Properties

Label 504.2.ch.b.269.11
Level $504$
Weight $2$
Character 504.269
Analytic conductor $4.024$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(269,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.269");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.ch (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.11
Character \(\chi\) \(=\) 504.269
Dual form 504.2.ch.b.341.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.447766 - 1.34146i) q^{2} +(-1.59901 + 1.20132i) q^{4} +(-0.331990 + 0.191675i) q^{5} +(-2.03027 + 1.69647i) q^{7} +(2.32750 + 1.60709i) q^{8} +O(q^{10})\) \(q+(-0.447766 - 1.34146i) q^{2} +(-1.59901 + 1.20132i) q^{4} +(-0.331990 + 0.191675i) q^{5} +(-2.03027 + 1.69647i) q^{7} +(2.32750 + 1.60709i) q^{8} +(0.405777 + 0.359525i) q^{10} +(2.28107 - 3.95093i) q^{11} +2.84195 q^{13} +(3.18483 + 1.96389i) q^{14} +(1.11367 - 3.84184i) q^{16} +(2.46500 - 4.26950i) q^{17} +(-4.18535 - 7.24924i) q^{19} +(0.300594 - 0.705316i) q^{20} +(-6.32139 - 1.29086i) q^{22} +(5.41792 - 3.12804i) q^{23} +(-2.42652 + 4.20286i) q^{25} +(-1.27253 - 3.81236i) q^{26} +(1.20841 - 5.15167i) q^{28} -0.292746 q^{29} +(4.93966 + 2.85191i) q^{31} +(-5.65233 + 0.226308i) q^{32} +(-6.83109 - 1.39495i) q^{34} +(0.348858 - 0.952363i) q^{35} +(6.12469 - 3.53609i) q^{37} +(-7.85048 + 8.86043i) q^{38} +(-1.08075 - 0.0874167i) q^{40} +4.92280 q^{41} +4.35631i q^{43} +(1.09887 + 9.05788i) q^{44} +(-6.62209 - 5.86728i) q^{46} +(-4.73214 - 8.19631i) q^{47} +(1.24396 - 6.88858i) q^{49} +(6.72447 + 1.37317i) q^{50} +(-4.54431 + 3.41409i) q^{52} +(-2.33050 + 4.03655i) q^{53} +1.74890i q^{55} +(-7.45183 + 0.685712i) q^{56} +(0.131082 + 0.392706i) q^{58} +(-5.72506 - 3.30537i) q^{59} +(1.40098 + 2.42656i) q^{61} +(1.61390 - 7.90332i) q^{62} +(2.83450 + 7.48102i) q^{64} +(-0.943501 + 0.544730i) q^{65} +(-7.81560 - 4.51234i) q^{67} +(1.18747 + 9.78822i) q^{68} +(-1.43376 - 0.0415413i) q^{70} +4.37059i q^{71} +(10.9929 + 6.34673i) q^{73} +(-7.48595 - 6.63267i) q^{74} +(15.4011 + 6.56367i) q^{76} +(2.07147 + 11.8912i) q^{77} +(-0.0352186 - 0.0610004i) q^{79} +(0.366656 + 1.48892i) q^{80} +(-2.20426 - 6.60372i) q^{82} -6.48166i q^{83} +1.88991i q^{85} +(5.84380 - 1.95061i) q^{86} +(11.6587 - 5.52990i) q^{88} +(-1.63404 - 2.83024i) q^{89} +(-5.76992 + 4.82130i) q^{91} +(-4.90555 + 11.5104i) q^{92} +(-8.87609 + 10.0180i) q^{94} +(2.77899 + 1.60445i) q^{95} +0.349243i q^{97} +(-9.79774 + 1.41576i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.447766 1.34146i −0.316619 0.948553i
\(3\) 0 0
\(4\) −1.59901 + 1.20132i −0.799505 + 0.600659i
\(5\) −0.331990 + 0.191675i −0.148471 + 0.0857195i −0.572395 0.819978i \(-0.693986\pi\)
0.423924 + 0.905698i \(0.360652\pi\)
\(6\) 0 0
\(7\) −2.03027 + 1.69647i −0.767368 + 0.641206i
\(8\) 2.32750 + 1.60709i 0.822895 + 0.568193i
\(9\) 0 0
\(10\) 0.405777 + 0.359525i 0.128318 + 0.113692i
\(11\) 2.28107 3.95093i 0.687769 1.19125i −0.284789 0.958590i \(-0.591923\pi\)
0.972558 0.232661i \(-0.0747432\pi\)
\(12\) 0 0
\(13\) 2.84195 0.788216 0.394108 0.919064i \(-0.371054\pi\)
0.394108 + 0.919064i \(0.371054\pi\)
\(14\) 3.18483 + 1.96389i 0.851181 + 0.524872i
\(15\) 0 0
\(16\) 1.11367 3.84184i 0.278417 0.960460i
\(17\) 2.46500 4.26950i 0.597850 1.03551i −0.395288 0.918557i \(-0.629355\pi\)
0.993138 0.116949i \(-0.0373113\pi\)
\(18\) 0 0
\(19\) −4.18535 7.24924i −0.960185 1.66309i −0.722030 0.691861i \(-0.756791\pi\)
−0.238154 0.971227i \(-0.576542\pi\)
\(20\) 0.300594 0.705316i 0.0672148 0.157713i
\(21\) 0 0
\(22\) −6.32139 1.29086i −1.34773 0.275213i
\(23\) 5.41792 3.12804i 1.12971 0.652241i 0.185852 0.982578i \(-0.440496\pi\)
0.943863 + 0.330337i \(0.107162\pi\)
\(24\) 0 0
\(25\) −2.42652 + 4.20286i −0.485304 + 0.840572i
\(26\) −1.27253 3.81236i −0.249564 0.747665i
\(27\) 0 0
\(28\) 1.20841 5.15167i 0.228369 0.973575i
\(29\) −0.292746 −0.0543616 −0.0271808 0.999631i \(-0.508653\pi\)
−0.0271808 + 0.999631i \(0.508653\pi\)
\(30\) 0 0
\(31\) 4.93966 + 2.85191i 0.887188 + 0.512218i 0.873022 0.487681i \(-0.162157\pi\)
0.0141665 + 0.999900i \(0.495490\pi\)
\(32\) −5.65233 + 0.226308i −0.999199 + 0.0400059i
\(33\) 0 0
\(34\) −6.83109 1.39495i −1.17152 0.239232i
\(35\) 0.348858 0.952363i 0.0589677 0.160979i
\(36\) 0 0
\(37\) 6.12469 3.53609i 1.00689 0.581330i 0.0966129 0.995322i \(-0.469199\pi\)
0.910281 + 0.413992i \(0.135866\pi\)
\(38\) −7.85048 + 8.86043i −1.27352 + 1.43735i
\(39\) 0 0
\(40\) −1.08075 0.0874167i −0.170881 0.0138218i
\(41\) 4.92280 0.768812 0.384406 0.923164i \(-0.374406\pi\)
0.384406 + 0.923164i \(0.374406\pi\)
\(42\) 0 0
\(43\) 4.35631i 0.664332i 0.943221 + 0.332166i \(0.107779\pi\)
−0.943221 + 0.332166i \(0.892221\pi\)
\(44\) 1.09887 + 9.05788i 0.165661 + 1.36553i
\(45\) 0 0
\(46\) −6.62209 5.86728i −0.976374 0.865083i
\(47\) −4.73214 8.19631i −0.690253 1.19555i −0.971755 0.235993i \(-0.924166\pi\)
0.281501 0.959561i \(-0.409168\pi\)
\(48\) 0 0
\(49\) 1.24396 6.88858i 0.177709 0.984083i
\(50\) 6.72447 + 1.37317i 0.950983 + 0.194196i
\(51\) 0 0
\(52\) −4.54431 + 3.41409i −0.630183 + 0.473449i
\(53\) −2.33050 + 4.03655i −0.320119 + 0.554462i −0.980512 0.196458i \(-0.937056\pi\)
0.660393 + 0.750920i \(0.270390\pi\)
\(54\) 0 0
\(55\) 1.74890i 0.235821i
\(56\) −7.45183 + 0.685712i −0.995793 + 0.0916321i
\(57\) 0 0
\(58\) 0.131082 + 0.392706i 0.0172119 + 0.0515649i
\(59\) −5.72506 3.30537i −0.745340 0.430322i 0.0786677 0.996901i \(-0.474933\pi\)
−0.824008 + 0.566579i \(0.808267\pi\)
\(60\) 0 0
\(61\) 1.40098 + 2.42656i 0.179376 + 0.310689i 0.941667 0.336546i \(-0.109259\pi\)
−0.762291 + 0.647235i \(0.775925\pi\)
\(62\) 1.61390 7.90332i 0.204966 1.00372i
\(63\) 0 0
\(64\) 2.83450 + 7.48102i 0.354313 + 0.935127i
\(65\) −0.943501 + 0.544730i −0.117027 + 0.0675655i
\(66\) 0 0
\(67\) −7.81560 4.51234i −0.954827 0.551270i −0.0602503 0.998183i \(-0.519190\pi\)
−0.894577 + 0.446913i \(0.852523\pi\)
\(68\) 1.18747 + 9.78822i 0.144002 + 1.18700i
\(69\) 0 0
\(70\) −1.43376 0.0415413i −0.171367 0.00496514i
\(71\) 4.37059i 0.518694i 0.965784 + 0.259347i \(0.0835073\pi\)
−0.965784 + 0.259347i \(0.916493\pi\)
\(72\) 0 0
\(73\) 10.9929 + 6.34673i 1.28662 + 0.742829i 0.978049 0.208374i \(-0.0668171\pi\)
0.308568 + 0.951202i \(0.400150\pi\)
\(74\) −7.48595 6.63267i −0.870224 0.771032i
