Properties

Label 429.2.bd.b.76.6
Level $429$
Weight $2$
Character 429.76
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(76,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bd (of order \(12\), 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 \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 76.6
Character \(\chi\) \(=\) 429.76
Dual form 429.2.bd.b.175.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.391582 - 0.104924i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.58972 - 0.917827i) q^{4} +(2.00961 + 2.00961i) q^{5} +(-0.104924 - 0.391582i) q^{6} +(-3.95482 + 1.05969i) q^{7} +(1.09952 + 1.09952i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.391582 - 0.104924i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.58972 - 0.917827i) q^{4} +(2.00961 + 2.00961i) q^{5} +(-0.104924 - 0.391582i) q^{6} +(-3.95482 + 1.05969i) q^{7} +(1.09952 + 1.09952i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.576070 - 0.997782i) q^{10} +(-2.31890 - 2.37123i) q^{11} -1.83565i q^{12} +(-3.35978 + 1.30837i) q^{13} +1.65982 q^{14} +(-0.735567 + 2.74517i) q^{15} +(1.52047 + 2.63353i) q^{16} +(-0.407381 + 0.705605i) q^{17} +(0.286658 - 0.286658i) q^{18} +(-0.953793 - 3.55960i) q^{19} +(-1.35025 - 5.03919i) q^{20} +(-2.89513 - 2.89513i) q^{21} +(0.659241 + 1.17184i) q^{22} +(-3.35891 + 1.93927i) q^{23} +(-0.402453 + 1.50197i) q^{24} +3.07703i q^{25} +(1.45291 - 0.159814i) q^{26} -1.00000 q^{27} +(7.25968 + 1.94523i) q^{28} +(-4.70672 + 2.71742i) q^{29} +(0.576070 - 0.997782i) q^{30} +(4.88323 + 4.88323i) q^{31} +(-1.12397 - 4.19472i) q^{32} +(0.894092 - 3.19384i) q^{33} +(0.233558 - 0.233558i) q^{34} +(-10.0772 - 5.81807i) q^{35} +(1.58972 - 0.917827i) q^{36} +(-2.24755 - 0.602228i) q^{37} +1.49395i q^{38} +(-2.81298 - 2.25547i) q^{39} +4.41921i q^{40} +(6.89125 + 1.84650i) q^{41} +(0.829912 + 1.43745i) q^{42} +(-4.75179 + 8.23034i) q^{43} +(1.51003 + 5.89794i) q^{44} +(-2.74517 + 0.735567i) q^{45} +(1.51877 - 0.406952i) q^{46} +(-5.58658 + 5.58658i) q^{47} +(-1.52047 + 2.63353i) q^{48} +(8.45547 - 4.88177i) q^{49} +(0.322855 - 1.20491i) q^{50} -0.814762 q^{51} +(6.54199 + 1.00375i) q^{52} -3.97736 q^{53} +(0.391582 + 0.104924i) q^{54} +(0.105156 - 9.42530i) q^{55} +(-5.51356 - 3.18326i) q^{56} +(2.60581 - 2.60581i) q^{57} +(2.12819 - 0.570247i) q^{58} +(-2.78917 - 10.4093i) q^{59} +(3.68894 - 3.68894i) q^{60} +(9.30427 + 5.37182i) q^{61} +(-1.39982 - 2.42455i) q^{62} +(1.05969 - 3.95482i) q^{63} -4.32136i q^{64} +(-9.38116 - 4.12253i) q^{65} +(-0.685221 + 1.15684i) q^{66} +(1.10134 - 4.11026i) q^{67} +(1.29525 - 0.747811i) q^{68} +(-3.35891 - 1.93927i) q^{69} +(3.33559 + 3.33559i) q^{70} +(-0.994820 + 0.266561i) q^{71} +(-1.50197 + 0.402453i) q^{72} +(9.57876 + 9.57876i) q^{73} +(0.816911 + 0.471644i) q^{74} +(-2.66479 + 1.53852i) q^{75} +(-1.75083 + 6.53420i) q^{76} +(11.6836 + 6.92045i) q^{77} +(0.864859 + 1.17835i) q^{78} +4.76856i q^{79} +(-2.23681 + 8.34789i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.50475 - 1.44612i) q^{82} +(5.63465 - 5.63465i) q^{83} +(1.94523 + 7.25968i) q^{84} +(-2.23666 + 0.599312i) q^{85} +(2.72428 - 2.72428i) q^{86} +(-4.70672 - 2.71742i) q^{87} +(0.0575343 - 5.15689i) q^{88} +(14.1263 + 3.78514i) q^{89} +1.15214 q^{90} +(11.9009 - 8.73472i) q^{91} +7.11965 q^{92} +(-1.78738 + 6.67061i) q^{93} +(2.77377 - 1.60144i) q^{94} +(5.23665 - 9.07015i) q^{95} +(3.07075 - 3.07075i) q^{96} +(-8.44167 + 2.26194i) q^{97} +(-3.82323 + 1.02443i) q^{98} +(3.21299 - 0.822612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9} - 4 q^{11} - 24 q^{14} - 8 q^{15} + 4 q^{16} + 80 q^{20} - 10 q^{22} - 12 q^{23} + 40 q^{26} - 56 q^{27} - 12 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{37} - 12 q^{42} + 24 q^{44} - 4 q^{45} - 40 q^{47} - 4 q^{48} + 24 q^{49} - 88 q^{53} - 18 q^{55} + 72 q^{56} + 40 q^{58} + 8 q^{59} + 52 q^{60} - 20 q^{66} - 4 q^{67} - 12 q^{69} + 40 q^{70} - 24 q^{71} + 12 q^{75} - 4 q^{78} - 188 q^{80} - 28 q^{81} - 12 q^{82} + 32 q^{86} + 18 q^{88} - 16 q^{89} + 28 q^{91} - 96 q^{92} - 12 q^{93} - 28 q^{97} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.391582 0.104924i −0.276890 0.0741926i 0.117702 0.993049i \(-0.462447\pi\)
−0.394592 + 0.918856i \(0.629114\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −1.58972 0.917827i −0.794862 0.458914i
\(5\) 2.00961 + 2.00961i 0.898723 + 0.898723i 0.995323 0.0966002i \(-0.0307968\pi\)
−0.0966002 + 0.995323i \(0.530797\pi\)
\(6\) −0.104924 0.391582i −0.0428351 0.159863i
\(7\) −3.95482 + 1.05969i −1.49478 + 0.400525i −0.911348 0.411636i \(-0.864957\pi\)
−0.583433 + 0.812162i \(0.698291\pi\)
\(8\) 1.09952 + 1.09952i 0.388739 + 0.388739i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.576070 0.997782i −0.182169 0.315526i
\(11\) −2.31890 2.37123i −0.699174 0.714951i
\(12\) 1.83565i 0.529908i
\(13\) −3.35978 + 1.30837i −0.931837 + 0.362878i
\(14\) 1.65982 0.443607
\(15\) −0.735567 + 2.74517i −0.189923 + 0.708801i
\(16\) 1.52047 + 2.63353i 0.380117 + 0.658382i
\(17\) −0.407381 + 0.705605i −0.0988044 + 0.171134i −0.911190 0.411986i \(-0.864835\pi\)
0.812386 + 0.583121i \(0.198168\pi\)
\(18\) 0.286658 0.286658i 0.0675660 0.0675660i
\(19\) −0.953793 3.55960i −0.218815 0.816629i −0.984789 0.173757i \(-0.944409\pi\)
0.765973 0.642872i \(-0.222257\pi\)
\(20\) −1.35025 5.03919i −0.301924 1.12680i
\(21\) −2.89513 2.89513i −0.631769 0.631769i
\(22\) 0.659241 + 1.17184i 0.140551 + 0.249837i
\(23\) −3.35891 + 1.93927i −0.700381 + 0.404365i −0.807489 0.589882i \(-0.799174\pi\)
0.107108 + 0.994247i \(0.465841\pi\)
\(24\) −0.402453 + 1.50197i −0.0821503 + 0.306589i
\(25\) 3.07703i 0.615406i
\(26\) 1.45291 0.159814i 0.284940 0.0313421i
\(27\) −1.00000 −0.192450
\(28\) 7.25968 + 1.94523i 1.37195 + 0.367613i
\(29\) −4.70672 + 2.71742i −0.874015 + 0.504613i −0.868680 0.495373i \(-0.835031\pi\)
−0.00533471 + 0.999986i \(0.501698\pi\)
\(30\) 0.576070 0.997782i 0.105175 0.182169i
\(31\) 4.88323 + 4.88323i 0.877053 + 0.877053i 0.993229 0.116176i \(-0.0370635\pi\)
−0.116176 + 0.993229i \(0.537064\pi\)
\(32\) −1.12397 4.19472i −0.198692 0.741530i
\(33\) 0.894092 3.19384i 0.155641 0.555976i
\(34\) 0.233558 0.233558i 0.0400549 0.0400549i
\(35\) −10.0772 5.81807i −1.70336 0.983433i
\(36\) 1.58972 0.917827i 0.264954 0.152971i
\(37\) −2.24755 0.602228i −0.369494 0.0990057i 0.0692938 0.997596i \(-0.477925\pi\)
−0.438788 + 0.898591i \(0.644592\pi\)
\(38\) 1.49395i 0.242351i
\(39\) −2.81298 2.25547i −0.450437 0.361165i
\(40\) 4.41921i 0.698738i
\(41\) 6.89125 + 1.84650i 1.07623 + 0.288375i 0.753051 0.657962i \(-0.228581\pi\)
0.323181 + 0.946337i \(0.395248\pi\)
\(42\) 0.829912 + 1.43745i 0.128058 + 0.221803i
\(43\) −4.75179 + 8.23034i −0.724641 + 1.25511i 0.234481 + 0.972121i \(0.424661\pi\)
−0.959122 + 0.282994i \(0.908672\pi\)
\(44\) 1.51003 + 5.89794i 0.227646 + 0.889148i
\(45\) −2.74517 + 0.735567i −0.409226 + 0.109652i
\(46\) 1.51877 0.406952i 0.223930 0.0600018i
\(47\) −5.58658 + 5.58658i −0.814886 + 0.814886i −0.985362 0.170476i \(-0.945469\pi\)
0.170476 + 0.985362i \(0.445469\pi\)
\(48\) −1.52047 + 2.63353i −0.219461 + 0.380117i
\(49\) 8.45547 4.88177i 1.20792 0.697395i
\(50\) 0.322855 1.20491i 0.0456586 0.170400i
\(51\) −0.814762 −0.114090
\(52\) 6.54199 + 1.00375i 0.907211 + 0.139195i
\(53\) −3.97736 −0.546333 −0.273166 0.961967i \(-0.588071\pi\)
−0.273166 + 0.961967i \(0.588071\pi\)
\(54\) 0.391582 + 0.104924i 0.0532876 + 0.0142784i
\(55\) 0.105156 9.42530i 0.0141792 1.27091i
\(56\) −5.51356 3.18326i −0.736780 0.425380i
\(57\) 2.60581 2.60581i 0.345148 0.345148i
\(58\) 2.12819 0.570247i 0.279445 0.0748771i
\(59\) −2.78917 10.4093i −0.363120 1.35518i −0.869952 0.493136i \(-0.835850\pi\)
0.506832 0.862045i \(-0.330816\pi\)
