Properties

 Label 722.2.e.f.389.1 Level $722$ Weight $2$ Character 722.389 Analytic conductor $5.765$ Analytic rank $0$ Dimension $6$ CM no Inner twists $6$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$722 = 2 \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 722.e (of order $$9$$, degree $$6$$, not minimal)

Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$5.76519902594$$ Analytic rank: $$0$$ Dimension: $$6$$ 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: no (minimal twist has level 38) Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

 Embedding label 389.1 Root $$-0.766044 + 0.642788i$$ of defining polynomial Character $$\chi$$ $$=$$ 722.389 Dual form 722.2.e.f.245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.766044 - 0.642788i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.347296 + 1.96962i) q^{9} +O(q^{10})$$ $$q+(-0.173648 - 0.984808i) q^{2} +(0.766044 - 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.766044 - 0.642788i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.347296 + 1.96962i) q^{9} +(3.00000 + 5.19615i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(3.83022 + 3.21394i) q^{13} +(-0.939693 - 0.342020i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.520945 + 2.95442i) q^{17} +2.00000 q^{18} +(-0.173648 - 0.984808i) q^{21} +(4.59627 - 3.85673i) q^{22} +(-2.81908 + 1.02606i) q^{23} +(0.939693 + 0.342020i) q^{24} +(-3.83022 - 3.21394i) q^{25} +(2.50000 - 4.33013i) q^{26} +(2.50000 + 4.33013i) q^{27} +(-0.173648 + 0.984808i) q^{28} +(1.56283 - 8.86327i) q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(5.63816 + 2.05212i) q^{33} +(2.81908 - 1.02606i) q^{34} +(-0.347296 - 1.96962i) q^{36} +2.00000 q^{37} +5.00000 q^{39} +(-0.939693 + 0.342020i) q^{42} +(-7.51754 - 2.73616i) q^{43} +(-4.59627 - 3.85673i) q^{44} +(1.50000 + 2.59808i) q^{46} +(0.173648 - 0.984808i) q^{48} +(3.00000 + 5.19615i) q^{49} +(-2.50000 + 4.33013i) q^{50} +(2.29813 + 1.92836i) q^{51} +(-4.69846 - 1.71010i) q^{52} +(2.81908 - 1.02606i) q^{53} +(3.83022 - 3.21394i) q^{54} +1.00000 q^{56} -9.00000 q^{58} +(1.56283 + 8.86327i) q^{59} +(9.39693 - 3.42020i) q^{61} +(-3.75877 - 1.36808i) q^{62} +(1.53209 + 1.28558i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.04189 - 5.90885i) q^{66} +(0.868241 - 4.92404i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(-1.50000 + 2.59808i) q^{69} +(5.63816 + 2.05212i) q^{71} +(-1.87939 + 0.684040i) q^{72} +(-5.36231 + 4.49951i) q^{73} +(-0.347296 - 1.96962i) q^{74} -5.00000 q^{75} +6.00000 q^{77} +(-0.868241 - 4.92404i) q^{78} +(-7.66044 + 6.42788i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(3.00000 - 5.19615i) q^{83} +(0.500000 + 0.866025i) q^{84} +(-1.38919 + 7.87846i) q^{86} +(-4.50000 - 7.79423i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-9.19253 - 7.71345i) q^{89} +(4.69846 - 1.71010i) q^{91} +(2.29813 - 1.92836i) q^{92} +(-0.694593 - 3.93923i) q^{93} -1.00000 q^{96} +(-1.73648 - 9.84808i) q^{97} +(4.59627 - 3.85673i) q^{98} +(-11.2763 + 4.10424i) 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 $$6 q + 3 q^{7} + 3 q^{8} + 18 q^{11} - 3 q^{12} + 12 q^{18} + 15 q^{26} + 15 q^{27} + 12 q^{31} + 12 q^{37} + 30 q^{39} + 9 q^{46} + 18 q^{49} - 15 q^{50} + 6 q^{56} - 54 q^{58} - 3 q^{64} - 9 q^{68} - 9 q^{69} - 30 q^{75} + 36 q^{77} + 18 q^{83} + 3 q^{84} - 27 q^{87} - 18 q^{88} - 6 q^{96}+O(q^{100})$$ 6 * q + 3 * q^7 + 3 * q^8 + 18 * q^11 - 3 * q^12 + 12 * q^18 + 15 * q^26 + 15 * q^27 + 12 * q^31 + 12 * q^37 + 30 * q^39 + 9 * q^46 + 18 * q^49 - 15 * q^50 + 6 * q^56 - 54 * q^58 - 3 * q^64 - 9 * q^68 - 9 * q^69 - 30 * q^75 + 36 * q^77 + 18 * q^83 + 3 * q^84 - 27 * q^87 - 18 * q^88 - 6 * q^96

Character values

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

 $$n$$ $$363$$ $$\chi(n)$$ $$e\left(\frac{4}{9}\right)$$

Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.173648 0.984808i −0.122788 0.696364i
$$3$$ 0.766044 0.642788i 0.442276 0.371114i −0.394284 0.918989i $$-0.629007\pi$$
0.836560 + 0.547875i $$0.184563\pi$$
$$4$$ −0.939693 + 0.342020i −0.469846 + 0.171010i
$$5$$ 0 0 0.342020 0.939693i $$-0.388889\pi$$
−0.342020 + 0.939693i $$0.611111\pi$$
$$6$$ −0.766044 0.642788i −0.312736 0.262417i
$$7$$ 0.500000 0.866025i 0.188982 0.327327i −0.755929 0.654654i $$-0.772814\pi$$
0.944911 + 0.327327i $$0.106148\pi$$
$$8$$ 0.500000 + 0.866025i 0.176777 + 0.306186i
$$9$$ −0.347296 + 1.96962i −0.115765 + 0.656539i
$$10$$ 0 0
$$11$$ 3.00000 + 5.19615i 0.904534 + 1.56670i 0.821541 + 0.570149i $$0.193114\pi$$
0.0829925 + 0.996550i $$0.473552\pi$$
$$12$$ −0.500000 + 0.866025i −0.144338 + 0.250000i
$$13$$ 3.83022 + 3.21394i 1.06231 + 0.891386i 0.994334 0.106301i $$-0.0339006\pi$$
0.0679785 + 0.997687i $$0.478345\pi$$
$$14$$ −0.939693 0.342020i −0.251143 0.0914087i
$$15$$ 0 0
$$16$$ 0.766044 0.642788i 0.191511 0.160697i
$$17$$ 0.520945 + 2.95442i 0.126348 + 0.716553i 0.980498 + 0.196527i $$0.0629665\pi$$
−0.854151 + 0.520026i $$0.825922\pi$$
$$18$$ 2.00000 0.471405
$$19$$ 0 0
$$20$$ 0 0
$$21$$ −0.173648 0.984808i −0.0378931 0.214903i
$$22$$ 4.59627 3.85673i 0.979927 0.822257i
$$23$$ −2.81908 + 1.02606i −0.587818 + 0.213948i −0.618770 0.785573i $$-0.712369\pi$$
0.0309512 + 0.999521i $$0.490146\pi$$
$$24$$ 0.939693 + 0.342020i 0.191814 + 0.0698146i
