Properties

Label 585.2.bt.b.571.33
Level $585$
Weight $2$
Character 585.571
Analytic conductor $4.671$
Analytic rank $0$
Dimension $108$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [585,2,Mod(376,585)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("585.376");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.bt (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: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(54\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 571.33
Character \(\chi\) \(=\) 585.571
Dual form 585.2.bt.b.376.33

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.569525 - 0.328815i) q^{2} +(1.49163 - 0.880367i) q^{3} +(-0.783761 + 1.35751i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.560040 - 0.991861i) q^{6} +(0.282702 - 0.163218i) q^{7} +2.34611i q^{8} +(1.44991 - 2.62636i) q^{9} +O(q^{10})\) \(q+(0.569525 - 0.328815i) q^{2} +(1.49163 - 0.880367i) q^{3} +(-0.783761 + 1.35751i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.560040 - 0.991861i) q^{6} +(0.282702 - 0.163218i) q^{7} +2.34611i q^{8} +(1.44991 - 2.62636i) q^{9} +0.657630 q^{10} +(-1.86962 + 1.07943i) q^{11} +(0.0260313 + 2.71490i) q^{12} +(3.53934 + 0.687825i) q^{13} +(0.107337 - 0.185913i) q^{14} +(1.73197 - 0.0166067i) q^{15} +(-0.796086 - 1.37886i) q^{16} +7.02806 q^{17} +(-0.0378299 - 1.97253i) q^{18} +1.98213i q^{19} +(-1.35751 + 0.783761i) q^{20} +(0.277994 - 0.492341i) q^{21} +(-0.709864 + 1.22952i) q^{22} +(1.07152 - 1.85592i) q^{23} +(2.06544 + 3.49952i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.24191 - 0.772054i) q^{26} +(-0.149442 - 5.19400i) q^{27} +0.511695i q^{28} +(1.80200 + 3.12115i) q^{29} +(0.980940 - 0.578956i) q^{30} +(-6.45532 - 3.72698i) q^{31} +(-4.97036 - 2.86964i) q^{32} +(-1.83849 + 3.25606i) q^{33} +(4.00265 - 2.31093i) q^{34} +0.326436 q^{35} +(2.42894 + 4.02671i) q^{36} +7.86547i q^{37} +(0.651755 + 1.12887i) q^{38} +(5.88491 - 2.08994i) q^{39} +(-1.17306 + 2.03179i) q^{40} +(-3.36407 - 1.94224i) q^{41} +(-0.00356502 - 0.371809i) q^{42} +(-2.83158 - 4.90444i) q^{43} -3.38405i q^{44} +(2.56884 - 1.54954i) q^{45} -1.40932i q^{46} +(0.0831560 - 0.0480102i) q^{47} +(-2.40137 - 1.35590i) q^{48} +(-3.44672 + 5.96989i) q^{49} +(0.569525 + 0.328815i) q^{50} +(10.4832 - 6.18727i) q^{51} +(-3.70773 + 4.26561i) q^{52} -2.33484 q^{53} +(-1.79298 - 2.90897i) q^{54} -2.15885 q^{55} +(0.382927 + 0.663249i) q^{56} +(1.74500 + 2.95660i) q^{57} +(2.05256 + 1.18505i) q^{58} +(8.49087 + 4.90221i) q^{59} +(-1.33491 + 2.36419i) q^{60} +(-7.60709 - 13.1759i) q^{61} -4.90195 q^{62} +(-0.0187781 - 0.979127i) q^{63} -0.589982 q^{64} +(2.72124 + 2.36534i) q^{65} +(0.0235770 + 2.45893i) q^{66} +(-4.62569 - 2.67064i) q^{67} +(-5.50832 + 9.54069i) q^{68} +(-0.0355886 - 3.71167i) q^{69} +(0.185913 - 0.107337i) q^{70} -11.6852i q^{71} +(6.16173 + 3.40164i) q^{72} -12.1088i q^{73} +(2.58629 + 4.47958i) q^{74} +(1.50823 + 0.851604i) q^{75} +(-2.69077 - 1.55352i) q^{76} +(-0.352364 + 0.610312i) q^{77} +(2.66440 - 3.12532i) q^{78} +(-5.54372 - 9.60200i) q^{79} -1.59217i q^{80} +(-4.79554 - 7.61596i) q^{81} -2.55456 q^{82} +(-13.8398 + 7.99043i) q^{83} +(0.450480 + 0.763259i) q^{84} +(6.08648 + 3.51403i) q^{85} +(-3.22531 - 1.86213i) q^{86} +(5.43567 + 3.06918i) q^{87} +(-2.53246 - 4.38634i) q^{88} +7.29707i q^{89} +(0.953502 - 1.72717i) q^{90} +(1.11284 - 0.383233i) q^{91} +(1.67962 + 2.90920i) q^{92} +(-12.9100 + 0.123786i) q^{93} +(0.0315729 - 0.0546859i) q^{94} +(-0.991066 + 1.71658i) q^{95} +(-9.94027 + 0.0953104i) q^{96} +(1.55370 - 0.897027i) q^{97} +4.53333i q^{98} +(0.124187 + 6.47537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.569525 0.328815i 0.402715 0.232507i −0.284940 0.958545i \(-0.591974\pi\)
0.687655 + 0.726038i \(0.258640\pi\)
\(3\) 1.49163 0.880367i 0.861192 0.508280i
\(4\) −0.783761 + 1.35751i −0.391881 + 0.678757i
\(5\) 0.866025 + 0.500000i 0.387298 + 0.223607i
\(6\) 0.560040 0.991861i 0.228636 0.404925i
\(7\) 0.282702 0.163218i 0.106851 0.0616905i −0.445622 0.895221i \(-0.647017\pi\)
0.552473 + 0.833531i \(0.313684\pi\)
\(8\) 2.34611i 0.829475i
\(9\) 1.44991 2.62636i 0.483302 0.875454i
\(10\) 0.657630 0.207961
\(11\) −1.86962 + 1.07943i −0.563713 + 0.325460i −0.754634 0.656146i \(-0.772186\pi\)
0.190922 + 0.981605i \(0.438852\pi\)
\(12\) 0.0260313 + 2.71490i 0.00751460 + 0.783725i
\(13\) 3.53934 + 0.687825i 0.981635 + 0.190768i
\(14\) 0.107337 0.185913i 0.0286870 0.0496874i
\(15\) 1.73197 0.0166067i 0.447193 0.00428783i
\(16\) −0.796086 1.37886i −0.199021 0.344715i
\(17\) 7.02806 1.70455 0.852277 0.523090i \(-0.175221\pi\)
0.852277 + 0.523090i \(0.175221\pi\)
\(18\) −0.0378299 1.97253i −0.00891659 0.464929i
\(19\) 1.98213i 0.454732i 0.973809 + 0.227366i \(0.0730114\pi\)
−0.973809 + 0.227366i \(0.926989\pi\)
\(20\) −1.35751 + 0.783761i −0.303549 + 0.175254i
\(21\) 0.277994 0.492341i 0.0606632 0.107438i
\(22\) −0.709864 + 1.22952i −0.151344 + 0.262135i
\(23\) 1.07152 1.85592i 0.223426 0.386986i −0.732420 0.680853i \(-0.761609\pi\)
0.955846 + 0.293867i \(0.0949424\pi\)
\(24\) 2.06544 + 3.49952i 0.421606 + 0.714337i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 2.24191 0.772054i 0.439674 0.151412i
\(27\) −0.149442 5.19400i −0.0287601 0.999586i
\(28\) 0.511695i 0.0967013i
\(29\) 1.80200 + 3.12115i 0.334623 + 0.579583i 0.983412 0.181384i \(-0.0580578\pi\)
−0.648790 + 0.760968i \(0.724724\pi\)
\(30\) 0.980940 0.578956i 0.179094 0.105702i
\(31\) −6.45532 3.72698i −1.15941 0.669386i −0.208247 0.978076i \(-0.566776\pi\)
−0.951163 + 0.308691i \(0.900109\pi\)
\(32\) −4.97036 2.86964i −0.878644 0.507286i
\(33\) −1.83849 + 3.25606i −0.320040 + 0.566807i
\(34\) 4.00265 2.31093i 0.686449 0.396322i
\(35\) 0.326436 0.0551777
\(36\) 2.42894 + 4.02671i 0.404824 + 0.671118i
\(37\) 7.86547i 1.29308i 0.762882 + 0.646538i \(0.223784\pi\)
−0.762882 + 0.646538i \(0.776216\pi\)
\(38\) 0.651755 + 1.12887i 0.105729 + 0.183127i
\(39\) 5.88491 2.08994i 0.942340 0.334658i
\(40\) −1.17306 + 2.03179i −0.185476 + 0.321254i
\(41\) −3.36407 1.94224i −0.525379 0.303328i 0.213754 0.976888i \(-0.431431\pi\)
−0.739133 + 0.673560i \(0.764764\pi\)
\(42\) −0.00356502 0.371809i −0.000550095 0.0573714i
\(43\) −2.83158 4.90444i −0.431812 0.747920i 0.565217 0.824942i \(-0.308792\pi\)
−0.997029 + 0.0770217i \(0.975459\pi\)
\(44\) 3.38405i 0.510165i
\(45\) 2.56884 1.54954i 0.382939 0.230992i
\(46\) 1.40932i 0.207793i
\(47\) 0.0831560 0.0480102i 0.0121296 0.00700300i −0.493923 0.869506i \(-0.664438\pi\)
0.506053 + 0.862503i \(0.331104\pi\)
\(48\) −2.40137 1.35590i −0.346608 0.195707i
\(49\) −3.44672 + 5.96989i −0.492389 + 0.852842i
\(50\) 0.569525 + 0.328815i 0.0805429 + 0.0465015i
\(51\) 10.4832 6.18727i 1.46795 0.866391i
\(52\) −3.70773 + 4.26561i −0.514169 + 0.591533i
\(53\) −2.33484 −0.320715 −0.160358 0.987059i \(-0.551265\pi\)
−0.160358 + 0.987059i \(0.551265\pi\)
\(54\) −1.79298 2.90897i −0.243993 0.395861i
\(55\) −2.15885 −0.291100
\(56\) 0.382927 + 0.663249i 0.0511708 + 0.0886304i
\(57\) 1.74500 + 2.95660i 0.231131 + 0.391612i
\(58\) 2.05256 + 1.18505i 0.269515 + 0.155604i
\(59\) 8.49087 + 4.90221i 1.10542 + 0.638213i 0.937638 0.347612i \(-0.113007\pi\)
0.167778 + 0.985825i \(0.446341\pi\)
\(60\) −1.33491 + 2.36419i −0.172336 + 0.305216i
\(61\) −7.60709 13.1759i −0.973989 1.68700i −0.683233 0.730201i \(-0.739427\pi\)
−0.290756 0.956797i \(-0.593907\pi\)
\(62\) −4.90195 −0.622548
\(63\) −0.0187781 0.979127i −0.00236581 0.123358i
\(64\) −0.589982 −0.0737478
\(65\) 2.72124 + 2.36534i 0.337529 + 0.293385i
