Properties

Label 315.2.z.b.104.17
Level $315$
Weight $2$
Character 315.104
Analytic conductor $2.515$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,2,Mod(104,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.104");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.z (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 104.17
Character \(\chi\) \(=\) 315.104
Dual form 315.2.z.b.209.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.430691 - 0.745979i) q^{2} +(-0.0265195 - 1.73185i) q^{3} +(0.629010 - 1.08948i) q^{4} +(-2.22929 + 0.173963i) q^{5} +(-1.28050 + 0.765674i) q^{6} +(1.96991 - 1.76620i) q^{7} -2.80640 q^{8} +(-2.99859 + 0.0918554i) q^{9} +O(q^{10})\) \(q+(-0.430691 - 0.745979i) q^{2} +(-0.0265195 - 1.73185i) q^{3} +(0.629010 - 1.08948i) q^{4} +(-2.22929 + 0.173963i) q^{5} +(-1.28050 + 0.765674i) q^{6} +(1.96991 - 1.76620i) q^{7} -2.80640 q^{8} +(-2.99859 + 0.0918554i) q^{9} +(1.08991 + 1.58808i) q^{10} +(0.938031 - 0.541572i) q^{11} +(-1.90349 - 1.06046i) q^{12} +(-0.585327 + 1.01382i) q^{13} +(-2.16597 - 0.708826i) q^{14} +(0.360397 + 3.85618i) q^{15} +(-0.0493285 - 0.0854395i) q^{16} -2.85626i q^{17} +(1.35999 + 2.19733i) q^{18} +1.67469i q^{19} +(-1.21272 + 2.53819i) q^{20} +(-3.11103 - 3.36475i) q^{21} +(-0.808003 - 0.466501i) q^{22} +(-2.16794 + 3.75498i) q^{23} +(0.0744243 + 4.86026i) q^{24} +(4.93947 - 0.775628i) q^{25} +1.00838 q^{26} +(0.238601 + 5.19067i) q^{27} +(-0.685139 - 3.25713i) q^{28} +(5.10403 - 2.94681i) q^{29} +(2.72141 - 1.92967i) q^{30} +(-4.66158 - 2.69137i) q^{31} +(-2.84889 + 4.93443i) q^{32} +(-0.962797 - 1.61016i) q^{33} +(-2.13071 + 1.23016i) q^{34} +(-4.08425 + 4.28006i) q^{35} +(-1.78607 + 3.32468i) q^{36} -6.09133i q^{37} +(1.24928 - 0.721274i) q^{38} +(1.77130 + 0.986812i) q^{39} +(6.25628 - 0.488210i) q^{40} +(0.718725 - 1.24487i) q^{41} +(-1.17014 + 3.76993i) q^{42} +(-3.85576 + 2.22612i) q^{43} -1.36262i q^{44} +(6.66876 - 0.726416i) q^{45} +3.73485 q^{46} +(8.32143 - 4.80438i) q^{47} +(-0.146660 + 0.0876953i) q^{48} +(0.761092 - 6.95850i) q^{49} +(-2.70599 - 3.35069i) q^{50} +(-4.94660 + 0.0757465i) q^{51} +(0.736354 + 1.27540i) q^{52} -9.26253 q^{53} +(3.76937 - 2.41357i) q^{54} +(-1.99693 + 1.37050i) q^{55} +(-5.52836 + 4.95666i) q^{56} +(2.90031 - 0.0444119i) q^{57} +(-4.39652 - 2.53833i) q^{58} +(6.02182 - 10.4301i) q^{59} +(4.42791 + 2.03293i) q^{60} +(10.0506 - 5.80270i) q^{61} +4.63659i q^{62} +(-5.74472 + 5.47706i) q^{63} +4.71066 q^{64} +(1.12850 - 2.36192i) q^{65} +(-0.786481 + 1.41171i) q^{66} +(3.28867 + 1.89871i) q^{67} +(-3.11183 - 1.79662i) q^{68} +(6.56054 + 3.65496i) q^{69} +(4.95188 + 1.20338i) q^{70} -7.45367i q^{71} +(8.41526 - 0.257783i) q^{72} +1.13156 q^{73} +(-4.54400 + 2.62348i) q^{74} +(-1.47426 - 8.53385i) q^{75} +(1.82454 + 1.05340i) q^{76} +(0.891313 - 2.72360i) q^{77} +(-0.0267417 - 1.74636i) q^{78} +(3.13677 + 5.43305i) q^{79} +(0.124831 + 0.181888i) q^{80} +(8.98313 - 0.550874i) q^{81} -1.23819 q^{82} +(-3.12835 + 1.80615i) q^{83} +(-5.62268 + 1.27293i) q^{84} +(0.496883 + 6.36743i) q^{85} +(3.32128 + 1.91754i) q^{86} +(-5.23879 - 8.76126i) q^{87} +(-2.63249 + 1.51987i) q^{88} +9.15999 q^{89} +(-3.41407 - 4.66189i) q^{90} +(0.637558 + 3.03093i) q^{91} +(2.72731 + 4.72384i) q^{92} +(-4.53741 + 8.14452i) q^{93} +(-7.16793 - 4.13841i) q^{94} +(-0.291334 - 3.73337i) q^{95} +(8.62122 + 4.80299i) q^{96} +(9.64743 + 16.7098i) q^{97} +(-5.51869 + 2.42921i) q^{98} +(-2.76303 + 1.71012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 52 q^{4} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 52 q^{4} - 4 q^{9} - 24 q^{11} - 12 q^{14} - 34 q^{15} - 28 q^{16} + 20 q^{21} - 22 q^{25} - 48 q^{29} + 36 q^{30} - 40 q^{36} + 16 q^{39} - 24 q^{46} + 20 q^{49} - 42 q^{50} - 8 q^{51} + 24 q^{56} + 116 q^{60} + 128 q^{64} + 90 q^{65} - 6 q^{70} + 12 q^{74} - 32 q^{79} + 68 q^{81} - 4 q^{84} - 2 q^{85} + 156 q^{86} - 8 q^{91} - 24 q^{95} - 116 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.430691 0.745979i −0.304545 0.527487i 0.672615 0.739992i \(-0.265171\pi\)
−0.977160 + 0.212506i \(0.931838\pi\)
\(3\) −0.0265195 1.73185i −0.0153110 0.999883i
\(4\) 0.629010 1.08948i 0.314505 0.544739i
\(5\) −2.22929 + 0.173963i −0.996969 + 0.0777986i
\(6\) −1.28050 + 0.765674i −0.522762 + 0.312585i
\(7\) 1.96991 1.76620i 0.744556 0.667560i
\(8\) −2.80640 −0.992213
\(9\) −2.99859 + 0.0918554i −0.999531 + 0.0306185i
\(10\) 1.08991 + 1.58808i 0.344659 + 0.502195i
\(11\) 0.938031 0.541572i 0.282827 0.163290i −0.351876 0.936047i \(-0.614456\pi\)
0.634703 + 0.772757i \(0.281123\pi\)
\(12\) −1.90349 1.06046i −0.549490 0.306128i
\(13\) −0.585327 + 1.01382i −0.162341 + 0.281182i −0.935708 0.352776i \(-0.885238\pi\)
0.773367 + 0.633958i \(0.218571\pi\)
\(14\) −2.16597 0.708826i −0.578880 0.189442i
\(15\) 0.360397 + 3.85618i 0.0930541 + 0.995661i
\(16\) −0.0493285 0.0854395i −0.0123321 0.0213599i
\(17\) 2.85626i 0.692744i −0.938097 0.346372i \(-0.887413\pi\)
0.938097 0.346372i \(-0.112587\pi\)
\(18\) 1.35999 + 2.19733i 0.320553 + 0.517915i
\(19\) 1.67469i 0.384200i 0.981375 + 0.192100i \(0.0615298\pi\)
−0.981375 + 0.192100i \(0.938470\pi\)
\(20\) −1.21272 + 2.53819i −0.271172 + 0.567556i
\(21\) −3.11103 3.36475i −0.678882 0.734248i
\(22\) −0.808003 0.466501i −0.172267 0.0994583i
\(23\) −2.16794 + 3.75498i −0.452046 + 0.782967i −0.998513 0.0545137i \(-0.982639\pi\)
0.546467 + 0.837481i \(0.315972\pi\)
\(24\) 0.0744243 + 4.86026i 0.0151918 + 0.992096i
\(25\) 4.93947 0.775628i 0.987895 0.155126i
\(26\) 1.00838 0.197760
\(27\) 0.238601 + 5.19067i 0.0459187 + 0.998945i
\(28\) −0.685139 3.25713i −0.129479 0.615540i
\(29\) 5.10403 2.94681i 0.947795 0.547210i 0.0553996 0.998464i \(-0.482357\pi\)
0.892395 + 0.451255i \(0.149023\pi\)
\(30\) 2.72141 1.92967i 0.496859 0.352308i
\(31\) −4.66158 2.69137i −0.837245 0.483383i 0.0190820 0.999818i \(-0.493926\pi\)
−0.856327 + 0.516434i \(0.827259\pi\)
\(32\) −2.84889 + 4.93443i −0.503618 + 0.872291i
\(33\) −0.962797 1.61016i −0.167601 0.280294i
\(34\) −2.13071 + 1.23016i −0.365413 + 0.210972i
\(35\) −4.08425 + 4.28006i −0.690364 + 0.723462i
\(36\) −1.78607 + 3.32468i −0.297679 + 0.554113i
\(37\) 6.09133i 1.00141i −0.865619 0.500704i \(-0.833075\pi\)
0.865619 0.500704i \(-0.166925\pi\)
\(38\) 1.24928 0.721274i 0.202661 0.117006i
\(39\) 1.77130 + 0.986812i 0.283635 + 0.158016i
\(40\) 6.25628 0.488210i 0.989205 0.0771927i
\(41\) 0.718725 1.24487i 0.112246 0.194416i −0.804430 0.594048i \(-0.797529\pi\)
0.916675 + 0.399632i \(0.130862\pi\)
\(42\) −1.17014 + 3.76993i −0.180556 + 0.581712i
\(43\) −3.85576 + 2.22612i −0.587997 + 0.339480i −0.764305 0.644855i \(-0.776918\pi\)
0.176308 + 0.984335i \(0.443585\pi\)
\(44\) 1.36262i 0.205422i
\(45\) 6.66876 0.726416i 0.994120 0.108288i
\(46\) 3.73485 0.550673
\(47\) 8.32143 4.80438i 1.21381 0.700791i 0.250219 0.968189i \(-0.419497\pi\)
0.963586 + 0.267398i \(0.0861639\pi\)
\(48\) −0.146660 + 0.0876953i −0.0211685 + 0.0126577i
\(49\) 0.761092 6.95850i 0.108727 0.994072i
\(50\) −2.70599 3.35069i −0.382685 0.473859i
\(51\) −4.94660 + 0.0757465i −0.692663 + 0.0106066i
\(52\) 0.736354 + 1.27540i 0.102114 + 0.176866i
\(53\) −9.26253 −1.27231 −0.636153 0.771563i \(-0.719475\pi\)
−0.636153 + 0.771563i \(0.719475\pi\)
\(54\) 3.76937 2.41357i 0.512946 0.328445i
\(55\) −1.99693 + 1.37050i −0.269266 + 0.184799i
\(56\) −5.52836 + 4.95666i −0.738758 + 0.662361i
\(57\) 2.90031 0.0444119i 0.384155 0.00588250i
\(58\) −4.39652 2.53833i −0.577292 0.333299i
\(59\) 6.02182 10.4301i 0.783974 1.35788i −0.145636 0.989338i \(-0.546523\pi\)
0.929610 0.368544i \(-0.120144\pi\)
\(60\) 4.42791 + 2.03293i 0.571641 + 0.262450i
\(61\) 10.0506 5.80270i 1.28684 0.742960i 0.308754 0.951142i \(-0.400088\pi\)
0.978090 + 0.208182i \(0.0667547\pi\)
\(62\) 4.63659i 0.588847i
