Properties

Label 702.2.bb.a.71.5
Level $702$
Weight $2$
Character 702.71
Analytic conductor $5.605$
Analytic rank $0$
Dimension $56$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [702,2,Mod(71,702)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(702, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("702.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 702.bb (of order \(12\), degree \(4\), not 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: \(5.60549822189\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 234)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 71.5
Character \(\chi\) \(=\) 702.71
Dual form 702.2.bb.a.89.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.670386 - 0.179629i) q^{5} +(-4.43374 + 1.18802i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.670386 - 0.179629i) q^{5} +(-4.43374 + 1.18802i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.601052 - 0.347017i) q^{10} +(1.59115 - 1.59115i) q^{11} +(3.60547 - 0.0239902i) q^{13} +(3.97518 + 2.29507i) q^{14} -1.00000 q^{16} +(-2.32181 - 4.02149i) q^{17} +(-2.81042 - 0.753050i) q^{19} +(0.179629 + 0.670386i) q^{20} -2.25023 q^{22} +(-2.37251 - 4.10931i) q^{23} +(-3.91298 + 2.25916i) q^{25} +(-2.56642 - 2.53249i) q^{26} +(-1.18802 - 4.43374i) q^{28} -4.88226i q^{29} +(-1.74651 - 6.51808i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.20186 + 4.48539i) q^{34} +(-2.75891 + 1.59286i) q^{35} +(3.44953 - 0.924299i) q^{37} +(1.45478 + 2.51976i) q^{38} +(0.347017 - 0.601052i) q^{40} +(1.48606 - 5.54605i) q^{41} +(4.59562 + 2.65328i) q^{43} +(1.59115 + 1.59115i) q^{44} +(-1.22810 + 4.58334i) q^{46} +(-11.6601 - 3.12430i) q^{47} +(12.1845 - 7.03470i) q^{49} +(4.36436 + 1.16943i) q^{50} +(0.0239902 + 3.60547i) q^{52} +5.06576i q^{53} +(0.780869 - 1.35250i) q^{55} +(-2.29507 + 3.97518i) q^{56} +(-3.45228 + 3.45228i) q^{58} +(-3.79710 + 3.79710i) q^{59} +(-1.56055 + 2.70295i) q^{61} +(-3.37401 + 5.84395i) q^{62} -1.00000i q^{64} +(2.41275 - 0.663731i) q^{65} +(-12.6377 - 3.38625i) q^{67} +(4.02149 - 2.32181i) q^{68} +(3.07717 + 0.824524i) q^{70} +(4.16970 - 15.5615i) q^{71} +(-5.55110 - 5.55110i) q^{73} +(-3.09276 - 1.78561i) q^{74} +(0.753050 - 2.81042i) q^{76} +(-5.16444 + 8.94507i) q^{77} +(-1.55400 - 2.69161i) q^{79} +(-0.670386 + 0.179629i) q^{80} +(-4.97245 + 2.87085i) q^{82} +(-2.45977 + 9.17998i) q^{83} +(-2.27888 - 2.27888i) q^{85} +(-1.37344 - 5.12575i) q^{86} -2.25023i q^{88} +(0.648204 + 2.41913i) q^{89} +(-15.9572 + 4.38972i) q^{91} +(4.10931 - 2.37251i) q^{92} +(6.03569 + 10.4541i) q^{94} -2.01934 q^{95} +(-0.317765 - 1.18591i) q^{97} +(-13.5900 - 3.64143i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73} - 48 q^{74} + 4 q^{76} + 24 q^{77} - 24 q^{79} + 60 q^{83} - 48 q^{86} + 4 q^{91} + 24 q^{92} + 20 q^{97} + 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/702\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(677\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 0.670386 0.179629i 0.299806 0.0803327i −0.105780 0.994390i \(-0.533734\pi\)
0.405586 + 0.914057i \(0.367067\pi\)
\(6\) 0 0
\(7\) −4.43374 + 1.18802i −1.67579 + 0.449028i −0.966664 0.256049i \(-0.917579\pi\)
−0.709131 + 0.705077i \(0.750912\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0 0
\(10\) −0.601052 0.347017i −0.190069 0.109736i
\(11\) 1.59115 1.59115i 0.479751 0.479751i −0.425301 0.905052i \(-0.639832\pi\)
0.905052 + 0.425301i \(0.139832\pi\)
\(12\) 0 0
\(13\) 3.60547 0.0239902i 0.999978 0.00665368i
\(14\) 3.97518 + 2.29507i 1.06241 + 0.613383i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −2.32181 4.02149i −0.563121 0.975354i −0.997222 0.0744895i \(-0.976267\pi\)
0.434101 0.900864i \(-0.357066\pi\)
\(18\) 0 0
\(19\) −2.81042 0.753050i −0.644755 0.172762i −0.0783988 0.996922i \(-0.524981\pi\)
−0.566356 + 0.824160i \(0.691647\pi\)
\(20\) 0.179629 + 0.670386i 0.0401663 + 0.149903i
\(21\) 0 0
\(22\) −2.25023 −0.479751
\(23\) −2.37251 4.10931i −0.494703 0.856851i 0.505278 0.862957i \(-0.331390\pi\)
−0.999981 + 0.00610531i \(0.998057\pi\)
\(24\) 0 0
\(25\) −3.91298 + 2.25916i −0.782595 + 0.451832i
\(26\) −2.56642 2.53249i −0.503316 0.496662i
\(27\) 0 0
\(28\) −1.18802 4.43374i −0.224514 0.837897i
\(29\) 4.88226i 0.906613i −0.891355 0.453307i \(-0.850244\pi\)
0.891355 0.453307i \(-0.149756\pi\)
\(30\) 0 0
\(31\) −1.74651 6.51808i −0.313683 1.17068i −0.925209 0.379457i \(-0.876111\pi\)
0.611526 0.791224i \(-0.290556\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 0 0
\(34\) −1.20186 + 4.48539i −0.206116 + 0.769237i
\(35\) −2.75891 + 1.59286i −0.466341 + 0.269242i
\(36\) 0 0
\(37\) 3.44953 0.924299i 0.567099 0.151954i 0.0361333 0.999347i \(-0.488496\pi\)
0.530966 + 0.847393i \(0.321829\pi\)
\(38\) 1.45478 + 2.51976i 0.235997 + 0.408758i
\(39\) 0 0
\(40\) 0.347017 0.601052i 0.0548682 0.0950346i
\(41\) 1.48606 5.54605i 0.232083 0.866147i −0.747358 0.664421i \(-0.768678\pi\)
