# Properties

 Label 169.2.e.b.147.2 Level $169$ Weight $2$ Character 169.147 Analytic conductor $1.349$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(23,169)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$169 = 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 169.e (of order $$6$$, degree $$2$$, 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: $$1.34947179416$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{6})$$ Coefficient field: 12.0.17213603549184.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1$$ x^12 - 5*x^10 + 19*x^8 - 28*x^6 + 31*x^4 - 6*x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 147.2 Root $$1.56052 - 0.900969i$$ of defining polynomial Character $$\chi$$ $$=$$ 169.147 Dual form 169.2.e.b.23.2

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.694498 - 0.400969i) q^{2} +(1.12349 - 1.94594i) q^{3} +(-0.678448 - 1.17511i) q^{4} +0.246980i q^{5} +(-1.56052 + 0.900969i) q^{6} +(2.04113 - 1.17845i) q^{7} +2.69202i q^{8} +(-1.02446 - 1.77441i) q^{9} +O(q^{10})$$ $$q+(-0.694498 - 0.400969i) q^{2} +(1.12349 - 1.94594i) q^{3} +(-0.678448 - 1.17511i) q^{4} +0.246980i q^{5} +(-1.56052 + 0.900969i) q^{6} +(2.04113 - 1.17845i) q^{7} +2.69202i q^{8} +(-1.02446 - 1.77441i) q^{9} +(0.0990311 - 0.171527i) q^{10} +(-3.67799 - 2.12349i) q^{11} -3.04892 q^{12} -1.89008 q^{14} +(0.480608 + 0.277479i) q^{15} +(-0.277479 + 0.480608i) q^{16} +(1.07942 + 1.86960i) q^{17} +1.64310i q^{18} +(-0.0763367 + 0.0440730i) q^{19} +(0.290227 - 0.167563i) q^{20} -5.29590i q^{21} +(1.70291 + 2.94952i) q^{22} +(0.746980 - 1.29381i) q^{23} +(5.23852 + 3.02446i) q^{24} +4.93900 q^{25} +2.13706 q^{27} +(-2.76960 - 1.59903i) q^{28} +(-2.31551 + 4.01058i) q^{29} +(-0.222521 - 0.385418i) q^{30} -6.63102i q^{31} +(5.04814 - 2.91454i) q^{32} +(-8.26437 + 4.77144i) q^{33} -1.73125i q^{34} +(0.291053 + 0.504118i) q^{35} +(-1.39008 + 2.40770i) q^{36} +(4.92944 + 2.84601i) q^{37} +0.0706876 q^{38} -0.664874 q^{40} +(10.0388 + 5.79590i) q^{41} +(-2.12349 + 3.67799i) q^{42} +(-0.147948 - 0.256254i) q^{43} +5.76271i q^{44} +(0.438244 - 0.253020i) q^{45} +(-1.03755 + 0.599031i) q^{46} +7.35690i q^{47} +(0.623490 + 1.07992i) q^{48} +(-0.722521 + 1.25144i) q^{49} +(-3.43013 - 1.98039i) q^{50} +4.85086 q^{51} -10.3937 q^{53} +(-1.48419 - 0.856896i) q^{54} +(0.524459 - 0.908389i) q^{55} +(3.17241 + 5.49477i) q^{56} +0.198062i q^{57} +(3.21624 - 1.85690i) q^{58} +(5.87180 - 3.39008i) q^{59} -0.753020i q^{60} +(-1.73609 - 3.00700i) q^{61} +(-2.65883 + 4.60523i) q^{62} +(-4.18211 - 2.41454i) q^{63} -3.56465 q^{64} +7.65279 q^{66} +(-6.65102 - 3.83997i) q^{67} +(1.46466 - 2.53686i) q^{68} +(-1.67845 - 2.90716i) q^{69} -0.466812i q^{70} +(-7.50400 + 4.33244i) q^{71} +(4.77676 - 2.75786i) q^{72} -6.73556i q^{73} +(-2.28232 - 3.95310i) q^{74} +(5.54892 - 9.61101i) q^{75} +(0.103581 + 0.0598025i) q^{76} -10.0097 q^{77} +9.97046 q^{79} +(-0.118700 - 0.0685317i) q^{80} +(5.47434 - 9.48184i) q^{81} +(-4.64795 - 8.05048i) q^{82} +1.60925i q^{83} +(-6.22324 + 3.59299i) q^{84} +(-0.461754 + 0.266594i) q^{85} +0.237291i q^{86} +(5.20291 + 9.01170i) q^{87} +(5.71648 - 9.90123i) q^{88} +(-2.49823 - 1.44235i) q^{89} -0.405813 q^{90} -2.02715 q^{92} +(-12.9036 - 7.44989i) q^{93} +(2.94989 - 5.10935i) q^{94} +(-0.0108851 - 0.0188536i) q^{95} -13.0978i q^{96} +(-6.97896 + 4.02930i) q^{97} +(1.00358 - 0.579417i) q^{98} +8.70171i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + 4 q^{3} + 6 q^{9}+O(q^{10})$$ 12 * q + 4 * q^3 + 6 * q^9 $$12 q + 4 q^{3} + 6 q^{9} + 10 q^{10} - 20 q^{14} - 4 q^{16} - 4 q^{17} - 6 q^{22} - 10 q^{23} + 20 q^{25} + 4 q^{27} + 2 q^{29} - 2 q^{30} - 8 q^{35} - 14 q^{36} - 48 q^{38} - 12 q^{40} - 16 q^{42} + 26 q^{43} - 2 q^{48} - 8 q^{49} + 4 q^{51} + 4 q^{53} - 12 q^{55} - 8 q^{56} - 8 q^{61} + 2 q^{62} + 44 q^{64} + 20 q^{66} + 42 q^{68} - 12 q^{69} + 16 q^{74} + 30 q^{75} - 32 q^{77} - 20 q^{79} + 2 q^{81} - 28 q^{82} + 36 q^{87} + 30 q^{88} + 48 q^{90} - 10 q^{94} + 6 q^{95}+O(q^{100})$$ 12 * q + 4 * q^3 + 6 * q^9 + 10 * q^10 - 20 * q^14 - 4 * q^16 - 4 * q^17 - 6 * q^22 - 10 * q^23 + 20 * q^25 + 4 * q^27 + 2 * q^29 - 2 * q^30 - 8 * q^35 - 14 * q^36 - 48 * q^38 - 12 * q^40 - 16 * q^42 + 26 * q^43 - 2 * q^48 - 8 * q^49 + 4 * q^51 + 4 * q^53 - 12 * q^55 - 8 * q^56 - 8 * q^61 + 2 * q^62 + 44 * q^64 + 20 * q^66 + 42 * q^68 - 12 * q^69 + 16 * q^74 + 30 * q^75 - 32 * q^77 - 20 * q^79 + 2 * q^81 - 28 * q^82 + 36 * q^87 + 30 * q^88 + 48 * q^90 - 10 * q^94 + 6 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$$.