\(63\) −5.74472 + 5.47706i −0.723767 + 0.690044i
\(64\) 4.71066 0.588832
\(65\) 1.12850 2.36192i 0.139973 0.292960i
\(66\) −0.786481 + 1.41171i −0.0968091 + 0.173769i
\(67\) 3.28867 + 1.89871i 0.401775 + 0.231965i 0.687250 0.726421i \(-0.258818\pi\)
−0.285475 + 0.958386i \(0.592151\pi\)
\(68\) −3.11183 1.79662i −0.377365 0.217872i
\(69\) 6.56054 + 3.65496i 0.789797 + 0.440005i
\(70\) 4.95188 + 1.20338i 0.591863 + 0.143832i
\(71\) 7.45367i 0.884588i −0.896870 0.442294i \(-0.854165\pi\)
0.896870 0.442294i \(-0.145835\pi\)
\(72\) 8.41526 0.257783i 0.991747 0.0303800i
\(73\) 1.13156 0.132439 0.0662193 0.997805i \(-0.478906\pi\)
0.0662193 + 0.997805i \(0.478906\pi\)
\(74\) −4.54400 + 2.62348i −0.528229 + 0.304973i
\(75\) −1.47426 8.53385i −0.170233 0.985404i
\(76\) 1.82454 + 1.05340i 0.209289 + 0.120833i
\(77\) 0.891313 2.72360i 0.101575 0.310383i
\(78\) −0.0267417 1.74636i −0.00302791 0.197737i
\(79\) 3.13677 + 5.43305i 0.352915 + 0.611266i 0.986759 0.162195i \(-0.0518572\pi\)
−0.633844 + 0.773461i \(0.718524\pi\)
\(80\) 0.124831 + 0.181888i 0.0139565 + 0.0203357i
\(81\) 8.98313 0.550874i 0.998125 0.0612082i
\(82\) −1.23819 −0.136736
\(83\) −3.12835 + 1.80615i −0.343381 + 0.198251i −0.661766 0.749710i \(-0.730193\pi\)
0.318385 + 0.947961i \(0.396859\pi\)
\(84\) −5.62268 + 1.27293i −0.613485 + 0.138889i
\(85\) 0.496883 + 6.36743i 0.0538945 + 0.690645i
\(86\) 3.32128 + 1.91754i 0.358143 + 0.206774i
\(87\) −5.23879 8.76126i −0.561657 0.939305i
\(88\) −2.63249 + 1.51987i −0.280625 + 0.162019i
\(89\) 9.15999 0.970957 0.485478 0.874249i \(-0.338645\pi\)
0.485478 + 0.874249i \(0.338645\pi\)
\(90\) −3.41407 4.66189i −0.359874 0.491406i
\(91\) 0.637558 + 3.03093i 0.0668342 + 0.317728i
\(92\) 2.72731 + 4.72384i 0.284342 + 0.492494i
\(93\) −4.53741 + 8.14452i −0.470508 + 0.844548i
\(94\) −7.16793 4.13841i −0.739316 0.426844i
\(95\) −0.291334 3.73337i −0.0298902 0.383036i
\(96\) 8.62122 + 4.80299i 0.879900 + 0.490203i
\(97\) 9.64743 + 16.7098i 0.979548 + 1.69663i 0.664027 + 0.747708i \(0.268846\pi\)
0.315521 + 0.948919i \(0.397821\pi\)
\(98\) −5.51869 + 2.42921i −0.557472 + 0.245387i
\(99\) −2.76303 + 1.71012i −0.277695 + 0.171873i
\(100\) 2.26195 5.86932i 0.226195 0.586932i
\(101\) 2.69879 + 4.67444i 0.268539 + 0.465124i 0.968485 0.249072i \(-0.0801257\pi\)
−0.699946 + 0.714196i \(0.746792\pi\)
\(102\) 2.18696 + 3.65744i 0.216542 + 0.362140i
\(103\) 8.67459 15.0248i 0.854733 1.48044i −0.0221593 0.999754i \(-0.507054\pi\)
0.876892 0.480687i \(-0.159613\pi\)
\(104\) 1.64266 2.84518i 0.161076 0.278992i
\(105\) 7.52072 + 6.95979i 0.733947 + 0.679206i
\(106\) 3.98929 + 6.90965i 0.387474 + 0.671125i
\(107\) 11.5521 1.11678 0.558392 0.829577i \(-0.311419\pi\)
0.558392 + 0.829577i \(0.311419\pi\)
\(108\) 5.80520 + 3.00504i 0.558606 + 0.289160i
\(109\) −17.3043 −1.65745 −0.828727 0.559653i \(-0.810935\pi\)
−0.828727 + 0.559653i \(0.810935\pi\)
\(110\) 1.88243 + 0.899404i 0.179482 + 0.0857548i
\(111\) −10.5492 + 0.161539i −1.00129 + 0.0153326i
\(112\) −0.248076 0.0811842i −0.0234410 0.00767119i
\(113\) 2.69608 4.66975i 0.253626 0.439293i −0.710896 0.703298i \(-0.751710\pi\)
0.964521 + 0.264005i \(0.0850435\pi\)
\(114\) −1.28227 2.14444i −0.120095 0.200845i
\(115\) 4.17974 8.74808i 0.389762 0.815763i
\(116\) 7.41431i 0.688401i
\(117\) 1.66203 3.09379i 0.153655 0.286021i
\(118\) −10.3742 −0.955020
\(119\) −5.04471 5.62657i −0.462448 0.515787i
\(120\) −1.01142 10.8220i −0.0923294 0.987907i
\(121\) −4.91340 + 8.51026i −0.446673 + 0.773660i
\(122\) −8.65739 4.99834i −0.783803 0.452529i
\(123\) −2.17498 1.21171i −0.196111 0.109256i
\(124\) −5.86437 + 3.38579i −0.526636 + 0.304053i
\(125\) −10.8766 + 2.58838i −0.972832 + 0.231512i
\(126\) 6.55997 + 1.92652i 0.584409 + 0.171628i
\(127\) 4.42463i 0.392622i 0.980542 + 0.196311i \(0.0628962\pi\)
−0.980542 + 0.196311i \(0.937104\pi\)
\(128\) 3.66895 + 6.35480i 0.324292 + 0.561690i
\(129\) 3.95756 + 6.61855i 0.348444 + 0.582731i
\(130\) −2.24797 + 0.175421i −0.197160 + 0.0153854i
\(131\) −8.34082 + 14.4467i −0.728741 + 1.26222i 0.228675 + 0.973503i \(0.426561\pi\)
−0.957416 + 0.288713i \(0.906773\pi\)
\(132\) −2.35985 + 0.0361359i −0.205398 + 0.00314523i
\(133\) 2.95783 + 3.29899i 0.256477 + 0.286059i
\(134\) 3.27104i 0.282575i
\(135\) −1.43489 11.5300i −0.123496 0.992345i
\(136\) 8.01580i 0.687350i
\(137\) −9.93186 17.2025i −0.848536 1.46971i −0.882515 0.470284i \(-0.844151\pi\)
0.0339793 0.999423i \(-0.489182\pi\)
\(138\) −0.0990462 6.46819i −0.00843137 0.550609i
\(139\) −19.3156 11.1519i −1.63833 0.945890i −0.981408 0.191931i \(-0.938525\pi\)
−0.656921 0.753959i \(-0.728142\pi\)
\(140\) 2.09399 + 7.14190i 0.176975 + 0.603601i
\(141\) −8.54114 14.2840i −0.719293 1.20293i
\(142\) −5.56028 + 3.21023i −0.466608 + 0.269396i
\(143\) 1.26799i 0.106034i
\(144\) 0.155764 + 0.251667i 0.0129804 + 0.0209723i
\(145\) −10.8657 + 7.45722i −0.902350 + 0.619288i
\(146\) −0.487351 0.844117i −0.0403335 0.0698597i
\(147\) −12.0712 1.13356i −0.995620 0.0934945i
\(148\) −6.63636 3.83151i −0.545506 0.314948i
\(149\) 8.01245 + 4.62599i 0.656405 + 0.378976i 0.790906 0.611938i \(-0.209610\pi\)
−0.134501 + 0.990913i \(0.542943\pi\)
\(150\) −5.73112 + 4.77522i −0.467944 + 0.389895i
\(151\) −8.99201 15.5746i −0.731759 1.26744i −0.956131 0.292941i \(-0.905366\pi\)
0.224371 0.974504i \(-0.427967\pi\)
\(152\) 4.69985i 0.381208i
\(153\) 0.262363 + 8.56475i 0.0212108 + 0.692419i
\(154\) −2.41563 + 0.508128i −0.194657 + 0.0409462i
\(155\) 10.8602 + 5.18889i 0.872314 + 0.416782i
\(156\) 2.18927 1.30908i 0.175282 0.104810i
\(157\) −1.97351 + 3.41821i −0.157503 + 0.272803i −0.933968 0.357358i \(-0.883678\pi\)
0.776465 + 0.630161i \(0.217011\pi\)
\(158\) 2.70196 4.67994i 0.214957 0.372316i
\(159\) 0.245637 + 16.0413i 0.0194803 + 1.27216i
\(160\) 5.49260 11.4959i 0.434228 0.908828i
\(161\) 2.36139 + 11.2260i 0.186104 + 0.884731i
\(162\) −4.27989 6.46397i −0.336260 0.507857i
\(163\) 12.6517i 0.990961i 0.868619 + 0.495481i \(0.165008\pi\)
−0.868619 + 0.495481i \(0.834992\pi\)
\(164\) −0.904170 1.56607i −0.0706038 0.122289i
\(165\) 2.42646 + 3.42203i 0.188900 + 0.266405i
\(166\) 2.69470 + 1.55579i 0.209150 + 0.120753i
\(167\) 10.8034 + 6.23735i 0.835992 + 0.482660i 0.855900 0.517141i \(-0.173004\pi\)
−0.0199075 + 0.999802i \(0.506337\pi\)
\(168\) 8.73079 + 9.44283i 0.673595 + 0.728530i
\(169\) 5.81478 + 10.0715i 0.447291 + 0.774731i
\(170\) 4.53596 3.11306i 0.347893 0.238761i
\(171\) −0.153829 5.02171i −0.0117636 0.384020i
\(172\) 5.60102i 0.427073i
\(173\) −3.93214 + 2.27022i −0.298955 + 0.172602i −0.641973 0.766727i \(-0.721884\pi\)
0.343019 + 0.939329i \(0.388551\pi\)
\(174\) −4.27941 + 7.68142i −0.324421 + 0.582327i
\(175\) 8.36041 10.2520i 0.631987 0.774979i
\(176\) −0.0925433 0.0534299i −0.00697572 0.00402743i
\(177\) −18.2230 10.1523i −1.36973 0.763091i
\(178\) −3.94512 6.83316i −0.295700 0.512167i
\(179\) 13.8148i 1.03257i 0.856417 + 0.516284i \(0.172685\pi\)
−0.856417 + 0.516284i \(0.827315\pi\)
\(180\) 3.40330 7.72239i 0.253667 0.575593i
\(181\) 13.0785i 0.972118i 0.873926 + 0.486059i \(0.161566\pi\)
−0.873926 + 0.486059i \(0.838434\pi\)
\(182\) 1.98642 1.78100i 0.147243 0.132016i
\(183\) −10.3159 17.2522i −0.762576 1.27532i
\(184\) 6.08410 10.5380i 0.448526 0.776870i
\(185\) 1.05966 + 13.5793i 0.0779081 + 0.998373i
\(186\) 8.02987 0.122960i 0.588778 0.00901586i
\(187\) −1.54687 2.67926i −0.113118 0.195927i
\(188\) 12.0880i 0.881610i
\(189\) 9.63777 + 9.80374i 0.701045 + 0.713117i
\(190\) −2.65954 + 1.82526i −0.192943 + 0.132418i
\(191\) −5.96653 + 3.44478i −0.431723 + 0.249255i −0.700080 0.714064i \(-0.746853\pi\)
0.268357 + 0.963319i \(0.413519\pi\)
\(192\) −0.124924 8.15814i −0.00901562 0.588763i
\(193\) 17.0989 + 9.87208i 1.23081 + 0.710608i 0.967198 0.254022i \(-0.0817535\pi\)