0.979442 0.201726i \(-0.0646551\pi\)
\(42\) 0 0
\(43\) 4.59562 + 2.65328i 0.700826 + 0.404622i 0.807655 0.589655i \(-0.200736\pi\)
−0.106829 + 0.994277i \(0.534070\pi\)
\(44\) 1.59115 + 1.59115i 0.239875 + 0.239875i
\(45\) 0 0
\(46\) −1.22810 + 4.58334i −0.181074 + 0.675777i
\(47\) −11.6601 3.12430i −1.70080 0.455727i −0.727656 0.685943i \(-0.759390\pi\)
−0.973140 + 0.230216i \(0.926057\pi\)
\(48\) 0 0
\(49\) 12.1845 7.03470i 1.74064 1.00496i
\(50\) 4.36436 + 1.16943i 0.617213 + 0.165382i
\(51\) 0 0
\(52\) 0.0239902 + 3.60547i 0.00332684 + 0.499989i
\(53\) 5.06576i 0.695835i 0.937525 + 0.347918i \(0.113111\pi\)
−0.937525 + 0.347918i \(0.886889\pi\)
\(54\) 0 0
\(55\) 0.780869 1.35250i 0.105292 0.182372i
\(56\) −2.29507 + 3.97518i −0.306692 + 0.531206i
\(57\) 0 0
\(58\) −3.45228 + 3.45228i −0.453307 + 0.453307i
\(59\) −3.79710 + 3.79710i −0.494341 + 0.494341i −0.909671 0.415330i \(-0.863666\pi\)
0.415330 + 0.909671i \(0.363666\pi\)
\(60\) 0 0
\(61\) −1.56055 + 2.70295i −0.199808 + 0.346078i −0.948466 0.316879i \(-0.897365\pi\)
0.748658 + 0.662956i \(0.230699\pi\)
\(62\) −3.37401 + 5.84395i −0.428499 + 0.742182i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 2.41275 0.663731i 0.299265 0.0823257i
\(66\) 0 0
\(67\) −12.6377 3.38625i −1.54393 0.413696i −0.616400 0.787433i \(-0.711410\pi\)
−0.927535 + 0.373737i \(0.878076\pi\)
\(68\) 4.02149 2.32181i 0.487677 0.281560i
\(69\) 0 0
\(70\) 3.07717 + 0.824524i 0.367792 + 0.0985495i
\(71\) 4.16970 15.5615i 0.494852 1.84681i −0.0360054 0.999352i \(-0.511463\pi\)
0.530857 0.847461i \(-0.321870\pi\)
\(72\) 0 0
\(73\) −5.55110 5.55110i −0.649707 0.649707i 0.303215 0.952922i \(-0.401940\pi\)
−0.952922 + 0.303215i \(0.901940\pi\)
\(74\) −3.09276 1.78561i −0.359526 0.207573i
\(75\) 0 0
\(76\) 0.753050 2.81042i 0.0863808 0.322378i
\(77\) −5.16444 + 8.94507i −0.588542 + 1.01939i
\(78\) 0 0
\(79\) −1.55400 2.69161i −0.174839 0.302829i 0.765267 0.643713i \(-0.222607\pi\)
−0.940105 + 0.340884i \(0.889274\pi\)
\(80\) −0.670386 + 0.179629i −0.0749514 + 0.0200832i
\(81\) 0 0
\(82\) −4.97245 + 2.87085i −0.549115 + 0.317032i
\(83\) −2.45977 + 9.17998i −0.269995 + 1.00763i 0.689127 + 0.724640i \(0.257994\pi\)
−0.959122 + 0.282993i \(0.908673\pi\)
\(84\) 0 0
\(85\) −2.27888 2.27888i −0.247180 0.247180i
\(86\) −1.37344 5.12575i −0.148102 0.552724i
\(87\) 0 0
\(88\) 2.25023i 0.239875i
\(89\) 0.648204 + 2.41913i 0.0687095 + 0.256427i 0.991733 0.128315i \(-0.0409569\pi\)
−0.923024 + 0.384743i \(0.874290\pi\)
\(90\) 0 0
\(91\) −15.9572 + 4.38972i −1.67277 + 0.460168i
\(92\) 4.10931 2.37251i 0.428426 0.247352i
\(93\) 0 0
\(94\) 6.03569 + 10.4541i 0.622534 + 1.07826i
\(95\) −2.01934 −0.207180
\(96\) 0 0
\(97\) −0.317765 1.18591i −0.0322641 0.120411i 0.947916 0.318521i \(-0.103186\pi\)
−0.980180 + 0.198110i \(0.936520\pi\)
\(98\) −13.5900 3.64143i −1.37280 0.367840i
\(99\) 0 0
\(100\) −2.25916 3.91298i −0.225916 0.391298i
\(101\) 3.76440 0.374572 0.187286 0.982305i \(-0.440031\pi\)
0.187286 + 0.982305i \(0.440031\pi\)
\(102\) 0 0
\(103\) 13.1567 + 7.59604i 1.29637 + 0.748460i 0.979775 0.200100i \(-0.0641268\pi\)
0.316596 + 0.948561i \(0.397460\pi\)
\(104\) 2.53249 2.56642i 0.248331 0.251658i
\(105\) 0 0
\(106\) 3.58203 3.58203i 0.347918 0.347918i
\(107\) 4.73458 + 2.73351i 0.457709 + 0.264259i 0.711081 0.703111i \(-0.248206\pi\)
−0.253371 + 0.967369i \(0.581539\pi\)
\(108\) 0 0
\(109\) 5.10130 5.10130i 0.488616 0.488616i −0.419253 0.907869i \(-0.637708\pi\)
0.907869 + 0.419253i \(0.137708\pi\)
\(110\) −1.50852 + 0.404207i −0.143832 + 0.0385397i
\(111\) 0 0
\(112\) 4.43374 1.18802i 0.418949 0.112257i
\(113\) 0.472893i 0.0444861i −0.999753 0.0222430i \(-0.992919\pi\)
0.999753 0.0222430i \(-0.00708076\pi\)
\(114\) 0 0
\(115\) −2.32865 2.32865i −0.217148 0.217148i
\(116\) 4.88226 0.453307
\(117\) 0 0
\(118\) 5.36992 0.494341
\(119\) 15.0719 + 15.0719i 1.38164 + 1.38164i
\(120\) 0 0
\(121\) 5.93646i 0.539678i
\(122\) 3.01475 0.807800i 0.272943 0.0731348i
\(123\) 0 0
\(124\) 6.51808 1.74651i 0.585341 0.156842i
\(125\) −4.67118 + 4.67118i −0.417803 + 0.417803i
\(126\) 0 0
\(127\) −0.377096 0.217716i −0.0334618 0.0193192i 0.483176 0.875523i \(-0.339483\pi\)
−0.516638 + 0.856204i \(0.672817\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) −2.17540 1.23674i −0.190795 0.108469i
\(131\) 9.02321 + 5.20955i 0.788361 + 0.455161i 0.839385 0.543537i \(-0.182915\pi\)
−0.0510241 + 0.998697i \(0.516249\pi\)
\(132\) 0 0
\(133\) 13.3553 1.15805
\(134\) 6.54173 + 11.3306i 0.565119 + 0.978815i
\(135\) 0 0
\(136\) −4.48539 1.20186i −0.384619 0.103058i
\(137\) −1.97943 7.38734i −0.169114 0.631143i −0.997480 0.0709549i \(-0.977395\pi\)
0.828365 0.560188i \(-0.189271\pi\)
\(138\) 0 0
\(139\) 11.1732 0.947702 0.473851 0.880605i \(-0.342863\pi\)
0.473851 + 0.880605i \(0.342863\pi\)
\(140\) −1.59286 2.75891i −0.134621 0.233171i
\(141\) 0 0
\(142\) −13.9521 + 8.05524i −1.17083 + 0.675980i