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.694498 0.400969i −0.491085 0.283528i 0.233940 0.972251i $$-0.424838\pi$$
−0.725024 + 0.688723i $$0.758171\pi$$
$$3$$ 1.12349 1.94594i 0.648647 1.12349i −0.334799 0.942290i $$-0.608668\pi$$
0.983446 0.181200i $$-0.0579982\pi$$
$$4$$ −0.678448 1.17511i −0.339224 0.587553i
$$5$$ 0.246980i 0.110453i 0.998474 + 0.0552263i $$0.0175880\pi$$
−0.998474 + 0.0552263i $$0.982412\pi$$
$$6$$ −1.56052 + 0.900969i −0.637081 + 0.367819i
$$7$$ 2.04113 1.17845i 0.771475 0.445411i −0.0619254 0.998081i $$-0.519724\pi$$
0.833401 + 0.552669i $$0.186391\pi$$
$$8$$ 2.69202i 0.951773i
$$9$$ −1.02446 1.77441i −0.341486 0.591471i
$$10$$ 0.0990311 0.171527i 0.0313164 0.0542416i
$$11$$ −3.67799 2.12349i −1.10896 0.640256i −0.170397 0.985375i $$-0.554505\pi$$
−0.938559 + 0.345119i $$0.887839\pi$$
$$12$$ −3.04892 −0.880147
$$13$$ 0 0
$$14$$ −1.89008 −0.505146
$$15$$ 0.480608 + 0.277479i 0.124092 + 0.0716448i
$$16$$ −0.277479 + 0.480608i −0.0693698 + 0.120152i
$$17$$ 1.07942 + 1.86960i 0.261797 + 0.453446i 0.966720 0.255839i $$-0.0823516\pi$$
−0.704922 + 0.709284i $$0.749018\pi$$
$$18$$ 1.64310i 0.387283i
$$19$$ −0.0763367 + 0.0440730i −0.0175128 + 0.0101110i −0.508731 0.860926i $$-0.669885\pi$$
0.491218 + 0.871037i $$0.336552\pi$$
$$20$$ 0.290227 0.167563i 0.0648968 0.0374682i
$$21$$ 5.29590i 1.15566i
$$22$$ 1.70291 + 2.94952i 0.363061 + 0.628840i
$$23$$ 0.746980 1.29381i 0.155756 0.269777i −0.777578 0.628786i $$-0.783552\pi$$
0.933334 + 0.359009i $$0.116885\pi$$
$$24$$ 5.23852 + 3.02446i 1.06931 + 0.617365i
$$25$$ 4.93900 0.987800
$$26$$ 0 0
$$27$$ 2.13706 0.411278
$$28$$ −2.76960 1.59903i −0.523406 0.302188i
$$29$$ −2.31551 + 4.01058i −0.429980 + 0.744747i −0.996871 0.0790460i $$-0.974813\pi$$
0.566891 + 0.823793i $$0.308146\pi$$
$$30$$ −0.222521 0.385418i −0.0406266 0.0703673i
$$31$$ 6.63102i 1.19097i −0.803368 0.595483i $$-0.796961\pi$$
0.803368 0.595483i $$-0.203039\pi$$
$$32$$ 5.04814 2.91454i 0.892393 0.515223i
$$33$$ −8.26437 + 4.77144i −1.43864 + 0.830601i
$$34$$ 1.73125i 0.296907i
$$35$$ 0.291053 + 0.504118i 0.0491969 + 0.0852115i
$$36$$ −1.39008 + 2.40770i −0.231681 + 0.401283i
$$37$$ 4.92944 + 2.84601i 0.810394 + 0.467881i 0.847093 0.531445i $$-0.178351\pi$$
−0.0366986 + 0.999326i $$0.511684\pi$$
$$38$$ 0.0706876 0.0114670
$$39$$ 0 0
$$40$$ −0.664874 −0.105126
$$41$$ 10.0388 + 5.79590i 1.56780 + 0.905167i 0.996426 + 0.0844742i $$0.0269210\pi$$
0.571370 + 0.820693i $$0.306412\pi$$
$$42$$ −2.12349 + 3.67799i −0.327662 + 0.567527i
$$43$$ −0.147948 0.256254i −0.0225619 0.0390784i 0.854524 0.519412i $$-0.173849\pi$$
−0.877086 + 0.480334i $$0.840516\pi$$
$$44$$ 5.76271i 0.868761i
$$45$$ 0.438244 0.253020i 0.0653296 0.0377181i
$$46$$ −1.03755 + 0.599031i −0.152979 + 0.0883223i
$$47$$ 7.35690i 1.07311i 0.843864 + 0.536557i $$0.180275\pi$$
−0.843864 + 0.536557i $$0.819725\pi$$
$$48$$ 0.623490 + 1.07992i 0.0899930 + 0.155872i
$$49$$ −0.722521 + 1.25144i −0.103217 + 0.178778i
$$50$$ −3.43013 1.98039i −0.485093 0.280069i
$$51$$ 4.85086 0.679256
$$52$$ 0 0
$$53$$ −10.3937 −1.42769 −0.713844 0.700304i $$-0.753048\pi$$
−0.713844 + 0.700304i $$0.753048\pi$$
$$54$$ −1.48419 0.856896i −0.201972 0.116609i
$$55$$ 0.524459 0.908389i 0.0707180 0.122487i
$$56$$ 3.17241 + 5.49477i 0.423931 + 0.734270i
$$57$$ 0.198062i 0.0262340i
$$58$$ 3.21624 1.85690i 0.422313 0.243822i
$$59$$ 5.87180 3.39008i 0.764443 0.441351i −0.0664458 0.997790i $$-0.521166\pi$$
0.830889 + 0.556439i $$0.187833\pi$$
$$60$$ 0.753020i 0.0972145i
$$61$$ −1.73609 3.00700i −0.222284 0.385007i 0.733217 0.679995i $$-0.238018\pi$$
−0.955501 + 0.294987i $$0.904685\pi$$
$$62$$ −2.65883 + 4.60523i −0.337672 + 0.584865i
$$63$$ −4.18211 2.41454i −0.526896 0.304204i
$$64$$ −3.56465 −0.445581
$$65$$ 0 0
$$66$$ 7.65279 0.941994
$$67$$ −6.65102 3.83997i −0.812552 0.469127i 0.0352895 0.999377i $$-0.488765\pi$$
−0.847841 + 0.530250i $$0.822098\pi$$
$$68$$ 1.46466 2.53686i 0.177616 0.307639i
$$69$$ −1.67845 2.90716i −0.202061 0.349981i
$$70$$ 0.466812i 0.0557947i
$$71$$ −7.50400 + 4.33244i −0.890561 + 0.514166i −0.874126 0.485699i $$-0.838565\pi$$
−0.0164351 + 0.999865i $$0.505232\pi$$
$$72$$ 4.77676 2.75786i 0.562947 0.325017i
$$73$$ 6.73556i 0.788338i −0.919038 0.394169i $$-0.871032\pi$$
0.919038 0.394169i $$-0.128968\pi$$
$$74$$ −2.28232 3.95310i −0.265315 0.459539i
$$75$$ 5.54892 9.61101i 0.640734 1.10978i
$$76$$ 0.103581 + 0.0598025i 0.0118815 + 0.00685981i
$$77$$ −10.0097 −1.14071
$$78$$ 0 0
$$79$$ 9.97046 1.12176 0.560882 0.827896i $$-0.310462\pi$$
0.560882 + 0.827896i $$0.310462\pi$$
$$80$$ −0.118700 0.0685317i −0.0132711 0.00766207i
$$81$$ 5.47434 9.48184i 0.608261 1.05354i
$$82$$ −4.64795 8.05048i −0.513280 0.889027i
$$83$$ 1.60925i 0.176638i 0.996092 + 0.0883192i $$0.0281495\pi$$
−0.996092 + 0.0883192i $$0.971850\pi$$
$$84$$ −6.22324 + 3.59299i −0.679011 + 0.392027i
$$85$$ −0.461754 + 0.266594i −0.0500843 + 0.0289162i
$$86$$ 0.237291i 0.0255877i
$$87$$ 5.20291 + 9.01170i 0.557810 + 0.966156i
$$88$$ 5.71648 9.90123i 0.609379 1.05548i
$$89$$ −2.49823 1.44235i −0.264812 0.152889i 0.361716 0.932288i $$-0.382191\pi$$
−0.626528 + 0.779399i $$0.715524\pi$$
$$90$$ −0.405813 −0.0427765
$$91$$ 0 0
$$92$$ −2.02715 −0.211345
$$93$$ −12.9036 7.44989i −1.33804 0.772517i
$$94$$ 2.94989 5.10935i 0.304258 0.526990i
$$95$$ −0.0108851 0.0188536i −0.00111679 0.00193434i
$$96$$ 13.0978i 1.33679i
$$97$$ −6.97896 + 4.02930i −0.708606 + 0.409114i −0.810545 0.585677i $$-0.800829\pi$$
0.101939 + 0.994791i $$0.467495\pi$$
$$98$$ 1.00358 0.579417i 0.101377 0.0585299i
$$99$$ 8.70171i 0.874555i
$$100$$ −3.35086 5.80385i −0.335086 0.580385i
$$101$$ −6.67725 + 11.5653i −0.664411 + 1.15079i 0.315033 + 0.949081i $$0.397984\pi$$
−0.979445 + 0.201714i $$0.935349\pi$$
