Properties

Label 475.2.u.c.74.2
Level $475$
Weight $2$
Character 475.74
Analytic conductor $3.793$
Analytic rank $0$
Dimension $36$
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] = [475,2,Mod(24,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.24");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.u (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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 74.2
Character \(\chi\) \(=\) 475.74
Dual form 475.2.u.c.199.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.44009 - 0.253927i) q^{2} +(0.970838 - 1.15700i) q^{3} +(0.130002 + 0.0473169i) q^{4} +(-1.69189 + 1.41966i) q^{6} +(3.52622 - 2.03586i) q^{7} +(2.35759 + 1.36116i) q^{8} +(0.124823 + 0.707907i) q^{9} +O(q^{10})\) \(q+(-1.44009 - 0.253927i) q^{2} +(0.970838 - 1.15700i) q^{3} +(0.130002 + 0.0473169i) q^{4} +(-1.69189 + 1.41966i) q^{6} +(3.52622 - 2.03586i) q^{7} +(2.35759 + 1.36116i) q^{8} +(0.124823 + 0.707907i) q^{9} +(0.310503 - 0.537807i) q^{11} +(0.180957 - 0.104475i) q^{12} +(3.27390 + 3.90168i) q^{13} +(-5.59504 + 2.03643i) q^{14} +(-3.26147 - 2.73670i) q^{16} +(-0.262435 - 0.0462744i) q^{17} -1.05115i q^{18} +(-0.399960 + 4.34051i) q^{19} +(1.06789 - 6.05632i) q^{21} +(-0.583716 + 0.695646i) q^{22} +(1.99799 - 5.48944i) q^{23} +(3.86370 - 1.40627i) q^{24} +(-3.72398 - 6.45012i) q^{26} +(4.86425 + 2.80837i) q^{27} +(0.554747 - 0.0978169i) q^{28} +(-0.708058 - 4.01560i) q^{29} +(3.24496 + 5.62043i) q^{31} +(0.502163 + 0.598455i) q^{32} +(-0.320794 - 0.881374i) q^{33} +(0.366180 + 0.133279i) q^{34} +(-0.0172687 + 0.0979357i) q^{36} -8.83927i q^{37} +(1.67815 - 6.14918i) q^{38} +7.69267 q^{39} +(-3.43252 - 2.88022i) q^{41} +(-3.07573 + 8.45050i) q^{42} +(-0.615885 - 1.69213i) q^{43} +(0.0658134 - 0.0552240i) q^{44} +(-4.27121 + 7.39795i) q^{46} +(-11.3711 + 2.00502i) q^{47} +(-6.33272 + 1.11663i) q^{48} +(4.78947 - 8.29561i) q^{49} +(-0.308321 + 0.258712i) q^{51} +(0.240999 + 0.662139i) q^{52} +(0.862891 - 2.37077i) q^{53} +(-6.29184 - 5.27948i) q^{54} +11.0845 q^{56} +(4.63367 + 4.67668i) q^{57} +5.96263i q^{58} +(-0.154624 + 0.876916i) q^{59} +(-2.03905 - 0.742153i) q^{61} +(-3.24586 - 8.91792i) q^{62} +(1.88135 + 2.24211i) q^{63} +(3.68635 + 6.38495i) q^{64} +(0.238168 + 1.35072i) q^{66} +(13.8649 - 2.44476i) q^{67} +(-0.0319276 - 0.0184334i) q^{68} +(-4.41155 - 7.64103i) q^{69} +(1.54737 - 0.563198i) q^{71} +(-0.669290 + 1.83886i) q^{72} +(1.15493 - 1.37639i) q^{73} +(-2.24453 + 12.7294i) q^{74} +(-0.257375 + 0.545351i) q^{76} -2.52856i q^{77} +(-11.0782 - 1.95338i) q^{78} +(-3.94242 - 3.30809i) q^{79} +(5.94525 - 2.16389i) q^{81} +(4.21177 + 5.01940i) q^{82} +(-11.9367 + 6.89167i) q^{83} +(0.425395 - 0.736806i) q^{84} +(0.457253 + 2.59321i) q^{86} +(-5.33345 - 3.07927i) q^{87} +(1.46408 - 0.845286i) q^{88} +(0.000572418 - 0.000480315i) q^{89} +(19.4878 + 7.09297i) q^{91} +(0.519487 - 0.619100i) q^{92} +(9.65316 + 1.70211i) q^{93} +16.8845 q^{94} +1.17993 q^{96} +(-10.2642 - 1.80985i) q^{97} +(-9.00376 + 10.7303i) q^{98} +(0.419475 + 0.152676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9} - 48 q^{14} + 42 q^{16} + 24 q^{19} + 6 q^{21} - 42 q^{24} - 42 q^{26} + 18 q^{29} + 60 q^{31} - 48 q^{34} - 42 q^{36} - 24 q^{39} - 12 q^{41} + 60 q^{44} + 42 q^{46} + 6 q^{49} + 54 q^{51} - 60 q^{54} - 144 q^{56} - 36 q^{59} + 12 q^{61} + 48 q^{64} - 66 q^{66} - 54 q^{69} + 48 q^{71} + 78 q^{74} + 54 q^{76} - 18 q^{79} + 30 q^{81} + 24 q^{84} - 66 q^{86} + 12 q^{89} - 12 q^{91} + 132 q^{94} - 36 q^{96} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.44009 0.253927i −1.01830 0.179554i −0.360510 0.932755i \(-0.617397\pi\)
−0.657789 + 0.753202i \(0.728508\pi\)
\(3\) 0.970838 1.15700i 0.560513 0.667994i −0.409142 0.912471i \(-0.634172\pi\)
0.969655 + 0.244477i \(0.0786163\pi\)
\(4\) 0.130002 + 0.0473169i 0.0650011 + 0.0236585i
\(5\) 0 0
\(6\) −1.69189 + 1.41966i −0.690711 + 0.579575i
\(7\) 3.52622 2.03586i 1.33278 0.769484i 0.347059 0.937843i \(-0.387180\pi\)
0.985726 + 0.168360i \(0.0538470\pi\)
\(8\) 2.35759 + 1.36116i 0.833535 + 0.481241i
\(9\) 0.124823 + 0.707907i 0.0416077 + 0.235969i
\(10\) 0 0
\(11\) 0.310503 0.537807i 0.0936201 0.162155i −0.815412 0.578881i \(-0.803489\pi\)
0.909032 + 0.416727i \(0.136823\pi\)
\(12\) 0.180957 0.104475i 0.0522377 0.0301595i
\(13\) 3.27390 + 3.90168i 0.908017 + 1.08213i 0.996292 + 0.0860363i \(0.0274201\pi\)
−0.0882750 + 0.996096i \(0.528135\pi\)
\(14\) −5.59504 + 2.03643i −1.49534 + 0.544258i
\(15\) 0 0
\(16\) −3.26147 2.73670i −0.815368 0.684175i
\(17\) −0.262435 0.0462744i −0.0636498 0.0112232i 0.141733 0.989905i \(-0.454733\pi\)
−0.205382 + 0.978682i \(0.565844\pi\)
\(18\) 1.05115i 0.247758i
\(19\) −0.399960 + 4.34051i −0.0917571 + 0.995781i
\(20\) 0 0
\(21\) 1.06789 6.05632i 0.233033 1.32160i
\(22\) −0.583716 + 0.695646i −0.124449 + 0.148312i
\(23\) 1.99799 5.48944i 0.416610 1.14463i −0.537000 0.843582i \(-0.680442\pi\)
0.953610 0.301045i \(-0.0973353\pi\)
\(24\) 3.86370 1.40627i 0.788674 0.287054i
\(25\) 0 0
\(26\) −3.72398 6.45012i −0.730332 1.26497i
\(27\) 4.86425 + 2.80837i 0.936125 + 0.540472i
\(28\) 0.554747 0.0978169i 0.104837 0.0184856i
\(29\) −0.708058 4.01560i −0.131483 0.745678i −0.977244 0.212116i \(-0.931964\pi\)
0.845761 0.533561i \(-0.179147\pi\)
\(30\) 0 0
\(31\) 3.24496 + 5.62043i 0.582811 + 1.00946i 0.995144 + 0.0984257i \(0.0313807\pi\)
−0.412333 + 0.911033i \(0.635286\pi\)
\(32\) 0.502163 + 0.598455i 0.0887708 + 0.105793i
\(33\) −0.320794 0.881374i −0.0558431 0.153428i
\(34\) 0.366180 + 0.133279i 0.0627994 + 0.0228571i
\(35\) 0 0
\(36\) −0.0172687 + 0.0979357i −0.00287812 + 0.0163226i
\(37\) 8.83927i 1.45317i −0.687078 0.726584i \(-0.741107\pi\)
0.687078 0.726584i \(-0.258893\pi\)
\(38\) 1.67815 6.14918i 0.272232 0.997528i
\(39\) 7.69267 1.23181
\(40\) 0 0
\(41\) −3.43252 2.88022i −0.536069 0.449815i 0.334122 0.942530i \(-0.391560\pi\)
−0.870191 + 0.492714i \(0.836005\pi\)
\(42\) −3.07573 + 8.45050i −0.474595 + 1.30394i
\(43\) −0.615885 1.69213i −0.0939215 0.258047i 0.883832 0.467804i \(-0.154955\pi\)
−0.977753 + 0.209757i \(0.932733\pi\)
\(44\) 0.0658134 0.0552240i 0.00992175 0.00832533i
\(45\) 0 0
\(46\) −4.27121 + 7.39795i −0.629756 + 1.09077i
\(47\) −11.3711 + 2.00502i −1.65864 + 0.292463i −0.922968 0.384877i \(-0.874244\pi\)
−0.735671 + 0.677339i \(0.763133\pi\)
\(48\) −6.33272 + 1.11663i −0.914050 + 0.161172i
\(49\) 4.78947 8.29561i 0.684210 1.18509i
\(50\) 0 0
\(51\) −0.308321 + 0.258712i −0.0431736 + 0.0362269i
\(52\) 0.240999 + 0.662139i 0.0334205 + 0.0918221i
\(53\) 0.862891 2.37077i 0.118527 0.325651i −0.866215 0.499672i \(-0.833454\pi\)
0.984742 + 0.174021i \(0.0556761\pi\)
\(54\) −6.29184 5.27948i −0.856212 0.718447i
\(55\) 0 0
\(56\) 11.0845 1.48123
\(57\) 4.63367 + 4.67668i 0.613745 + 0.619442i
\(58\) 5.96263i 0.782931i
\(59\) −0.154624 + 0.876916i −0.0201303 + 0.114165i −0.993217 0.116274i \(-0.962905\pi\)
0.973087 + 0.230439i \(0.0740161\pi\)
\(60\) 0 0
\(61\) −2.03905 0.742153i −0.261073 0.0950229i 0.208167 0.978093i \(-0.433250\pi\)
