LMFDB - Embedded newform 216.2.q.b.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(25,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("216.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.q (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			121.3
Character	$\chi$	$=$	216.121
Dual form			216.2.q.b.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.198479 - 1.72064i) q^{3} +(-2.79870 - 2.34839i) q^{5} +(0.843226 + 0.306909i) q^{7} +(-2.92121 + 0.683023i) q^{9} +O(q^{10})$	\(q+(-0.198479 - 1.72064i) q^{3} +(-2.79870 - 2.34839i) q^{5} +(0.843226 + 0.306909i) q^{7} +(-2.92121 + 0.683023i) q^{9} +(-4.12074 + 3.45771i) q^{11} +(0.560278 - 3.17749i) q^{13} +(-3.48525 + 5.28166i) q^{15} +(3.01773 - 5.22685i) q^{17} +(-1.24138 - 2.15013i) q^{19} +(0.360718 - 1.51180i) q^{21} +(3.10693 - 1.13083i) q^{23} +(1.44955 + 8.22082i) q^{25} +(1.75504 + 4.89079i) q^{27} +(-1.45963 - 8.27795i) q^{29} +(6.00898 - 2.18709i) q^{31} +(6.76735 + 6.40402i) q^{33} +(-1.63919 - 2.83917i) q^{35} +(0.854321 - 1.47973i) q^{37} +(-5.57853 - 0.333371i) q^{39} +(-0.766855 + 4.34905i) q^{41} +(-0.679214 + 0.569928i) q^{43} +(9.77960 + 4.94856i) q^{45} +(-2.22292 - 0.809076i) q^{47} +(-4.74547 - 3.98193i) q^{49} +(-9.59250 - 4.15500i) q^{51} +3.93007 q^{53} +19.6527 q^{55} +(-3.45322 + 2.56272i) q^{57} +(9.65346 + 8.10021i) q^{59} +(5.55274 + 2.02103i) q^{61} +(-2.67287 - 0.320604i) q^{63} +(-9.03003 + 7.57710i) q^{65} +(-1.25539 + 7.11964i) q^{67} +(-2.56242 - 5.12147i) q^{69} +(-0.922706 + 1.59817i) q^{71} +(1.38518 + 2.39920i) q^{73} +(13.8574 - 4.12582i) q^{75} +(-4.53591 + 1.65094i) q^{77} +(-0.942692 - 5.34627i) q^{79} +(8.06696 - 3.99051i) q^{81} +(-1.46974 - 8.33532i) q^{83} +(-20.7204 + 7.54160i) q^{85} +(-13.9537 + 4.15449i) q^{87} +(-6.85499 - 11.8732i) q^{89} +(1.44764 - 2.50739i) q^{91} +(-4.95585 - 9.90521i) q^{93} +(-1.57509 + 8.93281i) q^{95} +(-8.16171 + 6.84849i) q^{97} +(9.67585 - 12.9153i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) $ 30 * q + 3 * q^7 - 6 * q^9	$ 30 q + 3 q^{7} - 6 q^{9} - 3 q^{11} - 12 q^{13} + 15 q^{15} + 6 q^{17} - 9 q^{19} + 30 q^{21} - 12 q^{23} + 24 q^{25} - 15 q^{27} - 9 q^{29} + 27 q^{31} - 30 q^{33} - 18 q^{35} - 15 q^{37} - 21 q^{39} - 15 q^{41} - 30 q^{43} + 15 q^{45} - 18 q^{47} + 15 q^{49} - 6 q^{51} - 18 q^{53} + 54 q^{55} - 72 q^{57} - 12 q^{59} + 6 q^{61} - 54 q^{63} - 54 q^{65} - 45 q^{67} + 9 q^{69} - 36 q^{73} + 69 q^{75} + 12 q^{77} + 45 q^{79} - 30 q^{81} - 3 q^{83} + 57 q^{85} - 60 q^{87} + 36 q^{89} - 39 q^{91} + 30 q^{93} + 51 q^{95} - 84 q^{97} + 162 q^{99}+O(q^{100}) $ 30 * q + 3 * q^7 - 6 * q^9 - 3 * q^11 - 12 * q^13 + 15 * q^15 + 6 * q^17 - 9 * q^19 + 30 * q^21 - 12 * q^23 + 24 * q^25 - 15 * q^27 - 9 * q^29 + 27 * q^31 - 30 * q^33 - 18 * q^35 - 15 * q^37 - 21 * q^39 - 15 * q^41 - 30 * q^43 + 15 * q^45 - 18 * q^47 + 15 * q^49 - 6 * q^51 - 18 * q^53 + 54 * q^55 - 72 * q^57 - 12 * q^59 + 6 * q^61 - 54 * q^63 - 54 * q^65 - 45 * q^67 + 9 * q^69 - 36 * q^73 + 69 * q^75 + 12 * q^77 + 45 * q^79 - 30 * q^81 - 3 * q^83 + 57 * q^85 - 60 * q^87 + 36 * q^89 - 39 * q^91 + 30 * q^93 + 51 * q^95 - 84 * q^97 + 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{9}\right)$

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 (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			0
$2$		0			0
$3$	−0.198479	−	1.72064i	−0.114592	−	0.993413i
$3$	−0.198479	−	1.72064i	−0.114592	−	0.993413i
$4$		0			0
$5$	−2.79870	−	2.34839i	−1.25162	−	1.05023i	−0.996523	−	0.0833141i	$-0.973450\pi$
$5$	−2.79870	−	2.34839i	−1.25162	−	1.05023i	−0.255093	−	0.966917i	$-0.582106\pi$
$6$		0			0
$7$	0.843226	+	0.306909i	0.318710	+	0.116001i	0.496421	−	0.868082i	$-0.334647\pi$
$7$	0.843226	+	0.306909i	0.318710	+	0.116001i	−0.177712	+	0.984083i	$0.556869\pi$
$8$		0			0
$9$	−2.92121	+	0.683023i	−0.973737	+	0.227674i
$10$		0			0
$11$	−4.12074	+	3.45771i	−1.24245	+	1.04254i	−0.245120	+	0.969493i	$0.578827\pi$
$11$	−4.12074	+	3.45771i	−1.24245	+	1.04254i	−0.997329	+	0.0730452i	$0.976728\pi$
$12$		0			0
$13$	0.560278	−	3.17749i	0.155393	−	0.881278i	−0.803032	−	0.595935i	$-0.796781\pi$
$13$	0.560278	−	3.17749i	0.155393	−	0.881278i	0.958426	−	0.285343i	$-0.0921074\pi$
$14$		0			0
$15$	−3.48525	+	5.28166i	−0.899887	+	1.36372i
$16$		0			0
$17$	3.01773	−	5.22685i	0.731906	−	1.26770i	−0.224162	−	0.974552i	$-0.571964\pi$
$17$	3.01773	−	5.22685i	0.731906	−	1.26770i	0.956068	−	0.293146i	$-0.0947023\pi$
$18$		0			0
$19$	−1.24138	−	2.15013i	−0.284792	−	0.493274i	0.687767	−	0.725932i	$-0.258591\pi$
$19$	−1.24138	−	2.15013i	−0.284792	−	0.493274i	−0.972559	+	0.232658i	$0.925258\pi$
$20$		0			0
$21$	0.360718	−	1.51180i	0.0787151	−	0.329903i
$22$		0			0
$23$	3.10693	−	1.13083i	0.647841	−	0.235795i	0.00286273	−	0.999996i	$-0.499089\pi$
$23$	3.10693	−	1.13083i	0.647841	−	0.235795i	0.644978	+	0.764201i	$0.276867\pi$
$24$		0			0
$25$	1.44955	+	8.22082i	0.289910	+	1.64416i
$26$		0			0
$27$	1.75504	+	4.89079i	0.337757	+	0.941233i
$28$		0			0
$29$	−1.45963	−	8.27795i	−0.271046	−	1.53718i	−0.751249	−	0.660019i	$-0.770548\pi$
$29$	−1.45963	−	8.27795i	−0.271046	−	1.53718i	0.480203	−	0.877157i	$-0.340563\pi$
$30$		0			0
$31$	6.00898	−	2.18709i	1.07924	−	0.392813i	0.259618	−	0.965711i	$-0.416403\pi$
$31$	6.00898	−	2.18709i	1.07924	−	0.392813i	0.819626	+	0.572898i	$0.194181\pi$
$32$		0			0
$33$	6.76735	+	6.40402i	1.17805	+	1.11480i
$34$		0			0
$35$	−1.63919	−	2.83917i	−0.277074	−	0.479907i
$36$		0			0
$37$	0.854321	−	1.47973i	0.140450	−	0.243266i	−0.787216	−	0.616677i	$-0.788479\pi$
$37$	0.854321	−	1.47973i	0.140450	−	0.243266i	0.927666	+	0.373411i	$0.121812\pi$
$38$		0			0
$39$	−5.57853	−	0.333371i	−0.893280	−	0.0533820i
$40$		0			0
$41$	−0.766855	+	4.34905i	−0.119763	+	0.679208i	0.864519	+	0.502601i	$0.167623\pi$
$41$	−0.766855	+	4.34905i	−0.119763	+	0.679208i	−0.984281	+	0.176607i	$0.943488\pi$
$42$		0			0
$43$	−0.679214	+	0.569928i	−0.103579	+	0.0869132i	−0.693107	−	0.720835i	$-0.743758\pi$
