Properties

Label 429.2.n.b.196.3
Level $429$
Weight $2$
Character 429.196
Analytic conductor $3.426$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(157,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.157");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.n (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + 4 x^{18} + 4 x^{17} + 37 x^{16} - 74 x^{15} + 398 x^{14} - 224 x^{13} + 978 x^{12} + 115 x^{11} + 1963 x^{10} + 323 x^{9} + 3007 x^{8} + 1828 x^{7} + 6736 x^{6} + \cdots + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 196.3
Root \(0.169480 + 0.521606i\) of defining polynomial
Character \(\chi\) \(=\) 429.196
Dual form 429.2.n.b.313.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.169480 - 0.521606i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.37468 + 0.998767i) q^{4} +(-0.266070 - 0.818878i) q^{5} +(-0.169480 - 0.521606i) q^{6} +(2.33406 + 1.69579i) q^{7} +(1.64135 - 1.19251i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(0.169480 - 0.521606i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.37468 + 0.998767i) q^{4} +(-0.266070 - 0.818878i) q^{5} +(-0.169480 - 0.521606i) q^{6} +(2.33406 + 1.69579i) q^{7} +(1.64135 - 1.19251i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.472225 q^{10} +(-2.07523 - 2.58716i) q^{11} +1.69920 q^{12} +(-0.309017 + 0.951057i) q^{13} +(1.28011 - 0.930055i) q^{14} +(-0.696579 - 0.506094i) q^{15} +(0.706320 + 2.17383i) q^{16} +(0.732462 + 2.25429i) q^{17} +(-0.443705 - 0.322370i) q^{18} +(-1.91727 + 1.39298i) q^{19} +(0.452106 - 1.39144i) q^{20} +2.88505 q^{21} +(-1.70119 + 0.643981i) q^{22} +1.81427 q^{23} +(0.626941 - 1.92953i) q^{24} +(3.44532 - 2.50317i) q^{25} +(0.443705 + 0.322370i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.51489 + 4.66236i) q^{28} +(-3.43067 - 2.49253i) q^{29} +(-0.382038 + 0.277567i) q^{30} +(-0.318476 + 0.980168i) q^{31} +5.31124 q^{32} +(-3.19959 - 0.873268i) q^{33} +1.29999 q^{34} +(0.767625 - 2.36251i) q^{35} +(1.37468 - 0.998767i) q^{36} +(-8.78740 - 6.38442i) q^{37} +(0.401647 + 1.23614i) q^{38} +(0.309017 + 0.951057i) q^{39} +(-1.41324 - 1.02678i) q^{40} +(-1.61597 + 1.17407i) q^{41} +(0.488959 - 1.50486i) q^{42} +1.67092 q^{43} +(-0.268817 - 5.62921i) q^{44} -0.861019 q^{45} +(0.307483 - 0.946334i) q^{46} +(-2.12809 + 1.54615i) q^{47} +(1.84917 + 1.34350i) q^{48} +(0.408994 + 1.25875i) q^{49} +(-0.721756 - 2.22134i) q^{50} +(1.91761 + 1.39323i) q^{51} +(-1.37468 + 0.998767i) q^{52} +(-2.34937 + 7.23063i) q^{53} -0.548449 q^{54} +(-1.56641 + 2.38773i) q^{55} +5.85327 q^{56} +(-0.732333 + 2.25389i) q^{57} +(-1.88155 + 1.36703i) q^{58} +(-4.27373 - 3.10505i) q^{59} +(-0.452106 - 1.39144i) q^{60} +(0.526405 + 1.62011i) q^{61} +(0.457286 + 0.332238i) q^{62} +(2.33406 - 1.69579i) q^{63} +(-0.512491 + 1.57729i) q^{64} +0.861019 q^{65} +(-0.997769 + 1.52093i) q^{66} -7.33979 q^{67} +(-1.24460 + 3.83049i) q^{68} +(1.46777 - 1.06640i) q^{69} +(-1.10220 - 0.800795i) q^{70} +(-1.30904 - 4.02882i) q^{71} +(-0.626941 - 1.92953i) q^{72} +(8.36680 + 6.07883i) q^{73} +(-4.81944 + 3.50153i) q^{74} +(1.31599 - 4.05021i) q^{75} -4.02691 q^{76} +(-0.456421 - 9.55775i) q^{77} +0.548449 q^{78} +(-1.70314 + 5.24171i) q^{79} +(1.59217 - 1.15678i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.338528 + 1.04188i) q^{82} +(0.438561 + 1.34975i) q^{83} +(3.96604 + 2.88150i) q^{84} +(1.65110 - 1.19959i) q^{85} +(0.283188 - 0.871564i) q^{86} -4.24054 q^{87} +(-6.49142 - 1.77171i) q^{88} +6.01572 q^{89} +(-0.145926 + 0.449113i) q^{90} +(-2.33406 + 1.69579i) q^{91} +(2.49405 + 1.81203i) q^{92} +(0.318476 + 0.980168i) q^{93} +(0.445812 + 1.37207i) q^{94} +(1.65081 + 1.19938i) q^{95} +(4.29688 - 3.12187i) q^{96} +(-1.05099 + 3.23462i) q^{97} +0.725890 q^{98} +(-3.10182 + 1.17419i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.169480 0.521606i 0.119841 0.368831i −0.873085 0.487567i \(-0.837884\pi\)
0.992926 + 0.118736i \(0.0378843\pi\)
\(3\) 0.809017 0.587785i 0.467086 0.339358i
\(4\) 1.37468 + 0.998767i 0.687342 + 0.499383i
\(5\) −0.266070 0.818878i −0.118990 0.366213i 0.873768 0.486342i \(-0.161669\pi\)
−0.992758 + 0.120129i \(0.961669\pi\)
\(6\) −0.169480 0.521606i −0.0691899 0.212945i
\(7\) 2.33406 + 1.69579i 0.882191 + 0.640949i 0.933830 0.357717i \(-0.116445\pi\)
−0.0516395 + 0.998666i \(0.516445\pi\)
\(8\) 1.64135 1.19251i 0.580306 0.421617i
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) −0.472225 −0.149331
\(11\) −2.07523 2.58716i −0.625706 0.780059i
\(12\) 1.69920 0.490518
\(13\) −0.309017 + 0.951057i −0.0857059 + 0.263776i
\(14\) 1.28011 0.930055i 0.342124 0.248568i
\(15\) −0.696579 0.506094i −0.179856 0.130673i
\(16\) 0.706320 + 2.17383i 0.176580 + 0.543458i
\(17\) 0.732462 + 2.25429i 0.177648 + 0.546745i 0.999745 0.0226037i \(-0.00719561\pi\)
−0.822096 + 0.569348i \(0.807196\pi\)
\(18\) −0.443705 0.322370i −0.104582 0.0759834i
\(19\) −1.91727 + 1.39298i −0.439852 + 0.319571i −0.785576 0.618765i \(-0.787633\pi\)
0.345724 + 0.938336i \(0.387633\pi\)
\(20\) 0.452106 1.39144i 0.101094 0.311135i
\(21\) 2.88505 0.629570
\(22\) −1.70119 + 0.643981i −0.362695 + 0.137297i
\(23\) 1.81427 0.378301 0.189151 0.981948i \(-0.439427\pi\)
0.189151 + 0.981948i \(0.439427\pi\)
\(24\) 0.626941 1.92953i 0.127974 0.393863i
\(25\) 3.44532 2.50317i 0.689063 0.500634i
\(26\) 0.443705 + 0.322370i 0.0870176 + 0.0632220i
\(27\) −0.309017 0.951057i −0.0594703 0.183031i
\(28\) 1.51489 + 4.66236i 0.286288 + 0.881103i
\(29\) −3.43067 2.49253i −0.637060 0.462851i 0.221779 0.975097i \(-0.428814\pi\)
−0.858839 + 0.512246i \(0.828814\pi\)
\(30\) −0.382038 + 0.277567i −0.0697503 + 0.0506766i
\(31\) −0.318476 + 0.980168i −0.0572000 + 0.176043i −0.975574 0.219669i \(-0.929502\pi\)
0.918374 + 0.395712i \(0.129502\pi\)
\(32\) 5.31124 0.938903
\(33\) −3.19959 0.873268i −0.556978 0.152016i
\(34\) 1.29999 0.222946
\(35\) 0.767625 2.36251i 0.129752 0.399336i
\(36\) 1.37468 0.998767i 0.229114 0.166461i
\(37\) −8.78740 6.38442i −1.44464 1.04959i −0.987047 0.160429i \(-0.948712\pi\)
−0.457592 0.889162i \(-0.651288\pi\)
\(38\) 0.401647 + 1.23614i 0.0651558 + 0.200529i
\(39\) 0.309017 + 0.951057i 0.0494823 + 0.152291i
\(40\) −1.41324 1.02678i −0.223452 0.162348i
\(41\) −1.61597 + 1.17407i −0.252372 + 0.183359i −0.706778 0.707436i \(-0.749852\pi\)
0.454405 + 0.890795i \(0.349852\pi\)
\(42\) 0.488959 1.50486i 0.0754480 0.232205i
\(43\) 1.67092 0.254814 0.127407 0.991851i \(-0.459335\pi\)
0.127407 + 0.991851i \(0.459335\pi\)
\(44\) −0.268817 5.62921i −0.0405257 0.848635i
\(45\) −0.861019 −0.128353
\(46\) 0.307483 0.946334i 0.0453358 0.139529i
\(47\) −2.12809 + 1.54615i −0.310414 + 0.225529i −0.732074 0.681225i \(-0.761448\pi\)
0.421660 + 0.906754i \(0.361448\pi\)
\(48\) 1.84917 + 1.34350i 0.266905 + 0.193918i
\(49\) 0.408994 + 1.25875i 0.0584277 + 0.179822i
\(50\) −0.721756 2.22134i −0.102072 0.314144i
\(51\) 1.91761 + 1.39323i 0.268519 + 0.195091i
\(52\) −1.37468 + 0.998767i −0.190634 + 0.138504i
\(53\) −2.34937 + 7.23063i −0.322711 + 0.993204i 0.649752 + 0.760147i \(0.274873\pi\)
−0.972463 + 0.233057i \(0.925127\pi\)
\(54\) −0.548449 −0.0746345
\(55\) −1.56641 + 2.38773i −0.211215 + 0.321961i
\(56\) 5.85327 0.782176
\(57\) −0.732333 + 2.25389i −0.0969998 + 0.298535i
\(58\) −1.88155 + 1.36703i −0.247059 + 0.179499i
\(59\) −4.27373 3.10505i −0.556392 0.404242i 0.273745 0.961802i \(-0.411738\pi\)
−0.830137 + 0.557560i \(0.811738\pi\)
\(60\) −0.452106 1.39144i −0.0583667 0.179634i
\(61\) 0.526405 + 1.62011i 0.0673993 + 0.207434i 0.979084 0.203457i \(-0.0652177\pi\)
−0.911685 + 0.410891i \(0.865218\pi\)
