Properties

Label 225.2.q.a.121.17
Level $225$
Weight $2$
Character 225.121
Analytic conductor $1.797$
Analytic rank $0$
Dimension $224$
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] = [225,2,Mod(16,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.q (of order \(15\), 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: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 121.17
Character \(\chi\) \(=\) 225.121
Dual form 225.2.q.a.106.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.367877 - 0.0781947i) q^{2} +(0.776923 + 1.54803i) q^{3} +(-1.69787 + 0.755941i) q^{4} +(1.98576 - 1.02799i) q^{5} +(0.406860 + 0.508733i) q^{6} +(1.17975 + 2.04339i) q^{7} +(-1.17403 + 0.852985i) q^{8} +(-1.79278 + 2.40540i) q^{9} +O(q^{10})\) \(q+(0.367877 - 0.0781947i) q^{2} +(0.776923 + 1.54803i) q^{3} +(-1.69787 + 0.755941i) q^{4} +(1.98576 - 1.02799i) q^{5} +(0.406860 + 0.508733i) q^{6} +(1.17975 + 2.04339i) q^{7} +(-1.17403 + 0.852985i) q^{8} +(-1.79278 + 2.40540i) q^{9} +(0.650132 - 0.533449i) q^{10} +(-0.366949 + 0.0779975i) q^{11} +(-2.48933 - 2.04104i) q^{12} +(-0.347527 - 0.0738691i) q^{13} +(0.593785 + 0.659465i) q^{14} +(3.13414 + 2.27534i) q^{15} +(2.12203 - 2.35675i) q^{16} +(3.45606 - 2.51098i) q^{17} +(-0.471434 + 1.02508i) q^{18} +(-3.26679 + 2.37346i) q^{19} +(-2.59447 + 3.24651i) q^{20} +(-2.24664 + 3.41384i) q^{21} +(-0.128893 + 0.0573870i) q^{22} +(3.07582 + 3.41605i) q^{23} +(-2.23258 - 1.15473i) q^{24} +(2.88648 - 4.08267i) q^{25} -0.133623 q^{26} +(-5.11648 - 0.906467i) q^{27} +(-3.54774 - 2.57759i) q^{28} +(0.0385018 - 0.366320i) q^{29} +(1.33090 + 0.591974i) q^{30} +(-0.614589 - 5.84742i) q^{31} +(2.04755 - 3.54645i) q^{32} +(-0.405834 - 0.507450i) q^{33} +(1.07506 - 1.19398i) q^{34} +(4.44328 + 2.84490i) q^{35} +(1.22557 - 5.43929i) q^{36} +(-3.03352 - 9.33621i) q^{37} +(-1.01618 + 1.12859i) q^{38} +(-0.155650 - 0.595372i) q^{39} +(-1.45449 + 2.90072i) q^{40} +(8.44348 + 1.79472i) q^{41} +(-0.559545 + 1.43155i) q^{42} +(-3.86472 - 6.69390i) q^{43} +(0.564071 - 0.409822i) q^{44} +(-1.08731 + 6.61950i) q^{45} +(1.39864 + 1.01617i) q^{46} +(0.0700054 - 0.666057i) q^{47} +(5.29697 + 1.45394i) q^{48} +(0.716381 - 1.24081i) q^{49} +(0.742627 - 1.72763i) q^{50} +(6.57216 + 3.39925i) q^{51} +(0.645896 - 0.137289i) q^{52} +(-8.98419 - 6.52740i) q^{53} +(-1.95312 + 0.0666126i) q^{54} +(-0.648493 + 0.532104i) q^{55} +(-3.12804 - 1.39270i) q^{56} +(-6.21222 - 3.21308i) q^{57} +(-0.0144804 - 0.137771i) q^{58} +(11.3428 + 2.41099i) q^{59} +(-7.04139 - 1.49402i) q^{60} +(-6.33351 + 1.34623i) q^{61} +(-0.683331 - 2.10308i) q^{62} +(-7.03019 - 0.825578i) q^{63} +(-1.48405 + 4.56744i) q^{64} +(-0.766041 + 0.210567i) q^{65} +(-0.188977 - 0.154945i) q^{66} +(1.33023 + 12.6563i) q^{67} +(-3.96980 + 6.87589i) q^{68} +(-2.89846 + 7.41547i) q^{69} +(1.85704 + 0.699135i) q^{70} +(-1.67206 - 1.21482i) q^{71} +(0.0530170 - 4.35323i) q^{72} +(1.94846 - 5.99673i) q^{73} +(-1.84600 - 3.19737i) q^{74} +(8.56267 + 1.29643i) q^{75} +(3.75239 - 6.49933i) q^{76} +(-0.592287 - 0.657802i) q^{77} +(-0.103815 - 0.206853i) q^{78} +(-1.24358 + 11.8319i) q^{79} +(1.79112 - 6.86136i) q^{80} +(-2.57187 - 8.62470i) q^{81} +3.24650 q^{82} +(-8.03305 - 3.57654i) q^{83} +(1.23385 - 7.49459i) q^{84} +(4.28165 - 8.53899i) q^{85} +(-1.94517 - 2.16033i) q^{86} +(0.596986 - 0.225001i) q^{87} +(0.364280 - 0.404574i) q^{88} +(-0.603343 + 1.85690i) q^{89} +(0.117613 + 2.52018i) q^{90} +(-0.259051 - 0.797278i) q^{91} +(-7.80469 - 3.47487i) q^{92} +(8.57449 - 5.49440i) q^{93} +(-0.0263287 - 0.250501i) q^{94} +(-4.04716 + 8.07133i) q^{95} +(7.08079 + 0.414337i) q^{96} +(-1.17621 + 11.1909i) q^{97} +(0.166516 - 0.512483i) q^{98} +(0.470245 - 1.02249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.367877 0.0781947i 0.260128 0.0552920i −0.0760012 0.997108i \(-0.524215\pi\)
0.336130 + 0.941816i \(0.390882\pi\)
\(3\) 0.776923 + 1.54803i 0.448557 + 0.893754i
\(4\) −1.69787 + 0.755941i −0.848936 + 0.377971i
\(5\) 1.98576 1.02799i 0.888059 0.459730i
\(6\) 0.406860 + 0.508733i 0.166100 + 0.207689i
\(7\) 1.17975 + 2.04339i 0.445903 + 0.772327i 0.998115 0.0613768i \(-0.0195491\pi\)
−0.552211 + 0.833704i \(0.686216\pi\)
\(8\) −1.17403 + 0.852985i −0.415084 + 0.301576i
\(9\) −1.79278 + 2.40540i −0.597594 + 0.801799i
\(10\) 0.650132 0.533449i 0.205590 0.168692i
\(11\) −0.366949 + 0.0779975i −0.110639 + 0.0235171i −0.262899 0.964823i \(-0.584678\pi\)
0.152259 + 0.988341i \(0.451345\pi\)
\(12\) −2.48933 2.04104i −0.718609 0.589199i
\(13\) −0.347527 0.0738691i −0.0963865 0.0204876i 0.159466 0.987203i \(-0.449023\pi\)
−0.255852 + 0.966716i \(0.582356\pi\)
\(14\) 0.593785 + 0.659465i 0.158696 + 0.176249i
\(15\) 3.13414 + 2.27534i 0.809231 + 0.587491i
\(16\) 2.12203 2.35675i 0.530507 0.589187i
\(17\) 3.45606 2.51098i 0.838218 0.609001i −0.0836542 0.996495i \(-0.526659\pi\)
0.921872 + 0.387494i \(0.126659\pi\)
\(18\) −0.471434 + 1.02508i −0.111118 + 0.241613i
\(19\) −3.26679 + 2.37346i −0.749452 + 0.544509i −0.895657 0.444746i \(-0.853294\pi\)
0.146205 + 0.989254i \(0.453294\pi\)
\(20\) −2.59447 + 3.24651i −0.580140 + 0.725942i
\(21\) −2.24664 + 3.41384i −0.490258 + 0.744961i
\(22\) −0.128893 + 0.0573870i −0.0274801 + 0.0122349i
\(23\) 3.07582 + 3.41605i 0.641354 + 0.712295i 0.972921 0.231136i \(-0.0742442\pi\)
−0.331568 + 0.943431i \(0.607578\pi\)
\(24\) −2.23258 1.15473i −0.455723 0.235709i
\(25\) 2.88648 4.08267i 0.577296 0.816535i
\(26\) −0.133623 −0.0262057
\(27\) −5.11648 0.906467i −0.984666 0.174450i
\(28\) −3.54774 2.57759i −0.670460 0.487118i
\(29\) 0.0385018 0.366320i 0.00714960 0.0680239i −0.990365 0.138479i \(-0.955779\pi\)
0.997515 + 0.0704554i \(0.0224452\pi\)
\(30\) 1.33090 + 0.591974i 0.242988 + 0.108079i
\(31\) −0.614589 5.84742i −0.110383 1.05023i −0.899780 0.436344i \(-0.856273\pi\)
0.789396 0.613884i \(-0.210394\pi\)
\(32\) 2.04755 3.54645i 0.361958 0.626930i
\(33\) −0.405834 0.507450i −0.0706466 0.0883357i
\(34\) 1.07506 1.19398i 0.184372 0.204765i
\(35\) 4.44328 + 2.84490i 0.751051 + 0.480877i
\(36\) 1.22557 5.43929i 0.204262 0.906549i
\(37\) −3.03352 9.33621i −0.498707 1.53486i −0.811099 0.584910i \(-0.801130\pi\)
0.312391 0.949953i \(-0.398870\pi\)
\(38\) −1.01618 + 1.12859i −0.164847 + 0.183081i
\(39\) −0.155650 0.595372i −0.0249240 0.0953357i
\(40\) −1.45449 + 2.90072i −0.229975 + 0.458644i
\(41\) 8.44348 + 1.79472i 1.31865 + 0.280288i 0.812905 0.582396i \(-0.197885\pi\)
0.505744 + 0.862683i \(0.331218\pi\)
\(42\) −0.559545 + 1.43155i −0.0863397 + 0.220893i
\(43\) −3.86472 6.69390i −0.589365 1.02081i −0.994316 0.106471i \(-0.966045\pi\)
0.404951 0.914338i \(-0.367289\pi\)
\(44\) 0.564071 0.409822i 0.0850370 0.0617830i
\(45\) −1.08731 + 6.61950i −0.162087 + 0.986776i
\(46\) 1.39864 + 1.01617i 0.206219 + 0.149827i
\(47\) 0.0700054 0.666057i 0.0102113 0.0971544i −0.988229 0.152981i \(-0.951113\pi\)
0.998440 + 0.0558265i \(0.0177794\pi\)
\(48\) 5.29697 + 1.45394i 0.764551 + 0.209859i
\(49\) 0.716381 1.24081i 0.102340 0.177258i
\(50\) 0.742627 1.72763i 0.105023 0.244324i
\(51\) 6.57216 + 3.39925i 0.920286 + 0.475990i
\(52\) 0.645896 0.137289i 0.0895697 0.0190386i
\(53\) −8.98419 6.52740i −1.23407 0.896607i −0.236885 0.971538i \(-0.576126\pi\)
−0.997189 + 0.0749310i \(0.976126\pi\)
\(54\) −1.95312 + 0.0666126i −0.265785 + 0.00906483i
\(55\) −0.648493 + 0.532104i −0.0874427 + 0.0717489i
\(56\) −3.12804 1.39270i −0.418002 0.186107i
\(57\) −6.21222 3.21308i −0.822829 0.425583i
\(58\) −0.0144804 0.137771i −0.00190136 0.0180903i
\(59\) 11.3428 + 2.41099i 1.47671 + 0.313885i 0.874724 0.484622i \(-0.161043\pi\)
0.601987 + 0.798506i \(0.294376\pi\)
\(60\) −7.04139 1.49402i −0.909039 0.192877i
\(61\) −6.33351 + 1.34623i −0.810923 + 0.172367i −0.594670 0.803970i \(-0.702717\pi\)
−0.216254 + 0.976337i \(0.569384\pi\)
\(62\) −0.683331 2.10308i −0.0867831 0.267091i
\(63\) −7.03019 0.825578i −0.885721 0.104013i
\(64\) −1.48405 + 4.56744i −0.185506 + 0.570930i
\(65\) −0.766041 + 0.210567i −0.0950157 + 0.0261176i
\(66\) −0.188977 0.154945i −0.0232614 0.0190724i