\(66\) 0.0235770 + 2.45893i 0.00290212 + 0.302673i
\(67\) −4.62569 2.67064i −0.565118 0.326271i 0.190079 0.981769i \(-0.439125\pi\)
−0.755197 + 0.655498i \(0.772459\pi\)
\(68\) −5.50832 + 9.54069i −0.667982 + 1.15698i
\(69\) −0.0355886 3.71167i −0.00428437 0.446832i
\(70\) 0.185913 0.107337i 0.0222209 0.0128292i
\(71\) 11.6852i 1.38678i −0.720562 0.693390i \(-0.756116\pi\)
0.720562 0.693390i \(-0.243884\pi\)
\(72\) 6.16173 + 3.40164i 0.726167 + 0.400887i
\(73\) 12.1088i 1.41723i −0.705596 0.708614i \(-0.749321\pi\)
0.705596 0.708614i \(-0.250679\pi\)
\(74\) 2.58629 + 4.47958i 0.300650 + 0.520740i
\(75\) 1.50823 + 0.851604i 0.174156 + 0.0983347i
\(76\) −2.69077 1.55352i −0.308653 0.178201i
\(77\) −0.352364 + 0.610312i −0.0401556 + 0.0695515i
\(78\) 2.66440 3.12532i 0.301684 0.353873i
\(79\) −5.54372 9.60200i −0.623717 1.08031i −0.988787 0.149330i \(-0.952288\pi\)
0.365070 0.930980i \(-0.381045\pi\)
\(80\) 1.59217i 0.178010i
\(81\) −4.79554 7.61596i −0.532838 0.846217i
\(82\) −2.55456 −0.282104
\(83\) −13.8398 + 7.99043i −1.51912 + 0.877063i −0.519372 + 0.854548i \(0.673834\pi\)
−0.999747 + 0.0225150i \(0.992833\pi\)
\(84\) 0.450480 + 0.763259i 0.0491514 + 0.0832783i
\(85\) 6.08648 + 3.51403i 0.660171 + 0.381150i
\(86\) −3.22531 1.86213i −0.347794 0.200799i
\(87\) 5.43567 + 3.06918i 0.582765 + 0.329050i
\(88\) −2.53246 4.38634i −0.269961 0.467586i
\(89\) 7.29707i 0.773488i 0.922187 + 0.386744i \(0.126400\pi\)
−0.922187 + 0.386744i \(0.873600\pi\)
\(90\) 0.953502 1.72717i 0.100508 0.182060i
\(91\) 1.11284 0.383233i 0.116657 0.0401738i
\(92\) 1.67962 + 2.90920i 0.175113 + 0.303305i
\(93\) −12.9100 + 0.123786i −1.33871 + 0.0128360i
\(94\) 0.0315729 0.0546859i 0.00325650 0.00564042i
\(95\) −0.991066 + 1.71658i −0.101681 + 0.176117i
\(96\) −9.94027 + 0.0953104i −1.01452 + 0.00972758i
\(97\) 1.55370 0.897027i 0.157754 0.0910793i −0.419045 0.907966i \(-0.637635\pi\)
0.576799 + 0.816886i \(0.304302\pi\)
\(98\) 4.53333i 0.457936i
\(99\) 0.124187 + 6.47537i 0.0124813 + 0.650800i
\(100\) −1.56752 −0.156752
\(101\) 5.13309 + 8.89076i 0.510761 + 0.884664i 0.999922 + 0.0124707i \(0.00396965\pi\)
−0.489161 + 0.872193i \(0.662697\pi\)
\(102\) 3.93600 6.97085i 0.389722 0.690217i
\(103\) −6.44957 + 11.1710i −0.635495 + 1.10071i 0.350916 + 0.936407i \(0.385870\pi\)
−0.986410 + 0.164302i \(0.947463\pi\)
\(104\) −1.61371 + 8.30367i −0.158238 + 0.814242i
\(105\) 0.486920 0.287383i 0.0475186 0.0280457i
\(106\) −1.32975 + 0.767731i −0.129157 + 0.0745687i
\(107\) 10.6783 1.03231 0.516157 0.856494i \(-0.327362\pi\)
0.516157 + 0.856494i \(0.327362\pi\)
\(108\) 7.16806 + 3.86799i 0.689747 + 0.372197i
\(109\) 13.2609i 1.27017i −0.772444 0.635083i \(-0.780966\pi\)
0.772444 0.635083i \(-0.219034\pi\)
\(110\) −1.22952 + 0.709864i −0.117230 + 0.0676829i
\(111\) 6.92450 + 11.7324i 0.657245 + 1.11359i
\(112\) −0.450109 0.259871i −0.0425313 0.0245555i
\(113\) 3.73784 6.47413i 0.351626 0.609035i −0.634908 0.772588i \(-0.718962\pi\)
0.986535 + 0.163553i \(0.0522954\pi\)
\(114\) 1.96600 + 1.11007i 0.184133 + 0.103968i
\(115\) 1.85592 1.07152i 0.173065 0.0999194i
\(116\) −5.64935 −0.524529
\(117\) 6.93818 8.29829i 0.641435 0.767177i
\(118\) 6.44768 0.593557
\(119\) 1.98684 1.14710i 0.182134 0.105155i
\(120\) 0.0389611 + 4.06340i 0.00355665 + 0.370936i
\(121\) −3.16967 + 5.49003i −0.288152 + 0.499094i
\(122\) −8.66485 5.00266i −0.784479 0.452919i
\(123\) −6.72782 + 0.0645085i −0.606627 + 0.00581653i
\(124\) 10.1189 5.84213i 0.908701 0.524639i
\(125\) 1.00000i 0.0894427i
\(126\) −0.332646 0.551462i −0.0296345 0.0491282i
\(127\) −11.9857 −1.06355 −0.531777 0.846884i \(-0.678476\pi\)
−0.531777 + 0.846884i \(0.678476\pi\)
\(128\) 9.60472 5.54529i 0.848945 0.490139i
\(129\) −8.54137 4.82277i −0.752026 0.424621i
\(130\) 2.32757 + 0.452335i 0.204142 + 0.0396724i
\(131\) −9.46251 + 16.3895i −0.826743 + 1.43196i 0.0738364 + 0.997270i \(0.476476\pi\)
−0.900580 + 0.434691i \(0.856858\pi\)
\(132\) −2.97921 5.04775i −0.259307 0.439350i
\(133\) 0.323519 + 0.560352i 0.0280527 + 0.0485887i
\(134\) −3.51259 −0.303441
\(135\) 2.46758 4.57286i 0.212376 0.393569i
\(136\) 16.4886i 1.41389i
\(137\) −7.06326 + 4.07797i −0.603455 + 0.348405i −0.770399 0.637562i \(-0.779943\pi\)
0.166945 + 0.985966i \(0.446610\pi\)
\(138\) −1.24072 2.10218i −0.105617 0.178950i
\(139\) −2.58206 + 4.47226i −0.219008 + 0.379333i −0.954505 0.298195i \(-0.903615\pi\)
0.735497 + 0.677528i \(0.236949\pi\)
\(140\) −0.255848 + 0.443141i −0.0216231 + 0.0374522i
\(141\) 0.0817713 0.144821i 0.00688638 0.0121961i
\(142\) −3.84228 6.65502i −0.322437 0.558477i
\(143\) −7.35968 + 2.53448i −0.615447 + 0.211944i
\(144\) −4.77564 + 0.0915890i −0.397970 + 0.00763242i
\(145\) 3.60400i 0.299296i
\(146\) −3.98156 6.89626i −0.329516 0.570739i
\(147\) 0.114477 + 11.9392i 0.00944192 + 0.984732i
\(148\) −10.6775 6.16465i −0.877684 0.506731i
\(149\) 18.7254 + 10.8111i 1.53404 + 0.885680i 0.999169 + 0.0407488i \(0.0129743\pi\)
0.534874 + 0.844932i \(0.320359\pi\)
\(150\) 1.13900 0.0109211i 0.0929987 0.000891700i
\(151\) 10.6056 6.12314i 0.863071 0.498294i −0.00196859 0.999998i \(-0.500627\pi\)
0.865039 + 0.501704i \(0.167293\pi\)
\(152\) −4.65030 −0.377189
\(153\) 10.1900 18.4582i 0.823815 1.49226i
\(154\) 0.463450i 0.0373459i
\(155\) −3.72698 6.45532i −0.299358 0.518504i
\(156\) −1.77525 + 9.62686i −0.142133 + 0.770766i
\(157\) −1.42241 + 2.46369i −0.113521 + 0.196624i −0.917188 0.398456i \(-0.869546\pi\)
0.803667 + 0.595080i \(0.202880\pi\)
\(158\) −6.31457 3.64572i −0.502360 0.290038i
\(159\) −3.48271 + 2.05552i −0.276197 + 0.163013i
\(160\) −2.86964 4.97036i −0.226865 0.392942i
\(161\) 0.699562i 0.0551332i
\(162\) −5.23542 2.76063i −0.411333 0.216895i
\(163\) 0.319490i 0.0250244i 0.999922 + 0.0125122i \(0.00398286\pi\)
−0.999922 + 0.0125122i \(0.996017\pi\)
\(164\) 5.27325 3.04451i 0.411772 0.237736i
\(165\) −3.22021 + 1.90059i −0.250693 + 0.147960i
\(166\) −5.25475 + 9.10149i −0.407847 + 0.706413i
\(167\) −13.8413 7.99125i −1.07107 0.618382i −0.142596 0.989781i \(-0.545545\pi\)
−0.928473 + 0.371399i \(0.878878\pi\)
\(168\) 1.15509 + 0.652204i 0.0891169 + 0.0503186i
\(169\) 12.0538 + 4.86889i 0.927215 + 0.374530i
\(170\) 4.62186 0.354481
\(171\) 5.20579 + 2.87391i 0.398097 + 0.219773i
\(172\) 8.87713 0.676875
\(173\) 0.891038 + 1.54332i 0.0677443 + 0.117337i 0.897908 0.440183i \(-0.145086\pi\)
−0.830164 + 0.557520i \(0.811753\pi\)
\(174\) 4.10494 0.0393594i 0.311195 0.00298383i
\(175\) 0.282702 + 0.163218i 0.0213702 + 0.0123381i
\(176\) 2.97676 + 1.71863i 0.224382 + 0.129547i
\(177\) 16.9810 0.162819i 1.27637 0.0122382i
\(178\) 2.39939 + 4.15586i 0.179842 + 0.311495i
\(179\) 2.89894 0.216677 0.108338 0.994114i \(-0.465447\pi\)
0.108338 + 0.994114i \(0.465447\pi\)
\(180\) 0.0901711 + 4.70170i 0.00672096 + 0.350444i
\(181\) 1.44881 0.107689 0.0538445 0.998549i \(-0.482852\pi\)
0.0538445 + 0.998549i \(0.482852\pi\)
\(182\) 0.507777 0.584180i 0.0376390 0.0433023i
\(183\) −22.9466 12.9565i −1.69626 0.957769i
\(184\) 4.35419 + 2.51389i 0.320995 + 0.185327i
\(185\) −3.93273 + 6.81170i −0.289140 + 0.500806i
\(186\) −7.31189 + 4.31552i −0.536134 + 0.316429i
\(187\) −13.1398 + 7.58628i −0.960879 + 0.554764i
\(188\) 0.150514i 0.0109774i
\(189\) −0.890001 1.44396i −0.0647381 0.105033i
\(190\) 1.30351i 0.0945666i
\(191\) −1.55424 2.69202i −0.112461 0.194788i 0.804301 0.594222i \(-0.202540\pi\)
−0.916762 + 0.399434i \(0.869207\pi\)
\(192\) −0.880034 + 0.519401i −0.0635110 + 0.0374845i
\(193\) −15.9475 9.20727i −1.14792 0.662754i −0.199543 0.979889i \(-0.563946\pi\)
