Properties

Label 324.3.j.a.307.33
Level $324$
Weight $3$
Character 324.307
Analytic conductor $8.828$
Analytic rank $0$
Dimension $204$
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] = [324,3,Mod(19,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 16]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.j (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(34\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 307.33
Character \(\chi\) \(=\) 324.307
Dual form 324.3.j.a.19.33

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.95123 - 0.438997i) q^{2} +(3.61456 - 1.71316i) q^{4} +(-0.0372686 + 0.211361i) q^{5} +(7.43930 + 8.86581i) q^{7} +(6.30076 - 4.92955i) q^{8} +O(q^{10})\) \(q+(1.95123 - 0.438997i) q^{2} +(3.61456 - 1.71316i) q^{4} +(-0.0372686 + 0.211361i) q^{5} +(7.43930 + 8.86581i) q^{7} +(6.30076 - 4.92955i) q^{8} +(0.0200672 + 0.428773i) q^{10} +(9.50415 - 1.67584i) q^{11} +(-18.7145 + 6.81150i) q^{13} +(18.4078 + 14.0334i) q^{14} +(10.1301 - 12.3847i) q^{16} +(0.856471 - 1.48345i) q^{17} +(-5.28896 + 3.05358i) q^{19} +(0.227386 + 0.827824i) q^{20} +(17.8091 - 7.44223i) q^{22} +(20.2195 - 24.0967i) q^{23} +(23.4490 + 8.53475i) q^{25} +(-33.5259 + 21.5064i) q^{26} +(42.0784 + 19.3013i) q^{28} +(-8.13847 - 2.96216i) q^{29} +(-0.101324 + 0.120753i) q^{31} +(14.3294 - 28.6124i) q^{32} +(1.01994 - 3.27054i) q^{34} +(-2.15114 + 1.24196i) q^{35} +(24.1007 - 41.7436i) q^{37} +(-8.97943 + 8.28006i) q^{38} +(0.807093 + 1.51545i) q^{40} +(-19.2926 + 7.02193i) q^{41} +(-45.0838 + 7.94949i) q^{43} +(31.4824 - 22.3396i) q^{44} +(28.8744 - 55.8943i) q^{46} +(-23.9050 - 28.4889i) q^{47} +(-14.7507 + 83.6553i) q^{49} +(49.5011 + 6.35918i) q^{50} +(-55.9754 + 56.6815i) q^{52} -98.4809 q^{53} +2.07126i q^{55} +(90.5777 + 19.1890i) q^{56} +(-17.1804 - 2.20708i) q^{58} +(12.4095 + 2.18814i) q^{59} +(-62.8227 + 52.7145i) q^{61} +(-0.144696 + 0.280098i) q^{62} +(15.3991 - 62.1198i) q^{64} +(-0.742223 - 4.20936i) q^{65} +(18.1950 + 49.9905i) q^{67} +(0.554376 - 6.82930i) q^{68} +(-3.65214 + 3.36769i) q^{70} +(-65.5561 - 37.8488i) q^{71} +(13.3902 + 23.1924i) q^{73} +(28.7005 - 92.0312i) q^{74} +(-13.8860 + 20.0982i) q^{76} +(85.5619 + 71.7950i) q^{77} +(39.9006 - 109.626i) q^{79} +(2.24010 + 2.60268i) q^{80} +(-34.5616 + 22.1707i) q^{82} +(-38.5038 + 105.788i) q^{83} +(0.281624 + 0.236311i) q^{85} +(-84.4788 + 35.3029i) q^{86} +(51.6222 - 57.4102i) q^{88} +(-59.4575 - 102.983i) q^{89} +(-199.612 - 115.246i) q^{91} +(31.8032 - 121.738i) q^{92} +(-59.1506 - 45.0941i) q^{94} +(-0.448295 - 1.23168i) q^{95} +(-4.27138 - 24.2242i) q^{97} +(7.94247 + 169.706i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.95123 0.438997i 0.975613 0.219498i
\(3\) 0 0
\(4\) 3.61456 1.71316i 0.903641 0.428291i
\(5\) −0.0372686 + 0.211361i −0.00745372 + 0.0422722i −0.988308 0.152472i \(-0.951277\pi\)
0.980854 + 0.194744i \(0.0623877\pi\)
\(6\) 0 0
\(7\) 7.43930 + 8.86581i 1.06276 + 1.26654i 0.962412 + 0.271592i \(0.0875502\pi\)
0.100345 + 0.994953i \(0.468005\pi\)
\(8\) 6.30076 4.92955i 0.787595 0.616194i
\(9\) 0 0
\(10\) 0.0200672 + 0.428773i 0.00200672 + 0.0428773i
\(11\) 9.50415 1.67584i 0.864014 0.152349i 0.275958 0.961170i \(-0.411005\pi\)
0.588055 + 0.808821i \(0.299894\pi\)
\(12\) 0 0
\(13\) −18.7145 + 6.81150i −1.43957 + 0.523962i −0.939659 0.342113i \(-0.888858\pi\)
−0.499915 + 0.866075i \(0.666635\pi\)
\(14\) 18.4078 + 14.0334i 1.31484 + 1.00238i
\(15\) 0 0
\(16\) 10.1301 12.3847i 0.633134 0.774042i
\(17\) 0.856471 1.48345i 0.0503806 0.0872618i −0.839735 0.542996i \(-0.817290\pi\)
0.890116 + 0.455734i \(0.150623\pi\)
\(18\) 0 0
\(19\) −5.28896 + 3.05358i −0.278366 + 0.160715i −0.632683 0.774410i \(-0.718047\pi\)
0.354317 + 0.935125i \(0.384713\pi\)
\(20\) 0.227386 + 0.827824i 0.0113693 + 0.0413912i
\(21\) 0 0
\(22\) 17.8091 7.44223i 0.809503 0.338283i
\(23\) 20.2195 24.0967i 0.879108 1.04768i −0.119387 0.992848i \(-0.538093\pi\)
0.998496 0.0548328i \(-0.0174626\pi\)
\(24\) 0 0
\(25\) 23.4490 + 8.53475i 0.937961 + 0.341390i
\(26\) −33.5259 + 21.5064i −1.28946 + 0.827168i
\(27\) 0 0
\(28\) 42.0784 + 19.3013i 1.50280 + 0.689333i
\(29\) −8.13847 2.96216i −0.280637 0.102144i 0.197867 0.980229i \(-0.436599\pi\)
−0.478504 + 0.878085i \(0.658821\pi\)
\(30\) 0 0
\(31\) −0.101324 + 0.120753i −0.00326852 + 0.00389527i −0.767676 0.640838i \(-0.778587\pi\)
0.764408 + 0.644733i \(0.223032\pi\)
\(32\) 14.3294 28.6124i 0.447793 0.894137i
\(33\) 0 0
\(34\) 1.01994 3.27054i 0.0299982 0.0961922i
\(35\) −2.15114 + 1.24196i −0.0614611 + 0.0354846i
\(36\) 0 0
\(37\) 24.1007 41.7436i 0.651369 1.12820i −0.331422 0.943483i \(-0.607528\pi\)
0.982791 0.184722i \(-0.0591383\pi\)
\(38\) −8.97943 + 8.28006i −0.236301 + 0.217896i
\(39\) 0 0
\(40\) 0.807093 + 1.51545i 0.0201773 + 0.0378863i
\(41\) −19.2926 + 7.02193i −0.470551 + 0.171267i −0.566402 0.824129i \(-0.691665\pi\)
0.0958510 + 0.995396i \(0.469443\pi\)
\(42\) 0 0
\(43\) −45.0838 + 7.94949i −1.04846 + 0.184872i −0.671231 0.741248i \(-0.734234\pi\)
−0.377229 + 0.926120i \(0.623123\pi\)
\(44\) 31.4824 22.3396i 0.715509 0.507718i
\(45\) 0 0
\(46\) 28.8744 55.8943i 0.627705 1.21509i
\(47\) −23.9050 28.4889i −0.508618 0.606147i 0.449233 0.893415i \(-0.351697\pi\)
−0.957850 + 0.287268i \(0.907253\pi\)
\(48\) 0 0
\(49\) −14.7507 + 83.6553i −0.301035 + 1.70725i
\(50\) 49.5011 + 6.35918i 0.990022 + 0.127184i
\(51\) 0 0
\(52\) −55.9754 + 56.6815i −1.07645 + 1.09003i
\(53\) −98.4809 −1.85813 −0.929065 0.369917i \(-0.879386\pi\)
−0.929065 + 0.369917i \(0.879386\pi\)
\(54\) 0 0
\(55\) 2.07126i 0.0376593i
\(56\) 90.5777 + 19.1890i 1.61746 + 0.342660i
\(57\) 0 0
\(58\) −17.1804 2.20708i −0.296213 0.0380532i
\(59\) 12.4095 + 2.18814i 0.210331 + 0.0370871i 0.277821 0.960633i \(-0.410388\pi\)
−0.0674896 + 0.997720i \(0.521499\pi\)
\(60\) 0 0
\(61\) −62.8227 + 52.7145i −1.02988 + 0.864172i −0.990837 0.135065i \(-0.956876\pi\)
−0.0390434 + 0.999238i \(0.512431\pi\)
\(62\) −0.144696 + 0.280098i −0.00233381 + 0.00451771i
\(63\) 0 0
\(64\) 15.3991 62.1198i 0.240611 0.970622i
\(65\) −0.742223 4.20936i −0.0114188 0.0647593i
\(66\) 0 0
\(67\) 18.1950 + 49.9905i 0.271568 + 0.746126i 0.998249 + 0.0591515i \(0.0188395\pi\)
−0.726681 + 0.686975i \(0.758938\pi\)
\(68\) 0.554376 6.82930i 0.00815259 0.100431i
\(69\) 0 0
\(70\) −3.65214 + 3.36769i −0.0521734 + 0.0481098i
