# Properties

 Label 475.2.e.f.201.4 Level $475$ Weight $2$ Character 475.201 Analytic conductor $3.793$ Analytic rank $0$ Dimension $12$ 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: $$x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} + \cdots + 1$$ 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 201.4 Root $$1.62208 + 2.80952i$$ of defining polynomial Character $$\chi$$ $$=$$ 475.201 Dual form 475.2.e.f.26.4

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.155554 + 0.269427i) q^{2} +(1.12208 - 1.94349i) q^{3} +(0.951606 + 1.64823i) q^{4} +(0.349087 + 0.604636i) q^{6} +3.96928 q^{7} -1.21432 q^{8} +(-1.01811 - 1.76343i) q^{9} +O(q^{10})$$ $$q+(-0.155554 + 0.269427i) q^{2} +(1.12208 - 1.94349i) q^{3} +(0.951606 + 1.64823i) q^{4} +(0.349087 + 0.604636i) q^{6} +3.96928 q^{7} -1.21432 q^{8} +(-1.01811 - 1.76343i) q^{9} +0.361495 q^{11} +4.27110 q^{12} +(-1.25807 - 2.17905i) q^{13} +(-0.617436 + 1.06943i) q^{14} +(-1.71432 + 2.96929i) q^{16} +(-0.00464089 + 0.00803826i) q^{17} +0.633487 q^{18} +(-3.45680 + 2.65529i) q^{19} +(4.45383 - 7.71427i) q^{21} +(-0.0562320 + 0.0973967i) q^{22} +(2.70404 + 4.68354i) q^{23} +(-1.36256 + 2.36002i) q^{24} +0.782793 q^{26} +2.16285 q^{27} +(3.77719 + 6.54228i) q^{28} +(-4.72735 - 8.18801i) q^{29} +3.66745 q^{31} +(-1.74766 - 3.02703i) q^{32} +(0.405626 - 0.702564i) q^{33} +(-0.00144382 - 0.00250076i) q^{34} +(1.93769 - 3.35617i) q^{36} +0.0596692 q^{37} +(-0.177689 - 1.34440i) q^{38} -5.64662 q^{39} +(-1.85906 + 3.21998i) q^{41} +(1.38562 + 2.39997i) q^{42} +(2.10671 - 3.64894i) q^{43} +(0.344001 + 0.595827i) q^{44} -1.68250 q^{46} +(-6.45659 - 11.1831i) q^{47} +(3.84720 + 6.66354i) q^{48} +8.75515 q^{49} +(0.0104149 + 0.0180391i) q^{51} +(2.39438 - 4.14719i) q^{52} +(-5.48564 - 9.50140i) q^{53} +(-0.336440 + 0.582731i) q^{54} -4.81997 q^{56} +(1.28175 + 9.69770i) q^{57} +2.94143 q^{58} +(2.65944 - 4.60629i) q^{59} +(4.44875 + 7.70546i) q^{61} +(-0.570486 + 0.988111i) q^{62} +(-4.04118 - 6.99952i) q^{63} -5.76986 q^{64} +(0.126193 + 0.218573i) q^{66} +(2.32498 + 4.02699i) q^{67} -0.0176652 q^{68} +12.1366 q^{69} +(-7.68968 + 13.3189i) q^{71} +(1.23632 + 2.14136i) q^{72} +(-4.83162 + 8.36861i) q^{73} +(-0.00928178 + 0.0160765i) q^{74} +(-7.66603 - 3.17081i) q^{76} +1.43487 q^{77} +(0.878354 - 1.52135i) q^{78} +(-6.70596 + 11.6151i) q^{79} +(5.48123 - 9.49377i) q^{81} +(-0.578367 - 1.00176i) q^{82} -15.5409 q^{83} +16.9532 q^{84} +(0.655415 + 1.13521i) q^{86} -21.2178 q^{87} -0.438971 q^{88} +(2.08578 + 3.61267i) q^{89} +(-4.99364 - 8.64923i) q^{91} +(-5.14637 + 8.91377i) q^{92} +(4.11516 - 7.12767i) q^{93} +4.01739 q^{94} -7.84403 q^{96} +(1.87094 - 3.24056i) q^{97} +(-1.36190 + 2.35888i) q^{98} +(-0.368044 - 0.637470i) 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 $$\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.155554 + 0.269427i −0.109993 + 0.190514i −0.915767 0.401709i $$-0.868416\pi$$
0.805774 + 0.592223i $$0.201750\pi$$
$$3$$ 1.12208 1.94349i 0.647832 1.12208i −0.335808 0.941930i $$-0.609009\pi$$
0.983640 0.180147i $$-0.0576573\pi$$
$$4$$ 0.951606 + 1.64823i 0.475803 + 0.824115i
$$5$$ 0 0
$$6$$ 0.349087 + 0.604636i 0.142514 + 0.246842i
$$7$$ 3.96928 1.50025 0.750123 0.661299i $$-0.229994\pi$$
0.750123 + 0.661299i $$0.229994\pi$$
$$8$$ −1.21432 −0.429327
$$9$$ −1.01811 1.76343i −0.339371 0.587809i
$$10$$ 0 0
$$11$$ 0.361495 0.108995 0.0544975 0.998514i $$-0.482644\pi$$
0.0544975 + 0.998514i $$0.482644\pi$$
$$12$$ 4.27110 1.23296
$$13$$ −1.25807 2.17905i −0.348927 0.604359i 0.637132 0.770754i $$-0.280120\pi$$
−0.986059 + 0.166396i $$0.946787\pi$$
$$14$$ −0.617436 + 1.06943i −0.165017 + 0.285817i
$$15$$ 0 0
$$16$$ −1.71432 + 2.96929i −0.428580 + 0.742322i
$$17$$ −0.00464089 + 0.00803826i −0.00112558 + 0.00194956i −0.866588 0.499025i $$-0.833692\pi$$
0.865462 + 0.500974i $$0.167025\pi$$
$$18$$ 0.633487 0.149314
$$19$$ −3.45680 + 2.65529i −0.793043 + 0.609165i
$$20$$ 0 0
$$21$$ 4.45383 7.71427i 0.971906 1.68339i
$$22$$ −0.0562320 + 0.0973967i −0.0119887 + 0.0207650i
$$23$$ 2.70404 + 4.68354i 0.563832 + 0.976586i 0.997157 + 0.0753481i $$0.0240068\pi$$
−0.433325 + 0.901238i $$0.642660\pi$$
$$24$$ −1.36256 + 2.36002i −0.278131 + 0.481738i
$$25$$ 0 0
$$26$$ 0.782793 0.153518
$$27$$ 2.16285 0.416241
$$28$$ 3.77719 + 6.54228i 0.713821 + 1.23637i
$$29$$ −4.72735 8.18801i −0.877847 1.52047i −0.853699 0.520766i $$-0.825646\pi$$
−0.0241473 0.999708i $$-0.507687\pi$$
$$30$$ 0 0
$$31$$ 3.66745 0.658693 0.329347 0.944209i $$-0.393172\pi$$
0.329347 + 0.944209i $$0.393172\pi$$
$$32$$ −1.74766 3.02703i −0.308945 0.535109i
$$33$$ 0.405626 0.702564i 0.0706103 0.122301i
$$34$$ −0.00144382 0.00250076i −0.000247613 0.000428878i
$$35$$ 0 0
$$36$$ 1.93769 3.35617i 0.322948 0.559362i
$$37$$ 0.0596692 0.00980956 0.00490478 0.999988i $$-0.498439\pi$$
0.00490478 + 0.999988i $$0.498439\pi$$
$$38$$ −0.177689 1.34440i −0.0288250 0.218090i
$$39$$ −5.64662 −0.904183
$$40$$ 0 0
$$41$$ −1.85906 + 3.21998i −0.290336 + 0.502877i −0.973889 0.227024i $$-0.927100\pi$$
0.683553 + 0.729901i $$0.260434\pi$$