0.263610 + 0.964629i \(0.415087\pi\)
\(194\) 8.31012 14.3936i 0.596632 1.03340i
\(195\) −4.12041 1.89175i −0.295068 0.135471i
\(196\) −7.10240 5.20616i −0.507314 0.371869i
\(197\) 14.8453 1.05768 0.528842 0.848721i \(-0.322627\pi\)
0.528842 + 0.848721i \(0.322627\pi\)
\(198\) 2.46572 + 1.32463i 0.175231 + 0.0941371i
\(199\) 12.8149i 0.908426i 0.890893 + 0.454213i \(0.150080\pi\)
−0.890893 + 0.454213i \(0.849920\pi\)
\(200\) −13.8621 + 2.17672i −0.980202 + 0.153918i
\(201\) 3.20107 5.74583i 0.225786 0.405279i
\(202\) 2.32469 4.02648i 0.163564 0.283302i
\(203\) 4.84983 14.8197i 0.340391 1.04014i
\(204\) −3.02894 + 5.43686i −0.212068 + 0.380656i
\(205\) −1.38569 + 2.90020i −0.0967804 + 0.202559i
\(206\) −14.9443 −1.04122
\(207\) 6.15585 11.4588i 0.427861 0.796441i
\(208\) 0.115493 0.00800802
\(209\) 0.906966 + 1.57091i 0.0627362 + 0.108662i
\(210\) 1.95275 8.60782i 0.134753 0.593996i
\(211\) −4.83474 + 8.37401i −0.332837 + 0.576491i −0.983067 0.183247i \(-0.941339\pi\)
0.650230 + 0.759738i \(0.274673\pi\)
\(212\) −5.82623 + 10.0913i −0.400147 + 0.693075i
\(213\) −12.9086 + 0.197667i −0.884484 + 0.0135439i
\(214\) −4.97539 8.61763i −0.340111 0.589089i
\(215\) 8.20834 5.63343i 0.559804 0.384197i
\(216\) −0.669609 14.5671i −0.0455611 0.991166i
\(217\) −13.9364 + 2.93153i −0.946063 + 0.199005i
\(218\) 7.45282 + 12.9087i 0.504769 + 0.874285i
\(219\) −0.0300083 1.95968i −0.00202777 0.132423i
\(220\) 0.237045 + 3.03767i 0.0159816 + 0.204800i
\(221\) 2.89572 + 1.67184i 0.194787 + 0.112460i
\(222\) 4.66397 + 7.79994i 0.313025 + 0.523498i
\(223\) −0.910329 1.57674i −0.0609601 0.105586i 0.833935 0.551863i \(-0.186083\pi\)
−0.894895 + 0.446277i \(0.852750\pi\)
\(224\) 3.10311 + 14.7521i 0.207335 + 0.985665i
\(225\) −14.7402 + 2.77951i −0.982682 + 0.185301i
\(226\) −4.64471 −0.308962
\(227\) −7.63563 + 4.40843i −0.506795 + 0.292598i −0.731515 0.681825i \(-0.761186\pi\)
0.224720 + 0.974423i \(0.427853\pi\)
\(228\) 1.77594 3.18776i 0.117614 0.211114i
\(229\) −13.7883 7.96066i −0.911155 0.526055i −0.0303522 0.999539i \(-0.509663\pi\)
−0.880803 + 0.473484i \(0.842996\pi\)
\(230\) −8.32606 + 0.649725i −0.549004 + 0.0428416i
\(231\) −4.74049 1.47139i −0.311902 0.0968103i
\(232\) −14.3240 + 8.26994i −0.940414 + 0.542948i
\(233\) 13.5982 0.890847 0.445423 0.895320i \(-0.353053\pi\)
0.445423 + 0.895320i \(0.353053\pi\)
\(234\) −3.02372 + 0.0926252i −0.197667 + 0.00605510i
\(235\) −17.7151 + 12.1580i −1.15561 + 0.793099i
\(236\) −7.57557 13.1213i −0.493128 0.854122i
\(237\) 9.32604 5.57650i 0.605791 0.362232i
\(238\) −2.02459 + 6.18656i −0.131235 + 0.401015i
\(239\) 12.1584 + 7.01966i 0.786462 + 0.454064i 0.838715 0.544570i \(-0.183307\pi\)
−0.0522537 + 0.998634i \(0.516640\pi\)
\(240\) 0.311692 0.221012i 0.0201196 0.0142662i
\(241\) 23.4330 13.5290i 1.50945 0.871482i 0.509512 0.860463i \(-0.329826\pi\)
0.999939 0.0110187i \(-0.00350742\pi\)
\(242\) 8.46463 0.544127
\(243\) −1.19226 15.5428i −0.0764834 0.997071i
\(244\) 14.5998i 0.934659i
\(245\) −0.486175 + 15.6449i −0.0310606 + 0.999518i
\(246\) 0.0328362 + 2.14436i 0.00209356 + 0.136720i
\(247\) −1.69783 0.980242i −0.108030 0.0623713i
\(248\) 13.0823 + 7.55305i 0.830725 + 0.479619i
\(249\) 3.21095 + 5.36993i 0.203485 + 0.340305i
\(250\) 6.61533 + 6.99891i 0.418390 + 0.442650i
\(251\) −3.10117 −0.195744 −0.0978719 0.995199i \(-0.531204\pi\)
−0.0978719 + 0.995199i \(0.531204\pi\)
\(252\) 2.35364 + 9.70387i 0.148265 + 0.611287i
\(253\) 4.69638i 0.295259i
\(254\) 3.30068 1.90565i 0.207103 0.119571i
\(255\) 11.0142 1.02939i 0.689738 0.0644627i
\(256\) 7.87102 13.6330i 0.491939 0.852063i
\(257\) −2.82082 1.62860i −0.175958 0.101589i 0.409434 0.912340i \(-0.365726\pi\)
−0.585392 + 0.810750i \(0.699059\pi\)
\(258\) 3.23281 5.80280i 0.201266 0.361267i
\(259\) −10.7585 11.9994i −0.668500 0.745604i
\(260\) −1.86342 2.71514i −0.115564 0.168386i
\(261\) −15.0342 + 9.30513i −0.930596 + 0.575973i
\(262\) 14.3693 0.887736
\(263\) −0.134435 0.232848i −0.00828959 0.0143580i 0.861851 0.507162i \(-0.169305\pi\)
−0.870140 + 0.492804i \(0.835972\pi\)
\(264\) 2.70199 + 4.51877i 0.166296 + 0.278111i
\(265\) 20.6489 1.61134i 1.26845 0.0989836i
\(266\) 1.18706 3.62733i 0.0727835 0.222406i
\(267\) −0.242918 15.8637i −0.0148663 0.970843i
\(268\) 4.13721 2.38862i 0.252721 0.145908i
\(269\) 17.9055 1.09172 0.545859 0.837877i \(-0.316203\pi\)
0.545859 + 0.837877i \(0.316203\pi\)
\(270\) −7.98315 + 6.03627i −0.485839 + 0.367356i
\(271\) 13.7292i 0.833991i −0.908908 0.416996i \(-0.863083\pi\)
0.908908 0.416996i \(-0.136917\pi\)
\(272\) −0.244037 + 0.140895i −0.0147969 + 0.00854301i
\(273\) 5.23220 1.18453i 0.316667 0.0716911i
\(274\) −8.55512 + 14.8179i −0.516834 + 0.895183i
\(275\) 4.21332 3.40265i 0.254073 0.205187i
\(276\) 8.10865 4.84856i 0.488083 0.291849i
\(277\) 7.98974 4.61288i 0.480057 0.277161i −0.240383 0.970678i \(-0.577273\pi\)
0.720440 + 0.693517i \(0.243940\pi\)
\(278\) 19.2121i 1.15226i
\(279\) 14.2254 + 7.64212i 0.851653 + 0.457522i
\(280\) 11.4620 12.0116i 0.684988 0.717828i
\(281\) 22.1999 12.8171i 1.32434 0.764605i 0.339918 0.940455i \(-0.389601\pi\)
0.984417 + 0.175850i \(0.0562673\pi\)
\(282\) −6.97700 + 12.5235i −0.415475 + 0.745765i
\(283\) −5.75333 + 9.96506i −0.342000 + 0.592361i −0.984804 0.173669i \(-0.944438\pi\)
0.642804 + 0.766031i \(0.277771\pi\)
\(284\) −8.12061 4.68843i −0.481869 0.278207i
\(285\) −6.45790 + 0.603553i −0.382533 + 0.0357514i
\(286\) 0.945892 0.546111i 0.0559318 0.0322922i
\(287\) −0.782859 3.72169i −0.0462107 0.219684i
\(288\) 8.08941 15.0580i 0.476673 0.887302i
\(289\) 8.84179 0.520106
\(290\) 10.2427 + 4.89385i 0.601472 + 0.287377i
\(291\) 28.6831 17.1510i 1.68143 1.00541i
\(292\) 0.711761 1.23281i 0.0416527 0.0721445i
\(293\) 3.81488 + 2.20252i 0.222868 + 0.128673i 0.607277 0.794490i \(-0.292262\pi\)
−0.384410 + 0.923163i \(0.625595\pi\)
\(294\) 4.35337 + 9.49311i 0.253894 + 0.553649i
\(295\) −11.6099 + 24.2993i −0.675956 + 1.41476i
\(296\) 17.0947i 0.993610i
\(297\) 3.03494 + 4.73979i 0.176105 + 0.275031i
\(298\) 7.96949i 0.461660i
\(299\) −2.53791 4.39578i −0.146771 0.254215i
\(300\) −10.2248 3.76170i −0.590327 0.217182i
\(301\) −3.66372 + 11.1953i −0.211173 + 0.645286i
\(302\) −7.74556 + 13.4157i −0.445707 + 0.771987i
\(303\) 8.02384 4.79785i 0.460958 0.275629i
\(304\) 0.143085 0.0826100i 0.00820647 0.00473801i
\(305\) −21.3962 + 14.6843i −1.22514 + 0.840823i
\(306\) 6.27613 3.88448i 0.358782 0.222061i
\(307\) 7.36693 0.420453 0.210226 0.977653i \(-0.432580\pi\)
0.210226 + 0.977653i \(0.432580\pi\)
\(308\) −2.40665 2.68424i −0.137132 0.152949i
\(309\) −26.2508 14.6246i −1.49335 0.831966i
\(310\) −0.806594 10.3363i −0.0458115 0.587063i
\(311\) −8.14412 + 14.1060i −0.461811 + 0.799880i −0.999051 0.0435492i \(-0.986133\pi\)
0.537240 + 0.843429i \(0.319467\pi\)
\(312\) −4.97097 2.76939i −0.281426 0.156786i
\(313\) 13.1038 + 22.6965i 0.740673 + 1.28288i 0.952189 + 0.305508i \(0.0988264\pi\)
−0.211517 + 0.977374i \(0.567840\pi\)
\(314\) 3.39989 0.191867
\(315\) 11.8539 13.2093i 0.667889 0.744261i
\(316\) 7.89225 0.443974
\(317\) −9.49482 16.4455i −0.533282 0.923671i −0.999244 0.0388670i \(-0.987625\pi\)
0.465962 0.884805i \(-0.345708\pi\)
\(318\) 11.8607 7.09208i 0.665113 0.397704i
\(319\) 3.19183 5.52841i 0.178708 0.309531i
\(320\) −10.5014 + 0.819479i −0.587047 + 0.0458103i
\(321\) −0.306356 20.0065i −0.0170991 1.11665i
\(322\) 7.35731 6.59648i 0.410007 0.367607i
\(323\) 4.78335 0.266152
\(324\) 5.05031 10.1334i 0.280573 0.562968i
\(325\) −2.10486 + 5.46171i −0.116757 + 0.302961i
\(326\) 9.43794 5.44900i 0.522719 0.301792i
\(327\) 0.458902 + 29.9685i 0.0253773 + 1.65726i
\(328\) −2.01703 + 3.49360i −0.111372 + 0.192902i
\(329\) 7.90699 24.1615i 0.435926 1.33207i
\(330\) 1.50771 3.28393i 0.0829966 0.180774i
