# Properties

 Label 475.2.e.f.26.1 Level $475$ Weight $2$ Character 475.26 Analytic conductor $3.793$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$475 = 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 475.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$3.79289409601$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} - 552 x^{3} + 1107 x^{2} + 33 x + 1$$ x^12 - 3*x^11 + 17*x^10 - 18*x^9 + 109*x^8 - 93*x^7 + 484*x^6 - 147*x^5 + 1009*x^4 - 552*x^3 + 1107*x^2 + 33*x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 26.1 Root $$-0.975939 + 1.69038i$$ of defining polynomial Character $$\chi$$ $$=$$ 475.26 Dual form 475.2.e.f.201.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.08504 - 1.87935i) q^{2} +(-1.47594 - 2.55640i) q^{3} +(-1.35464 + 2.34630i) q^{4} +(-3.20292 + 5.54761i) q^{6} +0.591620 q^{7} +1.53919 q^{8} +(-2.85679 + 4.94811i) q^{9} +O(q^{10})$$ $$q+(-1.08504 - 1.87935i) q^{2} +(-1.47594 - 2.55640i) q^{3} +(-1.35464 + 2.34630i) q^{4} +(-3.20292 + 5.54761i) q^{6} +0.591620 q^{7} +1.53919 q^{8} +(-2.85679 + 4.94811i) q^{9} +2.58045 q^{11} +7.99745 q^{12} +(-3.43332 + 5.94669i) q^{13} +(-0.641933 - 1.11186i) q^{14} +(1.03919 + 1.79993i) q^{16} +(2.61787 + 4.53429i) q^{17} +12.3990 q^{18} +(-2.26423 - 3.72468i) q^{19} +(-0.873195 - 1.51242i) q^{21} +(-2.79990 - 4.84957i) q^{22} +(-1.45072 + 2.51271i) q^{23} +(-2.27175 - 3.93478i) q^{24} +14.9012 q^{26} +8.01017 q^{27} +(-0.801431 + 1.38812i) q^{28} +(-3.52494 + 6.10538i) q^{29} -6.81421 q^{31} +(3.79432 - 6.57195i) q^{32} +(-3.80859 - 6.59667i) q^{33} +(5.68101 - 9.83980i) q^{34} +(-7.73984 - 13.4058i) q^{36} -4.82538 q^{37} +(-4.54320 + 8.29672i) q^{38} +20.2695 q^{39} +(-3.11419 - 5.39393i) q^{41} +(-1.89491 + 3.28208i) q^{42} +(-2.18013 - 3.77609i) q^{43} +(-3.49558 + 6.05452i) q^{44} +6.29636 q^{46} +(-1.27941 + 2.21600i) q^{47} +(3.06756 - 5.31317i) q^{48} -6.64999 q^{49} +(7.72764 - 13.3847i) q^{51} +(-9.30181 - 16.1112i) q^{52} +(4.79573 - 8.30645i) q^{53} +(-8.69138 - 15.0539i) q^{54} +0.910615 q^{56} +(-6.17993 + 11.2857i) q^{57} +15.2989 q^{58} +(1.46221 + 2.53263i) q^{59} +(-1.16586 + 2.01932i) q^{61} +(7.39371 + 12.8063i) q^{62} +(-1.69013 + 2.92740i) q^{63} -12.3112 q^{64} +(-8.26497 + 14.3153i) q^{66} +(-2.15122 + 3.72603i) q^{67} -14.1851 q^{68} +8.56468 q^{69} +(6.74645 + 11.6852i) q^{71} +(-4.39714 + 7.61607i) q^{72} +(4.21337 + 7.29777i) q^{73} +(5.23574 + 9.06858i) q^{74} +(11.8064 - 0.266962i) q^{76} +1.52665 q^{77} +(-21.9933 - 38.0935i) q^{78} +(-2.93630 - 5.08583i) q^{79} +(-3.25215 - 5.63288i) q^{81} +(-6.75806 + 11.7053i) q^{82} -4.02036 q^{83} +4.73145 q^{84} +(-4.73107 + 8.19445i) q^{86} +20.8104 q^{87} +3.97180 q^{88} +(-1.85823 + 3.21855i) q^{89} +(-2.03122 + 3.51818i) q^{91} +(-3.93039 - 6.80764i) q^{92} +(10.0574 + 17.4199i) q^{93} +5.55285 q^{94} -22.4007 q^{96} +(-1.26285 - 2.18732i) q^{97} +(7.21552 + 12.4977i) q^{98} +(-7.37182 + 12.7684i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9}+O(q^{10})$$ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 $$12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24} + 38 q^{26} + 36 q^{27} + 4 q^{28} - 3 q^{29} - 6 q^{31} + 6 q^{32} + 18 q^{33} + q^{34} - 13 q^{36} - 12 q^{37} - 18 q^{38} + 16 q^{39} - 11 q^{41} + 11 q^{42} - 13 q^{43} - 21 q^{44} - 24 q^{46} + 6 q^{47} + 19 q^{48} + 8 q^{49} + 17 q^{51} + q^{52} - 18 q^{53} - 18 q^{54} + 8 q^{56} - 20 q^{57} + 10 q^{58} - 4 q^{59} - 25 q^{61} + 21 q^{62} - 43 q^{63} - 44 q^{64} - 34 q^{66} - 6 q^{67} - 2 q^{68} + 26 q^{69} - 18 q^{71} - 13 q^{72} - q^{73} + 6 q^{74} + 24 q^{76} - 22 q^{77} - 72 q^{78} - 3 q^{79} - 2 q^{81} - 31 q^{82} - 46 q^{83} + 74 q^{84} - 9 q^{86} + 22 q^{87} + 22 q^{88} - 12 q^{89} + 11 q^{91} - 28 q^{92} + 13 q^{93} + 16 q^{94} - 26 q^{96} - 3 q^{97} + 22 q^{98} + 20 q^{99}+O(q^{100})$$ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.08504 1.87935i −0.767241 1.32890i −0.939053 0.343771i $$-0.888295\pi$$
0.171812 0.985130i $$-0.445038\pi$$
$$3$$ −1.47594 2.55640i −0.852134 1.47594i −0.879279 0.476308i $$-0.841975\pi$$
0.0271449 0.999632i $$-0.491358\pi$$
$$4$$ −1.35464 + 2.34630i −0.677319 + 1.17315i
$$5$$ 0 0
$$6$$ −3.20292 + 5.54761i −1.30758 + 2.26480i
$$7$$ 0.591620 0.223611 0.111806 0.993730i $$-0.464337\pi$$
0.111806 + 0.993730i $$0.464337\pi$$
$$8$$ 1.53919 0.544185
$$9$$ −2.85679 + 4.94811i −0.952264 + 1.64937i
$$10$$ 0 0
$$11$$ 2.58045 0.778036 0.389018 0.921230i $$-0.372814\pi$$
0.389018 + 0.921230i $$0.372814\pi$$
$$12$$ 7.99745 2.30867
$$13$$ −3.43332 + 5.94669i −0.952232 + 1.64931i −0.211653 + 0.977345i $$0.567885\pi$$
−0.740579 + 0.671969i $$0.765449\pi$$
$$14$$ −0.641933 1.11186i −0.171564 0.297157i
$$15$$ 0 0
$$16$$ 1.03919 + 1.79993i 0.259797 + 0.449982i
$$17$$ 2.61787 + 4.53429i 0.634927 + 1.09973i 0.986531 + 0.163577i $$0.0523033\pi$$
−0.351603 + 0.936149i $$0.614363\pi$$
$$18$$ 12.3990 2.92247
$$19$$ −2.26423 3.72468i −0.519449 0.854501i
$$20$$ 0 0
$$21$$ −0.873195 1.51242i −0.190547 0.330037i
$$22$$ −2.79990 4.84957i −0.596941 1.03393i
$$23$$ −1.45072 + 2.51271i −0.302495 + 0.523937i −0.976701 0.214607i $$-0.931153\pi$$
