Properties

Label 429.2.bb.a.25.10
Level $429$
Weight $2$
Character 429.25
Analytic conductor $3.426$
Analytic rank $0$
Dimension $56$
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] = [429,2,Mod(25,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bb (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 25.10
Character \(\chi\) \(=\) 429.25
Dual form 429.2.bb.a.103.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.817916 + 1.12577i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.0196739 - 0.0605500i) q^{4} +(1.89008 - 2.60147i) q^{5} +(-0.817916 + 1.12577i) q^{6} +(-2.89956 - 0.942124i) q^{7} +(2.73109 - 0.887385i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(0.817916 + 1.12577i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.0196739 - 0.0605500i) q^{4} +(1.89008 - 2.60147i) q^{5} +(-0.817916 + 1.12577i) q^{6} +(-2.89956 - 0.942124i) q^{7} +(2.73109 - 0.887385i) q^{8} +(-0.809017 + 0.587785i) q^{9} +4.47458 q^{10} +(3.20270 + 0.861794i) q^{11} +0.0636661 q^{12} +(-0.446557 + 3.57779i) q^{13} +(-1.31099 - 4.03480i) q^{14} +(3.05822 + 0.993674i) q^{15} +(3.12977 + 2.27391i) q^{16} +(-2.20231 - 1.60007i) q^{17} +(-1.32342 - 0.430004i) q^{18} +(6.82897 - 2.21887i) q^{19} +(-0.120334 - 0.165626i) q^{20} -3.04878i q^{21} +(1.64937 + 4.31037i) q^{22} +1.60068 q^{23} +(1.68791 + 2.32320i) q^{24} +(-1.65017 - 5.07871i) q^{25} +(-4.39300 + 2.42362i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.114091 + 0.157033i) q^{28} +(-1.98527 + 6.11004i) q^{29} +(1.38272 + 4.25557i) q^{30} +(-0.650284 - 0.895040i) q^{31} -0.360011i q^{32} +(0.170075 + 3.31226i) q^{33} -3.78802i q^{34} +(-7.93131 + 5.76244i) q^{35} +(0.0196739 + 0.0605500i) q^{36} +(-6.24791 - 2.03007i) q^{37} +(8.08345 + 5.87297i) q^{38} +(-3.54067 + 0.680898i) q^{39} +(2.85347 - 8.78208i) q^{40} +(-7.24015 + 2.35247i) q^{41} +(3.43221 - 2.49364i) q^{42} -10.3286 q^{43} +(0.115191 - 0.176969i) q^{44} +3.21560i q^{45} +(1.30922 + 1.80199i) q^{46} +(-1.74095 + 0.565669i) q^{47} +(-1.19547 + 3.67927i) q^{48} +(1.85673 + 1.34899i) q^{49} +(4.36773 - 6.01166i) q^{50} +(0.841209 - 2.58898i) q^{51} +(0.207850 + 0.0974281i) q^{52} +(-5.83535 + 4.23963i) q^{53} -1.39152i q^{54} +(8.29530 - 6.70289i) q^{55} -8.75498 q^{56} +(4.22054 + 5.80907i) q^{57} +(-8.50225 + 2.76255i) q^{58} +(-3.67607 - 1.19443i) q^{59} +(0.120334 - 0.165626i) q^{60} +(11.6399 + 8.45686i) q^{61} +(0.475726 - 1.46413i) q^{62} +(2.89956 - 0.942124i) q^{63} +(6.66484 - 4.84229i) q^{64} +(8.46350 + 7.92402i) q^{65} +(-3.58972 + 2.90062i) q^{66} -11.8916i q^{67} +(-0.140213 + 0.101871i) q^{68} +(0.494638 + 1.52234i) q^{69} +(-12.9743 - 4.21561i) q^{70} +(0.240603 - 0.331162i) q^{71} +(-1.68791 + 2.32320i) q^{72} +(8.99648 + 2.92313i) q^{73} +(-2.82488 - 8.69410i) q^{74} +(4.32021 - 3.13881i) q^{75} -0.457148i q^{76} +(-8.47451 - 5.51617i) q^{77} +(-3.66251 - 3.42905i) q^{78} +(-4.62118 + 3.35748i) q^{79} +(11.8311 - 3.84414i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-8.57016 - 6.22659i) q^{82} +(-7.51164 + 10.3389i) q^{83} +(-0.184604 - 0.0599814i) q^{84} +(-8.32510 + 2.70499i) q^{85} +(-8.44792 - 11.6276i) q^{86} -6.42447 q^{87} +(9.51161 - 0.488394i) q^{88} -2.58760i q^{89} +(-3.62001 + 2.63009i) q^{90} +(4.66554 - 9.95331i) q^{91} +(0.0314917 - 0.0969214i) q^{92} +(0.650284 - 0.895040i) q^{93} +(-2.06076 - 1.49723i) q^{94} +(7.13499 - 21.9592i) q^{95} +(0.342391 - 0.111250i) q^{96} +(2.17811 + 2.99791i) q^{97} +3.19361i q^{98} +(-3.09759 + 1.18530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.817916 + 1.12577i 0.578354 + 0.796036i 0.993514 0.113712i \(-0.0362743\pi\)
−0.415160 + 0.909749i \(0.636274\pi\)
\(3\) 0.309017 + 0.951057i 0.178411 + 0.549093i
\(4\) 0.0196739 0.0605500i 0.00983695 0.0302750i
\(5\) 1.89008 2.60147i 0.845270 1.16341i −0.139615 0.990206i \(-0.544587\pi\)
0.984885 0.173208i \(-0.0554134\pi\)
\(6\) −0.817916 + 1.12577i −0.333913 + 0.459592i
\(7\) −2.89956 0.942124i −1.09593 0.356089i −0.295395 0.955375i \(-0.595451\pi\)
−0.800535 + 0.599286i \(0.795451\pi\)
\(8\) 2.73109 0.887385i 0.965586 0.313738i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) 4.47458 1.41498
\(11\) 3.20270 + 0.861794i 0.965652 + 0.259841i
\(12\) 0.0636661 0.0183788
\(13\) −0.446557 + 3.57779i −0.123853 + 0.992301i
\(14\) −1.31099 4.03480i −0.350376 1.07835i
\(15\) 3.05822 + 0.993674i 0.789628 + 0.256566i
\(16\) 3.12977 + 2.27391i 0.782444 + 0.568479i
\(17\) −2.20231 1.60007i −0.534140 0.388075i 0.287764 0.957701i \(-0.407088\pi\)
−0.821904 + 0.569626i \(0.807088\pi\)
\(18\) −1.32342 0.430004i −0.311932 0.101353i
\(19\) 6.82897 2.21887i 1.56667 0.509043i 0.608094 0.793865i \(-0.291935\pi\)
0.958580 + 0.284822i \(0.0919345\pi\)
\(20\) −0.120334 0.165626i −0.0269075 0.0370350i
\(21\) 3.04878i 0.665298i
\(22\) 1.64937 + 4.31037i 0.351646 + 0.918973i
\(23\) 1.60068 0.333765 0.166883 0.985977i \(-0.446630\pi\)
0.166883 + 0.985977i \(0.446630\pi\)
\(24\) 1.68791 + 2.32320i 0.344542 + 0.474222i
\(25\) −1.65017 5.07871i −0.330034 1.01574i
\(26\) −4.39300 + 2.42362i −0.861538 + 0.475310i
\(27\) −0.809017 0.587785i −0.155695 0.113119i
\(28\) −0.114091 + 0.157033i −0.0215612 + 0.0296765i
\(29\) −1.98527 + 6.11004i −0.368656 + 1.13461i 0.579005 + 0.815324i \(0.303441\pi\)
−0.947660 + 0.319281i \(0.896559\pi\)
\(30\) 1.38272 + 4.25557i 0.252449 + 0.776958i
\(31\) −0.650284 0.895040i −0.116795 0.160754i 0.746617 0.665254i \(-0.231677\pi\)
−0.863412 + 0.504500i \(0.831677\pi\)
\(32\) 0.360011i 0.0636416i
\(33\) 0.170075 + 3.31226i 0.0296063 + 0.576591i
\(34\) 3.78802i 0.649639i
\(35\) −7.93131 + 5.76244i −1.34064 + 0.974030i
\(36\) 0.0196739 + 0.0605500i 0.00327898 + 0.0100917i
\(37\) −6.24791 2.03007i −1.02715 0.333741i −0.253487 0.967339i \(-0.581577\pi\)
−0.773663 + 0.633598i \(0.781577\pi\)
\(38\) 8.08345 + 5.87297i 1.31131 + 0.952722i
\(39\) −3.54067 + 0.680898i −0.566962 + 0.109031i
\(40\) 2.85347 8.78208i 0.451174 1.38857i
\(41\) −7.24015 + 2.35247i −1.13072 + 0.367394i −0.813850 0.581075i \(-0.802632\pi\)
−0.316871 + 0.948469i \(0.602632\pi\)
\(42\) 3.43221 2.49364i 0.529601 0.384778i
\(43\) −10.3286 −1.57510 −0.787548 0.616253i \(-0.788650\pi\)
−0.787548 + 0.616253i \(0.788650\pi\)
\(44\) 0.115191 0.176969i 0.0173657 0.0266791i
\(45\) 3.21560i 0.479353i
\(46\) 1.30922 + 1.80199i 0.193035 + 0.265689i
\(47\) −1.74095 + 0.565669i −0.253944 + 0.0825113i −0.433223 0.901287i \(-0.642624\pi\)
0.179279 + 0.983798i \(0.442624\pi\)
\(48\) −1.19547 + 3.67927i −0.172551 + 0.531057i
\(49\) 1.85673 + 1.34899i 0.265247 + 0.192713i
\(50\) 4.36773 6.01166i 0.617690 0.850177i
\(51\) 0.841209 2.58898i 0.117793 0.362529i
\(52\) 0.207850 + 0.0974281i 0.0288236 + 0.0135109i
\(53\) −5.83535 + 4.23963i −0.801547 + 0.582358i −0.911368 0.411593i \(-0.864972\pi\)
0.109821 + 0.993951i \(0.464972\pi\)
\(54\) 1.39152i 0.189362i
\(55\) 8.29530 6.70289i 1.11854 0.903817i
\(56\) −8.75498 −1.16993
\(57\) 4.22054 + 5.80907i 0.559024 + 0.769430i
\(58\) −8.50225 + 2.76255i −1.11640 + 0.362740i
\(59\) −3.67607 1.19443i −0.478584 0.155501i 0.0597841 0.998211i \(-0.480959\pi\)
−0.538368 + 0.842710i \(0.680959\pi\)
\(60\) 0.120334 0.165626i 0.0155351 0.0213822i
\(61\) 11.6399 + 8.45686i 1.49033 + 1.08279i 0.974040 + 0.226377i \(0.0726881\pi\)
0.516292 + 0.856413i \(0.327312\pi\)
\(62\) 0.475726 1.46413i 0.0604173 0.185945i
\(63\) 2.89956 0.942124i 0.365310 0.118696i
\(64\) 6.66484 4.84229i 0.833105 0.605286i
\(65\) 8.46350 + 7.92402i 1.04977 + 0.982854i
\(66\) −3.58972 + 2.90062i −0.441864 + 0.357041i
\(67\) 11.8916i 1.45279i −0.687279 0.726394i \(-0.741195\pi\)
0.687279 0.726394i \(-0.258805\pi\)
