Properties

Label 252.2.bi.c.139.13
Level $252$
Weight $2$
Character 252.139
Analytic conductor $2.012$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [252,2,Mod(139,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.139");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bi (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 139.13
Character \(\chi\) \(=\) 252.139
Dual form 252.2.bi.c.223.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.801205 - 1.16536i) q^{2} +(-0.420223 + 1.68030i) q^{3} +(-0.716141 + 1.86739i) q^{4} +(2.25662 + 1.30286i) q^{5} +(2.29485 - 0.856554i) q^{6} +(-2.51837 + 0.811054i) q^{7} +(2.74996 - 0.661599i) q^{8} +(-2.64683 - 1.41220i) q^{9} +O(q^{10})\) \(q+(-0.801205 - 1.16536i) q^{2} +(-0.420223 + 1.68030i) q^{3} +(-0.716141 + 1.86739i) q^{4} +(2.25662 + 1.30286i) q^{5} +(2.29485 - 0.856554i) q^{6} +(-2.51837 + 0.811054i) q^{7} +(2.74996 - 0.661599i) q^{8} +(-2.64683 - 1.41220i) q^{9} +(-0.289711 - 3.67364i) q^{10} +(-3.80655 + 2.19771i) q^{11} +(-2.83684 - 1.98805i) q^{12} +(-2.58681 - 1.49349i) q^{13} +(2.96290 + 2.28499i) q^{14} +(-3.13748 + 3.24431i) q^{15} +(-2.97429 - 2.67463i) q^{16} +6.35108i q^{17} +(0.474923 + 4.21598i) q^{18} +4.43265 q^{19} +(-4.04901 + 3.28096i) q^{20} +(-0.304538 - 4.57245i) q^{21} +(5.61096 + 2.67519i) q^{22} +(1.50500 + 0.868910i) q^{23} +(-0.0439117 + 4.89878i) q^{24} +(0.894893 + 1.55000i) q^{25} +(0.332101 + 4.21116i) q^{26} +(3.48518 - 3.85402i) q^{27} +(0.288954 - 5.28361i) q^{28} +(0.886455 + 1.53538i) q^{29} +(6.29457 + 1.05695i) q^{30} +(-1.41210 + 2.44584i) q^{31} +(-0.733897 + 5.60905i) q^{32} +(-2.09322 - 7.31968i) q^{33} +(7.40132 - 5.08852i) q^{34} +(-6.73970 - 1.45084i) q^{35} +(4.53263 - 3.93132i) q^{36} -4.47624 q^{37} +(-3.55146 - 5.16565i) q^{38} +(3.59656 - 3.71902i) q^{39} +(7.06759 + 2.08984i) q^{40} +(6.88823 + 3.97692i) q^{41} +(-5.08456 + 4.01836i) q^{42} +(-0.939597 + 0.542477i) q^{43} +(-1.37796 - 8.68218i) q^{44} +(-4.13298 - 6.63525i) q^{45} +(-0.193215 - 2.45004i) q^{46} +(4.58720 + 7.94527i) q^{47} +(5.74404 - 3.87376i) q^{48} +(5.68438 - 4.08507i) q^{49} +(1.08932 - 2.28474i) q^{50} +(-10.6717 - 2.66887i) q^{51} +(4.64145 - 3.76102i) q^{52} +4.31655 q^{53} +(-7.28368 - 0.973636i) q^{54} -11.4533 q^{55} +(-6.38883 + 3.89652i) q^{56} +(-1.86270 + 7.44819i) q^{57} +(1.07905 - 2.26320i) q^{58} +(4.10217 - 7.10516i) q^{59} +(-3.81151 - 8.18228i) q^{60} +(-3.57562 + 2.06438i) q^{61} +(3.98167 - 0.314003i) q^{62} +(7.81106 + 1.40973i) q^{63} +(7.12457 - 3.63874i) q^{64} +(-3.89163 - 6.74050i) q^{65} +(-6.85299 + 8.30393i) q^{66} +(-3.92432 - 2.26571i) q^{67} +(-11.8599 - 4.54827i) q^{68} +(-2.09246 + 2.16371i) q^{69} +(3.70912 + 9.01662i) q^{70} -11.8806i q^{71} +(-8.21298 - 2.13237i) q^{72} +7.69032i q^{73} +(3.58638 + 5.21644i) q^{74} +(-2.98052 + 0.852344i) q^{75} +(-3.17440 + 8.27749i) q^{76} +(7.80384 - 8.62198i) q^{77} +(-7.21558 - 1.21160i) q^{78} +(11.7375 - 6.77665i) q^{79} +(-3.22717 - 9.91070i) q^{80} +(5.01137 + 7.47571i) q^{81} +(-0.884330 - 11.2136i) q^{82} +(0.518194 + 0.897538i) q^{83} +(8.75663 + 2.70582i) q^{84} +(-8.27458 + 14.3320i) q^{85} +(1.38499 + 0.660336i) q^{86} +(-2.95242 + 0.844307i) q^{87} +(-9.01386 + 8.56204i) q^{88} +0.167616i q^{89} +(-4.42111 + 10.1326i) q^{90} +(7.72584 + 1.66313i) q^{91} +(-2.70038 + 2.18815i) q^{92} +(-3.51634 - 3.40056i) q^{93} +(5.58383 - 11.7115i) q^{94} +(10.0028 + 5.77513i) q^{95} +(-9.11649 - 3.59022i) q^{96} +(-5.35479 + 3.09159i) q^{97} +(-9.31494 - 3.35139i) q^{98} +(13.1789 - 0.441344i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.801205 1.16536i −0.566538 0.824036i
\(3\) −0.420223 + 1.68030i −0.242616 + 0.970122i
\(4\) −0.716141 + 1.86739i −0.358070 + 0.933695i
\(5\) 2.25662 + 1.30286i 1.00919 + 0.582657i 0.910955 0.412506i \(-0.135346\pi\)
0.0982368 + 0.995163i \(0.468680\pi\)
\(6\) 2.29485 0.856554i 0.936867 0.349687i
\(7\) −2.51837 + 0.811054i −0.951855 + 0.306550i
\(8\) 2.74996 0.661599i 0.972258 0.233910i
\(9\) −2.64683 1.41220i −0.882275 0.470734i
\(10\) −0.289711 3.67364i −0.0916147 1.16171i
\(11\) −3.80655 + 2.19771i −1.14772 + 0.662636i −0.948330 0.317285i \(-0.897229\pi\)
−0.199388 + 0.979921i \(0.563895\pi\)
\(12\) −2.83684 1.98805i −0.818925 0.573901i
\(13\) −2.58681 1.49349i −0.717451 0.414221i 0.0963626 0.995346i \(-0.469279\pi\)
−0.813814 + 0.581126i \(0.802612\pi\)
\(14\) 2.96290 + 2.28499i 0.791869 + 0.610690i
\(15\) −3.13748 + 3.24431i −0.810095 + 0.837678i
\(16\) −2.97429 2.67463i −0.743571 0.668657i
\(17\) 6.35108i 1.54036i 0.637824 + 0.770182i \(0.279835\pi\)
−0.637824 + 0.770182i \(0.720165\pi\)
\(18\) 0.474923 + 4.21598i 0.111940 + 0.993715i
\(19\) 4.43265 1.01692 0.508460 0.861086i \(-0.330215\pi\)
0.508460 + 0.861086i \(0.330215\pi\)
\(20\) −4.04901 + 3.28096i −0.905385 + 0.733645i
\(21\) −0.304538 4.57245i −0.0664557 0.997789i
\(22\) 5.61096 + 2.67519i 1.19626 + 0.570353i
\(23\) 1.50500 + 0.868910i 0.313813 + 0.181180i 0.648632 0.761102i \(-0.275342\pi\)
−0.334818 + 0.942283i \(0.608675\pi\)
\(24\) −0.0439117 + 4.89878i −0.00896345 + 0.999960i
\(25\) 0.894893 + 1.55000i 0.178979 + 0.310000i
\(26\) 0.332101 + 4.21116i 0.0651304 + 0.825877i
\(27\) 3.48518 3.85402i 0.670724 0.741707i
\(28\) 0.288954 5.28361i 0.0546071 0.998508i
\(29\) 0.886455 + 1.53538i 0.164611 + 0.285114i 0.936517 0.350622i \(-0.114030\pi\)
−0.771906 + 0.635736i \(0.780697\pi\)
\(30\) 6.29457 + 1.05695i 1.14923 + 0.192971i
\(31\) −1.41210 + 2.44584i −0.253621 + 0.439285i −0.964520 0.264009i \(-0.914955\pi\)
0.710899 + 0.703294i \(0.248288\pi\)
\(32\) −0.733897 + 5.60905i −0.129736 + 0.991549i
\(33\) −2.09322 7.31968i −0.364383 1.27419i
\(34\) 7.40132 5.08852i 1.26932 0.872674i
\(35\) −6.73970 1.45084i −1.13922 0.245238i
\(36\) 4.53263 3.93132i 0.755438 0.655220i
\(37\) −4.47624 −0.735889 −0.367944 0.929848i \(-0.619938\pi\)
−0.367944 + 0.929848i \(0.619938\pi\)
\(38\) −3.55146 5.16565i −0.576124 0.837979i
\(39\) 3.59656 3.71902i 0.575910 0.595519i
\(40\) 7.06759 + 2.08984i 1.11748 + 0.330433i
\(41\) 6.88823 + 3.97692i 1.07576 + 0.621091i 0.929750 0.368192i \(-0.120023\pi\)
0.146011 + 0.989283i \(0.453356\pi\)
\(42\) −5.08456 + 4.01836i −0.784565 + 0.620047i
\(43\) −0.939597 + 0.542477i −0.143287 + 0.0827269i −0.569930 0.821693i \(-0.693030\pi\)
0.426643 + 0.904420i \(0.359696\pi\)
\(44\) −1.37796 8.68218i −0.207735 1.30889i
\(45\) −4.13298 6.63525i −0.616108 0.989125i
\(46\) −0.193215 2.45004i −0.0284881 0.361239i
\(47\) 4.58720 + 7.94527i 0.669112 + 1.15894i 0.978153 + 0.207887i \(0.0666588\pi\)
−0.309041 + 0.951049i \(0.600008\pi\)
\(48\) 5.74404 3.87376i 0.829081 0.559129i
\(49\) 5.68438 4.08507i 0.812055 0.583581i
\(50\) 1.08932 2.28474i 0.154053 0.323111i
\(51\) −10.6717 2.66887i −1.49434 0.373717i
\(52\) 4.64145 3.76102i 0.643654 0.521560i
\(53\) 4.31655 0.592923 0.296462 0.955045i \(-0.404193\pi\)
0.296462 + 0.955045i \(0.404193\pi\)
\(54\) −7.28368 0.973636i −0.991184 0.132495i
\(55\) −11.4533 −1.54436
\(56\) −6.38883 + 3.89652i −0.853743 + 0.520694i
\(57\) −1.86270 + 7.44819i −0.246721 + 0.986537i
\(58\) 1.07905 2.26320i 0.141686 0.297173i
\(59\) 4.10217 7.10516i 0.534056 0.925013i −0.465152 0.885231i \(-0.654000\pi\)
0.999208 0.0397821i \(-0.0126664\pi\)
\(60\) −3.81151 8.18228i −0.492064 1.05633i
\(61\) −3.57562 + 2.06438i −0.457811 + 0.264317i −0.711123 0.703067i \(-0.751813\pi\)
0.253313 + 0.967384i \(0.418480\pi\)
\(62\) 3.98167 0.314003i 0.505673 0.0398784i
\(63\) 7.81106 + 1.40973i 0.984101 + 0.177609i
\(64\) 7.12457 3.63874i 0.890572 0.454843i
\(65\) −3.89163 6.74050i −0.482697 0.836056i
\(66\) −6.85299 + 8.30393i −0.843544 + 1.02214i
\(67\) −3.92432 2.26571i −0.479433 0.276801i 0.240747 0.970588i \(-0.422607\pi\)
−0.720180 + 0.693787i \(0.755941\pi\)
\(68\) −11.8599 4.54827i −1.43823 0.551559i
\(69\) −2.09246 + 2.16371i −0.251903 + 0.260480i