−0.469241 + 0.883070i \(0.655472\pi\)
\(62\) −3.24586 8.91792i −0.412224 1.13258i
\(63\) 1.88135 + 2.24211i 0.237028 + 0.282479i
\(64\) 3.68635 + 6.38495i 0.460794 + 0.798119i
\(65\) 0 0
\(66\) 0.238168 + 1.35072i 0.0293165 + 0.166262i
\(67\) 13.8649 2.44476i 1.69387 0.298674i 0.758322 0.651881i \(-0.226020\pi\)
0.935546 + 0.353206i \(0.114909\pi\)
\(68\) −0.0319276 0.0184334i −0.00387179 0.00223538i
\(69\) −4.41155 7.64103i −0.531088 0.919872i
\(70\) 0 0
\(71\) 1.54737 0.563198i 0.183639 0.0668393i −0.248564 0.968616i \(-0.579959\pi\)
0.432203 + 0.901776i \(0.357736\pi\)
\(72\) −0.669290 + 1.83886i −0.0788766 + 0.216712i
\(73\) 1.15493 1.37639i 0.135174 0.161095i −0.694211 0.719772i \(-0.744246\pi\)
0.829385 + 0.558677i \(0.188691\pi\)
\(74\) −2.24453 + 12.7294i −0.260922 + 1.47976i
\(75\) 0 0
\(76\) −0.257375 + 0.545351i −0.0295230 + 0.0625561i
\(77\) 2.52856i 0.288157i
\(78\) −11.0782 1.95338i −1.25435 0.221177i
\(79\) −3.94242 3.30809i −0.443557 0.372189i 0.393481 0.919333i \(-0.371271\pi\)
−0.837039 + 0.547144i \(0.815715\pi\)
\(80\) 0 0
\(81\) 5.94525 2.16389i 0.660584 0.240433i
\(82\) 4.21177 + 5.01940i 0.465113 + 0.554300i
\(83\) −11.9367 + 6.89167i −1.31023 + 0.756459i −0.982133 0.188187i \(-0.939739\pi\)
−0.328092 + 0.944646i \(0.606406\pi\)
\(84\) 0.425395 0.736806i 0.0464144 0.0803921i
\(85\) 0 0
\(86\) 0.457253 + 2.59321i 0.0493069 + 0.279633i
\(87\) −5.33345 3.07927i −0.571806 0.330132i
\(88\) 1.46408 0.845286i 0.156071 0.0901078i
\(89\) 0.000572418 0 0.000480315i 6.06762e−5 0 5.09133e-5i −0.642757 0.766070i \(-0.722210\pi\)
0.642818 + 0.766019i \(0.277765\pi\)
\(90\) 0 0
\(91\) 19.4878 + 7.09297i 2.04287 + 0.743545i
\(92\) 0.519487 0.619100i 0.0541603 0.0645457i
\(93\) 9.65316 + 1.70211i 1.00099 + 0.176501i
\(94\) 16.8845 1.74150
\(95\) 0 0
\(96\) 1.17993 0.120426
\(97\) −10.2642 1.80985i −1.04217 0.183762i −0.373736 0.927535i \(-0.621923\pi\)
−0.668432 + 0.743773i \(0.733034\pi\)
\(98\) −9.00376 + 10.7303i −0.909517 + 1.08392i
\(99\) 0.419475 + 0.152676i 0.0421588 + 0.0153445i
\(100\) 0 0
\(101\) −9.36086 + 7.85469i −0.931440 + 0.781571i −0.976075 0.217432i \(-0.930232\pi\)
0.0446350 + 0.999003i \(0.485788\pi\)
\(102\) 0.509705 0.294278i 0.0504683 0.0291379i
\(103\) −6.75822 3.90186i −0.665908 0.384462i 0.128617 0.991694i \(-0.458946\pi\)
−0.794524 + 0.607232i \(0.792280\pi\)
\(104\) 2.40772 + 13.6549i 0.236097 + 1.33897i
\(105\) 0 0
\(106\) −1.84465 + 3.19502i −0.179168 + 0.310328i
\(107\) 4.93993 2.85207i 0.477561 0.275720i −0.241839 0.970316i \(-0.577750\pi\)
0.719399 + 0.694597i \(0.244417\pi\)
\(108\) 0.499479 + 0.595256i 0.0480624 + 0.0572786i
\(109\) −6.32712 + 2.30288i −0.606029 + 0.220576i −0.626765 0.779209i \(-0.715621\pi\)
0.0207361 + 0.999785i \(0.493399\pi\)
\(110\) 0 0
\(111\) −10.2270 8.58150i −0.970707 0.814520i
\(112\) −17.0722 3.01029i −1.61317 0.284446i
\(113\) 4.78878i 0.450490i 0.974302 + 0.225245i \(0.0723183\pi\)
−0.974302 + 0.225245i \(0.927682\pi\)
\(114\) −5.48538 7.91147i −0.513753 0.740977i
\(115\) 0 0
\(116\) 0.0979567 0.555540i 0.00909505 0.0515806i
\(117\) −2.35337 + 2.80464i −0.217569 + 0.259289i
\(118\) 0.445346 1.22358i 0.0409974 0.112639i
\(119\) −1.01961 + 0.371108i −0.0934676 + 0.0340194i
\(120\) 0 0
\(121\) 5.30718 + 9.19230i 0.482471 + 0.835664i
\(122\) 2.74796 + 1.58654i 0.248789 + 0.143638i
\(123\) −6.66483 + 1.17519i −0.600948 + 0.105963i
\(124\) 0.155910 + 0.884210i 0.0140011 + 0.0794044i
\(125\) 0 0
\(126\) −2.13999 3.70657i −0.190646 0.330208i
\(127\) 11.8894 + 14.1693i 1.05502 + 1.25732i 0.965242 + 0.261356i \(0.0841698\pi\)
0.0897732 + 0.995962i \(0.471386\pi\)
\(128\) −4.22177 11.5992i −0.373155 1.02524i
\(129\) −2.55572 0.930204i −0.225018 0.0818999i
\(130\) 0 0
\(131\) −3.40080 + 19.2869i −0.297129 + 1.68510i 0.361291 + 0.932453i \(0.382336\pi\)
−0.658420 + 0.752650i \(0.728775\pi\)
\(132\) 0.129760i 0.0112941i
\(133\) 7.42634 + 16.1198i 0.643945 + 1.39777i
\(134\) −20.5875 −1.77849
\(135\) 0 0
\(136\) −0.555728 0.466311i −0.0476533 0.0399858i
\(137\) −0.806027 + 2.21454i −0.0688635 + 0.189201i −0.969350 0.245682i \(-0.920988\pi\)
0.900487 + 0.434883i \(0.143210\pi\)
\(138\) 4.41278 + 12.1240i 0.375640 + 1.03206i
\(139\) −2.93433 + 2.46220i −0.248887 + 0.208841i −0.758693 0.651448i \(-0.774162\pi\)
0.509806 + 0.860289i \(0.329717\pi\)
\(140\) 0 0
\(141\) −8.71964 + 15.1029i −0.734326 + 1.27189i
\(142\) −2.37137 + 0.418137i −0.199001 + 0.0350893i
\(143\) 3.11491 0.549242i 0.260482 0.0459299i
\(144\) 1.53022 2.65042i 0.127519 0.220869i
\(145\) 0 0
\(146\) −2.01271 + 1.68887i −0.166573 + 0.139772i
\(147\) −4.94821 13.5951i −0.408122 1.12130i
\(148\) 0.418247 1.14913i 0.0343797 0.0944575i
\(149\) −13.9310 11.6895i −1.14127 0.957638i −0.141789 0.989897i \(-0.545286\pi\)
−0.999480 + 0.0322585i \(0.989730\pi\)
\(150\) 0 0
\(151\) −2.29340 −0.186634 −0.0933170 0.995636i \(-0.529747\pi\)
−0.0933170 + 0.995636i \(0.529747\pi\)
\(152\) −6.85106 + 9.68875i −0.555694 + 0.785861i
\(153\) 0.191556i 0.0154863i
\(154\) −0.642071 + 3.64137i −0.0517396 + 0.293430i
\(155\) 0 0
\(156\) 1.00006 + 0.363994i 0.0800693 + 0.0291428i
\(157\) 7.12925 + 19.5874i 0.568976 + 1.56325i 0.806106 + 0.591771i \(0.201571\pi\)
−0.237130 + 0.971478i \(0.576207\pi\)
\(158\) 4.83744 + 5.76504i 0.384846 + 0.458642i
\(159\) −1.90526 3.30000i −0.151097 0.261707i
\(160\) 0 0
\(161\) −4.13039 23.4246i −0.325520 1.84612i
\(162\) −9.11119 + 1.60655i −0.715842 + 0.126222i
\(163\) −6.85624 3.95845i −0.537022 0.310050i 0.206849 0.978373i \(-0.433679\pi\)
−0.743871 + 0.668323i \(0.767012\pi\)
\(164\) −0.309952 0.536852i −0.0242031 0.0419211i
\(165\) 0 0
\(166\) 18.9400 6.89358i 1.47003 0.535046i
\(167\) 4.82025 13.2435i 0.373002 1.02482i −0.601192 0.799105i \(-0.705307\pi\)
0.974194 0.225711i \(-0.0724705\pi\)
\(168\) 10.7613 12.8248i 0.830249 0.989452i
\(169\) −2.24728 + 12.7450i −0.172868 + 0.980382i
\(170\) 0 0
\(171\) −3.12260 + 0.258662i −0.238791 + 0.0197803i
\(172\) 0.249122i 0.0189954i
\(173\) 10.3531 + 1.82553i 0.787130 + 0.138792i 0.552744 0.833351i \(-0.313581\pi\)
0.234386 + 0.972144i \(0.424692\pi\)
\(174\) 6.89876 + 5.78874i 0.522993 + 0.438843i
\(175\) 0 0
\(176\) −2.48451 + 0.904289i −0.187277 + 0.0681633i
\(177\) 0.864477 + 1.03024i 0.0649780 + 0.0774378i
\(178\) −0.000946300 0 0.000546346i −7.09282e−5 0 4.09504e-5i
\(179\) 2.50164 4.33298i 0.186982 0.323862i −0.757261 0.653113i \(-0.773463\pi\)
0.944243 + 0.329251i \(0.106796\pi\)
\(180\) 0 0
\(181\) −4.60022 26.0891i −0.341932 1.93919i −0.343395 0.939191i \(-0.611577\pi\)
0.00146347 0.999999i \(-0.499534\pi\)
\(182\) −26.2631 15.1630i −1.94675 1.12396i
\(183\) −2.83825 + 1.63867i −0.209810 + 0.121134i
\(184\) 12.1824 10.2223i 0.898101 0.753596i
\(185\) 0 0
\(186\) −13.4692 4.90240i −0.987612 0.359461i
\(187\) −0.106373 + 0.126771i −0.00777879 + 0.00927041i
\(188\) −1.57313 0.277386i −0.114733 0.0202305i
\(189\) 22.8699 1.66354
\(190\) 0 0
\(191\) −0.143815 −0.0104061 −0.00520303 0.999986i \(-0.501656\pi\)
−0.00520303 + 0.999986i \(0.501656\pi\)