\(67\) 1.33023 + 12.6563i 0.162513 + 1.54621i 0.706861 + 0.707352i \(0.250111\pi\)
−0.544348 + 0.838860i \(0.683223\pi\)
\(68\) −3.96980 + 6.87589i −0.481409 + 0.833825i
\(69\) −2.89846 + 7.41547i −0.348934 + 0.892718i
\(70\) 1.85704 + 0.699135i 0.221958 + 0.0835626i
\(71\) −1.67206 1.21482i −0.198437 0.144173i 0.484129 0.874996i \(-0.339136\pi\)
−0.682567 + 0.730823i \(0.739136\pi\)
\(72\) 0.0530170 4.35323i 0.00624812 0.513033i
\(73\) 1.94846 5.99673i 0.228050 0.701864i −0.769918 0.638143i \(-0.779703\pi\)
0.997968 0.0637218i \(-0.0202970\pi\)
\(74\) −1.84600 3.19737i −0.214594 0.371687i
\(75\) 8.56267 + 1.29643i 0.988732 + 0.149699i
\(76\) 3.75239 6.49933i 0.430428 0.745524i
\(77\) −0.592287 0.657802i −0.0674974 0.0749635i
\(78\) −0.103815 0.206853i −0.0117547 0.0234214i
\(79\) −1.24358 + 11.8319i −0.139914 + 1.33119i 0.668997 + 0.743265i \(0.266724\pi\)
−0.808912 + 0.587930i \(0.799943\pi\)
\(80\) 1.79112 6.86136i 0.200254 0.767123i
\(81\) −2.57187 8.62470i −0.285763 0.958300i
\(82\) 3.24650 0.358516
\(83\) −8.03305 3.57654i −0.881741 0.392577i −0.0846325 0.996412i \(-0.526972\pi\)
−0.797109 + 0.603836i \(0.793638\pi\)
\(84\) 1.23385 7.49459i 0.134624 0.817727i
\(85\) 4.28165 8.53899i 0.464410 0.926183i
\(86\) −1.94517 2.16033i −0.209753 0.232954i
\(87\) 0.596986 0.225001i 0.0640037 0.0241226i
\(88\) 0.364280 0.404574i 0.0388324 0.0431277i
\(89\) −0.603343 + 1.85690i −0.0639542 + 0.196831i −0.977928 0.208943i \(-0.932998\pi\)
0.913974 + 0.405774i \(0.132998\pi\)
\(90\) 0.117613 + 2.52018i 0.0123974 + 0.265651i
\(91\) −0.259051 0.797278i −0.0271560 0.0835775i
\(92\) −7.80469 3.47487i −0.813695 0.362280i
\(93\) 8.57449 5.49440i 0.889133 0.569743i
\(94\) −0.0263287 0.250501i −0.00271560 0.0258372i
\(95\) −4.04716 + 8.07133i −0.415230 + 0.828101i
\(96\) 7.08079 + 0.414337i 0.722680 + 0.0422881i
\(97\) −1.17621 + 11.1909i −0.119426 + 1.13626i 0.756561 + 0.653924i \(0.226878\pi\)
−0.875986 + 0.482336i \(0.839788\pi\)
\(98\) 0.166516 0.512483i 0.0168206 0.0517686i
\(99\) 0.470245 1.02249i 0.0472614 0.102764i
\(100\) −1.81461 + 9.11387i −0.181461 + 0.911387i
\(101\) 7.92712 + 13.7302i 0.788778 + 1.36620i 0.926716 + 0.375762i \(0.122619\pi\)
−0.137938 + 0.990441i \(0.544048\pi\)
\(102\) 2.68355 + 0.736597i 0.265711 + 0.0729340i
\(103\) −1.29330 + 0.575813i −0.127432 + 0.0567365i −0.469462 0.882953i \(-0.655552\pi\)
0.342030 + 0.939689i \(0.388886\pi\)
\(104\) 0.471017 0.209710i 0.0461870 0.0205638i
\(105\) −0.951908 + 9.08859i −0.0928967 + 0.886955i
\(106\) −3.81549 1.69876i −0.370593 0.164999i
\(107\) 7.97644 0.771112 0.385556 0.922684i \(-0.374010\pi\)
0.385556 + 0.922684i \(0.374010\pi\)
\(108\) 9.37235 2.32869i 0.901855 0.224078i
\(109\) 2.73023 + 8.40279i 0.261509 + 0.804841i 0.992477 + 0.122430i \(0.0390687\pi\)
−0.730968 + 0.682411i \(0.760931\pi\)
\(110\) −0.196958 + 0.246458i −0.0187792 + 0.0234988i
\(111\) 12.0959 11.9495i 1.14809 1.13419i
\(112\) 7.31921 + 1.55575i 0.691600 + 0.147004i
\(113\) −16.2878 3.46209i −1.53223 0.325686i −0.636850 0.770988i \(-0.719763\pi\)
−0.895380 + 0.445302i \(0.853096\pi\)
\(114\) −2.53658 0.696256i −0.237573 0.0652104i
\(115\) 9.61951 + 3.62154i 0.897023 + 0.337710i
\(116\) 0.211545 + 0.651069i 0.0196415 + 0.0604503i
\(117\) 0.800724 0.703508i 0.0740269 0.0650394i
\(118\) 4.36130 0.401490
\(119\) 9.20818 + 4.09975i 0.844113 + 0.375823i
\(120\) −5.62042 + 0.00204349i −0.513071 + 0.000186545i
\(121\) −9.92043 + 4.41686i −0.901857 + 0.401533i
\(122\) −2.22469 + 0.990495i −0.201414 + 0.0896752i
\(123\) 3.78166 + 14.4651i 0.340981 + 1.30427i
\(124\) 5.46380 + 9.46358i 0.490664 + 0.849855i
\(125\) 1.53491 11.0745i 0.137287 0.990531i
\(126\) −2.65080 + 0.246012i −0.236152 + 0.0219165i
\(127\) 2.85948 8.80056i 0.253738 0.780924i −0.740338 0.672235i \(-0.765335\pi\)
0.994076 0.108689i \(-0.0346653\pi\)
\(128\) −1.04491 + 9.94162i −0.0923575 + 0.878723i
\(129\) 7.35975 11.1833i 0.647989 0.984638i
\(130\) −0.265344 + 0.137363i −0.0232722 + 0.0120475i
\(131\) 1.66169 + 15.8099i 0.145183 + 1.38132i 0.788177 + 0.615449i \(0.211025\pi\)
−0.642994 + 0.765871i \(0.722308\pi\)
\(132\) 1.07266 + 0.554798i 0.0933627 + 0.0482890i
\(133\) −8.70388 3.87522i −0.754722 0.336024i
\(134\) 1.47902 + 4.55194i 0.127768 + 0.393228i
\(135\) −11.0919 + 3.45965i −0.954641 + 0.297759i
\(136\) −1.91571 + 5.89594i −0.164271 + 0.505573i
\(137\) −4.68846 + 5.20706i −0.400562 + 0.444870i −0.909356 0.416019i \(-0.863425\pi\)
0.508794 + 0.860889i \(0.330092\pi\)
\(138\) −0.486427 + 2.95463i −0.0414074 + 0.251515i
\(139\) −10.7197 11.9055i −0.909236 1.00981i −0.999903 0.0139277i \(-0.995567\pi\)
0.0906670 0.995881i \(-0.471100\pi\)
\(140\) −9.69469 1.47143i −0.819351 0.124358i
\(141\) 1.08546 0.409104i 0.0914125 0.0344528i
\(142\) −0.710106 0.316160i −0.0595908 0.0265315i
\(143\) 0.133286 0.0111460
\(144\) 1.86459 + 9.32945i 0.155382 + 0.777454i
\(145\) −0.300117 0.767002i −0.0249234 0.0636961i
\(146\) 0.247880 2.35842i 0.0205147 0.195184i
\(147\) 2.47738 + 0.144965i 0.204331 + 0.0119565i
\(148\) 12.2081 + 13.5585i 1.00350 + 1.11450i
\(149\) 5.59996 9.69941i 0.458766 0.794606i −0.540130 0.841582i \(-0.681625\pi\)
0.998896 + 0.0469753i \(0.0149582\pi\)
\(150\) 3.25138 0.192629i 0.265474 0.0157281i
\(151\) −1.72821 2.99334i −0.140640 0.243595i 0.787098 0.616828i \(-0.211583\pi\)
−0.927738 + 0.373233i \(0.878249\pi\)
\(152\) 1.81079 5.57304i 0.146874 0.452033i
\(153\) −0.156069 + 12.8148i −0.0126174 + 1.03602i
\(154\) −0.269326 0.195677i −0.0217029 0.0157681i
\(155\) −7.23151 10.9798i −0.580849 0.881918i
\(156\) 0.714340 + 0.893202i 0.0571929 + 0.0715134i
\(157\) −0.881657 + 1.52708i −0.0703639 + 0.121874i −0.899061 0.437824i \(-0.855749\pi\)
0.828697 + 0.559698i \(0.189083\pi\)
\(158\) 0.467707 + 4.44994i 0.0372088 + 0.354018i
\(159\) 3.12457 18.9791i 0.247794 1.50514i
\(160\) 0.420220 9.14725i 0.0332213 0.723154i
\(161\) −3.35161 + 10.3152i −0.264143 + 0.812950i
\(162\) −1.62054 2.97172i −0.127322 0.233481i
\(163\) 2.57870 + 7.93644i 0.201980 + 0.621630i 0.999824 + 0.0187660i \(0.00597376\pi\)
−0.797844 + 0.602864i \(0.794026\pi\)
\(164\) −15.6926 + 3.33557i −1.22539 + 0.260465i
\(165\) −1.32754 0.590481i −0.103349 0.0459689i
\(166\) −3.23484 0.687587i −0.251072 0.0533671i
\(167\) −1.20283 11.4442i −0.0930778 0.885577i −0.937051 0.349192i \(-0.886456\pi\)
0.843973 0.536385i \(-0.180210\pi\)
\(168\) −0.274319 5.92432i −0.0211641 0.457071i
\(169\) −11.7608 5.23623i −0.904675 0.402787i
\(170\) 0.907419 3.47610i 0.0695959 0.266605i
\(171\) 0.147522 12.1130i 0.0112813 0.926305i
\(172\) 11.6220 + 8.44387i 0.886169 + 0.643839i
\(173\) 17.7210 3.76672i 1.34731 0.286379i 0.522908 0.852389i \(-0.324847\pi\)
0.824398 + 0.566011i \(0.191514\pi\)
\(174\) 0.202024 0.129454i 0.0153154 0.00981386i
\(175\) 11.7478 + 1.08166i 0.888051 + 0.0817657i
\(176\) −0.594856 + 1.03032i −0.0448389 + 0.0776633i
\(177\) 5.08022 + 19.4322i 0.381853 + 1.46061i
\(178\) −0.0767565 + 0.730289i −0.00575314 + 0.0547375i
\(179\) −5.91468 4.29726i −0.442084 0.321193i 0.344379 0.938831i \(-0.388090\pi\)
−0.786462 + 0.617638i \(0.788090\pi\)
\(180\) −3.15784 12.0610i −0.235371 0.898974i
\(181\) −7.81043 + 5.67461i −0.580544 + 0.421790i −0.838920 0.544254i \(-0.816813\pi\)
0.258376 + 0.966044i \(0.416813\pi\)
\(182\) −0.157642 0.273044i −0.0116852 0.0202394i
\(183\) −7.00465 8.75854i −0.517799 0.647450i
\(184\) −6.52496 1.38692i −0.481026 0.102245i
\(185\) −15.6213 15.4210i −1.14850 1.13378i
\(186\) 2.72473 2.69174i 0.199787 0.197368i
\(187\) −1.07235 + 1.19097i −0.0784180 + 0.0870920i
\(188\) 0.384640 + 1.18380i 0.0280527 + 0.0863374i
\(189\) −4.18390 11.5243i −0.304334 0.838272i
\(190\) −0.857723 + 3.28573i −0.0622258 + 0.238372i
\(191\) 8.77381 9.74430i 0.634850 0.705073i −0.336778 0.941584i \(-0.609337\pi\)
0.971629 + 0.236511i \(0.0760040\pi\)
\(192\) −8.22352 + 1.25120i −0.593481 + 0.0902973i
\(193\) 8.40007 14.5494i 0.604650 1.04729i −0.387456 0.921888i \(-0.626646\pi\)
0.992107 0.125397i \(-0.0400205\pi\)
\(194\) 0.442367 + 4.20884i 0.0317601 + 0.302177i
\(195\) −0.921119 1.02226i −0.0659627 0.0732054i
