Properties

Label 136.2.s.c.107.5
Level $136$
Weight $2$
Character 136.107
Analytic conductor $1.086$
Analytic rank $0$
Dimension $112$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [136,2,Mod(3,136)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(136, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([8, 8, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("136.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 136.s (of order \(16\), degree \(8\), 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: \(1.08596546749\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(14\) over \(\Q(\zeta_{16})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 107.5
Character \(\chi\) \(=\) 136.107
Dual form 136.2.s.c.75.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.896947 + 1.09338i) q^{2} +(-0.456483 - 0.683175i) q^{3} +(-0.390973 - 1.96141i) q^{4} +(-1.61884 - 0.322007i) q^{5} +(1.15641 + 0.113661i) q^{6} +(4.21158 - 0.837735i) q^{7} +(2.49526 + 1.33180i) q^{8} +(0.889699 - 2.14792i) q^{9} +O(q^{10})\) \(q+(-0.896947 + 1.09338i) q^{2} +(-0.456483 - 0.683175i) q^{3} +(-0.390973 - 1.96141i) q^{4} +(-1.61884 - 0.322007i) q^{5} +(1.15641 + 0.113661i) q^{6} +(4.21158 - 0.837735i) q^{7} +(2.49526 + 1.33180i) q^{8} +(0.889699 - 2.14792i) q^{9} +(1.80409 - 1.48119i) q^{10} +(-0.106698 - 0.0712931i) q^{11} +(-1.16152 + 1.16246i) q^{12} +(2.31804 - 2.31804i) q^{13} +(-2.86160 + 5.35627i) q^{14} +(0.518985 + 1.25294i) q^{15} +(-3.69428 + 1.53372i) q^{16} +(-2.89543 - 2.93539i) q^{17} +(1.55049 + 2.89935i) q^{18} +(1.68438 + 4.06645i) q^{19} +(0.00133407 + 3.30110i) q^{20} +(-2.49484 - 2.49484i) q^{21} +(0.173653 - 0.0527153i) q^{22} +(2.14808 + 1.43530i) q^{23} +(-0.229191 - 2.31264i) q^{24} +(-2.10245 - 0.870864i) q^{25} +(0.455347 + 4.61366i) q^{26} +(-4.29112 + 0.853557i) q^{27} +(-3.28976 - 7.93311i) q^{28} +(0.908461 - 4.56714i) q^{29} +(-1.83545 - 0.556371i) q^{30} +(2.02231 + 3.02660i) q^{31} +(1.63663 - 5.41493i) q^{32} +0.105437i q^{33} +(5.80655 - 0.532927i) q^{34} -7.08762 q^{35} +(-4.56081 - 0.905286i) q^{36} +(-7.00926 + 4.68344i) q^{37} +(-5.95698 - 1.80572i) q^{38} +(-2.64177 - 0.525481i) q^{39} +(-3.61057 - 2.95946i) q^{40} +(2.02785 + 10.1947i) q^{41} +(4.96554 - 0.490077i) q^{42} +(3.26274 - 7.87696i) q^{43} +(-0.0981193 + 0.237152i) q^{44} +(-2.13192 + 3.19065i) q^{45} +(-3.49605 + 1.06129i) q^{46} +(-4.90893 + 4.90893i) q^{47} +(2.73418 + 1.82372i) q^{48} +(10.5684 - 4.37759i) q^{49} +(2.83798 - 1.51767i) q^{50} +(-0.683670 + 3.31804i) q^{51} +(-5.45291 - 3.64033i) q^{52} +(1.32699 - 0.549659i) q^{53} +(2.91564 - 5.45743i) q^{54} +(0.149769 + 0.149769i) q^{55} +(11.6247 + 3.51861i) q^{56} +(2.00921 - 3.00699i) q^{57} +(4.17880 + 5.08978i) q^{58} +(12.6911 + 5.25683i) q^{59} +(2.25462 - 1.50781i) q^{60} +(0.813692 + 4.09070i) q^{61} +(-5.12313 - 0.503539i) q^{62} +(1.94765 - 9.79148i) q^{63} +(4.45262 + 6.64636i) q^{64} +(-4.49895 + 3.00610i) q^{65} +(-0.115283 - 0.0945717i) q^{66} +3.72469i q^{67} +(-4.62547 + 6.82679i) q^{68} -2.12271i q^{69} +(6.35722 - 7.74948i) q^{70} +(-0.759116 + 0.507225i) q^{71} +(5.08063 - 4.17472i) q^{72} +(-0.631605 + 3.17529i) q^{73} +(1.16614 - 11.8646i) q^{74} +(0.364781 + 1.83388i) q^{75} +(7.31744 - 4.89363i) q^{76} +(-0.509091 - 0.210872i) q^{77} +(2.94408 - 2.41714i) q^{78} +(-6.49126 + 9.71485i) q^{79} +(6.47431 - 1.29326i) q^{80} +(-2.38989 - 2.38989i) q^{81} +(-12.9656 - 6.92687i) q^{82} +(-4.75872 + 1.97112i) q^{83} +(-3.91799 + 5.86882i) q^{84} +(3.74201 + 5.68426i) q^{85} +(5.68603 + 10.6326i) q^{86} +(-3.53486 + 1.46419i) q^{87} +(-0.171290 - 0.319995i) q^{88} +(-0.886097 + 0.886097i) q^{89} +(-1.57638 - 5.19285i) q^{90} +(7.82069 - 11.7045i) q^{91} +(1.97538 - 4.77444i) q^{92} +(1.14455 - 2.76318i) q^{93} +(-0.964293 - 9.77039i) q^{94} +(-1.41731 - 7.12530i) q^{95} +(-4.44644 + 1.35372i) q^{96} +(-8.67498 - 1.72556i) q^{97} +(-4.69294 + 15.4818i) q^{98} +(-0.248061 + 0.165749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 8 q^{20} - 8 q^{22} - 56 q^{24} - 16 q^{25} - 40 q^{26} + 32 q^{27} + 40 q^{28} - 72 q^{30} + 32 q^{32} - 72 q^{34} - 32 q^{35} + 56 q^{36} + 48 q^{38} + 56 q^{40} - 16 q^{41} - 56 q^{42} - 96 q^{43} + 24 q^{44} - 24 q^{46} + 16 q^{48} - 16 q^{49} - 16 q^{51} - 16 q^{52} - 24 q^{54} + 32 q^{56} + 32 q^{57} + 48 q^{58} - 16 q^{59} + 96 q^{60} + 48 q^{62} + 40 q^{64} + 64 q^{65} - 16 q^{66} + 80 q^{68} + 64 q^{70} + 96 q^{72} - 96 q^{73} + 40 q^{74} - 16 q^{75} + 48 q^{76} + 96 q^{78} + 8 q^{80} - 96 q^{81} + 32 q^{82} + 128 q^{83} + 64 q^{86} - 72 q^{88} - 16 q^{89} + 152 q^{90} - 16 q^{91} - 120 q^{92} + 88 q^{94} - 160 q^{96} - 16 q^{97} + 128 q^{98} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).

\(n\) \(69\) \(103\) \(105\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{16}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.896947 + 1.09338i −0.634237 + 0.773139i
\(3\) −0.456483 0.683175i −0.263551 0.394431i 0.675967 0.736932i \(-0.263726\pi\)
−0.939518 + 0.342500i \(0.888726\pi\)
\(4\) −0.390973 1.96141i −0.195487 0.980706i
\(5\) −1.61884 0.322007i −0.723966 0.144006i −0.180666 0.983544i \(-0.557825\pi\)
−0.543300 + 0.839539i \(0.682825\pi\)
\(6\) 1.15641 + 0.113661i 0.472104 + 0.0464019i
\(7\) 4.21158 0.837735i 1.59183 0.316634i 0.681914 0.731432i \(-0.261148\pi\)
0.909913 + 0.414798i \(0.136148\pi\)
\(8\) 2.49526 + 1.33180i 0.882207 + 0.470862i
\(9\) 0.889699 2.14792i 0.296566 0.715974i
\(10\) 1.80409 1.48119i 0.570503 0.468392i
\(11\) −0.106698 0.0712931i −0.0321706 0.0214957i 0.539381 0.842062i \(-0.318658\pi\)
−0.571552 + 0.820566i \(0.693658\pi\)
\(12\) −1.16152 + 1.16246i −0.335301 + 0.335572i
\(13\) 2.31804 2.31804i 0.642907 0.642907i −0.308362 0.951269i \(-0.599781\pi\)
0.951269 + 0.308362i \(0.0997807\pi\)
\(14\) −2.86160 + 5.35627i −0.764794 + 1.43152i
\(15\) 0.518985 + 1.25294i 0.134001 + 0.323508i
\(16\) −3.69428 + 1.53372i −0.923570 + 0.383430i
\(17\) −2.89543 2.93539i −0.702244 0.711936i
\(18\) 1.55049 + 2.89935i 0.365454 + 0.683384i
\(19\) 1.68438 + 4.06645i 0.386423 + 0.932907i 0.990691 + 0.136127i \(0.0434654\pi\)
−0.604269 + 0.796781i \(0.706535\pi\)
\(20\) 0.00133407 + 3.30110i 0.000298307 + 0.738149i
\(21\) −2.49484 2.49484i −0.544418 0.544418i
\(22\) 0.173653 0.0527153i 0.0370229 0.0112389i
\(23\) 2.14808 + 1.43530i 0.447906 + 0.299281i 0.758991 0.651101i \(-0.225692\pi\)
−0.311085 + 0.950382i \(0.600692\pi\)
\(24\) −0.229191 2.31264i −0.0467834 0.472066i
\(25\) −2.10245 0.870864i −0.420490 0.174173i
\(26\) 0.455347 + 4.61366i 0.0893008 + 0.904812i
\(27\) −4.29112 + 0.853557i −0.825827 + 0.164267i
\(28\) −3.28976 7.93311i −0.621706 1.49922i
\(29\) 0.908461 4.56714i 0.168697 0.848097i −0.800028 0.599962i \(-0.795182\pi\)
0.968725 0.248135i \(-0.0798177\pi\)
\(30\) −1.83545 0.556371i −0.335105 0.101579i
\(31\) 2.02231 + 3.02660i 0.363217 + 0.543593i 0.967400 0.253253i \(-0.0815005\pi\)
−0.604183 + 0.796845i \(0.706500\pi\)
\(32\) 1.63663 5.41493i 0.289318 0.957233i
\(33\) 0.105437i 0.0183543i
\(34\) 5.80655 0.532927i 0.995815 0.0913962i
\(35\) −7.08762 −1.19803
\(36\) −4.56081 0.905286i −0.760135 0.150881i
\(37\) −7.00926 + 4.68344i −1.15231 + 0.769952i −0.976722 0.214511i \(-0.931184\pi\)
−0.175593 + 0.984463i \(0.556184\pi\)
\(38\) −5.95698 1.80572i −0.966350 0.292926i
\(39\) −2.64177 0.525481i −0.423022 0.0841442i
\(40\) −3.61057 2.95946i −0.570881 0.467931i
\(41\) 2.02785 + 10.1947i 0.316696 + 1.59214i 0.731246 + 0.682114i \(0.238939\pi\)
−0.414550 + 0.910027i \(0.636061\pi\)
\(42\) 4.96554 0.490077i 0.766200 0.0756205i
\(43\) 3.26274 7.87696i 0.497564 1.20122i −0.453228 0.891394i \(-0.649728\pi\)
0.950792 0.309830i \(-0.100272\pi\)
\(44\) −0.0981193 + 0.237152i −0.0147920 + 0.0357520i
\(45\) −2.13192 + 3.19065i −0.317808 + 0.475634i
\(46\) −3.49605 + 1.06129i −0.515465 + 0.156478i
\(47\) −4.90893 + 4.90893i −0.716041 + 0.716041i −0.967792 0.251751i \(-0.918994\pi\)
0.251751 + 0.967792i \(0.418994\pi\)
\(48\) 2.73418 + 1.82372i 0.394644 + 0.263232i
\(49\) 10.5684 4.37759i 1.50978 0.625370i
\(50\) 2.83798 1.51767i 0.401350 0.214630i