$43$	−0.679214	+	0.569928i	−0.103579	+	0.0869132i	0.589527	+	0.807748i	$0.299314\pi$
$44$		0			0
$45$	9.77960	+	4.94856i	1.45786	+	0.737688i
$46$		0			0
$47$	−2.22292	−	0.809076i	−0.324246	−	0.118016i	0.174769	−	0.984610i	$-0.444082\pi$
$47$	−2.22292	−	0.809076i	−0.324246	−	0.118016i	−0.499014	+	0.866594i	$0.666305\pi$
$48$		0			0
$49$	−4.74547	−	3.98193i	−0.677925	−	0.568846i
$50$		0			0
$51$	−9.59250	−	4.15500i	−1.34322	−	0.581817i
$52$		0			0
$53$	3.93007			0.539837			0.269919	−	0.962883i	$-0.413003\pi$
$53$	3.93007			0.539837			0.269919	+	0.962883i	$0.413003\pi$
$54$		0			0
$55$	19.6527			2.64997
$56$		0			0
$57$	−3.45322	+	2.56272i	−0.457390	+	0.339441i
$58$		0			0
$59$	9.65346	+	8.10021i	1.25677	+	1.05456i	0.996018	+	0.0891532i	$0.0284161\pi$
$59$	9.65346	+	8.10021i	1.25677	+	1.05456i	0.260755	+	0.965405i	$0.416028\pi$
$60$		0			0
$61$	5.55274	+	2.02103i	0.710956	+	0.258767i	0.672081	−	0.740477i	$-0.265401\pi$
$61$	5.55274	+	2.02103i	0.710956	+	0.258767i	0.0388744	+	0.999244i	$0.487623\pi$
$62$		0			0
$63$	−2.67287	−	0.320604i	−0.336750	−	0.0403923i
$64$		0			0
$65$	−9.03003	+	7.57710i	−1.12004	+	0.939823i
$66$		0			0
$67$	−1.25539	+	7.11964i	−0.153370	+	0.869803i	0.806891	+	0.590700i	$0.201148\pi$
$67$	−1.25539	+	7.11964i	−0.153370	+	0.869803i	−0.960261	+	0.279103i	$0.909963\pi$
$68$		0			0
$69$	−2.56242	−	5.12147i	−0.308479	−	0.616553i
$70$		0			0
$71$	−0.922706	+	1.59817i	−0.109505	+	0.189668i	−0.915570	−	0.402159i	$-0.868260\pi$
$71$	−0.922706	+	1.59817i	−0.109505	+	0.189668i	0.806065	+	0.591827i	$0.201593\pi$
$72$		0			0
$73$	1.38518	+	2.39920i	0.162123	+	0.280805i	0.935630	−	0.352983i	$-0.114833\pi$
$73$	1.38518	+	2.39920i	0.162123	+	0.280805i	−0.773507	+	0.633788i	$0.781499\pi$
$74$		0			0
$75$	13.8574	−	4.12582i	1.60011	−	0.476409i
$76$		0			0
$77$	−4.53591	+	1.65094i	−0.516915	+	0.188142i
$78$		0			0
$79$	−0.942692	−	5.34627i	−0.106061	−	0.601502i	−0.990791	−	0.135399i	$-0.956768\pi$
$79$	−0.942692	−	5.34627i	−0.106061	−	0.601502i	0.884730	−	0.466104i	$-0.154343\pi$
$80$		0			0
$81$	8.06696	−	3.99051i	0.896329	−	0.443390i
$82$		0			0
$83$	−1.46974	−	8.33532i	−0.161325	−	0.914920i	−0.952773	−	0.303683i	$-0.901783\pi$
$83$	−1.46974	−	8.33532i	−0.161325	−	0.914920i	0.791448	−	0.611237i	$-0.209328\pi$
$84$		0			0
$85$	−20.7204	+	7.54160i	−2.24744	+	0.818002i
$86$		0			0
$87$	−13.9537	+	4.15449i	−1.49599	+	0.445408i
$88$		0			0
$89$	−6.85499	−	11.8732i	−0.726628	−	1.25856i	−0.958301	−	0.285762i	$-0.907753\pi$
$89$	−6.85499	−	11.8732i	−0.726628	−	1.25856i	0.231673	−	0.972794i	$-0.425580\pi$
$90$		0			0
$91$	1.44764	−	2.50739i	0.151754	−	0.262846i
$92$		0			0
$93$	−4.95585	−	9.90521i	−0.513898	−	1.02712i
$94$		0			0
$95$	−1.57509	+	8.93281i	−0.161601	+	0.916487i
$96$		0			0
$97$	−8.16171	+	6.84849i	−0.828696	+	0.695359i	−0.954991	−	0.296634i	$-0.904136\pi$
$97$	−8.16171	+	6.84849i	−0.828696	+	0.695359i	0.126295	+	0.991993i	$0.459691\pi$
$98$		0			0
$99$	9.67585	−	12.9153i	0.972459	−	1.29803i
$100$		0			0
$101$	7.66773	+	2.79083i	0.762968	+	0.277698i	0.694052	−	0.719925i	$-0.255824\pi$
$101$	7.66773	+	2.79083i	0.762968	+	0.277698i	0.0689160	+	0.997622i	$0.478046\pi$
$102$		0			0
$103$	−11.8495	−	9.94288i	−1.16756	−	0.979701i	−0.167581	−	0.985858i	$-0.553595\pi$
$103$	−11.8495	−	9.94288i	−1.16756	−	0.979701i	−0.999981	+	0.00615772i	$0.998040\pi$
$104$		0			0
$105$	−4.55984	+	3.38398i	−0.444995	+	0.330243i
$106$		0			0
$107$	1.28827			0.124542			0.0622710	−	0.998059i	$-0.480166\pi$
$107$	1.28827			0.124542			0.0622710	+	0.998059i	$0.480166\pi$
$108$		0			0
$109$	5.54002			0.530638			0.265319	−	0.964161i	$-0.414523\pi$
$109$	5.54002			0.530638			0.265319	+	0.964161i	$0.414523\pi$
$110$		0			0
$111$	−2.71565	−	1.17629i	−0.257758	−	0.111648i
$112$		0			0
$113$	10.1136	+	8.48632i	0.951407	+	0.798326i	0.979534	−	0.201279i	$-0.0645097\pi$
$113$	10.1136	+	8.48632i	0.951407	+	0.798326i	−0.0281266	+	0.999604i	$0.508954\pi$
$114$		0			0
$115$	−11.3510	−	4.13143i	−1.05849	−	0.385258i
$116$		0			0
$117$	0.533611	+	9.66481i	0.0493323	+	0.893512i
$118$		0			0
$119$	4.14880	−	3.48125i	0.380319	−	0.319126i
$120$		0			0
$121$	3.11459	−	17.6637i	0.283144	−	1.60579i
$122$		0			0
$123$	7.63536	+	0.456286i	0.688458	+	0.0411419i
$124$		0			0
$125$	6.11520	−	10.5918i	0.546960	−	0.947363i
$126$		0			0
$127$	−8.77861	−	15.2050i	−0.778976	−	1.34923i	−0.932533	−	0.361085i	$-0.882406\pi$
$127$	−8.77861	−	15.2050i	−0.778976	−	1.34923i	0.153557	−	0.988140i	$-0.450927\pi$
$128$		0			0
$129$	1.11545	+	1.05556i	0.0982100	+	0.0929373i
$130$		0			0
$131$	2.44488	−	0.889863i	0.213610	−	0.0777477i	−0.232999	−	0.972477i	$-0.574854\pi$
$131$	2.44488	−	0.889863i	0.213610	−	0.0777477i	0.446609	+	0.894729i	$0.352632\pi$
$132$		0			0
$133$	−0.386868	−	2.19404i	−0.0335457	−	0.190247i
$134$		0			0
$135$	6.57365	−	17.8094i	0.565770	−	1.53279i
$136$		0			0
$137$	1.56897	+	8.89810i	0.134047	+	0.760216i	0.975519	+	0.219916i	$0.0705782\pi$
$137$	1.56897	+	8.89810i	0.134047	+	0.760216i	−0.841472	+	0.540300i	$0.818311\pi$
$138$		0			0
$139$	−5.33190	+	1.94065i	−0.452246	+	0.164604i	−0.558093	−	0.829778i	$-0.688467\pi$
$139$	−5.33190	+	1.94065i	−0.452246	+	0.164604i	0.105847	+	0.994382i	$0.466245\pi$
$140$		0			0
$141$	−0.950926	+	3.98543i	−0.0800824	+	0.335634i
$142$		0			0
$143$	8.67809	+	15.0309i	0.725698	+	1.25695i
$144$		0			0
$145$	−15.3548	+	26.5952i	−1.27514	+	2.20862i
$146$		0			0
$147$	−5.90959	+	8.95559i	−0.487414	+	0.738644i
$148$		0			0
$149$	0.842223	−	4.77648i	0.0689976	−	0.391305i	−0.930678	−	0.365839i	$-0.880782\pi$
$149$	0.842223	−	4.77648i	0.0689976	−	0.391305i	0.999676	−	0.0254656i	$-0.00810683\pi$
$150$		0			0
$151$	−11.1789	+	9.38020i	−0.909725	+	0.763350i	−0.972067	−	0.234705i	$-0.924588\pi$
$151$	−11.1789	+	9.38020i	−0.909725	+	0.763350i	0.0623418	+	0.998055i	$0.480143\pi$
$152$		0			0
$153$	−5.24535	+	17.3299i	−0.424062	+	1.40104i
$154$		0			0
$155$	−21.9535	−	7.99041i	−1.76334	−	0.641805i