$$102$$ −3.36891 1.94504i −0.333572 0.192588i
$$103$$ −1.36227 −0.134229 −0.0671144 0.997745i $$-0.521379\pi$$
−0.0671144 + 0.997745i $$0.521379\pi$$
$$104$$ 0 0
$$105$$ 1.30798 0.127646
$$106$$ 7.21843 + 4.16756i 0.701116 + 0.404789i
$$107$$ −1.63437 + 2.83082i −0.158001 + 0.273666i −0.934148 0.356887i $$-0.883838\pi$$
0.776147 + 0.630552i $$0.217172\pi$$
$$108$$ −1.44989 2.51128i −0.139515 0.241648i
$$109$$ 15.7017i 1.50395i 0.659191 + 0.751976i $$0.270899\pi$$
−0.659191 + 0.751976i $$0.729101\pi$$
$$110$$ −0.728471 + 0.420583i −0.0694570 + 0.0401010i
$$111$$ 11.0763 6.39493i 1.05132 0.606980i
$$112$$ 1.30798i 0.123592i
$$113$$ −6.02446 10.4347i −0.566733 0.981611i −0.996886 0.0788549i $$-0.974874\pi$$
0.430153 0.902756i $$-0.358460\pi$$
$$114$$ 0.0794168 0.137554i 0.00743806 0.0128831i
$$115$$ 0.319544 + 0.184489i 0.0297976 + 0.0172037i
$$116$$ 6.28382 0.583438
$$117$$ 0 0
$$118$$ −5.43727 −0.500541
$$119$$ 4.40646 + 2.54407i 0.403940 + 0.233215i
$$120$$ −0.746980 + 1.29381i −0.0681896 + 0.118108i
$$121$$ 3.51842 + 6.09408i 0.319856 + 0.554007i
$$122$$ 2.78448i 0.252095i
$$123$$ 22.5570 13.0233i 2.03389 1.17427i
$$124$$ −7.79216 + 4.49880i −0.699756 + 0.404004i
$$125$$ 2.45473i 0.219558i
$$126$$ 1.93631 + 3.35379i 0.172500 + 0.298780i
$$127$$ −4.90366 + 8.49338i −0.435129 + 0.753666i −0.997306 0.0733510i $$-0.976631\pi$$
0.562177 + 0.827017i $$0.309964\pi$$
$$128$$ −7.62063 4.39977i −0.673575 0.388889i
$$129$$ −0.664874 −0.0585389
$$130$$ 0 0
$$131$$ −6.57673 −0.574611 −0.287306 0.957839i $$-0.592760\pi$$
−0.287306 + 0.957839i $$0.592760\pi$$
$$132$$ 11.2139 + 6.47434i 0.976044 + 0.563519i
$$133$$ −0.103875 + 0.179918i −0.00900715 + 0.0156008i
$$134$$ 3.07942 + 5.33371i 0.266021 + 0.460762i
$$135$$ 0.527811i 0.0454267i
$$136$$ −5.03302 + 2.90581i −0.431578 + 0.249171i
$$137$$ −5.38653 + 3.10992i −0.460203 + 0.265698i −0.712129 0.702048i $$-0.752269\pi$$
0.251927 + 0.967746i $$0.418936\pi$$
$$138$$ 2.69202i 0.229160i
$$139$$ 7.35354 + 12.7367i 0.623719 + 1.08031i 0.988787 + 0.149333i $$0.0477125\pi$$
−0.365068 + 0.930981i $$0.618954\pi$$
$$140$$ 0.394928 0.684035i 0.0333775 0.0578116i
$$141$$ 14.3161 + 8.26540i 1.20563 + 0.696072i
$$142$$ 6.94869 0.583121
$$143$$ 0 0
$$144$$ 1.13706 0.0947553
$$145$$ −0.990532 0.571884i −0.0822592 0.0474924i
$$146$$ −2.70075 + 4.67784i −0.223516 + 0.387141i
$$147$$ 1.62349 + 2.81197i 0.133903 + 0.231927i
$$148$$ 7.72348i 0.634866i
$$149$$ 3.75433 2.16756i 0.307567 0.177574i −0.338270 0.941049i $$-0.609842\pi$$
0.645837 + 0.763475i $$0.276509\pi$$
$$150$$ −7.70743 + 4.44989i −0.629309 + 0.363332i
$$151$$ 3.94438i 0.320989i −0.987037 0.160494i $$-0.948691\pi$$
0.987037 0.160494i $$-0.0513089\pi$$
$$152$$ −0.118645 0.205500i −0.00962342 0.0166682i
$$153$$ 2.21164 3.83067i 0.178800 0.309691i
$$154$$ 6.95171 + 4.01357i 0.560185 + 0.323423i
$$155$$ 1.63773 0.131545
$$156$$ 0 0
$$157$$ 4.45473 0.355526 0.177763 0.984073i $$-0.443114\pi$$
0.177763 + 0.984073i $$0.443114\pi$$
$$158$$ −6.92447 3.99784i −0.550881 0.318051i
$$159$$ −11.6773 + 20.2256i −0.926066 + 1.60399i
$$160$$ 0.719833 + 1.24679i 0.0569078 + 0.0985671i
$$161$$ 3.52111i 0.277502i
$$162$$ −7.60385 + 4.39008i −0.597415 + 0.344918i
$$163$$ −13.9940 + 8.07942i −1.09609 + 0.632829i −0.935192 0.354142i $$-0.884773\pi$$
−0.160900 + 0.986971i $$0.551440\pi$$
$$164$$ 15.7289i 1.22822i
$$165$$ −1.17845 2.04113i −0.0917420 0.158902i
$$166$$ 0.645260 1.11762i 0.0500819 0.0867444i
$$167$$ 13.9579 + 8.05861i 1.08010 + 0.623594i 0.930922 0.365217i $$-0.119005\pi$$
0.149174 + 0.988811i $$0.452339\pi$$
$$168$$ 14.2567 1.09993
$$169$$ 0 0
$$170$$ 0.427583 0.0327942
$$171$$ 0.156408 + 0.0903019i 0.0119608 + 0.00690556i
$$172$$ −0.200751 + 0.347710i −0.0153071 + 0.0265127i
$$173$$ −10.7681 18.6509i −0.818682 1.41800i −0.906653 0.421876i $$-0.861372\pi$$
0.0879709 0.996123i $$-0.471962\pi$$
$$174$$ 8.34481i 0.632619i
$$175$$ 10.0812 5.82036i 0.762063 0.439978i
$$176$$ 2.04113 1.17845i 0.153856 0.0888289i
$$177$$ 15.2349i 1.14513i
$$178$$ 1.15668 + 2.00342i 0.0866967 + 0.150163i
$$179$$ 5.71648 9.90123i 0.427270 0.740053i −0.569360 0.822089i $$-0.692809\pi$$
0.996629 + 0.0820356i $$0.0261421\pi$$
$$180$$ −0.594652 0.343322i −0.0443227 0.0255897i
$$181$$ −20.9705 −1.55872 −0.779361 0.626575i $$-0.784456\pi$$
−0.779361 + 0.626575i $$0.784456\pi$$
$$182$$ 0 0
$$183$$ −7.80194 −0.576736
$$184$$ 3.48296 + 2.01089i 0.256767 + 0.148244i
$$185$$ −0.702907 + 1.21747i −0.0516787 + 0.0895102i
$$186$$ 5.97434 + 10.3479i 0.438060 + 0.758743i
$$187$$ 9.16852i 0.670469i
$$188$$ 8.64513 4.99127i 0.630511 0.364026i
$$189$$ 4.36203 2.51842i 0.317291 0.183188i
$$190$$ 0.0174584i 0.00126657i
$$191$$ 7.21864 + 12.5030i 0.522322 + 0.904689i 0.999663 + 0.0259702i $$0.00826749\pi$$
−0.477341 + 0.878718i $$0.658399\pi$$
$$192$$ −4.00484 + 6.93659i −0.289025 + 0.500606i
$$193$$ −11.7604 6.78986i −0.846530 0.488745i 0.0129483 0.999916i $$-0.495878\pi$$
−0.859479 + 0.511172i $$0.829212\pi$$
$$194$$ 6.46250 0.463980
$$195$$ 0 0
$$196$$ 1.96077 0.140055
$$197$$ 0.485264 + 0.280167i 0.0345736 + 0.0199611i 0.517187 0.855872i $$-0.326979\pi$$
−0.482614 + 0.875833i $$0.660312\pi$$
$$198$$ 3.48911 6.04332i 0.247961 0.429480i
$$199$$ 5.74578 + 9.95199i 0.407308 + 0.705478i 0.994587 0.103907i $$-0.0331343\pi$$
−0.587279 + 0.809384i $$0.699801\pi$$
$$200$$ 13.2959i 0.940162i
$$201$$ −14.9447 + 8.62833i −1.05412 + 0.608596i
$$202$$ 9.27468 5.35474i 0.652564 0.376758i
$$203$$ 10.9148i 0.766071i
$$204$$ −3.29105 5.70027i −0.230420 0.399099i
$$205$$ −1.43147 + 2.47938i −0.0999781 + 0.173167i
$$206$$ 0.946096 + 0.546229i 0.0659177 + 0.0380576i
$$207$$ −3.06100 −0.212754
$$208$$ 0 0
$$209$$ 0.374354 0.0258946
$$210$$ −0.908389 0.524459i −0.0626848 0.0361911i