$$42$$ 1.38562 + 2.39997i 0.213806 + 0.370323i
$$43$$ 2.10671 3.64894i 0.321271 0.556458i −0.659480 0.751722i $$-0.729223\pi$$
0.980751 + 0.195265i $$0.0625566\pi$$
$$44$$ 0.344001 + 0.595827i 0.0518601 + 0.0898243i
$$45$$ 0 0
$$46$$ −1.68250 −0.248071
$$47$$ −6.45659 11.1831i −0.941790 1.63123i −0.762055 0.647513i $$-0.775809\pi$$
−0.179735 0.983715i $$-0.557524\pi$$
$$48$$ 3.84720 + 6.66354i 0.555295 + 0.961800i
$$49$$ 8.75515 1.25074
$$50$$ 0 0
$$51$$ 0.0104149 + 0.0180391i 0.00145837 + 0.00252598i
$$52$$ 2.39438 4.14719i 0.332041 0.575111i
$$53$$ −5.48564 9.50140i −0.753510 1.30512i −0.946112 0.323841i $$-0.895026\pi$$
0.192601 0.981277i $$-0.438308\pi$$
$$54$$ −0.336440 + 0.582731i −0.0457837 + 0.0792997i
$$55$$ 0 0
$$56$$ −4.81997 −0.644095
$$57$$ 1.28175 + 9.69770i 0.169772 + 1.28449i
$$58$$ 2.94143 0.386229
$$59$$ 2.65944 4.60629i 0.346230 0.599688i −0.639346 0.768919i $$-0.720795\pi$$
0.985576 + 0.169231i $$0.0541283\pi$$
$$60$$ 0 0
$$61$$ 4.44875 + 7.70546i 0.569604 + 0.986583i 0.996605 + 0.0823316i $$0.0262366\pi$$
−0.427001 + 0.904251i $$0.640430\pi$$
$$62$$ −0.570486 + 0.988111i −0.0724518 + 0.125490i
$$63$$ −4.04118 6.99952i −0.509140 0.881857i
$$64$$ −5.76986 −0.721232
$$65$$ 0 0
$$66$$ 0.126193 + 0.218573i 0.0155333 + 0.0269045i
$$67$$ 2.32498 + 4.02699i 0.284042 + 0.491975i 0.972376 0.233418i $$-0.0749912\pi$$
−0.688334 + 0.725393i $$0.741658\pi$$
$$68$$ −0.0176652 −0.00214222
$$69$$ 12.1366 1.46107
$$70$$ 0 0
$$71$$ −7.68968 + 13.3189i −0.912597 + 1.58066i −0.102215 + 0.994762i $$0.532593\pi$$
−0.810382 + 0.585902i $$0.800740\pi$$
$$72$$ 1.23632 + 2.14136i 0.145701 + 0.252362i
$$73$$ −4.83162 + 8.36861i −0.565498 + 0.979471i 0.431505 + 0.902110i $$0.357983\pi$$
−0.997003 + 0.0773609i $$0.975351\pi$$
$$74$$ −0.00928178 + 0.0160765i −0.00107898 + 0.00186886i
$$75$$ 0 0
$$76$$ −7.66603 3.17081i −0.879354 0.363716i
$$77$$ 1.43487 0.163519
$$78$$ 0.878354 1.52135i 0.0994540 0.172259i
$$79$$ −6.70596 + 11.6151i −0.754480 + 1.30680i 0.191153 + 0.981560i $$0.438777\pi$$
−0.945632 + 0.325237i $$0.894556\pi$$
$$80$$ 0 0
$$81$$ 5.48123 9.49377i 0.609025 1.05486i
$$82$$ −0.578367 1.00176i −0.0638700 0.110626i
$$83$$ −15.5409 −1.70583 −0.852916 0.522048i $$-0.825168\pi$$
−0.852916 + 0.522048i $$0.825168\pi$$
$$84$$ 16.9532 1.84974
$$85$$ 0 0
$$86$$ 0.655415 + 1.13521i 0.0706753 + 0.122413i
$$87$$ −21.2178 −2.27479
$$88$$ −0.438971 −0.0467944
$$89$$ 2.08578 + 3.61267i 0.221092 + 0.382942i 0.955140 0.296155i $$-0.0957046\pi$$
−0.734048 + 0.679098i $$0.762371\pi$$
$$90$$ 0 0
$$91$$ −4.99364 8.64923i −0.523475 0.906686i
$$92$$ −5.14637 + 8.91377i −0.536546 + 0.929325i
$$93$$ 4.11516 7.12767i 0.426722 0.739105i
$$94$$ 4.01739 0.414362
$$95$$ 0 0
$$96$$ −7.84403 −0.800578
$$97$$ 1.87094 3.24056i 0.189965 0.329029i −0.755273 0.655410i $$-0.772496\pi$$
0.945238 + 0.326381i $$0.105829\pi$$
$$98$$ −1.36190 + 2.35888i −0.137572 + 0.238282i
$$99$$ −0.368044 0.637470i −0.0369898 0.0640682i
$$100$$ 0 0
$$101$$ 8.61953 + 14.9295i 0.857675 + 1.48554i 0.874141 + 0.485672i $$0.161425\pi$$
−0.0164664 + 0.999864i $$0.505242\pi$$
$$102$$ −0.00648030 −0.000641645
$$103$$ 8.81660 0.868725 0.434362 0.900738i $$-0.356974\pi$$
0.434362 + 0.900738i $$0.356974\pi$$
$$104$$ 1.52770 + 2.64606i 0.149804 + 0.259467i
$$105$$ 0 0
$$106$$ 3.41325 0.331524
$$107$$ −1.30581 −0.126238 −0.0631188 0.998006i $$-0.520105\pi$$
−0.0631188 + 0.998006i $$0.520105\pi$$
$$108$$ 2.05818 + 3.56488i 0.198049 + 0.343030i
$$109$$ 3.04839 5.27997i 0.291983 0.505730i −0.682295 0.731077i $$-0.739018\pi$$
0.974279 + 0.225347i $$0.0723515\pi$$
$$110$$ 0 0
$$111$$ 0.0669535 0.115967i 0.00635494 0.0110071i
$$112$$ −6.80461 + 11.7859i −0.642975 + 1.11367i
$$113$$ −11.2382 −1.05720 −0.528599 0.848872i $$-0.677282\pi$$
−0.528599 + 0.848872i $$0.677282\pi$$
$$114$$ −2.81221 1.16318i −0.263387 0.108942i
$$115$$ 0 0
$$116$$ 8.99715 15.5835i 0.835364 1.44689i
$$117$$ −2.56172 + 4.43704i −0.236831 + 0.410204i
$$118$$ 0.827374 + 1.43305i 0.0761659 + 0.131923i
$$119$$ −0.0184210 + 0.0319061i −0.00168865 + 0.00292482i
$$120$$ 0 0
$$121$$ −10.8693 −0.988120
$$122$$ −2.76808 −0.250610
$$123$$ 4.17201 + 7.22613i 0.376178 + 0.651559i
$$124$$ 3.48997 + 6.04480i 0.313408 + 0.542839i
$$125$$ 0 0
$$126$$ 2.51448 0.224008
$$127$$ −5.92682 10.2656i −0.525921 0.910921i −0.999544 0.0301937i $$-0.990388\pi$$
0.473624 0.880727i $$-0.342946\pi$$
$$128$$ 4.39284 7.60862i 0.388276 0.672514i
$$129$$ −4.72779 8.18878i −0.416259 0.720982i
$$130$$ 0 0
$$131$$ 1.20298 2.08362i 0.105105 0.182047i −0.808676 0.588254i $$-0.799816\pi$$
0.913781 + 0.406207i $$0.133149\pi$$
$$132$$ 1.54398 0.134386
$$133$$ −13.7210 + 10.5396i −1.18976 + 0.913897i
$$134$$ −1.44664 −0.124971
$$135$$ 0 0
$$136$$ 0.00563552 0.00976101i 0.000483242 0.000837000i
$$137$$ −2.50867 4.34514i −0.214330 0.371230i 0.738735 0.673996i $$-0.235423\pi$$
−0.953065 + 0.302765i $$0.902090\pi$$
$$138$$ −1.88789 + 3.26993i −0.160708 + 0.278355i
$$139$$ −5.84248 10.1195i −0.495553 0.858323i 0.504434 0.863450i $$-0.331701\pi$$
−0.999987 + 0.00512757i $$0.998368\pi$$
