Properties

Label 731.2.k.b.35.14
Level $731$
Weight $2$
Character 731.35
Analytic conductor $5.837$
Analytic rank $0$
Dimension $180$
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] = [731,2,Mod(35,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.k (of order \(7\), degree \(6\), 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: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(180\)
Relative dimension: \(30\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 35.14
Character \(\chi\) \(=\) 731.35
Dual form 731.2.k.b.188.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0946208 + 0.414561i) q^{2} +(-0.485779 - 2.12833i) q^{3} +(1.63903 + 0.789315i) q^{4} +(-0.816059 + 1.02331i) q^{5} +0.928289 q^{6} -4.53691 q^{7} +(-1.01255 + 1.26970i) q^{8} +(-1.59092 + 0.766147i) q^{9} +O(q^{10})\) \(q+(-0.0946208 + 0.414561i) q^{2} +(-0.485779 - 2.12833i) q^{3} +(1.63903 + 0.789315i) q^{4} +(-0.816059 + 1.02331i) q^{5} +0.928289 q^{6} -4.53691 q^{7} +(-1.01255 + 1.26970i) q^{8} +(-1.59092 + 0.766147i) q^{9} +(-0.347007 - 0.435132i) q^{10} +(3.80652 - 1.83312i) q^{11} +(0.883722 - 3.87184i) q^{12} +(-4.05863 + 5.08937i) q^{13} +(0.429287 - 1.88083i) q^{14} +(2.57436 + 1.23975i) q^{15} +(1.83793 + 2.30469i) q^{16} +(-0.623490 - 0.781831i) q^{17} +(-0.167080 - 0.732027i) q^{18} +(-5.11082 - 2.46124i) q^{19} +(-2.14526 + 1.03310i) q^{20} +(2.20394 + 9.65607i) q^{21} +(0.399765 + 1.75148i) q^{22} +(-5.76289 + 2.77526i) q^{23} +(3.19421 + 1.53825i) q^{24} +(0.731402 + 3.20448i) q^{25} +(-1.72582 - 2.16411i) q^{26} +(-1.67991 - 2.10654i) q^{27} +(-7.43614 - 3.58106i) q^{28} +(-1.22255 + 5.35633i) q^{29} +(-0.757539 + 0.949924i) q^{30} +(0.705545 - 3.09119i) q^{31} +(-4.05569 + 1.95312i) q^{32} +(-5.75062 - 7.21105i) q^{33} +(0.383112 - 0.184497i) q^{34} +(3.70239 - 4.64265i) q^{35} -3.21230 q^{36} -0.568857 q^{37} +(1.50393 - 1.88586i) q^{38} +(12.8035 + 6.16583i) q^{39} +(-0.472988 - 2.07230i) q^{40} +(-1.45522 + 6.37574i) q^{41} -4.21157 q^{42} +(4.55222 + 4.71988i) q^{43} +7.68591 q^{44} +(0.514283 - 2.25322i) q^{45} +(-0.605225 - 2.65167i) q^{46} +(-4.47293 - 2.15405i) q^{47} +(4.01233 - 5.03130i) q^{48} +13.5836 q^{49} -1.39766 q^{50} +(-1.36112 + 1.70679i) q^{51} +(-10.6693 + 5.13808i) q^{52} +(5.95948 + 7.47295i) q^{53} +(1.03224 - 0.497102i) q^{54} +(-1.23050 + 5.39117i) q^{55} +(4.59385 - 5.76050i) q^{56} +(-2.75562 + 12.0732i) q^{57} +(-2.10485 - 1.01364i) q^{58} +(-2.87966 - 3.61098i) q^{59} +(3.24091 + 4.06397i) q^{60} +(-0.979013 - 4.28934i) q^{61} +(1.21473 + 0.584983i) q^{62} +(7.21787 - 3.47595i) q^{63} +(0.885965 + 3.88167i) q^{64} +(-1.89589 - 8.30645i) q^{65} +(3.53355 - 1.70167i) q^{66} +(-4.83874 - 2.33021i) q^{67} +(-0.404807 - 1.77358i) q^{68} +(8.70617 + 10.9172i) q^{69} +(1.57434 + 1.97416i) q^{70} +(-2.62253 - 1.26295i) q^{71} +(0.638112 - 2.79575i) q^{72} +(9.83465 - 12.3323i) q^{73} +(0.0538257 - 0.235826i) q^{74} +(6.46491 - 3.11334i) q^{75} +(-6.43410 - 8.06810i) q^{76} +(-17.2698 + 8.31672i) q^{77} +(-3.76759 + 4.72440i) q^{78} -15.3459 q^{79} -3.85826 q^{80} +(-6.97021 + 8.74037i) q^{81} +(-2.50544 - 1.20656i) q^{82} +(0.813344 + 3.56349i) q^{83} +(-4.00937 + 17.5662i) q^{84} +1.30886 q^{85} +(-2.38741 + 1.44058i) q^{86} +11.9940 q^{87} +(-1.52678 + 6.68925i) q^{88} +(2.54458 + 11.1485i) q^{89} +(0.885436 + 0.426403i) q^{90} +(18.4137 - 23.0900i) q^{91} -11.6361 q^{92} -6.92183 q^{93} +(1.31622 - 1.65048i) q^{94} +(6.68934 - 3.22142i) q^{95} +(6.12706 + 7.68309i) q^{96} +(8.93808 - 4.30435i) q^{97} +(-1.28529 + 5.63122i) q^{98} +(-4.65143 + 5.83271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 180 q + 2 q^{3} - 34 q^{4} + 2 q^{5} + 6 q^{6} - 54 q^{7} + 14 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 180 q + 2 q^{3} - 34 q^{4} + 2 q^{5} + 6 q^{6} - 54 q^{7} + 14 q^{8} - 18 q^{9} - 8 q^{10} + 4 q^{11} - 4 q^{12} - 5 q^{13} + 24 q^{14} + 11 q^{15} - 58 q^{16} + 30 q^{17} - 84 q^{18} - 4 q^{20} - 28 q^{21} - 49 q^{22} - 23 q^{23} - 6 q^{24} - 14 q^{25} + 14 q^{26} + 20 q^{27} - 14 q^{28} - 60 q^{29} - 5 q^{30} + 36 q^{31} + 39 q^{32} - 39 q^{33} - 14 q^{35} + 224 q^{36} - 184 q^{37} + 32 q^{38} + 58 q^{39} + 22 q^{40} - 48 q^{41} - 58 q^{42} + 2 q^{43} + 134 q^{44} - 54 q^{45} - 5 q^{46} - 35 q^{47} + 44 q^{48} + 174 q^{49} - 70 q^{50} - 2 q^{51} - 22 q^{52} + 8 q^{53} + 70 q^{54} + 51 q^{55} - 61 q^{56} + 72 q^{57} + 29 q^{58} + 35 q^{59} + 96 q^{60} - 40 q^{61} + 20 q^{62} - 35 q^{63} - 18 q^{64} - 17 q^{65} - 218 q^{66} + 16 q^{67} + 27 q^{68} + 50 q^{69} + 72 q^{70} - 20 q^{71} - 143 q^{72} - 4 q^{73} - 35 q^{74} - 45 q^{75} - 148 q^{76} + 40 q^{77} - 220 q^{78} - 12 q^{79} - 222 q^{80} + 12 q^{81} + 50 q^{82} + 16 q^{83} - 170 q^{84} - 2 q^{85} + 108 q^{86} + 78 q^{87} - 14 q^{88} + 55 q^{89} + 105 q^{90} - 53 q^{91} - 28 q^{92} - 142 q^{93} + 108 q^{94} - 49 q^{95} - 148 q^{96} + 73 q^{97} + 6 q^{98} - 73 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{7}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0946208 + 0.414561i −0.0669070 + 0.293139i −0.997301 0.0734225i \(-0.976608\pi\)
0.930394 + 0.366561i \(0.119465\pi\)
\(3\) −0.485779 2.12833i −0.280464 1.22879i −0.897200 0.441624i \(-0.854402\pi\)
0.616736 0.787170i \(-0.288455\pi\)
\(4\) 1.63903 + 0.789315i 0.819515 + 0.394658i
\(5\) −0.816059 + 1.02331i −0.364953 + 0.457636i −0.930074 0.367371i \(-0.880258\pi\)
0.565122 + 0.825008i \(0.308829\pi\)
\(6\) 0.928289 0.378972
\(7\) −4.53691 −1.71479 −0.857396 0.514657i \(-0.827919\pi\)
−0.857396 + 0.514657i \(0.827919\pi\)
\(8\) −1.01255 + 1.26970i −0.357990 + 0.448905i
\(9\) −1.59092 + 0.766147i −0.530307 + 0.255382i
\(10\) −0.347007 0.435132i −0.109733 0.137601i
\(11\) 3.80652 1.83312i 1.14771 0.552707i 0.239364 0.970930i \(-0.423061\pi\)
0.908344 + 0.418223i \(0.137347\pi\)
\(12\) 0.883722 3.87184i 0.255108 1.11770i
\(13\) −4.05863 + 5.08937i −1.12566 + 1.41154i −0.226451 + 0.974023i \(0.572712\pi\)
−0.899212 + 0.437514i \(0.855859\pi\)
\(14\) 0.429287 1.88083i 0.114732 0.502672i
\(15\) 2.57436 + 1.23975i 0.664697 + 0.320101i
\(16\) 1.83793 + 2.30469i 0.459482 + 0.576173i
\(17\) −0.623490 0.781831i −0.151218 0.189622i
\(18\) −0.167080 0.732027i −0.0393813 0.172541i
\(19\) −5.11082 2.46124i −1.17250 0.564648i −0.256785 0.966469i \(-0.582663\pi\)
−0.915718 + 0.401821i \(0.868378\pi\)
\(20\) −2.14526 + 1.03310i −0.479694 + 0.231008i
\(21\) 2.20394 + 9.65607i 0.480938 + 2.10713i
\(22\) 0.399765 + 1.75148i 0.0852302 + 0.373418i
\(23\) −5.76289 + 2.77526i −1.20165 + 0.578682i −0.924144 0.382043i \(-0.875220\pi\)
−0.277501 + 0.960725i \(0.589506\pi\)
\(24\) 3.19421 + 1.53825i 0.652016 + 0.313994i
\(25\) 0.731402 + 3.20448i 0.146280 + 0.640896i
\(26\) −1.72582 2.16411i −0.338461 0.424417i
\(27\) −1.67991 2.10654i −0.323299 0.405404i
\(28\) −7.43614 3.58106i −1.40530 0.676756i
\(29\) −1.22255 + 5.35633i −0.227021 + 0.994646i 0.725032 + 0.688715i \(0.241825\pi\)
−0.952054 + 0.305931i \(0.901032\pi\)
\(30\) −0.757539 + 0.949924i −0.138307 + 0.173432i
\(31\) 0.705545 3.09119i 0.126720 0.555195i −0.871212 0.490907i \(-0.836665\pi\)
0.997931 0.0642875i \(-0.0204775\pi\)
\(32\) −4.05569 + 1.95312i −0.716952 + 0.345266i
\(33\) −5.75062 7.21105i −1.00105 1.25528i
\(34\) 0.383112 0.184497i 0.0657032 0.0316410i
\(35\) 3.70239 4.64265i 0.625818 0.784751i
\(36\) −3.21230 −0.535383
\(37\) −0.568857 −0.0935195 −0.0467598 0.998906i \(-0.514890\pi\)
−0.0467598 + 0.998906i \(0.514890\pi\)
\(38\) 1.50393 1.88586i 0.243969 0.305927i
\(39\) 12.8035 + 6.16583i 2.05020 + 0.987323i
\(40\) −0.472988 2.07230i −0.0747859 0.327659i
\(41\) −1.45522 + 6.37574i −0.227267 + 0.995723i 0.724590 + 0.689181i \(0.242029\pi\)
−0.951857 + 0.306543i \(0.900828\pi\)
\(42\) −4.21157 −0.649859
\(43\) 4.55222 + 4.71988i 0.694208 + 0.719775i
