Properties

Label 117.2.bc.a.20.4
Level $117$
Weight $2$
Character 117.20
Analytic conductor $0.934$
Analytic rank $0$
Dimension $48$
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] = [117,2,Mod(20,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.20");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 117.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.934249703649\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 20.4
Character \(\chi\) \(=\) 117.20
Dual form 117.2.bc.a.41.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.55681 - 0.417145i) q^{2} +(-1.30216 + 1.14210i) q^{3} +(0.517589 + 0.298830i) q^{4} +(-0.690114 - 0.184916i) q^{5} +(2.50363 - 1.23483i) q^{6} +(3.10547 - 3.10547i) q^{7} +(1.59819 + 1.59819i) q^{8} +(0.391235 - 2.97438i) q^{9} +O(q^{10})\) \(q+(-1.55681 - 0.417145i) q^{2} +(-1.30216 + 1.14210i) q^{3} +(0.517589 + 0.298830i) q^{4} +(-0.690114 - 0.184916i) q^{5} +(2.50363 - 1.23483i) q^{6} +(3.10547 - 3.10547i) q^{7} +(1.59819 + 1.59819i) q^{8} +(0.391235 - 2.97438i) q^{9} +(0.997239 + 0.575756i) q^{10} +(0.453556 - 1.69270i) q^{11} +(-1.01528 + 0.202012i) q^{12} +(3.59178 + 0.314864i) q^{13} +(-6.13006 + 3.53919i) q^{14} +(1.10983 - 0.547387i) q^{15} +(-2.41906 - 4.18994i) q^{16} +(-2.96481 - 5.13520i) q^{17} +(-1.84983 + 4.46734i) q^{18} +(-0.836286 + 3.12106i) q^{19} +(-0.301937 - 0.301937i) q^{20} +(-0.497071 + 7.59056i) q^{21} +(-1.41220 + 2.44600i) q^{22} +7.99307 q^{23} +(-3.90639 - 0.255812i) q^{24} +(-3.88806 - 2.24477i) q^{25} +(-5.46036 - 1.98848i) q^{26} +(2.88758 + 4.31994i) q^{27} +(2.53537 - 0.679350i) q^{28} +(-0.579056 + 0.334318i) q^{29} +(-1.95613 + 0.389216i) q^{30} +(-0.300031 + 1.11973i) q^{31} +(0.848242 + 3.16568i) q^{32} +(1.34262 + 2.72216i) q^{33} +(2.47351 + 9.23127i) q^{34} +(-2.71738 + 1.56888i) q^{35} +(1.09133 - 1.42259i) q^{36} +(-0.0149826 - 0.0559159i) q^{37} +(2.60387 - 4.51004i) q^{38} +(-5.03667 + 3.69215i) q^{39} +(-0.807405 - 1.39847i) q^{40} +(-1.40774 + 1.40774i) q^{41} +(3.94021 - 11.6097i) q^{42} -4.14155i q^{43} +(0.740585 - 0.740585i) q^{44} +(-0.820006 + 1.98032i) q^{45} +(-12.4437 - 3.33427i) q^{46} +(5.58909 - 1.49759i) q^{47} +(7.93531 + 2.69316i) q^{48} -12.2879i q^{49} +(5.11657 + 5.11657i) q^{50} +(9.72554 + 3.30075i) q^{51} +(1.76497 + 1.23630i) q^{52} -4.09535i q^{53} +(-2.69336 - 7.92986i) q^{54} +(-0.626011 + 1.08428i) q^{55} +9.92629 q^{56} +(-2.47557 - 5.01924i) q^{57} +(1.04094 - 0.278919i) q^{58} +(-1.34291 + 0.359831i) q^{59} +(0.738012 + 0.0483290i) q^{60} -8.19005 q^{61} +(0.934180 - 1.61805i) q^{62} +(-8.02188 - 10.4518i) q^{63} +4.39405i q^{64} +(-2.42051 - 0.881468i) q^{65} +(-0.954660 - 4.79795i) q^{66} +(8.56537 + 8.56537i) q^{67} -3.54390i q^{68} +(-10.4082 + 9.12885i) q^{69} +(4.88489 - 1.30890i) q^{70} +(3.11758 + 0.835353i) q^{71} +(5.37890 - 4.12837i) q^{72} +(-3.59223 + 3.59223i) q^{73} +0.0933002i q^{74} +(7.62662 - 1.51749i) q^{75} +(-1.36552 + 1.36552i) q^{76} +(-3.84811 - 6.66512i) q^{77} +(9.38129 - 3.64694i) q^{78} +(-4.63097 + 8.02108i) q^{79} +(0.894644 + 3.33886i) q^{80} +(-8.69387 - 2.32736i) q^{81} +(2.77882 - 1.60435i) q^{82} +(2.23189 + 8.32953i) q^{83} +(-2.52557 + 3.78025i) q^{84} +(1.09648 + 4.09211i) q^{85} +(-1.72763 + 6.44760i) q^{86} +(0.372200 - 1.09667i) q^{87} +(3.43013 - 1.98038i) q^{88} +(-4.89110 + 1.31057i) q^{89} +(2.10267 - 2.74091i) q^{90} +(12.1320 - 10.1764i) q^{91} +(4.13712 + 2.38857i) q^{92} +(-0.888151 - 1.80073i) q^{93} -9.32585 q^{94} +(1.15427 - 1.99925i) q^{95} +(-4.72006 - 3.15345i) q^{96} +(9.26652 + 9.26652i) q^{97} +(-5.12584 + 19.1299i) q^{98} +(-4.85727 - 2.01129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9} - 12 q^{10} + 6 q^{11} - 18 q^{12} - 2 q^{13} - 12 q^{14} + 4 q^{15} + 14 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{20} + 22 q^{21} + 2 q^{22} - 12 q^{23} - 18 q^{24} + 48 q^{26} - 32 q^{27} - 6 q^{29} + 66 q^{30} + 6 q^{31} + 30 q^{32} - 56 q^{33} - 6 q^{34} - 6 q^{35} - 6 q^{36} - 6 q^{37} - 36 q^{38} - 32 q^{39} - 12 q^{40} + 18 q^{41} + 80 q^{42} - 12 q^{44} + 34 q^{45} - 12 q^{46} + 30 q^{47} + 22 q^{48} - 12 q^{50} - 16 q^{52} - 56 q^{54} - 4 q^{55} - 12 q^{56} - 2 q^{57} - 28 q^{58} + 30 q^{59} - 58 q^{60} - 4 q^{61} - 18 q^{62} - 2 q^{63} + 30 q^{65} + 32 q^{66} - 16 q^{67} - 48 q^{69} - 46 q^{70} + 48 q^{71} + 126 q^{72} - 22 q^{73} + 24 q^{75} - 18 q^{76} - 72 q^{77} + 94 q^{78} + 8 q^{79} + 54 q^{80} - 14 q^{81} - 12 q^{82} + 72 q^{83} - 110 q^{84} + 78 q^{85} + 102 q^{86} + 14 q^{87} - 6 q^{88} + 114 q^{90} - 16 q^{91} + 120 q^{92} - 44 q^{93} - 52 q^{94} - 6 q^{95} + 16 q^{96} + 48 q^{97} - 36 q^{98} - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.55681 0.417145i −1.10083 0.294966i −0.337727 0.941244i \(-0.609658\pi\)
−0.763102 + 0.646278i \(0.776325\pi\)
\(3\) −1.30216 + 1.14210i −0.751802 + 0.659389i
\(4\) 0.517589 + 0.298830i 0.258795 + 0.149415i
\(5\) −0.690114 0.184916i −0.308629 0.0826968i 0.101181 0.994868i \(-0.467738\pi\)
−0.409809 + 0.912171i \(0.634405\pi\)
\(6\) 2.50363 1.23483i 1.02210 0.504119i
\(7\) 3.10547 3.10547i 1.17376 1.17376i 0.192451 0.981306i \(-0.438356\pi\)
0.981306 0.192451i \(-0.0616438\pi\)
\(8\) 1.59819 + 1.59819i 0.565047 + 0.565047i
\(9\) 0.391235 2.97438i 0.130412 0.991460i
\(10\) 0.997239 + 0.575756i 0.315355 + 0.182070i
\(11\) 0.453556 1.69270i 0.136752 0.510367i −0.863232 0.504807i \(-0.831564\pi\)
0.999985 0.00555973i \(-0.00176973\pi\)
\(12\) −1.01528 + 0.202012i −0.293085 + 0.0583158i
\(13\) 3.59178 + 0.314864i 0.996180 + 0.0873276i
\(14\) −6.13006 + 3.53919i −1.63833 + 0.945888i
\(15\) 1.10983 0.547387i 0.286557 0.141335i
\(16\) −2.41906 4.18994i −0.604765 1.04748i
\(17\) −2.96481 5.13520i −0.719071 1.24547i −0.961368 0.275266i \(-0.911234\pi\)
0.242297 0.970202i \(-0.422099\pi\)
\(18\) −1.84983 + 4.46734i −0.436008 + 1.05296i
\(19\) −0.836286 + 3.12106i −0.191857 + 0.716021i 0.801201 + 0.598395i \(0.204195\pi\)
−0.993058 + 0.117625i \(0.962472\pi\)
\(20\) −0.301937 0.301937i −0.0675152 0.0675152i
\(21\) −0.497071 + 7.59056i −0.108470 + 1.65640i
\(22\) −1.41220 + 2.44600i −0.301082 + 0.521489i
\(23\) 7.99307 1.66667 0.833335 0.552769i \(-0.186429\pi\)
0.833335 + 0.552769i \(0.186429\pi\)
\(24\) −3.90639 0.255812i −0.797389 0.0522174i
\(25\) −3.88806 2.24477i −0.777613 0.448955i
\(26\) −5.46036 1.98848i −1.07087 0.389972i
\(27\) 2.88758 + 4.31994i 0.555714 + 0.831373i
\(28\) 2.53537 0.679350i 0.479139 0.128385i
\(29\) −0.579056 + 0.334318i −0.107528 + 0.0620814i −0.552800 0.833314i \(-0.686440\pi\)
0.445272 + 0.895396i \(0.353107\pi\)
\(30\) −1.95613 + 0.389216i −0.357139 + 0.0710608i
\(31\) −0.300031 + 1.11973i −0.0538871 + 0.201109i −0.987621 0.156858i \(-0.949863\pi\)
0.933734 + 0.357967i \(0.116530\pi\)
\(32\) 0.848242 + 3.16568i 0.149949 + 0.559619i
\(33\) 1.34262 + 2.72216i 0.233720 + 0.473868i
\(34\) 2.47351 + 9.23127i 0.424204 + 1.58315i
\(35\) −2.71738 + 1.56888i −0.459321 + 0.265189i
\(36\) 1.09133 1.42259i 0.181889 0.237099i
\(37\) −0.0149826 0.0559159i −0.00246313 0.00919251i 0.964683 0.263412i \(-0.0848480\pi\)
−0.967146 + 0.254220i \(0.918181\pi\)
\(38\) 2.60387 4.51004i 0.422404 0.731625i
\(39\) −5.03667 + 3.69215i −0.806512 + 0.591217i
\(40\) −0.807405 1.39847i −0.127662 0.221117i
\(41\) −1.40774 + 1.40774i −0.219853 + 0.219853i −0.808436 0.588584i \(-0.799686\pi\)
0.588584 + 0.808436i \(0.299686\pi\)
\(42\) 3.94021 11.6097i 0.607988 1.79142i
\(43\) 4.14155i 0.631581i −0.948829 0.315790i \(-0.897730\pi\)
0.948829 0.315790i \(-0.102270\pi\)
\(44\) 0.740585 0.740585i 0.111647 0.111647i
\(45\) −0.820006 + 1.98032i −0.122239 + 0.295208i
\(46\) −12.4437 3.33427i −1.83472 0.491611i
\(47\) 5.58909 1.49759i 0.815252 0.218446i 0.172983 0.984925i \(-0.444660\pi\)
0.642270 + 0.766479i \(0.277993\pi\)
\(48\) 7.93531 + 2.69316i 1.14536 + 0.388725i
\(49\) 12.2879i 1.75542i
\(50\) 5.11657 + 5.11657i 0.723592 + 0.723592i
\(51\) 9.72554 + 3.30075i 1.36185 + 0.462197i