$$140$$ 0 0
$$141$$ −28.9791 −2.44048
$$142$$ −2.39232 4.14362i −0.200759 0.347725i
$$143$$ −0.454787 0.787715i −0.0380312 0.0658720i
$$144$$ 6.98149 0.581791
$$145$$ 0 0
$$146$$ −1.50315 2.60354i −0.124402 0.215470i
$$147$$ 9.82395 17.0156i 0.810266 1.40342i
$$148$$ 0.0567816 + 0.0983486i 0.00466742 + 0.00808420i
$$149$$ 3.13033 5.42188i 0.256446 0.444178i −0.708841 0.705368i $$-0.750782\pi$$
0.965287 + 0.261190i $$0.0841150\pi$$
$$150$$ 0 0
$$151$$ −15.3436 −1.24864 −0.624322 0.781167i $$-0.714625\pi$$
−0.624322 + 0.781167i $$0.714625\pi$$
$$152$$ 4.19766 3.22437i 0.340475 0.261531i
$$153$$ 0.0188998 0.00152796
$$154$$ −0.223200 + 0.386594i −0.0179860 + 0.0311527i
$$155$$ 0 0
$$156$$ −5.37336 9.30693i −0.430213 0.745151i
$$157$$ −7.50595 + 13.0007i −0.599040 + 1.03757i 0.393923 + 0.919143i $$0.371118\pi$$
−0.992963 + 0.118424i $$0.962216\pi$$
$$158$$ −2.08628 3.61354i −0.165975 0.287478i
$$159$$ −24.6212 −1.95259
$$160$$ 0 0
$$161$$ 10.7331 + 18.5903i 0.845886 + 1.46512i
$$162$$ 1.70525 + 2.95359i 0.133977 + 0.232056i
$$163$$ 11.8894 0.931250 0.465625 0.884982i $$-0.345830\pi$$
0.465625 + 0.884982i $$0.345830\pi$$
$$164$$ −7.07636 −0.552571
$$165$$ 0 0
$$166$$ 2.41744 4.18714i 0.187630 0.324985i
$$167$$ 3.61678 + 6.26445i 0.279875 + 0.484757i 0.971353 0.237640i $$-0.0763737\pi$$
−0.691479 + 0.722397i $$0.743040\pi$$
$$168$$ −5.40838 + 9.36758i −0.417265 + 0.722725i
$$169$$ 3.33451 5.77553i 0.256500 0.444272i
$$170$$ 0 0
$$171$$ 8.20182 + 3.39242i 0.627209 + 0.259425i
$$172$$ 8.01905 0.611447
$$173$$ −1.72229 + 2.98309i −0.130943 + 0.226800i −0.924040 0.382295i $$-0.875134\pi$$
0.793097 + 0.609095i $$0.208467\pi$$
$$174$$ 3.30051 5.71665i 0.250211 0.433378i
$$175$$ 0 0
$$176$$ −0.619718 + 1.07338i −0.0467130 + 0.0809094i
$$177$$ −5.96820 10.3372i −0.448597 0.776994i
$$178$$ −1.29780 −0.0972744
$$179$$ −5.87847 −0.439378 −0.219689 0.975570i $$-0.570504\pi$$
−0.219689 + 0.975570i $$0.570504\pi$$
$$180$$ 0 0
$$181$$ −0.552356 0.956709i −0.0410563 0.0711116i 0.844767 0.535134i $$-0.179739\pi$$
−0.885823 + 0.464023i $$0.846406\pi$$
$$182$$ 3.10712 0.230315
$$183$$ 19.9674 1.47603
$$184$$ −3.28357 5.68732i −0.242068 0.419274i
$$185$$ 0 0
$$186$$ 1.28026 + 2.21747i 0.0938731 + 0.162593i
$$187$$ −0.00167766 + 0.00290579i −0.000122683 + 0.000212493i
$$188$$ 12.2883 21.2839i 0.896213 1.55229i
$$189$$ 8.58495 0.624463
$$190$$ 0 0
$$191$$ 21.2415 1.53698 0.768491 0.639860i $$-0.221008\pi$$
0.768491 + 0.639860i $$0.221008\pi$$
$$192$$ −6.47423 + 11.2137i −0.467237 + 0.809278i
$$193$$ 4.77026 8.26233i 0.343371 0.594736i −0.641686 0.766968i $$-0.721765\pi$$
0.985056 + 0.172232i $$0.0550979\pi$$
$$194$$ 0.582064 + 1.00816i 0.0417897 + 0.0723820i
$$195$$ 0 0
$$196$$ 8.33145 + 14.4305i 0.595104 + 1.03075i
$$197$$ −2.05919 −0.146711 −0.0733556 0.997306i $$-0.523371\pi$$
−0.0733556 + 0.997306i $$0.523371\pi$$
$$198$$ 0.229002 0.0162745
$$199$$ 9.95070 + 17.2351i 0.705386 + 1.22176i 0.966552 + 0.256471i $$0.0825598\pi$$
−0.261166 + 0.965294i $$0.584107\pi$$
$$200$$ 0 0
$$201$$ 10.4352 0.736045
$$202$$ −5.36320 −0.377354
$$203$$ −18.7641 32.5005i −1.31698 2.28108i
$$204$$ −0.0198217 + 0.0343322i −0.00138780 + 0.00240374i
$$205$$ 0 0
$$206$$ −1.37146 + 2.37543i −0.0955539 + 0.165504i
$$207$$ 5.50605 9.53676i 0.382697 0.662851i
$$208$$ 8.62696 0.598172
$$209$$ −1.24962 + 0.959874i −0.0864377 + 0.0663959i
$$210$$ 0 0
$$211$$ 10.7586 18.6345i 0.740655 1.28285i −0.211542 0.977369i $$-0.567848\pi$$
0.952197 0.305484i $$-0.0988182\pi$$
$$212$$ 10.4403 18.0832i 0.717045 1.24196i
$$213$$ 17.2568 + 29.8897i 1.18242 + 2.04801i
$$214$$ 0.203124 0.351822i 0.0138853 0.0240500i
$$215$$ 0 0
$$216$$ −2.62639 −0.178703
$$217$$ 14.5571 0.988201
$$218$$ 0.948379 + 1.64264i 0.0642323 + 0.111254i
$$219$$ 10.8429 + 18.7804i 0.732695 + 1.26906i
$$220$$ 0 0
$$221$$ 0.0233543 0.00157098
$$222$$ 0.0208297 + 0.0360782i 0.00139800 + 0.00242141i
$$223$$ 2.76965 4.79718i 0.185470 0.321243i −0.758265 0.651946i $$-0.773953\pi$$
0.943735 + 0.330704i $$0.107286\pi$$
$$224$$ −6.93694 12.0151i −0.463494 0.802794i
$$225$$ 0 0
$$226$$ 1.74814 3.02787i 0.116285 0.201411i
$$227$$ 16.2401 1.07789 0.538947 0.842340i $$-0.318822\pi$$
0.538947 + 0.842340i $$0.318822\pi$$
$$228$$ −14.7643 + 11.3410i −0.977791 + 0.751077i
$$229$$ 10.5436 0.696739 0.348369 0.937357i $$-0.386736\pi$$
0.348369 + 0.937357i $$0.386736\pi$$
$$230$$ 0 0
$$231$$ 1.61004 2.78867i 0.105933 0.183481i
$$232$$ 5.74051 + 9.94286i 0.376883 + 0.652781i
$$233$$ −8.08922 + 14.0109i −0.529942 + 0.917887i 0.469447 + 0.882960i $$0.344453\pi$$
−0.999390 + 0.0349268i $$0.988880\pi$$
$$234$$ −0.796972 1.38040i −0.0520997 0.0902394i
$$235$$ 0 0
$$236$$ 10.1230 0.658949
$$237$$ 15.0492 + 26.0660i 0.977552 + 1.69317i
$$238$$ −0.00573091 0.00992622i −0.000371480 0.000643421i
$$239$$ −9.62683 −0.622708 −0.311354 0.950294i $$-0.600782\pi$$
−0.311354 + 0.950294i $$0.600782\pi$$
$$240$$ 0 0
$$241$$ 9.84997 + 17.0606i 0.634492 + 1.09897i 0.986622 + 0.163022i $$0.0521241\pi$$
−0.352130 + 0.935951i $$0.614543\pi$$
$$242$$ 1.69077 2.92849i 0.108687 0.188251i