\(71\) −65.5561 37.8488i −0.923325 0.533082i −0.0386308 0.999254i \(-0.512300\pi\)
−0.884694 + 0.466172i \(0.845633\pi\)
\(72\) 0 0
\(73\) 13.3902 + 23.1924i 0.183427 + 0.317705i 0.943045 0.332664i \(-0.107948\pi\)
−0.759618 + 0.650369i \(0.774614\pi\)
\(74\) 28.7005 92.0312i 0.387845 1.24367i
\(75\) 0 0
\(76\) −13.8860 + 20.0982i −0.182710 + 0.264450i
\(77\) 85.5619 + 71.7950i 1.11119 + 0.932402i
\(78\) 0 0
\(79\) 39.9006 109.626i 0.505071 1.38767i −0.381194 0.924495i \(-0.624487\pi\)
0.886266 0.463177i \(-0.153291\pi\)
\(80\) 2.24010 + 2.60268i 0.0280012 + 0.0325334i
\(81\) 0 0
\(82\) −34.5616 + 22.1707i −0.421483 + 0.270375i
\(83\) −38.5038 + 105.788i −0.463901 + 1.27456i 0.458628 + 0.888628i \(0.348341\pi\)
−0.922529 + 0.385928i \(0.873881\pi\)
\(84\) 0 0
\(85\) 0.281624 + 0.236311i 0.00331322 + 0.00278012i
\(86\) −84.4788 + 35.3029i −0.982312 + 0.410498i
\(87\) 0 0
\(88\) 51.6222 57.4102i 0.586616 0.652389i
\(89\) −59.4575 102.983i −0.668061 1.15712i −0.978446 0.206505i \(-0.933791\pi\)
0.310384 0.950611i \(-0.399542\pi\)
\(90\) 0 0
\(91\) −199.612 115.246i −2.19354 1.26644i
\(92\) 31.8032 121.738i 0.345687 1.32324i
\(93\) 0 0
\(94\) −59.1506 45.0941i −0.629262 0.479724i
\(95\) −0.448295 1.23168i −0.00471889 0.0129651i
\(96\) 0 0
\(97\) −4.27138 24.2242i −0.0440349 0.249734i 0.954842 0.297114i \(-0.0960241\pi\)
−0.998877 + 0.0473796i \(0.984913\pi\)
\(98\) 7.94247 + 169.706i 0.0810456 + 1.73169i
\(99\) 0 0
\(100\) 99.3794 9.32261i 0.993794 0.0932261i
\(101\) −36.2218 + 30.3937i −0.358632 + 0.300928i −0.804245 0.594298i \(-0.797430\pi\)
0.445613 + 0.895226i \(0.352986\pi\)
\(102\) 0 0
\(103\) 52.3436 + 9.22958i 0.508190 + 0.0896076i 0.421864 0.906659i \(-0.361376\pi\)
0.0863264 + 0.996267i \(0.472487\pi\)
\(104\) −84.3376 + 135.171i −0.810939 + 1.29973i
\(105\) 0 0
\(106\) −192.158 + 43.2328i −1.81282 + 0.407856i
\(107\) 31.1755i 0.291360i −0.989332 0.145680i \(-0.953463\pi\)
0.989332 0.145680i \(-0.0465369\pi\)
\(108\) 0 0
\(109\) 62.5881 0.574203 0.287101 0.957900i \(-0.407308\pi\)
0.287101 + 0.957900i \(0.407308\pi\)
\(110\) 0.909277 + 4.04150i 0.00826615 + 0.0367409i
\(111\) 0 0
\(112\) 185.161 2.32132i 1.65323 0.0207260i
\(113\) −22.6665 + 128.548i −0.200589 + 1.13760i 0.703643 + 0.710554i \(0.251555\pi\)
−0.904232 + 0.427042i \(0.859556\pi\)
\(114\) 0 0
\(115\) 4.33953 + 5.17166i 0.0377351 + 0.0449709i
\(116\) −34.4917 + 3.23560i −0.297342 + 0.0278931i
\(117\) 0 0
\(118\) 25.1744 1.17820i 0.213342 0.00998471i
\(119\) 19.5236 3.44253i 0.164063 0.0289288i
\(120\) 0 0
\(121\) −26.1823 + 9.52958i −0.216383 + 0.0787569i
\(122\) −99.4398 + 130.437i −0.815080 + 1.06915i
\(123\) 0 0
\(124\) −0.159372 + 0.610056i −0.00128526 + 0.00491980i
\(125\) −5.36059 + 9.28482i −0.0428847 + 0.0742785i
\(126\) 0 0
\(127\) 26.2396 15.1494i 0.206611 0.119287i −0.393124 0.919485i \(-0.628606\pi\)
0.599735 + 0.800198i \(0.295273\pi\)
\(128\) 2.77676 127.970i 0.0216934 0.999765i
\(129\) 0 0
\(130\) −3.29614 7.88757i −0.0253549 0.0606736i
\(131\) 118.464 141.179i 0.904302 1.07770i −0.0923324 0.995728i \(-0.529432\pi\)
0.996634 0.0819767i \(-0.0261233\pi\)
\(132\) 0 0
\(133\) −66.4186 24.1744i −0.499388 0.181762i
\(134\) 57.4483 + 89.5551i 0.428718 + 0.668322i
\(135\) 0 0
\(136\) −1.91633 13.5689i −0.0140907 0.0997712i
\(137\) 23.6048 + 8.59145i 0.172298 + 0.0627113i 0.426729 0.904380i \(-0.359666\pi\)
−0.254431 + 0.967091i \(0.581888\pi\)
\(138\) 0 0
\(139\) 5.61100 6.68693i 0.0403669 0.0481074i −0.745483 0.666524i \(-0.767781\pi\)
0.785850 + 0.618417i \(0.212226\pi\)
\(140\) −5.64775 + 8.17439i −0.0403410 + 0.0583885i
\(141\) 0 0
\(142\) −144.530 45.0727i −1.01782 0.317413i
\(143\) −166.450 + 96.1000i −1.16399 + 0.672028i
\(144\) 0 0
\(145\) 0.929394 1.60976i 0.00640962 0.0111018i
\(146\) 36.3086 + 39.3755i 0.248689 + 0.269695i
\(147\) 0 0
\(148\) 15.5999 192.173i 0.105404 1.29847i
\(149\) 9.12132 3.31989i 0.0612169 0.0222811i −0.311230 0.950335i \(-0.600741\pi\)
0.372447 + 0.928053i \(0.378519\pi\)
\(150\) 0 0
\(151\) 92.5096 16.3119i 0.612646 0.108026i 0.141289 0.989968i \(-0.454875\pi\)
0.471357 + 0.881942i \(0.343764\pi\)
\(152\) −18.2717 + 45.3120i −0.120208 + 0.298105i
\(153\) 0 0
\(154\) 198.468 + 102.527i 1.28876 + 0.665759i
\(155\) −0.0217463 0.0259163i −0.000140299 0.000167202i
\(156\) 0 0
\(157\) −23.4101 + 132.765i −0.149109 + 0.845639i 0.814867 + 0.579649i \(0.196810\pi\)
−0.963976 + 0.265991i \(0.914301\pi\)
\(158\) 29.7297 231.422i 0.188163 1.46469i
\(159\) 0 0
\(160\) 5.51350 + 4.09501i 0.0344594 + 0.0255938i
\(161\) 364.055 2.26121
\(162\) 0 0
\(163\) 202.543i 1.24260i 0.783575 + 0.621298i \(0.213394\pi\)
−0.783575 + 0.621298i \(0.786606\pi\)
\(164\) −57.7046 + 58.4326i −0.351857 + 0.356296i
\(165\) 0 0
\(166\) −28.6889 + 223.320i −0.172824 + 1.34530i
\(167\) 147.033 + 25.9260i 0.880440 + 0.155245i 0.595553 0.803316i \(-0.296933\pi\)
0.284887 + 0.958561i \(0.408044\pi\)
\(168\) 0 0
\(169\) 174.373 146.316i 1.03179 0.865776i
\(170\) 0.653251 + 0.337463i 0.00384266 + 0.00198508i
\(171\) 0 0
\(172\) −149.339 + 105.970i −0.868252 + 0.616103i
\(173\) −54.2893 307.890i −0.313811 1.77971i −0.578809 0.815463i \(-0.696482\pi\)
0.264998 0.964249i \(-0.414629\pi\)
\(174\) 0 0
\(175\) 98.7769 + 271.387i 0.564439 + 1.55078i
\(176\) 75.5238 134.682i 0.429112 0.765240i
\(177\) 0 0
\(178\) −161.224 174.842i −0.905754 0.982259i
\(179\) −23.2554 13.4265i −0.129919 0.0750086i 0.433632 0.901090i \(-0.357232\pi\)
−0.563551 + 0.826081i \(0.690565\pi\)
\(180\) 0 0
\(181\) −144.044 249.492i −0.795823 1.37841i −0.922315 0.386439i \(-0.873705\pi\)
0.126492 0.991968i \(-0.459628\pi\)
\(182\) −440.081 137.242i −2.41803 0.754077i
\(183\) 0 0
\(184\) 8.61251 251.500i 0.0468071 1.36685i
\(185\) 7.92475 + 6.64966i 0.0428365 + 0.0359441i
\(186\) 0 0
\(187\) 5.65401 15.5343i 0.0302353 0.0830709i
\(188\) −135.212 62.0218i −0.719215 0.329903i
\(189\) 0 0
\(190\) −1.41543 2.20649i −0.00744962 0.0116131i
\(191\) −77.1124 + 211.865i −0.403730 + 1.10924i 0.556699 + 0.830714i \(0.312068\pi\)
−0.960429 + 0.278525i \(0.910155\pi\)
\(192\) 0 0
\(193\) −157.892 132.487i −0.818095 0.686463i 0.134430 0.990923i \(-0.457080\pi\)
−0.952525 + 0.304460i \(0.901524\pi\)
\(194\) −18.9688 45.3918i −0.0977772 0.233978i
\(195\) 0 0
\(196\) 89.9979 + 327.648i 0.459173 + 1.67167i
\(197\) 63.0398 + 109.188i 0.319999 + 0.554255i 0.980487 0.196581i \(-0.0629840\pi\)
