Properties

Label 378.2.z.a.83.8
Level $378$
Weight $2$
Character 378.83
Analytic conductor $3.018$
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] = [378,2,Mod(41,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([17, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.z (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 83.8
Character \(\chi\) \(=\) 378.83
Dual form 378.2.z.a.41.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.984808 - 0.173648i) q^{2} +(0.754516 + 1.55907i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.486827 + 0.408497i) q^{5} +(-0.472323 - 1.66641i) q^{6} +(-2.18779 - 1.48781i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.86141 + 2.35269i) q^{9} +O(q^{10})\) \(q+(-0.984808 - 0.173648i) q^{2} +(0.754516 + 1.55907i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.486827 + 0.408497i) q^{5} +(-0.472323 - 1.66641i) q^{6} +(-2.18779 - 1.48781i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.86141 + 2.35269i) q^{9} +(0.550366 - 0.317754i) q^{10} +(-3.72295 + 4.43684i) q^{11} +(0.175779 + 1.72311i) q^{12} +(0.505415 - 0.0891184i) q^{13} +(1.89620 + 1.84511i) q^{14} +(-1.00419 - 0.450782i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.66709 + 2.88748i) q^{17} +(2.24167 - 1.99372i) q^{18} +(-3.56339 - 2.05732i) q^{19} +(-0.597182 + 0.217357i) q^{20} +(0.668877 - 4.53350i) q^{21} +(4.43684 - 3.72295i) q^{22} +(-0.488119 + 1.34109i) q^{23} +(0.126106 - 1.72745i) q^{24} +(-0.798110 + 4.52630i) q^{25} -0.513212 q^{26} +(-5.07248 - 1.12694i) q^{27} +(-1.54699 - 2.14635i) q^{28} +(-3.07257 - 0.541776i) q^{29} +(0.910661 + 0.618310i) q^{30} +(2.46439 - 6.77086i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-9.72638 - 2.45669i) q^{33} +(-1.14036 - 3.13310i) q^{34} +(1.67284 - 0.169400i) q^{35} +(-2.55382 + 1.57416i) q^{36} +(-0.189555 - 0.328318i) q^{37} +(3.15200 + 2.64485i) q^{38} +(0.520286 + 0.720738i) q^{39} +(0.625853 - 0.110355i) q^{40} +(0.877198 + 4.97484i) q^{41} +(-1.44595 + 4.34847i) q^{42} +(7.02881 + 5.89787i) q^{43} +(-5.01592 + 2.89594i) q^{44} +(-0.0548789 - 1.90573i) q^{45} +(0.713582 - 1.23596i) q^{46} +(-5.23895 + 1.90682i) q^{47} +(-0.424160 + 1.67931i) q^{48} +(2.57286 + 6.51002i) q^{49} +(1.57197 - 4.31895i) q^{50} +(-3.24395 + 4.77776i) q^{51} +(0.505415 + 0.0891184i) q^{52} +3.85391i q^{53} +(4.79972 + 1.99064i) q^{54} -3.68079i q^{55} +(1.15078 + 2.38237i) q^{56} +(0.518884 - 7.10787i) q^{57} +(2.93181 + 1.06709i) q^{58} +(2.85807 - 2.39820i) q^{59} +(-0.789458 - 0.767051i) q^{60} +(-0.871745 - 2.39510i) q^{61} +(-3.60270 + 6.24006i) q^{62} +(7.57273 - 2.37777i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.209646 + 0.249846i) q^{65} +(9.15202 + 4.10833i) q^{66} +(-1.36783 - 7.75736i) q^{67} +(0.578974 + 3.28353i) q^{68} +(-2.45916 + 0.250865i) q^{69} +(-1.67684 - 0.123659i) q^{70} +(-2.67680 + 1.54545i) q^{71} +(2.78837 - 1.10678i) q^{72} +(11.5451 + 6.66557i) q^{73} +(0.129663 + 0.356246i) q^{74} +(-7.65902 + 2.17086i) q^{75} +(-2.64485 - 3.15200i) q^{76} +(14.7462 - 4.16785i) q^{77} +(-0.387227 - 0.800135i) q^{78} +(-0.238325 + 1.35161i) q^{79} -0.635508 q^{80} +(-2.07029 - 8.75865i) q^{81} -5.05158i q^{82} +(1.33547 - 7.57382i) q^{83} +(2.17909 - 4.03133i) q^{84} +(-1.99111 - 0.724706i) q^{85} +(-5.89787 - 7.02881i) q^{86} +(-1.47363 - 5.19913i) q^{87} +(5.44259 - 1.98094i) q^{88} +(2.08703 - 3.61484i) q^{89} +(-0.276882 + 1.88631i) q^{90} +(-1.23833 - 0.556988i) q^{91} +(-0.917363 + 1.09327i) q^{92} +(12.4157 - 1.26655i) q^{93} +(5.49047 - 0.968119i) q^{94} +(2.57517 - 0.454071i) q^{95} +(0.709325 - 1.58014i) q^{96} +(-11.4055 + 13.5925i) q^{97} +(-1.40332 - 6.85789i) q^{98} +(-3.50856 - 17.0177i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.984808 0.173648i −0.696364 0.122788i
\(3\) 0.754516 + 1.55907i 0.435620 + 0.900131i
\(4\) 0.939693 + 0.342020i 0.469846 + 0.171010i
\(5\) −0.486827 + 0.408497i −0.217716 + 0.182685i −0.745122 0.666928i \(-0.767609\pi\)
0.527407 + 0.849613i \(0.323164\pi\)
\(6\) −0.472323 1.66641i −0.192825 0.680308i
\(7\) −2.18779 1.48781i −0.826907 0.562338i
\(8\) −0.866025 0.500000i −0.306186 0.176777i
\(9\) −1.86141 + 2.35269i −0.620471 + 0.784230i
\(10\) 0.550366 0.317754i 0.174041 0.100483i
\(11\) −3.72295 + 4.43684i −1.12251 + 1.33776i −0.187859 + 0.982196i \(0.560155\pi\)
−0.934653 + 0.355562i \(0.884289\pi\)
\(12\) 0.175779 + 1.72311i 0.0507429 + 0.497418i
\(13\) 0.505415 0.0891184i 0.140177 0.0247170i −0.103119 0.994669i \(-0.532882\pi\)
0.243296 + 0.969952i \(0.421771\pi\)
\(14\) 1.89620 + 1.84511i 0.506780 + 0.493126i
\(15\) −1.00419 0.450782i −0.259282 0.116391i
\(16\) 0.766044 + 0.642788i 0.191511 + 0.160697i
\(17\) 1.66709 + 2.88748i 0.404329 + 0.700318i 0.994243 0.107148i \(-0.0341719\pi\)
−0.589914 + 0.807466i \(0.700839\pi\)
\(18\) 2.24167 1.99372i 0.528368 0.469923i
\(19\) −3.56339 2.05732i −0.817498 0.471983i 0.0320550 0.999486i \(-0.489795\pi\)
−0.849553 + 0.527503i \(0.823128\pi\)
\(20\) −0.597182 + 0.217357i −0.133534 + 0.0486024i
\(21\) 0.668877 4.53350i 0.145961 0.989290i
\(22\) 4.43684 3.72295i 0.945938 0.793736i
\(23\) −0.488119 + 1.34109i −0.101780 + 0.279638i −0.980122 0.198394i \(-0.936427\pi\)
0.878343 + 0.478032i \(0.158650\pi\)
\(24\) 0.126106 1.72745i 0.0257414 0.352615i
\(25\) −0.798110 + 4.52630i −0.159622 + 0.905261i
\(26\) −0.513212 −0.100649
\(27\) −5.07248 1.12694i −0.976198 0.216879i
\(28\) −1.54699 2.14635i −0.292354 0.405622i
\(29\) −3.07257 0.541776i −0.570561 0.100605i −0.119078 0.992885i \(-0.537994\pi\)
−0.451483 + 0.892280i \(0.649105\pi\)
\(30\) 0.910661 + 0.618310i 0.166263 + 0.112887i
\(31\) 2.46439 6.77086i 0.442618 1.21608i −0.495147 0.868809i \(-0.664886\pi\)
0.937764 0.347273i \(-0.112892\pi\)
\(32\) −0.642788 0.766044i −0.113630 0.135419i
\(33\) −9.72638 2.45669i −1.69315 0.427654i
\(34\) −1.14036 3.13310i −0.195570 0.537323i
\(35\) 1.67284 0.169400i 0.282762 0.0286338i
\(36\) −2.55382 + 1.57416i −0.425637 + 0.262361i
\(37\) −0.189555 0.328318i −0.0311626 0.0539752i 0.850023 0.526745i \(-0.176588\pi\)
−0.881186 + 0.472770i \(0.843254\pi\)
\(38\) 3.15200 + 2.64485i 0.511323 + 0.429051i
\(39\) 0.520286 + 0.720738i 0.0833124 + 0.115410i
\(40\) 0.625853 0.110355i 0.0989561 0.0174486i
\(41\) 0.877198 + 4.97484i 0.136995 + 0.776939i 0.973449 + 0.228902i \(0.0735135\pi\)
−0.836454 + 0.548037i \(0.815375\pi\)
\(42\) −1.44595 + 4.34847i −0.223115 + 0.670984i
\(43\) 7.02881 + 5.89787i 1.07188 + 0.899417i 0.995222 0.0976401i \(-0.0311294\pi\)
0.0766617 + 0.997057i \(0.475574\pi\)
\(44\) −5.01592 + 2.89594i −0.756178 + 0.436580i
\(45\) −0.0548789 1.90573i −0.00818086 0.284090i
\(46\) 0.713582 1.23596i 0.105212 0.182232i
\(47\) −5.23895 + 1.90682i −0.764179 + 0.278139i −0.694560 0.719435i \(-0.744401\pi\)
−0.0696196 + 0.997574i \(0.522179\pi\)
\(48\) −0.424160 + 1.67931i −0.0612222 + 0.242388i
\(49\) 2.57286 + 6.51002i 0.367551 + 0.930003i
\(50\) 1.57197 4.31895i 0.222310 0.610792i
\(51\) −3.24395 + 4.77776i −0.454244 + 0.669021i
\(52\) 0.505415 + 0.0891184i 0.0700885 + 0.0123585i
\(53\) 3.85391i 0.529376i 0.964334 + 0.264688i \(0.0852689\pi\)
−0.964334 + 0.264688i \(0.914731\pi\)
\(54\) 4.79972 + 1.99064i 0.653160 + 0.270892i
\(55\) 3.68079i 0.496318i
\(56\) 1.15078 + 2.38237i 0.153779 + 0.318358i
\(57\) 0.518884 7.10787i 0.0687278 0.941460i
\(58\) 2.93181 + 1.06709i 0.384965 + 0.140116i
\(59\) 2.85807 2.39820i 0.372089 0.312220i −0.437498 0.899219i \(-0.644135\pi\)
0.809587 + 0.587000i \(0.199691\pi\)
\(60\) −0.789458 0.767051i −0.101919 0.0990259i
\(61\) −0.871745 2.39510i −0.111616 0.306661i 0.871291 0.490767i \(-0.163283\pi\)
−0.982906 + 0.184106i \(0.941061\pi\)
\(62\) −3.60270 + 6.24006i −0.457543 + 0.792488i
\(63\) 7.57273 2.37777i 0.954074 0.299571i
\(64\) 0.500000 + 0.866025i 0.0625000 + 0.108253i
\(65\) −0.209646 + 0.249846i −0.0260033 + 0.0309896i
\(66\) 9.15202 + 4.10833i 1.12654 + 0.505701i