\(68\) −0.140213 + 0.101871i −0.0170033 + 0.0123536i
\(69\) 0.494638 + 1.52234i 0.0595474 + 0.183268i
\(70\) −12.9743 4.21561i −1.55073 0.503861i
\(71\) 0.240603 0.331162i 0.0285543 0.0393017i −0.794501 0.607263i \(-0.792268\pi\)
0.823055 + 0.567961i \(0.192268\pi\)
\(72\) −1.68791 + 2.32320i −0.198922 + 0.273792i
\(73\) 8.99648 + 2.92313i 1.05296 + 0.342127i 0.783829 0.620977i \(-0.213264\pi\)
0.269129 + 0.963104i \(0.413264\pi\)
\(74\) −2.82488 8.69410i −0.328386 1.01067i
\(75\) 4.32021 3.13881i 0.498854 0.362439i
\(76\) 0.457148i 0.0524385i
\(77\) −8.47451 5.51617i −0.965761 0.628626i
\(78\) −3.66251 3.42905i −0.414697 0.388264i
\(79\) −4.62118 + 3.35748i −0.519923 + 0.377746i −0.816575 0.577239i \(-0.804130\pi\)
0.296652 + 0.954986i \(0.404130\pi\)
\(80\) 11.8311 3.84414i 1.32275 0.429788i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) −8.57016 6.22659i −0.946416 0.687611i
\(83\) −7.51164 + 10.3389i −0.824510 + 1.13484i 0.164410 + 0.986392i \(0.447428\pi\)
−0.988920 + 0.148448i \(0.952572\pi\)
\(84\) −0.184604 0.0599814i −0.0201419 0.00654450i
\(85\) −8.32510 + 2.70499i −0.902984 + 0.293397i
\(86\) −8.44792 11.6276i −0.910963 1.25383i
\(87\) −6.42447 −0.688776
\(88\) 9.51161 0.488394i 1.01394 0.0520630i
\(89\) 2.58760i 0.274285i −0.990551 0.137143i \(-0.956208\pi\)
0.990551 0.137143i \(-0.0437919\pi\)
\(90\) −3.62001 + 2.63009i −0.381582 + 0.277236i
\(91\) 4.66554 9.95331i 0.489082 1.04339i
\(92\) 0.0314917 0.0969214i 0.00328323 0.0101048i
\(93\) 0.650284 0.895040i 0.0674314 0.0928113i
\(94\) −2.06076 1.49723i −0.212551 0.154428i
\(95\) 7.13499 21.9592i 0.732034 2.25297i
\(96\) 0.342391 0.111250i 0.0349452 0.0113544i
\(97\) 2.17811 + 2.99791i 0.221154 + 0.304392i 0.905149 0.425095i \(-0.139759\pi\)
−0.683995 + 0.729486i \(0.739759\pi\)
\(98\) 3.19361i 0.322603i
\(99\) −3.09759 + 1.18530i −0.311320 + 0.119127i
\(100\) −0.339981 −0.0339981
\(101\) −6.63234 + 4.81867i −0.659942 + 0.479476i −0.866643 0.498928i \(-0.833727\pi\)
0.206701 + 0.978404i \(0.433727\pi\)
\(102\) 3.60262 1.17056i 0.356712 0.115903i
\(103\) 3.36950 10.3703i 0.332007 1.02181i −0.636171 0.771548i \(-0.719483\pi\)
0.968178 0.250264i \(-0.0805175\pi\)
\(104\) 1.95529 + 10.1675i 0.191732 + 0.997009i
\(105\) −7.93131 5.76244i −0.774017 0.562356i
\(106\) −9.54565 3.10157i −0.927156 0.301251i
\(107\) −1.43141 4.40543i −0.138380 0.425889i 0.857721 0.514116i \(-0.171880\pi\)
−0.996100 + 0.0882268i \(0.971880\pi\)
\(108\) −0.0515069 + 0.0374220i −0.00495626 + 0.00360093i
\(109\) 13.5684i 1.29962i 0.760097 + 0.649810i \(0.225151\pi\)
−0.760097 + 0.649810i \(0.774849\pi\)
\(110\) 14.3307 + 3.85616i 1.36638 + 0.367671i
\(111\) 6.56944i 0.623543i
\(112\) −6.93266 9.54199i −0.655075 0.901633i
\(113\) 0.711611 + 2.19011i 0.0669427 + 0.206029i 0.978932 0.204185i \(-0.0654543\pi\)
−0.911990 + 0.410213i \(0.865454\pi\)
\(114\) −3.08760 + 9.50267i −0.289181 + 0.890006i
\(115\) 3.02542 4.16413i 0.282122 0.388307i
\(116\) 0.330905 + 0.240416i 0.0307237 + 0.0223221i
\(117\) −1.74170 3.15697i −0.161020 0.291862i
\(118\) −1.66207 5.11533i −0.153006 0.470905i
\(119\) 4.87827 + 6.71437i 0.447191 + 0.615505i
\(120\) 9.23403 0.842948
\(121\) 9.51462 + 5.52014i 0.864966 + 0.501831i
\(122\) 20.0208i 1.81259i
\(123\) −4.47466 6.15884i −0.403466 0.555324i
\(124\) −0.0669883 + 0.0217658i −0.00601573 + 0.00195463i
\(125\) −1.04000 0.337917i −0.0930206 0.0302242i
\(126\) 3.43221 + 2.49364i 0.305765 + 0.222152i
\(127\) 0.870936 + 0.632772i 0.0772831 + 0.0561494i 0.625756 0.780019i \(-0.284791\pi\)
−0.548473 + 0.836168i \(0.684791\pi\)
\(128\) 10.2178 + 3.31996i 0.903132 + 0.293445i
\(129\) −3.19171 9.82308i −0.281014 0.864874i
\(130\) −1.99815 + 16.0091i −0.175249 + 1.40409i
\(131\) 10.2897 0.899014 0.449507 0.893277i \(-0.351600\pi\)
0.449507 + 0.893277i \(0.351600\pi\)
\(132\) 0.203904 + 0.0548670i 0.0177475 + 0.00477556i
\(133\) −21.8915 −1.89823
\(134\) 13.3871 9.72632i 1.15647 0.840226i
\(135\) −3.05822 + 0.993674i −0.263209 + 0.0855219i
\(136\) −7.43460 2.41565i −0.637512 0.207140i
\(137\) 7.22116 9.93907i 0.616945 0.849152i −0.380181 0.924912i \(-0.624138\pi\)
0.997126 + 0.0757601i \(0.0241383\pi\)
\(138\) −1.30922 + 1.80199i −0.111449 + 0.153396i
\(139\) 0.00498869 0.0153536i 0.000423135 0.00130228i −0.950845 0.309668i \(-0.899782\pi\)
0.951268 + 0.308366i \(0.0997821\pi\)
\(140\) 0.192876 + 0.593611i 0.0163010 + 0.0501693i
\(141\) −1.07597 1.48094i −0.0906127 0.124718i
\(142\) 0.569603 0.0478001
\(143\) −4.51351 + 11.0738i −0.377438 + 0.926035i
\(144\) −3.86861 −0.322385
\(145\) 12.1428 + 16.7131i 1.00840 + 1.38795i
\(146\) 4.06760 + 12.5188i 0.336637 + 1.03606i
\(147\) −0.709208 + 2.18272i −0.0584945 + 0.180028i
\(148\) −0.245841 + 0.338372i −0.0202080 + 0.0278140i
\(149\) −11.5025 + 15.8318i −0.942322 + 1.29699i 0.0125331 + 0.999921i \(0.496010\pi\)
−0.954855 + 0.297073i \(0.903990\pi\)
\(150\) 7.06713 + 2.29625i 0.577029 + 0.187488i
\(151\) 5.78001 1.87804i 0.470370 0.152833i −0.0642345 0.997935i \(-0.520461\pi\)
0.534605 + 0.845102i \(0.320461\pi\)
\(152\) 16.6815 12.1199i 1.35305 0.983050i
\(153\) 2.72221 0.220078
\(154\) −0.721534 14.0521i −0.0581429 1.13235i
\(155\) −3.55751 −0.285746
\(156\) −0.0284305 + 0.227784i −0.00227626 + 0.0182373i
\(157\) 5.62075 + 17.2989i 0.448584 + 1.38060i 0.878505 + 0.477734i \(0.158542\pi\)
−0.429920 + 0.902867i \(0.641458\pi\)
\(158\) −7.55947 2.45622i −0.601399 0.195406i
\(159\) −5.83535 4.23963i −0.462773 0.336225i
\(160\) −0.936560 0.680451i −0.0740416 0.0537944i
\(161\) −4.64128 1.50804i −0.365784 0.118850i
\(162\) 1.32342 0.430004i 0.103977 0.0337843i
\(163\) −7.22195 9.94016i −0.565667 0.778574i 0.426366 0.904551i \(-0.359793\pi\)
−0.992033 + 0.125977i \(0.959793\pi\)
\(164\) 0.484674i 0.0378467i
\(165\) 8.93821 + 5.81800i 0.695839 + 0.452930i
\(166\) −17.7831 −1.38023
\(167\) −2.41921 3.32975i −0.187204 0.257664i 0.705091 0.709117i \(-0.250906\pi\)
−0.892295 + 0.451452i \(0.850906\pi\)
\(168\) −2.70544 8.32648i −0.208729 0.642402i
\(169\) −12.6012 3.19537i −0.969321 0.245798i
\(170\) −9.85442 7.15966i −0.755800 0.549121i
\(171\) −4.22054 + 5.80907i −0.322753 + 0.444231i
\(172\) −0.203204 + 0.625397i −0.0154941 + 0.0476861i
\(173\) −5.67003 17.4506i −0.431084 1.32674i −0.897046 0.441936i \(-0.854292\pi\)
0.465962 0.884805i \(-0.345708\pi\)
\(174\) −5.25468 7.23245i −0.398356 0.548290i
\(175\) 16.2807i 1.23070i
\(176\) 8.06410 + 9.97990i 0.607854 + 0.752263i
\(177\) 3.86525i 0.290530i
\(178\) 2.91303 2.11644i 0.218341 0.158634i
\(179\) 3.08404 + 9.49171i 0.230512 + 0.709444i 0.997685 + 0.0680035i \(0.0216629\pi\)
−0.767173 + 0.641441i \(0.778337\pi\)
\(180\) 0.194705 + 0.0632634i 0.0145124 + 0.00471537i
\(181\) −8.89365 6.46162i −0.661060 0.480288i 0.205961 0.978560i \(-0.433968\pi\)
−0.867021 + 0.498272i \(0.833968\pi\)
\(182\) 15.0211 2.88867i 1.11344 0.214122i
\(183\) −4.44603 + 13.6835i −0.328660 + 1.01151i
\(184\) 4.37161 1.42042i 0.322279 0.104715i
\(185\) −17.0902 + 12.4168i −1.25650 + 0.912899i
\(186\) 1.53948 0.112880
\(187\) −5.67442 7.02251i −0.414955 0.513537i
\(188\) 0.116544i 0.00849981i
\(189\) 1.79203 + 2.46651i 0.130351 + 0.179412i
\(190\) 30.5568 9.92849i 2.21682 0.720289i
\(191\) −4.97166 + 15.3012i −0.359737 + 1.10716i 0.593475 + 0.804852i \(0.297755\pi\)
−0.953212 + 0.302303i \(0.902245\pi\)
\(192\) 6.66484 + 4.84229i 0.480993 + 0.349462i
\(193\) 14.7012 20.2345i 1.05822 1.45651i 0.176754 0.984255i \(-0.443440\pi\)
0.881462 0.472254i \(-0.156560\pi\)
\(194\) −1.59343 + 4.90408i −0.114402 + 0.352092i
\(195\) −4.92083 + 10.4979i −0.352388 + 0.751772i
