0.467355\pi\)
\(422\) −10.2225 + 21.9223i −0.497624 + 1.06716i
\(423\) −8.00936 17.1761i −0.389428 0.835132i
\(424\) −6.76214 + 8.05881i −0.328399 + 0.391370i
\(425\) 0 0
\(426\) 4.97510 2.87238i 0.241044 0.139167i
\(427\) −4.62143 6.60008i −0.223647 0.319400i
\(428\) 4.04791 + 5.78101i 0.195663 + 0.279436i
\(429\) −2.78198 + 1.60618i −0.134315 + 0.0775469i
\(430\) 0 0
\(431\) −11.0078 + 13.1186i −0.530229 + 0.631903i −0.962968 0.269617i \(-0.913103\pi\)
0.432738 + 0.901520i \(0.357547\pi\)
\(432\) −1.17143 2.51214i −0.0563604 0.120865i
\(433\) 1.73279 3.71598i 0.0832725 0.178578i −0.860262 0.509851i \(-0.829700\pi\)
0.943535 + 0.331273i \(0.107478\pi\)
\(434\) 4.55928 + 5.43354i 0.218852 + 0.260818i
\(435\) 0 0
\(436\) 2.97979i 0.142706i
\(437\) 7.02030 + 8.84556i 0.335827 + 0.423140i
\(438\) −3.56708 3.56708i −0.170442 0.170442i
\(439\) 3.06889 + 17.4045i 0.146470 + 0.830673i 0.966175 + 0.257887i \(0.0830262\pi\)
−0.819705 + 0.572786i \(0.805863\pi\)
\(440\) 0 0
\(441\) −18.4542 + 6.71677i −0.878771 + 0.319846i
\(442\) −5.71043 + 2.66282i −0.271617 + 0.126657i
\(443\) 0.839479 + 9.59529i 0.0398849 + 0.455886i 0.989708 + 0.143100i \(0.0457069\pi\)
−0.949823 + 0.312787i \(0.898738\pi\)
\(444\) 3.40906 + 1.96822i 0.161787 + 0.0934076i
\(445\) 0 0
\(446\) −0.288250 + 1.63475i −0.0136490 + 0.0774075i
\(447\) 3.18102 2.22737i 0.150457 0.105351i
\(448\) −0.971585 + 3.62600i −0.0459031 + 0.171313i
\(449\) 10.4806 18.1529i 0.494610 0.856689i −0.505371 0.862902i \(-0.668644\pi\)
0.999981 + 0.00621314i \(0.00197772\pi\)
\(450\) 0 0
\(451\) 15.9580 43.8442i 0.751432 2.06454i
\(452\) −7.72986 3.60449i −0.363582 0.169541i
\(453\) 5.44749 + 0.476594i 0.255945 + 0.0223923i
\(454\) −15.4678 + 2.72739i −0.725940 + 0.128003i
\(455\) 0 0
\(456\) 1.52070 1.43994i 0.0712134 0.0674312i
\(457\) −23.9786 + 23.9786i −1.12167 + 1.12167i −0.130179 + 0.991491i \(0.541555\pi\)
−0.991491 + 0.130179i \(0.958445\pi\)
\(458\) 3.14748 + 2.20389i 0.147072 + 0.102981i
\(459\) −9.98109 + 8.37513i −0.465877 + 0.390917i
\(460\) 0 0
\(461\) 10.5002 + 3.82175i 0.489042 + 0.177997i 0.574759 0.818323i \(-0.305096\pi\)
−0.0857169 + 0.996320i \(0.527318\pi\)
\(462\) 8.96220 0.784091i 0.416959 0.0364792i
\(463\) 27.8891 7.47287i 1.29612 0.347294i 0.456137 0.889910i \(-0.349233\pi\)
0.839981 + 0.542616i \(0.182566\pi\)
\(464\) −0.873409 1.51279i −0.0405470 0.0702294i
\(465\) 0 0
\(466\) 6.97385 + 1.22968i 0.323057 + 0.0569637i
\(467\) −14.8914 3.99015i −0.689094 0.184642i −0.102753 0.994707i \(-0.532765\pi\)
−0.586341 + 0.810065i \(0.699432\pi\)
\(468\) 0.960685 + 3.58533i 0.0444077 + 0.165732i
\(469\) −0.727857 0.610745i −0.0336093 0.0282016i
\(470\) 0 0
\(471\) 0.411760 + 1.13130i 0.0189729 + 0.0521277i
\(472\) −0.798184 + 9.12329i −0.0367394 + 0.419933i
\(473\) 5.58831 7.98093i 0.256951 0.366964i
\(474\) 4.61312 0.211888
\(475\) 0 0
\(476\) 17.6458 0.808792
\(477\) 16.7092 23.8632i 0.765063 1.09262i
\(478\) −0.753879 + 8.61687i −0.0344816 + 0.394127i
\(479\) 3.53261 + 9.70577i 0.161409 + 0.443468i 0.993862 0.110628i \(-0.0352863\pi\)
−0.832453 + 0.554096i \(0.813064\pi\)
\(480\) 0 0
\(481\) −8.41278 7.05916i −0.383590 0.321870i
\(482\) −5.31711 19.8437i −0.242188 0.903857i
\(483\) −4.51347 1.20938i −0.205370 0.0550287i
\(484\) 13.6698 + 2.41035i 0.621354 + 0.109561i
\(485\) 0 0
\(486\) 5.83353 + 10.1040i 0.264614 + 0.458325i
\(487\) −19.9832 + 5.35450i −0.905527 + 0.242635i −0.681389 0.731922i \(-0.738624\pi\)
−0.224139 + 0.974557i \(0.571957\pi\)
\(488\) 2.13818 0.187067i 0.0967910 0.00846811i
\(489\) 5.98188 + 2.17723i 0.270510 + 0.0984575i
\(490\) 0 0
\(491\) 27.5015 23.0765i 1.24112 1.04143i 0.243688 0.969854i \(-0.421643\pi\)
0.997435 0.0715726i \(-0.0228018\pi\)
\(492\) 3.68142 + 2.57776i 0.165971 + 0.116214i