\(44\) 7.68591 1.15869
\(45\) 0.514283 2.25322i 0.0766648 0.335890i
\(46\) −0.605225 2.65167i −0.0892356 0.390967i
\(47\) −4.47293 2.15405i −0.652444 0.314201i 0.0782215 0.996936i \(-0.475076\pi\)
−0.730666 + 0.682735i \(0.760790\pi\)
\(48\) 4.01233 5.03130i 0.579130 0.726205i
\(49\) 13.5836 1.94051
\(50\) −1.39766 −0.197659
\(51\) −1.36112 + 1.70679i −0.190595 + 0.238999i
\(52\) −10.6693 + 5.13808i −1.47957 + 0.712524i
\(53\) 5.95948 + 7.47295i 0.818598 + 1.02649i 0.999079 + 0.0429106i \(0.0136631\pi\)
−0.180481 + 0.983578i \(0.557766\pi\)
\(54\) 1.03224 0.497102i 0.140471 0.0676471i
\(55\) −1.23050 + 5.39117i −0.165920 + 0.726945i
\(56\) 4.59385 5.76050i 0.613879 0.769780i
\(57\) −2.75562 + 12.0732i −0.364991 + 1.59913i
\(58\) −2.10485 1.01364i −0.276380 0.133098i
\(59\) −2.87966 3.61098i −0.374899 0.470109i 0.558211 0.829699i \(-0.311488\pi\)
−0.933110 + 0.359590i \(0.882917\pi\)
\(60\) 3.24091 + 4.06397i 0.418399 + 0.524656i
\(61\) −0.979013 4.28934i −0.125350 0.549193i −0.998133 0.0610845i \(-0.980544\pi\)
0.872783 0.488109i \(-0.162313\pi\)
\(62\) 1.21473 + 0.584983i 0.154271 + 0.0742929i
\(63\) 7.21787 3.47595i 0.909367 0.437928i
\(64\) 0.885965 + 3.88167i 0.110746 + 0.485208i
\(65\) −1.89589 8.30645i −0.235157 1.03029i
\(66\) 3.53355 1.70167i 0.434950 0.209461i
\(67\) −4.83874 2.33021i −0.591146 0.284681i 0.114298 0.993447i \(-0.463538\pi\)
−0.705444 + 0.708766i \(0.749252\pi\)
\(68\) −0.404807 1.77358i −0.0490901 0.215078i
\(69\) 8.70617 + 10.9172i 1.04810 + 1.31428i
\(70\) 1.57434 + 1.97416i 0.188169 + 0.235957i
\(71\) −2.62253 1.26295i −0.311237 0.149884i 0.271744 0.962370i \(-0.412400\pi\)
−0.582981 + 0.812486i \(0.698114\pi\)
\(72\) 0.638112 2.79575i 0.0752022 0.329482i
\(73\) 9.83465 12.3323i 1.15106 1.44338i 0.274827 0.961494i \(-0.411380\pi\)
0.876232 0.481889i \(-0.160049\pi\)
\(74\) 0.0538257 0.235826i 0.00625711 0.0274142i
\(75\) 6.46491 3.11334i 0.746504 0.359497i
\(76\) −6.43410 8.06810i −0.738042 0.925475i
\(77\) −17.2698 + 8.31672i −1.96808 + 0.947778i
\(78\) −3.76759 + 4.72440i −0.426595 + 0.534933i
\(79\) −15.3459 −1.72655 −0.863273 0.504737i \(-0.831589\pi\)
−0.863273 + 0.504737i \(0.831589\pi\)
\(80\) −3.85826 −0.431367
\(81\) −6.97021 + 8.74037i −0.774468 + 0.971152i
\(82\) −2.50544 1.20656i −0.276679 0.133242i
\(83\) 0.813344 + 3.56349i 0.0892761 + 0.391144i 0.999749 0.0224256i \(-0.00713890\pi\)
−0.910472 + 0.413570i \(0.864282\pi\)
\(84\) −4.00937 + 17.5662i −0.437458 + 1.91663i
\(85\) 1.30886 0.141966
\(86\) −2.38741 + 1.44058i −0.257441 + 0.155341i
\(87\) 11.9940 1.28589
\(88\) −1.52678 + 6.68925i −0.162755 + 0.713076i
\(89\) 2.54458 + 11.1485i 0.269724 + 1.18174i 0.910334 + 0.413874i \(0.135824\pi\)
−0.640610 + 0.767867i \(0.721318\pi\)
\(90\) 0.885436 + 0.426403i 0.0933331 + 0.0449469i
\(91\) 18.4137 23.0900i 1.93028 2.42049i
\(92\) −11.6361 −1.21315
\(93\) −6.92183 −0.717761
\(94\) 1.31622 1.65048i 0.135757 0.170234i
\(95\) 6.68934 3.22142i 0.686312 0.330510i
\(96\) 6.12706 + 7.68309i 0.625340 + 0.784152i
\(97\) 8.93808 4.30435i 0.907524 0.437041i 0.0789236 0.996881i \(-0.474852\pi\)
0.828601 + 0.559840i \(0.189137\pi\)
\(98\) −1.28529 + 5.63122i −0.129834 + 0.568840i
\(99\) −4.65143 + 5.83271i −0.467486 + 0.586209i
\(100\) −1.33056 + 5.82955i −0.133056 + 0.582955i
\(101\) −14.4356 6.95180i −1.43639 0.691730i −0.456218 0.889868i \(-0.650796\pi\)
−0.980174 + 0.198138i \(0.936511\pi\)
\(102\) −0.578779 0.725766i −0.0573076 0.0718615i
\(103\) 3.16399 + 3.96752i 0.311757 + 0.390931i 0.912882 0.408224i \(-0.133852\pi\)
−0.601125 + 0.799155i \(0.705280\pi\)
\(104\) −2.35238 10.3065i −0.230670 1.01063i
\(105\) −11.6797 5.62463i −1.13982 0.548907i
\(106\) −3.66189 + 1.76347i −0.355674 + 0.171283i
\(107\) 1.49169 + 6.53552i 0.144207 + 0.631812i 0.994431 + 0.105391i \(0.0336094\pi\)
−0.850224 + 0.526421i \(0.823533\pi\)
\(108\) −1.09070 4.77866i −0.104952 0.459827i
\(109\) 10.2021 4.91305i 0.977180 0.470585i 0.124046 0.992277i \(-0.460413\pi\)
0.853134 + 0.521692i \(0.174699\pi\)
\(110\) −2.11854 1.02023i −0.201995 0.0972755i
\(111\) 0.276339 + 1.21072i 0.0262289 + 0.114916i
\(112\) −8.33853 10.4562i −0.787917 0.988017i
\(113\) −3.94966 4.95272i −0.371553 0.465912i 0.560543 0.828126i \(-0.310593\pi\)
−0.932095 + 0.362213i \(0.882021\pi\)
\(114\) −4.74432 2.28475i −0.444347 0.213986i
\(115\) 1.86292 8.16198i 0.173718 0.761108i
\(116\) −6.23163 + 7.81421i −0.578592 + 0.725531i
\(117\) 2.55776 11.2063i 0.236465 1.03602i
\(118\) 1.76944 0.852120i 0.162891 0.0784440i
\(119\) 2.82872 + 3.54710i 0.259308 + 0.325162i
\(120\) −4.18077 + 2.01335i −0.381650 + 0.183793i
\(121\) 4.27085 5.35548i 0.388259 0.486861i
\(122\) 1.87083 0.169377
\(123\) 14.2766 1.28728
\(124\) 3.59634 4.50966i 0.322961 0.404980i
\(125\) −9.77223 4.70606i −0.874055 0.420923i
\(126\) 0.758030 + 3.32115i 0.0675307 + 0.295871i
\(127\) 2.92519 12.8161i 0.259568 1.13724i −0.662146 0.749374i \(-0.730354\pi\)
0.921715 0.387868i \(-0.126789\pi\)
\(128\) −10.6960 −0.945400
\(129\) 7.83411 11.9815i 0.689755 1.05491i
\(130\) 3.62292 0.317751
\(131\) −0.331944 + 1.45434i −0.0290020 + 0.127066i −0.987357 0.158515i \(-0.949329\pi\)
0.958355 + 0.285581i \(0.0921866\pi\)
\(132\) −3.73365 16.3582i −0.324972 1.42380i
\(133\) 23.1874 + 11.1664i 2.01060 + 0.968254i
\(134\) 1.42386 1.78547i 0.123003 0.154241i
\(135\) 3.52654 0.303516
\(136\) 1.62400 0.139257
\(137\) 7.19034 9.01640i 0.614312 0.770323i −0.373220 0.927743i \(-0.621746\pi\)
0.987532 + 0.157420i \(0.0503176\pi\)
\(138\) −5.34963 + 2.57624i −0.455391 + 0.219305i
\(139\) 0.514765 + 0.645494i 0.0436618 + 0.0547501i 0.803183 0.595732i \(-0.203138\pi\)
−0.759521 + 0.650483i \(0.774567\pi\)
\(140\) 9.73285 4.68709i 0.822576 0.396132i
\(141\) −2.41169 + 10.5663i −0.203101 + 0.889842i
\(142\) 0.771714 0.967699i 0.0647608 0.0812075i
\(143\) −6.11983 + 26.8127i −0.511766 + 2.24219i
\(144\) −4.68974 2.25846i −0.390811 0.188205i
\(145\) −4.48349 5.62212i −0.372334 0.466892i
\(146\) 4.18191 + 5.24395i 0.346098 + 0.433993i
\(147\) −6.59862 28.9104i −0.544245 2.38449i
\(148\) −0.932374 0.449008i −0.0766407 0.0369082i
\(149\) −10.5565 + 5.08374i −0.864822 + 0.416476i −0.813058 0.582183i \(-0.802199\pi\)
−0.0517641 + 0.998659i \(0.516484\pi\)
\(150\) 0.678953 + 2.97469i 0.0554363 + 0.242882i
\(151\) 0.923775 + 4.04732i 0.0751757 + 0.329366i 0.998506 0.0546401i \(-0.0174012\pi\)
−0.923330 + 0.384007i \(0.874544\pi\)
\(152\) 8.29999 3.99706i 0.673218 0.324205i
\(153\) 1.59092 + 0.766147i 0.128618 + 0.0619394i
\(154\) −1.81370 7.94634i −0.146152 0.640334i
\(155\) 2.58747 + 3.24459i 0.207831 + 0.260611i
\(156\) 16.1185 + 20.2120i 1.29051 + 1.61825i
\(157\) −11.0285 5.31103i −0.880167 0.423866i −0.0614815 0.998108i \(-0.519583\pi\)
−0.818686 + 0.574242i \(0.805297\pi\)
\(158\) 1.45204 6.36180i 0.115518 0.506118i
\(159\) 13.0100 16.3140i 1.03176 1.29378i
\(160\) 1.31105 5.74408i 0.103647 0.454109i
\(161\) 26.1457 12.5911i 2.06057 0.992319i
\(162\) −2.96389 3.71660i −0.232865 0.292004i
\(163\) 13.2860 6.39821i 1.04064 0.501147i 0.166106 0.986108i \(-0.446881\pi\)
0.874536 + 0.484961i \(0.161166\pi\)
\(164\) −7.41762 + 9.30140i −0.579219 + 0.726317i
\(165\) 12.0720 0.939801
\(166\) −1.55424 −0.120633
\(167\) −3.31549 + 4.15749i −0.256560 + 0.321717i −0.893385 0.449292i \(-0.851676\pi\)
0.636824 + 0.771009i \(0.280248\pi\)
\(168\) −14.4919 6.97892i −1.11807 0.538435i
\(169\) −6.53636 28.6377i −0.502797 2.20290i
\(170\) −0.123845 + 0.542601i −0.00949849 + 0.0416156i
\(171\) 10.0166 0.765988
\(172\) 3.73576 + 11.3292i 0.284849 + 0.863841i
\(173\) 3.23540 0.245983 0.122991 0.992408i \(-0.460751\pi\)
0.122991 + 0.992408i \(0.460751\pi\)
\(174\) −1.13488 + 4.97222i −0.0860349 + 0.376943i
\(175\) −3.31831 14.5385i −0.250841 1.09900i
\(176\) 11.2209 + 5.40370i 0.845806 + 0.407319i