−0.660488 + 0.750836i \(0.729651\pi\)
\(198\) 0 0
\(199\) −64.5454 37.2653i −0.324348 0.187263i 0.328981 0.944337i \(-0.393295\pi\)
−0.653329 + 0.757074i \(0.726628\pi\)
\(200\) 189.819 61.8177i 0.949096 0.309089i
\(201\) 0 0
\(202\) −57.3343 + 75.2063i −0.283833 + 0.372308i
\(203\) −34.2826 94.1906i −0.168880 0.463993i
\(204\) 0 0
\(205\) −0.765152 4.33939i −0.00373245 0.0211678i
\(206\) 106.186 4.96965i 0.515465 0.0241245i
\(207\) 0 0
\(208\) −105.222 + 300.774i −0.505875 + 1.44603i
\(209\) −45.1497 + 37.8851i −0.216027 + 0.181269i
\(210\) 0 0
\(211\) −26.9666 4.75493i −0.127804 0.0225352i 0.109380 0.994000i \(-0.465113\pi\)
−0.237184 + 0.971465i \(0.576224\pi\)
\(212\) −355.965 + 168.714i −1.67908 + 0.795820i
\(213\) 0 0
\(214\) −13.6859 60.8304i −0.0639529 0.284254i
\(215\) 9.82521i 0.0456986i
\(216\) 0 0
\(217\) −1.82436 −0.00840718
\(218\) 122.123 27.4760i 0.560200 0.126036i
\(219\) 0 0
\(220\) 3.54841 + 7.48671i 0.0161291 + 0.0340305i
\(221\) −5.92385 + 33.5958i −0.0268048 + 0.152017i
\(222\) 0 0
\(223\) −25.4525 30.3332i −0.114137 0.136023i 0.705951 0.708261i \(-0.250520\pi\)
−0.820088 + 0.572238i \(0.806075\pi\)
\(224\) 360.273 85.8146i 1.60836 0.383101i
\(225\) 0 0
\(226\) 12.2047 + 260.777i 0.0540033 + 1.15388i
\(227\) 367.121 64.7334i 1.61727 0.285169i 0.709524 0.704681i \(-0.248910\pi\)
0.907750 + 0.419512i \(0.137799\pi\)
\(228\) 0 0
\(229\) 270.130 98.3193i 1.17961 0.429342i 0.323544 0.946213i \(-0.395126\pi\)
0.856063 + 0.516871i \(0.172903\pi\)
\(230\) 10.7378 + 8.18603i 0.0466859 + 0.0355914i
\(231\) 0 0
\(232\) −65.8807 + 21.4551i −0.283968 + 0.0924790i
\(233\) 183.876 318.482i 0.789166 1.36688i −0.137312 0.990528i \(-0.543846\pi\)
0.926478 0.376348i \(-0.122820\pi\)
\(234\) 0 0
\(235\) 6.91234 3.99084i 0.0294142 0.0169823i
\(236\) 48.6037 13.3504i 0.205948 0.0565695i
\(237\) 0 0
\(238\) 36.5836 15.2879i 0.153713 0.0642350i
\(239\) −114.381 + 136.314i −0.478581 + 0.570350i −0.950275 0.311412i \(-0.899198\pi\)
0.471694 + 0.881762i \(0.343643\pi\)
\(240\) 0 0
\(241\) 327.606 + 119.239i 1.35936 + 0.494766i 0.915856 0.401507i \(-0.131513\pi\)
0.443503 + 0.896273i \(0.353736\pi\)
\(242\) −46.9041 + 30.0883i −0.193819 + 0.124332i
\(243\) 0 0
\(244\) −136.768 + 298.165i −0.560525 + 1.22199i
\(245\) −17.1317 6.23544i −0.0699254 0.0254508i
\(246\) 0 0
\(247\) 78.1804 93.1718i 0.316520 0.377214i
\(248\) −0.0431591 + 1.26032i −0.000174029 + 0.00508194i
\(249\) 0 0
\(250\) −6.38372 + 20.4701i −0.0255349 + 0.0818802i
\(251\) 110.893 64.0244i 0.441806 0.255077i −0.262557 0.964916i \(-0.584566\pi\)
0.704364 + 0.709839i \(0.251232\pi\)
\(252\) 0 0
\(253\) 151.787 262.903i 0.599949 1.03914i
\(254\) 44.5488 41.0790i 0.175389 0.161729i
\(255\) 0 0
\(256\) −50.7603 250.917i −0.198282 0.980145i
\(257\) 251.532 91.5503i 0.978725 0.356227i 0.197381 0.980327i \(-0.436756\pi\)
0.781344 + 0.624100i \(0.214534\pi\)
\(258\) 0 0
\(259\) 549.383 96.8710i 2.12117 0.374019i
\(260\) −9.89413 13.9434i −0.0380543 0.0536286i
\(261\) 0 0
\(262\) 169.172 327.478i 0.645694 1.24992i
\(263\) 167.815 + 199.995i 0.638081 + 0.760436i 0.984066 0.177805i \(-0.0568995\pi\)
−0.345985 + 0.938240i \(0.612455\pi\)
\(264\) 0 0
\(265\) 3.67024 20.8150i 0.0138500 0.0785471i
\(266\) −140.210 18.0122i −0.527106 0.0677149i
\(267\) 0 0
\(268\) 151.409 + 149.523i 0.564959 + 0.557920i
\(269\) −316.834 −1.17782 −0.588910 0.808199i \(-0.700443\pi\)
−0.588910 + 0.808199i \(0.700443\pi\)
\(270\) 0 0
\(271\) 175.899i 0.649072i −0.945873 0.324536i \(-0.894792\pi\)
0.945873 0.324536i \(-0.105208\pi\)
\(272\) −9.69588 25.6347i −0.0356466 0.0942452i
\(273\) 0 0
\(274\) 49.8300 + 6.40143i 0.181861 + 0.0233629i
\(275\) 237.166 + 41.8188i 0.862422 + 0.152068i
\(276\) 0 0
\(277\) 12.2521 10.2807i 0.0442313 0.0371144i −0.620404 0.784282i \(-0.713031\pi\)
0.664635 + 0.747168i \(0.268587\pi\)
\(278\) 8.01279 15.5109i 0.0288230 0.0557947i
\(279\) 0 0
\(280\) −7.43150 + 18.4294i −0.0265411 + 0.0658194i
\(281\) 55.2824 + 313.522i 0.196734 + 1.11574i 0.909927 + 0.414768i \(0.136137\pi\)
−0.713193 + 0.700968i \(0.752752\pi\)
\(282\) 0 0
\(283\) 70.4466 + 193.550i 0.248928 + 0.683924i 0.999726 + 0.0233925i \(0.00744673\pi\)
−0.750798 + 0.660531i \(0.770331\pi\)
\(284\) −301.798 24.4988i −1.06267 0.0862632i
\(285\) 0 0
\(286\) −282.594 + 260.584i −0.988091 + 0.911132i
\(287\) −205.778 118.806i −0.716998 0.413959i
\(288\) 0 0
\(289\) 143.033 + 247.740i 0.494924 + 0.857233i
\(290\) 1.10678 3.54900i 0.00381648 0.0122379i
\(291\) 0 0
\(292\) 88.1320 + 60.8911i 0.301822 + 0.208531i
\(293\) −74.1234 62.1969i −0.252981 0.212276i 0.507474 0.861667i \(-0.330579\pi\)
−0.760455 + 0.649391i \(0.775024\pi\)
\(294\) 0 0
\(295\) −0.924972 + 2.54134i −0.00313550 + 0.00861471i
\(296\) −53.9245 381.821i −0.182177 1.28994i
\(297\) 0 0
\(298\) 16.3403 10.4821i 0.0548333 0.0351748i
\(299\) −214.262 + 588.681i −0.716596 + 1.96883i
\(300\) 0 0
\(301\) −405.870 340.566i −1.34841 1.13145i
\(302\) 173.346 72.4397i 0.573994 0.239866i
\(303\) 0 0
\(304\) −15.7603 + 96.4352i −0.0518431 + 0.317221i
\(305\) −8.80046 15.2428i −0.0288540 0.0499765i
\(306\) 0 0
\(307\) 234.193 + 135.212i 0.762845 + 0.440429i 0.830316 0.557293i \(-0.188160\pi\)
−0.0674715 + 0.997721i \(0.521493\pi\)
\(308\) 432.266 + 112.926i 1.40346 + 0.366643i
\(309\) 0 0
\(310\) −0.0538091 0.0410219i −0.000173578 0.000132329i
\(311\) −6.59888 18.1303i −0.0212183 0.0582967i 0.928631 0.371004i \(-0.120986\pi\)
−0.949850 + 0.312707i \(0.898764\pi\)
\(312\) 0 0
\(313\) 84.3023 + 478.102i 0.269337 + 1.52748i 0.756396 + 0.654114i \(0.226959\pi\)
−0.487059 + 0.873369i \(0.661930\pi\)
\(314\) 12.6051 + 269.332i 0.0401437 + 0.857746i
\(315\) 0 0
\(316\) −43.5839 464.607i −0.137924 1.47028i
\(317\) −420.029 + 352.446i −1.32501 + 1.11182i −0.339796 + 0.940499i \(0.610358\pi\)
−0.985216 + 0.171318i \(0.945198\pi\)
\(318\) 0 0
\(319\) −82.3134 14.5141i −0.258036 0.0454987i
\(320\) 12.5558 + 5.56988i 0.0392368 + 0.0174059i
\(321\) 0 0
\(322\) 710.354 159.819i 2.20607 0.496332i
\(323\) 10.4612i 0.0323876i
\(324\) 0 0
\(325\) −496.970 −1.52914
\(326\) 88.9157 + 395.207i 0.272748 + 1.21229i
\(327\) 0 0
\(328\) −86.9430 + 139.347i −0.265070 + 0.424839i
\(329\) 74.7406 423.875i 0.227175 1.28837i
\(330\) 0 0
\(331\) −349.160 416.112i −1.05486 1.25714i −0.965297 0.261156i \(-0.915896\pi\)
−0.0895664 0.995981i \(-0.528548\pi\)