0.674205 + 0.738544i $$0.264486\pi$$
$$24$$ −2.27175 3.93478i −0.463719 0.803185i
$$25$$ 0 0
$$26$$ 14.9012 2.92237
$$27$$ 8.01017 1.54156
$$28$$ −0.801431 + 1.38812i −0.151456 + 0.262330i
$$29$$ −3.52494 + 6.10538i −0.654565 + 1.13374i 0.327438 + 0.944873i $$0.393815\pi$$
−0.982003 + 0.188867i $$0.939518\pi$$
$$30$$ 0 0
$$31$$ −6.81421 −1.22387 −0.611934 0.790909i $$-0.709608\pi$$
−0.611934 + 0.790909i $$0.709608\pi$$
$$32$$ 3.79432 6.57195i 0.670747 1.16177i
$$33$$ −3.80859 6.59667i −0.662990 1.14833i
$$34$$ 5.68101 9.83980i 0.974285 1.68751i
$$35$$ 0 0
$$36$$ −7.73984 13.4058i −1.28997 2.23430i
$$37$$ −4.82538 −0.793287 −0.396644 0.917973i $$-0.629825\pi$$
−0.396644 + 0.917973i $$0.629825\pi$$
$$38$$ −4.54320 + 8.29672i −0.737005 + 1.34591i
$$39$$ 20.2695 3.24572
$$40$$ 0 0
$$41$$ −3.11419 5.39393i −0.486355 0.842391i 0.513522 0.858076i $$-0.328340\pi$$
−0.999877 + 0.0156852i $$0.995007\pi$$
$$42$$ −1.89491 + 3.28208i −0.292391 + 0.506436i
$$43$$ −2.18013 3.77609i −0.332467 0.575849i 0.650528 0.759482i $$-0.274548\pi$$
−0.982995 + 0.183633i $$0.941214\pi$$
$$44$$ −3.49558 + 6.05452i −0.526978 + 0.912753i
$$45$$ 0 0
$$46$$ 6.29636 0.928348
$$47$$ −1.27941 + 2.21600i −0.186621 + 0.323237i −0.944121 0.329598i $$-0.893087\pi$$
0.757501 + 0.652834i $$0.226420\pi$$
$$48$$ 3.06756 5.31317i 0.442764 0.766890i
$$49$$ −6.64999 −0.949998
$$50$$ 0 0
$$51$$ 7.72764 13.3847i 1.08209 1.87423i
$$52$$ −9.30181 16.1112i −1.28993 2.23422i
$$53$$ 4.79573 8.30645i 0.658745 1.14098i −0.322196 0.946673i $$-0.604421\pi$$
0.980941 0.194306i $$-0.0622456\pi$$
$$54$$ −8.69138 15.0539i −1.18275 2.04858i
$$55$$ 0 0
$$56$$ 0.910615 0.121686
$$57$$ −6.17993 + 11.2857i −0.818551 + 1.49483i
$$58$$ 15.2989 2.00884
$$59$$ 1.46221 + 2.53263i 0.190364 + 0.329720i 0.945371 0.325997i $$-0.105700\pi$$
−0.755007 + 0.655717i $$0.772367\pi$$
$$60$$ 0 0
$$61$$ −1.16586 + 2.01932i −0.149273 + 0.258548i −0.930959 0.365124i $$-0.881027\pi$$
0.781686 + 0.623672i $$0.214360\pi$$
$$62$$ 7.39371 + 12.8063i 0.939003 + 1.62640i
$$63$$ −1.69013 + 2.92740i −0.212937 + 0.368818i
$$64$$ −12.3112 −1.53891
$$65$$ 0 0
$$66$$ −8.26497 + 14.3153i −1.01735 + 1.76210i
$$67$$ −2.15122 + 3.72603i −0.262814 + 0.455207i −0.966989 0.254820i $$-0.917984\pi$$
0.704175 + 0.710027i $$0.251317\pi$$
$$68$$ −14.1851 −1.72019
$$69$$ 8.56468 1.03107
$$70$$ 0 0
$$71$$ 6.74645 + 11.6852i 0.800656 + 1.38678i 0.919185 + 0.393827i $$0.128849\pi$$
−0.118528 + 0.992951i $$0.537818\pi$$
$$72$$ −4.39714 + 7.61607i −0.518208 + 0.897563i
$$73$$ 4.21337 + 7.29777i 0.493137 + 0.854139i 0.999969 0.00790620i $$-0.00251665\pi$$
−0.506831 + 0.862045i $$0.669183\pi$$
$$74$$ 5.23574 + 9.06858i 0.608643 + 1.05420i
$$75$$ 0 0
$$76$$ 11.8064 0.266962i 1.35429 0.0306226i
$$77$$ 1.52665 0.173978
$$78$$ −21.9933 38.0935i −2.49025 4.31324i
$$79$$ −2.93630 5.08583i −0.330360 0.572200i 0.652222 0.758028i $$-0.273837\pi$$
−0.982582 + 0.185827i $$0.940503\pi$$
$$80$$ 0 0
$$81$$ −3.25215 5.63288i −0.361350 0.625876i
$$82$$ −6.75806 + 11.7053i −0.746303 + 1.29263i
$$83$$ −4.02036 −0.441292 −0.220646 0.975354i $$-0.570816\pi$$
−0.220646 + 0.975354i $$0.570816\pi$$
$$84$$ 4.73145 0.516244
$$85$$ 0 0
$$86$$ −4.73107 + 8.19445i −0.510164 + 0.883630i
$$87$$ 20.8104 2.23111
$$88$$ 3.97180 0.423396
$$89$$ −1.85823 + 3.21855i −0.196972 + 0.341166i −0.947545 0.319622i $$-0.896444\pi$$
0.750573 + 0.660787i $$0.229778\pi$$
$$90$$ 0 0
$$91$$ −2.03122 + 3.51818i −0.212930 + 0.368805i
$$92$$ −3.93039 6.80764i −0.409772 0.709745i
$$93$$ 10.0574 + 17.4199i 1.04290 + 1.80636i
$$94$$ 5.55285 0.572733
$$95$$ 0 0
$$96$$ −22.4007 −2.28627
$$97$$ −1.26285 2.18732i −0.128223 0.222089i 0.794765 0.606917i $$-0.207594\pi$$
−0.922988 + 0.384828i $$0.874261\pi$$
$$98$$ 7.21552 + 12.4977i 0.728878 + 1.26245i
$$99$$ −7.37182 + 12.7684i −0.740895 + 1.28327i
$$100$$ 0 0
$$101$$ −0.692736 + 1.19985i −0.0689298 + 0.119390i −0.898430 0.439116i $$-0.855292\pi$$
0.829501 + 0.558506i $$0.188625\pi$$
$$102$$ −33.5393 −3.32088
$$103$$ 0.166774 0.0164328 0.00821638 0.999966i $$-0.497385\pi$$
0.00821638 + 0.999966i $$0.497385\pi$$
$$104$$ −5.28453 + 9.15307i −0.518191 + 0.897533i
$$105$$ 0 0
$$106$$ −20.8143 −2.02166
$$107$$ −4.51729 −0.436703 −0.218351 0.975870i $$-0.570068\pi$$
−0.218351 + 0.975870i $$0.570068\pi$$
$$108$$ −10.8509 + 18.7943i −1.04413 + 1.80848i
$$109$$ 5.35464 + 9.27450i 0.512881 + 0.888336i 0.999888 + 0.0149384i $$0.00475523\pi$$
−0.487007 + 0.873398i $$0.661911\pi$$
$$110$$ 0 0
$$111$$ 7.12196 + 12.3356i 0.675987 + 1.17084i
$$112$$ 0.614805 + 1.06487i 0.0580936 + 0.100621i
$$113$$ 13.2065 1.24237 0.621183 0.783665i $$-0.286652\pi$$
0.621183 + 0.783665i $$0.286652\pi$$
$$114$$ 27.9152 0.631206i 2.61450 0.0591178i
$$115$$ 0 0
$$116$$ −9.55004 16.5411i −0.886699 1.53581i
$$117$$ −19.6166 33.9769i −1.81355 3.14117i
$$118$$ 3.17313 5.49602i 0.292110 0.505950i
$$119$$ 1.54879 + 2.68257i 0.141977 + 0.245911i
$$120$$ 0 0
$$121$$ −4.34127 −0.394661
$$122$$ 5.06002 0.458113
$$123$$ −9.19271 + 15.9222i −0.828879 + 1.43566i
$$124$$ 9.23079 15.9882i 0.828949 1.43578i
$$125$$ 0 0
$$126$$ 7.33548 0.653496
