Properties

Label 630.2.t.c.551.2
Level $630$
Weight $2$
Character 630.551
Analytic conductor $5.031$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [630,2,Mod(311,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.311");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.t (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 551.2
Character \(\chi\) \(=\) 630.551
Dual form 630.2.t.c.311.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-1.35238 + 1.08216i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(0.630115 - 1.61337i) q^{6} +(-1.80382 - 1.93552i) q^{7} +1.00000i q^{8} +(0.657860 - 2.92698i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-1.35238 + 1.08216i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(0.630115 - 1.61337i) q^{6} +(-1.80382 - 1.93552i) q^{7} +1.00000i q^{8} +(0.657860 - 2.92698i) q^{9} +(-0.866025 + 0.500000i) q^{10} +0.781517i q^{11} +(0.260988 + 1.71227i) q^{12} +(-2.26905 + 1.31003i) q^{13} +(2.52991 + 0.774302i) q^{14} +(-1.35238 + 1.08216i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.02795 + 5.24457i) q^{17} +(0.893768 + 2.86377i) q^{18} +(6.09668 + 3.51992i) q^{19} +(0.500000 - 0.866025i) q^{20} +(4.53399 + 0.665540i) q^{21} +(-0.390758 - 0.676813i) q^{22} -4.60919i q^{23} +(-1.08216 - 1.35238i) q^{24} +1.00000 q^{25} +(1.31003 - 2.26905i) q^{26} +(2.27779 + 4.67030i) q^{27} +(-2.57812 + 0.594391i) q^{28} +(3.96237 + 2.28767i) q^{29} +(0.630115 - 1.61337i) q^{30} +(-6.47842 - 3.74031i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.845726 - 1.05691i) q^{33} +(-5.24457 - 3.02795i) q^{34} +(-1.80382 - 1.93552i) q^{35} +(-2.20591 - 2.03321i) q^{36} +(-5.42975 + 9.40460i) q^{37} -7.03984 q^{38} +(1.65094 - 4.22714i) q^{39} +1.00000i q^{40} +(5.46910 + 9.47275i) q^{41} +(-4.25932 + 1.69062i) q^{42} +(-4.45098 + 7.70932i) q^{43} +(0.676813 + 0.390758i) q^{44} +(0.657860 - 2.92698i) q^{45} +(2.30460 + 3.99168i) q^{46} +(0.501266 + 0.868218i) q^{47} +(1.61337 + 0.630115i) q^{48} +(-0.492485 + 6.98265i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-9.77040 - 3.81592i) q^{51} +2.62007i q^{52} +(8.30234 - 4.79336i) q^{53} +(-4.30777 - 2.90570i) q^{54} +0.781517i q^{55} +(1.93552 - 1.80382i) q^{56} +(-12.0541 + 1.83732i) q^{57} -4.57535 q^{58} +(1.32003 - 2.28635i) q^{59} +(0.260988 + 1.71227i) q^{60} +(1.84617 - 1.06588i) q^{61} +7.48063 q^{62} +(-6.85189 + 4.00644i) q^{63} -1.00000 q^{64} +(-2.26905 + 1.31003i) q^{65} +(1.26087 + 0.492445i) q^{66} +(-6.02939 + 10.4432i) q^{67} +6.05590 q^{68} +(4.98788 + 6.23338i) q^{69} +(2.52991 + 0.774302i) q^{70} +10.1200i q^{71} +(2.92698 + 0.657860i) q^{72} +(7.67003 - 4.42830i) q^{73} -10.8595i q^{74} +(-1.35238 + 1.08216i) q^{75} +(6.09668 - 3.51992i) q^{76} +(1.51264 - 1.40971i) q^{77} +(0.683808 + 4.48628i) q^{78} +(-7.96847 - 13.8018i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-8.13444 - 3.85109i) q^{81} +(-9.47275 - 5.46910i) q^{82} +(-2.03248 + 3.52036i) q^{83} +(2.84337 - 3.59378i) q^{84} +(3.02795 + 5.24457i) q^{85} -8.90195i q^{86} +(-7.83425 + 1.19411i) q^{87} -0.781517 q^{88} +(-3.78927 + 6.56320i) q^{89} +(0.893768 + 2.86377i) q^{90} +(6.62855 + 2.02872i) q^{91} +(-3.99168 - 2.30460i) q^{92} +(12.8089 - 1.95236i) q^{93} +(-0.868218 - 0.501266i) q^{94} +(6.09668 + 3.51992i) q^{95} +(-1.71227 + 0.260988i) q^{96} +(5.00436 + 2.88927i) q^{97} +(-3.06482 - 6.29340i) q^{98} +(2.28748 + 0.514128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −1.35238 + 1.08216i −0.780797 + 0.624785i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.00000 0.447214
\(6\) 0.630115 1.61337i 0.257243 0.658655i
\(7\) −1.80382 1.93552i −0.681779 0.731558i
\(8\) 1.00000i 0.353553i
\(9\) 0.657860 2.92698i 0.219287 0.975660i
\(10\) −0.866025 + 0.500000i −0.273861 + 0.158114i
\(11\) 0.781517i 0.235636i 0.993035 + 0.117818i \(0.0375900\pi\)
−0.993035 + 0.117818i \(0.962410\pi\)
\(12\) 0.260988 + 1.71227i 0.0753408 + 0.494291i
\(13\) −2.26905 + 1.31003i −0.629320 + 0.363338i −0.780489 0.625170i \(-0.785030\pi\)
0.151168 + 0.988508i \(0.451696\pi\)
\(14\) 2.52991 + 0.774302i 0.676148 + 0.206941i
\(15\) −1.35238 + 1.08216i −0.349183 + 0.279412i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.02795 + 5.24457i 0.734386 + 1.27199i 0.954992 + 0.296631i \(0.0958632\pi\)
−0.220606 + 0.975363i \(0.570803\pi\)
\(18\) 0.893768 + 2.86377i 0.210663 + 0.674997i
\(19\) 6.09668 + 3.51992i 1.39867 + 0.807525i 0.994254 0.107048i \(-0.0341397\pi\)
0.404421 + 0.914573i \(0.367473\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 4.53399 + 0.665540i 0.989398 + 0.145233i
\(22\) −0.390758 0.676813i −0.0833100 0.144297i
\(23\) 4.60919i 0.961083i −0.876972 0.480542i \(-0.840440\pi\)
0.876972 0.480542i \(-0.159560\pi\)
\(24\) −1.08216 1.35238i −0.220895 0.276053i
\(25\) 1.00000 0.200000
\(26\) 1.31003 2.26905i 0.256919 0.444997i
\(27\) 2.27779 + 4.67030i 0.438360 + 0.898799i
\(28\) −2.57812 + 0.594391i −0.487219 + 0.112329i
\(29\) 3.96237 + 2.28767i 0.735793 + 0.424810i 0.820538 0.571592i \(-0.193674\pi\)
−0.0847445 + 0.996403i \(0.527007\pi\)
\(30\) 0.630115 1.61337i 0.115043 0.294559i
\(31\) −6.47842 3.74031i −1.16356 0.671780i −0.211404 0.977399i \(-0.567803\pi\)
−0.952154 + 0.305618i \(0.901137\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −0.845726 1.05691i −0.147222 0.183984i
\(34\) −5.24457 3.02795i −0.899436 0.519289i
\(35\) −1.80382 1.93552i −0.304901 0.327163i
\(36\) −2.20591 2.03321i −0.367652 0.338869i
\(37\) −5.42975 + 9.40460i −0.892645 + 1.54611i −0.0559531 + 0.998433i \(0.517820\pi\)
−0.836692 + 0.547673i \(0.815514\pi\)
\(38\) −7.03984 −1.14201
\(39\) 1.65094 4.22714i 0.264363 0.676883i
\(40\) 1.00000i 0.158114i
\(41\) 5.46910 + 9.47275i 0.854129 + 1.47940i 0.877450 + 0.479667i \(0.159243\pi\)
−0.0233211 + 0.999728i \(0.507424\pi\)
\(42\) −4.25932 + 1.69062i −0.657227 + 0.260868i
\(43\) −4.45098 + 7.70932i −0.678768 + 1.17566i 0.296585 + 0.955007i \(0.404152\pi\)
−0.975352 + 0.220654i \(0.929181\pi\)
\(44\) 0.676813 + 0.390758i 0.102033 + 0.0589090i
\(45\) 0.657860 2.92698i 0.0980679 0.436329i
\(46\) 2.30460 + 3.99168i 0.339794 + 0.588541i
\(47\) 0.501266 + 0.868218i 0.0731172 + 0.126643i 0.900266 0.435340i \(-0.143372\pi\)
−0.827149 + 0.561983i \(0.810039\pi\)
\(48\) 1.61337 + 0.630115i 0.232870 + 0.0909492i
\(49\) −0.492485 + 6.98265i −0.0703549 + 0.997522i
\(50\) −0.866025 + 0.500000i −0.122474 + 0.0707107i
\(51\) −9.77040 3.81592i −1.36813 0.534335i
\(52\) 2.62007i 0.363338i
\(53\) 8.30234 4.79336i 1.14041 0.658418i 0.193881 0.981025i \(-0.437893\pi\)
0.946533 + 0.322607i \(0.104559\pi\)
\(54\) −4.30777 2.90570i −0.586213 0.395416i
\(55\) 0.781517i 0.105380i
\(56\) 1.93552 1.80382i 0.258645 0.241045i
\(57\) −12.0541 + 1.83732i −1.59661 + 0.243359i
\(58\) −4.57535 −0.600773
\(59\) 1.32003 2.28635i 0.171853 0.297658i −0.767215 0.641390i \(-0.778358\pi\)
0.939068 + 0.343733i \(0.111691\pi\)
\(60\) 0.260988 + 1.71227i 0.0336935 + 0.221054i
\(61\) 1.84617 1.06588i 0.236377 0.136473i −0.377133 0.926159i \(-0.623090\pi\)
0.613511 + 0.789686i \(0.289757\pi\)
\(62\) 7.48063 0.950041
\(63\) −6.85189 + 4.00644i −0.863257 + 0.504764i
\(64\) −1.00000 −0.125000
\(65\) −2.26905 + 1.31003i −0.281441 + 0.162490i
\(66\) 1.26087 + 0.492445i 0.155203 + 0.0606158i
\(67\) −6.02939 + 10.4432i −0.736607 + 1.27584i 0.217407 + 0.976081i \(0.430240\pi\)
−0.954015 + 0.299760i \(0.903093\pi\)
\(68\) 6.05590 0.734386
\(69\) 4.98788 + 6.23338i 0.600471 + 0.750410i
\(70\) 2.52991 + 0.774302i 0.302382 + 0.0925468i