\(493\) −5.80615 + 5.80615i −0.261496 + 0.261496i
\(494\) −4.87567 + 3.21947i −0.219367 + 0.144851i
\(495\) 0 0
\(496\) −1.86078 + 0.328106i −0.0835516 + 0.0147324i
\(497\) 44.7141 + 3.91198i 2.00570 + 0.175476i
\(498\) −6.50967 3.03551i −0.291705 0.136024i
\(499\) 3.78694 10.4045i 0.169527 0.465771i −0.825614 0.564236i \(-0.809171\pi\)
0.995141 + 0.0984645i \(0.0313931\pi\)
\(500\) 0 0
\(501\) −2.64058 + 4.57361i −0.117972 + 0.204334i
\(502\) −0.537439 + 2.00575i −0.0239871 + 0.0895210i
\(503\) 25.1961 17.6425i 1.12344 0.786640i 0.144240 0.989543i \(-0.453926\pi\)
0.979199 + 0.202902i \(0.0650374\pi\)
\(504\) 1.80511 10.2373i 0.0804058 0.456004i
\(505\) 0 0
\(506\) −11.1915 6.46142i −0.497523 0.287245i
\(507\) −0.469135 5.36223i −0.0208350 0.238145i
\(508\) −6.89445 + 3.21493i −0.305892 + 0.142640i
\(509\) 36.5051 13.2868i 1.61806 0.588925i 0.635048 0.772473i \(-0.280980\pi\)
0.983011 + 0.183548i \(0.0587581\pi\)
\(510\) 0 0
\(511\) −6.84428 38.8158i −0.302773 1.71711i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −8.01577 + 9.04025i −0.353905 + 0.399137i
\(514\) 15.9583i 0.703891i
\(515\) 0 0
\(516\) 0.603227 + 0.718898i 0.0265556 + 0.0316477i
\(517\) −14.4272 + 30.9391i −0.634505 + 1.36070i
\(518\) 12.9981 + 27.8746i 0.571105 + 1.22474i
\(519\) 5.43849 6.48134i 0.238723 0.284499i
\(520\) 0 0
\(521\) −14.3093 + 8.26150i −0.626904 + 0.361943i −0.779552 0.626338i \(-0.784553\pi\)
0.152648 + 0.988281i \(0.451220\pi\)
\(522\) 2.77451 + 3.96242i 0.121437 + 0.173430i
\(523\) 4.58197 + 6.54373i 0.200356 + 0.286137i 0.906739 0.421692i \(-0.138564\pi\)
−0.706384 + 0.707829i \(0.749675\pi\)
\(524\) 8.91869 5.14921i 0.389615 0.224944i
\(525\) 0 0
\(526\) −4.15064 + 4.94655i −0.180977 + 0.215680i
\(527\) 3.75361 + 8.04963i 0.163510 + 0.350648i
\(528\) −1.01283 + 2.17201i −0.0440776 + 0.0945246i
\(529\) −10.4697 12.4773i −0.455205 0.542492i
\(530\) 0 0
\(531\) 25.3603i 1.10055i
\(532\) 16.1858 2.40090i 0.701745 0.104092i
\(533\) −8.86579 8.86579i −0.384020 0.384020i
\(534\) 1.11167 + 6.30458i 0.0481065 + 0.272826i
\(535\) 0 0
\(536\) 0.237845 0.0865685i 0.0102733 0.00373919i
\(537\) 8.66506 4.04058i 0.373925 0.174364i
\(538\) −1.88663 21.5643i −0.0813386 0.929704i
\(539\) 30.6353 + 17.6873i 1.31956 + 0.761847i
\(540\) 0 0
\(541\) 1.47824 8.38349i 0.0635543 0.360434i −0.936401 0.350933i \(-0.885864\pi\)
0.999955 0.00950131i \(-0.00302441\pi\)
\(542\) −21.2118 + 14.8526i −0.911124 + 0.637976i
\(543\) −0.913145 + 3.40790i −0.0391868 + 0.146247i
\(544\) −2.35031 + 4.07086i −0.100769 + 0.174537i
\(545\) 0 0
\(546\) 0.826853 2.27176i 0.0353860 0.0972223i
\(547\) 32.4549 + 15.1340i 1.38767 + 0.647082i 0.965732 0.259542i \(-0.0835716\pi\)
0.421940 + 0.906624i \(0.361349\pi\)
\(548\) 14.0200 + 1.22659i 0.598905 + 0.0523974i
\(549\) −5.85329 + 1.03209i −0.249812 + 0.0440487i
\(550\) 0 0
\(551\) −4.53579 + 6.11577i −0.193231 + 0.260541i
\(552\) 0.880171 0.880171i 0.0374626 0.0374626i
\(553\) 29.5249 + 20.6736i 1.25553 + 0.879130i
\(554\) 6.35501 5.33249i 0.269999 0.226556i
\(555\) 0 0
\(556\) 17.4292 + 6.34369i 0.739161 + 0.269032i
\(557\) −9.40447 + 0.822784i −0.398480 + 0.0348625i −0.284635 0.958636i \(-0.591872\pi\)
−0.113845 + 0.993498i \(0.536317\pi\)
\(558\) 5.05401 1.35422i 0.213953 0.0573286i
\(559\) −1.30908 2.26739i −0.0553680 0.0959003i
\(560\) 0 0
\(561\) 11.0941 + 1.95620i 0.468395 + 0.0825907i
\(562\) 23.3227 + 6.24931i 0.983811 + 0.263611i
\(563\) 0.717612 + 2.67816i 0.0302437 + 0.112871i 0.979398 0.201941i \(-0.0647250\pi\)
−0.949154 + 0.314813i \(0.898058\pi\)
\(564\) −2.51890 2.11361i −0.106065 0.0889989i
\(565\) 0 0
\(566\) −3.03904 8.34971i −0.127741 0.350964i
\(567\) −2.28229 + 26.0866i −0.0958470 + 1.09554i
\(568\) −6.85816 + 9.79446i −0.287762 + 0.410966i
\(569\) −5.49736 −0.230461 −0.115231 0.993339i \(-0.536761\pi\)
