LMFDB - Embedded newform 731.2.m.c.689.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			689.20
Character	$\chi$	$=$	731.689
Dual form			731.2.m.c.87.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.810350 - 0.810350i) q^{2} +(3.13521 + 1.29865i) q^{3} +0.686666i q^{4} +(1.23003 - 2.96956i) q^{5} +(3.59298 - 1.48826i) q^{6} +(-0.604922 - 1.46041i) q^{7} +(2.17714 + 2.17714i) q^{8} +(6.02174 + 6.02174i) q^{9} +O(q^{10})$	\(q+(0.810350 - 0.810350i) q^{2} +(3.13521 + 1.29865i) q^{3} +0.686666i q^{4} +(1.23003 - 2.96956i) q^{5} +(3.59298 - 1.48826i) q^{6} +(-0.604922 - 1.46041i) q^{7} +(2.17714 + 2.17714i) q^{8} +(6.02174 + 6.02174i) q^{9} +(-1.40963 - 3.40314i) q^{10} +(-4.91459 + 2.03569i) q^{11} +(-0.891736 + 2.15284i) q^{12} -1.77520i q^{13} +(-1.67364 - 0.693246i) q^{14} +(7.71281 - 7.71281i) q^{15} +2.15516 q^{16} +(-4.01260 - 0.948189i) q^{17} +9.75943 q^{18} +(-2.37035 + 2.37035i) q^{19} +(2.03909 + 0.844620i) q^{20} -5.36428i q^{21} +(-2.33292 + 5.63216i) q^{22} +(3.32148 - 1.37580i) q^{23} +(3.99846 + 9.65312i) q^{24} +(-3.76976 - 3.76976i) q^{25} +(-1.43853 - 1.43853i) q^{26} +(7.16337 + 17.2939i) q^{27} +(1.00281 - 0.415379i) q^{28} +(3.17390 - 7.66248i) q^{29} -12.5002i q^{30} +(-7.90431 - 3.27407i) q^{31} +(-2.60785 + 2.60785i) q^{32} -18.0519 q^{33} +(-4.01997 + 2.48324i) q^{34} -5.08085 q^{35} +(-4.13492 + 4.13492i) q^{36} +(-3.49145 - 1.44620i) q^{37} +3.84163i q^{38} +(2.30536 - 5.56563i) q^{39} +(9.14309 - 3.78719i) q^{40} +(1.94976 + 4.70713i) q^{41} +(-4.34694 - 4.34694i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(-1.39784 - 3.37468i) q^{44} +(25.2888 - 10.4750i) q^{45} +(1.57668 - 3.80645i) q^{46} -1.99825i q^{47} +(6.75688 + 2.79879i) q^{48} +(3.18288 - 3.18288i) q^{49} -6.10965 q^{50} +(-11.3490 - 8.18372i) q^{51} +1.21897 q^{52} +(-5.93359 + 5.93359i) q^{53} +(19.8189 + 8.20927i) q^{54} +17.0981i q^{55} +(1.86252 - 4.49652i) q^{56} +(-10.5098 + 4.35330i) q^{57} +(-3.63732 - 8.78126i) q^{58} +(2.04099 + 2.04099i) q^{59} +(5.29612 + 5.29612i) q^{60} +(0.209778 + 0.506448i) q^{61} +(-9.05840 + 3.75211i) q^{62} +(5.15153 - 12.4369i) q^{63} +8.53685i q^{64} +(-5.27156 - 2.18355i) q^{65} +(-14.6284 + 14.6284i) q^{66} +4.80863 q^{67} +(0.651089 - 2.75531i) q^{68} +12.2002 q^{69} +(-4.11727 + 4.11727i) q^{70} +(7.00308 + 2.90077i) q^{71} +26.2203i q^{72} +(-1.29534 + 3.12722i) q^{73} +(-4.00122 + 1.65736i) q^{74} +(-6.92340 - 16.7146i) q^{75} +(-1.62764 - 1.62764i) q^{76} +(5.94589 + 5.94589i) q^{77} +(-2.64196 - 6.37825i) q^{78} +(6.79229 - 2.81346i) q^{79} +(2.65091 - 6.39987i) q^{80} +37.9746i q^{81} +(5.39441 + 2.23444i) q^{82} +(-1.85608 + 1.85608i) q^{83} +3.68347 q^{84} +(-7.75132 + 10.7493i) q^{85} -1.14601 q^{86} +(19.9017 - 19.9017i) q^{87} +(-15.1317 - 6.26777i) q^{88} +9.53974i q^{89} +(12.0044 - 28.9812i) q^{90} +(-2.59252 + 1.07386i) q^{91} +(0.944717 + 2.28075i) q^{92} +(-20.5298 - 20.5298i) q^{93} +(-1.61928 - 1.61928i) q^{94} +(4.12329 + 9.95449i) q^{95} +(-11.5628 + 4.78948i) q^{96} +(4.96439 - 11.9851i) q^{97} -5.15849i q^{98} +(-41.8528 - 17.3360i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.810350	−	0.810350i	0.573004	−	0.573004i	−0.359963	−	0.932967i	$-0.617211\pi$
$2$	0.810350	−	0.810350i	0.573004	−	0.573004i	0.932967	+	0.359963i	$0.117211\pi$
$3$	3.13521	+	1.29865i	1.81011	+	0.749774i	0.981910	+	0.189347i	$0.0606372\pi$
$3$	3.13521	+	1.29865i	1.81011	+	0.749774i	0.828204	+	0.560427i	$0.189363\pi$
$4$			0.686666i			0.343333i
$5$	1.23003	−	2.96956i	0.550086	−	1.32803i	−0.367327	−	0.930092i	$-0.619727\pi$
$5$	1.23003	−	2.96956i	0.550086	−	1.32803i	0.917414	−	0.397935i	$-0.130273\pi$
$6$	3.59298	−	1.48826i	1.46683	−	0.607579i
$7$	−0.604922	−	1.46041i	−0.228639	−	0.551984i	0.767373	−	0.641201i	$-0.221563\pi$
$7$	−0.604922	−	1.46041i	−0.228639	−	0.551984i	−0.996012	+	0.0892172i	$0.971563\pi$
$8$	2.17714	+	2.17714i	0.769735	+	0.769735i
$9$	6.02174	+	6.02174i	2.00725	+	2.00725i
$10$	−1.40963	−	3.40314i	−0.445763	−	1.07617i
$11$	−4.91459	+	2.03569i	−1.48180	+	0.613783i	−0.969516	−	0.245030i	$-0.921202\pi$
$11$	−4.91459	+	2.03569i	−1.48180	+	0.613783i	−0.512289	+	0.858813i	$0.671202\pi$
$12$	−0.891736	+	2.15284i	−0.257422	+	0.621472i
$13$		−	1.77520i		−	0.492352i	−0.969225	−	0.246176i	$-0.920826\pi$
$13$		−	1.77520i		−	0.492352i	0.969225	−	0.246176i	$-0.0791742\pi$
$14$	−1.67364	−	0.693246i	−0.447300	−	0.185278i
$15$	7.71281	−	7.71281i	1.99144	−	1.99144i
$16$	2.15516			0.538790
$17$	−4.01260	−	0.948189i	−0.973198	−	0.229970i
$17$	−4.01260	−	0.948189i	−0.973198	−	0.229970i
$18$	9.75943			2.30032
$19$	−2.37035	+	2.37035i	−0.543796	+	0.543796i	−0.924639	−	0.380844i	$-0.875634\pi$
$19$	−2.37035	+	2.37035i	−0.543796	+	0.543796i	0.380844	+	0.924639i	$0.375634\pi$
$20$	2.03909	+	0.844620i	0.455955	+	0.188863i
$21$		−	5.36428i		−	1.17058i
$22$	−2.33292	+	5.63216i	−0.497379	+	1.20078i
$23$	3.32148	−	1.37580i	0.692577	−	0.286875i	−0.00849611	−	0.999964i	$-0.502704\pi$
$23$	3.32148	−	1.37580i	0.692577	−	0.286875i	0.701074	+	0.713089i	$0.252704\pi$
$24$	3.99846	+	9.65312i	0.816181	+	1.97044i
$25$	−3.76976	−	3.76976i	−0.753952	−	0.753952i
$26$	−1.43853	−	1.43853i	−0.282120	−	0.282120i
$27$	7.16337	+	17.2939i	1.37859	+	3.32821i
$28$	1.00281	−	0.415379i	0.189514	−	0.0784993i
$29$	3.17390	−	7.66248i	0.589379	−	1.42289i	−0.294719	−	0.955584i	$-0.595226\pi$
$29$	3.17390	−	7.66248i	0.589379	−	1.42289i	0.884098	−	0.467302i	$-0.154774\pi$
$30$		−	12.5002i		−	2.28220i
$31$	−7.90431	−	3.27407i	−1.41966	−	0.588040i	−0.464881	−	0.885373i	$-0.653903\pi$
$31$	−7.90431	−	3.27407i	−1.41966	−	0.588040i	−0.954774	+	0.297333i	$0.903903\pi$
$32$	−2.60785	+	2.60785i	−0.461006	+	0.461006i
$33$	−18.0519			−3.14243
$34$	−4.01997	+	2.48324i	−0.689420	+	0.425873i
$35$	−5.08085			−0.858820
$36$	−4.13492	+	4.13492i	−0.689154	+	0.689154i
$37$	−3.49145	−	1.44620i	−0.573990	−	0.237754i	0.0767560	−	0.997050i	$-0.475544\pi$
$37$	−3.49145	−	1.44620i	−0.573990	−	0.237754i	−0.650746	+	0.759295i	$0.725544\pi$
$38$			3.84163i			0.623194i
$39$	2.30536	−	5.56563i	0.369153	−	0.891214i
$40$	9.14309	−	3.78719i	1.44565	−	0.598808i
$41$	1.94976	+	4.70713i	0.304501	+	0.735131i	0.999864	+	0.0164722i	$0.00524349\pi$
$41$	1.94976	+	4.70713i	0.304501	+	0.735131i	−0.695363	+	0.718658i	$0.744757\pi$
$42$	−4.34694	−	4.34694i	−0.670748	−	0.670748i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$44$	−1.39784	−	3.37468i	−0.210732	−	0.508752i
$45$	25.2888	−	10.4750i	3.76983	−	1.56152i
$46$	1.57668	−	3.80645i	0.232469	−	0.561230i
$47$		−	1.99825i		−	0.291475i	−0.989323	−	0.145737i	$-0.953445\pi$
$47$		−	1.99825i		−	0.291475i	0.989323	−	0.145737i	$-0.0465555\pi$
$48$	6.75688	+	2.79879i	0.975271	+	0.403970i
$49$	3.18288	−	3.18288i	0.454697	−	0.454697i
$50$	−6.10965			−0.864035
$51$	−11.3490	−	8.18372i	−1.58917	−	1.14595i
$52$	1.21897			0.169041
$53$	−5.93359	+	5.93359i	−0.815041	+	0.815041i	−0.985385	−	0.170343i	$-0.945512\pi$
$53$	−5.93359	+	5.93359i	−0.815041	+	0.815041i	0.170343	+	0.985385i	$0.445512\pi$
$54$	19.8189	+	8.20927i	2.69702	+	1.11714i
$55$			17.0981i			2.30551i
$56$	1.86252	−	4.49652i	0.248890	−	0.600873i
$57$	−10.5098	+	4.35330i	−1.39206	+	0.576608i
$58$	−3.63732	−	8.78126i	−0.477603	−	1.15304i
$59$	2.04099	+	2.04099i	0.265715	+	0.265715i	0.827371	−	0.561656i	$-0.189836\pi$
$59$	2.04099	+	2.04099i	0.265715	+	0.265715i	−0.561656	+	0.827371i	$0.689836\pi$
$60$	5.29612	+	5.29612i	0.683726	+	0.683726i
$61$	0.209778	+	0.506448i	0.0268593	+	0.0648440i	0.936740	−	0.350026i	$-0.113827\pi$
$61$	0.209778	+	0.506448i	0.0268593	+	0.0648440i	−0.909881	+	0.414870i	$0.863827\pi$
$62$	−9.05840	+	3.75211i	−1.15042	+	0.476519i
$63$	5.15153	−	12.4369i	0.649032	−	1.56690i
$64$			8.53685i			1.06711i
$65$	−5.27156	−	2.18355i	−0.653857	−	0.270836i
$66$	−14.6284	+	14.6284i	−1.80063	+	1.80063i
$67$	4.80863			0.587468			0.293734	−	0.955887i	$-0.405102\pi$
$67$	4.80863			0.587468			0.293734	+	0.955887i	$0.405102\pi$
$68$	0.651089	−	2.75531i	0.0789561	−	0.334131i
$69$	12.2002			1.46874
$70$	−4.11727	+	4.11727i	−0.492107	+	0.492107i
$71$	7.00308	+	2.90077i	0.831113	+	0.344258i	0.757343	−	0.653017i	$-0.226497\pi$
$71$	7.00308	+	2.90077i	0.831113	+	0.344258i	0.0737696	+	0.997275i	$0.476497\pi$
$72$			26.2203i			3.09010i
$73$	−1.29534	+	3.12722i	−0.151608	+	0.366013i	−0.981377	−	0.192094i	$-0.938472\pi$
$73$	−1.29534	+	3.12722i	−0.151608	+	0.366013i	0.829769	+	0.558107i	$0.188472\pi$
$74$	−4.00122	+	1.65736i	−0.465133	+	0.192664i
$75$	−6.92340	−	16.7146i	−0.799446	−	1.93003i
$76$	−1.62764	−	1.62764i	−0.186703	−	0.186703i
