Properties

Label 731.2.e.b.307.9
Level $731$
Weight $2$
Character 731.307
Analytic conductor $5.837$
Analytic rank $0$
Dimension $58$
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(307,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.307");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.9
Character \(\chi\) \(=\) 731.307
Dual form 731.2.e.b.681.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.32448 q^{2} +(1.04438 - 1.80892i) q^{3} -0.245749 q^{4} +(1.40548 - 2.43436i) q^{5} +(-1.38326 + 2.39588i) q^{6} +(0.178508 + 0.309184i) q^{7} +2.97445 q^{8} +(-0.681454 - 1.18031i) q^{9} +O(q^{10})\) \(q-1.32448 q^{2} +(1.04438 - 1.80892i) q^{3} -0.245749 q^{4} +(1.40548 - 2.43436i) q^{5} +(-1.38326 + 2.39588i) q^{6} +(0.178508 + 0.309184i) q^{7} +2.97445 q^{8} +(-0.681454 - 1.18031i) q^{9} +(-1.86153 + 3.22427i) q^{10} -3.97943 q^{11} +(-0.256655 + 0.444539i) q^{12} +(-2.36455 - 4.09553i) q^{13} +(-0.236430 - 0.409509i) q^{14} +(-2.93571 - 5.08480i) q^{15} -3.44811 q^{16} +(-0.500000 - 0.866025i) q^{17} +(0.902573 + 1.56330i) q^{18} +(1.25318 - 2.17057i) q^{19} +(-0.345395 + 0.598242i) q^{20} +0.745719 q^{21} +5.27068 q^{22} +(0.569368 - 0.986175i) q^{23} +(3.10646 - 5.38054i) q^{24} +(-1.45076 - 2.51278i) q^{25} +(3.13181 + 5.42445i) q^{26} +3.41949 q^{27} +(-0.0438680 - 0.0759816i) q^{28} +(0.524106 + 0.907778i) q^{29} +(3.88829 + 6.73472i) q^{30} +(2.49198 - 4.31623i) q^{31} -1.38195 q^{32} +(-4.15603 + 7.19846i) q^{33} +(0.662241 + 1.14703i) q^{34} +1.00356 q^{35} +(0.167466 + 0.290060i) q^{36} +(-4.47170 + 7.74521i) q^{37} +(-1.65982 + 2.87488i) q^{38} -9.87796 q^{39} +(4.18054 - 7.24090i) q^{40} -10.1140 q^{41} -0.987690 q^{42} +(6.55501 + 0.178430i) q^{43} +0.977940 q^{44} -3.83108 q^{45} +(-0.754118 + 1.30617i) q^{46} -13.0872 q^{47} +(-3.60113 + 6.23735i) q^{48} +(3.43627 - 5.95179i) q^{49} +(1.92150 + 3.32813i) q^{50} -2.08876 q^{51} +(0.581086 + 1.00647i) q^{52} +(3.33610 - 5.77830i) q^{53} -4.52905 q^{54} +(-5.59302 + 9.68739i) q^{55} +(0.530963 + 0.919654i) q^{56} +(-2.61759 - 4.53380i) q^{57} +(-0.694168 - 1.20233i) q^{58} +5.56077 q^{59} +(0.721447 + 1.24958i) q^{60} +(0.395036 + 0.684222i) q^{61} +(-3.30058 + 5.71677i) q^{62} +(0.243290 - 0.421390i) q^{63} +8.72658 q^{64} -13.2933 q^{65} +(5.50459 - 9.53423i) q^{66} +(-7.02236 + 12.1631i) q^{67} +(0.122874 + 0.212825i) q^{68} +(-1.18927 - 2.05988i) q^{69} -1.32919 q^{70} +(-0.353987 - 0.613124i) q^{71} +(-2.02695 - 3.51079i) q^{72} +(-1.13731 - 1.96987i) q^{73} +(5.92268 - 10.2584i) q^{74} -6.06055 q^{75} +(-0.307968 + 0.533415i) q^{76} +(-0.710359 - 1.23038i) q^{77} +13.0832 q^{78} +(0.704747 + 1.22066i) q^{79} +(-4.84625 + 8.39396i) q^{80} +(5.61560 - 9.72651i) q^{81} +13.3958 q^{82} +(4.87520 - 8.44409i) q^{83} -0.183259 q^{84} -2.81096 q^{85} +(-8.68199 - 0.236327i) q^{86} +2.18946 q^{87} -11.8366 q^{88} +(1.58885 - 2.75197i) q^{89} +5.07420 q^{90} +(0.844182 - 1.46217i) q^{91} +(-0.139921 + 0.242351i) q^{92} +(-5.20514 - 9.01556i) q^{93} +17.3337 q^{94} +(-3.52265 - 6.10140i) q^{95} +(-1.44328 + 2.49983i) q^{96} -7.36932 q^{97} +(-4.55128 + 7.88304i) q^{98} +(2.71180 + 4.69698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32448 −0.936550 −0.468275 0.883583i \(-0.655124\pi\)
−0.468275 + 0.883583i \(0.655124\pi\)
\(3\) 1.04438 1.80892i 0.602972 1.04438i −0.389396 0.921070i \(-0.627316\pi\)
0.992368 0.123308i \(-0.0393504\pi\)
\(4\) −0.245749 −0.122874
\(5\) 1.40548 2.43436i 0.628550 1.08868i −0.359292 0.933225i \(-0.616982\pi\)
0.987843 0.155456i \(-0.0496847\pi\)
\(6\) −1.38326 + 2.39588i −0.564714 + 0.978113i
\(7\) 0.178508 + 0.309184i 0.0674696 + 0.116861i 0.897787 0.440430i \(-0.145174\pi\)
−0.830317 + 0.557291i \(0.811841\pi\)
\(8\) 2.97445 1.05163
\(9\) −0.681454 1.18031i −0.227151 0.393438i
\(10\) −1.86153 + 3.22427i −0.588669 + 1.01960i
\(11\) −3.97943 −1.19984 −0.599922 0.800059i \(-0.704802\pi\)
−0.599922 + 0.800059i \(0.704802\pi\)
\(12\) −0.256655 + 0.444539i −0.0740898 + 0.128327i
\(13\) −2.36455 4.09553i −0.655809 1.13589i −0.981690 0.190484i \(-0.938994\pi\)
0.325881 0.945411i \(-0.394339\pi\)
\(14\) −0.236430 0.409509i −0.0631886 0.109446i
\(15\) −2.93571 5.08480i −0.757997 1.31289i
\(16\) −3.44811 −0.862028
\(17\) −0.500000 0.866025i −0.121268 0.210042i
\(18\) 0.902573 + 1.56330i 0.212739 + 0.368474i
\(19\) 1.25318 2.17057i 0.287500 0.497964i −0.685713 0.727872i \(-0.740509\pi\)
0.973212 + 0.229909i \(0.0738427\pi\)
\(20\) −0.345395 + 0.598242i −0.0772327 + 0.133771i
\(21\) 0.745719 0.162729
\(22\) 5.27068 1.12371
\(23\) 0.569368 0.986175i 0.118721 0.205632i −0.800540 0.599280i \(-0.795454\pi\)
0.919261 + 0.393648i \(0.128787\pi\)
\(24\) 3.10646 5.38054i 0.634103 1.09830i
\(25\) −1.45076 2.51278i −0.290151 0.502556i
\(26\) 3.13181 + 5.42445i 0.614198 + 1.06382i
\(27\) 3.41949 0.658081
\(28\) −0.0438680 0.0759816i −0.00829028 0.0143592i
\(29\) 0.524106 + 0.907778i 0.0973240 + 0.168570i 0.910576 0.413341i \(-0.135638\pi\)
−0.813252 + 0.581911i \(0.802305\pi\)
\(30\) 3.88829 + 6.73472i 0.709902 + 1.22959i
\(31\) 2.49198 4.31623i 0.447572 0.775218i −0.550655 0.834733i \(-0.685622\pi\)
0.998227 + 0.0595147i \(0.0189553\pi\)
\(32\) −1.38195 −0.244296
\(33\) −4.15603 + 7.19846i −0.723473 + 1.25309i
\(34\) 0.662241 + 1.14703i 0.113573 + 0.196715i
\(35\) 1.00356 0.169632
\(36\) 0.167466 + 0.290060i 0.0279111 + 0.0483434i
\(37\) −4.47170 + 7.74521i −0.735142 + 1.27330i 0.219518 + 0.975608i \(0.429551\pi\)
−0.954661 + 0.297696i \(0.903782\pi\)
\(38\) −1.65982 + 2.87488i −0.269258 + 0.466368i
\(39\) −9.87796 −1.58174
\(40\) 4.18054 7.24090i 0.661001 1.14489i
\(41\) −10.1140 −1.57954 −0.789771 0.613401i \(-0.789801\pi\)
−0.789771 + 0.613401i \(0.789801\pi\)
\(42\) −0.987690 −0.152404
\(43\) 6.55501 + 0.178430i 0.999630 + 0.0272103i
\(44\) 0.977940 0.147430
\(45\) −3.83108 −0.571104
\(46\) −0.754118 + 1.30617i −0.111189 + 0.192584i
\(47\) −13.0872 −1.90896 −0.954481 0.298271i \(-0.903590\pi\)
−0.954481 + 0.298271i \(0.903590\pi\)
\(48\) −3.60113 + 6.23735i −0.519779 + 0.900283i
\(49\) 3.43627 5.95179i 0.490896 0.850256i
\(50\) 1.92150 + 3.32813i 0.271741 + 0.470669i
\(51\) −2.08876 −0.292485
\(52\) 0.581086 + 1.00647i 0.0805821 + 0.139572i
\(53\) 3.33610 5.77830i 0.458249 0.793711i −0.540619 0.841267i \(-0.681810\pi\)
0.998869 + 0.0475564i \(0.0151434\pi\)
\(54\) −4.52905 −0.616325
\(55\) −5.59302 + 9.68739i −0.754162 + 1.30625i
\(56\) 0.530963 + 0.919654i 0.0709529 + 0.122894i
\(57\) −2.61759 4.53380i −0.346709 0.600517i
\(58\) −0.694168 1.20233i −0.0911488 0.157874i
\(59\) 5.56077 0.723950 0.361975 0.932188i \(-0.382102\pi\)
0.361975 + 0.932188i \(0.382102\pi\)
\(60\) 0.721447 + 1.24958i 0.0931384 + 0.161320i
\(61\) 0.395036 + 0.684222i 0.0505792 + 0.0876057i 0.890207 0.455557i \(-0.150560\pi\)
−0.839627 + 0.543163i \(0.817227\pi\)
\(62\) −3.30058 + 5.71677i −0.419174 + 0.726031i
\(63\) 0.243290 0.421390i 0.0306516 0.0530901i
\(64\) 8.72658 1.09082
\(65\) −13.2933 −1.64884
\(66\) 5.50459 9.53423i 0.677568 1.17358i
\(67\) −7.02236 + 12.1631i −0.857918 + 1.48596i 0.0159938 + 0.999872i \(0.494909\pi\)