\(62\) 0.457286 + 0.332238i 0.0580754 + 0.0421943i
\(63\) 2.33406 1.69579i 0.294064 0.213650i
\(64\) −0.512491 + 1.57729i −0.0640614 + 0.197161i
\(65\) 0.861019 0.106796
\(66\) −0.997769 + 1.52093i −0.122817 + 0.187213i
\(67\) −7.33979 −0.896698 −0.448349 0.893858i \(-0.647988\pi\)
−0.448349 + 0.893858i \(0.647988\pi\)
\(68\) −1.24460 + 3.83049i −0.150930 + 0.464515i
\(69\) 1.46777 1.06640i 0.176699 0.128380i
\(70\) −1.10220 0.800795i −0.131738 0.0957133i
\(71\) −1.30904 4.02882i −0.155355 0.478133i 0.842842 0.538161i \(-0.180881\pi\)
−0.998197 + 0.0600283i \(0.980881\pi\)
\(72\) −0.626941 1.92953i −0.0738857 0.227397i
\(73\) 8.36680 + 6.07883i 0.979259 + 0.711474i 0.957543 0.288291i \(-0.0930869\pi\)
0.0217165 + 0.999764i \(0.493087\pi\)
\(74\) −4.81944 + 3.50153i −0.560248 + 0.407044i
\(75\) 1.31599 4.05021i 0.151958 0.467678i
\(76\) −4.02691 −0.461918
\(77\) −0.456421 9.55775i −0.0520140 1.08921i
\(78\) 0.548449 0.0620996
\(79\) −1.70314 + 5.24171i −0.191618 + 0.589739i 0.808382 + 0.588659i \(0.200344\pi\)
−0.999999 + 0.00108015i \(0.999656\pi\)
\(80\) 1.59217 1.15678i 0.178010 0.129332i
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 0.338528 + 1.04188i 0.0373842 + 0.115057i
\(83\) 0.438561 + 1.34975i 0.0481384 + 0.148155i 0.972236 0.234001i \(-0.0751819\pi\)
−0.924098 + 0.382156i \(0.875182\pi\)
\(84\) 3.96604 + 2.88150i 0.432730 + 0.314397i
\(85\) 1.65110 1.19959i 0.179087 0.130114i
\(86\) 0.283188 0.871564i 0.0305370 0.0939832i
\(87\) −4.24054 −0.454634
\(88\) −6.49142 1.77171i −0.691987 0.188865i
\(89\) 6.01572 0.637665 0.318832 0.947811i \(-0.396709\pi\)
0.318832 + 0.947811i \(0.396709\pi\)
\(90\) −0.145926 + 0.449113i −0.0153819 + 0.0473406i
\(91\) −2.33406 + 1.69579i −0.244676 + 0.177767i
\(92\) 2.49405 + 1.81203i 0.260023 + 0.188917i
\(93\) 0.318476 + 0.980168i 0.0330244 + 0.101639i
\(94\) 0.445812 + 1.37207i 0.0459820 + 0.141518i
\(95\) 1.65081 + 1.19938i 0.169369 + 0.123054i
\(96\) 4.29688 3.12187i 0.438549 0.318624i
\(97\) −1.05099 + 3.23462i −0.106712 + 0.328426i −0.990128 0.140163i \(-0.955237\pi\)
0.883416 + 0.468589i \(0.155237\pi\)
\(98\) 0.725890 0.0733260
\(99\) −3.10182 + 1.17419i −0.311745 + 0.118010i
\(100\) 7.23631 0.723631
\(101\) −3.71677 + 11.4390i −0.369832 + 1.13823i 0.577067 + 0.816697i \(0.304197\pi\)
−0.946899 + 0.321530i \(0.895803\pi\)
\(102\) 1.05171 0.764113i 0.104135 0.0756584i
\(103\) −7.45807 5.41861i −0.734866 0.533911i 0.156233 0.987720i \(-0.450065\pi\)
−0.891099 + 0.453809i \(0.850065\pi\)
\(104\) 0.626941 + 1.92953i 0.0614767 + 0.189206i
\(105\) −0.767625 2.36251i −0.0749125 0.230557i
\(106\) 3.37337 + 2.45090i 0.327651 + 0.238052i
\(107\) −12.0751 + 8.77306i −1.16734 + 0.848123i −0.990688 0.136150i \(-0.956527\pi\)
−0.176653 + 0.984273i \(0.556527\pi\)
\(108\) 0.525083 1.61604i 0.0505261 0.155503i
\(109\) −8.27227 −0.792340 −0.396170 0.918177i \(-0.629661\pi\)
−0.396170 + 0.918177i \(0.629661\pi\)
\(110\) 0.979977 + 1.22172i 0.0934371 + 0.116487i
\(111\) −10.8618 −1.03096
\(112\) −2.03777 + 6.27162i −0.192551 + 0.592612i
\(113\) −2.65827 + 1.93135i −0.250069 + 0.181686i −0.705757 0.708454i \(-0.749393\pi\)
0.455688 + 0.890139i \(0.349393\pi\)
\(114\) 1.05153 + 0.763978i 0.0984844 + 0.0715531i
\(115\) −0.482722 1.48566i −0.0450140 0.138539i
\(116\) −2.22664 6.85288i −0.206738 0.636274i
\(117\) 0.809017 + 0.587785i 0.0747936 + 0.0543408i
\(118\) −2.34392 + 1.70296i −0.215775 + 0.156770i
\(119\) −2.11319 + 6.50373i −0.193716 + 0.596196i
\(120\) −1.74686 −0.159465
\(121\) −2.38682 + 10.7379i −0.216984 + 0.976175i
\(122\) 0.934274 0.0845852
\(123\) −0.617246 + 1.89969i −0.0556552 + 0.171289i
\(124\) −1.41676 + 1.02934i −0.127229 + 0.0924374i
\(125\) −6.44938 4.68575i −0.576850 0.419106i
\(126\) −0.488959 1.50486i −0.0435599 0.134064i
\(127\) 4.62472 + 14.2334i 0.410378 + 1.26301i 0.916321 + 0.400445i \(0.131145\pi\)
−0.505943 + 0.862567i \(0.668855\pi\)
\(128\) 9.32963 + 6.77837i 0.824631 + 0.599129i
\(129\) 1.35181 0.982145i 0.119020 0.0864730i
\(130\) 0.145926 0.449113i 0.0127985 0.0393898i
\(131\) 4.75880 0.415779 0.207889 0.978152i \(-0.433341\pi\)
0.207889 + 0.978152i \(0.433341\pi\)
\(132\) −3.52624 4.39612i −0.306920 0.382633i
\(133\) −6.83723 −0.592863
\(134\) −1.24395 + 3.82848i −0.107461 + 0.330730i
\(135\) −0.696579 + 0.506094i −0.0599520 + 0.0435577i
\(136\) 3.89049 + 2.82661i 0.333607 + 0.242380i
\(137\) −6.48027 19.9442i −0.553647 1.70395i −0.699491 0.714641i \(-0.746590\pi\)
0.145844 0.989308i \(-0.453410\pi\)
\(138\) −0.307483 0.946334i −0.0261746 0.0805573i
\(139\) 9.87558 + 7.17503i 0.837636 + 0.608578i 0.921709 0.387882i \(-0.126793\pi\)
−0.0840734 + 0.996460i \(0.526793\pi\)
\(140\) 3.41483 2.48102i 0.288606 0.209685i
\(141\) −0.812859 + 2.50172i −0.0684551 + 0.210683i
\(142\) −2.32331 −0.194968
\(143\) 3.10182 1.17419i 0.259387 0.0981903i
\(144\) 2.28570 0.190475
\(145\) −1.12828 + 3.47249i −0.0936985 + 0.288374i
\(146\) 4.58876 3.33393i 0.379769 0.275918i
\(147\) 1.07076 + 0.777953i 0.0883148 + 0.0641645i
\(148\) −5.70335 17.5531i −0.468813 1.44286i
\(149\) −1.82404 5.61381i −0.149431 0.459901i 0.848123 0.529799i \(-0.177733\pi\)
−0.997554 + 0.0698979i \(0.977733\pi\)
\(150\) −1.88958 1.37286i −0.154284 0.112094i
\(151\) −2.71948 + 1.97582i −0.221308 + 0.160790i −0.692915 0.721019i \(-0.743674\pi\)
0.471607 + 0.881809i \(0.343674\pi\)
\(152\) −1.48577 + 4.57274i −0.120512 + 0.370898i
\(153\) 2.37030 0.191627
\(154\) −5.06273 1.38178i −0.407967 0.111347i
\(155\) 0.887375 0.0712757
\(156\) −0.525083 + 1.61604i −0.0420403 + 0.129387i
\(157\) 10.5387 7.65679i 0.841077 0.611078i −0.0815941 0.996666i \(-0.526001\pi\)
0.922671 + 0.385587i \(0.126001\pi\)
\(158\) 2.44546 + 1.77673i 0.194551 + 0.141349i
\(159\) 2.34937 + 7.23063i 0.186318 + 0.573426i
\(160\) −1.41316 4.34926i −0.111720 0.343839i
\(161\) 4.23461 + 3.07662i 0.333734 + 0.242472i
\(162\) −0.443705 + 0.322370i −0.0348607 + 0.0253278i
\(163\) 4.04880 12.4609i 0.317127 0.976015i −0.657744 0.753242i \(-0.728489\pi\)
0.974870 0.222773i \(-0.0715110\pi\)
\(164\) −3.39408 −0.265033
\(165\) 0.136215 + 2.85243i 0.0106043 + 0.222061i
\(166\) 0.778367 0.0604130
\(167\) 4.81141 14.8080i 0.372318 1.14588i −0.572953 0.819589i \(-0.694202\pi\)
0.945270 0.326288i \(-0.105798\pi\)
\(168\) 4.73539 3.44046i 0.365343 0.265438i
\(169\) −0.809017 0.587785i −0.0622321 0.0452143i
\(170\) −0.345887 1.06453i −0.0265283 0.0816457i
\(171\) 0.732333 + 2.25389i 0.0560029 + 0.172359i
\(172\) 2.29699 + 1.66886i 0.175144 + 0.127250i
\(173\) −1.23479 + 0.897126i −0.0938792 + 0.0682072i −0.633735 0.773550i \(-0.718479\pi\)
0.539855 + 0.841758i \(0.318479\pi\)
\(174\) −0.718688 + 2.21189i −0.0544836 + 0.167683i
\(175\) 12.2864 0.928766
\(176\) 4.15827 6.33857i 0.313442 0.477788i
\(177\) −5.28262 −0.397066
\(178\) 1.01954 3.13783i 0.0764180 0.235191i
\(179\) 13.6531 9.91956i 1.02048 0.741423i 0.0540993 0.998536i \(-0.482771\pi\)
0.966381 + 0.257113i \(0.0827712\pi\)
\(180\) −1.18363 0.859957i −0.0882225 0.0640974i
\(181\) −7.42763 22.8599i −0.552091 1.69916i −0.703504 0.710691i \(-0.748382\pi\)
0.151413 0.988471i \(-0.451618\pi\)
\(182\) 0.488959 + 1.50486i 0.0362441 + 0.111548i
\(183\) 1.37815 + 1.00128i 0.101876 + 0.0740169i
\(184\) 2.97786 2.16354i 0.219531 0.159498i
\(185\) −2.89000 + 8.89450i −0.212477 + 0.653937i
\(186\) 0.565237 0.0414452
\(187\) 4.31218 6.57316i 0.315337 0.480677i
\(188\) −4.46970 −0.325986
\(189\) 0.891530 2.74385i 0.0648493 0.199586i
\(190\) 0.905384 0.657800i 0.0656834 0.0477218i
\(191\) 14.4595 + 10.5054i 1.04625 + 0.760145i 0.971496 0.237057i \(-0.0761828\pi\)
0.0747541 + 0.997202i \(0.476183\pi\)