$$243$$ −9.05645 15.6862i −0.580971 1.00627i
$$244$$ −8.46691 + 14.6651i −0.542038 + 0.938838i
$$245$$ 0 0
$$246$$ −2.59589 −0.165508
$$247$$ 10.1349 + 4.19197i 0.644868 + 0.266729i
$$248$$ −4.45346 −0.282795
$$249$$ −17.4381 + 30.2036i −1.10509 + 1.91408i
$$250$$ 0 0
$$251$$ −4.60240 7.97158i −0.290501 0.503162i 0.683428 0.730018i $$-0.260489\pi$$
−0.973928 + 0.226856i $$0.927155\pi$$
$$252$$ 7.69121 13.3216i 0.484501 0.839180i
$$253$$ 0.977499 + 1.69308i 0.0614548 + 0.106443i
$$254$$ 3.68776 0.231391
$$255$$ 0 0
$$256$$ −4.40321 7.62659i −0.275201 0.476662i
$$257$$ −0.229133 0.396869i −0.0142929 0.0247560i 0.858790 0.512327i $$-0.171216\pi$$
−0.873083 + 0.487571i $$0.837883\pi$$
$$258$$ 2.94171 0.183143
$$259$$ 0.236844 0.0147167
$$260$$ 0 0
$$261$$ −9.62596 + 16.6727i −0.595832 + 1.03201i
$$262$$ 0.374256 + 0.648230i 0.0231216 + 0.0400478i
$$263$$ 5.87774 10.1806i 0.362437 0.627760i −0.625924 0.779884i $$-0.715278\pi$$
0.988361 + 0.152124i $$0.0486114\pi$$
$$264$$ −0.492559 + 0.853137i −0.0303149 + 0.0525070i
$$265$$ 0 0
$$266$$ −0.705297 5.33628i −0.0432445 0.327188i
$$267$$ 9.36161 0.572921
$$268$$ −4.42494 + 7.66421i −0.270296 + 0.468166i
$$269$$ −2.38296 + 4.12742i −0.145292 + 0.251653i −0.929482 0.368868i $$-0.879745\pi$$
0.784190 + 0.620521i $$0.213079\pi$$
$$270$$ 0 0
$$271$$ 7.75620 13.4341i 0.471155 0.816065i −0.528300 0.849058i $$-0.677170\pi$$
0.999456 + 0.0329925i $$0.0105038\pi$$
$$272$$ −0.0159119 0.0275603i −0.000964803 0.00167109i
$$273$$ −22.4130 −1.35650
$$274$$ 1.56093 0.0942994
$$275$$ 0 0
$$276$$ 11.5492 + 20.0039i 0.695183 + 1.20409i
$$277$$ 4.90677 0.294819 0.147410 0.989076i $$-0.452906\pi$$
0.147410 + 0.989076i $$0.452906\pi$$
$$278$$ 3.63528 0.218030
$$279$$ −3.73388 6.46727i −0.223542 0.387186i
$$280$$ 0 0
$$281$$ −6.84266 11.8518i −0.408199 0.707021i 0.586489 0.809957i $$-0.300510\pi$$
−0.994688 + 0.102936i $$0.967176\pi$$
$$282$$ 4.50782 7.80777i 0.268437 0.464946i
$$283$$ −8.43386 + 14.6079i −0.501341 + 0.868348i 0.498658 + 0.866799i $$0.333826\pi$$
−0.999999 + 0.00154919i $$0.999507\pi$$
$$284$$ −29.2702 −1.73687
$$285$$ 0 0
$$286$$ 0.282976 0.0167327
$$287$$ −7.37911 + 12.7810i −0.435575 + 0.754438i
$$288$$ −3.55863 + 6.16373i −0.209694 + 0.363201i
$$289$$ 8.49996 + 14.7224i 0.499997 + 0.866021i
$$290$$ 0 0
$$291$$ −4.19868 7.27232i −0.246131 0.426311i
$$292$$ −18.3912 −1.07626
$$293$$ 25.8794 1.51189 0.755944 0.654636i $$-0.227178\pi$$
0.755944 + 0.654636i $$0.227178\pi$$
$$294$$ 3.05631 + 5.29368i 0.178247 + 0.308734i
$$295$$ 0 0
$$296$$ −0.0724575 −0.00421151
$$297$$ 0.781861 0.0453681
$$298$$ 0.973869 + 1.68679i 0.0564147 + 0.0977132i
$$299$$ 6.80377 11.7845i 0.393472 0.681514i
$$300$$ 0 0
$$301$$ 8.36213 14.4836i 0.481985 0.834823i
$$302$$ 2.38676 4.13398i 0.137342 0.237884i
$$303$$ 38.6871 2.22252
$$304$$ −1.95827 14.8162i −0.112314 0.849770i
$$305$$ 0 0
$$306$$ −0.00293994 + 0.00509213i −0.000168065 + 0.000291098i
$$307$$ 1.64721 2.85305i 0.0940111 0.162832i −0.815184 0.579202i $$-0.803364\pi$$
0.909195 + 0.416370i $$0.136698\pi$$
$$308$$ 1.36543 + 2.36500i 0.0778029 + 0.134759i
$$309$$ 9.89290 17.1350i 0.562787 0.974776i
$$310$$ 0 0
$$311$$ 30.4253 1.72526 0.862629 0.505837i $$-0.168816\pi$$
0.862629 + 0.505837i $$0.168816\pi$$
$$312$$ 6.85680 0.388190
$$313$$ −4.37696 7.58112i −0.247401 0.428510i 0.715403 0.698712i $$-0.246243\pi$$
−0.962804 + 0.270201i $$0.912910\pi$$
$$314$$ −2.33516 4.04461i −0.131781 0.228251i
$$315$$ 0 0
$$316$$ −25.5257 −1.43594
$$317$$ 4.18690 + 7.25192i 0.235160 + 0.407308i 0.959319 0.282324i $$-0.0911054\pi$$
−0.724159 + 0.689633i $$0.757772\pi$$
$$318$$ 3.82993 6.63363i 0.214772 0.371996i
$$319$$ −1.70891 2.95993i −0.0956808 0.165724i
$$320$$ 0 0
$$321$$ −1.46522 + 2.53784i −0.0817808 + 0.141648i
$$322$$ −6.67830 −0.372167
$$323$$ −0.00530128 0.0401095i −0.000294971 0.00223175i
$$324$$ 20.8639 1.15910
$$325$$ 0 0
$$326$$ −1.84944 + 3.20333i −0.102431 + 0.177416i
$$327$$ −6.84107 11.8491i −0.378312 0.655255i
$$328$$ 2.25749 3.91009i 0.124649 0.215898i
$$329$$ −25.6280 44.3889i −1.41292 2.44724i
$$330$$ 0 0
$$331$$ −17.8536 −0.981321 −0.490661 0.871351i $$-0.663245\pi$$
−0.490661 + 0.871351i $$0.663245\pi$$
$$332$$ −14.7888 25.6149i −0.811640 1.40580i
$$333$$ −0.0607501 0.105222i −0.00332908 0.00576614i
$$334$$ −2.25042 −0.123137
$$335$$ 0 0
$$336$$ 15.2706 + 26.4494i 0.833079 + 1.44293i
$$337$$ −5.04723 + 8.74205i −0.274940 + 0.476210i −0.970120 0.242626i $$-0.921991\pi$$
0.695180 + 0.718836i $$0.255325\pi$$
$$338$$ 1.03739 + 1.79681i 0.0564266 + 0.0977338i
$$339$$ −12.6101 + 21.8413i −0.684886 + 1.18626i
$$340$$ 0 0
$$341$$ 1.32577 0.0717942
$$342$$ −2.18983 + 1.68209i −0.118413 + 0.0909570i
$$343$$ 6.96666 0.376164
$$344$$ −2.55823 + 4.43098i −0.137930 + 0.238902i
$$345$$ 0 0
$$346$$ −0.535818 0.928063i −0.0288057 0.0498930i
$$347$$ −1.35145 + 2.34077i −0.0725494 + 0.125659i −0.900018 0.435853i $$-0.856447\pi$$
0.827469 + 0.561512i $$0.189780\pi$$
$$348$$ −20.1910 34.9718i −1.08235 1.87469i
$$349$$ −11.2187 −0.600524 −0.300262 0.953857i $$-0.597074\pi$$