−0.873912 + 0.486085i \(0.838425\pi\)
\(68\) 0.122874 + 0.212825i 0.0149007 + 0.0258088i
\(69\) −1.18927 2.05988i −0.143172 0.247980i
\(70\) −1.32919 −0.158869
\(71\) −0.353987 0.613124i −0.0420106 0.0727644i 0.844256 0.535941i \(-0.180043\pi\)
−0.886266 + 0.463176i \(0.846710\pi\)
\(72\) −2.02695 3.51079i −0.238879 0.413750i
\(73\) −1.13731 1.96987i −0.133112 0.230556i 0.791763 0.610829i \(-0.209164\pi\)
−0.924874 + 0.380273i \(0.875830\pi\)
\(74\) 5.92268 10.2584i 0.688498 1.19251i
\(75\) −6.06055 −0.699812
\(76\) −0.307968 + 0.533415i −0.0353263 + 0.0611869i
\(77\) −0.710359 1.23038i −0.0809529 0.140215i
\(78\) 13.0832 1.48138
\(79\) 0.704747 + 1.22066i 0.0792902 + 0.137335i 0.902944 0.429758i \(-0.141401\pi\)
−0.823654 + 0.567093i \(0.808068\pi\)
\(80\) −4.84625 + 8.39396i −0.541828 + 0.938473i
\(81\) 5.61560 9.72651i 0.623956 1.08072i
\(82\) 13.3958 1.47932
\(83\) 4.87520 8.44409i 0.535122 0.926859i −0.464035 0.885817i \(-0.653599\pi\)
0.999157 0.0410421i \(-0.0130678\pi\)
\(84\) −0.183259 −0.0199952
\(85\) −2.81096 −0.304892
\(86\) −8.68199 0.236327i −0.936203 0.0254838i
\(87\) 2.18946 0.234735
\(88\) −11.8366 −1.26179
\(89\) 1.58885 2.75197i 0.168418 0.291708i −0.769446 0.638712i \(-0.779468\pi\)
0.937864 + 0.347004i \(0.112801\pi\)
\(90\) 5.07420 0.534868
\(91\) 0.844182 1.46217i 0.0884943 0.153277i
\(92\) −0.139921 + 0.242351i −0.0145878 + 0.0252668i
\(93\) −5.20514 9.01556i −0.539748 0.934870i
\(94\) 17.3337 1.78784
\(95\) −3.52265 6.10140i −0.361416 0.625991i
\(96\) −1.44328 + 2.49983i −0.147304 + 0.255138i
\(97\) −7.36932 −0.748241 −0.374120 0.927380i \(-0.622055\pi\)
−0.374120 + 0.927380i \(0.622055\pi\)
\(98\) −4.55128 + 7.88304i −0.459748 + 0.796307i
\(99\) 2.71180 + 4.69698i 0.272546 + 0.472064i
\(100\) 0.356521 + 0.617513i 0.0356521 + 0.0617513i
\(101\) −1.55157 2.68739i −0.154387 0.267406i 0.778449 0.627708i \(-0.216007\pi\)
−0.932836 + 0.360302i \(0.882674\pi\)
\(102\) 2.76652 0.273926
\(103\) 2.41493 + 4.18277i 0.237950 + 0.412141i 0.960126 0.279568i \(-0.0901913\pi\)
−0.722176 + 0.691709i \(0.756858\pi\)
\(104\) −7.03325 12.1819i −0.689667 1.19454i
\(105\) 1.04809 1.81535i 0.102283 0.177160i
\(106\) −4.41861 + 7.65326i −0.429173 + 0.743350i
\(107\) 14.6213 1.41349 0.706747 0.707467i \(-0.250162\pi\)
0.706747 + 0.707467i \(0.250162\pi\)
\(108\) −0.840334 −0.0808612
\(109\) −4.63683 + 8.03123i −0.444128 + 0.769252i −0.997991 0.0633558i \(-0.979820\pi\)
0.553863 + 0.832608i \(0.313153\pi\)
\(110\) 7.40785 12.8308i 0.706311 1.22337i
\(111\) 9.34029 + 16.1779i 0.886541 + 1.53553i
\(112\) −0.615514 1.06610i −0.0581606 0.100737i
\(113\) −3.76954 −0.354608 −0.177304 0.984156i \(-0.556738\pi\)
−0.177304 + 0.984156i \(0.556738\pi\)
\(114\) 3.46695 + 6.00494i 0.324710 + 0.562414i
\(115\) −1.60047 2.77210i −0.149245 0.258500i
\(116\) −0.128798 0.223085i −0.0119586 0.0207129i
\(117\) −3.22267 + 5.58183i −0.297936 + 0.516040i
\(118\) −7.36514 −0.678016
\(119\) 0.178508 0.309184i 0.0163638 0.0283429i
\(120\) −8.73213 15.1245i −0.797131 1.38067i
\(121\) 4.83588 0.439625
\(122\) −0.523218 0.906240i −0.0473699 0.0820471i
\(123\) −10.5629 + 18.2954i −0.952421 + 1.64964i
\(124\) −0.612400 + 1.06071i −0.0549952 + 0.0952544i
\(125\) 5.89878 0.527603
\(126\) −0.322233 + 0.558123i −0.0287068 + 0.0497216i
\(127\) −8.71353 −0.773200 −0.386600 0.922247i \(-0.626351\pi\)
−0.386600 + 0.922247i \(0.626351\pi\)
\(128\) −8.79431 −0.777314
\(129\) 7.16868 11.6711i 0.631167 1.02759i
\(130\) 17.6068 1.54422
\(131\) −0.0278540 −0.00243362 −0.00121681 0.999999i \(-0.500387\pi\)
−0.00121681 + 0.999999i \(0.500387\pi\)
\(132\) 1.02134 1.76901i 0.0888962 0.153973i
\(133\) 0.894810 0.0775899
\(134\) 9.30099 16.1098i 0.803483 1.39167i
\(135\) 4.80603 8.32428i 0.413637 0.716440i
\(136\) −1.48723 2.57595i −0.127529 0.220886i
\(137\) 0.941787 0.0804623 0.0402311 0.999190i \(-0.487191\pi\)
0.0402311 + 0.999190i \(0.487191\pi\)
\(138\) 1.57517 + 2.72827i 0.134087 + 0.232246i
\(139\) 6.05172 10.4819i 0.513300 0.889062i −0.486581 0.873636i \(-0.661756\pi\)
0.999881 0.0154265i \(-0.00491061\pi\)
\(140\) −0.246623 −0.0208434
\(141\) −13.6680 + 23.6736i −1.15105 + 1.99368i
\(142\) 0.468850 + 0.812071i 0.0393450 + 0.0681475i
\(143\) 9.40958 + 16.2979i 0.786868 + 1.36290i
\(144\) 2.34973 + 4.06985i 0.195811 + 0.339154i
\(145\) 2.94648 0.244692
\(146\) 1.50634 + 2.60906i 0.124666 + 0.215927i
\(147\) −7.17754 12.4319i −0.591993 1.02536i
\(148\) 1.09891 1.90337i 0.0903301 0.156456i
\(149\) 7.50590 13.0006i 0.614907 1.06505i −0.375493 0.926825i \(-0.622527\pi\)
0.990401 0.138226i \(-0.0441399\pi\)
\(150\) 8.02709 0.655409
\(151\) 14.5323 1.18262 0.591309 0.806445i \(-0.298611\pi\)
0.591309 + 0.806445i \(0.298611\pi\)
\(152\) 3.72753 6.45627i 0.302342 0.523673i
\(153\) −0.681454 + 1.18031i −0.0550923 + 0.0954227i
\(154\) 0.940858 + 1.62961i 0.0758165 + 0.131318i
\(155\) −7.00486 12.1328i −0.562644 0.974527i
\(156\) 2.42749 0.194355
\(157\) 1.79702 + 3.11253i 0.143418 + 0.248407i 0.928782 0.370628i \(-0.120857\pi\)
−0.785364 + 0.619035i \(0.787524\pi\)
\(158\) −0.933424 1.61674i −0.0742592 0.128621i
\(159\) −6.96831 12.0695i −0.552623 0.957172i
\(160\) −1.94230 + 3.36416i −0.153552 + 0.265960i
\(161\) 0.406546 0.0320403
\(162\) −7.43776 + 12.8826i −0.584366 + 1.01215i
\(163\) 5.34492 + 9.25767i 0.418646 + 0.725116i 0.995804 0.0915166i \(-0.0291714\pi\)
−0.577157 + 0.816633i \(0.695838\pi\)
\(164\) 2.48550 0.194085
\(165\) 11.6825 + 20.2346i 0.909478 + 1.57526i
\(166\) −6.45711 + 11.1840i −0.501169 + 0.868050i
\(167\) 8.21461 14.2281i 0.635666 1.10101i −0.350708 0.936485i \(-0.614059\pi\)
0.986374 0.164521i \(-0.0526077\pi\)
\(168\) 2.21810 0.171130
\(169\) −4.68222 + 8.10985i −0.360171 + 0.623834i
\(170\) 3.72307 0.285546
\(171\) −3.41594 −0.261224
\(172\) −1.61088 0.0438488i −0.122829 0.00334344i
\(173\) 4.44011 0.337575 0.168788 0.985652i \(-0.446015\pi\)
0.168788 + 0.985652i \(0.446015\pi\)
\(174\) −2.89990 −0.219841
\(175\) 0.517942 0.897102i 0.0391527 0.0678145i
\(176\) 13.7215 1.03430
\(177\) 5.80755 10.0590i 0.436522 0.756078i
\(178\) −2.10440 + 3.64493i −0.157731 + 0.273199i
\(179\) −5.44729 9.43498i −0.407150 0.705204i 0.587419 0.809283i \(-0.300144\pi\)
−0.994569 + 0.104079i \(0.966811\pi\)
\(180\) 0.941484 0.0701740
\(181\) −5.75467 9.96737i −0.427741 0.740869i 0.568931 0.822385i \(-0.307357\pi\)
−0.996672 + 0.0815161i \(0.974024\pi\)
\(182\) −1.11810 + 1.93661i −0.0828793 + 0.143551i
\(183\) 1.65027 0.121991
\(184\) 1.69356 2.93333i 0.124851 0.216248i
\(185\) 12.5698 + 21.7715i 0.924148 + 1.60067i
\(186\) 6.89411 + 11.9409i 0.505501 + 0.875553i
\(187\) 1.98972 + 3.44629i 0.145502 + 0.252018i
\(188\) 3.21616 0.234562
\(189\) 0.610405 + 1.05725i 0.0444004 + 0.0769038i
\(190\) 4.66568 + 8.08119i 0.338484 + 0.586271i
\(191\) −9.82211 + 17.0124i −0.710703 + 1.23097i 0.253891 + 0.967233i \(0.418290\pi\)
−0.964594 + 0.263741i \(0.915044\pi\)
\(192\) 9.11386 15.7857i 0.657736 1.13923i
\(193\) 16.6576 1.19904 0.599519 0.800361i \(-0.295359\pi\)
0.599519 + 0.800361i \(0.295359\pi\)
\(194\) 9.76053 0.700765
\(195\) −13.8833 + 24.0466i −0.994203 + 1.72201i
