# Properties

 Label 570.2.u.c.61.1 Level $570$ Weight $2$ Character 570.61 Analytic conductor $4.551$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 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("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.u (of order $$9$$, degree $$6$$, 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: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: $$\Q(\zeta_{18})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} - x^{3} + 1$$ x^6 - x^3 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

## Embedding invariants

 Embedding label 61.1 Root $$-0.173648 - 0.984808i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.61 Dual form 570.2.u.c.271.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-1.43969 + 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$$ $$q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-1.43969 + 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.939693 - 0.342020i) q^{10} +(0.266044 + 0.460802i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.673648 + 3.82045i) q^{13} +(-2.20574 + 1.85083i) q^{14} +(0.766044 + 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-0.673648 - 0.245188i) q^{17} -1.00000 q^{18} +(4.21688 + 1.10359i) q^{19} +1.00000 q^{20} +(-2.70574 - 0.984808i) q^{21} +(0.0923963 + 0.524005i) q^{22} +(1.20574 + 1.01173i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-1.93969 + 3.35965i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-2.70574 + 0.984808i) q^{28} +(2.91875 - 1.06234i) q^{29} +(0.500000 + 0.866025i) q^{30} +(2.41875 - 4.18939i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.407604 + 0.342020i) q^{33} +(-0.549163 - 0.460802i) q^{34} +(0.500000 + 2.83564i) q^{35} +(-0.939693 - 0.342020i) q^{36} -5.92127 q^{37} +(3.58512 + 2.47929i) q^{38} -3.87939 q^{39} +(0.939693 + 0.342020i) q^{40} +(-0.687319 - 3.89798i) q^{41} +(-2.20574 - 1.85083i) q^{42} +(-0.748970 + 0.628461i) q^{43} +(-0.0923963 + 0.524005i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(0.786989 + 1.36310i) q^{46} +(7.23783 - 2.63435i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(-0.645430 - 1.11792i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.124485 - 0.705990i) q^{51} +(-2.97178 + 2.49362i) q^{52} +(-2.07532 - 1.74140i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(0.500000 + 0.181985i) q^{55} -2.87939 q^{56} +(-0.354570 + 4.34445i) q^{57} +3.10607 q^{58} +(7.21688 + 2.62673i) q^{59} +(0.173648 + 0.984808i) q^{60} +(-11.1873 - 9.38728i) q^{61} +(3.70574 - 3.10948i) q^{62} +(0.500000 - 2.83564i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.93969 + 3.35965i) q^{65} +(-0.500000 + 0.181985i) q^{66} +(2.27972 - 0.829748i) q^{67} +(-0.358441 - 0.620838i) q^{68} +(-0.786989 + 1.36310i) q^{69} +(-0.500000 + 2.83564i) q^{70} +(6.16637 - 5.17420i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(-0.982926 - 5.57445i) q^{73} +(-5.56418 - 2.02520i) q^{74} +1.00000 q^{75} +(2.52094 + 3.55596i) q^{76} -1.53209 q^{77} +(-3.64543 - 1.32683i) q^{78} +(-0.254900 - 1.44561i) q^{79} +(0.766044 + 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(0.687319 - 3.89798i) q^{82} +(-1.85844 + 3.21891i) q^{83} +(-1.43969 - 2.49362i) q^{84} +(-0.673648 + 0.245188i) q^{85} +(-0.918748 + 0.334397i) q^{86} +(1.55303 + 2.68993i) q^{87} +(-0.266044 + 0.460802i) q^{88} +(-2.68479 + 15.2262i) q^{89} +(-0.766044 + 0.642788i) q^{90} +(-8.55690 - 7.18009i) q^{91} +(0.273318 + 1.55007i) q^{92} +(4.54576 + 1.65452i) q^{93} +7.70233 q^{94} +(3.93969 - 1.86516i) q^{95} -1.00000 q^{96} +(-12.4572 - 4.53406i) q^{97} +(-0.224155 - 1.27125i) q^{98} +(-0.407604 - 0.342020i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 3 q^{7} + 3 q^{8}+O(q^{10})$$ 6 * q - 3 * q^7 + 3 * q^8 $$6 q - 3 q^{7} + 3 q^{8} - 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 6 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} - 3 q^{22} - 3 q^{23} - 6 q^{26} - 3 q^{27} - 6 q^{28} + 15 q^{29} + 3 q^{30} + 12 q^{31} - 6 q^{33} - 15 q^{34} + 3 q^{35} - 18 q^{37} - 12 q^{39} + 18 q^{41} - 3 q^{42} + 21 q^{43} + 3 q^{44} - 3 q^{45} - 3 q^{46} + 24 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{51} - 3 q^{52} + 12 q^{53} + 3 q^{55} - 6 q^{56} - 18 q^{57} - 6 q^{58} + 27 q^{59} - 45 q^{61} + 12 q^{62} + 3 q^{63} - 3 q^{64} + 6 q^{65} - 3 q^{66} - 12 q^{67} + 6 q^{68} + 3 q^{69} - 3 q^{70} + 18 q^{71} + 15 q^{73} - 15 q^{74} + 6 q^{75} + 12 q^{76} - 6 q^{78} - 3 q^{79} - 18 q^{82} - 3 q^{83} - 3 q^{84} - 3 q^{85} - 3 q^{86} - 3 q^{87} + 3 q^{88} - 9 q^{89} - 15 q^{91} + 15 q^{92} - 3 q^{93} - 6 q^{94} + 18 q^{95} - 6 q^{96} - 24 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100})$$ 6 * q - 3 * q^7 + 3 * q^8 - 3 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 - 3 * q^17 - 6 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 - 3 * q^22 - 3 * q^23 - 6 * q^26 - 3 * q^27 - 6 * q^28 + 15 * q^29 + 3 * q^30 + 12 * q^31 - 6 * q^33 - 15 * q^34 + 3 * q^35 - 18 * q^37 - 12 * q^39 + 18 * q^41 - 3 * q^42 + 21 * q^43 + 3 * q^44 - 3 * q^45 - 3 * q^46 + 24 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^51 - 3 * q^52 + 12 * q^53 + 3 * q^55 - 6 * q^56 - 18 * q^57 - 6 * q^58 + 27 * q^59 - 45 * q^61 + 12 * q^62 + 3 * q^63 - 3 * q^64 + 6 * q^65 - 3 * q^66 - 12 * q^67 + 6 * q^68 + 3 * q^69 - 3 * q^70 + 18 * q^71 + 15 * q^73 - 15 * q^74 + 6 * q^75 + 12 * q^76 - 6 * q^78 - 3 * q^79 - 18 * q^82 - 3 * q^83 - 3 * q^84 - 3 * q^85 - 3 * q^86 - 3 * q^87 + 3 * q^88 - 9 * q^89 - 15 * q^91 + 15 * q^92 - 3 * q^93 - 6 * q^94 + 18 * q^95 - 6 * q^96 - 24 * q^97 - 3 * q^98 - 6 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.939693 + 0.342020i 0.664463 + 0.241845i
$$3$$ 0.173648 + 0.984808i 0.100256 + 0.568579i
$$4$$ 0.766044 + 0.642788i 0.383022 + 0.321394i
$$5$$ 0.766044 0.642788i 0.342585 0.287463i
$$6$$ −0.173648 + 0.984808i −0.0708916 + 0.402046i
$$7$$ −1.43969 + 2.49362i −0.544153 + 0.942500i 0.454507 + 0.890743i $$0.349815\pi$$
−0.998660 + 0.0517569i $$0.983518\pi$$
$$8$$ 0.500000 + 0.866025i 0.176777 + 0.306186i
$$9$$ −0.939693 + 0.342020i −0.313231 + 0.114007i
$$10$$ 0.939693 0.342020i 0.297157 0.108156i
$$11$$ 0.266044 + 0.460802i 0.0802154 + 0.138937i 0.903342 0.428920i $$-0.141106\pi$$
−0.823127 + 0.567857i $$0.807773\pi$$
$$12$$ −0.500000 + 0.866025i −0.144338 + 0.250000i