\(52\) 1.76497 + 1.23630i 0.244758 + 0.171444i
\(53\) 4.09535i 0.562540i −0.959629 0.281270i \(-0.909244\pi\)
0.959629 0.281270i \(-0.0907556\pi\)
\(54\) −2.69336 7.92986i −0.366519 1.07912i
\(55\) −0.626011 + 1.08428i −0.0844114 + 0.146205i
\(56\) 9.92629 1.32646
\(57\) −2.47557 5.01924i −0.327898 0.664814i
\(58\) 1.04094 0.278919i 0.136682 0.0366238i
\(59\) −1.34291 + 0.359831i −0.174832 + 0.0468460i −0.345173 0.938539i \(-0.612180\pi\)
0.170341 + 0.985385i \(0.445513\pi\)
\(60\) 0.738012 + 0.0483290i 0.0952769 + 0.00623925i
\(61\) −8.19005 −1.04863 −0.524315 0.851525i \(-0.675678\pi\)
−0.524315 + 0.851525i \(0.675678\pi\)
\(62\) 0.934180 1.61805i 0.118641 0.205492i
\(63\) −8.02188 10.4518i −1.01066 1.31681i
\(64\) 4.39405i 0.549256i
\(65\) −2.42051 0.881468i −0.300228 0.109333i
\(66\) −0.954660 4.79795i −0.117511 0.590587i
\(67\) 8.56537 + 8.56537i 1.04643 + 1.04643i 0.998868 + 0.0475582i \(0.0151440\pi\)
0.0475582 + 0.998868i \(0.484856\pi\)
\(68\) 3.54390i 0.429761i
\(69\) −10.4082 + 9.12885i −1.25301 + 1.09898i
\(70\) 4.88489 1.30890i 0.583856 0.156444i
\(71\) 3.11758 + 0.835353i 0.369988 + 0.0991381i 0.439022 0.898476i \(-0.355325\pi\)
−0.0690337 + 0.997614i \(0.521992\pi\)
\(72\) 5.37890 4.12837i 0.633910 0.486533i
\(73\) −3.59223 + 3.59223i −0.420439 + 0.420439i −0.885355 0.464916i \(-0.846085\pi\)
0.464916 + 0.885355i \(0.346085\pi\)
\(74\) 0.0933002i 0.0108459i
\(75\) 7.62662 1.51749i 0.880646 0.175224i
\(76\) −1.36552 + 1.36552i −0.156636 + 0.156636i
\(77\) −3.84811 6.66512i −0.438533 0.759561i
\(78\) 9.38129 3.64694i 1.06222 0.412935i
\(79\) −4.63097 + 8.02108i −0.521025 + 0.902441i 0.478676 + 0.877992i \(0.341117\pi\)
−0.999701 + 0.0244500i \(0.992217\pi\)
\(80\) 0.894644 + 3.33886i 0.100024 + 0.373296i
\(81\) −8.69387 2.32736i −0.965986 0.258596i
\(82\) 2.77882 1.60435i 0.306869 0.177171i
\(83\) 2.23189 + 8.32953i 0.244982 + 0.914285i 0.973393 + 0.229144i \(0.0735926\pi\)
−0.728411 + 0.685141i \(0.759741\pi\)
\(84\) −2.52557 + 3.78025i −0.275562 + 0.412459i
\(85\) 1.09648 + 4.09211i 0.118930 + 0.443852i
\(86\) −1.72763 + 6.44760i −0.186295 + 0.695262i
\(87\) 0.372200 1.09667i 0.0399040 0.117576i
\(88\) 3.43013 1.98038i 0.365653 0.211110i
\(89\) −4.89110 + 1.31057i −0.518455 + 0.138920i −0.508552 0.861031i \(-0.669819\pi\)
−0.00990324 + 0.999951i \(0.503152\pi\)
\(90\) 2.10267 2.74091i 0.221641 0.288917i
\(91\) 12.1320 10.1764i 1.27178 1.06677i
\(92\) 4.13712 + 2.38857i 0.431325 + 0.249026i
\(93\) −0.888151 1.80073i −0.0920969 0.186727i
\(94\) −9.32585 −0.961888
\(95\) 1.15427 1.99925i 0.118425 0.205118i
\(96\) −4.72006 3.15345i −0.481739 0.321847i
\(97\) 9.26652 + 9.26652i 0.940872 + 0.940872i 0.998347 0.0574745i \(-0.0183048\pi\)
−0.0574745 + 0.998347i \(0.518305\pi\)
\(98\) −5.12584 + 19.1299i −0.517788 + 1.93241i
\(99\) −4.85727 2.01129i −0.488174 0.202142i
\(100\) −1.34161 2.32374i −0.134161 0.232374i
\(101\) 6.11679 + 10.5946i 0.608644 + 1.05420i 0.991464 + 0.130379i \(0.0416194\pi\)
−0.382820 + 0.923823i \(0.625047\pi\)
\(102\) −13.7639 9.19559i −1.36283 0.910499i
\(103\) −9.33513 + 5.38964i −0.919818 + 0.531057i −0.883577 0.468286i \(-0.844872\pi\)
−0.0362409 + 0.999343i \(0.511538\pi\)
\(104\) 5.23714 + 6.24357i 0.513544 + 0.612232i
\(105\) 1.74665 5.14644i 0.170456 0.502241i
\(106\) −1.70836 + 6.37567i −0.165930 + 0.619260i
\(107\) 2.85766 + 1.64987i 0.276261 + 0.159499i 0.631729 0.775189i \(-0.282345\pi\)
−0.355469 + 0.934688i \(0.615679\pi\)
\(108\) 0.203649 + 3.09885i 0.0195961 + 0.298187i
\(109\) 0.650028 + 0.650028i 0.0622613 + 0.0622613i 0.737552 0.675291i \(-0.235982\pi\)
−0.675291 + 0.737552i \(0.735982\pi\)
\(110\) 1.42688 1.42688i 0.136048 0.136048i
\(111\) 0.0833710 + 0.0556998i 0.00791322 + 0.00528679i
\(112\) −20.5241 5.49941i −1.93934 0.519645i
\(113\) −15.6325 9.02543i −1.47058 0.849041i −0.471128 0.882065i \(-0.656153\pi\)
−0.999455 + 0.0330238i \(0.989486\pi\)
\(114\) 1.76024 + 8.84666i 0.164862 + 0.828566i
\(115\) −5.51613 1.47804i −0.514382 0.137828i
\(116\) −0.399618 −0.0371036
\(117\) 2.34175 10.5601i 0.216495 0.976284i
\(118\) 2.24075 0.206278
\(119\) −25.1543 6.74008i −2.30589 0.617862i
\(120\) 2.64855 + 0.898892i 0.241779 + 0.0820572i
\(121\) 6.86678 + 3.96453i 0.624252 + 0.360412i
\(122\) 12.7503 + 3.41644i 1.15436 + 0.309310i
\(123\) 0.225328 3.44088i 0.0203171 0.310254i
\(124\) −0.489902 + 0.489902i −0.0439945 + 0.0439945i
\(125\) 4.79411 + 4.79411i 0.428798 + 0.428798i
\(126\) 8.12860 + 19.6178i 0.724153 + 1.74769i
\(127\) 0.642814 + 0.371129i 0.0570405 + 0.0329323i 0.528249 0.849089i \(-0.322849\pi\)
−0.471209 + 0.882022i \(0.656182\pi\)
\(128\) 3.52944 13.1721i 0.311961 1.16426i
\(129\) 4.73005 + 5.39296i 0.416457 + 0.474823i
\(130\) 3.40057 + 2.38198i 0.298250 + 0.208914i
\(131\) −3.97273 + 2.29366i −0.347099 + 0.200398i −0.663407 0.748259i \(-0.730890\pi\)
0.316308 + 0.948657i \(0.397557\pi\)
\(132\) −0.118540 + 1.81018i −0.0103176 + 0.157556i
\(133\) 7.09531 + 12.2894i 0.615241 + 1.06563i
\(134\) −9.76163 16.9076i −0.843277 1.46060i
\(135\) −1.19393 3.51521i −0.102757 0.302541i
\(136\) 3.46870 12.9454i 0.297439 1.11006i
\(137\) 3.13976 + 3.13976i 0.268248 + 0.268248i 0.828394 0.560146i \(-0.189255\pi\)
−0.560146 + 0.828394i \(0.689255\pi\)
\(138\) 20.0117 9.87011i 1.70351 0.840199i
\(139\) 11.2215 19.4363i 0.951799 1.64856i 0.210269 0.977644i \(-0.432566\pi\)
0.741530 0.670920i \(-0.234101\pi\)
\(140\) −1.87532 −0.158493
\(141\) −5.56749 + 8.33338i −0.468867 + 0.701797i
\(142\) −4.50501 2.60097i −0.378052 0.218268i
\(143\) 2.16204 5.93698i 0.180799 0.496475i
\(144\) −13.4089 + 5.55596i −1.11741 + 0.462996i
\(145\) 0.461436 0.123641i 0.0383202 0.0102679i
\(146\) 7.09089 4.09393i 0.586847 0.338816i
\(147\) 14.0340 + 16.0008i 1.15750 + 1.31972i
\(148\) 0.00895451 0.0334187i 0.000736057 0.00274700i
\(149\) −1.48515 5.54265i −0.121668 0.454072i 0.878031 0.478604i \(-0.158857\pi\)
−0.999699 + 0.0245323i \(0.992190\pi\)
\(150\) −12.5062 0.818974i −1.02113 0.0668689i
\(151\) −5.81580 21.7048i −0.473283 1.76632i −0.627851 0.778333i \(-0.716065\pi\)
0.154568 0.987982i \(-0.450601\pi\)
\(152\) −6.32461 + 3.65151i −0.512993 + 0.296177i
\(153\) −16.4340 + 6.80939i −1.32861 + 0.550507i
\(154\) 3.21044 + 11.9815i 0.258705 + 0.965500i
\(155\) 0.414111 0.717261i 0.0332622 0.0576118i
\(156\) −3.71025 + 0.405908i −0.297058 + 0.0324986i
\(157\) 3.80152 + 6.58443i 0.303394 + 0.525494i 0.976903 0.213685i \(-0.0685467\pi\)
−0.673508 + 0.739180i \(0.735213\pi\)
\(158\) 10.5555 10.5555i 0.839749 0.839749i
\(159\) 4.67728 + 5.33280i 0.370933 + 0.422918i
\(160\) 2.34154i 0.185115i
\(161\) 24.8222 24.8222i 1.95627 1.95627i
\(162\) 12.5638 + 7.24986i 0.987108 + 0.569603i
\(163\) −3.50378 0.938834i −0.274437 0.0735352i 0.118976 0.992897i \(-0.462039\pi\)
−0.393413 + 0.919362i \(0.628706\pi\)
\(164\) −1.14931 + 0.307957i −0.0897460 + 0.0240474i
\(165\) −0.423189 2.12687i −0.0329452 0.165577i
\(166\) 13.8985i 1.07873i
\(167\) 14.8746 + 14.8746i 1.15103 + 1.15103i 0.986346 + 0.164688i \(0.0526618\pi\)
0.164688 + 0.986346i \(0.447338\pi\)
\(168\) −12.9256 + 11.3368i −0.997232 + 0.874651i
\(169\) 12.8017 + 2.26184i 0.984748 + 0.173988i
\(170\) 6.82802i 0.523685i
\(171\) 8.95604 + 3.70850i 0.684885 + 0.283596i
\(172\) 1.23762 2.14362i 0.0943677 0.163450i
\(173\) −18.3298 −1.39359 −0.696793 0.717272i \(-0.745390\pi\)
−0.696793 + 0.717272i \(0.745390\pi\)
\(174\) −1.03692 + 1.55205i −0.0786084 + 0.117660i
\(175\) −19.0454 + 5.10319i −1.43969 + 0.385765i
\(176\) −8.18947 + 2.19436i −0.617304 + 0.165406i
\(177\) 1.33772 2.00229i 0.100549 0.150501i
\(178\) 8.16119 0.611707
\(179\) −8.60225 + 14.8995i −0.642962 + 1.11364i 0.341806 + 0.939771i \(0.388961\pi\)
−0.984768 + 0.173872i \(0.944372\pi\)
\(180\) −1.01620 + 0.779948i −0.0757434 + 0.0581339i
\(181\) 1.08994i 0.0810148i 0.999179 + 0.0405074i \(0.0128974\pi\)
−0.999179 + 0.0405074i \(0.987103\pi\)