−0.300262 + 0.953857i $$0.597074\pi$$
$$350$$ 0 0
$$351$$ −2.72102 4.71295i −0.145238 0.251559i
$$352$$ −0.631770 1.09426i −0.0336735 0.0583241i
$$353$$ 9.37058 0.498746 0.249373 0.968408i $$-0.419776\pi$$
0.249373 + 0.968408i $$0.419776\pi$$
$$354$$ 3.71351 0.197371
$$355$$ 0 0
$$356$$ −3.96967 + 6.87568i −0.210392 + 0.364410i
$$357$$ 0.0413395 + 0.0716021i 0.00218792 + 0.00378959i
$$358$$ 0.914419 1.58382i 0.0483286 0.0837075i
$$359$$ 10.7443 18.6097i 0.567064 0.982184i −0.429790 0.902929i $$-0.641413\pi$$
0.996854 0.0792550i $$-0.0252541\pi$$
$$360$$ 0 0
$$361$$ 4.89888 18.3576i 0.257836 0.966189i
$$362$$ 0.343685 0.0180637
$$363$$ −12.1962 + 21.1245i −0.640135 + 1.10875i
$$364$$ 9.50395 16.4613i 0.498142 0.862808i
$$365$$ 0 0
$$366$$ −3.10600 + 5.37975i −0.162353 + 0.281204i
$$367$$ −15.0567 26.0790i −0.785953 1.36131i −0.928428 0.371512i $$-0.878839\pi$$
0.142475 0.989798i $$-0.454494\pi$$
$$368$$ −18.5424 −0.966588
$$369$$ 7.57093 0.394127
$$370$$ 0 0
$$371$$ −21.7740 37.7137i −1.13045 1.95800i
$$372$$ 15.6640 0.812143
$$373$$ 26.7206 1.38354 0.691769 0.722119i $$-0.256831\pi$$
0.691769 + 0.722119i $$0.256831\pi$$
$$374$$ −0.000521933 0 0.000904015i −2.69885e−5 0 4.67455e-5i
$$375$$ 0 0
$$376$$ 7.84036 + 13.5799i 0.404336 + 0.700330i
$$377$$ −11.8947 + 20.6022i −0.612608 + 1.06107i
$$378$$ −1.33542 + 2.31302i −0.0686867 + 0.118969i
$$379$$ 22.9732 1.18005 0.590026 0.807384i $$-0.299117\pi$$
0.590026 + 0.807384i $$0.299117\pi$$
$$380$$ 0 0
$$381$$ −26.6014 −1.36283
$$382$$ −3.30420 + 5.72305i −0.169058 + 0.292816i
$$383$$ −14.5442 + 25.1913i −0.743174 + 1.28722i 0.207868 + 0.978157i $$0.433347\pi$$
−0.951043 + 0.309059i $$0.899986\pi$$
$$384$$ −9.85821 17.0749i −0.503075 0.871351i
$$385$$ 0 0
$$386$$ 1.48407 + 2.57048i 0.0755369 + 0.130834i
$$387$$ −8.57951 −0.436121
$$388$$ 7.12159 0.361544
$$389$$ −1.81882 3.15029i −0.0922178 0.159726i 0.816226 0.577732i $$-0.196062\pi$$
−0.908444 + 0.418006i $$0.862729\pi$$
$$390$$ 0 0
$$391$$ −0.0501967 −0.00253855
$$392$$ −10.6315 −0.536974
$$393$$ −2.69967 4.67596i −0.136180 0.235871i
$$394$$ 0.320315 0.554802i 0.0161372 0.0279505i
$$395$$ 0 0
$$396$$ 0.700465 1.21324i 0.0351997 0.0609676i
$$397$$ 6.96707 12.0673i 0.349667 0.605641i −0.636523 0.771258i $$-0.719628\pi$$
0.986190 + 0.165616i $$0.0529613\pi$$
$$398$$ −6.19148 −0.310351
$$399$$ 5.08761 + 38.4929i 0.254699 + 1.92705i
$$400$$ 0 0
$$401$$ −13.2751 + 22.9931i −0.662925 + 1.14822i 0.316918 + 0.948453i $$0.397352\pi$$
−0.979843 + 0.199767i $$0.935981\pi$$
$$402$$ −1.62324 + 2.81154i −0.0809600 + 0.140227i
$$403$$ −4.61392 7.99154i −0.229836 0.398087i
$$404$$ −16.4048 + 28.4139i −0.816168 + 1.41365i
$$405$$ 0 0
$$406$$ 11.6753 0.579438
$$407$$ 0.0215701 0.00106919
$$408$$ −0.0126470 0.0219052i −0.000626119 0.00108447i
$$409$$ −7.49800 12.9869i −0.370752 0.642162i 0.618929 0.785447i $$-0.287567\pi$$
−0.989681 + 0.143285i $$0.954234\pi$$
$$410$$ 0 0
$$411$$ −11.2597 −0.555399
$$412$$ 8.38993 + 14.5318i 0.413342 + 0.715929i
$$413$$ 10.5561 18.2836i 0.519430 0.899679i
$$414$$ 1.71298 + 2.96696i 0.0841881 + 0.145818i
$$415$$ 0 0
$$416$$ −4.39736 + 7.61646i −0.215598 + 0.373427i
$$417$$ −26.2229 −1.28414
$$418$$ −0.0642337 0.485993i −0.00314177 0.0237707i
$$419$$ 30.4528 1.48772 0.743859 0.668337i $$-0.232993\pi$$
0.743859 + 0.668337i $$0.232993\pi$$
$$420$$ 0 0
$$421$$ 0.444876 0.770547i 0.0216819 0.0375542i −0.854981 0.518660i $$-0.826431\pi$$
0.876663 + 0.481105i $$0.159765\pi$$
$$422$$ 3.34710 + 5.79734i 0.162934 + 0.282210i
$$423$$ −13.1471 + 22.7714i −0.639233 + 1.10718i
$$424$$ 6.66132 + 11.5377i 0.323502 + 0.560322i
$$425$$ 0 0
$$426$$ −10.7375 −0.520232
$$427$$ 17.6583 + 30.5851i 0.854545 + 1.48012i
$$428$$ −1.24262 2.15228i −0.0600643 0.104034i
$$429$$ −2.04123 −0.0985513
$$430$$ 0 0
$$431$$ −7.36739 12.7607i −0.354875 0.614661i 0.632222 0.774787i $$-0.282143\pi$$
−0.987097 + 0.160126i $$0.948810\pi$$
$$432$$ −3.70782 + 6.42213i −0.178393 + 0.308985i
$$433$$ −0.742440 1.28594i −0.0356794 0.0617985i 0.847634 0.530581i $$-0.178026\pi$$
−0.883314 + 0.468782i $$0.844693\pi$$
$$434$$ −2.26442 + 3.92208i −0.108695 + 0.188266i
$$435$$ 0 0
$$436$$ 11.6035 0.555706
$$437$$ −21.7835 9.01003i −1.04205 0.431008i
$$438$$ −6.74662 −0.322366
$$439$$ 7.34789 12.7269i 0.350696 0.607423i −0.635676 0.771956i $$-0.719278\pi$$
0.986372 + 0.164533i $$0.0526118\pi$$
$$440$$ 0 0
$$441$$ −8.91374 15.4391i −0.424464 0.735193i
$$442$$ −0.00363285 + 0.00629229i −0.000172797 + 0.000299294i
$$443$$ −9.32539 16.1520i −0.443062 0.767407i 0.554853 0.831949i $$-0.312775\pi$$
−0.997915 + 0.0645421i $$0.979441\pi$$
$$444$$ 0.254853 0.0120948
$$445$$ 0 0
$$446$$ 0.861660 + 1.49244i 0.0408008 + 0.0706690i
$$447$$ −7.02494 12.1675i −0.332268 0.575505i
$$448$$ −22.9022 −1.08203
$$449$$ 5.17365 0.244160 0.122080 0.992520i $$-0.461044\pi$$
0.122080 + 0.992520i $$0.461044\pi$$
$$450$$ 0 0
$$451$$ −0.672040 + 1.16401i −0.0316451 + 0.0548110i
$$452$$ −10.6943 18.5231i −0.503018 0.871252i
$$453$$ −17.2167 + 29.8202i −0.808911 + 1.40107i
$$454$$ −2.52621 + 4.37553i −0.118561 + 0.205354i
$$455$$ 0 0