\(67\) −1.36783 7.75736i −0.167107 0.947712i −0.946865 0.321631i \(-0.895769\pi\)
0.779758 0.626081i \(-0.215342\pi\)
\(68\) 0.578974 + 3.28353i 0.0702109 + 0.398186i
\(69\) −2.45916 + 0.250865i −0.296048 + 0.0302006i
\(70\) −1.67684 0.123659i −0.200421 0.0147801i
\(71\) −2.67680 + 1.54545i −0.317678 + 0.183412i −0.650357 0.759629i \(-0.725381\pi\)
0.332679 + 0.943040i \(0.392047\pi\)
\(72\) 2.78837 1.10678i 0.328613 0.130435i
\(73\) 11.5451 + 6.66557i 1.35125 + 0.780146i 0.988425 0.151710i \(-0.0484781\pi\)
0.362827 + 0.931856i \(0.381811\pi\)
\(74\) 0.129663 + 0.356246i 0.0150730 + 0.0414128i
\(75\) −7.65902 + 2.17086i −0.884388 + 0.250669i
\(76\) −2.64485 3.15200i −0.303385 0.361560i
\(77\) 14.7462 4.16785i 1.68049 0.474970i
\(78\) −0.387227 0.800135i −0.0438448 0.0905975i
\(79\) −0.238325 + 1.35161i −0.0268136 + 0.152068i −0.995275 0.0970961i \(-0.969045\pi\)
0.968461 + 0.249164i \(0.0801557\pi\)
\(80\) −0.635508 −0.0710520
\(81\) −2.07029 8.75865i −0.230032 0.973183i
\(82\) 5.05158i 0.557854i
\(83\) 1.33547 7.57382i 0.146587 0.831334i −0.819493 0.573090i \(-0.805745\pi\)
0.966079 0.258245i \(-0.0831442\pi\)
\(84\) 2.17909 4.03133i 0.237758 0.439854i
\(85\) −1.99111 0.724706i −0.215966 0.0786054i
\(86\) −5.89787 7.02881i −0.635984 0.757936i
\(87\) −1.47363 5.19913i −0.157990 0.557405i
\(88\) 5.44259 1.98094i 0.580182 0.211169i
\(89\) 2.08703 3.61484i 0.221225 0.383172i −0.733955 0.679198i \(-0.762328\pi\)
0.955180 + 0.296025i \(0.0956613\pi\)
\(90\) −0.276882 + 1.88631i −0.0291859 + 0.198835i
\(91\) −1.23833 0.556988i −0.129813 0.0583882i
\(92\) −0.917363 + 1.09327i −0.0956417 + 0.113981i
\(93\) 12.4157 1.26655i 1.28745 0.131336i
\(94\) 5.49047 0.968119i 0.566299 0.0998538i
\(95\) 2.57517 0.454071i 0.264207 0.0465867i
\(96\) 0.709325 1.58014i 0.0723952 0.161273i
\(97\) −11.4055 + 13.5925i −1.15805 + 1.38011i −0.246389 + 0.969171i \(0.579244\pi\)
−0.911662 + 0.410941i \(0.865200\pi\)
\(98\) −1.40332 6.85789i −0.141757 0.692752i
\(99\) −3.50856 17.0177i −0.352623 1.71035i
\(100\) −2.29806 + 3.98036i −0.229806 + 0.398036i
\(101\) 17.2906 6.29325i 1.72048 0.626202i 0.722595 0.691272i \(-0.242949\pi\)
0.997881 + 0.0650697i \(0.0207270\pi\)
\(102\) 4.02432 4.14187i 0.398467 0.410107i
\(103\) 9.45121 + 11.2635i 0.931255 + 1.10983i 0.993733 + 0.111780i \(0.0356553\pi\)
−0.0624778 + 0.998046i \(0.519900\pi\)
\(104\) −0.482262 0.175529i −0.0472897 0.0172120i
\(105\) 1.52629 + 2.48027i 0.148951 + 0.242049i
\(106\) 0.669225 3.79536i 0.0650009 0.368638i
\(107\) 1.98291i 0.191695i −0.995396 0.0958475i \(-0.969444\pi\)
0.995396 0.0958475i \(-0.0305561\pi\)
\(108\) −4.38113 2.79386i −0.421575 0.268840i
\(109\) 9.10407 0.872012 0.436006 0.899944i \(-0.356393\pi\)
0.436006 + 0.899944i \(0.356393\pi\)
\(110\) −0.639162 + 3.62487i −0.0609417 + 0.345618i
\(111\) 0.368850 0.543251i 0.0350097 0.0515631i
\(112\) −0.719601 2.54601i −0.0679959 0.240575i
\(113\) 12.8426 + 15.3052i 1.20813 + 1.43979i 0.865928 + 0.500169i \(0.166729\pi\)
0.342204 + 0.939626i \(0.388827\pi\)
\(114\) −1.74527 + 6.90978i −0.163459 + 0.647160i
\(115\) −0.310203 0.852277i −0.0289266 0.0794752i
\(116\) −2.70197 1.55998i −0.250872 0.144841i
\(117\) −0.731119 + 1.35497i −0.0675920 + 0.125267i
\(118\) −3.23109 + 1.86547i −0.297446 + 0.171731i
\(119\) 0.648776 8.79752i 0.0594732 0.806467i
\(120\) 0.644267 + 0.892486i 0.0588133 + 0.0814725i
\(121\) −3.91506 22.2034i −0.355914 2.01849i
\(122\) 0.442597 + 2.51009i 0.0400708 + 0.227253i
\(123\) −7.09427 + 5.12121i −0.639669 + 0.461764i
\(124\) 4.63154 5.51965i 0.415925 0.495680i
\(125\) −3.04921 5.28138i −0.272730 0.472381i
\(126\) −7.87058 + 1.02665i −0.701167 + 0.0914616i
\(127\) −7.02060 + 12.1600i −0.622978 + 1.07903i 0.365951 + 0.930634i \(0.380744\pi\)
−0.988928 + 0.148395i \(0.952589\pi\)
\(128\) −0.342020 0.939693i −0.0302306 0.0830579i
\(129\) −3.89186 + 15.4085i −0.342659 + 1.35664i
\(130\) 0.249846 0.209646i 0.0219129 0.0183871i
\(131\) 2.64877 + 0.964074i 0.231424 + 0.0842315i 0.455129 0.890425i \(-0.349593\pi\)
−0.223705 + 0.974657i \(0.571815\pi\)
\(132\) −8.29957 5.63515i −0.722385 0.490477i
\(133\) 4.73505 + 9.80263i 0.410581 + 0.849996i
\(134\) 7.87703i 0.680472i
\(135\) 2.92977 1.52347i 0.252154 0.131119i
\(136\) 3.33418i 0.285904i
\(137\) −16.1337 2.84480i −1.37839 0.243048i −0.565157 0.824983i \(-0.691185\pi\)
−0.813235 + 0.581935i \(0.802296\pi\)
\(138\) 2.46536 + 0.179975i 0.209865 + 0.0153205i
\(139\) 4.76880 13.1022i 0.404484 1.11131i −0.555563 0.831474i \(-0.687497\pi\)
0.960047 0.279837i \(-0.0902805\pi\)
\(140\) 1.62989 + 0.412961i 0.137751 + 0.0349016i
\(141\) −6.92574 6.72917i −0.583253 0.566699i
\(142\) 2.90450 1.05715i 0.243740 0.0887143i
\(143\) −1.48623 + 2.57423i −0.124285 + 0.215268i
\(144\) −2.93820 + 0.605771i −0.244850 + 0.0504809i
\(145\) 1.71712 0.991381i 0.142599 0.0823297i
\(146\) −10.2122 8.56909i −0.845171 0.709183i
\(147\) −8.20833 + 8.92319i −0.677012 + 0.735972i
\(148\) −0.0658317 0.373350i −0.00541133 0.0306892i
\(149\) 21.7811 3.84060i 1.78438 0.314634i 0.818671 0.574263i \(-0.194711\pi\)
0.965708 + 0.259629i \(0.0836004\pi\)
\(150\) 7.91963 0.807901i 0.646635 0.0659649i
\(151\) 8.15215 + 6.84046i 0.663412 + 0.556669i 0.911107 0.412169i \(-0.135229\pi\)
−0.247695 + 0.968838i \(0.579673\pi\)
\(152\) 2.05732 + 3.56339i 0.166871 + 0.289029i
\(153\) −9.89649 1.45266i −0.800084 0.117440i
\(154\) −15.2459 + 1.54388i −1.22855 + 0.124409i
\(155\) 1.56614 + 4.30294i 0.125795 + 0.345620i
\(156\) 0.242402 + 0.855220i 0.0194077 + 0.0684724i
\(157\) 6.16172 + 7.34326i 0.491759 + 0.586056i 0.953664 0.300874i \(-0.0972783\pi\)
−0.461905 + 0.886929i \(0.652834\pi\)
\(158\) 0.469408 1.28969i 0.0373441 0.102602i
\(159\) −6.00853 + 2.90784i −0.476507 + 0.230607i
\(160\) 0.625853 + 0.110355i 0.0494780 + 0.00872431i
\(161\) 3.06319 2.20781i 0.241413 0.174000i
\(162\) 0.517911 + 8.98509i 0.0406910 + 0.705935i
\(163\) −11.0908 −0.868699 −0.434350 0.900744i \(-0.643022\pi\)
−0.434350 + 0.900744i \(0.643022\pi\)
\(164\) −0.877198 + 4.97484i −0.0684976 + 0.388469i
\(165\) 5.73862 2.77721i 0.446751 0.216206i
\(166\) −2.63036 + 7.22685i −0.204155 + 0.560913i
\(167\) −16.7437 + 14.0496i −1.29567 + 1.08719i −0.304791 + 0.952419i \(0.598587\pi\)
−0.990876 + 0.134775i \(0.956969\pi\)
\(168\) −2.84601 + 3.59169i −0.219575 + 0.277105i
\(169\) −11.9685 + 4.35618i −0.920654 + 0.335091i
\(170\) 1.83502 + 1.05945i 0.140740 + 0.0812560i
\(171\) 11.4732 4.55402i 0.877376 0.348255i
\(172\) 4.58773 + 7.94618i 0.349811 + 0.605891i
\(173\) −15.6285 13.1139i −1.18821 0.997030i −0.999889 0.0149227i \(-0.995250\pi\)
−0.188325 0.982107i \(-0.560306\pi\)
\(174\) 0.548423 + 5.37604i 0.0415758 + 0.407556i
\(175\) 8.48036 8.71517i 0.641055 0.658805i
\(176\) −5.70389 + 1.00575i −0.429947 + 0.0758113i
\(177\) 5.89543 + 2.64645i 0.443128 + 0.198920i
\(178\) −2.68303 + 3.19751i −0.201102 + 0.239664i
\(179\) −13.4545 + 7.76794i −1.00563 + 0.580603i −0.909911 0.414805i \(-0.863850\pi\)
−0.0957240 + 0.995408i \(0.530517\pi\)
\(180\) 0.600230 1.80957i 0.0447385 0.134878i
\(181\) −5.90948 3.41184i −0.439248 0.253600i 0.264030 0.964514i \(-0.414948\pi\)
−0.703279 + 0.710914i \(0.748281\pi\)
\(182\) 1.12280 + 0.763561i 0.0832276 + 0.0565989i
\(183\) 3.07639 3.16625i 0.227413 0.234056i
\(184\) 1.09327 0.917363i 0.0805970 0.0676289i
\(185\) 0.226397 + 0.0824019i 0.0166451 + 0.00605831i
\(186\) −12.4470 0.908647i −0.912658 0.0666252i
\(187\) −19.0178 3.35335i −1.39072 0.245221i
\(188\) −5.57517 −0.406611
\(189\) 9.42085 + 10.0124i 0.685266 + 0.728293i
\(190\) −2.61489 −0.189704
\(191\) −15.6102 2.75250i −1.12951 0.199164i −0.422500 0.906363i \(-0.638847\pi\)
−0.707015 + 0.707199i \(0.749959\pi\)
\(192\) −0.972938 + 1.43297i −0.0702158 + 0.103415i
\(193\) 10.2343 + 3.72497i 0.736679 + 0.268129i 0.682989 0.730429i \(-0.260680\pi\)
0.0536896 + 0.998558i \(0.482902\pi\)
\(194\) 13.5925 11.4055i 0.975886 0.818866i