\(332\) 42.0581 + 448.341i 0.126681 + 1.35043i
\(333\) 0 0
\(334\) 298.277 13.9598i 0.893045 0.0417957i
\(335\) −11.2441 + 1.98264i −0.0335646 + 0.00591834i
\(336\) 0 0
\(337\) 187.444 68.2240i 0.556214 0.202445i −0.0485915 0.998819i \(-0.515473\pi\)
0.604805 + 0.796374i \(0.293251\pi\)
\(338\) 276.008 362.045i 0.816593 1.07114i
\(339\) 0 0
\(340\) 1.42279 + 0.371692i 0.00418467 + 0.00109321i
\(341\) −0.760637 + 1.31746i −0.00223061 + 0.00386352i
\(342\) 0 0
\(343\) −360.283 + 208.010i −1.05039 + 0.606442i
\(344\) −244.875 + 272.330i −0.711845 + 0.791658i
\(345\) 0 0
\(346\) −241.094 576.930i −0.696802 1.66743i
\(347\) 19.9944 23.8284i 0.0576208 0.0686697i −0.736464 0.676477i \(-0.763506\pi\)
0.794085 + 0.607807i \(0.207950\pi\)
\(348\) 0 0
\(349\) −181.722 66.1414i −0.520694 0.189517i 0.0682846 0.997666i \(-0.478247\pi\)
−0.588978 + 0.808149i \(0.700470\pi\)
\(350\) 311.874 + 486.175i 0.891069 + 1.38907i
\(351\) 0 0
\(352\) 88.2388 295.950i 0.250678 0.840768i
\(353\) 247.782 + 90.1852i 0.701932 + 0.255482i 0.668235 0.743950i \(-0.267050\pi\)
0.0336962 + 0.999432i \(0.489272\pi\)
\(354\) 0 0
\(355\) 10.4429 12.4454i 0.0294167 0.0350575i
\(356\) −391.340 270.380i −1.09927 0.759493i
\(357\) 0 0
\(358\) −51.2708 15.9891i −0.143215 0.0446624i
\(359\) 250.254 144.484i 0.697086 0.402463i −0.109175 0.994023i \(-0.534821\pi\)
0.806261 + 0.591560i \(0.201488\pi\)
\(360\) 0 0
\(361\) −161.851 + 280.335i −0.448342 + 0.776550i
\(362\) −390.588 423.580i −1.07897 1.17011i
\(363\) 0 0
\(364\) −918.946 74.5964i −2.52458 0.204935i
\(365\) −5.40101 + 1.96581i −0.0147973 + 0.00538577i
\(366\) 0 0
\(367\) −443.020 + 78.1163i −1.20714 + 0.212851i −0.740782 0.671746i \(-0.765545\pi\)
−0.466356 + 0.884597i \(0.654434\pi\)
\(368\) −93.6027 494.514i −0.254355 1.34379i
\(369\) 0 0
\(370\) 18.3822 + 9.49604i 0.0496815 + 0.0256650i
\(371\) −732.629 873.113i −1.97474 2.35340i
\(372\) 0 0
\(373\) −40.7778 + 231.262i −0.109324 + 0.620006i 0.880081 + 0.474824i \(0.157488\pi\)
−0.989405 + 0.145183i \(0.953623\pi\)
\(374\) 4.21276 32.7929i 0.0112641 0.0876816i
\(375\) 0 0
\(376\) −291.057 61.6607i −0.774088 0.163991i
\(377\) 172.484 0.457517
\(378\) 0 0
\(379\) 24.5603i 0.0648028i −0.999475 0.0324014i \(-0.989685\pi\)
0.999475 0.0324014i \(-0.0103155\pi\)
\(380\) −3.73046 3.68399i −0.00981700 0.00969470i
\(381\) 0 0
\(382\) −57.4559 + 447.248i −0.150408 + 1.17081i
\(383\) −586.109 103.347i −1.53031 0.269835i −0.655835 0.754905i \(-0.727683\pi\)
−0.874475 + 0.485070i \(0.838794\pi\)
\(384\) 0 0
\(385\) −18.3634 + 15.4087i −0.0476972 + 0.0400227i
\(386\) −366.245 189.199i −0.948822 0.490152i
\(387\) 0 0
\(388\) −56.9392 80.2424i −0.146751 0.206810i
\(389\) 57.6262 + 326.814i 0.148139 + 0.840139i 0.964793 + 0.263011i \(0.0847156\pi\)
−0.816654 + 0.577128i \(0.804173\pi\)
\(390\) 0 0
\(391\) −18.4288 50.6327i −0.0471325 0.129495i
\(392\) 319.443 + 599.806i 0.814904 + 1.53012i
\(393\) 0 0
\(394\) 170.938 + 185.377i 0.433853 + 0.470499i
\(395\) 21.6836 + 12.5190i 0.0548952 + 0.0316938i
\(396\) 0 0
\(397\) −42.7323 74.0146i −0.107638 0.186435i 0.807175 0.590312i \(-0.200995\pi\)
−0.914813 + 0.403878i \(0.867662\pi\)
\(398\) −142.302 44.3778i −0.357542 0.111502i
\(399\) 0 0
\(400\) 343.242 203.950i 0.858106 0.509876i
\(401\) −129.017 108.258i −0.321738 0.269970i 0.467586 0.883948i \(-0.345124\pi\)
−0.789323 + 0.613978i \(0.789568\pi\)
\(402\) 0 0
\(403\) 1.07371 2.95000i 0.00266430 0.00732011i
\(404\) −78.8568 + 171.914i −0.195190 + 0.425530i
\(405\) 0 0
\(406\) −108.242 168.737i −0.266607 0.415609i
\(407\) 159.101 437.126i 0.390911 1.07402i
\(408\) 0 0
\(409\) −106.572 89.4245i −0.260567 0.218642i 0.503139 0.864205i \(-0.332178\pi\)
−0.763707 + 0.645563i \(0.776623\pi\)
\(410\) −3.39796 8.13124i −0.00828772 0.0198323i
\(411\) 0 0
\(412\) 205.011 56.3121i 0.497599 0.136680i
\(413\) 72.9187 + 126.299i 0.176559 + 0.305808i
\(414\) 0 0
\(415\) −20.9245 12.0808i −0.0504205 0.0291103i
\(416\) −73.2730 + 633.070i −0.176137 + 1.52180i
\(417\) 0 0
\(418\) −71.4659 + 93.7430i −0.170971 + 0.224266i
\(419\) 48.4909 + 133.228i 0.115730 + 0.317966i 0.984011 0.178107i \(-0.0569972\pi\)
−0.868281 + 0.496073i \(0.834775\pi\)
\(420\) 0 0
\(421\) 18.5532 + 105.220i 0.0440694 + 0.249930i 0.998882 0.0472796i \(-0.0150552\pi\)
−0.954812 + 0.297209i \(0.903944\pi\)
\(422\) −54.7053 + 2.56028i −0.129633 + 0.00606702i
\(423\) 0 0
\(424\) −620.504 + 485.466i −1.46345 + 1.14497i
\(425\) 32.7443 27.4757i 0.0770454 0.0646488i
\(426\) 0 0
\(427\) −934.714 164.815i −2.18903 0.385984i
\(428\) −53.4087 112.686i −0.124787 0.263284i
\(429\) 0 0
\(430\) −4.31323 19.1712i −0.0100308 0.0445842i
\(431\) 560.222i 1.29982i −0.760012 0.649910i \(-0.774807\pi\)
0.760012 0.649910i \(-0.225193\pi\)
\(432\) 0 0
\(433\) 381.789 0.881731 0.440865 0.897573i \(-0.354672\pi\)
0.440865 + 0.897573i \(0.354672\pi\)
\(434\) −3.55973 + 0.800887i −0.00820215 + 0.00184536i
\(435\) 0 0
\(436\) 226.229 107.224i 0.518873 0.245926i
\(437\) −33.3589 + 189.188i −0.0763362 + 0.432924i
\(438\) 0 0
\(439\) 310.625 + 370.189i 0.707575 + 0.843255i 0.993361 0.115038i \(-0.0366991\pi\)
−0.285786 + 0.958293i \(0.592255\pi\)
\(440\) 10.2104 + 13.0505i 0.0232054 + 0.0296603i
\(441\) 0 0
\(442\) 3.18968 + 68.1536i 0.00721648 + 0.154194i
\(443\) 310.302 54.7146i 0.700456 0.123509i 0.187932 0.982182i \(-0.439822\pi\)
0.512524 + 0.858673i \(0.328711\pi\)
\(444\) 0 0
\(445\) 23.9825 8.72893i 0.0538933 0.0196156i
\(446\) −62.9798 48.0133i −0.141210 0.107653i
\(447\) 0 0
\(448\) 665.301 325.602i 1.48505 0.726791i
\(449\) −408.322 + 707.234i −0.909402 + 1.57513i −0.0945056 + 0.995524i \(0.530127\pi\)
−0.814897 + 0.579606i \(0.803206\pi\)
\(450\) 0 0
\(451\) −171.592 + 99.0687i −0.380470 + 0.219665i
\(452\) 138.295 + 503.478i 0.305961 + 1.11389i
\(453\) 0 0
\(454\) 687.919 287.474i 1.51524 0.633204i
\(455\) 31.7978 37.8951i 0.0698852 0.0832859i
\(456\) 0 0
\(457\) 48.2527 + 17.5625i 0.105586 + 0.0384301i 0.394273 0.918993i \(-0.370996\pi\)
−0.288687 + 0.957424i \(0.593219\pi\)
\(458\) 483.923 310.429i 1.05660 0.677793i
\(459\) 0 0
\(460\) 24.5454 + 11.2590i 0.0533596 + 0.0244760i
\(461\) −559.359 203.590i −1.21336 0.441627i −0.345492 0.938422i \(-0.612288\pi\)
−0.867868 + 0.496795i \(0.834510\pi\)
\(462\) 0 0
\(463\) 277.457 330.660i 0.599259 0.714169i −0.378098 0.925766i \(-0.623422\pi\)
0.977357 + 0.211597i \(0.0678663\pi\)