\(75\) 0 0
\(76\) 15.4011 + 6.56367i 1.76662 + 0.752905i
\(77\) 2.07147 + 11.8912i 0.236066 + 1.35513i
\(78\) 0 0
\(79\) −0.0352186 0.0610004i −0.00396240 0.00686308i 0.864037 0.503428i \(-0.167928\pi\)
−0.868000 + 0.496565i \(0.834595\pi\)
\(80\) 0.366656 + 1.48892i 0.0409934 + 0.166466i
\(81\) 0 0
\(82\) −2.20426 6.60372i −0.243420 0.729259i
\(83\) 6.48166i 0.711454i −0.934590 0.355727i \(-0.884233\pi\)
0.934590 0.355727i \(-0.115767\pi\)
\(84\) 0 0
\(85\) 1.88991i 0.204990i
\(86\) 5.84380 1.95061i 0.630154 0.210340i
\(87\) 0 0
\(88\) 11.6587 5.52990i 1.24282 0.589489i
\(89\) −1.63404 2.83024i −0.173208 0.300004i 0.766332 0.642445i \(-0.222080\pi\)
−0.939540 + 0.342441i \(0.888746\pi\)
\(90\) 0 0
\(91\) −5.76992 + 4.82130i −0.604852 + 0.505409i
\(92\) −4.90555 + 11.5104i −0.511438 + 1.20004i
\(93\) 0 0
\(94\) −8.87609 + 10.0180i −0.915499 + 1.03328i
\(95\) 2.77899 + 1.60445i 0.285118 + 0.164613i
\(96\) 0 0
\(97\) 0.349243i 0.0354602i 0.999843 + 0.0177301i \(0.00564396\pi\)
−0.999843 + 0.0177301i \(0.994356\pi\)
\(98\) −9.79774 + 1.41576i −0.989721 + 0.143013i
\(99\) 0 0
\(100\) −1.16894 9.63544i −0.116894 0.963544i
\(101\) −13.3130 7.68628i −1.32470 0.764814i −0.340222 0.940345i \(-0.610502\pi\)
−0.984474 + 0.175531i \(0.943836\pi\)
\(102\) 0 0
\(103\) 2.06085 1.18983i 0.203062 0.117238i −0.395021 0.918672i \(-0.629263\pi\)
0.598083 + 0.801434i \(0.295929\pi\)
\(104\) 6.61464 + 4.56728i 0.648619 + 0.447859i
\(105\) 0 0
\(106\) 6.45837 + 1.31884i 0.627292 + 0.128097i
\(107\) −0.412090 0.713762i −0.0398383 0.0690019i 0.845419 0.534104i \(-0.179351\pi\)
−0.885257 + 0.465102i \(0.846018\pi\)
\(108\) 0 0
\(109\) 14.1259 + 8.15558i 1.35301 + 0.781163i 0.988670 0.150102i \(-0.0479603\pi\)
0.364343 + 0.931265i \(0.381294\pi\)
\(110\) 2.34607 0.783096i 0.223689 0.0746653i
\(111\) 0 0
\(112\) 4.25653 + 9.68927i 0.402204 + 0.915550i
\(113\) 3.02323i 0.284401i −0.989838 0.142201i \(-0.954582\pi\)
0.989838 0.142201i \(-0.0454178\pi\)
\(114\) 0 0
\(115\) −1.19913 + 2.07696i −0.111820 + 0.193677i
\(116\) 0.468104 0.351681i 0.0434624 0.0326528i
\(117\) 0 0
\(118\) −1.87052 + 9.15996i −0.172195 + 0.843242i
\(119\) 2.23849 + 12.8500i 0.205202 + 1.17796i
\(120\) 0 0
\(121\) −4.90658 8.49845i −0.446053 0.772586i
\(122\) 2.62782 2.96588i 0.237911 0.268518i
\(123\) 0 0
\(124\) −11.3246 + 1.37386i −1.01698 + 0.123376i
\(125\) 3.77716i 0.337839i
\(126\) 0 0
\(127\) 2.89959 0.257297 0.128649 0.991690i \(-0.458936\pi\)
0.128649 + 0.991690i \(0.458936\pi\)
\(128\) 8.76626 7.15211i 0.774835 0.632163i
\(129\) 0 0
\(130\) 1.15320 + 1.02175i 0.101142 + 0.0896137i
\(131\) 10.5535 6.09304i 0.922059 0.532351i 0.0377678 0.999287i \(-0.487975\pi\)
0.884291 + 0.466935i \(0.154642\pi\)
\(132\) 0 0
\(133\) 20.7955 + 7.61755i 1.80320 + 0.660525i
\(134\) −2.55354 + 12.5048i −0.220593 + 1.08025i
\(135\) 0 0
\(136\) 12.5988 5.97578i 1.08034 0.512419i
\(137\) 15.9155 + 9.18879i 1.35975 + 0.785051i 0.989590 0.143917i \(-0.0459699\pi\)
0.370159 + 0.928968i \(0.379303\pi\)
\(138\) 0 0
\(139\) −6.40327 −0.543118 −0.271559 0.962422i \(-0.587539\pi\)
−0.271559 + 0.962422i \(0.587539\pi\)
\(140\) 0.586264 + 1.94193i 0.0495483 + 0.164123i
\(141\) 0 0
\(142\) 5.86296 1.95700i 0.492008 0.164228i
\(143\) 6.48270 11.2284i 0.542111 0.938963i
\(144\) 0 0
\(145\) 0.0971889 0.0561120i 0.00807110 0.00465985i
\(146\) 3.59163 17.5883i 0.297245 1.45562i
\(147\) 0 0
\(148\) −5.54548 + 13.0120i −0.455835 + 1.06958i
\(149\) 9.21714 + 15.9646i 0.755098 + 1.30787i 0.945326 + 0.326128i \(0.105744\pi\)
−0.190228 + 0.981740i \(0.560923\pi\)
\(150\) 0 0
\(151\) −7.38424 + 12.7899i −0.600921 + 1.04083i 0.391761 + 0.920067i \(0.371866\pi\)
−0.992682 + 0.120758i \(0.961467\pi\)
\(152\) 1.90880 23.5988i 0.154824 1.91412i
\(153\) 0 0
\(154\) 15.0240 8.10327i 1.21067 0.652980i
\(155\) −2.18656 −0.175628
\(156\) 0 0
\(157\) −3.02939 + 5.24706i −0.241772 + 0.418761i −0.961219 0.275786i \(-0.911062\pi\)
0.719447 + 0.694547i \(0.244395\pi\)
\(158\) −0.0660597 + 0.0745582i −0.00525543 + 0.00593153i
\(159\) 0 0
\(160\) 1.83314 1.15854i 0.144922 0.0915906i
\(161\) −5.69319 + 15.5421i −0.448686 + 1.22489i
\(162\) 0 0
\(163\) 3.88592 2.24354i 0.304369 0.175727i −0.340035 0.940413i \(-0.610439\pi\)
0.644404 + 0.764685i \(0.277106\pi\)
\(164\) −7.87161 + 5.91385i −0.614670 + 0.461794i
\(165\) 0 0
\(166\) −8.69486 + 2.90227i −0.674852 + 0.225260i
\(167\) −15.9351 −1.23309 −0.616546 0.787319i \(-0.711468\pi\)
−0.616546 + 0.787319i \(0.711468\pi\)
\(168\) 0 0
\(169\) −4.92330 −0.378715
\(170\) 2.53523 0.846238i 0.194443 0.0649035i
\(171\) 0 0
\(172\) −5.23332 6.96579i −0.399037 0.531137i
\(173\) −16.5050 + 9.52916i −1.25485 + 0.724488i −0.972069 0.234696i \(-0.924591\pi\)
−0.282782 + 0.959184i \(0.591257\pi\)
\(174\) 0 0
\(175\) −2.20355 12.6494i −0.166573 0.956208i
\(176\) −12.6385 13.1636i −0.952662 0.992240i
\(177\) 0 0
\(178\) −3.06497 + 3.45927i −0.229729 + 0.259284i
\(179\) 1.74852 3.02853i 0.130691 0.226363i −0.793252 0.608893i \(-0.791614\pi\)
0.923943 + 0.382530i \(0.124947\pi\)
\(180\) 0 0
\(181\) −21.3086 −1.58386 −0.791929 0.610613i \(-0.790923\pi\)
−0.791929 + 0.610613i \(0.790923\pi\)
\(182\) 9.05114 + 5.58128i 0.670915 + 0.413712i
\(183\) 0 0
\(184\) 17.6373 + 1.42660i 1.30024 + 0.105170i
\(185\) −1.35556 + 2.34790i −0.0996627 + 0.172621i
\(186\) 0 0
\(187\) −11.2457 19.4781i −0.822365 1.42438i
\(188\) 17.4131 + 7.42118i 1.26998 + 0.541245i
\(189\) 0 0
\(190\) 0.907962 4.44631i 0.0658705 0.322569i
\(191\) −17.2191 + 9.94147i −1.24593 + 0.719340i −0.970296 0.241922i \(-0.922222\pi\)
−0.275637 + 0.961262i \(0.588889\pi\)
\(192\) 0 0
\(193\) 5.21260 9.02849i 0.375211 0.649885i −0.615147 0.788412i \(-0.710903\pi\)
0.990359 + 0.138527i \(0.0442368\pi\)
\(194\) 0.468494 0.156379i 0.0336359 0.0112274i
\(195\) 0 0
\(196\) 6.28627 + 12.5093i 0.449019 + 0.893522i
\(197\) 16.0387 1.14271 0.571355 0.820703i \(-0.306418\pi\)
0.571355 + 0.820703i \(0.306418\pi\)
\(198\) 0 0
\(199\) 2.00128 + 1.15544i 0.141867 + 0.0819069i 0.569253 0.822162i \(-0.307232\pi\)
−0.427387 + 0.904069i \(0.640566\pi\)
\(200\) −12.4021 + 5.88250i −0.876962 + 0.415956i
\(201\) 0 0
\(202\) −4.34969 + 21.3005i −0.306043 + 1.49870i
\(203\) 0.594353 0.496636i 0.0417154 0.0348570i