−0.948380 + 0.317136i \(0.897279\pi\)
\(194\) 0.589912 1.02176i 0.0423532 0.0733580i
\(195\) 6.14145 + 1.13252i 0.439798 + 0.0811012i
\(196\) −5.40281 9.35794i −0.385915 0.668424i
\(197\) 9.35543i 0.666546i −0.942830 0.333273i \(-0.891847\pi\)
0.942830 0.333273i \(-0.108153\pi\)
\(198\) 2.19993 + 3.64705i 0.156342 + 0.259185i
\(199\) 1.93111 0.136893 0.0684463 0.997655i \(-0.478196\pi\)
0.0684463 + 0.997655i \(0.478196\pi\)
\(200\) −2.03179 + 1.17306i −0.143669 + 0.0829475i
\(201\) −9.25095 + 0.0887010i −0.652512 + 0.00625648i
\(202\) 5.84684 + 3.37567i 0.411382 + 0.237511i
\(203\) 1.01886 + 0.588236i 0.0715096 + 0.0412861i
\(204\) 0.182950 + 19.0805i 0.0128090 + 1.33590i
\(205\) −1.94224 3.36407i −0.135652 0.234957i
\(206\) 8.48286i 0.591029i
\(207\) −3.32072 5.50510i −0.230806 0.382631i
\(208\) −1.86920 5.42782i −0.129606 0.376352i
\(209\) −2.13957 3.70584i −0.147997 0.256338i
\(210\) 0.182817 0.323779i 0.0126156 0.0223428i
\(211\) 1.33361 2.30988i 0.0918095 0.159019i −0.816463 0.577398i \(-0.804068\pi\)
0.908273 + 0.418379i \(0.137402\pi\)
\(212\) 1.82996 3.16958i 0.125682 0.217688i
\(213\) −10.2873 17.4300i −0.704873 1.19428i
\(214\) 6.08158 3.51120i 0.415728 0.240021i
\(215\) 5.66316i 0.386224i
\(216\) 12.1857 0.350607i 0.829132 0.0238558i
\(217\) −2.43324 −0.165179
\(218\) −4.36039 7.55242i −0.295323 0.511514i
\(219\) −10.6602 18.0618i −0.720349 1.22051i
\(220\) 1.69203 2.93068i 0.114076 0.197586i
\(221\) 24.8747 + 4.83408i 1.67325 + 0.325175i
\(222\) 7.80145 + 4.40498i 0.523599 + 0.295643i
\(223\) 3.70928 2.14155i 0.248392 0.143409i −0.370636 0.928778i \(-0.620860\pi\)
0.619028 + 0.785369i \(0.287527\pi\)
\(224\) −1.87351 −0.125179
\(225\) 2.99945 0.0575246i 0.199963 0.00383497i
\(226\) 4.91623i 0.327023i
\(227\) 21.5080 12.4176i 1.42753 0.824187i 0.430608 0.902539i \(-0.358299\pi\)
0.996926 + 0.0783523i \(0.0249659\pi\)
\(228\) −5.38130 + 0.0515976i −0.356385 + 0.00341713i
\(229\) −3.19530 1.84480i −0.211151 0.121908i 0.390695 0.920520i \(-0.372235\pi\)
−0.601846 + 0.798612i \(0.705568\pi\)
\(230\) 0.704661 1.22051i 0.0464640 0.0804780i
\(231\) 0.0117032 + 1.22057i 0.000770013 + 0.0803074i
\(232\) −7.32257 + 4.22769i −0.480750 + 0.277561i
\(233\) 11.0442 0.723531 0.361766 0.932269i \(-0.382174\pi\)
0.361766 + 0.932269i \(0.382174\pi\)
\(234\) 1.22286 7.00746i 0.0799410 0.458092i
\(235\) 0.0960203 0.00626367
\(236\) −13.3096 + 7.68432i −0.866383 + 0.500206i
\(237\) −16.7225 9.44210i −1.08624 0.613330i
\(238\) 0.754370 1.30661i 0.0488986 0.0846948i
\(239\) 4.39448 + 2.53715i 0.284255 + 0.164115i 0.635348 0.772226i \(-0.280857\pi\)
−0.351093 + 0.936341i \(0.614190\pi\)
\(240\) −1.40170 2.37493i −0.0904791 0.153301i
\(241\) −11.7182 + 6.76552i −0.754837 + 0.435805i −0.827439 0.561556i \(-0.810203\pi\)
0.0726019 + 0.997361i \(0.476870\pi\)
\(242\) 4.16895i 0.267990i
\(243\) −13.8580 7.13833i −0.888991 0.457924i
\(244\) 23.8486 1.52675
\(245\) −5.96989 + 3.44672i −0.381403 + 0.220203i
\(246\) −3.81045 + 2.24895i −0.242945 + 0.143388i
\(247\) −1.36336 + 7.01543i −0.0867485 + 0.446381i
\(248\) 8.74391 15.1449i 0.555239 0.961702i
\(249\) −13.6094 + 24.1029i −0.862458 + 1.52746i
\(250\) 0.328815 + 0.569525i 0.0207961 + 0.0360199i
\(251\) 14.9804 0.945554 0.472777 0.881182i \(-0.343252\pi\)
0.472777 + 0.881182i \(0.343252\pi\)
\(252\) 1.34390 + 0.741910i 0.0846575 + 0.0467359i
\(253\) 4.62649i 0.290865i
\(254\) −6.82612 + 3.94106i −0.428309 + 0.247284i
\(255\) 12.1724 0.116713i 0.762265 0.00730883i
\(256\) 4.23673 7.33823i 0.264796 0.458639i
\(257\) 10.6951 18.5244i 0.667141 1.15552i −0.311559 0.950227i \(-0.600851\pi\)
0.978700 0.205295i \(-0.0658155\pi\)
\(258\) −6.45032 + 0.0618477i −0.401579 + 0.00385047i
\(259\) 1.28378 + 2.22358i 0.0797705 + 0.138167i
\(260\) −5.34379 + 1.84026i −0.331408 + 0.114128i
\(261\) 10.8100 0.207318i 0.669122 0.0128327i
\(262\) 12.4457i 0.768896i
\(263\) 7.48463 + 12.9638i 0.461522 + 0.799380i 0.999037 0.0438743i \(-0.0139701\pi\)
−0.537515 + 0.843254i \(0.680637\pi\)
\(264\) −7.63908 4.31330i −0.470153 0.265465i
\(265\) −2.02203 1.16742i −0.124212 0.0717141i
\(266\) 0.368504 + 0.212756i 0.0225944 + 0.0130449i
\(267\) 6.42410 + 10.8845i 0.393149 + 0.666122i
\(268\) 7.25087 4.18629i 0.442917 0.255718i
\(269\) 4.48895 0.273696 0.136848 0.990592i \(-0.456303\pi\)
0.136848 + 0.990592i \(0.456303\pi\)
\(270\) −0.0982775 3.41573i −0.00598098 0.207875i
\(271\) 19.1023i 1.16038i −0.814481 0.580190i \(-0.802978\pi\)
0.814481 0.580190i \(-0.197022\pi\)
\(272\) −5.59494 9.69071i −0.339243 0.587586i
\(273\) 1.32256 1.55135i 0.0800449 0.0938920i
\(274\) −2.68180 + 4.64501i −0.162013 + 0.280615i
\(275\) −1.86962 1.07943i −0.112743 0.0650919i
\(276\) 5.06654 + 2.86075i 0.304970 + 0.172197i
\(277\) 9.77781 + 16.9357i 0.587492 + 1.01757i 0.994560 + 0.104168i \(0.0332179\pi\)
−0.407068 + 0.913398i \(0.633449\pi\)
\(278\) 3.39609i 0.203684i
\(279\) −19.1480 + 11.5502i −1.14636 + 0.691494i
\(280\) 0.765854i 0.0457685i
\(281\) −0.681142 + 0.393257i −0.0406335 + 0.0234598i −0.520179 0.854057i \(-0.674135\pi\)
0.479546 + 0.877517i \(0.340801\pi\)
\(282\) −0.00104864 0.109367i −6.24458e−5 0.00651270i
\(283\) 9.11042 15.7797i 0.541558 0.938007i −0.457256 0.889335i \(-0.651168\pi\)
0.998815 0.0486719i \(-0.0154989\pi\)
\(284\) 15.8629 + 9.15842i 0.941287 + 0.543452i
\(285\) 0.0329166 + 3.43300i 0.00194981 + 0.203353i
\(286\) −3.35814 + 3.86342i −0.198571 + 0.228449i
\(287\) −1.26804 −0.0748498
\(288\) −14.7433 + 8.89326i −0.868756 + 0.524040i
\(289\) 32.3936 1.90551
\(290\) 1.18505 + 2.05256i 0.0695884 + 0.120531i
\(291\) 1.52782 2.70585i 0.0895626 0.158620i
\(292\) 16.4379 + 9.49041i 0.961954 + 0.555384i
\(293\) −10.6694 6.16000i −0.623315 0.359871i 0.154844 0.987939i \(-0.450513\pi\)
−0.778158 + 0.628068i \(0.783846\pi\)
\(294\) 3.99100 + 6.76205i 0.232760 + 0.394371i
\(295\) 4.90221 + 8.49087i 0.285417 + 0.494358i
\(296\) −18.4533 −1.07257
\(297\) 5.88595 + 9.54952i 0.341537 + 0.554119i
\(298\) 14.2194 0.823709
\(299\) 5.06900 5.83171i 0.293148 0.337256i
\(300\) −2.33816 + 1.38000i −0.134994 + 0.0796741i
\(301\) −1.60098 0.924329i −0.0922792 0.0532774i
\(302\) 4.02676 6.97456i 0.231714 0.401341i
\(303\) 15.4838 + 8.74271i 0.889521 + 0.502256i
\(304\) 2.73308 1.57795i 0.156753 0.0905015i
\(305\) 15.2142i 0.871162i
\(306\) −0.265871 13.8630i −0.0151988 0.792497i
\(307\) 34.9414i 1.99421i 0.0760427 + 0.997105i \(0.475771\pi\)
−0.0760427 + 0.997105i \(0.524229\pi\)
\(308\) −0.552338 0.956677i −0.0314724 0.0545117i
\(309\) 0.214212 + 22.3409i 0.0121861 + 1.27093i
\(310\) −4.24521 2.45098i −0.241112 0.139206i
\(311\) −1.64637 + 2.85160i −0.0933571 + 0.161699i −0.908922 0.416967i \(-0.863093\pi\)
0.815565 + 0.578666i \(0.196427\pi\)
\(312\) 4.90322 + 13.8067i 0.277590 + 0.781648i
\(313\) 13.3187 + 23.0687i 0.752819 + 1.30392i 0.946451 + 0.322846i \(0.104640\pi\)
−0.193633 + 0.981074i \(0.562027\pi\)
\(314\) 1.87085i 0.105578i
\(315\) 0.473301 0.857338i 0.0266675 0.0483055i
\(316\) 17.3798 0.977690
\(317\) −20.0163 + 11.5564i −1.12422 + 0.649071i −0.942476 0.334274i \(-0.891509\pi\)
−0.181749 + 0.983345i \(0.558176\pi\)
\(318\) −1.30761 + 2.31584i −0.0733269 + 0.129866i
\(319\) −6.73812 3.89025i −0.377262 0.217812i
\(320\) −0.510939 0.294991i −0.0285624 0.0164905i
\(321\) 15.9281 9.40087i 0.889021 0.524705i
\(322\) −0.230026 0.398418i −0.0128189 0.0222029i
\(323\) 13.9305i 0.775116i
\(324\) 14.0973 0.540927i 0.783185 0.0300515i
\(325\) 1.17399 + 3.40907i 0.0651215 + 0.189101i
\(326\) 0.105053 + 0.181957i 0.00581835 + 0.0100777i
