Properties

Label 224.2.x.b.27.4
Level $224$
Weight $2$
Character 224.27
Analytic conductor $1.789$
Analytic rank $0$
Dimension $112$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [224,2,Mod(27,224)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(224, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 1, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("224.27");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.x (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: \(1.78864900528\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(28\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 27.4
Character \(\chi\) \(=\) 224.27
Dual form 224.2.x.b.83.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36868 + 0.355955i) q^{2} +(1.01638 + 2.45376i) q^{3} +(1.74659 - 0.974380i) q^{4} +(-1.11188 + 2.68430i) q^{5} +(-2.26454 - 2.99664i) q^{6} +(2.64539 - 0.0435134i) q^{7} +(-2.04370 + 1.95533i) q^{8} +(-2.86660 + 2.86660i) q^{9} +O(q^{10})\) \(q+(-1.36868 + 0.355955i) q^{2} +(1.01638 + 2.45376i) q^{3} +(1.74659 - 0.974380i) q^{4} +(-1.11188 + 2.68430i) q^{5} +(-2.26454 - 2.99664i) q^{6} +(2.64539 - 0.0435134i) q^{7} +(-2.04370 + 1.95533i) q^{8} +(-2.86660 + 2.86660i) q^{9} +(0.566314 - 4.06974i) q^{10} +(1.44195 + 0.597277i) q^{11} +(4.16610 + 3.29538i) q^{12} +(-1.41757 - 3.42231i) q^{13} +(-3.60522 + 1.00120i) q^{14} -7.71674 q^{15} +(2.10117 - 3.40369i) q^{16} +2.54645 q^{17} +(2.90309 - 4.94386i) q^{18} +(-1.94460 + 0.805480i) q^{19} +(0.673541 + 5.77177i) q^{20} +(2.79550 + 6.44694i) q^{21} +(-2.18618 - 0.304212i) q^{22} +(-6.51022 - 6.51022i) q^{23} +(-6.87509 - 3.02739i) q^{24} +(-2.43369 - 2.43369i) q^{25} +(3.15839 + 4.17947i) q^{26} +(-2.58624 - 1.07126i) q^{27} +(4.57802 - 2.65362i) q^{28} +(2.87982 + 6.95251i) q^{29} +(10.5618 - 2.74681i) q^{30} -3.98396 q^{31} +(-1.66427 + 5.40650i) q^{32} +4.14527i q^{33} +(-3.48528 + 0.906421i) q^{34} +(-2.82454 + 7.14942i) q^{35} +(-2.21362 + 7.79995i) q^{36} +(6.26182 + 2.59373i) q^{37} +(2.37483 - 1.79464i) q^{38} +(6.95676 - 6.95676i) q^{39} +(-2.97636 - 7.65998i) q^{40} +(1.24468 + 1.24468i) q^{41} +(-6.12098 - 7.82876i) q^{42} +(0.455327 + 0.188603i) q^{43} +(3.10048 - 0.361812i) q^{44} +(-4.50753 - 10.8821i) q^{45} +(11.2278 + 6.59309i) q^{46} -11.5542i q^{47} +(10.4874 + 1.69632i) q^{48} +(6.99621 - 0.230220i) q^{49} +(4.19724 + 2.46467i) q^{50} +(2.58816 + 6.24838i) q^{51} +(-5.81055 - 4.59613i) q^{52} +(5.01182 - 12.0996i) q^{53} +(3.92106 + 0.545625i) q^{54} +(-3.20654 + 3.20654i) q^{55} +(-5.32130 + 5.26154i) q^{56} +(-3.95291 - 3.95291i) q^{57} +(-6.41635 - 8.49070i) q^{58} +(8.98416 + 3.72136i) q^{59} +(-13.4780 + 7.51904i) q^{60} +(-5.57916 + 2.31096i) q^{61} +(5.45278 - 1.41811i) q^{62} +(-7.45856 + 7.70803i) q^{63} +(0.353393 - 7.99219i) q^{64} +10.7627 q^{65} +(-1.47553 - 5.67357i) q^{66} +(4.31852 - 1.78879i) q^{67} +(4.44761 - 2.48121i) q^{68} +(9.35768 - 22.5914i) q^{69} +(1.32104 - 10.7907i) q^{70} +(-1.46443 + 1.46443i) q^{71} +(0.253321 - 11.4636i) q^{72} +(6.10360 + 6.10360i) q^{73} +(-9.49371 - 1.32107i) q^{74} +(3.49814 - 8.44526i) q^{75} +(-2.61158 + 3.30162i) q^{76} +(3.84052 + 1.51729i) q^{77} +(-7.04531 + 11.9979i) q^{78} +10.3715 q^{79} +(6.80030 + 9.42465i) q^{80} +4.72714i q^{81} +(-2.14662 - 1.26052i) q^{82} +(-11.1362 + 4.61276i) q^{83} +(11.1644 + 8.53630i) q^{84} +(-2.83133 + 6.83544i) q^{85} +(-0.690333 - 0.0960614i) q^{86} +(-14.1328 + 14.1328i) q^{87} +(-4.11479 + 1.59884i) q^{88} +(-1.98481 + 1.98481i) q^{89} +(10.0429 + 13.2897i) q^{90} +(-3.89894 - 8.99168i) q^{91} +(-17.7141 - 5.02727i) q^{92} +(-4.04922 - 9.77569i) q^{93} +(4.11278 + 15.8141i) q^{94} -6.11549i q^{95} +(-14.9578 + 1.41133i) q^{96} +2.83003i q^{97} +(-9.49366 + 2.80544i) q^{98} +(-5.84566 + 2.42135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{11} - 20 q^{14} - 16 q^{15} + 16 q^{16} - 16 q^{18} - 4 q^{21} + 32 q^{22} - 48 q^{23} - 8 q^{25} - 24 q^{28} - 8 q^{29} + 16 q^{30} - 8 q^{32} + 20 q^{35} + 32 q^{36} - 8 q^{37} - 8 q^{39} + 16 q^{42} + 32 q^{43} - 144 q^{44} - 8 q^{46} + 16 q^{50} - 32 q^{51} - 32 q^{53} + 64 q^{56} - 8 q^{57} - 72 q^{58} - 88 q^{60} + 112 q^{64} - 16 q^{65} - 64 q^{67} - 40 q^{70} + 56 q^{71} - 8 q^{72} - 168 q^{74} + 52 q^{77} + 192 q^{78} - 16 q^{79} - 24 q^{84} - 48 q^{85} - 8 q^{86} - 96 q^{88} - 52 q^{91} - 8 q^{92} - 32 q^{93} + 88 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{8}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36868 + 0.355955i −0.967806 + 0.251698i
\(3\) 1.01638 + 2.45376i 0.586809 + 1.41668i 0.886538 + 0.462657i \(0.153104\pi\)
−0.299729 + 0.954024i \(0.596896\pi\)
\(4\) 1.74659 0.974380i 0.873296 0.487190i
\(5\) −1.11188 + 2.68430i −0.497246 + 1.20046i 0.453715 + 0.891147i \(0.350098\pi\)
−0.950961 + 0.309311i \(0.899902\pi\)
\(6\) −2.26454 2.99664i −0.924493 1.22337i
\(7\) 2.64539 0.0435134i 0.999865 0.0164465i
\(8\) −2.04370 + 1.95533i −0.722556 + 0.691312i
\(9\) −2.86660 + 2.86660i −0.955534 + 0.955534i
\(10\) 0.566314 4.06974i 0.179084 1.28697i
\(11\) 1.44195 + 0.597277i 0.434765 + 0.180086i 0.589322 0.807898i \(-0.299395\pi\)
−0.154557 + 0.987984i \(0.549395\pi\)
\(12\) 4.16610 + 3.29538i 1.20265 + 0.951295i
\(13\) −1.41757 3.42231i −0.393163 0.949179i −0.989247 0.146257i \(-0.953277\pi\)
0.596084 0.802922i \(-0.296723\pi\)
\(14\) −3.60522 + 1.00120i −0.963535 + 0.267581i
\(15\) −7.71674 −1.99245
\(16\) 2.10117 3.40369i 0.525292 0.850922i
\(17\) 2.54645 0.617604 0.308802 0.951126i \(-0.400072\pi\)
0.308802 + 0.951126i \(0.400072\pi\)
\(18\) 2.90309 4.94386i 0.684265 1.16528i
\(19\) −1.94460 + 0.805480i −0.446122 + 0.184790i −0.594423 0.804152i \(-0.702620\pi\)
0.148301 + 0.988942i \(0.452620\pi\)
\(20\) 0.673541 + 5.77177i 0.150608 + 1.29061i
\(21\) 2.79550 + 6.44694i 0.610029 + 1.40684i
\(22\) −2.18618 0.304212i −0.466096 0.0648583i
\(23\) −6.51022 6.51022i −1.35748 1.35748i −0.877018 0.480458i \(-0.840471\pi\)
−0.480458 0.877018i \(-0.659529\pi\)
\(24\) −6.87509 3.02739i −1.40337 0.617963i
\(25\) −2.43369 2.43369i −0.486738 0.486738i
\(26\) 3.15839 + 4.17947i 0.619412 + 0.819662i
\(27\) −2.58624 1.07126i −0.497722 0.206163i
\(28\) 4.57802 2.65362i 0.865165 0.501487i
\(29\) 2.87982 + 6.95251i 0.534770 + 1.29105i 0.928333 + 0.371751i \(0.121242\pi\)
−0.393563 + 0.919298i \(0.628758\pi\)
\(30\) 10.5618 2.74681i 1.92831 0.501497i
\(31\) −3.98396 −0.715540 −0.357770 0.933810i \(-0.616463\pi\)
−0.357770 + 0.933810i \(0.616463\pi\)
\(32\) −1.66427 + 5.40650i −0.294205 + 0.955742i
\(33\) 4.14527i 0.721600i
\(34\) −3.48528 + 0.906421i −0.597721 + 0.155450i
\(35\) −2.82454 + 7.14942i −0.477435 + 1.20847i
\(36\) −2.21362 + 7.79995i −0.368937 + 1.29999i
\(37\) 6.26182 + 2.59373i 1.02944 + 0.426407i 0.832509 0.554011i \(-0.186903\pi\)
0.196928 + 0.980418i \(0.436903\pi\)
\(38\) 2.37483 1.79464i 0.385248 0.291129i
\(39\) 6.95676 6.95676i 1.11397 1.11397i
\(40\) −2.97636 7.65998i −0.470603 1.21115i
\(41\) 1.24468 + 1.24468i 0.194386 + 0.194386i 0.797588 0.603202i \(-0.206109\pi\)
−0.603202 + 0.797588i \(0.706109\pi\)
\(42\) −6.12098 7.82876i −0.944488 1.20800i
\(43\) 0.455327 + 0.188603i 0.0694367 + 0.0287616i 0.417131 0.908846i \(-0.363035\pi\)
−0.347695 + 0.937608i \(0.613035\pi\)
\(44\) 3.10048 0.361812i 0.467415 0.0545452i
\(45\) −4.50753 10.8821i −0.671943 1.62221i
\(46\) 11.2278 + 6.59309i 1.65545 + 0.972098i
\(47\) 11.5542i 1.68536i −0.538418 0.842678i \(-0.680978\pi\)
0.538418 0.842678i \(-0.319022\pi\)
\(48\) 10.4874 + 1.69632i 1.51373 + 0.244842i
\(49\) 6.99621 0.230220i 0.999459 0.0328886i
\(50\) 4.19724 + 2.46467i 0.593579 + 0.348557i
\(51\) 2.58816 + 6.24838i 0.362416 + 0.874949i
\(52\) −5.81055 4.59613i −0.805778 0.637369i
\(53\) 5.01182 12.0996i 0.688426 1.66201i −0.0595011 0.998228i \(-0.518951\pi\)
0.747928 0.663780i \(-0.231049\pi\)