\(192\) 0.512491 + 1.57729i 0.0369859 + 0.113831i
\(193\) −4.95832 15.2601i −0.356908 1.09845i −0.954895 0.296943i \(-0.904033\pi\)
0.597988 0.801505i \(-0.295967\pi\)
\(194\) 1.50907 + 1.09641i 0.108345 + 0.0787174i
\(195\) 0.696579 0.506094i 0.0498831 0.0362422i
\(196\) −0.694964 + 2.13888i −0.0496403 + 0.152777i
\(197\) −20.1579 −1.43619 −0.718097 0.695943i \(-0.754986\pi\)
−0.718097 + 0.695943i \(0.754986\pi\)
\(198\) 0.0867657 + 1.81693i 0.00616617 + 0.129124i
\(199\) 14.9087 1.05685 0.528423 0.848981i \(-0.322783\pi\)
0.528423 + 0.848981i \(0.322783\pi\)
\(200\) 2.66992 8.21717i 0.188792 0.581042i
\(201\) −5.93802 + 4.31422i −0.418835 + 0.304302i
\(202\) 5.33675 + 3.87738i 0.375492 + 0.272811i
\(203\) −3.78057 11.6354i −0.265344 0.816646i
\(204\) 1.24460 + 3.83049i 0.0871395 + 0.268188i
\(205\) 1.39138 + 1.01090i 0.0971784 + 0.0706042i
\(206\) −4.09037 + 2.97183i −0.284990 + 0.207057i
\(207\) 0.560640 1.72547i 0.0389672 0.119929i
\(208\) −2.28570 −0.158485
\(209\) 7.58265 + 2.06954i 0.524503 + 0.143153i
\(210\) −1.36239 −0.0940141
\(211\) −1.97745 + 6.08595i −0.136133 + 0.418974i −0.995765 0.0919403i \(-0.970693\pi\)
0.859632 + 0.510914i \(0.170693\pi\)
\(212\) −10.4514 + 7.59336i −0.717803 + 0.521514i
\(213\) −3.42712 2.48995i −0.234822 0.170608i
\(214\) 2.52959 + 7.78529i 0.172919 + 0.532191i
\(215\) −0.444582 1.36828i −0.0303202 0.0933161i
\(216\) −1.64135 1.19251i −0.111680 0.0811402i
\(217\) −2.40550 + 1.74770i −0.163296 + 0.118642i
\(218\) −1.40198 + 4.31487i −0.0949544 + 0.292240i
\(219\) 10.3419 0.698843
\(220\) −4.53811 + 1.71789i −0.305959 + 0.115820i
\(221\) −2.37030 −0.159443
\(222\) −1.84086 + 5.66559i −0.123551 + 0.380249i
\(223\) 21.0317 15.2804i 1.40839 1.02325i 0.414831 0.909898i \(-0.363841\pi\)
0.993555 0.113354i \(-0.0361595\pi\)
\(224\) 12.3967 + 9.00676i 0.828292 + 0.601789i
\(225\) −1.31599 4.05021i −0.0877329 0.270014i
\(226\) 0.556878 + 1.71389i 0.0370430 + 0.114006i
\(227\) 21.6386 + 15.7213i 1.43620 + 1.04346i 0.988819 + 0.149119i \(0.0476437\pi\)
0.447383 + 0.894343i \(0.352356\pi\)
\(228\) −3.25784 + 2.36696i −0.215755 + 0.156755i
\(229\) −0.755999 + 2.32673i −0.0499578 + 0.153754i −0.972923 0.231129i \(-0.925758\pi\)
0.922965 + 0.384883i \(0.125758\pi\)
\(230\) −0.856743 −0.0564920
\(231\) −5.98716 7.46410i −0.393926 0.491102i
\(232\) −8.60332 −0.564836
\(233\) 5.71402 17.5859i 0.374338 1.15209i −0.569586 0.821932i \(-0.692897\pi\)
0.943924 0.330162i \(-0.107103\pi\)
\(234\) 0.443705 0.322370i 0.0290059 0.0210740i
\(235\) 1.83233 + 1.33126i 0.119528 + 0.0868421i
\(236\) −2.77381 8.53692i −0.180560 0.555706i
\(237\) 1.70314 + 5.24171i 0.110631 + 0.340486i
\(238\) 3.03424 + 2.20451i 0.196681 + 0.142897i
\(239\) −16.9174 + 12.2912i −1.09429 + 0.795051i −0.980119 0.198410i \(-0.936422\pi\)
−0.114175 + 0.993461i \(0.536422\pi\)
\(240\) 0.608155 1.87171i 0.0392562 0.120818i
\(241\) 23.3711 1.50546 0.752731 0.658328i \(-0.228736\pi\)
0.752731 + 0.658328i \(0.228736\pi\)
\(242\) 5.19645 + 3.06485i 0.334040 + 0.197016i
\(243\) −1.00000 −0.0641500
\(244\) −0.894470 + 2.75289i −0.0572626 + 0.176236i
\(245\) 0.921945 0.669832i 0.0589009 0.0427940i
\(246\) 0.886278 + 0.643919i 0.0565070 + 0.0410548i
\(247\) −0.732333 2.25389i −0.0465972 0.143411i
\(248\) 0.646132 + 1.98859i 0.0410294 + 0.126276i
\(249\) 1.14817 + 0.834193i 0.0727622 + 0.0528649i
\(250\) −3.53716 + 2.56989i −0.223709 + 0.162534i
\(251\) −8.11719 + 24.9821i −0.512353 + 1.57686i 0.275695 + 0.961245i \(0.411092\pi\)
−0.788048 + 0.615614i \(0.788908\pi\)
\(252\) 4.90229 0.308815
\(253\) −3.76503 4.69381i −0.236705 0.295097i
\(254\) 8.20804 0.515018
\(255\) 0.630663 1.94098i 0.0394937 0.121549i
\(256\) 2.43339 1.76796i 0.152087 0.110497i
\(257\) −6.89518 5.00964i −0.430109 0.312493i 0.351583 0.936157i \(-0.385643\pi\)
−0.781693 + 0.623664i \(0.785643\pi\)
\(258\) −0.283188 0.871564i −0.0176305 0.0542612i
\(259\) −9.68364 29.8032i −0.601712 1.85188i
\(260\) 1.18363 + 0.859957i 0.0734056 + 0.0533323i
\(261\) −3.43067 + 2.49253i −0.212353 + 0.154284i
\(262\) 0.806522 2.48222i 0.0498271 0.153352i
\(263\) 25.4425 1.56885 0.784427 0.620221i \(-0.212957\pi\)
0.784427 + 0.620221i \(0.212957\pi\)
\(264\) −6.29305 + 2.38222i −0.387310 + 0.146615i
\(265\) 6.54610 0.402124
\(266\) −1.15877 + 3.56634i −0.0710490 + 0.218666i
\(267\) 4.86682 3.53595i 0.297844 0.216397i
\(268\) −10.0899 7.33074i −0.616339 0.447796i
\(269\) 6.08164 + 18.7173i 0.370804 + 1.14122i 0.946266 + 0.323389i \(0.104822\pi\)
−0.575462 + 0.817828i \(0.695178\pi\)
\(270\) 0.145926 + 0.449113i 0.00888075 + 0.0273321i
\(271\) 8.61902 + 6.26208i 0.523568 + 0.380395i 0.817946 0.575294i \(-0.195113\pi\)
−0.294378 + 0.955689i \(0.595113\pi\)
\(272\) −4.38308 + 3.18450i −0.265763 + 0.193088i
\(273\) −0.891530 + 2.74385i −0.0539579 + 0.166065i
\(274\) −11.5013 −0.694819
\(275\) −13.6259 3.71894i −0.821675 0.224260i
\(276\) 3.08281 0.185564
\(277\) 3.32125 10.2217i 0.199554 0.614165i −0.800339 0.599548i \(-0.795347\pi\)
0.999893 0.0146171i \(-0.00465292\pi\)
\(278\) 5.41625 3.93514i 0.324845 0.236014i
\(279\) 0.833781 + 0.605777i 0.0499172 + 0.0362669i
\(280\) −1.55738 4.79311i −0.0930710 0.286443i
\(281\) 1.19919 + 3.69072i 0.0715376 + 0.220170i 0.980433 0.196855i \(-0.0630728\pi\)
−0.908895 + 0.417025i \(0.863073\pi\)
\(282\) 1.16715 + 0.847984i 0.0695028 + 0.0504967i
\(283\) 18.3333 13.3199i 1.08980 0.791786i 0.110434 0.993883i \(-0.464776\pi\)
0.979365 + 0.202098i \(0.0647758\pi\)
\(284\) 2.22433 6.84579i 0.131990 0.406223i
\(285\) 2.04051 0.120869
\(286\) −0.0867657 1.81693i −0.00513056 0.107437i
\(287\) −5.76275 −0.340165
\(288\) 1.64126 5.05129i 0.0967124 0.297650i
\(289\) 9.20799 6.68999i 0.541646 0.393529i
\(290\) 1.62005 + 1.17703i 0.0951326 + 0.0691179i
\(291\) 1.05099 + 3.23462i 0.0616102 + 0.189617i
\(292\) 5.43037 + 16.7130i 0.317788 + 0.978052i
\(293\) −21.0141 15.2676i −1.22766 0.891944i −0.230943 0.972967i \(-0.574181\pi\)
−0.996712 + 0.0810236i \(0.974181\pi\)
\(294\) 0.587257 0.426668i 0.0342495 0.0248838i
\(295\) −1.40554 + 4.32582i −0.0818339 + 0.251859i
\(296\) −22.0367 −1.28086
\(297\) −1.81926 + 2.77314i −0.105564 + 0.160914i
\(298\) −3.23733 −0.187534
\(299\) −0.560640 + 1.72547i −0.0324227 + 0.0997867i
\(300\) 5.85430 4.25339i 0.337998 0.245570i
\(301\) 3.90003 + 2.83354i 0.224794 + 0.163323i
\(302\) 0.569702 + 1.75336i 0.0327826 + 0.100895i
\(303\) 3.71677 + 11.4390i 0.213523 + 0.657155i
\(304\) −4.38231 3.18393i −0.251343 0.182611i
\(305\) 1.18661 0.862123i 0.0679451 0.0493650i
\(306\) 0.401718 1.23636i 0.0229647 0.0706780i
\(307\) 23.7938 1.35798 0.678991 0.734146i \(-0.262417\pi\)
0.678991 + 0.734146i \(0.262417\pi\)
\(308\) 8.91853 13.5947i 0.508180 0.774633i
\(309\) −9.21869 −0.524433
\(310\) 0.150392 0.462860i 0.00854171 0.0262887i
\(311\) 0.260256 0.189087i 0.0147578 0.0107221i −0.580382 0.814344i \(-0.697097\pi\)
0.595140 + 0.803622i \(0.297097\pi\)
\(312\) 1.64135 + 1.19251i 0.0929233 + 0.0675128i
\(313\) −9.45290 29.0930i −0.534309 1.64444i −0.745136 0.666912i \(-0.767616\pi\)
0.210827 0.977523i \(-0.432384\pi\)
\(314\) −2.20773 6.79471i −0.124590 0.383447i
\(315\) −2.00967 1.46011i −0.113232 0.0822678i
\(316\) −7.57653 + 5.50467i −0.426213 + 0.309662i
\(317\) −7.91864 + 24.3711i −0.444755 + 1.36882i 0.437996 + 0.898977i \(0.355688\pi\)
−0.882752 + 0.469840i \(0.844312\pi\)
\(318\) 4.16971 0.233826
\(319\) 0.670862 + 14.0483i 0.0375611 + 0.786553i
\(320\) 1.42796 0.0798256
\(321\) −4.61227 + 14.1951i −0.257432 + 0.792293i
\(322\) 2.32247 1.68737i 0.129426 0.0940335i
\(323\) −4.54450 3.30177i −0.252863 0.183716i