\(51\) −0.683670 + 3.31804i −0.0957329 + 0.464619i
\(52\) −5.45291 3.64033i −0.756183 0.504824i
\(53\) 1.32699 0.549659i 0.182277 0.0755015i −0.289679 0.957124i \(-0.593548\pi\)
0.471955 + 0.881623i \(0.343548\pi\)
\(54\) 2.91564 5.45743i 0.396769 0.742663i
\(55\) 0.149769 + 0.149769i 0.0201949 + 0.0201949i
\(56\) 11.6247 + 3.51861i 1.55341 + 0.470194i
\(57\) 2.00921 3.00699i 0.266126 0.398286i
\(58\) 4.17880 + 5.08978i 0.548703 + 0.668321i
\(59\) 12.6911 + 5.25683i 1.65224 + 0.684381i 0.997446 0.0714255i \(-0.0227548\pi\)
0.654795 + 0.755806i \(0.272755\pi\)
\(60\) 2.25462 1.50781i 0.291071 0.194657i
\(61\) 0.813692 + 4.09070i 0.104183 + 0.523761i 0.997268 + 0.0738732i \(0.0235360\pi\)
−0.893085 + 0.449888i \(0.851464\pi\)
\(62\) −5.12313 0.503539i −0.650638 0.0639495i
\(63\) 1.94765 9.79148i 0.245380 1.23361i
\(64\) 4.45262 + 6.64636i 0.556578 + 0.830795i
\(65\) −4.49895 + 3.00610i −0.558026 + 0.372861i
\(66\) −0.115283 0.0945717i −0.0141904 0.0116410i
\(67\) 3.72469i 0.455044i 0.973773 + 0.227522i \(0.0730623\pi\)
−0.973773 + 0.227522i \(0.926938\pi\)
\(68\) −4.62547 + 6.82679i −0.560921 + 0.827870i
\(69\) 2.12271i 0.255544i
\(70\) 6.35722 7.74948i 0.759833 0.926240i
\(71\) −0.759116 + 0.507225i −0.0900904 + 0.0601965i −0.599800 0.800150i \(-0.704753\pi\)
0.509709 + 0.860347i \(0.329753\pi\)
\(72\) 5.08063 4.17472i 0.598758 0.491996i
\(73\) −0.631605 + 3.17529i −0.0739238 + 0.371640i −0.999984 0.00573683i \(-0.998174\pi\)
0.926060 + 0.377377i \(0.123174\pi\)
\(74\) 1.16614 11.8646i 0.135561 1.37923i
\(75\) 0.364781 + 1.83388i 0.0421213 + 0.211758i
\(76\) 7.31744 4.89363i 0.839367 0.561338i
\(77\) −0.509091 0.210872i −0.0580163 0.0240311i
\(78\) 2.94408 2.41714i 0.333351 0.273687i
\(79\) −6.49126 + 9.71485i −0.730323 + 1.09301i 0.261477 + 0.965210i \(0.415790\pi\)
−0.991800 + 0.127796i \(0.959210\pi\)
\(80\) 6.47431 1.29326i 0.723849 0.144591i
\(81\) −2.38989 2.38989i −0.265544 0.265544i
\(82\) −12.9656 6.92687i −1.43181 0.764944i
\(83\) −4.75872 + 1.97112i −0.522337 + 0.216359i −0.628243 0.778017i \(-0.716226\pi\)
0.105906 + 0.994376i \(0.466226\pi\)
\(84\) −3.91799 + 5.86882i −0.427487 + 0.640340i
\(85\) 3.74201 + 5.68426i 0.405878 + 0.616545i
\(86\) 5.68603 + 10.6326i 0.613140 + 1.14655i
\(87\) −3.53486 + 1.46419i −0.378976 + 0.156977i
\(88\) −0.171290 0.319995i −0.0182596 0.0341115i
\(89\) −0.886097 + 0.886097i −0.0939261 + 0.0939261i −0.752509 0.658582i \(-0.771156\pi\)
0.658582 + 0.752509i \(0.271156\pi\)
\(90\) −1.57638 5.19285i −0.166165 0.547374i
\(91\) 7.82069 11.7045i 0.819831 1.22696i
\(92\) 1.97538 4.77444i 0.205947 0.497770i
\(93\) 1.14455 2.76318i 0.118684 0.286528i
\(94\) −0.964293 9.77039i −0.0994592 1.00774i
\(95\) −1.41731 7.12530i −0.145413 0.731040i
\(96\) −4.44644 + 1.35372i −0.453813 + 0.138163i
\(97\) −8.67498 1.72556i −0.880811 0.175204i −0.266089 0.963948i \(-0.585732\pi\)
−0.614721 + 0.788744i \(0.710732\pi\)
\(98\) −4.69294 + 15.4818i −0.474059 + 1.56390i
\(99\) −0.248061 + 0.165749i −0.0249311 + 0.0166584i
\(100\) −0.886121 + 4.46426i −0.0886121 + 0.446426i
\(101\) 12.7602 1.26968 0.634842 0.772642i \(-0.281065\pi\)
0.634842 + 0.772642i \(0.281065\pi\)
\(102\) −3.01467 3.72362i −0.298497 0.368693i
\(103\) 8.51240i 0.838752i −0.907813 0.419376i \(-0.862249\pi\)
0.907813 0.419376i \(-0.137751\pi\)
\(104\) 8.87125 2.69694i 0.869898 0.264457i
\(105\) 3.23538 + 4.84209i 0.315741 + 0.472539i
\(106\) −0.589255 + 1.94393i −0.0572335 + 0.188811i
\(107\) 0.542503 2.72735i 0.0524457 0.263662i −0.945662 0.325151i \(-0.894585\pi\)
0.998108 + 0.0614887i \(0.0195848\pi\)
\(108\) 3.35189 + 8.08294i 0.322536 + 0.777781i
\(109\) −13.8733 + 2.75956i −1.32882 + 0.264318i −0.807915 0.589298i \(-0.799404\pi\)
−0.520902 + 0.853617i \(0.674404\pi\)
\(110\) −0.298090 + 0.0294202i −0.0284218 + 0.00280510i
\(111\) 6.39922 + 2.65064i 0.607387 + 0.251588i
\(112\) −14.2739 + 9.55421i −1.34876 + 0.902788i
\(113\) 6.43022 + 4.29653i 0.604904 + 0.404184i 0.819962 0.572417i \(-0.193994\pi\)
−0.215059 + 0.976601i \(0.568994\pi\)
\(114\) 1.48564 + 4.89394i 0.139143 + 0.458360i
\(115\) −3.01522 3.01522i −0.281171 0.281171i
\(116\) −9.31324 + 0.00376374i −0.864712 + 0.000349454i
\(117\) −2.91661 7.04131i −0.269640 0.650970i
\(118\) −17.1310 + 9.16115i −1.57703 + 0.843352i
\(119\) −14.6534 9.93701i −1.34328 0.910924i
\(120\) −0.373664 + 3.81759i −0.0341107 + 0.348497i
\(121\) −4.20322 10.1475i −0.382111 0.922496i
\(122\) −5.20254 2.77947i −0.471016 0.251641i
\(123\) 6.03907 6.03907i 0.544525 0.544525i
\(124\) 5.14574 5.14990i 0.462101 0.462474i
\(125\) 9.98502 + 6.67178i 0.893088 + 0.596742i
\(126\) 8.95890 + 10.9120i 0.798122 + 0.972114i
\(127\) 4.46964 10.7907i 0.396616 0.957516i −0.591846 0.806051i \(-0.701601\pi\)
0.988463 0.151465i \(-0.0483992\pi\)
\(128\) −11.2608 1.09301i −0.995322 0.0966094i
\(129\) −6.87073 + 1.36667i −0.604934 + 0.120329i
\(130\) 0.748496 7.61538i 0.0656474 0.667913i
\(131\) −18.8074 3.74102i −1.64321 0.326855i −0.715060 0.699063i \(-0.753601\pi\)
−0.928149 + 0.372208i \(0.878601\pi\)
\(132\) 0.206806 0.0412232i 0.0180002 0.00358802i
\(133\) 10.5005 + 15.7151i 0.910509 + 1.36267i
\(134\) −4.07252 3.34085i −0.351812 0.288606i
\(135\) 7.22148 0.621526
\(136\) −3.31549 11.1807i −0.284301 0.958735i
\(137\) −8.21097 −0.701511 −0.350755 0.936467i \(-0.614075\pi\)
−0.350755 + 0.936467i \(0.614075\pi\)
\(138\) 2.32093 + 1.90396i 0.197571 + 0.162076i
\(139\) 6.37970 + 9.54790i 0.541119 + 0.809842i 0.996769 0.0803166i \(-0.0255931\pi\)
−0.455650 + 0.890159i \(0.650593\pi\)
\(140\) 2.77107 + 13.9017i 0.234198 + 1.17491i
\(141\) 5.59450 + 1.11282i 0.471142 + 0.0937160i
\(142\) 0.126295 1.28496i 0.0105985 0.107831i
\(143\) −0.412589 + 0.0820691i −0.0345024 + 0.00686296i
\(144\) 0.00751644 + 9.29957i 0.000626370 + 0.774965i
\(145\) −2.94130 + 7.10093i −0.244262 + 0.589700i
\(146\) −2.90530 3.53866i −0.240444 0.292861i
\(147\) −7.81498 5.22180i −0.644568 0.430687i
\(148\) 11.9266 + 11.9169i 0.980359 + 0.979567i
\(149\) 15.9196 15.9196i 1.30418 1.30418i 0.378635 0.925546i \(-0.376394\pi\)
0.925546 0.378635i \(-0.123606\pi\)
\(150\) −2.33232 1.24605i −0.190433 0.101739i
\(151\) 6.91534 + 16.6951i 0.562762 + 1.35863i 0.907549 + 0.419947i \(0.137951\pi\)
−0.344786 + 0.938681i \(0.612049\pi\)
\(152\) −1.21273 + 12.3901i −0.0983657 + 1.00497i
\(153\) −8.88104 + 3.60755i −0.717990 + 0.291653i
\(154\) 0.687191 0.367490i 0.0553754 0.0296132i
\(155\) −2.29920 5.55076i −0.184676 0.445848i
\(156\) 0.00217706 + 5.38705i 0.000174304 + 0.431309i
\(157\) 4.46396 + 4.46396i 0.356263 + 0.356263i 0.862433 0.506170i \(-0.168939\pi\)
−0.506170 + 0.862433i \(0.668939\pi\)
\(158\) −4.79974 15.8111i −0.381847 1.25787i
\(159\) −0.981264 0.655660i −0.0778193 0.0519972i
\(160\) −4.39308 + 8.23888i −0.347303 + 0.651341i
\(161\) 10.2492 + 4.24537i 0.807752 + 0.334582i
\(162\) 4.75667 0.469462i 0.373720 0.0368844i
\(163\) 2.19822 0.437254i 0.172178 0.0342484i −0.108248 0.994124i \(-0.534524\pi\)
0.280426 + 0.959876i \(0.409524\pi\)
\(164\) 19.2031 7.96329i 1.49951 0.621828i
\(165\) 0.0339515 0.170686i 0.00264312 0.0132879i
\(166\) 2.11312 6.97109i 0.164010 0.541062i
\(167\) −3.16809 4.74138i −0.245154 0.366899i 0.688403 0.725329i \(-0.258312\pi\)
−0.933557 + 0.358430i \(0.883312\pi\)
\(168\) −2.90264 9.54788i −0.223943 0.736635i
\(169\) 2.25342i 0.173340i
\(170\) −9.57146 1.00703i −0.734098 0.0772353i
\(171\) 10.2330 0.782537
\(172\) −16.7256 3.31990i −1.27532 0.253140i
\(173\) −0.701217 + 0.468538i −0.0533125 + 0.0356223i −0.581941 0.813231i \(-0.697707\pi\)
0.528628 + 0.848853i \(0.322707\pi\)
\(174\) 1.56966 5.17825i 0.118996 0.392562i
\(175\) −9.58419 1.90641i −0.724497 0.144111i
\(176\) 0.503515 + 0.0997323i 0.0379539 + 0.00751761i
\(177\) −2.20194 11.0699i −0.165508 0.832065i
\(178\) −0.174062 1.76363i −0.0130465 0.132189i
\(179\) −1.92271 + 4.64184i −0.143710 + 0.346947i −0.979302 0.202403i \(-0.935125\pi\)
0.835592 + 0.549351i \(0.185125\pi\)
\(180\) 7.09170 + 2.93412i 0.528584 + 0.218697i
\(181\) 2.50824 3.75385i 0.186436 0.279022i −0.726464 0.687205i \(-0.758838\pi\)
