Properties

Label 96.2.n.a.61.4
Level $96$
Weight $2$
Character 96.61
Analytic conductor $0.767$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [96,2,Mod(13,96)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(96, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("96.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 96.n (of order \(8\), 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: \(0.766563859404\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 61.4
Character \(\chi\) \(=\) 96.61
Dual form 96.2.n.a.85.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.607577 - 1.27705i) q^{2} +(0.923880 + 0.382683i) q^{3} +(-1.26170 + 1.55181i) q^{4} +(-1.35803 - 3.27858i) q^{5} +(-0.0726234 - 1.41235i) q^{6} +(2.48546 - 2.48546i) q^{7} +(2.74831 + 0.668405i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.607577 - 1.27705i) q^{2} +(0.923880 + 0.382683i) q^{3} +(-1.26170 + 1.55181i) q^{4} +(-1.35803 - 3.27858i) q^{5} +(-0.0726234 - 1.41235i) q^{6} +(2.48546 - 2.48546i) q^{7} +(2.74831 + 0.668405i) q^{8} +(0.707107 + 0.707107i) q^{9} +(-3.36179 + 3.72626i) q^{10} +(0.420646 - 0.174237i) q^{11} +(-1.75951 + 0.950854i) q^{12} +(-1.98881 + 4.80141i) q^{13} +(-4.68416 - 1.66394i) q^{14} -3.54871i q^{15} +(-0.816228 - 3.91584i) q^{16} +4.75470i q^{17} +(0.473387 - 1.33263i) q^{18} +(-0.402518 + 0.971765i) q^{19} +(6.80116 + 2.02917i) q^{20} +(3.24741 - 1.34512i) q^{21} +(-0.478084 - 0.431322i) q^{22} +(0.739125 + 0.739125i) q^{23} +(2.28332 + 1.66926i) q^{24} +(-5.36930 + 5.36930i) q^{25} +(7.33998 - 0.377424i) q^{26} +(0.382683 + 0.923880i) q^{27} +(0.721057 + 6.99286i) q^{28} +(-0.153117 - 0.0634229i) q^{29} +(-4.53187 + 2.15611i) q^{30} +8.57458 q^{31} +(-4.50479 + 3.42154i) q^{32} +0.455304 q^{33} +(6.07198 - 2.88885i) q^{34} +(-11.5241 - 4.77344i) q^{35} +(-1.98945 + 0.205139i) q^{36} +(-2.67583 - 6.46002i) q^{37} +(1.48555 - 0.0763875i) q^{38} +(-3.67484 + 3.67484i) q^{39} +(-1.54088 - 9.91828i) q^{40} +(-1.39247 - 1.39247i) q^{41} +(-3.69083 - 3.32983i) q^{42} +(2.84883 - 1.18002i) q^{43} +(-0.260346 + 0.872597i) q^{44} +(1.35803 - 3.27858i) q^{45} +(0.494822 - 1.39297i) q^{46} +0.715661i q^{47} +(0.744429 - 3.93012i) q^{48} -5.35501i q^{49} +(10.1191 + 3.59458i) q^{50} +(-1.81955 + 4.39277i) q^{51} +(-4.94159 - 9.14418i) q^{52} +(-10.4455 + 4.32668i) q^{53} +(0.947328 - 1.05003i) q^{54} +(-1.14250 - 1.14250i) q^{55} +(8.49212 - 5.16953i) q^{56} +(-0.743756 + 0.743756i) q^{57} +(0.0120360 + 0.234071i) q^{58} +(2.09568 + 5.05941i) q^{59} +(5.50692 + 4.47740i) q^{60} +(-2.81202 - 1.16478i) q^{61} +(-5.20972 - 10.9501i) q^{62} +3.51497 q^{63} +(7.10647 + 3.67398i) q^{64} +18.4427 q^{65} +(-0.276632 - 0.581444i) q^{66} +(-5.39384 - 2.23420i) q^{67} +(-7.37840 - 5.99901i) q^{68} +(0.400012 + 0.965714i) q^{69} +(0.905876 + 17.6171i) q^{70} +(-8.26068 + 8.26068i) q^{71} +(1.47072 + 2.41599i) q^{72} +(4.37354 + 4.37354i) q^{73} +(-6.62398 + 7.34212i) q^{74} +(-7.01532 + 2.90584i) q^{75} +(-1.00014 - 1.85071i) q^{76} +(0.612439 - 1.47856i) q^{77} +(6.92569 + 2.46019i) q^{78} -9.46948i q^{79} +(-11.7299 + 7.99390i) q^{80} +1.00000i q^{81} +(-0.932218 + 2.62429i) q^{82} +(2.85195 - 6.88522i) q^{83} +(-2.00988 + 6.73650i) q^{84} +(15.5887 - 6.45704i) q^{85} +(-3.23783 - 2.92114i) q^{86} +(-0.117190 - 0.117190i) q^{87} +(1.27253 - 0.197697i) q^{88} +(8.60493 - 8.60493i) q^{89} +(-5.01201 + 0.257719i) q^{90} +(6.99060 + 16.8768i) q^{91} +(-2.07954 + 0.214428i) q^{92} +(7.92188 + 3.28135i) q^{93} +(0.913933 - 0.434819i) q^{94} +3.73264 q^{95} +(-5.47124 + 1.43718i) q^{96} -10.2117 q^{97} +(-6.83860 + 3.25358i) q^{98} +(0.420646 + 0.174237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/96\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(65\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{8}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.607577 1.27705i −0.429622 0.903009i
\(3\) 0.923880 + 0.382683i 0.533402 + 0.220942i
\(4\) −1.26170 + 1.55181i −0.630850 + 0.775905i
\(5\) −1.35803 3.27858i −0.607330 1.46623i −0.865892 0.500230i \(-0.833249\pi\)
0.258562 0.965995i \(-0.416751\pi\)
\(6\) −0.0726234 1.41235i −0.0296484 0.576589i
\(7\) 2.48546 2.48546i 0.939415 0.939415i −0.0588516 0.998267i \(-0.518744\pi\)
0.998267 + 0.0588516i \(0.0187439\pi\)
\(8\) 2.74831 + 0.668405i 0.971676 + 0.236317i
\(9\) 0.707107 + 0.707107i 0.235702 + 0.235702i
\(10\) −3.36179 + 3.72626i −1.06309 + 1.17835i
\(11\) 0.420646 0.174237i 0.126829 0.0525345i −0.318366 0.947968i \(-0.603134\pi\)
0.445196 + 0.895433i \(0.353134\pi\)
\(12\) −1.75951 + 0.950854i −0.507927 + 0.274488i
\(13\) −1.98881 + 4.80141i −0.551596 + 1.33167i 0.364684 + 0.931131i \(0.381177\pi\)
−0.916280 + 0.400539i \(0.868823\pi\)
\(14\) −4.68416 1.66394i −1.25189 0.444707i
\(15\) 3.54871i 0.916273i
\(16\) −0.816228 3.91584i −0.204057 0.978959i
\(17\) 4.75470i 1.15318i 0.817032 + 0.576592i \(0.195618\pi\)
−0.817032 + 0.576592i \(0.804382\pi\)
\(18\) 0.473387 1.33263i 0.111578 0.314104i
\(19\) −0.402518 + 0.971765i −0.0923440 + 0.222938i −0.963302 0.268419i \(-0.913499\pi\)
0.870958 + 0.491357i \(0.163499\pi\)
\(20\) 6.80116 + 2.02917i 1.52079 + 0.453737i
\(21\) 3.24741 1.34512i 0.708643 0.293529i
\(22\) −0.478084 0.431322i −0.101928 0.0919582i
\(23\) 0.739125 + 0.739125i 0.154118 + 0.154118i 0.779955 0.625836i \(-0.215242\pi\)
−0.625836 + 0.779955i \(0.715242\pi\)
\(24\) 2.28332 + 1.66926i 0.466082 + 0.340736i
\(25\) −5.36930 + 5.36930i −1.07386 + 1.07386i
\(26\) 7.33998 0.377424i 1.43949 0.0740190i
\(27\) 0.382683 + 0.923880i 0.0736475 + 0.177801i
\(28\) 0.721057 + 6.99286i 0.136267 + 1.32153i
\(29\) −0.153117 0.0634229i −0.0284330 0.0117773i 0.368422 0.929659i \(-0.379898\pi\)
−0.396855 + 0.917881i \(0.629898\pi\)
\(30\) −4.53187 + 2.15611i −0.827402 + 0.393651i
\(31\) 8.57458 1.54004 0.770020 0.638020i \(-0.220246\pi\)
0.770020 + 0.638020i \(0.220246\pi\)
\(32\) −4.50479 + 3.42154i −0.796341 + 0.604848i
\(33\) 0.455304 0.0792582
\(34\) 6.07198 2.88885i 1.04134 0.495434i
\(35\) −11.5241 4.77344i −1.94793 0.806859i
\(36\) −1.98945 + 0.205139i −0.331575 + 0.0341898i
\(37\) −2.67583 6.46002i −0.439903 1.06202i −0.975982 0.217852i \(-0.930095\pi\)
0.536079 0.844168i \(-0.319905\pi\)
\(38\) 1.48555 0.0763875i 0.240988 0.0123917i
\(39\) −3.67484 + 3.67484i −0.588445 + 0.588445i
\(40\) −1.54088 9.91828i −0.243634 1.56822i
\(41\) −1.39247 1.39247i −0.217467 0.217467i 0.589963 0.807430i \(-0.299142\pi\)
−0.807430 + 0.589963i \(0.799142\pi\)
\(42\) −3.69083 3.32983i −0.569508 0.513804i
\(43\) 2.84883 1.18002i 0.434443 0.179952i −0.154734 0.987956i \(-0.549452\pi\)
0.589177 + 0.808004i \(0.299452\pi\)
\(44\) −0.260346 + 0.872597i −0.0392486 + 0.131549i
\(45\) 1.35803 3.27858i 0.202443 0.488742i
\(46\) 0.494822 1.39297i 0.0729576 0.205383i
\(47\) 0.715661i 0.104390i 0.998637 + 0.0521949i \(0.0166217\pi\)
−0.998637 + 0.0521949i \(0.983378\pi\)
\(48\) 0.744429 3.93012i 0.107449 0.567264i
\(49\) 5.35501i 0.765002i
\(50\) 10.1191 + 3.59458i 1.43106 + 0.508351i
\(51\) −1.81955 + 4.39277i −0.254787 + 0.615111i
\(52\) −4.94159 9.14418i −0.685275 1.26807i
\(53\) −10.4455 + 4.32668i −1.43480 + 0.594316i −0.958533 0.284982i \(-0.908012\pi\)
−0.476272 + 0.879298i \(0.658012\pi\)
\(54\) 0.947328 1.05003i 0.128915 0.142891i
\(55\) −1.14250 1.14250i −0.154055 0.154055i
\(56\) 8.49212 5.16953i 1.13481 0.690807i
\(57\) −0.743756 + 0.743756i −0.0985130 + 0.0985130i
\(58\) 0.0120360 + 0.234071i 0.00158041 + 0.0307351i
\(59\) 2.09568 + 5.05941i 0.272834 + 0.658679i 0.999602 0.0282033i \(-0.00897857\pi\)
−0.726768 + 0.686883i \(0.758979\pi\)
\(60\) 5.50692 + 4.47740i 0.710940 + 0.578030i
\(61\) −2.81202 1.16478i −0.360042 0.149134i 0.195327 0.980738i \(-0.437423\pi\)
−0.555369 + 0.831604i \(0.687423\pi\)
\(62\) −5.20972 10.9501i −0.661635 1.39067i
