Properties

Label 570.2.s.b.521.10
Level $570$
Weight $2$
Character 570.521
Analytic conductor $4.551$
Analytic rank $0$
Dimension $24$
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] = [570,2,Mod(221,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("570.221");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.s (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 521.10
Character \(\chi\) \(=\) 570.521
Dual form 570.2.s.b.221.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.32792 + 1.11204i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.62701 - 0.593994i) q^{6} -0.387589 q^{7} -1.00000 q^{8} +(0.526745 + 2.95339i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.32792 + 1.11204i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.62701 - 0.593994i) q^{6} -0.387589 q^{7} -1.00000 q^{8} +(0.526745 + 2.95339i) q^{9} +(0.866025 - 0.500000i) q^{10} +6.28666i q^{11} +(0.299093 - 1.70603i) q^{12} +(5.96278 - 3.44261i) q^{13} +(-0.193795 + 0.335662i) q^{14} +(0.593994 + 1.62701i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.63331 - 2.67504i) q^{17} +(2.82109 + 1.02052i) q^{18} +(0.936449 + 4.25712i) q^{19} -1.00000i q^{20} +(-0.514688 - 0.431014i) q^{21} +(5.44441 + 3.14333i) q^{22} +(5.57852 - 3.22076i) q^{23} +(-1.32792 - 1.11204i) q^{24} +(0.500000 + 0.866025i) q^{25} -6.88523i q^{26} +(-2.58481 + 4.50763i) q^{27} +(0.193795 + 0.335662i) q^{28} +(-2.15245 - 3.72815i) q^{29} +(1.70603 + 0.299093i) q^{30} -5.87016i q^{31} +(0.500000 + 0.866025i) q^{32} +(-6.99100 + 8.34818i) q^{33} +(-4.63331 + 2.67504i) q^{34} +(-0.335662 - 0.193795i) q^{35} +(2.29434 - 1.93287i) q^{36} -2.54580i q^{37} +(4.15500 + 1.31757i) q^{38} +(11.7464 + 2.05932i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(1.40194 - 2.42823i) q^{41} +(-0.630613 + 0.230226i) q^{42} +(-0.588721 + 1.01969i) q^{43} +(5.44441 - 3.14333i) q^{44} +(-1.02052 + 2.82109i) q^{45} -6.44153i q^{46} +(-6.74336 + 3.89328i) q^{47} +(-1.62701 + 0.593994i) q^{48} -6.84977 q^{49} +1.00000 q^{50} +(-3.17792 - 8.70465i) q^{51} +(-5.96278 - 3.44261i) q^{52} +(1.97481 + 3.42047i) q^{53} +(2.61132 + 4.49233i) q^{54} +(-3.14333 + 5.44441i) q^{55} +0.387589 q^{56} +(-3.49055 + 6.69448i) q^{57} -4.30489 q^{58} +(-0.556791 + 0.964390i) q^{59} +(1.11204 - 1.32792i) q^{60} +(1.28373 + 2.22348i) q^{61} +(-5.08371 - 2.93508i) q^{62} +(-0.204161 - 1.14470i) q^{63} +1.00000 q^{64} +6.88523 q^{65} +(3.73424 + 10.2285i) q^{66} +(6.95760 - 4.01697i) q^{67} +5.35008i q^{68} +(10.9894 + 1.92661i) q^{69} +(-0.335662 + 0.193795i) q^{70} +(4.17799 - 7.23648i) q^{71} +(-0.526745 - 2.95339i) q^{72} +(-0.890700 + 1.54274i) q^{73} +(-2.20473 - 1.27290i) q^{74} +(-0.299093 + 1.70603i) q^{75} +(3.21855 - 2.93955i) q^{76} -2.43664i q^{77} +(7.65663 - 9.14304i) q^{78} +(-12.3862 - 7.15117i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(-8.44508 + 3.11137i) q^{81} +(-1.40194 - 2.42823i) q^{82} +3.22583i q^{83} +(-0.115925 + 0.661239i) q^{84} +(-2.67504 - 4.63331i) q^{85} +(0.588721 + 1.01969i) q^{86} +(1.28756 - 7.34428i) q^{87} -6.28666i q^{88} +(-7.49847 - 12.9877i) q^{89} +(1.93287 + 2.29434i) q^{90} +(-2.31111 + 1.33432i) q^{91} +(-5.57852 - 3.22076i) q^{92} +(6.52784 - 7.79511i) q^{93} +7.78656i q^{94} +(-1.31757 + 4.15500i) q^{95} +(-0.299093 + 1.70603i) q^{96} +(-5.33880 - 3.08236i) q^{97} +(-3.42489 + 5.93208i) q^{98} +(-18.5670 + 3.31146i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 1.32792 + 1.11204i 0.766675 + 0.642035i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.866025 + 0.500000i 0.387298 + 0.223607i
\(6\) 1.62701 0.593994i 0.664225 0.242497i
\(7\) −0.387589 −0.146495 −0.0732475 0.997314i \(-0.523336\pi\)
−0.0732475 + 0.997314i \(0.523336\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.526745 + 2.95339i 0.175582 + 0.984465i
\(10\) 0.866025 0.500000i 0.273861 0.158114i
\(11\) 6.28666i 1.89550i 0.319015 + 0.947750i \(0.396648\pi\)
−0.319015 + 0.947750i \(0.603352\pi\)
\(12\) 0.299093 1.70603i 0.0863406 0.492489i
\(13\) 5.96278 3.44261i 1.65378 0.954809i 0.678280 0.734804i \(-0.262726\pi\)
0.975499 0.220006i \(-0.0706076\pi\)
\(14\) −0.193795 + 0.335662i −0.0517938 + 0.0897095i
\(15\) 0.593994 + 1.62701i 0.153369 + 0.420093i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −4.63331 2.67504i −1.12374 0.648793i −0.181389 0.983411i \(-0.558059\pi\)
−0.942354 + 0.334619i \(0.891393\pi\)
\(18\) 2.82109 + 1.02052i 0.664937 + 0.240540i
\(19\) 0.936449 + 4.25712i 0.214836 + 0.976650i
\(20\) 1.00000i 0.223607i
\(21\) −0.514688 0.431014i −0.112314 0.0940549i
\(22\) 5.44441 + 3.14333i 1.16075 + 0.670160i
\(23\) 5.57852 3.22076i 1.16320 0.671575i 0.211133 0.977457i \(-0.432285\pi\)
0.952069 + 0.305882i \(0.0989513\pi\)
\(24\) −1.32792 1.11204i −0.271061 0.226994i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 6.88523i 1.35030i
\(27\) −2.58481 + 4.50763i −0.497447 + 0.867494i
\(28\) 0.193795 + 0.335662i 0.0366237 + 0.0634342i
\(29\) −2.15245 3.72815i −0.399699 0.692299i 0.593989 0.804473i \(-0.297552\pi\)
−0.993689 + 0.112173i \(0.964219\pi\)
\(30\) 1.70603 + 0.299093i 0.311477 + 0.0546066i
\(31\) 5.87016i 1.05431i −0.849769 0.527156i \(-0.823258\pi\)
0.849769 0.527156i \(-0.176742\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −6.99100 + 8.34818i −1.21698 + 1.45323i
\(34\) −4.63331 + 2.67504i −0.794606 + 0.458766i
\(35\) −0.335662 0.193795i −0.0567373 0.0327573i
\(36\) 2.29434 1.93287i 0.382390 0.322145i
\(37\) 2.54580i 0.418527i −0.977859 0.209264i \(-0.932893\pi\)
0.977859 0.209264i \(-0.0671067\pi\)
\(38\) 4.15500 + 1.31757i 0.674030 + 0.213738i
\(39\) 11.7464 + 2.05932i 1.88093 + 0.329755i
\(40\) −0.866025 0.500000i −0.136931 0.0790569i
\(41\) 1.40194 2.42823i 0.218946 0.379226i −0.735540 0.677481i \(-0.763071\pi\)
0.954486 + 0.298256i \(0.0964048\pi\)
\(42\) −0.630613 + 0.230226i −0.0973057 + 0.0355246i
\(43\) −0.588721 + 1.01969i −0.0897791 + 0.155502i −0.907418 0.420230i \(-0.861949\pi\)
0.817639 + 0.575732i \(0.195283\pi\)
\(44\) 5.44441 3.14333i 0.820775 0.473875i
\(45\) −1.02052 + 2.82109i −0.152131 + 0.420543i
\(46\) 6.44153i 0.949751i
\(47\) −6.74336 + 3.89328i −0.983620 + 0.567893i −0.903361 0.428881i \(-0.858908\pi\)
−0.0802589 + 0.996774i \(0.525575\pi\)
\(48\) −1.62701 + 0.593994i −0.234839 + 0.0857356i
\(49\) −6.84977 −0.978539
\(50\) 1.00000 0.141421
\(51\) −3.17792 8.70465i −0.444997 1.21890i
\(52\) −5.96278 3.44261i −0.826889 0.477405i
\(53\) 1.97481 + 3.42047i 0.271261 + 0.469837i 0.969185 0.246334i \(-0.0792261\pi\)
−0.697924 + 0.716172i \(0.745893\pi\)
\(54\) 2.61132 + 4.49233i 0.355355 + 0.611328i
\(55\) −3.14333 + 5.44441i −0.423846 + 0.734124i
\(56\) 0.387589 0.0517938
\(57\) −3.49055 + 6.69448i −0.462334 + 0.886706i
\(58\) −4.30489 −0.565260
\(59\) −0.556791 + 0.964390i −0.0724880 + 0.125553i −0.899991 0.435908i \(-0.856427\pi\)
0.827503 + 0.561461i \(0.189761\pi\)
\(60\) 1.11204 1.32792i 0.143563 0.171434i
\(61\) 1.28373 + 2.22348i 0.164365 + 0.284688i 0.936429 0.350856i \(-0.114109\pi\)
−0.772065 + 0.635544i \(0.780776\pi\)
\(62\) −5.08371 2.93508i −0.645632 0.372756i
\(63\) −0.204161 1.14470i −0.0257218 0.144219i
\(64\) 1.00000 0.125000
\(65\) 6.88523 0.854008
\(66\) 3.73424 + 10.2285i 0.459653 + 1.25904i
\(67\) 6.95760 4.01697i 0.850006 0.490751i −0.0106470 0.999943i \(-0.503389\pi\)
0.860653 + 0.509192i \(0.170056\pi\)
\(68\) 5.35008i 0.648793i
\(69\) 10.9894 + 1.92661i 1.32297 + 0.231937i