\(71\) 10.1200i 1.20103i 0.799614 + 0.600514i \(0.205037\pi\)
−0.799614 + 0.600514i \(0.794963\pi\)
\(72\) 2.92698 + 0.657860i 0.344948 + 0.0775295i
\(73\) 7.67003 4.42830i 0.897710 0.518293i 0.0212532 0.999774i \(-0.493234\pi\)
0.876456 + 0.481481i \(0.159901\pi\)
\(74\) 10.8595i 1.26239i
\(75\) −1.35238 + 1.08216i −0.156159 + 0.124957i
\(76\) 6.09668 3.51992i 0.699337 0.403763i
\(77\) 1.51264 1.40971i 0.172382 0.160652i
\(78\) 0.683808 + 4.48628i 0.0774260 + 0.507971i
\(79\) −7.96847 13.8018i −0.896523 1.55282i −0.831909 0.554912i \(-0.812752\pi\)
−0.0646137 0.997910i \(-0.520582\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −8.13444 3.85109i −0.903827 0.427898i
\(82\) −9.47275 5.46910i −1.04609 0.603961i
\(83\) −2.03248 + 3.52036i −0.223094 + 0.386410i −0.955746 0.294194i \(-0.904949\pi\)
0.732652 + 0.680603i \(0.238282\pi\)
\(84\) 2.84337 3.59378i 0.310237 0.392114i
\(85\) 3.02795 + 5.24457i 0.328428 + 0.568853i
\(86\) 8.90195i 0.959922i
\(87\) −7.83425 + 1.19411i −0.839920 + 0.128022i
\(88\) −0.781517 −0.0833100
\(89\) −3.78927 + 6.56320i −0.401662 + 0.695698i −0.993927 0.110045i \(-0.964901\pi\)
0.592265 + 0.805743i \(0.298234\pi\)
\(90\) 0.893768 + 2.86377i 0.0942114 + 0.301868i
\(91\) 6.62855 + 2.02872i 0.694860 + 0.212668i
\(92\) −3.99168 2.30460i −0.416161 0.240271i
\(93\) 12.8089 1.95236i 1.32822 0.202450i
\(94\) −0.868218 0.501266i −0.0895499 0.0517017i
\(95\) 6.09668 + 3.51992i 0.625506 + 0.361136i
\(96\) −1.71227 + 0.260988i −0.174758 + 0.0266370i
\(97\) 5.00436 + 2.88927i 0.508115 + 0.293361i 0.732059 0.681242i \(-0.238560\pi\)
−0.223943 + 0.974602i \(0.571893\pi\)
\(98\) −3.06482 6.29340i −0.309594 0.635729i
\(99\) 2.28748 + 0.514128i 0.229901 + 0.0516718i
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 0.998784 0.0993827 0.0496914 0.998765i \(-0.484176\pi\)
0.0496914 + 0.998765i \(0.484176\pi\)
\(102\) 10.3694 1.58052i 1.02672 0.156495i
\(103\) 5.87358i 0.578741i −0.957217 0.289370i \(-0.906554\pi\)
0.957217 0.289370i \(-0.0934459\pi\)
\(104\) −1.31003 2.26905i −0.128459 0.222498i
\(105\) 4.53399 + 0.665540i 0.442472 + 0.0649500i
\(106\) −4.79336 + 8.30234i −0.465572 + 0.806394i
\(107\) 4.22082 + 2.43689i 0.408042 + 0.235583i 0.689948 0.723859i \(-0.257633\pi\)
−0.281906 + 0.959442i \(0.590967\pi\)
\(108\) 5.18349 + 0.362528i 0.498782 + 0.0348843i
\(109\) 0.338969 + 0.587111i 0.0324673 + 0.0562350i 0.881802 0.471619i \(-0.156330\pi\)
−0.849335 + 0.527854i \(0.822997\pi\)
\(110\) −0.390758 0.676813i −0.0372573 0.0645316i
\(111\) −2.83420 18.5944i −0.269011 1.76491i
\(112\) −0.774302 + 2.52991i −0.0731646 + 0.239054i
\(113\) −2.66192 + 1.53686i −0.250413 + 0.144576i −0.619953 0.784639i \(-0.712848\pi\)
0.369541 + 0.929215i \(0.379515\pi\)
\(114\) 9.52054 7.61824i 0.891680 0.713513i
\(115\) 4.60919i 0.429809i
\(116\) 3.96237 2.28767i 0.367897 0.212405i
\(117\) 2.34173 + 7.50328i 0.216493 + 0.693678i
\(118\) 2.64005i 0.243036i
\(119\) 4.68910 15.3209i 0.429849 1.40447i
\(120\) −1.08216 1.35238i −0.0987872 0.123455i
\(121\) 10.3892 0.944476
\(122\) −1.06588 + 1.84617i −0.0965006 + 0.167144i
\(123\) −17.6473 6.89232i −1.59121 0.621459i
\(124\) −6.47842 + 3.74031i −0.581779 + 0.335890i
\(125\) 1.00000 0.0894427
\(126\) 3.93069 6.89562i 0.350174 0.614311i
\(127\) −0.401239 −0.0356042 −0.0178021 0.999842i \(-0.505667\pi\)
−0.0178021 + 0.999842i \(0.505667\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −2.32331 15.2426i −0.204556 1.34204i
\(130\) 1.31003 2.26905i 0.114898 0.199009i
\(131\) 22.1595 1.93608 0.968042 0.250787i \(-0.0806894\pi\)
0.968042 + 0.250787i \(0.0806894\pi\)
\(132\) −1.33817 + 0.203967i −0.116473 + 0.0177530i
\(133\) −4.18442 18.1496i −0.362835 1.57377i
\(134\) 12.0588i 1.04172i
\(135\) 2.27779 + 4.67030i 0.196041 + 0.401955i
\(136\) −5.24457 + 3.02795i −0.449718 + 0.259645i
\(137\) 19.2002i 1.64039i −0.572086 0.820194i \(-0.693866\pi\)
0.572086 0.820194i \(-0.306134\pi\)
\(138\) −7.43632 2.90432i −0.633022 0.247232i
\(139\) −0.151908 + 0.0877042i −0.0128847 + 0.00743897i −0.506429 0.862282i \(-0.669035\pi\)
0.493544 + 0.869721i \(0.335701\pi\)
\(140\) −2.57812 + 0.594391i −0.217891 + 0.0502352i
\(141\) −1.61745 0.631711i −0.136214 0.0531996i
\(142\) −5.06002 8.76422i −0.424628 0.735477i
\(143\) −1.02381 1.77330i −0.0856156 0.148291i
\(144\) −2.86377 + 0.893768i −0.238648 + 0.0744806i
\(145\) 3.96237 + 2.28767i 0.329057 + 0.189981i
\(146\) −4.42830 + 7.67003i −0.366488 + 0.634777i
\(147\) −6.89032 9.97614i −0.568304 0.822818i
\(148\) 5.42975 + 9.40460i 0.446323 + 0.773053i
\(149\) 1.23022i 0.100784i 0.998730 + 0.0503918i \(0.0160470\pi\)
−0.998730 + 0.0503918i \(0.983953\pi\)
\(150\) 0.630115 1.61337i 0.0514487 0.131731i
\(151\) 1.87265 0.152394 0.0761969 0.997093i \(-0.475722\pi\)
0.0761969 + 0.997093i \(0.475722\pi\)
\(152\) −3.51992 + 6.09668i −0.285503 + 0.494506i
\(153\) 17.3427 5.41257i 1.40208 0.437580i
\(154\) −0.605130 + 1.97717i −0.0487627 + 0.159325i
\(155\) −6.47842 3.74031i −0.520359 0.300429i
\(156\) −2.83533 3.54333i −0.227008 0.283693i
\(157\) 5.99822 + 3.46308i 0.478710 + 0.276383i 0.719879 0.694100i \(-0.244197\pi\)
−0.241169 + 0.970483i \(0.577531\pi\)
\(158\) 13.8018 + 7.96847i 1.09801 + 0.633937i
\(159\) −6.04073 + 15.4669i −0.479061 + 1.22660i
\(160\) 0.866025 + 0.500000i 0.0684653 + 0.0395285i
\(161\) −8.92119 + 8.31414i −0.703088 + 0.655246i
\(162\) 8.97018 0.732082i 0.704764 0.0575178i
\(163\) 9.12797 15.8101i 0.714958 1.23834i −0.248018 0.968756i \(-0.579779\pi\)
0.962976 0.269588i \(-0.0868876\pi\)
\(164\) 10.9382 0.854129
\(165\) −0.845726 1.05691i −0.0658397 0.0822801i
\(166\) 4.06496i 0.315502i
\(167\) 10.7511 + 18.6214i 0.831942 + 1.44097i 0.896496 + 0.443051i \(0.146104\pi\)
−0.0645545 + 0.997914i \(0.520563\pi\)
\(168\) −0.665540 + 4.53399i −0.0513475 + 0.349805i
\(169\) −3.06762 + 5.31327i −0.235971 + 0.408713i
\(170\) −5.24457 3.02795i −0.402240 0.232233i
\(171\) 14.3135 15.5293i 1.09458 1.18755i
\(172\) 4.45098 + 7.70932i 0.339384 + 0.587830i
\(173\) −3.31016 5.73336i −0.251667 0.435900i 0.712318 0.701857i \(-0.247645\pi\)
−0.963985 + 0.265957i \(0.914312\pi\)
\(174\) 6.18761 4.95126i 0.469081 0.375354i
\(175\) −1.80382 1.93552i −0.136356 0.146312i
\(176\) 0.676813 0.390758i 0.0510167 0.0294545i
\(177\) 0.689023 + 4.52049i 0.0517901 + 0.339781i
\(178\) 7.57854i 0.568035i
\(179\) −8.99427 + 5.19284i −0.672263 + 0.388131i −0.796934 0.604067i \(-0.793546\pi\)
0.124671 + 0.992198i \(0.460213\pi\)
\(180\) −2.20591 2.03321i −0.164419 0.151547i
\(181\) 0.766824i 0.0569975i 0.999594 + 0.0284988i \(0.00907267\pi\)
−0.999594 + 0.0284988i \(0.990927\pi\)
\(182\) −6.75485 + 1.55735i −0.500703 + 0.115438i
\(183\) −1.34326 + 3.43933i −0.0992966 + 0.254242i
\(184\) 4.60919 0.339794
\(185\) −5.42975 + 9.40460i −0.399203 + 0.691440i
\(186\) −10.1166 + 8.09524i −0.741789 + 0.593572i
\(187\) −4.09872 + 2.36639i −0.299728 + 0.173048i
\(188\) 1.00253 0.0731172
\(189\) 4.93075 12.8331i 0.358659 0.933469i
\(190\) −7.03984 −0.510724
\(191\) −11.7224 + 6.76794i −0.848204 + 0.489711i −0.860044 0.510219i \(-0.829564\pi\)
0.0118406 + 0.999930i \(0.496231\pi\)
\(192\) 1.35238 1.08216i 0.0975996 0.0780982i
\(193\) 4.69750 8.13632i 0.338134 0.585665i −0.645948 0.763381i \(-0.723538\pi\)
0.984082 + 0.177717i \(0.0568710\pi\)
\(194\) −5.77853 −0.414874
\(195\) 1.65094 4.22714i 0.118227 0.302711i
\(196\) 5.80091 + 3.91783i 0.414351 + 0.279845i
\(197\) 12.0072i 0.855480i 0.903902 + 0.427740i \(0.140690\pi\)
−0.903902 + 0.427740i \(0.859310\pi\)
\(198\) −2.23808 + 0.698494i −0.159054 + 0.0496398i
