Properties

Label 722.2.e.r.423.3
Level $722$
Weight $2$
Character 722.423
Analytic conductor $5.765$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $6$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [722,2,Mod(99,722)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(722, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("722.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.e (of order \(9\), degree \(6\), 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: \(5.76519902594\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 423.3
Character \(\chi\) \(=\) 722.423
Dual form 722.2.e.r.99.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.939693 + 0.342020i) q^{2} +(0.222978 - 1.26457i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.83108 + 2.37556i) q^{5} +(0.222978 + 1.26457i) q^{6} +(0.221232 + 0.383185i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.26966 + 0.462117i) q^{9} +O(q^{10})\) \(q+(-0.939693 + 0.342020i) q^{2} +(0.222978 - 1.26457i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.83108 + 2.37556i) q^{5} +(0.222978 + 1.26457i) q^{6} +(0.221232 + 0.383185i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.26966 + 0.462117i) q^{9} +(-3.47284 - 1.26401i) q^{10} +(2.01484 - 3.48980i) q^{11} +(-0.642040 - 1.11205i) q^{12} +(0.849399 + 4.81718i) q^{13} +(-0.338947 - 0.284410i) q^{14} +(3.63534 - 3.05041i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.250797 + 0.0912828i) q^{17} -1.35114 q^{18} +3.69572 q^{20} +(0.533894 - 0.194322i) q^{21} +(-0.699745 + 3.96845i) q^{22} +(-7.05473 + 5.91962i) q^{23} +(0.983662 + 0.825390i) q^{24} +(1.50350 + 8.52679i) q^{25} +(-2.44575 - 4.23616i) q^{26} +(2.79360 - 4.83866i) q^{27} +(0.415780 + 0.151331i) q^{28} +(0.210098 + 0.0764694i) q^{29} +(-2.37280 + 4.10980i) q^{30} +(-1.73993 - 3.01364i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-3.96383 - 3.32605i) q^{33} +(0.204452 - 0.171556i) q^{34} +(-0.283953 + 1.61038i) q^{35} +(1.26966 - 0.462117i) q^{36} +1.44903 q^{37} +6.28106 q^{39} +(-3.47284 + 1.26401i) q^{40} +(-1.36569 + 7.74524i) q^{41} +(-0.435234 + 0.365205i) q^{42} +(-4.31683 - 3.62225i) q^{43} +(-0.699745 - 3.96845i) q^{44} +(2.49672 + 4.32444i) q^{45} +(4.60465 - 7.97549i) q^{46} +(-2.06608 - 0.751992i) q^{47} +(-1.20664 - 0.439181i) q^{48} +(3.40211 - 5.89263i) q^{49} +(-4.32916 - 7.49833i) q^{50} +(0.0595113 + 0.337505i) q^{51} +(3.74710 + 3.14419i) q^{52} +(7.61633 - 6.39086i) q^{53} +(-0.970209 + 5.50233i) q^{54} +(13.9944 - 5.09355i) q^{55} -0.442463 q^{56} -0.223582 q^{58} +(3.29788 - 1.20033i) q^{59} +(0.824064 - 4.67350i) q^{60} +(3.12512 - 2.62228i) q^{61} +(2.66572 + 2.23681i) q^{62} +(0.103812 + 0.588748i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-9.03879 + 15.6556i) q^{65} +(4.86236 + 1.76976i) q^{66} +(-0.138852 - 0.0505379i) q^{67} +(-0.133446 + 0.231136i) q^{68} +(5.91273 + 10.2412i) q^{69} +(-0.283953 - 1.61038i) q^{70} +(8.78585 + 7.37221i) q^{71} +(-1.03503 + 0.868497i) q^{72} +(0.246973 - 1.40065i) q^{73} +(-1.36164 + 0.495597i) q^{74} +11.1180 q^{75} +1.78298 q^{77} +(-5.90227 + 2.14825i) q^{78} +(1.77180 - 10.0484i) q^{79} +(2.83108 - 2.37556i) q^{80} +(-2.39082 - 2.00614i) q^{81} +(-1.36569 - 7.74524i) q^{82} +(1.64439 + 2.84817i) q^{83} +(0.284079 - 0.492039i) q^{84} +(-0.926876 - 0.337355i) q^{85} +(5.29537 + 1.92736i) q^{86} +(0.143548 - 0.248633i) q^{87} +(2.01484 + 3.48980i) q^{88} +(-1.03507 - 5.87019i) q^{89} +(-3.82519 - 3.20972i) q^{90} +(-1.65795 + 1.39119i) q^{91} +(-1.59918 + 9.06939i) q^{92} +(-4.19893 + 1.52828i) q^{93} +2.19868 q^{94} +1.28408 q^{96} +(-3.83842 + 1.39707i) q^{97} +(-1.18154 + 6.70085i) q^{98} +(4.17085 - 3.49976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{7} - 12 q^{8} - 6 q^{11} - 6 q^{12} + 24 q^{18} - 12 q^{20} - 54 q^{26} + 12 q^{27} - 12 q^{30} - 78 q^{31} + 24 q^{37} - 36 q^{39} + 66 q^{45} + 30 q^{46} + 36 q^{49} - 18 q^{50} - 12 q^{56} - 12 q^{58} - 12 q^{64} + 12 q^{65} - 18 q^{68} + 60 q^{69} + 48 q^{75} + 24 q^{77} + 36 q^{83} - 12 q^{84} + 78 q^{87} - 6 q^{88} - 72 q^{94} + 12 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.939693 + 0.342020i −0.664463 + 0.241845i
\(3\) 0.222978 1.26457i 0.128736 0.730100i −0.850282 0.526328i \(-0.823569\pi\)
0.979018 0.203773i \(-0.0653204\pi\)
\(4\) 0.766044 0.642788i 0.383022 0.321394i
\(5\) 2.83108 + 2.37556i 1.26610 + 1.06238i 0.995004 + 0.0998307i \(0.0318301\pi\)
0.271095 + 0.962553i \(0.412614\pi\)
\(6\) 0.222978 + 1.26457i 0.0910304 + 0.516259i
\(7\) 0.221232 + 0.383185i 0.0836177 + 0.144830i 0.904801 0.425834i \(-0.140019\pi\)
−0.821184 + 0.570664i \(0.806686\pi\)
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) 1.26966 + 0.462117i 0.423219 + 0.154039i
\(10\) −3.47284 1.26401i −1.09821 0.399715i
\(11\) 2.01484 3.48980i 0.607496 1.05221i −0.384156 0.923268i \(-0.625507\pi\)
0.991652 0.128946i \(-0.0411593\pi\)
\(12\) −0.642040 1.11205i −0.185341 0.321020i
\(13\) 0.849399 + 4.81718i 0.235581 + 1.33604i 0.841387 + 0.540433i \(0.181740\pi\)
−0.605806 + 0.795612i \(0.707149\pi\)
\(14\) −0.338947 0.284410i −0.0905873 0.0760118i
\(15\) 3.63534 3.05041i 0.938640 0.787612i
\(16\) 0.173648 0.984808i 0.0434120 0.246202i
\(17\) −0.250797 + 0.0912828i −0.0608273 + 0.0221393i −0.372255 0.928131i \(-0.621415\pi\)
0.311427 + 0.950270i \(0.399193\pi\)
\(18\) −1.35114 −0.318467
\(19\) 0 0
\(20\) 3.69572 0.826388
\(21\) 0.533894 0.194322i 0.116505 0.0424044i
\(22\) −0.699745 + 3.96845i −0.149186 + 0.846077i
\(23\) −7.05473 + 5.91962i −1.47101 + 1.23433i −0.555826 + 0.831299i \(0.687598\pi\)
−0.915188 + 0.403028i \(0.867958\pi\)
\(24\) 0.983662 + 0.825390i 0.200789 + 0.168482i
\(25\) 1.50350 + 8.52679i 0.300701 + 1.70536i
\(26\) −2.44575 4.23616i −0.479650 0.830779i
\(27\) 2.79360 4.83866i 0.537629 0.931201i
\(28\) 0.415780 + 0.151331i 0.0785750 + 0.0285990i
\(29\) 0.210098 + 0.0764694i 0.0390142 + 0.0142000i 0.361454 0.932390i \(-0.382281\pi\)
−0.322439 + 0.946590i \(0.604503\pi\)
\(30\) −2.37280 + 4.10980i −0.433211 + 0.750344i
\(31\) −1.73993 3.01364i −0.312500 0.541266i 0.666403 0.745592i \(-0.267833\pi\)
−0.978903 + 0.204326i \(0.934500\pi\)
\(32\) 0.173648 + 0.984808i 0.0306970 + 0.174091i
\(33\) −3.96383 3.32605i −0.690015 0.578991i
\(34\) 0.204452 0.171556i 0.0350632 0.0294215i
\(35\) −0.283953 + 1.61038i −0.0479968 + 0.272203i
\(36\) 1.26966 0.462117i 0.211610 0.0770196i
\(37\) 1.44903 0.238219 0.119109 0.992881i \(-0.461996\pi\)
0.119109 + 0.992881i \(0.461996\pi\)
\(38\) 0 0
\(39\) 6.28106 1.00577
\(40\) −3.47284 + 1.26401i −0.549104 + 0.199858i
\(41\) −1.36569 + 7.74524i −0.213286 + 1.20960i 0.670571 + 0.741845i \(0.266049\pi\)
−0.883857 + 0.467758i \(0.845062\pi\)
\(42\) −0.435234 + 0.365205i −0.0671581 + 0.0563524i
\(43\) −4.31683 3.62225i −0.658310 0.552388i 0.251270 0.967917i \(-0.419152\pi\)
−0.909580 + 0.415529i \(0.863596\pi\)
\(44\) −0.699745 3.96845i −0.105491 0.598267i
\(45\) 2.49672 + 4.32444i 0.372189 + 0.644650i
\(46\) 4.60465 7.97549i 0.678919 1.17592i
\(47\) −2.06608 0.751992i −0.301369 0.109689i 0.186910 0.982377i \(-0.440153\pi\)
−0.488279 + 0.872688i \(0.662375\pi\)
\(48\) −1.20664 0.439181i −0.174163 0.0633903i
\(49\) 3.40211 5.89263i 0.486016 0.841805i
\(50\) −4.32916 7.49833i −0.612236 1.06042i
\(51\) 0.0595113 + 0.337505i 0.00833324 + 0.0472602i
\(52\) 3.74710 + 3.14419i 0.519629 + 0.436021i
\(53\) 7.61633 6.39086i 1.04618 0.877852i 0.0534958 0.998568i \(-0.482964\pi\)
0.992687 + 0.120716i \(0.0385192\pi\)
\(54\) −0.970209 + 5.50233i −0.132029 + 0.748772i
\(55\) 13.9944 5.09355i 1.88700 0.686814i
\(56\) −0.442463 −0.0591267
\(57\) 0 0
\(58\) −0.223582 −0.0293577
\(59\) 3.29788 1.20033i 0.429347 0.156269i −0.118302 0.992978i \(-0.537745\pi\)
0.547649 + 0.836708i \(0.315523\pi\)