−0.115231 + 0.993339i \(0.536761\pi\)
\(570\) 0 0
\(571\) −4.01384 −0.167974 −0.0839871 0.996467i \(-0.526765\pi\)
−0.0839871 + 0.996467i \(0.526765\pi\)
\(572\) 3.83494 5.47687i 0.160347 0.228999i
\(573\) −0.124196 + 1.41957i −0.00518837 + 0.0593033i
\(574\) 12.0097 + 32.9963i 0.501274 + 1.37724i
\(575\) 0 0
\(576\) 2.12130 + 1.77998i 0.0883875 + 0.0741659i
\(577\) −3.50041 13.0637i −0.145724 0.543849i −0.999722 0.0235733i \(-0.992496\pi\)
0.853998 0.520276i \(-0.174171\pi\)
\(578\) 4.92228 + 1.31892i 0.204740 + 0.0548599i
\(579\) 4.64325 + 0.818730i 0.192967 + 0.0340253i
\(580\) 0 0
\(581\) −28.0597 48.6008i −1.16411 2.01630i
\(582\) −6.53195 + 1.75023i −0.270758 + 0.0725494i
\(583\) −52.2747 + 4.57345i −2.16500 + 0.189413i
\(584\) 9.86641 + 3.59108i 0.408275 + 0.148600i
\(585\) 0 0
\(586\) 10.5455 8.84875i 0.435632 0.365538i
\(587\) 1.69635 + 1.18780i 0.0700160 + 0.0490257i 0.608060 0.793891i \(-0.291948\pi\)
−0.538044 + 0.842916i \(0.680837\pi\)
\(588\) −2.40936 + 2.40936i −0.0993602 + 0.0993602i
\(589\) 4.53829 + 6.87292i 0.186997 + 0.283194i
\(590\) 0 0
\(591\) 4.38670 0.773494i 0.180445 0.0318173i
\(592\) −8.16193 0.714076i −0.335453 0.0293483i
\(593\) −29.7681 13.8811i −1.22243 0.570028i −0.299167 0.954201i \(-0.596709\pi\)
−0.923261 + 0.384173i \(0.874487\pi\)
\(594\) 4.72880 12.9923i 0.194025 0.533079i
\(595\) 0 0
\(596\) −4.04125 + 6.99966i −0.165536 + 0.286717i
\(597\) −1.24550 + 4.64828i −0.0509750 + 0.190241i
\(598\) −2.84465 + 1.99184i −0.116326 + 0.0814525i
\(599\) 0.983279 5.57645i 0.0401757 0.227848i −0.958108 0.286406i \(-0.907539\pi\)
0.998284 + 0.0585585i \(0.0186504\pi\)
\(600\) 0 0
\(601\) −0.0640903 0.0370026i −0.00261430 0.00150937i 0.498692 0.866779i \(-0.333814\pi\)
−0.501307 + 0.865270i \(0.667147\pi\)
\(602\) 0.639056 + 7.30444i 0.0260460 + 0.297707i
\(603\) −0.635231 + 0.296213i −0.0258686 + 0.0120627i
\(604\) −10.6950 + 3.89268i −0.435175 + 0.158391i
\(605\) 0 0
\(606\) −0.938257 5.32112i −0.0381141 0.216156i
\(607\) −27.7146 27.7146i −1.12490 1.12490i −0.990994 0.133908i \(-0.957247\pi\)
−0.133908 0.990994i \(-0.542753\pi\)
\(608\) −1.60197 + 4.05385i −0.0649686 + 0.164405i
\(609\) 3.15056i 0.127667i
\(610\) 0 0
\(611\) 5.89665 + 7.02736i 0.238553 + 0.284297i
\(612\) 5.50114 11.7972i 0.222370 0.476875i
\(613\) −1.11748 2.39644i −0.0451345 0.0967913i 0.882447 0.470411i \(-0.155894\pi\)
−0.927582 + 0.373620i \(0.878117\pi\)
\(614\) −3.45111 + 4.11288i −0.139276 + 0.165982i
\(615\) 0 0
\(616\) −16.2161 + 9.36236i −0.653365 + 0.377220i
\(617\) 21.9732 + 31.3810i 0.884608 + 1.26335i 0.963836 + 0.266495i \(0.0858656\pi\)
−0.0792280 + 0.996857i \(0.525246\pi\)
\(618\) −0.657775 0.939400i −0.0264596 0.0377882i
\(619\) −6.00501 + 3.46700i −0.241362 + 0.139350i −0.615802 0.787901i \(-0.711168\pi\)
0.374441 + 0.927251i \(0.377835\pi\)
\(620\) 0 0
\(621\) −4.61596 + 5.50109i −0.185232 + 0.220751i
\(622\) −4.43178 9.50399i −0.177698 0.381075i
\(623\) −21.1389 + 45.3325i −0.846911 + 1.81621i
\(624\) 0.413961 + 0.493340i 0.0165717 + 0.0197494i
\(625\) 0 0
\(626\) 6.23781i 0.249313i
\(627\) 10.4424 + 0.284867i 0.417030 + 0.0113765i
\(628\) −1.77183 1.77183i −0.0707038 0.0707038i
\(629\) 6.68767 + 37.9277i 0.266655 + 1.51227i
\(630\) 0 0
\(631\) −38.0296 + 13.8416i −1.51393 + 0.551026i −0.959624 0.281285i \(-0.909239\pi\)
−0.554308 + 0.832311i \(0.687017\pi\)
\(632\) −8.70193 + 4.05778i −0.346144 + 0.161410i
\(633\) −1.01289 11.5773i −0.0402586 0.460158i
\(634\) 11.2837 + 6.51463i 0.448132 + 0.258729i
\(635\) 0 0
\(636\) 0.877692 4.97764i 0.0348028 0.197376i
\(637\) 7.78686 5.45242i 0.308527 0.216033i
\(638\) 2.25515 8.41632i 0.0892821 0.333205i
\(639\) 16.5552 28.6744i 0.654913 1.13434i
\(640\) 0 0
\(641\) −1.32749 + 3.64724i −0.0524325 + 0.144057i −0.963144 0.268985i \(-0.913312\pi\)
