Properties

Label 315.2.cc.a.92.19
Level $315$
Weight $2$
Character 315.92
Analytic conductor $2.515$
Analytic rank $0$
Dimension $144$
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] = [315,2,Mod(92,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.92");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.cc (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(36\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 92.19
Character \(\chi\) \(=\) 315.92
Dual form 315.2.cc.a.113.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0573303 + 0.213960i) q^{2} +(-1.05605 - 1.37287i) q^{3} +(1.68956 - 0.975467i) q^{4} +(1.86575 - 1.23247i) q^{5} +(0.233194 - 0.304659i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.618832 + 0.618832i) q^{8} +(-0.769518 + 2.89963i) q^{9} +O(q^{10})\) \(q+(0.0573303 + 0.213960i) q^{2} +(-1.05605 - 1.37287i) q^{3} +(1.68956 - 0.975467i) q^{4} +(1.86575 - 1.23247i) q^{5} +(0.233194 - 0.304659i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.618832 + 0.618832i) q^{8} +(-0.769518 + 2.89963i) q^{9} +(0.370664 + 0.328536i) q^{10} +(2.09032 + 1.20685i) q^{11} +(-3.12344 - 1.28939i) q^{12} +(-3.96308 - 1.06190i) q^{13} +(0.110754 + 0.191831i) q^{14} +(-3.66234 - 1.25986i) q^{15} +(1.85401 - 3.21123i) q^{16} +(-1.21585 + 1.21585i) q^{17} +(-0.664520 + 0.00159073i) q^{18} -5.58574i q^{19} +(1.95005 - 3.90231i) q^{20} +(-1.37539 - 1.05276i) q^{21} +(-0.138378 + 0.516433i) q^{22} +(-1.58542 + 5.91686i) q^{23} +(0.196056 - 1.50309i) q^{24} +(1.96201 - 4.59897i) q^{25} -0.908819i q^{26} +(4.79345 - 2.00571i) q^{27} +(1.37952 - 1.37952i) q^{28} +(-0.551542 + 0.955299i) q^{29} +(0.0595967 - 0.855822i) q^{30} +(4.32039 + 7.48313i) q^{31} +(2.48405 + 0.665599i) q^{32} +(-0.550643 - 4.14422i) q^{33} +(-0.329848 - 0.190438i) q^{34} +(1.48318 - 1.67337i) q^{35} +(1.52835 + 5.64973i) q^{36} +(-4.25538 - 4.25538i) q^{37} +(1.19512 - 0.320232i) q^{38} +(2.72736 + 6.56220i) q^{39} +(1.91728 + 0.391889i) q^{40} +(-6.77814 + 3.91336i) q^{41} +(0.146397 - 0.354633i) q^{42} +(-0.867684 - 3.23824i) q^{43} +4.70896 q^{44} +(2.13799 + 6.35838i) q^{45} -1.35686 q^{46} +(-1.35770 - 5.06702i) q^{47} +(-6.36652 + 0.845921i) q^{48} +(0.866025 - 0.500000i) q^{49} +(1.09648 + 0.156131i) q^{50} +(2.95320 + 0.385200i) q^{51} +(-7.73171 + 2.07171i) q^{52} +(3.35477 + 3.35477i) q^{53} +(0.703950 + 0.910617i) q^{54} +(5.38741 - 0.324597i) q^{55} +(0.757912 + 0.437581i) q^{56} +(-7.66847 + 5.89882i) q^{57} +(-0.236016 - 0.0632402i) q^{58} +(1.40196 + 2.42826i) q^{59} +(-7.41670 + 1.44388i) q^{60} +(-0.309791 + 0.536573i) q^{61} +(-1.35340 + 1.35340i) q^{62} +(0.00718138 + 2.99999i) q^{63} -6.84638i q^{64} +(-8.70287 + 2.90315i) q^{65} +(0.855127 - 0.355405i) q^{66} +(-4.13397 + 15.4282i) q^{67} +(-0.868229 + 3.24027i) q^{68} +(9.79733 - 4.07193i) q^{69} +(0.443065 + 0.221407i) q^{70} +16.5772i q^{71} +(-2.27059 + 1.31818i) q^{72} +(-0.642131 + 0.642131i) q^{73} +(0.666517 - 1.15444i) q^{74} +(-8.38575 + 2.16316i) q^{75} +(-5.44871 - 9.43744i) q^{76} +(2.33145 + 0.624710i) q^{77} +(-1.24769 + 0.959758i) q^{78} +(10.6181 + 6.13038i) q^{79} +(-0.498659 - 8.27636i) q^{80} +(-7.81568 - 4.46263i) q^{81} +(-1.22589 - 1.22589i) q^{82} +(9.56030 - 2.56167i) q^{83} +(-3.35073 - 0.437053i) q^{84} +(-0.769963 + 3.76697i) q^{85} +(0.643108 - 0.371299i) q^{86} +(1.89395 - 0.251650i) q^{87} +(0.546722 + 2.04039i) q^{88} +8.40572 q^{89} +(-1.23787 + 0.821972i) q^{90} -4.10288 q^{91} +(3.09305 + 11.5434i) q^{92} +(5.71079 - 13.8339i) q^{93} +(1.00630 - 0.580988i) q^{94} +(-6.88428 - 10.4216i) q^{95} +(-1.70950 - 4.11317i) q^{96} +(1.39759 - 0.374484i) q^{97} +(0.156629 + 0.156629i) q^{98} +(-5.10794 + 5.13246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 4 q^{3} - 12 q^{11} - 16 q^{12} + 16 q^{15} + 72 q^{16} - 64 q^{18} - 48 q^{20} - 4 q^{21} - 24 q^{23} - 12 q^{25} - 32 q^{27} - 20 q^{30} - 60 q^{32} - 16 q^{33} - 16 q^{36} - 24 q^{37} + 72 q^{38} + 48 q^{41} - 40 q^{42} + 40 q^{45} - 48 q^{46} + 12 q^{47} + 104 q^{48} - 76 q^{51} - 24 q^{55} - 4 q^{57} - 92 q^{60} + 8 q^{63} - 72 q^{65} - 80 q^{66} - 12 q^{67} - 64 q^{72} - 108 q^{75} - 24 q^{76} + 72 q^{78} + 32 q^{81} - 96 q^{82} + 120 q^{83} - 48 q^{85} - 144 q^{86} + 116 q^{87} - 48 q^{88} + 252 q^{90} + 24 q^{91} + 156 q^{92} - 44 q^{93} + 120 q^{95} - 96 q^{96} - 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0573303 + 0.213960i 0.0405387 + 0.151292i 0.983229 0.182378i \(-0.0583794\pi\)
−0.942690 + 0.333670i \(0.891713\pi\)
\(3\) −1.05605 1.37287i −0.609711 0.792624i
\(4\) 1.68956 0.975467i 0.844779 0.487734i
\(5\) 1.86575 1.23247i 0.834387 0.551179i
\(6\) 0.233194 0.304659i 0.0952011 0.124376i
\(7\) 0.965926 0.258819i 0.365086 0.0978244i
\(8\) 0.618832 + 0.618832i 0.218790 + 0.218790i
\(9\) −0.769518 + 2.89963i −0.256506 + 0.966543i
\(10\) 0.370664 + 0.328536i 0.117214 + 0.103892i
\(11\) 2.09032 + 1.20685i 0.630255 + 0.363878i 0.780851 0.624718i \(-0.214786\pi\)
−0.150596 + 0.988595i \(0.548119\pi\)
\(12\) −3.12344 1.28939i −0.901660 0.372216i
\(13\) −3.96308 1.06190i −1.09916 0.294519i −0.336738 0.941598i \(-0.609324\pi\)
−0.762423 + 0.647079i \(0.775990\pi\)
\(14\) 0.110754 + 0.191831i 0.0296002 + 0.0512690i
\(15\) −3.66234 1.25986i −0.945613 0.325295i
\(16\) 1.85401 3.21123i 0.463502 0.802809i
\(17\) −1.21585 + 1.21585i −0.294887 + 0.294887i −0.839007 0.544120i \(-0.816864\pi\)
0.544120 + 0.839007i \(0.316864\pi\)
\(18\) −0.664520 + 0.00159073i −0.156629 + 0.000374938i
\(19\) 5.58574i 1.28146i −0.767768 0.640728i \(-0.778632\pi\)
0.767768 0.640728i \(-0.221368\pi\)
\(20\) 1.95005 3.90231i 0.436044 0.872583i
\(21\) −1.37539 1.05276i −0.300135 0.229731i
\(22\) −0.138378 + 0.516433i −0.0295022 + 0.110104i
\(23\) −1.58542 + 5.91686i −0.330582 + 1.23375i 0.577997 + 0.816039i \(0.303834\pi\)
−0.908580 + 0.417712i \(0.862832\pi\)
\(24\) 0.196056 1.50309i 0.0400197 0.306817i
\(25\) 1.96201 4.59897i 0.392403 0.919794i
\(26\) 0.908819i 0.178234i
\(27\) 4.79345 2.00571i 0.922499 0.385998i
\(28\) 1.37952 1.37952i 0.260705 0.260705i
\(29\) −0.551542 + 0.955299i −0.102419 + 0.177395i −0.912681 0.408673i \(-0.865992\pi\)
0.810262 + 0.586068i \(0.199325\pi\)
\(30\) 0.0595967 0.855822i 0.0108808 0.156251i
\(31\) 4.32039 + 7.48313i 0.775965 + 1.34401i 0.934251 + 0.356617i \(0.116070\pi\)
−0.158286 + 0.987393i \(0.550597\pi\)
\(32\) 2.48405 + 0.665599i 0.439122 + 0.117662i
\(33\) −0.550643 4.14422i −0.0958547 0.721415i
\(34\) −0.329848 0.190438i −0.0565685 0.0326598i
\(35\) 1.48318 1.67337i 0.250704 0.282851i
\(36\) 1.52835 + 5.64973i 0.254724 + 0.941622i
\(37\) −4.25538 4.25538i −0.699580 0.699580i 0.264740 0.964320i \(-0.414714\pi\)
−0.964320 + 0.264740i \(0.914714\pi\)
\(38\) 1.19512 0.320232i 0.193875 0.0519486i
\(39\) 2.72736 + 6.56220i 0.436727 + 1.05079i
\(40\) 1.91728 + 0.391889i 0.303148 + 0.0619630i
\(41\) −6.77814 + 3.91336i −1.05857 + 0.611164i −0.925036 0.379880i \(-0.875965\pi\)
−0.133532 + 0.991045i \(0.542632\pi\)
\(42\) 0.146397 0.354633i 0.0225895 0.0547211i
\(43\) −0.867684 3.23824i −0.132321 0.493827i 0.867674 0.497134i \(-0.165614\pi\)
−0.999995 + 0.00330670i \(0.998947\pi\)
\(44\) 4.70896 0.709902
\(45\) 2.13799 + 6.35838i 0.318713 + 0.947851i
\(46\) −1.35686 −0.200058
\(47\) −1.35770 5.06702i −0.198042 0.739101i −0.991459 0.130423i \(-0.958367\pi\)
0.793417 0.608678i \(-0.208300\pi\)
\(48\) −6.36652 + 0.845921i −0.918927 + 0.122098i
\(49\) 0.866025 0.500000i 0.123718 0.0714286i
\(50\) 1.09648 + 0.156131i 0.155065 + 0.0220803i
\(51\) 2.95320 + 0.385200i 0.413530 + 0.0539389i
\(52\) −7.73171 + 2.07171i −1.07220 + 0.287294i
\(53\) 3.35477 + 3.35477i 0.460813 + 0.460813i 0.898922 0.438109i \(-0.144352\pi\)
−0.438109 + 0.898922i \(0.644352\pi\)
\(54\) 0.703950 + 0.910617i 0.0957955 + 0.123919i
\(55\) 5.38741 0.324597i 0.726438 0.0437686i
\(56\) 0.757912 + 0.437581i 0.101280 + 0.0584742i
\(57\) −7.66847 + 5.89882i −1.01571 + 0.781318i
\(58\) −0.236016 0.0632402i −0.0309904 0.00830384i