\(331\) 3.42267 + 5.92824i 0.188127 + 0.325846i 0.944626 0.328149i \(-0.106425\pi\)
−0.756499 + 0.653995i \(0.773092\pi\)
\(332\) 4.54436i 0.249404i
\(333\) 0.559521 + 18.2654i 0.0306616 + 1.00094i
\(334\) 10.7455i 0.587967i
\(335\) −7.66171 3.66068i −0.418604 0.200004i
\(336\) −0.134020 + 0.431782i −0.00731138 + 0.0235557i
\(337\) −3.12437 1.80386i −0.170195 0.0982623i 0.412483 0.910965i \(-0.364662\pi\)
−0.582678 + 0.812703i \(0.697995\pi\)
\(338\) 5.00875 8.67541i 0.272440 0.471880i
\(339\) −8.15879 4.54536i −0.443125 0.246870i
\(340\) 7.24972 + 3.46384i 0.393171 + 0.187853i
\(341\) −5.83028 −0.315727
\(342\) −3.67984 + 2.27756i −0.198983 + 0.123156i
\(343\) −10.7908 15.0519i −0.582649 0.812724i
\(344\) 10.8208 6.24739i 0.583418 0.336837i
\(345\) −15.2612 7.00667i −0.821635 0.377227i
\(346\) 3.38707 + 1.95553i 0.182090 + 0.105130i
\(347\) −4.56560 + 7.90786i −0.245094 + 0.424516i −0.962158 0.272492i \(-0.912152\pi\)
0.717064 + 0.697008i \(0.245486\pi\)
\(348\) −12.8404 + 0.196624i −0.688320 + 0.0105401i
\(349\) −13.9418 + 8.04933i −0.746290 + 0.430871i −0.824352 0.566078i \(-0.808460\pi\)
0.0780620 + 0.996949i \(0.475127\pi\)
\(350\) −11.2485 1.82124i −0.601259 0.0973495i
\(351\) −5.40205 2.79634i −0.288340 0.149258i
\(352\) 6.17153i 0.328943i
\(353\) −0.0335173 + 0.0193512i −0.00178395 + 0.00102996i −0.500892 0.865510i \(-0.666995\pi\)
0.499108 + 0.866540i \(0.333661\pi\)
\(354\) 0.275118 + 17.9665i 0.0146223 + 0.954908i
\(355\) 1.29666 + 16.6164i 0.0688197 + 0.881907i
\(356\) 5.76173 9.97960i 0.305371 0.528918i
\(357\) −9.61058 + 8.88589i −0.508646 + 0.470291i
\(358\) 10.3056 5.94992i 0.544666 0.314463i
\(359\) 15.2509i 0.804911i −0.915440 0.402455i \(-0.868157\pi\)
0.915440 0.402455i \(-0.131843\pi\)
\(360\) −18.7152 + 2.03862i −0.986378 + 0.107444i
\(361\) 16.1954 0.852390
\(362\) 9.75629 5.63280i 0.512779 0.296053i
\(363\) 14.8688 + 8.28357i 0.780408 + 0.434775i
\(364\) 3.70316 + 1.21188i 0.194098 + 0.0635198i
\(365\) −2.52257 + 0.196849i −0.132037 + 0.0103035i
\(366\) −8.42678 + 15.1258i −0.440475 + 0.790640i
\(367\) −9.67829 16.7633i −0.505203 0.875037i −0.999982 0.00601803i \(-0.998084\pi\)
0.494779 0.869019i \(-0.335249\pi\)
\(368\) 0.427765 0.0222988
\(369\) −2.04081 + 3.79887i −0.106241 + 0.197761i
\(370\) 9.67351 6.63899i 0.502902 0.345145i
\(371\) −18.2464 + 16.3595i −0.947303 + 0.849341i
\(372\) 6.01920 + 10.0664i 0.312081 + 0.521918i
\(373\) 12.3657 + 7.13934i 0.640272 + 0.369661i 0.784719 0.619851i \(-0.212807\pi\)
−0.144447 + 0.989512i \(0.546140\pi\)
\(374\) −1.33245 + 2.30787i −0.0688992 + 0.119337i
\(375\) 4.77113 + 18.7680i 0.246380 + 0.969173i
\(376\) −23.3533 + 13.4830i −1.20435 + 0.695334i
\(377\) 6.89940i 0.355337i
\(378\) 3.16248 11.4120i 0.162660 0.586968i
\(379\) −3.44813 −0.177119 −0.0885593 0.996071i \(-0.528226\pi\)
−0.0885593 + 0.996071i \(0.528226\pi\)
\(380\) −4.25068 2.03093i −0.218055 0.104184i
\(381\) 7.66278 0.117339i 0.392576 0.00601145i
\(382\) 5.13946 + 2.96727i 0.262958 + 0.151819i
\(383\) 8.42092 + 4.86182i 0.430289 + 0.248427i 0.699470 0.714662i \(-0.253420\pi\)
−0.269181 + 0.963090i \(0.586753\pi\)
\(384\) 10.9082 6.52258i 0.556659 0.332854i
\(385\) −1.51319 + 6.22674i −0.0771193 + 0.317344i
\(386\) 17.0073i 0.865647i
\(387\) 11.3574 7.02941i 0.577327 0.357325i
\(388\) 24.2733 1.23229
\(389\) −12.2161 + 7.05295i −0.619379 + 0.357599i −0.776627 0.629960i \(-0.783071\pi\)
0.157248 + 0.987559i \(0.449738\pi\)
\(390\) 0.363417 + 3.88850i 0.0184023 + 0.196902i
\(391\) 10.7252 + 6.19219i 0.542396 + 0.313152i
\(392\) −2.13593 + 19.5283i −0.107881 + 0.986330i
\(393\) 25.2407 + 14.0619i 1.27323 + 0.709329i
\(394\) −6.39373 11.0743i −0.322112 0.557914i
\(395\) −7.93793 11.5662i −0.399401 0.581957i
\(396\) 0.125164 + 4.08594i 0.00628972 + 0.205326i
\(397\) −27.9656 −1.40355 −0.701777 0.712396i \(-0.747610\pi\)
−0.701777 + 0.712396i \(0.747610\pi\)
\(398\) 9.55967 5.51928i 0.479183 0.276656i
\(399\) 5.63491 5.21001i 0.282098 0.260826i
\(400\) −0.309926 0.383766i −0.0154963 0.0191883i
\(401\) −30.3566 17.5264i −1.51594 0.875226i −0.999825 0.0187045i \(-0.994046\pi\)
−0.516111 0.856522i \(-0.672621\pi\)
\(402\) −5.66494 + 0.0867462i −0.282541 + 0.00432651i
\(403\) 5.45710 3.15066i 0.271838 0.156945i
\(404\) 6.79026 0.337828
\(405\) −19.9302 + 2.79079i −0.990338 + 0.138675i
\(406\) −13.1440 + 2.76484i −0.652323 + 0.137217i
\(407\) −3.29889 5.71385i −0.163520 0.283225i
\(408\) 13.8822 0.212575i 0.687269 0.0105240i
\(409\) −2.68401 1.54961i −0.132716 0.0766234i 0.432172 0.901791i \(-0.357747\pi\)
−0.564888 + 0.825168i \(0.691081\pi\)
\(410\) 2.76029 0.215400i 0.136321 0.0106378i
\(411\) −29.5287 + 17.6567i −1.45654 + 0.870939i
\(412\) −10.9128 18.9016i −0.537636 0.931213i
\(413\) −6.55917 31.1821i −0.322755 1.53437i
\(414\) −11.1993 + 0.343066i −0.550415 + 0.0168608i
\(415\) 6.65980 4.57066i 0.326917 0.224365i
\(416\) −3.33507 5.77651i −0.163515 0.283217i
\(417\) −18.8011 + 33.7475i −0.920695 + 1.65262i
\(418\) 0.781244 1.35316i 0.0382119 0.0661850i
\(419\) −3.42407 + 5.93067i −0.167277 + 0.289732i −0.937462 0.348089i \(-0.886831\pi\)
0.770185 + 0.637821i \(0.220164\pi\)
\(420\) 12.3132 3.81588i 0.600820 0.186196i
\(421\) 6.20547 + 10.7482i 0.302436 + 0.523834i 0.976687 0.214668i \(-0.0688668\pi\)
−0.674251 + 0.738502i \(0.735533\pi\)
\(422\) 8.32911 0.405455
\(423\) −24.5113 + 15.1708i −1.19178 + 0.737627i
\(424\) 25.9944 1.26240
\(425\) −2.21539 14.1084i −0.107462 0.684358i
\(426\) 5.70708 + 9.54443i 0.276509 + 0.462429i
\(427\) 9.55001 29.1821i 0.462157 1.41222i
\(428\) 7.26639 12.5858i 0.351234 0.608356i
\(429\) 2.19596 0.0336264i 0.106022 0.00162350i
\(430\) −7.73768 3.69698i −0.373144 0.178284i
\(431\) 0.948558i 0.0456904i 0.999739 + 0.0228452i \(0.00727249\pi\)
−0.999739 + 0.0228452i \(0.992728\pi\)
\(432\) 0.431718 0.276434i 0.0207711 0.0132999i
\(433\) −7.00223 −0.336506 −0.168253 0.985744i \(-0.553813\pi\)
−0.168253 + 0.985744i \(0.553813\pi\)
\(434\) 8.18913 + 9.13366i 0.393091 + 0.438430i
\(435\) 13.2029 + 18.6200i 0.633031 + 0.892762i
\(436\) −10.8846 + 18.8527i −0.521278 + 0.902880i
\(437\) −6.28843 3.63062i −0.300816 0.173676i
\(438\) −1.44896 + 0.866404i −0.0692339 + 0.0413984i
\(439\) −18.8107 + 10.8604i −0.897787 + 0.518337i −0.876481 0.481436i \(-0.840115\pi\)
−0.0213052 + 0.999773i \(0.506782\pi\)
\(440\) 5.60419 3.84619i 0.267169 0.183360i
\(441\) −1.64303 + 20.9356i −0.0782396 + 0.996935i
\(442\) 2.88019i 0.136997i
\(443\) 6.00689 + 10.4042i 0.285396 + 0.494321i 0.972705 0.232045i \(-0.0745415\pi\)
−0.687309 + 0.726365i \(0.741208\pi\)
\(444\) −6.45959 + 11.5948i −0.306559 + 0.550264i
\(445\) −20.4203 + 1.59350i −0.968014 + 0.0755390i
\(446\) −0.784141 + 1.35817i −0.0371302 + 0.0643113i
\(447\) 7.79902 13.9990i 0.368881 0.662131i
\(448\) 9.27957 8.31995i 0.438418 0.393081i
\(449\) 27.9268i 1.31795i −0.752166 0.658974i \(-0.770991\pi\)
0.752166 0.658974i \(-0.229009\pi\)
\(450\) 8.42194 + 9.79879i 0.397014 + 0.461919i
\(451\) 1.55697i 0.0733146i
\(452\) −3.39172 5.87464i −0.159533 0.276320i
\(453\) −26.7344 + 15.9858i −1.25609 + 0.751079i
\(454\) 6.57720 + 3.79735i 0.308683 + 0.178218i
\(455\) −1.94857 6.64591i −0.0913504 0.311565i
\(456\) −8.13943 + 0.124638i −0.381164 + 0.00583669i
\(457\) 9.20125 5.31234i 0.430416 0.248501i −0.269108 0.963110i \(-0.586729\pi\)
0.699524 + 0.714609i \(0.253395\pi\)
\(458\) 13.7143i 0.640829i
\(459\) 14.8259 0.681505i 0.692013 0.0318099i
\(460\) −6.90174 10.0564i −0.321795 0.468880i
\(461\) 12.3743 + 21.4329i 0.576327 + 0.998228i 0.995896 + 0.0905045i \(0.0288480\pi\)
−0.419569 + 0.907724i \(0.637819\pi\)
\(462\) 0.944062 + 4.17002i 0.0439218 + 0.194007i
\(463\) −32.3275 18.6643i −1.50239 0.867403i −0.999996 0.00276150i \(-0.999121\pi\)
−0.502390 0.864641i \(-0.667546\pi\)