\(196\) 0.118211 0.0858852i 0.00844363 0.00613466i
\(197\) 22.0441i 1.57058i −0.619130 0.785288i \(-0.712515\pi\)
0.619130 0.785288i \(-0.287485\pi\)
\(198\) −3.86794 2.51769i −0.274882 0.178924i
\(199\) 18.1393 1.28586 0.642932 0.765923i \(-0.277718\pi\)
0.642932 + 0.765923i \(0.277718\pi\)
\(200\) −9.01353 12.4061i −0.637353 0.877241i
\(201\) 11.3096 3.67470i 0.797715 0.259193i
\(202\) −10.8494 3.52518i −0.763360 0.248031i
\(203\) 11.5128 15.8460i 0.808042 1.11217i
\(204\) −0.140213 0.101871i −0.00981685 0.00713236i
\(205\) −7.56459 + 23.2814i −0.528334 + 1.62604i
\(206\) 14.4305 4.68874i 1.00542 0.326680i
\(207\) −1.29498 + 0.940858i −0.0900073 + 0.0653941i
\(208\) −9.53321 + 10.1822i −0.661009 + 0.706012i
\(209\) 23.7834 1.22121i 1.64513 0.0844728i
\(210\) 13.6420i 0.941386i
\(211\) 7.01517 5.09682i 0.482944 0.350880i −0.319520 0.947579i \(-0.603522\pi\)
0.802464 + 0.596700i \(0.203522\pi\)
\(212\) 0.141906 + 0.436741i 0.00974612 + 0.0299955i
\(213\) 0.389304 + 0.126493i 0.0266747 + 0.00866712i
\(214\) 3.78871 5.21471i 0.258991 0.356470i
\(215\) −19.5219 + 26.8696i −1.33138 + 1.83249i
\(216\) −2.73109 0.887385i −0.185827 0.0603789i
\(217\) 1.04230 + 3.20787i 0.0707559 + 0.217764i
\(218\) −15.2749 + 11.0978i −1.03454 + 0.751640i
\(219\) 9.45946i 0.639211i
\(220\) −0.242659 0.634153i −0.0163601 0.0427546i
\(221\) 6.70819 7.16490i 0.451242 0.481963i
\(222\) 7.39564 5.37325i 0.496363 0.360629i
\(223\) 11.7683 3.82374i 0.788062 0.256057i 0.112783 0.993620i \(-0.464023\pi\)
0.675279 + 0.737563i \(0.264023\pi\)
\(224\) −0.339175 + 1.04387i −0.0226621 + 0.0697468i
\(225\) 4.32021 + 3.13881i 0.288014 + 0.209254i
\(226\) −1.88352 + 2.59244i −0.125290 + 0.172446i
\(227\) −12.6268 4.10269i −0.838068 0.272305i −0.141628 0.989920i \(-0.545234\pi\)
−0.696440 + 0.717615i \(0.745234\pi\)
\(228\) 0.434774 0.141267i 0.0287936 0.00935561i
\(229\) 6.24048 + 8.58929i 0.412383 + 0.567596i 0.963798 0.266635i \(-0.0859118\pi\)
−0.551415 + 0.834231i \(0.685912\pi\)
\(230\) 7.16238 0.472273
\(231\) 2.62742 9.76433i 0.172871 0.642446i
\(232\) 18.4487i 1.21122i
\(233\) −22.4787 + 16.3317i −1.47263 + 1.06993i −0.492789 + 0.870149i \(0.664022\pi\)
−0.979841 + 0.199779i \(0.935978\pi\)
\(234\) 2.12944 4.54289i 0.139206 0.296978i
\(235\) −1.81896 + 5.59819i −0.118656 + 0.365186i
\(236\) −0.144645 + 0.199087i −0.00941561 + 0.0129595i
\(237\) −4.62118 3.35748i −0.300178 0.218092i
\(238\) −3.56878 + 10.9836i −0.231330 + 0.711960i
\(239\) 0.0290695 0.00944525i 0.00188035 0.000610962i −0.308077 0.951362i \(-0.599685\pi\)
0.309957 + 0.950751i \(0.399685\pi\)
\(240\) 7.31199 + 10.0641i 0.471987 + 0.649635i
\(241\) 8.99759i 0.579586i −0.957089 0.289793i \(-0.906414\pi\)
0.957089 0.289793i \(-0.0935864\pi\)
\(242\) 1.56778 + 15.2262i 0.100781 + 0.978780i
\(243\) 1.00000 0.0641500
\(244\) 0.741065 0.538415i 0.0474418 0.0344685i
\(245\) 7.01875 2.28053i 0.448411 0.145698i
\(246\) 3.27351 10.0748i 0.208711 0.642348i
\(247\) 4.88912 + 25.4235i 0.311087 + 1.61766i
\(248\) −2.57023 1.86738i −0.163210 0.118579i
\(249\) −12.1541 3.94910i −0.770234 0.250264i
\(250\) −0.470219 1.44719i −0.0297393 0.0915280i
\(251\) 19.1837 13.9378i 1.21086 0.879744i 0.215555 0.976492i \(-0.430844\pi\)
0.995309 + 0.0967471i \(0.0308438\pi\)
\(252\) 0.194104i 0.0122274i
\(253\) 5.12651 + 1.37946i 0.322301 + 0.0867258i
\(254\) 1.49802i 0.0939944i
\(255\) −5.14520 7.08176i −0.322205 0.443477i
\(256\) −0.471690 1.45171i −0.0294806 0.0907321i
\(257\) 0.0297171 0.0914599i 0.00185370 0.00570511i −0.950125 0.311868i \(-0.899045\pi\)
0.951979 + 0.306163i \(0.0990453\pi\)
\(258\) 8.44792 11.6276i 0.525945 0.723901i
\(259\) 16.2036 + 11.7726i 1.00684 + 0.731514i
\(260\) 0.646310 0.356569i 0.0400824 0.0221135i
\(261\) −1.98527 6.11004i −0.122885 0.378202i
\(262\) 8.41610 + 11.5838i 0.519948 + 0.715647i
\(263\) 15.8394 0.976698 0.488349 0.872648i \(-0.337599\pi\)
0.488349 + 0.872648i \(0.337599\pi\)
\(264\) 3.40374 + 8.89516i 0.209486 + 0.547459i
\(265\) 23.1938i 1.42478i
\(266\) −17.9054 24.6447i −1.09785 1.51106i
\(267\) 2.46096 0.799613i 0.150608 0.0489355i
\(268\) −0.720036 0.233954i −0.0439832 0.0142910i
\(269\) −2.60791 1.89476i −0.159007 0.115526i 0.505436 0.862864i \(-0.331331\pi\)
−0.664444 + 0.747338i \(0.731331\pi\)
\(270\) −3.62001 2.63009i −0.220307 0.160062i
\(271\) −4.37008 1.41993i −0.265464 0.0862544i 0.173261 0.984876i \(-0.444570\pi\)
−0.438725 + 0.898622i \(0.644570\pi\)
\(272\) −3.25431 10.0157i −0.197322 0.607294i
\(273\) 10.9079 + 1.36145i 0.660175 + 0.0823988i
\(274\) 17.0954 1.03277
\(275\) −0.908213 17.6877i −0.0547673 1.06661i
\(276\) 0.101909 0.00613421
\(277\) −21.1133 + 15.3397i −1.26858 + 0.921676i −0.999145 0.0413434i \(-0.986836\pi\)
−0.269433 + 0.963019i \(0.586836\pi\)
\(278\) 0.0213649 0.00694188i 0.00128138 0.000416346i
\(279\) 1.05218 + 0.341875i 0.0629925 + 0.0204675i
\(280\) −16.5476 + 22.7759i −0.988910 + 1.36112i
\(281\) 3.28611 4.52295i 0.196033 0.269816i −0.699673 0.714463i \(-0.746671\pi\)
0.895706 + 0.444647i \(0.146671\pi\)
\(282\) 0.787141 2.42257i 0.0468736 0.144262i
\(283\) −0.0940650 0.289502i −0.00559158 0.0172091i 0.948222 0.317609i \(-0.102880\pi\)
−0.953813 + 0.300400i \(0.902880\pi\)
\(284\) −0.0153183 0.0210838i −0.000908971 0.00125109i
\(285\) 23.0893 1.36769
\(286\) −16.1581 + 3.97626i −0.955450 + 0.235121i
\(287\) 23.2096 1.37002
\(288\) 0.211609 + 0.291255i 0.0124692 + 0.0171624i
\(289\) −2.96334 9.12023i −0.174314 0.536484i
\(290\) −8.88324 + 27.3398i −0.521642 + 1.60545i
\(291\) −2.17811 + 2.99791i −0.127683 + 0.175741i
\(292\) 0.353992 0.487228i 0.0207158 0.0285128i
\(293\) 9.67826 + 3.14466i 0.565410 + 0.183713i 0.577754 0.816211i \(-0.303929\pi\)
−0.0123439 + 0.999924i \(0.503929\pi\)
\(294\) −3.03730 + 0.986879i −0.177139 + 0.0575560i
\(295\) −10.0553 + 7.30563i −0.585445 + 0.425350i
\(296\) −18.8650 −1.09651
\(297\) −2.08449 2.57971i −0.120954 0.149690i
\(298\) −27.2310 −1.57745
\(299\) −0.714796 + 5.72691i −0.0413377 + 0.331196i
\(300\) −0.105060 0.323341i −0.00606564 0.0186681i
\(301\) 29.9484 + 9.73082i 1.72620 + 0.560875i
\(302\) 6.84179 + 4.97085i 0.393701 + 0.286040i
\(303\) −6.63234 4.81867i −0.381018 0.276826i
\(304\) 26.4187 + 8.58395i 1.51521 + 0.492323i
\(305\) 44.0006 14.2967i 2.51947 0.818624i
\(306\) 2.22654 + 3.06457i 0.127283 + 0.175190i
\(307\) 8.56615i 0.488896i 0.969662 + 0.244448i \(0.0786067\pi\)
−0.969662 + 0.244448i \(0.921393\pi\)
\(308\) −0.500731 + 0.404608i −0.0285318 + 0.0230547i
\(309\) 10.9039 0.620304
\(310\) −2.90975 4.00492i −0.165262 0.227464i
\(311\) −6.07774 18.7053i −0.344637 1.06068i −0.961778 0.273830i \(-0.911709\pi\)
0.617141 0.786852i \(-0.288291\pi\)
\(312\) −9.06568 + 5.00153i −0.513243 + 0.283156i
\(313\) −16.0973 11.6954i −0.909873 0.661062i 0.0311094 0.999516i \(-0.490096\pi\)
−0.940983 + 0.338454i \(0.890096\pi\)
\(314\) −14.8772 + 20.4767i −0.839567 + 1.15557i
\(315\) 3.02949 9.32382i 0.170693 0.525338i
\(316\) 0.112379 + 0.345867i 0.00632182 + 0.0194566i
\(317\) −2.10265 2.89405i −0.118096 0.162546i 0.745876 0.666085i \(-0.232031\pi\)
−0.863973 + 0.503539i \(0.832031\pi\)
\(318\) 10.0369i 0.562841i
\(319\) −11.6238 + 17.8577i −0.650809 + 0.999841i
\(320\) 26.4907i 1.48088i
\(321\) 3.74749 2.72271i 0.209164 0.151967i
\(322\) −2.09847 6.45844i −0.116943 0.359915i
\(323\) −18.5899 6.04022i −1.03437 0.336087i
\(324\) −0.0515069 0.0374220i −0.00286150 0.00207900i
\(325\) 18.9074 3.63604i 1.04880 0.201691i
\(326\) 5.28334 16.2604i 0.292617 0.900582i
\(327\) −12.9043 + 4.19287i −0.713612 + 0.231866i
\(328\) −17.6860 + 12.8496i −0.976543 + 0.709500i
\(329\) 5.58092 0.307686
