Properties

Label 315.2.i.e.211.5
Level $315$
Weight $2$
Character 315.211
Analytic conductor $2.515$
Analytic rank $0$
Dimension $12$
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] = [315,2,Mod(106,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.106");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 2 x^{10} - x^{9} - 4 x^{8} + 20 x^{7} - 38 x^{6} + 60 x^{5} - 36 x^{4} - 27 x^{3} + 162 x^{2} - 243 x + 729 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.5
Root \(1.65373 + 0.514941i\) of defining polynomial
Character \(\chi\) \(=\) 315.211
Dual form 315.2.i.e.106.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.09108 + 1.88981i) q^{2} +(1.65373 - 0.514941i) q^{3} +(-1.38091 + 2.39181i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.77750 + 2.56340i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.66244 q^{8} +(2.46967 - 1.70315i) q^{9} +O(q^{10})\) \(q+(1.09108 + 1.88981i) q^{2} +(1.65373 - 0.514941i) q^{3} +(-1.38091 + 2.39181i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.77750 + 2.56340i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.66244 q^{8} +(2.46967 - 1.70315i) q^{9} +2.18216 q^{10} +(0.754827 + 1.30740i) q^{11} +(-1.05202 + 4.66651i) q^{12} +(-1.12609 + 1.95044i) q^{13} +(1.09108 - 1.88981i) q^{14} +(0.380915 - 1.68965i) q^{15} +(0.947978 + 1.64195i) q^{16} -6.96525 q^{17} +(5.91324 + 2.80893i) q^{18} -5.73716 q^{19} +(1.38091 + 2.39181i) q^{20} +(-1.27282 - 1.17470i) q^{21} +(-1.64715 + 2.85296i) q^{22} +(2.03268 - 3.52071i) q^{23} +(-2.74923 + 0.856056i) q^{24} +(-0.500000 - 0.866025i) q^{25} -4.91461 q^{26} +(3.20716 - 4.08829i) q^{27} +2.76183 q^{28} +(-2.65373 - 4.59640i) q^{29} +(3.60871 - 1.12368i) q^{30} +(-1.40659 + 2.43629i) q^{31} +(-3.73108 + 6.46242i) q^{32} +(1.92152 + 1.77340i) q^{33} +(-7.59966 - 13.1630i) q^{34} -1.00000 q^{35} +(0.663217 + 8.25890i) q^{36} +11.6509 q^{37} +(-6.25970 - 10.8421i) q^{38} +(-0.857887 + 3.80538i) q^{39} +(-0.831218 + 1.43971i) q^{40} +(0.815937 - 1.41324i) q^{41} +(0.831218 - 3.68708i) q^{42} +(0.539685 + 0.934761i) q^{43} -4.16941 q^{44} +(-0.240137 - 2.99037i) q^{45} +8.87128 q^{46} +(-2.18138 - 3.77826i) q^{47} +(2.41321 + 2.22719i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(1.09108 - 1.88981i) q^{50} +(-11.5187 + 3.58670i) q^{51} +(-3.11006 - 5.38679i) q^{52} -10.2968 q^{53} +(11.2254 + 1.60025i) q^{54} +1.50965 q^{55} +(0.831218 + 1.43971i) q^{56} +(-9.48773 + 2.95430i) q^{57} +(5.79088 - 10.0301i) q^{58} +(-2.65183 + 4.59311i) q^{59} +(3.51531 + 3.24433i) q^{60} +(2.28577 + 3.95908i) q^{61} -6.13883 q^{62} +(-2.70981 - 1.28722i) q^{63} -12.4917 q^{64} +(1.12609 + 1.95044i) q^{65} +(-1.25485 + 5.56622i) q^{66} +(2.01492 - 3.48995i) q^{67} +(9.61842 - 16.6596i) q^{68} +(1.54856 - 6.86903i) q^{69} +(-1.09108 - 1.88981i) q^{70} +0.400307 q^{71} +(-4.10567 + 2.83138i) q^{72} +14.2573 q^{73} +(12.7121 + 22.0180i) q^{74} +(-1.27282 - 1.17470i) q^{75} +(7.92252 - 13.7222i) q^{76} +(0.754827 - 1.30740i) q^{77} +(-8.12746 + 2.53074i) q^{78} +(7.28217 + 12.6131i) q^{79} +1.89596 q^{80} +(3.19855 - 8.41245i) q^{81} +3.56101 q^{82} +(-3.07603 - 5.32784i) q^{83} +(4.56733 - 1.42218i) q^{84} +(-3.48263 + 6.03209i) q^{85} +(-1.17768 + 2.03980i) q^{86} +(-6.75545 - 6.23471i) q^{87} +(-1.25485 - 2.17347i) q^{88} +9.94438 q^{89} +(5.38922 - 3.71655i) q^{90} +2.25218 q^{91} +(5.61392 + 9.72360i) q^{92} +(-1.07159 + 4.75329i) q^{93} +(4.76012 - 8.24478i) q^{94} +(-2.86858 + 4.96852i) q^{95} +(-2.84244 + 12.6084i) q^{96} +(-7.24949 - 12.5565i) q^{97} -2.18216 q^{98} +(4.09087 + 1.94326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} + q^{3} - 11 q^{4} + 6 q^{5} - 6 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} + q^{3} - 11 q^{4} + 6 q^{5} - 6 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9} + 6 q^{10} + 7 q^{11} - 37 q^{12} - 10 q^{13} + 3 q^{14} - q^{15} - 13 q^{16} + 14 q^{17} + 24 q^{18} + 30 q^{19} + 11 q^{20} - 2 q^{21} + 7 q^{22} + 14 q^{23} + 6 q^{24} - 6 q^{25} - 26 q^{26} - 2 q^{27} + 22 q^{28} - 13 q^{29} - 9 q^{30} - 10 q^{31} - 18 q^{32} - 14 q^{33} - 15 q^{34} - 12 q^{35} - 4 q^{36} + 42 q^{37} - 4 q^{38} - 11 q^{39} + 3 q^{40} - 4 q^{41} - 3 q^{42} - 13 q^{43} - 78 q^{44} - 30 q^{46} + 8 q^{47} + 42 q^{48} - 6 q^{49} + 3 q^{50} - 19 q^{51} - 31 q^{52} + 20 q^{53} + 84 q^{54} + 14 q^{55} - 3 q^{56} - 22 q^{57} - 3 q^{58} + 21 q^{59} - 17 q^{60} - 2 q^{61} + 50 q^{62} + 3 q^{63} + 62 q^{64} + 10 q^{65} + 19 q^{66} - 6 q^{67} - 33 q^{68} - 19 q^{69} - 3 q^{70} - 58 q^{71} + 51 q^{72} + 16 q^{73} - 5 q^{74} - 2 q^{75} - 31 q^{76} + 7 q^{77} - 5 q^{78} + 22 q^{79} - 26 q^{80} + 21 q^{81} + 36 q^{82} + 5 q^{83} + 20 q^{84} + 7 q^{85} + 23 q^{86} - 19 q^{87} + 19 q^{88} + 2 q^{89} + 9 q^{90} + 20 q^{91} + 9 q^{92} + 31 q^{93} - 31 q^{94} + 15 q^{95} - 66 q^{96} - 32 q^{97} - 6 q^{98} + 38 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.09108 + 1.88981i 0.771511 + 1.33630i 0.936735 + 0.350040i \(0.113832\pi\)
−0.165224 + 0.986256i \(0.552835\pi\)
\(3\) 1.65373 0.514941i 0.954784 0.297301i
\(4\) −1.38091 + 2.39181i −0.690457 + 1.19591i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 2.77750 + 2.56340i 1.13391 + 1.04650i
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) −1.66244 −0.587760
\(9\) 2.46967 1.70315i 0.823224 0.567717i
\(10\) 2.18216 0.690060
\(11\) 0.754827 + 1.30740i 0.227589 + 0.394196i 0.957093 0.289781i \(-0.0935824\pi\)
−0.729504 + 0.683976i \(0.760249\pi\)
\(12\) −1.05202 + 4.66651i −0.303692 + 1.34711i
\(13\) −1.12609 + 1.95044i −0.312321 + 0.540955i −0.978864 0.204511i \(-0.934440\pi\)
0.666544 + 0.745466i \(0.267773\pi\)
\(14\) 1.09108 1.88981i 0.291604 0.505072i
\(15\) 0.380915 1.68965i 0.0983518 0.436265i
\(16\) 0.947978 + 1.64195i 0.236995 + 0.410487i
\(17\) −6.96525 −1.68932 −0.844661 0.535301i \(-0.820198\pi\)
−0.844661 + 0.535301i \(0.820198\pi\)
\(18\) 5.91324 + 2.80893i 1.39376 + 0.662070i
\(19\) −5.73716 −1.31619 −0.658097 0.752933i \(-0.728638\pi\)
−0.658097 + 0.752933i \(0.728638\pi\)
\(20\) 1.38091 + 2.39181i 0.308782 + 0.534826i
\(21\) −1.27282 1.17470i −0.277752 0.256342i
\(22\) −1.64715 + 2.85296i −0.351175 + 0.608252i
\(23\) 2.03268 3.52071i 0.423844 0.734119i −0.572468 0.819927i \(-0.694014\pi\)
0.996312 + 0.0858084i \(0.0273473\pi\)
\(24\) −2.74923 + 0.856056i −0.561183 + 0.174742i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −4.91461 −0.963834
\(27\) 3.20716 4.08829i 0.617217 0.786793i
\(28\) 2.76183 0.521937
\(29\) −2.65373 4.59640i −0.492786 0.853530i 0.507179 0.861840i \(-0.330688\pi\)
−0.999965 + 0.00831007i \(0.997355\pi\)
\(30\) 3.60871 1.12368i 0.658858 0.205156i
\(31\) −1.40659 + 2.43629i −0.252632 + 0.437571i −0.964250 0.264996i \(-0.914629\pi\)
0.711618 + 0.702567i \(0.247963\pi\)
\(32\) −3.73108 + 6.46242i −0.659568 + 1.14240i
\(33\) 1.92152 + 1.77340i 0.334493 + 0.308709i
\(34\) −7.59966 13.1630i −1.30333 2.25743i
\(35\) −1.00000 −0.169031
\(36\) 0.663217 + 8.25890i 0.110536 + 1.37648i
\(37\) 11.6509 1.91540 0.957700 0.287770i \(-0.0929138\pi\)
0.957700 + 0.287770i \(0.0929138\pi\)
\(38\) −6.25970 10.8421i −1.01546 1.75882i
\(39\) −0.857887 + 3.80538i −0.137372 + 0.609348i
\(40\) −0.831218 + 1.43971i −0.131427 + 0.227638i
\(41\) 0.815937 1.41324i 0.127428 0.220712i −0.795251 0.606280i \(-0.792661\pi\)
0.922679 + 0.385568i \(0.125994\pi\)
\(42\) 0.831218 3.68708i 0.128260 0.568929i
\(43\) 0.539685 + 0.934761i 0.0823011 + 0.142550i 0.904238 0.427029i \(-0.140440\pi\)
−0.821937 + 0.569579i \(0.807106\pi\)
\(44\) −4.16941 −0.628562