$$25$$ −3.83022 3.21394i −0.766044 0.642788i
$$26$$ 2.50000 4.33013i 0.490290 0.849208i
$$27$$ 2.50000 + 4.33013i 0.481125 + 0.833333i
$$28$$ −0.173648 + 0.984808i −0.0328164 + 0.186111i
$$29$$ 1.56283 8.86327i 0.290211 1.64587i −0.395844 0.918318i $$-0.629548\pi$$
0.686055 0.727550i $$-0.259341\pi$$
$$30$$ 0 0
$$31$$ 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i $$-0.716379\pi$$
0.987829 + 0.155543i $$0.0497126\pi$$
$$32$$ −0.766044 0.642788i −0.135419 0.113630i
$$33$$ 5.63816 + 2.05212i 0.981477 + 0.357228i
$$34$$ 2.81908 1.02606i 0.483468 0.175968i
$$35$$ 0 0
$$36$$ −0.347296 1.96962i −0.0578827 0.328269i
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 0 0
$$39$$ 5.00000 0.800641
$$40$$ 0 0
$$41$$ 0 0 −0.642788 0.766044i $$-0.722222\pi$$
0.642788 + 0.766044i $$0.277778\pi$$
$$42$$ −0.939693 + 0.342020i −0.144998 + 0.0527749i
$$43$$ −7.51754 2.73616i −1.14641 0.417261i −0.302188 0.953248i $$-0.597717\pi$$
−0.844226 + 0.535988i $$0.819939\pi$$
$$44$$ −4.59627 3.85673i −0.692913 0.581423i
$$45$$ 0 0
$$46$$ 1.50000 + 2.59808i 0.221163 + 0.383065i
$$47$$ 0 0 −0.984808 0.173648i $$-0.944444\pi$$
0.984808 + 0.173648i $$0.0555556\pi$$
$$48$$ 0.173648 0.984808i 0.0250640 0.142145i
$$49$$ 3.00000 + 5.19615i 0.428571 + 0.742307i
$$50$$ −2.50000 + 4.33013i −0.353553 + 0.612372i
$$51$$ 2.29813 + 1.92836i 0.321803 + 0.270025i
$$52$$ −4.69846 1.71010i −0.651560 0.237148i
$$53$$ 2.81908 1.02606i 0.387230 0.140940i −0.141066 0.990000i $$-0.545053\pi$$
0.528297 + 0.849060i $$0.322831\pi$$
$$54$$ 3.83022 3.21394i 0.521227 0.437362i
$$55$$ 0 0
$$56$$ 1.00000 0.133631
$$57$$ 0 0
$$58$$ −9.00000 −1.18176
$$59$$ 1.56283 + 8.86327i 0.203464 + 1.15390i 0.899839 + 0.436222i $$0.143684\pi$$
−0.696376 + 0.717678i $$0.745205\pi$$
$$60$$ 0 0
$$61$$ 9.39693 3.42020i 1.20315 0.437912i 0.338829 0.940848i $$-0.389969\pi$$
0.864324 + 0.502936i $$0.167747\pi$$
$$62$$ −3.75877 1.36808i −0.477364 0.173746i
$$63$$ 1.53209 + 1.28558i 0.193025 + 0.161967i
$$64$$ −0.500000 + 0.866025i −0.0625000 + 0.108253i
$$65$$ 0 0
$$66$$ 1.04189 5.90885i 0.128248 0.727329i
$$67$$ 0.868241 4.92404i 0.106073 0.601567i −0.884714 0.466134i $$-0.845646\pi$$
0.990787 0.135433i $$-0.0432425\pi$$
$$68$$ −1.50000 2.59808i −0.181902 0.315063i
$$69$$ −1.50000 + 2.59808i −0.180579 + 0.312772i
$$70$$ 0 0
$$71$$ 5.63816 + 2.05212i 0.669126 + 0.243542i 0.654172 0.756346i $$-0.273017\pi$$
0.0149545 + 0.999888i $$0.495240\pi$$
$$72$$ −1.87939 + 0.684040i −0.221488 + 0.0806149i
$$73$$ −5.36231 + 4.49951i −0.627611 + 0.526628i −0.900186 0.435506i $$-0.856569\pi$$
0.272575 + 0.962135i $$0.412125\pi$$
$$74$$ −0.347296 1.96962i −0.0403724 0.228963i
$$75$$ −5.00000 −0.577350
$$76$$ 0 0
$$77$$ 6.00000 0.683763
$$78$$ −0.868241 4.92404i −0.0983089 0.557538i
$$79$$ −7.66044 + 6.42788i −0.861867 + 0.723193i −0.962369 0.271744i $$-0.912400\pi$$
0.100502 + 0.994937i $$0.467955\pi$$
$$80$$ 0 0
$$81$$ −0.939693 0.342020i −0.104410 0.0380022i
$$82$$ 0 0
$$83$$ 3.00000 5.19615i 0.329293 0.570352i −0.653079 0.757290i $$-0.726523\pi$$
0.982372 + 0.186938i $$0.0598564\pi$$
$$84$$ 0.500000 + 0.866025i 0.0545545 + 0.0944911i
$$85$$ 0 0
$$86$$ −1.38919 + 7.87846i −0.149800 + 0.849556i
$$87$$ −4.50000 7.79423i −0.482451 0.835629i
$$88$$ −3.00000 + 5.19615i −0.319801 + 0.553912i
$$89$$ −9.19253 7.71345i −0.974407 0.817624i 0.00882955 0.999961i $$-0.497189\pi$$
−0.983236 + 0.182337i $$0.941634\pi$$
$$90$$ 0 0
$$91$$ 4.69846 1.71010i 0.492533 0.179267i
$$92$$ 2.29813 1.92836i 0.239597 0.201046i
$$93$$ −0.694593 3.93923i −0.0720259 0.408479i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ −1.73648 9.84808i −0.176313 0.999921i −0.936617 0.350354i $$-0.886061\pi$$
0.760304 0.649567i $$-0.225050\pi$$
$$98$$ 4.59627 3.85673i 0.464293 0.389588i
$$99$$ −11.2763 + 4.10424i −1.13331 + 0.412492i
$$100$$ 4.69846 + 1.71010i 0.469846 + 0.171010i
$$101$$ 13.7888 + 11.5702i 1.37204 + 1.15128i 0.972055 + 0.234753i $$0.0754280\pi$$
0.399982 + 0.916523i $$0.369016\pi$$
$$102$$ 1.50000 2.59808i 0.148522 0.257248i
$$103$$ −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i $$-0.924396\pi$$
0.282194 0.959357i $$-0.408938\pi$$
$$104$$ −0.868241 + 4.92404i −0.0851380 + 0.482842i
$$105$$ 0 0
$$106$$ −1.50000 2.59808i −0.145693 0.252347i
$$107$$ 4.50000 7.79423i 0.435031 0.753497i −0.562267 0.826956i $$-0.690071\pi$$
0.997298 + 0.0734594i $$0.0234039\pi$$
$$108$$ −3.83022 3.21394i −0.368563 0.309261i
$$109$$ −10.3366 3.76222i −0.990069 0.360355i −0.204322 0.978904i $$-0.565499\pi$$
−0.785747 + 0.618548i $$0.787721\pi$$
$$110$$ 0 0
$$111$$ 1.53209 1.28558i 0.145419 0.122021i
$$112$$ −0.173648 0.984808i −0.0164082 0.0930556i
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 1.56283 + 8.86327i 0.145105 + 0.822934i
$$117$$ −7.66044 + 6.42788i −0.708208 + 0.594257i
$$118$$ 8.45723 3.07818i 0.778551 0.283370i
$$119$$ 2.81908 + 1.02606i 0.258424 + 0.0940588i
$$120$$ 0 0
$$121$$ −12.5000 + 21.6506i −1.13636 + 1.96824i
$$122$$ −5.00000 8.66025i −0.452679 0.784063i
$$123$$ 0 0
$$124$$ −0.694593 + 3.93923i −0.0623763 + 0.353753i
$$125$$ 0 0
$$126$$ 1.00000 1.73205i 0.0890871 0.154303i
$$127$$ 1.53209 + 1.28558i 0.135951 + 0.114076i 0.708227 0.705984i $$-0.249495\pi$$
−0.572276 + 0.820061i $$0.693940\pi$$
$$128$$ 0.939693 + 0.342020i 0.0830579 + 0.0302306i