\(59\) 1.40196 + 2.42826i 0.182519 + 0.316133i 0.942738 0.333535i \(-0.108241\pi\)
−0.760218 + 0.649667i \(0.774908\pi\)
\(60\) −7.41670 + 1.44388i −0.957491 + 0.186404i
\(61\) −0.309791 + 0.536573i −0.0396646 + 0.0687012i −0.885176 0.465256i \(-0.845962\pi\)
0.845512 + 0.533957i \(0.179296\pi\)
\(62\) −1.35340 + 1.35340i −0.171882 + 0.171882i
\(63\) 0.00718138 + 2.99999i 0.000904768 + 0.377963i
\(64\) 6.84638i 0.855798i
\(65\) −8.70287 + 2.90315i −1.07946 + 0.360092i
\(66\) 0.855127 0.355405i 0.105259 0.0437473i
\(67\) −4.13397 + 15.4282i −0.505045 + 1.88485i −0.0407542 + 0.999169i \(0.512976\pi\)
−0.464290 + 0.885683i \(0.653691\pi\)
\(68\) −0.868229 + 3.24027i −0.105288 + 0.392941i
\(69\) 9.79733 4.07193i 1.17946 0.490203i
\(70\) 0.443065 + 0.221407i 0.0529564 + 0.0264632i
\(71\) 16.5772i 1.96735i 0.179960 + 0.983674i \(0.442403\pi\)
−0.179960 + 0.983674i \(0.557597\pi\)
\(72\) −2.27059 + 1.31818i −0.267591 + 0.155349i
\(73\) −0.642131 + 0.642131i −0.0751557 + 0.0751557i −0.743685 0.668530i \(-0.766924\pi\)
0.668530 + 0.743685i \(0.266924\pi\)
\(74\) 0.666517 1.15444i 0.0774811 0.134201i
\(75\) −8.38575 + 2.16316i −0.968303 + 0.249780i
\(76\) −5.44871 9.43744i −0.625010 1.08255i
\(77\) 2.33145 + 0.624710i 0.265693 + 0.0711923i
\(78\) −1.24769 + 0.959758i −0.141273 + 0.108671i
\(79\) 10.6181 + 6.13038i 1.19463 + 0.689721i 0.959354 0.282206i \(-0.0910663\pi\)
0.235279 + 0.971928i \(0.424400\pi\)
\(80\) −0.498659 8.27636i −0.0557518 0.925326i
\(81\) −7.81568 4.46263i −0.868409 0.495848i
\(82\) −1.22589 1.22589i −0.135377 0.135377i
\(83\) 9.56030 2.56167i 1.04938 0.281180i 0.307384 0.951586i \(-0.400546\pi\)
0.741995 + 0.670405i \(0.233880\pi\)
\(84\) −3.35073 0.437053i −0.365595 0.0476864i
\(85\) −0.769963 + 3.76697i −0.0835142 + 0.408586i
\(86\) 0.643108 0.371299i 0.0693481 0.0400382i
\(87\) 1.89395 0.251650i 0.203053 0.0269797i
\(88\) 0.546722 + 2.04039i 0.0582807 + 0.217507i
\(89\) 8.40572 0.891004 0.445502 0.895281i \(-0.353025\pi\)
0.445502 + 0.895281i \(0.353025\pi\)
\(90\) −1.23787 + 0.821972i −0.130482 + 0.0866435i
\(91\) −4.10288 −0.430099
\(92\) 3.09305 + 11.5434i 0.322472 + 1.20348i
\(93\) 5.71079 13.8339i 0.592181 1.43451i
\(94\) 1.00630 0.580988i 0.103792 0.0599243i
\(95\) −6.88428 10.4216i −0.706312 1.06923i
\(96\) −1.70950 4.11317i −0.174475 0.419798i
\(97\) 1.39759 0.374484i 0.141904 0.0380231i −0.187168 0.982328i \(-0.559931\pi\)
0.329072 + 0.944305i \(0.393264\pi\)
\(98\) 0.156629 + 0.156629i 0.0158220 + 0.0158220i
\(99\) −5.10794 + 5.13246i −0.513368 + 0.515831i
\(100\) −1.17121 9.68411i −0.117121 0.968411i
\(101\) −9.14981 5.28265i −0.910440 0.525643i −0.0298674 0.999554i \(-0.509509\pi\)
−0.880573 + 0.473911i \(0.842842\pi\)
\(102\) 0.0868904 + 0.653949i 0.00860343 + 0.0647506i
\(103\) −4.73510 1.26877i −0.466563 0.125015i 0.0178758 0.999840i \(-0.494310\pi\)
−0.484439 + 0.874825i \(0.660976\pi\)
\(104\) −1.79534 3.10962i −0.176048 0.304924i
\(105\) −3.86363 0.269051i −0.377051 0.0262566i
\(106\) −0.525456 + 0.910116i −0.0510368 + 0.0883983i
\(107\) 2.10252 2.10252i 0.203259 0.203259i −0.598136 0.801395i \(-0.704092\pi\)
0.801395 + 0.598136i \(0.204092\pi\)
\(108\) 6.14231 8.06461i 0.591044 0.776017i
\(109\) 1.93280i 0.185129i −0.995707 0.0925644i \(-0.970494\pi\)
0.995707 0.0925644i \(-0.0295064\pi\)
\(110\) 0.378313 + 1.13408i 0.0360707 + 0.108130i
\(111\) −1.34817 + 10.3360i −0.127963 + 0.981045i
\(112\) 0.959705 3.58167i 0.0906836 0.338436i
\(113\) −0.835339 + 3.11753i −0.0785820 + 0.293272i −0.994022 0.109183i \(-0.965176\pi\)
0.915440 + 0.402455i \(0.131843\pi\)
\(114\) −1.70175 1.30256i −0.159383 0.121996i
\(115\) 4.33439 + 12.9933i 0.404184 + 1.21164i
\(116\) 2.15204i 0.199812i
\(117\) 6.12879 10.6743i 0.566607 0.986840i
\(118\) −0.439175 + 0.439175i −0.0404294 + 0.0404294i
\(119\) −0.859736 + 1.48911i −0.0788119 + 0.136506i
\(120\) −1.48673 3.04602i −0.135719 0.278062i
\(121\) −2.58704 4.48089i −0.235186 0.407354i
\(122\) −0.132565 0.0355208i −0.0120019 0.00321590i
\(123\) 12.5306 + 5.17277i 1.12984 + 0.466413i
\(124\) 14.5991 + 8.42880i 1.31104 + 0.756928i
\(125\) −2.00749 10.9986i −0.179556 0.983748i
\(126\) −0.641466 + 0.173527i −0.0571463 + 0.0154590i
\(127\) 7.64856 + 7.64856i 0.678700 + 0.678700i 0.959706 0.281006i \(-0.0906681\pi\)
−0.281006 + 0.959706i \(0.590668\pi\)
\(128\) 6.43295 1.72370i 0.568597 0.152355i
\(129\) −3.52935 + 4.61095i −0.310742 + 0.405972i
\(130\) −1.12010 1.69563i −0.0982389 0.148716i
\(131\) 5.75997 3.32552i 0.503251 0.290552i −0.226804 0.973940i \(-0.572828\pi\)
0.730055 + 0.683388i \(0.239494\pi\)
\(132\) −4.97289 6.46476i −0.432835 0.562685i
\(133\) −1.44570 5.39541i −0.125358 0.467841i
\(134\) −3.53801 −0.305638
\(135\) 6.47137 9.64994i 0.556967 0.830535i
\(136\) −1.50482 −0.129037
\(137\) 2.01885 + 7.53445i 0.172482 + 0.643712i 0.996967 + 0.0778276i \(0.0247984\pi\)
−0.824485 + 0.565884i \(0.808535\pi\)
\(138\) 1.43291 + 1.86279i 0.121978 + 0.158571i
\(139\) −6.00656 + 3.46789i −0.509470 + 0.294142i −0.732616 0.680643i \(-0.761701\pi\)
0.223146 + 0.974785i \(0.428367\pi\)
\(140\) 0.873609 4.27405i 0.0738335 0.361223i
\(141\) −5.52253 + 7.21497i −0.465081 + 0.607610i
\(142\) −3.54685 + 0.950375i −0.297645 + 0.0797537i
\(143\) −7.00255 7.00255i −0.585582 0.585582i
\(144\) 7.88469 + 7.84703i 0.657058 + 0.653920i
\(145\) 0.148344 + 2.46211i 0.0123193 + 0.204467i
\(146\) −0.174204 0.100577i −0.0144172 0.00832377i
\(147\) −1.60100 0.660911i −0.132048 0.0545111i
\(148\) −11.3407 3.03873i −0.932199 0.249782i
\(149\) −7.67726 13.2974i −0.628946 1.08937i −0.987764 0.155958i \(-0.950153\pi\)
0.358818 0.933408i \(-0.383180\pi\)
\(150\) −0.943587 1.67020i −0.0770435 0.136371i
\(151\) 8.47154 14.6731i 0.689404 1.19408i −0.282627 0.959230i \(-0.591206\pi\)
0.972031 0.234853i \(-0.0754609\pi\)
\(152\) 3.45664 3.45664i 0.280370 0.280370i
\(153\) −2.58990 4.46113i −0.209381 0.360661i
\(154\) 0.534651i 0.0430834i
\(155\) 17.2835 + 8.63685i 1.38825 + 0.693729i
\(156\) 11.0092 + 8.42677i 0.881445 + 0.674682i
\(157\) −3.95091 + 14.7450i −0.315317 + 1.17678i 0.608377 + 0.793648i \(0.291821\pi\)
−0.923694 + 0.383131i \(0.874846\pi\)
\(158\) −0.702913 + 2.62331i −0.0559208 + 0.208699i
\(159\) 1.06284 8.14845i 0.0842890 0.646214i
\(160\) 5.45493 1.81969i 0.431250 0.143859i
\(161\) 6.12558i 0.482764i
\(162\) 0.506748 1.92809i 0.0398139 0.151485i
\(163\) 7.87805 7.87805i 0.617057 0.617057i −0.327719 0.944775i \(-0.606280\pi\)
0.944775 + 0.327719i \(0.106280\pi\)
\(164\) −7.63471 + 13.2237i −0.596171 + 1.03260i
\(165\) −6.13500 7.05340i −0.477609 0.549106i
\(166\) 1.09619 + 1.89866i 0.0850809 + 0.147364i
\(167\) 14.7429 + 3.95035i 1.14084 + 0.305687i 0.779289 0.626665i \(-0.215581\pi\)
0.361551 + 0.932352i \(0.382247\pi\)
\(168\) −0.199653 1.50262i −0.0154036 0.115929i
\(169\) 3.32004 + 1.91682i 0.255388 + 0.147448i
\(170\) −0.850123 + 0.0512207i −0.0652014 + 0.00392845i
\(171\) 16.1966 + 4.29833i 1.23858 + 0.328701i
\(172\) −4.62480 4.62480i −0.352638 0.352638i
\(173\) −22.9969 + 6.16200i −1.74842 + 0.468488i −0.984288 0.176570i \(-0.943500\pi\)
−0.764133 + 0.645058i \(0.776833\pi\)
\(174\) 0.162424 + 0.390802i 0.0123133 + 0.0296267i
\(175\) 0.704859 4.95007i 0.0532823 0.374190i
\(176\) 7.75093 4.47500i 0.584248 0.337316i
\(177\) 1.85314 4.48906i 0.139290 0.337419i
\(178\) 0.481903 + 1.79849i 0.0361201 + 0.134802i
\(179\) −16.8068 −1.25620 −0.628101 0.778132i \(-0.716167\pi\)
−0.628101 + 0.778132i \(0.716167\pi\)
\(180\) 9.81465 + 8.65731i 0.731541 + 0.645278i
\(181\) 2.26580 0.168416 0.0842080 0.996448i \(-0.473164\pi\)
0.0842080 + 0.996448i \(0.473164\pi\)
\(182\) −0.235220 0.877852i −0.0174356 0.0650707i
\(183\) 1.06380 0.141347i 0.0786381 0.0104487i
\(184\) −4.64265 + 2.68044i −0.342261 + 0.197604i
\(185\) −13.1841 2.69481i −0.969314 0.198126i
\(186\) 3.28729 + 0.428778i 0.241036 + 0.0314395i
\(187\) −4.00886 + 1.07417i −0.293157 + 0.0785512i
\(188\) −7.23663 7.23663i −0.527786 0.527786i
