Properties

Label 240.2.bk.b.11.1
Level $240$
Weight $2$
Character 240.11
Analytic conductor $1.916$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [240,2,Mod(11,240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(240, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("240.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.bk (of order \(4\), 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: \(1.91640964851\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(30\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 11.1
Character \(\chi\) \(=\) 240.11
Dual form 240.2.bk.b.131.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39972 + 0.201959i) q^{2} +(1.67583 - 0.437717i) q^{3} +(1.91842 - 0.565372i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-2.25729 + 0.951130i) q^{6} +2.03158 q^{7} +(-2.57107 + 1.17881i) q^{8} +(2.61681 - 1.46708i) q^{9} +O(q^{10})\) \(q+(-1.39972 + 0.201959i) q^{2} +(1.67583 - 0.437717i) q^{3} +(1.91842 - 0.565372i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-2.25729 + 0.951130i) q^{6} +2.03158 q^{7} +(-2.57107 + 1.17881i) q^{8} +(2.61681 - 1.46708i) q^{9} +(-0.846944 + 1.13256i) q^{10} +(-1.16221 - 1.16221i) q^{11} +(2.96748 - 1.78720i) q^{12} +(-2.26609 + 2.26609i) q^{13} +(-2.84364 + 0.410296i) q^{14} +(0.875477 - 1.49450i) q^{15} +(3.36071 - 2.16925i) q^{16} -1.83642i q^{17} +(-3.36650 + 2.58199i) q^{18} +(-1.52831 - 1.52831i) q^{19} +(0.956753 - 1.75631i) q^{20} +(3.40457 - 0.889256i) q^{21} +(1.86148 + 1.39204i) q^{22} +5.97972i q^{23} +(-3.79270 + 3.10088i) q^{24} -1.00000i q^{25} +(2.71423 - 3.62954i) q^{26} +(3.74316 - 3.60400i) q^{27} +(3.89743 - 1.14860i) q^{28} +(4.80376 + 4.80376i) q^{29} +(-0.923593 + 2.26869i) q^{30} -8.98136i q^{31} +(-4.26595 + 3.71506i) q^{32} +(-2.45638 - 1.43894i) q^{33} +(0.370883 + 2.57048i) q^{34} +(1.43654 - 1.43654i) q^{35} +(4.19070 - 4.29395i) q^{36} +(3.47568 + 3.47568i) q^{37} +(2.44786 + 1.83055i) q^{38} +(-2.80567 + 4.78948i) q^{39} +(-0.984481 + 2.65156i) q^{40} +7.70891 q^{41} +(-4.58585 + 1.93229i) q^{42} +(-4.45355 + 4.45355i) q^{43} +(-2.88668 - 1.57252i) q^{44} +(0.812981 - 2.88774i) q^{45} +(-1.20766 - 8.36993i) q^{46} -8.73867 q^{47} +(4.68246 - 5.10633i) q^{48} -2.87270 q^{49} +(0.201959 + 1.39972i) q^{50} +(-0.803835 - 3.07753i) q^{51} +(-3.06614 + 5.62850i) q^{52} +(-6.76795 + 6.76795i) q^{53} +(-4.51151 + 5.80054i) q^{54} -1.64361 q^{55} +(-5.22333 + 2.39483i) q^{56} +(-3.23015 - 1.89222i) q^{57} +(-7.69408 - 5.75375i) q^{58} +(-8.78054 - 8.78054i) q^{59} +(0.834587 - 3.36206i) q^{60} +(-8.76931 + 8.76931i) q^{61} +(1.81387 + 12.5714i) q^{62} +(5.31624 - 2.98048i) q^{63} +(5.22083 - 6.06159i) q^{64} +3.20473i q^{65} +(3.72884 + 1.51802i) q^{66} +(-6.12925 - 6.12925i) q^{67} +(-1.03826 - 3.52304i) q^{68} +(2.61743 + 10.0210i) q^{69} +(-1.72063 + 2.30088i) q^{70} +1.43394i q^{71} +(-4.99860 + 6.85667i) q^{72} +11.4230i q^{73} +(-5.56692 - 4.16303i) q^{74} +(-0.437717 - 1.67583i) q^{75} +(-3.79601 - 2.06788i) q^{76} +(-2.36111 - 2.36111i) q^{77} +(2.95987 - 7.27056i) q^{78} +7.96512i q^{79} +(0.842489 - 3.91027i) q^{80} +(4.69536 - 7.67812i) q^{81} +(-10.7903 + 1.55689i) q^{82} +(5.54053 - 5.54053i) q^{83} +(6.02866 - 3.63082i) q^{84} +(-1.29855 - 1.29855i) q^{85} +(5.33428 - 7.13315i) q^{86} +(10.1530 + 5.94760i) q^{87} +(4.35813 + 1.61810i) q^{88} +10.0685 q^{89} +(-0.554738 + 4.20622i) q^{90} +(-4.60373 + 4.60373i) q^{91} +(3.38077 + 11.4716i) q^{92} +(-3.93130 - 15.0512i) q^{93} +(12.2317 - 1.76486i) q^{94} -2.16135 q^{95} +(-5.52285 + 8.09309i) q^{96} +6.88053 q^{97} +(4.02097 - 0.580168i) q^{98} +(-4.74631 - 1.33622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39972 + 0.201959i −0.989751 + 0.142807i
\(3\) 1.67583 0.437717i 0.967540 0.252716i
\(4\) 1.91842 0.565372i 0.959212 0.282686i
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) −2.25729 + 0.951130i −0.921534 + 0.388297i
\(7\) 2.03158 0.767864 0.383932 0.923361i \(-0.374570\pi\)
0.383932 + 0.923361i \(0.374570\pi\)
\(8\) −2.57107 + 1.17881i −0.909012 + 0.416771i
\(9\) 2.61681 1.46708i 0.872269 0.489026i
\(10\) −0.846944 + 1.13256i −0.267827 + 0.358146i
\(11\) −1.16221 1.16221i −0.350418 0.350418i 0.509847 0.860265i \(-0.329702\pi\)
−0.860265 + 0.509847i \(0.829702\pi\)
\(12\) 2.96748 1.78720i 0.856637 0.515919i
\(13\) −2.26609 + 2.26609i −0.628500 + 0.628500i −0.947691 0.319191i \(-0.896589\pi\)
0.319191 + 0.947691i \(0.396589\pi\)
\(14\) −2.84364 + 0.410296i −0.759994 + 0.109656i
\(15\) 0.875477 1.49450i 0.226047 0.385879i
\(16\) 3.36071 2.16925i 0.840177 0.542312i
\(17\) 1.83642i 0.445398i −0.974887 0.222699i \(-0.928513\pi\)
0.974887 0.222699i \(-0.0714868\pi\)
\(18\) −3.36650 + 2.58199i −0.793493 + 0.608580i
\(19\) −1.52831 1.52831i −0.350618 0.350618i 0.509721 0.860339i \(-0.329748\pi\)
−0.860339 + 0.509721i \(0.829748\pi\)
\(20\) 0.956753 1.75631i 0.213936 0.392723i
\(21\) 3.40457 0.889256i 0.742939 0.194052i
\(22\) 1.86148 + 1.39204i 0.396869 + 0.296784i
\(23\) 5.97972i 1.24686i 0.781880 + 0.623429i \(0.214261\pi\)
−0.781880 + 0.623429i \(0.785739\pi\)
\(24\) −3.79270 + 3.10088i −0.774181 + 0.632965i
\(25\) 1.00000i 0.200000i
\(26\) 2.71423 3.62954i 0.532304 0.711812i
\(27\) 3.74316 3.60400i 0.720371 0.693589i
\(28\) 3.89743 1.14860i 0.736544 0.217064i
\(29\) 4.80376 + 4.80376i 0.892037 + 0.892037i 0.994715 0.102678i \(-0.0327412\pi\)
−0.102678 + 0.994715i \(0.532741\pi\)
\(30\) −0.923593 + 2.26869i −0.168624 + 0.414205i
\(31\) 8.98136i 1.61310i −0.591166 0.806550i \(-0.701332\pi\)
0.591166 0.806550i \(-0.298668\pi\)
\(32\) −4.26595 + 3.71506i −0.754120 + 0.656737i
\(33\) −2.45638 1.43894i −0.427600 0.250487i
\(34\) 0.370883 + 2.57048i 0.0636059 + 0.440833i
\(35\) 1.43654 1.43654i 0.242820 0.242820i
\(36\) 4.19070 4.29395i 0.698450 0.715658i
\(37\) 3.47568 + 3.47568i 0.571398 + 0.571398i 0.932519 0.361121i \(-0.117606\pi\)
−0.361121 + 0.932519i \(0.617606\pi\)
\(38\) 2.44786 + 1.83055i 0.397095 + 0.296954i
\(39\) −2.80567 + 4.78948i −0.449267 + 0.766931i
\(40\) −0.984481 + 2.65156i −0.155660 + 0.419249i
\(41\) 7.70891 1.20393 0.601964 0.798523i \(-0.294385\pi\)
0.601964 + 0.798523i \(0.294385\pi\)
\(42\) −4.58585 + 1.93229i −0.707613 + 0.298159i
\(43\) −4.45355 + 4.45355i −0.679160 + 0.679160i −0.959810 0.280650i \(-0.909450\pi\)
0.280650 + 0.959810i \(0.409450\pi\)
\(44\) −2.88668 1.57252i −0.435184 0.237067i
\(45\) 0.812981 2.88774i 0.121192 0.430479i
\(46\) −1.20766 8.36993i −0.178060 1.23408i
\(47\) −8.73867 −1.27467 −0.637333 0.770588i \(-0.719963\pi\)
−0.637333 + 0.770588i \(0.719963\pi\)
\(48\) 4.68246 5.10633i 0.675854 0.737035i
\(49\) −2.87270 −0.410385
\(50\) 0.201959 + 1.39972i 0.0285614 + 0.197950i
\(51\) −0.803835 3.07753i −0.112559 0.430941i
\(52\) −3.06614 + 5.62850i −0.425197 + 0.780533i
\(53\) −6.76795 + 6.76795i −0.929649 + 0.929649i −0.997683 0.0680339i \(-0.978327\pi\)
0.0680339 + 0.997683i \(0.478327\pi\)
\(54\) −4.51151 + 5.80054i −0.613938 + 0.789354i
\(55\) −1.64361 −0.221624
\(56\) −5.22333 + 2.39483i −0.697997 + 0.320023i
\(57\) −3.23015 1.89222i −0.427844 0.250630i
\(58\) −7.69408 5.75375i −1.01028 0.755505i
\(59\) −8.78054 8.78054i −1.14313 1.14313i −0.987875 0.155254i \(-0.950380\pi\)
−0.155254 0.987875i \(-0.549620\pi\)
\(60\) 0.834587 3.36206i 0.107745 0.434040i
\(61\) −8.76931 + 8.76931i −1.12280 + 1.12280i −0.131476 + 0.991319i \(0.541972\pi\)
−0.991319 + 0.131476i \(0.958028\pi\)
\(62\) 1.81387 + 12.5714i 0.230362 + 1.59657i
\(63\) 5.31624 2.98048i 0.669784 0.375505i
\(64\) 5.22083 6.06159i 0.652604 0.757699i
\(65\) 3.20473i 0.397498i