$$129$$ −7.51754 + 2.73616i −0.661883 + 0.240906i
$$130$$ 0 0
$$131$$ 0 0 0.984808 0.173648i $$-0.0555556\pi$$
−0.984808 + 0.173648i $$0.944444\pi$$
$$132$$ −6.00000 −0.522233
$$133$$ 0 0
$$134$$ −5.00000 −0.431934
$$135$$ 0 0
$$136$$ −2.29813 + 1.92836i −0.197063 + 0.165356i
$$137$$ 8.45723 3.07818i 0.722550 0.262987i 0.0455422 0.998962i $$-0.485498\pi$$
0.677008 + 0.735976i $$0.263276\pi$$
$$138$$ 2.81908 + 1.02606i 0.239976 + 0.0873441i
$$139$$ −3.06418 2.57115i −0.259900 0.218082i 0.503521 0.863983i $$-0.332038\pi$$
−0.763421 + 0.645901i $$0.776482\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 1.04189 5.90885i 0.0874334 0.495859i
$$143$$ −5.20945 + 29.5442i −0.435636 + 2.47061i
$$144$$ 1.00000 + 1.73205i 0.0833333 + 0.144338i
$$145$$ 0 0
$$146$$ 5.36231 + 4.49951i 0.443788 + 0.372382i
$$147$$ 5.63816 + 2.05212i 0.465027 + 0.169256i
$$148$$ −1.87939 + 0.684040i −0.154485 + 0.0562278i
$$149$$ 0 0 −0.642788 0.766044i $$-0.722222\pi$$
0.642788 + 0.766044i $$0.277778\pi$$
$$150$$ 0.868241 + 4.92404i 0.0708916 + 0.402046i
$$151$$ −10.0000 −0.813788 −0.406894 0.913475i $$-0.633388\pi$$
−0.406894 + 0.913475i $$0.633388\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ −1.04189 5.90885i −0.0839578 0.476148i
$$155$$ 0 0
$$156$$ −4.69846 + 1.71010i −0.376178 + 0.136918i
$$157$$ 20.6732 + 7.52444i 1.64990 + 0.600516i 0.988729 0.149716i $$-0.0478359\pi$$
0.661175 + 0.750232i $$0.270058\pi$$
$$158$$ 7.66044 + 6.42788i 0.609432 + 0.511374i
$$159$$ 1.50000 2.59808i 0.118958 0.206041i
$$160$$ 0 0
$$161$$ −0.520945 + 2.95442i −0.0410562 + 0.232841i
$$162$$ −0.173648 + 0.984808i −0.0136431 + 0.0773738i
$$163$$ −10.0000 17.3205i −0.783260 1.35665i −0.930033 0.367477i $$-0.880222\pi$$
0.146772 0.989170i $$-0.453112\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −5.63816 2.05212i −0.437606 0.159275i
$$167$$ −11.2763 + 4.10424i −0.872587 + 0.317596i −0.739214 0.673470i $$-0.764803\pi$$
−0.133373 + 0.991066i $$0.542581\pi$$
$$168$$ 0.766044 0.642788i 0.0591016 0.0495921i
$$169$$ 2.08378 + 11.8177i 0.160291 + 0.909053i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 8.00000 0.609994
$$173$$ 1.04189 + 5.90885i 0.0792134 + 0.449241i 0.998456 + 0.0555496i $$0.0176911\pi$$
−0.919243 + 0.393692i $$0.871198\pi$$
$$174$$ −6.89440 + 5.78509i −0.522663 + 0.438566i
$$175$$ −4.69846 + 1.71010i −0.355170 + 0.129271i
$$176$$ 5.63816 + 2.05212i 0.424992 + 0.154684i
$$177$$ 6.89440 + 5.78509i 0.518215 + 0.434834i
$$178$$ −6.00000 + 10.3923i −0.449719 + 0.778936i
$$179$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$180$$ 0 0
$$181$$ 0.347296 1.96962i 0.0258143 0.146400i −0.969176 0.246368i $$-0.920763\pi$$
0.994991 + 0.0999676i $$0.0318739\pi$$
$$182$$ −2.50000 4.33013i −0.185312 0.320970i
$$183$$ 5.00000 8.66025i 0.369611 0.640184i
$$184$$ −2.29813 1.92836i −0.169421 0.142161i
$$185$$ 0 0
$$186$$ −3.75877 + 1.36808i −0.275606 + 0.100313i
$$187$$ −13.7888 + 11.5702i −1.00834 + 0.846095i
$$188$$ 0 0
$$189$$ 5.00000 0.363696
$$190$$ 0 0
$$191$$ 3.00000 0.217072 0.108536 0.994092i $$-0.465384\pi$$
0.108536 + 0.994092i $$0.465384\pi$$
$$192$$ 0.173648 + 0.984808i 0.0125320 + 0.0710724i
$$193$$ 10.7246 8.99903i 0.771975 0.647764i −0.169239 0.985575i $$-0.554131\pi$$
0.941214 + 0.337811i $$0.109686\pi$$
$$194$$ −9.39693 + 3.42020i −0.674660 + 0.245556i
$$195$$ 0 0
$$196$$ −4.59627 3.85673i −0.328305 0.275480i
$$197$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$198$$ 6.00000 + 10.3923i 0.426401 + 0.738549i
$$199$$ 1.91013 10.8329i 0.135406 0.767923i −0.839171 0.543868i $$-0.816959\pi$$
0.974576 0.224055i $$-0.0719296\pi$$
$$200$$ 0.868241 4.92404i 0.0613939 0.348182i
$$201$$ −2.50000 4.33013i −0.176336 0.305424i
$$202$$ 9.00000 15.5885i 0.633238 1.09680i
$$203$$ −6.89440 5.78509i −0.483892 0.406034i
$$204$$ −2.81908 1.02606i −0.197375 0.0718386i
$$205$$ 0 0
$$206$$ −10.7246 + 8.99903i −0.747220 + 0.626992i
$$207$$ −1.04189 5.90885i −0.0724163 0.410693i
$$208$$ 5.00000 0.346688
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0.868241 + 4.92404i 0.0597722 + 0.338985i 0.999999 0.00156464i $$-0.000498040\pi$$
−0.940227 + 0.340549i $$0.889387\pi$$
$$212$$ −2.29813 + 1.92836i −0.157836 + 0.132441i
$$213$$ 5.63816 2.05212i 0.386320 0.140609i
$$214$$ −8.45723 3.07818i −0.578125 0.210420i
$$215$$ 0 0
$$216$$ −2.50000 + 4.33013i −0.170103 + 0.294628i
$$217$$ −2.00000 3.46410i −0.135769 0.235159i
$$218$$ −1.91013 + 10.8329i −0.129370 + 0.733696i
$$219$$ −1.21554 + 6.89365i −0.0821384 + 0.465830i
$$220$$ 0 0
$$221$$ −7.50000 + 12.9904i −0.504505 + 0.873828i
$$222$$ −1.53209 1.28558i −0.102827 0.0862822i
$$223$$ −24.4320 8.89252i −1.63609 0.595487i −0.649739 0.760157i $$-0.725122\pi$$
−0.986349 + 0.164670i $$0.947344\pi$$
$$224$$ −0.939693 + 0.342020i −0.0627859 + 0.0228522i
$$225$$ 7.66044 6.42788i 0.510696 0.428525i
$$226$$ −1.04189 5.90885i −0.0693054 0.393051i
$$227$$ −15.0000 −0.995585 −0.497792 0.867296i $$-0.665856\pi$$
−0.497792 + 0.867296i $$0.665856\pi$$
$$228$$ 0 0
$$229$$ −22.0000 −1.45380 −0.726900 0.686743i $$-0.759040\pi$$
−0.726900 + 0.686743i $$0.759040\pi$$
$$230$$ 0 0
$$231$$ 4.59627 3.85673i 0.302412 0.253754i
$$232$$ 8.45723 3.07818i 0.555245 0.202093i
$$233$$ 5.63816 + 2.05212i 0.369368 + 0.134439i 0.520033 0.854146i $$-0.325919\pi$$