0.912900 + 0.408183i \(0.133838\pi\)
\(182\) 5.78275 + 19.0493i 0.428646 + 1.41203i
\(183\) 2.42323 2.42323i 0.179130 0.179130i
\(184\) 3.44849 + 6.44227i 0.254226 + 0.474930i
\(185\) 12.8549 5.32469i 0.945114 0.391479i
\(186\) 1.99462 + 3.72985i 0.146252 + 0.273486i
\(187\) 0.0996626 + 0.519623i 0.00728805 + 0.0379986i
\(188\) 11.5477 + 7.70918i 0.842202 + 0.562249i
\(189\) −17.3573 + 7.18965i −1.26256 + 0.522970i
\(190\) 9.06193 + 4.84135i 0.657422 + 0.351228i
\(191\) −7.24027 7.24027i −0.523888 0.523888i 0.394856 0.918743i \(-0.370795\pi\)
−0.918743 + 0.394856i \(0.870795\pi\)
\(192\) 2.50808 6.07588i 0.181005 0.438489i
\(193\) 6.38433 9.55482i 0.459554 0.687771i −0.527246 0.849712i \(-0.676775\pi\)
0.986800 + 0.161941i \(0.0517755\pi\)
\(194\) 9.66769 7.93734i 0.694100 0.569868i
\(195\) 4.10739 + 1.70134i 0.294136 + 0.121835i
\(196\) −12.7182 19.0176i −0.908446 1.35840i
\(197\) −3.26593 16.4189i −0.232688 1.16980i −0.903637 0.428298i \(-0.859113\pi\)
0.670949 0.741503i \(-0.265887\pi\)
\(198\) 0.0412702 0.419894i 0.00293295 0.0298405i
\(199\) −1.30692 + 6.57032i −0.0926450 + 0.465758i 0.906414 + 0.422390i \(0.138809\pi\)
−0.999059 + 0.0433677i \(0.986191\pi\)
\(200\) −4.08634 4.97307i −0.288948 0.351649i
\(201\) 2.54462 1.70026i 0.179484 0.119927i
\(202\) −11.4452 + 13.9518i −0.805281 + 0.981642i
\(203\) 19.9959i 1.40344i
\(204\) 6.77534 + 0.0436934i 0.474369 + 0.00305915i
\(205\) 17.1565i 1.19826i
\(206\) 9.30732 + 7.63517i 0.648472 + 0.531968i
\(207\) 4.99407 3.33693i 0.347112 0.231933i
\(208\) −5.00825 + 12.1187i −0.347260 + 0.840280i
\(209\) 0.110191 0.553965i 0.00762204 0.0383186i
\(210\) −8.19622 0.805585i −0.565593 0.0555906i
\(211\) 4.19940 + 21.1118i 0.289099 + 1.45340i 0.803221 + 0.595681i \(0.203118\pi\)
−0.514122 + 0.857717i \(0.671882\pi\)
\(212\) −1.59693 2.38788i −0.109677 0.164000i
\(213\) 0.693047 + 0.287069i 0.0474868 + 0.0196697i
\(214\) 2.49544 + 3.03945i 0.170585 + 0.207772i
\(215\) −7.81828 + 11.7009i −0.533203 + 0.797994i
\(216\) −11.8442 3.58507i −0.805897 0.243933i
\(217\) 11.0526 + 11.0526i 0.750299 + 0.750299i
\(218\) 9.42631 17.6440i 0.638431 1.19500i
\(219\) 2.45760 1.01797i 0.166069 0.0687881i
\(220\) 0.235204 0.352315i 0.0158574 0.0237531i
\(221\) −13.5160 0.0926259i −0.909187 0.00623069i
\(222\) −8.63792 + 4.61931i −0.579739 + 0.310028i
\(223\) 10.8572 4.49720i 0.727051 0.301154i 0.0117116 0.999931i \(-0.496272\pi\)
0.715340 + 0.698777i \(0.246272\pi\)
\(224\) 2.35651 24.1765i 0.157451 1.61536i
\(225\) −3.74110 + 3.74110i −0.249406 + 0.249406i
\(226\) −10.4653 + 3.17693i −0.696143 + 0.211326i
\(227\) 1.55096 2.32117i 0.102941 0.154062i −0.776423 0.630212i \(-0.782968\pi\)
0.879364 + 0.476150i \(0.157968\pi\)
\(228\) −6.68350 2.76523i −0.442625 0.183132i
\(229\) −11.3819 + 27.4784i −0.752138 + 1.81582i −0.205037 + 0.978754i \(0.565731\pi\)
−0.547101 + 0.837067i \(0.684269\pi\)
\(230\) 6.00128 0.592299i 0.395713 0.0390550i
\(231\) 0.0883286 + 0.444058i 0.00581159 + 0.0292169i
\(232\) 8.34936 10.1863i 0.548162 0.668764i
\(233\) −6.35323 1.26374i −0.416214 0.0827901i −0.0174590 0.999848i \(-0.505558\pi\)
−0.398755 + 0.917057i \(0.630558\pi\)
\(234\) 10.3149 + 3.12671i 0.674306 + 0.204400i
\(235\) 9.52747 6.36605i 0.621503 0.415275i
\(236\) 5.34893 26.9478i 0.348185 1.75415i
\(237\) 9.60010 0.623593
\(238\) 24.0083 7.10881i 1.55623 0.460796i
\(239\) 12.7854i 0.827016i 0.910500 + 0.413508i \(0.135697\pi\)
−0.910500 + 0.413508i \(0.864303\pi\)
\(240\) −3.83894 3.83273i −0.247802 0.247402i
\(241\) 1.59519 + 2.38736i 0.102755 + 0.153784i 0.879284 0.476298i \(-0.158022\pi\)
−0.776529 + 0.630081i \(0.783022\pi\)
\(242\) 14.8651 + 4.50601i 0.955566 + 0.289657i
\(243\) −3.10244 + 15.5970i −0.199022 + 1.00055i
\(244\) 7.70543 3.19534i 0.493289 0.204561i
\(245\) −18.5182 + 3.68350i −1.18308 + 0.235330i
\(246\) 1.18629 + 12.0197i 0.0756353 + 0.766351i
\(247\) 13.3306 + 5.52172i 0.848207 + 0.351339i
\(248\) 1.01536 + 10.2454i 0.0644754 + 0.650586i
\(249\) 3.51890 + 2.35125i 0.223001 + 0.149005i
\(250\) −16.2508 + 4.93323i −1.02779 + 0.312005i
\(251\) −4.86266 4.86266i −0.306928 0.306928i 0.536789 0.843717i \(-0.319637\pi\)
−0.843717 + 0.536789i \(0.819637\pi\)
\(252\) −19.9666 + 0.00806907i −1.25778 + 0.000508303i
\(253\) −0.126868 0.306287i −0.00797614 0.0192561i
\(254\) 7.78930 + 14.5657i 0.488744 + 0.913931i
\(255\) 2.17518 5.15122i 0.136215 0.322582i
\(256\) 11.2954 11.3320i 0.705963 0.708249i
\(257\) 3.21534 + 7.76252i 0.200567 + 0.484213i 0.991877 0.127204i \(-0.0406001\pi\)
−0.791309 + 0.611416i \(0.790600\pi\)
\(258\) 4.66838 8.73817i 0.290641 0.544015i
\(259\) −25.5966 + 25.5966i −1.59049 + 1.59049i
\(260\) 7.65517 + 7.64898i 0.474753 + 0.474370i
\(261\) −9.00161 6.01468i −0.557186 0.372300i
\(262\) 20.9596 17.2082i 1.29489 1.06313i
\(263\) −4.88181 + 11.7857i −0.301025 + 0.726739i 0.698908 + 0.715211i \(0.253670\pi\)
−0.999934 + 0.0115280i \(0.996330\pi\)
\(264\) −0.140421 + 0.263093i −0.00864234 + 0.0161923i
\(265\) −2.32518 + 0.462507i −0.142835 + 0.0284116i
\(266\) −26.6010 2.61454i −1.63101 0.160308i
\(267\) 1.00985 + 0.200871i 0.0618017 + 0.0122931i
\(268\) 7.30566 1.45626i 0.446264 0.0889550i
\(269\) 5.07304 + 7.59234i 0.309309 + 0.462913i 0.953259 0.302154i \(-0.0977057\pi\)
−0.643950 + 0.765067i \(0.722706\pi\)
\(270\) −6.47728 + 7.89584i −0.394195 + 0.480526i
\(271\) 12.5928 0.764955 0.382478 0.923965i \(-0.375071\pi\)
0.382478 + 0.923965i \(0.375071\pi\)
\(272\) 15.1986 + 6.40336i 0.921549 + 0.388261i
\(273\) −11.5662 −0.700020
\(274\) 7.36480 8.97774i 0.444924 0.542365i
\(275\) 0.162240 + 0.242810i 0.00978345 + 0.0146420i
\(276\) −4.16351 + 0.829923i −0.250614 + 0.0499555i
\(277\) −25.2468 5.02190i −1.51693 0.301737i −0.634777 0.772695i \(-0.718908\pi\)
−0.882155 + 0.470959i \(0.843908\pi\)
\(278\) −16.1618 1.58850i −0.969319 0.0952718i
\(279\) 8.30014 1.65100i 0.496916 0.0988428i
\(280\) −17.6854 9.43928i −1.05691 0.564105i
\(281\) 12.5687 30.3435i 0.749784 1.81014i 0.189414 0.981897i \(-0.439341\pi\)
0.560370 0.828242i \(-0.310659\pi\)
\(282\) −6.23471 + 5.11880i −0.371271 + 0.304820i
\(283\) 15.7022 + 10.4918i 0.933396 + 0.623675i 0.926497 0.376301i \(-0.122804\pi\)
0.00689850 + 0.999976i \(0.497804\pi\)
\(284\) 1.29167 + 1.29063i 0.0766466 + 0.0765846i
\(285\) −4.22085 + 4.22085i −0.250022 + 0.250022i
\(286\) 0.280337 0.524730i 0.0165767 0.0310279i
\(287\) 17.0809 + 41.2369i 1.00825 + 2.43414i
\(288\) −10.1747 8.33300i −0.599552 0.491027i
\(289\) −0.232992 + 16.9984i −0.0137054 + 0.999906i
\(290\) −5.12585 9.58513i −0.301000 0.562858i
\(291\) 2.78112 + 6.71422i 0.163032 + 0.393595i
\(292\) 6.47500 0.00261673i 0.378921 0.000153133i
\(293\) 2.94002 + 2.94002i 0.171758 + 0.171758i 0.787751 0.615994i \(-0.211245\pi\)
−0.615994 + 0.787751i \(0.711245\pi\)
\(294\) 12.7190 3.86109i 0.741790 0.225183i
\(295\) −18.8521 12.5966i −1.09761 0.733401i
\(296\) −23.7273 + 2.35146i −1.37912 + 0.136676i
\(297\) 0.518706 + 0.214855i 0.0300983 + 0.0124671i
\(298\) 3.12718 + 31.6852i 0.181153 + 1.83547i
\(299\) 8.30642 1.65225i 0.480372 0.0955520i
\(300\) 3.45437 1.43248i 0.199438 0.0827045i
\(301\) 7.14249 35.9077i 0.411687 2.06969i
\(302\) −24.4568 7.41350i −1.40733 0.426599i
\(303\) −5.82480 8.71743i −0.334626 0.500804i
\(304\) −12.4594 12.4392i −0.714593 0.713439i
\(305\) 6.88420i 0.394188i
\(306\) 4.02139 12.9462i 0.229888 0.740083i
\(307\) −17.5822 −1.00347 −0.501734 0.865022i \(-0.667304\pi\)
−0.501734 + 0.865022i \(0.667304\pi\)
\(308\) −0.214567 + 1.08098i −0.0122261 + 0.0615947i
\(309\) −5.81546 + 3.88577i −0.330830 + 0.221054i
\(310\) 8.13137 + 2.46483i 0.461831 + 0.139993i
\(311\) −12.9719 2.58028i −0.735571 0.146314i −0.186931 0.982373i \(-0.559854\pi\)
−0.548640 + 0.836059i \(0.684854\pi\)
\(312\) −5.89206 4.82951i −0.333572 0.273417i
\(313\) −6.19591 31.1489i −0.350213 1.76064i −0.607513 0.794310i \(-0.707833\pi\)
0.257299 0.966332i \(-0.417167\pi\)
\(314\) −8.88476 + 0.876885i −0.501396 + 0.0494855i
\(315\) −6.30584 + 15.2237i −0.355294 + 0.857756i
\(316\) 21.5927 + 8.93378i 1.21469 + 0.502565i