$$13$$ −0.673648 + 3.82045i −0.186836 + 1.05960i 0.736737 + 0.676180i $$0.236366\pi$$
−0.923573 + 0.383422i $$0.874745\pi$$
$$14$$ −2.20574 + 1.85083i −0.589508 + 0.494656i
$$15$$ 0.766044 + 0.642788i 0.197792 + 0.165967i
$$16$$ 0.173648 + 0.984808i 0.0434120 + 0.246202i
$$17$$ −0.673648 0.245188i −0.163384 0.0594668i 0.259033 0.965868i $$-0.416596\pi$$
−0.422417 + 0.906402i $$0.638818\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ 4.21688 + 1.10359i 0.967419 + 0.253181i
$$20$$ 1.00000 0.223607
$$21$$ −2.70574 0.984808i −0.590440 0.214903i
$$22$$ 0.0923963 + 0.524005i 0.0196989 + 0.111718i
$$23$$ 1.20574 + 1.01173i 0.251414 + 0.210961i 0.759781 0.650179i $$-0.225306\pi$$
−0.508367 + 0.861140i $$0.669751\pi$$
$$24$$ −0.766044 + 0.642788i −0.156368 + 0.131208i
$$25$$ 0.173648 0.984808i 0.0347296 0.196962i
$$26$$ −1.93969 + 3.35965i −0.380405 + 0.658881i
$$27$$ −0.500000 0.866025i −0.0962250 0.166667i
$$28$$ −2.70574 + 0.984808i −0.511336 + 0.186111i
$$29$$ 2.91875 1.06234i 0.541998 0.197271i −0.0564897 0.998403i $$-0.517991\pi$$
0.598488 + 0.801132i $$0.295769\pi$$
$$30$$ 0.500000 + 0.866025i 0.0912871 + 0.158114i
$$31$$ 2.41875 4.18939i 0.434420 0.752437i −0.562828 0.826574i $$-0.690287\pi$$
0.997248 + 0.0741365i $$0.0236200\pi$$
$$32$$ −0.173648 + 0.984808i −0.0306970 + 0.174091i
$$33$$ −0.407604 + 0.342020i −0.0709547 + 0.0595381i
$$34$$ −0.549163 0.460802i −0.0941807 0.0790270i
$$35$$ 0.500000 + 2.83564i 0.0845154 + 0.479311i
$$36$$ −0.939693 0.342020i −0.156615 0.0570034i
$$37$$ −5.92127 −0.973451 −0.486726 0.873555i $$-0.661809\pi$$
−0.486726 + 0.873555i $$0.661809\pi$$
$$38$$ 3.58512 + 2.47929i 0.581584 + 0.402195i
$$39$$ −3.87939 −0.621199
$$40$$ 0.939693 + 0.342020i 0.148578 + 0.0540781i
$$41$$ −0.687319 3.89798i −0.107341 0.608762i −0.990259 0.139235i $$-0.955536\pi$$
0.882918 0.469527i $$-0.155575\pi$$
$$42$$ −2.20574 1.85083i −0.340353 0.285590i
$$43$$ −0.748970 + 0.628461i −0.114217 + 0.0958394i −0.698107 0.715993i $$-0.745974\pi$$
0.583890 + 0.811832i $$0.301530\pi$$
$$44$$ −0.0923963 + 0.524005i −0.0139293 + 0.0789968i
$$45$$ −0.500000 + 0.866025i −0.0745356 + 0.129099i
$$46$$ 0.786989 + 1.36310i 0.116035 + 0.200979i
$$47$$ 7.23783 2.63435i 1.05575 0.384260i 0.244917 0.969544i $$-0.421239\pi$$
0.810828 + 0.585284i $$0.199017\pi$$
$$48$$ −0.939693 + 0.342020i −0.135633 + 0.0493664i
$$49$$ −0.645430 1.11792i −0.0922042 0.159702i
$$50$$ 0.500000 0.866025i 0.0707107 0.122474i
$$51$$ 0.124485 0.705990i 0.0174314 0.0988584i
$$52$$ −2.97178 + 2.49362i −0.412112 + 0.345803i
$$53$$ −2.07532 1.74140i −0.285067 0.239200i 0.489029 0.872267i $$-0.337351\pi$$
−0.774097 + 0.633067i $$0.781796\pi$$
$$54$$ −0.173648 0.984808i −0.0236305 0.134015i
$$55$$ 0.500000 + 0.181985i 0.0674200 + 0.0245389i
$$56$$ −2.87939 −0.384774
$$57$$ −0.354570 + 4.34445i −0.0469640 + 0.575437i
$$58$$ 3.10607 0.407847
$$59$$ 7.21688 + 2.62673i 0.939558 + 0.341971i 0.765991 0.642851i $$-0.222249\pi$$
0.173567 + 0.984822i $$0.444471\pi$$
$$60$$ 0.173648 + 0.984808i 0.0224179 + 0.127138i
$$61$$ −11.1873 9.38728i −1.43239 1.20192i −0.944284 0.329133i $$-0.893244\pi$$
−0.488106 0.872784i $$-0.662312\pi$$
$$62$$ 3.70574 3.10948i 0.470629 0.394905i
$$63$$ 0.500000 2.83564i 0.0629941 0.357257i
$$64$$ −0.500000 + 0.866025i −0.0625000 + 0.108253i
$$65$$ 1.93969 + 3.35965i 0.240589 + 0.416713i
$$66$$ −0.500000 + 0.181985i −0.0615457 + 0.0224008i
$$67$$ 2.27972 0.829748i 0.278512 0.101370i −0.198988 0.980002i $$-0.563765\pi$$
0.477499 + 0.878632i $$0.341543\pi$$
$$68$$ −0.358441 0.620838i −0.0434673 0.0752876i
$$69$$ −0.786989 + 1.36310i −0.0947423 + 0.164099i
$$70$$ −0.500000 + 2.83564i −0.0597614 + 0.338924i
$$71$$ 6.16637 5.17420i 0.731814 0.614065i −0.198812 0.980038i $$-0.563708\pi$$
0.930626 + 0.365973i $$0.119264\pi$$
$$72$$ −0.766044 0.642788i −0.0902792 0.0757532i
$$73$$ −0.982926 5.57445i −0.115043 0.652440i −0.986729 0.162376i $$-0.948084\pi$$
0.871686 0.490064i $$-0.163027\pi$$
$$74$$ −5.56418 2.02520i −0.646823 0.235424i
$$75$$ 1.00000 0.115470
$$76$$ 2.52094 + 3.55596i 0.289172 + 0.407896i
$$77$$ −1.53209 −0.174598
$$78$$ −3.64543 1.32683i −0.412764 0.150234i
$$79$$ −0.254900 1.44561i −0.0286785 0.162644i 0.967105 0.254377i $$-0.0818704\pi$$
−0.995784 + 0.0917332i $$0.970759\pi$$
$$80$$ 0.766044 + 0.642788i 0.0856464 + 0.0718658i
$$81$$ 0.766044 0.642788i 0.0851160 0.0714208i
$$82$$ 0.687319 3.89798i 0.0759017 0.430460i
$$83$$ −1.85844 + 3.21891i −0.203990 + 0.353322i −0.949811 0.312826i $$-0.898724\pi$$
0.745820 + 0.666147i $$0.232058\pi$$
$$84$$ −1.43969 2.49362i −0.157083 0.272076i
$$85$$ −0.673648 + 0.245188i −0.0730674 + 0.0265944i
$$86$$ −0.918748 + 0.334397i −0.0990712 + 0.0360590i
$$87$$ 1.55303 + 2.68993i 0.166503 + 0.288391i
$$88$$ −0.266044 + 0.460802i −0.0283604 + 0.0491217i
$$89$$ −2.68479 + 15.2262i −0.284587 + 1.61398i 0.422168 + 0.906518i $$0.361269\pi$$
−0.706755 + 0.707458i $$0.749842\pi$$
$$90$$ −0.766044 + 0.642788i −0.0807482 + 0.0677558i
$$91$$ −8.55690 7.18009i −0.897007 0.752678i
$$92$$ 0.273318 + 1.55007i 0.0284954 + 0.161606i
$$93$$ 4.54576 + 1.65452i 0.471373 + 0.171566i
$$94$$ 7.70233 0.794435
$$95$$ 3.93969 1.86516i 0.404204 0.191361i
$$96$$ −1.00000 −0.102062
$$97$$ −12.4572 4.53406i −1.26484 0.460364i −0.379450 0.925212i $$-0.623887\pi$$
−0.885390 + 0.464848i $$0.846109\pi$$
$$98$$ −0.224155 1.27125i −0.0226431 0.128415i
$$99$$ −0.407604 0.342020i −0.0409657 0.0343743i
$$100$$ 0.766044 0.642788i 0.0766044 0.0642788i
$$101$$ 2.55690 14.5009i 0.254421 1.44290i −0.543132 0.839647i $$-0.682762\pi$$
0.797553 0.603248i $$-0.206127\pi$$
$$102$$ 0.358441 0.620838i 0.0354909 0.0614721i
$$103$$ 5.36824 + 9.29807i 0.528948 + 0.916166i 0.999430 + 0.0337559i $$0.0107469\pi$$
−0.470482 + 0.882410i $$0.655920\pi$$
$$104$$ −3.64543 + 1.32683i −0.357464 + 0.130106i
$$105$$ −2.70574 + 0.984808i −0.264053 + 0.0961074i
$$106$$ −1.35457 2.34618i −0.131567 0.227882i
$$107$$ 7.85844 13.6112i 0.759704 1.31585i −0.183297 0.983058i $$-0.558677\pi$$
0.943001 0.332789i $$-0.107990\pi$$
$$108$$ 0.173648 0.984808i 0.0167093 0.0947632i
$$109$$ 10.3871 8.71583i 0.994906 0.834825i 0.00863564 0.999963i $$-0.497251\pi$$
0.986271 + 0.165137i $$0.0528067\pi$$
$$110$$ 0.407604 + 0.342020i 0.0388635 + 0.0326103i
$$111$$ −1.02822 5.83132i −0.0975942 0.553484i
$$112$$ −2.70574 0.984808i −0.255668 0.0930556i