\(330\) 0.761014 + 14.8210i 0.0418925 + 0.815867i
\(331\) 32.1710i 1.76828i −0.467224 0.884139i \(-0.654746\pi\)
0.467224 0.884139i \(-0.345254\pi\)
\(332\) 0.478237 + 0.658236i 0.0262467 + 0.0361254i
\(333\) 6.24791 2.03007i 0.342383 0.111247i
\(334\) 1.76981 5.44692i 0.0968398 0.298042i
\(335\) −30.9356 22.4760i −1.69019 1.22800i
\(336\) 6.93266 9.54199i 0.378208 0.520558i
\(337\) 5.62079 17.2990i 0.306184 0.942338i −0.673049 0.739598i \(-0.735016\pi\)
0.979233 0.202740i \(-0.0649845\pi\)
\(338\) −6.70947 16.7995i −0.364947 0.913773i
\(339\) −1.86302 + 1.35356i −0.101185 + 0.0735155i
\(340\) 0.557303i 0.0302240i
\(341\) −1.31133 3.42696i −0.0710124 0.185580i
\(342\) −9.99170 −0.540289
\(343\) 8.43140 + 11.6048i 0.455253 + 0.626602i
\(344\) −28.2083 + 9.16544i −1.52089 + 0.494167i
\(345\) 4.89523 + 1.59056i 0.263550 + 0.0856327i
\(346\) 15.0076 20.6562i 0.806814 1.11048i
\(347\) −26.9181 19.5571i −1.44504 1.04988i −0.986959 0.160969i \(-0.948538\pi\)
−0.458078 0.888912i \(-0.651462\pi\)
\(348\) −0.126394 + 0.389002i −0.00677545 + 0.0208527i
\(349\) 20.5198 6.66728i 1.09840 0.356891i 0.296912 0.954905i \(-0.404043\pi\)
0.801486 + 0.598013i \(0.204043\pi\)
\(350\) −18.3282 + 13.3162i −0.979685 + 0.711783i
\(351\) 2.46424 2.63201i 0.131532 0.140487i
\(352\) 0.310256 1.15301i 0.0165367 0.0614556i
\(353\) 8.91882i 0.474701i −0.971424 0.237350i \(-0.923721\pi\)
0.971424 0.237350i \(-0.0762790\pi\)
\(354\) 4.35136 3.16145i 0.231272 0.168029i
\(355\) −0.406749 1.25184i −0.0215880 0.0664410i
\(356\) −0.156679 0.0509083i −0.00830400 0.00269813i
\(357\) −4.87827 + 6.71437i −0.258186 + 0.355362i
\(358\) −8.16295 + 11.2353i −0.431425 + 0.593806i
\(359\) 8.10039 + 2.63198i 0.427522 + 0.138910i 0.514872 0.857267i \(-0.327840\pi\)
−0.0873493 + 0.996178i \(0.527840\pi\)
\(360\) 2.85347 + 8.78208i 0.150391 + 0.462856i
\(361\) 26.3402 19.1373i 1.38633 1.00722i
\(362\) 15.2972i 0.804004i
\(363\) −2.30979 + 10.7548i −0.121232 + 0.564479i
\(364\) −0.510884 0.478319i −0.0267776 0.0250707i
\(365\) 24.6085 17.8791i 1.28807 0.935837i
\(366\) −19.0409 + 6.18675i −0.995282 + 0.323387i
\(367\) 1.04722 3.22300i 0.0546642 0.168239i −0.919997 0.391925i \(-0.871809\pi\)
0.974661 + 0.223686i \(0.0718091\pi\)
\(368\) 5.00978 + 3.63982i 0.261153 + 0.189739i
\(369\) 4.47466 6.15884i 0.232941 0.320616i
\(370\) −27.9567 9.08369i −1.45340 0.472239i
\(371\) 20.9142 6.79544i 1.08581 0.352802i
\(372\) −0.0414011 0.0569837i −0.00214655 0.00295447i
\(373\) −9.79834 −0.507339 −0.253669 0.967291i \(-0.581638\pi\)
−0.253669 + 0.967291i \(0.581638\pi\)
\(374\) 3.26449 12.1319i 0.168803 0.627325i
\(375\) 1.09352i 0.0564693i
\(376\) −4.25272 + 3.08978i −0.219317 + 0.159343i
\(377\) −20.9739 9.83136i −1.08021 0.506341i
\(378\) −1.31099 + 4.03480i −0.0674299 + 0.207528i
\(379\) 7.10341 9.77700i 0.364877 0.502211i −0.586622 0.809861i \(-0.699543\pi\)
0.951500 + 0.307650i \(0.0995426\pi\)
\(380\) −1.18926 0.864048i −0.0610077 0.0443247i
\(381\) −0.332668 + 1.02385i −0.0170431 + 0.0524532i
\(382\) −21.2919 + 6.91817i −1.08939 + 0.353965i
\(383\) 13.7260 + 18.8922i 0.701364 + 0.965345i 0.999940 + 0.0109590i \(0.00348844\pi\)
−0.298576 + 0.954386i \(0.596512\pi\)
\(384\) 10.7436i 0.548257i
\(385\) −30.3677 + 11.6202i −1.54768 + 0.592221i
\(386\) 34.8036 1.77146
\(387\) 8.35601 6.07100i 0.424760 0.308606i
\(388\) 0.224376 0.0729040i 0.0113909 0.00370114i
\(389\) −8.94512 + 27.5302i −0.453535 + 1.39584i 0.419311 + 0.907843i \(0.362272\pi\)
−0.872846 + 0.487996i \(0.837728\pi\)
\(390\) −15.8430 + 3.04673i −0.802242 + 0.154277i
\(391\) −3.52521 2.56121i −0.178277 0.129526i
\(392\) 6.26798 + 2.03659i 0.316581 + 0.102863i
\(393\) 3.17969 + 9.78607i 0.160394 + 0.493642i
\(394\) 24.8165 18.0302i 1.25024 0.908350i
\(395\) 18.3678i 0.924183i
\(396\) 0.0108280 + 0.210879i 0.000544129 + 0.0105971i
\(397\) 8.63454i 0.433355i 0.976243 + 0.216678i \(0.0695220\pi\)
−0.976243 + 0.216678i \(0.930478\pi\)
\(398\) 14.8365 + 20.4206i 0.743685 + 1.02359i
\(399\) −6.76484 20.8200i −0.338665 1.04230i
\(400\) 6.38388 19.6476i 0.319194 0.982378i
\(401\) −7.79030 + 10.7224i −0.389029 + 0.535452i −0.957948 0.286941i \(-0.907362\pi\)
0.568919 + 0.822393i \(0.307362\pi\)
\(402\) 13.3871 + 9.72632i 0.667689 + 0.485105i
\(403\) 3.49265 1.92690i 0.173981 0.0959855i
\(404\) 0.161287 + 0.496390i 0.00802433 + 0.0246963i
\(405\) −1.89008 2.60147i −0.0939189 0.129268i
\(406\) 27.2554 1.35267
\(407\) −18.2607 11.8861i −0.905149 0.589173i
\(408\) 7.81720i 0.387009i
\(409\) −4.92749 6.78211i −0.243649 0.335354i 0.669626 0.742699i \(-0.266455\pi\)
−0.913274 + 0.407345i \(0.866455\pi\)
\(410\) −32.3966 + 10.5263i −1.59995 + 0.519857i
\(411\) 11.6841 + 3.79639i 0.576333 + 0.187262i
\(412\) −0.561629 0.408047i −0.0276695 0.0201030i
\(413\) 9.53369 + 6.92663i 0.469122 + 0.340837i
\(414\) −2.11837 0.688300i −0.104112 0.0338281i
\(415\) 12.6987 + 39.0827i 0.623356 + 1.91849i
\(416\) 1.28805 + 0.160766i 0.0631516 + 0.00788218i
\(417\) 0.0161437 0.000790563
\(418\) 20.8276 + 25.7757i 1.01871 + 1.26073i
\(419\) 13.2656 0.648067 0.324034 0.946046i \(-0.394961\pi\)
0.324034 + 0.946046i \(0.394961\pi\)
\(420\) −0.504956 + 0.366872i −0.0246393 + 0.0179015i
\(421\) −16.0487 + 5.21452i −0.782164 + 0.254140i −0.672764 0.739857i \(-0.734893\pi\)
−0.109400 + 0.993998i \(0.534893\pi\)
\(422\) 11.4756 + 3.72866i 0.558626 + 0.181508i
\(423\) 1.07597 1.48094i 0.0523153 0.0720058i
\(424\) −12.1747 + 16.7570i −0.591255 + 0.813792i
\(425\) −4.49211 + 13.8253i −0.217900 + 0.670626i
\(426\) 0.176017 + 0.541725i 0.00852806 + 0.0262467i
\(427\) −25.7831 35.4874i −1.24773 1.71735i
\(428\) −0.294911 −0.0142550
\(429\) −11.9265 0.870619i −0.575818 0.0420339i
\(430\) −46.2161 −2.22874
\(431\) −19.5151 26.8602i −0.940008 1.29381i −0.955825 0.293935i \(-0.905035\pi\)
0.0158177 0.999875i \(-0.494965\pi\)
\(432\) −1.19547 3.67927i −0.0575170 0.177019i
\(433\) −7.27826 + 22.4002i −0.349771 + 1.07648i 0.609209 + 0.793009i \(0.291487\pi\)
−0.958980 + 0.283474i \(0.908513\pi\)
\(434\) −2.75879 + 3.79715i −0.132426 + 0.182269i
\(435\) −12.1428 + 16.7131i −0.582201 + 0.801331i
\(436\) 0.821569 + 0.266944i 0.0393460 + 0.0127843i
\(437\) 10.9310 3.55170i 0.522902 0.169901i
\(438\) −10.6491 + 7.73704i −0.508835 + 0.369690i
\(439\) 14.6392 0.698692 0.349346 0.936994i \(-0.386404\pi\)
0.349346 + 0.936994i \(0.386404\pi\)
\(440\) 16.7072 25.6673i 0.796483 1.22364i
\(441\) −2.29505 −0.109288
\(442\) 13.5527 + 1.69156i 0.644637 + 0.0804595i
\(443\) 3.42284 + 10.5344i 0.162624 + 0.500505i 0.998853 0.0478748i \(-0.0152448\pi\)
−0.836229 + 0.548380i \(0.815245\pi\)
\(444\) −0.397780 0.129246i −0.0188778 0.00613377i
\(445\) −6.73158 4.89078i −0.319107 0.231845i
\(446\) 13.9301 + 10.1208i 0.659609 + 0.479234i
\(447\) −18.6114 6.04722i −0.880291 0.286024i
\(448\) −23.8871 + 7.76140i −1.12856 + 0.366692i
\(449\) −9.00409 12.3931i −0.424929 0.584865i 0.541851 0.840475i \(-0.317724\pi\)
−0.966780 + 0.255610i \(0.917724\pi\)
\(450\) 7.43082i 0.350292i
\(451\) −25.2154 + 1.29474i −1.18735 + 0.0609669i
\(452\) 0.146612 0.00689603
\(453\) 3.57224 + 4.91677i 0.167838 + 0.231010i
\(454\) −5.70898 17.5704i −0.267936 0.824621i
\(455\) −17.0750 30.9498i −0.800489 1.45095i
\(456\) 16.6815 + 12.1199i 0.781185 + 0.567564i
\(457\) 22.8294 31.4219i 1.06791 1.46986i 0.195740 0.980656i \(-0.437289\pi\)
0.872172 0.489199i \(-0.162711\pi\)
\(458\) −4.56533 + 14.0506i −0.213324 + 0.656543i
\(459\) 0.841209 + 2.58898i 0.0392643 + 0.120843i
\(460\) −0.192617 0.265114i −0.00898080 0.0123610i
\(461\) 12.1630i 0.566489i 0.959048 + 0.283244i \(0.0914107\pi\)
−0.959048 + 0.283244i \(0.908589\pi\)