\(189\) 4.11100 3.17800i 0.299031 0.231165i
\(190\) 1.83512 2.07043i 0.133133 0.150205i
\(191\) −22.2399 12.8402i −1.60922 0.929086i −0.989544 0.144230i \(-0.953929\pi\)
−0.619679 0.784855i \(-0.712737\pi\)
\(192\) −9.39916 + 7.23012i −0.678326 + 0.521789i
\(193\) −4.31078 1.15507i −0.310296 0.0831437i 0.100310 0.994956i \(-0.468016\pi\)
−0.410607 + 0.911813i \(0.634683\pi\)
\(194\) 0.160249 + 0.277559i 0.0115052 + 0.0199276i
\(195\) 13.1763 + 8.88200i 0.943575 + 0.636053i
\(196\) 0.975467 1.68956i 0.0696762 0.120683i
\(197\) 14.3209 14.3209i 1.02032 1.02032i 0.0205332 0.999789i \(-0.493464\pi\)
0.999789 0.0205332i \(-0.00653638\pi\)
\(198\) −1.39098 0.798649i −0.0988526 0.0567575i
\(199\) 3.13470i 0.222213i 0.993808 + 0.111107i \(0.0354395\pi\)
−0.993808 + 0.111107i \(0.964561\pi\)
\(200\) 4.06015 1.63183i 0.287096 0.115388i
\(201\) 25.5465 10.6175i 1.80191 0.748904i
\(202\) 0.605712 2.26055i 0.0426177 0.159052i
\(203\) −0.285499 + 1.06550i −0.0200381 + 0.0747833i
\(204\) 5.36535 2.22993i 0.375650 0.156126i
\(205\) −7.82316 + 15.6552i −0.546393 + 1.09341i
\(206\) 1.08586i 0.0756554i
\(207\) −15.9367 9.15025i −1.10768 0.635986i
\(208\) −10.7576 + 10.7576i −0.745906 + 0.745906i
\(209\) 6.74113 11.6760i 0.466294 0.807644i
\(210\) −0.163937 0.842085i −0.0113127 0.0581094i
\(211\) −5.14418 8.90999i −0.354140 0.613389i 0.632830 0.774291i \(-0.281893\pi\)
−0.986970 + 0.160902i \(0.948560\pi\)
\(212\) 8.94055 + 2.39561i 0.614040 + 0.164531i
\(213\) 22.7582 17.5063i 1.55937 1.19951i
\(214\) 0.570394 + 0.329317i 0.0389913 + 0.0225116i
\(215\) −5.60992 4.97233i −0.382594 0.339110i
\(216\) 4.20754 + 1.72515i 0.286287 + 0.117381i
\(217\) 6.10995 + 6.10995i 0.414771 + 0.414771i
\(218\) 0.413542 0.110808i 0.0280086 0.00750488i
\(219\) 1.55968 + 0.203437i 0.105393 + 0.0137470i
\(220\) 8.78571 5.80367i 0.592333 0.391283i
\(221\) 6.10963 3.52740i 0.410978 0.237278i
\(222\) −2.28877 + 0.304109i −0.153612 + 0.0204105i
\(223\) 1.06153 + 3.96168i 0.0710851 + 0.265293i 0.992317 0.123720i \(-0.0394826\pi\)
−0.921232 + 0.389014i \(0.872816\pi\)
\(224\) 2.57168 0.171827
\(225\) 11.8255 + 9.22810i 0.788366 + 0.615207i
\(226\) −0.714915 −0.0475555
\(227\) −6.66140 24.8607i −0.442132 1.65006i −0.723399 0.690431i \(-0.757421\pi\)
0.281266 0.959630i \(-0.409246\pi\)
\(228\) −7.20222 + 17.4467i −0.476979 + 1.15544i
\(229\) 3.31073 1.91145i 0.218779 0.126312i −0.386606 0.922245i \(-0.626352\pi\)
0.605385 + 0.795933i \(0.293019\pi\)
\(230\) −2.53156 + 1.67230i −0.166926 + 0.110268i
\(231\) −1.60448 3.86049i −0.105567 0.254001i
\(232\) −0.932482 + 0.249858i −0.0612205 + 0.0164040i
\(233\) −11.7144 11.7144i −0.767433 0.767433i 0.210221 0.977654i \(-0.432582\pi\)
−0.977654 + 0.210221i \(0.932582\pi\)
\(234\) 2.63524 + 0.699353i 0.172271 + 0.0457181i
\(235\) −8.77811 7.78044i −0.572620 0.507540i
\(236\) 4.73738 + 2.73513i 0.308377 + 0.178042i
\(237\) −2.79709 21.0512i −0.181690 1.36743i
\(238\) −0.367898 0.0985779i −0.0238473 0.00638986i
\(239\) −11.0621 19.1601i −0.715548 1.23937i −0.962748 0.270401i \(-0.912844\pi\)
0.247200 0.968964i \(-0.420490\pi\)
\(240\) −10.8357 + 9.42484i −0.699443 + 0.608371i
\(241\) −12.3545 + 21.3986i −0.795822 + 1.37840i 0.126495 + 0.991967i \(0.459627\pi\)
−0.922316 + 0.386436i \(0.873706\pi\)
\(242\) 0.810414 0.810414i 0.0520954 0.0520954i
\(243\) 2.12716 + 15.4426i 0.136457 + 0.990646i
\(244\) 1.20876i 0.0773831i
\(245\) 0.999546 2.00023i 0.0638586 0.127790i
\(246\) −0.388382 + 2.97759i −0.0247624 + 0.189844i
\(247\) −5.93152 + 22.1367i −0.377414 + 1.40853i
\(248\) −1.95721 + 7.30440i −0.124283 + 0.463830i
\(249\) −13.6130 10.4197i −0.862688 0.660325i
\(250\) 2.23817 1.06008i 0.141555 0.0670452i
\(251\) 20.9686i 1.32353i 0.749712 + 0.661764i \(0.230192\pi\)
−0.749712 + 0.661764i \(0.769808\pi\)
\(252\) 2.93853 + 5.06166i 0.185110 + 0.318854i
\(253\) −10.4548 + 10.4548i −0.657286 + 0.657286i
\(254\) −1.19799 + 2.07498i −0.0751686 + 0.130196i
\(255\) 5.98467 2.92105i 0.374774 0.182924i
\(256\) −6.10878 10.5807i −0.381799 0.661295i
\(257\) −8.42379 2.25715i −0.525461 0.140797i −0.0136697 0.999907i \(-0.504351\pi\)
−0.511792 + 0.859110i \(0.671018\pi\)
\(258\) −1.18890 0.490791i −0.0740175 0.0305553i
\(259\) −5.21175 3.00901i −0.323843 0.186971i
\(260\) −11.8721 + 13.3944i −0.736275 + 0.830686i
\(261\) −2.34559 2.33439i −0.145188 0.144495i
\(262\) 1.04175 + 1.04175i 0.0643595 + 0.0643595i
\(263\) 18.9629 5.08109i 1.16930 0.313313i 0.378627 0.925550i \(-0.376396\pi\)
0.790675 + 0.612236i \(0.209730\pi\)
\(264\) 2.22382 2.90533i 0.136867 0.178811i
\(265\) 10.3938 + 2.12448i 0.638487 + 0.130506i
\(266\) 1.07152 0.618641i 0.0656990 0.0379313i
\(267\) −8.87686 11.5399i −0.543255 0.706232i
\(268\) 8.06510 + 30.0994i 0.492654 + 1.83861i
\(269\) −17.0169 −1.03754 −0.518770 0.854914i \(-0.673610\pi\)
−0.518770 + 0.854914i \(0.673610\pi\)
\(270\) 2.43570 + 0.831379i 0.148232 + 0.0505961i
\(271\) −18.1080 −1.09998 −0.549991 0.835171i \(-0.685369\pi\)
−0.549991 + 0.835171i \(0.685369\pi\)
\(272\) 1.65019 + 6.15858i 0.100057 + 0.373419i
\(273\) 4.33285 + 5.63271i 0.262236 + 0.340907i
\(274\) −1.49633 + 0.863905i −0.0903965 + 0.0521904i
\(275\) 9.65148 7.24546i 0.582006 0.436918i
\(276\) 12.5811 16.4367i 0.757295 0.989376i
\(277\) 21.9777 5.88891i 1.32051 0.353830i 0.471343 0.881950i \(-0.343770\pi\)
0.849170 + 0.528120i \(0.177103\pi\)
\(278\) −1.08635 1.08635i −0.0651547 0.0651547i
\(279\) −25.0229 + 6.76911i −1.49808 + 0.405256i
\(280\) 1.95338 0.117693i 0.116737 0.00703350i
\(281\) −7.89538 4.55840i −0.470999 0.271931i 0.245659 0.969356i \(-0.420996\pi\)
−0.716658 + 0.697425i \(0.754329\pi\)
\(282\) −1.86032 0.767963i −0.110781 0.0457315i
\(283\) 19.2332 + 5.15353i 1.14330 + 0.306345i 0.780276 0.625435i \(-0.215079\pi\)
0.363021 + 0.931781i \(0.381745\pi\)
\(284\) 16.1705 + 28.0081i 0.959542 + 1.66197i
\(285\) −7.03727 + 20.4569i −0.416852 + 1.21176i
\(286\) 1.09680 1.89972i 0.0648554 0.112333i
\(287\) −5.53433 + 5.53433i −0.326681 + 0.326681i
\(288\) −3.84151 + 6.69062i −0.226363 + 0.394249i
\(289\) 14.0434i 0.826083i
\(290\) −0.518287 + 0.172893i −0.0304349 + 0.0101526i
\(291\) −1.99004 1.52323i −0.116658 0.0892935i
\(292\) −0.458540 + 1.71129i −0.0268340 + 0.100146i
\(293\) −3.11371 + 11.6205i −0.181905 + 0.678879i 0.813367 + 0.581751i \(0.197632\pi\)
−0.995272 + 0.0971278i \(0.969034\pi\)
\(294\) 0.0496226 0.380439i 0.00289405 0.0221877i
\(295\) 5.60847 + 2.80264i 0.326538 + 0.163176i
\(296\) 5.26673i 0.306123i
\(297\) 12.4404 + 1.59239i 0.721866 + 0.0923998i
\(298\) 2.40497 2.40497i 0.139316 0.139316i
\(299\) 12.5663 21.7654i 0.726726 1.25873i
\(300\) −12.0581 + 11.8348i −0.696176 + 0.683283i
\(301\) −1.67624 2.90333i −0.0966166 0.167345i
\(302\) 3.62514 + 0.971353i 0.208603 + 0.0558951i
\(303\) 2.41029 + 18.1402i 0.138468 + 1.04213i
\(304\) −17.9371 10.3560i −1.02876 0.593957i
\(305\) 0.0833222 + 1.38292i 0.00477102 + 0.0791857i
\(306\) 0.806023 0.809892i 0.0460773 0.0462984i
\(307\) −9.89052 9.89052i −0.564482 0.564482i 0.366095 0.930577i \(-0.380694\pi\)
−0.930577 + 0.366095i \(0.880694\pi\)
\(308\) 4.54850 1.21877i 0.259175 0.0694457i
\(309\) 3.25866 + 7.84054i 0.185378 + 0.446033i
\(310\) −0.857069 + 4.19313i −0.0486783 + 0.238154i
\(311\) −8.52730 + 4.92324i −0.483539 + 0.279171i −0.721890 0.692008i \(-0.756726\pi\)
0.238351 + 0.971179i \(0.423393\pi\)
\(312\) −2.37312 + 5.74868i −0.134352 + 0.325455i
\(313\) −7.18679 26.8215i −0.406221 1.51604i −0.801792 0.597603i \(-0.796120\pi\)
0.395570 0.918436i \(-0.370547\pi\)
\(314\) −3.38134 −0.190820
\(315\) 3.71081 + 5.58837i 0.209081 + 0.314869i
\(316\) 23.9199 1.34560
\(317\) 4.20490 + 15.6929i 0.236171 + 0.881402i 0.977618 + 0.210390i \(0.0674734\pi\)
−0.741447 + 0.671012i \(0.765860\pi\)
\(318\) 1.80437 0.239748i 0.101184 0.0134444i
\(319\) −2.30580 + 1.33125i −0.129100 + 0.0745359i
\(320\) −8.43799 12.7736i −0.471698 0.714066i
\(321\) −5.10685 0.666112i −0.285037 0.0371788i