\(199\) 3.77973 2.18223i 0.267938 0.154694i −0.360012 0.932948i \(-0.617227\pi\)
0.627950 + 0.778253i \(0.283894\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −3.14720 20.6480i −0.221987 1.45639i
\(202\) −0.864973 + 0.499392i −0.0608593 + 0.0351371i
\(203\) −2.71955 11.7958i −0.190875 0.827902i
\(204\) −8.18988 + 6.55346i −0.573406 + 0.458834i
\(205\) 5.46910 + 9.47275i 0.381978 + 0.661606i
\(206\) 2.93679 + 5.08667i 0.204616 + 0.354405i
\(207\) −13.4910 3.03220i −0.937691 0.210753i
\(208\) 2.26905 + 1.31003i 0.157330 + 0.0908346i
\(209\) −2.75088 + 4.76466i −0.190282 + 0.329578i
\(210\) −4.25932 + 1.69062i −0.293921 + 0.116664i
\(211\) −5.82791 10.0942i −0.401210 0.694916i 0.592662 0.805451i \(-0.298077\pi\)
−0.993872 + 0.110535i \(0.964744\pi\)
\(212\) 9.58671i 0.658418i
\(213\) −10.9515 13.6861i −0.750385 0.937759i
\(214\) −4.87379 −0.333165
\(215\) −4.45098 + 7.70932i −0.303554 + 0.525771i
\(216\) −4.67030 + 2.27779i −0.317774 + 0.154984i
\(217\) 4.44642 + 19.2860i 0.301843 + 1.30922i
\(218\) −0.587111 0.338969i −0.0397642 0.0229579i
\(219\) −5.58067 + 14.2889i −0.377107 + 0.965557i
\(220\) 0.676813 + 0.390758i 0.0456307 + 0.0263449i
\(221\) −13.7411 7.93344i −0.924328 0.533661i
\(222\) 11.7517 + 14.6862i 0.788723 + 0.985671i
\(223\) 8.63803 + 4.98717i 0.578446 + 0.333966i 0.760515 0.649320i \(-0.224946\pi\)
−0.182070 + 0.983286i \(0.558280\pi\)
\(224\) −0.594391 2.57812i −0.0397144 0.172258i
\(225\) 0.657860 2.92698i 0.0438573 0.195132i
\(226\) 1.53686 2.66192i 0.102231 0.177068i
\(227\) 17.1596 1.13893 0.569463 0.822017i \(-0.307151\pi\)
0.569463 + 0.822017i \(0.307151\pi\)
\(228\) −4.43591 + 11.3579i −0.293775 + 0.752192i
\(229\) 12.8942i 0.852070i −0.904707 0.426035i \(-0.859910\pi\)
0.904707 0.426035i \(-0.140090\pi\)
\(230\) 2.30460 + 3.99168i 0.151961 + 0.263203i
\(231\) −0.520130 + 3.54339i −0.0342221 + 0.233138i
\(232\) −2.28767 + 3.96237i −0.150193 + 0.260142i
\(233\) −12.8761 7.43401i −0.843540 0.487018i 0.0149261 0.999889i \(-0.495249\pi\)
−0.858466 + 0.512871i \(0.828582\pi\)
\(234\) −5.77964 5.32716i −0.377827 0.348247i
\(235\) 0.501266 + 0.868218i 0.0326990 + 0.0566363i
\(236\) −1.32003 2.28635i −0.0859263 0.148829i
\(237\) 25.7121 + 10.0421i 1.67018 + 0.652304i
\(238\) 3.59958 + 15.6128i 0.233326 + 1.01203i
\(239\) −1.84122 + 1.06303i −0.119099 + 0.0687617i −0.558366 0.829595i \(-0.688571\pi\)
0.439267 + 0.898356i \(0.355238\pi\)
\(240\) 1.61337 + 0.630115i 0.104142 + 0.0406737i
\(241\) 18.4443i 1.18810i 0.804426 + 0.594052i \(0.202473\pi\)
−0.804426 + 0.594052i \(0.797527\pi\)
\(242\) −8.99734 + 5.19462i −0.578371 + 0.333923i
\(243\) 15.1683 3.59464i 0.973050 0.230596i
\(244\) 2.13177i 0.136473i
\(245\) −0.492485 + 6.98265i −0.0314637 + 0.446105i
\(246\) 18.7292 2.85474i 1.19413 0.182012i
\(247\) −18.4449 −1.17362
\(248\) 3.74031 6.47842i 0.237510 0.411380i
\(249\) −1.06091 6.96033i −0.0672323 0.441093i
\(250\) −0.866025 + 0.500000i −0.0547723 + 0.0316228i
\(251\) −14.4909 −0.914655 −0.457328 0.889298i \(-0.651193\pi\)
−0.457328 + 0.889298i \(0.651193\pi\)
\(252\) 0.0437315 + 7.93713i 0.00275482 + 0.499992i
\(253\) 3.60216 0.226466
\(254\) 0.347483 0.200619i 0.0218030 0.0125880i
\(255\) −9.77040 3.81592i −0.611846 0.238962i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.81867 −0.425337 −0.212669 0.977124i \(-0.568215\pi\)
−0.212669 + 0.977124i \(0.568215\pi\)
\(258\) 9.63334 + 12.0388i 0.599745 + 0.749504i
\(259\) 27.9971 6.45479i 1.73965 0.401081i
\(260\) 2.62007i 0.162490i
\(261\) 9.30266 10.0928i 0.575820 0.624729i
\(262\) −19.1907 + 11.0798i −1.18560 + 0.684509i
\(263\) 18.5629i 1.14464i −0.820031 0.572319i \(-0.806044\pi\)
0.820031 0.572319i \(-0.193956\pi\)
\(264\) 1.05691 0.845726i 0.0650481 0.0520508i
\(265\) 8.30234 4.79336i 0.510008 0.294454i
\(266\) 12.6986 + 13.6258i 0.778601 + 0.835449i
\(267\) −1.97791 12.9765i −0.121046 0.794151i
\(268\) 6.02939 + 10.4432i 0.368304 + 0.637921i
\(269\) −0.646992 1.12062i −0.0394478 0.0683256i 0.845627 0.533774i \(-0.179227\pi\)
−0.885075 + 0.465448i \(0.845893\pi\)
\(270\) −4.30777 2.90570i −0.262163 0.176836i
\(271\) −23.9309 13.8165i −1.45370 0.839295i −0.455012 0.890485i \(-0.650365\pi\)
−0.998689 + 0.0511902i \(0.983699\pi\)
\(272\) 3.02795 5.24457i 0.183597 0.317999i
\(273\) −11.1597 + 4.42954i −0.675417 + 0.268088i
\(274\) 9.60012 + 16.6279i 0.579964 + 1.00453i
\(275\) 0.781517i 0.0471272i
\(276\) 7.89220 1.20295i 0.475055 0.0724088i
\(277\) −24.4527 −1.46922 −0.734611 0.678488i \(-0.762635\pi\)
−0.734611 + 0.678488i \(0.762635\pi\)
\(278\) 0.0877042 0.151908i 0.00526015 0.00911084i
\(279\) −15.2097 + 16.5016i −0.910582 + 0.987925i
\(280\) 1.93552 1.80382i 0.115670 0.107799i
\(281\) 2.32984 + 1.34513i 0.138986 + 0.0802438i 0.567881 0.823111i \(-0.307763\pi\)
−0.428894 + 0.903355i \(0.641097\pi\)
\(282\) 1.71661 0.261649i 0.102223 0.0155810i
\(283\) 6.19520 + 3.57680i 0.368266 + 0.212619i 0.672701 0.739915i \(-0.265134\pi\)
−0.304434 + 0.952533i \(0.598467\pi\)
\(284\) 8.76422 + 5.06002i 0.520061 + 0.300257i
\(285\) −12.0541 + 1.83732i −0.714026 + 0.108833i
\(286\) 1.77330 + 1.02381i 0.104857 + 0.0605394i
\(287\) 8.46946 27.6727i 0.499936 1.63347i
\(288\) 2.03321 2.20591i 0.119808 0.129985i
\(289\) −9.83699 + 17.0382i −0.578646 + 1.00224i
\(290\) −4.57535 −0.268674
\(291\) −9.89444 + 1.50813i −0.580022 + 0.0884081i
\(292\) 8.85659i 0.518293i
\(293\) −2.65334 4.59573i −0.155010 0.268485i 0.778053 0.628199i \(-0.216208\pi\)
−0.933063 + 0.359714i \(0.882874\pi\)
\(294\) 10.9553 + 5.19443i 0.638924 + 0.302945i
\(295\) 1.32003 2.28635i 0.0768549 0.133117i
\(296\) −9.40460 5.42975i −0.546631 0.315598i
\(297\) −3.64992 + 1.78013i −0.211790 + 0.103294i
\(298\) −0.615111 1.06540i −0.0356324 0.0617171i
\(299\) 6.03820 + 10.4585i 0.349198 + 0.604829i
\(300\) 0.260988 + 1.71227i 0.0150682 + 0.0988582i
\(301\) 22.9503 5.29124i 1.32283 0.304982i
\(302\) −1.62176 + 0.936323i −0.0933218 + 0.0538794i
\(303\) −1.35074 + 1.08084i −0.0775977 + 0.0620929i
\(304\) 7.03984i 0.403763i
\(305\) 1.84617 1.06588i 0.105711 0.0610324i
\(306\) −12.3129 + 13.3588i −0.703884 + 0.763671i
\(307\) 28.5768i 1.63097i −0.578782 0.815483i \(-0.696472\pi\)
0.578782 0.815483i \(-0.303528\pi\)
\(308\) −0.464527 2.01484i −0.0264689 0.114806i
\(309\) 6.35615 + 7.94330i 0.361589 + 0.451879i
\(310\) 7.48063 0.424871
\(311\) −14.1734 + 24.5491i −0.803702 + 1.39205i 0.113462 + 0.993542i \(0.463806\pi\)
−0.917164 + 0.398510i \(0.869527\pi\)
\(312\) 4.22714 + 1.65094i 0.239314 + 0.0934663i
\(313\) 12.0568 6.96097i 0.681488 0.393457i −0.118927 0.992903i \(-0.537946\pi\)
0.800416 + 0.599446i \(0.204612\pi\)
\(314\) −6.92615 −0.390865
\(315\) −6.85189 + 4.00644i −0.386060 + 0.225737i
\(316\) −15.9369 −0.896523
\(317\) 5.61708 3.24302i 0.315487 0.182146i −0.333892 0.942611i \(-0.608362\pi\)
0.649379 + 0.760465i \(0.275029\pi\)
\(318\) −2.50202 16.4151i −0.140306 0.920512i
\(319\) −1.78786 + 3.09666i −0.100101 + 0.173379i
\(320\) −1.00000 −0.0559017
\(321\) −8.34526 + 1.27200i −0.465787 + 0.0709962i
\(322\) 3.56891 11.6609i 0.198887 0.649834i
\(323\) 42.6326i 2.37214i
\(324\) −7.40236 + 5.11909i −0.411242 + 0.284394i
\(325\) −2.26905 + 1.31003i −0.125864 + 0.0726677i
\(326\) 18.2559i 1.01110i
\(327\) −1.09376 0.427178i −0.0604852 0.0236230i
\(328\) −9.47275 + 5.46910i −0.523045 + 0.301980i
\(329\) 0.776263 2.53632i 0.0427967 0.139832i
\(330\) 1.26087 + 0.492445i 0.0694088 + 0.0271082i
\(331\) 10.1155 + 17.5206i 0.556001 + 0.963021i 0.997825 + 0.0659198i \(0.0209982\pi\)