$$211$$ −4.39224 + 7.60758i −0.302374 + 0.523728i −0.976673 0.214731i $$-0.931113\pi$$
0.674299 + 0.738458i $$0.264446\pi$$
$$212$$ 7.05161 + 12.2137i 0.484306 + 0.838843i
$$213$$ 19.4698i 1.33405i
$$214$$ 2.27014 1.31067i 0.155184 0.0895953i
$$215$$ 0.0632896 0.0365403i 0.00431631 0.00249202i
$$216$$ 5.75302i 0.391443i
$$217$$ −7.81431 13.5348i −0.530470 0.918801i
$$218$$ 6.29590 10.9048i 0.426412 0.738567i
$$219$$ −13.1070 7.56734i −0.885690 0.511353i
$$220$$ −1.42327 −0.0959570
$$221$$ 0 0
$$222$$ −10.2567 −0.688383
$$223$$ 1.95640 + 1.12953i 0.131011 + 0.0756390i 0.564073 0.825725i $$-0.309234\pi$$
−0.433062 + 0.901364i $$0.642567\pi$$
$$224$$ 6.86927 11.8979i 0.458973 0.794964i
$$225$$ −5.05980 8.76383i −0.337320 0.584256i
$$226$$ 9.66248i 0.642739i
$$227$$ −6.03286 + 3.48307i −0.400415 + 0.231180i −0.686663 0.726976i $$-0.740925\pi$$
0.286248 + 0.958156i $$0.407592\pi$$
$$228$$ 0.232744 0.134375i 0.0154139 0.00889920i
$$229$$ 24.1739i 1.59746i 0.601692 + 0.798728i $$0.294493\pi$$
−0.601692 + 0.798728i $$0.705507\pi$$
$$230$$ −0.147948 0.256254i −0.00975543 0.0168969i
$$231$$ −11.2458 + 19.4783i −0.739918 + 1.28158i
$$232$$ −10.7966 6.23341i −0.708830 0.409243i
$$233$$ 3.06100 0.200533 0.100266 0.994961i $$-0.468031\pi$$
0.100266 + 0.994961i $$0.468031\pi$$
$$234$$ 0 0
$$235$$ −1.81700 −0.118528
$$236$$ −7.96742 4.59999i −0.518635 0.299434i
$$237$$ 11.2017 19.4019i 0.727629 1.26029i
$$238$$ −2.04019 3.53371i −0.132246 0.229056i
$$239$$ 25.1468i 1.62661i −0.581839 0.813304i $$-0.697667\pi$$
0.581839 0.813304i $$-0.302333\pi$$
$$240$$ −0.266717 + 0.153989i −0.0172165 + 0.00993996i
$$241$$ 17.5512 10.1332i 1.13057 0.652735i 0.186492 0.982456i $$-0.440288\pi$$
0.944078 + 0.329721i $$0.106955\pi$$
$$242$$ 5.64310i 0.362752i
$$243$$ −9.09515 15.7533i −0.583454 1.01057i
$$244$$ −2.35570 + 4.08019i −0.150808 + 0.261207i
$$245$$ −0.309081 0.178448i −0.0197465 0.0114006i
$$246$$ −20.8877 −1.33175
$$247$$ 0 0
$$248$$ 17.8509 1.13353
$$249$$ 3.13151 + 1.80798i 0.198451 + 0.114576i
$$250$$ 0.984271 1.70481i 0.0622507 0.107821i
$$251$$ −11.8605 20.5431i −0.748631 1.29667i −0.948479 0.316840i $$-0.897378\pi$$
0.199848 0.979827i $$-0.435955\pi$$
$$252$$ 6.55257i 0.412773i
$$253$$ −5.49477 + 3.17241i −0.345453 + 0.199448i
$$254$$ 6.81116 3.93243i 0.427370 0.246742i
$$255$$ 1.19806i 0.0750256i
$$256$$ 7.09299 + 12.2854i 0.443312 + 0.767839i
$$257$$ 7.11207 12.3185i 0.443639 0.768405i −0.554317 0.832305i $$-0.687021\pi$$
0.997956 + 0.0639003i $$0.0203540\pi$$
$$258$$ 0.461754 + 0.266594i 0.0287476 + 0.0165974i
$$259$$ 13.4155 0.833599
$$260$$ 0 0
$$261$$ 9.48858 0.587329
$$262$$ 4.56753 + 2.63706i 0.282183 + 0.162918i
$$263$$ 8.54772 14.8051i 0.527075 0.912921i −0.472427 0.881370i $$-0.656622\pi$$
0.999502 0.0315510i $$-0.0100447\pi$$
$$264$$ −12.8448 22.2479i −0.790544 1.36926i
$$265$$ 2.56704i 0.157692i
$$266$$ 0.144283 0.0833017i 0.00884654 0.00510755i
$$267$$ −5.61347 + 3.24094i −0.343539 + 0.198342i
$$268$$ 10.4209i 0.636556i
$$269$$ 3.23341 + 5.60042i 0.197144 + 0.341464i 0.947601 0.319455i $$-0.103500\pi$$
−0.750457 + 0.660919i $$0.770167\pi$$
$$270$$ 0.211636 0.366564i 0.0128797 0.0223084i
$$271$$ 5.58415 + 3.22401i 0.339213 + 0.195845i 0.659924 0.751332i $$-0.270588\pi$$
−0.320711 + 0.947177i $$0.603922\pi$$
$$272$$ −1.19806 −0.0726432
$$273$$ 0 0
$$274$$ 4.98792 0.301331
$$275$$ −18.1656 10.4879i −1.09543 0.632445i
$$276$$ −2.27748 + 3.94471i −0.137088 + 0.237444i
$$277$$ 6.73005 + 11.6568i 0.404370 + 0.700389i 0.994248 0.107103i $$-0.0341576\pi$$
−0.589878 + 0.807492i $$0.700824\pi$$
$$278$$ 11.7942i 0.707367i
$$279$$ −11.7662 + 6.79321i −0.704423 + 0.406699i
$$280$$ −1.35710 + 0.783520i −0.0811020 + 0.0468243i
$$281$$ 5.03684i 0.300472i −0.988650 0.150236i $$-0.951997\pi$$
0.988650 0.150236i $$-0.0480034\pi$$
$$282$$ −6.62833 11.4806i −0.394712 0.683660i
$$283$$ 11.0640 19.1634i 0.657686 1.13914i −0.323528 0.946219i $$-0.604869\pi$$
0.981213 0.192926i $$-0.0617977\pi$$
$$284$$ 10.1821 + 5.87867i 0.604199 + 0.348835i
$$285$$ −0.0489173 −0.00289761
$$286$$ 0 0
$$287$$ 27.3207 1.61269
$$288$$ −10.3432 5.97166i −0.609480 0.351883i
$$289$$ 6.16972 10.6863i 0.362925 0.628604i
$$290$$ 0.458615 + 0.794345i 0.0269308 + 0.0466456i
$$291$$ 18.1075i 1.06148i
$$292$$ −7.91500 + 4.56973i −0.463190 + 0.267423i
$$293$$ −12.9439 + 7.47315i −0.756189 + 0.436586i −0.827926 0.560838i $$-0.810479\pi$$
0.0717367 + 0.997424i $$0.477146\pi$$
$$294$$ 2.60388i 0.151861i
$$295$$ 0.837282 + 1.45021i 0.0487484 + 0.0844347i
$$296$$ −7.66152 + 13.2701i −0.445317 + 0.771312i
$$297$$ −7.86010 4.53803i −0.456089 0.263323i
$$298$$ −3.47650 −0.201388
$$299$$ 0 0
$$300$$ −15.0586 −0.869409
$$301$$ −0.603965 0.348699i −0.0348119 0.0200987i
$$302$$ −1.58157 + 2.73936i −0.0910093 + 0.157633i
$$303$$ 15.0036 + 25.9871i 0.861937 + 1.49292i
$$304$$ 0.0489173i 0.00280560i
$$305$$ 0.742669 0.428780i 0.0425251 0.0245519i
$$306$$ −3.07196 + 1.77359i −0.175612 + 0.101390i
$$307$$ 19.1293i 1.09177i −0.837861 0.545883i $$-0.816194\pi$$
0.837861 0.545883i $$-0.183806\pi$$
$$308$$ 6.79105 + 11.7624i 0.386956 + 0.670228i
$$309$$ −1.53050 + 2.65090i −0.0870671 + 0.150805i
$$310$$ −1.13740 0.656678i −0.0645999 0.0372968i
$$311$$ 0.269815 0.0152998 0.00764990 0.999971i $$-0.497565\pi$$
0.00764990 + 0.999971i $$0.497565\pi$$
$$312$$ 0 0
$$313$$ −23.3937 −1.32229 −0.661146 0.750257i $$-0.729930\pi$$
−0.661146 + 0.750257i $$0.729930\pi$$
$$314$$ −3.09380 1.78621i −0.174593 0.100802i
$$315$$ 0.596343 1.03290i 0.0336001 0.0581971i
$$316$$ −6.76444 11.7164i −0.380529 0.659096i
$$317$$ 13.9952i 0.786050i −0.919528 0.393025i $$-0.871429\pi$$
0.919528 0.393025i $$-0.128571\pi$$
$$318$$ 16.2197 9.36443i 0.909554 0.525131i
$$319$$ 17.0329 9.83393i 0.953657 0.550594i