\(192\) 10.9662 + 1.93364i 0.791420 + 0.139549i
\(193\) 1.32488 1.57893i 0.0953669 0.113654i −0.716250 0.697843i \(-0.754143\pi\)
0.811617 + 0.584190i \(0.198588\pi\)
\(194\) 14.3218 + 5.21270i 1.02824 + 0.374250i
\(195\) 0 0
\(196\) 1.01516 0.851824i 0.0725118 0.0608446i
\(197\) 15.8035 9.12413i 1.12595 0.650068i 0.183037 0.983106i \(-0.441407\pi\)
0.942913 + 0.333038i \(0.108074\pi\)
\(198\) −0.565314 0.326384i −0.0401751 0.0231951i
\(199\) −1.38971 7.88142i −0.0985137 0.558699i −0.993614 0.112834i \(-0.964007\pi\)
0.895100 0.445865i \(-0.147104\pi\)
\(200\) 0 0
\(201\) 10.6320 18.4151i 0.749922 1.29890i
\(202\) 15.4750 8.93451i 1.08882 0.628630i
\(203\) −10.6720 12.7184i −0.749026 0.892654i
\(204\) −0.0523239 + 0.0190443i −0.00366341 + 0.00133337i
\(205\) 0 0
\(206\) 8.74168 + 7.33514i 0.609062 + 0.511063i
\(207\) 4.13541 + 0.729184i 0.287431 + 0.0506818i
\(208\) 21.6849i 1.50358i
\(209\) 2.21017 + 1.56284i 0.152880 + 0.108104i
\(210\) 0 0
\(211\) −2.44545 + 13.8689i −0.168352 + 0.954772i 0.777189 + 0.629268i \(0.216645\pi\)
−0.945541 + 0.325504i \(0.894466\pi\)
\(212\) 0.224356 0.267377i 0.0154088 0.0183635i
\(213\) 0.850628 2.33708i 0.0582841 0.160134i
\(214\) −7.83817 + 2.85286i −0.535806 + 0.195018i
\(215\) 0 0
\(216\) 7.64528 + 13.2420i 0.520195 + 0.901004i
\(217\) 22.8848 + 13.2126i 1.55352 + 0.896928i
\(218\) 9.69641 1.70974i 0.656724 0.115798i
\(219\) −0.471235 2.67251i −0.0318431 0.180591i
\(220\) 0 0
\(221\) −0.678638 1.17544i −0.0456501 0.0790684i
\(222\) 12.5488 + 14.9551i 0.842220 + 1.00372i
\(223\) 1.67798 + 4.61022i 0.112366 + 0.308723i 0.983111 0.183012i \(-0.0585848\pi\)
−0.870744 + 0.491736i \(0.836363\pi\)
\(224\) 2.98911 + 1.08795i 0.199718 + 0.0726915i
\(225\) 0 0
\(226\) 1.21600 6.89629i 0.0808872 0.458734i
\(227\) 2.65246i 0.176050i 0.996118 + 0.0880250i \(0.0280555\pi\)
−0.996118 + 0.0880250i \(0.971944\pi\)
\(228\) 0.381101 + 0.827231i 0.0252390 + 0.0547847i
\(229\) 23.1372 1.52895 0.764473 0.644655i \(-0.222999\pi\)
0.764473 + 0.644655i \(0.222999\pi\)
\(230\) 0 0
\(231\) −2.92555 2.45482i −0.192487 0.161516i
\(232\) 3.79654 10.4309i 0.249255 0.684823i
\(233\) −9.88772 27.1663i −0.647766 1.77972i −0.625824 0.779964i \(-0.715237\pi\)
−0.0219420 0.999759i \(-0.506985\pi\)
\(234\) 4.10124 3.44135i 0.268107 0.224968i
\(235\) 0 0
\(236\) −0.0615945 + 0.106685i −0.00400946 + 0.00694458i
\(237\) −7.65490 + 1.34977i −0.497239 + 0.0876767i
\(238\) 1.56257 0.275523i 0.101286 0.0178595i
\(239\) −10.3736 + 17.9677i −0.671016 + 1.16223i 0.306601 + 0.951838i \(0.400808\pi\)
−0.977616 + 0.210395i \(0.932525\pi\)
\(240\) 0 0
\(241\) 4.74748 3.98361i 0.305812 0.256607i −0.476946 0.878932i \(-0.658256\pi\)
0.782759 + 0.622326i \(0.213812\pi\)
\(242\) −5.30865 14.5854i −0.341253 0.937585i
\(243\) −2.49487 + 6.85461i −0.160046 + 0.439724i
\(244\) −0.229964 0.192963i −0.0147220 0.0123532i
\(245\) 0 0
\(246\) 9.89639 0.630971
\(247\) −18.2447 + 12.6499i −1.16088 + 0.804893i
\(248\) 17.6676i 1.12189i
\(249\) −3.61496 + 20.5015i −0.229089 + 1.29923i
\(250\) 0 0
\(251\) −7.32016 2.66432i −0.462044 0.168170i 0.100501 0.994937i \(-0.467956\pi\)
−0.562545 + 0.826767i \(0.690178\pi\)
\(252\) 0.138490 + 0.380499i 0.00872408 + 0.0239692i
\(253\) −2.33187 2.77902i −0.146604 0.174715i
\(254\) −13.5239 23.4241i −0.848565 1.46976i
\(255\) 0 0
\(256\) 0.573868 + 3.25456i 0.0358667 + 0.203410i
\(257\) −19.8510 + 3.50026i −1.23827 + 0.218340i −0.754174 0.656675i \(-0.771962\pi\)
−0.484096 + 0.875015i \(0.660851\pi\)
\(258\) 3.44426 + 1.98855i 0.214430 + 0.123801i
\(259\) −17.9955 31.1692i −1.11819 1.93676i
\(260\) 0 0
\(261\) 2.75429 1.00248i 0.170486 0.0620518i
\(262\) 9.79493 26.9114i 0.605133 1.66259i
\(263\) 6.86869 8.18579i 0.423542 0.504758i −0.511506 0.859280i \(-0.670912\pi\)
0.935048 + 0.354522i \(0.115357\pi\)
\(264\) 0.443387 2.51457i 0.0272886 0.154761i
\(265\) 0 0
\(266\) −6.60135 25.0998i −0.404754 1.53897i
\(267\) 0.00112860i 6.90689e-5i
\(268\) 1.91815 + 0.338221i 0.117169 + 0.0206601i
\(269\) 18.3284 + 15.3793i 1.11750 + 0.937693i 0.998475 0.0551980i \(-0.0175790\pi\)
0.119024 + 0.992891i \(0.462023\pi\)
\(270\) 0 0
\(271\) −24.4040 + 8.88231i −1.48243 + 0.539562i −0.951446 0.307817i \(-0.900402\pi\)
−0.530989 + 0.847379i \(0.678179\pi\)
\(272\) 0.729285 + 0.869129i 0.0442194 + 0.0526987i
\(273\) 27.1260 15.6612i 1.64174 0.947860i
\(274\) 1.72309 2.98447i 0.104095 0.180299i
\(275\) 0 0
\(276\) −0.211961 1.20209i −0.0127586 0.0723574i
\(277\) 1.58803 + 0.916850i 0.0954156 + 0.0550882i 0.546949 0.837166i \(-0.315789\pi\)
−0.451533 + 0.892254i \(0.649123\pi\)
\(278\) 4.85093 2.80069i 0.290940 0.167974i
\(279\) −3.57369 + 2.99869i −0.213951 + 0.179527i
\(280\) 0 0
\(281\) 12.8592 + 4.68035i 0.767114 + 0.279207i 0.695789 0.718247i \(-0.255055\pi\)
0.0713251 + 0.997453i \(0.477277\pi\)
\(282\) 16.3921 19.5354i 0.976136 1.16331i
\(283\) −10.3762 1.82961i −0.616803 0.108759i −0.143488 0.989652i \(-0.545832\pi\)
−0.473315 + 0.880893i \(0.656943\pi\)
\(284\) 0.227811 0.0135181
\(285\) 0 0
\(286\) −4.62522 −0.273495
\(287\) −17.9675 3.16816i −1.06059 0.187011i
\(288\) −0.360969 + 0.430186i −0.0212703 + 0.0253489i
\(289\) −15.9080 5.79005i −0.935767 0.340591i
\(290\) 0 0
\(291\) −12.0588 + 10.1186i −0.706901 + 0.593161i
\(292\) 0.215270 0.124286i 0.0125977 0.00727331i
\(293\) 20.7017 + 11.9521i 1.20941 + 0.698251i 0.962630 0.270822i \(-0.0872953\pi\)
0.246776 + 0.969072i \(0.420629\pi\)
\(294\) 3.67372 + 20.8347i 0.214256 + 1.21510i
\(295\) 0 0
\(296\) 12.0316 20.8394i 0.699325 1.21127i
\(297\) 3.02072 1.74402i 0.175280 0.101198i
\(298\) 17.0936 + 20.3714i 0.990206 + 1.18008i
\(299\) 27.9593 10.1763i 1.61693 0.588513i
\(300\) 0 0
\(301\) −5.61668 4.71296i −0.323740 0.271650i
\(302\) 3.30271 + 0.582356i 0.190049 + 0.0335108i
\(303\) 18.4561i 1.06028i
\(304\) 13.1831 13.0619i 0.756105 0.749151i
\(305\) 0 0
\(306\) −0.0486412 + 0.275858i −0.00278063 + 0.0157697i
\(307\) −10.0716 + 12.0029i −0.574817 + 0.685040i −0.972612 0.232434i \(-0.925331\pi\)
0.397795 + 0.917474i \(0.369775\pi\)
\(308\) 0.119644 0.328719i 0.00681734 0.0187305i
\(309\) −11.0756 + 4.03118i −0.630068 + 0.229326i
\(310\) 0 0
\(311\) 1.75605 + 3.04157i 0.0995764 + 0.172471i 0.911509 0.411279i \(-0.134918\pi\)
−0.811933 + 0.583751i \(0.801585\pi\)
\(312\) 18.1362 + 10.4709i 1.02676 + 0.592800i
\(313\) 1.15525 0.203702i 0.0652987 0.0115139i −0.140903 0.990023i \(-0.545001\pi\)
0.206202 + 0.978509i \(0.433890\pi\)
\(314\) −5.29299 30.0180i −0.298701 1.69402i
\(315\) 0 0
\(316\) −0.355995 0.616602i −0.0200263 0.0346866i
\(317\) −0.843086 1.00475i −0.0473524 0.0564324i 0.741848 0.670568i \(-0.233949\pi\)
−0.789201 + 0.614135i \(0.789505\pi\)
\(318\) 1.90579 + 5.23610i 0.106871 + 0.293626i
\(319\) −2.37947 0.866056i −0.133225 0.0484898i
\(320\) 0 0
\(321\) 1.49603 8.48439i 0.0835000 0.473552i
\(322\) 34.7824i 1.93835i
\(323\) 0.305818 1.12059i 0.0170162 0.0623515i
\(324\) 0.875285 0.0486270
\(325\) 0 0
\(326\) 8.86847 + 7.44153i 0.491179 + 0.412148i
\(327\) −3.47817 + 9.55620i −0.192343 + 0.528459i
