Properties

Label 585.2.i.h.196.12
Level $585$
Weight $2$
Character 585.196
Analytic conductor $4.671$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [585,2,Mod(196,585)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("585.196");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.i (of order \(3\), degree \(2\), 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: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(15\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 196.12
Character \(\chi\) \(=\) 585.196
Dual form 585.2.i.h.391.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.909537 - 1.57536i) q^{2} +(1.33257 + 1.10646i) q^{3} +(-0.654515 - 1.13365i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.95510 - 1.09292i) q^{6} +(-1.45386 + 2.51816i) q^{7} +1.25693 q^{8} +(0.551488 + 2.94887i) q^{9} +O(q^{10})\) \(q+(0.909537 - 1.57536i) q^{2} +(1.33257 + 1.10646i) q^{3} +(-0.654515 - 1.13365i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.95510 - 1.09292i) q^{6} +(-1.45386 + 2.51816i) q^{7} +1.25693 q^{8} +(0.551488 + 2.94887i) q^{9} +1.81907 q^{10} +(-1.59030 + 2.75449i) q^{11} +(0.382156 - 2.23487i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(2.64468 + 4.58073i) q^{14} +(-0.291938 + 1.70727i) q^{15} +(2.45225 - 4.24742i) q^{16} -1.97843 q^{17} +(5.14715 + 1.81332i) q^{18} +6.13227 q^{19} +(0.654515 - 1.13365i) q^{20} +(-4.72362 + 1.74699i) q^{21} +(2.89288 + 5.01062i) q^{22} +(-2.79077 - 4.83376i) q^{23} +(1.67494 + 1.39074i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.81907 q^{26} +(-2.52792 + 4.53978i) q^{27} +3.80630 q^{28} +(1.83351 - 3.17573i) q^{29} +(2.42404 + 2.01273i) q^{30} +(-4.09477 - 7.09235i) q^{31} +(-3.20390 - 5.54932i) q^{32} +(-5.16693 + 1.91094i) q^{33} +(-1.79945 + 3.11675i) q^{34} -2.90773 q^{35} +(2.98204 - 2.55528i) q^{36} +8.77322 q^{37} +(5.57752 - 9.66055i) q^{38} +(0.291938 - 1.70727i) q^{39} +(0.628463 + 1.08853i) q^{40} +(-1.03484 - 1.79239i) q^{41} +(-1.54417 + 9.03038i) q^{42} +(-0.928705 + 1.60856i) q^{43} +4.16351 q^{44} +(-2.27806 + 1.95204i) q^{45} -10.1532 q^{46} +(4.03187 - 6.98341i) q^{47} +(7.96740 - 2.94667i) q^{48} +(-0.727433 - 1.25995i) q^{49} +(0.909537 + 1.57536i) q^{50} +(-2.63640 - 2.18905i) q^{51} +(-0.654515 + 1.13365i) q^{52} +3.09517 q^{53} +(4.85258 + 8.11149i) q^{54} -3.18061 q^{55} +(-1.82740 + 3.16514i) q^{56} +(8.17168 + 6.78511i) q^{57} +(-3.33529 - 5.77689i) q^{58} +(-2.01856 - 3.49624i) q^{59} +(2.12653 - 0.786478i) q^{60} +(1.50866 - 2.61308i) q^{61} -14.8974 q^{62} +(-8.22754 - 2.89852i) q^{63} -1.84726 q^{64} +(0.500000 - 0.866025i) q^{65} +(-1.68908 + 9.87786i) q^{66} +(-2.84693 - 4.93103i) q^{67} +(1.29491 + 2.24285i) q^{68} +(1.62946 - 9.52920i) q^{69} +(-2.64468 + 4.58073i) q^{70} +0.716107 q^{71} +(0.693179 + 3.70651i) q^{72} +1.12563 q^{73} +(7.97957 - 13.8210i) q^{74} +(-1.62451 + 0.600809i) q^{75} +(-4.01366 - 6.95186i) q^{76} +(-4.62417 - 8.00929i) q^{77} +(-2.42404 - 2.01273i) q^{78} +(-7.28558 + 12.6190i) q^{79} +4.90450 q^{80} +(-8.39172 + 3.25254i) q^{81} -3.76490 q^{82} +(-0.0540476 + 0.0936133i) q^{83} +(5.07216 + 4.21152i) q^{84} +(-0.989215 - 1.71337i) q^{85} +(1.68938 + 2.92610i) q^{86} +(5.95710 - 2.20318i) q^{87} +(-1.99889 + 3.46219i) q^{88} -2.32728 q^{89} +(1.00320 + 5.36422i) q^{90} +2.90773 q^{91} +(-3.65320 + 6.32753i) q^{92} +(2.39084 - 13.9818i) q^{93} +(-7.33428 - 12.7033i) q^{94} +(3.06613 + 5.31070i) q^{95} +(1.87068 - 10.9398i) q^{96} +(-6.46887 + 11.2044i) q^{97} -2.64651 q^{98} +(-8.99967 - 3.17054i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.909537 1.57536i 0.643140 1.11395i −0.341588 0.939850i \(-0.610965\pi\)
0.984728 0.174101i \(-0.0557019\pi\)
\(3\) 1.33257 + 1.10646i 0.769360 + 0.638816i
\(4\) −0.654515 1.13365i −0.327258 0.566827i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 2.95510 1.09292i 1.20642 0.446181i
\(7\) −1.45386 + 2.51816i −0.549508 + 0.951777i 0.448800 + 0.893632i \(0.351852\pi\)
−0.998308 + 0.0581442i \(0.981482\pi\)
\(8\) 1.25693 0.444390
\(9\) 0.551488 + 2.94887i 0.183829 + 0.982958i
\(10\) 1.81907 0.575242
\(11\) −1.59030 + 2.75449i −0.479495 + 0.830509i −0.999723 0.0235177i \(-0.992513\pi\)
0.520229 + 0.854027i \(0.325847\pi\)
\(12\) 0.382156 2.23487i 0.110319 0.645151i
\(13\) −0.500000 0.866025i −0.138675 0.240192i
\(14\) 2.64468 + 4.58073i 0.706821 + 1.22425i
\(15\) −0.291938 + 1.70727i −0.0753781 + 0.440815i
\(16\) 2.45225 4.24742i 0.613063 1.06186i
\(17\) −1.97843 −0.479840 −0.239920 0.970793i \(-0.577121\pi\)
−0.239920 + 0.970793i \(0.577121\pi\)
\(18\) 5.14715 + 1.81332i 1.21319 + 0.427403i
\(19\) 6.13227 1.40684 0.703419 0.710775i \(-0.251656\pi\)
0.703419 + 0.710775i \(0.251656\pi\)
\(20\) 0.654515 1.13365i 0.146354 0.253493i
\(21\) −4.72362 + 1.74699i −1.03078 + 0.381224i
\(22\) 2.89288 + 5.01062i 0.616764 + 1.06827i
\(23\) −2.79077 4.83376i −0.581916 1.00791i −0.995252 0.0973293i \(-0.968970\pi\)
0.413336 0.910578i \(-0.364363\pi\)
\(24\) 1.67494 + 1.39074i 0.341896 + 0.283883i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −1.81907 −0.356750
\(27\) −2.52792 + 4.53978i −0.486498 + 0.873682i
\(28\) 3.80630 0.719323
\(29\) 1.83351 3.17573i 0.340474 0.589718i −0.644047 0.764986i \(-0.722746\pi\)
0.984521 + 0.175268i \(0.0560792\pi\)
\(30\) 2.42404 + 2.01273i 0.442568 + 0.367473i
\(31\) −4.09477 7.09235i −0.735443 1.27382i −0.954529 0.298119i \(-0.903641\pi\)
0.219086 0.975706i \(-0.429692\pi\)
\(32\) −3.20390 5.54932i −0.566375 0.980990i
\(33\) −5.16693 + 1.91094i −0.899446 + 0.332652i
\(34\) −1.79945 + 3.11675i −0.308604 + 0.534518i
\(35\) −2.90773 −0.491495
\(36\) 2.98204 2.55528i 0.497007 0.425880i
\(37\) 8.77322 1.44231 0.721155 0.692774i \(-0.243612\pi\)
0.721155 + 0.692774i \(0.243612\pi\)
\(38\) 5.57752 9.66055i 0.904794 1.56715i
\(39\) 0.291938 1.70727i 0.0467475 0.273382i
\(40\) 0.628463 + 1.08853i 0.0993687 + 0.172112i
\(41\) −1.03484 1.79239i −0.161615 0.279925i 0.773833 0.633389i \(-0.218337\pi\)
−0.935448 + 0.353465i \(0.885004\pi\)
\(42\) −1.54417 + 9.03038i −0.238270 + 1.39342i
\(43\) −0.928705 + 1.60856i −0.141626 + 0.245304i −0.928109 0.372308i \(-0.878566\pi\)
0.786483 + 0.617612i \(0.211900\pi\)
\(44\) 4.16351 0.627673
\(45\) −2.27806 + 1.95204i −0.339593 + 0.290993i
\(46\) −10.1532 −1.49701
\(47\) 4.03187 6.98341i 0.588109 1.01864i −0.406371 0.913708i \(-0.633206\pi\)
0.994480 0.104927i \(-0.0334609\pi\)
\(48\) 7.96740 2.94667i 1.15000 0.425315i
\(49\) −0.727433 1.25995i −0.103919 0.179993i
\(50\) 0.909537 + 1.57536i 0.128628 + 0.222790i
\(51\) −2.63640 2.18905i −0.369169 0.306529i
\(52\) −0.654515 + 1.13365i −0.0907649 + 0.157209i
\(53\) 3.09517 0.425154 0.212577 0.977144i \(-0.431814\pi\)
0.212577 + 0.977144i \(0.431814\pi\)
\(54\) 4.85258 + 8.11149i 0.660352 + 1.10383i
\(55\) −3.18061 −0.428873
\(56\) −1.82740 + 3.16514i −0.244196 + 0.422960i
\(57\) 8.17168 + 6.78511i 1.08236 + 0.898710i
\(58\) −3.33529 5.77689i −0.437945 0.758542i
\(59\) −2.01856 3.49624i −0.262794 0.455172i 0.704189 0.710012i \(-0.251311\pi\)
−0.966983 + 0.254840i \(0.917977\pi\)
\(60\) 2.12653 0.786478i 0.274534 0.101534i
\(61\) 1.50866 2.61308i 0.193164 0.334570i −0.753133 0.657868i \(-0.771458\pi\)
0.946297 + 0.323298i \(0.104792\pi\)
\(62\) −14.8974 −1.89197
\(63\) −8.22754 2.89852i −1.03657 0.365179i
\(64\) −1.84726 −0.230907
\(65\) 0.500000 0.866025i 0.0620174 0.107417i
\(66\) −1.68908 + 9.87786i −0.207912 + 1.21588i