\(60\) 3.68894 3.68894i 0.476240 0.476240i
\(61\) 9.30427 + 5.37182i 1.19129 + 0.687791i 0.958599 0.284759i \(-0.0919137\pi\)
0.232691 + 0.972551i \(0.425247\pi\)
\(62\) −1.39982 2.42455i −0.177777 0.307918i
\(63\) 1.05969 3.95482i 0.133508 0.498260i
\(64\) 4.32136i 0.540170i
\(65\) −9.38116 4.12253i −1.16359 0.511336i
\(66\) −0.685221 + 1.15684i −0.0843449 + 0.142397i
\(67\) 1.10134 4.11026i 0.134550 0.502148i −0.865449 0.500997i \(-0.832967\pi\)
0.999999 0.00115109i \(-0.000366402\pi\)
\(68\) 1.29525 0.747811i 0.157072 0.0906854i
\(69\) −3.35891 1.93927i −0.404365 0.233460i
\(70\) 3.33559 + 3.33559i 0.398679 + 0.398679i
\(71\) −0.994820 + 0.266561i −0.118063 + 0.0316350i −0.317367 0.948303i \(-0.602799\pi\)
0.199304 + 0.979938i \(0.436132\pi\)
\(72\) −1.50197 + 0.402453i −0.177009 + 0.0474295i
\(73\) 9.57876 + 9.57876i 1.12111 + 1.12111i 0.991575 + 0.129534i \(0.0413481\pi\)
0.129534 + 0.991575i \(0.458652\pi\)
\(74\) 0.816911 + 0.471644i 0.0949639 + 0.0548274i
\(75\) −2.66479 + 1.53852i −0.307703 + 0.177653i
\(76\) −1.75083 + 6.53420i −0.200834 + 0.749525i
\(77\) 11.6836 + 6.92045i 1.33147 + 0.788659i
\(78\) 0.864859 + 1.17835i 0.0979260 + 0.133422i
\(79\) 4.76856i 0.536505i 0.963349 + 0.268252i \(0.0864461\pi\)
−0.963349 + 0.268252i \(0.913554\pi\)
\(80\) −2.23681 + 8.34789i −0.250083 + 0.933323i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.50475 1.44612i −0.276603 0.159697i
\(83\) 5.63465 5.63465i 0.618484 0.618484i −0.326659 0.945142i \(-0.605923\pi\)
0.945142 + 0.326659i \(0.105923\pi\)
\(84\) 1.94523 + 7.25968i 0.212241 + 0.792096i
\(85\) −2.23666 + 0.599312i −0.242600 + 0.0650045i
\(86\) 2.72428 2.72428i 0.293766 0.293766i
\(87\) −4.70672 2.71742i −0.504613 0.291338i
\(88\) 0.0575343 5.15689i 0.00613317 0.549726i
\(89\) 14.1263 + 3.78514i 1.49739 + 0.401224i 0.912225 0.409690i \(-0.134363\pi\)
0.585165 + 0.810914i \(0.301030\pi\)
\(90\) 1.15214 0.121446
\(91\) 11.9009 8.73472i 1.24755 0.915647i
\(92\) 7.11965 0.742275
\(93\) −1.78738 + 6.67061i −0.185343 + 0.691710i
\(94\) 2.77377 1.60144i 0.286093 0.165176i
\(95\) 5.23665 9.07015i 0.537269 0.930578i
\(96\) 3.07075 3.07075i 0.313407 0.313407i
\(97\) −8.44167 + 2.26194i −0.857122 + 0.229665i −0.660511 0.750816i \(-0.729660\pi\)
−0.196611 + 0.980482i \(0.562994\pi\)
\(98\) −3.82323 + 1.02443i −0.386204 + 0.103483i
\(99\) 3.21299 0.822612i 0.322918 0.0826757i
\(100\) 2.82418 4.89163i 0.282418 0.489163i
\(101\) 2.03636 + 3.52707i 0.202625 + 0.350957i 0.949373 0.314150i \(-0.101719\pi\)
−0.746748 + 0.665107i \(0.768386\pi\)
\(102\) 0.319046 + 0.0854882i 0.0315903 + 0.00846459i
\(103\) 2.51492i 0.247802i 0.992295 + 0.123901i \(0.0395405\pi\)
−0.992295 + 0.123901i \(0.960459\pi\)
\(104\) −5.13274 2.25557i −0.503307 0.221177i
\(105\) 11.6361i 1.13557i
\(106\) 1.55746 + 0.417321i 0.151274 + 0.0405338i
\(107\) −4.69636 + 2.71144i −0.454014 + 0.262125i −0.709524 0.704681i \(-0.751090\pi\)
0.255510 + 0.966806i \(0.417757\pi\)
\(108\) 1.58972 + 0.917827i 0.152971 + 0.0883180i
\(109\) 6.02896 6.02896i 0.577470 0.577470i −0.356736 0.934205i \(-0.616110\pi\)
0.934205 + 0.356736i \(0.116110\pi\)
\(110\) −1.03012 + 3.67975i −0.0982180 + 0.350850i
\(111\) −0.602228 2.24755i −0.0571609 0.213328i
\(112\) −8.80390 8.80390i −0.831890 0.831890i
\(113\) 4.45504 7.71635i 0.419095 0.725893i −0.576754 0.816918i \(-0.695681\pi\)
0.995849 + 0.0910247i \(0.0290142\pi\)
\(114\) −1.29380 + 0.746977i −0.121176 + 0.0699608i
\(115\) −10.6472 2.85292i −0.992861 0.266036i
\(116\) 9.97650 0.926295
\(117\) 0.546807 3.56385i 0.0505523 0.329478i
\(118\) 4.36877i 0.402177i
\(119\) 0.863396 3.22224i 0.0791474 0.295382i
\(120\) −3.82715 + 2.20960i −0.349369 + 0.201708i
\(121\) −0.245418 + 10.9973i −0.0223108 + 0.999751i
\(122\) −3.07975 3.07975i −0.278828 0.278828i
\(123\) 1.84650 + 6.89125i 0.166494 + 0.621363i
\(124\) −3.28102 12.2449i −0.294644 1.09963i
\(125\) 3.86441 3.86441i 0.345643 0.345643i
\(126\) −0.829912 + 1.43745i −0.0739344 + 0.128058i
\(127\) 1.79483 + 3.10873i 0.159265 + 0.275855i 0.934604 0.355690i \(-0.115754\pi\)
−0.775339 + 0.631546i \(0.782421\pi\)
\(128\) −2.70136 + 10.0816i −0.238769 + 0.891097i
\(129\) −9.50357 −0.836743
\(130\) 3.24094 + 2.59862i 0.284250 + 0.227914i
\(131\) 7.05407i 0.616317i −0.951335 0.308159i \(-0.900287\pi\)
0.951335 0.308159i \(-0.0997128\pi\)
\(132\) −4.35275 + 4.25670i −0.378858 + 0.370498i
\(133\) 7.54416 + 13.0669i 0.654161 + 1.13304i
\(134\) −0.862530 + 1.49395i −0.0745112 + 0.129057i
\(135\) −2.00961 2.00961i −0.172959 0.172959i
\(136\) −1.22375 + 0.327903i −0.104936 + 0.0281175i
\(137\) −2.81361 10.5005i −0.240383 0.897120i −0.975648 0.219341i \(-0.929609\pi\)
0.735266 0.677779i \(-0.237057\pi\)
\(138\) 1.11181 + 1.11181i 0.0946438 + 0.0946438i
\(139\) 6.60159 + 3.81143i 0.559940 + 0.323281i 0.753121 0.657882i \(-0.228547\pi\)
−0.193182 + 0.981163i \(0.561881\pi\)
\(140\) 10.6800 + 18.4982i 0.902621 + 1.56339i
\(141\) −7.63141 2.04483i −0.642680 0.172206i
\(142\) 0.417523 0.0350377
\(143\) 10.8935 + 4.93282i 0.910956 + 0.412503i
\(144\) −3.04094 −0.253411
\(145\) −14.9196 3.99769i −1.23900 0.331990i
\(146\) −2.74583 4.75592i −0.227246 0.393602i
\(147\) 8.45547 + 4.88177i 0.697395 + 0.402641i
\(148\) 3.02023 + 3.02023i 0.248262 + 0.248262i
\(149\) 2.59701 + 9.69215i 0.212755 + 0.794012i 0.986945 + 0.161059i \(0.0514909\pi\)
−0.774190 + 0.632953i \(0.781842\pi\)
\(150\) 1.20491 0.322855i 0.0983806 0.0263610i
\(151\) −14.9563 14.9563i −1.21713 1.21713i −0.968634 0.248492i \(-0.920065\pi\)
−0.248492 0.968634i \(-0.579935\pi\)
\(152\) 2.86515 4.96258i 0.232394 0.402518i
\(153\) −0.407381 0.705605i −0.0329348 0.0570448i
\(154\) −3.84896 3.93582i −0.310158 0.317157i
\(155\) 19.6267i 1.57646i
\(156\) 2.40172 + 6.16740i 0.192292 + 0.493787i
\(157\) −22.2134 −1.77282 −0.886411 0.462899i \(-0.846809\pi\)
−0.886411 + 0.462899i \(0.846809\pi\)
\(158\) 0.500337 1.86728i 0.0398047 0.148553i
\(159\) −1.98868 3.44450i −0.157713 0.273166i
\(160\) 6.17100 10.6885i 0.487860 0.844999i
\(161\) 11.2289 11.2289i 0.884958 0.884958i
\(162\) 0.104924 + 0.391582i 0.00824362 + 0.0307656i
\(163\) 3.45186 + 12.8825i 0.270370 + 1.00904i 0.958881 + 0.283810i \(0.0915983\pi\)
−0.688510 + 0.725227i \(0.741735\pi\)
\(164\) −9.26040 9.26040i −0.723116 0.723116i
\(165\) 8.21513 4.62158i 0.639547 0.359790i
\(166\) −2.79764 + 1.61522i −0.217139 + 0.125365i
\(167\) 4.51531 16.8514i 0.349405 1.30400i −0.537976 0.842960i \(-0.680811\pi\)
0.887381 0.461037i \(-0.152522\pi\)
\(168\) 6.36651i 0.491187i
\(169\) 9.57631 8.79172i 0.736639 0.676286i
\(170\) 0.938720 0.0719965
\(171\) 3.55960 + 0.953793i 0.272210 + 0.0729384i
\(172\) 15.1081 8.72264i 1.15198 0.665095i
\(173\) −6.42530 + 11.1289i −0.488507 + 0.846118i −0.999913 0.0132209i \(-0.995792\pi\)
0.511406 + 0.859339i \(0.329125\pi\)
\(174\) 1.55794 + 1.55794i 0.118107 + 0.118107i
\(175\) −3.26070 12.1691i −0.246486 0.919898i
\(176\) 2.71888 9.71225i 0.204943 0.732089i
\(177\) 7.62017 7.62017i 0.572767 0.572767i
\(178\) −5.13447 2.96439i −0.384845 0.222190i
\(179\) −16.8258 + 9.71437i −1.25762 + 0.726086i −0.972611 0.232439i \(-0.925329\pi\)
−0.285007 + 0.958525i \(0.591996\pi\)
\(180\) 5.03919 + 1.35025i 0.375599 + 0.100641i
\(181\) 20.6946i 1.53822i 0.639117 + 0.769109i \(0.279300\pi\)
−0.639117 + 0.769109i \(0.720700\pi\)
\(182\) −5.57665 + 2.17167i −0.413369 + 0.160975i
\(183\) 10.7436i 0.794193i
\(184\) −5.82546 1.56093i −0.429458 0.115073i
\(185\) −3.30644 5.72692i −0.243094 0.421052i
\(186\) 1.39982 2.42455i 0.102639 0.177777i
\(187\) 2.61782 0.670233i 0.191434 0.0490123i
\(188\) 14.0086 3.75360i 1.02168 0.273759i
\(189\) 3.95482 1.05969i 0.287671 0.0770811i
\(190\) −3.00226 + 3.00226i −0.217807 + 0.217807i