\(196\) −0.844459 + 1.46265i −0.0603185 + 0.104475i
\(197\) −4.23702 7.33873i −0.301875 0.522863i 0.674686 0.738105i \(-0.264279\pi\)
−0.976561 + 0.215242i \(0.930946\pi\)
\(198\) −3.59173 6.22106i −0.255253 0.442111i
\(199\) 24.5628 1.74121 0.870605 0.491983i \(-0.163728\pi\)
0.870605 + 0.491983i \(0.163728\pi\)
\(200\) −4.31520 7.47415i −0.305131 0.528502i
\(201\) 14.6680 + 25.4057i 1.03460 + 1.79198i
\(202\) 2.05502 + 3.55940i 0.144591 + 0.250439i
\(203\) −0.187114 + 0.324091i −0.0131328 + 0.0227467i
\(204\) 0.513309 0.0359388
\(205\) −14.2151 + 24.6212i −0.992822 + 1.71962i
\(206\) −3.19852 5.54001i −0.222852 0.385990i
\(207\) −1.55199 −0.107871
\(208\) 8.15324 + 14.1218i 0.565325 + 0.979172i
\(209\) −4.98695 + 8.63765i −0.344954 + 0.597479i
\(210\) −1.38818 + 2.40440i −0.0957936 + 0.165919i
\(211\) 25.1280 1.72988 0.864942 0.501872i \(-0.167355\pi\)
0.864942 + 0.501872i \(0.167355\pi\)
\(212\) −0.819843 + 1.42001i −0.0563071 + 0.0975267i
\(213\) −1.47879 −0.101325
\(214\) −19.3656 −1.32381
\(215\) 9.64731 15.7065i 0.657941 1.07117i
\(216\) 10.1711 0.692056
\(217\) 1.77935 0.120790
\(218\) 6.14140 10.6372i 0.415948 0.720443i
\(219\) −4.75111 −0.321050
\(220\) 1.37448 2.38066i 0.0926672 0.160504i
\(221\) −2.36455 + 4.09553i −0.159057 + 0.275495i
\(222\) −12.3710 21.4273i −0.830290 1.43810i
\(223\) 3.74978 0.251104 0.125552 0.992087i \(-0.459930\pi\)
0.125552 + 0.992087i \(0.459930\pi\)
\(224\) −0.246688 0.427276i −0.0164825 0.0285486i
\(225\) −1.97725 + 3.42469i −0.131816 + 0.228313i
\(226\) 4.99269 0.332109
\(227\) 13.4759 23.3409i 0.894424 1.54919i 0.0599077 0.998204i \(-0.480919\pi\)
0.834516 0.550984i \(-0.185747\pi\)
\(228\) 0.643270 + 1.11418i 0.0426016 + 0.0737881i
\(229\) 11.5732 + 20.0454i 0.764780 + 1.32464i 0.940363 + 0.340173i \(0.110486\pi\)
−0.175583 + 0.984465i \(0.556181\pi\)
\(230\) 2.11980 + 3.67160i 0.139775 + 0.242098i
\(231\) −2.96754 −0.195250
\(232\) 1.55893 + 2.70014i 0.102349 + 0.177273i
\(233\) 6.96795 + 12.0688i 0.456486 + 0.790656i 0.998772 0.0495373i \(-0.0157747\pi\)
−0.542287 + 0.840193i \(0.682441\pi\)
\(234\) 4.26837 7.39303i 0.279032 0.483297i
\(235\) −18.3938 + 31.8590i −1.19988 + 2.07825i
\(236\) −1.36655 −0.0889549
\(237\) 2.94409 0.191239
\(238\) −0.236430 + 0.409509i −0.0153255 + 0.0265445i
\(239\) 13.9045 24.0833i 0.899409 1.55782i 0.0711579 0.997465i \(-0.477331\pi\)
0.828251 0.560357i \(-0.189336\pi\)
\(240\) 10.1227 + 17.5329i 0.653414 + 1.13175i
\(241\) −3.74510 6.48671i −0.241243 0.417846i 0.719825 0.694155i \(-0.244222\pi\)
−0.961069 + 0.276310i \(0.910889\pi\)
\(242\) −6.40503 −0.411731
\(243\) −6.60040 11.4322i −0.423416 0.733378i
\(244\) −0.0970796 0.168147i −0.00621488 0.0107645i
\(245\) −9.65923 16.7303i −0.617105 1.06886i
\(246\) 13.9903 24.2319i 0.891990 1.54497i
\(247\) −11.8529 −0.754179
\(248\) 7.41227 12.8384i 0.470680 0.815241i
\(249\) −10.1831 17.6376i −0.645328 1.11774i
\(250\) −7.81282 −0.494126
\(251\) −13.4352 23.2704i −0.848021 1.46882i −0.882971 0.469427i \(-0.844460\pi\)
0.0349498 0.999389i \(-0.488873\pi\)
\(252\) −0.0597881 + 0.103556i −0.00376629 + 0.00652341i
\(253\) −2.26576 + 3.92442i −0.142447 + 0.246726i
\(254\) 11.5409 0.724141
\(255\) −2.93571 + 5.08480i −0.183841 + 0.318422i
\(256\) −5.80527 −0.362829
\(257\) −15.9810 −0.996868 −0.498434 0.866928i \(-0.666091\pi\)
−0.498434 + 0.866928i \(0.666091\pi\)
\(258\) −9.49478 + 15.4582i −0.591119 + 0.962385i
\(259\) −3.19293 −0.198399
\(260\) 3.26682 0.202600
\(261\) 0.714308 1.23722i 0.0442146 0.0765818i
\(262\) 0.0368921 0.00227920
\(263\) −1.04702 + 1.81349i −0.0645619 + 0.111824i −0.896500 0.443045i \(-0.853898\pi\)
0.831938 + 0.554869i \(0.187232\pi\)
\(264\) −12.3619 + 21.4115i −0.760824 + 1.31779i
\(265\) −9.37767 16.2426i −0.576065 0.997775i
\(266\) −1.18516 −0.0726668
\(267\) −3.31872 5.74819i −0.203102 0.351783i
\(268\) 1.72574 2.98906i 0.105416 0.182586i
\(269\) 6.46541 0.394203 0.197102 0.980383i \(-0.436847\pi\)
0.197102 + 0.980383i \(0.436847\pi\)
\(270\) −6.36549 + 11.0254i −0.387392 + 0.670982i
\(271\) 7.27343 + 12.5979i 0.441829 + 0.765270i 0.997825 0.0659144i \(-0.0209964\pi\)
−0.555996 + 0.831185i \(0.687663\pi\)
\(272\) 1.72406 + 2.98615i 0.104536 + 0.181062i
\(273\) −1.76329 3.05411i −0.106719 0.184843i
\(274\) −1.24738 −0.0753570
\(275\) 5.77318 + 9.99944i 0.348136 + 0.602989i
\(276\) 0.292262 + 0.506213i 0.0175921 + 0.0304704i
\(277\) 9.82609 17.0193i 0.590392 1.02259i −0.403787 0.914853i \(-0.632306\pi\)
0.994179 0.107737i \(-0.0343603\pi\)
\(278\) −8.01539 + 13.8831i −0.480731 + 0.832651i
\(279\) −6.79267 −0.406667
\(280\) 2.98503 0.178390
\(281\) 1.49084 2.58221i 0.0889359 0.154041i −0.818126 0.575039i \(-0.804987\pi\)
0.907062 + 0.420998i \(0.138320\pi\)
\(282\) 18.1030 31.3553i 1.07802 1.86718i
\(283\) −2.01758 3.49455i −0.119933 0.207730i 0.799808 0.600256i \(-0.204935\pi\)
−0.919741 + 0.392526i \(0.871601\pi\)
\(284\) 0.0869919 + 0.150674i 0.00516202 + 0.00894088i
\(285\) −14.7159 −0.871695
\(286\) −12.4628 21.5862i −0.736942 1.27642i
\(287\) −1.80543 3.12709i −0.106571 0.184587i
\(288\) 0.941733 + 1.63113i 0.0554922 + 0.0961152i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) −3.90256 −0.229166
\(291\) −7.69636 + 13.3305i −0.451169 + 0.781447i
\(292\) 0.279491 + 0.484093i 0.0163560 + 0.0283294i
\(293\) −32.3236 −1.88837 −0.944183 0.329422i \(-0.893146\pi\)
−0.944183 + 0.329422i \(0.893146\pi\)
\(294\) 9.50651 + 16.4658i 0.554431 + 0.960303i
\(295\) 7.81556 13.5369i 0.455039 0.788151i
\(296\) −13.3009 + 23.0377i −0.773096 + 1.33904i
\(297\) −13.6076 −0.789594
\(298\) −9.94143 + 17.2191i −0.575891 + 0.997473i
\(299\) −5.38521 −0.311435
\(300\) 1.48937 0.0859889
\(301\) 1.11495 + 2.05856i 0.0642648 + 0.118653i
\(302\) −19.2477 −1.10758
\(303\) −6.48170 −0.372364
\(304\) −4.32111 + 7.48438i −0.247833 + 0.429258i
\(305\) 2.22086 0.127166
\(306\) 0.902573 1.56330i 0.0515967 0.0893681i
\(307\) 6.19107 10.7232i 0.353343 0.612008i −0.633490 0.773751i \(-0.718378\pi\)
0.986833 + 0.161743i \(0.0517115\pi\)
\(308\) 0.174570 + 0.302364i 0.00994704 + 0.0172288i
\(309\) 10.0884 0.573908
\(310\) 9.27780 + 16.0696i 0.526944 + 0.912693i
\(311\) 7.11938 12.3311i 0.403703 0.699234i −0.590467 0.807062i \(-0.701056\pi\)
0.994170 + 0.107828i \(0.0343897\pi\)
\(312\) −29.3815 −1.66340
\(313\) 12.1823 21.1004i 0.688587 1.19267i −0.283709 0.958911i \(-0.591565\pi\)
0.972295 0.233756i \(-0.0751018\pi\)
\(314\) −2.38012 4.12249i −0.134318 0.232646i
\(315\) −0.683878 1.18451i −0.0385322 0.0667397i
\(316\) −0.173191 0.299975i −0.00974273 0.0168749i
\(317\) 0.641654 0.0360389 0.0180194 0.999838i \(-0.494264\pi\)
0.0180194 + 0.999838i \(0.494264\pi\)
\(318\) 9.22940 + 15.9858i 0.517559 + 0.896439i
\(319\) −2.08564 3.61244i −0.116774 0.202258i
\(320\) 12.2650 21.2437i 0.685637 1.18756i
\(321\) 15.2702 26.4487i 0.852298 1.47622i
\(322\) −0.538463 −0.0300074
\(323\) −2.50636 −0.139458
\(324\) −1.38003 + 2.39028i −0.0766681 + 0.132793i
\(325\) −6.86078 + 11.8832i −0.380567 + 0.659162i
\(326\) −7.07924 12.2616i −0.392083 0.679108i
\(327\) 9.68521 + 16.7753i 0.535594 + 0.927675i