\(328\) −4.17204 11.4626i −0.230362 0.632915i
\(329\) −36.0148 + 30.2200i −1.98556 + 1.66609i
\(330\) 0 0
\(331\) 6.36245 11.0201i 0.349712 0.605718i −0.636487 0.771288i \(-0.719613\pi\)
0.986198 + 0.165570i \(0.0529462\pi\)
\(332\) −1.87789 + 0.331123i −0.103063 + 0.0181727i
\(333\) 6.25738 1.10335i 0.342902 0.0604629i
\(334\) −10.3045 + 17.8479i −0.563837 + 0.976595i
\(335\) 0 0
\(336\) −20.0572 + 16.8300i −1.09421 + 0.918153i
\(337\) −5.20541 14.3017i −0.283557 0.779066i −0.996931 0.0782827i \(-0.975056\pi\)
0.713374 0.700783i \(-0.247166\pi\)
\(338\) 6.47258 17.7833i 0.352062 0.967283i
\(339\) 5.54061 + 4.64913i 0.300925 + 0.252506i
\(340\) 0 0
\(341\) 4.03027 0.218251
\(342\) 4.56251 + 0.420417i 0.246713 + 0.0227335i
\(343\) 10.5007i 0.566987i
\(344\) 0.851248 4.82766i 0.0458962 0.260290i
\(345\) 0 0
\(346\) −14.4458 5.25786i −0.776613 0.282664i
\(347\) −6.84652 18.8107i −0.367541 1.00981i −0.976294 0.216450i \(-0.930552\pi\)
0.608753 0.793360i \(-0.291670\pi\)
\(348\) −0.547659 0.652675i −0.0293576 0.0349870i
\(349\) 11.1408 + 19.2964i 0.596353 + 1.03291i 0.993354 + 0.115095i \(0.0367174\pi\)
−0.397002 + 0.917818i \(0.629949\pi\)
\(350\) 0 0
\(351\) 4.96768 + 28.1731i 0.265155 + 1.50377i
\(352\) 0.477776 0.0842448i 0.0254655 0.00449026i
\(353\) −22.7029 13.1075i −1.20835 0.697642i −0.245952 0.969282i \(-0.579101\pi\)
−0.962399 + 0.271640i \(0.912434\pi\)
\(354\) −0.983319 1.70316i −0.0522628 0.0905219i
\(355\) 0 0
\(356\) 9.71426e−5 0 3.53570e-5i 5.14855e−6 0 1.87392e-6i
\(357\) −0.560505 + 1.53997i −0.0296651 + 0.0815041i
\(358\) −4.70286 + 5.60465i −0.248554 + 0.296215i
\(359\) −4.91047 + 27.8486i −0.259164 + 1.46979i 0.525988 + 0.850492i \(0.323696\pi\)
−0.785152 + 0.619303i \(0.787415\pi\)
\(360\) 0 0
\(361\) −18.6801 3.47206i −0.983161 0.182740i
\(362\) 38.7389i 2.03607i
\(363\) 15.7879 + 2.78383i 0.828649 + 0.146113i
\(364\) 2.19784 + 1.84420i 0.115198 + 0.0966626i
\(365\) 0 0
\(366\) 4.50345 1.63912i 0.235399 0.0856783i
\(367\) −6.16747 7.35010i −0.321939 0.383672i 0.580666 0.814142i \(-0.302792\pi\)
−0.902605 + 0.430470i \(0.858348\pi\)
\(368\) −21.5394 + 12.4358i −1.12282 + 0.648258i
\(369\) 1.61047 2.78942i 0.0838378 0.145211i
\(370\) 0 0
\(371\) −1.78383 10.1166i −0.0926117 0.525227i
\(372\) 1.17439 + 0.678036i 0.0608895 + 0.0351545i
\(373\) −11.2930 + 6.52003i −0.584731 + 0.337595i −0.763011 0.646385i \(-0.776280\pi\)
0.178280 + 0.983980i \(0.442947\pi\)
\(374\) 0.185378 0.155551i 0.00958568 0.00804334i
\(375\) 0 0
\(376\) −29.5375 10.7508i −1.52328 0.554428i
\(377\) 13.3495 15.9093i 0.687533 0.819370i
\(378\) −32.9347 5.80728i −1.69398 0.298694i
\(379\) −9.93895 −0.510530 −0.255265 0.966871i \(-0.582163\pi\)
−0.255265 + 0.966871i \(0.582163\pi\)
\(380\) 0 0
\(381\) 27.9365 1.43123
\(382\) 0.207106 + 0.0365184i 0.0105965 + 0.00186845i
\(383\) −11.5885 + 13.8106i −0.592144 + 0.705689i −0.976017 0.217697i \(-0.930146\pi\)
0.383873 + 0.923386i \(0.374590\pi\)
\(384\) −17.5189 6.37637i −0.894009 0.325393i
\(385\) 0 0
\(386\) −2.30888 + 1.93738i −0.117519 + 0.0986102i
\(387\) 1.12099 0.647205i 0.0569833 0.0328993i
\(388\) −1.24873 0.720954i −0.0633946 0.0366009i
\(389\) −4.22852 23.9811i −0.214395 1.21589i −0.881954 0.471336i \(-0.843772\pi\)
0.667559 0.744557i \(-0.267339\pi\)
\(390\) 0 0
\(391\) −0.778363 + 1.34816i −0.0393635 + 0.0681796i
\(392\) 22.5832 13.0384i 1.14063 0.658541i
\(393\) 19.0133 + 22.6592i 0.959094 + 1.14300i
\(394\) −25.0753 + 9.12667i −1.26328 + 0.459795i
\(395\) 0 0
\(396\) 0.0473085 + 0.0396965i 0.00237734 + 0.00199483i
\(397\) −19.6684 3.46808i −0.987131 0.174058i −0.343300 0.939226i \(-0.611545\pi\)
−0.643831 + 0.765168i \(0.722656\pi\)
\(398\) 11.7029i 0.586611i
\(399\) 25.8604 + 7.05749i 1.29464 + 0.353316i
\(400\) 0 0
\(401\) −2.84848 + 16.1545i −0.142246 + 0.806718i 0.827291 + 0.561774i \(0.189881\pi\)
−0.969537 + 0.244944i \(0.921230\pi\)
\(402\) −19.9871 + 23.8198i −0.996868 + 1.18802i
\(403\) −11.3055 + 31.0615i −0.563166 + 1.54728i
\(404\) −1.58859 + 0.578201i −0.0790355 + 0.0287666i
\(405\) 0 0
\(406\) 12.1391 + 21.0255i 0.602453 + 1.04348i
\(407\) −4.75382 2.74462i −0.235638 0.136046i
\(408\) −1.07904 + 0.190264i −0.0534206 + 0.00941949i
\(409\) −1.44702 8.20643i −0.0715503 0.405782i −0.999456 0.0329680i \(-0.989504\pi\)
0.927906 0.372814i \(-0.121607\pi\)
\(410\) 0 0
\(411\) 1.77970 + 3.08253i 0.0877862 + 0.152050i
\(412\) −0.693960 0.827029i −0.0341890 0.0407448i
\(413\) 1.24004 + 3.40699i 0.0610185 + 0.167647i
\(414\) −5.77021 2.10018i −0.283590 0.103218i
\(415\) 0 0
\(416\) −0.690949 + 3.91856i −0.0338765 + 0.192123i
\(417\) 5.78542i 0.283313i
\(418\) −2.78600 2.81186i −0.136268 0.137532i
\(419\) 11.6553 0.569397 0.284698 0.958617i \(-0.408107\pi\)
0.284698 + 0.958617i \(0.408107\pi\)
\(420\) 0 0
\(421\) 16.2337 + 13.6217i 0.791182 + 0.663881i 0.946038 0.324056i \(-0.105047\pi\)
−0.154855 + 0.987937i \(0.549491\pi\)
\(422\) 7.04336 19.3515i 0.342866 0.942015i
\(423\) −2.83874 7.79937i −0.138024 0.379218i
\(424\) 5.26134 4.41479i 0.255513 0.214401i
\(425\) 0 0
\(426\) −1.81843 + 3.14962i −0.0881033 + 0.152599i
\(427\) −8.70105 + 1.53423i −0.421073 + 0.0742465i
\(428\) 0.777153 0.137033i 0.0375651 0.00662374i
\(429\) 2.38860 4.13717i 0.115322 0.199744i
\(430\) 0 0
\(431\) 0.300492 0.252142i 0.0144742 0.0121453i −0.635522 0.772083i \(-0.719215\pi\)
0.649996 + 0.759938i \(0.274771\pi\)
\(432\) −8.17893 22.4714i −0.393509 1.08116i
\(433\) −4.43639 + 12.1889i −0.213199 + 0.585761i −0.999485 0.0321031i \(-0.989780\pi\)
0.786285 + 0.617864i \(0.212002\pi\)
\(434\) −29.6013 24.8384i −1.42091 1.19228i
\(435\) 0 0
\(436\) −0.931506 −0.0446110
\(437\) 23.0278 + 10.8679i 1.10157 + 0.519880i
\(438\) 3.96832i 0.189614i
\(439\) 0.946035 5.36523i 0.0451518 0.256068i −0.953874 0.300209i \(-0.902944\pi\)
0.999025 + 0.0441401i \(0.0140548\pi\)
\(440\) 0 0
\(441\) 6.47035 + 2.35502i 0.308112 + 0.112144i
\(442\) 0.678827 + 1.86506i 0.0322885 + 0.0887119i
\(443\) −15.9043 18.9540i −0.755636 0.900532i 0.241928 0.970294i \(-0.422220\pi\)
−0.997564 + 0.0697627i \(0.977776\pi\)
\(444\) −0.923487 1.59953i −0.0438267 0.0759102i
\(445\) 0 0
\(446\) −1.24579 7.06523i −0.0589899 0.334549i
\(447\) −27.0494 + 4.76954i −1.27939 + 0.225591i
\(448\) 25.9978 + 15.0098i 1.22828 + 0.709147i
\(449\) 17.2809 + 29.9315i 0.815538 + 1.41255i 0.908941 + 0.416925i \(0.136892\pi\)
−0.0934033 + 0.995628i \(0.529775\pi\)
\(450\) 0 0
\(451\) −2.61481 + 0.951713i −0.123127 + 0.0448144i
\(452\) −0.226590 + 0.622552i −0.0106579 + 0.0292824i
\(453\) −2.22652 + 2.65346i −0.104611 + 0.124670i
\(454\) 0.673532 3.81979i 0.0316104 0.179272i
\(455\) 0 0
\(456\) 4.55861 + 17.3329i 0.213476 + 0.811686i
\(457\) 11.6425i 0.544613i −0.962211 0.272307i \(-0.912214\pi\)
0.962211 0.272307i \(-0.0877865\pi\)
\(458\) −33.3197 5.87515i −1.55693 0.274528i
\(459\) −1.14659 0.962106i −0.0535184 0.0449072i
\(460\) 0 0
\(461\) −2.80943 + 1.02255i −0.130848 + 0.0476248i −0.406614 0.913600i \(-0.633291\pi\)
0.275766 + 0.961225i \(0.411068\pi\)