\(191\) −8.11011 + 14.0471i −0.586827 + 1.01641i 0.407818 + 0.913063i \(0.366290\pi\)
−0.994645 + 0.103351i \(0.967044\pi\)
\(192\) 3.74241 2.16068i 0.270085 0.155934i
\(193\) −6.28919 + 23.4716i −0.452706 + 1.68952i 0.242041 + 0.970266i \(0.422183\pi\)
−0.694747 + 0.719254i \(0.744484\pi\)
\(194\) 3.54294 0.254368
\(195\) −1.12037 10.1856i −0.0802313 0.729405i
\(196\) −17.9225 −1.28018
\(197\) −20.9622 5.61680i −1.49349 0.400180i −0.582578 0.812775i \(-0.697956\pi\)
−0.910915 + 0.412594i \(0.864623\pi\)
\(198\) −1.34446 0.0149999i −0.0955467 0.00106599i
\(199\) 5.75748 + 3.32408i 0.408137 + 0.235638i 0.689989 0.723820i \(-0.257615\pi\)
−0.281852 + 0.959458i \(0.590949\pi\)
\(200\) −3.38326 + 3.38326i −0.239233 + 0.239233i
\(201\) 4.11026 1.10134i 0.289915 0.0776825i
\(202\) −0.427326 1.59480i −0.0300665 0.112210i
\(203\) 15.7346 15.7346i 1.10435 1.10435i
\(204\) 1.29525 + 0.747811i 0.0906854 + 0.0523572i
\(205\) 10.1379 + 17.5594i 0.708065 + 1.22640i
\(206\) 0.263876 0.984797i 0.0183851 0.0686141i
\(207\) 3.87853i 0.269577i
\(208\) −8.55409 6.85874i −0.593119 0.475568i
\(209\) −6.22887 + 10.5160i −0.430860 + 0.727408i
\(210\) −1.22091 + 4.55650i −0.0842509 + 0.314429i
\(211\) 16.9556 9.78932i 1.16727 0.673925i 0.214236 0.976782i \(-0.431274\pi\)
0.953036 + 0.302857i \(0.0979406\pi\)
\(212\) 6.32291 + 3.65053i 0.434259 + 0.250720i
\(213\) −0.728259 0.728259i −0.0498995 0.0498995i
\(214\) 2.12351 0.568992i 0.145160 0.0388955i
\(215\) −26.0890 + 6.99051i −1.77925 + 0.476749i
\(216\) −1.09952 1.09952i −0.0748130 0.0748130i
\(217\) −24.4870 14.1376i −1.66228 0.959720i
\(218\) −2.99342 + 1.72825i −0.202740 + 0.117052i
\(219\) −3.50607 + 13.0848i −0.236918 + 0.884191i
\(220\) −8.81797 + 14.8871i −0.594507 + 1.00369i
\(221\) 0.445517 2.90369i 0.0299687 0.195323i
\(222\) 0.943287i 0.0633093i
\(223\) 1.56442 5.83849i 0.104761 0.390974i −0.893557 0.448950i \(-0.851798\pi\)
0.998318 + 0.0579759i \(0.0184647\pi\)
\(224\) 8.89022 + 15.3983i 0.594003 + 1.02884i
\(225\) −2.66479 1.53852i −0.177653 0.102568i
\(226\) −2.55414 + 2.55414i −0.169899 + 0.169899i
\(227\) −3.79339 14.1571i −0.251776 0.939641i −0.969856 0.243680i \(-0.921645\pi\)
0.718080 0.695961i \(-0.245021\pi\)
\(228\) −6.53420 + 1.75083i −0.432738 + 0.115952i
\(229\) 2.63621 2.63621i 0.174206 0.174206i −0.614619 0.788824i \(-0.710690\pi\)
0.788824 + 0.614619i \(0.210690\pi\)
\(230\) 3.86993 + 2.23431i 0.255176 + 0.147326i
\(231\) −0.151492 + 13.5785i −0.00996746 + 0.893400i
\(232\) −8.16300 2.18727i −0.535927 0.143601i
\(233\) −12.6584 −0.829277 −0.414639 0.909986i \(-0.636092\pi\)
−0.414639 + 0.909986i \(0.636092\pi\)
\(234\) −0.588053 + 1.33817i −0.0384422 + 0.0874786i
\(235\) −22.4536 −1.46471
\(236\) −5.11996 + 19.1080i −0.333281 + 1.24382i
\(237\) −4.12969 + 2.38428i −0.268252 + 0.154876i
\(238\) −0.676181 + 1.17118i −0.0438303 + 0.0759163i
\(239\) −15.5478 + 15.5478i −1.00570 + 1.00570i −0.00571889 + 0.999984i \(0.501820\pi\)
−0.999984 + 0.00571889i \(0.998180\pi\)
\(240\) −8.34789 + 2.23681i −0.538854 + 0.144386i
\(241\) −22.6969 + 6.08161i −1.46203 + 0.391751i −0.900192 0.435493i \(-0.856574\pi\)
−0.561843 + 0.827244i \(0.689907\pi\)
\(242\) 1.24998 4.28058i 0.0803517 0.275166i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −9.86081 17.0794i −0.631274 1.09340i
\(245\) 26.8026 + 7.18173i 1.71235 + 0.458824i
\(246\) 2.89223i 0.184402i
\(247\) 7.86184 + 10.7116i 0.500237 + 0.681562i
\(248\) 10.7384i 0.681890i
\(249\) 7.69708 + 2.06243i 0.487783 + 0.130701i
\(250\) −1.91870 + 1.10776i −0.121349 + 0.0700611i
\(251\) −1.66319 0.960242i −0.104980 0.0606099i 0.446591 0.894738i \(-0.352638\pi\)
−0.551571 + 0.834128i \(0.685971\pi\)
\(252\) −5.31445 + 5.31445i −0.334779 + 0.334779i
\(253\) 12.3874 + 3.46777i 0.778790 + 0.218017i
\(254\) −0.376641 1.40564i −0.0236326 0.0881980i
\(255\) −1.63735 1.63735i −0.102535 0.102535i
\(256\) −2.20575 + 3.82047i −0.137859 + 0.238779i
\(257\) −17.6940 + 10.2156i −1.10372 + 0.637234i −0.937196 0.348803i \(-0.886588\pi\)
−0.166526 + 0.986037i \(0.553255\pi\)
\(258\) 3.72143 + 0.997154i 0.231686 + 0.0620801i
\(259\) 9.52681 0.591967
\(260\) 11.1297 + 15.1640i 0.690234 + 0.940429i
\(261\) 5.43485i 0.336409i
\(262\) −0.740143 + 2.76225i −0.0457262 + 0.170652i
\(263\) 3.90007 2.25171i 0.240489 0.138846i −0.374913 0.927060i \(-0.622327\pi\)
0.615401 + 0.788214i \(0.288994\pi\)
\(264\) 4.49477 2.52862i 0.276634 0.155626i
\(265\) −7.99293 7.99293i −0.491002 0.491002i
\(266\) −1.58313 5.90832i −0.0970678 0.362262i
\(267\) 3.78514 + 14.1263i 0.231647 + 0.864518i
\(268\) −5.52333 + 5.52333i −0.337391 + 0.337391i
\(269\) −1.50710 + 2.61037i −0.0918894 + 0.159157i −0.908306 0.418306i \(-0.862624\pi\)
0.816417 + 0.577463i \(0.195957\pi\)
\(270\) 0.576070 + 0.997782i 0.0350585 + 0.0607231i
\(271\) 1.20307 4.48992i 0.0730814 0.272743i −0.919710 0.392598i \(-0.871576\pi\)
0.992791 + 0.119855i \(0.0382429\pi\)
\(272\) −2.47764 −0.150229
\(273\) 13.5149 + 5.93910i 0.817960 + 0.359450i
\(274\) 4.40703i 0.266238i
\(275\) 7.29634 7.13533i 0.439986 0.430276i
\(276\) 3.55982 + 6.16580i 0.214276 + 0.371137i
\(277\) −4.04445 + 7.00520i −0.243008 + 0.420902i −0.961570 0.274561i \(-0.911467\pi\)
0.718562 + 0.695463i \(0.244801\pi\)
\(278\) −2.18515 2.18515i −0.131057 0.131057i
\(279\) −6.67061 + 1.78738i −0.399359 + 0.107008i
\(280\) −4.68299 17.4772i −0.279862 1.04446i
\(281\) −11.7836 11.7836i −0.702952 0.702952i 0.262091 0.965043i \(-0.415588\pi\)
−0.965043 + 0.262091i \(0.915588\pi\)
\(282\) 2.77377 + 1.60144i 0.165176 + 0.0953642i
\(283\) −5.79787 10.0422i −0.344648 0.596947i 0.640642 0.767840i \(-0.278668\pi\)
−0.985290 + 0.170892i \(0.945335\pi\)
\(284\) 1.82615 + 0.489314i 0.108362 + 0.0290355i
\(285\) 10.4733 0.620385
\(286\) −3.74811 3.07459i −0.221630 0.181804i
\(287\) −29.2103 −1.72423
\(288\) 4.19472 + 1.12397i 0.247177 + 0.0662307i
\(289\) 8.16808 + 14.1475i 0.480475 + 0.832208i
\(290\) 5.42279 + 3.13085i 0.318437 + 0.183850i
\(291\) −6.17973 6.17973i −0.362262 0.362262i
\(292\) −6.43593 24.0192i −0.376634 1.40562i
\(293\) 23.4225 6.27605i 1.36836 0.366651i 0.501480 0.865169i \(-0.332789\pi\)
0.866879 + 0.498519i \(0.166123\pi\)
\(294\) −2.79880 2.79880i −0.163229 0.163229i
\(295\) 15.3135 26.5238i 0.891588 1.54428i
\(296\) −1.80906 3.13339i −0.105150 0.182124i
\(297\) 2.31890 + 2.37123i 0.134556 + 0.137592i
\(298\) 4.06776i 0.235639i
\(299\) 8.74793 10.9102i 0.505906 0.630955i
\(300\) 5.64837 0.326109
\(301\) 10.0708 37.5849i 0.580474 2.16636i
\(302\) 4.28734 + 7.42589i 0.246709 + 0.427312i
\(303\) −2.03636 + 3.52707i −0.116986 + 0.202625i
\(304\) 7.92410 7.92410i 0.454479 0.454479i
\(305\) 7.90267 + 29.4932i 0.452506 + 1.68877i
\(306\) 0.0854882 + 0.319046i 0.00488704 + 0.0182387i
\(307\) 11.3350 + 11.3350i 0.646920 + 0.646920i 0.952247 0.305327i \(-0.0987659\pi\)
−0.305327 + 0.952247i \(0.598766\pi\)
\(308\) −12.2219 21.7251i −0.696407 1.23790i
\(309\) −2.17798 + 1.25746i −0.123901 + 0.0715343i
\(310\) 2.05932 7.68547i 0.116961 0.436506i
\(311\) 7.64419i 0.433462i −0.976231 0.216731i \(-0.930461\pi\)
0.976231 0.216731i \(-0.0695395\pi\)
\(312\) −0.612991 5.57287i −0.0347038 0.315502i
\(313\) −10.6415 −0.601494 −0.300747 0.953704i \(-0.597236\pi\)
−0.300747 + 0.953704i \(0.597236\pi\)
\(314\) 8.69837 + 2.33072i 0.490878 + 0.131530i
\(315\) 10.0772 5.81807i 0.567785 0.327811i
\(316\) 4.37671 7.58069i 0.246209 0.426447i
\(317\) 15.4997 + 15.4997i 0.870552 + 0.870552i 0.992532 0.121981i \(-0.0389246\pi\)
−0.121981 + 0.992532i \(0.538925\pi\)
\(318\) 0.417321 + 1.55746i 0.0234022 + 0.0873383i
\(319\) 17.3580 + 4.85925i 0.971863 + 0.272066i
\(320\) 8.68423 8.68423i 0.485463 0.485463i
\(321\) −4.69636 2.71144i −0.262125 0.151338i