$$320$$ 0.880395i 0.0492156i
$$321$$ 3.67241 + 6.36080i 0.204974 + 0.355025i
$$322$$ −1.41185 + 2.44540i −0.0786795 + 0.136277i
$$323$$ −0.164798 0.0951463i −0.00916962 0.00529408i
$$324$$ −14.8562 −0.825346
$$325$$ 0 0
$$326$$ 12.9584 0.717698
$$327$$ 30.5546 + 17.6407i 1.68967 + 0.975534i
$$328$$ −15.6027 + 27.0246i −0.861514 + 1.49219i
$$329$$ 8.66972 + 15.0164i 0.477977 + 0.827881i
$$330$$ 1.89008i 0.104046i
$$331$$ 15.4337 8.91066i 0.848314 0.489774i −0.0117680 0.999931i $$-0.503746\pi$$
0.860081 + 0.510157i $$0.170413\pi$$
$$332$$ 1.89104 1.09179i 0.103784 0.0599200i
$$333$$ 11.6625i 0.639100i
$$334$$ −6.46250 11.1934i −0.353612 0.612474i
$$335$$ 0.948394 1.64267i 0.0518163 0.0897485i
$$336$$ 2.54525 + 1.46950i 0.138855 + 0.0801678i
$$337$$ 27.8485 1.51700 0.758501 0.651672i $$-0.225932\pi$$
0.758501 + 0.651672i $$0.225932\pi$$
$$338$$ 0 0
$$339$$ −27.0737 −1.47044
$$340$$ 0.626552 + 0.361740i 0.0339796 + 0.0196181i
$$341$$ −14.0809 + 24.3888i −0.762524 + 1.32073i
$$342$$ −0.0724165 0.125429i −0.00391584 0.00678243i
$$343$$ 19.9041i 1.07472i
$$344$$ 0.689842 0.398280i 0.0371938 0.0214738i
$$345$$ 0.718009 0.414542i 0.0386563 0.0223182i
$$346$$ 17.2707i 0.928477i
$$347$$ −0.751824 1.30220i −0.0403600 0.0699056i 0.845140 0.534545i $$-0.179517\pi$$
−0.885500 + 0.464640i $$0.846184\pi$$
$$348$$ 7.05980 12.2279i 0.378445 0.655486i
$$349$$ −12.2854 7.09299i −0.657623 0.379679i 0.133747 0.991015i $$-0.457299\pi$$
−0.791371 + 0.611336i $$0.790632\pi$$
$$350$$ −9.33513 −0.498983
$$351$$ 0 0
$$352$$ −24.7560 −1.31950
$$353$$ 6.20812 + 3.58426i 0.330425 + 0.190771i 0.656030 0.754735i $$-0.272235\pi$$
−0.325605 + 0.945506i $$0.605568\pi$$
$$354$$ −6.10872 + 10.5806i −0.324675 + 0.562353i
$$355$$ −1.07002 1.85334i −0.0567910 0.0983648i
$$356$$ 3.91425i 0.207455i
$$357$$ 9.90123 5.71648i 0.524029 0.302548i
$$358$$ −7.94017 + 4.58426i −0.419651 + 0.242286i
$$359$$ 19.8853i 1.04951i −0.851255 0.524753i $$-0.824158\pi$$
0.851255 0.524753i $$-0.175842\pi$$
$$360$$ 0.681136 + 1.17976i 0.0358990 + 0.0621790i
$$361$$ −9.49612 + 16.4478i −0.499796 + 0.865671i
$$362$$ 14.5640 + 8.40850i 0.765464 + 0.441941i
$$363$$ 15.8116 0.829895
$$364$$ 0 0
$$365$$ 1.66355 0.0870740
$$366$$ 5.41843 + 3.12833i 0.283226 + 0.163521i
$$367$$ −0.541917 + 0.938628i −0.0282878 + 0.0489960i −0.879823 0.475302i $$-0.842339\pi$$
0.851535 + 0.524298i $$0.175672\pi$$
$$368$$ 0.414542 + 0.718009i 0.0216095 + 0.0374288i
$$369$$ 23.7506i 1.23641i
$$370$$ 0.976335 0.563687i 0.0507572 0.0293047i
$$371$$ −21.2150 + 12.2485i −1.10143 + 0.635909i
$$372$$ 20.2174i 1.04823i
$$373$$ 3.06518 + 5.30905i 0.158709 + 0.274892i 0.934403 0.356217i $$-0.115934\pi$$
−0.775694 + 0.631109i $$0.782600\pi$$
$$374$$ −3.67629 + 6.36752i −0.190097 + 0.329257i
$$375$$ 4.77676 + 2.75786i 0.246671 + 0.142416i
$$376$$ −19.8049 −1.02136
$$377$$ 0 0
$$378$$ −4.03923 −0.207756
$$379$$ 2.08608 + 1.20440i 0.107155 + 0.0618658i 0.552620 0.833434i $$-0.313628\pi$$
−0.445465 + 0.895299i $$0.646962\pi$$
$$380$$ −0.0147700 + 0.0255824i −0.000757685 + 0.00131235i
$$381$$ 11.0184 + 19.0845i 0.564491 + 0.977726i
$$382$$ 11.5778i 0.592371i
$$383$$ −26.3197 + 15.1957i −1.34487 + 0.776462i −0.987518 0.157506i $$-0.949655\pi$$
−0.357354 + 0.933969i $$0.616321\pi$$
$$384$$ −17.1234 + 9.88620i −0.873825 + 0.504503i
$$385$$ 2.47219i 0.125994i
$$386$$ 5.44504 + 9.43109i 0.277145 + 0.480030i
$$387$$ −0.303134 + 0.525044i −0.0154092 + 0.0266895i
$$388$$ 9.46972 + 5.46734i 0.480752 + 0.277562i
$$389$$ 15.9409 0.808237 0.404118 0.914707i $$-0.367578\pi$$
0.404118 + 0.914707i $$0.367578\pi$$
$$390$$ 0 0
$$391$$ 3.22521 0.163106
$$392$$ −3.36891 1.94504i −0.170156 0.0982394i
$$393$$ −7.38889 + 12.7979i −0.372720 + 0.645570i
$$394$$ −0.224677 0.389152i −0.0113191 0.0196052i
$$395$$ 2.46250i 0.123902i
$$396$$ 10.2254 5.90366i 0.513847 0.296670i
$$397$$ −14.6487 + 8.45742i −0.735196 + 0.424466i −0.820320 0.571905i $$-0.806205\pi$$
0.0851239 + 0.996370i $$0.472871\pi$$
$$398$$ 9.21552i 0.461932i
$$399$$ 0.233406 + 0.404271i 0.0116849 + 0.0202389i
$$400$$ −1.37047 + 2.37372i −0.0685235 + 0.118686i
$$401$$ 23.0904 + 13.3312i 1.15308 + 0.665730i 0.949636 0.313356i $$-0.101453\pi$$
0.203443 + 0.979087i $$0.434787\pi$$
$$402$$ 13.8388 0.690215
$$403$$ 0 0
$$404$$ 18.1207 0.901537
$$405$$ 2.34182 + 1.35205i 0.116366 + 0.0671840i
$$406$$ 4.37651 7.58034i 0.217203 0.376206i
$$407$$ −12.0869 20.9352i −0.599128 1.03772i
$$408$$ 13.0586i 0.646497i
$$409$$ 24.6959 14.2582i 1.22113 0.705021i 0.255972 0.966684i $$-0.417604\pi$$
0.965159 + 0.261663i $$0.0842710\pi$$
$$410$$ 1.98831 1.14795i 0.0981954 0.0566931i
$$411$$ 13.9758i 0.689377i
$$412$$ 0.924231 + 1.60082i 0.0455336 + 0.0788665i
$$413$$ 7.99007 13.8392i 0.393166 0.680983i
$$414$$ 2.12586 + 1.22737i 0.104480 + 0.0603217i
$$415$$ −0.397452 −0.0195102
$$416$$ 0 0
$$417$$ 33.0465 1.61830
$$418$$ −0.259988 0.150104i −0.0127165 0.00734185i
$$419$$ 14.8046 25.6424i 0.723253 1.25271i −0.236436 0.971647i $$-0.575979\pi$$
0.959689 0.281064i $$-0.0906874\pi$$
$$420$$ −0.887395 1.53701i −0.0433005 0.0749986i
$$421$$ 11.6606i 0.568301i −0.958780 0.284151i $$-0.908288\pi$$
0.958780 0.284151i $$-0.0917115\pi$$
$$422$$ 6.10081 3.52230i 0.296983 0.171463i
$$423$$ 13.0542 7.53684i 0.634716 0.366453i
$$424$$ 27.9801i 1.35884i
$$425$$ 5.33124 + 9.23398i 0.258603 + 0.447914i
$$426$$ 7.80678 13.5217i 0.378240 0.655131i
$$427$$ −7.08719 4.09179i −0.342973 0.198016i
$$428$$ 4.43535 0.214391
$$429$$ 0 0
$$430$$ −0.0586060 −0.00282623
$$431$$ −3.76645 2.17456i −0.181424 0.104745i 0.406538 0.913634i $$-0.366736\pi$$
−0.587961 + 0.808889i $$0.700069\pi$$
$$432$$ −0.592990 + 1.02709i −0.0285303 + 0.0494159i
$$433$$ −7.19418 12.4607i −0.345730 0.598822i 0.639756 0.768578i $$-0.279035\pi$$