$156$		0			0
$157$	7.28606	+	6.11373i	0.581491	+	0.487929i	0.885436	−	0.464760i	$-0.153860\pi$
$157$	7.28606	+	6.11373i	0.581491	+	0.487929i	−0.303945	+	0.952689i	$0.598304\pi$
$158$		0			0
$159$	−0.780038	−	6.76225i	−0.0618610	−	0.536281i
$160$		0			0
$161$	2.96691			0.233825
$162$		0			0
$163$	8.08350			0.633149			0.316574	−	0.948568i	$-0.397467\pi$
$163$	8.08350			0.633149			0.316574	+	0.948568i	$0.397467\pi$
$164$		0			0
$165$	−3.90066	−	33.8153i	−0.303666	−	2.63252i
$166$		0			0
$167$	9.40177	+	7.88902i	0.727531	+	0.610471i	0.929457	−	0.368930i	$-0.120276\pi$
$167$	9.40177	+	7.88902i	0.727531	+	0.610471i	−0.201927	+	0.979401i	$0.564720\pi$
$168$		0			0
$169$	2.43345	+	0.885704i	0.187189	+	0.0681311i
$170$		0			0
$171$	5.09492	+	5.43310i	0.389618	+	0.415479i
$172$		0			0
$173$	−9.89387	+	8.30194i	−0.752217	+	0.631185i	−0.936088	−	0.351765i	$-0.885581\pi$
$173$	−9.89387	+	8.30194i	−0.752217	+	0.631185i	0.183871	+	0.982950i	$0.441137\pi$
$174$		0			0
$175$	−1.30074	+	7.37689i	−0.0983271	+	0.557641i
$176$		0			0
$177$	12.0216	−	18.2179i	0.903595	−	1.36934i
$178$		0			0
$179$	−2.61960	+	4.53728i	−0.195798	+	0.339133i	−0.947162	−	0.320756i	$-0.896063\pi$
$179$	−2.61960	+	4.53728i	−0.195798	+	0.339133i	0.751364	+	0.659888i	$0.229396\pi$
$180$		0			0
$181$	−12.8889	−	22.3243i	−0.958027	−	1.65935i	−0.727283	−	0.686337i	$-0.759217\pi$
$181$	−12.8889	−	22.3243i	−0.958027	−	1.65935i	−0.230744	−	0.973014i	$-0.574116\pi$
$182$		0			0
$183$	2.37537	−	9.95541i	0.175592	−	0.735925i
$184$		0			0
$185$	−5.86596	+	2.13504i	−0.431274	+	0.156971i
$186$		0			0
$187$	5.63768	+	31.9729i	0.412268	+	2.33809i
$188$		0			0
$189$	−0.0211356	+	4.66268i	−0.00153739	+	0.339160i
$190$		0			0
$191$	3.64355	+	20.6636i	0.263638	+	1.49517i	0.772885	+	0.634546i	$0.218813\pi$
$191$	3.64355	+	20.6636i	0.263638	+	1.49517i	−0.509247	+	0.860620i	$0.670076\pi$
$192$		0			0
$193$	24.0997	−	8.77156i	1.73473	−	0.631391i	0.735783	−	0.677218i	$-0.236815\pi$
$193$	24.0997	−	8.77156i	1.73473	−	0.631391i	0.998949	+	0.0458270i	$0.0145923\pi$
$194$		0			0
$195$	14.8297	+	14.0336i	1.06198	+	1.00496i
$196$		0			0
$197$	8.99297	+	15.5763i	0.640722	+	1.10976i	0.985272	+	0.170995i	$0.0546983\pi$
$197$	8.99297	+	15.5763i	0.640722	+	1.10976i	−0.344550	+	0.938768i	$0.611968\pi$
$198$		0			0
$199$	3.36078	−	5.82104i	0.238239	−	0.412642i	−0.721970	−	0.691924i	$-0.756763\pi$
$199$	3.36078	−	5.82104i	0.238239	−	0.412642i	0.960209	+	0.279282i	$0.0900964\pi$
$200$		0			0
$201$	12.4995	+	0.746966i	0.881648	+	0.0526869i
$202$		0			0
$203$	1.30978	−	7.42816i	0.0919288	−	0.521354i
$204$		0			0
$205$	12.3595	−	10.3708i	0.863222	−	0.724329i
$206$		0			0
$207$	−8.30363	+	5.42551i	−0.577142	+	0.377099i
$208$		0			0
$209$	12.5499	+	4.56780i	0.868096	+	0.315961i
$210$		0			0
$211$	2.03291	+	1.70582i	0.139951	+	0.117433i	0.710076	−	0.704125i	$-0.248661\pi$
$211$	2.03291	+	1.70582i	0.139951	+	0.117433i	−0.570124	+	0.821558i	$0.693105\pi$
$212$		0			0
$213$	2.93302	+	1.27044i	0.200967	+	0.0870492i
$214$		0			0
$215$	3.23933			0.220920
$216$		0			0
$217$	5.73817			0.389532
$218$		0			0
$219$	3.85323	−	2.85958i	0.260377	−	0.193233i
$220$		0			0
$221$	−14.9175	−	12.5173i	−1.00346	−	0.842004i
$222$		0			0
$223$	4.21867	+	1.53547i	0.282503	+	0.102823i	0.479386	−	0.877604i	$-0.340860\pi$
$223$	4.21867	+	1.53547i	0.282503	+	0.102823i	−0.196883	+	0.980427i	$0.563082\pi$
$224$		0			0
$225$	−9.84946	−	23.0247i	−0.656631	−	1.53498i
$226$		0			0
$227$	19.5055	−	16.3670i	1.29462	−	1.08632i	0.303576	−	0.952807i	$-0.401819\pi$
$227$	19.5055	−	16.3670i	1.29462	−	1.08632i	0.991047	−	0.133511i	$-0.0426251\pi$
$228$		0			0
$229$	1.66837	−	9.46180i	0.110249	−	0.625254i	−0.878744	−	0.477293i	$-0.841618\pi$
$229$	1.66837	−	9.46180i	0.110249	−	0.625254i	0.988993	−	0.147961i	$-0.0472709\pi$
$230$		0			0
$231$	3.74096	+	7.47700i	0.246137	+	0.491951i
$232$		0			0
$233$	4.35891	−	7.54985i	0.285562	−	0.494607i	−0.687184	−	0.726484i	$-0.741153\pi$
$233$	4.35891	−	7.54985i	0.285562	−	0.494607i	0.972745	+	0.231877i	$0.0744866\pi$
$234$		0			0
$235$	4.32125	+	7.48463i	0.281887	+	0.488243i
$236$		0			0
$237$	−9.01191	+	2.68316i	−0.585386	+	0.174290i
$238$		0			0
$239$	9.87343	−	3.59363i	0.638659	−	0.232453i	−0.00233675	−	0.999997i	$-0.500744\pi$
$239$	9.87343	−	3.59363i	0.638659	−	0.232453i	0.640996	+	0.767544i	$0.278522\pi$
$240$		0			0
$241$	−0.149183	−	0.846056i	−0.00960969	−	0.0544993i	0.979626	−	0.200831i	$-0.0643643\pi$
$241$	−0.149183	−	0.846056i	−0.00960969	−	0.0544993i	−0.989236	+	0.146332i	$0.953253\pi$
$242$		0			0
$243$	−8.46736	−	13.0883i	−0.543181	−	0.839615i
$244$		0			0
$245$	3.93005	+	22.2884i	0.251082	+	1.42395i
$246$		0			0
$247$	−7.52754	+	2.73980i	−0.478966	+	0.174329i
$248$		0			0
$249$	−14.0504	+	4.18329i	−0.890407	+	0.265105i
$250$		0			0
$251$	−7.94278	−	13.7573i	−0.501344	−	0.868353i	−0.999999	−	0.00155212i	$-0.999506\pi$
$251$	−7.94278	−	13.7573i	−0.501344	−	0.868353i	0.498655	−	0.866800i	$-0.333827\pi$
$252$		0			0
$253$	−8.89277	+	15.4027i	−0.559084	+	0.968361i
$254$		0			0
$255$	17.0890	+	34.1555i	1.07015	+	2.13890i
$256$		0			0
$257$	−2.18317	+	12.3814i	−0.136183	+	0.772330i	0.837846	+	0.545906i	$0.183814\pi$
$257$	−2.18317	+	12.3814i	−0.136183	+	0.772330i	−0.974029	+	0.226424i	$0.927297\pi$
$258$		0			0
$259$	1.17453	−	0.985547i	0.0729817	−	0.0612389i
$260$		0			0
$261$	9.91790	+	23.1847i	0.613903	+	1.43510i
$262$		0			0
$263$	−24.5032	−	8.91843i	−1.51093	−	0.549934i	−0.552067	−	0.833800i	$-0.686161\pi$
$263$	−24.5032	−	8.91843i	−1.51093	−	0.549934i	−0.958864	+	0.283866i	$0.908383\pi$
$264$		0			0
$265$	−10.9991	−	9.22934i	−0.675669	−	0.566954i
$266$		0			0
$267$	−19.0689	+	14.1516i	−1.16700	+	0.866062i
$268$		0			0
$269$	6.66987			0.406669			0.203335	−	0.979109i	$-0.434822\pi$
$269$	6.66987			0.406669			0.203335	+	0.979109i	$0.434822\pi$
$270$		0			0
$271$	−2.20901			−0.134188			−0.0670938	−	0.997747i	$-0.521373\pi$