\(328\) −30.0836 −1.66109
\(329\) −2.33616 4.04635i −0.128797 0.223083i
\(330\) −15.4732 26.8004i −0.851771 1.47531i
\(331\) 14.4327 + 24.9982i 0.793294 + 1.37403i 0.923917 + 0.382593i \(0.124969\pi\)
−0.130623 + 0.991432i \(0.541698\pi\)
\(332\) −1.19807 + 2.07512i −0.0657528 + 0.113887i
\(333\) 12.1890 0.667954
\(334\) −10.8801 + 18.8449i −0.595333 + 1.03115i
\(335\) 19.7396 + 34.1900i 1.07849 + 1.86800i
\(336\) −2.57132 −0.140277
\(337\) −12.6770 21.9572i −0.690560 1.19608i −0.971655 0.236405i \(-0.924031\pi\)
0.281095 0.959680i \(-0.409302\pi\)
\(338\) 6.20152 10.7413i 0.337318 0.584252i
\(339\) −3.93683 + 6.81879i −0.213819 + 0.370346i
\(340\) 0.690790 0.0374634
\(341\) −9.91666 + 17.1762i −0.537017 + 0.930141i
\(342\) 4.52435 0.244649
\(343\) 4.95271 0.267421
\(344\) 19.4976 + 0.530731i 1.05124 + 0.0286151i
\(345\) −6.68600 −0.359962
\(346\) −5.88084 −0.316156
\(347\) −0.224642 + 0.389091i −0.0120594 + 0.0208875i −0.871992 0.489520i \(-0.837172\pi\)
0.859933 + 0.510407i \(0.170505\pi\)
\(348\) −0.538057 −0.0288429
\(349\) −8.43559 + 14.6109i −0.451547 + 0.782102i −0.998482 0.0550729i \(-0.982461\pi\)
0.546936 + 0.837175i \(0.315794\pi\)
\(350\) −0.686005 + 1.18819i −0.0366685 + 0.0635117i
\(351\) −8.08556 14.0046i −0.431575 0.747510i
\(352\) 5.49936 0.293117
\(353\) 6.06714 + 10.5086i 0.322921 + 0.559316i 0.981089 0.193555i \(-0.0620018\pi\)
−0.658168 + 0.752871i \(0.728668\pi\)
\(354\) −7.69199 + 13.3229i −0.408825 + 0.708105i
\(355\) −1.99009 −0.105623
\(356\) −0.390457 + 0.676292i −0.0206942 + 0.0358434i
\(357\) −0.372859 0.645811i −0.0197338 0.0341800i
\(358\) 7.21484 + 12.4965i 0.381316 + 0.660459i
\(359\) −17.3845 30.1109i −0.917520 1.58919i −0.803170 0.595750i \(-0.796855\pi\)
−0.114350 0.993441i \(-0.536478\pi\)
\(360\) −11.3954 −0.600589
\(361\) 6.35907 + 11.0142i 0.334688 + 0.579697i
\(362\) 7.62195 + 13.2016i 0.400601 + 0.693861i
\(363\) 5.05049 8.74770i 0.265082 0.459135i
\(364\) −0.207457 + 0.359325i −0.0108737 + 0.0188338i
\(365\) −6.39385 −0.334669
\(366\) −2.18575 −0.114251
\(367\) −5.03134 + 8.71453i −0.262634 + 0.454895i −0.966941 0.255000i \(-0.917924\pi\)
0.704307 + 0.709895i \(0.251258\pi\)
\(368\) −1.96324 + 3.40044i −0.102341 + 0.177260i
\(369\) 6.89223 + 11.9377i 0.358795 + 0.621452i
\(370\) −16.6484 28.8359i −0.865511 1.49911i
\(371\) 2.38208 0.123671
\(372\) 1.27916 + 2.21556i 0.0663211 + 0.114872i
\(373\) −8.03969 13.9251i −0.416279 0.721017i 0.579283 0.815127i \(-0.303333\pi\)
−0.995562 + 0.0941101i \(0.969999\pi\)
\(374\) −2.63534 4.56455i −0.136270 0.236027i
\(375\) 6.16056 10.6704i 0.318130 0.551017i
\(376\) −38.9272 −2.00752
\(377\) 2.47855 4.29298i 0.127652 0.221100i
\(378\) −0.808470 1.40031i −0.0415832 0.0720242i
\(379\) 23.1774 1.19054 0.595272 0.803525i \(-0.297044\pi\)
0.595272 + 0.803525i \(0.297044\pi\)
\(380\) 0.865685 + 1.49941i 0.0444087 + 0.0769182i
\(381\) −9.10022 + 15.7620i −0.466219 + 0.807514i
\(382\) 13.0092 22.5326i 0.665609 1.15287i
\(383\) 16.4355 0.839814 0.419907 0.907567i \(-0.362063\pi\)
0.419907 + 0.907567i \(0.362063\pi\)
\(384\) −9.18459 + 15.9082i −0.468699 + 0.811810i
\(385\) −3.99359 −0.203532
\(386\) −22.0626 −1.12296
\(387\) −4.25634 7.85856i −0.216362 0.399473i
\(388\) 1.81100 0.0919396
\(389\) −33.9128 −1.71945 −0.859724 0.510760i \(-0.829364\pi\)
−0.859724 + 0.510760i \(0.829364\pi\)
\(390\) 18.3882 31.8492i 0.931120 1.61275i
\(391\) −1.13874 −0.0575884
\(392\) 10.2210 17.7033i 0.516240 0.894153i
\(393\) −0.0290902 + 0.0503856i −0.00146740 + 0.00254162i
\(394\) 5.61185 + 9.72001i 0.282721 + 0.489687i
\(395\) 3.96203 0.199352
\(396\) −0.666421 1.15428i −0.0334889 0.0580045i
\(397\) −5.49988 + 9.52607i −0.276031 + 0.478100i −0.970395 0.241524i \(-0.922353\pi\)
0.694364 + 0.719624i \(0.255686\pi\)
\(398\) −32.5330 −1.63073
\(399\) 0.934521 1.61864i 0.0467845 0.0810332i
\(400\) 5.00236 + 8.66435i 0.250118 + 0.433217i
\(401\) 16.4027 + 28.4102i 0.819109 + 1.41874i 0.906339 + 0.422551i \(0.138865\pi\)
−0.0872299 + 0.996188i \(0.527801\pi\)
\(402\) −19.4275 33.6494i −0.968956 1.67828i
\(403\) −23.5697 −1.17409
\(404\) 0.381296 + 0.660423i 0.0189702 + 0.0328573i
\(405\) −15.7852 27.3409i −0.784375 1.35858i
\(406\) 0.247829 0.429252i 0.0122995 0.0213034i
\(407\) 17.7948 30.8215i 0.882056 1.52777i
\(408\) −6.21291 −0.307585
\(409\) −11.8274 −0.584825 −0.292412 0.956292i \(-0.594458\pi\)
−0.292412 + 0.956292i \(0.594458\pi\)
\(410\) 18.8276 32.6103i 0.929828 1.61051i
\(411\) 0.983582 1.70361i 0.0485165 0.0840331i
\(412\) −0.593464 1.02791i −0.0292379 0.0506415i
\(413\) 0.992640 + 1.71930i 0.0488446 + 0.0846014i
\(414\) 2.05559 0.101027
\(415\) −13.7040 23.7360i −0.672702 1.16515i
\(416\) 3.26769 + 5.65980i 0.160211 + 0.277494i
\(417\) −12.6406 21.8941i −0.619012 1.07216i
\(418\) 6.60512 11.4404i 0.323067 0.559569i
\(419\) 5.84162 0.285382 0.142691 0.989767i \(-0.454425\pi\)
0.142691 + 0.989767i \(0.454425\pi\)
\(420\) −0.257568 + 0.446120i −0.0125680 + 0.0217684i
\(421\) 7.70598 + 13.3472i 0.375567 + 0.650501i 0.990412 0.138147i \(-0.0441148\pi\)
−0.614845 + 0.788648i \(0.710781\pi\)
\(422\) −33.2816 −1.62012
\(423\) 8.91832 + 15.4470i 0.433623 + 0.751058i
\(424\) 9.92309 17.1873i 0.481908 0.834688i
\(425\) −1.45076 + 2.51278i −0.0703720 + 0.121888i
\(426\) 1.95863 0.0948958
\(427\) −0.141034 + 0.244278i −0.00682511 + 0.0118214i
\(428\) −3.59316 −0.173682
\(429\) 39.3087 1.89784
\(430\) −12.7777 + 20.8030i −0.616194 + 1.00321i
\(431\) −17.5524 −0.845470 −0.422735 0.906253i \(-0.638930\pi\)
−0.422735 + 0.906253i \(0.638930\pi\)
\(432\) −11.7908 −0.567284
\(433\) 10.5919 18.3456i 0.509012 0.881635i −0.490934 0.871197i \(-0.663344\pi\)
0.999946 0.0104375i \(-0.00332243\pi\)
\(434\) −2.35671 −0.113126
\(435\) 3.07724 5.32994i 0.147543 0.255551i
\(436\) 1.13949 1.97366i 0.0545719 0.0945213i
\(437\) −1.42704 2.47171i −0.0682647 0.118238i
\(438\) 6.29276 0.300680
\(439\) 15.3257 + 26.5449i 0.731457 + 1.26692i 0.956260 + 0.292516i \(0.0944926\pi\)
−0.224804 + 0.974404i \(0.572174\pi\)
\(440\) −16.6362 + 28.8147i −0.793098 + 1.37369i
\(441\) −9.36664 −0.446031
\(442\) 3.13181 5.42445i 0.148965 0.258015i
\(443\) −4.32851 7.49720i −0.205654 0.356203i 0.744687 0.667414i \(-0.232599\pi\)
−0.950341 + 0.311211i \(0.899265\pi\)
\(444\) −2.29536 3.97569i −0.108933 0.188678i
\(445\) −4.46619 7.73567i −0.211718 0.366706i
\(446\) −4.96651 −0.235171
\(447\) −15.6780 27.1551i −0.741544 1.28439i
\(448\) 1.55776 + 2.69812i 0.0735973 + 0.127474i
\(449\) −14.8605 + 25.7391i −0.701309 + 1.21470i 0.266698 + 0.963780i \(0.414067\pi\)
−0.968007 + 0.250923i \(0.919266\pi\)
\(450\) 2.61883 4.53594i 0.123453 0.213826i
\(451\) 40.2480 1.89520
\(452\) 0.926359 0.0435723
\(453\) 15.1772 26.2876i 0.713086 1.23510i
\(454\) −17.8485 + 30.9145i −0.837673 + 1.45089i
\(455\) −2.37296 4.11009i −0.111246 0.192684i
\(456\) −7.78590 13.4856i −0.364608 0.631520i
\(457\) −38.3052 −1.79184 −0.895922 0.444212i \(-0.853484\pi\)
−0.895922 + 0.444212i \(0.853484\pi\)
\(458\) −15.3285 26.5498i −0.716255 1.24059i
\(459\) −1.70974 2.96136i −0.0798040 0.138225i