\(60\) 0.824064 4.67350i 0.106386 0.603346i
\(61\) 3.12512 2.62228i 0.400130 0.335749i −0.420414 0.907332i \(-0.638115\pi\)
0.820544 + 0.571583i \(0.193671\pi\)
\(62\) 2.66572 + 2.23681i 0.338547 + 0.284075i
\(63\) 0.103812 + 0.588748i 0.0130791 + 0.0741753i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) −9.03879 + 15.6556i −1.12112 + 1.94184i
\(66\) 4.86236 + 1.76976i 0.598515 + 0.217842i
\(67\) −0.138852 0.0505379i −0.0169634 0.00617418i 0.333524 0.942741i \(-0.391762\pi\)
−0.350488 + 0.936567i \(0.613984\pi\)
\(68\) −0.133446 + 0.231136i −0.0161828 + 0.0280294i
\(69\) 5.91273 + 10.2412i 0.711810 + 1.23289i
\(70\) −0.283953 1.61038i −0.0339389 0.192477i
\(71\) 8.78585 + 7.37221i 1.04269 + 0.874920i 0.992306 0.123810i \(-0.0395113\pi\)
0.0503832 + 0.998730i \(0.483956\pi\)
\(72\) −1.03503 + 0.868497i −0.121980 + 0.102353i
\(73\) 0.246973 1.40065i 0.0289060 0.163934i −0.966938 0.255013i \(-0.917920\pi\)
0.995844 + 0.0910787i \(0.0290315\pi\)
\(74\) −1.36164 + 0.495597i −0.158288 + 0.0576120i
\(75\) 11.1180 1.28379
\(76\) 0 0
\(77\) 1.78298 0.203190
\(78\) −5.90227 + 2.14825i −0.668300 + 0.243241i
\(79\) 1.77180 10.0484i 0.199343 1.13053i −0.706754 0.707459i \(-0.749841\pi\)
0.906097 0.423070i \(-0.139048\pi\)
\(80\) 2.83108 2.37556i 0.316525 0.265596i
\(81\) −2.39082 2.00614i −0.265647 0.222904i
\(82\) −1.36569 7.74524i −0.150816 0.855319i
\(83\) 1.64439 + 2.84817i 0.180495 + 0.312627i 0.942049 0.335475i \(-0.108897\pi\)
−0.761554 + 0.648101i \(0.775563\pi\)
\(84\) 0.284079 0.492039i 0.0309956 0.0536859i
\(85\) −0.926876 0.337355i −0.100534 0.0365913i
\(86\) 5.29537 + 1.92736i 0.571015 + 0.207832i
\(87\) 0.143548 0.248633i 0.0153900 0.0266562i
\(88\) 2.01484 + 3.48980i 0.214782 + 0.372014i
\(89\) −1.03507 5.87019i −0.109717 0.622239i −0.989231 0.146364i \(-0.953243\pi\)
0.879513 0.475874i \(-0.157868\pi\)
\(90\) −3.82519 3.20972i −0.403211 0.338334i
\(91\) −1.65795 + 1.39119i −0.173801 + 0.145836i
\(92\) −1.59918 + 9.06939i −0.166726 + 0.945549i
\(93\) −4.19893 + 1.52828i −0.435409 + 0.158476i
\(94\) 2.19868 0.226776
\(95\) 0 0
\(96\) 1.28408 0.131056
\(97\) −3.83842 + 1.39707i −0.389732 + 0.141851i −0.529451 0.848340i \(-0.677602\pi\)
0.139719 + 0.990191i \(0.455380\pi\)
\(98\) −1.18154 + 6.70085i −0.119354 + 0.676889i
\(99\) 4.17085 3.49976i 0.419186 0.351739i
\(100\) 6.63266 + 5.56547i 0.663266 + 0.556547i
\(101\) 0.0738486 + 0.418817i 0.00734822 + 0.0416738i 0.988261 0.152772i \(-0.0488201\pi\)
−0.980913 + 0.194446i \(0.937709\pi\)
\(102\) −0.171356 0.296797i −0.0169668 0.0293873i
\(103\) 2.26809 3.92845i 0.223482 0.387081i −0.732381 0.680895i \(-0.761591\pi\)
0.955863 + 0.293813i \(0.0949244\pi\)
\(104\) −4.59650 1.67299i −0.450724 0.164050i
\(105\) 1.97312 + 0.718157i 0.192557 + 0.0700850i
\(106\) −4.97120 + 8.61038i −0.482846 + 0.836314i
\(107\) 1.58576 + 2.74661i 0.153301 + 0.265525i 0.932439 0.361327i \(-0.117676\pi\)
−0.779138 + 0.626852i \(0.784343\pi\)
\(108\) −0.970209 5.50233i −0.0933584 0.529462i
\(109\) −5.19464 4.35882i −0.497556 0.417499i 0.359169 0.933273i \(-0.383060\pi\)
−0.856725 + 0.515773i \(0.827505\pi\)
\(110\) −11.4083 + 9.57273i −1.08774 + 0.912724i
\(111\) 0.323101 1.83240i 0.0306674 0.173924i
\(112\) 0.415780 0.151331i 0.0392875 0.0142995i
\(113\) −10.0444 −0.944893 −0.472447 0.881359i \(-0.656629\pi\)
−0.472447 + 0.881359i \(0.656629\pi\)
\(114\) 0 0
\(115\) −34.0350 −3.17378
\(116\) 0.210098 0.0764694i 0.0195071 0.00710001i
\(117\) −1.14766 + 6.50869i −0.106101 + 0.601728i
\(118\) −2.68845 + 2.25588i −0.247492 + 0.207671i
\(119\) −0.0904625 0.0759070i −0.00829268 0.00695839i
\(120\) 0.824064 + 4.67350i 0.0752264 + 0.426630i
\(121\) −2.61913 4.53647i −0.238103 0.412406i
\(122\) −2.03977 + 3.53299i −0.184672 + 0.319862i
\(123\) 9.48989 + 3.45404i 0.855674 + 0.311440i
\(124\) −3.26999 1.19018i −0.293654 0.106881i
\(125\) −6.76007 + 11.7088i −0.604639 + 1.04727i
\(126\) −0.298915 0.517736i −0.0266295 0.0461236i
\(127\) 2.44507 + 13.8667i 0.216965 + 1.23047i 0.877464 + 0.479642i \(0.159233\pi\)
−0.660500 + 0.750826i \(0.729655\pi\)
\(128\) 0.766044 + 0.642788i 0.0677094 + 0.0568149i
\(129\) −5.54315 + 4.65125i −0.488047 + 0.409520i
\(130\) 3.13914 17.8029i 0.275321 1.56142i
\(131\) −14.8861 + 5.41811i −1.30061 + 0.473383i −0.897195 0.441635i \(-0.854399\pi\)
−0.403414 + 0.915018i \(0.632176\pi\)
\(132\) −5.17442 −0.450375
\(133\) 0 0
\(134\) 0.147763 0.0127648
\(135\) 19.4035 7.06229i 1.66999 0.607825i
\(136\) 0.0463455 0.262838i 0.00397409 0.0225382i
\(137\) 1.69099 1.41891i 0.144471 0.121226i −0.567688 0.823244i \(-0.692162\pi\)
0.712159 + 0.702018i \(0.247717\pi\)
\(138\) −9.05883 7.60127i −0.771139 0.647063i
\(139\) −2.96321 16.8052i −0.251336 1.42540i −0.805305 0.592861i \(-0.797998\pi\)
0.553969 0.832537i \(-0.313113\pi\)
\(140\) 0.817610 + 1.41614i 0.0691007 + 0.119686i
\(141\) −1.41164 + 2.44503i −0.118881 + 0.205909i
\(142\) −10.7774 3.92267i −0.904423 0.329183i
\(143\) 18.5224 + 6.74160i 1.54892 + 0.563761i
\(144\) 0.675571 1.17012i 0.0562975 0.0975102i
\(145\) 0.413147 + 0.715592i 0.0343100 + 0.0594267i
\(146\) 0.246973 + 1.40065i 0.0204396 + 0.115919i
\(147\) −6.69306 5.61614i −0.552034 0.463211i
\(148\) 1.11002 0.931417i 0.0912431 0.0765620i
\(149\) 2.35220 13.3400i 0.192699 1.09285i −0.722957 0.690893i \(-0.757218\pi\)
0.915657 0.401961i \(-0.131671\pi\)
\(150\) −10.4475 + 3.80257i −0.853033 + 0.310479i
\(151\) −9.15317 −0.744875 −0.372437 0.928057i \(-0.621478\pi\)
−0.372437 + 0.928057i \(0.621478\pi\)
\(152\) 0 0
\(153\) −0.360610 −0.0291536
\(154\) −1.67546 + 0.609816i −0.135012 + 0.0491404i
\(155\) 2.23321 12.6652i 0.179376 1.01729i
\(156\) 4.81157 4.03739i 0.385234 0.323250i
\(157\) −12.5557 10.5355i −1.00205 0.840822i −0.0147852 0.999891i \(-0.504706\pi\)
−0.987268 + 0.159069i \(0.949151\pi\)
\(158\) 1.77180 + 10.0484i 0.140957 + 0.799405i
\(159\) −6.38342 11.0564i −0.506238 0.876830i
\(160\) −1.84786 + 3.20059i −0.146086 + 0.253028i
\(161\) −3.82904 1.39366i −0.301771 0.109836i
\(162\) 2.93278 + 1.06744i 0.230421 + 0.0838663i
\(163\) 6.88612 11.9271i 0.539363 0.934204i −0.459576 0.888139i \(-0.651998\pi\)
0.998938 0.0460652i \(-0.0146682\pi\)
\(164\) 3.93236 + 6.81105i 0.307066 + 0.531854i
\(165\) −3.32071 18.8327i −0.258517 1.46612i
\(166\) −2.51935 2.11399i −0.195540 0.164077i
\(167\) −7.91539 + 6.64180i −0.612511 + 0.513958i −0.895439 0.445183i \(-0.853139\pi\)
0.282929 + 0.959141i \(0.408694\pi\)
\(168\) −0.0986596 + 0.559526i −0.00761175 + 0.0431684i
\(169\) −10.2677 + 3.73715i −0.789825 + 0.287473i
\(170\) 0.986361 0.0756504
\(171\) 0 0
\(172\) −5.63522 −0.429682
\(173\) 9.22028 3.35591i 0.701005 0.255145i 0.0331648 0.999450i \(-0.489441\pi\)
0.667840 + 0.744305i \(0.267219\pi\)
\(174\) −0.0498538 + 0.282735i −0.00377940 + 0.0214341i
\(175\) −2.93471 + 2.46252i −0.221843 + 0.186149i
\(176\) −3.08691 2.59022i −0.232684 0.195245i
\(177\) −0.782547 4.43804i −0.0588198 0.333584i
\(178\) 2.98037 + 5.16216i 0.223388 + 0.386920i
\(179\) 4.39915 7.61955i 0.328808 0.569512i −0.653468 0.756955i \(-0.726686\pi\)
0.982276 + 0.187442i \(0.0600197\pi\)
\(180\) 4.69229 + 1.70786i 0.349743 + 0.127296i
\(181\) −13.6516 4.96878i −1.01472 0.369327i −0.219474 0.975618i \(-0.570434\pi\)
−0.795243 + 0.606291i \(0.792656\pi\)
\(182\) 1.08215 1.87434i 0.0802145 0.138936i
\(183\) −2.61923 4.53664i −0.193619 0.335358i
\(184\) −1.59918 9.06939i −0.117893 0.668604i
\(185\) 4.10232 + 3.44225i 0.301609 + 0.253080i
\(186\) 3.42300 2.87224i 0.250986 0.210603i
\(187\) −0.186757 + 1.05915i −0.0136570 + 0.0774529i
\(188\) −2.06608 + 0.751992i −0.150685 + 0.0548447i
\(189\) 2.47214 0.179821
\(190\) 0 0
\(191\) 12.7302 0.921122 0.460561 0.887628i \(-0.347648\pi\)
0.460561 + 0.887628i \(0.347648\pi\)
\(192\) −1.20664 + 0.439181i −0.0870817 + 0.0316952i