$77$	5.94589	+	5.94589i	0.677597	+	0.677597i
$78$	−2.64196	−	6.37825i	−0.299143	−	0.722195i
$79$	6.79229	−	2.81346i	0.764192	−	0.316539i	0.0336749	−	0.999433i	$-0.489279\pi$
$79$	6.79229	−	2.81346i	0.764192	−	0.316539i	0.730517	+	0.682894i	$0.239279\pi$
$80$	2.65091	−	6.39987i	0.296381	−	0.715527i
$81$			37.9746i			4.21940i
$82$	5.39441	+	2.23444i	0.595713	+	0.246752i
$83$	−1.85608	+	1.85608i	−0.203731	+	0.203731i	−0.801596	−	0.597866i	$-0.796016\pi$
$83$	−1.85608	+	1.85608i	−0.203731	+	0.203731i	0.597866	+	0.801596i	$0.296016\pi$
$84$	3.68347			0.401899
$85$	−7.75132	+	10.7493i	−0.840749	+	1.16593i
$86$	−1.14601			−0.123577
$87$	19.9017	−	19.9017i	2.13369	−	2.13369i
$88$	−15.1317	−	6.26777i	−1.61305	−	0.668146i
$89$			9.53974i			1.01121i	0.862765	+	0.505605i	$0.168731\pi$
$89$			9.53974i			1.01121i	−0.862765	+	0.505605i	$0.831269\pi$
$90$	12.0044	−	28.9812i	1.26537	−	3.05489i
$91$	−2.59252	+	1.07386i	−0.271770	+	0.112571i
$92$	0.944717	+	2.28075i	0.0984936	+	0.237785i
$93$	−20.5298	−	20.5298i	−2.12884	−	2.12884i
$94$	−1.61928	−	1.61928i	−0.167016	−	0.167016i
$95$	4.12329	+	9.95449i	0.423040	+	1.02131i
$96$	−11.5628	+	4.78948i	−1.18012	+	0.488824i
$97$	4.96439	−	11.9851i	0.504057	−	1.21690i	−0.443198	−	0.896424i	$-0.646156\pi$
$97$	4.96439	−	11.9851i	0.504057	−	1.21690i	0.947256	−	0.320479i	$-0.103844\pi$
$98$		−	5.15849i		−	0.521086i
$99$	−41.8528	−	17.3360i	−4.20636	−	1.74233i
$100$	2.58856	−	2.58856i	0.258856	−	0.258856i
$101$	−11.1739			−1.11185			−0.555923	−	0.831234i	$-0.687635\pi$
$101$	−11.1739			−1.11185			−0.555923	+	0.831234i	$0.687635\pi$
$102$	−15.8283	+	2.56497i	−1.56724	+	0.253970i
$103$	13.3054			1.31102			0.655508	−	0.755188i	$-0.272454\pi$
$103$	13.3054			1.31102			0.655508	+	0.755188i	$0.272454\pi$
$104$	3.86486	−	3.86486i	0.378981	−	0.378981i
$105$	−15.9295	−	6.59823i	−1.55456	−	0.643921i
$106$			9.61657i			0.934044i
$107$	1.70378	−	4.11330i	0.164711	−	0.397648i	−0.819876	−	0.572540i	$-0.805958\pi$
$107$	1.70378	−	4.11330i	0.164711	−	0.397648i	0.984587	+	0.174893i	$0.0559579\pi$
$108$	−11.8751	+	4.91884i	−1.14268	+	0.473315i
$109$	−2.78980	−	6.73516i	−0.267214	−	0.645112i	0.732136	−	0.681158i	$-0.238524\pi$
$109$	−2.78980	−	6.73516i	−0.267214	−	0.645112i	−0.999350	+	0.0360466i	$0.988524\pi$
$110$	13.8555	+	13.8555i	1.32107	+	1.32107i
$111$	−9.06831	−	9.06831i	−0.860726	−	0.860726i
$112$	−1.30370	−	3.14742i	−0.123188	−	0.297403i
$113$	−1.71581	+	0.710712i	−0.161410	+	0.0668581i	−0.461925	−	0.886919i	$-0.652841\pi$
$113$	−1.71581	+	0.710712i	−0.161410	+	0.0668581i	0.300516	+	0.953777i	$0.402841\pi$
$114$	−4.98891	+	12.0443i	−0.467255	+	1.12805i
$115$		−	11.5556i		−	1.07757i
$116$	5.26156	+	2.17941i	0.488524	+	0.202353i
$117$	10.6898	−	10.6898i	0.988272	−	0.988272i
$118$	3.30784			0.304511
$119$	1.04256	+	6.43362i	0.0955717	+	0.589769i
$120$	33.5837			3.06576
$121$	12.2310	−	12.2310i	1.11191	−	1.11191i
$122$	0.580393	+	0.240407i	0.0525464	+	0.0217654i
$123$			17.2899i			1.55898i
$124$	2.24819	−	5.42762i	0.201894	−	0.487414i
$125$	−0.983649	+	0.407441i	−0.0879802	+	0.0364426i
$126$	−5.90370	−	14.2528i	−0.525943	−	1.26974i
$127$	−5.58303	−	5.58303i	−0.495414	−	0.495414i	0.414593	−	0.910007i	$-0.363924\pi$
$127$	−5.58303	−	5.58303i	−0.495414	−	0.495414i	−0.910007	+	0.414593i	$0.863924\pi$
$128$	1.70215	+	1.70215i	0.150450	+	0.150450i
$129$	−1.29865	−	3.13521i	−0.114339	−	0.276040i
$130$	−6.04125	+	2.50237i	−0.529853	+	0.219472i
$131$	−3.81481	+	9.20978i	−0.333302	+	0.804662i	0.665024	+	0.746822i	$0.268421\pi$
$131$	−3.81481	+	9.20978i	−0.333302	+	0.804662i	−0.998326	+	0.0578398i	$0.981579\pi$
$132$		−	12.3956i		−	1.07890i
$133$	4.89556	+	2.02781i	0.424499	+	0.175833i
$134$	3.89667	−	3.89667i	0.336621	−	0.336621i
$135$	60.1664			5.17830
$136$	−6.67165	−	10.8003i	−0.572089	−	0.926120i
$137$	−17.8433			−1.52446			−0.762228	−	0.647309i	$-0.775895\pi$
$137$	−17.8433			−1.52446			−0.762228	+	0.647309i	$0.775895\pi$
$138$	9.88646	−	9.88646i	0.841591	−	0.841591i
$139$	3.15629	+	1.30738i	0.267713	+	0.110890i	0.512502	−	0.858686i	$-0.328719\pi$
$139$	3.15629	+	1.30738i	0.267713	+	0.110890i	−0.244789	+	0.969576i	$0.578719\pi$
$140$		−	3.48884i		−	0.294861i
$141$	2.59502	−	6.26493i	0.218540	−	0.527603i
$142$	8.02559	−	3.32431i	0.673492	−	0.278970i
$143$	3.61376	+	8.72438i	0.302198	+	0.729570i
$144$	12.9778	+	12.9778i	1.08148	+	1.08148i
$145$	−18.8502	−	18.8502i	−1.56542	−	1.56542i
$146$	1.48447	+	3.58382i	0.122855	+	0.296599i
$147$	14.1124	−	5.84555i	1.16397	−	0.482133i
$148$	0.993059	−	2.39746i	0.0816289	−	0.197070i
$149$			5.74817i			0.470908i	0.971885	+	0.235454i	$0.0756578\pi$
$149$			5.74817i			0.470908i	−0.971885	+	0.235454i	$0.924342\pi$
$150$	−19.1550	−	7.93427i	−1.56400	−	0.647831i
$151$	−6.93901	+	6.93901i	−0.564689	+	0.564689i	−0.930636	−	0.365947i	$-0.880745\pi$
$151$	−6.93901	+	6.93901i	−0.564689	+	0.564689i	0.365947	+	0.930636i	$0.380745\pi$
$152$	−10.3212			−0.837157
$153$	−18.4531	−	29.8726i	−1.49184	−	2.41505i
$154$	9.63650			0.776531
$155$	−19.4451	+	19.4451i	−1.56187	+	1.56187i
$156$	3.82173	+	1.58301i	0.305983	+	0.126742i
$157$		−	17.9634i		−	1.43363i	−0.697262	−	0.716816i	$-0.745599\pi$
$157$		−	17.9634i		−	1.43363i	0.697262	−	0.716816i	$-0.254401\pi$
$158$	3.22425	−	7.78402i	0.256507	−	0.619263i
$159$	−26.3087	+	10.8974i	−2.08641	+	0.864221i
$160$	4.53642	+	10.9519i	0.358635	+	0.865822i
$161$	−4.01848	−	4.01848i	−0.316701	−	0.316701i
$162$	30.7727	+	30.7727i	2.41773	+	2.41773i
$163$	7.41463	+	17.9005i	0.580759	+	1.40208i	0.892126	+	0.451786i	$0.149213\pi$
$163$	7.41463	+	17.9005i	0.580759	+	1.40208i	−0.311368	+	0.950289i	$0.600787\pi$
$164$	−3.23223	+	1.33883i	−0.252394	+	0.104545i
$165$	−22.2044	+	53.6062i	−1.72861	+	4.17323i
$166$			3.00814i			0.233477i
$167$	−21.6131	−	8.95243i	−1.67247	−	0.692759i	−0.673546	−	0.739146i	$-0.735230\pi$
$167$	−21.6131	−	8.95243i	−1.67247	−	0.692759i	−0.998924	+	0.0463860i	$0.985230\pi$
$168$	11.6788	−	11.6788i	0.901037	−	0.901037i
$169$	9.84866			0.757589
$170$	2.42944	+	14.9920i	0.186330	+	1.14983i
$171$	−28.5473			−2.18306
$172$	0.485546	−	0.485546i	0.0370225	−	0.0370225i
$173$	13.7539	+	5.69706i	1.04569	+	0.433139i	0.838352	−	0.545130i	$-0.183520\pi$
$173$	13.7539	+	5.69706i	1.04569	+	0.433139i	0.207339	+	0.978269i	$0.433520\pi$
$174$		−	32.2547i		−	2.44522i
$175$	−3.22499	+	7.78581i	−0.243786	+	0.588552i
$176$	−10.5917	+	4.38723i	−0.798381	+	0.330700i
$177$	3.74841	+	9.04947i	0.281748	+	0.680200i
$178$	7.73053	+	7.73053i	0.579428	+	0.579428i
$179$	8.99052	+	8.99052i	0.671983	+	0.671983i	0.958173	−	0.286190i	$-0.0923887\pi$
$179$	8.99052	+	8.99052i	0.671983	+	0.671983i	−0.286190	+	0.958173i	$0.592389\pi$
$180$	7.19280	+	17.3650i	0.536120	+	1.29431i
$181$	−14.1593	+	5.86496i	−1.05245	+	0.435939i	−0.840766	−	0.541399i	$-0.817895\pi$
$181$	−14.1593	+	5.86496i	−1.05245	+	0.435939i	−0.211685	+	0.977338i	$0.567895\pi$
$182$	−1.23065	+	2.97105i	−0.0912219	+	0.220229i
$183$			1.86025i			0.137513i
$184$	10.2267	+	4.23602i	0.753919	+	0.312283i
$185$	−8.58917	+	8.58917i	−0.631488	+	0.631488i
$186$	−33.2726			−2.43967
$187$	21.6505	−	3.50844i	1.58324	−	0.256563i
$188$	1.37213			0.100073
$189$	20.9229	−	20.9229i	1.52192	−	1.52192i
$190$	11.4079	+	4.72532i	0.827618	+	0.342811i
$191$		−	0.444488i		−	0.0321620i	−0.999871	−	0.0160810i	$-0.994881\pi$
$191$		−	0.444488i		−	0.0321620i	0.999871	−	0.0160810i	$-0.00511897\pi$
$192$	−11.0864	+	26.7648i	−0.800089	+	1.93159i
$193$	0.537629	−	0.222693i	0.0386994	−	0.0160298i	−0.363250	−	0.931692i	$-0.618333\pi$
$193$	0.537629	−	0.222693i	0.0386994	−	0.0160298i	0.401949	+	0.915662i	$0.368333\pi$
$194$	−5.68923	−	13.7350i	−0.408463	−	0.986117i
$195$	−13.6918	−	13.6918i	−0.980489	−	0.980489i
$196$	2.18557	+	2.18557i	0.156112	+	0.156112i
$197$	−2.75232	−	6.64468i	−0.196094	−	0.473414i	0.794994	−	0.606617i	$-0.207474\pi$
$197$	−2.75232	−	6.64468i	−0.196094	−	0.473414i	−0.991089	+	0.133203i	$0.957474\pi$
$198$	−47.9636	+	19.8672i	−3.40862	+	1.41190i
$199$	5.39773	−	13.0313i	0.382635	−	0.923762i	−0.608820	−	0.793309i	$-0.708357\pi$
$199$	5.39773	−	13.0313i	0.382635	−	0.923762i	0.991454	−	0.130453i	$-0.0416433\pi$
$200$		−	16.4146i		−	1.16069i
$201$	15.0761	+	6.24471i	1.06338	+	0.440468i
$202$	−9.05478	+	9.05478i	−0.637092	+	0.637092i
$203$	−13.1103			−0.920165
$204$	5.61948	−	7.79295i	0.393442	−	0.545616i
$205$	16.3764			1.14377
$206$	10.7820	−	10.7820i	0.751218	−	0.751218i
$207$	28.2858	+	11.7164i	1.96600	+	0.814345i
$208$		−	3.82584i		−	0.265274i
$209$	6.82400	−	16.4746i	0.472026	−	1.13957i