\(327\) −11.6745 19.7804i −0.645600 1.09386i
\(328\) 4.55672 7.89247i 0.251603 0.435789i
\(329\) 0.0156722 0.0271451i 0.000864038 0.00149656i
\(330\) −1.20905 + 2.14128i −0.0665558 + 0.117874i
\(331\) 16.3568 9.44361i 0.899052 0.519068i 0.0221596 0.999754i \(-0.492946\pi\)
0.876893 + 0.480686i \(0.159612\pi\)
\(332\) 25.0503i 1.37482i
\(333\) 20.6576 + 11.4042i 1.13203 + 0.624946i
\(334\) −10.5106 −0.575113
\(335\) −2.67064 4.62569i −0.145913 0.252728i
\(336\) −0.900177 + 0.00863118i −0.0491087 + 0.000470869i
\(337\) −3.75322 + 6.50077i −0.204451 + 0.354120i −0.949958 0.312379i \(-0.898874\pi\)
0.745507 + 0.666498i \(0.232208\pi\)
\(338\) 8.46589 1.19052i 0.460484 0.0647557i
\(339\) −0.124146 12.9477i −0.00674270 0.703220i
\(340\) −9.54069 + 5.50832i −0.517416 + 0.298731i
\(341\) 16.0920 0.871432
\(342\) 3.90981 0.0749839i 0.211418 0.00405466i
\(343\) 4.53531i 0.244884i
\(344\) 11.5064 6.64320i 0.620382 0.358177i
\(345\) 1.82501 3.23219i 0.0982554 0.174015i
\(346\) 1.01494 + 0.585973i 0.0545633 + 0.0315021i
\(347\) 7.31677 12.6730i 0.392785 0.680324i −0.600031 0.799977i \(-0.704845\pi\)
0.992816 + 0.119653i \(0.0381783\pi\)
\(348\) −8.42672 + 4.97350i −0.451720 + 0.266608i
\(349\) −10.8180 + 6.24575i −0.579072 + 0.334327i −0.760764 0.649028i \(-0.775176\pi\)
0.181693 + 0.983355i \(0.441842\pi\)
\(350\) 0.214674 0.0114748
\(351\) 3.04364 18.4861i 0.162458 0.986716i
\(352\) 12.3903 0.660404
\(353\) 16.2880 9.40390i 0.866925 0.500519i 0.000599592 1.00000i \(-0.499809\pi\)
0.866325 + 0.499481i \(0.166476\pi\)
\(354\) 9.61753 5.67632i 0.511166 0.301693i
\(355\) 5.84261 10.1197i 0.310094 0.537098i
\(356\) −9.90588 5.71916i −0.525011 0.303115i
\(357\) 1.95376 3.46020i 0.103404 0.183133i
\(358\) 1.65102 0.953214i 0.0872589 0.0503789i
\(359\) 16.0915i 0.849279i 0.905363 + 0.424639i \(0.139599\pi\)
−0.905363 + 0.424639i \(0.860401\pi\)
\(360\) 3.63540 + 6.02677i 0.191602 + 0.317639i
\(361\) 15.0712 0.793219
\(362\) 0.825132 0.476390i 0.0433680 0.0250385i
\(363\) 0.105275 + 10.9796i 0.00552553 + 0.576278i
\(364\) −0.351957 + 1.81106i −0.0184475 + 0.0949254i
\(365\) 6.05440 10.4865i 0.316902 0.548890i
\(366\) −17.3289 + 0.166155i −0.905797 + 0.00868506i
\(367\) −13.3103 23.0540i −0.694790 1.20341i −0.970252 0.242099i \(-0.922164\pi\)
0.275462 0.961312i \(-0.411169\pi\)
\(368\) −3.41207 −0.177867
\(369\) −9.97862 + 6.01918i −0.519466 + 0.313346i
\(370\) 5.17257i 0.268909i
\(371\) −0.660063 + 0.381088i −0.0342688 + 0.0197851i
\(372\) 9.95036 17.6226i 0.515902 0.913689i
\(373\) −7.45606 + 12.9143i −0.386060 + 0.668676i −0.991916 0.126899i \(-0.959498\pi\)
0.605855 + 0.795575i \(0.292831\pi\)
\(374\) −4.98897 + 8.64114i −0.257973 + 0.446823i
\(375\) 0.880367 + 1.49163i 0.0454620 + 0.0770273i
\(376\) 0.112637 + 0.195093i 0.00580882 + 0.0100612i
\(377\) 4.23107 + 12.2863i 0.217911 + 0.632775i
\(378\) −0.981674 0.529725i −0.0504918 0.0272461i
\(379\) 11.1367i 0.572052i −0.958222 0.286026i \(-0.907666\pi\)
0.958222 0.286026i \(-0.0923345\pi\)
\(380\) −1.55352 2.69077i −0.0796938 0.138034i
\(381\) −17.8781 + 10.5518i −0.915925 + 0.540584i
\(382\) −1.77036 1.02212i −0.0905793 0.0522960i
\(383\) 10.5980 + 6.11875i 0.541532 + 0.312654i 0.745700 0.666282i \(-0.232115\pi\)
−0.204167 + 0.978936i \(0.565449\pi\)
\(384\) 9.44477 16.7272i 0.481977 0.853606i
\(385\) −0.610312 + 0.352364i −0.0311044 + 0.0179581i
\(386\) −12.1100 −0.616380
\(387\) −16.9864 + 0.325771i −0.863465 + 0.0165599i
\(388\) 2.81222i 0.142769i
\(389\) −11.9098 20.6284i −0.603851 1.04590i −0.992232 0.124401i \(-0.960299\pi\)
0.388381 0.921499i \(-0.373034\pi\)
\(390\) 3.87009 1.37441i 0.195970 0.0695957i
\(391\) 7.53067 13.0435i 0.380843 0.659639i
\(392\) −14.0060 8.08639i −0.707411 0.408424i
\(393\) 0.314282 + 32.7776i 0.0158534 + 1.65341i
\(394\) −3.07621 5.32814i −0.154977 0.268428i
\(395\) 11.0874i 0.557869i
\(396\) −8.88775 4.90656i −0.446626 0.246564i
\(397\) 13.0095i 0.652928i −0.945210 0.326464i \(-0.894143\pi\)
0.945210 0.326464i \(-0.105857\pi\)
\(398\) 1.09981 0.634978i 0.0551287 0.0318286i
\(399\) 0.975886 + 0.551020i 0.0488554 + 0.0275855i
\(400\) 0.796086 1.37886i 0.0398043 0.0689431i
\(401\) 3.74595 + 2.16272i 0.187064 + 0.108001i 0.590607 0.806959i \(-0.298888\pi\)
−0.403544 + 0.914960i \(0.632222\pi\)
\(402\) −5.23948 + 3.09237i −0.261321 + 0.154233i
\(403\) −20.2840 17.6312i −1.01042 0.878271i
\(404\) −16.0925 −0.800629
\(405\) −0.345084 8.99338i −0.0171474 0.446885i
\(406\) 0.773684 0.0383973
\(407\) −8.49020 14.7055i −0.420844 0.728923i
\(408\) 14.5160 + 24.5949i 0.718650 + 1.21763i
\(409\) 12.3517 + 7.13127i 0.610753 + 0.352618i 0.773260 0.634089i \(-0.218625\pi\)
−0.162507 + 0.986707i \(0.551958\pi\)
\(410\) −2.21231 1.27728i −0.109258 0.0630803i
\(411\) −6.94563 + 12.3011i −0.342603 + 0.606767i
\(412\) −10.1098 17.5108i −0.498076 0.862693i
\(413\) 3.20051 0.157487
\(414\) −3.70139 2.04339i −0.181913 0.100427i
\(415\) −15.9809 −0.784469
\(416\) −15.6180 13.5754i −0.765734 0.665587i
\(417\) 0.0857590 + 8.94412i 0.00419964 + 0.437995i
\(418\) −2.43707 1.40704i −0.119201 0.0688208i
\(419\) −7.23754 + 12.5358i −0.353577 + 0.612413i −0.986873 0.161496i \(-0.948368\pi\)
0.633297 + 0.773909i \(0.281701\pi\)
\(420\) 0.00849756 + 0.886241i 0.000414638 + 0.0432441i
\(421\) −3.86957 + 2.23410i −0.188591 + 0.108883i −0.591323 0.806435i \(-0.701394\pi\)
0.402732 + 0.915318i \(0.368061\pi\)
\(422\) 1.75404i 0.0853855i
\(423\) −0.00552353 0.288008i −0.000268563 0.0140034i
\(424\) 5.47780i 0.266025i
\(425\) 3.51403 + 6.08648i 0.170455 + 0.295237i
\(426\) −11.5901 6.54420i −0.561543 0.317067i
\(427\) −4.30107 2.48323i −0.208144 0.120172i
\(428\) −8.36927 + 14.4960i −0.404544 + 0.700691i
\(429\) −8.74663 + 10.2597i −0.422291 + 0.495344i
\(430\) −1.86213 3.22531i −0.0898000 0.155538i
\(431\) 19.8690i 0.957057i −0.878072 0.478529i \(-0.841170\pi\)
0.878072 0.478529i \(-0.158830\pi\)
\(432\) −7.04284 + 4.34093i −0.338849 + 0.208853i
\(433\) −12.0708 −0.580087 −0.290044 0.957013i \(-0.593670\pi\)
−0.290044 + 0.957013i \(0.593670\pi\)
\(434\) −1.38579 + 0.800086i −0.0665200 + 0.0384053i
\(435\) 3.17284 + 5.37582i 0.152126 + 0.257751i
\(436\) 18.0019 + 10.3934i 0.862134 + 0.497753i
\(437\) 3.67868 + 2.12389i 0.175975 + 0.101599i
\(438\) −12.0102 6.78142i −0.573872 0.324029i
\(439\) 7.91595 + 13.7108i 0.377808 + 0.654382i 0.990743 0.135751i \(-0.0433446\pi\)
−0.612935 + 0.790133i \(0.710011\pi\)
\(440\) 5.06491i 0.241460i
\(441\) 10.6817 + 17.7081i 0.508651 + 0.843244i
\(442\) 15.7562 5.42604i 0.749448 0.258090i
\(443\) −0.0730197 0.126474i −0.00346927 0.00600895i 0.864286 0.503001i \(-0.167771\pi\)
−0.867755 + 0.496993i \(0.834438\pi\)
\(444\) −21.3540 + 0.204749i −1.01342 + 0.00971695i
\(445\) −3.64854 + 6.31945i −0.172957 + 0.299571i
\(446\) 1.40835 2.43933i 0.0666873 0.115506i
\(447\) 37.4491 0.359073i 1.77128 0.0169836i
\(448\) −0.166789 + 0.0962956i −0.00788003 + 0.00454954i
\(449\) 1.68576i 0.0795562i 0.999209 + 0.0397781i \(0.0126651\pi\)
−0.999209 + 0.0397781i \(0.987335\pi\)
\(450\) 1.68934 1.01903i 0.0796365 0.0480373i
\(451\) 8.38605 0.394884
\(452\) 5.85915 + 10.1483i 0.275591 + 0.477338i
\(453\) 10.4290 18.4703i 0.489996 0.867809i
\(454\) 8.16621 14.1443i 0.383259 0.663824i
\(455\) 1.15537 + 0.224531i 0.0541644 + 0.0105262i
\(456\) −6.93652 + 4.09397i −0.324832 + 0.191718i
\(457\) −18.8050 + 10.8571i −0.879662 + 0.507873i −0.870547 0.492085i \(-0.836235\pi\)
−0.00911515 + 0.999958i \(0.502901\pi\)
\(458\) −2.42640 −0.113378
\(459\) −1.05029 36.5038i −0.0490231 1.70385i
\(460\) 3.35925i 0.156626i