\(193\) 3.03503 17.2125i 0.218466 1.23898i −0.656322 0.754481i \(-0.727889\pi\)
0.874789 0.484504i \(-0.161000\pi\)
\(194\) 3.12911 2.62563i 0.224657 0.188509i
\(195\) 17.7822 + 14.9210i 1.27341 + 1.06852i
\(196\) −1.18154 6.70085i −0.0843958 0.478632i
\(197\) 12.2556 + 21.2274i 0.873178 + 1.51239i 0.858691 + 0.512494i \(0.171278\pi\)
0.0144872 + 0.999895i \(0.495388\pi\)
\(198\) −2.72233 + 4.71521i −0.193467 + 0.335095i
\(199\) −15.4731 5.63174i −1.09686 0.399223i −0.270700 0.962664i \(-0.587255\pi\)
−0.826157 + 0.563440i \(0.809477\pi\)
\(200\) −8.13617 2.96132i −0.575314 0.209397i
\(201\) −0.0948696 + 0.164319i −0.00669159 + 0.0115902i
\(202\) −0.212639 0.368301i −0.0149612 0.0259136i
\(203\) 0.0171784 + 0.0974238i 0.00120569 + 0.00683781i
\(204\) 0.262532 + 0.220291i 0.0183809 + 0.0154234i
\(205\) −22.2657 + 18.6831i −1.55510 + 1.30489i
\(206\) −0.787699 + 4.46727i −0.0548816 + 0.311249i
\(207\) −11.6927 + 4.25578i −0.812696 + 0.295797i
\(208\) 4.89149 0.339164
\(209\) 0 0
\(210\) −2.09975 −0.144897
\(211\) −25.8232 + 9.39887i −1.77774 + 0.647045i −0.777915 + 0.628369i \(0.783723\pi\)
−0.999826 + 0.0186757i \(0.994055\pi\)
\(212\) 1.72648 9.79136i 0.118575 0.672473i
\(213\) 11.2817 9.46650i 0.773012 0.648634i
\(214\) −2.42952 2.03861i −0.166079 0.139356i
\(215\) −3.61643 20.5098i −0.246638 1.39876i
\(216\) 2.79360 + 4.83866i 0.190081 + 0.329229i
\(217\) 0.769854 1.33343i 0.0522611 0.0905189i
\(218\) 6.37217 + 2.31928i 0.431578 + 0.157081i
\(219\) −1.71616 0.624629i −0.115967 0.0422085i
\(220\) 7.44627 12.8973i 0.502027 0.869536i
\(221\) −0.652752 1.13060i −0.0439089 0.0760524i
\(222\) 0.323101 + 1.83240i 0.0216851 + 0.122983i
\(223\) 15.6048 + 13.0940i 1.04497 + 0.876837i 0.992556 0.121789i \(-0.0388630\pi\)
0.0524171 + 0.998625i \(0.483307\pi\)
\(224\) −0.338947 + 0.284410i −0.0226468 + 0.0190029i
\(225\) −2.03144 + 11.5209i −0.135430 + 0.768060i
\(226\) 9.43860 3.43537i 0.627847 0.228517i
\(227\) −22.1493 −1.47010 −0.735051 0.678011i \(-0.762842\pi\)
−0.735051 + 0.678011i \(0.762842\pi\)
\(228\) 0 0
\(229\) 12.7148 0.840216 0.420108 0.907474i \(-0.361992\pi\)
0.420108 + 0.907474i \(0.361992\pi\)
\(230\) 31.9824 11.6406i 2.10886 0.767561i
\(231\) 0.397566 2.25471i 0.0261579 0.148349i
\(232\) −0.171273 + 0.143715i −0.0112447 + 0.00943538i
\(233\) −6.65062 5.58053i −0.435696 0.365593i 0.398400 0.917212i \(-0.369566\pi\)
−0.834096 + 0.551619i \(0.814010\pi\)
\(234\) −1.14766 6.50869i −0.0750247 0.425486i
\(235\) −4.06285 7.03706i −0.265031 0.459047i
\(236\) 1.75476 3.03934i 0.114225 0.197844i
\(237\) −12.3118 4.48113i −0.799737 0.291081i
\(238\) 0.110969 + 0.0403893i 0.00719303 + 0.00261805i
\(239\) −10.9375 + 18.9442i −0.707485 + 1.22540i 0.258302 + 0.966064i \(0.416837\pi\)
−0.965787 + 0.259336i \(0.916496\pi\)
\(240\) −2.37280 4.10980i −0.153163 0.265287i
\(241\) −3.29293 18.6751i −0.212116 1.20297i −0.885841 0.463988i \(-0.846418\pi\)
0.673725 0.738982i \(-0.264693\pi\)
\(242\) 4.01274 + 3.36709i 0.257949 + 0.216445i
\(243\) 9.77015 8.19813i 0.626755 0.525910i
\(244\) 0.708406 4.01757i 0.0453511 0.257199i
\(245\) 23.6300 8.60061i 1.50966 0.549473i
\(246\) −10.0989 −0.643884
\(247\) 0 0
\(248\) 3.47985 0.220971
\(249\) 3.96837 1.44437i 0.251485 0.0915332i
\(250\) 2.34775 13.3147i 0.148485 0.842098i
\(251\) 2.22364 1.86586i 0.140355 0.117772i −0.569907 0.821709i \(-0.693021\pi\)
0.710262 + 0.703937i \(0.248576\pi\)
\(252\) 0.457965 + 0.384278i 0.0288491 + 0.0242072i
\(253\) 6.44416 + 36.5467i 0.405141 + 2.29767i
\(254\) −7.04029 12.1941i −0.441747 0.765129i
\(255\) −0.633283 + 1.09688i −0.0396577 + 0.0686892i
\(256\) −0.939693 0.342020i −0.0587308 0.0213763i
\(257\) −21.5237 7.83398i −1.34261 0.488670i −0.431976 0.901885i \(-0.642184\pi\)
−0.910634 + 0.413215i \(0.864406\pi\)
\(258\) 3.61803 6.26662i 0.225249 0.390143i
\(259\) 0.320571 + 0.555245i 0.0199193 + 0.0345013i
\(260\) 3.13914 + 17.8029i 0.194681 + 1.10409i
\(261\) 0.231415 + 0.194180i 0.0143242 + 0.0120194i
\(262\) 12.1353 10.1827i 0.749721 0.629091i
\(263\) −0.879070 + 4.98545i −0.0542058 + 0.307416i −0.999841 0.0178119i \(-0.994330\pi\)
0.945636 + 0.325228i \(0.105441\pi\)
\(264\) 4.86236 1.76976i 0.299258 0.108921i
\(265\) 36.7443 2.25719
\(266\) 0 0
\(267\) −7.65407 −0.468421
\(268\) −0.138852 + 0.0505379i −0.00848172 + 0.00308709i
\(269\) −3.60180 + 20.4268i −0.219606 + 1.24545i 0.653128 + 0.757248i \(0.273456\pi\)
−0.872733 + 0.488197i \(0.837655\pi\)
\(270\) −15.8179 + 13.2728i −0.962644 + 0.807754i
\(271\) 4.82202 + 4.04616i 0.292917 + 0.245786i 0.777389 0.629020i \(-0.216544\pi\)
−0.484472 + 0.874807i \(0.660988\pi\)
\(272\) 0.0463455 + 0.262838i 0.00281011 + 0.0159369i
\(273\) 1.38957 + 2.40681i 0.0841006 + 0.145667i
\(274\) −1.10372 + 1.91169i −0.0666780 + 0.115490i
\(275\) 32.7861 + 11.9332i 1.97708 + 0.719597i
\(276\) 11.1123 + 4.04455i 0.668882 + 0.243453i
\(277\) −3.58804 + 6.21467i −0.215584 + 0.373403i −0.953453 0.301541i \(-0.902499\pi\)
0.737869 + 0.674944i \(0.235832\pi\)
\(278\) 8.53222 + 14.7782i 0.511729 + 0.886340i
\(279\) −0.816454 4.63034i −0.0488798 0.277211i
\(280\) −1.25265 1.05110i −0.0748602 0.0628152i
\(281\) 2.12494 1.78304i 0.126763 0.106367i −0.577202 0.816601i \(-0.695855\pi\)
0.703965 + 0.710234i \(0.251411\pi\)
\(282\) 0.490257 2.78039i 0.0291944 0.165570i
\(283\) −7.28131 + 2.65018i −0.432829 + 0.157537i −0.549241 0.835664i \(-0.685083\pi\)
0.116412 + 0.993201i \(0.462861\pi\)
\(284\) 11.4691 0.680567
\(285\) 0 0
\(286\) −19.7111 −1.16554
\(287\) −3.26999 + 1.19018i −0.193022 + 0.0702541i
\(288\) −0.234623 + 1.33061i −0.0138253 + 0.0784072i
\(289\) −12.9682 + 10.8816i −0.762835 + 0.640094i
\(290\) −0.632978 0.531132i −0.0371698 0.0311891i
\(291\) 0.910811 + 5.16547i 0.0533927 + 0.302805i
\(292\) −0.711130 1.23171i −0.0416157 0.0720806i
\(293\) 0.391435 0.677985i 0.0228679 0.0396083i −0.854365 0.519673i \(-0.826054\pi\)
0.877233 + 0.480065i \(0.159387\pi\)
\(294\) 8.21025 + 2.98829i 0.478831 + 0.174280i
\(295\) 12.1880 + 4.43607i 0.709614 + 0.258278i
\(296\) −0.724514 + 1.25490i −0.0421115 + 0.0729393i
\(297\) −11.2573 19.4982i −0.653215 1.13140i
\(298\) 2.35220 + 13.3400i 0.136259 + 0.772764i
\(299\) −34.5082 28.9558i −1.99566 1.67456i
\(300\) 8.51686 7.14650i 0.491721 0.412603i
\(301\) 0.432971 2.45550i 0.0249560 0.141533i
\(302\) 8.60117 3.13057i 0.494942 0.180144i
\(303\) 0.546090 0.0313720
\(304\) 0 0
\(305\) 15.0769 0.863298
\(306\) 0.338863 0.123336i 0.0193715 0.00705064i
\(307\) −4.89146 + 27.7408i −0.279170 + 1.58325i 0.446225 + 0.894921i \(0.352768\pi\)
−0.725395 + 0.688332i \(0.758343\pi\)
\(308\) 1.36584 1.14608i 0.0778262 0.0653039i
\(309\) −4.46207 3.74412i −0.253838 0.212995i
\(310\) 2.23321 + 12.6652i 0.126838 + 0.719333i
\(311\) −1.93414 3.35002i −0.109675 0.189962i 0.805964 0.591965i \(-0.201648\pi\)
−0.915639 + 0.402003i \(0.868314\pi\)
\(312\) −3.14053 + 5.43956i −0.177798 + 0.307954i
\(313\) −28.5552 10.3932i −1.61403 0.587460i −0.631801 0.775130i \(-0.717684\pi\)
−0.982232 + 0.187670i \(0.939906\pi\)
\(314\) 15.4018 + 5.60581i 0.869175 + 0.316354i
\(315\) −1.10471 + 1.91341i −0.0622432 + 0.107808i
\(316\) −5.10169 8.83638i −0.286992 0.497085i
\(317\) 0.925203 + 5.24709i 0.0519646 + 0.294706i 0.999704 0.0243404i \(-0.00774857\pi\)
−0.947739 + 0.319046i \(0.896637\pi\)
\(318\) 9.77996 + 8.20636i 0.548433 + 0.460190i
\(319\) 0.690176 0.579126i 0.0386424 0.0324248i
\(320\) 0.641755 3.63957i 0.0358752 0.203458i
\(321\) 3.82687 1.39287i 0.213595 0.0777423i
\(322\) 4.07478 0.227079
\(323\) 0 0
\(324\) −3.12099 −0.173389
\(325\) −39.7980 + 14.4853i −2.20760 + 0.803499i
\(326\) −2.39153 + 13.5630i −0.132454 + 0.751186i
\(327\) −6.67033 + 5.59707i −0.368870 + 0.309519i
\(328\) −6.02473 5.05535i −0.332660 0.279135i