\(195\) −0.547708 0.138340i −0.0392222 0.00990673i
\(196\) 0.191138 + 6.99739i 0.0136527 + 0.499814i
\(197\) 19.7320 + 11.3923i 1.40585 + 0.811667i 0.994984 0.100030i \(-0.0318938\pi\)
0.410864 + 0.911697i \(0.365227\pi\)
\(198\) 0.500154 + 17.3685i 0.0355444 + 1.23432i
\(199\) −9.06480 + 5.23356i −0.642586 + 0.370997i −0.785610 0.618722i \(-0.787651\pi\)
0.143024 + 0.989719i \(0.454317\pi\)
\(200\) 2.95434 3.52084i 0.208903 0.248961i
\(201\) 11.0622 7.98560i 0.780270 0.563261i
\(202\) −18.1207 + 3.19517i −1.27497 + 0.224811i
\(203\) 5.91607 + 5.75668i 0.415227 + 0.404040i
\(204\) −4.68241 + 3.38013i −0.327834 + 0.236657i
\(205\) −2.45925 2.06355i −0.171761 0.144125i
\(206\) −7.35173 12.7336i −0.512220 0.887190i
\(207\) −2.24659 3.64472i −0.156149 0.253326i
\(208\) 0.444455 + 0.256606i 0.0308174 + 0.0177924i
\(209\) 22.3944 8.15088i 1.54905 0.563808i
\(210\) −1.07241 2.70762i −0.0740033 0.186844i
\(211\) −7.28487 + 6.11273i −0.501511 + 0.420818i −0.858130 0.513432i \(-0.828374\pi\)
0.356619 + 0.934250i \(0.383929\pi\)
\(212\) −1.31812 + 3.62149i −0.0905286 + 0.248725i
\(213\) −4.42916 3.00726i −0.303481 0.206054i
\(214\) −0.344329 + 1.95278i −0.0235378 + 0.133490i
\(215\) −5.83108 −0.397676
\(216\) 3.82942 + 3.51219i 0.260559 + 0.238975i
\(217\) −15.4653 + 11.1467i −1.04985 + 0.756686i
\(218\) −8.96576 1.58091i −0.607238 0.107072i
\(219\) −1.68114 + 23.0289i −0.113601 + 1.55615i
\(220\) 1.25890 3.45881i 0.0848753 0.233193i
\(221\) 1.09990 + 1.31081i 0.0739873 + 0.0881747i
\(222\) −0.457581 + 0.470948i −0.0307108 + 0.0316079i
\(223\) 8.69071 + 23.8775i 0.581973 + 1.59896i 0.784804 + 0.619745i \(0.212764\pi\)
−0.202830 + 0.979214i \(0.565014\pi\)
\(224\) 0.266558 + 2.63229i 0.0178102 + 0.175877i
\(225\) −9.16337 10.3030i −0.610892 0.686868i
\(226\) −9.98978 17.3028i −0.664510 1.15097i
\(227\) −8.24824 6.92110i −0.547455 0.459369i 0.326623 0.945155i \(-0.394089\pi\)
−0.874078 + 0.485785i \(0.838534\pi\)
\(228\) 2.91862 6.50174i 0.193291 0.430588i
\(229\) −11.3312 + 1.99800i −0.748788 + 0.132032i −0.535004 0.844849i \(-0.679690\pi\)
−0.213784 + 0.976881i \(0.568579\pi\)
\(230\) 0.157494 + 0.893195i 0.0103849 + 0.0588955i
\(231\) 17.6242 + 19.8457i 1.15959 + 1.30575i
\(232\) 2.39003 + 2.00547i 0.156913 + 0.131666i
\(233\) 10.9246 6.30731i 0.715694 0.413206i −0.0974721 0.995238i \(-0.531076\pi\)
0.813166 + 0.582032i \(0.197742\pi\)
\(234\) 0.955300 1.20743i 0.0624499 0.0789321i
\(235\) 1.77153 3.06839i 0.115562 0.200159i
\(236\) 3.50594 1.27606i 0.228217 0.0830643i
\(237\) −2.28707 + 0.648242i −0.148561 + 0.0421079i
\(238\) −2.16659 + 8.55121i −0.140439 + 0.554292i
\(239\) 5.39158 14.8133i 0.348753 0.958190i −0.634011 0.773324i \(-0.718593\pi\)
0.982764 0.184866i \(-0.0591851\pi\)
\(240\) −0.479501 0.990803i −0.0309516 0.0639561i
\(241\) −10.2809 1.81281i −0.662254 0.116773i −0.167589 0.985857i \(-0.553598\pi\)
−0.494665 + 0.869084i \(0.664709\pi\)
\(242\) 22.5459i 1.44931i
\(243\) 12.0933 9.83626i 0.775786 0.630997i
\(244\) 2.54881i 0.163171i
\(245\) −3.91186 2.11825i −0.249920 0.135330i
\(246\) 7.87578 3.81150i 0.502141 0.243012i
\(247\) −1.98434 0.722240i −0.126260 0.0459550i
\(248\) −5.51965 + 4.63154i −0.350498 + 0.294103i
\(249\) 12.8158 3.63247i 0.812166 0.230199i
\(250\) 2.08578 + 5.73064i 0.131916 + 0.362437i
\(251\) 2.66950 4.62370i 0.168497 0.291846i −0.769395 0.638774i \(-0.779442\pi\)
0.937892 + 0.346928i \(0.112775\pi\)
\(252\) 7.92928 + 0.355655i 0.499498 + 0.0224041i
\(253\) −4.13298 7.15854i −0.259838 0.450053i
\(254\) 9.02551 10.7562i 0.566311 0.674903i
\(255\) −0.372457 3.65109i −0.0233242 0.228640i
\(256\) 0.173648 + 0.984808i 0.0108530 + 0.0615505i
\(257\) −3.11009 17.6382i −0.194002 1.10024i −0.913833 0.406090i \(-0.866892\pi\)
0.719831 0.694149i \(-0.244219\pi\)
\(258\) 6.50839 14.4986i 0.405194 0.902641i
\(259\) −0.0737684 + 1.00031i −0.00458374 + 0.0621564i
\(260\) −0.282455 + 0.163075i −0.0175171 + 0.0101135i
\(261\) 6.99394 6.22032i 0.432914 0.385028i
\(262\) −2.44112 1.40938i −0.150813 0.0870719i
\(263\) 1.75653 + 4.82602i 0.108312 + 0.297585i 0.981994 0.188913i \(-0.0604964\pi\)
−0.873682 + 0.486498i \(0.838274\pi\)
\(264\) 7.19495 + 6.99074i 0.442819 + 0.430250i
\(265\) −1.57431 1.87619i −0.0967092 0.115253i
\(266\) −2.96091 10.4759i −0.181545 0.642321i
\(267\) 7.21049 + 0.526376i 0.441275 + 0.0322137i
\(268\) 1.36783 7.75736i 0.0835536 0.473856i
\(269\) −18.0618 −1.10125 −0.550624 0.834754i \(-0.685610\pi\)
−0.550624 + 0.834754i \(0.685610\pi\)
\(270\) −3.14981 + 0.991572i −0.191691 + 0.0603452i
\(271\) 9.13586i 0.554964i −0.960731 0.277482i \(-0.910500\pi\)
0.960731 0.277482i \(-0.0894999\pi\)
\(272\) −0.578974 + 3.28353i −0.0351055 + 0.199093i
\(273\) −0.0659574 2.35091i −0.00399193 0.142283i
\(274\) 15.3946 + 5.60316i 0.930020 + 0.338500i
\(275\) −17.1112 20.3923i −1.03184 1.22970i
\(276\) −2.39665 0.605345i −0.144262 0.0364375i
\(277\) 26.8186 9.76116i 1.61137 0.586492i 0.629661 0.776870i \(-0.283194\pi\)
0.981711 + 0.190378i \(0.0609714\pi\)
\(278\) −6.97152 + 12.0750i −0.418124 + 0.724212i
\(279\) 11.3425 + 18.4013i 0.679056 + 1.10166i
\(280\) −1.53342 0.689716i −0.0916395 0.0412184i
\(281\) 3.73499 4.45119i 0.222811 0.265536i −0.643046 0.765828i \(-0.722330\pi\)
0.865857 + 0.500292i \(0.166774\pi\)
\(282\) 5.65202 + 7.82959i 0.336573 + 0.466245i
\(283\) −22.8862 + 4.03545i −1.36044 + 0.239883i −0.805791 0.592200i \(-0.798260\pi\)
−0.554652 + 0.832083i \(0.687149\pi\)
\(284\) −3.04395 + 0.536730i −0.180625 + 0.0318491i
\(285\) 2.65093 + 3.67227i 0.157028 + 0.217526i
\(286\) 1.91066 2.27704i 0.112980 0.134644i
\(287\) 5.48247 12.1890i 0.323620 0.719494i
\(288\) 2.99876 0.0863543i 0.176703 0.00508848i
\(289\) 2.94162 5.09504i 0.173037 0.299708i
\(290\) −1.86319 + 0.678145i −0.109410 + 0.0398220i
\(291\) −29.7973 7.52620i −1.74675 0.441194i
\(292\) 8.56909 + 10.2122i 0.501468 + 0.597626i
\(293\) −15.6864 5.70937i −0.916407 0.333545i −0.159599 0.987182i \(-0.551020\pi\)
−0.756808 + 0.653637i \(0.773242\pi\)
\(294\) 9.63313 7.36226i 0.561815 0.429376i
\(295\) −0.411727 + 2.33502i −0.0239717 + 0.135950i
\(296\) 0.379109i 0.0220353i
\(297\) 23.8846 18.3102i 1.38593 1.06247i
\(298\) −22.1171 −1.28121
\(299\) −0.127186 + 0.721310i −0.00735538 + 0.0417145i
\(300\) −7.93960 0.579602i −0.458393 0.0334633i
\(301\) −6.60267 23.3608i −0.380572 1.34650i
\(302\) −6.84046 8.15215i −0.393624 0.469103i
\(303\) 22.8576 + 22.2089i 1.31314 + 1.27587i
\(304\) −1.40729 3.86651i −0.0807138 0.221759i
\(305\) 1.40278 + 0.809895i 0.0803229 + 0.0463745i
\(306\) 9.49389 + 3.14909i 0.542730 + 0.180022i
\(307\) 3.43942 1.98575i 0.196298 0.113333i −0.398630 0.917112i \(-0.630514\pi\)
0.594928 + 0.803779i \(0.297181\pi\)
\(308\) 15.2824 + 1.12700i 0.870795 + 0.0642170i
\(309\) −10.4295 + 23.2336i −0.593316 + 1.32171i
\(310\) −0.795150 4.50952i −0.0451615 0.256124i
\(311\) −0.777795 4.41110i −0.0441047 0.250130i 0.954782 0.297307i \(-0.0960886\pi\)
−0.998887 + 0.0471771i \(0.984977\pi\)
\(312\) −0.0902117 0.884320i −0.00510723 0.0500648i
\(313\) −13.5703 + 16.1725i −0.767039 + 0.914122i −0.998271 0.0587768i \(-0.981280\pi\)
0.231232 + 0.972899i \(0.425724\pi\)
\(314\) −4.79297 8.30167i −0.270483 0.468490i
\(315\) −2.71530 + 4.25100i −0.152990 + 0.239517i
\(316\) −0.686228 + 1.18858i −0.0386034 + 0.0668630i
\(317\) −4.74188 13.0282i −0.266331 0.731737i −0.998707 0.0508372i \(-0.983811\pi\)
0.732376 0.680900i \(-0.238411\pi\)
\(318\) 6.42219 1.82029i 0.360138 0.102077i
\(319\) 13.8428 11.6155i 0.775047 0.650342i
\(320\) −0.597182 0.217357i −0.0333835 0.0121506i
\(321\) 3.09150 1.49614i 0.172551 0.0835061i
\(322\) −3.40004 + 1.64235i −0.189477 + 0.0915246i
\(323\) 13.7190i 0.763344i
\(324\) 1.05020 8.93852i 0.0583445 0.496584i
\(325\) 2.35879i 0.130842i
\(326\) 10.9223 + 1.92590i 0.604931 + 0.106666i
\(327\) 6.86916 + 14.1939i 0.379866 + 0.784925i
\(328\) 1.72774 4.74693i 0.0953986 0.262106i