$$127$$ −0.860805 + 1.49096i −0.0763841 + 0.132301i −0.901687 0.432389i $$-0.857671\pi$$
0.825303 + 0.564690i $$0.191004\pi$$
$$128$$ 5.76959 + 9.99323i 0.509965 + 0.883285i
$$129$$ −6.43548 + 11.1466i −0.566612 + 0.981401i
$$130$$ 0 0
$$131$$ −1.64201 2.84405i −0.143463 0.248486i 0.785335 0.619071i $$-0.212491\pi$$
−0.928799 + 0.370585i $$0.879157\pi$$
$$132$$ 20.6370 1.79622
$$133$$ −1.33956 2.20360i −0.116155 0.191076i
$$134$$ 9.33668 0.806567
$$135$$ 0 0
$$136$$ 4.02940 + 6.97913i 0.345518 + 0.598455i
$$137$$ −4.07541 + 7.05882i −0.348186 + 0.603075i −0.985927 0.167175i $$-0.946536\pi$$
0.637741 + 0.770251i $$0.279869\pi$$
$$138$$ −9.29304 16.0960i −0.791076 1.37018i
$$139$$ 7.81401 13.5343i 0.662776 1.14796i −0.317108 0.948390i $$-0.602712\pi$$
0.979883 0.199571i $$-0.0639550\pi$$
$$140$$ 0 0
$$141$$ 7.55331 0.636103
$$142$$ 14.6404 25.3579i 1.22859 2.12799i
$$143$$ −8.85952 + 15.3451i −0.740870 + 1.28323i
$$144$$ −11.8750 −0.989582
$$145$$ 0 0
$$146$$ 9.14337 15.8368i 0.756711 1.31066i
$$147$$ 9.81497 + 17.0000i 0.809525 + 1.40214i
$$148$$ 6.53664 11.3218i 0.537308 0.930646i
$$149$$ −1.61005 2.78869i −0.131900 0.228458i 0.792509 0.609861i $$-0.208775\pi$$
−0.924409 + 0.381402i $$0.875441\pi$$
$$150$$ 0 0
$$151$$ −11.1226 −0.905142 −0.452571 0.891728i $$-0.649493\pi$$
−0.452571 + 0.891728i $$0.649493\pi$$
$$152$$ −3.48507 5.73299i −0.282677 0.465007i
$$153$$ −29.9149 −2.41847
$$154$$ −1.65648 2.86910i −0.133483 0.231199i
$$155$$ 0 0
$$156$$ −27.4578 + 47.5583i −2.19838 + 3.80771i
$$157$$ −10.7157 18.5602i −0.855209 1.48127i −0.876451 0.481491i $$-0.840095\pi$$
0.0212418 0.999774i $$-0.493238\pi$$
$$158$$ −6.37203 + 11.0367i −0.506932 + 0.878032i
$$159$$ −28.3128 −2.24535
$$160$$ 0 0
$$161$$ −0.858273 + 1.48657i −0.0676414 + 0.117158i
$$162$$ −7.05744 + 12.2238i −0.554485 + 0.960396i
$$163$$ 10.3129 0.807768 0.403884 0.914810i $$-0.367660\pi$$
0.403884 + 0.914810i $$0.367660\pi$$
$$164$$ 16.8744 1.31767
$$165$$ 0 0
$$166$$ 4.36226 + 7.55566i 0.338577 + 0.586433i
$$167$$ −3.25342 + 5.63509i −0.251757 + 0.436056i −0.964010 0.265867i $$-0.914342\pi$$
0.712252 + 0.701923i $$0.247675\pi$$
$$168$$ −1.34401 2.32790i −0.103693 0.179601i
$$169$$ −17.0754 29.5754i −1.31349 2.27503i
$$170$$ 0 0
$$171$$ 24.8986 0.562995i 1.90404 0.0430533i
$$172$$ 11.8131 0.900744
$$173$$ −3.13027 5.42179i −0.237990 0.412211i 0.722147 0.691739i $$-0.243155\pi$$
−0.960137 + 0.279528i $$0.909822\pi$$
$$174$$ −22.5802 39.1100i −1.71180 2.96492i
$$175$$ 0 0
$$176$$ 2.68158 + 4.64463i 0.202131 + 0.350102i
$$177$$ 4.31628 7.47601i 0.324431 0.561931i
$$178$$ 8.06505 0.604501
$$179$$ 23.1893 1.73325 0.866624 0.498961i $$-0.166285\pi$$
0.866624 + 0.498961i $$0.166285\pi$$
$$180$$ 0 0
$$181$$ 1.59948 2.77039i 0.118889 0.205921i −0.800439 0.599414i $$-0.795400\pi$$
0.919328 + 0.393493i $$0.128733\pi$$
$$182$$ 8.81585 0.653474
$$183$$ 6.88294 0.508801
$$184$$ −2.23293 + 3.86754i −0.164614 + 0.285119i
$$185$$ 0 0
$$186$$ 21.8253 37.8026i 1.60031 2.77182i
$$187$$ 6.75529 + 11.7005i 0.493996 + 0.855626i
$$188$$ −3.46627 6.00375i −0.252803 0.437868i
$$189$$ 4.73898 0.344710
$$190$$ 0 0
$$191$$ 18.9443 1.37076 0.685382 0.728184i $$-0.259635\pi$$
0.685382 + 0.728184i $$0.259635\pi$$
$$192$$ 18.1706 + 31.4725i 1.31135 + 2.27133i
$$193$$ 0.515269 + 0.892472i 0.0370899 + 0.0642415i 0.883974 0.467535i $$-0.154858\pi$$
−0.846885 + 0.531777i $$0.821525\pi$$
$$194$$ −2.74049 + 4.74667i −0.196756 + 0.340791i
$$195$$ 0 0
$$196$$ 9.00832 15.6029i 0.643452 1.11449i
$$197$$ −18.5515 −1.32174 −0.660868 0.750502i $$-0.729812\pi$$
−0.660868 + 0.750502i $$0.729812\pi$$
$$198$$ 31.9950 2.27378
$$199$$ −11.3166 + 19.6010i −0.802215 + 1.38948i 0.115940 + 0.993256i $$0.463012\pi$$
−0.918155 + 0.396221i $$0.870321\pi$$
$$200$$ 0 0
$$201$$ 12.7003 0.895810
$$202$$ 3.00659 0.211543
$$203$$ −2.08542 + 3.61206i −0.146368 + 0.253517i
$$204$$ 20.9363 + 36.2627i 1.46583 + 2.53890i
$$205$$ 0 0
$$206$$ −0.180957 0.313427i −0.0126079 0.0218375i
$$207$$ −8.28879 14.3566i −0.576111 0.997853i
$$208$$ −14.2715 −0.989549
$$209$$ −5.84273 9.61137i −0.404150 0.664832i
$$210$$ 0 0
$$211$$ −6.21978 10.7730i −0.428187 0.741642i 0.568525 0.822666i $$-0.307514\pi$$
−0.996712 + 0.0810240i $$0.974181\pi$$
$$212$$ 12.9930 + 22.5045i 0.892360 + 1.54561i
$$213$$ 19.9147 34.4933i 1.36453 2.36344i
$$214$$ 4.90145 + 8.48956i 0.335056 + 0.580335i
$$215$$ 0 0
$$216$$ 12.3292 0.838893
$$217$$ −4.03142 −0.273671
$$218$$ 11.6200 20.1265i 0.787008 1.36314i
$$219$$ 12.4373 21.5421i 0.840438 1.45568i
$$220$$ 0 0
$$221$$ −35.9520 −2.41839
$$222$$ 15.4553 26.7693i 1.03729 1.79664i
$$223$$ 9.58654 + 16.6044i 0.641962 + 1.11191i 0.984994 + 0.172588i $$0.0552128\pi$$
−0.343032 + 0.939324i $$0.611454\pi$$
$$224$$ 2.24479 3.88810i 0.149987 0.259784i
$$225$$ 0 0
$$226$$ −14.3297 24.8197i −0.953195 1.65098i
$$227$$ −26.5208 −1.76025 −0.880123 0.474745i $$-0.842540\pi$$
−0.880123 + 0.474745i $$0.842540\pi$$
$$228$$ −18.1080 29.7880i −1.19923 1.97276i
$$229$$ −8.81023 −0.582196 −0.291098 0.956693i $$-0.594021\pi$$
−0.291098 + 0.956693i $$0.594021\pi$$
$$230$$ 0 0