\(66\) 3.72884 + 1.51802i 0.458989 + 0.186856i
\(67\) −6.12925 6.12925i −0.748807 0.748807i 0.225448 0.974255i \(-0.427615\pi\)
−0.974255 + 0.225448i \(0.927615\pi\)
\(68\) −1.03826 3.52304i −0.125908 0.427232i
\(69\) 2.61743 + 10.0210i 0.315101 + 1.20639i
\(70\) −1.72063 + 2.30088i −0.205655 + 0.275007i
\(71\) 1.43394i 0.170177i 0.996373 + 0.0850886i \(0.0271173\pi\)
−0.996373 + 0.0850886i \(0.972883\pi\)
\(72\) −4.99860 + 6.85667i −0.589091 + 0.808067i
\(73\) 11.4230i 1.33696i 0.743732 + 0.668478i \(0.233054\pi\)
−0.743732 + 0.668478i \(0.766946\pi\)
\(74\) −5.56692 4.16303i −0.647141 0.483942i
\(75\) −0.437717 1.67583i −0.0505432 0.193508i
\(76\) −3.79601 2.06788i −0.435432 0.237202i
\(77\) −2.36111 2.36111i −0.269073 0.269073i
\(78\) 2.95987 7.27056i 0.335139 0.823229i
\(79\) 7.96512i 0.896147i 0.893997 + 0.448073i \(0.147890\pi\)
−0.893997 + 0.448073i \(0.852110\pi\)
\(80\) 0.842489 3.91027i 0.0941931 0.437181i
\(81\) 4.69536 7.67812i 0.521707 0.853125i
\(82\) −10.7903 + 1.55689i −1.19159 + 0.171929i
\(83\) 5.54053 5.54053i 0.608153 0.608153i −0.334310 0.942463i \(-0.608503\pi\)
0.942463 + 0.334310i \(0.108503\pi\)
\(84\) 6.02866 3.63082i 0.657781 0.396155i
\(85\) −1.29855 1.29855i −0.140847 0.140847i
\(86\) 5.33428 7.13315i 0.575210 0.769188i
\(87\) 10.1530 + 5.94760i 1.08851 + 0.637649i
\(88\) 4.35813 + 1.61810i 0.464578 + 0.172490i
\(89\) 10.0685 1.06726 0.533632 0.845717i \(-0.320827\pi\)
0.533632 + 0.845717i \(0.320827\pi\)
\(90\) −0.554738 + 4.20622i −0.0584745 + 0.443374i
\(91\) −4.60373 + 4.60373i −0.482602 + 0.482602i
\(92\) 3.38077 + 11.4716i 0.352470 + 1.19600i
\(93\) −3.93130 15.0512i −0.407656 1.56074i
\(94\) 12.2317 1.76486i 1.26160 0.182031i
\(95\) −2.16135 −0.221750
\(96\) −5.52285 + 8.09309i −0.563673 + 0.825998i
\(97\) 6.88053 0.698612 0.349306 0.937009i \(-0.386417\pi\)
0.349306 + 0.937009i \(0.386417\pi\)
\(98\) 4.02097 0.580168i 0.406179 0.0586058i
\(99\) −4.74631 1.33622i −0.477023 0.134295i
\(100\) −0.565372 1.91842i −0.0565372 0.191842i
\(101\) −2.21559 + 2.21559i −0.220460 + 0.220460i −0.808692 0.588232i \(-0.799824\pi\)
0.588232 + 0.808692i \(0.299824\pi\)
\(102\) 1.74668 + 4.14534i 0.172947 + 0.410450i
\(103\) 1.08629 0.107035 0.0535177 0.998567i \(-0.482957\pi\)
0.0535177 + 0.998567i \(0.482957\pi\)
\(104\) 3.15500 8.49756i 0.309373 0.833254i
\(105\) 1.77860 3.03620i 0.173573 0.296302i
\(106\) 8.10637 10.8401i 0.787361 1.05288i
\(107\) −5.47594 5.47594i −0.529380 0.529380i 0.391008 0.920387i \(-0.372127\pi\)
−0.920387 + 0.391008i \(0.872127\pi\)
\(108\) 5.14336 9.03027i 0.494921 0.868938i
\(109\) −2.73926 + 2.73926i −0.262373 + 0.262373i −0.826018 0.563644i \(-0.809399\pi\)
0.563644 + 0.826018i \(0.309399\pi\)
\(110\) 2.30059 0.331942i 0.219352 0.0316494i
\(111\) 7.34601 + 4.30328i 0.697252 + 0.408449i
\(112\) 6.82754 4.40699i 0.645141 0.416422i
\(113\) 3.30775i 0.311167i −0.987823 0.155583i \(-0.950274\pi\)
0.987823 0.155583i \(-0.0497257\pi\)
\(114\) 4.90345 + 1.99621i 0.459251 + 0.186962i
\(115\) 4.22830 + 4.22830i 0.394291 + 0.394291i
\(116\) 11.9316 + 6.49974i 1.10782 + 0.603486i
\(117\) −2.60539 + 9.25445i −0.240868 + 0.855574i
\(118\) 14.0636 + 10.5170i 1.29466 + 0.968166i
\(119\) 3.73084i 0.342005i
\(120\) −0.489187 + 4.87449i −0.0446565 + 0.444978i
\(121\) 8.29856i 0.754414i
\(122\) 10.5035 14.0456i 0.950945 1.27163i
\(123\) 12.9188 3.37432i 1.16485 0.304252i
\(124\) −5.07781 17.2301i −0.456001 1.54731i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) −6.83931 + 5.24550i −0.609294 + 0.467306i
\(127\) 2.95044i 0.261809i −0.991395 0.130905i \(-0.958212\pi\)
0.991395 0.130905i \(-0.0417882\pi\)
\(128\) −6.08350 + 9.53892i −0.537711 + 0.843129i
\(129\) −5.51399 + 9.41279i −0.485480 + 0.828750i
\(130\) −0.647226 4.48572i −0.0567654 0.393424i
\(131\) −12.1289 + 12.1289i −1.05971 + 1.05971i −0.0616099 + 0.998100i \(0.519623\pi\)
−0.998100 + 0.0616099i \(0.980377\pi\)
\(132\) −5.52591 1.37173i −0.480969 0.119394i
\(133\) −3.10488 3.10488i −0.269227 0.269227i
\(134\) 9.81709 + 7.34137i 0.848067 + 0.634198i
\(135\) 0.0984018 5.19522i 0.00846908 0.447133i
\(136\) 2.16479 + 4.72158i 0.185629 + 0.404872i
\(137\) 4.93466 0.421597 0.210798 0.977530i \(-0.432394\pi\)
0.210798 + 0.977530i \(0.432394\pi\)
\(138\) −5.68749 13.4980i −0.484152 1.14902i
\(139\) −11.2261 + 11.2261i −0.952189 + 0.952189i −0.998908 0.0467191i \(-0.985123\pi\)
0.0467191 + 0.998908i \(0.485123\pi\)
\(140\) 1.94372 3.56808i 0.164274 0.301558i
\(141\) −14.6445 + 3.82507i −1.23329 + 0.322129i
\(142\) −0.289597 2.00711i −0.0243024 0.168433i
\(143\) 5.26732 0.440475
\(144\) 5.61187 10.6069i 0.467656 0.883911i
\(145\) 6.79355 0.564173
\(146\) −2.30697 15.9889i −0.190926 1.32325i
\(147\) −4.81415 + 1.25743i −0.397064 + 0.103711i
\(148\) 8.63288 + 4.70278i 0.709618 + 0.386566i
\(149\) 2.18417 2.18417i 0.178934 0.178934i −0.611957 0.790891i \(-0.709617\pi\)
0.790891 + 0.611957i \(0.209617\pi\)
\(150\) 0.951130 + 2.25729i 0.0776595 + 0.184307i
\(151\) 18.3162 1.49055 0.745276 0.666756i \(-0.232318\pi\)
0.745276 + 0.666756i \(0.232318\pi\)
\(152\) 5.73097 + 2.12781i 0.464843 + 0.172588i
\(153\) −2.69418 4.80557i −0.217812 0.388507i
\(154\) 3.78174 + 2.82804i 0.304741 + 0.227890i
\(155\) −6.35078 6.35078i −0.510107 0.510107i
\(156\) −2.67463 + 10.7745i −0.214142 + 0.862651i
\(157\) 13.1686 13.1686i 1.05097 1.05097i 0.0523376 0.998629i \(-0.483333\pi\)
0.998629 0.0523376i \(-0.0166672\pi\)
\(158\) −1.60863 11.1489i −0.127976 0.886962i
\(159\) −8.37948 + 14.3044i −0.664536 + 1.13441i
\(160\) −0.389532 + 5.64343i −0.0307952 + 0.446152i
\(161\) 12.1483i 0.957417i
\(162\) −5.02151 + 11.6955i −0.394527 + 0.918884i
\(163\) 13.9396 + 13.9396i 1.09183 + 1.09183i 0.995333 + 0.0964965i \(0.0307637\pi\)
0.0964965 + 0.995333i \(0.469236\pi\)
\(164\) 14.7890 4.35840i 1.15482 0.340334i
\(165\) −2.75440 + 0.719435i −0.214430 + 0.0560079i
\(166\) −6.63623 + 8.87415i −0.515071 + 0.688768i
\(167\) 11.0540i 0.855387i −0.903924 0.427693i \(-0.859326\pi\)
0.903924 0.427693i \(-0.140674\pi\)
\(168\) −7.70515 + 6.29968i −0.594465 + 0.486031i
\(169\) 2.72969i 0.209976i
\(170\) 2.07986 + 1.55535i 0.159518 + 0.119290i
\(171\) −6.24144 1.75714i −0.477295 0.134372i
\(172\) −6.02589 + 11.0617i −0.459470 + 0.843448i
\(173\) −10.3602 10.3602i −0.787671 0.787671i 0.193441 0.981112i \(-0.438035\pi\)
−0.981112 + 0.193441i \(0.938035\pi\)
\(174\) −15.4125 6.27447i −1.16842 0.475667i
\(175\) 2.03158i 0.153573i
\(176\) −6.42695 1.38472i −0.484449 0.104377i
\(177\) −18.5581 10.8713i −1.39491 0.817136i
\(178\) −14.0931 + 2.03344i −1.05632 + 0.152412i
\(179\) 4.19924 4.19924i 0.313866 0.313866i −0.532539 0.846405i \(-0.678762\pi\)
0.846405 + 0.532539i \(0.178762\pi\)
\(180\) −0.0730079 5.99956i −0.00544169 0.447180i
\(181\) −11.3450 11.3450i −0.843267 0.843267i 0.146015 0.989282i \(-0.453355\pi\)
−0.989282 + 0.146015i \(0.953355\pi\)
\(182\) 5.51416 7.37370i 0.408737 0.546575i
\(183\) −10.8574 + 18.5343i −0.802601 + 1.37010i
\(184\) −7.04893 15.3743i −0.519654 1.13341i
\(185\) 4.91535 0.361384
\(186\) 8.54244 + 20.2735i 0.626362 + 1.48653i
\(187\) −2.13430 + 2.13430i −0.156076 + 0.156076i
\(188\) −16.7645 + 4.94061i −1.22268 + 0.360331i
\(189\) 7.60451 7.32179i 0.553147 0.532582i
\(190\) 3.02529 0.436506i 0.219477 0.0316674i
\(191\) 15.1652 1.09731 0.548656 0.836048i \(-0.315140\pi\)
0.548656 + 0.836048i \(0.315140\pi\)
\(192\) 6.09596 12.4434i 0.439938 0.898028i
\(193\) −22.1526 −1.59458 −0.797288 0.603599i \(-0.793733\pi\)
−0.797288 + 0.603599i \(0.793733\pi\)
\(194\) −9.63081 + 1.38959i −0.691452 + 0.0997665i