$$113$$ 18.6655 1.75590 0.877951 0.478750i $$-0.158910\pi$$
0.877951 + 0.478750i $$0.158910\pi$$
$$114$$ −1.81908 + 3.96118i −0.170372 + 0.370999i
$$115$$ 1.57398 0.146774
$$116$$ 2.91875 + 1.06234i 0.270999 + 0.0986356i
$$117$$ −0.673648 3.82045i −0.0622788 0.353201i
$$118$$ 5.88326 + 4.93664i 0.541598 + 0.454454i
$$119$$ 1.58125 1.32683i 0.144953 0.121630i
$$120$$ −0.173648 + 0.984808i −0.0158518 + 0.0899002i
$$121$$ 5.35844 9.28109i 0.487131 0.843736i
$$122$$ −7.30200 12.6474i −0.661092 1.14505i
$$123$$ 3.71941 1.35375i 0.335368 0.122064i
$$124$$ 4.54576 1.65452i 0.408221 0.148580i
$$125$$ −0.500000 0.866025i −0.0447214 0.0774597i
$$126$$ 1.43969 2.49362i 0.128258 0.222149i
$$127$$ −0.819078 + 4.64522i −0.0726814 + 0.412197i 0.926660 + 0.375901i $$0.122667\pi$$
−0.999341 + 0.0362954i $$0.988444\pi$$
$$128$$ −0.766044 + 0.642788i −0.0677094 + 0.0568149i
$$129$$ −0.748970 0.628461i −0.0659432 0.0553329i
$$130$$ 0.673648 + 3.82045i 0.0590829 + 0.335076i
$$131$$ 2.22668 + 0.810446i 0.194546 + 0.0708090i 0.437456 0.899240i $$-0.355880\pi$$
−0.242910 + 0.970049i $$0.578102\pi$$
$$132$$ −0.532089 −0.0463124
$$133$$ −8.82295 + 8.92647i −0.765047 + 0.774023i
$$134$$ 2.42602 0.209576
$$135$$ −0.939693 0.342020i −0.0808759 0.0294364i
$$136$$ −0.124485 0.705990i −0.0106745 0.0605382i
$$137$$ −0.956767 0.802823i −0.0817421 0.0685898i 0.601001 0.799248i $$-0.294769\pi$$
−0.682743 + 0.730658i $$0.739213\pi$$
$$138$$ −1.20574 + 1.01173i −0.102639 + 0.0861245i
$$139$$ 1.52481 8.64766i 0.129333 0.733485i −0.849306 0.527900i $$-0.822979\pi$$
0.978639 0.205584i $$-0.0659094\pi$$
$$140$$ −1.43969 + 2.49362i −0.121676 + 0.210749i
$$141$$ 3.85117 + 6.67042i 0.324327 + 0.561750i
$$142$$ 7.56418 2.75314i 0.634772 0.231038i
$$143$$ −1.93969 + 0.705990i −0.162205 + 0.0590379i
$$144$$ −0.500000 0.866025i −0.0416667 0.0721688i
$$145$$ 1.55303 2.68993i 0.128972 0.223387i
$$146$$ 0.982926 5.57445i 0.0813475 0.461345i
$$147$$ 0.988856 0.829748i 0.0815594 0.0684365i
$$148$$ −4.53596 3.80612i −0.372854 0.312861i
$$149$$ 1.16503 + 6.60721i 0.0954430 + 0.541284i 0.994611 + 0.103680i $$0.0330618\pi$$
−0.899168 + 0.437604i $$0.855827\pi$$
$$150$$ 0.939693 + 0.342020i 0.0767256 + 0.0279258i
$$151$$ −19.2422 −1.56591 −0.782953 0.622081i $$-0.786287\pi$$
−0.782953 + 0.622081i $$0.786287\pi$$
$$152$$ 1.15270 + 4.20372i 0.0934966 + 0.340967i
$$153$$ 0.716881 0.0579564
$$154$$ −1.43969 0.524005i −0.116014 0.0422255i
$$155$$ −0.840022 4.76400i −0.0674722 0.382654i
$$156$$ −2.97178 2.49362i −0.237933 0.199649i
$$157$$ −10.6152 + 8.90717i −0.847181 + 0.710870i −0.959167 0.282840i $$-0.908723\pi$$
0.111986 + 0.993710i $$0.464279\pi$$
$$158$$ 0.254900 1.44561i 0.0202788 0.115007i
$$159$$ 1.35457 2.34618i 0.107424 0.186065i
$$160$$ 0.500000 + 0.866025i 0.0395285 + 0.0684653i
$$161$$ −4.25877 + 1.55007i −0.335638 + 0.122162i
$$162$$ 0.939693 0.342020i 0.0738292 0.0268716i
$$163$$ 6.81180 + 11.7984i 0.533542 + 0.924121i 0.999232 + 0.0391737i $$0.0124726\pi$$
−0.465691 + 0.884948i $$0.654194\pi$$
$$164$$ 1.97906 3.42782i 0.154538 0.267668i
$$165$$ −0.0923963 + 0.524005i −0.00719304 + 0.0407938i
$$166$$ −2.84730 + 2.38917i −0.220993 + 0.185435i
$$167$$ −8.93036 7.49346i −0.691052 0.579861i 0.228160 0.973624i $$-0.426729\pi$$
−0.919212 + 0.393762i $$0.871173\pi$$
$$168$$ −0.500000 2.83564i −0.0385758 0.218774i
$$169$$ −1.92602 0.701015i −0.148156 0.0539242i
$$170$$ −0.716881 −0.0549823
$$171$$ −4.34002 + 0.405223i −0.331890 + 0.0309882i
$$172$$ −0.977711 −0.0745498
$$173$$ 5.67277 + 2.06472i 0.431293 + 0.156978i 0.548539 0.836125i $$-0.315184\pi$$
−0.117246 + 0.993103i $$0.537407\pi$$
$$174$$ 0.539363 + 3.05888i 0.0408890 + 0.231893i
$$175$$ 2.20574 + 1.85083i 0.166738 + 0.139910i
$$176$$ −0.407604 + 0.342020i −0.0307243 + 0.0257807i
$$177$$ −1.33363 + 7.56337i −0.100241 + 0.568498i
$$178$$ −7.73055 + 13.3897i −0.579429 + 1.00360i
$$179$$ −0.610815 1.05796i −0.0456544 0.0790758i 0.842295 0.539017i $$-0.181204\pi$$
−0.887950 + 0.459941i $$0.847871\pi$$
$$180$$ −0.939693 + 0.342020i −0.0700406 + 0.0254927i
$$181$$ −16.9217 + 6.15901i −1.25778 + 0.457796i −0.883025 0.469327i $$-0.844497\pi$$
−0.374759 + 0.927122i $$0.622274\pi$$
$$182$$ −5.58512 9.67372i −0.413997 0.717064i
$$183$$ 7.30200 12.6474i 0.539780 0.934926i
$$184$$ −0.273318 + 1.55007i −0.0201493 + 0.114272i
$$185$$ −4.53596 + 3.80612i −0.333490 + 0.279832i
$$186$$ 3.70574 + 3.10948i 0.271718 + 0.227998i
$$187$$ −0.0662372 0.375650i −0.00484374 0.0274702i
$$188$$ 7.23783 + 2.63435i 0.527873 + 0.192130i
$$189$$ 2.87939 0.209444
$$190$$ 4.34002 0.405223i 0.314858 0.0293980i
$$191$$ −1.69459 −0.122616 −0.0613082 0.998119i $$-0.519527\pi$$
−0.0613082 + 0.998119i $$0.519527\pi$$
$$192$$ −0.939693 0.342020i −0.0678165 0.0246832i
$$193$$ −0.0482857 0.273842i −0.00347568 0.0197116i 0.983021 0.183495i $$-0.0587412\pi$$
−0.986496 + 0.163784i $$0.947630\pi$$
$$194$$ −10.1552 8.52125i −0.729103 0.611790i
$$195$$ −2.97178 + 2.49362i −0.212814 + 0.178572i
$$196$$ 0.224155 1.27125i 0.0160111 0.0908035i
$$197$$ −3.62701 + 6.28217i −0.258414 + 0.447586i −0.965817 0.259224i $$-0.916533\pi$$
0.707403 + 0.706810i $$0.249866\pi$$
$$198$$ −0.266044 0.460802i −0.0189070 0.0327478i
$$199$$ −1.34002 + 0.487728i −0.0949917 + 0.0345741i −0.389079 0.921204i $$-0.627207\pi$$
0.294087 + 0.955779i $$0.404984\pi$$
$$200$$ 0.939693 0.342020i 0.0664463 0.0241845i
$$201$$ 1.21301 + 2.10100i 0.0855592 + 0.148193i
$$202$$ 7.36231 12.7519i 0.518010 0.897220i
$$203$$ −1.55303 + 8.80769i −0.109002 + 0.618179i
$$204$$ 0.549163 0.460802i 0.0384491 0.0322626i
$$205$$ −3.03209 2.54422i −0.211770 0.177696i
$$206$$ 1.86437 + 10.5734i 0.129897 + 0.736682i
$$207$$ −1.47906 0.538332i −0.102801 0.0374167i
$$208$$ −3.87939 −0.268987
$$209$$ 0.613341 + 2.23675i 0.0424257 + 0.154719i
$$210$$ −2.87939 −0.198696
$$211$$ −4.01114 1.45994i −0.276139 0.100506i 0.200239 0.979747i $$-0.435828\pi$$
−0.476377 + 0.879241i $$0.658050\pi$$
$$212$$ −0.470437 2.66798i −0.0323098 0.183238i
$$213$$ 6.16637 + 5.17420i 0.422513 + 0.354531i
$$214$$ 12.0398 10.1026i 0.823026 0.690601i
$$215$$ −0.169778 + 0.962858i −0.0115787 + 0.0656663i
$$216$$ 0.500000 0.866025i 0.0340207 0.0589256i
$$217$$ 6.96451 + 12.0629i 0.472782 + 0.818882i
$$218$$ 12.7417 4.63760i 0.862977 0.314098i
$$219$$ 5.31908 1.93599i 0.359430 0.130822i
$$220$$ 0.266044 + 0.460802i 0.0179367 + 0.0310673i