\(324\) −0.525083 1.61604i −0.0291713 0.0897799i
\(325\) 1.31599 + 4.05021i 0.0729982 + 0.224665i
\(326\) −5.81350 4.22376i −0.321980 0.233932i
\(327\) −6.69241 + 4.86232i −0.370091 + 0.268887i
\(328\) −1.25228 + 3.85414i −0.0691459 + 0.212809i
\(329\) −7.58904 −0.418397
\(330\) 1.51093 + 0.412379i 0.0831739 + 0.0227007i
\(331\) 6.92200 0.380467 0.190234 0.981739i \(-0.439075\pi\)
0.190234 + 0.981739i \(0.439075\pi\)
\(332\) −0.745205 + 2.29351i −0.0408984 + 0.125872i
\(333\) −8.78740 + 6.38442i −0.481546 + 0.349864i
\(334\) −6.90850 5.01932i −0.378016 0.274645i
\(335\) 1.95290 + 6.01039i 0.106698 + 0.328383i
\(336\) 2.03777 + 6.27162i 0.111170 + 0.342145i
\(337\) −24.0335 17.4613i −1.30919 0.951180i −1.00000 0.000178979i \(-0.999943\pi\)
−0.309187 0.951001i \(-0.600057\pi\)
\(338\) −0.443705 + 0.322370i −0.0241343 + 0.0175346i
\(339\) −1.01537 + 3.12498i −0.0551472 + 0.169726i
\(340\) 3.46785 0.188071
\(341\) 3.19677 1.21013i 0.173115 0.0655321i
\(342\) 1.29976 0.0702828
\(343\) 5.06074 15.5754i 0.273254 0.840991i
\(344\) 2.74258 1.99260i 0.147870 0.107434i
\(345\) −1.26378 0.918191i −0.0680397 0.0494338i
\(346\) 0.258674 + 0.796118i 0.0139064 + 0.0427996i
\(347\) −7.00782 21.5679i −0.376200 1.15782i −0.942666 0.333739i \(-0.891690\pi\)
0.566466 0.824085i \(-0.308310\pi\)
\(348\) −5.82941 4.23531i −0.312489 0.227037i
\(349\) 3.69218 2.68253i 0.197638 0.143592i −0.484565 0.874755i \(-0.661022\pi\)
0.682203 + 0.731163i \(0.261022\pi\)
\(350\) 2.08230 6.40867i 0.111304 0.342558i
\(351\) 1.00000 0.0533761
\(352\) −11.0221 13.7410i −0.587477 0.732400i
\(353\) 9.80944 0.522104 0.261052 0.965325i \(-0.415931\pi\)
0.261052 + 0.965325i \(0.415931\pi\)
\(354\) −0.895298 + 2.75545i −0.0475846 + 0.146450i
\(355\) −2.95082 + 2.14389i −0.156613 + 0.113786i
\(356\) 8.26971 + 6.00830i 0.438294 + 0.318439i
\(357\) 2.11319 + 6.50373i 0.111842 + 0.344214i
\(358\) −2.86017 8.80271i −0.151165 0.465238i
\(359\) −0.0584317 0.0424531i −0.00308391 0.00224059i 0.586242 0.810136i \(-0.300607\pi\)
−0.589326 + 0.807895i \(0.700607\pi\)
\(360\) −1.41324 + 1.02678i −0.0744841 + 0.0541159i
\(361\) −4.13578 + 12.7286i −0.217673 + 0.669928i
\(362\) −13.1827 −0.692867
\(363\) 4.38061 + 10.0901i 0.229923 + 0.529593i
\(364\) −4.90229 −0.256950
\(365\) 2.75167 8.46878i 0.144029 0.443276i
\(366\) 0.755843 0.549152i 0.0395086 0.0287047i
\(367\) 11.8065 + 8.57791i 0.616293 + 0.447763i 0.851625 0.524152i \(-0.175618\pi\)
−0.235331 + 0.971915i \(0.575618\pi\)
\(368\) 1.28146 + 3.94391i 0.0668005 + 0.205591i
\(369\) 0.617246 + 1.89969i 0.0321326 + 0.0988939i
\(370\) 4.14963 + 3.01488i 0.215729 + 0.156736i
\(371\) −17.7452 + 12.8927i −0.921286 + 0.669353i
\(372\) −0.541156 + 1.66551i −0.0280576 + 0.0863525i
\(373\) −12.0924 −0.626122 −0.313061 0.949733i \(-0.601354\pi\)
−0.313061 + 0.949733i \(0.601354\pi\)
\(374\) −2.69777 3.36328i −0.139499 0.173911i
\(375\) −7.97187 −0.411666
\(376\) −1.64915 + 5.07556i −0.0850483 + 0.261752i
\(377\) 3.43067 2.49253i 0.176689 0.128372i
\(378\) −1.28011 0.930055i −0.0658418 0.0478369i
\(379\) 6.13245 + 18.8737i 0.315003 + 0.969479i 0.975753 + 0.218873i \(0.0702381\pi\)
−0.660751 + 0.750606i \(0.729762\pi\)
\(380\) 1.07144 + 3.29754i 0.0549635 + 0.169160i
\(381\) 12.1077 + 8.79674i 0.620295 + 0.450671i
\(382\) 7.93028 5.76168i 0.405748 0.294793i
\(383\) −11.6345 + 35.8072i −0.594493 + 1.82966i −0.0372574 + 0.999306i \(0.511862\pi\)
−0.557235 + 0.830355i \(0.688138\pi\)
\(384\) 11.5321 0.588493
\(385\) −7.70519 + 2.91678i −0.392693 + 0.148653i
\(386\) −8.80012 −0.447914
\(387\) 0.516344 1.58914i 0.0262472 0.0807807i
\(388\) −4.67541 + 3.39689i −0.237358 + 0.172451i
\(389\) 26.5462 + 19.2869i 1.34595 + 0.977887i 0.999203 + 0.0399270i \(0.0127125\pi\)
0.346743 + 0.937960i \(0.387287\pi\)
\(390\) −0.145926 0.449113i −0.00738923 0.0227417i
\(391\) 1.32888 + 4.08988i 0.0672045 + 0.206834i
\(392\) 2.17238 + 1.57833i 0.109722 + 0.0797177i
\(393\) 3.84995 2.79715i 0.194204 0.141098i
\(394\) −3.41637 + 10.5145i −0.172114 + 0.529713i
\(395\) 4.74548 0.238771
\(396\) −5.43676 1.48386i −0.273208 0.0745668i
\(397\) −6.97595 −0.350113 −0.175057 0.984558i \(-0.556011\pi\)
−0.175057 + 0.984558i \(0.556011\pi\)
\(398\) 2.52672 7.77644i 0.126653 0.389798i
\(399\) −5.53143 + 4.01882i −0.276918 + 0.201193i
\(400\) 7.87496 + 5.72150i 0.393748 + 0.286075i
\(401\) −5.88124 18.1006i −0.293695 0.903900i −0.983657 0.180054i \(-0.942373\pi\)
0.689962 0.723846i \(-0.257627\pi\)
\(402\) 1.24395 + 3.82848i 0.0620425 + 0.190947i
\(403\) −0.833781 0.605777i −0.0415336 0.0301759i
\(404\) −16.5343 + 12.0129i −0.822613 + 0.597663i
\(405\) −0.266070 + 0.818878i −0.0132211 + 0.0406904i
\(406\) −6.70983 −0.333003
\(407\) 1.71836 + 35.9836i 0.0851760 + 1.78364i
\(408\) 4.80891 0.238077
\(409\) −5.94251 + 18.2892i −0.293838 + 0.904341i 0.689771 + 0.724028i \(0.257711\pi\)
−0.983609 + 0.180314i \(0.942289\pi\)
\(410\) 0.763102 0.554426i 0.0376869 0.0273812i
\(411\) −16.9656 12.3262i −0.836849 0.608007i
\(412\) −4.84057 14.8978i −0.238478 0.733960i
\(413\) −4.70962 14.4947i −0.231745 0.713238i
\(414\) −0.805000 0.584866i −0.0395636 0.0287446i
\(415\) 0.988595 0.718256i 0.0485282 0.0352578i
\(416\) −1.64126 + 5.05129i −0.0804696 + 0.247660i
\(417\) 12.2069 0.597774
\(418\) 2.36459 3.60441i 0.115656 0.176297i
\(419\) −7.92185 −0.387008 −0.193504 0.981100i \(-0.561985\pi\)
−0.193504 + 0.981100i \(0.561985\pi\)
\(420\) 1.30435 4.01438i 0.0636458 0.195882i
\(421\) −11.2643 + 8.18398i −0.548987 + 0.398863i −0.827412 0.561595i \(-0.810188\pi\)
0.278425 + 0.960458i \(0.410188\pi\)
\(422\) 2.83933 + 2.06289i 0.138216 + 0.100420i
\(423\) 0.812859 + 2.50172i 0.0395226 + 0.121638i
\(424\) 4.76647 + 14.6697i 0.231480 + 0.712423i
\(425\) 8.16642 + 5.93325i 0.396130 + 0.287805i
\(426\) −1.87960 + 1.36561i −0.0910669 + 0.0661640i
\(427\) −1.51871 + 4.67410i −0.0734954 + 0.226196i
\(428\) −25.3617 −1.22590
\(429\) 1.81926 2.77314i 0.0878345 0.133888i
\(430\) −0.789052 −0.0380515
\(431\) −4.12564 + 12.6974i −0.198725 + 0.611613i 0.801188 + 0.598413i \(0.204202\pi\)
−0.999913 + 0.0131998i \(0.995798\pi\)
\(432\) 1.84917 1.34350i 0.0889683 0.0646392i
\(433\) −21.4217 15.5638i −1.02946 0.747949i −0.0612619 0.998122i \(-0.519512\pi\)
−0.968201 + 0.250173i \(0.919512\pi\)
\(434\) 0.503926 + 1.55093i 0.0241892 + 0.0744468i
\(435\) 1.12828 + 3.47249i 0.0540969 + 0.166493i
\(436\) −11.3718 8.26207i −0.544609 0.395681i
\(437\) −3.47845 + 2.52724i −0.166397 + 0.120894i
\(438\) 1.75275 5.39441i 0.0837497 0.257755i
\(439\) 33.1329 1.58134 0.790672 0.612240i \(-0.209731\pi\)
0.790672 + 0.612240i \(0.209731\pi\)
\(440\) 0.276356 + 5.78707i 0.0131748 + 0.275888i
\(441\) 1.32353 0.0630254
\(442\) −0.401718 + 1.23636i −0.0191078 + 0.0588077i
\(443\) −2.21514 + 1.60939i −0.105244 + 0.0764646i −0.639163 0.769071i \(-0.720719\pi\)
0.533918 + 0.845536i \(0.320719\pi\)
\(444\) −14.9316 10.8484i −0.708621 0.514843i
\(445\) −1.60060 4.92614i −0.0758756 0.233521i
\(446\) −4.40591 13.5600i −0.208626 0.642084i
\(447\) −4.77539 3.46952i −0.225868 0.164103i
\(448\) −3.87093 + 2.81240i −0.182884 + 0.132873i
\(449\) 8.30204 25.5510i 0.391797 1.20583i −0.539630 0.841902i \(-0.681436\pi\)
0.931428 0.363926i \(-0.118564\pi\)
\(450\) −2.33565 −0.110104
\(451\) 6.39103 + 1.74431i 0.300942 + 0.0821364i
\(452\) −5.58324 −0.262614
\(453\) −1.03875 + 3.19694i −0.0488047 + 0.150206i
\(454\) 11.8676 8.62235i 0.556976 0.404667i
\(455\) 2.00967 + 1.46011i 0.0942147 + 0.0684510i
\(456\) 1.48577 + 4.57274i 0.0695778 + 0.214138i
\(457\) 1.49423 + 4.59878i 0.0698973 + 0.215122i 0.979903 0.199474i \(-0.0639232\pi\)