\(70\) −0.335662 + 0.193795i −0.0401193 + 0.0231629i
\(71\) 4.17799 7.23648i 0.495836 0.858813i −0.504153 0.863614i \(-0.668195\pi\)
0.999988 + 0.00480188i \(0.00152849\pi\)
\(72\) −0.526745 2.95339i −0.0620775 0.348061i
\(73\) −0.890700 + 1.54274i −0.104249 + 0.180564i −0.913431 0.406994i \(-0.866577\pi\)
0.809182 + 0.587557i \(0.199910\pi\)
\(74\) −2.20473 1.27290i −0.256294 0.147972i
\(75\) −0.299093 + 1.70603i −0.0345362 + 0.196996i
\(76\) 3.21855 2.93955i 0.369193 0.337189i
\(77\) 2.43664i 0.277681i
\(78\) 7.65663 9.14304i 0.866943 1.03524i
\(79\) −12.3862 7.15117i −1.39355 0.804569i −0.399848 0.916581i \(-0.630937\pi\)
−0.993707 + 0.112012i \(0.964270\pi\)
\(80\) −0.866025 + 0.500000i −0.0968246 + 0.0559017i
\(81\) −8.44508 + 3.11137i −0.938342 + 0.345708i
\(82\) −1.40194 2.42823i −0.154818 0.268153i
\(83\) 3.22583i 0.354081i 0.984204 + 0.177040i \(0.0566523\pi\)
−0.984204 + 0.177040i \(0.943348\pi\)
\(84\) −0.115925 + 0.661239i −0.0126485 + 0.0721471i
\(85\) −2.67504 4.63331i −0.290149 0.502553i
\(86\) 0.588721 + 1.01969i 0.0634834 + 0.109956i
\(87\) 1.28756 7.34428i 0.138041 0.787390i
\(88\) 6.28666i 0.670160i
\(89\) −7.49847 12.9877i −0.794836 1.37670i −0.922943 0.384936i \(-0.874223\pi\)
0.128107 0.991760i \(-0.459110\pi\)
\(90\) 1.93287 + 2.29434i 0.203743 + 0.241845i
\(91\) −2.31111 + 1.33432i −0.242270 + 0.139875i
\(92\) −5.57852 3.22076i −0.581601 0.335788i
\(93\) 6.52784 7.79511i 0.676905 0.808315i
\(94\) 7.78656i 0.803122i
\(95\) −1.31757 + 4.15500i −0.135180 + 0.426294i
\(96\) −0.299093 + 1.70603i −0.0305260 + 0.174121i
\(97\) −5.33880 3.08236i −0.542073 0.312966i 0.203846 0.979003i \(-0.434656\pi\)
−0.745919 + 0.666037i \(0.767989\pi\)
\(98\) −3.42489 + 5.93208i −0.345966 + 0.599230i
\(99\) −18.5670 + 3.31146i −1.86605 + 0.332815i
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −3.63539 + 2.09889i −0.361734 + 0.208847i −0.669841 0.742504i \(-0.733638\pi\)
0.308107 + 0.951352i \(0.400305\pi\)
\(102\) −9.12741 1.60017i −0.903748 0.158441i
\(103\) 14.4685i 1.42562i −0.701356 0.712811i \(-0.747422\pi\)
0.701356 0.712811i \(-0.252578\pi\)
\(104\) −5.96278 + 3.44261i −0.584699 + 0.337576i
\(105\) −0.230226 0.630613i −0.0224677 0.0615415i
\(106\) 3.94962 0.383621
\(107\) 2.46390 0.238194 0.119097 0.992883i \(-0.462000\pi\)
0.119097 + 0.992883i \(0.462000\pi\)
\(108\) 5.19613 0.0153044i 0.499998 0.00147267i
\(109\) 2.32388 + 1.34169i 0.222587 + 0.128511i 0.607148 0.794589i \(-0.292314\pi\)
−0.384561 + 0.923100i \(0.625647\pi\)
\(110\) 3.14333 + 5.44441i 0.299705 + 0.519104i
\(111\) 2.83103 3.38062i 0.268709 0.320874i
\(112\) 0.193795 0.335662i 0.0183119 0.0317171i
\(113\) 0.146598 0.0137908 0.00689539 0.999976i \(-0.497805\pi\)
0.00689539 + 0.999976i \(0.497805\pi\)
\(114\) 4.05232 + 6.37014i 0.379534 + 0.596619i
\(115\) 6.44153 0.600675
\(116\) −2.15245 + 3.72815i −0.199850 + 0.346150i
\(117\) 13.3083 + 15.7971i 1.23035 + 1.46044i
\(118\) 0.556791 + 0.964390i 0.0512567 + 0.0887793i
\(119\) 1.79582 + 1.03682i 0.164623 + 0.0950449i
\(120\) −0.593994 1.62701i −0.0542240 0.148525i
\(121\) −28.5221 −2.59292
\(122\) 2.56746 0.232447
\(123\) 4.56195 1.66549i 0.411337 0.150172i
\(124\) −5.08371 + 2.93508i −0.456530 + 0.263578i
\(125\) 1.00000i 0.0894427i
\(126\) −1.09342 0.395544i −0.0974099 0.0352378i
\(127\) −14.1674 + 8.17952i −1.25715 + 0.725815i −0.972519 0.232822i \(-0.925204\pi\)
−0.284630 + 0.958638i \(0.591871\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −1.91571 + 0.699393i −0.168669 + 0.0615781i
\(130\) 3.44261 5.96278i 0.301937 0.522971i
\(131\) −2.32705 1.34352i −0.203316 0.117384i 0.394886 0.918730i \(-0.370784\pi\)
−0.598201 + 0.801346i \(0.704118\pi\)
\(132\) 10.7252 + 1.88029i 0.933512 + 0.163659i
\(133\) −0.362957 1.65001i −0.0314724 0.143074i
\(134\) 8.03394i 0.694027i
\(135\) −4.49233 + 2.61132i −0.386638 + 0.224747i
\(136\) 4.63331 + 2.67504i 0.397303 + 0.229383i
\(137\) 11.8037 6.81488i 1.00846 0.582234i 0.0977189 0.995214i \(-0.468845\pi\)
0.910740 + 0.412980i \(0.135512\pi\)
\(138\) 7.16322 8.55383i 0.609774 0.728151i
\(139\) 11.3319 + 19.6275i 0.961162 + 1.66478i 0.719590 + 0.694399i \(0.244330\pi\)
0.241572 + 0.970383i \(0.422337\pi\)
\(140\) 0.387589i 0.0327573i
\(141\) −13.2841 2.32890i −1.11872 0.196129i
\(142\) −4.17799 7.23648i −0.350609 0.607272i
\(143\) 21.6425 + 37.4860i 1.80984 + 3.13474i
\(144\) −2.82109 1.02052i −0.235091 0.0850436i
\(145\) 4.30489i 0.357502i
\(146\) 0.890700 + 1.54274i 0.0737148 + 0.127678i
\(147\) −9.09595 7.61721i −0.750222 0.628257i
\(148\) −2.20473 + 1.27290i −0.181228 + 0.104632i
\(149\) 2.36838 + 1.36738i 0.194025 + 0.112020i 0.593866 0.804564i \(-0.297601\pi\)
−0.399840 + 0.916585i \(0.630934\pi\)
\(150\) 1.32792 + 1.11204i 0.108424 + 0.0907975i
\(151\) 5.03506i 0.409747i 0.978788 + 0.204874i \(0.0656784\pi\)
−0.978788 + 0.204874i \(0.934322\pi\)
\(152\) −0.936449 4.25712i −0.0759560 0.345298i
\(153\) 5.45988 15.0931i 0.441405 1.22020i
\(154\) −2.11019 1.21832i −0.170044 0.0981751i
\(155\) 2.93508 5.08371i 0.235751 0.408333i
\(156\) −4.08978 11.2024i −0.327445 0.896906i
\(157\) 0.931580 1.61354i 0.0743482 0.128775i −0.826454 0.563004i \(-0.809646\pi\)
0.900803 + 0.434229i \(0.142979\pi\)
\(158\) −12.3862 + 7.15117i −0.985392 + 0.568916i
\(159\) −1.18130 + 6.73817i −0.0936833 + 0.534372i
\(160\) 1.00000i 0.0790569i
\(161\) −2.16218 + 1.24833i −0.170403 + 0.0983824i
\(162\) −1.52801 + 8.86934i −0.120052 + 0.696841i
\(163\) −15.6424 −1.22521 −0.612604 0.790390i \(-0.709878\pi\)
−0.612604 + 0.790390i \(0.709878\pi\)
\(164\) −2.80388 −0.218946
\(165\) −10.2285 + 3.73424i −0.796286 + 0.290710i
\(166\) 2.79365 + 1.61291i 0.216829 + 0.125186i
\(167\) 2.58979 + 4.48565i 0.200404 + 0.347110i 0.948659 0.316302i \(-0.102441\pi\)
−0.748255 + 0.663412i \(0.769108\pi\)
\(168\) 0.514688 + 0.431014i 0.0397090 + 0.0332534i
\(169\) 17.2032 29.7968i 1.32332 2.29206i
\(170\) −5.35008 −0.410333
\(171\) −12.0797 + 5.00812i −0.923756 + 0.382980i
\(172\) 1.17744 0.0897791
\(173\) −4.91408 + 8.51144i −0.373611 + 0.647113i −0.990118 0.140236i \(-0.955214\pi\)
0.616507 + 0.787349i \(0.288547\pi\)
\(174\) −5.71655 4.78720i −0.433371 0.362917i
\(175\) −0.193795 0.335662i −0.0146495 0.0253737i
\(176\) −5.44441 3.14333i −0.410388 0.236937i
\(177\) −1.81181 + 0.661461i −0.136184 + 0.0497184i
\(178\) −14.9969 −1.12407
\(179\) 19.6374 1.46777 0.733884 0.679275i \(-0.237706\pi\)
0.733884 + 0.679275i \(0.237706\pi\)
\(180\) 2.95339 0.526745i 0.220133 0.0392612i
\(181\) −19.3105 + 11.1489i −1.43534 + 0.828691i −0.997521 0.0703737i \(-0.977581\pi\)
−0.437815 + 0.899065i \(0.644247\pi\)
\(182\) 2.66864i 0.197813i
\(183\) −0.767908 + 4.38017i −0.0567654 + 0.323791i
\(184\) −5.57852 + 3.22076i −0.411254 + 0.237438i
\(185\) 1.27290 2.20473i 0.0935855 0.162095i
\(186\) −3.48684 9.55083i −0.255667 0.700301i
\(187\) 16.8171 29.1280i 1.22979 2.13005i
\(188\) 6.74336 + 3.89328i 0.491810 + 0.283947i
\(189\) 1.00184 1.74711i 0.0728735 0.127084i
\(190\) 2.93955 + 3.21855i 0.213257 + 0.233498i
\(191\) 17.2742i 1.24992i −0.780658 0.624958i \(-0.785116\pi\)
0.780658 0.624958i \(-0.214884\pi\)
\(192\) 1.32792 + 1.11204i 0.0958344 + 0.0802544i
\(193\) 8.44254 + 4.87430i 0.607707 + 0.350860i 0.772068 0.635540i \(-0.219223\pi\)
−0.164360 + 0.986400i \(0.552556\pi\)
\(194\) −5.33880 + 3.08236i −0.383304 + 0.221300i
\(195\) 9.14304 + 7.65663i 0.654746 + 0.548303i
\(196\) 3.42489 + 5.93208i 0.244635 + 0.423720i