\(329\) 14.2987 + 3.62282i 0.788313 + 0.199733i
\(330\) −6.13369 + 1.73852i −0.337649 + 0.0957024i
\(331\) −0.858086 + 0.312318i −0.0471647 + 0.0171665i −0.365495 0.930813i \(-0.619100\pi\)
0.318330 + 0.947980i \(0.396878\pi\)
\(332\) 3.84533 6.66030i 0.211040 0.365532i
\(333\) 1.12527 + 0.165173i 0.0616644 + 0.00905141i
\(334\) 18.9290 10.9287i 1.03575 0.597991i
\(335\) 3.83475 + 3.21774i 0.209515 + 0.175804i
\(336\) 3.42647 3.04292i 0.186929 0.166005i
\(337\) −1.72863 9.80357i −0.0941647 0.534035i −0.995000 0.0998738i \(-0.968156\pi\)
0.900835 0.434161i \(-0.142955\pi\)
\(338\) 12.5431 2.21169i 0.682256 0.120300i
\(339\) −14.1720 + 31.5706i −0.769718 + 1.71468i
\(340\) −1.62317 1.36200i −0.0880287 0.0738649i
\(341\) 20.8664 + 36.1417i 1.12998 + 1.95718i
\(342\) −12.0897 + 2.49254i −0.653735 + 0.134781i
\(343\) 4.05678 18.0705i 0.219046 0.975715i
\(344\) −3.13819 8.62211i −0.169200 0.464873i
\(345\) 1.09471 1.12669i 0.0589371 0.0606587i
\(346\) 13.1139 + 15.6285i 0.705006 + 0.840194i
\(347\) −4.67022 + 12.8313i −0.250710 + 0.688821i 0.748946 + 0.662631i \(0.230560\pi\)
−0.999657 + 0.0261909i \(0.991662\pi\)
\(348\) 0.393448 5.38960i 0.0210910 0.288913i
\(349\) 11.1326 + 1.96297i 0.595912 + 0.105075i 0.463466 0.886115i \(-0.346606\pi\)
0.132446 + 0.991190i \(0.457717\pi\)
\(350\) −9.86490 + 7.11017i −0.527301 + 0.380055i
\(351\) −2.66414 0.117520i −0.142201 0.00627277i
\(352\) 5.79188 0.308708
\(353\) −3.50744 + 19.8917i −0.186682 + 1.05873i 0.737093 + 0.675791i \(0.236198\pi\)
−0.923775 + 0.382935i \(0.874913\pi\)
\(354\) −5.34631 3.62998i −0.284153 0.192931i
\(355\) 0.671829 1.84583i 0.0356570 0.0979667i
\(356\) 3.19751 2.68303i 0.169468 0.142200i
\(357\) 14.2055 5.62638i 0.751834 0.297779i
\(358\) 14.5990 5.31359i 0.771579 0.280832i
\(359\) 0.0633911 + 0.0365989i 0.00334566 + 0.00193162i 0.501672 0.865058i \(-0.332718\pi\)
−0.498326 + 0.866990i \(0.666052\pi\)
\(360\) −0.905341 + 1.67785i −0.0477156 + 0.0884307i
\(361\) −1.03483 1.79238i −0.0544648 0.0943359i
\(362\) 5.22724 + 4.38618i 0.274738 + 0.230532i
\(363\) 31.6627 22.8567i 1.66186 1.19966i
\(364\) −0.973152 0.946933i −0.0510070 0.0496328i
\(365\) −8.34334 + 1.47116i −0.436710 + 0.0770038i
\(366\) −3.57947 + 2.58394i −0.187102 + 0.135065i
\(367\) 19.7388 23.5238i 1.03036 1.22793i 0.0570611 0.998371i \(-0.481827\pi\)
0.973295 0.229559i \(-0.0737285\pi\)
\(368\) −1.23596 + 0.713582i −0.0644289 + 0.0371980i
\(369\) −13.3371 7.19645i −0.694300 0.374632i
\(370\) −0.208649 0.120464i −0.0108471 0.00626260i
\(371\) 5.73388 8.43156i 0.297688 0.437745i
\(372\) 12.1001 + 3.05624i 0.627361 + 0.158459i
\(373\) −23.4944 + 19.7142i −1.21650 + 1.02076i −0.217495 + 0.976061i \(0.569789\pi\)
−0.999000 + 0.0446993i \(0.985767\pi\)
\(374\) 18.1466 + 6.60481i 0.938337 + 0.341527i
\(375\) 5.93338 8.73882i 0.306399 0.451271i
\(376\) 5.49047 + 0.968119i 0.283150 + 0.0499269i
\(377\) −1.60120 −0.0824662
\(378\) −7.53910 11.4962i −0.387769 0.591299i
\(379\) 10.9028 0.560038 0.280019 0.959995i \(-0.409659\pi\)
0.280019 + 0.959995i \(0.409659\pi\)
\(380\) 2.57517 + 0.454071i 0.132103 + 0.0232934i
\(381\) −24.2555 1.77069i −1.24265 0.0907150i
\(382\) 14.8951 + 5.42137i 0.762099 + 0.277381i
\(383\) −4.68369 + 3.93008i −0.239325 + 0.200818i −0.754559 0.656232i \(-0.772149\pi\)
0.515234 + 0.857049i \(0.327705\pi\)
\(384\) 1.20699 1.24225i 0.0615939 0.0633931i
\(385\) −5.47631 + 8.05280i −0.279098 + 0.410409i
\(386\) −9.43195 5.44554i −0.480074 0.277171i
\(387\) −26.9594 + 5.55823i −1.37042 + 0.282541i
\(388\) −15.3666 + 8.87189i −0.780119 + 0.450402i
\(389\) −11.8344 + 14.1037i −0.600027 + 0.715084i −0.977500 0.210937i \(-0.932349\pi\)
0.377473 + 0.926021i \(0.376793\pi\)
\(390\) 0.515365 + 0.231347i 0.0260965 + 0.0117147i
\(391\) −4.68613 + 0.826291i −0.236988 + 0.0417873i
\(392\) 1.02685 6.92427i 0.0518638 0.349729i
\(393\) 0.495478 + 4.85703i 0.0249936 + 0.245005i
\(394\) −17.4540 14.6456i −0.879320 0.737837i
\(395\) −0.436104 0.755353i −0.0219428 0.0380060i
\(396\) 2.52344 17.1914i 0.126808 0.863902i
\(397\) 24.3764 + 14.0737i 1.22342 + 0.706340i 0.965645 0.259866i \(-0.0836784\pi\)
0.257772 + 0.966206i \(0.417012\pi\)
\(398\) 9.83588 3.57997i 0.493028 0.179448i
\(399\) −11.7103 + 14.7785i −0.586251 + 0.739852i
\(400\) −3.52084 + 2.95434i −0.176042 + 0.147717i
\(401\) −10.3696 + 28.4901i −0.517831 + 1.42273i 0.355074 + 0.934838i \(0.384456\pi\)
−0.872905 + 0.487891i \(0.837766\pi\)
\(402\) −12.2809 + 5.94334i −0.612513 + 0.296427i
\(403\) 0.642133 3.64172i 0.0319869 0.181407i
\(404\) 18.4002 0.915446
\(405\) 4.58575 + 3.41824i 0.227868 + 0.169854i
\(406\) −4.82656 6.69654i −0.239538 0.332344i
\(407\) 2.16240 + 0.381289i 0.107186 + 0.0188998i
\(408\) 5.19823 2.51569i 0.257351 0.124545i
\(409\) −3.44095 + 9.45394i −0.170144 + 0.467467i −0.995232 0.0975374i \(-0.968903\pi\)
0.825088 + 0.565005i \(0.191126\pi\)
\(410\) 2.06355 + 2.45925i 0.101912 + 0.121454i
\(411\) −7.73785 27.3000i −0.381680 1.34661i
\(412\) 5.02888 + 13.8167i 0.247755 + 0.680702i
\(413\) −9.82092 + 0.994514i −0.483256 + 0.0489369i
\(414\) 1.57956 + 3.97947i 0.0776311 + 0.195580i
\(415\) 2.44374 + 4.23268i 0.119958 + 0.207774i
\(416\) −0.393143 0.329886i −0.0192754 0.0161740i
\(417\) 24.0254 2.45089i 1.17653 0.120021i
\(418\) −23.4695 + 4.13831i −1.14793 + 0.202411i
\(419\) 4.20764 + 23.8627i 0.205556 + 1.16577i 0.896562 + 0.442919i \(0.146057\pi\)
−0.691005 + 0.722850i \(0.742832\pi\)
\(420\) 0.585944 + 2.85271i 0.0285912 + 0.139198i
\(421\) 0.481683 + 0.404180i 0.0234758 + 0.0196985i 0.654450 0.756105i \(-0.272900\pi\)
−0.630974 + 0.775804i \(0.717345\pi\)
\(422\) 8.23566 4.75486i 0.400905 0.231463i
\(423\) 5.26569 15.8750i 0.256027 0.771869i
\(424\) 1.92696 3.33759i 0.0935813 0.162088i
\(425\) −14.4002 + 5.24123i −0.698510 + 0.254237i
\(426\) 3.83967 + 3.73069i 0.186033 + 0.180753i
\(427\) −1.65625 + 6.53697i −0.0801516 + 0.316346i
\(428\) 0.678195 1.86332i 0.0327818 0.0900672i
\(429\) −5.13480 0.374847i −0.247910 0.0180978i
\(430\) 5.74249 + 1.01256i 0.276928 + 0.0488298i
\(431\) 2.89765i 0.139575i −0.997562 0.0697875i \(-0.977768\pi\)
0.997562 0.0697875i \(-0.0222321\pi\)
\(432\) −3.16136 4.12381i −0.152101 0.198407i
\(433\) 5.77940i 0.277740i −0.990311 0.138870i \(-0.955653\pi\)
0.990311 0.138870i \(-0.0443471\pi\)
\(434\) 17.1660 8.29182i 0.823992 0.398020i
\(435\) 2.84123 + 1.92911i 0.136227 + 0.0924936i
\(436\) 8.55503 + 3.11378i 0.409712 + 0.149123i
\(437\) 4.49842 3.77463i 0.215189 0.180565i
\(438\) 5.65453 22.3871i 0.270184 1.06970i
\(439\) −12.9832 35.6709i −0.619652 1.70248i −0.707837 0.706376i \(-0.750329\pi\)
0.0881850 0.996104i \(-0.471893\pi\)
\(440\) −1.84039 + 3.18766i −0.0877374 + 0.151966i
\(441\) −20.1052 6.06470i −0.957391 0.288795i
\(442\) −0.855571 1.48189i −0.0406954 0.0704864i
\(443\) 1.51019 1.79977i 0.0717512 0.0855097i −0.728975 0.684541i \(-0.760003\pi\)
0.800726 + 0.599031i \(0.204447\pi\)
\(444\) 0.532408 0.384335i 0.0252670 0.0182397i
\(445\) 0.460627 + 2.61235i 0.0218358 + 0.123837i
\(446\) −4.41239 25.0239i −0.208933 1.18492i
\(447\) 22.4220 + 31.0605i 1.06052 + 1.46911i
\(448\) 0.194583 2.63859i 0.00919320 0.124661i
\(449\) 7.90828 4.56585i 0.373215 0.215476i −0.301647 0.953420i \(-0.597536\pi\)
0.674862 + 0.737944i \(0.264203\pi\)
\(450\) 7.23506 + 11.7377i 0.341064 + 0.553320i
\(451\) −25.3383 14.6291i −1.19314 0.688857i
\(452\) 6.83341 + 18.7746i 0.321417 + 0.883085i
\(453\) −4.51386 + 17.8710i −0.212079 + 0.839654i
\(454\) 6.92110 + 8.24824i 0.324823 + 0.387109i
\(455\) 0.830383 0.234698i 0.0389290 0.0110028i
\(456\) −4.00330 + 5.89615i −0.187472 + 0.276113i
\(457\) −4.03573 + 22.8878i −0.188783 + 1.07064i 0.732214 + 0.681075i \(0.238487\pi\)
−0.920997 + 0.389569i \(0.872624\pi\)
\(458\) 11.5060 0.537641
\(459\) −5.20226 16.5254i −0.242821 0.771340i
\(460\) 0.906974i 0.0422879i
\(461\) 4.45849 25.2853i 0.207652 1.17766i −0.685559 0.728017i \(-0.740442\pi\)