$210$	−18.2554	+	7.56162i	−1.25974	+	0.521801i
$211$	−1.74586	−	4.21488i	−0.120190	−	0.290164i	0.852322	−	0.523018i	$-0.175194\pi$
$211$	−1.74586	−	4.21488i	−0.120190	−	0.290164i	−0.972512	+	0.232853i	$0.925194\pi$
$212$	−4.07439	−	4.07439i	−0.279830	−	0.279830i
$213$	18.1890	+	18.1890i	1.24629	+	1.24629i
$214$	−1.95255	−	4.71387i	−0.133474	−	0.322234i
$215$	−2.96956	+	1.23003i	−0.202522	+	0.0838874i
$216$	−22.0556	+	53.2469i	−1.50069	+	3.62299i
$217$			13.5241i			0.918076i
$218$	−7.71855	−	3.19713i	−0.522766	−	0.216537i
$219$	−8.12230	+	8.12230i	−0.548854	+	0.548854i
$220$	−11.7407			−0.791557
$221$	−1.68323	+	7.12317i	−0.113226	+	0.479156i
$222$	−14.6970			−0.986398
$223$	−3.27691	+	3.27691i	−0.219438	+	0.219438i	−0.808262	−	0.588823i	$-0.799591\pi$
$223$	−3.27691	+	3.27691i	−0.219438	+	0.219438i	0.588823	+	0.808262i	$0.299591\pi$
$224$	5.38607	+	2.23098i	0.359872	+	0.149064i
$225$		−	45.4010i		−	3.02673i
$226$	−0.814481	+	1.96633i	−0.0541785	+	0.130798i
$227$	−8.50128	+	3.52135i	−0.564250	+	0.233720i	−0.646529	−	0.762889i	$-0.723780\pi$
$227$	−8.50128	+	3.52135i	−0.564250	+	0.233720i	0.0822792	+	0.996609i	$0.473780\pi$
$228$	−2.98926	−	7.21671i	−0.197969	−	0.477938i
$229$	15.3361	+	15.3361i	1.01344	+	1.01344i	0.999908	+	0.0135301i	$0.00430691\pi$
$229$	15.3361	+	15.3361i	1.01344	+	1.01344i	0.0135301	+	0.999908i	$0.495693\pi$
$230$	−9.36410	−	9.36410i	−0.617450	−	0.617450i
$231$	10.9200	+	26.3632i	0.718483	+	1.73457i
$232$	23.5923	−	9.77225i	1.54891	−	0.641580i
$233$	9.13752	−	22.0599i	0.598619	−	1.44519i	−0.276370	−	0.961051i	$-0.589132\pi$
$233$	9.13752	−	22.0599i	0.598619	−	1.44519i	0.874989	−	0.484142i	$-0.160868\pi$
$234$		−	17.3250i		−	1.13257i
$235$	−5.93392	−	2.45791i	−0.387086	−	0.160336i
$236$	−1.40148	+	1.40148i	−0.0912286	+	0.0912286i
$237$	24.9489			1.62061
$238$	6.05833	+	4.36865i	0.392703	+	0.283177i
$239$	4.66754			0.301918			0.150959	−	0.988540i	$-0.451764\pi$
$239$	4.66754			0.301918			0.150959	+	0.988540i	$0.451764\pi$
$240$	16.6223	−	16.6223i	1.07297	−	1.07297i
$241$	−3.60404	−	1.49284i	−0.232157	−	0.0961624i	0.263573	−	0.964640i	$-0.415099\pi$
$241$	−3.60404	−	1.49284i	−0.232157	−	0.0961624i	−0.495729	+	0.868477i	$0.665099\pi$
$242$		−	19.8227i		−	1.27425i
$243$	−27.8255	+	67.1766i	−1.78501	+	4.30938i
$244$	−0.347760	+	0.144047i	−0.0222631	+	0.00922167i
$245$	−5.53670	−	13.3668i	−0.353727	−	0.853972i
$246$	14.0109	+	14.0109i	0.893300	+	0.893300i
$247$	4.20785	+	4.20785i	0.267739	+	0.267739i
$248$	−10.0807	−	24.3369i	−0.640123	−	1.54539i
$249$	−8.22958	+	3.40880i	−0.521528	+	0.216024i
$250$	−0.466930	+	1.12727i	−0.0295313	+	0.0712948i
$251$			16.3442i			1.03163i	0.856699	+	0.515817i	$0.172512\pi$
$251$			16.3442i			1.03163i	−0.856699	+	0.515817i	$0.827488\pi$
$252$	8.53999	+	3.53738i	0.537969	+	0.222834i
$253$	−13.5230	+	13.5230i	−0.850185	+	0.850185i
$254$	−9.04841			−0.567748
$255$	−38.2616	+	23.6352i	−2.39603	+	1.48009i
$256$	−14.3150			−0.894690
$257$	10.7528	−	10.7528i	0.670742	−	0.670742i	−0.287145	−	0.957887i	$-0.592706\pi$
$257$	10.7528	−	10.7528i	0.670742	−	0.670742i	0.957887	+	0.287145i	$0.0927062\pi$
$258$	−3.59298	−	1.48826i	−0.223689	−	0.0926550i
$259$			5.97379i			0.371193i
$260$	1.49937	−	3.61980i	0.0929870	−	0.224490i
$261$	65.2538	−	27.0290i	4.03911	−	1.67305i
$262$	4.37181	+	10.5545i	0.270091	+	0.652058i
$263$	15.2689	+	15.2689i	0.941519	+	0.941519i	0.998382	−	0.0568626i	$-0.0181097\pi$
$263$	15.2689	+	15.2689i	0.941519	+	0.941519i	−0.0568626	+	0.998382i	$0.518110\pi$
$264$	−39.3015	−	39.3015i	−2.41884	−	2.41884i
$265$	10.3216	+	24.9186i	0.634053	+	1.53074i
$266$	5.61036	−	2.32389i	0.343993	−	0.142487i
$267$	−12.3887	+	29.9091i	−0.758179	+	1.83041i
$268$			3.30192i			0.201697i
$269$	14.0934	+	5.83768i	0.859290	+	0.355929i	0.768430	−	0.639934i	$-0.221038\pi$
$269$	14.0934	+	5.83768i	0.859290	+	0.355929i	0.0908599	+	0.995864i	$0.471038\pi$
$270$	48.7558	−	48.7558i	2.96718	−	2.96718i
$271$	6.00809			0.364965			0.182483	−	0.983209i	$-0.441587\pi$
$271$	6.00809			0.364965			0.182483	+	0.983209i	$0.441587\pi$
$272$	−8.64778	−	2.04350i	−0.524349	−	0.123905i
$273$	−9.52267			−0.576338
$274$	−14.4593	+	14.4593i	−0.873519	+	0.873519i
$275$	26.2009	+	10.8528i	1.57997	+	0.654446i
$276$			8.37748i			0.504265i
$277$	7.18164	−	17.3380i	0.431503	−	1.04174i	−0.547300	−	0.836936i	$-0.684344\pi$
$277$	7.18164	−	17.3380i	0.431503	−	1.04174i	0.978803	−	0.204804i	$-0.0656556\pi$
$278$	3.61714	−	1.49827i	0.216941	−	0.0898601i
$279$	−27.8821	−	67.3133i	−1.66926	−	4.02994i
$280$	−11.0617	−	11.0617i	−0.661064	−	0.661064i
$281$	−13.8956	−	13.8956i	−0.828941	−	0.828941i	0.158429	−	0.987370i	$-0.449357\pi$
$281$	−13.8956	−	13.8956i	−0.828941	−	0.828941i	−0.987370	+	0.158429i	$0.949357\pi$
$282$	−2.97391	−	7.17967i	−0.177094	−	0.427543i
$283$	6.05053	−	2.50621i	0.359666	−	0.148979i	−0.195531	−	0.980698i	$-0.562643\pi$
$283$	6.05053	−	2.50621i	0.359666	−	0.148979i	0.555197	+	0.831719i	$0.312643\pi$
$284$	−1.99186	+	4.80877i	−0.118195	+	0.285348i
$285$			36.5641i			2.16587i
$286$	9.99821	+	4.14140i	0.591207	+	0.244886i
$287$	5.69490	−	5.69490i	0.336159	−	0.336159i
$288$	−31.4075			−1.85071
$289$	15.2019	+	7.60940i	0.894228	+	0.447612i
$290$	−30.5505			−1.79398
$291$	31.1288	−	31.1288i	1.82480	−	1.82480i
$292$	−2.14735	−	0.889463i	−0.125664	−	0.0520519i
$293$		−	15.9670i		−	0.932803i	−0.884573	−	0.466402i	$-0.845550\pi$
$293$		−	15.9670i		−	0.932803i	0.884573	−	0.466402i	$-0.154450\pi$
$294$	6.69905	−	16.1729i	0.390697	−	0.943225i
$295$	8.57133	−	3.55036i	0.499042	−	0.206710i
$296$	−4.45278	−	10.7500i	−0.258812	−	0.624828i
$297$	−70.4100	−	70.4100i	−4.08560	−	4.08560i
$298$	4.65803	+	4.65803i	0.269832	+	0.269832i
$299$	−2.44233	−	5.89630i	−0.141244	−	0.340992i
$300$	11.4773	−	4.75406i	0.662643	−	0.274476i
$301$	−0.604922	+	1.46041i	−0.0348671	+	0.0841767i
$302$			11.2461i			0.647138i
$303$	−35.0326	−	14.5110i	−2.01257	−	0.833633i
$304$	−5.10848	+	5.10848i	−0.292991	+	0.292991i
$305$	1.76196			0.100889
$306$	−39.1607	−	9.25378i	−2.23867	−	0.529004i
$307$	15.3519			0.876179			0.438089	−	0.898931i	$-0.355655\pi$
$307$	15.3519			0.876179			0.438089	+	0.898931i	$0.355655\pi$
$308$	−4.08284	+	4.08284i	−0.232641	+	0.232641i
$309$	41.7151	+	17.2790i	2.37309	+	0.982966i
$310$			31.5146i			1.78991i
$311$	−6.78506	+	16.3806i	−0.384745	+	0.928858i	0.606288	+	0.795245i	$0.292658\pi$
$311$	−6.78506	+	16.3806i	−0.384745	+	0.928858i	−0.991034	+	0.133613i	$0.957342\pi$
$312$	17.1362	−	7.09806i	0.970148	−	0.401849i
$313$	−6.42256	−	15.5054i	−0.363025	−	0.876419i	−0.994855	−	0.101312i	$-0.967696\pi$
$313$	−6.42256	−	15.5054i	−0.363025	−	0.876419i	0.631830	−	0.775107i	$-0.282304\pi$
$314$	−14.5566	−	14.5566i	−0.821477	−	0.821477i
$315$	−30.5955	−	30.5955i	−1.72386	−	1.72386i
$316$	1.93191	+	4.66403i	0.108678	+	0.262372i
$317$	−12.0607	+	4.99570i	−0.677395	+	0.280586i	−0.694738	−	0.719263i	$-0.744479\pi$
$317$	−12.0607	+	4.99570i	−0.677395	+	0.280586i	0.0173424	+	0.999850i	$0.494479\pi$
$318$	−12.4885	+	30.1500i	−0.700322	+	1.69073i
$319$			44.1190i			2.47019i
$320$	25.3507	+	10.5006i	1.41715	+	0.587001i
$321$	10.6834	−	10.6834i	0.596291	−	0.596291i
$322$	−6.51275			−0.362941
$323$	11.7588	−	7.26372i	0.654277	−	0.404164i
$324$	−26.0759			−1.44866
$325$	−6.69208	+	6.69208i	−0.371210	+	0.371210i
$326$	20.5141	+	8.49722i	1.13617	+	0.470618i
$327$		−	24.7391i		−	1.36808i
$328$	−6.00319	+	14.4930i	−0.331471	+	0.800241i
$329$	−2.91827	+	1.20879i	−0.160889	+	0.0666425i
$330$	25.4464	+	61.4331i	1.40078	+	3.38178i
$331$	22.4116	+	22.4116i	1.23185	+	1.23185i	0.963252	+	0.268600i	$0.0865609\pi$
$331$	22.4116	+	22.4116i	1.23185	+	1.23185i	0.268600	+	0.963252i	$0.413439\pi$
$332$	−1.27450	−	1.27450i	−0.0699475	−	0.0699475i
$333$	−12.3159	−	29.7332i	−0.674908	−	1.62937i
$334$	−24.7687	+	10.2596i	−1.35529	+	0.561378i
$335$	5.91476	−	14.2795i	0.323158	−	0.780172i
$336$		−	11.5609i		−	0.630697i
$337$	22.9751	+	9.51659i	1.25153	+	0.518402i	0.907301	−	0.420483i	$-0.138139\pi$
$337$	22.9751	+	9.51659i	1.25153	+	0.518402i	0.344232	+	0.938885i	$0.388139\pi$
$338$	7.98086	−	7.98086i	0.434102	−	0.434102i
$339$	−6.30239			−0.342299
$340$	−7.38120	−	5.32256i	−0.400302	−	0.288657i
$341$	45.5114			2.46458
$342$	−23.1333	+	23.1333i	−1.25090	+	1.25090i
$343$	−16.7966	−	6.95737i	−0.906930	−	0.375663i
$344$		−	3.07894i		−	0.166005i
$345$	15.0067	−	36.2293i	0.807932	−	1.95052i
$346$	15.7621	−	6.52888i	0.847376	−	0.350995i
$347$	9.15919	+	22.1123i	0.491691	+	1.18705i	0.953859	+	0.300255i	$0.0970719\pi$
$347$	9.15919	+	22.1123i	0.491691	+	1.18705i	−0.462168	+	0.886793i	$0.652928\pi$