\(45\) −0.240137 2.99037i −0.0357975 0.445779i
\(46\) 8.87128 1.30800
\(47\) −2.18138 3.77826i −0.318187 0.551116i 0.661923 0.749572i \(-0.269741\pi\)
−0.980110 + 0.198456i \(0.936407\pi\)
\(48\) 2.41321 + 2.22719i 0.348317 + 0.321467i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 1.09108 1.88981i 0.154302 0.267259i
\(51\) −11.5187 + 3.58670i −1.61294 + 0.502238i
\(52\) −3.11006 5.38679i −0.431288 0.747013i
\(53\) −10.2968 −1.41437 −0.707187 0.707027i \(-0.750036\pi\)
−0.707187 + 0.707027i \(0.750036\pi\)
\(54\) 11.2254 + 1.60025i 1.52758 + 0.217766i
\(55\) 1.50965 0.203562
\(56\) 0.831218 + 1.43971i 0.111076 + 0.192389i
\(57\) −9.48773 + 2.95430i −1.25668 + 0.391306i
\(58\) 5.79088 10.0301i 0.760379 1.31702i
\(59\) −2.65183 + 4.59311i −0.345239 + 0.597972i −0.985397 0.170271i \(-0.945536\pi\)
0.640158 + 0.768243i \(0.278869\pi\)
\(60\) 3.51531 + 3.24433i 0.453824 + 0.418842i
\(61\) 2.28577 + 3.95908i 0.292663 + 0.506908i 0.974439 0.224654i \(-0.0721251\pi\)
−0.681775 + 0.731562i \(0.738792\pi\)
\(62\) −6.13883 −0.779633
\(63\) −2.70981 1.28722i −0.341404 0.162175i
\(64\) −12.4917 −1.56146
\(65\) 1.12609 + 1.95044i 0.139674 + 0.241922i
\(66\) −1.25485 + 5.56622i −0.154462 + 0.685154i
\(67\) 2.01492 3.48995i 0.246162 0.426365i −0.716296 0.697797i \(-0.754164\pi\)
0.962458 + 0.271432i \(0.0874972\pi\)
\(68\) 9.61842 16.6596i 1.16640 2.02027i
\(69\) 1.54856 6.86903i 0.186424 0.826934i
\(70\) −1.09108 1.88981i −0.130409 0.225875i
\(71\) 0.400307 0.0475077 0.0237539 0.999718i \(-0.492438\pi\)
0.0237539 + 0.999718i \(0.492438\pi\)
\(72\) −4.10567 + 2.83138i −0.483858 + 0.333681i
\(73\) 14.2573 1.66870 0.834348 0.551238i \(-0.185844\pi\)
0.834348 + 0.551238i \(0.185844\pi\)
\(74\) 12.7121 + 22.0180i 1.47775 + 2.55954i
\(75\) −1.27282 1.17470i −0.146972 0.135643i
\(76\) 7.92252 13.7222i 0.908776 1.57405i
\(77\) 0.754827 1.30740i 0.0860205 0.148992i
\(78\) −8.12746 + 2.53074i −0.920253 + 0.286549i
\(79\) 7.28217 + 12.6131i 0.819309 + 1.41908i 0.906192 + 0.422866i \(0.138976\pi\)
−0.0868836 + 0.996218i \(0.527691\pi\)
\(80\) 1.89596 0.211974
\(81\) 3.19855 8.41245i 0.355395 0.934716i
\(82\) 3.56101 0.393248
\(83\) −3.07603 5.32784i −0.337638 0.584807i 0.646350 0.763041i \(-0.276295\pi\)
−0.983988 + 0.178235i \(0.942961\pi\)
\(84\) 4.56733 1.42218i 0.498337 0.155173i
\(85\) −3.48263 + 6.03209i −0.377744 + 0.654272i
\(86\) −1.17768 + 2.03980i −0.126992 + 0.219957i
\(87\) −6.75545 6.23471i −0.724260 0.668431i
\(88\) −1.25485 2.17347i −0.133768 0.231692i
\(89\) 9.94438 1.05410 0.527051 0.849834i \(-0.323298\pi\)
0.527051 + 0.849834i \(0.323298\pi\)
\(90\) 5.38922 3.71655i 0.568074 0.391759i
\(91\) 2.25218 0.236092
\(92\) 5.61392 + 9.72360i 0.585292 + 1.01376i
\(93\) −1.07159 + 4.75329i −0.111118 + 0.492894i
\(94\) 4.76012 8.24478i 0.490969 0.850384i
\(95\) −2.86858 + 4.96852i −0.294310 + 0.509760i
\(96\) −2.84244 + 12.6084i −0.290106 + 1.28684i
\(97\) −7.24949 12.5565i −0.736074 1.27492i −0.954250 0.299009i \(-0.903344\pi\)
0.218176 0.975909i \(-0.429989\pi\)
\(98\) −2.18216 −0.220432
\(99\) 4.09087 + 1.94326i 0.411148 + 0.195305i
\(100\) 2.76183 0.276183
\(101\) 4.09072 + 7.08534i 0.407042 + 0.705018i 0.994557 0.104196i \(-0.0332269\pi\)
−0.587515 + 0.809214i \(0.699894\pi\)
\(102\) −19.3460 17.8547i −1.91554 1.76788i
\(103\) −4.28577 + 7.42318i −0.422290 + 0.731428i −0.996163 0.0875166i \(-0.972107\pi\)
0.573873 + 0.818944i \(0.305440\pi\)
\(104\) 1.87205 3.24248i 0.183569 0.317951i
\(105\) −1.65373 + 0.514941i −0.161388 + 0.0502531i
\(106\) −11.2346 19.4590i −1.09120 1.89002i
\(107\) 4.41335 0.426654 0.213327 0.976981i \(-0.431570\pi\)
0.213327 + 0.976981i \(0.431570\pi\)
\(108\) 5.34963 + 13.3165i 0.514769 + 1.28138i
\(109\) −10.9433 −1.04818 −0.524088 0.851664i \(-0.675594\pi\)
−0.524088 + 0.851664i \(0.675594\pi\)
\(110\) 1.64715 + 2.85296i 0.157050 + 0.272019i
\(111\) 19.2675 5.99954i 1.82879 0.569451i
\(112\) 0.947978 1.64195i 0.0895755 0.155149i
\(113\) −1.31168 + 2.27190i −0.123393 + 0.213722i −0.921104 0.389318i \(-0.872711\pi\)
0.797711 + 0.603040i \(0.206044\pi\)
\(114\) −15.9349 14.7066i −1.49244 1.37740i
\(115\) −2.03268 3.52071i −0.189549 0.328308i
\(116\) 14.6583 1.36099
\(117\) 0.540830 + 6.73485i 0.0499998 + 0.622637i
\(118\) −11.5735 −1.06542
\(119\) 3.48263 + 6.03209i 0.319252 + 0.552960i
\(120\) −0.633246 + 2.80893i −0.0578072 + 0.256419i
\(121\) 4.36047 7.55256i 0.396407 0.686596i
\(122\) −4.98793 + 8.63935i −0.451586 + 0.782170i
\(123\) 0.621605 2.75729i 0.0560482 0.248617i
\(124\) −3.88477 6.72863i −0.348863 0.604249i
\(125\) −1.00000 −0.0894427
\(126\) −0.524017 6.52548i −0.0466832 0.581336i
\(127\) 1.83032 0.162415 0.0812073 0.996697i \(-0.474122\pi\)
0.0812073 + 0.996697i \(0.474122\pi\)
\(128\) −6.16732 10.6821i −0.545119 0.944173i
\(129\) 1.37384 + 1.26794i 0.120960 + 0.111636i
\(130\) −2.45731 + 4.25618i −0.215520 + 0.373291i
\(131\) 8.82154 15.2794i 0.770741 1.33496i −0.166416 0.986056i \(-0.553219\pi\)
0.937157 0.348907i \(-0.113447\pi\)
\(132\) −6.89509 + 2.14700i −0.600141 + 0.186872i
\(133\) 2.86858 + 4.96852i 0.248737 + 0.430826i
\(134\) 8.79377 0.759666
\(135\) −1.93699 4.82163i −0.166709 0.414979i
\(136\) 11.5793 0.992915
\(137\) −8.21586 14.2303i −0.701928 1.21578i −0.967789 0.251764i \(-0.918989\pi\)
0.265860 0.964012i \(-0.414344\pi\)
\(138\) 14.6707 4.56819i 1.24886 0.388870i
\(139\) −8.16323 + 14.1391i −0.692396 + 1.19926i 0.278655 + 0.960391i \(0.410111\pi\)
−0.971051 + 0.238873i \(0.923222\pi\)
\(140\) 1.38091 2.39181i 0.116709 0.202145i
\(141\) −5.55300 5.12496i −0.467647 0.431599i
\(142\) 0.436767 + 0.756503i 0.0366527 + 0.0634844i
\(143\) −3.40001 −0.284323
\(144\) 5.13768 + 2.44052i 0.428140 + 0.203376i
\(145\) −5.30747 −0.440761
\(146\) 15.5559 + 26.9436i 1.28742 + 2.22987i
\(147\) −0.380915 + 1.68965i −0.0314173 + 0.139360i
\(148\) −16.0889 + 27.8668i −1.32250 + 2.29064i
\(149\) −7.65407 + 13.2572i −0.627046 + 1.08607i 0.361096 + 0.932529i \(0.382403\pi\)
−0.988141 + 0.153546i \(0.950931\pi\)
\(150\) 0.831218 3.68708i 0.0678686 0.301049i
\(151\) 6.59239 + 11.4184i 0.536481 + 0.929213i 0.999090 + 0.0426501i \(0.0135801\pi\)
−0.462609 + 0.886562i \(0.653087\pi\)
\(152\) 9.53765 0.773606
\(153\) −17.2019 + 11.8629i −1.39069 + 0.959057i
\(154\) 3.29431 0.265463
\(155\) 1.40659 + 2.43629i 0.112980 + 0.195688i
\(156\) −7.91709 7.30681i −0.633875 0.585013i
\(157\) −4.56785 + 7.91174i −0.364554 + 0.631426i −0.988704 0.149878i \(-0.952112\pi\)
0.624151 + 0.781304i \(0.285445\pi\)
\(158\) −15.8909 + 27.5238i −1.26421 + 2.18968i
\(159\) −17.0282 + 5.30225i −1.35042 + 0.420495i
\(160\) 3.73108 + 6.46242i 0.294968 + 0.510899i
\(161\) −4.06536 −0.320396
\(162\) 19.3878 3.13401i 1.52325 0.246231i
\(163\) −4.25754 −0.333476 −0.166738 0.986001i \(-0.553323\pi\)
−0.166738 + 0.986001i \(0.553323\pi\)
\(164\) 2.25348 + 3.90314i 0.175967 + 0.304784i
\(165\) 2.49657 0.777383i 0.194357 0.0605192i
\(166\) 6.71240 11.6262i 0.520983 0.902369i
\(167\) −4.55777 + 7.89429i −0.352691 + 0.610879i −0.986720 0.162430i \(-0.948067\pi\)
0.634029 + 0.773309i \(0.281400\pi\)
\(168\) 2.11598 + 1.95287i 0.163251 + 0.150667i
\(169\) 3.96385 + 6.86560i 0.304912 + 0.528123i
\(170\) −15.1993 −1.16573
\(171\) −14.1689 + 9.77124i −1.08352 + 0.747226i
\(172\) −2.98103 −0.227302
\(173\) −4.72807 8.18925i −0.359468 0.622617i 0.628404 0.777887i \(-0.283709\pi\)
−0.987872 + 0.155270i \(0.950375\pi\)
\(174\) 4.41166 19.5691i 0.334447 1.48353i
\(175\) −0.500000 + 0.866025i −0.0377964 + 0.0654654i
\(176\) −1.43112 + 2.47877i −0.107875 + 0.186844i