\(63\) 3.51497 0.442845
\(64\) 7.10647 + 3.67398i 0.888309 + 0.459247i
\(65\) 18.4427 2.28753
\(66\) −0.276632 0.581444i −0.0340511 0.0715709i
\(67\) −5.39384 2.23420i −0.658962 0.272951i 0.0280395 0.999607i \(-0.491074\pi\)
−0.687002 + 0.726656i \(0.741074\pi\)
\(68\) −7.37840 5.99901i −0.894762 0.727486i
\(69\) 0.400012 + 0.965714i 0.0481558 + 0.116258i
\(70\) 0.905876 + 17.6171i 0.108273 + 2.10564i
\(71\) −8.26068 + 8.26068i −0.980363 + 0.980363i −0.999811 0.0194483i \(-0.993809\pi\)
0.0194483 + 0.999811i \(0.493809\pi\)
\(72\) 1.47072 + 2.41599i 0.173326 + 0.284727i
\(73\) 4.37354 + 4.37354i 0.511884 + 0.511884i 0.915103 0.403219i \(-0.132109\pi\)
−0.403219 + 0.915103i \(0.632109\pi\)
\(74\) −6.62398 + 7.34212i −0.770022 + 0.853504i
\(75\) −7.01532 + 2.90584i −0.810060 + 0.335538i
\(76\) −1.00014 1.85071i −0.114724 0.212291i
\(77\) 0.612439 1.47856i 0.0697938 0.168497i
\(78\) 6.92569 + 2.46019i 0.784180 + 0.278562i
\(79\) 9.46948i 1.06540i −0.846304 0.532700i \(-0.821177\pi\)
0.846304 0.532700i \(-0.178823\pi\)
\(80\) −11.7299 + 7.99390i −1.31144 + 0.893745i
\(81\) 1.00000i 0.111111i
\(82\) −0.932218 + 2.62429i −0.102946 + 0.289804i
\(83\) 2.85195 6.88522i 0.313042 0.755751i −0.686547 0.727086i \(-0.740874\pi\)
0.999589 0.0286653i \(-0.00912568\pi\)
\(84\) −2.00988 + 6.73650i −0.219296 + 0.735012i
\(85\) 15.5887 6.45704i 1.69083 0.700364i
\(86\) −3.23783 2.92114i −0.349144 0.314994i
\(87\) −0.117190 0.117190i −0.0125641 0.0125641i
\(88\) 1.27253 0.197697i 0.135652 0.0210745i
\(89\) 8.60493 8.60493i 0.912120 0.912120i −0.0843186 0.996439i \(-0.526871\pi\)
0.996439 + 0.0843186i \(0.0268713\pi\)
\(90\) −5.01201 + 0.257719i −0.528312 + 0.0271660i
\(91\) 6.99060 + 16.8768i 0.732814 + 1.76917i
\(92\) −2.07954 + 0.214428i −0.216807 + 0.0223557i
\(93\) 7.92188 + 3.28135i 0.821460 + 0.340260i
\(94\) 0.913933 0.434819i 0.0942650 0.0448482i
\(95\) 3.73264 0.382961
\(96\) −5.47124 + 1.43718i −0.558407 + 0.146682i
\(97\) −10.2117 −1.03684 −0.518420 0.855126i \(-0.673480\pi\)
−0.518420 + 0.855126i \(0.673480\pi\)
\(98\) −6.83860 + 3.25358i −0.690803 + 0.328662i
\(99\) 0.420646 + 0.174237i 0.0422765 + 0.0175115i
\(100\) −1.55769 15.1066i −0.155769 1.51066i
\(101\) −1.92210 4.64035i −0.191256 0.461732i 0.798941 0.601409i \(-0.205394\pi\)
−0.990197 + 0.139677i \(0.955394\pi\)
\(102\) 6.71529 0.345303i 0.664913 0.0341901i
\(103\) −2.99647 + 2.99647i −0.295251 + 0.295251i −0.839150 0.543900i \(-0.816947\pi\)
0.543900 + 0.839150i \(0.316947\pi\)
\(104\) −8.67515 + 11.8664i −0.850669 + 1.16360i
\(105\) −8.82017 8.82017i −0.860760 0.860760i
\(106\) 11.8719 + 10.7107i 1.15310 + 1.04031i
\(107\) −0.420364 + 0.174120i −0.0406381 + 0.0168328i −0.402910 0.915240i \(-0.632001\pi\)
0.362272 + 0.932072i \(0.382001\pi\)
\(108\) −1.91652 0.571806i −0.184417 0.0550221i
\(109\) −1.97979 + 4.77963i −0.189629 + 0.457806i −0.989888 0.141849i \(-0.954695\pi\)
0.800259 + 0.599655i \(0.204695\pi\)
\(110\) −0.764870 + 2.15319i −0.0729275 + 0.205298i
\(111\) 6.99227i 0.663677i
\(112\) −11.7614 7.70395i −1.11134 0.727955i
\(113\) 6.63496i 0.624164i −0.950055 0.312082i \(-0.898974\pi\)
0.950055 0.312082i \(-0.101026\pi\)
\(114\) 1.40170 + 0.497923i 0.131281 + 0.0466347i
\(115\) 1.41953 3.42704i 0.132371 0.319573i
\(116\) 0.291607 0.157587i 0.0270751 0.0146316i
\(117\) −4.80141 + 1.98881i −0.443890 + 0.183865i
\(118\) 5.18782 5.75026i 0.477578 0.529355i
\(119\) 11.8176 + 11.8176i 1.08332 + 1.08332i
\(120\) 2.37198 9.75297i 0.216531 0.890320i
\(121\) −7.63159 + 7.63159i −0.693781 + 0.693781i
\(122\) 0.221044 + 4.29877i 0.0200124 + 0.389192i
\(123\) −0.753600 1.81935i −0.0679498 0.164045i
\(124\) −10.8185 + 13.3061i −0.971534 + 1.19492i
\(125\) 8.50244 + 3.52183i 0.760481 + 0.315002i
\(126\) −2.13562 4.48878i −0.190256 0.399893i
\(127\) −19.1639 −1.70052 −0.850262 0.526360i \(-0.823557\pi\)
−0.850262 + 0.526360i \(0.823557\pi\)
\(128\) 0.374113 11.3075i 0.0330673 0.999453i
\(129\) 3.08355 0.271492
\(130\) −11.2053 23.5521i −0.982773 2.06566i
\(131\) 16.6367 + 6.89115i 1.45356 + 0.602083i 0.963042 0.269350i \(-0.0868089\pi\)
0.490514 + 0.871433i \(0.336809\pi\)
\(132\) −0.574457 + 0.706545i −0.0500000 + 0.0614968i
\(133\) 1.41484 + 3.41572i 0.122682 + 0.296181i
\(134\) 0.423994 + 8.24564i 0.0366275 + 0.712315i
\(135\) 2.50932 2.50932i 0.215968 0.215968i
\(136\) −3.17807 + 13.0674i −0.272517 + 1.12052i
\(137\) −4.17579 4.17579i −0.356762 0.356762i 0.505856 0.862618i \(-0.331177\pi\)
−0.862618 + 0.505856i \(0.831177\pi\)
\(138\) 0.990224 1.09758i 0.0842935 0.0934322i
\(139\) 17.1703 7.11217i 1.45636 0.603246i 0.492661 0.870221i \(-0.336024\pi\)
0.963703 + 0.266975i \(0.0860242\pi\)
\(140\) 21.9474 11.8606i 1.85490 1.00240i
\(141\) −0.273872 + 0.661185i −0.0230642 + 0.0556818i
\(142\) 15.5683 + 5.53028i 1.30646 + 0.464091i
\(143\) 2.36622i 0.197873i
\(144\) 2.19175 3.34607i 0.182646 0.278840i
\(145\) 0.588135i 0.0488420i
\(146\) 2.92795 8.24248i 0.242319 0.682152i
\(147\) 2.04927 4.94739i 0.169021 0.408054i
\(148\) 13.4008 + 3.99823i 1.10154 + 0.328652i
\(149\) 7.65604 3.17123i 0.627207 0.259798i −0.0463589 0.998925i \(-0.514762\pi\)
0.673566 + 0.739127i \(0.264762\pi\)
\(150\) 7.97325 + 7.19338i 0.651013 + 0.587337i
\(151\) −8.34642 8.34642i −0.679222 0.679222i 0.280602 0.959824i \(-0.409466\pi\)
−0.959824 + 0.280602i \(0.909466\pi\)
\(152\) −1.75578 + 2.40167i −0.142413 + 0.194801i
\(153\) −3.36208 + 3.36208i −0.271808 + 0.271808i
\(154\) −2.26029 + 0.116225i −0.182139 + 0.00936568i
\(155\) −11.6445 28.1124i −0.935313 2.25804i
\(156\) −1.06611 10.3392i −0.0853570 0.827798i
\(157\) 1.13210 + 0.468931i 0.0903514 + 0.0374248i 0.427401 0.904062i \(-0.359429\pi\)
−0.337050 + 0.941487i \(0.609429\pi\)
\(158\) −12.0930 + 5.75344i −0.962066 + 0.457719i
\(159\) −11.3062 −0.896637
\(160\) 17.3354 + 10.1227i 1.37049 + 0.800273i
\(161\) 3.67413 0.289562
\(162\) 1.27705 0.607577i 0.100334 0.0477358i
\(163\) −12.5235 5.18742i −0.980920 0.406310i −0.166154 0.986100i \(-0.553135\pi\)
−0.814766 + 0.579790i \(0.803135\pi\)
\(164\) 3.91773 0.403970i 0.305923 0.0315448i
\(165\) −0.618317 1.49275i −0.0481359 0.116210i
\(166\) −10.5255 + 0.541227i −0.816940 + 0.0420073i
\(167\) −6.60580 + 6.60580i −0.511172 + 0.511172i −0.914886 0.403713i \(-0.867719\pi\)
0.403713 + 0.914886i \(0.367719\pi\)
\(168\) 9.82399 1.52623i 0.757937 0.117751i
\(169\) −9.90575 9.90575i −0.761981 0.761981i
\(170\) −17.7173 15.9843i −1.35885 1.22594i
\(171\) −0.971765 + 0.402518i −0.0743127 + 0.0307813i
\(172\) −1.76320 + 5.90968i −0.134442 + 0.450609i
\(173\) −7.14385 + 17.2468i −0.543137 + 1.31125i 0.379361 + 0.925249i \(0.376144\pi\)
−0.922499 + 0.386000i \(0.873856\pi\)
\(174\) −0.0784554 + 0.220860i −0.00594769 + 0.0167433i
\(175\) 26.6903i 2.01760i
\(176\) −1.02563 1.50496i −0.0773096 0.113441i
\(177\) 5.47627i 0.411622i
\(178\) −16.2171 5.76074i −1.21552 0.431786i
\(179\) 3.80659 9.18993i 0.284518 0.686887i −0.715412 0.698703i \(-0.753761\pi\)
0.999930 + 0.0118153i \(0.00376101\pi\)
\(180\) 3.37430 + 6.24399i 0.251506 + 0.465399i
\(181\) −5.55971 + 2.30291i −0.413250 + 0.171174i −0.579615 0.814890i \(-0.696797\pi\)
0.166365 + 0.986064i \(0.446797\pi\)
\(182\) 17.3051 19.1813i 1.28274 1.42181i
\(183\) −2.15222 2.15222i −0.159097 0.159097i
\(184\) 1.53731 + 2.52538i 0.113332 + 0.186174i
\(185\) −17.5458 + 17.5458i −1.28999 + 1.28999i
\(186\) −0.622715 12.1103i −0.0456597 0.887969i
\(187\) 0.828446 + 2.00005i 0.0605820 + 0.146258i
\(188\) −1.11057 0.902949i −0.0809966 0.0658543i
\(189\) 3.24741 + 1.34512i 0.236214 + 0.0978431i
\(190\) −2.26787 4.76676i −0.164528 0.345817i
\(191\) 5.75185 0.416190 0.208095 0.978109i \(-0.433274\pi\)
0.208095 + 0.978109i \(0.433274\pi\)
\(192\) 5.15955 + 6.11384i 0.372358 + 0.441228i
\(193\) −2.02898 −0.146049 −0.0730246 0.997330i \(-0.523265\pi\)