\(460\) 0.393314 + 0.681240i 0.0183384 + 0.0317630i
\(461\) −2.89850 + 5.02035i −0.134997 + 0.233821i −0.925596 0.378513i \(-0.876436\pi\)
0.790600 + 0.612334i \(0.209769\pi\)
\(462\) 3.93045 0.182861
\(463\) −0.701480 + 1.21500i −0.0326006 + 0.0564658i −0.881865 0.471501i \(-0.843712\pi\)
0.849265 + 0.527967i \(0.177046\pi\)
\(464\) −1.80717 3.13012i −0.0838960 0.145312i
\(465\) −29.2629 −1.35703
\(466\) −9.22892 15.9850i −0.427521 0.740489i
\(467\) −10.1240 + 17.5352i −0.468482 + 0.811434i −0.999351 0.0360196i \(-0.988532\pi\)
0.530869 + 0.847454i \(0.321865\pi\)
\(468\) 0.791966 1.37173i 0.0366087 0.0634081i
\(469\) −5.01418 −0.231533
\(470\) 24.3622 42.1966i 1.12375 1.94639i
\(471\) 7.50708 0.345908
\(472\) 16.5402 0.761326
\(473\) −26.0852 0.710049i −1.19940 0.0326481i
\(474\) −3.89939 −0.179105
\(475\) −7.27224 −0.333673
\(476\) −0.0438680 + 0.0759816i −0.00201069 + 0.00348261i
\(477\) −9.09361 −0.416368
\(478\) −18.4163 + 31.8979i −0.842341 + 1.45898i
\(479\) 11.6743 20.2205i 0.533413 0.923898i −0.465825 0.884877i \(-0.654243\pi\)
0.999238 0.0390216i \(-0.0124241\pi\)
\(480\) 4.05699 + 7.02692i 0.185176 + 0.320734i
\(481\) 42.2943 1.92845
\(482\) 4.96032 + 8.59153i 0.225936 + 0.391333i
\(483\) 0.424588 0.735409i 0.0193194 0.0334623i
\(484\) −1.18841 −0.0540186
\(485\) −10.3574 + 17.9396i −0.470307 + 0.814596i
\(486\) 8.74211 + 15.1418i 0.396550 + 0.686845i
\(487\) −10.2567 17.7651i −0.464776 0.805015i 0.534416 0.845222i \(-0.320532\pi\)
−0.999191 + 0.0402068i \(0.987198\pi\)
\(488\) 1.17502 + 2.03519i 0.0531905 + 0.0921286i
\(489\) 22.3285 1.00973
\(490\) 12.7935 + 22.1589i 0.577950 + 1.00104i
\(491\) 14.5516 + 25.2042i 0.656706 + 1.13745i 0.981463 + 0.191651i \(0.0613843\pi\)
−0.324757 + 0.945798i \(0.605282\pi\)
\(492\) 2.59581 4.49607i 0.117028 0.202699i
\(493\) 0.524106 0.907778i 0.0236045 0.0408842i
\(494\) 15.6989 0.706326
\(495\) 15.2455 0.685236
\(496\) −8.59262 + 14.8828i −0.385820 + 0.668260i
\(497\) 0.126379 0.218895i 0.00566887 0.00981877i
\(498\) 13.4873 + 23.3607i 0.604382 + 1.04682i
\(499\) 12.6818 + 21.9655i 0.567714 + 0.983310i 0.996791 + 0.0800420i \(0.0255054\pi\)
−0.429077 + 0.903268i \(0.641161\pi\)
\(500\) −1.44962 −0.0648288
\(501\) −17.1583 29.7191i −0.766578 1.32775i
\(502\) 17.7947 + 30.8212i 0.794214 + 1.37562i
\(503\) 13.8934 + 24.0641i 0.619476 + 1.07296i 0.989581 + 0.143974i \(0.0459883\pi\)
−0.370105 + 0.928990i \(0.620678\pi\)
\(504\) 0.723653 1.25340i 0.0322341 0.0558311i
\(505\) −8.72280 −0.388159
\(506\) 3.00096 5.19782i 0.133409 0.231071i
\(507\) 9.78003 + 16.9395i 0.434346 + 0.752310i
\(508\) 2.14134 0.0950065
\(509\) 4.48123 + 7.76171i 0.198627 + 0.344032i 0.948083 0.318022i \(-0.103018\pi\)
−0.749457 + 0.662054i \(0.769685\pi\)
\(510\) 3.88829 6.73472i 0.172177 0.298218i
\(511\) 0.406036 0.703274i 0.0179620 0.0311110i
\(512\) 25.2776 1.11712
\(513\) 4.28524 7.42225i 0.189198 0.327700i
\(514\) 21.1665 0.933616
\(515\) 13.5765 0.598253
\(516\) −1.76169 + 2.86816i −0.0775542 + 0.126264i
\(517\) 52.0796 2.29046
\(518\) 4.22898 0.185811
\(519\) 4.63715 8.03179i 0.203548 0.352556i
\(520\) −39.5404 −1.73396
\(521\) 6.60683 11.4434i 0.289450 0.501343i −0.684228 0.729268i \(-0.739861\pi\)
0.973679 + 0.227925i \(0.0731941\pi\)
\(522\) −0.946088 + 1.63867i −0.0414091 + 0.0717227i
\(523\) −6.26508 10.8514i −0.273953 0.474500i 0.695918 0.718122i \(-0.254998\pi\)
−0.969870 + 0.243621i \(0.921665\pi\)
\(524\) 0.00684509 0.000299029
\(525\) −1.08186 1.87383i −0.0472160 0.0817806i
\(526\) 1.38676 2.40193i 0.0604654 0.104729i
\(527\) −4.98396 −0.217105
\(528\) 14.3305 24.8211i 0.623653 1.08020i
\(529\) 10.8516 + 18.7956i 0.471810 + 0.817200i
\(530\) 12.4205 + 21.5130i 0.539514 + 0.934466i
\(531\) −3.78941 6.56345i −0.164446 0.284829i
\(532\) −0.219898 −0.00953380
\(533\) 23.9151 + 41.4222i 1.03588 + 1.79419i
\(534\) 4.39558 + 7.61337i 0.190215 + 0.329463i
\(535\) 20.5500 35.5936i 0.888452 1.53884i
\(536\) −20.8877 + 36.1785i −0.902210 + 1.56267i
\(537\) −22.7561 −0.982000
\(538\) −8.56332 −0.369191
\(539\) −13.6744 + 23.6848i −0.588998 + 1.02017i
\(540\) −1.18107 + 2.04568i −0.0508253 + 0.0880321i
\(541\) 15.2447 + 26.4046i 0.655420 + 1.13522i 0.981788 + 0.189978i \(0.0608418\pi\)
−0.326368 + 0.945243i \(0.605825\pi\)
\(542\) −9.63352 16.6857i −0.413795 0.716714i
\(543\) −24.0402 −1.03166
\(544\) 0.690973 + 1.19680i 0.0296252 + 0.0513124i
\(545\) 13.0340 + 22.5755i 0.558313 + 0.967027i
\(546\) 2.33545 + 4.04511i 0.0999479 + 0.173115i
\(547\) −6.54873 + 11.3427i −0.280003 + 0.484980i −0.971385 0.237510i \(-0.923669\pi\)
0.691382 + 0.722489i \(0.257002\pi\)
\(548\) −0.231443 −0.00988675
\(549\) 0.538398 0.932532i 0.0229783 0.0397995i
\(550\) −7.64647 13.2441i −0.326047 0.564729i
\(551\) 2.62720 0.111922
\(552\) −3.53743 6.12702i −0.150563 0.260783i
\(553\) −0.251605 + 0.435793i −0.0106994 + 0.0185318i
\(554\) −13.0145 + 22.5417i −0.552932 + 0.957706i
\(555\) 52.5104 2.22894
\(556\) −1.48720 + 2.57591i −0.0630714 + 0.109243i
\(557\) −15.3484 −0.650333 −0.325167 0.945657i \(-0.605420\pi\)
−0.325167 + 0.945657i \(0.605420\pi\)
\(558\) 8.99677 0.380864
\(559\) −14.7689 27.2681i −0.624658 1.15332i
\(560\) −3.46037 −0.146228
\(561\) 8.31207 0.350936
\(562\) −1.97459 + 3.42008i −0.0832929 + 0.144268i
\(563\) −20.8536 −0.878875 −0.439438 0.898273i \(-0.644822\pi\)
−0.439438 + 0.898273i \(0.644822\pi\)
\(564\) 3.35889 5.81776i 0.141435 0.244972i
\(565\) −5.29802 + 9.17644i −0.222889 + 0.386056i
\(566\) 2.67225 + 4.62847i 0.112323 + 0.194549i
\(567\) 4.00971 0.168392
\(568\) −1.05292 1.82371i −0.0441795 0.0765211i
\(569\) −3.51989 + 6.09663i −0.147562 + 0.255584i −0.930326 0.366734i \(-0.880476\pi\)
0.782764 + 0.622318i \(0.213809\pi\)
\(570\) 19.4909 0.816386
\(571\) −10.3376 + 17.9053i −0.432617 + 0.749315i −0.997098 0.0761315i \(-0.975743\pi\)
0.564481 + 0.825446i \(0.309076\pi\)
\(572\) −2.31239 4.00518i −0.0966859 0.167465i
\(573\) 20.5160 + 35.5348i 0.857068 + 1.48449i
\(574\) 2.39126 + 4.14178i 0.0998091 + 0.172874i
\(575\) −3.30406 −0.137789
\(576\) −5.94677 10.3001i −0.247782 0.429171i
\(577\) 21.0641 + 36.4841i 0.876910 + 1.51885i 0.854714 + 0.519100i \(0.173733\pi\)
0.0221966 + 0.999754i \(0.492934\pi\)
\(578\) 0.662241 1.14703i 0.0275456 0.0477104i
\(579\) 17.3968 30.1322i 0.722987 1.25225i
\(580\) −0.724094 −0.0300664
\(581\) 3.48104 0.144418
\(582\) 10.1937 17.6560i 0.422542 0.731864i
\(583\) −13.2758 + 22.9944i −0.549827 + 0.952329i
\(584\) −3.38286 5.85929i −0.139984 0.242459i
\(585\) 9.05880 + 15.6903i 0.374535 + 0.648714i
\(586\) 42.8120 1.76855
\(587\) 17.5169 + 30.3401i 0.722998 + 1.25227i 0.959793 + 0.280710i \(0.0905700\pi\)
−0.236794 + 0.971560i \(0.576097\pi\)
\(588\) 1.76387 + 3.05511i 0.0727407 + 0.125991i
\(589\) −6.24580 10.8180i −0.257354 0.445750i
\(590\) −10.3516 + 17.9294i −0.426167 + 0.738143i
\(591\) −17.7002 −0.728089
\(592\) 15.4189 26.7063i 0.633713 1.09762i
\(593\) 1.72507 + 2.98791i 0.0708401 + 0.122699i 0.899270 0.437395i \(-0.144099\pi\)
−0.828430 + 0.560093i \(0.810765\pi\)
\(594\) 18.0230 0.739494
\(595\) −0.501778 0.869106i −0.0205709 0.0356299i