−0.985486 + 0.169756i $$0.945702\pi$$
$$434$$ 12.5332i 0.601612i
$$435$$ −2.22571 + 1.28501i −0.106714 + 0.0616116i
$$436$$ 18.4512 10.6528i 0.883651 0.510176i
$$437$$ 0.131687i 0.00629942i
$$438$$ 6.06853 + 10.5110i 0.289966 + 0.502235i
$$439$$ −10.1163 + 17.5219i −0.482822 + 0.836273i −0.999805 0.0197227i $$-0.993722\pi$$
0.516983 + 0.855996i $$0.327055\pi$$
$$440$$ 2.44540 + 1.41185i 0.116580 + 0.0673075i
$$441$$ 2.96077 0.140989
$$442$$ 0 0
$$443$$ 8.12200 0.385888 0.192944 0.981210i $$-0.438196\pi$$
0.192944 + 0.981210i $$0.438196\pi$$
$$444$$ −15.0294 8.67725i −0.713266 0.411804i
$$445$$ 0.356232 0.617012i 0.0168870 0.0292492i
$$446$$ −0.905813 1.56891i −0.0428915 0.0742903i
$$447$$ 9.74094i 0.460731i
$$448$$ −7.27591 + 4.20075i −0.343755 + 0.198467i
$$449$$ −10.8180 + 6.24578i −0.510534 + 0.294757i −0.733053 0.680172i $$-0.761905\pi$$
0.222519 + 0.974928i $$0.428572\pi$$
$$450$$ 8.11529i 0.382559i
$$451$$ −24.6151 42.6345i −1.15908 2.00758i
$$452$$ −8.17456 + 14.1588i −0.384499 + 0.665972i
$$453$$ −7.67553 4.43147i −0.360628 0.208209i
$$454$$ 5.58642 0.262184
$$455$$ 0 0
$$456$$ −0.533188 −0.0249688
$$457$$ −5.17988 2.99061i −0.242305 0.139895i 0.373931 0.927457i $$-0.378010\pi$$
−0.616236 + 0.787562i $$0.711343\pi$$
$$458$$ 9.69298 16.7887i 0.452923 0.784486i
$$459$$ 2.30678 + 3.99546i 0.107671 + 0.186492i
$$460$$ 0.500664i 0.0233436i
$$461$$ −1.78114 + 1.02834i −0.0829561 + 0.0478947i −0.540904 0.841084i $$-0.681918\pi$$
0.457948 + 0.888979i $$0.348585\pi$$
$$462$$ 15.6204 9.01842i 0.726725 0.419575i
$$463$$ 8.44935i 0.392675i 0.980536 + 0.196337i $$0.0629048\pi$$
−0.980536 + 0.196337i $$0.937095\pi$$
$$464$$ −1.28501 2.22571i −0.0596552 0.103326i
$$465$$ 1.83997 3.18692i 0.0853266 0.147790i
$$466$$ −2.12586 1.22737i −0.0984785 0.0568566i
$$467$$ −33.5139 −1.55084 −0.775420 0.631446i $$-0.782462\pi$$
−0.775420 + 0.631446i $$0.782462\pi$$
$$468$$ 0 0
$$469$$ −18.1008 −0.835818
$$470$$ 1.26191 + 0.728562i 0.0582074 + 0.0336060i
$$471$$ 5.00484 8.66864i 0.230611 0.399430i
$$472$$ 9.12618 + 15.8070i 0.420066 + 0.727576i
$$473$$ 1.25667i 0.0577817i
$$474$$ −15.5591 + 8.98307i −0.714655 + 0.412606i
$$475$$ −0.377027 + 0.217677i −0.0172992 + 0.00998769i
$$476$$ 6.90408i 0.316448i
$$477$$ 10.6479 + 18.4428i 0.487536 + 0.844437i
$$478$$ −10.0831 + 17.4644i −0.461189 + 0.798802i
$$479$$ −21.4179 12.3656i −0.978608 0.565000i −0.0767587 0.997050i $$-0.524457\pi$$
−0.901850 + 0.432050i $$0.857790\pi$$
$$480$$ 3.23490 0.147652
$$481$$ 0 0
$$482$$ −16.2524 −0.740275
$$483$$ −6.85187 3.95593i −0.311771 0.180001i
$$484$$ 4.77413 8.26903i 0.217006 0.375865i
$$485$$ −0.995156 1.72366i −0.0451877 0.0782674i
$$486$$ 14.5875i 0.661702i
$$487$$ −32.6972 + 18.8778i −1.48165 + 0.855433i −0.999783 0.0208094i $$-0.993376\pi$$
−0.481870 + 0.876243i $$0.660042\pi$$
$$488$$ 8.09492 4.67360i 0.366440 0.211564i
$$489$$ 36.3086i 1.64193i
$$490$$ 0.143104 + 0.247864i 0.00646479 + 0.0111973i
$$491$$ 15.6555 27.1161i 0.706522 1.22373i −0.259617 0.965712i $$-0.583596\pi$$
0.966139 0.258020i $$-0.0830702\pi$$
$$492$$ −30.6074 17.6712i −1.37989 0.796680i
$$493$$ −9.99761 −0.450270
$$494$$ 0 0
$$495$$ −2.14914 −0.0965969
$$496$$ 3.18692 + 1.83997i 0.143097 + 0.0826171i
$$497$$ −10.2111 + 17.6861i −0.458031 + 0.793332i
$$498$$ −1.44989 2.51128i −0.0649710 0.112533i
$$499$$ 21.4873i 0.961902i 0.876748 + 0.480951i $$0.159708\pi$$
−0.876748 + 0.480951i $$0.840292\pi$$
$$500$$ 2.88457 1.66541i 0.129002 0.0744793i
$$501$$ 31.3632 18.1075i 1.40120 0.808984i
$$502$$ 19.0228i 0.849031i
$$503$$ −18.7962 32.5560i −0.838081 1.45160i −0.891497 0.453026i $$-0.850344\pi$$
0.0534164 0.998572i $$-0.482989\pi$$
$$504$$ 6.50000 11.2583i 0.289533 0.501486i
$$505$$ −2.85640 1.64914i −0.127108 0.0733860i
$$506$$ 5.08815 0.226196
$$507$$ 0 0
$$508$$ 13.3075 0.590425
$$509$$ 14.8155 + 8.55376i 0.656688 + 0.379139i 0.791014 0.611798i $$-0.209554\pi$$
−0.134326 + 0.990937i $$0.542887\pi$$
$$510$$ 0.480386 0.832052i 0.0212718 0.0368439i
$$511$$ −7.93751 13.7482i −0.351135 0.608183i
$$512$$ 6.22282i 0.275012i
$$513$$ −0.163136 + 0.0941868i −0.00720264 + 0.00415845i
$$514$$ −9.87865 + 5.70344i −0.435728 + 0.251568i
$$515$$ 0.336454i 0.0148259i
$$516$$ 0.451083 + 0.781298i 0.0198578 + 0.0343947i
$$517$$ 15.6223 27.0586i 0.687068 1.19004i
$$518$$ −9.31705 5.37920i −0.409367 0.236348i
$$519$$ −48.3913 −2.12414
$$520$$ 0 0
$$521$$ −19.8465 −0.869493 −0.434746 0.900553i $$-0.643162\pi$$
−0.434746 + 0.900553i $$0.643162\pi$$
$$522$$ −6.58981 3.80463i −0.288428 0.166524i
$$523$$ 5.71499 9.89865i 0.249899 0.432838i −0.713599 0.700555i $$-0.752936\pi$$
0.963498 + 0.267717i $$0.0862693\pi$$
$$524$$ 4.46197 + 7.72835i 0.194922 + 0.337615i
$$525$$ 26.1564i 1.14156i
$$526$$ −11.8728 + 6.85474i −0.517677 + 0.298881i
$$527$$ 12.3974 7.15764i 0.540039 0.311792i
$$528$$ 5.29590i 0.230474i
$$529$$ 10.3840 + 17.9857i 0.451480 + 0.781987i
$$530$$ −1.02930 + 1.78281i −0.0447101 + 0.0774401i
$$531$$ −12.0308 6.94600i −0.522093 0.301431i
$$532$$ 0.281896 0.0122218
$$533$$ 0 0
$$534$$ 5.19806 0.224942
$$535$$ −0.699155 0.403657i −0.0302271 0.0174516i
$$536$$ 10.3373 17.9047i 0.446503 0.773365i
$$537$$ −12.8448 22.2479i −0.554295 0.960066i
$$538$$ 5.18598i 0.223584i
$$539$$ 5.31485 3.06853i 0.228927 0.132171i
$$540$$ 0.620234 0.358092i 0.0266906 0.0154098i
$$541$$ 16.1884i 0.695993i −0.937496 0.347996i $$-0.886862\pi$$
0.937496 0.347996i $$-0.113138\pi$$
$$542$$ −2.58546 4.47814i −0.111055 0.192353i
$$543$$ −23.5601 + 40.8073i −1.01106 + 1.75121i
$$544$$ 10.8981 + 6.29201i 0.467252 + 0.269768i
$$545$$ −3.87800 −0.166115
$$546$$ 0 0
$$547$$ 5.33081 0.227929 0.113965 0.993485i $$-0.463645\pi$$
0.113965 + 0.993485i $$0.463645\pi$$
$$548$$ 7.30896 + 4.21983i 0.312223 + 0.180262i