\(322\) −5.57520 + 3.21884i −0.310694 + 0.179379i
\(323\) 2.90023 + 0.777115i 0.161373 + 0.0432398i
\(324\) 1.83565i 0.101981i
\(325\) −4.02591 10.3382i −0.223317 0.573458i
\(326\) 5.40675i 0.299452i
\(327\) 8.23571 + 2.20675i 0.455436 + 0.122034i
\(328\) 5.54680 + 9.60734i 0.306271 + 0.530477i
\(329\) 16.1739 28.0139i 0.891693 1.54446i
\(330\) −3.70181 + 0.947764i −0.203778 + 0.0521727i
\(331\) −1.50410 + 0.403023i −0.0826729 + 0.0221521i −0.299918 0.953965i \(-0.596959\pi\)
0.217245 + 0.976117i \(0.430293\pi\)
\(332\) −14.1292 + 3.78590i −0.775439 + 0.207778i
\(333\) 1.64532 1.64532i 0.0901628 0.0901628i
\(334\) −3.53623 + 6.12493i −0.193494 + 0.335141i
\(335\) 10.4733 6.04674i 0.572215 0.330368i
\(336\) 3.22245 12.0263i 0.175799 0.656091i
\(337\) 21.6012 1.17669 0.588347 0.808609i \(-0.299779\pi\)
0.588347 + 0.808609i \(0.299779\pi\)
\(338\) −4.67238 + 2.43789i −0.254144 + 0.132604i
\(339\) 8.91007 0.483929
\(340\) 4.10574 + 1.10013i 0.222665 + 0.0596629i
\(341\) 0.255523 22.9029i 0.0138373 1.24026i
\(342\) −1.29380 0.746977i −0.0699608 0.0403919i
\(343\) −8.00079 + 8.00079i −0.432002 + 0.432002i
\(344\) −14.2741 + 3.82474i −0.769609 + 0.206216i
\(345\) −2.85292 10.6472i −0.153596 0.573229i
\(346\) 3.68373 3.68373i 0.198039 0.198039i
\(347\) 30.5530 + 17.6398i 1.64017 + 0.946953i 0.980772 + 0.195159i \(0.0625222\pi\)
0.659398 + 0.751794i \(0.270811\pi\)
\(348\) 4.98825 + 8.63990i 0.267398 + 0.463147i
\(349\) 6.28137 23.4424i 0.336234 1.25484i −0.566291 0.824206i \(-0.691622\pi\)
0.902525 0.430638i \(-0.141711\pi\)
\(350\) 5.10733i 0.272998i
\(351\) 3.35978 1.30837i 0.179332 0.0698359i
\(352\) −7.34026 + 12.3923i −0.391237 + 0.660514i
\(353\) 3.68953 13.7695i 0.196374 0.732878i −0.795533 0.605910i \(-0.792809\pi\)
0.991907 0.126967i \(-0.0405243\pi\)
\(354\) −3.78346 + 2.18438i −0.201089 + 0.116099i
\(355\) −2.53488 1.46351i −0.134537 0.0776752i
\(356\) −18.9829 18.9829i −1.00609 1.00609i
\(357\) 3.22224 0.863396i 0.170539 0.0456957i
\(358\) 7.60795 2.03854i 0.402093 0.107740i
\(359\) −6.70912 6.70912i −0.354094 0.354094i 0.507536 0.861630i \(-0.330556\pi\)
−0.861630 + 0.507536i \(0.830556\pi\)
\(360\) −3.82715 2.20960i −0.201708 0.116456i
\(361\) 4.69342 2.70975i 0.247022 0.142618i
\(362\) 2.17137 8.10364i 0.114124 0.425918i
\(363\) −9.64662 + 5.28609i −0.506316 + 0.277448i
\(364\) −26.9360 + 2.96284i −1.41183 + 0.155295i
\(365\) 38.4991i 2.01513i
\(366\) 1.12727 4.20702i 0.0589232 0.219905i
\(367\) 16.3714 + 28.3560i 0.854579 + 1.48017i 0.877035 + 0.480426i \(0.159518\pi\)
−0.0224568 + 0.999748i \(0.507149\pi\)
\(368\) −10.2142 5.89719i −0.532453 0.307412i
\(369\) −5.04474 + 5.04474i −0.262619 + 0.262619i
\(370\) 0.693851 + 2.58949i 0.0360716 + 0.134621i
\(371\) 15.7297 4.21477i 0.816648 0.218820i
\(372\) 8.96391 8.96391i 0.464757 0.464757i
\(373\) −2.60807 1.50577i −0.135041 0.0779660i 0.430958 0.902372i \(-0.358176\pi\)
−0.565999 + 0.824406i \(0.691509\pi\)
\(374\) −1.09542 0.0122213i −0.0566426 0.000631949i
\(375\) 5.27888 + 1.41447i 0.272600 + 0.0730430i
\(376\) −12.2851 −0.633557
\(377\) 12.2581 15.2881i 0.631327 0.787378i
\(378\) −1.65982 −0.0853721
\(379\) −0.105875 + 0.395132i −0.00543844 + 0.0202965i −0.968592 0.248656i \(-0.920011\pi\)
0.963153 + 0.268953i \(0.0866776\pi\)
\(380\) −16.6497 + 9.61269i −0.854110 + 0.493120i
\(381\) −1.79483 + 3.10873i −0.0919518 + 0.159265i
\(382\) 4.64965 4.64965i 0.237897 0.237897i
\(383\) −17.2452 + 4.62084i −0.881189 + 0.236114i −0.670920 0.741530i \(-0.734101\pi\)
−0.210269 + 0.977644i \(0.567434\pi\)
\(384\) −10.0816 + 2.70136i −0.514475 + 0.137853i
\(385\) 9.57203 + 37.3868i 0.487836 + 1.90541i
\(386\) 4.92547 8.53116i 0.250700 0.434225i
\(387\) −4.75179 8.23034i −0.241547 0.418372i
\(388\) 15.4960 + 4.15214i 0.786690 + 0.210793i
\(389\) 17.4218i 0.883322i −0.897182 0.441661i \(-0.854389\pi\)
0.897182 0.441661i \(-0.145611\pi\)
\(390\) −0.629997 + 4.10605i −0.0319012 + 0.207918i
\(391\) 3.16008i 0.159812i
\(392\) 14.6646 + 3.92936i 0.740673 + 0.198463i
\(393\) 6.10901 3.52704i 0.308159 0.177915i
\(394\) 7.61908 + 4.39888i 0.383844 + 0.221612i
\(395\) −9.58292 + 9.58292i −0.482169 + 0.482169i
\(396\) −5.86278 1.64124i −0.294616 0.0824756i
\(397\) −4.49773 16.7858i −0.225735 0.842453i −0.982109 0.188314i \(-0.939698\pi\)
0.756374 0.654139i \(-0.226969\pi\)
\(398\) −1.90575 1.90575i −0.0955267 0.0955267i
\(399\) −7.54416 + 13.0669i −0.377680 + 0.654161i
\(400\) −8.10345 + 4.67853i −0.405172 + 0.233926i
\(401\) 1.03360 + 0.276953i 0.0516157 + 0.0138304i 0.284534 0.958666i \(-0.408161\pi\)
−0.232919 + 0.972496i \(0.574828\pi\)
\(402\) −1.72506 −0.0860382
\(403\) −22.7957 10.0175i −1.13553 0.499007i
\(404\) 7.47609i 0.371950i
\(405\) 0.735567 2.74517i 0.0365506 0.136409i
\(406\) −7.81232 + 4.51044i −0.387719 + 0.223850i
\(407\) 3.78381 + 6.72594i 0.187557 + 0.333393i
\(408\) −0.895848 0.895848i −0.0443511 0.0443511i
\(409\) 6.44859 + 24.0665i 0.318862 + 1.19001i 0.920340 + 0.391120i \(0.127912\pi\)
−0.601478 + 0.798890i \(0.705421\pi\)
\(410\) −2.12743 7.93968i −0.105066 0.392113i
\(411\) 7.68691 7.68691i 0.379167 0.379167i
\(412\) 2.30826 3.99802i 0.113720 0.196968i
\(413\) 22.0614 + 38.2114i 1.08557 + 1.88026i
\(414\) −0.406952 + 1.51877i −0.0200006 + 0.0746432i
\(415\) 22.6469 1.11169
\(416\) 9.26458 + 12.6228i 0.454233 + 0.618883i
\(417\) 7.62286i 0.373293i
\(418\) 3.54250 3.46433i 0.173269 0.169446i
\(419\) −3.42080 5.92500i −0.167117 0.289455i 0.770288 0.637696i \(-0.220112\pi\)
−0.937405 + 0.348241i \(0.886779\pi\)
\(420\) −10.6800 + 18.4982i −0.521129 + 0.902621i
\(421\) 11.7634 + 11.7634i 0.573313 + 0.573313i 0.933053 0.359739i \(-0.117134\pi\)
−0.359739 + 0.933053i \(0.617134\pi\)
\(422\) −7.66665 + 2.05427i −0.373207 + 0.100000i
\(423\) −2.04483 7.63141i −0.0994230 0.371052i
\(424\) −4.37320 4.37320i −0.212381 0.212381i
\(425\) −2.17117 1.25352i −0.105317 0.0608049i
\(426\) 0.208761 + 0.361585i 0.0101145 + 0.0175189i
\(427\) −42.4892 11.3849i −2.05620 0.550956i
\(428\) 9.95455 0.481171
\(429\) 1.17478 + 11.9004i 0.0567189 + 0.574557i
\(430\) 10.9494 0.528029
\(431\) −14.9754 4.01264i −0.721338 0.193282i −0.120569 0.992705i \(-0.538472\pi\)
−0.600768 + 0.799423i \(0.705139\pi\)
\(432\) −1.52047 2.63353i −0.0731535 0.126706i
\(433\) 8.34486 + 4.81791i 0.401029 + 0.231534i 0.686928 0.726726i \(-0.258959\pi\)
−0.285899 + 0.958260i \(0.592292\pi\)
\(434\) 8.10529 + 8.10529i 0.389067 + 0.389067i
\(435\) −3.99769 14.9196i −0.191675 0.715340i
\(436\) −15.1179 + 4.05083i −0.724017 + 0.194000i
\(437\) 10.1067 + 10.1067i 0.483470 + 0.483470i
\(438\) 2.74583 4.75592i 0.131201 0.227246i
\(439\) −10.6942 18.5228i −0.510404 0.884046i −0.999927 0.0120558i \(-0.996162\pi\)
0.489523 0.871990i \(-0.337171\pi\)
\(440\) 10.4789 10.2477i 0.499564 0.488540i
\(441\) 9.76353i 0.464930i
\(442\) −0.479124 + 1.09029i −0.0227896 + 0.0518597i
\(443\) 25.5779 1.21524 0.607622 0.794226i \(-0.292123\pi\)
0.607622 + 0.794226i \(0.292123\pi\)
\(444\) −1.10548 + 4.12572i −0.0524639 + 0.195798i
\(445\) 20.7817 + 35.9950i 0.985149 + 1.70633i
\(446\) −1.22520 + 2.12211i −0.0580148 + 0.100485i
\(447\) −7.09515 + 7.09515i −0.335589 + 0.335589i
\(448\) 4.57930 + 17.0902i 0.216352 + 0.807436i
\(449\) 0.642646 + 2.39839i 0.0303283 + 0.113187i 0.979431 0.201781i \(-0.0646729\pi\)
−0.949102 + 0.314968i \(0.898006\pi\)
\(450\) 0.882056 + 0.882056i 0.0415805 + 0.0415805i
\(451\) −11.6016 20.6226i −0.546299 0.971078i
\(452\) −14.1646 + 8.17791i −0.666245 + 0.384656i
\(453\) 5.47438 20.4307i 0.257209 0.959917i
\(454\) 5.94169i 0.278857i
\(455\) 41.4694 + 6.36271i 1.94412 + 0.298289i
\(456\) 5.73029 0.268345
\(457\) −12.5267 3.35652i −0.585974 0.157011i −0.0463613 0.998925i \(-0.514763\pi\)