\(195\) 1.40277 + 5.37059i 0.100454 + 0.384596i
\(196\) −5.51105 + 1.62414i −0.393647 + 0.116010i
\(197\) 2.77239 2.77239i 0.197525 0.197525i −0.601413 0.798938i \(-0.705396\pi\)
0.798938 + 0.601413i \(0.205396\pi\)
\(198\) 6.91337 + 0.911771i 0.491312 + 0.0647967i
\(199\) 2.19199 0.155386 0.0776932 0.996977i \(-0.475245\pi\)
0.0776932 + 0.996977i \(0.475245\pi\)
\(200\) 1.17881 + 2.57107i 0.0833542 + 0.181802i
\(201\) −12.9545 7.58870i −0.913737 0.535266i
\(202\) 2.65375 3.54867i 0.186717 0.249683i
\(203\) 9.75921 + 9.75921i 0.684962 + 0.684962i
\(204\) −3.28205 5.44955i −0.229789 0.381545i
\(205\) 5.45102 5.45102i 0.380716 0.380716i
\(206\) −1.52050 + 0.219387i −0.105938 + 0.0152854i
\(207\) 8.77272 + 15.6478i 0.609746 + 1.08760i
\(208\) −2.69995 + 12.5314i −0.187208 + 0.868894i
\(209\) 3.55242i 0.245726i
\(210\) −1.87635 + 4.60903i −0.129480 + 0.318053i
\(211\) −4.49084 4.49084i −0.309162 0.309162i 0.535422 0.844584i \(-0.320152\pi\)
−0.844584 + 0.535422i \(0.820152\pi\)
\(212\) −9.15739 + 16.8102i −0.628932 + 1.15453i
\(213\) 0.627659 + 2.40303i 0.0430065 + 0.164653i
\(214\) 8.77070 + 6.55886i 0.599553 + 0.448355i
\(215\) 6.29827i 0.429539i
\(216\) −5.37552 + 13.6786i −0.365758 + 0.930710i
\(217\) 18.2463i 1.23864i
\(218\) 3.28097 4.38741i 0.222215 0.297153i
\(219\) 5.00003 + 19.1429i 0.337870 + 1.29356i
\(220\) −3.15314 + 0.929250i −0.212584 + 0.0626500i
\(221\) 4.16150 + 4.16150i 0.279933 + 0.279933i
\(222\) −11.1514 4.53979i −0.748435 0.304690i
\(223\) 16.6495i 1.11493i −0.830199 0.557467i \(-0.811773\pi\)
0.830199 0.557467i \(-0.188227\pi\)
\(224\) −8.66659 + 7.54744i −0.579061 + 0.504284i
\(225\) −1.46708 2.61681i −0.0978053 0.174454i
\(226\) 0.668030 + 4.62992i 0.0444367 + 0.307977i
\(227\) 13.3713 13.3713i 0.887487 0.887487i −0.106794 0.994281i \(-0.534059\pi\)
0.994281 + 0.106794i \(0.0340587\pi\)
\(228\) −7.26661 1.80384i −0.481243 0.119462i
\(229\) −11.5035 11.5035i −0.760172 0.760172i 0.216181 0.976353i \(-0.430640\pi\)
−0.976353 + 0.216181i \(0.930640\pi\)
\(230\) −6.77238 5.06449i −0.446557 0.333942i
\(231\) −4.99031 2.92332i −0.328339 0.192340i
\(232\) −18.0135 6.68812i −1.18265 0.439097i
\(233\) 11.5869 0.759083 0.379541 0.925175i \(-0.376082\pi\)
0.379541 + 0.925175i \(0.376082\pi\)
\(234\) 1.77779 13.4798i 0.116218 0.881202i
\(235\) −6.17918 + 6.17918i −0.403085 + 0.403085i
\(236\) −21.8091 11.8805i −1.41965 0.773356i
\(237\) 3.48647 + 13.3482i 0.226471 + 0.867058i
\(238\) 0.753477 + 5.22212i 0.0488407 + 0.338500i
\(239\) −10.8530 −0.702025 −0.351013 0.936371i \(-0.614163\pi\)
−0.351013 + 0.936371i \(0.614163\pi\)
\(240\) −0.299725 6.92172i −0.0193472 0.446795i
\(241\) 28.5856 1.84136 0.920681 0.390316i \(-0.127634\pi\)
0.920681 + 0.390316i \(0.127634\pi\)
\(242\) 1.67597 + 11.6156i 0.107735 + 0.746682i
\(243\) 4.50777 14.9225i 0.289174 0.957277i
\(244\) −11.8653 + 21.7812i −0.759601 + 1.39440i
\(245\) −2.03130 + 2.03130i −0.129775 + 0.129775i
\(246\) −17.4012 + 7.33217i −1.10946 + 0.467482i
\(247\) 6.92656 0.440727
\(248\) 10.5873 + 23.0917i 0.672293 + 1.46633i
\(249\) 6.85980 11.7102i 0.434722 0.742102i
\(250\) 1.13256 + 0.846944i 0.0716292 + 0.0535654i
\(251\) 13.7062 + 13.7062i 0.865130 + 0.865130i 0.991928 0.126799i \(-0.0404703\pi\)
−0.126799 + 0.991928i \(0.540470\pi\)
\(252\) 8.51373 8.72349i 0.536315 0.549528i
\(253\) 6.94966 6.94966i 0.436922 0.436922i
\(254\) 0.595869 + 4.12979i 0.0373882 + 0.259126i
\(255\) −2.74454 1.60775i −0.171870 0.100681i
\(256\) 6.58872 14.5804i 0.411795 0.911277i
\(257\) 12.6394i 0.788422i −0.919020 0.394211i \(-0.871018\pi\)
0.919020 0.394211i \(-0.128982\pi\)
\(258\) 5.81704 14.2889i 0.362153 0.889585i
\(259\) 7.06111 + 7.06111i 0.438756 + 0.438756i
\(260\) 1.81187 + 6.14804i 0.112367 + 0.381285i
\(261\) 19.6180 + 5.52302i 1.21433 + 0.341867i
\(262\) 14.5275 19.4267i 0.897515 1.20018i
\(263\) 1.82039i 0.112250i −0.998424 0.0561251i \(-0.982125\pi\)
0.998424 0.0561251i \(-0.0178746\pi\)
\(264\) 8.01175 + 0.804031i 0.493089 + 0.0494847i
\(265\) 9.57132i 0.587962i
\(266\) 4.97301 + 3.71889i 0.304915 + 0.228020i
\(267\) 16.8732 4.40717i 1.03262 0.269715i
\(268\) −15.2238 8.29320i −0.929943 0.506588i
\(269\) 21.5211 + 21.5211i 1.31217 + 1.31217i 0.919815 + 0.392351i \(0.128338\pi\)
0.392351 + 0.919815i \(0.371662\pi\)
\(270\) 0.911488 + 7.29172i 0.0554714 + 0.443760i
\(271\) 0.935084i 0.0568023i −0.999597 0.0284012i \(-0.990958\pi\)
0.999597 0.0284012i \(-0.00904159\pi\)
\(272\) −3.98366 6.17169i −0.241545 0.374213i
\(273\) −5.69994 + 9.73020i −0.344976 + 0.588899i
\(274\) −6.90714 + 0.996601i −0.417275 + 0.0602069i
\(275\) −1.16221 + 1.16221i −0.0700836 + 0.0700836i
\(276\) 10.6869 + 17.7447i 0.643278 + 1.06811i
\(277\) −6.83941 6.83941i −0.410940 0.410940i 0.471126 0.882066i \(-0.343848\pi\)
−0.882066 + 0.471126i \(0.843848\pi\)
\(278\) 13.4462 17.9807i 0.806451 1.07841i
\(279\) −13.1764 23.5025i −0.788848 1.40706i
\(280\) −2.00005 + 5.38686i −0.119526 + 0.321926i
\(281\) −32.5245 −1.94025 −0.970124 0.242610i \(-0.921996\pi\)
−0.970124 + 0.242610i \(0.921996\pi\)
\(282\) 19.7257 8.31162i 1.17465 0.494950i
\(283\) 10.3797 10.3797i 0.617012 0.617012i −0.327752 0.944764i \(-0.606291\pi\)
0.944764 + 0.327752i \(0.106291\pi\)
\(284\) 0.810709 + 2.75090i 0.0481067 + 0.163236i
\(285\) −3.62206 + 0.946062i −0.214552 + 0.0560399i
\(286\) −7.37277 + 1.06378i −0.435961 + 0.0629029i
\(287\) 15.6612 0.924453
\(288\) −5.71287 + 15.9801i −0.336634 + 0.941636i
\(289\) 13.6275 0.801620
\(290\) −9.50906 + 1.37202i −0.558391 + 0.0805678i
\(291\) 11.5306 3.01173i 0.675935 0.176551i
\(292\) 6.45823 + 21.9141i 0.377939 + 1.28242i
\(293\) 9.39190 9.39190i 0.548681 0.548681i −0.377378 0.926059i \(-0.623174\pi\)
0.926059 + 0.377378i \(0.123174\pi\)
\(294\) 6.48451 2.73231i 0.378184 0.159352i
\(295\) −12.4176 −0.722978
\(296\) −13.0334 4.83907i −0.757549 0.281265i
\(297\) −8.53890 0.161734i −0.495477 0.00938475i
\(298\) −2.61611 + 3.49833i −0.151547 + 0.202653i
\(299\) −13.5506 13.5506i −0.783650 0.783650i
\(300\) −1.78720 2.96748i −0.103184 0.171327i
\(301\) −9.04773 + 9.04773i −0.521502 + 0.521502i
\(302\) −25.6376 + 3.69913i −1.47528 + 0.212861i
\(303\) −2.74315 + 4.68276i −0.157590 + 0.269017i
\(304\) −8.45148 1.82092i −0.484726 0.104437i
\(305\) 12.4017i 0.710118i
\(306\) 4.74162 + 6.18233i 0.271061 + 0.353420i
\(307\) −10.5579 10.5579i −0.602572 0.602572i 0.338423 0.940994i \(-0.390107\pi\)
−0.940994 + 0.338423i \(0.890107\pi\)
\(308\) −5.86452 3.19470i −0.334162 0.182035i
\(309\) 1.82044 0.475488i 0.103561 0.0270496i
\(310\) 10.1719 + 7.60670i 0.577725 + 0.432032i
\(311\) 2.32185i 0.131660i −0.997831 0.0658299i \(-0.979031\pi\)
0.997831 0.0658299i \(-0.0209695\pi\)
\(312\) 1.56771 15.6215i 0.0887543 0.884391i
\(313\) 30.9881i 1.75155i 0.482720 + 0.875775i \(0.339649\pi\)
−0.482720 + 0.875775i \(0.660351\pi\)
\(314\) −15.7728 + 21.0918i −0.890110 + 1.19028i
\(315\) 1.65163 5.86667i 0.0930589 0.330549i
\(316\) 4.50326 + 15.2805i 0.253328 + 0.859595i
\(317\) −1.40300 1.40300i −0.0788005 0.0788005i 0.666608 0.745408i \(-0.267746\pi\)
−0.745408 + 0.666608i \(0.767746\pi\)
\(318\) 8.84001 21.7144i 0.495723 1.21768i
\(319\) 11.1659i 0.625172i
\(320\) −0.594507 7.97788i −0.0332340 0.445977i
\(321\) −11.5737 6.77983i −0.645979 0.378413i
\(322\) −2.45345 17.0041i −0.136726 0.947604i
\(323\) −2.80662 + 2.80662i −0.156165 + 0.156165i
\(324\) 4.66670 17.3845i 0.259261 0.965807i
\(325\) 2.26609 + 2.26609i 0.125700 + 0.125700i
\(326\) −22.3267 16.6962i −1.23656 0.924719i
\(327\) −3.39151 + 5.78955i −0.187551 + 0.320163i
\(328\) −19.8202 + 9.08731i −1.09439 + 0.501762i