$$231$$ −2.25324 3.90272i −0.148252 0.256780i
$$232$$ −5.42555 + 9.39733i −0.356205 + 0.616965i
$$233$$ 2.25616 + 3.90778i 0.147806 + 0.256007i 0.930416 0.366505i $$-0.119446\pi$$
−0.782610 + 0.622512i $$0.786112\pi$$
$$234$$ −42.5697 + 73.7328i −2.78287 + 4.82006i
$$235$$ 0 0
$$236$$ −7.92308 −0.515749
$$237$$ −8.66761 + 15.0127i −0.563022 + 0.975182i
$$238$$ 3.36100 5.82142i 0.217861 0.377347i
$$239$$ −7.82431 −0.506112 −0.253056 0.967452i $$-0.581436\pi$$
−0.253056 + 0.967452i $$0.581436\pi$$
$$240$$ 0 0
$$241$$ −13.6697 + 23.6766i −0.880541 + 1.52514i −0.0298010 + 0.999556i $$0.509487\pi$$
−0.850740 + 0.525586i $$0.823846\pi$$
$$242$$ 4.71046 + 8.15876i 0.302800 + 0.524465i
$$243$$ 2.41531 4.18345i 0.154942 0.268368i
$$244$$ −3.15863 5.47091i −0.202210 0.350239i
$$245$$ 0 0
$$246$$ 39.8979 2.54380
$$247$$ 29.9233 0.676612i 1.90398 0.0430518i
$$248$$ −10.4884 −0.666011
$$249$$ 5.93380 + 10.2777i 0.376040 + 0.651320i
$$250$$ 0 0
$$251$$ 8.11886 14.0623i 0.512458 0.887603i −0.487438 0.873158i $$-0.662068\pi$$
0.999896 0.0144451i $$-0.00459818\pi$$
$$252$$ −4.57904 7.93113i −0.288452 0.499614i
$$253$$ −3.74350 + 6.48394i −0.235352 + 0.407642i
$$254$$ 3.73604 0.234420
$$255$$ 0 0
$$256$$ 0.209275 0.362476i 0.0130797 0.0226547i
$$257$$ 4.57174 7.91848i 0.285177 0.493941i −0.687475 0.726208i $$-0.741281\pi$$
0.972652 + 0.232267i $$0.0746143\pi$$
$$258$$ 27.9311 1.73891
$$259$$ −2.85479 −0.177388
$$260$$ 0 0
$$261$$ −20.1400 34.8836i −1.24664 2.15924i
$$262$$ −3.56331 + 6.17183i −0.220142 + 0.381297i
$$263$$ 7.64861 + 13.2478i 0.471634 + 0.816894i 0.999473 0.0324505i $$-0.0103311\pi$$
−0.527840 + 0.849344i $$0.676998\pi$$
$$264$$ −5.86214 10.1535i −0.360790 0.624906i
$$265$$ 0 0
$$266$$ −2.68785 + 4.90850i −0.164803 + 0.300960i
$$267$$ 10.9705 0.671386
$$268$$ −5.82826 10.0948i −0.356017 0.616640i
$$269$$ 7.07334 + 12.2514i 0.431269 + 0.746981i 0.996983 0.0776213i $$-0.0247325\pi$$
−0.565714 + 0.824602i $$0.691399\pi$$
$$270$$ 0 0
$$271$$ 5.68158 + 9.84078i 0.345131 + 0.597785i 0.985378 0.170385i $$-0.0545010\pi$$
−0.640246 + 0.768170i $$0.721168\pi$$
$$272$$ −5.44093 + 9.42396i −0.329905 + 0.571412i
$$273$$ 11.9918 0.725779
$$274$$ 17.6880 1.06857
$$275$$ 0 0
$$276$$ −11.6020 + 20.0953i −0.698360 + 1.20960i
$$277$$ 18.9102 1.13620 0.568101 0.822959i $$-0.307678\pi$$
0.568101 + 0.822959i $$0.307678\pi$$
$$278$$ −33.9142 −2.03404
$$279$$ 19.4668 33.7175i 1.16545 2.01861i
$$280$$ 0 0
$$281$$ 13.9438 24.1513i 0.831816 1.44075i −0.0647802 0.997900i $$-0.520635\pi$$
0.896596 0.442849i $$-0.146032\pi$$
$$282$$ −8.19567 14.1953i −0.488045 0.845318i
$$283$$ −7.19798 12.4673i −0.427876 0.741102i 0.568809 0.822470i $$-0.307405\pi$$
−0.996684 + 0.0813677i $$0.974071\pi$$
$$284$$ −36.5560 −2.16920
$$285$$ 0 0
$$286$$ 38.4519 2.27371
$$287$$ −1.84242 3.19116i −0.108754 0.188368i
$$288$$ 21.6792 + 37.5494i 1.27746 + 2.21262i
$$289$$ −5.20651 + 9.01794i −0.306265 + 0.530467i
$$290$$ 0 0
$$291$$ −3.72778 + 6.45670i −0.218526 + 0.378498i
$$292$$ −22.8303 −1.33605
$$293$$ 2.63178 0.153750 0.0768752 0.997041i $$-0.475506\pi$$
0.0768752 + 0.997041i $$0.475506\pi$$
$$294$$ 21.2993 36.8915i 1.24220 2.15156i
$$295$$ 0 0
$$296$$ −7.42717 −0.431695
$$297$$ 20.6699 1.19939
$$298$$ −3.49395 + 6.05169i −0.202399 + 0.350565i
$$299$$ −9.96155 17.2539i −0.576091 0.997819i
$$300$$ 0 0
$$301$$ −1.28981 2.23401i −0.0743433 0.128766i
$$302$$ 12.0685 + 20.9032i 0.694463 + 1.20284i
$$303$$ 4.08974 0.234950
$$304$$ 4.35120 7.94610i 0.249559 0.455740i
$$305$$ 0 0
$$306$$ 32.4589 + 56.2205i 1.85555 + 3.21391i
$$307$$ 8.41257 + 14.5710i 0.480131 + 0.831611i 0.999740 0.0227929i $$-0.00725584\pi$$
−0.519609 + 0.854404i $$0.673923\pi$$
$$308$$ −2.06805 + 3.58197i −0.117838 + 0.204102i
$$309$$ −0.246149 0.426342i −0.0140029 0.0242538i
$$310$$ 0 0
$$311$$ −18.3273 −1.03924 −0.519622 0.854396i $$-0.673927\pi$$
−0.519622 + 0.854396i $$0.673927\pi$$
$$312$$ 31.1986 1.76627
$$313$$ 11.7527 20.3562i 0.664299 1.15060i −0.315176 0.949033i $$-0.602063\pi$$
0.979475 0.201567i $$-0.0646033\pi$$
$$314$$ −23.2541 + 40.2772i −1.31230 + 2.27298i
$$315$$ 0 0
$$316$$ 15.9105 0.895036
$$317$$ 1.94177 3.36324i 0.109061 0.188899i −0.806329 0.591467i $$-0.798549\pi$$
0.915390 + 0.402568i $$0.131882\pi$$
$$318$$ 30.7207 + 53.2097i 1.72273 + 2.98385i
$$319$$ −9.09594 + 15.7546i −0.509275 + 0.882090i
$$320$$ 0 0
$$321$$ 6.66724 + 11.5480i 0.372129 + 0.644546i
$$322$$ 3.72505 0.207589
$$323$$ 10.9613 20.0174i 0.609905 1.11380i
$$324$$ 17.6219 0.978996
$$325$$ 0 0
$$326$$ −11.1899 19.3815i −0.619753 1.07344i
$$327$$ 15.8062 27.3772i 0.874087 1.51396i
$$328$$ −4.79333 8.30228i −0.264667 0.458417i
$$329$$ −0.756923 + 1.31103i −0.0417305 + 0.0722793i
$$330$$ 0 0
$$331$$ 3.25821 0.179087 0.0895437 0.995983i $$-0.471459\pi$$
0.0895437 + 0.995983i $$0.471459\pi$$
$$332$$ 5.44613 9.43297i 0.298895 0.517702i
$$333$$ 13.7851 23.8765i 0.755419 1.30842i
$$334$$ 14.1204 0.772635
$$335$$ 0 0
$$336$$ 1.81483 3.14338i 0.0990070 0.171485i
$$337$$ 11.0987 + 19.2234i 0.604582 + 1.04717i 0.992117 + 0.125312i $$0.0399933\pi$$
−0.387535 + 0.921855i $$0.626673\pi$$