\(67\) −2.84693 4.93103i −0.347808 0.602421i 0.638052 0.769993i \(-0.279741\pi\)
−0.985860 + 0.167572i \(0.946407\pi\)
\(68\) 1.29491 + 2.24285i 0.157031 + 0.271986i
\(69\) 1.62946 9.52920i 0.196164 1.14718i
\(70\) −2.64468 + 4.58073i −0.316100 + 0.547502i
\(71\) 0.716107 0.0849862 0.0424931 0.999097i \(-0.486470\pi\)
0.0424931 + 0.999097i \(0.486470\pi\)
\(72\) 0.693179 + 3.70651i 0.0816919 + 0.436817i
\(73\) 1.12563 0.131745 0.0658727 0.997828i \(-0.479017\pi\)
0.0658727 + 0.997828i \(0.479017\pi\)
\(74\) 7.97957 13.8210i 0.927606 1.60666i
\(75\) −1.62451 + 0.600809i −0.187582 + 0.0693755i
\(76\) −4.01366 6.95186i −0.460398 0.797433i
\(77\) −4.62417 8.00929i −0.526973 0.912744i
\(78\) −2.42404 2.01273i −0.274469 0.227897i
\(79\) −7.28558 + 12.6190i −0.819692 + 1.41975i 0.0862169 + 0.996276i \(0.472522\pi\)
−0.905909 + 0.423472i \(0.860811\pi\)
\(80\) 4.90450 0.548340
\(81\) −8.39172 + 3.25254i −0.932414 + 0.361393i
\(82\) −3.76490 −0.415763
\(83\) −0.0540476 + 0.0936133i −0.00593250 + 0.0102754i −0.868976 0.494854i \(-0.835222\pi\)
0.863044 + 0.505129i \(0.168555\pi\)
\(84\) 5.07216 + 4.21152i 0.553418 + 0.459515i
\(85\) −0.989215 1.71337i −0.107295 0.185841i
\(86\) 1.68938 + 2.92610i 0.182171 + 0.315529i
\(87\) 5.95710 2.20318i 0.638668 0.236205i
\(88\) −1.99889 + 3.46219i −0.213083 + 0.369070i
\(89\) −2.32728 −0.246691 −0.123345 0.992364i \(-0.539362\pi\)
−0.123345 + 0.992364i \(0.539362\pi\)
\(90\) 1.00320 + 5.36422i 0.105746 + 0.565439i
\(91\) 2.90773 0.304812
\(92\) −3.65320 + 6.32753i −0.380873 + 0.659691i
\(93\) 2.39084 13.9818i 0.247919 1.44984i
\(94\) −7.33428 12.7033i −0.756473 1.31025i
\(95\) 3.06613 + 5.31070i 0.314579 + 0.544866i
\(96\) 1.87068 10.9398i 0.190926 1.11654i
\(97\) −6.46887 + 11.2044i −0.656814 + 1.13763i 0.324622 + 0.945844i \(0.394763\pi\)
−0.981436 + 0.191791i \(0.938570\pi\)
\(98\) −2.64651 −0.267338
\(99\) −8.99967 3.17054i −0.904501 0.318651i
\(100\) 1.30903 0.130903
\(101\) 6.36352 11.0219i 0.633194 1.09672i −0.353701 0.935359i \(-0.615077\pi\)
0.986895 0.161365i \(-0.0515897\pi\)
\(102\) −5.84646 + 2.16226i −0.578886 + 0.214095i
\(103\) 5.19805 + 9.00329i 0.512179 + 0.887121i 0.999900 + 0.0141211i \(0.00449504\pi\)
−0.487721 + 0.873000i \(0.662172\pi\)
\(104\) −0.628463 1.08853i −0.0616258 0.106739i
\(105\) −3.87475 3.21728i −0.378137 0.313975i
\(106\) 2.81517 4.87601i 0.273433 0.473600i
\(107\) −18.2669 −1.76593 −0.882965 0.469439i \(-0.844456\pi\)
−0.882965 + 0.469439i \(0.844456\pi\)
\(108\) 6.80110 0.105573i 0.654436 0.0101588i
\(109\) 15.8134 1.51465 0.757326 0.653036i \(-0.226505\pi\)
0.757326 + 0.653036i \(0.226505\pi\)
\(110\) −2.89288 + 5.01062i −0.275825 + 0.477744i
\(111\) 11.6909 + 9.70723i 1.10965 + 0.921370i
\(112\) 7.13047 + 12.3503i 0.673766 + 1.16700i
\(113\) −8.02121 13.8931i −0.754572 1.30696i −0.945587 0.325370i \(-0.894511\pi\)
0.191015 0.981587i \(-0.438822\pi\)
\(114\) 18.1215 6.70206i 1.69723 0.627705i
\(115\) 2.79077 4.83376i 0.260241 0.450750i
\(116\) −4.80024 −0.445691
\(117\) 2.27806 1.95204i 0.210606 0.180466i
\(118\) −7.34381 −0.676053
\(119\) 2.87636 4.98201i 0.263676 0.456700i
\(120\) −0.366944 + 2.14591i −0.0334973 + 0.195894i
\(121\) 0.441865 + 0.765332i 0.0401695 + 0.0695757i
\(122\) −2.74436 4.75338i −0.248463 0.430351i
\(123\) 0.604218 3.53350i 0.0544805 0.318605i
\(124\) −5.36018 + 9.28411i −0.481358 + 0.833737i
\(125\) −1.00000 −0.0894427
\(126\) −12.0495 + 10.3251i −1.07345 + 0.919829i
\(127\) −20.0387 −1.77814 −0.889072 0.457768i \(-0.848649\pi\)
−0.889072 + 0.457768i \(0.848649\pi\)
\(128\) 4.72765 8.18853i 0.417869 0.723770i
\(129\) −3.01738 + 1.11595i −0.265665 + 0.0982538i
\(130\) −0.909537 1.57536i −0.0797717 0.138169i
\(131\) 1.17947 + 2.04290i 0.103051 + 0.178489i 0.912940 0.408094i \(-0.133806\pi\)
−0.809889 + 0.586583i \(0.800473\pi\)
\(132\) 5.54817 + 4.60676i 0.482907 + 0.400967i
\(133\) −8.91547 + 15.4421i −0.773069 + 1.33900i
\(134\) −10.3576 −0.894756
\(135\) −5.19553 + 0.0806501i −0.447160 + 0.00694125i
\(136\) −2.48674 −0.213236
\(137\) −2.63619 + 4.56601i −0.225225 + 0.390101i −0.956387 0.292103i \(-0.905645\pi\)
0.731162 + 0.682204i \(0.238978\pi\)
\(138\) −13.5299 11.2342i −1.15174 0.956315i
\(139\) 9.48703 + 16.4320i 0.804680 + 1.39375i 0.916507 + 0.400018i \(0.130996\pi\)
−0.111827 + 0.993728i \(0.535670\pi\)
\(140\) 1.90315 + 3.29635i 0.160846 + 0.278593i
\(141\) 13.0996 4.84478i 1.10319 0.408004i
\(142\) 0.651325 1.12813i 0.0546580 0.0946705i
\(143\) 3.18061 0.265976
\(144\) 13.8775 + 4.88898i 1.15646 + 0.407415i
\(145\) 3.66702 0.304529
\(146\) 1.02381 1.77328i 0.0847307 0.146758i
\(147\) 0.424731 2.48385i 0.0350312 0.204865i
\(148\) −5.74221 9.94580i −0.472007 0.817539i
\(149\) 7.43448 + 12.8769i 0.609056 + 1.05492i 0.991396 + 0.130895i \(0.0417850\pi\)
−0.382340 + 0.924022i \(0.624882\pi\)
\(150\) −0.531057 + 3.10565i −0.0433606 + 0.253575i
\(151\) 5.78021 10.0116i 0.470387 0.814734i −0.529040 0.848597i \(-0.677448\pi\)
0.999426 + 0.0338632i \(0.0107810\pi\)
\(152\) 7.70780 0.625185
\(153\) −1.09108 5.83414i −0.0882086 0.471662i
\(154\) −16.8234 −1.35567
\(155\) 4.09477 7.09235i 0.328900 0.569672i
\(156\) −2.12653 + 0.786478i −0.170259 + 0.0629686i
\(157\) 5.53134 + 9.58056i 0.441449 + 0.764612i 0.997797 0.0663372i \(-0.0211313\pi\)
−0.556348 + 0.830949i \(0.687798\pi\)
\(158\) 13.2530 + 22.9549i 1.05435 + 1.82619i
\(159\) 4.12453 + 3.42468i 0.327096 + 0.271595i
\(160\) 3.20390 5.54932i 0.253290 0.438712i
\(161\) 16.2296 1.27907
\(162\) −2.50865 + 16.1783i −0.197098 + 1.27109i
\(163\) −9.81467 −0.768745 −0.384372 0.923178i \(-0.625582\pi\)
−0.384372 + 0.923178i \(0.625582\pi\)
\(164\) −1.35464 + 2.34630i −0.105779 + 0.183215i
\(165\) −4.23838 3.51922i −0.329958 0.273971i
\(166\) 0.0983167 + 0.170289i 0.00763085 + 0.0132170i
\(167\) −2.25236 3.90120i −0.174293 0.301884i 0.765624 0.643289i \(-0.222431\pi\)
−0.939916 + 0.341405i \(0.889097\pi\)
\(168\) −5.93724 + 2.19583i −0.458068 + 0.169412i
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) −3.59891 −0.276024
\(171\) 3.38187 + 18.0833i 0.258618 + 1.38286i
\(172\) 2.43141 0.185393
\(173\) −11.6012 + 20.0939i −0.882024 + 1.52771i −0.0329360 + 0.999457i \(0.510486\pi\)
−0.849088 + 0.528252i \(0.822848\pi\)
\(174\) 1.94740 11.3885i 0.147632 0.863358i
\(175\) −1.45386 2.51816i −0.109902 0.190355i
\(176\) 7.79965 + 13.5094i 0.587921 + 1.01831i
\(177\) 1.17859 6.89245i 0.0885881 0.518068i
\(178\) −2.11674 + 3.66631i −0.158657 + 0.274801i
\(179\) −7.59652 −0.567790 −0.283895 0.958855i \(-0.591627\pi\)
−0.283895 + 0.958855i \(0.591627\pi\)
\(180\) 3.70396 + 1.30489i 0.276077 + 0.0972605i
\(181\) −6.85284 −0.509367 −0.254684 0.967024i \(-0.581971\pi\)
−0.254684 + 0.967024i \(0.581971\pi\)
\(182\) 2.64468 4.58073i 0.196037 0.339546i
\(183\) 4.90166 1.81283i 0.362341 0.134009i
\(184\) −3.50779 6.07567i −0.258598 0.447904i
\(185\) 4.38661 + 7.59784i 0.322510 + 0.558604i
\(186\) −19.8518 16.4834i −1.45561 1.20862i
\(187\) 3.14630 5.44956i 0.230081 0.398511i
\(188\) −10.5557 −0.769853
\(189\) −7.75667 12.9659i −0.564215 0.943133i
\(190\) 11.1550 0.809272
\(191\) −4.33199 + 7.50323i −0.313452 + 0.542915i −0.979107 0.203345i \(-0.934819\pi\)
0.665655 + 0.746259i \(0.268152\pi\)
\(192\) −2.46160 2.04392i −0.177651 0.147507i
\(193\) −11.9561 20.7085i −0.860617 1.49063i −0.871334 0.490690i \(-0.836745\pi\)
0.0107172 0.999943i \(-0.496589\pi\)