\(329\) −17.7533 −0.978770
\(330\) 3.71009 1.56328i 0.204234 0.0860560i
\(331\) 1.73406 1.73406i 0.0953125 0.0953125i −0.657843 0.753155i \(-0.728531\pi\)
0.753155 + 0.657843i \(0.228531\pi\)
\(332\) 7.49663 13.7616i 0.411431 0.755264i
\(333\) 14.1943 + 3.99609i 0.777841 + 0.218984i
\(334\) 2.23246 + 15.4725i 0.122155 + 0.846620i
\(335\) −8.66807 −0.473587
\(336\) 9.51277 10.3739i 0.518964 0.565943i
\(337\) 23.4104 1.27524 0.637622 0.770350i \(-0.279918\pi\)
0.637622 + 0.770350i \(0.279918\pi\)
\(338\) −0.551285 3.82079i −0.0299860 0.207824i
\(339\) −1.44786 5.54322i −0.0786368 0.301066i
\(340\) −3.22533 1.75700i −0.174918 0.0952869i
\(341\) −10.4382 + 10.4382i −0.565259 + 0.565259i
\(342\) 9.09113 + 1.19899i 0.491592 + 0.0648337i
\(343\) −20.0571 −1.08298
\(344\) 6.20053 16.7003i 0.334310 0.900418i
\(345\) 8.93671 + 5.23511i 0.481136 + 0.281849i
\(346\) 16.5937 + 12.4090i 0.892083 + 0.667113i
\(347\) 8.79774 + 8.79774i 0.472288 + 0.472288i 0.902654 0.430367i \(-0.141616\pi\)
−0.430367 + 0.902654i \(0.641616\pi\)
\(348\) 22.8403 + 5.66981i 1.22437 + 0.303933i
\(349\) 5.73650 5.73650i 0.307068 0.307068i −0.536703 0.843771i \(-0.680331\pi\)
0.843771 + 0.536703i \(0.180331\pi\)
\(350\) 0.410296 + 2.84364i 0.0219312 + 0.151999i
\(351\) −0.315352 + 16.6493i −0.0168322 + 0.888674i
\(352\) 9.27557 + 0.640237i 0.494390 + 0.0341248i
\(353\) 2.51474i 0.133846i −0.997758 0.0669231i \(-0.978682\pi\)
0.997758 0.0669231i \(-0.0213182\pi\)
\(354\) 28.1716 + 11.4688i 1.49731 + 0.609558i
\(355\) 1.01395 + 1.01395i 0.0538147 + 0.0538147i
\(356\) 19.3157 5.69248i 1.02373 0.301701i
\(357\) −1.63305 6.25225i −0.0864303 0.330904i
\(358\) −5.02968 + 6.72583i −0.265827 + 0.355471i
\(359\) 7.69152i 0.405943i −0.979185 0.202971i \(-0.934940\pi\)
0.979185 0.202971i \(-0.0650599\pi\)
\(360\) 1.31386 + 8.38295i 0.0692463 + 0.441820i
\(361\) 14.3285i 0.754134i
\(362\) 18.1710 + 13.5886i 0.955049 + 0.714200i
\(363\) −3.63242 13.9070i −0.190653 0.729926i
\(364\) −6.22909 + 11.4347i −0.326493 + 0.599343i
\(365\) 8.07725 + 8.07725i 0.422783 + 0.422783i
\(366\) 11.4541 28.1356i 0.598716 1.47067i
\(367\) 5.64136i 0.294476i 0.989101 + 0.147238i \(0.0470384\pi\)
−0.989101 + 0.147238i \(0.952962\pi\)
\(368\) 12.9715 + 20.0961i 0.676186 + 1.04758i
\(369\) 20.1727 11.3096i 1.05015 0.588753i
\(370\) −6.88011 + 0.992701i −0.357680 + 0.0516081i
\(371\) −13.7496 + 13.7496i −0.713844 + 0.713844i
\(372\) −16.0514 26.6520i −0.832228 1.38184i
\(373\) −6.44235 6.44235i −0.333572 0.333572i 0.520369 0.853941i \(-0.325794\pi\)
−0.853941 + 0.520369i \(0.825794\pi\)
\(374\) 2.55638 3.41847i 0.132187 0.176765i
\(375\) −1.49450 0.875477i −0.0771758 0.0452095i
\(376\) 22.4678 10.3012i 1.15869 0.531244i
\(377\) −21.7715 −1.12129
\(378\) −9.16547 + 11.7842i −0.471421 + 0.606116i
\(379\) 17.1713 17.1713i 0.882031 0.882031i −0.111710 0.993741i \(-0.535633\pi\)
0.993741 + 0.111710i \(0.0356326\pi\)
\(380\) −4.14640 + 1.22197i −0.212706 + 0.0626858i
\(381\) −1.29146 4.94444i −0.0661635 0.253311i
\(382\) −21.2269 + 3.06274i −1.08607 + 0.156704i
\(383\) −21.9150 −1.11981 −0.559903 0.828558i \(-0.689162\pi\)
−0.559903 + 0.828558i \(0.689162\pi\)
\(384\) −6.01956 + 18.6485i −0.307184 + 0.951650i
\(385\) −3.33911 −0.170177
\(386\) 31.0074 4.47392i 1.57823 0.227716i
\(387\) −5.12037 + 18.1878i −0.260283 + 0.924537i
\(388\) 13.1998 3.89006i 0.670117 0.197488i
\(389\) 16.6859 16.6859i 0.846006 0.846006i −0.143626 0.989632i \(-0.545876\pi\)
0.989632 + 0.143626i \(0.0458762\pi\)
\(390\) −3.04812 7.23401i −0.154347 0.366308i
\(391\) 10.9813 0.555349
\(392\) 7.38592 3.38635i 0.373045 0.171037i
\(393\) −15.0170 + 25.6351i −0.757507 + 1.29312i
\(394\) −3.32065 + 4.44047i −0.167292 + 0.223708i
\(395\) 5.63219 + 5.63219i 0.283386 + 0.283386i
\(396\) −9.86091 + 0.119996i −0.495529 + 0.00603004i
\(397\) −23.8246 + 23.8246i −1.19572 + 1.19572i −0.220288 + 0.975435i \(0.570700\pi\)
−0.975435 + 0.220288i \(0.929300\pi\)
\(398\) −3.06817 + 0.442693i −0.153794 + 0.0221902i
\(399\) −6.56230 3.84418i −0.328526 0.192450i
\(400\) −2.16925 3.36071i −0.108462 0.168035i
\(401\) 10.3923i 0.518968i −0.965747 0.259484i \(-0.916448\pi\)
0.965747 0.259484i \(-0.0835524\pi\)
\(402\) 19.6652 + 8.00577i 0.980811 + 0.399292i
\(403\) 20.3526 + 20.3526i 1.01383 + 1.01383i
\(404\) −2.99781 + 5.50308i −0.149147 + 0.273789i
\(405\) −2.10913 8.74937i −0.104804 0.434760i
\(406\) −15.6311 11.6892i −0.775759 0.580125i
\(407\) 8.07890i 0.400456i
\(408\) 5.69453 + 6.96500i 0.281921 + 0.344819i
\(409\) 18.3523i 0.907465i −0.891138 0.453732i \(-0.850092\pi\)
0.891138 0.453732i \(-0.149908\pi\)
\(410\) −6.52901 + 8.73078i −0.322445 + 0.431182i
\(411\) 8.26965 2.15999i 0.407912 0.106544i
\(412\) 2.08397 0.614159i 0.102670 0.0302574i
\(413\) −17.8383 17.8383i −0.877767 0.877767i
\(414\) −15.4396 20.1308i −0.758813 0.989373i
\(415\) 7.83550i 0.384629i
\(416\) 1.24835 18.0857i 0.0612052 0.886723i
\(417\) −13.8992 + 23.7270i −0.680648 + 1.16191i
\(418\) −0.717444 4.97238i −0.0350913 0.243207i
\(419\) −6.34178 + 6.34178i −0.309816 + 0.309816i −0.844838 0.535022i \(-0.820303\pi\)
0.535022 + 0.844838i \(0.320303\pi\)
\(420\) 1.69553 6.83029i 0.0827332 0.333284i
\(421\) 12.6283 + 12.6283i 0.615467 + 0.615467i 0.944365 0.328899i \(-0.106677\pi\)
−0.328899 + 0.944365i \(0.606677\pi\)
\(422\) 7.19288 + 5.37895i 0.350144 + 0.261843i
\(423\) −22.8674 + 12.8203i −1.11185 + 0.623345i
\(424\) 9.42279 25.3790i 0.457611 1.23251i
\(425\) −1.83642 −0.0890797
\(426\) −1.36386 3.23681i −0.0660793 0.156824i
\(427\) −17.8155 + 17.8155i −0.862154 + 0.862154i
\(428\) −13.6011 7.40924i −0.657436 0.358139i
\(429\) 8.82713 2.30560i 0.426178 0.111315i
\(430\) −1.27199 8.81581i −0.0613410 0.425136i
\(431\) −12.4078 −0.597661 −0.298831 0.954306i \(-0.596597\pi\)
−0.298831 + 0.954306i \(0.596597\pi\)
\(432\) 4.76169 20.2318i 0.229097 0.973404i
\(433\) 12.0310 0.578173 0.289086 0.957303i \(-0.406649\pi\)
0.289086 + 0.957303i \(0.406649\pi\)
\(434\) 3.68501 + 25.5397i 0.176886 + 1.22595i
\(435\) 11.3848 2.97365i 0.545861 0.142576i
\(436\) −3.70636 + 6.80376i −0.177502 + 0.325841i
\(437\) 9.13886 9.13886i 0.437171 0.437171i
\(438\) −10.8647 25.7849i −0.519136 1.23205i
\(439\) 30.6420 1.46246 0.731231 0.682130i \(-0.238946\pi\)
0.731231 + 0.682130i \(0.238946\pi\)
\(440\) 4.22583 1.93749i 0.201459 0.0923664i
\(441\) −7.51730 + 4.21447i −0.357966 + 0.200689i
\(442\) −6.66538 4.98448i −0.317040 0.237087i
\(443\) −5.33011 5.33011i −0.253241 0.253241i 0.569057 0.822298i \(-0.307308\pi\)
−0.822298 + 0.569057i \(0.807308\pi\)
\(444\) 16.5257 + 4.10229i 0.784276 + 0.194686i
\(445\) 7.11953 7.11953i 0.337498 0.337498i
\(446\) 3.36252 + 23.3046i 0.159220 + 1.10351i
\(447\) 2.70424 4.61634i 0.127906 0.218345i
\(448\) 10.6065 12.3146i 0.501111 0.581810i
\(449\) 7.58164i 0.357800i 0.983867 + 0.178900i \(0.0572538\pi\)
−0.983867 + 0.178900i \(0.942746\pi\)
\(450\) 2.58199 + 3.36650i 0.121716 + 0.158699i
\(451\) −8.95933 8.95933i −0.421878 0.421878i
\(452\) −1.87011 6.34566i −0.0879625 0.298475i
\(453\) 30.6949 8.01732i 1.44217 0.376687i
\(454\) −16.0156 + 21.4166i −0.751651 + 1.00513i
\(455\) 6.51066i 0.305224i
\(456\) 10.5355 + 1.05731i 0.493371 + 0.0495129i
\(457\) 36.7260i 1.71797i 0.512002 + 0.858984i \(0.328904\pi\)
−0.512002 + 0.858984i \(0.671096\pi\)
\(458\) 18.4249 + 13.7784i 0.860938 + 0.643823i
\(459\) −6.61847 6.87402i −0.308924 0.320852i
\(460\) 10.5022 + 5.72111i 0.489670 + 0.266748i
\(461\) 9.99393 + 9.99393i 0.465464 + 0.465464i 0.900441 0.434978i \(-0.143244\pi\)
−0.434978 + 0.900441i \(0.643244\pi\)