\(70\) 3.70912 + 9.01662i 0.443325 + 1.07769i
\(71\) 11.8806i 1.40996i −0.709226 0.704981i \(-0.750955\pi\)
0.709226 0.704981i \(-0.249045\pi\)
\(72\) −8.21298 2.13237i −0.967909 0.251302i
\(73\) 7.69032i 0.900084i 0.893007 + 0.450042i \(0.148591\pi\)
−0.893007 + 0.450042i \(0.851409\pi\)
\(74\) 3.58638 + 5.21644i 0.416909 + 0.606399i
\(75\) −2.98052 + 0.852344i −0.344161 + 0.0984203i
\(76\) −3.17440 + 8.27749i −0.364129 + 0.949493i
\(77\) 7.80384 8.62198i 0.889330 0.982565i
\(78\) −7.21558 1.21160i −0.817004 0.137186i
\(79\) 11.7375 6.77665i 1.32057 0.762432i 0.336752 0.941593i \(-0.390672\pi\)
0.983820 + 0.179161i \(0.0573383\pi\)
\(80\) −3.22717 9.91070i −0.360809 1.10805i
\(81\) 5.01137 + 7.47571i 0.556819 + 0.830634i
\(82\) −0.884330 11.2136i −0.0976579 1.23834i
\(83\) 0.518194 + 0.897538i 0.0568792 + 0.0985176i 0.893063 0.449932i \(-0.148552\pi\)
−0.836184 + 0.548449i \(0.815218\pi\)
\(84\) 8.75663 + 2.70582i 0.955426 + 0.295229i
\(85\) −8.27458 + 14.3320i −0.897504 + 1.55452i
\(86\) 1.38499 + 0.660336i 0.149348 + 0.0712059i
\(87\) −2.95242 + 0.844307i −0.316532 + 0.0905193i
\(88\) −9.01386 + 8.56204i −0.960881 + 0.912716i
\(89\) 0.167616i 0.0177672i 0.999961 + 0.00888361i \(0.00282778\pi\)
−0.999961 + 0.00888361i \(0.997172\pi\)
\(90\) −4.42111 + 10.1326i −0.466026 + 1.06807i
\(91\) 7.72584 + 1.66313i 0.809889 + 0.174343i
\(92\) −2.70038 + 2.18815i −0.281534 + 0.228131i
\(93\) −3.51634 3.40056i −0.364628 0.352621i
\(94\) 5.58383 11.7115i 0.575928 1.20795i
\(95\) 10.0028 + 5.77513i 1.02627 + 0.592516i
\(96\) −9.11649 3.59022i −0.930448 0.366425i
\(97\) −5.35479 + 3.09159i −0.543696 + 0.313903i −0.746576 0.665300i \(-0.768303\pi\)
0.202879 + 0.979204i \(0.434970\pi\)
\(98\) −9.31494 3.35139i −0.940952 0.338541i
\(99\) 13.1789 0.441344i 1.32453 0.0443567i
\(100\) −3.53532 + 0.561096i −0.353532 + 0.0561096i
\(101\) 12.6134 7.28234i 1.25508 0.724620i 0.282965 0.959130i \(-0.408682\pi\)
0.972114 + 0.234510i \(0.0753486\pi\)
\(102\) 5.44005 + 14.5748i 0.538645 + 1.44312i
\(103\) 8.96940 15.5355i 0.883781 1.53075i 0.0366767 0.999327i \(-0.488323\pi\)
0.847104 0.531427i \(-0.178344\pi\)
\(104\) −8.10171 2.39562i −0.794438 0.234910i
\(105\) 5.27003 10.7150i 0.514303 1.04568i
\(106\) −3.45844 5.03034i −0.335913 0.488590i
\(107\) 10.4277i 1.00808i 0.863679 + 0.504042i \(0.168154\pi\)
−0.863679 + 0.504042i \(0.831846\pi\)
\(108\) 4.70108 + 9.26821i 0.452362 + 0.891834i
\(109\) 10.8402 1.03830 0.519149 0.854684i \(-0.326249\pi\)
0.519149 + 0.854684i \(0.326249\pi\)
\(110\) 9.17641 + 13.3472i 0.874936 + 1.27261i
\(111\) 1.88102 7.52143i 0.178538 0.713902i
\(112\) 9.65962 + 4.32339i 0.912748 + 0.408522i
\(113\) −6.45034 + 11.1723i −0.606797 + 1.05100i 0.384968 + 0.922930i \(0.374212\pi\)
−0.991765 + 0.128073i \(0.959121\pi\)
\(114\) 10.1723 3.79681i 0.952719 0.355604i
\(115\) 2.26414 + 3.92160i 0.211132 + 0.365691i
\(116\) −3.50199 + 0.555805i −0.325151 + 0.0516052i
\(117\) 4.73771 + 7.60611i 0.438002 + 0.703185i
\(118\) −11.5668 + 0.912180i −1.06481 + 0.0839729i
\(119\) −5.15107 15.9944i −0.472198 1.46620i
\(120\) −6.48152 + 10.9975i −0.591680 + 1.00393i
\(121\) 4.15989 7.20514i 0.378172 0.655013i
\(122\) 5.27056 + 2.51290i 0.477174 + 0.227507i
\(123\) −9.57702 + 9.90311i −0.863531 + 0.892933i
\(124\) −3.55606 4.38851i −0.319344 0.394100i
\(125\) 8.36492i 0.748182i
\(126\) −4.61542 10.2322i −0.411174 0.911557i
\(127\) 12.1610i 1.07911i 0.841949 + 0.539557i \(0.181408\pi\)
−0.841949 + 0.539557i \(0.818592\pi\)
\(128\) −9.94870 5.38734i −0.879349 0.476178i
\(129\) −0.516684 1.80677i −0.0454915 0.159077i
\(130\) −4.73713 + 9.93568i −0.415474 + 0.871417i
\(131\) −7.69288 + 13.3245i −0.672130 + 1.16416i 0.305169 + 0.952298i \(0.401287\pi\)
−0.977299 + 0.211865i \(0.932046\pi\)
\(132\) 15.1677 + 1.33306i 1.32018 + 0.116028i
\(133\) −11.1631 + 3.59512i −0.967960 + 0.311737i
\(134\) 0.503815 + 6.38856i 0.0435230 + 0.551888i
\(135\) 12.8860 4.15637i 1.10905 0.357723i
\(136\) 4.20187 + 17.4652i 0.360307 + 1.49763i
\(137\) 2.13470 + 3.69741i 0.182380 + 0.315891i 0.942690 0.333669i \(-0.108287\pi\)
−0.760311 + 0.649560i \(0.774953\pi\)
\(138\) 4.19800 + 0.704903i 0.357358 + 0.0600053i
\(139\) −10.7224 + 18.5717i −0.909459 + 1.57523i −0.0946405 + 0.995512i \(0.530170\pi\)
−0.814818 + 0.579717i \(0.803163\pi\)
\(140\) 7.53586 11.5466i 0.636897 0.975869i
\(141\) −15.2781 + 4.36910i −1.28665 + 0.367945i
\(142\) −13.8452 + 9.51876i −1.16186 + 0.798797i
\(143\) 13.1291 1.09791
\(144\) 4.09530 + 11.2796i 0.341275 + 0.939963i
\(145\) 4.61971i 0.383646i
\(146\) 8.96201 6.16152i 0.741701 0.509931i
\(147\) 4.47544 + 11.2681i 0.369128 + 0.929379i
\(148\) 3.20561 8.35888i 0.263500 0.687095i
\(149\) −5.22512 + 9.05017i −0.428058 + 0.741419i −0.996701 0.0811663i \(-0.974136\pi\)
0.568642 + 0.822585i \(0.307469\pi\)
\(150\) 3.38130 + 2.79049i 0.276082 + 0.227842i
\(151\) 10.5519 6.09213i 0.858700 0.495771i −0.00487656 0.999988i \(-0.501552\pi\)
0.863577 + 0.504217i \(0.168219\pi\)
\(152\) 12.1896 2.93264i 0.988709 0.237868i
\(153\) 8.96901 16.8102i 0.725102 1.35903i
\(154\) −16.3002 2.18634i −1.31351 0.176180i
\(155\) −6.37317 + 3.67955i −0.511905 + 0.295549i
\(156\) 4.36921 + 9.37951i 0.349817 + 0.750962i
\(157\) −13.1637 7.60005i −1.05057 0.606550i −0.127765 0.991805i \(-0.540780\pi\)
−0.922810 + 0.385255i \(0.874114\pi\)
\(158\) −17.3014 8.24896i −1.37643 0.656252i
\(159\) −1.81391 + 7.25310i −0.143853 + 0.575208i
\(160\) −8.96393 + 11.7013i −0.708661 + 0.925071i
\(161\) −4.49487 0.967604i −0.354245 0.0762579i
\(162\) 4.69677 11.8296i 0.369013 0.929424i
\(163\) 3.98564i 0.312179i 0.987743 + 0.156090i \(0.0498889\pi\)
−0.987743 + 0.156090i \(0.950111\pi\)
\(164\) −12.3594 + 10.0150i −0.965107 + 0.782038i
\(165\) 4.81292 19.2449i 0.374685 1.49822i
\(166\) 0.630778 1.32300i 0.0489579 0.102684i
\(167\) 1.70062 2.94557i 0.131598 0.227935i −0.792695 0.609619i \(-0.791322\pi\)
0.924293 + 0.381684i \(0.124656\pi\)
\(168\) −3.86259 12.3726i −0.298005 0.954564i
\(169\) −2.03895 3.53157i −0.156842 0.271659i
\(170\) 23.3316 1.83998i 1.78945 0.141120i
\(171\) −11.7325 6.25980i −0.897203 0.478699i
\(172\) −0.340132 2.14308i −0.0259348 0.163409i
\(173\) −5.09957 + 2.94424i −0.387713 + 0.223846i −0.681169 0.732127i \(-0.738528\pi\)
0.293456 + 0.955973i \(0.405195\pi\)
\(174\) 3.34942 + 2.76417i 0.253919 + 0.209551i
\(175\) −3.51081 3.17767i −0.265392 0.240209i
\(176\) 17.1998 + 3.64447i 1.29649 + 0.274713i
\(177\) 10.2150 + 9.87863i 0.767805 + 0.742523i
\(178\) 0.195333 0.134294i 0.0146408 0.0100658i
\(179\) 14.2559i 1.06553i −0.846262 0.532767i \(-0.821152\pi\)
0.846262 0.532767i \(-0.178848\pi\)
\(180\) 15.3504 2.96611i 1.14415 0.221081i
\(181\) 4.24221i 0.315321i −0.987493 0.157660i \(-0.949605\pi\)
0.987493 0.157660i \(-0.0503951\pi\)
\(182\) −4.25184 10.3359i −0.315167 0.766149i
\(183\) −1.96623 6.87561i −0.145348 0.508260i
\(184\) 4.71355 + 1.39377i 0.347488 + 0.102750i
\(185\) −10.1012 5.83191i −0.742653 0.428771i
\(186\) −1.14557 + 6.82236i −0.0839972 + 0.500240i
\(187\) −13.9579 24.1757i −1.02070 1.76790i
\(188\) −18.1220 + 2.87616i −1.32168 + 0.209766i
\(189\) −5.65116 + 12.5325i −0.411061 + 0.911608i
\(190\) −1.28419 16.2840i −0.0931649 1.18136i
\(191\) −2.00820 + 1.15943i −0.145308 + 0.0838937i −0.570891 0.821026i \(-0.693402\pi\)
0.425583 + 0.904919i \(0.360069\pi\)
\(192\) 3.12027 + 13.5005i 0.225186 + 0.974316i
\(193\) 0.803389 1.39151i 0.0578292 0.100163i −0.835662 0.549245i \(-0.814915\pi\)
0.893491 + 0.449082i \(0.148249\pi\)
\(194\) 7.89311 + 3.76327i 0.566692 + 0.270187i
\(195\) 12.9614 3.70660i 0.928187 0.265435i
\(196\) 3.55760 + 13.5404i 0.254114 + 0.967174i
\(197\) −9.41145 −0.670538 −0.335269 0.942122i \(-0.608827\pi\)
−0.335269 + 0.942122i \(0.608827\pi\)
\(198\) −11.0733 15.0046i −0.786947 1.06633i