\(317\) 10.3583 15.5022i 0.581778 0.870693i −0.417500 0.908677i \(-0.637094\pi\)
0.999278 + 0.0379839i \(0.0120936\pi\)
\(318\) 1.59703 0.484806i 0.0895569 0.0271866i
\(319\) −0.422537 + 0.422537i −0.0236575 + 0.0236575i
\(320\) −5.06790 12.1932i −0.283304 0.681618i
\(321\) −2.11090 + 0.874363i −0.117819 + 0.0488022i
\(322\) −13.8348 + 7.39846i −0.770984 + 0.412300i
\(323\) 7.05960 16.7184i 0.392807 0.930237i
\(324\) −3.75318 + 5.62195i −0.208510 + 0.312330i
\(325\) −6.89225 + 2.85486i −0.382313 + 0.158359i
\(326\) −1.49360 + 2.79569i −0.0827230 + 0.154839i
\(327\) 8.21818 + 8.21818i 0.454466 + 0.454466i
\(328\) −8.51726 + 28.1390i −0.470287 + 1.55372i
\(329\) −16.5620 + 24.7867i −0.913091 + 1.36654i
\(330\) 0.156172 + 0.190218i 0.00859701 + 0.0104712i
\(331\) −28.8044 11.9312i −1.58323 0.655796i −0.594311 0.804235i \(-0.702575\pi\)
−0.988922 + 0.148439i \(0.952575\pi\)
\(332\) 5.72672 + 8.56315i 0.314295 + 0.469964i
\(333\) 3.82353 + 19.2222i 0.209528 + 1.05337i
\(334\) 8.02575 + 0.788830i 0.439150 + 0.0431629i
\(335\) 1.19938 6.02967i 0.0655290 0.329436i
\(336\) 13.0430 + 5.39024i 0.711554 + 0.294062i
\(337\) 11.8732 7.93343i 0.646775 0.432161i −0.188440 0.982085i \(-0.560343\pi\)
0.835215 + 0.549923i \(0.185343\pi\)
\(338\) −2.46385 2.02120i −0.134016 0.109939i
\(339\) 6.35426i 0.345116i
\(340\) 9.68616 9.56203i 0.525306 0.518574i
\(341\) 0.467107i 0.0252953i
\(342\) −9.17846 + 11.1886i −0.496314 + 0.605010i
\(343\) 15.8497 10.5904i 0.855805 0.571831i
\(344\) 18.6319 15.3097i 1.00457 0.825445i
\(345\) −0.683527 + 3.43632i −0.0367998 + 0.185005i
\(346\) 0.116662 1.18695i 0.00627181 0.0638109i
\(347\) 3.56365 + 17.9157i 0.191307 + 0.961765i 0.950459 + 0.310851i \(0.100614\pi\)
−0.759152 + 0.650914i \(0.774386\pi\)
\(348\) 4.25391 + 6.36086i 0.228033 + 0.340978i
\(349\) −18.5330 7.67664i −0.992051 0.410921i −0.173175 0.984891i \(-0.555403\pi\)
−0.818876 + 0.573970i \(0.805403\pi\)
\(350\) 10.6810 8.76924i 0.570921 0.468736i
\(351\) −7.96840 + 11.9255i −0.425322 + 0.636539i
\(352\) −0.560672 + 0.461080i −0.0298839 + 0.0245757i
\(353\) 4.65183 + 4.65183i 0.247592 + 0.247592i 0.819982 0.572390i \(-0.193984\pi\)
−0.572390 + 0.819982i \(0.693984\pi\)
\(354\) 14.0787 + 7.52155i 0.748273 + 0.399766i
\(355\) 1.39221 0.576674i 0.0738911 0.0306067i
\(356\) 2.08444 + 1.39156i 0.110475 + 0.0737526i
\(357\) −0.0996905 + 14.5469i −0.00527618 + 0.769905i
\(358\) −3.35074 6.26574i −0.177092 0.331155i
\(359\) 17.9010 7.41484i 0.944779 0.391340i 0.143513 0.989648i \(-0.454160\pi\)
0.801266 + 0.598308i \(0.204160\pi\)
\(360\) −9.56900 + 5.12220i −0.504331 + 0.269963i
\(361\) −0.263841 + 0.263841i −0.0138864 + 0.0138864i
\(362\) 1.85464 + 6.10948i 0.0974776 + 0.321107i
\(363\) −5.01380 + 7.50368i −0.263156 + 0.393841i
\(364\) −26.0150 10.7635i −1.36356 0.564158i
\(365\) 2.04493 4.93690i 0.107037 0.258409i
\(366\) 0.476011 + 4.82303i 0.0248815 + 0.252104i
\(367\) −0.558331 2.80692i −0.0291446 0.146520i 0.963473 0.267805i \(-0.0862984\pi\)
−0.992618 + 0.121285i \(0.961298\pi\)
\(368\) −10.1370 2.00785i −0.528426 0.104667i
\(369\) 23.7015 + 4.71453i 1.23385 + 0.245429i
\(370\) −5.70827 + 18.8313i −0.296759 + 0.978995i
\(371\) 5.12827 3.42660i 0.266247 0.177900i
\(372\) −5.86722 1.16460i −0.304201 0.0603816i
\(373\) 18.3339 0.949292 0.474646 0.880177i \(-0.342576\pi\)
0.474646 + 0.880177i \(0.342576\pi\)
\(374\) −0.657539 0.357105i −0.0340005 0.0184655i
\(375\) 9.86708i 0.509534i
\(376\) −18.7868 + 5.71134i −0.968853 + 0.294540i
\(377\) −8.48095 12.6926i −0.436791 0.653704i
\(378\) 7.70757 25.4270i 0.396435 1.30782i
\(379\) 6.92319 34.8052i 0.355620 1.78782i −0.225750 0.974185i \(-0.572483\pi\)
0.581371 0.813639i \(-0.302517\pi\)
\(380\) −13.4215 + 5.56573i −0.688510 + 0.285516i
\(381\) −9.41222 + 1.87221i −0.482203 + 0.0959161i
\(382\) 14.4105 1.42225i 0.737307 0.0727688i
\(383\) −13.2592 5.49215i −0.677515 0.280636i 0.0172729 0.999851i \(-0.494502\pi\)
−0.694787 + 0.719215i \(0.744502\pi\)
\(384\) 4.39364 + 8.19203i 0.224212 + 0.418048i
\(385\) 0.756233 + 0.505298i 0.0385412 + 0.0257524i
\(386\) 4.72068 + 15.5507i 0.240276 + 0.791509i
\(387\) −14.0162 14.0162i −0.712485 0.712485i
\(388\) 0.00714897 + 17.6899i 0.000362934 + 0.898067i
\(389\) −12.8699 31.0706i −0.652529 1.57534i −0.809096 0.587676i \(-0.800043\pi\)
0.156567 0.987667i \(-0.449957\pi\)
\(390\) −5.54432 + 2.96494i −0.280747 + 0.150136i
\(391\) −2.00645 10.4613i −0.101471 0.529049i
\(392\) 32.2011 + 3.15182i 1.62640 + 0.159191i
\(393\) 6.02948 + 14.5565i 0.304147 + 0.734276i
\(394\) 20.8816 + 11.1560i 1.05200 + 0.562032i
\(395\) 13.6365 13.6365i 0.686129 0.686129i
\(396\) 0.422087 + 0.421746i 0.0212107 + 0.0211936i
\(397\) 14.3219 + 9.56956i 0.718794 + 0.480283i 0.860386 0.509642i \(-0.170222\pi\)
−0.141593 + 0.989925i \(0.545222\pi\)
\(398\) −6.01164 7.32219i −0.301336 0.367028i
\(399\) 5.94287 14.3474i 0.297516 0.718266i
\(400\) 9.10271 0.00735732i 0.455135 0.000367866i
\(401\) −14.9183 + 2.96743i −0.744984 + 0.148187i −0.552965 0.833205i \(-0.686504\pi\)
−0.192019 + 0.981391i \(0.561504\pi\)
\(402\) −0.423352 + 4.30729i −0.0211149 + 0.214828i
\(403\) 11.7035 + 2.32798i 0.582995 + 0.115965i
\(404\) −4.98889 25.0280i −0.248206 1.24519i
\(405\) 3.09929 + 4.63841i 0.154005 + 0.230484i
\(406\) 21.8632 + 17.9353i 1.08505 + 0.890113i
\(407\) 1.08177 0.0536213
\(408\) −6.12489 + 7.36885i −0.303227 + 0.364813i
\(409\) 18.7470 0.926980 0.463490 0.886102i \(-0.346597\pi\)
0.463490 + 0.886102i \(0.346597\pi\)
\(410\) 18.7586 + 15.3885i 0.926423 + 0.759982i
\(411\) 3.74817 + 5.60953i 0.184884 + 0.276698i
\(412\) −16.6963 + 3.32812i −0.822569 + 0.163965i
\(413\) 57.8534 + 11.5078i 2.84678 + 0.566260i
\(414\) −0.830870 + 8.45347i −0.0408350 + 0.415466i
\(415\) 8.33830 1.65859i 0.409311 0.0814171i
\(416\) −8.75823 16.3458i −0.429408 0.801417i
\(417\) 3.61066 8.71691i 0.176815 0.426869i
\(418\) 0.506861 + 0.617358i 0.0247914 + 0.0301960i
\(419\) −10.2065 6.81973i −0.498618 0.333166i 0.280699 0.959796i \(-0.409434\pi\)
−0.779317 + 0.626630i \(0.784434\pi\)
\(420\) 8.23238 8.23904i 0.401699 0.402024i
\(421\) 19.1632 19.1632i 0.933956 0.933956i −0.0639943 0.997950i \(-0.520384\pi\)
0.997950 + 0.0639943i \(0.0203840\pi\)
\(422\) −26.8500 14.3446i −1.30704 0.698285i
\(423\) 6.17653 + 14.9115i 0.300313 + 0.725020i
\(424\) 4.04323 + 0.395749i 0.196357 + 0.0192193i
\(425\) 3.53117 + 8.69303i 0.171287 + 0.421674i
\(426\) −0.935503 + 0.500280i −0.0453253 + 0.0242386i
\(427\) 6.85385 + 16.5467i 0.331681 + 0.800749i
\(428\) −5.56155 + 0.00224758i −0.268828 + 0.000108641i
\(429\) 0.244408 + 0.244408i 0.0118001 + 0.0118001i
\(430\) −5.78097 19.0435i −0.278783 0.918357i
\(431\) 18.4061 + 12.2986i 0.886591 + 0.592401i 0.913320 0.407242i \(-0.133509\pi\)
−0.0267298 + 0.999643i \(0.508509\pi\)
\(432\) 14.5435 9.73466i 0.699724 0.468359i
\(433\) −28.9741 12.0015i −1.39241 0.576754i −0.444638 0.895710i \(-0.646668\pi\)
−0.947770 + 0.318956i \(0.896668\pi\)
\(434\) −21.9983 + 2.17113i −1.05595 + 0.104218i
\(435\) 6.19384 1.23203i 0.296972 0.0590713i
\(436\) 10.8367 + 26.1323i 0.518985 + 1.25151i
\(437\) −2.21840 + 11.1527i −0.106121 + 0.533504i
\(438\) −1.09130 + 3.60017i −0.0521445 + 0.172023i
\(439\) 3.06257 + 4.58346i 0.146168 + 0.218756i 0.897328 0.441364i \(-0.145505\pi\)
−0.751160 + 0.660120i \(0.770505\pi\)
\(440\) 0.174250 + 0.573176i 0.00830707 + 0.0273251i
\(441\) 26.5949i 1.26643i
\(442\) 12.2244 14.6951i 0.581457 0.698976i
\(443\) 7.96439 0.378399 0.189200 0.981939i \(-0.439411\pi\)
0.189200 + 0.981939i \(0.439411\pi\)
\(444\) 2.69708 13.5878i 0.127998 0.644850i
\(445\) 1.71978 1.14912i 0.0815252 0.0544734i
\(446\) −4.82116 + 15.9048i −0.228289 + 0.753115i
\(447\) −18.1429 3.60884i −0.858128 0.170692i
\(448\) 24.3205 + 24.2616i 1.14903 + 1.14625i
\(449\) 1.14085 + 5.73542i 0.0538398 + 0.270671i 0.998323 0.0578886i \(-0.0184368\pi\)
−0.944483 + 0.328560i \(0.893437\pi\)
\(450\) −0.734888 7.44602i −0.0346429 0.351009i
\(451\) 0.510444 1.23232i 0.0240359 0.0580277i
\(452\) 5.91323 14.2921i 0.278135 0.672246i
\(453\) 8.24895 12.3454i 0.387569 0.580039i