\(194\) 11.7673 + 20.3816i 0.844846 + 1.46332i
\(195\) 1.62451 0.600809i 0.116333 0.0430248i
\(196\) −0.952232 + 1.64931i −0.0680166 + 0.117808i
\(197\) 2.57489 0.183453 0.0917267 0.995784i \(-0.470761\pi\)
0.0917267 + 0.995784i \(0.470761\pi\)
\(198\) −13.1803 + 11.2940i −0.936683 + 0.802632i
\(199\) −9.19810 −0.652036 −0.326018 0.945364i \(-0.605707\pi\)
−0.326018 + 0.945364i \(0.605707\pi\)
\(200\) −0.628463 + 1.08853i −0.0444390 + 0.0769706i
\(201\) 1.66226 9.72096i 0.117246 0.685664i
\(202\) −11.5757 20.0497i −0.814464 1.41069i
\(203\) 5.33134 + 9.23415i 0.374187 + 0.648110i
\(204\) −0.756068 + 4.42153i −0.0529354 + 0.309569i
\(205\) 1.03484 1.79239i 0.0722763 0.125186i
\(206\) 18.9113 1.31761
\(207\) 12.7151 10.8954i 0.883758 0.757282i
\(208\) −4.90450 −0.340066
\(209\) −9.75217 + 16.8913i −0.674572 + 1.16839i
\(210\) −8.59262 + 3.17790i −0.592947 + 0.219296i
\(211\) 5.06507 + 8.77295i 0.348694 + 0.603955i 0.986018 0.166641i \(-0.0532921\pi\)
−0.637324 + 0.770596i \(0.719959\pi\)
\(212\) −2.02583 3.50884i −0.139135 0.240988i
\(213\) 0.954263 + 0.792344i 0.0653850 + 0.0542905i
\(214\) −16.6144 + 28.7770i −1.13574 + 1.96716i
\(215\) −1.85741 −0.126674
\(216\) −3.17740 + 5.70617i −0.216195 + 0.388256i
\(217\) 23.8129 1.61653
\(218\) 14.3829 24.9119i 0.974134 1.68725i
\(219\) 1.49999 + 1.24547i 0.101360 + 0.0841610i
\(220\) 2.08176 + 3.60571i 0.140352 + 0.243097i
\(221\) 0.989215 + 1.71337i 0.0665418 + 0.115254i
\(222\) 25.9258 9.58840i 1.74002 0.643531i
\(223\) −7.01972 + 12.1585i −0.470075 + 0.814194i −0.999414 0.0342160i \(-0.989107\pi\)
0.529339 + 0.848410i \(0.322440\pi\)
\(224\) 18.6321 1.24491
\(225\) −2.82954 0.996835i −0.188636 0.0664556i
\(226\) −29.1824 −1.94118
\(227\) 8.54222 14.7956i 0.566967 0.982016i −0.429896 0.902878i \(-0.641450\pi\)
0.996864 0.0791379i \(-0.0252167\pi\)
\(228\) 2.34348 13.7048i 0.155201 0.907623i
\(229\) 7.87595 + 13.6415i 0.520457 + 0.901458i 0.999717 + 0.0237854i \(0.00757183\pi\)
−0.479260 + 0.877673i \(0.659095\pi\)
\(230\) −5.07662 8.79296i −0.334742 0.579791i
\(231\) 2.69994 15.7894i 0.177643 1.03887i
\(232\) 2.30458 3.99165i 0.151303 0.262065i
\(233\) −23.3774 −1.53150 −0.765751 0.643137i \(-0.777633\pi\)
−0.765751 + 0.643137i \(0.777633\pi\)
\(234\) −1.00320 5.36422i −0.0655811 0.350670i
\(235\) 8.06375 0.526021
\(236\) −2.64235 + 4.57669i −0.172003 + 0.297917i
\(237\) −23.6710 + 8.75449i −1.53760 + 0.568665i
\(238\) −5.23232 9.06264i −0.339161 0.587444i
\(239\) 0.604547 + 1.04711i 0.0391049 + 0.0677316i 0.884915 0.465752i \(-0.154216\pi\)
−0.845811 + 0.533483i \(0.820883\pi\)
\(240\) 6.53559 + 5.42664i 0.421871 + 0.350288i
\(241\) 12.2678 21.2484i 0.790238 1.36873i −0.135582 0.990766i \(-0.543290\pi\)
0.925820 0.377966i \(-0.123376\pi\)
\(242\) 1.60757 0.103338
\(243\) −14.7814 4.95088i −0.948225 0.317599i
\(244\) −3.94976 −0.252858
\(245\) 0.727433 1.25995i 0.0464740 0.0804953i
\(246\) −5.01699 4.16571i −0.319872 0.265596i
\(247\) −3.06613 5.31070i −0.195093 0.337912i
\(248\) −5.14682 8.91456i −0.326824 0.566075i
\(249\) −0.175602 + 0.0649447i −0.0111283 + 0.00411570i
\(250\) −0.909537 + 1.57536i −0.0575242 + 0.0996348i
\(251\) −0.457299 −0.0288645 −0.0144322 0.999896i \(-0.504594\pi\)
−0.0144322 + 0.999896i \(0.504594\pi\)
\(252\) 2.09913 + 11.2243i 0.132233 + 0.707065i
\(253\) 17.7527 1.11610
\(254\) −18.2259 + 31.5682i −1.14359 + 1.98076i
\(255\) 0.577579 3.37771i 0.0361694 0.211521i
\(256\) −10.4472 18.0951i −0.652950 1.13094i
\(257\) −6.66062 11.5365i −0.415478 0.719629i 0.580001 0.814616i \(-0.303052\pi\)
−0.995478 + 0.0949873i \(0.969719\pi\)
\(258\) −0.986391 + 5.76847i −0.0614100 + 0.359129i
\(259\) −12.7551 + 22.0924i −0.792561 + 1.37276i
\(260\) −1.30903 −0.0811826
\(261\) 10.3760 + 3.65541i 0.642257 + 0.226264i
\(262\) 4.29108 0.265104
\(263\) 11.5770 20.0519i 0.713866 1.23645i −0.249529 0.968367i \(-0.580276\pi\)
0.963395 0.268085i \(-0.0863907\pi\)
\(264\) −6.49444 + 2.40191i −0.399705 + 0.147827i
\(265\) 1.54758 + 2.68049i 0.0950673 + 0.164661i
\(266\) 16.2179 + 28.0902i 0.994383 + 1.72232i
\(267\) −3.10126 2.57504i −0.189794 0.157590i
\(268\) −3.72672 + 6.45486i −0.227646 + 0.394294i
\(269\) 16.2398 0.990159 0.495080 0.868848i \(-0.335139\pi\)
0.495080 + 0.868848i \(0.335139\pi\)
\(270\) −4.59847 + 8.25820i −0.279854 + 0.502578i
\(271\) 29.0860 1.76685 0.883424 0.468574i \(-0.155232\pi\)
0.883424 + 0.468574i \(0.155232\pi\)
\(272\) −4.85160 + 8.40322i −0.294172 + 0.509520i
\(273\) 3.87475 + 3.21728i 0.234510 + 0.194719i
\(274\) 4.79542 + 8.30591i 0.289702 + 0.501779i
\(275\) −1.59030 2.75449i −0.0958990 0.166102i
\(276\) −11.8693 + 4.38976i −0.714449 + 0.264232i
\(277\) 7.05950 12.2274i 0.424164 0.734674i −0.572178 0.820130i \(-0.693901\pi\)
0.996342 + 0.0854555i \(0.0272345\pi\)
\(278\) 34.5152 2.07009
\(279\) 18.6562 15.9863i 1.11692 0.957076i
\(280\) −3.65479 −0.218416
\(281\) 10.5837 18.3316i 0.631373 1.09357i −0.355898 0.934525i \(-0.615825\pi\)
0.987271 0.159046i \(-0.0508417\pi\)
\(282\) 4.28231 25.0432i 0.255008 1.49130i
\(283\) −8.59973 14.8952i −0.511201 0.885426i −0.999916 0.0129824i \(-0.995867\pi\)
0.488715 0.872444i \(-0.337466\pi\)
\(284\) −0.468703 0.811817i −0.0278124 0.0481725i
\(285\) −1.79024 + 10.4694i −0.106045 + 0.620156i
\(286\) 2.89288 5.01062i 0.171060 0.296284i
\(287\) 6.01806 0.355235
\(288\) 14.5973 12.5083i 0.860156 0.737057i
\(289\) −13.0858 −0.769754
\(290\) 3.33529 5.77689i 0.195855 0.339230i
\(291\) −21.0175 + 7.77311i −1.23207 + 0.455668i
\(292\) −0.736744 1.27608i −0.0431147 0.0746768i
\(293\) −6.63650 11.4947i −0.387708 0.671530i 0.604433 0.796656i \(-0.293400\pi\)
−0.992141 + 0.125126i \(0.960067\pi\)
\(294\) −3.52666 2.92826i −0.205679 0.170780i
\(295\) 2.01856 3.49624i 0.117525 0.203559i
\(296\) 11.0273 0.640948
\(297\) −8.48462 14.1828i −0.492327 0.822967i
\(298\) 27.0477 1.56683
\(299\) −2.79077 + 4.83376i −0.161394 + 0.279543i
\(300\) 1.74437 + 1.44839i 0.100712 + 0.0836229i
\(301\) −2.70042 4.67726i −0.155650 0.269593i
\(302\) −10.5146 18.2119i −0.605049 1.04798i
\(303\) 20.6752 7.64652i 1.18776 0.439281i
\(304\) 15.0379 26.0463i 0.862480 1.49386i
\(305\) 3.01732 0.172771
\(306\) −10.1833 3.58752i −0.582139 0.205085i
\(307\) 31.0270 1.77080 0.885402 0.464826i \(-0.153883\pi\)
0.885402 + 0.464826i \(0.153883\pi\)
\(308\) −6.05318 + 10.4844i −0.344912 + 0.597405i
\(309\) −3.03502 + 17.7490i −0.172656 + 1.00970i
\(310\) −7.44869 12.9015i −0.423057 0.732757i
\(311\) −12.6825 21.9666i −0.719156 1.24561i −0.961335 0.275383i \(-0.911195\pi\)
0.242179 0.970232i \(-0.422138\pi\)
\(312\) 0.366944 2.14591i 0.0207741 0.121488i
\(313\) 1.55085 2.68615i 0.0876593 0.151830i −0.818862 0.573990i \(-0.805395\pi\)
0.906521 + 0.422160i \(0.138728\pi\)
\(314\) 20.1238 1.13565
\(315\) −1.60358 8.57452i −0.0903512 0.483119i
\(316\) 19.0741 1.07300
\(317\) −2.16385 + 3.74790i −0.121534 + 0.210503i −0.920373 0.391042i \(-0.872115\pi\)
0.798839 + 0.601545i \(0.205448\pi\)
\(318\) 9.14653 3.38276i 0.512912 0.189696i
\(319\) 5.83167 + 10.1008i 0.326511 + 0.565534i
\(320\) −0.923629 1.59977i −0.0516325 0.0894300i
\(321\) −24.3420 20.2116i −1.35864 1.12810i
\(322\) 14.7614 25.5675i 0.822621 1.42482i
\(323\) −12.1323 −0.675057
\(324\) 9.17976 + 7.38447i 0.509987 + 0.410248i
\(325\) 1.00000 0.0554700
\(326\) −8.92681 + 15.4617i −0.494410 + 0.856344i
\(327\) 21.0725 + 17.4970i 1.16531 + 0.967584i