$271$	−2.20901			−0.134188			−0.0670938	+	0.997747i	$0.521373\pi$
$272$		0			0
$273$	−4.60165	−	1.99321i	−0.278504	−	0.120635i
$274$		0			0
$275$	−34.3984	−	28.8637i	−2.07430	−	1.74055i
$276$		0			0
$277$	8.50637	+	3.09606i	0.511098	+	0.186024i	0.584679	−	0.811265i	$-0.301220\pi$
$277$	8.50637	+	3.09606i	0.511098	+	0.186024i	−0.0735809	+	0.997289i	$0.523443\pi$
$278$		0			0
$279$	−16.0597	+	10.4932i	−0.961467	+	0.628213i
$280$		0			0
$281$	12.3528	−	10.3653i	0.736909	−	0.618340i	−0.195097	−	0.980784i	$-0.562502\pi$
$281$	12.3528	−	10.3653i	0.736909	−	0.618340i	0.932005	+	0.362444i	$0.118058\pi$
$282$		0			0
$283$	−2.98234	+	16.9137i	−0.177282	+	1.00542i	0.758195	+	0.652028i	$0.226081\pi$
$283$	−2.98234	+	16.9137i	−0.177282	+	1.00542i	−0.935477	+	0.353388i	$0.885030\pi$
$284$		0			0
$285$	15.6828	+	0.937196i	0.928968	+	0.0555147i
$286$		0			0
$287$	−1.98140	+	3.43188i	−0.116958	+	0.202578i
$288$		0			0
$289$	−9.71334	−	16.8240i	−0.571373	−	0.989647i
$290$		0			0
$291$	13.4037	+	12.6841i	0.785740	+	0.743555i
$292$		0			0
$293$	5.69658	−	2.07338i	0.332798	−	0.121128i	−0.170216	−	0.985407i	$-0.554447\pi$
$293$	5.69658	−	2.07338i	0.332798	−	0.121128i	0.503014	+	0.864278i	$0.332224\pi$
$294$		0			0
$295$	−7.99469	−	45.3401i	−0.465469	−	2.63980i
$296$		0			0
$297$	−24.1430	−	14.0853i	−1.40092	−	0.817309i
$298$		0			0
$299$	−1.85246	−	10.5058i	−0.107131	−	0.607569i
$300$		0			0
$301$	−0.747647	+	0.272121i	−0.0430937	+	0.0156848i
$302$		0			0
$303$	3.28013	−	13.7473i	0.188438	−	0.789764i
$304$		0			0
$305$	−10.7943	−	18.6962i	−0.618079	−	1.07054i
$306$		0			0
$307$	−12.8088	+	22.1855i	−0.731037	+	1.26619i	0.225403	+	0.974266i	$0.427630\pi$
$307$	−12.8088	+	22.1855i	−0.731037	+	1.26619i	−0.956440	+	0.291928i	$0.905703\pi$
$308$		0			0
$309$	−14.7562	+	22.3621i	−0.839454	+	1.27214i
$310$		0			0
$311$	0.251203	−	1.42464i	0.0142444	−	0.0807842i	−0.976857	−	0.213894i	$-0.931385\pi$
$311$	0.251203	−	1.42464i	0.0142444	−	0.0807842i	0.991101	+	0.133110i	$0.0424963\pi$
$312$		0			0
$313$	18.4648	−	15.4938i	1.04369	−	0.875762i	0.0512760	−	0.998685i	$-0.483671\pi$
$313$	18.4648	−	15.4938i	1.04369	−	0.875762i	0.992416	+	0.122923i	$0.0392267\pi$
$314$		0			0
$315$	6.72765	+	7.17421i	0.379060	+	0.404221i
$316$		0			0
$317$	−6.37558	−	2.32052i	−0.358088	−	0.130334i	0.156710	−	0.987645i	$-0.449911\pi$
$317$	−6.37558	−	2.32052i	−0.358088	−	0.130334i	−0.514799	+	0.857311i	$0.672133\pi$
$318$		0			0
$319$	34.6375	+	29.0643i	1.93932	+	1.62729i
$320$		0			0
$321$	−0.255695	−	2.21666i	−0.0142715	−	0.123722i
$322$		0			0
$323$	−14.9846			−0.833763
$324$		0			0
$325$	26.9337			1.49402
$326$		0			0
$327$	−1.09958	−	9.53239i	−0.0608069	−	0.527142i
$328$		0			0
$329$	−1.62611	−	1.36447i	−0.0896503	−	0.0752255i
$330$		0			0
$331$	−26.8565	−	9.77497i	−1.47617	−	0.537281i	−0.526399	−	0.850238i	$-0.676458\pi$
$331$	−26.8565	−	9.77497i	−1.47617	−	0.537281i	−0.949767	+	0.312957i	$0.898680\pi$
$332$		0			0
$333$	−1.48497	+	4.90612i	−0.0813756	+	0.268854i
$334$		0			0
$335$	20.2331	−	16.9776i	1.10545	−	0.927586i
$336$		0			0
$337$	−1.10727	+	6.27963i	−0.0603168	+	0.342073i	0.939683	+	0.342046i	$0.111120\pi$
$337$	−1.10727	+	6.27963i	−0.0603168	+	0.342073i	−1.00000		2.74009e-5i	$0.999991\pi$
$338$		0			0
$339$	12.5946	−	19.0862i	0.684043	−	1.03662i
$340$		0			0
$341$	−17.1991	+	29.7897i	−0.931383	+	1.61320i
$342$		0			0
$343$	−5.92012	−	10.2539i	−0.319656	−	0.553661i
$344$		0			0
$345$	−4.85577	+	20.3510i	−0.261426	+	1.09566i
$346$		0			0
$347$	6.76842	−	2.46350i	0.363348	−	0.132248i	−0.153893	−	0.988087i	$-0.549181\pi$
$347$	6.76842	−	2.46350i	0.363348	−	0.132248i	0.517241	+	0.855840i	$0.326959\pi$
$348$		0			0
$349$	−0.191649	−	1.08689i	−0.0102587	−	0.0581801i	0.979249	−	0.202662i	$-0.0649594\pi$
$349$	−0.191649	−	1.08689i	−0.0102587	−	0.0581801i	−0.989507	+	0.144482i	$0.953848\pi$
$350$		0			0
$351$	16.5238	−	2.83642i	0.881973	−	0.151397i
$352$		0			0
$353$	−5.31972	−	30.1696i	−0.283140	−	1.60577i	−0.711855	−	0.702327i	$-0.752145\pi$
$353$	−5.31972	−	30.1696i	−0.283140	−	1.60577i	0.428715	−	0.903440i	$-0.358966\pi$
$354$		0			0
$355$	6.33550	−	2.30594i	0.336254	−	0.122386i
$356$		0			0
$357$	−6.81344	−	6.44763i	−0.360605	−	0.341245i
$358$		0			0
$359$	0.154723	+	0.267989i	0.00816598	+	0.0141439i	0.870080	−	0.492911i	$-0.164067\pi$
$359$	0.154723	+	0.267989i	0.00816598	+	0.0141439i	−0.861914	+	0.507055i	$0.830734\pi$
$360$		0			0
$361$	6.41796	−	11.1162i	0.337787	−	0.585065i
$362$		0			0
$363$	−31.0111	−	1.85321i	−1.62766	−	0.0972683i
$364$		0			0
$365$	1.75755	−	9.96756i	0.0919944	−	0.521726i
$366$		0			0
$367$	7.09619	−	5.95441i	0.370418	−	0.310818i	−0.438509	−	0.898727i	$-0.644493\pi$
$367$	7.09619	−	5.95441i	0.370418	−	0.310818i	0.808927	+	0.587909i	$0.200049\pi$
$368$		0			0
$369$	−0.730356	−	13.2283i	−0.0380208	−	0.688637i
$370$		0			0
$371$	3.31394	+	1.20618i	0.172051	+	0.0626216i
$372$		0			0
$373$	6.75819	+	5.67079i	0.349926	+	0.293622i	0.800760	−	0.598985i	$-0.204429\pi$
$373$	6.75819	+	5.67079i	0.349926	+	0.293622i	−0.450835	+	0.892608i	$0.648874\pi$
$374$		0			0
$375$	−19.4385	−	8.41981i	−1.00380	−	0.434797i
$376$		0			0
$377$	−27.1209			−1.39680
$378$		0			0
$379$	12.5677			0.645561			0.322781	−	0.946474i	$-0.395382\pi$
$379$	12.5677			0.645561			0.322781	+	0.946474i	$0.395382\pi$
$380$		0			0
$381$	−24.4200	+	18.1227i	−1.25107	+	0.928455i
$382$		0			0
$383$	13.4485	+	11.2846i	0.687184	+	0.576616i	0.918096	−	0.396359i	$-0.129726\pi$
$383$	13.4485	+	11.2846i	0.687184	+	0.576616i	−0.230912	+	0.972975i	$0.574171\pi$
$384$		0			0
$385$	16.5717	+	6.03161i	0.844572	+	0.307399i
$386$		0			0
$387$	1.59485	−	2.12880i	0.0810710	−	0.108213i
$388$		0			0
$389$	−4.14041	+	3.47421i	−0.209927	+	0.176150i	−0.741688	−	0.670745i	$-0.765975\pi$
$389$	−4.14041	+	3.47421i	−0.209927	+	0.176150i	0.531762	+	0.846894i	$0.321530\pi$
$390$		0			0
$391$	3.46518	−	19.6520i	0.175242	−	0.993846i
$392$		0			0
$393$	−2.01639	−	4.03014i	−0.101714	−	0.203294i