\(596\) −1.84456 + 3.19488i −0.0755563 + 0.130867i
\(597\) 25.6529 44.4321i 1.04990 1.81848i
\(598\) 7.13261 0.291674
\(599\) −13.3331 + 23.0935i −0.544774 + 0.943577i 0.453847 + 0.891080i \(0.350051\pi\)
−0.998621 + 0.0524969i \(0.983282\pi\)
\(600\) −18.0268 −0.735942
\(601\) 5.40057 0.220294 0.110147 0.993915i \(-0.464868\pi\)
0.110147 + 0.993915i \(0.464868\pi\)
\(602\) −1.47673 2.72652i −0.0601872 0.111125i
\(603\) 19.1417 0.779509
\(604\) −3.57128 −0.145313
\(605\) 6.79673 11.7723i 0.276327 0.478612i
\(606\) 8.58489 0.348737
\(607\) 8.84568 15.3212i 0.359035 0.621867i −0.628765 0.777595i \(-0.716439\pi\)
0.987800 + 0.155729i \(0.0497726\pi\)
\(608\) −1.73183 + 2.99962i −0.0702350 + 0.121651i
\(609\) 0.390835 + 0.676947i 0.0158374 + 0.0274313i
\(610\) −2.94149 −0.119098
\(611\) 30.9453 + 53.5989i 1.25191 + 2.16838i
\(612\) 0.167466 0.290060i 0.00676943 0.0117250i
\(613\) −36.3494 −1.46814 −0.734070 0.679074i \(-0.762381\pi\)
−0.734070 + 0.679074i \(0.762381\pi\)
\(614\) −8.19996 + 14.2027i −0.330923 + 0.573176i
\(615\) 29.6918 + 51.4277i 1.19729 + 2.07376i
\(616\) −2.11293 3.65970i −0.0851324 0.147454i
\(617\) −7.04369 12.2000i −0.283568 0.491155i 0.688693 0.725053i \(-0.258185\pi\)
−0.972261 + 0.233899i \(0.924852\pi\)
\(618\) −13.3619 −0.537494
\(619\) −5.74484 9.95035i −0.230905 0.399938i 0.727170 0.686457i \(-0.240835\pi\)
−0.958075 + 0.286519i \(0.907502\pi\)
\(620\) 1.72143 + 2.98161i 0.0691344 + 0.119744i
\(621\) 1.94695 3.37221i 0.0781283 0.135322i
\(622\) −9.42948 + 16.3323i −0.378088 + 0.654867i
\(623\) 1.13449 0.0454522
\(624\) 34.0603 1.36350
\(625\) 15.5444 26.9237i 0.621776 1.07695i
\(626\) −16.1353 + 27.9471i −0.644896 + 1.11699i
\(627\) 10.4165 + 18.0420i 0.415996 + 0.720526i
\(628\) −0.441615 0.764900i −0.0176224 0.0305229i
\(629\) 8.94339 0.356596
\(630\) 0.905784 + 1.56886i 0.0360873 + 0.0625050i
\(631\) −14.9497 25.8936i −0.595137 1.03081i −0.993528 0.113591i \(-0.963765\pi\)
0.398391 0.917216i \(-0.369569\pi\)
\(632\) 2.09624 + 3.63079i 0.0833838 + 0.144425i
\(633\) 26.2432 45.4545i 1.04307 1.80665i
\(634\) −0.849859 −0.0337522
\(635\) −12.2467 + 21.2119i −0.485995 + 0.841769i
\(636\) 1.71245 + 2.96606i 0.0679032 + 0.117612i
\(637\) −32.5010 −1.28774
\(638\) 2.76240 + 4.78461i 0.109364 + 0.189424i
\(639\) −0.482452 + 0.835632i −0.0190855 + 0.0330571i
\(640\) −12.3602 + 21.4086i −0.488581 + 0.846247i
\(641\) 38.3573 1.51502 0.757512 0.652821i \(-0.226415\pi\)
0.757512 + 0.652821i \(0.226415\pi\)
\(642\) −20.2251 + 35.0308i −0.798219 + 1.38256i
\(643\) 27.8773 1.09937 0.549686 0.835371i \(-0.314747\pi\)
0.549686 + 0.835371i \(0.314747\pi\)
\(644\) −0.0999082 −0.00393694
\(645\) −18.3363 33.8547i −0.721992 1.33303i
\(646\) 3.31963 0.130609
\(647\) −4.71992 −0.185559 −0.0927796 0.995687i \(-0.529575\pi\)
−0.0927796 + 0.995687i \(0.529575\pi\)
\(648\) 16.7033 28.9310i 0.656169 1.13652i
\(649\) −22.1287 −0.868627
\(650\) 9.08697 15.7391i 0.356420 0.617338i
\(651\) 1.85831 3.21869i 0.0728331 0.126151i
\(652\) −1.31351 2.27506i −0.0514408 0.0890982i
\(653\) −19.0543 −0.745653 −0.372827 0.927901i \(-0.621611\pi\)
−0.372827 + 0.927901i \(0.621611\pi\)
\(654\) −12.8279 22.2186i −0.501610 0.868814i
\(655\) −0.0391483 + 0.0678069i −0.00152965 + 0.00264943i
\(656\) 34.8742 1.36161
\(657\) −1.55004 + 2.68475i −0.0604729 + 0.104742i
\(658\) 3.09421 + 5.35932i 0.120625 + 0.208928i
\(659\) 6.88143 + 11.9190i 0.268063 + 0.464298i 0.968361 0.249552i \(-0.0802833\pi\)
−0.700299 + 0.713850i \(0.746950\pi\)
\(660\) −2.87095 4.97263i −0.111751 0.193559i
\(661\) −6.32246 −0.245915 −0.122958 0.992412i \(-0.539238\pi\)
−0.122958 + 0.992412i \(0.539238\pi\)
\(662\) −19.1159 33.1096i −0.742959 1.28684i
\(663\) 4.93898 + 8.55456i 0.191814 + 0.332232i
\(664\) 14.5010 25.1165i 0.562749 0.974711i
\(665\) 1.25764 2.17829i 0.0487691 0.0844706i
\(666\) −16.1441 −0.625573
\(667\) 1.19364 0.0462178
\(668\) −2.01873 + 3.49654i −0.0781070 + 0.135285i
\(669\) 3.91619 6.78304i 0.151409 0.262247i
\(670\) −26.1447 45.2840i −1.01006 1.74947i
\(671\) −1.57202 2.72282i −0.0606871 0.105113i
\(672\) −1.03054 −0.0397541
\(673\) −12.3506 21.3919i −0.476081 0.824596i 0.523544 0.851999i \(-0.324610\pi\)
−0.999624 + 0.0274028i \(0.991276\pi\)
\(674\) 16.7904 + 29.0819i 0.646744 + 1.12019i
\(675\) −4.96084 8.59243i −0.190943 0.330723i
\(676\) 1.15065 1.99298i 0.0442558 0.0766532i
\(677\) 20.9415 0.804846 0.402423 0.915454i \(-0.368168\pi\)
0.402423 + 0.915454i \(0.368168\pi\)
\(678\) 5.21426 9.03136i 0.200252 0.346847i
\(679\) −1.31548 2.27848i −0.0504835 0.0874400i
\(680\) −8.36107 −0.320633
\(681\) −28.1478 48.7534i −1.07863 1.86823i
\(682\) 13.1344 22.7495i 0.502943 0.871123i
\(683\) 0.611462 1.05908i 0.0233969 0.0405247i −0.854090 0.520125i \(-0.825885\pi\)
0.877487 + 0.479601i \(0.159219\pi\)
\(684\) 0.839463 0.0320977
\(685\) 1.32366 2.29265i 0.0505746 0.0875978i
\(686\) −6.55977 −0.250453
\(687\) 48.3473 1.84456
\(688\) −22.6024 0.615245i −0.861708 0.0234560i
\(689\) −31.5536 −1.20210
\(690\) 8.85548 0.337122
\(691\) −2.04517 + 3.54233i −0.0778018 + 0.134757i −0.902301 0.431106i \(-0.858123\pi\)
0.824499 + 0.565863i \(0.191457\pi\)
\(692\) −1.09115 −0.0414793
\(693\) −0.968154 + 1.67689i −0.0367771 + 0.0636999i
\(694\) 0.297534 0.515344i 0.0112942 0.0195622i
\(695\) −17.0112 29.4642i −0.645270 1.11764i
\(696\) 6.51244 0.246854
\(697\) 5.05700 + 8.75899i 0.191548 + 0.331770i
\(698\) 11.1728 19.3518i 0.422896 0.732477i
\(699\) 29.1087 1.10099
\(700\) −0.127284 + 0.220462i −0.00481086 + 0.00833266i
\(701\) −13.3092 23.0521i −0.502680 0.870667i −0.999995 0.00309698i \(-0.999014\pi\)
0.497316 0.867570i \(-0.334319\pi\)
\(702\) 10.7092 + 18.5488i 0.404192 + 0.700081i
\(703\) 11.2077 + 19.4123i 0.422706 + 0.732149i
\(704\) −34.7268 −1.30882
\(705\) 38.4202 + 66.5457i 1.44699 + 2.50626i
\(706\) −8.03581 13.9184i −0.302432 0.523827i
\(707\) 0.553934 0.959441i 0.0208328 0.0360835i
\(708\) −1.42720 + 2.47198i −0.0536374 + 0.0929026i
\(709\) −45.0283 −1.69107 −0.845536 0.533918i \(-0.820719\pi\)
−0.845536 + 0.533918i \(0.820719\pi\)
\(710\) 2.63584 0.0989212
\(711\) 0.960505 1.66364i 0.0360218 0.0623915i
\(712\) 4.72595 8.18559i 0.177113 0.306768i
\(713\) −2.83771 4.91505i −0.106273 0.184070i
\(714\) 0.493845 + 0.855365i 0.0184817 + 0.0320112i
\(715\) 52.8999 1.97835
\(716\) 1.33866 + 2.31863i 0.0500282 + 0.0866514i
\(717\) −29.0432 50.3043i −1.08464 1.87865i
\(718\) 23.0255 + 39.8813i 0.859303 + 1.48836i
\(719\) −0.252554 + 0.437436i −0.00941868 + 0.0163136i −0.870696 0.491821i \(-0.836331\pi\)
0.861278 + 0.508135i \(0.169665\pi\)
\(720\) 13.2100 0.492308
\(721\) −0.862165 + 1.49331i −0.0321087 + 0.0556139i
\(722\) −8.42248 14.5882i −0.313452 0.542915i
\(723\) −15.6452 −0.581852
\(724\) 1.41420 + 2.44947i 0.0525584 + 0.0910338i
\(725\) 1.52070 2.63393i 0.0564773 0.0978216i
\(726\) −6.68928 + 11.5862i −0.248262 + 0.430003i
\(727\) 6.17679 0.229084 0.114542 0.993418i \(-0.463460\pi\)
0.114542 + 0.993418i \(0.463460\pi\)
\(728\) 2.51098 4.34914i 0.0930631 0.161190i
\(729\) 6.12034 0.226679
\(730\) 8.46853 0.313434