\(328\) −1.30072 2.25291i −0.0718200 0.124396i
\(329\) 11.7236 + 20.3058i 0.646342 + 1.11950i
\(330\) −9.39902 + 3.47614i −0.517399 + 0.191355i
\(331\) −0.904396 + 1.56646i −0.0497101 + 0.0861004i −0.889810 0.456332i \(-0.849163\pi\)
0.840100 + 0.542432i \(0.182496\pi\)
\(332\) 0.141500 0.00776582
\(333\) 4.83833 + 25.8711i 0.265139 + 1.41773i
\(334\) −8.19441 −0.448378
\(335\) 2.84693 4.93103i 0.155544 0.269411i
\(336\) −4.16331 + 24.3473i −0.227127 + 1.32825i
\(337\) 7.87660 + 13.6427i 0.429066 + 0.743164i 0.996790 0.0800548i \(-0.0255095\pi\)
−0.567725 + 0.823218i \(0.692176\pi\)
\(338\) 0.909537 + 1.57536i 0.0494723 + 0.0856885i
\(339\) 4.68340 27.3888i 0.254367 1.48755i
\(340\) −1.29491 + 2.24285i −0.0702264 + 0.121636i
\(341\) 26.0477 1.41056
\(342\) 31.5637 + 11.1197i 1.70677 + 0.601286i
\(343\) −16.1237 −0.870599
\(344\) −1.16731 + 2.02184i −0.0629373 + 0.109011i
\(345\) 9.06726 3.35344i 0.488165 0.180543i
\(346\) 21.1035 + 36.5523i 1.13453 + 1.96506i
\(347\) −12.6985 21.9945i −0.681692 1.18072i −0.974464 0.224543i \(-0.927911\pi\)
0.292772 0.956182i \(-0.405422\pi\)
\(348\) −6.39665 5.31127i −0.342896 0.284714i
\(349\) 13.1045 22.6977i 0.701469 1.21498i −0.266481 0.963840i \(-0.585861\pi\)
0.967951 0.251140i \(-0.0808056\pi\)
\(350\) −5.28937 −0.282729
\(351\) 5.19553 0.0806501i 0.277317 0.00430478i
\(352\) 20.3807 1.08629
\(353\) −15.6137 + 27.0437i −0.831034 + 1.43939i 0.0661851 + 0.997807i \(0.478917\pi\)
−0.897219 + 0.441586i \(0.854416\pi\)
\(354\) −9.78615 8.12564i −0.520128 0.431873i
\(355\) 0.358053 + 0.620167i 0.0190035 + 0.0329150i
\(356\) 1.52324 + 2.63832i 0.0807314 + 0.139831i
\(357\) 9.34536 3.45629i 0.494609 0.182926i
\(358\) −6.90931 + 11.9673i −0.365169 + 0.632491i
\(359\) −15.6733 −0.827207 −0.413604 0.910457i \(-0.635730\pi\)
−0.413604 + 0.910457i \(0.635730\pi\)
\(360\) −2.86335 + 2.45357i −0.150912 + 0.129314i
\(361\) 18.6047 0.979194
\(362\) −6.23291 + 10.7957i −0.327594 + 0.567410i
\(363\) −0.257994 + 1.50877i −0.0135412 + 0.0791896i
\(364\) −1.90315 3.29635i −0.0997522 0.172776i
\(365\) 0.562817 + 0.974827i 0.0294592 + 0.0510248i
\(366\) 1.60237 9.37074i 0.0837572 0.489816i
\(367\) −15.7212 + 27.2298i −0.820638 + 1.42139i 0.0845702 + 0.996418i \(0.473048\pi\)
−0.905208 + 0.424969i \(0.860285\pi\)
\(368\) −27.3747 −1.42700
\(369\) 4.71484 4.04009i 0.245445 0.210319i
\(370\) 15.9591 0.829676
\(371\) −4.49995 + 7.79413i −0.233626 + 0.404651i
\(372\) −17.4153 + 6.44089i −0.902942 + 0.333945i
\(373\) −14.4658 25.0555i −0.749012 1.29733i −0.948297 0.317385i \(-0.897195\pi\)
0.199285 0.979942i \(-0.436138\pi\)
\(374\) −5.72336 9.91315i −0.295948 0.512597i
\(375\) −1.33257 1.10646i −0.0688136 0.0571374i
\(376\) 5.06777 8.77763i 0.261350 0.452672i
\(377\) −3.66702 −0.188861
\(378\) −27.4810 + 0.426588i −1.41347 + 0.0219413i
\(379\) −6.55238 −0.336573 −0.168287 0.985738i \(-0.553823\pi\)
−0.168287 + 0.985738i \(0.553823\pi\)
\(380\) 4.01366 6.95186i 0.205896 0.356623i
\(381\) −26.7029 22.1720i −1.36803 1.13591i
\(382\) 7.88022 + 13.6489i 0.403187 + 0.698340i
\(383\) 10.1929 + 17.6546i 0.520834 + 0.902110i 0.999707 + 0.0242260i \(0.00771214\pi\)
−0.478873 + 0.877884i \(0.658955\pi\)
\(384\) 15.3602 5.68083i 0.783847 0.289899i
\(385\) 4.62417 8.00929i 0.235669 0.408191i
\(386\) −43.4980 −2.21399
\(387\) −5.25562 1.85153i −0.267158 0.0941186i
\(388\) 16.9359 0.859789
\(389\) −2.18988 + 3.79299i −0.111031 + 0.192312i −0.916186 0.400752i \(-0.868749\pi\)
0.805155 + 0.593065i \(0.202082\pi\)
\(390\) 0.531057 3.10565i 0.0268911 0.157261i
\(391\) 5.52134 + 9.56324i 0.279226 + 0.483634i
\(392\) −0.914329 1.58366i −0.0461806 0.0799871i
\(393\) −0.688664 + 4.02734i −0.0347385 + 0.203153i
\(394\) 2.34196 4.05639i 0.117986 0.204358i
\(395\) −14.5712 −0.733155
\(396\) 2.29613 + 12.2777i 0.115385 + 0.616976i
\(397\) 17.0748 0.856959 0.428479 0.903552i \(-0.359049\pi\)
0.428479 + 0.903552i \(0.359049\pi\)
\(398\) −8.36601 + 14.4904i −0.419350 + 0.726336i
\(399\) −28.9665 + 10.7130i −1.45014 + 0.536321i
\(400\) 2.45225 + 4.24742i 0.122613 + 0.212371i
\(401\) 2.08563 + 3.61242i 0.104152 + 0.180396i 0.913391 0.407083i \(-0.133454\pi\)
−0.809240 + 0.587479i \(0.800121\pi\)
\(402\) −13.8022 11.4602i −0.688390 0.571584i
\(403\) −4.09477 + 7.09235i −0.203975 + 0.353295i
\(404\) −16.6601 −0.828870
\(405\) −7.01264 5.64118i −0.348461 0.280312i
\(406\) 19.3962 0.962617
\(407\) −13.9521 + 24.1657i −0.691580 + 1.19785i
\(408\) −3.31375 2.75148i −0.164055 0.136218i
\(409\) −6.39405 11.0748i −0.316165 0.547614i 0.663519 0.748159i \(-0.269062\pi\)
−0.979685 + 0.200545i \(0.935729\pi\)
\(410\) −1.88245 3.26050i −0.0929675 0.161024i
\(411\) −8.56502 + 3.16769i −0.422481 + 0.156251i
\(412\) 6.80441 11.7856i 0.335229 0.580634i
\(413\) 11.7388 0.577630
\(414\) −5.59939 29.9406i −0.275195 1.47150i
\(415\) −0.108095 −0.00530619
\(416\) −3.20390 + 5.54932i −0.157084 + 0.272078i
\(417\) −5.53925 + 32.3939i −0.271258 + 1.58633i
\(418\) 17.7399 + 30.7264i 0.867688 + 1.50288i
\(419\) −0.801447 1.38815i −0.0391532 0.0678154i 0.845785 0.533524i \(-0.179133\pi\)
−0.884938 + 0.465709i \(0.845799\pi\)
\(420\) −1.11120 + 6.49838i −0.0542212 + 0.317089i
\(421\) −10.2518 + 17.7566i −0.499642 + 0.865405i −1.00000 0.000413253i \(-0.999868\pi\)
0.500358 + 0.865819i \(0.333202\pi\)
\(422\) 18.4275 0.897035
\(423\) 22.8167 + 8.03823i 1.10939 + 0.390832i
\(424\) 3.89039 0.188934
\(425\) 0.989215 1.71337i 0.0479840 0.0831106i
\(426\) 2.11617 0.782645i 0.102529 0.0379193i
\(427\) 4.38677 + 7.59810i 0.212291 + 0.367698i
\(428\) 11.9560 + 20.7084i 0.577914 + 1.00098i
\(429\) 4.23838 + 3.51922i 0.204631 + 0.169910i
\(430\) −1.68938 + 2.92610i −0.0814693 + 0.141109i
\(431\) −34.2496 −1.64974 −0.824872 0.565319i \(-0.808753\pi\)
−0.824872 + 0.565319i \(0.808753\pi\)
\(432\) 13.0833 + 21.8698i 0.629470 + 1.05221i
\(433\) 9.63935 0.463238 0.231619 0.972807i \(-0.425598\pi\)
0.231619 + 0.972807i \(0.425598\pi\)
\(434\) 21.6588 37.5141i 1.03965 1.80073i
\(435\) 4.88656 + 4.05741i 0.234293 + 0.194538i
\(436\) −10.3501 17.9270i −0.495682 0.858546i
\(437\) −17.1137 29.6419i −0.818661 1.41796i
\(438\) 3.32636 1.23022i 0.158940 0.0587823i
\(439\) −2.92186 + 5.06080i −0.139453 + 0.241539i −0.927290 0.374345i \(-0.877868\pi\)
0.787837 + 0.615884i \(0.211201\pi\)
\(440\) −3.99779 −0.190587
\(441\) 3.31427 2.83996i 0.157822 0.135236i
\(442\) 3.59891 0.171183
\(443\) −18.1976 + 31.5192i −0.864595 + 1.49752i 0.00285335 + 0.999996i \(0.499092\pi\)
−0.867449 + 0.497527i \(0.834242\pi\)
\(444\) 3.35274 19.6070i 0.159114 0.930507i
\(445\) −1.16364 2.01548i −0.0551617 0.0955429i
\(446\) 12.7694 + 22.1172i 0.604648 + 1.04728i
\(447\) −4.34082 + 25.3853i −0.205314 + 1.20069i
\(448\) 2.68566 4.65170i 0.126886 0.219772i
\(449\) 27.6598 1.30535 0.652673 0.757639i \(-0.273647\pi\)
0.652673 + 0.757639i \(0.273647\pi\)
\(450\) −4.14395 + 3.55090i −0.195348 + 0.167391i
\(451\) 6.58284 0.309974
\(452\) −10.5000 + 18.1865i −0.493879 + 0.855423i
\(453\) 18.7800 6.94561i 0.882362 0.326333i
\(454\) −15.5389 26.9142i −0.729278 1.26315i
\(455\) 1.45386 + 2.51816i 0.0681581 + 0.118053i
\(456\) 10.2712 + 8.52838i 0.480992 + 0.399378i
\(457\) 7.91720 13.7130i 0.370351 0.641467i −0.619268 0.785179i \(-0.712571\pi\)
0.989620 + 0.143712i \(0.0459040\pi\)
\(458\) 28.6539 1.33891
\(459\) 5.00131 8.98164i 0.233441 0.419227i
\(460\) −7.30640 −0.340663
\(461\) 6.59008 11.4144i 0.306931 0.531620i −0.670759 0.741676i \(-0.734031\pi\)