\(197\) 7.99412i 0.569557i 0.958593 + 0.284779i \(0.0919201\pi\)
−0.958593 + 0.284779i \(0.908080\pi\)
\(198\) −6.41568 + 17.7352i −0.455943 + 1.26039i
\(199\) 2.50783 + 4.34368i 0.177775 + 0.307915i 0.941118 0.338078i \(-0.109777\pi\)
−0.763343 + 0.645993i \(0.776443\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 13.7062 + 2.40289i 0.966758 + 0.169487i
\(202\) 4.19778i 0.295355i
\(203\) 0.834265 + 1.44499i 0.0585539 + 0.101418i
\(204\) −5.94949 + 7.10448i −0.416548 + 0.497413i
\(205\) 2.42823 1.40194i 0.169595 0.0979157i
\(206\) −12.5301 7.23425i −0.873012 0.504034i
\(207\) 12.4506 + 14.7791i 0.865379 + 1.02722i
\(208\) 6.88523i 0.477405i
\(209\) −26.7631 + 5.88714i −1.85124 + 0.407222i
\(210\) −0.661239 0.115925i −0.0456299 0.00799959i
\(211\) −0.901047 0.520219i −0.0620306 0.0358134i 0.468664 0.883377i \(-0.344736\pi\)
−0.530695 + 0.847563i \(0.678069\pi\)
\(212\) 1.97481 3.42047i 0.135630 0.234919i
\(213\) 13.5953 4.96340i 0.931533 0.340086i
\(214\) 1.23195 2.13380i 0.0842144 0.145864i
\(215\) −1.01969 + 0.588721i −0.0695426 + 0.0401504i
\(216\) 2.58481 4.50763i 0.175874 0.306706i
\(217\) 2.27521i 0.154451i
\(218\) 2.32388 1.34169i 0.157393 0.0908708i
\(219\) −2.89836 + 1.05814i −0.195853 + 0.0715025i
\(220\) 6.28666 0.423846
\(221\) −36.8365 −2.47789
\(222\) −1.51219 4.14205i −0.101492 0.277996i
\(223\) −3.44225 1.98738i −0.230510 0.133085i 0.380297 0.924864i \(-0.375822\pi\)
−0.610807 + 0.791779i \(0.709155\pi\)
\(224\) −0.193795 0.335662i −0.0129484 0.0224274i
\(225\) −2.29434 + 1.93287i −0.152956 + 0.128858i
\(226\) 0.0732990 0.126958i 0.00487578 0.00844509i
\(227\) 20.9613 1.39125 0.695626 0.718404i \(-0.255127\pi\)
0.695626 + 0.718404i \(0.255127\pi\)
\(228\) 7.54286 0.324338i 0.499538 0.0214798i
\(229\) −8.17578 −0.540271 −0.270135 0.962822i \(-0.587068\pi\)
−0.270135 + 0.962822i \(0.587068\pi\)
\(230\) 3.22076 5.57852i 0.212371 0.367837i
\(231\) 2.70964 3.23567i 0.178281 0.212891i
\(232\) 2.15245 + 3.72815i 0.141315 + 0.244765i
\(233\) −3.05627 1.76454i −0.200223 0.115599i 0.396537 0.918019i \(-0.370212\pi\)
−0.596759 + 0.802420i \(0.703545\pi\)
\(234\) 20.3348 3.62676i 1.32933 0.237089i
\(235\) −7.78656 −0.507939
\(236\) 1.11358 0.0724880
\(237\) −8.49550 23.2701i −0.551842 1.51155i
\(238\) 1.79582 1.03682i 0.116406 0.0672069i
\(239\) 15.8539i 1.02550i −0.858537 0.512751i \(-0.828626\pi\)
0.858537 0.512751i \(-0.171374\pi\)
\(240\) −1.70603 0.299093i −0.110124 0.0193063i
\(241\) 3.16963 1.82999i 0.204174 0.117880i −0.394427 0.918927i \(-0.629057\pi\)
0.598601 + 0.801047i \(0.295724\pi\)
\(242\) −14.2610 + 24.7009i −0.916735 + 1.58783i
\(243\) −14.6744 5.25960i −0.941360 0.337403i
\(244\) 1.28373 2.22348i 0.0821823 0.142344i
\(245\) −5.93208 3.42489i −0.378987 0.218808i
\(246\) 0.838620 4.78351i 0.0534684 0.304985i
\(247\) 20.2395 + 22.1604i 1.28781 + 1.41004i
\(248\) 5.87016i 0.372756i
\(249\) −3.58724 + 4.28364i −0.227332 + 0.271465i
\(250\) 0.866025 + 0.500000i 0.0547723 + 0.0316228i
\(251\) 9.75160 5.63009i 0.615516 0.355368i −0.159605 0.987181i \(-0.551022\pi\)
0.775121 + 0.631813i \(0.217689\pi\)
\(252\) −0.889262 + 0.749160i −0.0560183 + 0.0471927i
\(253\) 20.2478 + 35.0703i 1.27297 + 2.20485i
\(254\) 16.3590i 1.02646i
\(255\) 1.60017 9.12741i 0.100207 0.571581i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −13.6499 23.6423i −0.851456 1.47477i −0.879894 0.475170i \(-0.842386\pi\)
0.0284374 0.999596i \(-0.490947\pi\)
\(258\) −0.352164 + 2.00875i −0.0219248 + 0.125059i
\(259\) 0.986725i 0.0613121i
\(260\) −3.44261 5.96278i −0.213502 0.369796i
\(261\) 9.87690 8.32080i 0.611365 0.515045i
\(262\) −2.32705 + 1.34352i −0.143766 + 0.0830032i
\(263\) 16.4659 + 9.50659i 1.01533 + 0.586202i 0.912748 0.408523i \(-0.133956\pi\)
0.102583 + 0.994724i \(0.467289\pi\)
\(264\) 6.99100 8.34818i 0.430266 0.513795i
\(265\) 3.94962i 0.242623i
\(266\) −1.61043 0.510676i −0.0987419 0.0313116i
\(267\) 4.48547 25.5853i 0.274507 1.56579i
\(268\) −6.95760 4.01697i −0.425003 0.245376i
\(269\) 9.43473 16.3414i 0.575246 0.996355i −0.420769 0.907168i \(-0.638240\pi\)
0.996015 0.0891869i \(-0.0284268\pi\)
\(270\) 0.0153044 + 5.19613i 0.000931395 + 0.316226i
\(271\) 9.90543 17.1567i 0.601712 1.04220i −0.390850 0.920454i \(-0.627819\pi\)
0.992562 0.121741i \(-0.0388478\pi\)
\(272\) 4.63331 2.67504i 0.280936 0.162198i
\(273\) −4.55278 0.798171i −0.275547 0.0483075i
\(274\) 13.6298i 0.823403i
\(275\) −5.44441 + 3.14333i −0.328310 + 0.189550i
\(276\) −3.82623 10.4804i −0.230312 0.630849i
\(277\) 13.1915 0.792598 0.396299 0.918121i \(-0.370294\pi\)
0.396299 + 0.918121i \(0.370294\pi\)
\(278\) 22.6639 1.35929
\(279\) 17.3369 3.09208i 1.03793 0.185118i
\(280\) 0.335662 + 0.193795i 0.0200596 + 0.0115814i
\(281\) 8.39558 + 14.5416i 0.500838 + 0.867477i 1.00000 0.000967983i \(0.000308119\pi\)
−0.499161 + 0.866509i \(0.666359\pi\)
\(282\) −8.65895 + 10.3399i −0.515633 + 0.615734i
\(283\) 3.98624 6.90437i 0.236958 0.410422i −0.722882 0.690971i \(-0.757183\pi\)
0.959840 + 0.280549i \(0.0905164\pi\)
\(284\) −8.35597 −0.495836
\(285\) −6.37014 + 4.05232i −0.377335 + 0.240039i
\(286\) 43.2851 2.55950
\(287\) −0.543377 + 0.941156i −0.0320745 + 0.0555547i
\(288\) −2.29434 + 1.93287i −0.135195 + 0.113896i
\(289\) 5.81170 + 10.0662i 0.341864 + 0.592127i
\(290\) −3.72815 2.15245i −0.218924 0.126396i
\(291\) −3.66180 10.0301i −0.214659 0.587973i
\(292\) 1.78140 0.104249
\(293\) 4.52893 0.264583 0.132292 0.991211i \(-0.457766\pi\)
0.132292 + 0.991211i \(0.457766\pi\)
\(294\) −11.1447 + 4.06872i −0.649970 + 0.237293i
\(295\) −0.964390 + 0.556791i −0.0561489 + 0.0324176i
\(296\) 2.54580i 0.147972i
\(297\) −28.3380 16.2498i −1.64433 0.942911i
\(298\) 2.36838 1.36738i 0.137196 0.0792104i
\(299\) 22.1757 38.4094i 1.28245 2.22127i
\(300\) 1.62701 0.593994i 0.0939356 0.0342943i
\(301\) 0.228182 0.395223i 0.0131522 0.0227802i
\(302\) 4.36049 + 2.51753i 0.250918 + 0.144868i
\(303\) −7.16155 1.25553i −0.411420 0.0721281i
\(304\) −4.15500 1.31757i −0.238305 0.0755679i
\(305\) 2.56746i 0.147012i
\(306\) −10.3410 12.2749i −0.591157 0.701711i
\(307\) 20.5036 + 11.8378i 1.17020 + 0.675618i 0.953728 0.300670i \(-0.0972104\pi\)
0.216476 + 0.976288i \(0.430544\pi\)
\(308\) −2.11019 + 1.21832i −0.120239 + 0.0694203i
\(309\) 16.0895 19.2130i 0.915300 1.09299i
\(310\) −2.93508 5.08371i −0.166701 0.288735i
\(311\) 21.2557i 1.20530i 0.798006 + 0.602650i \(0.205888\pi\)
−0.798006 + 0.602650i \(0.794112\pi\)
\(312\) −11.7464 2.05932i −0.665010 0.116586i
\(313\) 16.1860 + 28.0351i 0.914889 + 1.58463i 0.807063 + 0.590465i \(0.201056\pi\)
0.107826 + 0.994170i \(0.465611\pi\)
\(314\) −0.931580 1.61354i −0.0525721 0.0910575i
\(315\) 0.395544 1.09342i 0.0222864 0.0616074i
\(316\) 14.3023i 0.804569i
\(317\) −0.273517 0.473746i −0.0153623 0.0266082i 0.858242 0.513245i \(-0.171557\pi\)
−0.873604 + 0.486637i \(0.838223\pi\)
\(318\) 5.24478 + 4.39212i 0.294112 + 0.246298i
\(319\) 23.4376 13.5317i 1.31225 0.757630i
\(320\) 0.866025 + 0.500000i 0.0484123 + 0.0279508i
\(321\) 3.27186 + 2.73995i 0.182618 + 0.152929i
\(322\) 2.49667i 0.139134i
\(323\) 7.04911 22.2296i 0.392223 1.23689i
\(324\) 6.91707 + 5.75797i 0.384281 + 0.319887i
\(325\) 5.96278 + 3.44261i 0.330756 + 0.190962i
\(326\) −7.82120 + 13.5467i −0.433176 + 0.750284i
\(327\) 1.59391 + 4.36590i 0.0881436 + 0.241435i
\(328\) −1.40194 + 2.42823i −0.0774091 + 0.134077i
\(329\) 2.61365 1.50899i 0.144095 0.0831935i
\(330\) −1.88029 + 10.7252i −0.103507 + 0.590405i
