Properties

Label 630.2.bk.b.131.2
Level $630$
Weight $2$
Character 630.131
Analytic conductor $5.031$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [630,2,Mod(101,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.bk (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 131.2
Character \(\chi\) \(=\) 630.131
Dual form 630.2.bk.b.101.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-1.67419 + 0.443962i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.443962 + 1.67419i) q^{6} +(-1.17317 + 2.37143i) q^{7} +1.00000i q^{8} +(2.60580 - 1.48655i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-1.67419 + 0.443962i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.443962 + 1.67419i) q^{6} +(-1.17317 + 2.37143i) q^{7} +1.00000i q^{8} +(2.60580 - 1.48655i) q^{9} +(-0.866025 + 0.500000i) q^{10} +(-0.179928 - 0.103881i) q^{11} +(1.67419 - 0.443962i) q^{12} +(-1.22567 - 0.707642i) q^{13} +(2.37143 + 1.17317i) q^{14} +(1.22158 + 1.22791i) q^{15} +1.00000 q^{16} +(-0.680447 - 1.17857i) q^{17} +(-1.48655 - 2.60580i) q^{18} +(5.73160 + 3.30914i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.911277 - 4.49105i) q^{21} +(-0.103881 + 0.179928i) q^{22} +(5.53808 - 3.19741i) q^{23} +(-0.443962 - 1.67419i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.707642 + 1.22567i) q^{26} +(-3.70262 + 3.64563i) q^{27} +(1.17317 - 2.37143i) q^{28} +(6.11758 - 3.53199i) q^{29} +(1.22791 - 1.22158i) q^{30} -4.74509i q^{31} -1.00000i q^{32} +(0.347352 + 0.0940356i) q^{33} +(-1.17857 + 0.680447i) q^{34} +(2.64030 - 0.169721i) q^{35} +(-2.60580 + 1.48655i) q^{36} +(1.32889 - 2.30171i) q^{37} +(3.30914 - 5.73160i) q^{38} +(2.36617 + 0.640573i) q^{39} +(0.866025 - 0.500000i) q^{40} +(1.41245 - 2.44643i) q^{41} +(-4.49105 - 0.911277i) q^{42} +(1.06723 + 1.84849i) q^{43} +(0.179928 + 0.103881i) q^{44} +(-2.59029 - 1.51341i) q^{45} +(-3.19741 - 5.53808i) q^{46} -0.114683 q^{47} +(-1.67419 + 0.443962i) q^{48} +(-4.24735 - 5.56417i) q^{49} +(0.866025 + 0.500000i) q^{50} +(1.66243 + 1.67105i) q^{51} +(1.22567 + 0.707642i) q^{52} +(8.40507 - 4.85267i) q^{53} +(3.64563 + 3.70262i) q^{54} +0.207763i q^{55} +(-2.37143 - 1.17317i) q^{56} +(-11.0649 - 2.99551i) q^{57} +(-3.53199 - 6.11758i) q^{58} +8.68947 q^{59} +(-1.22158 - 1.22791i) q^{60} -2.13738i q^{61} -4.74509 q^{62} +(0.468209 + 7.92343i) q^{63} -1.00000 q^{64} +1.41528i q^{65} +(0.0940356 - 0.347352i) q^{66} +0.0470446 q^{67} +(0.680447 + 1.17857i) q^{68} +(-7.85224 + 7.81175i) q^{69} +(-0.169721 - 2.64030i) q^{70} +3.45539i q^{71} +(1.48655 + 2.60580i) q^{72} +(-11.5793 + 6.68529i) q^{73} +(-2.30171 - 1.32889i) q^{74} +(0.452611 - 1.67187i) q^{75} +(-5.73160 - 3.30914i) q^{76} +(0.457433 - 0.304816i) q^{77} +(0.640573 - 2.36617i) q^{78} +15.9531 q^{79} +(-0.500000 - 0.866025i) q^{80} +(4.58034 - 7.74729i) q^{81} +(-2.44643 - 1.41245i) q^{82} +(8.06016 + 13.9606i) q^{83} +(-0.911277 + 4.49105i) q^{84} +(-0.680447 + 1.17857i) q^{85} +(1.84849 - 1.06723i) q^{86} +(-8.67390 + 8.62918i) q^{87} +(0.103881 - 0.179928i) q^{88} +(1.40976 - 2.44178i) q^{89} +(-1.51341 + 2.59029i) q^{90} +(3.11604 - 2.07641i) q^{91} +(-5.53808 + 3.19741i) q^{92} +(2.10664 + 7.94416i) q^{93} +0.114683i q^{94} -6.61828i q^{95} +(0.443962 + 1.67419i) q^{96} +(-1.39248 + 0.803947i) q^{97} +(-5.56417 + 4.24735i) q^{98} +(-0.623280 - 0.00322214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9} - 2 q^{12} + 2 q^{15} + 28 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} + 14 q^{20} + 16 q^{21} - 6 q^{22} + 30 q^{23} - 8 q^{24} - 14 q^{25} - 12 q^{26} - 28 q^{27} - 8 q^{28} - 4 q^{30} - 20 q^{33} - 4 q^{35} - 6 q^{36} + 4 q^{37} - 6 q^{38} - 42 q^{39} - 18 q^{41} + 28 q^{43} - 12 q^{45} - 18 q^{46} + 60 q^{47} + 2 q^{48} - 20 q^{49} - 74 q^{51} + 42 q^{53} + 10 q^{54} - 30 q^{57} + 6 q^{58} - 48 q^{59} - 2 q^{60} + 12 q^{62} - 28 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{67} - 6 q^{68} - 8 q^{69} + 6 q^{70} - 8 q^{72} + 6 q^{73} - 4 q^{75} + 6 q^{76} - 18 q^{77} + 14 q^{78} - 4 q^{79} - 14 q^{80} + 38 q^{81} + 24 q^{82} + 18 q^{83} - 16 q^{84} + 6 q^{85} - 96 q^{86} + 52 q^{87} + 6 q^{88} - 6 q^{89} - 4 q^{90} + 66 q^{91} - 30 q^{92} + 22 q^{93} + 8 q^{96} + 72 q^{97} + 24 q^{98} - 42 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.67419 + 0.443962i −0.966592 + 0.256321i
\(4\) −1.00000 −0.500000
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0.443962 + 1.67419i 0.181247 + 0.683483i
\(7\) −1.17317 + 2.37143i −0.443416 + 0.896316i
\(8\) 1.00000i 0.353553i
\(9\) 2.60580 1.48655i 0.868599 0.495516i
\(10\) −0.866025 + 0.500000i −0.273861 + 0.158114i
\(11\) −0.179928 0.103881i −0.0542502 0.0313214i 0.472630 0.881261i \(-0.343305\pi\)
−0.526880 + 0.849940i \(0.676638\pi\)
\(12\) 1.67419 0.443962i 0.483296 0.128161i
\(13\) −1.22567 0.707642i −0.339940 0.196265i 0.320305 0.947314i \(-0.396214\pi\)
−0.660246 + 0.751050i \(0.729548\pi\)
\(14\) 2.37143 + 1.17317i 0.633791 + 0.313542i
\(15\) 1.22158 + 1.22791i 0.315409 + 0.317044i
\(16\) 1.00000 0.250000
\(17\) −0.680447 1.17857i −0.165033 0.285845i 0.771634 0.636067i \(-0.219440\pi\)
−0.936667 + 0.350222i \(0.886106\pi\)
\(18\) −1.48655 2.60580i −0.350383 0.614192i
\(19\) 5.73160 + 3.30914i 1.31492 + 0.759169i 0.982906 0.184106i \(-0.0589389\pi\)
0.332013 + 0.943275i \(0.392272\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) 0.911277 4.49105i 0.198857 0.980029i
\(22\) −0.103881 + 0.179928i −0.0221476 + 0.0383607i
\(23\) 5.53808 3.19741i 1.15477 0.666706i 0.204724 0.978820i \(-0.434370\pi\)
0.950045 + 0.312114i \(0.101037\pi\)
\(24\) −0.443962 1.67419i −0.0906233 0.341742i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −0.707642 + 1.22567i −0.138780 + 0.240374i
\(27\) −3.70262 + 3.64563i −0.712569 + 0.701602i
\(28\) 1.17317 2.37143i 0.221708 0.448158i
\(29\) 6.11758 3.53199i 1.13601 0.655874i 0.190568 0.981674i \(-0.438967\pi\)
0.945439 + 0.325800i \(0.105634\pi\)
\(30\) 1.22791 1.22158i 0.224184 0.223028i
\(31\) 4.74509i 0.852244i −0.904666 0.426122i \(-0.859880\pi\)
0.904666 0.426122i \(-0.140120\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.347352 + 0.0940356i 0.0604662 + 0.0163695i
\(34\) −1.17857 + 0.680447i −0.202123 + 0.116696i
\(35\) 2.64030 0.169721i 0.446292 0.0286881i
\(36\) −2.60580 + 1.48655i −0.434299 + 0.247758i
\(37\) 1.32889 2.30171i 0.218468 0.378398i −0.735872 0.677121i \(-0.763227\pi\)
0.954340 + 0.298723i \(0.0965607\pi\)
\(38\) 3.30914 5.73160i 0.536814 0.929788i
\(39\) 2.36617 + 0.640573i 0.378890 + 0.102574i
\(40\) 0.866025 0.500000i 0.136931 0.0790569i
\(41\) 1.41245 2.44643i 0.220587 0.382068i −0.734399 0.678718i \(-0.762536\pi\)
0.954986 + 0.296650i \(0.0958693\pi\)
\(42\) −4.49105 0.911277i −0.692985 0.140613i
\(43\) 1.06723 + 1.84849i 0.162751 + 0.281893i 0.935854 0.352387i \(-0.114630\pi\)
−0.773103 + 0.634280i \(0.781297\pi\)
\(44\) 0.179928 + 0.103881i 0.0271251 + 0.0156607i
\(45\) −2.59029 1.51341i −0.386137 0.225606i
\(46\) −3.19741 5.53808i −0.471432 0.816545i
\(47\) −0.114683 −0.0167282 −0.00836410 0.999965i \(-0.502662\pi\)
−0.00836410 + 0.999965i \(0.502662\pi\)
\(48\) −1.67419 + 0.443962i −0.241648 + 0.0640804i
\(49\) −4.24735 5.56417i −0.606765 0.794881i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) 1.66243 + 1.67105i 0.232787 + 0.233994i
\(52\) 1.22567 + 0.707642i 0.169970 + 0.0981323i
\(53\) 8.40507 4.85267i 1.15452 0.666565i 0.204539 0.978858i \(-0.434430\pi\)
0.949986 + 0.312293i \(0.101097\pi\)
\(54\) 3.64563 + 3.70262i 0.496108 + 0.503862i
\(55\) 0.207763i 0.0280147i
\(56\) −2.37143 1.17317i −0.316896 0.156771i
\(57\) −11.0649 2.99551i −1.46558 0.396764i
\(58\) −3.53199 6.11758i −0.463773 0.803278i
\(59\) 8.68947 1.13127 0.565636 0.824655i \(-0.308631\pi\)