0.910712 + 0.413043i \(0.135534\pi\)
\(642\) −3.07306 1.43299i −0.121284 0.0565556i
\(643\) 41.0713 + 3.59328i 1.61970 + 0.141705i 0.860602 0.509278i \(-0.170087\pi\)
0.759093 + 0.650982i \(0.225643\pi\)
\(644\) 9.57773 1.68881i 0.377416 0.0665486i
\(645\) 0 0
\(646\) 20.3553 + 2.34174i 0.800869 + 0.0921344i
\(647\) 4.81659 4.81659i 0.189360 0.189360i −0.606060 0.795419i \(-0.707251\pi\)
0.795419 + 0.606060i \(0.207251\pi\)
\(648\) −5.71418 4.00111i −0.224474 0.157179i
\(649\) −34.9939 + 29.3633i −1.37363 + 1.15261i
\(650\) 0 0
\(651\) −3.20236 1.16556i −0.125510 0.0456820i
\(652\) −13.1990 + 1.15476i −0.516912 + 0.0452240i
\(653\) −21.3360 + 5.71697i −0.834944 + 0.223722i −0.650869 0.759190i \(-0.725595\pi\)
−0.184074 + 0.982912i \(0.558929\pi\)
\(654\) −0.715832 1.23986i −0.0279913 0.0484823i
\(655\) 0 0
\(656\) −9.21185 1.62430i −0.359662 0.0634182i
\(657\) −28.0844 7.52519i −1.09568 0.293586i
\(658\) −6.64939 24.8159i −0.259220 0.967423i
\(659\) −10.2912 8.63535i −0.400889 0.336385i 0.419948 0.907548i \(-0.362048\pi\)
−0.820837 + 0.571163i \(0.806493\pi\)
\(660\) 0 0
\(661\) 16.8993 + 46.4304i 0.657305 + 1.80593i 0.588797 + 0.808281i \(0.299602\pi\)
0.0685088 + 0.997651i \(0.478176\pi\)
\(662\) −1.37408 + 15.7059i −0.0534053 + 0.610426i
\(663\) 1.73636 2.47978i 0.0674346 0.0963066i
\(664\) 14.9495 0.580155
\(665\) 0 0
\(666\) 22.6880 0.879143
\(667\) −2.59577 + 3.70714i −0.100509 + 0.143541i
\(668\) 0.958009 10.9501i 0.0370665 0.423672i
\(669\) −0.272776 0.749446i −0.0105461 0.0289752i
\(670\) 0 0
\(671\) 8.20135 + 6.88175i 0.316610 + 0.265667i
\(672\) −0.466805 1.74214i −0.0180074 0.0672046i
\(673\) −7.21919 1.93437i −0.278279 0.0745647i 0.116980 0.993134i \(-0.462679\pi\)
−0.395259 + 0.918570i \(0.629345\pi\)
\(674\) −27.6149 4.86926i −1.06369 0.187557i
\(675\) 0 0
\(676\) 5.60165 + 9.70235i 0.215448 + 0.373167i
\(677\) 26.7103 7.15701i 1.02656 0.275066i 0.294027 0.955797i \(-0.405004\pi\)
0.732534 + 0.680731i \(0.238338\pi\)
\(678\) 4.08221 0.357147i 0.156776 0.0137162i
\(679\) −49.6494 18.0709i −1.90537 0.693497i
\(680\) 0 0
\(681\) 5.78078 4.85065i 0.221520 0.185877i
\(682\) −7.72040 5.40588i −0.295629 0.207002i
\(683\) 25.9136 25.9136i 0.991557 0.991557i −0.00840797 0.999965i \(-0.502676\pi\)
0.999965 + 0.00840797i \(0.00267637\pi\)
\(684\) 3.44085 11.5697i 0.131564 0.442377i
\(685\) 0 0
\(686\) −0.339645 + 0.0598886i −0.0129677 + 0.00228656i
\(687\) −1.83907 0.160898i −0.0701649 0.00613863i
\(688\) −1.77025 0.825480i −0.0674901 0.0314711i
\(689\) −4.82287 + 13.2507i −0.183737 + 0.504812i
\(690\) 0 0
\(691\) −7.30289 + 12.6490i −0.277815 + 0.481190i −0.970842 0.239722i \(-0.922944\pi\)
0.693026 + 0.720912i \(0.256277\pi\)
\(692\) −4.55777 + 17.0098i −0.173260 + 0.646616i
\(693\) 42.4745 29.7409i 1.61347 1.12976i
\(694\) −0.340193 + 1.92933i −0.0129135 + 0.0732363i
\(695\) 0 0
\(696\) 0.726831 + 0.419636i 0.0275505 + 0.0159063i
\(697\) 3.83219 + 43.8022i 0.145155 + 1.65913i
\(698\) 16.3413 7.62005i 0.618526 0.288423i
\(699\) −3.19714 + 1.16367i −0.120927 + 0.0440139i
\(700\) 0 0
\(701\) 8.46076 + 47.9834i 0.319559 + 1.81231i 0.545438 + 0.838151i \(0.316363\pi\)
−0.225879 + 0.974155i \(0.572526\pi\)
\(702\) −2.62718 2.62718i −0.0991565 0.0991565i
\(703\) 11.2948 + 33.8798i 0.425993 + 1.27780i
\(704\) 4.98805i 0.187994i
\(705\) 0 0
\(706\) 4.15344 + 4.94987i 0.156317 + 0.186291i
\(707\) 17.8414 38.2610i 0.670995 1.43895i
\(708\) −1.85956 3.98784i −0.0698866 0.149872i
\(709\) 11.3359 13.5096i 0.425729 0.507364i −0.509956 0.860200i \(-0.670338\pi\)
0.935685 + 0.352836i \(0.114783\pi\)
\(710\) 0 0
\(711\) 23.0260 13.2941i 0.863543 0.498567i
\(712\) −7.64259 10.9148i −0.286418 0.409048i
\(713\) 2.80778 + 4.00992i 0.105152 + 0.150173i
\(714\) −7.34220 + 4.23902i −0.274775 + 0.158641i