\(143\) 5.69869 5.77503i 0.476548 0.482932i
\(144\) 0 0
\(145\) −0.876997 3.27300i −0.0728307 0.271808i
\(146\) 7.85044i 0.649707i
\(147\) 0 0
\(148\) 0.924299 + 3.44953i 0.0759769 + 0.283550i
\(149\) 5.23203 + 5.23203i 0.428625 + 0.428625i 0.888160 0.459535i \(-0.151984\pi\)
−0.459535 + 0.888160i \(0.651984\pi\)
\(150\) 0 0
\(151\) −3.70881 + 13.8415i −0.301818 + 1.12640i 0.633831 + 0.773471i \(0.281481\pi\)
−0.935650 + 0.352930i \(0.885185\pi\)
\(152\) −2.51976 + 1.45478i −0.204379 + 0.117998i
\(153\) 0 0
\(154\) 9.97693 2.67331i 0.803964 0.215421i
\(155\) −2.34168 4.05590i −0.188088 0.325778i
\(156\) 0 0
\(157\) −2.86104 + 4.95546i −0.228336 + 0.395489i −0.957315 0.289047i \(-0.906662\pi\)
0.728979 + 0.684536i \(0.239995\pi\)
\(158\) −0.804409 + 3.00210i −0.0639954 + 0.238834i
\(159\) 0 0
\(160\) 0.601052 + 0.347017i 0.0475173 + 0.0274341i
\(161\) 15.4010 + 15.4010i 1.21377 + 1.21377i
\(162\) 0 0
\(163\) −1.44621 + 5.39731i −0.113276 + 0.422750i −0.999152 0.0411708i \(-0.986891\pi\)
0.885877 + 0.463921i \(0.153558\pi\)
\(164\) 5.54605 + 1.48606i 0.433074 + 0.116042i
\(165\) 0 0
\(166\) 8.23054 4.75191i 0.638814 0.368819i
\(167\) −23.6549 6.33832i −1.83047 0.490474i −0.832495 0.554033i \(-0.813088\pi\)
−0.997978 + 0.0635593i \(0.979755\pi\)
\(168\) 0 0
\(169\) 12.9988 0.172992i 0.999911 0.0133071i
\(170\) 3.22283i 0.247180i
\(171\) 0 0
\(172\) −2.65328 + 4.59562i −0.202311 + 0.350413i
\(173\) 5.29699 9.17465i 0.402722 0.697536i −0.591331 0.806429i \(-0.701397\pi\)
0.994053 + 0.108893i \(0.0347307\pi\)
\(174\) 0 0
\(175\) 14.6652 14.6652i 1.10858 1.10858i
\(176\) −1.59115 + 1.59115i −0.119938 + 0.119938i
\(177\) 0 0
\(178\) 1.25223 2.16893i 0.0938590 0.162569i
\(179\) 6.22591 10.7836i 0.465346 0.806003i −0.533871 0.845566i \(-0.679263\pi\)
0.999217 + 0.0395630i \(0.0125966\pi\)
\(180\) 0 0
\(181\) 18.4465i 1.37112i −0.728018 0.685558i \(-0.759558\pi\)
0.728018 0.685558i \(-0.240442\pi\)
\(182\) 14.3875 + 8.17945i 1.06647 + 0.606301i
\(183\) 0 0
\(184\) −4.58334 1.22810i −0.337889 0.0905370i
\(185\) 2.14648 1.23927i 0.157813 0.0911132i
\(186\) 0 0
\(187\) −10.0932 2.70445i −0.738084 0.197769i
\(188\) 3.12430 11.6601i 0.227863 0.850398i
\(189\) 0 0
\(190\) 1.42789 + 1.42789i 0.103590 + 0.103590i
\(191\) −7.37477 4.25783i −0.533620 0.308085i 0.208870 0.977944i \(-0.433022\pi\)
−0.742489 + 0.669858i \(0.766355\pi\)
\(192\) 0 0
\(193\) −4.89947 + 18.2851i −0.352671 + 1.31619i 0.530718 + 0.847548i \(0.321922\pi\)
−0.883390 + 0.468639i \(0.844744\pi\)
\(194\) −0.613875 + 1.06326i −0.0440736 + 0.0763378i
\(195\) 0 0
\(196\) 7.03470 + 12.1845i 0.502478 + 0.870318i
\(197\) 16.8453 4.51369i 1.20018 0.321587i 0.397278 0.917698i \(-0.369955\pi\)
0.802902 + 0.596111i \(0.203288\pi\)
\(198\) 0 0
\(199\) 20.0170 11.5568i 1.41897 0.819243i 0.422761 0.906241i \(-0.361061\pi\)
0.996208 + 0.0869986i \(0.0277276\pi\)
\(200\) −1.16943 + 4.36436i −0.0826909 + 0.308607i
\(201\) 0 0
\(202\) −2.66184 2.66184i −0.187286 0.187286i
\(203\) 5.80020 + 21.6467i 0.407095 + 1.51930i
\(204\) 0 0
\(205\) 3.98493i 0.278320i
\(206\) −3.93200 14.6744i −0.273955 1.02242i
\(207\) 0 0
\(208\) −3.60547 + 0.0239902i −0.249994 + 0.00166342i
\(209\) −5.67003 + 3.27359i −0.392204 + 0.226439i
\(210\) 0 0
\(211\) 5.19424 + 8.99669i 0.357586 + 0.619358i 0.987557 0.157261i \(-0.0502665\pi\)
−0.629971 + 0.776619i \(0.716933\pi\)
\(212\) −5.06576 −0.347918
\(213\) 0 0
\(214\) −1.41497 5.28074i −0.0967254 0.360984i
\(215\) 3.55745 + 0.953215i 0.242616 + 0.0650087i
\(216\) 0 0
\(217\) 15.4872 + 26.8246i 1.05134 + 1.82097i
\(218\) −7.21433 −0.488616
\(219\) 0 0
\(220\) 1.35250 + 0.780869i 0.0911858 + 0.0526462i
\(221\) −8.46768 14.4437i −0.569598 0.971585i
\(222\) 0 0
\(223\) 11.2191 11.2191i 0.751283 0.751283i −0.223435 0.974719i \(-0.571727\pi\)
0.974719 + 0.223435i \(0.0717271\pi\)
\(224\) −3.97518 2.29507i −0.265603 0.153346i
\(225\) 0 0
\(226\) −0.334386 + 0.334386i −0.0222430 + 0.0222430i
\(227\) −6.15723 + 1.64982i −0.408669 + 0.109503i −0.457296 0.889314i \(-0.651182\pi\)
0.0486270 + 0.998817i \(0.484515\pi\)
\(228\) 0 0
\(229\) 12.3575 3.31118i 0.816606 0.218809i 0.173744 0.984791i \(-0.444414\pi\)
0.642862 + 0.765982i \(0.277747\pi\)
\(230\) 3.29321i 0.217148i
\(231\) 0 0
\(232\) −3.45228 3.45228i −0.226653 0.226653i
\(233\) −18.2644 −1.19654 −0.598271 0.801294i \(-0.704145\pi\)
−0.598271 + 0.801294i \(0.704145\pi\)
\(234\) 0 0
\(235\) −8.37796 −0.546518
\(236\) −3.79710 3.79710i −0.247170 0.247170i
\(237\) 0 0
\(238\) 21.3148i 1.38164i
\(239\) −19.3192 + 5.17656i −1.24965 + 0.334844i −0.822203 0.569195i \(-0.807255\pi\)
−0.427451 + 0.904039i \(0.640588\pi\)
\(240\) 0 0
\(241\) −14.5426 + 3.89667i −0.936768 + 0.251006i −0.694739 0.719262i \(-0.744480\pi\)
−0.242030 + 0.970269i \(0.577813\pi\)
\(242\) 4.19771 4.19771i 0.269839 0.269839i
\(243\) 0 0
\(244\) −2.70295 1.56055i −0.173039 0.0999040i