−0.910006 + 0.414595i \(0.863923\pi\)
\(458\) 1.08551 + 0.788668i 0.0507224 + 0.0368520i
\(459\) 1.91761 1.39323i 0.0895064 0.0650302i
\(460\) 0.820243 2.52445i 0.0382440 0.117703i
\(461\) −2.49419 −0.116166 −0.0580829 0.998312i \(-0.518499\pi\)
−0.0580829 + 0.998312i \(0.518499\pi\)
\(462\) −4.90802 + 1.85792i −0.228342 + 0.0864382i
\(463\) 38.3608 1.78278 0.891389 0.453239i \(-0.149731\pi\)
0.891389 + 0.453239i \(0.149731\pi\)
\(464\) 2.99518 9.21822i 0.139048 0.427945i
\(465\) 0.717901 0.521586i 0.0332919 0.0241880i
\(466\) −8.20452 5.96094i −0.380067 0.276135i
\(467\) 0.510228 + 1.57032i 0.0236105 + 0.0726658i 0.962168 0.272459i \(-0.0878368\pi\)
−0.938557 + 0.345124i \(0.887837\pi\)
\(468\) 0.525083 + 1.61604i 0.0242720 + 0.0747014i
\(469\) −17.1315 12.4468i −0.791059 0.574738i
\(470\) 1.00494 0.730131i 0.0463544 0.0336784i
\(471\) 4.02541 12.3889i 0.185481 0.570853i
\(472\) −10.7175 −0.493313
\(473\) −3.46756 4.32295i −0.159438 0.198770i
\(474\) 3.02276 0.138840
\(475\) −3.11875 + 9.59851i −0.143098 + 0.440410i
\(476\) −9.40069 + 6.83000i −0.430880 + 0.313052i
\(477\) 6.15074 + 4.46878i 0.281623 + 0.204611i
\(478\) 3.54400 + 10.9073i 0.162099 + 0.498889i
\(479\) −5.30948 16.3409i −0.242596 0.746635i −0.996022 0.0891023i \(-0.971600\pi\)
0.753426 0.657533i \(-0.228400\pi\)
\(480\) −3.69970 2.68799i −0.168867 0.122689i
\(481\) 8.78740 6.38442i 0.400671 0.291104i
\(482\) 3.96093 12.1905i 0.180415 0.555261i
\(483\) 5.23426 0.238167
\(484\) −14.0058 + 12.3774i −0.636628 + 0.562608i
\(485\) 2.92839 0.132972
\(486\) −0.169480 + 0.521606i −0.00768777 + 0.0236605i
\(487\) −18.3025 + 13.2975i −0.829365 + 0.602569i −0.919380 0.393371i \(-0.871309\pi\)
0.0900145 + 0.995940i \(0.471309\pi\)
\(488\) 2.79602 + 2.03143i 0.126570 + 0.0919583i
\(489\) −4.04880 12.4609i −0.183093 0.563503i
\(490\) −0.193137 0.594415i −0.00872505 0.0268529i
\(491\) −14.0339 10.1962i −0.633340 0.460148i 0.224216 0.974540i \(-0.428018\pi\)
−0.857556 + 0.514391i \(0.828018\pi\)
\(492\) −2.74587 + 1.99499i −0.123793 + 0.0899410i
\(493\) 3.10604 9.55940i 0.139889 0.430534i
\(494\) −1.29976 −0.0584788
\(495\) 1.78681 + 2.22760i 0.0803113 + 0.100123i
\(496\) −2.35567 −0.105773
\(497\) 3.77666 11.6234i 0.169406 0.521379i
\(498\) 0.629712 0.457513i 0.0282181 0.0205016i
\(499\) −18.2528 13.2614i −0.817107 0.593663i 0.0987757 0.995110i \(-0.468507\pi\)
−0.915882 + 0.401447i \(0.868507\pi\)
\(500\) −4.18589 12.8829i −0.187199 0.576139i
\(501\) −4.81141 14.8080i −0.214958 0.661572i
\(502\) 11.6551 + 8.46795i 0.520194 + 0.377943i
\(503\) −0.311011 + 0.225963i −0.0138673 + 0.0100752i −0.594697 0.803950i \(-0.702728\pi\)
0.580830 + 0.814025i \(0.302728\pi\)
\(504\) 1.80876 5.56679i 0.0805685 0.247964i
\(505\) 10.3561 0.460840
\(506\) −3.08642 + 1.16836i −0.137208 + 0.0519397i
\(507\) −1.00000 −0.0444116
\(508\) −7.85834 + 24.1855i −0.348658 + 1.07306i
\(509\) 21.1729 15.3830i 0.938472 0.681840i −0.00958015 0.999954i \(-0.503050\pi\)
0.948052 + 0.318114i \(0.103050\pi\)
\(510\) −0.905543 0.657916i −0.0400981 0.0291330i
\(511\) 9.22015 + 28.3767i 0.407875 + 1.25531i
\(512\) 6.61744 + 20.3664i 0.292452 + 0.900075i
\(513\) 1.91727 + 1.39298i 0.0846496 + 0.0615015i
\(514\) −3.78165 + 2.74753i −0.166802 + 0.121188i
\(515\) −2.45281 + 7.54898i −0.108084 + 0.332648i
\(516\) 2.83924 0.124991
\(517\) 8.41643 + 2.29710i 0.370154 + 0.101026i
\(518\) −17.1867 −0.755140
\(519\) −0.471647 + 1.45158i −0.0207030 + 0.0637173i
\(520\) 1.41324 1.02678i 0.0619745 0.0450271i
\(521\) 19.8204 + 14.4004i 0.868347 + 0.630891i 0.930143 0.367198i \(-0.119683\pi\)
−0.0617957 + 0.998089i \(0.519683\pi\)
\(522\) 0.718688 + 2.21189i 0.0314561 + 0.0968119i
\(523\) −3.25528 10.0187i −0.142343 0.438088i 0.854316 0.519753i \(-0.173976\pi\)
−0.996660 + 0.0816653i \(0.973976\pi\)
\(524\) 6.54185 + 4.75294i 0.285782 + 0.207633i
\(525\) 9.93992 7.22178i 0.433814 0.315184i
\(526\) 4.31200 13.2710i 0.188012 0.578642i
\(527\) −2.44285 −0.106412
\(528\) −0.361602 7.57218i −0.0157367 0.329537i
\(529\) −19.7084 −0.856888
\(530\) 1.10943 3.41449i 0.0481907 0.148316i
\(531\) −4.27373 + 3.10505i −0.185464 + 0.134747i
\(532\) −9.39903 6.82879i −0.407500 0.296066i
\(533\) −0.617246 1.89969i −0.0267359 0.0822847i
\(534\) −1.01954 3.13783i −0.0441200 0.135787i
\(535\) 10.3969 + 7.55377i 0.449496 + 0.326578i
\(536\) −12.0472 + 8.75280i −0.520360 + 0.378063i
\(537\) 5.21502 16.0502i 0.225045 0.692617i
\(538\) 10.7938 0.465354
\(539\) 2.40784 3.67034i 0.103713 0.158093i
\(540\) −1.46305 −0.0629595
\(541\) −9.94607 + 30.6108i −0.427615 + 1.31606i 0.472853 + 0.881141i \(0.343224\pi\)
−0.900468 + 0.434922i \(0.856776\pi\)
\(542\) 4.72709 3.43443i 0.203046 0.147522i
\(543\) −19.4458 14.1282i −0.834498 0.606298i
\(544\) 3.89028 + 11.9730i 0.166794 + 0.513340i
\(545\) 2.20100 + 6.77398i 0.0942804 + 0.290165i
\(546\) 1.28011 + 0.930055i 0.0547837 + 0.0398027i
\(547\) 2.19772 1.59674i 0.0939679 0.0682716i −0.539809 0.841787i \(-0.681504\pi\)
0.633777 + 0.773516i \(0.281504\pi\)
\(548\) 11.0113 33.8893i 0.470379 1.44768i
\(549\) 1.70348 0.0727029
\(550\) −4.24915 + 6.47709i −0.181184 + 0.276184i
\(551\) 10.0496 0.428126
\(552\) 1.13744 3.50068i 0.0484127 0.148999i
\(553\) −12.8641 + 9.34630i −0.547036 + 0.397445i
\(554\) −4.76884 3.46476i −0.202608 0.147204i
\(555\) 2.89000 + 8.89450i 0.122674 + 0.377551i
\(556\) 6.40963 + 19.7268i 0.271829 + 0.836603i
\(557\) 21.0858 + 15.3197i 0.893433 + 0.649117i 0.936771 0.349943i \(-0.113799\pi\)
−0.0433378 + 0.999060i \(0.513799\pi\)
\(558\) 0.457286 0.332238i 0.0193585 0.0140648i
\(559\) −0.516344 + 1.58914i −0.0218390 + 0.0672136i
\(560\) 5.67788 0.239934
\(561\) −0.374985 7.85243i −0.0158319 0.331530i
\(562\) 2.12834 0.0897787
\(563\) 6.27595 19.3154i 0.264500 0.814047i −0.727308 0.686311i \(-0.759229\pi\)
0.991808 0.127736i \(-0.0407710\pi\)
\(564\) −3.61606 + 2.62722i −0.152264 + 0.110626i
\(565\) 2.28882 + 1.66292i 0.0962914 + 0.0699598i
\(566\) −3.84062 11.8202i −0.161433 0.496840i
\(567\) −0.891530 2.74385i −0.0374408 0.115231i
\(568\) −6.95302 5.05167i −0.291742 0.211963i
\(569\) 8.31780 6.04324i 0.348700 0.253346i −0.399623 0.916679i \(-0.630859\pi\)
0.748324 + 0.663334i \(0.230859\pi\)
\(570\) 0.345826 1.06434i 0.0144850 0.0445804i
\(571\) −7.56987 −0.316789 −0.158395 0.987376i \(-0.550632\pi\)
−0.158395 + 0.987376i \(0.550632\pi\)
\(572\) 5.43676 + 1.48386i 0.227322 + 0.0620433i
\(573\) 17.8729 0.746650
\(574\) −0.976672 + 3.00589i −0.0407655 + 0.125463i
\(575\) 6.25073 4.54142i 0.260674 0.189390i
\(576\) 1.34172 + 0.974817i 0.0559050 + 0.0406174i
\(577\) 2.68657 + 8.26841i 0.111843 + 0.344218i 0.991276 0.131806i \(-0.0420775\pi\)
−0.879432 + 0.476024i \(0.842078\pi\)
\(578\) −1.92897 5.93676i −0.0802346 0.246937i
\(579\) −12.9810 9.43128i −0.539474 0.391951i
\(580\) −5.01923 + 3.64669i −0.208412 + 0.151420i
\(581\) −1.26527 + 3.89411i −0.0524924 + 0.161555i
\(582\) 1.86532 0.0773199
\(583\) 23.5823 8.92702i 0.976680 0.369720i
\(584\) 20.9820 0.868240
\(585\) 0.266070 0.818878i 0.0110006 0.0338564i
\(586\) −11.5251 + 8.37351i −0.476099 + 0.345906i
\(587\) 13.4552 + 9.77576i 0.555355 + 0.403489i 0.829756 0.558126i \(-0.188480\pi\)
−0.274401 + 0.961615i \(0.588480\pi\)
\(588\) 0.694964 + 2.13888i 0.0286598 + 0.0882059i
\(589\) −0.754749 2.32288i −0.0310989 0.0957126i
\(590\) 2.01816 + 1.46628i 0.0830864 + 0.0603658i
\(591\) −16.3081 + 11.8485i −0.670826 + 0.487384i
\(592\) 7.67192 23.6118i 0.315314 0.970437i
\(593\) 13.8633 0.569297 0.284649 0.958632i \(-0.408123\pi\)
0.284649 + 0.958632i \(0.408123\pi\)
\(594\) 1.13816 + 1.41893i 0.0466992 + 0.0582193i