\(177\) −2.02024 + 8.96132i −0.151851 + 0.673574i
\(178\) 10.8501 + 18.7930i 0.813251 + 1.40859i
\(179\) −12.0166 −0.898164 −0.449082 0.893491i \(-0.648249\pi\)
−0.449082 + 0.893491i \(0.648249\pi\)
\(180\) 7.48403 + 3.55509i 0.557826 + 0.264981i
\(181\) 16.2695 1.20930 0.604652 0.796490i \(-0.293312\pi\)
0.604652 + 0.796490i \(0.293312\pi\)
\(182\) 2.45731 + 4.25618i 0.182148 + 0.315489i
\(183\) 5.81876 + 5.37022i 0.430135 + 0.396978i
\(184\) −3.37920 + 5.85295i −0.249118 + 0.431485i
\(185\) 5.82546 10.0900i 0.428296 0.741831i
\(186\) −10.1520 + 3.16114i −0.744381 + 0.231786i
\(187\) −5.25756 9.10637i −0.384471 0.665923i
\(188\) 12.0492 0.878778
\(189\) −5.14414 0.733331i −0.374181 0.0533420i
\(190\) −12.5194 −0.908253
\(191\) 0.805501 + 1.39517i 0.0582840 + 0.100951i 0.893695 0.448675i \(-0.148104\pi\)
−0.835411 + 0.549625i \(0.814770\pi\)
\(192\) −20.6580 + 6.43250i −1.49086 + 0.464226i
\(193\) 6.93614 12.0137i 0.499274 0.864768i −0.500726 0.865606i \(-0.666933\pi\)
1.00000 0.000838059i \(0.000266763\pi\)
\(194\) 15.8196 27.4003i 1.13578 1.96723i
\(195\) 2.86661 + 2.64564i 0.205282 + 0.189458i
\(196\) −1.38091 2.39181i −0.0986368 0.170844i
\(197\) 26.5726 1.89322 0.946609 0.322383i \(-0.104484\pi\)
0.946609 + 0.322383i \(0.104484\pi\)
\(198\) 0.791085 + 9.85122i 0.0562200 + 0.700096i
\(199\) 1.74626 0.123789 0.0618946 0.998083i \(-0.480286\pi\)
0.0618946 + 0.998083i \(0.480286\pi\)
\(200\) 0.831218 + 1.43971i 0.0587760 + 0.101803i
\(201\) 1.53503 6.80901i 0.108272 0.480271i
\(202\) −8.92662 + 15.4614i −0.628075 + 1.08786i
\(203\) −2.65373 + 4.59640i −0.186256 + 0.322604i
\(204\) 7.32760 32.5035i 0.513034 2.27570i
\(205\) −0.815937 1.41324i −0.0569875 0.0987053i
\(206\) −18.7045 −1.30320
\(207\) −0.976243 12.1570i −0.0678536 0.844967i
\(208\) −4.27003 −0.296073
\(209\) −4.33056 7.50075i −0.299551 0.518838i
\(210\) −2.77750 2.56340i −0.191666 0.176891i
\(211\) −9.32245 + 16.1470i −0.641784 + 1.11160i 0.343250 + 0.939244i \(0.388472\pi\)
−0.985034 + 0.172359i \(0.944861\pi\)
\(212\) 14.2190 24.6280i 0.976565 1.69146i
\(213\) 0.662001 0.206135i 0.0453596 0.0141241i
\(214\) 4.81532 + 8.34037i 0.329168 + 0.570136i
\(215\) 1.07937 0.0736124
\(216\) −5.33169 + 6.79652i −0.362775 + 0.462445i
\(217\) 2.81319 0.190972
\(218\) −11.9400 20.6807i −0.808679 1.40067i
\(219\) 23.5779 7.34169i 1.59324 0.496106i
\(220\) −2.08470 + 3.61081i −0.140551 + 0.243441i
\(221\) 7.84349 13.5853i 0.527610 0.913847i
\(222\) 32.3604 + 29.8659i 2.17189 + 2.00447i
\(223\) 10.3101 + 17.8576i 0.690417 + 1.19584i 0.971701 + 0.236212i \(0.0759061\pi\)
−0.281285 + 0.959624i \(0.590761\pi\)
\(224\) 7.46215 0.498586
\(225\) −2.70981 1.28722i −0.180654 0.0858148i
\(226\) −5.72461 −0.380795
\(227\) −9.97409 17.2756i −0.662003 1.14662i −0.980088 0.198561i \(-0.936373\pi\)
0.318085 0.948062i \(-0.396960\pi\)
\(228\) 6.03561 26.7725i 0.399718 1.77305i
\(229\) 2.26958 3.93103i 0.149978 0.259770i −0.781241 0.624230i \(-0.785413\pi\)
0.931219 + 0.364460i \(0.118746\pi\)
\(230\) 4.43564 7.68276i 0.292478 0.506586i
\(231\) 0.575050 2.55078i 0.0378355 0.167829i
\(232\) 4.41166 + 7.64122i 0.289640 + 0.501671i
\(233\) 13.5757 0.889375 0.444688 0.895686i \(-0.353315\pi\)
0.444688 + 0.895686i \(0.353315\pi\)
\(234\) −12.1375 + 8.37033i −0.793451 + 0.547185i
\(235\) −4.36276 −0.284595
\(236\) −7.32391 12.6854i −0.476746 0.825748i
\(237\) 18.5378 + 17.1088i 1.20416 + 1.11134i
\(238\) −7.59966 + 13.1630i −0.492612 + 0.853230i
\(239\) −14.1388 + 24.4891i −0.914564 + 1.58407i −0.107025 + 0.994256i \(0.534132\pi\)
−0.807539 + 0.589814i \(0.799201\pi\)
\(240\) 3.13541 0.976306i 0.202390 0.0630203i
\(241\) 3.10501 + 5.37804i 0.200012 + 0.346430i 0.948532 0.316682i \(-0.102569\pi\)
−0.748520 + 0.663112i \(0.769235\pi\)
\(242\) 19.0305 1.22333
\(243\) 0.957636 15.5590i 0.0614324 0.998111i
\(244\) −12.6258 −0.808287
\(245\) 0.500000 + 0.866025i 0.0319438 + 0.0553283i
\(246\) 5.88897 1.83371i 0.375467 0.116913i
\(247\) 6.46054 11.1900i 0.411074 0.712002i
\(248\) 2.33837 4.05018i 0.148487 0.257187i
\(249\) −7.83046 7.22686i −0.496236 0.457984i
\(250\) −1.09108 1.88981i −0.0690060 0.119522i
\(251\) 25.6455 1.61873 0.809365 0.587307i \(-0.199812\pi\)
0.809365 + 0.587307i \(0.199812\pi\)
\(252\) 6.82081 4.70381i 0.429671 0.296312i
\(253\) 6.13730 0.385848
\(254\) 1.99703 + 3.45895i 0.125305 + 0.217034i
\(255\) −2.65317 + 11.7688i −0.166148 + 0.736992i
\(256\) 0.966365 1.67379i 0.0603978 0.104612i
\(257\) 4.79108 8.29839i 0.298859 0.517639i −0.677016 0.735968i \(-0.736727\pi\)
0.975875 + 0.218329i \(0.0700606\pi\)
\(258\) −0.897191 + 3.97972i −0.0558567 + 0.247767i
\(259\) −5.82546 10.0900i −0.361976 0.626962i
\(260\) −6.22012 −0.385756
\(261\) −14.3822 6.83189i −0.890237 0.422883i
\(262\) 38.5000 2.37854
\(263\) −3.53980 6.13112i −0.218274 0.378061i 0.736007 0.676974i \(-0.236709\pi\)
−0.954280 + 0.298913i \(0.903376\pi\)
\(264\) −3.19440 2.94816i −0.196602 0.181447i
\(265\) −5.14840 + 8.91729i −0.316264 + 0.547785i
\(266\) −6.25970 + 10.8421i −0.383807 + 0.664773i
\(267\) 16.4454 5.12077i 1.00644 0.313386i
\(268\) 5.56487 + 9.63864i 0.339929 + 0.588774i
\(269\) 6.53680 0.398556 0.199278 0.979943i \(-0.436140\pi\)
0.199278 + 0.979943i \(0.436140\pi\)
\(270\) 6.99853 8.92132i 0.425917 0.542934i
\(271\) −9.56585 −0.581084 −0.290542 0.956862i \(-0.593836\pi\)
−0.290542 + 0.956862i \(0.593836\pi\)
\(272\) −6.60291 11.4366i −0.400360 0.693444i
\(273\) 3.72450 1.15974i 0.225417 0.0701905i
\(274\) 17.9283 31.0528i 1.08309 1.87597i
\(275\) 0.754827 1.30740i 0.0455178 0.0788391i
\(276\) 14.2910 + 13.1894i 0.860218 + 0.793909i
\(277\) −4.62684 8.01392i −0.278000 0.481510i 0.692888 0.721045i \(-0.256338\pi\)
−0.970888 + 0.239536i \(0.923005\pi\)
\(278\) −35.6270 −2.13676
\(279\) 0.675550 + 8.41249i 0.0404441 + 0.503642i
\(280\) 1.66244 0.0993495
\(281\) −5.26343 9.11652i −0.313990 0.543846i 0.665232 0.746636i \(-0.268332\pi\)
−0.979222 + 0.202790i \(0.934999\pi\)
\(282\) 3.62640 16.0858i 0.215949 0.957898i
\(283\) −9.09363 + 15.7506i −0.540560 + 0.936278i 0.458312 + 0.888792i \(0.348454\pi\)
−0.998872 + 0.0474862i \(0.984879\pi\)
\(284\) −0.552790 + 0.957460i −0.0328021 + 0.0568148i
\(285\) −2.18537 + 9.69376i −0.129450 + 0.574209i
\(286\) −3.70968 6.42536i −0.219358 0.379939i
\(287\) −1.63187 −0.0963265
\(288\) 1.79194 + 22.3146i 0.105591 + 1.31490i
\(289\) 31.5148 1.85381
\(290\) −5.79088 10.0301i −0.340052 0.588987i
\(291\) −18.4546 17.0320i −1.08183 0.998435i
\(292\) −19.6882 + 34.1009i −1.15216 + 1.99561i
\(293\) 15.3521 26.5906i 0.896879 1.55344i 0.0654166 0.997858i \(-0.479162\pi\)
0.831462 0.555581i \(-0.187504\pi\)
\(294\) −3.60871 + 1.12368i −0.210465 + 0.0655346i
\(295\) 2.65183 + 4.59311i 0.154396 + 0.267421i
\(296\) −19.3689 −1.12579
\(297\) 7.76588 + 1.10708i 0.450622 + 0.0642391i
\(298\) −33.4048 −1.93509
\(299\) 4.57796 + 7.92925i 0.264750 + 0.458561i
\(300\) 4.56733 1.42218i 0.263695 0.0821096i
\(301\) 0.539685 0.934761i 0.0311069 0.0538787i
\(302\) −14.3857 + 24.9167i −0.827802 + 1.43379i
\(303\) 10.4135 + 9.61078i 0.598240 + 0.552125i
\(304\) −5.43870 9.42010i −0.311931 0.540280i
\(305\) 4.57155 0.261766
\(306\) −41.1872 19.5649i −2.35452 1.11845i
\(307\) −18.2136 −1.03951 −0.519754 0.854316i \(-0.673976\pi\)
−0.519754 + 0.854316i \(0.673976\pi\)
\(308\) 2.08470 + 3.61081i 0.118787 + 0.205745i
\(309\) −3.26503 + 14.4829i −0.185741 + 0.823903i
\(310\) −3.06942 + 5.31639i −0.174331 + 0.301950i
\(311\) −7.66394 + 13.2743i −0.434582 + 0.752718i −0.997261 0.0739571i \(-0.976437\pi\)