0.893211 0.449638i \(-0.148447\pi\)
\(462\) −13.9103 22.6046i −0.647165 1.05166i
\(463\) 24.6191 + 8.96061i 1.14415 + 0.416435i 0.843409 0.537272i \(-0.180545\pi\)
0.300737 + 0.953707i \(0.402767\pi\)
\(464\) −2.00547 2.39003i −0.0931018 0.110954i
\(465\) −5.52691 + 5.68836i −0.256304 + 0.263791i
\(466\) −11.8539 + 4.31446i −0.549120 + 0.199863i
\(467\) 3.89959 6.75429i 0.180452 0.312551i −0.761583 0.648068i \(-0.775577\pi\)
0.942034 + 0.335516i \(0.108911\pi\)
\(468\) −1.15045 + 1.02320i −0.0531798 + 0.0472974i
\(469\) −8.54893 + 19.0066i −0.394753 + 0.877641i
\(470\) −2.27744 + 2.71415i −0.105050 + 0.125194i
\(471\) −6.79955 + 15.1472i −0.313307 + 0.697945i
\(472\) −3.67426 + 0.647871i −0.169122 + 0.0298207i
\(473\) −52.3358 + 9.22822i −2.40640 + 0.424314i
\(474\) 2.36489 0.241248i 0.108623 0.0110809i
\(475\) 12.1561 14.4870i 0.557758 0.664710i
\(476\) 3.61858 8.04507i 0.165857 0.368745i
\(477\) −9.06706 7.17372i −0.415152 0.328462i
\(478\) −7.88197 + 13.6520i −0.360513 + 0.624426i
\(479\) −37.5764 + 13.6767i −1.71691 + 0.624903i −0.997564 0.0697511i \(-0.977779\pi\)
−0.719344 + 0.694655i \(0.755557\pi\)
\(480\) 0.300165 + 1.05901i 0.0137006 + 0.0483372i
\(481\) −0.125063 0.149044i −0.00570239 0.00679584i
\(482\) 9.80996 + 3.57053i 0.446831 + 0.162633i
\(483\) 5.75336 + 3.10991i 0.261787 + 0.141506i
\(484\) 3.91506 22.2034i 0.177957 1.00925i
\(485\) 11.2763i 0.512031i
\(486\) −13.6176 + 7.58685i −0.617708 + 0.344146i
\(487\) 33.9761 1.53961 0.769803 0.638282i \(-0.220355\pi\)
0.769803 + 0.638282i \(0.220355\pi\)
\(488\) −0.442597 + 2.51009i −0.0200354 + 0.113626i
\(489\) −8.36819 17.2914i −0.378422 0.781943i
\(490\) 3.48460 + 2.76536i 0.157418 + 0.124926i
\(491\) 10.8839 + 12.9710i 0.491185 + 0.585371i 0.953518 0.301335i \(-0.0974322\pi\)
−0.462334 + 0.886706i \(0.652988\pi\)
\(492\) −8.41799 + 2.38598i −0.379512 + 0.107568i
\(493\) −3.55787 9.77517i −0.160239 0.440252i
\(494\) 1.82878 + 1.05584i 0.0822805 + 0.0475047i
\(495\) 8.65975 + 6.85147i 0.389227 + 0.307951i
\(496\) 6.24006 3.60270i 0.280187 0.161766i
\(497\) 8.15562 + 0.601439i 0.365830 + 0.0269782i
\(498\) −13.2518 + 1.35185i −0.593829 + 0.0605780i
\(499\) 2.91424 + 16.5275i 0.130459 + 0.739872i 0.977915 + 0.209005i \(0.0670225\pi\)
−0.847455 + 0.530867i \(0.821866\pi\)
\(500\) −1.05898 6.00577i −0.0473590 0.268586i
\(501\) −34.5378 15.5040i −1.54304 0.692667i
\(502\) −3.43184 + 4.08991i −0.153170 + 0.182541i
\(503\) 16.1195 + 27.9198i 0.718734 + 1.24488i 0.961502 + 0.274799i \(0.0886113\pi\)
−0.242768 + 0.970084i \(0.578055\pi\)
\(504\) −7.74706 1.72716i −0.345081 0.0769337i
\(505\) −5.84675 + 10.1269i −0.260177 + 0.450640i
\(506\) 2.82713 + 7.76747i 0.125681 + 0.345306i
\(507\) −15.8220 15.3730i −0.702680 0.682737i
\(508\) −10.7562 + 9.02551i −0.477229 + 0.400442i
\(509\) −27.2666 9.92421i −1.20857 0.439883i −0.342362 0.939568i \(-0.611227\pi\)
−0.866207 + 0.499685i \(0.833449\pi\)
\(510\) −0.267207 + 3.66030i −0.0118321 + 0.162081i
\(511\) −15.3412 31.7598i −0.678655 1.40497i
\(512\) 1.00000i 0.0441942i
\(513\) 15.7567 + 14.4514i 0.695677 + 0.638047i
\(514\) 17.9103i 0.789989i
\(515\) −9.20221 1.62260i −0.405498 0.0715002i
\(516\) −8.92716 + 13.1481i −0.392996 + 0.578814i
\(517\) 11.0441 30.3434i 0.485719 1.33450i
\(518\) 0.246350 0.972306i 0.0108240 0.0427207i
\(519\) 8.65353 34.2606i 0.379848 1.50387i
\(520\) 0.306481 0.111550i 0.0134401 0.00489179i
\(521\) 10.9353 18.9406i 0.479086 0.829801i −0.520626 0.853785i \(-0.674302\pi\)
0.999712 + 0.0239834i \(0.00763490\pi\)
\(522\) −7.96784 + 4.91133i −0.348743 + 0.214963i
\(523\) 34.5237 19.9323i 1.50961 0.871576i 0.509678 0.860365i \(-0.329765\pi\)
0.999937 0.0112110i \(-0.00356864\pi\)
\(524\) 2.15930 + 1.81187i 0.0943294 + 0.0791517i
\(525\) 19.9862 + 6.64577i 0.872267 + 0.290045i
\(526\) −0.891812 5.05772i −0.0388849 0.220527i
\(527\) 23.6591 4.17174i 1.03061 0.181724i
\(528\) −5.87171 8.13393i −0.255534 0.353984i
\(529\) 16.0587 + 13.4749i 0.698206 + 0.585865i
\(530\) 1.22460 + 2.12106i 0.0531931 + 0.0921331i
\(531\) 0.322183 + 11.1882i 0.0139816 + 0.485526i
\(532\) 1.09679 + 10.8309i 0.0475521 + 0.469581i
\(533\) 0.886699 + 2.43618i 0.0384072 + 0.105523i
\(534\) −7.00955 1.77047i −0.303333 0.0766156i
\(535\) 0.810012 + 0.965334i 0.0350199 + 0.0417350i
\(536\) −2.69410 + 7.40199i −0.116368 + 0.319717i
\(537\) −22.2624 15.1155i −0.960693 0.652280i
\(538\) 17.7874 + 3.13640i 0.766869 + 0.135220i
\(539\) −38.4626 12.8211i −1.65670 0.552245i
\(540\) 3.27414 0.429550i 0.140897 0.0184849i
\(541\) −12.4848 −0.536763 −0.268382 0.963313i \(-0.586489\pi\)
−0.268382 + 0.963313i \(0.586489\pi\)
\(542\) −1.58643 + 8.99706i −0.0681428 + 0.386457i
\(543\) 0.860510 11.7876i 0.0369280 0.505854i
\(544\) 1.14036 3.13310i 0.0488924 0.134331i
\(545\) −4.43211 + 3.71898i −0.189851 + 0.159304i
\(546\) −0.343276 + 2.32665i −0.0146908 + 0.0995713i
\(547\) −8.02394 + 2.92048i −0.343079 + 0.124871i −0.507813 0.861468i \(-0.669546\pi\)
0.164734 + 0.986338i \(0.447324\pi\)
\(548\) −14.1877 8.19128i −0.606069 0.349914i
\(549\) 7.25760 + 2.40732i 0.309747 + 0.102742i
\(550\) 13.3101 + 23.0538i 0.567546 + 0.983018i
\(551\) 9.83414 + 8.25182i 0.418949 + 0.351540i
\(552\) 2.25512 + 1.01232i 0.0959845 + 0.0430873i
\(553\) 2.53233 2.60245i 0.107686 0.110667i
\(554\) −28.1062 + 4.95587i −1.19412 + 0.210555i
\(555\) 0.0423498 + 0.415143i 0.00179765 + 0.0176219i
\(556\) 8.96241 10.6810i 0.380091 0.452975i
\(557\) −12.2712 + 7.08480i −0.519949 + 0.300193i −0.736914 0.675987i \(-0.763718\pi\)
0.216965 + 0.976179i \(0.430384\pi\)
\(558\) −7.97480 20.0913i −0.337600 0.850535i
\(559\) 4.07808 + 2.35448i 0.172484 + 0.0995839i
\(560\) 1.39036 + 0.945514i 0.0587534 + 0.0399552i
\(561\) −9.12111 32.1803i −0.385094 1.35865i
\(562\) −4.45119 + 3.73499i −0.187762 + 0.157551i
\(563\) −4.30657 1.56746i −0.181500 0.0660607i 0.249671 0.968331i \(-0.419677\pi\)
−0.431172 + 0.902270i \(0.641900\pi\)
\(564\) −4.20656 8.69210i −0.177128 0.366003i
\(565\) −12.5043 2.20484i −0.526059 0.0927583i
\(566\) 23.2392 0.976819
\(567\) −8.50182 + 22.2423i −0.357043 + 0.934088i
\(568\) 3.09091 0.129692
\(569\) 34.0499 + 6.00391i 1.42744 + 0.251697i 0.833371 0.552714i \(-0.186408\pi\)
0.594073 + 0.804411i \(0.297519\pi\)
\(570\) −1.97298 4.07681i −0.0826389 0.170759i
\(571\) 18.2532 + 6.64362i 0.763872 + 0.278027i 0.694431 0.719559i \(-0.255656\pi\)
0.0694413 + 0.997586i \(0.477878\pi\)
\(572\) −2.27704 + 1.91066i −0.0952079 + 0.0798889i
\(573\) −7.48680 26.4142i −0.312765 1.10347i
\(574\) −7.51578 + 11.0518i −0.313703 + 0.461293i
\(575\) −5.68063 3.27971i −0.236899 0.136774i
\(576\) −2.96819 0.435686i −0.123675 0.0181536i
\(577\) 13.5159 7.80342i 0.562675 0.324860i −0.191544 0.981484i \(-0.561349\pi\)
0.754218 + 0.656624i \(0.228016\pi\)
\(578\) −3.78168 + 4.50683i −0.157297 + 0.187459i
\(579\) 1.91442 + 18.7665i 0.0795605 + 0.779910i
\(580\) 1.95264 0.344303i 0.0810790 0.0142964i
\(581\) −14.1901 + 14.5830i −0.588705 + 0.605005i
\(582\) 28.0377 + 12.5861i 1.16220 + 0.521711i
\(583\) −17.0992 14.3479i −0.708177 0.594231i
\(584\) −6.66557 11.5451i −0.275823 0.477740i
\(585\) −0.197573 0.958297i −0.00816862 0.0396207i
\(586\) 14.4566 + 8.34654i 0.597198 + 0.344792i
\(587\) 20.1730 7.34238i 0.832630 0.303053i 0.109692 0.993966i \(-0.465013\pi\)
0.722938 + 0.690913i \(0.242791\pi\)
\(588\) −10.7652 + 5.57764i −0.443950 + 0.230018i
\(589\) −22.7114 + 19.0572i −0.935809 + 0.785237i
\(590\) 0.810945 2.22805i 0.0333861 0.0917275i
\(591\) −2.87328 + 39.3593i −0.118191 + 1.61903i
\(592\) 0.0658317 0.373350i 0.00270566 0.0153446i
\(593\) 48.5176 1.99238 0.996189 0.0872183i \(-0.0277978\pi\)
0.996189 + 0.0872183i \(0.0277978\pi\)
\(594\) −26.7013 + 13.8845i −1.09557 + 0.569690i
\(595\) 3.27792 + 4.54790i 0.134381 + 0.186446i
\(596\) 21.7811 + 3.84060i 0.892189 + 0.157317i
\(597\) −14.9990 10.1839i −0.613870 0.416798i