0.565636 + 0.824655i \(0.308631\pi\)
\(60\) −1.22158 1.22791i −0.157705 0.158522i
\(61\) 2.13738i 0.273663i −0.990594 0.136832i \(-0.956308\pi\)
0.990594 0.136832i \(-0.0436919\pi\)
\(62\) −4.74509 −0.602627
\(63\) 0.468209 + 7.92343i 0.0589888 + 0.998259i
\(64\) −1.00000 −0.125000
\(65\) 1.41528i 0.175544i
\(66\) 0.0940356 0.347352i 0.0115750 0.0427560i
\(67\) 0.0470446 0.00574741 0.00287371 0.999996i \(-0.499085\pi\)
0.00287371 + 0.999996i \(0.499085\pi\)
\(68\) 0.680447 + 1.17857i 0.0825163 + 0.142922i
\(69\) −7.85224 + 7.81175i −0.945299 + 0.940424i
\(70\) −0.169721 2.64030i −0.0202856 0.315576i
\(71\) 3.45539i 0.410079i 0.978754 + 0.205040i \(0.0657323\pi\)
−0.978754 + 0.205040i \(0.934268\pi\)
\(72\) 1.48655 + 2.60580i 0.175191 + 0.307096i
\(73\) −11.5793 + 6.68529i −1.35525 + 0.782454i −0.988979 0.148054i \(-0.952699\pi\)
−0.366271 + 0.930508i \(0.619366\pi\)
\(74\) −2.30171 1.32889i −0.267568 0.154480i
\(75\) 0.452611 1.67187i 0.0522630 0.193051i
\(76\) −5.73160 3.30914i −0.657460 0.379585i
\(77\) 0.457433 0.304816i 0.0521293 0.0347370i
\(78\) 0.640573 2.36617i 0.0725306 0.267916i
\(79\) 15.9531 1.79487 0.897434 0.441148i \(-0.145429\pi\)
0.897434 + 0.441148i \(0.145429\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) 4.58034 7.74729i 0.508927 0.860810i
\(82\) −2.44643 1.41245i −0.270163 0.155979i
\(83\) 8.06016 + 13.9606i 0.884717 + 1.53237i 0.846038 + 0.533123i \(0.178982\pi\)
0.0386794 + 0.999252i \(0.487685\pi\)
\(84\) −0.911277 + 4.49105i −0.0994285 + 0.490014i
\(85\) −0.680447 + 1.17857i −0.0738048 + 0.127834i
\(86\) 1.84849 1.06723i 0.199328 0.115082i
\(87\) −8.67390 + 8.62918i −0.929940 + 0.925145i
\(88\) 0.103881 0.179928i 0.0110738 0.0191804i
\(89\) 1.40976 2.44178i 0.149435 0.258828i −0.781584 0.623800i \(-0.785588\pi\)
0.931019 + 0.364972i \(0.118921\pi\)
\(90\) −1.51341 + 2.59029i −0.159528 + 0.273040i
\(91\) 3.11604 2.07641i 0.326650 0.217667i
\(92\) −5.53808 + 3.19741i −0.577384 + 0.333353i
\(93\) 2.10664 + 7.94416i 0.218448 + 0.823771i
\(94\) 0.114683i 0.0118286i
\(95\) 6.61828i 0.679021i
\(96\) 0.443962 + 1.67419i 0.0453117 + 0.170871i
\(97\) −1.39248 + 0.803947i −0.141385 + 0.0816284i −0.569024 0.822321i \(-0.692679\pi\)
0.427639 + 0.903950i \(0.359345\pi\)
\(98\) −5.56417 + 4.24735i −0.562066 + 0.429047i
\(99\) −0.623280 0.00322214i −0.0626420 0.000323837i
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −3.05401 + 5.28971i −0.303886 + 0.526346i −0.977013 0.213181i \(-0.931617\pi\)
0.673127 + 0.739527i \(0.264951\pi\)
\(102\) 1.67105 1.66243i 0.165459 0.164606i
\(103\) −5.72998 + 3.30820i −0.564591 + 0.325967i −0.754986 0.655741i \(-0.772356\pi\)
0.190395 + 0.981708i \(0.439023\pi\)
\(104\) 0.707642 1.22567i 0.0693900 0.120187i
\(105\) −4.34501 + 1.45634i −0.424029 + 0.142124i
\(106\) −4.85267 8.40507i −0.471333 0.816372i
\(107\) 4.64917 + 2.68420i 0.449452 + 0.259491i 0.707599 0.706614i \(-0.249778\pi\)
−0.258147 + 0.966106i \(0.583112\pi\)
\(108\) 3.70262 3.64563i 0.356284 0.350801i
\(109\) 9.12274 + 15.8011i 0.873800 + 1.51347i 0.858035 + 0.513591i \(0.171685\pi\)
0.0157652 + 0.999876i \(0.494982\pi\)
\(110\) 0.207763 0.0198094
\(111\) −1.20294 + 4.44346i −0.114178 + 0.421755i
\(112\) −1.17317 + 2.37143i −0.110854 + 0.224079i
\(113\) −3.64375 2.10372i −0.342775 0.197901i 0.318723 0.947848i \(-0.396746\pi\)
−0.661498 + 0.749947i \(0.730079\pi\)
\(114\) −2.99551 + 11.0649i −0.280555 + 1.03632i
\(115\) −5.53808 3.19741i −0.516428 0.298160i
\(116\) −6.11758 + 3.53199i −0.568003 + 0.327937i
\(117\) −4.24580 0.0219493i −0.392524 0.00202921i
\(118\) 8.68947i 0.799930i
\(119\) 3.59317 0.230973i 0.329385 0.0211732i
\(120\) −1.22791 + 1.22158i −0.112092 + 0.111514i
\(121\) −5.47842 9.48890i −0.498038 0.862627i
\(122\) −2.13738 −0.193509
\(123\) −1.27858 + 4.72285i −0.115285 + 0.425845i
\(124\) 4.74509i 0.426122i
\(125\) 1.00000 0.0894427
\(126\) 7.92343 0.468209i 0.705875 0.0417114i
\(127\) −14.9591 −1.32741 −0.663704 0.747995i \(-0.731017\pi\)
−0.663704 + 0.747995i \(0.731017\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −2.60740 2.62091i −0.229569 0.230759i
\(130\) 1.41528 0.124129
\(131\) −8.39654 14.5432i −0.733609 1.27065i −0.955331 0.295538i \(-0.904501\pi\)
0.221722 0.975110i \(-0.428832\pi\)
\(132\) −0.347352 0.0940356i −0.0302331 0.00818475i
\(133\) −14.5715 + 9.70991i −1.26351 + 0.841956i
\(134\) 0.0470446i 0.00406403i
\(135\) 5.00852 + 1.38374i 0.431065 + 0.119094i
\(136\) 1.17857 0.680447i 0.101061 0.0583478i
\(137\) 2.93746 + 1.69594i 0.250964 + 0.144894i 0.620206 0.784439i \(-0.287049\pi\)
−0.369241 + 0.929334i \(0.620382\pi\)
\(138\) 7.81175 + 7.85224i 0.664981 + 0.668427i
\(139\) −5.07662 2.93099i −0.430593 0.248603i 0.269006 0.963138i \(-0.413305\pi\)
−0.699599 + 0.714535i \(0.746638\pi\)
\(140\) −2.64030 + 0.169721i −0.223146 + 0.0143441i
\(141\) 0.192000 0.0509148i 0.0161693 0.00428780i
\(142\) 3.45539 0.289970
\(143\) 0.147022 + 0.254649i 0.0122946 + 0.0212948i
\(144\) 2.60580 1.48655i 0.217150 0.123879i
\(145\) −6.11758 3.53199i −0.508038 0.293316i
\(146\) 6.68529 + 11.5793i 0.553279 + 0.958307i
\(147\) 9.58114 + 7.42979i 0.790239 + 0.612799i
\(148\) −1.32889 + 2.30171i −0.109234 + 0.189199i
\(149\) 19.3671 11.1816i 1.58661 0.916033i 0.592755 0.805382i \(-0.298040\pi\)
0.993859 0.110650i \(-0.0352933\pi\)
\(150\) −1.67187 0.452611i −0.136507 0.0369555i
\(151\) −6.31191 + 10.9325i −0.513656 + 0.889678i 0.486219 + 0.873837i \(0.338376\pi\)
−0.999875 + 0.0158405i \(0.994958\pi\)
\(152\) −3.30914 + 5.73160i −0.268407 + 0.464894i
\(153\) −3.52511 2.05959i −0.284988 0.166508i
\(154\) −0.304816 0.457433i −0.0245627 0.0368610i
\(155\) −4.10937 + 2.37255i −0.330072 + 0.190567i
\(156\) −2.36617 0.640573i −0.189445 0.0512869i
\(157\) 5.80220i 0.463066i 0.972827 + 0.231533i \(0.0743741\pi\)
−0.972827 + 0.231533i \(0.925626\pi\)
\(158\) 15.9531i 1.26916i
\(159\) −11.9172 + 11.8558i −0.945099 + 0.940226i
\(160\) −0.866025 + 0.500000i −0.0684653 + 0.0395285i
\(161\) 1.08534 + 16.8843i 0.0855365 + 1.33067i
\(162\) −7.74729 4.58034i −0.608684 0.359866i
\(163\) 8.98690 15.5658i 0.703908 1.21920i −0.263176 0.964748i \(-0.584770\pi\)
0.967084 0.254457i \(-0.0818967\pi\)
\(164\) −1.41245 + 2.44643i −0.110294 + 0.191034i
\(165\) −0.0922387 0.347833i −0.00718077 0.0270788i
\(166\) 13.9606 8.06016i 1.08355 0.625589i
\(167\) 5.00537 8.66956i 0.387327 0.670870i −0.604762 0.796406i \(-0.706732\pi\)
0.992089 + 0.125536i \(0.0400650\pi\)
\(168\) 4.49105 + 0.911277i 0.346492 + 0.0703066i
\(169\) −5.49849 9.52366i −0.422960 0.732589i
\(170\) 1.17857 + 0.680447i 0.0903921 + 0.0521879i
\(171\) 19.8546 + 0.102641i 1.51832 + 0.00784918i
\(172\) −1.06723 1.84849i −0.0813754 0.140946i
\(173\) 7.20429 0.547732 0.273866 0.961768i \(-0.411698\pi\)
0.273866 + 0.961768i \(0.411698\pi\)
\(174\) 8.62918 + 8.67390i 0.654176 + 0.657567i
\(175\) −1.46713 2.20171i −0.110905 0.166433i
\(176\) −0.179928 0.103881i −0.0135626 0.00783035i
\(177\) −14.5478 + 3.85779i −1.09348 + 0.289969i
\(178\) −2.44178 1.40976i −0.183019 0.105666i
\(179\) −12.7104 + 7.33833i −0.950016 + 0.548492i −0.893086 0.449886i \(-0.851465\pi\)
−0.0569303 + 0.998378i \(0.518131\pi\)
\(180\) 2.59029 + 1.51341i 0.193069 + 0.112803i
\(181\) 20.6504i 1.53493i 0.641090 + 0.767465i \(0.278482\pi\)
−0.641090 + 0.767465i \(0.721518\pi\)
\(182\) −2.07641 3.11604i −0.153914 0.230976i
\(183\) 0.948914 + 3.57837i 0.0701458 + 0.264521i
\(184\) 3.19741 + 5.53808i 0.235716 + 0.408272i
\(185\) −2.65778 −0.195404
\(186\) 7.94416 2.10664i 0.582494 0.154466i
\(187\) 0.282743i 0.0206762i
\(188\) 0.114683 0.00836410
\(189\) −4.30157 13.0574i −0.312893 0.949788i
\(190\) −6.61828 −0.480141