\(54\) 3.92106 + 0.545625i 0.533589 + 0.0742502i
\(55\) −3.20654 + 3.20654i −0.432370 + 0.432370i
\(56\) −5.32130 + 5.26154i −0.711089 + 0.703102i
\(57\) −3.95291 3.95291i −0.523576 0.523576i
\(58\) −6.41635 8.49070i −0.842508 1.11488i
\(59\) 8.98416 + 3.72136i 1.16964 + 0.484480i 0.881073 0.472980i \(-0.156822\pi\)
0.288565 + 0.957460i \(0.406822\pi\)
\(60\) −13.4780 + 7.51904i −1.74000 + 0.970704i
\(61\) −5.57916 + 2.31096i −0.714338 + 0.295888i −0.710098 0.704103i \(-0.751349\pi\)
−0.00423949 + 0.999991i \(0.501349\pi\)
\(62\) 5.45278 1.41811i 0.692504 0.180100i
\(63\) −7.45856 + 7.70803i −0.939690 + 0.971120i
\(64\) 0.353393 7.99219i 0.0441742 0.999024i
\(65\) 10.7627 1.33495
\(66\) −1.47553 5.67357i −0.181625 0.698368i
\(67\) 4.31852 1.78879i 0.527591 0.218535i −0.102957 0.994686i \(-0.532830\pi\)
0.630548 + 0.776151i \(0.282830\pi\)
\(68\) 4.44761 2.48121i 0.539351 0.300891i
\(69\) 9.35768 22.5914i 1.12653 2.71969i
\(70\) 1.32104 10.7907i 0.157894 1.28974i
\(71\) −1.46443 + 1.46443i −0.173796 + 0.173796i −0.788645 0.614849i \(-0.789217\pi\)
0.614849 + 0.788645i \(0.289217\pi\)
\(72\) 0.253321 11.4636i 0.0298542 1.35100i
\(73\) 6.10360 + 6.10360i 0.714372 + 0.714372i 0.967447 0.253075i \(-0.0814418\pi\)
−0.253075 + 0.967447i \(0.581442\pi\)
\(74\) −9.49371 1.32107i −1.10362 0.153571i
\(75\) 3.49814 8.44526i 0.403930 0.975174i
\(76\) −2.61158 + 3.30162i −0.299569 + 0.378722i
\(77\) 3.84052 + 1.51729i 0.437668 + 0.172911i
\(78\) −7.04531 + 11.9979i −0.797724 + 1.35849i
\(79\) 10.3715 1.16688 0.583441 0.812156i \(-0.301706\pi\)
0.583441 + 0.812156i \(0.301706\pi\)
\(80\) 6.80030 + 9.42465i 0.760297 + 1.05371i
\(81\) 4.72714i 0.525238i
\(82\) −2.14662 1.26052i −0.237055 0.139202i
\(83\) −11.1362 + 4.61276i −1.22235 + 0.506316i −0.898157 0.439674i \(-0.855094\pi\)
−0.324197 + 0.945990i \(0.605094\pi\)
\(84\) 11.1644 + 8.53630i 1.21813 + 0.931386i
\(85\) −2.83133 + 6.83544i −0.307101 + 0.741408i
\(86\) −0.690333 0.0960614i −0.0744405 0.0103586i
\(87\) −14.1328 + 14.1328i −1.51520 + 1.51520i
\(88\) −4.11479 + 1.59884i −0.438638 + 0.170437i
\(89\) −1.98481 + 1.98481i −0.210390 + 0.210390i −0.804433 0.594043i \(-0.797531\pi\)
0.594043 + 0.804433i \(0.297531\pi\)
\(90\) 10.0429 + 13.2897i 1.05862 + 1.40086i
\(91\) −3.89894 8.99168i −0.408720 0.942584i
\(92\) −17.7141 5.02727i −1.84683 0.524129i
\(93\) −4.04922 9.77569i −0.419885 1.01369i
\(94\) 4.11278 + 15.8141i 0.424201 + 1.63110i
\(95\) 6.11549i 0.627436i
\(96\) −14.9578 + 1.41133i −1.52662 + 0.144044i
\(97\) 2.83003i 0.287346i 0.989625 + 0.143673i \(0.0458914\pi\)
−0.989625 + 0.143673i \(0.954109\pi\)
\(98\) −9.49366 + 2.80544i −0.959004 + 0.283392i
\(99\) −5.84566 + 2.42135i −0.587511 + 0.243355i
\(100\) −6.62200 1.87932i −0.662200 0.187932i
\(101\) −3.19363 + 7.71009i −0.317778 + 0.767183i 0.681594 + 0.731731i \(0.261287\pi\)
−0.999371 + 0.0354522i \(0.988713\pi\)
\(102\) −5.76652 7.63079i −0.570971 0.755561i
\(103\) −2.33186 2.33186i −0.229765 0.229765i 0.582830 0.812594i \(-0.301945\pi\)
−0.812594 + 0.582830i \(0.801945\pi\)
\(104\) 9.58882 + 4.22236i 0.940261 + 0.414036i
\(105\) −20.4138 + 0.335781i −1.99218 + 0.0327689i
\(106\) −2.55268 + 18.3445i −0.247938 + 1.78178i
\(107\) −3.03494 1.25711i −0.293398 0.121530i 0.231129 0.972923i \(-0.425758\pi\)
−0.524527 + 0.851394i \(0.675758\pi\)
\(108\) −5.56091 + 0.648934i −0.535099 + 0.0624437i
\(109\) 0.155030 0.0642157i 0.0148492 0.00615075i −0.375246 0.926925i \(-0.622442\pi\)
0.390096 + 0.920774i \(0.372442\pi\)
\(110\) 3.24736 5.53013i 0.309624 0.527277i
\(111\) 18.0013i 1.70860i
\(112\) 5.41031 9.09553i 0.511226 0.859446i
\(113\) 2.84861i 0.267975i −0.990983 0.133987i \(-0.957222\pi\)
0.990983 0.133987i \(-0.0427781\pi\)
\(114\) 6.81735 + 4.00323i 0.638503 + 0.374937i
\(115\) 24.7140 10.2369i 2.30459 0.954593i
\(116\) 11.8043 + 9.33715i 1.09600 + 0.866933i
\(117\) 13.8740 + 5.74681i 1.28265 + 0.531292i
\(118\) −13.6211 1.89541i −1.25392 0.174487i
\(119\) 6.73636 0.110805i 0.617521 0.0101574i
\(120\) 15.7707 15.0887i 1.43966 1.37741i
\(121\) −6.05568 6.05568i −0.550517 0.550517i
\(122\) 6.81350 5.14891i 0.616866 0.466160i
\(123\) −1.78908 + 4.31922i −0.161316 + 0.389451i
\(124\) −6.95835 + 3.88189i −0.624878 + 0.348604i
\(125\) −4.18280 + 1.73257i −0.374121 + 0.154966i
\(126\) 7.46470 13.2048i 0.665008 1.17637i
\(127\) 0.210031i 0.0186372i −0.999957 0.00931862i \(-0.997034\pi\)
0.999957 0.00931862i \(-0.00296625\pi\)
\(128\) 2.36118 + 11.0646i 0.208701 + 0.977980i
\(129\) 1.30896i 0.115247i
\(130\) −14.7307 + 3.83103i −1.29197 + 0.336004i
\(131\) −1.90334 4.59506i −0.166295 0.401473i 0.818661 0.574278i \(-0.194717\pi\)
−0.984956 + 0.172805i \(0.944717\pi\)
\(132\) 4.03907 + 7.24010i 0.351556 + 0.630170i
\(133\) −5.10918 + 2.21543i −0.443022 + 0.192102i
\(134\) −5.27395 + 3.98548i −0.455600 + 0.344293i
\(135\) 5.75115 5.75115i 0.494980 0.494980i
\(136\) −5.20417 + 4.97914i −0.446254 + 0.426958i
\(137\) 1.73401 1.73401i 0.148146 0.148146i −0.629143 0.777289i \(-0.716594\pi\)
0.777289 + 0.629143i \(0.216594\pi\)
\(138\) −4.76617 + 34.2514i −0.405723 + 2.91568i
\(139\) 7.45866 18.0068i 0.632635 1.52732i −0.203662 0.979041i \(-0.565284\pi\)
0.836298 0.548276i \(-0.184716\pi\)
\(140\) 2.03293 + 15.2393i 0.171814 + 1.28796i
\(141\) 28.3513 11.7435i 2.38761 0.988981i
\(142\) 1.48307 2.52562i 0.124457 0.211945i
\(143\) 5.78150i 0.483473i
\(144\) 3.73381 + 15.7802i 0.311151 + 1.31502i
\(145\) −21.8647 −1.81576
\(146\) −10.5265 6.18129i −0.871180 0.511567i
\(147\) 7.67573 + 16.9331i 0.633084 + 1.39662i
\(148\) 13.4641 1.57120i 1.10674 0.129152i
\(149\) −2.82390 + 6.81750i −0.231343 + 0.558511i −0.996336 0.0855276i \(-0.972742\pi\)
0.764993 + 0.644039i \(0.222742\pi\)
\(150\) −1.78172 + 12.8041i −0.145476 + 1.04545i
\(151\) −4.18735 4.18735i −0.340762 0.340762i 0.515892 0.856654i \(-0.327461\pi\)
−0.856654 + 0.515892i \(0.827461\pi\)
\(152\) 2.39920 5.44849i 0.194601 0.441931i
\(153\) −7.29966 + 7.29966i −0.590142 + 0.590142i
\(154\) −5.79655 0.709633i −0.467099 0.0571839i
\(155\) 4.42966 10.6942i 0.355799 0.858975i
\(156\) 5.37209 18.9291i 0.430111 1.51554i
\(157\) 0.672912 0.278729i 0.0537042 0.0222450i −0.355670 0.934612i \(-0.615747\pi\)
0.409374 + 0.912367i \(0.365747\pi\)
\(158\) −14.1953 + 3.69178i −1.12931 + 0.293702i
\(159\) 34.7835 2.75851
\(160\) −12.6622 10.4788i −1.00104 0.828419i
\(161\) −17.5054 16.9388i −1.37962 1.33497i
\(162\) −1.68265 6.46996i −0.132202 0.508328i
\(163\) −18.7174 + 7.75302i −1.46606 + 0.607263i −0.965958 0.258701i \(-0.916706\pi\)
−0.500106 + 0.865964i \(0.666706\pi\)
\(164\) 3.38674 + 0.961157i 0.264460 + 0.0750537i
\(165\) −11.1272 4.60903i −0.866250 0.358812i
\(166\) 13.6000 10.2774i 1.05556 0.797680i
\(167\) −11.4569 11.4569i −0.886565 0.886565i 0.107627 0.994191i \(-0.465675\pi\)
−0.994191 + 0.107627i \(0.965675\pi\)
\(168\) −18.3190 7.70948i −1.41334 0.594799i
\(169\) −0.510336 + 0.510336i −0.0392566 + 0.0392566i
\(170\) 1.44209 10.3634i 0.110603 0.794836i
\(171\) 3.26541 7.88339i 0.249712 0.602858i
\(172\) 0.979041 0.114250i 0.0746512 0.00871147i
\(173\) −0.276248 0.666921i −0.0210027 0.0507051i 0.913030 0.407892i \(-0.133736\pi\)
−0.934033 + 0.357187i \(0.883736\pi\)
\(174\) 14.3127 24.3740i 1.08504 1.84779i
\(175\) −6.54396 6.33217i −0.494677 0.478667i
\(176\) 5.06273 3.65298i 0.381617 0.275354i
\(177\) 25.8273i 1.94130i
\(178\) 2.01008 3.42308i 0.150662 0.256571i
\(179\) −7.20523 17.3950i −0.538544 1.30016i −0.925739 0.378163i \(-0.876556\pi\)
0.387195 0.921998i \(-0.373444\pi\)
\(180\) −18.4762 14.6146i −1.37713 1.08931i
\(181\) −5.82097 2.41113i −0.432670 0.179218i 0.155709 0.987803i \(-0.450234\pi\)
−0.588379 + 0.808585i \(0.700234\pi\)
\(182\) 8.53705 + 10.9189i 0.632809 + 0.809364i
\(183\) −11.3411 11.3411i −0.838359 0.838359i
\(184\) 26.0345 + 0.575308i 1.91929 + 0.0424123i