\(329\) −0.168931 0.958055i −0.00931347 0.0528193i
\(330\) 9.56159 + 16.5612i 0.526348 + 0.911662i
\(331\) 10.2740 17.7951i 0.564711 0.978108i −0.432366 0.901698i \(-0.642321\pi\)
0.997077 0.0764094i \(-0.0243456\pi\)
\(332\) 3.09044 + 1.12483i 0.169610 + 0.0617330i
\(333\) 1.83977 + 0.669621i 0.100819 + 0.0366950i
\(334\) 5.16640 8.94847i 0.282693 0.489638i
\(335\) −0.273045 0.472928i −0.0149180 0.0258388i
\(336\) −0.0986596 0.559526i −0.00538232 0.0305247i
\(337\) 10.1749 + 8.53777i 0.554263 + 0.465082i 0.876382 0.481617i \(-0.159950\pi\)
−0.322118 + 0.946699i \(0.604395\pi\)
\(338\) 8.37033 7.02354i 0.455286 0.382030i
\(339\) −2.23967 + 12.7018i −0.121642 + 0.689867i
\(340\) −0.926876 + 0.337355i −0.0502669 + 0.0182957i
\(341\) −14.0227 −0.759370
\(342\) 0 0
\(343\) 6.10787 0.329794
\(344\) 5.29537 1.92736i 0.285507 0.103916i
\(345\) −7.58905 + 43.0396i −0.408581 + 2.31718i
\(346\) −7.51644 + 6.30704i −0.404086 + 0.339069i
\(347\) 23.0904 + 19.3751i 1.23956 + 1.04011i 0.997559 + 0.0698336i \(0.0222468\pi\)
0.241997 + 0.970277i \(0.422198\pi\)
\(348\) −0.0498538 0.282735i −0.00267244 0.0151562i
\(349\) −17.5326 30.3674i −0.938501 1.62553i −0.768269 0.640127i \(-0.778882\pi\)
−0.170232 0.985404i \(-0.554452\pi\)
\(350\) 1.91550 3.31774i 0.102388 0.177341i
\(351\) 25.6816 + 9.34734i 1.37078 + 0.498924i
\(352\) 3.78665 + 1.37823i 0.201829 + 0.0734599i
\(353\) −6.77053 + 11.7269i −0.360359 + 0.624160i −0.988020 0.154327i \(-0.950679\pi\)
0.627661 + 0.778487i \(0.284012\pi\)
\(354\) 2.25325 + 3.90275i 0.119759 + 0.207429i
\(355\) 7.36036 + 41.7427i 0.390647 + 2.21547i
\(356\) −4.56620 3.83149i −0.242008 0.203069i
\(357\) −0.116161 + 0.0974706i −0.00614789 + 0.00515869i
\(358\) −1.52781 + 8.66464i −0.0807472 + 0.457940i
\(359\) 22.0896 8.03994i 1.16584 0.424332i 0.314661 0.949204i \(-0.398109\pi\)
0.851181 + 0.524872i \(0.175887\pi\)
\(360\) −4.99344 −0.263177
\(361\) 0 0
\(362\) 14.5278 0.763562
\(363\) −6.32069 + 2.30054i −0.331750 + 0.120747i
\(364\) −0.375828 + 2.13143i −0.0196987 + 0.111717i
\(365\) 4.02654 3.37867i 0.210759 0.176847i
\(366\) 4.01290 + 3.36722i 0.209757 + 0.176007i
\(367\) −2.20410 12.5000i −0.115053 0.652497i −0.986724 0.162406i \(-0.948075\pi\)
0.871671 0.490091i \(-0.163037\pi\)
\(368\) 4.60465 + 7.97549i 0.240034 + 0.415751i
\(369\) −5.31318 + 9.20269i −0.276593 + 0.479073i
\(370\) −5.03224 1.83159i −0.261614 0.0952196i
\(371\) 4.13385 + 1.50460i 0.214619 + 0.0781149i
\(372\) −2.23420 + 3.86975i −0.115838 + 0.200637i
\(373\) −1.32475 2.29454i −0.0685930 0.118807i 0.829689 0.558226i \(-0.188518\pi\)
−0.898282 + 0.439419i \(0.855184\pi\)
\(374\) −0.186757 1.05915i −0.00965698 0.0547675i
\(375\) 13.2992 + 11.1594i 0.686770 + 0.576269i
\(376\) 1.68429 1.41328i 0.0868604 0.0728845i
\(377\) −0.189910 + 1.07703i −0.00978086 + 0.0554700i
\(378\) −2.32305 + 0.845520i −0.119485 + 0.0434889i
\(379\) 18.1672 0.933187 0.466593 0.884472i \(-0.345481\pi\)
0.466593 + 0.884472i \(0.345481\pi\)
\(380\) 0 0
\(381\) 18.0806 0.926297
\(382\) −11.9624 + 4.35397i −0.612052 + 0.222769i
\(383\) 3.99535 22.6588i 0.204153 1.15781i −0.694614 0.719383i \(-0.744425\pi\)
0.898767 0.438426i \(-0.144464\pi\)
\(384\) 0.983662 0.825390i 0.0501973 0.0421205i
\(385\) 5.04777 + 4.23559i 0.257258 + 0.215865i
\(386\) 3.03503 + 17.2125i 0.154479 + 0.876095i
\(387\) −3.80699 6.59390i −0.193520 0.335187i
\(388\) −2.04238 + 3.53750i −0.103686 + 0.179590i
\(389\) 15.5713 + 5.66749i 0.789496 + 0.287353i 0.705126 0.709082i \(-0.250890\pi\)
0.0843694 + 0.996435i \(0.473112\pi\)
\(390\) −21.8131 7.93932i −1.10455 0.402023i
\(391\) 1.22895 2.12860i 0.0621506 0.107648i
\(392\) 3.40211 + 5.89263i 0.171833 + 0.297623i
\(393\) 3.53231 + 20.0327i 0.178181 + 1.01052i
\(394\) −18.7767 15.7555i −0.945958 0.793753i
\(395\) 28.8866 24.2388i 1.45344 1.21958i
\(396\) 0.945455 5.36194i 0.0475109 0.269448i
\(397\) 16.7217 6.08619i 0.839236 0.305457i 0.113592 0.993527i \(-0.463764\pi\)
0.725644 + 0.688070i \(0.241542\pi\)
\(398\) 16.4661 0.825371
\(399\) 0 0
\(400\) 8.65833 0.432916
\(401\) −28.7748 + 10.4732i −1.43694 + 0.523005i −0.938913 0.344155i \(-0.888165\pi\)
−0.498030 + 0.867160i \(0.665943\pi\)
\(402\) 0.0329479 0.186857i 0.00164329 0.00931956i
\(403\) 13.0394 10.9413i 0.649537 0.545026i
\(404\) 0.325781 + 0.273363i 0.0162082 + 0.0136003i
\(405\) −2.00291 11.3591i −0.0995255 0.564437i
\(406\) −0.0494633 0.0856730i −0.00245482 0.00425188i
\(407\) 2.91955 5.05682i 0.144717 0.250657i
\(408\) −0.322044 0.117214i −0.0159435 0.00580297i
\(409\) −8.59187 3.12719i −0.424841 0.154629i 0.120747 0.992683i \(-0.461471\pi\)
−0.545587 + 0.838054i \(0.683693\pi\)
\(410\) 14.5329 25.1717i 0.717729 1.24314i
\(411\) −1.41726 2.45477i −0.0699083 0.121085i
\(412\) −0.787699 4.46727i −0.0388072 0.220086i
\(413\) 1.18954 + 0.998144i 0.0585335 + 0.0491155i
\(414\) 9.53194 7.99825i 0.468469 0.393092i
\(415\) −2.11059 + 11.9697i −0.103605 + 0.587572i
\(416\) −4.59650 + 1.67299i −0.225362 + 0.0820250i
\(417\) −21.9121 −1.07304
\(418\) 0 0
\(419\) 12.6157 0.616315 0.308158 0.951335i \(-0.400288\pi\)
0.308158 + 0.951335i \(0.400288\pi\)
\(420\) 1.97312 0.718157i 0.0962785 0.0350425i
\(421\) 5.77473 32.7501i 0.281443 1.59614i −0.436278 0.899812i \(-0.643704\pi\)
0.717721 0.696331i \(-0.245185\pi\)
\(422\) 21.0512 17.6641i 1.02476 0.859875i
\(423\) −2.27571 1.90955i −0.110649 0.0928453i
\(424\) 1.72648 + 9.79136i 0.0838453 + 0.475510i
\(425\) −1.15542 2.00125i −0.0560463 0.0970750i
\(426\) −7.36363 + 12.7542i −0.356769 + 0.617942i
\(427\) 1.69619 + 0.617364i 0.0820845 + 0.0298763i
\(428\) 2.98025 + 1.08472i 0.144056 + 0.0524320i
\(429\) 12.6553 21.9196i 0.611004 1.05829i
\(430\) 10.4131 + 18.0360i 0.502164 + 0.869773i
\(431\) −3.99242 22.6422i −0.192308 1.09063i −0.916200 0.400721i \(-0.868760\pi\)
0.723892 0.689914i \(-0.242351\pi\)
\(432\) −4.28005 3.59139i −0.205924 0.172791i
\(433\) 26.5888 22.3107i 1.27778 1.07218i 0.284231 0.958756i \(-0.408262\pi\)
0.993546 0.113427i \(-0.0361827\pi\)
\(434\) −0.267367 + 1.51632i −0.0128340 + 0.0727855i
\(435\) 0.997039 0.362893i 0.0478044 0.0173994i
\(436\) −6.78112 −0.324757
\(437\) 0 0
\(438\) 1.82629 0.0872637
\(439\) 34.2817 12.4775i 1.63618 0.595519i 0.649812 0.760095i \(-0.274848\pi\)
0.986364 + 0.164576i \(0.0526255\pi\)
\(440\) −2.58606 + 14.6663i −0.123286 + 0.699187i
\(441\) 7.04261 5.90945i 0.335362 0.281402i
\(442\) 1.00007 + 0.839162i 0.0475687 + 0.0399149i
\(443\) 2.04181 + 11.5797i 0.0970091 + 0.550166i 0.994113 + 0.108347i \(0.0345557\pi\)
−0.897104 + 0.441819i \(0.854333\pi\)
\(444\) −0.930333 1.61138i −0.0441517 0.0764729i
\(445\) 11.0146 19.0779i 0.522143 0.904378i
\(446\) −19.1421 6.96715i −0.906404 0.329904i
\(447\) −16.3449 5.94904i −0.773085 0.281380i
\(448\) 0.221232 0.383185i 0.0104522 0.0181038i
\(449\) 4.34551 + 7.52664i 0.205077 + 0.355204i 0.950157 0.311771i \(-0.100922\pi\)
−0.745080 + 0.666975i \(0.767589\pi\)
\(450\) −2.03144 11.5209i −0.0957632 0.543100i
\(451\) 24.2777 + 20.3714i 1.14319 + 0.959251i
\(452\) −7.69442 + 6.45638i −0.361915 + 0.303683i
\(453\) −2.04096 + 11.5748i −0.0958925 + 0.543833i
\(454\) 20.8136 7.57552i 0.976829 0.355537i
\(455\) −7.99866 −0.374983
\(456\) 0 0
\(457\) −13.0286 −0.609454 −0.304727 0.952440i \(-0.598565\pi\)
−0.304727 + 0.952440i \(0.598565\pi\)
\(458\) −11.9480 + 4.34871i −0.558292 + 0.203202i
\(459\) −0.258942 + 1.46853i −0.0120864 + 0.0685452i
\(460\) −26.0723 + 21.8773i −1.21563 + 1.02003i
\(461\) 6.92703 + 5.81247i 0.322624 + 0.270714i 0.789686 0.613511i \(-0.210243\pi\)
−0.467062 + 0.884224i \(0.654688\pi\)
\(462\) 0.397566 + 2.25471i 0.0184964 + 0.104899i
\(463\) 8.86025 + 15.3464i 0.411771 + 0.713208i 0.995083 0.0990396i \(-0.0315771\pi\)
−0.583313 + 0.812248i \(0.698244\pi\)
\(464\) 0.111791 0.193627i 0.00518976 0.00898892i