−0.150666 + 0.988585i $$0.548142\pi$$
$$234$$ 7.66044 + 6.42788i 0.500779 + 0.420203i
$$235$$ 0 0
$$236$$ −4.50000 7.79423i −0.292925 0.507361i
$$237$$ −1.73648 + 9.84808i −0.112797 + 0.639701i
$$238$$ 0.520945 2.95442i 0.0337678 0.191507i
$$239$$ 10.5000 + 18.1865i 0.679189 + 1.17639i 0.975226 + 0.221213i $$0.0710015\pi$$
−0.296037 + 0.955176i $$0.595665\pi$$
$$240$$ 0 0
$$241$$ 6.12836 + 5.14230i 0.394762 + 0.331245i 0.818465 0.574557i $$-0.194825\pi$$
−0.423703 + 0.905801i $$0.639270\pi$$
$$242$$ 23.4923 + 8.55050i 1.51014 + 0.549647i
$$243$$ −15.0351 + 5.47232i −0.964501 + 0.351050i
$$244$$ −7.66044 + 6.42788i −0.490410 + 0.411503i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 4.00000 0.254000
$$249$$ −1.04189 5.90885i −0.0660270 0.374458i
$$250$$ 0 0
$$251$$ −5.63816 + 2.05212i −0.355877 + 0.129529i −0.513771 0.857927i $$-0.671752\pi$$
0.157894 + 0.987456i $$0.449530\pi$$
$$252$$ −1.87939 0.684040i −0.118390 0.0430905i
$$253$$ −13.7888 11.5702i −0.866894 0.727411i
$$254$$ 1.00000 1.73205i 0.0627456 0.108679i
$$255$$ 0 0
$$256$$ 0.173648 0.984808i 0.0108530 0.0615505i
$$257$$ 2.08378 11.8177i 0.129983 0.737167i −0.848241 0.529611i $$-0.822338\pi$$
0.978223 0.207556i $$-0.0665510\pi$$
$$258$$ 4.00000 + 6.92820i 0.249029 + 0.431331i
$$259$$ 1.00000 1.73205i 0.0621370 0.107624i
$$260$$ 0 0
$$261$$ 16.9145 + 6.15636i 1.04698 + 0.381069i
$$262$$ 0 0
$$263$$ 18.3851 15.4269i 1.13367 0.951264i 0.134458 0.990919i $$-0.457071\pi$$
0.999213 + 0.0396557i $$0.0126261\pi$$
$$264$$ 1.04189 + 5.90885i 0.0641238 + 0.363664i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −12.0000 −0.734388
$$268$$ 0.868241 + 4.92404i 0.0530363 + 0.300784i
$$269$$ −4.59627 + 3.85673i −0.280239 + 0.235149i −0.772063 0.635546i $$-0.780775\pi$$
0.491824 + 0.870695i $$0.336331\pi$$
$$270$$ 0 0
$$271$$ −10.3366 3.76222i −0.627905 0.228539i 0.00841427 0.999965i $$-0.497322\pi$$
−0.636319 + 0.771426i $$0.719544\pi$$
$$272$$ 2.29813 + 1.92836i 0.139345 + 0.116924i
$$273$$ 2.50000 4.33013i 0.151307 0.262071i
$$274$$ −4.50000 7.79423i −0.271855 0.470867i
$$275$$ 5.20945 29.5442i 0.314141 1.78158i
$$276$$ 0.520945 2.95442i 0.0313572 0.177835i
$$277$$ −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i $$-0.243925\pi$$
−0.960810 + 0.277207i $$0.910591\pi$$
$$278$$ −2.00000 + 3.46410i −0.119952 + 0.207763i
$$279$$ 6.12836 + 5.14230i 0.366895 + 0.307862i
$$280$$ 0 0
$$281$$ 0 0 −0.342020 0.939693i $$-0.611111\pi$$
0.342020 + 0.939693i $$0.388889\pi$$
$$282$$ 0 0
$$283$$ −3.82026 21.6658i −0.227091 1.28790i −0.858647 0.512567i $$-0.828695\pi$$
0.631557 0.775330i $$-0.282416\pi$$
$$284$$ −6.00000 −0.356034
$$285$$ 0 0
$$286$$ 30.0000 1.77394
$$287$$ 0 0
$$288$$ 1.53209 1.28558i 0.0902792 0.0757532i
$$289$$ 7.51754 2.73616i 0.442208 0.160951i
$$290$$ 0 0
$$291$$ −7.66044 6.42788i −0.449063 0.376809i
$$292$$ 3.50000 6.06218i 0.204822 0.354762i
$$293$$ 10.5000 + 18.1865i 0.613417 + 1.06247i 0.990660 + 0.136355i $$0.0435386\pi$$
−0.377244 + 0.926114i $$0.623128\pi$$
$$294$$ 1.04189 5.90885i 0.0607642 0.344611i
$$295$$ 0 0
$$296$$ 1.00000 + 1.73205i 0.0581238 + 0.100673i
$$297$$ −15.0000 + 25.9808i −0.870388 + 1.50756i
$$298$$ 0 0
$$299$$ −14.0954 5.13030i −0.815157 0.296693i
$$300$$ 4.69846 1.71010i 0.271266 0.0987327i
$$301$$ −6.12836 + 5.14230i −0.353233 + 0.296397i
$$302$$ 1.73648 + 9.84808i 0.0999233 + 0.566693i
$$303$$ 18.0000 1.03407
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 1.04189 + 5.90885i 0.0595608 + 0.337786i
$$307$$ 15.3209 12.8558i 0.874409 0.733717i −0.0906125 0.995886i $$-0.528882\pi$$
0.965022 + 0.262170i $$0.0844380\pi$$
$$308$$ −5.63816 + 2.05212i −0.321264 + 0.116930i
$$309$$ −13.1557 4.78828i −0.748401 0.272396i
$$310$$ 0 0
$$311$$ 10.5000 18.1865i 0.595400 1.03126i −0.398090 0.917346i $$-0.630327\pi$$
0.993490 0.113917i $$-0.0363399\pi$$
$$312$$ 2.50000 + 4.33013i 0.141535 + 0.245145i
$$313$$ −3.29932 + 18.7113i −0.186488 + 1.05763i 0.737540 + 0.675304i $$0.235987\pi$$
−0.924028 + 0.382324i $$0.875124\pi$$
$$314$$ 3.82026 21.6658i 0.215590 1.22267i
$$315$$ 0 0
$$316$$ 5.00000 8.66025i 0.281272 0.487177i
$$317$$ −6.89440 5.78509i −0.387228 0.324923i 0.428304 0.903635i $$-0.359111\pi$$
−0.815532 + 0.578712i $$0.803556\pi$$
$$318$$ −2.81908 1.02606i −0.158086 0.0575386i
$$319$$ 50.7434 18.4691i 2.84109 1.03407i
$$320$$ 0 0
$$321$$ −1.56283 8.86327i −0.0872289 0.494699i
$$322$$ 3.00000 0.167183
$$323$$ 0 0
$$324$$ 1.00000 0.0555556
$$325$$ −4.34120 24.6202i −0.240807 1.36568i
$$326$$ −15.3209 + 12.8558i −0.848546 + 0.712014i
$$327$$ −10.3366 + 3.76222i −0.571616 + 0.208051i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0.500000 + 0.866025i 0.0274825 + 0.0476011i 0.879440 0.476011i $$-0.157918\pi$$
−0.851957 + 0.523612i $$0.824584\pi$$
$$332$$ −1.04189 + 5.90885i −0.0571811 + 0.324290i
$$333$$ −0.694593 + 3.93923i −0.0380634 + 0.215869i
$$334$$ 6.00000 + 10.3923i 0.328305 + 0.568642i
$$335$$ 0 0
$$336$$ −0.766044 0.642788i −0.0417912 0.0350669i
$$337$$ 3.75877 + 1.36808i 0.204753 + 0.0745241i 0.442361 0.896837i $$-0.354141\pi$$
−0.237608 + 0.971361i $$0.576363\pi$$
$$338$$ 11.2763 4.10424i 0.613350 0.223241i
$$339$$ 4.59627 3.85673i 0.249635 0.209469i
$$340$$ 0 0
$$341$$ 24.0000 1.29967
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ −1.38919 7.87846i −0.0748999 0.424778i