\(462\) 13.1414 5.02855i 0.611391 0.233949i
\(463\) 8.23544i 0.382733i −0.981519 0.191367i \(-0.938708\pi\)
0.981519 0.191367i \(-0.0612920\pi\)
\(464\) −20.1071 + 14.6087i −0.933451 + 0.678192i
\(465\) −1.09933 3.38339i −0.0509803 0.156901i
\(466\) −36.7714 11.9478i −1.70340 0.553469i
\(467\) −3.10334 2.25471i −0.143605 0.104335i 0.513663 0.857992i \(-0.328288\pi\)
−0.657268 + 0.753657i \(0.728288\pi\)
\(468\) −0.225421 + 0.0433501i −0.0104201 + 0.00200386i
\(469\) −11.2033 + 34.4804i −0.517322 + 1.59215i
\(470\) −7.79001 + 2.53113i −0.359326 + 0.116752i
\(471\) −14.7153 + 10.6913i −0.678045 + 0.492629i
\(472\) −11.0996 −0.510900
\(473\) −33.0794 8.90112i −1.52099 0.409274i
\(474\) 7.94850i 0.365087i
\(475\) −22.5380 31.0208i −1.03411 1.42333i
\(476\) 0.502530 0.163282i 0.0230334 0.00748401i
\(477\) 2.22891 6.85987i 0.102055 0.314092i
\(478\) 0.0344095 + 0.0250000i 0.00157386 + 0.00114347i
\(479\) 7.93170 10.9171i 0.362409 0.498813i −0.588409 0.808563i \(-0.700246\pi\)
0.950818 + 0.309750i \(0.100246\pi\)
\(480\) 0.357734 1.10099i 0.0163283 0.0502532i
\(481\) 10.0532 21.4472i 0.458387 0.977906i
\(482\) 10.1292 7.35928i 0.461371 0.335206i
\(483\) 4.88013i 0.222053i
\(484\) 0.521435 0.467508i 0.0237016 0.0212504i
\(485\) 11.9158 0.541068
\(486\) 0.817916 + 1.12577i 0.0371014 + 0.0510657i
\(487\) −16.9669 + 5.51287i −0.768842 + 0.249812i −0.667069 0.744996i \(-0.732452\pi\)
−0.101773 + 0.994808i \(0.532452\pi\)
\(488\) 39.2940 + 12.7674i 1.77876 + 0.577953i
\(489\) 7.22195 9.94016i 0.326588 0.449510i
\(490\) 8.30808 + 6.03618i 0.375321 + 0.272687i
\(491\) 9.57615 29.4724i 0.432166 1.33007i −0.463798 0.885941i \(-0.653514\pi\)
0.895963 0.444128i \(-0.146486\pi\)
\(492\) −0.460952 + 0.149772i −0.0207813 + 0.00675226i
\(493\) 14.1487 10.2796i 0.637226 0.462971i
\(494\) −24.6220 + 26.2983i −1.10780 + 1.18322i
\(495\) −2.77118 + 10.2986i −0.124555 + 0.462888i
\(496\) 4.27996i 0.192176i
\(497\) −1.00964 + 0.733545i −0.0452885 + 0.0329040i
\(498\) −5.49527 16.9127i −0.246249 0.757876i
\(499\) 32.8955 + 10.6884i 1.47261 + 0.478479i 0.931895 0.362729i \(-0.118155\pi\)
0.540712 + 0.841208i \(0.318155\pi\)
\(500\) −0.0409218 + 0.0563240i −0.00183008 + 0.00251889i
\(501\) 2.41921 3.32975i 0.108082 0.148762i
\(502\) 31.3813 + 10.1964i 1.40062 + 0.455088i
\(503\) 4.68909 + 14.4315i 0.209076 + 0.643470i 0.999521 + 0.0309375i \(0.00984928\pi\)
−0.790445 + 0.612533i \(0.790151\pi\)
\(504\) 7.08293 5.14605i 0.315499 0.229223i
\(505\) 26.3615i 1.17307i
\(506\) 2.64011 + 6.89953i 0.117367 + 0.306722i
\(507\) −0.854997 12.9719i −0.0379718 0.576100i
\(508\) 0.0554491 0.0402861i 0.00246015 0.00178741i
\(509\) −28.4796 + 9.25357i −1.26233 + 0.410157i −0.862326 0.506354i \(-0.830993\pi\)
−0.400009 + 0.916511i \(0.630993\pi\)
\(510\) 3.76405 11.5846i 0.166675 0.512973i
\(511\) −23.3319 16.9516i −1.03214 0.749895i
\(512\) 13.8783 19.1019i 0.613342 0.844193i
\(513\) −6.82897 2.21887i −0.301507 0.0979654i
\(514\) 0.127268 0.0413520i 0.00561357 0.00182396i
\(515\) −20.6093 28.3663i −0.908156 1.24997i
\(516\) −0.657581 −0.0289484
\(517\) −6.06324 + 0.311330i −0.266661 + 0.0136923i
\(518\) 27.8705i 1.22456i
\(519\) 14.8443 10.7850i 0.651594 0.473410i
\(520\) 30.1462 + 14.1308i 1.32200 + 0.619678i
\(521\) −1.19705 + 3.68415i −0.0524438 + 0.161405i −0.973848 0.227200i \(-0.927043\pi\)
0.921404 + 0.388605i \(0.127043\pi\)
\(522\) 5.25468 7.23245i 0.229991 0.316556i
\(523\) 24.7603 + 17.9894i 1.08269 + 0.786622i 0.978150 0.207898i \(-0.0666623\pi\)
0.104542 + 0.994520i \(0.466662\pi\)
\(524\) 0.202438 0.623041i 0.00884355 0.0272177i
\(525\) −15.4838 + 5.03101i −0.675771 + 0.219571i
\(526\) 12.9553 + 17.8314i 0.564877 + 0.777487i
\(527\) 3.01166i 0.131190i
\(528\) −6.99950 + 10.7534i −0.304614 + 0.467980i
\(529\) −20.4378 −0.888601
\(530\) −26.1107 + 18.9705i −1.13418 + 0.824028i
\(531\) 3.67607 1.19443i 0.159528 0.0518337i
\(532\) −0.430691 + 1.32553i −0.0186728 + 0.0574690i
\(533\) −5.18350 26.9543i −0.224522 1.16752i
\(534\) 2.91303 + 2.11644i 0.126059 + 0.0915874i
\(535\) −14.1661 4.60285i −0.612454 0.198998i
\(536\) −10.5524 32.4770i −0.455795 1.40279i
\(537\) −8.07413 + 5.86620i −0.348425 + 0.253145i
\(538\) 4.48565i 0.193390i
\(539\) 4.78401 + 5.92055i 0.206062 + 0.255016i
\(540\) 0.204725i 0.00880994i
\(541\) −1.64461 2.26361i −0.0707072 0.0973201i 0.772199 0.635381i \(-0.219157\pi\)
−0.842906 + 0.538061i \(0.819157\pi\)
\(542\) −1.97586 6.08107i −0.0848704 0.261204i
\(543\) 3.39707 10.4551i 0.145782 0.448672i
\(544\) −0.576045 + 0.792858i −0.0246977 + 0.0339935i
\(545\) 35.2979 + 25.6454i 1.51200 + 1.09853i
\(546\) 7.38906 + 13.3933i 0.316223 + 0.573179i
\(547\) −8.60655 26.4882i −0.367990 1.13256i −0.948088 0.318009i \(-0.896986\pi\)
0.580098 0.814547i \(-0.303014\pi\)
\(548\) −0.459743 0.632782i −0.0196392 0.0270311i
\(549\) −14.3877 −0.614050
\(550\) 19.1694 15.4895i 0.817384 0.660474i
\(551\) 46.1303i 1.96522i
\(552\) 2.70180 + 3.71871i 0.114996 + 0.158279i
\(553\) 16.5625 5.38150i 0.704311 0.228845i
\(554\) −34.5379 11.2220i −1.46737 0.476779i
\(555\) −17.0902 12.4168i −0.725439 0.527062i
\(556\) −0.000831515 0 0.000604131i −3.52641e−5 0 2.56209e-5i
\(557\) 42.1587 + 13.6982i 1.78632 + 0.580411i 0.999332 0.0365563i \(-0.0116388\pi\)
0.786989 + 0.616967i \(0.211639\pi\)
\(558\) 0.475726 + 1.46413i 0.0201391 + 0.0619818i
\(559\) 4.61230 36.9535i 0.195080 1.56297i
\(560\) −37.9265 −1.60269
\(561\) 4.92531 7.56677i 0.207947 0.319469i
\(562\) 7.77954 0.328160
\(563\) −18.3079 + 13.3015i −0.771585 + 0.560589i −0.902442 0.430812i \(-0.858227\pi\)
0.130857 + 0.991401i \(0.458227\pi\)
\(564\) −0.110839 + 0.0360139i −0.00466718 + 0.00151646i
\(565\) 7.04252 + 2.28825i 0.296281 + 0.0962676i
\(566\) 0.248974 0.342684i 0.0104652 0.0144041i
\(567\) −1.79203 + 2.46651i −0.0752580 + 0.103584i
\(568\) 0.363241 1.11794i 0.0152412 0.0469077i
\(569\) 13.4106 + 41.2735i 0.562201 + 1.73028i 0.676126 + 0.736786i \(0.263657\pi\)
−0.113926 + 0.993489i \(0.536343\pi\)
\(570\) 18.8851 + 25.9931i 0.791010 + 1.08873i
\(571\) 7.31359 0.306064 0.153032 0.988221i \(-0.451096\pi\)
0.153032 + 0.988221i \(0.451096\pi\)
\(572\) 0.581719 + 0.491157i 0.0243229 + 0.0205363i
\(573\) −16.0886 −0.672112
\(574\) 18.9835 + 26.1285i 0.792355 + 1.09058i
\(575\) −2.64140 8.12940i −0.110154 0.339019i
\(576\) −2.54574 + 7.83499i −0.106073 + 0.326458i
\(577\) 7.12951 9.81292i 0.296805 0.408517i −0.634404 0.773001i \(-0.718755\pi\)
0.931210 + 0.364484i \(0.118755\pi\)
\(578\) 7.84347 10.7956i 0.326245 0.449038i
\(579\) 23.7871 + 7.72888i 0.988556 + 0.321201i
\(580\) 1.25087 0.406434i 0.0519397 0.0168762i
\(581\) 31.5210 22.9013i 1.30771 0.950107i
\(582\) −5.15646 −0.213742
\(583\) −22.3426 + 8.54941i −0.925335 + 0.354080i
\(584\) 27.1641 1.12406
\(585\) −11.5047 1.43595i −0.475662 0.0593691i
\(586\) 4.37586 + 13.4675i 0.180765 + 0.556338i
\(587\) 40.3507 + 13.1107i 1.66545 + 0.541138i 0.982004 0.188861i \(-0.0604794\pi\)
0.683448 + 0.729999i \(0.260479\pi\)
\(588\) 0.118211 + 0.0858852i 0.00487493 + 0.00354185i
\(589\) −6.42675 4.66931i −0.264810 0.192395i
\(590\) −16.4489 5.34456i −0.677188 0.220032i
\(591\) 20.9652 6.81200i 0.862392 0.280208i
\(592\) −14.9383 20.5609i −0.613962 0.845046i
\(593\) 22.1805i 0.910843i 0.890276 + 0.455422i \(0.150511\pi\)
−0.890276 + 0.455422i \(0.849489\pi\)
\(594\) 1.19921 4.45663i 0.0492040 0.182858i
\(595\) 26.6876 1.09408
\(596\) 0.732319 + 1.00795i 0.0299970 + 0.0412873i
\(597\) 5.60537 + 17.2515i 0.229412 + 0.706059i
\(598\) −7.03180 + 3.87944i −0.287552 + 0.158642i
\(599\) −2.88085 2.09306i −0.117708 0.0855202i 0.527374 0.849634i \(-0.323177\pi\)