\(177\) −6.28649 + 7.88301i −0.472521 + 0.592523i
\(178\) −4.86251 −0.364460
\(179\) 3.48273 0.260311 0.130156 0.991494i \(-0.458452\pi\)
0.130156 + 0.991494i \(0.458452\pi\)
\(180\) 2.62143 3.28717i 0.195390 0.245011i
\(181\) −2.94724 + 1.41932i −0.219067 + 0.105497i −0.540199 0.841537i \(-0.681651\pi\)
0.321132 + 0.947034i \(0.395937\pi\)
\(182\) 7.82990 + 9.81839i 0.580391 + 0.727787i
\(183\) −8.65356 + 4.16734i −0.639690 + 0.308058i
\(184\) 2.31147 10.1272i 0.170404 0.746588i
\(185\) 0.464221 0.582115i 0.0341302 0.0427979i
\(186\) 0.654950 2.86952i 0.0480232 0.210404i
\(187\) −3.80652 1.83312i −0.278360 0.134051i
\(188\) −5.63104 7.06111i −0.410686 0.514984i
\(189\) 7.62161 + 9.55719i 0.554390 + 0.695183i
\(190\) 0.702523 + 3.07795i 0.0509663 + 0.223298i
\(191\) 8.47081 + 4.07933i 0.612926 + 0.295170i 0.714475 0.699661i \(-0.246666\pi\)
−0.101549 + 0.994831i \(0.532380\pi\)
\(192\) 7.83111 3.77126i 0.565161 0.272167i
\(193\) −1.74521 7.64629i −0.125623 0.550392i −0.998093 0.0617240i \(-0.980340\pi\)
0.872470 0.488668i \(-0.162517\pi\)
\(194\) 0.938688 + 4.11266i 0.0673938 + 0.295272i
\(195\) −16.7579 + 8.07019i −1.20006 + 0.577918i
\(196\) 22.2639 + 10.7217i 1.59028 + 0.765838i
\(197\) −1.29824 5.68796i −0.0924958 0.405250i 0.907391 0.420287i \(-0.138071\pi\)
−0.999887 + 0.0150367i \(0.995213\pi\)
\(198\) −1.97789 2.48020i −0.140563 0.176260i
\(199\) 13.2987 + 16.6760i 0.942717 + 1.18213i 0.983123 + 0.182947i \(0.0585636\pi\)
−0.0404056 + 0.999183i \(0.512865\pi\)
\(200\) −4.80930 2.31604i −0.340069 0.163769i
\(201\) −2.60892 + 11.4304i −0.184019 + 0.806240i
\(202\) 4.24785 5.32664i 0.298878 0.374781i
\(203\) 5.54659 24.3012i 0.389295 1.70561i
\(204\) −3.57812 + 1.72313i −0.250518 + 0.120643i
\(205\) −5.33679 6.69212i −0.372737 0.467398i
\(206\) −1.94416 + 0.936256i −0.135456 + 0.0652321i
\(207\) 7.04205 8.83045i 0.489456 0.613758i
\(208\) −19.1889 −1.33051
\(209\) −23.9662 −1.65778
\(210\) 3.43689 4.30972i 0.237168 0.297399i
\(211\) −22.4179 10.7959i −1.54331 0.743220i −0.547689 0.836682i \(-0.684492\pi\)
−0.995623 + 0.0934623i \(0.970207\pi\)
\(212\) 3.86925 + 16.9523i 0.265741 + 1.16429i
\(213\) −1.41400 + 6.19514i −0.0968857 + 0.424484i
\(214\) −2.85052 −0.194857
\(215\) −8.54477 + 0.806616i −0.582748 + 0.0550108i
\(216\) 4.37566 0.297726
\(217\) −3.20100 + 14.0245i −0.217298 + 0.952044i
\(218\) 1.07143 + 4.69425i 0.0725665 + 0.317935i
\(219\) −31.0247 14.9407i −2.09645 1.00960i
\(220\) −6.27216 + 7.86504i −0.422869 + 0.530261i
\(221\) 6.50954 0.437879
\(222\) −0.528064 −0.0354413
\(223\) 2.97164 3.72632i 0.198996 0.249533i −0.672314 0.740266i \(-0.734700\pi\)
0.871310 + 0.490733i \(0.163271\pi\)
\(224\) 18.4003 8.86113i 1.22942 0.592059i
\(225\) −3.61871 4.53772i −0.241247 0.302515i
\(226\) 2.42692 1.16874i 0.161436 0.0777437i
\(227\) −1.99018 + 8.71957i −0.132093 + 0.578738i 0.864948 + 0.501862i \(0.167352\pi\)
−0.997041 + 0.0768757i \(0.975506\pi\)
\(228\) −14.0461 + 17.6132i −0.930224 + 1.16646i
\(229\) 1.46507 6.41887i 0.0968142 0.424171i −0.903173 0.429277i \(-0.858768\pi\)
0.999987 + 0.00510642i \(0.00162543\pi\)
\(230\) 3.20737 + 1.54459i 0.211487 + 0.101847i
\(231\) 26.0901 + 32.7159i 1.71660 + 2.15255i
\(232\) −5.56302 6.97581i −0.365230 0.457984i
\(233\) 4.48627 + 19.6556i 0.293905 + 1.28768i 0.879040 + 0.476748i \(0.158184\pi\)
−0.585135 + 0.810936i \(0.698958\pi\)
\(234\) 4.40367 + 2.12070i 0.287877 + 0.138634i
\(235\) 5.85443 2.81935i 0.381901 0.183914i
\(236\) −1.86965 8.19145i −0.121704 0.533218i
\(237\) 7.45470 + 32.6612i 0.484235 + 2.12157i
\(238\) −1.73815 + 0.837047i −0.112667 + 0.0542577i
\(239\) 12.6145 + 6.07484i 0.815966 + 0.392949i 0.794833 0.606828i \(-0.207558\pi\)
0.0211331 + 0.999777i \(0.493273\pi\)
\(240\) 1.87426 + 8.21168i 0.120983 + 0.530062i
\(241\) 13.2639 + 16.6324i 0.854402 + 1.07139i 0.996669 + 0.0815580i \(0.0259896\pi\)
−0.142266 + 0.989828i \(0.545439\pi\)
\(242\) 1.81606 + 2.27727i 0.116741 + 0.146388i
\(243\) 14.7058 + 7.08194i 0.943377 + 0.454307i
\(244\) 1.78101 7.80310i 0.114017 0.499542i
\(245\) −11.0850 + 13.9002i −0.708196 + 0.888049i
\(246\) −1.35087 + 5.91853i −0.0861281 + 0.377352i
\(247\) 33.2691 16.0216i 2.11686 1.01943i
\(248\) 3.21048 + 4.02581i 0.203866 + 0.255639i
\(249\) 7.18920 3.46214i 0.455597 0.219404i
\(250\) 2.87561 3.60590i 0.181869 0.228057i
\(251\) 20.4144 1.28854 0.644272 0.764796i \(-0.277160\pi\)
0.644272 + 0.764796i \(0.277160\pi\)
\(252\) 14.5739 0.918071
\(253\) −16.8491 + 21.1282i −1.05930 + 1.32832i
\(254\) 5.03626 + 2.42534i 0.316003 + 0.152179i
\(255\) −0.635815 2.78569i −0.0398163 0.174447i
\(256\) −0.759868 + 3.32920i −0.0474918 + 0.208075i
\(257\) −29.2807 −1.82648 −0.913240 0.407423i \(-0.866428\pi\)
−0.913240 + 0.407423i \(0.866428\pi\)
\(258\) 4.22578 + 4.38141i 0.263086 + 0.272775i
\(259\) 2.58086 0.160367
\(260\) 3.44898 15.1110i 0.213897 0.937143i
\(261\) −2.15876 9.45815i −0.133624 0.585445i
\(262\) −0.571504 0.275222i −0.0353076 0.0170033i
\(263\) 1.44614 1.81340i 0.0891727 0.111819i −0.735244 0.677803i \(-0.762932\pi\)
0.824416 + 0.565984i \(0.191504\pi\)
\(264\) 14.9786 0.921871
\(265\) −12.5104 −0.768508
\(266\) −6.82318 + 8.55600i −0.418356 + 0.524602i
\(267\) 22.4917 10.8314i 1.37647 0.662872i
\(268\) −6.09157 7.63858i −0.372102 0.466601i
\(269\) 22.1904 10.6863i 1.35297 0.651556i 0.389913 0.920852i \(-0.372505\pi\)
0.963058 + 0.269296i \(0.0867909\pi\)
\(270\) −0.333684 + 1.46197i −0.0203074 + 0.0889724i
\(271\) −7.75813 + 9.72839i −0.471273 + 0.590958i −0.959482 0.281769i \(-0.909079\pi\)
0.488209 + 0.872727i \(0.337650\pi\)
\(272\) 0.655950 2.87390i 0.0397728 0.174256i
\(273\) −58.0883 27.9738i −3.51566 1.69305i
\(274\) 3.05749 + 3.83397i 0.184710 + 0.231619i
\(275\) 8.65830 + 10.8572i 0.522115 + 0.654712i
\(276\) 5.65257 + 24.7655i 0.340245 + 1.49071i
\(277\) −4.09838 1.97368i −0.246248 0.118587i 0.306689 0.951810i \(-0.400779\pi\)
−0.552937 + 0.833223i \(0.686493\pi\)
\(278\) −0.316304 + 0.152324i −0.0189707 + 0.00913579i
\(279\) 1.24584 + 5.45840i 0.0745867 + 0.326786i
\(280\) 2.14591 + 9.40182i 0.128242 + 0.561866i
\(281\) −1.55713 + 0.749876i −0.0928908 + 0.0447338i −0.479752 0.877404i \(-0.659273\pi\)
0.386861 + 0.922138i \(0.373559\pi\)
\(282\) −4.15217 1.99958i −0.247258 0.119073i
\(283\) 5.22187 + 22.8785i 0.310408 + 1.35999i 0.853842 + 0.520533i \(0.174267\pi\)
−0.543434 + 0.839452i \(0.682876\pi\)
\(284\) −3.30155 4.14001i −0.195911 0.245664i
\(285\) −10.1058 12.6723i −0.598615 0.750640i
\(286\) −10.5364 5.07409i −0.623033 0.300037i
\(287\) 6.60221 28.9262i 0.389716 1.70746i
\(288\) 4.95591 6.21452i 0.292030 0.366194i
\(289\) −0.222521 + 0.974928i −0.0130895 + 0.0573487i
\(290\) 2.75495 1.32671i 0.161776 0.0779072i
\(291\) −13.5030 16.9323i −0.791561 0.992587i
\(292\) 25.8533 12.4503i 1.51295 0.728599i
\(293\) −12.2020 + 15.3009i −0.712851 + 0.893887i −0.997910 0.0646231i \(-0.979415\pi\)
0.285059 + 0.958510i \(0.407987\pi\)
\(294\) 12.6095 0.735401
\(295\) 6.04510 0.351960
\(296\) 0.575996 0.722276i 0.0334791 0.0419814i
\(297\) −10.2562 4.93910i −0.595122 0.286596i
\(298\) −1.10866 4.85734i −0.0642227 0.281378i
\(299\) 9.26514 40.5932i 0.535817 2.34757i
\(300\) 13.0536 0.753649
\(301\) −20.6530 21.4137i −1.19042 1.23426i
\(302\) −1.76527 −0.101580
\(303\) −7.78327 + 34.1008i −0.447137 + 1.95904i
\(304\) −3.72093 16.3025i −0.213410 0.935010i
\(305\) 5.18824 + 2.49852i 0.297078 + 0.143065i
\(306\) −0.468149 + 0.587040i −0.0267623 + 0.0335589i
\(307\) 4.71301 0.268986 0.134493 0.990915i \(-0.457059\pi\)
0.134493 + 0.990915i \(0.457059\pi\)
\(308\) −34.8703 −1.98692
\(309\) 6.90721 8.66136i 0.392937 0.492728i
\(310\) −1.58991 + 0.765659i −0.0903007 + 0.0434865i
\(311\) −12.4413 15.6009i −0.705483 0.884648i 0.291937 0.956438i \(-0.405700\pi\)