\(464\) −0.503549 0.290724i −0.0233767 0.0134965i
\(465\) 8.69837 18.9459i 0.403377 0.878593i
\(466\) −5.85662 10.1440i −0.271303 0.469910i
\(467\) 11.8237i 0.547137i 0.961853 + 0.273568i \(0.0882040\pi\)
−0.961853 + 0.273568i \(0.911796\pi\)
\(468\) −2.32518 3.75677i −0.107481 0.173657i
\(469\) 9.83189 2.06814i 0.453994 0.0954980i
\(470\) 16.6993 + 7.97876i 0.770283 + 0.368033i
\(471\) 5.97216 + 3.32716i 0.275183 + 0.153308i
\(472\) −16.8996 + 29.2710i −0.777869 + 1.34731i
\(473\) −2.41121 + 4.17634i −0.110868 + 0.192028i
\(474\) −8.17659 4.55528i −0.375563 0.209231i
\(475\) 1.29894 + 8.27209i 0.0595993 + 0.379549i
\(476\) −9.30320 + 1.95693i −0.426412 + 0.0896959i
\(477\) 27.7746 0.850813i 1.27171 0.0389561i
\(478\) 12.0932i 0.553131i
\(479\) −19.1743 33.2108i −0.876095 1.51744i −0.855592 0.517652i \(-0.826806\pi\)
−0.0205036 0.999790i \(-0.506527\pi\)
\(480\) −20.0548 9.20748i −0.915370 0.420262i
\(481\) 6.17549 + 3.56542i 0.281578 + 0.162569i
\(482\) −20.1848 11.6537i −0.919391 0.530810i
\(483\) 19.3791 4.38728i 0.881778 0.199628i
\(484\) 6.18116 + 10.7061i 0.280962 + 0.486640i
\(485\) −24.4138 35.5728i −1.10857 1.61528i
\(486\) −11.0811 + 7.58354i −0.502649 + 0.343997i
\(487\) 33.1836i 1.50369i −0.659338 0.751847i \(-0.729163\pi\)
0.659338 0.751847i \(-0.270837\pi\)
\(488\) −28.2059 + 16.2847i −1.27682 + 0.737174i
\(489\) 21.9109 0.335518i 0.990845 0.0151726i
\(490\) 11.8802 6.37545i 0.536692 0.288014i
\(491\) 10.6956 + 6.17510i 0.482685 + 0.278678i 0.721535 0.692378i \(-0.243437\pi\)
−0.238850 + 0.971057i \(0.576770\pi\)
\(492\) −2.68821 + 1.60742i −0.121194 + 0.0724679i
\(493\) −8.41686 14.5784i −0.379076 0.656579i
\(494\) 1.68873i 0.0759793i
\(495\) 5.86209 4.29302i 0.263482 0.192957i
\(496\) 0.531044i 0.0238446i
\(497\) −13.1647 14.6831i −0.590515 0.658625i
\(498\) 2.62293 4.70808i 0.117536 0.210974i
\(499\) −0.754345 + 1.30656i −0.0337691 + 0.0584898i −0.882416 0.470470i \(-0.844084\pi\)
0.848647 + 0.528960i \(0.177418\pi\)
\(500\) −4.02150 + 13.4779i −0.179847 + 0.602751i
\(501\) 10.5156 18.8753i 0.469804 0.843285i
\(502\) 1.33564 + 2.31340i 0.0596127 + 0.103252i
\(503\) 37.6353i 1.67807i −0.544074 0.839037i \(-0.683119\pi\)
0.544074 0.839037i \(-0.316881\pi\)
\(504\) 16.1220 15.3708i 0.718131 0.684670i
\(505\) −6.82956 9.95119i −0.303911 0.442822i
\(506\) 3.50340 2.02269i 0.155745 0.0899195i
\(507\) 17.2881 10.3374i 0.767792 0.459101i
\(508\) 4.82053 + 2.78314i 0.213877 + 0.123482i
\(509\) −13.3960 + 23.2025i −0.593766 + 1.02843i 0.399954 + 0.916535i \(0.369026\pi\)
−0.993720 + 0.111897i \(0.964307\pi\)
\(510\) −5.51164 7.77304i −0.244059 0.344196i
\(511\) 2.22907 1.99855i 0.0986080 0.0884108i
\(512\) 1.11587 0.0493149
\(513\) −8.69277 + 0.399582i −0.383795 + 0.0176420i
\(514\) 2.80569i 0.123754i
\(515\) −16.7244 + 35.0038i −0.736966 + 1.54245i
\(516\) 9.70011 0.148536i 0.427023 0.00653893i
\(517\) 5.20384 9.01332i 0.228865 0.396405i
\(518\) −4.31769 + 13.1936i −0.189708 + 0.579695i
\(519\) 4.03595 + 6.74965i 0.177159 + 0.296277i
\(520\) −3.16702 + 6.62848i −0.138883 + 0.290678i
\(521\) 26.3458 1.15423 0.577115 0.816663i \(-0.304178\pi\)
0.577115 + 0.816663i \(0.304178\pi\)
\(522\) 13.4165 + 7.20759i 0.587226 + 0.315467i
\(523\) 35.7678 1.56402 0.782009 0.623267i \(-0.214195\pi\)
0.782009 + 0.623267i \(0.214195\pi\)
\(524\) 10.4929 + 18.1743i 0.458385 + 0.793947i
\(525\) −17.9766 14.2071i −0.784564 0.620048i
\(526\) −0.115800 + 0.200571i −0.00504910 + 0.00874530i
\(527\) −7.68723 + 13.3147i −0.334861 + 0.579996i
\(528\) −0.0900783 + 0.161688i −0.00392015 + 0.00703656i
\(529\) 2.10009 + 3.63746i 0.0913083 + 0.158151i
\(530\) −10.0953 14.7096i −0.438512 0.638946i
\(531\) −17.0989 + 31.8287i −0.742030 + 1.38125i
\(532\) 5.45468 1.14740i 0.236491 0.0497459i
\(533\) 0.841378 + 1.45731i 0.0364441 + 0.0631231i
\(534\) −11.7294 + 7.01357i −0.507579 + 0.303507i
\(535\) −25.7530 + 2.00964i −1.11340 + 0.0868842i
\(536\) −9.22933 5.32855i −0.398646 0.230158i
\(537\) 23.9252 0.366362i 1.03245 0.0158097i
\(538\) −7.71174 13.3571i −0.332477 0.575867i
\(539\) −3.05460 6.93948i −0.131571 0.298904i
\(540\) −13.4643 5.68921i −0.579409 0.244825i
\(541\) 14.9279 0.641801 0.320901 0.947113i \(-0.396014\pi\)
0.320901 + 0.947113i \(0.396014\pi\)
\(542\) −10.2417 + 5.91306i −0.439919 + 0.253988i
\(543\) 22.6500 0.346835i 0.972004 0.0148841i
\(544\) 14.0940 + 8.13717i 0.604275 + 0.348878i
\(545\) 38.5764 3.01031i 1.65243 0.128948i
\(546\) −3.13710 3.39295i −0.134255 0.145205i
\(547\) −6.29286 + 3.63319i −0.269063 + 0.155344i −0.628462 0.777840i \(-0.716315\pi\)
0.359399 + 0.933184i \(0.382982\pi\)
\(548\) −24.9890 −1.06748
\(549\) −29.6046 + 18.3231i −1.26349 + 0.782013i
\(550\) −4.35294 1.67756i −0.185610 0.0715314i
\(551\) 4.93500 + 8.54767i 0.210238 + 0.364143i
\(552\) −18.4115 10.2573i −0.783646 0.436579i
\(553\) 15.7750 + 5.16246i 0.670822 + 0.219530i
\(554\) −6.88222 3.97345i −0.292398 0.168816i
\(555\) 23.4892 2.19529i 0.997063 0.0931851i
\(556\) −24.2994 + 14.0293i −1.03053 + 0.594975i
\(557\) −9.15146 −0.387760 −0.193880 0.981025i \(-0.562107\pi\)
−0.193880 + 0.981025i \(0.562107\pi\)
\(558\) −0.425896 13.9032i −0.0180296 0.588571i
\(559\) 5.21204i 0.220446i
\(560\) 0.567156 + 0.137827i 0.0239667 + 0.00582426i
\(561\) −4.59904 + 2.75000i −0.194172 + 0.116105i
\(562\) −19.1226 11.0404i −0.806638 0.465713i
\(563\) −27.9044 16.1106i −1.17603 0.678981i −0.220937 0.975288i \(-0.570912\pi\)
−0.955093 + 0.296307i \(0.904245\pi\)
\(564\) −20.9346 + 0.320568i −0.881506 + 0.0134983i
\(565\) −5.19798 + 10.8792i −0.218681 + 0.457693i
\(566\) 9.91163 0.416617
\(567\) 16.7230 16.9511i 0.702300 0.711881i
\(568\) 20.9180i 0.877699i
\(569\) −0.103976 + 0.0600303i −0.00435888 + 0.00251660i −0.502178 0.864764i \(-0.667468\pi\)
0.497819 + 0.867281i \(0.334134\pi\)
\(570\) 3.23160 + 4.55752i 0.135357 + 0.190893i
\(571\) 14.2444 24.6720i 0.596109 1.03249i −0.397280 0.917697i \(-0.630046\pi\)
0.993389 0.114794i \(-0.0366208\pi\)
\(572\) 1.38144 + 0.797578i 0.0577611 + 0.0333484i
\(573\) 6.12406 + 10.2418i 0.255836 + 0.427856i
\(574\) −2.43913 + 2.18689i −0.101807 + 0.0912792i
\(575\) −7.79601 + 20.2291i −0.325116 + 0.843613i
\(576\) −14.1253 + 0.432699i −0.588556 + 0.0180291i
\(577\) 37.1817 1.54789 0.773947 0.633251i \(-0.218280\pi\)
0.773947 + 0.633251i \(0.218280\pi\)
\(578\) −3.80808 6.59579i −0.158395 0.274349i
\(579\) 16.6435 29.8746i 0.691679 1.24154i
\(580\) 1.28981 + 16.5286i 0.0535566 + 0.686314i
\(581\) −2.97254 + 9.08324i −0.123322 + 0.376836i
\(582\) −25.1478 14.0102i −1.04241 0.580740i
\(583\) −8.68854 + 5.01633i −0.359843 + 0.207755i
\(584\) −3.17560 −0.131407
\(585\) −3.16695 + 7.18609i −0.130937 + 0.297108i
\(586\) 3.79442i 0.156746i
\(587\) −15.1312 + 8.73600i −0.624532 + 0.360573i −0.778631 0.627482i \(-0.784086\pi\)
0.154100 + 0.988055i \(0.450752\pi\)
\(588\) −8.82793 + 12.4383i −0.364058 + 0.512948i
\(589\) 4.50720 7.80670i 0.185716 0.321670i
\(590\) 23.1270 1.80472i 0.952125 0.0742992i
\(591\) −0.393689 25.7098i −0.0161942 1.05756i
\(592\) −0.520440 + 0.300476i −0.0213899 + 0.0123495i
\(593\) 46.2567i 1.89953i 0.312958 + 0.949767i \(0.398680\pi\)
−0.312958 + 0.949767i \(0.601320\pi\)
\(594\) 2.22866 4.30539i 0.0914431 0.176652i
\(595\) 12.2250 + 11.6657i 0.501174 + 0.478246i
\(596\) 10.0798 5.81959i 0.412886 0.238380i
\(597\) 22.1935 0.339845i 0.908320 0.0139089i
\(598\) −2.18611 + 3.78645i −0.0893966 + 0.154839i
\(599\) 0.819835 + 0.473332i 0.0334975 + 0.0193398i 0.516655 0.856194i \(-0.327177\pi\)
−0.483158 + 0.875533i \(0.660510\pi\)
\(600\) 4.13737 + 23.9494i 0.168907 + 0.977730i
\(601\) 14.7403 8.51032i 0.601270 0.347143i −0.168271 0.985741i \(-0.553818\pi\)
0.769541 + 0.638598i \(0.220485\pi\)
\(602\) 9.92938 2.08865i 0.404691 0.0851271i
\(603\) −10.0358 5.39139i −0.408689 0.219554i