\(204\) 0 0
\(205\) −1.63432 + 0.943576i −0.114146 + 0.0659022i
\(206\) −2.51889 2.23178i −0.175500 0.155495i
\(207\) 0 0
\(208\) 3.16500 10.9183i 0.219453 0.757050i
\(209\) −38.1883 −2.64154
\(210\) 0 0
\(211\) 12.7274i 0.876193i 0.898928 + 0.438096i \(0.144347\pi\)
−0.898928 + 0.438096i \(0.855653\pi\)
\(212\) −1.12268 9.25415i −0.0771060 0.635578i
\(213\) 0 0
\(214\) −0.772960 + 0.872400i −0.0528384 + 0.0596360i
\(215\) −0.834995 1.44625i −0.0569462 0.0986337i
\(216\) 0 0
\(217\) −14.8670 + 2.58985i −1.00924 + 0.175811i
\(218\) 4.61526 22.6010i 0.312585 1.53074i
\(219\) 0 0
\(220\) −2.10098 2.79650i −0.141648 0.188540i
\(221\) 7.00541 12.1337i 0.471235 0.816202i
\(222\) 0 0
\(223\) 11.4933i 0.769649i −0.922990 0.384824i \(-0.874262\pi\)
0.922990 0.384824i \(-0.125738\pi\)
\(224\) 11.0918 10.0485i 0.741102 0.671392i
\(225\) 0 0
\(226\) −4.05553 + 1.35370i −0.269770 + 0.0900468i
\(227\) 1.51766 + 0.876221i 0.100731 + 0.0581568i 0.549519 0.835481i \(-0.314811\pi\)
−0.448788 + 0.893638i \(0.648144\pi\)
\(228\) 0 0
\(229\) −2.91170 5.04322i −0.192411 0.333265i 0.753638 0.657290i \(-0.228297\pi\)
−0.946049 + 0.324025i \(0.894964\pi\)
\(230\) 3.32308 + 0.678591i 0.219117 + 0.0447450i
\(231\) 0 0
\(232\) −0.681367 0.470470i −0.0447339 0.0308879i
\(233\) 7.44335 4.29742i 0.487630 0.281533i −0.235961 0.971763i \(-0.575824\pi\)
0.723591 + 0.690229i \(0.242490\pi\)
\(234\) 0 0
\(235\) 3.14205 + 1.81406i 0.204965 + 0.118336i
\(236\) 13.1252 1.59231i 0.854380 0.103650i
\(237\) 0 0
\(238\) 16.2354 8.75664i 1.05239 0.567609i
\(239\) 2.17800i 0.140883i 0.997516 + 0.0704417i \(0.0224409\pi\)
−0.997516 + 0.0704417i \(0.977559\pi\)
\(240\) 0 0
\(241\) −5.08185 2.93401i −0.327351 0.188996i 0.327314 0.944916i \(-0.393857\pi\)
−0.654664 + 0.755920i \(0.727190\pi\)
\(242\) −9.20330 + 10.3873i −0.591610 + 0.667720i
\(243\) 0 0
\(244\) −5.15524 2.19708i −0.330031 0.140654i
\(245\) 0.907384 + 2.52538i 0.0579706 + 0.161340i
\(246\) 0 0
\(247\) −11.8946 20.6020i −0.756833 1.31087i
\(248\) 6.91376 + 14.5763i 0.439024 + 0.925596i
\(249\) 0 0
\(250\) −5.06689 + 1.69128i −0.320458 + 0.106966i
\(251\) 29.5645i 1.86609i 0.359755 + 0.933047i \(0.382860\pi\)
−0.359755 + 0.933047i \(0.617140\pi\)
\(252\) 0 0
\(253\) 28.5411i 1.79437i
\(254\) −1.29834 3.88967i −0.0814650 0.244060i
\(255\) 0 0
\(256\) −13.5195 8.55708i −0.844967 0.534818i
\(257\) −10.4608 18.1187i −0.652530 1.13021i −0.982507 0.186226i \(-0.940374\pi\)
0.329977 0.943989i \(-0.392959\pi\)
\(258\) 0 0
\(259\) −6.43587 + 17.5696i −0.399906 + 1.09172i
\(260\) 0.854273 2.00447i 0.0529798 0.124312i
\(261\) 0 0
\(262\) −12.8990 11.4287i −0.796904 0.706070i
\(263\) 10.3508 + 5.97604i 0.638258 + 0.368498i 0.783943 0.620833i \(-0.213205\pi\)
−0.145685 + 0.989331i \(0.546539\pi\)
\(264\) 0 0
\(265\) 1.78679i 0.109762i
\(266\) 0.907084 31.3071i 0.0556169 1.91956i
\(267\) 0 0
\(268\) 17.9180 2.17374i 1.09451 0.132783i
\(269\) 14.0600 + 8.11753i 0.857251 + 0.494934i 0.863091 0.505049i \(-0.168525\pi\)
−0.00583949 + 0.999983i \(0.501859\pi\)
\(270\) 0 0
\(271\) −22.0735 + 12.7441i −1.34087 + 0.774151i −0.986935 0.161119i \(-0.948490\pi\)
−0.353934 + 0.935270i \(0.615156\pi\)
\(272\) −13.6575 14.2249i −0.828110 0.862514i
\(273\) 0 0
\(274\) 5.19996 25.4643i 0.314141 1.53836i
\(275\) 11.0701 + 19.1741i 0.667555 + 1.15624i
\(276\) 0 0
\(277\) −9.51680 5.49453i −0.571809 0.330134i 0.186062 0.982538i \(-0.440427\pi\)
−0.757872 + 0.652404i \(0.773761\pi\)
\(278\) 2.86717 + 8.58970i 0.171961 + 0.515176i
\(279\) 0 0
\(280\) 2.34250 1.65598i 0.139991 0.0989635i
\(281\) 6.71345i 0.400491i 0.979746 + 0.200245i \(0.0641740\pi\)
−0.979746 + 0.200245i \(0.935826\pi\)
\(282\) 0 0
\(283\) 7.07673 12.2573i 0.420668 0.728619i −0.575337 0.817917i \(-0.695129\pi\)
0.996005 + 0.0892979i \(0.0284623\pi\)
\(284\) −5.25047 6.98862i −0.311558 0.414698i
\(285\) 0 0
\(286\) −17.9651 3.66858i −1.06230 0.216927i
\(287\) −9.99460 + 8.35140i −0.589962 + 0.492967i
\(288\) 0 0
\(289\) −3.65242 6.32618i −0.214848 0.372128i
\(290\) −0.118790 0.105250i −0.00697557 0.00618047i
\(291\) 0 0
\(292\) −25.2021 + 3.05743i −1.47484 + 0.178923i
\(293\) 7.73971i 0.452159i −0.974109 0.226079i \(-0.927409\pi\)
0.974109 0.226079i \(-0.0725909\pi\)
\(294\) 0 0
\(295\) 2.53422 0.147548
\(296\) 19.9381 + 1.61270i 1.15888 + 0.0937363i
\(297\) 0 0
\(298\) 17.2886 19.5128i 1.00150 1.13035i
\(299\) 15.3975 8.88974i 0.890459 0.514107i
\(300\) 0 0
\(301\) −7.39037 8.84447i −0.425974 0.509787i
\(302\) 20.4635 + 4.17876i 1.17754 + 0.240460i
\(303\) 0 0
\(304\) −32.5115 + 8.00619i −1.86466 + 0.459186i
\(305\) −0.930220 0.537063i −0.0532643 0.0307521i
\(306\) 0 0
\(307\) 24.8919 1.42066 0.710329 0.703870i \(-0.248546\pi\)
0.710329 + 0.703870i \(0.248546\pi\)
\(308\) −17.5974 16.5257i −1.00271 0.941639i
\(309\) 0 0
\(310\) 0.979066 + 2.93317i 0.0556072 + 0.166593i
\(311\) 4.24421 7.35119i 0.240667 0.416848i −0.720237 0.693728i \(-0.755967\pi\)
0.960904 + 0.276880i \(0.0893005\pi\)
\(312\) 0 0
\(313\) 6.06343 3.50072i 0.342725 0.197873i −0.318751 0.947838i \(-0.603263\pi\)
0.661477 + 0.749966i \(0.269930\pi\)
\(314\) 8.39517 + 1.71434i 0.473767 + 0.0967458i
\(315\) 0 0
\(316\) 0.129596 + 0.0552316i 0.00729034 + 0.00310702i
\(317\) −12.5953 21.8157i −0.707422 1.22529i −0.965810 0.259250i \(-0.916525\pi\)
0.258388 0.966041i \(-0.416809\pi\)
\(318\) 0 0
\(319\) −0.667775 + 1.15662i −0.0373882 + 0.0647583i
\(320\) −2.37495 1.94032i −0.132764 0.108467i
\(321\) 0 0
\(322\) 23.3983 + 0.677935i 1.30394 + 0.0377798i
\(323\) −41.2675 −2.29618
\(324\) 0 0
\(325\) −6.89606 + 11.9443i −0.382525 + 0.662552i
\(326\) −4.74959 4.20821i −0.263056 0.233071i
\(327\) 0 0
\(328\) 11.4578 + 7.91140i 0.632652 + 0.436834i
\(329\) 23.5123 + 8.61274i 1.29628 + 0.474836i
\(330\) 0 0
\(331\) 17.8109 10.2831i 0.978974 0.565211i 0.0770138 0.997030i \(-0.475461\pi\)
0.901960 + 0.431819i \(0.142128\pi\)
\(332\) 7.78653 + 10.3642i 0.427341 + 0.568811i
\(333\) 0 0
\(334\) 7.13518 + 21.3762i 0.390420 + 1.16965i
\(335\) 3.45960 0.189018
\(336\) 0 0
\(337\) 9.77045 0.532230 0.266115 0.963941i \(-0.414260\pi\)
0.266115 + 0.963941i \(0.414260\pi\)
\(338\) 2.20449 + 6.60439i 0.119908 + 0.359232i
\(339\) 0 0
\(340\) −2.27038 3.02199i −0.123129 0.163890i