\(462\) 7.57543 + 3.08398i 0.352441 + 0.143480i
\(463\) 21.1353i 0.982239i −0.871092 0.491119i \(-0.836588\pi\)
0.871092 0.491119i \(-0.163412\pi\)
\(464\) 26.5646 + 5.72349i 1.23323 + 0.265706i
\(465\) −13.4227 7.86298i −0.622461 0.364637i
\(466\) −16.2184 + 2.34008i −0.751303 + 0.108402i
\(467\) −17.1536 + 17.1536i −0.793775 + 0.793775i −0.982106 0.188331i \(-0.939692\pi\)
0.188331 + 0.982106i \(0.439692\pi\)
\(468\) 0.233971 + 19.2270i 0.0108153 + 0.888767i
\(469\) −12.4520 12.4520i −0.574982 0.574982i
\(470\) 7.40117 9.89705i 0.341390 0.456517i
\(471\) 16.3042 27.8324i 0.751257 1.28245i
\(472\) 32.9260 + 12.2249i 1.51554 + 0.562694i
\(473\) 10.3519 0.475980
\(474\) −7.57587 17.9796i −0.347971 0.825830i
\(475\) −1.52831 + 1.52831i −0.0701236 + 0.0701236i
\(476\) −2.10931 7.15733i −0.0966802 0.328056i
\(477\) −7.78130 + 27.6395i −0.356281 + 1.26553i
\(478\) 15.1912 2.19187i 0.694830 0.100254i
\(479\) 4.49348 0.205312 0.102656 0.994717i \(-0.467266\pi\)
0.102656 + 0.994717i \(0.467266\pi\)
\(480\) 1.81744 + 9.62792i 0.0829542 + 0.439453i
\(481\) −15.7524 −0.718247
\(482\) −40.0118 + 5.77313i −1.82249 + 0.262959i
\(483\) 5.31750 + 20.3584i 0.241955 + 0.926340i
\(484\) −4.69178 15.9202i −0.213263 0.723644i
\(485\) 4.86527 4.86527i 0.220920 0.220920i
\(486\) −3.29588 + 21.7976i −0.149504 + 0.988761i
\(487\) −26.7976 −1.21431 −0.607157 0.794582i \(-0.707690\pi\)
−0.607157 + 0.794582i \(0.707690\pi\)
\(488\) 12.2092 32.8839i 0.552686 1.48858i
\(489\) 29.4619 + 17.2587i 1.33231 + 0.780466i
\(490\) 2.43301 3.25349i 0.109912 0.146978i
\(491\) 14.5656 + 14.5656i 0.657337 + 0.657337i 0.954749 0.297412i \(-0.0961236\pi\)
−0.297412 + 0.954749i \(0.596124\pi\)
\(492\) 22.8760 13.7773i 1.03133 0.621130i
\(493\) 8.82175 8.82175i 0.397312 0.397312i
\(494\) −9.69524 + 1.39888i −0.436210 + 0.0629388i
\(495\) −4.30100 + 2.41130i −0.193316 + 0.108380i
\(496\) −19.4828 30.1837i −0.874804 1.35529i
\(497\) 2.91315i 0.130673i
\(498\) −7.23681 + 17.7764i −0.324289 + 0.796577i
\(499\) −1.70816 1.70816i −0.0764677 0.0764677i 0.667838 0.744306i \(-0.267220\pi\)
−0.744306 + 0.667838i \(0.767220\pi\)
\(500\) −1.75631 0.956753i −0.0785446 0.0427873i
\(501\) −4.83854 18.5247i −0.216170 0.827621i
\(502\) −21.9530 16.4168i −0.979809 0.732716i
\(503\) 5.48111i 0.244391i −0.992506 0.122195i \(-0.961007\pi\)
0.992506 0.122195i \(-0.0389934\pi\)
\(504\) −10.1550 + 13.9299i −0.452341 + 0.620485i
\(505\) 3.13332i 0.139431i
\(506\) −8.32403 + 11.1311i −0.370048 + 0.494839i
\(507\) 1.19483 + 4.57449i 0.0530643 + 0.203160i
\(508\) −1.66810 5.66020i −0.0740099 0.251131i
\(509\) −14.8244 14.8244i −0.657081 0.657081i 0.297607 0.954688i \(-0.403811\pi\)
−0.954688 + 0.297607i \(0.903811\pi\)
\(510\) 4.16629 + 1.69611i 0.184486 + 0.0751050i
\(511\) 23.2066i 1.02660i
\(512\) −6.27770 + 21.7391i −0.277438 + 0.960744i
\(513\) −11.2287 0.212681i −0.495760 0.00939010i
\(514\) 2.55264 + 17.6915i 0.112592 + 0.780341i
\(515\) 0.768124 0.768124i 0.0338476 0.0338476i
\(516\) −5.25645 + 21.1752i −0.231402 + 0.932185i
\(517\) 10.1561 + 10.1561i 0.446666 + 0.446666i
\(518\) −11.3096 8.45751i −0.496916 0.371601i
\(519\) −21.8968 12.8271i −0.961161 0.563047i
\(520\) −3.77776 8.23960i −0.165666 0.361330i
\(521\) 0.899984 0.0394290 0.0197145 0.999806i \(-0.493724\pi\)
0.0197145 + 0.999806i \(0.493724\pi\)
\(522\) −28.5751 3.76864i −1.25070 0.164949i
\(523\) 18.6524 18.6524i 0.815613 0.815613i −0.169856 0.985469i \(-0.554330\pi\)
0.985469 + 0.169856i \(0.0543303\pi\)
\(524\) −16.4111 + 30.1258i −0.716922 + 1.31605i
\(525\) −0.889256 3.40457i −0.0388103 0.148588i
\(526\) 0.367645 + 2.54804i 0.0160301 + 0.111100i
\(527\) −16.4936 −0.718472
\(528\) −11.3766 + 0.492631i −0.495102 + 0.0214390i
\(529\) −12.7571 −0.554655
\(530\) −1.93302 13.3972i −0.0839649 0.581935i
\(531\) −35.8587 10.0952i −1.55614 0.438096i
\(532\) −7.71188 4.20106i −0.334352 0.182139i
\(533\) −17.4691 + 17.4691i −0.756669 + 0.756669i
\(534\) −22.7276 + 9.57650i −0.983520 + 0.414416i
\(535\) −7.74416 −0.334809
\(536\) 22.9840 + 8.53355i 0.992756 + 0.368593i
\(537\) 5.19913 8.87529i 0.224359 0.382997i
\(538\) −34.4699 25.7771i −1.48610 1.11133i
\(539\) 3.33866 + 3.33866i 0.143806 + 0.143806i
\(540\) −2.74846 10.0223i −0.118275 0.431290i
\(541\) −3.93510 + 3.93510i −0.169183 + 0.169183i −0.786620 0.617437i \(-0.788171\pi\)
0.617437 + 0.786620i \(0.288171\pi\)
\(542\) 0.188849 + 1.30886i 0.00811176 + 0.0562201i
\(543\) −23.9782 14.0464i −1.02900 0.602788i
\(544\) 6.82244 + 7.83409i 0.292510 + 0.335884i
\(545\) 3.87390i 0.165939i
\(546\) 6.01320 14.7707i 0.257341 0.632128i
\(547\) −2.77378 2.77378i −0.118598 0.118598i 0.645317 0.763915i \(-0.276725\pi\)
−0.763915 + 0.645317i \(0.776725\pi\)
\(548\) 9.46678 2.78992i 0.404401 0.119180i
\(549\) −10.0823 + 35.8129i −0.430303 + 1.52846i
\(550\) 1.39204 1.86148i 0.0593569 0.0793737i
\(551\) 14.6833i 0.625528i
\(552\) −18.5424 22.6793i −0.789217 0.965294i
\(553\) 16.1818i 0.688118i
\(554\) 10.9545 + 8.19197i 0.465413 + 0.348043i
\(555\) 8.23729 2.15153i 0.349653 0.0913275i
\(556\) −15.1896 + 27.8835i −0.644181 + 1.18252i
\(557\) 3.60325 + 3.60325i 0.152674 + 0.152674i 0.779311 0.626637i \(-0.215569\pi\)
−0.626637 + 0.779311i \(0.715569\pi\)
\(558\) 23.1897 + 30.2358i 0.981700 + 1.27998i
\(559\) 20.1843i 0.853704i
\(560\) 1.71158 7.94401i 0.0723275 0.335696i
\(561\) −2.64251 + 4.51095i −0.111567 + 0.190452i
\(562\) 45.5251 6.56862i 1.92036 0.277081i
\(563\) −2.90080 + 2.90080i −0.122254 + 0.122254i −0.765587 0.643333i \(-0.777551\pi\)
0.643333 + 0.765587i \(0.277551\pi\)
\(564\) −25.9318 + 15.6177i −1.09193 + 0.657625i
\(565\) −2.33893 2.33893i −0.0983995 0.0983995i
\(566\) −12.4324 + 16.6250i −0.522574 + 0.698801i
\(567\) 9.53898 15.5987i 0.400600 0.655084i
\(568\) −1.69033 3.68676i −0.0709249 0.154693i
\(569\) −35.5959 −1.49226 −0.746129 0.665801i \(-0.768090\pi\)
−0.746129 + 0.665801i \(0.768090\pi\)
\(570\) 4.87880 2.05573i 0.204350 0.0861051i
\(571\) −3.81942 + 3.81942i −0.159838 + 0.159838i −0.782495 0.622657i \(-0.786053\pi\)
0.622657 + 0.782495i \(0.286053\pi\)
\(572\) 10.1050 2.97800i 0.422510 0.124516i
\(573\) 25.4142 6.63805i 1.06169 0.277308i
\(574\) −21.9213 + 3.16293i −0.914978 + 0.132018i
\(575\) 5.97972 0.249372
\(576\) 4.76908 23.5214i 0.198712 0.980058i
\(577\) 7.33300 0.305277 0.152638 0.988282i \(-0.451223\pi\)
0.152638 + 0.988282i \(0.451223\pi\)
\(578\) −19.0747 + 2.75221i −0.793404 + 0.114477i
\(579\) −37.1239 + 9.69656i −1.54282 + 0.402975i
\(580\) 13.0329 3.84088i 0.541162 0.159484i
\(581\) 11.2560 11.2560i 0.466978 0.466978i
\(582\) −15.5313 + 6.54428i −0.643795 + 0.271269i
\(583\) 15.7315 0.651532
\(584\) −13.4655 29.3693i −0.557204 1.21531i
\(585\) 4.70160 + 8.38617i 0.194387 + 0.346725i
\(586\) −11.2492 + 15.0428i −0.464702 + 0.621413i
\(587\) 18.7394 + 18.7394i 0.773459 + 0.773459i 0.978709 0.205251i \(-0.0658009\pi\)
−0.205251 + 0.978709i \(0.565801\pi\)
\(588\) −8.52467 + 5.13407i −0.351551 + 0.211726i
\(589\) −13.7263 + 13.7263i −0.565582 + 0.565582i
\(590\) 17.3811 2.50784i 0.715568 0.103246i
\(591\) 3.43253 5.85957i 0.141195 0.241031i
\(592\) 19.2204 + 4.14113i 0.789952 + 0.170199i
\(593\) 1.17391i 0.0482065i 0.999709 + 0.0241033i \(0.00767305\pi\)
−0.999709 + 0.0241033i \(0.992327\pi\)
\(594\) 11.9847 1.49813i 0.491739 0.0614689i
\(595\) −2.63810 2.63810i −0.108152 0.108152i
\(596\) 2.95529 5.42503i 0.121053 0.222218i
\(597\) 3.67341 0.959473i 0.150343 0.0392686i
\(598\) 21.7037 + 16.2303i 0.887529 + 0.663708i
\(599\) 29.5832i 1.20874i 0.796704 + 0.604369i \(0.206575\pi\)
−0.796704 + 0.604369i \(0.793425\pi\)