\(322\) −1.31063 + 0.351182i −0.0730384 + 0.0195706i
\(323\) 6.79143 + 6.79143i 0.377885 + 0.377885i
\(324\) −17.5582 + 0.0840621i −0.975456 + 0.00467012i
\(325\) −12.6593 + 16.1426i −0.702211 + 0.895431i
\(326\) 2.13724 + 1.23393i 0.118371 + 0.0683413i
\(327\) −2.65348 + 2.04113i −0.146738 + 0.112875i
\(328\) −6.61625 1.77282i −0.365321 0.0978875i
\(329\) −2.62288 4.54297i −0.144604 0.250462i
\(330\) 1.15742 1.71702i 0.0637140 0.0945187i
\(331\) 0.258873 0.448382i 0.0142290 0.0246453i −0.858823 0.512272i \(-0.828804\pi\)
0.873052 + 0.487627i \(0.162137\pi\)
\(332\) 13.6539 13.6539i 0.749353 0.749353i
\(333\) 15.6136 9.06442i 0.855620 0.496727i
\(334\) 3.38086i 0.184993i
\(335\) 11.3019 + 33.8801i 0.617489 + 1.85107i
\(336\) −5.93064 + 2.46487i −0.323543 + 0.134470i
\(337\) 0.620652 2.31630i 0.0338091 0.126177i −0.946959 0.321355i \(-0.895862\pi\)
0.980768 + 0.195178i \(0.0625284\pi\)
\(338\) −0.219784 + 0.820247i −0.0119547 + 0.0446155i
\(339\) 5.16210 2.14545i 0.280367 0.116525i
\(340\) 2.37366 + 7.11560i 0.128730 + 0.385897i
\(341\) 20.8562i 1.12943i
\(342\) 0.00888539 + 3.71184i 0.000480467 + 0.200713i
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 1.46698 2.54088i 0.0790941 0.136995i
\(345\) 13.2608 19.6721i 0.713936 1.05911i
\(346\) −2.63684 4.56714i −0.141757 0.245531i
\(347\) −5.27145 1.41248i −0.282986 0.0758259i 0.114534 0.993419i \(-0.463462\pi\)
−0.397520 + 0.917593i \(0.630129\pi\)
\(348\) 2.95447 2.27267i 0.158376 0.121828i
\(349\) 12.3075 + 7.10573i 0.658805 + 0.380361i 0.791821 0.610753i \(-0.209133\pi\)
−0.133017 + 0.991114i \(0.542466\pi\)
\(350\) 1.09953 0.132978i 0.0587721 0.00710796i
\(351\) −21.1267 + 2.85859i −1.12766 + 0.152580i
\(352\) 4.38918 + 4.38918i 0.233944 + 0.233944i
\(353\) −28.2771 + 7.57684i −1.50504 + 0.403274i −0.914785 0.403942i \(-0.867640\pi\)
−0.590256 + 0.807216i \(0.700973\pi\)
\(354\) 1.06672 + 0.139138i 0.0566955 + 0.00739508i
\(355\) 20.4309 + 30.9288i 1.08436 + 1.64153i
\(356\) 14.2020 8.19950i 0.752702 0.434573i
\(357\) 2.95227 0.392269i 0.156251 0.0207611i
\(358\) −0.963541 3.59598i −0.0509247 0.190054i
\(359\) −1.55204 −0.0819134 −0.0409567 0.999161i \(-0.513041\pi\)
−0.0409567 + 0.999161i \(0.513041\pi\)
\(360\) −2.61171 + 5.25783i −0.137649 + 0.277112i
\(361\) −12.2005 −0.642131
\(362\) 0.129899 + 0.484791i 0.00682736 + 0.0254800i
\(363\) −3.41961 + 8.28371i −0.179483 + 0.434782i
\(364\) −6.93206 + 4.00223i −0.363339 + 0.209774i
\(365\) −0.406643 + 1.98946i −0.0212847 + 0.104133i
\(366\) 0.0912304 + 0.219506i 0.00476869 + 0.0114738i
\(367\) 6.79574 1.82091i 0.354735 0.0950509i −0.0770509 0.997027i \(-0.524550\pi\)
0.431786 + 0.901976i \(0.357884\pi\)
\(368\) 16.0610 + 16.0610i 0.837240 + 0.837240i
\(369\) −6.13139 22.6655i −0.319187 1.17992i
\(370\) −0.179268 2.97536i −0.00931972 0.154682i
\(371\) 4.10874 + 2.37218i 0.213315 + 0.123158i
\(372\) −3.84578 28.9438i −0.199394 1.50067i
\(373\) 6.61758 + 1.77317i 0.342645 + 0.0918115i 0.426038 0.904705i \(-0.359909\pi\)
−0.0833928 + 0.996517i \(0.526576\pi\)
\(374\) −0.459659 0.796152i −0.0237684 0.0411680i
\(375\) −12.9796 + 14.3711i −0.670265 + 0.742122i
\(376\) 2.29545 3.97583i 0.118379 0.205038i
\(377\) 3.20024 3.20024i 0.164821 0.164821i
\(378\) 0.915649 + 0.697393i 0.0470959 + 0.0358700i
\(379\) 28.3518i 1.45633i −0.685400 0.728166i \(-0.740373\pi\)
0.685400 0.728166i \(-0.259627\pi\)
\(380\) −21.7973 10.8925i −1.11818 0.558772i
\(381\) 2.42318 18.5777i 0.124143 0.951765i
\(382\) 1.47227 5.49458i 0.0753278 0.281127i
\(383\) −4.48353 + 16.7328i −0.229098 + 0.855004i 0.751624 + 0.659592i \(0.229271\pi\)
−0.980721 + 0.195412i \(0.937396\pi\)
\(384\) −9.15992 7.01125i −0.467440 0.357791i
\(385\) 5.11983 1.70790i 0.260931 0.0870427i
\(386\) 0.988553i 0.0503160i
\(387\) 10.0574 0.0240754i 0.511246 0.00122382i
\(388\) 1.99602 1.99602i 0.101332 0.101332i
\(389\) −0.482813 + 0.836256i −0.0244796 + 0.0423999i −0.878006 0.478650i \(-0.841126\pi\)
0.853526 + 0.521050i \(0.174460\pi\)
\(390\) −1.14499 + 3.32841i −0.0579787 + 0.168540i
\(391\) −5.26639 9.12165i −0.266333 0.461302i
\(392\) 0.845341 + 0.226508i 0.0426962 + 0.0114404i
\(393\) −10.6483 4.39575i −0.537136 0.221736i
\(394\) 3.88512 + 2.24308i 0.195730 + 0.113004i
\(395\) 27.3663 1.64884i 1.37695 0.0829624i
\(396\) −3.62363 + 13.6542i −0.182094 + 0.686150i
\(397\) −6.76864 6.76864i −0.339708 0.339708i 0.516549 0.856258i \(-0.327216\pi\)
−0.856258 + 0.516549i \(0.827216\pi\)
\(398\) −0.670700 + 0.179714i −0.0336192 + 0.00900822i
\(399\) −5.88045 + 7.68257i −0.294390 + 0.384609i
\(400\) −11.1308 14.8270i −0.556539 0.741350i
\(401\) −10.0860 + 5.82314i −0.503670 + 0.290794i −0.730228 0.683204i \(-0.760586\pi\)
0.226558 + 0.973998i \(0.427253\pi\)
\(402\) 3.73632 + 4.85721i 0.186350 + 0.242256i
\(403\) −9.17568 34.2441i −0.457073 1.70582i
\(404\) −20.6122 −1.02549
\(405\) −20.0822 + 1.30649i −0.997890 + 0.0649201i
\(406\) −0.244341 −0.0121265
\(407\) −3.75951 14.0307i −0.186352 0.695475i
\(408\) 1.58916 + 2.06591i 0.0786751 + 0.102278i
\(409\) 27.1233 15.6597i 1.34116 0.774321i 0.354185 0.935176i \(-0.384758\pi\)
0.986978 + 0.160855i \(0.0514252\pi\)
\(410\) −3.79809 0.776323i −0.187574 0.0383399i
\(411\) 8.21178 10.7284i 0.405057 0.529191i
\(412\) −9.23787 + 2.47528i −0.455117 + 0.121948i
\(413\) 1.98267 + 1.98267i 0.0975607 + 0.0975607i
\(414\) 1.04413 3.93439i 0.0513162 0.193365i
\(415\) 14.6799 16.5623i 0.720607 0.813009i
\(416\) −9.13768 5.27564i −0.448012 0.258660i
\(417\) 11.1042 + 4.58393i 0.543773 + 0.224476i
\(418\) 2.88466 + 0.772942i 0.141093 + 0.0378059i
\(419\) 5.97779 + 10.3538i 0.292034 + 0.505818i 0.974291 0.225295i \(-0.0723345\pi\)
−0.682256 + 0.731113i \(0.739001\pi\)
\(420\) −6.79027 + 3.31426i −0.331331 + 0.161720i
\(421\) 17.9287 31.0535i 0.873793 1.51345i 0.0157499 0.999876i \(-0.494986\pi\)
0.858043 0.513578i \(-0.171680\pi\)
\(422\) 1.61146 1.61146i 0.0784447 0.0784447i
\(423\) 15.7373 0.0376718i 0.765172 0.00183167i
\(424\) 4.15208i 0.201643i
\(425\) 3.20614 + 7.97717i 0.155521 + 0.386950i
\(426\) 5.05038 + 3.86570i 0.244692 + 0.187294i
\(427\) −0.160359 + 0.598470i −0.00776034 + 0.0289620i
\(428\) 1.50139 5.60328i 0.0725726 0.270845i
\(429\) −2.21852 + 17.0086i −0.107111 + 0.821183i
\(430\) 0.742260 1.48536i 0.0357950 0.0716306i
\(431\) 7.62108i 0.367095i −0.983011 0.183547i \(-0.941242\pi\)
0.983011 0.183547i \(-0.0587580\pi\)
\(432\) 2.44629 19.1115i 0.117697 0.919501i
\(433\) 19.0999 19.0999i 0.917883 0.917883i −0.0789926 0.996875i \(-0.525170\pi\)
0.996875 + 0.0789926i \(0.0251703\pi\)
\(434\) −0.956998 + 1.65757i −0.0459374 + 0.0795659i
\(435\) 3.22348 2.80376i 0.154554 0.134430i
\(436\) −1.88538 3.26558i −0.0902935 0.156393i
\(437\) 33.0500 + 8.85573i 1.58100 + 0.423627i
\(438\) 0.0458897 + 0.345372i 0.00219269 + 0.0165025i
\(439\) −32.0247 18.4895i −1.52846 0.882454i −0.999427 0.0338507i \(-0.989223\pi\)
−0.529029 0.848604i \(-0.677444\pi\)
\(440\) 3.53478 + 3.13303i 0.168514 + 0.149362i
\(441\) 0.783392 + 2.89591i 0.0373044 + 0.137900i
\(442\) 1.10499 + 1.10499i 0.0525589 + 0.0525589i
\(443\) 32.5384 8.71865i 1.54595 0.414235i 0.617766 0.786362i \(-0.288038\pi\)
0.928182 + 0.372127i \(0.121371\pi\)
\(444\) 7.80457 + 18.7783i 0.370389 + 0.891179i
\(445\) 15.6829 10.3598i 0.743442 0.491103i
\(446\) −0.786781 + 0.454248i −0.0372552 + 0.0215093i
\(447\) −10.1480 + 24.5826i −0.479983 + 1.16272i
\(448\) −1.77197 6.61310i −0.0837179 0.312440i
\(449\) 7.27060 0.343121 0.171560 0.985174i \(-0.445119\pi\)
0.171560 + 0.985174i \(0.445119\pi\)
\(450\) −1.29648 + 3.05923i −0.0611167 + 0.144213i
\(451\) −18.8913 −0.889556
\(452\) 1.62969 + 6.08209i 0.0766542 + 0.286077i
\(453\) −29.0906 + 3.86528i −1.36680 + 0.181607i
\(454\) 4.93728 2.85054i 0.231718 0.133783i
\(455\) −7.65494 + 5.05670i −0.358869 + 0.237062i
\(456\) −8.39588 1.09512i −0.393173 0.0512835i
\(457\) −15.5098 + 4.15585i −0.725519 + 0.194402i −0.602633 0.798018i \(-0.705882\pi\)