\(464\) −119.129 + 70.7852i −0.256744 + 0.152554i
\(465\) 0 0
\(466\) 218.970 702.151i 0.469894 1.50676i
\(467\) −654.186 + 377.694i −1.40083 + 0.808767i −0.994477 0.104951i \(-0.966532\pi\)
−0.406349 + 0.913718i \(0.633198\pi\)
\(468\) 0 0
\(469\) −307.848 + 533.208i −0.656392 + 1.13690i
\(470\) 11.7356 10.8215i 0.0249693 0.0230245i
\(471\) 0 0
\(472\) 88.9760 47.3865i 0.188509 0.100395i
\(473\) −415.161 + 151.106i −0.877719 + 0.319464i
\(474\) 0 0
\(475\) −150.082 + 26.4636i −0.315963 + 0.0557128i
\(476\) 64.6715 45.8903i 0.135865 0.0964081i
\(477\) 0 0
\(478\) −163.342 + 316.192i −0.341719 + 0.661489i
\(479\) 379.355 + 452.098i 0.791974 + 0.943837i 0.999408 0.0344117i \(-0.0109557\pi\)
−0.207434 + 0.978249i \(0.566511\pi\)
\(480\) 0 0
\(481\) −166.694 + 945.370i −0.346558 + 1.96543i
\(482\) 691.578 + 88.8439i 1.43481 + 0.184323i
\(483\) 0 0
\(484\) −78.3119 + 79.2998i −0.161801 + 0.163843i
\(485\) 5.27924 0.0108850
\(486\) 0 0
\(487\) 474.186i 0.973688i −0.873489 0.486844i \(-0.838148\pi\)
0.873489 0.486844i \(-0.161852\pi\)
\(488\) −135.972 + 641.829i −0.278631 + 1.31522i
\(489\) 0 0
\(490\) −36.1652 4.64598i −0.0738065 0.00948159i
\(491\) −280.087 49.3868i −0.570441 0.100584i −0.119015 0.992892i \(-0.537974\pi\)
−0.451427 + 0.892308i \(0.649085\pi\)
\(492\) 0 0
\(493\) −11.3646 + 9.53602i −0.0230519 + 0.0193428i
\(494\) 111.646 216.120i 0.226003 0.437490i
\(495\) 0 0
\(496\) 0.469063 + 2.47812i 0.000945692 + 0.00499620i
\(497\) −152.131 862.777i −0.306098 1.73597i
\(498\) 0 0
\(499\) −128.475 352.983i −0.257465 0.707380i −0.999322 0.0368216i \(-0.988277\pi\)
0.741857 0.670559i \(-0.233946\pi\)
\(500\) −3.46980 + 42.7441i −0.00693960 + 0.0854883i
\(501\) 0 0
\(502\) 188.272 173.608i 0.375043 0.345832i
\(503\) 461.157 + 266.249i 0.916814 + 0.529323i 0.882617 0.470092i \(-0.155779\pi\)
0.0341967 + 0.999415i \(0.489113\pi\)
\(504\) 0 0
\(505\) −5.07411 8.78861i −0.0100477 0.0174032i
\(506\) 180.757 579.617i 0.357228 1.14549i
\(507\) 0 0
\(508\) 68.8912 99.7113i 0.135613 0.196282i
\(509\) −142.299 119.403i −0.279565 0.234583i 0.492213 0.870475i \(-0.336188\pi\)
−0.771778 + 0.635892i \(0.780633\pi\)
\(510\) 0 0
\(511\) −106.006 + 291.250i −0.207449 + 0.569962i
\(512\) −209.196 467.312i −0.408587 0.912719i
\(513\) 0 0
\(514\) 450.606 289.057i 0.876666 0.562368i
\(515\) −3.90154 + 10.7194i −0.00757581 + 0.0208144i
\(516\) 0 0
\(517\) −274.940 230.702i −0.531799 0.446232i
\(518\) 1029.44 430.194i 1.98734 0.830491i
\(519\) 0 0
\(520\) −25.4268 22.8633i −0.0488977 0.0439679i
\(521\) −87.3646 151.320i −0.167686 0.290441i 0.769920 0.638141i \(-0.220296\pi\)
−0.937606 + 0.347700i \(0.886963\pi\)
\(522\) 0 0
\(523\) 721.777 + 416.718i 1.38007 + 0.796784i 0.992167 0.124916i \(-0.0398662\pi\)
0.387903 + 0.921700i \(0.373200\pi\)
\(524\) 186.331 713.249i 0.355593 1.36116i
\(525\) 0 0
\(526\) 415.243 + 316.564i 0.789435 + 0.601833i
\(527\) 0.0923506 + 0.253731i 0.000175238 + 0.000481463i
\(528\) 0 0
\(529\) −79.9609 453.481i −0.151155 0.857242i
\(530\) −1.97623 42.2260i −0.00372874 0.0796716i
\(531\) 0 0
\(532\) −281.489 + 26.4060i −0.529115 + 0.0496353i
\(533\) 313.220 262.823i 0.587656 0.493102i
\(534\) 0 0
\(535\) 6.58927 + 1.16187i 0.0123164 + 0.00217171i
\(536\) 361.073 + 225.284i 0.673644 + 0.420307i
\(537\) 0 0
\(538\) −618.214 + 139.089i −1.14910 + 0.258530i
\(539\) 819.793i 1.52095i
\(540\) 0 0
\(541\) 313.109 0.578760 0.289380 0.957214i \(-0.406551\pi\)
0.289380 + 0.957214i \(0.406551\pi\)
\(542\) −77.2189 343.218i −0.142470 0.633243i
\(543\) 0 0
\(544\) −30.1724 45.7626i −0.0554640 0.0841225i
\(545\) −2.33257 + 13.2287i −0.00427995 + 0.0242728i
\(546\) 0 0
\(547\) 372.771 + 444.251i 0.681482 + 0.812158i 0.990297 0.138964i \(-0.0443771\pi\)
−0.308816 + 0.951122i \(0.599933\pi\)
\(548\) 100.040 9.38455i 0.182554 0.0171251i
\(549\) 0 0
\(550\) 481.123 22.5172i 0.874769 0.0409404i
\(551\) 52.0892 9.18473i 0.0945358 0.0166692i
\(552\) 0 0
\(553\) 1268.76 461.790i 2.29432 0.835063i
\(554\) 19.3933 25.4386i 0.0350060 0.0459180i
\(555\) 0 0
\(556\) 8.82552 33.7829i 0.0158732 0.0607606i
\(557\) 39.2530 67.9882i 0.0704722 0.122061i −0.828636 0.559788i \(-0.810883\pi\)
0.899108 + 0.437726i \(0.144216\pi\)
\(558\) 0 0
\(559\) 789.570 455.859i 1.41247 0.815489i
\(560\) −6.41007 + 39.2224i −0.0114466 + 0.0700400i
\(561\) 0 0
\(562\) 245.503 + 587.483i 0.436839 + 1.04534i
\(563\) −28.0423 + 33.4195i −0.0498087 + 0.0593597i −0.790374 0.612625i \(-0.790114\pi\)
0.740565 + 0.671985i \(0.234558\pi\)
\(564\) 0 0
\(565\) −26.3253 9.58163i −0.0465935 0.0169586i
\(566\) 222.425 + 346.735i 0.392977 + 0.612606i
\(567\) 0 0
\(568\) −599.631 + 84.6856i −1.05569 + 0.149094i
\(569\) 623.877 + 227.073i 1.09645 + 0.399074i 0.826005 0.563663i \(-0.190608\pi\)
0.270441 + 0.962737i \(0.412831\pi\)
\(570\) 0 0
\(571\) 316.761 377.501i 0.554747 0.661122i −0.413679 0.910423i \(-0.635756\pi\)
0.968426 + 0.249301i \(0.0802009\pi\)
\(572\) −437.010 + 632.516i −0.764003 + 1.10580i
\(573\) 0 0
\(574\) −453.676 141.482i −0.790376 0.246484i
\(575\) 679.786 392.475i 1.18224 0.682565i
\(576\) 0 0
\(577\) −4.25933 + 7.37738i −0.00738186 + 0.0127858i −0.869693 0.493594i \(-0.835683\pi\)
0.862311 + 0.506379i \(0.169016\pi\)
\(578\) 387.847 + 420.606i 0.671015 + 0.727692i
\(579\) 0 0
\(580\) 0.601578 7.41078i 0.00103720 0.0127772i
\(581\) −1224.34 + 445.623i −2.10730 + 0.766993i
\(582\) 0 0
\(583\) −935.977 + 165.038i −1.60545 + 0.283084i
\(584\) 198.696 + 80.1225i 0.340234 + 0.137196i
\(585\) 0 0
\(586\) −171.936 88.8203i −0.293406 0.151571i
\(587\) −265.990 316.994i −0.453134 0.540024i 0.490313 0.871546i \(-0.336882\pi\)
−0.943447 + 0.331522i \(0.892438\pi\)
\(588\) 0 0
\(589\) 0.167169 0.948061i 0.000283818 0.00160961i
\(590\) −0.689190 + 5.36479i −0.00116812 + 0.00909286i
\(591\) 0 0
\(592\) −272.837 721.347i −0.460874 1.21849i
\(593\) 105.821 0.178450 0.0892252 0.996011i \(-0.471561\pi\)
0.0892252 + 0.996011i \(0.471561\pi\)
\(594\) 0 0
\(595\) 4.25481i 0.00715094i
\(596\) 27.2821 27.6263i 0.0457753 0.0463528i
\(597\) 0 0
\(598\) −159.645 + 1242.71i −0.266965 + 2.07811i
\(599\) 430.103 + 75.8387i 0.718035 + 0.126609i 0.520715 0.853730i \(-0.325665\pi\)
0.197319 + 0.980339i \(0.436776\pi\)
\(600\) 0 0
\(601\) −756.042 + 634.394i −1.25797 + 1.05556i −0.262078 + 0.965047i \(0.584408\pi\)
−0.995895 + 0.0905178i \(0.971148\pi\)