\(199\) 4.61701 0.327291 0.163646 0.986519i \(-0.447675\pi\)
0.163646 + 0.986519i \(0.447675\pi\)
\(200\) 3.48640 + 3.67038i 0.246526 + 0.259535i
\(201\) 5.45617 5.64194i 0.384848 0.397952i
\(202\) −18.5925 8.86452i −1.30816 0.623705i
\(203\) −3.47770 3.14771i −0.244087 0.220926i
\(204\) 12.6263 18.0170i 0.884017 1.26144i
\(205\) 10.3628 + 17.9488i 0.723766 + 1.25360i
\(206\) −25.2908 + 1.99448i −1.76209 + 0.138962i
\(207\) −2.75639 4.42521i −0.191582 0.307573i
\(208\) 3.69937 + 11.3608i 0.256505 + 0.787731i
\(209\) −16.8731 + 9.74170i −1.16714 + 0.673847i
\(210\) −16.7093 + 2.44345i −1.15305 + 0.168614i
\(211\) −22.3255 12.8897i −1.53695 0.887360i −0.999015 0.0443764i \(-0.985870\pi\)
−0.537938 0.842984i \(-0.680797\pi\)
\(212\) −3.09125 + 8.06067i −0.212308 + 0.553609i
\(213\) 19.9629 + 4.99248i 1.36784 + 0.342079i
\(214\) 12.1521 8.35473i 0.830698 0.571118i
\(215\) −2.82709 −0.192806
\(216\) 7.03430 12.9042i 0.478623 0.878020i
\(217\) 1.57250 7.30481i 0.106748 0.495883i
\(218\) −8.68519 12.6327i −0.588235 0.855595i
\(219\) −12.9221 3.23165i −0.873192 0.218375i
\(220\) 8.20214 21.3877i 0.552988 1.44196i
\(221\) 9.48531 16.4290i 0.638051 1.10514i
\(222\) −10.2723 + 3.83414i −0.689430 + 0.257331i
\(223\) 4.03030 + 6.98069i 0.269889 + 0.467461i 0.968833 0.247715i \(-0.0796797\pi\)
−0.698944 + 0.715176i \(0.746346\pi\)
\(224\) −2.70102 14.7209i −0.180469 0.983581i
\(225\) −0.179712 5.36635i −0.0119808 0.357757i
\(226\) 18.1878 1.43433i 1.20984 0.0954103i
\(227\) 6.15006 + 10.6522i 0.408194 + 0.707013i 0.994687 0.102941i \(-0.0328253\pi\)
−0.586493 + 0.809954i \(0.699492\pi\)
\(228\) −12.5747 8.81234i −0.832781 0.583612i
\(229\) 5.55114 + 3.20495i 0.366830 + 0.211789i 0.672072 0.740485i \(-0.265404\pi\)
−0.305243 + 0.952275i \(0.598738\pi\)
\(230\) 2.75605 5.78055i 0.181728 0.381158i
\(231\) 11.2082 + 16.7360i 0.737443 + 1.10115i
\(232\) 3.45352 + 3.63577i 0.226735 + 0.238700i
\(233\) 14.6005 0.956512 0.478256 0.878220i \(-0.341269\pi\)
0.478256 + 0.878220i \(0.341269\pi\)
\(234\) 5.06800 11.6152i 0.331306 0.759310i
\(235\) 23.9059i 1.55945i
\(236\) 10.3304 + 12.7486i 0.672450 + 0.829865i
\(237\) 6.45445 + 22.5702i 0.419261 + 1.46609i
\(238\) −14.5122 + 18.8177i −0.940686 + 1.21977i
\(239\) 6.30063 + 3.63767i 0.407554 + 0.235302i 0.689738 0.724059i \(-0.257726\pi\)
−0.282184 + 0.959360i \(0.591059\pi\)
\(240\) 18.0091 1.25792i 1.16248 0.0811981i
\(241\) 9.84681 5.68506i 0.634289 0.366207i −0.148122 0.988969i \(-0.547323\pi\)
0.782411 + 0.622762i \(0.213990\pi\)
\(242\) −11.7295 + 0.925015i −0.754002 + 0.0594622i
\(243\) −14.6673 + 5.27915i −0.940910 + 0.338658i
\(244\) −1.29436 8.15546i −0.0828631 0.522100i
\(245\) 18.1498 1.81250i 1.15955 0.115796i
\(246\) 19.2139 + 3.22628i 1.22503 + 0.205700i
\(247\) −11.4664 6.62014i −0.729591 0.421229i
\(248\) −2.26507 + 7.66020i −0.143832 + 0.486423i
\(249\) −1.72589 + 0.493556i −0.109374 + 0.0312778i
\(250\) −9.74817 + 6.70202i −0.616528 + 0.423873i
\(251\) 10.0975 0.637350 0.318675 0.947864i \(-0.396762\pi\)
0.318675 + 0.947864i \(0.396762\pi\)
\(252\) −8.22633 + 13.5767i −0.518210 + 0.855253i
\(253\) −7.63846 −0.480226
\(254\) 14.1720 9.74346i 0.889229 0.611359i
\(255\) −20.6049 19.9264i −1.29033 1.24784i
\(256\) 1.69275 + 15.9102i 0.105797 + 0.994388i
\(257\) −5.68144 3.28018i −0.354398 0.204612i 0.312222 0.950009i \(-0.398927\pi\)
−0.666621 + 0.745397i \(0.732260\pi\)
\(258\) −1.69157 + 2.04972i −0.105313 + 0.127610i
\(259\) 11.2728 3.63047i 0.700459 0.225586i
\(260\) 15.3741 2.44004i 0.953461 0.151325i
\(261\) −0.178017 5.31575i −0.0110190 0.329037i
\(262\) 21.6914 1.71063i 1.34010 0.105683i
\(263\) −8.64854 + 4.99324i −0.533292 + 0.307896i −0.742356 0.670006i \(-0.766292\pi\)
0.209064 + 0.977902i \(0.432958\pi\)
\(264\) −10.5990 18.7440i −0.652321 1.15361i
\(265\) 9.74081 + 5.62386i 0.598373 + 0.345471i
\(266\) 13.1335 + 10.1286i 0.805268 + 0.621024i
\(267\) −0.281645 0.0704359i −0.0172364 0.00431061i
\(268\) 7.04133 5.70568i 0.430118 0.348530i
\(269\) 2.53470i 0.154543i −0.997010 0.0772716i \(-0.975379\pi\)
0.997010 0.0772716i \(-0.0246209\pi\)
\(270\) −15.1680 11.6868i −0.923095 0.711233i
\(271\) 10.4463 0.634569 0.317285 0.948330i \(-0.397229\pi\)
0.317285 + 0.948330i \(0.397229\pi\)
\(272\) 16.9868 18.8899i 1.02997 1.14537i
\(273\) −6.04114 + 12.2829i −0.365626 + 0.743393i
\(274\) 2.59849 5.45008i 0.156980 0.329251i
\(275\) −6.81291 3.93344i −0.410834 0.237195i
\(276\) −2.54199 5.45697i −0.153010 0.328471i
\(277\) −10.3949 18.0044i −0.624567 1.08178i −0.988624 0.150405i \(-0.951942\pi\)
0.364057 0.931377i \(-0.381391\pi\)
\(278\) 30.2335 2.38428i 1.81329 0.143000i
\(279\) 7.19161 4.47952i 0.430550 0.268182i
\(280\) −19.4938 + 0.469208i −1.16498 + 0.0280406i
\(281\) −4.47362 7.74854i −0.266874 0.462239i 0.701179 0.712985i \(-0.252657\pi\)
−0.968053 + 0.250746i \(0.919324\pi\)
\(282\) 17.3325 + 14.3040i 1.03213 + 0.851789i
\(283\) −11.3594 + 19.6750i −0.675243 + 1.16956i 0.301154 + 0.953575i \(0.402628\pi\)
−0.976398 + 0.215980i \(0.930705\pi\)
\(284\) 22.1856 + 8.50815i 1.31647 + 0.504866i
\(285\) −13.9074 + 14.3809i −0.823802 + 0.851851i
\(286\) −10.5191 15.3001i −0.622007 0.904717i
\(287\) −20.5726 4.42864i −1.21436 0.261414i
\(288\) 9.86360 13.8098i 0.581218 0.813748i
\(289\) −23.3363 −1.37272
\(290\) 5.38364 3.70133i 0.316138 0.217350i
\(291\) −2.94460 10.2968i −0.172615 0.603610i
\(292\) −14.3608 5.50735i −0.840403 0.322293i
\(293\) −5.14713 2.97170i −0.300699 0.173608i 0.342058 0.939679i \(-0.388876\pi\)
−0.642757 + 0.766070i \(0.722209\pi\)
\(294\) 9.54570 14.2436i 0.556716 0.830703i
\(295\) 18.5141 10.6891i 1.07793 0.622344i
\(296\) −12.3095 + 2.96147i −0.715474 + 0.172132i
\(297\) −4.79648 + 22.3300i −0.278320 + 1.29572i
\(298\) 14.7331 1.16188i 0.853467 0.0673062i
\(299\) −2.59542 4.49540i −0.150097 0.259976i
\(300\) 0.542814 6.17619i 0.0313394 0.356583i
\(301\) 1.92628 2.12822i 0.111029 0.122669i
\(302\) −15.5538 7.41572i −0.895019 0.426727i
\(303\) 6.93610 + 24.2545i 0.398468 + 1.39338i
\(304\) −13.1840 11.8557i −0.756153 0.679970i
\(305\) −10.7584 −0.616025
\(306\) −26.7760 + 3.01627i −1.53068 + 0.172429i
\(307\) 10.0769 0.575121 0.287560 0.957763i \(-0.407156\pi\)
0.287560 + 0.957763i \(0.407156\pi\)
\(308\) 10.5119 + 20.7474i 0.598973 + 1.18219i
\(309\) 22.3351 + 21.5996i 1.27060 + 1.22876i
\(310\) 9.39422 + 4.47898i 0.533556 + 0.254389i
\(311\) 0.0398807 0.0690754i 0.00226143 0.00391691i −0.864892 0.501957i \(-0.832613\pi\)
0.867154 + 0.498040i \(0.165947\pi\)
\(312\) 7.42989 12.6066i 0.420635 0.713710i
\(313\) 20.6585 11.9272i 1.16769 0.674164i 0.214553 0.976712i \(-0.431171\pi\)
0.953134 + 0.302548i \(0.0978373\pi\)
\(314\) 1.68999 + 21.4296i 0.0953715 + 1.20934i
\(315\) 15.7899 + 13.3580i 0.889661 + 0.752635i
\(316\) 4.24894 + 26.7715i 0.239022 + 1.50602i
\(317\) 1.98299 + 3.43465i 0.111376 + 0.192909i 0.916325 0.400435i \(-0.131141\pi\)
−0.804949 + 0.593344i \(0.797808\pi\)
\(318\) 9.90580 3.69735i 0.555490 0.207337i
\(319\) −6.74867 3.89635i −0.377853 0.218154i
\(320\) 20.8182 + 1.07107i 1.16377 + 0.0598746i
\(321\) −17.5217 4.38196i −0.977966 0.244577i
\(322\) 2.47370 + 6.01340i 0.137854 + 0.335114i
\(323\) 28.1521i 1.56643i
\(324\) −17.5489 + 4.00452i −0.974939 + 0.222474i
\(325\) 5.34607i 0.296547i
\(326\) 4.64472 3.19332i 0.257247 0.176861i
\(327\) −4.55528 + 18.2147i −0.251908 + 1.00728i
\(328\) 21.5735 + 6.37914i 1.19120 + 0.352229i
\(329\) −17.9963 16.2887i −0.992169 0.898023i
\(330\) −26.2835 + 9.81034i −1.44686 + 0.540041i
\(331\) −17.2122 + 9.93744i −0.946066 + 0.546211i −0.891857 0.452318i \(-0.850597\pi\)
−0.0542091 + 0.998530i \(0.517264\pi\)
\(332\) −2.04715 + 0.324906i −0.112352 + 0.0178315i
\(333\) 11.8478 + 6.32135i 0.649256 + 0.346408i
\(334\) −4.79520 + 0.378160i −0.262382 + 0.0206920i
\(335\) −5.90381 10.2257i −0.322560 0.558690i