\(604\) −22.6243 −0.920568
\(605\) 9.47293 19.8266i 0.385129 0.806065i
\(606\) −7.03489 3.91922i −0.285773 0.159208i
\(607\) −5.22945 + 9.05768i −0.212257 + 0.367640i −0.952421 0.304787i \(-0.901415\pi\)
0.740164 + 0.672427i \(0.234748\pi\)
\(608\) −8.26363 4.77101i −0.335135 0.193490i
\(609\) −25.7941 8.00615i −1.04523 0.324426i
\(610\) 20.1694 + 9.63670i 0.816633 + 0.390179i
\(611\) 11.2485i 0.455067i
\(612\) 9.49614 + 5.10148i 0.383859 + 0.206215i
\(613\) 18.4598i 0.745583i −0.927915 0.372792i \(-0.878401\pi\)
0.927915 0.372792i \(-0.121599\pi\)
\(614\) −3.17287 5.49557i −0.128047 0.221783i
\(615\) 5.05946 + 2.32288i 0.204017 + 0.0936677i
\(616\) −2.50138 + 7.64351i −0.100784 + 0.307966i
\(617\) −9.92135 + 17.1843i −0.399419 + 0.691813i −0.993654 0.112478i \(-0.964121\pi\)
0.594236 + 0.804291i \(0.297455\pi\)
\(618\) 0.396315 + 25.8812i 0.0159421 + 1.04110i
\(619\) 18.4929 10.6769i 0.743291 0.429139i −0.0799736 0.996797i \(-0.525484\pi\)
0.823265 + 0.567658i \(0.192150\pi\)
\(620\) 12.4844 8.56810i 0.501385 0.344103i
\(621\) −20.0081 10.3571i −0.802899 0.415617i
\(622\) 14.0304 0.562568
\(623\) 18.0444 16.1783i 0.722932 0.648172i
\(624\) −0.00306282 0.200017i −0.000122611 0.00800708i
\(625\) 23.7968 7.66238i 0.951872 0.306495i
\(626\) 11.2874 19.5504i 0.451136 0.781390i
\(627\) 2.69653 1.61239i 0.107689 0.0643925i
\(628\) 2.48271 + 4.30018i 0.0990710 + 0.171596i
\(629\) −17.3984 −0.693719
\(630\) −14.9592 3.15359i −0.595990 0.125642i
\(631\) 17.1185 0.681475 0.340738 0.940158i \(-0.389323\pi\)
0.340738 + 0.940158i \(0.389323\pi\)
\(632\) −8.80305 15.2473i −0.350166 0.606506i
\(633\) 14.6307 + 8.15095i 0.581519 + 0.323971i
\(634\) −8.17867 + 14.1659i −0.324816 + 0.562598i
\(635\) −0.769721 9.86378i −0.0305454 0.391432i
\(636\) 17.6311 + 9.82252i 0.699120 + 0.389488i
\(637\) 6.60915 + 4.84461i 0.261864 + 0.191950i
\(638\) −5.49877 −0.217698
\(639\) 0.684660 + 22.3505i 0.0270847 + 0.884173i
\(640\) −9.28465 13.5284i −0.367008 0.534758i
\(641\) 8.64424 4.99076i 0.341427 0.197123i −0.319476 0.947594i \(-0.603507\pi\)
0.660903 + 0.750471i \(0.270173\pi\)
\(642\) −14.7925 + 8.84515i −0.583812 + 0.349090i
\(643\) −16.4456 + 28.4847i −0.648552 + 1.12333i 0.334917 + 0.942248i \(0.391292\pi\)
−0.983469 + 0.181077i \(0.942042\pi\)
\(644\) 13.7158 + 4.48857i 0.540478 + 0.176875i
\(645\) −9.97393 14.0662i −0.392723 0.553856i
\(646\) −2.06014 3.56828i −0.0810553 0.140392i
\(647\) 25.1140i 0.987333i 0.869651 + 0.493666i \(0.164344\pi\)
−0.869651 + 0.493666i \(0.835656\pi\)
\(648\) −25.2103 + 1.54597i −0.990352 + 0.0607316i
\(649\) 13.0450i 0.512061i
\(650\) 4.98087 0.782128i 0.195366 0.0306776i
\(651\) 5.44654 + 24.0579i 0.213467 + 0.942905i
\(652\) 13.7838 + 7.95808i 0.539815 + 0.311662i
\(653\) −5.95761 + 10.3189i −0.233139 + 0.403809i −0.958730 0.284317i \(-0.908233\pi\)
0.725591 + 0.688126i \(0.241567\pi\)
\(654\) 22.1582 13.2495i 0.866454 0.518096i
\(655\) 16.0809 33.6569i 0.628333 1.31509i
\(656\) −0.141814 −0.00553692
\(657\) −3.39308 + 0.103940i −0.132377 + 0.00405507i
\(658\) −21.4294 + 4.50769i −0.835406 + 0.175728i
\(659\) −31.1669 + 17.9942i −1.21409 + 0.700956i −0.963648 0.267176i \(-0.913910\pi\)
−0.250443 + 0.968131i \(0.580576\pi\)
\(660\) 5.25450 0.491083i 0.204531 0.0191154i
\(661\) −32.5103 18.7699i −1.26451 0.730063i −0.290563 0.956856i \(-0.593843\pi\)
−0.973943 + 0.226793i \(0.927176\pi\)
\(662\) 2.94823 5.10648i 0.114586 0.198469i
\(663\) 2.81859 5.05928i 0.109465 0.196486i
\(664\) 8.77940 5.06879i 0.340707 0.196707i
\(665\) −7.16777 6.83985i −0.277954 0.265238i
\(666\) 13.3846 8.28414i 0.518644 0.321004i
\(667\) 25.5540i 0.989456i
\(668\) 13.5909 7.84671i 0.525848 0.303598i
\(669\) −2.70652 + 1.61837i −0.104640 + 0.0625696i
\(670\) 0.569039 + 7.29209i 0.0219839 + 0.281718i
\(671\) 6.28517 10.8862i 0.242636 0.420258i
\(672\) 25.4661 5.76533i 0.982375 0.222402i
\(673\) 8.68324 5.01327i 0.334714 0.193247i −0.323218 0.946325i \(-0.604765\pi\)
0.657932 + 0.753077i \(0.271431\pi\)
\(674\) 3.10762i 0.119701i
\(675\) 5.20459 + 25.4541i 0.200325 + 0.979730i
\(676\) 14.6302 0.562701
\(677\) 1.25812 0.726375i 0.0483534 0.0279169i −0.475628 0.879646i \(-0.657779\pi\)
0.523982 + 0.851729i \(0.324446\pi\)
\(678\) 0.123175 + 8.04393i 0.00473052 + 0.308925i
\(679\) 48.5174 + 15.8776i 1.86193 + 0.609327i
\(680\) −1.39445 17.8696i −0.0534748 0.685266i
\(681\) 7.83723 + 13.1068i 0.300323 + 0.502255i
\(682\) 2.51105 + 4.34926i 0.0961530 + 0.166542i
\(683\) 4.58360 0.175386 0.0876932 0.996148i \(-0.472050\pi\)
0.0876932 + 0.996148i \(0.472050\pi\)
\(684\) −5.56781 2.99112i −0.212890 0.114368i
\(685\) 25.1336 + 36.6216i 0.960305 + 1.39924i
\(686\) −6.58087 + 14.5324i −0.251259 + 0.554850i
\(687\) −13.4210 + 24.0903i −0.512043 + 0.919102i
\(688\) 0.380397 + 0.219623i 0.0145025 + 0.00837303i
\(689\) 5.42161 9.39050i 0.206547 0.357750i
\(690\) 1.34603 + 14.4022i 0.0512424 + 0.548284i
\(691\) 5.98573 3.45586i 0.227708 0.131467i −0.381806 0.924242i \(-0.624698\pi\)
0.609514 + 0.792775i \(0.291365\pi\)
\(692\) 5.71197i 0.217136i
\(693\) −2.42251 + 8.24883i −0.0920235 + 0.313347i
\(694\) 7.86546 0.298569
\(695\) 45.0001 + 21.5006i 1.70695 + 0.815563i
\(696\) 14.7021 + 24.5876i 0.557283 + 0.931991i
\(697\) −3.55566 2.05286i −0.134680 0.0777577i
\(698\) 12.0093 + 6.93355i 0.454557 + 0.262439i
\(699\) −0.360617 23.5500i −0.0136398 0.890742i
\(700\) −5.91055 15.5571i −0.223398 0.588003i
\(701\) 11.2311i 0.424191i 0.977249 + 0.212096i \(0.0680288\pi\)
−0.977249 + 0.212096i \(0.931971\pi\)
\(702\) 0.240600 + 5.23417i 0.00908088 + 0.197551i
\(703\) 10.2011 0.384741
\(704\) 4.41874 2.55116i 0.166538 0.0961505i
\(705\) 21.5256 + 30.3574i 0.810700 + 1.14333i
\(706\) 0.0288712 + 0.0166688i 0.00108658 + 0.000627339i
\(707\) 13.5723 + 4.44163i 0.510441 + 0.167045i
\(708\) −22.5231 + 13.4677i −0.846472 + 0.506147i
\(709\) 15.5040 + 26.8537i 0.582265 + 1.00851i 0.995210 + 0.0977563i \(0.0311666\pi\)
−0.412946 + 0.910756i \(0.635500\pi\)
\(710\) 11.8370 8.12382i 0.444235 0.304881i
\(711\) −9.90497 16.0034i −0.371465 0.600174i
\(712\) −25.7066 −0.963395
\(713\) 20.2120 11.6694i 0.756947 0.437023i
\(714\) 10.7679 + 3.34222i 0.402978 + 0.125079i
\(715\) −0.220583 2.82671i −0.00824933 0.105713i
\(716\) 15.0509 + 8.68966i 0.562480 + 0.324748i
\(717\) 11.8345 21.2427i 0.441969 0.793322i
\(718\) −11.3768 + 6.56842i −0.424580 + 0.245131i
\(719\) −17.0690 −0.636568 −0.318284 0.947995i \(-0.603107\pi\)
−0.318284 + 0.947995i \(0.603107\pi\)
\(720\) −0.391024 0.533942i −0.0145726 0.0198988i
\(721\) −9.44866 44.9186i −0.351886 1.67286i
\(722\) −6.97522 12.0814i −0.259591 0.449625i
\(723\) −24.0517 40.2236i −0.894491 1.49593i
\(724\) 14.2487 + 8.22652i 0.529550 + 0.305736i
\(725\) 22.9256 18.5145i 0.851435 0.687613i
\(726\) −0.224478 14.6594i −0.00833114 0.544063i
\(727\) −8.60852 14.9104i −0.319272 0.552996i 0.661064 0.750330i \(-0.270105\pi\)
−0.980336 + 0.197333i \(0.936772\pi\)
\(728\) −1.78924 8.50601i −0.0663138 0.315254i
\(729\) −26.8861 + 2.47700i −0.995783 + 0.0917406i
\(730\) 1.23329 + 1.79700i 0.0456462 + 0.0665100i
\(731\) 6.35838 + 11.0130i 0.235173 + 0.407332i
\(732\) −25.2847 + 0.387180i −0.934549 + 0.0143106i
\(733\) 19.0927 33.0696i 0.705205 1.22145i −0.261412 0.965227i \(-0.584188\pi\)
0.966617 0.256224i \(-0.0824786\pi\)
\(734\) −8.33671 + 14.4396i −0.307714 + 0.532975i
\(735\) 27.1075 + 0.427086i 0.999876 + 0.0157533i
\(736\) −12.3524 21.3951i −0.455317 0.788632i
\(737\) 4.11317 0.151510
\(738\) 3.71284 0.113735i 0.136671 0.00418663i
\(739\) −31.3305 −1.15251 −0.576255 0.817270i \(-0.695487\pi\)
−0.576255 + 0.817270i \(0.695487\pi\)
\(740\) 15.4609 + 7.38706i 0.568355 + 0.271554i
\(741\) −1.65260 + 2.96638i −0.0607099 + 0.108973i
\(742\) 20.0624 + 6.56552i 0.736512 + 0.241028i