\(715\) 0 0
\(716\) −12.7911 + 15.2438i −0.478026 + 0.569689i
\(717\) −1.75634 3.76649i −0.0655918 0.140662i
\(718\) −8.30528 + 17.8107i −0.309950 + 0.664691i
\(719\) 9.85702 + 11.7471i 0.367605 + 0.438094i 0.917861 0.396901i \(-0.129914\pi\)
−0.550256 + 0.834996i \(0.685470\pi\)
\(720\) 0 0
\(721\) 8.96015i 0.333693i
\(722\) 18.9898 0.621576i 0.706728 0.0231327i
\(723\) 6.97943 + 6.97943i 0.259568 + 0.259568i
\(724\) −1.27514 7.23169i −0.0473903 0.268764i
\(725\) 0 0
\(726\) −6.26688 + 2.28096i −0.232586 + 0.0846542i
\(727\) 31.4152 14.6492i 1.16513 0.543307i 0.258819 0.965926i \(-0.416667\pi\)
0.906308 + 0.422619i \(0.138889\pi\)
\(728\) 0.438548 + 5.01263i 0.0162537 + 0.185780i
\(729\) 13.2689 + 7.66083i 0.491442 + 0.283734i
\(730\) 0 0
\(731\) −1.59435 + 9.04203i −0.0589693 + 0.334431i
\(732\) −0.844735 + 0.591490i −0.0312223 + 0.0218621i
\(733\) 1.93064 7.20524i 0.0713098 0.266132i −0.921061 0.389417i \(-0.872676\pi\)
0.992371 + 0.123286i \(0.0393431\pi\)
\(734\) −7.05255 + 12.2154i −0.260314 + 0.450878i
\(735\) 0 0
\(736\) −0.886092 + 2.43452i −0.0326618 + 0.0897375i
\(737\) 1.14423 + 0.533565i 0.0421484 + 0.0196541i
\(738\) 25.8040 + 2.25756i 0.949860 + 0.0831020i
\(739\) 18.9290 3.33770i 0.696315 0.122779i 0.185723 0.982602i \(-0.440537\pi\)
0.510592 + 0.859823i \(0.329426\pi\)
\(740\) 0 0
\(741\) 1.25530 2.51086i 0.0461146 0.0922389i
\(742\) 27.9245 27.9245i 1.02514 1.02514i
\(743\) −29.1705 20.4254i −1.07016 0.749334i −0.100782 0.994908i \(-0.532135\pi\)
−0.969378 + 0.245574i \(0.921023\pi\)
\(744\) 0.695430 0.583535i 0.0254957 0.0213934i
\(745\) 0 0
\(746\) −34.1017 12.4120i −1.24855 0.454435i
\(747\) −41.2402 + 3.60805i −1.50890 + 0.132012i
\(748\) −22.6480 + 6.06853i −0.828095 + 0.221887i
\(749\) −13.2463 22.9432i −0.484008 0.838327i
\(750\) 0 0
\(751\) 1.29307 + 0.228003i 0.0471847 + 0.00831994i 0.197191 0.980365i \(-0.436818\pi\)
−0.150006 + 0.988685i \(0.547929\pi\)
\(752\) 6.61066 + 1.77132i 0.241066 + 0.0645935i
\(753\) −0.258217 0.963678i −0.00940994 0.0351184i
\(754\) −1.79365 1.50505i −0.0653210 0.0548108i
\(755\) 0 0
\(756\) 3.55880 + 9.77773i 0.129432 + 0.355613i
\(757\) −1.68000 + 19.2025i −0.0610608 + 0.697928i 0.902544 + 0.430598i \(0.141697\pi\)
−0.963605 + 0.267331i \(0.913858\pi\)
\(758\) 4.80867 6.86749i 0.174659 0.249439i
\(759\) 6.20888 0.225368
\(760\) 0 0
\(761\) 16.5439 0.599715 0.299857 0.953984i \(-0.403061\pi\)
0.299857 + 0.953984i \(0.403061\pi\)
\(762\) 2.09638 2.99394i 0.0759439 0.108459i
\(763\) 0.974914 11.1433i 0.0352943 0.403415i
\(764\) −1.01440 2.78704i −0.0366996 0.100831i
\(765\) 0 0
\(766\) −12.2323 10.2642i −0.441973 0.370859i
\(767\) 3.17717 + 11.8574i 0.114721 + 0.428144i
\(768\) 0.464087 + 0.124352i 0.0167463 + 0.00448715i
\(769\) −33.8306 5.96525i −1.21996 0.215112i −0.473653 0.880711i \(-0.657065\pi\)
−0.746310 + 0.665599i \(0.768176\pi\)
\(770\) 0 0
\(771\) 3.83365 + 6.64008i 0.138066 + 0.239137i
\(772\) −9.47893 + 2.53987i −0.341154 + 0.0914119i
\(773\) −11.3638 + 0.994208i −0.408729 + 0.0357592i −0.289667 0.957128i \(-0.593544\pi\)
−0.119063 + 0.992887i \(0.537989\pi\)
\(774\) 5.08267 + 1.84994i 0.182693 + 0.0664948i
\(775\) 0 0
\(776\) 10.7820 9.04713i 0.387050 0.324773i
\(777\) −12.1047 8.47578i −0.434252 0.304067i
\(778\) 19.5089 19.5089i 0.699426 0.699426i
\(779\) 9.47491 + 39.6568i 0.339474 + 1.42085i
\(780\) 0 0
\(781\) −58.7352 + 10.3566i −2.10171 + 0.370588i
\(782\) 12.1319 + 1.06140i 0.433834 + 0.0379556i
\(783\) −4.38825 2.04627i −0.156823 0.0731278i
\(784\) 2.42556 6.66418i 0.0866273 0.238006i
\(785\) 0 0
\(786\) −2.47398 + 4.28506i −0.0882439 + 0.152843i
\(787\) −6.46227 + 24.1175i −0.230355 + 0.859697i 0.749833 + 0.661627i \(0.230134\pi\)
−0.980188 + 0.198070i \(0.936533\pi\)
\(788\) −7.59444 + 5.31768i −0.270541 + 0.189435i