\(465\) −15.5181 5.64811i −0.719632 0.261925i
\(466\) 8.15819 + 2.96934i 0.377921 + 0.137552i
\(467\) 3.93886 6.82231i 0.182269 0.315699i −0.760384 0.649474i \(-0.774989\pi\)
0.942653 + 0.333775i \(0.108323\pi\)
\(468\) 3.30455 + 5.72364i 0.152753 + 0.264576i
\(469\) −0.0113531 0.0643864i −0.000524236 0.00297309i
\(470\) 6.22464 + 5.22310i 0.287121 + 0.240923i
\(471\) −16.1225 + 13.5284i −0.742885 + 0.623355i
\(472\) −0.609423 + 3.45621i −0.0280510 + 0.159085i
\(473\) −21.3386 + 7.76662i −0.981151 + 0.357110i
\(474\) 13.1019 0.601792
\(475\) 0 0
\(476\) −0.118090 −0.00541266
\(477\) 12.6234 4.59456i 0.577988 0.210370i
\(478\) 3.79854 21.5426i 0.173741 0.985334i
\(479\) −23.1191 + 19.3992i −1.05634 + 0.886373i −0.993746 0.111666i \(-0.964381\pi\)
−0.0625925 + 0.998039i \(0.519937\pi\)
\(480\) 3.63534 + 3.05041i 0.165930 + 0.139231i
\(481\) 1.23080 + 6.98023i 0.0561198 + 0.318271i
\(482\) 9.48160 + 16.4226i 0.431875 + 0.748030i
\(483\) −2.61617 + 4.53134i −0.119040 + 0.206183i
\(484\) −4.92235 1.79159i −0.223743 0.0814359i
\(485\) −14.1857 5.16317i −0.644140 0.234448i
\(486\) −6.37701 + 11.0453i −0.289267 + 0.501025i
\(487\) −17.8850 30.9777i −0.810445 1.40373i −0.912553 0.408959i \(-0.865892\pi\)
0.102107 0.994773i \(-0.467442\pi\)
\(488\) 0.708406 + 4.01757i 0.0320680 + 0.181867i
\(489\) −13.5472 11.3675i −0.612627 0.514055i
\(490\) −19.2633 + 16.1639i −0.870229 + 0.730209i
\(491\) −3.17301 + 17.9950i −0.143196 + 0.812104i 0.825602 + 0.564253i \(0.190836\pi\)
−0.968798 + 0.247852i \(0.920275\pi\)
\(492\) 9.48989 3.45404i 0.427837 0.155720i
\(493\) −0.0596724 −0.00268751
\(494\) 0 0
\(495\) 20.1219 0.904413
\(496\) −3.26999 + 1.19018i −0.146827 + 0.0534407i
\(497\) −0.881207 + 4.99757i −0.0395275 + 0.224172i
\(498\) −3.23505 + 2.71453i −0.144966 + 0.121641i
\(499\) 13.5574 + 11.3760i 0.606914 + 0.509262i 0.893660 0.448745i \(-0.148129\pi\)
−0.286745 + 0.958007i \(0.592573\pi\)
\(500\) 2.34775 + 13.3147i 0.104995 + 0.595454i
\(501\) 6.63407 + 11.4905i 0.296388 + 0.513360i
\(502\) −1.45138 + 2.51386i −0.0647782 + 0.112199i
\(503\) 9.57570 + 3.48527i 0.426959 + 0.155401i 0.546557 0.837422i \(-0.315938\pi\)
−0.119598 + 0.992822i \(0.538160\pi\)
\(504\) −0.561777 0.204470i −0.0250235 0.00910782i
\(505\) −0.785853 + 1.36114i −0.0349700 + 0.0605698i
\(506\) −18.5552 32.1386i −0.824881 1.42874i
\(507\) 2.43641 + 13.8176i 0.108205 + 0.613660i
\(508\) 10.7864 + 9.05083i 0.478567 + 0.401566i
\(509\) −6.46251 + 5.42269i −0.286446 + 0.240357i −0.774676 0.632358i \(-0.782087\pi\)
0.488230 + 0.872715i \(0.337643\pi\)
\(510\) 0.219937 1.24732i 0.00973897 0.0552324i
\(511\) 0.591347 0.215233i 0.0261596 0.00952133i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 22.9050 1.01030
\(515\) 15.7534 5.73378i 0.694179 0.252660i
\(516\) −1.25653 + 7.12614i −0.0553156 + 0.313711i
\(517\) −6.78712 + 5.69507i −0.298497 + 0.250469i
\(518\) −0.491143 0.412118i −0.0215796 0.0181074i
\(519\) −2.18786 12.4080i −0.0960365 0.544650i
\(520\) −9.03879 15.6556i −0.396377 0.686545i
\(521\) −4.48183 + 7.76275i −0.196352 + 0.340092i −0.947343 0.320221i \(-0.896243\pi\)
0.750991 + 0.660313i \(0.229576\pi\)
\(522\) −0.283872 0.103321i −0.0124247 0.00452223i
\(523\) 2.01088 + 0.731900i 0.0879296 + 0.0320038i 0.385610 0.922662i \(-0.373991\pi\)
−0.297681 + 0.954665i \(0.596213\pi\)
\(524\) −7.92075 + 13.7191i −0.346020 + 0.599324i
\(525\) 2.45965 + 4.26024i 0.107348 + 0.185932i
\(526\) −0.879070 4.98545i −0.0383293 0.217376i
\(527\) 0.711462 + 0.596988i 0.0309918 + 0.0260052i
\(528\) −3.96383 + 3.32605i −0.172504 + 0.144748i
\(529\) 10.7334 60.8722i 0.466670 2.64662i
\(530\) −34.5284 + 12.5673i −1.49982 + 0.545889i
\(531\) 4.74186 0.205779
\(532\) 0 0
\(533\) −38.4702 −1.66633
\(534\) 7.19247 2.61785i 0.311249 0.113285i
\(535\) −2.03533 + 11.5429i −0.0879951 + 0.499045i
\(536\) 0.113193 0.0949801i 0.00488919 0.00410252i
\(537\) −8.65455 7.26203i −0.373472 0.313380i
\(538\) −3.60180 20.4268i −0.155285 0.880663i
\(539\) −13.7094 23.7454i −0.590506 1.02279i
\(540\) 10.3244 17.8823i 0.444290 0.769533i
\(541\) 11.0053 + 4.00559i 0.473153 + 0.172214i 0.567580 0.823318i \(-0.307880\pi\)
−0.0944272 + 0.995532i \(0.530102\pi\)
\(542\) −5.91508 2.15291i −0.254075 0.0924756i
\(543\) −9.32739 + 16.1555i −0.400277 + 0.693299i
\(544\) −0.133446 0.231136i −0.00572147 0.00990988i
\(545\) −4.35181 24.6804i −0.186411 1.05719i
\(546\) −2.12895 1.78640i −0.0911104 0.0764507i
\(547\) −19.1432 + 16.0630i −0.818504 + 0.686806i −0.952621 0.304159i \(-0.901625\pi\)
0.134117 + 0.990965i \(0.457180\pi\)
\(548\) 0.383317 2.17390i 0.0163745 0.0928644i
\(549\) 5.17963 1.88523i 0.221061 0.0804597i
\(550\) −34.8902 −1.48772
\(551\) 0 0
\(552\) −11.8255 −0.503325
\(553\) 4.24236 1.54409i 0.180403 0.0656615i
\(554\) 1.24611 7.06706i 0.0529423 0.300251i
\(555\) 5.26770 4.42013i 0.223602 0.187624i
\(556\) −13.0721 10.9688i −0.554381 0.465181i
\(557\) 1.59681 + 9.05596i 0.0676590 + 0.383713i 0.999768 + 0.0215356i \(0.00685552\pi\)
−0.932109 + 0.362178i \(0.882033\pi\)
\(558\) 2.35089 + 4.07185i 0.0995209 + 0.172375i
\(559\) 13.7823 23.8717i 0.582930 1.00966i
\(560\) 1.53660 + 0.559278i 0.0649334 + 0.0236338i
\(561\) 1.29773 + 0.472335i 0.0547902 + 0.0199420i
\(562\) −1.38696 + 2.40228i −0.0585052 + 0.101334i
\(563\) −9.86122 17.0801i −0.415601 0.719842i 0.579890 0.814694i \(-0.303095\pi\)
−0.995491 + 0.0948526i \(0.969762\pi\)
\(564\) 0.490257 + 2.78039i 0.0206435 + 0.117075i
\(565\) −28.4364 23.8610i −1.19633 1.00384i
\(566\) 5.93578 4.98071i 0.249499 0.209355i
\(567\) 0.239795 1.35995i 0.0100705 0.0571124i
\(568\) −10.7774 + 3.92267i −0.452212 + 0.164592i
\(569\) 22.1469 0.928446 0.464223 0.885718i \(-0.346334\pi\)
0.464223 + 0.885718i \(0.346334\pi\)
\(570\) 0 0
\(571\) −3.02145 −0.126444 −0.0632218 0.998000i \(-0.520138\pi\)
−0.0632218 + 0.998000i \(0.520138\pi\)
\(572\) 18.5224 6.74160i 0.774460 0.281880i
\(573\) 2.83855 16.0982i 0.118582 0.672512i
\(574\) 2.66572 2.23681i 0.111265 0.0933625i
\(575\) −61.0822 51.2540i −2.54730 2.13744i
\(576\) −0.234623 1.33061i −0.00977597 0.0554423i
\(577\) −1.15469 1.99998i −0.0480704 0.0832603i 0.840989 0.541052i \(-0.181974\pi\)
−0.889059 + 0.457792i \(0.848641\pi\)
\(578\) 8.46438 14.6607i 0.352072 0.609807i
\(579\) −21.0897 7.67603i −0.876459 0.319005i
\(580\) 0.776463 + 0.282609i 0.0322409 + 0.0117347i
\(581\) −0.727582 + 1.26021i −0.0301852 + 0.0522823i
\(582\) −2.62258 4.54243i −0.108709 0.188290i
\(583\) −6.95715 39.4560i −0.288136 1.63410i
\(584\) 1.08951 + 0.914211i 0.0450844 + 0.0378303i
\(585\) −18.7109 + 15.7003i −0.773601 + 0.649128i
\(586\) −0.135944 + 0.770977i −0.00561579 + 0.0318487i
\(587\) −26.3950 + 9.60701i −1.08944 + 0.396524i −0.823413 0.567442i \(-0.807933\pi\)
−0.266027 + 0.963966i \(0.585711\pi\)
\(588\) −8.73716 −0.360315
\(589\) 0 0
\(590\) −12.9702 −0.533975
\(591\) 29.5763 10.7649i 1.21661 0.442808i
\(592\) 0.251621 1.42701i 0.0103416 0.0586499i
\(593\) −9.26446 + 7.77381i −0.380446 + 0.319232i −0.812877 0.582435i \(-0.802100\pi\)
0.432432 + 0.901667i \(0.357656\pi\)
\(594\) 17.2472 + 14.4721i 0.707661 + 0.593798i
\(595\) −0.0757851 0.429798i −0.00310688 0.0176200i
\(596\) −6.77288 11.7310i −0.277428 0.480519i
\(597\) −10.5719 + 18.3110i −0.432679 + 0.749421i
\(598\) 42.3305 + 15.4071i 1.73102 + 0.630041i
\(599\) −18.3264 6.67025i −0.748795 0.272539i −0.0606966 0.998156i \(-0.519332\pi\)
−0.688099 + 0.725617i \(0.741554\pi\)
\(600\) −5.55899 + 9.62845i −0.226945 + 0.393080i
\(601\) 19.4816 + 33.7431i 0.794671 + 1.37641i 0.923048 + 0.384685i \(0.125690\pi\)
−0.128376 + 0.991726i \(0.540977\pi\)
\(602\) 0.432971 + 2.45550i 0.0176466 + 0.100079i
\(603\) −0.152940 0.128332i −0.00622818 0.00522607i
\(604\) −7.01174 + 5.88355i −0.285304 + 0.239398i