\(743\) −13.8942 + 24.0655i −0.509730 + 0.882879i 0.490206 + 0.871606i \(0.336921\pi\)
−0.999936 + 0.0112721i \(0.996412\pi\)
\(744\) 12.7338 22.8568i 0.466844 0.837971i
\(745\) −18.6668 8.91880i −0.683899 0.326760i
\(746\) 12.2994i 0.450313i
\(747\) 9.21474 5.70328i 0.337150 0.208672i
\(748\) −3.89199 −0.142305
\(749\) 22.7566 20.4033i 0.831508 0.745520i
\(750\) 11.9456 11.6424i 0.436192 0.425119i
\(751\) −9.90503 + 17.1560i −0.361440 + 0.626032i −0.988198 0.153182i \(-0.951048\pi\)
0.626758 + 0.779214i \(0.284381\pi\)
\(752\) −0.820968 0.473986i −0.0299376 0.0172845i
\(753\) 0.0822413 + 5.37075i 0.00299704 + 0.195721i
\(754\) 5.14681 2.97151i 0.187436 0.108216i
\(755\) 22.7552 + 33.1561i 0.828147 + 1.20667i
\(756\) 16.7432 4.33349i 0.608945 0.157607i
\(757\) 27.0630i 0.983622i −0.870702 0.491811i \(-0.836335\pi\)
0.870702 0.491811i \(-0.163665\pi\)
\(758\) 1.48508 + 2.57223i 0.0539405 + 0.0934277i
\(759\) 8.13342 0.124546i 0.295224 0.00452072i
\(760\) 0.817600 + 10.4773i 0.0296575 + 0.380053i
\(761\) 15.7777 27.3278i 0.571942 0.990632i −0.424425 0.905463i \(-0.639524\pi\)
0.996367 0.0851690i \(-0.0271430\pi\)
\(762\) −3.38782 5.66574i −0.122728 0.205248i
\(763\) −34.0880 + 30.5629i −1.23407 + 1.10645i
\(764\) 8.66720i 0.313568i
\(765\) −2.07483 19.0477i −0.0750157 0.688671i
\(766\) 8.37577i 0.302629i
\(767\) 7.04947 + 12.2100i 0.254541 + 0.440879i
\(768\) −23.8190 13.2699i −0.859495 0.478835i
\(769\) −13.7774 7.95441i −0.496827 0.286843i 0.230575 0.973055i \(-0.425939\pi\)
−0.727402 + 0.686211i \(0.759273\pi\)
\(770\) 5.29674 1.55300i 0.190881 0.0559661i
\(771\) −2.74568 + 4.92842i −0.0988832 + 0.177493i
\(772\) 21.5108 12.4193i 0.774191 0.446979i
\(773\) 0.663048i 0.0238482i 0.999929 + 0.0119241i \(0.00379565\pi\)
−0.999929 + 0.0119241i \(0.996204\pi\)
\(774\) −10.1353 5.44485i −0.364306 0.195711i
\(775\) −25.1133 9.67828i −0.902095 0.347654i
\(776\) −27.0746 46.8945i −0.971920 1.68341i
\(777\) −20.4958 + 18.9503i −0.735281 + 0.679837i
\(778\) 10.5227 + 6.07528i 0.377257 + 0.217809i
\(779\) 2.08477 + 1.20364i 0.0746945 + 0.0431249i
\(780\) −4.65280 + 3.29916i −0.166597 + 0.118129i
\(781\) −4.03670 6.99177i −0.144445 0.250185i
\(782\) 10.6677i 0.381476i
\(783\) 16.5138 + 25.7902i 0.590154 + 0.921668i
\(784\) −0.632074 + 0.278225i −0.0225741 + 0.00993661i
\(785\) 3.80488 7.96351i 0.135802 0.284230i
\(786\) −0.381065 24.8854i −0.0135922 0.887632i
\(787\) −8.07852 + 13.9924i −0.287968 + 0.498775i −0.973325 0.229432i \(-0.926313\pi\)
0.685356 + 0.728208i \(0.259646\pi\)
\(788\) 9.33784 16.1736i 0.332647 0.576161i
\(789\) −0.399691 + 0.238995i −0.0142294 + 0.00850846i
\(790\) −5.20932 + 10.9030i −0.185339 + 0.387911i
\(791\) −2.93666 13.9608i −0.104416 0.496389i
\(792\) 7.75416 4.79928i 0.275532 0.170535i
\(793\) 13.5859i 0.482450i
\(794\) 12.0445 + 20.8618i 0.427445 + 0.740356i
\(795\) −3.33819 35.7180i −0.118393 1.26679i
\(796\) 13.9616 + 8.06072i 0.494855 + 0.285705i
\(797\) −18.4597 10.6577i −0.653877 0.377516i 0.136063 0.990700i \(-0.456555\pi\)
−0.789940 + 0.613184i \(0.789888\pi\)
\(798\) −6.31346 1.95962i −0.223494 0.0693698i
\(799\) −13.7225 23.7682i −0.485469 0.840857i
\(800\) −10.2448 + 26.5831i −0.362207 + 0.939856i
\(801\) −27.4671 + 0.841394i −0.970501 + 0.0297292i
\(802\) 30.1938i 1.06618i
\(803\) 1.06144 0.612820i 0.0374572 0.0216259i
\(804\) −4.24645 7.10168i −0.149761 0.250457i
\(805\) −7.21713 24.6152i −0.254370 0.867571i
\(806\) −4.70065 2.71392i −0.165573 0.0955938i
\(807\) −0.474845 31.0096i −0.0167153 1.09159i
\(808\) −7.57388 13.1183i −0.266448 0.461502i
\(809\) 49.0587i 1.72481i 0.506217 + 0.862406i \(0.331043\pi\)
−0.506217 + 0.862406i \(0.668957\pi\)
\(810\) 10.6656 + 13.6655i 0.374752 + 0.480157i
\(811\) 31.5984i 1.10957i −0.831994 0.554785i \(-0.812800\pi\)
0.831994 0.554785i \(-0.187200\pi\)
\(812\) −13.0951 14.6055i −0.459549 0.512553i
\(813\) −23.7769 + 0.364092i −0.833894 + 0.0127693i
\(814\) −2.84161 + 4.92181i −0.0995983 + 0.172509i
\(815\) −2.20093 28.2044i −0.0770954 0.987958i
\(816\) 0.250480 + 0.418899i 0.00876856 + 0.0146644i
\(817\) −3.72806 6.45720i −0.130428 0.225909i
\(818\) 2.66962i 0.0933410i
\(819\) −2.19018 9.02996i −0.0765312 0.315532i
\(820\) 2.28810 + 3.33393i 0.0799038 + 0.116426i
\(821\) 7.05006 4.07035i 0.246049 0.142056i −0.371905 0.928271i \(-0.621295\pi\)
0.617954 + 0.786214i \(0.287962\pi\)
\(822\) 25.8892 + 14.4232i 0.902991 + 0.503067i
\(823\) −42.2549 24.3959i −1.47291 0.850386i −0.473376 0.880860i \(-0.656965\pi\)
−0.999536 + 0.0304744i \(0.990298\pi\)
\(824\) −24.3444 + 42.1657i −0.848077 + 1.46891i
\(825\) −6.00460 7.20659i −0.209053 0.250901i
\(826\) −20.4362 + 18.3228i −0.711066 + 0.637533i
\(827\) 51.8090 1.80157 0.900787 0.434261i \(-0.142991\pi\)
0.900787 + 0.434261i \(0.142991\pi\)
\(828\) −8.61201 13.9144i −0.299288 0.483557i
\(829\) 29.4848i 1.02405i 0.858971 + 0.512025i \(0.171104\pi\)
−0.858971 + 0.512025i \(0.828896\pi\)
\(830\) −6.27793 2.99953i −0.217910 0.104115i
\(831\) −8.20069 13.7147i −0.284479 0.475757i
\(832\) −2.75727 + 4.77574i −0.0955913 + 0.165569i
\(833\) −19.8753 2.17388i −0.688637 0.0753203i
\(834\) 33.2724 0.509494i 1.15213 0.0176423i
\(835\) −25.1690 12.0255i −0.871009 0.416159i
\(836\) 2.28196 0.0789234
\(837\) 12.8577 24.8389i 0.444428 0.858558i
\(838\) 5.89887 0.203773
\(839\) 22.6019 + 39.1477i 0.780305 + 1.35153i 0.931764 + 0.363065i \(0.118270\pi\)
−0.151458 + 0.988464i \(0.548397\pi\)
\(840\) −21.1062 19.5320i −0.728232 0.673917i
\(841\) 2.86743 4.96653i 0.0988767 0.171260i
\(842\) 5.34528 9.25830i 0.184210 0.319062i
\(843\) −22.7860 38.1069i −0.784793 1.31247i
\(844\) 6.08220 + 10.5347i 0.209358 + 0.362619i
\(845\) −14.7149 21.4407i −0.506208 0.737584i
\(846\) 21.8739 + 11.7510i 0.752039 + 0.404007i
\(847\) 5.35184 + 25.4425i 0.183891 + 0.874214i
\(848\) 0.456907 + 0.791386i 0.0156902 + 0.0271763i
\(849\) 17.4105 + 9.69962i 0.597528 + 0.332890i
\(850\) −9.57043 + 7.72900i −0.328263 + 0.265103i
\(851\) 22.8728 + 13.2056i 0.784069 + 0.452683i
\(852\) −7.90430 + 14.1880i −0.270797 + 0.486073i
\(853\) −1.59707 2.76620i −0.0546825 0.0947128i 0.837388 0.546608i \(-0.184081\pi\)
−0.892071 + 0.451895i \(0.850748\pi\)
\(854\) −25.8823 + 5.44436i −0.885675 + 0.186302i
\(855\) 1.21652 + 11.1681i 0.0416042 + 0.381941i
\(856\) −32.4198 −1.10809
\(857\) 32.6079 18.8262i 1.11386 0.643089i 0.174036 0.984739i \(-0.444319\pi\)
0.939827 + 0.341650i \(0.110986\pi\)
\(858\) −0.970866 1.62366i −0.0331448 0.0554308i
\(859\) 30.9672 + 17.8789i 1.05659 + 0.610020i 0.924486 0.381216i \(-0.124495\pi\)
0.132100 + 0.991236i \(0.457828\pi\)
\(860\) −0.974369 12.4863i −0.0332257 0.425779i
\(861\) −6.42463 + 1.45449i −0.218951 + 0.0495689i
\(862\) 0.707604 0.408535i 0.0241011 0.0139148i
\(863\) −21.4669 −0.730741 −0.365371 0.930862i \(-0.619058\pi\)
−0.365371 + 0.930862i \(0.619058\pi\)
\(864\) −26.2927 13.6103i −0.894497 0.463032i
\(865\) 8.37094 5.74502i 0.284620 0.195337i
\(866\) 3.01580 + 5.22352i 0.102481 + 0.177502i
\(867\) −0.234480 15.3126i −0.00796335 0.520045i
\(868\) −5.57229 + 17.0273i −0.189136 + 0.577945i
\(869\) 5.88478 + 3.39758i 0.199628 + 0.115255i
\(870\) 8.20377 17.8686i 0.278134 0.605802i
\(871\) −3.84989 + 2.22274i −0.130449 + 0.0753146i
\(872\) 48.5629 1.64455
\(873\) −30.4636 49.2198i −1.03104 1.66584i
\(874\) 6.25471i 0.211569i
\(875\) −16.8543 + 24.3091i −0.569780 + 0.821797i
\(876\) −2.15391 1.19997i −0.0727738 0.0405432i
\(877\) 23.1310 + 13.3547i 0.781077 + 0.450955i 0.836812 0.547490i \(-0.184417\pi\)
−0.0557346 + 0.998446i \(0.517750\pi\)
\(878\) 16.2032 + 9.35493i 0.546832 + 0.315714i
\(879\) 3.71326 6.66520i 0.125245 0.224812i
\(880\) 0.215601 + 0.103012i 0.00726790 + 0.00347252i
\(881\) −33.2691 −1.12086 −0.560432 0.828201i \(-0.689365\pi\)