\(461\) 21.1304 12.1997i 0.984142 0.568195i 0.0806242 0.996745i \(-0.474309\pi\)
0.903518 + 0.428550i \(0.140975\pi\)
\(462\) 0.408006 + 0.691295i 0.0189822 + 0.0321619i
\(463\) 19.2118 + 11.0919i 0.892847 + 0.515486i 0.874873 0.484353i \(-0.160945\pi\)
0.0179744 + 0.999838i \(0.494278\pi\)
\(464\) 2.86909 4.96941i 0.133194 0.230699i
\(465\) −11.2423 6.34782i −0.521350 0.294373i
\(466\) 6.28996 3.63151i 0.291377 0.168226i
\(467\) −9.62358 −0.445326 −0.222663 0.974895i \(-0.571475\pi\)
−0.222663 + 0.974895i \(0.571475\pi\)
\(468\) 5.82717 + 15.9226i 0.269361 + 0.736021i
\(469\) −1.74358 −0.0805113
\(470\) 0.0546859 0.0315729i 0.00252247 0.00145635i
\(471\) 0.0472432 + 4.92716i 0.00217685 + 0.227032i
\(472\) −11.5011 + 19.9205i −0.529382 + 0.916916i
\(473\) 10.5880 + 6.11297i 0.486836 + 0.281075i
\(474\) −12.6286 + 0.121087i −0.580049 + 0.00556169i
\(475\) −1.71658 + 0.991066i −0.0787619 + 0.0454732i
\(476\) 3.59622i 0.164833i
\(477\) −3.38530 + 6.13214i −0.155002 + 0.280771i
\(478\) 3.33702 0.152632
\(479\) −9.15602 + 5.28623i −0.418349 + 0.241534i −0.694371 0.719617i \(-0.744317\pi\)
0.276022 + 0.961151i \(0.410984\pi\)
\(480\) −8.65618 4.88759i −0.395099 0.223087i
\(481\) −5.41007 + 27.8385i −0.246678 + 1.26933i
\(482\) −4.44921 + 7.70626i −0.202656 + 0.351010i
\(483\) −0.615871 1.04349i −0.0280231 0.0474802i
\(484\) −4.96853 8.60575i −0.225842 0.391171i
\(485\) 1.79405 0.0814638
\(486\) −10.2397 + 0.491267i −0.464481 + 0.0222843i
\(487\) 37.0636i 1.67951i 0.542964 + 0.839756i \(0.317302\pi\)
−0.542964 + 0.839756i \(0.682698\pi\)
\(488\) 30.9121 17.8471i 1.39932 0.807900i
\(489\) 0.281269 + 0.476560i 0.0127194 + 0.0215508i
\(490\) −2.26667 + 3.92598i −0.102398 + 0.177358i
\(491\) −4.25397 + 7.36810i −0.191979 + 0.332517i −0.945906 0.324441i \(-0.894824\pi\)
0.753927 + 0.656958i \(0.228157\pi\)
\(492\) 5.18544 9.18368i 0.233778 0.414032i
\(493\) 12.6645 + 21.9356i 0.570382 + 0.987931i
\(494\) 1.53031 + 4.44375i 0.0688520 + 0.199934i
\(495\) −3.13014 + 5.66993i −0.140689 + 0.254844i
\(496\) 11.8680i 0.532888i
\(497\) −1.90724 3.30343i −0.0855512 0.148179i
\(498\) 0.174528 + 18.2021i 0.00782078 + 0.815657i
\(499\) −25.6678 14.8193i −1.14905 0.663405i −0.200395 0.979715i \(-0.564222\pi\)
−0.948656 + 0.316311i \(0.897556\pi\)
\(500\) −1.35751 0.783761i −0.0607099 0.0350509i
\(501\) −27.6812 + 0.265416i −1.23671 + 0.0118579i
\(502\) 8.53170 4.92578i 0.380788 0.219848i
\(503\) −20.0429 −0.893668 −0.446834 0.894617i \(-0.647448\pi\)
−0.446834 + 0.894617i \(0.647448\pi\)
\(504\) 2.29714 0.0440554i 0.102323 0.00196239i
\(505\) 10.2662i 0.456839i
\(506\) 1.52126 + 2.63490i 0.0676283 + 0.117136i
\(507\) 22.2662 3.34920i 0.988876 0.148743i
\(508\) 9.39389 16.2707i 0.416787 0.721895i
\(509\) −30.7691 17.7645i −1.36382 0.787400i −0.373687 0.927555i \(-0.621907\pi\)
−0.990130 + 0.140155i \(0.955240\pi\)
\(510\) 6.89410 4.06894i 0.305276 0.180176i
\(511\) −1.97637 3.42318i −0.0874296 0.151432i
\(512\) 16.6087i 0.734010i
\(513\) 10.2952 0.296213i 0.454544 0.0130781i
\(514\) 14.0668i 0.620461i
\(515\) −11.1710 + 6.44957i −0.492252 + 0.284202i
\(516\) 13.2414 7.81514i 0.582919 0.344042i
\(517\) −0.103647 + 0.179522i −0.00455839 + 0.00789536i
\(518\) 1.46229 + 0.844256i 0.0642495 + 0.0370945i
\(519\) 2.68779 + 1.51762i 0.117981 + 0.0666162i
\(520\) −5.54935 + 6.38433i −0.243355 + 0.279972i
\(521\) −6.16502 −0.270095 −0.135047 0.990839i \(-0.543119\pi\)
−0.135047 + 0.990839i \(0.543119\pi\)
\(522\) 6.08839 3.67256i 0.266482 0.160744i
\(523\) −24.1503 −1.05602 −0.528010 0.849238i \(-0.677062\pi\)
−0.528010 + 0.849238i \(0.677062\pi\)
\(524\) −14.8327 25.6910i −0.647969 1.12232i
\(525\) 0.565377 0.00542101i 0.0246751 0.000236592i
\(526\) 8.52536 + 4.92212i 0.371724 + 0.214615i
\(527\) −45.3684 26.1934i −1.97628 1.14100i
\(528\) 5.95325 0.0570816i 0.259082 0.00248416i
\(529\) 9.20371 + 15.9413i 0.400161 + 0.693100i
\(530\) −1.53546 −0.0666962
\(531\) 25.1859 15.1923i 1.09298 0.659292i
\(532\) −1.01425 −0.0439732
\(533\) −10.5706 9.18815i −0.457865 0.397983i
\(534\) 7.23768 + 4.08666i 0.313205 + 0.176847i
\(535\) 9.24772 + 5.33917i 0.399814 + 0.230833i
\(536\) 6.26562 10.8524i 0.270634 0.468751i
\(537\) 4.32413 2.55213i 0.186600 0.110133i
\(538\) 2.55657 1.47603i 0.110221 0.0636364i
\(539\) 14.8819i 0.641010i
\(540\) 4.27373 + 6.93381i 0.183912 + 0.298384i
\(541\) 13.4591i 0.578650i −0.957231 0.289325i \(-0.906569\pi\)
0.957231 0.289325i \(-0.0934309\pi\)
\(542\) −6.28112 10.8792i −0.269797 0.467302i
\(543\) 2.16108 1.27548i 0.0927409 0.0547362i
\(544\) −34.9320 20.1680i −1.49770 0.864696i
\(545\) 6.63046 11.4843i 0.284018 0.491933i
\(546\) 0.243122 1.31841i 0.0104047 0.0564227i
\(547\) 6.88546 + 11.9260i 0.294401 + 0.509918i 0.974845 0.222882i \(-0.0715465\pi\)
−0.680444 + 0.732800i \(0.738213\pi\)
\(548\) 12.7846i 0.546132i
\(549\) −45.6342 + 0.875190i −1.94762 + 0.0373522i
\(550\) −1.41973 −0.0605374
\(551\) −6.18654 + 3.57180i −0.263555 + 0.152164i
\(552\) 8.70799 0.0834949i 0.370636 0.00355378i
\(553\) −3.13443 1.80967i −0.133290 0.0769549i
\(554\) 11.1374 + 6.43018i 0.473183 + 0.273192i
\(555\) 0.130619 + 13.6228i 0.00554448 + 0.578254i
\(556\) −4.04744 7.01038i −0.171650 0.297306i
\(557\) 12.2312i 0.518254i 0.965843 + 0.259127i \(0.0834348\pi\)
−0.965843 + 0.259127i \(0.916565\pi\)
\(558\) −7.10737 + 12.8743i −0.300879 + 0.545012i
\(559\) −6.64852 19.3061i −0.281202 0.816561i
\(560\) −0.259871 0.450109i −0.0109815 0.0190206i
\(561\) −12.9210 + 22.8838i −0.545525 + 0.966154i
\(562\) −0.258618 + 0.447939i −0.0109091 + 0.0188952i
\(563\) −13.9445 + 24.1526i −0.587691 + 1.01791i 0.406843 + 0.913498i \(0.366630\pi\)
−0.994534 + 0.104413i \(0.966704\pi\)
\(564\) 0.132508 + 0.224511i 0.00557958 + 0.00945361i
\(565\) 6.47413 3.73784i 0.272369 0.157252i
\(566\) 11.9826i 0.503665i
\(567\) −2.59877 1.37032i −0.109138 0.0575482i
\(568\) 27.4148 1.15030
\(569\) 22.6269 + 39.1909i 0.948567 + 1.64297i 0.748446 + 0.663196i \(0.230800\pi\)
0.200121 + 0.979771i \(0.435866\pi\)
\(570\) 1.14757 + 1.94435i 0.0480663 + 0.0814399i
\(571\) −15.4733 + 26.8006i −0.647539 + 1.12157i 0.336170 + 0.941801i \(0.390868\pi\)
−0.983709 + 0.179769i \(0.942465\pi\)
\(572\) 2.32764 11.9773i 0.0973234 0.500796i
\(573\) −4.68832 2.64719i −0.195857 0.110588i
\(574\) −0.722177 + 0.416949i −0.0301431 + 0.0174031i
\(575\) 2.14303 0.0893706
\(576\) −0.855419 + 1.54951i −0.0356424 + 0.0645627i
\(577\) 9.66715i 0.402449i 0.979545 + 0.201224i \(0.0644920\pi\)
−0.979545 + 0.201224i \(0.935508\pi\)
\(578\) 18.4489 10.6515i 0.767375 0.443044i
\(579\) −31.8934 + 0.305804i −1.32545 + 0.0127088i
\(580\) −4.89248 2.82467i −0.203149 0.117288i
\(581\) −2.60836 + 4.51781i −0.108213 + 0.187430i
\(582\) −0.0195930 2.04342i −0.000812155 0.0847026i
\(583\) 4.36527 2.52029i 0.180791 0.104380i
\(584\) 28.4086 1.17556
\(585\) 10.1578 3.71744i 0.419973 0.153697i
\(586\) −8.10200 −0.334691
\(587\) 6.08875 3.51534i 0.251310 0.145094i −0.369054 0.929408i \(-0.620318\pi\)
0.620364 + 0.784314i \(0.286985\pi\)
\(588\) −16.2974 9.20211i −0.672094 0.379489i
\(589\) 7.38737 12.7953i 0.304391 0.527221i
\(590\) 5.58385 + 3.22384i 0.229884 + 0.132723i
\(591\) −8.23621 13.9548i −0.338792 0.574024i
\(592\) 10.8454 6.26159i 0.445743 0.257350i
\(593\) 5.93635i 0.243777i 0.992544 + 0.121888i \(0.0388950\pi\)
−0.992544 + 0.121888i \(0.961105\pi\)
\(594\) 6.49222 + 3.50329i 0.266379 + 0.143742i
\(595\) 2.29421 0.0940534
\(596\) −29.3525 + 16.9467i −1.20232 + 0.694162i
\(597\) 2.88050 1.70009i 0.117891 0.0695799i
\(598\) 0.969367 4.98806i 0.0396404 0.203977i