0.562679 + 0.826675i \(0.309771\pi\)
\(312\) 1.42618 6.32620i 0.0807416 0.358150i
\(313\) −10.6445 18.4369i −0.601665 1.04211i −0.992569 0.121682i \(-0.961171\pi\)
0.390905 0.920431i \(-0.372162\pi\)
\(314\) −19.9356 −1.12503
\(315\) −2.46967 + 1.70315i −0.139150 + 0.0959617i
\(316\) −40.2243 −2.26279
\(317\) 5.97807 + 10.3543i 0.335762 + 0.581557i 0.983631 0.180195i \(-0.0576729\pi\)
−0.647869 + 0.761752i \(0.724340\pi\)
\(318\) −28.5993 26.3948i −1.60377 1.48015i
\(319\) 4.00622 6.93898i 0.224305 0.388508i
\(320\) −6.24586 + 10.8181i −0.349154 + 0.604752i
\(321\) 7.29850 2.27261i 0.407362 0.126845i
\(322\) −4.43564 7.68276i −0.247189 0.428143i
\(323\) 39.9607 2.22348
\(324\) 15.7041 + 19.2672i 0.872449 + 1.07040i
\(325\) 2.25218 0.124928
\(326\) −4.64532 8.04593i −0.257281 0.445623i
\(327\) −18.0973 + 5.63514i −1.00078 + 0.311624i
\(328\) −1.35644 + 2.34943i −0.0748970 + 0.129725i
\(329\) −2.18138 + 3.77826i −0.120263 + 0.208302i
\(330\) 4.19306 + 3.86984i 0.230820 + 0.213028i
\(331\) −7.76081 13.4421i −0.426573 0.738846i 0.569993 0.821650i \(-0.306946\pi\)
−0.996566 + 0.0828036i \(0.973613\pi\)
\(332\) 16.9910 0.932500
\(333\) 28.7739 19.8433i 1.57680 1.08740i
\(334\) −19.8916 −1.08842
\(335\) −2.01492 3.48995i −0.110087 0.190676i
\(336\) 0.722198 3.20350i 0.0393991 0.174765i
\(337\) −2.02012 + 3.49895i −0.110043 + 0.190600i −0.915787 0.401663i \(-0.868432\pi\)
0.805744 + 0.592263i \(0.201766\pi\)
\(338\) −8.64977 + 14.9818i −0.470485 + 0.814905i
\(339\) −0.999279 + 4.43256i −0.0542734 + 0.240744i
\(340\) −9.61842 16.6596i −0.521632 0.903493i
\(341\) −4.24694 −0.229985
\(342\) −33.9252 16.1153i −1.83446 0.871413i
\(343\) 1.00000 0.0539949
\(344\) −0.897191 1.55398i −0.0483733 0.0837850i
\(345\) −5.17447 4.77560i −0.278584 0.257110i
\(346\) 10.3174 17.8703i 0.554667 0.960712i
\(347\) 0.993330 1.72050i 0.0533248 0.0923612i −0.838131 0.545469i \(-0.816351\pi\)
0.891456 + 0.453108i \(0.149685\pi\)
\(348\) 24.2410 7.54817i 1.29945 0.404625i
\(349\) 16.6038 + 28.7587i 0.888783 + 1.53942i 0.841316 + 0.540544i \(0.181782\pi\)
0.0474671 + 0.998873i \(0.484885\pi\)
\(350\) −2.18216 −0.116641
\(351\) 4.36244 + 10.8591i 0.232850 + 0.579618i
\(352\) −11.2653 −0.600441
\(353\) −15.2884 26.4802i −0.813717 1.40940i −0.910245 0.414069i \(-0.864107\pi\)
0.0965280 0.995330i \(-0.469226\pi\)
\(354\) −19.1394 + 5.95965i −1.01725 + 0.316752i
\(355\) 0.200154 0.346676i 0.0106230 0.0183997i
\(356\) −13.7323 + 23.7851i −0.727813 + 1.26061i
\(357\) 8.86551 + 8.18212i 0.469212 + 0.433044i
\(358\) −13.1111 22.7091i −0.692943 1.20021i
\(359\) −15.4672 −0.816327 −0.408163 0.912909i \(-0.633831\pi\)
−0.408163 + 0.912909i \(0.633831\pi\)
\(360\) 0.399212 + 4.97130i 0.0210403 + 0.262011i
\(361\) 13.9150 0.732366
\(362\) 17.7514 + 30.7463i 0.932991 + 1.61599i
\(363\) 3.32194 14.7353i 0.174356 0.773403i
\(364\) −3.11006 + 5.38679i −0.163012 + 0.282344i
\(365\) 7.12867 12.3472i 0.373132 0.646283i
\(366\) −3.79995 + 16.8557i −0.198627 + 0.881060i
\(367\) −12.7930 22.1581i −0.667788 1.15664i −0.978521 0.206145i \(-0.933908\pi\)
0.310734 0.950497i \(-0.399425\pi\)
\(368\) 7.70776 0.401795
\(369\) −0.391873 4.87991i −0.0204001 0.254038i
\(370\) 25.4242 1.32174
\(371\) 5.14840 + 8.91729i 0.267292 + 0.462963i
\(372\) −9.88923 9.12693i −0.512733 0.473209i
\(373\) 9.53784 16.5200i 0.493850 0.855374i −0.506124 0.862460i \(-0.668922\pi\)
0.999975 + 0.00708638i \(0.00225568\pi\)
\(374\) 11.4729 19.8716i 0.593247 1.02753i
\(375\) −1.65373 + 0.514941i −0.0853984 + 0.0265914i
\(376\) 3.62640 + 6.28111i 0.187017 + 0.323924i
\(377\) 11.9533 0.615629
\(378\) −4.22682 10.5216i −0.217404 0.541171i
\(379\) 0.226342 0.0116264 0.00581321 0.999983i \(-0.498150\pi\)
0.00581321 + 0.999983i \(0.498150\pi\)
\(380\) −7.92252 13.7222i −0.406417 0.703935i
\(381\) 3.02686 0.942507i 0.155071 0.0482861i
\(382\) −1.75773 + 3.04448i −0.0899335 + 0.155769i
\(383\) −16.4392 + 28.4735i −0.840003 + 1.45493i 0.0498884 + 0.998755i \(0.484113\pi\)
−0.889891 + 0.456173i \(0.849220\pi\)
\(384\) −15.6998 14.4896i −0.801175 0.739417i
\(385\) −0.754827 1.30740i −0.0384696 0.0666312i
\(386\) 30.2715 1.54078
\(387\) 2.92488 + 1.38939i 0.148680 + 0.0706266i
\(388\) 40.0437 2.03291
\(389\) 0.919683 + 1.59294i 0.0466298 + 0.0807651i 0.888398 0.459074i \(-0.151819\pi\)
−0.841768 + 0.539839i \(0.818485\pi\)
\(390\) −1.87205 + 8.30395i −0.0947948 + 0.420487i
\(391\) −14.1581 + 24.5226i −0.716008 + 1.24016i
\(392\) 0.831218 1.43971i 0.0419828 0.0727164i
\(393\) 6.72051 29.8106i 0.339005 1.50374i
\(394\) 28.9928 + 50.2171i 1.46064 + 2.52990i
\(395\) 14.5643 0.732812
\(396\) −10.2971 + 7.10113i −0.517447 + 0.356845i
\(397\) 34.5990 1.73647 0.868237 0.496150i \(-0.165253\pi\)
0.868237 + 0.496150i \(0.165253\pi\)
\(398\) 1.90531 + 3.30010i 0.0955047 + 0.165419i
\(399\) 7.30236 + 6.73946i 0.365575 + 0.337395i
\(400\) 0.947978 1.64195i 0.0473989 0.0820973i
\(401\) 1.75214 3.03479i 0.0874977 0.151550i −0.818955 0.573858i \(-0.805446\pi\)
0.906453 + 0.422307i \(0.138780\pi\)
\(402\) 14.5426 4.52828i 0.725317 0.225850i
\(403\) −3.16790 5.48696i −0.157804 0.273325i
\(404\) −22.5958 −1.12418
\(405\) −5.68612 6.97625i −0.282545 0.346653i
\(406\) −11.5818 −0.574793
\(407\) 8.79443 + 15.2324i 0.435924 + 0.755042i
\(408\) 19.1491 5.96265i 0.948019 0.295195i
\(409\) 5.41258 9.37487i 0.267635 0.463557i −0.700616 0.713539i \(-0.747091\pi\)
0.968251 + 0.249982i \(0.0804245\pi\)
\(410\) 1.78051 3.08393i 0.0879330 0.152304i
\(411\) −20.9146 19.3024i −1.03164 0.952119i
\(412\) −11.8366 20.5016i −0.583146 1.01004i
\(413\) 5.30367 0.260976
\(414\) 21.9092 15.1091i 1.07678 0.742574i
\(415\) −6.15206 −0.301993
\(416\) −8.40304 14.5545i −0.411993 0.713593i
\(417\) −6.21899 + 27.5859i −0.304545 + 1.35089i
\(418\) 9.44998 16.3679i 0.462214 0.800578i
\(419\) 6.49695 11.2531i 0.317397 0.549748i −0.662547 0.749020i \(-0.730525\pi\)
0.979944 + 0.199273i \(0.0638579\pi\)
\(420\) 1.05202 4.66651i 0.0513334 0.227703i
\(421\) −16.6224 28.7908i −0.810124 1.40318i −0.912777 0.408459i \(-0.866066\pi\)
0.102653 0.994717i \(-0.467267\pi\)
\(422\) −40.6862 −1.98057
\(423\) −11.8222 5.61584i −0.574817 0.273052i
\(424\) 17.1178 0.831312
\(425\) 3.48263 + 6.03209i 0.168932 + 0.292599i
\(426\) 1.11185 + 1.02615i 0.0538694 + 0.0497169i
\(427\) 2.28577 3.95908i 0.110616 0.191593i
\(428\) −6.09445 + 10.5559i −0.294587 + 0.510239i
\(429\) −5.62270 + 1.75080i −0.271467 + 0.0845296i
\(430\) 1.17768 + 2.03980i 0.0567927 + 0.0983679i
\(431\) 22.6025 1.08873 0.544363 0.838850i \(-0.316771\pi\)
0.544363 + 0.838850i \(0.316771\pi\)
\(432\) 9.75308 + 1.39036i 0.469245 + 0.0668939i
\(433\) −13.9768 −0.671683 −0.335842 0.941918i \(-0.609021\pi\)
−0.335842 + 0.941918i \(0.609021\pi\)
\(434\) 3.06942 + 5.31639i 0.147337 + 0.255195i
\(435\) −8.77714 + 2.73303i −0.420832 + 0.131039i
\(436\) 15.1117 26.1743i 0.723721 1.25352i
\(437\) −11.6618 + 20.1989i −0.557860 + 0.966242i
\(438\) 39.5997 + 36.5472i 1.89215 + 1.74629i
\(439\) −8.76798 15.1866i −0.418473 0.724817i 0.577313 0.816523i \(-0.304101\pi\)
−0.995786 + 0.0917063i \(0.970768\pi\)
\(440\) −2.50970 −0.119645
\(441\) 0.240137 + 2.99037i 0.0114351 + 0.142399i
\(442\) 34.2315 1.62823
\(443\) 15.0793 + 26.1182i 0.716441 + 1.24091i 0.962401 + 0.271632i \(0.0875634\pi\)
−0.245960 + 0.969280i \(0.579103\pi\)
\(444\) −12.2570 + 54.3692i −0.581692 + 2.58025i
\(445\) 4.97219 8.61209i 0.235704 0.408252i
\(446\) −22.4983 + 38.9683i −1.06533 + 1.84520i
\(447\) −5.83109 + 25.8653i −0.275801 + 1.22339i
\(448\) 6.24586 + 10.8181i 0.295089 + 0.511109i