\(602\) −941.452 486.345i −1.56387 0.807882i
\(603\) 0 0
\(604\) 306.437 217.445i 0.507346 0.360008i
\(605\) −1.03840 5.88907i −0.00171637 0.00973400i
\(606\) 0 0
\(607\) 258.006 + 708.866i 0.425051 + 1.16782i 0.948781 + 0.315934i \(0.102318\pi\)
−0.523730 + 0.851884i \(0.675460\pi\)
\(608\) 11.5828 + 195.086i 0.0190507 + 0.320864i
\(609\) 0 0
\(610\) −23.8632 25.8789i −0.0391201 0.0424244i
\(611\) 641.422 + 370.325i 1.04979 + 0.606097i
\(612\) 0 0
\(613\) 88.3953 + 153.105i 0.144201 + 0.249764i 0.929075 0.369892i \(-0.120605\pi\)
−0.784874 + 0.619656i \(0.787272\pi\)
\(614\) 516.321 + 161.018i 0.840914 + 0.262245i
\(615\) 0 0
\(616\) 893.022 + 30.5811i 1.44971 + 0.0496447i
\(617\) 385.320 + 323.322i 0.624506 + 0.524023i 0.899216 0.437504i \(-0.144138\pi\)
−0.274710 + 0.961527i \(0.588582\pi\)
\(618\) 0 0
\(619\) 82.2498 225.980i 0.132875 0.365072i −0.855356 0.518041i \(-0.826661\pi\)
0.988231 + 0.152969i \(0.0488836\pi\)
\(620\) −0.123002 0.0564210i −0.000198391 9.10016e-5i
\(621\) 0 0
\(622\) −20.8350 32.4794i −0.0334968 0.0522177i
\(623\) 470.709 1293.26i 0.755552 2.07586i
\(624\) 0 0
\(625\) 476.133 + 399.523i 0.761813 + 0.639237i
\(626\) 374.378 + 895.877i 0.598048 + 1.43111i
\(627\) 0 0
\(628\) 142.831 + 519.994i 0.227438 + 0.828016i
\(629\) −41.2830 71.5043i −0.0656328 0.113679i
\(630\) 0 0
\(631\) −72.3715 41.7837i −0.114693 0.0662182i 0.441556 0.897234i \(-0.354427\pi\)
−0.556249 + 0.831016i \(0.687760\pi\)
\(632\) −289.003 887.420i −0.457283 1.40415i
\(633\) 0 0
\(634\) −664.848 + 872.093i −1.04866 + 1.37554i
\(635\) 2.22408 + 6.11062i 0.00350249 + 0.00962302i
\(636\) 0 0
\(637\) −293.768 1666.04i −0.461174 2.61545i
\(638\) −166.984 + 7.81506i −0.261730 + 0.0122493i
\(639\) 0 0
\(640\) 26.9443 + 5.35616i 0.0421005 + 0.00836899i
\(641\) 709.440 595.291i 1.10677 0.928691i 0.108909 0.994052i \(-0.465264\pi\)
0.997862 + 0.0653607i \(0.0208198\pi\)
\(642\) 0 0
\(643\) −0.379828 0.0669739i −0.000590712 0.000104159i 0.173353 0.984860i \(-0.444540\pi\)
−0.173944 + 0.984756i \(0.555651\pi\)
\(644\) 1315.90 623.686i 2.04333 0.968457i
\(645\) 0 0
\(646\) 4.59244 + 20.4122i 0.00710903 + 0.0315978i
\(647\) 295.175i 0.456222i 0.973635 + 0.228111i \(0.0732549\pi\)
−0.973635 + 0.228111i \(0.926745\pi\)
\(648\) 0 0
\(649\) 121.609 0.187379
\(650\) −969.701 + 218.168i −1.49185 + 0.335643i
\(651\) 0 0
\(652\) 346.989 + 732.105i 0.532192 + 1.12286i
\(653\) 19.2754 109.316i 0.0295182 0.167406i −0.966485 0.256723i \(-0.917357\pi\)
0.996003 + 0.0893167i \(0.0284683\pi\)
\(654\) 0 0
\(655\) 25.4248 + 30.3001i 0.0388165 + 0.0462597i
\(656\) −108.472 + 310.066i −0.165354 + 0.472661i
\(657\) 0 0
\(658\) −40.2439 859.887i −0.0611609 1.30682i
\(659\) −1084.88 + 191.294i −1.64626 + 0.290280i −0.918461 0.395512i \(-0.870567\pi\)
−0.727797 + 0.685792i \(0.759456\pi\)
\(660\) 0 0
\(661\) 471.148 171.484i 0.712781 0.259431i 0.0399230 0.999203i \(-0.487289\pi\)
0.672858 + 0.739772i \(0.265067\pi\)
\(662\) −863.961 658.649i −1.30508 0.994938i
\(663\) 0 0
\(664\) 278.885 + 856.352i 0.420008 + 1.28969i
\(665\) 7.58485 13.1373i 0.0114058 0.0197554i
\(666\) 0 0
\(667\) −235.934 + 136.217i −0.353724 + 0.204223i
\(668\) 575.877 158.181i 0.862092 0.236798i
\(669\) 0 0
\(670\) −21.0695 + 8.80472i −0.0314470 + 0.0131414i
\(671\) −508.735 + 606.287i −0.758175 + 0.903558i
\(672\) 0 0
\(673\) −745.558 271.361i −1.10781 0.403211i −0.277622 0.960690i \(-0.589546\pi\)
−0.830190 + 0.557480i \(0.811768\pi\)
\(674\) 335.795 215.408i 0.498213 0.319596i
\(675\) 0 0
\(676\) 379.618 827.598i 0.561565 1.22426i
\(677\) 524.604 + 190.940i 0.774896 + 0.282039i 0.699043 0.715080i \(-0.253610\pi\)
0.0758531 + 0.997119i \(0.475832\pi\)
\(678\) 0 0
\(679\) 182.991 218.080i 0.269501 0.321179i
\(680\) 2.93935 + 0.100657i 0.00432257 + 0.000148025i
\(681\) 0 0
\(682\) −0.905813 + 2.90458i −0.00132817 + 0.00425892i
\(683\) 921.593 532.082i 1.34933 0.779037i 0.361176 0.932498i \(-0.382375\pi\)
0.988155 + 0.153461i \(0.0490419\pi\)
\(684\) 0 0
\(685\) −2.69562 + 4.66894i −0.00393520 + 0.00681597i
\(686\) −611.679 + 564.037i −0.891660 + 0.822211i
\(687\) 0 0
\(688\) −358.253 + 638.877i −0.520717 + 0.928601i
\(689\) 1843.02 670.803i 2.67491 0.973589i
\(690\) 0 0
\(691\) −135.724 + 23.9318i −0.196417 + 0.0346336i −0.270991 0.962582i \(-0.587351\pi\)
0.0745742 + 0.997215i \(0.476240\pi\)
\(692\) −723.698 1019.88i −1.04581 1.47382i
\(693\) 0 0
\(694\) 28.5530 55.2721i 0.0411427 0.0796427i
\(695\) 1.20424 + 1.43516i 0.00173272 + 0.00206497i
\(696\) 0 0
\(697\) −6.10685 + 34.6337i −0.00876163 + 0.0496897i
\(698\) −383.617 49.2815i −0.549594 0.0706039i
\(699\) 0 0
\(700\) 821.966 + 811.726i 1.17424 + 1.15961i
\(701\) −1148.72 −1.63869 −0.819347 0.573298i \(-0.805664\pi\)
−0.819347 + 0.573298i \(0.805664\pi\)
\(702\) 0 0
\(703\) 294.373i 0.418738i
\(704\) 42.2527 616.202i 0.0600181 0.875287i
\(705\) 0 0
\(706\) 523.069 + 67.1963i 0.740891 + 0.0951789i
\(707\) −538.930 95.0280i −0.762278 0.134410i
\(708\) 0 0
\(709\) 166.685 139.866i 0.235099 0.197272i −0.517625 0.855608i \(-0.673184\pi\)
0.752724 + 0.658336i \(0.228739\pi\)
\(710\) 14.9130 28.8682i 0.0210043 0.0406595i
\(711\) 0 0
\(712\) −882.288 355.775i −1.23917 0.499683i
\(713\) 0.861030 + 4.88315i 0.00120762 + 0.00684873i
\(714\) 0 0
\(715\) −14.1084 38.7625i −0.0197320 0.0542133i
\(716\) −107.060 8.69072i −0.149525 0.0121379i
\(717\) 0 0
\(718\) 424.874 391.782i 0.591746 0.545657i
\(719\) −532.823 307.625i −0.741061 0.427852i 0.0813939 0.996682i \(-0.474063\pi\)
−0.822455 + 0.568830i \(0.807396\pi\)
\(720\) 0 0
\(721\) 307.572 + 532.730i 0.426591 + 0.738877i
\(722\) −192.742 + 618.048i −0.266956 + 0.856023i
\(723\) 0 0
\(724\) −948.076 655.032i −1.30950 0.904741i
\(725\) −165.558 138.920i −0.228356 0.191613i
\(726\) 0 0
\(727\) −263.701 + 724.511i −0.362724 + 0.996577i 0.615338 + 0.788264i \(0.289020\pi\)
−0.978062 + 0.208313i \(0.933203\pi\)
\(728\) −1825.82 + 257.860i −2.50799 + 0.354203i
\(729\) 0 0
\(730\) −9.67560 + 6.20675i −0.0132542 + 0.00850240i
\(731\) −26.8203 + 73.6881i −0.0366898 + 0.100804i
\(732\) 0 0
\(733\) −542.102 454.878i −0.739566 0.620570i 0.193155 0.981168i \(-0.438128\pi\)
−0.932721 + 0.360598i \(0.882572\pi\)
\(734\) −830.139 + 346.907i −1.13098 + 0.472625i
\(735\) 0 0
\(736\) −399.730 923.818i −0.543112 1.25519i
\(737\) 256.704 + 444.625i 0.348310 + 0.603291i