\(341\) 22.5354 13.0108i 1.22036 0.704576i
\(342\) 0 0
\(343\) 9.16072 + 16.0960i 0.494632 + 0.869102i
\(344\) −7.00100 + 10.1393i −0.377469 + 0.546675i
\(345\) 0 0
\(346\) 20.1733 + 17.8739i 1.08452 + 0.960906i
\(347\) 9.63809 16.6937i 0.517400 0.896163i −0.482396 0.875953i \(-0.660233\pi\)
0.999796 0.0202097i \(-0.00643338\pi\)
\(348\) 0 0
\(349\) −30.5766 −1.63673 −0.818363 0.574702i \(-0.805118\pi\)
−0.818363 + 0.574702i \(0.805118\pi\)
\(350\) −15.9820 + 8.61996i −0.854274 + 0.460757i
\(351\) 0 0
\(352\) −11.9992 + 22.8482i −0.639562 + 1.21781i
\(353\) 4.59814 7.96421i 0.244734 0.423892i −0.717323 0.696741i \(-0.754633\pi\)
0.962057 + 0.272849i \(0.0879659\pi\)
\(354\) 0 0
\(355\) −0.837731 1.45099i −0.0444622 0.0770107i
\(356\) 6.01286 + 2.56258i 0.318681 + 0.135816i
\(357\) 0 0
\(358\) −4.84557 0.989492i −0.256096 0.0522963i
\(359\) −0.890104 + 0.513902i −0.0469779 + 0.0271227i −0.523305 0.852145i \(-0.675301\pi\)
0.476327 + 0.879268i \(0.341968\pi\)
\(360\) 0 0
\(361\) −25.5343 + 44.2267i −1.34391 + 2.32772i
\(362\) 9.54128 + 28.5846i 0.501479 + 1.50237i
\(363\) 0 0
\(364\) 3.43426 14.6408i 0.180004 0.767387i
\(365\) −4.86603 −0.254700
\(366\) 0 0
\(367\) 22.9698 + 13.2616i 1.19902 + 0.692252i 0.960336 0.278846i \(-0.0899520\pi\)
0.238680 + 0.971098i \(0.423285\pi\)
\(368\) −5.98365 24.2984i −0.311919 1.26664i
\(369\) 0 0
\(370\) 3.75658 + 0.767114i 0.195295 + 0.0398804i
\(371\) −2.11635 12.1489i −0.109876 0.630739i
\(372\) 0 0
\(373\) −4.48008 + 2.58657i −0.231970 + 0.133928i −0.611480 0.791260i \(-0.709426\pi\)
0.379511 + 0.925187i \(0.376092\pi\)
\(374\) −21.0936 + 23.8072i −1.09072 + 1.23104i
\(375\) 0 0
\(376\) 2.15818 26.6819i 0.111300 1.37601i
\(377\) −0.831971 −0.0428487
\(378\) 0 0
\(379\) 28.2132i 1.44921i 0.689163 + 0.724606i \(0.257978\pi\)
−0.689163 + 0.724606i \(0.742022\pi\)
\(380\) −6.37109 + 0.772917i −0.326830 + 0.0396498i
\(381\) 0 0
\(382\) 21.0462 + 18.6473i 1.07682 + 0.954077i
\(383\) 1.84904 + 3.20262i 0.0944813 + 0.163646i 0.909392 0.415940i \(-0.136547\pi\)
−0.814911 + 0.579587i \(0.803214\pi\)
\(384\) 0 0
\(385\) −2.96695 3.55072i −0.151210 0.180962i
\(386\) −14.4454 2.94982i −0.735249 0.150142i
\(387\) 0 0
\(388\) −0.419551 0.558442i −0.0212995 0.0283506i
\(389\) −3.23187 + 5.59776i −0.163862 + 0.283818i −0.936251 0.351333i \(-0.885729\pi\)
0.772388 + 0.635151i \(0.219062\pi\)
\(390\) 0 0
\(391\) 30.8424i 1.55977i
\(392\) 13.9659 14.0340i 0.705385 0.708824i
\(393\) 0 0
\(394\) −7.18159 21.5152i −0.361803 1.08392i
\(395\) 0.0233845 + 0.0135010i 0.00117660 + 0.000679311i
\(396\) 0 0
\(397\) 14.7284 + 25.5104i 0.739198 + 1.28033i 0.952857 + 0.303421i \(0.0981287\pi\)
−0.213658 + 0.976908i \(0.568538\pi\)
\(398\) 0.653865 3.20199i 0.0327753 0.160501i
\(399\) 0 0
\(400\) 13.4444 + 14.0029i 0.672219 + 0.700145i
\(401\) −17.7242 + 10.2331i −0.885105 + 0.511016i −0.872338 0.488903i \(-0.837397\pi\)
−0.0127669 + 0.999918i \(0.504064\pi\)
\(402\) 0 0
\(403\) 14.0383 + 8.10500i 0.699296 + 0.403739i
\(404\) 30.5214 3.70274i 1.51849 0.184218i
\(405\) 0 0
\(406\) −0.932347 0.574921i −0.0462716 0.0285329i
\(407\) 32.2643i 1.59928i
\(408\) 0 0
\(409\) 11.5317 + 6.65785i 0.570207 + 0.329209i 0.757232 0.653146i \(-0.226551\pi\)
−0.187025 + 0.982355i \(0.559884\pi\)
\(410\) 1.99756 + 1.76987i 0.0986525 + 0.0874076i
\(411\) 0 0
\(412\) −1.86596 + 4.37830i −0.0919291 + 0.215703i
\(413\) 17.2309 3.00164i 0.847876 0.147701i
\(414\) 0 0
\(415\) 1.24237 + 2.15185i 0.0609855 + 0.105630i
\(416\) −16.0636 + 0.643155i −0.787585 + 0.0315333i
\(417\) 0 0
\(418\) 17.0994 + 51.2280i 0.836361 + 2.50564i
\(419\) 35.6073i 1.73953i 0.493467 + 0.869764i \(0.335729\pi\)
−0.493467 + 0.869764i \(0.664271\pi\)
\(420\) 0 0
\(421\) 16.1350i 0.786370i −0.919459 0.393185i \(-0.871373\pi\)
0.919459 0.393185i \(-0.128627\pi\)
\(422\) 17.0733 5.69892i 0.831115 0.277419i
\(423\) 0 0
\(424\) −11.9113 + 5.64973i −0.578466 + 0.274375i
\(425\) 11.9627 + 20.7201i 0.580278 + 1.00507i
\(426\) 0 0
\(427\) −6.96095 2.54985i −0.336864 0.123396i
\(428\) 1.51639 + 0.646261i 0.0732976 + 0.0312382i
\(429\) 0 0
\(430\) −1.56620 + 1.76769i −0.0755290 + 0.0852457i
\(431\) 27.7465 + 16.0194i 1.33650 + 0.771629i 0.986287 0.165041i \(-0.0527758\pi\)
0.350213 + 0.936670i \(0.386109\pi\)
\(432\) 0 0
\(433\) 25.4744i 1.22422i −0.790771 0.612112i \(-0.790320\pi\)
0.790771 0.612112i \(-0.209680\pi\)
\(434\) 10.1311 + 18.7838i 0.486309 + 0.901651i
\(435\) 0 0
\(436\) −32.3849 + 3.92881i −1.55095 + 0.188156i
\(437\) −45.3518 26.1839i −2.16947 1.25254i
\(438\) 0 0
\(439\) 18.7443 10.8220i 0.894615 0.516506i 0.0191655 0.999816i \(-0.493899\pi\)
0.875449 + 0.483310i \(0.160566\pi\)
\(440\) −2.81064 + 4.07055i −0.133992 + 0.194056i
\(441\) 0 0
\(442\) −19.4136 3.96438i −0.923413 0.188566i
\(443\) 7.35423 + 12.7379i 0.349410 + 0.605196i 0.986145 0.165887i \(-0.0530487\pi\)
−0.636735 + 0.771083i \(0.719715\pi\)
\(444\) 0 0
\(445\) 1.08497 + 0.626407i 0.0514325 + 0.0296945i
\(446\) −15.4178 + 5.14631i −0.730052 + 0.243685i
\(447\) 0 0
\(448\) −18.4461 10.3798i −0.871498 0.490399i
\(449\) 25.7754i 1.21642i −0.793778 0.608208i \(-0.791889\pi\)
0.793778 0.608208i \(-0.208111\pi\)
\(450\) 0 0
\(451\) 11.2293 19.4497i 0.528765 0.915849i
\(452\) 3.63186 + 4.83418i 0.170828 + 0.227380i
\(453\) 0 0
\(454\) 0.495855 2.42822i 0.0232716 0.113962i
\(455\) 0.991437 2.70657i 0.0464793 0.126886i
\(456\) 0 0
\(457\) 16.5498 + 28.6651i 0.774168 + 1.34090i 0.935261 + 0.353960i \(0.115165\pi\)
−0.161092 + 0.986939i \(0.551502\pi\)
\(458\) −5.46149 + 6.16411i −0.255199 + 0.288030i
\(459\) 0 0
\(460\) −0.577662 4.76161i −0.0269336 0.222011i
\(461\) 8.24676i 0.384090i −0.981386 0.192045i \(-0.938488\pi\)
0.981386 0.192045i \(-0.0615120\pi\)
\(462\) 0 0
\(463\) 16.2797 0.756582 0.378291 0.925687i \(-0.376512\pi\)
0.378291 + 0.925687i \(0.376512\pi\)
\(464\) −0.326023 + 1.12468i −0.0151352 + 0.0522122i
\(465\) 0 0
\(466\) −9.09768 8.06068i −0.421442 0.373404i
\(467\) −24.2507 + 14.0011i −1.12219 + 0.647895i −0.941959 0.335729i \(-0.891017\pi\)
−0.180229 + 0.983625i \(0.557684\pi\)
\(468\) 0 0
\(469\) 23.5228 4.09770i 1.08618 0.189214i
\(470\) 1.02658 5.02720i 0.0473527 0.231887i
\(471\) 0 0
\(472\) −8.01305 16.8940i −0.368830 0.777607i