$348$	13.6658	+	13.6658i	0.732564	+	0.732564i
$349$	−24.8433	−	24.8433i	−1.32983	−	1.32983i	−0.905514	−	0.424317i	$-0.860514\pi$
$349$	−24.8433	−	24.8433i	−1.32983	−	1.32983i	−0.424317	−	0.905514i	$-0.639486\pi$
$350$	3.69586	+	8.92260i	0.197552	+	0.476933i
$351$	30.7001	−	12.7164i	1.63865	−	0.678752i
$352$	7.50773	−	18.1253i	0.400163	−	0.966079i
$353$		−	20.1046i		−	1.07006i	−0.844832	−	0.535031i	$-0.820300\pi$
$353$		−	20.1046i		−	1.07006i	0.844832	−	0.535031i	$-0.179700\pi$
$354$	10.3708	+	4.29571i	0.551200	+	0.228315i
$355$	17.2280	−	17.2280i	0.914368	−	0.914368i
$356$	−6.55061			−0.347182
$357$	−5.08635	+	21.5247i	−0.269198	+	1.13921i
$358$	14.5709			0.770098
$359$	−8.38382	+	8.38382i	−0.442481	+	0.442481i	−0.892845	−	0.450364i	$-0.851294\pi$
$359$	−8.38382	+	8.38382i	−0.442481	+	0.442481i	0.450364	+	0.892845i	$0.351294\pi$
$360$	77.8628	+	32.2518i	4.10373	+	1.69982i
$361$			7.76288i			0.408573i
$362$	−6.72129	+	16.2266i	−0.353263	+	0.852853i
$363$	54.2304	−	22.4630i	2.84636	−	1.17900i
$364$	−0.737382	−	1.78020i	−0.0386493	−	0.0933077i
$365$	7.69315	+	7.69315i	0.402678	+	0.402678i
$366$	1.50745	+	1.50745i	0.0787958	+	0.0787958i
$367$	6.20252	+	14.9742i	0.323769	+	0.781647i	0.999029	+	0.0440670i	$0.0140315\pi$
$367$	6.20252	+	14.9742i	0.323769	+	0.781647i	−0.675260	+	0.737580i	$0.735968\pi$
$368$	7.15833	−	2.96508i	0.373154	−	0.154565i
$369$	−16.6042	+	40.0861i	−0.864379	+	2.08680i
$370$			13.9205i			0.723691i
$371$	12.2548	+	5.07612i	0.636240	+	0.263539i
$372$	14.0971	−	14.0971i	0.730901	−	0.730901i
$373$	−26.9809			−1.39702			−0.698510	−	0.715601i	$-0.746153\pi$
$373$	−26.9809			−1.39702			−0.698510	+	0.715601i	$0.746153\pi$
$374$	14.7014	−	20.3875i	0.760191	−	1.05421i
$375$	−3.61307			−0.186578
$376$	4.35047	−	4.35047i	0.224358	−	0.224358i
$377$	−13.6024	−	5.63431i	−0.700561	−	0.290182i
$378$		−	33.9098i		−	1.74413i
$379$	8.44037	−	20.3769i	0.433553	−	1.04669i	−0.544580	−	0.838709i	$-0.683311\pi$
$379$	8.44037	−	20.3769i	0.433553	−	1.04669i	0.978133	−	0.207980i	$-0.0666889\pi$
$380$	−6.83541	+	2.83132i	−0.350649	+	0.145244i
$381$	−10.2536	−	24.7543i	−0.525307	−	1.26820i
$382$	−0.360191	−	0.360191i	−0.0184290	−	0.0184290i
$383$	−10.7058	−	10.7058i	−0.547039	−	0.547039i	0.378544	−	0.925583i	$-0.376425\pi$
$383$	−10.7058	−	10.7058i	−0.547039	−	0.547039i	−0.925583	+	0.378544i	$0.876425\pi$
$384$	3.12610	+	7.54708i	0.159528	+	0.385135i
$385$	24.9703	−	10.3430i	1.27260	−	0.527130i
$386$	0.255208	−	0.616127i	0.0129898	−	0.0313600i
$387$		−	8.51602i		−	0.432894i
$388$	8.22975	+	3.40888i	0.417802	+	0.173059i
$389$	−12.2839	+	12.2839i	−0.622818	+	0.622818i	−0.946251	−	0.323433i	$-0.895163\pi$
$389$	−12.2839	+	12.2839i	−0.622818	+	0.622818i	0.323433	+	0.946251i	$0.395163\pi$
$390$	−22.1903			−1.12365
$391$	−14.6323	+	2.37115i	−0.739987	+	0.119914i
$392$	13.8591			0.699992
$393$	−23.9205	+	23.9205i	−1.20663	+	1.20663i
$394$	−7.61486	−	3.15418i	−0.383631	−	0.158905i
$395$		−	23.6307i		−	1.18899i
$396$	11.9040	−	28.7389i	0.598200	−	1.44418i
$397$	−25.9904	+	10.7656i	−1.30442	+	0.540309i	−0.923251	−	0.384196i	$-0.874479\pi$
$397$	−25.9904	+	10.7656i	−1.30442	+	0.540309i	−0.381169	+	0.924505i	$0.624479\pi$
$398$	−6.18584	−	14.9339i	−0.310068	−	0.748571i
$399$	12.7152	+	12.7152i	0.636557	+	0.636557i
$400$	−8.12443	−	8.12443i	−0.406221	−	0.406221i
$401$	−4.63547	−	11.1910i	−0.231484	−	0.558853i	0.764868	−	0.644187i	$-0.222804\pi$
$401$	−4.63547	−	11.1910i	−0.231484	−	0.558853i	−0.996352	+	0.0853344i	$0.972804\pi$
$402$	17.2773	−	7.15649i	0.861713	−	0.356933i
$403$	−5.81213	+	14.0317i	−0.289523	+	0.698970i
$404$		−	7.67275i		−	0.381733i
$405$	112.768	+	46.7099i	5.60347	+	2.32103i
$406$	−10.6240	+	10.6240i	−0.527258	+	0.527258i
$407$	20.1030			0.996471
$408$	−6.89121	−	42.5254i	−0.341166	−	2.10532i
$409$	33.6685			1.66480			0.832401	−	0.554174i	$-0.186966\pi$
$409$	33.6685			1.66480			0.832401	+	0.554174i	$0.186966\pi$
$410$	13.2706	−	13.2706i	0.655387	−	0.655387i
$411$	−55.9425	−	23.1721i	−2.75944	−	1.14300i
$412$			9.13634i			0.450115i
$413$	1.74605	−	4.21533i	0.0859174	−	0.207423i
$414$	32.4158	−	13.4271i	1.59315	−	0.659904i
$415$	3.22869	+	7.79476i	0.158490	+	0.382630i
$416$	4.62945	+	4.62945i	0.226978	+	0.226978i
$417$	8.19782	+	8.19782i	0.401449	+	0.401449i
$418$	−7.82036	−	18.8800i	−0.382506	−	0.923452i
$419$	15.5959	−	6.46004i	0.761910	−	0.315594i	0.0323196	−	0.999478i	$-0.489711\pi$
$419$	15.5959	−	6.46004i	0.761910	−	0.315594i	0.729591	+	0.683884i	$0.239711\pi$
$420$	4.53078	−	10.9383i	0.221079	−	0.533732i
$421$			6.97939i			0.340155i	0.985431	+	0.170077i	$0.0544018\pi$
$421$			6.97939i			0.340155i	−0.985431	+	0.170077i	$0.945598\pi$
$422$	−4.83028	−	2.00077i	−0.235135	−	0.0973959i
$423$	12.0329	−	12.0329i	0.585062	−	0.585062i
$424$	−25.8365			−1.25473
$425$	11.5521	+	18.7010i	0.560358	+	0.907130i
$426$	29.4790			1.42826
$427$	0.612723	−	0.612723i	0.0296518	−	0.0296518i
$428$	2.82446	+	1.16993i	0.136525	+	0.0565507i
$429$			32.0458i			1.54718i
$430$	−1.40963	+	3.40314i	−0.0679782	+	0.164114i
$431$	−11.0654	+	4.58343i	−0.533000	+	0.220776i	−0.632917	−	0.774220i	$-0.718142\pi$
$431$	−11.0654	+	4.58343i	−0.533000	+	0.220776i	0.0999163	+	0.994996i	$0.468142\pi$
$432$	15.4382	+	37.2711i	0.742770	+	1.79321i
$433$	−11.3846	−	11.3846i	−0.547107	−	0.547107i	0.378496	−	0.925603i	$-0.376441\pi$
$433$	−11.3846	−	11.3846i	−0.547107	−	0.547107i	−0.925603	+	0.378496i	$0.876441\pi$
$434$	10.9593	+	10.9593i	0.526061	+	0.526061i
$435$	−34.6195	−	83.5789i	−1.65988	−	4.00730i
$436$	4.62481	−	1.91566i	0.221488	−	0.0917434i
$437$	−4.61194	+	11.1342i	−0.220619	+	0.532622i
$438$			13.1638i			0.628991i
$439$	18.8575	+	7.81102i	0.900018	+	0.372800i	0.784227	−	0.620474i	$-0.213060\pi$
$439$	18.8575	+	7.81102i	0.900018	+	0.372800i	0.115791	+	0.993274i	$0.463060\pi$
$440$	−37.2250	+	37.2250i	−1.77463	+	1.77463i
$441$	38.3329			1.82538
$442$	4.40826	+	7.13626i	0.209679	+	0.339437i
$443$	28.7154			1.36431			0.682154	−	0.731209i	$-0.261043\pi$
$443$	28.7154			1.36431			0.682154	+	0.731209i	$0.261043\pi$
$444$	6.22689	−	6.22689i	0.295515	−	0.295515i
$445$	28.3288	+	11.7342i	1.34291	+	0.556253i
$446$			5.31089i			0.251478i
$447$	−7.46484	+	18.0217i	−0.353075	+	0.852398i
$448$	12.4673	−	5.16413i	0.589026	−	0.243982i
$449$	5.27334	+	12.7310i	0.248864	+	0.600811i	0.998108	−	0.0614828i	$-0.0195829\pi$
$449$	5.27334	+	12.7310i	0.248864	+	0.600811i	−0.749244	+	0.662294i	$0.769583\pi$
$450$	−36.7907	−	36.7907i	−1.73433	−	1.73433i
$451$	−19.1645	−	19.1645i	−0.902422	−	0.902422i
$452$	−0.488021	−	1.17819i	−0.0229546	−	0.0554173i
$453$	−30.7666	+	12.7439i	−1.44554	+	0.598762i
$454$	−4.03549	+	9.74253i	−0.189395	+	0.457240i
$455$			9.01953i			0.422842i
$456$	−32.3590	−	13.4035i	−1.51535	−	0.627678i
$457$	−2.40110	+	2.40110i	−0.112319	+	0.112319i	−0.761032	−	0.648714i	$-0.775307\pi$
$457$	−2.40110	+	2.40110i	−0.112319	+	0.112319i	0.648714	+	0.761032i	$0.275307\pi$
$458$	24.8552			1.16141
$459$	−12.3458	−	76.1857i	−0.576254	−	3.55604i
$460$	7.93485			0.369964
$461$	8.25353	−	8.25353i	0.384405	−	0.384405i	−0.488281	−	0.872686i	$-0.662376\pi$
$461$	8.25353	−	8.25353i	0.384405	−	0.384405i	0.872686	+	0.488281i	$0.162376\pi$
$462$	30.2125	+	12.5144i	1.40561	+	0.582223i
$463$			19.5438i			0.908277i	0.890931	+	0.454139i	$0.150053\pi$
$463$			19.5438i			0.908277i	−0.890931	+	0.454139i	$0.849947\pi$
$464$	6.84026	−	16.5139i	0.317551	−	0.766636i
$465$	−86.2167	+	35.7121i	−3.99820	+	1.65611i
$466$	−10.4717	−	25.2808i	−0.485091	−	1.17111i
$467$	−4.61711	−	4.61711i	−0.213655	−	0.213655i	0.592163	−	0.805818i	$-0.298274\pi$
$467$	−4.61711	−	4.61711i	−0.213655	−	0.213655i	−0.805818	+	0.592163i	$0.798274\pi$
$468$	7.34032	+	7.34032i	0.339306	+	0.339306i
$469$	−2.90885	−	7.02258i	−0.134318	−	0.324273i
$470$	−6.80032	+	2.81678i	−0.313675	+	0.129929i
$471$	23.3281	−	56.3189i	1.07490	−	2.59504i
$472$			8.88705i			0.409060i
$473$	4.91459	+	2.03569i	0.225973	+	0.0936011i
$474$	20.2174	−	20.2174i	0.928615	−	0.928615i
$475$	17.8713			0.819991
$476$	−4.41775	+	0.715893i	−0.202487	+	0.0328129i
$477$	−71.4611			−3.27198
$478$	3.78234	−	3.78234i	0.173000	−	0.173000i
$479$	−0.881094	−	0.364961i	−0.0402582	−	0.0166755i	0.362463	−	0.931998i	$-0.381936\pi$
$479$	−0.881094	−	0.364961i	−0.0402582	−	0.0166755i	−0.402722	+	0.915322i	$0.631936\pi$
$480$			40.2276i			1.83613i
$481$	−2.56730	+	6.19802i	−0.117059	+	0.282605i
$482$	−4.13026	+	1.71081i	−0.188128	+	0.0779252i
$483$	−7.38019	−	17.8174i	−0.335810	−	0.810718i
$484$	8.39859	+	8.39859i	0.381754	+	0.381754i