−0.997420 + 0.0717896i \(0.977129\pi\)
\(312\) −20.7929 + 10.0133i −1.17716 + 0.566893i
\(313\) −4.50855 + 19.7532i −0.254838 + 1.11652i 0.671850 + 0.740688i \(0.265500\pi\)
−0.926688 + 0.375832i \(0.877357\pi\)
\(314\) 3.24527 4.06944i 0.183141 0.229652i
\(315\) −2.33326 + 10.2227i −0.131464 + 0.575982i
\(316\) −25.1524 12.1127i −1.41493 0.681394i
\(317\) 3.06472 + 3.84304i 0.172132 + 0.215847i 0.860413 0.509598i \(-0.170206\pi\)
−0.688281 + 0.725444i \(0.741634\pi\)
\(318\) 5.53212 + 6.93706i 0.310226 + 0.389011i
\(319\) 5.16516 + 22.6300i 0.289193 + 1.26704i
\(320\) −4.69513 2.26106i −0.262466 0.126397i
\(321\) 13.1851 6.34963i 0.735923 0.354402i
\(322\) 2.74586 + 12.0304i 0.153021 + 0.670427i
\(323\) 1.26227 + 5.53036i 0.0702345 + 0.307718i
\(324\) −18.3233 + 8.82404i −1.01796 + 0.490224i
\(325\) −19.2773 9.28345i −1.06931 0.514953i
\(326\) 1.39531 + 6.11327i 0.0772793 + 0.338583i
\(327\) −15.4126 19.3267i −0.852316 1.06877i
\(328\) −6.62177 8.30344i −0.365626 0.458481i
\(329\) 20.2933 + 9.77274i 1.11881 + 0.538789i
\(330\) −1.14226 + 5.00456i −0.0628793 + 0.275492i
\(331\) −8.12772 + 10.1918i −0.446740 + 0.560194i −0.953306 0.302007i \(-0.902343\pi\)
0.506566 + 0.862201i \(0.330915\pi\)
\(332\) −1.47962 + 6.48266i −0.0812049 + 0.355782i
\(333\) 0.905007 0.435828i 0.0495941 0.0238832i
\(334\) −1.40982 1.76786i −0.0771419 0.0967329i
\(335\) 6.33322 3.04992i 0.346021 0.166635i
\(336\) −18.2036 + 22.8266i −0.993087 + 1.24529i
\(337\) −19.9122 −1.08469 −0.542343 0.840157i \(-0.682463\pi\)
−0.542343 + 0.840157i \(0.682463\pi\)
\(338\) 12.4905 0.679396
\(339\) −8.62238 + 10.8121i −0.468303 + 0.587234i
\(340\) 2.14526 + 1.03310i 0.116343 + 0.0560278i
\(341\) −2.98087 13.0600i −0.161423 0.707240i
\(342\) −0.947779 + 4.15249i −0.0512500 + 0.224541i
\(343\) −29.8692 −1.61278
\(344\) −10.6022 + 1.00083i −0.571630 + 0.0539612i
\(345\) −18.2764 −0.983967
\(346\) −0.306136 + 1.34127i −0.0164580 + 0.0721071i
\(347\) 0.138383 + 0.606295i 0.00742879 + 0.0325476i 0.978506 0.206216i \(-0.0661150\pi\)
−0.971078 + 0.238764i \(0.923258\pi\)
\(348\) 19.6585 + 9.46701i 1.05380 + 0.507485i
\(349\) 0.504708 0.632884i 0.0270164 0.0338775i −0.768140 0.640282i \(-0.778817\pi\)
0.795156 + 0.606405i \(0.207389\pi\)
\(350\) 6.34106 0.338944
\(351\) 17.5391 0.936167
\(352\) −11.8578 + 14.8692i −0.632021 + 0.792529i
\(353\) −4.96713 + 2.39204i −0.264374 + 0.127316i −0.561375 0.827561i \(-0.689728\pi\)
0.297002 + 0.954877i \(0.404013\pi\)
\(354\) −2.67315 3.35203i −0.142077 0.178158i
\(355\) 3.43252 1.65302i 0.182179 0.0877330i
\(356\) −4.62906 + 20.2812i −0.245340 + 1.07490i
\(357\) 6.17529 7.74357i 0.326831 0.409833i
\(358\) −0.329539 + 1.44380i −0.0174167 + 0.0763073i
\(359\) −16.7848 8.08311i −0.885865 0.426610i −0.0651020 0.997879i \(-0.520737\pi\)
−0.820763 + 0.571268i \(0.806452\pi\)
\(360\) 2.34017 + 2.93448i 0.123338 + 0.154661i
\(361\) 8.21650 + 10.3032i 0.432447 + 0.542272i
\(362\) −0.309523 1.35611i −0.0162682 0.0712755i
\(363\) −13.4729 6.48822i −0.707145 0.340543i
\(364\) 48.4059 23.3110i 2.53716 1.22183i
\(365\) 4.59402 + 20.1277i 0.240462 + 1.05353i
\(366\) −0.908807 3.98175i −0.0475041 0.208129i
\(367\) −9.25592 + 4.45742i −0.483155 + 0.232675i −0.659574 0.751640i \(-0.729263\pi\)
0.176418 + 0.984315i \(0.443549\pi\)
\(368\) −16.9879 8.18094i −0.885556 0.426461i
\(369\) −2.56961 11.2582i −0.133769 0.586079i
\(370\) 0.197397 + 0.247528i 0.0102622 + 0.0128684i
\(371\) −27.0377 33.9041i −1.40372 1.76022i
\(372\) −11.3451 5.46351i −0.588216 0.283270i
\(373\) 2.40388 10.5321i 0.124468 0.545332i −0.873788 0.486307i \(-0.838344\pi\)
0.998257 0.0590249i \(-0.0187991\pi\)
\(374\) 1.12012 1.40458i 0.0579199 0.0726292i
\(375\) −5.26893 + 23.0847i −0.272086 + 1.19209i
\(376\) 7.26405 3.49818i 0.374615 0.180405i
\(377\) −22.2985 27.9614i −1.14843 1.44008i
\(378\) −4.68320 + 2.25531i −0.240878 + 0.116001i
\(379\) 6.60677 8.28462i 0.339367 0.425553i −0.582637 0.812732i \(-0.697979\pi\)
0.922004 + 0.387180i \(0.126551\pi\)
\(380\) 13.5067 0.692881
\(381\) −28.6979 −1.47024
\(382\) −2.49264 + 3.12568i −0.127535 + 0.159924i
\(383\) 29.4834 + 14.1984i 1.50653 + 0.725507i 0.991309 0.131551i \(-0.0419957\pi\)
0.515221 + 0.857058i \(0.327710\pi\)
\(384\) 5.19588 + 22.7646i 0.265151 + 1.16170i
\(385\) 5.58267 24.4593i 0.284519 1.24656i
\(386\) 3.33499 0.169746
\(387\) −10.8584 4.02128i −0.551961 0.204413i
\(388\) 18.0473 0.916211
\(389\) −6.01546 + 26.3554i −0.304996 + 1.33627i 0.557487 + 0.830186i \(0.311766\pi\)
−0.862482 + 0.506087i \(0.831091\pi\)
\(390\) −1.75994 7.71079i −0.0891179 0.390451i
\(391\) 5.76289 + 2.77526i 0.291442 + 0.140351i
\(392\) −13.7540 + 17.2470i −0.694684 + 0.871107i
\(393\) 3.25657 0.164272
\(394\) 2.48085 0.124983
\(395\) 12.5231 15.7035i 0.630108 0.790130i
\(396\) −12.2277 + 5.88854i −0.614464 + 0.295910i
\(397\) 16.9005 + 21.1926i 0.848213 + 1.06363i 0.997200 + 0.0747865i \(0.0238275\pi\)
−0.148986 + 0.988839i \(0.547601\pi\)
\(398\) −8.17155 + 3.93521i −0.409603 + 0.197254i
\(399\) 12.5020 54.7749i 0.625884 2.74218i
\(400\) −6.04108 + 7.57527i −0.302054 + 0.378763i
\(401\) −5.99579 + 26.2693i −0.299416 + 1.31183i 0.571585 + 0.820543i \(0.306329\pi\)
−0.871000 + 0.491282i \(0.836528\pi\)
\(402\) −4.49175 2.16311i −0.224028 0.107886i
\(403\) 12.8687 + 16.1368i 0.641034 + 0.803831i
\(404\) −18.1732 22.7884i −0.904149 1.13377i
\(405\) −3.25597 14.2653i −0.161790 0.708850i
\(406\) 9.54951 + 4.59880i 0.473934 + 0.228235i
\(407\) −2.16536 + 1.04278i −0.107333 + 0.0516889i
\(408\) −0.788906 3.45642i −0.0390566 0.171118i
\(409\) 1.26937 + 5.56147i 0.0627663 + 0.274997i 0.996566 0.0827982i \(-0.0263857\pi\)
−0.933800 + 0.357795i \(0.883529\pi\)
\(410\) 3.27926 1.57921i 0.161951 0.0779916i
\(411\) −22.6828 10.9235i −1.11886 0.538815i
\(412\) 2.05425 + 9.00026i 0.101206 + 0.443411i
\(413\) 13.0648 + 16.3827i 0.642875 + 0.806139i
\(414\) 2.99443 + 3.75490i 0.147168 + 0.184543i
\(415\) −4.31028 2.07572i −0.211583 0.101893i
\(416\) 6.52044 28.5679i 0.319691 1.40066i
\(417\) 1.12377 1.40916i 0.0550311 0.0690068i
\(418\) 2.26770 9.93545i 0.110917 0.485959i
\(419\) −8.16548 + 3.93229i −0.398910 + 0.192105i −0.622573 0.782562i \(-0.713913\pi\)
0.223663 + 0.974666i \(0.428198\pi\)
\(420\) −14.7037 18.4379i −0.717468 0.899676i
\(421\) 21.6479 10.4251i 1.05505 0.508087i 0.175793 0.984427i \(-0.443751\pi\)
0.879261 + 0.476340i \(0.158037\pi\)
\(422\) 6.59675 8.27207i 0.321125 0.402678i
\(423\) 8.76640 0.426237
\(424\) −15.5226 −0.753846
\(425\) 2.04934 2.56980i 0.0994078 0.124653i
\(426\) −2.43447 1.17238i −0.117950 0.0568019i
\(427\) 4.44170 + 19.4604i 0.214949 + 0.941752i
\(428\) −2.71366 + 11.8893i −0.131170 + 0.574692i
\(429\) 60.0394 2.89873
\(430\) 0.474121 3.61865i 0.0228642 0.174507i
\(431\) −36.6108 −1.76348 −0.881741 0.471734i \(-0.843628\pi\)
−0.881741 + 0.471734i \(0.843628\pi\)
\(432\) 1.76737 7.74335i 0.0850325 0.372552i
\(433\) 1.76824 + 7.74718i 0.0849764 + 0.372306i 0.999479 0.0322740i \(-0.0102749\pi\)
−0.914503 + 0.404580i \(0.867418\pi\)
\(434\) −5.51112 2.65402i −0.264542 0.127397i
\(435\) −9.78778 + 12.2735i −0.469288 + 0.588469i
\(436\) 20.5994 0.986534
\(437\) 36.2837 1.73568
\(438\) 9.12940 11.4479i 0.436220 0.547002i
\(439\) −28.0284 + 13.4978i −1.33772 + 0.644214i −0.959555 0.281522i \(-0.909161\pi\)
−0.378169 + 0.925736i \(0.623446\pi\)
\(440\) −5.59921 7.02118i −0.266932 0.334722i
\(441\) −21.6104 + 10.4070i −1.02907 + 0.495573i
\(442\) −0.615938 + 2.69860i −0.0292972 + 0.128359i
\(443\) −13.0463 + 16.3595i −0.619847 + 0.777264i −0.988323 0.152373i \(-0.951308\pi\)
0.368476 + 0.929637i \(0.379880\pi\)
\(444\) −0.502711 + 2.20252i −0.0238576 + 0.104527i
\(445\) −13.4849 6.49397i −0.639244 0.307844i
\(446\) 1.26361 + 1.58451i 0.0598336 + 0.0750289i