\(185\) −13.9247 + 13.9247i −1.02377 + 1.02377i
\(186\) 9.02182 + 11.9385i 0.661512 + 0.875373i
\(187\) 3.67186 + 1.52093i 0.268513 + 0.111222i
\(188\) −11.2582 20.1805i −0.821089 1.47181i
\(189\) −6.88823 2.72136i −0.501045 0.197950i
\(190\) 2.17684 + 8.37018i 0.157925 + 0.607236i
\(191\) 12.9523i 0.937198i 0.883411 + 0.468599i \(0.155241\pi\)
−0.883411 + 0.468599i \(0.844759\pi\)
\(192\) 19.9701 7.25598i 1.44122 0.523655i
\(193\) 3.11927 0.224530 0.112265 0.993678i \(-0.464189\pi\)
0.112265 + 0.993678i \(0.464189\pi\)
\(194\) −1.00736 3.87342i −0.0723245 0.278095i
\(195\) 10.9390 + 26.4091i 0.783358 + 1.89119i
\(196\) 11.9952 7.21907i 0.856801 0.515648i
\(197\) 16.9862 + 7.03591i 1.21022 + 0.501288i 0.894287 0.447495i \(-0.147684\pi\)
0.315929 + 0.948783i \(0.397684\pi\)
\(198\) 7.13897 5.39486i 0.507345 0.383396i
\(199\) −6.91785 6.91785i −0.490393 0.490393i 0.418037 0.908430i \(-0.362718\pi\)
−0.908430 + 0.418037i \(0.862718\pi\)
\(200\) 9.73238 + 0.215065i 0.688183 + 0.0152074i
\(201\) 8.77852 + 8.77852i 0.619189 + 0.619189i
\(202\) 1.62662 11.6895i 0.114448 0.822468i
\(203\) 7.92079 + 18.2668i 0.555931 + 1.28208i
\(204\) 10.6088 + 8.39152i 0.742762 + 0.587524i
\(205\) −4.72503 + 1.95717i −0.330010 + 0.136695i
\(206\) 4.02161 + 2.36154i 0.280199 + 0.164536i
\(207\) 37.3245 2.59423
\(208\) −14.6270 2.36589i −1.01420 0.164045i
\(209\) −3.28512 −0.227236
\(210\) 27.8205 7.72598i 1.91980 0.533143i
\(211\) −1.25393 3.02726i −0.0863242 0.208405i 0.874822 0.484444i \(-0.160978\pi\)
−0.961146 + 0.276039i \(0.910978\pi\)
\(212\) −3.03601 26.0165i −0.208514 1.78682i
\(213\) −5.08179 2.10495i −0.348199 0.144229i
\(214\) 4.60134 + 0.640287i 0.314541 + 0.0437691i
\(215\) −1.01253 + 1.01253i −0.0690542 + 0.0690542i
\(216\) 7.38014 2.86762i 0.502155 0.195117i
\(217\) −10.5391 + 0.173355i −0.715443 + 0.0117681i
\(218\) −0.189330 + 0.143075i −0.0128230 + 0.00969026i
\(219\) −8.77320 + 21.1804i −0.592838 + 1.43124i
\(220\) −2.47613 + 8.72492i −0.166941 + 0.588234i
\(221\) −3.60976 8.71474i −0.242819 0.586217i
\(222\) −6.40764 24.6380i −0.430053 1.65360i
\(223\) 24.4613 1.63805 0.819025 0.573758i \(-0.194515\pi\)
0.819025 + 0.573758i \(0.194515\pi\)
\(224\) −4.16740 + 14.3747i −0.278446 + 0.960452i
\(225\) 13.9528 0.930189
\(226\) 1.01398 + 3.89885i 0.0674487 + 0.259347i
\(227\) −5.43354 13.1177i −0.360637 0.870654i −0.995207 0.0977890i \(-0.968823\pi\)
0.634570 0.772865i \(-0.281177\pi\)
\(228\) −10.7558 3.05249i −0.712318 0.202156i
\(229\) −7.45120 + 17.9888i −0.492389 + 1.18873i 0.461111 + 0.887342i \(0.347451\pi\)
−0.953501 + 0.301391i \(0.902549\pi\)
\(230\) −30.1818 + 22.8081i −1.99013 + 1.50392i
\(231\) 0.180375 + 10.9659i 0.0118678 + 0.721502i
\(232\) −19.4799 8.57783i −1.27892 0.563162i
\(233\) 14.7467 14.7467i 0.966090 0.966090i −0.0333540 0.999444i \(-0.510619\pi\)
0.999444 + 0.0333540i \(0.0106189\pi\)
\(234\) −21.0347 2.92703i −1.37508 0.191346i
\(235\) 31.0150 + 12.8468i 2.02320 + 0.838036i
\(236\) 19.3177 2.25429i 1.25747 0.146742i
\(237\) 10.5414 + 25.4491i 0.684736 + 1.65310i
\(238\) −9.18050 + 2.54950i −0.595084 + 0.165259i
\(239\) −5.33158 −0.344871 −0.172436 0.985021i \(-0.555164\pi\)
−0.172436 + 0.985021i \(0.555164\pi\)
\(240\) −16.2142 + 26.2654i −1.04662 + 1.69542i
\(241\) 19.9020 1.28200 0.641001 0.767540i \(-0.278519\pi\)
0.641001 + 0.767540i \(0.278519\pi\)
\(242\) 10.4439 + 6.13277i 0.671357 + 0.394229i
\(243\) −19.3580 + 8.01835i −1.24182 + 0.514377i
\(244\) −7.49275 + 9.47253i −0.479674 + 0.606416i
\(245\) −7.16094 + 19.0359i −0.457495 + 1.21616i
\(246\) 0.911236 6.54848i 0.0580983 0.417516i
\(247\) 5.51321 + 5.51321i 0.350797 + 0.350797i
\(248\) 8.14200 7.78994i 0.517018 0.494662i
\(249\) −22.6372 22.6372i −1.43458 1.43458i
\(250\) 5.10821 3.86023i 0.323072 0.244143i
\(251\) −3.81050 1.57836i −0.240517 0.0996253i 0.259169 0.965832i \(-0.416551\pi\)
−0.499686 + 0.866207i \(0.666551\pi\)
\(252\) −5.51651 + 20.7302i −0.347507 + 1.30588i
\(253\) −5.49903 13.2758i −0.345721 0.834645i
\(254\) 0.0747616 + 0.287466i 0.00469096 + 0.0180372i
\(255\) −19.6503 −1.23055
\(256\) −7.17020 14.3034i −0.448137 0.893965i
\(257\) 29.0776i 1.81381i −0.421337 0.906904i \(-0.638439\pi\)
0.421337 0.906904i \(-0.361561\pi\)
\(258\) −0.465930 1.79155i −0.0290075 0.111537i
\(259\) 16.6778 + 6.58897i 1.03631 + 0.409419i
\(260\) 18.7980 10.4869i 1.16580 0.650373i
\(261\) −28.1854 11.6748i −1.74463 0.722650i
\(262\) 4.24070 + 5.61169i 0.261992 + 0.346691i
\(263\) −11.7341 + 11.7341i −0.723558 + 0.723558i −0.969328 0.245770i \(-0.920959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(264\) −8.10537 8.47168i −0.498851 0.521396i
\(265\) 26.9065 + 26.9065i 1.65285 + 1.65285i
\(266\) 6.20427 4.85086i 0.380408 0.297425i
\(267\) −6.88759 2.85293i −0.421513 0.174597i
\(268\) 5.79972 7.33216i 0.354275 0.447883i
\(269\) −11.9934 28.9547i −0.731252 1.76540i −0.638382 0.769720i \(-0.720396\pi\)
−0.0928695 0.995678i \(-0.529604\pi\)
\(270\) −5.82436 + 9.91866i −0.354459 + 0.603630i
\(271\) 12.7659i 0.775475i 0.921770 + 0.387737i \(0.126743\pi\)
−0.921770 + 0.387737i \(0.873257\pi\)
\(272\) 5.35051 8.66732i 0.324422 0.525533i
\(273\) 18.1006 18.7061i 1.09550 1.13214i
\(274\) −1.75608 + 2.99054i −0.106089 + 0.180665i
\(275\) −2.05568 4.96285i −0.123962 0.299271i
\(276\) −5.66860 48.5759i −0.341210 2.92393i
\(277\) −8.35793 + 20.1778i −0.502179 + 1.21237i 0.446115 + 0.894976i \(0.352807\pi\)
−0.948294 + 0.317393i \(0.897193\pi\)
\(278\) −3.79894 + 27.3006i −0.227845 + 1.63738i
\(279\) 11.4204 11.4204i 0.683723 0.683723i
\(280\) −8.20695 20.1342i −0.490459 1.20325i
\(281\) 8.16285 + 8.16285i 0.486955 + 0.486955i 0.907344 0.420389i \(-0.138106\pi\)
−0.420389 + 0.907344i \(0.638106\pi\)
\(282\) −34.6238 + 26.1649i −2.06182 + 1.55810i
\(283\) −17.0660 7.06897i −1.01447 0.420207i −0.187386 0.982286i \(-0.560001\pi\)
−0.827083 + 0.562080i \(0.810001\pi\)
\(284\) −1.13085 + 3.98468i −0.0671037 + 0.236447i
\(285\) 15.0060 6.21568i 0.888877 0.368185i
\(286\) 2.05795 + 7.91304i 0.121689 + 0.467908i
\(287\) 3.34683 + 3.23851i 0.197557 + 0.191163i
\(288\) −10.7275 20.2691i −0.632122 1.19437i
\(289\) −10.5156 −0.618565
\(290\) 29.9258 7.78284i 1.75730 0.457024i
\(291\) −6.94423 + 2.87639i −0.407078 + 0.168617i
\(292\) 16.6077 + 4.71327i 0.971893 + 0.275823i
\(293\) 1.09885 2.65285i 0.0641953 0.154981i −0.888526 0.458826i \(-0.848270\pi\)
0.952722 + 0.303844i \(0.0982703\pi\)
\(294\) −16.5331 20.4438i −0.964228 1.19231i
\(295\) −19.9785 + 19.9785i −1.16319 + 1.16319i
\(296\) −17.8689 + 6.94311i −1.03861 + 0.403560i
\(297\) −3.08940 3.08940i −0.179265 0.179265i
\(298\) 1.43830 10.3362i 0.0833187 0.598759i
\(299\) −13.0513 + 31.5087i −0.754778 + 1.82220i
\(300\) −2.11907 18.1589i −0.122344 1.04841i
\(301\) 1.21273 + 0.479115i 0.0699004 + 0.0276157i
\(302\) 7.22167 + 4.24065i 0.415561 + 0.244022i
\(303\) −22.1647 −1.27333
\(304\) −1.34433 + 8.31126i −0.0771024 + 0.476684i
\(305\) 17.5457i 1.00466i
\(306\) 7.39257 12.5893i 0.422605 0.719681i
\(307\) 3.58306 1.48415i 0.204496 0.0847051i −0.278084 0.960557i \(-0.589700\pi\)
0.482581 + 0.875852i \(0.339700\pi\)
\(308\) 8.18624 1.09205i 0.466454 0.0622252i
\(309\) 3.35177 8.09189i 0.190675 0.460331i
\(310\) −2.25617 + 16.2137i −0.128142 + 0.920875i
\(311\) 0.798805 0.798805i 0.0452960 0.0452960i −0.684096 0.729392i \(-0.739803\pi\)
0.729392 + 0.684096i \(0.239803\pi\)
\(312\) −0.614768 + 27.8202i −0.0348044 + 1.57501i
\(313\) 10.4208 10.4208i 0.589021 0.589021i −0.348345 0.937366i \(-0.613256\pi\)
0.937366 + 0.348345i \(0.113256\pi\)
\(314\) −0.821788 + 0.621018i −0.0463762 + 0.0350461i
\(315\) −12.3977 28.5914i −0.698532 1.61094i
\(316\) 18.1147 10.1058i 1.01903 0.568493i
\(317\) −3.28997 7.94268i −0.184783 0.446105i 0.804158 0.594416i \(-0.202617\pi\)
−0.988941 + 0.148310i \(0.952617\pi\)