\(196\) −0.278345 + 2.64828i −0.0198818 + 0.189163i
\(197\) −9.40465 6.83288i −0.670054 0.486823i 0.199989 0.979798i \(-0.435909\pi\)
−0.870043 + 0.492976i \(0.835909\pi\)
\(198\) 0.0930390 0.412922i 0.00661199 0.0293451i
\(199\) 7.37976 0.523137 0.261568 0.965185i \(-0.415760\pi\)
0.261568 + 0.965185i \(0.415760\pi\)
\(200\) 0.0936376 + 7.25532i 0.00662118 + 0.513029i
\(201\) −18.5588 + 11.8922i −1.30904 + 0.838811i
\(202\) 3.98983 + 4.43116i 0.280724 + 0.311775i
\(203\) 0.793955 0.353492i 0.0557248 0.0248103i
\(204\) −13.7283 0.803320i −0.961174 0.0562437i
\(205\) 18.6117 5.11592i 1.29989 0.357312i
\(206\) −0.430749 + 0.312957i −0.0300117 + 0.0218048i
\(207\) −13.7312 + 1.27435i −0.954387 + 0.0885735i
\(208\) −0.911552 + 0.662281i −0.0632047 + 0.0459209i
\(209\) 1.01362 1.12574i 0.0701136 0.0778691i
\(210\) 0.360494 + 3.41792i 0.0248765 + 0.235859i
\(211\) 7.43482 + 8.25720i 0.511834 + 0.568449i 0.942561 0.334033i \(-0.108410\pi\)
−0.430727 + 0.902482i \(0.641743\pi\)
\(212\) 20.1883 + 4.29116i 1.38654 + 0.294718i
\(213\) 0.581518 3.53222i 0.0398450 0.242024i
\(214\) 2.93435 0.623716i 0.200588 0.0426363i
\(215\) −14.5557 9.31958i −0.992687 0.635590i
\(216\) 6.78012 3.30005i 0.461329 0.224540i
\(217\) 11.2235 8.15434i 0.761900 0.553553i
\(218\) 1.66144 + 2.87771i 0.112527 + 0.194903i
\(219\) 10.7969 1.64273i 0.729588 0.111006i
\(220\) 0.698818 1.39367i 0.0471143 0.0939610i
\(221\) −1.38656 + 0.617335i −0.0932699 + 0.0415264i
\(222\) 3.51542 5.34178i 0.235940 0.358517i
\(223\) 2.95847 0.628841i 0.198114 0.0421103i −0.107786 0.994174i \(-0.534376\pi\)
0.305900 + 0.952064i \(0.401043\pi\)
\(224\) 9.66236 0.645594
\(225\) 4.64563 + 14.2625i 0.309708 + 0.950832i
\(226\) −6.26264 −0.416585
\(227\) −8.94852 + 1.90207i −0.593934 + 0.126245i −0.495065 0.868856i \(-0.664856\pi\)
−0.0988690 + 0.995100i \(0.531522\pi\)
\(228\) 12.9765 + 0.759325i 0.859387 + 0.0502875i
\(229\) −26.9255 + 11.9880i −1.77929 + 0.792191i −0.797216 + 0.603694i \(0.793695\pi\)
−0.982074 + 0.188497i \(0.939638\pi\)
\(230\) 3.82198 + 0.580087i 0.252014 + 0.0382498i
\(231\) 0.558134 1.42794i 0.0367225 0.0939515i
\(232\) 0.267263 + 0.462913i 0.0175467 + 0.0303917i
\(233\) 6.59518 4.79168i 0.432064 0.313913i −0.350409 0.936597i \(-0.613958\pi\)
0.782474 + 0.622683i \(0.213958\pi\)
\(234\) 0.239557 0.321417i 0.0156604 0.0210117i
\(235\) −0.545685 1.39459i −0.0355965 0.0909732i
\(236\) −21.0812 + 4.48095i −1.37227 + 0.291685i
\(237\) −19.2823 + 7.26739i −1.25252 + 0.472067i
\(238\) 3.70806 + 0.788172i 0.240358 + 0.0510896i
\(239\) 3.17374 + 3.52480i 0.205292 + 0.228000i 0.836995 0.547211i \(-0.184310\pi\)
−0.631703 + 0.775211i \(0.717644\pi\)
\(240\) 12.0131 2.55804i 0.775445 0.165121i
\(241\) −16.7450 + 18.5973i −1.07864 + 1.19795i −0.0994459 + 0.995043i \(0.531707\pi\)
−0.979197 + 0.202911i \(0.934960\pi\)
\(242\) −3.30413 + 2.40059i −0.212397 + 0.154316i
\(243\) 11.3531 10.6821i 0.728304 0.685254i
\(244\) 9.73582 7.07349i 0.623272 0.452834i
\(245\) 0.147024 3.20038i 0.00939301 0.204465i
\(246\) 2.52228 + 5.02567i 0.160815 + 0.320425i
\(247\) 1.31062 0.583526i 0.0833928 0.0371288i
\(248\) 5.70932 + 6.34084i 0.362542 + 0.402644i
\(249\) −0.704470 15.2141i −0.0446440 0.964153i
\(250\) −0.301307 4.19407i −0.0190563 0.265256i
\(251\) −20.6780 −1.30518 −0.652591 0.757710i \(-0.726318\pi\)
−0.652591 + 0.757710i \(0.726318\pi\)
\(252\) 12.5604 3.91268i 0.791234 0.246476i
\(253\) −1.39511 1.01361i −0.0877101 0.0637251i
\(254\) 0.363779 3.46112i 0.0228255 0.217170i
\(255\) 16.5451 0.00601553i 1.03609 0.000376707i
\(256\) −0.611009 5.81337i −0.0381881 0.363335i
\(257\) 0.199971 0.346359i 0.0124738 0.0216053i −0.859721 0.510764i \(-0.829363\pi\)
0.872195 + 0.489158i \(0.162696\pi\)
\(258\) 1.83300 4.68959i 0.114118 0.291961i
\(259\) 15.4987 17.2130i 0.963042 1.06957i
\(260\) 1.14146 0.936598i 0.0707905 0.0580853i
\(261\) 0.812119 + 0.749343i 0.0502689 + 0.0463832i
\(262\) 1.84755 + 5.68618i 0.114142 + 0.351293i
\(263\) 1.78686 1.98451i 0.110182 0.122370i −0.685531 0.728044i \(-0.740430\pi\)
0.795713 + 0.605674i \(0.207096\pi\)
\(264\) 0.909310 + 0.249593i 0.0559641 + 0.0153614i
\(265\) −24.5505 3.72619i −1.50813 0.228898i
\(266\) −3.50498 0.745007i −0.214904 0.0456793i
\(267\) −3.34328 + 0.508676i −0.204606 + 0.0311304i
\(268\) −11.8260 20.4832i −0.722386 1.25121i
\(269\) 15.1805 11.0293i 0.925574 0.672469i −0.0193308 0.999813i \(-0.506154\pi\)
0.944905 + 0.327344i \(0.106154\pi\)
\(270\) −3.80994 + 2.14006i −0.231866 + 0.130240i
\(271\) −10.8085 7.85283i −0.656569 0.477025i 0.208934 0.977930i \(-0.433001\pi\)
−0.865503 + 0.500905i \(0.833001\pi\)
\(272\) 1.41611 13.4734i 0.0858646 0.816947i
\(273\) 1.03295 1.02044i 0.0625167 0.0617600i
\(274\) −1.31761 + 2.28217i −0.0795999 + 0.137871i
\(275\) −0.740753 + 1.72327i −0.0446691 + 0.103917i
\(276\) −0.684444 14.7816i −0.0411987 0.889747i
\(277\) −22.2737 + 4.73443i −1.33830 + 0.284464i −0.820798 0.571219i \(-0.806471\pi\)
−0.517500 + 0.855683i \(0.673137\pi\)
\(278\) −4.87449 3.54153i −0.292353 0.212407i
\(279\) 15.1672 + 9.00482i 0.908037 + 0.539105i
\(280\) −7.64322 + 0.450036i −0.456770 + 0.0268948i
\(281\) 8.19793 + 3.64996i 0.489048 + 0.217738i 0.636420 0.771343i \(-0.280415\pi\)
−0.147372 + 0.989081i \(0.547081\pi\)
\(282\) 0.367327 0.235378i 0.0218740 0.0140165i
\(283\) 0.679692 + 6.46684i 0.0404035 + 0.384414i 0.995973 + 0.0896492i \(0.0285746\pi\)
−0.955570 + 0.294765i \(0.904759\pi\)
\(284\) 3.75728 + 0.798635i 0.222954 + 0.0473903i
\(285\) −15.6390 + 0.00568608i −0.926374 + 0.000336815i
\(286\) 0.0490330 0.0104223i 0.00289938 0.000616282i
\(287\) 6.29389 + 19.3706i 0.371517 + 1.14341i
\(288\) 4.85983 + 11.2832i 0.286368 + 0.664867i
\(289\) 0.386075 1.18822i 0.0227103 0.0698951i
\(290\) −0.170382 0.258695i −0.0100052 0.0151911i
\(291\) −18.2376 + 6.87364i −1.06911 + 0.402940i
\(292\) 1.22495 + 11.6546i 0.0716847 + 0.682034i
\(293\) 8.56935 14.8426i 0.500627 0.867111i −0.499373 0.866387i \(-0.666436\pi\)
1.00000 0.000723948i \(-0.000230440\pi\)
\(294\) 0.922707 0.140389i 0.0538134 0.00818763i
\(295\) 25.0026 6.87264i 1.45571 0.400141i
\(296\) 11.5251 + 8.37347i 0.669883 + 0.486698i
\(297\) 1.94819 0.0664446i 0.113045 0.00385551i
\(298\) 1.30165 4.00608i 0.0754028 0.232066i
\(299\) −0.816590 1.41438i −0.0472246 0.0817955i
\(300\) −15.5183 + 4.27171i −0.895951 + 0.246627i
\(301\) 9.11881 15.7942i 0.525599 0.910365i
\(302\) −0.869832 0.966046i −0.0500532 0.0555897i
\(303\) −15.0959 + 22.9387i −0.867238 + 1.31779i
\(304\) −1.33856 + 12.7355i −0.0767716 + 0.730433i
\(305\) −11.1929 + 9.18407i −0.640905 + 0.525878i
\(306\) 0.944638 + 4.72649i 0.0540014 + 0.270195i
\(307\) −22.7466 −1.29822 −0.649109 0.760695i \(-0.724858\pi\)
−0.649109 + 0.760695i \(0.724858\pi\)
\(308\) 1.50289 + 0.669129i 0.0856350 + 0.0381271i
\(309\) −1.89617 1.55470i −0.107869 0.0884437i
\(310\) −3.51887 3.47375i −0.199858 0.197296i
\(311\) 9.62578 + 10.6905i 0.545828 + 0.606203i 0.951437 0.307843i \(-0.0996072\pi\)
−0.405609 + 0.914047i \(0.632941\pi\)
\(312\) 0.690582 + 0.566219i 0.0390965 + 0.0320558i
\(313\) 1.73060 1.92203i 0.0978194 0.108640i −0.692247 0.721660i \(-0.743379\pi\)
0.790067 + 0.613021i \(0.210046\pi\)
\(314\) −0.204932 + 0.630717i −0.0115650 + 0.0355934i
\(315\) −14.8089 + 5.58755i −0.834390 + 0.314823i
\(316\) −6.83279 21.0292i −0.384374 1.18298i
\(317\) 14.1723 + 6.30993i 0.795998 + 0.354401i 0.764106 0.645090i \(-0.223180\pi\)
0.0318914 + 0.999491i \(0.489847\pi\)
\(318\) −0.334605 7.22629i −0.0187637 0.405230i
\(319\) 0.0144438 + 0.137424i 0.000808699 + 0.00769426i
\(320\) 1.74831 + 10.5954i 0.0977333 + 0.592302i
\(321\) 6.19708 + 12.3478i 0.345887 + 0.689184i
\(322\) −0.426387 + 4.05680i −0.0237616 + 0.226077i
\(323\) −5.33052 + 16.4056i −0.296598 + 0.912834i
\(324\) 10.8865 + 12.6995i 0.604804 + 0.705525i
\(325\) −1.30471 + 1.20562i −0.0723724 + 0.0668756i
\(326\) 1.56923 + 2.71799i 0.0869119 + 0.150536i
\(327\) −10.8866 + 10.7548i −0.602029 + 0.594742i
\(328\) −11.4438 + 5.09511i −0.631878 + 0.281330i