\(731\) −3.12298 5.76602i −0.115508 0.213264i
\(732\) −0.405551 −0.0149896
\(733\) −6.44519 −0.238059 −0.119029 0.992891i \(-0.537978\pi\)
−0.119029 + 0.992891i \(0.537978\pi\)
\(734\) 6.66391 11.5422i 0.245970 0.426032i
\(735\) −40.3516 −1.48839
\(736\) −0.786837 + 1.36284i −0.0290032 + 0.0502350i
\(737\) 27.9450 48.4022i 1.02937 1.78292i
\(738\) −9.12864 15.8113i −0.336030 0.582021i
\(739\) −24.6756 −0.907708 −0.453854 0.891076i \(-0.649951\pi\)
−0.453854 + 0.891076i \(0.649951\pi\)
\(740\) −3.08900 5.35031i −0.113554 0.196681i
\(741\) −12.3789 + 21.4408i −0.454749 + 0.787649i
\(742\) −3.15502 −0.115825
\(743\) −8.18646 + 14.1794i −0.300332 + 0.520190i −0.976211 0.216822i \(-0.930431\pi\)
0.675879 + 0.737012i \(0.263764\pi\)
\(744\) −15.4824 26.8164i −0.567614 0.983136i
\(745\) −21.0988 36.5442i −0.773000 1.33888i
\(746\) 10.6484 + 18.4436i 0.389866 + 0.675268i
\(747\) −13.2889 −0.486215
\(748\) −0.488970 0.846921i −0.0178785 0.0309665i
\(749\) 2.61001 + 4.52067i 0.0953678 + 0.165182i
\(750\) −8.15954 + 14.1327i −0.297944 + 0.516055i
\(751\) −3.88963 + 6.73704i −0.141935 + 0.245838i −0.928225 0.372019i \(-0.878666\pi\)
0.786290 + 0.617857i \(0.211999\pi\)
\(752\) 45.1261 1.64558
\(753\) −56.1257 −2.04533
\(754\) −3.28280 + 5.68597i −0.119552 + 0.207071i
\(755\) 20.4248 35.3768i 0.743335 1.28749i
\(756\) −0.150006 0.259818i −0.00545567 0.00944950i
\(757\) −0.341751 0.591930i −0.0124211 0.0215140i 0.859748 0.510718i \(-0.170621\pi\)
−0.872169 + 0.489204i \(0.837287\pi\)
\(758\) −30.6980 −1.11500
\(759\) 4.73263 + 8.19715i 0.171784 + 0.297538i
\(760\) −10.4779 18.1483i −0.380075 0.658309i
\(761\) 7.68022 + 13.3025i 0.278408 + 0.482216i 0.970989 0.239123i \(-0.0768600\pi\)
−0.692581 + 0.721340i \(0.743527\pi\)
\(762\) 12.0531 20.8765i 0.436637 0.756277i
\(763\) −3.31084 −0.119860
\(764\) 2.41377 4.18077i 0.0873271 0.151255i
\(765\) 1.91554 + 3.31782i 0.0692566 + 0.119956i
\(766\) −21.7685 −0.786528
\(767\) −13.1487 22.7743i −0.474773 0.822331i
\(768\) −6.06290 + 10.5013i −0.218776 + 0.378931i
\(769\) 8.17314 14.1563i 0.294731 0.510489i −0.680191 0.733035i \(-0.738103\pi\)
0.974922 + 0.222546i \(0.0714366\pi\)
\(770\) 5.28943 0.190618
\(771\) −16.6902 + 28.9083i −0.601084 + 1.04111i
\(772\) −4.09357 −0.147331
\(773\) −10.0417 −0.361176 −0.180588 0.983559i \(-0.557800\pi\)
−0.180588 + 0.983559i \(0.557800\pi\)
\(774\) 5.63744 + 10.4085i 0.202634 + 0.374126i
\(775\) −14.4610 −0.519454
\(776\) −21.9197 −0.786871
\(777\) −3.33463 + 5.77574i −0.119629 + 0.207204i
\(778\) 44.9169 1.61035
\(779\) −12.6747 + 21.9532i −0.454118 + 0.786555i
\(780\) 3.41180 5.90941i 0.122162 0.211591i
\(781\) 1.40867 + 2.43989i 0.0504061 + 0.0873060i
\(782\) 1.50824 0.0539344
\(783\) 1.79217 + 3.10413i 0.0640470 + 0.110933i
\(784\) −11.8486 + 20.5224i −0.423166 + 0.732944i
\(785\) 10.1027 0.360582
\(786\) 0.0385294 0.0667348i 0.00137430 0.00238035i
\(787\) 26.4315 + 45.7807i 0.942182 + 1.63191i 0.761298 + 0.648402i \(0.224563\pi\)
0.180884 + 0.983504i \(0.442104\pi\)
\(788\) 1.04124 + 1.80348i 0.0370927 + 0.0642464i
\(789\) 2.18697 + 3.78794i 0.0778580 + 0.134854i
\(790\) −5.24764 −0.186703
\(791\) −0.672892 1.16548i −0.0239253 0.0414398i
\(792\) 8.06612 + 13.9709i 0.286617 + 0.496435i
\(793\) 1.86817 3.23576i 0.0663406 0.114905i
\(794\) 7.28449 12.6171i 0.258517 0.447764i
\(795\) −39.1753 −1.38941
\(796\) −6.03627 −0.213950
\(797\) 24.2486 41.9998i 0.858928 1.48771i −0.0140235 0.999902i \(-0.504464\pi\)
0.872952 0.487806i \(-0.162203\pi\)
\(798\) −1.23776 + 2.14385i −0.0438161 + 0.0758916i
\(799\) 6.54359 + 11.3338i 0.231496 + 0.400962i
\(800\) 2.00487 + 3.47253i 0.0708827 + 0.122772i
\(801\) −4.33091 −0.153025
\(802\) −21.7250 37.6288i −0.767137 1.32872i
\(803\) 4.52583 + 7.83897i 0.159713 + 0.276631i
\(804\) −3.60464 6.24342i −0.127126 0.220189i
\(805\) 0.571393 0.989682i 0.0201390 0.0348817i
\(806\) 31.2176 1.09959
\(807\) 6.75234 11.6954i 0.237694 0.411697i
\(808\) −4.61507 7.99353i −0.162357 0.281211i
\(809\) 19.7172 0.693219 0.346610 0.938009i \(-0.387333\pi\)
0.346610 + 0.938009i \(0.387333\pi\)
\(810\) 20.9073 + 36.2125i 0.734607 + 1.27238i
\(811\) 20.1546 34.9088i 0.707724 1.22581i −0.257976 0.966151i \(-0.583055\pi\)
0.965699 0.259662i \(-0.0836112\pi\)
\(812\) 0.0459830 0.0796448i 0.00161369 0.00279498i
\(813\) 30.3848 1.06564
\(814\) −23.5689 + 40.8225i −0.826090 + 1.43083i
\(815\) 30.0487 1.05256
\(816\) 7.20227 0.252130
\(817\) 8.60191 14.0045i 0.300943 0.489956i
\(818\) 15.6651 0.547718
\(819\) −2.30108 −0.0804064
\(820\) 3.49333 6.05062i 0.121992 0.211297i
\(821\) −13.3494 −0.465897 −0.232949 0.972489i \(-0.574837\pi\)
−0.232949 + 0.972489i \(0.574837\pi\)
\(822\) −1.30274 + 2.25641i −0.0454382 + 0.0787012i
\(823\) 7.12218 12.3360i 0.248264 0.430005i −0.714780 0.699349i \(-0.753473\pi\)
0.963044 + 0.269344i \(0.0868067\pi\)
\(824\) 7.18308 + 12.4415i 0.250234 + 0.433419i
\(825\) 24.1176 0.839665
\(826\) −1.31473 2.27718i −0.0457454 0.0792334i
\(827\) −10.0694 + 17.4407i −0.350148 + 0.606474i −0.986275 0.165110i \(-0.947202\pi\)
0.636127 + 0.771584i \(0.280535\pi\)
\(828\) 0.381400 0.0132546
\(829\) −10.5418 + 18.2590i −0.366133 + 0.634161i −0.988957 0.148201i \(-0.952652\pi\)
0.622824 + 0.782362i \(0.285985\pi\)
\(830\) 18.1507 + 31.4379i 0.630019 + 1.09123i
\(831\) −20.5243 35.5492i −0.711981 1.23319i
\(832\) −20.6345 35.7400i −0.715372 1.23906i
\(833\) −6.87254 −0.238119
\(834\) 16.7422 + 28.9984i 0.579735 + 1.00413i
\(835\) −23.0910 39.9947i −0.799096 1.38407i
\(836\) 1.22554 2.12269i 0.0423860 0.0734148i
\(837\) 8.52129 14.7593i 0.294539 0.510156i
\(838\) −7.73712 −0.267274
\(839\) −24.2961 −0.838796 −0.419398 0.907802i \(-0.637759\pi\)
−0.419398 + 0.907802i \(0.637759\pi\)
\(840\) 3.11750 5.39968i 0.107564 0.186307i
\(841\) 13.9506 24.1632i 0.481056 0.833214i
\(842\) −10.2064 17.6781i −0.351737 0.609226i
\(843\) −3.11400 5.39360i −0.107252 0.185766i
\(844\) −6.17517 −0.212558
\(845\) 13.1616 + 22.7965i 0.452771 + 0.784223i
\(846\) −11.8121 20.4592i −0.406110 0.703403i
\(847\) 0.863241 + 1.49518i 0.0296613 + 0.0513749i
\(848\) −11.5033 + 19.9242i −0.395023 + 0.684201i
\(849\) −8.42848 −0.289265
\(850\) 1.92150 3.32813i 0.0659069 0.114154i
\(851\) 5.09208 + 8.81975i 0.174554 + 0.302337i
\(852\) 0.363410 0.0124502
\(853\) 17.3422 + 30.0376i 0.593786 + 1.02847i 0.993717 + 0.111923i \(0.0357009\pi\)
−0.399931 + 0.916545i \(0.630966\pi\)
\(854\) 0.186797 0.323542i 0.00639206 0.0110714i
\(855\) −4.80104 + 8.31565i −0.164192 + 0.284389i
\(856\) 43.4903 1.48647
\(857\) −0.501912 + 0.869336i −0.0171450 + 0.0296960i −0.874471 0.485079i \(-0.838791\pi\)
0.857326 + 0.514774i \(0.172124\pi\)
\(858\) −52.0636 −1.77742
\(859\) 31.4412 1.07276 0.536379 0.843977i \(-0.319792\pi\)
0.536379 + 0.843977i \(0.319792\pi\)
\(860\) −2.37081 + 3.85985i −0.0808440 + 0.131620i
\(861\) −7.54220 −0.257038
\(862\) 23.2478 0.791825
\(863\) 12.6616 21.9305i 0.431006 0.746523i −0.565955 0.824436i \(-0.691492\pi\)
0.996960 + 0.0779129i \(0.0248256\pi\)
\(864\) −4.72555 −0.160766
\(865\) 6.24049 10.8088i 0.212183 0.367512i
\(866\) −14.0287 + 24.2984i −0.476715 + 0.825695i