\(191\) 21.9525i 1.58843i 0.607639 + 0.794214i \(0.292117\pi\)
−0.607639 + 0.794214i \(0.707883\pi\)
\(192\) 1.67419 0.443962i 0.120824 0.0320402i
\(193\) 20.6101 1.48354 0.741772 0.670652i \(-0.233985\pi\)
0.741772 + 0.670652i \(0.233985\pi\)
\(194\) 0.803947 + 1.39248i 0.0577200 + 0.0999740i
\(195\) −0.628332 2.36945i −0.0449958 0.169680i
\(196\) 4.24735 + 5.56417i 0.303382 + 0.397441i
\(197\) 9.49837i 0.676731i −0.941015 0.338365i \(-0.890126\pi\)
0.941015 0.338365i \(-0.109874\pi\)
\(198\) −0.00322214 + 0.623280i −0.000228987 + 0.0442946i
\(199\) 1.57005 0.906467i 0.111298 0.0642578i −0.443318 0.896365i \(-0.646199\pi\)
0.554616 + 0.832107i \(0.312865\pi\)
\(200\) −0.866025 0.500000i −0.0612372 0.0353553i
\(201\) −0.0787614 + 0.0208860i −0.00555540 + 0.00147318i
\(202\) 5.28971 + 3.05401i 0.372183 + 0.214880i
\(203\) 1.19891 + 18.6510i 0.0841468 + 1.30905i
\(204\) −1.66243 1.67105i −0.116394 0.116997i
\(205\) −2.82489 −0.197299
\(206\) 3.30820 + 5.72998i 0.230493 + 0.399226i
\(207\) 9.67799 16.5644i 0.672667 1.15131i
\(208\) −1.22567 0.707642i −0.0849851 0.0490661i
\(209\) −0.687516 1.19081i −0.0475565 0.0823702i
\(210\) 1.45634 + 4.34501i 0.100497 + 0.299834i
\(211\) 11.3768 19.7053i 0.783214 1.35657i −0.146847 0.989159i \(-0.546912\pi\)
0.930060 0.367407i \(-0.119754\pi\)
\(212\) −8.40507 + 4.85267i −0.577262 + 0.333283i
\(213\) −1.53406 5.78496i −0.105112 0.396379i
\(214\) 2.68420 4.64917i 0.183488 0.317811i
\(215\) 1.06723 1.84849i 0.0727844 0.126066i
\(216\) −3.64563 3.70262i −0.248054 0.251931i
\(217\) 11.2526 + 5.56679i 0.763879 + 0.377898i
\(218\) 15.8011 9.12274i 1.07018 0.617870i
\(219\) 16.4178 16.3332i 1.10941 1.10369i
\(220\) 0.207763i 0.0140074i
\(221\) 1.92605i 0.129560i
\(222\) 4.44346 + 1.20294i 0.298226 + 0.0807361i
\(223\) 8.80329 5.08258i 0.589512 0.340355i −0.175393 0.984499i \(-0.556119\pi\)
0.764904 + 0.644144i \(0.222786\pi\)
\(224\) 2.37143 + 1.17317i 0.158448 + 0.0783856i
\(225\) −0.0155088 + 2.99996i −0.00103392 + 0.199997i
\(226\) −2.10372 + 3.64375i −0.139937 + 0.242379i
\(227\) 8.59635 14.8893i 0.570560 0.988238i −0.425949 0.904747i \(-0.640060\pi\)
0.996509 0.0834912i \(-0.0266070\pi\)
\(228\) 11.0649 + 2.99551i 0.732791 + 0.198382i
\(229\) −3.11150 + 1.79643i −0.205614 + 0.118711i −0.599271 0.800546i \(-0.704543\pi\)
0.393657 + 0.919257i \(0.371210\pi\)
\(230\) −3.19741 + 5.53808i −0.210831 + 0.365170i
\(231\) −0.630501 + 0.713401i −0.0414839 + 0.0469383i
\(232\) 3.53199 + 6.11758i 0.231886 + 0.401639i
\(233\) −18.4117 10.6300i −1.20619 0.696396i −0.244268 0.969708i \(-0.578548\pi\)
−0.961926 + 0.273312i \(0.911881\pi\)
\(234\) −0.0219493 + 4.24580i −0.00143487 + 0.277556i
\(235\) 0.0573414 + 0.0993182i 0.00374054 + 0.00647881i
\(236\) −8.68947 −0.565636
\(237\) −26.7085 + 7.08258i −1.73490 + 0.460063i
\(238\) −0.230973 3.59317i −0.0149717 0.232911i
\(239\) −4.18867 2.41833i −0.270943 0.156429i 0.358373 0.933578i \(-0.383331\pi\)
−0.629316 + 0.777150i \(0.716665\pi\)
\(240\) 1.22158 + 1.22791i 0.0788523 + 0.0792610i
\(241\) 1.39424 + 0.804962i 0.0898106 + 0.0518522i 0.544233 0.838934i \(-0.316821\pi\)
−0.454422 + 0.890786i \(0.650154\pi\)
\(242\) −9.48890 + 5.47842i −0.609969 + 0.352166i
\(243\) −4.22885 + 15.0039i −0.271281 + 0.962500i
\(244\) 2.13738i 0.136832i
\(245\) −2.69504 + 6.46040i −0.172180 + 0.412740i
\(246\) 4.72285 + 1.27858i 0.301118 + 0.0815191i
\(247\) −4.68338 8.11184i −0.297996 0.516144i
\(248\) 4.74509 0.301314
\(249\) −19.6922 19.7942i −1.24794 1.25441i
\(250\) 1.00000i 0.0632456i
\(251\) −2.86313 −0.180719 −0.0903596 0.995909i \(-0.528802\pi\)
−0.0903596 + 0.995909i \(0.528802\pi\)
\(252\) −0.468209 7.92343i −0.0294944 0.499129i
\(253\) −1.32860 −0.0835287
\(254\) 14.9591i 0.938620i
\(255\) 0.615955 2.27524i 0.0385726 0.142481i
\(256\) 1.00000 0.0625000
\(257\) −15.7357 27.2551i −0.981567 1.70012i −0.656297 0.754503i \(-0.727878\pi\)
−0.325270 0.945621i \(-0.605455\pi\)
\(258\) −2.62091 + 2.60740i −0.163171 + 0.162330i
\(259\) 3.89932 + 5.85166i 0.242292 + 0.363604i
\(260\) 1.41528i 0.0877722i
\(261\) 10.6907 18.2977i 0.661738 1.13260i
\(262\) −14.5432 + 8.39654i −0.898484 + 0.518740i
\(263\) −2.85184 1.64651i −0.175852 0.101528i 0.409490 0.912314i \(-0.365706\pi\)
−0.585342 + 0.810786i \(0.699040\pi\)
\(264\) −0.0940356 + 0.347352i −0.00578749 + 0.0213780i
\(265\) −8.40507 4.85267i −0.516319 0.298097i
\(266\) 9.70991 + 14.5715i 0.595353 + 0.893438i
\(267\) −1.27615 + 4.71388i −0.0780990 + 0.288485i
\(268\) −0.0470446 −0.00287371
\(269\) −9.44456 16.3585i −0.575845 0.997393i −0.995949 0.0899173i \(-0.971340\pi\)
0.420104 0.907476i \(-0.361994\pi\)
\(270\) 1.38374 5.00852i 0.0842119 0.304809i
\(271\) 2.78962 + 1.61059i 0.169457 + 0.0978362i 0.582330 0.812953i \(-0.302141\pi\)
−0.412873 + 0.910789i \(0.635475\pi\)
\(272\) −0.680447 1.17857i −0.0412582 0.0714612i
\(273\) −4.29499 + 4.85970i −0.259944 + 0.294123i
\(274\) 1.69594 2.93746i 0.102456 0.177459i
\(275\) 0.179928 0.103881i 0.0108500 0.00626428i
\(276\) 7.85224 7.81175i 0.472649 0.470212i
\(277\) −0.0594767 + 0.103017i −0.00357361 + 0.00618967i −0.867807 0.496902i \(-0.834471\pi\)
0.864233 + 0.503092i \(0.167804\pi\)
\(278\) −2.93099 + 5.07662i −0.175789 + 0.304475i
\(279\) −7.05381 12.3647i −0.422301 0.740258i
\(280\) 0.169721 + 2.64030i 0.0101428 + 0.157788i
\(281\) −11.3489 + 6.55231i −0.677021 + 0.390878i −0.798732 0.601688i \(-0.794495\pi\)
0.121711 + 0.992566i \(0.461162\pi\)
\(282\) −0.0509148 0.192000i −0.00303193 0.0114335i
\(283\) 25.0528i 1.48923i 0.667492 + 0.744617i \(0.267368\pi\)
−0.667492 + 0.744617i \(0.732632\pi\)
\(284\) 3.45539i 0.205040i
\(285\) 2.93826 + 11.0802i 0.174048 + 0.656336i
\(286\) 0.254649 0.147022i 0.0150577 0.00869357i
\(287\) 4.14450 + 6.21959i 0.244642 + 0.367131i
\(288\) −1.48655 2.60580i −0.0875957 0.153548i
\(289\) 7.57398 13.1185i 0.445528 0.771678i
\(290\) −3.53199 + 6.11758i −0.207405 + 0.359237i
\(291\) 1.97434 1.96416i 0.115738 0.115141i
\(292\) 11.5793 6.68529i 0.677625 0.391227i
\(293\) 0.727716 1.26044i 0.0425136 0.0736358i −0.843986 0.536366i \(-0.819797\pi\)
0.886499 + 0.462730i \(0.153130\pi\)
\(294\) 7.42979 9.58114i 0.433314 0.558783i
\(295\) −4.34473 7.52530i −0.252960 0.438140i
\(296\) 2.30171 + 1.32889i 0.133784 + 0.0772402i
\(297\) 1.04492 0.271318i 0.0606322 0.0157435i
\(298\) −11.1816 19.3671i −0.647733 1.12191i
\(299\) −9.05049 −0.523403
\(300\) −0.452611 + 1.67187i −0.0261315 + 0.0965254i
\(301\) −5.63561 + 0.362263i −0.324831 + 0.0208805i
\(302\) 10.9325 + 6.31191i 0.629097 + 0.363209i
\(303\) 2.76456 10.2118i 0.158820 0.586654i
\(304\) 5.73160 + 3.30914i 0.328730 + 0.189792i
\(305\) −1.85102 + 1.06869i −0.105989 + 0.0611930i
\(306\) −2.05959 + 3.52511i −0.117739 + 0.201517i
\(307\) 0.302317i 0.0172541i −0.999963 0.00862706i \(-0.997254\pi\)
0.999963 0.00862706i \(-0.00274611\pi\)
\(308\) −0.457433 + 0.304816i −0.0260646 + 0.0173685i
\(309\) 8.12433 8.08244i 0.462177 0.459794i
\(310\) 2.37255 + 4.10937i 0.134752 + 0.233396i
\(311\) 0.317161 0.0179846 0.00899228 0.999960i \(-0.497138\pi\)
0.00899228 + 0.999960i \(0.497138\pi\)
\(312\) −0.640573 + 2.36617i −0.0362653 + 0.133958i
\(313\) 21.1311i 1.19440i −0.802091 0.597201i \(-0.796279\pi\)
0.802091 0.597201i \(-0.203721\pi\)
\(314\) 5.80220 0.327437
\(315\) 6.62779 4.36720i 0.373434 0.246064i
\(316\) −15.9531 −0.897434
\(317\) 10.1784i 0.571674i −0.958278 0.285837i \(-0.907728\pi\)
0.958278 0.285837i \(-0.0922715\pi\)
\(318\) 11.8558 + 11.9172i 0.664840 + 0.668286i
\(319\) −1.46763 −0.0821715
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) −8.97526 2.42980i −0.500950 0.135618i
\(322\) 16.8843 1.08534i 0.940923 0.0604835i
\(323\) 9.00678i 0.501151i