−0.0730246 + 0.997330i \(0.523265\pi\)
\(194\) 6.20439 + 13.0408i 0.445449 + 0.936275i
\(195\) 17.0388 + 7.05770i 1.22017 + 0.505412i
\(196\) 8.30996 + 6.75642i 0.593569 + 0.482601i
\(197\) 3.54890 + 8.56781i 0.252849 + 0.610431i 0.998432 0.0559816i \(-0.0178288\pi\)
−0.745583 + 0.666413i \(0.767829\pi\)
\(198\) −0.0330657 0.643047i −0.00234988 0.0456994i
\(199\) 12.7457 12.7457i 0.903520 0.903520i −0.0922191 0.995739i \(-0.529396\pi\)
0.995739 + 0.0922191i \(0.0293960\pi\)
\(200\) −18.3454 + 11.1676i −1.29721 + 0.789672i
\(201\) −4.12827 4.12827i −0.291185 0.291185i
\(202\) −4.75813 + 5.27398i −0.334781 + 0.371076i
\(203\) −0.538200 + 0.222930i −0.0377742 + 0.0156466i
\(204\) −4.52103 8.36595i −0.316535 0.585734i
\(205\) −2.67431 + 6.45635i −0.186782 + 0.450931i
\(206\) 5.64721 + 2.00604i 0.393460 + 0.139768i
\(207\) 1.04528i 0.0726521i
\(208\) 20.4248 + 3.86880i 1.41621 + 0.268253i
\(209\) 0.478902i 0.0331264i
\(210\) −5.90484 + 16.6227i −0.407473 + 1.14708i
\(211\) −8.49277 + 20.5034i −0.584666 + 1.41151i 0.303874 + 0.952712i \(0.401720\pi\)
−0.888541 + 0.458798i \(0.848280\pi\)
\(212\) 6.46494 21.6685i 0.444014 1.48820i
\(213\) −10.7931 + 4.47065i −0.739531 + 0.306324i
\(214\) 0.477763 + 0.431033i 0.0326592 + 0.0294648i
\(215\) −7.73761 7.73761i −0.527700 0.527700i
\(216\) 0.434208 + 2.79490i 0.0295441 + 0.190169i
\(217\) 21.3118 21.3118i 1.44674 1.44674i
\(218\) 7.30669 0.375713i 0.494872 0.0254465i
\(219\) 2.36694 + 5.71430i 0.159943 + 0.386137i
\(220\) 3.21444 0.331451i 0.216717 0.0223465i
\(221\) −22.8293 9.45619i −1.53566 0.636092i
\(222\) −8.92946 + 4.24835i −0.599306 + 0.285130i
\(223\) 1.93870 0.129825 0.0649123 0.997891i \(-0.479323\pi\)
0.0649123 + 0.997891i \(0.479323\pi\)
\(224\) −2.69237 + 19.7005i −0.179892 + 1.31630i
\(225\) −7.59333 −0.506222
\(226\) −8.47315 + 4.03125i −0.563626 + 0.268155i
\(227\) 19.8529 + 8.22334i 1.31768 + 0.545802i 0.927117 0.374773i \(-0.122279\pi\)
0.390566 + 0.920575i \(0.372279\pi\)
\(228\) −0.215771 2.09257i −0.0142898 0.138584i
\(229\) 9.21270 + 22.2414i 0.608792 + 1.46975i 0.864315 + 0.502951i \(0.167753\pi\)
−0.255522 + 0.966803i \(0.582247\pi\)
\(230\) −5.23896 + 0.269389i −0.345447 + 0.0177630i
\(231\) 1.13164 1.13164i 0.0744564 0.0744564i
\(232\) −0.378420 0.276650i −0.0248445 0.0181630i
\(233\) 7.56463 + 7.56463i 0.495575 + 0.495575i 0.910057 0.414482i \(-0.136037\pi\)
−0.414482 + 0.910057i \(0.636037\pi\)
\(234\) 5.45703 + 4.92327i 0.356737 + 0.321844i
\(235\) 2.34635 0.971890i 0.153059 0.0633991i
\(236\) −10.4954 3.13137i −0.683190 0.203835i
\(237\) 3.62381 8.74866i 0.235392 0.568287i
\(238\) 7.91154 22.2718i 0.512829 1.44366i
\(239\) 21.0655i 1.36261i −0.731997 0.681307i \(-0.761412\pi\)
0.731997 0.681307i \(-0.238588\pi\)
\(240\) −13.8962 + 2.89656i −0.896993 + 0.186972i
\(241\) 24.1957i 1.55858i −0.626664 0.779289i \(-0.715580\pi\)
0.626664 0.779289i \(-0.284420\pi\)
\(242\) 14.3827 + 5.10912i 0.924554 + 0.328427i
\(243\) −0.382683 + 0.923880i −0.0245492 + 0.0592669i
\(244\) 5.35543 2.89412i 0.342846 0.185277i
\(245\) −17.5568 + 7.27228i −1.12166 + 0.464609i
\(246\) −1.86553 + 2.06778i −0.118942 + 0.131837i
\(247\) −3.86531 3.86531i −0.245943 0.245943i
\(248\) 23.5656 + 5.73129i 1.49642 + 0.363938i
\(249\) 5.26972 5.26972i 0.333955 0.333955i
\(250\) −0.668352 12.9978i −0.0422703 0.822053i
\(251\) 0.0707278 + 0.170752i 0.00446430 + 0.0107778i 0.926096 0.377288i \(-0.123143\pi\)
−0.921632 + 0.388066i \(0.873143\pi\)
\(252\) −4.43484 + 5.45457i −0.279368 + 0.343605i
\(253\) 0.439693 + 0.182127i 0.0276433 + 0.0114502i
\(254\) 11.6436 + 24.4732i 0.730583 + 1.53559i
\(255\) 16.8731 1.05663
\(256\) −14.6675 + 6.39243i −0.916721 + 0.399527i
\(257\) −29.7460 −1.85550 −0.927751 0.373199i \(-0.878261\pi\)
−0.927751 + 0.373199i \(0.878261\pi\)
\(258\) −1.87350 3.93784i −0.116639 0.245159i
\(259\) −22.7068 9.40545i −1.41093 0.584426i
\(260\) −23.2691 + 28.6195i −1.44309 + 1.77491i
\(261\) −0.0634229 0.153117i −0.00392578 0.00947768i
\(262\) −1.30776 25.4328i −0.0807939 1.57124i
\(263\) 0.211270 0.211270i 0.0130275 0.0130275i −0.700563 0.713591i \(-0.747068\pi\)
0.713591 + 0.700563i \(0.247068\pi\)
\(264\) 1.25132 + 0.304328i 0.0770133 + 0.0187301i
\(265\) 28.3707 + 28.3707i 1.74280 + 1.74280i
\(266\) 3.50242 3.88213i 0.214747 0.238029i
\(267\) 11.2429 4.65695i 0.688053 0.285001i
\(268\) 10.2725 5.55132i 0.627490 0.339101i
\(269\) 9.18492 22.1744i 0.560014 1.35199i −0.349740 0.936847i \(-0.613730\pi\)
0.909754 0.415148i \(-0.136270\pi\)
\(270\) −4.72912 1.67991i −0.287805 0.102236i
\(271\) 15.5563i 0.944979i 0.881336 + 0.472489i \(0.156644\pi\)
−0.881336 + 0.472489i \(0.843356\pi\)
\(272\) 18.6186 3.88092i 1.12892 0.235316i
\(273\) 18.2673i 1.10559i
\(274\) −2.79556 + 7.86979i −0.168886 + 0.475431i
\(275\) −1.32304 + 3.19410i −0.0797824 + 0.192612i
\(276\) −2.00330 0.597699i −0.120584 0.0359772i
\(277\) 24.1714 10.0121i 1.45232 0.601570i 0.489570 0.871964i \(-0.337154\pi\)
0.962750 + 0.270394i \(0.0871539\pi\)
\(278\) −19.5148 17.6061i −1.17042 1.05594i
\(279\) 6.06314 + 6.06314i 0.362991 + 0.362991i
\(280\) −28.4813 20.8217i −1.70208 1.24433i
\(281\) 18.5324 18.5324i 1.10555 1.10555i 0.111820 0.993729i \(-0.464332\pi\)
0.993729 0.111820i \(-0.0356679\pi\)
\(282\) 1.01076 0.0519738i 0.0601900 0.00309499i
\(283\) −3.60189 8.69574i −0.214110 0.516908i 0.779937 0.625858i \(-0.215251\pi\)
−0.994047 + 0.108950i \(0.965251\pi\)
\(284\) −2.39651 23.2415i −0.142207 1.37913i
\(285\) 3.44851 + 1.42842i 0.204272 + 0.0846123i
\(286\) 3.02177 1.43766i 0.178681 0.0850106i
\(287\) −6.92186 −0.408584
\(288\) −5.60476 0.765974i −0.330263 0.0451354i
\(289\) −5.60720 −0.329836
\(290\) 0.751076 0.357338i 0.0441047 0.0209836i
\(291\) −9.43437 3.90784i −0.553052 0.229082i
\(292\) −12.3050 + 1.26881i −0.720095 + 0.0742514i
\(293\) 8.32183 + 20.0907i 0.486167 + 1.17371i 0.956634 + 0.291293i \(0.0940854\pi\)
−0.470467 + 0.882417i \(0.655915\pi\)
\(294\) −7.56314 + 0.388899i −0.441091 + 0.0226811i
\(295\) 13.7417 13.7417i 0.800072 0.800072i
\(296\) −3.03610 19.5427i −0.176470 1.13590i
\(297\) 0.321948 + 0.321948i 0.0186813 + 0.0186813i
\(298\) −8.70145 7.85035i −0.504061 0.454759i
\(299\) −5.01882 + 2.07886i −0.290246 + 0.120224i
\(300\) 4.34192 14.5527i 0.250681 0.840203i
\(301\) 4.14775 10.0136i 0.239072 0.577172i
\(302\) −5.58768 + 15.7299i −0.321535 + 0.905152i
\(303\) 5.02268i 0.288545i
\(304\) 4.13382 + 0.783013i 0.237091 + 0.0449089i
\(305\) 10.8012i 0.618476i
\(306\) 6.33626 + 2.25081i 0.362220 + 0.128670i
\(307\) 11.7750 28.4274i 0.672036 1.62244i −0.106111 0.994354i \(-0.533840\pi\)
0.778146 0.628083i \(-0.216160\pi\)
\(308\) 1.52173 + 2.81588i 0.0867084 + 0.160450i
\(309\) −3.91507 + 1.62168i −0.222721 + 0.0922539i
\(310\) −28.8259 + 31.9511i −1.63720 + 1.81470i
\(311\) −1.08506 1.08506i −0.0615284 0.0615284i 0.675673 0.737201i \(-0.263853\pi\)
−0.737201 + 0.675673i \(0.763853\pi\)
\(312\) −12.5559 + 7.64333i −0.710837 + 0.432718i
\(313\) 3.44537 3.44537i 0.194744 0.194744i −0.602998 0.797742i \(-0.706027\pi\)
0.797742 + 0.602998i \(0.206027\pi\)
\(314\) −0.0889910 1.73066i −0.00502205 0.0976666i
\(315\) −4.77344 11.5241i −0.268953 0.649310i
\(316\) 14.6948 + 11.9476i 0.826649 + 0.672108i
\(317\) 1.87234 + 0.775548i 0.105161 + 0.0435591i 0.434644 0.900603i \(-0.356874\pi\)
−0.329483 + 0.944162i \(0.606874\pi\)
\(318\) 6.86937 + 14.4385i 0.385215 + 0.809672i
\(319\) −0.0754585 −0.00422486
\(320\) 2.39461 28.2885i 0.133863 1.58137i
\(321\) −0.454998 −0.0253955
\(322\) −2.23232 4.69204i −0.124402 0.261477i
\(323\) −4.62045 1.91385i −0.257089 0.106490i
\(324\) −1.55181 1.26170i −0.0862117 0.0700944i
\(325\) −15.1017 36.4587i −0.837690 2.02236i
\(326\) 0.984439 + 19.1449i 0.0545230 + 1.06034i
\(327\) −3.65817 + 3.65817i −0.202297 + 0.202297i