$$221$$ 1.39053 2.40847i 0.0935371 0.162011i
$$222$$ 1.02822 5.83132i 0.0690095 0.391372i
$$223$$ −4.82816 + 4.05131i −0.323318 + 0.271296i −0.789971 0.613145i $$-0.789904\pi$$
0.466653 + 0.884441i $$0.345460\pi$$
$$224$$ −2.20574 1.85083i −0.147377 0.123664i
$$225$$ 0.173648 + 0.984808i 0.0115765 + 0.0656539i
$$226$$ 17.5398 + 6.38398i 1.16673 + 0.424656i
$$227$$ 22.2131 1.47433 0.737167 0.675711i $$-0.236163\pi$$
0.737167 + 0.675711i $$0.236163\pi$$
$$228$$ −3.06418 + 3.10013i −0.202930 + 0.205311i
$$229$$ −14.5321 −0.960307 −0.480154 0.877184i $$-0.659419\pi$$
−0.480154 + 0.877184i $$0.659419\pi$$
$$230$$ 1.47906 + 0.538332i 0.0975260 + 0.0354966i
$$231$$ −0.266044 1.50881i −0.0175044 0.0992726i
$$232$$ 2.37939 + 1.99654i 0.156214 + 0.131079i
$$233$$ −8.73648 + 7.33078i −0.572346 + 0.480255i −0.882423 0.470456i $$-0.844089\pi$$
0.310077 + 0.950711i $$0.399645\pi$$
$$234$$ 0.673648 3.82045i 0.0440378 0.249751i
$$235$$ 3.85117 6.67042i 0.251222 0.435130i
$$236$$ 3.84002 + 6.65111i 0.249964 + 0.432951i
$$237$$ 1.37939 0.502055i 0.0896007 0.0326120i
$$238$$ 1.93969 0.705990i 0.125732 0.0457626i
$$239$$ −5.79473 10.0368i −0.374830 0.649224i 0.615472 0.788159i $$-0.288966\pi$$
−0.990302 + 0.138935i $$0.955632\pi$$
$$240$$ −0.500000 + 0.866025i −0.0322749 + 0.0559017i
$$241$$ −2.64749 + 15.0147i −0.170540 + 0.967179i 0.772627 + 0.634860i $$0.218942\pi$$
−0.943167 + 0.332319i $$0.892169\pi$$
$$242$$ 8.20961 6.88868i 0.527734 0.442821i
$$243$$ 0.766044 + 0.642788i 0.0491418 + 0.0412348i
$$244$$ −2.53596 14.3821i −0.162348 0.920722i
$$245$$ −1.21301 0.441500i −0.0774964 0.0282064i
$$246$$ 3.95811 0.252360
$$247$$ −7.05690 + 15.3669i −0.449020 + 0.977775i
$$248$$ 4.83750 0.307181
$$249$$ −3.49273 1.27125i −0.221343 0.0805621i
$$250$$ −0.173648 0.984808i −0.0109825 0.0622847i
$$251$$ −9.07991 7.61895i −0.573119 0.480904i 0.309560 0.950880i $$-0.399818\pi$$
−0.882679 + 0.469976i $$0.844263\pi$$
$$252$$ 2.20574 1.85083i 0.138948 0.116592i
$$253$$ −0.145430 + 0.824773i −0.00914309 + 0.0518530i
$$254$$ −2.35844 + 4.08494i −0.147982 + 0.256312i
$$255$$ −0.358441 0.620838i −0.0224464 0.0388784i
$$256$$ −0.939693 + 0.342020i −0.0587308 + 0.0213763i
$$257$$ 0.280592 0.102127i 0.0175029 0.00637052i −0.333254 0.942837i $$-0.608147\pi$$
0.350757 + 0.936467i $$0.385924\pi$$
$$258$$ −0.488856 0.846723i −0.0304348 0.0527147i
$$259$$ 8.52481 14.7654i 0.529706 0.917478i
$$260$$ −0.673648 + 3.82045i −0.0417779 + 0.236934i
$$261$$ −2.37939 + 1.99654i −0.147280 + 0.123583i
$$262$$ 1.81521 + 1.52314i 0.112144 + 0.0940999i
$$263$$ 3.28746 + 18.6441i 0.202713 + 1.14964i 0.900998 + 0.433824i $$0.142836\pi$$
−0.698285 + 0.715820i $$0.746053\pi$$
$$264$$ −0.500000 0.181985i −0.0307729 0.0112004i
$$265$$ −2.70914 −0.166421
$$266$$ −11.3439 + 5.37051i −0.695539 + 0.329287i
$$267$$ −15.4611 −0.946204
$$268$$ 2.27972 + 0.829748i 0.139256 + 0.0506850i
$$269$$ 5.02141 + 28.4778i 0.306161 + 1.73632i 0.617990 + 0.786186i $$0.287947\pi$$
−0.311829 + 0.950138i $$0.600942\pi$$
$$270$$ −0.766044 0.642788i −0.0466200 0.0391188i
$$271$$ 2.36050 1.98069i 0.143390 0.120319i −0.568271 0.822841i $$-0.692388\pi$$
0.711661 + 0.702523i $$0.247943\pi$$
$$272$$ 0.124485 0.705990i 0.00754802 0.0428070i
$$273$$ 5.58512 9.67372i 0.338027 0.585480i
$$274$$ −0.624485 1.08164i −0.0377265 0.0653443i
$$275$$ 0.500000 0.181985i 0.0301511 0.0109741i
$$276$$ −1.47906 + 0.538332i −0.0890287 + 0.0324038i
$$277$$ 2.17499 + 3.76720i 0.130683 + 0.226349i 0.923940 0.382538i $$-0.124950\pi$$
−0.793257 + 0.608887i $$0.791616\pi$$
$$278$$ 4.39053 7.60462i 0.263326 0.456095i
$$279$$ −0.840022 + 4.76400i −0.0502908 + 0.285213i
$$280$$ −2.20574 + 1.85083i −0.131818 + 0.110608i
$$281$$ −15.6480 13.1302i −0.933479 0.783282i 0.0429599 0.999077i $$-0.486321\pi$$
−0.976439 + 0.215795i $$0.930766\pi$$
$$282$$ 1.33750 + 7.58532i 0.0796467 + 0.451699i
$$283$$ 15.2626 + 5.55515i 0.907270 + 0.330219i 0.753162 0.657835i $$-0.228528\pi$$
0.154108 + 0.988054i $$0.450750\pi$$
$$284$$ 8.04963 0.477658
$$285$$ 2.52094 + 3.55596i 0.149328 + 0.210637i
$$286$$ −2.06418 −0.122057
$$287$$ 10.7096 + 3.89798i 0.632168 + 0.230090i
$$288$$ −0.173648 0.984808i −0.0102323 0.0580304i
$$289$$ −12.6291 10.5970i −0.742887 0.623356i
$$290$$ 2.37939 1.99654i 0.139722 0.117241i
$$291$$ 2.30200 13.0553i 0.134946 0.765316i
$$292$$ 2.83022 4.90209i 0.165626 0.286873i
$$293$$ 1.70961 + 2.96113i 0.0998763 + 0.172991i 0.911633 0.411004i $$-0.134822\pi$$
−0.811757 + 0.583995i $$0.801489\pi$$
$$294$$ 1.21301 0.441500i 0.0707442 0.0257488i
$$295$$ 7.21688 2.62673i 0.420183 0.152934i
$$296$$ −2.96064 5.12797i −0.172084 0.298057i
$$297$$ 0.266044 0.460802i 0.0154375 0.0267385i
$$298$$ −1.16503 + 6.60721i −0.0674884 + 0.382746i
$$299$$ −4.67752 + 3.92490i −0.270508 + 0.226983i
$$300$$ 0.766044 + 0.642788i 0.0442276 + 0.0371114i
$$301$$ −0.488856 2.77244i −0.0281772 0.159801i
$$302$$ −18.0817 6.58121i −1.04049 0.378706i
$$303$$ 14.7246 0.845907
$$304$$ −0.354570 + 4.34445i −0.0203360 + 0.249172i
$$305$$ −14.6040 −0.836223
$$306$$ 0.673648 + 0.245188i 0.0385099 + 0.0140165i
$$307$$ 3.42943 + 19.4492i 0.195728 + 1.11003i 0.911379 + 0.411569i $$0.135019\pi$$
−0.715651 + 0.698458i $$0.753870\pi$$
$$308$$ −1.17365 0.984808i −0.0668748 0.0561146i
$$309$$ −8.22462 + 6.90128i −0.467882 + 0.392600i
$$310$$ 0.840022 4.76400i 0.0477101 0.270577i
$$311$$ −2.53074 + 4.38338i −0.143505 + 0.248559i −0.928814 0.370545i $$-0.879171\pi$$
0.785309 + 0.619104i $$0.212504\pi$$
$$312$$ −1.93969 3.35965i −0.109813 0.190203i
$$313$$ −17.6065 + 6.40825i −0.995180 + 0.362216i −0.787724 0.616028i $$-0.788741\pi$$
−0.207456 + 0.978244i $$0.566518\pi$$
$$314$$ −13.0214 + 4.73941i −0.734841 + 0.267460i
$$315$$ −1.43969 2.49362i −0.0811175 0.140500i
$$316$$ 0.733956 1.27125i 0.0412882 0.0715133i
$$317$$ 0.0243481 0.138085i 0.00136753 0.00775562i −0.984116 0.177525i $$-0.943191\pi$$
0.985484 + 0.169769i $$0.0543022\pi$$
$$318$$ 2.07532 1.74140i 0.116378 0.0976530i
$$319$$ 1.26604 + 1.06234i 0.0708849 + 0.0594795i
$$320$$ 0.173648 + 0.984808i 0.00970723 + 0.0550524i
$$321$$ 14.7690 + 5.37549i 0.824327 + 0.300031i
$$322$$ −4.53209 −0.252563
$$323$$ −2.57011 1.77736i −0.143005 0.0988949i
$$324$$ 1.00000 0.0555556
$$325$$ 3.64543 + 1.32683i 0.202212 + 0.0735992i
$$326$$ 2.36571 + 13.4166i 0.131025 + 0.743079i
$$327$$ 10.3871 + 8.71583i 0.574409 + 0.481987i