\(473\) 17.2115 + 9.93707i 0.791386 + 0.456907i
\(474\) 0 0
\(475\) 40.6233 1.86393
\(476\) −19.0163 17.8582i −0.871612 0.818528i
\(477\) 0 0
\(478\) 2.92170 0.975237i 0.133635 0.0446063i
\(479\) 5.42512 9.39658i 0.247880 0.429341i −0.715057 0.699066i \(-0.753600\pi\)
0.962937 + 0.269725i \(0.0869328\pi\)
\(480\) 0 0
\(481\) 17.4061 10.0494i 0.793650 0.458214i
\(482\) −1.66036 + 8.13083i −0.0756274 + 0.370349i
\(483\) 0 0
\(484\) 18.0550 + 7.69475i 0.820683 + 0.349761i
\(485\) −0.0669409 0.115945i −0.00303963 0.00526480i
\(486\) 0 0
\(487\) −5.75857 + 9.97414i −0.260946 + 0.451971i −0.966494 0.256691i \(-0.917368\pi\)
0.705548 + 0.708662i \(0.250701\pi\)
\(488\) −0.638940 + 7.89931i −0.0289235 + 0.357585i
\(489\) 0 0
\(490\) 2.98139 2.34799i 0.134685 0.106072i
\(491\) −5.61613 −0.253452 −0.126726 0.991938i \(-0.540447\pi\)
−0.126726 + 0.991938i \(0.540447\pi\)
\(492\) 0 0
\(493\) −0.721619 + 1.24988i −0.0325001 + 0.0562918i
\(494\) −22.3107 + 25.1809i −1.00381 + 1.13294i
\(495\) 0 0
\(496\) 16.4577 15.8013i 0.738974 0.709498i
\(497\) −7.41459 8.87346i −0.332590 0.398029i
\(498\) 0 0
\(499\) −12.5584 + 7.25061i −0.562193 + 0.324582i −0.754025 0.656846i \(-0.771890\pi\)
0.191832 + 0.981428i \(0.438557\pi\)
\(500\) 4.53757 + 6.03971i 0.202926 + 0.270104i
\(501\) 0 0
\(502\) 39.6595 13.2380i 1.77009 0.590840i
\(503\) −10.8393 −0.483301 −0.241651 0.970363i \(-0.577689\pi\)
−0.241651 + 0.970363i \(0.577689\pi\)
\(504\) 0 0
\(505\) 5.89306 0.262238
\(506\) −38.2867 + 12.7798i −1.70205 + 0.568130i
\(507\) 0 0
\(508\) −4.63648 + 3.48333i −0.205710 + 0.154548i
\(509\) −21.6861 + 12.5205i −0.961218 + 0.554959i −0.896548 0.442947i \(-0.853933\pi\)
−0.0646702 + 0.997907i \(0.520600\pi\)
\(510\) 0 0
\(511\) −33.0855 + 5.76353i −1.46362 + 0.254964i
\(512\) −5.42539 + 21.9674i −0.239770 + 0.970830i
\(513\) 0 0
\(514\) −19.6215 + 22.1457i −0.865465 + 0.976806i
\(515\) −0.456122 + 0.790027i −0.0200992 + 0.0348127i
\(516\) 0 0
\(517\) −43.1774 −1.89894
\(518\) 26.4506 + 0.766372i 1.16217 + 0.0336724i
\(519\) 0 0
\(520\) −3.07143 0.248434i −0.134691 0.0108946i
\(521\) 16.8507 29.1862i 0.738240 1.27867i −0.215047 0.976604i \(-0.568990\pi\)
0.953287 0.302066i \(-0.0976764\pi\)
\(522\) 0 0
\(523\) 9.74207 + 16.8738i 0.425991 + 0.737838i 0.996512 0.0834448i \(-0.0265922\pi\)
−0.570522 + 0.821283i \(0.693259\pi\)
\(524\) −9.55540 + 22.4209i −0.417430 + 0.979461i
\(525\) 0 0
\(526\) 3.38186 16.5610i 0.147456 0.722095i
\(527\) 24.3525 14.0599i 1.06081 0.612459i
\(528\) 0 0
\(529\) 8.06926 13.9764i 0.350837 0.607668i
\(530\) −2.39690 + 0.800065i −0.104115 + 0.0347526i
\(531\) 0 0
\(532\) −42.4033 + 12.8015i −1.83842 + 0.555014i
\(533\) 13.9904 0.605990
\(534\) 0 0
\(535\) 0.273620 + 0.157975i 0.0118296 + 0.00682984i
\(536\) −10.9391 23.0629i −0.472495 0.996164i
\(537\) 0 0
\(538\) 4.59373 22.4956i 0.198050 0.969854i
\(539\) −24.3788 20.6282i −1.05007 0.888518i
\(540\) 0 0
\(541\) −33.3111 + 19.2322i −1.43216 + 0.826856i −0.997285 0.0736362i \(-0.976540\pi\)
−0.434872 + 0.900492i \(0.643206\pi\)
\(542\) 26.9795 + 23.9042i 1.15887 + 1.02677i
\(543\) 0 0
\(544\) −12.9667 + 24.6905i −0.555945 + 1.05859i
\(545\) −6.25287 −0.267844
\(546\) 0 0
\(547\) 11.2961i 0.482985i 0.970403 + 0.241493i \(0.0776370\pi\)
−0.970403 + 0.241493i \(0.922363\pi\)
\(548\) −36.4876 + 4.42655i −1.55867 + 0.189093i
\(549\) 0 0
\(550\) 20.7643 23.4356i 0.885393 0.999298i
\(551\) 1.22524 + 2.12219i 0.0521972 + 0.0904082i
\(552\) 0 0
\(553\) 0.174989 + 0.0640997i 0.00744128 + 0.00272580i
\(554\) −3.10937 + 15.2266i −0.132104 + 0.646918i
\(555\) 0 0
\(556\) 10.2389 7.69236i 0.434226 0.326229i
\(557\) 10.9385 18.9460i 0.463477 0.802766i −0.535654 0.844438i \(-0.679935\pi\)
0.999131 + 0.0416711i \(0.0132682\pi\)
\(558\) 0 0
\(559\) 12.3804i 0.523637i
\(560\) −3.27031 2.40087i −0.138196 0.101455i
\(561\) 0 0
\(562\) 9.00580 3.00606i 0.379887 0.126803i
\(563\) 12.5783 + 7.26211i 0.530114 + 0.306061i 0.741063 0.671436i \(-0.234322\pi\)
−0.210949 + 0.977497i \(0.567655\pi\)
\(564\) 0 0
\(565\) 0.579476 + 1.00368i 0.0243788 + 0.0422252i
\(566\) −19.6113 4.00474i −0.824325 0.168332i
\(567\) 0 0
\(568\) −7.02395 + 10.1725i −0.294718 + 0.426830i
\(569\) 8.24719 4.76152i 0.345740 0.199613i −0.317067 0.948403i \(-0.602698\pi\)
0.662807 + 0.748790i \(0.269365\pi\)
\(570\) 0 0
\(571\) 6.63806 + 3.83248i 0.277794 + 0.160384i 0.632424 0.774622i \(-0.282060\pi\)
−0.354630 + 0.935007i \(0.615393\pi\)
\(572\) 3.12293 + 25.7421i 0.130576 + 1.07633i
\(573\) 0 0
\(574\) 15.6783 + 9.66784i 0.654399 + 0.403528i
\(575\) 30.3610i 1.26614i
\(576\) 0 0
\(577\) 26.5704 + 15.3405i 1.10614 + 0.638631i 0.937827 0.347102i \(-0.112834\pi\)
0.168315 + 0.985733i \(0.446168\pi\)
\(578\) −6.85086 + 7.73221i −0.284958 + 0.321618i
\(579\) 0 0
\(580\) −0.0879977 + 0.206478i −0.00365390 + 0.00857355i
\(581\) 10.9960 + 13.1595i 0.456189 + 0.545947i
\(582\) 0 0
\(583\) 10.6321 + 18.4153i 0.440336 + 0.762684i
\(584\) 15.3861 + 32.4386i 0.636681 + 1.34232i
\(585\) 0 0
\(586\) −10.3825 + 3.46558i −0.428897 + 0.143162i
\(587\) 12.2533i 0.505748i 0.967499 + 0.252874i \(0.0813758\pi\)
−0.967499 + 0.252874i \(0.918624\pi\)
\(588\) 0 0
\(589\) 47.7450i 1.96730i
\(590\) −1.13474 3.39955i −0.0467165 0.139957i
\(591\) 0 0
\(592\) −6.76422 27.4681i −0.278008 1.12893i
\(593\) −5.04004 8.72961i −0.206970 0.358482i 0.743789 0.668415i \(-0.233027\pi\)
−0.950759 + 0.309933i \(0.899694\pi\)
\(594\) 0 0
\(595\) −3.20618 3.83702i −0.131441 0.157302i
\(596\) −33.9168 14.4548i −1.38929 0.592091i
\(597\) 0 0
\(598\) −18.8197 16.6745i −0.769594 0.681872i
\(599\) −8.63004 4.98256i −0.352614 0.203582i 0.313222 0.949680i \(-0.398592\pi\)
−0.665836 + 0.746098i \(0.731925\pi\)
\(600\) 0 0
\(601\) 36.9998i 1.50925i 0.656154 + 0.754627i \(0.272182\pi\)
−0.656154 + 0.754627i \(0.727818\pi\)
\(602\) −8.55532 + 13.8741i −0.348689 + 0.565467i
\(603\) 0 0
\(604\) −3.55723 29.3220i −0.144742 1.19309i
\(605\) 3.25788 + 1.88094i 0.132451 + 0.0764709i
\(606\) 0 0
\(607\) 28.8906 16.6800i 1.17263 0.677021i 0.218335 0.975874i \(-0.429937\pi\)
0.954299 + 0.298853i \(0.0966041\pi\)
\(608\) 25.2975 + 40.0279i 1.02595 + 1.62334i
\(609\) 0 0
\(610\) −0.303925 + 1.48833i −0.0123056 + 0.0602607i
\(611\) −13.4485 23.2935i −0.544069 0.942355i