\(182\) −23.1322 + 10.7818i −1.71467 + 0.799203i
\(183\) 10.6648 9.35383i 0.788361 0.691455i
\(184\) 12.7745 + 12.7745i 0.941746 + 0.941746i
\(185\) 0.0413589i 0.00304076i
\(186\) 0.631514 + 3.17388i 0.0463048 + 0.232720i
\(187\) −10.0370 + 2.68941i −0.733980 + 0.196669i
\(188\) 3.34038 + 0.895051i 0.243622 + 0.0652783i
\(189\) 22.3827 + 4.44817i 1.62811 + 0.323557i
\(190\) −2.63095 + 2.63095i −0.190869 + 0.190869i
\(191\) 2.80156i 0.202714i −0.994850 0.101357i \(-0.967682\pi\)
0.994850 0.101357i \(-0.0323184\pi\)
\(192\) −5.01842 5.72175i −0.362174 0.412932i
\(193\) 1.80610 1.80610i 0.130006 0.130006i −0.639110 0.769115i \(-0.720697\pi\)
0.769115 + 0.639110i \(0.220697\pi\)
\(194\) −10.5607 18.2917i −0.758214 1.31327i
\(195\) 4.15861 1.61665i 0.297804 0.115770i
\(196\) 3.67200 6.36009i 0.262286 0.454292i
\(197\) 1.48877 + 5.55616i 0.106070 + 0.395860i 0.998464 0.0553970i \(-0.0176424\pi\)
−0.892394 + 0.451257i \(0.850976\pi\)
\(198\) 6.72284 + 5.15738i 0.477771 + 0.366519i
\(199\) −2.16918 + 1.25238i −0.153769 + 0.0887788i −0.574910 0.818216i \(-0.694963\pi\)
0.421141 + 0.906995i \(0.361630\pi\)
\(200\) −2.62629 9.80146i −0.185707 0.693068i
\(201\) −20.9359 1.37100i −1.47671 0.0967029i
\(202\) −5.10318 19.0453i −0.359059 1.34003i
\(203\) −0.760027 + 2.83646i −0.0533434 + 0.199080i
\(204\) 4.04747 + 4.61472i 0.283380 + 0.323095i
\(205\) 1.23182 0.711190i 0.0860339 0.0496717i
\(206\) 16.7813 4.49653i 1.16921 0.313288i
\(207\) 3.12717 23.7744i 0.217353 1.65244i
\(208\) −7.36947 15.8110i −0.510981 1.09630i
\(209\) 4.90370 + 2.83115i 0.339196 + 0.195835i
\(210\) −4.86601 + 7.28341i −0.335787 + 0.502603i
\(211\) −1.89494 −0.130453 −0.0652265 0.997870i \(-0.520777\pi\)
−0.0652265 + 0.997870i \(0.520777\pi\)
\(212\) 1.22381 2.11971i 0.0840520 0.145582i
\(213\) −5.01363 + 2.47281i −0.343529 + 0.169434i
\(214\) −3.76060 3.76060i −0.257069 0.257069i
\(215\) −0.765837 + 2.85814i −0.0522297 + 0.194924i
\(216\) −2.28920 + 11.5190i −0.155760 + 0.783769i
\(217\) 2.54555 + 4.40902i 0.172803 + 0.299304i
\(218\) −0.740812 1.28312i −0.0501741 0.0869041i
\(219\) 0.574983 8.78032i 0.0388538 0.593319i
\(220\) −0.648034 + 0.374142i −0.0436904 + 0.0252247i
\(221\) −9.03204 19.3780i −0.607561 1.30350i
\(222\) −0.106558 0.121492i −0.00715169 0.00815398i
\(223\) 3.93720 14.6938i 0.263655 0.983972i −0.699414 0.714717i \(-0.746556\pi\)
0.963069 0.269256i \(-0.0867777\pi\)
\(224\) 12.4651 + 7.19674i 0.832861 + 0.480853i
\(225\) −8.19796 + 10.6863i −0.546530 + 0.712423i
\(226\) 20.5719 + 20.5719i 1.36842 + 1.36842i
\(227\) −14.0889 + 14.0889i −0.935115 + 0.935115i −0.998020 0.0629043i \(-0.979964\pi\)
0.0629043 + 0.998020i \(0.479964\pi\)
\(228\) 0.218569 3.33768i 0.0144751 0.221043i
\(229\) 8.03772 + 2.15370i 0.531148 + 0.142321i 0.514418 0.857539i \(-0.328008\pi\)
0.0167295 + 0.999860i \(0.494675\pi\)
\(230\) 7.97099 + 4.60206i 0.525592 + 0.303451i
\(231\) 12.6231 + 4.28414i 0.830536 + 0.281876i
\(232\) −1.45975 0.391139i −0.0958373 0.0256795i
\(233\) 12.2606 0.803216 0.401608 0.915812i \(-0.368452\pi\)
0.401608 + 0.915812i \(0.368452\pi\)
\(234\) −8.05077 + 15.4632i −0.526295 + 1.01086i
\(235\) −4.13404 −0.269675
\(236\) −0.802603 0.215057i −0.0522450 0.0139990i
\(237\) −3.13058 15.7337i −0.203353 1.02202i
\(238\) 36.3489 + 20.9860i 2.35615 + 1.36032i
\(239\) −9.12224 2.44430i −0.590069 0.158108i −0.0485841 0.998819i \(-0.515471\pi\)
−0.541485 + 0.840711i \(0.682138\pi\)
\(240\) −4.97826 3.32595i −0.321346 0.214689i
\(241\) −3.84185 + 3.84185i −0.247476 + 0.247476i −0.819934 0.572458i \(-0.805990\pi\)
0.572458 + 0.819934i \(0.305990\pi\)
\(242\) −9.03646 9.03646i −0.580886 0.580886i
\(243\) 13.9789 6.89864i 0.896745 0.442548i
\(244\) −4.23908 2.44744i −0.271380 0.156681i
\(245\) −2.27223 + 8.48006i −0.145167 + 0.541771i
\(246\) −1.78614 + 5.26280i −0.113880 + 0.335544i
\(247\) −3.98646 + 10.9468i −0.253653 + 0.696531i
\(248\) −2.26905 + 1.31004i −0.144085 + 0.0831875i
\(249\) −12.4194 8.29734i −0.787047 0.525822i
\(250\) −5.46366 9.46334i −0.345552 0.598514i
\(251\) 8.35500 + 14.4713i 0.527363 + 0.913420i 0.999491 + 0.0318898i \(0.0101526\pi\)
−0.472128 + 0.881530i \(0.656514\pi\)
\(252\) −1.02872 7.80693i −0.0648032 0.491790i
\(253\) 3.62531 13.5298i 0.227921 0.850613i
\(254\) −0.845923 0.845923i −0.0530779 0.0530779i
\(255\) −6.10137 4.07630i −0.382083 0.255268i
\(256\) −6.59527 + 11.4233i −0.412205 + 0.713959i
\(257\) −18.2212 −1.13661 −0.568303 0.822819i \(-0.692400\pi\)
−0.568303 + 0.822819i \(0.692400\pi\)
\(258\) −5.11413 10.3689i −0.318392 0.645540i
\(259\) −0.220173 0.127117i −0.0136809 0.00789867i
\(260\) −0.989422 1.17956i −0.0613614 0.0731533i
\(261\) 0.767843 + 1.85313i 0.0475283 + 0.114706i
\(262\) 7.14157 1.91358i 0.441208 0.118221i
\(263\) −2.85890 + 1.65059i −0.176287 + 0.101779i −0.585547 0.810638i \(-0.699120\pi\)
0.409260 + 0.912418i \(0.365787\pi\)
\(264\) −2.20478 + 6.49631i −0.135695 + 0.399820i
\(265\) −0.757294 + 2.82626i −0.0465202 + 0.173616i
\(266\) −5.91955 22.0921i −0.362951 1.35455i
\(267\) 4.87219 7.29266i 0.298173 0.446304i
\(268\) 1.87375 + 6.99294i 0.114458 + 0.427162i
\(269\) −12.9794 + 7.49365i −0.791367 + 0.456896i −0.840444 0.541899i \(-0.817706\pi\)
0.0490765 + 0.998795i \(0.484372\pi\)
\(270\) 0.392370 + 5.97055i 0.0238789 + 0.363356i
\(271\) 6.77811 + 25.2963i 0.411741 + 1.53664i 0.791275 + 0.611460i \(0.209418\pi\)
−0.379534 + 0.925178i \(0.623916\pi\)
\(272\) −14.3441 + 24.8447i −0.869739 + 1.50643i
\(273\) −4.17537 + 27.1071i −0.252705 + 1.64060i
\(274\) −3.57827 6.19774i −0.216171 0.374419i
\(275\) −5.56317 + 5.56317i −0.335472 + 0.335472i
\(276\) −8.11517 + 1.61469i −0.488476 + 0.0971932i
\(277\) 18.4343i 1.10761i −0.832646 0.553806i \(-0.813175\pi\)
0.832646 0.553806i \(-0.186825\pi\)
\(278\) −25.5775 + 25.5775i −1.53404 + 1.53404i
\(279\) 3.21312 + 1.33048i 0.192364 + 0.0796539i
\(280\) −6.85027 1.83553i −0.409382 0.109694i
\(281\) 26.8908 7.20538i 1.60417 0.429837i 0.657873 0.753128i \(-0.271456\pi\)
0.946299 + 0.323292i \(0.104789\pi\)
\(282\) 12.1437 10.6510i 0.723149 0.634259i
\(283\) 7.98119i 0.474433i −0.971457 0.237216i \(-0.923765\pi\)
0.971457 0.237216i \(-0.0762350\pi\)
\(284\) 1.36400 + 1.36400i 0.0809383 + 0.0809383i
\(285\) 0.780294 + 3.92162i 0.0462206 + 0.232297i
\(286\) −5.84247 + 8.34084i −0.345472 + 0.493204i
\(287\) 8.74342i 0.516108i
\(288\) 9.74780 1.28447i 0.574395 0.0756880i
\(289\) −9.08016 + 15.7273i −0.534127 + 0.925136i
\(290\) −0.769943 −0.0452126
\(291\) −22.6497 1.48323i −1.32775 0.0869484i
\(292\) −2.93277 + 0.785832i −0.171627 + 0.0459874i
\(293\) 29.0957 7.79616i 1.69979 0.455457i 0.726901 0.686742i \(-0.240960\pi\)
0.972886 + 0.231286i \(0.0742931\pi\)
\(294\) −15.1735 30.7644i −0.884938 1.79422i
\(295\) 0.993298 0.0578321
\(296\) 0.0654193 0.113309i 0.00380242 0.00658598i
\(297\) 8.62203 2.92845i 0.500301 0.169926i
\(298\) 9.24836i 0.535743i
\(299\) 28.7093 + 2.51673i 1.66030 + 0.145546i
\(300\) 4.40093 + 1.49363i 0.254088 + 0.0862348i
\(301\) −12.8615 12.8615i −0.741323 0.741323i
\(302\) 36.2163i 2.08401i
\(303\) −20.0651 6.80988i −1.15271 0.391218i
\(304\) 15.1001 4.04605i 0.866049 0.232057i
\(305\) 5.65207 + 1.51447i 0.323637 + 0.0867182i
\(306\) 28.4250 3.74557i 1.62495 0.214120i
\(307\) −9.91862 + 9.91862i −0.566086 + 0.566086i −0.931029 0.364944i \(-0.881088\pi\)
0.364944 + 0.931029i \(0.381088\pi\)
\(308\) 4.59973i 0.262094i
\(309\) 6.00034 17.6798i 0.341347 1.00577i
\(310\) −0.943893 + 0.943893i −0.0536095 + 0.0536095i
\(311\) 4.71379 + 8.16452i 0.267294 + 0.462967i 0.968162 0.250324i \(-0.0805371\pi\)
−0.700868 + 0.713291i \(0.747204\pi\)
\(312\) −13.9503 2.14880i −0.789783 0.121652i
\(313\) −4.20593 + 7.28489i −0.237733 + 0.411766i −0.960064 0.279782i \(-0.909738\pi\)
0.722330 + 0.691548i \(0.243071\pi\)
\(314\) −3.17157 11.8365i −0.178982 0.667971i
\(315\) 3.60331 + 8.69632i 0.203024 + 0.489982i
\(316\) −4.79388 + 2.76775i −0.269677 + 0.155698i