\(245\) 6.90465 6.90465i 0.441122 0.441122i
\(246\) 0 0
\(247\) −10.1510 2.64768i −0.645890 0.168468i
\(248\) −5.84395 3.37401i −0.371091 0.214250i
\(249\) 0 0
\(250\) 6.60604 0.417803
\(251\) 13.1431 + 22.7645i 0.829586 + 1.43689i 0.898363 + 0.439253i \(0.144757\pi\)
−0.0687771 + 0.997632i \(0.521910\pi\)
\(252\) 0 0
\(253\) −10.3136 2.76352i −0.648409 0.173741i
\(254\) 0.112698 + 0.420596i 0.00707132 + 0.0263905i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −6.83291 11.8349i −0.426225 0.738244i 0.570309 0.821430i \(-0.306824\pi\)
−0.996534 + 0.0831866i \(0.973490\pi\)
\(258\) 0 0
\(259\) −14.1962 + 8.19619i −0.882110 + 0.509286i
\(260\) 0.663731 + 2.41275i 0.0411629 + 0.149632i
\(261\) 0 0
\(262\) −2.69666 10.0641i −0.166600 0.621761i
\(263\) 4.79600i 0.295734i −0.989007 0.147867i \(-0.952759\pi\)
0.989007 0.147867i \(-0.0472408\pi\)
\(264\) 0 0
\(265\) 0.909959 + 3.39601i 0.0558983 + 0.208615i
\(266\) −9.44363 9.44363i −0.579026 0.579026i
\(267\) 0 0
\(268\) 3.38625 12.6377i 0.206848 0.771967i
\(269\) −21.5499 + 12.4418i −1.31392 + 0.758591i −0.982743 0.184978i \(-0.940779\pi\)
−0.331176 + 0.943569i \(0.607445\pi\)
\(270\) 0 0
\(271\) −0.766787 + 0.205460i −0.0465790 + 0.0124808i −0.282033 0.959405i \(-0.591009\pi\)
0.235454 + 0.971885i \(0.424342\pi\)
\(272\) 2.32181 + 4.02149i 0.140780 + 0.243838i
\(273\) 0 0
\(274\) −3.82397 + 6.62331i −0.231015 + 0.400129i
\(275\) −2.63148 + 9.82081i −0.158684 + 0.592217i
\(276\) 0 0
\(277\) 28.5357 + 16.4751i 1.71455 + 0.989893i 0.928179 + 0.372133i \(0.121373\pi\)
0.786366 + 0.617760i \(0.211960\pi\)
\(278\) −7.90068 7.90068i −0.473851 0.473851i
\(279\) 0 0
\(280\) −0.824524 + 3.07717i −0.0492747 + 0.183896i
\(281\) 17.5706 + 4.70802i 1.04817 + 0.280857i 0.741496 0.670957i \(-0.234117\pi\)
0.306676 + 0.951814i \(0.400783\pi\)
\(282\) 0 0
\(283\) −21.1331 + 12.2012i −1.25624 + 0.725288i −0.972341 0.233568i \(-0.924960\pi\)
−0.283895 + 0.958856i \(0.591627\pi\)
\(284\) 15.5615 + 4.16970i 0.923406 + 0.247426i
\(285\) 0 0
\(286\) −8.11314 + 0.0539834i −0.479740 + 0.00319211i
\(287\) 26.3552i 1.55570i
\(288\) 0 0
\(289\) −2.28157 + 3.95179i −0.134210 + 0.232458i
\(290\) −1.69423 + 2.93449i −0.0994886 + 0.172319i
\(291\) 0 0
\(292\) 5.55110 5.55110i 0.324853 0.324853i
\(293\) −2.57215 + 2.57215i −0.150266 + 0.150266i −0.778237 0.627971i \(-0.783886\pi\)
0.627971 + 0.778237i \(0.283886\pi\)
\(294\) 0 0
\(295\) −1.86345 + 3.22760i −0.108494 + 0.187918i
\(296\) 1.78561 3.09276i 0.103786 0.179763i
\(297\) 0 0
\(298\) 7.39921i 0.428625i
\(299\) −8.65261 14.7591i −0.500394 0.853541i
\(300\) 0 0
\(301\) −23.5279 6.30429i −1.35613 0.363373i
\(302\) 12.4099 7.16486i 0.714110 0.412291i
\(303\) 0 0
\(304\) 2.81042 + 0.753050i 0.161189 + 0.0431904i
\(305\) −0.560641 + 2.09234i −0.0321022 + 0.119807i
\(306\) 0 0
\(307\) 10.8993 + 10.8993i 0.622055 + 0.622055i 0.946057 0.324001i \(-0.105028\pi\)
−0.324001 + 0.946057i \(0.605028\pi\)
\(308\) −8.94507 5.16444i −0.509693 0.294271i
\(309\) 0 0
\(310\) −1.21214 + 4.52377i −0.0688450 + 0.256933i
\(311\) 5.37895 9.31661i 0.305012 0.528296i −0.672252 0.740322i \(-0.734673\pi\)
0.977264 + 0.212026i \(0.0680062\pi\)
\(312\) 0 0
\(313\) 6.34655 + 10.9926i 0.358728 + 0.621336i 0.987749 0.156053i \(-0.0498771\pi\)
−0.629020 + 0.777389i \(0.716544\pi\)
\(314\) 5.52710 1.48098i 0.311912 0.0835766i
\(315\) 0 0
\(316\) 2.69161 1.55400i 0.151415 0.0874193i
\(317\) 6.74033 25.1552i 0.378574 1.41286i −0.469477 0.882945i \(-0.655557\pi\)
0.848051 0.529914i \(-0.177776\pi\)
\(318\) 0 0
\(319\) −7.76843 7.76843i −0.434948 0.434948i
\(320\) −0.179629 0.670386i −0.0100416 0.0374757i
\(321\) 0 0
\(322\) 21.7803i 1.21377i
\(323\) 3.49687 + 13.0505i 0.194571 + 0.726150i
\(324\) 0 0
\(325\) −14.0539 + 8.23920i −0.779572 + 0.457029i
\(326\) 4.83910 2.79386i 0.268013 0.154737i
\(327\) 0 0
\(328\) −2.87085 4.97245i −0.158516 0.274558i
\(329\) 55.4094 3.05482
\(330\) 0 0
\(331\) −5.24463 19.5732i −0.288271 1.07584i −0.946416 0.322950i \(-0.895325\pi\)
0.658145 0.752891i \(-0.271341\pi\)
\(332\) −9.17998 2.45977i −0.503817 0.134997i
\(333\) 0 0
\(334\) 12.2447 + 21.2084i 0.670000 + 1.16047i
\(335\) −9.08037 −0.496114
\(336\) 0 0
\(337\) −6.82932 3.94291i −0.372017 0.214784i 0.302322 0.953206i \(-0.402238\pi\)
−0.674339 + 0.738422i \(0.735571\pi\)
\(338\) −9.31390 9.06925i −0.506609 0.493302i
\(339\) 0 0
\(340\) 2.27888 2.27888i 0.123590 0.123590i
\(341\) −13.1502 7.59229i −0.712125 0.411146i
\(342\) 0 0
\(343\) −22.9453 + 22.9453i −1.23893 + 1.23893i
\(344\) 5.12575 1.37344i 0.276362 0.0740510i
\(345\) 0 0
\(346\) −10.2330 + 2.74192i −0.550129 + 0.147407i
\(347\) 16.9956i 0.912370i 0.889885 + 0.456185i \(0.150784\pi\)
−0.889885 + 0.456185i \(0.849216\pi\)
\(348\) 0 0
\(349\) −10.2799 10.2799i −0.550269 0.550269i 0.376250 0.926518i \(-0.377214\pi\)
−0.926518 + 0.376250i \(0.877214\pi\)
\(350\) −20.7397 −1.10858
\(351\) 0 0
\(352\) 2.25023 0.119938