\(447\) 15.9480 + 19.9982i 0.754315 + 0.945882i
\(448\) −4.01955 17.6108i −0.189906 0.832032i
\(449\) −2.31852 1.11654i −0.109418 0.0526927i 0.378374 0.925653i \(-0.376483\pi\)
−0.487792 + 0.872960i \(0.662198\pi\)
\(450\) 2.22357 1.07081i 0.104820 0.0504786i
\(451\) 6.14819 + 26.9370i 0.289507 + 1.26841i
\(452\) −2.56436 11.2352i −0.120617 0.528458i
\(453\) 8.16531 3.93220i 0.383640 0.184751i
\(454\) −3.42648 1.65011i −0.160813 0.0774433i
\(455\) 8.60150 + 37.6856i 0.403245 + 1.76673i
\(456\) −12.5390 15.7235i −0.587195 0.736319i
\(457\) 12.8905 + 16.1641i 0.602991 + 0.756126i 0.985841 0.167684i \(-0.0536289\pi\)
−0.382850 + 0.923810i \(0.625057\pi\)
\(458\) 2.52239 + 1.21472i 0.117863 + 0.0567600i
\(459\) −0.599553 + 2.62681i −0.0279847 + 0.122609i
\(460\) 9.49575 11.9073i 0.442742 0.555181i
\(461\) −1.79150 + 7.84906i −0.0834383 + 0.365567i −0.999359 0.0357916i \(-0.988605\pi\)
0.915921 + 0.401359i \(0.131462\pi\)
\(462\) −16.0314 + 7.72032i −0.745849 + 0.359182i
\(463\) 9.67112 + 12.1272i 0.449455 + 0.563599i 0.954008 0.299782i \(-0.0969140\pi\)
−0.504553 + 0.863381i \(0.668343\pi\)
\(464\) −14.5916 + 7.02697i −0.677400 + 0.326219i
\(465\) 5.64863 7.08316i 0.261949 0.328473i
\(466\) −8.57295 −0.397134
\(467\) 3.97642 0.184007 0.0920035 0.995759i \(-0.470673\pi\)
0.0920035 + 0.995759i \(0.470673\pi\)
\(468\) 13.0376 16.3486i 0.602661 0.755713i
\(469\) 21.9529 + 10.5720i 1.01369 + 0.488169i
\(470\) 0.614839 + 2.69379i 0.0283604 + 0.124255i
\(471\) −5.94625 + 26.0522i −0.273989 + 1.20042i
\(472\) 7.50064 0.345245
\(473\) 25.9802 + 9.62152i 1.19457 + 0.442398i
\(474\) −14.2454 −0.654313
\(475\) 4.14894 18.1777i 0.190367 0.834050i
\(476\) 1.83657 + 8.04656i 0.0841793 + 0.368813i
\(477\) −15.2065 7.32304i −0.696256 0.335299i
\(478\) −3.71199 + 4.65469i −0.169782 + 0.212900i
\(479\) 42.3918 1.93693 0.968466 0.249146i \(-0.0801499\pi\)
0.968466 + 0.249146i \(0.0801499\pi\)
\(480\) −12.8622 −0.587076
\(481\) 2.30878 2.89512i 0.105271 0.132006i
\(482\) −8.15018 + 3.92492i −0.371230 + 0.178775i
\(483\) −39.4992 49.5304i −1.79727 2.25371i
\(484\) 11.2272 5.40674i 0.510328 0.245761i
\(485\) −2.88933 + 12.6590i −0.131198 + 0.574815i
\(486\) −4.32737 + 5.42635i −0.196294 + 0.246144i
\(487\) 5.04756 22.1148i 0.228727 1.00212i −0.721953 0.691942i \(-0.756755\pi\)
0.950679 0.310175i \(-0.100388\pi\)
\(488\) 6.43745 + 3.10011i 0.291410 + 0.140336i
\(489\) −20.0716 25.1690i −0.907669 1.13818i
\(490\) −4.71359 5.91066i −0.212938 0.267016i
\(491\) 7.21760 + 31.6224i 0.325726 + 1.42710i 0.827192 + 0.561920i \(0.189937\pi\)
−0.501466 + 0.865177i \(0.667206\pi\)
\(492\) 23.3998 + 11.2688i 1.05495 + 0.508035i
\(493\) 4.94999 2.38379i 0.222937 0.107361i
\(494\) 3.49396 + 15.3081i 0.157201 + 0.688742i
\(495\) −2.17280 9.51967i −0.0976602 0.427877i
\(496\) 8.42099 4.05533i 0.378114 0.182090i
\(497\) 11.8982 + 5.72988i 0.533708 + 0.257020i
\(498\) 0.755019 + 3.30795i 0.0338332 + 0.148233i
\(499\) 9.64076 + 12.0891i 0.431580 + 0.541184i 0.949302 0.314365i \(-0.101792\pi\)
−0.517723 + 0.855549i \(0.673220\pi\)
\(500\) −12.3024 15.4267i −0.550181 0.689905i
\(501\) 10.4591 + 5.03685i 0.467280 + 0.225030i
\(502\) −1.93163 + 8.46301i −0.0862127 + 0.377722i
\(503\) −19.6527 + 24.6437i −0.876269 + 1.09881i 0.118118 + 0.993000i \(0.462314\pi\)
−0.994387 + 0.105807i \(0.966257\pi\)
\(504\) −2.89506 + 12.6841i −0.128956 + 0.564994i
\(505\) 18.8941 9.09892i 0.840776 0.404897i
\(506\) −7.16463 8.98416i −0.318507 0.399395i
\(507\) −57.7754 + 27.8231i −2.56589 + 1.23567i
\(508\) 14.9104 18.6970i 0.661542 0.829547i
\(509\) 33.6803 1.49285 0.746427 0.665467i \(-0.231768\pi\)
0.746427 + 0.665467i \(0.231768\pi\)
\(510\) 1.21500 0.0538010
\(511\) −44.6190 + 55.9504i −1.97383 + 2.47510i
\(512\) −20.5817 9.91164i −0.909593 0.438037i
\(513\) 3.40102 + 14.9008i 0.150158 + 0.657887i
\(514\) 2.77056 12.1386i 0.122204 0.535412i
\(515\) −6.64199 −0.292681
\(516\) 22.2975 13.4544i 0.981593 0.592297i
\(517\) −20.9749 −0.922476
\(518\) −0.244203 + 1.06992i −0.0107296 + 0.0470097i
\(519\) −1.57169 6.88601i −0.0689894 0.302262i
\(520\) 12.4664 + 6.00348i 0.546686 + 0.263270i
\(521\) −22.1552 + 27.7817i −0.970637 + 1.21714i 0.00550036 + 0.999985i \(0.498249\pi\)
−0.976137 + 0.217155i \(0.930322\pi\)
\(522\) 4.12525 0.180557
\(523\) −19.1893 −0.839090 −0.419545 0.907735i \(-0.637810\pi\)
−0.419545 + 0.907735i \(0.637810\pi\)
\(524\) −1.69200 + 2.12170i −0.0739153 + 0.0926868i
\(525\) −29.3307 + 14.1249i −1.28010 + 0.616463i
\(526\) 0.614930 + 0.771097i 0.0268122 + 0.0336214i
\(527\) −2.85669 + 1.37571i −0.124439 + 0.0599269i
\(528\) 6.05001 26.5068i 0.263293 1.15356i
\(529\) 11.1685 14.0049i 0.485589 0.608909i
\(530\) 1.18375 5.18633i 0.0514186 0.225280i
\(531\) 7.34785 + 3.53854i 0.318869 + 0.153559i
\(532\) 29.1909 + 36.6043i 1.26559 + 1.58700i
\(533\) −26.5423 33.2829i −1.14967 1.44164i
\(534\) 2.36210 + 10.3490i 0.102218 + 0.447847i
\(535\) −7.90514 3.80692i −0.341769 0.164587i
\(536\) 7.85813 3.78427i 0.339419 0.163456i
\(537\) −1.69183 7.41241i −0.0730080 0.319869i
\(538\) 2.33046 + 10.2104i 0.100473 + 0.440202i
\(539\) 51.7062 24.9004i 2.22714 1.07254i
\(540\) 5.78011 + 2.78355i 0.248736 + 0.119785i
\(541\) −0.609055 2.66844i −0.0261853 0.114725i 0.960146 0.279498i \(-0.0901681\pi\)
−0.986332 + 0.164773i \(0.947311\pi\)
\(542\) −3.29893 4.13673i −0.141701 0.177688i
\(543\) 4.45249 + 5.58324i 0.191075 + 0.239600i
\(544\) 4.05569 + 1.95312i 0.173886 + 0.0837393i
\(545\) −3.29793 + 14.4492i −0.141268 + 0.618934i
\(546\) 17.0932 21.4342i 0.731522 0.917300i
\(547\) −0.765978 + 3.35597i −0.0327508 + 0.143491i −0.988660 0.150172i \(-0.952017\pi\)
0.955909 + 0.293663i \(0.0948743\pi\)
\(548\) 18.9020 9.10271i 0.807452 0.388848i
\(549\) 4.84380 + 6.07393i 0.206728 + 0.259229i
\(550\) −5.32021 + 2.56208i −0.226855 + 0.109247i
\(551\) 19.4315 24.3663i 0.827808 1.03804i
\(552\) −22.6769 −0.965195
\(553\) 69.6229 2.96067
\(554\) 1.20600 1.51228i 0.0512381 0.0642505i
\(555\) −1.46444 0.705239i −0.0621622 0.0299357i
\(556\) 0.334216 + 1.46430i 0.0141739 + 0.0621000i
\(557\) 3.19054 13.9787i 0.135188 0.592296i −0.861266 0.508154i \(-0.830328\pi\)
0.996454 0.0841418i \(-0.0268149\pi\)
\(558\) −2.38072 −0.100784
\(559\) −42.4970 + 4.01167i −1.79743 + 0.169675i
\(560\) 17.5046 0.739705
\(561\) −2.05237 + 8.99203i −0.0866513 + 0.379644i
\(562\) −0.163532 0.716481i −0.00689818 0.0302229i
\(563\) 38.1842 + 18.3885i 1.60927 + 0.774984i 0.999841 0.0178563i \(-0.00568414\pi\)
0.609430 + 0.792840i \(0.291398\pi\)
\(564\) −12.2930 + 15.4149i −0.517627 + 0.649084i
\(565\) 8.29130 0.348818
\(566\) −9.97863 −0.419433
\(567\) 31.6233 39.6543i 1.32805 1.66532i
\(568\) 4.25900 2.05103i 0.178704 0.0860592i
\(569\) 22.3170 + 27.9847i 0.935579 + 1.17318i 0.984678 + 0.174385i \(0.0557936\pi\)
−0.0490988 + 0.998794i \(0.515635\pi\)
\(570\) 6.20964 2.99041i 0.260093 0.125254i
\(571\) −4.68207 + 20.5135i −0.195938 + 0.858462i 0.777385 + 0.629025i \(0.216546\pi\)
−0.973323 + 0.229437i \(0.926311\pi\)
\(572\) −31.1943 + 39.1164i −1.30430 + 1.63554i
\(573\) 4.56723 20.0104i 0.190799 0.835945i
\(574\) 11.3670 + 5.47404i 0.474448 + 0.228482i
\(575\) −13.1083 16.4372i −0.546652 0.685480i
\(576\) −4.38343 5.49665i −0.182643 0.229027i
\(577\) −7.64290 33.4857i −0.318178 1.39403i −0.840745 0.541431i \(-0.817883\pi\)
0.522567 0.852598i \(-0.324974\pi\)
\(578\) −0.383112 0.184497i −0.0159354 0.00767406i
\(579\) −15.4261 + 7.42880i −0.641086 + 0.308731i
\(580\) −2.91095 12.7537i −0.120871 0.529569i
\(581\) −3.69007 16.1673i −0.153090 0.670731i
\(582\) 8.29712 3.99568i 0.343927 0.165626i
\(583\) 36.3837 + 17.5215i 1.50686 + 0.725665i
\(584\) 5.70016 + 24.9740i 0.235874 + 1.03343i
\(585\) 9.38018 + 11.7624i 0.387823 + 0.486314i
\(586\) −5.18858 6.50627i −0.214338 0.268772i