$$338$$ −37.0551 + 64.1813i −2.01553 + 3.49100i
$$339$$ −19.4921 33.7612i −1.05866 1.83366i
$$340$$ 0 0
$$341$$ −17.5837 −0.952213
$$342$$ −28.0741 46.1823i −1.51807 2.49725i
$$343$$ −8.07560 −0.436042
$$344$$ −3.35563 5.81212i −0.180923 0.313369i
$$345$$ 0 0
$$346$$ −6.79296 + 11.7658i −0.365192 + 0.632531i
$$347$$ 1.49728 + 2.59336i 0.0803780 + 0.139219i 0.903412 0.428773i $$-0.141054\pi$$
−0.823034 + 0.567992i $$0.807721\pi$$
$$348$$ −28.1905 + 48.8274i −1.51117 + 2.61743i
$$349$$ 15.1407 0.810461 0.405230 0.914215i $$-0.367191\pi$$
0.405230 + 0.914215i $$0.367191\pi$$
$$350$$ 0 0
$$351$$ −27.5015 + 47.6340i −1.46792 + 2.54251i
$$352$$ 9.79106 16.9586i 0.521865 0.903897i
$$353$$ −34.4369 −1.83289 −0.916446 0.400159i $$-0.868955\pi$$
−0.916446 + 0.400159i $$0.868955\pi$$
$$354$$ −18.7334 −0.995668
$$355$$ 0 0
$$356$$ −5.03446 8.71994i −0.266826 0.462156i
$$357$$ 4.57182 7.91863i 0.241967 0.419098i
$$358$$ −25.1614 43.5808i −1.32982 2.30332i
$$359$$ −1.58165 2.73950i −0.0834763 0.144585i 0.821265 0.570548i $$-0.193269\pi$$
−0.904741 + 0.425962i $$0.859936\pi$$
$$360$$ 0 0
$$361$$ −8.74655 + 16.8671i −0.460345 + 0.887740i
$$362$$ −6.94204 −0.364865
$$363$$ 6.40744 + 11.0980i 0.336304 + 0.582495i
$$364$$ −5.50314 9.53171i −0.288443 0.499597i
$$365$$ 0 0
$$366$$ −7.46829 12.9354i −0.390374 0.676147i
$$367$$ −10.7270 + 18.5797i −0.559945 + 0.969853i 0.437556 + 0.899191i $$0.355844\pi$$
−0.997500 + 0.0706615i $$0.977489\pi$$
$$368$$ −6.03027 −0.314350
$$369$$ 35.5864 1.85255
$$370$$ 0 0
$$371$$ 2.83725 4.91426i 0.147303 0.255136i
$$372$$ −54.4963 −2.82550
$$373$$ −33.1587 −1.71689 −0.858446 0.512904i $$-0.828570\pi$$
−0.858446 + 0.512904i $$0.828570\pi$$
$$374$$ 14.6596 25.3911i 0.758028 1.31294i
$$375$$ 0 0
$$376$$ −1.96925 + 3.41084i −0.101556 + 0.175901i
$$377$$ −24.2045 41.9234i −1.24660 2.15917i
$$378$$ −5.14199 8.90619i −0.264476 0.458085i
$$379$$ −14.1646 −0.727589 −0.363795 0.931479i $$-0.618519\pi$$
−0.363795 + 0.931479i $$0.618519\pi$$
$$380$$ 0 0
$$381$$ 5.08198 0.260358
$$382$$ −20.5554 35.6030i −1.05171 1.82161i
$$383$$ −5.41036 9.37102i −0.276457 0.478837i 0.694045 0.719932i $$-0.255827\pi$$
−0.970502 + 0.241095i $$0.922494\pi$$
$$384$$ 17.0311 29.4988i 0.869117 1.50535i
$$385$$ 0 0
$$386$$ 1.11818 1.93674i 0.0569138 0.0985775i
$$387$$ 24.9127 1.26638
$$388$$ 6.84281 0.347391
$$389$$ −5.38703 + 9.33061i −0.273133 + 0.473081i −0.969662 0.244448i $$-0.921393\pi$$
0.696529 + 0.717529i $$0.254727\pi$$
$$390$$ 0 0
$$391$$ −15.1912 −0.768250
$$392$$ −10.2356 −0.516975
$$393$$ −4.84702 + 8.39529i −0.244500 + 0.423486i
$$394$$ 20.1291 + 34.8647i 1.01409 + 1.75646i
$$395$$ 0 0
$$396$$ −19.9723 34.5930i −1.00364 1.73836i
$$397$$ 1.55107 + 2.68653i 0.0778461 + 0.134833i 0.902320 0.431066i $$-0.141862\pi$$
−0.824474 + 0.565899i $$0.808529\pi$$
$$398$$ 49.1162 2.46197
$$399$$ −3.65617 + 6.67683i −0.183037 + 0.334260i
$$400$$ 0 0
$$401$$ 5.65671 + 9.79771i 0.282483 + 0.489274i 0.971996 0.234999i $$-0.0755088\pi$$
−0.689513 + 0.724273i $$0.742175\pi$$
$$402$$ −13.7804 23.8683i −0.687303 1.19044i
$$403$$ 23.3954 40.5220i 1.16541 2.01854i
$$404$$ −1.87681 3.25074i −0.0933749 0.161730i
$$405$$ 0 0
$$406$$ 9.05110 0.449199
$$407$$ −12.4517 −0.617206
$$408$$ 11.8943 20.6015i 0.588855 1.01993i
$$409$$ −7.11186 + 12.3181i −0.351659 + 0.609091i −0.986540 0.163519i $$-0.947716\pi$$
0.634882 + 0.772609i $$0.281049\pi$$
$$410$$ 0 0
$$411$$ 24.0602 1.18680
$$412$$ −0.225919 + 0.391303i −0.0111302 + 0.0192781i
$$413$$ 0.865075 + 1.49835i 0.0425675 + 0.0737291i
$$414$$ −17.9874 + 31.1551i −0.884032 + 1.53119i
$$415$$ 0 0
$$416$$ 26.0542 + 45.1272i 1.27741 + 2.21255i
$$417$$ −46.1320 −2.25909
$$418$$ −11.7235 + 21.4093i −0.573416 + 1.04716i
$$419$$ −11.0053 −0.537643 −0.268821 0.963190i $$-0.586634\pi$$
−0.268821 + 0.963190i $$0.586634\pi$$
$$420$$ 0 0
$$421$$ 11.4625 + 19.8536i 0.558646 + 0.967604i 0.997610 + 0.0690991i $$0.0220125\pi$$
−0.438963 + 0.898505i $$0.644654\pi$$
$$422$$ −13.4975 + 23.3783i −0.657046 + 1.13804i
$$423$$ −7.31000 12.6613i −0.355424 0.615613i
$$424$$ 7.38154 12.7852i 0.358479 0.620904i
$$425$$ 0 0
$$426$$ −86.4332 −4.18770
$$427$$ −0.689744 + 1.19467i −0.0333791 + 0.0578142i
$$428$$ 6.11929 10.5989i 0.295787 0.512318i
$$429$$ 52.3045 2.52528
$$430$$ 0 0
$$431$$ 8.49811 14.7192i 0.409340 0.708997i −0.585476 0.810690i $$-0.699092\pi$$
0.994816 + 0.101693i $$0.0324258\pi$$
$$432$$ 8.32408 + 14.4177i 0.400492 + 0.693673i
$$433$$ −15.7493 + 27.2786i −0.756863 + 1.31093i 0.187580 + 0.982249i $$0.439936\pi$$
−0.944443 + 0.328676i $$0.893398\pi$$
$$434$$ 4.37427 + 7.57645i 0.209972 + 0.363681i
$$435$$ 0 0
$$436$$ −29.0144 −1.38954
$$437$$ 12.6438 0.285896i 0.604836 0.0136763i
$$438$$ −53.9802 −2.57928
$$439$$ −1.57963 2.73600i −0.0753916 0.130582i 0.825865 0.563868i $$-0.190687\pi$$
−0.901256 + 0.433286i $$0.857354\pi$$
$$440$$ 0 0
$$441$$ 18.9976 32.9049i 0.904649 1.56690i
$$442$$ 39.0095 + 67.5664i 1.85549 + 3.21380i
$$443$$ 5.94720 10.3008i 0.282560 0.489408i −0.689455 0.724329i $$-0.742150\pi$$
0.972015 + 0.234921i $$0.0754831\pi$$
$$444$$ −38.5907 −1.83143
$$445$$ 0 0
$$446$$ 20.8036 36.0329i 0.985080 1.70621i