0.977689 + 0.210056i \(0.0673646\pi\)
\(462\) −22.4184 18.6144i −1.04300 0.866022i
\(463\) 11.5886 + 20.0720i 0.538567 + 0.932826i 0.998982 + 0.0451216i \(0.0143675\pi\)
−0.460414 + 0.887704i \(0.652299\pi\)
\(464\) −8.99244 15.5754i −0.417464 0.723068i
\(465\) 13.3040 4.92036i 0.616958 0.228176i
\(466\) −21.2626 + 36.8279i −0.984970 + 1.70602i
\(467\) −20.2503 −0.937072 −0.468536 0.883444i \(-0.655218\pi\)
−0.468536 + 0.883444i \(0.655218\pi\)
\(468\) −3.70396 1.30489i −0.171216 0.0603184i
\(469\) 16.5562 0.764493
\(470\) 7.33428 12.7033i 0.338305 0.585962i
\(471\) −3.22962 + 18.8870i −0.148813 + 0.870266i
\(472\) −2.53718 4.39452i −0.116783 0.202274i
\(473\) −2.95385 5.11621i −0.135818 0.235244i
\(474\) −7.73812 + 45.2530i −0.355424 + 2.07854i
\(475\) −3.06613 + 5.31070i −0.140684 + 0.243672i
\(476\) −7.53050 −0.345160
\(477\) 1.70695 + 9.12725i 0.0781557 + 0.417908i
\(478\) 2.19943 0.100600
\(479\) −15.0014 + 25.9832i −0.685431 + 1.18720i 0.287870 + 0.957669i \(0.407053\pi\)
−0.973301 + 0.229532i \(0.926280\pi\)
\(480\) 10.4095 3.84987i 0.475128 0.175721i
\(481\) −4.38661 7.59784i −0.200012 0.346431i
\(482\) −22.3160 38.6525i −1.01647 1.76057i
\(483\) 21.6271 + 17.9574i 0.984066 + 0.817090i
\(484\) 0.578414 1.00184i 0.0262916 0.0455383i
\(485\) −12.9377 −0.587472
\(486\) −21.2436 + 18.7830i −0.963631 + 0.852016i
\(487\) −24.6047 −1.11494 −0.557472 0.830196i \(-0.688229\pi\)
−0.557472 + 0.830196i \(0.688229\pi\)
\(488\) 1.89627 3.28444i 0.0858402 0.148680i
\(489\) −13.0787 10.8596i −0.591441 0.491086i
\(490\) −1.32325 2.29194i −0.0597786 0.103539i
\(491\) 13.2045 + 22.8708i 0.595909 + 1.03214i 0.993418 + 0.114546i \(0.0365415\pi\)
−0.397509 + 0.917598i \(0.630125\pi\)
\(492\) −4.40123 + 1.62776i −0.198423 + 0.0733849i
\(493\) −3.62747 + 6.28296i −0.163373 + 0.282970i
\(494\) −11.1550 −0.501889
\(495\) −1.75407 9.37922i −0.0788395 0.421564i
\(496\) −40.1656 −1.80349
\(497\) −1.04112 + 1.80327i −0.0467006 + 0.0808879i
\(498\) −0.0574048 + 0.335706i −0.00257237 + 0.0150434i
\(499\) 12.4508 + 21.5654i 0.557374 + 0.965399i 0.997715 + 0.0675687i \(0.0215242\pi\)
−0.440341 + 0.897831i \(0.645142\pi\)
\(500\) 0.654515 + 1.13365i 0.0292708 + 0.0506985i
\(501\) 1.31510 7.69077i 0.0587543 0.343598i
\(502\) −0.415931 + 0.720413i −0.0185639 + 0.0321536i
\(503\) 32.4888 1.44861 0.724303 0.689482i \(-0.242162\pi\)
0.724303 + 0.689482i \(0.242162\pi\)
\(504\) −10.3414 3.64322i −0.460643 0.162282i
\(505\) 12.7270 0.566346
\(506\) 16.1467 27.9670i 0.717810 1.24328i
\(507\) −1.62451 + 0.600809i −0.0721470 + 0.0266829i
\(508\) 13.1156 + 22.7169i 0.581911 + 1.00790i
\(509\) −4.58649 7.94403i −0.203293 0.352113i 0.746295 0.665616i \(-0.231831\pi\)
−0.949587 + 0.313503i \(0.898498\pi\)
\(510\) −4.79580 3.98205i −0.212362 0.176328i
\(511\) −1.63652 + 2.83453i −0.0723952 + 0.125392i
\(512\) −19.0979 −0.844015
\(513\) −15.5019 + 27.8392i −0.684424 + 1.22913i
\(514\) −24.2323 −1.06884
\(515\) −5.19805 + 9.00329i −0.229054 + 0.396732i
\(516\) 3.24002 + 2.69026i 0.142634 + 0.118432i
\(517\) 12.8238 + 22.2115i 0.563991 + 0.976861i
\(518\) 23.2024 + 40.1877i 1.01946 + 1.76575i
\(519\) −37.6925 + 13.9402i −1.65452 + 0.611908i
\(520\) 0.628463 1.08853i 0.0275599 0.0477352i
\(521\) 12.2681 0.537477 0.268739 0.963213i \(-0.413393\pi\)
0.268739 + 0.963213i \(0.413393\pi\)
\(522\) 15.1959 13.0212i 0.665108 0.569924i
\(523\) 33.6980 1.47351 0.736756 0.676159i \(-0.236357\pi\)
0.736756 + 0.676159i \(0.236357\pi\)
\(524\) 1.54396 2.67422i 0.0674482 0.116824i
\(525\) 0.848876 4.96427i 0.0370480 0.216659i
\(526\) −21.0593 36.4759i −0.918231 1.59042i
\(527\) 8.10122 + 14.0317i 0.352895 + 0.611231i
\(528\) −4.55403 + 26.6322i −0.198189 + 1.15902i
\(529\) −4.07680 + 7.06122i −0.177252 + 0.307009i
\(530\) 5.63034 0.244566
\(531\) 9.19678 7.88061i 0.399106 0.341989i
\(532\) 23.3412 1.01197
\(533\) −1.03484 + 1.79239i −0.0448239 + 0.0776372i
\(534\) −6.87734 + 2.54352i −0.297612 + 0.110069i
\(535\) −9.13346 15.8196i −0.394874 0.683941i
\(536\) −3.57838 6.19793i −0.154562 0.267710i
\(537\) −10.1229 8.40525i −0.436835 0.362713i
\(538\) 14.7707 25.5836i 0.636811 1.10299i
\(539\) 4.62736 0.199315
\(540\) 3.49198 + 5.83714i 0.150271 + 0.251190i
\(541\) 0.0987165 0.00424415 0.00212208 0.999998i \(-0.499325\pi\)
0.00212208 + 0.999998i \(0.499325\pi\)
\(542\) 26.4548 45.8210i 1.13633 1.96818i
\(543\) −9.13189 7.58240i −0.391887 0.325392i
\(544\) 6.33869 + 10.9789i 0.271769 + 0.470718i
\(545\) 7.90672 + 13.6948i 0.338687 + 0.586623i
\(546\) 8.59262 3.17790i 0.367730 0.136002i
\(547\) −4.62140 + 8.00450i −0.197597 + 0.342248i −0.947749 0.319018i \(-0.896647\pi\)
0.750152 + 0.661265i \(0.229980\pi\)
\(548\) 6.90170 0.294826
\(549\) 8.53764 + 3.00777i 0.364378 + 0.128368i
\(550\) −5.78576 −0.246706
\(551\) 11.2436 19.4744i 0.478992 0.829638i
\(552\) 2.04812 11.9775i 0.0871736 0.509796i
\(553\) −21.1845 36.6926i −0.900856 1.56033i
\(554\) −12.8418 22.2426i −0.545594 0.944997i
\(555\) −2.56124 + 14.9783i −0.108719 + 0.635792i
\(556\) 12.4188 21.5100i 0.526675 0.912228i
\(557\) 11.9568 0.506628 0.253314 0.967384i \(-0.418479\pi\)
0.253314 + 0.967384i \(0.418479\pi\)
\(558\) −8.21573 43.9305i −0.347800 1.85973i
\(559\) 1.85741 0.0785601
\(560\) −7.13047 + 12.3503i −0.301317 + 0.521897i
\(561\) 10.2224 3.78066i 0.431590 0.159620i
\(562\) −19.2526 33.3465i −0.812122 1.40664i
\(563\) −18.9637 32.8461i −0.799225 1.38430i −0.920121 0.391633i \(-0.871910\pi\)
0.120896 0.992665i \(-0.461423\pi\)
\(564\) −14.0662 11.6795i −0.592294 0.491794i
\(565\) 8.02121 13.8931i 0.337455 0.584489i
\(566\) −31.2871 −1.31509
\(567\) 4.00999 25.8605i 0.168404 1.08604i
\(568\) 0.900093 0.0377670
\(569\) −9.17271 + 15.8876i −0.384540 + 0.666043i −0.991705 0.128533i \(-0.958973\pi\)
0.607165 + 0.794575i \(0.292307\pi\)
\(570\) 14.8649 + 12.3426i 0.622621 + 0.516976i
\(571\) 17.7011 + 30.6592i 0.740768 + 1.28305i 0.952146 + 0.305643i \(0.0988715\pi\)
−0.211378 + 0.977404i \(0.567795\pi\)
\(572\) −2.08176 3.60571i −0.0870426 0.150762i
\(573\) −14.0747 + 5.20540i −0.587980 + 0.217459i
\(574\) 5.47364 9.48063i 0.228465 0.395714i
\(575\) 5.58154 0.232766
\(576\) −1.01874 5.44733i −0.0424475 0.226972i
\(577\) 2.55762 0.106475 0.0532376 0.998582i \(-0.483046\pi\)
0.0532376 + 0.998582i \(0.483046\pi\)
\(578\) −11.9020 + 20.6149i −0.495059 + 0.857468i
\(579\) 6.98087 40.8245i 0.290115 1.69661i
\(580\) −2.40012 4.15713i −0.0996595 0.172615i
\(581\) −0.157156 0.272202i −0.00651992 0.0112928i
\(582\) −6.87067 + 40.1801i −0.284799 + 1.66552i
\(583\) −4.92225 + 8.52560i −0.203859 + 0.353094i
\(584\) 1.41484 0.0585464
\(585\) 2.82954 + 0.996835i 0.116987 + 0.0412140i
\(586\) −24.1446 −0.997402
\(587\) −14.1759 + 24.5535i −0.585104 + 1.01343i 0.409759 + 0.912194i \(0.365613\pi\)
−0.994862 + 0.101236i \(0.967720\pi\)
\(588\) −3.09382 + 1.14422i −0.127587 + 0.0471868i
\(589\) −25.1102 43.4922i −1.03465 1.79206i
\(590\) −3.67191 6.35993i −0.151170 0.261834i
\(591\) 3.43123 + 2.84902i 0.141142 + 0.117193i
\(592\) 21.5141 37.2636i 0.884226 1.53152i
\(593\) −13.1857 −0.541470 −0.270735 0.962654i \(-0.587267\pi\)
−0.270735 + 0.962654i \(0.587267\pi\)
\(594\) −30.0601 + 0.466622i −1.23338 + 0.0191457i
\(595\) 5.75273 0.235839
\(596\) 9.73196 16.8562i 0.398637 0.690459i
\(597\) −12.2571 10.1773i −0.501650 0.416531i
\(598\) 5.07662 + 8.79296i 0.207598 + 0.359571i