\(353\) 6.02030 + 6.02030i 0.320428 + 0.320428i 0.848931 0.528503i \(-0.177246\pi\)
−0.528503 + 0.848931i \(0.677246\pi\)
\(354\) 0 0
\(355\) 11.1812i 0.593438i
\(356\) −2.41913 + 0.648204i −0.128214 + 0.0343548i
\(357\) 0 0
\(358\) −12.0275 + 3.22277i −0.635674 + 0.170328i
\(359\) −2.80645 + 2.80645i −0.148119 + 0.148119i −0.777277 0.629158i \(-0.783400\pi\)
0.629158 + 0.777277i \(0.283400\pi\)
\(360\) 0 0
\(361\) −9.12309 5.26722i −0.480163 0.277222i
\(362\) −13.0436 + 13.0436i −0.685558 + 0.685558i
\(363\) 0 0
\(364\) −4.38972 15.9572i −0.230084 0.836385i
\(365\) −4.71852 2.72424i −0.246979 0.142593i
\(366\) 0 0
\(367\) −24.3581 −1.27148 −0.635742 0.771901i \(-0.719306\pi\)
−0.635742 + 0.771901i \(0.719306\pi\)
\(368\) 2.37251 + 4.10931i 0.123676 + 0.214213i
\(369\) 0 0
\(370\) −2.39409 0.641495i −0.124463 0.0333497i
\(371\) −6.01820 22.4602i −0.312449 1.16608i
\(372\) 0 0
\(373\) −9.25807 −0.479365 −0.239682 0.970851i \(-0.577043\pi\)
−0.239682 + 0.970851i \(0.577043\pi\)
\(374\) 5.22460 + 9.04927i 0.270158 + 0.467927i
\(375\) 0 0
\(376\) −10.4541 + 6.03569i −0.539130 + 0.311267i
\(377\) −0.117126 17.6029i −0.00603231 0.906593i
\(378\) 0 0
\(379\) −3.58050 13.3626i −0.183918 0.686391i −0.994860 0.101264i \(-0.967711\pi\)
0.810942 0.585127i \(-0.198955\pi\)
\(380\) 2.01934i 0.103590i
\(381\) 0 0
\(382\) 2.20401 + 8.22549i 0.112767 + 0.420853i
\(383\) −12.5916 12.5916i −0.643398 0.643398i 0.307991 0.951389i \(-0.400343\pi\)
−0.951389 + 0.307991i \(0.900343\pi\)
\(384\) 0 0
\(385\) −1.85537 + 6.92433i −0.0945584 + 0.352897i
\(386\) 16.3939 9.46505i 0.834430 0.481758i
\(387\) 0 0
\(388\) 1.18591 0.317765i 0.0602057 0.0161321i
\(389\) −7.46970 12.9379i −0.378729 0.655978i 0.612149 0.790743i \(-0.290305\pi\)
−0.990878 + 0.134765i \(0.956972\pi\)
\(390\) 0 0
\(391\) −11.0170 + 19.0821i −0.557155 + 0.965021i
\(392\) 3.64143 13.5900i 0.183920 0.686398i
\(393\) 0 0
\(394\) −15.1031 8.71978i −0.760884 0.439296i
\(395\) −1.52527 1.52527i −0.0767447 0.0767447i
\(396\) 0 0
\(397\) 0.691339 2.58011i 0.0346973 0.129492i −0.946405 0.322983i \(-0.895314\pi\)
0.981102 + 0.193491i \(0.0619810\pi\)
\(398\) −22.3261 5.98226i −1.11911 0.299864i
\(399\) 0 0
\(400\) 3.91298 2.25916i 0.195649 0.112958i
\(401\) 0.0650204 + 0.0174222i 0.00324697 + 0.000870022i 0.260442 0.965489i \(-0.416132\pi\)
−0.257195 + 0.966359i \(0.582798\pi\)
\(402\) 0 0
\(403\) −6.45338 23.4588i −0.321466 1.16857i
\(404\) 3.76440i 0.187286i
\(405\) 0 0
\(406\) 11.2051 19.4079i 0.556101 0.963196i
\(407\) 4.01803 6.95943i 0.199166 0.344966i
\(408\) 0 0
\(409\) −14.4433 + 14.4433i −0.714173 + 0.714173i −0.967405 0.253233i \(-0.918506\pi\)
0.253233 + 0.967405i \(0.418506\pi\)
\(410\) −2.81777 + 2.81777i −0.139160 + 0.139160i
\(411\) 0 0
\(412\) −7.59604 + 13.1567i −0.374230 + 0.648186i
\(413\) 12.3243 21.3464i 0.606441 1.05039i
\(414\) 0 0
\(415\) 6.59597i 0.323784i
\(416\) 2.56642 + 2.53249i 0.125829 + 0.124166i
\(417\) 0 0
\(418\) 6.32410 + 1.69454i 0.309322 + 0.0828825i
\(419\) 19.8836 11.4798i 0.971378 0.560826i 0.0717221 0.997425i \(-0.477151\pi\)
0.899656 + 0.436599i \(0.143817\pi\)
\(420\) 0 0
\(421\) 10.9066 + 2.92242i 0.531556 + 0.142430i 0.514607 0.857426i \(-0.327938\pi\)
0.0169495 + 0.999856i \(0.494605\pi\)
\(422\) 2.68874 10.0345i 0.130886 0.488472i
\(423\) 0 0
\(424\) 3.58203 + 3.58203i 0.173959 + 0.173959i
\(425\) 18.1703 + 10.4907i 0.881391 + 0.508871i
\(426\) 0 0
\(427\) 3.70792 13.8381i 0.179439 0.669674i
\(428\) −2.73351 + 4.73458i −0.132129 + 0.228855i
\(429\) 0 0
\(430\) −1.84147 3.18952i −0.0888036 0.153812i
\(431\) −8.79469 + 2.35653i −0.423625 + 0.113510i −0.464332 0.885661i \(-0.653706\pi\)
0.0407069 + 0.999171i \(0.487039\pi\)
\(432\) 0 0
\(433\) 19.6096 11.3216i 0.942379 0.544083i 0.0516737 0.998664i \(-0.483544\pi\)
0.890705 + 0.454581i \(0.150211\pi\)
\(434\) 8.01675 29.9189i 0.384816 1.43615i
\(435\) 0 0
\(436\) 5.10130 + 5.10130i 0.244308 + 0.244308i
\(437\) 3.57325 + 13.3355i 0.170931 + 0.637925i
\(438\) 0 0
\(439\) 21.3894i 1.02086i −0.859920 0.510430i \(-0.829486\pi\)
0.859920 0.510430i \(-0.170514\pi\)
\(440\) −0.404207 1.50852i −0.0192698 0.0719160i
\(441\) 0 0
\(442\) −4.22565 + 16.2008i −0.200994 + 0.770592i
\(443\) −27.1059 + 15.6496i −1.28784 + 0.743535i −0.978269 0.207341i \(-0.933519\pi\)
−0.309571 + 0.950876i \(0.600186\pi\)
\(444\) 0 0
\(445\) 0.869094 + 1.50532i 0.0411990 + 0.0713588i
\(446\) −15.8661 −0.751283
\(447\) 0 0
\(448\) 1.18802 + 4.43374i 0.0561285 + 0.209474i
\(449\) −12.7731 3.42254i −0.602800 0.161520i −0.0555034 0.998458i \(-0.517676\pi\)
−0.547297 + 0.836939i \(0.684343\pi\)
\(450\) 0 0
\(451\) −6.46007 11.1892i −0.304193 0.526877i
\(452\) 0.472893 0.0222430
\(453\) 0 0
\(454\) 5.52042 + 3.18721i 0.259086 + 0.149583i
\(455\) −9.90896 + 5.80919i −0.464539 + 0.272339i
\(456\) 0 0
\(457\) 8.28185 8.28185i 0.387409 0.387409i −0.486354 0.873762i \(-0.661673\pi\)