\(336\) −11.3238 + 14.4143i −0.617764 + 0.786364i
\(337\) 0.692953 1.20023i 0.0377475 0.0653807i −0.846534 0.532334i \(-0.821315\pi\)
0.884282 + 0.466953i \(0.154648\pi\)
\(338\) −2.48194 + 5.20563i −0.135000 + 0.283149i
\(339\) −16.0623 15.5334i −0.872383 0.843657i
\(340\) −20.8376 25.7156i −1.13008 1.39462i
\(341\) 12.4136i 0.672234i
\(342\) 2.10517 + 18.6880i 0.113834 + 1.01053i
\(343\) −11.0022 + 14.8981i −0.594061 + 0.804420i
\(344\) −2.22495 + 2.11343i −0.119961 + 0.113948i
\(345\) −7.54091 + 2.15649i −0.405989 + 0.116101i
\(346\) 7.51690 + 3.58391i 0.404111 + 0.192672i
\(347\) −11.3727 6.56605i −0.610520 0.352484i 0.162649 0.986684i \(-0.447996\pi\)
−0.773169 + 0.634200i \(0.781329\pi\)
\(348\) 0.537695 6.11796i 0.0288235 0.327957i
\(349\) 23.7743 13.7261i 1.27261 0.734740i 0.297129 0.954837i \(-0.403971\pi\)
0.975478 + 0.220097i \(0.0706375\pi\)
\(350\) −0.890260 + 6.63733i −0.0475864 + 0.354780i
\(351\) −14.7715 + 4.76452i −0.788442 + 0.254311i
\(352\) −9.53346 22.9640i −0.508135 1.22399i
\(353\) −26.7734 + 15.4576i −1.42501 + 0.822727i −0.996721 0.0809166i \(-0.974215\pi\)
−0.428285 + 0.903644i \(0.640882\pi\)
\(354\) 3.32788 19.8190i 0.176875 1.05337i
\(355\) 15.4787 26.8099i 0.821525 1.42292i
\(356\) −0.313003 0.120036i −0.0165891 0.00636191i
\(357\) 29.0400 1.93415i 1.53696 0.102366i
\(358\) −16.6133 + 11.4219i −0.878038 + 0.603665i
\(359\) 11.1419i 0.588045i −0.955799 0.294022i \(-0.905006\pi\)
0.955799 0.294022i \(-0.0949940\pi\)
\(360\) −15.7554 15.5123i −0.830383 0.817571i
\(361\) 0.648409 0.0341268
\(362\) −4.94371 + 3.39888i −0.259836 + 0.178641i
\(363\) 10.3587 + 10.0176i 0.543692 + 0.525789i
\(364\) −8.63850 + 13.2361i −0.452781 + 0.693761i
\(365\) −10.0194 + 17.3541i −0.524440 + 0.908357i
\(366\) −6.43723 + 7.80015i −0.336479 + 0.407720i
\(367\) 11.9986 + 20.7821i 0.626319 + 1.08482i 0.988284 + 0.152625i \(0.0487727\pi\)
−0.361965 + 0.932192i \(0.617894\pi\)
\(368\) −2.15228 6.60969i −0.112195 0.344554i
\(369\) −12.6157 20.2538i −0.656749 1.05437i
\(370\) 1.29682 + 16.4441i 0.0674182 + 0.854887i
\(371\) −10.8707 + 3.50095i −0.564377 + 0.181760i
\(372\) 8.86836 4.13110i 0.459803 0.214188i
\(373\) 9.88561 17.1224i 0.511857 0.886563i −0.488048 0.872817i \(-0.662291\pi\)
0.999906 0.0137464i \(-0.00437575\pi\)
\(374\) −16.9904 + 35.6357i −0.878552 + 1.84268i
\(375\) 14.0556 + 3.51513i 0.725828 + 0.181521i
\(376\) 17.8712 + 18.8143i 0.921637 + 0.970273i
\(377\) 5.29566i 0.272740i
\(378\) 19.1327 3.45548i 0.984079 0.177731i
\(379\) 5.89248i 0.302676i −0.988482 0.151338i \(-0.951642\pi\)
0.988482 0.151338i \(-0.0483582\pi\)
\(380\) −17.9478 + 14.5434i −0.920705 + 0.746058i
\(381\) −20.4342 5.11033i −1.04687 0.261810i
\(382\) 2.96014 + 1.41134i 0.151454 + 0.0722102i
\(383\) −0.975897 + 1.69030i −0.0498660 + 0.0863704i −0.889881 0.456193i \(-0.849213\pi\)
0.840015 + 0.542563i \(0.182546\pi\)
\(384\) 13.2330 14.4529i 0.675295 0.737548i
\(385\) 28.8436 9.28921i 1.47000 0.473422i
\(386\) −2.26529 + 0.178646i −0.115300 + 0.00909283i
\(387\) 3.25304 0.108940i 0.165361 0.00553773i
\(388\) −1.93842 12.2135i −0.0984083 0.620046i
\(389\) −2.26752 3.92746i −0.114968 0.199130i 0.802799 0.596250i \(-0.203343\pi\)
−0.917767 + 0.397120i \(0.870010\pi\)
\(390\) −14.7043 12.1350i −0.744581 0.614480i
\(391\) −5.51852 + 9.55836i −0.279084 + 0.483387i
\(392\) 12.9292 14.9946i 0.653021 0.757340i
\(393\) −19.1564 18.5256i −0.966312 0.934493i
\(394\) 7.54051 + 10.9678i 0.379885 + 0.552548i
\(395\) 35.3161 1.77695
\(396\) −8.61378 + 24.9262i −0.432859 + 1.25259i
\(397\) 24.8829i 1.24883i −0.781091 0.624417i \(-0.785336\pi\)
0.781091 0.624417i \(-0.214664\pi\)
\(398\) −3.69917 5.38049i −0.185423 0.269700i
\(399\) −1.34991 20.2681i −0.0675802 1.01467i
\(400\) 1.48400 7.00365i 0.0742002 0.350182i
\(401\) −6.88532 + 11.9257i −0.343836 + 0.595542i −0.985142 0.171744i \(-0.945060\pi\)
0.641305 + 0.767286i \(0.278393\pi\)
\(402\) −10.9464 1.83806i −0.545958 0.0916740i
\(403\) 7.30568 4.21794i 0.363922 0.210110i
\(404\) 4.56601 + 28.7693i 0.227168 + 1.43133i
\(405\) 1.56896 + 23.3990i 0.0779623 + 1.16270i
\(406\) −0.881865 + 6.57474i −0.0437662 + 0.326299i
\(407\) 17.0390 9.83748i 0.844593 0.487626i
\(408\) −31.1126 0.278887i −1.54030 0.0138070i
\(409\) 31.0609 + 17.9330i 1.53586 + 0.886730i 0.999075 + 0.0430132i \(0.0136957\pi\)
0.536788 + 0.843717i \(0.319638\pi\)
\(410\) 12.6142 26.4570i 0.622970 1.30662i
\(411\) −7.10981 + 2.03320i −0.350701 + 0.100290i
\(412\) 22.5874 + 27.8749i 1.11280 + 1.37330i
\(413\) −4.56811 + 21.2205i −0.224782 + 1.04419i
\(414\) −2.94855 + 6.75769i −0.144913 + 0.332122i
\(415\) 2.70054i 0.132564i
\(416\) 10.2755 13.4135i 0.503799 0.657649i
\(417\) −26.7002 25.8210i −1.30752 1.26446i
\(418\) 24.8714 + 11.8582i 1.21650 + 0.580004i
\(419\) 5.05240 8.75102i 0.246826 0.427515i −0.715817 0.698287i \(-0.753946\pi\)
0.962643 + 0.270772i \(0.0872791\pi\)
\(420\) 16.2351 + 17.5147i 0.792191 + 0.854629i
\(421\) −5.04296 8.73465i −0.245779 0.425701i 0.716572 0.697514i \(-0.245710\pi\)
−0.962350 + 0.271812i \(0.912377\pi\)
\(422\) 2.86621 + 36.3446i 0.139525 + 1.76923i
\(423\) −0.921200 27.5078i −0.0447903 1.33747i
\(424\) 11.8703 2.85582i 0.576474 0.138691i
\(425\) −9.84418 + 5.68354i −0.477513 + 0.275692i
\(426\) −10.1763 27.2640i −0.493045 1.32095i
\(427\) 7.33040 8.09890i 0.354743 0.391933i
\(428\) −19.4726 7.46771i −0.941243 0.360965i
\(429\) −5.51714 + 22.0608i −0.266370 + 1.06511i
\(430\) 2.26508 + 3.29458i 0.109232 + 0.158879i
\(431\) 19.4883i 0.938719i 0.883007 + 0.469359i \(0.155515\pi\)
−0.883007 + 0.469359i \(0.844485\pi\)
\(432\) −20.6740 + 2.14141i −0.994678 + 0.103029i
\(433\) 4.11856i 0.197925i 0.995091 + 0.0989626i \(0.0315524\pi\)
−0.995091 + 0.0989626i \(0.968448\pi\)
\(434\) −9.77265 + 4.02013i −0.469102 + 0.192972i
\(435\) −7.76250 1.94131i −0.372184 0.0930786i
\(436\) −7.76307 + 20.2428i −0.371784 + 0.969454i
\(437\) 6.67112 + 3.85158i 0.319123 + 0.184246i
\(438\) 6.58718 + 17.6481i 0.314747 + 0.843259i
\(439\) −3.51549 6.08901i −0.167785 0.290613i 0.769856 0.638218i \(-0.220328\pi\)
−0.937641 + 0.347605i \(0.886995\pi\)
\(440\) −31.4960 + 7.57746i −1.50151 + 0.361241i
\(441\) −20.8145 + 2.78497i −0.991167 + 0.132618i
\(442\) −26.7455 + 2.10920i −1.27215 + 0.100325i
\(443\) 28.1700 16.2640i 1.33840 0.772724i 0.351827 0.936065i \(-0.385561\pi\)
0.986570 + 0.163341i \(0.0522272\pi\)
\(444\) 12.6984 + 8.89899i 0.602637 + 0.422327i
\(445\) −0.218380 + 0.378245i −0.0103522 + 0.0179305i
\(446\) 4.90593 10.2897i 0.232303 0.487233i
\(447\) −13.0113 12.5829i −0.615413 0.595149i
\(448\) −14.9911 + 14.9421i −0.708263 + 0.705949i
\(449\) 38.6596 1.82446 0.912229 0.409680i \(-0.134360\pi\)
0.912229 + 0.409680i \(0.134360\pi\)
\(450\) −6.10976 + 4.50898i −0.288017 + 0.212555i
\(451\) −34.9605 −1.64623
\(452\) −16.2437 20.0462i −0.764040 0.942896i
\(453\) 5.80248 + 20.2904i 0.272624 + 0.953326i
\(454\) 7.48624 15.7017i 0.351347 0.736916i
\(455\) 15.2675 + 13.8188i 0.715750 + 0.647833i
\(456\) −0.194646 + 21.7146i −0.00911511 + 1.01688i
\(457\) 11.4098 + 19.7623i 0.533727 + 0.924442i 0.999224 + 0.0393927i \(0.0125423\pi\)
−0.465497 + 0.885050i \(0.654124\pi\)
\(458\) −0.712670 9.03691i −0.0333009 0.422267i
\(459\) 24.4772 + 22.1347i 1.14250 + 1.03316i
\(460\) −8.94460 + 1.41961i −0.417044 + 0.0661896i
\(461\) 11.1596 6.44301i 0.519755 0.300081i −0.217079 0.976154i \(-0.569653\pi\)
0.736835 + 0.676073i \(0.236320\pi\)
\(462\) 10.5234 26.4705i 0.489594 1.23152i
\(463\) 24.8595 + 14.3527i 1.15532 + 0.667025i 0.950178 0.311707i \(-0.100901\pi\)
0.205143 + 0.978732i \(0.434234\pi\)
\(464\) 1.47001 6.93761i 0.0682435 0.322070i
\(465\) −3.50460 12.2551i −0.162522 0.568315i
\(466\) −11.6980 17.0149i −0.541900 0.788201i
\(467\) −25.4161 −1.17612 −0.588058 0.808819i \(-0.700107\pi\)
−0.588058 + 0.808819i \(0.700107\pi\)