\(605\) 3.36168 19.0650i 0.136672 0.775103i
\(606\) −0.513157 + 0.186774i −0.0208456 + 0.00758716i
\(607\) 8.46029 0.343393 0.171696 0.985150i \(-0.445075\pi\)
0.171696 + 0.985150i \(0.445075\pi\)
\(608\) 0 0
\(609\) 0.127030 0.00514750
\(610\) −14.1676 + 5.15659i −0.573630 + 0.208784i
\(611\) 1.86755 10.5914i 0.0755532 0.428483i
\(612\) −0.276243 + 0.231796i −0.0111665 + 0.00936978i
\(613\) −2.23296 1.87368i −0.0901885 0.0756772i 0.596579 0.802555i \(-0.296526\pi\)
−0.686767 + 0.726877i \(0.740971\pi\)
\(614\) −4.89146 27.7408i −0.197403 1.11953i
\(615\) 18.6614 + 32.3225i 0.752500 + 1.30337i
\(616\) −0.891491 + 1.54411i −0.0359192 + 0.0622139i
\(617\) 2.83698 + 1.03258i 0.114213 + 0.0415700i 0.398494 0.917171i \(-0.369533\pi\)
−0.284282 + 0.958741i \(0.591755\pi\)
\(618\) 5.47354 + 1.99220i 0.220178 + 0.0801382i
\(619\) 1.96406 3.40186i 0.0789423 0.136732i −0.823852 0.566806i \(-0.808179\pi\)
0.902794 + 0.430074i \(0.141512\pi\)
\(620\) −6.43028 11.1376i −0.258246 0.447295i
\(621\) 8.93494 + 50.6726i 0.358547 + 2.03342i
\(622\) 2.96327 + 2.48648i 0.118816 + 0.0996986i
\(623\) 2.02038 1.69530i 0.0809446 0.0679206i
\(624\) 1.09069 6.18564i 0.0436627 0.247624i
\(625\) −6.27245 + 2.28299i −0.250898 + 0.0913194i
\(626\) 30.3878 1.21454
\(627\) 0 0
\(628\) −16.3903 −0.654043
\(629\) −0.363412 + 0.132271i −0.0144902 + 0.00527400i
\(630\) 0.383661 2.17585i 0.0152854 0.0866878i
\(631\) 7.76517 6.51575i 0.309127 0.259388i −0.475004 0.879983i \(-0.657553\pi\)
0.784131 + 0.620595i \(0.213109\pi\)
\(632\) 7.81624 + 6.55861i 0.310913 + 0.260887i
\(633\) 6.12754 + 34.7510i 0.243548 + 1.38123i
\(634\) −2.66402 4.61421i −0.105802 0.183254i
\(635\) −26.0189 + 45.0661i −1.03253 + 1.78839i
\(636\) −11.9969 4.36652i −0.475708 0.173144i
\(637\) 31.2756 + 11.3834i 1.23918 + 0.451026i
\(638\) −0.450480 + 0.780255i −0.0178347 + 0.0308906i
\(639\) 7.74820 + 13.4203i 0.306514 + 0.530898i
\(640\) 0.641755 + 3.63957i 0.0253676 + 0.143867i
\(641\) 6.34308 + 5.32248i 0.250537 + 0.210225i 0.759403 0.650620i \(-0.225491\pi\)
−0.508867 + 0.860845i \(0.669935\pi\)
\(642\) −3.11970 + 2.61774i −0.123125 + 0.103314i
\(643\) 6.39964 36.2942i 0.252377 1.43130i −0.550339 0.834941i \(-0.685502\pi\)
0.802716 0.596361i \(-0.203387\pi\)
\(644\) −3.82904 + 1.39366i −0.150885 + 0.0549178i
\(645\) −26.7425 −1.05298
\(646\) 0 0
\(647\) −20.1901 −0.793753 −0.396876 0.917872i \(-0.629906\pi\)
−0.396876 + 0.917872i \(0.629906\pi\)
\(648\) 2.93278 1.06744i 0.115210 0.0419331i
\(649\) 2.45577 13.9274i 0.0963976 0.546698i
\(650\) 32.4436 27.2234i 1.27254 1.06779i
\(651\) −1.51455 1.27086i −0.0593600 0.0498089i
\(652\) −2.39153 13.5630i −0.0936594 0.531169i
\(653\) 11.0194 + 19.0861i 0.431221 + 0.746897i 0.996979 0.0776744i \(-0.0247495\pi\)
−0.565757 + 0.824572i \(0.691416\pi\)
\(654\) 4.35375 7.54091i 0.170245 0.294873i
\(655\) −55.0150 20.0238i −2.14961 0.782395i
\(656\) 7.39042 + 2.68989i 0.288548 + 0.105023i
\(657\) 0.960837 1.66422i 0.0374858 0.0649273i
\(658\) 0.486417 + 0.842500i 0.0189625 + 0.0328441i
\(659\) −4.72698 26.8080i −0.184137 1.04429i −0.927059 0.374915i \(-0.877672\pi\)
0.742922 0.669378i \(-0.233439\pi\)
\(660\) −14.6492 12.2921i −0.570220 0.478471i
\(661\) −6.82412 + 5.72611i −0.265427 + 0.222720i −0.765781 0.643101i \(-0.777648\pi\)
0.500354 + 0.865821i \(0.333203\pi\)
\(662\) −3.56813 + 20.2359i −0.138679 + 0.786489i
\(663\) −1.57527 + 0.573353i −0.0611786 + 0.0222672i
\(664\) −3.28878 −0.127629
\(665\) 0 0
\(666\) −1.95784 −0.0758648
\(667\) −1.93486 + 0.704230i −0.0749179 + 0.0272679i
\(668\) −1.79427 + 10.1758i −0.0694225 + 0.393714i
\(669\) 20.0378 16.8137i 0.774705 0.650055i
\(670\) 0.418329 + 0.351020i 0.0161615 + 0.0135611i
\(671\) −2.85464 16.1895i −0.110202 0.624989i
\(672\) 0.284079 + 0.492039i 0.0109586 + 0.0189808i
\(673\) −17.8505 + 30.9180i −0.688087 + 1.19180i 0.284370 + 0.958715i \(0.408216\pi\)
−0.972456 + 0.233086i \(0.925118\pi\)
\(674\) −12.4814 4.54285i −0.480765 0.174984i
\(675\) 45.4585 + 16.5455i 1.74970 + 0.636838i
\(676\) −5.46334 + 9.46279i −0.210129 + 0.363953i
\(677\) 13.6924 + 23.7160i 0.526243 + 0.911480i 0.999533 + 0.0305727i \(0.00973312\pi\)
−0.473290 + 0.880907i \(0.656934\pi\)
\(678\) −2.23967 12.7018i −0.0860140 0.487810i
\(679\) −1.38452 1.16175i −0.0531328 0.0445837i
\(680\) 0.755596 0.634021i 0.0289758 0.0243136i
\(681\) −4.93881 + 28.0094i −0.189256 + 1.07332i
\(682\) 13.1770 4.79603i 0.504573 0.183650i
\(683\) −38.1521 −1.45985 −0.729925 0.683528i \(-0.760445\pi\)
−0.729925 + 0.683528i \(0.760445\pi\)
\(684\) 0 0
\(685\) 8.15806 0.311703
\(686\) −5.73952 + 2.08901i −0.219136 + 0.0797589i
\(687\) 2.83511 16.0787i 0.108166 0.613442i
\(688\) −4.31683 + 3.62225i −0.164578 + 0.138097i
\(689\) 37.2552 + 31.2608i 1.41931 + 1.19094i
\(690\) −7.58905 43.0396i −0.288910 1.63849i
\(691\) 14.1029 + 24.4269i 0.536499 + 0.929244i 0.999089 + 0.0426714i \(0.0135868\pi\)
−0.462590 + 0.886572i \(0.653080\pi\)
\(692\) 4.90601 8.49745i 0.186498 0.323025i
\(693\) 2.26378 + 0.823948i 0.0859938 + 0.0312992i
\(694\) −28.3245 10.3093i −1.07518 0.391335i
\(695\) 31.5327 54.6162i 1.19610 2.07171i
\(696\) 0.143548 + 0.248633i 0.00544118 + 0.00942440i
\(697\) −0.364494 2.06715i −0.0138062 0.0782989i
\(698\) 26.8616 + 22.5395i 1.01673 + 0.853134i
\(699\) −8.53992 + 7.16584i −0.323009 + 0.271037i
\(700\) −0.665245 + 3.77279i −0.0251439 + 0.142598i
\(701\) −40.0448 + 14.5751i −1.51247 + 0.550495i −0.959255 0.282543i \(-0.908822\pi\)
−0.553217 + 0.833037i \(0.686600\pi\)
\(702\) −27.3298 −1.03150
\(703\) 0 0
\(704\) −4.02967 −0.151874
\(705\) −9.80478 + 3.56865i −0.369270 + 0.134403i
\(706\) 2.35138 13.3353i 0.0884954 0.501882i
\(707\) −0.144146 + 0.120953i −0.00542118 + 0.00454891i
\(708\) −3.45219 2.89673i −0.129741 0.108866i
\(709\) −3.93993 22.3445i −0.147967 0.839164i −0.964937 0.262483i \(-0.915459\pi\)
0.816969 0.576681i \(-0.195653\pi\)
\(710\) −21.1933 36.7079i −0.795371 1.37762i
\(711\) 6.89310 11.9392i 0.258511 0.447755i
\(712\) 5.60127 + 2.03870i 0.209916 + 0.0764033i
\(713\) 30.1143 + 10.9607i 1.12779 + 0.410482i
\(714\) 0.0758187 0.131322i 0.00283744 0.00491460i
\(715\) 36.4233 + 63.0871i 1.36216 + 2.35932i
\(716\) −1.52781 8.66464i −0.0570969 0.323813i
\(717\) 21.5175 + 18.0553i 0.803586 + 0.674289i
\(718\) −18.0076 + 15.1102i −0.672037 + 0.563906i
\(719\) −6.56953 + 37.2577i −0.245002 + 1.38948i 0.575486 + 0.817812i \(0.304813\pi\)
−0.820488 + 0.571664i \(0.806298\pi\)
\(720\) 4.69229 1.70786i 0.174871 0.0636480i
\(721\) 2.00709 0.0747481
\(722\) 0 0
\(723\) −24.3503 −0.905596
\(724\) −13.6516 + 4.96878i −0.507358 + 0.184663i
\(725\) −0.336156 + 1.90643i −0.0124845 + 0.0708031i
\(726\) 5.15268 4.32361i 0.191234 0.160464i
\(727\) −14.9687 12.5603i −0.555160 0.465835i 0.321524 0.946901i \(-0.395805\pi\)
−0.876684 + 0.481067i \(0.840249\pi\)
\(728\) −0.375828 2.13143i −0.0139291 0.0789959i
\(729\) −12.8701 22.2916i −0.476670 0.825616i
\(730\) −2.62814 + 4.55206i −0.0972717 + 0.168479i
\(731\) 1.41330 + 0.514399i 0.0522727 + 0.0190257i
\(732\) −4.92254 1.79166i −0.181942 0.0662216i
\(733\) −17.5550 + 30.4062i −0.648410 + 1.12308i 0.335092 + 0.942185i \(0.391232\pi\)
−0.983503 + 0.180894i \(0.942101\pi\)
\(734\) 6.34644 + 10.9924i 0.234251 + 0.405735i
\(735\) −5.60712 31.7995i −0.206822 1.17294i
\(736\) −7.05473 5.91962i −0.260041 0.218200i
\(737\) −0.456130 + 0.382739i −0.0168018 + 0.0140984i
\(738\) 1.84525 10.4649i 0.0679245 0.385219i
\(739\) 15.2958 5.56722i 0.562666 0.204794i −0.0449992 0.998987i \(-0.514329\pi\)
0.607665 + 0.794193i \(0.292106\pi\)
\(740\) 5.35520 0.196861
\(741\) 0 0
\(742\) −4.39915 −0.161498
\(743\) −31.2998 + 11.3922i −1.14828 + 0.417939i −0.844896 0.534930i \(-0.820338\pi\)
−0.303382 + 0.952869i \(0.598116\pi\)