−0.539612 + 0.841914i \(0.681429\pi\)
\(458\) −1.30889 + 0.755691i −0.0611606 + 0.0353111i
\(459\) 0.407381 0.705605i 0.0190149 0.0329348i
\(460\) 14.3077 + 14.3077i 0.667099 + 0.667099i
\(461\) −2.71188 10.1209i −0.126305 0.471376i 0.873578 0.486684i \(-0.161794\pi\)
−0.999883 + 0.0153081i \(0.995127\pi\)
\(462\) 1.48404 5.30121i 0.0690436 0.246635i
\(463\) 4.73643 4.73643i 0.220121 0.220121i −0.588429 0.808549i \(-0.700253\pi\)
0.808549 + 0.588429i \(0.200253\pi\)
\(464\) −14.3128 8.26351i −0.664456 0.383624i
\(465\) −16.9972 + 9.81336i −0.788228 + 0.455084i
\(466\) 4.95679 + 1.32817i 0.229619 + 0.0615262i
\(467\) 22.1757i 1.02617i −0.858338 0.513085i \(-0.828503\pi\)
0.858338 0.513085i \(-0.171497\pi\)
\(468\) −4.14027 + 5.16366i −0.191384 + 0.238690i
\(469\) 17.4224i 0.804491i
\(470\) 8.79244 + 2.35593i 0.405565 + 0.108671i
\(471\) −11.1067 19.2374i −0.511770 0.886411i
\(472\) 8.37854 14.5121i 0.385653 0.667971i
\(473\) 30.5349 7.81776i 1.40400 0.359461i
\(474\) 1.86728 0.500337i 0.0857671 0.0229812i
\(475\) 10.9530 2.93485i 0.502559 0.134660i
\(476\) −4.33002 + 4.33002i −0.198466 + 0.198466i
\(477\) 1.98868 3.44450i 0.0910555 0.157713i
\(478\) 7.71957 4.45690i 0.353085 0.203854i
\(479\) −8.47302 + 31.6217i −0.387142 + 1.44483i 0.447620 + 0.894224i \(0.352272\pi\)
−0.834762 + 0.550610i \(0.814395\pi\)
\(480\) 12.3420 0.563333
\(481\) 8.33921 0.917276i 0.380235 0.0418242i
\(482\) 9.52580 0.433889
\(483\) 15.3389 + 4.11005i 0.697944 + 0.187014i
\(484\) 10.4837 17.2574i 0.476533 0.784425i
\(485\) −21.5100 12.4188i −0.976721 0.563910i
\(486\) −0.286658 + 0.286658i −0.0130031 + 0.0130031i
\(487\) −2.40652 + 0.644825i −0.109050 + 0.0292198i −0.312931 0.949776i \(-0.601311\pi\)
0.203881 + 0.978996i \(0.434644\pi\)
\(488\) 4.32381 + 16.1367i 0.195730 + 0.730473i
\(489\) −9.43065 + 9.43065i −0.426469 + 0.426469i
\(490\) −9.74188 5.62448i −0.440093 0.254088i
\(491\) −8.28373 14.3478i −0.373839 0.647509i 0.616313 0.787501i \(-0.288626\pi\)
−0.990153 + 0.139992i \(0.955292\pi\)
\(492\) 3.38954 12.6499i 0.152812 0.570304i
\(493\) 4.42811i 0.199432i
\(494\) −1.95465 5.01936i −0.0879439 0.225832i
\(495\) 8.10997 + 4.80372i 0.364516 + 0.215911i
\(496\) −5.43532 + 20.2849i −0.244053 + 0.910819i
\(497\) 3.65186 2.10840i 0.163808 0.0945748i
\(498\) −2.79764 1.61522i −0.125365 0.0723797i
\(499\) −30.2590 30.2590i −1.35458 1.35458i −0.880462 0.474116i \(-0.842768\pi\)
−0.474116 0.880462i \(-0.657232\pi\)
\(500\) −9.69020 + 2.59648i −0.433359 + 0.116118i
\(501\) 16.8514 4.51531i 0.752863 0.201729i
\(502\) 0.550522 + 0.550522i 0.0245710 + 0.0245710i
\(503\) 14.8715 + 8.58605i 0.663087 + 0.382833i 0.793452 0.608633i \(-0.208282\pi\)
−0.130365 + 0.991466i \(0.541615\pi\)
\(504\) 5.51356 3.18326i 0.245593 0.141793i
\(505\) −2.99575 + 11.1803i −0.133309 + 0.497517i
\(506\) −4.48684 2.65765i −0.199464 0.118147i
\(507\) 12.4020 + 3.89747i 0.550792 + 0.173093i
\(508\) 6.58937i 0.292356i
\(509\) 6.27542 23.4202i 0.278153 1.03808i −0.675545 0.737318i \(-0.736092\pi\)
0.953699 0.300764i \(-0.0972416\pi\)
\(510\) 0.469360 + 0.812955i 0.0207836 + 0.0359983i
\(511\) −48.0328 27.7317i −2.12484 1.22678i
\(512\) 16.0251 16.0251i 0.708216 0.708216i
\(513\) 0.953793 + 3.55960i 0.0421110 + 0.157160i
\(514\) 8.00053 2.14373i 0.352888 0.0945561i
\(515\) −5.05399 + 5.05399i −0.222706 + 0.222706i
\(516\) 15.1081 + 8.72264i 0.665095 + 0.383993i
\(517\) 26.2017 + 0.292327i 1.15235 + 0.0128565i
\(518\) −3.73053 0.999592i −0.163910 0.0439196i
\(519\) −12.8506 −0.564079
\(520\) −5.78198 14.8476i −0.253557 0.651110i
\(521\) −20.9463 −0.917672 −0.458836 0.888521i \(-0.651733\pi\)
−0.458836 + 0.888521i \(0.651733\pi\)
\(522\) −0.570247 + 2.12819i −0.0249590 + 0.0931483i
\(523\) −23.3421 + 13.4766i −1.02068 + 0.589290i −0.914301 0.405035i \(-0.867259\pi\)
−0.106379 + 0.994326i \(0.533926\pi\)
\(524\) −6.47442 + 11.2140i −0.282836 + 0.489887i
\(525\) 8.90840 8.90840i 0.388795 0.388795i
\(526\) −1.76346 + 0.472517i −0.0768903 + 0.0206027i
\(527\) −5.43496 + 1.45629i −0.236751 + 0.0634371i
\(528\) 9.77050 2.50151i 0.425206 0.108864i
\(529\) −3.97848 + 6.89094i −0.172978 + 0.299606i
\(530\) 2.29124 + 3.96854i 0.0995250 + 0.172382i
\(531\) 10.4093 + 2.78917i 0.451727 + 0.121040i
\(532\) 27.6969i 1.20081i
\(533\) −25.5690 + 2.81248i −1.10752 + 0.121822i
\(534\) 5.92878i 0.256563i
\(535\) −14.8868 3.98890i −0.643611 0.172455i
\(536\) 5.73026 3.30837i 0.247510 0.142900i
\(537\) −16.8258 9.71437i −0.726086 0.419206i
\(538\) 0.864044 0.864044i 0.0372516 0.0372516i
\(539\) −31.1831 8.72950i −1.34315 0.376006i
\(540\) 1.35025 + 5.03919i 0.0581054 + 0.216852i
\(541\) 16.8496 + 16.8496i 0.724420 + 0.724420i 0.969502 0.245082i \(-0.0788150\pi\)
−0.245082 + 0.969502i \(0.578815\pi\)
\(542\) −0.942203 + 1.63194i −0.0404711 + 0.0700980i
\(543\) −17.9221 + 10.3473i −0.769109 + 0.444046i
\(544\) 3.41770 + 0.915771i 0.146533 + 0.0392633i
\(545\) 24.2317 1.03797
\(546\) −4.66905 3.74369i −0.199817 0.160215i
\(547\) 4.70387i 0.201123i 0.994931 + 0.100561i \(0.0320639\pi\)
−0.994931 + 0.100561i \(0.967936\pi\)
\(548\) −5.16481 + 19.2753i −0.220630 + 0.823401i
\(549\) −9.30427 + 5.37182i −0.397097 + 0.229264i
\(550\) −3.60578 + 2.02850i −0.153751 + 0.0864957i
\(551\) 14.1622 + 14.1622i 0.603329 + 0.603329i
\(552\) −1.56093 5.82546i −0.0664375 0.247948i
\(553\) −5.05319 18.8588i −0.214884 0.801957i
\(554\) 2.31875 2.31875i 0.0985143 0.0985143i
\(555\) 3.30644 5.72692i 0.140351 0.243094i
\(556\) −6.99647 12.1182i −0.296716 0.513928i
\(557\) 4.09358 15.2774i 0.173450 0.647325i −0.823360 0.567519i \(-0.807903\pi\)
0.996810 0.0798061i \(-0.0254301\pi\)
\(558\) 2.79963 0.118518
\(559\) 5.19662 33.8693i 0.219793 1.43252i
\(560\) 35.3847i 1.49528i
\(561\) 1.88935 + 1.93198i 0.0797685 + 0.0815685i
\(562\) 3.37787 + 5.85064i 0.142487 + 0.246794i
\(563\) −11.1080 + 19.2397i −0.468148 + 0.810856i −0.999337 0.0363972i \(-0.988412\pi\)
0.531190 + 0.847253i \(0.321745\pi\)
\(564\) 10.2550 + 10.2550i 0.431814 + 0.431814i
\(565\) 24.4597 6.55396i 1.02903 0.275727i
\(566\) 1.21667 + 4.54069i 0.0511406 + 0.190859i
\(567\) 2.89513 + 2.89513i 0.121584 + 0.121584i
\(568\) −1.38692 0.800736i −0.0581937 0.0335982i
\(569\) −18.7671 32.5056i −0.786759 1.36271i −0.927943 0.372723i \(-0.878424\pi\)
0.141184 0.989983i \(-0.454909\pi\)
\(570\) −4.10116 1.09890i −0.171779 0.0460280i
\(571\) 4.41199 0.184636 0.0923181 0.995730i \(-0.470572\pi\)
0.0923181 + 0.995730i \(0.470572\pi\)
\(572\) −12.7901 17.8401i −0.534781 0.745933i
\(573\) −16.2202 −0.677609
\(574\) 11.4383 + 3.06487i 0.477423 + 0.127925i
\(575\) −5.96719 10.3355i −0.248849 0.431019i
\(576\) 3.74241 + 2.16068i 0.155934 + 0.0900283i
\(577\) 25.6639 + 25.6639i 1.06840 + 1.06840i 0.997482 + 0.0709204i \(0.0225936\pi\)
0.0709204 + 0.997482i \(0.477406\pi\)
\(578\) −1.71406 6.39695i −0.0712954 0.266078i
\(579\) −23.4716 + 6.28919i −0.975445 + 0.261370i
\(580\) 20.0488 + 20.0488i 0.832483 + 0.832483i
\(581\) −16.3130 + 28.2550i −0.676779 + 1.17222i
\(582\) 1.77147 + 3.06828i 0.0734298 + 0.127184i
\(583\) 9.22310 + 9.43122i 0.381982 + 0.390601i
\(584\) 21.0641i 0.871639i
\(585\) 8.26079 6.06306i 0.341542 0.250677i
\(586\) −9.83035 −0.406088
\(587\) −11.3887 + 42.5032i −0.470061 + 1.75429i 0.169477 + 0.985534i \(0.445792\pi\)
−0.639538 + 0.768759i \(0.720874\pi\)
\(588\) −8.96124 15.5213i −0.369555 0.640088i
\(589\) 12.7248 22.0399i 0.524315 0.908140i
\(590\) −8.77950 + 8.77950i −0.361446 + 0.361446i
\(591\) −5.61680 20.9622i −0.231044 0.862269i
\(592\) −1.83134 6.83464i −0.0752675 0.280902i
\(593\) −20.3525 20.3525i −0.835778 0.835778i 0.152522 0.988300i \(-0.451261\pi\)
−0.988300 + 0.152522i \(0.951261\pi\)
\(594\) −0.659241 1.17184i −0.0270490 0.0480811i