\(599\) 15.0613 26.0869i 0.615387 1.06588i −0.374930 0.927053i \(-0.622333\pi\)
0.990316 0.138828i \(-0.0443336\pi\)
\(600\) −1.99796 + 3.53848i −0.0815662 + 0.144458i
\(601\) 7.99172 + 13.8421i 0.325989 + 0.564630i 0.981712 0.190372i \(-0.0609693\pi\)
−0.655723 + 0.755002i \(0.727636\pi\)
\(602\) −1.21573 −0.0495496
\(603\) −13.7209 + 8.27654i −0.558757 + 0.337047i
\(604\) 19.1963i 0.781087i
\(605\) −5.49003 + 3.16967i −0.223202 + 0.128866i
\(606\) 11.6931 0.112117i 0.475001 0.00455446i
\(607\) 1.38476 2.39848i 0.0562057 0.0973512i −0.836554 0.547885i \(-0.815433\pi\)
0.892759 + 0.450534i \(0.148766\pi\)
\(608\) 5.68801 9.85192i 0.230679 0.399548i
\(609\) 2.03762 0.0195373i 0.0825684 0.000791692i
\(610\) −5.00266 8.66485i −0.202552 0.350830i
\(611\) 0.327340 0.112727i 0.0132427 0.00456046i
\(612\) 17.0707 + 28.2999i 0.690044 + 1.14396i
\(613\) 13.9203i 0.562236i 0.959673 + 0.281118i \(0.0907053\pi\)
−0.959673 + 0.281118i \(0.909295\pi\)
\(614\) 11.4892 + 19.9000i 0.463668 + 0.803097i
\(615\) −5.85872 3.30805i −0.236246 0.133393i
\(616\) −1.43186 0.826684i −0.0576912 0.0333080i
\(617\) −34.2279 19.7615i −1.37796 0.795568i −0.386050 0.922478i \(-0.626161\pi\)
−0.991914 + 0.126910i \(0.959494\pi\)
\(618\) 7.46803 + 12.6533i 0.300408 + 0.508989i
\(619\) 32.2145 18.5990i 1.29481 0.747559i 0.315307 0.948990i \(-0.397892\pi\)
0.979503 + 0.201431i \(0.0645591\pi\)
\(620\) 11.6843 0.469251
\(621\) −9.79978 5.28810i −0.393252 0.212204i
\(622\) 2.16541i 0.0868249i
\(623\) 1.19101 + 2.06289i 0.0477169 + 0.0826481i
\(624\) −7.56663 6.45070i −0.302907 0.258235i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 15.1707 + 8.75879i 0.606342 + 0.350072i
\(627\) −6.45394 3.64413i −0.257746 0.145532i
\(628\) −2.22967 3.86190i −0.0889734 0.154106i
\(629\) 55.2790i 2.20412i
\(630\) −0.0123490 0.643903i −0.000491997 0.0256537i
\(631\) 0.503852i 0.0200580i −0.999950 0.0100290i \(-0.996808\pi\)
0.999950 0.0100290i \(-0.00319239\pi\)
\(632\) 22.5274 13.0062i 0.896090 0.517358i
\(633\) −0.0442937 4.61955i −0.00176051 0.183611i
\(634\) −7.59983 + 13.1633i −0.301828 + 0.522781i
\(635\) −10.3799 5.99283i −0.411913 0.237818i
\(636\) −0.0607791 6.33887i −0.00241005 0.251353i
\(637\) −16.3053 + 18.7587i −0.646041 + 0.743247i
\(638\) −5.11670 −0.202572
\(639\) −30.6896 16.9425i −1.21406 0.670234i
\(640\) 11.0906 0.438393
\(641\) 5.12505 + 8.87684i 0.202427 + 0.350614i 0.949310 0.314342i \(-0.101784\pi\)
−0.746883 + 0.664956i \(0.768450\pi\)
\(642\) 5.98030 10.5914i 0.236024 0.418010i
\(643\) 32.0632 + 18.5117i 1.26445 + 0.730029i 0.973932 0.226841i \(-0.0728397\pi\)
0.290516 + 0.956870i \(0.406173\pi\)
\(644\) 0.949665 + 0.548289i 0.0374220 + 0.0216056i
\(645\) −4.98566 8.44733i −0.196310 0.332613i
\(646\) 4.58057 + 7.93378i 0.180220 + 0.312151i
\(647\) −34.5539 −1.35845 −0.679227 0.733928i \(-0.737685\pi\)
−0.679227 + 0.733928i \(0.737685\pi\)
\(648\) 17.8679 11.2509i 0.701916 0.441976i
\(649\) −21.1663 −0.830850
\(650\) 1.78957 + 1.55552i 0.0701928 + 0.0610125i
\(651\) −3.62949 + 2.14214i −0.142251 + 0.0839572i
\(652\) −0.433712 0.250404i −0.0169855 0.00980657i
\(653\) 7.50748 13.0033i 0.293790 0.508860i −0.680912 0.732365i \(-0.738417\pi\)
0.974703 + 0.223505i \(0.0717499\pi\)
\(654\) −13.1530 7.42665i −0.514322 0.290405i
\(655\) −16.3895 + 9.46251i −0.640393 + 0.369731i
\(656\) 6.18477i 0.241475i
\(657\) −31.8021 17.5566i −1.24072 0.684949i
\(658\) 0.0206131i 0.000803581i
\(659\) −3.24346 5.61783i −0.126347 0.218840i 0.795912 0.605413i \(-0.206992\pi\)
−0.922259 + 0.386573i \(0.873659\pi\)
\(660\) −0.0561979 5.86108i −0.00218750 0.228142i
\(661\) −34.5991 19.9758i −1.34575 0.776968i −0.358104 0.933682i \(-0.616577\pi\)
−0.987644 + 0.156713i \(0.949910\pi\)
\(662\) 6.21041 10.7567i 0.241374 0.418073i
\(663\) 41.3595 14.6882i 1.60627 0.570442i
\(664\) −18.7464 32.4698i −0.727502 1.26007i
\(665\) 0.647038i 0.0250911i
\(666\) 15.5149 0.297550i 0.601189 0.0115298i
\(667\) 7.72348 0.299054
\(668\) 21.6965 12.5265i 0.839462 0.484664i
\(669\) 3.64751 6.45993i 0.141021 0.249755i
\(670\) −3.04199 1.75629i −0.117522 0.0678516i
\(671\) 28.4448 + 16.4226i 1.09810 + 0.633988i
\(672\) −2.79457 + 1.64937i −0.107803 + 0.0636260i
\(673\) 3.38993 + 5.87154i 0.130672 + 0.226331i 0.923936 0.382547i \(-0.124953\pi\)
−0.793264 + 0.608878i \(0.791620\pi\)
\(674\) 4.93647i 0.190146i
\(675\) 4.42342 2.72642i 0.170257 0.104940i
\(676\) −16.0569 + 12.5471i −0.617572 + 0.482583i
\(677\) 25.0490 + 43.3861i 0.962711 + 1.66746i 0.715642 + 0.698467i \(0.246134\pi\)
0.247069 + 0.968998i \(0.420533\pi\)
\(678\) −4.32809 7.33319i −0.166219 0.281629i
\(679\) 0.292822 0.507182i 0.0112375 0.0194639i
\(680\) −8.24430 + 14.2795i −0.316154 + 0.547596i
\(681\) 21.1498 37.4574i 0.810462 1.43537i
\(682\) 9.16480 5.29130i 0.350938 0.202614i
\(683\) 35.7445i 1.36773i 0.729611 + 0.683863i \(0.239701\pi\)
−0.729611 + 0.683863i \(0.760299\pi\)
\(684\) −7.98147 + 4.81448i −0.305179 + 0.184086i
\(685\) −8.15595 −0.311623
\(686\) 1.49128 + 2.58297i 0.0569373 + 0.0986183i
\(687\) −6.39030 + 0.0612722i −0.243805 + 0.00233768i
\(688\) −4.50836 + 7.80871i −0.171880 + 0.297704i
\(689\) −8.26379 1.60596i −0.314825 0.0611823i
\(690\) −0.0234042 2.44091i −0.000890981 0.0929237i
\(691\) 31.3027 18.0726i 1.19081 0.687514i 0.232319 0.972640i \(-0.425369\pi\)
0.958490 + 0.285125i \(0.0920352\pi\)
\(692\) −2.79344 −0.106191
\(693\) 1.09200 + 1.81033i 0.0414818 + 0.0687687i
\(694\) 9.62346i 0.365302i
\(695\) −4.47226 + 2.58206i −0.169643 + 0.0979432i
\(696\) −7.20063 + 12.7527i −0.272939 + 0.483389i
\(697\) −23.6429 13.6502i −0.895537 0.517039i
\(698\) −4.10739 + 7.11421i −0.155467 + 0.269277i
\(699\) 16.4739 9.72297i 0.623099 0.367757i
\(700\) −0.443141 + 0.255848i −0.0167492 + 0.00967013i
\(701\) −8.46862 −0.319856 −0.159928 0.987129i \(-0.551126\pi\)
−0.159928 + 0.987129i \(0.551126\pi\)
\(702\) −4.34508 11.5291i −0.163995 0.435137i
\(703\) −15.5904 −0.588003
\(704\) 1.10304 0.636843i 0.0415725 0.0240019i
\(705\) 0.143227 0.0845331i 0.00539422 0.00318370i
\(706\) 6.18429 10.7115i 0.232749 0.403133i
\(707\) 2.90226 + 1.67562i 0.109151 + 0.0630182i
\(708\) −13.0880 + 23.1795i −0.491877 + 0.871139i
\(709\) −39.3782 + 22.7350i −1.47888 + 0.853832i −0.999715 0.0238931i \(-0.992394\pi\)
−0.479165 + 0.877725i \(0.659061\pi\)
\(710\) 7.68455i 0.288396i
\(711\) −33.2562 + 0.637800i −1.24720 + 0.0239194i
\(712\) −17.1197 −0.641589
\(713\) −13.8340 + 7.98704i −0.518086 + 0.299117i
\(714\) −0.0250552 2.61310i −0.000937666 0.0977926i
\(715\) −7.64091 1.48491i −0.285754 0.0555327i
\(716\) −2.27207 + 3.93535i −0.0849114 + 0.147071i
\(717\) 8.78856 0.0842674i 0.328215 0.00314703i
\(718\) 5.29114 + 9.16452i 0.197464 + 0.342017i
\(719\) −34.7901 −1.29745 −0.648725 0.761023i \(-0.724697\pi\)
−0.648725 + 0.761023i \(0.724697\pi\)
\(720\) −4.18162 2.30850i −0.155840 0.0860327i
\(721\) 4.21074i 0.156816i
\(722\) 8.58339 4.95562i 0.319441 0.184429i
\(723\) −11.5231 + 20.4080i −0.428548 + 0.758981i
\(724\) −1.13552 + 1.96678i −0.0422012 + 0.0730947i
\(725\) −1.80200 + 3.12115i −0.0669245 + 0.115917i
\(726\) 3.67020 + 6.21851i 0.136214 + 0.230791i
\(727\) −19.5971 33.9432i −0.726817 1.25888i −0.958222 0.286026i \(-0.907666\pi\)
0.231405 0.972857i \(-0.425668\pi\)
\(728\) 0.899108 + 2.61085i 0.0333232 + 0.0967645i
\(729\) −26.9553 + 1.55240i −0.998346 + 0.0574964i
\(730\) 7.96312i 0.294728i
\(731\) −19.9005 34.4687i −0.736047 1.27487i
\(732\) 35.5732 20.9955i 1.31482 0.776017i
\(733\) 3.42447 + 1.97712i 0.126486 + 0.0730266i 0.561908 0.827200i \(-0.310068\pi\)