$$345$$ 0 0
$$346$$ 5.63816 2.05212i 0.303109 0.110323i
$$347$$ −16.9145 6.15636i −0.908016 0.330491i −0.154556 0.987984i $$-0.549395\pi$$
−0.753460 + 0.657493i $$0.771617\pi$$
$$348$$ 6.89440 + 5.78509i 0.369579 + 0.310113i
$$349$$ 5.00000 8.66025i 0.267644 0.463573i −0.700609 0.713545i $$-0.747088\pi$$
0.968253 + 0.249973i $$0.0804216\pi$$
$$350$$ 2.50000 + 4.33013i 0.133631 + 0.231455i
$$351$$ −4.34120 + 24.6202i −0.231716 + 1.31413i
$$352$$ 1.04189 5.90885i 0.0555329 0.314943i
$$353$$ 7.50000 + 12.9904i 0.399185 + 0.691408i 0.993626 0.112731i $$-0.0359599\pi$$
−0.594441 + 0.804139i $$0.702627\pi$$
$$354$$ 4.50000 7.79423i 0.239172 0.414259i
$$355$$ 0 0
$$356$$ 11.2763 + 4.10424i 0.597643 + 0.217524i
$$357$$ 2.81908 1.02606i 0.149201 0.0543049i
$$358$$ 0 0
$$359$$ 3.64661 + 20.6810i 0.192461 + 1.09150i 0.915989 + 0.401204i $$0.131408\pi$$
−0.723528 + 0.690295i $$0.757481\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ −2.00000 −0.105118
$$363$$ 4.34120 + 24.6202i 0.227854 + 1.29223i
$$364$$ −3.83022 + 3.21394i −0.200758 + 0.168456i
$$365$$ 0 0
$$366$$ −9.39693 3.42020i −0.491185 0.178777i
$$367$$ −21.4492 17.9981i −1.11964 0.939491i −0.121055 0.992646i $$-0.538628\pi$$
−0.998586 + 0.0531551i $$0.983072\pi$$
$$368$$ −1.50000 + 2.59808i −0.0781929 + 0.135434i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0.520945 2.95442i 0.0270461 0.153386i
$$372$$ 2.00000 + 3.46410i 0.103695 + 0.179605i
$$373$$ −11.5000 + 19.9186i −0.595447 + 1.03135i 0.398036 + 0.917370i $$0.369692\pi$$
−0.993484 + 0.113975i $$0.963641\pi$$
$$374$$ 13.7888 + 11.5702i 0.713002 + 0.598280i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 34.4720 28.9254i 1.77540 1.48974i
$$378$$ −0.868241 4.92404i −0.0446575 0.253265i
$$379$$ −7.00000 −0.359566 −0.179783 0.983706i $$-0.557540\pi$$
−0.179783 + 0.983706i $$0.557540\pi$$
$$380$$ 0 0
$$381$$ 2.00000 0.102463
$$382$$ −0.520945 2.95442i −0.0266538 0.151161i
$$383$$ 13.7888 11.5702i 0.704575 0.591208i −0.218496 0.975838i $$-0.570115\pi$$
0.923071 + 0.384629i $$0.125671\pi$$
$$384$$ 0.939693 0.342020i 0.0479535 0.0174536i
$$385$$ 0 0
$$386$$ −10.7246 8.99903i −0.545869 0.458038i
$$387$$ 8.00000 13.8564i 0.406663 0.704361i
$$388$$ 5.00000 + 8.66025i 0.253837 + 0.439658i
$$389$$ 3.12567 17.7265i 0.158478 0.898771i −0.797060 0.603901i $$-0.793612\pi$$
0.955537 0.294871i $$-0.0952765\pi$$
$$390$$ 0 0
$$391$$ −4.50000 7.79423i −0.227575 0.394171i
$$392$$ −3.00000 + 5.19615i −0.151523 + 0.262445i
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 9.19253 7.71345i 0.461942 0.387616i
$$397$$ 3.47296 + 19.6962i 0.174303 + 0.988522i 0.938945 + 0.344067i $$0.111805\pi$$
−0.764642 + 0.644455i $$0.777084\pi$$
$$398$$ −11.0000 −0.551380
$$399$$ 0 0
$$400$$ −5.00000 −0.250000
$$401$$ 0 0 0.984808 0.173648i $$-0.0555556\pi$$
−0.984808 + 0.173648i $$0.944444\pi$$
$$402$$ −3.83022 + 3.21394i −0.191034 + 0.160297i
$$403$$ 18.7939 6.84040i 0.936188 0.340745i
$$404$$ −16.9145 6.15636i −0.841526 0.306290i
$$405$$ 0 0
$$406$$ −4.50000 + 7.79423i −0.223331 + 0.386821i
$$407$$ 6.00000 + 10.3923i 0.297409 + 0.515127i
$$408$$ −0.520945 + 2.95442i −0.0257906 + 0.146266i
$$409$$ 5.55674 31.5138i 0.274763 1.55826i −0.464950 0.885337i $$-0.653928\pi$$
0.739713 0.672922i $$-0.234961\pi$$
$$410$$ 0 0
$$411$$ 4.50000 7.79423i 0.221969 0.384461i
$$412$$ 10.7246 + 8.99903i 0.528364 + 0.443350i
$$413$$ 8.45723 + 3.07818i 0.416153 + 0.151467i
$$414$$ −5.63816 + 2.05212i −0.277100 + 0.100856i
$$415$$ 0 0
$$416$$ −0.868241 4.92404i −0.0425690 0.241421i
$$417$$ −4.00000 −0.195881
$$418$$ 0 0
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ 13.0228 10.9274i 0.634690 0.532568i −0.267692 0.963504i $$-0.586261\pi$$
0.902382 + 0.430936i $$0.141817\pi$$
$$422$$ 4.69846 1.71010i 0.228718 0.0832464i
$$423$$ 0 0
$$424$$ 2.29813 + 1.92836i 0.111607 + 0.0936496i
$$425$$ 7.50000 12.9904i 0.363803 0.630126i
$$426$$ −3.00000 5.19615i −0.145350 0.251754i
$$427$$ 1.73648 9.84808i 0.0840342 0.476582i
$$428$$ −1.56283 + 8.86327i −0.0755424 + 0.428422i
$$429$$ 15.0000 + 25.9808i 0.724207 + 1.25436i
$$430$$ 0 0
$$431$$ 4.59627 + 3.85673i 0.221394 + 0.185772i 0.746738 0.665118i $$-0.231619\pi$$
−0.525344 + 0.850890i $$0.676063\pi$$
$$432$$ 4.69846 + 1.71010i 0.226055 + 0.0822773i
$$433$$ −1.87939 + 0.684040i −0.0903175 + 0.0328729i −0.386784 0.922170i $$-0.626414\pi$$
0.296466 + 0.955043i $$0.404192\pi$$
$$434$$ −3.06418 + 2.57115i −0.147085 + 0.123419i
$$435$$ 0 0
$$436$$ 11.0000 0.526804
$$437$$ 0 0
$$438$$ 7.00000 0.334473
$$439$$ −4.86215 27.5746i −0.232058 1.31606i −0.848722 0.528839i $$-0.822628\pi$$
0.616665 0.787226i $$-0.288483\pi$$
$$440$$ 0 0
$$441$$ −11.2763 + 4.10424i −0.536967 + 0.195440i
$$442$$ 14.0954 + 5.13030i 0.670449 + 0.244024i
$$443$$ −13.7888 11.5702i −0.655126 0.549716i 0.253496 0.967336i $$-0.418420\pi$$
−0.908621 + 0.417621i $$0.862864\pi$$
$$444$$ −1.00000 + 1.73205i −0.0474579 + 0.0821995i
$$445$$ 0 0
$$446$$ −4.51485 + 25.6050i −0.213784 + 1.21243i
$$447$$ 0 0
$$448$$ 0.500000 + 0.866025i 0.0236228 + 0.0409159i
$$449$$ 9.00000 15.5885i 0.424736 0.735665i −0.571660 0.820491i $$-0.693700\pi$$
0.996396 + 0.0848262i $$0.0270335\pi$$
$$450$$ −7.66044 6.42788i −0.361117 0.303013i
$$451$$ 0 0