\(468\) −17.5964 + 3.40011i −0.813396 + 0.157170i
\(469\) 11.7205 + 2.52306i 0.541203 + 0.116504i
\(470\) 27.8591 19.1536i 1.28504 0.883488i
\(471\) 18.3020 18.9252i 0.843314 0.872028i
\(472\) 6.58003 22.2529i 0.302871 1.02427i
\(473\) 2.38442 4.12993i 0.109636 0.189894i
\(474\) 21.1312 25.6052i 0.970587 1.17608i
\(475\) 3.96675 + 6.87061i 0.182007 + 0.315245i
\(476\) 33.5566 + 1.83517i 1.53807 + 0.0841148i
\(477\) −11.4251 6.09584i −0.523121 0.279109i
\(478\) −0.808893 10.2570i −0.0369979 0.469146i
\(479\) 15.7078 + 27.2068i 0.717709 + 1.24311i 0.961905 + 0.273383i \(0.0881426\pi\)
−0.244196 + 0.969726i \(0.578524\pi\)
\(480\) −15.8949 19.9793i −0.725500 0.911925i
\(481\) 11.5792 + 6.68523i 0.527964 + 0.304820i
\(482\) −14.5145 6.92021i −0.661116 0.315207i
\(483\) 3.51471 7.14613i 0.159925 0.325160i
\(484\) 10.4757 + 12.9280i 0.476170 + 0.587637i
\(485\) −16.1116 −0.731592
\(486\) 17.9037 + 12.8631i 0.812127 + 0.583481i
\(487\) 27.8663i 1.26274i −0.775481 0.631371i \(-0.782493\pi\)
0.775481 0.631371i \(-0.217507\pi\)
\(488\) −8.46701 + 8.04260i −0.383284 + 0.364071i
\(489\) −6.69708 1.67486i −0.302852 0.0757397i
\(490\) −16.6539 19.6989i −0.752347 0.889905i
\(491\) −24.8087 14.3233i −1.11960 0.646403i −0.178304 0.983976i \(-0.557061\pi\)
−0.941300 + 0.337572i \(0.890394\pi\)
\(492\) −11.6345 24.9760i −0.524522 1.12601i
\(493\) −9.75136 + 5.62995i −0.439179 + 0.253560i
\(494\) 1.47209 + 18.6666i 0.0662325 + 0.839851i
\(495\) 30.3148 + 16.1743i 1.36255 + 0.726982i
\(496\) 10.7417 3.49776i 0.482316 0.157054i
\(497\) 9.63577 + 29.9196i 0.432224 + 1.34208i
\(498\) 1.95796 + 1.61585i 0.0877385 + 0.0724080i
\(499\) 21.5390 + 12.4355i 0.964218 + 0.556691i 0.897469 0.441078i \(-0.145404\pi\)
0.0667492 + 0.997770i \(0.478737\pi\)
\(500\) 15.6206 + 5.99046i 0.698573 + 0.267902i
\(501\) 4.23480 + 4.09535i 0.189197 + 0.182967i
\(502\) −8.09019 11.7673i −0.361083 0.525199i
\(503\) −26.2058 −1.16846 −0.584229 0.811589i \(-0.698603\pi\)
−0.584229 + 0.811589i \(0.698603\pi\)
\(504\) 22.4128 1.29108i 0.998345 0.0575094i
\(505\) 37.9515 1.68882
\(506\) 6.11997 + 8.90158i 0.272066 + 0.395723i
\(507\) 6.79091 1.94201i 0.301595 0.0862476i
\(508\) −22.7093 8.70899i −1.00756 0.386399i
\(509\) 4.29958 + 2.48236i 0.190575 + 0.110029i 0.592252 0.805753i \(-0.298239\pi\)
−0.401677 + 0.915782i \(0.631572\pi\)
\(510\) −6.71275 + 39.9773i −0.297246 + 1.77023i
\(511\) −6.23727 19.3671i −0.275920 0.856749i
\(512\) 17.1849 14.7200i 0.759473 0.650538i
\(513\) 15.4486 17.0836i 0.682072 0.754257i
\(514\) 0.729398 + 9.24903i 0.0321724 + 0.407957i
\(515\) 40.4811 23.3718i 1.78381 1.02988i
\(516\) 3.74396 + 0.329049i 0.164819 + 0.0144856i
\(517\) −34.9228 20.1627i −1.53590 0.886755i
\(518\) −13.2627 10.2282i −0.582728 0.449400i
\(519\) −2.80425 9.80604i −0.123093 0.430438i
\(520\) −15.1613 15.9614i −0.664869 0.699955i
\(521\) 13.6674i 0.598781i 0.954131 + 0.299391i \(0.0967834\pi\)
−0.954131 + 0.299391i \(0.903217\pi\)
\(522\) −6.05215 + 4.46646i −0.264895 + 0.195492i
\(523\) 27.0038 1.18079 0.590397 0.807113i \(-0.298971\pi\)
0.590397 + 0.807113i \(0.298971\pi\)
\(524\) −19.3728 23.9078i −0.846303 1.04442i
\(525\) 6.81476 4.56388i 0.297421 0.199184i
\(526\) 12.7482 + 6.07808i 0.555847 + 0.265017i
\(527\) −15.5337 8.96839i −0.676659 0.390669i
\(528\) −13.3516 + 27.3694i −0.581053 + 1.19110i
\(529\) −9.98999 17.3032i −0.434347 0.752312i
\(530\) −1.25055 15.8574i −0.0543205 0.688803i
\(531\) −20.8916 + 13.0130i −0.906620 + 0.564717i
\(532\) 1.28083 23.4204i 0.0555311 1.01540i
\(533\) −11.8790 20.5751i −0.514537 0.891205i
\(534\) 0.143572 + 0.384652i 0.00621296 + 0.0166455i
\(535\) −13.5859 + 23.5314i −0.587368 + 1.01735i
\(536\) −12.2907 3.63429i −0.530879 0.156977i
\(537\) 23.9542 + 5.99064i 1.03370 + 0.258515i
\(538\) −2.95384 + 2.03081i −0.127349 + 0.0875546i
\(539\) −12.6601 + 28.0427i −0.545308 + 1.20788i
\(540\) −1.46663 + 27.0397i −0.0631136 + 1.16360i
\(541\) −30.2237 −1.29942 −0.649710 0.760182i \(-0.725110\pi\)
−0.649710 + 0.760182i \(0.725110\pi\)
\(542\) −8.36965 12.1738i −0.359507 0.522908i
\(543\) 7.12818 + 1.78267i 0.305900 + 0.0765018i
\(544\) −35.6235 4.66104i −1.52735 0.199840i
\(545\) 24.4621 + 14.1232i 1.04784 + 0.604972i
\(546\) 19.1542 2.80098i 0.819723 0.119871i
\(547\) 5.08073 2.93336i 0.217236 0.125421i −0.387434 0.921898i \(-0.626638\pi\)
0.604670 + 0.796476i \(0.293305\pi\)
\(548\) −8.43324 + 1.33845i −0.360250 + 0.0571758i
\(549\) 12.3794 0.414568i 0.528338 0.0176934i
\(550\) 0.874660 + 11.0910i 0.0372956 + 0.472922i
\(551\) 3.92935 + 6.80583i 0.167396 + 0.289938i
\(552\) −4.32269 + 7.33449i −0.183986 + 0.312177i
\(553\) −24.0631 + 26.5859i −1.02327 + 1.13055i
\(554\) −12.6533 + 26.5390i −0.537586 + 1.12754i
\(555\) 14.0441 14.5223i 0.596139 0.616438i
\(556\) −27.0018 33.3227i −1.14513 1.41320i
\(557\) −26.6804 −1.13049 −0.565243 0.824925i \(-0.691217\pi\)
−0.565243 + 0.824925i \(0.691217\pi\)
\(558\) −10.9822 4.79181i −0.464915 0.202854i
\(559\) 3.24074 0.137069
\(560\) 16.1653 + 22.3414i 0.683110 + 0.944097i
\(561\) 46.4879 13.2942i 1.96272 0.561282i
\(562\) −5.44557 + 11.4216i −0.229708 + 0.481790i
\(563\) 16.4713 28.5292i 0.694184 1.20236i −0.276271 0.961080i \(-0.589099\pi\)
0.970455 0.241282i \(-0.0775679\pi\)
\(564\) 2.78245 31.6590i 0.117162 1.33309i
\(565\) −29.1119 + 16.8078i −1.22475 + 0.707109i
\(566\) 32.0297 2.52593i 1.34631 0.106173i
\(567\) −18.6837 14.7621i −0.784641 0.619950i
\(568\) −7.86016 32.6711i −0.329805 1.37085i
\(569\) 0.320991 + 0.555972i 0.0134566 + 0.0233076i 0.872675 0.488301i \(-0.162383\pi\)
−0.859219 + 0.511609i \(0.829050\pi\)
\(570\) 27.9016 + 4.68507i 1.16867 + 0.196236i
\(571\) −11.6295 6.71428i −0.486679 0.280984i 0.236517 0.971627i \(-0.423994\pi\)
−0.723196 + 0.690643i \(0.757327\pi\)
\(572\) −9.40227 + 24.5171i −0.393129 + 1.02511i
\(573\) −1.10431 3.86160i −0.0461331 0.161321i
\(574\) 11.3219 + 27.5228i 0.472568 + 1.14878i
\(575\) 3.11033i 0.129710i
\(576\) −23.9961 0.430228i −0.999839 0.0179262i
\(577\) 24.9083i 1.03695i −0.855094 0.518473i \(-0.826501\pi\)
0.855094 0.518473i \(-0.173499\pi\)
\(578\) 18.6971 + 27.1952i 0.777698 + 1.13117i
\(579\) 2.00055 + 1.93468i 0.0831402 + 0.0804025i
\(580\) −8.62680 3.30836i −0.358208 0.137372i
\(581\) −2.03296 1.84005i −0.0843412 0.0763382i
\(582\) −9.64030 + 11.6814i −0.399603 + 0.484209i
\(583\) −16.4312 + 9.48653i −0.680509 + 0.392892i
\(584\) 5.08790 + 21.1481i 0.210539 + 0.875114i
\(585\) 0.781515 + 23.3367i 0.0323117 + 0.964854i
\(586\) 0.660803 + 8.37922i 0.0272975 + 0.346142i
\(587\) −12.8056 22.1799i −0.528542 0.915462i −0.999446 0.0332777i \(-0.989405\pi\)
0.470904 0.882185i \(-0.343928\pi\)
\(588\) −24.2470 + 0.287837i −0.999930 + 0.0118702i
\(589\) −6.25937 + 10.8415i −0.257913 + 0.446718i
\(590\) −27.2902 13.0114i −1.12352 0.535673i
\(591\) 3.95491 15.8141i 0.162683 0.650504i
\(592\) 13.3136 + 11.9723i 0.547186 + 0.492057i
\(593\) 16.0701i 0.659921i 0.943995 + 0.329960i \(0.107035\pi\)
−0.943995 + 0.329960i \(0.892965\pi\)
\(594\) 29.8655 12.3013i 1.22540 0.504726i
\(595\) 9.21444 42.8044i 0.377755 1.75481i
\(596\) −13.1583 16.2385i −0.538984 0.665156i
\(597\) −1.94017 + 7.75796i −0.0794060 + 0.317512i
\(598\) −3.15931 + 6.62635i −0.129194 + 0.270972i
\(599\) −13.6480 7.87965i −0.557640 0.321954i 0.194557 0.980891i \(-0.437673\pi\)
−0.752198 + 0.658937i \(0.771006\pi\)
\(600\) −7.63241 + 4.31582i −0.311592 + 0.176193i
\(601\) −29.4617 + 17.0097i −1.20177 + 0.693840i −0.960948 0.276730i \(-0.910749\pi\)
−0.240818 + 0.970570i \(0.577416\pi\)
\(602\) −4.02349 0.539668i −0.163985 0.0219952i
\(603\) 7.18736 + 11.5389i 0.292692 + 0.469899i
\(604\) 3.81975 + 24.0673i 0.155424 + 0.979285i
\(605\) 18.7746 10.8395i 0.763295 0.440689i
\(606\) 22.7081 27.5159i 0.922451 1.11776i
\(607\) 8.74550 15.1477i 0.354969 0.614824i −0.632144 0.774851i \(-0.717825\pi\)