$$456$$ −1.55645 11.7761i −0.0728875 0.551467i
$$457$$ −20.2319 −0.946409 −0.473204 0.880953i $$-0.656903\pi$$
−0.473204 + 0.880953i $$0.656903\pi$$
$$458$$ −1.64009 + 2.84072i −0.0766365 + 0.132738i
$$459$$ −0.0100376 + 0.0173856i −0.000468513 + 0.000811488i
$$460$$ 0 0
$$461$$ −15.1012 + 26.1561i −0.703334 + 1.21821i 0.263955 + 0.964535i $$0.414973\pi$$
−0.967289 + 0.253675i $$0.918361\pi$$
$$462$$ 0.500896 + 0.867577i 0.0233038 + 0.0403633i
$$463$$ −20.4060 −0.948345 −0.474173 0.880432i $$-0.657253\pi$$
−0.474173 + 0.880432i $$0.657253\pi$$
$$464$$ 32.4167 1.50491
$$465$$ 0 0
$$466$$ −2.51662 4.35891i −0.116580 0.201923i
$$467$$ 15.9143 0.736425 0.368212 0.929742i $$-0.379970\pi$$
0.368212 + 0.929742i $$0.379970\pi$$
$$468$$ −9.75101 −0.450741
$$469$$ 9.22850 + 15.9842i 0.426132 + 0.738083i
$$470$$ 0 0
$$471$$ 16.8445 + 29.1755i 0.776154 + 1.34434i
$$472$$ −3.22941 + 5.59351i −0.148646 + 0.257462i
$$473$$ 0.761567 1.31907i 0.0350169 0.0606511i
$$474$$ −9.36386 −0.430096
$$475$$ 0 0
$$476$$ −0.0701180 −0.00321385
$$477$$ −11.1700 + 19.3470i −0.511440 + 0.885839i
$$478$$ 1.49749 2.59373i 0.0684936 0.118634i
$$479$$ 18.6782 + 32.3515i 0.853428 + 1.47818i 0.878096 + 0.478484i $$0.158814\pi$$
−0.0246685 + 0.999696i $$0.507853\pi$$
$$480$$ 0 0
$$481$$ −0.0750682 0.130022i −0.00342282 0.00592849i
$$482$$ −6.12881 −0.279159
$$483$$ 48.1734 2.19197
$$484$$ −10.3433 17.9151i −0.470150 0.814325i
$$485$$ 0 0
$$486$$ 5.63506 0.255612
$$487$$ 39.0070 1.76757 0.883787 0.467889i $$-0.154985\pi$$
0.883787 + 0.467889i $$0.154985\pi$$
$$488$$ −5.40220 9.35689i −0.244546 0.423566i
$$489$$ 13.3408 23.1070i 0.603293 1.04493i
$$490$$ 0 0
$$491$$ 10.2673 17.7835i 0.463357 0.802557i −0.535769 0.844365i $$-0.679978\pi$$
0.999126 + 0.0418074i $$0.0133116\pi$$
$$492$$ −7.94022 + 13.7529i −0.357973 + 0.620027i
$$493$$ 0.0877564 0.00395235
$$494$$ −2.70595 + 2.07854i −0.121747 + 0.0935180i
$$495$$ 0 0
$$496$$ −6.28718 + 10.8897i −0.282303 + 0.488963i
$$497$$ −30.5225 + 52.8664i −1.36912 + 2.37138i
$$498$$ −5.42512 9.39658i −0.243105 0.421071i
$$499$$ −0.368486 + 0.638237i −0.0164957 + 0.0285714i −0.874155 0.485646i $$-0.838584\pi$$
0.857660 + 0.514218i $$0.171918\pi$$
$$500$$ 0 0
$$501$$ 16.2332 0.725247
$$502$$ 2.86368 0.127812
$$503$$ 4.99035 + 8.64354i 0.222509 + 0.385397i 0.955569 0.294767i $$-0.0952420\pi$$
−0.733060 + 0.680164i $$0.761909\pi$$
$$504$$ 4.90728 + 8.49966i 0.218588 + 0.378605i
$$505$$ 0 0
$$506$$ −0.608215 −0.0270385
$$507$$ −7.48314 12.9612i −0.332338 0.575626i
$$508$$ 11.2800 19.5375i 0.500469 0.866838i
$$509$$ 15.2505 + 26.4147i 0.675968 + 1.17081i 0.976185 + 0.216940i $$0.0696075\pi$$
−0.300217 + 0.953871i $$0.597059\pi$$
$$510$$ 0 0
$$511$$ −19.1780 + 33.2173i −0.848386 + 1.46945i
$$512$$ 20.3111 0.897633
$$513$$ −7.47654 + 5.74300i −0.330097 + 0.253559i
$$514$$ 0.142570 0.00628849
$$515$$ 0 0
$$516$$ 8.99799 15.5850i 0.396115 0.686090i
$$517$$ −2.33402 4.04265i −0.102650 0.177796i
$$518$$ −0.0368419 + 0.0638121i −0.00161874 + 0.00280374i
$$519$$ 3.86508 + 6.69452i 0.169658 + 0.293857i
$$520$$ 0 0
$$521$$ 23.5752 1.03285 0.516424 0.856333i $$-0.327263\pi$$
0.516424 + 0.856333i $$0.327263\pi$$
$$522$$ −2.99471 5.18699i −0.131075 0.227029i
$$523$$ 5.46896 + 9.47252i 0.239141 + 0.414204i 0.960468 0.278390i $$-0.0898009\pi$$
−0.721327 + 0.692595i $$0.756468\pi$$
$$524$$ 4.57904 0.200036
$$525$$ 0 0
$$526$$ 1.82861 + 3.16725i 0.0797313 + 0.138099i
$$527$$ −0.0170202 + 0.0294799i −0.000741413 + 0.00128416i
$$528$$ 1.39074 + 2.40884i 0.0605244 + 0.104831i
$$529$$ −3.12370 + 5.41041i −0.135813 + 0.235235i
$$530$$ 0 0
$$531$$ −10.8305 −0.470002
$$532$$ −30.4286 12.5858i −1.31925 0.545664i
$$533$$ 9.35532 0.405224
$$534$$ −1.45623 + 2.52227i −0.0630174 + 0.109149i
$$535$$ 0 0
$$536$$ −2.82327 4.89005i −0.121947 0.211218i
$$537$$ −6.59610 + 11.4248i −0.284643 + 0.493016i
$$538$$ −0.741359 1.28407i −0.0319623 0.0553603i
$$539$$ 3.16494 0.136324
$$540$$ 0 0
$$541$$ −14.7076 25.4743i −0.632328 1.09522i −0.987075 0.160261i $$-0.948766\pi$$
0.354747 0.934962i $$-0.384567\pi$$
$$542$$ 2.41301 + 4.17946i 0.103648 + 0.179523i
$$543$$ −2.47914 −0.106390
$$544$$ 0.0324428 0.00139097
$$545$$ 0 0
$$546$$ 3.48643 6.03867i 0.149205 0.258431i
$$547$$ −16.3667 28.3480i −0.699790 1.21207i −0.968539 0.248861i $$-0.919944\pi$$
0.268750 0.963210i $$-0.413390\pi$$
$$548$$ 4.77453 8.26973i 0.203958 0.353265i
$$549$$ 9.05867 15.6901i 0.386614 0.669636i
$$550$$ 0 0
$$551$$ 38.0830 + 15.7518i 1.62239 + 0.671049i
$$552$$ −14.7377 −0.627278
$$553$$ −26.6178 + 46.1034i −1.13190 + 1.96052i
$$554$$ −0.763267 + 1.32202i −0.0324281 + 0.0561671i
$$555$$ 0 0
$$556$$ 11.1195 19.2595i 0.471571 0.816785i
$$557$$ −4.74905 8.22560i −0.201224 0.348530i 0.747699 0.664038i $$-0.231159\pi$$
−0.948923 + 0.315508i $$0.897825\pi$$
$$558$$ 2.32328 0.0983523
$$559$$ −10.6016 −0.448400
$$560$$ 0 0
$$561$$ 0.00376493 + 0.00652105i 0.000158955 + 0.000275319i
$$562$$ 4.25761 0.179596
$$563$$ −33.1253 −1.39607 −0.698033 0.716065i $$-0.745941\pi$$
−0.698033 + 0.716065i $$0.745941\pi$$