0.873762 + 0.486354i \(0.161673\pi\)
\(458\) −11.0794 6.39671i −0.517707 0.298898i
\(459\) 0 0
\(460\) 2.32865 2.32865i 0.108574 0.108574i
\(461\) −7.07647 + 1.89613i −0.329584 + 0.0883118i −0.419817 0.907609i \(-0.637906\pi\)
0.0902326 + 0.995921i \(0.471239\pi\)
\(462\) 0 0
\(463\) −14.1615 + 3.79457i −0.658142 + 0.176349i −0.572407 0.819969i \(-0.693990\pi\)
−0.0857346 + 0.996318i \(0.527324\pi\)
\(464\) 4.88226i 0.226653i
\(465\) 0 0
\(466\) 12.9149 + 12.9149i 0.598271 + 0.598271i
\(467\) 18.0118 0.833488 0.416744 0.909024i \(-0.363171\pi\)
0.416744 + 0.909024i \(0.363171\pi\)
\(468\) 0 0
\(469\) 60.0549 2.77308
\(470\) 5.92411 + 5.92411i 0.273259 + 0.273259i
\(471\) 0 0
\(472\) 5.36992i 0.247170i
\(473\) 11.5341 3.09056i 0.530339 0.142104i
\(474\) 0 0
\(475\) 12.6984 3.40252i 0.582641 0.156118i
\(476\) −15.0719 + 15.0719i −0.690818 + 0.690818i
\(477\) 0 0
\(478\) 17.3211 + 10.0003i 0.792249 + 0.457405i
\(479\) 5.08536 5.08536i 0.232356 0.232356i −0.581319 0.813675i \(-0.697463\pi\)
0.813675 + 0.581319i \(0.197463\pi\)
\(480\) 0 0
\(481\) 12.4150 3.41529i 0.566075 0.155724i
\(482\) 13.0385 + 7.52778i 0.593887 + 0.342881i
\(483\) 0 0
\(484\) −5.93646 −0.269839
\(485\) −0.426050 0.737940i −0.0193459 0.0335082i
\(486\) 0 0
\(487\) 0.324094 + 0.0868407i 0.0146861 + 0.00393513i 0.266155 0.963930i \(-0.414247\pi\)
−0.251469 + 0.967865i \(0.580913\pi\)
\(488\) 0.807800 + 3.01475i 0.0365674 + 0.136471i
\(489\) 0 0
\(490\) −9.76464 −0.441122
\(491\) 1.96382 + 3.40144i 0.0886260 + 0.153505i 0.906931 0.421280i \(-0.138419\pi\)
−0.818305 + 0.574785i \(0.805086\pi\)
\(492\) 0 0
\(493\) −19.6339 + 11.3357i −0.884269 + 0.510533i
\(494\) 5.30562 + 9.05001i 0.238711 + 0.407179i
\(495\) 0 0
\(496\) 1.74651 + 6.51808i 0.0784208 + 0.292670i
\(497\) 73.9493i 3.31708i
\(498\) 0 0
\(499\) −5.25372 19.6072i −0.235189 0.877737i −0.978064 0.208307i \(-0.933205\pi\)
0.742875 0.669431i \(-0.233462\pi\)
\(500\) −4.67118 4.67118i −0.208901 0.208901i
\(501\) 0 0
\(502\) 6.80338 25.3906i 0.303650 1.13324i
\(503\) −24.7833 + 14.3086i −1.10503 + 0.637991i −0.937538 0.347882i \(-0.886901\pi\)
−0.167494 + 0.985873i \(0.553568\pi\)
\(504\) 0 0
\(505\) 2.52360 0.676198i 0.112299 0.0300904i
\(506\) 5.33870 + 9.24691i 0.237334 + 0.411075i
\(507\) 0 0
\(508\) 0.217716 0.377096i 0.00965960 0.0167309i
\(509\) 4.15448 15.5047i 0.184144 0.687235i −0.810668 0.585506i \(-0.800896\pi\)
0.994812 0.101729i \(-0.0324375\pi\)
\(510\) 0 0
\(511\) 31.2069 + 18.0173i 1.38051 + 0.797039i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0 0
\(514\) −3.53697 + 13.2002i −0.156009 + 0.582235i
\(515\) 10.1846 + 2.72894i 0.448785 + 0.120252i
\(516\) 0 0
\(517\) −23.5242 + 13.5817i −1.03459 + 0.597323i
\(518\) 15.8338 + 4.24266i 0.695698 + 0.186412i
\(519\) 0 0
\(520\) 1.23674 2.17540i 0.0542347 0.0953976i
\(521\) 19.3205i 0.846448i −0.906025 0.423224i \(-0.860898\pi\)
0.906025 0.423224i \(-0.139102\pi\)
\(522\) 0 0
\(523\) 4.17667 7.23421i 0.182633 0.316330i −0.760143 0.649755i \(-0.774871\pi\)
0.942776 + 0.333426i \(0.108205\pi\)
\(524\) −5.20955 + 9.02321i −0.227580 + 0.394181i
\(525\) 0 0
\(526\) −3.39129 + 3.39129i −0.147867 + 0.147867i
\(527\) −22.1573 + 22.1573i −0.965187 + 0.965187i
\(528\) 0 0
\(529\) 0.242357 0.419774i 0.0105372 0.0182510i
\(530\) 1.75791 3.04478i 0.0763585 0.132257i
\(531\) 0 0
\(532\) 13.3553i 0.579026i
\(533\) 5.22489 20.0318i 0.226315 0.867672i
\(534\) 0 0
\(535\) 3.66502 + 0.982038i 0.158452 + 0.0424572i
\(536\) −11.3306 + 6.54173i −0.489408 + 0.282560i
\(537\) 0 0
\(538\) 24.0358 + 6.44036i 1.03625 + 0.277664i
\(539\) 8.19405 30.5806i 0.352943 1.31720i
\(540\) 0 0
\(541\) 18.5480 + 18.5480i 0.797443 + 0.797443i 0.982692 0.185249i \(-0.0593092\pi\)
−0.185249 + 0.982692i \(0.559309\pi\)
\(542\) 0.687482 + 0.396918i 0.0295299 + 0.0170491i
\(543\) 0 0
\(544\) 1.20186 4.48539i 0.0515291 0.192309i
\(545\) 2.50350 4.33618i 0.107238 0.185742i
\(546\) 0 0
\(547\) −11.1826 19.3688i −0.478133 0.828151i 0.521552 0.853219i \(-0.325353\pi\)
−0.999686 + 0.0250681i \(0.992020\pi\)
\(548\) 7.38734 1.97943i 0.315572 0.0845572i
\(549\) 0 0
\(550\) 8.80510 5.08363i 0.375451 0.216767i
\(551\) −3.67659 + 13.7212i −0.156628 + 0.584544i
\(552\) 0 0
\(553\) 10.0877 + 10.0877i 0.428972 + 0.428972i
\(554\) −8.52814 31.8275i −0.362326 1.35222i
\(555\) 0 0
\(556\) 11.1732i 0.473851i
\(557\) 3.13004 + 11.6815i 0.132624 + 0.494959i 0.999996 0.00270033i \(-0.000859542\pi\)
−0.867372 + 0.497660i \(0.834193\pi\)
\(558\) 0 0
\(559\) 16.6330 + 9.45609i 0.703503 + 0.399950i
\(560\) 2.75891 1.59286i 0.116585 0.0673105i
\(561\) 0 0
\(562\) −9.09520 15.7533i −0.383658 0.664515i
\(563\) −35.1807 −1.48269 −0.741345 0.671124i \(-0.765812\pi\)
−0.741345 + 0.671124i \(0.765812\pi\)
\(564\) 0 0
\(565\) −0.0849455 0.317021i −0.00357368 0.0133372i
\(566\) 23.5710 + 6.31582i 0.990761 + 0.265474i
\(567\) 0 0
\(568\) −8.05524 13.9521i −0.337990 0.585416i