$$328$$ 3.03209 2.54422i 0.167419 0.140481i
$$329$$ −3.85117 + 21.8411i −0.212322 + 1.20414i
$$330$$ −0.266044 + 0.460802i −0.0146453 + 0.0253663i
$$331$$ 8.64930 + 14.9810i 0.475409 + 0.823432i 0.999603 0.0281667i $$-0.00896693\pi$$
−0.524195 + 0.851598i $$0.675634\pi$$
$$332$$ −3.49273 + 1.27125i −0.191688 + 0.0697688i
$$333$$ 5.56418 2.02520i 0.304915 0.110980i
$$334$$ −5.82888 10.0959i −0.318942 0.552424i
$$335$$ 1.21301 2.10100i 0.0662739 0.114790i
$$336$$ 0.500000 2.83564i 0.0272772 0.154697i
$$337$$ 26.0128 21.8273i 1.41701 1.18901i 0.464087 0.885790i $$-0.346383\pi$$
0.952920 0.303220i $$-0.0980618\pi$$
$$338$$ −1.57011 1.31748i −0.0854026 0.0716613i
$$339$$ 3.24123 + 18.3819i 0.176039 + 0.998369i
$$340$$ −0.673648 0.245188i −0.0365337 0.0132972i
$$341$$ 2.57398 0.139389
$$342$$ −4.21688 1.10359i −0.228023 0.0596753i
$$343$$ −16.4388 −0.887613
$$344$$ −0.918748 0.334397i −0.0495356 0.0180295i
$$345$$ 0.273318 + 1.55007i 0.0147150 + 0.0834527i
$$346$$ 4.62449 + 3.88040i 0.248614 + 0.208612i
$$347$$ −10.2005 + 8.55925i −0.547593 + 0.459485i −0.874125 0.485701i $$-0.838564\pi$$
0.326532 + 0.945186i $$0.394120\pi$$
$$348$$ −0.539363 + 3.05888i −0.0289129 + 0.163973i
$$349$$ −2.63563 + 4.56504i −0.141082 + 0.244361i −0.927904 0.372818i $$-0.878391\pi$$
0.786822 + 0.617180i $$0.211725\pi$$
$$350$$ 1.43969 + 2.49362i 0.0769548 + 0.133290i
$$351$$ 3.64543 1.32683i 0.194579 0.0708208i
$$352$$ −0.500000 + 0.181985i −0.0266501 + 0.00969984i
$$353$$ −16.9290 29.3219i −0.901041 1.56065i −0.826146 0.563457i $$-0.809471\pi$$
−0.0748949 0.997191i $$-0.523862\pi$$
$$354$$ −3.84002 + 6.65111i −0.204095 + 0.353503i
$$355$$ 1.39780 7.92734i 0.0741877 0.420739i
$$356$$ −11.8439 + 9.93821i −0.627725 + 0.526724i
$$357$$ 1.58125 + 1.32683i 0.0836887 + 0.0702232i
$$358$$ −0.212134 1.20307i −0.0112116 0.0635842i
$$359$$ −29.6339 10.7858i −1.56402 0.569255i −0.592364 0.805670i $$-0.701805\pi$$
−0.971652 + 0.236415i $$0.924027\pi$$
$$360$$ −1.00000 −0.0527046
$$361$$ 16.5642 + 9.30742i 0.871799 + 0.489864i
$$362$$ −18.0077 −0.946466
$$363$$ 10.0706 + 3.66539i 0.528568 + 0.192383i
$$364$$ −1.93969 11.0005i −0.101668 0.576585i
$$365$$ −4.33615 3.63846i −0.226965 0.190446i
$$366$$ 11.1873 9.38728i 0.584771 0.490681i
$$367$$ −1.90255 + 10.7899i −0.0993124 + 0.563228i 0.894028 + 0.448011i $$0.147868\pi$$
−0.993340 + 0.115217i $$0.963244\pi$$
$$368$$ −0.786989 + 1.36310i −0.0410246 + 0.0710568i
$$369$$ 1.97906 + 3.42782i 0.103026 + 0.178445i
$$370$$ −5.56418 + 2.02520i −0.289268 + 0.105285i
$$371$$ 7.33022 2.66798i 0.380566 0.138515i
$$372$$ 2.41875 + 4.18939i 0.125406 + 0.217210i
$$373$$ 2.06893 3.58348i 0.107125 0.185546i −0.807479 0.589896i $$-0.799169\pi$$
0.914604 + 0.404350i $$0.132502\pi$$
$$374$$ 0.0662372 0.375650i 0.00342504 0.0194244i
$$375$$ 0.766044 0.642788i 0.0395584 0.0331934i
$$376$$ 5.90033 + 4.95096i 0.304286 + 0.255327i
$$377$$ 2.09240 + 11.8666i 0.107764 + 0.611159i
$$378$$ 2.70574 + 0.984808i 0.139168 + 0.0506530i
$$379$$ 33.8631 1.73943 0.869715 0.493555i $$-0.164303\pi$$
0.869715 + 0.493555i $$0.164303\pi$$
$$380$$ 4.21688 + 1.10359i 0.216321 + 0.0566130i
$$381$$ −4.71688 −0.241653
$$382$$ −1.59240 0.579585i −0.0814741 0.0296541i
$$383$$ 3.36366 + 19.0762i 0.171875 + 0.974750i 0.941690 + 0.336483i $$0.109237\pi$$
−0.769815 + 0.638267i $$0.779651\pi$$
$$384$$ −0.766044 0.642788i −0.0390920 0.0328021i
$$385$$ −1.17365 + 0.984808i −0.0598146 + 0.0501905i
$$386$$ 0.0482857 0.273842i 0.00245768 0.0139382i
$$387$$ 0.488856 0.846723i 0.0248499 0.0430413i
$$388$$ −6.62836 11.4806i −0.336504 0.582842i
$$389$$ −25.1570 + 9.15641i −1.27551 + 0.464249i −0.888946 0.458013i $$-0.848561\pi$$
−0.386567 + 0.922261i $$0.626339\pi$$
$$390$$ −3.64543 + 1.32683i −0.184594 + 0.0671865i
$$391$$ −0.564178 0.977185i −0.0285317 0.0494183i
$$392$$ 0.645430 1.11792i 0.0325991 0.0564633i
$$393$$ −0.411474 + 2.33359i −0.0207561 + 0.117714i
$$394$$ −5.55690 + 4.66280i −0.279953 + 0.234908i
$$395$$ −1.12449 0.943555i −0.0565790 0.0474754i
$$396$$ −0.0923963 0.524005i −0.00464309 0.0263323i
$$397$$ −2.04664 0.744915i −0.102718 0.0373862i 0.290150 0.956981i $$-0.406295\pi$$
−0.392868 + 0.919595i $$0.628517\pi$$
$$398$$ −1.42602 −0.0714800
$$399$$ −10.3229 7.13884i −0.516794 0.357389i
$$400$$ 1.00000 0.0500000
$$401$$ 8.61721 + 3.13641i 0.430323 + 0.156625i 0.548095 0.836416i $$-0.315353\pi$$
−0.117772 + 0.993041i $$0.537575\pi$$
$$402$$ 0.421274 + 2.38917i 0.0210113 + 0.119161i
$$403$$ 14.3760 + 12.0629i 0.716119 + 0.600895i
$$404$$ 11.2797 9.46480i 0.561187 0.470892i
$$405$$ 0.173648 0.984808i 0.00862865 0.0489355i
$$406$$ −4.47178 + 7.74535i −0.221931 + 0.384395i
$$407$$ −1.57532 2.72854i −0.0780858 0.135249i
$$408$$ 0.673648 0.245188i 0.0333506 0.0121386i
$$409$$ 17.9402 6.52968i 0.887084 0.322872i 0.142019 0.989864i $$-0.454641\pi$$
0.745065 + 0.666992i $$0.232418\pi$$
$$410$$ −1.97906 3.42782i −0.0977386 0.169288i
$$411$$ 0.624485 1.08164i 0.0308036 0.0533534i
$$412$$ −1.86437 + 10.5734i −0.0918509 + 0.520913i
$$413$$ −16.9402 + 14.2145i −0.833571 + 0.699449i
$$414$$ −1.20574 1.01173i −0.0592587 0.0497240i
$$415$$ 0.645430 + 3.66041i 0.0316829 + 0.179683i
$$416$$ −3.64543 1.32683i −0.178732 0.0650531i
$$417$$ 8.78106 0.430010
$$418$$ −0.188663 + 2.31164i −0.00922781 + 0.113066i
$$419$$ −16.1557 −0.789257 −0.394629 0.918841i $$-0.629127\pi$$
−0.394629 + 0.918841i $$0.629127\pi$$
$$420$$ −2.70574 0.984808i −0.132026 0.0480537i
$$421$$ 2.77941 + 15.7628i 0.135460 + 0.768233i 0.974538 + 0.224222i $$0.0719840\pi$$
−0.839078 + 0.544011i $$0.816905\pi$$
$$422$$ −3.26991 2.74378i −0.159177 0.133565i
$$423$$ −5.90033 + 4.95096i −0.286884 + 0.240724i
$$424$$ 0.470437 2.66798i 0.0228465 0.129569i
$$425$$ −0.358441 + 0.620838i −0.0173869 + 0.0301150i
$$426$$ 4.02481 + 6.97118i 0.195003 + 0.337755i
$$427$$ 39.5146 14.3821i 1.91225 0.696001i
$$428$$ 14.7690 5.37549i 0.713888 0.259834i
$$429$$ −1.03209 1.78763i −0.0498297 0.0863076i
$$430$$ −0.488856 + 0.846723i −0.0235747 + 0.0408326i
$$431$$ 4.28817 24.3194i 0.206554 1.17143i −0.688422 0.725311i $$-0.741696\pi$$
0.894976 0.446115i $$-0.147193\pi$$
$$432$$ 0.766044 0.642788i 0.0368563 0.0309261i
$$433$$ −29.8350 25.0346i −1.43378 1.20308i −0.943436 0.331555i $$-0.892427\pi$$
−0.490344 0.871529i $$-0.663129\pi$$
$$434$$ 2.41875 + 13.7174i 0.116104 + 0.658456i