\(738\) 0 0
\(739\) 328.811 + 189.839i 0.444940 + 0.256887i 0.705691 0.708520i \(-0.250637\pi\)
−0.260751 + 0.965406i \(0.583970\pi\)
\(740\) 40.0365 + 10.4592i 0.0541033 + 0.0141341i
\(741\) 0 0
\(742\) −1812.82 1382.02i −2.44315 1.86256i
\(743\) 410.605 + 1128.13i 0.552631 + 1.51834i 0.830104 + 0.557608i \(0.188281\pi\)
−0.277473 + 0.960733i \(0.589497\pi\)
\(744\) 0 0
\(745\) 0.361755 + 2.05162i 0.000485578 + 0.00275385i
\(746\) 21.9567 + 469.146i 0.0294326 + 0.628883i
\(747\) 0 0
\(748\) −6.17594 65.8358i −0.00825660 0.0880158i
\(749\) 276.396 231.924i 0.369020 0.309644i
\(750\) 0 0
\(751\) −338.515 59.6894i −0.450753 0.0794799i −0.0563366 0.998412i \(-0.517942\pi\)
−0.394416 + 0.918932i \(0.629053\pi\)
\(752\) −594.987 + 7.45919i −0.791206 + 0.00991913i
\(753\) 0 0
\(754\) 336.555 75.7198i 0.446359 0.100424i
\(755\) 20.1608i 0.0267031i
\(756\) 0 0
\(757\) −185.105 −0.244525 −0.122262 0.992498i \(-0.539015\pi\)
−0.122262 + 0.992498i \(0.539015\pi\)
\(758\) −10.7819 47.9226i −0.0142241 0.0632225i
\(759\) 0 0
\(760\) −8.89623 5.55063i −0.0117056 0.00730346i
\(761\) −107.060 + 607.165i −0.140683 + 0.797851i 0.830050 + 0.557689i \(0.188312\pi\)
−0.970733 + 0.240162i \(0.922799\pi\)
\(762\) 0 0
\(763\) 465.612 + 554.894i 0.610238 + 0.727253i
\(764\) 84.2308 + 897.904i 0.110250 + 1.17527i
\(765\) 0 0
\(766\) −1189.00 + 55.6468i −1.55222 + 0.0726460i
\(767\) −247.142 + 43.5778i −0.322219 + 0.0568160i
\(768\) 0 0
\(769\) 120.247 43.7664i 0.156368 0.0569134i −0.262650 0.964891i \(-0.584596\pi\)
0.419018 + 0.907978i \(0.362374\pi\)
\(770\) −29.0668 + 38.1274i −0.0377491 + 0.0495161i
\(771\) 0 0
\(772\) −797.684 208.389i −1.03327 0.269934i
\(773\) 156.807 271.599i 0.202856 0.351356i −0.746592 0.665283i \(-0.768311\pi\)
0.949447 + 0.313926i \(0.101644\pi\)
\(774\) 0 0
\(775\) −3.40655 + 1.96677i −0.00439555 + 0.00253777i
\(776\) −146.327 131.575i −0.188566 0.169555i
\(777\) 0 0
\(778\) 255.912 + 612.391i 0.328936 + 0.787135i
\(779\) 80.5956 96.0501i 0.103460 0.123299i
\(780\) 0 0
\(781\) −686.484 249.860i −0.878980 0.319923i
\(782\) −58.1863 90.7057i −0.0744071 0.115992i
\(783\) 0 0
\(784\) 886.617 + 1030.12i 1.13089 + 1.31393i
\(785\) −27.1889 9.89596i −0.0346356 0.0126063i
\(786\) 0 0
\(787\) 335.127 399.389i 0.425828 0.507483i −0.509886 0.860242i \(-0.670312\pi\)
0.935714 + 0.352760i \(0.114757\pi\)
\(788\) 414.919 + 286.670i 0.526547 + 0.363795i
\(789\) 0 0
\(790\) 47.8055 + 14.9084i 0.0605132 + 0.0188715i
\(791\) −1308.31 + 755.352i −1.65399 + 0.954934i
\(792\) 0 0
\(793\) 816.627 1414.44i 1.02979 1.78366i
\(794\) −115.873 125.660i −0.145935 0.158262i
\(795\) 0 0
\(796\) −297.145 24.1210i −0.373297 0.0303028i
\(797\) 260.173 94.6953i 0.326441 0.118815i −0.173601 0.984816i \(-0.555540\pi\)
0.500041 + 0.866001i \(0.333318\pi\)
\(798\) 0 0
\(799\) −62.7359 + 11.0620i −0.0785180 + 0.0138448i
\(800\) 580.210 548.635i 0.725262 0.685794i
\(801\) 0 0
\(802\) −299.266 154.598i −0.373149 0.192765i
\(803\) 166.129 + 197.985i 0.206885 + 0.246556i
\(804\) 0 0
\(805\) −13.5678 + 76.9470i −0.0168545 + 0.0955864i
\(806\) 0.800016 6.22748i 0.000992576 0.00772640i
\(807\) 0 0
\(808\) −78.3977 + 370.061i −0.0970268 + 0.457996i
\(809\) −638.629 −0.789405 −0.394702 0.918809i \(-0.629152\pi\)
−0.394702 + 0.918809i \(0.629152\pi\)
\(810\) 0 0
\(811\) 260.263i 0.320916i −0.987043 0.160458i \(-0.948703\pi\)
0.987043 0.160458i \(-0.0512971\pi\)
\(812\) −285.280 281.726i −0.351331 0.346954i
\(813\) 0 0
\(814\) 118.545 922.776i 0.145633 1.13363i
\(815\) −42.8097 7.54850i −0.0525272 0.00926196i
\(816\) 0 0
\(817\) 214.172 179.711i 0.262144 0.219965i
\(818\) −247.203 127.703i −0.302204 0.156116i
\(819\) 0 0
\(820\) −10.1998 14.3742i −0.0124388 0.0175295i
\(821\) 179.659 + 1018.90i 0.218830 + 1.24104i 0.874136 + 0.485681i \(0.161428\pi\)
−0.655307 + 0.755363i \(0.727461\pi\)
\(822\) 0 0
\(823\) −206.443 567.198i −0.250842 0.689183i −0.999652 0.0263979i \(-0.991596\pi\)
0.748809 0.662786i \(-0.230626\pi\)
\(824\) 375.302 199.877i 0.455463 0.242569i
\(825\) 0 0
\(826\) 197.726 + 214.427i 0.239377 + 0.259596i
\(827\) 584.555 + 337.493i 0.706838 + 0.408093i 0.809889 0.586583i \(-0.199527\pi\)
−0.103051 + 0.994676i \(0.532860\pi\)
\(828\) 0 0
\(829\) 109.326 + 189.359i 0.131877 + 0.228418i 0.924400 0.381424i \(-0.124566\pi\)
−0.792523 + 0.609842i \(0.791233\pi\)
\(830\) −46.1318 14.3865i −0.0555805 0.0173331i
\(831\) 0 0
\(832\) 134.943 + 1267.43i 0.162192 + 1.52335i
\(833\) 111.465 + 93.5303i 0.133812 + 0.112281i
\(834\) 0 0
\(835\) −10.9595 + 30.1109i −0.0131251 + 0.0360609i
\(836\) −98.2932 + 214.287i −0.117576 + 0.256324i
\(837\) 0 0
\(838\) 153.103 + 238.670i 0.182701 + 0.284809i
\(839\) 257.800 708.300i 0.307270 0.844219i −0.685916 0.727681i \(-0.740598\pi\)
0.993186 0.116538i \(-0.0371796\pi\)
\(840\) 0 0
\(841\) −586.783 492.369i −0.697721 0.585457i
\(842\) 82.3929 + 197.164i 0.0978538 + 0.234162i
\(843\) 0 0
\(844\) −105.618 + 29.0111i −0.125140 + 0.0343734i
\(845\) 24.4269 + 42.3086i 0.0289075 + 0.0500693i
\(846\) 0 0
\(847\) −279.266 161.234i −0.329711 0.190359i
\(848\) −997.626 + 1219.65i −1.17645 + 1.43827i
\(849\) 0 0
\(850\) 51.8298 67.9860i 0.0609762 0.0799835i
\(851\) −518.577 1424.78i −0.609374 1.67424i
\(852\) 0 0
\(853\) 198.372 + 1125.02i 0.232558 + 1.31890i 0.847696 + 0.530482i \(0.177989\pi\)
−0.615138 + 0.788419i \(0.710900\pi\)
\(854\) −1896.19 + 88.7443i −2.22036 + 0.103916i
\(855\) 0 0
\(856\) −153.681 196.429i −0.179534 0.229473i
\(857\) 226.349 189.929i 0.264117 0.221621i −0.501106 0.865386i \(-0.667073\pi\)
0.765223 + 0.643765i \(0.222629\pi\)
\(858\) 0 0
\(859\) −156.184 27.5395i −0.181821 0.0320600i 0.0819961 0.996633i \(-0.473870\pi\)
−0.263817 + 0.964573i \(0.584982\pi\)
\(860\) −16.8322 35.5138i −0.0195723 0.0412952i
\(861\) 0 0
\(862\) −245.936 1093.12i −0.285308 1.26812i
\(863\) 222.807i 0.258177i 0.991633 + 0.129089i \(0.0412052\pi\)
−0.991633 + 0.129089i \(0.958795\pi\)
\(864\) 0 0
\(865\) 67.0992 0.0775713
\(866\) 744.957 167.604i 0.860228 0.193538i
\(867\) 0 0
\(868\) −6.59426 + 3.12542i −0.00759707 + 0.00360072i
\(869\) 195.506 1108.77i 0.224978 1.27592i
\(870\) 0 0
\(871\) −681.021 811.609i −0.781884 0.931813i
\(872\) 394.352 308.531i 0.452239 0.353820i
\(873\) 0 0
\(874\) 17.9620 + 383.793i 0.0205515 + 0.439122i
\(875\) −122.197 + 21.5465i −0.139653 + 0.0246246i
\(876\) 0 0