\(598\) 0.250508 0.688266i 0.0102441 0.0281453i
\(599\) 14.5703 + 17.3642i 0.595327 + 0.709483i 0.976620 0.214971i \(-0.0689657\pi\)
−0.381293 + 0.924454i \(0.624521\pi\)
\(600\) 7.71833 + 1.94949i 0.315100 + 0.0795877i
\(601\) 6.19093 + 17.0094i 0.252533 + 0.693829i 0.999578 + 0.0290552i \(0.00924987\pi\)
−0.747045 + 0.664774i \(0.768528\pi\)
\(602\) 2.44580 + 24.1525i 0.0996832 + 0.984381i
\(603\) 20.7967 + 11.2216i 0.846909 + 0.456977i
\(604\) 5.32094 + 9.21613i 0.216506 + 0.374999i
\(605\) 10.9760 + 9.20994i 0.446237 + 0.374437i
\(606\) −18.6538 25.8407i −0.757761 1.04971i
\(607\) −20.1947 + 3.56086i −0.819676 + 0.144531i −0.567735 0.823211i \(-0.692180\pi\)
−0.251941 + 0.967743i \(0.581069\pi\)
\(608\) 0.714501 + 4.05214i 0.0289769 + 0.164336i
\(609\) −4.51131 + 13.5671i −0.182807 + 0.549766i
\(610\) −1.24083 1.04118i −0.0502398 0.0421562i
\(611\) −2.47791 + 1.43062i −0.100246 + 0.0578768i
\(612\) −8.80282 4.74985i −0.355833 0.192001i
\(613\) 20.5244 35.5492i 0.828971 1.43582i −0.0698747 0.997556i \(-0.522260\pi\)
0.898846 0.438265i \(-0.144407\pi\)
\(614\) −3.73199 + 1.35833i −0.150611 + 0.0548178i
\(615\) 1.36169 5.39113i 0.0549086 0.217391i
\(616\) −14.8545 3.76364i −0.598505 0.151641i
\(617\) −9.04615 + 24.8541i −0.364184 + 1.00059i 0.613350 + 0.789811i \(0.289822\pi\)
−0.977534 + 0.210777i \(0.932401\pi\)
\(618\) 14.3056 21.0696i 0.575454 0.847542i
\(619\) 22.7108 + 4.00453i 0.912824 + 0.160956i 0.610286 0.792182i \(-0.291055\pi\)
0.302539 + 0.953137i \(0.402166\pi\)
\(620\) 4.57909i 0.183901i
\(621\) 3.98730 6.25259i 0.160005 0.250908i
\(622\) 4.47914i 0.179597i
\(623\) −9.94417 + 4.80342i −0.398405 + 0.192445i
\(624\) −0.0647194 + 0.886551i −0.00259085 + 0.0354904i
\(625\) −17.9529 6.53431i −0.718115 0.261373i
\(626\) 16.1725 13.5703i 0.646382 0.542379i
\(627\) 29.6047 + 28.7644i 1.18230 + 1.14874i
\(628\) 3.27858 + 9.00784i 0.130830 + 0.359452i
\(629\) 0.632009 1.09467i 0.0251999 0.0436475i
\(630\) 3.41223 3.71491i 0.135946 0.148005i
\(631\) −8.92423 15.4572i −0.355268 0.615343i 0.631896 0.775053i \(-0.282277\pi\)
−0.987164 + 0.159711i \(0.948944\pi\)
\(632\) 0.882198 1.05136i 0.0350920 0.0418210i
\(633\) −15.0267 6.74548i −0.597259 0.268109i
\(634\) 2.40752 + 13.6537i 0.0956147 + 0.542258i
\(635\) −1.54951 8.78773i −0.0614906 0.348731i
\(636\) −6.64071 + 0.677436i −0.263321 + 0.0268621i
\(637\) 1.88053 + 3.06098i 0.0745091 + 0.121280i
\(638\) −15.6495 + 9.03524i −0.619569 + 0.357709i
\(639\) 1.34667 9.17441i 0.0532733 0.362934i
\(640\) 0.550366 + 0.317754i 0.0217551 + 0.0125603i
\(641\) −2.07231 5.69363i −0.0818514 0.224885i 0.892015 0.452005i \(-0.149291\pi\)
−0.973867 + 0.227120i \(0.927069\pi\)
\(642\) −3.30433 + 0.936573i −0.130412 + 0.0369636i
\(643\) −2.10930 2.51377i −0.0831827 0.0991333i 0.722848 0.691007i \(-0.242833\pi\)
−0.806031 + 0.591874i \(0.798388\pi\)
\(644\) 3.63357 1.02699i 0.143183 0.0404690i
\(645\) −4.39964 9.09107i −0.173236 0.357961i
\(646\) −2.38228 + 13.5106i −0.0937294 + 0.531566i
\(647\) 4.11102 0.161621 0.0808105 0.996729i \(-0.474249\pi\)
0.0808105 + 0.996729i \(0.474249\pi\)
\(648\) −2.58640 + 8.62035i −0.101604 + 0.338640i
\(649\) 21.6092i 0.848235i
\(650\) 0.409600 2.32295i 0.0160658 0.0911138i
\(651\) −29.0473 15.7012i −1.13845 0.615378i
\(652\) −10.4219 3.79328i −0.408155 0.148556i
\(653\) −7.45623 8.88599i −0.291785 0.347736i 0.600160 0.799880i \(-0.295104\pi\)
−0.891945 + 0.452144i \(0.850659\pi\)
\(654\) −4.30006 15.1711i −0.168146 0.593236i
\(655\) −1.68332 + 0.612677i −0.0657726 + 0.0239393i
\(656\) −2.52579 + 4.37480i −0.0986156 + 0.170807i
\(657\) −37.1722 + 14.7547i −1.45023 + 0.575634i
\(658\) −13.4524 6.05073i −0.524429 0.235882i
\(659\) −1.35660 + 1.61674i −0.0528458 + 0.0629791i −0.791820 0.610755i \(-0.790866\pi\)
0.738974 + 0.673734i \(0.235311\pi\)
\(660\) 6.34240 0.647004i 0.246878 0.0251846i
\(661\) −9.69896 + 1.71019i −0.377246 + 0.0665186i −0.359056 0.933316i \(-0.616901\pi\)
−0.0181896 + 0.999835i \(0.505790\pi\)
\(662\) 0.899283 0.158568i 0.0349516 0.00616291i
\(663\) −1.21376 + 2.70385i −0.0471384 + 0.105009i
\(664\) −4.94346 + 5.89138i −0.191843 + 0.228630i
\(665\) −6.30950 2.83794i −0.244672 0.110051i
\(666\) −1.07949 0.358065i −0.0418295 0.0138747i
\(667\) 2.22635 3.85615i 0.0862046 0.149311i
\(668\) −20.5392 + 7.47566i −0.794686 + 0.289242i
\(669\) −30.6695 + 31.5654i −1.18575 + 1.22039i
\(670\) −3.21774 3.83475i −0.124312 0.148149i
\(671\) 13.8721 + 5.04905i 0.535528 + 0.194916i
\(672\) −3.90281 + 2.40169i −0.150554 + 0.0926471i
\(673\) −3.66938 + 20.8101i −0.141444 + 0.802169i 0.828710 + 0.559679i \(0.189075\pi\)
−0.970154 + 0.242490i \(0.922036\pi\)
\(674\) 9.95481i 0.383445i
\(675\) 9.14925 22.0602i 0.352155 0.849096i
\(676\) −12.7366 −0.489870
\(677\) −3.60031 + 20.4184i −0.138371 + 0.784743i 0.834081 + 0.551642i \(0.185998\pi\)
−0.972453 + 0.233101i \(0.925113\pi\)
\(678\) 19.4389 28.6300i 0.746546 1.09953i
\(679\) 45.1759 12.7684i 1.73369 0.490008i
\(680\) 1.36200 + 1.62317i 0.0522304 + 0.0622457i
\(681\) 4.56706 18.0817i 0.175010 0.692892i
\(682\) −14.2735 39.2160i −0.546559 1.50166i
\(683\) −20.8519 12.0389i −0.797877 0.460654i 0.0448513 0.998994i \(-0.485719\pi\)
−0.842728 + 0.538339i \(0.819052\pi\)
\(684\) 12.3388 0.355318i 0.471787 0.0135859i
\(685\) 9.01640 5.20562i 0.344499 0.198897i
\(686\) −7.13306 + 17.0915i −0.272341 + 0.652557i
\(687\) −11.6646 16.1587i −0.445032 0.616492i
\(688\) 1.59330 + 9.03606i 0.0607441 + 0.344497i
\(689\) 0.343455 + 1.94783i 0.0130846 + 0.0742063i
\(690\) −1.27372 + 0.919475i −0.0484898 + 0.0350038i
\(691\) 8.80297 10.4910i 0.334881 0.399095i −0.572157 0.820144i \(-0.693893\pi\)
0.907038 + 0.421049i \(0.138338\pi\)
\(692\) −10.2008 17.6683i −0.387776 0.671647i
\(693\) −17.6431 + 42.4513i −0.670207 + 1.61259i
\(694\) 6.82740 11.8254i 0.259165 0.448886i
\(695\) 3.03061 + 8.32654i 0.114958 + 0.315843i
\(696\) −1.32336 + 5.23939i −0.0501620 + 0.198599i
\(697\) −12.9024 + 10.8264i −0.488713 + 0.410079i
\(698\) −10.6226 3.86630i −0.402070 0.146342i
\(699\) 18.0763 + 12.2733i 0.683710 + 0.464217i
\(700\) 10.9497 5.28913i 0.413860 0.199910i
\(701\) 3.27800i 0.123808i −0.998082 0.0619042i \(-0.980283\pi\)
0.998082 0.0619042i \(-0.0197173\pi\)
\(702\) 2.60326 + 0.578358i 0.0982536 + 0.0218287i
\(703\) 1.55990i 0.0588328i
\(704\) −5.70389 1.00575i −0.214974 0.0379056i
\(705\) 6.12049 + 0.446804i 0.230511 + 0.0168276i
\(706\) 6.90830 18.9804i 0.259997 0.714337i
\(707\) −47.1913 11.9567i −1.77481 0.449678i
\(708\) 4.63475 + 4.50321i 0.174185 + 0.169241i
\(709\) 3.87481 1.41031i 0.145521 0.0529655i −0.268233 0.963354i \(-0.586440\pi\)
0.413754 + 0.910389i \(0.364217\pi\)
\(710\) −0.982148 + 1.70113i −0.0368594 + 0.0638423i
\(711\) −2.73629 3.07660i −0.102619 0.115381i
\(712\) −3.61484 + 2.08703i −0.135472 + 0.0782147i
\(713\) 7.87745 + 6.60996i 0.295013 + 0.247545i
\(714\) −14.9667 + 3.07414i −0.560114 + 0.115047i
\(715\) −0.328026 1.86033i −0.0122675 0.0695723i
\(716\) −15.2999 + 2.69778i −0.571783 + 0.100821i
\(717\) 27.1630 2.77096i 1.01442 0.103483i
\(718\) −0.0560727 0.0470506i −0.00209262 0.00175591i
\(719\) 8.74299 + 15.1433i 0.326059 + 0.564750i 0.981726 0.190300i \(-0.0609460\pi\)
−0.655668 + 0.755050i \(0.727613\pi\)
\(720\) 1.18294 1.49515i 0.0440857 0.0557210i
\(721\) −3.91933 38.7038i −0.145964 1.44140i
\(722\) 0.707867 + 1.94485i 0.0263441 + 0.0723797i
\(723\) −4.93083 17.3965i −0.183380 0.646984i
\(724\) −4.38618 5.22724i −0.163011 0.194269i
\(725\) 4.90449 13.4750i 0.182148 0.500448i
\(726\) −35.1507 + 17.0113i −1.30457 + 0.631347i
\(727\) 36.7468 + 6.47944i 1.36286 + 0.240309i 0.806797 0.590829i \(-0.201199\pi\)
0.556065 + 0.831139i \(0.312310\pi\)
\(728\) 0.793935 + 1.10153i 0.0294252 + 0.0408255i
\(729\) 24.4600 + 11.4327i 0.905927 + 0.423434i
\(730\) 8.47205 0.313565
\(731\) −5.31235 + 30.1279i −0.196485 + 1.11432i
\(732\) 3.97378 1.92312i 0.146875 0.0710805i