\(328\) −2.89621 4.75768i −0.159917 0.262699i
\(329\) 1.77875 + 1.77875i 0.0980654 + 0.0980654i
\(330\) −1.53064 + 1.69658i −0.0842587 + 0.0933937i
\(331\) −27.3713 + 11.3376i −1.50446 + 0.623168i −0.974406 0.224795i \(-0.927829\pi\)
−0.530055 + 0.847963i \(0.677829\pi\)
\(332\) 7.08625 + 13.1128i 0.388908 + 0.719656i
\(333\) 2.67583 6.46002i 0.146634 0.354007i
\(334\) 12.4495 + 4.42238i 0.681204 + 0.241982i
\(335\) 20.7182i 1.13196i
\(336\) −7.91790 11.6184i −0.431957 0.633835i
\(337\) 8.28014i 0.451048i −0.974238 0.225524i \(-0.927591\pi\)
0.974238 0.225524i \(-0.0724094\pi\)
\(338\) −6.63160 + 18.6686i −0.360712 + 1.01544i
\(339\) 2.53909 6.12990i 0.137904 0.332930i
\(340\) −9.64812 + 32.3375i −0.523243 + 1.75375i
\(341\) 3.60686 1.49401i 0.195322 0.0809052i
\(342\) 1.10446 + 0.996429i 0.0597222 + 0.0538807i
\(343\) 4.08855 + 4.08855i 0.220761 + 0.220761i
\(344\) 8.61822 1.33890i 0.464663 0.0721889i
\(345\) 2.62294 2.62294i 0.141214 0.141214i
\(346\) 26.3654 1.35572i 1.41741 0.0728839i
\(347\) 7.72315 + 18.6453i 0.414601 + 1.00093i 0.983886 + 0.178795i \(0.0572198\pi\)
−0.569286 + 0.822140i \(0.692780\pi\)
\(348\) 0.329716 0.0339981i 0.0176746 0.00182249i
\(349\) −1.13179 0.468804i −0.0605835 0.0250945i 0.352186 0.935930i \(-0.385438\pi\)
−0.412769 + 0.910836i \(0.635438\pi\)
\(350\) 34.0848 16.2164i 1.82191 0.866805i
\(351\) −5.19700 −0.277396
\(352\) −1.29876 + 2.22416i −0.0692242 + 0.118548i
\(353\) −11.9551 −0.636306 −0.318153 0.948039i \(-0.603063\pi\)
−0.318153 + 0.948039i \(0.603063\pi\)
\(354\) 6.99345 3.32726i 0.371698 0.176842i
\(355\) 38.3016 + 15.8650i 2.03284 + 0.842028i
\(356\) 2.49638 + 24.2100i 0.132308 + 1.28313i
\(357\) 6.39565 + 15.4405i 0.338494 + 0.817196i
\(358\) −14.0488 + 0.722393i −0.742501 + 0.0381797i
\(359\) 5.02082 5.02082i 0.264989 0.264989i −0.562088 0.827077i \(-0.690002\pi\)
0.827077 + 0.562088i \(0.190002\pi\)
\(360\) 5.92372 8.10285i 0.312207 0.427058i
\(361\) 12.6527 + 12.6527i 0.665933 + 0.665933i
\(362\) 6.31888 + 5.70082i 0.332113 + 0.299629i
\(363\) −9.97115 + 4.13019i −0.523350 + 0.216779i
\(364\) −35.0096 10.4454i −1.83500 0.547486i
\(365\) 8.39959 20.2784i 0.439655 1.06142i
\(366\) −1.44085 + 4.05614i −0.0753144 + 0.212018i
\(367\) 23.7760i 1.24109i 0.784169 + 0.620547i \(0.213090\pi\)
−0.784169 + 0.620547i \(0.786910\pi\)
\(368\) 2.29100 3.49759i 0.119427 0.182324i
\(369\) 1.96925i 0.102515i
\(370\) 33.0673 + 11.7464i 1.71909 + 0.610666i
\(371\) −15.2082 + 36.7157i −0.789568 + 1.90619i
\(372\) −15.0871 + 8.15317i −0.782228 + 0.422722i
\(373\) 3.85917 1.59852i 0.199820 0.0827683i −0.280529 0.959846i \(-0.590510\pi\)
0.480349 + 0.877077i \(0.340510\pi\)
\(374\) 2.05081 2.27315i 0.106045 0.117542i
\(375\) 6.50749 + 6.50749i 0.336045 + 0.336045i
\(376\) −0.478352 + 1.96686i −0.0246691 + 0.101433i
\(377\) 0.609039 0.609039i 0.0313671 0.0313671i
\(378\) −0.255269 4.96436i −0.0131296 0.255339i
\(379\) −3.43755 8.29899i −0.176575 0.426290i 0.810669 0.585505i \(-0.199104\pi\)
−0.987244 + 0.159215i \(0.949104\pi\)
\(380\) −4.70947 + 5.79235i −0.241591 + 0.297141i
\(381\) −17.7052 7.33372i −0.907063 0.375718i
\(382\) −3.49470 7.34539i −0.178804 0.375823i
\(383\) −9.61765 −0.491439 −0.245720 0.969341i \(-0.579024\pi\)
−0.245720 + 0.969341i \(0.579024\pi\)
\(384\) 4.67284 10.3036i 0.238460 0.525804i
\(385\) −5.67928 −0.289443
\(386\) 1.23276 + 2.59110i 0.0627460 + 0.131884i
\(387\) 2.84883 + 1.18002i 0.144814 + 0.0599840i
\(388\) 12.8841 15.8466i 0.654090 0.804489i
\(389\) −11.3406 27.3786i −0.574991 1.38815i −0.897260 0.441503i \(-0.854445\pi\)
0.322269 0.946648i \(-0.395555\pi\)
\(390\) −1.33937 26.0474i −0.0678216 1.31896i
\(391\) −3.51432 + 3.51432i −0.177727 + 0.177727i
\(392\) 3.57932 14.7173i 0.180783 0.743334i
\(393\) 12.7332 + 12.7332i 0.642305 + 0.642305i
\(394\) 8.78527 9.73773i 0.442595 0.490580i
\(395\) −31.0465 + 12.8599i −1.56212 + 0.647050i
\(396\) −0.801112 + 0.432927i −0.0402574 + 0.0217554i
\(397\) 0.283457 0.684326i 0.0142263 0.0343453i −0.916607 0.399790i \(-0.869083\pi\)
0.930833 + 0.365445i \(0.119083\pi\)
\(398\) −24.0209 8.53287i −1.20406 0.427714i
\(399\) 3.69715i 0.185089i
\(400\) 25.4079 + 16.6427i 1.27039 + 0.832135i
\(401\) 4.48635i 0.224038i 0.993706 + 0.112019i \(0.0357317\pi\)
−0.993706 + 0.112019i \(0.964268\pi\)
\(402\) −2.76375 + 7.78023i −0.137843 + 0.388043i
\(403\) −17.0532 + 41.1700i −0.849480 + 2.05083i
\(404\) 9.62605 + 2.87200i 0.478914 + 0.142887i
\(405\) 3.27858 1.35803i 0.162914 0.0674811i
\(406\) 0.611690 + 0.551860i 0.0303577 + 0.0273883i
\(407\) −2.25115 2.25115i −0.111585 0.111585i
\(408\) −7.93684 + 10.8565i −0.392932 + 0.537478i
\(409\) −15.2251 + 15.2251i −0.752833 + 0.752833i −0.975007 0.222174i \(-0.928685\pi\)
0.222174 + 0.975007i \(0.428685\pi\)
\(410\) 9.86991 0.507514i 0.487440 0.0250643i
\(411\) −2.25992 5.45593i −0.111474 0.269121i
\(412\) −0.869306 8.43059i −0.0428276 0.415345i
\(413\) 17.7837 + 7.36624i 0.875078 + 0.362469i
\(414\) 1.33487 0.635089i 0.0656055 0.0312129i
\(415\) −26.4468 −1.29822
\(416\) −7.46903 28.4341i −0.366199 1.39410i
\(417\) 18.5850 0.910111
\(418\) 0.611581 0.290970i 0.0299134 0.0142318i
\(419\) −13.2128 5.47292i −0.645487 0.267369i 0.0358301 0.999358i \(-0.488592\pi\)
−0.681317 + 0.731988i \(0.738592\pi\)
\(420\) 24.8156 2.55882i 1.21088 0.124858i
\(421\) 5.77775 + 13.9487i 0.281590 + 0.679819i 0.999873 0.0159320i \(-0.00507152\pi\)
−0.718283 + 0.695751i \(0.755072\pi\)
\(422\) 31.3438 1.61171i 1.52579 0.0784567i
\(423\) −0.506049 + 0.506049i −0.0246049 + 0.0246049i
\(424\) −31.5996 + 4.90923i −1.53461 + 0.238413i
\(425\) −25.5294 25.5294i −1.23836 1.23836i
\(426\) 12.2669 + 11.0670i 0.594332 + 0.536200i
\(427\) −9.88415 + 4.09415i −0.478328 + 0.198130i
\(428\) 0.260171 0.872012i 0.0125758 0.0421503i
\(429\) −0.905512 + 2.18610i −0.0437185 + 0.105546i
\(430\) −5.18010 + 14.5825i −0.249806 + 0.703230i
\(431\) 30.9700i 1.49177i −0.666073 0.745886i \(-0.732026\pi\)
0.666073 0.745886i \(-0.267974\pi\)
\(432\) 3.30540 2.25262i 0.159031 0.108379i
\(433\) 38.8143i 1.86529i 0.360790 + 0.932647i \(0.382507\pi\)
−0.360790 + 0.932647i \(0.617493\pi\)
\(434\) −40.1647 14.2676i −1.92797 0.684866i
\(435\) −0.225070 + 0.543366i −0.0107913 + 0.0260524i
\(436\) −4.91918 9.10272i −0.235586 0.435941i
\(437\) −1.01577 + 0.420745i −0.0485907 + 0.0201269i
\(438\) 5.85934 6.49458i 0.279970 0.310323i
\(439\) −4.15330 4.15330i −0.198226 0.198226i 0.601013 0.799239i \(-0.294764\pi\)
−0.799239 + 0.601013i \(0.794764\pi\)
\(440\) −2.37630 3.90361i −0.113286 0.186097i
\(441\) 3.78657 3.78657i 0.180313 0.180313i
\(442\) 1.79454 + 34.8994i 0.0853576 + 1.66000i
\(443\) −2.26978 5.47973i −0.107840 0.260350i 0.860742 0.509041i \(-0.170000\pi\)
−0.968583 + 0.248691i \(0.920000\pi\)
\(444\) 10.8507 + 8.82215i 0.514950 + 0.418681i
\(445\) −39.8977 16.5262i −1.89133 0.783415i
\(446\) −1.17791 2.47581i −0.0557755 0.117233i
\(447\) 8.28683 0.391954
\(448\) 26.7944 8.53132i 1.26591 0.403067i
\(449\) 7.31556 0.345243 0.172621 0.984988i \(-0.444776\pi\)
0.172621 + 0.984988i \(0.444776\pi\)
\(450\) 4.61354 + 9.69704i 0.217484 + 0.457123i
\(451\) −0.828358 0.343117i −0.0390058 0.0161567i
\(452\) 10.2962 + 8.37132i 0.484292 + 0.393754i
\(453\) −4.51705 10.9051i −0.212230 0.512367i
\(454\) −1.56058 30.3494i −0.0732415 1.42437i
\(455\) 45.8385 45.8385i 2.14894 2.14894i
\(456\) −2.54121 + 1.54695i −0.119003 + 0.0724424i
\(457\) 1.80714 + 1.80714i 0.0845343 + 0.0845343i 0.748110 0.663575i \(-0.230962\pi\)
−0.663575 + 0.748110i \(0.730962\pi\)
\(458\) 22.8059 25.2784i 1.06565 1.18118i
\(459\) −4.39277 + 1.81955i −0.205037 + 0.0849291i
\(460\) 3.52710 + 6.52672i 0.164452 + 0.304310i
\(461\) 5.44672 13.1495i 0.253679 0.612436i −0.744816 0.667269i \(-0.767463\pi\)
0.998495 + 0.0548340i \(0.0174629\pi\)