−0.441824 + 0.897102i \(0.645669\pi\)
\(332\) 2.03248 + 3.52036i 0.111547 + 0.193205i
\(333\) 23.9551 + 22.0797i 1.31273 + 1.20996i
\(334\) −18.6214 10.7511i −1.01892 0.588272i
\(335\) −6.02939 + 10.4432i −0.329421 + 0.570574i
\(336\) −1.69062 4.25932i −0.0922309 0.232365i
\(337\) −6.26528 10.8518i −0.341292 0.591134i 0.643381 0.765546i \(-0.277531\pi\)
−0.984673 + 0.174412i \(0.944198\pi\)
\(338\) 6.13524i 0.333713i
\(339\) 1.93680 4.95905i 0.105192 0.269338i
\(340\) 6.05590 0.328428
\(341\) 2.92312 5.06299i 0.158296 0.274176i
\(342\) −4.63123 + 20.6055i −0.250428 + 1.11422i
\(343\) 14.4034 11.6422i 0.777712 0.628621i
\(344\) −7.70932 4.45098i −0.415659 0.239981i
\(345\) 4.98788 + 6.23338i 0.268539 + 0.335594i
\(346\) 5.73336 + 3.31016i 0.308228 + 0.177955i
\(347\) 0.249731 + 0.144182i 0.0134063 + 0.00774011i 0.506688 0.862129i \(-0.330870\pi\)
−0.493282 + 0.869870i \(0.664203\pi\)
\(348\) −2.88299 + 7.38172i −0.154545 + 0.395702i
\(349\) −6.77506 3.91159i −0.362661 0.209382i 0.307586 0.951520i \(-0.400479\pi\)
−0.670247 + 0.742138i \(0.733812\pi\)
\(350\) 2.52991 + 0.774302i 0.135230 + 0.0413882i
\(351\) −11.2867 7.61315i −0.602437 0.406360i
\(352\) −0.390758 + 0.676813i −0.0208275 + 0.0360743i
\(353\) 4.24919 0.226162 0.113081 0.993586i \(-0.463928\pi\)
0.113081 + 0.993586i \(0.463928\pi\)
\(354\) −2.85696 3.57035i −0.151846 0.189762i
\(355\) 10.1200i 0.537116i
\(356\) 3.78927 + 6.56320i 0.200831 + 0.347849i
\(357\) 10.2382 + 25.7940i 0.541865 + 1.36516i
\(358\) 5.19284 8.99427i 0.274450 0.475362i
\(359\) 9.71995 + 5.61182i 0.513000 + 0.296180i 0.734066 0.679078i \(-0.237620\pi\)
−0.221066 + 0.975259i \(0.570954\pi\)
\(360\) 2.92698 + 0.657860i 0.154265 + 0.0346722i
\(361\) 15.2797 + 26.4652i 0.804194 + 1.39291i
\(362\) −0.383412 0.664089i −0.0201517 0.0349037i
\(363\) −14.0502 + 11.2428i −0.737443 + 0.590095i
\(364\) 5.07120 4.72613i 0.265803 0.247716i
\(365\) 7.67003 4.42830i 0.401468 0.231788i
\(366\) −0.556367 3.65017i −0.0290818 0.190798i
\(367\) 6.63431i 0.346308i 0.984895 + 0.173154i \(0.0553958\pi\)
−0.984895 + 0.173154i \(0.944604\pi\)
\(368\) −3.99168 + 2.30460i −0.208081 + 0.120135i
\(369\) 31.3245 9.77620i 1.63069 0.508929i
\(370\) 10.8595i 0.564558i
\(371\) −24.2535 7.42301i −1.25918 0.385383i
\(372\) 4.71366 12.0690i 0.244392 0.625749i
\(373\) −30.4025 −1.57418 −0.787091 0.616837i \(-0.788414\pi\)
−0.787091 + 0.616837i \(0.788414\pi\)
\(374\) 2.36639 4.09872i 0.122363 0.211940i
\(375\) −1.35238 + 1.08216i −0.0698366 + 0.0558825i
\(376\) −0.868218 + 0.501266i −0.0447749 + 0.0258508i
\(377\) −11.9877 −0.617400
\(378\) 2.14638 + 13.5791i 0.110398 + 0.698436i
\(379\) −7.50620 −0.385568 −0.192784 0.981241i \(-0.561752\pi\)
−0.192784 + 0.981241i \(0.561752\pi\)
\(380\) 6.09668 3.51992i 0.312753 0.180568i
\(381\) 0.542627 0.434205i 0.0277996 0.0222450i
\(382\) 6.76794 11.7224i 0.346278 0.599771i
\(383\) −4.17818 −0.213495 −0.106748 0.994286i \(-0.534044\pi\)
−0.106748 + 0.994286i \(0.534044\pi\)
\(384\) −0.630115 + 1.61337i −0.0321554 + 0.0823318i
\(385\) 1.51264 1.40971i 0.0770914 0.0718456i
\(386\) 9.39501i 0.478193i
\(387\) 19.6369 + 18.0996i 0.998201 + 0.920053i
\(388\) 5.00436 2.88927i 0.254058 0.146680i
\(389\) 14.2487i 0.722439i −0.932481 0.361220i \(-0.882360\pi\)
0.932481 0.361220i \(-0.117640\pi\)
\(390\) 0.683808 + 4.48628i 0.0346259 + 0.227172i
\(391\) 24.1732 13.9564i 1.22249 0.705806i
\(392\) −6.98265 0.492485i −0.352677 0.0248742i
\(393\) −29.9681 + 23.9801i −1.51169 + 1.20964i
\(394\) −6.00362 10.3986i −0.302458 0.523872i
\(395\) −7.96847 13.8018i −0.400937 0.694443i
\(396\) 1.58899 1.72396i 0.0798498 0.0866320i
\(397\) 15.1562 + 8.75045i 0.760669 + 0.439172i 0.829536 0.558453i \(-0.188605\pi\)
−0.0688669 + 0.997626i \(0.521938\pi\)
\(398\) −2.18223 + 3.77973i −0.109385 + 0.189461i
\(399\) 25.2996 + 20.0169i 1.26657 + 1.00210i
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 12.0735i 0.602924i −0.953478 0.301462i \(-0.902525\pi\)
0.953478 0.301462i \(-0.0974746\pi\)
\(402\) 13.0495 + 16.3080i 0.650852 + 0.813372i
\(403\) 19.5998 0.976334
\(404\) 0.499392 0.864973i 0.0248457 0.0430340i
\(405\) −8.13444 3.85109i −0.404204 0.191362i
\(406\) 8.25309 + 8.85568i 0.409594 + 0.439500i
\(407\) −7.34985 4.24344i −0.364319 0.210339i
\(408\) 3.81592 9.77040i 0.188916 0.483707i
\(409\) −30.4287 17.5680i −1.50460 0.868683i −0.999986 0.00533893i \(-0.998301\pi\)
−0.504617 0.863344i \(-0.668366\pi\)
\(410\) −9.47275 5.46910i −0.467826 0.270099i
\(411\) 20.7777 + 25.9660i 1.02489 + 1.28081i
\(412\) −5.08667 2.93679i −0.250602 0.144685i
\(413\) −6.80637 + 1.56922i −0.334919 + 0.0772164i
\(414\) 13.1997 4.11955i 0.648728 0.202465i
\(415\) −2.03248 + 3.52036i −0.0997706 + 0.172808i
\(416\) −2.62007 −0.128459
\(417\) 0.110527 0.282998i 0.00541255 0.0138585i
\(418\) 5.50175i 0.269100i
\(419\) −1.20192 2.08178i −0.0587176 0.101702i 0.835172 0.549988i \(-0.185368\pi\)
−0.893890 + 0.448286i \(0.852034\pi\)
\(420\) 2.84337 3.59378i 0.138742 0.175359i
\(421\) 0.667716 1.15652i 0.0325425 0.0563652i −0.849295 0.527918i \(-0.822973\pi\)
0.881838 + 0.471553i \(0.156306\pi\)
\(422\) 10.0942 + 5.82791i 0.491380 + 0.283698i
\(423\) 2.87102 0.896031i 0.139594 0.0435665i
\(424\) 4.79336 + 8.30234i 0.232786 + 0.403197i
\(425\) 3.02795 + 5.24457i 0.146877 + 0.254399i
\(426\) 16.3274 + 6.37679i 0.791063 + 0.308957i
\(427\) −5.39319 1.65063i −0.260995 0.0798797i
\(428\) 4.22082 2.43689i 0.204021 0.117792i
\(429\) 3.30358 + 1.29024i 0.159498 + 0.0622934i
\(430\) 8.90195i 0.429290i
\(431\) −27.5465 + 15.9040i −1.32687 + 0.766067i −0.984814 0.173613i \(-0.944456\pi\)
−0.342054 + 0.939680i \(0.611122\pi\)
\(432\) 2.90570 4.30777i 0.139801 0.207258i
\(433\) 33.1620i 1.59367i −0.604200 0.796833i \(-0.706507\pi\)
0.604200 0.796833i \(-0.293493\pi\)
\(434\) −13.4937 14.4789i −0.647718 0.695010i
\(435\) −7.83425 + 1.19411i −0.375624 + 0.0572533i
\(436\) 0.677937 0.0324673
\(437\) 16.2240 28.1008i 0.776099 1.34424i
\(438\) −2.31147 15.1649i −0.110446 0.724608i
\(439\) −24.7576 + 14.2938i −1.18162 + 0.682207i −0.956388 0.292099i \(-0.905646\pi\)
−0.225229 + 0.974306i \(0.572313\pi\)
\(440\) −0.781517 −0.0372573
\(441\) 20.1141 + 6.03510i 0.957815 + 0.287386i
\(442\) 15.8669 0.754711
\(443\) −30.2830 + 17.4839i −1.43879 + 0.830684i −0.997766 0.0668124i \(-0.978717\pi\)
−0.441022 + 0.897497i \(0.645384\pi\)
\(444\) −17.5204 6.84273i −0.831480 0.324742i
\(445\) −3.78927 + 6.56320i −0.179629 + 0.311126i
\(446\) −9.97434 −0.472299
\(447\) −1.33130 1.66373i −0.0629681 0.0786915i
\(448\) 1.80382 + 1.93552i 0.0852224 + 0.0914448i
\(449\) 12.6187i 0.595515i 0.954642 + 0.297758i \(0.0962387\pi\)
−0.954642 + 0.297758i \(0.903761\pi\)
\(450\) 0.893768 + 2.86377i 0.0421326 + 0.134999i
\(451\) −7.40311 + 4.27419i −0.348599 + 0.201264i
\(452\) 3.07372i 0.144576i
\(453\) −2.53253 + 2.02650i −0.118989 + 0.0952134i
\(454\) −14.8607 + 8.57982i −0.697447 + 0.402671i
\(455\) 6.62855 + 2.02872i 0.310751 + 0.0951081i
\(456\) −1.83732 12.0541i −0.0860403 0.564487i
\(457\) −15.1831 26.2979i −0.710236 1.23016i −0.964768 0.263100i \(-0.915255\pi\)
0.254533 0.967064i \(-0.418078\pi\)
\(458\) 6.44708 + 11.1667i 0.301252 + 0.521784i
\(459\) −17.5967 + 26.0874i −0.821342 + 1.21766i
\(460\) −3.99168 2.30460i −0.186113 0.107452i
\(461\) 0.772644 1.33826i 0.0359856 0.0623289i −0.847472 0.530841i \(-0.821876\pi\)
0.883457 + 0.468512i \(0.155210\pi\)
\(462\) −1.32125 3.32873i −0.0614700 0.154866i
\(463\) −7.01500 12.1503i −0.326015 0.564674i 0.655703 0.755019i \(-0.272373\pi\)