$$435$$ 2.91875 + 1.06234i 0.139943 + 0.0509352i
$$436$$ 13.5594 0.649379
$$437$$ 3.96791 + 5.59700i 0.189811 + 0.267741i
$$438$$ 5.66044 0.270466
$$439$$ −8.37433 3.04801i −0.399685 0.145473i 0.134354 0.990933i $$-0.457104\pi$$
−0.534039 + 0.845460i $$0.679326\pi$$
$$440$$ 0.0923963 + 0.524005i 0.00440482 + 0.0249810i
$$441$$ 0.988856 + 0.829748i 0.0470884 + 0.0395118i
$$442$$ 2.13041 1.78763i 0.101334 0.0850289i
$$443$$ 3.12495 17.7225i 0.148471 0.842021i −0.816043 0.577990i $$-0.803837\pi$$
0.964514 0.264030i $$-0.0850518\pi$$
$$444$$ 2.96064 5.12797i 0.140506 0.243363i
$$445$$ 7.73055 + 13.3897i 0.366463 + 0.634733i
$$446$$ −5.92262 + 2.15566i −0.280444 + 0.102073i
$$447$$ −6.30453 + 2.29466i −0.298194 + 0.108534i
$$448$$ −1.43969 2.49362i −0.0680191 0.117813i
$$449$$ −2.33662 + 4.04714i −0.110272 + 0.190996i −0.915880 0.401452i $$-0.868505\pi$$
0.805608 + 0.592449i $$0.201839\pi$$
$$450$$ −0.173648 + 0.984808i −0.00818585 + 0.0464243i
$$451$$ 1.61334 1.35375i 0.0759693 0.0637458i
$$452$$ 14.2986 + 11.9980i 0.672550 + 0.564336i
$$453$$ −3.34137 18.9498i −0.156991 0.890341i
$$454$$ 20.8735 + 7.59732i 0.979640 + 0.356560i
$$455$$ −11.1702 −0.523669
$$456$$ −3.93969 + 1.86516i −0.184493 + 0.0873441i
$$457$$ −7.20708 −0.337133 −0.168567 0.985690i $$-0.553914\pi$$
−0.168567 + 0.985690i $$0.553914\pi$$
$$458$$ −13.6557 4.97027i −0.638089 0.232245i
$$459$$ 0.124485 + 0.705990i 0.00581047 + 0.0329528i
$$460$$ 1.20574 + 1.01173i 0.0562178 + 0.0471723i
$$461$$ 26.1616 21.9522i 1.21847 1.02242i 0.219565 0.975598i $$-0.429536\pi$$
0.998903 0.0468185i $$-0.0149083\pi$$
$$462$$ 0.266044 1.50881i 0.0123775 0.0701963i
$$463$$ 3.25965 5.64588i 0.151489 0.262386i −0.780286 0.625423i $$-0.784927\pi$$
0.931775 + 0.363036i $$0.118260\pi$$
$$464$$ 1.55303 + 2.68993i 0.0720978 + 0.124877i
$$465$$ 4.54576 1.65452i 0.210805 0.0767266i
$$466$$ −10.7169 + 3.90063i −0.496450 + 0.180693i
$$467$$ −4.09240 7.08824i −0.189374 0.328005i 0.755668 0.654955i $$-0.227312\pi$$
−0.945042 + 0.326950i $$0.893979\pi$$
$$468$$ 1.93969 3.35965i 0.0896623 0.155300i
$$469$$ −1.21301 + 6.87933i −0.0560116 + 0.317658i
$$470$$ 5.90033 4.95096i 0.272162 0.228371i
$$471$$ −10.6152 8.90717i −0.489120 0.410421i
$$472$$ 1.33363 + 7.56337i 0.0613851 + 0.348132i
$$473$$ −0.488856 0.177929i −0.0224776 0.00818118i
$$474$$ 1.46791 0.0674234
$$475$$ 1.81908 3.96118i 0.0834650 0.181751i
$$476$$ 2.06418 0.0946114
$$477$$ 2.54576 + 0.926581i 0.116562 + 0.0424252i
$$478$$ −2.01249 11.4134i −0.0920491 0.522036i
$$479$$ −18.5141 15.5352i −0.845933 0.709822i 0.112957 0.993600i $$-0.463968\pi$$
−0.958890 + 0.283778i $$0.908412\pi$$
$$480$$ −0.766044 + 0.642788i −0.0349650 + 0.0293391i
$$481$$ 3.98886 22.6219i 0.181876 1.03147i
$$482$$ −7.62314 + 13.2037i −0.347225 + 0.601411i
$$483$$ −2.26604 3.92490i −0.103109 0.178589i
$$484$$ 10.0706 3.66539i 0.457753 0.166609i
$$485$$ −12.4572 + 4.53406i −0.565654 + 0.205881i
$$486$$ 0.500000 + 0.866025i 0.0226805 + 0.0392837i
$$487$$ 10.9500 18.9659i 0.496190 0.859426i −0.503800 0.863820i $$-0.668065\pi$$
0.999990 + 0.00439380i $$0.00139859\pi$$
$$488$$ 2.53596 14.3821i 0.114797 0.651049i
$$489$$ −10.4363 + 8.75709i −0.471945 + 0.396009i
$$490$$ −0.988856 0.829748i −0.0446719 0.0374842i
$$491$$ 2.35875 + 13.3771i 0.106449 + 0.603701i 0.990632 + 0.136560i $$0.0436047\pi$$
−0.884183 + 0.467140i $$0.845284\pi$$
$$492$$ 3.71941 + 1.35375i 0.167684 + 0.0610319i
$$493$$ −2.22668 −0.100285
$$494$$ −11.8871 + 12.0266i −0.534827 + 0.541102i
$$495$$ −0.532089 −0.0239156
$$496$$ 4.54576 + 1.65452i 0.204111 + 0.0742902i
$$497$$ 4.02481 + 22.8259i 0.180538 + 1.02388i
$$498$$ −2.84730 2.38917i −0.127590 0.107061i
$$499$$ 30.0069 25.1787i 1.34329 1.12716i 0.362525 0.931974i $$-0.381915\pi$$
0.980767 0.195181i $$-0.0625295\pi$$
$$500$$ 0.173648 0.984808i 0.00776578 0.0440419i
$$501$$ 5.82888 10.0959i 0.260415 0.451052i
$$502$$ −5.92649 10.2650i −0.264512 0.458148i
$$503$$ −28.0035 + 10.1924i −1.24861 + 0.454458i −0.879933 0.475099i $$-0.842412\pi$$
−0.368680 + 0.929556i $$0.620190\pi$$
$$504$$ 2.70574 0.984808i 0.120523 0.0438668i
$$505$$ −7.36231 12.7519i −0.327619 0.567452i
$$506$$ −0.418748 + 0.725293i −0.0186156 + 0.0322432i
$$507$$ 0.355914 2.01849i 0.0158067 0.0896443i
$$508$$ −3.61334 + 3.03195i −0.160316 + 0.134521i
$$509$$ −10.0419 8.42615i −0.445099 0.373482i 0.392514 0.919746i $$-0.371605\pi$$
−0.837613 + 0.546263i $$0.816050\pi$$
$$510$$ −0.124485 0.705990i −0.00551230 0.0312618i
$$511$$ 15.3157 + 5.57445i 0.677526 + 0.246599i
$$512$$ −1.00000 −0.0441942
$$513$$ −1.15270 4.20372i −0.0508931 0.185599i
$$514$$ 0.298600 0.0131707
$$515$$ 10.0890 + 3.67209i 0.444574 + 0.161812i
$$516$$ −0.169778 0.962858i −0.00747405 0.0423874i
$$517$$ 3.13950 + 2.63435i 0.138075 + 0.115859i
$$518$$ 13.0608 10.9593i 0.573857 0.481524i
$$519$$ −1.04829 + 5.94512i −0.0460146 + 0.260962i
$$520$$ −1.93969 + 3.35965i −0.0850611 + 0.147330i
$$521$$ 13.7959 + 23.8952i 0.604410 + 1.04687i 0.992144 + 0.125098i $$0.0399244\pi$$
−0.387735 + 0.921771i $$0.626742\pi$$
$$522$$ −2.91875 + 1.06234i −0.127750 + 0.0464972i
$$523$$ −4.51114 + 1.64192i −0.197259 + 0.0717962i −0.438760 0.898604i $$-0.644582\pi$$
0.241502 + 0.970400i $$0.422360\pi$$
$$524$$ 1.18479 + 2.05212i 0.0517579 + 0.0896473i
$$525$$ −1.43969 + 2.49362i −0.0628333 + 0.108831i
$$526$$ −3.28746 + 18.6441i −0.143340 + 0.812921i
$$527$$ −2.65657 + 2.22913i −0.115722 + 0.0971024i
$$528$$ −0.407604 0.342020i −0.0177387 0.0148845i
$$529$$ −3.56371 20.2108i −0.154944 0.878731i
$$530$$ −2.54576 0.926581i −0.110581 0.0402481i
$$531$$ −7.68004 −0.333286
$$532$$ −12.4966 + 1.16679i −0.541796 + 0.0505869i
$$533$$ 15.3550 0.665100
$$534$$ −14.5287 5.28801i −0.628718 0.228835i
$$535$$ −2.72921 15.4781i −0.117994 0.669177i
$$536$$ 1.85844 + 1.55942i 0.0802724 + 0.0673566i
$$537$$ 0.935822 0.785248i 0.0403837 0.0338860i
$$538$$ −5.02141 + 28.4778i −0.216488 + 1.22777i
$$539$$ 0.343426 0.594831i 0.0147924 0.0256212i
$$540$$ −0.500000 0.866025i −0.0215166 0.0372678i
$$541$$ −39.7340 + 14.4620i −1.70830 + 0.621770i −0.996727 0.0808436i $$-0.974239\pi$$
−0.711572 + 0.702613i $$0.752016\pi$$
$$542$$ 2.89558 1.05391i 0.124376 0.0452691i
$$543$$ −9.00387 15.5952i −0.386393 0.669252i
$$544$$ 0.358441 0.620838i 0.0153680 0.0266182i
$$545$$ 2.35457 13.3534i 0.100859 0.571998i
$$546$$ 8.55690 7.18009i 0.366202 0.307280i