\(318\) −47.6076 + 12.3814i −2.66970 + 0.694312i
\(319\) 11.7452i 0.657608i
\(320\) 21.0605 + 9.83493i 1.17732 + 0.549790i
\(321\) 8.72472i 0.486966i
\(322\) 29.9888 + 16.9528i 1.67121 + 0.944741i
\(323\) −4.95183 + 2.05111i −0.275527 + 0.114127i
\(324\) 4.60603 + 8.25639i 0.255891 + 0.458688i
\(325\) −4.87892 + 11.7788i −0.270634 + 0.653368i
\(326\) 22.8585 17.2740i 1.26602 0.956719i
\(327\) 0.315140 + 0.315140i 0.0174273 + 0.0174273i
\(328\) −4.97751 0.109992i −0.274837 0.00607331i
\(329\) −0.502763 30.5655i −0.0277182 1.68513i
\(330\) 16.8702 + 2.34753i 0.928674 + 0.129227i
\(331\) −3.24224 1.34298i −0.178209 0.0738168i 0.291795 0.956481i \(-0.405748\pi\)
−0.470004 + 0.882664i \(0.655748\pi\)
\(332\) −14.9558 + 18.9075i −0.820805 + 1.03768i
\(333\) −25.3854 + 10.5150i −1.39111 + 0.576216i
\(334\) 19.7591 + 11.6028i 1.08117 + 0.634876i
\(335\) 13.5811i 0.742016i
\(336\) 27.8172 + 4.03108i 1.51755 + 0.219914i
\(337\) 6.62627i 0.360956i −0.983579 0.180478i \(-0.942236\pi\)
0.983579 0.180478i \(-0.0577645\pi\)
\(338\) 0.516832 0.880145i 0.0281119 0.0478736i
\(339\) 6.98981 2.89528i 0.379635 0.157250i
\(340\) 1.71514 + 14.6975i 0.0930163 + 0.797085i
\(341\) −5.74468 2.37953i −0.311092 0.128859i
\(342\) −1.66318 + 11.9522i −0.0899343 + 0.646301i
\(343\) 18.4977 0.913451i 0.998783 0.0493217i
\(344\) −1.29933 + 0.504867i −0.0700552 + 0.0272206i
\(345\) 50.2377 + 50.2377i 2.70471 + 2.70471i
\(346\) 0.615490 + 0.814472i 0.0330889 + 0.0437863i
\(347\) 3.51612 8.48867i 0.188755 0.455696i −0.800965 0.598711i \(-0.795680\pi\)
0.989720 + 0.143015i \(0.0456798\pi\)
\(348\) −10.9135 + 38.4550i −0.585026 + 2.06140i
\(349\) −16.0265 + 6.63840i −0.857879 + 0.355345i −0.767878 0.640596i \(-0.778687\pi\)
−0.0900016 + 0.995942i \(0.528687\pi\)
\(350\) 11.2106 + 6.33738i 0.599231 + 0.338747i
\(351\) 10.3695i 0.553483i
\(352\) −5.62898 + 6.80188i −0.300025 + 0.362542i
\(353\) 11.9218i 0.634532i 0.948337 + 0.317266i \(0.102765\pi\)
−0.948337 + 0.317266i \(0.897235\pi\)
\(354\) −9.19337 35.3494i −0.488622 1.87880i
\(355\) −2.30271 5.55924i −0.122215 0.295054i
\(356\) −1.53270 + 5.40062i −0.0812327 + 0.286232i
\(357\) 7.11860 + 16.4168i 0.376756 + 0.868870i
\(358\) 16.0535 + 21.2435i 0.848454 + 1.12275i
\(359\) 18.5210 18.5210i 0.977501 0.977501i −0.0222516 0.999752i \(-0.507083\pi\)
0.999752 + 0.0222516i \(0.00708348\pi\)
\(360\) 30.4902 + 13.4261i 1.60697 + 0.707618i
\(361\) −10.3024 + 10.3024i −0.542229 + 0.542229i
\(362\) 8.82533 + 1.22806i 0.463849 + 0.0645456i
\(363\) 8.70433 21.0141i 0.456859 1.10295i
\(364\) −15.5712 11.9057i −0.816151 0.624031i
\(365\) −23.1704 + 9.59747i −1.21279 + 0.502355i
\(366\) 19.5593 + 11.4855i 1.02238 + 0.600355i
\(367\) 25.5647i 1.33447i −0.744848 0.667234i \(-0.767478\pi\)
0.744848 0.667234i \(-0.232522\pi\)
\(368\) −35.8378 + 8.47971i −1.86818 + 0.442036i
\(369\) −7.13601 −0.371486
\(370\) 14.1020 24.0151i 0.733127 1.24849i
\(371\) 12.7317 32.2263i 0.660999 1.67311i
\(372\) −16.5976 13.1287i −0.860545 0.680689i
\(373\) −5.80739 + 14.0203i −0.300695 + 0.725943i 0.699244 + 0.714883i \(0.253520\pi\)
−0.999939 + 0.0110591i \(0.996480\pi\)
\(374\) −5.56700 0.774661i −0.287863 0.0400568i
\(375\) −8.50265 8.50265i −0.439075 0.439075i
\(376\) 22.5923 + 23.6133i 1.16511 + 1.21776i
\(377\) 19.7113 19.7113i 1.01518 1.01518i
\(378\) 10.3965 + 1.27277i 0.534738 + 0.0654644i
\(379\) 4.18045 10.0925i 0.214735 0.518417i −0.779404 0.626522i \(-0.784478\pi\)
0.994140 + 0.108104i \(0.0344780\pi\)
\(380\) −5.95882 10.6813i −0.305681 0.547938i
\(381\) 0.515366 0.213472i 0.0264030 0.0109365i
\(382\) −4.61045 17.7277i −0.235891 0.907026i
\(383\) −6.58969 −0.336717 −0.168359 0.985726i \(-0.553847\pi\)
−0.168359 + 0.985726i \(0.553847\pi\)
\(384\) −24.7500 + 17.0396i −1.26302 + 0.869549i
\(385\) −8.34304 + 8.62210i −0.425201 + 0.439423i
\(386\) −4.26929 + 1.11032i −0.217301 + 0.0565137i
\(387\) −1.84589 + 0.764593i −0.0938319 + 0.0388664i
\(388\) 2.75753 + 4.94291i 0.139992 + 0.250938i
\(389\) 8.24678 + 3.41593i 0.418128 + 0.173194i 0.581821 0.813317i \(-0.302341\pi\)
−0.163693 + 0.986511i \(0.552341\pi\)
\(390\) −24.3725 32.2519i −1.23415 1.63314i
\(391\) −16.5780 16.5780i −0.838383 0.838383i
\(392\) −13.8480 + 14.1504i −0.699429 + 0.714702i
\(393\) 9.34068 9.34068i 0.471175 0.471175i
\(394\) −25.7532 3.58362i −1.29743 0.180540i
\(395\) −11.5318 + 27.8402i −0.580227 + 1.40079i
\(396\) −7.85067 + 9.92501i −0.394511 + 0.498751i
\(397\) −4.29181 10.3614i −0.215400 0.520021i 0.778837 0.627226i \(-0.215810\pi\)
−0.994237 + 0.107205i \(0.965810\pi\)
\(398\) 11.9308 + 7.00591i 0.598037 + 0.351174i
\(399\) −10.6290 10.2850i −0.532117 0.514895i
\(400\) −13.3971 + 3.16994i −0.669855 + 0.158497i
\(401\) 8.48921i 0.423931i −0.977277 0.211966i \(-0.932014\pi\)
0.977277 0.211966i \(-0.0679865\pi\)
\(402\) −15.1398 8.89026i −0.755104 0.443406i
\(403\) 5.64753 + 13.6344i 0.281324 + 0.679175i
\(404\) 1.93460 + 16.5782i 0.0962501 + 0.824796i
\(405\) −12.6891 5.25599i −0.630526 0.261172i
\(406\) −17.3432 22.1820i −0.860730 1.10088i
\(407\) 7.48008 + 7.48008i 0.370774 + 0.370774i
\(408\) −17.5071 7.70909i −0.866728 0.381657i
\(409\) −1.96856 + 1.96856i −0.0973391 + 0.0973391i −0.754099 0.656760i \(-0.771926\pi\)
0.656760 + 0.754099i \(0.271926\pi\)
\(410\) 5.77041 4.36065i 0.284980 0.215357i
\(411\) 6.01726 + 2.49243i 0.296810 + 0.122943i
\(412\) −6.34492 1.80069i −0.312592 0.0887135i
\(413\) 23.9286 + 9.45353i 1.17745 + 0.465178i
\(414\) −51.0854 + 13.2858i −2.51071 + 0.652963i
\(415\) 35.0217i 1.71915i
\(416\) 20.8619 1.96842i 1.02284 0.0965095i
\(417\) 51.7653 2.53496
\(418\) 4.49629 1.16935i 0.219921 0.0571950i
\(419\) −3.68570 8.89807i −0.180058 0.434699i 0.807920 0.589292i \(-0.200593\pi\)
−0.987978 + 0.154593i \(0.950593\pi\)
\(420\) −35.3274 + 20.4773i −1.72380 + 0.999189i
\(421\) 22.8873 + 9.48022i 1.11546 + 0.462038i 0.862814 0.505522i \(-0.168700\pi\)
0.252644 + 0.967559i \(0.418700\pi\)
\(422\) 2.79381 + 3.69702i 0.136000 + 0.179968i
\(423\) 33.1214 + 33.1214i 1.61042 + 1.61042i
\(424\) 13.4160 + 34.5277i 0.651541 + 1.67681i
\(425\) −6.19726 6.19726i −0.300611 0.300611i
\(426\) 7.70463 + 1.07212i 0.373291 + 0.0519443i
\(427\) −14.6585 + 6.35617i −0.709375 + 0.307597i
\(428\) −6.52570 + 0.761520i −0.315431 + 0.0368095i
\(429\) 14.1864 5.87621i 0.684927 0.283706i
\(430\) 1.02542 1.74626i 0.0494502 0.0842119i
\(431\) 5.76864 0.277865 0.138933 0.990302i \(-0.455633\pi\)
0.138933 + 0.990302i \(0.455633\pi\)
\(432\) −9.08034 + 6.55187i −0.436878 + 0.315227i
\(433\) −24.4362 −1.17433 −0.587163 0.809469i \(-0.699755\pi\)
−0.587163 + 0.809469i \(0.699755\pi\)
\(434\) 14.3630 3.98873i 0.689448 0.191465i
\(435\) −22.2228 53.6507i −1.06550 2.57235i
\(436\) 0.208204 0.263217i 0.00997118 0.0126058i
\(437\) 17.9036 + 7.41593i 0.856447 + 0.354752i
\(438\) 4.46847 32.1121i 0.213512 1.53438i
\(439\) −24.7270 + 24.7270i −1.18016 + 1.18016i −0.200453 + 0.979703i \(0.564242\pi\)
−0.979703 + 0.200453i \(0.935758\pi\)
\(440\) 0.283362 12.8230i 0.0135088 0.611315i
\(441\) −19.3954 + 20.7153i −0.923591 + 0.986444i
\(442\) 8.04268 + 10.6428i 0.382551 + 0.506227i
\(443\) −1.81762 + 4.38813i −0.0863578 + 0.208486i −0.961159 0.275997i \(-0.910992\pi\)
0.874801 + 0.484483i \(0.160992\pi\)
\(444\) 17.5401 + 31.4408i 0.832415 + 1.49212i
\(445\) −3.12098 7.53470i −0.147948 0.357179i
\(446\) −33.4798 + 8.70713i −1.58531 + 0.412294i
\(447\) −19.5987 −0.926986
\(448\) 0.587097 21.1579i 0.0277377 0.999615i
\(449\) 3.44160 0.162419 0.0812097 0.996697i \(-0.474122\pi\)
0.0812097 + 0.996697i \(0.474122\pi\)
\(450\) −19.0970 + 4.96659i −0.900243 + 0.234127i
\(451\) 1.05135 + 2.53819i 0.0495063 + 0.119519i
\(452\) −2.77563 4.97536i −0.130555 0.234021i
\(453\) 6.01882 14.5307i 0.282789 0.682713i
\(454\) 12.1061 + 16.0199i 0.568168 + 0.751852i
\(455\) 28.4715 0.468321i 1.33477 0.0219552i