−0.981717 + 0.190346i \(0.939039\pi\)
\(464\) 4.57535i 0.212405i
\(465\) 12.8089 1.95236i 0.593998 0.0905384i
\(466\) 14.8680 0.688747
\(467\) 5.25258 9.09774i 0.243061 0.420993i −0.718524 0.695502i \(-0.755182\pi\)
0.961585 + 0.274509i \(0.0885153\pi\)
\(468\) 7.66889 + 1.72364i 0.354495 + 0.0796752i
\(469\) 31.0890 7.16763i 1.43556 0.330971i
\(470\) −0.868218 0.501266i −0.0400479 0.0231217i
\(471\) −11.8595 + 1.80764i −0.546456 + 0.0832919i
\(472\) 2.28635 + 1.32003i 0.105238 + 0.0607591i
\(473\) −6.02496 3.47851i −0.277028 0.159942i
\(474\) −27.2884 + 4.15935i −1.25340 + 0.191045i
\(475\) 6.09668 + 3.51992i 0.279735 + 0.161505i
\(476\) −10.9237 11.7213i −0.500689 0.537246i
\(477\) −8.56829 27.4541i −0.392315 1.25704i
\(478\) 1.06303 1.84122i 0.0486219 0.0842155i
\(479\) 9.77353 0.446564 0.223282 0.974754i \(-0.428323\pi\)
0.223282 + 0.974754i \(0.428323\pi\)
\(480\) −1.71227 + 0.260988i −0.0781543 + 0.0119124i
\(481\) 28.4526i 1.29733i
\(482\) −9.22217 15.9733i −0.420058 0.727563i
\(483\) 3.06760 20.8980i 0.139581 0.950893i
\(484\) 5.19462 8.99734i 0.236119 0.408970i
\(485\) 5.00436 + 2.88927i 0.227236 + 0.131195i
\(486\) −11.3389 + 10.6972i −0.514341 + 0.485236i
\(487\) 0.414656 + 0.718204i 0.0187898 + 0.0325449i 0.875267 0.483639i \(-0.160685\pi\)
−0.856478 + 0.516184i \(0.827352\pi\)
\(488\) 1.06588 + 1.84617i 0.0482503 + 0.0835720i
\(489\) 4.76459 + 31.2592i 0.215462 + 1.41359i
\(490\) −3.06482 6.29340i −0.138455 0.284307i
\(491\) 21.3419 12.3218i 0.963147 0.556073i 0.0660068 0.997819i \(-0.478974\pi\)
0.897140 + 0.441746i \(0.145641\pi\)
\(492\) −14.7926 + 11.8369i −0.666901 + 0.533647i
\(493\) 27.7079i 1.24790i
\(494\) 15.9737 9.22244i 0.718692 0.414937i
\(495\) 2.28748 + 0.514128i 0.102815 + 0.0231083i
\(496\) 7.48063i 0.335890i
\(497\) 19.5876 18.2547i 0.878623 0.818836i
\(498\) 4.39894 + 5.49737i 0.197121 + 0.246343i
\(499\) 29.0471 1.30033 0.650164 0.759794i \(-0.274700\pi\)
0.650164 + 0.759794i \(0.274700\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) −34.6908 13.5488i −1.54987 0.605316i
\(502\) 12.5495 7.24543i 0.560110 0.323379i
\(503\) −1.72372 −0.0768570 −0.0384285 0.999261i \(-0.512235\pi\)
−0.0384285 + 0.999261i \(0.512235\pi\)
\(504\) −4.00644 6.85189i −0.178461 0.305208i
\(505\) 0.998784 0.0444453
\(506\) −3.11956 + 1.80108i −0.138681 + 0.0800678i
\(507\) −1.60123 10.5052i −0.0711129 0.466553i
\(508\) −0.200619 + 0.347483i −0.00890105 + 0.0154171i
\(509\) −12.6782 −0.561952 −0.280976 0.959715i \(-0.590658\pi\)
−0.280976 + 0.959715i \(0.590658\pi\)
\(510\) 10.3694 1.58052i 0.459164 0.0699866i
\(511\) −22.4064 6.85768i −0.991201 0.303366i
\(512\) 1.00000i 0.0441942i
\(513\) −2.55214 + 36.4910i −0.112680 + 1.61112i
\(514\) 5.90514 3.40934i 0.260465 0.150379i
\(515\) 5.87358i 0.258821i
\(516\) −14.3621 5.60925i −0.632257 0.246934i
\(517\) −0.678527 + 0.391748i −0.0298416 + 0.0172291i
\(518\) −21.0188 + 19.5886i −0.923513 + 0.860672i
\(519\) 10.6810 + 4.17156i 0.468844 + 0.183111i
\(520\) −1.31003 2.26905i −0.0574488 0.0995043i
\(521\) 20.9088 + 36.2152i 0.916032 + 1.58661i 0.805383 + 0.592755i \(0.201960\pi\)
0.110650 + 0.993859i \(0.464707\pi\)
\(522\) −3.00994 + 13.3920i −0.131741 + 0.586150i
\(523\) −23.2073 13.3987i −1.01478 0.585885i −0.102195 0.994764i \(-0.532586\pi\)
−0.912589 + 0.408879i \(0.865920\pi\)
\(524\) 11.0798 19.1907i 0.484021 0.838349i
\(525\) 4.53399 + 0.665540i 0.197880 + 0.0290465i
\(526\) 9.28146 + 16.0760i 0.404691 + 0.700945i
\(527\) 45.3020i 1.97339i
\(528\) −0.492445 + 1.26087i −0.0214309 + 0.0548725i
\(529\) 1.75534 0.0763192
\(530\) −4.79336 + 8.30234i −0.208210 + 0.360630i
\(531\) −5.82372 5.36779i −0.252728 0.232942i
\(532\) −17.8102 5.45096i −0.772169 0.236329i
\(533\) −24.8193 14.3294i −1.07504 0.620676i
\(534\) 8.20119 + 10.2491i 0.354900 + 0.443520i
\(535\) 4.22082 + 2.43689i 0.182482 + 0.105356i
\(536\) −10.4432 6.02939i −0.451078 0.260430i
\(537\) 6.54417 16.7559i 0.282402 0.723072i
\(538\) 1.12062 + 0.646992i 0.0483135 + 0.0278938i
\(539\) −5.45706 0.384885i −0.235052 0.0165782i
\(540\) 5.18349 + 0.362528i 0.223062 + 0.0156007i
\(541\) 5.58077 9.66618i 0.239936 0.415581i −0.720760 0.693185i \(-0.756207\pi\)
0.960696 + 0.277604i \(0.0895402\pi\)
\(542\) 27.6331 1.18694
\(543\) −0.829826 1.03704i −0.0356112 0.0445035i
\(544\) 6.05590i 0.259645i
\(545\) 0.338969 + 0.587111i 0.0145198 + 0.0251491i
\(546\) 7.44982 9.41595i 0.318823 0.402966i
\(547\) 1.68877 2.92504i 0.0722067 0.125066i −0.827661 0.561228i \(-0.810329\pi\)
0.899868 + 0.436162i \(0.143663\pi\)
\(548\) −16.6279 9.60012i −0.710308 0.410097i
\(549\) −1.90531 6.10490i −0.0813165 0.260551i
\(550\) −0.390758 0.676813i −0.0166620 0.0288594i
\(551\) 16.1049 + 27.8944i 0.686090 + 1.18834i
\(552\) −6.23338 + 4.98788i −0.265310 + 0.212298i
\(553\) −12.3400 + 40.3190i −0.524750 + 1.71454i
\(554\) 21.1767 12.2264i 0.899711 0.519449i
\(555\) −2.83420 18.5944i −0.120305 0.789290i
\(556\) 0.175408i 0.00743897i
\(557\) 19.1518 11.0573i 0.811489 0.468513i −0.0359839 0.999352i \(-0.511456\pi\)
0.847473 + 0.530839i \(0.178123\pi\)
\(558\) 4.92120 21.8957i 0.208331 0.926917i
\(559\) 23.3237i 0.986489i
\(560\) −0.774302 + 2.52991i −0.0327202 + 0.106908i
\(561\) 2.98220 7.63573i 0.125909 0.322381i
\(562\) −2.69026 −0.113482
\(563\) −6.56999 + 11.3796i −0.276892 + 0.479591i −0.970611 0.240655i \(-0.922638\pi\)
0.693719 + 0.720246i \(0.255971\pi\)
\(564\) −1.35580 + 1.08490i −0.0570896 + 0.0456825i
\(565\) −2.66192 + 1.53686i −0.111988 + 0.0646563i
\(566\) −7.15360 −0.300688
\(567\) 7.21919 + 22.6910i 0.303177 + 0.952934i
\(568\) −10.1200 −0.424628
\(569\) 14.3290 8.27287i 0.600704 0.346817i −0.168614 0.985682i \(-0.553929\pi\)
0.769319 + 0.638865i \(0.220596\pi\)
\(570\) 9.52054 7.61824i 0.398771 0.319093i
\(571\) 20.9898 36.3554i 0.878397 1.52143i 0.0252972 0.999680i \(-0.491947\pi\)
0.853100 0.521748i \(-0.174720\pi\)
\(572\) −2.04763 −0.0856156
\(573\) 8.52915 21.8383i 0.356311 0.912310i
\(574\) 6.50157 + 28.2000i 0.271370 + 1.17704i
\(575\) 4.60919i 0.192217i
\(576\) −0.657860 + 2.92698i −0.0274108 + 0.121958i
\(577\) 0.965716 0.557556i 0.0402033 0.0232114i −0.479764 0.877398i \(-0.659278\pi\)
0.519967 + 0.854186i \(0.325944\pi\)
\(578\) 19.6740i 0.818329i
\(579\) 2.45199 + 16.0868i 0.101901 + 0.668546i
\(580\) 3.96237 2.28767i 0.164528 0.0949905i
\(581\) 10.4800 2.41618i 0.434782 0.100240i
\(582\) 7.81477 6.25330i 0.323933 0.259207i
\(583\) 3.74609 + 6.48841i 0.155147 + 0.268723i
\(584\) 4.42830 + 7.67003i 0.183244 + 0.317388i
\(585\) 2.34173 + 7.50328i 0.0968188 + 0.310222i
\(586\) 4.59573 + 2.65334i 0.189848 + 0.109609i
\(587\) 7.06492 12.2368i 0.291600 0.505067i −0.682588 0.730803i \(-0.739146\pi\)
0.974188 + 0.225737i \(0.0724789\pi\)
\(588\) −12.0848 + 0.979123i −0.498367 + 0.0403783i
\(589\) −26.3312 45.6070i −1.08496 1.87920i
\(590\) 2.64005i 0.108689i
\(591\) −12.9937 16.2383i −0.534491 0.667956i
\(592\) 10.8595 0.446323
\(593\) 1.63329 2.82894i 0.0670711 0.116171i −0.830540 0.556959i \(-0.811968\pi\)
0.897611 + 0.440789i \(0.145301\pi\)
\(594\) 2.27086 3.36659i 0.0931744 0.138133i
\(595\) 4.68910 15.3209i 0.192234 0.628096i
\(596\) 1.06540 + 0.615111i 0.0436406 + 0.0251959i
\(597\) −2.75011 + 7.04148i −0.112555 + 0.288189i
\(598\) −10.4585 6.03820i −0.427679 0.246920i
\(599\) 9.28550 + 5.36099i 0.379395 + 0.219044i 0.677555 0.735472i \(-0.263040\pi\)
−0.298160 + 0.954516i \(0.596373\pi\)
\(600\) −1.08216 1.35238i −0.0441790 0.0552107i
\(601\) 34.1874 + 19.7381i 1.39453 + 0.805134i 0.993813 0.111067i \(-0.0354268\pi\)