\(462\) −2.13271 0.757598i −0.0992229 0.0352467i
\(463\) 28.6674i 1.33229i −0.745824 0.666143i \(-0.767944\pi\)
0.745824 0.666143i \(-0.232056\pi\)
\(464\) −0.123376 + 0.651347i −0.00572758 + 0.0302380i
\(465\) 30.4287i 1.41110i
\(466\) 5.06429 14.2565i 0.234599 0.660419i
\(467\) −0.0184119 + 0.0444502i −0.000852000 + 0.00205691i −0.924305 0.381655i \(-0.875354\pi\)
0.923453 + 0.383712i \(0.125354\pi\)
\(468\) 2.97168 9.96015i 0.137366 0.460408i
\(469\) −18.9592 + 7.85315i −0.875454 + 0.362625i
\(470\) −2.66674 2.40590i −0.123008 0.110976i
\(471\) 0.866471 + 0.866471i 0.0399249 + 0.0399249i
\(472\) 2.37784 + 15.3056i 0.109449 + 0.704498i
\(473\) 0.992745 0.992745i 0.0456465 0.0456465i
\(474\) −13.3742 + 0.687706i −0.614298 + 0.0315874i
\(475\) −3.05645 7.37893i −0.140240 0.338569i
\(476\) −33.2490 + 3.42841i −1.52396 + 0.157141i
\(477\) −10.4455 4.32668i −0.478268 0.198105i
\(478\) −26.9017 + 12.7989i −1.23045 + 0.585409i
\(479\) 8.64155 0.394843 0.197421 0.980319i \(-0.436743\pi\)
0.197421 + 0.980319i \(0.436743\pi\)
\(480\) 12.1420 + 15.9862i 0.554205 + 0.729666i
\(481\) 36.3389 1.65691
\(482\) −30.8990 + 14.7007i −1.40741 + 0.669600i
\(483\) 3.39446 + 1.40603i 0.154453 + 0.0639766i
\(484\) −2.21400 21.4716i −0.100637 0.975980i
\(485\) 13.8678 + 33.4798i 0.629704 + 1.52024i
\(486\) 1.41235 0.0726234i 0.0640654 0.00329427i
\(487\) 2.15820 2.15820i 0.0977973 0.0977973i −0.656515 0.754313i \(-0.727970\pi\)
0.754313 + 0.656515i \(0.227970\pi\)
\(488\) −6.94977 5.08074i −0.314601 0.229994i
\(489\) −9.58511 9.58511i −0.433454 0.433454i
\(490\) 19.9542 + 18.0024i 0.901438 + 0.813267i
\(491\) 24.4583 10.1310i 1.10379 0.457204i 0.244994 0.969525i \(-0.421214\pi\)
0.858794 + 0.512321i \(0.171214\pi\)
\(492\) 3.77410 + 1.12603i 0.170150 + 0.0507654i
\(493\) 0.301557 0.728024i 0.0135815 0.0327885i
\(494\) −2.58771 + 7.28465i −0.116426 + 0.327752i
\(495\) 1.61574i 0.0726221i
\(496\) −6.99881 33.5766i −0.314256 1.50764i
\(497\) 41.0632i 1.84193i
\(498\) −9.93144 3.52792i −0.445038 0.158090i
\(499\) 4.98970 12.0462i 0.223370 0.539263i −0.771974 0.635655i \(-0.780730\pi\)
0.995343 + 0.0963921i \(0.0307303\pi\)
\(500\) −16.1927 + 8.75068i −0.724161 + 0.391343i
\(501\) −8.63089 + 3.57503i −0.385600 + 0.159721i
\(502\) 0.175086 0.194068i 0.00781446 0.00866167i
\(503\) −7.59295 7.59295i −0.338553 0.338553i 0.517270 0.855823i \(-0.326948\pi\)
−0.855823 + 0.517270i \(0.826948\pi\)
\(504\) 9.66024 + 2.34942i 0.430301 + 0.104652i
\(505\) −12.6035 + 12.6035i −0.560848 + 0.560848i
\(506\) −0.0345630 0.672165i −0.00153651 0.0298814i
\(507\) −5.36096 12.9425i −0.238088 0.574796i
\(508\) 24.1791 29.7388i 1.07278 1.31945i
\(509\) 12.9910 + 5.38103i 0.575814 + 0.238510i 0.651534 0.758619i \(-0.274126\pi\)
−0.0757202 + 0.997129i \(0.524126\pi\)
\(510\) −10.2517 21.5477i −0.453952 0.954148i
\(511\) 21.7405 0.961743
\(512\) 17.0751 + 14.8472i 0.754620 + 0.656162i
\(513\) −1.05183 −0.0464395
\(514\) 18.0730 + 37.9870i 0.797165 + 1.67553i
\(515\) 13.8934 + 5.75485i 0.612218 + 0.253589i
\(516\) −3.89052 + 4.78509i −0.171270 + 0.210652i
\(517\) 0.124695 + 0.301040i 0.00548407 + 0.0132397i
\(518\) 1.78491 + 34.7122i 0.0784245 + 1.52516i
\(519\) −13.2001 + 13.2001i −0.579421 + 0.579421i
\(520\) 50.6862 + 12.3272i 2.22274 + 0.540582i
\(521\) 17.0333 + 17.0333i 0.746242 + 0.746242i 0.973771 0.227529i \(-0.0730647\pi\)
−0.227529 + 0.973771i \(0.573065\pi\)
\(522\) −0.157003 + 0.174024i −0.00687182 + 0.00761683i
\(523\) 38.4247 15.9160i 1.68020 0.695960i 0.680860 0.732414i \(-0.261606\pi\)
0.999335 + 0.0364542i \(0.0116063\pi\)
\(524\) −31.6843 + 17.1225i −1.38414 + 0.747998i
\(525\) −10.2139 + 24.6586i −0.445773 + 1.07619i
\(526\) −0.398165 0.141439i −0.0173608 0.00616703i
\(527\) 40.7696i 1.77595i
\(528\) −0.371632 1.78289i −0.0161732 0.0775905i
\(529\) 21.9074i 0.952495i
\(530\) 18.9934 53.4682i 0.825019 2.32251i
\(531\) −2.09568 + 5.05941i −0.0909447 + 0.219560i
\(532\) −7.08566 2.11406i −0.307202 0.0916559i
\(533\) 9.45518 3.91646i 0.409549 0.169641i
\(534\) −12.7781 11.5282i −0.552961 0.498875i
\(535\) 1.14173 + 1.14173i 0.0493615 + 0.0493615i
\(536\) −13.3306 9.74556i −0.575795 0.420944i
\(537\) 7.03367 7.03367i 0.303525 0.303525i
\(538\) −33.8983 + 1.74306i −1.46146 + 0.0751487i
\(539\) −0.933042 2.25256i −0.0401890 0.0970248i
\(540\) 0.727979 + 7.05998i 0.0313272 + 0.303813i
\(541\) −8.78427 3.63857i −0.377665 0.156434i 0.185772 0.982593i \(-0.440521\pi\)
−0.563437 + 0.826159i \(0.690521\pi\)
\(542\) 19.8661 9.45166i 0.853324 0.405984i
\(543\) −6.01779 −0.258248
\(544\) −16.2684 21.4189i −0.697501 0.918329i
\(545\) 18.3590 0.786414
\(546\) 23.3282 11.0988i 0.998356 0.474985i
\(547\) 3.07217 + 1.27253i 0.131357 + 0.0544097i 0.447393 0.894337i \(-0.352352\pi\)
−0.316037 + 0.948747i \(0.602352\pi\)
\(548\) 11.7486 1.21144i 0.501876 0.0517501i
\(549\) −1.16478 2.81202i −0.0497114 0.120014i
\(550\) 4.88287 0.251079i 0.208206 0.0107060i
\(551\) 0.123264 0.123264i 0.00525124 0.00525124i
\(552\) 0.453870 + 2.92146i 0.0193180 + 0.124345i
\(553\) −23.5360 23.5360i −1.00085 1.00085i
\(554\) −27.4720 24.7849i −1.16717 1.05301i
\(555\) −22.9247 + 9.49573i −0.973100 + 0.403071i
\(556\) −10.6270 + 35.6184i −0.450686 + 1.51056i
\(557\) 0.215669 0.520670i 0.00913817 0.0220615i −0.919245 0.393687i \(-0.871199\pi\)
0.928383 + 0.371625i \(0.121199\pi\)
\(558\) 4.05909 11.4267i 0.171835 0.483733i
\(559\) 16.0252i 0.677795i
\(560\) −9.28571 + 49.0227i −0.392393 + 2.07159i
\(561\) 2.16483i 0.0913994i
\(562\) −34.9265 12.4069i −1.47329 0.523352i
\(563\) 11.9538 28.8591i 0.503793 1.21626i −0.443610 0.896220i \(-0.646302\pi\)
0.947403 0.320044i \(-0.103698\pi\)
\(564\) −0.680489 1.25921i −0.0286538 0.0530224i
\(565\) −21.7532 + 9.01048i −0.915165 + 0.379074i
\(566\) −8.91644 + 9.88312i −0.374786 + 0.415419i
\(567\) 2.48546 + 2.48546i 0.104379 + 0.104379i
\(568\) −28.2244 + 17.1815i −1.18427 + 0.720918i
\(569\) −22.2286 + 22.2286i −0.931873 + 0.931873i −0.997823 0.0659498i \(-0.978992\pi\)
0.0659498 + 0.997823i \(0.478992\pi\)
\(570\) −0.271077 5.27178i −0.0113542 0.220811i
\(571\) −2.84886 6.87776i −0.119221 0.287825i 0.852991 0.521925i \(-0.174786\pi\)
−0.972213 + 0.234099i \(0.924786\pi\)
\(572\) −3.67192 2.98545i −0.153531 0.124828i
\(573\) 5.31402 + 2.20114i 0.221996 + 0.0919539i
\(574\) 4.20557 + 8.83954i 0.175537 + 0.368955i
\(575\) −7.93717 −0.331003
\(576\) 2.42714 + 7.62293i 0.101131 + 0.317622i
\(577\) −31.1728 −1.29774 −0.648871 0.760899i \(-0.724758\pi\)
−0.648871 + 0.760899i \(0.724758\pi\)
\(578\) 3.40681 + 7.16066i 0.141705 + 0.297844i
\(579\) −1.87453 0.776457i −0.0779029 0.0322685i
\(580\) −0.912674 0.742050i −0.0378967 0.0308119i
\(581\) −10.0245 24.2013i −0.415887 1.00404i
\(582\) 0.741607 + 14.4224i 0.0307406 + 0.597830i
\(583\) −3.64000 + 3.64000i −0.150754 + 0.150754i
\(584\) 9.09657 + 14.9432i 0.376419 + 0.618352i
\(585\) 13.0409 + 13.0409i 0.539176 + 0.539176i
\(586\) 20.6006 22.8340i 0.851003 0.943265i
\(587\) −13.5567 + 5.61536i −0.559544 + 0.231771i −0.644487 0.764615i \(-0.722929\pi\)
0.0849433 + 0.996386i \(0.472929\pi\)
\(588\) 5.09183 + 9.42220i 0.209984 + 0.388565i
\(589\) −3.45142 + 8.33247i −0.142213 + 0.343334i
\(590\) −25.8979 9.19965i −1.06620 0.378744i
\(591\) 9.27373i 0.381470i
\(592\) −23.1123 + 15.7509i −0.949909 + 0.647360i
\(593\) 20.0872i 0.824883i −0.910984 0.412442i \(-0.864676\pi\)
0.910984 0.412442i \(-0.135324\pi\)
\(594\) 0.215535 0.606752i 0.00884350 0.0248953i
\(595\) 22.6963 54.7937i 0.930457 2.24632i
\(596\) −4.73847 + 15.8819i −0.194095 + 0.650546i
\(597\) 16.6531 6.89793i 0.681565 0.282313i
\(598\) 5.70413 + 5.14620i 0.233259 + 0.210444i
\(599\) 22.9392 + 22.9392i 0.937271 + 0.937271i 0.998145 0.0608749i \(-0.0193891\pi\)
−0.0608749 + 0.998145i \(0.519389\pi\)
\(600\) −21.2226 + 3.29709i −0.866409 + 0.134603i