\(867\) 1.04438 + 1.80892i 0.0354690 + 0.0614340i
\(868\) −0.437273 −0.0148420
\(869\) −2.80449 4.85752i −0.0951359 0.164780i
\(870\) −4.07575 + 7.05941i −0.138181 + 0.239336i
\(871\) 66.4190 2.25052
\(872\) −13.7920 + 23.8885i −0.467057 + 0.808967i
\(873\) 5.02185 + 8.69810i 0.169964 + 0.294386i
\(874\) 1.89009 + 3.27374i 0.0639333 + 0.110736i
\(875\) 1.05298 + 1.82381i 0.0355971 + 0.0616560i
\(876\) 1.16758 0.0394488
\(877\) 3.06721 + 5.31256i 0.103572 + 0.179392i 0.913154 0.407615i \(-0.133639\pi\)
−0.809582 + 0.587007i \(0.800306\pi\)
\(878\) −20.2986 35.1583i −0.685046 1.18653i
\(879\) −33.7581 + 58.4707i −1.13863 + 1.97217i
\(880\) 19.2853 33.4032i 0.650109 1.12602i
\(881\) −36.8129 −1.24026 −0.620130 0.784499i \(-0.712920\pi\)
−0.620130 + 0.784499i \(0.712920\pi\)
\(882\) 12.4059 0.417730
\(883\) −15.3041 + 26.5075i −0.515025 + 0.892049i 0.484823 + 0.874612i \(0.338884\pi\)
−0.999848 + 0.0174367i \(0.994449\pi\)
\(884\) 0.581086 1.00647i 0.0195440 0.0338512i
\(885\) −16.3248 28.2754i −0.548752 0.950467i
\(886\) 5.73303 + 9.92990i 0.192605 + 0.333601i
\(887\) 13.7973 0.463268 0.231634 0.972803i \(-0.425593\pi\)
0.231634 + 0.972803i \(0.425593\pi\)
\(888\) 27.7823 + 48.1203i 0.932311 + 1.61481i
\(889\) −1.55543 2.69409i −0.0521675 0.0903568i
\(890\) 5.91539 + 10.2458i 0.198284 + 0.343438i
\(891\) −22.3469 + 38.7060i −0.748650 + 1.29670i
\(892\) −0.921503 −0.0308542
\(893\) −16.4006 + 28.4067i −0.548826 + 0.950594i
\(894\) 20.7652 + 35.9664i 0.694493 + 1.20290i
\(895\) −30.6243 −1.02366
\(896\) −1.56985 2.71906i −0.0524450 0.0908375i
\(897\) −5.62419 + 9.74139i −0.187786 + 0.325256i
\(898\) 19.6824 34.0910i 0.656811 1.13763i
\(899\) 5.22424 0.174238
\(900\) 0.485906 0.841613i 0.0161969 0.0280538i
\(901\) −6.67221 −0.222284
\(902\) −53.3077 −1.77495
\(903\) 4.88819 + 0.133058i 0.162669 + 0.00442790i
\(904\) −11.2123 −0.372916
\(905\) −32.3523 −1.07543
\(906\) −20.1019 + 34.8175i −0.667841 + 1.15673i
\(907\) −53.1994 −1.76646 −0.883229 0.468941i \(-0.844636\pi\)
−0.883229 + 0.468941i \(0.844636\pi\)
\(908\) −3.31167 + 5.73598i −0.109902 + 0.190355i
\(909\) −2.11464 + 3.66267i −0.0701383 + 0.121483i
\(910\) 3.14295 + 5.44374i 0.104188 + 0.180458i
\(911\) 13.0310 0.431735 0.215868 0.976423i \(-0.430742\pi\)
0.215868 + 0.976423i \(0.430742\pi\)
\(912\) 9.02575 + 15.6331i 0.298872 + 0.517662i
\(913\) −19.4005 + 33.6027i −0.642063 + 1.11209i
\(914\) 50.7346 1.67815
\(915\) 2.31942 4.01736i 0.0766777 0.132810i
\(916\) −2.84410 4.92613i −0.0939718 0.162764i
\(917\) −0.00497216 0.00861203i −0.000164195 0.000284394i
\(918\) 2.26452 + 3.92227i 0.0747404 + 0.129454i
\(919\) −20.4333 −0.674031 −0.337015 0.941499i \(-0.609417\pi\)
−0.337015 + 0.941499i \(0.609417\pi\)
\(920\) −4.76053 8.24548i −0.156950 0.271845i
\(921\) −12.9316 22.3983i −0.426112 0.738048i
\(922\) 3.83901 6.64936i 0.126431 0.218985i
\(923\) −1.67404 + 2.89953i −0.0551018 + 0.0954391i
\(924\) 0.729268 0.0239912
\(925\) 25.9494 0.853209
\(926\) 0.929098 1.60924i 0.0305321 0.0528831i
\(927\) 3.29132 5.70074i 0.108101 0.187237i
\(928\) −0.724286 1.25450i −0.0237759 0.0411810i
\(929\) 27.9368 + 48.3880i 0.916577 + 1.58756i 0.804576 + 0.593850i \(0.202393\pi\)
0.112001 + 0.993708i \(0.464274\pi\)
\(930\) 38.7582 1.27093
\(931\) −8.61254 14.9174i −0.282265 0.488897i
\(932\) −1.71236 2.96590i −0.0560903 0.0971513i
\(933\) −14.8707 25.7567i −0.486843 0.843237i
\(934\) 13.4090 23.2251i 0.438756 0.759948i
\(935\) 11.1860 0.365822
\(936\) −9.58568 + 16.6029i −0.313318 + 0.542682i
\(937\) 25.8992 + 44.8587i 0.846090 + 1.46547i 0.884671 + 0.466216i \(0.154383\pi\)
−0.0385810 + 0.999255i \(0.512284\pi\)
\(938\) 6.64119 0.216843
\(939\) −25.4460 44.0737i −0.830397 1.43829i
\(940\) 4.52025 7.82930i 0.147434 0.255364i
\(941\) −27.8664 + 48.2660i −0.908418 + 1.57343i −0.0921550 + 0.995745i \(0.529376\pi\)
−0.816263 + 0.577681i \(0.803958\pi\)
\(942\) −9.94299 −0.323960
\(943\) −5.75860 + 9.97418i −0.187526 + 0.324804i
\(944\) −19.1741 −0.624065
\(945\) 3.43165 0.111632
\(946\) 34.5494 + 0.940446i 1.12330 + 0.0305765i
\(947\) 2.64708 0.0860185 0.0430093 0.999075i \(-0.486305\pi\)
0.0430093 + 0.999075i \(0.486305\pi\)
\(948\) −0.723506 −0.0234984
\(949\) −5.37844 + 9.31573i −0.174592 + 0.302401i
\(950\) 9.63194 0.312502
\(951\) 0.670130 1.16070i 0.0217304 0.0376382i
\(952\) 0.530963 0.919654i 0.0172086 0.0298062i
\(953\) −15.7864 27.3428i −0.511371 0.885720i −0.999913 0.0131800i \(-0.995805\pi\)
0.488542 0.872540i \(-0.337529\pi\)
\(954\) 12.0443 0.389949
\(955\) 27.6096 + 47.8212i 0.893425 + 1.54746i
\(956\) −3.41702 + 5.91845i −0.110514 + 0.191416i
\(957\) −8.71280 −0.281645
\(958\) −15.4624 + 26.7817i −0.499568 + 0.865277i
\(959\) 0.168116 + 0.291186i 0.00542876 + 0.00940288i
\(960\) −25.6187 44.3729i −0.826840 1.43213i
\(961\) 3.08009 + 5.33488i 0.0993578 + 0.172093i
\(962\) −56.0180 −1.80609
\(963\) −9.96374 17.2577i −0.321077 0.556122i
\(964\) 0.920354 + 1.59410i 0.0296426 + 0.0513425i
\(965\) 23.4119 40.5506i 0.753656 1.30537i
\(966\) −0.562360 + 0.974035i −0.0180936 + 0.0313391i
\(967\) 13.8022 0.443848 0.221924 0.975064i \(-0.428766\pi\)
0.221924 + 0.975064i \(0.428766\pi\)
\(968\) 14.3841 0.462322
\(969\) −2.61759 + 4.53380i −0.0840892 + 0.145647i
\(970\) 13.7182 23.7607i 0.440466 0.762910i
\(971\) 23.9605 + 41.5007i 0.768928 + 1.33182i 0.938145 + 0.346243i \(0.112543\pi\)
−0.169217 + 0.985579i \(0.554124\pi\)
\(972\) 1.62204 + 2.80945i 0.0520269 + 0.0901133i
\(973\) 4.32111 0.138529
\(974\) 13.5848 + 23.5296i 0.435285 + 0.753937i
\(975\) 14.3305 + 24.8211i 0.458943 + 0.794913i
\(976\) −1.36213 2.35927i −0.0436006 0.0755185i
\(977\) −18.9377 + 32.8011i −0.605871 + 1.04940i 0.386042 + 0.922481i \(0.373842\pi\)
−0.991913 + 0.126918i \(0.959491\pi\)
\(978\) −29.5736 −0.945661
\(979\) −6.32271 + 10.9513i −0.202075 + 0.350004i
\(980\) 2.37374 + 4.11144i 0.0758264 + 0.131335i
\(981\) 12.6391 0.403537
\(982\) −19.2734 33.3825i −0.615038 1.06528i
\(983\) 14.8151 25.6606i 0.472530 0.818445i −0.526976 0.849880i \(-0.676674\pi\)
0.999506 + 0.0314347i \(0.0100076\pi\)
\(984\) −31.4187 + 54.4188i −1.00159 + 1.73481i
\(985\) −23.8202 −0.758974
\(986\) −0.694168 + 1.20233i −0.0221068 + 0.0382901i
\(987\) −9.75936 −0.310644
\(988\) 2.91282 0.0926692
\(989\) 3.90818 6.36279i 0.124273 0.202325i
\(990\) −20.1924 −0.641758
\(991\) 29.5593 0.938984 0.469492 0.882937i \(-0.344437\pi\)
0.469492 + 0.882937i \(0.344437\pi\)
\(992\) −3.44378 + 5.96480i −0.109340 + 0.189383i
\(993\) 60.2929 1.91334
\(994\) −0.167387 + 0.289922i −0.00530918 + 0.00919577i
\(995\) 34.5225 59.7948i 1.09444 1.89562i
\(996\) 2.50248 + 4.33443i 0.0792942 + 0.137342i
\(997\) −42.3784 −1.34214 −0.671068 0.741396i \(-0.734164\pi\)
−0.671068 + 0.741396i \(0.734164\pi\)
\(998\) −16.7968 29.0929i −0.531693 0.920919i
\(999\) −15.2909 + 26.4846i −0.483783 + 0.837937i
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.e.b.307.9 58
43.36 even 3 inner 731.2.e.b.681.9 yes 58
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.e.b.307.9 58 1.1 even 1 trivial
731.2.e.b.681.9 yes 58 43.36 even 3 inner