$$452$$ −5.63816 + 2.05212i −0.265197 + 0.0965236i
$$453$$ −7.66044 + 6.42788i −0.359919 + 0.302008i
$$454$$ 2.60472 + 14.7721i 0.122246 + 0.693290i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 17.0000 0.795226 0.397613 0.917553i $$-0.369839\pi$$
0.397613 + 0.917553i $$0.369839\pi$$
$$458$$ 3.82026 + 21.6658i 0.178509 + 1.01237i
$$459$$ −11.4907 + 9.64181i −0.536338 + 0.450041i
$$460$$ 0 0
$$461$$ 11.2763 + 4.10424i 0.525190 + 0.191154i 0.590989 0.806679i $$-0.298737\pi$$
−0.0657993 + 0.997833i $$0.520960\pi$$
$$462$$ −4.59627 3.85673i −0.213838 0.179431i
$$463$$ 2.00000 3.46410i 0.0929479 0.160990i −0.815802 0.578331i $$-0.803704\pi$$
0.908750 + 0.417340i $$0.137038\pi$$
$$464$$ −4.50000 7.79423i −0.208907 0.361838i
$$465$$ 0 0
$$466$$ 1.04189 5.90885i 0.0482646 0.273722i
$$467$$ −9.00000 15.5885i −0.416470 0.721348i 0.579111 0.815249i $$-0.303400\pi$$
−0.995582 + 0.0939008i $$0.970066\pi$$
$$468$$ 5.00000 8.66025i 0.231125 0.400320i
$$469$$ −3.83022 3.21394i −0.176863 0.148406i
$$470$$ 0 0
$$471$$ 20.6732 7.52444i 0.952573 0.346708i
$$472$$ −6.89440 + 5.78509i −0.317340 + 0.266280i
$$473$$ −8.33511 47.2708i −0.383249 2.17351i
$$474$$ 10.0000 0.459315
$$475$$ 0 0
$$476$$ −3.00000 −0.137505
$$477$$ 1.04189 + 5.90885i 0.0477048 + 0.270547i
$$478$$ 16.0869 13.4985i 0.735799 0.617409i
$$479$$ −33.8289 + 12.3127i −1.54568 + 0.562583i −0.967400 0.253253i $$-0.918499\pi$$
−0.578283 + 0.815836i $$0.696277\pi$$
$$480$$ 0 0
$$481$$ 7.66044 + 6.42788i 0.349286 + 0.293086i
$$482$$ 4.00000 6.92820i 0.182195 0.315571i
$$483$$ 1.50000 + 2.59808i 0.0682524 + 0.118217i
$$484$$ 4.34120 24.6202i 0.197327 1.11910i
$$485$$ 0 0
$$486$$ 8.00000 + 13.8564i 0.362887 + 0.628539i
$$487$$ −1.00000 + 1.73205i −0.0453143 + 0.0784867i −0.887793 0.460243i $$-0.847762\pi$$
0.842479 + 0.538730i $$0.181096\pi$$
$$488$$ 7.66044 + 6.42788i 0.346772 + 0.290976i
$$489$$ −18.7939 6.84040i −0.849887 0.309334i
$$490$$ 0 0
$$491$$ −27.5776 + 23.1404i −1.24456 + 1.04431i −0.247406 + 0.968912i $$0.579578\pi$$
−0.997154 + 0.0753977i $$0.975977\pi$$
$$492$$ 0 0
$$493$$ 27.0000 1.21602
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −0.694593 3.93923i −0.0311881 0.176877i
$$497$$ 4.59627 3.85673i 0.206171 0.172998i
$$498$$ −5.63816 + 2.05212i −0.252652 + 0.0919577i
$$499$$ 3.75877 + 1.36808i 0.168266 + 0.0612437i 0.424779 0.905297i $$-0.360352\pi$$
−0.256514 + 0.966541i $$0.582574\pi$$
$$500$$ 0 0
$$501$$ −6.00000 + 10.3923i −0.268060 + 0.464294i
$$502$$ 3.00000 + 5.19615i 0.133897 + 0.231916i
$$503$$ −3.64661 + 20.6810i −0.162594 + 0.922119i 0.788916 + 0.614501i $$0.210643\pi$$
−0.951510 + 0.307617i $$0.900468\pi$$
$$504$$ −0.347296 + 1.96962i −0.0154698 + 0.0877336i
$$505$$ 0 0
$$506$$ −9.00000 + 15.5885i −0.400099 + 0.692991i
$$507$$ 9.19253 + 7.71345i 0.408255 + 0.342566i
$$508$$ −1.87939 0.684040i −0.0833842 0.0303494i
$$509$$ −28.1908 + 10.2606i −1.24953 + 0.454793i −0.880244 0.474521i $$-0.842621\pi$$
−0.369290 + 0.929314i $$0.620399\pi$$
$$510$$ 0 0
$$511$$ 1.21554 + 6.89365i 0.0537722 + 0.304957i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −12.0000 −0.529297
$$515$$ 0 0
$$516$$ 6.12836 5.14230i 0.269786 0.226377i
$$517$$ 0 0
$$518$$ −1.87939 0.684040i −0.0825754 0.0300550i
$$519$$ 4.59627 + 3.85673i 0.201754 + 0.169291i
$$520$$ 0 0
$$521$$ 18.0000 + 31.1769i 0.788594 + 1.36589i 0.926828 + 0.375486i $$0.122524\pi$$
−0.138234 + 0.990400i $$0.544143\pi$$
$$522$$ 3.12567 17.7265i 0.136807 0.775870i
$$523$$ 1.91013 10.8329i 0.0835242 0.473689i −0.914141 0.405396i $$-0.867134\pi$$
0.997665 0.0682930i $$-0.0217553\pi$$
$$524$$ 0 0
$$525$$ −2.50000 + 4.33013i −0.109109 + 0.188982i
$$526$$ −18.3851 15.4269i −0.801627 0.672645i
$$527$$ 11.2763 + 4.10424i 0.491204 + 0.178784i
$$528$$ 5.63816 2.05212i 0.245369 0.0893071i
$$529$$ −10.7246 + 8.99903i −0.466288 + 0.391262i
$$530$$ 0 0
$$531$$ −18.0000 −0.781133
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 2.08378 + 11.8177i 0.0901739 + 0.511402i
$$535$$ 0 0
$$536$$ 4.69846 1.71010i 0.202943 0.0738651i
$$537$$ 0 0
$$538$$ 4.59627 + 3.85673i 0.198159 + 0.166275i
$$539$$ −18.0000 + 31.1769i −0.775315 + 1.34288i
$$540$$ 0 0
$$541$$ 0.347296 1.96962i 0.0149314 0.0846804i −0.976431 0.215828i $$-0.930755\pi$$
0.991363 + 0.131147i $$0.0418661\pi$$
$$542$$ −1.91013 + 10.8329i −0.0820471 + 0.465312i
$$543$$ −1.00000 1.73205i −0.0429141 0.0743294i
$$544$$ 1.50000 2.59808i 0.0643120 0.111392i
$$545$$ 0 0
$$546$$ −4.69846 1.71010i −0.201076 0.0731856i
$$547$$ −41.3465 + 15.0489i −1.76785 + 0.643444i −0.767852 + 0.640628i $$0.778674\pi$$
−0.999996 + 0.00281615i $$0.999104\pi$$
$$548$$ −6.89440 + 5.78509i −0.294514 + 0.247127i
$$549$$ 3.47296 + 19.6962i 0.148222 + 0.840611i
$$550$$ −30.0000 −1.27920
$$551$$ 0 0
$$552$$ −3.00000 −0.127688
$$553$$ 1.73648 + 9.84808i 0.0738427 + 0.418783i
$$554$$ −6.12836 + 5.14230i −0.260369 + 0.218475i
$$555$$ 0 0
$$556$$ 3.75877 + 1.36808i 0.159407 + 0.0580195i
$$557$$ 18.3851 + 15.4269i 0.779000 + 0.653659i 0.942997 0.332802i $$-0.107994\pi$$
−0.163996 + 0.986461i $$0.552439\pi$$
$$558$$ 4.00000 6.92820i 0.169334 0.293294i
$$559$$ −20.0000 34.6410i −0.845910 1.46516i
$$560$$ 0 0
$$561$$ −3.12567 + 17.7265i −0.131966 + 0.748415i
$$562$$ 0 0
$$563$$ 6.00000 10.3923i 0.252870 0.437983i −0.711445 0.702742i $$-0.751959\pi$$