\(329\) 1.44360 0.642732i 0.0795882 0.0354350i
\(330\) −0.534544 0.113418i −0.0294257 0.00624344i
\(331\) 7.91509 + 3.52403i 0.435053 + 0.193698i 0.612564 0.790421i \(-0.290138\pi\)
−0.177511 + 0.984119i \(0.556805\pi\)
\(332\) 16.3427 0.896924
\(333\) 27.8957 + 9.44096i 1.52868 + 0.517362i
\(334\) −1.33737 4.11600i −0.0731775 0.225217i
\(335\) 15.6520 + 23.7649i 0.855162 + 1.29841i
\(336\) 3.27812 + 12.5390i 0.178836 + 0.684061i
\(337\) 16.1508 + 3.43295i 0.879789 + 0.187005i 0.625594 0.780148i \(-0.284856\pi\)
0.254194 + 0.967153i \(0.418190\pi\)
\(338\) −4.73597 1.00666i −0.257603 0.0547551i
\(339\) −7.29499 27.9038i −0.396209 1.51553i
\(340\) −0.814727 + 17.7348i −0.0441848 + 0.961803i
\(341\) 0.681607 + 2.09777i 0.0369111 + 0.113601i
\(342\) −0.892903 4.46764i −0.0482827 0.241582i
\(343\) 19.8971 1.07434
\(344\) 10.2471 + 4.56231i 0.552487 + 0.245983i
\(345\) 1.86737 + 17.7049i 0.100536 + 0.953201i
\(346\) 6.22463 2.77138i 0.334638 0.148990i
\(347\) 0.512906 0.228361i 0.0275342 0.0122590i −0.392923 0.919571i \(-0.628536\pi\)
0.420458 + 0.907312i \(0.361870\pi\)
\(348\) −0.843519 + 0.833309i −0.0452174 + 0.0446700i
\(349\) −17.9910 31.1614i −0.963037 1.66803i −0.714798 0.699331i \(-0.753481\pi\)
−0.248239 0.968699i \(-0.579852\pi\)
\(350\) 4.40633 0.520699i 0.235528 0.0278325i
\(351\) 1.71115 + 0.692971i 0.0913345 + 0.0369880i
\(352\) −0.474731 + 1.46107i −0.0253032 + 0.0778754i
\(353\) −1.37659 + 13.0974i −0.0732685 + 0.697103i 0.894809 + 0.446450i \(0.147312\pi\)
−0.968077 + 0.250653i \(0.919355\pi\)
\(354\) 3.38839 + 6.75141i 0.180091 + 0.358833i
\(355\) −4.56914 0.693488i −0.242505 0.0368065i
\(356\) −0.379307 3.60887i −0.0201033 0.191270i
\(357\) 0.807526 + 17.4397i 0.0427388 + 0.923007i
\(358\) −2.51190 1.11837i −0.132758 0.0591077i
\(359\) 11.4732 + 35.3108i 0.605532 + 1.86364i 0.493093 + 0.869976i \(0.335866\pi\)
0.112438 + 0.993659i \(0.464134\pi\)
\(360\) −4.36979 8.69897i −0.230308 0.458476i
\(361\) −0.832742 + 2.56292i −0.0438285 + 0.134890i
\(362\) −2.42955 + 2.69829i −0.127694 + 0.141819i
\(363\) −14.5448 11.9255i −0.763406 0.625929i
\(364\) 1.04253 + 1.15785i 0.0546435 + 0.0606877i
\(365\) −2.29541 13.9111i −0.120147 0.728138i
\(366\) −3.26172 2.67434i −0.170493 0.139790i
\(367\) 23.4860 + 10.4566i 1.22596 + 0.545832i 0.914561 0.404448i \(-0.132536\pi\)
0.311397 + 0.950280i \(0.399203\pi\)
\(368\) 14.5778 0.759918
\(369\) −19.4543 + 17.0924i −1.01275 + 0.889794i
\(370\) −6.95258 4.45154i −0.361448 0.231425i
\(371\) 2.73890 26.0589i 0.142196 1.35291i
\(372\) −10.4049 + 15.8106i −0.539471 + 0.819741i
\(373\) −3.11442 3.45891i −0.161259 0.179096i 0.657101 0.753803i \(-0.271783\pi\)
−0.818359 + 0.574707i \(0.805116\pi\)
\(374\) −0.301366 + 0.521981i −0.0155833 + 0.0269910i
\(375\) 18.3361 6.22793i 0.946873 0.321609i
\(376\) 0.485948 + 0.841686i 0.0250609 + 0.0434067i
\(377\) −0.0404401 + 0.124462i −0.00208277 + 0.00641011i
\(378\) −2.44030 3.91238i −0.125516 0.201231i
\(379\) 20.4895 + 14.8865i 1.05247 + 0.764666i 0.972681 0.232145i \(-0.0745745\pi\)
0.0797917 + 0.996812i \(0.474574\pi\)
\(380\) 0.770107 16.7635i 0.0395056 0.859950i
\(381\) 15.8451 2.41081i 0.811770 0.123510i
\(382\) 2.46573 4.27077i 0.126158 0.218512i
\(383\) −0.712744 6.78131i −0.0364195 0.346509i −0.997524 0.0703242i \(-0.977597\pi\)
0.961105 0.276184i \(-0.0890701\pi\)
\(384\) −16.2017 + 6.10633i −0.826790 + 0.311612i
\(385\) −1.85235 0.697371i −0.0944046 0.0355413i
\(386\) 1.95251 6.00922i 0.0993803 0.305861i
\(387\) 23.0301 + 2.70450i 1.17068 + 0.137477i
\(388\) −6.46258 19.8898i −0.328088 1.00975i
\(389\) 2.17285 0.461853i 0.110168 0.0234169i −0.152498 0.988304i \(-0.548732\pi\)
0.262666 + 0.964887i \(0.415398\pi\)
\(390\) −0.418794 0.304039i −0.0212064 0.0153956i
\(391\) 19.2079 + 4.08276i 0.971383 + 0.206474i
\(392\) 0.217336 + 2.06781i 0.0109771 + 0.104440i
\(393\) −23.1832 + 14.8554i −1.16944 + 0.749358i
\(394\) −3.99405 1.77827i −0.201217 0.0895878i
\(395\) 9.69362 + 24.7737i 0.487739 + 1.24650i
\(396\) −0.0254724 + 2.09154i −0.00128003 + 0.105104i
\(397\) −18.7858 13.6487i −0.942831 0.685007i 0.00626974 0.999980i \(-0.498004\pi\)
−0.949100 + 0.314974i \(0.898004\pi\)
\(398\) 2.71484 0.577058i 0.136083 0.0289253i
\(399\) −0.763300 16.4846i −0.0382128 0.825262i
\(400\) −3.49665 15.4663i −0.174833 0.773313i
\(401\) 7.72116 13.3734i 0.385576 0.667837i −0.606273 0.795257i \(-0.707336\pi\)
0.991849 + 0.127419i \(0.0406694\pi\)
\(402\) −5.89745 + 5.82607i −0.294138 + 0.290578i
\(403\) −0.218358 + 2.07753i −0.0108772 + 0.103489i
\(404\) −23.8384 17.3196i −1.18601 0.861684i
\(405\) −13.9732 14.4827i −0.694334 0.719653i
\(406\) 0.264437 0.192125i 0.0131238 0.00953499i
\(407\) 1.84135 + 3.18931i 0.0912722 + 0.158088i
\(408\) −10.6154 + 1.61512i −0.525542 + 0.0799605i
\(409\) 26.5034 + 5.63347i 1.31051 + 0.278557i 0.809620 0.586955i \(-0.199673\pi\)
0.500888 + 0.865512i \(0.333007\pi\)
\(410\) 6.44677 3.33737i 0.318383 0.164821i
\(411\) −11.7033 3.21238i −0.577279 0.158455i
\(412\) 1.76057 1.95531i 0.0867371 0.0963314i
\(413\) 8.45511 + 26.0221i 0.416049 + 1.28047i
\(414\) −4.95176 + 1.54251i −0.243366 + 0.0758104i
\(415\) −19.6283 + 1.15573i −0.963517 + 0.0567323i
\(416\) −0.973550 + 1.08124i −0.0477322 + 0.0530120i
\(417\) 10.1016 25.8441i 0.494677 1.26559i
\(418\) 0.284861 0.493394i 0.0139330 0.0241327i
\(419\) −1.68365 16.0188i −0.0822516 0.782572i −0.955439 0.295188i \(-0.904618\pi\)
0.873188 0.487384i \(-0.162049\pi\)
\(420\) −5.25422 16.1508i −0.256380 0.788080i
\(421\) −1.78347 + 16.9686i −0.0869212 + 0.827000i 0.861024 + 0.508565i \(0.169824\pi\)
−0.947945 + 0.318435i \(0.896843\pi\)
\(422\) 3.38077 + 2.45627i 0.164573 + 0.119570i
\(423\) 1.47663 + 1.36248i 0.0717960 + 0.0662463i
\(424\) 16.1155 0.782639
\(425\) −0.275646 21.3579i −0.0133708 1.03601i
\(426\) −0.0622739 1.34490i −0.00301718 0.0651604i
\(427\) −10.2228 11.3536i −0.494717 0.549439i
\(428\) −13.5430 + 6.02972i −0.654624 + 0.291458i
\(429\) 0.103553 + 0.206331i 0.00499959 + 0.00996175i
\(430\) −6.08344 2.29028i −0.293369 0.110447i
\(431\) 8.91750 6.47894i 0.429541 0.312080i −0.351925 0.936028i \(-0.614473\pi\)
0.781465 + 0.623949i \(0.214473\pi\)
\(432\) −12.9936 + 10.1347i −0.625155 + 0.487606i
\(433\) 14.8065 10.7575i 0.711555 0.516975i −0.172120 0.985076i \(-0.555062\pi\)
0.883675 + 0.468101i \(0.155062\pi\)
\(434\) 3.49124 3.87741i 0.167585 0.186122i
\(435\) 0.954173 1.06049i 0.0457491 0.0508467i
\(436\) −10.9876 12.2030i −0.526211 0.584416i
\(437\) −18.1559 3.85916i −0.868515 0.184609i
\(438\) 3.84348 1.44859i 0.183649 0.0692161i
\(439\) 20.6213 4.38319i 0.984200 0.209198i 0.312416 0.949945i \(-0.398862\pi\)
0.671784 + 0.740747i \(0.265528\pi\)
\(440\) 0.307475 1.17786i 0.0146583 0.0561524i
\(441\) 1.70032 + 3.94768i 0.0809678 + 0.187985i
\(442\) −0.461810 + 0.335525i −0.0219661 + 0.0159593i
\(443\) −15.9033 27.5452i −0.755586 1.30871i −0.945082 0.326833i \(-0.894019\pi\)
0.189496 0.981882i \(-0.439315\pi\)
\(444\) −11.5042 + 29.4325i −0.545964 + 1.39680i
\(445\) 0.710777 + 4.30758i 0.0336940 + 0.204199i
\(446\) 1.03918 0.462673i 0.0492066 0.0219082i
\(447\) 19.3657 + 1.13320i 0.915966 + 0.0535983i
\(448\) −11.0839 + 2.35595i −0.523663 + 0.111308i
\(449\) −14.3360 −0.676559 −0.338280 0.941046i \(-0.609845\pi\)
−0.338280 + 0.941046i \(0.609845\pi\)
\(450\) 2.82427 + 4.88358i 0.133137 + 0.230214i
\(451\) −3.23831 −0.152486
\(452\) 30.2718 6.43447i 1.42387 0.302652i
\(453\) 3.29110 5.00091i 0.154629 0.234963i
\(454\) −3.14323 + 1.39945i −0.147519 + 0.0656796i
\(455\) −1.33401 1.31690i −0.0625392 0.0617373i
\(456\) 10.0341 1.52667i 0.469888 0.0714928i
\(457\) −11.2914 19.5574i −0.528191 0.914854i −0.999460 0.0328645i \(-0.989537\pi\)
0.471268 0.881990i \(-0.343796\pi\)
\(458\) −8.96789 + 6.51556i −0.419042 + 0.304452i
\(459\) −19.9590 + 9.71454i −0.931605 + 0.453436i
\(460\) −19.0704 + 1.12287i −0.889160 + 0.0523541i
\(461\) 25.8932 5.50378i 1.20597 0.256337i 0.439277 0.898352i \(-0.355235\pi\)
0.766692 + 0.642015i \(0.221901\pi\)
\(462\) 0.0936675 0.568949i 0.00435780 0.0264699i