\(324\) −4.58034 + 7.74729i −0.254464 + 0.430405i
\(325\) 1.22567 0.707642i 0.0679880 0.0392529i
\(326\) −15.5658 8.98690i −0.862108 0.497738i
\(327\) −22.2882 22.4038i −1.23254 1.23893i
\(328\) 2.44643 + 1.41245i 0.135081 + 0.0779893i
\(329\) 0.134542 0.271962i 0.00741755 0.0149938i
\(330\) −0.347833 + 0.0922387i −0.0191476 + 0.00507757i
\(331\) −22.1801 −1.21913 −0.609566 0.792736i \(-0.708656\pi\)
−0.609566 + 0.792736i \(0.708656\pi\)
\(332\) −8.06016 13.9606i −0.442359 0.766187i
\(333\) 0.0412189 7.97324i 0.00225878 0.436931i
\(334\) −8.66956 5.00537i −0.474377 0.273882i
\(335\) −0.0235223 0.0407418i −0.00128516 0.00222596i
\(336\) 0.911277 4.49105i 0.0497143 0.245007i
\(337\) −13.9347 + 24.1356i −0.759070 + 1.31475i 0.184256 + 0.982878i \(0.441013\pi\)
−0.943325 + 0.331869i \(0.892321\pi\)
\(338\) −9.52366 + 5.49849i −0.518019 + 0.299078i
\(339\) 7.03428 + 1.90433i 0.382050 + 0.103429i
\(340\) 0.680447 1.17857i 0.0369024 0.0639169i
\(341\) −0.492926 + 0.853773i −0.0266935 + 0.0462344i
\(342\) 0.102641 19.8546i 0.00555021 1.07361i
\(343\) 18.1779 3.54459i 0.981514 0.191390i
\(344\) −1.84849 + 1.06723i −0.0996641 + 0.0575411i
\(345\) 10.6913 + 2.89436i 0.575600 + 0.155827i
\(346\) 7.20429i 0.387305i
\(347\) 8.89161i 0.477327i 0.971102 + 0.238663i \(0.0767093\pi\)
−0.971102 + 0.238663i \(0.923291\pi\)
\(348\) 8.67390 8.62918i 0.464970 0.462572i
\(349\) 22.9898 13.2732i 1.23062 0.710497i 0.263459 0.964671i \(-0.415137\pi\)
0.967159 + 0.254173i \(0.0818033\pi\)
\(350\) −2.20171 + 1.46713i −0.117686 + 0.0784216i
\(351\) 7.11800 1.84822i 0.379930 0.0986509i
\(352\) −0.103881 + 0.179928i −0.00553689 + 0.00959018i
\(353\) 14.9024 25.8117i 0.793175 1.37382i −0.130817 0.991407i \(-0.541760\pi\)
0.923992 0.382412i \(-0.124907\pi\)
\(354\) 3.85779 + 14.5478i 0.205039 + 0.773206i
\(355\) 2.99245 1.72769i 0.158823 0.0916965i
\(356\) −1.40976 + 2.44178i −0.0747173 + 0.129414i
\(357\) −5.91309 + 1.98192i −0.312954 + 0.104894i
\(358\) 7.33833 + 12.7104i 0.387843 + 0.671763i
\(359\) −14.6722 8.47101i −0.774370 0.447083i 0.0600612 0.998195i \(-0.480870\pi\)
−0.834431 + 0.551112i \(0.814204\pi\)
\(360\) 1.51341 2.59029i 0.0797638 0.136520i
\(361\) 12.4008 + 21.4789i 0.652675 + 1.13047i
\(362\) 20.6504 1.08536
\(363\) 13.3846 + 13.4540i 0.702509 + 0.706150i
\(364\) −3.11604 + 2.07641i −0.163325 + 0.108834i
\(365\) 11.5793 + 6.68529i 0.606086 + 0.349924i
\(366\) 3.57837 0.948914i 0.187044 0.0496005i
\(367\) 18.2244 + 10.5218i 0.951305 + 0.549236i 0.893486 0.449091i \(-0.148252\pi\)
0.0578186 + 0.998327i \(0.481585\pi\)
\(368\) 5.53808 3.19741i 0.288692 0.166677i
\(369\) 0.0438106 8.47457i 0.00228069 0.441168i
\(370\) 2.65778i 0.138171i
\(371\) 1.64720 + 25.6250i 0.0855184 + 1.33038i
\(372\) −2.10664 7.94416i −0.109224 0.411886i
\(373\) 5.61566 + 9.72660i 0.290768 + 0.503624i 0.973991 0.226585i \(-0.0727560\pi\)
−0.683224 + 0.730209i \(0.739423\pi\)
\(374\) 0.282743 0.0146203
\(375\) −1.67419 + 0.443962i −0.0864546 + 0.0229261i
\(376\) 0.114683i 0.00591431i
\(377\) −9.99753 −0.514899
\(378\) −13.0574 + 4.30157i −0.671602 + 0.221249i
\(379\) 2.41836 0.124223 0.0621113 0.998069i \(-0.480217\pi\)
0.0621113 + 0.998069i \(0.480217\pi\)
\(380\) 6.61828i 0.339511i
\(381\) 25.0444 6.64129i 1.28306 0.340243i
\(382\) 21.9525 1.12319
\(383\) −8.75083 15.1569i −0.447146 0.774480i 0.551053 0.834471i \(-0.314226\pi\)
−0.998199 + 0.0599902i \(0.980893\pi\)
\(384\) −0.443962 1.67419i −0.0226558 0.0854354i
\(385\) −0.492694 0.243740i −0.0251100 0.0124222i
\(386\) 20.6101i 1.04902i
\(387\) 5.52885 + 3.23031i 0.281047 + 0.164206i
\(388\) 1.39248 0.803947i 0.0706923 0.0408142i
\(389\) −5.81070 3.35481i −0.294614 0.170096i 0.345407 0.938453i \(-0.387741\pi\)
−0.640021 + 0.768358i \(0.721074\pi\)
\(390\) −2.36945 + 0.628332i −0.119982 + 0.0318168i
\(391\) −7.53673 4.35134i −0.381149 0.220057i
\(392\) 5.56417 4.24735i 0.281033 0.214524i
\(393\) 20.5140 + 20.6203i 1.03479 + 1.04016i
\(394\) −9.49837 −0.478521
\(395\) −7.97657 13.8158i −0.401345 0.695149i
\(396\) 0.623280 + 0.00322214i 0.0313210 + 0.000161919i
\(397\) 6.02981 + 3.48131i 0.302628 + 0.174722i 0.643623 0.765343i \(-0.277431\pi\)
−0.340995 + 0.940065i \(0.610764\pi\)
\(398\) −0.906467 1.57005i −0.0454371 0.0786994i
\(399\) 20.0846 22.7254i 1.00549 1.13769i
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) −10.0251 + 5.78798i −0.500629 + 0.289038i −0.728973 0.684542i \(-0.760002\pi\)
0.228345 + 0.973580i \(0.426669\pi\)
\(402\) 0.0208860 + 0.0787614i 0.00104170 + 0.00392826i
\(403\) −3.35783 + 5.81593i −0.167265 + 0.289712i
\(404\) 3.05401 5.28971i 0.151943 0.263173i
\(405\) −8.99952 0.0930513i −0.447190 0.00462376i
\(406\) 18.6510 1.19891i 0.925635 0.0595008i
\(407\) −0.478209 + 0.276094i −0.0237039 + 0.0136855i
\(408\) −1.67105 + 1.66243i −0.0827293 + 0.0823028i
\(409\) 36.3280i 1.79630i 0.439686 + 0.898151i \(0.355090\pi\)
−0.439686 + 0.898151i \(0.644910\pi\)
\(410\) 2.82489i 0.139512i
\(411\) −5.67079 1.53521i −0.279720 0.0757261i
\(412\) 5.72998 3.30820i 0.282296 0.162983i
\(413\) −10.1942 + 20.6065i −0.501624 + 1.01398i
\(414\) −16.5644 9.67799i −0.814097 0.475647i
\(415\) 8.06016 13.9606i 0.395657 0.685299i
\(416\) −0.707642 + 1.22567i −0.0346950 + 0.0600935i
\(417\) 9.80044 + 2.65319i 0.479930 + 0.129927i
\(418\) −1.19081 + 0.687516i −0.0582445 + 0.0336275i
\(419\) −16.0393 + 27.7808i −0.783570 + 1.35718i 0.146280 + 0.989243i \(0.453270\pi\)
−0.929850 + 0.367939i \(0.880063\pi\)
\(420\) 4.34501 1.45634i 0.212015 0.0710620i
\(421\) −5.92162 10.2565i −0.288602 0.499873i 0.684874 0.728661i \(-0.259857\pi\)
−0.973476 + 0.228788i \(0.926524\pi\)
\(422\) −19.7053 11.3768i −0.959237 0.553816i
\(423\) −0.298840 + 0.170482i −0.0145301 + 0.00828910i
\(424\) 4.85267 + 8.40507i 0.235666 + 0.408186i
\(425\) 1.36089 0.0660131
\(426\) −5.78496 + 1.53406i −0.280282 + 0.0743254i
\(427\) 5.06864 + 2.50750i 0.245289 + 0.121347i
\(428\) −4.64917 2.68420i −0.224726 0.129746i
\(429\) −0.359196 0.361058i −0.0173421 0.0174320i
\(430\) −1.84849 1.06723i −0.0891423 0.0514663i
\(431\) −28.2466 + 16.3082i −1.36059 + 0.785538i −0.989703 0.143139i \(-0.954280\pi\)
−0.370890 + 0.928677i \(0.620947\pi\)
\(432\) −3.70262 + 3.64563i −0.178142 + 0.175401i
\(433\) 1.82172i 0.0875462i 0.999041 + 0.0437731i \(0.0139379\pi\)
−0.999041 + 0.0437731i \(0.986062\pi\)
\(434\) 5.56679 11.2526i 0.267214 0.540144i
\(435\) 11.8100 + 3.19723i 0.566248 + 0.153296i
\(436\) −9.12274 15.8011i −0.436900 0.756733i
\(437\) 42.3227 2.02457
\(438\) −16.3332 16.4178i −0.780429 0.784474i
\(439\) 23.8749i 1.13949i 0.821822 + 0.569744i \(0.192958\pi\)
−0.821822 + 0.569744i \(0.807042\pi\)
\(440\) −0.207763 −0.00990470
\(441\) −19.3391 8.18519i −0.920912 0.389771i
\(442\) 1.92605 0.0916129
\(443\) 23.6199i 1.12222i 0.827742 + 0.561109i \(0.189625\pi\)
−0.827742 + 0.561109i \(0.810375\pi\)
\(444\) 1.20294 4.44346i 0.0570890 0.210877i
\(445\) −2.81953 −0.133658
\(446\) −5.08258 8.80329i −0.240667 0.416848i
\(447\) −27.4599 + 27.3183i −1.29881 + 1.29211i
\(448\) 1.17317 2.37143i 0.0554270 0.112040i
\(449\) 33.6640i 1.58870i −0.607459 0.794351i \(-0.707811\pi\)
0.607459 0.794351i \(-0.292189\pi\)
\(450\) 2.99996 + 0.0155088i 0.141419 + 0.000731090i
\(451\) −0.508277 + 0.293454i −0.0239338 + 0.0138182i
\(452\) 3.64375 + 2.10372i 0.171387 + 0.0989506i
\(453\) 5.71367 21.1053i 0.268452 0.991616i
\(454\) −14.8893 8.59635i −0.698790 0.403447i
\(455\) −3.35625 1.66037i −0.157343 0.0778392i
\(456\) 2.99551 11.0649i 0.140277 0.518161i
\(457\) 18.1990 0.851316 0.425658 0.904884i \(-0.360043\pi\)
0.425658 + 0.904884i \(0.360043\pi\)
\(458\) 1.79643 + 3.11150i 0.0839415 + 0.145391i
\(459\) 6.81606 + 1.88313i 0.318147 + 0.0878968i