\(317\) −2.48579 9.27710i −0.139616 0.521054i −0.999936 0.0112997i \(-0.996403\pi\)
0.860320 0.509754i \(-0.170264\pi\)
\(318\) −5.05708 10.2532i −0.283587 0.574974i
\(319\) 0.303264 + 1.13180i 0.0169796 + 0.0633686i
\(320\) 0.812528 3.03240i 0.0454217 0.169516i
\(321\) −5.60544 + 1.11533i −0.312865 + 0.0622516i
\(322\) −48.9979 + 28.2890i −2.73055 + 1.57648i
\(323\) 18.5067 4.95885i 1.02974 0.275918i
\(324\) −3.80437 3.80261i −0.211354 0.211256i
\(325\) −13.2583 9.28694i −0.735436 0.515147i
\(326\) 5.06308 + 2.92317i 0.280418 + 0.161899i
\(327\) −1.58883 0.104045i −0.0878626 0.00575373i
\(328\) −4.49969 −0.248454
\(329\) 12.7060 22.0075i 0.700506 1.21331i
\(330\) −0.228391 + 3.48767i −0.0125725 + 0.191990i
\(331\) 3.27323 + 3.27323i 0.179913 + 0.179913i 0.791318 0.611405i \(-0.209395\pi\)
−0.611405 + 0.791318i \(0.709395\pi\)
\(332\) −1.33391 + 4.97823i −0.0732080 + 0.273216i
\(333\) −0.172177 + 0.0226877i −0.00943523 + 0.00124328i
\(334\) −16.9521 29.3618i −0.927576 1.60661i
\(335\) −4.32721 7.49496i −0.236421 0.409493i
\(336\) 33.0064 16.2793i 1.80065 0.888111i
\(337\) 19.8285 11.4480i 1.08013 0.623612i 0.149197 0.988808i \(-0.452331\pi\)
0.930931 + 0.365196i \(0.118998\pi\)
\(338\) −18.9863 8.86143i −1.03272 0.481998i
\(339\) 30.6639 6.10127i 1.66544 0.331376i
\(340\) −0.655322 + 2.44569i −0.0355398 + 0.132636i
\(341\) 1.75928 + 1.01572i 0.0952704 + 0.0550044i
\(342\) −12.3958 9.50939i −0.670291 0.514209i
\(343\) −16.4215 16.4215i −0.886675 0.886675i
\(344\) 6.61900 6.61900i 0.356873 0.356873i
\(345\) 8.87094 4.37530i 0.477595 0.235558i
\(346\) 28.5359 + 7.64617i 1.53410 + 0.411061i
\(347\) 20.9258 + 12.0815i 1.12336 + 0.648570i 0.942256 0.334895i \(-0.108701\pi\)
0.181101 + 0.983465i \(0.442034\pi\)
\(348\) 0.520366 0.456402i 0.0278945 0.0244657i
\(349\) 12.3456 + 3.30800i 0.660846 + 0.177073i 0.573628 0.819116i \(-0.305536\pi\)
0.0872181 + 0.996189i \(0.472202\pi\)
\(350\) 31.7787 1.69864
\(351\) 9.01133 + 16.4255i 0.480989 + 0.876726i
\(352\) 5.74326 0.306117
\(353\) 19.8223 + 5.31136i 1.05503 + 0.282695i 0.744330 0.667812i \(-0.232769\pi\)
0.310703 + 0.950507i \(0.399436\pi\)
\(354\) −2.91781 + 2.55915i −0.155080 + 0.136017i
\(355\) −1.99702 1.15298i −0.105991 0.0611937i
\(356\) −2.92322 0.783273i −0.154930 0.0415134i
\(357\) 40.4528 19.9520i 2.14099 1.05597i
\(358\) 19.6073 19.6073i 1.03628 1.03628i
\(359\) −9.59235 9.59235i −0.506265 0.506265i 0.407113 0.913378i \(-0.366536\pi\)
−0.913378 + 0.407113i \(0.866536\pi\)
\(360\) −4.47546 + 1.85440i −0.235877 + 0.0977355i
\(361\) 7.41283 + 4.27980i 0.390149 + 0.225253i
\(362\) 0.454664 1.69683i 0.0238966 0.0891834i
\(363\) −13.4695 + 2.68006i −0.706966 + 0.140667i
\(364\) 9.32038 1.64178i 0.488521 0.0860525i
\(365\) 3.14331 1.81479i 0.164528 0.0949905i
\(366\) −20.5049 + 10.1134i −1.07181 + 0.528634i
\(367\) 6.40843 + 11.0997i 0.334517 + 0.579401i 0.983392 0.181494i \(-0.0580934\pi\)
−0.648875 + 0.760895i \(0.724760\pi\)
\(368\) −19.3357 33.4904i −1.00794 1.74581i
\(369\) 3.63641 + 4.73792i 0.189304 + 0.246646i
\(370\) 0.0172527 0.0643878i 0.000896923 0.00334736i
\(371\) −12.7180 12.7180i −0.660286 0.660286i
\(372\) 0.0784152 1.19744i 0.00406564 0.0620846i
\(373\) −2.50103 + 4.33190i −0.129498 + 0.224297i −0.923482 0.383641i \(-0.874670\pi\)
0.793984 + 0.607939i \(0.208003\pi\)
\(374\) 16.7476 0.865998
\(375\) −11.7180 0.767360i −0.605116 0.0396263i
\(376\) 11.3259 + 6.53900i 0.584088 + 0.337223i
\(377\) −2.18511 + 1.01847i −0.112539 + 0.0524540i
\(378\) −32.9901 16.2618i −1.69683 0.836417i
\(379\) −14.1436 + 3.78976i −0.726507 + 0.194667i −0.603073 0.797686i \(-0.706057\pi\)
−0.123434 + 0.992353i \(0.539391\pi\)
\(380\) 1.19487 0.689859i 0.0612956 0.0353890i
\(381\) −1.26091 + 0.250886i −0.0645984 + 0.0128533i
\(382\) −1.16866 + 4.36149i −0.0597938 + 0.223153i
\(383\) 3.94548 + 14.7247i 0.201605 + 0.752399i 0.990458 + 0.137817i \(0.0440086\pi\)
−0.788853 + 0.614582i \(0.789325\pi\)
\(384\) 10.4479 + 21.1831i 0.533165 + 1.08099i
\(385\) 1.42315 + 5.31127i 0.0725305 + 0.270688i
\(386\) −3.56515 + 2.05834i −0.181461 + 0.104767i
\(387\) −12.3185 1.62032i −0.626187 0.0823655i
\(388\) 2.02713 + 7.56537i 0.102912 + 0.384073i
\(389\) −6.32765 + 10.9598i −0.320824 + 0.555684i −0.980658 0.195727i \(-0.937293\pi\)
0.659834 + 0.751411i \(0.270627\pi\)
\(390\) −7.14854 + 0.782062i −0.361980 + 0.0396013i
\(391\) −23.6979 41.0460i −1.19845 2.07578i
\(392\) 19.6385 19.6385i 0.991892 0.991892i
\(393\) 2.55355 7.52395i 0.128810 0.379533i
\(394\) 9.27091i 0.467061i
\(395\) 4.67912 4.67912i 0.235432 0.235432i
\(396\) −1.91304 2.49252i −0.0961337 0.125254i
\(397\) −25.0026 6.69943i −1.25485 0.336235i −0.430639 0.902524i \(-0.641712\pi\)
−0.824207 + 0.566289i \(0.808378\pi\)
\(398\) 3.89942 1.04485i 0.195461 0.0523735i
\(399\) −23.2749 7.89927i −1.16520 0.395458i
\(400\) 21.7210i 1.08605i
\(401\) −13.5641 13.5641i −0.677360 0.677360i 0.282042 0.959402i \(-0.408988\pi\)
−0.959402 + 0.282042i \(0.908988\pi\)
\(402\) 32.0213 + 10.8677i 1.59708 + 0.542032i
\(403\) −1.43021 + 3.92735i −0.0712436 + 0.195635i
\(404\) 7.31153i 0.363762i
\(405\) 5.56940 + 3.21378i 0.276746 + 0.159694i
\(406\) 2.36643 4.09878i 0.117444 0.203419i
\(407\) −0.101444 −0.00502839
\(408\) 10.2681 + 20.8185i 0.508344 + 1.03067i
\(409\) −16.2586 + 4.35649i −0.803938 + 0.215415i −0.637312 0.770606i \(-0.719954\pi\)
−0.166626 + 0.986020i \(0.553287\pi\)
\(410\) −2.21437 + 0.593340i −0.109360 + 0.0293030i
\(411\) −7.67438 0.502560i −0.378549 0.0247895i
\(412\) −6.44235 −0.317392
\(413\) −3.05292 + 5.28781i −0.150224 + 0.260196i
\(414\) −14.7858 + 35.7077i −0.726682 + 1.75494i
\(415\) 6.16104i 0.302433i
\(416\) 2.04994 + 11.6375i 0.100506 + 0.570575i
\(417\) 7.58586 + 38.1252i 0.371481 + 1.86700i
\(418\) −6.45312 6.45312i −0.315632 0.315632i
\(419\) 19.5930i 0.957183i −0.878038 0.478591i \(-0.841148\pi\)
0.878038 0.478591i \(-0.158852\pi\)
\(420\) 2.44196 2.14179i 0.119155 0.104509i
\(421\) −38.7080 + 10.3718i −1.88651 + 0.505489i −0.887511 + 0.460787i \(0.847567\pi\)
−0.999000 + 0.0447018i \(0.985766\pi\)
\(422\) 2.95006 + 0.790465i 0.143606 + 0.0384792i
\(423\) −2.26776 17.2100i −0.110262 0.836778i
\(424\) 6.54516 6.54516i 0.317861 0.317861i
\(425\) 26.6213i 1.29132i
\(426\) 8.83679 1.75828i 0.428144 0.0851888i
\(427\) −25.4340 + 25.4340i −1.23084 + 1.23084i
\(428\) 0.986064 + 1.70791i 0.0476632 + 0.0825551i
\(429\) 3.96527 + 10.2001i 0.191445 + 0.492468i
\(430\) 2.38452 4.13011i 0.114992 0.199172i
\(431\) 0.489822 + 1.82804i 0.0235939 + 0.0880536i 0.976719 0.214523i \(-0.0688198\pi\)
−0.953125 + 0.302577i \(0.902153\pi\)
\(432\) 11.1151 22.5490i 0.534774 1.08489i
\(433\) 8.22301 4.74756i 0.395173 0.228153i −0.289226 0.957261i \(-0.593398\pi\)
0.684399 + 0.729108i \(0.260065\pi\)
\(434\) −2.12373 7.92587i −0.101942 0.380454i
\(435\) −0.459652 + 0.688005i −0.0220386 + 0.0329873i
\(436\) 0.142199 + 0.530695i 0.00681011 + 0.0254157i
\(437\) −6.68449 + 24.9469i −0.319763 + 1.19337i
\(438\) −4.55781 + 13.4294i −0.217781 + 0.641683i
\(439\) 5.45516 3.14954i 0.260361 0.150319i −0.364138 0.931345i \(-0.618636\pi\)
0.624499 + 0.781025i \(0.285303\pi\)
\(440\) −2.73338 + 0.732408i −0.130309 + 0.0349162i
\(441\) −36.5489 4.80746i −1.74042 0.228927i
\(442\) 5.97771 + 33.9355i 0.284330 + 1.61415i
\(443\) −5.45146 3.14740i −0.259007 0.149538i 0.364875 0.931057i \(-0.381112\pi\)
−0.623881 + 0.781519i \(0.714445\pi\)
\(444\) 0.0265072 + 0.0537434i 0.00125797 + 0.00255055i
\(445\) 3.61776 0.171498
\(446\) −12.2589 + 21.2331i −0.580477 + 1.00542i
\(447\) 8.26414 + 5.52123i 0.390880 + 0.261145i
\(448\) 13.6456 + 13.6456i 0.644694 + 0.644694i
\(449\) −9.61952 + 35.9005i −0.453973 + 1.69425i 0.237115 + 0.971481i \(0.423798\pi\)
−0.691089 + 0.722770i \(0.742869\pi\)
\(450\) 17.2204 13.2168i 0.811778 0.623048i
\(451\) 1.74439 + 3.02137i 0.0821401 + 0.142271i
\(452\) −5.39414 9.34293i −0.253719 0.439455i