\(463\) −5.61991 1.19455i −0.261179 0.0555154i 0.0754608 0.997149i \(-0.475957\pi\)
−0.336640 + 0.941633i \(0.609291\pi\)
\(464\) −0.781622 0.868080i −0.0362859 0.0402996i
\(465\) 11.3787 19.7250i 0.527674 0.914726i
\(466\) 2.05153 2.27846i 0.0950354 0.105547i
\(467\) −14.6975 + 10.6783i −0.680118 + 0.494135i −0.873397 0.487009i \(-0.838088\pi\)
0.193279 + 0.981144i \(0.438088\pi\)
\(468\) −0.827715 + 1.79977i −0.0382611 + 0.0831943i
\(469\) −24.2924 + 17.6494i −1.12172 + 0.814975i
\(470\) −0.309795 0.470369i −0.0142898 0.0216965i
\(471\) −3.04893 0.178410i −0.140487 0.00822071i
\(472\) −15.3734 + 6.84468i −0.707618 + 0.315052i
\(473\) 1.94026 + 2.15488i 0.0892134 + 0.0990816i
\(474\) −6.52525 + 4.18128i −0.299715 + 0.192053i
\(475\) 0.260550 + 20.1882i 0.0119548 + 0.926296i
\(476\) −18.7335 −0.858648
\(477\) 31.8077 9.90835i 1.45637 0.453672i
\(478\) 1.44317 + 1.04852i 0.0660090 + 0.0479583i
\(479\) 0.0346271 0.329455i 0.00158215 0.0150532i −0.993702 0.112052i \(-0.964258\pi\)
0.995284 + 0.0969989i \(0.0309243\pi\)
\(480\) 14.4867 6.45620i 0.661224 0.294684i
\(481\) 0.364571 + 3.46866i 0.0166230 + 0.158157i
\(482\) −4.70591 + 8.15088i −0.214348 + 0.371262i
\(483\) −18.5721 + 2.82572i −0.845061 + 0.128575i
\(484\) 13.5047 14.9985i 0.613852 0.681751i
\(485\) 9.16841 + 23.4315i 0.416316 + 1.06397i
\(486\) 3.34128 4.81744i 0.151564 0.218524i
\(487\) −6.16698 18.9800i −0.279452 0.860066i −0.988007 0.154410i \(-0.950652\pi\)
0.708555 0.705656i \(-0.249348\pi\)
\(488\) 6.28744 6.98291i 0.284619 0.316102i
\(489\) −10.2824 + 10.1579i −0.464985 + 0.459356i
\(490\) −0.196166 1.18884i −0.00886188 0.0537065i
\(491\) −35.3373 7.51118i −1.59475 0.338975i −0.676954 0.736025i \(-0.736701\pi\)
−0.917797 + 0.397050i \(0.870034\pi\)
\(492\) −17.3555 21.7012i −0.782448 0.978364i
\(493\) −0.786756 1.36270i −0.0354337 0.0613730i
\(494\) 0.436519 0.317149i 0.0196399 0.0142692i
\(495\) −0.117316 2.51383i −0.00527296 0.112988i
\(496\) −15.0851 10.9600i −0.677340 0.492117i
\(497\) 0.509741 4.84986i 0.0228650 0.217546i
\(498\) −1.44882 5.54183i −0.0649231 0.248335i
\(499\) −13.7067 + 23.7407i −0.613596 + 1.06278i 0.377033 + 0.926200i \(0.376944\pi\)
−0.990629 + 0.136579i \(0.956389\pi\)
\(500\) 5.76557 + 19.9633i 0.257844 + 0.892788i
\(501\) 16.7814 10.7533i 0.749737 0.480420i
\(502\) −7.60696 + 1.61691i −0.339515 + 0.0721662i
\(503\) −1.33405 0.969242i −0.0594822 0.0432164i 0.557647 0.830078i \(-0.311704\pi\)
−0.617129 + 0.786862i \(0.711704\pi\)
\(504\) 8.95788 5.02739i 0.399016 0.223938i
\(505\) 29.8558 + 19.1158i 1.32857 + 0.850643i
\(506\) −0.592490 0.263794i −0.0263394 0.0117271i
\(507\) −1.03138 22.2742i −0.0458051 0.989230i
\(508\) 1.79768 + 17.1038i 0.0797594 + 0.758860i
\(509\) −24.1747 5.13850i −1.07153 0.227760i −0.361813 0.932251i \(-0.617842\pi\)
−0.709713 + 0.704491i \(0.751176\pi\)
\(510\) 6.08610 1.29595i 0.269497 0.0573857i
\(511\) 14.5523 3.09319i 0.643757 0.136835i
\(512\) −6.85745 21.1051i −0.303059 0.932721i
\(513\) 18.8659 9.18251i 0.832949 0.405418i
\(514\) 0.0464812 0.143054i 0.00205020 0.00630986i
\(515\) −1.97625 + 2.47292i −0.0870839 + 0.108970i
\(516\) −4.04196 + 24.5514i −0.177937 + 1.08082i
\(517\) 0.0262623 + 0.249869i 0.00115502 + 0.0109892i
\(518\) 4.35565 7.54420i 0.191376 0.331473i
\(519\) 19.5989 + 24.5062i 0.860295 + 1.07570i
\(520\) 0.719747 0.900634i 0.0315630 0.0394954i
\(521\) 0.868044 + 0.630671i 0.0380297 + 0.0276302i 0.606638 0.794978i \(-0.292518\pi\)
−0.568608 + 0.822609i \(0.692518\pi\)
\(522\) 0.357355 + 0.212163i 0.0156410 + 0.00928612i
\(523\) −4.86221 + 14.9643i −0.212610 + 0.654345i 0.786705 + 0.617329i \(0.211785\pi\)
−0.999315 + 0.0370160i \(0.988215\pi\)
\(524\) −14.7727 25.5871i −0.645349 1.11778i
\(525\) 7.45270 + 19.0263i 0.325263 + 0.830376i
\(526\) 0.502166 0.869777i 0.0218955 0.0379241i
\(527\) −16.8068 18.6658i −0.732116 0.813097i
\(528\) −2.05712 0.120374i −0.0895247 0.00523859i
\(529\) 0.195459 1.85967i 0.00849823 0.0808553i
\(530\) −9.32295 + 0.548939i −0.404963 + 0.0238444i
\(531\) −26.1346 + 22.9616i −1.13415 + 0.996450i
\(532\) 17.7075 0.767718
\(533\) −2.80176 1.24742i −0.121358 0.0540319i
\(534\) −1.19014 + 0.448557i −0.0515025 + 0.0194110i
\(535\) 15.8393 8.19969i 0.684792 0.354503i
\(536\) −12.3574 13.7242i −0.533757 0.592797i
\(537\) 2.05704 12.4947i 0.0887677 0.539187i
\(538\) 4.72214 5.24447i 0.203586 0.226105i
\(539\) −0.166096 + 0.511190i −0.00715425 + 0.0220185i
\(540\) 16.2174 14.2589i 0.697885 0.613605i
\(541\) 5.82440 + 17.9257i 0.250410 + 0.770684i 0.994699 + 0.102826i \(0.0327886\pi\)
−0.744289 + 0.667858i \(0.767211\pi\)
\(542\) −4.59025 2.04371i −0.197168 0.0877848i
\(543\) −14.8525 7.68203i −0.637384 0.329667i
\(544\) −1.82861 17.3981i −0.0784012 0.745937i
\(545\) 14.0596 + 13.8793i 0.602245 + 0.594523i
\(546\) 0.300204 0.456168i 0.0128475 0.0195222i
\(547\) 0.239907 2.28257i 0.0102577 0.0975955i −0.988195 0.153200i \(-0.951042\pi\)
0.998453 + 0.0556048i \(0.0177087\pi\)
\(548\) 4.02417 12.3851i 0.171904 0.529067i
\(549\) 8.11639 17.6481i 0.346399 0.753203i
\(550\) −0.137755 + 0.691876i −0.00587391 + 0.0295017i
\(551\) 0.743668 + 1.28807i 0.0316813 + 0.0548737i
\(552\) −2.92240 11.1784i −0.124385 0.475782i
\(553\) −25.6443 + 11.4176i −1.09051 + 0.485525i
\(554\) −7.82379 + 3.48337i −0.332401 + 0.147994i
\(555\) 11.7356 36.1632i 0.498149 1.53504i
\(556\) 27.2006 + 12.1105i 1.15356 + 0.513599i
\(557\) 26.8111 1.13602 0.568012 0.823020i \(-0.307713\pi\)
0.568012 + 0.823020i \(0.307713\pi\)
\(558\) 6.28380 + 2.12667i 0.266014 + 0.0900293i
\(559\) 0.848622 + 2.61179i 0.0358929 + 0.110467i
\(560\) 16.1335 4.43473i 0.681764 0.187401i
\(561\) −2.67678 0.734739i −0.113014 0.0310207i
\(562\) 3.30124 + 0.701700i 0.139254 + 0.0295994i
\(563\) −20.7742 4.41570i −0.875529 0.186100i −0.251837 0.967770i \(-0.581035\pi\)
−0.623692 + 0.781670i \(0.714368\pi\)
\(564\) −1.53372 + 1.51515i −0.0645812 + 0.0637995i
\(565\) −35.9027 + 9.86884i −1.51044 + 0.415185i
\(566\) 0.755716 + 2.32586i 0.0317651 + 0.0977630i
\(567\) 14.5894 15.4303i 0.612699 0.648012i
\(568\) 2.99928 0.125847
\(569\) 37.4475 + 16.6727i 1.56988 + 0.698955i 0.993026 0.117893i \(-0.0376140\pi\)
0.576853 + 0.816848i \(0.304281\pi\)
\(570\) −5.75278 + 1.22498i −0.240958 + 0.0513087i
\(571\) 40.3376 17.9594i 1.68807 0.751579i 0.688420 0.725312i \(-0.258305\pi\)
0.999655 0.0262671i \(-0.00836204\pi\)
\(572\) −0.226303 + 0.100757i −0.00946220 + 0.00421284i
\(573\) 21.9010 + 6.01153i 0.914928 + 0.251135i
\(574\) 3.83006 + 6.63386i 0.159864 + 0.276892i
\(575\) 22.8249 2.69723i 0.951865 0.112482i
\(576\) −8.32593 11.7582i −0.346914 0.489923i
\(577\) −1.18692 + 3.65297i −0.0494122 + 0.152075i −0.972718 0.231990i \(-0.925476\pi\)
0.923306 + 0.384065i \(0.125476\pi\)
\(578\) 0.0491159 0.467307i 0.00204295 0.0194374i
\(579\) 29.0490 + 1.69982i 1.20724 + 0.0706421i
\(580\) 1.08937 + 1.07540i 0.0452336 + 0.0446536i
\(581\) −2.16873 20.6340i −0.0899739 0.856044i
\(582\) −6.17171 + 3.95474i −0.255826 + 0.163929i
\(583\) 3.80586 + 1.69448i 0.157623 + 0.0701782i
\(584\) 2.82757 + 8.70237i 0.117006 + 0.360107i
\(585\) 0.866846 2.22013i 0.0358397 0.0917912i
\(586\) 1.99186 6.13031i 0.0822830 0.253241i
\(587\) −26.5121 + 29.4447i −1.09427 + 1.21531i −0.119332 + 0.992854i \(0.538075\pi\)
−0.974942 + 0.222459i \(0.928592\pi\)
\(588\) −4.31586 + 1.62662i −0.177983 + 0.0670807i
\(589\) 15.8863 + 17.6436i 0.654586 + 0.726991i
\(590\) 8.66048 4.48336i 0.356546 0.184577i
\(591\) 3.27080 19.8673i 0.134543 0.817231i
\(592\) −28.4403 12.6624i −1.16889 0.520423i
\(593\) −23.7687 −0.976065 −0.488033 0.872825i \(-0.662285\pi\)
−0.488033 + 0.872825i \(0.662285\pi\)
\(594\) 0.711499 0.176782i 0.0291932 0.00725344i
\(595\) 22.4997 1.32479i 0.922399 0.0543113i
\(596\) −2.17582 + 20.7016i −0.0891252 + 0.847970i
\(597\) 5.73350 + 11.4241i 0.234657 + 0.467556i
\(598\) −0.411002 0.456464i −0.0168071 0.0186662i
\(599\) −21.3498 + 36.9790i −0.872330 + 1.51092i −0.0127494 + 0.999919i \(0.504058\pi\)
−0.859580 + 0.511001i \(0.829275\pi\)
\(600\) −11.1587 + 5.78178i −0.455552 + 0.236040i