\(462\) 3.58971 + 4.27805i 0.167008 + 0.199033i
\(463\) 7.35009 4.24358i 0.341588 0.197216i −0.319386 0.947625i \(-0.603477\pi\)
0.660974 + 0.750409i \(0.270143\pi\)
\(464\) −8.68018 + 15.0345i −0.402967 + 0.697960i
\(465\) 0 0
\(466\) 7.34098 + 41.6327i 0.340064 + 1.92860i
\(467\) −15.5280 8.96512i −0.718552 0.414856i 0.0956676 0.995413i \(-0.469501\pi\)
−0.814219 + 0.580557i \(0.802835\pi\)
\(468\) −0.438650 + 0.253255i −0.0202766 + 0.0117067i
\(469\) 43.9135 36.8478i 2.02774 1.70147i
\(470\) 0 0
\(471\) 29.5840 + 10.7677i 1.36316 + 0.496149i
\(472\) −1.55816 + 1.85694i −0.0717201 + 0.0854727i
\(473\) −1.10127 0.194184i −0.0506365 0.00892859i
\(474\) 11.3665 0.522081
\(475\) 0 0
\(476\) −0.150111 −0.00688034
\(477\) 1.78599 + 0.314919i 0.0817751 + 0.0144192i
\(478\) 19.5015 23.2410i 0.891978 1.06302i
\(479\) 3.18514 + 1.15929i 0.145533 + 0.0529695i 0.413759 0.910386i \(-0.364215\pi\)
−0.268227 + 0.963356i \(0.586438\pi\)
\(480\) 0 0
\(481\) 34.4881 28.9389i 1.57252 1.31950i
\(482\) −7.84836 + 4.53125i −0.357483 + 0.206393i
\(483\) −31.1122 17.9626i −1.41565 0.817327i
\(484\) 0.254993 + 1.44614i 0.0115906 + 0.0657336i
\(485\) 0 0
\(486\) 5.33342 9.23776i 0.241929 0.419033i
\(487\) −9.66655 + 5.58098i −0.438033 + 0.252899i −0.702763 0.711424i \(-0.748051\pi\)
0.264730 + 0.964323i \(0.414717\pi\)
\(488\) −3.79706 4.52516i −0.171885 0.204844i
\(489\) −11.2362 + 4.08965i −0.508120 + 0.184940i
\(490\) 0 0
\(491\) 17.6060 + 14.7732i 0.794547 + 0.666704i 0.946866 0.321627i \(-0.104230\pi\)
−0.152320 + 0.988331i \(0.548674\pi\)
\(492\) −0.922050 0.162582i −0.0415692 0.00732977i
\(493\) 1.08660i 0.0489379i
\(494\) 29.4862 13.5842i 1.32665 0.611181i
\(495\) 0 0
\(496\) 4.79810 27.2114i 0.215441 1.22183i
\(497\) 4.30978 5.13620i 0.193320 0.230390i
\(498\) 10.4118 28.6061i 0.466562 1.28187i
\(499\) 0.921587 0.335430i 0.0412559 0.0150159i −0.321310 0.946974i \(-0.604123\pi\)
0.362566 + 0.931958i \(0.381901\pi\)
\(500\) 0 0
\(501\) −10.6431 18.4343i −0.475498 0.823586i
\(502\) 9.86516 + 5.69566i 0.440304 + 0.254210i
\(503\) 3.51768 0.620262i 0.156846 0.0276561i −0.0946739 0.995508i \(-0.530181\pi\)
0.251520 + 0.967852i \(0.419070\pi\)
\(504\) 1.38360 + 7.84680i 0.0616305 + 0.349524i
\(505\) 0 0
\(506\) 2.65245 + 4.59417i 0.117916 + 0.204236i
\(507\) 12.5642 + 14.9734i 0.557994 + 0.664991i
\(508\) 0.875205 + 2.40461i 0.0388310 + 0.106687i
\(509\) −12.2069 4.44293i −0.541059 0.196929i 0.0570105 0.998374i \(-0.481843\pi\)
−0.598070 + 0.801444i \(0.704065\pi\)
\(510\) 0 0
\(511\) 1.27039 7.20474i 0.0561988 0.318719i
\(512\) 19.8547i 0.877460i
\(513\) −14.1353 + 19.9901i −0.624088 + 0.882584i
\(514\) 29.4761 1.30013
\(515\) 0 0
\(516\) −0.288234 0.241857i −0.0126888 0.0106472i
\(517\) −2.45243 + 6.73799i −0.107858 + 0.296337i
\(518\) 18.0005 + 49.4561i 0.790898 + 2.17298i
\(519\) 12.1633 10.2062i 0.533909 0.448003i
\(520\) 0 0
\(521\) −11.4598 + 19.8490i −0.502064 + 0.869601i 0.497933 + 0.867216i \(0.334093\pi\)
−0.999997 + 0.00238537i \(0.999241\pi\)
\(522\) −4.22098 + 0.744273i −0.184747 + 0.0325760i
\(523\) 1.94240 0.342497i 0.0849352 0.0149764i −0.131019 0.991380i \(-0.541825\pi\)
0.215954 + 0.976403i \(0.430714\pi\)
\(524\) −1.35471 + 2.34642i −0.0591807 + 0.102504i
\(525\) 0 0
\(526\) −11.9702 + 10.0441i −0.521923 + 0.437946i
\(527\) −0.591508 1.62515i −0.0257665 0.0707929i
\(528\) −1.36580 + 3.75250i −0.0594387 + 0.163306i
\(529\) −8.52294 7.15159i −0.370563 0.310939i
\(530\) 0 0
\(531\) −0.640075 −0.0277769
\(532\) 0.202699 + 2.44701i 0.00878810 + 0.106091i
\(533\) 22.8222i 0.988538i
\(534\) −0.000286581 0.00162528i −1.24016e−5 7.03328e-5i
\(535\) 0 0
\(536\) 36.0155 + 13.1086i 1.55563 + 0.566204i
\(537\) −2.58456 7.10102i −0.111532 0.306431i
\(538\) −22.4893 26.8017i −0.969583 1.15550i
\(539\) −2.97429 5.15162i −0.128112 0.221896i
\(540\) 0 0
\(541\) −4.78002 27.1088i −0.205509 1.16550i −0.896637 0.442767i \(-0.853997\pi\)
0.691128 0.722733i \(-0.257114\pi\)
\(542\) 37.3994 6.59452i 1.60644 0.283259i
\(543\) −34.6512 20.0059i −1.48702 0.858534i
\(544\) −0.104092 0.180293i −0.00446291 0.00772999i
\(545\) 0 0
\(546\) −43.0408 + 15.6656i −1.84198 + 0.670425i
\(547\) 2.85466 7.84310i 0.122056 0.335347i −0.863584 0.504205i \(-0.831786\pi\)
0.985640 + 0.168858i \(0.0540079\pi\)
\(548\) −0.209571 + 0.249757i −0.00895241 + 0.0106691i
\(549\) 0.270855 1.53609i 0.0115598 0.0655589i
\(550\) 0 0
\(551\) 17.7129 1.46726i 0.754597 0.0625072i
\(552\) 24.0192i 1.02233i
\(553\) −20.6366 3.63880i −0.877559 0.154737i
\(554\) −2.05410 1.72359i −0.0872703 0.0732285i
\(555\) 0 0
\(556\) −0.497974 + 0.181248i −0.0211188 + 0.00768661i
\(557\) 15.3198 + 18.2574i 0.649120 + 0.773591i 0.985781 0.168035i \(-0.0537421\pi\)
−0.336661 + 0.941626i \(0.609298\pi\)
\(558\) 5.90790 3.41093i 0.250101 0.144396i
\(559\) 4.58581 7.94285i 0.193959 0.335947i
\(560\) 0 0
\(561\) 0.0434025 + 0.246148i 0.00183246 + 0.0103924i
\(562\) −17.3299 10.0054i −0.731019 0.422054i
\(563\) 16.9979 9.81371i 0.716374 0.413599i −0.0970426 0.995280i \(-0.530938\pi\)
0.813417 + 0.581681i \(0.197605\pi\)
\(564\) −1.84819 + 1.55082i −0.0778230 + 0.0653012i
\(565\) 0 0
\(566\) 14.4782 + 5.26962i 0.608562 + 0.221499i
\(567\) 16.5589 19.7341i 0.695407 0.828753i
\(568\) 4.41467 + 0.778426i 0.185236 + 0.0326620i
\(569\) −23.7705 −0.996510 −0.498255 0.867030i \(-0.666026\pi\)
−0.498255 + 0.867030i \(0.666026\pi\)
\(570\) 0 0
\(571\) −17.5361 −0.733865 −0.366933 0.930248i \(-0.619592\pi\)
−0.366933 + 0.930248i \(0.619592\pi\)
\(572\) 0.430933 + 0.0759852i 0.0180182 + 0.00317710i
\(573\) −0.139621 + 0.166393i −0.00583273 + 0.00695118i
\(574\) 25.0704 + 9.12489i 1.04642 + 0.380866i
\(575\) 0 0
\(576\) −4.05981 + 3.40658i −0.169159 + 0.141941i
\(577\) −22.4543 + 12.9640i −0.934786 + 0.539699i −0.888322 0.459221i \(-0.848128\pi\)
−0.0464636 + 0.998920i \(0.514795\pi\)
\(578\) 21.4388 + 12.3777i 0.891737 + 0.514844i
\(579\) −0.540578 3.06577i −0.0224656 0.127409i
\(580\) 0 0
\(581\) −28.0610 + 48.6030i −1.16417 + 2.01639i
\(582\) 19.9352 11.5096i 0.826341 0.477088i
\(583\) −1.00709 1.20020i −0.0417093 0.0497072i
\(584\) 4.59634 1.67293i 0.190198 0.0692264i
\(585\) 0 0
\(586\) −26.7774 22.4689i −1.10616 0.928182i
\(587\) −3.98064 0.701894i −0.164299 0.0289703i 0.0908937 0.995861i \(-0.471028\pi\)
−0.255192 + 0.966890i \(0.582139\pi\)
\(588\) 2.00153i 0.0825416i
\(589\) −25.6934 + 11.8368i −1.05868 + 0.487728i
\(590\) 0 0
\(591\) 4.78598 27.1426i 0.196869 1.11650i
\(592\) −24.1905 + 28.8291i −0.994221 + 1.18487i
\(593\) −6.44918 + 17.7190i −0.264836 + 0.727631i 0.733988 + 0.679162i \(0.237657\pi\)
−0.998825 + 0.0484695i \(0.984566\pi\)
\(594\) −4.79298 + 1.74450i −0.196658 + 0.0715777i
\(595\) 0 0
\(596\) −1.25795 2.17883i −0.0515275 0.0892482i
\(597\) −10.4680 6.04369i −0.428426 0.247352i
\(598\) −42.8480 + 7.55526i −1.75219 + 0.308958i
\(599\) 6.74122 + 38.2313i 0.275439 + 1.56209i 0.737565 + 0.675276i \(0.235976\pi\)
−0.462126 + 0.886814i \(0.652913\pi\)
\(600\) 0 0
\(601\) −0.179210 0.310400i −0.00731011 0.0126615i 0.862347 0.506317i \(-0.168994\pi\)