\(601\) 19.0481 19.0481i 0.776990 0.776990i −0.202328 0.979318i \(-0.564851\pi\)
0.979318 + 0.202328i \(0.0648507\pi\)
\(602\) −15.3079 + 0.787136i −0.623902 + 0.0320813i
\(603\) −2.23420 5.39384i −0.0909837 0.219654i
\(604\) 23.4827 2.42138i 0.955499 0.0985247i
\(605\) 35.3847 + 14.6568i 1.43859 + 0.595885i
\(606\) −6.41420 + 3.05167i −0.260559 + 0.123965i
\(607\) 39.8682 1.61820 0.809100 0.587672i \(-0.199955\pi\)
0.809100 + 0.587672i \(0.199955\pi\)
\(608\) −1.51167 5.75482i −0.0613063 0.233389i
\(609\) −0.582543 −0.0236059
\(610\) 13.7937 6.56258i 0.558489 0.265711i
\(611\) −3.43618 1.42331i −0.139013 0.0575810i
\(612\) −0.975375 9.45925i −0.0394272 0.382368i
\(613\) 7.28252 + 17.5816i 0.294138 + 0.710113i 0.999998 + 0.00176143i \(0.000560680\pi\)
−0.705860 + 0.708351i \(0.749439\pi\)
\(614\) −43.4574 + 2.23459i −1.75380 + 0.0901809i
\(615\) −4.94147 + 4.94147i −0.199259 + 0.199259i
\(616\) 2.67145 3.65418i 0.107636 0.147231i
\(617\) −17.7361 17.7361i −0.714027 0.714027i 0.253348 0.967375i \(-0.418468\pi\)
−0.967375 + 0.253348i \(0.918468\pi\)
\(618\) 4.44967 + 4.01444i 0.178992 + 0.161484i
\(619\) 7.84831 3.25088i 0.315450 0.130664i −0.219340 0.975648i \(-0.570391\pi\)
0.534790 + 0.844985i \(0.320391\pi\)
\(620\) 58.3171 + 17.3993i 2.34207 + 0.698773i
\(621\) −0.400012 + 0.965714i −0.0160519 + 0.0387528i
\(622\) −0.726418 + 2.04494i −0.0291267 + 0.0819946i
\(623\) 42.7744i 1.71372i
\(624\) 17.3896 + 11.3906i 0.696140 + 0.455987i
\(625\) 5.30798i 0.212319i
\(626\) −6.49324 2.30657i −0.259522 0.0921893i
\(627\) −0.183268 + 0.442448i −0.00731902 + 0.0176697i
\(628\) −2.15606 + 1.16515i −0.0860362 + 0.0464947i
\(629\) 30.7155 12.7228i 1.22471 0.507290i
\(630\) −11.8166 + 13.0977i −0.470784 + 0.521825i
\(631\) 29.7910 + 29.7910i 1.18596 + 1.18596i 0.978174 + 0.207785i \(0.0666256\pi\)
0.207785 + 0.978174i \(0.433374\pi\)
\(632\) 6.32946 26.0251i 0.251772 1.03522i
\(633\) −15.6926 + 15.6926i −0.623725 + 0.623725i
\(634\) −0.147179 2.86227i −0.00584522 0.113675i
\(635\) 26.0252 + 62.8305i 1.03278 + 2.49335i
\(636\) 14.2650 17.5450i 0.565644 0.695705i
\(637\) 25.7116 + 10.6501i 1.01873 + 0.421972i
\(638\) 0.0458469 + 0.0963640i 0.00181509 + 0.00381509i
\(639\) −11.6824 −0.462147
\(640\) −37.5807 + 14.1294i −1.48551 + 0.558514i
\(641\) −25.6481 −1.01304 −0.506520 0.862228i \(-0.669068\pi\)
−0.506520 + 0.862228i \(0.669068\pi\)
\(642\) 0.276447 + 0.581054i 0.0109105 + 0.0229324i
\(643\) −24.6616 10.2152i −0.972559 0.402847i −0.160895 0.986972i \(-0.551438\pi\)
−0.811664 + 0.584125i \(0.801438\pi\)
\(644\) −4.63565 + 5.70155i −0.182670 + 0.224673i
\(645\) −4.18756 10.1097i −0.164885 0.398068i
\(646\) 0.363200 + 7.06335i 0.0142899 + 0.277904i
\(647\) −33.8051 + 33.8051i −1.32902 + 1.32902i −0.422786 + 0.906230i \(0.638948\pi\)
−0.906230 + 0.422786i \(0.861052\pi\)
\(648\) −0.668405 + 2.74831i −0.0262574 + 0.107964i
\(649\) 1.76308 + 1.76308i 0.0692068 + 0.0692068i
\(650\) −37.3840 + 41.4370i −1.46632 + 1.62529i
\(651\) 27.8452 11.5338i 1.09134 0.452047i
\(652\) 23.8508 12.8892i 0.934071 0.504780i
\(653\) −12.1078 + 29.2307i −0.473813 + 1.14389i 0.488652 + 0.872479i \(0.337489\pi\)
−0.962465 + 0.271407i \(0.912511\pi\)
\(654\) 6.89428 + 2.44904i 0.269588 + 0.0957649i
\(655\) 63.9032i 2.49690i
\(656\) −4.31611 + 6.58926i −0.168516 + 0.257268i
\(657\) 6.18512i 0.241304i
\(658\) 1.19082 3.35227i 0.0464229 0.130685i
\(659\) −0.896470 + 2.16427i −0.0349215 + 0.0843080i −0.940378 0.340131i \(-0.889529\pi\)
0.905457 + 0.424439i \(0.139529\pi\)
\(660\) 3.09659 + 0.923891i 0.120535 + 0.0359624i
\(661\) −24.9607 + 10.3391i −0.970859 + 0.402143i −0.811032 0.585002i \(-0.801094\pi\)
−0.159827 + 0.987145i \(0.551094\pi\)
\(662\) 31.1088 + 28.0660i 1.20908 + 1.09082i
\(663\) −17.4728 17.4728i −0.678586 0.678586i
\(664\) 12.4402 17.0165i 0.482772 0.660368i
\(665\) 9.27732 9.27732i 0.359759 0.359759i
\(666\) −9.87552 + 0.507803i −0.382669 + 0.0196770i
\(667\) −0.0662948 0.160050i −0.00256695 0.00619715i
\(668\) −1.91641 18.5855i −0.0741482 0.719094i
\(669\) 1.79112 + 0.741907i 0.0692487 + 0.0286838i
\(670\) 26.4582 12.5879i 1.02217 0.486314i
\(671\) −1.38581 −0.0534986
\(672\) −10.0265 + 17.1706i −0.386781 + 0.662370i
\(673\) −29.0320 −1.11910 −0.559550 0.828797i \(-0.689026\pi\)
−0.559550 + 0.828797i \(0.689026\pi\)
\(674\) −10.5741 + 5.03083i −0.407300 + 0.193780i
\(675\) −7.01532 2.90584i −0.270020 0.111846i
\(676\) 27.8699 2.87376i 1.07192 0.110529i
\(677\) 4.97128 + 12.0017i 0.191062 + 0.461264i 0.990161 0.139936i \(-0.0446897\pi\)
−0.799099 + 0.601200i \(0.794690\pi\)
\(678\) −9.37086 + 0.481853i −0.359886 + 0.0185055i
\(679\) −25.3807 + 25.3807i −0.974023 + 0.974023i
\(680\) 47.1585 7.32642i 1.80845 0.280955i
\(681\) 15.1947 + 15.1947i 0.582264 + 0.582264i
\(682\) −4.09937 3.69840i −0.156973 0.141619i
\(683\) 31.6243 13.0992i 1.21007 0.501227i 0.315830 0.948816i \(-0.397717\pi\)
0.894239 + 0.447589i \(0.147717\pi\)
\(684\) 0.601443 2.01585i 0.0229968 0.0770780i
\(685\) −8.01980 + 19.3615i −0.306421 + 0.739765i
\(686\) 2.73716 7.70538i 0.104505 0.294193i
\(687\) 24.0739i 0.918478i
\(688\) −6.94608 10.1924i −0.264817 0.388581i
\(689\) 58.7582i 2.23851i
\(690\) −4.94326 1.75598i −0.188187 0.0668490i
\(691\) −4.38682 + 10.5907i −0.166883 + 0.402890i −0.985092 0.172031i \(-0.944967\pi\)
0.818209 + 0.574921i \(0.194967\pi\)
\(692\) −17.7503 32.8462i −0.674767 1.24862i
\(693\) 1.47856 0.612439i 0.0561658 0.0232646i
\(694\) 19.1186 21.1913i 0.725731 0.804412i
\(695\) −46.6356 46.6356i −1.76899 1.76899i
\(696\) −0.243745 0.400407i −0.00923914 0.0151774i
\(697\) 6.62079 6.62079i 0.250780 0.250780i
\(698\) 0.0889670 + 1.73019i 0.00336745 + 0.0654886i
\(699\) 4.09395 + 9.88366i 0.154847 + 0.373834i
\(700\) −41.4183 33.6752i −1.56547 1.27280i
\(701\) 1.31276 + 0.543761i 0.0495821 + 0.0205376i 0.407337 0.913278i \(-0.366458\pi\)
−0.357755 + 0.933816i \(0.616458\pi\)
\(702\) 3.15758 + 6.63682i 0.119175 + 0.250491i
\(703\) 7.35469 0.277387
\(704\) 3.62945 + 0.307232i 0.136790 + 0.0115792i
\(705\) 2.53967 0.0956496
\(706\) 7.26365 + 15.2672i 0.273371 + 0.574590i
\(707\) −16.3107 6.75611i −0.613427 0.254090i
\(708\) −8.49813 6.90941i −0.319379 0.259671i
\(709\) 2.19698 + 5.30398i 0.0825094 + 0.199195i 0.959750 0.280856i \(-0.0906182\pi\)
−0.877241 + 0.480051i \(0.840618\pi\)
\(710\) −3.01077 58.5521i −0.112992 2.19742i
\(711\) 6.69594 6.69594i 0.251117 0.251117i
\(712\) 29.4006 17.8975i 1.10183 0.670736i
\(713\) 6.33769 + 6.33769i 0.237348 + 0.237348i
\(714\) 15.8324 17.5488i 0.592511 0.656748i
\(715\) 7.75782 3.21340i 0.290126 0.120174i
\(716\) 9.45825 + 17.5020i 0.353471 + 0.654082i
\(717\) 8.06142 19.4620i 0.301059 0.726822i
\(718\) −9.46237 3.36129i −0.353132 0.125442i
\(719\) 7.05462i 0.263093i −0.991310 0.131547i \(-0.958006\pi\)
0.991310 0.131547i \(-0.0419943\pi\)
\(720\) −13.9468 2.64176i −0.519768 0.0984526i
\(721\) 14.8952i 0.554726i
\(722\) 8.47062 23.8456i 0.315244 0.887443i
\(723\) 9.25928 22.3539i 0.344356 0.831349i
\(724\) 3.44101 11.5332i 0.127884 0.428628i
\(725\) 1.16266 0.481591i 0.0431803 0.0178859i
\(726\) 11.3327 + 10.2242i 0.420596 + 0.379457i
\(727\) 6.68778 + 6.68778i 0.248036 + 0.248036i 0.820164 0.572128i \(-0.193882\pi\)
−0.572128 + 0.820164i \(0.693882\pi\)
\(728\) 7.93182 + 51.0553i 0.293973 + 1.89224i
\(729\) −0.707107 + 0.707107i −0.0261891 + 0.0261891i
\(730\) −30.9999 + 1.59402i −1.14736 + 0.0589975i
\(731\) 5.61067 + 13.5453i 0.207518 + 0.500993i
\(732\) 6.05530 0.624383i 0.223810 0.0230779i
\(733\) −1.39035 0.575901i −0.0513537 0.0212714i 0.356859 0.934158i \(-0.383848\pi\)
−0.408212 + 0.912887i \(0.633848\pi\)
\(734\) 30.3630 14.4457i 1.12072 0.533202i
\(735\) −19.0034 −0.700950
\(736\) −5.85855 0.800658i −0.215949 0.0295126i
\(737\) −2.65818 −0.0979152