\(456\) 15.8078 + 0.349319i 0.740268 + 0.0163583i
\(457\) −17.6622 + 17.6622i −0.826202 + 0.826202i −0.986989 0.160787i \(-0.948597\pi\)
0.160787 + 0.986989i \(0.448597\pi\)
\(458\) 3.79514 27.2733i 0.177335 1.27440i
\(459\) −6.58572 2.72790i −0.307395 0.127327i
\(460\) 33.1906 41.9604i 1.54752 1.95642i
\(461\) 13.7497 + 33.1948i 0.640389 + 1.54604i 0.826155 + 0.563442i \(0.190523\pi\)
−0.185766 + 0.982594i \(0.559477\pi\)
\(462\) −4.15024 14.9446i −0.193087 0.695287i
\(463\) 9.55536 0.444075 0.222038 0.975038i \(-0.428729\pi\)
0.222038 + 0.975038i \(0.428729\pi\)
\(464\) 29.7152 + 4.80636i 1.37949 + 0.223129i
\(465\) 30.7432 1.42568
\(466\) −14.9344 + 25.4328i −0.691824 + 1.17815i
\(467\) −13.5473 + 5.61148i −0.626895 + 0.259668i −0.673433 0.739248i \(-0.735181\pi\)
0.0465384 + 0.998917i \(0.485181\pi\)
\(468\) 29.8318 3.48124i 1.37898 0.160920i
\(469\) 11.3463 4.91996i 0.523925 0.227183i
\(470\) −47.0227 6.54332i −2.16899 0.301821i
\(471\) 1.36787 + 1.36787i 0.0630281 + 0.0630281i
\(472\) −25.6374 + 9.96164i −1.18006 + 0.458521i
\(473\) 0.543912 + 0.543912i 0.0250091 + 0.0250091i
\(474\) −23.4866 31.0796i −1.07877 1.42753i
\(475\) 6.69284 + 2.77227i 0.307089 + 0.127200i
\(476\) 11.6577 6.75730i 0.534330 0.309721i
\(477\) 20.3179 + 49.0517i 0.930291 + 2.24592i
\(478\) 7.29725 1.89780i 0.333768 0.0868035i
\(479\) 12.7617 0.583096 0.291548 0.956556i \(-0.405830\pi\)
0.291548 + 0.956556i \(0.405830\pi\)
\(480\) 12.8428 41.7205i 0.586189 1.90427i
\(481\) 25.1067i 1.14477i
\(482\) −27.2396 + 7.08423i −1.24073 + 0.322678i
\(483\) 23.7717 60.1704i 1.08165 2.73785i
\(484\) −16.4773 4.67627i −0.748970 0.212558i
\(485\) −7.59666 3.14664i −0.344947 0.142882i
\(486\) 23.6408 17.8652i 1.07237 0.810380i
\(487\) −5.86287 + 5.86287i −0.265672 + 0.265672i −0.827354 0.561681i \(-0.810155\pi\)
0.561681 + 0.827354i \(0.310155\pi\)
\(488\) 6.88342 15.6320i 0.311598 0.707626i
\(489\) −38.0482 38.0482i −1.72060 1.72060i
\(490\) 3.02512 28.6032i 0.136661 1.29216i
\(491\) −3.95295 1.63736i −0.178394 0.0738932i 0.291699 0.956510i \(-0.405780\pi\)
−0.470093 + 0.882617i \(0.655780\pi\)
\(492\) 1.08377 + 9.28716i 0.0488602 + 0.418698i
\(493\) 7.33332 + 17.7042i 0.330276 + 0.797357i
\(494\) −9.50829 5.58339i −0.427798 0.251208i
\(495\) 18.3838i 0.826289i
\(496\) −8.37096 + 13.5602i −0.375867 + 0.608869i
\(497\) −3.81028 + 3.93772i −0.170914 + 0.176631i
\(498\) 39.0410 + 22.9254i 1.74947 + 1.02731i
\(499\) 14.0448 + 33.9073i 0.628734 + 1.51790i 0.841197 + 0.540728i \(0.181851\pi\)
−0.212464 + 0.977169i \(0.568149\pi\)
\(500\) −5.61746 + 7.10173i −0.251220 + 0.317599i
\(501\) 16.4680 39.7573i 0.735736 1.77622i
\(502\) 5.77720 + 0.803911i 0.257849 + 0.0358803i
\(503\) 10.8605 10.8605i 0.484248 0.484248i −0.422237 0.906485i \(-0.638755\pi\)
0.906485 + 0.422237i \(0.138755\pi\)
\(504\) 0.171314 30.3368i 0.00763095 1.35131i
\(505\) −17.1453 17.1453i −0.762957 0.762957i
\(506\) 12.2520 + 16.2130i 0.544670 + 0.720757i
\(507\) −1.77094 0.733547i −0.0786502 0.0325780i
\(508\) −0.204650 0.366838i −0.00907988 0.0162758i
\(509\) 2.94065 1.21806i 0.130342 0.0539895i −0.316559 0.948573i \(-0.602528\pi\)
0.446901 + 0.894583i \(0.352528\pi\)
\(510\) 26.8950 6.99462i 1.19093 0.309727i
\(511\) 16.4120 + 15.8808i 0.726024 + 0.702527i
\(512\) 14.9051 + 17.0246i 0.658719 + 0.752389i
\(513\) 5.89208 0.260142
\(514\) 10.3503 + 39.7980i 0.456532 + 1.75541i
\(515\) 8.85215 3.66668i 0.390072 0.161573i
\(516\) 1.27542 + 2.28621i 0.0561473 + 0.100645i
\(517\) 6.90106 16.6606i 0.303508 0.732734i
\(518\) −25.1721 3.08165i −1.10600 0.135400i
\(519\) 1.35569 1.35569i 0.0595083 0.0595083i
\(520\) −21.9957 + 21.0446i −0.964574 + 0.922866i
\(521\) −19.6375 19.6375i −0.860335 0.860335i 0.131042 0.991377i \(-0.458168\pi\)
−0.991377 + 0.131042i \(0.958168\pi\)
\(522\) 42.7326 + 5.94634i 1.87036 + 0.260264i
\(523\) 1.73006 4.17674i 0.0756503 0.182636i −0.881530 0.472127i \(-0.843486\pi\)
0.957181 + 0.289492i \(0.0934862\pi\)
\(524\) −7.80169 6.17113i −0.340819 0.269587i
\(525\) 8.88647 22.4932i 0.387838 0.981686i
\(526\) 11.8835 20.2372i 0.518146 0.882382i
\(527\) −10.1449 −0.441921
\(528\) 14.1092 + 8.70991i 0.614025 + 0.379050i
\(529\) 61.7660i 2.68548i
\(530\) −46.4040 27.2490i −2.01566 1.18362i
\(531\) −36.4217 + 15.0864i −1.58057 + 0.654692i
\(532\) −6.76499 + 8.84774i −0.293300 + 0.383598i
\(533\) 2.49527 6.02410i 0.108082 0.260933i
\(534\) 10.4424 + 1.45309i 0.451889 + 0.0628814i
\(535\) 6.74894 6.74894i 0.291782 0.291782i
\(536\) −5.32807 + 12.0998i −0.230138 + 0.522634i
\(537\) 35.3599 35.3599i 1.52589 1.52589i
\(538\) 26.7218 + 35.3607i 1.15206 + 1.52451i
\(539\) 10.2257 + 3.84671i 0.440453 + 0.165689i
\(540\) 4.44111 15.6487i 0.191115 0.673414i
\(541\) −11.1799 26.9906i −0.480660 1.16042i −0.959296 0.282403i \(-0.908869\pi\)
0.478636 0.878013i \(-0.341131\pi\)
\(542\) −4.54410 17.4725i −0.195186 0.750509i
\(543\) 16.7339i 0.718121i
\(544\) −4.23798 + 13.7674i −0.181702 + 0.590271i
\(545\) 0.487549i 0.0208843i
\(546\) −18.1155 + 32.0457i −0.775274 + 1.37143i
\(547\) 6.06574 2.51251i 0.259352 0.107427i −0.249219 0.968447i \(-0.580174\pi\)
0.508571 + 0.861020i \(0.330174\pi\)
\(548\) 1.33902 4.71819i 0.0572002 0.201551i
\(549\) 9.36861 22.6178i 0.399843 0.965306i
\(550\) 4.58013 + 6.06085i 0.195297 + 0.258435i
\(551\) −11.2002 11.2002i −0.477145 0.477145i
\(552\) 25.0494 + 64.4673i 1.06617 + 2.74391i
\(553\) 27.4366 0.451298i 1.16672 0.0191911i
\(554\) 4.25697 30.5921i 0.180861 1.29973i
\(555\) −48.3208 20.0151i −2.05111 0.849596i
\(556\) −4.51823 38.7181i −0.191616 1.64201i
\(557\) −28.0175 + 11.6052i −1.18714 + 0.491730i −0.886823 0.462109i \(-0.847093\pi\)
−0.300318 + 0.953839i \(0.597093\pi\)
\(558\) −11.5658 + 19.6961i −0.489619 + 0.833803i
\(559\) 1.82563i 0.0772159i
\(560\) 18.3996 + 24.6360i 0.777524 + 1.04106i
\(561\) 10.5557i 0.445663i
\(562\) −14.0780 8.26675i −0.593843 0.348712i
\(563\) −32.8788 + 13.6189i −1.38568 + 0.573966i −0.945993 0.324186i \(-0.894910\pi\)
−0.439684 + 0.898152i \(0.644910\pi\)
\(564\) 38.0756 48.1361i 1.60327 2.02689i
\(565\) 7.64653 + 3.16730i 0.321692 + 0.133249i
\(566\) 25.8742 + 3.60046i 1.08757 + 0.151338i
\(567\) 0.205694 + 12.5052i 0.00863833 + 0.525167i
\(568\) 0.129412 5.85630i 0.00542999 0.245725i
\(569\) 13.5586 + 13.5586i 0.568406 + 0.568406i 0.931682 0.363276i \(-0.118342\pi\)
−0.363276 + 0.931682i \(0.618342\pi\)
\(570\) −18.3259 + 13.8488i −0.767589 + 0.580060i
\(571\) −9.21862 + 22.2557i −0.385787 + 0.931372i 0.605035 + 0.796199i \(0.293159\pi\)
−0.990822 + 0.135173i \(0.956841\pi\)
\(572\) −5.63337 10.0979i −0.235543 0.422215i
\(573\) −31.7820 + 13.1645i −1.32771 + 0.549956i
\(574\) −5.73352 3.24117i −0.239312 0.135284i
\(575\) 31.6877i 1.32147i
\(576\) 21.8974 + 23.9235i 0.912392 + 0.996811i
\(577\) 1.13890i 0.0474131i 0.999719 + 0.0237066i \(0.00754674\pi\)
−0.999719 + 0.0237066i \(0.992453\pi\)
\(578\) 14.3925 3.74308i 0.598650 0.155692i
\(579\) 3.17037 + 7.65394i 0.131756 + 0.318087i
\(580\) −38.1886 + 21.3045i −1.58570 + 0.884621i
\(581\) −29.2589 + 12.6871i −1.21386 + 0.526351i
\(582\) 8.48058 6.40870i 0.351532 0.265649i
\(583\) 14.4536 14.4536i 0.598608 0.598608i
\(584\) −24.4084 0.539374i −1.01003 0.0223195i
\(585\) −30.8524 + 30.8524i −1.27559 + 1.27559i
\(586\) −0.559678 + 4.02205i −0.0231201 + 0.166149i
\(587\) 9.62366 23.2336i 0.397211 0.958952i −0.591113 0.806588i \(-0.701311\pi\)
0.988324 0.152364i \(-0.0486886\pi\)
\(588\) 29.9056 + 22.0961i 1.23329 + 0.911226i
\(589\) 7.74721 3.20900i 0.319218 0.132224i
\(590\) 20.2328 34.4558i 0.832973 1.41852i
\(591\) 48.8313i 2.00865i
\(592\) 21.9854 15.8634i 0.903594 0.651983i
\(593\) 19.9388 0.818789 0.409395 0.912357i \(-0.365740\pi\)
0.409395 + 0.912357i \(0.365740\pi\)
\(594\) 5.32810 + 3.12872i 0.218615 + 0.128373i
\(595\) −7.19256 + 18.2056i −0.294866 + 0.746358i