$394$		0			0
$395$	−9.91680	+	17.1764i	−0.498968	+	0.864239i
$396$		0			0
$397$	14.3040	+	24.7753i	0.717898	+	1.24344i	0.961831	+	0.273644i	$0.0882289\pi$
$397$	14.3040	+	24.7753i	0.717898	+	1.24344i	−0.243933	+	0.969792i	$0.578438\pi$
$398$		0			0
$399$	−3.69837	+	1.10113i	−0.185150	+	0.0551255i
$400$		0			0
$401$	−22.4984	+	8.18873i	−1.12351	+	0.408926i	−0.835934	−	0.548830i	$-0.815073\pi$
$401$	−22.4984	+	8.18873i	−1.12351	+	0.408926i	−0.287581	+	0.957756i	$0.592851\pi$
$402$		0			0
$403$	−3.58277	−	20.3189i	−0.178470	−	1.01216i
$404$		0			0
$405$	−31.9483	−	7.77611i	−1.58752	−	0.386398i
$406$		0			0
$407$	1.59603	+	9.05156i	0.0791125	+	0.448669i
$408$		0			0
$409$	14.2298	−	5.17922i	0.703618	−	0.256096i	0.0346630	−	0.999399i	$-0.488964\pi$
$409$	14.2298	−	5.17922i	0.703618	−	0.256096i	0.668955	+	0.743303i	$0.266742\pi$
$410$		0			0
$411$	14.9990	−	4.46573i	0.739847	−	0.220278i
$412$		0			0
$413$	5.65402	+	9.79305i	0.278216	+	0.481884i
$414$		0			0
$415$	−15.4612	+	26.7796i	−0.758960	+	1.31456i
$416$		0			0
$417$	4.39744	+	8.78911i	0.215344	+	0.430405i
$418$		0			0
$419$	4.36466	−	24.7532i	0.213228	−	1.20927i	−0.670728	−	0.741703i	$-0.734018\pi$
$419$	4.36466	−	24.7532i	0.213228	−	1.20927i	0.883956	−	0.467570i	$-0.154871\pi$
$420$		0			0
$421$	−3.90582	+	3.27737i	−0.190358	+	0.159729i	−0.732986	−	0.680244i	$-0.761874\pi$
$421$	−3.90582	+	3.27737i	−0.190358	+	0.159729i	0.542628	+	0.839973i	$0.317429\pi$
$422$		0			0
$423$	7.04623	+	0.845178i	0.342599	+	0.0410940i
$424$		0			0
$425$	47.3434	+	17.2316i	2.29649	+	0.835854i
$426$		0			0
$427$	4.06194	+	3.40838i	0.196571	+	0.164943i
$428$		0			0
$429$	24.1403	−	17.9152i	1.16551	−	0.864954i
$430$		0			0
$431$	−39.2236			−1.88933			−0.944667	−	0.328030i	$-0.893615\pi$
$431$	−39.2236			−1.88933			−0.944667	+	0.328030i	$0.893615\pi$
$432$		0			0
$433$	−15.8305			−0.760765			−0.380382	−	0.924829i	$-0.624208\pi$
$433$	−15.8305			−0.760765			−0.380382	+	0.924829i	$0.624208\pi$
$434$		0			0
$435$	48.8085	+	21.1415i	2.34019	+	1.01366i
$436$		0			0
$437$	−6.28832	−	5.27653i	−0.300811	−	0.252410i
$438$		0			0
$439$	35.2430	+	12.8274i	1.68205	+	0.612218i	0.993589	−	0.113051i	$-0.0360624\pi$
$439$	35.2430	+	12.8274i	1.68205	+	0.612218i	0.688465	+	0.725269i	$0.258285\pi$
$440$		0			0
$441$	16.5823	+	8.39078i	0.789632	+	0.399561i
$442$		0			0
$443$	7.61356	−	6.38854i	0.361731	−	0.303528i	−0.443749	−	0.896151i	$-0.646352\pi$
$443$	7.61356	−	6.38854i	0.361731	−	0.303528i	0.805480	+	0.592623i	$0.201907\pi$
$444$		0			0
$445$	−8.69780	+	49.3277i	−0.412315	+	2.33836i
$446$		0			0
$447$	−8.38578	−	0.501131i	−0.396634	−	0.0237027i
$448$		0			0
$449$	−4.71824	+	8.17222i	−0.222667	+	0.385671i	−0.955617	−	0.294612i	$-0.904810\pi$
$449$	−4.71824	+	8.17222i	−0.222667	+	0.385671i	0.732950	+	0.680283i	$0.238143\pi$
$450$		0			0
$451$	−11.8777	−	20.5729i	−0.559301	−	0.968738i
$452$		0			0
$453$	18.3587	+	17.3731i	0.862569	+	0.816258i
$454$		0			0
$455$	−9.93984	+	3.61781i	−0.465987	+	0.169605i
$456$		0			0
$457$	0.951590	+	5.39673i	0.0445135	+	0.252449i	0.998942	−	0.0459917i	$-0.0146448\pi$
$457$	0.951590	+	5.39673i	0.0445135	+	0.252449i	−0.954428	+	0.298440i	$0.903534\pi$
$458$		0			0
$459$	30.8597	+	5.58574i	1.44041	+	0.260720i
$460$		0			0
$461$	−4.82989	−	27.3917i	−0.224951	−	1.27576i	−0.862780	−	0.505580i	$-0.831279\pi$
$461$	−4.82989	−	27.3917i	−0.224951	−	1.27576i	0.637829	−	0.770178i	$-0.279833\pi$
$462$		0			0
$463$	8.63987	−	3.14466i	0.401529	−	0.146145i	−0.133359	−	0.991068i	$-0.542576\pi$
$463$	8.63987	−	3.14466i	0.401529	−	0.146145i	0.534888	+	0.844923i	$0.320354\pi$
$464$		0			0
$465$	−9.39132	+	39.3600i	−0.435512	+	1.82527i
$466$		0			0
$467$	0.993280	+	1.72041i	0.0459635	+	0.0796111i	0.888092	−	0.459666i	$-0.152031\pi$
$467$	0.993280	+	1.72041i	0.0459635	+	0.0796111i	−0.842128	+	0.539277i	$0.818698\pi$
$468$		0			0
$469$	−3.24366	+	5.61818i	−0.149778	+	0.259424i
$470$		0			0
$471$	9.07341	−	13.7501i	0.418081	−	0.633573i
$472$		0			0
$473$	0.828216	−	4.69705i	0.0380814	−	0.215970i
$474$		0			0
$475$	15.8764	−	13.3219i	0.728459	−	0.611250i
$476$		0			0
$477$	−11.4806	+	2.68433i	−0.525660	+	0.122907i
$478$		0			0
$479$	18.4628	+	6.71990i	0.843585	+	0.307040i	0.727422	−	0.686190i	$-0.240718\pi$
$479$	18.4628	+	6.71990i	0.843585	+	0.307040i	0.116163	+	0.993230i	$0.462940\pi$
$480$		0			0
$481$	−4.22317	−	3.54366i	−0.192560	−	0.161577i
$482$		0			0
$483$	−0.588870	−	5.10499i	−0.0267945	−	0.232285i
$484$		0			0
$485$	38.9251			1.76750
$486$		0			0
$487$	−8.91122			−0.403806			−0.201903	−	0.979406i	$-0.564713\pi$
$487$	−8.91122			−0.403806			−0.201903	+	0.979406i	$0.564713\pi$
$488$		0			0
$489$	−1.60441	−	13.9088i	−0.0725538	−	0.628978i
$490$		0			0
$491$	15.7899	+	13.2493i	0.712590	+	0.597934i	0.925325	−	0.379176i	$-0.123792\pi$
$491$	15.7899	+	13.2493i	0.712590	+	0.597934i	−0.212734	+	0.977110i	$0.568237\pi$
$492$		0			0
$493$	−47.6724	−	17.3513i	−2.14706	−	0.781464i
$494$		0			0
$495$	−57.4098	+	13.4233i	−2.58038	+	0.603331i
$496$		0			0
$497$	−1.26854	+	1.06443i	−0.0569020	+	0.0477464i
$498$		0			0
$499$	0.372283	−	2.11132i	0.0166657	−	0.0945158i	−0.975340	−	0.220706i	$-0.929164\pi$
$499$	0.372283	−	2.11132i	0.0166657	−	0.0945158i	0.992006	+	0.126190i	$0.0402750\pi$
$500$		0			0
$501$	11.7081	−	17.7429i	0.523080	−	0.792693i
$502$		0			0
$503$	16.9717	−	29.3959i	0.756733	−	1.31070i	−0.187776	−	0.982212i	$-0.560128\pi$
$503$	16.9717	−	29.3959i	0.756733	−	1.31070i	0.944508	−	0.328487i	$-0.106539\pi$
$504$		0			0
$505$	−14.9057	−	25.8175i	−0.663297	−	1.14886i
$506$		0			0
$507$	1.04099	−	4.36289i	0.0462319	−	0.193763i
$508$		0			0
$509$	−0.239732	+	0.0872553i	−0.0106259	+	0.00386752i	−0.347328	−	0.937744i	$-0.612911\pi$
$509$	−0.239732	+	0.0872553i	−0.0106259	+	0.00386752i	0.336702	+	0.941611i	$0.390689\pi$
$510$		0			0
$511$	0.431682	+	2.44819i	0.0190965	+	0.108302i
$512$		0			0
$513$	8.33718	−	9.84488i	0.368095	−	0.434662i
$514$		0			0