\(744\) 0.775931 4.40052i 0.0284470 0.161331i
\(745\) 38.3492 32.1788i 1.40501 1.17894i
\(746\) 2.02964 + 1.70307i 0.0743103 + 0.0623537i
\(747\) 0.771624 + 4.37610i 0.0282322 + 0.160113i
\(748\) 0.537746 + 0.931403i 0.0196619 + 0.0340555i
\(749\) −0.701639 + 1.21528i −0.0256373 + 0.0444052i
\(750\) −16.3139 5.93779i −0.595701 0.216817i
\(751\) −18.0984 6.58727i −0.660419 0.240373i −0.0100020 0.999950i \(-0.503184\pi\)
−0.650417 + 0.759577i \(0.725406\pi\)
\(752\) −1.09934 + 1.90411i −0.0400888 + 0.0694358i
\(753\) −1.86368 3.22800i −0.0679164 0.117635i
\(754\) −0.189910 1.07703i −0.00691611 0.0392232i
\(755\) −25.9134 21.7439i −0.943085 0.791343i
\(756\) 1.89377 1.58906i 0.0688756 0.0577935i
\(757\) −4.15808 + 23.5816i −0.151128 + 0.857089i 0.811113 + 0.584890i \(0.198862\pi\)
−0.962241 + 0.272200i \(0.912249\pi\)
\(758\) −17.0716 + 6.21355i −0.620068 + 0.225686i
\(759\) 47.6528 1.72969
\(760\) 0 0
\(761\) −44.7968 −1.62388 −0.811941 0.583739i \(-0.801589\pi\)
−0.811941 + 0.583739i \(0.801589\pi\)
\(762\) −16.9902 + 6.18393i −0.615490 + 0.224020i
\(763\) 0.521013 2.95481i 0.0188620 0.106971i
\(764\) 9.75187 8.18279i 0.352810 0.296043i
\(765\) −1.02092 0.856651i −0.0369113 0.0309723i
\(766\) 3.99535 + 22.6588i 0.144358 + 0.818695i
\(767\) 8.58341 + 14.8669i 0.309929 + 0.536813i
\(768\) −0.642040 + 1.11205i −0.0231676 + 0.0401275i
\(769\) 29.8228 + 10.8546i 1.07544 + 0.391427i 0.818207 0.574924i \(-0.194968\pi\)
0.257229 + 0.966350i \(0.417190\pi\)
\(770\) −6.19201 2.25371i −0.223145 0.0812180i
\(771\) −14.7059 + 25.4714i −0.529621 + 0.917330i
\(772\) −8.73903 15.1364i −0.314525 0.544772i
\(773\) −3.86032 21.8929i −0.138846 0.787434i −0.972104 0.234550i \(-0.924638\pi\)
0.833258 0.552884i \(-0.186473\pi\)
\(774\) 5.83264 + 4.89417i 0.209650 + 0.175917i
\(775\) 23.0807 19.3670i 0.829083 0.695683i
\(776\) 0.709311 4.02270i 0.0254628 0.144407i
\(777\) 0.773627 0.281577i 0.0277537 0.0101015i
\(778\) −16.5706 −0.594086
\(779\) 0 0
\(780\) 23.2130 0.831160
\(781\) 43.4296 15.8071i 1.55403 0.565622i
\(782\) −0.426809 + 2.42056i −0.0152627 + 0.0865589i
\(783\) 0.956940 0.802968i 0.0341983 0.0286957i
\(784\) −5.21234 4.37367i −0.186155 0.156203i
\(785\) −10.5185 59.6536i −0.375423 2.12913i
\(786\) −10.1709 17.6165i −0.362783 0.628358i
\(787\) −12.2298 + 21.1826i −0.435945 + 0.755080i −0.997372 0.0724468i \(-0.976919\pi\)
0.561427 + 0.827526i \(0.310253\pi\)
\(788\) 23.0331 + 8.38335i 0.820519 + 0.298645i
\(789\) 6.10845 + 2.22329i 0.217466 + 0.0791513i
\(790\) −18.8544 + 32.6568i −0.670810 + 1.16188i
\(791\) −2.22213 3.84884i −0.0790098 0.136849i
\(792\) 0.945455 + 5.36194i 0.0335953 + 0.190528i
\(793\) 15.2865 + 12.8269i 0.542839 + 0.455496i
\(794\) −13.6316 + 11.4383i −0.483768 + 0.405930i
\(795\) 8.19318 46.4658i 0.290582 1.64797i
\(796\) −15.4731 + 5.63174i −0.548429 + 0.199612i
\(797\) 41.6933 1.47685 0.738426 0.674334i \(-0.235569\pi\)
0.738426 + 0.674334i \(0.235569\pi\)
\(798\) 0 0
\(799\) 0.586812 0.0207599
\(800\) −8.13617 + 2.96132i −0.287657 + 0.104699i
\(801\) 1.39853 7.93145i 0.0494146 0.280244i
\(802\) 23.4574 19.6831i 0.828310 0.695034i
\(803\) −4.39039 3.68397i −0.154933 0.130005i
\(804\) 0.0329479 + 0.186857i 0.00116198 + 0.00658993i
\(805\) −7.52962 13.0417i −0.265384 0.459659i
\(806\) −8.51084 + 14.7412i −0.299781 + 0.519237i
\(807\) 25.0280 + 9.10946i 0.881029 + 0.320668i
\(808\) −0.399630 0.145453i −0.0140589 0.00511703i
\(809\) 24.6244 42.6507i 0.865748 1.49952i −0.000555336 1.00000i \(-0.500177\pi\)
0.866303 0.499519i \(-0.166490\pi\)
\(810\) 5.76716 + 9.98901i 0.202637 + 0.350978i
\(811\) 9.03760 + 51.2548i 0.317353 + 1.79980i 0.558710 + 0.829363i \(0.311296\pi\)
−0.241357 + 0.970436i \(0.577593\pi\)
\(812\) 0.0757822 + 0.0635888i 0.00265944 + 0.00223153i
\(813\) 6.19186 5.19558i 0.217158 0.182217i
\(814\) −1.01395 + 5.75040i −0.0355389 + 0.201551i
\(815\) 47.8288 17.4083i 1.67537 0.609785i
\(816\) 0.342712 0.0119973
\(817\) 0 0
\(818\) 9.14328 0.319687
\(819\) −2.74793 + 1.00016i −0.0960203 + 0.0349485i
\(820\) −5.04722 + 28.6242i −0.176257 + 0.999601i
\(821\) −32.3717 + 27.1631i −1.12978 + 0.947998i −0.999057 0.0434212i \(-0.986174\pi\)
−0.130723 + 0.991419i \(0.541730\pi\)
\(822\) 2.17137 + 1.82200i 0.0757352 + 0.0635494i
\(823\) 5.63959 + 31.9837i 0.196584 + 1.11488i 0.910145 + 0.414290i \(0.135970\pi\)
−0.713561 + 0.700593i \(0.752919\pi\)
\(824\) 2.26809 + 3.92845i 0.0790127 + 0.136854i
\(825\) 22.4009 38.7995i 0.779899 1.35083i
\(826\) −1.45919 0.531101i −0.0507717 0.0184794i
\(827\) 20.2181 + 7.35879i 0.703052 + 0.255890i 0.668713 0.743520i \(-0.266845\pi\)
0.0343387 + 0.999410i \(0.489068\pi\)
\(828\) −6.22153 + 10.7760i −0.216213 + 0.374492i
\(829\) −2.82531 4.89357i −0.0981269 0.169961i 0.812782 0.582567i \(-0.197952\pi\)
−0.910909 + 0.412607i \(0.864618\pi\)
\(830\) −2.11059 11.9697i −0.0732596 0.415476i
\(831\) 7.05883 + 5.92307i 0.244868 + 0.205469i
\(832\) 3.74710 3.14419i 0.129907 0.109005i
\(833\) −0.315345 + 1.78841i −0.0109261 + 0.0619648i
\(834\) 20.5906 7.49438i 0.712995 0.259509i
\(835\) −38.1871 −1.32152
\(836\) 0 0
\(837\) −19.4427 −0.672037
\(838\) −11.8548 + 4.31481i −0.409519 + 0.149053i
\(839\) −1.85398 + 10.5144i −0.0640064 + 0.362998i 0.935935 + 0.352173i \(0.114557\pi\)
−0.999941 + 0.0108254i \(0.996554\pi\)
\(840\) −1.60850 + 1.34969i −0.0554986 + 0.0465689i
\(841\) −22.1770 18.6087i −0.764724 0.641680i
\(842\) 5.77473 + 32.7501i 0.199010 + 1.12864i
\(843\) −1.78096 3.08471i −0.0613395 0.106243i
\(844\) −13.7402 + 23.7988i −0.472958 + 0.819187i
\(845\) −37.9466 13.8114i −1.30540 0.475128i
\(846\) 2.79157 + 1.01605i 0.0959761 + 0.0349324i
\(847\) 1.15887 2.00722i 0.0398192 0.0689689i
\(848\) −4.97120 8.61038i −0.170712 0.295682i
\(849\) 1.72777 + 9.79867i 0.0592969 + 0.336289i
\(850\) 1.77021 + 1.48538i 0.0607178 + 0.0509482i
\(851\) −10.2225 + 8.57770i −0.350423 + 0.294040i
\(852\) 2.55736 14.5035i 0.0876137 0.496882i
\(853\) −9.64743 + 3.51138i −0.330322 + 0.120227i −0.501857 0.864951i \(-0.667350\pi\)
0.171535 + 0.985178i \(0.445127\pi\)
\(854\) −1.80505 −0.0617676
\(855\) 0 0
\(856\) −3.17151 −0.108400
\(857\) 35.0869 12.7706i 1.19855 0.436235i 0.335830 0.941923i \(-0.390983\pi\)
0.862717 + 0.505687i \(0.168761\pi\)
\(858\) −4.39514 + 24.9261i −0.150048 + 0.850963i
\(859\) −18.6064 + 15.6127i −0.634844 + 0.532697i −0.902430 0.430837i \(-0.858218\pi\)
0.267586 + 0.963534i \(0.413774\pi\)
\(860\) −15.9538 13.3868i −0.544019 0.456486i
\(861\) 0.775931 + 4.40052i 0.0264436 + 0.149969i
\(862\) 11.4957 + 19.9112i 0.391546 + 0.678178i
\(863\) 11.7864 20.4146i 0.401214 0.694922i −0.592659 0.805453i \(-0.701922\pi\)
0.993873 + 0.110531i \(0.0352552\pi\)
\(864\) 5.25026 + 1.91094i 0.178617 + 0.0650114i
\(865\) 34.0755 + 12.4025i 1.15860 + 0.421697i
\(866\) −17.3546 + 30.0591i −0.589734 + 1.02145i
\(867\) 10.8689 + 18.8256i 0.369128 + 0.639349i
\(868\) −0.267367 1.51632i −0.00907504 0.0514671i
\(869\) −31.4969 26.4290i −1.06846 0.896543i
\(870\) −0.812794 + 0.682015i −0.0275563 + 0.0231225i
\(871\) 0.125510 0.711800i 0.00425273 0.0241184i
\(872\) 6.37217 2.31928i 0.215789 0.0785407i
\(873\) −5.51908 −0.186793
\(874\) 0 0
\(875\) −5.98217 −0.202234
\(876\) −1.71616 + 0.624629i −0.0579835 + 0.0211043i
\(877\) −5.45918 + 30.9606i −0.184344 + 1.04546i 0.742452 + 0.669899i \(0.233663\pi\)
−0.926796 + 0.375565i \(0.877449\pi\)
\(878\) −27.9467 + 23.4501i −0.943155 + 0.791401i
\(879\) −0.770079 0.646173i −0.0259741 0.0217949i
\(880\) −2.58606 14.6663i −0.0871761 0.494400i
\(881\) 20.8800 + 36.1653i 0.703466 + 1.21844i 0.967242 + 0.253855i \(0.0816985\pi\)
−0.263776 + 0.964584i \(0.584968\pi\)
\(882\) −4.59673 + 7.96178i −0.154780 + 0.268087i
\(883\) −0.510291 0.185731i −0.0171727 0.00625034i 0.333420 0.942779i \(-0.391797\pi\)