\(331\) 12.2880i 0.675410i 0.941252 + 0.337705i \(0.109651\pi\)
−0.941252 + 0.337705i \(0.890349\pi\)
\(332\) 2.79365 1.61291i 0.153321 0.0885202i
\(333\) 7.51876 1.34099i 0.412025 0.0734857i
\(334\) 5.17958 0.283414
\(335\) 8.03394 0.438941
\(336\) 0.630613 0.230226i 0.0344027 0.0125598i
\(337\) 12.8425 + 7.41464i 0.699577 + 0.403901i 0.807190 0.590292i \(-0.200987\pi\)
−0.107613 + 0.994193i \(0.534321\pi\)
\(338\) −17.2032 29.7968i −0.935730 1.62073i
\(339\) 0.194670 + 0.163022i 0.0105730 + 0.00885416i
\(340\) −2.67504 + 4.63331i −0.145074 + 0.251276i
\(341\) 36.9037 1.99845
\(342\) −1.70268 + 12.9654i −0.0920706 + 0.701087i
\(343\) 5.36802 0.289846
\(344\) 0.588721 1.01969i 0.0317417 0.0549782i
\(345\) 8.55383 + 7.16322i 0.460523 + 0.385655i
\(346\) 4.91408 + 8.51144i 0.264183 + 0.457578i
\(347\) −8.34699 4.81914i −0.448090 0.258705i 0.258933 0.965895i \(-0.416629\pi\)
−0.707023 + 0.707190i \(0.749962\pi\)
\(348\) −7.00412 + 2.55708i −0.375460 + 0.137074i
\(349\) −25.2299 −1.35053 −0.675263 0.737577i \(-0.735970\pi\)
−0.675263 + 0.737577i \(0.735970\pi\)
\(350\) −0.387589 −0.0207175
\(351\) 0.105374 + 35.7765i 0.00562446 + 1.90961i
\(352\) −5.44441 + 3.14333i −0.290188 + 0.167540i
\(353\) 10.0563i 0.535241i −0.963524 0.267620i \(-0.913763\pi\)
0.963524 0.267620i \(-0.0862373\pi\)
\(354\) −0.333064 + 1.89980i −0.0177022 + 0.100973i
\(355\) 7.23648 4.17799i 0.384073 0.221744i
\(356\) −7.49847 + 12.9877i −0.397418 + 0.688348i
\(357\) 1.23173 + 3.37383i 0.0651899 + 0.178562i
\(358\) 9.81870 17.0065i 0.518934 0.898821i
\(359\) 9.76791 + 5.63951i 0.515531 + 0.297642i 0.735104 0.677954i \(-0.237133\pi\)
−0.219573 + 0.975596i \(0.570467\pi\)
\(360\) 1.02052 2.82109i 0.0537863 0.148684i
\(361\) −17.2461 + 7.97315i −0.907691 + 0.419639i
\(362\) 22.2978i 1.17195i
\(363\) −37.8751 31.7176i −1.98793 1.66474i
\(364\) 2.31111 + 1.33432i 0.121135 + 0.0699374i
\(365\) −1.54274 + 0.890700i −0.0807505 + 0.0466213i
\(366\) 3.40938 + 2.85511i 0.178211 + 0.149239i
\(367\) −13.2097 22.8799i −0.689540 1.19432i −0.971987 0.235036i \(-0.924479\pi\)
0.282447 0.959283i \(-0.408854\pi\)
\(368\) 6.44153i 0.335788i
\(369\) 7.90999 + 2.86142i 0.411777 + 0.148960i
\(370\) −1.27290 2.20473i −0.0661750 0.114618i
\(371\) −0.765414 1.32574i −0.0397383 0.0688288i
\(372\) −10.0147 1.75572i −0.519237 0.0910299i
\(373\) 9.42090i 0.487796i 0.969801 + 0.243898i \(0.0784262\pi\)
−0.969801 + 0.243898i \(0.921574\pi\)
\(374\) −16.8171 29.1280i −0.869590 1.50617i
\(375\) −1.11204 + 1.32792i −0.0574254 + 0.0685735i
\(376\) 6.74336 3.89328i 0.347762 0.200781i
\(377\) −25.6691 14.8201i −1.32203 0.763273i
\(378\) −1.01212 1.74118i −0.0520578 0.0895565i
\(379\) 18.4868i 0.949601i 0.880093 + 0.474801i \(0.157480\pi\)
−0.880093 + 0.474801i \(0.842520\pi\)
\(380\) 4.25712 0.936449i 0.218386 0.0480388i
\(381\) −27.9091 4.89287i −1.42982 0.250669i
\(382\) −14.9599 8.63710i −0.765415 0.441912i
\(383\) −8.39580 + 14.5419i −0.429005 + 0.743059i −0.996785 0.0801217i \(-0.974469\pi\)
0.567780 + 0.823180i \(0.307802\pi\)
\(384\) 1.62701 0.593994i 0.0830282 0.0303121i
\(385\) 1.21832 2.11019i 0.0620914 0.107545i
\(386\) 8.44254 4.87430i 0.429714 0.248096i
\(387\) −3.32167 1.20161i −0.168850 0.0610811i
\(388\) 6.16472i 0.312966i
\(389\) −3.31963 + 1.91659i −0.168312 + 0.0971748i −0.581790 0.813339i \(-0.697647\pi\)
0.413478 + 0.910514i \(0.364314\pi\)
\(390\) 11.2024 4.08978i 0.567253 0.207094i
\(391\) −34.4627 −1.74285
\(392\) 6.84977 0.345966
\(393\) −1.59609 4.37186i −0.0805121 0.220531i
\(394\) 6.92311 + 3.99706i 0.348781 + 0.201369i
\(395\) −7.15117 12.3862i −0.359814 0.623217i
\(396\) 12.1513 + 14.4237i 0.610626 + 0.724821i
\(397\) 6.16028 10.6699i 0.309176 0.535508i −0.669007 0.743257i \(-0.733280\pi\)
0.978182 + 0.207748i \(0.0666135\pi\)
\(398\) 5.01565 0.251412
\(399\) 1.35290 2.59471i 0.0677296 0.129898i
\(400\) −1.00000 −0.0500000
\(401\) 3.20325 5.54818i 0.159962 0.277063i −0.774892 0.632093i \(-0.782196\pi\)
0.934855 + 0.355030i \(0.115529\pi\)
\(402\) 8.93405 10.6684i 0.445590 0.532093i
\(403\) −20.2087 35.0025i −1.00667 1.74360i
\(404\) 3.63539 + 2.09889i 0.180867 + 0.104424i
\(405\) −8.86934 1.52801i −0.440721 0.0759277i
\(406\) 1.66853 0.0828078
\(407\) 16.0046 0.793318
\(408\) 3.17792 + 8.70465i 0.157330 + 0.430945i
\(409\) −28.7986 + 16.6269i −1.42400 + 0.822147i −0.996638 0.0819327i \(-0.973891\pi\)
−0.427363 + 0.904080i \(0.640557\pi\)
\(410\) 2.80388i 0.138474i
\(411\) 23.2528 + 4.07656i 1.14698 + 0.201082i
\(412\) −12.5301 + 7.23425i −0.617313 + 0.356406i
\(413\) 0.215806 0.373787i 0.0106191 0.0183929i
\(414\) 19.0244 3.39304i 0.934997 0.166759i
\(415\) −1.61291 + 2.79365i −0.0791748 + 0.137135i
\(416\) 5.96278 + 3.44261i 0.292349 + 0.168788i
\(417\) −6.77860 + 38.6653i −0.331949 + 1.89345i
\(418\) −8.28312 + 26.1211i −0.405141 + 1.27762i
\(419\) 26.2177i 1.28082i 0.768034 + 0.640409i \(0.221235\pi\)
−0.768034 + 0.640409i \(0.778765\pi\)
\(420\) −0.431014 + 0.514688i −0.0210313 + 0.0251142i
\(421\) 16.2792 + 9.39883i 0.793402 + 0.458071i 0.841159 0.540788i \(-0.181874\pi\)
−0.0477568 + 0.998859i \(0.515207\pi\)
\(422\) −0.901047 + 0.520219i −0.0438623 + 0.0253239i
\(423\) −15.0504 17.8650i −0.731777 0.868628i
\(424\) −1.97481 3.42047i −0.0959052 0.166113i
\(425\) 5.35008i 0.259517i
\(426\) 2.49921 14.2556i 0.121087 0.690684i
\(427\) −0.497560 0.861799i −0.0240786 0.0417054i
\(428\) −1.23195 2.13380i −0.0595485 0.103141i
\(429\) −12.9463 + 73.8457i −0.625051 + 3.56531i
\(430\) 1.17744i 0.0567813i
\(431\) 16.8907 + 29.2555i 0.813595 + 1.40919i 0.910333 + 0.413877i \(0.135826\pi\)
−0.0967380 + 0.995310i \(0.530841\pi\)
\(432\) −2.61132 4.49233i −0.125637 0.216137i
\(433\) 18.8094 10.8596i 0.903920 0.521879i 0.0254504 0.999676i \(-0.491898\pi\)
0.878470 + 0.477797i \(0.158565\pi\)
\(434\) 1.97039 + 1.13761i 0.0945818 + 0.0546068i
\(435\) 4.78720 5.71655i 0.229529 0.274088i
\(436\) 2.68338i 0.128511i
\(437\) 18.9352 + 20.7324i 0.905792 + 0.991763i
\(438\) −0.532803 + 3.03912i −0.0254583 + 0.145215i
\(439\) −4.46634 2.57864i −0.213167 0.123072i 0.389616 0.920978i \(-0.372608\pi\)
−0.602782 + 0.797906i \(0.705941\pi\)
\(440\) 3.14333 5.44441i 0.149852 0.259552i
\(441\) −3.60808 20.2301i −0.171813 0.963338i
\(442\) −18.4183 + 31.9014i −0.876068 + 1.51739i
\(443\) −28.7183 + 16.5805i −1.36445 + 0.787765i −0.990212 0.139568i \(-0.955429\pi\)
−0.374237 + 0.927333i \(0.622095\pi\)
\(444\) −4.34322 0.761431i −0.206120 0.0361359i
\(445\) 14.9969i 0.710923i
\(446\) −3.44225 + 1.98738i −0.162995 + 0.0941053i
\(447\) 1.62444 + 4.44950i 0.0768332 + 0.210454i
\(448\) −0.387589 −0.0183119
\(449\) −28.6061 −1.35001 −0.675004 0.737815i \(-0.735858\pi\)
−0.675004 + 0.737815i \(0.735858\pi\)
\(450\) 0.526745 + 2.95339i 0.0248310 + 0.139224i
\(451\) 15.2655 + 8.81352i 0.718822 + 0.415012i
\(452\) −0.0732990 0.126958i −0.00344769 0.00597158i
\(453\) −5.59918 + 6.68616i −0.263072 + 0.314143i
\(454\) 10.4807 18.1530i 0.491882 0.851964i
\(455\) −2.66864 −0.125108
\(456\) 3.49055 6.69448i 0.163460 0.313498i
\(457\) 12.0944 0.565752 0.282876 0.959156i \(-0.408711\pi\)
0.282876 + 0.959156i \(0.408711\pi\)
\(458\) −4.08789 + 7.08043i −0.191015 + 0.330847i
\(459\) 24.0343 13.9708i 1.12183 0.652100i
\(460\) −3.22076 5.57852i −0.150169 0.260100i
\(461\) −23.9736 13.8412i −1.11656 0.644647i −0.176040 0.984383i \(-0.556329\pi\)
−0.940521 + 0.339736i \(0.889662\pi\)