\(454\) 1.14680 + 3.77776i 0.0538222 + 0.177299i
\(455\) −16.4294 + 16.4294i −0.770220 + 0.770220i
\(456\) 9.01820 4.82736i 0.422316 0.226062i
\(457\) −9.51504 + 3.94126i −0.445095 + 0.184364i −0.593962 0.804493i \(-0.702437\pi\)
0.148868 + 0.988857i \(0.452437\pi\)
\(458\) −19.8354 37.0914i −0.926848 1.73317i
\(459\) 14.9302 + 10.1247i 0.696880 + 0.472580i
\(460\) −4.73522 + 7.09296i −0.220781 + 0.330711i
\(461\) −7.51342 + 3.11216i −0.349935 + 0.144948i −0.550725 0.834686i \(-0.685649\pi\)
0.200791 + 0.979634i \(0.435649\pi\)
\(462\) −0.564751 0.301719i −0.0262746 0.0140372i
\(463\) −26.0197 26.0197i −1.20924 1.20924i −0.971274 0.237964i \(-0.923520\pi\)
−0.237964 0.971274i \(-0.576480\pi\)
\(464\) 3.64861 + 18.2656i 0.169382 + 0.847960i
\(465\) −2.74260 + 4.10459i −0.127185 + 0.190346i
\(466\) 7.08026 5.81301i 0.327987 0.269283i
\(467\) 0.560574 + 0.232198i 0.0259403 + 0.0107448i 0.395616 0.918416i \(-0.370531\pi\)
−0.369676 + 0.929161i \(0.620531\pi\)
\(468\) −12.6706 + 8.47364i −0.585699 + 0.391694i
\(469\) 3.12031 + 15.6868i 0.144082 + 0.724351i
\(470\) −1.58510 + 16.1272i −0.0731151 + 0.743891i
\(471\) 1.01195 5.08739i 0.0466280 0.234415i
\(472\) 24.6665 + 30.0191i 1.13537 + 1.38174i
\(473\) −0.909700 + 0.607842i −0.0418281 + 0.0279486i
\(474\) −8.61077 + 10.4966i −0.395506 + 0.482124i
\(475\) 10.0164i 0.459583i
\(476\) −13.7615 + 32.6265i −0.630757 + 1.49543i
\(477\) 3.33931i 0.152897i
\(478\) −13.9793 11.4678i −0.639398 0.524524i
\(479\) −26.8598 + 17.9471i −1.22725 + 0.820025i −0.988524 0.151061i \(-0.951731\pi\)
−0.238730 + 0.971086i \(0.576731\pi\)
\(480\) 7.63397 0.759669i 0.348441 0.0346740i
\(481\) −5.39134 + 27.1041i −0.245824 + 1.23584i
\(482\) −4.04110 0.397189i −0.184067 0.0180915i
\(483\) −1.77827 8.93996i −0.0809140 0.406782i
\(484\) −18.2600 + 12.2116i −0.830001 + 0.555074i
\(485\) 13.4877 + 5.58680i 0.612447 + 0.253684i
\(486\) −14.2708 17.3819i −0.647337 0.788457i
\(487\) 3.03440 4.54130i 0.137502 0.205786i −0.756328 0.654193i \(-0.773008\pi\)
0.893830 + 0.448407i \(0.148008\pi\)
\(488\) −3.41762 + 11.2910i −0.154709 + 0.511121i
\(489\) −1.30217 1.30217i −0.0588863 0.0588863i
\(490\) 12.5824 23.5514i 0.568413 1.06394i
\(491\) −11.2995 + 4.68043i −0.509941 + 0.211225i −0.622792 0.782387i \(-0.714002\pi\)
0.112851 + 0.993612i \(0.464002\pi\)
\(492\) −14.2062 9.48400i −0.640466 0.427572i
\(493\) −16.0367 + 10.5571i −0.722257 + 0.475470i
\(494\) −17.9942 + 9.62278i −0.809598 + 0.432949i
\(495\) 0.454943 0.188443i 0.0204481 0.00846990i
\(496\) −12.1129 8.07944i −0.543886 0.362777i
\(497\) −2.77215 + 2.77215i −0.124348 + 0.124348i
\(498\) −5.72708 + 1.73856i −0.256637 + 0.0779065i
\(499\) −6.26864 + 9.38168i −0.280623 + 0.419982i −0.944827 0.327569i \(-0.893770\pi\)
0.664204 + 0.747551i \(0.268770\pi\)
\(500\) 9.18223 22.1932i 0.410642 0.992512i
\(501\) −1.79301 + 4.32872i −0.0801060 + 0.193393i
\(502\) 9.67830 0.955204i 0.431963 0.0426328i
\(503\) −8.11441 40.7939i −0.361804 1.81891i −0.548095 0.836416i \(-0.684647\pi\)
0.186291 0.982495i \(-0.440353\pi\)
\(504\) 17.9002 21.8384i 0.797336 0.972759i
\(505\) −20.6566 4.10886i −0.919208 0.182842i
\(506\) 0.448683 + 0.136008i 0.0199464 + 0.00604627i
\(507\) 1.53948 1.02865i 0.0683708 0.0456839i
\(508\) −22.9124 4.54794i −1.01658 0.201782i
\(509\) −32.7742 −1.45269 −0.726345 0.687330i \(-0.758783\pi\)
−0.726345 + 0.687330i \(0.758783\pi\)
\(510\) 3.68124 + 6.99868i 0.163008 + 0.309907i
\(511\) 13.9021i 0.614994i
\(512\) 2.25882 + 22.5144i 0.0998268 + 0.995005i
\(513\) −10.6988 16.0119i −0.472364 0.706943i
\(514\) −11.3714 3.44697i −0.501571 0.152039i
\(515\) −2.74105 + 13.7802i −0.120785 + 0.607228i
\(516\) 5.36688 + 12.9420i 0.236264 + 0.569740i
\(517\) 0.873745 0.173799i 0.0384272 0.00764365i
\(518\) −5.02810 50.9456i −0.220922 2.23842i
\(519\) 0.640187 + 0.265174i 0.0281011 + 0.0116399i
\(520\) −15.2296 + 1.50930i −0.667860 + 0.0661873i
\(521\) 18.0123 + 12.0354i 0.789133 + 0.527282i 0.883598 0.468246i \(-0.155114\pi\)
−0.0944646 + 0.995528i \(0.530114\pi\)
\(522\) 14.6503 4.44736i 0.641227 0.194656i
\(523\) −7.97077 7.97077i −0.348537 0.348537i 0.511027 0.859565i \(-0.329265\pi\)
−0.859565 + 0.511027i \(0.829265\pi\)
\(524\) 0.0154990 + 38.3517i 0.000677077 + 1.67540i
\(525\) 3.07261 + 7.41793i 0.134100 + 0.323745i
\(526\) −8.50760 15.9089i −0.370949 0.693659i
\(527\) 3.02879 14.6995i 0.131936 0.640322i
\(528\) −0.161711 0.389515i −0.00703759 0.0169515i
\(529\) −6.24755 15.0829i −0.271633 0.655780i
\(530\) 1.57987 2.95716i 0.0686250 0.128451i
\(531\) 22.5825 22.5825i 0.979998 0.979998i
\(532\) 26.7184 26.7400i 1.15839 1.15933i
\(533\) 28.3322 + 18.9310i 1.22721 + 0.819992i
\(534\) −1.12541 + 0.923980i −0.0487012 + 0.0399845i
\(535\) −1.75645 + 4.24044i −0.0759378 + 0.183330i
\(536\) −4.96054 + 9.29407i −0.214263 + 0.401443i
\(537\) 4.04888 0.805372i 0.174722 0.0347544i
\(538\) −12.8516 1.26315i −0.554071 0.0544582i
\(539\) −1.43972 0.286378i −0.0620132 0.0123352i
\(540\) −2.82341 14.1643i −0.121500 0.609534i
\(541\) −1.41516 2.11794i −0.0608425 0.0910573i 0.799801 0.600265i \(-0.204938\pi\)
−0.860643 + 0.509208i \(0.829938\pi\)
\(542\) −11.2950 + 13.7687i −0.485163 + 0.591416i
\(543\) −3.70951 −0.159190
\(544\) −20.6336 + 10.8744i −0.884660 + 0.466236i
\(545\) 23.3471 1.00008
\(546\) 10.3743 12.6463i 0.443979 0.541213i
\(547\) −5.58404 8.35711i −0.238756 0.357324i 0.692670 0.721255i \(-0.256434\pi\)
−0.931426 + 0.363931i \(0.881434\pi\)
\(548\) 3.21027 + 16.1051i 0.137136 + 0.687976i
\(549\) 9.51046 + 1.89175i 0.405896 + 0.0807378i
\(550\) −0.411005 0.0403966i −0.0175253 0.00172252i
\(551\) 20.1022 3.99858i 0.856384 0.170345i
\(552\) 2.82702 5.29671i 0.120326 0.225443i
\(553\) −19.2000 + 46.3528i −0.816466 + 1.97112i
\(554\) 28.1359 23.1000i 1.19538 0.981426i
\(555\) −9.50577 6.35155i −0.403497 0.269608i
\(556\) 16.2331 16.2462i 0.688436 0.688993i
\(557\) −8.39351 + 8.39351i −0.355644 + 0.355644i −0.862205 0.506560i \(-0.830917\pi\)
0.506560 + 0.862205i \(0.330917\pi\)
\(558\) −5.63960 + 10.5561i −0.238743 + 0.446875i
\(559\) −10.6959 25.8222i −0.452389 1.09216i
\(560\) 26.1836 10.8704i 1.10646 0.459359i
\(561\) 0.309499 0.305286i 0.0130671 0.0128892i
\(562\) 21.9036 + 40.9589i 0.923948 + 1.72774i
\(563\) −3.70762 8.95099i −0.156258 0.377239i 0.826291 0.563243i \(-0.190446\pi\)
−0.982549 + 0.186003i \(0.940446\pi\)
\(564\) −0.00461038 11.4082i −0.000194132 0.480372i
\(565\) −9.02596 9.02596i −0.379725 0.379725i
\(566\) −25.5556 + 7.75784i −1.07418 + 0.326087i
\(567\) −12.0673 8.06312i −0.506780 0.338619i
\(568\) −2.56971 + 0.254667i −0.107823 + 0.0106856i
\(569\) 3.81051 + 1.57837i 0.159745 + 0.0661685i 0.461123 0.887336i \(-0.347447\pi\)
−0.301378 + 0.953505i \(0.597447\pi\)
\(570\) −0.829129 8.40088i −0.0347284 0.351874i
\(571\) −15.3808 + 3.05943i −0.643667 + 0.128033i −0.506122 0.862462i \(-0.668921\pi\)
−0.137545 + 0.990495i \(0.543921\pi\)
\(572\) 0.322283 + 0.777171i 0.0134753 + 0.0324951i
\(573\) −1.64131 + 8.25144i −0.0685668 + 0.344709i
\(574\) −60.4083 18.3113i −2.52140 0.764301i
\(575\) −3.26629 4.88834i −0.136214 0.203858i
\(576\) 18.2374 3.65063i 0.759890 0.152110i
\(577\) 14.5403i 0.605319i 0.953099 + 0.302660i \(0.0978746\pi\)
−0.953099 + 0.302660i \(0.902125\pi\)
\(578\) −18.3768 15.5014i −0.764374 0.644774i
\(579\) −9.44196 −0.392394
\(580\) 15.0778 + 2.99283i 0.626073 + 0.124271i
\(581\) −18.3904 + 12.2881i −0.762964 + 0.509796i
\(582\) −9.83573 2.98147i −0.407704 0.123586i
\(583\) −0.180774 0.0359582i −0.00748690 0.00148924i
\(584\) −5.80487 + 7.08201i −0.240207 + 0.293056i
\(585\) 2.45416 + 12.3379i 0.101467 + 0.510110i
\(586\) −5.85161 + 0.577527i −0.241728 + 0.0238574i
\(587\) −9.18052 + 22.1637i −0.378921 + 0.914795i 0.613248 + 0.789890i \(0.289863\pi\)
−0.992169 + 0.124905i \(0.960137\pi\)
\(588\) −7.18666 + 17.3700i −0.296373 + 0.716326i
\(589\) −8.90117 + 13.3215i −0.366766 + 0.548904i
\(590\) 30.6822 9.31412i 1.26317 0.383456i
\(591\) −9.72618 + 9.72618i −0.400082 + 0.400082i
\(592\) 18.7111 28.0522i 0.769020 1.15294i