\(449\) −9.06230 −0.427676 −0.213838 0.976869i \(-0.568597\pi\)
−0.213838 + 0.976869i \(0.568597\pi\)
\(450\) −0.524017 6.52548i −0.0247024 0.307614i
\(451\) 2.46357 0.116005
\(452\) −3.62264 6.27460i −0.170395 0.295133i
\(453\) 16.7818 + 15.4882i 0.788480 + 0.727700i
\(454\) 21.7651 37.6982i 1.02149 1.76926i
\(455\) 1.12609 1.95044i 0.0527918 0.0914381i
\(456\) 15.7727 4.91133i 0.738626 0.229994i
\(457\) −10.2326 17.7234i −0.478662 0.829066i 0.521039 0.853533i \(-0.325545\pi\)
−0.999701 + 0.0244665i \(0.992211\pi\)
\(458\) 9.90519 0.462839
\(459\) −22.3387 + 28.4760i −1.04268 + 1.32915i
\(460\) 11.2278 0.523501
\(461\) 2.29576 + 3.97638i 0.106924 + 0.185198i 0.914523 0.404534i \(-0.132566\pi\)
−0.807598 + 0.589733i \(0.799233\pi\)
\(462\) 5.44791 1.69638i 0.253460 0.0789225i
\(463\) 20.7405 35.9236i 0.963892 1.66951i 0.251331 0.967901i \(-0.419132\pi\)
0.712562 0.701609i \(-0.247535\pi\)
\(464\) 5.03136 8.71458i 0.233575 0.404564i
\(465\) 3.58068 + 3.30467i 0.166050 + 0.153250i
\(466\) 14.8122 + 25.6555i 0.686162 + 1.18847i
\(467\) 6.36603 0.294585 0.147292 0.989093i \(-0.452944\pi\)
0.147292 + 0.989093i \(0.452944\pi\)
\(468\) −16.8553 8.00668i −0.779138 0.370109i
\(469\) −4.02984 −0.186081
\(470\) −4.76012 8.24478i −0.219568 0.380303i
\(471\) −3.47992 + 15.4361i −0.160346 + 0.711257i
\(472\) 4.40850 7.63575i 0.202918 0.351464i
\(473\) −0.814737 + 1.41117i −0.0374617 + 0.0648855i
\(474\) −12.1061 + 53.6999i −0.556054 + 2.46652i
\(475\) 2.86858 + 4.96852i 0.131619 + 0.227971i
\(476\) −19.2368 −0.881719
\(477\) −25.4297 + 17.5370i −1.16435 + 0.802964i
\(478\) −61.7063 −2.82238
\(479\) −10.5752 18.3169i −0.483195 0.836918i 0.516619 0.856216i \(-0.327190\pi\)
−0.999814 + 0.0192973i \(0.993857\pi\)
\(480\) 9.49797 + 8.76583i 0.433521 + 0.400104i
\(481\) −13.1200 + 22.7244i −0.598218 + 1.03614i
\(482\) −6.77564 + 11.7358i −0.308622 + 0.534549i
\(483\) −6.72303 + 2.09342i −0.305909 + 0.0952541i
\(484\) 12.0429 + 20.8589i 0.547404 + 0.948131i
\(485\) −14.4990 −0.658365
\(486\) 30.4484 15.1664i 1.38117 0.687962i
\(487\) 5.09422 0.230841 0.115421 0.993317i \(-0.463178\pi\)
0.115421 + 0.993317i \(0.463178\pi\)
\(488\) −3.79995 6.58171i −0.172016 0.297940i
\(489\) −7.04084 + 2.19238i −0.318398 + 0.0991430i
\(490\) −1.09108 + 1.88981i −0.0492900 + 0.0853728i
\(491\) −11.8110 + 20.4572i −0.533023 + 0.923222i 0.466234 + 0.884662i \(0.345611\pi\)
−0.999256 + 0.0385605i \(0.987723\pi\)
\(492\) 5.73654 + 5.29435i 0.258623 + 0.238688i
\(493\) 18.4839 + 32.0151i 0.832474 + 1.44189i
\(494\) 28.1959 1.26859
\(495\) 3.72835 2.57117i 0.167577 0.115565i
\(496\) −5.33369 −0.239490
\(497\) −0.200154 0.346676i −0.00897811 0.0155506i
\(498\) 5.11370 22.6832i 0.229151 1.01646i
\(499\) 1.60691 2.78326i 0.0719354 0.124596i −0.827814 0.561003i \(-0.810416\pi\)
0.899749 + 0.436407i \(0.143749\pi\)
\(500\) 1.38091 2.39181i 0.0617564 0.106965i
\(501\) −3.47225 + 15.4020i −0.155129 + 0.688113i
\(502\) 27.9813 + 48.4650i 1.24887 + 2.16310i
\(503\) −13.1848 −0.587883 −0.293942 0.955823i \(-0.594967\pi\)
−0.293942 + 0.955823i \(0.594967\pi\)
\(504\) 4.50488 + 2.13992i 0.200663 + 0.0953198i
\(505\) 8.18145 0.364070
\(506\) 6.69629 + 11.5983i 0.297686 + 0.515608i
\(507\) 10.0905 + 9.31272i 0.448136 + 0.413592i
\(508\) −2.52752 + 4.37779i −0.112140 + 0.194233i
\(509\) 11.4102 19.7630i 0.505747 0.875979i −0.494231 0.869330i \(-0.664550\pi\)
0.999978 0.00664837i \(-0.00211626\pi\)
\(510\) −25.1356 + 7.82675i −1.11302 + 0.346574i
\(511\) −7.12867 12.3472i −0.315354 0.546209i
\(512\) −20.4517 −0.903847
\(513\) −18.4000 + 23.4552i −0.812378 + 1.03557i
\(514\) 20.9098 0.922292
\(515\) 4.28577 + 7.42318i 0.188854 + 0.327104i
\(516\) −4.92984 + 1.53506i −0.217024 + 0.0675771i
\(517\) 3.29313 5.70387i 0.144832 0.250856i
\(518\) 12.7121 22.0180i 0.558537 0.967415i
\(519\) −12.0359 11.1082i −0.528319 0.487594i
\(520\) −1.87205 3.24248i −0.0820947 0.142192i
\(521\) 11.5314 0.505201 0.252600 0.967571i \(-0.418714\pi\)
0.252600 + 0.967571i \(0.418714\pi\)
\(522\) −2.78120 34.6338i −0.121730 1.51588i
\(523\) 7.50782 0.328294 0.164147 0.986436i \(-0.447513\pi\)
0.164147 + 0.986436i \(0.447513\pi\)
\(524\) 24.3636 + 42.1990i 1.06433 + 1.84347i
\(525\) −0.380915 + 1.68965i −0.0166245 + 0.0737422i
\(526\) 7.72443 13.3791i 0.336801 0.583356i
\(527\) 9.79729 16.9694i 0.426777 0.739199i
\(528\) −1.09027 + 4.83617i −0.0474479 + 0.210467i
\(529\) 3.23641 + 5.60562i 0.140713 + 0.243723i
\(530\) −22.4693 −0.976003
\(531\) 1.27361 + 15.8599i 0.0552698 + 0.688263i
\(532\) −15.8450 −0.686970
\(533\) 1.83763 + 3.18288i 0.0795968 + 0.137866i
\(534\) 27.6205 + 25.4914i 1.19526 + 1.10312i
\(535\) 2.20667 3.82207i 0.0954028 0.165242i
\(536\) −3.34968 + 5.80181i −0.144684 + 0.250600i
\(537\) −19.8723 + 6.18785i −0.857552 + 0.267025i
\(538\) 7.13217 + 12.3533i 0.307490 + 0.532588i
\(539\) −1.50965 −0.0650254
\(540\) 14.2073 + 2.02534i 0.611383 + 0.0871566i
\(541\) −17.9217 −0.770513 −0.385256 0.922810i \(-0.625887\pi\)
−0.385256 + 0.922810i \(0.625887\pi\)
\(542\) −10.4371 18.0776i −0.448313 0.776500i
\(543\) 26.9054 8.37784i 1.15462 0.359528i
\(544\) 25.9879 45.0124i 1.11422 1.92989i
\(545\) −5.47164 + 9.47715i −0.234379 + 0.405957i
\(546\) 6.25541 + 5.77322i 0.267707 + 0.247071i
\(547\) −7.36929 12.7640i −0.315088 0.545749i 0.664368 0.747406i \(-0.268701\pi\)
−0.979456 + 0.201657i \(0.935367\pi\)
\(548\) 45.3816 1.93861
\(549\) 12.3880 + 5.88460i 0.528708 + 0.251149i
\(550\) 3.29431 0.140470
\(551\) 15.2249 + 26.3703i 0.648602 + 1.12341i
\(552\) −2.57438 + 11.4193i −0.109573 + 0.486038i
\(553\) 7.28217 12.6131i 0.309670 0.536363i
\(554\) 10.0965 17.4877i 0.428960 0.742980i
\(555\) 4.43801 19.6859i 0.188383 0.835621i
\(556\) −22.5454 39.0498i −0.956139 1.65608i
\(557\) −21.8306 −0.924992 −0.462496 0.886621i \(-0.653046\pi\)
−0.462496 + 0.886621i \(0.653046\pi\)
\(558\) −15.1609 + 10.4554i −0.641812 + 0.442611i
\(559\) −2.43093 −0.102817
\(560\) −0.947978 1.64195i −0.0400594 0.0693849i
\(561\) −13.3839 12.3522i −0.565067 0.521509i
\(562\) 11.4856 19.8937i 0.484493 0.839166i
\(563\) −14.8302 + 25.6867i −0.625018 + 1.08256i 0.363519 + 0.931587i \(0.381575\pi\)
−0.988537 + 0.150977i \(0.951758\pi\)
\(564\) 19.9262 6.20463i 0.839043 0.261262i
\(565\) 1.31168 + 2.27190i 0.0551829 + 0.0955796i
\(566\) −39.6875 −1.66819
\(567\) −8.88467 + 1.43620i −0.373121 + 0.0603146i
\(568\) −0.665485 −0.0279231
\(569\) −19.0696 33.0295i −0.799439 1.38467i −0.919982 0.391961i \(-0.871797\pi\)
0.120543 0.992708i \(-0.461536\pi\)
\(570\) −20.7038 + 6.44676i −0.867185 + 0.270025i
\(571\) −17.9601 + 31.1078i −0.751608 + 1.30182i 0.195436 + 0.980717i \(0.437388\pi\)
−0.947043 + 0.321106i \(0.895945\pi\)
\(572\) 4.69512 8.13218i 0.196313 0.340024i
\(573\) 2.05052 + 1.89245i 0.0856615 + 0.0790584i
\(574\) −1.78051 3.08393i −0.0743169 0.128721i
\(575\) −4.06536 −0.169537
\(576\) −30.8504 + 21.2753i −1.28543 + 0.886470i
\(577\) 22.0851 0.919415 0.459708 0.888070i \(-0.347954\pi\)
0.459708 + 0.888070i \(0.347954\pi\)
\(578\) 34.3852 + 59.5568i 1.43023 + 2.47724i
\(579\) 5.28415 23.4392i 0.219602 0.974101i
\(580\) 7.32916 12.6945i 0.304327 0.527110i
\(581\) −3.07603 + 5.32784i −0.127615 + 0.221036i
\(582\) 12.0518 53.4589i 0.499564 2.21594i
\(583\) −7.77230 13.4620i −0.321896 0.557540i
\(584\) −23.7019 −0.980792
\(585\) 6.10296 + 2.89905i 0.252326 + 0.119861i
\(586\) 67.0015 2.76781
\(587\) −2.50433 4.33763i −0.103365 0.179033i 0.809704 0.586838i \(-0.199628\pi\)
−0.913069 + 0.407805i \(0.866294\pi\)
\(588\) −3.51531 3.24433i −0.144969 0.133794i