$485$	−29.4841	−	29.4841i	−1.33880	−	1.33880i
$486$	31.8882	+	76.9850i	1.44648	+	3.49211i
$487$	−8.72830	+	3.61538i	−0.395517	+	0.163829i	−0.571572	−	0.820552i	$-0.693666\pi$
$487$	−8.72830	+	3.61538i	−0.395517	+	0.163829i	0.176055	+	0.984380i	$0.443666\pi$
$488$	−0.645893	+	1.55932i	−0.0292382	+	0.0705872i
$489$			65.7508i			2.97335i
$490$	−15.3184	−	6.34510i	−0.692016	−	0.286642i
$491$	−18.3353	+	18.3353i	−0.827461	+	0.827461i	−0.987165	−	0.159704i	$-0.948946\pi$
$491$	−18.3353	+	18.3353i	−0.827461	+	0.827461i	0.159704	+	0.987165i	$0.448946\pi$
$492$	−11.8724			−0.535248
$493$	−20.0011	+	27.7370i	−0.900803	+	1.24921i
$494$	6.81966			0.306831
$495$	−102.960	+	102.960i	−4.62772	+	4.62772i
$496$	−17.0350	−	7.05614i	−0.764896	−	0.316830i
$497$		−	11.9821i		−	0.537472i
$498$	−3.90651	+	9.43116i	−0.175055	+	0.422620i
$499$	38.7209	−	16.0387i	1.73339	−	0.717992i	0.734147	−	0.678990i	$-0.237582\pi$
$499$	38.7209	−	16.0387i	1.73339	−	0.717992i	0.999239	−	0.0390019i	$-0.0124178\pi$
$500$	−0.279776	−	0.675438i	−0.0125119	−	0.0302065i
$501$	−56.1355	−	56.1355i	−2.50795	−	2.50795i
$502$	13.2445	+	13.2445i	0.591131	+	0.591131i
$503$	−13.9777	−	33.7452i	−0.623237	−	1.50463i	−0.847882	−	0.530185i	$-0.822122\pi$
$503$	−13.9777	−	33.7452i	−0.623237	−	1.50463i	0.224645	−	0.974441i	$-0.427878\pi$
$504$	38.2925	−	15.8613i	1.70568	−	0.706517i
$505$	−13.7443	+	33.1816i	−0.611612	+	1.47656i
$506$			21.9168i			0.974319i
$507$	30.8776	+	12.7899i	1.37132	+	0.568021i
$508$	3.83367	−	3.83367i	0.170092	−	0.170092i
$509$	−7.10896			−0.315099			−0.157550	−	0.987511i	$-0.550359\pi$
$509$	−7.10896			−0.315099			−0.157550	+	0.987511i	$0.550359\pi$
$510$	−11.8525	+	50.1581i	−0.524838	+	2.22104i
$511$	5.35060			0.236697
$512$	−15.0045	+	15.0045i	−0.663111	+	0.663111i
$513$	−57.9723	−	24.0129i	−2.55954	−	1.06020i
$514$		−	17.4271i		−	0.768676i
$515$	16.3660	−	39.5110i	0.721172	−	1.74106i
$516$	2.15284	−	0.891736i	0.0947735	−	0.0392565i
$517$	4.06782	+	9.82058i	0.178902	+	0.431909i
$518$	4.84086	+	4.84086i	0.212695	+	0.212695i
$519$	35.7230	+	35.7230i	1.56806	+	1.56806i
$520$	−6.72303	−	16.2308i	−0.294824	−	0.711769i
$521$	17.0798	−	7.07469i	0.748280	−	0.309948i	0.0242405	−	0.999706i	$-0.492283\pi$
$521$	17.0798	−	7.07469i	0.748280	−	0.309948i	0.724040	+	0.689758i	$0.242283\pi$
$522$	30.9755	−	74.7814i	1.35576	−	3.27309i
$523$		−	20.0606i		−	0.877190i	−0.898685	−	0.438595i	$-0.855476\pi$
$523$		−	20.0606i		−	0.877190i	0.898685	−	0.438595i	$-0.144524\pi$
$524$	−6.32404	−	2.61950i	−0.276267	−	0.114433i
$525$	−20.2220	+	20.2220i	−0.882562	+	0.882562i
$526$	24.7463			1.07899
$527$	28.6124	+	20.6323i	1.24637	+	0.898757i
$528$	−38.9047			−1.69311
$529$	−7.12403	+	7.12403i	−0.309740	+	0.309740i
$530$	28.5570	+	11.8287i	1.24043	+	0.513805i
$531$			24.5807i			1.06671i
$532$	−1.39243	+	3.36162i	−0.0603694	+	0.145745i
$533$	8.35611	−	3.46121i	0.361943	−	0.149922i
$534$	14.1976	+	34.2760i	0.614390	+	1.48327i
$535$	−10.1190	−	10.1190i	−0.437481	−	0.437481i
$536$	10.4691	+	10.4691i	0.452194	+	0.452194i
$537$	16.5117	+	39.8627i	0.712531	+	1.72020i
$538$	16.1511	−	6.69002i	0.696325	−	0.288427i
$539$	−9.16318	+	22.1219i	−0.394686	+	0.952857i
$540$			41.3142i			1.77788i
$541$	−16.9187	−	7.00796i	−0.727392	−	0.301296i	−0.0119121	−	0.999929i	$-0.503792\pi$
$541$	−16.9187	−	7.00796i	−0.727392	−	0.301296i	−0.715480	+	0.698633i	$0.753792\pi$
$542$	4.86865	−	4.86865i	0.209127	−	0.209127i
$543$	−52.0088			−2.23191
$544$	12.9370	−	7.99151i	0.554668	−	0.342633i
$545$	−23.4320			−1.00372
$546$	−7.71670	+	7.71670i	−0.330244	+	0.330244i
$547$	−20.9107	−	8.66150i	−0.894078	−	0.370339i	−0.112138	−	0.993693i	$-0.535770\pi$
$547$	−20.9107	−	8.66150i	−0.894078	−	0.370339i	−0.781940	+	0.623354i	$0.785770\pi$
$548$		−	12.2524i		−	0.523396i
$549$	−1.78647	+	4.31292i	−0.0762447	+	0.184071i
$550$	30.0264	−	12.4373i	1.28033	−	0.530330i
$551$	10.6395	+	25.6860i	0.453258	+	1.09426i
$552$	26.5616	+	26.5616i	1.13054	+	1.13054i
$553$	−8.21762	−	8.21762i	−0.349449	−	0.349449i
$554$	−8.23022	−	19.8695i	−0.349668	−	0.844174i
$555$	−38.0831	+	15.7746i	−1.61654	+	0.669593i
$556$	−0.897732	+	2.16732i	−0.0380723	+	0.0919148i
$557$			9.37961i			0.397427i	0.980058	+	0.198713i	$0.0636763\pi$
$557$			9.37961i			0.397427i	−0.980058	+	0.198713i	$0.936324\pi$
$558$	−77.1415	−	31.9531i	−3.26566	−	1.35268i
$559$	−1.25526	+	1.25526i	−0.0530917	+	0.0530917i
$560$	−10.9500			−0.462723
$561$	72.4350	+	17.1166i	3.05821	+	0.722664i
$562$	−22.5206			−0.949973
$563$	−10.4100	+	10.4100i	−0.438728	+	0.438728i	−0.891584	−	0.452856i	$-0.850405\pi$
$563$	−10.4100	+	10.4100i	−0.438728	+	0.438728i	0.452856	+	0.891584i	$0.350405\pi$
$564$	4.30192	+	1.78191i	0.181143	+	0.0750320i
$565$			5.96939i			0.251134i
$566$	2.87214	−	6.93395i	0.120725	−	0.291456i
$567$	55.4585	−	22.9717i	2.32904	−	0.964720i
$568$	8.93130	+	21.5621i	0.374749	+	0.904724i
$569$	9.59991	+	9.59991i	0.402449	+	0.402449i	0.879095	−	0.476646i	$-0.158148\pi$
$569$	9.59991	+	9.59991i	0.402449	+	0.402449i	−0.476646	+	0.879095i	$0.658148\pi$
$570$	29.6297	+	29.6297i	1.24105	+	1.24105i
$571$	7.40989	+	17.8891i	0.310094	+	0.748633i	0.999701	+	0.0244496i	$0.00778332\pi$
$571$	7.40989	+	17.8891i	0.310094	+	0.748633i	−0.689607	+	0.724184i	$0.742217\pi$
$572$	−5.99074	+	2.48144i	−0.250485	+	0.103754i
$573$	0.577233	−	1.39356i	0.0241142	−	0.0582169i
$574$		−	9.22972i		−	0.385241i
$575$	−17.7076	−	7.33475i	−0.738460	−	0.305880i
$576$	−51.4067	+	51.4067i	−2.14195	+	2.14195i
$577$	3.21303			0.133760			0.0668801	−	0.997761i	$-0.478695\pi$
$577$	3.21303			0.133760			0.0668801	+	0.997761i	$0.478695\pi$
$578$	18.4851	−	6.15256i	0.768880	−	0.255913i
$579$	1.97478			0.0820690
$580$	12.9438	−	12.9438i	0.537460	−	0.537460i
$581$	3.83342	+	1.58785i	0.159037	+	0.0658753i
$582$		−	50.4505i		−	2.09124i
$583$	17.0822	−	41.2401i	0.707473	−	1.70799i
$584$	−9.62852	+	3.98826i	−0.398431	+	0.165035i
$585$	−18.5952	−	44.8927i	−0.768816	−	1.85609i
$586$	−12.9389	−	12.9389i	−0.534500	−	0.534500i
$587$	−23.0027	−	23.0027i	−0.949425	−	0.949425i	0.0493564	−	0.998781i	$-0.484283\pi$
$587$	−23.0027	−	23.0027i	−0.949425	−	0.949425i	−0.998781	+	0.0493564i	$0.984283\pi$
$588$	4.01394	+	9.69051i	0.165532	+	0.399630i
$589$	26.4967	−	10.9753i	1.09178	−	0.452228i
$590$	4.06874	−	9.82281i	0.167507	−	0.404399i
$591$		−	24.4068i		−	1.00396i
$592$	−7.52462	−	3.11680i	−0.309260	−	0.128100i
$593$	8.34611	−	8.34611i	0.342734	−	0.342734i	−0.514660	−	0.857394i	$-0.672082\pi$
$593$	8.34611	−	8.34611i	0.342734	−	0.342734i	0.857394	+	0.514660i	$0.172082\pi$
$594$	−114.113			−4.68213
$595$	20.3874	+	4.81760i	0.835802	+	0.197502i
$596$	−3.94707			−0.161678
$597$	33.8460	−	33.8460i	1.38523	−	1.38523i
$598$	−6.75721	−	2.79893i	−0.276323	−	0.114457i
$599$			21.5156i			0.879103i	0.898217	+	0.439551i	$0.144863\pi$
$599$			21.5156i			0.879103i	−0.898217	+	0.439551i	$0.855137\pi$
$600$	21.3167	−	51.4632i	0.870252	−	2.10097i
$601$	3.40944	−	1.41224i	0.139074	−	0.0576064i	−0.312061	−	0.950062i	$-0.601019\pi$
$601$	3.40944	−	1.41224i	0.139074	−	0.0576064i	0.451135	+	0.892456i	$0.351019\pi$
$602$	0.693246	+	1.67364i	0.0282546	+	0.0682126i
$603$	28.9563	+	28.9563i	1.17919	+	1.17919i
$604$	−4.76478	−	4.76478i	−0.193876	−	0.193876i
$605$	−21.2761	−	51.3651i	−0.864997	−	2.08829i
$606$	−40.1476	+	16.6297i	−1.63089	+	0.675535i
$607$	14.7555	−	35.6229i	0.598907	−	1.44589i	−0.275790	−	0.961218i	$-0.588939\pi$
$607$	14.7555	−	35.6229i	0.598907	−	1.44589i	0.874696	−	0.484671i	$-0.161061\pi$
$608$		−	12.3630i		−	0.501386i
$609$	−41.1036	−	17.0257i	−1.66560	−	0.689916i
$610$	1.42780	−	1.42780i	0.0578101	−	0.0578101i
$611$	−3.54730			−0.143508
$612$	20.5125	−	12.6711i	0.829167	−	0.512198i
$613$	−7.68277			−0.310304			−0.155152	−	0.987891i	$-0.549587\pi$
$613$	−7.68277			−0.310304			−0.155152	+	0.987891i	$0.549587\pi$
$614$	12.4404	−	12.4404i	0.502054	−	0.502054i
$615$	51.3433	+	21.2671i	2.07036	+	0.857572i
$616$			25.8901i			1.04314i
$617$	5.33140	−	12.8711i	0.214634	−	0.518172i	−0.779491	−	0.626414i	$-0.784522\pi$
$617$	5.33140	−	12.8711i	0.214634	−	0.518172i	0.994125	+	0.108242i	$0.0345220\pi$
$618$	47.8058	−	19.8018i	1.92303	−	0.796546i
$619$	−2.09066	−	5.04730i	−0.0840308	−	0.202868i	0.876279	−	0.481804i	$-0.160018\pi$
$619$	−2.09066	−	5.04730i	−0.0840308	−	0.202868i	−0.960310	+	0.278936i	$0.910018\pi$
$620$	−13.3523	−	13.3523i	−0.536240	−	0.536240i
$621$	47.5860	+	47.5860i	1.90956	+	1.90956i
$622$	7.77573	+	18.7723i	0.311778	+	0.752700i
$623$	13.9319	−	5.77080i	0.558172	−	0.231202i
$624$	4.96841	−	11.9948i	0.198896	−	0.480177i