−0.645082 + 0.764113i \(0.723177\pi\)
\(600\) 9.01353 12.4061i 0.367976 0.506475i
\(601\) −3.50614 + 10.7908i −0.143019 + 0.440166i −0.996751 0.0805462i \(-0.974334\pi\)
0.853732 + 0.520712i \(0.174334\pi\)
\(602\) 13.5406 + 41.6738i 0.551876 + 1.69850i
\(603\) 6.98970 + 9.62049i 0.284642 + 0.391777i
\(604\) 0.386928i 0.0157439i
\(605\) 32.3439 14.3185i 1.31497 0.582131i
\(606\) 11.4077i 0.463407i
\(607\) 15.7523 11.4447i 0.639367 0.464527i −0.220266 0.975440i \(-0.570692\pi\)
0.859633 + 0.510913i \(0.170692\pi\)
\(608\) −0.798818 2.45851i −0.0323963 0.0997057i
\(609\) 18.6281 + 6.05265i 0.754850 + 0.245266i
\(610\) 52.0834 + 37.8408i 2.10880 + 1.53213i
\(611\) −1.24641 6.48136i −0.0504244 0.262208i
\(612\) 0.0535565 0.164830i 0.00216489 0.00666286i
\(613\) −21.5657 + 7.00713i −0.871032 + 0.283015i −0.710228 0.703971i \(-0.751408\pi\)
−0.160803 + 0.986987i \(0.551408\pi\)
\(614\) −9.64347 + 7.00639i −0.389179 + 0.282755i
\(615\) −24.4795 −0.987110
\(616\) −28.0396 7.54499i −1.12975 0.303996i
\(617\) 2.59709i 0.104555i −0.998633 0.0522774i \(-0.983352\pi\)
0.998633 0.0522774i \(-0.0166480\pi\)
\(618\) 8.91851 + 12.2753i 0.358755 + 0.493784i
\(619\) 26.0889 8.47681i 1.04860 0.340712i 0.266483 0.963840i \(-0.414138\pi\)
0.782120 + 0.623128i \(0.214138\pi\)
\(620\) −0.0699901 + 0.215408i −0.00281087 + 0.00865097i
\(621\) −1.29498 0.940858i −0.0519657 0.0377553i
\(622\) 16.0867 22.1415i 0.645020 0.887794i
\(623\) −2.43784 + 7.50291i −0.0976701 + 0.300598i
\(624\) −12.6298 5.92014i −0.505597 0.236995i
\(625\) 18.7563 13.6272i 0.750250 0.545089i
\(626\) 27.6876i 1.10662i
\(627\) 8.51091 + 22.2420i 0.339893 + 0.888259i
\(628\) 1.15803 0.0462104
\(629\) 10.5116 + 14.4680i 0.419125 + 0.576875i
\(630\) 12.9743 4.21561i 0.516908 0.167954i
\(631\) −26.7218 8.68245i −1.06378 0.345643i −0.275717 0.961239i \(-0.588915\pi\)
−0.788062 + 0.615596i \(0.788915\pi\)
\(632\) −9.64147 + 13.2703i −0.383517 + 0.527866i
\(633\) 7.01517 + 5.09682i 0.278828 + 0.202580i
\(634\) 1.53823 4.73418i 0.0610908 0.188018i
\(635\) 3.29228 1.06973i 0.130650 0.0424508i
\(636\) −0.371514 + 0.269921i −0.0147315 + 0.0107031i
\(637\) −5.65556 + 6.04059i −0.224081 + 0.239337i
\(638\) −29.6109 + 1.52044i −1.17231 + 0.0601947i
\(639\) 0.409338i 0.0161932i
\(640\) 27.9492 20.3063i 1.10479 0.802676i
\(641\) 14.0483 + 43.2361i 0.554873 + 1.70772i 0.696280 + 0.717771i \(0.254837\pi\)
−0.141407 + 0.989952i \(0.545163\pi\)
\(642\) 6.13026 + 1.99184i 0.241942 + 0.0786117i
\(643\) 4.13004 5.68451i 0.162873 0.224175i −0.719778 0.694204i \(-0.755757\pi\)
0.882651 + 0.470029i \(0.155757\pi\)
\(644\) −0.182624 + 0.251360i −0.00719639 + 0.00990499i
\(645\) −31.5871 10.2633i −1.24374 0.404115i
\(646\) −8.40511 25.8683i −0.330695 1.01777i
\(647\) −29.8982 + 21.7223i −1.17542 + 0.853993i −0.991648 0.128976i \(-0.958831\pi\)
−0.183772 + 0.982969i \(0.558831\pi\)
\(648\) 2.87164i 0.112809i
\(649\) −10.7440 6.99341i −0.421739 0.274515i
\(650\) 19.5580 + 18.3114i 0.767129 + 0.718231i
\(651\) −2.72878 + 1.98257i −0.106949 + 0.0777031i
\(652\) −0.743961 + 0.241728i −0.0291358 + 0.00946678i
\(653\) 1.75250 5.39363i 0.0685805 0.211069i −0.910893 0.412643i \(-0.864606\pi\)
0.979473 + 0.201574i \(0.0646057\pi\)
\(654\) −15.2749 11.0978i −0.597294 0.433960i
\(655\) 19.4483 26.7683i 0.759909 1.04593i
\(656\) −28.0093 9.10079i −1.09358 0.355326i
\(657\) −8.99648 + 2.92313i −0.350986 + 0.114042i
\(658\) 4.56472 + 6.28280i 0.177951 + 0.244929i
\(659\) 0.0891110 0.00347127 0.00173564 0.999998i \(-0.499448\pi\)
0.00173564 + 0.999998i \(0.499448\pi\)
\(660\) 0.528129 0.426747i 0.0205574 0.0166111i
\(661\) 7.27774i 0.283071i 0.989933 + 0.141536i \(0.0452040\pi\)
−0.989933 + 0.141536i \(0.954796\pi\)
\(662\) 36.2170 26.3132i 1.40761 1.02269i
\(663\) 8.88717 + 4.16579i 0.345149 + 0.161786i
\(664\) −11.3404 + 34.9021i −0.440093 + 1.35447i
\(665\) −41.3766 + 56.9501i −1.60452 + 2.20843i
\(666\) 7.39564 + 5.37325i 0.286575 + 0.208209i
\(667\) −3.17779 + 9.78023i −0.123044 + 0.378692i
\(668\) −0.249212 + 0.0809739i −0.00964230 + 0.00313297i
\(669\) 7.27319 + 10.0107i 0.281198 + 0.387036i
\(670\) 53.2098i 2.05567i
\(671\) 29.9910 + 37.1160i 1.15779 + 1.43285i
\(672\) −1.09759 −0.0423406
\(673\) 18.8063 13.6635i 0.724928 0.526691i −0.163027 0.986622i \(-0.552126\pi\)
0.887955 + 0.459931i \(0.152126\pi\)
\(674\) 24.0720 7.82146i 0.927218 0.301271i
\(675\) −1.65017 + 5.07871i −0.0635151 + 0.195480i
\(676\) −0.441394 + 0.700136i −0.0169767 + 0.0269283i
\(677\) 23.3516 + 16.9659i 0.897476 + 0.652054i 0.937816 0.347132i \(-0.112844\pi\)
−0.0403407 + 0.999186i \(0.512844\pi\)
\(678\) −3.04759 0.990223i −0.117042 0.0380293i
\(679\) −3.49116 10.7447i −0.133978 0.412343i
\(680\) −20.3362 + 14.7751i −0.779859 + 0.566601i
\(681\) 13.2766i 0.508760i
\(682\) 2.78539 4.27921i 0.106658 0.163860i
\(683\) 23.8036i 0.910821i 0.890282 + 0.455410i \(0.150507\pi\)
−0.890282 + 0.455410i \(0.849493\pi\)
\(684\) 0.268705 + 0.369841i 0.0102742 + 0.0141412i
\(685\) −12.2077 37.5713i −0.466430 1.43553i
\(686\) −6.16813 + 18.9836i −0.235500 + 0.724796i
\(687\) −6.24048 + 8.58929i −0.238089 + 0.327702i
\(688\) −32.3262 23.4863i −1.23242 0.895408i
\(689\) −12.5627 22.7709i −0.478601 0.867502i
\(690\) 2.21330 + 6.81182i 0.0842587 + 0.259322i
\(691\) 6.39262 + 8.79869i 0.243187 + 0.334718i 0.913111 0.407712i \(-0.133673\pi\)
−0.669924 + 0.742430i \(0.733673\pi\)
\(692\) −1.16818 −0.0444077
\(693\) 10.0983 0.518522i 0.383605 0.0196970i
\(694\) 46.2995i 1.75750i
\(695\) −0.0305130 0.0419975i −0.00115742 0.00159306i
\(696\) −17.5458 + 5.70098i −0.665072 + 0.216095i
\(697\) 19.7092 + 6.40391i 0.746539 + 0.242565i
\(698\) 24.2892 + 17.6472i 0.919362 + 0.667955i
\(699\) −22.4787 16.3317i −0.850223 0.617723i
\(700\) 0.985796 + 0.320305i 0.0372596 + 0.0121064i
\(701\) −7.19231 22.1357i −0.271650 0.836053i −0.990086 0.140460i \(-0.955142\pi\)
0.718436 0.695593i \(-0.244858\pi\)
\(702\) 4.97858 + 0.621393i 0.187904 + 0.0234530i
\(703\) −47.1712 −1.77910
\(704\) 25.5186 9.76470i 0.961767 0.368021i
\(705\) −5.88629 −0.221691
\(706\) 10.0405 7.29485i 0.377879 0.274545i
\(707\) 23.7706 7.72355i 0.893987 0.290474i
\(708\) −0.234041 0.0760445i −0.00879580 0.00285793i
\(709\) 1.47867 2.03522i 0.0555328 0.0764343i −0.780347 0.625346i \(-0.784958\pi\)
0.835880 + 0.548912i \(0.184958\pi\)
\(710\) 1.07660 1.48181i 0.0404039 0.0556113i
\(711\) 1.76513 5.43252i 0.0661976 0.203735i
\(712\) −2.29620 7.06697i −0.0860537 0.264846i
\(713\) −1.04090 1.43267i −0.0389820 0.0536541i
\(714\) −11.5488 −0.432204
\(715\) 20.2772 + 32.6721i 0.758325 + 1.22187i
\(716\) 0.635399 0.0237460
\(717\) 0.0179659 + 0.0247280i 0.000670950 + 0.000923484i
\(718\) 3.66245 + 11.2719i 0.136682 + 0.420663i
\(719\) 5.64689 17.3793i 0.210593 0.648139i −0.788844 0.614594i \(-0.789320\pi\)
0.999437 0.0335459i \(-0.0106800\pi\)
\(720\) −7.31199 + 10.0641i −0.272502 + 0.375067i
\(721\) −19.5402 + 26.8947i −0.727713 + 1.00161i
\(722\) 43.0881 + 14.0002i 1.60357 + 0.521033i
\(723\) 8.55722 2.78041i 0.318246 0.103405i
\(724\) −0.566224 + 0.411386i −0.0210435 + 0.0152890i
\(725\) 34.3071 1.27413
\(726\) −13.9965 + 6.19622i −0.519461 + 0.229963i
\(727\) 41.2474 1.52978 0.764891 0.644159i \(-0.222793\pi\)
0.764891 + 0.644159i \(0.222793\pi\)
\(728\) 3.90960 31.3235i 0.144899 1.16093i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 40.2554 + 13.0798i 1.48992 + 0.484104i
\(731\) 22.7468 + 16.5265i 0.841321 + 0.611256i
\(732\) 0.741065 + 0.538415i 0.0273905 + 0.0199004i
\(733\) 25.0555 + 8.14103i 0.925446 + 0.300696i 0.732699 0.680553i \(-0.238260\pi\)