$$447$$ −4.75267 + 8.23186i −0.224794 + 0.389354i
$$448$$ −7.28358 −0.344117
$$449$$ 21.2175 1.00132 0.500659 0.865645i $$-0.333091\pi$$
0.500659 + 0.865645i $$0.333091\pi$$
$$450$$ 0 0
$$451$$ −8.03602 13.9188i −0.378401 0.655410i
$$452$$ −17.8901 + 30.9865i −0.841479 + 1.45748i
$$453$$ 16.4162 + 28.4338i 0.771302 + 1.33593i
$$454$$ 28.7762 + 49.8418i 1.35053 + 2.33919i
$$455$$ 0 0
$$456$$ −9.51208 + 17.3708i −0.445444 + 0.813462i
$$457$$ −9.41670 −0.440495 −0.220247 0.975444i $$-0.570686\pi$$
−0.220247 + 0.975444i $$0.570686\pi$$
$$458$$ 9.55948 + 16.5575i 0.446685 + 0.773682i
$$459$$ 20.9696 + 36.3204i 0.978777 + 1.69529i
$$460$$ 0 0
$$461$$ −1.16004 2.00924i −0.0540282 0.0935797i 0.837746 0.546060i $$-0.183873\pi$$
−0.891775 + 0.452480i $$0.850539\pi$$
$$462$$ −4.88972 + 8.46924i −0.227490 + 0.394025i
$$463$$ −14.7160 −0.683909 −0.341955 0.939716i $$-0.611089\pi$$
−0.341955 + 0.939716i $$0.611089\pi$$
$$464$$ −14.6523 −0.680217
$$465$$ 0 0
$$466$$ 4.89606 8.48023i 0.226806 0.392839i
$$467$$ 11.7747 0.544867 0.272434 0.962175i $$-0.412172\pi$$
0.272434 + 0.962175i $$0.412172\pi$$
$$468$$ 106.293 4.91341
$$469$$ −1.27271 + 2.20439i −0.0587681 + 0.101789i
$$470$$ 0 0
$$471$$ −31.6316 + 54.7875i −1.45751 + 2.52447i
$$472$$ 2.25062 + 3.89819i 0.103593 + 0.179429i
$$473$$ −5.62572 9.74403i −0.258671 0.448031i
$$474$$ 37.6189 1.72789
$$475$$ 0 0
$$476$$ −8.39217 −0.384655
$$477$$ 27.4008 + 47.4596i 1.25460 + 2.17303i
$$478$$ 8.48971 + 14.7046i 0.388310 + 0.672573i
$$479$$ −5.69219 + 9.85915i −0.260083 + 0.450476i −0.966264 0.257555i $$-0.917083\pi$$
0.706181 + 0.708031i $$0.250416\pi$$
$$480$$ 0 0
$$481$$ 16.5671 28.6950i 0.755394 1.30838i
$$482$$ 59.3288 2.70235
$$483$$ 5.06703 0.230558
$$484$$ 5.88084 10.1859i 0.267311 0.462996i
$$485$$ 0 0
$$486$$ −10.4829 −0.475513
$$487$$ 4.77063 0.216178 0.108089 0.994141i $$-0.465527\pi$$
0.108089 + 0.994141i $$0.465527\pi$$
$$488$$ −1.79447 + 3.10812i −0.0812321 + 0.140698i
$$489$$ −15.2212 26.3639i −0.688326 1.19222i
$$490$$ 0 0
$$491$$ 2.50665 + 4.34165i 0.113124 + 0.195936i 0.917028 0.398822i $$-0.130581\pi$$
−0.803904 + 0.594758i $$0.797248\pi$$
$$492$$ −24.9056 43.1377i −1.12283 1.94480i
$$493$$ −36.9114 −1.66240
$$494$$ −33.7397 55.5023i −1.51802 2.49717i
$$495$$ 0 0
$$496$$ −7.08125 12.2651i −0.317958 0.550719i
$$497$$ 3.99133 + 6.91319i 0.179036 + 0.310099i
$$498$$ 12.8769 22.3034i 0.577026 0.999439i
$$499$$ −10.9112 18.8987i −0.488450 0.846021i 0.511461 0.859306i $$-0.329104\pi$$
−0.999912 + 0.0132853i $$0.995771\pi$$
$$500$$ 0 0
$$501$$ 19.2074 0.858124
$$502$$ −35.2372 −1.57272
$$503$$ 7.58583 13.1391i 0.338236 0.585841i −0.645865 0.763451i $$-0.723503\pi$$
0.984101 + 0.177610i $$0.0568366\pi$$
$$504$$ −2.60144 + 4.50582i −0.115877 + 0.200705i
$$505$$ 0 0
$$506$$ 16.2475 0.722288
$$507$$ −50.4045 + 87.3031i −2.23854 + 3.87727i
$$508$$ −2.33216 4.03941i −0.103473 0.179220i
$$509$$ −2.59122 + 4.48812i −0.114854 + 0.198933i −0.917721 0.397225i $$-0.869973\pi$$
0.802868 + 0.596157i $$0.203307\pi$$
$$510$$ 0 0
$$511$$ 2.49271 + 4.31750i 0.110271 + 0.190995i
$$512$$ 22.1701 0.979789
$$513$$ −18.1368 29.8354i −0.800761 1.31726i
$$514$$ −19.8421 −0.875199
$$515$$ 0 0
$$516$$ −17.4355 30.1991i −0.767554 1.32944i
$$517$$ −3.30145 + 5.71828i −0.145198 + 0.251490i
$$518$$ 3.09757 + 5.36515i 0.136099 + 0.235731i
$$519$$ −9.24018 + 16.0045i −0.405599 + 0.702518i
$$520$$ 0 0
$$521$$ 11.2091 0.491079 0.245540 0.969387i $$-0.421035\pi$$
0.245540 + 0.969387i $$0.421035\pi$$
$$522$$ −43.7056 + 75.7004i −1.91294 + 3.31332i
$$523$$ −2.71940 + 4.71014i −0.118911 + 0.205960i −0.919336 0.393472i $$-0.871274\pi$$
0.800425 + 0.599433i $$0.204607\pi$$
$$524$$ 8.89733 0.388682
$$525$$ 0 0
$$526$$ 16.5982 28.7488i 0.723714 1.25351i
$$527$$ −17.8387 30.8976i −0.777067 1.34592i
$$528$$ 7.91569 13.7104i 0.344486 0.596668i
$$529$$ 7.29084 + 12.6281i 0.316993 + 0.549048i
$$530$$ 0 0
$$531$$ −16.7090 −0.725107
$$532$$ 6.98492 0.157940i 0.302835 0.00684756i
$$533$$ 42.7680 1.85249
$$534$$ −11.9035 20.6175i −0.515116 0.892206i
$$535$$ 0 0
$$536$$ −3.31114 + 5.73506i −0.143019 + 0.247717i
$$537$$ −34.2260 59.2811i −1.47696 2.55817i
$$538$$ 15.3498 26.5866i 0.661776 1.14623i
$$539$$ −17.1600 −0.739132
$$540$$ 0 0
$$541$$ −7.14111 + 12.3688i −0.307020 + 0.531775i −0.977709 0.209964i $$-0.932665\pi$$
0.670689 + 0.741739i $$0.265999\pi$$
$$542$$ 12.3295 21.3554i 0.529598 0.917291i
$$543$$ −9.44296 −0.405236
$$544$$ 39.7322 1.70350
$$545$$ 0 0
$$546$$ −13.0117 22.5369i −0.556848 0.964488i
$$547$$ 12.5122 21.6717i 0.534982 0.926616i −0.464182 0.885740i $$-0.653652\pi$$
0.999164 0.0408766i $$-0.0130151\pi$$
$$548$$ −11.0414 19.1243i −0.471666 0.816949i
$$549$$ −6.66122 11.5376i −0.284294 0.492412i
$$550$$ 0 0
$$551$$ 30.7219 0.694668i 1.30880 0.0295939i
$$552$$ 13.1827 0.561091
$$553$$ −1.73718 3.00888i −0.0738722 0.127950i
$$554$$ −20.5184 35.5388i −0.871741 1.50990i
$$555$$ 0 0
$$556$$ 21.1703 + 36.6680i 0.897821 + 1.55507i
$$557$$ 3.57846 6.19807i 0.151624 0.262621i −0.780201 0.625529i $$-0.784883\pi$$
0.931825 + 0.362909i $$0.118216\pi$$