\(600\) 3.10088 + 3.79270i 0.126593 + 0.154836i
\(601\) 7.84624i 0.320055i 0.987113 + 0.160027i \(0.0511583\pi\)
−0.987113 + 0.160027i \(0.948842\pi\)
\(602\) 10.8370 14.4915i 0.441683 0.590631i
\(603\) −25.0312 7.04697i −1.01935 0.286975i
\(604\) 35.1383 10.3555i 1.42976 0.421359i
\(605\) −5.86797 5.86797i −0.238567 0.238567i
\(606\) 2.89391 7.10855i 0.117557 0.288765i
\(607\) 10.9548i 0.444643i 0.974973 + 0.222322i \(0.0713635\pi\)
−0.974973 + 0.222322i \(0.928637\pi\)
\(608\) 12.1974 + 0.841917i 0.494672 + 0.0341442i
\(609\) 20.6265 + 12.0830i 0.835830 + 0.489628i
\(610\) −2.50463 17.3589i −0.101410 0.702840i
\(611\) 19.8026 19.8026i 0.801128 0.801128i
\(612\) −7.88552 7.69591i −0.318753 0.311089i
\(613\) −16.4952 16.4952i −0.666234 0.666234i 0.290609 0.956842i \(-0.406142\pi\)
−0.956842 + 0.290609i \(0.906142\pi\)
\(614\) 16.9104 + 12.6458i 0.682447 + 0.510344i
\(615\) 6.74897 11.5210i 0.272145 0.464571i
\(616\) 8.85387 + 3.28729i 0.356733 + 0.132449i
\(617\) 10.9317 0.440092 0.220046 0.975489i \(-0.429379\pi\)
0.220046 + 0.975489i \(0.429379\pi\)
\(618\) −2.45207 + 1.03320i −0.0986368 + 0.0415616i
\(619\) 8.41624 8.41624i 0.338277 0.338277i −0.517442 0.855719i \(-0.673115\pi\)
0.855719 + 0.517442i \(0.173115\pi\)
\(620\) −15.7740 8.59294i −0.633501 0.345101i
\(621\) 21.5509 + 22.3830i 0.864807 + 0.898200i
\(622\) 0.468918 + 3.24993i 0.0188019 + 0.130310i
\(623\) 20.4550 0.819513
\(624\) 0.960540 + 22.1823i 0.0384524 + 0.888001i
\(625\) −1.00000 −0.0400000
\(626\) −6.25833 43.3746i −0.250133 1.73360i
\(627\) 1.55495 + 5.95324i 0.0620989 + 0.237750i
\(628\) 17.8178 32.7081i 0.711007 1.30519i
\(629\) 6.38282 6.38282i 0.254500 0.254500i
\(630\) −1.12699 + 8.54525i −0.0449004 + 0.340451i
\(631\) −8.95905 −0.356654 −0.178327 0.983971i \(-0.557069\pi\)
−0.178327 + 0.983971i \(0.557069\pi\)
\(632\) −9.38934 20.4789i −0.373488 0.814608i
\(633\) −9.49160 5.56016i −0.377257 0.220997i
\(634\) 2.24716 + 1.68046i 0.0892461 + 0.0667396i
\(635\) −2.08628 2.08628i −0.0827914 0.0827914i
\(636\) −7.98810 + 32.1794i −0.316749 + 1.27600i
\(637\) 6.50979 6.50979i 0.257927 0.257927i
\(638\) 2.25506 + 15.6291i 0.0892787 + 0.618764i
\(639\) 2.10370 + 3.75234i 0.0832211 + 0.148440i
\(640\) 2.44335 + 11.0467i 0.0965819 + 0.436660i
\(641\) 24.7747i 0.978541i −0.872132 0.489270i \(-0.837263\pi\)
0.872132 0.489270i \(-0.162737\pi\)
\(642\) 17.5691 + 7.15245i 0.693398 + 0.282285i
\(643\) −15.9062 15.9062i −0.627281 0.627281i 0.320102 0.947383i \(-0.396283\pi\)
−0.947383 + 0.320102i \(0.896283\pi\)
\(644\) 6.86829 + 23.3055i 0.270649 + 0.918366i
\(645\) 2.75686 + 10.5548i 0.108551 + 0.415596i
\(646\) 3.36166 4.49531i 0.132263 0.176865i
\(647\) 14.4592i 0.568448i −0.958758 0.284224i \(-0.908264\pi\)
0.958758 0.284224i \(-0.0917360\pi\)
\(648\) −3.02109 + 25.2759i −0.118680 + 0.992933i
\(649\) 20.4096i 0.801146i
\(650\) −3.62954 2.71423i −0.142362 0.106461i
\(651\) −7.98673 30.5777i −0.313024 1.19843i
\(652\) 34.6230 + 18.8609i 1.35594 + 0.738652i
\(653\) −18.9295 18.9295i −0.740769 0.740769i 0.231957 0.972726i \(-0.425487\pi\)
−0.972726 + 0.231957i \(0.925487\pi\)
\(654\) 3.57790 8.78869i 0.139907 0.343665i
\(655\) 17.1529i 0.670220i
\(656\) 25.9074 16.7225i 1.01151 0.652905i
\(657\) 16.7584 + 29.8917i 0.653807 + 1.16619i
\(658\) 24.8496 3.58544i 0.968738 0.139775i
\(659\) 7.04721 7.04721i 0.274520 0.274520i −0.556396 0.830917i \(-0.687816\pi\)
0.830917 + 0.556396i \(0.187816\pi\)
\(660\) −4.87737 + 2.93745i −0.189851 + 0.114340i
\(661\) −0.261608 0.261608i −0.0101754 0.0101754i 0.702001 0.712176i \(-0.252290\pi\)
−0.712176 + 0.702001i \(0.752290\pi\)
\(662\) −2.07698 + 2.77740i −0.0807243 + 0.107947i
\(663\) 8.79553 + 5.15240i 0.341590 + 0.200103i
\(664\) −7.71390 + 20.7763i −0.299357 + 0.806278i
\(665\) −4.39096 −0.170274
\(666\) −20.6750 2.72673i −0.801141 0.105659i
\(667\) −28.7252 + 28.7252i −1.11224 + 1.11224i
\(668\) −6.24965 21.2063i −0.241806 0.820498i
\(669\) −7.28778 27.9017i −0.281762 1.07874i
\(670\) 12.1329 1.75060i 0.468733 0.0676315i
\(671\) 20.3835 0.786896
\(672\) −11.2201 + 16.4417i −0.432824 + 0.634254i
\(673\) −7.74885 −0.298696 −0.149348 0.988785i \(-0.547718\pi\)
−0.149348 + 0.988785i \(0.547718\pi\)
\(674\) −32.7679 + 4.72794i −1.26217 + 0.182113i
\(675\) −3.60400 3.74316i −0.138718 0.144074i
\(676\) 1.54329 + 5.23670i 0.0593573 + 0.201411i
\(677\) 5.98942 5.98942i 0.230192 0.230192i −0.582581 0.812773i \(-0.697957\pi\)
0.812773 + 0.582581i \(0.197957\pi\)
\(678\) 3.14610 + 7.46654i 0.120825 + 0.286751i
\(679\) 13.9783 0.536439
\(680\) 4.86940 + 1.80793i 0.186733 + 0.0693308i
\(681\) 16.5552 28.2609i 0.634397 1.08296i
\(682\) 12.5024 16.7186i 0.478743 0.640189i
\(683\) 27.2713 + 27.2713i 1.04351 + 1.04351i 0.999009 + 0.0444991i \(0.0141692\pi\)
0.0444991 + 0.999009i \(0.485831\pi\)
\(684\) −12.9672 + 0.157796i −0.495812 + 0.00603348i
\(685\) 3.48933 3.48933i 0.133321 0.133321i
\(686\) 28.0744 4.05073i 1.07188 0.154657i
\(687\) −24.3132 14.2426i −0.927605 0.543389i
\(688\) −5.30622 + 24.6279i −0.202298 + 0.938932i
\(689\) 30.6735i 1.16857i
\(690\) −13.5662 5.52283i −0.516455 0.210251i
\(691\) −28.8250 28.8250i −1.09656 1.09656i −0.994811 0.101745i \(-0.967557\pi\)
−0.101745 0.994811i \(-0.532443\pi\)
\(692\) −25.7326 14.0179i −0.978208 0.532880i
\(693\) −9.64250 2.71463i −0.366288 0.103120i
\(694\) −14.0911 10.5376i −0.534893 0.400001i
\(695\) 15.8762i 0.602217i
\(696\) −33.1151 3.32331i −1.25523 0.125970i
\(697\) 14.1568i 0.536228i
\(698\) −6.87094 + 9.18802i −0.260069 + 0.347772i
\(699\) 19.4177 5.07179i 0.734444 0.191833i
\(700\) −1.14860 3.89743i −0.0434129 0.147309i
\(701\) 14.6526 + 14.6526i 0.553421 + 0.553421i 0.927427 0.374005i \(-0.122016\pi\)
−0.374005 + 0.927427i \(0.622016\pi\)
\(702\) −2.92108 23.3680i −0.110249 0.881969i
\(703\) 10.6238i 0.400685i
\(704\) −13.1125 + 0.977136i −0.494196 + 0.0368272i
\(705\) −7.65051 + 13.0600i −0.288135 + 0.491867i
\(706\) 0.507876 + 3.51993i 0.0191142 + 0.132474i
\(707\) −4.50115 + 4.50115i −0.169283 + 0.169283i
\(708\) −41.7486 10.3635i −1.56901 0.389485i
\(709\) 25.4427 + 25.4427i 0.955520 + 0.955520i 0.999052 0.0435320i \(-0.0138610\pi\)
−0.0435320 + 0.999052i \(0.513861\pi\)
\(710\) −1.62402 1.21446i −0.0609483 0.0455780i
\(711\) 11.6855 + 20.8432i 0.438239 + 0.781681i
\(712\) −25.8870 + 11.8689i −0.970155 + 0.444804i
\(713\) 53.7060 2.01131
\(714\) 3.54851 + 8.42157i 0.132800 + 0.315170i
\(715\) 3.72456 3.72456i 0.139291 0.139291i
\(716\) 5.68179 10.4301i 0.212338 0.389790i
\(717\) −18.1879 + 4.75057i −0.679238 + 0.177413i
\(718\) 1.55337 + 10.7660i 0.0579714 + 0.401782i
\(719\) 32.2840 1.20399 0.601996 0.798499i \(-0.294372\pi\)
0.601996 + 0.798499i \(0.294372\pi\)
\(720\) −3.53204 11.4684i −0.131631 0.427403i
\(721\) 2.20688 0.0821886
\(722\) 2.89378 + 20.0559i 0.107695 + 0.746405i
\(723\) 47.9046 12.5124i 1.78159 0.465342i
\(724\) −28.1787 15.3504i −1.04725 0.570492i
\(725\) 4.80376 4.80376i 0.178407 0.178407i
\(726\) 7.89301 + 18.7322i 0.292937 + 0.695219i
\(727\) −18.4129 −0.682898 −0.341449 0.939900i \(-0.610918\pi\)
−0.341449 + 0.939900i \(0.610918\pi\)
\(728\) 6.40962 17.2634i 0.237556 0.639826i
\(729\) 1.02244 26.9806i 0.0378681 0.999283i
\(730\) −12.9372 9.67460i −0.478826 0.358073i
\(731\) 8.17861 + 8.17861i 0.302497 + 0.302497i
\(732\) −10.3503 + 41.6952i −0.382557 + 1.54110i
\(733\) 25.7677 25.7677i 0.951753 0.951753i −0.0471356 0.998889i \(-0.515009\pi\)
0.998889 + 0.0471356i \(0.0150093\pi\)
\(734\) −1.13932 7.89631i −0.0420532 0.291458i
\(735\) −2.51498 + 4.29326i −0.0927665 + 0.158359i