0.192747 + 0.981248i \(0.438260\pi\)
\(734\) 4.48488 1.45722i 0.165540 0.0537871i
\(735\) 4.33782 + 5.97050i 0.160003 + 0.220225i
\(736\) 0.576264i 0.0212414i
\(737\) 10.2481 38.0852i 0.377493 1.40289i
\(738\) 10.5933 0.389945
\(739\) −14.6349 20.1432i −0.538354 0.740980i 0.450021 0.893018i \(-0.351416\pi\)
−0.988375 + 0.152038i \(0.951416\pi\)
\(740\) 0.415605 + 1.27910i 0.0152779 + 0.0470206i
\(741\) −22.6684 + 12.5061i −0.832743 + 0.459424i
\(742\) 24.7561 + 17.9864i 0.908826 + 0.660301i
\(743\) −6.26470 + 8.62263i −0.229830 + 0.316333i −0.908320 0.418276i \(-0.862635\pi\)
0.678490 + 0.734609i \(0.262635\pi\)
\(744\) 0.981740 3.02149i 0.0359923 0.110773i
\(745\) 19.4454 + 59.8469i 0.712426 + 2.19262i
\(746\) −8.01422 11.0306i −0.293422 0.403860i
\(747\) 12.7796i 0.467580i
\(748\) −0.536851 + 0.205427i −0.0196292 + 0.00751114i
\(749\) 14.1224i 0.516021i
\(750\) 1.23105 0.894410i 0.0449516 0.0326592i
\(751\) −9.27231 28.5372i −0.338351 1.04134i −0.965048 0.262075i \(-0.915593\pi\)
0.626696 0.779264i \(-0.284407\pi\)
\(752\) −6.73506 2.18836i −0.245603 0.0798011i
\(753\) 19.1837 + 13.9378i 0.699093 + 0.507921i
\(754\) −6.08708 31.6529i −0.221679 1.15273i
\(755\) 6.03901 18.5862i 0.219782 0.676420i
\(756\) 0.184604 0.0599814i 0.00671397 0.00218150i
\(757\) 5.87848 4.27096i 0.213657 0.155231i −0.475810 0.879548i \(-0.657845\pi\)
0.689467 + 0.724317i \(0.257845\pi\)
\(758\) 16.8166 0.610806
\(759\) 0.272237 + 5.30188i 0.00988156 + 0.192446i
\(760\) 66.3041i 2.40510i
\(761\) −21.4831 29.5690i −0.778762 1.07187i −0.995417 0.0956258i \(-0.969515\pi\)
0.216655 0.976248i \(-0.430485\pi\)
\(762\) −1.42470 + 0.462915i −0.0516116 + 0.0167696i
\(763\) 12.7831 39.3425i 0.462781 1.42429i
\(764\) 0.828676 + 0.602068i 0.0299804 + 0.0217821i
\(765\) 5.14520 7.08176i 0.186025 0.256041i
\(766\) −10.0415 + 30.9044i −0.362813 + 1.11662i
\(767\) 5.91499 12.6188i 0.213578 0.455640i
\(768\) 1.23490 0.897208i 0.0445606 0.0323752i
\(769\) 52.8371i 1.90535i −0.303985 0.952677i \(-0.598317\pi\)
0.303985 0.952677i \(-0.401683\pi\)
\(770\) −37.9199 24.6825i −1.36654 0.889496i
\(771\) 0.0961666 0.00346336
\(772\) −0.935968 1.28825i −0.0336862 0.0463651i
\(773\) 37.5037 12.1857i 1.34891 0.438289i 0.456587 0.889679i \(-0.349072\pi\)
0.892327 + 0.451390i \(0.149072\pi\)
\(774\) 13.6690 + 4.44134i 0.491323 + 0.159641i
\(775\) −3.47256 + 4.77957i −0.124738 + 0.171687i
\(776\) 8.60891 + 6.25474i 0.309042 + 0.224532i
\(777\) −6.18923 + 19.0485i −0.222037 + 0.683360i
\(778\) −38.3089 + 12.4473i −1.37344 + 0.446258i
\(779\) −44.2230 + 32.1299i −1.58445 + 1.15117i
\(780\) 0.538838 + 0.504491i 0.0192935 + 0.0180637i
\(781\) 1.05597 0.853263i 0.0377857 0.0305321i
\(782\) 6.06341i 0.216827i
\(783\) 5.19751 3.77621i 0.185744 0.134951i
\(784\) 2.74365 + 8.44410i 0.0979876 + 0.301575i
\(785\) 55.6262 + 18.0741i 1.98539 + 0.645091i
\(786\) −8.41610 + 11.5838i −0.300192 + 0.413179i
\(787\) −30.7335 + 42.3011i −1.09553 + 1.50787i −0.254354 + 0.967111i \(0.581863\pi\)
−0.841178 + 0.540759i \(0.818137\pi\)
\(788\) −1.33477 0.433693i −0.0475492 0.0154497i
\(789\) 4.89464 + 15.0642i 0.174254 + 0.536298i
\(790\) −20.6778 + 15.0233i −0.735683 + 0.534505i
\(791\) 7.02079i 0.249631i
\(792\) −7.40798 + 5.98590i −0.263231 + 0.212700i
\(793\) −35.4547 + 37.8685i −1.25903 + 1.34475i
\(794\) −9.72046 + 7.06233i −0.344966 + 0.250633i
\(795\) −22.0586 + 7.16726i −0.782337 + 0.254197i
\(796\) 0.356872 1.09834i 0.0126490 0.0389296i
\(797\) −24.5818 17.8597i −0.870731 0.632623i 0.0600522 0.998195i \(-0.480873\pi\)
−0.930783 + 0.365572i \(0.880873\pi\)
\(798\) 17.9054 24.6447i 0.633844 0.872411i
\(799\) 4.73923 + 1.53987i 0.167662 + 0.0544767i
\(800\) −1.82839 + 0.594081i −0.0646434 + 0.0210039i
\(801\) 1.52095 + 2.09341i 0.0537403 + 0.0739672i
\(802\) −18.4427 −0.651236
\(803\) 26.2939 + 17.1150i 0.927892 + 0.603977i
\(804\) 0.757090i 0.0267005i
\(805\) −12.6955 + 9.22383i −0.447458 + 0.325097i
\(806\) 5.02593 + 2.35587i 0.177031 + 0.0829819i
\(807\) 0.996135 3.06579i 0.0350656 0.107921i
\(808\) −13.8375 + 19.0457i −0.486801 + 0.670024i
\(809\) −41.8354 30.3952i −1.47085 1.06864i −0.980365 0.197192i \(-0.936818\pi\)
−0.490490 0.871447i \(-0.663182\pi\)
\(810\) 1.38272 4.25557i 0.0485838 0.149526i
\(811\) −37.4761 + 12.1767i −1.31596 + 0.427582i −0.881106 0.472918i \(-0.843201\pi\)
−0.434856 + 0.900500i \(0.643201\pi\)
\(812\) −0.732976 1.00886i −0.0257224 0.0354039i
\(813\) 4.59498i 0.161153i
\(814\) −1.55475 30.2791i −0.0544938 1.06128i
\(815\) −39.5091 −1.38394
\(816\) 8.51990 6.19007i 0.298256 0.216696i
\(817\) −70.5337 + 22.9178i −2.46766 + 0.801792i
\(818\) 3.60479 11.0944i 0.126038 0.387906i
\(819\) 2.07591 + 10.7947i 0.0725380 + 0.377198i
\(820\) 1.26087 + 0.916072i 0.0440313 + 0.0319906i
\(821\) −7.16964 2.32956i −0.250222 0.0813021i 0.181220 0.983443i \(-0.441995\pi\)
−0.431443 + 0.902140i \(0.641995\pi\)
\(822\) 5.28276 + 16.2587i 0.184257 + 0.567086i
\(823\) 12.5196 9.09601i 0.436405 0.317067i −0.347800 0.937569i \(-0.613071\pi\)
0.784205 + 0.620502i \(0.213071\pi\)
\(824\) 31.3122i 1.09081i
\(825\) 16.5413 6.32956i 0.575896 0.220367i
\(826\) 16.3981i 0.570563i
\(827\) −21.7183 29.8927i −0.755219 1.03947i −0.997597 0.0692875i \(-0.977927\pi\)
0.242378 0.970182i \(-0.422073\pi\)
\(828\) 0.0314917 + 0.0969214i 0.00109441 + 0.00336825i
\(829\) −7.62280 + 23.4606i −0.264751 + 0.814819i 0.727000 + 0.686637i \(0.240914\pi\)
−0.991751 + 0.128181i \(0.959086\pi\)
\(830\) −33.6114 + 46.2621i −1.16667 + 1.60578i
\(831\) −21.1133 15.3397i −0.732414 0.532130i
\(832\) 14.3485 + 26.0078i 0.497444 + 0.901657i
\(833\) −1.93061 5.94182i −0.0668918 0.205872i
\(834\) 0.0132042 + 0.0181741i 0.000457225 + 0.000629317i
\(835\) −13.2348 −0.458008
\(836\) 0.393968 1.46411i 0.0136257 0.0506373i
\(837\) 1.10633i 0.0382404i
\(838\) 10.8502 + 14.9340i 0.374812 + 0.515885i
\(839\) −6.66516 + 2.16564i −0.230107 + 0.0747662i −0.421801 0.906688i \(-0.638602\pi\)
0.191694 + 0.981455i \(0.438602\pi\)
\(840\) −26.7746 8.69960i −0.923812 0.300165i
\(841\) −9.92974 7.21438i −0.342405 0.248772i
\(842\) −18.9968 13.8020i −0.654672 0.475647i
\(843\) 5.31704 + 1.72761i 0.183129 + 0.0595021i
\(844\) −0.170597 0.525043i −0.00587219 0.0180727i
\(845\) −32.1299 + 26.7421i −1.10530 + 0.919956i
\(846\) 2.54724 0.0875760
\(847\) −22.3876 24.9699i −0.769246 0.857977i
\(848\) −27.9039 −0.958223
\(849\) 0.246265 0.178922i 0.00845181 0.00614060i
\(850\) −19.2382 + 6.25088i −0.659865 + 0.214403i
\(851\) −10.0009 3.24949i −0.342827 0.111391i
\(852\) 0.0153183 0.0210838i 0.000524795 0.000722318i
\(853\) −10.1565 + 13.9792i −0.347751 + 0.478638i −0.946685 0.322160i \(-0.895591\pi\)
0.598934 + 0.800798i \(0.295591\pi\)
\(854\) 18.8620 58.0514i 0.645446 1.98648i
\(855\) 7.13499 + 21.9592i 0.244011 + 0.750990i
\(856\) −7.81863 10.7614i −0.267235 0.367818i
\(857\) 8.36334 0.285686 0.142843 0.989745i \(-0.454376\pi\)
0.142843 + 0.989745i \(0.454376\pi\)
\(858\) −8.77479 14.1386i −0.299566 0.482682i
\(859\) 46.8951 1.60004 0.800020 0.599973i \(-0.204822\pi\)
0.800020 + 0.599973i \(0.204822\pi\)
\(860\) 1.24288 + 1.71068i 0.0423819 + 0.0583337i
\(861\) 7.17215 + 22.0736i 0.244426 + 0.752267i
\(862\) 14.2766 43.9388i 0.486262 1.49656i
\(863\) 16.4052 22.5798i 0.558440 0.768626i −0.432687 0.901544i \(-0.642435\pi\)
0.991127 + 0.132918i \(0.0424346\pi\)
\(864\) −0.211609 + 0.291255i −0.00719910 + 0.00990871i
\(865\) −56.1140 18.2325i −1.90793 0.619925i
\(866\) −31.1703 + 10.1279i −1.05921 + 0.344158i
\(867\) 7.75813 5.63661i 0.263480 0.191429i
\(868\) 0.214743 0.00728885
\(869\) −17.6937 + 6.77052i −0.600218 + 0.229674i