$625$		−	23.2341i		−	0.929362i
$626$	−17.7694	−	7.36031i	−0.710206	−	0.294177i
$627$	42.7893	−	42.7893i	1.70884	−	1.70884i
$628$	12.3348			0.492213
$629$	12.6385	+	9.11358i	0.503930	+	0.363382i
$630$	−49.5862			−1.97556
$631$	17.6233	−	17.6233i	0.701572	−	0.701572i	−0.263176	−	0.964748i	$-0.584770\pi$
$631$	17.6233	−	17.6233i	0.701572	−	0.701572i	0.964748	+	0.263176i	$0.0847701\pi$
$632$	20.9131	+	8.66247i	0.831877	+	0.344575i
$633$		−	15.4818i		−	0.615346i
$634$	−5.72511	+	13.8216i	−0.227373	+	0.548927i
$635$	−23.4464	+	9.71182i	−0.930443	+	0.385402i
$636$	−7.48288	−	18.0653i	−0.296716	−	0.716335i
$637$	−5.65025	−	5.65025i	−0.223871	−	0.223871i
$638$	35.7518	+	35.7518i	1.41543	+	1.41543i
$639$	24.7030	+	59.6384i	0.977237	+	2.35926i
$640$	7.14832	−	2.96093i	0.282562	−	0.117041i
$641$	−12.2981	+	29.6903i	−0.485746	+	1.17270i	0.471095	+	0.882083i	$0.343859\pi$
$641$	−12.2981	+	29.6903i	−0.485746	+	1.17270i	−0.956841	+	0.290612i	$0.906141\pi$
$642$		−	17.3147i		−	0.683355i
$643$	44.1993	+	18.3080i	1.74305	+	0.721995i	0.998519	+	0.0544084i	$0.0173273\pi$
$643$	44.1993	+	18.3080i	1.74305	+	0.721995i	0.744532	+	0.667587i	$0.232673\pi$
$644$	2.75935	−	2.75935i	0.108734	−	0.108734i
$645$	−10.9076			−0.429485
$646$	3.64259	−	15.4149i	0.143316	−	0.606491i
$647$	−43.4177			−1.70693			−0.853463	−	0.521153i	$-0.825502\pi$
$647$	−43.4177			−1.70693			−0.853463	+	0.521153i	$0.825502\pi$
$648$	−82.6760	+	82.6760i	−3.24782	+	3.24782i
$649$	−14.1855	−	5.87581i	−0.556828	−	0.230646i
$650$			10.8459i			0.425409i
$651$	−17.5630	+	42.4009i	−0.688349	+	1.66182i
$652$	−12.2917	+	5.09137i	−0.481379	+	0.199394i
$653$	−1.48976	−	3.59659i	−0.0582987	−	0.140746i	0.892046	−	0.451944i	$-0.149269\pi$
$653$	−1.48976	−	3.59659i	−0.0582987	−	0.140746i	−0.950345	+	0.311199i	$0.899269\pi$
$654$	−20.0473	−	20.0473i	−0.783913	−	0.783913i
$655$	22.6566	+	22.6566i	0.885267	+	0.885267i
$656$	4.20204	+	10.1446i	0.164062	+	0.396081i
$657$	−26.6315	+	11.0311i	−1.03899	+	0.430365i
$658$	−1.38528	+	3.34436i	−0.0540038	+	0.130377i
$659$			11.0855i			0.431829i	0.976412	+	0.215914i	$0.0692732\pi$
$659$			11.0855i			0.431829i	−0.976412	+	0.215914i	$0.930727\pi$
$660$	−36.8095	−	15.2470i	−1.43281	−	0.593489i
$661$	12.0407	−	12.0407i	0.468327	−	0.468327i	−0.433045	−	0.901372i	$-0.642561\pi$
$661$	12.0407	−	12.0407i	0.468327	−	0.468327i	0.901372	+	0.433045i	$0.142561\pi$
$662$	36.3224			1.41171
$663$	−14.5277	+	20.1467i	−0.564211	+	0.782433i
$664$	−8.08188			−0.313638
$665$	12.0434	−	12.0434i	0.467023	−	0.467023i
$666$	−34.0745	−	14.1141i	−1.32036	−	0.546911i
$667$		−	29.8175i		−	1.15454i
$668$	6.14732	−	14.8410i	0.237847	−	0.574214i
$669$	−14.5294	+	6.01826i	−0.561738	+	0.232679i
$670$	−6.77836	−	16.3644i	−0.261871	−	0.632213i
$671$	−2.06194	−	2.06194i	−0.0796004	−	0.0796004i
$672$	13.9892	+	13.9892i	0.539645	+	0.539645i
$673$	7.46818	+	18.0298i	0.287877	+	0.694997i	0.999975	−	0.00708318i	$-0.00225467\pi$
$673$	7.46818	+	18.0298i	0.287877	+	0.694997i	−0.712098	+	0.702080i	$0.752255\pi$
$674$	26.3296	−	10.9061i	1.01418	−	0.420087i
$675$	38.1897	−	92.1980i	1.46992	−	3.54870i
$676$			6.76274i			0.260105i
$677$	26.8514	+	11.1222i	1.03198	+	0.427462i	0.833428	−	0.552628i	$-0.186375\pi$
$677$	26.8514	+	11.1222i	1.03198	+	0.427462i	0.198556	+	0.980090i	$0.436375\pi$
$678$	−5.10714	+	5.10714i	−0.196139	+	0.196139i
$679$	−20.5062			−0.786957
$680$	−40.2785	+	6.52710i	−1.54461	+	0.250303i
$681$	−31.2263			−1.19659
$682$	36.8802	−	36.8802i	1.41221	−	1.41221i
$683$	−32.0395	−	13.2712i	−1.22596	−	0.507808i	−0.326658	−	0.945143i	$-0.605922\pi$
$683$	−32.0395	−	13.2712i	−1.22596	−	0.507808i	−0.899299	+	0.437335i	$0.855922\pi$
$684$		−	19.6024i		−	0.749517i
$685$	−21.9478	+	52.9867i	−0.838583	+	2.02452i
$686$	−19.2490	+	7.97320i	−0.734931	+	0.304418i
$687$	28.1657	+	67.9981i	1.07459	+	2.59429i
$688$	−1.52393	−	1.52393i	−0.0580992	−	0.0580992i
$689$	10.5333	+	10.5333i	0.401287	+	0.401287i
$690$	−17.1978	−	41.5191i	−0.654707	−	1.58060i
$691$	30.8116	−	12.7626i	1.17213	−	0.485511i	0.290232	−	0.956956i	$-0.406268\pi$
$691$	30.8116	−	12.7626i	1.17213	−	0.485511i	0.881895	+	0.471446i	$0.156268\pi$
$692$	−3.91198	+	9.44434i	−0.148711	+	0.359020i
$693$			71.6092i			2.72021i
$694$	25.3408	+	10.4965i	0.961924	+	0.398442i
$695$	7.76467	−	7.76467i	0.294531	−	0.294531i
$696$	86.6575			3.28475
$697$	−3.36034	−	20.7366i	−0.127282	−	0.785453i
$698$	−40.2635			−1.52400
$699$	57.2961	−	57.2961i	2.16714	−	2.16714i
$700$	−5.34625	−	2.21449i	−0.202069	−	0.0836998i
$701$		−	7.43050i		−	0.280646i	−0.990106	−	0.140323i	$-0.955186\pi$
$701$		−	7.43050i		−	0.280646i	0.990106	−	0.140323i	$-0.0448141\pi$
$702$	14.5731	−	35.1826i	0.550027	−	1.32788i
$703$	11.7040	−	4.84794i	0.441423	−	0.182843i
$704$	−17.3784	−	41.9551i	−0.654972	−	1.58124i
$705$	−15.4121	−	15.4121i	−0.580454	−	0.580454i
$706$	−16.2918	−	16.2918i	−0.613150	−	0.613150i
$707$	6.75935	+	16.3185i	0.254212	+	0.613721i
$708$	−6.21396	+	2.57391i	−0.233535	+	0.0967334i
$709$	−6.71448	+	16.2102i	−0.252168	+	0.608787i	−0.998379	−	0.0569229i	$-0.981871\pi$
$709$	−6.71448	+	16.2102i	−0.252168	+	0.608787i	0.746211	+	0.665710i	$0.231871\pi$
$710$		−	27.9214i		−	1.04787i
$711$	57.8433	+	23.9595i	2.16929	+	0.898551i
$712$	−20.7693	+	20.7693i	−0.778364	+	0.778364i
$713$	−30.7585			−1.15192
$714$	13.3208	+	21.5642i	0.498519	+	0.807022i
$715$	30.3526			1.13512
$716$	−6.17348	+	6.17348i	−0.230714	+	0.230714i
$717$	14.6337	+	6.06148i	0.546506	+	0.226370i
$718$			13.5877i			0.507087i
$719$	−5.63222	+	13.5974i	−0.210046	+	0.507097i	−0.993430	−	0.114442i	$-0.963492\pi$
$719$	−5.63222	+	13.5974i	−0.210046	+	0.507097i	0.783384	+	0.621539i	$0.213492\pi$
$720$	54.5014	−	22.5752i	2.03115	−	0.841329i
$721$	−8.04871	−	19.4313i	−0.299750	−	0.723660i
$722$	6.29065	+	6.29065i	0.234114	+	0.234114i
$723$	−9.36075	−	9.36075i	−0.348130	−	0.348130i
$724$	−4.02727	−	9.72269i	−0.149672	−	0.361341i
$725$	−40.8505	+	16.9208i	−1.51715	+	0.628424i
$726$	25.7427	−	62.1485i	0.955403	−	2.30655i
$727$			26.0781i			0.967182i	0.875294	+	0.483591i	$0.160668\pi$
$727$			26.0781i			0.967182i	−0.875294	+	0.483591i	$0.839332\pi$
$728$	−7.98223	−	3.30635i	−0.295841	−	0.122541i
$729$	−93.9211	+	93.9211i	−3.47856	+	3.47856i
$730$	12.4683			0.461472
$731$	2.16686	+	3.50781i	0.0801444	+	0.129741i
$732$	−1.27737			−0.0472129
$733$	−12.7631	+	12.7631i	−0.471417	+	0.471417i	−0.902373	−	0.430956i	$-0.858177\pi$
$733$	−12.7631	+	12.7631i	−0.471417	+	0.471417i	0.430956	+	0.902373i	$0.358177\pi$
$734$	17.1606	+	7.10813i	0.633408	+	0.262366i
$735$		−	49.0978i		−	1.81100i
$736$	−5.07404	+	12.2498i	−0.187031	+	0.451534i
$737$	−23.6324	+	9.78888i	−0.870512	+	0.360578i
$738$	19.0285	+	45.9389i	0.700450	+	1.69104i
$739$	−24.8634	−	24.8634i	−0.914615	−	0.914615i	0.0820156	−	0.996631i	$-0.473864\pi$
$739$	−24.8634	−	24.8634i	−0.914615	−	0.914615i	−0.996631	+	0.0820156i	$0.973864\pi$
$740$	−5.89789	−	5.89789i	−0.216811	−	0.216811i
$741$	7.72798	+	18.6570i	0.283894	+	0.685382i
$742$	14.0442	−	5.81728i	0.515577	−	0.213559i
$743$	−8.38588	+	20.2453i	−0.307648	+	0.742728i	0.692132	+	0.721771i	$0.256671\pi$
$743$	−8.38588	+	20.2453i	−0.307648	+	0.742728i	−0.999780	+	0.0209575i	$0.993329\pi$
$744$		−	89.3925i		−	3.27729i
$745$	17.0695	+	7.07043i	0.625379	+	0.259040i
$746$	−21.8640	+	21.8640i	−0.800498	+	0.800498i
$747$	−22.3536			−0.817876
$748$	2.40913	+	14.8666i	0.0880865	+	0.543578i
$749$	−7.03776			−0.257154
$750$	−2.92785	+	2.92785i	−0.106910	+	0.106910i
$751$	−46.6377	−	19.3180i	−1.70183	−	0.704922i	−0.701860	−	0.712314i	$-0.747647\pi$
$751$	−46.6377	−	19.3180i	−1.70183	−	0.704922i	−0.999973	+	0.00739212i	$0.997647\pi$
$752$		−	4.30655i		−	0.157044i
$753$	−21.2253	+	51.2424i	−0.773493	+	1.86738i
$754$	−15.5885	+	6.45697i	−0.567700	+	0.235149i
$755$	12.0706	+	29.1410i	0.439294	+	1.06055i
$756$	14.3671	+	14.3671i	0.522525	+	0.522525i
$757$	1.16834	+	1.16834i	0.0424641	+	0.0424641i	0.728020	−	0.685556i	$-0.240441\pi$
$757$	1.16834	+	1.16834i	0.0424641	+	0.0424641i	−0.685556	+	0.728020i	$0.740441\pi$
$758$	−9.67273	−	23.3520i	−0.351329	−	0.848184i
$759$	−59.9591	+	24.8359i	−2.17638	+	0.901486i
$760$	−12.6954	+	30.6493i	−0.460509	+	1.11177i
$761$		−	3.89048i		−	0.141030i	−0.997511	−	0.0705149i	$-0.977536\pi$
$761$		−	3.89048i		−	0.141030i	0.997511	−	0.0705149i	$-0.0224642\pi$
$762$	−28.3687	−	11.7507i	−1.02769	−	0.425683i
$763$	−8.14850	+	8.14850i	−0.294996	+	0.294996i
$764$	0.305215			0.0110423
$765$	−111.406	+	18.0533i	−4.02790	+	0.652718i
$766$	−17.3508			−0.626911
$767$	3.62317	−	3.62317i	0.130825	−	0.130825i