\(460\) 5.53808 + 3.19741i 0.258214 + 0.149080i
\(461\) 7.33169 + 12.6989i 0.341471 + 0.591445i 0.984706 0.174224i \(-0.0557415\pi\)
−0.643235 + 0.765669i \(0.722408\pi\)
\(462\) 0.713401 + 0.630501i 0.0331904 + 0.0293335i
\(463\) −3.20796 + 5.55635i −0.149087 + 0.258226i −0.930890 0.365299i \(-0.880967\pi\)
0.781804 + 0.623525i \(0.214300\pi\)
\(464\) 6.11758 3.53199i 0.284002 0.163968i
\(465\) 5.82653 5.79648i 0.270199 0.268806i
\(466\) −10.6300 + 18.4117i −0.492426 + 0.852907i
\(467\) 13.0712 22.6399i 0.604862 1.04765i −0.387212 0.921991i \(-0.626562\pi\)
0.992073 0.125660i \(-0.0401049\pi\)
\(468\) 4.24580 + 0.0219493i 0.196262 + 0.00101461i
\(469\) −0.0551912 + 0.111563i −0.00254849 + 0.00515150i
\(470\) 0.0993182 0.0573414i 0.00458121 0.00264496i
\(471\) −2.57595 9.71395i −0.118694 0.447595i
\(472\) 8.68947i 0.399965i
\(473\) 0.443460i 0.0203903i
\(474\) 7.08258 + 26.7085i 0.325314 + 1.22676i
\(475\) −5.73160 + 3.30914i −0.262984 + 0.151834i
\(476\) −3.59317 + 0.230973i −0.164693 + 0.0105866i
\(477\) 14.6882 25.1396i 0.672525 1.15106i
\(478\) −2.41833 + 4.18867i −0.110612 + 0.191585i
\(479\) 16.8626 29.2068i 0.770470 1.33449i −0.166835 0.985985i \(-0.553355\pi\)
0.937306 0.348509i \(-0.113312\pi\)
\(480\) 1.22791 1.22158i 0.0560460 0.0557570i
\(481\) −3.25757 + 1.88076i −0.148532 + 0.0857552i
\(482\) 0.804962 1.39424i 0.0366650 0.0635057i
\(483\) −9.31302 27.7855i −0.423757 1.26429i
\(484\) 5.47842 + 9.48890i 0.249019 + 0.431314i
\(485\) 1.39248 + 0.803947i 0.0632291 + 0.0365053i
\(486\) 15.0039 + 4.22885i 0.680590 + 0.191824i
\(487\) 3.38529 + 5.86349i 0.153402 + 0.265700i 0.932476 0.361232i \(-0.117644\pi\)
−0.779074 + 0.626932i \(0.784310\pi\)
\(488\) 2.13738 0.0967546
\(489\) −8.13513 + 30.0498i −0.367883 + 1.35890i
\(490\) 6.46040 + 2.69504i 0.291851 + 0.121749i
\(491\) −7.86871 4.54300i −0.355110 0.205023i 0.311824 0.950140i \(-0.399060\pi\)
−0.666934 + 0.745117i \(0.732393\pi\)
\(492\) 1.27858 4.72285i 0.0576427 0.212923i
\(493\) −8.32538 4.80666i −0.374956 0.216481i
\(494\) −8.11184 + 4.68338i −0.364969 + 0.210715i
\(495\) 0.308849 + 0.541387i 0.0138817 + 0.0243335i
\(496\) 4.74509i 0.213061i
\(497\) −8.19421 4.05375i −0.367560 0.181836i
\(498\) −19.7942 + 19.6922i −0.887001 + 0.882427i
\(499\) 21.0294 + 36.4240i 0.941407 + 1.63056i 0.762791 + 0.646645i \(0.223829\pi\)
0.178616 + 0.983919i \(0.442838\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −4.53097 + 16.7366i −0.202429 + 0.747738i
\(502\) 2.86313i 0.127788i
\(503\) 19.9162 0.888021 0.444011 0.896021i \(-0.353555\pi\)
0.444011 + 0.896021i \(0.353555\pi\)
\(504\) −7.92343 + 0.468209i −0.352938 + 0.0208557i
\(505\) 6.10803 0.271804
\(506\) 1.32860i 0.0590637i
\(507\) 13.4336 + 13.5033i 0.596608 + 0.599700i
\(508\) 14.9591 0.663704
\(509\) 12.0143 + 20.8094i 0.532524 + 0.922359i 0.999279 + 0.0379721i \(0.0120898\pi\)
−0.466755 + 0.884387i \(0.654577\pi\)
\(510\) −2.27524 0.615955i −0.100749 0.0272750i
\(511\) −2.26927 35.3024i −0.100387 1.56168i
\(512\) 1.00000i 0.0441942i
\(513\) −33.2858 + 8.64284i −1.46961 + 0.381590i
\(514\) −27.2551 + 15.7357i −1.20217 + 0.694073i
\(515\) 5.72998 + 3.30820i 0.252493 + 0.145777i
\(516\) 2.60740 + 2.62091i 0.114784 + 0.115379i
\(517\) 0.0206346 + 0.0119134i 0.000907509 + 0.000523951i
\(518\) 5.85166 3.89932i 0.257107 0.171326i
\(519\) −12.0613 + 3.19843i −0.529433 + 0.140395i
\(520\) −1.41528 −0.0620643
\(521\) 16.5020 + 28.5823i 0.722965 + 1.25221i 0.959806 + 0.280663i \(0.0905545\pi\)
−0.236841 + 0.971548i \(0.576112\pi\)
\(522\) −18.2977 10.6907i −0.800870 0.467919i
\(523\) −26.4518 15.2720i −1.15666 0.667797i −0.206157 0.978519i \(-0.566096\pi\)
−0.950501 + 0.310722i \(0.899429\pi\)
\(524\) 8.39654 + 14.5432i 0.366805 + 0.635324i
\(525\) 3.43373 + 3.03472i 0.149860 + 0.132446i
\(526\) −1.64651 + 2.85184i −0.0717912 + 0.124346i
\(527\) −5.59242 + 3.22878i −0.243609 + 0.140648i
\(528\) 0.347352 + 0.0940356i 0.0151165 + 0.00409237i
\(529\) 8.94686 15.4964i 0.388994 0.673757i
\(530\) −4.85267 + 8.40507i −0.210786 + 0.365093i
\(531\) 22.6430 12.9173i 0.982622 0.560564i
\(532\) 14.5715 9.70991i 0.631756 0.420978i
\(533\) −3.46239 + 1.99901i −0.149973 + 0.0865869i
\(534\) 4.71388 + 1.27615i 0.203990 + 0.0552243i
\(535\) 5.36840i 0.232096i
\(536\) 0.0470446i 0.00203202i
\(537\) 18.0216 17.9286i 0.777687 0.773678i
\(538\) −16.3585 + 9.44456i −0.705264 + 0.407184i
\(539\) 0.186203 + 1.44237i 0.00802034 + 0.0621272i
\(540\) −5.00852 1.38374i −0.215532 0.0595468i
\(541\) −14.4385 + 25.0082i −0.620760 + 1.07519i 0.368585 + 0.929594i \(0.379842\pi\)
−0.989345 + 0.145593i \(0.953491\pi\)
\(542\) 1.61059 2.78962i 0.0691806 0.119824i
\(543\) −9.16798 34.5726i −0.393436 1.48365i
\(544\) −1.17857 + 0.680447i −0.0505307 + 0.0291739i
\(545\) 9.12274 15.8011i 0.390775 0.676843i
\(546\) 4.85970 + 4.29499i 0.207976 + 0.183808i
\(547\) 14.0094 + 24.2650i 0.598999 + 1.03750i 0.992969 + 0.118374i \(0.0377681\pi\)
−0.393970 + 0.919123i \(0.628899\pi\)
\(548\) −2.93746 1.69594i −0.125482 0.0724472i
\(549\) −3.17732 5.56957i −0.135605 0.237703i
\(550\) −0.103881 0.179928i −0.00442951 0.00767214i
\(551\) 46.7514 1.99168
\(552\) −7.81175 7.85224i −0.332490 0.334214i
\(553\) −18.7157 + 37.8317i −0.795873 + 1.60877i
\(554\) 0.103017 + 0.0594767i 0.00437676 + 0.00252692i
\(555\) 4.44962 1.17995i 0.188876 0.0500862i
\(556\) 5.07662 + 2.93099i 0.215296 + 0.124301i
\(557\) −8.62658 + 4.98056i −0.365520 + 0.211033i −0.671499 0.741005i \(-0.734349\pi\)
0.305980 + 0.952038i \(0.401016\pi\)
\(558\) −12.3647 + 7.05381i −0.523441 + 0.298612i
\(559\) 3.02086i 0.127769i
\(560\) 2.64030 0.169721i 0.111573 0.00717203i
\(561\) −0.125527 0.473364i −0.00529976 0.0199855i
\(562\) 6.55231 + 11.3489i 0.276392 + 0.478726i
\(563\) −38.5239 −1.62359 −0.811794 0.583945i \(-0.801509\pi\)
−0.811794 + 0.583945i \(0.801509\pi\)
\(564\) −0.192000 + 0.0509148i −0.00808467 + 0.00214390i
\(565\) 4.20744i 0.177008i
\(566\) 25.0528 1.05305
\(567\) 12.9986 + 19.9508i 0.545891 + 0.837856i
\(568\) −3.45539 −0.144985
\(569\) 15.3964i 0.645451i 0.946493 + 0.322725i \(0.104599\pi\)
−0.946493 + 0.322725i \(0.895401\pi\)
\(570\) 11.0802 2.93826i 0.464100 0.123070i
\(571\) 4.64392 0.194342 0.0971709 0.995268i \(-0.469021\pi\)
0.0971709 + 0.995268i \(0.469021\pi\)
\(572\) −0.147022 0.254649i −0.00614728 0.0106474i
\(573\) −9.74607 36.7526i −0.407148 1.53536i
\(574\) 6.21959 4.14450i 0.259601 0.172988i
\(575\) 6.39482i 0.266682i
\(576\) −2.60580 + 1.48655i −0.108575 + 0.0619395i
\(577\) −16.2075 + 9.35741i −0.674727 + 0.389554i −0.797865 0.602836i \(-0.794037\pi\)
0.123138 + 0.992390i \(0.460704\pi\)
\(578\) −13.1185 7.57398i −0.545659 0.315036i
\(579\) −34.5051 + 9.15008i −1.43398 + 0.380264i
\(580\) 6.11758 + 3.53199i 0.254019 + 0.146658i
\(581\) −42.5625 + 2.73596i −1.76579 + 0.113507i
\(582\) −1.96416 1.97434i −0.0814172 0.0818391i
\(583\) −2.01641 −0.0835110
\(584\) −6.68529 11.5793i −0.276639 0.479153i
\(585\) 2.10389 + 3.68794i 0.0869851 + 0.152478i
\(586\) −1.26044 0.727716i −0.0520684 0.0300617i
\(587\) −5.45638 9.45073i −0.225209 0.390073i 0.731173 0.682192i \(-0.238973\pi\)
−0.956382 + 0.292119i \(0.905640\pi\)
\(588\) −9.58114 7.42979i −0.395119 0.306399i
\(589\) 15.7022 27.1970i 0.646997 1.12063i
\(590\) −7.52530 + 4.34473i −0.309812 + 0.178870i
\(591\) 4.21691 + 15.9020i 0.173461 + 0.654122i
\(592\) 1.32889 2.30171i 0.0546171 0.0945995i
\(593\) 9.60114 16.6297i 0.394272 0.682899i −0.598736 0.800946i \(-0.704330\pi\)
0.993008 + 0.118048i \(0.0376635\pi\)
\(594\) −0.271318 1.04492i −0.0111323 0.0428734i
\(595\) −1.99661 2.99629i −0.0818532 0.122836i
\(596\) −19.3671 + 11.1816i −0.793307 + 0.458016i
\(597\) −2.22611 + 2.21464i −0.0911088 + 0.0906390i