\(596\) 1.71063 + 14.6589i 0.0700703 + 0.600453i
\(597\) 9.94359 24.0060i 0.406964 0.982498i
\(598\) 6.64747 47.7712i 0.271835 1.95351i
\(599\) 14.7541 + 14.7541i 0.602835 + 0.602835i 0.941064 0.338229i \(-0.109828\pi\)
−0.338229 + 0.941064i \(0.609828\pi\)
\(600\) 9.36410 + 24.0996i 0.382288 + 0.983860i
\(601\) 14.0509 14.0509i 0.573148 0.573148i −0.359858 0.933007i \(-0.617175\pi\)
0.933007 + 0.359858i \(0.117175\pi\)
\(602\) −1.83038 0.224082i −0.0746008 0.00913288i
\(603\) −7.25172 + 17.5072i −0.295313 + 0.712949i
\(604\) −11.3937 3.23352i −0.463602 0.131570i
\(605\) 22.9885 9.52213i 0.934614 0.387130i
\(606\) 30.3365 7.88964i 1.23233 0.320495i
\(607\) −17.8857 −0.725956 −0.362978 0.931798i \(-0.618240\pi\)
−0.362978 + 0.931798i \(0.618240\pi\)
\(608\) −1.11848 11.8540i −0.0453603 0.480744i
\(609\) −36.7719 + 38.0018i −1.49007 + 1.53991i
\(610\) 6.24547 + 24.0145i 0.252871 + 0.972317i
\(611\) −39.5421 + 16.3789i −1.59970 + 0.662619i
\(612\) −5.63688 + 19.8622i −0.227857 + 0.802880i
\(613\) −27.8036 11.5166i −1.12298 0.465152i −0.257588 0.966255i \(-0.582928\pi\)
−0.865388 + 0.501103i \(0.832928\pi\)
\(614\) −4.37579 + 3.30675i −0.176592 + 0.133449i
\(615\) −9.60487 9.60487i −0.387306 0.387306i
\(616\) −10.8157 + 4.40860i −0.435775 + 0.177628i
\(617\) 1.18385 1.18385i 0.0476600 0.0476600i −0.682875 0.730535i \(-0.739271\pi\)
0.730535 + 0.682875i \(0.239271\pi\)
\(618\) −1.70716 + 12.2683i −0.0686722 + 0.493504i
\(619\) −1.51142 + 3.64890i −0.0607493 + 0.146662i −0.951339 0.308145i \(-0.900292\pi\)
0.890590 + 0.454807i \(0.150292\pi\)
\(620\) −2.68336 22.9945i −0.107766 0.923482i
\(621\) 9.86288 + 23.8111i 0.395784 + 0.955507i
\(622\) −0.808972 + 1.37765i −0.0324368 + 0.0552387i
\(623\) −5.16424 + 5.33697i −0.206901 + 0.213821i
\(624\) −9.06133 38.2959i −0.362744 1.53306i
\(625\) 30.3631i 1.21452i
\(626\) −10.5535 + 17.9722i −0.421803 + 0.718314i
\(627\) −3.33893 8.06090i −0.133344 0.321921i
\(628\) 0.903714 1.14250i 0.0360621 0.0455906i
\(629\) 15.9454 + 6.60480i 0.635785 + 0.263351i
\(630\) 27.1458 + 34.7196i 1.08151 + 1.38326i
\(631\) −25.8833 25.8833i −1.03040 1.03040i −0.999523 0.0308730i \(-0.990171\pi\)
−0.0308730 0.999523i \(-0.509829\pi\)
\(632\) −21.1961 + 20.2796i −0.843137 + 0.806680i
\(633\) 6.15371 6.15371i 0.244588 0.244588i
\(634\) 7.33016 + 9.69994i 0.291118 + 0.385234i
\(635\) 0.563787 + 0.233528i 0.0223732 + 0.00926729i
\(636\) 60.7526 33.8923i 2.40900 1.34392i
\(637\) −10.7055 23.6169i −0.424167 0.935735i
\(638\) −4.18078 16.0755i −0.165519 0.636436i
\(639\) 8.39589i 0.332136i
\(640\) −32.3260 5.96431i −1.27780 0.235760i
\(641\) −29.7504 −1.17507 −0.587536 0.809198i \(-0.699902\pi\)
−0.587536 + 0.809198i \(0.699902\pi\)
\(642\) 3.10561 + 11.9414i 0.122569 + 0.471289i
\(643\) 0.683163 + 1.64930i 0.0269413 + 0.0650421i 0.936778 0.349925i \(-0.113793\pi\)
−0.909836 + 0.414967i \(0.863793\pi\)
\(644\) −47.0796 12.5283i −1.85520 0.493685i
\(645\) −3.51364 1.45540i −0.138349 0.0573062i
\(646\) 6.04738 4.56995i 0.237931 0.179802i
\(647\) 25.2116 + 25.2116i 0.991169 + 0.991169i 0.999961 0.00879259i \(-0.00279880\pi\)
−0.00879259 + 0.999961i \(0.502799\pi\)
\(648\) −9.24311 9.66084i −0.363104 0.379514i
\(649\) 10.7321 + 10.7321i 0.421270 + 0.421270i
\(650\) 2.48499 17.8581i 0.0974695 0.700452i
\(651\) −11.1372 25.6844i −0.436500 1.00665i
\(652\) −25.1374 + 31.7793i −0.984455 + 1.24457i
\(653\) 6.65610 2.75705i 0.260473 0.107892i −0.248625 0.968600i \(-0.579979\pi\)
0.509099 + 0.860708i \(0.329979\pi\)
\(654\) −0.543503 0.319152i −0.0212527 0.0124798i
\(655\) 14.4508 0.564640
\(656\) 6.85178 1.62122i 0.267517 0.0632982i
\(657\) −34.9932 −1.36521
\(658\) 11.5681 + 41.6555i 0.450970 + 1.62390i
\(659\) 11.2233 + 27.0954i 0.437197 + 1.05549i 0.976912 + 0.213640i \(0.0685320\pi\)
−0.539715 + 0.841848i \(0.681468\pi\)
\(660\) −23.9256 + 2.79201i −0.931302 + 0.108679i
\(661\) 20.5741 + 8.52207i 0.800239 + 0.331470i 0.745052 0.667006i \(-0.232424\pi\)
0.0551871 + 0.998476i \(0.482424\pi\)
\(662\) 4.91564 + 0.684022i 0.191052 + 0.0265853i
\(663\) 17.7150 17.7150i 0.687994 0.687994i
\(664\) 13.7395 31.2019i 0.533197 1.21087i
\(665\) −0.266106 16.1779i −0.0103191 0.627351i
\(666\) 31.0017 23.4277i 1.20129 0.907805i
\(667\) 26.5141 64.0107i 1.02663 2.47850i
\(668\) −31.1740 8.84718i −1.20616 0.342308i
\(669\) 24.8620 + 60.0223i 0.961222 + 2.32059i
\(670\) −4.83427 18.5883i −0.186764 0.718127i
\(671\) −9.42517 −0.363854
\(672\) −39.5079 + 4.38440i −1.52405 + 0.169132i
\(673\) 6.25912 0.241271 0.120636 0.992697i \(-0.461507\pi\)
0.120636 + 0.992697i \(0.461507\pi\)
\(674\) 2.35866 + 9.06927i 0.0908520 + 0.349335i
\(675\) 3.68700 + 8.90120i 0.141913 + 0.342608i
\(676\) −0.394087 + 1.38861i −0.0151572 + 0.0534080i
\(677\) 5.52143 13.3299i 0.212206 0.512310i −0.781556 0.623835i \(-0.785574\pi\)
0.993762 + 0.111525i \(0.0355737\pi\)
\(678\) −8.53626 + 6.45078i −0.327833 + 0.247741i
\(679\) 0.123144 + 7.48654i 0.00472584 + 0.287307i
\(680\) −7.57914 19.5058i −0.290647 0.748012i
\(681\) 26.6652 26.6652i 1.02181 1.02181i
\(682\) 8.70966 + 1.21197i 0.333510 + 0.0464087i
\(683\) −18.2503 7.55952i −0.698328 0.289257i 0.00513711 0.999987i \(-0.498365\pi\)
−0.703465 + 0.710730i \(0.748365\pi\)
\(684\) −1.97809 16.9508i −0.0756340 0.648130i
\(685\) 2.72661 + 6.58261i 0.104178 + 0.251509i
\(686\) −24.9924 + 7.83458i −0.954214 + 0.299126i
\(687\) −51.7135 −1.97299
\(688\) 1.59866 1.15351i 0.0609484 0.0439770i
\(689\) −48.5132 −1.84821
\(690\) −86.6419 50.8772i −3.29840 1.93686i
\(691\) 22.5623 9.34562i 0.858311 0.355524i 0.0902645 0.995918i \(-0.471229\pi\)
0.768047 + 0.640394i \(0.221229\pi\)
\(692\) −1.13233 0.895669i −0.0430446 0.0340482i
\(693\) −15.3587 + 6.65980i −0.583429 + 0.252985i
\(694\) −1.79087 + 12.8699i −0.0679807 + 0.488534i
\(695\) 40.0426 + 40.0426i 1.51890 + 1.51890i
\(696\) 1.24892 56.5175i 0.0473400 2.14229i
\(697\) 3.16951 + 3.16951i 0.120054 + 0.120054i
\(698\) 19.5723 14.7906i 0.740821 0.559832i
\(699\) 51.1733 + 21.1967i 1.93555 + 0.801731i
\(700\) −17.5996 4.68340i −0.665201 0.177016i
\(701\) 13.8010 + 33.3185i 0.521255 + 1.25842i 0.937124 + 0.348997i \(0.113478\pi\)
−0.415869 + 0.909425i \(0.636522\pi\)
\(702\) −3.69108 14.1926i −0.139311 0.535664i
\(703\) −14.2659 −0.538050
\(704\) 5.28313 11.3133i 0.199115 0.426386i
\(705\) 89.1609i 3.35799i
\(706\) −4.24362 16.3172i −0.159711 0.614104i
\(707\) −8.11290 + 20.5352i −0.305117 + 0.772306i
\(708\) 25.1656 + 45.1098i 0.945782 + 1.69533i
\(709\) −23.5630 9.76010i −0.884926 0.366548i −0.106521 0.994310i \(-0.533971\pi\)
−0.778405 + 0.627762i \(0.783971\pi\)
\(710\) 5.13053 + 6.78919i 0.192545 + 0.254794i
\(711\) −29.7309 + 29.7309i −1.11500 + 1.11500i
\(712\) 0.175398 7.93731i 0.00657330 0.297463i
\(713\) 25.9365 + 25.9365i 0.971328 + 0.971328i
\(714\) −15.5868 19.9355i −0.583320 0.746068i
\(715\) 15.5193 + 6.42830i 0.580389 + 0.240405i
\(716\) −29.5339 23.3613i −1.10373 0.873052i
\(717\) −5.41892 13.0824i −0.202373 0.488572i
\(718\) −18.7567 + 31.9420i −0.699996 + 1.19207i
\(719\) 48.7896i 1.81955i 0.415106 + 0.909773i \(0.363744\pi\)
−0.415106 + 0.909773i \(0.636256\pi\)
\(720\) −46.5105 7.52296i −1.73334 0.280364i
\(721\) −6.27015 6.06721i −0.233513 0.225955i
\(722\) 10.4335 17.7678i 0.388294 0.661251i
\(723\) 20.2281 + 48.8349i 0.752290 + 1.81619i
\(724\) −12.5162 + 1.46059i −0.465162 + 0.0542823i
\(725\) 9.91165 23.9288i 0.368110 0.888695i
\(726\) −4.43340 + 31.8600i −0.164539 + 1.18244i
\(727\) −24.0403 + 24.0403i −0.891606 + 0.891606i −0.994674 0.103068i \(-0.967134\pi\)
0.103068 + 0.994674i \(0.467134\pi\)
\(728\) 25.5499 + 10.7526i 0.946943 + 0.398516i
\(729\) −29.3225 29.3225i −1.08602 1.08602i
\(730\) 28.2966 21.3835i 1.04731 0.791439i
\(731\) 1.15947 + 0.480267i 0.0428844 + 0.0177633i
\(732\) −30.8588 8.75774i −1.14058 0.323695i