$$564$$ −27.5767 47.7643i −1.16119 2.01124i
$$565$$ 0 0
$$566$$ −2.62384 4.54462i −0.110288 0.191025i
$$567$$ 21.7565 37.6834i 0.913687 1.58255i
$$568$$ 9.33773 16.1734i 0.391802 0.678622i
$$569$$ 26.5756 1.11411 0.557054 0.830476i $$-0.311932\pi$$
0.557054 + 0.830476i $$0.311932\pi$$
$$570$$ 0 0
$$571$$ −6.14212 −0.257040 −0.128520 0.991707i $$-0.541023\pi$$
−0.128520 + 0.991707i $$0.541023\pi$$
$$572$$ 0.865557 1.49919i 0.0361907 0.0626842i
$$573$$ 23.8346 41.2828i 0.995706 1.72461i
$$574$$ −2.29570 3.97627i −0.0958206 0.165966i
$$575$$ 0 0
$$576$$ 5.87438 + 10.1747i 0.244766 + 0.423947i
$$577$$ 11.1455 0.463992 0.231996 0.972717i $$-0.425474\pi$$
0.231996 + 0.972717i $$0.425474\pi$$
$$578$$ −5.28881 −0.219985
$$579$$ −10.7052 18.5420i −0.444893 0.770577i
$$580$$ 0 0
$$581$$ −61.6860 −2.55917
$$582$$ 2.61248 0.108291
$$583$$ −1.98303 3.43471i −0.0821288 0.142251i
$$584$$ 5.86713 10.1622i 0.242784 0.420513i
$$585$$ 0 0
$$586$$ −4.02564 + 6.97261i −0.166297 + 0.288036i
$$587$$ 10.8330 18.7633i 0.447126 0.774445i −0.551072 0.834458i $$-0.685781\pi$$
0.998198 + 0.0600130i $$0.0191142\pi$$
$$588$$ 37.3941 1.54211
$$589$$ −12.6776 + 9.73814i −0.522372 + 0.401253i
$$590$$ 0 0
$$591$$ −2.31057 + 4.00202i −0.0950441 + 0.164621i
$$592$$ −0.102292 + 0.177175i −0.00420418 + 0.00728185i
$$593$$ 12.1707 + 21.0803i 0.499791 + 0.865664i 1.00000 0.000240828i $$-7.66580e-5\pi$$
−0.500209 + 0.865905i $$0.666743\pi$$
$$594$$ −0.121621 + 0.210655i −0.00499019 + 0.00864326i
$$595$$ 0 0
$$596$$ 11.9153 0.488072
$$597$$ 44.6618 1.82789
$$598$$ 2.11671 + 3.66624i 0.0865585 + 0.149924i
$$599$$ 9.47682 + 16.4143i 0.387212 + 0.670672i 0.992073 0.125659i $$-0.0401046\pi$$
−0.604861 + 0.796331i $$0.706771\pi$$
$$600$$ 0 0
$$601$$ 4.40461 0.179668 0.0898339 0.995957i $$-0.471366\pi$$
0.0898339 + 0.995957i $$0.471366\pi$$
$$602$$ 2.60152 + 4.50597i 0.106030 + 0.183650i
$$603$$ 4.73420 8.19987i 0.192791 0.333925i
$$604$$ −14.6011 25.2898i −0.594108 1.02903i
$$605$$ 0 0
$$606$$ −6.01793 + 10.4234i −0.244462 + 0.423420i
$$607$$ 17.3015 0.702246 0.351123 0.936329i $$-0.385800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$608$$ 14.0789 + 5.82330i 0.570977 + 0.236166i
$$609$$ −84.2193 −3.41274
$$610$$ 0 0
$$611$$ −16.2457 + 28.1384i −0.657231 + 1.13836i
$$612$$ 0.0179852 + 0.0311513i 0.000727008 + 0.00125922i
$$613$$ −1.85860 + 3.21918i −0.0750680 + 0.130022i −0.901116 0.433578i $$-0.857251\pi$$
0.826048 + 0.563600i $$0.190584\pi$$
$$614$$ 0.512459 + 0.887606i 0.0206812 + 0.0358208i
$$615$$ 0 0
$$616$$ −1.74240 −0.0702031
$$617$$ 9.04453 + 15.6656i 0.364119 + 0.630673i 0.988634 0.150340i $$-0.0480368\pi$$
−0.624515 + 0.781013i $$0.714703\pi$$
$$618$$ 3.07776 + 5.33083i 0.123806 + 0.214438i
$$619$$ −40.6682 −1.63459 −0.817297 0.576216i $$-0.804529\pi$$
−0.817297 + 0.576216i $$0.804529\pi$$
$$620$$ 0 0
$$621$$ 5.84844 + 10.1298i 0.234690 + 0.406495i
$$622$$ −4.73277 + 8.19739i −0.189767 + 0.328686i
$$623$$ 8.27902 + 14.3397i 0.331692 + 0.574507i
$$624$$ 9.68011 16.7664i 0.387515 0.671195i
$$625$$ 0 0
$$626$$ 2.72342 0.108850
$$627$$ 0.463346 + 3.50567i 0.0185042 + 0.140003i
$$628$$ −28.5708 −1.14010
$$629$$ −0.000276918 0 0.000479637i −1.10415e−5 0 1.91244e-5i
$$630$$ 0 0
$$631$$ −8.14602 14.1093i −0.324288 0.561683i 0.657080 0.753821i $$-0.271791\pi$$
−0.981368 + 0.192138i $$0.938458\pi$$
$$632$$ 8.14318 14.1044i 0.323918 0.561043i
$$633$$ −24.1441 41.8187i −0.959640 1.66215i
$$634$$ −2.60515 −0.103464
$$635$$ 0 0
$$636$$ −23.4297 40.5814i −0.929048 1.60916i
$$637$$ −11.0146 19.0779i −0.436415 0.755893i
$$638$$ 1.06331 0.0420970
$$639$$ 31.3159 1.23884
$$640$$ 0 0
$$641$$ −5.03530 + 8.72139i −0.198882 + 0.344474i −0.948166 0.317775i $$-0.897064\pi$$
0.749284 + 0.662249i $$0.230398\pi$$
$$642$$ −0.455842 0.789542i −0.0179907 0.0311607i
$$643$$ 2.14765 3.71984i 0.0846950 0.146696i −0.820566 0.571552i $$-0.806342\pi$$
0.905261 + 0.424855i $$0.139675\pi$$
$$644$$ −20.4273 + 35.3812i −0.804950 + 1.39421i
$$645$$ 0 0
$$646$$ 0.0116312 + 0.00481088i 0.000457625 + 0.000189282i
$$647$$ −11.5451 −0.453884 −0.226942 0.973908i $$-0.572873\pi$$
−0.226942 + 0.973908i $$0.572873\pi$$
$$648$$ −6.65597 + 11.5285i −0.261471 + 0.452881i
$$649$$ 0.961376 1.66515i 0.0377373 0.0653629i
$$650$$ 0 0
$$651$$ 16.3342 28.2917i 0.640188 1.10884i
$$652$$ 11.3140 + 19.5965i 0.443092 + 0.767457i
$$653$$ 46.8302 1.83261 0.916304 0.400483i $$-0.131158\pi$$
0.916304 + 0.400483i $$0.131158\pi$$
$$654$$ 4.25662 0.166447
$$655$$ 0 0
$$656$$ −6.37404 11.0402i −0.248864 0.431046i
$$657$$ 19.6766 0.767656
$$658$$ 15.9461 0.621644
$$659$$ −22.0463 38.1854i −0.858803 1.48749i −0.873071 0.487593i $$-0.837875\pi$$
0.0142676 0.999898i $$-0.495458\pi$$
$$660$$ 0 0
$$661$$ 22.0688 + 38.2243i 0.858378 + 1.48675i 0.873475 + 0.486869i $$0.161861\pi$$
−0.0150971 + 0.999886i $$0.504806\pi$$
$$662$$ 2.77719 4.81024i 0.107939 0.186955i
$$663$$ 0.0262053 0.0453890i 0.00101773 0.00176276i
$$664$$ 18.8716 0.732360
$$665$$ 0 0
$$666$$ 0.0377997 0.00146471
$$667$$ 25.5659 44.2815i 0.989916 1.71458i
$$668$$ −6.88350 + 11.9226i −0.266331 + 0.461298i