0.400720 + 0.916201i \(0.368760\pi\)
\(602\) −17.2299 + 16.0575i −0.702239 + 0.654455i
\(603\) 26.6006 + 24.5181i 1.08326 + 0.998454i
\(604\) 0.936323 1.62176i 0.0380985 0.0659885i
\(605\) 10.3892 0.422382
\(606\) 0.629349 1.61141i 0.0255655 0.0654589i
\(607\) 23.4972i 0.953721i 0.878979 + 0.476861i \(0.158225\pi\)
−0.878979 + 0.476861i \(0.841775\pi\)
\(608\) 3.51992 + 6.09668i 0.142752 + 0.247253i
\(609\) 16.4428 + 13.0094i 0.666296 + 0.527168i
\(610\) −1.06588 + 1.84617i −0.0431564 + 0.0747491i
\(611\) −2.27479 1.31335i −0.0920283 0.0531325i
\(612\) 3.98393 17.7255i 0.161041 0.716512i
\(613\) 4.76729 + 8.25719i 0.192549 + 0.333505i 0.946094 0.323891i \(-0.104991\pi\)
−0.753545 + 0.657396i \(0.771658\pi\)
\(614\) 14.2884 + 24.7483i 0.576633 + 0.998758i
\(615\) −17.6473 6.89232i −0.711609 0.277925i
\(616\) 1.40971 + 1.51264i 0.0567990 + 0.0609461i
\(617\) −22.4936 + 12.9867i −0.905559 + 0.522825i −0.879000 0.476823i \(-0.841788\pi\)
−0.0265594 + 0.999647i \(0.508455\pi\)
\(618\) −9.47624 3.70103i −0.381190 0.148877i
\(619\) 12.8707i 0.517317i 0.965969 + 0.258658i \(0.0832804\pi\)
−0.965969 + 0.258658i \(0.916720\pi\)
\(620\) −6.47842 + 3.74031i −0.260179 + 0.150215i
\(621\) 21.5263 10.4988i 0.863821 0.421301i
\(622\) 28.3469i 1.13661i
\(623\) 19.5384 4.50461i 0.782788 0.180474i
\(624\) −4.48628 + 0.683808i −0.179595 + 0.0273742i
\(625\) 1.00000 0.0400000
\(626\) −6.96097 + 12.0568i −0.278216 + 0.481885i
\(627\) −1.43589 9.42052i −0.0573441 0.376219i
\(628\) 5.99822 3.46308i 0.239355 0.138192i
\(629\) −65.7641 −2.62219
\(630\) 3.93069 6.89562i 0.156603 0.274728i
\(631\) 25.3213 1.00802 0.504012 0.863697i \(-0.331857\pi\)
0.504012 + 0.863697i \(0.331857\pi\)
\(632\) 13.8018 7.96847i 0.549006 0.316969i
\(633\) 18.8051 + 7.34451i 0.747437 + 0.291918i
\(634\) −3.24302 + 5.61708i −0.128797 + 0.223083i
\(635\) −0.401239 −0.0159227
\(636\) 10.3744 + 12.9649i 0.411370 + 0.514091i
\(637\) −8.03005 16.4891i −0.318162 0.653324i
\(638\) 3.57571i 0.141564i
\(639\) 29.6212 + 6.65757i 1.17180 + 0.263369i
\(640\) 0.866025 0.500000i 0.0342327 0.0197642i
\(641\) 20.8838i 0.824859i −0.910989 0.412430i \(-0.864680\pi\)
0.910989 0.412430i \(-0.135320\pi\)
\(642\) 6.59121 5.27422i 0.260134 0.208157i
\(643\) −1.18971 + 0.686880i −0.0469177 + 0.0270879i −0.523275 0.852164i \(-0.675290\pi\)
0.476358 + 0.879252i \(0.341957\pi\)
\(644\) 2.73966 + 11.8830i 0.107958 + 0.468258i
\(645\) −2.32331 15.2426i −0.0914801 0.600177i
\(646\) −21.3163 36.9209i −0.838679 1.45263i
\(647\) 18.1195 + 31.3838i 0.712349 + 1.23383i 0.963973 + 0.266000i \(0.0857022\pi\)
−0.251624 + 0.967825i \(0.580964\pi\)
\(648\) 3.85109 8.13444i 0.151285 0.319551i
\(649\) 1.78682 + 1.03162i 0.0701389 + 0.0404947i
\(650\) 1.31003 2.26905i 0.0513838 0.0889993i
\(651\) −26.8837 21.2702i −1.05366 0.833644i
\(652\) −9.12797 15.8101i −0.357479 0.619172i
\(653\) 31.8472i 1.24628i −0.782112 0.623138i \(-0.785857\pi\)
0.782112 0.623138i \(-0.214143\pi\)
\(654\) 1.16081 0.176934i 0.0453915 0.00691866i
\(655\) 22.1595 0.865843
\(656\) 5.46910 9.47275i 0.213532 0.369849i
\(657\) −7.91574 25.3632i −0.308822 0.989514i
\(658\) 0.595896 + 2.58465i 0.0232305 + 0.100760i
\(659\) 20.7307 + 11.9689i 0.807552 + 0.466240i 0.846105 0.533016i \(-0.178942\pi\)
−0.0385530 + 0.999257i \(0.512275\pi\)
\(660\) −1.33817 + 0.203967i −0.0520882 + 0.00793939i
\(661\) 33.4391 + 19.3061i 1.30063 + 0.750920i 0.980512 0.196458i \(-0.0629439\pi\)
0.320119 + 0.947378i \(0.396277\pi\)
\(662\) −17.5206 10.1155i −0.680959 0.393152i
\(663\) 27.1685 4.14107i 1.05514 0.160826i
\(664\) −3.52036 2.03248i −0.136616 0.0788755i
\(665\) −4.18442 18.1496i −0.162265 0.703810i
\(666\) −31.7855 7.14403i −1.23167 0.276825i
\(667\) 10.5443 18.2633i 0.408278 0.707158i
\(668\) 21.5021 0.831942
\(669\) −17.0788 + 2.60319i −0.660305 + 0.100645i
\(670\) 12.0588i 0.465871i
\(671\) 0.833006 + 1.44281i 0.0321579 + 0.0556990i
\(672\) 3.59378 + 2.84337i 0.138633 + 0.109685i
\(673\) −7.83794 + 13.5757i −0.302131 + 0.523305i −0.976618 0.214981i \(-0.931031\pi\)
0.674488 + 0.738286i \(0.264365\pi\)
\(674\) 10.8518 + 6.26528i 0.417995 + 0.241330i
\(675\) 2.27779 + 4.67030i 0.0876720 + 0.179760i
\(676\) 3.06762 + 5.31327i 0.117985 + 0.204357i
\(677\) −0.750432 1.29979i −0.0288414 0.0499548i 0.851244 0.524769i \(-0.175848\pi\)
−0.880086 + 0.474815i \(0.842515\pi\)
\(678\) 0.802206 + 5.26306i 0.0308085 + 0.202127i
\(679\) −3.43471 14.8977i −0.131812 0.571723i
\(680\) −5.24457 + 3.02795i −0.201120 + 0.116117i
\(681\) −23.2064 + 18.5695i −0.889269 + 0.711584i
\(682\) 5.84624i 0.223864i
\(683\) 42.4921 24.5328i 1.62591 0.938722i 0.640619 0.767859i \(-0.278678\pi\)
0.985295 0.170862i \(-0.0546554\pi\)
\(684\) −6.29198 20.1605i −0.240580 0.770856i
\(685\) 19.2002i 0.733603i
\(686\) −6.65262 + 17.2842i −0.253998 + 0.659913i
\(687\) 13.9535 + 17.4378i 0.532361 + 0.665293i
\(688\) 8.90195 0.339384
\(689\) −12.5589 + 21.7527i −0.478457 + 0.828712i
\(690\) −7.43632 2.90432i −0.283096 0.110566i
\(691\) −14.7193 + 8.49821i −0.559950 + 0.323287i −0.753125 0.657877i \(-0.771455\pi\)
0.193175 + 0.981164i \(0.438121\pi\)
\(692\) −6.62032 −0.251667
\(693\) −3.13110 5.35487i −0.118941 0.203415i
\(694\) −0.288364 −0.0109462
\(695\) −0.151908 + 0.0877042i −0.00576220 + 0.00332681i
\(696\) −1.19411 7.83425i −0.0452627 0.296957i
\(697\) −33.1203 + 57.3661i −1.25452 + 2.17290i
\(698\) 7.82317 0.296111
\(699\) 25.4581 3.88038i 0.962915 0.146769i
\(700\) −2.57812 + 0.594391i −0.0974437 + 0.0224659i
\(701\) 27.6593i 1.04468i −0.852738 0.522338i \(-0.825060\pi\)
0.852738 0.522338i \(-0.174940\pi\)
\(702\) 13.5811 + 0.949850i 0.512586 + 0.0358498i
\(703\) −66.2069 + 38.2246i −2.49704 + 1.44167i
\(704\) 0.781517i 0.0294545i
\(705\) −1.61745 0.631711i −0.0609168 0.0237916i
\(706\) −3.67991 + 2.12459i −0.138495 + 0.0799602i
\(707\) −1.80162 1.93317i −0.0677571 0.0727043i
\(708\) 4.25937 + 1.66354i 0.160077 + 0.0625195i
\(709\) 14.5417 + 25.1870i 0.546125 + 0.945917i 0.998535 + 0.0541066i \(0.0172311\pi\)
−0.452410 + 0.891810i \(0.649436\pi\)
\(710\) −5.06002 8.76422i −0.189899 0.328915i
\(711\) −45.6397 + 14.2439i −1.71162 + 0.534189i
\(712\) −6.56320 3.78927i −0.245966 0.142009i
\(713\) −17.2398 + 29.8603i −0.645637 + 1.11828i
\(714\) −21.7636 17.2192i −0.814482 0.644411i
\(715\) −1.02381 1.77330i −0.0382885 0.0663176i
\(716\) 10.3857i 0.388131i
\(717\) 1.33966 3.43012i 0.0500306 0.128100i
\(718\) −11.2236 −0.418862
\(719\) 19.0668 33.0246i 0.711070 1.23161i −0.253385 0.967365i \(-0.581544\pi\)
0.964456 0.264245i \(-0.0851226\pi\)
\(720\) −2.86377 + 0.893768i −0.106726 + 0.0333088i
\(721\) −11.3684 + 10.5949i −0.423383 + 0.394573i
\(722\) −26.4652 15.2797i −0.984933 0.568651i
\(723\) −19.9597 24.9438i −0.742310 0.927668i
\(724\) 0.664089 + 0.383412i 0.0246807 + 0.0142494i
\(725\) 3.96237 + 2.28767i 0.147159 + 0.0849621i
\(726\) 6.54641 16.7617i 0.242960 0.622083i
\(727\) −9.20054 5.31193i −0.341229 0.197009i 0.319586 0.947557i \(-0.396456\pi\)
−0.660815 + 0.750548i \(0.729789\pi\)
\(728\) −2.02872 + 6.62855i −0.0751895 + 0.245670i
\(729\) −16.6234 + 21.2759i −0.615681 + 0.787996i
\(730\) −4.42830 + 7.67003i −0.163899 + 0.283881i
\(731\) −53.9094 −1.99391
\(732\) 2.30691 + 2.88296i 0.0852660 + 0.106557i
\(733\) 3.60653i 0.133210i 0.997779 + 0.0666051i \(0.0212168\pi\)
−0.997779 + 0.0666051i \(0.978783\pi\)
\(734\) −3.31715 5.74548i −0.122438 0.212070i
\(735\) −6.89032 9.97614i −0.254153 0.367976i
\(736\) 2.30460 3.99168i 0.0849485 0.147135i
\(737\) −8.16154 4.71207i −0.300634 0.173571i