\(733\) 3.33963 9.17556i 0.123352 0.338907i −0.862612 0.505867i \(-0.831173\pi\)
0.985964 + 0.166960i \(0.0533950\pi\)
\(734\) −23.5238 + 19.7388i −0.868278 + 0.728572i
\(735\) 0.350949 7.69713i 0.0129450 0.283913i
\(736\) 1.34109 0.488119i 0.0494334 0.0179923i
\(737\) 39.5105 + 22.8114i 1.45539 + 0.840270i
\(738\) 11.8848 + 9.40308i 0.437485 + 0.346132i
\(739\) 13.3646 + 23.1482i 0.491624 + 0.851518i 0.999953 0.00964443i \(-0.00306997\pi\)
−0.508329 + 0.861163i \(0.669737\pi\)
\(740\) 0.184561 + 0.154865i 0.00678459 + 0.00569295i
\(741\) −0.371190 3.63867i −0.0136360 0.133670i
\(742\) −7.11090 + 7.30779i −0.261049 + 0.268277i
\(743\) 11.1754 1.97053i 0.409986 0.0722916i 0.0351486 0.999382i \(-0.488810\pi\)
0.374838 + 0.927090i \(0.377698\pi\)
\(744\) −11.3856 5.11097i −0.417415 0.187377i
\(745\) −9.03477 + 10.7672i −0.331009 + 0.394481i
\(746\) 26.5608 15.3349i 0.972461 0.561450i
\(747\) 15.3330 + 17.2399i 0.561004 + 0.630776i
\(748\) −16.7240 9.65559i −0.611489 0.353043i
\(749\) −2.95019 + 4.33819i −0.107797 + 0.158514i
\(750\) −7.36072 + 7.57574i −0.268776 + 0.276627i
\(751\) 12.2746 10.2996i 0.447906 0.375837i −0.390752 0.920496i \(-0.627785\pi\)
0.838658 + 0.544658i \(0.183341\pi\)
\(752\) −5.23895 1.90682i −0.191045 0.0695346i
\(753\) 9.22287 + 0.673282i 0.336100 + 0.0245358i
\(754\) 1.57688 + 0.278046i 0.0574265 + 0.0101258i
\(755\) −6.76300 −0.246131
\(756\) 5.42827 + 12.6307i 0.197424 + 0.459373i
\(757\) 42.1339 1.53138 0.765691 0.643209i \(-0.222397\pi\)
0.765691 + 0.643209i \(0.222397\pi\)
\(758\) −10.7371 1.89325i −0.389990 0.0687658i
\(759\) 8.04228 11.8448i 0.291916 0.429941i
\(760\) −2.45720 0.894346i −0.0891318 0.0324413i
\(761\) 31.5496 26.4733i 1.14367 0.959656i 0.144121 0.989560i \(-0.453965\pi\)
0.999553 + 0.0299041i \(0.00952018\pi\)
\(762\) 23.5796 + 5.95571i 0.854197 + 0.215753i
\(763\) −19.9178 13.5451i −0.721073 0.490366i
\(764\) −13.7274 7.92551i −0.496639 0.286735i
\(765\) 5.41129 3.33549i 0.195646 0.120595i
\(766\) 5.29498 3.05706i 0.191315 0.110456i
\(767\) 1.23079 1.46680i 0.0444412 0.0529629i
\(768\) −1.40437 + 1.01378i −0.0506757 + 0.0365817i
\(769\) −33.0863 + 5.83400i −1.19312 + 0.210380i −0.734723 0.678367i \(-0.762688\pi\)
−0.458399 + 0.888747i \(0.651577\pi\)
\(770\) 6.79146 6.97951i 0.244747 0.251524i
\(771\) 25.1526 18.1571i 0.905849 0.653913i
\(772\) 8.34305 + 7.00065i 0.300273 + 0.251959i
\(773\) 5.04004 + 8.72960i 0.181277 + 0.313982i 0.942316 0.334725i \(-0.108643\pi\)
−0.761038 + 0.648707i \(0.775310\pi\)
\(774\) 27.5150 0.792341i 0.989005 0.0284801i
\(775\) 28.6801 + 16.5585i 1.03022 + 0.594798i
\(776\) 16.6737 6.06873i 0.598551 0.217855i
\(777\) −1.61522 + 0.639741i −0.0579457 + 0.0229506i
\(778\) 14.1037 11.8344i 0.505641 0.424283i
\(779\) 7.10905 19.5320i 0.254708 0.699805i
\(780\) −0.467363 0.317324i −0.0167343 0.0113620i
\(781\) 3.10868 17.6302i 0.111237 0.630858i
\(782\) 4.75842 0.170161
\(783\) 14.9750 + 6.21073i 0.535162 + 0.221953i
\(784\) −2.21364 + 6.64077i −0.0790585 + 0.237170i
\(785\) −5.99939 1.05785i −0.214127 0.0377564i
\(786\) 0.355464 4.86928i 0.0126790 0.173682i
\(787\) 3.38555 9.30172i 0.120682 0.331570i −0.864612 0.502440i \(-0.832436\pi\)
0.985294 + 0.170870i \(0.0546578\pi\)
\(788\) 14.6456 + 17.4540i 0.521729 + 0.621773i
\(789\) −6.19878 + 6.37986i −0.220683 + 0.227129i
\(790\) 0.298312 + 0.819607i 0.0106135 + 0.0291603i
\(791\) −5.32572 52.5920i −0.189361 1.86996i
\(792\) −5.47037 + 16.4921i −0.194381 + 0.586020i
\(793\) −0.654041 1.13283i −0.0232257 0.0402280i
\(794\) −21.5622 18.0928i −0.765214 0.642090i
\(795\) 1.73727 3.87008i 0.0616148 0.137258i
\(796\) −10.3081 + 1.81760i −0.365361 + 0.0644230i
\(797\) 0.793459 + 4.49993i 0.0281058 + 0.159396i 0.995630 0.0933808i \(-0.0297674\pi\)
−0.967525 + 0.252776i \(0.918656\pi\)
\(798\) 14.0987 12.5205i 0.499089 0.443222i
\(799\) −14.2397 11.9485i −0.503765 0.422709i
\(800\) 3.98036 2.29806i 0.140727 0.0812489i
\(801\) 4.61977 + 11.6388i 0.163232 + 0.411238i
\(802\) 15.1593 26.2566i 0.535293 0.927154i
\(803\) −72.5559 + 26.4082i −2.56044 + 0.931925i
\(804\) 13.1263 3.72050i 0.462930 0.131212i
\(805\) −0.589363 + 2.32613i −0.0207723 + 0.0819852i
\(806\) −1.26476 + 3.47489i −0.0445491 + 0.122398i
\(807\) −13.6279 28.1596i −0.479725 0.991266i
\(808\) −18.1207 3.19517i −0.637484 0.112406i
\(809\) 24.5688i 0.863791i −0.901924 0.431896i \(-0.857845\pi\)
0.901924 0.431896i \(-0.142155\pi\)
\(810\) −3.92251 4.16262i −0.137823 0.146260i
\(811\) 19.8079i 0.695548i 0.937578 + 0.347774i \(0.113062\pi\)
−0.937578 + 0.347774i \(0.886938\pi\)
\(812\) 3.59039 + 7.43292i 0.125998 + 0.260845i
\(813\) 14.2435 6.89315i 0.499540 0.241753i
\(814\) −2.06334 0.750994i −0.0723200 0.0263223i
\(815\) 5.39931 4.53056i 0.189130 0.158699i
\(816\) −5.55610 + 1.57481i −0.194502 + 0.0551293i
\(817\) −12.9126 35.4770i −0.451753 1.24118i
\(818\) 5.03034 8.71280i 0.175882 0.304636i
\(819\) 3.61547 1.87663i 0.126335 0.0655748i
\(820\) −1.60516 2.78022i −0.0560546 0.0970895i
\(821\) 6.40767 7.63636i 0.223629 0.266511i −0.642551 0.766243i \(-0.722124\pi\)
0.866180 + 0.499732i \(0.166568\pi\)
\(822\) 2.87970 + 28.2289i 0.100441 + 0.984597i
\(823\) −2.85161 16.1723i −0.0994010 0.563731i −0.993310 0.115482i \(-0.963159\pi\)
0.893909 0.448249i \(-0.147952\pi\)
\(824\) −2.55323 14.4801i −0.0889460 0.504438i
\(825\) 18.8824 42.0639i 0.657401 1.46448i
\(826\) 9.84441 + 0.725979i 0.342531 + 0.0252601i
\(827\) −20.3061 + 11.7237i −0.706112 + 0.407674i −0.809620 0.586955i \(-0.800327\pi\)
0.103508 + 0.994629i \(0.466993\pi\)
\(828\) −0.864534 4.19330i −0.0300446 0.145727i
\(829\) 11.6276 + 6.71317i 0.403842 + 0.233158i 0.688140 0.725578i \(-0.258427\pi\)
−0.284299 + 0.958736i \(0.591761\pi\)
\(830\) −1.67161 4.59272i −0.0580226 0.159416i
\(831\) 35.4534 + 34.4472i 1.22986 + 1.19496i
\(832\) 0.329886 + 0.393143i 0.0114368 + 0.0136298i
\(833\) −14.5084 + 18.2819i −0.502686 + 0.633430i
\(834\) −24.0860 1.75831i −0.834029 0.0608852i
\(835\) 2.41207 13.6795i 0.0834730 0.473399i
\(836\) 23.8316 0.824232
\(837\) −20.1309 + 31.5678i −0.695825 + 1.09114i
\(838\) 24.2308i 0.837039i
\(839\) 1.69849 9.63259i 0.0586382 0.332554i −0.941350 0.337432i \(-0.890442\pi\)
0.999988 + 0.00487812i \(0.00155276\pi\)
\(840\) −0.0816747 2.91112i −0.00281805 0.100443i
\(841\) −18.1039 6.58930i −0.624274 0.227217i
\(842\) −0.404180 0.481683i −0.0139290 0.0165999i
\(843\) 9.75784 + 2.46463i 0.336078 + 0.0848864i
\(844\) −8.93621 + 3.25251i −0.307597 + 0.111956i
\(845\) 4.04711 7.00980i 0.139225 0.241144i
\(846\) −7.94236 + 14.7194i −0.273064 + 0.506065i
\(847\) −24.4691 + 54.4013i −0.840767 + 1.86925i
\(848\) −2.47725 + 2.95227i −0.0850690 + 0.101381i
\(849\) −23.5596 32.6364i −0.808562 1.12008i
\(850\) 15.0915 2.66104i 0.517634 0.0912729i
\(851\) 0.532831 0.0939525i 0.0182652 0.00322065i
\(852\) −3.13351 4.34077i −0.107352 0.148712i
\(853\) −4.34115 + 5.17358i −0.148638 + 0.177140i −0.835226 0.549907i \(-0.814663\pi\)
0.686588 + 0.727047i \(0.259108\pi\)
\(854\) 2.76622 6.15005i 0.0946581 0.210450i
\(855\) −3.72516 + 6.90378i −0.127398 + 0.236104i
\(856\) −0.991454 + 1.71725i −0.0338872 + 0.0586944i
\(857\) 52.1248 18.9719i 1.78055 0.648067i 0.780820 0.624756i \(-0.214801\pi\)
0.999728 0.0233112i \(-0.00742085\pi\)
\(858\) 4.99170 + 1.26080i 0.170414 + 0.0430430i
\(859\) 16.4364 + 19.5882i 0.560804 + 0.668340i 0.969716 0.244233i \(-0.0785363\pi\)
−0.408912 + 0.912574i \(0.634092\pi\)
\(860\) −5.47942 1.99435i −0.186847 0.0680067i
\(861\) 23.1401 0.649223i 0.788614 0.0221255i
\(862\) −0.503172 + 2.85363i −0.0171381 + 0.0971950i
\(863\) 50.5355i 1.72025i −0.510086 0.860123i \(-0.670386\pi\)
0.510086 0.860123i \(-0.329614\pi\)
\(864\) 2.39724 + 4.61012i 0.0815558 + 0.156840i
\(865\) 12.9654 0.440836
\(866\) −1.00358 + 5.69160i −0.0341031 + 0.193408i
\(867\) 10.1630 + 0.741916i 0.345155 + 0.0251968i
\(868\) −18.3450 + 5.18501i −0.622671 + 0.175991i