\(593\) 12.4965 5.17620i 0.513168 0.212561i −0.111045 0.993815i \(-0.535420\pi\)
0.624213 + 0.781254i \(0.285420\pi\)
\(594\) −0.700170 + 0.374431i −0.0287283 + 0.0153631i
\(595\) 20.5217 + 20.8049i 0.841307 + 0.852918i
\(596\) −37.4490 25.0007i −1.53397 1.02407i
\(597\) 5.08527 2.10639i 0.208126 0.0862087i
\(598\) −5.64387 + 10.5641i −0.230795 + 0.431997i
\(599\) 7.44471 + 7.44471i 0.304183 + 0.304183i 0.842648 0.538465i \(-0.180996\pi\)
−0.538465 + 0.842648i \(0.680996\pi\)
\(600\) −1.53213 + 5.06181i −0.0625491 + 0.206648i
\(601\) 1.02713 1.53720i 0.0418974 0.0627039i −0.809930 0.586527i \(-0.800495\pi\)
0.851827 + 0.523823i \(0.175495\pi\)
\(602\) 32.8545 + 40.0168i 1.33905 + 1.63096i
\(603\) 8.00035 + 3.31386i 0.325800 + 0.134951i
\(604\) 30.0423 20.0912i 1.22240 0.817498i
\(605\) 3.53677 + 17.7806i 0.143790 + 0.722882i
\(606\) 14.7560 + 1.45033i 0.599423 + 0.0589157i
\(607\) −7.66107 + 38.5148i −0.310953 + 1.56327i 0.436966 + 0.899478i \(0.356053\pi\)
−0.747919 + 0.663790i \(0.768947\pi\)
\(608\) 24.7762 2.46552i 1.00481 0.0999901i
\(609\) −13.6607 + 9.12781i −0.553561 + 0.369877i
\(610\) 7.52707 + 6.17476i 0.304762 + 0.250009i
\(611\) 22.7581i 0.920696i
\(612\) 10.5481 + 16.0089i 0.426383 + 0.647123i
\(613\) 8.51336i 0.343852i 0.985110 + 0.171926i \(0.0549989\pi\)
−0.985110 + 0.171926i \(0.945001\pi\)
\(614\) 15.7703 19.2241i 0.636437 0.775820i
\(615\) −11.7209 + 7.83165i −0.472632 + 0.315803i
\(616\) −0.989473 1.20419i −0.0398670 0.0485181i
\(617\) −3.79851 + 19.0964i −0.152922 + 0.768791i 0.825858 + 0.563878i \(0.190691\pi\)
−0.978780 + 0.204913i \(0.934309\pi\)
\(618\) 0.967527 9.84386i 0.0389196 0.395978i
\(619\) −3.33048 16.7435i −0.133863 0.672977i −0.988189 0.153239i \(-0.951030\pi\)
0.854326 0.519738i \(-0.173970\pi\)
\(620\) −9.98841 + 6.67988i −0.401144 + 0.268271i
\(621\) −10.4428 4.32555i −0.419055 0.173578i
\(622\) 14.4564 11.8689i 0.579648 0.475901i
\(623\) −2.98955 + 4.47418i −0.119774 + 0.179254i
\(624\) 10.5654 2.11046i 0.422953 0.0844861i
\(625\) −5.97004 5.97004i −0.238801 0.238801i
\(626\) 39.6151 + 21.1644i 1.58334 + 0.845901i
\(627\) −0.428756 + 0.177596i −0.0171228 + 0.00709252i
\(628\) 7.01038 10.5010i 0.279745 0.419034i
\(629\) 34.0425 + 7.01433i 1.35736 + 0.279680i
\(630\) −10.9893 20.5495i −0.437823 0.818712i
\(631\) −6.51453 + 2.69841i −0.259339 + 0.107422i −0.508565 0.861024i \(-0.669824\pi\)
0.249226 + 0.968445i \(0.419824\pi\)
\(632\) −29.1356 + 15.5960i −1.15895 + 0.620376i
\(633\) 12.5061 12.5061i 0.497074 0.497074i
\(634\) 7.65908 + 25.2302i 0.304181 + 1.00202i
\(635\) −10.7103 + 16.0291i −0.425024 + 0.636094i
\(636\) −0.902371 + 2.18101i −0.0357814 + 0.0864827i
\(637\) 14.3506 34.6454i 0.568592 1.37270i
\(638\) −0.0830016 0.840987i −0.00328606 0.0332950i
\(639\) 0.414095 + 2.08180i 0.0163814 + 0.0823547i
\(640\) 17.8774 + 5.39546i 0.706667 + 0.213274i
\(641\) 19.0576 + 3.79080i 0.752730 + 0.149727i 0.556520 0.830834i \(-0.312136\pi\)
0.196211 + 0.980562i \(0.437136\pi\)
\(642\) 0.937350 3.09228i 0.0369942 0.122042i
\(643\) 39.0244 26.0753i 1.53897 1.02831i 0.559000 0.829168i \(-0.311185\pi\)
0.979971 0.199140i \(-0.0638149\pi\)
\(644\) 4.31974 21.7628i 0.170222 0.857574i
\(645\) 11.5627 0.455280
\(646\) 11.9475 + 22.7144i 0.470070 + 0.893685i
\(647\) 6.68386i 0.262770i −0.991331 0.131385i \(-0.958058\pi\)
0.991331 0.131385i \(-0.0419424\pi\)
\(648\) −2.78054 9.14625i −0.109230 0.359299i
\(649\) −0.979336 1.46568i −0.0384423 0.0575330i
\(650\) 3.06052 10.0965i 0.120044 0.396019i
\(651\) 2.50554 12.5962i 0.0981997 0.493683i
\(652\) −1.71708 4.14067i −0.0672461 0.162161i
\(653\) −35.9272 + 7.14636i −1.40594 + 0.279659i −0.839014 0.544110i \(-0.816867\pi\)
−0.566926 + 0.823769i \(0.691867\pi\)
\(654\) −16.3569 + 1.61435i −0.639605 + 0.0631261i
\(655\) 29.2415 + 12.1122i 1.14256 + 0.473263i
\(656\) −23.1272 34.5518i −0.902966 1.34902i
\(657\) 6.25835 + 4.18169i 0.244161 + 0.163143i
\(658\) −12.2462 40.3409i −0.477406 1.57265i
\(659\) 7.78629 + 7.78629i 0.303311 + 0.303311i 0.842308 0.538997i \(-0.181197\pi\)
−0.538997 + 0.842308i \(0.681197\pi\)
\(660\) −0.348060 0.000140661i −0.0135482 5.47521e-6i
\(661\) −13.9674 33.7202i −0.543267 1.31156i −0.922405 0.386223i \(-0.873780\pi\)
0.379138 0.925340i \(-0.376220\pi\)
\(662\) 38.8813 20.7926i 1.51117 0.808128i
\(663\) 6.10656 + 9.27611i 0.237159 + 0.360254i
\(664\) −14.4994 1.41919i −0.562685 0.0550752i
\(665\) −11.9382 28.8214i −0.462945 1.11765i
\(666\) −24.4467 13.0607i −0.947291 0.506092i
\(667\) 8.50668 8.50668i 0.329380 0.329380i
\(668\) −8.06117 + 8.06768i −0.311896 + 0.312148i
\(669\) −8.02850 5.36447i −0.310400 0.207402i
\(670\) 5.51697 + 6.71967i 0.213139 + 0.259604i
\(671\) 0.204820 0.494479i 0.00790699 0.0190892i
\(672\) −17.5925 + 9.42624i −0.678644 + 0.363625i
\(673\) 18.9914 3.77763i 0.732066 0.145617i 0.185038 0.982731i \(-0.440759\pi\)
0.547028 + 0.837114i \(0.315759\pi\)
\(674\) −1.97536 + 20.0978i −0.0760882 + 0.774140i
\(675\) 9.76521 + 1.94242i 0.375863 + 0.0747638i
\(676\) 4.41989 0.881028i 0.169996 0.0338857i
\(677\) −8.13684 12.1776i −0.312724 0.468025i 0.641497 0.767125i \(-0.278313\pi\)
−0.954222 + 0.299100i \(0.903313\pi\)
\(678\) 6.94764 + 5.69943i 0.266823 + 0.218885i
\(679\) −37.9809 −1.45757
\(680\) 1.76699 + 19.1673i 0.0677611 + 0.735033i
\(681\) −2.29375 −0.0878968
\(682\) 0.510727 + 0.418970i 0.0195568 + 0.0160432i
\(683\) 8.74789 + 13.0921i 0.334729 + 0.500957i 0.960209 0.279283i \(-0.0900968\pi\)
−0.625480 + 0.780240i \(0.715097\pi\)
\(684\) −4.00083 20.0711i −0.152976 0.767439i
\(685\) 13.2922 + 2.64399i 0.507870 + 0.101022i
\(686\) −2.63694 + 26.8289i −0.100679 + 1.02433i
\(687\) 23.9682 4.76757i 0.914443 0.181894i
\(688\) 0.0275646 + 34.1038i 0.00105089 + 1.30020i
\(689\) 1.80189 4.35015i 0.0686466 0.165728i
\(690\) −3.14413 3.82955i −0.119695 0.145789i
\(691\) 5.11972 + 3.42089i 0.194763 + 0.130137i 0.649128 0.760679i \(-0.275134\pi\)
−0.454365 + 0.890816i \(0.650134\pi\)
\(692\) 1.19315 + 1.19219i 0.0453569 + 0.0453202i
\(693\) −0.905874 + 0.905874i −0.0344113 + 0.0344113i
\(694\) −22.7851 12.1730i −0.864912 0.462080i
\(695\) −7.25321 17.5108i −0.275130 0.664223i
\(696\) −10.7704 1.05420i −0.408250 0.0399593i
\(697\) 24.0538 35.4705i 0.911104 1.34354i
\(698\) 25.0167 13.3782i 0.946894 0.506372i
\(699\) 2.03679 + 4.91725i 0.0770385 + 0.185987i
\(700\) 0.00789825 + 19.5439i 0.000298526 + 0.738691i
\(701\) 3.72512 + 3.72512i 0.140696 + 0.140696i 0.773947 0.633251i \(-0.218280\pi\)
−0.633251 + 0.773947i \(0.718280\pi\)
\(702\) −5.89197 19.4091i −0.222378 0.732549i
\(703\) −30.8512 20.6141i −1.16357 0.777476i
\(704\) −0.00124463 1.02659i −4.69086e−5 0.0386912i
\(705\) −8.69826 3.60294i −0.327595 0.135694i
\(706\) −9.25868 + 0.913789i −0.348455 + 0.0343909i
\(707\) 53.7405 10.6896i 2.02112 0.402025i
\(708\) −20.8518 + 8.64695i −0.783657 + 0.324972i
\(709\) 2.64917 13.3183i 0.0994916 0.500178i −0.898619 0.438731i \(-0.855428\pi\)
0.998110 0.0614477i \(-0.0195717\pi\)
\(710\) −0.618216 + 2.03947i −0.0232012 + 0.0765399i
\(711\) 15.0915 + 22.5860i 0.565975 + 0.847041i
\(712\) −3.39114 + 1.03094i −0.127089 + 0.0386360i
\(713\) 9.40400i 0.352183i
\(714\) −15.8159 13.1568i −0.591897 0.492381i
\(715\) 0.694341 0.0259669
\(716\) 9.85629 + 1.95640i 0.368347 + 0.0731140i
\(717\) 8.73464 5.83630i 0.326201 0.217961i
\(718\) −7.94899 + 26.2234i −0.296654 + 0.978648i
\(719\) 1.34159 + 0.266860i 0.0500330 + 0.00995218i 0.220043 0.975490i \(-0.429380\pi\)
−0.170010 + 0.985442i \(0.554380\pi\)
\(720\) 2.98236 15.0569i 0.111146 0.561138i
\(721\) −7.13114 35.8507i −0.265578 1.33515i
\(722\) −0.0518280 0.525131i −0.00192884 0.0195433i
\(723\) 0.902813 2.17958i 0.0335760 0.0810596i
\(724\) −8.34351 3.45205i −0.310084 0.128294i
\(725\) −5.88736 + 8.81105i −0.218651 + 0.327234i
\(726\) −3.70729 12.2124i −0.137590 0.453245i
\(727\) −24.5142 + 24.5142i −0.909180 + 0.909180i −0.996206 0.0870256i \(-0.972264\pi\)
0.0870256 + 0.996206i \(0.472264\pi\)
\(728\) 35.1027 18.7901i 1.30099 0.696409i
\(729\) 2.70408 1.12007i 0.100151 0.0414840i
\(730\) 3.56373 + 6.66404i 0.131900 + 0.246647i