\(599\) 11.4054 + 19.7548i 0.466013 + 0.807159i 0.999247 0.0388095i \(-0.0123565\pi\)
−0.533233 + 0.845968i \(0.679023\pi\)
\(600\) −2.04189 + 0.755172i −0.0833596 + 0.0308298i
\(601\) 21.1641 36.6573i 0.863302 1.49528i −0.00542157 0.999985i \(-0.501726\pi\)
0.868723 0.495297i \(-0.164941\pi\)
\(602\) −9.82452 −0.400418
\(603\) 12.9709 11.1146i 0.528217 0.452623i
\(604\) −15.1329 −0.615751
\(605\) −0.441865 + 0.765332i −0.0179644 + 0.0311152i
\(606\) 6.75878 39.5257i 0.274557 1.60562i
\(607\) 10.9919 + 19.0384i 0.446146 + 0.772747i 0.998131 0.0611069i \(-0.0194630\pi\)
−0.551986 + 0.833854i \(0.686130\pi\)
\(608\) −19.6472 34.0299i −0.796798 1.38009i
\(609\) −3.11284 + 18.2041i −0.126139 + 0.737666i
\(610\) 2.74436 4.75338i 0.111116 0.192459i
\(611\) −8.06375 −0.326224
\(612\) −5.89976 + 5.05544i −0.238484 + 0.204354i
\(613\) −28.1827 −1.13829 −0.569145 0.822237i \(-0.692726\pi\)
−0.569145 + 0.822237i \(0.692726\pi\)
\(614\) 28.2202 48.8788i 1.13887 1.97259i
\(615\) 3.36221 1.24348i 0.135577 0.0501420i
\(616\) −5.81223 10.0671i −0.234182 0.405614i
\(617\) 8.42902 + 14.5995i 0.339339 + 0.587753i 0.984309 0.176455i \(-0.0564632\pi\)
−0.644969 + 0.764209i \(0.723130\pi\)
\(618\) 25.2006 + 20.9246i 1.01372 + 0.841711i
\(619\) −1.14190 + 1.97782i −0.0458967 + 0.0794953i −0.888061 0.459725i \(-0.847948\pi\)
0.842164 + 0.539221i \(0.181281\pi\)
\(620\) −10.7204 −0.430540
\(621\) 28.9990 0.450152i 1.16369 0.0180640i
\(622\) −46.1406 −1.85007
\(623\) 3.38354 5.86046i 0.135559 0.234795i
\(624\) −6.53559 5.42664i −0.261633 0.217239i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −2.82111 4.88631i −0.112754 0.195296i
\(627\) −31.6850 + 11.7184i −1.26538 + 0.467987i
\(628\) 7.24069 12.5412i 0.288935 0.500450i
\(629\) −17.3572 −0.692077
\(630\) −14.9665 5.27262i −0.596280 0.210066i
\(631\) −37.7800 −1.50400 −0.752000 0.659163i \(-0.770911\pi\)
−0.752000 + 0.659163i \(0.770911\pi\)
\(632\) −9.15743 + 15.8611i −0.364263 + 0.630922i
\(633\) −2.95737 + 17.2949i −0.117545 + 0.687410i
\(634\) 3.93620 + 6.81770i 0.156327 + 0.270766i
\(635\) −10.0193 17.3540i −0.397605 0.688672i
\(636\) 1.18284 6.91729i 0.0469025 0.274288i
\(637\) −0.727433 + 1.25995i −0.0288220 + 0.0499211i
\(638\) 21.2165 0.839969
\(639\) 0.394924 + 2.11171i 0.0156230 + 0.0835379i
\(640\) 9.45530 0.373753
\(641\) 0.335000 0.580236i 0.0132317 0.0229180i −0.859334 0.511415i \(-0.829121\pi\)
0.872565 + 0.488497i \(0.162455\pi\)
\(642\) −53.9806 + 19.9642i −2.13044 + 0.787925i
\(643\) −15.8896 27.5216i −0.626625 1.08535i −0.988224 0.153013i \(-0.951102\pi\)
0.361599 0.932334i \(-0.382231\pi\)
\(644\) −10.6225 18.3987i −0.418585 0.725011i
\(645\) −2.47513 2.05515i −0.0974581 0.0809215i
\(646\) −11.0347 + 19.1127i −0.434156 + 0.751980i
\(647\) 2.41571 0.0949715 0.0474857 0.998872i \(-0.484879\pi\)
0.0474857 + 0.998872i \(0.484879\pi\)
\(648\) −10.5478 + 4.08820i −0.414355 + 0.160600i
\(649\) 12.8405 0.504033
\(650\) 0.909537 1.57536i 0.0356750 0.0617909i
\(651\) 31.7324 + 26.3481i 1.24369 + 1.03266i
\(652\) 6.42385 + 11.1264i 0.251577 + 0.435745i
\(653\) −9.23529 15.9960i −0.361405 0.625972i 0.626787 0.779190i \(-0.284369\pi\)
−0.988192 + 0.153219i \(0.951036\pi\)
\(654\) 46.7303 17.2828i 1.82730 0.675810i
\(655\) −1.17947 + 2.04290i −0.0460857 + 0.0798227i
\(656\) −10.1507 −0.396320
\(657\) 0.620773 + 3.31935i 0.0242187 + 0.129500i
\(658\) 42.6521 1.66275
\(659\) −23.3833 + 40.5010i −0.910883 + 1.57770i −0.0980634 + 0.995180i \(0.531265\pi\)
−0.812820 + 0.582515i \(0.802069\pi\)
\(660\) −1.21549 + 7.10824i −0.0473128 + 0.276688i
\(661\) 9.09998 + 15.7616i 0.353948 + 0.613056i 0.986937 0.161104i \(-0.0515056\pi\)
−0.632989 + 0.774161i \(0.718172\pi\)
\(662\) 1.64516 + 2.84951i 0.0639411 + 0.110749i
\(663\) −0.577579 + 3.37771i −0.0224313 + 0.131180i
\(664\) −0.0679339 + 0.117665i −0.00263634 + 0.00456628i
\(665\) −17.8309 −0.691454
\(666\) 45.1571 + 15.9086i 1.74980 + 0.616447i
\(667\) −20.4676 −0.792509
\(668\) −2.94840 + 5.10679i −0.114077 + 0.197587i
\(669\) −22.8072 + 8.43503i −0.881777 + 0.326117i
\(670\) −5.17878 8.96990i −0.200074 0.346538i
\(671\) 4.79846 + 8.31117i 0.185242 + 0.320849i
\(672\) 24.8286 + 20.6157i 0.957784 + 0.795268i
\(673\) −24.8617 + 43.0616i −0.958346 + 1.65990i −0.231829 + 0.972757i \(0.574471\pi\)
−0.726517 + 0.687148i \(0.758862\pi\)
\(674\) 28.6562 1.10380
\(675\) −2.66761 4.45913i −0.102676 0.171632i
\(676\) 1.30903 0.0503473
\(677\) −8.76931 + 15.1889i −0.337032 + 0.583757i −0.983873 0.178868i \(-0.942756\pi\)
0.646841 + 0.762625i \(0.276090\pi\)
\(678\) −38.8875 32.2891i −1.49347 1.24006i
\(679\) −18.8097 32.5793i −0.721849 1.25028i
\(680\) −1.24337 2.15358i −0.0476810 0.0825859i
\(681\) 27.7538 10.2645i 1.06353 0.393336i
\(682\) 23.6914 41.0347i 0.907190 1.57130i
\(683\) 0.869524 0.0332714 0.0166357 0.999862i \(-0.494704\pi\)
0.0166357 + 0.999862i \(0.494704\pi\)
\(684\) 18.2867 15.6697i 0.699209 0.599144i
\(685\) −5.27238 −0.201447
\(686\) −14.6651 + 25.4007i −0.559917 + 0.969805i
\(687\) −4.59858 + 26.8927i −0.175447 + 1.02602i
\(688\) 4.55483 + 7.88920i 0.173651 + 0.300773i
\(689\) −1.54758 2.68049i −0.0589582 0.102119i
\(690\) 2.96412 17.3343i 0.112842 0.659906i
\(691\) −10.8101 + 18.7237i −0.411236 + 0.712282i −0.995025 0.0996232i \(-0.968236\pi\)
0.583789 + 0.811906i \(0.301570\pi\)
\(692\) 30.3727 1.15460
\(693\) 21.0682 18.0531i 0.800316 0.685781i
\(694\) −46.1991 −1.75369
\(695\) −9.48703 + 16.4320i −0.359864 + 0.623302i
\(696\) 7.48763 2.76923i 0.283818 0.104967i
\(697\) 2.04736 + 3.54612i 0.0775491 + 0.134319i
\(698\) −23.8381 41.2888i −0.902286 1.56280i
\(699\) −31.1520 25.8662i −1.17828 0.978348i
\(700\) −1.90315 + 3.29635i −0.0719323 + 0.124590i
\(701\) 20.9223 0.790225 0.395113 0.918633i \(-0.370706\pi\)
0.395113 + 0.918633i \(0.370706\pi\)
\(702\) 4.59847 8.25820i 0.173558 0.311686i
\(703\) 53.7997 2.02910
\(704\) 2.93770 5.08825i 0.110719 0.191771i
\(705\) 10.7455 + 8.92222i 0.404699 + 0.336030i
\(706\) 28.4025 + 49.1946i 1.06894 + 1.85146i
\(707\) 18.5034 + 32.0488i 0.695891 + 1.20532i
\(708\) −8.58505 + 3.17510i −0.322646 + 0.119328i
\(709\) 6.56161 11.3650i 0.246427 0.426823i −0.716105 0.697992i \(-0.754077\pi\)
0.962532 + 0.271169i \(0.0874102\pi\)
\(710\) 1.30265 0.0488876
\(711\) −41.2298 14.5250i −1.54624 0.544732i
\(712\) −2.92521 −0.109627
\(713\) −22.8551 + 39.5863i −0.855932 + 1.48252i
\(714\) 3.05503 17.8660i 0.114332 0.668617i
\(715\) 1.59030 + 2.75449i 0.0594740 + 0.103012i
\(716\) 4.97204 + 8.61182i 0.185814 + 0.321839i
\(717\) −0.352981 + 2.06425i −0.0131823 + 0.0770908i
\(718\) −14.2555 + 24.6912i −0.532010 + 0.921468i
\(719\) 32.1004 1.19714 0.598571 0.801069i \(-0.295735\pi\)
0.598571 + 0.801069i \(0.295735\pi\)
\(720\) 2.70477 + 14.4628i 0.100801 + 0.538995i
\(721\) −30.2290 −1.12579
\(722\) 16.9216 29.3092i 0.629759 1.09077i
\(723\) 39.8583 14.7412i 1.48234 0.548231i
\(724\) 4.48529 + 7.76874i 0.166694 + 0.288723i
\(725\) 1.83351 + 3.17573i 0.0680948 + 0.117944i
\(726\) 2.14220 + 1.77871i 0.0795045 + 0.0660142i
\(727\) 14.3942 24.9314i 0.533851 0.924656i −0.465368 0.885118i \(-0.654078\pi\)
0.999218 0.0395387i \(-0.0125888\pi\)
\(728\) 3.65479 0.135456
\(729\) −14.2193 22.9524i −0.526639 0.850089i
\(730\) 2.04761 0.0757854
\(731\) 1.83738 3.18243i 0.0679578 0.117706i
\(732\) −5.26334 4.37026i −0.194538 0.161529i
\(733\) −11.3369 19.6362i −0.418740 0.725278i 0.577073 0.816692i \(-0.304195\pi\)