\(733\) −10.2746 + 4.25589i −0.379502 + 0.157195i −0.564276 0.825586i \(-0.690845\pi\)
0.184774 + 0.982781i \(0.440845\pi\)
\(734\) 9.09990 + 34.9900i 0.335883 + 1.29151i
\(735\) −53.9879 + 1.77655i −1.99138 + 0.0655289i
\(736\) 46.0323 24.3627i 1.69677 0.898021i
\(737\) 7.29550 0.268733
\(738\) 9.76694 2.54010i 0.359526 0.0935023i
\(739\) −11.9282 + 4.94082i −0.438786 + 0.181751i −0.591130 0.806576i \(-0.701318\pi\)
0.152344 + 0.988328i \(0.451318\pi\)
\(740\) −10.7528 + 37.8888i −0.395282 + 1.39282i
\(741\) −7.92458 + 19.1316i −0.291117 + 0.702818i
\(742\) −5.95462 + 48.6395i −0.218601 + 1.78561i
\(743\) −31.5613 + 31.5613i −1.15787 + 1.15787i −0.172939 + 0.984932i \(0.555326\pi\)
−0.984932 + 0.172939i \(0.944674\pi\)
\(744\) 27.3901 + 12.0610i 1.00417 + 0.442177i
\(745\) −15.1604 15.1604i −0.555435 0.555435i
\(746\) 2.95789 21.2565i 0.108296 0.778256i
\(747\) 18.7001 45.1459i 0.684199 1.65180i
\(748\) 7.89521 0.921336i 0.288677 0.0336874i
\(749\) −8.08330 3.19349i −0.295357 0.116688i
\(750\) 14.6640 + 8.61088i 0.535453 + 0.314425i
\(751\) 21.8090 0.795822 0.397911 0.917424i \(-0.369735\pi\)
0.397911 + 0.917424i \(0.369735\pi\)
\(752\) −39.3270 24.2773i −1.43411 0.885303i
\(753\) 10.9543i 0.399197i
\(754\) −19.9622 + 33.9949i −0.726981 + 1.23802i
\(755\) 15.8959 6.58432i 0.578513 0.239628i
\(756\) −14.6826 + 1.95866i −0.534000 + 0.0712358i
\(757\) 10.9057 26.3287i 0.396374 0.956931i −0.592145 0.805832i \(-0.701719\pi\)
0.988519 0.151100i \(-0.0482814\pi\)
\(758\) −2.12924 + 15.3015i −0.0773375 + 0.555776i
\(759\) 26.9867 26.9867i 0.979554 0.979554i
\(760\) 11.9578 + 12.4982i 0.433755 + 0.453358i
\(761\) −30.2009 + 30.2009i −1.09478 + 1.09478i −0.0997698 + 0.995011i \(0.531811\pi\)
−0.995011 + 0.0997698i \(0.968189\pi\)
\(762\) −0.629387 + 0.475623i −0.0228003 + 0.0172300i
\(763\) 0.407322 0.176622i 0.0147461 0.00639414i
\(764\) 12.6205 + 22.6224i 0.456594 + 0.818451i
\(765\) −11.4782 27.7108i −0.414995 1.00189i
\(766\) 9.01920 2.34563i 0.325877 0.0847512i
\(767\) 36.0219i 1.30067i
\(768\) 27.8096 32.1317i 1.00349 1.15945i
\(769\) 3.97118i 0.143204i 0.997433 + 0.0716022i \(0.0228112\pi\)
−0.997433 + 0.0716022i \(0.977189\pi\)
\(770\) 8.34991 14.7707i 0.300910 0.532298i
\(771\) 71.3495 29.5539i 2.56959 1.06436i
\(772\) 5.44809 3.03935i 0.196081 0.109389i
\(773\) −13.9301 + 33.6303i −0.501031 + 1.20960i 0.447891 + 0.894088i \(0.352175\pi\)
−0.948923 + 0.315509i \(0.897825\pi\)
\(774\) 2.25428 1.70354i 0.0810284 0.0612325i
\(775\) 9.69572 + 9.69572i 0.348280 + 0.348280i
\(776\) −5.53363 5.78372i −0.198646 0.207624i
\(777\) 0.783295 + 47.6204i 0.0281006 + 1.70837i
\(778\) −12.5031 1.73984i −0.448260 0.0623764i
\(779\) −3.42297 1.41784i −0.122641 0.0507994i
\(780\) 44.8385 + 35.4672i 1.60547 + 1.26993i
\(781\) −2.98631 + 1.23697i −0.106859 + 0.0442623i
\(782\) 28.5910 + 16.7890i 1.02241 + 0.600372i
\(783\) 21.0659i 0.752833i
\(784\) 13.9166 24.2967i 0.497022 0.867738i
\(785\) 2.11621i 0.0755308i
\(786\) −9.45958 + 16.1093i −0.337412 + 0.574600i
\(787\) 4.94464 2.04814i 0.176257 0.0730082i −0.292810 0.956171i \(-0.594590\pi\)
0.469067 + 0.883163i \(0.344590\pi\)
\(788\) 36.5236 4.26214i 1.30110 0.151833i
\(789\) −40.7192 16.8664i −1.44964 0.600461i
\(790\) 5.87351 42.2092i 0.208970 1.50174i
\(791\) −0.123953 7.53569i −0.00440725 0.267938i
\(792\) 7.21223 16.3787i 0.256275 0.581991i
\(793\) 15.8177 + 15.8177i 0.561702 + 0.561702i
\(794\) 9.56231 + 12.6537i 0.339354 + 0.449064i
\(795\) −38.6749 + 93.3695i −1.37166 + 3.31147i
\(796\) −18.8233 5.34205i −0.667173 0.189344i
\(797\) 32.9963 13.6675i 1.16879 0.484128i 0.287996 0.957632i \(-0.407011\pi\)
0.880792 + 0.473504i \(0.157011\pi\)
\(798\) 18.2088 + 10.2935i 0.644584 + 0.364385i
\(799\) 29.4222i 1.04088i
\(800\) 17.2081 9.10741i 0.608397 0.321996i
\(801\) 11.3793i 0.402069i
\(802\) 3.02178 + 11.6190i 0.106703 + 0.410283i
\(803\) 5.15557 + 12.4466i 0.181936 + 0.439232i
\(804\) 23.8861 + 6.77888i 0.842398 + 0.239073i
\(805\) 64.9328 28.1559i 2.28858 0.992366i
\(806\) −12.5829 16.6509i −0.443214 0.586501i
\(807\) 58.8580 58.8580i 2.07190 2.07190i
\(808\) −8.54895 22.0017i −0.300751 0.774016i
\(809\) 26.9368 26.9368i 0.947048 0.947048i −0.0516192 0.998667i \(-0.516438\pi\)
0.998667 + 0.0516192i \(0.0164382\pi\)
\(810\) 19.2382 + 2.67705i 0.675963 + 0.0940618i
\(811\) −8.88461 + 21.4493i −0.311981 + 0.753188i 0.687651 + 0.726042i \(0.258642\pi\)
−0.999631 + 0.0271465i \(0.991358\pi\)
\(812\) 31.6332 + 24.1868i 1.11011 + 0.848790i
\(813\) −31.3246 + 12.9751i −1.09860 + 0.455055i
\(814\) −12.9004 7.57529i −0.452160 0.265514i
\(815\) 58.8637i 2.06191i
\(816\) 26.7057 + 4.31958i 0.934887 + 0.151216i
\(817\) −1.03734 −0.0362921
\(818\) 1.99362 3.39506i 0.0697053 0.118705i
\(819\) 36.9523 + 14.5989i 1.29122 + 0.510125i
\(820\) −6.34567 + 8.02235i −0.221600 + 0.280153i
\(821\) −13.0349 + 31.4690i −0.454921 + 1.09828i 0.515507 + 0.856886i \(0.327604\pi\)
−0.970428 + 0.241392i \(0.922396\pi\)
\(822\) −9.12293 1.26948i −0.318199 0.0442781i
\(823\) 13.1260 + 13.1260i 0.457542 + 0.457542i 0.897848 0.440306i \(-0.145130\pi\)
−0.440306 + 0.897848i \(0.645130\pi\)
\(824\) 9.32515 + 0.206066i 0.324857 + 0.00717865i
\(825\) 10.0883 10.0883i 0.351230 0.351230i
\(826\) −36.1157 4.42140i −1.25663 0.153840i
\(827\) −6.18534 + 14.9327i −0.215085 + 0.519262i −0.994191 0.107631i \(-0.965674\pi\)
0.779106 + 0.626893i \(0.215674\pi\)
\(828\) 65.1906 36.3682i 2.26553 1.26388i
\(829\) −2.24820 + 0.931237i −0.0780834 + 0.0323432i −0.421383 0.906883i \(-0.638455\pi\)
0.343300 + 0.939226i \(0.388455\pi\)
\(830\) 12.4662 + 47.9336i 0.432706 + 1.66380i
\(831\) −58.0065 −2.01222
\(832\) −27.8527 + 10.1201i −0.965620 + 0.350850i
\(833\) 17.8155 0.586243i 0.617270 0.0203121i
\(834\) −70.8503 + 18.4261i −2.45335 + 0.638044i
\(835\) 43.4926 18.0152i 1.50512 0.623443i
\(836\) −5.73776 + 3.20095i −0.198445 + 0.110707i
\(837\) 10.3035 + 4.26784i 0.356140 + 0.147518i
\(838\) 8.21187 + 10.8667i 0.283674 + 0.375384i
\(839\) −7.35290 7.35290i −0.253850 0.253850i 0.568697 0.822547i \(-0.307448\pi\)
−0.822547 + 0.568697i \(0.807448\pi\)
\(840\) 41.0631 40.6019i 1.41681 1.40090i
\(841\) −19.5379 + 19.5379i −0.673721 + 0.673721i
\(842\) −34.7000 4.82858i −1.19584 0.166404i
\(843\) −11.7331 + 28.3263i −0.404110 + 0.975608i
\(844\) −5.13981 4.06558i −0.176920 0.139943i
\(845\) −0.802467 1.93733i −0.0276057 0.0666460i
\(846\) −57.1224 33.5430i −1.96391 1.15323i
\(847\) −16.2832 15.7562i −0.559496 0.541388i
\(848\) −30.6526 42.4820i −1.05262 1.45884i
\(849\) 49.0607i 1.68376i
\(850\) 10.6880 + 6.27615i 0.366597 + 0.215270i
\(851\) −23.8801 57.6516i −0.818599 1.97627i
\(852\) −10.9268 + 1.27511i −0.374347 + 0.0436847i
\(853\) −43.8860 18.1782i −1.50263 0.622409i −0.528607 0.848867i \(-0.677285\pi\)
−0.974021 + 0.226458i \(0.927285\pi\)
\(854\) 17.8003 13.9174i 0.609115 0.476242i
\(855\) 17.5307 + 17.5307i 0.599537 + 0.599537i
\(856\) 8.66055 3.36514i 0.296012 0.115018i
\(857\) 34.8771 34.8771i 1.19138 1.19138i 0.214697 0.976681i \(-0.431123\pi\)
0.976681 0.214697i \(-0.0688765\pi\)
\(858\) −17.3251 + 13.0924i −0.591468 + 0.446967i
\(859\) 23.3888 + 9.68796i 0.798015 + 0.330549i 0.744161 0.668000i \(-0.232849\pi\)
0.0538542 + 0.998549i \(0.482849\pi\)
\(860\) −0.781890 + 2.75508i −0.0266622 + 0.0939473i
\(861\) −4.54488 + 11.5039i −0.154889 + 0.392052i
\(862\) −7.89544 + 2.05338i −0.268920 + 0.0699383i
\(863\) 33.9995i 1.15736i −0.815556 0.578678i \(-0.803569\pi\)
0.815556 0.578678i \(-0.196431\pi\)
\(864\) 10.0959 12.1996i 0.343471 0.415040i
\(865\) 2.09737 0.0713128
\(866\) 33.4454 8.69817i 1.13652 0.295576i
\(867\) −10.6879 25.8028i −0.362979 0.876309i
\(868\) −18.2387 + 10.5719i −0.619060 + 0.358834i
\(869\) 14.9552 + 6.19464i 0.507320 + 0.210139i
\(870\) 49.5133 + 65.5205i 1.67866 + 2.22135i
\(871\) −12.2436 12.2436i −0.414858 0.414858i