−0.122886 + 0.992421i \(0.539215\pi\)
\(458\) 0.598779 + 0.598779i 0.0279791 + 0.0279791i
\(459\) −3.38948 + 8.26676i −0.158207 + 0.385859i
\(460\) 19.9978 + 17.7250i 0.932402 + 0.826430i
\(461\) −5.56834 3.21488i −0.259344 0.149732i 0.364692 0.931128i \(-0.381174\pi\)
−0.624035 + 0.781396i \(0.714508\pi\)
\(462\) 0.734003 0.564618i 0.0341489 0.0262684i
\(463\) −17.6450 4.72796i −0.820032 0.219727i −0.175672 0.984449i \(-0.556210\pi\)
−0.644360 + 0.764722i \(0.722876\pi\)
\(464\) 2.04513 + 3.54226i 0.0949426 + 0.164445i
\(465\) −6.39502 32.8489i −0.296562 1.52333i
\(466\) 1.83481 3.17799i 0.0849961 0.147217i
\(467\) 6.37687 6.37687i 0.295086 0.295086i −0.543999 0.839086i \(-0.683091\pi\)
0.839086 + 0.543999i \(0.183091\pi\)
\(468\) −0.0574830 24.0133i −0.00265715 1.11002i
\(469\) 15.9724i 0.737538i
\(470\) 1.16145 2.32422i 0.0535736 0.107208i
\(471\) 24.4152 10.1474i 1.12500 0.467567i
\(472\) −0.635110 + 2.37026i −0.0292333 + 0.109100i
\(473\) 2.09432 7.81611i 0.0962970 0.359385i
\(474\) 4.34376 1.80534i 0.199516 0.0829219i
\(475\) −25.6886 10.9593i −1.17868 0.502847i
\(476\) 3.35458i 0.153757i
\(477\) −12.3091 + 7.14603i −0.563597 + 0.327194i
\(478\) 3.46530 3.46530i 0.158499 0.158499i
\(479\) −2.02650 + 3.51001i −0.0925933 + 0.160376i −0.908602 0.417664i \(-0.862849\pi\)
0.816008 + 0.578040i \(0.196182\pi\)
\(480\) −8.25887 5.56721i −0.376964 0.254107i
\(481\) 12.3456 + 21.3832i 0.562911 + 0.974991i
\(482\) −5.28672 1.41657i −0.240803 0.0645231i
\(483\) 8.40960 6.46892i 0.382650 0.294346i
\(484\) −8.74193 5.04715i −0.397360 0.229416i
\(485\) 2.14601 2.42119i 0.0974453 0.109941i
\(486\) −3.18215 + 1.34046i −0.144345 + 0.0608044i
\(487\) 19.4032 + 19.4032i 0.879243 + 0.879243i 0.993456 0.114213i \(-0.0364346\pi\)
−0.114213 + 0.993456i \(0.536435\pi\)
\(488\) −0.523758 + 0.140340i −0.0237094 + 0.00635291i
\(489\) −19.1351 2.49589i −0.865320 0.112868i
\(490\) 0.485272 + 0.0991889i 0.0219224 + 0.00448090i
\(491\) 13.1879 7.61405i 0.595163 0.343617i −0.171974 0.985102i \(-0.555014\pi\)
0.767136 + 0.641484i \(0.221681\pi\)
\(492\) 26.2170 3.48346i 1.18195 0.157047i
\(493\) −0.490908 1.83209i −0.0221094 0.0825133i
\(494\) −5.07643 −0.228399
\(495\) −3.20450 + 15.8713i −0.144032 + 0.713360i
\(496\) 32.0401 1.43864
\(497\) 4.29049 + 16.0123i 0.192455 + 0.718250i
\(498\) 1.44897 3.51000i 0.0649299 0.157287i
\(499\) −26.6773 + 15.4021i −1.19424 + 0.689494i −0.959265 0.282508i \(-0.908834\pi\)
−0.234973 + 0.972002i \(0.575500\pi\)
\(500\) −14.1206 16.6246i −0.631492 0.743475i
\(501\) −10.1459 24.4118i −0.453287 1.09064i
\(502\) −4.48644 + 1.20214i −0.200240 + 0.0536541i
\(503\) 16.5256 + 16.5256i 0.736841 + 0.736841i 0.971965 0.235124i \(-0.0755497\pi\)
−0.235124 + 0.971965i \(0.575550\pi\)
\(504\) −1.85205 + 1.86094i −0.0824968 + 0.0828927i
\(505\) −23.5819 + 1.42084i −1.04938 + 0.0632264i
\(506\) −2.83627 1.63752i −0.126088 0.0727968i
\(507\) −0.874583 6.58223i −0.0388416 0.292327i
\(508\) 20.3836 + 5.46177i 0.904377 + 0.242327i
\(509\) 10.7964 + 18.7000i 0.478543 + 0.828861i 0.999697 0.0246016i \(-0.00783172\pi\)
−0.521154 + 0.853462i \(0.674498\pi\)
\(510\) 0.968091 + 1.11301i 0.0428678 + 0.0492850i
\(511\) −0.454055 + 0.786446i −0.0200862 + 0.0347903i
\(512\) 11.3321 11.3321i 0.500813 0.500813i
\(513\) −11.2034 26.7750i −0.494640 1.18214i
\(514\) 1.93175i 0.0852060i
\(515\) −10.3982 + 3.46870i −0.458200 + 0.152849i
\(516\) −1.46521 + 11.2332i −0.0645022 + 0.494516i
\(517\) 3.27708 12.2302i 0.144126 0.537885i
\(518\) 0.345015 1.28761i 0.0151591 0.0565745i
\(519\) 32.7455 + 25.0643i 1.43737 + 1.10020i
\(520\) −7.18218 3.58905i −0.314960 0.157390i
\(521\) 27.2554i 1.19408i −0.802211 0.597041i \(-0.796343\pi\)
0.802211 0.597041i \(-0.203657\pi\)
\(522\) 0.364991 0.635693i 0.0159752 0.0278235i
\(523\) −5.79009 + 5.79009i −0.253183 + 0.253183i −0.822274 0.569091i \(-0.807295\pi\)
0.569091 + 0.822274i \(0.307295\pi\)
\(524\) 6.48788 11.2373i 0.283424 0.490905i
\(525\) −7.54014 + 4.25984i −0.329079 + 0.185915i
\(526\) 2.17430 + 3.76599i 0.0948039 + 0.164205i
\(527\) −14.3513 3.84542i −0.625153 0.167509i
\(528\) −14.3289 5.91516i −0.623587 0.257424i
\(529\) −12.5771 7.26138i −0.546830 0.315712i
\(530\) 0.141328 + 2.34566i 0.00613890 + 0.101889i
\(531\) −8.11989 + 2.19656i −0.352373 + 0.0953227i
\(532\) −7.70563 7.70563i −0.334082 0.334082i
\(533\) 31.0179 8.31123i 1.34354 0.359999i
\(534\) 1.96016 2.56088i 0.0848246 0.110820i
\(535\) 1.33147 6.51408i 0.0575643 0.281628i
\(536\) −12.1057 + 6.98923i −0.522886 + 0.301889i
\(537\) 17.7488 + 23.0735i 0.765919 + 0.995695i
\(538\) −0.975586 3.64094i −0.0420605 0.156972i
\(539\) 2.41369 0.103965
\(540\) 1.52056 22.6168i 0.0654347 0.973270i
\(541\) 11.2560 0.483934 0.241967 0.970284i \(-0.422207\pi\)
0.241967 + 0.970284i \(0.422207\pi\)
\(542\) −1.03814 3.87438i −0.0445918 0.166419i
\(543\) −2.39280 3.11064i −0.102685 0.133491i
\(544\) −3.82950 + 2.21096i −0.164188 + 0.0947942i
\(545\) −2.38213 3.60612i −0.102039 0.154469i
\(546\) −0.956769 + 1.24998i −0.0409459 + 0.0534942i
\(547\) 7.06681 1.89355i 0.302155 0.0809622i −0.104556 0.994519i \(-0.533342\pi\)
0.406711 + 0.913557i \(0.366676\pi\)
\(548\) 10.7606 + 10.7606i 0.459669 + 0.459669i
\(549\) −1.31747 1.31118i −0.0562284 0.0559598i
\(550\) 2.10356 + 1.64964i 0.0896961 + 0.0703410i
\(551\) 5.33605 + 3.08077i 0.227323 + 0.131245i
\(552\) 8.58275 + 3.54306i 0.365306 + 0.150803i
\(553\) 11.8430 + 3.17332i 0.503615 + 0.134943i
\(554\) 2.51998 + 4.36473i 0.107064 + 0.185440i
\(555\) 10.2235 + 20.9458i 0.433962 + 0.889102i
\(556\) −6.76562 + 11.7184i −0.286926 + 0.496971i
\(557\) 0.101718 0.101718i 0.00430991 0.00430991i −0.704949 0.709258i \(-0.749030\pi\)
0.709258 + 0.704949i \(0.249030\pi\)
\(558\) −2.88289 4.96582i −0.122042 0.210220i
\(559\) 13.7548i 0.581766i
\(560\) −2.62375 7.86529i −0.110874 0.332369i
\(561\) 5.70825 + 4.36925i 0.241002 + 0.184470i
\(562\) 0.522669 1.95063i 0.0220475 0.0822823i
\(563\) −7.14204 + 26.6544i −0.301001 + 1.12335i 0.635332 + 0.772239i \(0.280863\pi\)
−0.936333 + 0.351112i \(0.885804\pi\)
\(564\) −2.29268 + 17.5772i −0.0965392 + 0.740132i
\(565\) 2.28374 + 6.84604i 0.0960777 + 0.288015i
\(566\) 4.41059i 0.185391i
\(567\) −8.70438 2.28772i −0.365550 0.0960754i
\(568\) −10.2585 + 10.2585i −0.430437 + 0.430437i
\(569\) 2.33597 4.04603i 0.0979291 0.169618i −0.812898 0.582406i \(-0.802111\pi\)
0.910827 + 0.412788i \(0.135445\pi\)
\(570\) −4.78040 0.332892i −0.200229 0.0139433i
\(571\) −0.566249 0.980773i −0.0236968 0.0410441i 0.853934 0.520382i \(-0.174210\pi\)
−0.877631 + 0.479338i \(0.840877\pi\)
\(572\) −18.6620 5.00046i −0.780296 0.209080i
\(573\) 5.85856 + 44.0923i 0.244745 + 1.84198i
\(574\) −1.50141 0.866838i −0.0626675 0.0361811i
\(575\) 24.1008 + 18.9002i 1.00507 + 0.788194i
\(576\) 19.8520 + 5.26842i 0.827165 + 0.219517i
\(577\) 15.0500 + 15.0500i 0.626541 + 0.626541i 0.947196 0.320655i \(-0.103903\pi\)
−0.320655 + 0.947196i \(0.603903\pi\)
\(578\) −3.00473 + 0.805114i −0.124980 + 0.0334883i
\(579\) 2.96664 + 7.13793i 0.123289 + 0.296642i
\(580\) 2.65234 + 4.01517i 0.110132 + 0.166721i
\(581\) 8.57153 4.94878i 0.355607 0.205310i
\(582\) 0.211821 0.513116i 0.00878025 0.0212694i
\(583\) 2.96385 + 11.0612i 0.122750 + 0.458110i
\(584\) −0.794742 −0.0328867
\(585\) −1.72105 27.4691i −0.0711565 1.13571i
\(586\) −2.66484 −0.110083
\(587\) 2.29950 + 8.58186i 0.0949106 + 0.354211i 0.997006 0.0773257i \(-0.0246381\pi\)
−0.902095 + 0.431537i \(0.857971\pi\)
\(588\) −3.34968 + 0.445073i −0.138138 + 0.0183545i
\(589\) 41.7988 24.1326i 1.72229 0.994365i
\(590\) −0.278117 + 1.36066i −0.0114499 + 0.0560176i
\(591\) −34.7843 4.53709i −1.43083 0.186631i
\(592\) −21.5545 + 5.77552i −0.885885 + 0.237372i
\(593\) −29.9869 29.9869i −1.23141 1.23141i −0.963421 0.267994i \(-0.913639\pi\)
−0.267994 0.963421i \(-0.586361\pi\)
\(594\) 0.372506 + 2.75304i 0.0152841 + 0.112959i
\(595\) 0.231237 + 3.83790i 0.00947980 + 0.157338i