−0.869657 + 0.493656i \(0.835660\pi\)
\(602\) 6.89180 + 8.21332i 0.280889 + 0.334750i
\(603\) 3.46132 + 9.50989i 0.140956 + 0.387273i
\(604\) −0.298147 0.108517i −0.0121314 0.00441548i
\(605\) 0 0
\(606\) 4.68652 26.5785i 0.190377 1.07968i
\(607\) 4.56885i 0.185444i 0.995692 + 0.0927219i \(0.0295568\pi\)
−0.995692 + 0.0927219i \(0.970443\pi\)
\(608\) −2.79844 + 1.94029i −0.113492 + 0.0786890i
\(609\) −25.0759 −1.01613
\(610\) 0 0
\(611\) −45.0507 37.8020i −1.82256 1.52931i
\(612\) 0.00906382 0.0249026i 0.000366383 0.00100663i
\(613\) 5.77762 + 15.8739i 0.233356 + 0.641140i 1.00000 0.000932984i \(-0.000296978\pi\)
−0.766644 + 0.642073i \(0.778075\pi\)
\(614\) 17.5519 14.7278i 0.708337 0.594365i
\(615\) 0 0
\(616\) 3.44177 5.96132i 0.138673 0.240188i
\(617\) −23.9952 + 4.23101i −0.966011 + 0.170334i −0.634334 0.773059i \(-0.718726\pi\)
−0.331677 + 0.943393i \(0.607615\pi\)
\(618\) 16.9735 2.99289i 0.682774 0.120392i
\(619\) −16.6616 + 28.8588i −0.669687 + 1.15993i 0.308305 + 0.951288i \(0.400238\pi\)
−0.977992 + 0.208644i \(0.933095\pi\)
\(620\) 0 0
\(621\) 25.1351 21.0909i 1.00864 0.846348i
\(622\) −1.75654 4.82605i −0.0704307 0.193507i
\(623\) 0.00104061 0.00285906i 4.16913e−5 0.000114546i
\(624\) −25.0894 21.0525i −1.00438 0.842776i
\(625\) 0 0
\(626\) −1.71540 −0.0685610
\(627\) 3.95392 1.03990i 0.157904 0.0415294i
\(628\) 2.88375i 0.115074i
\(629\) −0.409032 + 2.31973i −0.0163092 + 0.0924939i
\(630\) 0 0
\(631\) −35.2681 12.8365i −1.40400 0.511014i −0.474637 0.880181i \(-0.657421\pi\)
−0.929363 + 0.369167i \(0.879643\pi\)
\(632\) −4.79180 13.1654i −0.190608 0.523690i
\(633\) 13.6721 + 16.2938i 0.543418 + 0.647621i
\(634\) 0.958988 + 1.66102i 0.0380863 + 0.0659674i
\(635\) 0 0
\(636\) −0.0915416 0.519158i −0.00362986 0.0205860i
\(637\) 48.0471 8.47200i 1.90370 0.335673i
\(638\) 3.20674 + 1.85141i 0.126956 + 0.0732981i
\(639\) 0.591839 + 1.02510i 0.0234128 + 0.0405522i
\(640\) 0 0
\(641\) 6.62106 2.40987i 0.261516 0.0951841i −0.207935 0.978143i \(-0.566674\pi\)
0.469451 + 0.882959i \(0.344452\pi\)
\(642\) −4.30883 + 11.8384i −0.170056 + 0.467225i
\(643\) 9.82279 11.7063i 0.387373 0.461653i −0.536754 0.843739i \(-0.680350\pi\)
0.924127 + 0.382086i \(0.124794\pi\)
\(644\) 0.571420 3.24069i 0.0225171 0.127701i
\(645\) 0 0
\(646\) −0.724955 + 1.53610i −0.0285230 + 0.0604372i
\(647\) 23.8972i 0.939495i 0.882801 + 0.469748i \(0.155655\pi\)
−0.882801 + 0.469748i \(0.844345\pi\)
\(648\) 16.9619 + 2.99084i 0.666326 + 0.117491i
\(649\) 0.423600 + 0.355443i 0.0166278 + 0.0139523i
\(650\) 0 0
\(651\) 37.5044 13.6505i 1.46991 0.535005i
\(652\) −0.704025 0.839024i −0.0275718 0.0328587i
\(653\) 23.5046 13.5704i 0.919805 0.531050i 0.0362323 0.999343i \(-0.488464\pi\)
0.883573 + 0.468294i \(0.155131\pi\)
\(654\) 7.43547 12.8786i 0.290750 0.503594i
\(655\) 0 0
\(656\) 3.31275 + 18.7875i 0.129341 + 0.733530i
\(657\) 1.11852 + 0.645778i 0.0436376 + 0.0251942i
\(658\) 59.5384 34.3745i 2.32105 1.34006i
\(659\) 35.1081 29.4592i 1.36762 1.14757i 0.394073 0.919079i \(-0.371066\pi\)
0.973546 0.228490i \(-0.0733787\pi\)
\(660\) 0 0
\(661\) −17.2794 6.28920i −0.672092 0.244622i −0.0166438 0.999861i \(-0.505298\pi\)
−0.655448 + 0.755240i \(0.727520\pi\)
\(662\) −11.9608 + 14.2543i −0.464870 + 0.554010i
\(663\) −2.01883 0.355973i −0.0784047 0.0138249i
\(664\) −37.5226 −1.45616
\(665\) 0 0
\(666\) −9.29138 −0.360034
\(667\) −23.4581 4.13629i −0.908300 0.160158i
\(668\) 1.25329 1.49361i 0.0484911 0.0577895i
\(669\) 6.96308 + 2.53435i 0.269208 + 0.0979837i
\(670\) 0 0
\(671\) −1.03226 + 0.866173i −0.0398501 + 0.0334382i
\(672\) 4.16069 2.40218i 0.160502 0.0926660i
\(673\) −5.04007 2.90989i −0.194280 0.112168i 0.399704 0.916644i \(-0.369113\pi\)
−0.593985 + 0.804476i \(0.702446\pi\)
\(674\) 3.86467 + 21.9176i 0.148862 + 0.844236i
\(675\) 0 0
\(676\) −0.895204 + 1.55054i −0.0344309 + 0.0596361i
\(677\) 15.4877 8.94182i 0.595240 0.343662i −0.171926 0.985110i \(-0.554999\pi\)
0.767167 + 0.641448i \(0.221666\pi\)
\(678\) −6.79846 8.10209i −0.261093 0.311159i
\(679\) −39.8783 + 14.5145i −1.53039 + 0.557016i
\(680\) 0 0
\(681\) 3.06890 + 2.57511i 0.117600 + 0.0986784i
\(682\) −5.80396 1.02340i −0.222245 0.0391878i
\(683\) 13.4534i 0.514779i 0.966308 + 0.257390i \(0.0828624\pi\)
−0.966308 + 0.257390i \(0.917138\pi\)
\(684\) −0.418184 0.114125i −0.0159897 0.00436369i
\(685\) 0 0
\(686\) −2.66642 + 15.1220i −0.101804 + 0.577362i
\(687\) 22.4624 26.7697i 0.856995 1.02133i
\(688\) −2.62216 + 7.20433i −0.0999689 + 0.274662i
\(689\) 12.0750 4.39495i 0.460022 0.167434i
\(690\) 0 0
\(691\) −1.15757 2.00498i −0.0440362 0.0762729i 0.843167 0.537651i \(-0.180688\pi\)
−0.887203 + 0.461379i \(0.847355\pi\)
\(692\) 1.25955 + 0.727199i 0.0478807 + 0.0276439i
\(693\) 1.78999 0.315623i 0.0679960 0.0119895i
\(694\) 5.08309 + 28.8276i 0.192951 + 1.09428i
\(695\) 0 0
\(696\) −8.38274 14.5193i −0.317747 0.550354i
\(697\) 0.767532 + 0.914709i 0.0290723 + 0.0346471i
\(698\) −11.1439 30.6176i −0.421802 1.15889i
\(699\) −41.0308 14.9340i −1.55193 0.564855i
\(700\) 0 0
\(701\) 0.542849 3.07865i 0.0205031 0.116279i −0.972839 0.231485i \(-0.925642\pi\)
0.993342 + 0.115206i \(0.0367528\pi\)
\(702\) 41.8333i 1.57890i
\(703\) 38.3670 + 3.53535i 1.44704 + 0.133338i
\(704\) 4.57849 0.172558
\(705\) 0 0
\(706\) 29.3659 + 24.6409i 1.10520 + 0.927372i
\(707\) −17.0173 + 46.7548i −0.640003 + 1.75839i
\(708\) 0.0636359 + 0.174838i 0.00239158 + 0.00657083i
\(709\) 21.5824 18.1098i 0.810544 0.680127i −0.140193 0.990124i \(-0.544772\pi\)
0.950738 + 0.309997i \(0.100328\pi\)
\(710\) 0 0
\(711\) 1.84971 3.20379i 0.0693696 0.120152i
\(712\) 0.00200331 0.000353238i 7.50773e−5 1.32382e-5i
\(713\) 37.3364 6.58341i 1.39826 0.246551i
\(714\) 1.19822 2.07538i 0.0448423 0.0776691i
\(715\) 0 0
\(716\) 0.530243 0.444926i 0.0198161 0.0166277i
\(717\) 10.7175 + 29.4460i 0.400251 + 1.09968i
\(718\) 14.1431 38.8577i 0.527814 1.45016i
\(719\) 0.929140 + 0.779641i 0.0346511 + 0.0290757i 0.659949 0.751311i \(-0.270578\pi\)
−0.625298 + 0.780386i \(0.715022\pi\)
\(720\) 0 0
\(721\) −31.7746 −1.18335
\(722\) 26.0194 + 9.74346i 0.968341 + 0.362614i
\(723\) 9.36027i 0.348112i
\(724\) 0.636420 3.60931i 0.0236523 0.134139i
\(725\) 0 0
\(726\) −22.0291 8.01795i −0.817578 0.297574i
\(727\) −12.2347 33.6146i −0.453761 1.24670i −0.930058 0.367413i \(-0.880244\pi\)
0.476297 0.879284i \(-0.341979\pi\)
\(728\) 36.2896 + 43.2482i 1.34498 + 1.60289i
\(729\) 14.9989 + 25.9788i 0.555514 + 0.962178i
\(730\) 0 0
\(731\) 0.0833274 + 0.472573i 0.00308198 + 0.0174788i
\(732\) −0.446516 + 0.0787328i −0.0165037 + 0.00291005i
\(733\) 32.7765 + 18.9235i 1.21063 + 0.698957i 0.962896 0.269872i \(-0.0869813\pi\)
0.247732 + 0.968828i \(0.420315\pi\)
\(734\) 7.01533 + 12.1509i 0.258941 + 0.448498i
\(735\) 0 0
\(736\) 4.28850 1.56089i 0.158076 0.0575350i
\(737\) 2.99028 8.21574i 0.110149 0.302631i
\(738\) −3.02754 + 3.60808i −0.111445 + 0.132815i
\(739\) −1.31048 + 7.43210i −0.0482067 + 0.273394i −0.999378 0.0352702i \(-0.988771\pi\)