−0.995813 + 0.0914140i \(0.970861\pi\)
\(734\) 28.5980 + 49.5331i 1.05557 + 1.82830i
\(735\) 2.36344 0.874097i 0.0871769 0.0322416i
\(736\) −17.8827 + 30.9737i −0.659165 + 1.14171i
\(737\) 18.1099 0.667088
\(738\) −2.07630 11.1022i −0.0764295 0.408678i
\(739\) −0.143434 −0.00527631 −0.00263816 0.999997i \(-0.500840\pi\)
−0.00263816 + 0.999997i \(0.500840\pi\)
\(740\) 5.74221 9.94580i 0.211088 0.365615i
\(741\) 1.79024 10.4694i 0.0657662 0.384604i
\(742\) 8.18573 + 14.1781i 0.300508 + 0.520495i
\(743\) 18.7987 + 32.5603i 0.689658 + 1.19452i 0.971948 + 0.235194i \(0.0755726\pi\)
−0.282290 + 0.959329i \(0.591094\pi\)
\(744\) 3.00511 17.5740i 0.110173 0.644295i
\(745\) −7.43448 + 12.8769i −0.272378 + 0.471773i
\(746\) −52.6288 −1.92688
\(747\) −0.305860 0.107753i −0.0111908 0.00394248i
\(748\) −8.23721 −0.301182
\(749\) 26.5576 45.9991i 0.970393 1.68077i
\(750\) −2.95510 + 1.09292i −0.107905 + 0.0399077i
\(751\) 1.99105 + 3.44859i 0.0726543 + 0.125841i 0.900064 0.435758i \(-0.143520\pi\)
−0.827410 + 0.561599i \(0.810186\pi\)
\(752\) −19.7743 34.2501i −0.721096 1.24897i
\(753\) −0.609384 0.505984i −0.0222072 0.0184391i
\(754\) −3.33529 + 5.77689i −0.121464 + 0.210382i
\(755\) 11.5604 0.420727
\(756\) −9.62202 + 17.2798i −0.349949 + 0.628459i
\(757\) −14.4846 −0.526450 −0.263225 0.964734i \(-0.584786\pi\)
−0.263225 + 0.964734i \(0.584786\pi\)
\(758\) −5.95964 + 10.3224i −0.216464 + 0.374926i
\(759\) 23.6567 + 19.6427i 0.858684 + 0.712984i
\(760\) 3.85390 + 6.67515i 0.139796 + 0.242133i
\(761\) −11.0363 19.1154i −0.400064 0.692931i 0.593669 0.804709i \(-0.297679\pi\)
−0.993733 + 0.111778i \(0.964345\pi\)
\(762\) −59.2163 + 21.9006i −2.14518 + 0.793374i
\(763\) −22.9906 + 39.8208i −0.832315 + 1.44161i
\(764\) 11.3414 0.410318
\(765\) 4.50697 3.86197i 0.162950 0.139630i
\(766\) 37.0833 1.33988
\(767\) −2.01856 + 3.49624i −0.0728859 + 0.126242i
\(768\) 6.09987 35.6724i 0.220110 1.28722i
\(769\) −10.5490 18.2714i −0.380408 0.658885i 0.610713 0.791852i \(-0.290883\pi\)
−0.991120 + 0.132967i \(0.957550\pi\)
\(770\) −8.41170 14.5695i −0.303137 0.525048i
\(771\) 3.88898 22.7429i 0.140058 0.819067i
\(772\) −15.6509 + 27.1081i −0.563287 + 0.975641i
\(773\) 50.8006 1.82717 0.913585 0.406647i \(-0.133302\pi\)
0.913585 + 0.406647i \(0.133302\pi\)
\(774\) −7.69702 + 6.59549i −0.276664 + 0.237070i
\(775\) 8.18955 0.294177
\(776\) −8.13088 + 14.0831i −0.291882 + 0.505554i
\(777\) −41.4414 + 15.3267i −1.48670 + 0.549843i
\(778\) 3.98356 + 6.89973i 0.142818 + 0.247367i
\(779\) −6.34591 10.9914i −0.227366 0.393809i
\(780\) −1.74437 1.44839i −0.0624586 0.0518607i
\(781\) −1.13883 + 1.97251i −0.0407504 + 0.0705818i
\(782\) 20.0875 0.718326
\(783\) 9.78216 + 16.3517i 0.349586 + 0.584363i
\(784\) −7.13539 −0.254835
\(785\) −5.53134 + 9.58056i −0.197422 + 0.341945i
\(786\) 5.71817 + 4.74792i 0.203960 + 0.169353i
\(787\) 14.5258 + 25.1595i 0.517789 + 0.896838i 0.999786 + 0.0206647i \(0.00657826\pi\)
−0.481997 + 0.876173i \(0.660088\pi\)
\(788\) −1.68531 2.91904i −0.0600365 0.103986i
\(789\) 37.6137 13.9111i 1.33908 0.495248i
\(790\) −13.2530 + 22.9549i −0.471521 + 0.816699i
\(791\) 46.6470 1.65857
\(792\) −11.3119 3.98513i −0.401951 0.141606i
\(793\) −3.01732 −0.107148
\(794\) 15.5301 26.8990i 0.551144 0.954610i
\(795\) −0.903597 + 5.28428i −0.0320473 + 0.187414i
\(796\) 6.02029 + 10.4275i 0.213384 + 0.369591i
\(797\) 5.94043 + 10.2891i 0.210421 + 0.364459i 0.951846 0.306576i \(-0.0991833\pi\)
−0.741426 + 0.671035i \(0.765850\pi\)
\(798\) −9.46925 + 55.3767i −0.335208 + 1.96031i
\(799\) −7.97678 + 13.8162i −0.282198 + 0.488782i
\(800\) 6.40780 0.226550
\(801\) −1.28346 6.86285i −0.0453490 0.242487i
\(802\) 7.58784 0.267936
\(803\) −1.79010 + 3.10054i −0.0631712 + 0.109416i
\(804\) −12.1082 + 4.47809i −0.427022 + 0.157930i
\(805\) 8.11479 + 14.0552i 0.286009 + 0.495382i
\(806\) 7.44869 + 12.9015i 0.262369 + 0.454437i
\(807\) 21.6407 + 17.9687i 0.761789 + 0.632529i
\(808\) 7.99847 13.8538i 0.281385 0.487373i
\(809\) −3.96416 −0.139372 −0.0696862 0.997569i \(-0.522200\pi\)
−0.0696862 + 0.997569i \(0.522200\pi\)
\(810\) −15.2652 + 5.91661i −0.536363 + 0.207888i
\(811\) −34.5850 −1.21444 −0.607222 0.794532i \(-0.707716\pi\)
−0.607222 + 0.794532i \(0.707716\pi\)
\(812\) 6.97888 12.0878i 0.244911 0.424198i
\(813\) 38.7591 + 32.1825i 1.35934 + 1.12869i
\(814\) 25.3799 + 43.9593i 0.889565 + 1.54077i
\(815\) −4.90734 8.49976i −0.171897 0.297734i
\(816\) −15.7629 + 5.82978i −0.551813 + 0.204083i
\(817\) −5.69507 + 9.86414i −0.199245 + 0.345103i
\(818\) −23.2625 −0.813354
\(819\) 1.60358 + 8.57452i 0.0560335 + 0.299618i
\(820\) −2.70927 −0.0946119
\(821\) −9.97836 + 17.2830i −0.348247 + 0.603182i −0.985938 0.167111i \(-0.946556\pi\)
0.637691 + 0.770292i \(0.279890\pi\)
\(822\) −2.79993 + 16.3742i −0.0976589 + 0.571115i
\(823\) −14.6620 25.3953i −0.511086 0.885226i −0.999917 0.0128482i \(-0.995910\pi\)
0.488832 0.872378i \(-0.337423\pi\)
\(824\) 6.53356 + 11.3165i 0.227607 + 0.394228i
\(825\) 0.928541 5.43016i 0.0323276 0.189054i
\(826\) 10.6769 18.4929i 0.371497 0.643451i
\(827\) 8.79948 0.305988 0.152994 0.988227i \(-0.451109\pi\)
0.152994 + 0.988227i \(0.451109\pi\)
\(828\) −20.6738 7.28328i −0.718464 0.253111i
\(829\) 19.9330 0.692301 0.346151 0.938179i \(-0.387489\pi\)
0.346151 + 0.938179i \(0.387489\pi\)
\(830\) −0.0983167 + 0.170289i −0.00341262 + 0.00591083i
\(831\) 22.9364 8.48283i 0.795656 0.294266i
\(832\) 0.923629 + 1.59977i 0.0320211 + 0.0554622i
\(833\) 1.43917 + 2.49272i 0.0498645 + 0.0863678i
\(834\) 45.9940 + 38.1898i 1.59264 + 1.32240i
\(835\) 2.25236 3.90120i 0.0779460 0.135007i
\(836\) 25.5318 0.883035
\(837\) 42.5490 0.660487i 1.47071 0.0228298i
\(838\) −2.91578 −0.100724
\(839\) −12.0692 + 20.9044i −0.416674 + 0.721701i −0.995603 0.0936773i \(-0.970138\pi\)
0.578928 + 0.815379i \(0.303471\pi\)
\(840\) −4.87027 4.04389i −0.168040 0.139527i
\(841\) 7.77650 + 13.4693i 0.268155 + 0.464458i
\(842\) 18.6488 + 32.3006i 0.642679 + 1.11315i
\(843\) 34.3868 12.7176i 1.18434 0.438018i
\(844\) 6.63032 11.4841i 0.228225 0.395298i
\(845\) −1.00000 −0.0344010
\(846\) 33.4158 28.6336i 1.14886 0.984444i
\(847\) −2.56964 −0.0882940
\(848\) 7.59012 13.1465i 0.260646 0.451452i
\(849\) 5.02118 29.3641i 0.172326 1.00777i
\(850\) −1.79945 3.11675i −0.0617208 0.106904i
\(851\) −24.4841 42.4076i −0.839303 1.45371i
\(852\) 0.273664 1.60040i 0.00937559 0.0548289i
\(853\) −6.23323 + 10.7963i −0.213422 + 0.369657i −0.952783 0.303651i \(-0.901794\pi\)
0.739361 + 0.673309i \(0.235127\pi\)
\(854\) 15.9597 0.546130
\(855\) −13.9696 + 11.9704i −0.477752 + 0.409380i
\(856\) −22.9601 −0.784762
\(857\) −6.62425 + 11.4735i −0.226280 + 0.391929i −0.956703 0.291067i \(-0.905990\pi\)
0.730423 + 0.682996i \(0.239323\pi\)
\(858\) 9.39902 3.47614i 0.320877 0.118673i
\(859\) −3.05398 5.28965i −0.104200 0.180480i 0.809211 0.587518i \(-0.199895\pi\)
−0.913411 + 0.407038i \(0.866562\pi\)
\(860\) 1.21570 + 2.10566i 0.0414551 + 0.0718024i
\(861\) 8.01948 + 6.65874i 0.273303 + 0.226929i
\(862\) −31.1513 + 53.9556i −1.06102 + 1.83773i
\(863\) 38.1347 1.29812 0.649061 0.760737i \(-0.275162\pi\)
0.649061 + 0.760737i \(0.275162\pi\)
\(864\) 33.2919 0.516789i 1.13261 0.0175815i
\(865\) −23.2024 −0.788906
\(866\) 8.76735 15.1855i 0.297927 0.516024i
\(867\) −17.4378 14.4789i −0.592218 0.491731i
\(868\) −15.5859 26.9956i −0.529021 0.916291i
\(869\) −23.1726 40.1361i −0.786076 1.36152i