\(453\) 32.3621 + 21.6210i 1.52050 + 1.01584i
\(454\) 27.8109 16.0566i 1.30523 0.753575i
\(455\) −10.2542 + 4.77946i −0.480725 + 0.224065i
\(456\) 4.06527 11.9782i 0.190373 0.560929i
\(457\) 1.79799 6.71017i 0.0841062 0.313889i −0.911037 0.412324i \(-0.864717\pi\)
0.995143 + 0.0984354i \(0.0313838\pi\)
\(458\) −11.6148 6.70580i −0.542723 0.313341i
\(459\) 13.6226 27.6361i 0.635851 1.28994i
\(460\) −2.41341 2.41341i −0.112526 0.112526i
\(461\) −8.84076 + 8.84076i −0.411755 + 0.411755i −0.882350 0.470594i \(-0.844040\pi\)
0.470594 + 0.882350i \(0.344040\pi\)
\(462\) −17.8646 11.9352i −0.831135 0.555277i
\(463\) −19.1811 5.13957i −0.891423 0.238856i −0.216094 0.976373i \(-0.569332\pi\)
−0.675329 + 0.737517i \(0.735998\pi\)
\(464\) 2.80155 + 1.61747i 0.130059 + 0.0750893i
\(465\) 0.279943 + 1.40694i 0.0129820 + 0.0652454i
\(466\) −19.0873 5.11443i −0.884203 0.236922i
\(467\) 17.4746 0.808628 0.404314 0.914620i \(-0.367510\pi\)
0.404314 + 0.914620i \(0.367510\pi\)
\(468\) 4.36775 4.76602i 0.201899 0.220309i
\(469\) 53.1990 2.45650
\(470\) 6.43590 + 1.72449i 0.296866 + 0.0795450i
\(471\) −12.4702 4.23227i −0.574598 0.195013i
\(472\) −2.72131 1.57115i −0.125258 0.0723179i
\(473\) −7.01038 1.87843i −0.322338 0.0863702i
\(474\) −1.68954 + 25.8003i −0.0776033 + 1.18505i
\(475\) 10.2576 10.2576i 0.470652 0.470652i
\(476\) −11.0055 11.0055i −0.504435 0.504435i
\(477\) −12.1811 1.60224i −0.557736 0.0733617i
\(478\) 13.1819 + 7.61060i 0.602928 + 0.348101i
\(479\) 7.19802 26.8634i 0.328886 1.22742i −0.581461 0.813574i \(-0.697519\pi\)
0.910347 0.413845i \(-0.135814\pi\)
\(480\) 2.67426 + 3.04905i 0.122063 + 0.139169i
\(481\) −0.0362083 0.205555i −0.00165096 0.00937249i
\(482\) 7.58364 4.37842i 0.345425 0.199431i
\(483\) −3.97313 + 60.6719i −0.180783 + 2.76067i
\(484\) 2.36945 + 4.10400i 0.107702 + 0.186545i
\(485\) −4.68143 8.10848i −0.212573 0.368187i
\(486\) −24.6401 + 4.90863i −1.11770 + 0.222660i
\(487\) 3.96000 14.7789i 0.179445 0.669696i −0.816307 0.577618i \(-0.803982\pi\)
0.995752 0.0920783i \(-0.0293510\pi\)
\(488\) −13.0893 13.0893i −0.592524 0.592524i
\(489\) 5.63471 2.77914i 0.254810 0.125677i
\(490\) 7.07484 12.2540i 0.319609 0.553578i
\(491\) −34.3549 −1.55041 −0.775207 0.631707i \(-0.782355\pi\)
−0.775207 + 0.631707i \(0.782355\pi\)
\(492\) 1.14487 1.71363i 0.0516146 0.0772564i
\(493\) 3.43358 + 1.98238i 0.154641 + 0.0892819i
\(494\) 10.7726 15.3792i 0.484681 0.691943i
\(495\) 2.98015 + 2.28621i 0.133948 + 0.102757i
\(496\) 5.41739 1.45158i 0.243248 0.0651781i
\(497\) 12.2757 7.08739i 0.550641 0.317913i
\(498\) 15.8734 + 18.0981i 0.711305 + 0.810993i
\(499\) −8.85813 + 33.0590i −0.396545 + 1.47992i 0.422589 + 0.906321i \(0.361121\pi\)
−0.819133 + 0.573603i \(0.805545\pi\)
\(500\) 1.04875 + 3.91400i 0.0469017 + 0.175040i
\(501\) −36.3574 2.38088i −1.62433 0.106370i
\(502\) −6.97050 26.0143i −0.311109 1.16107i
\(503\) −24.2079 + 13.9764i −1.07938 + 0.623179i −0.930728 0.365711i \(-0.880826\pi\)
−0.148649 + 0.988890i \(0.547492\pi\)
\(504\) 3.88351 29.5246i 0.172985 1.31513i
\(505\) −2.26218 8.44257i −0.100666 0.375690i
\(506\) −11.2878 + 19.5511i −0.501804 + 0.869151i
\(507\) −19.2531 + 11.6755i −0.855061 + 0.518528i
\(508\) 0.221809 + 0.384184i 0.00984118 + 0.0170454i
\(509\) −11.2497 + 11.2497i −0.498634 + 0.498634i −0.911012 0.412379i \(-0.864698\pi\)
0.412379 + 0.911012i \(0.364698\pi\)
\(510\) 7.79825 + 8.89117i 0.345313 + 0.393708i
\(511\) 22.3111i 0.986987i
\(512\) −4.25246 + 4.25246i −0.187934 + 0.187934i
\(513\) −15.8976 + 5.39960i −0.701898 + 0.238398i
\(514\) 28.3669 + 7.60088i 1.25121 + 0.335260i
\(515\) 7.43894 1.99326i 0.327799 0.0878334i
\(516\) 0.836643 + 4.20482i 0.0368311 + 0.185107i
\(517\) 10.1399i 0.445951i
\(518\) 0.289741 + 0.289741i 0.0127305 + 0.0127305i
\(519\) 23.8683 20.9343i 1.04770 0.918915i
\(520\) −2.45969 5.27720i −0.107865 0.231421i
\(521\) 42.9931i 1.88356i −0.336227 0.941781i \(-0.609151\pi\)
0.336227 0.941781i \(-0.390849\pi\)
\(522\) −0.422359 3.20527i −0.0184861 0.140291i
\(523\) 12.4275 21.5251i 0.543417 0.941226i −0.455288 0.890344i \(-0.650464\pi\)
0.998705 0.0508813i \(-0.0162030\pi\)
\(524\) −2.74166 −0.119770
\(525\) 18.9717 28.3968i 0.827995 1.23934i
\(526\) 5.13929 1.37707i 0.224084 0.0600430i
\(527\) 6.63956 1.77907i 0.289224 0.0774973i
\(528\) 8.15782 12.2106i 0.355023 0.531397i
\(529\) 40.8891 1.77779
\(530\) 2.35792 4.08404i 0.102422 0.177399i
\(531\) 0.544882 + 4.13510i 0.0236459 + 0.179448i
\(532\) 8.48117i 0.367705i
\(533\) −5.49955 + 4.61305i −0.238212 + 0.199814i
\(534\) −10.6272 + 9.32086i −0.459883 + 0.403353i
\(535\) −1.66703 1.66703i −0.0720719 0.0720719i
\(536\) 27.3782i 1.18256i
\(537\) −5.81520 29.2261i −0.250944 1.26120i
\(538\) 23.3324 6.25188i 1.00593 0.269538i
\(539\) −20.7997 5.57326i −0.895906 0.240057i
\(540\) 0.432485 2.17622i 0.0186112 0.0936496i
\(541\) 27.8867 27.8867i 1.19894 1.19894i 0.224459 0.974484i \(-0.427938\pi\)
0.974484 0.224459i \(-0.0720615\pi\)
\(542\) 42.2089i 1.81303i
\(543\) −1.24482 1.41928i −0.0534203 0.0609071i
\(544\) 13.7415 13.7415i 0.589163 0.589163i
\(545\) −0.328393 0.568794i −0.0140668 0.0243644i
\(546\) 17.8078 40.4588i 0.762105 1.73148i
\(547\) −8.19854 + 14.2003i −0.350544 + 0.607161i −0.986345 0.164693i \(-0.947337\pi\)
0.635801 + 0.771853i \(0.280670\pi\)
\(548\) 0.686851 + 2.56336i 0.0293408 + 0.109501i
\(549\) −3.20424 + 24.3603i −0.136753 + 1.03967i
\(550\) 10.9814 6.34014i 0.468250 0.270345i
\(551\) −0.559172 2.08686i −0.0238215 0.0889031i
\(552\) −31.2240 2.04472i −1.32898 0.0870291i
\(553\) 10.5279 + 39.2906i 0.447691 + 1.67080i
\(554\) −7.68980 + 28.6987i −0.326708 + 1.21929i
\(555\) −0.0472358 0.0538558i −0.00200505 0.00228605i
\(556\) 11.6163 6.70667i 0.492641 0.284426i
\(557\) 3.78199 1.01338i 0.160248 0.0429384i −0.177803 0.984066i \(-0.556899\pi\)
0.338051 + 0.941128i \(0.390232\pi\)
\(558\) −4.44720 3.41164i −0.188265 0.144426i
\(559\) 1.30403 14.8755i 0.0551544 0.629168i
\(560\) 13.1470 + 7.59044i 0.555563 + 0.320754i
\(561\) 9.99824 14.9653i 0.422126 0.631835i
\(562\) −44.8696 −1.89271
\(563\) −16.8089 + 29.1139i −0.708412 + 1.22701i 0.257034 + 0.966402i \(0.417255\pi\)
−0.965446 + 0.260603i \(0.916079\pi\)
\(564\) −5.37194 + 2.64953i −0.226199 + 0.111565i
\(565\) 9.11927 + 9.11927i 0.383651 + 0.383651i
\(566\) −3.32932 + 12.4252i −0.139942 + 0.522269i
\(567\) −34.2261 + 19.7710i −1.43736 + 0.830304i
\(568\) 3.64744 + 6.31755i 0.153043 + 0.265078i
\(569\) −18.2286 31.5729i −0.764183 1.32360i −0.940678 0.339302i \(-0.889809\pi\)
0.176495 0.984302i \(-0.443524\pi\)
\(570\) 0.421118 6.43070i 0.0176387 0.269353i
\(571\) 11.6292 6.71410i 0.486665 0.280976i −0.236525 0.971625i \(-0.576008\pi\)
0.723190 + 0.690649i \(0.242675\pi\)
\(572\) 2.89320 2.42683i 0.120971 0.101471i
\(573\) 3.19965 + 3.64808i 0.133667 + 0.152401i
\(574\) 3.64728 13.6118i 0.152234 0.568146i
\(575\) −31.0775 17.9426i −1.29602 0.748259i
\(576\) 13.0696 + 1.71911i 0.544565 + 0.0716294i
\(577\) 16.9279 + 16.9279i 0.704716 + 0.704716i 0.965419 0.260703i \(-0.0839544\pi\)
−0.260703 + 0.965419i \(0.583954\pi\)
\(578\) 20.6966 20.6966i 0.860867 0.860867i
\(579\) −0.289089 + 4.41456i −0.0120141 + 0.183463i
\(580\) 0.275782 + 0.0738956i 0.0114512 + 0.00306835i
\(581\) 32.7982 + 18.9360i 1.36070 + 0.785600i
\(582\) 34.6426 + 11.7573i 1.43598 + 0.487357i
\(583\) −6.93218 1.85747i −0.287102 0.0769287i
\(584\) −11.4822 −0.475135
\(585\) −3.56881 + 6.85466i −0.147552 + 0.283406i
\(586\) −48.5485 −2.00552
\(587\) 16.6205 + 4.45344i 0.686000 + 0.183813i 0.584951 0.811069i \(-0.301114\pi\)
0.101048 + 0.994882i \(0.467780\pi\)
\(588\) 2.48230 + 12.4756i 0.102369 + 0.514486i
\(589\) −3.24383 1.87283i −0.133660 0.0771685i
\(590\) −1.54637 0.414350i −0.0636632 0.0170585i
\(591\) −8.28428 5.53469i −0.340770 0.227667i
\(592\) −0.198040 + 0.198040i −0.00813940 + 0.00813940i
\(593\) −6.78670 6.78670i −0.278696 0.278696i 0.553892 0.832589i \(-0.313142\pi\)