$768$	−44.8806	−	18.5902i	−1.61949	−	0.670815i
$769$			5.78082i			0.208462i	0.994553	+	0.104231i	$0.0332381\pi$
$769$			5.78082i			0.208462i	−0.994553	+	0.104231i	$0.966762\pi$
$770$	11.8532	−	28.6161i	0.427159	−	1.03125i
$771$	47.6764	−	19.7482i	1.71702	−	0.711215i
$772$	0.152916	+	0.369171i	0.00550356	+	0.0132868i
$773$	−23.5406	−	23.5406i	−0.846695	−	0.846695i	0.143024	−	0.989719i	$-0.454317\pi$
$773$	−23.5406	−	23.5406i	−0.846695	−	0.846695i	−0.989719	+	0.143024i	$0.954317\pi$
$774$	−6.90096	−	6.90096i	−0.248050	−	0.248050i
$775$	17.4549	+	42.1398i	0.626997	+	1.51371i
$776$	36.9014	−	15.2851i	1.32468	−	0.548702i
$777$	−7.75784	+	18.7291i	−0.278311	+	0.671902i
$778$			19.9085i			0.713755i
$779$	−15.7792	−	6.53594i	−0.565347	−	0.234174i
$780$	9.40168	−	9.40168i	0.336634	−	0.336634i
$781$	−40.3223			−1.44285
$782$	−9.93582	+	13.7788i	−0.355304	+	0.492727i
$783$	155.250			5.54818
$784$	6.85960	−	6.85960i	0.244986	−	0.244986i
$785$	−53.3432	−	22.0955i	−1.90390	−	0.788622i
$786$			38.7679i			1.38281i
$787$	14.9128	−	36.0027i	0.531585	−	1.28336i	−0.398889	−	0.916999i	$-0.630604\pi$
$787$	14.9128	−	36.0027i	0.531585	−	1.28336i	0.930473	−	0.366359i	$-0.119396\pi$
$788$	4.56267	−	1.88992i	0.162539	−	0.0673257i
$789$	28.0423	+	67.7000i	0.998331	+	2.41018i
$790$	−19.1492	−	19.1492i	−0.681297	−	0.681297i
$791$	2.07586	+	2.07586i	0.0738092	+	0.0738092i
$792$	−53.3764	−	128.862i	−1.89665	−	4.57892i
$793$	0.899047	−	0.372398i	0.0319261	−	0.0132242i
$794$	−12.3374	+	29.7852i	−0.437839	+	1.05704i
$795$			91.5293i			3.24621i
$796$	8.94812	+	3.70643i	0.317158	+	0.131371i
$797$	−19.3610	+	19.3610i	−0.685801	+	0.685801i	−0.961301	−	0.275500i	$-0.911157\pi$
$797$	−19.3610	+	19.3610i	−0.685801	+	0.685801i	0.275500	+	0.961301i	$0.411157\pi$
$798$	20.6075			0.729499
$799$	−1.89472	+	8.01817i	−0.0670303	+	0.283663i
$800$	19.6619			0.695153
$801$	−57.4458	+	57.4458i	−2.02975	+	2.02975i
$802$	−12.8250	−	5.31228i	−0.452866	−	0.187583i
$803$		−	18.0059i		−	0.635414i
$804$	−4.28803	+	10.3522i	−0.151227	+	0.365094i
$805$	−16.8760	+	6.99025i	−0.594799	+	0.246374i
$806$	6.66075	+	16.0805i	0.234615	+	0.566411i
$807$	36.6047	+	36.6047i	1.28855	+	1.28855i
$808$	−24.3272	−	24.3272i	−0.855827	−	0.855827i
$809$	−15.8930	−	38.3692i	−0.558770	−	1.34899i	−0.910741	−	0.412978i	$-0.864488\pi$
$809$	−15.8930	−	38.3692i	−0.558770	−	1.34899i	0.351971	−	0.936011i	$-0.385512\pi$
$810$	129.233	−	53.5299i	4.54077	−	1.88085i
$811$	8.71039	−	21.0287i	0.305863	−	0.738419i	−0.693967	−	0.720006i	$-0.744139\pi$
$811$	8.71039	−	21.0287i	0.305863	−	0.738419i	0.999830	−	0.0184124i	$-0.00586118\pi$
$812$		−	9.00242i		−	0.315923i
$813$	18.8366	+	7.80238i	0.660629	+	0.273641i
$814$	16.2905	−	16.2905i	0.570982	−	0.570982i
$815$	62.2768			2.18146
$816$	−24.4588	−	17.6372i	−0.856231	−	0.617426i
$817$	3.35218			0.117278
$818$	27.2833	−	27.2833i	0.953938	−	0.953938i
$819$	−22.0780	−	9.14501i	−0.771468	−	0.319552i
$820$			11.2451i			0.392695i
$821$	−9.36674	+	22.6133i	−0.326902	+	0.789210i	0.671917	+	0.740626i	$0.265471\pi$
$821$	−9.36674	+	22.6133i	−0.326902	+	0.789210i	−0.998819	+	0.0485843i	$0.984529\pi$
$822$	−64.1105	+	26.5555i	−2.23611	+	0.926228i
$823$	2.50665	+	6.05159i	0.0873764	+	0.210945i	0.961527	−	0.274709i	$-0.0885815\pi$
$823$	2.50665	+	6.05159i	0.0873764	+	0.210945i	−0.874151	+	0.485654i	$0.838581\pi$
$824$	28.9676	+	28.9676i	1.00914	+	1.00914i
$825$	68.0513	+	68.0513i	2.36924	+	2.36924i
$826$	−2.00098	−	4.83080i	−0.0696232	−	0.168085i
$827$	14.4318	−	5.97787i	0.501845	−	0.207871i	−0.117377	−	0.993087i	$-0.537448\pi$
$827$	14.4318	−	5.97787i	0.501845	−	0.207871i	0.619221	+	0.785217i	$0.287448\pi$
$828$	−8.04524	+	19.4229i	−0.279591	+	0.674993i
$829$		−	1.35950i		−	0.0472174i	−0.999721	−	0.0236087i	$-0.992484\pi$
$829$		−	1.35950i		−	0.0472174i	0.999721	−	0.0236087i	$-0.00751558\pi$
$830$	8.93285	+	3.70011i	0.310064	+	0.128433i
$831$	45.0319	−	45.0319i	1.56214	−	1.56214i
$832$	15.1546			0.525392
$833$	−15.7896	+	9.75363i	−0.547076	+	0.337943i
$834$	13.2862			0.460064
$835$	−53.1695	+	53.1695i	−1.84001	+	1.84001i
$836$	11.3125	+	4.68581i	0.391252	+	0.162062i
$837$		−	160.150i		−	5.53558i
$838$	7.40326	−	17.8730i	0.255741	−	0.617414i
$839$	0.215892	−	0.0894256i	0.00745344	−	0.00308731i	−0.378954	−	0.925416i	$-0.623716\pi$
$839$	0.215892	−	0.0894256i	0.00745344	−	0.00308731i	0.386407	+	0.922328i	$0.373716\pi$
$840$	−20.3155	−	49.0461i	−0.700953	−	1.69225i
$841$	−28.1338	−	28.1338i	−0.970131	−	0.970131i
$842$	5.65575	+	5.65575i	0.194910	+	0.194910i
$843$	−25.5201	−	61.6111i	−0.878960	−	2.12200i
$844$	2.89421	−	1.19882i	0.0996229	−	0.0412652i
$845$	12.1142	−	29.2462i	0.416740	−	1.00610i
$846$		−	19.5018i		−	0.670485i
$847$	−25.2611	−	10.4635i	−0.867980	−	0.359529i
$848$	−12.7878	+	12.7878i	−0.439136	+	0.439136i
$849$	22.2243			0.762738
$850$	24.5156	+	5.79310i	0.840877	+	0.198702i
$851$	−13.5865			−0.465738
$852$	−12.4898	+	12.4898i	−0.427893	+	0.427893i
$853$	37.9875	+	15.7349i	1.30067	+	0.538754i	0.922147	−	0.386839i	$-0.126433\pi$
$853$	37.9875	+	15.7349i	1.30067	+	0.538754i	0.378520	+	0.925593i	$0.376433\pi$
$854$		−	0.993041i		−	0.0339812i
$855$	−35.1140	+	84.7727i	−1.20087	+	2.89916i
$856$	12.6646	−	5.24585i	0.432867	−	0.179299i
$857$	3.28565	+	7.93226i	0.112236	+	0.270961i	0.970010	−	0.243066i	$-0.0781532\pi$
$857$	3.28565	+	7.93226i	0.112236	+	0.270961i	−0.857774	+	0.514027i	$0.828153\pi$
$858$	25.9683	+	25.9683i	0.886543	+	0.886543i
$859$	−28.1551	−	28.1551i	−0.960638	−	0.960638i	0.0386157	−	0.999254i	$-0.487705\pi$
$859$	−28.1551	−	28.1551i	−0.960638	−	0.960638i	−0.999254	+	0.0386157i	$0.987705\pi$
$860$	−0.844620	−	2.03909i	−0.0288013	−	0.0695325i
$861$	25.2504	−	10.4590i	0.860530	−	0.356443i
$862$	−5.25265	+	12.6810i	−0.178906	+	0.431917i
$863$			9.28191i			0.315960i	0.987442	+	0.157980i	$0.0504982\pi$
$863$			9.28191i			0.315960i	−0.987442	+	0.157980i	$0.949502\pi$
$864$	−63.7808	−	26.4189i	−2.16987	−	0.898788i
$865$	33.8355	−	33.8355i	1.15044	−	1.15044i
$866$	−18.4510			−0.626989
$867$	37.7792	+	43.5989i	1.28305	+	1.48070i
$868$	−9.28653			−0.315206
$869$	−27.6540	+	27.6540i	−0.938097	+	0.938097i
$870$	−95.7821	−	39.6742i	−3.24732	−	1.34508i
$871$		−	8.53628i		−	0.289241i
$872$	8.58962	−	20.7372i	0.290881	−	0.702249i
$873$	102.065	−	42.2769i	3.45439	−	1.43085i
$874$	5.28532	+	12.7599i	0.178779	+	0.431610i
$875$	1.19006	+	1.19006i	0.0402314	+	0.0402314i
$876$	−5.57731	−	5.57731i	−0.188440	−	0.188440i
$877$	2.69226	+	6.49970i	0.0909113	+	0.219479i	0.962795	−	0.270235i	$-0.0871012\pi$
$877$	2.69226	+	6.49970i	0.0909113	+	0.219479i	−0.871883	+	0.489714i	$0.837101\pi$
$878$	21.6108	−	8.95149i	0.729330	−	0.302098i
$879$	20.7355	−	50.0600i	0.699391	−	1.68848i
$880$			36.8491i			1.24218i
$881$	−4.73253	−	1.96028i	−0.159443	−	0.0660435i	0.301535	−	0.953455i	$-0.402501\pi$
$881$	−4.73253	−	1.96028i	−0.159443	−	0.0660435i	−0.460978	+	0.887412i	$0.652501\pi$
$882$	31.0631	−	31.0631i	1.04595	−	1.04595i
$883$	9.97520			0.335692			0.167846	−	0.985813i	$-0.446319\pi$
$883$	9.97520			0.335692			0.167846	+	0.985813i	$0.446319\pi$
$884$	−4.89124	−	1.15581i	−0.164510	−	0.0388742i
$885$	31.4836			1.05831
$886$	23.2695	−	23.2695i	0.781754	−	0.781754i
$887$	−47.3231	−	19.6019i	−1.58895	−	0.658167i	−0.599155	−	0.800633i	$-0.704497\pi$
$887$	−47.3231	−	19.6019i	−1.58895	−	0.658167i	−0.989800	+	0.142466i	$0.954497\pi$
$888$		−	39.4859i		−	1.32506i
$889$	−4.77622	+	11.5308i	−0.160189	+	0.386731i
$890$	32.4650	−	13.4475i	1.08823	−	0.450760i
$891$	−77.3045	−	186.630i	−2.58980	−	6.25232i
$892$	−2.25014	−	2.25014i	−0.0753404	−	0.0753404i
$893$	4.73655	+	4.73655i	0.158503	+	0.158503i
$894$	8.55477	+	20.6530i	0.286114	+	0.690741i
$895$	37.7565	−	15.6393i	1.26206	−	0.522763i
$896$	1.45617	−	3.51550i	0.0486472	−	0.117445i
$897$		−	21.6579i		−	0.723135i
$898$	14.5898	+	6.04329i	0.486867	+	0.201667i
$899$	−50.1750	+	50.1750i	−1.67343	+	1.67343i
$900$	31.1753			1.03918
$901$	29.4353	−	18.1829i	0.980631	−	0.605762i
$902$	−31.0599			−1.03418
$903$	−3.79312	+	3.79312i	−0.126227	+	0.126227i
$904$	−5.28288	−	2.18824i	−0.175706	−	0.0727798i
$905$			49.2608i			1.63749i
$906$	−14.6046	+	35.2587i	−0.485207	+	1.17139i
$907$	−35.2249	+	14.5906i	−1.16962	+	0.484474i	−0.881069	−	0.472989i	$-0.843175\pi$
$907$	−35.2249	+	14.5906i	−1.16962	+	0.484474i	−0.288556	+	0.957463i	$0.593175\pi$
$908$	−2.41799	−	5.83754i	−0.0802437	−	0.193725i
$909$	−67.2864	−	67.2864i	−2.23175	−	2.23175i
$910$	7.30898	+	7.30898i	0.242290	+	0.242290i
$911$	16.0124	+	38.6573i	0.530513	+	1.28077i	0.931184	+	0.364550i	$0.118777\pi$