$$558$$ −84.4892 −3.57671
$$559$$ 29.9403 1.26634
$$560$$ 0 0
$$561$$ 19.9408 34.5385i 0.841901 1.45822i
$$562$$ −60.5184 −2.55282
$$563$$ 28.9386 1.21962 0.609809 0.792548i $$-0.291246\pi$$
0.609809 + 0.792548i $$0.291246\pi$$
$$564$$ −10.2320 + 17.7223i −0.430845 + 0.746245i
$$565$$ 0 0
$$566$$ −15.6202 + 27.0551i −0.656568 + 1.13721i
$$567$$ −1.92403 3.33253i −0.0808019 0.139953i
$$568$$ 10.3841 + 17.9857i 0.435706 + 0.754664i
$$569$$ 38.8864 1.63020 0.815100 0.579320i $$-0.196682\pi$$
0.815100 + 0.579320i $$0.196682\pi$$
$$570$$ 0 0
$$571$$ 15.1613 0.634480 0.317240 0.948345i $$-0.397244\pi$$
0.317240 + 0.948345i $$0.397244\pi$$
$$572$$ −24.0029 41.5742i −1.00361 1.73831i
$$573$$ −27.9607 48.4293i −1.16807 2.02316i
$$574$$ −3.99820 + 6.92509i −0.166882 + 0.289048i
$$575$$ 0 0
$$576$$ 35.1707 60.9174i 1.46544 2.53822i
$$577$$ 20.6412 0.859303 0.429651 0.902995i $$-0.358636\pi$$
0.429651 + 0.902995i $$0.358636\pi$$
$$578$$ 22.5972 0.939918
$$579$$ 1.52101 2.63447i 0.0632111 0.109485i
$$580$$ 0 0
$$581$$ −2.37852 −0.0986778
$$582$$ 16.1792 0.670649
$$583$$ 12.3752 21.4344i 0.512527 0.887723i
$$584$$ 6.48517 + 11.2326i 0.268358 + 0.464810i
$$585$$ 0 0
$$586$$ −2.85560 4.94604i −0.117964 0.204319i
$$587$$ −3.58942 6.21706i −0.148151 0.256606i 0.782393 0.622785i $$-0.213999\pi$$
−0.930544 + 0.366180i $$0.880666\pi$$
$$588$$ −53.1829 −2.19323
$$589$$ 15.4289 + 25.3808i 0.635738 + 1.04580i
$$590$$ 0 0
$$591$$ 27.3808 + 47.4250i 1.12630 + 1.95080i
$$592$$ −5.01448 8.68533i −0.206094 0.356965i
$$593$$ −18.3743 + 31.8253i −0.754543 + 1.30691i 0.191058 + 0.981579i $$0.438808\pi$$
−0.945601 + 0.325328i $$0.894525\pi$$
$$594$$ −22.4277 38.8459i −0.920219 1.59387i
$$595$$ 0 0
$$596$$ 8.72413 0.357354
$$597$$ 66.8107 2.73438
$$598$$ −21.6174 + 37.4425i −0.884002 + 1.53114i
$$599$$ 0.926876 1.60540i 0.0378711 0.0655947i −0.846469 0.532439i $$-0.821276\pi$$
0.884340 + 0.466844i $$0.154609\pi$$
$$600$$ 0 0
$$601$$ −38.1633 −1.55671 −0.778356 0.627823i $$-0.783946\pi$$
−0.778356 + 0.627823i $$0.783946\pi$$
$$602$$ −2.79899 + 4.84800i −0.114078 + 0.197590i
$$603$$ −12.2912 21.2890i −0.500536 0.866954i
$$604$$ 15.0671 26.0969i 0.613070 1.06187i
$$605$$ 0 0
$$606$$ −4.43755 7.68606i −0.180263 0.312225i
$$607$$ 7.44914 0.302351 0.151176 0.988507i $$-0.451694\pi$$
0.151176 + 0.988507i $$0.451694\pi$$
$$608$$ −33.0696 + 0.747755i −1.34115 + 0.0303255i
$$609$$ 12.3118 0.498901
$$610$$ 0 0
$$611$$ −8.78523 15.2165i −0.355412 0.615592i
$$612$$ 40.5238 70.1893i 1.63808 2.83723i
$$613$$ 10.6049 + 18.3682i 0.428326 + 0.741883i 0.996725 0.0808706i $$-0.0257700\pi$$
−0.568398 + 0.822754i $$0.692437\pi$$
$$614$$ 18.2560 31.6203i 0.736753 1.27609i
$$615$$ 0 0
$$616$$ 2.34980 0.0946760
$$617$$ 15.4076 26.6868i 0.620287 1.07437i −0.369145 0.929372i $$-0.620349\pi$$
0.989432 0.144997i $$-0.0463172\pi$$
$$618$$ −0.534164 + 0.925199i −0.0214872 + 0.0372170i
$$619$$ 7.32036 0.294230 0.147115 0.989119i $$-0.453001\pi$$
0.147115 + 0.989119i $$0.453001\pi$$
$$620$$ 0 0
$$621$$ −11.6205 + 20.1273i −0.466314 + 0.807680i
$$622$$ 19.8859 + 34.4434i 0.797352 + 1.38105i
$$623$$ −1.09937 + 1.90416i −0.0440452 + 0.0762885i
$$624$$ 21.0638 + 36.4836i 0.843228 + 1.46051i
$$625$$ 0 0
$$626$$ −51.0086 −2.03871
$$627$$ −15.9470 + 29.1222i −0.636862 + 1.16303i
$$628$$ 58.0638 2.31700
$$629$$ −12.6322 21.8797i −0.503680 0.872399i
$$630$$ 0 0
$$631$$ −2.25414 + 3.90429i −0.0897360 + 0.155427i −0.907399 0.420269i $$-0.861936\pi$$
0.817664 + 0.575696i $$0.195269\pi$$
$$632$$ −4.51953 7.82805i −0.179777 0.311383i
$$633$$ −18.3600 + 31.8005i −0.729746 + 1.26396i
$$634$$ −8.42762 −0.334704
$$635$$ 0 0
$$636$$ 38.3536 66.4305i 1.52082 2.63414i
$$637$$ 22.8315 39.5454i 0.904618 1.56685i
$$638$$ 39.4780 1.56295
$$639$$ −77.0928 −3.04975
$$640$$ 0 0
$$641$$ 8.48158 + 14.6905i 0.335002 + 0.580241i 0.983485 0.180988i $$-0.0579296\pi$$
−0.648483 + 0.761229i $$0.724596\pi$$
$$642$$ 14.4685 25.0602i 0.571026 0.989046i
$$643$$ −4.64306 8.04202i −0.183104 0.317146i 0.759832 0.650120i $$-0.225281\pi$$
−0.942936 + 0.332974i $$0.891948\pi$$
$$644$$ −2.32530 4.02753i −0.0916295 0.158707i
$$645$$ 0 0
$$646$$ −49.5132 + 1.11957i −1.94807 + 0.0440489i
$$647$$ 39.2779 1.54418 0.772088 0.635516i $$-0.219213\pi$$
0.772088 + 0.635516i $$0.219213\pi$$
$$648$$ −5.00567 8.67007i −0.196641 0.340593i
$$649$$ 3.77317 + 6.53533i 0.148110 + 0.256534i
$$650$$ 0 0
$$651$$ 5.95013 + 10.3059i 0.233204 + 0.403921i
$$652$$ −13.9702 + 24.1972i −0.547116 + 0.947634i
$$653$$ 26.5513 1.03903 0.519517 0.854460i $$-0.326112\pi$$
0.519517 + 0.854460i $$0.326112\pi$$
$$654$$ −68.6018 −2.68254
$$655$$ 0 0
$$656$$ 6.47246 11.2106i 0.252707 0.437702i
$$657$$ −48.1469 −1.87839
$$658$$ 3.28518 0.128069
$$659$$ −16.3143 + 28.2573i −0.635517 + 1.10075i 0.350889 + 0.936417i $$0.385880\pi$$
−0.986405 + 0.164330i $$0.947454\pi$$
$$660$$ 0 0
$$661$$ −3.13332 + 5.42707i −0.121872 + 0.211088i −0.920506 0.390729i $$-0.872223\pi$$
0.798634 + 0.601817i $$0.205556\pi$$
$$662$$ −3.53530 6.12332i −0.137403 0.237989i
$$663$$ 53.0629 + 91.9077i 2.06079 + 3.56940i
$$664$$ −6.18809 −0.240145
$$665$$ 0 0