$$669$$ −6.21552 10.7656i −0.240306 0.416222i
$$670$$ 0 0
$$671$$ 1.60820 + 2.78549i 0.0620839 + 0.107532i
$$672$$ −31.1351 −1.20106
$$673$$ 26.1730 1.00889 0.504447 0.863443i $$-0.331696\pi$$
0.504447 + 0.863443i $$0.331696\pi$$
$$674$$ −1.57023 2.71972i −0.0604831 0.104760i
$$675$$ 0 0
$$676$$ 12.6925 0.488175
$$677$$ −19.7693 −0.759796 −0.379898 0.925028i $$-0.624041\pi$$
−0.379898 + 0.925028i $$0.624041\pi$$
$$678$$ −3.92310 6.79500i −0.150666 0.260960i
$$679$$ 7.42627 12.8627i 0.284994 0.493624i
$$680$$ 0 0
$$681$$ 18.2227 31.5626i 0.698294 1.20948i
$$682$$ −0.206228 + 0.357197i −0.00789688 + 0.0136778i
$$683$$ −38.8945 −1.48826 −0.744128 0.668037i $$-0.767135\pi$$
−0.744128 + 0.668037i $$0.767135\pi$$
$$684$$ 2.21342 + 16.7467i 0.0846321 + 0.640327i
$$685$$ 0 0
$$686$$ −1.08369 + 1.87701i −0.0413755 + 0.0716645i
$$687$$ 11.8307 20.4914i 0.451369 0.781795i
$$688$$ 7.22317 + 12.5109i 0.275381 + 0.476973i
$$689$$ −13.8027 + 23.9069i −0.525840 + 0.910781i
$$690$$ 0 0
$$691$$ 22.6319 0.860959 0.430479 0.902600i $$-0.358345\pi$$
0.430479 + 0.902600i $$0.358345\pi$$
$$692$$ −6.55576 −0.249213
$$693$$ −1.46087 2.53029i −0.0554937 0.0961179i
$$694$$ −0.420445 0.728233i −0.0159599 0.0276433i
$$695$$ 0 0
$$696$$ 25.7652 0.976627
$$697$$ −0.0172554 0.0298872i −0.000653593 0.00113206i
$$698$$ 1.74511 3.02263i 0.0660535 0.114408i
$$699$$ 18.1535 + 31.4427i 0.686627 + 1.18927i
$$700$$ 0 0
$$701$$ 10.9167 18.9083i 0.412319 0.714158i −0.582824 0.812599i $$-0.698052\pi$$
0.995143 + 0.0984408i $$0.0313855\pi$$
$$702$$ 1.69306 0.0639006
$$703$$ −0.206264 + 0.158439i −0.00777941 + 0.00597564i
$$704$$ −2.08578 −0.0786107
$$705$$ 0 0
$$706$$ −1.45763 + 2.52469i −0.0548586 + 0.0950179i
$$707$$ 34.2133 + 59.2591i 1.28672 + 2.22867i
$$708$$ 11.3588 19.6739i 0.426888 0.739392i
$$709$$ 0.325939 + 0.564543i 0.0122409 + 0.0212019i 0.872081 0.489362i $$-0.162770\pi$$
−0.859840 + 0.510563i $$0.829437\pi$$
$$710$$ 0 0
$$711$$ 27.3098 1.02420
$$712$$ −2.53280 4.38694i −0.0949206 0.164407i
$$713$$ 9.91694 + 17.1766i 0.371392 + 0.643270i
$$714$$ −0.0257221 −0.000962625
$$715$$ 0 0
$$716$$ −5.59399 9.68907i −0.209057 0.362098i
$$717$$ −10.8020 + 18.7097i −0.403410 + 0.698726i
$$718$$ 3.34264 + 5.78963i 0.124746 + 0.216067i
$$719$$ 2.31346 4.00704i 0.0862777 0.149437i −0.819657 0.572854i $$-0.805836\pi$$
0.905935 + 0.423417i $$0.139169\pi$$
$$720$$ 0 0
$$721$$ 34.9955 1.30330
$$722$$ 4.18399 + 4.17549i 0.155712 + 0.155396i
$$723$$ 44.2097 1.64418
$$724$$ 1.05125 1.82082i 0.0390694 0.0676702i
$$725$$ 0 0
$$726$$ −3.79434 6.57199i −0.140821 0.243909i
$$727$$ −7.91445 + 13.7082i −0.293531 + 0.508410i −0.974642 0.223770i $$-0.928164\pi$$
0.681111 + 0.732180i $$0.261497\pi$$
$$728$$ 6.06387 + 10.5029i 0.224742 + 0.389265i
$$729$$ −7.76076 −0.287435
$$730$$ 0 0
$$731$$ 0.0195541 + 0.0338686i 0.000723233 + 0.00125268i
$$732$$ 19.0011 + 32.9108i 0.702299 + 1.21642i
$$733$$ −28.8257 −1.06470 −0.532350 0.846524i $$-0.678691\pi$$
−0.532350 + 0.846524i $$0.678691\pi$$
$$734$$ 9.36851 0.345798
$$735$$ 0 0
$$736$$ 9.45149 16.3705i 0.348386 0.603423i
$$737$$ 0.840470 + 1.45574i 0.0309591 + 0.0536228i
$$738$$ −1.17769 + 2.03981i −0.0433513 + 0.0750866i
$$739$$ −13.8458 + 23.9817i −0.509327 + 0.882180i 0.490614 + 0.871377i $$0.336772\pi$$
−0.999942 + 0.0108038i $$0.996561\pi$$
$$740$$ 0 0
$$741$$ 19.5192 14.9934i 0.717056 0.550797i
$$742$$ 13.5481 0.497367
$$743$$ −22.4228 + 38.8374i −0.822611 + 1.42480i 0.0811199 + 0.996704i $$0.474150\pi$$
−0.903731 + 0.428100i $$0.859183\pi$$
$$744$$ −4.99712 + 8.65527i −0.183203 + 0.317318i
$$745$$ 0 0
$$746$$ −4.15649 + 7.19925i −0.152180 + 0.263583i
$$747$$ 15.8224 + 27.4052i 0.578911 + 1.00270i
$$748$$ −0.00638588 −0.000233491
$$749$$ −5.18313 −0.189387
$$750$$ 0 0
$$751$$ 12.3257 + 21.3488i 0.449772 + 0.779029i 0.998371 0.0570573i $$-0.0181718\pi$$
−0.548599 + 0.836086i $$0.684838\pi$$
$$752$$ 44.2746 1.61453
$$753$$ −20.6570 −0.752782
$$754$$ −3.70053 6.40951i −0.134765 0.233421i
$$755$$ 0 0
$$756$$ 8.16949 + 14.1500i 0.297122 + 0.514630i
$$757$$ 23.1313 40.0646i 0.840721 1.45617i −0.0485649 0.998820i $$-0.515465\pi$$
0.889286 0.457352i $$-0.151202\pi$$
$$758$$ −3.57356 + 6.18960i −0.129798 + 0.224816i
$$759$$ 4.38732 0.159250
$$760$$ 0 0
$$761$$ −18.7036 −0.678004 −0.339002 0.940786i $$-0.610089\pi$$
−0.339002 + 0.940786i $$0.610089\pi$$
$$762$$ 4.13795 7.16715i 0.149902 0.259638i
$$763$$ 12.0999 20.9577i 0.438046 0.758719i
$$764$$ 20.2136 + 35.0109i 0.731301 + 1.26665i
$$765$$ 0 0
$$766$$ −4.52482 7.83721i −0.163488 0.283170i
$$767$$ −13.3831 −0.483235
$$768$$ −19.7630 −0.713135
$$769$$ 5.45393 + 9.44648i 0.196674 + 0.340649i 0.947448 0.319910i $$-0.103653\pi$$
−0.750774 + 0.660559i $$0.770319\pi$$
$$770$$ 0 0
$$771$$ −1.02842 −0.0370376
$$772$$ 18.1576 0.653508
$$773$$ 3.94152 + 6.82692i 0.141767 + 0.245547i 0.928162 0.372176i $$-0.121388\pi$$
−0.786395 + 0.617724i $$0.788055\pi$$
$$774$$ 1.33458 2.31155i 0.0479703 0.0830871i
$$775$$ 0 0
$$776$$ −2.27192 + 3.93508i −0.0815571 + 0.141261i
$$777$$ 0.265757 0.460304i 0.00953397 0.0165133i