\(595\) 5.88802 0.241385
\(596\) 3.09941 9.53900i 0.126957 0.390733i
\(597\) 12.0614 8.76309i 0.493638 0.358649i
\(598\) 0.805000 + 0.584866i 0.0329189 + 0.0239170i
\(599\) −12.8816 39.6455i −0.526329 1.61987i −0.761674 0.647961i \(-0.775622\pi\)
0.235345 0.971912i \(-0.424378\pi\)
\(600\) −2.66992 8.21717i −0.108999 0.335465i
\(601\) −15.3781 11.1729i −0.627287 0.455751i 0.228172 0.973621i \(-0.426725\pi\)
−0.855459 + 0.517870i \(0.826725\pi\)
\(602\) 2.13897 1.55405i 0.0871779 0.0633384i
\(603\) −2.26812 + 6.98056i −0.0923650 + 0.284270i
\(604\) −5.71182 −0.232410
\(605\) 9.42811 0.902519i 0.383307 0.0366926i
\(606\) 6.59659 0.267968
\(607\) −13.3917 + 41.2154i −0.543552 + 1.67288i 0.180855 + 0.983510i \(0.442113\pi\)
−0.724408 + 0.689372i \(0.757887\pi\)
\(608\) −10.1831 + 7.39845i −0.412979 + 0.300047i
\(609\) −9.89767 7.19108i −0.401074 0.291397i
\(610\) −0.248582 0.765056i −0.0100648 0.0309762i
\(611\) −0.812859 2.50172i −0.0328848 0.101209i
\(612\) 3.25841 + 2.36737i 0.131713 + 0.0956954i
\(613\) 5.58239 4.05584i 0.225471 0.163814i −0.469315 0.883031i \(-0.655499\pi\)
0.694786 + 0.719217i \(0.255499\pi\)
\(614\) 4.03257 12.4110i 0.162741 0.500866i
\(615\) 1.71984 0.0693508
\(616\) −12.1469 15.1434i −0.489412 0.610143i
\(617\) −26.7547 −1.07710 −0.538552 0.842592i \(-0.681029\pi\)
−0.538552 + 0.842592i \(0.681029\pi\)
\(618\) −1.56238 + 4.80852i −0.0628483 + 0.193427i
\(619\) 6.30059 4.57765i 0.253242 0.183991i −0.453920 0.891042i \(-0.649975\pi\)
0.707162 + 0.707051i \(0.249975\pi\)
\(620\) 1.21986 + 0.886281i 0.0489908 + 0.0355939i
\(621\) −0.560640 1.72547i −0.0224977 0.0692408i
\(622\) −0.0545207 0.167797i −0.00218608 0.00672806i
\(623\) 14.0410 + 10.2014i 0.562542 + 0.408710i
\(624\) −1.84917 + 1.34350i −0.0740261 + 0.0537831i
\(625\) 4.45890 13.7231i 0.178356 0.548923i
\(626\) −16.7772 −0.670551
\(627\) 7.35094 2.78268i 0.293568 0.111129i
\(628\) 22.1347 0.883270
\(629\) 7.95587 24.4856i 0.317221 0.976306i
\(630\) −1.10220 + 0.800795i −0.0439127 + 0.0319044i
\(631\) 4.68114 + 3.40104i 0.186353 + 0.135393i 0.677050 0.735937i \(-0.263258\pi\)
−0.490697 + 0.871330i \(0.663258\pi\)
\(632\) 3.45536 + 10.6345i 0.137447 + 0.423018i
\(633\) 1.97745 + 6.08595i 0.0785964 + 0.241895i
\(634\) 11.3701 + 8.26083i 0.451562 + 0.328079i
\(635\) 10.4249 7.57416i 0.413701 0.300571i
\(636\) −3.99207 + 12.2863i −0.158296 + 0.487184i
\(637\) −1.32353 −0.0524403
\(638\) 7.44137 + 2.03098i 0.294607 + 0.0804072i
\(639\) −4.23615 −0.167580
\(640\) 3.06833 9.44335i 0.121286 0.373281i
\(641\) 19.6740 14.2940i 0.777077 0.564580i −0.127023 0.991900i \(-0.540542\pi\)
0.904100 + 0.427320i \(0.140542\pi\)
\(642\) 6.62256 + 4.81157i 0.261372 + 0.189898i
\(643\) −3.62688 11.1624i −0.143030 0.440201i 0.853722 0.520728i \(-0.174340\pi\)
−0.996752 + 0.0805273i \(0.974340\pi\)
\(644\) 2.74842 + 8.45877i 0.108303 + 0.333322i
\(645\) −1.16393 0.845645i −0.0458297 0.0332973i
\(646\) −2.49243 + 1.81085i −0.0980632 + 0.0712471i
\(647\) −7.43368 + 22.8785i −0.292248 + 0.899447i 0.691884 + 0.722009i \(0.256781\pi\)
−0.984132 + 0.177438i \(0.943219\pi\)
\(648\) −2.02882 −0.0796998
\(649\) 0.835720 + 17.5005i 0.0328049 + 0.686955i
\(650\) 2.33565 0.0916117
\(651\) −0.918820 + 2.82784i −0.0360114 + 0.110832i
\(652\) 18.0114 13.0860i 0.705380 0.512489i
\(653\) 15.8385 + 11.5073i 0.619808 + 0.450317i 0.852855 0.522149i \(-0.174869\pi\)
−0.233046 + 0.972466i \(0.574869\pi\)
\(654\) 1.40198 + 4.31487i 0.0548219 + 0.168725i
\(655\) −1.26617 3.89688i −0.0494735 0.152264i
\(656\) −3.69363 2.68358i −0.144212 0.104776i
\(657\) 8.36680 6.07883i 0.326420 0.237158i
\(658\) −1.28619 + 3.95849i −0.0501409 + 0.154318i
\(659\) 9.76928 0.380557 0.190279 0.981730i \(-0.439061\pi\)
0.190279 + 0.981730i \(0.439061\pi\)
\(660\) −2.66166 + 4.05723i −0.103605 + 0.157928i
\(661\) 7.70930 0.299857 0.149929 0.988697i \(-0.452096\pi\)
0.149929 + 0.988697i \(0.452096\pi\)
\(662\) 1.17314 3.61056i 0.0455954 0.140328i
\(663\) −1.91761 + 1.39323i −0.0744738 + 0.0541084i
\(664\) 2.32943 + 1.69243i 0.0903995 + 0.0656791i
\(665\) 1.81918 + 5.59885i 0.0705447 + 0.217114i
\(666\) 1.84086 + 5.66559i 0.0713319 + 0.219537i
\(667\) −6.22416 4.52212i −0.241001 0.175097i
\(668\) 21.4039 15.5508i 0.828142 0.601680i
\(669\) 8.03339 24.7242i 0.310589 0.955894i
\(670\) 3.46603 0.133905
\(671\) 3.09907 4.72400i 0.119638 0.182368i
\(672\) 15.3232 0.591106
\(673\) −8.99157 + 27.6732i −0.346599 + 1.06672i 0.614123 + 0.789211i \(0.289510\pi\)
−0.960722 + 0.277513i \(0.910490\pi\)
\(674\) −13.1811 + 9.57666i −0.507719 + 0.368879i
\(675\) −3.44532 2.50317i −0.132610 0.0963470i
\(676\) −0.525083 1.61604i −0.0201955 0.0621553i
\(677\) 11.8305 + 36.4106i 0.454683 + 1.39937i 0.871506 + 0.490384i \(0.163143\pi\)
−0.416823 + 0.908988i \(0.636857\pi\)
\(678\) 1.45792 + 1.05924i 0.0559913 + 0.0406800i
\(679\) −7.93831 + 5.76752i −0.304645 + 0.221337i
\(680\) 1.27951 3.93791i 0.0490668 0.151012i
\(681\) 26.7467 1.02494
\(682\) −0.0894216 1.87255i −0.00342413 0.0717035i
\(683\) 20.9870 0.803046 0.401523 0.915849i \(-0.368481\pi\)
0.401523 + 0.915849i \(0.368481\pi\)
\(684\) −1.24438 + 3.82982i −0.0475801 + 0.146437i
\(685\) −14.6077 + 10.6131i −0.558130 + 0.405505i
\(686\) −7.26651 5.27943i −0.277437 0.201570i
\(687\) 0.755999 + 2.32673i 0.0288432 + 0.0887702i
\(688\) 1.18021 + 3.63231i 0.0449950 + 0.138480i
\(689\) −6.15074 4.46878i −0.234325 0.170247i
\(690\) −0.693120 + 0.503581i −0.0263866 + 0.0191710i
\(691\) 0.814167 2.50575i 0.0309724 0.0953232i −0.934375 0.356290i \(-0.884041\pi\)
0.965348 + 0.260967i \(0.0840414\pi\)
\(692\) −2.59346 −0.0985887
\(693\) −9.23100 2.51942i −0.350657 0.0957050i
\(694\) −12.4376 −0.472125
\(695\) 3.24788 9.99595i 0.123199 0.379168i
\(696\) −6.96023 + 5.05690i −0.263827 + 0.191681i
\(697\) −3.83033 2.78290i −0.145084 0.105410i
\(698\) −0.773472 2.38050i −0.0292763 0.0901033i
\(699\) −5.71402 17.5859i −0.216124 0.665162i
\(700\) 16.8900 + 12.2713i 0.638380 + 0.463810i
\(701\) 13.6947 9.94975i 0.517240 0.375797i −0.298323 0.954465i \(-0.596427\pi\)
0.815563 + 0.578668i \(0.196427\pi\)
\(702\) 0.169480 0.521606i 0.00639661 0.0196868i
\(703\) 25.7412 0.970847
\(704\) 5.14424 1.94734i 0.193881 0.0733930i
\(705\) 2.26488 0.0853004
\(706\) 1.66250 5.11666i 0.0625692 0.192568i
\(707\) −28.0734 + 20.3965i −1.05581 + 0.767089i
\(708\) −7.26193 5.27610i −0.272920 0.198288i
\(709\) 12.8151 + 39.4409i 0.481283 + 1.48124i 0.837293 + 0.546754i \(0.184137\pi\)
−0.356011 + 0.934482i \(0.615863\pi\)
\(710\) 0.618163 + 1.90251i 0.0231992 + 0.0713999i
\(711\) 4.45887 + 3.23956i 0.167221 + 0.121493i
\(712\) 9.87392 7.17382i 0.370041 0.268850i
\(713\) −0.577801 + 1.77829i −0.0216388 + 0.0665975i
\(714\) 3.75053 0.140360
\(715\) −1.78681 2.22760i −0.0668231 0.0833074i
\(716\) 28.6760 1.07167
\(717\) −6.46186 + 19.8876i −0.241323 + 0.742715i
\(718\) −0.0320468 + 0.0232834i −0.00119598 + 0.000868928i
\(719\) 21.0968 + 15.3277i 0.786777 + 0.571627i 0.907005 0.421119i \(-0.138363\pi\)
−0.120228 + 0.992746i \(0.538363\pi\)
\(720\) −0.608155 1.87171i −0.0226646 0.0697545i
\(721\) −8.21874 25.2947i −0.306082 0.942023i
\(722\) 5.93840 + 4.31450i 0.221004 + 0.160569i
\(723\) 18.9076 13.7372i 0.703180 0.510891i
\(724\) 12.6210 38.8436i 0.469058 1.44361i
\(725\) −18.0590 −0.670694
\(726\) 6.00549 0.574883i 0.222884 0.0213359i
\(727\) −48.9788 −1.81652 −0.908261 0.418403i \(-0.862590\pi\)
−0.908261 + 0.418403i \(0.862590\pi\)
\(728\) −1.80876 + 5.56679i −0.0670371 + 0.206319i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) −3.95101 2.87058i −0.146233 0.106245i
\(731\) 1.22389 + 3.76674i 0.0452671 + 0.139318i