\(598\) 9.05049i 0.370102i
\(599\) 21.9105i 0.895241i 0.894224 + 0.447620i \(0.147728\pi\)
−0.894224 + 0.447620i \(0.852272\pi\)
\(600\) 1.67187 + 0.452611i 0.0682537 + 0.0184778i
\(601\) 38.2477 22.0823i 1.56016 0.900756i 0.562915 0.826515i \(-0.309680\pi\)
0.997240 0.0742412i \(-0.0236535\pi\)
\(602\) 0.362263 + 5.63561i 0.0147647 + 0.229690i
\(603\) 0.122589 0.0699341i 0.00499219 0.00284794i
\(604\) 6.31191 10.9325i 0.256828 0.444839i
\(605\) −5.47842 + 9.48890i −0.222729 + 0.385779i
\(606\) −10.2118 2.76456i −0.414827 0.112303i
\(607\) −22.3770 + 12.9194i −0.908256 + 0.524382i −0.879870 0.475215i \(-0.842370\pi\)
−0.0283865 + 0.999597i \(0.509037\pi\)
\(608\) 3.30914 5.73160i 0.134203 0.232447i
\(609\) −10.2875 30.6930i −0.416872 1.24374i
\(610\) 1.06869 + 1.85102i 0.0432700 + 0.0749458i
\(611\) 0.140563 + 0.0811544i 0.00568659 + 0.00328315i
\(612\) 3.52511 + 2.05959i 0.142494 + 0.0832541i
\(613\) 20.3696 + 35.2812i 0.822720 + 1.42499i 0.903650 + 0.428273i \(0.140878\pi\)
−0.0809298 + 0.996720i \(0.525789\pi\)
\(614\) −0.302317 −0.0122005
\(615\) 4.72940 1.25414i 0.190708 0.0505720i
\(616\) 0.304816 + 0.457433i 0.0122814 + 0.0184305i
\(617\) 18.7258 + 10.8114i 0.753874 + 0.435249i 0.827092 0.562067i \(-0.189994\pi\)
−0.0732181 + 0.997316i \(0.523327\pi\)
\(618\) −8.08244 8.12433i −0.325123 0.326808i
\(619\) −35.9899 20.7788i −1.44656 0.835170i −0.448282 0.893892i \(-0.647964\pi\)
−0.998274 + 0.0587223i \(0.981297\pi\)
\(620\) 4.10937 2.37255i 0.165036 0.0952837i
\(621\) −8.84878 + 32.0286i −0.355089 + 1.28526i
\(622\) 0.317161i 0.0127170i
\(623\) 4.13663 + 6.20778i 0.165730 + 0.248709i
\(624\) 2.36617 + 0.640573i 0.0947226 + 0.0256434i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −21.1311 −0.844570
\(627\) 1.67970 + 1.68841i 0.0670809 + 0.0674286i
\(628\) 5.80220i 0.231533i
\(629\) −3.61696 −0.144218
\(630\) −4.36720 6.62779i −0.173993 0.264057i
\(631\) −24.7896 −0.986860 −0.493430 0.869785i \(-0.664257\pi\)
−0.493430 + 0.869785i \(0.664257\pi\)
\(632\) 15.9531i 0.634582i
\(633\) −10.2986 + 38.0411i −0.409331 + 1.51200i
\(634\) −10.1784 −0.404234
\(635\) 7.47957 + 12.9550i 0.296818 + 0.514103i
\(636\) 11.9172 11.8558i 0.472549 0.470113i
\(637\) 1.26842 + 9.82545i 0.0502567 + 0.389299i
\(638\) 1.46763i 0.0581040i
\(639\) 5.13660 + 9.00403i 0.203201 + 0.356194i
\(640\) 0.866025 0.500000i 0.0342327 0.0197642i
\(641\) −30.6815 17.7140i −1.21185 0.699660i −0.248686 0.968584i \(-0.579999\pi\)
−0.963161 + 0.268924i \(0.913332\pi\)
\(642\) −2.42980 + 8.97526i −0.0958964 + 0.354225i
\(643\) 25.1223 + 14.5043i 0.990726 + 0.571996i 0.905491 0.424365i \(-0.139503\pi\)
0.0852345 + 0.996361i \(0.472836\pi\)
\(644\) −1.08534 16.8843i −0.0427683 0.665333i
\(645\) −0.966078 + 3.56853i −0.0380393 + 0.140511i
\(646\) −9.00678 −0.354367
\(647\) −14.2851 24.7426i −0.561607 0.972731i −0.997357 0.0726633i \(-0.976850\pi\)
0.435750 0.900068i \(-0.356483\pi\)
\(648\) 7.74729 + 4.58034i 0.304342 + 0.179933i
\(649\) −1.56348 0.902674i −0.0613718 0.0354330i
\(650\) −0.707642 1.22567i −0.0277560 0.0480748i
\(651\) −21.3105 4.32409i −0.835223 0.169475i
\(652\) −8.98690 + 15.5658i −0.351954 + 0.609602i
\(653\) 20.1958 11.6601i 0.790324 0.456294i −0.0497523 0.998762i \(-0.515843\pi\)
0.840077 + 0.542468i \(0.182510\pi\)
\(654\) −22.4038 + 22.2882i −0.876056 + 0.871539i
\(655\) −8.39654 + 14.5432i −0.328080 + 0.568251i
\(656\) 1.41245 2.44643i 0.0551468 0.0955170i
\(657\) −20.2352 + 34.6336i −0.789450 + 1.35119i
\(658\) −0.271962 0.134542i −0.0106022 0.00524500i
\(659\) −41.6998 + 24.0754i −1.62440 + 0.937845i −0.638670 + 0.769481i \(0.720515\pi\)
−0.985725 + 0.168364i \(0.946151\pi\)
\(660\) 0.0922387 + 0.347833i 0.00359039 + 0.0135394i
\(661\) 43.3165i 1.68482i 0.538840 + 0.842408i \(0.318863\pi\)
−0.538840 + 0.842408i \(0.681137\pi\)
\(662\) 22.1801i 0.862056i
\(663\) −0.855093 3.22457i −0.0332091 0.125232i
\(664\) −13.9606 + 8.06016i −0.541776 + 0.312795i
\(665\) 15.6948 + 7.76436i 0.608618 + 0.301089i
\(666\) −7.97324 0.0412189i −0.308957 0.00159720i
\(667\) 22.5864 39.1208i 0.874550 1.51476i
\(668\) −5.00537 + 8.66956i −0.193664 + 0.335435i
\(669\) −12.4819 + 12.4175i −0.482577 + 0.480089i
\(670\) −0.0407418 + 0.0235223i −0.00157399 + 0.000908746i
\(671\) −0.222034 + 0.384574i −0.00857151 + 0.0148463i
\(672\) −4.49105 0.911277i −0.173246 0.0351533i
\(673\) −10.7910 18.6906i −0.415964 0.720471i 0.579565 0.814926i \(-0.303222\pi\)
−0.995529 + 0.0944550i \(0.969889\pi\)
\(674\) 24.1356 + 13.9347i 0.929667 + 0.536743i
\(675\) −1.30590 5.02938i −0.0502642 0.193581i
\(676\) 5.49849 + 9.52366i 0.211480 + 0.366294i
\(677\) 36.5408 1.40438 0.702188 0.711991i \(-0.252207\pi\)
0.702188 + 0.711991i \(0.252207\pi\)
\(678\) 1.90433 7.03428i 0.0731354 0.270150i
\(679\) −0.272894 4.24532i −0.0104727 0.162921i
\(680\) −1.17857 0.680447i −0.0451960 0.0260940i
\(681\) −7.78160 + 28.7439i −0.298192 + 1.10147i
\(682\) 0.853773 + 0.492926i 0.0326927 + 0.0188751i
\(683\) −36.6115 + 21.1377i −1.40090 + 0.808811i −0.994485 0.104878i \(-0.966555\pi\)
−0.406416 + 0.913688i \(0.633222\pi\)
\(684\) −19.8546 0.102641i −0.759159 0.00392459i
\(685\) 3.39189i 0.129597i
\(686\) −3.54459 18.1779i −0.135333 0.694035i
\(687\) 4.41169 4.38894i 0.168316 0.167449i
\(688\) 1.06723 + 1.84849i 0.0406877 + 0.0704731i
\(689\) −13.7358 −0.523293
\(690\) 2.89436 10.6913i 0.110187 0.407011i
\(691\) 31.0692i 1.18193i −0.806698 0.590964i \(-0.798748\pi\)
0.806698 0.590964i \(-0.201252\pi\)
\(692\) −7.20429 −0.273866
\(693\) 0.738853 1.47428i 0.0280667 0.0560034i
\(694\) 8.89161 0.337521
\(695\) 5.86197i 0.222357i
\(696\) −8.62918 8.67390i −0.327088 0.328783i
\(697\) −3.84438 −0.145616
\(698\) −13.2732 22.9898i −0.502398 0.870178i
\(699\) 35.5440 + 9.62253i 1.34440 + 0.363957i
\(700\) 1.46713 + 2.20171i 0.0554524 + 0.0832167i
\(701\) 27.7518i 1.04817i 0.851666 + 0.524085i \(0.175593\pi\)
−0.851666 + 0.524085i \(0.824407\pi\)
\(702\) −1.84822 7.11800i −0.0697567 0.268651i
\(703\) 15.2333 8.79497i 0.574536 0.331709i
\(704\) 0.179928 + 0.103881i 0.00678128 + 0.00391517i
\(705\) −0.140094 0.140820i −0.00527623 0.00530358i
\(706\) −25.8117 14.9024i −0.971437 0.560859i
\(707\) −8.96130 13.4481i −0.337024 0.505768i
\(708\) 14.5478 3.85779i 0.546739 0.144985i
\(709\) 14.2174 0.533944 0.266972 0.963704i \(-0.413977\pi\)
0.266972 + 0.963704i \(0.413977\pi\)
\(710\) −1.72769 2.99245i −0.0648392 0.112305i
\(711\) 41.5706 23.7151i 1.55902 0.889387i
\(712\) 2.44178 + 1.40976i 0.0915097 + 0.0528331i
\(713\) −15.1720 26.2787i −0.568196 0.984144i
\(714\) 1.98192 + 5.91309i 0.0741716 + 0.221292i
\(715\) 0.147022 0.254649i 0.00549830 0.00952333i
\(716\) 12.7104 7.33833i 0.475008 0.274246i
\(717\) 8.08626 + 2.18912i 0.301987 + 0.0817543i
\(718\) −8.47101 + 14.6722i −0.316135 + 0.547562i
\(719\) −21.6234 + 37.4528i −0.806415 + 1.39675i 0.108916 + 0.994051i \(0.465262\pi\)
−0.915332 + 0.402701i \(0.868071\pi\)
\(720\) −2.59029 1.51341i −0.0965343 0.0564015i
\(721\) −1.12294 17.4693i −0.0418207 0.650591i
\(722\) 21.4789 12.4008i 0.799361 0.461511i
\(723\) −2.69158 0.728669i −0.100101 0.0270995i
\(724\) 20.6504i 0.767465i
\(725\) 7.06398i 0.262349i
\(726\) 13.4540 13.3846i 0.499324 0.496749i
\(727\) 2.32159 1.34037i 0.0861032 0.0497117i −0.456330 0.889811i \(-0.650836\pi\)
0.542433 + 0.840099i \(0.317503\pi\)
\(728\) 2.07641 + 3.11604i 0.0769569 + 0.115488i
\(729\) 0.418721 26.9968i 0.0155082 0.999880i
\(730\) 6.68529 11.5793i 0.247434 0.428568i
\(731\) 1.45238 2.51560i 0.0537184 0.0930430i
\(732\) −0.948914 3.57837i −0.0350729 0.132260i
\(733\) 18.7946 10.8511i 0.694196 0.400794i −0.110986 0.993822i \(-0.535401\pi\)
0.805182 + 0.593028i \(0.202068\pi\)