\(738\) −2.51483 + 1.19647i −0.0925721 + 0.0440428i
\(739\) −4.78590 1.98239i −0.176052 0.0729233i 0.292916 0.956138i \(-0.405374\pi\)
−0.468969 + 0.883215i \(0.655374\pi\)
\(740\) −5.09023 49.3653i −0.187120 1.81471i
\(741\) −2.09189 5.05026i −0.0768474 0.185526i
\(742\) 56.1279 2.88612i 2.06052 0.105953i
\(743\) −5.78338 + 5.78338i −0.212172 + 0.212172i −0.805189 0.593018i \(-0.797936\pi\)
0.593018 + 0.805189i \(0.297936\pi\)
\(744\) 19.5785 + 14.3132i 0.717784 + 0.524748i
\(745\) −20.7943 20.7943i −0.761844 0.761844i
\(746\) −4.38613 3.95712i −0.160588 0.144880i
\(747\) 6.88522 2.85195i 0.251917 0.104347i
\(748\) −4.14894 1.23787i −0.151700 0.0452609i
\(749\) −0.612028 + 1.47757i −0.0223630 + 0.0539891i
\(750\) 4.35657 12.2642i 0.159079 0.447824i
\(751\) 16.4504i 0.600283i −0.953895 0.300141i \(-0.902966\pi\)
0.953895 0.300141i \(-0.0970338\pi\)
\(752\) 2.80241 0.584143i 0.102193 0.0213015i
\(753\) 0.184821i 0.00673524i
\(754\) −1.14781 0.407733i −0.0418007 0.0148488i
\(755\) −16.0297 + 38.6991i −0.583380 + 1.40840i
\(756\) −6.18463 + 3.34222i −0.224933 + 0.121555i
\(757\) −6.29845 + 2.60890i −0.228921 + 0.0948222i −0.494196 0.869351i \(-0.664537\pi\)
0.265275 + 0.964173i \(0.414537\pi\)
\(758\) −8.50962 + 9.43219i −0.309083 + 0.342593i
\(759\) 0.336527 + 0.336527i 0.0122151 + 0.0122151i
\(760\) 10.2585 + 2.49492i 0.372114 + 0.0905001i
\(761\) −8.75540 + 8.75540i −0.317383 + 0.317383i −0.847761 0.530378i \(-0.822050\pi\)
0.530378 + 0.847761i \(0.322050\pi\)
\(762\) 1.39175 + 27.0661i 0.0504178 + 0.980503i
\(763\) 6.95890 + 16.8003i 0.251929 + 0.608211i
\(764\) −7.25711 + 8.92579i −0.262553 + 0.322924i
\(765\) 15.5887 + 6.45704i 0.563610 + 0.233455i
\(766\) 5.84347 + 12.2822i 0.211133 + 0.443774i
\(767\) −28.4602 −1.02764
\(768\) −15.9973 + 0.292813i −0.577254 + 0.0105660i
\(769\) 31.9426 1.15188 0.575940 0.817492i \(-0.304636\pi\)
0.575940 + 0.817492i \(0.304636\pi\)
\(770\) 3.45060 + 7.25271i 0.124351 + 0.261369i
\(771\) −27.4817 11.3833i −0.989729 0.409959i
\(772\) 2.55996 3.14859i 0.0921351 0.113320i
\(773\) −11.4245 27.5812i −0.410911 0.992027i −0.984894 0.173159i \(-0.944602\pi\)
0.573983 0.818867i \(-0.305398\pi\)
\(774\) −0.223938 4.35505i −0.00804929 0.156539i
\(775\) −46.0394 + 46.0394i −1.65379 + 1.65379i
\(776\) −28.0649 6.82555i −1.00747 0.245023i
\(777\) −17.3790 17.3790i −0.623468 0.623468i
\(778\) −28.0735 + 31.1171i −1.00648 + 1.11560i
\(779\) 1.91365 0.792659i 0.0685636 0.0284000i
\(780\) −32.4500 + 17.5363i −1.16190 + 0.627899i
\(781\) −2.03550 + 4.91414i −0.0728360 + 0.175842i
\(782\) 6.62318 + 2.35273i 0.236844 + 0.0841336i
\(783\) 0.165732i 0.00592278i
\(784\) −20.9693 + 4.37091i −0.748905 + 0.156104i
\(785\) 4.34850i 0.155205i
\(786\) 8.52449 23.9973i 0.304058 0.855955i
\(787\) 4.33415 10.4636i 0.154496 0.372986i −0.827613 0.561299i \(-0.810302\pi\)
0.982109 + 0.188313i \(0.0603019\pi\)
\(788\) −17.7733 5.30278i −0.633146 0.188904i
\(789\) 0.276038 0.114338i 0.00982720 0.00407056i
\(790\) 35.2858 + 31.8344i 1.25541 + 1.13262i
\(791\) −16.4909 16.4909i −0.586349 0.586349i
\(792\) 1.03961 + 0.760021i 0.0369408 + 0.0270062i
\(793\) 11.1851 11.1851i 0.397195 0.397195i
\(794\) −1.04614 + 0.0537928i −0.0371261 + 0.00190903i
\(795\) 15.3541 + 37.0682i 0.544555 + 1.31467i
\(796\) 3.69766 + 35.8602i 0.131060 + 1.27103i
\(797\) −46.7451 19.3624i −1.65580 0.685853i −0.658050 0.752974i \(-0.728619\pi\)
−0.997745 + 0.0671211i \(0.978619\pi\)
\(798\) 4.72144 2.24631i 0.167137 0.0795184i
\(799\) −3.40276 −0.120381
\(800\) 5.81629 42.5588i 0.205637 1.50468i
\(801\) 12.1692 0.429978
\(802\) 5.72929 2.72581i 0.202308 0.0962516i
\(803\) 2.60174 + 1.07768i 0.0918136 + 0.0380304i
\(804\) 11.6149 1.19765i 0.409627 0.0422380i
\(805\) −4.98959 12.0459i −0.175860 0.424563i
\(806\) 62.9372 3.23625i 2.21687 0.113992i
\(807\) 16.9715 16.9715i 0.597426 0.597426i
\(808\) −2.18089 14.0379i −0.0767234 0.493851i
\(809\) −1.47101 1.47101i −0.0517179 0.0517179i 0.680775 0.732493i \(-0.261643\pi\)
−0.732493 + 0.680775i \(0.761643\pi\)
\(810\) −3.72626 3.36179i −0.130927 0.118121i
\(811\) −27.3097 + 11.3120i −0.958972 + 0.397219i −0.806596 0.591103i \(-0.798693\pi\)
−0.152376 + 0.988323i \(0.548693\pi\)
\(812\) 0.333102 1.11645i 0.0116896 0.0391799i
\(813\) −5.95314 + 14.3722i −0.208786 + 0.504054i
\(814\) −1.50708 + 4.24257i −0.0528231 + 0.148702i
\(815\) 48.1041i 1.68501i
\(816\) 18.6865 + 3.53954i 0.654160 + 0.123909i
\(817\) 3.24337i 0.113471i
\(818\) 28.6936 + 10.1927i 1.00325 + 0.356381i
\(819\) −6.99060 + 16.8768i −0.244271 + 0.589723i
\(820\) −6.64485 12.2960i −0.232048 0.429394i
\(821\) −2.95519 + 1.22408i −0.103137 + 0.0427207i −0.433655 0.901079i \(-0.642776\pi\)
0.330518 + 0.943800i \(0.392776\pi\)
\(822\) −5.59440 + 6.20092i −0.195127 + 0.216282i
\(823\) −11.2350 11.2350i −0.391626 0.391626i 0.483640 0.875267i \(-0.339314\pi\)
−0.875267 + 0.483640i \(0.839314\pi\)
\(824\) −10.2381 + 6.23238i −0.356661 + 0.217115i
\(825\) −2.44466 + 2.44466i −0.0851122 + 0.0851122i
\(826\) −1.39792 27.1862i −0.0486399 0.945928i
\(827\) −16.2758 39.2934i −0.565967 1.36636i −0.904928 0.425564i \(-0.860076\pi\)
0.338962 0.940800i \(-0.389924\pi\)
\(828\) −1.62208 1.31883i −0.0563711 0.0458325i
\(829\) 41.9981 + 17.3962i 1.45866 + 0.604195i 0.964240 0.265031i \(-0.0853821\pi\)
0.494416 + 0.869226i \(0.335382\pi\)
\(830\) 16.0685 + 33.7738i 0.557744 + 1.17230i
\(831\) 26.1629 0.907583
\(832\) −31.7737 + 26.8142i −1.10155 + 0.929615i
\(833\) 25.4615 0.882188
\(834\) −11.2918 23.7339i −0.391004 0.821838i
\(835\) 30.6285 + 12.6867i 1.05994 + 0.439043i
\(836\) −0.743166 0.604231i −0.0257029 0.0208978i
\(837\) 3.28135 + 7.92188i 0.113420 + 0.273820i
\(838\) 1.03862 + 20.1986i 0.0358785 + 0.697748i
\(839\) −36.5559 + 36.5559i −1.26205 + 1.26205i −0.311954 + 0.950097i \(0.600983\pi\)
−0.950097 + 0.311954i \(0.899017\pi\)
\(840\) −18.3452 30.1360i −0.632968 1.03979i
\(841\) −20.4867 20.4867i −0.706437 0.706437i
\(842\) 14.3028 15.8534i 0.492905 0.546344i
\(843\) 24.2137 10.0296i 0.833964 0.345439i
\(844\) −21.1020 39.0483i −0.726361 1.34410i
\(845\) −19.0245 + 45.9291i −0.654462 + 1.58001i
\(846\) 0.953712 + 0.338784i 0.0327893 + 0.0116476i
\(847\) 37.9360i 1.30350i
\(848\) 25.4685 + 37.3714i 0.874593 + 1.28334i
\(849\) 9.41220i 0.323026i
\(850\) −17.0912 + 48.1134i −0.586222 + 1.65027i
\(851\) 2.79699 6.75254i 0.0958796 0.231474i
\(852\) 6.68005 22.3895i 0.228855 0.767050i
\(853\) 37.5279 15.5446i 1.28493 0.532236i 0.367461 0.930039i \(-0.380227\pi\)
0.917471 + 0.397802i \(0.130227\pi\)
\(854\) 11.2338 + 10.1350i 0.384413 + 0.346813i
\(855\) 2.63937 + 2.63937i 0.0902647 + 0.0902647i
\(856\) −1.27167 + 0.197564i −0.0434649 + 0.00675260i
\(857\) −14.0544 + 14.0544i −0.480088 + 0.480088i −0.905160 0.425072i \(-0.860249\pi\)
0.425072 + 0.905160i \(0.360249\pi\)
\(858\) 3.34192 0.171843i 0.114091 0.00586661i
\(859\) 2.44981 + 5.91435i 0.0835863 + 0.201795i 0.960147 0.279497i \(-0.0901677\pi\)
−0.876560 + 0.481292i \(0.840168\pi\)
\(860\) 21.7698 2.24476i 0.742345 0.0765457i
\(861\) −6.39496 2.64888i −0.217940 0.0902736i
\(862\) −39.5502 + 18.8167i −1.34708 + 0.640899i
\(863\) 49.2474 1.67640 0.838201 0.545361i \(-0.183608\pi\)
0.838201 + 0.545361i \(0.183608\pi\)
\(864\) −4.88499 2.85251i −0.166191 0.0970445i
\(865\) 66.2465 2.25245
\(866\) 49.5676 23.5827i 1.68438 0.801372i
\(867\) −5.18038 2.14578i −0.175935 0.0728746i
\(868\) 6.18276 + 59.9608i 0.209857 + 2.03520i
\(869\) −1.64994 3.98330i −0.0559703 0.135124i
\(870\) 0.830651 0.0427124i 0.0281617 0.00144809i
\(871\) 21.4546 21.4546i 0.726962 0.726962i
\(872\) −8.63582 + 11.8126i −0.292446 + 0.400026i
\(873\) −7.22075 7.22075i −0.244385 0.244385i
\(874\) 1.15447 + 1.04155i 0.0390505 + 0.0352309i
\(875\) 29.8858 12.3791i 1.01033 0.418490i
\(876\) −11.8539 3.53669i −0.400506 0.119494i