−0.435422 + 0.900226i \(0.643401\pi\)
\(734\) −15.1610 8.75323i −0.559604 0.323087i
\(735\) −5.87048 + 10.3969i −0.216536 + 0.383496i
\(736\) −10.6516 + 6.14973i −0.392625 + 0.226682i
\(737\) 11.5311 0.424752
\(738\) −3.70387 + 6.70919i −0.136341 + 0.246969i
\(739\) 33.3471i 1.22669i −0.789814 0.613347i \(-0.789823\pi\)
0.789814 0.613347i \(-0.210177\pi\)
\(740\) −6.16465 10.6775i −0.226617 0.392512i
\(741\) 4.14253 + 11.6647i 0.152180 + 0.428512i
\(742\) −0.250615 + 0.434078i −0.00920036 + 0.0159355i
\(743\) −5.97731 3.45100i −0.219286 0.126605i 0.386333 0.922359i \(-0.373741\pi\)
−0.605620 + 0.795754i \(0.707075\pi\)
\(744\) −0.290415 30.2884i −0.0106471 1.11043i
\(745\) 10.8111 + 18.7254i 0.396088 + 0.686045i
\(746\) 9.80666i 0.359047i
\(747\) 0.919292 + 47.9338i 0.0336351 + 1.75380i
\(748\) 23.7833i 0.869604i
\(749\) 3.01878 1.74290i 0.110304 0.0636840i
\(750\) 0.991861 + 0.560040i 0.0362176 + 0.0204498i
\(751\) 11.5467 19.9994i 0.421344 0.729789i −0.574727 0.818345i \(-0.694892\pi\)
0.996071 + 0.0885558i \(0.0282252\pi\)
\(752\) −0.132399 0.0764404i −0.00482808 0.00278749i
\(753\) 22.3452 13.1882i 0.814303 0.480606i
\(754\) 6.44961 + 5.60609i 0.234881 + 0.204162i
\(755\) 12.2463 0.445688
\(756\) 2.65775 0.0764686i 0.0966613 0.00278114i
\(757\) −12.6259 −0.458894 −0.229447 0.973321i \(-0.573692\pi\)
−0.229447 + 0.973321i \(0.573692\pi\)
\(758\) −3.66191 6.34261i −0.133006 0.230374i
\(759\) 4.07301 + 6.90101i 0.147841 + 0.250491i
\(760\) −4.02728 2.32515i −0.146085 0.0843421i
\(761\) 35.4456 + 20.4645i 1.28490 + 0.741838i 0.977740 0.209820i \(-0.0672877\pi\)
0.307161 + 0.951658i \(0.400621\pi\)
\(762\) −6.71245 + 11.8881i −0.243166 + 0.430660i
\(763\) −2.16442 3.74888i −0.0783572 0.135719i
\(764\) 4.87261 0.176285
\(765\) 18.0539 10.8903i 0.652741 0.393739i
\(766\) 8.04776 0.290777
\(767\) 26.6802 + 23.1908i 0.963365 + 0.837371i
\(768\) −0.140716 14.6758i −0.00507765 0.529567i
\(769\) 24.5247 + 14.1593i 0.884382 + 0.510598i 0.872101 0.489327i \(-0.162757\pi\)
0.0122811 + 0.999925i \(0.496091\pi\)
\(770\) −0.231725 + 0.401359i −0.00835079 + 0.0144640i
\(771\) −0.355220 37.0472i −0.0127929 1.33422i
\(772\) 24.9980 14.4326i 0.899697 0.519441i
\(773\) 37.9270i 1.36414i −0.731286 0.682071i \(-0.761080\pi\)
0.731286 0.682071i \(-0.238920\pi\)
\(774\) −9.56703 + 5.77091i −0.343880 + 0.207431i
\(775\) 7.45396i 0.267754i
\(776\) 2.10453 + 3.64514i 0.0755481 + 0.130853i
\(777\) 3.87250 + 2.18655i 0.138925 + 0.0784421i
\(778\) −13.5658 7.83224i −0.486359 0.280799i
\(779\) 3.84979 6.66802i 0.137933 0.238907i
\(780\) −6.35084 + 7.44948i −0.227396 + 0.266734i
\(781\) 12.6133 + 21.8470i 0.451341 + 0.781746i
\(782\) 9.90480i 0.354195i
\(783\) 15.9420 9.82601i 0.569720 0.351153i
\(784\) 10.9755 0.391984
\(785\) −2.46369 + 1.42241i −0.0879330 + 0.0507682i
\(786\) 10.9568 + 18.5643i 0.390815 + 0.662167i
\(787\) 28.2750 + 16.3246i 1.00790 + 0.581909i 0.910575 0.413344i \(-0.135639\pi\)
0.0973205 + 0.995253i \(0.468973\pi\)
\(788\) 12.7001 + 7.33242i 0.452423 + 0.261207i
\(789\) 22.5772 + 12.7479i 0.803768 + 0.453837i
\(790\) −3.64572 6.31457i −0.129709 0.224662i
\(791\) 2.44033i 0.0867681i
\(792\) −15.1919 + 0.291357i −0.539822 + 0.0103529i
\(793\) −17.8614 51.8662i −0.634276 1.84182i
\(794\) −4.27772 7.40923i −0.151811 0.262944i
\(795\) −4.04388 + 0.0387740i −0.143422 + 0.00137517i
\(796\) −1.51353 + 2.62151i −0.0536456 + 0.0929169i
\(797\) 7.91250 13.7048i 0.280275 0.485451i −0.691177 0.722685i \(-0.742908\pi\)
0.971452 + 0.237235i \(0.0762410\pi\)
\(798\) 0.736975 0.00706634i 0.0260886 0.000250146i
\(799\) 0.584425 0.337418i 0.0206755 0.0119370i
\(800\) 5.73928i 0.202914i
\(801\) 19.1647 + 10.5801i 0.677153 + 0.373828i
\(802\) 2.84455 0.100444
\(803\) 13.0706 + 22.6389i 0.461251 + 0.798909i
\(804\) 7.13012 12.6278i 0.251460 0.445349i
\(805\) 0.349781 0.605838i 0.0123282 0.0213530i
\(806\) −17.3497 3.37169i −0.611115 0.118763i
\(807\) 6.69584 3.95192i 0.235705 0.139114i
\(808\) −20.8587 + 12.0428i −0.733807 + 0.423664i
\(809\) 6.20843 0.218277 0.109138 0.994027i \(-0.465191\pi\)
0.109138 + 0.994027i \(0.465191\pi\)
\(810\) −3.15369 5.00848i −0.110810 0.175980i
\(811\) 18.5979i 0.653060i −0.945187 0.326530i \(-0.894121\pi\)
0.945187 0.326530i \(-0.105879\pi\)
\(812\) −1.59708 + 0.922074i −0.0560465 + 0.0323584i
\(813\) −16.8170 28.4935i −0.589799 0.999310i
\(814\) −9.67076 5.58341i −0.338960 0.195699i
\(815\) −0.159745 + 0.276686i −0.00559562 + 0.00969190i
\(816\) −16.8770 9.52934i −0.590811 0.333594i
\(817\) 9.72125 5.61257i 0.340104 0.196359i
\(818\) 9.37947 0.327946
\(819\) 0.607006 3.47837i 0.0212105 0.121544i
\(820\) 6.08902 0.212638
\(821\) −7.08387 + 4.08987i −0.247229 + 0.142738i −0.618495 0.785789i \(-0.712257\pi\)
0.371266 + 0.928527i \(0.378924\pi\)
\(822\) 0.0890715 + 9.28959i 0.00310673 + 0.324012i
\(823\) −13.0281 + 22.5654i −0.454133 + 0.786581i −0.998638 0.0521766i \(-0.983384\pi\)
0.544505 + 0.838757i \(0.316717\pi\)
\(824\) −26.2083 15.1314i −0.913011 0.527127i
\(825\) −3.73907 + 0.0358514i −0.130178 + 0.00124819i
\(826\) 1.82277 1.05238i 0.0634222 0.0366168i
\(827\) 6.63409i 0.230690i 0.993325 + 0.115345i \(0.0367974\pi\)
−0.993325 + 0.115345i \(0.963203\pi\)
\(828\) 10.0759 0.193239i 0.350162 0.00671554i
\(829\) −3.16728 −0.110004 −0.0550021 0.998486i \(-0.517517\pi\)
−0.0550021 + 0.998486i \(0.517517\pi\)
\(830\) −9.10149 + 5.25475i −0.315917 + 0.182395i
\(831\) 29.4945 + 16.6536i 1.02315 + 0.577708i
\(832\) −2.08814 0.405805i −0.0723934 0.0140687i
\(833\) −24.2237 + 41.9568i −0.839303 + 1.45372i
\(834\) 2.98980 + 5.06570i 0.103528 + 0.175411i
\(835\) −7.99125 13.8413i −0.276549 0.478997i
\(836\) 6.70764 0.231989
\(837\) −18.3933 + 34.0859i −0.635764 + 1.17818i
\(838\) 9.51925i 0.328837i
\(839\) 29.8526 17.2354i 1.03063 0.595032i 0.113462 0.993542i \(-0.463806\pi\)
0.917164 + 0.398510i \(0.130473\pi\)
\(840\) 0.674233 + 1.14237i 0.0232632 + 0.0394155i
\(841\) 8.00561 13.8661i 0.276055 0.478142i
\(842\) −1.46921 + 2.54475i −0.0506324 + 0.0876978i
\(843\) −0.669799 + 1.18625i −0.0230691 + 0.0408566i
\(844\) 2.09046 + 3.62079i 0.0719567 + 0.124633i
\(845\) 8.00445 + 10.2435i 0.275361 + 0.352386i
\(846\) −0.0978472 0.162211i −0.00336405 0.00557694i
\(847\) 2.06939i 0.0711050i
\(848\) 1.85873 + 3.21942i 0.0638292 + 0.110555i
\(849\) −0.302588 31.5580i −0.0103848 1.08307i
\(850\) 4.00265 + 2.31093i 0.137290 + 0.0792643i
\(851\) 14.5977 + 8.42797i 0.500402 + 0.288907i
\(852\) 31.7243 0.304182i 1.08685 0.0104211i
\(853\) 18.1118 10.4568i 0.620135 0.358035i −0.156786 0.987633i \(-0.550113\pi\)
0.776922 + 0.629597i \(0.216780\pi\)
\(854\) −3.26609 −0.111763
\(855\) 3.07140 + 5.09177i 0.105040 + 0.174135i
\(856\) 25.0526i 0.856280i
\(857\) 11.8102 + 20.4558i 0.403427 + 0.698757i 0.994137 0.108127i \(-0.0344855\pi\)
−0.590710 + 0.806884i \(0.701152\pi\)
\(858\) −1.60787 + 8.71919i −0.0548916 + 0.297668i
\(859\) 1.47856 2.56094i 0.0504478 0.0873781i −0.839699 0.543052i \(-0.817268\pi\)
0.890147 + 0.455674i \(0.150602\pi\)
\(860\) 7.68782 + 4.43857i 0.262153 + 0.151354i
\(861\) −1.89144 + 1.11634i −0.0644600 + 0.0380447i
\(862\) −6.53324 11.3159i −0.222523 0.385421i
\(863\) 0.569343i 0.0193807i 0.999953 + 0.00969033i \(0.00308458\pi\)
−0.999953 + 0.00969033i \(0.996915\pi\)
\(864\) −14.1621 + 26.2449i −0.481806 + 0.892871i
\(865\) 1.78208i 0.0605924i
\(866\) −6.87463 + 3.96907i −0.233610 + 0.134875i
\(867\) 48.3192 28.5183i 1.64101 0.968531i
\(868\) 1.90708 3.30316i 0.0647305 0.112116i
\(869\) 20.7293 + 11.9681i 0.703194 + 0.405989i