\(732\) 0.894470 + 2.75289i 0.0330606 + 0.101750i
\(733\) −41.5744 30.2056i −1.53559 1.11567i −0.953028 0.302881i \(-0.902052\pi\)
−0.582559 0.812789i \(-0.697948\pi\)
\(734\) 6.47525 4.70455i 0.239006 0.173648i
\(735\) 0.352152 1.08381i 0.0129893 0.0399770i
\(736\) 9.63602 0.355188
\(737\) 15.2318 + 18.9892i 0.561070 + 0.699478i
\(738\) 1.09550 0.0403259
\(739\) −0.611781 + 1.88287i −0.0225047 + 0.0692624i −0.961678 0.274181i \(-0.911593\pi\)
0.939173 + 0.343443i \(0.111593\pi\)
\(740\) −12.8564 + 9.34070i −0.472610 + 0.343371i
\(741\) −1.91727 1.39298i −0.0704327 0.0511724i
\(742\) 3.71743 + 11.4411i 0.136471 + 0.420015i
\(743\) −6.53858 20.1237i −0.239877 0.738267i −0.996437 0.0843418i \(-0.973121\pi\)
0.756560 0.653925i \(-0.226879\pi\)
\(744\) 1.69160 + 1.22902i 0.0620169 + 0.0450579i
\(745\) −4.11170 + 2.98733i −0.150641 + 0.109447i
\(746\) −2.04943 + 6.30748i −0.0750348 + 0.230933i
\(747\) 1.41921 0.0519263
\(748\) 12.4929 4.72917i 0.456787 0.172916i
\(749\) −43.0612 −1.57342
\(750\) −1.35107 + 4.15818i −0.0493342 + 0.151835i
\(751\) 6.84228 4.97121i 0.249678 0.181402i −0.455906 0.890028i \(-0.650685\pi\)
0.705584 + 0.708626i \(0.250685\pi\)
\(752\) −4.86418 3.53403i −0.177378 0.128873i
\(753\) 8.11719 + 24.9821i 0.295807 + 0.910400i
\(754\) −0.718688 2.21189i −0.0261731 0.0805524i
\(755\) 2.34153 + 1.70122i 0.0852169 + 0.0619137i
\(756\) 3.96604 2.88150i 0.144243 0.104799i
\(757\) 9.41677 28.9818i 0.342258 1.05336i −0.620777 0.783987i \(-0.713183\pi\)
0.963035 0.269375i \(-0.0868172\pi\)
\(758\) 10.8840 0.395324
\(759\) −5.80493 1.58434i −0.210705 0.0575080i
\(760\) 4.13984 0.150168
\(761\) −4.00923 + 12.3391i −0.145334 + 0.447293i −0.997054 0.0767048i \(-0.975560\pi\)
0.851719 + 0.523998i \(0.175560\pi\)
\(762\) 6.64044 4.82456i 0.240558 0.174776i
\(763\) −19.3079 14.0280i −0.698995 0.507849i
\(764\) 9.38474 + 28.8833i 0.339528 + 1.04496i
\(765\) −0.630663 1.94098i −0.0228017 0.0701764i
\(766\) 16.7054 + 12.1372i 0.603591 + 0.438535i
\(767\) 4.27373 3.10505i 0.154315 0.112117i
\(768\) 0.929471 2.86062i 0.0335394 0.103224i
\(769\) −46.6018 −1.68050 −0.840252 0.542196i \(-0.817593\pi\)
−0.840252 + 0.542196i \(0.817593\pi\)
\(770\) 0.215533 + 4.51341i 0.00776728 + 0.162652i
\(771\) −8.52291 −0.306945
\(772\) 8.42519 25.9301i 0.303229 0.933244i
\(773\) 16.4000 11.9153i 0.589866 0.428563i −0.252401 0.967623i \(-0.581220\pi\)
0.842268 + 0.539060i \(0.181220\pi\)
\(774\) −0.741397 0.538656i −0.0266490 0.0193616i
\(775\) 1.35628 + 4.17419i 0.0487189 + 0.149941i
\(776\) 2.13228 + 6.56247i 0.0765443 + 0.235579i
\(777\) −25.3521 18.4194i −0.909502 0.660792i
\(778\) 14.5592 10.5779i 0.521974 0.379236i
\(779\) 1.46280 4.50203i 0.0524102 0.161302i
\(780\) 1.46305 0.0523855
\(781\) −7.70665 + 11.7474i −0.275765 + 0.420357i
\(782\) 2.35853 0.0843407
\(783\) −1.31040 + 4.03300i −0.0468299 + 0.144128i
\(784\) −2.44744 + 1.77817i −0.0874085 + 0.0635060i
\(785\) −9.07399 6.59264i −0.323865 0.235301i
\(786\) −0.806522 2.48222i −0.0287677 0.0885379i
\(787\) 14.0965 + 43.3847i 0.502487 + 1.54650i 0.804954 + 0.593337i \(0.202190\pi\)
−0.302466 + 0.953160i \(0.597810\pi\)
\(788\) −27.7108 20.1331i −0.987157 0.717211i
\(789\) 20.5834 14.9548i 0.732790 0.532403i
\(790\) 0.804263 2.47527i 0.0286144 0.0880661i
\(791\) −9.47971 −0.337060
\(792\) −3.69095 + 5.62622i −0.131152 + 0.199919i
\(793\) −1.70348 −0.0604925
\(794\) −1.18229 + 3.63870i −0.0419577 + 0.129133i
\(795\) 5.29591 3.84770i 0.187826 0.136464i
\(796\) 20.4947 + 14.8903i 0.726415 + 0.527772i
\(797\) −5.38118 16.5616i −0.190611 0.586641i 0.809389 0.587273i \(-0.199799\pi\)
−1.00000 0.000632438i \(0.999799\pi\)
\(798\) 1.15877 + 3.56634i 0.0410201 + 0.126247i
\(799\) −5.04421 3.66483i −0.178451 0.129652i
\(800\) 18.2989 13.2949i 0.646964 0.470047i
\(801\) 1.85896 5.72129i 0.0656831 0.202152i
\(802\) −10.4381 −0.368583
\(803\) −1.63611 34.2613i −0.0577372 1.20905i
\(804\) −12.4718 −0.439847
\(805\) 1.39268 4.28622i 0.0490855 0.151069i
\(806\) −0.457286 + 0.332238i −0.0161072 + 0.0117026i
\(807\) 15.9219 + 11.5680i 0.560478 + 0.407211i
\(808\) 7.54067 + 23.2078i 0.265280 + 0.816447i
\(809\) −12.5402 38.5946i −0.440889 1.35692i −0.886930 0.461903i \(-0.847167\pi\)
0.446042 0.895012i \(-0.352833\pi\)
\(810\) 0.382038 + 0.277567i 0.0134234 + 0.00975271i
\(811\) −10.4341 + 7.58083i −0.366391 + 0.266199i −0.755713 0.654903i \(-0.772710\pi\)
0.389322 + 0.921102i \(0.372710\pi\)
\(812\) 6.42397 19.7709i 0.225437 0.693824i
\(813\) 10.6537 0.373641
\(814\) 19.0605 + 5.20219i 0.668069 + 0.182337i
\(815\) −11.2812 −0.395165
\(816\) −1.67419 + 5.15262i −0.0586083 + 0.180378i
\(817\) −3.20362 + 2.32756i −0.112080 + 0.0814311i
\(818\) 8.53261 + 6.19930i 0.298336 + 0.216753i
\(819\) 0.891530 + 2.74385i 0.0311526 + 0.0958778i
\(820\) 0.903060 + 2.77933i 0.0315362 + 0.0970586i
\(821\) 12.9638 + 9.41874i 0.452439 + 0.328716i 0.790558 0.612387i \(-0.209791\pi\)
−0.338119 + 0.941103i \(0.609791\pi\)
\(822\) −9.30474 + 6.76029i −0.324540 + 0.235792i
\(823\) 14.7850 45.5037i 0.515374 1.58616i −0.267226 0.963634i \(-0.586107\pi\)
0.782600 0.622524i \(-0.213893\pi\)
\(824\) −18.7031 −0.651553
\(825\) −13.2096 + 5.00044i −0.459898 + 0.174093i
\(826\) −8.35871 −0.290837
\(827\) 13.7889 42.4379i 0.479488 1.47571i −0.360321 0.932828i \(-0.617333\pi\)
0.839809 0.542882i \(-0.182667\pi\)
\(828\) 2.49405 1.81203i 0.0866742 0.0629725i
\(829\) 22.2096 + 16.1362i 0.771370 + 0.560433i 0.902377 0.430948i \(-0.141821\pi\)
−0.131007 + 0.991382i \(0.541821\pi\)
\(830\) −0.207100 0.637387i −0.00718853 0.0221240i
\(831\) −3.32125 10.2217i −0.115213 0.354588i
\(832\) −1.34172 0.974817i −0.0465158 0.0337957i
\(833\) −2.53802 + 1.84398i −0.0879371 + 0.0638901i
\(834\) 2.06882 6.36719i 0.0716375 0.220478i
\(835\) −13.4061 −0.463937
\(836\) 8.35676 + 10.4183i 0.289025 + 0.360323i
\(837\) 1.03061 0.0356231
\(838\) −1.34260 + 4.13209i −0.0463792 + 0.142741i
\(839\) −35.7959 + 26.0072i −1.23581 + 0.897869i −0.997312 0.0732743i \(-0.976655\pi\)
−0.238498 + 0.971143i \(0.576655\pi\)
\(840\) −4.07726 2.96230i −0.140679 0.102209i
\(841\) −3.40468 10.4785i −0.117403 0.361329i
\(842\) 2.35974 + 7.26254i 0.0813221 + 0.250284i
\(843\) 3.13952 + 2.28099i 0.108131 + 0.0785615i
\(844\) −8.79681 + 6.39126i −0.302799 + 0.219996i
\(845\) −0.266070 + 0.818878i −0.00915307 + 0.0281703i
\(846\) 1.44268 0.0496003
\(847\) −23.7803 + 21.0154i −0.817100 + 0.722097i
\(848\) −17.3776 −0.596748
\(849\) 7.00269 21.5521i 0.240332 0.739664i
\(850\) 4.47887 3.25409i 0.153624 0.111614i
\(851\) −15.9427 11.5831i −0.546509 0.397062i
\(852\) −2.22433 6.84579i −0.0762043 0.234533i
\(853\) 4.46809 + 13.7514i 0.152985 + 0.470838i 0.997951 0.0639810i \(-0.0203797\pi\)
−0.844966 + 0.534819i \(0.820380\pi\)
\(854\) 2.18065 + 1.58433i 0.0746202 + 0.0542148i
\(855\) 1.65081 1.19938i 0.0564564 0.0410180i
\(856\) −9.35748 + 28.7994i −0.319832 + 0.984342i
\(857\) −57.2894 −1.95697 −0.978483 0.206325i \(-0.933850\pi\)
−0.978483 + 0.206325i \(0.933850\pi\)
\(858\) −1.13816 1.41893i −0.0388561 0.0484414i
\(859\) −6.09124 −0.207830 −0.103915 0.994586i \(-0.533137\pi\)
−0.103915 + 0.994586i \(0.533137\pi\)
\(860\) 0.755435 2.32499i 0.0257601 0.0792815i
\(861\) −4.66217 + 3.38726i −0.158886 + 0.115438i
\(862\) 5.92383 + 4.30392i 0.201767 + 0.146592i
\(863\) 1.91899 + 5.90605i 0.0653232 + 0.201044i 0.978391 0.206764i \(-0.0662932\pi\)
−0.913068 + 0.407808i \(0.866293\pi\)
\(864\) −1.64126 5.05129i −0.0558369 0.171848i
\(865\) 1.06318 + 0.772443i 0.0361491 + 0.0262638i
\(866\) −11.7487 + 8.53595i −0.399238 + 0.290063i