\(462\) −1.44735 3.96445i −0.0673368 0.184443i
\(463\) 22.5239 1.04678 0.523388 0.852094i \(-0.324668\pi\)
0.523388 + 0.852094i \(0.324668\pi\)
\(464\) 4.30489 0.199850
\(465\) 9.55083 3.48684i 0.442909 0.161698i
\(466\) −3.05627 + 1.76454i −0.141579 + 0.0817407i
\(467\) 22.4617i 1.03940i 0.854348 + 0.519701i \(0.173957\pi\)
−0.854348 + 0.519701i \(0.826043\pi\)
\(468\) 7.02653 19.4238i 0.324802 0.897867i
\(469\) −2.69669 + 1.55693i −0.124522 + 0.0718926i
\(470\) −3.89328 + 6.74336i −0.179584 + 0.311048i
\(471\) 3.03139 1.10671i 0.139679 0.0509943i
\(472\) 0.556791 0.964390i 0.0256284 0.0443896i
\(473\) −6.41047 3.70109i −0.294754 0.170176i
\(474\) −24.4002 4.27772i −1.12074 0.196482i
\(475\) −3.21855 + 2.93955i −0.147677 + 0.134876i
\(476\) 2.07363i 0.0950449i
\(477\) −9.06177 + 7.63410i −0.414910 + 0.349542i
\(478\) −13.7299 7.92694i −0.627989 0.362570i
\(479\) −14.0462 + 8.10959i −0.641788 + 0.370537i −0.785303 0.619111i \(-0.787493\pi\)
0.143515 + 0.989648i \(0.454160\pi\)
\(480\) −1.11204 + 1.32792i −0.0507573 + 0.0606110i
\(481\) −8.76421 15.1801i −0.399614 0.692151i
\(482\) 3.65997i 0.166707i
\(483\) −4.25939 0.746734i −0.193809 0.0339776i
\(484\) 14.2610 + 24.7009i 0.648229 + 1.12277i
\(485\) −3.08236 5.33880i −0.139963 0.242423i
\(486\) −11.8921 + 10.0786i −0.539438 + 0.457173i
\(487\) 26.2560i 1.18977i 0.803809 + 0.594887i \(0.202803\pi\)
−0.803809 + 0.594887i \(0.797197\pi\)
\(488\) −1.28373 2.22348i −0.0581117 0.100652i
\(489\) −20.7719 17.3949i −0.939337 0.786627i
\(490\) −5.93208 + 3.42489i −0.267984 + 0.154721i
\(491\) 20.1138 + 11.6127i 0.907723 + 0.524074i 0.879698 0.475533i \(-0.157745\pi\)
0.0280250 + 0.999607i \(0.491078\pi\)
\(492\) −3.72333 3.11802i −0.167861 0.140571i
\(493\) 23.0315i 1.03729i
\(494\) 29.3112 6.44766i 1.31878 0.290094i
\(495\) −17.7352 6.41568i −0.797139 0.288363i
\(496\) 5.08371 + 2.93508i 0.228265 + 0.131789i
\(497\) −1.61934 + 2.80478i −0.0726374 + 0.125812i
\(498\) 1.91612 + 5.24846i 0.0858635 + 0.235189i
\(499\) −5.68385 + 9.84472i −0.254444 + 0.440710i −0.964744 0.263189i \(-0.915226\pi\)
0.710300 + 0.703899i \(0.248559\pi\)
\(500\) 0.866025 0.500000i 0.0387298 0.0223607i
\(501\) −1.54917 + 8.83653i −0.0692120 + 0.394787i
\(502\) 11.2602i 0.502567i
\(503\) −11.7374 + 6.77660i −0.523346 + 0.302154i −0.738302 0.674470i \(-0.764372\pi\)
0.214957 + 0.976624i \(0.431039\pi\)
\(504\) 0.204161 + 1.14470i 0.00909403 + 0.0509892i
\(505\) −4.19778 −0.186799
\(506\) 40.4957 1.80025
\(507\) 55.9796 20.4372i 2.48614 0.907647i
\(508\) 14.1674 + 8.17952i 0.628575 + 0.362908i
\(509\) −15.5217 26.8843i −0.687986 1.19163i −0.972488 0.232951i \(-0.925162\pi\)
0.284502 0.958675i \(-0.408172\pi\)
\(510\) −7.10448 5.94949i −0.314592 0.263448i
\(511\) 0.345226 0.597948i 0.0152719 0.0264517i
\(512\) −1.00000 −0.0441942
\(513\) −21.6101 6.78268i −0.954108 0.299463i
\(514\) −27.2998 −1.20414
\(515\) 7.23425 12.5301i 0.318779 0.552141i
\(516\) 1.56355 + 1.30936i 0.0688314 + 0.0576413i
\(517\) −24.4757 42.3932i −1.07644 1.86445i
\(518\) 0.854529 + 0.493363i 0.0375459 + 0.0216771i
\(519\) −15.9906 + 5.83787i −0.701908 + 0.256254i
\(520\) −6.88523 −0.301937
\(521\) 7.63094 0.334317 0.167159 0.985930i \(-0.446541\pi\)
0.167159 + 0.985930i \(0.446541\pi\)
\(522\) −2.26758 12.7140i −0.0992492 0.556479i
\(523\) −14.6044 + 8.43187i −0.638607 + 0.368700i −0.784078 0.620663i \(-0.786864\pi\)
0.145471 + 0.989363i \(0.453530\pi\)
\(524\) 2.68705i 0.117384i
\(525\) 0.115925 0.661239i 0.00505939 0.0288589i
\(526\) 16.4659 9.50659i 0.717948 0.414507i
\(527\) −15.7029 + 27.1983i −0.684030 + 1.18477i
\(528\) −3.73424 10.2285i −0.162512 0.445137i
\(529\) 9.24662 16.0156i 0.402027 0.696331i
\(530\) 3.42047 + 1.97481i 0.148576 + 0.0857802i
\(531\) −3.14151 1.13644i −0.136330 0.0493171i
\(532\) −1.24747 + 1.13934i −0.0540849 + 0.0493965i
\(533\) 19.3053i 0.836207i
\(534\) −19.9147 16.6772i −0.861795 0.721691i
\(535\) 2.13380 + 1.23195i 0.0922522 + 0.0532618i
\(536\) −6.95760 + 4.01697i −0.300522 + 0.173507i
\(537\) 26.0769 + 21.8375i 1.12530 + 0.942359i
\(538\) −9.43473 16.3414i −0.406760 0.704529i
\(539\) 43.0622i 1.85482i
\(540\) 4.50763 + 2.58481i 0.193978 + 0.111233i
\(541\) −11.3322 19.6279i −0.487208 0.843869i 0.512684 0.858577i \(-0.328651\pi\)
−0.999892 + 0.0147085i \(0.995318\pi\)
\(542\) −9.90543 17.1567i −0.425475 0.736944i
\(543\) −38.0408 6.66911i −1.63249 0.286199i
\(544\) 5.35008i 0.229383i
\(545\) 1.34169 + 2.32388i 0.0574717 + 0.0995440i
\(546\) −2.96763 + 3.54374i −0.127003 + 0.151658i
\(547\) −1.44092 + 0.831914i −0.0616091 + 0.0355701i −0.530488 0.847692i \(-0.677991\pi\)
0.468879 + 0.883262i \(0.344658\pi\)
\(548\) −11.8037 6.81488i −0.504230 0.291117i
\(549\) −5.89063 + 4.96257i −0.251406 + 0.211797i
\(550\) 6.28666i 0.268064i
\(551\) 13.8555 12.6544i 0.590264 0.539097i
\(552\) −10.9894 1.92661i −0.467742 0.0820021i
\(553\) 4.80075 + 2.77172i 0.204149 + 0.117865i
\(554\) 6.59573 11.4241i 0.280226 0.485365i
\(555\) 4.14205 1.51219i 0.175820 0.0641889i
\(556\) 11.3319 19.6275i 0.480581 0.832391i
\(557\) 7.03591 4.06218i 0.298121 0.172120i −0.343477 0.939161i \(-0.611605\pi\)
0.641599 + 0.767041i \(0.278272\pi\)
\(558\) 5.99063 16.5602i 0.253604 0.701051i
\(559\) 8.10695i 0.342888i
\(560\) 0.335662 0.193795i 0.0141843 0.00818932i
\(561\) 54.7232 19.9785i 2.31042 0.843492i
\(562\) 16.7912 0.708292
\(563\) −6.21069 −0.261749 −0.130875 0.991399i \(-0.541779\pi\)
−0.130875 + 0.991399i \(0.541779\pi\)
\(564\) 4.62517 + 12.6688i 0.194755 + 0.533454i
\(565\) 0.126958 + 0.0732990i 0.00534114 + 0.00308371i
\(566\) −3.98624 6.90437i −0.167554 0.290213i
\(567\) 3.27322 1.20593i 0.137462 0.0506444i
\(568\) −4.17799 + 7.23648i −0.175304 + 0.303636i
\(569\) −24.7474 −1.03747 −0.518733 0.854936i \(-0.673596\pi\)
−0.518733 + 0.854936i \(0.673596\pi\)
\(570\) 0.324338 + 7.54286i 0.0135850 + 0.315936i
\(571\) −2.91055 −0.121803 −0.0609014 0.998144i \(-0.519398\pi\)
−0.0609014 + 0.998144i \(0.519398\pi\)
\(572\) 21.6425 37.4860i 0.904920 1.56737i
\(573\) 19.2096 22.9388i 0.802491 0.958280i
\(574\) 0.543377 + 0.941156i 0.0226801 + 0.0392831i
\(575\) 5.57852 + 3.22076i 0.232641 + 0.134315i
\(576\) 0.526745 + 2.95339i 0.0219477 + 0.123058i
\(577\) 11.1520 0.464264 0.232132 0.972684i \(-0.425430\pi\)
0.232132 + 0.972684i \(0.425430\pi\)
\(578\) 11.6234 0.483469
\(579\) 5.79061 + 15.8611i 0.240650 + 0.659165i
\(580\) −3.72815 + 2.15245i −0.154803 + 0.0893755i
\(581\) 1.25030i 0.0518710i
\(582\) −10.5172 1.84382i −0.435952 0.0764289i
\(583\) −21.5033 + 12.4149i −0.890577 + 0.514175i
\(584\) 0.890700 1.54274i 0.0368574 0.0638389i
\(585\) 3.62676 + 20.3348i 0.149948 + 0.840740i
\(586\) 2.26447 3.92217i 0.0935443 0.162023i
\(587\) −28.0297 16.1829i −1.15691 0.667942i −0.206348 0.978479i \(-0.566158\pi\)
−0.950561 + 0.310537i \(0.899491\pi\)
\(588\) −2.04872 + 11.6859i −0.0844877 + 0.481920i
\(589\) 24.9900 5.49711i 1.02969 0.226504i
\(590\) 1.11358i 0.0458454i
\(591\) −8.88976 + 10.6156i −0.365676 + 0.436665i
\(592\) 2.20473 + 1.27290i 0.0906138 + 0.0523159i
\(593\) −11.3927 + 6.57758i −0.467842 + 0.270109i −0.715336 0.698781i \(-0.753726\pi\)
0.247494 + 0.968889i \(0.420393\pi\)
\(594\) −28.2417 + 16.4165i −1.15877 + 0.673576i
\(595\) 1.03682 + 1.79582i 0.0425054 + 0.0736215i
\(596\) 2.73477i 0.112020i
\(597\) −1.50014 + 8.55686i −0.0613968 + 0.350209i
\(598\) −22.1757 38.4094i −0.906831 1.57068i
\(599\) 19.9168 + 34.4969i 0.813777 + 1.40950i 0.910203 + 0.414163i \(0.135926\pi\)