\(612\) 0 0
\(613\) 6.37477 + 3.68047i 0.257474 + 0.148653i 0.623182 0.782077i \(-0.285840\pi\)
−0.365708 + 0.930730i \(0.619173\pi\)
\(614\) −11.1458 33.3915i −0.449807 1.34757i
\(615\) 0 0
\(616\) −14.2890 + 31.0058i −0.575719 + 1.24926i
\(617\) 16.0597i 0.646540i −0.946307 0.323270i \(-0.895218\pi\)
0.946307 0.323270i \(-0.104782\pi\)
\(618\) 0 0
\(619\) −0.283019 + 0.490203i −0.0113755 + 0.0197029i −0.871657 0.490116i \(-0.836954\pi\)
0.860282 + 0.509819i \(0.170288\pi\)
\(620\) 3.49633 2.62675i 0.140416 0.105493i
\(621\) 0 0
\(622\) −11.7617 2.40181i −0.471602 0.0963038i
\(623\) 8.11895 + 2.97403i 0.325279 + 0.119152i
\(624\) 0 0
\(625\) −11.4086 19.7603i −0.456345 0.790413i
\(626\) −7.41107 6.56632i −0.296206 0.262443i
\(627\) 0 0
\(628\) −1.45936 12.0294i −0.0582348 0.480024i
\(629\) 34.8658i 1.39019i
\(630\) 0 0
\(631\) 32.2928 1.28556 0.642779 0.766052i \(-0.277781\pi\)
0.642779 + 0.766052i \(0.277781\pi\)
\(632\) 0.0160621 0.198578i 0.000638915 0.00789901i
\(633\) 0 0
\(634\) −23.6251 + 26.6644i −0.938271 + 1.05898i
\(635\) −0.962636 + 0.555778i −0.0382010 + 0.0220554i
\(636\) 0 0
\(637\) 3.53528 19.5770i 0.140073 0.775670i
\(638\) 1.85056 + 0.377896i 0.0732645 + 0.0149610i
\(639\) 0 0
\(640\) −1.53944 + 4.05470i −0.0608515 + 0.160276i
\(641\) −7.35118 4.24421i −0.290354 0.167636i 0.347747 0.937588i \(-0.386947\pi\)
−0.638102 + 0.769952i \(0.720280\pi\)
\(642\) 0 0
\(643\) 29.1690 1.15031 0.575156 0.818044i \(-0.304942\pi\)
0.575156 + 0.818044i \(0.304942\pi\)
\(644\) −9.56754 31.6913i −0.377014 1.24881i
\(645\) 0 0
\(646\) 18.4782 + 55.3585i 0.727015 + 2.17805i
\(647\) 4.70856 8.15546i 0.185113 0.320624i −0.758502 0.651671i \(-0.774068\pi\)
0.943614 + 0.331046i \(0.107402\pi\)
\(648\) 0 0
\(649\) −26.1186 + 15.0796i −1.02524 + 0.591925i
\(650\) 19.1106 + 3.90250i 0.749580 + 0.153069i
\(651\) 0 0
\(652\) −3.51843 + 8.25567i −0.137792 + 0.323317i
\(653\) −6.88850 11.9312i −0.269568 0.466905i 0.699182 0.714943i \(-0.253548\pi\)
−0.968750 + 0.248038i \(0.920214\pi\)
\(654\) 0 0
\(655\) −2.33576 + 4.04566i −0.0912658 + 0.158077i
\(656\) 5.48237 18.9126i 0.214051 0.738414i
\(657\) 0 0
\(658\) 1.02559 35.3972i 0.0399816 1.37993i
\(659\) 3.86377 0.150511 0.0752555 0.997164i \(-0.476023\pi\)
0.0752555 + 0.997164i \(0.476023\pi\)
\(660\) 0 0
\(661\) 1.46098 2.53049i 0.0568255 0.0984247i −0.836213 0.548404i \(-0.815235\pi\)
0.893039 + 0.449980i \(0.148569\pi\)
\(662\) −21.7695 19.2881i −0.846094 0.749652i
\(663\) 0 0
\(664\) 10.4166 15.0860i 0.404243 0.585452i
\(665\) −8.36399 + 1.45702i −0.324342 + 0.0565008i
\(666\) 0 0
\(667\) −1.58608 + 0.915722i −0.0614131 + 0.0354569i
\(668\) 25.4803 19.1431i 0.985863 0.740668i
\(669\) 0 0
\(670\) −1.54909 4.64091i −0.0598467 0.179294i
\(671\) 12.7829 0.493479
\(672\) 0 0
\(673\) −38.7127 −1.49227 −0.746133 0.665797i \(-0.768092\pi\)
−0.746133 + 0.665797i \(0.768092\pi\)
\(674\) −4.37488 13.1066i −0.168514 0.504848i
\(675\) 0 0
\(676\) 7.87241 5.91445i 0.302785 0.227479i
\(677\) −39.7095 + 22.9263i −1.52616 + 0.881130i −0.526644 + 0.850086i \(0.676550\pi\)
−0.999518 + 0.0310437i \(0.990117\pi\)
\(678\) 0 0
\(679\) −0.592480 0.709055i −0.0227373 0.0272110i
\(680\) −3.03726 + 4.39876i −0.116474 + 0.168685i
\(681\) 0 0
\(682\) −27.5441 24.4045i −1.05472 0.934496i
\(683\) −19.9744 + 34.5968i −0.764301 + 1.32381i 0.176315 + 0.984334i \(0.443582\pi\)
−0.940615 + 0.339474i \(0.889751\pi\)
\(684\) 0 0
\(685\) −7.04503 −0.269177
\(686\) 17.4902 19.4960i 0.667780 0.744359i
\(687\) 0 0
\(688\) 16.7363 + 4.85149i 0.638064 + 0.184961i
\(689\) −6.62318 + 11.4717i −0.252323 + 0.437036i
\(690\) 0 0
\(691\) −13.9816 24.2169i −0.531886 0.921253i −0.999307 0.0372183i \(-0.988150\pi\)
0.467422 0.884035i \(-0.345183\pi\)
\(692\) 14.9441 35.0650i 0.568089 1.33297i
\(693\) 0 0
\(694\) −26.7094 5.45422i −1.01388 0.207039i
\(695\) 2.12582 1.22734i 0.0806370 0.0465558i
\(696\) 0 0
\(697\) 12.1347 21.0179i 0.459634 0.796110i
\(698\) 13.6912 + 41.0171i 0.518218 + 1.55252i
\(699\) 0 0
\(700\) 18.7195 + 17.5794i 0.707531 + 0.664440i
\(701\) 47.3436 1.78814 0.894072 0.447923i \(-0.147836\pi\)
0.894072 + 0.447923i \(0.147836\pi\)
\(702\) 0 0
\(703\) −51.2680 29.5996i −1.93361 1.11637i
\(704\) 36.0227 + 5.86581i 1.35766 + 0.221076i
\(705\) 0 0
\(706\) −12.7425 2.60210i −0.479572 0.0979313i
\(707\) 40.0686 6.98000i 1.50693 0.262510i
\(708\) 0 0
\(709\) 8.16943 4.71662i 0.306810 0.177137i −0.338688 0.940899i \(-0.609983\pi\)
0.645498 + 0.763762i \(0.276650\pi\)
\(710\) −1.57134 + 1.77349i −0.0589712 + 0.0665577i
\(711\) 0 0
\(712\) 0.745232 9.21342i 0.0279288 0.345287i
\(713\) 35.6836 1.33636
\(714\) 0 0
\(715\) 4.97028i 0.185878i
\(716\) 0.842321 + 6.94318i 0.0314790 + 0.259479i
\(717\) 0 0
\(718\) 1.08794 + 0.963928i 0.0406014 + 0.0359735i
\(719\) −22.0452 38.1835i −0.822148 1.42400i −0.904079 0.427364i \(-0.859442\pi\)
0.0819312 0.996638i \(-0.473891\pi\)
\(720\) 0 0
\(721\) −2.16556 + 5.91186i −0.0806497 + 0.220169i
\(722\) 70.7615 + 14.4499i 2.63347 + 0.537770i
\(723\) 0 0
\(724\) 34.0727 25.5984i 1.26630 0.951358i
\(725\) 0.710355 1.23037i 0.0263819 0.0456948i
\(726\) 0 0
\(727\) 0.998475i 0.0370314i 0.999829 + 0.0185157i \(0.00589406\pi\)
−0.999829 + 0.0185157i \(0.994106\pi\)
\(728\) −21.1778 + 1.94876i −0.784900 + 0.0722259i
\(729\) 0 0
\(730\) 2.17884 + 6.52757i 0.0806426 + 0.241596i
\(731\) 18.5993 + 10.7383i 0.687919 + 0.397170i
\(732\) 0 0
\(733\) 21.6087 + 37.4274i 0.798136 + 1.38241i 0.920829 + 0.389967i \(0.127514\pi\)
−0.122693 + 0.992445i \(0.539153\pi\)
\(734\) 7.50479 36.7511i 0.277007 1.35651i
\(735\) 0 0
\(736\) −29.9160 + 18.9068i −1.10272 + 0.696914i
\(737\) −35.6559 + 20.5859i −1.31340 + 0.758293i
\(738\) 0 0
\(739\) −20.3992 11.7775i −0.750398 0.433243i 0.0754395 0.997150i \(-0.475964\pi\)
−0.825838 + 0.563908i \(0.809297\pi\)
\(740\) −0.653018 5.38277i −0.0240054 0.197875i
\(741\) 0 0
\(742\) −15.3496 + 8.27886i −0.563501 + 0.303927i
\(743\) 0.745461i 0.0273483i 0.999907 + 0.0136742i \(0.00435275\pi\)
−0.999907 + 0.0136742i \(0.995647\pi\)
\(744\) 0 0
\(745\) −6.12000 3.53339i −0.224220 0.129453i
\(746\) 5.47580 + 4.85165i 0.200483 + 0.177631i
\(747\) 0 0
\(748\) 41.3813 + 17.6360i 1.51305 + 0.644837i
\(749\) 2.04753 + 0.750026i 0.0748151 + 0.0274053i