0.964315 + 0.264758i $$0.0852922\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −20.6732 + 7.52444i −0.868961 + 0.316276i
$$567$$ −0.766044 + 0.642788i −0.0321708 + 0.0269945i
$$568$$ 1.04189 + 5.90885i 0.0437167 + 0.247930i
$$569$$ −24.0000 −1.00613 −0.503066 0.864248i $$-0.667795\pi$$
−0.503066 + 0.864248i $$0.667795\pi$$
$$570$$ 0 0
$$571$$ −4.00000 −0.167395 −0.0836974 0.996491i $$-0.526673\pi$$
−0.0836974 + 0.996491i $$0.526673\pi$$
$$572$$ −5.20945 29.5442i −0.217818 1.23531i
$$573$$ 2.29813 1.92836i 0.0960059 0.0805585i
$$574$$ 0 0
$$575$$ 14.0954 + 5.13030i 0.587818 + 0.213948i
$$576$$ −1.53209 1.28558i −0.0638370 0.0535656i
$$577$$ −5.50000 + 9.52628i −0.228968 + 0.396584i −0.957503 0.288425i $$-0.906868\pi$$
0.728535 + 0.685009i $$0.240202\pi$$
$$578$$ −4.00000 6.92820i −0.166378 0.288175i
$$579$$ 2.43107 13.7873i 0.101032 0.572981i
$$580$$ 0 0
$$581$$ −3.00000 5.19615i −0.124461 0.215573i
$$582$$ −5.00000 + 8.66025i −0.207257 + 0.358979i
$$583$$ 13.7888 + 11.5702i 0.571074 + 0.479188i
$$584$$ −6.57785 2.39414i −0.272193 0.0990703i
$$585$$ 0 0
$$586$$ 16.0869 13.4985i 0.664545 0.557620i
$$587$$ −2.08378 11.8177i −0.0860067 0.487768i −0.997135 0.0756451i $$-0.975898\pi$$
0.911128 0.412123i $$-0.135213\pi$$
$$588$$ −6.00000 −0.247436
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 1.53209 1.28558i 0.0629685 0.0528368i
$$593$$ 28.1908 10.2606i 1.15766 0.421353i 0.309397 0.950933i $$-0.399873\pi$$
0.848260 + 0.529580i $$0.177651\pi$$
$$594$$ 28.1908 + 10.2606i 1.15668 + 0.420998i
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −5.50000 9.52628i −0.225100 0.389885i
$$598$$ −2.60472 + 14.7721i −0.106515 + 0.604077i
$$599$$ −4.16756 + 23.6354i −0.170282 + 0.965716i 0.773168 + 0.634201i $$0.218671\pi$$
−0.943450 + 0.331515i $$0.892440\pi$$
$$600$$ −2.50000 4.33013i −0.102062 0.176777i
$$601$$ 14.0000 24.2487i 0.571072 0.989126i −0.425384 0.905013i $$-0.639861\pi$$
0.996456 0.0841128i $$-0.0268056\pi$$
$$602$$ 6.12836 + 5.14230i 0.249773 + 0.209585i
$$603$$ 9.39693 + 3.42020i 0.382672 + 0.139281i
$$604$$ 9.39693 3.42020i 0.382356 0.139166i
$$605$$ 0 0
$$606$$ −3.12567 17.7265i −0.126972 0.720091i
$$607$$ −22.0000 −0.892952 −0.446476 0.894795i $$-0.647321\pi$$
−0.446476 + 0.894795i $$0.647321\pi$$
$$608$$ 0 0
$$609$$ −9.00000 −0.364698
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 5.63816 2.05212i 0.227909 0.0829521i
$$613$$ −1.87939 0.684040i −0.0759077 0.0276281i 0.303787 0.952740i $$-0.401749\pi$$
−0.379695 + 0.925112i $$0.623971\pi$$
$$614$$ −15.3209 12.8558i −0.618301 0.518816i
$$615$$ 0 0
$$616$$ 3.00000 + 5.19615i 0.120873 + 0.209359i
$$617$$ −1.04189 + 5.90885i −0.0419449 + 0.237881i −0.998571 0.0534364i $$-0.982983\pi$$
0.956626 + 0.291318i $$0.0940937\pi$$
$$618$$ −2.43107 + 13.7873i −0.0977922 + 0.554607i
$$619$$ 5.00000 + 8.66025i 0.200967 + 0.348085i 0.948840 0.315757i $$-0.102258\pi$$
−0.747873 + 0.663842i $$0.768925\pi$$
$$620$$ 0 0
$$621$$ −11.4907 9.64181i −0.461105 0.386913i
$$622$$ −19.7335 7.18242i −0.791243 0.287989i
$$623$$ −11.2763 + 4.10424i −0.451776 + 0.164433i
$$624$$ 3.83022 3.21394i 0.153332 0.128660i
$$625$$ 4.34120 + 24.6202i 0.173648 + 0.984808i
$$626$$ 19.0000 0.759393
$$627$$ 0 0
$$628$$ −22.0000 −0.877896
$$629$$ 1.04189 + 5.90885i 0.0415428 + 0.235601i
$$630$$ 0 0
$$631$$ 15.0351 5.47232i 0.598537 0.217850i −0.0249430 0.999689i $$-0.507940\pi$$
0.623480 + 0.781839i $$0.285718\pi$$
$$632$$ −9.39693 3.42020i −0.373790 0.136048i
$$633$$ 3.83022 + 3.21394i 0.152238 + 0.127743i
$$634$$ −4.50000 + 7.79423i −0.178718 + 0.309548i
$$635$$ 0 0
$$636$$ −0.520945 + 2.95442i −0.0206568 + 0.117151i
$$637$$ −5.20945 + 29.5442i −0.206406 + 1.17059i
$$638$$ −27.0000 46.7654i −1.06894 1.85146i
$$639$$ −6.00000 + 10.3923i −0.237356 + 0.411113i
$$640$$ 0 0
$$641$$ −5.63816 2.05212i −0.222694 0.0810539i 0.228264 0.973599i $$-0.426695\pi$$
−0.450957 + 0.892545i $$0.648917\pi$$
$$642$$ −8.45723 + 3.07818i −0.333780 + 0.121486i
$$643$$ −16.8530 + 14.1413i −0.664617 + 0.557680i −0.911467 0.411374i $$-0.865049\pi$$
0.246850 + 0.969054i $$0.420605\pi$$
$$644$$ −0.520945 2.95442i −0.0205281 0.116421i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 27.0000 1.06148 0.530740 0.847535i $$-0.321914\pi$$
0.530740 + 0.847535i $$0.321914\pi$$
$$648$$ −0.173648 0.984808i −0.00682154 0.0386869i
$$649$$ −41.3664 + 34.7105i −1.62377 + 1.36251i
$$650$$ −23.4923 + 8.55050i −0.921444 + 0.335378i
$$651$$ −3.75877 1.36808i −0.147318 0.0536193i
$$652$$ 15.3209 + 12.8558i 0.600012 + 0.503470i
$$653$$ −12.0000 + 20.7846i −0.469596 + 0.813365i −0.999396 0.0347583i $$-0.988934\pi$$
0.529799 + 0.848123i $$0.322267\pi$$
$$654$$ 5.50000 + 9.52628i 0.215067 + 0.372507i
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −7.00000 12.1244i −0.273096 0.473016i
$$658$$ 0 0
$$659$$ −34.4720 28.9254i −1.34284 1.12678i −0.980887 0.194578i $$-0.937666\pi$$
−0.361951 0.932197i $$-0.617889\pi$$
$$660$$ 0 0
$$661$$ 12.2160 4.44626i 0.475147 0.172940i −0.0933352 0.995635i $$-0.529753\pi$$
0.568483 + 0.822695i $$0.307531\pi$$
$$662$$ 0.766044 0.642788i 0.0297732 0.0249826i
$$663$$ 2.60472 + 14.7721i 0.101159 + 0.573701i
$$664$$ 6.00000 0.232845
$$665$$ 0 0
$$666$$ 4.00000 0.154997
$$667$$ 4.68850 + 26.5898i 0.181539 + 1.02956i