\(870\) 3.57466 + 2.01838i 0.121192 + 0.0684296i
\(871\) −14.5349 12.6340i −0.492497 0.428085i
\(872\) 31.1116 1.05357
\(873\) −0.103202 5.38117i −0.00349287 0.182125i
\(874\) 2.79346 0.0944903
\(875\) 0.163218 + 0.282702i 0.00551777 + 0.00955706i
\(876\) 32.8742 0.315208i 1.11072 0.0106499i
\(877\) 32.2837 + 18.6390i 1.09014 + 0.629395i 0.933615 0.358279i \(-0.116636\pi\)
0.156529 + 0.987673i \(0.449970\pi\)
\(878\) 9.01666 + 5.20577i 0.304298 + 0.175686i
\(879\) −21.3379 + 0.204594i −0.719709 + 0.00690079i
\(880\) 1.71863 + 2.97676i 0.0579351 + 0.100347i
\(881\) 53.2952 1.79556 0.897780 0.440443i \(-0.145179\pi\)
0.897780 + 0.440443i \(0.145179\pi\)
\(882\) 11.9062 + 6.57291i 0.400902 + 0.221321i
\(883\) 12.5410 0.422038 0.211019 0.977482i \(-0.432322\pi\)
0.211019 + 0.977482i \(0.432322\pi\)
\(884\) −26.0581 + 29.9789i −0.876429 + 1.00830i
\(885\) 14.7873 + 8.34947i 0.497071 + 0.280664i
\(886\) −0.0831730 0.0480200i −0.00279425 0.00161326i
\(887\) −28.7562 + 49.8072i −0.965538 + 1.67236i −0.257377 + 0.966311i \(0.582858\pi\)
−0.708162 + 0.706050i \(0.750475\pi\)
\(888\) −27.5254 + 16.2456i −0.923692 + 0.545168i
\(889\) −3.38836 + 1.95627i −0.113642 + 0.0656113i
\(890\) 4.79878i 0.160855i
\(891\) 17.1867 + 9.06253i 0.575777 + 0.303606i
\(892\) 6.71386i 0.224797i
\(893\) 0.0951625 + 0.164826i 0.00318449 + 0.00551570i
\(894\) 21.2101 12.5183i 0.709371 0.418675i
\(895\) 2.51055 + 1.44947i 0.0839185 + 0.0484504i
\(896\) 1.81018 3.13532i 0.0604738 0.104744i
\(897\) 2.42702 13.1613i 0.0810358 0.439444i
\(898\) 0.554305 + 0.960084i 0.0184974 + 0.0320384i
\(899\) 26.8641i 0.895966i
\(900\) −2.27276 + 4.11688i −0.0757587 + 0.137229i
\(901\) −16.4094 −0.546676
\(902\) 4.77606 2.75746i 0.159025 0.0918134i
\(903\) −3.20182 + 0.0307001i −0.106550 + 0.00102163i
\(904\) 15.1890 + 8.76939i 0.505179 + 0.291665i
\(905\) 1.25470 + 0.724404i 0.0417078 + 0.0240800i
\(906\) −0.133742 13.9485i −0.00444329 0.463407i
\(907\) −19.6520 34.0383i −0.652535 1.13022i −0.982506 0.186232i \(-0.940372\pi\)
0.329971 0.943991i \(-0.392961\pi\)
\(908\) 38.9298i 1.29193i
\(909\) 30.7928 0.590557i 1.02133 0.0195875i
\(910\) 0.731838 0.252026i 0.0242602 0.00835457i
\(911\) 17.0985 + 29.6154i 0.566498 + 0.981203i 0.996909 + 0.0785697i \(0.0250353\pi\)
−0.430411 + 0.902633i \(0.641631\pi\)
\(912\) 2.68757 4.75983i 0.0889944 0.157614i
\(913\) 17.2502 29.8782i 0.570897 0.988823i
\(914\) −7.13995 + 12.3668i −0.236169 + 0.409056i
\(915\) −13.3941 22.6939i −0.442795 0.750237i
\(916\) 5.00870 2.89177i 0.165492 0.0955469i
\(917\) 6.17780i 0.204009i
\(918\) −12.6011 20.4444i −0.415900 0.674767i
\(919\) −25.6556 −0.846301 −0.423150 0.906059i \(-0.639076\pi\)
−0.423150 + 0.906059i \(0.639076\pi\)
\(920\) 2.51389 + 4.35419i 0.0828806 + 0.143553i
\(921\) 30.7612 + 52.1195i 1.01362 + 1.71740i
\(922\) 8.02287 13.8960i 0.264219 0.457641i
\(923\) 8.03739 41.3579i 0.264554 1.36131i
\(924\) −1.66611 0.940746i −0.0548110 0.0309483i
\(925\) −6.81170 + 3.93273i −0.223967 + 0.129308i
\(926\) 14.5888 0.479417
\(927\) 19.9877 + 33.1358i 0.656484 + 1.08832i
\(928\) 20.6843i 0.678997i
\(929\) 4.22076 2.43686i 0.138479 0.0799507i −0.429160 0.903228i \(-0.641190\pi\)
0.567639 + 0.823278i \(0.307857\pi\)
\(930\) −8.49004 + 0.0814051i −0.278399 + 0.00266938i
\(931\) −11.8331 6.83185i −0.387815 0.223905i
\(932\) −8.65603 + 14.9927i −0.283538 + 0.491102i
\(933\) 0.0546815 + 5.70293i 0.00179019 + 0.186706i
\(934\) −5.48086 + 3.16438i −0.179339 + 0.103542i
\(935\) −15.1726 −0.496196
\(936\) 19.4687 + 16.2777i 0.636355 + 0.532055i
\(937\) 9.44461 0.308542 0.154271 0.988029i \(-0.450697\pi\)
0.154271 + 0.988029i \(0.450697\pi\)
\(938\) −0.993014 + 0.573317i −0.0324231 + 0.0187195i
\(939\) 40.1755 + 22.6845i 1.31108 + 0.740282i
\(940\) −0.0752570 + 0.130349i −0.00245461 + 0.00425151i
\(941\) 14.3094 + 8.26153i 0.466473 + 0.269318i 0.714762 0.699368i \(-0.246535\pi\)
−0.248289 + 0.968686i \(0.579868\pi\)
\(942\) 1.64703 + 2.79061i 0.0536632 + 0.0909229i
\(943\) −7.20930 + 4.16229i −0.234767 + 0.135543i
\(944\) 15.6103i 0.508072i
\(945\) −0.0487831 1.69551i −0.00158692 0.0551549i
\(946\) 8.04015 0.261408
\(947\) −11.6573 + 6.73036i −0.378812 + 0.218707i −0.677301 0.735706i \(-0.736851\pi\)
0.298489 + 0.954413i \(0.403517\pi\)
\(948\) 25.9242 15.3006i 0.841979 0.496941i
\(949\) 8.32874 42.8571i 0.270362 1.39120i
\(950\) −0.651755 + 1.12887i −0.0211457 + 0.0366255i
\(951\) −19.6829 + 34.8595i −0.638263 + 1.13040i
\(952\) 2.69123 + 4.66135i 0.0872234 + 0.151075i
\(953\) 50.2664 1.62829 0.814144 0.580664i \(-0.197207\pi\)
0.814144 + 0.580664i \(0.197207\pi\)
\(954\) 0.0883268 + 4.60554i 0.00285969 + 0.149110i
\(955\) 3.10848i 0.100588i
\(956\) −6.88845 + 3.97705i −0.222788 + 0.128627i
\(957\) −13.4756 + 0.129208i −0.435605 + 0.00417671i
\(958\) −3.47638 + 6.02127i −0.112317 + 0.194539i
\(959\) −1.33120 + 2.30570i −0.0429865 + 0.0744549i
\(960\) −1.02183 + 0.00979764i −0.0329795 + 0.000316218i
\(961\) 12.2808 + 21.2709i 0.396154 + 0.686159i
\(962\) 6.07257 + 17.6336i 0.195787 + 0.568531i
\(963\) 15.4826 28.0452i 0.498920 0.903744i
\(964\) 21.2102i 0.683135i
\(965\) −9.20727 15.9475i −0.296392 0.513367i
\(966\) −0.693868 0.391783i −0.0223248 0.0126054i
\(967\) −42.3381 24.4439i −1.36150 0.786063i −0.371678 0.928362i \(-0.621217\pi\)
−0.989824 + 0.142299i \(0.954551\pi\)
\(968\) −12.8802 7.43640i −0.413986 0.239015i
\(969\) 12.2640 + 20.7792i 0.393976 + 0.667523i
\(970\) 1.02176 0.589912i 0.0328067 0.0189409i
\(971\) 20.9990 0.673891 0.336945 0.941524i \(-0.390606\pi\)
0.336945 + 0.941524i \(0.390606\pi\)
\(972\) 20.5518 13.2177i 0.659198 0.423958i
\(973\) 1.68575i 0.0540428i
\(974\) 12.1871 + 21.1086i 0.390499 + 0.676364i
\(975\) 4.75239 + 4.05151i 0.152198 + 0.129752i
\(976\) −12.1118 + 20.9783i −0.387689 + 0.671497i
\(977\) 0.570511 + 0.329385i 0.0182523 + 0.0105379i 0.509098 0.860708i \(-0.329979\pi\)
−0.490846 + 0.871246i \(0.663312\pi\)
\(978\) 0.316889 + 0.178927i 0.0101330 + 0.00572146i
\(979\) −7.87666 13.6428i −0.251739 0.436025i
\(980\) 10.8056i 0.345173i
\(981\) −34.8280 19.2271i −1.11197 0.613874i
\(982\) 5.59508i 0.178546i
\(983\) −44.5459 + 25.7186i −1.42079 + 0.820296i −0.996367 0.0851662i \(-0.972858\pi\)
−0.424427 + 0.905462i \(0.639525\pi\)
\(984\) −0.151344 15.7842i −0.00482467 0.503183i
\(985\) 4.67771 8.10204i 0.149044 0.258152i
\(986\) 14.4255 + 8.32859i 0.459403 + 0.265236i
\(987\) −0.000520527 0.0542877i −1.65686e−5 0.00172800i
\(988\) −8.45500 7.34920i −0.268989 0.233809i
\(989\) −12.1363 −0.385913
\(990\) 0.0816693 + 4.25840i 0.00259562 + 0.135341i
\(991\) −56.2188 −1.78585 −0.892924 0.450208i \(-0.851350\pi\)
−0.892924 + 0.450208i \(0.851350\pi\)
\(992\) 21.3902 + 37.0489i 0.679139 + 1.17630i
\(993\) 16.0844 28.4864i 0.510424 0.903988i
\(994\) −2.17244 1.25426i −0.0689055 0.0397826i
\(995\) 1.67239 + 0.965555i 0.0530183 + 0.0306101i
\(996\) −22.0535 37.3658i −0.698792 1.18398i
\(997\) 19.3082 + 33.4428i 0.611498 + 1.05915i 0.990988 + 0.133950i \(0.0427661\pi\)
−0.379490 + 0.925196i \(0.623901\pi\)
\(998\) −19.4913 −0.616986
\(999\) 40.8533 1.17543i 1.29254 0.0371890i
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 585.2.bt.b.571.33 yes 108
9.7 even 3 inner 585.2.bt.b.376.22 108
13.12 even 2 inner 585.2.bt.b.571.22 yes 108
117.25 even 6 inner 585.2.bt.b.376.33 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.bt.b.376.22 108 9.7 even 3 inner
585.2.bt.b.376.33 yes 108 117.25 even 6 inner
585.2.bt.b.571.22 yes 108 13.12 even 2 inner
585.2.bt.b.571.33 yes 108 1.1 even 1 trivial