\(877\) 3.14641 7.59609i 0.106247 0.256502i −0.861811 0.507229i \(-0.830670\pi\)
0.968058 + 0.250727i \(0.0806698\pi\)
\(878\) −2.78051 + 7.82741i −0.0938376 + 0.264162i
\(879\) 21.7460i 0.733474i
\(880\) −3.54130 + 5.40639i −0.119377 + 0.182249i
\(881\) 0.591830i 0.0199392i 0.999950 + 0.00996962i \(0.00317348\pi\)
−0.999950 + 0.00996962i \(0.996827\pi\)
\(882\) −7.13625 2.53499i −0.240290 0.0853576i
\(883\) −12.2234 + 29.5100i −0.411352 + 0.993091i 0.573424 + 0.819259i \(0.305615\pi\)
−0.984775 + 0.173832i \(0.944385\pi\)
\(884\) 43.4779 23.4958i 1.46232 0.790249i
\(885\) 17.9544 7.43695i 0.603530 0.249990i
\(886\) −5.61881 + 6.22797i −0.188768 + 0.209233i
\(887\) 19.3889 + 19.3889i 0.651017 + 0.651017i 0.953238 0.302221i \(-0.0977281\pi\)
−0.302221 + 0.953238i \(0.597728\pi\)
\(888\) 4.67367 19.2170i 0.156838 0.644879i
\(889\) −47.6312 + 47.6312i −1.59750 + 1.59750i
\(890\) 3.13624 + 60.9922i 0.105127 + 2.04446i
\(891\) 0.174237 + 0.420646i 0.00583717 + 0.0140922i
\(892\) −2.44605 + 3.00849i −0.0818999 + 0.100732i
\(893\) −0.695454 0.288067i −0.0232725 0.00963978i
\(894\) −5.03489 10.5827i −0.168392 0.353938i
\(895\) −35.2994 −1.17993
\(896\) −27.1745 29.0342i −0.907838 0.969965i
\(897\) −5.43233 −0.181380
\(898\) −4.44477 9.34232i −0.148324 0.311757i
\(899\) −1.31291 0.543825i −0.0437880 0.0181376i
\(900\) 9.58050 11.7834i 0.319350 0.392780i
\(901\) −20.5721 49.6654i −0.685356 1.65460i
\(902\) 0.0651147 + 1.26632i 0.00216808 + 0.0421639i
\(903\) 7.66404 7.66404i 0.255043 0.255043i
\(904\) 4.43484 18.2349i 0.147501 0.606485i
\(905\) 15.1005 + 15.1005i 0.501959 + 0.501959i
\(906\) −11.1819 + 12.3942i −0.371494 + 0.411769i
\(907\) −7.79114 + 3.22719i −0.258700 + 0.107157i −0.508264 0.861201i \(-0.669713\pi\)
0.249564 + 0.968358i \(0.419713\pi\)
\(908\) −37.8095 + 20.4325i −1.25475 + 0.678078i
\(909\) 1.92210 4.64035i 0.0637519 0.153911i
\(910\) −86.3883 30.6875i −2.86374 1.01728i
\(911\) 32.8156i 1.08723i −0.839335 0.543615i \(-0.817055\pi\)
0.839335 0.543615i \(-0.182945\pi\)
\(912\) 3.51950 + 2.30535i 0.116542 + 0.0763379i
\(913\) 3.39315i 0.112297i
\(914\) 1.20982 3.40577i 0.0400174 0.112653i
\(915\) −4.13345 + 9.97903i −0.136648 + 0.329896i
\(916\) −46.1381 13.7656i −1.52445 0.454829i
\(917\) 58.4776 24.2222i 1.93110 0.799887i
\(918\) 4.99260 + 4.50426i 0.164780 + 0.148663i
\(919\) −3.20080 3.20080i −0.105584 0.105584i 0.652341 0.757926i \(-0.273787\pi\)
−0.757926 + 0.652341i \(0.773787\pi\)
\(920\) 6.19195 8.46976i 0.204143 0.279240i
\(921\) 21.7574 21.7574i 0.716930 0.716930i
\(922\) −20.1019 + 1.03365i −0.662021 + 0.0340413i
\(923\) −23.2340 56.0918i −0.764756 1.84628i
\(924\) 0.328300 + 3.18388i 0.0108003 + 0.104742i
\(925\) 49.0531 + 20.3184i 1.61285 + 0.668066i
\(926\) −36.6096 + 17.4177i −1.20307 + 0.572380i
\(927\) −4.23764 −0.139182
\(928\) 0.906761 0.238187i 0.0297659 0.00781887i
\(929\) −5.46430 −0.179278 −0.0896389 0.995974i \(-0.528571\pi\)
−0.0896389 + 0.995974i \(0.528571\pi\)
\(930\) −38.8589 + 18.4878i −1.27423 + 0.606238i
\(931\) 5.20381 + 2.15549i 0.170548 + 0.0706433i
\(932\) −21.2831 + 2.19458i −0.697153 + 0.0718858i
\(933\) −0.587233 1.41771i −0.0192251 0.0464136i
\(934\) 0.0679517 0.00349410i 0.00222345 0.000114330i
\(935\) 5.43225 5.43225i 0.177654 0.177654i
\(936\) −14.5251 + 2.25658i −0.474768 + 0.0737587i
\(937\) −20.1655 20.1655i −0.658779 0.658779i 0.296312 0.955091i \(-0.404243\pi\)
−0.955091 + 0.296312i \(0.904243\pi\)
\(938\) 21.5480 + 19.4404i 0.703568 + 0.634751i
\(939\) 4.50160 1.86462i 0.146904 0.0608497i
\(940\) −1.45220 + 4.86732i −0.0473656 + 0.158755i
\(941\) −10.4612 + 25.2557i −0.341027 + 0.823311i 0.656586 + 0.754251i \(0.272000\pi\)
−0.997613 + 0.0690598i \(0.978000\pi\)
\(942\) 0.580077 1.63297i 0.0188999 0.0532052i
\(943\) 2.05842i 0.0670314i
\(944\) 18.1013 12.3360i 0.589146 0.401501i
\(945\) 12.4736i 0.405766i
\(946\) −1.87095 0.664613i −0.0608299 0.0216084i
\(947\) 7.10795 17.1601i 0.230977 0.557628i −0.765316 0.643655i \(-0.777417\pi\)
0.996293 + 0.0860269i \(0.0274171\pi\)
\(948\) 9.00410 + 16.6617i 0.292439 + 0.541145i
\(949\) −29.6973 + 12.3010i −0.964014 + 0.399308i
\(950\) −7.56621 + 8.38651i −0.245480 + 0.272094i
\(951\) 1.43303 + 1.43303i 0.0464690 + 0.0464690i
\(952\) 24.5796 + 40.3775i 0.796629 + 1.30864i
\(953\) −8.36834 + 8.36834i −0.271077 + 0.271077i −0.829534 0.558457i \(-0.811394\pi\)
0.558457 + 0.829534i \(0.311394\pi\)
\(954\) 0.821093 + 15.9682i 0.0265839 + 0.516991i
\(955\) −7.81120 18.8579i −0.252765 0.610228i
\(956\) 32.6897 + 26.5783i 1.05726 + 0.859605i
\(957\) −0.0697145 0.0288767i −0.00225355 0.000933451i
\(958\) −5.25041 11.0357i −0.169633 0.356546i
\(959\) −20.7575 −0.670294
\(960\) 13.0379 25.2188i 0.420796 0.813933i
\(961\) 42.5234 1.37172
\(962\) −22.0787 46.4065i −0.711845 1.49620i
\(963\) −0.420364 0.174120i −0.0135460 0.00561095i
\(964\) 37.5471 + 30.5276i 1.20931 + 0.983229i
\(965\) 2.75542 + 6.65217i 0.0887001 + 0.214141i
\(966\) −0.266828 5.18915i −0.00858505 0.166958i
\(967\) 15.9921 15.9921i 0.514273 0.514273i −0.401560 0.915833i \(-0.631532\pi\)
0.915833 + 0.401560i \(0.131532\pi\)
\(968\) −26.0750 + 15.8730i −0.838083 + 0.510178i
\(969\) −3.53634 3.53634i −0.113604 0.113604i
\(970\) 34.3295 38.0514i 1.10226 1.22176i
\(971\) −30.0555 + 12.4494i −0.964528 + 0.399521i −0.808673 0.588259i \(-0.799814\pi\)
−0.155856 + 0.987780i \(0.549814\pi\)
\(972\) −0.950854 1.75951i −0.0304987 0.0564363i
\(973\) 24.9990 60.3530i 0.801433 1.93483i
\(974\) −4.06739 1.44485i −0.130328 0.0462959i
\(975\) 39.4626i 1.26381i
\(976\) −2.26582 + 11.9621i −0.0725272 + 0.382898i
\(977\) 25.2550i 0.807979i −0.914764 0.403989i \(-0.867623\pi\)
0.914764 0.403989i \(-0.132377\pi\)
\(978\) −6.41694 + 18.0643i −0.205191 + 0.577634i
\(979\) 2.12033 5.11892i 0.0677660 0.163602i
\(980\) 10.8663 36.4203i 0.347110 1.16340i
\(981\) −4.77963 + 1.97979i −0.152602 + 0.0632098i
\(982\) −27.7980 25.0791i −0.887071 0.800305i
\(983\) 37.2730 + 37.2730i 1.18882 + 1.18882i 0.977393 + 0.211432i \(0.0678128\pi\)
0.211432 + 0.977393i \(0.432187\pi\)
\(984\) −0.855066 5.50386i −0.0272585 0.175457i
\(985\) 23.2707 23.2707i 0.741467 0.741467i
\(986\) −1.11294 + 0.0572278i −0.0354432 + 0.00182250i
\(987\) 0.962650 + 2.32404i 0.0306415 + 0.0739751i
\(988\) 10.8751 1.12137i 0.345982 0.0356754i
\(989\) 2.97783 + 1.23346i 0.0946895 + 0.0392217i
\(990\) −2.06338 + 0.981687i −0.0655784 + 0.0312001i
\(991\) −21.7711 −0.691581 −0.345791 0.938312i \(-0.612389\pi\)
−0.345791 + 0.938312i \(0.612389\pi\)
\(992\) −38.6266 + 29.3382i −1.22640 + 0.931489i
\(993\) −29.6265 −0.940167
\(994\) 52.4396 24.9491i 1.66328 0.791336i
\(995\) −59.0969 24.4787i −1.87350 0.776028i
\(996\) 1.52880 + 14.8264i 0.0484419 + 0.469792i
\(997\) 7.63502 + 18.4326i 0.241803 + 0.583765i 0.997462 0.0712005i \(-0.0226830\pi\)
−0.755659 + 0.654966i \(0.772683\pi\)
\(998\) −18.4152 + 0.946917i −0.582923 + 0.0299741i
\(999\) 4.94428 4.94428i 0.156430 0.156430i
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 96.2.n.a.61.4 32
3.2 odd 2 288.2.v.d.253.5 32
4.3 odd 2 384.2.n.a.337.1 32
8.3 odd 2 768.2.n.b.673.8 32
8.5 even 2 768.2.n.a.673.4 32
12.11 even 2 1152.2.v.c.721.7 32
32.5 even 8 768.2.n.a.97.4 32
32.11 odd 8 384.2.n.a.49.1 32
32.21 even 8 inner 96.2.n.a.85.4 yes 32
32.27 odd 8 768.2.n.b.97.8 32
96.11 even 8 1152.2.v.c.433.7 32
96.53 odd 8 288.2.v.d.181.5 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.2.n.a.61.4 32 1.1 even 1 trivial
96.2.n.a.85.4 yes 32 32.21 even 8 inner
288.2.v.d.181.5 32 96.53 odd 8
288.2.v.d.253.5 32 3.2 odd 2
384.2.n.a.49.1 32 32.11 odd 8
384.2.n.a.337.1 32 4.3 odd 2
768.2.n.a.97.4 32 32.5 even 8
768.2.n.a.673.4 32 8.5 even 2
768.2.n.b.97.8 32 32.27 odd 8
768.2.n.b.673.8 32 8.3 odd 2
1152.2.v.c.433.7 32 96.11 even 8
1152.2.v.c.721.7 32 12.11 even 2