−0.832589 + 0.553892i \(0.813142\pi\)
\(594\) −14.6444 + 0.962395i −0.600868 + 0.0394875i
\(595\) 16.1130 + 9.30286i 0.660569 + 0.381380i
\(596\) 0.887615 3.31262i 0.0363581 0.135690i
\(597\) 1.39428 4.10821i 0.0570643 0.168138i
\(598\) −43.6450 15.8940i −1.78478 0.649955i
\(599\) 5.90268 3.40791i 0.241177 0.139244i −0.374541 0.927210i \(-0.622200\pi\)
0.615718 + 0.787967i \(0.288866\pi\)
\(600\) 14.6141 + 9.76358i 0.596616 + 0.398596i
\(601\) 2.00814 + 3.47821i 0.0819139 + 0.141879i 0.904072 0.427380i \(-0.140563\pi\)
−0.822158 + 0.569259i \(0.807230\pi\)
\(602\) 14.6577 + 25.3879i 0.597405 + 1.03474i
\(603\) 28.8277 22.1256i 1.17396 0.901024i
\(604\) 3.47587 12.9721i 0.141431 0.527829i
\(605\) −4.00576 4.00576i −0.162857 0.162857i
\(606\) 28.3968 + 18.9717i 1.15354 + 0.770674i
\(607\) 10.8153 18.7326i 0.438979 0.760333i −0.558632 0.829415i \(-0.688674\pi\)
0.997611 + 0.0690822i \(0.0220071\pi\)
\(608\) −10.5897 −0.429467
\(609\) −2.24983 4.56154i −0.0911678 0.184843i
\(610\) −8.16744 4.71547i −0.330690 0.190924i
\(611\) 20.5463 3.61921i 0.831214 0.146418i
\(612\) −10.5409 1.38650i −0.426090 0.0560458i
\(613\) −43.4028 + 11.6297i −1.75302 + 0.469721i −0.985267 0.171024i \(-0.945292\pi\)
−0.767754 + 0.640745i \(0.778626\pi\)
\(614\) 19.5789 11.3039i 0.790140 0.456187i
\(615\) −0.791775 + 2.33294i −0.0319274 + 0.0940731i
\(616\) 4.50213 16.8022i 0.181396 0.676979i
\(617\) 0.337260 + 1.25867i 0.0135776 + 0.0506723i 0.972382 0.233394i \(-0.0749831\pi\)
−0.958805 + 0.284066i \(0.908316\pi\)
\(618\) −16.7164 + 25.0210i −0.672433 + 1.00649i
\(619\) 5.84752 + 21.8232i 0.235032 + 0.877150i 0.978135 + 0.207973i \(0.0666866\pi\)
−0.743103 + 0.669177i \(0.766647\pi\)
\(620\) 0.428679 0.247498i 0.0172161 0.00993975i
\(621\) 23.0806 + 34.5296i 0.926192 + 1.38562i
\(622\) −3.93267 14.6769i −0.157686 0.588491i
\(623\) −11.1192 + 19.2591i −0.445483 + 0.771599i
\(624\) 27.6539 + 12.1718i 1.10704 + 0.487262i
\(625\) 8.80189 + 15.2453i 0.352076 + 0.609813i
\(626\) 9.58669 9.58669i 0.383161 0.383161i
\(627\) −9.61885 + 1.91389i −0.384140 + 0.0764332i
\(628\) 4.54404i 0.181327i
\(629\) −0.242718 + 0.242718i −0.00967782 + 0.00967782i
\(630\) −1.98203 15.0416i −0.0789661 0.599272i
\(631\) −5.14920 1.37972i −0.204986 0.0549259i 0.154865 0.987936i \(-0.450506\pi\)
−0.359851 + 0.933010i \(0.617173\pi\)
\(632\) −20.2204 + 5.41804i −0.804325 + 0.215518i
\(633\) 2.46751 2.16420i 0.0980748 0.0860193i
\(634\) 15.4796i 0.614773i
\(635\) −0.374988 0.374988i −0.0148809 0.0148809i
\(636\) 0.827310 + 4.15791i 0.0328050 + 0.164872i
\(637\) 3.86902 44.1354i 0.153296 1.74871i
\(638\) 1.88850i 0.0747664i
\(639\) 3.70436 8.94604i 0.146542 0.353900i
\(640\) −4.87143 + 8.43757i −0.192560 + 0.333524i
\(641\) 15.8415 0.625700 0.312850 0.949803i \(-0.398716\pi\)
0.312850 + 0.949803i \(0.398716\pi\)
\(642\) 9.19185 + 0.601933i 0.362773 + 0.0237564i
\(643\) 12.7912 3.42738i 0.504434 0.135163i 0.00237717 0.999997i \(-0.499243\pi\)
0.502057 + 0.864834i \(0.332577\pi\)
\(644\) 20.2654 5.43009i 0.798567 0.213975i
\(645\) −2.26703 4.59642i −0.0892643 0.180984i
\(646\) −30.8799 −1.21495
\(647\) 8.92652 15.4612i 0.350938 0.607842i −0.635476 0.772120i \(-0.719196\pi\)
0.986414 + 0.164278i \(0.0525296\pi\)
\(648\) −10.1749 17.6141i −0.399708 0.691946i
\(649\) 2.43634i 0.0956346i
\(650\) 16.7666 + 19.9886i 0.657638 + 0.784017i
\(651\) −8.35024 2.83399i −0.327272 0.111073i
\(652\) −1.53296 1.53296i −0.0600355 0.0600355i
\(653\) 24.2387i 0.948534i −0.880381 0.474267i \(-0.842713\pi\)
0.880381 0.474267i \(-0.157287\pi\)
\(654\) 2.43010 + 0.824753i 0.0950246 + 0.0322504i
\(655\) 3.16577 0.848267i 0.123697 0.0331445i
\(656\) 9.30378 + 2.49294i 0.363251 + 0.0973329i
\(657\) 9.27925 + 12.0901i 0.362018 + 0.471678i
\(658\) −28.9612 + 28.9612i −1.12902 + 1.12902i
\(659\) 28.8750i 1.12481i −0.826862 0.562405i \(-0.809876\pi\)
0.826862 0.562405i \(-0.190124\pi\)
\(660\) 0.416536 1.22731i 0.0162137 0.0477729i
\(661\) 7.00438 7.00438i 0.272439 0.272439i −0.557642 0.830081i \(-0.688294\pi\)
0.830081 + 0.557642i \(0.188294\pi\)
\(662\) −3.73038 6.46120i −0.144985 0.251122i
\(663\) 33.8927 + 14.9178i 1.31628 + 0.579358i
\(664\) −9.74521 + 16.8792i −0.378187 + 0.655040i
\(665\) −2.62407 9.79315i −0.101757 0.379762i
\(666\) 0.277510 + 0.0365023i 0.0107533 + 0.00141443i
\(667\) −4.62844 + 2.67223i −0.179214 + 0.103469i
\(668\) 3.25396 + 12.1439i 0.125899 + 0.469863i
\(669\) 11.6549 + 23.6304i 0.450605 + 0.913603i
\(670\) 3.61016 + 13.4733i 0.139472 + 0.520518i
\(671\) −3.71465 + 13.8633i −0.143403 + 0.535186i
\(672\) −24.4509 + 4.86506i −0.943216 + 0.187674i
\(673\) 3.77343 2.17859i 0.145455 0.0839785i −0.425506 0.904955i \(-0.639904\pi\)
0.570961 + 0.820977i \(0.306571\pi\)
\(674\) −35.6446 + 9.55095i −1.37298 + 0.367889i
\(675\) −1.52978 23.2782i −0.0588814 0.895977i
\(676\) 5.95013 + 4.99625i 0.228851 + 0.192163i
\(677\) 0.418860 + 0.241829i 0.0160981 + 0.00929424i 0.508027 0.861341i \(-0.330375\pi\)
−0.491929 + 0.870635i \(0.663708\pi\)
\(678\) −50.2829 3.29280i −1.93110 0.126459i
\(679\) 57.5538 2.20871
\(680\) −4.78760 + 8.29237i −0.183596 + 0.317998i
\(681\) 2.25512 34.4369i 0.0864163 1.31963i
\(682\) −2.31516 2.31516i −0.0886520 0.0886520i
\(683\) 9.36965 34.9680i 0.358520 1.33801i −0.517477 0.855697i \(-0.673129\pi\)
0.875997 0.482317i \(-0.160205\pi\)
\(684\) 3.52734 + 4.59582i 0.134871 + 0.175725i
\(685\) −1.58620 2.74739i −0.0606057 0.104972i
\(686\) 18.7149 + 32.4152i 0.714539 + 1.23762i
\(687\) −12.9261 + 6.37539i −0.493162 + 0.243236i
\(688\) −17.3528 + 10.0187i −0.661571 + 0.381958i
\(689\) 1.28948 14.7096i 0.0491252 0.560391i
\(690\) −15.6355 + 3.11103i −0.595233 + 0.118435i
\(691\) 5.17254 19.3042i 0.196773 0.734365i −0.795028 0.606572i \(-0.792544\pi\)
0.991801 0.127793i \(-0.0407892\pi\)
\(692\) −9.48728 5.47749i −0.360652 0.208223i
\(693\) −21.3301 + 8.83811i −0.810265 + 0.335732i
\(694\) −27.5377 27.5377i −1.04532 1.04532i
\(695\) −11.3382 + 11.3382i −0.430083 + 0.430083i
\(696\) 2.34754 1.15785i 0.0889834 0.0438882i
\(697\) 11.4027 + 3.05535i 0.431909 + 0.115730i
\(698\) −17.8398 10.2998i −0.675248 0.389855i
\(699\) −15.9652 + 14.0027i −0.603859 + 0.529632i
\(700\) −11.3827 3.04997i −0.430224 0.115278i
\(701\) −35.3690 −1.33587 −0.667933 0.744221i \(-0.732821\pi\)
−0.667933 + 0.744221i \(0.732821\pi\)
\(702\) −7.17711 29.3303i −0.270883 1.10700i
\(703\) 0.187047 0.00705460
\(704\) 7.43779 + 1.99295i 0.280322 + 0.0751121i
\(705\) 5.38317 4.72147i 0.202742 0.177821i
\(706\) −28.6438 16.5375i −1.07803 0.622398i
\(707\) 51.8968 + 13.9057i 1.95178 + 0.522977i
\(708\) 1.29073 0.636611i 0.0485087 0.0239253i
\(709\) −33.6112 + 33.6112i −1.26229 + 1.26229i −0.312316 + 0.949978i \(0.601105\pi\)
−0.949978 + 0.312316i \(0.898895\pi\)
\(710\) 2.62801 + 2.62801i 0.0986275 + 0.0986275i
\(711\) 22.0459 + 16.9124i 0.826787 + 0.634264i
\(712\) −9.91146 5.72238i −0.371447 0.214455i
\(713\) −2.39816 + 8.95007i −0.0898120 + 0.335183i
\(714\) −71.3000 + 14.1867i −2.66834 + 0.530925i
\(715\) −2.58990 + 3.69740i −0.0968566 + 0.138275i
\(716\) −8.90486 + 5.14122i −0.332790 + 0.192137i
\(717\) 14.6702 7.23561i 0.547870 0.270219i
\(718\) 10.9320 + 18.9349i 0.407980 + 0.706643i
\(719\) 17.0324 + 29.5010i 0.635201 + 1.10020i 0.986472 + 0.163927i \(0.0524162\pi\)
−0.351271 + 0.936274i \(0.614251\pi\)
\(720\) 10.2810 1.35473i 0.383152 0.0504880i
\(721\) −12.2526 + 45.7274i −0.456311 + 1.70298i
\(722\) −9.75505 9.75505i −0.363045 0.363045i
\(723\) 0.614939 9.39047i 0.0228698 0.349235i
\(724\) −0.325708 + 0.564142i −0.0121048 + 0.0209662i
\(725\) 3.00188 0.111487
\(726\) 22.0874 + 1.44640i 0.819741 + 0.0536811i
\(727\) −32.3631 18.6848i −1.20028 0.692983i −0.239663 0.970856i \(-0.577037\pi\)
−0.960618 + 0.277873i \(0.910370\pi\)
\(728\) 35.6530 + 3.12543i 1.32139 + 0.115836i
\(729\) −10.3238 + 24.9483i −0.382363 + 0.924012i
\(730\) −5.65056 + 1.51406i −0.209137 + 0.0560380i