\(595\) 8.21051 4.74034i 0.336598 0.194335i
\(596\) 4.76720 17.7914i 0.195272 0.728766i
\(597\) 6.64817i 0.272091i
\(598\) −4.57028 + 3.35439i −0.186893 + 0.137171i
\(599\) −7.10192 −0.290177 −0.145088 0.989419i \(-0.546347\pi\)
−0.145088 + 0.989419i \(0.546347\pi\)
\(600\) −4.62162 1.23836i −0.188677 0.0505558i
\(601\) −15.5542 + 8.98021i −0.634468 + 0.366310i −0.782480 0.622675i \(-0.786046\pi\)
0.148012 + 0.988986i \(0.452712\pi\)
\(602\) −7.88713 + 13.6609i −0.321455 + 0.556777i
\(603\) 3.00892 + 3.00892i 0.122533 + 0.122533i
\(604\) 10.0491 + 37.5037i 0.408891 + 1.52600i
\(605\) −22.5934 + 21.6070i −0.918551 + 0.878448i
\(606\) 1.16748 1.16748i 0.0474255 0.0474255i
\(607\) 7.54902 + 4.35843i 0.306405 + 0.176903i 0.645317 0.763915i \(-0.276725\pi\)
−0.338912 + 0.940818i \(0.610059\pi\)
\(608\) −13.8595 + 8.00180i −0.562078 + 0.324516i
\(609\) 21.4938 + 5.75926i 0.870974 + 0.233377i
\(610\) 12.3782i 0.501178i
\(611\) 11.4604 26.0790i 0.463637 1.05504i
\(612\) 1.49562i 0.0604569i
\(613\) −4.81573 1.29037i −0.194506 0.0521176i 0.160251 0.987076i \(-0.448770\pi\)
−0.354757 + 0.934959i \(0.615436\pi\)
\(614\) −3.24926 5.62788i −0.131129 0.227123i
\(615\) −10.1379 + 17.5594i −0.408801 + 0.708065i
\(616\) 5.23717 + 20.4555i 0.211012 + 0.824177i
\(617\) 32.7446 8.77389i 1.31825 0.353223i 0.469926 0.882706i \(-0.344280\pi\)
0.848321 + 0.529482i \(0.177614\pi\)
\(618\) 0.984797 0.263876i 0.0396143 0.0106146i
\(619\) −30.6722 + 30.6722i −1.23282 + 1.23282i −0.269942 + 0.962877i \(0.587004\pi\)
−0.962877 + 0.269942i \(0.912996\pi\)
\(620\) 18.0139 31.2010i 0.723457 1.25306i
\(621\) 3.35891 1.93927i 0.134788 0.0778201i
\(622\) −0.802060 + 2.99333i −0.0321597 + 0.120022i
\(623\) −59.8782 −2.39897
\(624\) 1.66280 10.8374i 0.0665654 0.433844i
\(625\) 30.9170 1.23668
\(626\) 4.16703 + 1.11655i 0.166548 + 0.0446264i
\(627\) −12.2216 0.136353i −0.488083 0.00544543i
\(628\) 35.3132 + 20.3881i 1.40915 + 0.813572i
\(629\) 1.34054 1.34054i 0.0534509 0.0534509i
\(630\) −4.55650 + 1.22091i −0.181535 + 0.0486423i
\(631\) 10.2920 + 38.4104i 0.409720 + 1.52909i 0.795182 + 0.606371i \(0.207375\pi\)
−0.385463 + 0.922723i \(0.625958\pi\)
\(632\) −5.24313 + 5.24313i −0.208561 + 0.208561i
\(633\) 16.9556 + 9.78932i 0.673925 + 0.389091i
\(634\) −4.44312 7.69572i −0.176459 0.305636i
\(635\) −2.64043 + 9.85422i −0.104782 + 0.391053i
\(636\) 7.30106i 0.289506i
\(637\) −22.0214 + 27.4646i −0.872519 + 1.08819i
\(638\) −6.28724 3.72407i −0.248914 0.147437i
\(639\) 0.266561 0.994820i 0.0105450 0.0393545i
\(640\) −25.6887 + 14.8314i −1.01544 + 0.586263i
\(641\) −18.5437 10.7062i −0.732433 0.422870i 0.0868788 0.996219i \(-0.472311\pi\)
−0.819311 + 0.573349i \(0.805644\pi\)
\(642\) 1.55451 + 1.55451i 0.0613518 + 0.0613518i
\(643\) 23.1088 6.19199i 0.911324 0.244188i 0.227451 0.973790i \(-0.426961\pi\)
0.683873 + 0.729601i \(0.260294\pi\)
\(644\) −28.1569 + 7.54462i −1.10954 + 0.297300i
\(645\) −19.0984 19.0984i −0.752000 0.752000i
\(646\) −1.05414 0.608608i −0.0414746 0.0239454i
\(647\) 40.4881 23.3758i 1.59175 0.918998i 0.598745 0.800940i \(-0.295666\pi\)
0.993007 0.118059i \(-0.0376672\pi\)
\(648\) 0.402453 1.50197i 0.0158098 0.0590031i
\(649\) −18.2151 + 30.7520i −0.715004 + 1.20712i
\(650\) 0.491752 + 4.47066i 0.0192881 + 0.175354i
\(651\) 28.2751i 1.10819i
\(652\) 6.33642 23.6478i 0.248153 0.926121i
\(653\) 13.1820 + 22.8319i 0.515851 + 0.893480i 0.999831 + 0.0184010i \(0.00585755\pi\)
−0.483980 + 0.875079i \(0.660809\pi\)
\(654\) −2.99342 1.72825i −0.117052 0.0675799i
\(655\) 14.1759 14.1759i 0.553899 0.553899i
\(656\) 5.61510 + 20.9558i 0.219233 + 0.818188i
\(657\) −13.0848 + 3.50607i −0.510488 + 0.136785i
\(658\) −9.27273 + 9.27273i −0.361489 + 0.361489i
\(659\) 1.77308 + 1.02369i 0.0690695 + 0.0398773i 0.534137 0.845398i \(-0.320637\pi\)
−0.465068 + 0.885275i \(0.653970\pi\)
\(660\) −17.3016 0.193030i −0.673464 0.00751368i
\(661\) 10.2379 + 2.74324i 0.398209 + 0.106700i 0.452365 0.891833i \(-0.350580\pi\)
−0.0541564 + 0.998532i \(0.517247\pi\)
\(662\) 0.631267 0.0245349
\(663\) 2.73743 1.06601i 0.106313 0.0414006i
\(664\) 12.3908 0.480858
\(665\) −11.0985 + 41.4200i −0.430380 + 1.60620i
\(666\) −0.816911 + 0.471644i −0.0316546 + 0.0182758i
\(667\) 10.5396 18.2552i 0.408096 0.706843i
\(668\) −22.6447 + 22.6447i −0.876151 + 0.876151i
\(669\) 5.83849 1.56442i 0.225729 0.0604840i
\(670\) −4.73559 + 1.26890i −0.182952 + 0.0490218i
\(671\) −8.83786 34.5192i −0.341182 1.33260i
\(672\) −8.89022 + 15.3983i −0.342948 + 0.594003i
\(673\) 4.53777 + 7.85965i 0.174918 + 0.302967i 0.940133 0.340808i \(-0.110701\pi\)
−0.765215 + 0.643775i \(0.777367\pi\)
\(674\) −8.45866 2.26649i −0.325815 0.0873020i
\(675\) 3.07703i 0.118435i
\(676\) −23.2930 + 5.18700i −0.895883 + 0.199500i
\(677\) 24.9170i 0.957636i 0.877914 + 0.478818i \(0.158935\pi\)
−0.877914 + 0.478818i \(0.841065\pi\)
\(678\) −3.48903 0.934882i −0.133995 0.0359039i
\(679\) 30.9883 17.8911i 1.18922 0.686598i
\(680\) −3.11821 1.80030i −0.119578 0.0690384i
\(681\) 10.3637 10.3637i 0.397139 0.397139i
\(682\) −2.50313 + 8.94157i −0.0958498 + 0.342390i
\(683\) 1.31828 + 4.91990i 0.0504427 + 0.188255i 0.986550 0.163460i \(-0.0522654\pi\)
−0.936107 + 0.351715i \(0.885599\pi\)
\(684\) −4.78337 4.78337i −0.182897 0.182897i
\(685\) 15.4477 26.7561i 0.590225 1.02230i
\(686\) 3.97244 2.29349i 0.151669 0.0875659i
\(687\) 3.60113 + 0.964920i 0.137392 + 0.0368140i
\(688\) −28.8998 −1.10179
\(689\) 13.3631 5.20388i 0.509093 0.198252i
\(690\) 4.46861i 0.170117i
\(691\) −12.9353 + 48.2753i −0.492083 + 1.83648i 0.0537042 + 0.998557i \(0.482897\pi\)
−0.545788 + 0.837924i \(0.683769\pi\)
\(692\) 20.4289 11.7946i 0.776590 0.448365i
\(693\) −11.8351 + 6.65806i −0.449578 + 0.252919i
\(694\) −10.1132 10.1132i −0.383891 0.383891i
\(695\) 5.60712 + 20.9261i 0.212690 + 0.793771i
\(696\) −2.18727 8.16300i −0.0829082 0.309418i
\(697\) −4.11026 + 4.11026i −0.155687 + 0.155687i
\(698\) −4.91935 + 8.52056i −0.186200 + 0.322508i
\(699\) −6.32918 10.9625i −0.239392 0.414639i
\(700\) −5.98552 + 22.3383i −0.226231 + 0.844307i
\(701\) −8.59749 −0.324723 −0.162361 0.986731i \(-0.551911\pi\)
−0.162361 + 0.986731i \(0.551911\pi\)
\(702\) −1.45291 + 0.159814i −0.0548366 + 0.00603178i
\(703\) 8.57477i 0.323404i
\(704\) −10.2469 + 10.0208i −0.386195 + 0.377673i
\(705\) −11.2268 19.4454i −0.422826 0.732357i
\(706\) −2.88951 + 5.00478i −0.108748 + 0.188357i
\(707\) −11.7910 11.7910i −0.443447 0.443447i
\(708\) −19.1080 + 5.11996i −0.718121 + 0.192420i
\(709\) −10.5778 39.4768i −0.397257 1.48258i −0.817902 0.575358i \(-0.804863\pi\)
0.420645 0.907225i \(-0.361804\pi\)
\(710\) 0.839056 + 0.839056i 0.0314892 + 0.0314892i
\(711\) −4.12969 2.38428i −0.154876 0.0894174i
\(712\) 11.3704 + 19.6941i 0.426123 + 0.738066i
\(713\) −25.8722 6.93243i −0.968921 0.259622i
\(714\) −1.35236 −0.0506109
\(715\) 11.9785 + 31.8046i 0.447971 + 1.18942i
\(716\) 35.6645 1.33284
\(717\) −21.2387 5.69088i −0.793173 0.212530i
\(718\) 1.92322 + 3.33112i 0.0717741 + 0.124316i
\(719\) 9.22484 + 5.32596i 0.344028 + 0.198625i 0.662052 0.749458i \(-0.269686\pi\)
−0.318024 + 0.948083i \(0.603019\pi\)
\(720\) −6.11108 6.11108i −0.227747 0.227747i
\(721\) −2.66503 9.94604i −0.0992510 0.370410i
\(722\) −2.12218 + 0.568636i −0.0789793 + 0.0211624i
\(723\) −16.6153 16.6153i −0.617929 0.617929i
\(724\) 18.9941 32.8987i 0.705910 1.22267i
\(725\) −8.36160 14.4827i −0.310542 0.537874i
\(726\) 4.33208 1.05778i 0.160779 0.0392578i
\(727\) 9.87894i 0.366390i −0.983077 0.183195i \(-0.941356\pi\)
0.983077 0.183195i \(-0.0586439\pi\)
\(728\) 22.6893 + 3.48125i 0.840920 + 0.129024i
\(729\) 1.00000 0.0370370
\(730\) 4.03948 15.0755i 0.149508 0.557971i