\(734\) 10.5218 18.2244i 0.388368 0.672674i
\(735\) 1.64382 12.0124i 0.0606332 0.443084i
\(736\) −3.19741 5.53808i −0.117858 0.204136i
\(737\) −0.00846463 0.00488705i −0.000311799 0.000180017i
\(738\) −8.47457 0.0438106i −0.311953 0.00161269i
\(739\) −0.779082 1.34941i −0.0286590 0.0496389i 0.851340 0.524614i \(-0.175790\pi\)
−0.879999 + 0.474975i \(0.842457\pi\)
\(740\) 2.65778 0.0977020
\(741\) 11.4422 + 11.5015i 0.420339 + 0.422518i
\(742\) 25.6250 1.64720i 0.940724 0.0604707i
\(743\) −5.56936 3.21547i −0.204320 0.117964i 0.394349 0.918961i \(-0.370970\pi\)
−0.598669 + 0.800997i \(0.704303\pi\)
\(744\) −7.94416 + 2.10664i −0.291247 + 0.0772331i
\(745\) −19.3671 11.1816i −0.709556 0.409662i
\(746\) 9.72660 5.61566i 0.356116 0.205604i
\(747\) 41.7562 + 24.3967i 1.52778 + 0.892627i
\(748\) 0.282743i 0.0103381i
\(749\) −11.8197 + 7.87616i −0.431881 + 0.287789i
\(750\) 0.443962 + 1.67419i 0.0162112 + 0.0611326i
\(751\) −27.3420 47.3577i −0.997722 1.72811i −0.557280 0.830324i \(-0.688155\pi\)
−0.440442 0.897781i \(-0.645178\pi\)
\(752\) −0.114683 −0.00418205
\(753\) 4.79341 1.27112i 0.174682 0.0463222i
\(754\) 9.99753i 0.364089i
\(755\) 12.6238 0.459427
\(756\) 4.30157 + 13.0574i 0.156447 + 0.474894i
\(757\) 6.88087 0.250089 0.125045 0.992151i \(-0.460093\pi\)
0.125045 + 0.992151i \(0.460093\pi\)
\(758\) 2.41836i 0.0878387i
\(759\) 2.22433 0.589850i 0.0807381 0.0214102i
\(760\) 6.61828 0.240070
\(761\) −10.1827 17.6370i −0.369123 0.639340i 0.620306 0.784360i \(-0.287009\pi\)
−0.989429 + 0.145020i \(0.953675\pi\)
\(762\) −6.64129 25.0444i −0.240588 0.907262i
\(763\) −48.1736 + 3.09665i −1.74400 + 0.112106i
\(764\) 21.9525i 0.794214i
\(765\) −0.0211058 + 4.08263i −0.000763081 + 0.147608i
\(766\) −15.1569 + 8.75083i −0.547640 + 0.316180i
\(767\) −10.6504 6.14903i −0.384565 0.222029i
\(768\) −1.67419 + 0.443962i −0.0604120 + 0.0160201i
\(769\) −17.8787 10.3223i −0.644721 0.372230i 0.141710 0.989908i \(-0.454740\pi\)
−0.786431 + 0.617678i \(0.788073\pi\)
\(770\) −0.243740 + 0.492694i −0.00878380 + 0.0177555i
\(771\) 38.4447 + 38.6440i 1.38455 + 1.39173i
\(772\) −20.6101 −0.741772
\(773\) 13.4607 + 23.3145i 0.484146 + 0.838566i 0.999834 0.0182107i \(-0.00579695\pi\)
−0.515688 + 0.856776i \(0.672464\pi\)
\(774\) 3.23031 5.52885i 0.116111 0.198731i
\(775\) 4.10937 + 2.37255i 0.147613 + 0.0852244i
\(776\) −0.803947 1.39248i −0.0288600 0.0499870i
\(777\) −9.12610 8.06561i −0.327397 0.289352i
\(778\) −3.35481 + 5.81070i −0.120276 + 0.208324i
\(779\) 16.1912 9.34797i 0.580109 0.334926i
\(780\) 0.628332 + 2.36945i 0.0224979 + 0.0848399i
\(781\) 0.358950 0.621720i 0.0128442 0.0222469i
\(782\) −4.35134 + 7.53673i −0.155603 + 0.269513i
\(783\) −9.77472 + 35.3801i −0.349320 + 1.26438i
\(784\) −4.24735 5.56417i −0.151691 0.198720i
\(785\) 5.02485 2.90110i 0.179345 0.103545i
\(786\) 20.6203 20.5140i 0.735503 0.731711i
\(787\) 27.2324i 0.970730i −0.874311 0.485365i \(-0.838687\pi\)
0.874311 0.485365i \(-0.161313\pi\)
\(788\) 9.49837i 0.338365i
\(789\) 5.50549 + 1.49045i 0.196001 + 0.0530616i
\(790\) −13.8158 + 7.97657i −0.491545 + 0.283794i
\(791\) 9.26355 6.17287i 0.329374 0.219482i
\(792\) 0.00322214 0.623280i 0.000114494 0.0221473i
\(793\) −1.51250 + 2.61972i −0.0537104 + 0.0930291i
\(794\) 3.48131 6.02981i 0.123547 0.213990i
\(795\) 16.2260 + 4.39274i 0.575478 + 0.155794i
\(796\) −1.57005 + 0.906467i −0.0556489 + 0.0321289i
\(797\) 12.9468 22.4246i 0.458601 0.794319i −0.540287 0.841481i \(-0.681684\pi\)
0.998887 + 0.0471616i \(0.0150176\pi\)
\(798\) −22.7254 20.0846i −0.804470 0.710988i
\(799\) 0.0780356 + 0.135162i 0.00276070 + 0.00478167i
\(800\) 0.866025 + 0.500000i 0.0306186 + 0.0176777i
\(801\) 0.0437274 8.45847i 0.00154503 0.298865i
\(802\) 5.78798 + 10.0251i 0.204381 + 0.353998i
\(803\) 2.77791 0.0980302
\(804\) 0.0787614 0.0208860i 0.00277770 0.000736592i
\(805\) 14.0795 9.38206i 0.496238 0.330674i
\(806\) 5.81593 + 3.35783i 0.204857 + 0.118274i
\(807\) 23.0745 + 23.1941i 0.812260 + 0.816470i
\(808\) −5.28971 3.05401i −0.186091 0.107440i
\(809\) 20.9833 12.1147i 0.737734 0.425931i −0.0835110 0.996507i \(-0.526613\pi\)
0.821245 + 0.570576i \(0.193280\pi\)
\(810\) −0.0930513 + 8.99952i −0.00326949 + 0.316211i
\(811\) 26.9699i 0.947040i −0.880783 0.473520i \(-0.842983\pi\)
0.880783 0.473520i \(-0.157017\pi\)
\(812\) −1.19891 18.6510i −0.0420734 0.654523i
\(813\) −5.38538 1.45794i −0.188873 0.0511321i
\(814\) 0.276094 + 0.478209i 0.00967708 + 0.0167612i
\(815\) −17.9738 −0.629595
\(816\) 1.66243 + 1.67105i 0.0581968 + 0.0584985i
\(817\) 14.1264i 0.494221i
\(818\) 36.3280 1.27018
\(819\) 5.03308 10.0429i 0.175870 0.350926i
\(820\) 2.82489 0.0986496
\(821\) 1.99919i 0.0697722i 0.999391 + 0.0348861i \(0.0111068\pi\)
−0.999391 + 0.0348861i \(0.988893\pi\)
\(822\) −1.53521 + 5.67079i −0.0535464 + 0.197792i
\(823\) −6.28847 −0.219202 −0.109601 0.993976i \(-0.534957\pi\)
−0.109601 + 0.993976i \(0.534957\pi\)
\(824\) −3.30820 5.72998i −0.115247 0.199613i
\(825\) −0.255113 + 0.253798i −0.00888190 + 0.00883610i
\(826\) 20.6065 + 10.1942i 0.716990 + 0.354702i
\(827\) 43.5204i 1.51335i 0.653789 + 0.756677i \(0.273178\pi\)
−0.653789 + 0.756677i \(0.726822\pi\)
\(828\) −9.67799 + 16.5644i −0.336333 + 0.575653i
\(829\) −28.3927 + 16.3926i −0.986120 + 0.569337i −0.904112 0.427295i \(-0.859467\pi\)
−0.0820080 + 0.996632i \(0.526133\pi\)
\(830\) −13.9606 8.06016i −0.484579 0.279772i
\(831\) 0.0538396 0.198874i 0.00186767 0.00689888i
\(832\) 1.22567 + 0.707642i 0.0424925 + 0.0245331i
\(833\) −3.66766 + 8.79192i −0.127077 + 0.304622i
\(834\) 2.65319 9.80044i 0.0918725 0.339362i
\(835\) −10.0107 −0.346436
\(836\) 0.687516 + 1.19081i 0.0237782 + 0.0411851i
\(837\) 17.2989 + 17.5692i 0.597936 + 0.607282i
\(838\) 27.7808 + 16.0393i 0.959673 + 0.554067i
\(839\) 4.60486 + 7.97586i 0.158978 + 0.275357i 0.934500 0.355962i \(-0.115847\pi\)
−0.775523 + 0.631320i \(0.782514\pi\)
\(840\) −1.45634 4.34501i −0.0502484 0.149917i
\(841\) 10.4499 18.0997i 0.360341 0.624128i
\(842\) −10.2565 + 5.92162i −0.353464 + 0.204072i
\(843\) 16.0912 16.0083i 0.554212 0.551354i
\(844\) −11.3768 + 19.7053i −0.391607 + 0.678283i
\(845\) −5.49849 + 9.52366i −0.189154 + 0.327624i
\(846\) 0.170482 + 0.298840i 0.00586128 + 0.0102743i
\(847\) 28.9294 1.85961i 0.994024 0.0638969i
\(848\) 8.40507 4.85267i 0.288631 0.166641i
\(849\) −11.1225 41.9430i −0.381722 1.43948i
\(850\) 1.36089i 0.0466783i
\(851\) 16.9960i 0.582616i
\(852\) 1.53406 + 5.78496i 0.0525560 + 0.198189i
\(853\) 34.0668 19.6685i 1.16642 0.673435i 0.213589 0.976924i \(-0.431485\pi\)
0.952835 + 0.303489i \(0.0981514\pi\)
\(854\) 2.50750 5.06864i 0.0858050 0.173445i
\(855\) −9.83840 17.2459i −0.336466 0.589797i
\(856\) −2.68420 + 4.64917i −0.0917441 + 0.158905i
\(857\) 16.2056 28.0689i 0.553573 0.958816i −0.444440 0.895809i \(-0.646597\pi\)
0.998013 0.0630079i \(-0.0200693\pi\)
\(858\) −0.361058 + 0.359196i −0.0123263 + 0.0122627i
\(859\) −22.8803 + 13.2099i −0.780665 + 0.450717i −0.836666 0.547713i \(-0.815498\pi\)
0.0560006 + 0.998431i \(0.482165\pi\)
\(860\) −1.06723 + 1.84849i −0.0363922 + 0.0630331i
\(861\) −9.69992 8.57275i −0.330572 0.292159i
\(862\) 16.3082 + 28.2466i 0.555459 + 0.962084i
\(863\) −24.4007 14.0878i −0.830610 0.479553i 0.0234518 0.999725i \(-0.492534\pi\)
−0.854061 + 0.520172i \(0.825868\pi\)
\(864\) 3.64563 + 3.70262i 0.124027 + 0.125966i
\(865\) −3.60215 6.23910i −0.122477 0.212136i
\(866\) 1.82172 0.0619045
\(867\) −6.85613 + 25.3254i −0.232846 + 0.860096i
\(868\) −11.2526 5.56679i −0.381940 0.188949i
\(869\) −2.87041 1.65723i −0.0973721 0.0562178i
\(870\) 3.19723 11.8100i 0.108396 0.400398i
\(871\) −0.0576612 0.0332907i −0.00195378 0.00112801i