\(601\) 15.2463 + 26.4074i 0.621910 + 1.07718i 0.989130 + 0.147045i \(0.0469764\pi\)
−0.367220 + 0.930134i \(0.619690\pi\)
\(602\) 2.11958 6.52338i 0.0863875 0.265873i
\(603\) −32.8282 19.4902i −1.33687 0.793704i
\(604\) 5.19707 + 3.77589i 0.211466 + 0.153639i
\(605\) −15.1591 + 18.9689i −0.616305 + 0.771196i
\(606\) −3.75976 + 9.61904i −0.152730 + 0.390747i
\(607\) 13.5546 23.4772i 0.550163 0.952910i −0.448099 0.893984i \(-0.647899\pi\)
0.998262 0.0589263i \(-0.0187677\pi\)
\(608\) 1.72847 + 16.4453i 0.0700986 + 0.666943i
\(609\) 1.16406 + 0.954429i 0.0471700 + 0.0386754i
\(610\) −3.39948 + 4.25384i −0.137641 + 0.172233i
\(611\) −0.0735297 + 0.226301i −0.00297469 + 0.00915517i
\(612\) −9.42227 21.8759i −0.380873 0.884282i
\(613\) 6.76831 + 20.8307i 0.273370 + 0.841345i 0.989646 + 0.143529i \(0.0458449\pi\)
−0.716277 + 0.697816i \(0.754155\pi\)
\(614\) −8.36797 + 1.77867i −0.337704 + 0.0717811i
\(615\) 22.3794 + 24.8367i 0.902425 + 1.00151i
\(616\) 1.25646 + 0.267069i 0.0506242 + 0.0107605i
\(617\) 2.94074 + 27.9793i 0.118390 + 1.12640i 0.878876 + 0.477050i \(0.158294\pi\)
−0.760486 + 0.649354i \(0.775039\pi\)
\(618\) −0.819126 0.423668i −0.0329501 0.0170424i
\(619\) −33.5139 14.9214i −1.34704 0.599740i −0.398723 0.917071i \(-0.630546\pi\)
−0.948315 + 0.317332i \(0.897213\pi\)
\(620\) 20.5782 + 13.1757i 0.826442 + 0.529148i
\(621\) −12.6408 20.2663i −0.507259 0.813257i
\(622\) 4.37705 + 3.18011i 0.175504 + 0.127511i
\(623\) −4.50616 + 0.957813i −0.180535 + 0.0383740i
\(624\) −1.73343 0.896566i −0.0693929 0.0358914i
\(625\) −8.33647 23.5691i −0.333459 0.942765i
\(626\) 0.486357 0.842395i 0.0194387 0.0336689i
\(627\) 2.53018 + 0.694500i 0.101046 + 0.0277357i
\(628\) 0.342562 3.25926i 0.0136697 0.130059i
\(629\) −33.9270 24.6494i −1.35276 0.982837i
\(630\) −5.01096 + 3.21351i −0.199641 + 0.128029i
\(631\) −9.47939 + 6.88718i −0.377369 + 0.274174i −0.760260 0.649619i \(-0.774928\pi\)
0.382891 + 0.923793i \(0.374928\pi\)
\(632\) −8.63244 14.9518i −0.343380 0.594752i
\(633\) −7.00610 + 17.9245i −0.278467 + 0.712436i
\(634\) 5.70708 + 1.21308i 0.226657 + 0.0481775i
\(635\) −3.36865 20.4153i −0.133681 0.810157i
\(636\) 9.04194 + 34.5860i 0.358536 + 1.37142i
\(637\) −0.340619 + 0.378296i −0.0134958 + 0.0149886i
\(638\) 0.0160594 + 0.0494257i 0.000635797 + 0.00195678i
\(639\) 5.91978 1.84406i 0.234183 0.0729499i
\(640\) 8.14493 + 20.8158i 0.321957 + 0.822817i
\(641\) −18.9229 + 21.0160i −0.747410 + 0.830083i −0.990150 0.140009i \(-0.955287\pi\)
0.242741 + 0.970091i \(0.421954\pi\)
\(642\) 3.24529 + 4.05788i 0.128082 + 0.160152i
\(643\) −24.9228 + 43.1676i −0.982861 + 1.70237i −0.331780 + 0.943357i \(0.607649\pi\)
−0.651081 + 0.759009i \(0.725684\pi\)
\(644\) −2.10707 20.0475i −0.0830303 0.789981i
\(645\) 3.11834 29.7732i 0.122785 1.17232i
\(646\) −0.678141 + 6.45208i −0.0266811 + 0.253854i
\(647\) −36.4560 26.4868i −1.43323 1.04131i −0.989403 0.145194i \(-0.953619\pi\)
−0.443830 0.896111i \(-0.646381\pi\)
\(648\) 10.3762 + 7.93192i 0.407616 + 0.311595i
\(649\) −4.35029 −0.170764
\(650\) −0.385701 + 0.545540i −0.0151284 + 0.0213979i
\(651\) 21.3429 + 11.0390i 0.836495 + 0.432652i
\(652\) −10.3778 11.5257i −0.406426 0.451381i
\(653\) 39.5029 17.5878i 1.54587 0.688265i 0.556123 0.831100i \(-0.312288\pi\)
0.989747 + 0.142835i \(0.0456217\pi\)
\(654\) −3.16395 + 4.80772i −0.123720 + 0.187997i
\(655\) 19.5521 + 29.6865i 0.763965 + 1.15995i
\(656\) 22.1470 16.0907i 0.864694 0.628237i
\(657\) 10.9314 + 15.4376i 0.426473 + 0.602280i
\(658\) 0.480809 0.349328i 0.0187439 0.0136182i
\(659\) −22.7712 + 25.2900i −0.887039 + 0.985157i −0.999964 0.00844655i \(-0.997311\pi\)
0.112925 + 0.993604i \(0.463978\pi\)
\(660\) 2.70036 0.000981808i 0.105111 3.82168e-5i
\(661\) −2.00144 2.22282i −0.0778469 0.0864577i 0.702963 0.711226i \(-0.251860\pi\)
−0.780810 + 0.624769i \(0.785193\pi\)
\(662\) 3.18734 + 0.677491i 0.123880 + 0.0263314i
\(663\) −2.03290 1.66681i −0.0789513 0.0647334i
\(664\) 12.4818 2.65309i 0.484388 0.102960i
\(665\) −21.2675 + 1.25224i −0.824718 + 0.0485598i
\(666\) 11.0004 + 1.29182i 0.426258 + 0.0500569i
\(667\) 1.36979 0.995212i 0.0530385 0.0385347i
\(668\) 10.6934 + 18.5215i 0.413739 + 0.716617i
\(669\) 3.27196 + 4.09123i 0.126501 + 0.158176i
\(670\) 7.61632 + 7.51865i 0.294244 + 0.290471i
\(671\) 2.21908 0.987996i 0.0856665 0.0381412i
\(672\) 7.50691 + 14.9576i 0.289585 + 0.577002i
\(673\) 6.93118 1.47327i 0.267178 0.0567903i −0.0723748 0.997378i \(-0.523058\pi\)
0.339552 + 0.940587i \(0.389724\pi\)
\(674\) 6.20994 0.239198
\(675\) −18.4694 + 18.2724i −0.710888 + 0.703305i
\(676\) 23.9266 0.920253
\(677\) 35.2596 7.49466i 1.35514 0.288043i 0.527618 0.849482i \(-0.323085\pi\)
0.827519 + 0.561438i \(0.189752\pi\)
\(678\) −4.86559 9.69474i −0.186862 0.372324i
\(679\) −24.2549 + 10.7990i −0.930817 + 0.414426i
\(680\) 2.25682 + 13.6772i 0.0865453 + 0.524498i
\(681\) −9.89676 12.3748i −0.379245 0.474203i
\(682\) 0.414783 + 0.718424i 0.0158828 + 0.0275099i
\(683\) 21.8805 15.8971i 0.837236 0.608287i −0.0843615 0.996435i \(-0.526885\pi\)
0.921597 + 0.388148i \(0.126885\pi\)
\(684\) 8.90625 + 20.6779i 0.340539 + 0.790637i
\(685\) −3.95736 + 15.1597i −0.151203 + 0.579221i
\(686\) 7.31969 1.55585i 0.279467 0.0594026i
\(687\) −39.4769 32.3677i −1.50614 1.23491i
\(688\) −23.9769 5.09644i −0.914110 0.194300i
\(689\) 2.64007 + 2.93210i 0.100579 + 0.111704i
\(690\) 2.07139 + 6.36722i 0.0788566 + 0.242396i
\(691\) −8.47233 + 9.40948i −0.322303 + 0.357953i −0.882422 0.470458i \(-0.844089\pi\)
0.560119 + 0.828412i \(0.310755\pi\)
\(692\) −27.2406 + 19.7915i −1.03553 + 0.752359i
\(693\) 2.64412 0.245392i 0.100442 0.00932166i
\(694\) 0.170830 0.124115i 0.00648462 0.00471135i
\(695\) −33.5255 12.6216i −1.27169 0.478766i
\(696\) −0.508960 + 0.773379i −0.0192921 + 0.0293148i
\(697\) 33.6877 14.9987i 1.27601 0.568117i
\(698\) −9.05514 10.0568i −0.342742 0.380654i
\(699\) 12.5416 + 6.48675i 0.474367 + 0.245352i
\(700\) −20.7639 + 7.04413i −0.784803 + 0.266243i
\(701\) 38.2015 1.44285 0.721426 0.692492i \(-0.243487\pi\)
0.721426 + 0.692492i \(0.243487\pi\)
\(702\) 0.683680 + 0.121125i 0.0258038 + 0.00457157i
\(703\) 32.0690 + 23.2995i 1.20950 + 0.878756i
\(704\) 0.188323 1.79177i 0.00709768 0.0675299i
\(705\) 1.73491 1.92823i 0.0653406 0.0726212i
\(706\) 0.517730 + 4.92587i 0.0194850 + 0.185388i
\(707\) −18.7040 + 32.3963i −0.703437 + 1.21839i
\(708\) −23.3151 29.1530i −0.876237 1.09564i
\(709\) 26.4187 29.3409i 0.992175 1.10192i −0.00261676 0.999997i \(-0.500833\pi\)
0.994792 0.101926i \(-0.0325004\pi\)
\(710\) −1.73511 + 0.102164i −0.0651175 + 0.00383415i
\(711\) −26.2310 24.2034i −0.983739 0.907697i
\(712\) −0.875563 2.69470i −0.0328131 0.100988i
\(713\) 18.0847 20.0851i 0.677278 0.752194i
\(714\) 1.66076 + 6.35253i 0.0621525 + 0.237737i
\(715\) 0.264674 0.137017i 0.00989826 0.00512413i
\(716\) 13.2908 + 2.82506i 0.496702 + 0.105577i
\(717\) −2.99073 + 7.65154i −0.111691 + 0.285752i
\(718\) 6.98185 + 12.0929i 0.260560 + 0.451304i
\(719\) 8.24606 5.99111i 0.307526 0.223431i −0.423308 0.905986i \(-0.639131\pi\)
0.730834 + 0.682555i \(0.239131\pi\)
\(720\) 13.2932 + 16.6093i 0.495408 + 0.618991i
\(721\) −2.70238 1.96339i −0.100642 0.0731205i
\(722\) −0.105940 + 1.00795i −0.00394269 + 0.0375122i
\(723\) −41.7987 11.4732i −1.55451 0.426691i
\(724\) 8.97143 15.5390i 0.333421 0.577501i
\(725\) −1.38443 1.21457i −0.0514165 0.0451078i
\(726\) −6.28323 3.24981i −0.233192 0.120612i
\(727\) −26.9467 + 5.72770i −0.999399 + 0.212429i −0.678433 0.734662i \(-0.737341\pi\)
−0.320966 + 0.947091i \(0.604007\pi\)
\(728\) 0.984202 + 0.715064i 0.0364769 + 0.0265020i
\(729\) 25.3566 + 9.27584i 0.939135 + 0.343549i
\(730\) −1.93220 4.93807i −0.0715139 0.182766i
\(731\) −30.1649 13.4303i −1.11569 0.496737i
\(732\) 18.5139 + 9.57577i 0.684295 + 0.353931i
\(733\) −0.396743 3.77476i −0.0146540 0.139424i 0.984749 0.173983i \(-0.0556639\pi\)
−0.999403 + 0.0345595i \(0.988997\pi\)
\(734\) 9.45761 + 2.01028i 0.349087 + 0.0742007i
\(735\) 5.06850 2.25885i 0.186955 0.0833190i
\(736\) 18.4127 3.91375i 0.678703 0.144263i