$$666$$ −59.8297 −2.31836
$$667$$ −10.2274 17.7143i −0.396006 0.685902i
$$668$$ −8.81442 15.2670i −0.341040 0.590699i
$$669$$ 28.2983 49.0141i 1.09408 1.89499i
$$670$$ 0 0
$$671$$ −3.00844 + 5.21077i −0.116140 + 0.201160i
$$672$$ −13.2527 −0.511235
$$673$$ −7.39044 −0.284881 −0.142440 0.989803i $$-0.545495\pi$$
−0.142440 + 0.989803i $$0.545495\pi$$
$$674$$ 24.0850 41.7165i 0.927721 1.60686i
$$675$$ 0 0
$$676$$ 92.5238 3.55861
$$677$$ −20.2751 −0.779234 −0.389617 0.920977i $$-0.627393\pi$$
−0.389617 + 0.920977i $$0.627393\pi$$
$$678$$ −42.2994 + 73.2648i −1.62450 + 2.81372i
$$679$$ −0.747127 1.29406i −0.0286721 0.0496615i
$$680$$ 0 0
$$681$$ 39.1431 + 67.7978i 1.49997 + 2.59802i
$$682$$ 19.0791 + 33.0460i 0.730577 + 1.26540i
$$683$$ 24.6563 0.943448 0.471724 0.881746i $$-0.343632\pi$$
0.471724 + 0.881746i $$0.343632\pi$$
$$684$$ −32.4076 + 59.1822i −1.23914 + 2.26289i
$$685$$ 0 0
$$686$$ 8.76238 + 15.1769i 0.334549 + 0.579456i
$$687$$ 13.0034 + 22.5225i 0.496109 + 0.859286i
$$688$$ 4.53113 7.84815i 0.172748 0.299208i
$$689$$ 32.9306 + 57.0374i 1.25456 + 2.17295i
$$690$$ 0 0
$$691$$ −41.7299 −1.58748 −0.793739 0.608258i $$-0.791869\pi$$
−0.793739 + 0.608258i $$0.791869\pi$$
$$692$$ 16.9615 0.644781
$$693$$ −4.36131 + 7.55402i −0.165673 + 0.286953i
$$694$$ 3.24922 5.62782i 0.123339 0.213629i
$$695$$ 0 0
$$696$$ 32.0311 1.21414
$$697$$ 16.3051 28.2413i 0.617600 1.06971i
$$698$$ −16.4283 28.4546i −0.621819 1.07702i
$$699$$ 6.65991 11.5353i 0.251901 0.436305i
$$700$$ 0 0
$$701$$ 3.60840 + 6.24993i 0.136287 + 0.236057i 0.926089 0.377306i $$-0.123150\pi$$
−0.789801 + 0.613363i $$0.789816\pi$$
$$702$$ 119.361 4.50500
$$703$$ 10.9258 + 17.9730i 0.412073 + 0.677865i
$$704$$ −31.7686 −1.19732
$$705$$ 0 0
$$706$$ 37.3655 + 64.7190i 1.40627 + 2.43573i
$$707$$ −0.409836 + 0.709857i −0.0154135 + 0.0266969i
$$708$$ 11.6940 + 20.2546i 0.439487 + 0.761213i
$$709$$ 10.3172 17.8700i 0.387472 0.671122i −0.604636 0.796502i $$-0.706682\pi$$
0.992109 + 0.125380i $$0.0400149\pi$$
$$710$$ 0 0
$$711$$ 33.5536 1.25836
$$712$$ −2.86017 + 4.95396i −0.107189 + 0.185657i
$$713$$ 9.88549 17.1222i 0.370214 0.641230i
$$714$$ −19.8425 −0.742587
$$715$$ 0 0
$$716$$ −31.4131 + 54.4091i −1.17396 + 2.03336i
$$717$$ 11.5482 + 20.0021i 0.431275 + 0.746991i
$$718$$ −3.43232 + 5.94495i −0.128093 + 0.221864i
$$719$$ −0.748958 1.29723i −0.0279314 0.0483787i 0.851722 0.523994i $$-0.175559\pi$$
−0.879653 + 0.475616i $$0.842225\pi$$
$$720$$ 0 0
$$721$$ 0.0986670 0.00367455
$$722$$ 41.1895 1.86367i 1.53291 0.0693585i
$$723$$ 80.7024 3.00136
$$724$$ 4.33344 + 7.50574i 0.161051 + 0.278949i
$$725$$ 0 0
$$726$$ 13.9047 24.0837i 0.516052 0.893828i
$$727$$ 5.68222 + 9.84190i 0.210742 + 0.365016i 0.951947 0.306263i $$-0.0990787\pi$$
−0.741205 + 0.671279i $$0.765745\pi$$
$$728$$ −3.12643 + 5.41514i −0.115873 + 0.200698i
$$729$$ −33.7723 −1.25083
$$730$$ 0 0
$$731$$ 11.4146 19.7707i 0.422184 0.731244i
$$732$$ −9.32389 + 16.1494i −0.344621 + 0.596901i
$$733$$ 45.6910 1.68764 0.843818 0.536630i $$-0.180303\pi$$
0.843818 + 0.536630i $$0.180303\pi$$
$$734$$ 46.5570 1.71845
$$735$$ 0 0
$$736$$ 11.0090 + 19.0681i 0.405796 + 0.702859i
$$737$$ −5.55113 + 9.61484i −0.204479 + 0.354167i
$$738$$ −38.6127 66.8792i −1.42135 2.46186i
$$739$$ 1.78276 + 3.08783i 0.0655799 + 0.113588i 0.896951 0.442130i $$-0.145777\pi$$
−0.831371 + 0.555718i $$0.812444\pi$$
$$740$$ 0 0
$$741$$ −45.8947 75.4975i −1.68599 2.77347i
$$742$$ −12.3142 −0.452067
$$743$$ −21.2482 36.8030i −0.779522 1.35017i −0.932218 0.361898i $$-0.882129\pi$$
0.152696 0.988273i $$-0.451205\pi$$
$$744$$ 15.4802 + 26.8125i 0.567531 + 0.982992i
$$745$$ 0 0
$$746$$ 35.9786 + 62.3168i 1.31727 + 2.28158i
$$747$$ 11.4853 19.8932i 0.420226 0.727853i
$$748$$ −36.6039 −1.33837
$$749$$ −2.67252 −0.0976516
$$750$$ 0 0
$$751$$ 6.38588 11.0607i 0.233024 0.403610i −0.725672 0.688040i $$-0.758471\pi$$
0.958697 + 0.284431i $$0.0918045\pi$$
$$752$$ −5.31818 −0.193934
$$753$$ −47.9317 −1.74673
$$754$$ −52.5259 + 90.9775i −1.91288 + 3.31320i
$$755$$ 0 0
$$756$$ −6.41960 + 11.1191i −0.233478 + 0.404396i
$$757$$ 5.67306 + 9.82603i 0.206191 + 0.357133i 0.950512 0.310689i $$-0.100560\pi$$
−0.744321 + 0.667822i $$0.767227\pi$$
$$758$$ 15.3693 + 26.6203i 0.558237 + 0.966894i
$$759$$ 22.1007 0.802206
$$760$$ 0 0
$$761$$ −36.9214 −1.33840 −0.669199 0.743083i $$-0.733363\pi$$
−0.669199 + 0.743083i $$0.733363\pi$$
$$762$$ −5.51417 9.55082i −0.199757 0.345990i
$$763$$ 3.16791 + 5.48698i 0.114686 + 0.198642i
$$764$$ −25.6627 + 44.4491i −0.928444 + 1.60811i
$$765$$ 0 0
$$766$$ −11.7410 + 20.3359i −0.424218 + 0.734767i
$$767$$ −20.0810 −0.725083
$$768$$ −1.23551 −0.0445827
$$769$$ −14.2528 + 24.6866i −0.513971 + 0.890223i 0.485898 + 0.874015i $$0.338493\pi$$
−0.999869 + 0.0162076i $$0.994841\pi$$
$$770$$ 0 0
$$771$$ −26.9904 −0.972036
$$772$$ −2.79201 −0.100487
$$773$$ 7.60956 13.1801i 0.273697 0.474057i −0.696109 0.717936i $$-0.745087\pi$$
0.969805 + 0.243880i $$0.0784202\pi$$
$$774$$ −27.0314 46.8197i −0.971622 1.68290i
$$775$$ 0 0
$$776$$ −1.94376 3.36670i −0.0697770 0.120857i
$$777$$ 4.21350 + 7.29799i 0.151158 + 0.261814i
$$778$$