0.987113 + 0.160027i \(0.0511581\pi\)
\(608\) −3.25311 + 24.8630i −0.131931 + 1.00833i
\(609\) 6.75050 4.52085i 0.273544 0.183194i
\(610\) 8.61970 + 12.5375i 0.349001 + 0.507627i
\(611\) 27.4038i 1.10864i
\(612\) 24.9681 + 28.7871i 1.00928 + 1.16365i
\(613\) 4.11918 0.166372 0.0831860 0.996534i \(-0.473490\pi\)
0.0831860 + 0.996534i \(0.473490\pi\)
\(614\) −8.07369 11.7433i −0.325827 0.473920i
\(615\) −34.5141 + 9.87005i −1.39174 + 0.397999i
\(616\) 15.7560 28.8731i 0.634827 1.16333i
\(617\) 14.7264 25.5069i 0.592863 1.02687i −0.400982 0.916086i \(-0.631331\pi\)
0.993845 0.110783i \(-0.0353358\pi\)
\(618\) 7.27643 43.3342i 0.292701 1.74316i
\(619\) −4.03999 6.99747i −0.162381 0.281252i 0.773341 0.633990i \(-0.218584\pi\)
−0.935722 + 0.352738i \(0.885251\pi\)
\(620\) −2.30707 14.5363i −0.0926541 0.583790i
\(621\) 8.59399 2.77198i 0.344865 0.111236i
\(622\) −0.112450 + 0.00886808i −0.00450885 + 0.000355578i
\(623\) −0.135945 0.422118i −0.00544653 0.0169118i
\(624\) −20.6442 + 1.44197i −0.826428 + 0.0577251i
\(625\) 15.3728 26.6265i 0.614912 1.06506i
\(626\) −30.4512 14.5185i −1.21707 0.580276i
\(627\) −9.27852 32.4456i −0.370548 1.29575i
\(628\) 23.6193 19.1390i 0.942512 0.763729i
\(629\) 28.4290i 1.13354i
\(630\) 2.91589 29.1034i 0.116172 1.15951i
\(631\) 1.61516i 0.0642986i −0.999483 0.0321493i \(-0.989765\pi\)
0.999483 0.0321493i \(-0.0102352\pi\)
\(632\) 27.7942 26.4010i 1.10560 1.05018i
\(633\) 31.0402 32.0971i 1.23374 1.27575i
\(634\) 2.41382 5.06277i 0.0958652 0.201068i
\(635\) −15.8441 + 27.4428i −0.628754 + 1.08903i
\(636\) −12.2453 8.58152i −0.485559 0.340279i
\(637\) −20.8054 + 2.07770i −0.824341 + 0.0823214i
\(638\) 0.866413 + 10.9864i 0.0343016 + 0.434957i
\(639\) −16.7777 + 31.4458i −0.663717 + 1.24397i
\(640\) −15.4315 25.1189i −0.609983 0.992914i
\(641\) 15.1794 + 26.2915i 0.599551 + 1.03845i 0.992887 + 0.119058i \(0.0379875\pi\)
−0.393336 + 0.919395i \(0.628679\pi\)
\(642\) 8.93190 + 23.9300i 0.352514 + 0.944441i
\(643\) 7.27667 12.6036i 0.286964 0.497036i −0.686120 0.727489i \(-0.740687\pi\)
0.973084 + 0.230453i \(0.0740207\pi\)
\(644\) 5.02585 7.70073i 0.198046 0.303451i
\(645\) 1.18801 4.75036i 0.0467777 0.187045i
\(646\) 32.8075 22.5556i 1.29079 0.887440i
\(647\) 40.4385 1.58980 0.794900 0.606740i \(-0.207523\pi\)
0.794900 + 0.606740i \(0.207523\pi\)
\(648\) 18.7270 + 17.2424i 0.735666 + 0.677345i
\(649\) 36.0615i 1.41554i
\(650\) −6.23011 + 4.28330i −0.244365 + 0.168005i
\(651\) 11.6135 + 5.71192i 0.455169 + 0.223868i
\(652\) −7.44274 2.85428i −0.291480 0.111782i
\(653\) 15.9077 27.5529i 0.622515 1.07823i −0.366501 0.930418i \(-0.619444\pi\)
0.989016 0.147810i \(-0.0472224\pi\)
\(654\) 24.8765 9.28518i 0.972747 0.363079i
\(655\) −34.7198 + 20.0455i −1.35662 + 0.783243i
\(656\) −9.85079 30.2519i −0.384609 1.18114i
\(657\) 10.8603 20.3549i 0.423700 0.794122i
\(658\) −4.56345 + 34.0228i −0.177902 + 1.32635i
\(659\) 2.88773 1.66723i 0.112490 0.0649460i −0.442699 0.896670i \(-0.645979\pi\)
0.555189 + 0.831724i \(0.312646\pi\)
\(660\) 32.4910 + 22.7697i 1.26471 + 0.886308i
\(661\) −26.0572 15.0442i −1.01351 0.585150i −0.101292 0.994857i \(-0.532298\pi\)
−0.912217 + 0.409707i \(0.865631\pi\)
\(662\) 25.3712 + 12.0965i 0.986079 + 0.470143i
\(663\) 23.6198 + 22.8420i 0.917316 + 0.887111i
\(664\) 2.01882 + 2.12536i 0.0783455 + 0.0824799i
\(665\) −29.8747 6.43109i −1.15849 0.249387i
\(666\) −2.12587 18.8717i −0.0823756 0.731264i
\(667\) 3.08100i 0.119297i
\(668\) 4.28263 + 5.28517i 0.165700 + 0.204489i
\(669\) −13.4233 + 3.83868i −0.518974 + 0.148412i
\(670\) −7.18648 + 15.0730i −0.277638 + 0.582319i
\(671\) 9.07384 15.7164i 0.350292 0.606723i
\(672\) 25.8706 + 1.64753i 0.997978 + 0.0635550i
\(673\) −15.0593 26.0835i −0.580493 1.00544i −0.995421 0.0955891i \(-0.969527\pi\)
0.414928 0.909854i \(-0.363807\pi\)
\(674\) −1.95390 + 0.154089i −0.0752614 + 0.00593528i
\(675\) 9.09260 + 1.95309i 0.349974 + 0.0751746i
\(676\) 8.05499 1.27842i 0.309807 0.0491699i
\(677\) 28.3970 16.3950i 1.09138 0.630111i 0.157439 0.987529i \(-0.449676\pi\)
0.933945 + 0.357418i \(0.116343\pi\)
\(678\) −5.23284 + 31.1638i −0.200966 + 1.19684i
\(679\) 10.9779 12.1288i 0.421293 0.465460i
\(680\) −13.2727 + 44.8869i −0.508987 + 1.72133i
\(681\) −20.4833 + 5.85765i −0.784923 + 0.224466i
\(682\) −14.4663 + 9.94584i −0.553945 + 0.380846i
\(683\) 35.6698i 1.36487i 0.730948 + 0.682433i \(0.239078\pi\)
−0.730948 + 0.682433i \(0.760922\pi\)
\(684\) 20.0916 17.4262i 0.768221 0.666306i
\(685\) 11.1249i 0.425059i
\(686\) 26.1766 + 0.885114i 0.999429 + 0.0337938i
\(687\) −7.71800 + 7.98079i −0.294460 + 0.304486i
\(688\) 4.24555 + 0.899591i 0.161860 + 0.0342966i
\(689\) −11.1661 6.44673i −0.425393 0.245601i
\(690\) 8.55491 + 7.06011i 0.325680 + 0.268774i
\(691\) 7.74976 + 13.4230i 0.294815 + 0.510634i 0.974942 0.222460i \(-0.0714087\pi\)
−0.680127 + 0.733094i \(0.738075\pi\)
\(692\) −1.84603 11.6314i −0.0701755 0.442158i
\(693\) −32.8314 + 11.8003i −1.24716 + 0.448255i
\(694\) 1.46006 + 18.5141i 0.0554232 + 0.702786i
\(695\) −48.3926 + 27.9395i −1.83564 + 1.05980i
\(696\) −7.56044 + 4.27513i −0.286578 + 0.162048i
\(697\) −25.2578 + 43.7477i −0.956706 + 1.65706i
\(698\) −35.0439 16.7082i −1.32643 0.632416i
\(699\) −6.13548 + 24.5333i −0.232065 + 0.927934i
\(700\) 8.44817 4.28038i 0.319311 0.161783i
\(701\) 30.0954 1.13669 0.568344 0.822791i \(-0.307584\pi\)
0.568344 + 0.822791i \(0.307584\pi\)
\(702\) 17.3874 + 13.3967i 0.656244 + 0.505628i
\(703\) −19.8416 −0.748340
\(704\) −19.1231 + 29.5088i −0.720731 + 1.11216i
\(705\) −40.1692 10.0458i −1.51286 0.378348i
\(706\) 39.4648 + 18.8160i 1.48528 + 0.708150i
\(707\) −25.8588 + 28.5698i −0.972521 + 1.07448i
\(708\) −25.7626 + 12.0009i −0.968218 + 0.451020i
\(709\) 9.74971 + 16.8870i 0.366158 + 0.634204i 0.988961 0.148174i \(-0.0473396\pi\)
−0.622803 + 0.782379i \(0.714006\pi\)
\(710\) −43.6449 + 3.44193i −1.63796 + 0.129173i
\(711\) −40.6371 + 1.36088i −1.52401 + 0.0510371i
\(712\) 0.110894 + 0.460936i 0.00415594 + 0.0172743i
\(713\) −4.25042 + 2.45398i −0.159180 + 0.0919023i
\(714\) −25.5210 32.2925i −0.955098 1.20852i
\(715\) 29.6274 + 17.1054i 1.10800 + 0.639705i
\(716\) 26.6213 + 10.2092i 0.994883 + 0.381536i
\(717\) −8.76006 + 9.05833i −0.327150 + 0.338290i
\(718\) −12.9843 + 8.92691i −0.484570 + 0.333149i
\(719\) −8.18208 −0.305140 −0.152570 0.988293i \(-0.548755\pi\)
−0.152570 + 0.988293i \(0.548755\pi\)
\(720\) −5.45415 + 30.7893i −0.203264 + 1.14745i
\(721\) −9.98818 + 46.3987i −0.371979 + 1.72798i
\(722\) −0.519508 0.755631i −0.0193341 0.0281217i
\(723\) 5.41476 + 18.9346i 0.201377 + 0.704185i
\(724\) 7.92185 + 3.03802i 0.294413 + 0.112907i
\(725\) −1.58656 + 2.74801i −0.0589235 + 0.102059i
\(726\) 3.37471 20.0978i 0.125247 0.745901i
\(727\) 1.20415 + 2.08565i 0.0446595 + 0.0773525i 0.887491 0.460825i \(-0.152446\pi\)
−0.842832 + 0.538177i \(0.819113\pi\)
\(728\) 22.3461 0.537862i 0.828201 0.0199345i
\(729\) −2.70701 26.8640i −0.100260 0.994961i
\(730\) 28.2515 2.22797i 1.04563 0.0824609i
\(731\) −3.44532 5.96746i −0.127430 0.220715i
\(732\) 14.2475 + 1.25219i 0.526604 + 0.0462822i
\(733\) −19.7132 11.3814i −0.728123 0.420382i 0.0896122 0.995977i \(-0.471437\pi\)
−0.817735 + 0.575595i \(0.804771\pi\)
\(734\) 14.6054 30.6334i 0.539095 1.13070i
\(735\) −4.58141 + 31.2587i −0.168988 + 1.15300i
\(736\) −5.97827 + 7.80390i −0.220362 + 0.287656i
\(737\) 19.9175 0.733671
\(738\) −13.4952 + 30.9293i −0.496766 + 1.13852i
\(739\) 12.2257i 0.449729i 0.974390 + 0.224865i \(0.0721940\pi\)
−0.974390 + 0.224865i \(0.927806\pi\)
\(740\) 18.1243 14.6863i 0.666263 0.539881i
\(741\) 15.9423 16.4851i 0.585654 0.605595i
\(742\) 12.7895 + 9.86328i 0.469518 + 0.362093i
\(743\) 9.48896 + 5.47845i 0.348116 + 0.200985i 0.663855 0.747861i \(-0.268919\pi\)