\(872\) −15.8011 + 9.12274i −0.535091 + 0.308935i
\(873\) −2.43340 + 4.16491i −0.0823582 + 0.140961i
\(874\) 42.3227i 1.43159i
\(875\) −1.17317 + 2.37143i −0.0396603 + 0.0801689i
\(876\) −16.4178 + 16.3332i −0.554707 + 0.551847i
\(877\) −18.1740 31.4782i −0.613691 1.06294i −0.990613 0.136699i \(-0.956351\pi\)
0.376921 0.926245i \(-0.376983\pi\)
\(878\) 23.8749 0.805739
\(879\) −0.658744 + 2.43329i −0.0222189 + 0.0820729i
\(880\) 0.207763i 0.00700368i
\(881\) −0.589367 −0.0198563 −0.00992814 0.999951i \(-0.503160\pi\)
−0.00992814 + 0.999951i \(0.503160\pi\)
\(882\) −8.18519 + 19.3391i −0.275610 + 0.651183i
\(883\) 55.1932 1.85740 0.928700 0.370833i \(-0.120928\pi\)
0.928700 + 0.370833i \(0.120928\pi\)
\(884\) 1.92605i 0.0647801i
\(885\) 10.6148 + 10.6699i 0.356814 + 0.358663i
\(886\) 23.6199 0.793527
\(887\) 25.4014 + 43.9965i 0.852896 + 1.47726i 0.878584 + 0.477588i \(0.158489\pi\)
−0.0256882 + 0.999670i \(0.508178\pi\)
\(888\) −4.44346 1.20294i −0.149113 0.0403680i
\(889\) 17.5496 35.4745i 0.588594 1.18978i
\(890\) 2.81953i 0.0945108i
\(891\) −1.62893 + 0.918139i −0.0545712 + 0.0307588i
\(892\) −8.80329 + 5.08258i −0.294756 + 0.170177i
\(893\) −0.657316 0.379502i −0.0219962 0.0126995i
\(894\) 27.3183 + 27.4599i 0.913662 + 0.918397i
\(895\) 12.7104 + 7.33833i 0.424860 + 0.245293i
\(896\) −2.37143 1.17317i −0.0792239 0.0391928i
\(897\) 15.1522 4.01807i 0.505917 0.134159i
\(898\) −33.6640 −1.12338
\(899\) −16.7596 29.0285i −0.558964 0.968154i
\(900\) 0.0155088 2.99996i 0.000516958 0.0999987i
\(901\) −11.4384 6.60397i −0.381068 0.220010i
\(902\) 0.293454 + 0.508277i 0.00977094 + 0.0169238i
\(903\) 9.27423 3.10849i 0.308627 0.103444i
\(904\) 2.10372 3.64375i 0.0699687 0.121189i
\(905\) 17.8838 10.3252i 0.594476 0.343221i
\(906\) −21.1053 5.71367i −0.701178 0.189824i
\(907\) 9.74779 16.8837i 0.323670 0.560613i −0.657572 0.753392i \(-0.728417\pi\)
0.981242 + 0.192778i \(0.0617499\pi\)
\(908\) −8.59635 + 14.8893i −0.285280 + 0.494119i
\(909\) −0.0947279 + 18.3238i −0.00314193 + 0.607764i
\(910\) −1.66037 + 3.35625i −0.0550406 + 0.111258i
\(911\) 29.5749 17.0751i 0.979860 0.565723i 0.0776324 0.996982i \(-0.475264\pi\)
0.902228 + 0.431259i \(0.141931\pi\)
\(912\) −11.0649 2.99551i −0.366395 0.0991911i
\(913\) 3.34920i 0.110842i
\(914\) 18.1990i 0.601971i
\(915\) 2.62450 2.61097i 0.0867633 0.0863159i
\(916\) 3.11150 1.79643i 0.102807 0.0593556i
\(917\) 44.3388 2.85014i 1.46420 0.0941200i
\(918\) 1.88313 6.81606i 0.0621524 0.224964i
\(919\) −8.23460 + 14.2627i −0.271634 + 0.470484i −0.969280 0.245958i \(-0.920897\pi\)
0.697646 + 0.716442i \(0.254231\pi\)
\(920\) 3.19741 5.53808i 0.105415 0.182585i
\(921\) 0.134217 + 0.506134i 0.00442260 + 0.0166777i
\(922\) 12.6989 7.33169i 0.418215 0.241456i
\(923\) 2.44518 4.23517i 0.0804840 0.139402i
\(924\) 0.630501 0.713401i 0.0207420 0.0234692i
\(925\) 1.32889 + 2.30171i 0.0436937 + 0.0756796i
\(926\) 5.55635 + 3.20796i 0.182593 + 0.105420i
\(927\) −10.0133 + 17.1384i −0.328881 + 0.562899i
\(928\) −3.53199 6.11758i −0.115943 0.200820i
\(929\) −11.7221 −0.384589 −0.192294 0.981337i \(-0.561593\pi\)
−0.192294 + 0.981337i \(0.561593\pi\)
\(930\) −5.79648 5.82653i −0.190074 0.191059i
\(931\) −5.93151 45.9467i −0.194397 1.50584i
\(932\) 18.4117 + 10.6300i 0.603097 + 0.348198i
\(933\) −0.530987 + 0.140807i −0.0173837 + 0.00460983i
\(934\) −22.6399 13.0712i −0.740801 0.427702i
\(935\) 0.244863 0.141371i 0.00800786 0.00462334i
\(936\) 0.0219493 4.24580i 0.000717435 0.138778i
\(937\) 10.5888i 0.345922i 0.984929 + 0.172961i \(0.0553334\pi\)
−0.984929 + 0.172961i \(0.944667\pi\)
\(938\) 0.111563 + 0.0551912i 0.00364266 + 0.00180206i
\(939\) 9.38142 + 35.3775i 0.306151 + 1.15450i
\(940\) −0.0573414 0.0993182i −0.00187027 0.00323940i
\(941\) 11.6282 0.379070 0.189535 0.981874i \(-0.439302\pi\)
0.189535 + 0.981874i \(0.439302\pi\)
\(942\) −9.71395 + 2.57595i −0.316498 + 0.0839291i
\(943\) 18.0647i 0.588267i
\(944\) 8.68947 0.282818
\(945\) −9.15728 + 10.2540i −0.297886 + 0.333562i
\(946\) −0.443460 −0.0144181
\(947\) 2.07406i 0.0673978i 0.999432 + 0.0336989i \(0.0107287\pi\)
−0.999432 + 0.0336989i \(0.989271\pi\)
\(948\) 26.7085 7.08258i 0.867452 0.230032i
\(949\) 18.9232 0.614272
\(950\) 3.30914 + 5.73160i 0.107363 + 0.185958i
\(951\) 4.51880 + 17.0405i 0.146532 + 0.552575i
\(952\) 0.230973 + 3.59317i 0.00748587 + 0.116455i
\(953\) 28.8160i 0.933442i 0.884405 + 0.466721i \(0.154565\pi\)
−0.884405 + 0.466721i \(0.845435\pi\)
\(954\) −25.1396 14.6882i −0.813925 0.475547i
\(955\) 19.0114 10.9763i 0.615195 0.355183i
\(956\) 4.18867 + 2.41833i 0.135471 + 0.0782144i
\(957\) 2.45709 0.651572i 0.0794263 0.0210623i
\(958\) −29.2068 16.8626i −0.943629 0.544805i
\(959\) −7.46795 + 4.97636i −0.241153 + 0.160695i
\(960\) −1.22158 1.22791i −0.0394262 0.0396305i
\(961\) 8.48411 0.273681
\(962\) 1.88076 + 3.25757i 0.0606381 + 0.105028i
\(963\) 16.1050 + 0.0832572i 0.518976 + 0.00268293i
\(964\) −1.39424 0.804962i −0.0449053 0.0259261i
\(965\) −10.3050 17.8488i −0.331731 0.574574i
\(966\) −27.7855 + 9.31302i −0.893985 + 0.299641i
\(967\) −9.12278 + 15.8011i −0.293369 + 0.508130i −0.974604 0.223935i \(-0.928110\pi\)
0.681235 + 0.732065i \(0.261443\pi\)
\(968\) 9.48890 5.47842i 0.304985 0.176083i
\(969\) 3.99867 + 15.0790i 0.128456 + 0.484408i
\(970\) 0.803947 1.39248i 0.0258132 0.0447097i
\(971\) 1.09564 1.89770i 0.0351606 0.0609000i −0.847910 0.530141i \(-0.822139\pi\)
0.883070 + 0.469241i \(0.155472\pi\)
\(972\) 4.22885 15.0039i 0.135640 0.481250i
\(973\) 12.9063 8.60030i 0.413759 0.275713i
\(974\) 5.86349 3.38529i 0.187878 0.108472i
\(975\) −1.73784 + 1.72888i −0.0556553 + 0.0553683i
\(976\) 2.13738i 0.0684158i
\(977\) 0.250099i 0.00800137i −0.999992 0.00400068i \(-0.998727\pi\)
0.999992 0.00400068i \(-0.00127346\pi\)
\(978\) 30.0498 + 8.13513i 0.960887 + 0.260133i
\(979\) −0.507311 + 0.292896i −0.0162137 + 0.00936101i
\(980\) 2.69504 6.46040i 0.0860898 0.206370i
\(981\) 47.2611 + 27.6129i 1.50893 + 0.881613i
\(982\) −4.54300 + 7.86871i −0.144973 + 0.251101i
\(983\) −1.60860 + 2.78618i −0.0513064 + 0.0888654i −0.890538 0.454909i \(-0.849672\pi\)
0.839232 + 0.543774i \(0.183005\pi\)
\(984\) −4.72285 1.27858i −0.150559 0.0407595i
\(985\) −8.22583 + 4.74918i −0.262097 + 0.151322i
\(986\) −4.80666 + 8.32538i −0.153075 + 0.265134i
\(987\) −0.104508 + 0.515047i −0.00332652 + 0.0163941i
\(988\) 4.68338 + 8.11184i 0.148998 + 0.258072i
\(989\) 11.8208 + 6.82473i 0.375879 + 0.217014i
\(990\) 0.541387 0.308849i 0.0172064 0.00981588i
\(991\) −0.704168 1.21966i −0.0223686 0.0387436i 0.854624 0.519247i \(-0.173787\pi\)
−0.876993 + 0.480503i \(0.840454\pi\)
\(992\) −4.74509 −0.150657
\(993\) 37.1337 9.84714i 1.17840 0.312489i
\(994\) −4.05375 + 8.19421i −0.128577 + 0.259904i
\(995\) −1.57005 0.906467i −0.0497739 0.0287369i
\(996\) 19.6922 + 19.7942i 0.623970 + 0.627204i
\(997\) −31.0456 17.9242i −0.983224 0.567664i −0.0799817 0.996796i \(-0.525486\pi\)
−0.903242 + 0.429132i \(0.858820\pi\)
\(998\) 36.4240 21.0294i 1.15298 0.665675i
\(999\) 3.47080 + 13.3670i 0.109811 + 0.422913i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 630.2.bk.b.131.2 yes 28
3.2 odd 2 1890.2.bk.b.341.7 28
7.3 odd 6 630.2.t.b.311.10 28
9.2 odd 6 630.2.t.b.551.10 yes 28
9.7 even 3 1890.2.t.b.1601.6 28
21.17 even 6 1890.2.t.b.1151.6 28
63.38 even 6 inner 630.2.bk.b.101.9 yes 28
63.52 odd 6 1890.2.bk.b.521.7 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.t.b.311.10 28 7.3 odd 6
630.2.t.b.551.10 yes 28 9.2 odd 6
630.2.bk.b.101.9 yes 28 63.38 even 6 inner
630.2.bk.b.131.2 yes 28 1.1 even 1 trivial
1890.2.t.b.1151.6 28 21.17 even 6
1890.2.t.b.1601.6 28 9.7 even 3
1890.2.bk.b.341.7 28 3.2 odd 2
1890.2.bk.b.521.7 28 63.52 odd 6