\(731\) −3.87158 6.70577i −0.143195 0.248022i
\(732\) 9.86081 17.0794i 0.364466 0.631274i
\(733\) −7.78756 + 7.78756i −0.287640 + 0.287640i −0.836146 0.548506i \(-0.815197\pi\)
0.548506 + 0.836146i \(0.315197\pi\)
\(734\) −3.43550 12.8215i −0.126807 0.473249i
\(735\) 7.18173 + 26.8026i 0.264902 + 0.988628i
\(736\) 11.9100 + 11.9100i 0.439009 + 0.439009i
\(737\) −12.3002 + 6.91974i −0.453085 + 0.254892i
\(738\) 2.50475 1.44612i 0.0922010 0.0532323i
\(739\) −1.41605 + 5.28476i −0.0520902 + 0.194403i −0.987068 0.160304i \(-0.948753\pi\)
0.934978 + 0.354707i \(0.115419\pi\)
\(740\) 12.1390i 0.446237i
\(741\) −5.34559 + 12.1643i −0.196375 + 0.446868i
\(742\) −6.60172 −0.242357
\(743\) 19.8362 + 5.31509i 0.727719 + 0.194992i 0.603613 0.797277i \(-0.293727\pi\)
0.124106 + 0.992269i \(0.460394\pi\)
\(744\) −9.29975 + 5.36921i −0.340945 + 0.196845i
\(745\) −14.2585 + 24.6964i −0.522389 + 0.904805i
\(746\) 0.863284 + 0.863284i 0.0316071 + 0.0316071i
\(747\) 2.06243 + 7.69708i 0.0754602 + 0.281621i
\(748\) −4.77677 1.33722i −0.174656 0.0488937i
\(749\) 15.7000 15.7000i 0.573664 0.573664i
\(750\) −1.91870 1.10776i −0.0700611 0.0404498i
\(751\) −11.4288 + 6.59844i −0.417044 + 0.240780i −0.693812 0.720156i \(-0.744070\pi\)
0.276768 + 0.960937i \(0.410737\pi\)
\(752\) −23.2066 6.21819i −0.846258 0.226754i
\(753\) 1.92048i 0.0699863i
\(754\) −6.40416 + 4.70038i −0.233226 + 0.171178i
\(755\) 60.1125i 2.18772i
\(756\) −7.25968 1.94523i −0.264032 0.0707472i
\(757\) 1.43465 + 2.48488i 0.0521431 + 0.0903144i 0.890919 0.454163i \(-0.150061\pi\)
−0.838776 + 0.544477i \(0.816728\pi\)
\(758\) 0.0829177 0.143618i 0.00301171 0.00521643i
\(759\) 3.19053 + 12.4617i 0.115809 + 0.452331i
\(760\) 15.7306 4.21501i 0.570610 0.152895i
\(761\) 43.9456 11.7752i 1.59303 0.426850i 0.650099 0.759850i \(-0.274727\pi\)
0.942927 + 0.332999i \(0.108061\pi\)
\(762\) 1.02900 1.02900i 0.0372769 0.0372769i
\(763\) −17.4546 + 30.2323i −0.631899 + 1.09448i
\(764\) 25.7856 14.8874i 0.932892 0.538605i
\(765\) 0.599312 2.23666i 0.0216682 0.0808667i
\(766\) 7.23775 0.261511
\(767\) 22.9903 + 31.3239i 0.830133 + 1.13104i
\(768\) −4.41150 −0.159186
\(769\) −9.50710 2.54742i −0.342835 0.0918623i 0.0832935 0.996525i \(-0.473456\pi\)
−0.426128 + 0.904663i \(0.640123\pi\)
\(770\) 0.174540 15.6443i 0.00629000 0.563783i
\(771\) −17.6940 10.2156i −0.637234 0.367907i
\(772\) 31.5409 31.5409i 1.13518 1.13518i
\(773\) 27.5842 7.39115i 0.992133 0.265841i 0.273987 0.961733i \(-0.411658\pi\)
0.718146 + 0.695892i \(0.244991\pi\)
\(774\) 0.997154 + 3.72143i 0.0358420 + 0.133764i
\(775\) −15.0258 + 15.0258i −0.539744 + 0.539744i
\(776\) −11.7688 6.79475i −0.422477 0.243917i
\(777\) 4.76340 + 8.25046i 0.170886 + 0.295984i
\(778\) −1.82797 + 6.82208i −0.0655360 + 0.244584i
\(779\) 26.2913i 0.941983i
\(780\) −7.56753 + 17.2206i −0.270961 + 0.616595i
\(781\) 2.93896 + 1.74081i 0.105164 + 0.0622912i
\(782\) −0.331569 + 1.23743i −0.0118569 + 0.0442505i
\(783\) 4.70672 2.71742i 0.168204 0.0971128i
\(784\) 25.7125 + 14.8451i 0.918305 + 0.530183i
\(785\) −44.6402 44.6402i −1.59328 1.59328i
\(786\) −2.76225 + 0.740143i −0.0985262 + 0.0264000i
\(787\) −9.31415 + 2.49572i −0.332014 + 0.0889628i −0.420975 0.907072i \(-0.638312\pi\)
0.0889612 + 0.996035i \(0.471645\pi\)
\(788\) 28.1688 + 28.1688i 1.00347 + 1.00347i
\(789\) 3.90007 + 2.25171i 0.138846 + 0.0801629i
\(790\) 4.75798 2.74702i 0.169281 0.0977346i
\(791\) −9.44192 + 35.2377i −0.335716 + 1.25291i
\(792\) 4.43723 + 2.62827i 0.157670 + 0.0933916i
\(793\) −38.2887 5.87470i −1.35967 0.208617i
\(794\) 7.04493i 0.250015i
\(795\) 2.92562 10.9185i 0.103761 0.387241i
\(796\) −6.10187 10.5687i −0.216275 0.374599i
\(797\) −43.0405 24.8495i −1.52457 0.880213i −0.999576 0.0291101i \(-0.990733\pi\)
−0.524998 0.851103i \(-0.675934\pi\)
\(798\) 4.32519 4.32519i 0.153110 0.153110i
\(799\) −1.66605 6.21778i −0.0589406 0.219969i
\(800\) 12.9073 3.45850i 0.456342 0.122276i
\(801\) −10.3412 + 10.3412i −0.365388 + 0.365388i
\(802\) −0.375682 0.216900i −0.0132658 0.00765900i
\(803\) 0.501224 44.9256i 0.0176878 1.58539i
\(804\) −7.54501 2.02168i −0.266092 0.0712991i
\(805\) 45.1311 1.59066
\(806\) 7.87530 + 6.31449i 0.277396 + 0.222418i
\(807\) −3.01420 −0.106105
\(808\) −1.63907 + 6.11711i −0.0576624 + 0.215199i
\(809\) 21.1719 12.2236i 0.744366 0.429760i −0.0792887 0.996852i \(-0.525265\pi\)
0.823655 + 0.567092i \(0.191932\pi\)
\(810\) −0.576070 + 0.997782i −0.0202410 + 0.0350585i
\(811\) 24.8203 24.8203i 0.871559 0.871559i −0.121083 0.992642i \(-0.538637\pi\)
0.992642 + 0.121083i \(0.0386367\pi\)
\(812\) −39.4552 + 10.5720i −1.38461 + 0.371005i
\(813\) 4.48992 1.20307i 0.157469 0.0421936i
\(814\) −0.775960 3.03077i −0.0271974 0.106229i
\(815\) −18.9519 + 32.8256i −0.663856 + 1.14983i
\(816\) −1.23882 2.14570i −0.0433674 0.0751145i
\(817\) 33.8290 + 9.06444i 1.18353 + 0.317125i
\(818\) 10.1006i 0.353159i
\(819\) 1.61405 + 14.6738i 0.0563996 + 0.512745i
\(820\) 37.2195i 1.29976i
\(821\) −25.6077 6.86157i −0.893716 0.239471i −0.217401 0.976082i \(-0.569758\pi\)
−0.676316 + 0.736612i \(0.736424\pi\)
\(822\) −3.81660 + 2.20352i −0.133119 + 0.0768564i
\(823\) 32.9786 + 19.0402i 1.14956 + 0.663700i 0.948781 0.315936i \(-0.102318\pi\)
0.200782 + 0.979636i \(0.435652\pi\)
\(824\) −2.76521 + 2.76521i −0.0963305 + 0.0963305i
\(825\) 9.82754 + 2.75115i 0.342151 + 0.0957827i
\(826\) −4.62954 17.2777i −0.161082 0.601167i
\(827\) −7.09916 7.09916i −0.246862 0.246862i 0.572820 0.819681i \(-0.305850\pi\)
−0.819681 + 0.572820i \(0.805850\pi\)
\(828\) −3.55982 + 6.16580i −0.123712 + 0.214276i
\(829\) 30.4168 17.5612i 1.05642 0.609924i 0.131980 0.991252i \(-0.457866\pi\)
0.924440 + 0.381328i \(0.124533\pi\)
\(830\) −8.86811 2.37620i −0.307817 0.0824792i
\(831\) −8.08891 −0.280601
\(832\) 5.65396 + 14.5188i 0.196016 + 0.503350i
\(833\) 7.95496i 0.275623i
\(834\) 0.799822 2.98498i 0.0276956 0.103361i
\(835\) 42.9386 24.7906i 1.48595 0.857914i
\(836\) 19.5541 11.0005i 0.676292 0.380461i
\(837\) −4.88323 4.88323i −0.168789 0.168789i
\(838\) 0.717849 + 2.67905i 0.0247977 + 0.0925462i
\(839\) 2.59301 + 9.67723i 0.0895205 + 0.334095i 0.996132 0.0878716i \(-0.0280065\pi\)
−0.906611 + 0.421967i \(0.861340\pi\)
\(840\) 12.7942 12.7942i 0.441441 0.441441i
\(841\) 0.268781 0.465542i 0.00926831 0.0160532i
\(842\) −3.37208 5.84061i −0.116209 0.201281i
\(843\) 4.31310 16.0967i 0.148551 0.554401i
\(844\) −35.9396 −1.23709
\(845\) 36.9125 + 1.57672i 1.26983 + 0.0542409i
\(846\) 3.20287i 0.110117i
\(847\) −10.6831 43.7522i −0.367076 1.50334i
\(848\) −6.04745 10.4745i −0.207670 0.359696i
\(849\) 5.79787 10.0422i 0.198982 0.344648i
\(850\) 0.718666 + 0.718666i 0.0246500 + 0.0246500i
\(851\) 8.71718 2.33576i 0.298821 0.0800689i
\(852\) 0.489314 + 1.82615i 0.0167636 + 0.0625627i
\(853\) 20.4127 + 20.4127i 0.698919 + 0.698919i 0.964177 0.265258i \(-0.0854573\pi\)
−0.265258 + 0.964177i \(0.585457\pi\)
\(854\) 15.4435 + 8.91628i 0.528464 + 0.305109i
\(855\) 5.23665 + 9.07015i 0.179090 + 0.310193i
\(856\) −8.14504 2.18246i −0.278392 0.0745948i
\(857\) 20.7248 0.707947 0.353973 0.935255i \(-0.384830\pi\)
0.353973 + 0.935255i \(0.384830\pi\)
\(858\) 0.788618 4.78325i 0.0269230 0.163298i
\(859\) −17.2940 −0.590065 −0.295033 0.955487i \(-0.595331\pi\)
−0.295033 + 0.955487i \(0.595331\pi\)
\(860\) 47.8903 + 12.8322i 1.63305 + 0.437573i
\(861\) −14.6052 25.2969i −0.497743 0.862116i
\(862\) 5.44306 + 3.14255i 0.185391 + 0.107036i
\(863\) 30.2785 + 30.2785i 1.03069 + 1.03069i 0.999514 + 0.0311793i \(0.00992630\pi\)
0.0311793 + 0.999514i \(0.490074\pi\)
\(864\) 1.12397 + 4.19472i 0.0382383 + 0.142707i
\(865\) −35.2771 + 9.45248i −1.19946 + 0.321394i
\(866\) −2.76219 2.76219i −0.0938629 0.0938629i