0.951171 + 0.308664i \(0.0998819\pi\)
\(740\) 0 0
\(741\) −3.07676 + 33.3901i −0.113028 + 1.22662i
\(742\) 15.0218i 0.551467i
\(743\) 9.03644 + 1.59337i 0.331515 + 0.0584550i 0.336928 0.941530i \(-0.390612\pi\)
−0.00541343 + 0.999985i \(0.501723\pi\)
\(744\) 20.4414 + 17.1523i 0.749417 + 0.628835i
\(745\) 0 0
\(746\) 17.9186 6.52185i 0.656047 0.238782i
\(747\) −6.36864 7.58984i −0.233016 0.277698i
\(748\) −0.0198272 + 0.0114472i −0.000724954 + 0.000418552i
\(749\) 11.6128 20.1140i 0.424324 0.734950i
\(750\) 0 0
\(751\) 1.81833 + 10.3123i 0.0663519 + 0.376300i 0.999843 + 0.0177006i \(0.00563457\pi\)
−0.933491 + 0.358600i \(0.883254\pi\)
\(752\) 42.5735 + 24.5798i 1.55250 + 0.896335i
\(753\) −10.1893 + 5.88280i −0.371319 + 0.214381i
\(754\) −23.2643 + 19.5211i −0.847235 + 0.710915i
\(755\) 0 0
\(756\) 2.97313 + 1.08213i 0.108132 + 0.0393568i
\(757\) 34.1163 40.6582i 1.23998 1.47775i 0.417779 0.908549i \(-0.362809\pi\)
0.822199 0.569199i \(-0.192747\pi\)
\(758\) 14.3130 + 2.52377i 0.519872 + 0.0916675i
\(759\) −5.47919 −0.198882
\(760\) 0 0
\(761\) −16.6886 −0.604960 −0.302480 0.953156i \(-0.597815\pi\)
−0.302480 + 0.953156i \(0.597815\pi\)
\(762\) −40.2312 7.09384i −1.45742 0.256983i
\(763\) −17.6225 + 21.0016i −0.637976 + 0.760310i
\(764\) −0.0186962 0.00680487i −0.000676405 0.000246191i
\(765\) 0 0
\(766\) 20.1954 16.9459i 0.729689 0.612281i
\(767\) −3.92767 + 2.26764i −0.141820 + 0.0818799i
\(768\) 4.32266 + 2.49569i 0.155981 + 0.0900554i
\(769\) 1.07276 + 6.08395i 0.0386849 + 0.219393i 0.998022 0.0628711i \(-0.0200257\pi\)
−0.959337 + 0.282264i \(0.908915\pi\)
\(770\) 0 0
\(771\) −15.2223 + 26.3657i −0.548217 + 0.949539i
\(772\) 0.246947 0.142575i 0.00888783 0.00513139i
\(773\) −18.0982 21.5686i −0.650948 0.775769i 0.335109 0.942179i \(-0.391227\pi\)
−0.986057 + 0.166410i \(0.946782\pi\)
\(774\) −1.77868 + 0.647385i −0.0639332 + 0.0232698i
\(775\) 0 0
\(776\) −21.7352 18.2380i −0.780249 0.654707i
\(777\) −53.5335 9.43940i −1.92050 0.338637i
\(778\) 35.6088i 1.27664i
\(779\) 13.8745 13.7469i 0.497106 0.492534i
\(780\) 0 0
\(781\) 0.177572 1.00706i 0.00635403 0.0360355i
\(782\) 1.46325 1.74383i 0.0523257 0.0623594i
\(783\) 7.83313 21.5214i 0.279933 0.769111i
\(784\) −38.3233 + 13.9486i −1.36869 + 0.498163i
\(785\) 0 0
\(786\) −21.6271 37.4593i −0.771414 1.33613i
\(787\) −4.73601 2.73433i −0.168820 0.0974685i 0.413209 0.910636i \(-0.364408\pi\)
−0.582030 + 0.813168i \(0.697741\pi\)
\(788\) 2.48621 0.438386i 0.0885676 0.0156169i
\(789\) −2.80257 15.8941i −0.0997740 0.565847i
\(790\) 0 0
\(791\) 9.74930 + 16.8863i 0.346645 + 0.600407i
\(792\) 0.781134 + 0.930919i 0.0277564 + 0.0330788i
\(793\) −3.78000 10.3855i −0.134232 0.368798i
\(794\) 27.4437 + 9.98870i 0.973942 + 0.354486i
\(795\) 0 0
\(796\) 0.192260 1.09036i 0.00681447 0.0386468i
\(797\) 47.2273i 1.67288i −0.548061 0.836439i \(-0.684634\pi\)
0.548061 0.836439i \(-0.315366\pi\)
\(798\) −35.4493 16.7301i −1.25489 0.592239i
\(799\) 3.07694 0.108854
\(800\) 0 0
\(801\) 0.000411469 0 0.000345264i 1.45386e−5 0 1.21993e-5i
\(802\) 8.20414 22.5407i 0.289698 0.795939i
\(803\) −0.381624 1.04850i −0.0134672 0.0370009i
\(804\) 2.25353 1.89094i 0.0794759 0.0666882i
\(805\) 0 0
\(806\) 24.1683 41.8607i 0.851292 1.47448i
\(807\) 35.5877 6.27507i 1.25275 0.220893i
\(808\) −32.7606 + 5.77657i −1.15251 + 0.203219i
\(809\) −3.06691 + 5.31204i −0.107827 + 0.186762i −0.914890 0.403704i \(-0.867723\pi\)
0.807063 + 0.590466i \(0.201056\pi\)
\(810\) 0 0
\(811\) 20.6831 17.3552i 0.726281 0.609422i −0.202834 0.979213i \(-0.565015\pi\)
0.929115 + 0.369791i \(0.120571\pi\)
\(812\) −0.785586 2.15838i −0.0275687 0.0757443i
\(813\) −13.4154 + 36.8586i −0.470500 + 1.29269i
\(814\) 6.14901 + 5.15963i 0.215523 + 0.180845i
\(815\) 0 0
\(816\) 1.71360 0.0599880
\(817\) 7.59103 1.99647i 0.265577 0.0698476i
\(818\) 12.1855i 0.426055i
\(819\) −2.58864 + 14.6809i −0.0904543 + 0.512992i
\(820\) 0 0
\(821\) 42.5186 + 15.4755i 1.48391 + 0.540099i 0.951838 0.306600i \(-0.0991914\pi\)
0.532072 + 0.846699i \(0.321414\pi\)
\(822\) −1.78020 4.89105i −0.0620914 0.170595i
\(823\) −19.3760 23.0915i −0.675407 0.804918i 0.314102 0.949389i \(-0.398296\pi\)
−0.989509 + 0.144471i \(0.953852\pi\)
\(824\) −10.6221 18.3980i −0.370038 0.640925i
\(825\) 0 0
\(826\) −0.920649 5.22126i −0.0320335 0.181671i
\(827\) 20.1600 3.55475i 0.701032 0.123611i 0.188239 0.982123i \(-0.439722\pi\)
0.512793 + 0.858512i \(0.328611\pi\)
\(828\) 0.503109 + 0.290470i 0.0174843 + 0.0100945i
\(829\) −10.4604 18.1179i −0.363303 0.629259i 0.625199 0.780465i \(-0.285018\pi\)
−0.988502 + 0.151206i \(0.951684\pi\)
\(830\) 0 0
\(831\) 2.60252 0.947238i 0.0902803 0.0328593i
\(832\) −12.8433 + 35.2867i −0.445262 + 1.22335i
\(833\) −1.64080 + 1.95543i −0.0568503 + 0.0677515i
\(834\) 1.46907 8.33154i 0.0508699 0.288498i
\(835\) 0 0
\(836\) 0.213378 + 0.307751i 0.00737982 + 0.0106438i
\(837\) 36.4522i 1.25997i
\(838\) −16.7847 2.95959i −0.579816 0.102237i
\(839\) −3.25369 2.73017i −0.112330 0.0942559i 0.584893 0.811111i \(-0.301137\pi\)
−0.697222 + 0.716855i \(0.745581\pi\)
\(840\) 0 0
\(841\) 11.6274 4.23203i 0.400945 0.145932i
\(842\) −19.9191 23.7387i −0.686458 0.818089i
\(843\) 17.8993 10.3342i 0.616486 0.355928i
\(844\) −0.974147 + 1.68727i −0.0335315 + 0.0580783i
\(845\) 0 0
\(846\) 2.10757 + 11.9526i 0.0724599 + 0.410941i
\(847\) 37.4285 + 21.6094i 1.28606 + 0.742506i
\(848\) −9.30239 + 5.37074i −0.319446 + 0.184432i
\(849\) −12.1905 + 10.2290i −0.418377 + 0.351060i
\(850\) 0 0
\(851\) −48.5226 17.6608i −1.66334 0.605404i
\(852\) 0.221167 0.263577i 0.00757706 0.00902999i
\(853\) 1.64409 + 0.289897i 0.0562926 + 0.00992590i 0.201724 0.979443i \(-0.435346\pi\)
−0.145431 + 0.989368i \(0.546457\pi\)
\(854\) 12.9199 0.442110
\(855\) 0 0
\(856\) 15.5284 0.530751
\(857\) 0.843653 + 0.148759i 0.0288186 + 0.00508150i 0.188039 0.982162i \(-0.439787\pi\)
−0.159220 + 0.987243i \(0.550898\pi\)
\(858\) −4.49034 + 5.35138i −0.153298 + 0.182693i
\(859\) −49.8985 18.1616i −1.70251 0.619665i −0.706407 0.707806i \(-0.749685\pi\)
−0.996108 + 0.0881416i \(0.971907\pi\)
\(860\) 0 0
\(861\) −21.1091 + 17.7127i −0.719397 + 0.603646i
\(862\) −0.496761 + 0.286805i −0.0169198 + 0.00976863i
\(863\) 25.6004 + 14.7804i 0.871447 + 0.503130i 0.867829 0.496864i \(-0.165515\pi\)
0.00361786 + 0.999993i \(0.498848\pi\)
\(864\) 0.761961 + 4.32130i 0.0259224 + 0.147013i
\(865\) 0 0
\(866\) 9.48391 16.4266i 0.322276 0.558199i
\(867\) −22.1432 + 12.7844i −0.752023 + 0.434181i
\(868\) 2.34990 + 2.80050i 0.0797609 + 0.0950553i
\(869\) −3.00324 + 1.09309i −0.101878 + 0.0370806i
\(870\) 0 0
\(871\) 54.9310 + 46.0926i 1.86127 + 1.56179i
\(872\) −18.0514 3.18294i −0.611296 0.107788i
\(873\) 7.49198i 0.253565i
\(874\) −30.4026 21.4981i −1.02838 0.727185i
\(875\) 0 0
\(876\) 0.0651933 0.369730i 0.00220268 0.0124920i
\(877\) −5.65060 + 6.73412i −0.190807 + 0.227395i −0.852963 0.521971i \(-0.825197\pi\)
0.662156 + 0.749366i \(0.269641\pi\)
\(878\) −2.72476 + 7.48620i −0.0919560 + 0.252647i
\(879\) 33.9266 12.3483i 1.14432 0.416497i