−0.0964255 + 0.995340i \(0.530741\pi\)
\(600\) 0.299093 1.70603i 0.0122104 0.0696484i
\(601\) 2.09040i 0.0852692i 0.999091 + 0.0426346i \(0.0135751\pi\)
−0.999091 + 0.0426346i \(0.986425\pi\)
\(602\) −0.228182 0.395223i −0.00930000 0.0161081i
\(603\) 15.5286 + 18.4326i 0.632373 + 0.750634i
\(604\) 4.36049 2.51753i 0.177426 0.102437i
\(605\) −24.7009 14.2610i −1.00423 0.579794i
\(606\) −4.66809 + 5.57432i −0.189628 + 0.226441i
\(607\) 5.53538i 0.224674i −0.993670 0.112337i \(-0.964166\pi\)
0.993670 0.112337i \(-0.0358336\pi\)
\(608\) −3.21855 + 2.93955i −0.130529 + 0.119214i
\(609\) −0.499045 + 2.84656i −0.0202223 + 0.115349i
\(610\) 2.22348 + 1.28373i 0.0900263 + 0.0519767i
\(611\) −26.8061 + 46.4296i −1.08446 + 1.87834i
\(612\) −15.8009 + 2.81813i −0.638714 + 0.113916i
\(613\) −10.6274 + 18.4073i −0.429238 + 0.743462i −0.996806 0.0798646i \(-0.974551\pi\)
0.567568 + 0.823327i \(0.307885\pi\)
\(614\) 20.5036 11.8378i 0.827459 0.477734i
\(615\) 4.78351 + 0.838620i 0.192890 + 0.0338164i
\(616\) 2.43664i 0.0981751i
\(617\) −3.00091 + 1.73258i −0.120812 + 0.0697509i −0.559188 0.829041i \(-0.688887\pi\)
0.438376 + 0.898792i \(0.355554\pi\)
\(618\) −8.59420 23.5404i −0.345709 0.946935i
\(619\) 20.0769 0.806960 0.403480 0.914989i \(-0.367801\pi\)
0.403480 + 0.914989i \(0.367801\pi\)
\(620\) −5.87016 −0.235751
\(621\) 0.0985836 + 33.4710i 0.00395602 + 1.34315i
\(622\) 18.4080 + 10.6278i 0.738092 + 0.426138i
\(623\) 2.90633 + 5.03390i 0.116440 + 0.201679i
\(624\) −7.65663 + 9.14304i −0.306511 + 0.366014i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 32.3721 1.29385
\(627\) −42.0859 21.9439i −1.68075 0.876354i
\(628\) −1.86316 −0.0743482
\(629\) −6.81012 + 11.7955i −0.271537 + 0.470317i
\(630\) −0.749160 0.889262i −0.0298473 0.0354291i
\(631\) −3.03717 5.26053i −0.120908 0.209418i 0.799218 0.601041i \(-0.205247\pi\)
−0.920126 + 0.391623i \(0.871914\pi\)
\(632\) 12.3862 + 7.15117i 0.492696 + 0.284458i
\(633\) −0.618014 1.69281i −0.0245639 0.0672831i
\(634\) −0.547035 −0.0217255
\(635\) −16.3590 −0.649189
\(636\) 6.42608 2.34605i 0.254811 0.0930269i
\(637\) −40.8437 + 23.5811i −1.61829 + 0.934319i
\(638\) 27.0634i 1.07145i
\(639\) 23.5729 + 8.52746i 0.932530 + 0.337341i
\(640\) 0.866025 0.500000i 0.0342327 0.0197642i
\(641\) 2.26142 3.91689i 0.0893206 0.154708i −0.817904 0.575355i \(-0.804864\pi\)
0.907224 + 0.420648i \(0.138197\pi\)
\(642\) 4.00880 1.46354i 0.158215 0.0577614i
\(643\) 5.12601 8.87852i 0.202150 0.350135i −0.747071 0.664745i \(-0.768540\pi\)
0.949221 + 0.314610i \(0.101874\pi\)
\(644\) 2.16218 + 1.24833i 0.0852017 + 0.0491912i
\(645\) −2.00875 0.352164i −0.0790945 0.0138664i
\(646\) −15.7268 17.2195i −0.618764 0.677492i
\(647\) 32.4311i 1.27500i −0.770451 0.637500i \(-0.779969\pi\)
0.770451 0.637500i \(-0.220031\pi\)
\(648\) 8.44508 3.11137i 0.331754 0.122226i
\(649\) −6.06279 3.50035i −0.237985 0.137401i
\(650\) 5.96278 3.44261i 0.233880 0.135030i
\(651\) −2.53012 + 3.02130i −0.0991632 + 0.118414i
\(652\) 7.82120 + 13.5467i 0.306302 + 0.530531i
\(653\) 34.6967i 1.35778i 0.734238 + 0.678892i \(0.237540\pi\)
−0.734238 + 0.678892i \(0.762460\pi\)
\(654\) 4.57793 + 0.802580i 0.179011 + 0.0313834i
\(655\) −1.34352 2.32705i −0.0524958 0.0909255i
\(656\) 1.40194 + 2.42823i 0.0547365 + 0.0948065i
\(657\) −5.02548 1.81796i −0.196063 0.0709253i
\(658\) 3.01799i 0.117653i
\(659\) −3.29288 5.70344i −0.128272 0.222174i 0.794735 0.606957i \(-0.207610\pi\)
−0.923007 + 0.384782i \(0.874277\pi\)
\(660\) 8.34818 + 6.99100i 0.324953 + 0.272124i
\(661\) 33.4091 19.2887i 1.29946 0.750245i 0.319152 0.947704i \(-0.396602\pi\)
0.980311 + 0.197458i \(0.0632687\pi\)
\(662\) 10.6417 + 6.14400i 0.413602 + 0.238793i
\(663\) −48.9160 40.9636i −1.89974 1.59090i
\(664\) 3.22583i 0.125186i
\(665\) 0.510676 1.61043i 0.0198032 0.0624499i
\(666\) 2.59805 7.18193i 0.100672 0.278294i
\(667\) −24.0149 13.8650i −0.929862 0.536856i
\(668\) 2.58979 4.48565i 0.100202 0.173555i
\(669\) −2.36099 6.46699i −0.0912810 0.250028i
\(670\) 4.01697 6.95760i 0.155189 0.268795i
\(671\) −13.9783 + 8.07037i −0.539626 + 0.311553i
\(672\) 0.115925 0.661239i 0.00447191 0.0255079i
\(673\) 27.8104i 1.07201i −0.844214 0.536006i \(-0.819932\pi\)
0.844214 0.536006i \(-0.180068\pi\)
\(674\) 12.8425 7.41464i 0.494676 0.285601i
\(675\) −5.19613 + 0.0153044i −0.199999 + 0.000589066i
\(676\) −34.4064 −1.32332
\(677\) 20.4612 0.786387 0.393193 0.919456i \(-0.371370\pi\)
0.393193 + 0.919456i \(0.371370\pi\)
\(678\) 0.238517 0.0870783i 0.00916018 0.00334422i
\(679\) 2.06926 + 1.19469i 0.0794110 + 0.0458480i
\(680\) 2.67504 + 4.63331i 0.102583 + 0.177679i
\(681\) 27.8350 + 23.3098i 1.06664 + 0.893233i
\(682\) 18.4518 31.9595i 0.706558 1.22379i
\(683\) −6.27342 −0.240046 −0.120023 0.992771i \(-0.538297\pi\)
−0.120023 + 0.992771i \(0.538297\pi\)
\(684\) 10.3770 + 7.95725i 0.396774 + 0.304253i
\(685\) 13.6298 0.520766
\(686\) 2.68401 4.64884i 0.102476 0.177494i
\(687\) −10.8568 9.09177i −0.414212 0.346873i
\(688\) −0.588721 1.01969i −0.0224448 0.0388755i
\(689\) 23.5507 + 13.5970i 0.897211 + 0.518005i
\(690\) 10.4804 3.82623i 0.398984 0.145662i
\(691\) −39.8978 −1.51778 −0.758891 0.651217i \(-0.774259\pi\)
−0.758891 + 0.651217i \(0.774259\pi\)
\(692\) 9.82817 0.373611
\(693\) 7.19636 1.28349i 0.273367 0.0487557i
\(694\) −8.34699 + 4.81914i −0.316847 + 0.182932i
\(695\) 22.6639i 0.859690i
\(696\) −1.28756 + 7.34428i −0.0488049 + 0.278384i
\(697\) −12.9912 + 7.50049i −0.492078 + 0.284101i
\(698\) −12.6150 + 21.8497i −0.477483 + 0.827025i
\(699\) −2.09625 5.74185i −0.0792875 0.217177i
\(700\) −0.193795 + 0.335662i −0.00732475 + 0.0126868i
\(701\) 8.46297 + 4.88610i 0.319642 + 0.184545i 0.651233 0.758878i \(-0.274252\pi\)
−0.331591 + 0.943423i \(0.607585\pi\)
\(702\) 31.0361 + 17.7970i 1.17138 + 0.671705i
\(703\) 10.8378 2.38401i 0.408755 0.0899147i
\(704\) 6.28666i 0.236937i
\(705\) −10.3399 8.65895i −0.389424 0.326115i
\(706\) −8.70898 5.02813i −0.327767 0.189236i
\(707\) 1.40904 0.813507i 0.0529923 0.0305951i
\(708\) 1.47875 + 1.23834i 0.0555747 + 0.0465398i
\(709\) −9.26925 16.0548i −0.348114 0.602951i 0.637800 0.770202i \(-0.279844\pi\)
−0.985914 + 0.167251i \(0.946511\pi\)
\(710\) 8.35597i 0.313594i
\(711\) 14.5959 40.3481i 0.547388 1.51317i
\(712\) 7.49847 + 12.9877i 0.281017 + 0.486736i
\(713\) −18.9064 32.7468i −0.708050 1.22638i
\(714\) 3.53769 + 0.620209i 0.132395 + 0.0232107i
\(715\) 43.2851i 1.61877i
\(716\) −9.81870 17.0065i −0.366942 0.635562i
\(717\) 17.6301 21.0527i 0.658408 0.786227i
\(718\) 9.76791 5.63951i 0.364535 0.210465i
\(719\) −29.2721 16.9002i −1.09166 0.630273i −0.157645 0.987496i \(-0.550390\pi\)
−0.934019 + 0.357223i \(0.883724\pi\)
\(720\) −1.93287 2.29434i −0.0720339 0.0855051i
\(721\) 5.60783i 0.208847i
\(722\) −1.71811 + 18.9222i −0.0639416 + 0.704210i
\(723\) 6.24403 + 1.09467i 0.232218 + 0.0407113i
\(724\) 19.3105 + 11.1489i 0.717668 + 0.414346i
\(725\) 2.15245 3.72815i 0.0799398 0.138460i
\(726\) −46.4058 + 16.9419i −1.72228 + 0.628775i
\(727\) −15.8883 + 27.5193i −0.589264 + 1.02064i 0.405065 + 0.914288i \(0.367249\pi\)
−0.994329 + 0.106347i \(0.966084\pi\)
\(728\) 2.31111 1.33432i 0.0856555 0.0494532i
\(729\) −13.6375 23.3028i −0.505093 0.863065i
\(730\) 1.78140i 0.0659325i
\(731\) 5.45545 3.14971i 0.201777 0.116496i
\(732\) 4.17729 1.52505i 0.154397 0.0563676i
\(733\) 24.0223 0.887283 0.443642 0.896204i \(-0.353686\pi\)