\(587\) −20.1574 9.70730i −0.831986 0.400663i −0.0311261 0.999515i \(-0.509909\pi\)
−0.800859 + 0.598852i \(0.795624\pi\)
\(588\) 12.0041 52.5934i 0.495041 2.16892i
\(589\) −11.2141 + 14.0620i −0.462069 + 0.579416i
\(590\) −0.571993 + 2.50606i −0.0235486 + 0.103173i
\(591\) −11.4752 + 5.52618i −0.472028 + 0.227317i
\(592\) −1.04552 1.31104i −0.0429706 0.0538834i
\(593\) −23.0170 + 11.0844i −0.945195 + 0.455182i −0.841999 0.539479i \(-0.818621\pi\)
−0.103196 + 0.994661i \(0.532907\pi\)
\(594\) 3.01800 3.78446i 0.123830 0.155278i
\(595\) −5.93817 −0.243441
\(596\) −21.3151 −0.873100
\(597\) 29.0319 36.4048i 1.18820 1.48995i
\(598\) 15.9517 + 7.68193i 0.652313 + 0.314137i
\(599\) 0.927707 + 4.06455i 0.0379051 + 0.166073i 0.990338 0.138676i \(-0.0442846\pi\)
−0.952433 + 0.304749i \(0.901427\pi\)
\(600\) −2.59305 + 11.3609i −0.105861 + 0.463806i
\(601\) 10.4772 0.427373 0.213686 0.976902i \(-0.431453\pi\)
0.213686 + 0.976902i \(0.431453\pi\)
\(602\) 10.8315 6.53577i 0.441458 0.266378i
\(603\) 9.48334 0.386192
\(604\) −1.68052 + 7.36283i −0.0683793 + 0.299589i
\(605\) 1.99502 + 8.74077i 0.0811093 + 0.355363i
\(606\) −13.4004 6.45328i −0.544353 0.262147i
\(607\) −9.04864 + 11.3466i −0.367273 + 0.460546i −0.930788 0.365560i \(-0.880877\pi\)
0.563515 + 0.826106i \(0.309449\pi\)
\(608\) 25.5350 1.03558
\(609\) −54.4155 −2.20503
\(610\) −1.52671 + 1.91443i −0.0618145 + 0.0775129i
\(611\) 29.1167 14.0219i 1.17794 0.567265i
\(612\) 2.00284 + 2.51148i 0.0809599 + 0.101520i
\(613\) 22.0504 10.6189i 0.890606 0.428893i 0.0681193 0.997677i \(-0.478300\pi\)
0.822487 + 0.568784i \(0.192586\pi\)
\(614\) −0.445949 + 1.95383i −0.0179970 + 0.0788501i
\(615\) −11.6506 + 14.6094i −0.469796 + 0.589106i
\(616\) 6.92686 30.3485i 0.279091 1.22278i
\(617\) −21.2721 10.2441i −0.856382 0.412412i −0.0464396 0.998921i \(-0.514788\pi\)
−0.809943 + 0.586509i \(0.800502\pi\)
\(618\) 2.93710 + 3.68300i 0.118147 + 0.148152i
\(619\) −12.3644 15.5045i −0.496967 0.623177i 0.468575 0.883424i \(-0.344767\pi\)
−0.965542 + 0.260247i \(0.916196\pi\)
\(620\) 1.67994 + 7.36031i 0.0674681 + 0.295597i
\(621\) 15.5273 + 7.47757i 0.623090 + 0.300064i
\(622\) 7.64475 3.68152i 0.306527 0.147615i
\(623\) −11.5445 50.5798i −0.462521 2.02644i
\(624\) 9.32156 + 40.8404i 0.373161 + 1.63492i
\(625\) −2.01647 + 0.971082i −0.0806589 + 0.0388433i
\(626\) −7.76232 3.73814i −0.310245 0.149406i
\(627\) 11.6423 + 51.0081i 0.464947 + 2.03707i
\(628\) −13.8839 17.4099i −0.554028 0.694729i
\(629\) 0.354677 + 0.444750i 0.0141419 + 0.0177334i
\(630\) −4.01715 1.93456i −0.160047 0.0770745i
\(631\) −4.98776 + 21.8528i −0.198560 + 0.869947i 0.773235 + 0.634119i \(0.218637\pi\)
−0.971795 + 0.235828i \(0.924220\pi\)
\(632\) 15.5385 19.4846i 0.618086 0.775056i
\(633\) −12.0871 + 52.9572i −0.480421 + 2.10486i
\(634\) −1.88316 + 0.906883i −0.0747899 + 0.0360169i
\(635\) 10.7276 + 13.4520i 0.425714 + 0.533828i
\(636\) 34.2006 16.4701i 1.35614 0.653083i
\(637\) −55.1308 + 69.1319i −2.18436 + 2.73910i
\(638\) −9.87026 −0.390768
\(639\) 5.13985 0.203329
\(640\) 8.72855 10.9453i 0.345026 0.432649i
\(641\) −27.8199 13.3974i −1.09882 0.529164i −0.205533 0.978650i \(-0.565893\pi\)
−0.893287 + 0.449486i \(0.851607\pi\)
\(642\) 1.38472 + 6.06685i 0.0546505 + 0.239439i
\(643\) 3.07034 13.4520i 0.121082 0.530496i −0.877610 0.479375i \(-0.840863\pi\)
0.998692 0.0511211i \(-0.0162795\pi\)
\(644\) 52.7920 2.08030
\(645\) 5.86761 + 17.7943i 0.231037 + 0.700649i
\(646\) −2.41211 −0.0949032
\(647\) −0.610407 + 2.67437i −0.0239976 + 0.105140i −0.985508 0.169627i \(-0.945744\pi\)
0.961511 + 0.274767i \(0.0886008\pi\)
\(648\) −4.03993 17.7001i −0.158704 0.695326i
\(649\) −17.5808 8.46648i −0.690108 0.332338i
\(650\) 5.67259 7.11320i 0.222497 0.279003i
\(651\) 31.4038 1.23081
\(652\) 26.8264 1.05060
\(653\) 1.82139 2.28395i 0.0712764 0.0893778i −0.744915 0.667159i \(-0.767510\pi\)
0.816191 + 0.577782i \(0.196081\pi\)
\(654\) 9.47046 4.56073i 0.370324 0.178339i
\(655\) −1.21735 1.52651i −0.0475658 0.0596456i
\(656\) −17.3687 + 8.36433i −0.678134 + 0.326572i
\(657\) −6.19783 + 27.1545i −0.241800 + 1.05940i
\(658\) −5.97157 + 7.48811i −0.232796 + 0.291917i
\(659\) 1.93259 8.46721i 0.0752829 0.329836i −0.923237 0.384232i \(-0.874466\pi\)
0.998519 + 0.0543963i \(0.0173234\pi\)
\(660\) 19.7863 + 9.52858i 0.770181 + 0.370900i
\(661\) −17.8521 22.3858i −0.694367 0.870708i 0.302222 0.953238i \(-0.402272\pi\)
−0.996589 + 0.0825295i \(0.973700\pi\)
\(662\) −3.45609 4.33380i −0.134325 0.168438i
\(663\) −3.16220 13.8545i −0.122810 0.538064i
\(664\) −5.34810 2.57551i −0.207547 0.0999492i
\(665\) −30.3490 + 14.6153i −1.17688 + 0.566757i
\(666\) 0.0950449 + 0.416419i 0.00368292 + 0.0161359i
\(667\) −7.81981 34.2608i −0.302784 1.32658i
\(668\) −8.71576 + 4.19729i −0.337223 + 0.162398i
\(669\) −9.37442 4.51448i −0.362436 0.174540i
\(670\) 0.665122 + 2.91409i 0.0256959 + 0.112581i
\(671\) −11.5895 14.5328i −0.447408 0.561032i
\(672\) −27.7979 34.8575i −1.07233 1.34466i
\(673\) −23.9768 11.5466i −0.924237 0.445089i −0.0896553 0.995973i \(-0.528577\pi\)
−0.834582 + 0.550884i \(0.814291\pi\)
\(674\) 1.88411 8.25482i 0.0725731 0.317964i
\(675\) 5.52168 6.92397i 0.212530 0.266504i
\(676\) 11.8909 52.0973i 0.457341 2.00374i
\(677\) −2.94145 + 1.41653i −0.113049 + 0.0544416i −0.489554 0.871973i \(-0.662840\pi\)
0.376504 + 0.926415i \(0.377126\pi\)
\(678\) −3.66643 4.59755i −0.140808 0.176568i
\(679\) −40.5513 + 19.5285i −1.55622 + 0.749434i
\(680\) −1.32528 + 1.66185i −0.0508223 + 0.0637291i
\(681\) 19.5249 0.748198
\(682\) 5.69623 0.218120
\(683\) −18.9167 + 23.7208i −0.723828 + 0.907652i −0.998548 0.0538728i \(-0.982843\pi\)
0.274720 + 0.961524i \(0.411415\pi\)
\(684\) 16.4175 + 7.90625i 0.627739 + 0.302303i
\(685\) 3.35879 + 14.7158i 0.128333 + 0.562263i
\(686\) 2.82625 12.3826i 0.107907 0.472770i
\(687\) −14.3732 −0.548372
\(688\) −2.51120 + 19.1663i −0.0957385 + 0.730707i
\(689\) −62.2199 −2.37039
\(690\) 1.72933 7.57668i 0.0658343 0.288439i
\(691\) −6.06416 26.5688i −0.230692 1.01073i −0.949068 0.315072i \(-0.897971\pi\)
0.718376 0.695655i \(-0.244886\pi\)
\(692\) 5.30292 + 2.55375i 0.201587 + 0.0970790i
\(693\) 21.1031 26.4625i 0.801642 1.00523i
\(694\) −0.264440 −0.0100380
\(695\) −1.08062 −0.0409901
\(696\) −12.1445 + 15.2287i −0.460335 + 0.577242i
\(697\) 5.89207 2.83747i 0.223178 0.107477i
\(698\) 0.214613 + 0.269116i 0.00812322 + 0.0101862i
\(699\) 39.6544 19.0966i 1.49987 0.722299i
\(700\) 6.03662 26.4482i 0.228163 0.999647i
\(701\) 21.7071 27.2199i 0.819868 1.02808i −0.179152 0.983821i \(-0.557335\pi\)
0.999020 0.0442602i \(-0.0140931\pi\)
\(702\) −1.65956 + 7.27102i −0.0626362 + 0.274427i
\(703\) 2.90733 + 1.40010i 0.109652 + 0.0528056i
\(704\) 10.4880 + 13.1516i 0.395282 + 0.495668i
\(705\) −8.84447 11.0906i −0.333102 0.417697i
\(706\) −0.521654 2.28552i −0.0196327 0.0860165i
\(707\) 65.4929 + 31.5397i 2.46311 + 1.18617i
\(708\) −16.5259 + 7.95847i −0.621082 + 0.299097i
\(709\) −7.94683 34.8173i −0.298449 1.30759i −0.872436 0.488728i \(-0.837461\pi\)
0.573987 0.818864i \(-0.305396\pi\)
\(710\) 0.360488 + 1.57940i 0.0135289 + 0.0592738i
\(711\) 24.4141 11.7572i 0.915600 0.440930i
\(712\) −16.7317 8.05758i −0.627048 0.301971i
\(713\) 4.51289 + 19.7723i 0.169009 + 0.740478i
\(714\) 2.62587 + 3.29274i 0.0982707 + 0.123228i
\(715\) −22.4435 28.1432i −0.839339 1.05250i
\(716\) 5.70829 + 2.74897i 0.213329 + 0.102734i
\(717\) 6.80142 29.7990i 0.254004 1.11286i
\(718\) 4.93913 6.19347i 0.184327 0.231138i
\(719\) 9.00141 39.4377i 0.335696 1.47078i −0.472219 0.881481i \(-0.656547\pi\)
0.807915 0.589299i \(-0.200596\pi\)
\(720\) 6.13820 2.95600i 0.228757 0.110164i
\(721\) −14.3547 18.0003i −0.534599 0.670365i
\(722\) −5.04874 + 2.43135i −0.187895 + 0.0904853i
\(723\) 28.9560 36.3097i 1.07688 1.35037i