\(569\) 11.2623 0.472141 0.236071 0.971736i \(-0.424140\pi\)
0.236071 + 0.971736i \(0.424140\pi\)
\(570\) 0 0
\(571\) 27.0909 + 15.6409i 1.13372 + 0.654553i 0.944868 0.327452i \(-0.106190\pi\)
0.188852 + 0.982006i \(0.439523\pi\)
\(572\) 5.77503 + 5.69869i 0.241466 + 0.238274i
\(573\) 0 0
\(574\) 18.6359 18.6359i 0.777848 0.777848i
\(575\) 18.5672 + 10.7198i 0.774305 + 0.447045i
\(576\) 0 0
\(577\) −26.9790 + 26.9790i −1.12315 + 1.12315i −0.131887 + 0.991265i \(0.542103\pi\)
−0.991265 + 0.131887i \(0.957897\pi\)
\(578\) 4.40765 1.18103i 0.183334 0.0491242i
\(579\) 0 0
\(580\) 3.27300 0.876997i 0.135904 0.0364153i
\(581\) 43.6238i 1.80982i
\(582\) 0 0
\(583\) 8.06040 + 8.06040i 0.333828 + 0.333828i
\(584\) −7.85044 −0.324853
\(585\) 0 0
\(586\) 3.63756 0.150266
\(587\) −1.61436 1.61436i −0.0666316 0.0666316i 0.673006 0.739637i \(-0.265003\pi\)
−0.739637 + 0.673006i \(0.765003\pi\)
\(588\) 0 0
\(589\) 19.6338i 0.808995i
\(590\) 3.59992 0.964595i 0.148206 0.0397117i
\(591\) 0 0
\(592\) −3.44953 + 0.924299i −0.141775 + 0.0379884i
\(593\) 21.4122 21.4122i 0.879295 0.879295i −0.114166 0.993462i \(-0.536420\pi\)
0.993462 + 0.114166i \(0.0364197\pi\)
\(594\) 0 0
\(595\) 12.8113 + 7.39662i 0.525213 + 0.303232i
\(596\) −5.23203 + 5.23203i −0.214312 + 0.214312i
\(597\) 0 0
\(598\) −4.31794 + 16.5546i −0.176574 + 0.676967i
\(599\) 27.0669 + 15.6271i 1.10593 + 0.638506i 0.937771 0.347255i \(-0.112886\pi\)
0.168154 + 0.985761i \(0.446219\pi\)
\(600\) 0 0
\(601\) −27.8755 −1.13707 −0.568533 0.822661i \(-0.692489\pi\)
−0.568533 + 0.822661i \(0.692489\pi\)
\(602\) 12.1789 + 21.0946i 0.496377 + 0.859750i
\(603\) 0 0
\(604\) −13.8415 3.70881i −0.563201 0.150909i
\(605\) 1.06636 + 3.97972i 0.0433538 + 0.161799i
\(606\) 0 0
\(607\) −2.84557 −0.115498 −0.0577490 0.998331i \(-0.518392\pi\)
−0.0577490 + 0.998331i \(0.518392\pi\)
\(608\) −1.45478 2.51976i −0.0589992 0.102190i
\(609\) 0 0
\(610\) 1.87594 1.08308i 0.0759547 0.0438525i
\(611\) −42.1150 10.9849i −1.70379 0.444400i
\(612\) 0 0
\(613\) 0.202550 + 0.755928i 0.00818093 + 0.0305316i 0.969896 0.243521i \(-0.0783024\pi\)
−0.961715 + 0.274053i \(0.911636\pi\)
\(614\) 15.4139i 0.622055i
\(615\) 0 0
\(616\) 2.67331 + 9.97693i 0.107711 + 0.401982i
\(617\) 19.5997 + 19.5997i 0.789055 + 0.789055i 0.981339 0.192284i \(-0.0615896\pi\)
−0.192284 + 0.981339i \(0.561590\pi\)
\(618\) 0 0
\(619\) 1.73266 6.46639i 0.0696417 0.259906i −0.922323 0.386419i \(-0.873712\pi\)
0.991965 + 0.126513i \(0.0403785\pi\)
\(620\) 4.05590 2.34168i 0.162889 0.0940440i
\(621\) 0 0
\(622\) −10.3913 + 2.78435i −0.416654 + 0.111642i
\(623\) −5.74793 9.95571i −0.230286 0.398867i
\(624\) 0 0
\(625\) 9.00338 15.5943i 0.360135 0.623772i
\(626\) 3.28522 12.2606i 0.131304 0.490032i
\(627\) 0 0
\(628\) −4.95546 2.86104i −0.197744 0.114168i
\(629\) −11.7262 11.7262i −0.467554 0.467554i
\(630\) 0 0
\(631\) −1.16111 + 4.33331i −0.0462230 + 0.172506i −0.985179 0.171532i \(-0.945128\pi\)
0.938956 + 0.344038i \(0.111795\pi\)
\(632\) −3.00210 0.804409i −0.119417 0.0319977i
\(633\) 0 0
\(634\) −22.5536 + 13.0213i −0.895717 + 0.517142i
\(635\) −0.291908 0.0782165i −0.0115840 0.00310393i
\(636\) 0 0
\(637\) 43.7619 25.6557i 1.73391 1.01652i
\(638\) 10.9862i 0.434948i
\(639\) 0 0
\(640\) −0.347017 + 0.601052i −0.0137171 + 0.0237586i
\(641\) −21.4910 + 37.2236i −0.848845 + 1.47024i 0.0333945 + 0.999442i \(0.489368\pi\)
−0.882240 + 0.470801i \(0.843965\pi\)
\(642\) 0 0
\(643\) 16.1469 16.1469i 0.636771 0.636771i −0.312987 0.949758i \(-0.601329\pi\)
0.949758 + 0.312987i \(0.101329\pi\)
\(644\) −15.4010 + 15.4010i −0.606886 + 0.606886i
\(645\) 0 0
\(646\) 6.75544 11.7008i 0.265789 0.460361i
\(647\) 18.2315 31.5780i 0.716756 1.24146i −0.245523 0.969391i \(-0.578960\pi\)
0.962278 0.272067i \(-0.0877071\pi\)
\(648\) 0 0
\(649\) 12.0836i 0.474321i
\(650\) 15.7636 + 4.11163i 0.618300 + 0.161271i
\(651\) 0 0
\(652\) −5.39731 1.44621i −0.211375 0.0566378i
\(653\) 2.93974 1.69726i 0.115041 0.0664190i −0.441375 0.897323i \(-0.645509\pi\)
0.556416 + 0.830904i \(0.312176\pi\)
\(654\) 0 0
\(655\) 6.98482 + 1.87158i 0.272919 + 0.0731285i
\(656\) −1.48606 + 5.54605i −0.0580209 + 0.216537i
\(657\) 0 0
\(658\) −39.1803 39.1803i −1.52741 1.52741i
\(659\) 23.7208 + 13.6952i 0.924032 + 0.533490i 0.884919 0.465745i \(-0.154214\pi\)
0.0391126 + 0.999235i \(0.487547\pi\)
\(660\) 0 0
\(661\) 11.8777 44.3282i 0.461990 1.72417i −0.204692 0.978826i \(-0.565619\pi\)
0.666682 0.745342i \(-0.267714\pi\)
\(662\) −10.1318 + 17.5489i −0.393785 + 0.682056i
\(663\) 0 0
\(664\) 4.75191 + 8.23054i 0.184410 + 0.319407i
\(665\) 8.95321 2.39900i 0.347191 0.0930294i
\(666\) 0 0
\(667\) −20.0627 + 11.5832i −0.776833 + 0.448505i
\(668\) 6.33832 23.6549i 0.245237 0.915236i
\(669\) 0 0
\(670\) 6.42079 + 6.42079i 0.248057 + 0.248057i
\(671\) 1.81774 + 6.78389i 0.0701730 + 0.261889i
\(672\) 0 0
\(673\) 20.6898i 0.797535i −0.917052 0.398767i \(-0.869438\pi\)