\(731\) −32.5690 + 13.2298i −1.20461 + 0.489320i
\(732\) −5.70038 3.80554i −0.210692 0.140657i
\(733\) −11.7341 + 4.86043i −0.433409 + 0.179524i −0.588712 0.808343i \(-0.700365\pi\)
0.155303 + 0.987867i \(0.450365\pi\)
\(734\) 3.56983 + 1.90719i 0.131765 + 0.0703956i
\(735\) 10.9697 + 10.9697i 0.404624 + 0.404624i
\(736\) 11.2877 9.28266i 0.416069 0.342163i
\(737\) 0.265545 0.397416i 0.00978148 0.0146390i
\(738\) −26.4138 + 21.6862i −0.972306 + 0.798279i
\(739\) −17.2497 7.14505i −0.634540 0.262835i 0.0421407 0.999112i \(-0.486582\pi\)
−0.676681 + 0.736277i \(0.736582\pi\)
\(740\) −15.4699 23.1320i −0.568683 0.850351i
\(741\) −2.31290 11.6277i −0.0849664 0.427155i
\(742\) −0.853198 + 8.68065i −0.0313219 + 0.318677i
\(743\) −1.83763 + 9.23837i −0.0674159 + 0.338923i −0.999742 0.0226948i \(-0.992775\pi\)
0.932326 + 0.361618i \(0.117775\pi\)
\(744\) 6.53594 5.37054i 0.239619 0.196894i
\(745\) −30.8974 + 20.6450i −1.13199 + 0.756373i
\(746\) −16.4445 + 20.0460i −0.602076 + 0.733934i
\(747\) 11.9751i 0.438145i
\(748\) 0.980230 0.398638i 0.0358408 0.0145757i
\(749\) 11.9409i 0.436311i
\(750\) 10.7885 + 8.85024i 0.393940 + 0.323165i
\(751\) 39.0008 26.0595i 1.42316 0.950925i 0.424189 0.905574i \(-0.360559\pi\)
0.998971 0.0453512i \(-0.0144407\pi\)
\(752\) 10.6060 25.6639i 0.386762 0.935866i
\(753\) −1.10233 + 5.54177i −0.0401710 + 0.201953i
\(754\) 21.4849 + 2.11169i 0.782433 + 0.0769033i
\(755\) −5.81887 29.2534i −0.211770 1.06464i
\(756\) 20.8881 + 31.2339i 0.759694 + 1.13597i
\(757\) −7.19106 2.97863i −0.261363 0.108260i 0.248154 0.968721i \(-0.420176\pi\)
−0.509517 + 0.860460i \(0.670176\pi\)
\(758\) 31.8457 + 38.7881i 1.15669 + 1.40885i
\(759\) −0.151335 + 0.226488i −0.00549310 + 0.00822100i
\(760\) 5.95291 19.6670i 0.215935 0.713398i
\(761\) −6.55025 6.55025i −0.237446 0.237446i 0.578346 0.815792i \(-0.303699\pi\)
−0.815792 + 0.578346i \(0.803699\pi\)
\(762\) 6.39522 11.9704i 0.231674 0.433643i
\(763\) −56.1165 + 23.2442i −2.03156 + 0.841498i
\(764\) −11.3704 + 17.0319i −0.411367 + 0.616193i
\(765\) 15.5386 2.98027i 0.561800 0.107752i
\(766\) 17.8978 9.57124i 0.646675 0.345823i
\(767\) 41.6040 17.2329i 1.50223 0.622245i
\(768\) −12.8979 2.54388i −0.465413 0.0917945i
\(769\) −16.3062 + 16.3062i −0.588016 + 0.588016i −0.937094 0.349078i \(-0.886495\pi\)
0.349078 + 0.937094i \(0.386495\pi\)
\(770\) −1.23079 + 0.373626i −0.0443544 + 0.0134646i
\(771\) 3.83541 5.74010i 0.138129 0.206725i
\(772\) −21.2371 8.78662i −0.764338 0.316237i
\(773\) −5.81873 + 14.0477i −0.209285 + 0.505259i −0.993311 0.115469i \(-0.963163\pi\)
0.784026 + 0.620728i \(0.213163\pi\)
\(774\) 27.8969 2.75330i 1.00273 0.0989653i
\(775\) −1.61605 8.12442i −0.0580502 0.291838i
\(776\) −19.3482 15.8590i −0.694560 0.569307i
\(777\) 29.1713 + 5.80254i 1.04652 + 0.208165i
\(778\) 45.5157 + 13.7970i 1.63182 + 0.494646i
\(779\) −38.0404 + 25.4178i −1.36294 + 0.910688i
\(780\) 1.73114 8.72146i 0.0619848 0.312278i
\(781\) 0.117158 0.00419223
\(782\) 13.2379 + 7.18938i 0.473385 + 0.257092i
\(783\) 20.3736i 0.728093i
\(784\) −32.3288 + 32.3811i −1.15460 + 1.15647i
\(785\) −5.78900 8.66386i −0.206618 0.309226i
\(786\) −21.3239 6.46383i −0.760599 0.230557i
\(787\) 1.24633 6.26575i 0.0444270 0.223350i −0.952193 0.305496i \(-0.901178\pi\)
0.996620 + 0.0821467i \(0.0261776\pi\)
\(788\) −30.9274 + 12.8252i −1.10174 + 0.456879i
\(789\) 10.2802 2.04486i 0.365984 0.0727988i
\(790\) 2.67871 + 27.1412i 0.0953043 + 0.965641i
\(791\) 30.6807 + 12.7084i 1.09088 + 0.451858i
\(792\) −0.839720 + 0.0832192i −0.0298382 + 0.00295707i
\(793\) 11.3686 + 7.59623i 0.403710 + 0.269750i
\(794\) −23.3092 + 7.07590i −0.827211 + 0.251114i
\(795\) 1.37738 + 1.37738i 0.0488506 + 0.0488506i
\(796\) 13.3981 0.00541454i 0.474882 0.000191913i
\(797\) 0.792947 + 1.91434i 0.0280876 + 0.0678095i 0.937301 0.348521i \(-0.113316\pi\)
−0.909213 + 0.416330i \(0.863316\pi\)
\(798\) 10.3567 + 19.3667i 0.366624 + 0.685572i
\(799\) 28.6231 + 0.196155i 1.01261 + 0.00693946i
\(800\) −8.15660 + 9.95934i −0.288379 + 0.352116i
\(801\) 1.11491 + 2.69163i 0.0393934 + 0.0951040i
\(802\) 10.1364 18.9730i 0.357928 0.669961i
\(803\) 0.293768 0.293768i 0.0103668 0.0103668i
\(804\) −4.32979 4.32629i −0.152700 0.152577i
\(805\) −15.2248 10.1729i −0.536603 0.358547i
\(806\) −13.0428 + 10.7084i −0.459414 + 0.377186i
\(807\) 2.87114 6.93156i 0.101069 0.244002i
\(808\) 31.8399 + 16.9940i 1.12012 + 0.597846i
\(809\) −2.74562 + 0.546138i −0.0965310 + 0.0192012i −0.243119 0.969996i \(-0.578171\pi\)
0.146588 + 0.989198i \(0.453171\pi\)
\(810\) −7.85145 0.771699i −0.275872 0.0271147i
\(811\) −29.0513 5.77867i −1.02013 0.202917i −0.343433 0.939177i \(-0.611590\pi\)
−0.676698 + 0.736261i \(0.736590\pi\)
\(812\) −39.2203 + 7.81788i −1.37636 + 0.274354i
\(813\) −5.74838 8.60306i −0.201604 0.301722i
\(814\) −0.970289 + 1.18279i −0.0340086 + 0.0414567i
\(815\) −3.69936 −0.129583
\(816\) −2.56328 13.3063i −0.0897327 0.465815i
\(817\) 37.5269 1.31290
\(818\) −16.8151 + 20.4977i −0.587925 + 0.716684i
\(819\) −18.1823 27.2117i −0.635340 0.950854i
\(820\) −33.6510 + 6.70773i −1.17514 + 0.234244i
\(821\) −14.8916 2.96213i −0.519722 0.103379i −0.0717428 0.997423i \(-0.522856\pi\)
−0.447979 + 0.894044i \(0.647856\pi\)
\(822\) −9.49528 0.933266i −0.331186 0.0325514i
\(823\) 48.5611 9.65941i 1.69274 0.336706i 0.747790 0.663935i \(-0.231115\pi\)
0.944945 + 0.327229i \(0.106115\pi\)
\(824\) 11.3368 21.2406i 0.394937 0.739953i
\(825\) 0.0918216 0.221677i 0.00319682 0.00771780i
\(826\) −64.4738 + 52.9341i −2.24333 + 1.84181i
\(827\) −22.3231 14.9158i −0.776252 0.518675i 0.103201 0.994660i \(-0.467091\pi\)
−0.879453 + 0.475986i \(0.842091\pi\)
\(828\) −8.49764 8.49077i −0.295313 0.295075i
\(829\) 5.46751 5.46751i 0.189894 0.189894i −0.605756 0.795650i \(-0.707129\pi\)
0.795650 + 0.605756i \(0.207129\pi\)
\(830\) −5.66554 + 10.6046i −0.196654 + 0.368092i
\(831\) 8.09389 + 19.5404i 0.280774 + 0.677849i
\(832\) 25.7278 + 5.08517i 0.891953 + 0.176296i
\(833\) −43.4501 18.3475i −1.50546 0.635702i
\(834\) 6.29235 + 11.7664i 0.217886 + 0.407439i
\(835\) 3.60186 + 8.69567i 0.124648 + 0.300926i
\(836\) −1.12964 0.000456518i −0.0390693 1.57890e-5i
\(837\) −11.2613 11.2613i −0.389249 0.389249i
\(838\) 16.6112 5.04263i 0.573825 0.174195i
\(839\) 21.4706 + 14.3462i 0.741247 + 0.495285i 0.867948 0.496656i \(-0.165439\pi\)
−0.126701 + 0.991941i \(0.540439\pi\)
\(840\) 1.62442 + 16.3911i 0.0560478 + 0.565548i
\(841\) 6.75902 + 2.79968i 0.233070 + 0.0965406i
\(842\) 3.76435 + 38.1410i 0.129728 + 1.31443i
\(843\) −26.4673 + 5.26467i −0.911582 + 0.181325i
\(844\) 39.7671 16.4909i 1.36884 0.567641i
\(845\) 0.725617 3.64792i 0.0249620 0.125492i
\(846\) −21.8440 6.62148i −0.751011 0.227651i
\(847\) −26.2031 39.2157i −0.900348 1.34747i
\(848\) −4.05927 + 4.06583i −0.139396 + 0.139621i
\(849\) 15.5167i 0.532531i
\(850\) −12.6721 3.93626i −0.434649 0.135013i
\(851\) −21.7786 −0.746561
\(852\) 0.292099 1.47159i 0.0100071 0.0504158i
\(853\) 8.10721 5.41706i 0.277585 0.185477i −0.408983 0.912542i \(-0.634116\pi\)
0.686568 + 0.727065i \(0.259116\pi\)
\(854\) −24.2394 7.34759i −0.829455 0.251429i
\(855\) −16.5656 3.29510i −0.566530 0.112690i
\(856\) 4.98596 6.08292i 0.170417 0.207910i
\(857\) 2.51232 + 12.6303i 0.0858192 + 0.431442i 0.999677 + 0.0254083i \(0.00808857\pi\)
−0.913858 + 0.406034i \(0.866911\pi\)
\(858\) −0.486452 + 0.0480106i −0.0166072 + 0.00163905i
\(859\) 8.15299 19.6831i 0.278177 0.671578i −0.721609 0.692301i \(-0.756597\pi\)
0.999785 + 0.0207235i \(0.00659697\pi\)
\(860\) 26.0070 + 10.7601i 0.886832 + 0.366918i
\(861\) 20.3749 30.4932i 0.694374 1.03920i
\(862\) −29.9563 + 9.09376i −1.02032 + 0.309735i
\(863\) 22.6525 22.6525i 0.771101 0.771101i −0.207198 0.978299i \(-0.566434\pi\)
0.978299 + 0.207198i \(0.0664344\pi\)
\(864\) −2.40102 + 24.6331i −0.0816843 + 0.838034i
\(865\) 1.28603 0.532690i 0.0437263 0.0181120i
\(866\) 39.1105 20.9151i 1.32903 0.710725i
\(867\) 11.7192 7.60031i 0.398007 0.258120i
\(868\) 17.3574 26.0000i 0.589149 0.882496i
\(869\) 1.38520 0.573770i 0.0469898 0.0194638i