\(589\) 8.06985 13.9774i 0.332512 0.575929i
\(590\) −5.78673 + 10.0229i −0.238236 + 0.412637i
\(591\) 43.9440 13.6833i 1.80761 0.562857i
\(592\) 11.0448 + 19.1302i 0.453939 + 0.786246i
\(593\) 0.443763 0.0182231 0.00911157 0.999958i \(-0.497100\pi\)
0.00911157 + 0.999958i \(0.497100\pi\)
\(594\) 6.38104 + 15.8839i 0.261817 + 0.651725i
\(595\) 6.96525 0.285548
\(596\) −21.1392 36.6142i −0.865896 1.49978i
\(597\) 2.88785 0.899222i 0.118192 0.0368027i
\(598\) −9.98984 + 17.3029i −0.408515 + 0.707569i
\(599\) 7.62637 13.2093i 0.311605 0.539716i −0.667105 0.744964i \(-0.732467\pi\)
0.978710 + 0.205248i \(0.0658001\pi\)
\(600\) 2.11598 + 1.95287i 0.0863845 + 0.0797256i
\(601\) −12.5895 21.8057i −0.513538 0.889474i −0.999877 0.0157036i \(-0.995001\pi\)
0.486339 0.873770i \(-0.338332\pi\)
\(602\) 2.35536 0.0959972
\(603\) −0.967714 12.0507i −0.0394083 0.490744i
\(604\) −36.4141 −1.48167
\(605\) −4.36047 7.55256i −0.177278 0.307055i
\(606\) −6.80056 + 30.1657i −0.276254 + 1.22540i
\(607\) −4.51571 + 7.82144i −0.183287 + 0.317462i −0.942998 0.332799i \(-0.892007\pi\)
0.759711 + 0.650261i \(0.225340\pi\)
\(608\) 21.4058 37.0759i 0.868119 1.50363i
\(609\) −2.02169 + 8.96774i −0.0819231 + 0.363391i
\(610\) 4.98793 + 8.63935i 0.201955 + 0.349797i
\(611\) 9.82570 0.397505
\(612\) −4.61947 57.5254i −0.186731 2.32532i
\(613\) −40.6655 −1.64246 −0.821231 0.570596i \(-0.806712\pi\)
−0.821231 + 0.570596i \(0.806712\pi\)
\(614\) −19.8725 34.4203i −0.801991 1.38909i
\(615\) −2.07708 1.91697i −0.0837560 0.0772997i
\(616\) −1.25485 + 2.17347i −0.0505594 + 0.0875714i
\(617\) −22.1187 + 38.3108i −0.890467 + 1.54233i −0.0511506 + 0.998691i \(0.516289\pi\)
−0.839316 + 0.543643i \(0.817044\pi\)
\(618\) −30.9323 + 9.63172i −1.24428 + 0.387445i
\(619\) −9.57864 16.5907i −0.384998 0.666836i 0.606771 0.794877i \(-0.292465\pi\)
−0.991769 + 0.128041i \(0.959131\pi\)
\(620\) −7.76955 −0.312033
\(621\) −7.87457 19.6017i −0.315995 0.786588i
\(622\) −33.4479 −1.34114
\(623\) −4.97219 8.61209i −0.199207 0.345036i
\(624\) −7.06149 + 2.19881i −0.282686 + 0.0880230i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 23.2281 40.2322i 0.928381 1.60800i
\(627\) −11.0240 10.1743i −0.440258 0.406321i
\(628\) −12.6156 21.8509i −0.503418 0.871945i
\(629\) −81.1516 −3.23573
\(630\) −5.91324 2.80893i −0.235589 0.111910i
\(631\) −39.5474 −1.57436 −0.787179 0.616725i \(-0.788459\pi\)
−0.787179 + 0.616725i \(0.788459\pi\)
\(632\) −12.1061 20.9685i −0.481557 0.834080i
\(633\) −7.10212 + 31.5033i −0.282284 + 1.25214i
\(634\) −13.0451 + 22.5948i −0.518088 + 0.897355i
\(635\) 0.915160 1.58510i 0.0363170 0.0629029i
\(636\) 10.8325 48.0502i 0.429535 1.90531i
\(637\) −1.12609 1.95044i −0.0446172 0.0772793i
\(638\) 17.4844 0.692216
\(639\) 0.988627 0.681784i 0.0391095 0.0269709i
\(640\) −12.3346 −0.487569
\(641\) −14.2408 24.6658i −0.562478 0.974240i −0.997279 0.0737136i \(-0.976515\pi\)
0.434802 0.900526i \(-0.356818\pi\)
\(642\) 12.2581 + 11.3132i 0.483787 + 0.446495i
\(643\) −3.38899 + 5.86990i −0.133649 + 0.231486i −0.925080 0.379771i \(-0.876003\pi\)
0.791432 + 0.611258i \(0.209336\pi\)
\(644\) 5.61392 9.72360i 0.221220 0.383163i
\(645\) 1.78499 0.555812i 0.0702839 0.0218851i
\(646\) 43.6004 + 75.5181i 1.71543 + 2.97122i
\(647\) −4.88796 −0.192165 −0.0960827 0.995373i \(-0.530631\pi\)
−0.0960827 + 0.995373i \(0.530631\pi\)
\(648\) −5.31738 + 13.9851i −0.208887 + 0.549389i
\(649\) −8.00670 −0.314291
\(650\) 2.45731 + 4.25618i 0.0963834 + 0.166941i
\(651\) 4.65227 1.44863i 0.182337 0.0567762i
\(652\) 5.87930 10.1832i 0.230251 0.398807i
\(653\) −2.84057 + 4.92001i −0.111160 + 0.192535i −0.916238 0.400634i \(-0.868790\pi\)
0.805078 + 0.593169i \(0.202123\pi\)
\(654\) −30.3949 28.0519i −1.18854 1.09692i
\(655\) −8.82154 15.2794i −0.344686 0.597014i
\(656\) 3.09396 0.120799
\(657\) 35.2110 24.2824i 1.37371 0.947347i
\(658\) −9.52025 −0.371138
\(659\) −4.77505 8.27063i −0.186009 0.322178i 0.757907 0.652363i \(-0.226222\pi\)
−0.943916 + 0.330185i \(0.892889\pi\)
\(660\) −1.58819 + 7.04482i −0.0618202 + 0.274219i
\(661\) −1.92056 + 3.32651i −0.0747013 + 0.129386i −0.900956 0.433910i \(-0.857134\pi\)
0.826255 + 0.563296i \(0.190467\pi\)
\(662\) 16.9354 29.3329i 0.658211 1.14006i
\(663\) 5.97540 26.5054i 0.232065 1.02939i
\(664\) 5.11370 + 8.85720i 0.198450 + 0.343726i
\(665\) 5.73716 0.222477
\(666\) 68.8947 + 32.7266i 2.66961 + 1.26813i
\(667\) −21.5768 −0.835457
\(668\) −12.5878 21.8027i −0.487036 0.843572i
\(669\) 26.2458 + 24.2227i 1.01472 + 0.936503i
\(670\) 4.39689 7.61563i 0.169867 0.294217i
\(671\) −3.45073 + 5.97684i −0.133214 + 0.230733i
\(672\) 12.3404 3.84257i 0.476042 0.148230i
\(673\) 14.7759 + 25.5926i 0.569569 + 0.986522i 0.996609 + 0.0822890i \(0.0262230\pi\)
−0.427040 + 0.904233i \(0.640444\pi\)
\(674\) −8.81646 −0.339597
\(675\) −5.14414 0.733331i −0.197998 0.0282259i
\(676\) −21.8950 −0.842114
\(677\) 14.8529 + 25.7260i 0.570844 + 0.988730i 0.996480 + 0.0838357i \(0.0267171\pi\)
−0.425636 + 0.904894i \(0.639950\pi\)
\(678\) −9.46698 + 2.94784i −0.363577 + 0.113211i
\(679\) −7.24949 + 12.5565i −0.278210 + 0.481874i
\(680\) 5.78964 10.0280i 0.222023 0.384554i
\(681\) −25.3904 23.4332i −0.972963 0.897963i
\(682\) −4.63376 8.02591i −0.177436 0.307328i
\(683\) −44.2805 −1.69435 −0.847174 0.531316i \(-0.821698\pi\)
−0.847174 + 0.531316i \(0.821698\pi\)
\(684\) −3.80498 47.3826i −0.145487 1.81172i
\(685\) −16.4317 −0.627824
\(686\) 1.09108 + 1.88981i 0.0416577 + 0.0721532i
\(687\) 1.72904 7.66958i 0.0659668 0.292613i
\(688\) −1.02322 + 1.77227i −0.0390099 + 0.0675670i
\(689\) 11.5951 20.0833i 0.441738 0.765113i
\(690\) 3.37920 14.9893i 0.128644 0.570634i
\(691\) 16.1568 + 27.9843i 0.614632 + 1.06457i 0.990449 + 0.137880i \(0.0440288\pi\)
−0.375817 + 0.926694i \(0.622638\pi\)
\(692\) 26.1162 0.992790
\(693\) −0.362523 4.51443i −0.0137711 0.171489i
\(694\) 4.33521 0.164562
\(695\) 8.16323 + 14.1391i 0.309649 + 0.536327i
\(696\) 11.2305 + 10.3648i 0.425691 + 0.392877i
\(697\) −5.68321 + 9.84361i −0.215267 + 0.372853i
\(698\) −36.2322 + 62.7561i −1.37141 + 2.37535i
\(699\) 22.4506 6.99070i 0.849161 0.264413i
\(700\) −1.38091 2.39181i −0.0521937 0.0904021i
\(701\) 31.3623 1.18454 0.592269 0.805740i \(-0.298232\pi\)
0.592269 + 0.805740i \(0.298232\pi\)
\(702\) −15.7619 + 20.0924i −0.594895 + 0.758338i
\(703\) −66.8431 −2.52104
\(704\) −9.42908 16.3317i −0.355372 0.615522i
\(705\) −7.21484 + 2.24656i −0.271727 + 0.0846105i
\(706\) 33.3617 57.7841i 1.25558 2.17473i
\(707\) 4.09072 7.08534i 0.153847 0.266472i
\(708\) −18.6440 17.2069i −0.700685 0.646674i
\(709\) −17.7983 30.8276i −0.668429 1.15775i −0.978343 0.206989i \(-0.933634\pi\)
0.309914 0.950765i \(-0.399700\pi\)
\(710\) 0.873535 0.0327832
\(711\) 39.4666 + 18.7476i 1.48011 + 0.703088i
\(712\) −16.5319 −0.619559
\(713\) 5.71832 + 9.90442i 0.214153 + 0.370923i
\(714\) −5.78964 + 25.6815i −0.216672 + 0.961104i
\(715\) −1.70000 + 2.94449i −0.0635765 + 0.110118i
\(716\) 16.5939 28.7415i 0.620144 1.07412i
\(717\) −10.7714 + 47.7792i −0.402264 + 1.78435i
\(718\) −16.8759 29.2300i −0.629805 1.09085i
\(719\) −3.70852 −0.138304 −0.0691522 0.997606i \(-0.522029\pi\)
−0.0691522 + 0.997606i \(0.522029\pi\)
\(720\) 4.68239 3.22910i 0.174502 0.120341i
\(721\) 8.57155 0.319221
\(722\) 15.1823 + 26.2966i 0.565028 + 0.978658i
\(723\) 7.90424 + 7.29495i 0.293962 + 0.271302i
\(724\) −22.4668 + 38.9137i −0.834973 + 1.44622i
\(725\) −2.65373 + 4.59640i −0.0985572 + 0.170706i
\(726\) 31.4714 9.79959i 1.16801 0.363697i