$515$	9.81334	+	55.6542i	0.432428	+	2.45242i
$516$		0			0
$517$	11.9576	−	4.35221i	0.525895	−	0.191410i
$518$		0			0
$519$	16.2484	+	15.3760i	0.713225	+	0.674933i
$520$		0			0
$521$	19.4337	+	33.6602i	0.851408	+	1.47468i	0.879938	+	0.475089i	$0.157584\pi$
$521$	19.4337	+	33.6602i	0.851408	+	1.47468i	−0.0285298	+	0.999593i	$0.509083\pi$
$522$		0			0
$523$	−10.9212	+	18.9162i	−0.477553	+	0.827146i	−0.999669	−	0.0257286i	$-0.991809\pi$
$523$	−10.9212	+	18.9162i	−0.477553	+	0.827146i	0.522116	+	0.852874i	$0.325143\pi$
$524$		0			0
$525$	12.9512	+	0.773956i	0.565235	+	0.0337782i
$526$		0			0
$527$	6.70185	−	38.0081i	0.291937	−	1.65566i
$528$		0			0
$529$	−9.24476	+	7.75727i	−0.401946	+	0.337273i
$530$		0			0
$531$	−33.7324	−	17.0689i	−1.46386	−	0.740728i
$532$		0			0
$533$	13.3894	+	4.87336i	0.579961	+	0.211088i
$534$		0			0
$535$	−3.60549	−	3.02536i	−0.155879	−	0.130798i
$536$		0			0
$537$	8.32697	+	3.60684i	0.359335	+	0.155647i
$538$		0			0
$539$	33.3232			1.43533
$540$		0			0
$541$	−3.52613			−0.151600			−0.0758001	−	0.997123i	$-0.524151\pi$
$541$	−3.52613			−0.151600			−0.0758001	+	0.997123i	$0.524151\pi$
$542$		0			0
$543$	−35.8539	+	26.6081i	−1.53864	+	1.14186i
$544$		0			0
$545$	−15.5049	−	13.0101i	−0.664155	−	0.557292i
$546$		0			0
$547$	−3.56080	−	1.29603i	−0.152249	−	0.0554140i	0.264772	−	0.964311i	$-0.414703\pi$
$547$	−3.56080	−	1.29603i	−0.152249	−	0.0554140i	−0.417020	+	0.908897i	$0.636926\pi$
$548$		0			0
$549$	−17.6011	−	2.11121i	−0.751199	−	0.0901044i
$550$		0			0
$551$	−15.9867	+	13.4145i	−0.681057	+	0.571475i
$552$		0			0
$553$	0.845917	−	4.79744i	0.0359721	−	0.204008i
$554$		0			0
$555$	4.83790	+	9.66946i	0.205358	+	0.410446i
$556$		0			0
$557$	0.558686	−	0.967672i	0.0236723	−	0.0410016i	−0.853947	−	0.520361i	$-0.825798\pi$
$557$	0.558686	−	0.967672i	0.0236723	−	0.0410016i	0.877619	+	0.479359i	$0.159131\pi$
$558$		0			0
$559$	1.43039	+	2.47752i	0.0604992	+	0.104788i
$560$		0			0
$561$	53.8949	−	16.0464i	2.27545	−	0.677479i
$562$		0			0
$563$	−17.5695	+	6.39479i	−0.740468	+	0.269508i	−0.684589	−	0.728929i	$-0.740018\pi$
$563$	−17.5695	+	6.39479i	−0.740468	+	0.269508i	−0.0558789	+	0.998438i	$0.517796\pi$
$564$		0			0
$565$	−8.37576	−	47.5013i	−0.352371	−	1.99839i
$566$		0			0
$567$	8.02700	−	0.889079i	0.337102	−	0.0373378i
$568$		0			0
$569$	−3.04166	−	17.2501i	−0.127513	−	0.723163i	−0.979783	−	0.200061i	$-0.935886\pi$
$569$	−3.04166	−	17.2501i	−0.127513	−	0.723163i	0.852270	−	0.523102i	$-0.175225\pi$
$570$		0			0
$571$	−14.7128	+	5.35501i	−0.615710	+	0.224100i	−0.631000	−	0.775783i	$-0.717355\pi$
$571$	−14.7128	+	5.35501i	−0.615710	+	0.224100i	0.0152897	+	0.999883i	$0.495133\pi$
$572$		0			0
$573$	34.8315	−	10.3705i	1.45511	−	0.433236i
$574$		0			0
$575$	13.8000	+	23.9023i	0.575501	+	0.996797i
$576$		0			0
$577$	−11.2988	+	19.5701i	−0.470374	+	0.814712i	−0.999426	−	0.0338776i	$-0.989214\pi$
$577$	−11.2988	+	19.5701i	−0.470374	+	0.814712i	0.529052	+	0.848590i	$0.322548\pi$
$578$		0			0
$579$	−19.8760	−	39.7259i	−0.826018	−	1.65095i
$580$		0			0
$581$	1.31886	−	7.47964i	0.0547156	−	0.310308i
$582$		0			0
$583$	−16.1948	+	13.5890i	−0.670720	+	0.562801i
$584$		0			0
$585$	21.2033	−	28.3020i	0.876649	−	1.17014i
$586$		0			0
$587$	6.47895	+	2.35814i	0.267415	+	0.0973310i	0.472248	−	0.881466i	$-0.343443\pi$
$587$	6.47895	+	2.35814i	0.267415	+	0.0973310i	−0.204833	+	0.978797i	$0.565665\pi$
$588$		0			0
$589$	−12.1619	−	10.2051i	−0.501124	−	0.420493i
$590$		0			0
$591$	25.0163	−	18.5652i	1.02903	−	0.763672i
$592$		0			0
$593$	−13.5617			−0.556912			−0.278456	−	0.960449i	$-0.589823\pi$
$593$	−13.5617			−0.556912			−0.278456	+	0.960449i	$0.589823\pi$
$594$		0			0
$595$	−19.7866			−0.811170
$596$		0			0
$597$	−10.6830	−	4.62734i	−0.437225	−	0.189384i
$598$		0			0
$599$	−21.9848	−	18.4474i	−0.898274	−	0.753742i	0.0715779	−	0.997435i	$-0.477197\pi$
$599$	−21.9848	−	18.4474i	−0.898274	−	0.753742i	−0.969852	+	0.243693i	$0.921641\pi$
$600$		0			0
$601$	26.1491	+	9.51751i	1.06665	+	0.388227i	0.814921	−	0.579572i	$-0.196780\pi$
$601$	26.1491	+	9.51751i	1.06665	+	0.388227i	0.251725	+	0.967799i	$0.419002\pi$
$602$		0			0
$603$	−1.19563	−	21.6554i	−0.0486900	−	0.881878i
$604$		0			0
$605$	−50.1980	+	42.1211i	−2.04084	+	1.71247i
$606$		0			0
$607$	2.39142	−	13.5624i	0.0970646	−	0.550481i	−0.897031	−	0.441969i	$-0.854280\pi$
$607$	2.39142	−	13.5624i	0.0970646	−	0.550481i	0.994095	−	0.108512i	$-0.0346086\pi$
$608$		0			0
$609$	−13.0412	−	0.779334i	−0.528454	−	0.0315802i
$610$		0			0
$611$	−3.81628	+	6.61000i	−0.154390	+	0.267412i
$612$		0			0
$613$	8.72001	+	15.1035i	0.352198	+	0.610025i	0.986634	−	0.162950i	$-0.0521010\pi$
$613$	8.72001	+	15.1035i	0.352198	+	0.610025i	−0.634436	+	0.772975i	$0.718768\pi$
$614$		0			0
$615$	−20.2975	−	19.2078i	−0.818476	−	0.774533i
$616$		0			0
$617$	21.1681	−	7.70455i	0.852194	−	0.310173i	0.121260	−	0.992621i	$-0.461307\pi$
$617$	21.1681	−	7.70455i	0.852194	−	0.310173i	0.730935	+	0.682447i	$0.239084\pi$
$618$		0			0
$619$	8.02691	+	45.5229i	0.322629	+	1.82972i	0.525840	+	0.850583i	$0.323751\pi$
$619$	8.02691	+	45.5229i	0.322629	+	1.82972i	−0.203212	+	0.979135i	$0.565138\pi$
$620$		0			0
$621$	10.9834	+	13.2107i	0.440751	+	0.530128i
$622$		0			0
$623$	−2.13632	−	12.1156i	−0.0855897	−	0.485403i
$624$		0			0
$625$	−2.76727	+	1.00720i	−0.110691	+	0.0402882i
$626$		0			0
$627$	5.36864	−	22.5005i	0.214403	−	0.898584i
$628$		0			0
$629$	−5.15622	−	8.93083i	−0.205592	−	0.356095i
$630$		0			0
$631$	14.9908	−	25.9649i	0.596776	−	1.03365i	−0.396517	−	0.918027i	$-0.629781\pi$
$631$	14.9908	−	25.9649i	0.596776	−	1.03365i	0.993294	−	0.115619i	$-0.0368853\pi$
$632$		0			0
$633$	2.53161	−	3.83648i	0.100622	−	0.152486i
$634$		0			0
$635$	−11.1385	+	63.1698i	−0.442019	+	2.50682i
$636$		0			0
$637$	−15.3113	+	12.8477i	−0.606657	+	0.509045i
$638$		0			0
$639$	1.60383	−	5.29883i	0.0634465	−	0.209619i
$640$		0			0
$641$	3.31478	+	1.20648i	0.130926	+	0.0476532i	0.406652	−	0.913583i	$-0.366696\pi$