\(870\) −4.20846 + 7.87730i −0.142680 + 0.267066i
\(871\) 8.63397 + 8.63397i 0.292551 + 0.292551i
\(872\) −38.2925 11.5906i −1.29675 0.392506i
\(873\) −11.4245 + 17.0980i −0.386660 + 0.578678i
\(874\) −10.2043 12.4289i −0.345167 0.420414i
\(875\) 47.6419 + 19.7339i 1.61059 + 0.667128i
\(876\) −2.95752 4.42237i −0.0999253 0.149418i
\(877\) 4.17129 + 20.9705i 0.140855 + 0.708124i 0.985075 + 0.172127i \(0.0550640\pi\)
−0.844220 + 0.535996i \(0.819936\pi\)
\(878\) −7.75843 0.762556i −0.261834 0.0257350i
\(879\) 0.666479 3.35062i 0.0224798 0.113014i
\(880\) −0.782994 0.323586i −0.0263947 0.0109081i
\(881\) 18.4972 12.3594i 0.623187 0.416400i −0.203490 0.979077i \(-0.565228\pi\)
0.826677 + 0.562677i \(0.190228\pi\)
\(882\) 29.0784 + 23.8542i 0.979122 + 0.803214i
\(883\) 13.4575i 0.452881i 0.974025 + 0.226440i \(0.0727088\pi\)
−0.974025 + 0.226440i \(0.927291\pi\)
\(884\) 5.10273 + 26.5467i 0.171623 + 0.892864i
\(885\) 18.6294i 0.626221i
\(886\) −7.14363 + 8.70812i −0.239995 + 0.292555i
\(887\) 9.75945 6.52106i 0.327690 0.218956i −0.380832 0.924644i \(-0.624362\pi\)
0.708522 + 0.705689i \(0.249362\pi\)
\(888\) 12.4376 + 15.1365i 0.417378 + 0.507948i
\(889\) 9.78451 49.1901i 0.328162 1.64978i
\(890\) −0.286122 + 2.91107i −0.00959082 + 0.0975794i
\(891\) 0.0846131 + 0.425379i 0.00283465 + 0.0142507i
\(892\) −13.0657 19.5371i −0.437473 0.654152i
\(893\) −28.2304 11.6934i −0.944694 0.391305i
\(894\) 20.2190 16.6002i 0.676225 0.555193i
\(895\) 4.60726 6.89526i 0.154004 0.230483i
\(896\) −48.3413 + 4.83026i −1.61497 + 0.161368i
\(897\) −4.92051 4.92051i −0.164291 0.164291i
\(898\) −7.29429 3.89698i −0.243413 0.130044i
\(899\) 15.6601 6.48662i 0.522293 0.216341i
\(900\) 8.80050 + 5.87517i 0.293350 + 0.195839i
\(901\) −5.45568 2.30374i −0.181755 0.0767488i
\(902\) 0.889557 + 1.66344i 0.0296190 + 0.0553863i
\(903\) −27.7917 + 11.5117i −0.924850 + 0.383086i
\(904\) 10.3229 + 19.2847i 0.343335 + 0.641400i
\(905\) −5.26920 + 5.26920i −0.175154 + 0.175154i
\(906\) 6.09941 + 20.0924i 0.202639 + 0.667527i
\(907\) 0.826092 1.23633i 0.0274299 0.0410518i −0.817501 0.575927i \(-0.804641\pi\)
0.844931 + 0.534875i \(0.179641\pi\)
\(908\) −5.15916 2.13455i −0.171213 0.0708376i
\(909\) 11.3527 27.4079i 0.376545 0.909061i
\(910\) −3.22732 32.6998i −0.106985 1.08399i
\(911\) 7.64631 + 38.4406i 0.253334 + 1.27359i 0.872609 + 0.488420i \(0.162427\pi\)
−0.619275 + 0.785174i \(0.712573\pi\)
\(912\) −2.81069 + 14.1902i −0.0930713 + 0.469885i
\(913\) 0.648272 + 0.128949i 0.0214547 + 0.00426760i
\(914\) 4.22518 13.9387i 0.139756 0.461051i
\(915\) −4.70311 + 3.14252i −0.155480 + 0.103889i
\(916\) 58.3464 + 11.5813i 1.92782 + 0.382657i
\(917\) −82.3428 −2.71920
\(918\) −24.4617 + 7.24307i −0.807357 + 0.239057i
\(919\) 34.1022i 1.12493i 0.826821 + 0.562465i \(0.190147\pi\)
−0.826821 + 0.562465i \(0.809853\pi\)
\(920\) −3.50808 11.5394i −0.115658 0.380443i
\(921\) 8.02597 + 12.0117i 0.264465 + 0.395800i
\(922\) 3.33635 11.0065i 0.109877 0.362479i
\(923\) −0.583892 + 2.93542i −0.0192190 + 0.0966206i
\(924\) 0.836446 0.346864i 0.0275171 0.0114110i
\(925\) 18.8153 3.74259i 0.618642 0.123056i
\(926\) 51.7878 5.11122i 1.70185 0.167965i
\(927\) −18.2840 7.57347i −0.600525 0.248746i
\(928\) −23.2439 12.3940i −0.763020 0.406852i
\(929\) −39.0848 26.1156i −1.28233 0.856826i −0.287441 0.957798i \(-0.592805\pi\)
−0.994889 + 0.100972i \(0.967805\pi\)
\(930\) −2.02792 6.68031i −0.0664982 0.219056i
\(931\) 35.6025 + 35.6025i 1.16682 + 1.16682i
\(932\) 0.00523564 + 12.9554i 0.000171499 + 0.424368i
\(933\) 4.15869 + 10.0400i 0.136149 + 0.328694i
\(934\) −0.756686 + 0.404654i −0.0247595 + 0.0132407i
\(935\) 0.00598460 0.873277i 0.000195717 0.0285592i
\(936\) 2.09993 21.4542i 0.0686382 0.701253i
\(937\) −5.85996 14.1472i −0.191437 0.462169i 0.798795 0.601604i \(-0.205471\pi\)
−0.990231 + 0.139435i \(0.955471\pi\)
\(938\) −19.9505 10.6586i −0.651406 0.348015i
\(939\) −18.4519 + 18.4519i −0.602154 + 0.602154i
\(940\) −16.2114 16.1983i −0.528759 0.528332i
\(941\) −4.36730 2.91814i −0.142370 0.0951286i 0.482345 0.875981i \(-0.339785\pi\)
−0.624715 + 0.780852i \(0.714785\pi\)
\(942\) 4.65481 + 5.66957i 0.151662 + 0.184724i
\(943\) −10.2765 + 24.8096i −0.334648 + 0.807911i
\(944\) −54.9470 + 0.0444113i −1.78837 + 0.00144546i
\(945\) 30.4138 6.04969i 0.989362 0.196796i
\(946\) 0.151348 1.53985i 0.00492075 0.0500649i
\(947\) 40.3489 + 8.02589i 1.31116 + 0.260806i 0.800685 0.599085i \(-0.204469\pi\)
0.510477 + 0.859892i \(0.329469\pi\)
\(948\) −3.75338 18.8298i −0.121904 0.611562i
\(949\) 5.89636 + 8.82453i 0.191404 + 0.286456i
\(950\) 10.9517 + 8.98415i 0.355321 + 0.291484i
\(951\) −15.3191 −0.496757
\(952\) −23.3299 44.3108i −0.756127 1.43612i
\(953\) −39.1075 −1.26682 −0.633408 0.773818i \(-0.718345\pi\)
−0.633408 + 0.773818i \(0.718345\pi\)
\(954\) 3.65115 + 2.99518i 0.118210 + 0.0969727i
\(955\) 9.38941 + 14.0522i 0.303834 + 0.454720i
\(956\) 25.0774 4.99873i 0.811060 0.161671i
\(957\) 0.481547 + 0.0957857i 0.0155662 + 0.00309631i
\(958\) 4.46870 45.4656i 0.144377 1.46893i
\(959\) −34.5812 + 6.87862i −1.11668 + 0.222122i
\(960\) −6.01665 + 9.02823i −0.194187 + 0.291385i
\(961\) 6.79263 16.3989i 0.219117 0.528995i
\(962\) −24.7994 30.2057i −0.799565 0.973871i
\(963\) −5.37546 3.59177i −0.173222 0.115743i
\(964\) 4.05893 4.06221i 0.130729 0.130835i
\(965\) −13.4119 + 13.4119i −0.431745 + 0.431745i
\(966\) 11.3698 + 6.07434i 0.365818 + 0.195439i
\(967\) −3.78282 9.13255i −0.121647 0.293683i 0.851312 0.524660i \(-0.175808\pi\)
−0.972959 + 0.230977i \(0.925808\pi\)
\(968\) 3.02627 30.9184i 0.0972680 0.993754i
\(969\) −14.6442 + 2.80873i −0.470439 + 0.0902293i
\(970\) −18.2063 + 9.73620i −0.584569 + 0.312611i
\(971\) 12.6614 + 30.5674i 0.406324 + 0.980954i 0.986096 + 0.166175i \(0.0531416\pi\)
−0.579772 + 0.814779i \(0.696858\pi\)
\(972\) 31.8052 0.0128534i 1.02015 0.000412272i
\(973\) 34.8672 + 34.8672i 1.11779 + 1.11779i
\(974\) 2.24369 + 7.39107i 0.0718924 + 0.236825i
\(975\) 5.09657 + 3.40542i 0.163221 + 0.109061i
\(976\) −9.28000 13.8642i −0.297046 0.443783i
\(977\) 0.554837 + 0.229821i 0.0177508 + 0.00735263i 0.391541 0.920161i \(-0.371942\pi\)
−0.373790 + 0.927513i \(0.621942\pi\)
\(978\) 2.59175 0.255794i 0.0828751 0.00817940i
\(979\) 0.157717 0.0313719i 0.00504066 0.00100265i
\(980\) 14.4650 + 34.8817i 0.462067 + 1.11425i
\(981\) −6.41569 + 32.2539i −0.204837 + 1.02979i
\(982\) 5.01759 16.5528i 0.160118 0.528222i
\(983\) −16.9723 25.4009i −0.541333 0.810162i 0.455454 0.890259i \(-0.349477\pi\)
−0.996787 + 0.0800974i \(0.974477\pi\)
\(984\) 23.1119 7.02621i 0.736780 0.223987i
\(985\) 27.6313i 0.880405i
\(986\) 2.84107 27.0035i 0.0904781 0.859966i
\(987\) 24.4939 0.779651
\(988\) 5.61846 28.3057i 0.178747 0.900524i
\(989\) 18.3145 12.2373i 0.582366 0.389125i
\(990\) −0.202018 + 0.666450i −0.00642057 + 0.0211812i
\(991\) 19.2840 + 3.83582i 0.612576 + 0.121849i 0.491621 0.870809i \(-0.336404\pi\)
0.120955 + 0.992658i \(0.461404\pi\)
\(992\) 19.6986 5.99723i 0.625430 0.190412i
\(993\) 4.99764 + 25.1248i 0.158595 + 0.797312i
\(994\) −0.544552 5.51750i −0.0172721 0.175005i
\(995\) 4.23137 10.2154i 0.134144 0.323851i
\(996\) 3.23598 7.82129i 0.102536 0.247827i
\(997\) 12.9291 19.3497i 0.409468 0.612813i −0.568219 0.822877i \(-0.692367\pi\)
0.977688 + 0.210065i \(0.0673674\pi\)
\(998\) −4.63513 15.2689i −0.146723 0.483328i
\(999\) 26.0800 26.0800i 0.825134 0.825134i
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 136.2.s.c.107.5 yes 112
4.3 odd 2 544.2.cc.c.175.7 112
8.3 odd 2 inner 136.2.s.c.107.14 yes 112
8.5 even 2 544.2.cc.c.175.8 112
17.7 odd 16 inner 136.2.s.c.75.14 yes 112
68.7 even 16 544.2.cc.c.143.8 112
136.75 even 16 inner 136.2.s.c.75.5 112
136.109 odd 16 544.2.cc.c.143.7 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
136.2.s.c.75.5 112 136.75 even 16 inner
136.2.s.c.75.14 yes 112 17.7 odd 16 inner
136.2.s.c.107.5 yes 112 1.1 even 1 trivial
136.2.s.c.107.14 yes 112 8.3 odd 2 inner
544.2.cc.c.143.7 112 136.109 odd 16
544.2.cc.c.143.8 112 68.7 even 16
544.2.cc.c.175.7 112 4.3 odd 2
544.2.cc.c.175.8 112 8.5 even 2