\(750\) 0 0
\(751\) 10.2168 + 17.6961i 0.372817 + 0.645738i 0.989998 0.141083i \(-0.0450585\pi\)
−0.617180 + 0.786822i \(0.711725\pi\)
\(752\) −36.7589 + 9.05215i −1.34046 + 0.330098i
\(753\) 0 0
\(754\) 0.372529 + 1.11605i 0.0135667 + 0.0406443i
\(755\) 5.66148i 0.206042i
\(756\) 0 0
\(757\) 12.6416i 0.459465i −0.973254 0.229733i \(-0.926215\pi\)
0.973254 0.229733i \(-0.0737852\pi\)
\(758\) 37.8467 12.6329i 1.37465 0.458848i
\(759\) 0 0
\(760\) 3.88959 + 8.20045i 0.141090 + 0.297462i
\(761\) 20.0783 + 34.7767i 0.727839 + 1.26065i 0.957795 + 0.287452i \(0.0928083\pi\)
−0.229956 + 0.973201i \(0.573858\pi\)
\(762\) 0 0
\(763\) −42.5150 + 7.40617i −1.53915 + 0.268121i
\(764\) 15.5907 36.5822i 0.564052 1.32350i
\(765\) 0 0
\(766\) 3.46824 3.91443i 0.125313 0.141434i
\(767\) −16.2704 9.39370i −0.587489 0.339187i
\(768\) 0 0
\(769\) 9.78731i 0.352939i −0.984306 0.176470i \(-0.943532\pi\)
0.984306 0.176470i \(-0.0564678\pi\)
\(770\) −3.43464 + 5.56993i −0.123776 + 0.200726i
\(771\) 0 0
\(772\) 2.51109 + 20.6987i 0.0903759 + 0.744961i
\(773\) 36.3366 + 20.9789i 1.30694 + 0.754560i 0.981584 0.191033i \(-0.0611839\pi\)
0.325352 + 0.945593i \(0.394517\pi\)
\(774\) 0 0
\(775\) −23.9724 + 13.8404i −0.861113 + 0.497164i
\(776\) −0.561265 + 0.812862i −0.0201482 + 0.0291800i
\(777\) 0 0
\(778\) 8.95628 + 1.82892i 0.321098 + 0.0655701i
\(779\) −20.6036 35.6865i −0.738202 1.27860i
\(780\) 0 0
\(781\) 17.2679 + 9.96963i 0.617894 + 0.356741i
\(782\) −41.3738 + 13.8102i −1.47952 + 0.493852i
\(783\) 0 0
\(784\) −25.0795 12.4507i −0.895695 0.444668i
\(785\) 2.32263i 0.0828983i
\(786\) 0 0
\(787\) 15.7140 27.2175i 0.560145 0.970200i −0.437338 0.899297i \(-0.644079\pi\)
0.997483 0.0709026i \(-0.0225879\pi\)
\(788\) −25.6460 + 19.2676i −0.913603 + 0.686379i
\(789\) 0 0
\(790\) 0.00764026 0.0374146i 0.000271828 0.00133115i
\(791\) 5.12883 + 6.13796i 0.182360 + 0.218241i
\(792\) 0 0
\(793\) 3.98151 + 6.89617i 0.141387 + 0.244890i
\(794\) 27.6262 31.1802i 0.980416 1.10654i
\(795\) 0 0
\(796\) −4.58811 + 0.556613i −0.162621 + 0.0197286i
\(797\) 1.25772i 0.0445507i 0.999752 + 0.0222754i \(0.00709105\pi\)
−0.999752 + 0.0222754i \(0.992909\pi\)
\(798\) 0 0
\(799\) −46.6588 −1.65067
\(800\) 12.7644 24.3051i 0.451288 0.859314i
\(801\) 0 0
\(802\) 21.6635 + 19.1942i 0.764966 + 0.677772i
\(803\) 50.1510 28.9547i 1.76979 1.02179i
\(804\) 0 0
\(805\) −1.08894 6.25107i −0.0383802 0.220321i
\(806\) 4.58664 22.4609i 0.161557 0.791151i
\(807\) 0 0
\(808\) −18.6335 39.2851i −0.655524 1.38204i
\(809\) 24.5857 + 14.1945i 0.864386 + 0.499053i 0.865479 0.500946i \(-0.167014\pi\)
−0.00109260 + 0.999999i \(0.500348\pi\)
\(810\) 0 0
\(811\) −4.97465 −0.174684 −0.0873418 0.996178i \(-0.527837\pi\)
−0.0873418 + 0.996178i \(0.527837\pi\)
\(812\) −0.353759 + 1.50813i −0.0124145 + 0.0529251i
\(813\) 0 0
\(814\) −43.2812 + 14.4469i −1.51701 + 0.506363i
\(815\) −0.860059 + 1.48967i −0.0301265 + 0.0521807i
\(816\) 0 0
\(817\) 31.5799 18.2327i 1.10484 0.637881i
\(818\) 3.76769 18.4505i 0.131734 0.645106i
\(819\) 0 0
\(820\) 1.47976 3.47213i 0.0516756 0.121252i
\(821\) −5.02868 8.70993i −0.175502 0.303979i 0.764833 0.644229i \(-0.222822\pi\)
−0.940335 + 0.340250i \(0.889488\pi\)
\(822\) 0 0
\(823\) 2.27031 3.93230i 0.0791382 0.137071i −0.823740 0.566967i \(-0.808117\pi\)
0.902878 + 0.429896i \(0.141450\pi\)
\(824\) 6.70881 + 0.542646i 0.233713 + 0.0189040i
\(825\) 0 0
\(826\) −11.7420 21.7704i −0.408555 0.757490i
\(827\) −19.2538 −0.669520 −0.334760 0.942303i \(-0.608655\pi\)
−0.334760 + 0.942303i \(0.608655\pi\)
\(828\) 0 0
\(829\) 17.0503 29.5321i 0.592183 1.02569i −0.401755 0.915747i \(-0.631600\pi\)
0.993938 0.109943i \(-0.0350670\pi\)
\(830\) 2.33032 2.63011i 0.0808865 0.0912924i
\(831\) 0 0
\(832\) 8.05553 + 21.2607i 0.279275 + 0.737082i
\(833\) −26.3444 22.2914i −0.912781 0.772352i
\(834\) 0 0
\(835\) 5.29028 3.05435i 0.183078 0.105700i
\(836\) 61.0635 45.8763i 2.11193 1.58667i
\(837\) 0 0
\(838\) 47.7656 15.9437i 1.65003 0.550767i
\(839\) −12.0599 −0.416355 −0.208178 0.978091i \(-0.566753\pi\)
−0.208178 + 0.978091i \(0.566753\pi\)
\(840\) 0 0
\(841\) −28.9143 −0.997045
\(842\) −21.6443 + 7.22469i −0.745913 + 0.248979i
\(843\) 0 0
\(844\) −15.2897 20.3513i −0.526293 0.700521i
\(845\) 1.63449 0.943672i 0.0562281 0.0324633i
\(846\) 0 0
\(847\) 24.3791 + 8.93023i 0.837674 + 0.306846i
\(848\) 12.9124 + 13.4488i 0.443412 + 0.461833i
\(849\) 0 0
\(850\) 22.4386 25.3252i 0.769636 0.868649i
\(851\) 22.1221 38.3166i 0.758335 1.31348i
\(852\) 0 0
\(853\) 28.7232 0.983464 0.491732 0.870747i \(-0.336364\pi\)
0.491732 + 0.870747i \(0.336364\pi\)
\(854\) −0.303631 + 10.4795i −0.0103900 + 0.358603i
\(855\) 0 0
\(856\) 0.187941 2.32355i 0.00642370 0.0794172i
\(857\) 7.96109 13.7890i 0.271946 0.471024i −0.697414 0.716668i \(-0.745666\pi\)
0.969360 + 0.245644i \(0.0789996\pi\)
\(858\) 0 0
\(859\) −18.1568 31.4484i −0.619501 1.07301i −0.989577 0.144006i \(-0.954002\pi\)
0.370076 0.929002i \(-0.379332\pi\)
\(860\) 3.07258 + 1.30948i 0.104774 + 0.0446529i
\(861\) 0 0
\(862\) 9.06543 44.3936i 0.308770 1.51205i
\(863\) −26.8218 + 15.4856i −0.913025 + 0.527135i −0.881403 0.472365i \(-0.843401\pi\)
−0.0316219 + 0.999500i \(0.510067\pi\)
\(864\) 0 0
\(865\) 3.65300 6.32717i 0.124206 0.215130i
\(866\) −34.1729 + 11.4066i −1.16124 + 0.387612i
\(867\) 0 0
\(868\) 20.6613 22.0012i 0.701289 0.746769i
\(869\) −0.321345 −0.0109009
\(870\) 0 0
\(871\) −22.2116 12.8239i −0.752610 0.434520i
\(872\) 19.7712 + 41.6837i 0.669537 + 1.41159i
\(873\) 0 0
\(874\) −14.8175 + 72.5617i −0.501210 + 2.45444i
\(875\) 6.40784 + 7.66863i 0.216625 + 0.259247i
\(876\) 0 0
\(877\) −32.7909 + 18.9318i −1.10727 + 0.639282i −0.938121 0.346309i \(-0.887435\pi\)
−0.169148 + 0.985591i \(0.554102\pi\)
\(878\) −22.9103 20.2989i −0.773185 0.685054i
\(879\) 0 0
\(880\) 6.71898 + 1.94769i 0.226497 + 0.0656567i
\(881\) −23.9503 −0.806906 −0.403453 0.915000i \(-0.632190\pi\)
−0.403453 + 0.915000i \(0.632190\pi\)
\(882\) 0 0
\(883\) 10.2002i 0.343263i 0.985161 + 0.171631i \(0.0549038\pi\)
−0.985161 + 0.171631i \(0.945096\pi\)
\(884\) 3.37474 + 27.8177i 0.113505 + 0.935609i
\(885\) 0 0
\(886\) 13.7944 15.5690i 0.463430 0.523050i
\(887\) 13.8743 + 24.0310i 0.465854 + 0.806883i 0.999240 0.0389894i \(-0.0124139\pi\)