\(867\) 3.51714 10.8246i 0.119448 0.367624i
\(868\) −5.05235 −0.171488
\(869\) 17.0956 6.47148i 0.579928 0.219530i
\(870\) 2.00249 0.0678908
\(871\) 2.26812 6.98056i 0.0768523 0.236527i
\(872\) −13.5777 + 9.86479i −0.459800 + 0.334064i
\(873\) 2.75153 + 1.99910i 0.0931252 + 0.0676594i
\(874\) 0.728696 + 2.24270i 0.0246485 + 0.0758603i
\(875\) −7.10717 21.8736i −0.240266 0.739463i
\(876\) 14.2169 + 10.3292i 0.480344 + 0.348991i
\(877\) −31.7252 + 23.0497i −1.07128 + 0.778333i −0.976142 0.217131i \(-0.930330\pi\)
−0.0951408 + 0.995464i \(0.530330\pi\)
\(878\) 5.61536 17.2823i 0.189509 0.583249i
\(879\) −25.9748 −0.876109
\(880\) −6.29690 1.71862i −0.212269 0.0579346i
\(881\) −28.7305 −0.967956 −0.483978 0.875080i \(-0.660808\pi\)
−0.483978 + 0.875080i \(0.660808\pi\)
\(882\) 0.224312 0.690363i 0.00755299 0.0232457i
\(883\) −3.70137 + 2.68920i −0.124561 + 0.0904988i −0.648321 0.761367i \(-0.724529\pi\)
0.523760 + 0.851866i \(0.324529\pi\)
\(884\) −3.25841 2.36737i −0.109592 0.0796234i
\(885\) 1.40554 + 4.32582i 0.0472468 + 0.145411i
\(886\) 0.464047 + 1.42819i 0.0155900 + 0.0479810i
\(887\) −35.1359 25.5277i −1.17975 0.857137i −0.187605 0.982245i \(-0.560072\pi\)
−0.992143 + 0.125108i \(0.960072\pi\)
\(888\) −17.8281 + 12.9529i −0.598271 + 0.434670i
\(889\) −13.3426 + 41.0642i −0.447495 + 1.37725i
\(890\) −2.84077 −0.0952229
\(891\) 0.158202 + 3.31285i 0.00529996 + 0.110985i
\(892\) 44.1735 1.47904
\(893\) 1.92638 5.92878i 0.0644637 0.198399i
\(894\) −2.61906 + 1.90286i −0.0875944 + 0.0636411i
\(895\) −11.7556 8.54093i −0.392946 0.285492i
\(896\) 10.2812 + 31.6422i 0.343470 + 1.05709i
\(897\) 0.560640 + 1.72547i 0.0187192 + 0.0576119i
\(898\) −11.9206 8.66079i −0.397794 0.289014i
\(899\) 3.53569 2.56883i 0.117922 0.0856751i
\(900\) 2.23614 6.88214i 0.0745381 0.229405i
\(901\) −18.0207 −0.600358
\(902\) 1.99300 3.03798i 0.0663595 0.101154i
\(903\) 4.82071 0.160423
\(904\) −2.06000 + 6.34004i −0.0685147 + 0.210867i
\(905\) −16.7432 + 12.1646i −0.556562 + 0.404366i
\(906\) 1.49150 + 1.08364i 0.0495517 + 0.0360014i
\(907\) 8.94713 + 27.5364i 0.297085 + 0.914332i 0.982513 + 0.186193i \(0.0596149\pi\)
−0.685429 + 0.728140i \(0.740385\pi\)
\(908\) 14.0442 + 43.2238i 0.466075 + 1.43443i
\(909\) 9.73062 + 7.06971i 0.322744 + 0.234488i
\(910\) 1.10220 0.800795i 0.0365376 0.0265461i
\(911\) −17.4709 + 53.7699i −0.578837 + 1.78148i 0.0438890 + 0.999036i \(0.486025\pi\)
−0.622726 + 0.782440i \(0.713975\pi\)
\(912\) −5.41683 −0.179369
\(913\) 2.58191 3.93568i 0.0854489 0.130252i
\(914\) 2.65199 0.0877201
\(915\) 0.453245 1.39494i 0.0149838 0.0461154i
\(916\) −3.36312 + 2.44345i −0.111121 + 0.0807338i
\(917\) 11.1073 + 8.06994i 0.366796 + 0.266493i
\(918\) −0.401718 1.23636i −0.0132587 0.0408060i
\(919\) 7.67772 + 23.6296i 0.253265 + 0.779468i 0.994167 + 0.107855i \(0.0343982\pi\)
−0.740902 + 0.671613i \(0.765602\pi\)
\(920\) −2.56399 1.86285i −0.0845323 0.0614163i
\(921\) 19.2496 13.9856i 0.634295 0.460842i
\(922\) −0.422715 + 1.30098i −0.0139214 + 0.0428456i
\(923\) 4.23615 0.139435
\(924\) −0.775552 16.2406i −0.0255138 0.534275i
\(925\) −46.2566 −1.52091
\(926\) 6.50139 20.0092i 0.213649 0.657544i
\(927\) −7.45807 + 5.41861i −0.244955 + 0.177970i
\(928\) −18.2211 13.2384i −0.598138 0.434572i
\(929\) −7.01059 21.5764i −0.230010 0.707898i −0.997744 0.0671299i \(-0.978616\pi\)
0.767734 0.640769i \(-0.221384\pi\)
\(930\) −0.150392 0.462860i −0.00493156 0.0151778i
\(931\) −2.53757 1.84365i −0.0831655 0.0604233i
\(932\) 25.4192 18.4682i 0.832635 0.604945i
\(933\) 0.0994089 0.305949i 0.00325450 0.0100163i
\(934\) 0.905562 0.0296309
\(935\) −6.52996 1.78223i −0.213552 0.0582850i
\(936\) 2.02882 0.0663142
\(937\) 8.96952 27.6054i 0.293022 0.901828i −0.690857 0.722991i \(-0.742767\pi\)
0.983879 0.178836i \(-0.0572333\pi\)
\(938\) −9.39575 + 6.82641i −0.306782 + 0.222890i
\(939\) −24.7480 17.9805i −0.807621 0.586771i
\(940\) 1.18925 + 3.66014i 0.0387891 + 0.119381i
\(941\) 17.6921 + 54.4508i 0.576747 + 1.77504i 0.630152 + 0.776472i \(0.282993\pi\)
−0.0534048 + 0.998573i \(0.517007\pi\)
\(942\) −5.77992 4.19936i −0.188320 0.136823i
\(943\) −2.93181 + 2.13008i −0.0954728 + 0.0693651i
\(944\) 3.73122 11.4835i 0.121441 0.373757i
\(945\) −2.48409 −0.0808073
\(946\) −2.84256 + 1.07604i −0.0924196 + 0.0349852i
\(947\) 18.8001 0.610922 0.305461 0.952205i \(-0.401190\pi\)
0.305461 + 0.952205i \(0.401190\pi\)
\(948\) −2.89398 + 8.90674i −0.0939919 + 0.289277i
\(949\) −8.36680 + 6.07883i −0.271598 + 0.197327i
\(950\) 4.47808 + 3.25351i 0.145288 + 0.105558i
\(951\) 7.91864 + 24.3711i 0.256780 + 0.790287i
\(952\) 4.28729 + 13.1949i 0.138952 + 0.427650i
\(953\) −36.3494 26.4094i −1.17747 0.855484i −0.185589 0.982628i \(-0.559419\pi\)
−0.991884 + 0.127143i \(0.959419\pi\)
\(954\) 3.37337 2.45090i 0.109217 0.0793507i
\(955\) 4.75543 14.6357i 0.153882 0.473600i
\(956\) −35.5321 −1.14919
\(957\) 8.80011 + 10.9710i 0.284467 + 0.354641i
\(958\) −9.42337 −0.304455
\(959\) 18.6959 57.5401i 0.603723 1.85807i
\(960\) 1.15525 0.839336i 0.0372854 0.0270894i
\(961\) 24.2202 + 17.5970i 0.781298 + 0.567646i
\(962\) −1.84086 5.66559i −0.0593518 0.182666i
\(963\) 4.61227 + 14.1951i 0.148628 + 0.457431i
\(964\) 32.1278 + 23.3422i 1.03477 + 0.751803i
\(965\) −11.1769 + 8.12051i −0.359798 + 0.261409i
\(966\) 0.887103 2.73022i 0.0285421 0.0878435i
\(967\) 2.82220 0.0907560 0.0453780 0.998970i \(-0.485551\pi\)
0.0453780 + 0.998970i \(0.485551\pi\)
\(968\) 8.88750 + 20.4711i 0.285655 + 0.657965i
\(969\) −5.61731 −0.180454
\(970\) 0.496304 1.52747i 0.0159354 0.0490440i
\(971\) −39.0446 + 28.3676i −1.25300 + 0.910359i −0.998392 0.0566855i \(-0.981947\pi\)
−0.254609 + 0.967044i \(0.581947\pi\)
\(972\) −1.37468 0.998767i −0.0440930 0.0320355i
\(973\) 10.8828 + 33.4939i 0.348887 + 1.07376i
\(974\) 3.83417 + 11.8004i 0.122855 + 0.378108i
\(975\) 3.44532 + 2.50317i 0.110338 + 0.0801656i
\(976\) −3.15003 + 2.28863i −0.100830 + 0.0732573i
\(977\) −11.0552 + 34.0243i −0.353687 + 1.08854i 0.603081 + 0.797680i \(0.293940\pi\)
−0.956767 + 0.290855i \(0.906060\pi\)
\(978\) −7.18589 −0.229779
\(979\) −12.4840 15.5636i −0.398991 0.497416i
\(980\) 1.93639 0.0618557
\(981\) −2.55627 + 7.86740i −0.0816155 + 0.251187i
\(982\) −7.69687 + 5.59210i −0.245617 + 0.178451i
\(983\) 29.5985 + 21.5046i 0.944047 + 0.685890i 0.949391 0.314095i \(-0.101701\pi\)
−0.00534449 + 0.999986i \(0.501701\pi\)
\(984\) 1.25228 + 3.85414i 0.0399214 + 0.122865i
\(985\) 5.36341 + 16.5069i 0.170893 + 0.525953i
\(986\) −4.45983 3.24025i −0.142030 0.103191i
\(987\) −6.13966 + 4.46072i −0.195428 + 0.141986i
\(988\) 1.24438 3.82982i 0.0395891 0.121843i
\(989\) 3.03151 0.0963963
\(990\) 1.46476 0.554480i 0.0465530 0.0176225i
\(991\) 34.4494 1.09432 0.547161 0.837027i \(-0.315709\pi\)
0.547161 + 0.837027i \(0.315709\pi\)
\(992\) −1.69150 + 5.20591i −0.0537053 + 0.165288i
\(993\) 5.60001 4.06865i 0.177711 0.129115i
\(994\) −5.42275 3.93986i −0.171999 0.124965i
\(995\) −3.96674 12.2084i −0.125754 0.387031i
\(996\) 0.745205 + 2.29351i 0.0236127 + 0.0726725i
\(997\) −32.8352 23.8562i −1.03990 0.755532i −0.0696345 0.997573i \(-0.522183\pi\)
−0.970266 + 0.242041i \(0.922183\pi\)
\(998\) −10.0107 + 7.27321i −0.316884 + 0.230230i
\(999\) −3.35649 + 10.3302i −0.106195 + 0.326833i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 429.2.n.b.196.3 20
11.4 even 5 4719.2.a.bn.1.6 10
11.5 even 5 inner 429.2.n.b.313.3 yes 20
11.7 odd 10 4719.2.a.bi.1.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.n.b.196.3 20 1.1 even 1 trivial
429.2.n.b.313.3 yes 20 11.5 even 5 inner
4719.2.a.bi.1.5 10 11.7 odd 10
4719.2.a.bn.1.6 10 11.4 even 5