\(596\) −25.9424 14.9778i −1.06264 0.613516i
\(597\) 4.30352 3.31040i 0.176131 0.135486i
\(598\) 5.37735 + 1.44086i 0.219896 + 0.0589210i
\(599\) −5.93776 10.2845i −0.242610 0.420213i 0.718847 0.695169i \(-0.244670\pi\)
−0.961457 + 0.274955i \(0.911337\pi\)
\(600\) −6.52801 3.85074i −0.266505 0.157206i
\(601\) −6.61882 + 11.4641i −0.269987 + 0.467632i −0.968858 0.247616i \(-0.920353\pi\)
0.698871 + 0.715248i \(0.253686\pi\)
\(602\) 0.525096 0.525096i 0.0214013 0.0214013i
\(603\) −41.5548 23.8592i −1.69224 0.971623i
\(604\) 33.0548i 1.34498i
\(605\) −10.3494 5.17174i −0.420761 0.210261i
\(606\) −3.74309 + 1.55569i −0.152053 + 0.0631956i
\(607\) 11.3455 42.3421i 0.460501 1.71861i −0.210889 0.977510i \(-0.567636\pi\)
0.671390 0.741104i \(-0.265698\pi\)
\(608\) 3.71786 13.8752i 0.150779 0.562715i
\(609\) 1.76429 0.733266i 0.0714925 0.0297135i
\(610\) −0.291112 + 0.0971108i −0.0117868 + 0.00393190i
\(611\) 21.5228i 0.870718i
\(612\) −8.72747 5.01099i −0.352787 0.202557i
\(613\) −3.45641 + 3.45641i −0.139603 + 0.139603i −0.773455 0.633852i \(-0.781473\pi\)
0.633852 + 0.773455i \(0.281473\pi\)
\(614\) 1.54915 2.68320i 0.0625185 0.108285i
\(615\) 29.7542 5.79253i 1.19980 0.233577i
\(616\) 1.05619 + 1.82937i 0.0425549 + 0.0737073i
\(617\) −12.3112 3.29877i −0.495629 0.132803i 0.00234147 0.999997i \(-0.499255\pi\)
−0.497971 + 0.867194i \(0.665921\pi\)
\(618\) −1.49074 + 1.14672i −0.0599663 + 0.0461279i
\(619\) −11.5751 6.68290i −0.465244 0.268608i 0.249003 0.968503i \(-0.419897\pi\)
−0.714246 + 0.699894i \(0.753230\pi\)
\(620\) 37.6265 2.26703i 1.51112 0.0910463i
\(621\) 4.26786 + 31.5420i 0.171263 + 1.26574i
\(622\) −1.54225 1.54225i −0.0618385 0.0618385i
\(623\) 8.11930 2.17556i 0.325293 0.0871620i
\(624\) 26.1293 + 3.40818i 1.04601 + 0.136436i
\(625\) −17.3010 18.0465i −0.692040 0.721859i
\(626\) 5.32669 3.07537i 0.212897 0.122916i
\(627\) −23.1485 + 3.07575i −0.924463 + 0.122834i
\(628\) 7.70796 + 28.7665i 0.307581 + 1.14791i
\(629\) 10.3478 0.412594
\(630\) −0.982944 + 1.11435i −0.0391614 + 0.0443967i
\(631\) 19.7625 0.786733 0.393367 0.919382i \(-0.371310\pi\)
0.393367 + 0.919382i \(0.371310\pi\)
\(632\) 2.77716 + 10.3645i 0.110470 + 0.412278i
\(633\) −6.79970 + 16.4717i −0.270264 + 0.654690i
\(634\) −3.11658 + 1.79936i −0.123775 + 0.0714617i
\(635\) 23.6969 + 4.84361i 0.940384 + 0.192213i
\(636\) −6.15281 14.8041i −0.243975 0.587019i
\(637\) −3.96308 + 1.06190i −0.157023 + 0.0420742i
\(638\) −0.417027 0.417027i −0.0165102 0.0165102i
\(639\) −48.0676 12.7564i −1.90153 0.504637i
\(640\) 9.87782 11.1444i 0.390455 0.440522i
\(641\) 20.3879 + 11.7709i 0.805272 + 0.464924i 0.845311 0.534274i \(-0.179415\pi\)
−0.0400390 + 0.999198i \(0.512748\pi\)
\(642\) −0.150256 1.13085i −0.00593014 0.0446310i
\(643\) −21.8938 5.86642i −0.863406 0.231349i −0.200172 0.979761i \(-0.564150\pi\)
−0.663234 + 0.748412i \(0.730817\pi\)
\(644\) 5.97531 + 10.3495i 0.235460 + 0.407829i
\(645\) −0.901985 + 12.9527i −0.0355156 + 0.510012i
\(646\) −1.06374 + 1.84245i −0.0418522 + 0.0724901i
\(647\) −13.8366 + 13.8366i −0.543972 + 0.543972i −0.924691 0.380719i \(-0.875677\pi\)
0.380719 + 0.924691i \(0.375677\pi\)
\(648\) −2.07498 7.59822i −0.0815128 0.298486i
\(649\) 6.76779i 0.265659i
\(650\) −4.17963 1.78311i −0.163939 0.0699395i
\(651\) 1.93573 14.8406i 0.0758672 0.581647i
\(652\) 5.62565 20.9952i 0.220318 0.822236i
\(653\) 0.377082 1.40729i 0.0147564 0.0550715i −0.958155 0.286250i \(-0.907591\pi\)
0.972911 + 0.231178i \(0.0742580\pi\)
\(654\) −0.588845 0.450718i −0.0230257 0.0176245i
\(655\) 6.64802 13.3036i 0.259760 0.519815i
\(656\) 29.0216i 1.13310i
\(657\) −1.36781 2.35607i −0.0533633 0.0919191i
\(658\) 0.821641 0.821641i 0.0320309 0.0320309i
\(659\) −13.6365 + 23.6192i −0.531204 + 0.920072i 0.468133 + 0.883658i \(0.344927\pi\)
−0.999337 + 0.0364140i \(0.988407\pi\)
\(660\) −17.2458 5.93264i −0.671292 0.230928i
\(661\) 19.9575 + 34.5673i 0.776255 + 1.34451i 0.934086 + 0.357047i \(0.116217\pi\)
−0.157831 + 0.987466i \(0.550450\pi\)
\(662\) 0.110777 + 0.0296826i 0.00430547 + 0.00115365i
\(663\) −11.2947 4.66259i −0.438650 0.181080i
\(664\) 7.50147 + 4.33098i 0.291114 + 0.168075i
\(665\) −9.34701 8.28468i −0.362461 0.321266i
\(666\) 2.83455 + 2.82102i 0.109837 + 0.109312i
\(667\) −4.77794 4.77794i −0.185003 0.185003i
\(668\) 28.7624 7.70687i 1.11285 0.298188i
\(669\) 4.31782 5.64106i 0.166937 0.218096i
\(670\) −6.60103 + 4.36051i −0.255020 + 0.168461i
\(671\) −1.29512 + 0.747739i −0.0499977 + 0.0288662i
\(672\) −2.71582 3.53056i −0.104765 0.136194i
\(673\) −0.681737 2.54428i −0.0262790 0.0980747i 0.951541 0.307523i \(-0.0995000\pi\)
−0.977820 + 0.209448i \(0.932833\pi\)
\(674\) 0.531178 0.0204602
\(675\) 0.180630 25.9801i 0.00695246 0.999976i
\(676\) 7.47920 0.287661
\(677\) 4.18527 + 15.6196i 0.160853 + 0.600311i 0.998533 + 0.0541495i \(0.0172448\pi\)
−0.837680 + 0.546161i \(0.816089\pi\)
\(678\) 0.754986 + 0.981482i 0.0289951 + 0.0376936i
\(679\) 1.25305 0.723447i 0.0480875 0.0277634i
\(680\) −2.80760 + 1.85465i −0.107667 + 0.0711225i
\(681\) −27.0956 + 35.3993i −1.03831 + 1.35650i
\(682\) −4.46238 + 1.19569i −0.170873 + 0.0457854i
\(683\) −7.90415 7.90415i −0.302444 0.302444i 0.539526 0.841969i \(-0.318604\pi\)
−0.841969 + 0.539526i \(0.818604\pi\)
\(684\) 31.5579 8.53694i 1.20665 0.326418i
\(685\) 13.0527 + 11.5692i 0.498717 + 0.442036i
\(686\) 0.191831 + 0.110754i 0.00732414 + 0.00422860i
\(687\) −6.12047 2.52660i −0.233510 0.0963959i
\(688\) −12.0074 3.21738i −0.457779 0.122662i
\(689\) −9.73278 16.8577i −0.370790 0.642226i
\(690\) 4.96929 + 1.70946i 0.189178 + 0.0650780i
\(691\) −8.35950 + 14.4791i −0.318010 + 0.550810i −0.980073 0.198639i \(-0.936348\pi\)
0.662063 + 0.749449i \(0.269681\pi\)
\(692\) −32.8438 + 32.8438i −1.24853 + 1.24853i
\(693\) −3.60552 + 6.27961i −0.136962 + 0.238542i
\(694\) 1.20886i 0.0458875i
\(695\) −6.93263 + 13.8731i −0.262969 + 0.526238i
\(696\) 1.32777 + 1.01631i 0.0503289 + 0.0385231i
\(697\) 3.48314 12.9993i 0.131933 0.492382i
\(698\) −0.814748 + 3.04068i −0.0308387 + 0.115091i
\(699\) −3.71129 + 28.4532i −0.140374 + 1.07620i
\(700\) −3.63773 9.05100i −0.137493 0.342096i
\(701\) 28.5556i 1.07853i −0.842136 0.539266i \(-0.818702\pi\)
0.842136 0.539266i \(-0.181298\pi\)
\(702\) −1.82282 4.35638i −0.0687981 0.164421i
\(703\) −23.7694 + 23.7694i −0.896481 + 0.896481i
\(704\) 8.26253 14.3111i 0.311406 0.539371i
\(705\) −1.41138 + 20.2677i −0.0531555 + 0.763325i
\(706\) −3.24228 5.61579i −0.122025 0.211353i
\(707\) −10.2053 2.73450i −0.383809 0.102841i
\(708\) −1.24795 9.39221i −0.0469007 0.352981i
\(709\) 33.0480 + 19.0803i 1.24114 + 0.716574i 0.969327 0.245775i \(-0.0790426\pi\)
0.271816 + 0.962349i \(0.412376\pi\)
\(710\) −5.44620 + 6.14455i −0.204392 + 0.230601i
\(711\) −25.9467 + 26.0712i −0.973076 + 0.977746i
\(712\) 5.20173 + 5.20173i 0.194943 + 0.194943i
\(713\) −51.1263 + 13.6992i −1.91469 + 0.513041i
\(714\) 0.253184 + 0.609177i 0.00947518 + 0.0227979i
\(715\) −21.6954 4.43451i −0.811363 0.165841i
\(716\) −28.3961 + 16.3945i −1.06121 + 0.612692i
\(717\) −14.6221 + 35.4208i −0.546074 + 1.32281i
\(718\) −0.0889788 0.332074i −0.00332066 0.0123929i
\(719\) 40.4768 1.50953 0.754765 0.655995i \(-0.227751\pi\)
0.754765 + 0.655995i \(0.227751\pi\)
\(720\) 24.3821 + 4.92289i 0.908667 + 0.183465i
\(721\) −4.90214 −0.182565
\(722\) −0.699459 2.61041i −0.0260311 0.0971496i
\(723\) 42.4243 5.63693i 1.57778 0.209640i
\(724\) 3.82821 2.21022i 0.142274 0.0821421i
\(725\) 3.31126 + 4.41083i 0.122977 + 0.163814i
\(726\) −1.96843 0.256752i −0.0730552 0.00952896i
\(727\) 16.3478 4.38037i 0.606305 0.162459i 0.0574107 0.998351i \(-0.481716\pi\)
0.548894 + 0.835892i \(0.315049\pi\)
\(728\) −2.53900 2.53900i −0.0941015 0.0941015i
\(729\) 18.9543 19.2285i 0.702011 0.712167i
\(730\) −0.448978 + 0.0270513i −0.0166174 + 0.00100122i
\(731\) 4.99219 + 2.88224i 0.184643 + 0.106604i
\(732\) 1.65947 1.27651i 0.0613357 0.0471813i