−0.315739 + 0.948846i \(0.602252\pi\)
\(744\) −11.9196 7.02499i −0.436994 0.257549i
\(745\) −23.5822 + 13.6152i −0.863986 + 0.498822i
\(746\) −27.8742 + 2.19822i −1.02055 + 0.0804825i
\(747\) −0.104063 3.10742i −0.00380748 0.113695i
\(748\) 55.1413 8.75155i 2.01617 0.319988i
\(749\) −8.45744 26.2608i −0.309028 0.959550i
\(750\) −7.16501 19.1962i −0.261629 0.700946i
\(751\) −23.5744 13.6107i −0.860242 0.496661i 0.00385154 0.999993i \(-0.498774\pi\)
−0.864093 + 0.503332i \(0.832107\pi\)
\(752\) 7.60697 35.9005i 0.277398 1.30916i
\(753\) −4.24321 + 16.9669i −0.154631 + 0.618307i
\(754\) −6.17136 + 4.24291i −0.224748 + 0.154518i
\(755\) 31.7488 1.15546
\(756\) −19.3561 19.5280i −0.703974 0.710225i
\(757\) 24.4479 0.888572 0.444286 0.895885i \(-0.353457\pi\)
0.444286 + 0.895885i \(0.353457\pi\)
\(758\) −6.86688 + 4.72108i −0.249416 + 0.171478i
\(759\) 3.20986 12.8349i 0.116510 0.465878i
\(760\) 31.3282 + 9.26353i 1.13639 + 0.336024i
\(761\) −8.85621 5.11313i −0.321037 0.185351i 0.330818 0.943695i \(-0.392676\pi\)
−0.651855 + 0.758344i \(0.726009\pi\)
\(762\) 10.4166 + 27.9076i 0.377352 + 1.01099i
\(763\) −27.2995 + 8.79195i −0.988309 + 0.318290i
\(764\) −0.726962 4.58041i −0.0263006 0.165713i
\(765\) 42.1410 26.2489i 1.52361 0.949031i
\(766\) 2.75171 0.217006i 0.0994233 0.00784073i
\(767\) −21.2230 + 12.2531i −0.766319 + 0.442434i
\(768\) −27.4453 3.84150i −0.990346 0.138618i
\(769\) 43.5864 + 25.1646i 1.57177 + 0.907459i 0.995953 + 0.0898782i \(0.0286478\pi\)
0.575813 + 0.817581i \(0.304686\pi\)
\(770\) −33.9349 26.1706i −1.22293 0.943124i
\(771\) 7.89916 8.16812i 0.284481 0.294168i
\(772\) 2.02315 + 2.49676i 0.0728148 + 0.0898602i
\(773\) 2.39611i 0.0861820i −0.999071 0.0430910i \(-0.986279\pi\)
0.999071 0.0430910i \(-0.0137205\pi\)
\(774\) −2.73330 3.70368i −0.0982466 0.133126i
\(775\) −5.05473 −0.181571
\(776\) −12.6801 + 12.0445i −0.455188 + 0.432371i
\(777\) 1.36319 + 20.4673i 0.0489040 + 0.734262i
\(778\) −2.76017 + 5.78919i −0.0989568 + 0.207552i
\(779\) 30.5331 + 17.6283i 1.09396 + 0.631600i
\(780\) −2.36054 + 26.8585i −0.0845208 + 0.961687i
\(781\) 26.1101 + 45.2239i 0.934291 + 1.61824i
\(782\) 15.5604 1.22713i 0.556439 0.0438820i
\(783\) 9.00687 + 1.93468i 0.321879 + 0.0691397i
\(784\) −27.8330 3.05343i −0.994036 0.109051i
\(785\) −19.8036 34.3009i −0.706821 1.22425i
\(786\) −6.24085 + 37.1669i −0.222604 + 1.32570i
\(787\) −26.4412 + 45.7975i −0.942527 + 1.63251i −0.181899 + 0.983317i \(0.558224\pi\)
−0.760628 + 0.649188i \(0.775109\pi\)
\(788\) 6.73992 17.5748i 0.240100 0.626078i
\(789\) −4.75583 16.6304i −0.169312 0.592059i
\(790\) −28.2955 41.1561i −1.00671 1.46427i
\(791\) 7.18299 33.3676i 0.255398 1.18642i
\(792\) 35.9495 9.93281i 1.27741 0.352947i
\(793\) 12.3326 0.437943
\(794\) −28.9976 + 19.9363i −1.02908 + 0.707512i
\(795\) −13.5431 + 14.0042i −0.480324 + 0.496679i
\(796\) −3.30643 + 8.62175i −0.117193 + 0.305590i
\(797\) 10.7235 + 6.19123i 0.379847 + 0.219305i 0.677752 0.735291i \(-0.262954\pi\)
−0.297905 + 0.954596i \(0.596288\pi\)
\(798\) −22.5381 + 17.8120i −0.797840 + 0.630538i
\(799\) −50.4611 + 29.1337i −1.78518 + 1.03068i
\(800\) −9.35078 + 3.88196i −0.330600 + 0.137248i
\(801\) 0.236707 0.443649i 0.00836363 0.0156756i
\(802\) 19.4143 1.53106i 0.685544 0.0540635i
\(803\) −16.9011 29.2736i −0.596428 1.03304i
\(804\) 6.62833 + 14.2292i 0.233763 + 0.501826i
\(805\) −8.88257 8.03971i −0.313069 0.283362i
\(806\) −10.7688 5.13434i −0.379314 0.180849i
\(807\) 4.25906 + 1.06514i 0.149926 + 0.0374946i
\(808\) 29.8683 28.3712i 1.05076 0.998094i
\(809\) −22.4198 −0.788239 −0.394119 0.919059i \(-0.628950\pi\)
−0.394119 + 0.919059i \(0.628950\pi\)
\(810\) 26.0112 20.5758i 0.913941 0.722959i
\(811\) −4.09813 −0.143905 −0.0719525 0.997408i \(-0.522923\pi\)
−0.0719525 + 0.997408i \(0.522923\pi\)
\(812\) 8.36851 4.24002i 0.293677 0.148796i
\(813\) −4.38979 + 17.5530i −0.153957 + 0.615610i
\(814\) −25.1160 11.9748i −0.880315 0.419716i
\(815\) −5.19273 + 8.99408i −0.181894 + 0.315049i
\(816\) 24.6026 + 36.4809i 0.861262 + 1.27709i
\(817\) −4.16491 + 2.40461i −0.145712 + 0.0841267i
\(818\) −3.98768 50.5652i −0.139426 1.76797i
\(819\) −18.1003 15.3125i −0.632475 0.535061i
\(820\) −40.9386 + 6.49742i −1.42964 + 0.226900i
\(821\) −2.75549 4.77265i −0.0961674 0.166567i 0.813928 0.580966i \(-0.197325\pi\)
−0.910095 + 0.414399i \(0.863992\pi\)
\(822\) 8.06583 + 6.65649i 0.281328 + 0.232172i
\(823\) 42.9452 + 24.7944i 1.49697 + 0.864278i 0.999994 0.00348342i \(-0.00110881\pi\)
0.496980 + 0.867762i \(0.334442\pi\)
\(824\) 14.3873 48.6560i 0.501204 1.69501i
\(825\) 9.47230 9.79483i 0.329783 0.341012i
\(826\) 28.3896 11.6785i 0.987800 0.406346i
\(827\) 4.41558i 0.153545i −0.997049 0.0767723i \(-0.975539\pi\)
0.997049 0.0767723i \(-0.0244615\pi\)
\(828\) 10.2376 1.97817i 0.355780 0.0687462i
\(829\) 6.00543i 0.208577i 0.994547 + 0.104289i \(0.0332566\pi\)
−0.994547 + 0.104289i \(0.966743\pi\)
\(830\) 3.14711 2.16369i 0.109238 0.0751026i
\(831\) 34.6210 9.90063i 1.20099 0.343449i
\(832\) −23.8643 1.22779i −0.827347 0.0425659i
\(833\) 25.9446 + 36.1020i 0.898928 + 1.25086i
\(834\) −8.69851 + 51.8034i −0.301205 + 1.79380i
\(835\) 7.67533 4.43135i 0.265616 0.153353i
\(836\) −6.10802 38.4851i −0.211250 1.33104i
\(837\) 4.50487 + 13.9665i 0.155711 + 0.482752i
\(838\) −14.2461 + 1.12348i −0.492124 + 0.0388099i
\(839\) 13.2905 + 23.0198i 0.458839 + 0.794732i 0.998900 0.0468940i \(-0.0149323\pi\)
−0.540061 + 0.841626i \(0.681599\pi\)
\(840\) 7.40333 32.9526i 0.255439 1.13697i
\(841\) 12.9284 22.3926i 0.445807 0.772160i
\(842\) −6.13860 + 12.8751i −0.211550 + 0.443706i
\(843\) 14.8998 4.26092i 0.513176 0.146754i
\(844\) 40.0582 32.4597i 1.37886 1.11731i
\(845\) 10.6259i 0.365541i
\(846\) −31.3185 + 23.1129i −1.07675 + 0.794638i
\(847\) −4.63238 + 21.5191i −0.159171 + 0.739405i
\(848\) −12.8386 11.5451i −0.440881 0.396462i
\(849\) −28.2864 27.3550i −0.970788 0.938821i
\(850\) 14.5106 + 6.91836i 0.497709 + 0.237298i
\(851\) −6.73672 3.88945i −0.230932 0.133328i
\(852\) −23.6192 + 33.7032i −0.809179 + 1.15465i
\(853\) −19.9843 + 11.5380i −0.684250 + 0.395052i −0.801454 0.598056i \(-0.795940\pi\)
0.117204 + 0.993108i \(0.462607\pi\)
\(854\) −15.3113 2.05370i −0.523942 0.0702760i
\(855\) −18.3201 29.4118i −0.626533 1.00586i
\(856\) 6.89896 + 28.6758i 0.235802 + 0.980119i
\(857\) 32.3152 18.6572i 1.10387 0.637318i 0.166633 0.986019i \(-0.446711\pi\)
0.937234 + 0.348701i \(0.113377\pi\)
\(858\) 30.1292 11.2458i 1.02859 0.383924i
\(859\) −3.22640 + 5.58830i −0.110084 + 0.190670i −0.915804 0.401626i \(-0.868445\pi\)
0.805720 + 0.592296i \(0.201778\pi\)
\(860\) 2.02459 5.27927i 0.0690380 0.180022i
\(861\) 16.0865 32.7072i 0.548227 1.11466i
\(862\) 22.7109 15.6141i 0.773538 0.531819i
\(863\) 28.0729i 0.955612i 0.878465 + 0.477806i \(0.158568\pi\)
−0.878465 + 0.477806i \(0.841432\pi\)
\(864\) 19.0596 + 22.3770i 0.648422 + 0.761281i
\(865\) −15.3437 −0.521702
\(866\) 4.79961 3.29981i 0.163098 0.112132i
\(867\) 9.80643 39.2120i 0.333044 1.33171i
\(868\) 12.5148 + 8.16774i 0.424780 + 0.277231i
\(869\) −29.7863 + 51.5913i −1.01043 + 1.75012i
\(870\) 3.95703 + 10.6015i 0.134156 + 0.359425i
\(871\) 6.76765 + 11.7219i 0.229313 + 0.397182i
\(872\) 29.8100 7.17183i 1.00949 0.242869i
\(873\) 18.5391 0.620851i 0.627455 0.0210126i
\(874\) −0.856457 10.8602i −0.0289701 0.367351i
\(875\) 6.78441 + 21.0660i 0.229355 + 0.712160i
\(876\) 15.2888 21.8162i 0.516559 0.737101i
\(877\) 14.9954 25.9728i 0.506360 0.877041i −0.493613 0.869682i \(-0.664324\pi\)
0.999973 0.00735913i \(-0.00234250\pi\)
\(878\) −4.27928 + 8.97537i −0.144419 + 0.302904i
\(879\) 7.15629 7.39996i 0.241376 0.249594i
\(880\) 34.0653 + 30.6332i 1.14834 + 1.03264i
\(881\) 38.3766i 1.29294i 0.762939 + 0.646471i \(0.223756\pi\)
−0.762939 + 0.646471i \(0.776244\pi\)
\(882\) 19.9222 + 22.0251i 0.670815 + 0.741625i