\(877\) −443.850 + 161.548i −0.506100 + 0.184205i −0.582436 0.812877i \(-0.697900\pi\)
0.0763355 + 0.997082i \(0.475678\pi\)
\(878\) 768.612 + 585.959i 0.875412 + 0.667379i
\(879\) 0 0
\(880\) 25.6519 + 20.9822i 0.0291499 + 0.0238434i
\(881\) −40.2626 + 69.7369i −0.0457010 + 0.0791565i −0.887971 0.459899i \(-0.847885\pi\)
0.842270 + 0.539056i \(0.181219\pi\)
\(882\) 0 0
\(883\) 820.367 473.639i 0.929068 0.536398i 0.0425516 0.999094i \(-0.486451\pi\)
0.886517 + 0.462696i \(0.153118\pi\)
\(884\) 36.1430 + 131.583i 0.0408857 + 0.148849i
\(885\) 0 0
\(886\) 581.449 242.982i 0.656264 0.274246i
\(887\) −422.053 + 502.984i −0.475821 + 0.567062i −0.949553 0.313608i \(-0.898462\pi\)
0.473731 + 0.880669i \(0.342907\pi\)
\(888\) 0 0
\(889\) 329.516 + 119.934i 0.370659 + 0.134909i
\(890\) 42.9634 27.5604i 0.0482734 0.0309667i
\(891\) 0 0
\(892\) −143.966 66.0368i −0.161396 0.0740323i
\(893\) 213.426 + 77.6806i 0.238999 + 0.0869884i
\(894\) 0 0
\(895\) 3.70454 4.41490i 0.00413915 0.00493285i
\(896\) 1155.21 927.388i 1.28930 1.03503i
\(897\) 0 0
\(898\) −486.254 + 1559.22i −0.541486 + 1.73633i
\(899\) 1.18231 0.682610i 0.00131514 0.000759299i
\(900\) 0 0
\(901\) −84.3460 + 146.092i −0.0936138 + 0.162144i
\(902\) −291.324 + 268.634i −0.322976 + 0.297820i
\(903\) 0 0
\(904\) 490.869 + 921.688i 0.542997 + 1.01957i
\(905\) 58.1010 21.1471i 0.0642001 0.0233669i
\(906\) 0 0
\(907\) 1463.07 257.979i 1.61309 0.284431i 0.706902 0.707312i \(-0.250092\pi\)
0.906185 + 0.422881i \(0.138981\pi\)
\(908\) 1216.08 862.921i 1.33930 0.950354i
\(909\) 0 0
\(910\) 45.4088 87.9010i 0.0498998 0.0965945i
\(911\) 654.039 + 779.454i 0.717936 + 0.855603i 0.994428 0.105413i \(-0.0336166\pi\)
−0.276493 + 0.961016i \(0.589172\pi\)
\(912\) 0 0
\(913\) −188.662 + 1069.95i −0.206639 + 1.17191i
\(914\) 101.862 + 13.0857i 0.111446 + 0.0143170i
\(915\) 0 0
\(916\) 807.965 818.158i 0.882058 0.893186i
\(917\) 2132.96 2.32602
\(918\) 0 0
\(919\) 320.861i 0.349141i −0.984645 0.174571i \(-0.944146\pi\)
0.984645 0.174571i \(-0.0558537\pi\)
\(920\) 52.8363 + 11.1934i 0.0574307 + 0.0121667i
\(921\) 0 0
\(922\) −1180.81 151.693i −1.28071 0.164526i
\(923\) 1484.65 + 261.785i 1.60851 + 0.283624i
\(924\) 0 0
\(925\) 921.408 773.153i 0.996117 0.835841i
\(926\) 396.222 766.995i 0.427886 0.828289i
\(927\) 0 0
\(928\) −201.374 + 190.415i −0.216998 + 0.205189i
\(929\) 57.4894 + 326.039i 0.0618831 + 0.350957i 0.999989 + 0.00460898i \(0.00146709\pi\)
−0.938106 + 0.346348i \(0.887422\pi\)
\(930\) 0 0
\(931\) −177.433 487.492i −0.190583 0.523622i
\(932\) 119.019 1466.18i 0.127703 1.57316i
\(933\) 0 0
\(934\) −1110.66 + 1024.15i −1.18914 + 1.09652i
\(935\) 3.07262 + 1.77398i 0.00328622 + 0.00189730i
\(936\) 0 0
\(937\) −663.749 1149.65i −0.708376 1.22694i −0.965459 0.260554i \(-0.916095\pi\)
0.257083 0.966389i \(-0.417239\pi\)
\(938\) −366.604 + 1175.55i −0.390836 + 1.25326i
\(939\) 0 0
\(940\) 18.1481 26.2671i 0.0193065 0.0279438i
\(941\) −292.985 245.844i −0.311355 0.261258i 0.473697 0.880688i \(-0.342919\pi\)
−0.785052 + 0.619430i \(0.787364\pi\)
\(942\) 0 0
\(943\) −220.881 + 606.867i −0.234233 + 0.643549i
\(944\) 152.810 131.522i 0.161875 0.139324i
\(945\) 0 0
\(946\) −743.738 + 477.097i −0.786192 + 0.504331i
\(947\) −108.937 + 299.302i −0.115034 + 0.316053i −0.983827 0.179123i \(-0.942674\pi\)
0.868793 + 0.495176i \(0.164896\pi\)
\(948\) 0 0
\(949\) −408.565 342.827i −0.430522 0.361251i
\(950\) −281.227 + 117.522i −0.296029 + 0.123707i
\(951\) 0 0
\(952\) 106.043 117.933i 0.111390 0.123879i
\(953\) −61.8869 107.191i −0.0649391 0.112478i 0.831728 0.555183i \(-0.187352\pi\)
−0.896667 + 0.442706i \(0.854019\pi\)
\(954\) 0 0
\(955\) −41.9060 24.1944i −0.0438806 0.0253345i
\(956\) −179.909 + 688.668i −0.188189 + 0.720364i
\(957\) 0 0
\(958\) 938.677 + 715.610i 0.979830 + 0.746983i
\(959\) 99.4332 + 273.190i 0.103684 + 0.284870i
\(960\) 0 0
\(961\) 166.872 + 946.376i 0.173644 + 0.984782i
\(962\) 89.7560 + 1917.81i 0.0933015 + 1.99356i
\(963\) 0 0
\(964\) 1388.43 130.246i 1.44028 0.135110i
\(965\) 33.8871 28.4346i 0.0351161 0.0294659i
\(966\) 0 0
\(967\) 59.4973 + 10.4910i 0.0615277 + 0.0108490i 0.204327 0.978903i \(-0.434499\pi\)
−0.142800 + 0.989752i \(0.545610\pi\)
\(968\) −117.992 + 189.111i −0.121892 + 0.195362i
\(969\) 0 0
\(970\) 10.3010 2.31757i 0.0106196 0.00238924i
\(971\) 670.687i 0.690718i 0.938471 + 0.345359i \(0.112243\pi\)
−0.938471 + 0.345359i \(0.887757\pi\)
\(972\) 0 0
\(973\) 101.027 0.103830
\(974\) −208.166 925.244i −0.213723 0.949943i
\(975\) 0 0
\(976\) 16.4487 + 1312.04i 0.0168532 + 1.34431i
\(977\) −123.095 + 698.106i −0.125993 + 0.714540i 0.854721 + 0.519088i \(0.173728\pi\)
−0.980713 + 0.195452i \(0.937383\pi\)
\(978\) 0 0
\(979\) −737.676 879.128i −0.753500 0.897986i
\(980\) −72.6060 + 6.81104i −0.0740878 + 0.00695004i
\(981\) 0 0
\(982\) −568.193 + 26.5922i −0.578608 + 0.0270796i
\(983\) −668.074 + 117.799i −0.679628 + 0.119837i −0.502797 0.864405i \(-0.667696\pi\)
−0.176831 + 0.984241i \(0.556585\pi\)
\(984\) 0 0
\(985\) −25.4275 + 9.25486i −0.0258147 + 0.00939579i
\(986\) −17.9886 + 23.5959i −0.0182440 + 0.0239310i
\(987\) 0 0
\(988\) 122.970 470.711i 0.124463 0.476429i
\(989\) −720.015 + 1247.10i −0.728023 + 1.26097i
\(990\) 0 0
\(991\) 1062.37 613.362i 1.07202 0.618932i 0.143289 0.989681i \(-0.454232\pi\)
0.928733 + 0.370749i \(0.120899\pi\)
\(992\) 2.00313 + 4.62945i 0.00201929 + 0.00466678i
\(993\) 0 0
\(994\) −675.598 1616.69i −0.679676 1.62645i
\(995\) 10.2819 12.2535i 0.0103336 0.0123151i
\(996\) 0 0
\(997\) 1118.16 + 406.977i 1.12152 + 0.408202i 0.835209 0.549933i \(-0.185347\pi\)
0.286316 + 0.958135i \(0.407569\pi\)
\(998\) −405.642 632.349i −0.406455 0.633616i
\(999\) 0 0
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 324.3.j.a.307.33 204
3.2 odd 2 108.3.j.a.31.2 yes 204
4.3 odd 2 inner 324.3.j.a.307.26 204
12.11 even 2 108.3.j.a.31.9 yes 204
27.7 even 9 inner 324.3.j.a.19.26 204
27.20 odd 18 108.3.j.a.7.9 yes 204
108.7 odd 18 inner 324.3.j.a.19.33 204
108.47 even 18 108.3.j.a.7.2 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.j.a.7.2 204 108.47 even 18
108.3.j.a.7.9 yes 204 27.20 odd 18
108.3.j.a.31.2 yes 204 3.2 odd 2
108.3.j.a.31.9 yes 204 12.11 even 2
324.3.j.a.19.26 204 27.7 even 9 inner
324.3.j.a.19.33 204 108.7 odd 18 inner
324.3.j.a.307.26 204 4.3 odd 2 inner
324.3.j.a.307.33 204 1.1 even 1 trivial