\(733\) 1.91715 + 0.513699i 0.0708116 + 0.0189739i 0.294051 0.955790i \(-0.404996\pi\)
−0.223239 + 0.974764i \(0.571663\pi\)
\(734\) 0.779204 + 1.34962i 0.0287609 + 0.0498154i
\(735\) −3.80161 + 0.740097i −0.140225 + 0.0272989i
\(736\) −7.87650 + 13.6425i −0.290332 + 0.502869i
\(737\) −27.2608 + 27.2608i −1.00416 + 1.00416i
\(738\) 4.49799 2.61129i 0.165573 0.0961229i
\(739\) 11.0692i 0.407187i 0.979056 + 0.203593i \(0.0652621\pi\)
−0.979056 + 0.203593i \(0.934738\pi\)
\(740\) −24.9040 + 8.30762i −0.915490 + 0.305394i
\(741\) 36.6547 15.2343i 1.34655 0.559647i
\(742\) −0.271996 + 1.01510i −0.00998528 + 0.0372656i
\(743\) −10.3606 + 38.6662i −0.380093 + 1.41852i 0.465667 + 0.884960i \(0.345815\pi\)
−0.845759 + 0.533565i \(0.820852\pi\)
\(744\) 12.0949 5.02683i 0.443420 0.184292i
\(745\) −30.7125 15.3475i −1.12522 0.562291i
\(746\) 1.51755i 0.0555615i
\(747\) 0.0710780 + 29.6926i 0.00260061 + 1.08639i
\(748\) −5.72539 + 5.72539i −0.209341 + 0.209341i
\(749\) 1.48671 2.57505i 0.0543231 0.0940904i
\(750\) −3.81897 1.95322i −0.139449 0.0713214i
\(751\) −13.4102 23.2272i −0.489347 0.847573i 0.510578 0.859831i \(-0.329431\pi\)
−0.999925 + 0.0122579i \(0.996098\pi\)
\(752\) −18.7886 5.03439i −0.685149 0.183585i
\(753\) 28.7871 22.1439i 1.04906 0.806969i
\(754\) 0.868194 + 0.501252i 0.0316178 + 0.0182545i
\(755\) −2.27853 37.8173i −0.0829242 1.37631i
\(756\) 3.84574 9.37956i 0.139868 0.341131i
\(757\) −6.97073 6.97073i −0.253355 0.253355i 0.568989 0.822345i \(-0.307335\pi\)
−0.822345 + 0.568989i \(0.807335\pi\)
\(758\) 6.06614 1.62542i 0.220332 0.0590378i
\(759\) 25.3937 + 3.31223i 0.921734 + 0.120226i
\(760\) 2.18899 10.7094i 0.0794030 0.388472i
\(761\) 35.0482 20.2351i 1.27050 0.733522i 0.295415 0.955369i \(-0.404542\pi\)
0.975081 + 0.221847i \(0.0712086\pi\)
\(762\) 4.11380 0.546602i 0.149027 0.0198013i
\(763\) −0.500246 1.86694i −0.0181101 0.0675879i
\(764\) −50.1008 −1.81259
\(765\) −10.3303 5.13136i −0.373493 0.185525i
\(766\) −3.83718 −0.138643
\(767\) −2.97749 11.1121i −0.107511 0.401236i
\(768\) −8.07472 + 19.5603i −0.291371 + 0.705821i
\(769\) −13.1923 + 7.61659i −0.475727 + 0.274661i −0.718634 0.695388i \(-0.755232\pi\)
0.242907 + 0.970050i \(0.421899\pi\)
\(770\) 0.658943 + 0.997522i 0.0237467 + 0.0359482i
\(771\) 5.79718 + 13.9484i 0.208780 + 0.502339i
\(772\) −8.41004 + 2.25346i −0.302684 + 0.0811040i
\(773\) 4.10943 + 4.10943i 0.147806 + 0.147806i 0.777137 0.629331i \(-0.216671\pi\)
−0.629331 + 0.777137i \(0.716671\pi\)
\(774\) 0.581745 + 2.15050i 0.0209104 + 0.0772980i
\(775\) 42.8914 5.18732i 1.54070 0.186334i
\(776\) 1.09662 + 0.633133i 0.0393663 + 0.0227281i
\(777\) 1.37291 + 10.3327i 0.0492528 + 0.370683i
\(778\) −0.206605 0.0553596i −0.00740714 0.00198474i
\(779\) 21.8590 + 37.8609i 0.783180 + 1.35651i
\(780\) 30.9262 + 2.15360i 1.10734 + 0.0771114i
\(781\) −20.0061 + 34.6516i −0.715874 + 1.23993i
\(782\) 1.64974 1.64974i 0.0589946 0.0589946i
\(783\) −0.727739 + 5.68541i −0.0260073 + 0.203180i
\(784\) 3.70801i 0.132429i
\(785\) 10.8014 + 32.3798i 0.385520 + 1.15568i
\(786\) 0.330042 2.53032i 0.0117722 0.0902535i
\(787\) 2.57034 9.59262i 0.0916226 0.341940i −0.904863 0.425702i \(-0.860027\pi\)
0.996486 + 0.0837624i \(0.0266937\pi\)
\(788\) 10.2264 38.1656i 0.364302 1.35959i
\(789\) −27.0014 20.6676i −0.961275 0.735786i
\(790\) 1.92170 + 5.76075i 0.0683711 + 0.204958i
\(791\) 3.22750i 0.114757i
\(792\) −6.33709 + 0.0151697i −0.225179 + 0.000539033i
\(793\) 1.79752 1.79752i 0.0638316 0.0638316i
\(794\) 1.06017 1.83627i 0.0376240 0.0651666i
\(795\) −8.05977 16.5129i −0.285850 0.585651i
\(796\) 3.05780 + 5.29626i 0.108381 + 0.187721i
\(797\) −32.4043 8.68271i −1.14782 0.307557i −0.365729 0.930722i \(-0.619180\pi\)
−0.782091 + 0.623164i \(0.785847\pi\)
\(798\) −1.98089 0.817734i −0.0701227 0.0289475i
\(799\) 7.81151 + 4.50998i 0.276351 + 0.159551i
\(800\) 7.93480 10.1181i 0.280538 0.357730i
\(801\) −6.46835 + 24.3735i −0.228548 + 0.861194i
\(802\) −1.82415 1.82415i −0.0644130 0.0644130i
\(803\) −2.11721 + 0.567305i −0.0747147 + 0.0200198i
\(804\) 32.8052 42.8587i 1.15695 1.51151i
\(805\) 7.54962 + 11.4288i 0.266089 + 0.402812i
\(806\) 6.80081 3.92645i 0.239548 0.138303i
\(807\) 17.9707 + 23.3620i 0.632599 + 0.822380i
\(808\) −2.39313 8.93127i −0.0841899 0.314201i
\(809\) −23.3160 −0.819748 −0.409874 0.912142i \(-0.634427\pi\)
−0.409874 + 0.912142i \(0.634427\pi\)
\(810\) −1.43085 4.22187i −0.0502751 0.148341i
\(811\) −37.7095 −1.32416 −0.662081 0.749433i \(-0.730326\pi\)
−0.662081 + 0.749433i \(0.730326\pi\)
\(812\) 0.556990 + 2.07872i 0.0195465 + 0.0729486i
\(813\) 19.1229 + 24.8598i 0.670670 + 0.871872i
\(814\) 2.78647 1.60877i 0.0976656 0.0563873i
\(815\) 4.98894 24.4079i 0.174755 0.854973i
\(816\) 6.71222 8.76925i 0.234975 0.306985i
\(817\) −18.0880 + 4.84666i −0.632818 + 0.169563i
\(818\) 4.90553 + 4.90553i 0.171518 + 0.171518i
\(819\) 3.15724 11.8968i 0.110323 0.415709i
\(820\) 2.05345 + 34.0816i 0.0717097 + 1.19018i
\(821\) −21.2475 12.2672i −0.741542 0.428130i 0.0810877 0.996707i \(-0.474161\pi\)
−0.822630 + 0.568577i \(0.807494\pi\)
\(822\) 2.76622 + 1.14193i 0.0964831 + 0.0398294i
\(823\) 8.22162 + 2.20298i 0.286588 + 0.0767909i 0.399249 0.916843i \(-0.369271\pi\)
−0.112661 + 0.993633i \(0.535938\pi\)
\(824\) −2.14508 3.71539i −0.0747274 0.129432i
\(825\) −20.1395 5.59861i −0.701167 0.194919i
\(826\) −0.310544 + 0.537878i −0.0108052 + 0.0187152i
\(827\) 14.2802 14.2802i 0.496570 0.496570i −0.413799 0.910368i \(-0.635798\pi\)
0.910368 + 0.413799i \(0.135798\pi\)
\(828\) −35.8517 + 0.0858218i −1.24593 + 0.00298251i
\(829\) 29.7903i 1.03466i 0.855786 + 0.517330i \(0.173074\pi\)
−0.855786 + 0.517330i \(0.826926\pi\)
\(830\) 4.38526 + 2.19139i 0.152215 + 0.0760641i
\(831\) −31.2942 23.9535i −1.08558 0.830936i
\(832\) −7.27020 + 27.1328i −0.252049 + 0.940660i
\(833\) −0.445032 + 1.66088i −0.0154195 + 0.0575462i
\(834\) −0.344171 + 2.63864i −0.0119177 + 0.0913687i
\(835\) 32.3752 10.7999i 1.12039 0.373746i
\(836\) 26.3030i 0.909708i
\(837\) 35.7185 + 27.2046i 1.23461 + 0.940328i
\(838\) −1.87260 + 1.87260i −0.0646878 + 0.0646878i
\(839\) 24.9879 43.2802i 0.862676 1.49420i −0.00665959 0.999978i \(-0.502120\pi\)
0.869336 0.494222i \(-0.164547\pi\)
\(840\) −2.22444 2.55743i −0.0767505 0.0882399i
\(841\) 13.8916 + 24.0610i 0.479021 + 0.829688i
\(842\) 7.67205 + 2.05572i 0.264396 + 0.0708448i
\(843\) 2.07985 + 15.6532i 0.0716337 + 0.539125i
\(844\) −17.3828 10.0360i −0.598341 0.345452i
\(845\) 8.55678 0.515555i 0.294362 0.0177356i
\(846\) 0.910282 + 3.36498i 0.0312962 + 0.115690i
\(847\) −3.65863 3.65863i −0.125712 0.125712i
\(848\) 16.9927 4.55319i 0.583533 0.156357i
\(849\) −13.2361 31.8470i −0.454263 1.09299i
\(850\) −1.52298 + 1.14332i −0.0522379 + 0.0392155i
\(851\) 31.9250 18.4319i 1.09438 0.631838i
\(852\) 21.3745 51.7778i 0.732279 1.77388i
\(853\) 7.25470 + 27.0749i 0.248396 + 0.927027i 0.971646 + 0.236440i \(0.0759808\pi\)
−0.723250 + 0.690586i \(0.757353\pi\)
\(854\) −0.137242 −0.00469632
\(855\) 35.5163 11.9423i 1.21463 0.408417i
\(856\) 2.60222 0.0889420
\(857\) 1.38141 + 5.15548i 0.0471879 + 0.176108i 0.985498 0.169687i \(-0.0542758\pi\)
−0.938310 + 0.345795i \(0.887609\pi\)
\(858\) −3.76634 + 0.500435i −0.128581 + 0.0170846i
\(859\) 29.5785 17.0772i 1.00921 0.582665i 0.0982463 0.995162i \(-0.468677\pi\)
0.910959 + 0.412497i \(0.135343\pi\)
\(860\) −14.3286 2.92875i −0.488603 0.0998696i
\(861\) 13.4424 + 1.75336i 0.458116 + 0.0597544i
\(862\) 1.63060 0.436919i 0.0555386 0.0148815i
\(863\) −33.1610 33.1610i −1.12881 1.12881i −0.990370 0.138443i \(-0.955790\pi\)
−0.138443 0.990370i \(-0.544210\pi\)
\(864\) 13.2421 1.79176i 0.450507 0.0609568i
\(865\) −35.3118 + 39.8398i −1.20064 + 1.35459i
\(866\) 5.18161 + 2.99161i 0.176078 + 0.101659i
\(867\) 19.2797 14.8305i 0.654774 0.503672i
\(868\) 16.2832 + 4.36307i 0.552687 + 0.148092i
\(869\) 14.7968 + 25.6289i 0.501949 + 0.869401i
\(870\) 0.784696 + 0.528955i 0.0266037 + 0.0179332i
\(871\) 32.7665 56.7532i 1.11025 1.92301i