$911$	16.0124	+	38.6573i	0.530513	+	1.28077i	−0.400670	+	0.916222i	$0.631223\pi$
$912$	−22.6503	+	9.38205i	−0.750025	+	0.310671i
$913$	5.34346	−	12.9002i	0.176843	−	0.426936i
$914$			3.89146i			0.128718i
$915$	5.52411	+	2.28816i	0.182621	+	0.0756443i
$916$	−10.5308	+	10.5308i	−0.347947	+	0.347947i
$917$	15.7577			0.520366
$918$	−71.7415	−	51.7326i	−2.36782	−	1.70743i
$919$	−13.6593			−0.450580			−0.225290	−	0.974292i	$-0.572333\pi$
$919$	−13.6593			−0.450580			−0.225290	+	0.974292i	$0.572333\pi$
$920$	25.1582	−	25.1582i	0.829441	−	0.829441i
$921$	48.1314	+	19.9367i	1.58598	+	0.656936i
$922$		−	13.3765i		−	0.440531i
$923$	5.14945	−	12.4319i	0.169496	−	0.409200i
$924$	−18.1027	+	7.49839i	−0.595536	+	0.246679i
$925$	7.71007	+	18.6137i	0.253505	+	0.612016i
$926$	15.8373	+	15.8373i	0.520446	+	0.520446i
$927$	80.1214	+	80.1214i	2.63153	+	2.63153i
$928$	11.7055	+	28.2596i	0.384252	+	0.927667i
$929$	−32.5929	+	13.5004i	−1.06934	+	0.442935i	−0.846758	−	0.531979i	$-0.821449\pi$
$929$	−32.5929	+	13.5004i	−1.06934	+	0.442935i	−0.222582	+	0.974914i	$0.571449\pi$
$930$	−40.9264	+	98.8050i	−1.34203	+	3.23994i
$931$			15.0891i			0.494524i
$932$	15.1478	+	6.27442i	0.496182	+	0.205525i
$933$	−42.5452	+	42.5452i	−1.39287	+	1.39287i
$934$	−7.48296			−0.244850
$935$	16.2122	−	68.6078i	0.530197	−	2.24372i
$936$	46.5464			1.52142
$937$	−26.5436	+	26.5436i	−0.867141	+	0.867141i	−0.992155	−	0.125014i	$-0.960102\pi$
$937$	−26.5436	+	26.5436i	−0.867141	+	0.867141i	0.125014	+	0.992155i	$0.460102\pi$
$938$	−8.04793	−	3.33356i	−0.262774	−	0.108845i
$939$		−	56.9534i		−	1.85861i
$940$	1.68776	−	4.07462i	0.0550487	−	0.132899i
$941$	−2.39760	+	0.993118i	−0.0781595	+	0.0323747i	−0.421421	−	0.906865i	$-0.638468\pi$
$941$	−2.39760	+	0.993118i	−0.0781595	+	0.0323747i	0.343261	+	0.939240i	$0.388468\pi$
$942$	−26.7341	−	64.5419i	−0.871045	−	2.10289i
$943$	12.9522	+	12.9522i	0.421781	+	0.421781i
$944$	4.39866	+	4.39866i	0.143164	+	0.143164i
$945$	−36.3960	−	87.8677i	−1.18396	−	2.85833i
$946$	5.63216	−	2.33292i	0.183117	−	0.0758497i
$947$	−5.81156	+	14.0304i	−0.188850	+	0.455925i	−0.989739	−	0.142888i	$-0.954361\pi$
$947$	−5.81156	+	14.0304i	−0.188850	+	0.455925i	0.800888	+	0.598814i	$0.204361\pi$
$948$			17.1316i			0.556408i
$949$	5.55144	+	2.29948i	0.180207	+	0.0746443i
$950$	14.4820	−	14.4820i	0.469858	−	0.469858i
$951$	−44.3004			−1.43654
$952$	−11.7371	+	16.2767i	−0.380401	+	0.527531i
$953$	17.5884			0.569745			0.284873	−	0.958565i	$-0.408049\pi$
$953$	17.5884			0.569745			0.284873	+	0.958565i	$0.408049\pi$
$954$	−57.9085	+	57.9085i	−1.87486	+	1.87486i
$955$	−1.31993	−	0.546734i	−0.0427120	−	0.0176919i
$956$			3.20504i			0.103658i
$957$	−57.2950	+	138.322i	−1.85208	+	4.47133i
$958$	−1.00974	+	0.418248i	−0.0326232	+	0.0135130i
$959$	10.7938	+	26.0586i	0.348550	+	0.841475i
$960$	65.8431	+	65.8431i	2.12508	+	2.12508i
$961$	29.8382	+	29.8382i	0.962523	+	0.962523i
$962$	2.94215	+	7.10298i	0.0948587	+	0.229009i
$963$	35.0289	−	14.5095i	1.12879	−	0.467561i
$964$	1.02508	−	2.47477i	0.0330157	−	0.0797070i
$965$		−	1.87044i		−	0.0602116i
$966$	−20.4188	−	8.45776i	−0.656966	−	0.272124i
$967$	−14.7813	+	14.7813i	−0.475334	+	0.475334i	−0.903636	−	0.428302i	$-0.859112\pi$
$967$	−14.7813	+	14.7813i	−0.475334	+	0.475334i	0.428302	+	0.903636i	$0.359112\pi$
$968$	53.2571			1.71175
$969$	46.2993	−	7.50277i	1.48735	−	0.241024i
$970$	−47.7848			−1.53428
$971$	−15.7417	+	15.7417i	−0.505176	+	0.505176i	−0.913042	−	0.407866i	$-0.866273\pi$
$971$	−15.7417	+	15.7417i	−0.505176	+	0.505176i	0.407866	+	0.913042i	$0.366273\pi$
$972$	−46.1279	−	19.1068i	−1.47955	−	0.612851i
$973$		−	5.40035i		−	0.173127i
$974$	−4.14325	+	10.0027i	−0.132758	+	0.320507i
$975$	−29.6717	+	12.2904i	−0.950256	+	0.393609i
$976$	0.452104	+	1.09148i	0.0144715	+	0.0349373i
$977$	5.86938	+	5.86938i	0.187778	+	0.187778i	0.794735	−	0.606957i	$-0.207610\pi$
$977$	5.86938	+	5.86938i	0.187778	+	0.187778i	−0.606957	+	0.794735i	$0.707610\pi$
$978$	53.2812	+	53.2812i	1.70374	+	1.70374i
$979$	−19.4199	−	46.8839i	−0.620664	−	1.49842i
$980$	9.17850	−	3.80186i	0.293196	−	0.121446i
$981$	23.7580	−	57.3568i	0.758534	−	1.83126i
$982$			29.7160i			0.948277i
$983$	−36.6806	−	15.1936i	−1.16993	−	0.484601i	−0.288761	−	0.957401i	$-0.593243\pi$
$983$	−36.6806	−	15.1936i	−1.16993	−	0.484601i	−0.881170	+	0.472800i	$0.843243\pi$
$984$	−37.6425	+	37.6425i	−1.20000	+	1.20000i
$985$	−23.1172			−0.736575
$986$	6.26880	+	38.6845i	0.199639	+	1.23197i
$987$	−10.7192			−0.341195
$988$	−2.88938	+	2.88938i	−0.0919236	+	0.0919236i
$989$	−3.32148	−	1.37580i	−0.105617	−	0.0437480i
$990$			166.868i			5.30341i
$991$	−10.8417	+	26.1742i	−0.344398	+	0.831451i	0.652862	+	0.757477i	$0.273568\pi$
$991$	−10.8417	+	26.1742i	−0.344398	+	0.831451i	−0.997260	+	0.0739739i	$0.976432\pi$
$992$	29.1515	−	12.0749i	0.925561	−	0.383380i
$993$	41.1603	+	99.3697i	1.30618	+	3.15340i
$994$	−9.70971	−	9.70971i	−0.307973	−	0.307973i
$995$	−32.0577	−	32.0577i	−1.01630	−	1.01630i
$996$	−2.34071	−	5.65097i	−0.0741682	−	0.179058i
$997$	36.3630	−	15.0621i	1.15163	−	0.477020i	0.276549	−	0.961000i	$-0.410809\pi$
$997$	36.3630	−	15.0621i	1.15163	−	0.477020i	0.875079	+	0.483980i	$0.160809\pi$
$998$	18.3805	−	44.3745i	0.581825	−	1.40465i
$999$		−	70.7404i		−	2.23813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.689.20	yes	128
17.2	even	8	inner	731.2.m.c.87.20	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.20	✓	128	17.2	even	8	inner
731.2.m.c.689.20	yes	128	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.810350 - 0.810350i) q^{2} +(3.13521 + 1.29865i) q^{3} +0.686666i q^{4} +(1.23003 - 2.96956i) q^{5} +(3.59298 - 1.48826i) q^{6} +(-0.604922 - 1.46041i) q^{7} +(2.17714 + 2.17714i) q^{8} +(6.02174 + 6.02174i) q^{9} +O(q^{10})\)	\(q+(0.810350 - 0.810350i) q^{2} +(3.13521 + 1.29865i) q^{3} +0.686666i q^{4} +(1.23003 - 2.96956i) q^{5} +(3.59298 - 1.48826i) q^{6} +(-0.604922 - 1.46041i) q^{7} +(2.17714 + 2.17714i) q^{8} +(6.02174 + 6.02174i) q^{9} +(-1.40963 - 3.40314i) q^{10} +(-4.91459 + 2.03569i) q^{11} +(-0.891736 + 2.15284i) q^{12} -1.77520i q^{13} +(-1.67364 - 0.693246i) q^{14} +(7.71281 - 7.71281i) q^{15} +2.15516 q^{16} +(-4.01260 - 0.948189i) q^{17} +9.75943 q^{18} +(-2.37035 + 2.37035i) q^{19} +(2.03909 + 0.844620i) q^{20} -5.36428i q^{21} +(-2.33292 + 5.63216i) q^{22} +(3.32148 - 1.37580i) q^{23} +(3.99846 + 9.65312i) q^{24} +(-3.76976 - 3.76976i) q^{25} +(-1.43853 - 1.43853i) q^{26} +(7.16337 + 17.2939i) q^{27} +(1.00281 - 0.415379i) q^{28} +(3.17390 - 7.66248i) q^{29} -12.5002i q^{30} +(-7.90431 - 3.27407i) q^{31} +(-2.60785 + 2.60785i) q^{32} -18.0519 q^{33} +(-4.01997 + 2.48324i) q^{34} -5.08085 q^{35} +(-4.13492 + 4.13492i) q^{36} +(-3.49145 - 1.44620i) q^{37} +3.84163i q^{38} +(2.30536 - 5.56563i) q^{39} +(9.14309 - 3.78719i) q^{40} +(1.94976 + 4.70713i) q^{41} +(-4.34694 - 4.34694i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(-1.39784 - 3.37468i) q^{44} +(25.2888 - 10.4750i) q^{45} +(1.57668 - 3.80645i) q^{46} -1.99825i q^{47} +(6.75688 + 2.79879i) q^{48} +(3.18288 - 3.18288i) q^{49} -6.10965 q^{50} +(-11.3490 - 8.18372i) q^{51} +1.21897 q^{52} +(-5.93359 + 5.93359i) q^{53} +(19.8189 + 8.20927i) q^{54} +17.0981i q^{55} +(1.86252 - 4.49652i) q^{56} +(-10.5098 + 4.35330i) q^{57} +(-3.63732 - 8.78126i) q^{58} +(2.04099 + 2.04099i) q^{59} +(5.29612 + 5.29612i) q^{60} +(0.209778 + 0.506448i) q^{61} +(-9.05840 + 3.75211i) q^{62} +(5.15153 - 12.4369i) q^{63} +8.53685i q^{64} +(-5.27156 - 2.18355i) q^{65} +(-14.6284 + 14.6284i) q^{66} +4.80863 q^{67} +(0.651089 - 2.75531i) q^{68} +12.2002 q^{69} +(-4.11727 + 4.11727i) q^{70} +(7.00308 + 2.90077i) q^{71} +26.2203i q^{72} +(-1.29534 + 3.12722i) q^{73} +(-4.00122 + 1.65736i) q^{74} +(-6.92340 - 16.7146i) q^{75} +(-1.62764 - 1.62764i) q^{76} +(5.94589 + 5.94589i) q^{77} +(-2.64196 - 6.37825i) q^{78} +(6.79229 - 2.81346i) q^{79} +(2.65091 - 6.39987i) q^{80} +37.9746i q^{81} +(5.39441 + 2.23444i) q^{82} +(-1.85608 + 1.85608i) q^{83} +3.68347 q^{84} +(-7.75132 + 10.7493i) q^{85} -1.14601 q^{86} +(19.9017 - 19.9017i) q^{87} +(-15.1317 - 6.26777i) q^{88} +9.53974i q^{89} +(12.0044 - 28.9812i) q^{90} +(-2.59252 + 1.07386i) q^{91} +(0.944717 + 2.28075i) q^{92} +(-20.5298 - 20.5298i) q^{93} +(-1.61928 - 1.61928i) q^{94} +(4.12329 + 9.95449i) q^{95} +(-11.5628 + 4.78948i) q^{96} +(4.96439 - 11.9851i) q^{97} -5.15849i q^{98} +(-41.8528 - 17.3360i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

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