\(738\) −22.2397 + 24.1287i −0.818654 + 0.888189i
\(739\) −5.13310 8.89079i −0.188824 0.327053i 0.756034 0.654532i \(-0.227134\pi\)
−0.944858 + 0.327479i \(0.893801\pi\)
\(740\) 5.42975 + 9.40460i 0.199602 + 0.345720i
\(741\) 24.9445 19.9603i 0.916358 0.733260i
\(742\) 24.7157 5.69826i 0.907341 0.209190i
\(743\) 35.2305 20.3403i 1.29248 0.746214i 0.313388 0.949625i \(-0.398536\pi\)
0.979093 + 0.203411i \(0.0652027\pi\)
\(744\) 1.95236 + 12.8089i 0.0715769 + 0.469597i
\(745\) 1.23022i 0.0450718i
\(746\) 26.3293 15.2013i 0.963986 0.556557i
\(747\) 8.96694 + 8.26494i 0.328083 + 0.302398i
\(748\) 4.73279i 0.173048i
\(749\) −2.89694 12.5652i −0.105852 0.459122i
\(750\) 0.630115 1.61337i 0.0230085 0.0589119i
\(751\) −22.2824 −0.813095 −0.406547 0.913630i \(-0.633267\pi\)
−0.406547 + 0.913630i \(0.633267\pi\)
\(752\) 0.501266 0.868218i 0.0182793 0.0316607i
\(753\) 19.5971 15.6814i 0.714160 0.571463i
\(754\) 10.3817 5.99387i 0.378078 0.218284i
\(755\) 1.87265 0.0681526
\(756\) −8.64839 10.6867i −0.314539 0.388671i
\(757\) 40.9255 1.48746 0.743732 0.668478i \(-0.233054\pi\)
0.743732 + 0.668478i \(0.233054\pi\)
\(758\) 6.50056 3.75310i 0.236111 0.136319i
\(759\) −4.87149 + 3.89811i −0.176824 + 0.141493i
\(760\) −3.51992 + 6.09668i −0.127681 + 0.221150i
\(761\) −29.3512 −1.06398 −0.531990 0.846750i \(-0.678556\pi\)
−0.531990 + 0.846750i \(0.678556\pi\)
\(762\) −0.252827 + 0.647346i −0.00915894 + 0.0234509i
\(763\) 0.524928 1.71512i 0.0190037 0.0620916i
\(764\) 13.5359i 0.489711i
\(765\) 17.3427 5.41257i 0.627027 0.195692i
\(766\) 3.61841 2.08909i 0.130738 0.0754819i
\(767\) 6.91712i 0.249763i
\(768\) −0.260988 1.71227i −0.00941761 0.0617864i
\(769\) −31.8034 + 18.3617i −1.14686 + 0.662141i −0.948120 0.317912i \(-0.897018\pi\)
−0.198741 + 0.980052i \(0.563685\pi\)
\(770\) −0.605130 + 1.97717i −0.0218074 + 0.0712522i
\(771\) 9.22143 7.37889i 0.332102 0.265744i
\(772\) −4.69750 8.13632i −0.169067 0.292832i
\(773\) 16.9345 + 29.3314i 0.609091 + 1.05498i 0.991391 + 0.130938i \(0.0417990\pi\)
−0.382299 + 0.924039i \(0.624868\pi\)
\(774\) −26.0559 5.85624i −0.936558 0.210498i
\(775\) −6.47842 3.74031i −0.232712 0.134356i
\(776\) −2.88927 + 5.00436i −0.103719 + 0.179646i
\(777\) −30.8776 + 39.0266i −1.10773 + 1.40007i
\(778\) 7.12437 + 12.3398i 0.255421 + 0.442402i
\(779\) 77.0032i 2.75892i
\(780\) −2.83533 3.54333i −0.101521 0.126871i
\(781\) −7.90899 −0.283006
\(782\) −13.9564 + 24.1732i −0.499080 + 0.864433i
\(783\) −1.65869 + 23.7163i −0.0592769 + 0.847550i
\(784\) 6.29340 3.06482i 0.224764 0.109458i
\(785\) 5.99822 + 3.46308i 0.214086 + 0.123602i
\(786\) 13.9630 35.7514i 0.498045 1.27521i
\(787\) −2.83010 1.63396i −0.100882 0.0582443i 0.448710 0.893677i \(-0.351884\pi\)
−0.549592 + 0.835433i \(0.685217\pi\)
\(788\) 10.3986 + 6.00362i 0.370434 + 0.213870i
\(789\) 20.0880 + 25.1041i 0.715153 + 0.893730i
\(790\) 13.8018 + 7.96847i 0.491046 + 0.283505i
\(791\) 7.77625 + 2.37999i 0.276492 + 0.0846227i
\(792\) −0.514128 + 2.28748i −0.0182688 + 0.0812822i
\(793\) −2.79269 + 4.83708i −0.0991714 + 0.171770i
\(794\) −17.5009 −0.621084
\(795\) −6.04073 + 15.4669i −0.214243 + 0.548554i
\(796\) 4.36446i 0.154694i
\(797\) 13.7568 + 23.8275i 0.487292 + 0.844014i 0.999893 0.0146125i \(-0.00465148\pi\)
−0.512601 + 0.858627i \(0.671318\pi\)
\(798\) −31.9186 4.68529i −1.12991 0.165858i
\(799\) −3.03562 + 5.25785i −0.107393 + 0.186009i
\(800\) 0.866025 + 0.500000i 0.0306186 + 0.0176777i
\(801\) 16.7176 + 15.4088i 0.590686 + 0.544443i
\(802\) 6.03677 + 10.4560i 0.213166 + 0.369214i
\(803\) 3.46079 + 5.99426i 0.122129 + 0.211533i
\(804\) −19.4553 7.59842i −0.686134 0.267976i
\(805\) −8.92119 + 8.31414i −0.314431 + 0.293035i
\(806\) −16.9739 + 9.79988i −0.597880 + 0.345186i
\(807\) 2.08767 + 0.815359i 0.0734895 + 0.0287020i
\(808\) 0.998784i 0.0351371i
\(809\) 6.97997 4.02989i 0.245403 0.141683i −0.372255 0.928131i \(-0.621415\pi\)
0.617657 + 0.786447i \(0.288082\pi\)
\(810\) 8.97018 0.732082i 0.315180 0.0257228i
\(811\) 22.0290i 0.773544i −0.922175 0.386772i \(-0.873590\pi\)
0.922175 0.386772i \(-0.126410\pi\)
\(812\) −11.5752 3.54270i −0.406211 0.124324i
\(813\) 47.3154 7.21191i 1.65942 0.252933i
\(814\) 8.48688 0.297465
\(815\) 9.12797 15.8101i 0.319739 0.553804i
\(816\) 1.58052 + 10.3694i 0.0553293 + 0.363001i
\(817\) −54.2724 + 31.3342i −1.89875 + 1.09624i
\(818\) 35.1360 1.22850
\(819\) 10.2987 18.0670i 0.359865 0.631313i
\(820\) 10.9382 0.381978
\(821\) −25.5537 + 14.7535i −0.891832 + 0.514899i −0.874541 0.484951i \(-0.838837\pi\)
−0.0172906 + 0.999851i \(0.505504\pi\)
\(822\) −30.9770 12.0984i −1.08045 0.421979i
\(823\) −12.6232 + 21.8640i −0.440017 + 0.762132i −0.997690 0.0679284i \(-0.978361\pi\)
0.557673 + 0.830061i \(0.311694\pi\)
\(824\) 5.87358 0.204616
\(825\) −0.845726 1.05691i −0.0294444 0.0367968i
\(826\) 5.10988 4.76217i 0.177795 0.165697i
\(827\) 30.4760i 1.05975i −0.848075 0.529877i \(-0.822238\pi\)
0.848075 0.529877i \(-0.177762\pi\)
\(828\) −9.37147 + 10.1675i −0.325681 + 0.353344i
\(829\) −29.4517 + 17.0040i −1.02290 + 0.590572i −0.914943 0.403584i \(-0.867764\pi\)
−0.107958 + 0.994156i \(0.534431\pi\)
\(830\) 4.06496i 0.141097i
\(831\) 33.0694 26.4618i 1.14716 0.917949i
\(832\) 2.26905 1.31003i 0.0786650 0.0454173i
\(833\) −38.1122 + 18.5603i −1.32051 + 0.643075i
\(834\) 0.0457795 + 0.300347i 0.00158522 + 0.0104002i
\(835\) 10.7511 + 18.6214i 0.372056 + 0.644419i
\(836\) 2.75088 + 4.76466i 0.0951411 + 0.164789i
\(837\) 2.71194 38.7758i 0.0937384 1.34029i
\(838\) 2.08178 + 1.20192i 0.0719140 + 0.0415196i
\(839\) −11.5670 + 20.0346i −0.399336 + 0.691670i −0.993644 0.112567i \(-0.964093\pi\)
0.594308 + 0.804237i \(0.297426\pi\)
\(840\) −0.665540 + 4.53399i −0.0229633 + 0.156437i
\(841\) −4.03309 6.98552i −0.139072 0.240880i
\(842\) 1.33543i 0.0460220i
\(843\) −4.60647 + 0.702128i −0.158655 + 0.0241826i
\(844\) −11.6558 −0.401210
\(845\) −3.06762 + 5.31327i −0.105529 + 0.182782i
\(846\) −2.03836 + 2.21150i −0.0700804 + 0.0760328i
\(847\) −18.7403 20.1086i −0.643924 0.690939i
\(848\) −8.30234 4.79336i −0.285103 0.164605i
\(849\) −12.2489 + 1.86701i −0.420382 + 0.0640755i
\(850\) −5.24457 3.02795i −0.179887 0.103858i
\(851\) 43.3476 + 25.0268i 1.48594 + 0.857906i
\(852\) −17.3283 + 2.64121i −0.593658 + 0.0904865i
\(853\) 19.2922 + 11.1383i 0.660551 + 0.381369i 0.792487 0.609889i \(-0.208786\pi\)
−0.131936 + 0.991258i \(0.542119\pi\)
\(854\) 5.49595 1.26710i 0.188068 0.0433594i
\(855\) 14.3135 15.5293i 0.489512 0.531090i
\(856\) −2.43689 + 4.22082i −0.0832913 + 0.144265i
\(857\) 2.17164 0.0741817 0.0370908 0.999312i \(-0.488191\pi\)
0.0370908 + 0.999312i \(0.488191\pi\)
\(858\) −3.50610 + 0.534407i −0.119696 + 0.0182444i
\(859\) 3.62921i 0.123827i 0.998082 + 0.0619135i \(0.0197203\pi\)
−0.998082 + 0.0619135i \(0.980280\pi\)
\(860\) 4.45098 + 7.70932i 0.151777 + 0.262886i
\(861\) 18.4923 + 46.5893i 0.630217 + 1.58776i
\(862\) 15.9040 27.5465i 0.541691 0.938237i
\(863\) 16.4116 + 9.47522i 0.558656 + 0.322540i 0.752606 0.658471i \(-0.228797\pi\)
−0.193950 + 0.981011i \(0.562130\pi\)
\(864\) −0.362528 + 5.18349i −0.0123335 + 0.176346i
\(865\) −3.31016 5.73336i −0.112549 0.194940i
\(866\) 16.5810 + 28.7192i 0.563446 + 0.975917i
\(867\) −5.13468 33.6872i −0.174383 1.14408i
\(868\) 18.9253 + 5.79226i 0.642368 + 0.196602i
\(869\) 10.7863 6.22749i 0.365901 0.211253i
\(870\) 6.18761 4.95126i 0.209780 0.167863i
\(871\) 31.5949i 1.07055i
\(872\) −0.587111 + 0.338969i −0.0198821 + 0.0114789i
\(873\) 11.7490 12.7469i 0.397643 0.431418i