\(870\) 10.8364 4.00774i 0.367389 0.135875i
\(871\) −2.84693 + 4.93103i −0.0964646 + 0.167082i
\(872\) 19.8763 0.673097
\(873\) −36.6079 12.8968i −1.23899 0.436490i
\(874\) −62.2623 −2.10605
\(875\) 1.45386 2.51816i 0.0491495 0.0851295i
\(876\) 0.430167 2.51564i 0.0145340 0.0849957i
\(877\) −13.6611 23.6617i −0.461302 0.798999i 0.537724 0.843121i \(-0.319284\pi\)
−0.999026 + 0.0441220i \(0.985951\pi\)
\(878\) 5.31507 + 9.20597i 0.179375 + 0.310687i
\(879\) 3.87489 22.6606i 0.130697 0.764323i
\(880\) −7.79965 + 13.5094i −0.262926 + 0.455401i
\(881\) −22.5860 −0.760943 −0.380471 0.924793i \(-0.624238\pi\)
−0.380471 + 0.924793i \(0.624238\pi\)
\(882\) −1.45952 7.80422i −0.0491445 0.262782i
\(883\) −50.3248 −1.69356 −0.846782 0.531939i \(-0.821463\pi\)
−0.846782 + 0.531939i \(0.821463\pi\)
\(884\) 1.29491 2.24285i 0.0435526 0.0754353i
\(885\) 6.55833 2.42554i 0.220456 0.0815335i
\(886\) 33.1028 + 57.3358i 1.11211 + 1.92623i
\(887\) −3.58927 6.21680i −0.120516 0.208740i 0.799455 0.600725i \(-0.205122\pi\)
−0.919971 + 0.391986i \(0.871788\pi\)
\(888\) 14.6946 + 12.2013i 0.493120 + 0.409448i
\(889\) 29.1335 50.4606i 0.977105 1.69240i
\(890\) −4.23349 −0.141907
\(891\) 4.38632 28.2874i 0.146947 0.947664i
\(892\) 18.3781 0.615343
\(893\) 24.7245 42.8241i 0.827375 1.43306i
\(894\) 36.0430 + 29.9273i 1.20546 + 1.00092i
\(895\) −3.79826 6.57878i −0.126962 0.219904i
\(896\) 13.7467 + 23.8100i 0.459245 + 0.795436i
\(897\) −9.06726 + 3.35344i −0.302747 + 0.111968i
\(898\) 25.1576 43.5743i 0.839520 1.45409i
\(899\) −30.0312 −1.00160
\(900\) 0.721914 + 3.86017i 0.0240638 + 0.128672i
\(901\) −6.12357 −0.204006
\(902\) 5.98733 10.3704i 0.199356 0.345295i
\(903\) 1.57671 9.22069i 0.0524696 0.306845i
\(904\) −10.0821 17.4626i −0.335324 0.580799i
\(905\) −3.42642 5.93473i −0.113898 0.197277i
\(906\) 6.13924 35.9026i 0.203963 1.19279i
\(907\) −3.49203 + 6.04837i −0.115951 + 0.200833i −0.918159 0.396211i \(-0.870325\pi\)
0.802209 + 0.597044i \(0.203658\pi\)
\(908\) −22.3641 −0.742177
\(909\) 36.0117 + 12.6868i 1.19443 + 0.420793i
\(910\) 5.28937 0.175341
\(911\) 19.2461 33.3352i 0.637652 1.10445i −0.348295 0.937385i \(-0.613239\pi\)
0.985947 0.167060i \(-0.0534275\pi\)
\(912\) 48.8582 18.0698i 1.61786 0.598350i
\(913\) −0.171904 0.297747i −0.00568921 0.00985399i
\(914\) −14.4020 24.9450i −0.476375 0.825106i
\(915\) 4.02079 + 3.33855i 0.132923 + 0.110369i
\(916\) 10.3099 17.8572i 0.340647 0.590018i
\(917\) −6.85914 −0.226509
\(918\) −9.60048 16.0480i −0.316863 0.529663i
\(919\) 41.3551 1.36418 0.682089 0.731269i \(-0.261072\pi\)
0.682089 + 0.731269i \(0.261072\pi\)
\(920\) 3.50779 6.07567i 0.115648 0.200309i
\(921\) 41.3457 + 34.3302i 1.36239 + 1.13122i
\(922\) −11.9879 20.7636i −0.394799 0.683812i
\(923\) −0.358053 0.620167i −0.0117855 0.0204130i
\(924\) −19.6669 + 7.27361i −0.646993 + 0.239284i
\(925\) −4.38661 + 7.59784i −0.144231 + 0.249815i
\(926\) 42.1610 1.38550
\(927\) −23.6829 + 20.2936i −0.777849 + 0.666530i
\(928\) −23.4975 −0.771343
\(929\) 4.08864 7.08174i 0.134144 0.232344i −0.791126 0.611653i \(-0.790505\pi\)
0.925270 + 0.379309i \(0.123838\pi\)
\(930\) 4.34912 25.4339i 0.142613 0.834009i
\(931\) −4.46081 7.72636i −0.146197 0.253221i
\(932\) 15.3008 + 26.5018i 0.501196 + 0.868097i
\(933\) 7.40498 43.3047i 0.242428 1.41773i
\(934\) −18.4184 + 31.9016i −0.602668 + 1.04385i
\(935\) 6.29261 0.205790
\(936\) 2.86335 2.45357i 0.0935914 0.0801974i
\(937\) −15.3840 −0.502573 −0.251286 0.967913i \(-0.580854\pi\)
−0.251286 + 0.967913i \(0.580854\pi\)
\(938\) 15.0585 26.0820i 0.491676 0.851608i
\(939\) 5.03874 1.86353i 0.164433 0.0608140i
\(940\) −5.27785 9.14150i −0.172144 0.298163i
\(941\) 12.2527 + 21.2223i 0.399427 + 0.691828i 0.993655 0.112468i \(-0.0358757\pi\)
−0.594228 + 0.804297i \(0.702542\pi\)
\(942\) 26.8164 + 22.2662i 0.873726 + 0.725473i
\(943\) −5.77600 + 10.0043i −0.188092 + 0.325785i
\(944\) −19.8000 −0.644436
\(945\) 7.35049 13.2004i 0.239112 0.429410i
\(946\) −10.7465 −0.349400
\(947\) −4.98496 + 8.63420i −0.161989 + 0.280574i −0.935582 0.353109i \(-0.885124\pi\)
0.773593 + 0.633683i \(0.218458\pi\)
\(948\) 25.4176 + 21.1047i 0.825525 + 0.685450i
\(949\) −0.562817 0.974827i −0.0182698 0.0316442i
\(950\) 5.57752 + 9.66055i 0.180959 + 0.313430i
\(951\) −7.03039 + 2.60012i −0.227976 + 0.0843147i
\(952\) 3.61537 6.26201i 0.117175 0.202953i
\(953\) 37.3529 1.20998 0.604989 0.796234i \(-0.293178\pi\)
0.604989 + 0.796234i \(0.293178\pi\)
\(954\) 15.9313 + 5.61251i 0.515794 + 0.181712i
\(955\) −8.66399 −0.280360
\(956\) 0.791370 1.37069i 0.0255947 0.0443314i
\(957\) −3.40497 + 19.9125i −0.110067 + 0.643679i
\(958\) 27.2886 + 47.2653i 0.881656 + 1.52707i
\(959\) −7.66531 13.2767i −0.247526 0.428727i
\(960\) 0.539285 3.15377i 0.0174054 0.101787i
\(961\) −18.0343 + 31.2364i −0.581752 + 1.00762i
\(962\) −15.9591 −0.514543
\(963\) −10.0740 53.8668i −0.324630 1.73583i
\(964\) −32.1178 −1.03445
\(965\) 11.9561 20.7085i 0.384880 0.666631i
\(966\) 47.9601 17.7376i 1.54309 0.570697i
\(967\) −5.72260 9.91183i −0.184026 0.318743i 0.759222 0.650832i \(-0.225580\pi\)
−0.943248 + 0.332089i \(0.892247\pi\)
\(968\) 0.555391 + 0.961965i 0.0178509 + 0.0309187i
\(969\) −16.1671 13.4239i −0.519362 0.431237i
\(970\) −11.7673 + 20.3816i −0.377827 + 0.654415i
\(971\) −10.3317 −0.331559 −0.165780 0.986163i \(-0.553014\pi\)
−0.165780 + 0.986163i \(0.553014\pi\)
\(972\) 4.06205 + 19.9974i 0.130290 + 0.641416i
\(973\) −55.1714 −1.76871
\(974\) −22.3789 + 38.7613i −0.717065 + 1.24199i
\(975\) 1.33257 + 1.10646i 0.0426764 + 0.0354351i
\(976\) −7.39922 12.8158i −0.236843 0.410225i
\(977\) 18.0603 + 31.2814i 0.577800 + 1.00078i 0.995731 + 0.0923007i \(0.0294221\pi\)
−0.417931 + 0.908479i \(0.637245\pi\)
\(978\) −29.0034 + 10.7266i −0.927425 + 0.343000i
\(979\) 3.70108 6.41045i 0.118287 0.204879i
\(980\) −1.90446 −0.0608359
\(981\) 8.72092 + 46.6319i 0.278438 + 1.48884i
\(982\) 48.0398 1.53301
\(983\) 9.93766 17.2125i 0.316962 0.548994i −0.662891 0.748716i \(-0.730671\pi\)
0.979853 + 0.199722i \(0.0640039\pi\)
\(984\) 0.759457 4.44135i 0.0242106 0.141585i
\(985\) 1.28745 + 2.22992i 0.0410214 + 0.0710512i
\(986\) 6.59863 + 11.4292i 0.210143 + 0.363979i
\(987\) −6.84512 + 40.0307i −0.217883 + 1.27419i
\(988\) −4.01366 + 6.95186i −0.127692 + 0.221168i
\(989\) 10.3672 0.329658
\(990\) −16.3711 5.76745i −0.520307 0.183302i
\(991\) 37.6190 1.19501 0.597504 0.801866i \(-0.296159\pi\)
0.597504 + 0.801866i \(0.296159\pi\)
\(992\) −26.2385 + 45.4464i −0.833072 + 1.44292i
\(993\) −2.93840 + 1.08674i −0.0932472 + 0.0344866i
\(994\) 1.89388 + 3.28029i 0.0600701 + 0.104044i
\(995\) −4.59905 7.96579i −0.145800 0.252532i
\(996\) 0.188559 + 0.156564i 0.00597471 + 0.00496093i
\(997\) 28.1458 48.7499i 0.891386 1.54393i 0.0531718 0.998585i \(-0.483067\pi\)
0.838214 0.545341i \(-0.183600\pi\)
\(998\) 45.2978 1.43388
\(999\) −22.1780 + 39.8285i −0.701681 + 1.26012i
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 585.2.i.h.196.12 30
3.2 odd 2 1755.2.i.h.586.4 30
9.2 odd 6 5265.2.a.bl.1.12 15
9.4 even 3 inner 585.2.i.h.391.12 yes 30
9.5 odd 6 1755.2.i.h.1171.4 30
9.7 even 3 5265.2.a.bk.1.4 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.i.h.196.12 30 1.1 even 1 trivial
585.2.i.h.391.12 yes 30 9.4 even 3 inner
1755.2.i.h.586.4 30 3.2 odd 2
1755.2.i.h.1171.4 30 9.5 odd 6
5265.2.a.bk.1.4 15 9.7 even 3
5265.2.a.bl.1.12 15 9.2 odd 6