\(737\) −1.47529 4.54046i −0.0543428 0.167250i
\(738\) −5.82027 + 7.80912i −0.214247 + 0.287458i
\(739\) −6.92487 + 21.3125i −0.254735 + 0.783995i 0.739146 + 0.673545i \(0.235229\pi\)
−0.993882 + 0.110450i \(0.964771\pi\)
\(740\) 38.1804 + 14.3741i 1.40354 + 0.528403i
\(741\) 1.92156 + 1.57552i 0.0705904 + 0.0578782i
\(742\) −1.03009 9.80063i −0.0378157 0.359792i
\(743\) 0.543224 0.940891i 0.0199289 0.0345179i −0.855889 0.517160i \(-0.826989\pi\)
0.875818 + 0.482642i \(0.160323\pi\)
\(744\) −5.38009 + 13.7645i −0.197244 + 0.504632i
\(745\) 1.14929 25.0174i 0.0421066 0.916566i
\(746\) −1.41619 1.02892i −0.0518505 0.0376716i
\(747\) 23.0045 12.9107i 0.841691 0.472378i
\(748\) 0.920413 2.83274i 0.0336536 0.103575i
\(749\) 9.41020 + 16.2990i 0.343841 + 0.595551i
\(750\) 6.25845 3.72490i 0.228526 0.136014i
\(751\) −7.82702 + 13.5568i −0.285612 + 0.494694i −0.972757 0.231826i \(-0.925530\pi\)
0.687145 + 0.726520i \(0.258863\pi\)
\(752\) −1.42118 1.57838i −0.0518249 0.0575574i
\(753\) −16.0652 32.0101i −0.585448 1.16651i
\(754\) −0.00514473 + 0.0489489i −0.000187360 + 0.00178261i
\(755\) −6.50893 4.16748i −0.236884 0.151670i
\(756\) 15.8154 + 16.4041i 0.575202 + 0.596610i
\(757\) −8.77489 −0.318929 −0.159464 0.987204i \(-0.550977\pi\)
−0.159464 + 0.987204i \(0.550977\pi\)
\(758\) 8.70165 + 3.87422i 0.316058 + 0.140718i
\(759\) 0.485200 2.94717i 0.0176117 0.106976i
\(760\) −2.13323 12.9282i −0.0773803 0.468955i
\(761\) −12.7460 14.1558i −0.462041 0.513149i 0.466427 0.884560i \(-0.345541\pi\)
−0.928469 + 0.371411i \(0.878874\pi\)
\(762\) 5.64054 2.12589i 0.204335 0.0770127i
\(763\) −13.9492 + 15.4921i −0.504993 + 0.560852i
\(764\) −7.53068 + 23.1771i −0.272450 + 0.838516i
\(765\) 12.8636 + 25.6076i 0.465084 + 0.925845i
\(766\) −0.792465 2.43896i −0.0286329 0.0881231i
\(767\) −3.76384 1.67577i −0.135904 0.0605085i
\(768\) 8.52455 5.46240i 0.307603 0.197107i
\(769\) −2.89450 27.5393i −0.104378 0.993094i −0.913882 0.405979i \(-0.866930\pi\)
0.809504 0.587115i \(-0.199736\pi\)
\(770\) −0.735969 0.111703i −0.0265225 0.00402549i
\(771\) 0.691536 + 0.0404656i 0.0249051 + 0.00145733i
\(772\) −3.26379 + 31.0529i −0.117466 + 1.11762i
\(773\) 4.15971 12.8023i 0.149615 0.460466i −0.847961 0.530059i \(-0.822170\pi\)
0.997576 + 0.0695925i \(0.0221699\pi\)
\(774\) 8.68372 0.805907i 0.312130 0.0289677i
\(775\) −25.6471 14.3693i −0.921272 0.516161i
\(776\) −8.16473 14.1417i −0.293097 0.507659i
\(777\) 38.6875 + 10.6192i 1.38791 + 0.380962i
\(778\) 0.763226 0.339810i 0.0273630 0.0121828i
\(779\) −31.8427 + 14.1773i −1.14088 + 0.507954i
\(780\) 2.33671 + 1.03935i 0.0836676 + 0.0372148i
\(781\) 0.708315 + 0.315362i 0.0253455 + 0.0112846i
\(782\) 7.38538 0.264101
\(783\) −0.529050 + 1.83937i −0.0189067 + 0.0657336i
\(784\) −1.40410 4.32136i −0.0501463 0.154334i
\(785\) −0.180944 + 3.93874i −0.00645815 + 0.140580i
\(786\) −7.36696 + 7.27778i −0.262771 + 0.259590i
\(787\) 11.0803 + 2.35520i 0.394972 + 0.0839538i 0.401116 0.916027i \(-0.368622\pi\)
−0.00614432 + 0.999981i \(0.501956\pi\)
\(788\) 21.1331 + 4.49199i 0.752837 + 0.160020i
\(789\) 4.46032 + 1.22430i 0.158792 + 0.0435861i
\(790\) 5.50324 + 8.35570i 0.195796 + 0.297283i
\(791\) −12.1412 37.3667i −0.431691 1.32861i
\(792\) 0.320087 + 1.60155i 0.0113738 + 0.0569086i
\(793\) 2.30051 0.0816935
\(794\) −7.97811 3.55208i −0.283132 0.126059i
\(795\) −13.3056 40.8999i −0.471902 1.45057i
\(796\) −12.5299 + 5.57866i −0.444110 + 0.197730i
\(797\) −3.70507 + 1.64960i −0.131240 + 0.0584320i −0.471306 0.881970i \(-0.656217\pi\)
0.340066 + 0.940402i \(0.389551\pi\)
\(798\) −1.56981 6.00462i −0.0555706 0.212561i
\(799\) −1.43051 2.47772i −0.0506078 0.0876553i
\(800\) −8.56881 18.5962i −0.302953 0.657476i
\(801\) −3.38492 4.78029i −0.119600 0.168903i
\(802\) 1.79471 5.52354i 0.0633733 0.195043i
\(803\) −0.247255 + 2.35247i −0.00872543 + 0.0830169i
\(804\) 22.5207 34.2208i 0.794243 1.20687i
\(805\) 3.94840 + 23.9289i 0.139163 + 0.843382i
\(806\) 0.0821234 + 0.781352i 0.00289267 + 0.0275220i
\(807\) 28.8678 + 14.9310i 1.01619 + 0.525596i
\(808\) −21.0183 9.35797i −0.739423 0.329212i
\(809\) 1.08629 + 3.34324i 0.0381918 + 0.117542i 0.968335 0.249655i \(-0.0803173\pi\)
−0.930143 + 0.367198i \(0.880317\pi\)
\(810\) −6.27290 4.23524i −0.220407 0.148811i
\(811\) 13.6058 41.8744i 0.477765 1.47041i −0.364428 0.931232i \(-0.618735\pi\)
0.842193 0.539177i \(-0.181265\pi\)
\(812\) −1.08082 + 1.20037i −0.0379292 + 0.0421246i
\(813\) 3.75903 22.8329i 0.131835 0.800784i
\(814\) 0.926777 + 1.02929i 0.0324835 + 0.0360766i
\(815\) 13.2793 + 13.1090i 0.465152 + 0.459187i
\(816\) 21.9575 8.27563i 0.768665 0.289705i
\(817\) 28.5129 + 12.6948i 0.997540 + 0.444133i
\(818\) 10.1905 0.356302
\(819\) 2.38219 + 0.806224i 0.0832406 + 0.0281717i
\(820\) −27.7329 + 22.7555i −0.968474 + 0.794657i
\(821\) −1.84739 + 17.5767i −0.0644744 + 0.613433i 0.913807 + 0.406150i \(0.133129\pi\)
−0.978281 + 0.207283i \(0.933538\pi\)
\(822\) −4.55655 0.266629i −0.158928 0.00929977i
\(823\) 21.4671 + 23.8416i 0.748295 + 0.831066i 0.990262 0.139219i \(-0.0444591\pi\)
−0.241967 + 0.970285i \(0.577792\pi\)
\(824\) 1.02721 1.77919i 0.0357847 0.0619809i
\(825\) −3.24318 + 0.192143i −0.112913 + 0.00668957i
\(826\) 5.14524 + 8.91181i 0.179026 + 0.310082i
\(827\) −14.6544 + 45.1017i −0.509584 + 1.56834i 0.283341 + 0.959019i \(0.408557\pi\)
−0.792925 + 0.609320i \(0.791443\pi\)
\(828\) 22.3505 12.5437i 0.776735 0.435923i
\(829\) −1.12381 0.816496i −0.0390315 0.0283581i 0.568098 0.822961i \(-0.307679\pi\)
−0.607130 + 0.794603i \(0.707679\pi\)
\(830\) −7.13045 + 1.96000i −0.247501 + 0.0680325i
\(831\) −24.6340 30.8021i −0.854544 1.06851i
\(832\) 0.853140 1.47768i 0.0295773 0.0512294i
\(833\) −0.639783 6.08713i −0.0221672 0.210907i
\(834\) 1.69528 10.2973i 0.0587026 0.356568i
\(835\) −14.1530 21.4889i −0.489785 0.743653i
\(836\) −0.870005 + 2.67760i −0.0300897 + 0.0926067i
\(837\) −2.15597 + 30.4753i −0.0745212 + 1.05338i
\(838\) −1.87197 5.76132i −0.0646660 0.199021i
\(839\) −26.8889 + 5.71541i −0.928307 + 0.197318i −0.647166 0.762349i \(-0.724046\pi\)
−0.281141 + 0.959667i \(0.590713\pi\)
\(840\) −6.63486 11.4823i −0.228924 0.396176i
\(841\) 28.2336 + 6.00123i 0.973571 + 0.206939i
\(842\) 0.670757 + 6.38183i 0.0231158 + 0.219932i
\(843\) 0.718930 + 15.5264i 0.0247613 + 0.534756i
\(844\) −18.8653 8.39939i −0.649371 0.289119i
\(845\) −28.7369 + 1.69204i −0.988578 + 0.0582079i
\(846\) 0.649756 + 0.385763i 0.0223391 + 0.0132628i
\(847\) −20.7290 15.0605i −0.712256 0.517484i
\(848\) −34.4481 + 7.32218i −1.18295 + 0.251445i
\(849\) −9.48278 + 6.07642i −0.325448 + 0.208542i
\(850\) −1.77148 7.83552i −0.0607611 0.268756i
\(851\) 22.5624 39.0792i 0.773428 1.33962i
\(852\) 1.68281 + 6.43686i 0.0576521 + 0.220523i
\(853\) 0.747701 7.11390i 0.0256008 0.243575i −0.974236 0.225529i \(-0.927589\pi\)
0.999837 0.0180460i \(-0.00574452\pi\)
\(854\) −4.64854 3.37736i −0.159070 0.115571i
\(855\) −12.1591 24.2052i −0.415832 0.827799i
\(856\) −9.36461 + 6.80379i −0.320076 + 0.232549i
\(857\) 4.13554 + 7.16297i 0.141267 + 0.244682i 0.927974 0.372645i \(-0.121549\pi\)
−0.786707 + 0.617327i \(0.788216\pi\)
\(858\) 0.0542288 + 0.0678071i 0.00185134 + 0.00231490i
\(859\) −22.2616 4.73184i −0.759555 0.161448i −0.188177 0.982135i \(-0.560258\pi\)
−0.571378 + 0.820687i \(0.693591\pi\)
\(860\) 31.7587 + 4.82022i 1.08296 + 0.164368i
\(861\) −25.0964 + 24.7926i −0.855282 + 0.844929i
\(862\) 2.77393 3.08076i 0.0944803 0.104931i
\(863\) −6.39640 19.6861i −0.217736 0.670123i −0.998948 0.0458569i \(-0.985398\pi\)
0.781212 0.624266i \(-0.214602\pi\)
\(864\) −13.6910 + 16.2893i −0.465776 + 0.554173i
\(865\) 31.3176 25.6968i 1.06483 0.873718i
\(866\) 4.60579 5.11525i 0.156511 0.173823i
\(867\) 2.13934 0.325498i 0.0726559 0.0110545i
\(868\) −12.8918 + 22.3293i −0.437577 + 0.757906i
\(869\) −0.466527 4.43871i −0.0158259 0.150573i
\(870\) 0.268094 0.464742i 0.00908923 0.0157562i
\(871\) 0.472618 4.49666i 0.0160141 0.152364i
\(872\) −10.3728 7.53631i −0.351269 0.255212i
\(873\) −24.8098 22.8920i −0.839684 0.774777i