\(724\) −5.95091 −0.221164
\(725\) −18.0584 −0.670674
\(726\) 3.96458 4.97143i 0.147139 0.184507i
\(727\) 8.77073 + 4.22376i 0.325288 + 0.156651i 0.589400 0.807842i \(-0.299364\pi\)
−0.264111 + 0.964492i \(0.585079\pi\)
\(728\) 10.6726 + 46.7595i 0.395551 + 1.73302i
\(729\) 0.466055 2.04192i 0.0172613 0.0756267i
\(730\) −8.77886 −0.324920
\(731\) 0.851886 6.50187i 0.0315081 0.240480i
\(732\) −17.4728 −0.645813
\(733\) 0.0371825 0.162907i 0.00137337 0.00601711i −0.974237 0.225528i \(-0.927589\pi\)
0.975610 + 0.219511i \(0.0704463\pi\)
\(734\) −0.972068 4.25891i −0.0358797 0.157199i
\(735\) 34.9691 + 16.8402i 1.28985 + 0.621161i
\(736\) 17.9521 22.5112i 0.661723 0.829774i
\(737\) −22.6903 −0.835808
\(738\) 4.91036 0.180753
\(739\) 22.5966 28.3353i 0.831231 1.04233i −0.167177 0.985927i \(-0.553465\pi\)
0.998408 0.0564035i \(-0.0179633\pi\)
\(740\) 1.22034 0.587687i 0.0448608 0.0216038i
\(741\) −50.2607 63.0249i −1.84637 2.31528i
\(742\) 16.6137 8.00072i 0.609907 0.293716i
\(743\) −3.45156 + 15.1223i −0.126625 + 0.554782i 0.871320 + 0.490715i \(0.163264\pi\)
−0.997946 + 0.0640669i \(0.979593\pi\)
\(744\) 7.00870 8.78863i 0.256951 0.322207i
\(745\) 3.41250 14.9512i 0.125024 0.547768i
\(746\) 4.13874 + 1.99311i 0.151530 + 0.0729731i
\(747\) −4.02413 5.04610i −0.147235 0.184627i
\(748\) −4.79208 6.00908i −0.175216 0.219714i
\(749\) −6.76767 29.6511i −0.247285 1.08343i
\(750\) −9.07146 4.36858i −0.331243 0.159518i
\(751\) 27.6087 13.2957i 1.00746 0.485166i 0.143995 0.989578i \(-0.454005\pi\)
0.863463 + 0.504413i \(0.168291\pi\)
\(752\) −3.25651 14.2677i −0.118753 0.520290i
\(753\) −9.91687 43.4486i −0.361391 1.58336i
\(754\) 13.7016 6.59834i 0.498983 0.240297i
\(755\) −4.89550 2.35755i −0.178166 0.0858000i
\(756\) 4.94840 + 21.6804i 0.179972 + 0.788508i
\(757\) −4.72978 5.93095i −0.171907 0.215564i 0.688413 0.725319i \(-0.258308\pi\)
−0.860320 + 0.509755i \(0.829736\pi\)
\(758\) 2.80934 + 3.52281i 0.102040 + 0.127954i
\(759\) 53.1527 + 25.5970i 1.92932 + 0.929113i
\(760\) −2.68306 + 11.7553i −0.0973250 + 0.426409i
\(761\) 6.09425 7.64194i 0.220916 0.277020i −0.659006 0.752137i \(-0.729023\pi\)
0.879923 + 0.475117i \(0.157594\pi\)
\(762\) 2.71542 11.8970i 0.0983692 0.430984i
\(763\) −46.2859 + 22.2901i −1.67566 + 0.806956i
\(764\) 10.6640 + 13.3723i 0.385811 + 0.483792i
\(765\) −2.08229 + 1.00278i −0.0752854 + 0.0362555i
\(766\) −8.67586 + 10.8792i −0.313472 + 0.393081i
\(767\) 30.0650 1.08559
\(768\) 7.45478 0.269001
\(769\) −10.6486 + 13.3529i −0.383998 + 0.481518i −0.935837 0.352432i \(-0.885355\pi\)
0.551839 + 0.833950i \(0.313926\pi\)
\(770\) 9.61162 + 4.62871i 0.346379 + 0.166807i
\(771\) 14.2239 + 62.3191i 0.512262 + 2.24437i
\(772\) 3.17487 13.9100i 0.114266 0.500633i
\(773\) −13.0666 −0.469972 −0.234986 0.971999i \(-0.575504\pi\)
−0.234986 + 0.971999i \(0.575504\pi\)
\(774\) 2.69449 4.12095i 0.0968516 0.148125i
\(775\) 10.4217 0.374359
\(776\) −3.58502 + 15.7070i −0.128695 + 0.563849i
\(777\) −1.25372 5.49292i −0.0449771 0.197058i
\(778\) −10.3567 4.98755i −0.371307 0.178812i
\(779\) 23.1296 29.0036i 0.828705 1.03916i
\(780\) −33.8367 −1.21155
\(781\) −12.2979 −0.440052
\(782\) −1.69580 + 2.12647i −0.0606418 + 0.0760424i
\(783\) 13.3371 6.42281i 0.476629 0.229532i
\(784\) 24.9657 + 31.3060i 0.891631 + 1.11807i
\(785\) 14.4347 6.95138i 0.515196 0.248105i
\(786\) −0.308140 + 1.35005i −0.0109910 + 0.0481546i
\(787\) 3.30428 4.14344i 0.117785 0.147698i −0.719443 0.694551i \(-0.755603\pi\)
0.837228 + 0.546853i \(0.184175\pi\)
\(788\) 2.36174 10.3475i 0.0841335 0.368613i
\(789\) −4.56202 2.19695i −0.162412 0.0782137i
\(790\) 5.32512 + 6.67749i 0.189459 + 0.237574i
\(791\) 17.9193 + 22.4700i 0.637136 + 0.798943i
\(792\) −2.69597 11.8118i −0.0957970 0.419714i
\(793\) 25.8035 + 12.4263i 0.916308 + 0.441271i
\(794\) −10.3848 + 5.00104i −0.368541 + 0.177480i
\(795\) 6.07729 + 26.6263i 0.215539 + 0.944339i
\(796\) 8.63429 + 37.8293i 0.306034 + 1.34082i
\(797\) 25.0470 12.0620i 0.887210 0.427258i 0.0659574 0.997822i \(-0.478990\pi\)
0.821253 + 0.570565i \(0.193276\pi\)
\(798\) 21.5246 + 10.3657i 0.761962 + 0.366942i
\(799\) 1.10472 + 4.84011i 0.0390823 + 0.171231i
\(800\) −9.22508 11.5679i −0.326156 0.408986i
\(801\) −12.5896 15.7869i −0.444833 0.557802i
\(802\) −10.3229 4.97124i −0.364514 0.175541i
\(803\) 14.8292 64.9711i 0.523312 2.29278i
\(804\) −13.2983 + 16.6756i −0.468995 + 0.588101i
\(805\) −8.45190 + 37.0302i −0.297890 + 1.30514i
\(806\) −7.90733 + 3.80797i −0.278524 + 0.134130i
\(807\) −33.5237 42.0373i −1.18009 1.47978i
\(808\) 23.4434 11.2897i 0.824736 0.397172i
\(809\) −0.400645 + 0.502392i −0.0140859 + 0.0176632i −0.788825 0.614618i \(-0.789310\pi\)
0.774739 + 0.632282i \(0.217881\pi\)
\(810\) 6.22193 0.218616
\(811\) −6.69847 −0.235215 −0.117608 0.993060i \(-0.537523\pi\)
−0.117608 + 0.993060i \(0.537523\pi\)
\(812\) 28.2724 35.4524i 0.992165 1.24414i
\(813\) 24.4740 + 11.7861i 0.858341 + 0.413355i
\(814\) −0.227409 0.996344i −0.00797069 0.0349219i
\(815\) −4.29486 + 18.8170i −0.150442 + 0.659130i
\(816\) −6.43527 −0.225280
\(817\) −11.6488 35.3266i −0.407541 1.23592i
\(818\) −2.42568 −0.0848119
\(819\) −11.6044 + 50.8420i −0.405489 + 1.77656i
\(820\) −3.46496 15.1810i −0.121002 0.530143i
\(821\) 19.6128 + 9.44502i 0.684491 + 0.329634i 0.743606 0.668618i \(-0.233114\pi\)
−0.0591153 + 0.998251i \(0.518828\pi\)
\(822\) 6.67471 8.36983i 0.232807 0.291931i
\(823\) 9.83940 0.342980 0.171490 0.985186i \(-0.445142\pi\)
0.171490 + 0.985186i \(0.445142\pi\)
\(824\) −8.24123 −0.287097
\(825\) 18.9017 23.7019i 0.658072 0.825196i
\(826\) −8.02782 + 3.86599i −0.279324 + 0.134515i
\(827\) 20.2725 + 25.4209i 0.704944 + 0.883972i 0.997382 0.0723124i \(-0.0230378\pi\)
−0.292438 + 0.956285i \(0.594466\pi\)
\(828\) 18.5121 8.91497i 0.643341 0.309817i
\(829\) −5.92709 + 25.9683i −0.205856 + 0.901916i 0.761434 + 0.648243i \(0.224496\pi\)
−0.967290 + 0.253673i \(0.918361\pi\)
\(830\) 1.26836 1.59047i 0.0440253 0.0552059i
\(831\) −2.20974 + 9.68149i −0.0766550 + 0.335847i
\(832\) −23.3510 11.2453i −0.809552 0.389859i
\(833\) −8.46923 10.6201i −0.293441 0.367964i
\(834\) 0.477850 + 0.599206i 0.0165466 + 0.0207488i
\(835\) −1.54875 6.78552i −0.0535968 0.234823i
\(836\) −39.2813 18.9169i −1.35857 0.654254i
\(837\) −7.69698 + 3.70667i −0.266046 + 0.128121i
\(838\) −0.857548 3.75716i −0.0296235 0.129789i
\(839\) −0.167960 0.735879i −0.00579861 0.0254054i 0.971946 0.235205i \(-0.0755761\pi\)
−0.977744 + 0.209799i \(0.932719\pi\)
\(840\) 18.9678 9.13441i 0.654451 0.315167i
\(841\) −1.06756 0.514111i −0.0368125 0.0177280i
\(842\) 2.27349 + 9.96080i 0.0783496 + 0.343272i
\(843\) 2.35241 + 2.94983i 0.0810213 + 0.101597i
\(844\) −28.2222 35.3896i −0.971450 1.21816i
\(845\) 34.6392 + 16.6813i 1.19162 + 0.573856i
\(846\) −0.829484 + 3.63421i −0.0285183 + 0.124947i
\(847\) −19.3765 + 24.2973i −0.665784 + 0.834866i
\(848\) −6.26974 + 27.4695i −0.215304 + 0.943307i
\(849\) 46.1564 22.2278i 1.58408 0.762855i
\(850\) 0.871426 + 1.09273i 0.0298897 + 0.0374805i
\(851\) 3.27826 1.57873i 0.112377 0.0541181i
\(852\) −7.20751 + 9.03793i −0.246925 + 0.309634i
\(853\) −0.0566560 −0.00193987 −0.000969933 1.00000i \(-0.500309\pi\)
−0.000969933 1.00000i \(0.500309\pi\)
\(854\) −8.48778 −0.290446
\(855\) −8.17414 + 10.2500i −0.279550 + 0.350544i
\(856\) −9.80853 4.72354i −0.335249 0.161447i
\(857\) −7.45416 32.6588i −0.254629 1.11560i −0.926903 0.375301i \(-0.877539\pi\)
0.672274 0.740303i \(-0.265318\pi\)
\(858\) −5.68097 + 24.8900i −0.193945 + 0.849730i
\(859\) −46.3456 −1.58129 −0.790645 0.612274i \(-0.790255\pi\)
−0.790645 + 0.612274i \(0.790255\pi\)
\(860\) −14.6418 5.42245i −0.499281 0.184904i
\(861\) −64.7718 −2.20742
\(862\) 3.46415 15.1774i 0.117989 0.516945i
\(863\) −2.13933 9.37304i −0.0728238 0.319062i 0.925375 0.379053i \(-0.123750\pi\)