$$549$$ −3.55711 + 6.16110i −0.151814 + 0.262949i
$$550$$ 8.41066 + 14.5677i 0.358632 + 0.621168i
$$551$$ 0.408206i 0.0173902i
$$552$$ 7.82613 4.51842i 0.333102 0.192317i
$$553$$ 20.3510 11.7497i 0.865413 0.499647i
$$554$$ 10.7942i 0.458600i
$$555$$ 1.57942 + 2.73563i 0.0670425 + 0.116121i
$$556$$ 9.97799 17.2824i 0.423161 0.732937i
$$557$$ 6.40058 + 3.69537i 0.271201 + 0.156578i 0.629433 0.777054i $$-0.283287\pi$$
−0.358232 + 0.933633i $$0.616620\pi$$
$$558$$ 10.8955 0.461242
$$559$$ 0 0
$$560$$ −0.323044 −0.0136511
$$561$$ −17.8414 10.3007i −0.753265 0.434898i
$$562$$ −2.01961 + 3.49807i −0.0851923 + 0.147557i
$$563$$ −4.73945 8.20896i −0.199744 0.345967i 0.748701 0.662907i $$-0.230678\pi$$
−0.948445 + 0.316941i $$0.897344\pi$$
$$564$$ 22.4306i 0.944497i
$$565$$ 2.57715 1.48792i 0.108422 0.0625972i
$$566$$ −15.3678 + 8.87263i −0.645958 + 0.372944i
$$567$$ 25.8049i 1.08370i
$$568$$ −11.6630 20.2009i −0.489369 0.847612i
$$569$$ −5.07188 + 8.78476i −0.212624 + 0.368276i −0.952535 0.304429i $$-0.901534\pi$$
0.739911 + 0.672705i $$0.234868\pi$$
$$570$$ 0.0339730 + 0.0196143i 0.00142297 + 0.000821554i
$$571$$ 14.0925 0.589751 0.294876 0.955536i $$-0.404722\pi$$
0.294876 + 0.955536i $$0.404722\pi$$
$$572$$ 0 0
$$573$$ 32.4403 1.35521
$$574$$ −18.9741 10.9547i −0.791966 0.457242i
$$575$$ 3.68933 6.39011i 0.153856 0.266486i
$$576$$ 3.65183 + 6.32516i 0.152160 + 0.263548i
$$577$$ 25.1545i 1.04720i 0.851965 + 0.523598i $$0.175411\pi$$
−0.851965 + 0.523598i $$0.824589\pi$$
$$578$$ −8.56972 + 4.94773i −0.356453 + 0.205798i
$$579$$ −26.4253 + 15.2567i −1.09820 + 0.634045i
$$580$$ 1.55197i 0.0644422i
$$581$$ 1.89642 + 3.28470i 0.0786768 + 0.136272i
$$582$$ 7.26055 12.5756i 0.300960 0.521277i
$$583$$ 38.2281 + 22.0710i 1.58324 + 0.914087i
$$584$$ 18.1323 0.750319
$$585$$ 0 0
$$586$$ 11.9860 0.495137
$$587$$ −37.9625 21.9177i −1.56688 0.904639i −0.996530 0.0832369i $$-0.973474\pi$$
−0.570350 0.821402i $$-0.693192\pi$$
$$588$$ 2.20291 3.81555i 0.0908463 0.157350i
$$589$$ 0.292249 + 0.506190i 0.0120419 + 0.0208572i
$$590$$ 1.34290i 0.0552861i
$$591$$ 1.09038 0.629531i 0.0448522 0.0258954i
$$592$$ −2.73563 + 1.57942i −0.112434 + 0.0649136i
$$593$$ 24.9965i 1.02648i 0.858244 + 0.513242i $$0.171556\pi$$
−0.858244 + 0.513242i $$0.828444\pi$$
$$594$$ 3.63922 + 6.30331i 0.149319 + 0.258628i
$$595$$ −0.628334 + 1.08831i −0.0257592 + 0.0446162i
$$596$$ −5.09423 2.94116i −0.208668 0.120474i
$$597$$ 25.8213 1.05680
$$598$$ 0 0
$$599$$ −6.24027 −0.254971 −0.127485 0.991840i $$-0.540691\pi$$
−0.127485 + 0.991840i $$0.540691\pi$$
$$600$$ 25.8730 + 14.9378i 1.05626 + 0.609833i
$$601$$ −3.16487 + 5.48172i −0.129098 + 0.223604i −0.923327 0.384014i $$-0.874541\pi$$
0.794229 + 0.607618i $$0.207875\pi$$
$$602$$ 0.279635 + 0.484342i 0.0113971 + 0.0197403i
$$603$$ 15.7356i 0.640802i
$$604$$ −4.63506 + 2.67606i −0.188598 + 0.108887i
$$605$$ −1.50511 + 0.868977i −0.0611915 + 0.0353290i
$$606$$ 24.0640i 0.977532i
$$607$$ 21.8240 + 37.8003i 0.885809 + 1.53427i 0.844784 + 0.535108i $$0.179729\pi$$
0.0410253 + 0.999158i $$0.486938\pi$$
$$608$$ −0.256905 + 0.444973i −0.0104189 + 0.0180460i
$$609$$ 21.2396 + 12.2627i 0.860673 + 0.496910i
$$610$$ −0.687710 −0.0278445
$$611$$ 0 0
$$612$$ −6.00192 −0.242613
$$613$$ 22.4769 + 12.9770i 0.907833 + 0.524137i 0.879733 0.475468i $$-0.157721\pi$$
0.0280995 + 0.999605i $$0.491054\pi$$
$$614$$ −7.67025 + 13.2853i −0.309546 + 0.536150i
$$615$$ 3.21648 + 5.57111i 0.129701 + 0.224649i
$$616$$ 26.9463i 1.08570i
$$617$$ 39.7849 22.9698i 1.60168 0.924729i 0.610526 0.791996i $$-0.290958\pi$$
0.991152 0.132733i $$-0.0423753\pi$$
$$618$$ 2.12586 1.22737i 0.0855146 0.0493719i
$$619$$ 6.73556i 0.270725i −0.990796 0.135363i $$-0.956780\pi$$
0.990796 0.135363i $$-0.0432199\pi$$
$$620$$ −1.11111 1.92450i −0.0446234 0.0772899i
$$621$$ 1.59634 2.76495i 0.0640590 0.110953i
$$622$$ −0.187386 0.108187i −0.00751349 0.00433792i
$$623$$ −6.79895 −0.272394
$$624$$ 0 0
$$625$$ 24.0887 0.963549
$$626$$ 16.2469 + 9.38016i 0.649357 + 0.374907i
$$627$$ 0.420583 0.728471i 0.0167965 0.0290923i
$$628$$ −3.02230 5.23478i −0.120603 0.208891i
$$629$$ 12.2881i 0.489960i
$$630$$ −0.828318 + 0.478230i −0.0330010 + 0.0190531i
$$631$$ −39.0575 + 22.5499i −1.55486 + 0.897696i −0.557121 + 0.830432i $$0.688094\pi$$
−0.997735 + 0.0672649i $$0.978573\pi$$
$$632$$ 26.8407i 1.06767i
$$633$$ 9.86927 + 17.0941i 0.392268 + 0.679429i
$$634$$ −5.61165 + 9.71965i −0.222867 + 0.386017i
$$635$$ −2.09769 1.21110i −0.0832444 0.0480612i
$$636$$ 31.6896 1.25658
$$637$$ 0 0
$$638$$ −15.7724 −0.624435
$$639$$ 15.3751 + 8.87681i 0.608229 + 0.351161i
$$640$$ 1.08665 1.88214i 0.0429538 0.0743981i
$$641$$ 16.2911 + 28.2169i 0.643458 + 1.11450i 0.984655 + 0.174510i $$0.0558342\pi$$
−0.341197 + 0.939992i $$0.610832\pi$$
$$642$$ 5.89008i 0.232463i
$$643$$ 22.1489 12.7877i 0.873469 0.504298i 0.00496965 0.999988i $$-0.498418\pi$$
0.868500 + 0.495690i $$0.165085\pi$$
$$644$$ −4.13767 + 2.38889i −0.163047 + 0.0941353i
$$645$$ 0.164210i 0.00646578i
$$646$$ 0.0763014 + 0.132158i 0.00300204 + 0.00519968i
$$647$$ −15.0858 + 26.1293i −0.593082 + 1.02725i 0.400732 + 0.916195i $$0.368756\pi$$
−0.993814 + 0.111053i $$0.964578\pi$$
$$648$$ 25.5253 + 14.7371i 1.00273 + 0.578926i
$$649$$ −28.7952 −1.13031
$$650$$ 0 0
$$651$$ −35.1172 −1.37635
$$652$$ 18.9883 + 10.9629i 0.743641 + 0.429341i
$$653$$ −18.4514 + 31.9587i −0.722058 + 1.25064i 0.238115 + 0.971237i $$0.423470\pi$$
−0.960173 + 0.279405i $$0.909863\pi$$
$$654$$ −14.1468 24.5029i −0.553182 0.958139i
$$655$$ 1.62432i 0.0634673i
$$656$$ −5.57111 + 3.21648i −0.217515 + 0.125582i
$$657$$ −11.9517 + 6.90030i −0.466279 + 0.269207i
$$658$$ 13.9051i 0.542079i
$$659$$ −11.8433 20.5132i −0.461350 0.799082i 0.537678 0.843150i $$-0.319302\pi$$