\(736\) −22.2151 25.5092i −0.818858 0.940280i
\(737\) 14.2469i 0.524791i
\(738\) −25.9521 + 19.9043i −0.955309 + 0.732687i
\(739\) 28.5023 + 28.5023i 1.04847 + 1.04847i 0.998764 + 0.0497093i \(0.0158295\pi\)
0.0497093 + 0.998764i \(0.484171\pi\)
\(740\) 9.42973 2.77900i 0.346644 0.102158i
\(741\) 11.6077 3.03188i 0.426421 0.111379i
\(742\) 16.4687 22.0224i 0.604586 0.808469i
\(743\) 32.8315i 1.20447i −0.798319 0.602235i \(-0.794277\pi\)
0.798319 0.602235i \(-0.205723\pi\)
\(744\) 27.8501 + 34.0636i 1.02103 + 1.24883i
\(745\) 3.08888i 0.113168i
\(746\) 10.3186 + 7.71638i 0.377790 + 0.282517i
\(747\) 6.37011 22.6269i 0.233070 0.827875i
\(748\) −2.88782 + 5.30118i −0.105589 + 0.193830i
\(749\) −11.1248 11.1248i −0.406491 0.406491i
\(750\) 2.26869 + 0.923593i 0.0828410 + 0.0337249i
\(751\) 15.7955i 0.576386i 0.957572 + 0.288193i \(0.0930544\pi\)
−0.957572 + 0.288193i \(0.906946\pi\)
\(752\) −29.3681 + 18.9564i −1.07095 + 0.691267i
\(753\) 28.9688 + 16.9698i 1.05568 + 0.618416i
\(754\) 30.4740 4.39696i 1.10980 0.160128i
\(755\) 12.9515 12.9515i 0.471354 0.471354i
\(756\) 10.4491 18.3457i 0.380031 0.667226i
\(757\) 1.55620 + 1.55620i 0.0565611 + 0.0565611i 0.734822 0.678260i \(-0.237266\pi\)
−0.678260 + 0.734822i \(0.737266\pi\)
\(758\) −20.5671 + 27.5029i −0.747031 + 0.998951i
\(759\) 8.60446 14.6884i 0.312322 0.533157i
\(760\) 5.55700 2.54782i 0.201574 0.0924191i
\(761\) 29.7877 1.07980 0.539902 0.841728i \(-0.318461\pi\)
0.539902 + 0.841728i \(0.318461\pi\)
\(762\) 2.80626 + 6.66000i 0.101660 + 0.241266i
\(763\) −5.56501 + 5.56501i −0.201467 + 0.201467i
\(764\) 29.0932 8.57396i 1.05256 0.310195i
\(765\) −5.30312 1.49298i −0.191735 0.0539787i
\(766\) 30.6749 4.42595i 1.10833 0.159916i
\(767\) 39.7949 1.43691
\(768\) 4.65946 27.3183i 0.168134 0.985764i
\(769\) −36.2318 −1.30655 −0.653275 0.757120i \(-0.726606\pi\)
−0.653275 + 0.757120i \(0.726606\pi\)
\(770\) 4.67382 0.674365i 0.168433 0.0243024i
\(771\) −5.53247 21.1814i −0.199247 0.762830i
\(772\) −42.4980 + 12.5245i −1.52954 + 0.450765i
\(773\) −26.2882 + 26.2882i −0.945519 + 0.945519i −0.998591 0.0530715i \(-0.983099\pi\)
0.0530715 + 0.998591i \(0.483099\pi\)
\(774\) 3.49389 26.4919i 0.125585 0.952232i
\(775\) −8.98136 −0.322620
\(776\) −17.6903 + 8.11081i −0.635046 + 0.291161i
\(777\) 14.9240 + 8.74244i 0.535395 + 0.313633i
\(778\) −19.9856 + 26.7254i −0.716520 + 0.958151i
\(779\) −11.7816 11.7816i −0.422119 0.422119i
\(780\) 5.72748 + 9.50998i 0.205077 + 0.340512i
\(781\) 1.66653 1.66653i 0.0596331 0.0596331i
\(782\) −15.3707 + 2.21778i −0.549657 + 0.0793075i
\(783\) 35.2940 + 0.668497i 1.26130 + 0.0238901i
\(784\) −9.65430 + 6.23160i −0.344796 + 0.222557i
\(785\) 18.6232i 0.664690i
\(786\) 15.8423 38.9147i 0.565077 1.38804i
\(787\) 14.0210 + 14.0210i 0.499796 + 0.499796i 0.911374 0.411578i \(-0.135022\pi\)
−0.411578 + 0.911374i \(0.635022\pi\)
\(788\) 3.75119 6.88605i 0.133631 0.245305i
\(789\) −0.796817 3.05066i −0.0283674 0.108607i
\(790\) −9.02096 6.74601i −0.320951 0.240012i
\(791\) 6.71994i 0.238934i
\(792\) 13.7783 2.15946i 0.489589 0.0767332i
\(793\) 39.7441i 1.41135i
\(794\) 28.5361 38.1594i 1.01271 1.35422i
\(795\) 4.18953 + 16.0399i 0.148587 + 0.568877i
\(796\) 4.20518 1.23929i 0.149048 0.0439256i
\(797\) −3.36409 3.36409i −0.119162 0.119162i 0.645011 0.764173i \(-0.276853\pi\)
−0.764173 + 0.645011i \(0.776853\pi\)
\(798\) 9.96174 + 4.05546i 0.352642 + 0.143562i
\(799\) 16.0479i 0.567734i
\(800\) 3.71506 + 4.26595i 0.131347 + 0.150824i
\(801\) 26.3474 14.7713i 0.930941 0.521920i
\(802\) 2.09883 + 14.5463i 0.0741121 + 0.513649i
\(803\) 13.2758 13.2758i 0.468494 0.468494i
\(804\) −29.1426 7.23426i −1.02778 0.255133i
\(805\) 8.59012 + 8.59012i 0.302762 + 0.302762i
\(806\) −32.5982 24.3775i −1.14822 0.858659i
\(807\) 45.4859 + 26.6456i 1.60118 + 0.937969i
\(808\) 3.08470 8.30821i 0.108519 0.292282i
\(809\) −33.1370 −1.16503 −0.582517 0.812819i \(-0.697932\pi\)
−0.582517 + 0.812819i \(0.697932\pi\)
\(810\) 4.71921 + 11.8207i 0.165816 + 0.415337i
\(811\) 1.82888 1.82888i 0.0642205 0.0642205i −0.674267 0.738488i \(-0.735540\pi\)
0.738488 + 0.674267i \(0.235540\pi\)
\(812\) 24.2399 + 13.2047i 0.850654 + 0.463395i
\(813\) −0.409303 1.56704i −0.0143549 0.0549586i
\(814\) 1.63161 + 11.3082i 0.0571879 + 0.396352i
\(815\) 19.7135 0.690534
\(816\) −9.37739 8.59898i −0.328274 0.301024i
\(817\) 13.6128 0.476252
\(818\) 3.70643 + 25.6881i 0.129592 + 0.898164i
\(819\) −5.29304 + 18.8011i −0.184954 + 0.656964i
\(820\) 7.37552 13.5392i 0.257564 0.472810i
\(821\) −12.7110 + 12.7110i −0.443617 + 0.443617i −0.893225 0.449609i \(-0.851563\pi\)
0.449609 + 0.893225i \(0.351563\pi\)
\(822\) −11.1390 + 4.69351i −0.388516 + 0.163705i
\(823\) −35.6896 −1.24406 −0.622031 0.782993i \(-0.713692\pi\)
−0.622031 + 0.782993i \(0.713692\pi\)
\(824\) −2.79293 + 1.28053i −0.0972964 + 0.0446092i
\(825\) −1.43894 + 2.45638i −0.0500975 + 0.0855200i
\(826\) 28.5713 + 21.3660i 0.994121 + 0.743419i
\(827\) −33.5364 33.5364i −1.16618 1.16618i −0.983098 0.183078i \(-0.941394\pi\)
−0.183078 0.983098i \(-0.558606\pi\)
\(828\) 25.6766 + 25.0592i 0.892325 + 0.870869i
\(829\) −27.2066 + 27.2066i −0.944926 + 0.944926i −0.998561 0.0536349i \(-0.982919\pi\)
0.0536349 + 0.998561i \(0.482919\pi\)
\(830\) 1.58245 + 10.9675i 0.0549277 + 0.380687i
\(831\) −14.4554 8.46795i −0.501453 0.293750i
\(832\) 1.90524 + 25.5670i 0.0660522 + 0.886375i
\(833\) 5.27549i 0.182785i
\(834\) 14.6631 36.0182i 0.507742 1.24721i
\(835\) −7.81638 7.81638i −0.270497 0.270497i
\(836\) 2.00844 + 6.81504i 0.0694633 + 0.235703i
\(837\) −32.3688 33.6186i −1.11883 1.16203i
\(838\) 7.59593 10.1575i 0.262397 0.350885i
\(839\) 43.9736i 1.51814i 0.651011 + 0.759068i \(0.274345\pi\)
−0.651011 + 0.759068i \(0.725655\pi\)
\(840\) −0.993821 + 9.90291i −0.0342901 + 0.341683i
\(841\) 17.1523i 0.591458i
\(842\) −20.2265 15.1257i −0.697051 0.521266i
\(843\) −54.5055 + 14.2365i −1.87727 + 0.490332i
\(844\) −11.1543 6.07634i −0.383948 0.209156i
\(845\) 1.93018 + 1.93018i 0.0664002 + 0.0664002i
\(846\) 29.4188 22.5631i 1.01144 0.775737i
\(847\) 16.8592i 0.579287i
\(848\) −8.06373 + 37.4265i −0.276910 + 1.28523i
\(849\) 12.8513 21.9381i 0.441055 0.752913i
\(850\) 2.57048 0.370883i 0.0881667 0.0127212i
\(851\) −20.7836 + 20.7836i −0.712452 + 0.712452i
\(852\) 2.56273 + 4.25518i 0.0877976 + 0.145780i
\(853\) −13.0992 13.0992i −0.448507 0.448507i 0.446351 0.894858i \(-0.352723\pi\)
−0.894858 + 0.446351i \(0.852723\pi\)
\(854\) 21.3387 28.5347i 0.730196 0.976439i
\(855\) −5.65585 + 3.17088i −0.193426 + 0.108442i
\(856\) 20.5341 + 7.62398i 0.701842 + 0.260582i
\(857\) −1.30688 −0.0446423 −0.0223212 0.999751i \(-0.507106\pi\)
−0.0223212 + 0.999751i \(0.507106\pi\)
\(858\) −11.8899 + 5.00991i −0.405913 + 0.171035i
\(859\) −6.22051 + 6.22051i −0.212241 + 0.212241i −0.805219 0.592978i \(-0.797952\pi\)
0.592978 + 0.805219i \(0.297952\pi\)
\(860\) 3.56087 + 12.0828i 0.121425 + 0.412019i
\(861\) 26.2455 6.85519i 0.894446 0.233624i
\(862\) 17.3674 2.50587i 0.591536 0.0853501i
\(863\) −30.8875 −1.05142 −0.525712 0.850663i \(-0.676201\pi\)
−0.525712 + 0.850663i \(0.676201\pi\)
\(864\) −2.57903 + 29.2805i −0.0877403 + 0.996143i
\(865\) −14.6515 −0.498167
\(866\) −16.8400 + 2.42977i −0.572247 + 0.0825670i
\(867\) 22.8374 5.96501i 0.775600 0.202582i
\(868\) −10.3160 35.0042i −0.350147 1.18812i
\(869\) 9.25711 9.25711i 0.314026 0.314026i
\(870\) −15.3350 + 6.46155i −0.519905 + 0.219067i
\(871\) 27.7789 0.941251
\(872\) 3.81378 10.2719i 0.129151 0.347850i
\(873\) 18.0050 10.0943i 0.609378 0.341640i
\(874\) −10.9462 + 14.6375i −0.370259 + 0.495121i