−0.350592 + 0.936528i \(0.614020\pi\)
\(884\) −1.22677 0.446509i −0.0412608 0.0150177i
\(885\) 8.32739 14.4235i 0.279922 0.484839i
\(886\) −5.87915 10.1830i −0.197514 0.342104i
\(887\) 1.96653 + 11.1528i 0.0660297 + 0.374473i 0.999860 + 0.0167556i \(0.00533371\pi\)
−0.933830 + 0.357717i \(0.883555\pi\)
\(888\) 1.42535 + 1.19601i 0.0478317 + 0.0401356i
\(889\) −4.77257 + 4.00466i −0.160067 + 0.134312i
\(890\) −3.82534 + 21.6946i −0.128226 + 0.727203i
\(891\) −11.8181 + 4.30145i −0.395922 + 0.144104i
\(892\) 20.3706 0.682058
\(893\) 0 0
\(894\) 17.3938 0.581737
\(895\) 30.5551 11.1211i 1.02134 0.371739i
\(896\) −0.0768330 + 0.435741i −0.00256681 + 0.0145571i
\(897\) −44.3112 + 37.1815i −1.47951 + 1.24145i
\(898\) −6.65771 5.58648i −0.222171 0.186423i
\(899\) −0.135104 0.766211i −0.00450596 0.0255546i
\(900\) 5.84931 + 10.1313i 0.194977 + 0.337710i
\(901\) −1.32678 + 2.29805i −0.0442014 + 0.0765591i
\(902\) −29.7810 10.8394i −0.991598 0.360912i
\(903\) −3.00861 1.09504i −0.100120 0.0364408i
\(904\) 5.02218 8.69866i 0.167035 0.289313i
\(905\) −26.8452 46.4973i −0.892366 1.54562i
\(906\) −2.04096 11.5748i −0.0678062 0.384548i
\(907\) 8.36968 + 7.02300i 0.277911 + 0.233195i 0.771080 0.636739i \(-0.219717\pi\)
−0.493169 + 0.869934i \(0.664162\pi\)
\(908\) −16.9674 + 14.2373i −0.563082 + 0.472482i
\(909\) −0.0997799 + 0.565880i −0.00330949 + 0.0187691i
\(910\) 7.51629 2.73570i 0.249162 0.0906877i
\(911\) 47.4159 1.57096 0.785479 0.618888i \(-0.212416\pi\)
0.785479 + 0.618888i \(0.212416\pi\)
\(912\) 0 0
\(913\) 13.2527 0.438600
\(914\) 12.2429 4.45605i 0.404959 0.147393i
\(915\) 3.36181 19.0658i 0.111138 0.630295i
\(916\) 9.74008 8.17290i 0.321821 0.270040i
\(917\) −5.36942 4.50548i −0.177314 0.148784i
\(918\) −0.258942 1.46853i −0.00854636 0.0484688i
\(919\) −2.55534 4.42599i −0.0842930 0.146000i 0.820797 0.571220i \(-0.193530\pi\)
−0.905090 + 0.425221i \(0.860197\pi\)
\(920\) 17.0175 29.4752i 0.561050 0.971767i
\(921\) 33.9896 + 12.3712i 1.11999 + 0.407645i
\(922\) −8.49726 3.09275i −0.279842 0.101854i
\(923\) −28.0505 + 48.5850i −0.923295 + 1.59919i
\(924\) −1.14475 1.98276i −0.0376594 0.0652279i
\(925\) 2.17862 + 12.3556i 0.0716325 + 0.406248i
\(926\) −13.5747 11.3905i −0.446092 0.374316i
\(927\) 4.69510 3.93966i 0.154207 0.129395i
\(928\) −0.0388245 + 0.220185i −0.00127448 + 0.00722792i
\(929\) 40.2604 14.6536i 1.32090 0.480769i 0.417154 0.908836i \(-0.363028\pi\)
0.903747 + 0.428067i \(0.140805\pi\)
\(930\) 16.5140 0.541514
\(931\) 0 0
\(932\) −8.68176 −0.284381
\(933\) −4.66761 + 1.69887i −0.152811 + 0.0556185i
\(934\) −1.36795 + 7.75804i −0.0447607 + 0.253851i
\(935\) −3.04481 + 2.55490i −0.0995758 + 0.0835540i
\(936\) −5.06286 4.24824i −0.165485 0.138858i
\(937\) −0.638825 3.62296i −0.0208695 0.118357i 0.972593 0.232513i \(-0.0746948\pi\)
−0.993463 + 0.114156i \(0.963584\pi\)
\(938\) 0.0326898 + 0.0566205i 0.00106736 + 0.00184872i
\(939\) −19.5102 + 33.7926i −0.636690 + 1.10278i
\(940\) −7.63566 2.77915i −0.249048 0.0906459i
\(941\) −17.2711 6.28615i −0.563020 0.204923i 0.0448017 0.998996i \(-0.485734\pi\)
−0.607822 + 0.794073i \(0.707957\pi\)
\(942\) 10.5232 18.2267i 0.342865 0.593859i
\(943\) −36.2143 62.7250i −1.17930 2.04261i
\(944\) −0.609423 3.45621i −0.0198350 0.112490i
\(945\) 6.99882 + 5.87271i 0.227672 + 0.191039i
\(946\) 17.3954 14.5965i 0.565573 0.474572i
\(947\) 8.11962 46.0486i 0.263852 1.49638i −0.508432 0.861102i \(-0.669775\pi\)
0.772284 0.635277i \(-0.219114\pi\)
\(948\) −12.3118 + 4.48113i −0.399869 + 0.145540i
\(949\) 6.95697 0.225833
\(950\) 0 0
\(951\) 6.84162 0.221855
\(952\) 0.110969 0.0403893i 0.00359652 0.00130902i
\(953\) 4.35077 24.6744i 0.140935 0.799283i −0.829606 0.558349i \(-0.811435\pi\)
0.970541 0.240934i \(-0.0774538\pi\)
\(954\) −10.2907 + 8.63495i −0.333175 + 0.279567i
\(955\) 36.0401 + 30.2413i 1.16623 + 0.978585i
\(956\) 3.79854 + 21.5426i 0.122853 + 0.696737i
\(957\) −0.578452 1.00191i −0.0186987 0.0323871i
\(958\) 15.0899 26.1365i 0.487533 0.844432i
\(959\) 0.917807 + 0.334054i 0.0296375 + 0.0107872i
\(960\) −4.45940 1.62309i −0.143926 0.0523850i
\(961\) 9.44531 16.3598i 0.304687 0.527734i
\(962\) −3.54395 6.13831i −0.114262 0.197907i
\(963\) 0.744111 + 4.22006i 0.0239786 + 0.135990i
\(964\) −14.5267 12.1893i −0.467872 0.392591i
\(965\) 49.4818 41.5202i 1.59288 1.33658i
\(966\) 0.908586 5.15285i 0.0292333 0.165790i
\(967\) −6.67771 + 2.43049i −0.214741 + 0.0781592i −0.447151 0.894459i \(-0.647561\pi\)
0.232410 + 0.972618i \(0.425339\pi\)
\(968\) 5.23826 0.168364
\(969\) 0 0
\(970\) 15.0961 0.484707
\(971\) −57.0903 + 20.7792i −1.83212 + 0.666836i −0.839832 + 0.542846i \(0.817347\pi\)
−0.992284 + 0.123990i \(0.960431\pi\)
\(972\) 2.21471 12.5603i 0.0710369 0.402871i
\(973\) 5.78394 4.85330i 0.185424 0.155590i
\(974\) 27.4014 + 22.9925i 0.877996 + 0.736726i
\(975\) 9.44359 + 53.5573i 0.302437 + 1.71521i
\(976\) −2.03977 3.53299i −0.0652916 0.113088i
\(977\) 19.2706 33.3776i 0.616520 1.06784i −0.373595 0.927592i \(-0.621875\pi\)
0.990116 0.140253i \(-0.0447915\pi\)
\(978\) 16.6181 + 6.04851i 0.531390 + 0.193410i
\(979\) −22.5713 8.21527i −0.721381 0.262561i
\(980\) 12.5732 21.7775i 0.401638 0.695657i
\(981\) −4.58112 7.93474i −0.146264 0.253337i
\(982\) −3.17301 17.9950i −0.101255 0.574244i
\(983\) −5.74938 4.82430i −0.183377 0.153871i 0.546478 0.837473i \(-0.315968\pi\)
−0.729855 + 0.683602i \(0.760413\pi\)
\(984\) −7.73623 + 6.49146i −0.246622 + 0.206940i
\(985\) −15.7302 + 89.2105i −0.501207 + 2.84248i
\(986\) 0.0560737 0.0204091i 0.00178575 0.000649960i
\(987\) −1.24920 −0.0397624
\(988\) 0 0
\(989\) 51.8964 1.65021
\(990\) −18.9084 + 6.88210i −0.600949 + 0.218727i
\(991\) −3.71991 + 21.0967i −0.118167 + 0.670158i 0.866966 + 0.498367i \(0.166067\pi\)
−0.985133 + 0.171791i \(0.945044\pi\)
\(992\) 2.66572 2.23681i 0.0846368 0.0710187i
\(993\) −20.2123 16.9601i −0.641418 0.538214i
\(994\) −0.881207 4.99757i −0.0279502 0.158513i
\(995\) −30.4270 52.7012i −0.964602 1.67074i
\(996\) 2.11153 3.65727i 0.0669063 0.115885i
\(997\) 38.5279 + 14.0230i 1.22019 + 0.444113i 0.870227 0.492650i \(-0.163972\pi\)
0.349963 + 0.936763i \(0.386194\pi\)
\(998\) −16.6307 6.05307i −0.526434 0.191606i
\(999\) 4.04801 7.01136i 0.128073 0.221830i
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 722.2.e.r.423.3 24
19.2 odd 18 722.2.a.m.1.2 4
19.3 odd 18 722.2.c.n.653.3 8
19.4 even 9 inner 722.2.e.r.99.3 24
19.5 even 9 722.2.c.m.429.2 8
19.6 even 9 inner 722.2.e.r.389.3 24
19.7 even 3 inner 722.2.e.r.245.3 24
19.8 odd 6 722.2.e.s.415.3 24
19.9 even 9 inner 722.2.e.r.595.2 24
19.10 odd 18 722.2.e.s.595.3 24
19.11 even 3 inner 722.2.e.r.415.2 24
19.12 odd 6 722.2.e.s.245.2 24
19.13 odd 18 722.2.e.s.389.2 24
19.14 odd 18 722.2.c.n.429.3 8
19.15 odd 18 722.2.e.s.99.2 24
19.16 even 9 722.2.c.m.653.2 8
19.17 even 9 722.2.a.n.1.3 yes 4
19.18 odd 2 722.2.e.s.423.2 24
57.2 even 18 6498.2.a.ca.1.1 4
57.17 odd 18 6498.2.a.bx.1.1 4
76.55 odd 18 5776.2.a.bt.1.2 4
76.59 even 18 5776.2.a.bv.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
722.2.a.m.1.2 4 19.2 odd 18
722.2.a.n.1.3 yes 4 19.17 even 9
722.2.c.m.429.2 8 19.5 even 9
722.2.c.m.653.2 8 19.16 even 9
722.2.c.n.429.3 8 19.14 odd 18
722.2.c.n.653.3 8 19.3 odd 18
722.2.e.r.99.3 24 19.4 even 9 inner
722.2.e.r.245.3 24 19.7 even 3 inner
722.2.e.r.389.3 24 19.6 even 9 inner
722.2.e.r.415.2 24 19.11 even 3 inner
722.2.e.r.423.3 24 1.1 even 1 trivial
722.2.e.r.595.2 24 19.9 even 9 inner
722.2.e.s.99.2 24 19.15 odd 18
722.2.e.s.245.2 24 19.12 odd 6
722.2.e.s.389.2 24 19.13 odd 18
722.2.e.s.415.3 24 19.8 odd 6
722.2.e.s.423.2 24 19.18 odd 2
722.2.e.s.595.3 24 19.10 odd 18
5776.2.a.bt.1.2 4 76.55 odd 18
5776.2.a.bv.1.3 4 76.59 even 18
6498.2.a.bx.1.1 4 57.17 odd 18
6498.2.a.ca.1.1 4 57.2 even 18