\(869\) −5.10959 6.08937i −0.173331 0.206568i
\(870\) −2.46308 2.39317i −0.0835063 0.0811362i
\(871\) −1.38265 3.79879i −0.0468492 0.128717i
\(872\) −7.88436 4.55204i −0.266998 0.154151i
\(873\) −10.7487 52.1348i −0.363787 1.76450i
\(874\) −5.08554 + 2.93614i −0.172021 + 0.0993164i
\(875\) −1.18665 + 16.0912i −0.0401161 + 0.543982i
\(876\) −9.45612 + 21.0651i −0.319493 + 0.711725i
\(877\) 0.912675 + 5.17604i 0.0308189 + 0.174782i 0.996332 0.0855719i \(-0.0272717\pi\)
−0.965513 + 0.260354i \(0.916161\pi\)
\(878\) 6.59172 + 37.3835i 0.222460 + 1.26163i
\(879\) −2.93429 28.7640i −0.0989710 0.970185i
\(880\) 2.36597 2.81965i 0.0797567 0.0950503i
\(881\) 5.72759 + 9.92048i 0.192968 + 0.334230i 0.946232 0.323488i \(-0.104855\pi\)
−0.753265 + 0.657717i \(0.771522\pi\)
\(882\) 18.7466 + 9.46380i 0.631232 + 0.318663i
\(883\) −13.5072 + 23.3952i −0.454554 + 0.787310i −0.998662 0.0517044i \(-0.983535\pi\)
0.544109 + 0.839015i \(0.316868\pi\)
\(884\) 0.585245 + 1.60795i 0.0196839 + 0.0540811i
\(885\) −3.95112 + 1.11990i −0.132816 + 0.0376450i
\(886\) −1.79977 + 1.51019i −0.0604645 + 0.0507357i
\(887\) 24.1190 + 8.77858i 0.809835 + 0.294756i 0.713556 0.700598i \(-0.247084\pi\)
0.0962794 + 0.995354i \(0.469306\pi\)
\(888\) −0.591059 + 0.286044i −0.0198346 + 0.00959901i
\(889\) 33.4514 16.1583i 1.12192 0.541933i
\(890\) 2.65265i 0.0889170i
\(891\) 46.5683 + 23.4225i 1.56010 + 0.784683i
\(892\) 25.4099i 0.850788i
\(893\) 22.5914 + 3.98347i 0.755992 + 0.133302i
\(894\) −16.6877 34.4822i −0.558121 1.15326i
\(895\) 3.37683 9.27776i 0.112875 0.310121i
\(896\) −0.649813 + 2.56471i −0.0217087 + 0.0856810i
\(897\) −1.22054 + 0.345947i −0.0407526 + 0.0115508i
\(898\) −8.58099 + 3.12322i −0.286351 + 0.104223i
\(899\) −11.2403 + 19.4688i −0.374885 + 0.649319i
\(900\) −5.08691 12.8157i −0.169564 0.427191i
\(901\) −11.1281 + 6.42482i −0.370731 + 0.214042i
\(902\) 22.4131 + 18.8068i 0.746273 + 0.626198i
\(903\) 31.4394 27.9201i 1.04624 0.929124i
\(904\) −3.46941 19.6760i −0.115391 0.654415i
\(905\) 4.27062 0.753026i 0.141960 0.0250314i
\(906\) 7.54855 16.8157i 0.250784 0.558664i
\(907\) −38.9812 32.7091i −1.29435 1.08609i −0.991092 0.133181i \(-0.957481\pi\)
−0.303259 0.952908i \(-0.598075\pi\)
\(908\) −5.38366 9.32477i −0.178663 0.309453i
\(909\) −17.3788 + 52.3937i −0.576419 + 1.73779i
\(910\) −0.858523 + 0.0869382i −0.0284597 + 0.00288197i
\(911\) 16.7564 + 46.0378i 0.555164 + 1.52530i 0.826570 + 0.562834i \(0.190289\pi\)
−0.271406 + 0.962465i \(0.587489\pi\)
\(912\) 4.96634 5.11141i 0.164452 0.169256i
\(913\) 28.6319 + 34.1222i 0.947579 + 1.12928i
\(914\) 7.94883 21.8392i 0.262924 0.722378i
\(915\) −0.204266 + 2.79811i −0.00675283 + 0.0925028i
\(916\) −11.3312 1.99800i −0.374394 0.0660158i
\(917\) −4.36060 6.05005i −0.144000 0.199790i
\(918\) 2.25362 + 17.1777i 0.0743806 + 0.566949i
\(919\) 20.0385 0.661008 0.330504 0.943805i \(-0.392781\pi\)
0.330504 + 0.943805i \(0.392781\pi\)
\(920\) −0.157494 + 0.893195i −0.00519244 + 0.0294478i
\(921\) 5.69102 + 3.86402i 0.187526 + 0.127324i
\(922\) −8.78150 + 24.1270i −0.289203 + 0.794580i
\(923\) −1.21517 + 1.01965i −0.0399978 + 0.0335621i
\(924\) 9.77372 + 24.6767i 0.321532 + 0.811803i
\(925\) 1.63735 0.595948i 0.0538359 0.0195947i
\(926\) −22.6891 13.0995i −0.745609 0.430478i
\(927\) −44.0921 + 1.26971i −1.44818 + 0.0417027i
\(928\) 1.55998 + 2.70197i 0.0512089 + 0.0886965i
\(929\) −35.3221 29.6387i −1.15888 0.972416i −0.158991 0.987280i \(-0.550824\pi\)
−0.999890 + 0.0148643i \(0.995268\pi\)
\(930\) 6.43072 4.64220i 0.210871 0.152224i
\(931\) 4.22513 28.4910i 0.138473 0.933753i
\(932\) 12.4230 2.19051i 0.406928 0.0717524i
\(933\) 6.29036 4.54088i 0.205937 0.148662i
\(934\) −5.01322 + 5.97452i −0.164038 + 0.195492i
\(935\) 10.6282 6.13621i 0.347580 0.200675i
\(936\) 1.31065 0.807880i 0.0428400 0.0264064i
\(937\) −11.5715 6.68078i −0.378023 0.218252i 0.298935 0.954274i \(-0.403369\pi\)
−0.676958 + 0.736022i \(0.736702\pi\)
\(938\) 11.7195 17.2333i 0.382655 0.562687i
\(939\) −35.4531 8.95472i −1.15697 0.292226i
\(940\) 2.71415 2.27744i 0.0885257 0.0742819i
\(941\) −36.2054 13.1777i −1.18026 0.429580i −0.323967 0.946068i \(-0.605017\pi\)
−0.856294 + 0.516488i \(0.827239\pi\)
\(942\) 9.32653 13.7363i 0.303875 0.447554i
\(943\) −7.09990 1.25190i −0.231205 0.0407676i
\(944\) 3.73094 0.121432
\(945\) −8.67635 1.02591i −0.282242 0.0333728i
\(946\) 53.1432 1.72783
\(947\) 47.4571 + 8.36796i 1.54215 + 0.271922i 0.879093 0.476650i \(-0.158149\pi\)
0.663054 + 0.748572i \(0.269260\pi\)
\(948\) −2.37086 0.173076i −0.0770018 0.00562124i
\(949\) 6.42910 + 2.34000i 0.208697 + 0.0759596i
\(950\) −14.4870 + 12.1561i −0.470021 + 0.394394i
\(951\) 16.7341 17.2229i 0.542640 0.558492i
\(952\) −4.96062 + 7.29449i −0.160774 + 0.236416i
\(953\) −7.60492 4.39070i −0.246348 0.142229i 0.371743 0.928336i \(-0.378760\pi\)
−0.618091 + 0.786107i \(0.712094\pi\)
\(954\) 7.68361 + 8.63922i 0.248766 + 0.279705i
\(955\) 8.72386 5.03673i 0.282298 0.162985i
\(956\) 10.1329 12.0759i 0.327720 0.390562i
\(957\) 28.5540 + 12.8178i 0.923019 + 0.414342i
\(958\) 39.3804 6.94383i 1.27232 0.224345i
\(959\) 31.0646 + 30.2276i 1.00313 + 0.976101i
\(960\) −0.111709 1.09505i −0.00360538 0.0353426i
\(961\) −16.0239 13.4457i −0.516901 0.433731i
\(962\) 0.0972818 + 0.168497i 0.00313649 + 0.00543256i
\(963\) 4.66517 + 3.69101i 0.150333 + 0.118941i
\(964\) −9.04091 5.21977i −0.291188 0.168117i
\(965\) −6.50396 + 2.36725i −0.209370 + 0.0762044i
\(966\) −5.12592 4.06173i −0.164924 0.130684i
\(967\) 2.92554 2.45482i 0.0940791 0.0789417i −0.594535 0.804070i \(-0.702664\pi\)
0.688614 + 0.725128i \(0.258219\pi\)
\(968\) −7.71116 + 21.1862i −0.247846 + 0.680952i
\(969\) 21.3889 10.3512i 0.687110 0.332528i
\(970\) −1.95811 + 11.1050i −0.0628712 + 0.356560i
\(971\) 34.9807 1.12258 0.561291 0.827618i \(-0.310305\pi\)
0.561291 + 0.827618i \(0.310305\pi\)
\(972\) 14.7282 5.10691i 0.472407 0.163804i
\(973\) −29.9266 + 21.5698i −0.959404 + 0.691495i
\(974\) −33.4600 5.89989i −1.07213 0.189045i
\(975\) −3.67752 + 1.77974i −0.117775 + 0.0569974i
\(976\) 0.871745 2.39510i 0.0279039 0.0766653i
\(977\) 2.25071 + 2.68229i 0.0720065 + 0.0858141i 0.800845 0.598871i \(-0.204384\pi\)
−0.728839 + 0.684686i \(0.759940\pi\)
\(978\) 5.23844 + 18.4818i 0.167507 + 0.590983i
\(979\) 8.26856 + 22.7177i 0.264264 + 0.726061i
\(980\) −2.95146 3.32844i −0.0942810 0.106323i
\(981\) −16.9464 + 21.4190i −0.541058 + 0.683857i
\(982\) −8.46619 14.6639i −0.270167 0.467943i
\(983\) 5.06013 + 4.24596i 0.161393 + 0.135425i 0.719908 0.694070i \(-0.244184\pi\)
−0.558515 + 0.829495i \(0.688629\pi\)
\(984\) 8.70442 0.887960i 0.277487 0.0283071i
\(985\) −14.2598 + 2.51439i −0.454355 + 0.0801151i
\(986\) 1.80638 + 10.2445i 0.0575268 + 0.326251i
\(987\) 5.14036 + 25.0262i 0.163620 + 0.796593i
\(988\) −1.61765 1.35737i −0.0514642 0.0431836i
\(989\) −11.3405 + 6.54744i −0.360607 + 0.208197i
\(990\) −7.33845 8.25113i −0.233231 0.262238i
\(991\) −24.9020 + 43.1315i −0.791038 + 1.37012i 0.134288 + 0.990942i \(0.457125\pi\)
−0.925325 + 0.379175i \(0.876208\pi\)
\(992\) −6.77086 + 2.46439i −0.214975 + 0.0782445i
\(993\) −1.13436 1.10217i −0.0359980 0.0349763i
\(994\) −7.92728 2.00851i −0.251438 0.0637061i
\(995\) 2.27510 6.25078i 0.0721255 0.198163i
\(996\) 13.2853 + 0.969841i 0.420959 + 0.0307306i
\(997\) −31.5063 5.55541i −0.997815 0.175942i −0.349192 0.937051i \(-0.613544\pi\)
−0.648623 + 0.761110i \(0.724655\pi\)
\(998\) 16.7824i 0.531239i
\(999\) 0.591518 + 1.87900i 0.0187148 + 0.0594490i
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 378.2.z.a.83.8 yes 144
7.6 odd 2 inner 378.2.z.a.83.5 yes 144
27.14 odd 18 inner 378.2.z.a.41.5 144
189.41 even 18 inner 378.2.z.a.41.8 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.z.a.41.5 144 27.14 odd 18 inner
378.2.z.a.41.8 yes 144 189.41 even 18 inner
378.2.z.a.83.5 yes 144 7.6 odd 2 inner
378.2.z.a.83.8 yes 144 1.1 even 1 trivial