\(883\) 37.0722i 1.24758i −0.781593 0.623789i \(-0.785593\pi\)
0.781593 0.623789i \(-0.214407\pi\)
\(884\) 23.8866 + 29.4783i 0.803393 + 0.991461i
\(885\) 10.1809 + 35.6010i 0.342226 + 1.19672i
\(886\) −41.5233 19.7975i −1.39500 0.665110i
\(887\) 12.2145 21.1562i 0.410123 0.710355i −0.584779 0.811192i \(-0.698819\pi\)
0.994903 + 0.100838i \(0.0321523\pi\)
\(888\) 0.196559 21.9281i 0.00659610 0.735859i
\(889\) −9.86323 30.6259i −0.330802 1.02716i
\(890\) 0.615759 0.0485601i 0.0206403 0.00162774i
\(891\) −35.5055 17.4431i −1.18948 0.584366i
\(892\) −15.9219 + 2.52699i −0.533105 + 0.0846098i
\(893\) 20.3335 + 35.2186i 0.680434 + 1.17855i
\(894\) −4.23888 + 25.2443i −0.141769 + 0.844297i
\(895\) 18.5734 32.1701i 0.620841 1.07533i
\(896\) 29.4239 + 5.49838i 0.982985 + 0.183688i
\(897\) 8.64429 2.47202i 0.288624 0.0825384i
\(898\) −30.9743 45.0524i −1.03362 1.50342i
\(899\) −5.00706 −0.166995
\(900\) 10.1498 + 3.50747i 0.338325 + 0.116916i
\(901\) 27.4147i 0.913318i
\(902\) 28.0106 + 40.7417i 0.932650 + 1.35655i
\(903\) 2.76659 + 4.13105i 0.0920663 + 0.137473i
\(904\) −10.3466 + 34.9910i −0.344123 + 1.16378i
\(905\) 5.52700 9.57305i 0.183724 0.318219i
\(906\) 18.9967 23.0188i 0.631123 0.764747i
\(907\) 17.3676 10.0272i 0.576683 0.332948i −0.183131 0.983089i \(-0.558623\pi\)
0.759814 + 0.650140i \(0.225290\pi\)
\(908\) −24.2962 + 3.85608i −0.806296 + 0.127968i
\(909\) −43.6696 + 1.46244i −1.44843 + 0.0485060i
\(910\) 3.87148 28.8638i 0.128338 0.956826i
\(911\) −12.8106 + 7.39618i −0.424433 + 0.245046i −0.696972 0.717098i \(-0.745470\pi\)
0.272539 + 0.962145i \(0.412136\pi\)
\(912\) 25.4613 17.1710i 0.843109 0.568589i
\(913\) −3.94506 2.27768i −0.130563 0.0753803i
\(914\) 13.8887 29.1302i 0.459397 0.963542i
\(915\) 4.52093 18.0774i 0.149457 0.597620i
\(916\) −9.96029 + 8.07094i −0.329097 + 0.266671i
\(917\) 8.56667 39.7953i 0.282896 1.31416i
\(918\) 6.18365 46.2593i 0.204091 1.52678i
\(919\) 47.6023i 1.57026i −0.619333 0.785128i \(-0.712597\pi\)
0.619333 0.785128i \(-0.287403\pi\)
\(920\) 8.82082 + 9.28630i 0.290814 + 0.306160i
\(921\) −4.23455 + 16.9323i −0.139533 + 0.557937i
\(922\) −16.4496 7.84283i −0.541739 0.258290i
\(923\) −17.7435 + 30.7327i −0.584036 + 1.01158i
\(924\) −39.2792 + 8.94471i −1.29219 + 0.294259i
\(925\) −4.00575 6.93817i −0.131708 0.228126i
\(926\) −3.19153 40.4698i −0.104880 1.32992i
\(927\) −45.6796 + 28.4530i −1.50032 + 0.934520i
\(928\) −9.26261 + 3.84535i −0.304060 + 0.126230i
\(929\) 2.22951 1.28721i 0.0731477 0.0422318i −0.462980 0.886369i \(-0.653220\pi\)
0.536128 + 0.844137i \(0.319887\pi\)
\(930\) −11.4737 + 13.9030i −0.376237 + 0.455896i
\(931\) 25.1969 18.1077i 0.825795 0.593456i
\(932\) −10.4560 + 27.2649i −0.342499 + 0.893091i
\(933\) 0.0993087 + 0.0960386i 0.00325122 + 0.00314416i
\(934\) 20.3635 + 29.6190i 0.666314 + 0.969162i
\(935\) 72.7406i 2.37887i
\(936\) 18.0607 + 17.7821i 0.590333 + 0.581225i
\(937\) 10.0050i 0.326849i −0.986556 0.163424i \(-0.947746\pi\)
0.986556 0.163424i \(-0.0522539\pi\)
\(938\) −6.45026 15.6801i −0.210609 0.511975i
\(939\) 11.3601 + 39.7246i 0.370723 + 1.29636i
\(940\) −44.6417 17.1200i −1.45605 0.558393i
\(941\) 34.5062 + 19.9222i 1.12487 + 0.649445i 0.942640 0.333811i \(-0.108335\pi\)
0.182231 + 0.983256i \(0.441668\pi\)
\(942\) −36.7184 6.16554i −1.19635 0.200884i
\(943\) 6.91117 + 11.9705i 0.225059 + 0.389813i
\(944\) −31.2047 + 10.1610i −1.01563 + 0.330713i
\(945\) −29.0807 + 20.9185i −0.945994 + 0.680479i
\(946\) −6.72327 + 0.530212i −0.218593 + 0.0172387i
\(947\) 26.3058 15.1877i 0.854824 0.493533i −0.00745153 0.999972i \(-0.502372\pi\)
0.862276 + 0.506439i \(0.169039\pi\)
\(948\) −46.7697 4.11050i −1.51901 0.133503i
\(949\) 11.4854 19.8934i 0.372833 0.645766i
\(950\) 4.82857 10.1275i 0.156660 0.328579i
\(951\) −6.60454 + 1.88871i −0.214167 + 0.0612457i
\(952\) −24.7471 40.5760i −0.802059 1.31508i
\(953\) 27.5080 0.891073 0.445536 0.895264i \(-0.353013\pi\)
0.445536 + 0.895264i \(0.353013\pi\)
\(954\) 2.05002 + 18.1985i 0.0663720 + 0.589197i
\(955\) −6.04232 −0.195525
\(956\) −11.3051 + 9.16065i −0.365633 + 0.296277i
\(957\) 9.38298 9.70247i 0.303309 0.313636i
\(958\) 19.1206 40.1035i 0.617757 1.29569i
\(959\) −8.37476 7.58009i −0.270435 0.244774i
\(960\) −10.5480 + 34.5308i −0.340436 + 1.11448i
\(961\) 11.5119 + 19.9392i 0.371352 + 0.643201i
\(962\) −1.48656 18.8502i −0.0479287 0.607754i
\(963\) 14.7260 27.6003i 0.474540 0.889408i
\(964\) 3.56452 + 22.4591i 0.114805 + 0.723360i
\(965\) 3.62589 2.09341i 0.116721 0.0673892i
\(966\) −11.1438 + 1.62960i −0.358547 + 0.0524315i
\(967\) −51.9168 29.9742i −1.66953 0.963905i −0.967889 0.251377i \(-0.919117\pi\)
−0.701644 0.712528i \(-0.747550\pi\)
\(968\) 6.67262 22.5660i 0.214466 0.725300i
\(969\) −47.3041 11.8302i −1.51963 0.380040i
\(970\) 12.9087 + 18.7759i 0.414474 + 0.602858i
\(971\) −30.8420 −0.989768 −0.494884 0.868959i \(-0.664789\pi\)
−0.494884 + 0.868959i \(0.664789\pi\)
\(972\) 0.645642 31.1702i 0.0207090 0.999786i
\(973\) 11.9402 55.4668i 0.382787 1.77818i
\(974\) −32.4743 + 22.3266i −1.04054 + 0.715391i
\(975\) 8.98301 + 2.24654i 0.287686 + 0.0719469i
\(976\) 16.1564 + 3.42337i 0.517152 + 0.109579i
\(977\) −6.22072 + 10.7746i −0.199018 + 0.344710i −0.948210 0.317643i \(-0.897109\pi\)
0.749192 + 0.662353i \(0.230442\pi\)
\(978\) 3.41392 + 9.14643i 0.109165 + 0.292470i
\(979\) −0.368371 0.638037i −0.0117732 0.0203918i
\(980\) −9.61315 + 35.1907i −0.307081 + 1.12413i
\(981\) −28.6920 15.3085i −0.916065 0.488762i
\(982\) 3.18501 + 40.3871i 0.101638 + 1.28880i
\(983\) −0.588026 1.01849i −0.0187551 0.0324848i 0.856496 0.516154i \(-0.172637\pi\)
−0.875251 + 0.483670i \(0.839304\pi\)
\(984\) −19.7846 + 33.5693i −0.630708 + 1.07015i
\(985\) −21.2381 12.2618i −0.676702 0.390694i
\(986\) 14.3738 + 6.85312i 0.457754 + 0.218248i
\(987\) 34.9323 23.3944i 1.11191 0.744651i
\(988\) 20.5739 16.6713i 0.654544 0.530385i
\(989\) −1.88545 −0.0599539
\(990\) −5.43941 48.2867i −0.172876 1.53465i
\(991\) 7.08869i 0.225180i −0.993642 0.112590i \(-0.964085\pi\)
0.993642 0.112590i \(-0.0359146\pi\)
\(992\) −12.6825 9.71555i −0.402669 0.308469i
\(993\) −9.46496 33.0976i −0.300361 1.05032i
\(994\) 27.1470 35.2009i 0.861051 1.11651i
\(995\) 10.4188 + 6.01532i 0.330299 + 0.190698i
\(996\) 0.314320 3.57637i 0.00995961 0.113322i
\(997\) −22.9923 + 13.2746i −0.728173 + 0.420411i −0.817753 0.575569i \(-0.804781\pi\)
0.0895805 + 0.995980i \(0.471447\pi\)
\(998\) −2.76523 35.0642i −0.0875320 1.10994i
\(999\) −15.6005 + 17.2515i −0.493578 + 0.545814i
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 252.2.bi.c.139.13 80
3.2 odd 2 756.2.bi.c.307.27 80
4.3 odd 2 inner 252.2.bi.c.139.16 yes 80
7.6 odd 2 inner 252.2.bi.c.139.14 yes 80
9.2 odd 6 756.2.bi.c.559.26 80
9.7 even 3 inner 252.2.bi.c.223.15 yes 80
12.11 even 2 756.2.bi.c.307.25 80
21.20 even 2 756.2.bi.c.307.28 80
28.27 even 2 inner 252.2.bi.c.139.15 yes 80
36.7 odd 6 inner 252.2.bi.c.223.14 yes 80
36.11 even 6 756.2.bi.c.559.28 80
63.20 even 6 756.2.bi.c.559.25 80
63.34 odd 6 inner 252.2.bi.c.223.16 yes 80
84.83 odd 2 756.2.bi.c.307.26 80
252.83 odd 6 756.2.bi.c.559.27 80
252.223 even 6 inner 252.2.bi.c.223.13 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.bi.c.139.13 80 1.1 even 1 trivial
252.2.bi.c.139.14 yes 80 7.6 odd 2 inner
252.2.bi.c.139.15 yes 80 28.27 even 2 inner
252.2.bi.c.139.16 yes 80 4.3 odd 2 inner
252.2.bi.c.223.13 yes 80 252.223 even 6 inner
252.2.bi.c.223.14 yes 80 36.7 odd 6 inner
252.2.bi.c.223.15 yes 80 9.7 even 3 inner
252.2.bi.c.223.16 yes 80 63.34 odd 6 inner
756.2.bi.c.307.25 80 12.11 even 2
756.2.bi.c.307.26 80 84.83 odd 2
756.2.bi.c.307.27 80 3.2 odd 2
756.2.bi.c.307.28 80 21.20 even 2
756.2.bi.c.559.25 80 63.20 even 6
756.2.bi.c.559.26 80 9.2 odd 6
756.2.bi.c.559.27 80 252.83 odd 6
756.2.bi.c.559.28 80 36.11 even 6