0.443642 + 0.896204i \(0.353686\pi\)
\(734\) −26.4194 −0.975157
\(735\) −4.06872 11.1447i −0.150077 0.411077i
\(736\) 5.57852 + 3.22076i 0.205627 + 0.118719i
\(737\) 25.2533 + 43.7400i 0.930218 + 1.61119i
\(738\) 6.43306 5.41954i 0.236804 0.199496i
\(739\) −12.2978 + 21.3005i −0.452384 + 0.783551i −0.998534 0.0541361i \(-0.982760\pi\)
0.546150 + 0.837687i \(0.316093\pi\)
\(740\) −2.54580 −0.0935855
\(741\) 2.23314 + 51.9343i 0.0820365 + 1.90786i
\(742\) −1.53083 −0.0561985
\(743\) 1.48071 2.56467i 0.0543220 0.0940885i −0.837586 0.546306i \(-0.816034\pi\)
0.891908 + 0.452217i \(0.149367\pi\)
\(744\) −6.52784 + 7.79511i −0.239322 + 0.285782i
\(745\) 1.36738 + 2.36838i 0.0500971 + 0.0867707i
\(746\) 8.15874 + 4.71045i 0.298713 + 0.172462i
\(747\) −9.52714 + 1.69919i −0.348580 + 0.0621700i
\(748\) −33.6342 −1.22979
\(749\) −0.954981 −0.0348942
\(750\) 0.593994 + 1.62701i 0.0216896 + 0.0594101i
\(751\) 8.92680 5.15389i 0.325744 0.188068i −0.328206 0.944606i \(-0.606444\pi\)
0.653950 + 0.756538i \(0.273111\pi\)
\(752\) 7.78656i 0.283947i
\(753\) 19.2102 + 3.36784i 0.700060 + 0.122731i
\(754\) −25.6691 + 14.8201i −0.934815 + 0.539716i
\(755\) −2.51753 + 4.36049i −0.0916223 + 0.158695i
\(756\) −2.01396 + 0.00593182i −0.0732472 + 0.000215738i
\(757\) 9.26031 16.0393i 0.336572 0.582959i −0.647214 0.762308i \(-0.724066\pi\)
0.983785 + 0.179349i \(0.0573993\pi\)
\(758\) 16.0100 + 9.24338i 0.581510 + 0.335735i
\(759\) −12.1120 + 69.0869i −0.439636 + 2.50770i
\(760\) 1.31757 4.15500i 0.0477933 0.150718i
\(761\) 50.2106i 1.82013i 0.414462 + 0.910067i \(0.363970\pi\)
−0.414462 + 0.910067i \(0.636030\pi\)
\(762\) −18.1919 + 21.7235i −0.659022 + 0.786960i
\(763\) −0.900710 0.520025i −0.0326079 0.0188262i
\(764\) −14.9599 + 8.63710i −0.541230 + 0.312479i
\(765\) 12.2749 10.3410i 0.443801 0.373881i
\(766\) 8.39580 + 14.5419i 0.303352 + 0.525422i
\(767\) 7.66726i 0.276849i
\(768\) 0.299093 1.70603i 0.0107926 0.0615611i
\(769\) −17.5253 30.3547i −0.631979 1.09462i −0.987147 0.159817i \(-0.948910\pi\)
0.355168 0.934802i \(-0.384424\pi\)
\(770\) −1.21832 2.11019i −0.0439052 0.0760461i
\(771\) 8.16516 46.5743i 0.294061 1.67733i
\(772\) 9.74861i 0.350860i
\(773\) −20.0359 34.7031i −0.720640 1.24818i −0.960744 0.277438i \(-0.910515\pi\)
0.240104 0.970747i \(-0.422819\pi\)
\(774\) −2.70145 + 2.27584i −0.0971018 + 0.0818035i
\(775\) 5.08371 2.93508i 0.182612 0.105431i
\(776\) 5.33880 + 3.08236i 0.191652 + 0.110650i
\(777\) −1.09728 + 1.31029i −0.0393645 + 0.0470065i
\(778\) 3.83317i 0.137426i
\(779\) 11.6501 + 3.69431i 0.417408 + 0.132362i
\(780\) 2.05932 11.7464i 0.0737355 0.420589i
\(781\) 45.4933 + 26.2656i 1.62788 + 0.939856i
\(782\) −17.2313 + 29.8456i −0.616192 + 1.06728i
\(783\) 22.3688 0.0658837i 0.799395 0.00235449i
\(784\) 3.42489 5.93208i 0.122317 0.211860i
\(785\) 1.61354 0.931580i 0.0575898 0.0332495i
\(786\) −4.58419 0.803677i −0.163513 0.0286662i
\(787\) 1.76390i 0.0628763i 0.999506 + 0.0314382i \(0.0100087\pi\)
−0.999506 + 0.0314382i \(0.989991\pi\)
\(788\) 6.92311 3.99706i 0.246626 0.142389i
\(789\) 11.2937 + 30.9347i 0.402067 + 1.10130i
\(790\) −14.3023 −0.508854
\(791\) −0.0568198 −0.00202028
\(792\) 18.5670 3.31146i 0.659749 0.117668i
\(793\) 15.3092 + 8.83877i 0.543646 + 0.313874i
\(794\) −6.16028 10.6699i −0.218620 0.378661i
\(795\) −4.39212 + 5.24478i −0.155773 + 0.186013i
\(796\) 2.50783 4.34368i 0.0888875 0.153958i
\(797\) 24.2694 0.859666 0.429833 0.902908i \(-0.358572\pi\)
0.429833 + 0.902908i \(0.358572\pi\)
\(798\) −1.57063 2.46900i −0.0555999 0.0874016i
\(799\) 41.6587 1.47378
\(800\) −0.500000 + 0.866025i −0.0176777 + 0.0306186i
\(801\) 34.4081 28.9872i 1.21575 1.02421i
\(802\) −3.20325 5.54818i −0.113111 0.195913i
\(803\) −9.69866 5.59953i −0.342258 0.197603i
\(804\) −4.77211 13.0713i −0.168299 0.460990i
\(805\) −2.49667 −0.0879959
\(806\) −40.4174 −1.42364
\(807\) 30.7009 11.2083i 1.08072 0.394552i
\(808\) 3.63539 2.09889i 0.127892 0.0738387i
\(809\) 32.5685i 1.14505i 0.819888 + 0.572525i \(0.194036\pi\)
−0.819888 + 0.572525i \(0.805964\pi\)
\(810\) −5.75797 + 6.91707i −0.202314 + 0.243041i
\(811\) −40.2466 + 23.2364i −1.41325 + 0.815940i −0.995693 0.0927115i \(-0.970447\pi\)
−0.417556 + 0.908651i \(0.637113\pi\)
\(812\) 0.834265 1.44499i 0.0292770 0.0507092i
\(813\) 32.2325 11.7675i 1.13044 0.412705i
\(814\) 8.00229 13.8604i 0.280480 0.485806i
\(815\) −13.5467 7.82120i −0.474521 0.273965i
\(816\) 9.12741 + 1.60017i 0.319523 + 0.0560172i
\(817\) −4.89227 1.55136i −0.171159 0.0542753i
\(818\) 33.2538i 1.16269i
\(819\) −5.15814 6.12278i −0.180240 0.213947i
\(820\) −2.42823 1.40194i −0.0847975 0.0489578i
\(821\) −15.0238 + 8.67398i −0.524333 + 0.302724i −0.738706 0.674028i \(-0.764563\pi\)
0.214373 + 0.976752i \(0.431229\pi\)
\(822\) 15.1568 18.0992i 0.528654 0.631283i
\(823\) −1.52793 2.64645i −0.0532603 0.0922496i 0.838166 0.545415i \(-0.183628\pi\)
−0.891426 + 0.453166i \(0.850295\pi\)
\(824\) 14.4685i 0.504034i
\(825\) −10.7252 1.88029i −0.373405 0.0654634i
\(826\) −0.215806 0.373787i −0.00750885 0.0130057i
\(827\) 1.06321 + 1.84154i 0.0369715 + 0.0640366i 0.883919 0.467640i \(-0.154896\pi\)
−0.846948 + 0.531676i \(0.821562\pi\)
\(828\) 6.57372 18.1721i 0.228453 0.631524i
\(829\) 26.9654i 0.936546i 0.883584 + 0.468273i \(0.155124\pi\)
−0.883584 + 0.468273i \(0.844876\pi\)
\(830\) 1.61291 + 2.79365i 0.0559851 + 0.0969690i
\(831\) 17.5172 + 14.6694i 0.607665 + 0.508876i
\(832\) 5.96278 3.44261i 0.206722 0.119351i
\(833\) 31.7371 + 18.3234i 1.09963 + 0.634869i
\(834\) 30.0958 + 25.2031i 1.04213 + 0.872711i
\(835\) 5.17958i 0.179247i
\(836\) 18.4799 + 20.2339i 0.639142 + 0.699805i
\(837\) 26.4605 + 15.1733i 0.914610 + 0.524464i
\(838\) 22.7052 + 13.1089i 0.784338 + 0.452838i
\(839\) −6.48396 + 11.2305i −0.223851 + 0.387722i −0.955974 0.293451i \(-0.905196\pi\)
0.732123 + 0.681172i \(0.238530\pi\)
\(840\) 0.230226 + 0.630613i 0.00794354 + 0.0217582i
\(841\) 5.23395 9.06547i 0.180481 0.312602i
\(842\) 16.2792 9.39883i 0.561020 0.323905i
\(843\) −5.02211 + 28.6462i −0.172971 + 0.986629i
\(844\) 1.04044i 0.0358134i
\(845\) 29.7968 17.2032i 1.02504 0.591808i
\(846\) −22.9968 + 4.10153i −0.790646 + 0.141013i
\(847\) 11.0549 0.379849
\(848\) −3.94962 −0.135630
\(849\) 12.9713 4.73561i 0.445175 0.162526i
\(850\) −4.63331 2.67504i −0.158921 0.0917532i
\(851\) −8.19942 14.2018i −0.281073 0.486832i
\(852\) −11.0961 9.29215i −0.380145 0.318344i
\(853\) 19.8140 34.3188i 0.678418 1.17505i −0.297040 0.954865i \(-0.595999\pi\)
0.975457 0.220189i \(-0.0706673\pi\)
\(854\) −0.995119 −0.0340523
\(855\) −12.9654 1.70268i −0.443406 0.0582306i
\(856\) −2.46390 −0.0842144
\(857\) −18.7067 + 32.4009i −0.639008 + 1.10679i 0.346642 + 0.937997i \(0.387322\pi\)
−0.985651 + 0.168798i \(0.946012\pi\)
\(858\) 57.4791 + 48.1346i 1.96231 + 1.64329i
\(859\) −22.3252 38.6684i −0.761726 1.31935i −0.941960 0.335724i \(-0.891019\pi\)
0.180234 0.983624i \(-0.442314\pi\)
\(860\) 1.01969 + 0.588721i 0.0347713 + 0.0200752i
\(861\) −1.76816 + 0.645525i −0.0602588 + 0.0219994i
\(862\) 33.7813 1.15060
\(863\) −20.1867 −0.687163 −0.343581 0.939123i \(-0.611640\pi\)
−0.343581 + 0.939123i \(0.611640\pi\)
\(864\) −5.19613 + 0.0153044i −0.176776 + 0.000520666i
\(865\) −8.51144 + 4.91408i −0.289398 + 0.167084i
\(866\) 21.7192i 0.738048i
\(867\) −3.47647 + 19.8299i −0.118067 + 0.673458i
\(868\) 1.97039 1.13761i 0.0668794 0.0386128i
\(869\) 44.9570 77.8677i 1.52506 2.64148i