\(789\) 0.538733 3.05531i 0.0191794 0.108772i
\(790\) 0 0
\(791\) 27.7275 + 16.0085i 0.985877 + 0.569196i
\(792\) 1.20386 + 13.7602i 0.0427772 + 0.488946i
\(793\) 2.60743 1.21587i 0.0925926 0.0431767i
\(794\) 12.7831 4.65265i 0.453654 0.165116i
\(795\) 0 0
\(796\) −1.73926 9.86381i −0.0616463 0.349613i
\(797\) −20.9403 20.9403i −0.741744 0.741744i 0.231170 0.972913i \(-0.425745\pi\)
−0.972913 + 0.231170i \(0.925745\pi\)
\(798\) −6.15798 + 4.88729i −0.217990 + 0.173008i
\(799\) 32.1705i 1.13811i
\(800\) 0 0
\(801\) 23.7173 + 28.2652i 0.838009 + 0.998700i
\(802\) 10.2642 22.0117i 0.362443 0.777262i
\(803\) 22.1336 + 47.4657i 0.781078 + 1.67503i
\(804\) −0.0781683 + 0.0931574i −0.00275678 + 0.00328541i
\(805\) 0 0
\(806\) −2.19337 + 1.26634i −0.0772581 + 0.0446050i
\(807\) 5.96538 + 8.51945i 0.209991 + 0.299899i
\(808\) 6.45041 + 9.21214i 0.226925 + 0.324082i
\(809\) −30.2313 + 17.4540i −1.06288 + 0.613652i −0.926226 0.376968i \(-0.876967\pi\)
−0.136649 + 0.990619i \(0.543633\pi\)
\(810\) 0 0
\(811\) −27.0249 + 32.2070i −0.948972 + 1.13094i 0.0423000 + 0.999105i \(0.486531\pi\)
−0.991272 + 0.131835i \(0.957913\pi\)
\(812\) 2.77128 + 5.94303i 0.0972528 + 0.208559i
\(813\) 5.25795 11.2757i 0.184404 0.395456i
\(814\) −26.2692 31.3064i −0.920735 1.09729i
\(815\) 0 0
\(816\) 2.25845i 0.0790617i
\(817\) −0.232175 + 8.51086i −0.00812276 + 0.297757i
\(818\) 7.77901 + 7.77901i 0.271987 + 0.271987i
\(819\) −2.41958 13.7221i −0.0845469 0.479489i
\(820\) 0 0
\(821\) −34.0120 + 12.3793i −1.18703 + 0.432042i −0.858678 0.512515i \(-0.828714\pi\)
−0.328348 + 0.944557i \(0.606492\pi\)
\(822\) −6.12823 + 2.85764i −0.213747 + 0.0996717i
\(823\) −0.636069 7.27030i −0.0221720 0.253427i −0.999189 0.0402656i \(-0.987180\pi\)
0.977017 0.213161i \(-0.0683760\pi\)
\(824\) 2.06710 + 1.19344i 0.0720108 + 0.0415755i
\(825\) 0 0
\(826\) 5.96983 33.8566i 0.207717 1.17802i
\(827\) 3.26292 2.28472i 0.113463 0.0794475i −0.515468 0.856909i \(-0.672382\pi\)
0.628931 + 0.777461i \(0.283493\pi\)
\(828\) 1.85683 6.92977i 0.0645292 0.240826i
\(829\) 5.48124 9.49379i 0.190371 0.329733i −0.755002 0.655722i \(-0.772364\pi\)
0.945373 + 0.325990i \(0.105697\pi\)
\(830\) 0 0
\(831\) −1.36323 + 3.74545i −0.0472900 + 0.129928i
\(832\) −1.21482 0.566481i −0.0421164 0.0196392i
\(833\) −33.2094 2.90545i −1.15064 0.100668i
\(834\) −8.77601 + 1.54745i −0.303888 + 0.0535837i
\(835\) 0 0
\(836\) −19.9486 + 8.64797i −0.689935 + 0.299096i
\(837\) −3.70337 + 3.70337i −0.128007 + 0.128007i
\(838\) −16.5797 11.6092i −0.572736 0.401034i
\(839\) 6.03150 5.06103i 0.208230 0.174726i −0.532708 0.846299i \(-0.678826\pi\)
0.740938 + 0.671573i \(0.234381\pi\)
\(840\) 0 0
\(841\) 24.3837 + 8.87495i 0.840818 + 0.306033i
\(842\) −28.4614 + 2.49005i −0.980845 + 0.0858128i
\(843\) −11.2056 + 3.00253i −0.385941 + 0.103413i
\(844\) 12.0943 + 20.9479i 0.416302 + 0.721056i
\(845\) 0 0
\(846\) −18.6638 3.29094i −0.641676 0.113145i
\(847\) −50.3313 13.4862i −1.72940 0.463392i
\(848\) 2.72278 + 10.1616i 0.0935007 + 0.348950i
\(849\) 3.27035 + 2.74415i 0.112238 + 0.0941791i
\(850\) 0 0
\(851\) 7.25984 + 19.9463i 0.248864 + 0.683749i
\(852\) 0.500688 5.72289i 0.0171533 0.196063i
\(853\) 13.9668 19.9467i 0.478214 0.682961i −0.505474 0.862842i \(-0.668682\pi\)
0.983688 + 0.179881i \(0.0575713\pi\)
\(854\) −8.05721 −0.275712
\(855\) 0 0
\(856\) 7.05731 0.241214
\(857\) 28.6102 40.8596i 0.977307 1.39574i 0.0597146 0.998215i \(-0.480981\pi\)
0.917592 0.397523i \(-0.130130\pi\)
\(858\) −0.279975 + 3.20013i −0.00955818 + 0.109251i
\(859\) 16.1613 + 44.4029i 0.551418 + 1.51501i 0.831775 + 0.555113i \(0.187325\pi\)
−0.280357 + 0.959896i \(0.590453\pi\)
\(860\) 0 0
\(861\) −12.9238 10.8443i −0.440441 0.369574i
\(862\) 4.43232 + 16.5416i 0.150965 + 0.563410i