\(874\) 32.4480i 1.09757i
\(875\) −1.80382 1.93552i −0.0609802 0.0654326i
\(876\) 9.58425 + 11.9775i 0.323822 + 0.404681i
\(877\) 5.59790 0.189028 0.0945138 0.995524i \(-0.469870\pi\)
0.0945138 + 0.995524i \(0.469870\pi\)
\(878\) 14.2938 24.7576i 0.482393 0.835529i
\(879\) 8.56164 + 3.34382i 0.288777 + 0.112784i
\(880\) 0.676813 0.390758i 0.0228154 0.0131725i
\(881\) −39.1755 −1.31985 −0.659927 0.751330i \(-0.729413\pi\)
−0.659927 + 0.751330i \(0.729413\pi\)
\(882\) −20.4369 + 4.83051i −0.688146 + 0.162652i
\(883\) −30.6078 −1.03003 −0.515017 0.857180i \(-0.672214\pi\)
−0.515017 + 0.857180i \(0.672214\pi\)
\(884\) −13.7411 + 7.93344i −0.462164 + 0.266831i
\(885\) 0.689023 + 4.52049i 0.0231612 + 0.151955i
\(886\) 17.4839 30.2830i 0.587382 1.01738i
\(887\) 37.7239 1.26664 0.633322 0.773888i \(-0.281691\pi\)
0.633322 + 0.773888i \(0.281691\pi\)
\(888\) 18.5944 2.83420i 0.623989 0.0951096i
\(889\) 0.723762 + 0.776606i 0.0242742 + 0.0260465i
\(890\) 7.57854i 0.254033i
\(891\) 3.00969 6.35720i 0.100828 0.212974i
\(892\) 8.63803 4.98717i 0.289223 0.166983i
\(893\) 7.05767i 0.236176i
\(894\) 1.98480 + 0.775181i 0.0663816 + 0.0259259i
\(895\) −8.99427 + 5.19284i −0.300645 + 0.173578i
\(896\) −2.52991 0.774302i −0.0845184 0.0258676i
\(897\) −19.4837 7.60952i −0.650541 0.254075i
\(898\) −6.30937 10.9281i −0.210546 0.364677i
\(899\) −17.1132 29.6410i −0.570759 0.988583i
\(900\) −2.20591 2.03321i −0.0735304 0.0677738i
\(901\) 50.2782 + 29.0281i 1.67501 + 0.967066i
\(902\) 4.27419 7.40311i 0.142315 0.246497i
\(903\) −25.3115 + 31.9917i −0.842315 + 1.06462i
\(904\) −1.53686 2.66192i −0.0511153 0.0885342i
\(905\) 0.766824i 0.0254901i
\(906\) 1.17998 3.02127i 0.0392023 0.100375i
\(907\) 0.665419 0.0220949 0.0110474 0.999939i \(-0.496483\pi\)
0.0110474 + 0.999939i \(0.496483\pi\)
\(908\) 8.57982 14.8607i 0.284731 0.493169i
\(909\) 0.657060 2.92342i 0.0217933 0.0969638i
\(910\) −6.75485 + 1.55735i −0.223921 + 0.0516255i
\(911\) 16.9363 + 9.77817i 0.561124 + 0.323965i 0.753597 0.657337i \(-0.228317\pi\)
−0.192472 + 0.981302i \(0.561651\pi\)
\(912\) 7.61824 + 9.52054i 0.252265 + 0.315257i
\(913\) −2.75122 1.58842i −0.0910521 0.0525689i
\(914\) 26.2979 + 15.1831i 0.869858 + 0.502213i
\(915\) −1.34326 + 3.43933i −0.0444068 + 0.113701i
\(916\) −11.1667 6.44708i −0.368957 0.213017i
\(917\) −39.9717 42.8902i −1.31998 1.41636i
\(918\) 2.19544 31.3907i 0.0724602 1.03605i
\(919\) −0.579801 + 1.00424i −0.0191259 + 0.0331270i −0.875430 0.483345i \(-0.839422\pi\)
0.856304 + 0.516472i \(0.172755\pi\)
\(920\) 4.60919 0.151961
\(921\) 30.9247 + 38.6467i 1.01900 + 1.27345i
\(922\) 1.54529i 0.0508913i
\(923\) −13.2576 22.9629i −0.436380 0.755832i
\(924\) 2.80860 + 2.22214i 0.0923961 + 0.0731030i
\(925\) −5.42975 + 9.40460i −0.178529 + 0.309221i
\(926\) 12.1503 + 7.01500i 0.399285 + 0.230527i
\(927\) −17.1919 3.86399i −0.564654 0.126910i
\(928\) 2.28767 + 3.96237i 0.0750966 + 0.130071i
\(929\) −13.2868 23.0135i −0.435927 0.755048i 0.561444 0.827515i \(-0.310246\pi\)
−0.997371 + 0.0724671i \(0.976913\pi\)
\(930\) −10.1166 + 8.09524i −0.331738 + 0.265453i
\(931\) −27.5809 + 40.8375i −0.903928 + 1.33840i
\(932\) −12.8761 + 7.43401i −0.421770 + 0.243509i
\(933\) −7.39821 48.5376i −0.242206 1.58905i
\(934\) 10.5052i 0.343740i
\(935\) −4.09872 + 2.36639i −0.134042 + 0.0773894i
\(936\) −7.50328 + 2.34173i −0.245252 + 0.0765419i
\(937\) 23.9521i 0.782482i 0.920288 + 0.391241i \(0.127954\pi\)
−0.920288 + 0.391241i \(0.872046\pi\)
\(938\) −23.3400 + 21.7518i −0.762079 + 0.710223i
\(939\) −8.77242 + 22.4612i −0.286277 + 0.732994i
\(940\) 1.00253 0.0326990
\(941\) 21.6730 37.5387i 0.706519 1.22373i −0.259621 0.965711i \(-0.583598\pi\)
0.966140 0.258017i \(-0.0830689\pi\)
\(942\) 9.36678 7.49520i 0.305186 0.244207i
\(943\) 43.6617 25.2081i 1.42182 0.820889i
\(944\) −2.64005 −0.0859263
\(945\) 4.93075 12.8331i 0.160397 0.417460i
\(946\) 6.95703 0.226192
\(947\) −25.1709 + 14.5324i −0.817944 + 0.472240i −0.849707 0.527255i \(-0.823221\pi\)
0.0317631 + 0.999495i \(0.489888\pi\)
\(948\) 21.5528 17.2463i 0.700002 0.560134i
\(949\) −11.6024 + 20.0960i −0.376631 + 0.652344i
\(950\) −7.03984 −0.228403
\(951\) −4.08696 + 10.4644i −0.132529 + 0.339331i
\(952\) 15.3209 + 4.68910i 0.496553 + 0.151975i
\(953\) 11.6767i 0.378247i −0.981953 0.189123i \(-0.939435\pi\)
0.981953 0.189123i \(-0.0605646\pi\)
\(954\) 21.1474 + 19.4918i 0.684673 + 0.631072i
\(955\) −11.7224 + 6.76794i −0.379328 + 0.219005i
\(956\) 2.12606i 0.0687617i
\(957\) −0.933219 6.12260i −0.0301667 0.197916i
\(958\) −8.46413 + 4.88677i −0.273464 + 0.157884i
\(959\) −37.1625 + 34.6337i −1.20004 + 1.11838i
\(960\) 1.35238 1.08216i 0.0436479 0.0349266i
\(961\) 12.4799 + 21.6158i 0.402578 + 0.697285i
\(962\) 14.2263 + 24.6407i 0.458675 + 0.794448i
\(963\) 9.90945 10.7511i 0.319328 0.346451i
\(964\) 15.9733 + 9.22217i 0.514464 + 0.297026i
\(965\) 4.69750 8.13632i 0.151218 0.261917i
\(966\) 7.79239 + 19.6320i 0.250716 + 0.631650i
\(967\) 7.59505 + 13.1550i 0.244240 + 0.423037i 0.961918 0.273339i \(-0.0881280\pi\)
−0.717677 + 0.696376i \(0.754795\pi\)
\(968\) 10.3892i 0.333923i
\(969\) −46.1353 57.6555i −1.48208 1.85216i
\(970\) −5.77853 −0.185538
\(971\) 21.6059 37.4226i 0.693368 1.20095i −0.277360 0.960766i \(-0.589460\pi\)
0.970728 0.240182i \(-0.0772071\pi\)
\(972\) 4.47112 14.9335i 0.143411 0.478992i
\(973\) 0.443768 + 0.135819i 0.0142265 + 0.00435416i
\(974\) −0.718204 0.414656i −0.0230128 0.0132864i
\(975\) 1.65094 4.22714i 0.0528725 0.135377i
\(976\) −1.84617 1.06588i −0.0590943 0.0341181i
\(977\) 3.52150 + 2.03314i 0.112663 + 0.0650459i 0.555273 0.831668i \(-0.312614\pi\)
−0.442610 + 0.896714i \(0.645947\pi\)
\(978\) −19.7559 24.6890i −0.631723 0.789466i
\(979\) −5.12925 2.96138i −0.163932 0.0946460i
\(980\) 5.80091 + 3.91783i 0.185303 + 0.125151i
\(981\) 1.94146 0.605918i 0.0619859 0.0193455i
\(982\) −12.3218 + 21.3419i −0.393203 + 0.681048i
\(983\) 36.3092 1.15808 0.579041 0.815298i \(-0.303427\pi\)
0.579041 + 0.815298i \(0.303427\pi\)
\(984\) 6.89232 17.6473i 0.219719 0.562576i
\(985\) 12.0072i 0.382582i
\(986\) −13.8539 23.9957i −0.441199 0.764179i
\(987\) 1.69490 + 4.27011i 0.0539493 + 0.135919i
\(988\) −9.22244 + 15.9737i −0.293405 + 0.508192i
\(989\) 35.5337 + 20.5154i 1.12991 + 0.652352i
\(990\) −2.23808 + 0.698494i −0.0711310 + 0.0221996i
\(991\) 22.0204 + 38.1404i 0.699501 + 1.21157i 0.968640 + 0.248469i \(0.0799275\pi\)
−0.269139 + 0.963101i \(0.586739\pi\)
\(992\) −3.74031 6.47842i −0.118755 0.205690i
\(993\) −32.6402 12.7479i −1.03581 0.404543i
\(994\) −7.83597 + 25.6028i −0.248542 + 0.812073i
\(995\) 3.77973 2.18223i 0.119826 0.0691814i
\(996\) −6.55828 2.56139i −0.207807 0.0811608i
\(997\) 4.71325i 0.149270i 0.997211 + 0.0746350i \(0.0237792\pi\)
−0.997211 + 0.0746350i \(0.976221\pi\)
\(998\) −25.1555 + 14.5236i −0.796285 + 0.459735i
\(999\) −56.2901 3.93688i −1.78094 0.124557i
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 630.2.t.c.551.2 yes 32
3.2 odd 2 1890.2.t.c.1601.14 32
7.3 odd 6 630.2.bk.c.101.2 yes 32
9.4 even 3 1890.2.bk.c.341.7 32
9.5 odd 6 630.2.bk.c.131.10 yes 32
21.17 even 6 1890.2.bk.c.521.7 32
63.31 odd 6 1890.2.t.c.1151.14 32
63.59 even 6 inner 630.2.t.c.311.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.t.c.311.2 32 63.59 even 6 inner
630.2.t.c.551.2 yes 32 1.1 even 1 trivial
630.2.bk.c.101.2 yes 32 7.3 odd 6
630.2.bk.c.131.10 yes 32 9.5 odd 6
1890.2.t.c.1151.14 32 63.31 odd 6
1890.2.t.c.1601.14 32 3.2 odd 2
1890.2.bk.c.341.7 32 9.4 even 3
1890.2.bk.c.521.7 32 21.17 even 6