−0.533386 + 0.845872i \(0.679081\pi\)
\(888\) 0 0
\(889\) −5.88694 + 4.91908i −0.197442 + 0.164981i
\(890\) 0.354485 1.73592i 0.0118824 0.0581882i
\(891\) 0 0
\(892\) 13.8071 + 18.3779i 0.462296 + 0.615338i
\(893\) −39.6113 + 68.6088i −1.32554 + 2.29591i
\(894\) 0 0
\(895\) 1.34059i 0.0448109i
\(896\) −5.66448 + 29.3924i −0.189237 + 0.981931i
\(897\) 0 0
\(898\) −34.5766 + 11.5414i −1.15383 + 0.385140i
\(899\) −1.44607 0.834886i −0.0482290 0.0278450i
\(900\) 0 0
\(901\) 11.4894 + 19.9002i 0.382766 + 0.662970i
\(902\) −31.1190 6.35467i −1.03615 0.211587i
\(903\) 0 0
\(904\) 4.85861 7.03656i 0.161595 0.234033i
\(905\) 7.07426 4.08432i 0.235156 0.135767i
\(906\) 0 0
\(907\) −21.5836 12.4613i −0.716673 0.413771i 0.0968542 0.995299i \(-0.469122\pi\)
−0.813527 + 0.581527i \(0.802455\pi\)
\(908\) −3.47937 + 0.422105i −0.115467 + 0.0140080i
\(909\) 0 0
\(910\) −4.07468 0.118059i −0.135074 0.00391360i
\(911\) 27.2411i 0.902538i 0.892388 + 0.451269i \(0.149029\pi\)
−0.892388 + 0.451269i \(0.850971\pi\)
\(912\) 0 0
\(913\) −25.6086 14.7851i −0.847521 0.489316i
\(914\) 31.0426 35.0362i 1.02680 1.15889i
\(915\) 0 0
\(916\) 10.7144 + 4.56628i 0.354012 + 0.150874i
\(917\) −11.0896 + 30.2741i −0.366212 + 0.999740i
\(918\) 0 0
\(919\) 0.106387 + 0.184268i 0.00350938 + 0.00607843i 0.867775 0.496958i \(-0.165550\pi\)
−0.864265 + 0.503036i \(0.832216\pi\)
\(920\) −6.12884 + 2.90700i −0.202062 + 0.0958409i
\(921\) 0 0
\(922\) −11.0627 + 3.69262i −0.364330 + 0.121610i
\(923\) 12.4210i 0.408843i
\(924\) 0 0
\(925\) 34.3216i 1.12849i
\(926\) −7.28951 21.8385i −0.239548 0.717658i
\(927\) 0 0
\(928\) 1.65470 0.0662507i 0.0543181 0.00217478i
\(929\) −8.81604 15.2698i −0.289245 0.500987i 0.684385 0.729121i \(-0.260071\pi\)
−0.973630 + 0.228134i \(0.926738\pi\)
\(930\) 0 0
\(931\) −55.1434 + 19.8133i −1.80725 + 0.649356i
\(932\) −6.73942 + 15.8134i −0.220757 + 0.517987i
\(933\) 0 0
\(934\) 29.6406 + 26.2620i 0.969869 + 0.859319i
\(935\) 7.46691 + 4.31102i 0.244194 + 0.140985i
\(936\) 0 0
\(937\) 5.18135i 0.169267i −0.996412 0.0846337i \(-0.973028\pi\)
0.996412 0.0846337i \(-0.0269720\pi\)
\(938\) −16.0296 29.7200i −0.523385 0.970393i
\(939\) 0 0
\(940\) −7.20343 + 0.873894i −0.234950 + 0.0285033i
\(941\) −17.0687 9.85464i −0.556425 0.321252i 0.195284 0.980747i \(-0.437437\pi\)
−0.751709 + 0.659495i \(0.770770\pi\)
\(942\) 0 0
\(943\) 26.6714 15.3987i 0.868539 0.501451i
\(944\) −19.0745 + 18.3137i −0.620823 + 0.596060i
\(945\) 0 0
\(946\) 5.62341 27.5380i 0.182833 0.895336i
\(947\) 18.8273 + 32.6098i 0.611804 + 1.05968i 0.990936 + 0.134333i \(0.0428893\pi\)
−0.379132 + 0.925343i \(0.623777\pi\)
\(948\) 0 0
\(949\) 31.2412 + 18.0371i 1.01413 + 0.585509i
\(950\) −18.1898 54.4945i −0.590154 1.76803i
\(951\) 0 0
\(952\) −15.4411 + 33.5059i −0.500449 + 1.08593i
\(953\) 42.9398i 1.39096i 0.718547 + 0.695478i \(0.244808\pi\)
−0.718547 + 0.695478i \(0.755192\pi\)
\(954\) 0 0
\(955\) 3.81106 6.60094i 0.123323 0.213602i
\(956\) −2.61648 3.48265i −0.0846229 0.112637i
\(957\) 0 0
\(958\) −15.0343 3.07009i −0.485736 0.0991900i
\(959\) −47.9011 + 8.34444i −1.54681 + 0.269456i
\(960\) 0 0
\(961\) 0.766797 + 1.32813i 0.0247354 + 0.0428430i
\(962\) −21.2747 18.8497i −0.685924 0.607740i
\(963\) 0 0
\(964\) 11.6506 1.41341i 0.375241 0.0455229i
\(965\) 3.99650i 0.128652i
\(966\) 0 0
\(967\) −22.4334 −0.721408 −0.360704 0.932680i \(-0.617464\pi\)
−0.360704 + 0.932680i \(0.617464\pi\)
\(968\) 2.23774 27.6655i 0.0719236 0.889202i
\(969\) 0 0
\(970\) −0.125561 + 0.141715i −0.00403153 + 0.00455018i
\(971\) −7.50553 + 4.33332i −0.240864 + 0.139063i −0.615574 0.788079i \(-0.711076\pi\)
0.374710 + 0.927142i \(0.377742\pi\)
\(972\) 0 0
\(973\) 13.0003 10.8630i 0.416772 0.348251i
\(974\) 15.9584 + 3.25879i 0.511339 + 0.104418i
\(975\) 0 0
\(976\) 10.8827 2.67994i 0.348346 0.0857827i
\(977\) −48.7155 28.1259i −1.55855 0.899828i −0.997396 0.0721142i \(-0.977025\pi\)
−0.561151 0.827714i \(-0.689641\pi\)
\(978\) 0 0
\(979\) −14.9094 −0.476507
\(980\) −4.48470 2.94805i −0.143258 0.0941720i
\(981\) 0 0
\(982\) 2.51471 + 7.53379i 0.0802477 + 0.240413i
\(983\) −10.2462 + 17.7469i −0.326802 + 0.566038i −0.981875 0.189527i \(-0.939304\pi\)
0.655073 + 0.755565i \(0.272638\pi\)
\(984\) 0 0
\(985\) −5.32469 + 3.07421i −0.169659 + 0.0979525i
\(986\) 1.99978 + 0.408366i 0.0636858 + 0.0130050i
\(987\) 0 0
\(988\) 43.7691 + 18.6536i 1.39248 + 0.593451i
\(989\) 13.6267 + 23.6022i 0.433304 + 0.750505i
\(990\) 0 0
\(991\) 13.1943 22.8533i 0.419132 0.725958i −0.576720 0.816942i \(-0.695668\pi\)
0.995852 + 0.0909835i \(0.0290011\pi\)
\(992\) −28.5660 15.0021i −0.906970 0.476316i
\(993\) 0 0
\(994\) −8.58336 + 13.9196i −0.272248 + 0.441502i
\(995\) −0.885873 −0.0280841
\(996\) 0 0
\(997\) −19.5633 + 33.8847i −0.619577 + 1.07314i 0.369986 + 0.929038i \(0.379363\pi\)
−0.989563 + 0.144102i \(0.953971\pi\)
\(998\) 15.3496 + 13.6000i 0.485884 + 0.430501i
\(999\) 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 504.2.ch.b.269.11 yes 56
3.2 odd 2 inner 504.2.ch.b.269.18 yes 56
4.3 odd 2 2016.2.cp.b.17.14 56
7.5 odd 6 inner 504.2.ch.b.341.7 yes 56
8.3 odd 2 2016.2.cp.b.17.15 56
8.5 even 2 inner 504.2.ch.b.269.22 yes 56
12.11 even 2 2016.2.cp.b.17.16 56
21.5 even 6 inner 504.2.ch.b.341.22 yes 56
24.5 odd 2 inner 504.2.ch.b.269.7 56
24.11 even 2 2016.2.cp.b.17.13 56
28.19 even 6 2016.2.cp.b.593.13 56
56.5 odd 6 inner 504.2.ch.b.341.18 yes 56
56.19 even 6 2016.2.cp.b.593.16 56
84.47 odd 6 2016.2.cp.b.593.15 56
168.5 even 6 inner 504.2.ch.b.341.11 yes 56
168.131 odd 6 2016.2.cp.b.593.14 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.ch.b.269.7 56 24.5 odd 2 inner
504.2.ch.b.269.11 yes 56 1.1 even 1 trivial
504.2.ch.b.269.18 yes 56 3.2 odd 2 inner
504.2.ch.b.269.22 yes 56 8.5 even 2 inner
504.2.ch.b.341.7 yes 56 7.5 odd 6 inner
504.2.ch.b.341.11 yes 56 168.5 even 6 inner
504.2.ch.b.341.18 yes 56 56.5 odd 6 inner
504.2.ch.b.341.22 yes 56 21.5 even 6 inner
2016.2.cp.b.17.13 56 24.11 even 2
2016.2.cp.b.17.14 56 4.3 odd 2
2016.2.cp.b.17.15 56 8.3 odd 2
2016.2.cp.b.17.16 56 12.11 even 2
2016.2.cp.b.593.13 56 28.19 even 6
2016.2.cp.b.593.14 56 168.131 odd 6
2016.2.cp.b.593.15 56 84.47 odd 6
2016.2.cp.b.593.16 56 56.19 even 6