\(874\) −6.98091 −0.236133
\(875\) 24.4402 9.92869i 0.826231 0.335651i
\(876\) −17.0900 + 10.9510i −0.577416 + 0.369999i
\(877\) 7.92995 + 8.80710i 0.267775 + 0.297395i 0.862004 0.506902i \(-0.169209\pi\)
−0.594229 + 0.804296i \(0.702543\pi\)
\(878\) 7.24336 3.22495i 0.244452 0.108837i
\(879\) 29.6344 + 1.73408i 0.999544 + 0.0584889i
\(880\) −0.122083 + 2.65747i −0.00411541 + 0.0895834i
\(881\) 0.952966 0.692370i 0.0321062 0.0233265i −0.571616 0.820521i \(-0.693683\pi\)
0.603723 + 0.797194i \(0.293683\pi\)
\(882\) 0.934198 + 1.31931i 0.0314561 + 0.0444233i
\(883\) −5.30098 + 3.85139i −0.178392 + 0.129609i −0.673398 0.739280i \(-0.735166\pi\)
0.495006 + 0.868890i \(0.335166\pi\)
\(884\) 1.88753 2.09631i 0.0634844 0.0705066i
\(885\) 30.0641 + 33.3652i 1.01060 + 1.12156i
\(886\) −8.00434 8.88972i −0.268911 0.298656i
\(887\) 52.1642 + 11.0878i 1.75150 + 0.372293i 0.968362 0.249551i \(-0.0802830\pi\)
0.783141 + 0.621844i \(0.213616\pi\)
\(888\) −4.00826 + 24.3467i −0.134508 + 0.817022i
\(889\) 21.3564 4.53945i 0.716271 0.152248i
\(890\) 0.598309 + 1.52908i 0.0200554 + 0.0512550i
\(891\) 1.61645 + 2.96423i 0.0541532 + 0.0993054i
\(892\) −4.54773 + 3.30412i −0.152269 + 0.110630i
\(893\) 1.35217 + 2.34202i 0.0452485 + 0.0783727i
\(894\) 7.21281 1.09742i 0.241232 0.0367031i
\(895\) −16.1627 2.45311i −0.540258 0.0819985i
\(896\) −21.5473 + 9.59347i −0.719845 + 0.320495i
\(897\) 1.55507 2.36297i 0.0519221 0.0788971i
\(898\) −5.27390 + 1.12100i −0.175992 + 0.0374083i
\(899\) −2.16569 −0.0722298
\(900\) −18.6693 20.7040i −0.622309 0.690134i
\(901\) −47.4401 −1.58046
\(902\) −1.19130 + 0.253219i −0.0396660 + 0.00843127i
\(903\) 31.5345 + 1.84526i 1.04940 + 0.0614065i
\(904\) 22.0756 9.82868i 0.734223 0.326897i
\(905\) −9.67620 + 19.2974i −0.321648 + 0.641468i
\(906\) 0.819674 2.09707i 0.0272319 0.0696704i
\(907\) −23.7125 41.0712i −0.787360 1.36375i −0.927579 0.373626i \(-0.878114\pi\)
0.140220 0.990120i \(-0.455219\pi\)
\(908\) 13.7556 9.99402i 0.456495 0.331663i
\(909\) −47.2381 5.54733i −1.56679 0.183993i
\(910\) −0.593725 0.380146i −0.0196818 0.0126017i
\(911\) 9.88100 2.10027i 0.327372 0.0695851i −0.0412938 0.999147i \(-0.513148\pi\)
0.368666 + 0.929562i \(0.379815\pi\)
\(912\) −20.7549 + 7.82240i −0.687264 + 0.259026i
\(913\) 3.22668 + 0.685852i 0.106788 + 0.0226984i
\(914\) −5.68315 6.31177i −0.187982 0.208775i
\(915\) −22.9132 10.1916i −0.757488 0.336925i
\(916\) 36.6539 40.7083i 1.21108 1.34504i
\(917\) −30.3454 + 22.0472i −1.00209 + 0.728064i
\(918\) −6.58283 + 5.13444i −0.217266 + 0.169462i
\(919\) 16.4085 11.9215i 0.541266 0.393253i −0.283289 0.959035i \(-0.591426\pi\)
0.824555 + 0.565782i \(0.191426\pi\)
\(920\) −14.3827 + 3.95349i −0.474185 + 0.130343i
\(921\) −17.6724 35.2124i −0.582325 1.16029i
\(922\) 9.09517 4.04943i 0.299533 0.133361i
\(923\) 0.491348 + 0.545697i 0.0161729 + 0.0179619i
\(924\) 0.131798 + 2.84637i 0.00433584 + 0.0936388i
\(925\) −46.8729 14.5639i −1.54117 0.478858i
\(926\) −2.16084 −0.0710097
\(927\) 0.933540 4.14320i 0.0306615 0.136081i
\(928\) −1.22030 0.886601i −0.0400584 0.0291041i
\(929\) 3.77311 35.8988i 0.123792 1.17780i −0.739522 0.673133i \(-0.764948\pi\)
0.863314 0.504668i \(-0.168385\pi\)
\(930\) 2.64357 8.14614i 0.0866860 0.267123i
\(931\) 0.604744 + 5.75376i 0.0198197 + 0.188572i
\(932\) −7.57554 + 13.1212i −0.248145 + 0.429800i
\(933\) −9.07072 + 23.2067i −0.296962 + 0.759753i
\(934\) −4.57188 + 5.07758i −0.149596 + 0.166144i
\(935\) −0.905130 + 3.46733i −0.0296009 + 0.113394i
\(936\) −0.339994 + 1.50895i −0.0111131 + 0.0493215i
\(937\) −2.52174 7.76113i −0.0823818 0.253545i 0.901379 0.433032i \(-0.142556\pi\)
−0.983760 + 0.179487i \(0.942556\pi\)
\(938\) −7.55651 + 8.39236i −0.246729 + 0.274020i
\(939\) 4.31990 + 1.18575i 0.140975 + 0.0386956i
\(940\) 1.98073 + 1.95533i 0.0646044 + 0.0637760i
\(941\) 48.6857 + 10.3485i 1.58711 + 0.337350i 0.915111 0.403203i \(-0.132103\pi\)
0.671998 + 0.740553i \(0.265437\pi\)
\(942\) −1.13558 + 0.172778i −0.0369993 + 0.00562940i
\(943\) 19.8398 + 34.3636i 0.646073 + 1.11903i
\(944\) 29.7519 21.6160i 0.968342 0.703541i
\(945\) −20.1551 18.5836i −0.655645 0.604524i
\(946\) 0.882279 + 0.641013i 0.0286854 + 0.0208411i
\(947\) 0.803938 7.64896i 0.0261245 0.248558i −0.973664 0.227988i \(-0.926785\pi\)
0.999788 0.0205697i \(-0.00654801\pi\)
\(948\) 27.2452 26.9154i 0.884882 0.874171i
\(949\) −1.12011 + 1.94009i −0.0363604 + 0.0629781i
\(950\) 1.67446 + 7.40639i 0.0543266 + 0.240295i
\(951\) 1.24286 + 26.8415i 0.0403027 + 0.870395i
\(952\) −14.3077 + 3.04120i −0.463716 + 0.0985660i
\(953\) 8.32277 + 6.04685i 0.269601 + 0.195877i 0.714369 0.699769i \(-0.246714\pi\)
−0.444768 + 0.895646i \(0.646714\pi\)
\(954\) 10.9265 6.13225i 0.353760 0.198539i
\(955\) 7.40564 28.3692i 0.239641 0.918006i
\(956\) −8.05314 3.58549i −0.260457 0.115963i
\(957\) −0.201514 + 0.129127i −0.00651403 + 0.00417409i
\(958\) −0.0130231 0.123907i −0.000420758 0.00400324i
\(959\) −16.1713 3.43731i −0.522197 0.110996i
\(960\) −15.0437 + 10.9383i −0.485534 + 0.353031i
\(961\) −3.49208 + 0.742264i −0.112648 + 0.0239440i
\(962\) 0.405349 + 1.24753i 0.0130690 + 0.0402221i
\(963\) −14.3000 + 19.1865i −0.460812 + 0.618277i
\(964\) 14.3725 44.2340i 0.462907 1.42468i
\(965\) 1.72396 37.5267i 0.0554961 1.20803i
\(966\) −6.61131 + 2.49176i −0.212715 + 0.0801711i
\(967\) 1.88470 + 17.9317i 0.0606077 + 0.576644i 0.982115 + 0.188283i \(0.0602921\pi\)
−0.921507 + 0.388361i \(0.873041\pi\)
\(968\) 7.87940 13.6475i 0.253254 0.438648i
\(969\) −29.5378 + 4.49413i −0.948890 + 0.144372i
\(970\) 5.20507 + 7.90299i 0.167125 + 0.253750i
\(971\) 21.6172 + 15.7058i 0.693730 + 0.504025i 0.877884 0.478873i \(-0.158954\pi\)
−0.184154 + 0.982897i \(0.558954\pi\)
\(972\) −11.2012 + 26.7191i −0.359277 + 0.857014i
\(973\) 11.6809 35.9500i 0.374472 1.15251i
\(974\) −3.75283 6.50008i −0.120248 0.208276i
\(975\) −2.87999 1.08306i −0.0922335 0.0346857i
\(976\) −10.2672 + 17.7832i −0.328644 + 0.569228i
\(977\) −16.6448 18.4859i −0.532513 0.591416i 0.415521 0.909583i \(-0.363599\pi\)
−0.948034 + 0.318168i \(0.896932\pi\)
\(978\) −2.98836 + 4.54089i −0.0955571 + 0.145202i
\(979\) 0.0765629 0.728447i 0.00244696 0.0232813i
\(980\) 2.16967 + 5.54498i 0.0693076 + 0.177128i
\(981\) −25.1068 8.49707i −0.801597 0.271291i
\(982\) −13.5871 −0.433583
\(983\) −31.5050 14.0269i −1.00485 0.447390i −0.162728 0.986671i \(-0.552029\pi\)
−0.842126 + 0.539281i \(0.818696\pi\)
\(984\) −16.7783 13.7568i −0.534873 0.438551i
\(985\) −25.6995 3.90058i −0.818854 0.124283i
\(986\) −0.395986 0.439787i −0.0126108 0.0140057i
\(987\) 2.11653 + 1.73538i 0.0673700 + 0.0552377i
\(988\) −1.78415 + 1.98150i −0.0567615 + 0.0630400i
\(989\) 10.9795 33.7913i 0.349127 1.07450i
\(990\) −0.239726 0.915607i −0.00761899 0.0290999i
\(991\) −1.92211 5.91566i −0.0610580 0.187917i 0.915875 0.401464i \(-0.131498\pi\)
−0.976933 + 0.213547i \(0.931498\pi\)
\(992\) −21.9960 9.79326i −0.698374 0.310936i
\(993\) 0.694126 + 14.9907i 0.0220274 + 0.475715i
\(994\) −0.191711 1.82401i −0.00608071 0.0578541i
\(995\) 14.6544 7.58630i 0.464576 0.240502i
\(996\) 12.6970 + 25.2990i 0.402321 + 0.801630i
\(997\) 0.848789 8.07569i 0.0268814 0.255760i −0.972825 0.231541i \(-0.925623\pi\)
0.999707 0.0242190i \(-0.00770992\pi\)
\(998\) −3.18598 + 9.80545i −0.100851 + 0.310386i
\(999\) 7.05795 + 50.5183i 0.223304 + 1.59833i
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 225.2.q.a.121.17 yes 224
3.2 odd 2 675.2.r.a.496.12 224
9.2 odd 6 675.2.r.a.46.17 224
9.7 even 3 inner 225.2.q.a.196.12 yes 224
25.6 even 5 inner 225.2.q.a.31.12 224
75.56 odd 10 675.2.r.a.631.17 224
225.56 odd 30 675.2.r.a.181.12 224
225.106 even 15 inner 225.2.q.a.106.17 yes 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.q.a.31.12 224 25.6 even 5 inner
225.2.q.a.106.17 yes 224 225.106 even 15 inner
225.2.q.a.121.17 yes 224 1.1 even 1 trivial
225.2.q.a.196.12 yes 224 9.7 even 3 inner
675.2.r.a.46.17 224 9.2 odd 6
675.2.r.a.181.12 224 225.56 odd 30
675.2.r.a.496.12 224 3.2 odd 2
675.2.r.a.631.17 224 75.56 odd 10