\(731\) −21.2677 + 12.2789i −0.786613 + 0.454152i
\(732\) 8.31517 1.65449i 0.307337 0.0611517i
\(733\) 3.00419 11.2118i 0.110962 0.414116i −0.887991 0.459861i \(-0.847899\pi\)
0.998953 + 0.0457444i \(0.0145660\pi\)
\(734\) −5.34649 19.9534i −0.197343 0.736493i
\(735\) −6.72624 13.6375i −0.248101 0.503026i
\(736\) 6.78005 + 25.3035i 0.249916 + 0.932699i
\(737\) 18.3834 10.6137i 0.677163 0.390960i
\(738\) −3.68478 8.89295i −0.135639 0.327354i
\(739\) 0.0173171 + 0.0646284i 0.000637021 + 0.00237739i 0.966244 0.257630i \(-0.0829416\pi\)
−0.965607 + 0.260008i \(0.916275\pi\)
\(740\) −0.0123593 + 0.0214069i −0.000454336 + 0.000786933i
\(741\) −7.31133 18.8074i −0.268588 0.690909i
\(742\) 14.4942 + 25.1047i 0.532100 + 0.921624i
\(743\) 29.1133 29.1133i 1.06806 1.06806i 0.0705540 0.997508i \(-0.477523\pi\)
0.997508 0.0705540i \(-0.0224767\pi\)
\(744\) 1.45848 4.29735i 0.0534704 0.157548i
\(745\) 4.09969i 0.150201i
\(746\) 5.70065 5.70065i 0.208716 0.208716i
\(747\) 25.6484 3.37969i 0.938425 0.123656i
\(748\) −5.99874 1.60736i −0.219336 0.0587708i
\(749\) 13.9980 3.75076i 0.511477 0.137050i
\(750\) 17.9226 + 6.08275i 0.654441 + 0.222111i
\(751\) 3.51311i 0.128195i 0.997944 + 0.0640975i \(0.0204169\pi\)
−0.997944 + 0.0640975i \(0.979583\pi\)
\(752\) −19.7952 19.7952i −0.721855 0.721855i
\(753\) −27.4071 9.30170i −0.998772 0.338973i
\(754\) 3.82664 0.674060i 0.139358 0.0245478i
\(755\) 16.0543i 0.584274i
\(756\) 10.2558 + 8.99097i 0.373001 + 0.326998i
\(757\) 10.0417 17.3928i 0.364973 0.632152i −0.623799 0.781585i \(-0.714411\pi\)
0.988772 + 0.149433i \(0.0477448\pi\)
\(758\) 23.5997 0.857180
\(759\) 10.7316 + 21.7584i 0.389534 + 0.789781i
\(760\) 5.03992 1.35044i 0.182817 0.0489857i
\(761\) 18.8637 5.05453i 0.683810 0.183226i 0.0998426 0.995003i \(-0.468166\pi\)
0.583968 + 0.811777i \(0.301499\pi\)
\(762\) 2.06765 + 0.135401i 0.0749031 + 0.00490506i
\(763\) 4.03728 0.146160
\(764\) 0.837191 1.45006i 0.0302885 0.0524613i
\(765\) 12.6005 1.66036i 0.455571 0.0600306i
\(766\) 24.5694i 0.887729i
\(767\) −4.93672 + 0.869600i −0.178255 + 0.0313994i
\(768\) −4.45846 22.4074i −0.160881 0.808559i
\(769\) −14.9643 14.9643i −0.539625 0.539625i 0.383794 0.923419i \(-0.374617\pi\)
−0.923419 + 0.383794i \(0.874617\pi\)
\(770\) 8.86229i 0.319375i
\(771\) 23.7269 20.8103i 0.854502 0.749466i
\(772\) 1.47453 0.395100i 0.0530696 0.0142199i
\(773\) 25.5328 + 6.84148i 0.918349 + 0.246071i 0.686880 0.726771i \(-0.258980\pi\)
0.231470 + 0.972842i \(0.425647\pi\)
\(774\) 18.5017 + 7.66115i 0.665030 + 0.275374i
\(775\) 3.68008 3.68008i 0.132192 0.132192i
\(776\) 29.6194i 1.06327i
\(777\) 0.431880 0.0859323i 0.0154936 0.00308280i
\(778\) 14.4228 14.4228i 0.517081 0.517081i
\(779\) −3.21638 5.57093i −0.115239 0.199599i
\(780\) 2.63556 + 0.405960i 0.0943681 + 0.0145357i
\(781\) 2.82800 4.89823i 0.101194 0.175272i
\(782\) 19.7709 + 73.7862i 0.707007 + 2.63859i
\(783\) −3.11631 1.53612i −0.111368 0.0548965i
\(784\) −51.4856 + 29.7252i −1.83877 + 1.06161i
\(785\) −1.40592 5.24697i −0.0501795 0.187272i
\(786\) −7.11397 + 10.6481i −0.253747 + 0.379807i
\(787\) 2.75552 + 10.2837i 0.0982237 + 0.366576i 0.997488 0.0708289i \(-0.0225644\pi\)
−0.899265 + 0.437405i \(0.855898\pi\)
\(788\) −0.889778 + 3.32070i −0.0316970 + 0.118295i
\(789\) 1.83761 5.41446i 0.0654207 0.192760i
\(790\) −9.23636 + 5.33262i −0.328615 + 0.189726i
\(791\) −76.5745 + 20.5181i −2.72268 + 0.729539i
\(792\) −4.54843 10.9773i −0.161621 0.390061i
\(793\) −29.4168 2.57875i −1.04462 0.0915742i
\(794\) 36.1296 + 20.8595i 1.28219 + 0.740274i
\(795\) −2.24174 4.54514i −0.0795064 0.161200i
\(796\) −1.49699 −0.0530596
\(797\) −8.25442 + 14.2971i −0.292387 + 0.506428i −0.974374 0.224936i \(-0.927783\pi\)
0.681987 + 0.731364i \(0.261116\pi\)
\(798\) 32.9394 + 22.0067i 1.16604 + 0.779028i
\(799\) −24.2610 24.2610i −0.858292 0.858292i
\(800\) 3.80822 14.2125i 0.134641 0.502487i
\(801\) 1.98455 + 15.0607i 0.0701207 + 0.532144i
\(802\) 15.4585 + 26.7749i 0.545859 + 0.945456i
\(803\) 4.45127 + 7.70983i 0.157082 + 0.272074i
\(804\) −10.4265 6.96591i −0.367715 0.245669i
\(805\) −21.7202 + 12.5402i −0.765537 + 0.441983i
\(806\) 3.86483 5.51752i 0.136133 0.194346i
\(807\) 8.34275 24.5816i 0.293679 0.865314i
\(808\) −7.15640 + 26.7080i −0.251761 + 0.939585i
\(809\) 23.6058 + 13.6288i 0.829937 + 0.479164i 0.853831 0.520550i \(-0.174273\pi\)
−0.0238940 + 0.999714i \(0.507606\pi\)
\(810\) −7.32987 7.32648i −0.257545 0.257426i
\(811\) 8.22029 + 8.22029i 0.288654 + 0.288654i 0.836548 0.547894i \(-0.184570\pi\)
−0.547894 + 0.836548i \(0.684570\pi\)
\(812\) −1.24100 + 1.24100i −0.0435506 + 0.0435506i
\(813\) −37.7169 25.1985i −1.32279 0.883749i
\(814\) 0.157929 + 0.0423169i 0.00553540 + 0.00148321i
\(815\) 2.24440 + 1.29581i 0.0786179 + 0.0453901i
\(816\) −9.69674 48.7341i −0.339454 1.70603i
\(817\) 12.9260 + 3.46352i 0.452225 + 0.121173i
\(818\) 27.1289 0.948539
\(819\) −25.5219 40.0664i −0.891808 1.40003i
\(820\) 0.850101 0.0296868
\(821\) −25.7863 6.90942i −0.899948 0.241140i −0.220954 0.975284i \(-0.570917\pi\)
−0.678994 + 0.734144i \(0.737584\pi\)
\(822\) 11.7379 + 3.98372i 0.409406 + 0.138948i
\(823\) 22.6147 + 13.0566i 0.788298 + 0.455124i 0.839363 0.543571i \(-0.182928\pi\)
−0.0510651 + 0.998695i \(0.516262\pi\)
\(824\) −23.5330 6.30566i −0.819812 0.219668i
\(825\) 0.890459 13.5978i 0.0310018 0.473415i
\(826\) 6.95859 6.95859i 0.242120 0.242120i
\(827\) −15.0891 15.0891i −0.524701 0.524701i 0.394287 0.918988i \(-0.370992\pi\)
−0.918988 + 0.394287i \(0.870992\pi\)
\(828\) 8.72310 11.3709i 0.303149 0.395166i
\(829\) 12.8441 + 7.41555i 0.446095 + 0.257553i 0.706179 0.708033i \(-0.250417\pi\)
−0.260085 + 0.965586i \(0.583751\pi\)
\(830\) −2.57005 + 9.59155i −0.0892077 + 0.332928i
\(831\) 21.0538 + 24.0044i 0.730348 + 0.832705i
\(832\) −1.38353 + 15.7824i −0.0479652 + 0.547158i
\(833\) −63.1008 + 36.4313i −2.18631 + 1.26227i
\(834\) 4.09402 62.5180i 0.141764 2.16482i
\(835\) −7.51465 13.0158i −0.260055 0.450429i
\(836\) 1.69207 + 2.93075i 0.0585215 + 0.101362i
\(837\) −5.70353 + 1.93719i −0.197143 + 0.0669591i
\(838\) −8.17315 + 30.5026i −0.282337 + 1.05369i
\(839\) −17.7360 17.7360i −0.612315 0.612315i 0.331234 0.943549i \(-0.392535\pi\)
−0.943549 + 0.331234i \(0.892535\pi\)
\(840\) 11.0165 5.43352i 0.380105 0.187474i
\(841\) −14.2765 + 24.7276i −0.492292 + 0.852674i
\(842\) 64.5874 2.22583
\(843\) −26.7869 + 40.0945i −0.922590 + 1.38093i
\(844\) −0.980800 0.566265i −0.0337605 0.0194917i
\(845\) −8.41640 3.92817i −0.289533 0.135133i
\(846\) −3.64860 + 27.7386i −0.125441 + 0.953673i
\(847\) 33.6363 9.01283i 1.15576 0.309684i
\(848\) −17.1593 + 9.90691i −0.589252 + 0.340205i
\(849\) 9.11529 + 10.3928i 0.312836 + 0.356679i
\(850\) 11.1049 41.4442i 0.380897 1.42153i
\(851\) −0.119757 0.446939i −0.00410522 0.0153209i
\(852\) −3.33395 0.218325i −0.114219 0.00747971i
\(853\) −4.86952 18.1733i −0.166729 0.622242i −0.997813 0.0660950i \(-0.978946\pi\)
0.831084 0.556147i \(-0.187721\pi\)
\(854\) 50.2055 28.9862i 1.71800 0.991886i
\(855\) −5.49493 4.21540i −0.187923 0.144164i
\(856\) 1.93028 + 7.20392i 0.0659757 + 0.246225i
\(857\) 15.0231 26.0207i 0.513178 0.888850i −0.486705 0.873566i \(-0.661801\pi\)
0.999883 0.0152842i \(-0.00486529\pi\)
\(858\) −1.91822 17.5338i −0.0654870 0.598593i
\(859\) −4.29719 7.44295i −0.146618 0.253950i 0.783357 0.621572i \(-0.213506\pi\)
−0.929975 + 0.367622i \(0.880172\pi\)
\(860\) −1.25049 + 1.25049i −0.0426413 + 0.0426413i
\(861\) −9.98582 11.3853i −0.340316 0.388011i
\(862\) 3.05023i 0.103891i
\(863\) −22.4798 + 22.4798i −0.765221 + 0.765221i −0.977261 0.212040i \(-0.931989\pi\)
0.212040 + 0.977261i \(0.431989\pi\)
\(864\) −11.2262 + 12.8055i −0.381923 + 0.435652i
\(865\) 12.6496 + 3.38946i 0.430100 + 0.115245i
\(866\) −14.7821 + 3.96084i −0.502315 + 0.134595i
\(867\) −6.13827 30.8499i −0.208467 1.04772i
\(868\) 3.04275i 0.103278i
\(869\) 11.4768 + 11.4768i 0.389325 + 0.389325i