$$547$$ −25.3855 21.3010i −1.08541 0.910765i −0.0890485 0.996027i $$-0.528383\pi$$
−0.996359 + 0.0852626i $$0.972827\pi$$
$$548$$ −0.216881 1.23000i −0.00926471 0.0525428i
$$549$$ 13.7233 + 4.99486i 0.585695 + 0.213176i
$$550$$ 0.532089 0.0226883
$$551$$ 13.4804 1.25865i 0.574284 0.0536203i
$$552$$ −1.57398 −0.0669930
$$553$$ 3.97178 + 1.44561i 0.168897 + 0.0614736i
$$554$$ 0.755367 + 4.28390i 0.0320925 + 0.182005i
$$555$$ −4.53596 3.80612i −0.192541 0.161561i
$$556$$ 6.72668 5.64436i 0.285275 0.239374i
$$557$$ 2.40673 13.6492i 0.101976 0.578336i −0.890409 0.455162i $$-0.849581\pi$$
0.992385 0.123174i $$-0.0393075\pi$$
$$558$$ −2.41875 + 4.18939i −0.102394 + 0.177351i
$$559$$ −1.89646 3.28476i −0.0802117 0.138931i
$$560$$ −2.70574 + 0.984808i −0.114338 + 0.0416157i
$$561$$ 0.358441 0.130462i 0.0151334 0.00550810i
$$562$$ −10.2135 17.6903i −0.430830 0.746219i
$$563$$ 12.9003 22.3440i 0.543684 0.941688i −0.455004 0.890489i $$-0.650362\pi$$
0.998688 0.0511992i $$-0.0163044\pi$$
$$564$$ −1.33750 + 7.58532i −0.0563187 + 0.319399i
$$565$$ 14.2986 11.9980i 0.601547 0.504758i
$$566$$ 12.4422 + 10.4403i 0.522985 + 0.438837i
$$567$$ 0.500000 + 2.83564i 0.0209980 + 0.119086i
$$568$$ 7.56418 + 2.75314i 0.317386 + 0.115519i
$$569$$ 10.8553 0.455080 0.227540 0.973769i $$-0.426932\pi$$
0.227540 + 0.973769i $$0.426932\pi$$
$$570$$ 1.15270 + 4.20372i 0.0482814 + 0.176075i
$$571$$ 20.1239 0.842160 0.421080 0.907024i $$-0.361651\pi$$
0.421080 + 0.907024i $$0.361651\pi$$
$$572$$ −1.93969 0.705990i −0.0811026 0.0295189i
$$573$$ −0.294263 1.66885i −0.0122930 0.0697171i
$$574$$ 8.73055 + 7.32580i 0.364406 + 0.305773i
$$575$$ 1.20574 1.01173i 0.0502827 0.0421922i
$$576$$ 0.173648 0.984808i 0.00723534 0.0410337i
$$577$$ −6.70486 + 11.6132i −0.279127 + 0.483462i −0.971168 0.238396i $$-0.923378\pi$$
0.692041 + 0.721858i $$0.256712\pi$$
$$578$$ −8.24304 14.2774i −0.342865 0.593860i
$$579$$ 0.261297 0.0951042i 0.0108591 0.00395240i
$$580$$ 2.91875 1.06234i 0.121194 0.0441112i
$$581$$ −5.35117 9.26849i −0.222004 0.384522i
$$582$$ 6.62836 11.4806i 0.274754 0.475888i
$$583$$ 0.250314 1.41960i 0.0103670 0.0587940i
$$584$$ 4.33615 3.63846i 0.179431 0.150561i
$$585$$ −2.97178 2.49362i −0.122868 0.103099i
$$586$$ 0.593740 + 3.36727i 0.0245272 + 0.139101i
$$587$$ −23.3427 8.49605i −0.963457 0.350670i −0.188070 0.982156i $$-0.560223\pi$$
−0.775387 + 0.631486i $$0.782445\pi$$
$$588$$ 1.29086 0.0532341
$$589$$ 14.8229 14.9969i 0.610769 0.617935i
$$590$$ 7.68004 0.316182
$$591$$ −6.81655 2.48102i −0.280395 0.102056i
$$592$$ −1.02822 5.83132i −0.0422595 0.239666i
$$593$$ −35.1321 29.4793i −1.44270 1.21057i −0.937698 0.347452i $$-0.887047\pi$$
−0.505003 0.863117i $$-0.668509\pi$$
$$594$$ 0.407604 0.342020i 0.0167242 0.0140333i
$$595$$ 0.358441 2.03282i 0.0146946 0.0833374i
$$596$$ −3.35457 + 5.81029i −0.137409 + 0.237999i
$$597$$ −0.713011 1.23497i −0.0291816 0.0505440i
$$598$$ −5.73783 + 2.08840i −0.234637 + 0.0854009i
$$599$$ 45.7435 16.6493i 1.86903 0.680271i 0.898659 0.438649i $$-0.144543\pi$$
0.970370 0.241622i $$-0.0776795\pi$$
$$600$$ 0.500000 + 0.866025i 0.0204124 + 0.0353553i
$$601$$ 18.3981 31.8665i 0.750474 1.29986i −0.197118 0.980380i $$-0.563158\pi$$
0.947593 0.319480i $$-0.103508\pi$$
$$602$$ 0.488856 2.77244i 0.0199243 0.112996i
$$603$$ −1.85844 + 1.55942i −0.0756816 + 0.0635044i
$$604$$ −14.7404 12.3686i −0.599776 0.503272i
$$605$$ −1.86097 10.5541i −0.0756591 0.429084i
$$606$$ 13.8366 + 5.03612i 0.562074 + 0.204578i
$$607$$ −28.8881 −1.17253 −0.586265 0.810119i $$-0.699402\pi$$
−0.586265 + 0.810119i $$0.699402\pi$$
$$608$$ −1.81908 + 3.96118i −0.0737733 + 0.160647i
$$609$$ −8.94356 −0.362411
$$610$$ −13.7233 4.99486i −0.555639 0.202236i
$$611$$ 5.18866 + 29.4264i 0.209911 + 1.19046i
$$612$$ 0.549163 + 0.460802i 0.0221986 + 0.0186268i
$$613$$ 26.5612 22.2875i 1.07280 0.900185i 0.0774953 0.996993i $$-0.475308\pi$$
0.995303 + 0.0968080i $$0.0308633\pi$$
$$614$$ −3.42943 + 19.4492i −0.138400 + 0.784907i
$$615$$ 1.97906 3.42782i 0.0798032 0.138223i
$$616$$ −0.766044 1.32683i −0.0308648 0.0534594i
$$617$$ 32.7952 11.9365i 1.32028 0.480544i 0.416735 0.909028i $$-0.363174\pi$$
0.903550 + 0.428483i $$0.140952\pi$$
$$618$$ −10.0890 + 3.67209i −0.405839 + 0.147713i
$$619$$ 16.7935 + 29.0873i 0.674990 + 1.16912i 0.976472 + 0.215645i $$0.0691853\pi$$
−0.301482 + 0.953472i $$0.597481\pi$$
$$620$$ 2.41875 4.18939i 0.0971393 0.168250i
$$621$$ 0.273318 1.55007i 0.0109679 0.0622020i
$$622$$ −3.87733 + 3.25346i −0.155467 + 0.130452i
$$623$$ −34.1031 28.6159i −1.36631 1.14647i
$$624$$ −0.673648 3.82045i −0.0269675 0.152940i
$$625$$ −0.939693 0.342020i −0.0375877 0.0136808i
$$626$$ −18.7365 −0.748860
$$627$$ −2.09627 + 0.992431i −0.0837168 + 0.0396339i
$$628$$ −13.8571 −0.552958
$$629$$ 3.98886 + 1.45182i 0.159046 + 0.0578880i
$$630$$ −0.500000 2.83564i −0.0199205 0.112975i
$$631$$ −8.84595 7.42264i −0.352152 0.295490i 0.449502 0.893280i $$-0.351602\pi$$
−0.801653 + 0.597789i $$0.796046\pi$$
$$632$$ 1.12449 0.943555i 0.0447296 0.0375326i
$$633$$ 0.741230 4.20372i 0.0294612 0.167083i
$$634$$ 0.0701076 0.121430i 0.00278433 0.00482260i
$$635$$ 2.35844 + 4.08494i 0.0935919 + 0.162106i
$$636$$ 2.54576 0.926581i 0.100946 0.0367413i
$$637$$ 4.70574 1.71275i 0.186448 0.0678616i
$$638$$ 0.826352 + 1.43128i 0.0327156 + 0.0566651i
$$639$$ −4.02481 + 6.97118i −0.159219 + 0.275776i
$$640$$ −0.173648 + 0.984808i −0.00686405 + 0.0389279i
$$641$$ 34.8594 29.2505i 1.37686 1.15532i 0.406506 0.913648i $$-0.366747\pi$$
0.970357 0.241677i $$-0.0776973\pi$$
$$642$$ 12.0398 + 10.1026i 0.475174 + 0.398718i
$$643$$ 2.53895 + 14.3991i 0.100127 + 0.567846i 0.993055 + 0.117648i $$0.0375354\pi$$
−0.892929 + 0.450198i $$0.851353\pi$$
$$644$$ −4.25877 1.55007i −0.167819 0.0610811i
$$645$$ −0.977711 −0.0384973
$$646$$ −1.80722 2.54920i −0.0711041 0.100297i
$$647$$ −29.6742 −1.16661 −0.583306 0.812252i $$-0.698241\pi$$
−0.583306 + 0.812252i $$0.698241\pi$$
$$648$$ 0.939693 + 0.342020i 0.0369146 + 0.0134358i
$$649$$ 0.709607 + 4.02438i 0.0278545 + 0.157971i
$$650$$ 2.97178 + 2.49362i 0.116563 + 0.0978079i
$$651$$ −10.6702 + 8.95340i −0.418200 + 0.350911i
$$652$$ −2.36571 + 13.4166i −0.0926485 + 0.525436i
$$653$$ 4.67230 8.09267i 0.182841 0.316691i −0.760006 0.649916i $$-0.774804\pi$$
0.942847 + 0.333226i $$0.108137\pi$$
$$654$$ 6.77972 + 11.7428i 0.265108 + 0.459180i