\(875\) −1.43654 1.43654i −0.0485640 0.0485640i
\(876\) 20.4151 + 33.8974i 0.689761 + 1.14529i
\(877\) −6.95656 + 6.95656i −0.234907 + 0.234907i −0.814737 0.579831i \(-0.803119\pi\)
0.579831 + 0.814737i \(0.303119\pi\)
\(878\) −42.8901 + 6.18843i −1.44747 + 0.208849i
\(879\) 11.6282 19.8502i 0.392210 0.669531i
\(880\) −5.52368 + 3.56539i −0.186203 + 0.120189i
\(881\) 3.45874i 0.116528i −0.998301 0.0582639i \(-0.981444\pi\)
0.998301 0.0582639i \(-0.0185565\pi\)
\(882\) 9.67095 7.41727i 0.325638 0.249752i
\(883\) 32.6156 + 32.6156i 1.09760 + 1.09760i 0.994690 + 0.102913i \(0.0328162\pi\)
0.102913 + 0.994690i \(0.467184\pi\)
\(884\) 10.3363 + 5.63073i 0.347648 + 0.189382i
\(885\) −20.8097 + 5.43538i −0.699510 + 0.182708i
\(886\) 8.53711 + 6.38418i 0.286810 + 0.214481i
\(887\) 38.2122i 1.28304i 0.767107 + 0.641519i \(0.221696\pi\)
−0.767107 + 0.641519i \(0.778304\pi\)
\(888\) −23.9599 2.40453i −0.804040 0.0806906i
\(889\) 5.99405i 0.201034i
\(890\) −8.52749 + 11.4032i −0.285842 + 0.382236i
\(891\) −14.3805 + 3.46659i −0.481766 + 0.116135i
\(892\) −9.41317 31.9408i −0.315176 1.06946i
\(893\) 13.3554 + 13.3554i 0.446921 + 0.446921i
\(894\) −2.85287 + 7.00772i −0.0954141 + 0.234373i
\(895\) 5.93862i 0.198506i
\(896\) −12.3591 + 19.3790i −0.412889 + 0.647408i
\(897\) −28.6398 16.7771i −0.956254 0.560172i
\(898\) −1.53118 10.6122i −0.0510963 0.354133i
\(899\) 43.1443 43.1443i 1.43894 1.43894i
\(900\) −4.29395 4.19070i −0.143132 0.139690i
\(901\) 12.4288 + 12.4288i 0.414064 + 0.414064i
\(902\) 14.3500 + 10.7311i 0.477802 + 0.357307i
\(903\) −11.2021 + 19.1228i −0.372783 + 0.636367i
\(904\) 3.89919 + 8.50446i 0.129685 + 0.282854i
\(905\) −16.0443 −0.533329
\(906\) −41.3450 + 17.4211i −1.37360 + 0.578778i
\(907\) 1.86287 1.86287i 0.0618557 0.0618557i −0.675502 0.737358i \(-0.736073\pi\)
0.737358 + 0.675502i \(0.236073\pi\)
\(908\) 18.0921 33.2117i 0.600408 1.10217i
\(909\) −2.54733 + 9.04823i −0.0844896 + 0.300111i
\(910\) −1.31489 9.11309i −0.0435881 0.302096i
\(911\) −58.6122 −1.94191 −0.970954 0.239266i \(-0.923093\pi\)
−0.970954 + 0.239266i \(0.923093\pi\)
\(912\) −14.9603 + 0.647813i −0.495385 + 0.0214512i
\(913\) −12.8785 −0.426215
\(914\) −7.41715 51.4060i −0.245338 1.70036i
\(915\) 5.42843 + 20.7831i 0.179458 + 0.687068i
\(916\) −28.5723 15.5648i −0.944057 0.514276i
\(917\) −24.6409 + 24.6409i −0.813713 + 0.813713i
\(918\) 10.6523 + 8.28504i 0.351577 + 0.273447i
\(919\) −17.5232 −0.578039 −0.289019 0.957323i \(-0.593329\pi\)
−0.289019 + 0.957323i \(0.593329\pi\)
\(920\) −15.8556 5.88692i −0.522744 0.194086i
\(921\) −22.3146 13.0719i −0.735292 0.430733i
\(922\) −16.0071 11.9703i −0.527164 0.394221i
\(923\) −3.24943 3.24943i −0.106956 0.106956i
\(924\) −11.2263 2.78678i −0.369318 0.0916783i
\(925\) 3.47568 3.47568i 0.114280 0.114280i
\(926\) 4.26846 + 29.5834i 0.140270 + 0.972171i
\(927\) 2.84261 1.59367i 0.0933637 0.0523431i
\(928\) −38.3389 2.64630i −1.25854 0.0868692i
\(929\) 43.3977i 1.42383i 0.702265 + 0.711916i \(0.252172\pi\)
−0.702265 + 0.711916i \(0.747828\pi\)
\(930\) 20.3760 + 8.29512i 0.668154 + 0.272008i
\(931\) 4.39037 + 4.39037i 0.143889 + 0.143889i
\(932\) 22.2286 6.55091i 0.728122 0.214582i
\(933\) −1.01631 3.89102i −0.0332726 0.127386i
\(934\) 20.5459 27.4746i 0.672283 0.898995i
\(935\) 3.01836i 0.0987109i
\(936\) −4.21056 26.8651i −0.137626 0.878113i
\(937\) 55.5562i 1.81494i −0.420114 0.907471i \(-0.638010\pi\)
0.420114 0.907471i \(-0.361990\pi\)
\(938\) 19.9442 + 14.9146i 0.651200 + 0.486977i
\(939\) 13.5640 + 51.9307i 0.442645 + 1.69470i
\(940\) −8.36075 + 15.3478i −0.272698 + 0.500591i
\(941\) −15.9770 15.9770i −0.520836 0.520836i 0.396988 0.917824i \(-0.370055\pi\)
−0.917824 + 0.396988i \(0.870055\pi\)
\(942\) −17.2002 + 42.2503i −0.560414 + 1.37659i
\(943\) 46.0971i 1.50113i
\(944\) −48.5560 10.4617i −1.58036 0.340498i
\(945\) 0.199911 10.5545i 0.00650310 0.343337i
\(946\) −14.4897 + 2.09066i −0.471101 + 0.0679732i
\(947\) −21.0534 + 21.0534i −0.684145 + 0.684145i −0.960931 0.276787i \(-0.910730\pi\)
0.276787 + 0.960931i \(0.410730\pi\)
\(948\) 14.2352 + 23.6363i 0.462339 + 0.767673i
\(949\) −25.8854 25.8854i −0.840277 0.840277i
\(950\) 1.83055 2.44786i 0.0593908 0.0794190i
\(951\) −2.96531 1.73707i −0.0961568 0.0563285i
\(952\) 4.39793 + 9.59225i 0.142538 + 0.310887i
\(953\) −38.2352 −1.23856 −0.619281 0.785170i \(-0.712576\pi\)
−0.619281 + 0.785170i \(0.712576\pi\)
\(954\) 5.30957 40.2591i 0.171904 1.30344i
\(955\) 10.7234 10.7234i 0.347001 0.347001i
\(956\) −20.8208 + 6.13601i −0.673392 + 0.198453i
\(957\) −4.88752 18.7122i −0.157991 0.604879i
\(958\) −6.28960 + 0.907499i −0.203208 + 0.0293200i
\(959\) 10.0251 0.323729
\(960\) −4.48835 13.1093i −0.144861 0.423102i
\(961\) −49.6648 −1.60209
\(962\) 22.0489 3.18134i 0.710886 0.102571i
\(963\) −22.3631 6.29585i −0.720642 0.202881i
\(964\) 54.8394 16.1615i 1.76626 0.520528i
\(965\) −15.6642 + 15.6642i −0.504249 + 0.504249i
\(966\) −11.5546 27.4221i −0.371762 0.882293i
\(967\) −8.56913 −0.275565 −0.137782 0.990463i \(-0.543997\pi\)
−0.137782 + 0.990463i \(0.543997\pi\)
\(968\) 9.78239 + 21.3362i 0.314418 + 0.685771i
\(969\) −3.47491 + 5.93193i −0.111630 + 0.190561i
\(970\) −5.82742 + 7.79259i −0.187107 + 0.250205i
\(971\) −21.2325 21.2325i −0.681385 0.681385i 0.278927 0.960312i \(-0.410021\pi\)
−0.960312 + 0.278927i \(0.910021\pi\)
\(972\) 0.211075 31.1762i 0.00677023 0.999977i
\(973\) −22.8068 + 22.8068i −0.731151 + 0.731151i
\(974\) 37.5090 5.41202i 1.20187 0.173412i
\(975\) 4.78948 + 2.80567i 0.153386 + 0.0898534i
\(976\) −10.4483 + 48.4939i −0.334441 + 1.55225i
\(977\) 46.4074i 1.48470i −0.670010 0.742352i \(-0.733710\pi\)
0.670010 0.742352i \(-0.266290\pi\)
\(978\) −44.7239 18.2073i −1.43011 0.582204i
\(979\) −11.7017 11.7017i −0.373988 0.373988i
\(980\) −2.74846 + 5.04535i −0.0877964 + 0.161168i
\(981\) −3.14940 + 11.1868i −0.100553 + 0.357168i
\(982\) −23.3294 17.4461i −0.744472 0.556727i
\(983\) 31.9560i 1.01924i 0.860400 + 0.509620i \(0.170214\pi\)
−0.860400 + 0.509620i \(0.829786\pi\)
\(984\) −29.2375 + 23.9044i −0.932058 + 0.762044i
\(985\) 3.92075i 0.124925i
\(986\) −10.5663 + 14.1296i −0.336501 + 0.449978i
\(987\) −29.7515 + 7.77092i −0.947000 + 0.247351i
\(988\) 13.2881 3.91609i 0.422751 0.124587i
\(989\) −26.6310 26.6310i −0.846816 0.846816i
\(990\) 5.53321 4.24377i 0.175857 0.134876i
\(991\) 44.2060i 1.40425i 0.712053 + 0.702126i \(0.247765\pi\)
−0.712053 + 0.702126i \(0.752235\pi\)
\(992\) 33.3663 + 38.3140i 1.05938 + 1.21647i
\(993\) 2.14696 3.66501i 0.0681317 0.116306i
\(994\) −0.588339 4.07760i −0.0186610 0.129333i
\(995\) 1.54997 1.54997i 0.0491375 0.0491375i
\(996\) 6.53940 26.3434i 0.207209 0.834724i
\(997\) 29.8054 + 29.8054i 0.943946 + 0.943946i 0.998510 0.0545646i \(-0.0173771\pi\)
−0.0545646 + 0.998510i \(0.517377\pi\)
\(998\) 2.73592 + 2.04596i 0.0866041 + 0.0647639i
\(999\) 25.5363 + 0.483679i 0.807934 + 0.0153029i
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 240.2.bk.b.11.1 60
3.2 odd 2 inner 240.2.bk.b.11.30 yes 60
4.3 odd 2 960.2.bk.b.911.3 60
12.11 even 2 960.2.bk.b.911.19 60
16.3 odd 4 inner 240.2.bk.b.131.30 yes 60
16.13 even 4 960.2.bk.b.431.19 60
48.29 odd 4 960.2.bk.b.431.3 60
48.35 even 4 inner 240.2.bk.b.131.1 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.2.bk.b.11.1 60 1.1 even 1 trivial
240.2.bk.b.11.30 yes 60 3.2 odd 2 inner
240.2.bk.b.131.1 yes 60 48.35 even 4 inner
240.2.bk.b.131.30 yes 60 16.3 odd 4 inner
960.2.bk.b.431.3 60 48.29 odd 4
960.2.bk.b.431.19 60 16.13 even 4
960.2.bk.b.911.3 60 4.3 odd 2
960.2.bk.b.911.19 60 12.11 even 2