\(863\) −24.3265 6.51826i −0.828083 0.221884i −0.180206 0.983629i \(-0.557676\pi\)
−0.647877 + 0.761745i \(0.724343\pi\)
\(864\) −2.72973 0.481325i −0.0928672 0.0163750i
\(865\) 0 0
\(866\) −2.05006 3.55081i −0.0696640 0.120662i
\(867\) −2.36495 + 0.633686i −0.0803178 + 0.0215211i
\(868\) 7.06599 0.618194i 0.239835 0.0209829i
\(869\) −45.0046 16.3803i −1.52668 0.555664i
\(870\) 0 0
\(871\) 0.259895 0.218078i 0.00880622 0.00738930i
\(872\) 2.44090 + 1.70914i 0.0826594 + 0.0578787i
\(873\) −27.5598 + 27.5598i −0.932759 + 0.932759i
\(874\) 11.2725 0.677091i 0.381299 0.0229029i
\(875\) 0 0
\(876\) −4.96798 + 0.875989i −0.167853 + 0.0295969i
\(877\) −35.9584 3.14595i −1.21423 0.106231i −0.538014 0.842936i \(-0.680825\pi\)
−0.676214 + 0.736705i \(0.736381\pi\)
\(878\) 16.0172 + 7.46894i 0.540554 + 0.252065i
\(879\) −2.26215 + 6.21520i −0.0763004 + 0.209634i
\(880\) 0 0
\(881\) 1.46927 2.54486i 0.0495011 0.0857384i −0.840213 0.542256i \(-0.817570\pi\)
0.889714 + 0.456518i \(0.150904\pi\)
\(882\) −5.08283 + 18.9694i −0.171148 + 0.638732i
\(883\) −37.6354 + 26.3526i −1.26653 + 0.886836i −0.997094 0.0761812i \(-0.975727\pi\)
−0.269439 + 0.963017i \(0.586838\pi\)
\(884\) −1.09412 + 6.20504i −0.0367991 + 0.208698i
\(885\) 0 0
\(886\) 8.34151 + 4.81597i 0.280239 + 0.161796i
\(887\) −0.402514 4.60075i −0.0135151 0.154478i 0.986438 0.164132i \(-0.0524824\pi\)
−0.999953 + 0.00965430i \(0.996927\pi\)
\(888\) 3.56763 1.66361i 0.119722 0.0558272i
\(889\) 26.8345 9.76697i 0.900002 0.327574i
\(890\) 0 0
\(891\) −6.04214 34.2667i −0.202419 1.14798i
\(892\) 1.17377 + 1.17377i 0.0393008 + 0.0393008i
\(893\) −4.37715 29.5088i −0.146476 0.987476i
\(894\) 3.88330i 0.129877i
\(895\) 0 0
\(896\) 2.41297 + 2.87567i 0.0806117 + 0.0960692i
\(897\) 0.705127 1.51215i 0.0235435 0.0504892i
\(898\) −8.85858 18.9973i −0.295615 0.633947i
\(899\) −2.12158 + 2.52840i −0.0707586 + 0.0843269i
\(900\) 0 0
\(901\) 42.8256 24.7254i 1.42673 0.823721i
\(902\) −26.7619 38.2200i −0.891075 1.27259i
\(903\) −2.02064 2.88578i −0.0672427 0.0960326i
\(904\) −7.38629 + 4.26448i −0.245664 + 0.141834i
\(905\) 0 0
\(906\) 3.51496 4.18896i 0.116777 0.139169i
\(907\) 3.91880 + 8.40389i 0.130122 + 0.279047i 0.960565 0.278057i \(-0.0896904\pi\)
−0.830443 + 0.557104i \(0.811913\pi\)
\(908\) −6.63782 + 14.2348i −0.220284 + 0.472400i
\(909\) −20.0176 23.8560i −0.663941 0.791255i
\(910\) 0 0
\(911\) 1.34196i 0.0444610i 0.999753 + 0.0222305i \(0.00707677\pi\)
−0.999753 + 0.0222305i \(0.992923\pi\)
\(912\) −0.307288 2.07160i −0.0101753 0.0685976i
\(913\) 52.7283 + 52.7283i 1.74505 + 1.74505i
\(914\) 5.88855 + 33.3956i 0.194776 + 1.10463i
\(915\) 0 0
\(916\) 3.61064 1.31417i 0.119299 0.0434213i
\(917\) −35.0373 + 16.3382i −1.15703 + 0.539534i
\(918\) 1.13559 + 12.9798i 0.0374799 + 0.428397i
\(919\) 1.81672 + 1.04888i 0.0599279 + 0.0345994i 0.529665 0.848207i \(-0.322318\pi\)
−0.469737 + 0.882807i \(0.655651\pi\)
\(920\) 0 0
\(921\) 0.447937 2.54038i 0.0147600 0.0837083i
\(922\) 9.15325 6.40918i 0.301446 0.211075i
\(923\) −4.14810 + 15.4809i −0.136536 + 0.509561i
\(924\) 4.49822 7.79114i 0.147981 0.256310i
\(925\) 0 0
\(926\) 9.87513 27.1317i 0.324517 0.891603i
\(927\) −5.99038 2.79336i −0.196750 0.0917460i
\(928\) −1.74017 0.152245i −0.0571239 0.00499769i
\(929\) −52.4609 + 9.25027i −1.72119 + 0.303492i −0.945014 0.327029i \(-0.893952\pi\)
−0.776172 + 0.630521i \(0.782841\pi\)
\(930\) 0 0
\(931\) −30.8571 + 1.85345i −1.01130 + 0.0607444i
\(932\) 5.00733 5.00733i 0.164020 0.164020i
\(933\) 4.12715 + 2.88986i 0.135117 + 0.0946098i
\(934\) −11.8099 + 9.90970i −0.386432 + 0.324255i
\(935\) 0 0
\(936\) 3.48795 + 1.26951i 0.114007 + 0.0414953i
\(937\) 48.6745 4.25846i 1.59013 0.139118i 0.742549 0.669791i \(-0.233617\pi\)
0.847576 + 0.530673i \(0.178061\pi\)