−0.560432 + 0.828201i \(0.689365\pi\)
\(882\) 16.3252 7.79112i 0.549697 0.262341i
\(883\) 13.2867i 0.447134i 0.974689 + 0.223567i \(0.0717702\pi\)
−0.974689 + 0.223567i \(0.928230\pi\)
\(884\) 3.64288 2.10322i 0.122523 0.0707388i
\(885\) 42.3905 + 19.4622i 1.42494 + 0.654216i
\(886\) 5.17423 8.96203i 0.173832 0.301085i
\(887\) −21.7033 12.5304i −0.728724 0.420729i 0.0892311 0.996011i \(-0.471559\pi\)
−0.817955 + 0.575282i \(0.804892\pi\)
\(888\) 29.6054 0.453343i 0.993493 0.0152132i
\(889\) 7.81476 + 8.71612i 0.262099 + 0.292329i
\(890\) 9.98355 + 14.5468i 0.334649 + 0.487609i
\(891\) 8.12811 5.38175i 0.272302 0.180295i
\(892\) −2.29042 −0.0766891
\(893\) 8.04585 + 13.9358i 0.269244 + 0.466344i
\(894\) −13.8019 + 0.211347i −0.461606 + 0.00706849i
\(895\) −2.40327 30.7972i −0.0803323 1.02944i
\(896\) 18.4513 + 6.03830i 0.616416 + 0.201726i
\(897\) −7.54552 + 4.51184i −0.251938 + 0.150646i
\(898\) −20.8328 + 12.0278i −0.695200 + 0.401374i
\(899\) −31.7238 −1.05805
\(900\) −6.24354 + 17.8075i −0.208118 + 0.593583i
\(901\) 26.4562i 0.881383i
\(902\) −1.16146 + 0.670571i −0.0386725 + 0.0223276i
\(903\) 19.4857 + 6.04812i 0.648443 + 0.201269i
\(904\) −7.56628 + 13.1052i −0.251651 + 0.435872i
\(905\) −2.27517 29.1558i −0.0756294 0.969171i
\(906\) 23.4394 + 13.0583i 0.778720 + 0.433835i
\(907\) −33.4100 + 19.2892i −1.10936 + 0.640489i −0.938663 0.344835i \(-0.887935\pi\)
−0.170696 + 0.985324i \(0.554602\pi\)
\(908\) 11.0918i 0.368094i
\(909\) −8.52194 13.7688i −0.282655 0.456683i
\(910\) −4.11848 + 4.31593i −0.136526 + 0.143072i
\(911\) −43.4787 + 25.1024i −1.44051 + 0.831681i −0.997884 0.0650234i \(-0.979288\pi\)
−0.442630 + 0.896704i \(0.645954\pi\)
\(912\) −0.146862 0.245610i −0.00486310 0.00813296i
\(913\) −1.95633 + 3.38846i −0.0647449 + 0.112142i
\(914\) −7.92579 4.57596i −0.262162 0.151359i
\(915\) 25.9984 + 36.6655i 0.859482 + 1.21213i
\(916\) −17.3459 + 10.0147i −0.573126 + 0.330894i
\(917\) 9.08510 + 43.1903i 0.300016 + 1.42627i
\(918\) −6.89377 10.7663i −0.227528 0.355340i
\(919\) 2.16894 0.0715467 0.0357734 0.999360i \(-0.488611\pi\)
0.0357734 + 0.999360i \(0.488611\pi\)
\(920\) −11.7300 + 24.5506i −0.386727 + 0.809410i
\(921\) −0.195367 12.7584i −0.00643756 0.420403i
\(922\) 10.6590 18.4619i 0.351035 0.608010i
\(923\) 7.55665 + 4.36283i 0.248730 + 0.143604i
\(924\) −4.58487 + 4.23914i −0.150831 + 0.139458i
\(925\) −4.72460 30.0879i −0.155344 0.989286i
\(926\) 32.1542i 1.05665i
\(927\) −24.6315 + 45.8502i −0.809004 + 1.50592i
\(928\) 33.5806i 1.10234i
\(929\) 0.278887 + 0.483046i 0.00914998 + 0.0158482i 0.870564 0.492055i \(-0.163754\pi\)
−0.861414 + 0.507903i \(0.830421\pi\)
\(930\) −17.8795 + 1.67101i −0.586292 + 0.0547946i
\(931\) 11.6533 + 1.27459i 0.381923 + 0.0417731i
\(932\) 8.55340 14.8149i 0.280176 0.485279i
\(933\) 24.6455 + 13.7303i 0.806857 + 0.449510i
\(934\) 8.82025 5.09237i 0.288607 0.166628i
\(935\) 3.91451 + 5.70375i 0.128018 + 0.186532i
\(936\) −4.66433 + 8.68241i −0.152458 + 0.283793i
\(937\) −5.28555 −0.172671 −0.0863357 0.996266i \(-0.527516\pi\)
−0.0863357 + 0.996266i \(0.527516\pi\)
\(938\) −5.77730 6.44365i −0.188635 0.210393i
\(939\) 38.9594 23.2958i 1.27139 0.760228i
\(940\) 2.10287 + 26.9477i 0.0685879 + 0.878937i
\(941\) −16.2876 + 28.2110i −0.530962 + 0.919653i 0.468385 + 0.883524i \(0.344836\pi\)
−0.999347 + 0.0361284i \(0.988497\pi\)
\(942\) −0.0901632 5.88808i −0.00293768 0.191844i
\(943\) 3.11630 + 5.39759i 0.101481 + 0.175770i
\(944\) −1.18819 −0.0386723
\(945\) −23.1909 20.1788i −0.754400 0.656416i
\(946\) 4.15395 0.135057
\(947\) 16.8682 + 29.2165i 0.548142 + 0.949410i 0.998402 + 0.0565122i \(0.0179980\pi\)
−0.450260 + 0.892898i \(0.648669\pi\)
\(948\) −0.209298 13.6682i −0.00679770 0.443922i
\(949\) −0.662331 + 1.14719i −0.0215002 + 0.0372394i
\(950\) 5.61136 4.53169i 0.182057 0.147028i
\(951\) −28.2293 + 16.8797i −0.915398 + 0.547362i
\(952\) 14.1575 + 15.7904i 0.458847 + 0.511770i
\(953\) 15.1666 0.491295 0.245648 0.969359i \(-0.420999\pi\)
0.245648 + 0.969359i \(0.420999\pi\)
\(954\) −12.5969 20.3528i −0.407841 0.658946i
\(955\) 12.7019 8.71737i 0.411023 0.282087i
\(956\) 15.2955 8.83087i 0.494693 0.285611i
\(957\) −9.65900 5.38115i −0.312231 0.173948i
\(958\) −16.5164 + 28.6072i −0.533620 + 0.924257i
\(959\) −49.9478 16.3457i −1.61290 0.527831i
\(960\) 1.69771 + 18.1651i 0.0547932 + 0.586277i
\(961\) −1.01310 1.75475i −0.0326808 0.0566048i
\(962\) 6.14238i 0.198038i
\(963\) −34.6401 + 1.06112i −1.11626 + 0.0341942i
\(964\) 34.0396i 1.09634i
\(965\) −39.8359 19.0331i −1.28236 0.612699i
\(966\) −11.6192 12.5668i −0.373842 0.404330i
\(967\) 10.3311 + 5.96466i 0.332225 + 0.191810i 0.656829 0.754040i \(-0.271897\pi\)
−0.324603 + 0.945850i \(0.605231\pi\)
\(968\) 13.7890 23.8832i 0.443194 0.767635i
\(969\) −0.126852 8.28403i −0.00407507 0.266121i
\(970\) −16.0217 + 33.5331i −0.514427 + 1.07668i
\(971\) 50.1983 1.61094 0.805470 0.592637i \(-0.201913\pi\)
0.805470 + 0.592637i \(0.201913\pi\)
\(972\) −17.6835 8.47764i −0.567198 0.271920i
\(973\) −57.7465 + 12.1470i −1.85127 + 0.389415i
\(974\) −24.7543 + 14.2919i −0.793178 + 0.457942i
\(975\) 9.51468 + 3.50046i 0.304714 + 0.112105i
\(976\) −0.991560 0.572477i −0.0317390 0.0183245i
\(977\) −12.2344 + 21.1906i −0.391414 + 0.677948i −0.992636 0.121133i \(-0.961347\pi\)
0.601223 + 0.799081i \(0.294680\pi\)
\(978\) −9.68712 16.2006i −0.309760 0.518037i
\(979\) 8.59235 4.96080i 0.274613 0.158548i
\(980\) 16.7390 + 10.3705i 0.534707 + 0.331273i
\(981\) 51.8887 1.58950i 1.65668 0.0507487i
\(982\) 10.6382i 0.339480i
\(983\) −40.2035 + 23.2115i −1.28229 + 0.740331i −0.977267 0.212014i \(-0.931998\pi\)
−0.305024 + 0.952345i \(0.598665\pi\)
\(984\) 6.10387 + 3.40054i 0.194584 + 0.108405i
\(985\) −33.0945 + 2.58253i −1.05448 + 0.0822862i
\(986\) −7.25013 + 12.5576i −0.230891 + 0.399915i
\(987\) −42.0537 13.0529i −1.33858 0.415480i
\(988\) −2.13590 + 1.23316i −0.0679521 + 0.0392322i
\(989\) 19.3044i 0.613844i
\(990\) −5.72725 2.52403i −0.182024 0.0802191i
\(991\) −6.78859 −0.215647 −0.107823 0.994170i \(-0.534388\pi\)
−0.107823 + 0.994170i \(0.534388\pi\)
\(992\) 26.5607 15.3348i 0.843303 0.486881i
\(993\) 10.1760 6.08476i 0.322927 0.193094i
\(994\) −5.28335 + 16.1444i −0.167578 + 0.512070i
\(995\) −2.22932 28.5682i −0.0706743 0.905673i
\(996\) 7.87013 0.120514i 0.249375 0.00381863i
\(997\) −1.65733 2.87059i −0.0524883 0.0909124i 0.838587 0.544767i \(-0.183382\pi\)
−0.891076 + 0.453855i \(0.850049\pi\)
\(998\) 1.29956 0.0411368
\(999\) 31.6181 1.45339i 1.00035 0.0459834i
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 315.2.z.b.104.17 80
3.2 odd 2 945.2.z.b.314.24 80
5.4 even 2 inner 315.2.z.b.104.24 yes 80
7.6 odd 2 inner 315.2.z.b.104.18 yes 80
9.2 odd 6 inner 315.2.z.b.209.23 yes 80
9.7 even 3 945.2.z.b.629.18 80
15.14 odd 2 945.2.z.b.314.17 80
21.20 even 2 945.2.z.b.314.23 80
35.34 odd 2 inner 315.2.z.b.104.23 yes 80
45.29 odd 6 inner 315.2.z.b.209.18 yes 80
45.34 even 6 945.2.z.b.629.23 80
63.20 even 6 inner 315.2.z.b.209.24 yes 80
63.34 odd 6 945.2.z.b.629.17 80
105.104 even 2 945.2.z.b.314.18 80
315.34 odd 6 945.2.z.b.629.24 80
315.209 even 6 inner 315.2.z.b.209.17 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.z.b.104.17 80 1.1 even 1 trivial
315.2.z.b.104.18 yes 80 7.6 odd 2 inner
315.2.z.b.104.23 yes 80 35.34 odd 2 inner
315.2.z.b.104.24 yes 80 5.4 even 2 inner
315.2.z.b.209.17 yes 80 315.209 even 6 inner
315.2.z.b.209.18 yes 80 45.29 odd 6 inner
315.2.z.b.209.23 yes 80 9.2 odd 6 inner
315.2.z.b.209.24 yes 80 63.20 even 6 inner
945.2.z.b.314.17 80 15.14 odd 2
945.2.z.b.314.18 80 105.104 even 2
945.2.z.b.314.23 80 21.20 even 2
945.2.z.b.314.24 80 3.2 odd 2
945.2.z.b.629.17 80 63.34 odd 6
945.2.z.b.629.18 80 9.7 even 3
945.2.z.b.629.23 80 45.34 even 6
945.2.z.b.629.24 80 315.34 odd 6