\(870\) 1.00259 0.879349i 0.0339909 0.0298127i
\(871\) 28.0680 + 33.4618i 0.951047 + 1.13381i
\(872\) 2.07774i 0.0703611i
\(873\) 31.1875 23.9368i 1.05554 0.810137i
\(874\) 20.8129 36.0491i 0.704008 1.21938i
\(875\) 29.7759 1.00661
\(876\) 2.92143 4.37278i 0.0987060 0.147742i
\(877\) 21.4118 5.73729i 0.723027 0.193734i 0.121505 0.992591i \(-0.461228\pi\)
0.601522 + 0.798856i \(0.294561\pi\)
\(878\) −9.80646 + 2.62763i −0.330952 + 0.0886783i
\(879\) −28.9832 + 43.3819i −0.977580 + 1.46323i
\(880\) 6.05744 0.204196
\(881\) 4.67983 8.10570i 0.157667 0.273088i −0.776360 0.630290i \(-0.782936\pi\)
0.934027 + 0.357202i \(0.116269\pi\)
\(882\) 54.8942 + 22.7305i 1.84838 + 0.765376i
\(883\) 20.6234i 0.694033i −0.937859 0.347016i \(-0.887195\pi\)
0.937859 0.347016i \(-0.112805\pi\)
\(884\) 1.11585 12.7289i 0.0375300 0.428119i
\(885\) −1.29343 + 1.13444i −0.0434783 + 0.0381338i
\(886\) 7.17395 + 7.17395i 0.241014 + 0.241014i
\(887\) 43.4004i 1.45724i −0.684916 0.728622i \(-0.740161\pi\)
0.684916 0.728622i \(-0.259839\pi\)
\(888\) 0.0442240 + 0.222262i 0.00148406 + 0.00745862i
\(889\) 3.14877 0.843710i 0.105606 0.0282971i
\(890\) −5.63216 1.50913i −0.188790 0.0505862i
\(891\) −7.88268 + 13.6605i −0.264080 + 0.457643i
\(892\) 6.42882 6.42882i 0.215253 0.215253i
\(893\) 18.6963i 0.625648i
\(894\) −10.5625 12.0428i −0.353263 0.402773i
\(895\) 8.69169 8.69169i 0.290531 0.290531i
\(896\) −29.9449 51.8660i −1.00039 1.73272i
\(897\) −40.2584 + 29.5116i −1.34419 + 0.985364i
\(898\) 29.9515 51.8775i 0.999494 1.73117i
\(899\) −0.200612 0.748692i −0.00669077 0.0249703i
\(900\) −7.43658 + 3.08134i −0.247886 + 0.102711i
\(901\) −21.0304 + 12.1419i −0.700625 + 0.404506i
\(902\) −1.45533 5.43136i −0.0484571 0.180845i
\(903\) 31.4367 + 2.05865i 1.04615 + 0.0685075i
\(904\) −10.5594 39.4082i −0.351200 1.31070i
\(905\) 0.201547 0.752185i 0.00669966 0.0250035i
\(906\) −41.3625 47.1594i −1.37418 1.56677i
\(907\) 29.4275 16.9900i 0.977123 0.564142i 0.0757226 0.997129i \(-0.475874\pi\)
0.901400 + 0.432987i \(0.142540\pi\)
\(908\) −11.5025 + 3.08208i −0.381723 + 0.102282i
\(909\) 33.9055 14.0487i 1.12457 0.465966i
\(910\) 17.9576 3.16321i 0.595287 0.104859i
\(911\) −1.44338 0.833335i −0.0478213 0.0276096i 0.475899 0.879500i \(-0.342123\pi\)
−0.523720 + 0.851890i \(0.675456\pi\)
\(912\) −15.0417 + 22.5143i −0.498081 + 0.745524i
\(913\) 15.1116 0.500122
\(914\) −5.59824 + 9.69643i −0.185173 + 0.320729i
\(915\) −9.08957 + 4.48313i −0.300492 + 0.148208i
\(916\) 3.51665 + 3.51665i 0.116193 + 0.116193i
\(917\) −5.21432 + 19.4601i −0.172192 + 0.642629i
\(918\) −32.7361 + 37.3414i −1.08045 + 1.23245i
\(919\) 20.6189 + 35.7129i 0.680153 + 1.17806i 0.974934 + 0.222495i \(0.0714201\pi\)
−0.294781 + 0.955565i \(0.595247\pi\)
\(920\) −6.45364 11.1780i −0.212770 0.368529i
\(921\) 1.58761 24.2436i 0.0523134 0.798855i
\(922\) 17.4513 10.0755i 0.574726 0.331818i
\(923\) 10.9346 + 3.98201i 0.359918 + 0.131070i
\(924\) 5.25333 + 5.98958i 0.172822 + 0.197043i
\(925\) −0.0672651 + 0.251037i −0.00221166 + 0.00825404i
\(926\) 27.7174 + 16.0026i 0.910850 + 0.525879i
\(927\) 12.3786 + 29.8748i 0.406567 + 0.981219i
\(928\) −1.54953 1.54953i −0.0508657 0.0508657i
\(929\) −15.8786 + 15.8786i −0.520960 + 0.520960i −0.917861 0.396901i \(-0.870086\pi\)
0.396901 + 0.917861i \(0.370086\pi\)
\(930\) 0.151082 2.30711i 0.00495419 0.0756533i
\(931\) 38.3513 + 10.2762i 1.25691 + 0.336789i
\(932\) 6.34593 + 3.66382i 0.207868 + 0.120013i
\(933\) −15.4628 5.24790i −0.506228 0.171809i
\(934\) −27.2046 7.28945i −0.890161 0.238518i
\(935\) 7.42401 0.242791
\(936\) 20.6197 13.1345i 0.673976 0.429316i
\(937\) −25.0543 −0.818490 −0.409245 0.912425i \(-0.634208\pi\)
−0.409245 + 0.912425i \(0.634208\pi\)
\(938\) −82.8207 22.1917i −2.70419 0.724586i
\(939\) −2.84325 14.2897i −0.0927859 0.466325i
\(940\) −2.13973 1.23538i −0.0697904 0.0402935i
\(941\) 2.05537 + 0.550735i 0.0670032 + 0.0179535i 0.292165 0.956368i \(-0.405624\pi\)
−0.225162 + 0.974321i \(0.572291\pi\)
\(942\) 17.6483 + 11.7907i 0.575012 + 0.384163i
\(943\) −11.2522 + 11.2522i −0.366422 + 0.366422i
\(944\) 4.75625 + 4.75625i 0.154803 + 0.154803i
\(945\) −14.6241 7.20867i −0.475723 0.234498i
\(946\) 10.1302 + 5.84870i 0.329363 + 0.190158i
\(947\) 12.1738 45.4334i 0.395597 1.47639i −0.425164 0.905116i \(-0.639784\pi\)
0.820761 0.571272i \(-0.193550\pi\)
\(948\) 3.08136 9.07912i 0.100078 0.294876i
\(949\) −14.0336 + 11.7714i −0.455548 + 0.382117i
\(950\) −20.2480 + 11.6902i −0.656933 + 0.379281i
\(951\) 13.8322 + 9.24124i 0.448541 + 0.299668i
\(952\) −29.4295 50.9734i −0.953817 1.65206i
\(953\) −5.00845 8.67489i −0.162240 0.281007i 0.773432 0.633879i \(-0.218538\pi\)
−0.935672 + 0.352872i \(0.885205\pi\)
\(954\) 18.2953 + 7.57569i 0.592332 + 0.245272i
\(955\) −0.518052 + 1.93340i −0.0167638 + 0.0625633i
\(956\) −3.99114 3.99114i −0.129083 0.129083i
\(957\) −1.68752 1.12742i −0.0545498 0.0364445i
\(958\) −22.4119 + 38.8185i −0.724094 + 1.25417i
\(959\) 19.5009 0.629716
\(960\) 2.40525 + 4.87665i 0.0776290 + 0.157393i
\(961\) 25.6830 + 14.8281i 0.828484 + 0.478326i
\(962\) −0.0293769 + 0.335113i −0.000947148 + 0.0108045i
\(963\) 6.02537 7.85429i 0.194165 0.253101i
\(964\) −3.13656 + 0.840440i −0.101022 + 0.0270687i
\(965\) −1.58039 + 0.912437i −0.0508745 + 0.0293724i
\(966\) 31.4944 92.7971i 1.01332 2.98570i
\(967\) 3.10543 11.5896i 0.0998638 0.372697i −0.897848 0.440305i \(-0.854870\pi\)
0.997712 + 0.0676085i \(0.0215369\pi\)
\(968\) 4.63834 + 17.3105i 0.149082 + 0.556381i
\(969\) −18.4352 + 27.5936i −0.592223 + 0.886435i
\(970\) 3.90568 + 14.5762i 0.125404 + 0.468013i
\(971\) −19.6884 + 11.3671i −0.631831 + 0.364788i −0.781461 0.623954i \(-0.785525\pi\)
0.149630 + 0.988742i \(0.452192\pi\)
\(972\) 9.29683 + 0.606650i 0.298196 + 0.0194583i
\(973\) −25.5106 95.2070i −0.817833 3.05220i
\(974\) −12.3299 + 21.3560i −0.395076 + 0.684291i
\(975\) 27.8709 3.04913i 0.892584 0.0976502i
\(976\) 19.8122 + 34.3158i 0.634175 + 1.09842i
\(977\) −34.5738 + 34.5738i −1.10611 + 1.10611i −0.112456 + 0.993657i \(0.535872\pi\)
−0.993657 + 0.112456i \(0.964128\pi\)
\(978\) −9.93147 + 1.97609i −0.317573 + 0.0631883i
\(979\) 8.87355i 0.283600i
\(980\) −3.71018 + 3.71018i −0.118517 + 0.118517i
\(981\) 2.18774 1.67912i 0.0698492 0.0536100i
\(982\) 53.4839 + 14.3310i 1.70674 + 0.457320i
\(983\) 36.4645 9.77062i 1.16304 0.311634i 0.374858 0.927082i \(-0.377692\pi\)
0.788178 + 0.615448i \(0.211025\pi\)
\(984\) 5.85932 5.13908i 0.186788 0.163828i
\(985\) 4.10968i 0.130945i
\(986\) −4.51849 4.51849i −0.143898 0.143898i
\(987\) 8.58939 + 43.1687i 0.273403 + 1.37408i
\(988\) −5.33460 + 4.47469i −0.169716 + 0.142359i
\(989\) 33.1037i 1.05264i
\(990\) −3.68585 4.80234i −0.117144 0.152628i
\(991\) −20.1358 + 34.8762i −0.639635 + 1.10788i 0.345878 + 0.938279i \(0.387581\pi\)
−0.985513 + 0.169600i \(0.945752\pi\)
\(992\) −3.79920 −0.120625
\(993\) −8.00061 0.523923i −0.253892 0.0166262i
\(994\) −22.0674 + 5.91294i −0.699935 + 0.187547i
\(995\) 1.72857 0.463169i 0.0547993 0.0146834i
\(996\) −3.94865 8.00590i −0.125118 0.253677i
\(997\) −48.7084 −1.54261 −0.771306 0.636465i \(-0.780396\pi\)
−0.771306 + 0.636465i \(0.780396\pi\)
\(998\) 27.5808 47.7714i 0.873056 1.51218i
\(999\) 0.198290 0.226185i 0.00627361 0.00715619i
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 117.2.bc.a.20.4 yes 48
3.2 odd 2 351.2.bf.a.332.9 48
9.4 even 3 351.2.ba.a.98.9 48
9.5 odd 6 117.2.x.a.59.4 yes 48
13.2 odd 12 117.2.x.a.2.4 48
39.2 even 12 351.2.ba.a.197.9 48
117.41 even 12 inner 117.2.bc.a.41.4 yes 48
117.67 odd 12 351.2.bf.a.314.9 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.2.x.a.2.4 48 13.2 odd 12
117.2.x.a.59.4 yes 48 9.5 odd 6
117.2.bc.a.20.4 yes 48 1.1 even 1 trivial
117.2.bc.a.41.4 yes 48 117.41 even 12 inner
351.2.ba.a.98.9 48 9.4 even 3
351.2.ba.a.197.9 48 39.2 even 12
351.2.bf.a.314.9 48 117.67 odd 12
351.2.bf.a.332.9 48 3.2 odd 2