\(938\) −0.917775 + 0.245917i −0.0299664 + 0.00802947i
\(939\) −1.49850 2.59548i −0.0489018 0.0847004i
\(940\) 0 0
\(941\) 42.9034 + 7.56502i 1.39861 + 0.246613i 0.821572 0.570105i \(-0.193097\pi\)
0.577038 + 0.816717i \(0.304209\pi\)
\(942\) 1.16288 + 0.311594i 0.0378888 + 0.0101523i
\(943\) 6.27218 + 23.4081i 0.204250 + 0.762273i
\(944\) 7.01554 + 5.88674i 0.228336 + 0.191597i
\(945\) 0 0
\(946\) −3.33228 9.15535i −0.108342 0.297666i
\(947\) 0.241094 2.75571i 0.00783449 0.0895486i −0.991271 0.131842i \(-0.957911\pi\)
0.999105 + 0.0422934i \(0.0134664\pi\)
\(948\) 2.64598 3.77885i 0.0859374 0.122731i
\(949\) 14.0738 0.456853
\(950\) 0 0
\(951\) −6.26001 −0.202995
\(952\) 10.1212 14.4546i 0.328030 0.468475i
\(953\) −3.24039 + 37.0378i −0.104966 + 1.19977i 0.742841 + 0.669468i \(0.233478\pi\)
−0.847808 + 0.530304i \(0.822078\pi\)
\(954\) −9.96361 27.3748i −0.322584 0.886291i
\(955\) 0 0
\(956\) 6.62612 + 5.55998i 0.214304 + 0.179823i
\(957\) 1.08350 + 4.04369i 0.0350247 + 0.130714i
\(958\) 9.97672 + 2.67325i 0.322333 + 0.0863689i
\(959\) −52.0284 9.17400i −1.68008 0.296244i
\(960\) 0 0
\(961\) −13.7149 23.7549i −0.442417 0.766288i
\(962\) −10.6079 + 2.84238i −0.342012 + 0.0916419i
\(963\) −19.4685 + 1.70327i −0.627362 + 0.0548871i
\(964\) −19.3048 7.02637i −0.621766 0.226304i
\(965\) 0 0
\(966\) −3.57949 + 3.00354i −0.115168 + 0.0966375i
\(967\) −3.62688 2.53957i −0.116632 0.0816669i 0.513805 0.857907i \(-0.328236\pi\)
−0.630437 + 0.776240i \(0.717124\pi\)
\(968\) 9.81511 9.81511i 0.315469 0.315469i
\(969\) −9.03217 + 3.91556i −0.290155 + 0.125786i
\(970\) 0 0
\(971\) 9.49031 1.67340i 0.304558 0.0537019i −0.0192805 0.999814i \(-0.506138\pi\)
0.323839 + 0.946112i \(0.395026\pi\)
\(972\) 11.6227 + 1.01685i 0.372797 + 0.0326155i
\(973\) −63.1031 29.4254i −2.02299 0.943337i
\(974\) −7.07577 + 19.4405i −0.226722 + 0.622915i
\(975\) 0 0
\(976\) 1.07317 1.85879i 0.0343515 0.0594985i
\(977\) 7.84751 29.2873i 0.251064 0.936984i −0.719174 0.694830i \(-0.755479\pi\)
0.970238 0.242154i \(-0.0778539\pi\)
\(978\) 5.21454 3.65126i 0.166743 0.116754i
\(979\) 11.5412 65.4533i 0.368858 2.09190i
\(980\) 0 0
\(981\) −7.14603 4.12576i −0.228155 0.131725i
\(982\) −3.12894 35.7640i −0.0998486 1.14127i
\(983\) −32.3850 + 15.1014i −1.03292 + 0.481659i −0.863746 0.503927i \(-0.831888\pi\)
−0.169175 + 0.985586i \(0.554110\pi\)
\(984\) 4.22315 1.53710i 0.134629 0.0490010i
\(985\) 0 0
\(986\) 1.42585 + 8.08640i 0.0454083 + 0.257523i
\(987\) 8.72823 + 8.72823i 0.277823 + 0.277823i
\(988\) −0.159328 + 5.84053i −0.00506891 + 0.185812i
\(989\) 5.06040i 0.160912i
\(990\) 0 0
\(991\) −20.1912 24.0629i −0.641394 0.764383i 0.343196 0.939264i \(-0.388491\pi\)
−0.984590 + 0.174880i \(0.944046\pi\)
\(992\) −0.798532 + 1.71246i −0.0253534 + 0.0543706i
\(993\) −3.20126 6.86513i −0.101589 0.217858i
\(994\) 28.8515 34.3838i 0.915113 1.09059i
\(995\) 0 0
\(996\) −6.22034 + 3.59131i −0.197099 + 0.113795i
\(997\) −18.5401 26.4780i −0.587170 0.838566i 0.410128 0.912028i \(-0.365484\pi\)
−0.997298 + 0.0734621i \(0.976595\pi\)
\(998\) −6.35080 9.06988i −0.201031 0.287102i
\(999\) −19.6674 + 11.3550i −0.622249 + 0.359256i
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 950.2.bb.e.143.7 120
5.2 odd 4 inner 950.2.bb.e.257.9 120
5.3 odd 4 190.2.r.a.67.2 120
5.4 even 2 190.2.r.a.143.4 yes 120
19.2 odd 18 inner 950.2.bb.e.743.9 120
95.2 even 36 inner 950.2.bb.e.857.7 120
95.59 odd 18 190.2.r.a.173.2 yes 120
95.78 even 36 190.2.r.a.97.4 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.r.a.67.2 120 5.3 odd 4
190.2.r.a.97.4 yes 120 95.78 even 36
190.2.r.a.143.4 yes 120 5.4 even 2
190.2.r.a.173.2 yes 120 95.59 odd 18
950.2.bb.e.143.7 120 1.1 even 1 trivial
950.2.bb.e.257.9 120 5.2 odd 4 inner
950.2.bb.e.743.9 120 19.2 odd 18 inner
950.2.bb.e.857.7 120 95.2 even 36 inner