−0.998199 + 0.0599907i \(0.980893\pi\)
\(864\) 10.9275 + 5.26242i 0.371762 + 0.179031i
\(865\) −2.64028 + 3.31080i −0.0897721 + 0.112571i
\(866\) −3.37899 −0.114823
\(867\) 2.18307 0.0741409
\(868\) −16.3163 + 20.4600i −0.553810 + 0.694456i
\(869\) −58.4143 + 28.1309i −1.98157 + 0.954274i
\(870\) −4.16198 5.21896i −0.141104 0.176939i
\(871\) 31.4980 15.1686i 1.06727 0.513969i
\(872\) −4.09200 + 17.9282i −0.138573 + 0.607126i
\(873\) −10.9220 + 13.6958i −0.369654 + 0.463532i
\(874\) −3.43319 + 15.0418i −0.116130 + 0.508797i
\(875\) 44.3358 + 21.3510i 1.49882 + 0.721795i
\(876\) −39.0574 48.9765i −1.31963 1.65476i
\(877\) −10.1413 12.7168i −0.342447 0.429415i 0.580549 0.814226i \(-0.302838\pi\)
−0.922995 + 0.384811i \(0.874267\pi\)
\(878\) −2.94358 12.8967i −0.0993410 0.435241i
\(879\) 38.4929 + 18.5372i 1.29833 + 0.625244i
\(880\) −14.6865 + 7.07267i −0.495083 + 0.238420i
\(881\) −9.52611 41.7366i −0.320943 1.40614i −0.835879 0.548914i \(-0.815042\pi\)
0.514936 0.857228i \(-0.327816\pi\)
\(882\) −2.26955 9.94356i −0.0764198 0.334817i
\(883\) 6.93365 3.33907i 0.233336 0.112369i −0.313563 0.949567i \(-0.601523\pi\)
0.546899 + 0.837199i \(0.315808\pi\)
\(884\) 10.6693 + 5.13808i 0.358849 + 0.172812i
\(885\) −2.93658 12.8660i −0.0987121 0.432486i
\(886\) −5.54757 6.95643i −0.186374 0.233706i
\(887\) 12.1905 + 15.2864i 0.409316 + 0.513266i 0.943170 0.332311i \(-0.107828\pi\)
−0.533854 + 0.845577i \(0.679257\pi\)
\(888\) −1.81705 0.875046i −0.0609762 0.0293646i
\(889\) −13.2713 + 58.1454i −0.445106 + 1.95014i
\(890\) 3.96810 4.97583i 0.133011 0.166790i
\(891\) −10.5101 + 46.0476i −0.352101 + 1.54265i
\(892\) 7.81185 3.76199i 0.261560 0.125961i
\(893\) 17.5587 + 22.0179i 0.587580 + 0.736802i
\(894\) −9.79948 + 4.71918i −0.327744 + 0.157833i
\(895\) −2.84211 + 3.56390i −0.0950013 + 0.119128i
\(896\) 48.5267 1.62116
\(897\) −90.8968 −3.03495
\(898\) 0.682254 0.855519i 0.0227671 0.0285490i
\(899\) 15.6949 + 7.55826i 0.523454 + 0.252082i
\(900\) −2.34948 10.2938i −0.0783161 0.343125i
\(901\) 2.12691 9.31862i 0.0708578 0.310448i
\(902\) −11.7488 −0.391191
\(903\) −35.5427 + 54.3589i −1.18279 + 1.80895i
\(904\) 10.2877 0.342163
\(905\) 0.952729 4.17418i 0.0316698 0.138754i
\(906\) 0.857530 + 3.75709i 0.0284895 + 0.124821i
\(907\) 0.367608 + 0.177031i 0.0122062 + 0.00587821i 0.439977 0.898009i \(-0.354987\pi\)
−0.427771 + 0.903887i \(0.640701\pi\)
\(908\) −10.1445 + 12.7207i −0.336656 + 0.422153i
\(909\) 28.2920 0.938385
\(910\) −16.4369 −0.544877
\(911\) −37.4706 + 46.9867i −1.24146 + 1.55674i −0.547235 + 0.836979i \(0.684320\pi\)
−0.694223 + 0.719760i \(0.744252\pi\)
\(912\) −32.8895 + 15.8388i −1.08908 + 0.524474i
\(913\) 9.62833 + 12.0735i 0.318651 + 0.399576i
\(914\) −7.92072 + 3.81442i −0.261994 + 0.126170i
\(915\) 2.79736 12.2560i 0.0924779 0.405172i
\(916\) 7.46780 9.36432i 0.246743 0.309406i
\(917\) 1.50600 6.59822i 0.0497325 0.217892i
\(918\) −1.03224 0.497102i −0.0340691 0.0164068i
\(919\) 1.95543 + 2.45203i 0.0645036 + 0.0808849i 0.813037 0.582213i \(-0.197813\pi\)
−0.748533 + 0.663098i \(0.769241\pi\)
\(920\) 8.47694 + 10.6297i 0.279476 + 0.350452i
\(921\) −2.28948 10.0309i −0.0754409 0.330528i
\(922\) −3.08440 1.48537i −0.101579 0.0489180i
\(923\) 17.0715 8.22120i 0.561915 0.270604i
\(924\) 16.9392 + 74.2157i 0.557260 + 2.44152i
\(925\) −0.416063 1.82289i −0.0136801 0.0599363i
\(926\) −5.94255 + 2.86178i −0.195284 + 0.0940440i
\(927\) −8.07336 3.88793i −0.265164 0.127696i
\(928\) −5.50327 24.1114i −0.180654 0.791496i
\(929\) −27.2557 34.1776i −0.894231 1.12133i −0.992015 0.126122i \(-0.959747\pi\)
0.0977837 0.995208i \(-0.468825\pi\)
\(930\) 2.40192 + 3.01191i 0.0787621 + 0.0987646i
\(931\) −69.4233 33.4325i −2.27526 1.09571i
\(932\) −8.16136 + 35.7573i −0.267334 + 1.17127i
\(933\) −27.1603 + 34.0579i −0.889188 + 1.11501i
\(934\) −0.376253 + 1.64847i −0.0123114 + 0.0539396i
\(935\) 4.98219 2.39930i 0.162935 0.0784654i
\(936\) 11.6387 + 14.5945i 0.380424 + 0.477036i
\(937\) 42.6851 20.5561i 1.39446 0.671538i 0.422432 0.906394i \(-0.361176\pi\)
0.972030 + 0.234857i \(0.0754621\pi\)
\(938\) −6.45994 + 8.10050i −0.210924 + 0.264491i
\(939\) 44.2317 1.44345
\(940\) 11.8209 0.385557
\(941\) −22.7092 + 28.4765i −0.740300 + 0.928307i −0.999294 0.0375719i \(-0.988038\pi\)
0.258994 + 0.965879i \(0.416609\pi\)
\(942\) −10.2376 4.93017i −0.333559 0.160634i
\(943\) −9.30807 40.7813i −0.303112 1.32802i
\(944\) 3.02958 13.2734i 0.0986043 0.432014i
\(945\) −15.9996 −0.520467
\(946\) −6.44698 + 9.85999i −0.209609 + 0.320576i
\(947\) −0.177782 −0.00577713 −0.00288857 0.999996i \(-0.500919\pi\)
−0.00288857 + 0.999996i \(0.500919\pi\)
\(948\) −13.5615 + 59.4167i −0.440456 + 1.92977i
\(949\) 22.8482 + 100.104i 0.741682 + 3.24952i
\(950\) 7.14319 + 3.43998i 0.231756 + 0.111608i
\(951\) 6.69050 8.38962i 0.216954 0.272052i
\(952\) −7.36796 −0.238797
\(953\) 12.7098 0.411711 0.205855 0.978582i \(-0.434002\pi\)
0.205855 + 0.978582i \(0.434002\pi\)
\(954\) 4.47469 5.61109i 0.144874 0.181666i
\(955\) −11.0871 + 5.33926i −0.358769 + 0.172774i
\(956\) 15.8806 + 19.9137i 0.513616 + 0.644055i
\(957\) 45.6552 21.9864i 1.47582 0.710719i
\(958\) −4.01115 + 17.5740i −0.129594 + 0.567790i
\(959\) −32.6219 + 40.9066i −1.05342 + 1.32094i
\(960\) −2.53149 + 11.0912i −0.0817036 + 0.357967i
\(961\) 18.8723 + 9.08844i 0.608785 + 0.293176i
\(962\) 0.981745 + 1.23107i 0.0316527 + 0.0396913i
\(963\) −7.38033 9.25464i −0.237828 0.298227i
\(964\) 8.61171 + 37.7304i 0.277365 + 1.21521i
\(965\) 9.24869 + 4.45393i 0.297726 + 0.143377i
\(966\) 24.2708 11.6882i 0.780900 0.376062i
\(967\) −3.70494 16.2324i −0.119143 0.521998i −0.998914 0.0466005i \(-0.985161\pi\)
0.879771 0.475398i \(-0.157696\pi\)
\(968\) 2.47538 + 10.8454i 0.0795618 + 0.348583i
\(969\) 11.1573 5.37306i 0.358424 0.172608i
\(970\) −4.97453 2.39561i −0.159723 0.0769184i
\(971\) 2.19889 + 9.63398i 0.0705658 + 0.309169i 0.997877 0.0651214i \(-0.0207435\pi\)
−0.927312 + 0.374290i \(0.877886\pi\)
\(972\) 18.5134 + 23.2150i 0.593816 + 0.744622i
\(973\) −2.33544 2.92855i −0.0748709 0.0938851i
\(974\) 8.69033 + 4.18504i 0.278456 + 0.134097i
\(975\) −10.3938 + 45.5382i −0.332868 + 1.45839i
\(976\) 8.08624 10.1398i 0.258834 0.324568i
\(977\) −2.56813 + 11.2517i −0.0821617 + 0.359974i −0.999251 0.0387090i \(-0.987675\pi\)
0.917089 + 0.398683i \(0.130533\pi\)
\(978\) 12.3333 5.93939i 0.394375 0.189921i
\(979\) 30.1226 + 37.7725i 0.962721 + 1.20721i
\(980\) −29.1403 + 14.0332i −0.930852 + 0.448275i
\(981\) −12.4666 + 15.6326i −0.398026 + 0.499109i
\(982\) −13.7923 −0.440131
\(983\) −26.8003 −0.854798 −0.427399 0.904063i \(-0.640570\pi\)
−0.427399 + 0.904063i \(0.640570\pi\)
\(984\) −14.4558 + 18.1270i −0.460834 + 0.577867i
\(985\) 6.87997 + 3.31322i 0.219214 + 0.105568i
\(986\) 0.519854 + 2.27763i 0.0165555 + 0.0725345i
\(987\) 10.9416 47.9383i 0.348275 1.52589i
\(988\) 67.1752 2.13713
\(989\) −39.3329 14.5665i −1.25071 0.463189i
\(990\) 4.15208 0.131962
\(991\) 0.982339 4.30391i 0.0312050 0.136718i −0.956926 0.290332i \(-0.906234\pi\)
0.988131 + 0.153614i \(0.0490913\pi\)
\(992\) 3.17600 + 13.9149i 0.100838 + 0.441800i
\(993\) 25.6399 + 12.3475i 0.813658 + 0.391837i
\(994\) −3.50120 + 4.39037i −0.111051 + 0.139254i
\(995\) −27.9171 −0.885033
\(996\) 14.5160 0.459958
\(997\) −26.3583 + 33.0522i −0.834775 + 1.04678i 0.163410 + 0.986558i \(0.447751\pi\)
−0.998185 + 0.0602169i \(0.980821\pi\)
\(998\) −5.92390 + 2.85280i −0.187518 + 0.0903037i
\(999\) 0.955628 + 1.19832i 0.0302347 + 0.0379132i
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 731.2.k.b.35.14 180
43.16 even 7 inner 731.2.k.b.188.14 yes 180
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.k.b.35.14 180 1.1 even 1 trivial
731.2.k.b.188.14 yes 180 43.16 even 7 inner