0.917052 0.398767i \(-0.130562\pi\)
\(674\) 2.04100 + 7.61712i 0.0786164 + 0.293401i
\(675\) 0 0
\(676\) 0.172992 + 12.9988i 0.00665353 + 0.499956i
\(677\) −6.49755 + 3.75136i −0.249721 + 0.144176i −0.619636 0.784889i \(-0.712720\pi\)
0.369916 + 0.929065i \(0.379387\pi\)
\(678\) 0 0
\(679\) 2.81777 + 4.88052i 0.108136 + 0.187297i
\(680\) −3.22283 −0.123590
\(681\) 0 0
\(682\) 3.93006 + 14.6672i 0.150490 + 0.561635i
\(683\) 39.9739 + 10.7110i 1.52956 + 0.409844i 0.922875 0.385100i \(-0.125833\pi\)
0.606683 + 0.794944i \(0.292500\pi\)
\(684\) 0 0
\(685\) −2.65397 4.59681i −0.101403 0.175635i
\(686\) 32.4495 1.23893
\(687\) 0 0
\(688\) −4.59562 2.65328i −0.175206 0.101155i
\(689\) 0.121528 + 18.2644i 0.00462986 + 0.695820i
\(690\) 0 0
\(691\) 3.99681 3.99681i 0.152046 0.152046i −0.626985 0.779031i \(-0.715711\pi\)
0.779031 + 0.626985i \(0.215711\pi\)
\(692\) 9.17465 + 5.29699i 0.348768 + 0.201361i
\(693\) 0 0
\(694\) 12.0177 12.0177i 0.456185 0.456185i
\(695\) 7.49039 2.00704i 0.284127 0.0761315i
\(696\) 0 0
\(697\) −25.7537 + 6.90068i −0.975491 + 0.261382i
\(698\) 14.5379i 0.550269i
\(699\) 0 0
\(700\) 14.6652 + 14.6652i 0.554292 + 0.554292i
\(701\) −40.7022 −1.53730 −0.768651 0.639669i \(-0.779072\pi\)
−0.768651 + 0.639669i \(0.779072\pi\)
\(702\) 0 0
\(703\) −10.3907 −0.391892
\(704\) −1.59115 1.59115i −0.0599688 0.0599688i
\(705\) 0 0
\(706\) 8.51399i 0.320428i
\(707\) −16.6904 + 4.47217i −0.627706 + 0.168193i
\(708\) 0 0
\(709\) 1.65798 0.444255i 0.0622668 0.0166843i −0.227551 0.973766i \(-0.573072\pi\)
0.289818 + 0.957082i \(0.406405\pi\)
\(710\) −7.90632 + 7.90632i −0.296719 + 0.296719i
\(711\) 0 0
\(712\) 2.16893 + 1.25223i 0.0812843 + 0.0469295i
\(713\) −22.6412 + 22.6412i −0.847920 + 0.847920i
\(714\) 0 0
\(715\) 2.78295 4.89515i 0.104077 0.183068i
\(716\) 10.7836 + 6.22591i 0.403001 + 0.232673i
\(717\) 0 0
\(718\) 3.96892 0.148119
\(719\) 10.3528 + 17.9315i 0.386093 + 0.668732i 0.991920 0.126864i \(-0.0404911\pi\)
−0.605827 + 0.795596i \(0.707158\pi\)
\(720\) 0 0
\(721\) −67.3577 18.0484i −2.50853 0.672159i
\(722\) 2.72651 + 10.1755i 0.101470 + 0.378692i
\(723\) 0 0
\(724\) 18.4465 0.685558
\(725\) 11.0298 + 19.1042i 0.409637 + 0.709511i
\(726\) 0 0
\(727\) 38.1761 22.0410i 1.41587 0.817455i 0.419940 0.907552i \(-0.362051\pi\)
0.995933 + 0.0900971i \(0.0287178\pi\)
\(728\) −8.17945 + 14.3875i −0.303150 + 0.533234i
\(729\) 0 0
\(730\) 1.41017 + 5.26282i 0.0521927 + 0.194786i
\(731\) 24.6416i 0.911404i
\(732\) 0 0
\(733\) −5.25644 19.6173i −0.194151 0.724582i −0.992485 0.122367i \(-0.960952\pi\)
0.798334 0.602215i \(-0.205715\pi\)
\(734\) 17.2238 + 17.2238i 0.635742 + 0.635742i
\(735\) 0 0
\(736\) 1.22810 4.58334i 0.0452685 0.168944i
\(737\) −25.4965 + 14.7204i −0.939175 + 0.542233i
\(738\) 0 0
\(739\) 37.8060 10.1301i 1.39072 0.372642i 0.515715 0.856760i \(-0.327526\pi\)
0.875002 + 0.484118i \(0.160860\pi\)
\(740\) 1.23927 + 2.14648i 0.0455566 + 0.0789063i
\(741\) 0 0
\(742\) −11.6263 + 20.1373i −0.426814 + 0.739263i
\(743\) 13.6576 50.9709i 0.501049 1.86994i 0.00794786 0.999968i \(-0.497470\pi\)
0.493101 0.869972i \(-0.335863\pi\)
\(744\) 0 0
\(745\) 4.44731 + 2.56765i 0.162937 + 0.0940716i
\(746\) 6.54644 + 6.54644i 0.239682 + 0.239682i
\(747\) 0 0
\(748\) 2.70445 10.0932i 0.0988845 0.369042i
\(749\) −24.2393 6.49491i −0.885686 0.237319i
\(750\) 0 0
\(751\) −24.5558 + 14.1773i −0.896053 + 0.517336i −0.875917 0.482461i \(-0.839743\pi\)
−0.0201351 + 0.999797i \(0.506410\pi\)
\(752\) 11.6601 + 3.12430i 0.425199 + 0.113932i
\(753\) 0 0
\(754\) −12.3643 + 12.5299i −0.450280 + 0.456313i
\(755\) 9.94532i 0.361947i
\(756\) 0 0
\(757\) 24.6271 42.6555i 0.895089 1.55034i 0.0613944 0.998114i \(-0.480445\pi\)
0.833694 0.552226i \(-0.186221\pi\)
\(758\) −6.91700 + 11.9806i −0.251237 + 0.435155i
\(759\) 0 0
\(760\) −1.42789 + 1.42789i −0.0517949 + 0.0517949i
\(761\) 18.9582 18.9582i 0.687235 0.687235i −0.274385 0.961620i \(-0.588474\pi\)
0.961620 + 0.274385i \(0.0884744\pi\)
\(762\) 0 0
\(763\) −16.5574 + 28.6783i −0.599418 + 1.03822i
\(764\) 4.25783 7.37477i 0.154043 0.266810i
\(765\) 0 0
\(766\) 17.8071i 0.643398i
\(767\) −13.5993 + 13.7814i −0.491041 + 0.497619i
\(768\) 0 0
\(769\) 41.4115 + 11.0962i 1.49334 + 0.400138i 0.910862 0.412711i \(-0.135418\pi\)
0.582474 + 0.812849i \(0.302085\pi\)
\(770\) 6.20819 3.58430i 0.223728 0.129169i
\(771\) 0 0
\(772\) −18.2851 4.89947i −0.658094 0.176336i
\(773\) −1.46006 + 5.44904i −0.0525149 + 0.195988i −0.987200 0.159490i \(-0.949015\pi\)
0.934685 + 0.355478i \(0.115682\pi\)
\(774\) 0 0
\(775\) 21.5594 + 21.5594i 0.774438 + 0.774438i
\(776\) −1.06326 0.613875i −0.0381689 0.0220368i
\(777\) 0 0
\(778\) −3.86660 + 14.4304i −0.138624 + 0.517353i
\(779\) −8.35291 + 14.4677i −0.299274 + 0.518358i
\(780\) 0 0
\(781\) −18.1261 31.3954i −0.648604 1.12342i
\(782\) 21.2833 5.70284i 0.761088 0.203933i
\(783\) 0 0
\(784\) −12.1845 + 7.03470i −0.435159 +