\(727\) 10.6288 + 18.4096i 0.394199 + 0.682773i 0.992999 0.118126i \(-0.0376887\pi\)
−0.598800 + 0.800899i \(0.704355\pi\)
\(728\) −3.74410 −0.138765
\(729\) −6.42830 26.2236i −0.238085 0.971244i
\(730\) 31.1118 1.15150
\(731\) −3.75904 6.51085i −0.139033 0.240812i
\(732\) −20.8798 + 6.50157i −0.771739 + 0.240305i
\(733\) −14.2601 + 24.6992i −0.526707 + 0.912284i 0.472808 + 0.881165i \(0.343240\pi\)
−0.999516 + 0.0311188i \(0.990093\pi\)
\(734\) 27.9163 48.3525i 1.03041 1.78472i
\(735\) 1.27282 + 1.17470i 0.0469486 + 0.0433296i
\(736\) 15.1682 + 26.2721i 0.559107 + 0.968402i
\(737\) 6.08367 0.224095
\(738\) 8.79453 6.06495i 0.323731 0.223254i
\(739\) −5.88760 −0.216579 −0.108289 0.994119i \(-0.534537\pi\)
−0.108289 + 0.994119i \(0.534537\pi\)
\(740\) 16.0889 + 27.8668i 0.591441 + 1.02441i
\(741\) 4.92183 21.8321i 0.180808 0.802020i
\(742\) −11.2346 + 19.4590i −0.412437 + 0.714361i
\(743\) 18.8798 32.7008i 0.692633 1.19967i −0.278340 0.960483i \(-0.589784\pi\)
0.970972 0.239192i \(-0.0768826\pi\)
\(744\) 1.78144 7.90204i 0.0653108 0.289703i
\(745\) 7.65407 + 13.2572i 0.280423 + 0.485707i
\(746\) 41.6262 1.52404
\(747\) −16.6709 7.91907i −0.609957 0.289744i
\(748\) 29.0410 1.06184
\(749\) −2.20667 3.82207i −0.0806301 0.139655i
\(750\) −2.77750 2.56340i −0.101420 0.0936020i
\(751\) 7.63491 13.2241i 0.278602 0.482552i −0.692436 0.721480i \(-0.743462\pi\)
0.971037 + 0.238927i \(0.0767957\pi\)
\(752\) 4.13580 7.16342i 0.150817 0.261223i
\(753\) 42.4108 13.2059i 1.54554 0.481250i
\(754\) 13.0421 + 22.5895i 0.474964 + 0.822662i
\(755\) 13.1848 0.479843
\(756\) 8.85762 11.2912i 0.322148 0.410656i
\(757\) 17.2984 0.628720 0.314360 0.949304i \(-0.398210\pi\)
0.314360 + 0.949304i \(0.398210\pi\)
\(758\) 0.246958 + 0.427743i 0.00896990 + 0.0155363i
\(759\) 10.1495 3.16035i 0.368402 0.114713i
\(760\) 4.76882 8.25985i 0.172983 0.299616i
\(761\) 12.3241 21.3460i 0.446749 0.773791i −0.551424 0.834225i \(-0.685915\pi\)
0.998172 + 0.0604342i \(0.0192485\pi\)
\(762\) 5.08371 + 4.69184i 0.184163 + 0.169967i
\(763\) 5.47164 + 9.47715i 0.198087 + 0.343096i
\(764\) −4.44931 −0.160971
\(765\) 1.67261 + 20.8287i 0.0604735 + 0.753064i
\(766\) −71.7459 −2.59228
\(767\) −5.97239 10.3445i −0.215651 0.373518i
\(768\) 0.736205 3.26563i 0.0265655 0.117838i
\(769\) −8.50238 + 14.7266i −0.306604 + 0.531053i −0.977617 0.210392i \(-0.932526\pi\)
0.671013 + 0.741445i \(0.265859\pi\)
\(770\) 1.64715 2.85296i 0.0593593 0.102813i
\(771\) 3.64998 16.1905i 0.131451 0.583085i
\(772\) 19.1564 + 33.1799i 0.689455 + 1.19417i
\(773\) 13.6622 0.491396 0.245698 0.969346i \(-0.420983\pi\)
0.245698 + 0.969346i \(0.420983\pi\)
\(774\) 0.565608 + 7.04340i 0.0203304 + 0.253170i
\(775\) 2.81319 0.101053
\(776\) 12.0518 + 20.8743i 0.432635 + 0.749345i
\(777\) −14.8295 13.6864i −0.532006 0.490997i
\(778\) −2.00690 + 3.47605i −0.0719507 + 0.124622i
\(779\) −4.68116 + 8.10801i −0.167720 + 0.290499i
\(780\) −10.2864 + 3.20300i −0.368313 + 0.114686i
\(781\) 0.302163 + 0.523361i 0.0108122 + 0.0187273i
\(782\) −61.7907 −2.20963
\(783\) −27.3024 3.89213i −0.975708 0.139093i
\(784\) −1.89596 −0.0677127
\(785\) 4.56785 + 7.91174i 0.163033 + 0.282382i
\(786\) 63.6688 19.8253i 2.27099 0.707144i
\(787\) 20.0360 34.7034i 0.714208 1.23704i −0.249057 0.968489i \(-0.580121\pi\)
0.963264 0.268555i \(-0.0865461\pi\)
\(788\) −36.6945 + 63.5567i −1.30719 + 2.26411i
\(789\) −9.01106 8.31645i −0.320802 0.296074i
\(790\) 15.8909 + 27.5238i 0.565372 + 0.979253i
\(791\) 2.62337 0.0932761
\(792\) −6.80081 3.23054i −0.241656 0.114792i
\(793\) −10.2959 −0.365619
\(794\) 37.7503 + 65.3854i 1.33971 + 2.32044i
\(795\) −3.92220 + 17.3979i −0.139106 + 0.617042i
\(796\) −2.41144 + 4.17673i −0.0854712 + 0.148040i
\(797\) −22.6210 + 39.1807i −0.801277 + 1.38785i 0.117500 + 0.993073i \(0.462512\pi\)
−0.918776 + 0.394779i \(0.870821\pi\)
\(798\) −4.76882 + 21.1534i −0.168815 + 0.748821i
\(799\) 15.1939 + 26.3165i 0.537520 + 0.931013i
\(800\) 7.46215 0.263827
\(801\) 24.5594 16.9368i 0.867762 0.598432i
\(802\) 7.64690 0.270022
\(803\) 10.7618 + 18.6400i 0.379777 + 0.657793i
\(804\) 14.1661 + 13.0742i 0.499602 + 0.461090i
\(805\) −2.03268 + 3.52071i −0.0716426 + 0.124089i
\(806\) 6.91286 11.9734i 0.243495 0.421746i
\(807\) 10.8101 3.36607i 0.380534 0.118491i
\(808\) −6.80056 11.7789i −0.239243 0.414381i
\(809\) −27.0132 −0.949734 −0.474867 0.880058i \(-0.657504\pi\)
−0.474867 + 0.880058i \(0.657504\pi\)
\(810\) 6.97976 18.3573i 0.245244 0.645010i
\(811\) 10.1468 0.356301 0.178150 0.984003i \(-0.442989\pi\)
0.178150 + 0.984003i \(0.442989\pi\)
\(812\) −7.32916 12.6945i −0.257203 0.445489i
\(813\) −15.8194 + 4.92585i −0.554810 + 0.172757i
\(814\) −19.1909 + 33.2396i −0.672640 + 1.16505i
\(815\) −2.12877 + 3.68714i −0.0745676 + 0.129155i
\(816\) −16.8086 15.5129i −0.588419 0.543062i
\(817\) −3.09625 5.36287i −0.108324 0.187623i
\(818\) 23.6223 0.825933
\(819\) 5.56213 3.83580i 0.194357 0.134034i
\(820\) 4.50696 0.157390
\(821\) −12.0032 20.7902i −0.418915 0.725582i 0.576916 0.816804i \(-0.304256\pi\)
−0.995831 + 0.0912220i \(0.970923\pi\)
\(822\) 13.6583 60.5851i 0.476389 2.11315i
\(823\) 9.50147 16.4570i 0.331200 0.573656i −0.651547 0.758608i \(-0.725880\pi\)
0.982747 + 0.184952i \(0.0592131\pi\)
\(824\) 7.12482 12.3406i 0.248205 0.429904i
\(825\) 0.575050 2.55078i 0.0200207 0.0888068i
\(826\) 5.78673 + 10.0229i 0.201346 + 0.348742i
\(827\) −23.6824 −0.823518 −0.411759 0.911293i \(-0.635085\pi\)
−0.411759 + 0.911293i \(0.635085\pi\)
\(828\) 30.4253 + 14.4527i 1.05735 + 0.502267i
\(829\) 29.1824 1.01355 0.506774 0.862079i \(-0.330838\pi\)
0.506774 + 0.862079i \(0.330838\pi\)
\(830\) −6.71240 11.6262i −0.232991 0.403552i
\(831\) −11.7783 10.8703i −0.408583 0.377088i
\(832\) 14.0668 24.3644i 0.487677 0.844682i
\(833\) 3.48263 6.03209i 0.120666 0.208999i
\(834\) −58.9175 + 18.3458i −2.04015 + 0.635263i
\(835\) 4.55777 + 7.89429i 0.157728 + 0.273193i
\(836\) 23.9205 0.827309
\(837\) 5.44912 + 13.5641i 0.188349 + 0.468845i
\(838\) 28.3548 0.979501
\(839\) 3.81234 + 6.60317i 0.131617 + 0.227967i 0.924300 0.381667i \(-0.124650\pi\)
−0.792683 + 0.609634i \(0.791317\pi\)
\(840\) 2.74923 0.856056i 0.0948573 0.0295368i
\(841\) 0.415394 0.719483i 0.0143239 0.0248097i
\(842\) 36.2727 62.8261i 1.25004 2.16513i
\(843\) −13.3988 12.3659i −0.461479 0.425906i
\(844\) −25.7470 44.5952i −0.886249 1.53503i
\(845\) 7.92771 0.272721
\(846\) −2.28616 28.4691i −0.0785998 0.978788i
\(847\) −8.72094 −0.299655
\(848\) −9.76114 16.9068i −0.335199 0.580582i
\(849\) −6.92780 + 30.7300i −0.237761 + 1.05465i
\(850\) −7.59966 + 13.1630i −0.260666 + 0.451487i
\(851\) 23.6826 41.0195i 0.811830 1.40613i
\(852\) −0.421132 + 1.86804i −0.0144277 + 0.0639980i
\(853\) −11.9125 20.6330i −0.407876 0.706462i 0.586776 0.809750i \(-0.300397\pi\)
−0.994652 + 0.103288i \(0.967064\pi\)
\(854\) 9.97586 0.341367
\(855\) 1.37770 + 17.1562i 0.0471164 + 0.586731i
\(856\) −7.33690 −0.250770
\(857\) 7.85857 + 13.6114i 0.268444 + 0.464958i 0.968460 0.249169i \(-0.0801574\pi\)
−0.700016 + 0.714127i \(0.746824\pi\)
\(858\) −9.44351 8.71556i −0.322396 0.297544i
\(859\) 11.3041 19.5792i 0.385689 0.668033i −0.606175 0.795331i \(-0.707297\pi\)
0.991865 + 0.127298i \(0.0406303\pi\)
\(860\) −1.49052 + 2.58165i −0.0508262 + 0.0880336i
\(861\) −2.69869 + 0.840319i −0.0919710 + 0.0286380i
\(862\) 24.6612 + 42.7144i 0.839964 + 1.45486i
\(863\) −44.0266 −1.49868 −0.749342 0.662183i \(-0.769630\pi\)
−0.749342 + 0.662183i \(0.769630\pi\)
\(864\) 14.4541 + 35.9797i 0.491739 + 1.22405i
\(865\) −9.45613 −0.321518
\(866\) −15.2498 26.4135i −0.518211 0.897568i