\(867\) −8.16808 + 14.1475i −0.277403 + 0.480475i
\(868\) 25.9517 + 44.9496i 0.880857 + 1.52569i
\(869\) 11.3073 11.0578i 0.383575 0.375110i
\(870\) 6.26170i 0.212292i
\(871\) 1.67749 + 15.2505i 0.0568396 + 0.516745i
\(872\) 13.2579 0.448970
\(873\) 2.26194 8.44167i 0.0765550 0.285707i
\(874\) −2.89718 5.01806i −0.0979984 0.169738i
\(875\) −11.1880 + 19.3781i −0.378222 + 0.655100i
\(876\) 17.5833 17.5833i 0.594084 0.594084i
\(877\) −7.48595 27.9379i −0.252782 0.943397i −0.969311 0.245839i \(-0.920937\pi\)
0.716528 0.697558i \(-0.245730\pi\)
\(878\) 2.24415 + 8.37528i 0.0757364 + 0.282652i
\(879\) 17.1465 + 17.1465i 0.578336 + 0.578336i
\(880\) 24.9817 14.0539i 0.842132 0.473758i
\(881\) −24.5680 + 14.1843i −0.827716 + 0.477882i −0.853070 0.521797i \(-0.825262\pi\)
0.0253541 + 0.999679i \(0.491929\pi\)
\(882\) 1.02443 3.82323i 0.0344944 0.128735i
\(883\) 12.9290i 0.435096i 0.976050 + 0.217548i \(0.0698059\pi\)
−0.976050 + 0.217548i \(0.930194\pi\)
\(884\) −3.37333 + 4.20715i −0.113457 + 0.141502i
\(885\) 30.6271 1.02952
\(886\) −10.0159 2.68374i −0.336490 0.0901621i
\(887\) −27.8036 + 16.0524i −0.933555 + 0.538988i −0.887934 0.459971i \(-0.847860\pi\)
−0.0456208 + 0.998959i \(0.514527\pi\)
\(888\) 1.80906 3.13339i 0.0607081 0.105150i
\(889\) −10.3925 10.3925i −0.348554 0.348554i
\(890\) −4.36101 16.2755i −0.146182 0.545557i
\(891\) −0.894092 + 3.19384i −0.0299532 + 0.106998i
\(892\) −7.84572 + 7.84572i −0.262694 + 0.262694i
\(893\) 25.2144 + 14.5576i 0.843769 + 0.487150i
\(894\) 3.52279 2.03388i 0.117820 0.0680232i
\(895\) −53.3352 14.2911i −1.78280 0.477700i
\(896\) 42.7336i 1.42763i
\(897\) 13.8225 + 2.12081i 0.461520 + 0.0708117i
\(898\) 1.00659i 0.0335905i
\(899\) −36.2537 9.71416i −1.20913 0.323985i
\(900\) 2.82418 + 4.89163i 0.0941394 + 0.163054i
\(901\) 1.62030 2.80645i 0.0539801 0.0934963i
\(902\) 2.37919 + 9.29271i 0.0792182 + 0.309414i
\(903\) 37.5849 10.0708i 1.25075 0.335137i
\(904\) 13.3827 3.58588i 0.445102 0.119265i
\(905\) −41.5880 + 41.5880i −1.38243 + 1.38243i
\(906\) −4.28734 + 7.42589i −0.142437 + 0.246709i
\(907\) 33.9994 19.6295i 1.12893 0.651788i 0.185264 0.982689i \(-0.440686\pi\)
0.943666 + 0.330901i \(0.107353\pi\)
\(908\) −6.96335 + 25.9876i −0.231087 + 0.862428i
\(909\) −4.07271 −0.135083
\(910\) −15.5711 6.84267i −0.516176 0.226832i
\(911\) −8.71548 −0.288757 −0.144378 0.989523i \(-0.546118\pi\)
−0.144378 + 0.989523i \(0.546118\pi\)
\(912\) 10.8245 + 2.90042i 0.358436 + 0.0960426i
\(913\) −26.4272 0.294842i −0.874613 0.00975786i
\(914\) 4.55305 + 2.62870i 0.150601 + 0.0869498i
\(915\) −21.5905 + 21.5905i −0.713760 + 0.713760i
\(916\) −6.61043 + 1.77126i −0.218415 + 0.0585240i
\(917\) 7.47513 + 27.8976i 0.246851 + 0.921259i
\(918\) −0.233558 + 0.233558i −0.00770857 + 0.00770857i
\(919\) 35.1630 + 20.3014i 1.15992 + 0.669681i 0.951285 0.308312i \(-0.0997642\pi\)
0.208636 + 0.977993i \(0.433098\pi\)
\(920\) −8.57003 14.8437i −0.282545 0.489383i
\(921\) −4.14888 + 15.4838i −0.136710 + 0.510210i
\(922\) 4.24770i 0.139890i
\(923\) 2.99362 2.19719i 0.0985362 0.0723213i
\(924\) 12.7036 21.4470i 0.417916 0.705555i
\(925\) 1.85307 6.91577i 0.0609287 0.227389i
\(926\) −2.35167 + 1.35774i −0.0772806 + 0.0446180i
\(927\) −2.17798 1.25746i −0.0715343 0.0413004i
\(928\) 16.6891 + 16.6891i 0.547845 + 0.547845i
\(929\) 51.7369 13.8629i 1.69743 0.454825i 0.725141 0.688600i \(-0.241775\pi\)
0.972291 + 0.233775i \(0.0751079\pi\)
\(930\) 7.68547 2.05932i 0.252017 0.0675276i
\(931\) −25.4419 25.4419i −0.833826 0.833826i
\(932\) 20.1233 + 11.6182i 0.659161 + 0.380567i
\(933\) 6.62006 3.82209i 0.216731 0.125130i
\(934\) −2.32677 + 8.68361i −0.0761341 + 0.284136i
\(935\) 6.60770 + 3.91389i 0.216095 + 0.127998i
\(936\) 4.51975 3.31730i 0.147733 0.108429i
\(937\) 38.4606i 1.25645i −0.778030 0.628227i \(-0.783781\pi\)
0.778030 0.628227i \(-0.216219\pi\)
\(938\) 1.82803 6.82230i 0.0596873 0.222756i
\(939\) −5.32075 9.21582i −0.173636 0.300747i
\(940\) 35.6951 + 20.6086i 1.16424 + 0.672177i
\(941\) −26.2401 + 26.2401i −0.855402 + 0.855402i −0.990792 0.135391i \(-0.956771\pi\)
0.135391 + 0.990792i \(0.456771\pi\)
\(942\) 2.33072 + 8.69837i 0.0759390 + 0.283408i
\(943\) −26.7279 + 7.16173i −0.870381 + 0.233218i
\(944\) 23.1724 23.1724i 0.754199 0.754199i
\(945\) 10.0772 + 5.81807i 0.327811 + 0.189262i
\(946\) −12.7772 0.142552i −0.415422 0.00463477i
\(947\) −32.7023 8.76255i −1.06268 0.284745i −0.315199 0.949026i \(-0.602071\pi\)
−0.747483 + 0.664281i \(0.768738\pi\)
\(948\) 8.75342 0.284298
\(949\) −44.7152 19.6500i −1.45152 0.637865i
\(950\) −4.59694 −0.149145
\(951\) −5.67330 + 21.1730i −0.183969 + 0.686582i
\(952\) 4.49224 2.59360i 0.145594 0.0840589i
\(953\) 18.0820 31.3190i 0.585734 1.01452i −0.409049 0.912512i \(-0.634140\pi\)
0.994783 0.102009i \(-0.0325272\pi\)
\(954\) −1.14014 + 1.14014i −0.0369135 + 0.0369135i
\(955\) −44.5273 + 11.9310i −1.44087 + 0.386080i
\(956\) 38.9869 10.4465i 1.26092 0.337864i
\(957\) 4.47077 + 17.4621i 0.144520 + 0.564470i
\(958\) 6.63577 11.4935i 0.214392 0.371338i
\(959\) 22.2546 + 38.5461i 0.718638 + 1.24472i
\(960\) 11.8629 + 3.17865i 0.382873 + 0.102590i
\(961\) 16.6918i 0.538445i
\(962\) −3.36173 0.515796i −0.108387 0.0166299i
\(963\) 5.42289i 0.174750i
\(964\) 41.6636 + 11.1637i 1.34190 + 0.359560i
\(965\) −59.8074 + 34.5298i −1.92527 + 1.11155i
\(966\) −5.57520 3.21884i −0.179379 0.103565i
\(967\) −18.5937 + 18.5937i −0.597934 + 0.597934i −0.939762 0.341829i \(-0.888954\pi\)
0.341829 + 0.939762i \(0.388954\pi\)
\(968\) −12.3616 + 11.8219i −0.397316 + 0.379970i
\(969\) 0.777115 + 2.90023i 0.0249645 + 0.0931688i
\(970\) 7.11991 + 7.11991i 0.228607 + 0.228607i
\(971\) −15.4973 + 26.8422i −0.497333 + 0.861406i −0.999995 0.00307706i \(-0.999021\pi\)
0.502662 + 0.864483i \(0.332354\pi\)
\(972\) −1.58972 + 0.917827i −0.0509904 + 0.0294393i
\(973\) −30.1470 8.07787i −0.966469 0.258965i
\(974\) 1.01001 0.0323628
\(975\) 6.94016 8.65562i 0.222263 0.277202i
\(976\) 32.6707i 1.04576i
\(977\) 12.5294 46.7603i 0.400851 1.49600i −0.410731 0.911757i \(-0.634726\pi\)
0.811582 0.584239i \(-0.198607\pi\)
\(978\) 4.68238 2.70337i 0.149726 0.0864443i
\(979\) −23.7821 42.2741i −0.760080 1.35109i
\(980\) −36.0171 36.0171i −1.15052 1.15052i
\(981\) 2.20675 + 8.23571i 0.0704562 + 0.262946i
\(982\) 1.73833 + 6.48752i 0.0554722 + 0.207025i
\(983\) 21.4410 21.4410i 0.683860 0.683860i −0.277007 0.960868i \(-0.589343\pi\)
0.960868 + 0.277007i \(0.0893427\pi\)
\(984\) −5.54680 + 9.60734i −0.176826 + 0.306271i
\(985\) −30.8382 53.4133i −0.982585 1.70189i
\(986\) −0.464615 + 1.73397i −0.0147964 + 0.0552208i
\(987\) 32.3477 1.02964
\(988\) −2.66676 24.2443i −0.0848410 0.771313i
\(989\) 36.8599i 1.17208i
\(990\) −2.67169 2.73198i −0.0849120 0.0868281i
\(991\) 6.76841 + 11.7232i 0.215006 + 0.372401i 0.953274 0.302106i \(-0.0976897\pi\)
−0.738269 + 0.674507i \(0.764356\pi\)
\(992\) 14.9952 25.9724i 0.476097 0.824624i
\(993\) −1.10108 1.10108i −0.0349417 0.0349417i
\(994\) −1.65123 + 0.442445i −0.0523737 + 0.0140335i
\(995\) 4.89017 + 18.2504i 0.155029 + 0.578575i
\(996\) −10.3433 10.3433i −0.327739 0.327739i
\(997\) −45.1556 26.0706i −1.43009 0.825665i −0.432966 0.901410i \(-0.642533\pi\)
−0.997127 + 0.0757452i \(0.975866\pi\)
\(998\) 8.67398 + 15.0238i 0.274570 + 0.475570i
\(999\) 2.24755 + 0.602228i 0.0711092 + 0.0190536i
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.bd.b.76.6 56
11.10 odd 2 inner 429.2.bd.b.76.9 yes 56
13.6 odd 12 inner 429.2.bd.b.175.9 yes 56
143.32 even 12 inner 429.2.bd.b.175.6 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.bd.b.76.6 56 1.1 even 1 trivial
429.2.bd.b.76.9 yes 56 11.10 odd 2 inner
429.2.bd.b.175.6 yes 56 143.32 even 12 inner
429.2.bd.b.175.9 yes 56 13.6 odd 12 inner