\(872\) −0.191273 + 0.434373i −0.00647731 + 0.0147097i
\(873\) −8.11257 8.11257i −0.274569 0.274569i
\(874\) −27.1442 3.77717i −0.918165 0.127765i
\(875\) −10.9898 + 4.76534i −0.371522 + 0.161098i
\(876\) 5.31454 + 45.5419i 0.179562 + 1.53872i
\(877\) −3.64849 + 1.51126i −0.123201 + 0.0510315i −0.443432 0.896308i \(-0.646239\pi\)
0.320231 + 0.947339i \(0.396239\pi\)
\(878\) 25.0418 42.6452i 0.845119 1.43921i
\(879\) 7.62631 0.257229
\(880\) 4.17660 + 17.6516i 0.140793 + 0.595034i
\(881\) 17.7682 0.598626 0.299313 0.954155i \(-0.403243\pi\)
0.299313 + 0.954155i \(0.403243\pi\)
\(882\) 19.1725 35.2566i 0.645571 1.18715i
\(883\) 7.04198 + 17.0008i 0.236981 + 0.572124i 0.996968 0.0778151i \(-0.0247944\pi\)
−0.759986 + 0.649939i \(0.774794\pi\)
\(884\) −14.7963 11.7038i −0.497652 0.393642i
\(885\) −69.3284 28.7168i −2.33045 0.965304i
\(886\) 0.925773 6.65295i 0.0311020 0.223510i
\(887\) 28.9536 28.9536i 0.972168 0.972168i −0.0274550 0.999623i \(-0.508740\pi\)
0.999623 + 0.0274550i \(0.00874029\pi\)
\(888\) −35.1983 36.7891i −1.18118 1.23456i
\(889\) −0.00913916 0.555615i −0.000306518 0.0186347i
\(890\) 6.95365 + 9.20170i 0.233087 + 0.308442i
\(891\) −2.82341 + 6.81632i −0.0945878 + 0.228355i
\(892\) 42.7239 23.8346i 1.43050 0.798042i
\(893\) 9.30669 + 22.4683i 0.311437 + 0.751874i
\(894\) 26.8244 6.97625i 0.897143 0.233321i
\(895\) 54.7047 1.82858
\(896\) 6.72770 + 29.1674i 0.224757 + 0.974415i
\(897\) −90.5801 −3.02438
\(898\) −4.71047 + 1.22506i −0.157190 + 0.0408807i
\(899\) −11.4731 27.6985i −0.382649 0.923797i
\(900\) 24.3699 13.5954i 0.812331 0.453179i
\(901\) 12.7623 30.8110i 0.425175 1.02646i
\(902\) −2.34245 3.09974i −0.0779951 0.103210i
\(903\) 0.0569571 + 3.46271i 0.00189542 + 0.115232i
\(904\) 5.56996 + 5.82169i 0.185254 + 0.193627i
\(905\) 12.9444 12.9444i 0.430286 0.430286i
\(906\) −3.06558 + 22.0304i −0.101847 + 0.731911i
\(907\) 20.0839 + 8.31901i 0.666874 + 0.276228i 0.690328 0.723497i \(-0.257466\pi\)
−0.0234539 + 0.999725i \(0.507466\pi\)
\(908\) −22.2718 17.6170i −0.739117 0.584640i
\(909\) −12.9469 31.2566i −0.429422 1.03672i
\(910\) −38.8018 + 10.7756i −1.28627 + 0.357207i
\(911\) 37.5867 1.24530 0.622651 0.782500i \(-0.286056\pi\)
0.622651 + 0.782500i \(0.286056\pi\)
\(912\) −21.7602 + 5.14876i −0.720553 + 0.170492i
\(913\) −18.8129 −0.622617
\(914\) 17.8870 30.4609i 0.591649 1.00756i
\(915\) 43.0529 17.8331i 1.42328 0.589544i
\(916\) 4.51371 + 38.6794i 0.149137 + 1.27800i
\(917\) −5.23502 12.0729i −0.172876 0.398683i
\(918\) 9.98478 + 1.38941i 0.329547 + 0.0458572i
\(919\) −27.2040 27.2040i −0.897378 0.897378i 0.0978255 0.995204i \(-0.468811\pi\)
−0.995204 + 0.0978255i \(0.968811\pi\)
\(920\) −30.4915 + 69.2450i −1.00527 + 2.28294i
\(921\) 7.28352 + 7.28352i 0.240000 + 0.240000i
\(922\) −30.6349 40.5389i −1.00891 1.33508i
\(923\) 7.08767 + 2.93581i 0.233294 + 0.0966334i
\(924\) 11.0000 + 18.9772i 0.361873 + 0.624303i
\(925\) −8.92699 21.5517i −0.293518 0.708614i
\(926\) −13.0783 + 3.40128i −0.429778 + 0.111773i
\(927\) 13.3690 0.439096
\(928\) −42.3815 + 3.99888i −1.39124 + 0.131270i
\(929\) 32.6893i 1.07250i 0.844059 + 0.536250i \(0.180160\pi\)
−0.844059 + 0.536250i \(0.819840\pi\)
\(930\) −42.0777 + 10.9432i −1.37978 + 0.358841i
\(931\) −13.4194 + 6.08300i −0.439803 + 0.199362i
\(932\) 11.3876 40.1254i 0.373013 1.31435i
\(933\) 2.77197 + 1.14819i 0.0907502 + 0.0375899i
\(934\) 16.5445 12.5026i 0.541354 0.409097i
\(935\) −8.16530 + 8.16530i −0.267034 + 0.267034i
\(936\) −39.5912 + 15.3835i −1.29408 + 0.502826i
\(937\) 15.2455 + 15.2455i 0.498049 + 0.498049i 0.910830 0.412781i \(-0.135443\pi\)
−0.412781 + 0.910830i \(0.635443\pi\)
\(938\) −13.7783 + 10.7727i −0.449876 + 0.351740i
\(939\) 36.1619 + 14.9787i 1.18010 + 0.488813i
\(940\) 66.6883 7.78224i 2.17513 0.253829i
\(941\) 14.8950 + 35.9596i 0.485562 + 1.17225i 0.956931 + 0.290315i \(0.0937600\pi\)
−0.471369 + 0.881936i \(0.656240\pi\)
\(942\) −2.35908 1.38528i −0.0768631 0.0451349i
\(943\) 16.2063i 0.527750i
\(944\) 31.5436 22.7601i 1.02666 0.740778i
\(945\) 14.9638 15.4643i 0.486773 0.503054i
\(946\) −0.938053 0.550836i −0.0304987 0.0179092i
\(947\) 6.15679 + 14.8638i 0.200069 + 0.483008i 0.991791 0.127873i \(-0.0408151\pi\)
−0.791722 + 0.610882i \(0.790815\pi\)
\(948\) 43.2086 + 34.1779i 1.40335 + 1.11005i
\(949\) 12.2362 29.5407i 0.397202 0.958931i
\(950\) −10.1472 1.41200i −0.329218 0.0458115i
\(951\) 16.1456 16.1456i 0.523557 0.523557i
\(952\) −13.5504 + 13.3982i −0.439171 + 0.434239i
\(953\) 11.6145 + 11.6145i 0.376230 + 0.376230i 0.869740 0.493510i \(-0.164286\pi\)
−0.493510 + 0.869740i \(0.664286\pi\)
\(954\) −45.2689 59.9040i −1.46564 1.93946i
\(955\) −34.7680 14.4014i −1.12507 0.466018i
\(956\) −9.31209 + 5.19498i −0.301175 + 0.168018i
\(957\) −28.8201 + 11.9377i −0.931620 + 0.385890i
\(958\) −17.4667 + 4.54258i −0.564323 + 0.146764i
\(959\) 4.51168 4.66259i 0.145690 0.150563i
\(960\) −2.72704 + 61.6736i −0.0880150 + 1.99051i
\(961\) −15.1281 −0.488002
\(962\) 8.93686 + 34.3631i 0.288136 + 1.10791i
\(963\) 12.3036 5.09632i 0.396478 0.164226i
\(964\) 34.7607 19.3921i 1.11957 0.624579i
\(965\) −3.46824 + 8.37306i −0.111646 + 0.269538i
\(966\) −11.1180 + 90.8159i −0.357715 + 2.92195i
\(967\) −13.9698 + 13.9698i −0.449238 + 0.449238i −0.895101 0.445863i \(-0.852897\pi\)
0.445863 + 0.895101i \(0.352897\pi\)
\(968\) 24.2168 + 0.535140i 0.778358 + 0.0172001i
\(969\) −10.0659 10.0659i −0.323363 0.323363i
\(970\) 11.5175 + 1.60269i 0.369804 + 0.0514591i
\(971\) 3.44252 8.31098i 0.110476 0.266712i −0.858966 0.512032i \(-0.828893\pi\)
0.969442 + 0.245320i \(0.0788930\pi\)
\(972\) −25.9976 + 32.8668i −0.833874 + 1.05420i
\(973\) 18.9476 47.9596i 0.607431 1.53752i
\(974\) 5.93750 10.1113i 0.190250 0.323988i
\(975\) −33.8612 −1.08443
\(976\) −3.85694 + 23.8454i −0.123458 + 0.763274i
\(977\) 8.14594i 0.260612i 0.991474 + 0.130306i \(0.0415959\pi\)
−0.991474 + 0.130306i \(0.958404\pi\)
\(978\) 65.6193 + 38.5325i 2.09828 + 1.23213i
\(979\) −4.04749 + 1.67652i −0.129358 + 0.0535820i
\(980\) 6.04101 + 40.2255i 0.192973 + 1.28496i
\(981\) −0.260330 + 0.628492i −0.00831169 + 0.0200662i
\(982\) 5.99316 + 0.833962i 0.191249 + 0.0266128i
\(983\) 19.5156 19.5156i 0.622450 0.622450i −0.323707 0.946157i \(-0.604929\pi\)
0.946157 + 0.323707i \(0.104929\pi\)
\(984\) −4.78915 12.3254i −0.152673 0.392920i
\(985\) −37.7731 + 37.7731i −1.20355 + 1.20355i
\(986\) −16.3389 21.6211i −0.520337 0.688557i
\(987\) 74.4894 32.2998i 2.37102 1.02812i
\(988\) 15.0013 + 4.25736i 0.477254 + 0.135445i
\(989\) −1.73644 4.19213i −0.0552154 0.133302i
\(990\) 6.54380 + 25.1616i 0.207976 + 0.799688i
\(991\) 13.2077i 0.419558i 0.977749 + 0.209779i \(0.0672744\pi\)
−0.977749 + 0.209779i \(0.932726\pi\)
\(992\) 6.63039 21.5393i 0.210515 0.683872i
\(993\) 9.32066i 0.295782i
\(994\) 3.81341 6.74578i 0.120954 0.213963i
\(995\) 26.2614 10.8778i 0.832543 0.344850i
\(996\) −61.5952 17.4807i −1.95172 0.553898i
\(997\) −2.46442 + 5.94965i −0.0780491 + 0.188427i −0.958088 0.286475i \(-0.907517\pi\)
0.880039 + 0.474902i \(0.157517\pi\)
\(998\) −31.2924 41.4090i −0.990544 1.31078i
\(999\) −13.4160 13.4160i −0.424464 0.424464i
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 224.2.x.b.27.4 yes 112
4.3 odd 2 896.2.x.b.783.4 112
7.6 odd 2 inner 224.2.x.b.27.3 112
28.27 even 2 896.2.x.b.783.25 112
32.13 even 8 896.2.x.b.111.25 112
32.19 odd 8 inner 224.2.x.b.83.3 yes 112
224.13 odd 8 896.2.x.b.111.4 112
224.83 even 8 inner 224.2.x.b.83.4 yes 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.2.x.b.27.3 112 7.6 odd 2 inner
224.2.x.b.27.4 yes 112 1.1 even 1 trivial
224.2.x.b.83.3 yes 112 32.19 odd 8 inner
224.2.x.b.83.4 yes 112 224.83 even 8 inner
896.2.x.b.111.4 112 224.13 odd 8
896.2.x.b.111.25 112 32.13 even 8
896.2.x.b.783.4 112 4.3 odd 2
896.2.x.b.783.25 112 28.27 even 2