\(867\) 52.1170 16.2282i 1.76999 0.551140i
\(868\) −3.88477 + 6.72863i −0.131858 + 0.228384i
\(869\) −10.9936 + 19.0414i −0.372931 + 0.645936i
\(870\) −14.7415 13.6051i −0.499783 0.461257i
\(871\) 4.53796 + 7.85997i 0.153763 + 0.266325i
\(872\) 18.1925 0.616075
\(873\) −39.2895 18.6634i −1.32975 0.631661i
\(874\) −50.8959 −1.72158
\(875\) 0.500000 + 0.866025i 0.0169031 + 0.0292770i
\(876\) −14.9990 + 66.5321i −0.506770 + 2.24791i
\(877\) −23.9138 + 41.4199i −0.807512 + 1.39865i 0.107070 + 0.994252i \(0.465853\pi\)
−0.914582 + 0.404401i \(0.867480\pi\)
\(878\) 19.1332 33.1396i 0.645713 1.11841i
\(879\) 11.6957 51.8792i 0.394485 1.74984i
\(880\) 1.43112 + 2.47877i 0.0482430 + 0.0835594i
\(881\) −45.3688 −1.52851 −0.764257 0.644912i \(-0.776894\pi\)
−0.764257 + 0.644912i \(0.776894\pi\)
\(882\) −5.38922 + 3.71655i −0.181465 + 0.125143i
\(883\) 38.8987 1.30905 0.654523 0.756042i \(-0.272870\pi\)
0.654523 + 0.756042i \(0.272870\pi\)
\(884\) 21.6624 + 37.5203i 0.728584 + 1.26195i
\(885\) 6.75061 + 6.23024i 0.226919 + 0.209427i
\(886\) −32.9056 + 56.9941i −1.10548 + 1.91475i
\(887\) 13.3319 23.0915i 0.447641 0.775336i −0.550591 0.834775i \(-0.685598\pi\)
0.998232 + 0.0594387i \(0.0189311\pi\)
\(888\) −32.0310 + 9.97384i −1.07489 + 0.334700i
\(889\) −0.915160 1.58510i −0.0306935 0.0531627i
\(890\) 21.7002 0.727394
\(891\) 13.4128 2.16816i 0.449345 0.0726361i
\(892\) −56.9496 −1.90681
\(893\) 12.5149 + 21.6765i 0.418796 + 0.725375i
\(894\) −55.2427 + 17.2015i −1.84759 + 0.575305i
\(895\) −6.00831 + 10.4067i −0.200836 + 0.347857i
\(896\) −6.16732 + 10.6821i −0.206036 + 0.356864i
\(897\) 11.6538 + 10.7555i 0.389110 + 0.359116i
\(898\) −9.88770 17.1260i −0.329957 0.571502i
\(899\) 14.9309 0.497974
\(900\) 6.82081 4.70381i 0.227360 0.156794i
\(901\) 71.7198 2.38933
\(902\) 2.68795 + 4.65567i 0.0894990 + 0.155017i
\(903\) 0.411148 1.82375i 0.0136821 0.0606907i
\(904\) 2.18059 3.77689i 0.0725253 0.125617i
\(905\) 8.13476 14.0898i 0.270409 0.468361i
\(906\) −10.9594 + 48.6134i −0.364102 + 1.61507i
\(907\) −16.1330 27.9431i −0.535686 0.927836i −0.999130 0.0417093i \(-0.986720\pi\)
0.463444 0.886126i \(-0.346614\pi\)
\(908\) 55.0935 1.82834
\(909\) 22.1701 + 10.5313i 0.735337 + 0.349302i
\(910\) 4.91461 0.162918
\(911\) 8.06651 + 13.9716i 0.267255 + 0.462900i 0.968152 0.250363i \(-0.0805499\pi\)
−0.700897 + 0.713263i \(0.747217\pi\)
\(912\) −13.8450 12.7777i −0.458452 0.423113i
\(913\) 4.64375 8.04320i 0.153686 0.266191i
\(914\) 22.3292 38.6754i 0.738585 1.27927i
\(915\) 7.56013 2.35408i 0.249930 0.0778235i
\(916\) 6.26820 + 10.8568i 0.207107 + 0.358720i
\(917\) −17.6431 −0.582626
\(918\) −78.1875 11.1461i −2.58057 0.367877i
\(919\) 47.4357 1.56476 0.782380 0.622802i \(-0.214006\pi\)
0.782380 + 0.622802i \(0.214006\pi\)
\(920\) 3.37920 + 5.85295i 0.111409 + 0.192966i
\(921\) −30.1205 + 9.37895i −0.992504 + 0.309047i
\(922\) −5.00972 + 8.67710i −0.164986 + 0.285765i
\(923\) −0.450781 + 0.780775i −0.0148376 + 0.0256995i
\(924\) 5.30690 + 4.89782i 0.174584 + 0.161127i
\(925\) −5.82546 10.0900i −0.191540 0.331757i
\(926\) 90.5182 2.97461
\(927\) 2.05834 + 25.6321i 0.0676049 + 0.841870i
\(928\) 39.6051 1.30010
\(929\) 16.9992 + 29.4435i 0.557726 + 0.966010i 0.997686 + 0.0679924i \(0.0216594\pi\)
−0.439960 + 0.898017i \(0.645007\pi\)
\(930\) −2.33837 + 10.3725i −0.0766783 + 0.340126i
\(931\) 2.86858 4.96852i 0.0940138 0.162837i
\(932\) −18.7469 + 32.4706i −0.614076 + 1.06361i
\(933\) −5.83861 + 25.8987i −0.191148 + 0.847885i
\(934\) 6.94585 + 12.0306i 0.227275 + 0.393652i
\(935\) −10.5151 −0.343881
\(936\) −0.899095 11.1962i −0.0293878 0.365961i
\(937\) −17.3685 −0.567405 −0.283703 0.958912i \(-0.591563\pi\)
−0.283703 + 0.958912i \(0.591563\pi\)
\(938\) −4.39689 7.61563i −0.143563 0.248659i
\(939\) −27.0971 25.0084i −0.884281 0.816117i
\(940\) 6.02460 10.4349i 0.196501 0.340349i
\(941\) −20.8360 + 36.0891i −0.679235 + 1.17647i 0.295976 + 0.955195i \(0.404355\pi\)
−0.975212 + 0.221275i \(0.928978\pi\)
\(942\) −32.9681 + 10.2656i −1.07416 + 0.334473i
\(943\) −3.31708 5.74536i −0.108019 0.187095i
\(944\) −10.0555 −0.327279
\(945\) −3.20716 + 4.08829i −0.104329 + 0.132992i
\(946\) −3.55578 −0.115608
\(947\) 24.1437 + 41.8181i 0.784565 + 1.35891i 0.929258 + 0.369430i \(0.120447\pi\)
−0.144693 + 0.989477i \(0.546220\pi\)
\(948\) −66.5202 + 20.7131i −2.16048 + 0.672731i
\(949\) −16.0550 + 27.8081i −0.521168 + 0.902689i
\(950\) −6.25970 + 10.8421i −0.203092 + 0.351765i
\(951\) 15.2180 + 14.0449i 0.493478 + 0.455439i
\(952\) −5.78964 10.0280i −0.187643 0.325008i
\(953\) −22.7274 −0.736213 −0.368106 0.929784i \(-0.619994\pi\)
−0.368106 + 0.929784i \(0.619994\pi\)
\(954\) −60.8874 28.9230i −1.97130 0.936415i
\(955\) 1.61100 0.0521308
\(956\) −39.0490 67.6348i −1.26293 2.18747i
\(957\) 3.05206 13.5382i 0.0986590 0.437628i
\(958\) 23.0769 39.9703i 0.745580 1.29138i
\(959\) −8.21586 + 14.2303i −0.265304 + 0.459520i
\(960\) −4.75828 + 21.1066i −0.153573 + 0.681212i
\(961\) 11.5430 + 19.9930i 0.372354 + 0.644937i
\(962\) −57.2597 −1.84613
\(963\) 10.8995 7.51660i 0.351232 0.242219i
\(964\) −17.1510 −0.552398
\(965\) −6.93614 12.0137i −0.223282 0.386736i
\(966\) −11.2915 10.4211i −0.363299 0.335295i
\(967\) 16.0398 27.7818i 0.515805 0.893401i −0.484026 0.875053i \(-0.660826\pi\)
0.999832 0.0183477i \(-0.00584058\pi\)
\(968\) −7.24900 + 12.5556i −0.232992 + 0.403554i
\(969\) 66.0844 20.5774i 2.12294 0.661042i
\(970\) −15.8196 27.4003i −0.507936 0.879770i
\(971\) −19.7116 −0.632575 −0.316288 0.948663i \(-0.602437\pi\)
−0.316288 + 0.948663i \(0.602437\pi\)
\(972\) 35.8919 + 23.7762i 1.15123 + 0.762621i
\(973\) 16.3265 0.523402
\(974\) 5.55820 + 9.62709i 0.178096 + 0.308472i
\(975\) 3.72450 1.15974i 0.119279 0.0371413i
\(976\) −4.33373 + 7.50624i −0.138719 + 0.240269i
\(977\) 21.2412 36.7909i 0.679567 1.17704i −0.295544 0.955329i \(-0.595501\pi\)
0.975111 0.221716i \(-0.0711657\pi\)
\(978\) −11.8253 10.9138i −0.378132 0.348984i
\(979\) 7.50629 + 13.0013i 0.239902 + 0.415523i
\(980\) −2.76183 −0.0882234
\(981\) −27.0263 + 18.6381i −0.862883 + 0.595067i
\(982\) −51.5470 −1.64493
\(983\) 5.38194 + 9.32179i 0.171657 + 0.297319i 0.938999 0.343919i \(-0.111755\pi\)
−0.767342 + 0.641238i \(0.778421\pi\)
\(984\) −1.03338 + 4.58382i −0.0329429 + 0.146127i
\(985\) 13.2863 23.0125i 0.423336 0.733240i
\(986\) −40.3349 + 69.8621i −1.28453 + 2.22486i
\(987\) −1.66184 + 7.37152i −0.0528969 + 0.234638i
\(988\) 17.8429 + 30.9048i 0.567659 + 0.983213i
\(989\) 4.38803 0.139531
\(990\) 8.92695 + 4.24051i 0.283717 + 0.134772i
\(991\) 16.2759 0.517022 0.258511 0.966008i \(-0.416768\pi\)
0.258511 + 0.966008i \(0.416768\pi\)
\(992\) −10.4962 18.1800i −0.333256 0.577216i
\(993\) −19.7562 18.2333i −0.626945 0.578617i
\(994\) 0.436767 0.756503i 0.0138534 0.0239948i
\(995\) 0.873131 1.51231i 0.0276801 0.0479434i
\(996\) 28.0985 8.74934i 0.890335 0.277234i
\(997\) −2.26128 3.91664i −0.0716153 0.124041i 0.827994 0.560737i \(-0.189482\pi\)
−0.899609 + 0.436695i \(0.856149\pi\)
\(998\) 7.01310 0.221996
\(999\) 37.3663 47.6324i 1.18222 1.50702i
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 315.2.i.e.211.5 yes 12
3.2 odd 2 945.2.i.e.631.2 12
9.2 odd 6 945.2.i.e.316.2 12
9.4 even 3 2835.2.a.u.1.2 6
9.5 odd 6 2835.2.a.v.1.5 6
9.7 even 3 inner 315.2.i.e.106.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.i.e.106.5 12 9.7 even 3 inner
315.2.i.e.211.5 yes 12 1.1 even 1 trivial
945.2.i.e.316.2 12 9.2 odd 6
945.2.i.e.631.2 12 3.2 odd 2
2835.2.a.u.1.2 6 9.4 even 3
2835.2.a.v.1.5 6 9.5 odd 6