$641$	3.31478	+	1.20648i	0.130926	+	0.0476532i	−0.275726	+	0.961236i	$0.588918\pi$
$642$		0			0
$643$	13.5788	+	11.3940i	0.535496	+	0.449335i	0.869994	−	0.493062i	$-0.164122\pi$
$643$	13.5788	+	11.3940i	0.535496	+	0.449335i	−0.334498	+	0.942396i	$0.608567\pi$
$644$		0			0
$645$	−0.642939	−	5.57372i	−0.0253157	−	0.219465i
$646$		0			0
$647$	16.2920			0.640505			0.320252	−	0.947332i	$-0.396232\pi$
$647$	16.2920			0.640505			0.320252	+	0.947332i	$0.396232\pi$
$648$		0			0
$649$	−67.7875			−2.66089
$650$		0			0
$651$	−1.13891	−	9.87333i	−0.0446373	−	0.386966i
$652$		0			0
$653$	17.7984	+	14.9346i	0.696504	+	0.584436i	0.920777	−	0.390090i	$-0.127556\pi$
$653$	17.7984	+	14.9346i	0.696504	+	0.584436i	−0.224273	+	0.974526i	$0.572001\pi$
$654$		0			0
$655$	−8.93222	−	3.25106i	−0.349011	−	0.127030i
$656$		0			0
$657$	−5.68510	−	6.06246i	−0.221797	−	0.236519i
$658$		0			0
$659$	−11.5737	+	9.71151i	−0.450848	+	0.378307i	−0.839751	−	0.542972i	$-0.817299\pi$
$659$	−11.5737	+	9.71151i	−0.450848	+	0.378307i	0.388902	+	0.921279i	$0.372854\pi$
$660$		0			0
$661$	−1.43878	+	8.15971i	−0.0559619	+	0.317376i	−0.999919	−	0.0126910i	$-0.995960\pi$
$661$	−1.43878	+	8.15971i	−0.0559619	+	0.317376i	0.943958	+	0.330067i	$0.107071\pi$
$662$		0			0
$663$	−18.5770	+	28.1521i	−0.721469	+	1.09334i
$664$		0			0
$665$	−4.06972	+	7.04897i	−0.157817	+	0.273347i
$666$		0			0
$667$	−13.8959	−	24.0685i	−0.538052	−	0.931934i
$668$		0			0
$669$	1.80467	−	7.56357i	0.0697728	−	0.292425i
$670$		0			0
$671$	−29.8695	+	10.8716i	−1.15310	+	0.419694i
$672$		0			0
$673$	5.74268	+	32.5683i	0.221364	+	1.25542i	0.869516	+	0.493906i	$0.164431\pi$
$673$	5.74268	+	32.5683i	0.221364	+	1.25542i	−0.648152	+	0.761511i	$0.724458\pi$
$674$		0			0
$675$	−37.6623	+	21.5173i	−1.44962	+	0.828201i
$676$		0			0
$677$	−5.01235	−	28.4264i	−0.192640	−	1.09252i	−0.915739	−	0.401773i	$-0.868394\pi$
$677$	−5.01235	−	28.4264i	−0.192640	−	1.09252i	0.723099	−	0.690744i	$-0.242717\pi$
$678$		0			0
$679$	−8.98404	+	3.26992i	−0.344776	+	0.125488i
$680$		0			0
$681$	−32.0332	−	30.3134i	−1.22752	−	1.16161i
$682$		0			0
$683$	−4.92261	−	8.52621i	−0.188358	−	0.326246i	0.756345	−	0.654173i	$-0.226983\pi$
$683$	−4.92261	−	8.52621i	−0.188358	−	0.326246i	−0.944703	+	0.327927i	$0.893650\pi$
$684$		0			0
$685$	16.5051	−	28.5876i	0.630627	−	1.09228i
$686$		0			0
$687$	−16.6115	−	0.992697i	−0.633768	−	0.0378737i
$688$		0			0
$689$	2.20193	−	12.4878i	0.0838870	−	0.475747i
$690$		0			0
$691$	34.6824	−	29.1020i	1.31938	−	1.10709i	0.332945	−	0.942946i	$-0.391958\pi$
$691$	34.6824	−	29.1020i	1.31938	−	1.10709i	0.986436	−	0.164146i	$-0.0524868\pi$
$692$		0			0
$693$	12.1227	−	7.92087i	0.460505	−	0.300889i
$694$		0			0
$695$	19.4798	+	7.09006i	0.738911	+	0.268941i
$696$		0			0
$697$	20.4177	+	17.1325i	0.773376	+	0.648939i
$698$		0			0
$699$	−13.8557	−	6.00163i	−0.524072	−	0.227002i
$700$		0			0
$701$	−50.7267			−1.91592			−0.957960	−	0.286903i	$-0.907374\pi$
$701$	−50.7267			−1.91592			−0.957960	+	0.286903i	$0.907374\pi$
$702$		0			0
$703$	−4.24215			−0.159996
$704$		0			0
$705$	12.0207	−	8.92087i	0.452725	−	0.335979i
$706$		0			0
$707$	5.60910	+	4.70660i	0.210952	+	0.177010i
$708$		0			0
$709$	−44.0966	−	16.0498i	−1.65608	−	0.602765i	−0.666343	−	0.745646i	$-0.732141\pi$
$709$	−44.0966	−	16.0498i	−1.65608	−	0.602765i	−0.989740	+	0.142881i	$0.954363\pi$
$710$		0			0
$711$	6.40543	+	14.9737i	0.240222	+	0.561558i
$712$		0			0
$713$	16.1963	−	13.5903i	0.606555	−	0.508960i
$714$		0			0
$715$	11.0110	−	62.4464i	0.411788	−	2.33536i
$716$		0			0
$717$	−8.14303	−	16.2754i	−0.304107	−	0.607815i
$718$		0			0
$719$	−19.6803	+	34.0874i	−0.733953	+	1.27124i	0.221228	+	0.975222i	$0.428993\pi$
$719$	−19.6803	+	34.0874i	−0.733953	+	1.27124i	−0.955181	+	0.296022i	$0.904340\pi$
$720$		0			0
$721$	−6.94021	−	12.0208i	−0.258467	−	0.447678i
$722$		0			0
$723$	−1.42615	+	0.424614i	−0.0530391	+	0.0157916i
$724$		0			0
$725$	65.9357	−	23.9986i	2.44879	−	0.891287i
$726$		0			0
$727$	4.31819	+	24.4896i	0.160153	+	0.908271i	0.953923	+	0.300053i	$0.0970043\pi$
$727$	4.31819	+	24.4896i	0.160153	+	0.908271i	−0.793770	+	0.608218i	$0.791885\pi$
$728$		0			0
$729$	−20.8397	+	17.1670i	−0.771840	+	0.635816i
$730$		0			0
$731$	0.929250	+	5.27004i	0.0343696	+	0.194919i
$732$		0			0
$733$	0.0599323	−	0.0218136i	0.00221365	−	0.000805702i	−0.340913	−	0.940095i	$-0.610736\pi$
$733$	0.0599323	−	0.0218136i	0.00221365	−	0.000805702i	0.343127	+	0.939289i	$0.388514\pi$
$734$		0			0
$735$	37.5703	−	11.1860i	1.38580	−	0.412602i
$736$		0			0
$737$	−19.4445	−	33.6789i	−0.716249	−	1.24058i
$738$		0			0
$739$	−3.97754	+	6.88930i	−0.146316	+	0.253427i	−0.929863	−	0.367905i	$-0.880075\pi$
$739$	−3.97754	+	6.88930i	−0.146316	+	0.253427i	0.783547	+	0.621332i	$0.213408\pi$
$740$		0			0
$741$	6.20828	+	12.4084i	0.228067	+	0.455834i
$742$		0			0
$743$	−8.35810	+	47.4012i	−0.306629	+	1.73898i	0.309107	+	0.951027i	$0.399970\pi$
$743$	−8.35810	+	47.4012i	−0.306629	+	1.73898i	−0.615736	+	0.787953i	$0.711141\pi$
$744$		0			0
$745$	−13.5742	+	11.3901i	−0.497319	+	0.417300i
$746$		0			0
$747$	9.98664	+	23.3454i	0.365392	+	0.854162i
$748$		0			0
$749$	1.08631	+	0.395383i	0.0396928	+	0.0144470i
$750$		0			0
$751$	−29.9688	−	25.1468i	−1.09358	−	0.917619i	−0.0965996	−	0.995323i	$-0.530797\pi$
$751$	−29.9688	−	25.1468i	−1.09358	−	0.917619i	−0.996976	+	0.0777041i	$0.975241\pi$
$752$		0			0
$753$	−22.0949	+	16.3972i	−0.805182	+	0.597547i
$754$		0			0
$755$	53.3147			1.94032
$756$		0			0
$757$	48.7909			1.77333			0.886667	−	0.462408i	$-0.153015\pi$
$757$	48.7909			1.77333			0.886667	+	0.462408i	$0.153015\pi$
$758$		0			0
$759$	28.2676	+	12.2441i	1.02605	+	0.444434i
$760$		0			0
$761$	22.6042	+	18.9672i	0.819403	+	0.687561i	0.952832	−	0.303497i	$-0.0981543\pi$
$761$	22.6042	+	18.9672i	0.819403	+	0.687561i	−0.133429	+	0.991058i	$0.542599\pi$
$762$		0			0
$763$	4.67149	+	1.70028i	0.169119	+	0.0615544i
$764$		0			0