$$668$$ 9.19253 7.71345i 0.355670 0.298442i
$$669$$ −24.4320 + 8.89252i −0.944596 + 0.343805i
$$670$$ 0 0
$$671$$ 45.9627 + 38.5673i 1.77437 + 1.48887i
$$672$$ −0.500000 + 0.866025i −0.0192879 + 0.0334077i
$$673$$ −22.0000 38.1051i −0.848038 1.46884i −0.882957 0.469454i $$-0.844451\pi$$
0.0349191 0.999390i $$-0.488883\pi$$
$$674$$ 0.694593 3.93923i 0.0267547 0.151734i
$$675$$ 4.34120 24.6202i 0.167093 0.947632i
$$676$$ −6.00000 10.3923i −0.230769 0.399704i
$$677$$ 16.5000 28.5788i 0.634147 1.09837i −0.352549 0.935793i $$-0.614685\pi$$
0.986695 0.162581i $$-0.0519817\pi$$
$$678$$ −4.59627 3.85673i −0.176519 0.148117i
$$679$$ −9.39693 3.42020i −0.360621 0.131255i
$$680$$ 0 0
$$681$$ −11.4907 + 9.64181i −0.440323 + 0.369475i
$$682$$ −4.16756 23.6354i −0.159584 0.905046i
$$683$$ 36.0000 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −2.25743 12.8025i −0.0861889 0.488802i
$$687$$ −16.8530 + 14.1413i −0.642981 + 0.539525i
$$688$$ −7.51754 + 2.73616i −0.286604 + 0.104315i
$$689$$ 14.0954 + 5.13030i 0.536992 + 0.195449i
$$690$$ 0 0
$$691$$ 5.00000 8.66025i 0.190209 0.329452i −0.755110 0.655598i $$-0.772417\pi$$
0.945319 + 0.326146i $$0.105750\pi$$
$$692$$ −3.00000 5.19615i −0.114043 0.197528i
$$693$$ −2.08378 + 11.8177i −0.0791562 + 0.448917i
$$694$$ −3.12567 + 17.7265i −0.118649 + 0.672890i
$$695$$ 0 0
$$696$$ 4.50000 7.79423i 0.170572 0.295439i
$$697$$ 0 0
$$698$$ −9.39693 3.42020i −0.355679 0.129457i
$$699$$ 5.63816 2.05212i 0.213255 0.0776183i
$$700$$ 3.83022 3.21394i 0.144769 0.121475i
$$701$$ 2.08378 + 11.8177i 0.0787032 + 0.446348i 0.998539 + 0.0540435i $$0.0172110\pi$$
−0.919835 + 0.392305i $$0.871678\pi$$
$$702$$ 25.0000 0.943564
$$703$$ 0 0
$$704$$ −6.00000 −0.226134
$$705$$ 0 0
$$706$$ 11.4907 9.64181i 0.432457 0.362874i
$$707$$ 16.9145 6.15636i 0.636134 0.231534i
$$708$$ −8.45723 3.07818i −0.317842 0.115685i
$$709$$ −7.66044 6.42788i −0.287694 0.241404i 0.487506 0.873119i $$-0.337907\pi$$
−0.775200 + 0.631716i $$0.782351\pi$$
$$710$$ 0 0
$$711$$ −10.0000 17.3205i −0.375029 0.649570i
$$712$$ 2.08378 11.8177i 0.0780929 0.442887i
$$713$$ −2.08378 + 11.8177i −0.0780381 + 0.442576i
$$714$$ −1.50000 2.59808i −0.0561361 0.0972306i
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 19.7335 + 7.18242i 0.736963 + 0.268233i
$$718$$ 19.7335 7.18242i 0.736449 0.268046i
$$719$$ 29.8757 25.0687i 1.11418 0.934905i 0.115881 0.993263i $$-0.463031\pi$$
0.998296 + 0.0583577i $$0.0185864\pi$$
$$720$$ 0 0
$$721$$ −14.0000 −0.521387
$$722$$ 0 0
$$723$$ 8.00000 0.297523
$$724$$ 0.347296 + 1.96962i 0.0129072 + 0.0732002i
$$725$$ −34.4720 + 28.9254i −1.28026 + 1.07426i
$$726$$ 23.4923 8.55050i 0.871882 0.317339i
$$727$$ 34.7686 + 12.6547i 1.28950 + 0.469339i 0.893562 0.448940i $$-0.148198\pi$$
0.395935 + 0.918279i $$0.370421\pi$$
$$728$$ 3.83022 + 3.21394i 0.141957 + 0.119116i
$$729$$ −6.50000 + 11.2583i −0.240741 + 0.416975i
$$730$$ 0 0
$$731$$ 4.16756 23.6354i 0.154143 0.874186i
$$732$$ −1.73648 + 9.84808i −0.0641822 + 0.363995i
$$733$$ −16.0000 27.7128i −0.590973 1.02360i −0.994102 0.108453i $$-0.965410\pi$$
0.403128 0.915144i $$-0.367923\pi$$
$$734$$ −14.0000 + 24.2487i −0.516749 + 0.895036i
$$735$$ 0 0
$$736$$ 2.81908 + 1.02606i 0.103913 + 0.0378211i
$$737$$ 28.1908 10.2606i 1.03842 0.377954i
$$738$$ 0 0
$$739$$ −2.77837 15.7569i −0.102204 0.579628i −0.992300 0.123855i $$-0.960474\pi$$
0.890096 0.455773i $$-0.150637\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −3.00000 −0.110133
$$743$$ −6.25133 35.4531i −0.229339 1.30065i −0.854214 0.519922i $$-0.825961\pi$$
0.624874 0.780725i $$-0.285150\pi$$
$$744$$ 3.06418 2.57115i 0.112338 0.0942629i
$$745$$ 0 0
$$746$$ 21.6129 + 7.86646i 0.791306 + 0.288012i
$$747$$ 9.19253 + 7.71345i 0.336337 + 0.282220i
$$748$$ 9.00000 15.5885i 0.329073 0.569970i
$$749$$ −4.50000 7.79423i −0.164426 0.284795i
$$750$$ 0 0
$$751$$ −6.94593 + 39.3923i −0.253460 + 1.43745i 0.546533 + 0.837437i $$0.315947\pi$$
−0.799994 + 0.600008i $$0.795164\pi$$
$$752$$ 0 0
$$753$$ −3.00000 + 5.19615i −0.109326 + 0.189358i
$$754$$ −34.4720 28.9254i −1.25540 1.05340i
$$755$$ 0 0
$$756$$ −4.69846 + 1.71010i −0.170881 + 0.0621958i
$$757$$ 1.53209 1.28558i 0.0556847 0.0467250i −0.614521 0.788901i $$-0.710651\pi$$
0.670205 + 0.742176i $$0.266206\pi$$
$$758$$ 1.21554 + 6.89365i 0.0441503 + 0.250389i
$$759$$ −18.0000 −0.653359
$$760$$ 0 0
$$761$$ −21.0000 −0.761249 −0.380625 0.924730i $$-0.624291\pi$$
−0.380625 + 0.924730i $$0.624291\pi$$
$$762$$ −0.347296 1.96962i −0.0125812 0.0713516i
$$763$$ −8.42649 + 7.07066i −0.305059 + 0.255975i
$$764$$ −2.81908 + 1.02606i −0.101991 + 0.0371216i
$$765$$ 0 0
$$766$$ −13.7888 11.5702i −0.498210 0.418047i
$$767$$ −22.5000 + 38.9711i −0.812428 + 1.40717i
$$768$$ −0.500000 0.866025i −0.0180422 0.0312500i
$$769$$ 0.868241 4.92404i 0.0313096 0.177565i −0.965143 0.261724i $$-0.915709\pi$$
0.996452 + 0.0841584i $$0.0268202\pi$$
$$770$$ 0 0
$$771$$ −6.00000 10.3923i −0.216085 0.374270i
$$772$$ −7.00000 + 12.1244i −0.251936 + 0.436365i
$$773$$ 39.0683 + 32.7822i 1.40519 + 1.17909i 0.958740 + 0.284283i $$0.0917554\pi$$
0.446447 + 0.894810i $$0.352689\pi$$
$$774$$ −15.0351 5.47232i −0.540425 0.196699i
$$775$$ −18.7939 + 6.84040i −0.675095 + 0.245715i
$$776$$ 7.66044 6.42788i 0.274994 0.230747i
$$777$$ −0.347296 1.96962i −0.0124592