\(870\) −28.7468 −0.974607
\(871\) 42.5456 + 5.31026i 1.44160 + 0.179931i
\(872\) 12.0404 + 37.0566i 0.407740 + 1.25489i
\(873\) −3.52426 1.14510i −0.119278 0.0387558i
\(874\) 12.9390 + 9.40077i 0.437670 + 0.317986i
\(875\) 2.69719 + 1.95962i 0.0911816 + 0.0662473i
\(876\) 0.572770 + 0.186104i 0.0193521 + 0.00628789i
\(877\) −13.5837 + 4.41360i −0.458688 + 0.149037i −0.529241 0.848471i \(-0.677523\pi\)
0.0705537 + 0.997508i \(0.477523\pi\)
\(878\) 11.9737 + 16.4803i 0.404092 + 0.556184i
\(879\) 10.1763i 0.343239i
\(880\) 41.2042 2.11572i 1.38899 0.0713209i
\(881\) 1.01950 0.0343480 0.0171740 0.999853i \(-0.494533\pi\)
0.0171740 + 0.999853i \(0.494533\pi\)
\(882\) −1.87716 2.58368i −0.0632071 0.0869971i
\(883\) 17.2650 + 53.1363i 0.581014 + 1.78818i 0.614719 + 0.788747i \(0.289270\pi\)
−0.0337041 + 0.999432i \(0.510730\pi\)
\(884\) −0.301858 0.547143i −0.0101526 0.0184024i
\(885\) −10.0553 7.30563i −0.338007 0.245576i
\(886\) −9.05968 + 12.4696i −0.304366 + 0.418924i
\(887\) −8.99122 + 27.6721i −0.301896 + 0.929139i 0.678922 + 0.734210i \(0.262447\pi\)
−0.980817 + 0.194928i \(0.937553\pi\)
\(888\) −5.82962 17.9417i −0.195629 0.602085i
\(889\) −1.92918 2.65529i −0.0647027 0.0890556i
\(890\) 11.5784i 0.388110i
\(891\) 1.80930 2.77964i 0.0606140 0.0931216i
\(892\) 0.787797i 0.0263774i
\(893\) −10.6338 + 7.72588i −0.355845 + 0.258537i
\(894\) −8.41484 25.8982i −0.281435 0.866166i
\(895\) 30.5215 + 9.91705i 1.02022 + 0.331490i
\(896\) −26.4992 19.2528i −0.885278 0.643192i
\(897\) −5.66750 + 1.08990i −0.189232 + 0.0363907i
\(898\) 6.58709 20.2730i 0.219814 0.676518i
\(899\) 6.75971 2.19636i 0.225449 0.0732529i
\(900\) 0.275051 0.199836i 0.00916835 0.00666120i
\(901\) 19.6350 0.654137
\(902\) −22.0817 27.3276i −0.735239 0.909910i
\(903\) 31.4896i 1.04791i
\(904\) 3.88695 + 5.34992i 0.129278 + 0.177936i
\(905\) −33.6194 + 10.9236i −1.11755 + 0.363113i
\(906\) −2.61333 + 8.04301i −0.0868221 + 0.267211i
\(907\) 10.7990 + 7.84594i 0.358575 + 0.260520i 0.752458 0.658641i \(-0.228868\pi\)
−0.393882 + 0.919161i \(0.628868\pi\)
\(908\) −0.496836 + 0.683836i −0.0164881 + 0.0226939i
\(909\) 2.53333 7.79678i 0.0840251 0.258603i
\(910\) 20.8763 44.5368i 0.692043 1.47638i
\(911\) −12.8226 + 9.31615i −0.424831 + 0.308658i −0.779579 0.626304i \(-0.784567\pi\)
0.354748 + 0.934962i \(0.384567\pi\)
\(912\) 27.7782i 0.919829i
\(913\) −32.9676 + 26.6389i −1.09107 + 0.881619i
\(914\) 54.0462 1.78769
\(915\) 27.1938 + 37.4291i 0.899001 + 1.23737i
\(916\) 0.642856 0.208877i 0.0212406 0.00690148i
\(917\) −29.8355 9.69416i −0.985257 0.320129i
\(918\) −2.22654 + 3.06457i −0.0734868 + 0.101146i
\(919\) −17.1690 12.4740i −0.566352 0.411479i 0.267426 0.963578i \(-0.413827\pi\)
−0.833778 + 0.552100i \(0.813827\pi\)
\(920\) 4.56750 14.0573i 0.150586 0.463456i
\(921\) −8.14689 + 2.64709i −0.268449 + 0.0872244i
\(922\) −13.6927 + 9.94834i −0.450945 + 0.327631i
\(923\) 1.07738 + 1.00871i 0.0354625 + 0.0332021i
\(924\) −0.539539 0.351193i −0.0177495 0.0115534i
\(925\) 35.0812i 1.15346i
\(926\) 9.27117 6.73590i 0.304670 0.221355i
\(927\) 3.36950 + 10.3703i 0.110669 + 0.340604i
\(928\) 2.19968 + 0.714720i 0.0722081 + 0.0234618i
\(929\) 4.29907 5.91716i 0.141048 0.194136i −0.732649 0.680607i \(-0.761716\pi\)
0.873697 + 0.486471i \(0.161716\pi\)
\(930\) 2.90975 4.00492i 0.0954143 0.131327i
\(931\) 15.6728 + 5.09241i 0.513656 + 0.166897i
\(932\) 0.546644 + 1.68240i 0.0179059 + 0.0551087i
\(933\) 15.9117 11.5605i 0.520926 0.378475i
\(934\) 5.33779i 0.174658i
\(935\) −28.9940 + 1.48876i −0.948205 + 0.0486876i
\(936\) −7.55819 7.07642i −0.247047 0.231300i
\(937\) 26.2965 19.1055i 0.859070 0.624151i −0.0685620 0.997647i \(-0.521841\pi\)
0.927632 + 0.373496i \(0.121841\pi\)
\(938\) −47.9802 + 15.5897i −1.56661 + 0.509022i
\(939\) 6.14862 18.9235i 0.200653 0.617546i
\(940\) 0.303185 + 0.220277i 0.00988880 + 0.00718463i
\(941\) 10.5268 14.4889i 0.343164 0.472325i −0.602198 0.798347i \(-0.705708\pi\)
0.945362 + 0.326022i \(0.105708\pi\)
\(942\) −24.0718 7.82139i −0.784301 0.254835i
\(943\) −11.5892 + 3.76555i −0.377396 + 0.122623i
\(944\) −8.78924 12.0974i −0.286066 0.393735i
\(945\) 9.80364 0.318913
\(946\) −17.0356 44.5200i −0.553876 1.44747i
\(947\) 18.3127i 0.595082i 0.954709 + 0.297541i \(0.0961665\pi\)
−0.954709 + 0.297541i \(0.903833\pi\)
\(948\) −0.294212 + 0.213758i −0.00955557 + 0.00694253i
\(949\) −14.4758 + 30.8822i −0.469904 + 1.00248i
\(950\) 16.4880 50.7449i 0.534942 1.64638i
\(951\) 2.10265 2.89405i 0.0681830 0.0938459i
\(952\) 19.2812 + 14.0086i 0.624908 + 0.454022i
\(953\) −14.1773 + 43.6334i −0.459249 + 1.41342i 0.406824 + 0.913507i \(0.366636\pi\)
−0.866073 + 0.499917i \(0.833364\pi\)
\(954\) 9.54565 3.10157i 0.309052 0.100417i
\(955\) 30.4088 + 41.8541i 0.984006 + 1.35437i
\(956\) 0.00194598i 6.29376e-5i
\(957\) −20.5757 5.53657i −0.665117 0.178972i
\(958\) 18.7775 0.606674
\(959\) −30.3020 + 22.0157i −0.978503 + 0.710924i
\(960\) 25.1942 8.18608i 0.813138 0.264205i
\(961\) 9.20130 28.3187i 0.296816 0.913506i
\(962\) 32.3671 6.22444i 1.04356 0.200684i
\(963\) 3.74749 + 2.72271i 0.120761 + 0.0877380i
\(964\) −0.544805 0.177018i −0.0175470 0.00570136i
\(965\) −24.8530 76.4896i −0.800046 2.46229i
\(966\) 5.49388 3.99153i 0.176763 0.128426i
\(967\) 5.29215i 0.170184i −0.996373 0.0850920i \(-0.972882\pi\)
0.996373 0.0850920i \(-0.0271184\pi\)
\(968\) 30.8838 + 6.63287i 0.992642 + 0.213188i
\(969\) 19.5466i 0.627927i
\(970\) 9.74612 + 13.4144i 0.312929 + 0.430710i
\(971\) 16.2120 + 49.8955i 0.520269 + 1.60122i 0.773486 + 0.633813i \(0.218511\pi\)
−0.253218 + 0.967409i \(0.581489\pi\)
\(972\) 0.0196739 0.0605500i 0.000631041 0.00194214i
\(973\) −0.0289300 + 0.0398188i −0.000927454 + 0.00127653i
\(974\) −20.0837 14.5916i −0.643522 0.467546i
\(975\) 9.30080 + 16.8585i 0.297864 + 0.539903i
\(976\) 17.2000 + 52.9361i 0.550558 + 1.69444i
\(977\) 2.97853 + 4.09959i 0.0952915 + 0.131158i 0.854000 0.520272i \(-0.174170\pi\)
−0.758709 + 0.651430i \(0.774170\pi\)
\(978\) 17.0972 0.546709
\(979\) 2.22998 8.28733i 0.0712705 0.264864i
\(980\) 0.469852i 0.0150089i
\(981\) −7.97532 10.9771i −0.254632 0.350471i
\(982\) 41.0115 13.3254i 1.30873 0.425232i
\(983\) −36.1146 11.7344i −1.15188 0.374268i −0.330027 0.943971i \(-0.607058\pi\)
−0.821850 + 0.569704i \(0.807058\pi\)
\(984\) −17.6860 12.8496i −0.563808 0.409630i
\(985\) −57.3471 41.6651i −1.82723 1.32756i
\(986\) 23.1449 + 7.52024i 0.737084 + 0.239493i
\(987\) 1.72460 + 5.30777i 0.0548946 + 0.168948i
\(988\) 1.63558 + 0.204143i 0.0520348 + 0.00649464i
\(989\) −16.5328 −0.525713
\(990\) −13.8604 + 5.30370i −0.440513 + 0.168563i
\(991\) −30.0824 −0.955600 −0.477800 0.878469i \(-0.658566\pi\)
−0.477800 + 0.878469i \(0.658566\pi\)
\(992\) −0.322225 + 0.234110i −0.0102306 + 0.00743299i
\(993\) 30.5964 9.94138i 0.970948 0.315480i
\(994\) −1.65160 0.536637i −0.0523855 0.0170211i
\(995\) 34.2848 47.1890i 1.08690 1.49599i
\(996\) −0.478237 + 0.658236i −0.0151535 + 0.0208570i
\(997\) −7.89993 + 24.3135i −0.250193 + 0.770016i 0.744546 + 0.667572i \(0.232666\pi\)
−0.994739 + 0.102444i \(0.967334\pi\)
\(998\) 14.8732 + 45.7749i 0.470801 + 1.44898i
\(999\) 3.86142 + 5.31479i 0.122170 + 0.168152i
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 429.2.bb.a.25.10 yes 56
11.4 even 5 inner 429.2.bb.a.103.5 yes 56
13.12 even 2 inner 429.2.bb.a.25.5 56
143.103 even 10 inner 429.2.bb.a.103.10 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.bb.a.25.5 56 13.12 even 2 inner
429.2.bb.a.25.10 yes 56 1.1 even 1 trivial
429.2.bb.a.103.5 yes 56 11.4 even 5 inner
429.2.bb.a.103.10 yes 56 143.103 even 10 inner