−0.999029 + 0.0440679i $$0.985968\pi$$
$$660$$ −1.59903 + 2.76960i −0.0622422 + 0.107807i
$$661$$ −27.5041 15.8795i −1.06979 0.617641i −0.141662 0.989915i $$-0.545245\pi$$
−0.928123 + 0.372274i $$0.878578\pi$$
$$662$$ −14.2916 −0.555458
$$663$$ 0 0
$$664$$ −4.33214 −0.168120
$$665$$ −0.0444360 0.0256551i −0.00172315 0.000994863i
$$666$$ −4.67629 + 8.09958i −0.181203 + 0.313852i
$$667$$ 3.45928 + 5.99165i 0.133944 + 0.231998i
$$668$$ 21.8694i 0.846152i
$$669$$ 4.39600 2.53803i 0.169959 0.0981260i
$$670$$ −1.31732 + 0.760553i −0.0508924 + 0.0293827i
$$671$$ 14.7463i 0.569275i
$$672$$ −15.4351 26.7344i −0.595423 1.03130i
$$673$$ −3.75116 + 6.49720i −0.144597 + 0.250449i −0.929222 0.369521i $$-0.879522\pi$$
0.784626 + 0.619970i $$0.212855\pi$$
$$674$$ −19.3407 11.1664i −0.744976 0.430112i
$$675$$ 10.5550 0.406261
$$676$$ 0 0
$$677$$ −35.0315 −1.34637 −0.673184 0.739475i $$-0.735074\pi$$
−0.673184 + 0.739475i $$0.735074\pi$$
$$678$$ 18.8026 + 10.8557i 0.722110 + 0.416911i
$$679$$ −9.49665 + 16.4487i −0.364448 + 0.631242i
$$680$$ −0.717677 1.24305i −0.0275216 0.0476689i
$$681$$ 15.6528i 0.599816i
$$682$$ 19.5583 11.2920i 0.748927 0.432393i
$$683$$ 20.8568 12.0417i 0.798063 0.460762i −0.0447302 0.998999i $$-0.514243\pi$$
0.842794 + 0.538237i $$0.180909\pi$$
$$684$$ 0.245061i 0.00937013i
$$685$$ −0.768086 1.33036i −0.0293471 0.0508306i
$$686$$ 7.98092 13.8234i 0.304713 0.527778i
$$687$$ 47.0410 + 27.1591i 1.79473 + 1.03619i
$$688$$ 0.164210 0.00626046
$$689$$ 0 0
$$690$$ −0.664874 −0.0253113
$$691$$ −1.74459 1.00724i −0.0663672 0.0383171i 0.466449 0.884548i $$-0.345533\pi$$
−0.532816 + 0.846231i $$0.678866\pi$$
$$692$$ −14.6112 + 25.3073i −0.555433 + 0.962039i
$$693$$ 10.2545 + 17.7613i 0.389537 + 0.674697i
$$694$$ 1.20583i 0.0457728i
$$695$$ −3.14571 + 1.81618i −0.119323 + 0.0688915i
$$696$$ −24.2597 + 14.0063i −0.919561 + 0.530909i
$$697$$ 25.0248i 0.947880i
$$698$$ 5.68814 + 9.85214i 0.215299 + 0.372909i
$$699$$ 3.43900 5.95652i 0.130075 0.225296i
$$700$$ −13.6791 7.89762i −0.517020 0.298502i
$$701$$ 48.8189 1.84387 0.921933 0.387350i $$-0.126610\pi$$
0.921933 + 0.387350i $$0.126610\pi$$
$$702$$ 0 0
$$703$$ −0.501729 −0.0189231
$$704$$ 13.1107 + 7.56949i 0.494130 + 0.285286i
$$705$$ −2.04138 + 3.53578i −0.0768830 + 0.133165i
$$706$$ −2.87435 4.97853i −0.108178 0.187369i
$$707$$ 31.4752i 1.18375i
$$708$$ −17.9026 + 10.3361i −0.672822 + 0.388454i
$$709$$ 18.0185 10.4030i 0.676699 0.390693i −0.121911 0.992541i $$-0.538902\pi$$
0.798610 + 0.601848i $$0.205569\pi$$
$$710$$ 1.71618i 0.0644073i
$$711$$ −10.2143 17.6917i −0.383067 0.663492i
$$712$$ 3.88285 6.72529i 0.145516 0.252041i
$$713$$ −8.57926 4.95324i −0.321296 0.185500i
$$714$$ −9.16852 −0.343123
$$715$$ 0 0
$$716$$ −15.5133 −0.579761
$$717$$ −48.9341 28.2521i −1.82748 1.05509i
$$718$$ −7.97339 + 13.8103i −0.297564 + 0.515396i
$$719$$ 10.7153 + 18.5594i 0.399613 + 0.692149i 0.993678 0.112267i $$-0.0358113\pi$$
−0.594065 + 0.804417i $$0.702478\pi$$
$$720$$ 0.280831i 0.0104660i
$$721$$ −2.78058 + 1.60537i −0.103554 + 0.0597870i
$$722$$ 13.1901 7.61529i 0.490884 0.283412i
$$723$$ 45.5381i 1.69358i
$$724$$ 14.2274 + 24.6425i 0.528756 + 0.915832i
$$725$$ −11.4363 + 19.8083i −0.424734 + 0.735661i
$$726$$ −10.9812 6.33997i −0.407549 0.235298i
$$727$$ −13.4862 −0.500175 −0.250088 0.968223i $$-0.580459\pi$$
−0.250088 + 0.968223i $$0.580459\pi$$
$$728$$ 0 0
$$729$$ −8.02715 −0.297302
$$730$$ −1.15533 0.667030i −0.0427607 0.0246879i
$$731$$ 0.319396 0.553210i 0.0118133 0.0204612i
$$732$$ 5.29321 + 9.16811i 0.195643 + 0.338863i
$$733$$ 43.5424i 1.60828i −0.594443 0.804138i $$-0.702627\pi$$
0.594443 0.804138i $$-0.297373\pi$$
$$734$$ 0.752721 0.434584i 0.0277834 0.0160408i
$$735$$ −0.694498 + 0.400969i −0.0256170 + 0.0147900i
$$736$$ 8.70841i 0.320996i
$$737$$ 16.3083 + 28.2468i 0.600723 + 1.04048i
$$738$$ −9.52326 + 16.4948i −0.350556 + 0.607181i
$$739$$ 17.3675 + 10.0271i 0.638875 + 0.368855i 0.784181 0.620532i $$-0.213083\pi$$
−0.145306 + 0.989387i $$0.546417\pi$$
$$740$$ 1.90754 0.0701226
$$741$$ 0 0
$$742$$ 19.6450 0.721191
$$743$$ 28.7248 + 16.5843i 1.05381 + 0.608418i 0.923714 0.383084i $$-0.125138\pi$$
0.130096 + 0.991501i $$0.458471\pi$$
$$744$$ 20.0553 34.7367i 0.735261 1.27351i
$$745$$ 0.535344 + 0.927243i 0.0196135 + 0.0339715i
$$746$$ 4.91617i 0.179994i
$$747$$ 2.85548 1.64861i 0.104477 0.0603196i
$$748$$ −10.7740 + 6.22037i −0.393936 + 0.227439i
$$749$$ 7.70410i 0.281502i
$$750$$ −2.21164 3.83067i −0.0807575 0.139876i
$$751$$ 19.6407 34.0187i 0.716700 1.24136i −0.245601 0.969371i $$-0.578985\pi$$
0.962300 0.271989i $$-0.0876815\pi$$
$$752$$ −3.53578 2.04138i −0.128937 0.0744416i
$$753$$ −53.3008 −1.94239
$$754$$ 0 0
$$755$$ 0.974181 0.0354541
$$756$$ −5.91882 3.41723i −0.215265 0.124283i
$$757$$ 23.3213 40.3937i 0.847628 1.46813i −0.0356920 0.999363i $$-0.511364\pi$$
0.883320 0.468771i $$-0.155303\pi$$
$$758$$ −0.965853 1.67291i −0.0350813 0.0607627i
$$759$$ 14.2567i 0.517484i
$$760$$ 0.0507543 0.0293030i 0.00184105 0.00106293i
$$761$$ 18.9646 10.9492i 0.687467 0.396909i −0.115196 0.993343i $$-0.536750\pi$$
0.802662 + 0.596434i $$0.203416\pi$$
$$762$$ 17.6722i 0.640195i
$$763$$ 18.5036 + 32.0493i 0.669877 + 1.16026i
$$764$$ 9.79494 16.9653i 0.354368 0.613784i
$$765$$ 0.946096 + 0.546229i 0.0342062 + 0.0197489i
$$766$$ 24.3720 0.880595
$$767$$ 0 0
$$768$$ 31.8756 1.15021
$$769$$ −40.4517 23.3548i −1.45873 0.842196i −0.459777 0.888035i $$-0.652071\pi$$
−0.998949 + 0.0458390i $$0.985404\pi$$
$$770$$ −0.991271 + 1.71693i −0.0357229 + 0.0618739i
$$771$$ −15.9807 27.6794i −0.575530 0.996848i
$$772$$ 18.4263i 0.663175i
$$773$$ −26.1900 + 15.1208i −0.941989 + 0.543857i −0.890583 0.454820i $$-0.849703\pi$$
−0.0514055 + 0.998678i $$0.516370\pi$$