\(870\) −2.55708 7.00412i −0.0866931 0.237462i
\(871\) 27.6578 47.9047i 0.937148 1.62319i
\(872\) −2.32388 1.34169i −0.0786964 0.0454354i
\(873\) 6.29124 17.3912i 0.212926 0.588603i
\(874\) 27.4223 6.03216i 0.927574 0.204041i
\(875\) 0.387589i 0.0131029i
\(876\) 2.36556 + 1.98098i 0.0799247 + 0.0669312i
\(877\) −46.0744 26.6011i −1.55582 0.898254i −0.997649 0.0685295i \(-0.978169\pi\)
−0.558173 0.829725i \(-0.688497\pi\)
\(878\) −4.46634 + 2.57864i −0.150732 + 0.0870249i
\(879\) 6.01406 + 5.03634i 0.202849 + 0.169872i
\(880\) −3.14333 5.44441i −0.105962 0.183531i
\(881\) 29.5768i 0.996466i −0.867043 0.498233i \(-0.833982\pi\)
0.867043 0.498233i \(-0.166018\pi\)
\(882\) −19.3238 6.99035i −0.650667 0.235377i
\(883\) −8.68185 15.0374i −0.292168 0.506049i 0.682154 0.731208i \(-0.261043\pi\)
−0.974322 + 0.225159i \(0.927710\pi\)
\(884\) 18.4183 + 31.9014i 0.619474 + 1.07296i
\(885\) −1.89980 0.333064i −0.0638612 0.0111958i
\(886\) 33.1611i 1.11407i
\(887\) 19.2230 + 33.2953i 0.645446 + 1.11795i 0.984198 + 0.177070i \(0.0566620\pi\)
−0.338752 + 0.940876i \(0.610005\pi\)
\(888\) −2.83103 + 3.38062i −0.0950030 + 0.113446i
\(889\) 5.49111 3.17030i 0.184166 0.106328i
\(890\) −12.9877 7.49847i −0.435350 0.251349i
\(891\) −19.5601 53.0913i −0.655289 1.77863i
\(892\) 3.97476i 0.133085i
\(893\) −22.8890 25.0614i −0.765950 0.838649i
\(894\) 4.66560 + 0.817949i 0.156041 + 0.0273563i
\(895\) 17.0065 + 9.81870i 0.568464 + 0.328203i
\(896\) −0.193795 + 0.335662i −0.00647422 + 0.0112137i
\(897\) 72.1603 26.3444i 2.40936 0.879615i
\(898\) −14.3031 + 24.7736i −0.477300 + 0.826707i
\(899\) −21.8848 + 12.6352i −0.729899 + 0.421408i
\(900\) 2.82109 + 1.02052i 0.0940362 + 0.0340174i
\(901\) 21.1308i 0.703968i
\(902\) 15.2655 8.81352i 0.508284 0.293458i
\(903\) 0.742510 0.271077i 0.0247092 0.00902089i
\(904\) −0.146598 −0.00487578
\(905\) −22.2978 −0.741204
\(906\) 2.99080 + 8.19211i 0.0993625 + 0.272165i
\(907\) −5.28915 3.05369i −0.175623 0.101396i 0.409611 0.912260i \(-0.365664\pi\)
−0.585235 + 0.810864i \(0.698998\pi\)
\(908\) −10.4807 18.1530i −0.347813 0.602430i
\(909\) −8.11377 9.63115i −0.269117 0.319445i
\(910\) −1.33432 + 2.31111i −0.0442323 + 0.0766126i
\(911\) −30.0434 −0.995381 −0.497690 0.867355i \(-0.665818\pi\)
−0.497690 + 0.867355i \(0.665818\pi\)
\(912\) −4.05232 6.37014i −0.134186 0.210937i
\(913\) −20.2797 −0.671160
\(914\) 6.04720 10.4741i 0.200024 0.346451i
\(915\) −2.85511 + 3.40938i −0.0943870 + 0.112711i
\(916\) 4.08789 + 7.08043i 0.135068 + 0.233944i
\(917\) 0.901941 + 0.520736i 0.0297847 + 0.0171962i
\(918\) −0.0818798 27.7997i −0.00270243 0.917528i
\(919\) −5.87159 −0.193686 −0.0968429 0.995300i \(-0.530874\pi\)
−0.0968429 + 0.995300i \(0.530874\pi\)
\(920\) −6.44153 −0.212371
\(921\) 14.0631 + 38.5204i 0.463396 + 1.26929i
\(922\) −23.9736 + 13.8412i −0.789528 + 0.455834i
\(923\) 57.5328i 1.89371i
\(924\) −4.15699 0.728782i −0.136755 0.0239752i
\(925\) 2.20473 1.27290i 0.0724910 0.0418527i
\(926\) 11.2620 19.5063i 0.370091 0.641017i
\(927\) 42.7312 7.62120i 1.40348 0.250313i
\(928\) 2.15245 3.72815i 0.0706575 0.122382i
\(929\) 32.7353 + 18.8998i 1.07401 + 0.620081i 0.929275 0.369390i \(-0.120433\pi\)
0.144737 + 0.989470i \(0.453767\pi\)
\(930\) 1.75572 10.0147i 0.0575724 0.328394i
\(931\) −6.41446 29.1603i −0.210226 0.955690i
\(932\) 3.52908i 0.115599i
\(933\) −23.6371 + 28.2259i −0.773845 + 0.924073i
\(934\) 19.4524 + 11.2308i 0.636501 + 0.367484i
\(935\) 29.1280 16.8171i 0.952588 0.549977i
\(936\) −13.3083 15.7971i −0.434994 0.516343i
\(937\) 22.4831 + 38.9419i 0.734491 + 1.27218i 0.954946 + 0.296779i \(0.0959125\pi\)
−0.220455 + 0.975397i \(0.570754\pi\)
\(938\) 3.11387i 0.101671i
\(939\) −9.68226 + 55.2278i −0.315968 + 1.80229i
\(940\) 3.89328 + 6.74336i 0.126985 + 0.219944i
\(941\) 5.62832 + 9.74854i 0.183478 + 0.317793i 0.943063 0.332615i \(-0.107931\pi\)
−0.759585 + 0.650409i \(0.774598\pi\)
\(942\) 0.557257 3.17861i 0.0181564 0.103565i
\(943\) 18.0613i 0.588155i
\(944\) −0.556791 0.964390i −0.0181220 0.0313882i
\(945\) 1.74118 1.01212i 0.0566405 0.0329242i
\(946\) −6.41047 + 3.70109i −0.208422 + 0.120333i
\(947\) −35.4047 20.4409i −1.15050 0.664240i −0.201490 0.979491i \(-0.564578\pi\)
−0.949009 + 0.315250i \(0.897912\pi\)
\(948\) −15.9047 + 18.9924i −0.516562 + 0.616843i
\(949\) 12.2653i 0.398150i
\(950\) 0.936449 + 4.25712i 0.0303824 + 0.138119i
\(951\) 0.163614 0.933259i 0.00530555 0.0302630i
\(952\) −1.79582 1.03682i −0.0582029 0.0336034i
\(953\) −17.8170 + 30.8599i −0.577148 + 0.999651i 0.418656 + 0.908145i \(0.362501\pi\)
−0.995805 + 0.0915056i \(0.970832\pi\)
\(954\) 2.08044 + 11.6648i 0.0673567 + 0.377661i
\(955\) 8.63710 14.9599i 0.279490 0.484091i
\(956\) −13.7299 + 7.92694i −0.444055 + 0.256375i
\(957\) 46.1710 + 8.09446i 1.49250 + 0.261657i
\(958\) 16.2192i 0.524018i
\(959\) −4.57499 + 2.64137i −0.147734 + 0.0852944i
\(960\) 0.593994 + 1.62701i 0.0191711 + 0.0525116i
\(961\) −3.45878 −0.111574
\(962\) −17.5284 −0.565139
\(963\) 1.29785 + 7.27687i 0.0418225 + 0.234494i
\(964\) −3.16963 1.82999i −0.102087 0.0589399i
\(965\) 4.87430 + 8.44254i 0.156909 + 0.271775i
\(966\) −2.77639 + 3.31537i −0.0893288 + 0.106670i
\(967\) 9.57867 16.5907i 0.308029 0.533522i −0.669902 0.742450i \(-0.733664\pi\)
0.977931 + 0.208927i \(0.0669972\pi\)
\(968\) 28.5221 0.916735
\(969\) 34.0808 21.6802i 1.09483 0.696469i
\(970\) −6.16472 −0.197937
\(971\) −8.76880 + 15.1880i −0.281404 + 0.487406i −0.971731 0.236091i \(-0.924133\pi\)
0.690327 + 0.723498i \(0.257467\pi\)
\(972\) 2.78223 + 15.3382i 0.0892402 + 0.491972i
\(973\) −4.39214 7.60740i −0.140805 0.243882i
\(974\) 22.7384 + 13.1280i 0.728585 + 0.420649i
\(975\) 4.08978 + 11.2024i 0.130978 + 0.358763i
\(976\) −2.56746 −0.0821823
\(977\) 21.3473 0.682960 0.341480 0.939889i \(-0.389072\pi\)
0.341480 + 0.939889i \(0.389072\pi\)
\(978\) −25.4504 + 9.29150i −0.813814 + 0.297109i
\(979\) 81.6494 47.1403i 2.60953 1.50661i
\(980\) 6.84977i 0.218808i
\(981\) −2.73845 + 7.57005i −0.0874321 + 0.241693i
\(982\) 20.1138 11.6127i 0.641857 0.370576i
\(983\) 21.8784 37.8944i 0.697811 1.20864i −0.271413 0.962463i \(-0.587491\pi\)
0.969224 0.246181i \(-0.0791758\pi\)
\(984\) −4.56195 + 1.66549i −0.145430 + 0.0530938i
\(985\) −3.99706 + 6.92311i −0.127357 + 0.220589i
\(986\) 19.9459 + 11.5158i 0.635207 + 0.366737i
\(987\) 5.14878 + 0.902658i 0.163888 + 0.0287319i
\(988\) 9.07178 28.6081i 0.288612 0.910145i
\(989\) 7.58452i 0.241174i
\(990\) −14.4237 + 12.1513i −0.458417 + 0.386194i
\(991\) 25.4172 + 14.6746i 0.807405 + 0.466155i 0.846054 0.533097i \(-0.178972\pi\)
−0.0386489 + 0.999253i \(0.512305\pi\)
\(992\) 5.08371 2.93508i 0.161408 0.0931889i
\(993\) −13.6647 + 16.3175i −0.433637 + 0.517820i
\(994\) 1.61934 + 2.80478i 0.0513624 + 0.0889623i
\(995\) 5.01565i 0.159007i
\(996\) 5.50336 + 0.964822i 0.174381 + 0.0305715i
\(997\) 3.34562 + 5.79479i 0.105957 + 0.183523i 0.914129 0.405424i \(-0.132876\pi\)
−0.808172 + 0.588947i \(0.799543\pi\)
\(998\) 5.68385 + 9.84472i 0.179919 + 0.311629i
\(999\) 11.4755 + 6.58042i 0.363070 + 0.208195i
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 570.2.s.b.521.10 yes 24
3.2 odd 2 570.2.s.a.521.11 yes 24
19.12 odd 6 570.2.s.a.221.11 24
57.50 even 6 inner 570.2.s.b.221.10 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.s.a.221.11 24 19.12 odd 6
570.2.s.a.521.11 yes 24 3.2 odd 2
570.2.s.b.221.10 yes 24 57.50 even 6 inner
570.2.s.b.521.10 yes 24 1.1 even 1 trivial