\(872\) 1.19608 1.19608i 0.0405044 0.0405044i
\(873\) 0.0103907 + 4.34067i 0.000351672 + 0.146909i
\(874\) 7.57908i 0.256366i
\(875\) −4.78575 10.1043i −0.161788 0.341587i
\(876\) 2.83362 1.17770i 0.0957391 0.0397907i
\(877\) 9.51519 35.5112i 0.321305 1.19913i −0.596669 0.802488i \(-0.703509\pi\)
0.917974 0.396640i \(-0.129824\pi\)
\(878\) 2.12002 7.91201i 0.0715471 0.267017i
\(879\) 19.2417 7.99715i 0.649005 0.269737i
\(880\) 8.94594 17.9020i 0.301568 0.603478i
\(881\) 18.7387i 0.631322i 0.948872 + 0.315661i \(0.102226\pi\)
−0.948872 + 0.315661i \(0.897774\pi\)
\(882\) −0.574696 + 0.333638i −0.0193510 + 0.0112342i
\(883\) 10.9800 10.9800i 0.369505 0.369505i −0.497791 0.867297i \(-0.665856\pi\)
0.867297 + 0.497791i \(0.165856\pi\)
\(884\) 6.88172 11.9195i 0.231457 0.400896i
\(885\) −2.07517 10.6594i −0.0697561 0.358312i
\(886\) 3.73088 + 6.46207i 0.125341 + 0.217097i
\(887\) −9.47808 2.53964i −0.318243 0.0852729i 0.0961617 0.995366i \(-0.469343\pi\)
−0.414404 + 0.910093i \(0.636010\pi\)
\(888\) −7.23051 + 5.56193i −0.242640 + 0.186646i
\(889\) 9.36754 + 5.40835i 0.314177 + 0.181390i
\(890\) 3.11570 + 2.76158i 0.104438 + 0.0925685i
\(891\) −10.9516 18.7607i −0.366891 0.628506i
\(892\) 5.65800 + 5.65800i 0.189444 + 0.189444i
\(893\) −28.3031 + 7.58378i −0.947126 + 0.253782i
\(894\) −5.84147 0.761932i −0.195368 0.0254828i
\(895\) −31.3573 + 20.7140i −1.04816 + 0.692392i
\(896\) 5.76762 3.32994i 0.192683 0.111245i
\(897\) −43.1516 + 5.73357i −1.44079 + 0.191438i
\(898\) 0.416826 + 1.55562i 0.0139097 + 0.0519116i
\(899\) −9.53151 −0.317894
\(900\) 28.9816 + 4.05604i 0.966052 + 0.135201i
\(901\) −8.15780 −0.271776
\(902\) −1.08304 4.04198i −0.0360614 0.134583i
\(903\) −2.21569 + 5.36730i −0.0737334 + 0.178613i
\(904\) −2.44616 + 1.41229i −0.0813581 + 0.0469721i
\(905\) 4.22742 2.79255i 0.140524 0.0928274i
\(906\) −2.49479 6.00262i −0.0828838 0.199424i
\(907\) −4.51507 + 1.20981i −0.149921 + 0.0401711i −0.332999 0.942927i \(-0.608061\pi\)
0.183078 + 0.983098i \(0.441394\pi\)
\(908\) −35.5056 35.5056i −1.17829 1.17829i
\(909\) 22.3587 22.4660i 0.741590 0.745149i
\(910\) −1.52079 1.34795i −0.0504137 0.0446840i
\(911\) 3.38019 + 1.95155i 0.111991 + 0.0646578i 0.554949 0.831884i \(-0.312738\pi\)
−0.442958 + 0.896542i \(0.646071\pi\)
\(912\) 4.72510 + 35.5617i 0.156464 + 1.17757i
\(913\) 23.0756 + 6.18309i 0.763692 + 0.204631i
\(914\) −1.77837 3.08022i −0.0588232 0.101885i
\(915\) 1.81057 1.57482i 0.0598555 0.0520620i
\(916\) 3.72912 6.45902i 0.123214 0.213412i
\(917\) 4.70300 4.70300i 0.155307 0.155307i
\(918\) −1.96307 0.251276i −0.0647911 0.00829334i
\(919\) 24.8685i 0.820336i 0.912010 + 0.410168i \(0.134530\pi\)
−0.912010 + 0.410168i \(0.865470\pi\)
\(920\) −5.35844 + 10.7230i −0.176662 + 0.353526i
\(921\) −3.13347 + 24.0232i −0.103251 + 0.791592i
\(922\) 0.368621 1.37571i 0.0121399 0.0453066i
\(923\) 17.6034 65.6966i 0.579422 2.16243i
\(924\) −6.47665 4.95740i −0.213066 0.163087i
\(925\) −27.9195 + 11.2212i −0.917986 + 0.368952i
\(926\) 4.04637i 0.132972i
\(927\) 7.32270 12.7537i 0.240509 0.418886i
\(928\) −2.00590 + 2.00590i −0.0658470 + 0.0658470i
\(929\) 23.0525 39.9281i 0.756327 1.31000i −0.188384 0.982095i \(-0.560325\pi\)
0.944712 0.327902i \(-0.106342\pi\)
\(930\) 6.66171 3.25151i 0.218446 0.106621i
\(931\) −2.79287 4.83739i −0.0915326 0.158539i
\(932\) −31.2191 8.36512i −1.02261 0.274009i
\(933\) 15.7642 + 6.50765i 0.516097 + 0.213051i
\(934\) 1.72998 + 0.998805i 0.0566067 + 0.0326819i
\(935\) −6.15562 + 6.94495i −0.201310 + 0.227124i
\(936\) 10.3983 2.81291i 0.339879 0.0919429i
\(937\) −14.6972 14.6972i −0.480136 0.480136i 0.425039 0.905175i \(-0.360260\pi\)
−0.905175 + 0.425039i \(0.860260\pi\)
\(938\) −3.41746 + 0.915705i −0.111584 + 0.0298988i
\(939\) −29.2327 + 38.1913i −0.953972 + 1.24633i
\(940\) −22.4207 4.58275i −0.731282 0.149473i
\(941\) 20.8945 12.0634i 0.681141 0.393257i −0.119144 0.992877i \(-0.538015\pi\)
0.800285 + 0.599620i \(0.204682\pi\)
\(942\) 3.57086 + 4.64213i 0.116345 + 0.151249i
\(943\) −12.4086 46.3096i −0.404080 1.50805i
\(944\) 10.3970 0.338392
\(945\) 3.75328 10.9960i 0.122094 0.357701i
\(946\) 1.79240 0.0582760
\(947\) 1.12942 + 4.21504i 0.0367011 + 0.136970i 0.981845 0.189682i \(-0.0607459\pi\)
−0.945144 + 0.326653i \(0.894079\pi\)
\(948\) −25.2606 32.8388i −0.820427 1.06656i
\(949\) 3.22670 1.86293i 0.104743 0.0604734i
\(950\) 0.872110 6.12463i 0.0282950 0.198709i
\(951\) 17.1037 22.3453i 0.554625 0.724595i
\(952\) −1.45354 + 0.389475i −0.0471095 + 0.0126230i
\(953\) −30.6552 30.6552i −0.993020 0.993020i 0.00695595 0.999976i \(-0.497786\pi\)
−0.999976 + 0.00695595i \(0.997786\pi\)
\(954\) −2.23465 2.22398i −0.0723495 0.0720039i
\(955\) −57.3193 + 3.45354i −1.85481 + 0.111754i
\(956\) −37.3801 21.5814i −1.20896 0.697994i
\(957\) 4.26267 + 1.75968i 0.137792 + 0.0568824i
\(958\) −0.867181 0.232360i −0.0280173 0.00750722i
\(959\) 3.90012 + 6.75520i 0.125941 + 0.218137i
\(960\) −8.62551 + 25.0738i −0.278387 + 0.809253i
\(961\) −21.8315 + 37.8133i −0.704243 + 1.21978i
\(962\) −3.86737 + 3.86737i −0.124689 + 0.124689i
\(963\) 4.47860 + 7.71446i 0.144321 + 0.248595i
\(964\) 48.2055i 1.55260i
\(965\) −9.46641 + 3.15786i −0.304734 + 0.101655i
\(966\) 1.86621 + 1.42845i 0.0600444 + 0.0459596i
\(967\) −14.2214 + 53.0750i −0.457330 + 1.70678i 0.223817 + 0.974631i \(0.428148\pi\)
−0.681147 + 0.732147i \(0.738519\pi\)
\(968\) 1.17197 4.37387i 0.0376687 0.140581i
\(969\) 2.15163 16.4958i 0.0691203 0.529921i
\(970\) 0.641068 + 0.320352i 0.0205835 + 0.0102859i
\(971\) 15.6158i 0.501136i −0.968099 0.250568i \(-0.919383\pi\)
0.968099 0.250568i \(-0.0806174\pi\)
\(972\) 18.6577 + 24.0163i 0.598448 + 0.770323i
\(973\) −4.90433 + 4.90433i −0.157226 + 0.157226i
\(974\) −3.03911 + 5.26390i −0.0973795 + 0.168666i
\(975\) 35.5305 + 0.332088i 1.13789 + 0.0106353i
\(976\) 1.14871 + 1.98962i 0.0367693 + 0.0636862i
\(977\) −42.8953 11.4938i −1.37234 0.367718i −0.504008 0.863699i \(-0.668142\pi\)
−0.868333 + 0.495981i \(0.834809\pi\)
\(978\) −0.563003 4.23724i −0.0180028 0.135492i
\(979\) 17.5706 + 10.1444i 0.561560 + 0.324217i
\(980\) −0.262364 4.35453i −0.00838093 0.139100i
\(981\) 5.60440 + 1.48733i 0.178935 + 0.0474867i
\(982\) 2.38517 + 2.38517i 0.0761138 + 0.0761138i
\(983\) 60.4941 16.2093i 1.92946 0.516998i 0.951863 0.306523i \(-0.0991658\pi\)
0.977599 0.210474i \(-0.0675009\pi\)
\(984\) 4.55324 + 10.9554i 0.145152 + 0.349245i
\(985\) 9.06902 44.3693i 0.288963 1.41372i
\(986\) 0.363850 0.210069i 0.0115874 0.00668996i
\(987\) −3.46699 + 8.39846i −0.110355 + 0.267326i
\(988\) 11.5720 + 43.1873i 0.368155 + 1.37397i
\(989\) 20.5358 0.653002
\(990\) −3.57953 + 0.224271i −0.113765 + 0.00712780i
\(991\) 0.0755681 0.00240050 0.00120025 0.999999i \(-0.499618\pi\)
0.00120025 + 0.999999i \(0.499618\pi\)
\(992\) 5.75129 + 21.4641i 0.182604 + 0.681486i
\(993\) −0.888951 + 0.118115i −0.0282100 + 0.00374827i
\(994\) −3.18002 + 1.83598i −0.100864 + 0.0582338i
\(995\) 3.86344 + 5.84856i 0.122479 + 0.185412i
\(996\) −33.1641 4.32576i −1.05084 0.137067i
\(997\) 40.7049 10.9068i 1.28914 0.345423i 0.451804 0.892117i \(-0.350781\pi\)
0.837332 + 0.546695i \(0.184114\pi\)
\(998\) −4.82485 4.82485i −0.152728 0.152728i
\(999\) −28.9330 11.8629i −0.915399 0.375325i
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 315.2.cc.a.92.19 144
3.2 odd 2 945.2.cf.a.197.18 144
5.3 odd 4 inner 315.2.cc.a.218.19 yes 144
9.4 even 3 945.2.cf.a.827.18 144
9.5 odd 6 inner 315.2.cc.a.302.19 yes 144
15.8 even 4 945.2.cf.a.8.18 144
45.13 odd 12 945.2.cf.a.638.18 144
45.23 even 12 inner 315.2.cc.a.113.19 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.cc.a.92.19 144 1.1 even 1 trivial
315.2.cc.a.113.19 yes 144 45.23 even 12 inner
315.2.cc.a.218.19 yes 144 5.3 odd 4 inner
315.2.cc.a.302.19 yes 144 9.5 odd 6 inner
945.2.cf.a.8.18 144 15.8 even 4
945.2.cf.a.197.18 144 3.2 odd 2
945.2.cf.a.638.18 144 45.13 odd 12
945.2.cf.a.827.18 144 9.4 even 3