\(880\) 0 0
\(881\) −13.6335 23.6139i −0.459324 0.795572i 0.539602 0.841920i \(-0.318575\pi\)
−0.998925 + 0.0463485i \(0.985242\pi\)
\(882\) −8.71990 5.03444i −0.293614 0.169518i
\(883\) −8.51936 + 1.50219i −0.286699 + 0.0505528i −0.315148 0.949042i \(-0.602054\pi\)
0.0284490 + 0.999595i \(0.490943\pi\)
\(884\) −0.0326065 0.184920i −0.00109667 0.00621955i
\(885\) 0 0
\(886\) 18.0907 + 31.3340i 0.607769 + 1.05269i
\(887\) 25.4862 + 30.3733i 0.855744 + 1.01984i 0.999543 + 0.0302292i \(0.00962373\pi\)
−0.143799 + 0.989607i \(0.545932\pi\)
\(888\) −12.4304 34.1523i −0.417137 1.14607i
\(889\) 70.7713 + 25.7587i 2.37359 + 0.863918i
\(890\) 0 0
\(891\) 0.682260 3.86929i 0.0228566 0.129626i
\(892\) 0.678737i 0.0227258i
\(893\) −4.15486 50.1581i −0.139037 1.67848i
\(894\) 40.1648 1.34331
\(895\) 0 0
\(896\) −38.5013 32.3064i −1.28624 1.07928i
\(897\) 15.3699 42.2284i 0.513186 1.40997i
\(898\) −17.2857 47.4922i −0.576832 1.58483i
\(899\) 20.2718 17.0100i 0.676101 0.567316i
\(900\) 0 0
\(901\) −0.336159 + 0.582244i −0.0111991 + 0.0193974i
\(902\) 4.00723 0.706583i 0.133426 0.0235266i
\(903\) −10.9058 + 1.92298i −0.362921 + 0.0639929i
\(904\) −6.51828 + 11.2900i −0.216795 + 0.375499i
\(905\) 0 0
\(906\) 3.88018 3.25585i 0.128910 0.108169i
\(907\) 11.4157 + 31.3645i 0.379053 + 1.04144i 0.971750 + 0.236014i \(0.0758412\pi\)
−0.592696 + 0.805426i \(0.701937\pi\)
\(908\) −0.125506 + 0.344826i −0.00416508 + 0.0114435i
\(909\) −6.72884 5.64617i −0.223182 0.187272i
\(910\) 0 0
\(911\) −46.3977 −1.53722 −0.768611 0.639716i \(-0.779052\pi\)
−0.768611 + 0.639716i \(0.779052\pi\)
\(912\) −2.31391 27.9339i −0.0766212 0.924982i
\(913\) 8.55953i 0.283279i
\(914\) −2.95635 + 16.7663i −0.0977873 + 0.554579i
\(915\) 0 0
\(916\) 3.00788 + 1.09478i 0.0993833 + 0.0361726i
\(917\) 27.2735 + 74.9333i 0.900650 + 2.47452i
\(918\) 1.40689 + 1.67667i 0.0464345 + 0.0553384i
\(919\) 4.25997 + 7.37849i 0.140524 + 0.243394i 0.927694 0.373342i \(-0.121788\pi\)
−0.787170 + 0.616736i \(0.788455\pi\)
\(920\) 0 0
\(921\) 4.10942 + 23.3057i 0.135410 + 0.767948i
\(922\) 4.30549 0.759174i 0.141794 0.0250021i
\(923\) 7.26337 + 4.19351i 0.239077 + 0.138031i
\(924\) −0.264173 0.457561i −0.00869065 0.0150526i
\(925\) 0 0
\(926\) −11.6624 + 4.24475i −0.383249 + 0.139491i
\(927\) 1.91857 5.27123i 0.0630142 0.173130i
\(928\) 2.04759 2.44023i 0.0672155 0.0801044i
\(929\) 8.18896 46.4419i 0.268671 1.52371i −0.489702 0.871890i \(-0.662894\pi\)
0.758373 0.651820i \(-0.225994\pi\)
\(930\) 0 0
\(931\) 34.0916 + 24.1067i 1.11731 + 0.790064i
\(932\) 3.99954i 0.131009i
\(933\) 5.22393 + 0.921119i 0.171024 + 0.0301561i
\(934\) 20.0853 + 16.8536i 0.657212 + 0.551466i
\(935\) 0 0
\(936\) −9.36584 + 3.40889i −0.306132 + 0.111423i
\(937\) −18.9625 22.5986i −0.619477 0.738264i 0.361504 0.932371i \(-0.382264\pi\)
−0.980980 + 0.194107i \(0.937819\pi\)
\(938\) −72.5961 + 41.9134i −2.37035 + 1.36852i
\(939\) 0.885879 1.53439i 0.0289096 0.0500729i
\(940\) 0 0
\(941\) −1.64948 9.35464i −0.0537714 0.304953i 0.946047 0.324031i \(-0.105038\pi\)
−0.999818 + 0.0190779i \(0.993927\pi\)
\(942\) −39.8695 23.0187i −1.29902 0.749989i
\(943\) −22.6690 + 13.0879i −0.738203 + 0.426201i
\(944\) 2.90416 2.43688i 0.0945223 0.0793137i
\(945\) 0 0
\(946\) 1.53662 + 0.559286i 0.0499600 + 0.0181839i
\(947\) 6.33765 7.55292i 0.205946 0.245437i −0.653178 0.757204i \(-0.726565\pi\)
0.859124 + 0.511768i \(0.171009\pi\)
\(948\) −1.05902 0.186734i −0.0343954 0.00606484i
\(949\) 9.15138 0.297066
\(950\) 0 0
\(951\) −1.98099 −0.0642381
\(952\) −2.90896 0.512928i −0.0942800 0.0166241i
\(953\) 34.5014 41.1172i 1.11761 1.33192i 0.180223 0.983626i \(-0.442318\pi\)
0.937387 0.348290i \(-0.113237\pi\)
\(954\) −2.49203 0.907025i −0.0806825 0.0293660i
\(955\) 0 0
\(956\) −2.19877 + 1.84499i −0.0711134 + 0.0596712i
\(957\) −3.31210 + 1.91224i −0.107065 + 0.0618141i
\(958\) −4.29251 2.47828i −0.138685 0.0800697i
\(959\) 1.66627 + 9.44991i 0.0538068 + 0.305154i
\(960\) 0 0
\(961\) −5.55948 + 9.62930i −0.179338 + 0.310623i
\(962\) −57.0144 + 32.9173i −1.83822 + 1.06130i
\(963\) 2.63561 + 3.14100i 0.0849315 + 0.101217i
\(964\) 0.805675 0.293242i 0.0259491 0.00944468i
\(965\) 0 0
\(966\) 40.2432 + 33.7681i 1.29480 + 1.08647i
\(967\) 33.7173 + 5.94528i 1.08428 + 0.191187i 0.687106 0.726557i \(-0.258881\pi\)
0.397171 + 0.917745i \(0.369992\pi\)
\(968\) 28.8956i 0.928739i
\(969\) −0.999627 1.44175i −0.0321126 0.0463155i
\(970\) 0 0
\(971\) 2.46056 13.9545i 0.0789630 0.447821i −0.919534 0.393011i \(-0.871433\pi\)
0.998497 0.0548105i \(-0.0174555\pi\)
\(972\) −0.648679 + 0.773065i −0.0208064 + 0.0247961i
\(973\) −5.33440 + 14.6561i −0.171013 + 0.469855i
\(974\) 15.3379 5.58254i 0.491458 0.178876i
\(975\) 0 0
\(976\) 4.61925 + 8.00078i 0.147859 + 0.256099i
\(977\) −39.5060 22.8088i −1.26391 0.729717i −0.290079 0.957003i \(-0.593682\pi\)
−0.973828 + 0.227285i \(0.927015\pi\)
\(978\) 17.2197 3.03629i 0.550625 0.0970900i
\(979\) −8.05795e−5 0 0.000456989i −2.57533e−6 0 1.46054e-5i
\(980\) 0 0
\(981\) −2.42000 4.19156i −0.0772646 0.133826i
\(982\) −21.6029 25.7454i −0.689377 0.821568i
\(983\) 6.90400 + 18.9686i 0.220203 + 0.605004i 0.999773 0.0213117i \(-0.00678425\pi\)
−0.779569 + 0.626316i \(0.784562\pi\)
\(984\) −17.3126 6.30126i −0.551905 0.200877i
\(985\) 0 0
\(986\) 0.275917 1.56480i 0.00878698 0.0498334i
\(987\) 71.0079i 2.26021i
\(988\) −2.97041 + 0.781229i −0.0945013 + 0.0248542i
\(989\) −10.5194 −0.334496
\(990\) 0 0
\(991\) −8.46987 7.10707i −0.269054 0.225763i 0.498271 0.867021i \(-0.333968\pi\)
−0.767325 + 0.641258i \(0.778413\pi\)
\(992\) −1.73408 + 4.76433i −0.0550569 + 0.151268i
\(993\) −6.57332 18.0601i −0.208598 0.573118i
\(994\) −7.51070 + 6.30223i −0.238225 + 0.199894i
\(995\) 0 0
\(996\) −1.44002 + 2.49419i −0.0456288 + 0.0790314i
\(997\) −30.7526 + 5.42251i −0.973945 + 0.171733i −0.637905 0.770115i \(-0.720199\pi\)
−0.336040 + 0.941848i \(0.609088\pi\)
\(998\) −1.41235 + 0.249035i −0.0447070 + 0.00788305i
\(999\) 24.8240 42.9964i 0.785396 1.36035i
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 475.2.u.c.74.2 36
5.2 odd 4 475.2.l.b.226.3 18
5.3 odd 4 95.2.k.b.36.1 18
5.4 even 2 inner 475.2.u.c.74.5 36
15.8 even 4 855.2.bs.b.226.3 18
19.9 even 9 inner 475.2.u.c.199.5 36
95.3 even 36 1805.2.a.u.1.7 9
95.9 even 18 inner 475.2.u.c.199.2 36
95.22 even 36 9025.2.a.cd.1.3 9
95.28 odd 36 95.2.k.b.66.1 yes 18
95.47 odd 36 475.2.l.b.351.3 18
95.73 odd 36 1805.2.a.t.1.3 9
95.92 odd 36 9025.2.a.ce.1.7 9
285.218 even 36 855.2.bs.b.541.3 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.k.b.36.1 18 5.3 odd 4
95.2.k.b.66.1 yes 18 95.28 odd 36
475.2.l.b.226.3 18 5.2 odd 4
475.2.l.b.351.3 18 95.47 odd 36
475.2.u.c.74.2 36 1.1 even 1 trivial
475.2.u.c.74.5 36 5.4 even 2 inner
475.2.u.c.199.2 36 95.9 even 18 inner
475.2.u.c.199.5 36 19.9 even 9 inner
855.2.bs.b.226.3 18 15.8 even 4
855.2.bs.b.541.3 18 285.218 even 36
1805.2.a.t.1.3 9 95.73 odd 36
1805.2.a.u.1.7 9 95.3 even 36
9025.2.a.cd.1.3 9 95.22 even 36
9025.2.a.ce.1.7 9 95.92 odd 36