$$655$$ 2.22668 0.810446i 0.0870036 0.0316667i
$$656$$ 3.71941 1.35375i 0.145218 0.0528552i
$$657$$ 2.83022 + 4.90209i 0.110417 + 0.191249i
$$658$$ −11.0890 + 19.2067i −0.432294 + 0.748755i
$$659$$ 1.28787 7.30385i 0.0501681 0.284518i −0.949395 0.314086i $$-0.898302\pi$$
0.999563 + 0.0295680i $$0.00941317\pi$$
$$660$$ −0.407604 + 0.342020i −0.0158660 + 0.0133131i
$$661$$ 20.3648 + 17.0881i 0.792100 + 0.664651i 0.946264 0.323394i $$-0.104824\pi$$
−0.154164 + 0.988045i $$0.549268\pi$$
$$662$$ 3.00387 + 17.0358i 0.116749 + 0.662115i
$$663$$ 2.61334 + 0.951178i 0.101494 + 0.0369407i
$$664$$ −3.71688 −0.144243
$$665$$ −1.02094 + 12.5094i −0.0395905 + 0.485092i
$$666$$ 5.92127 0.229445
$$667$$ 4.59405 + 1.67210i 0.177882 + 0.0647438i
$$668$$ −2.02435 11.4806i −0.0783244 0.444200i
$$669$$ −4.82816 4.05131i −0.186668 0.156633i
$$670$$ 1.85844 1.55942i 0.0717978 0.0602455i
$$671$$ 1.34936 7.65258i 0.0520913 0.295424i
$$672$$ 1.43969 2.49362i 0.0555373 0.0961935i
$$673$$ −17.3118 29.9849i −0.667321 1.15583i −0.978650 0.205532i $$-0.934108\pi$$
0.311329 0.950302i $$-0.399226\pi$$
$$674$$ 31.9094 11.6141i 1.22910 0.447358i
$$675$$ −0.939693 + 0.342020i −0.0361688 + 0.0131644i
$$676$$ −1.02481 1.77503i −0.0394160 0.0682704i
$$677$$ 3.22075 5.57851i 0.123784 0.214399i −0.797473 0.603354i $$-0.793830\pi$$
0.921257 + 0.388955i $$0.127164\pi$$
$$678$$ −3.24123 + 18.3819i −0.124479 + 0.705954i
$$679$$ 29.2408 24.5360i 1.12216 0.941604i
$$680$$ −0.549163 0.460802i −0.0210594 0.0176710i
$$681$$ 3.85726 + 21.8756i 0.147810 + 0.838275i
$$682$$ 2.41875 + 0.880352i 0.0926187 + 0.0337104i
$$683$$ −11.9240 −0.456258 −0.228129 0.973631i $$-0.573261\pi$$
−0.228129 + 0.973631i $$0.573261\pi$$
$$684$$ −3.58512 2.47929i −0.137081 0.0947982i
$$685$$ −1.24897 −0.0477207
$$686$$ −15.4474 5.62241i −0.589786 0.214664i
$$687$$ −2.52347 14.3113i −0.0962764 0.546011i
$$688$$ −0.748970 0.628461i −0.0285542 0.0239598i
$$689$$ 8.05097 6.75557i 0.306718 0.257367i
$$690$$ −0.273318 + 1.55007i −0.0104051 + 0.0590100i
$$691$$ −23.8282 + 41.2716i −0.906466 + 1.57005i −0.0875289 + 0.996162i $$0.527897\pi$$
−0.818937 + 0.573883i $$0.805436\pi$$
$$692$$ 3.01842 + 5.22805i 0.114743 + 0.198741i
$$693$$ 1.43969 0.524005i 0.0546894 0.0199053i
$$694$$ −12.5128 + 4.55428i −0.474979 + 0.172878i
$$695$$ −4.39053 7.60462i −0.166542 0.288460i
$$696$$ −1.55303 + 2.68993i −0.0588676 + 0.101962i
$$697$$ −0.492726 + 2.79439i −0.0186633 + 0.105845i
$$698$$ −4.03802 + 3.38830i −0.152841 + 0.128249i
$$699$$ −8.73648 7.33078i −0.330444 0.277276i
$$700$$ 0.500000 + 2.83564i 0.0188982 + 0.107177i
$$701$$ 20.1074 + 7.31850i 0.759446 + 0.276416i 0.692575 0.721346i $$-0.256476\pi$$
0.0668713 + 0.997762i $$0.478698\pi$$
$$702$$ 3.87939 0.146418
$$703$$ −24.9693 6.53466i −0.941735 0.246459i
$$704$$ −0.532089 −0.0200539
$$705$$ 7.23783 + 2.63435i 0.272592 + 0.0992155i
$$706$$ −5.87939 33.3437i −0.221274 1.25490i
$$707$$ 32.4786 + 27.2528i 1.22149 + 1.02495i
$$708$$ −5.88326 + 4.93664i −0.221106 + 0.185530i
$$709$$ −6.72668 + 38.1489i −0.252626 + 1.43271i 0.549468 + 0.835515i $$0.314830\pi$$
−0.802094 + 0.597198i $$0.796281\pi$$
$$710$$ 4.02481 6.97118i 0.151049 0.261624i
$$711$$ 0.733956 + 1.27125i 0.0275255 + 0.0476755i
$$712$$ −14.5287 + 5.28801i −0.544486 + 0.198177i
$$713$$ 7.15493 2.60418i 0.267954 0.0975273i
$$714$$ 1.03209 + 1.78763i 0.0386250 + 0.0669004i
$$715$$ −1.03209 + 1.78763i −0.0385979 + 0.0668536i
$$716$$ 0.212134 1.20307i 0.00792781 0.0449608i
$$717$$ 8.87804 7.44956i 0.331557 0.278209i
$$718$$ −24.1578 20.2708i −0.901559 0.756498i
$$719$$ −8.19506 46.4765i −0.305624 1.73328i −0.620552 0.784165i $$-0.713092\pi$$
0.314928 0.949116i $$-0.398020\pi$$
$$720$$ −0.939693 0.342020i −0.0350203 0.0127463i
$$721$$ −30.9145 −1.15131
$$722$$ 12.3819 + 14.4114i 0.460807 + 0.536337i
$$723$$ −15.2463 −0.567015
$$724$$ −16.9217 6.15901i −0.628892 0.228898i
$$725$$ −0.539363 3.05888i −0.0200314 0.113604i
$$726$$ 8.20961 + 6.88868i 0.304687 + 0.255663i
$$727$$ −34.5979 + 29.0311i −1.28317 + 1.07670i −0.290366 + 0.956916i $$0.593777\pi$$
−0.992799 + 0.119788i $$0.961778\pi$$
$$728$$ 1.93969 11.0005i 0.0718898 0.407707i
$$729$$ −0.500000 + 0.866025i −0.0185185 + 0.0320750i
$$730$$ −2.83022 4.90209i −0.104751 0.181434i
$$731$$ 0.658633 0.239723i 0.0243604 0.00886647i
$$732$$ 13.7233 4.99486i 0.507227 0.184616i
$$733$$ 6.54710 + 11.3399i 0.241823 + 0.418849i 0.961234 0.275736i $$-0.0889214\pi$$
−0.719411 + 0.694585i $$0.755588\pi$$
$$734$$ −5.47818 + 9.48848i −0.202203 + 0.350226i
$$735$$ 0.224155 1.27125i 0.00826810 0.0468907i
$$736$$ −1.20574 + 1.01173i −0.0444441 + 0.0372930i
$$737$$ 0.988856 + 0.829748i 0.0364250 + 0.0305642i
$$738$$ 0.687319 + 3.89798i 0.0253006 + 0.143487i
$$739$$ 41.7845 + 15.2083i 1.53707 + 0.559447i 0.965340 0.260996i $$-0.0840509\pi$$
0.571728 + 0.820443i $$0.306273\pi$$
$$740$$ −5.92127 −0.217670
$$741$$ −16.3589 4.28125i −0.600959 0.157276i
$$742$$ 7.80066 0.286371
$$743$$ 2.96229 + 1.07818i 0.108676 + 0.0395547i 0.395786 0.918343i $$-0.370472\pi$$
−0.287110 + 0.957898i $$0.592695\pi$$
$$744$$ 0.840022 + 4.76400i 0.0307967 + 0.174657i
$$745$$ 5.13950 + 4.31255i 0.188297 + 0.158000i
$$746$$ 3.16978 2.65976i 0.116054 0.0973807i
$$747$$ 0.645430 3.66041i 0.0236150 0.133928i
$$748$$ 0.190722 0.330341i 0.00697350 0.0120785i
$$749$$ 22.6275 + 39.1919i 0.826790 + 1.43204i
$$750$$ 0.939693 0.342020i 0.0343127 0.0124888i
$$751$$ −3.36571 + 1.22502i −0.122817 + 0.0447016i −0.402697 0.915333i $$-0.631927\pi$$
0.279881 + 0.960035i $$0.409705\pi$$
$$752$$ 3.85117 + 6.67042i 0.140438 + 0.243245i
$$753$$ 5.92649 10.2650i 0.215973 0.374077i
$$754$$ −2.09240 + 11.8666i −0.0762006 + 0.432155i
$$755$$ −14.7404 + 12.3686i −0.536456 + 0.450140i
$$756$$ 2.20574 + 1.85083i 0.0802219 + 0.0673142i
$$757$$ −3.30390 18.7374i −0.120082 0.681021i −0.984108 0.177572i $$-0.943176\pi$$
0.864025 0.503448i $$-0.167936\pi$$
$$758$$ 31.8209 + 11.5819i 1.15579 + 0.420672i
$$759$$ −0.837496 −0.0303992
$$760$$ 3.58512 + 2.47929i 0.130046 + 0.0899334i
$$761$$ −1.87527 −0.0679784 −0.0339892 0.999422i $$-0.510821\pi$$
−0.0339892 + 0.999422i $$0.510821\pi$$
$$762$$ −4.43242 1.61327i −0.160570 0.0584426i
$$763$$ 6.77972 + 38.4497i 0.245442 + 1.39197i
$$764$$ −1.29813 1.08926i −0.0469648 0.0394082i
$$765$$ 0.549163 0.460802i 0.0198550 0.0166603i
$$766$$