$765$	55.3775	−	36.1831i	2.00218	−	1.30820i
$766$		0			0
$767$	31.1470	−	26.1354i	1.12465	−	0.943696i
$768$		0			0
$769$	−5.01390	+	28.4353i	−0.180806	+	1.02540i	0.750421	+	0.660961i	$0.229851\pi$
$769$	−5.01390	+	28.4353i	−0.180806	+	1.02540i	−0.931227	+	0.364441i	$0.881260\pi$
$770$		0			0
$771$	21.7372	+	1.29901i	0.782848	+	0.0467827i
$772$		0			0
$773$	18.5481	−	32.1262i	0.667128	−	1.15550i	−0.311575	−	0.950221i	$-0.600857\pi$
$773$	18.5481	−	32.1262i	0.667128	−	1.15550i	0.978704	−	0.205279i	$-0.0658100\pi$
$774$		0			0
$775$	26.6900	+	46.2284i	0.958733	+	1.66057i
$776$		0			0
$777$	−1.92889	−	1.82533i	−0.0691986	−	0.0654834i
$778$		0			0
$779$	10.3030	−	3.74998i	0.369143	−	0.134357i
$780$		0			0
$781$	−1.72379	−	9.77609i	−0.0616820	−	0.349816i
$782$		0			0
$783$	37.9240	−	21.6668i	1.35529	−	0.774309i
$784$		0			0
$785$	−6.03408	−	34.2210i	−0.215366	−	1.22140i
$786$		0			0
$787$	−27.7312	+	10.0933i	−0.988510	+	0.359788i	−0.785143	−	0.619315i	$-0.787411\pi$
$787$	−27.7312	+	10.0933i	−0.988510	+	0.359788i	−0.203367	+	0.979103i	$0.565188\pi$
$788$		0			0
$789$	−10.4820	+	43.9313i	−0.373171	+	1.56400i
$790$		0			0
$791$	5.92352	+	10.2598i	0.210616	+	0.364798i
$792$		0			0
$793$	9.53290	−	16.5115i	0.338523	−	0.586339i
$794$		0			0
$795$	−13.6973	+	20.7573i	−0.485793	+	0.736187i
$796$		0			0
$797$	6.45871	−	36.6292i	0.228779	−	1.29747i	−0.626548	−	0.779383i	$-0.715533\pi$
$797$	6.45871	−	36.6292i	0.228779	−	1.29747i	0.855327	−	0.518089i	$-0.173356\pi$
$798$		0			0
$799$	−10.9371	+	9.17730i	−0.386926	+	0.324669i
$800$		0			0
$801$	28.1345	+	30.0020i	0.994085	+	1.06007i
$802$		0			0
$803$	−14.0037	−	5.09692i	−0.494179	−	0.179866i
$804$		0			0
$805$	−8.30349	−	6.96746i	−0.292660	−	0.245571i
$806$		0			0
$807$	−1.32383	−	11.4765i	−0.0466011	−	0.403990i
$808$		0			0
$809$	13.5316			0.475747			0.237873	−	0.971296i	$-0.423550\pi$
$809$	13.5316			0.475747			0.237873	+	0.971296i	$0.423550\pi$
$810$		0			0
$811$	22.8317			0.801728			0.400864	−	0.916138i	$-0.368710\pi$
$811$	22.8317			0.801728			0.400864	+	0.916138i	$0.368710\pi$
$812$		0			0
$813$	0.438442	+	3.80091i	0.0153768	+	0.133304i
$814$		0			0
$815$	−22.6233	−	18.9832i	−0.792459	−	0.664952i
$816$		0			0
$817$	2.06858	+	0.752902i	0.0723705	+	0.0263407i
$818$		0			0
$819$	−2.51627	+	8.31340i	−0.0879255	+	0.290494i
$820$		0			0
$821$	−34.6662	+	29.0884i	−1.20986	+	1.01519i	−0.210566	+	0.977580i	$0.567531\pi$
$821$	−34.6662	+	29.0884i	−1.20986	+	1.01519i	−0.999292	+	0.0376116i	$0.988025\pi$
$822$		0			0
$823$	−1.71372	+	9.71896i	−0.0597364	+	0.338782i	−0.999999	−	0.00166926i	$-0.999469\pi$
$823$	−1.71372	+	9.71896i	−0.0597364	+	0.338782i	0.940262	+	0.340451i	$0.110580\pi$
$824$		0			0
$825$	−42.8367	+	64.9162i	−1.49138	+	2.26009i
$826$		0			0
$827$	1.43405	−	2.48385i	0.0498668	−	0.0863718i	−0.840015	−	0.542564i	$-0.817454\pi$
$827$	1.43405	−	2.48385i	0.0498668	−	0.0863718i	0.889881	+	0.456192i	$0.150787\pi$
$828$		0			0
$829$	21.8467	+	37.8396i	0.758768	+	1.31423i	0.943479	+	0.331432i	$0.107532\pi$
$829$	21.8467	+	37.8396i	0.758768	+	1.31423i	−0.184711	+	0.982793i	$0.559135\pi$
$830$		0			0
$831$	3.63888	−	15.2509i	0.126231	−	0.529048i
$832$		0			0
$833$	−35.1335	+	12.7875i	−1.21730	+	0.443062i
$834$		0			0
$835$	−7.78624	−	44.1580i	−0.269454	−	1.52815i
$836$		0			0
$837$	21.2426	+	25.5502i	0.734251	+	0.883146i
$838$		0			0
$839$	3.17194	+	17.9890i	0.109508	+	0.621049i	0.989324	+	0.145734i	$0.0465545\pi$
$839$	3.17194	+	17.9890i	0.109508	+	0.621049i	−0.879816	+	0.475314i	$0.842334\pi$
$840$		0			0
$841$	−39.1428	+	14.2468i	−1.34975	+	0.491270i
$842$		0			0
$843$	−20.2867	−	19.1975i	−0.698710	−	0.661197i
$844$		0			0
$845$	−4.73052	−	8.19350i	−0.162735	−	0.281865i
$846$		0			0
$847$	8.04746	−	13.9386i	0.276514	−	0.478936i
$848$		0			0
$849$	29.6943	+	1.77452i	1.01911	+	0.0609014i
$850$		0			0
$851$	0.980997	−	5.56351i	0.0336282	−	0.190715i
$852$		0			0
$853$	7.44368	−	6.24599i	0.254867	−	0.213859i	−0.506398	−	0.862300i	$-0.669023\pi$
$853$	7.44368	−	6.24599i	0.254867	−	0.213859i	0.761265	+	0.648441i	$0.224579\pi$
$854$		0			0
$855$	−1.50013	−	27.1704i	−0.0513033	−	0.929210i
$856$		0			0
$857$	0.627163	+	0.228269i	0.0214235	+	0.00779751i	0.352710	−	0.935733i	$-0.385260\pi$
$857$	0.627163	+	0.228269i	0.0214235	+	0.00779751i	−0.331286	+	0.943530i	$0.607483\pi$
$858$		0			0
$859$	−23.5431	−	19.7550i	−0.803280	−	0.674032i	0.145714	−	0.989327i	$-0.453452\pi$
$859$	−23.5431	−	19.7550i	−0.803280	−	0.674032i	−0.948994	+	0.315295i	$0.897897\pi$
$860$		0			0
$861$	6.29830	+	2.72812i	0.214646	+	0.0929740i
$862$		0			0
$863$	−19.8761			−0.676590			−0.338295	−	0.941040i	$-0.609850\pi$
$863$	−19.8761			−0.676590			−0.338295	+	0.941040i	$0.609850\pi$
$864$		0			0
$865$	47.1861			1.60438
$866$		0			0
$867$	−27.0202	+	20.0524i	−0.917653	+	0.681015i
$868$		0			0
$869$	22.3704	+	18.7710i	0.758864	+	0.636763i
$870$		0			0
$871$	21.9193	+	7.97796i	0.742706	+	0.270323i
$872$		0			0
$873$	19.1644	−	25.5805i	0.648617	−	0.865770i
$874$		0			0
$875$	8.40723	−	7.05450i	0.284216	−	0.238486i
$876$		0			0
$877$	−5.12978	+	29.0924i	−0.173220	+	0.982381i	0.766958	+	0.641697i	$0.221770\pi$
$877$	−5.12978	+	29.0924i	−0.173220	+	0.982381i	−0.940178	+	0.340683i	$0.889342\pi$
$878$		0			0
$879$	−4.69820	−	9.39024i	−0.158466	−	0.316725i
$880$		0			0
$881$	−13.7689	+	23.8485i	−0.463887	+	0.803476i	−0.999151	−	0.0412090i	$-0.986879\pi$
$881$	−13.7689	+	23.8485i	−0.463887	+	0.803476i	0.535263	+	0.844685i	$0.320212\pi$
$882$		0			0
$883$	19.4021	+	33.6055i	0.652934	+	1.13092i	0.982407	+	0.186750i	$0.0597955\pi$
$883$	19.4021	+	33.6055i	0.652934	+	1.13092i	−0.329473	+	0.944165i	$0.606871\pi$
$884$		0			0
$885$	−76.4273	+	22.7551i	−2.56908	+	0.764903i
$886$		0			0
$887$	27.1295	−	9.87432i	0.910919	−	0.331547i	0.156299	−	0.987710i	$-0.450044\pi$
$887$	27.1295	−	9.87432i	0.910919	−	0.331547i	0.754620	+	0.656163i	$0.227821\pi$
$888$		0			0
$889$	−2.73580	−	15.5155i	−0.0917558	−	0.520373i
$890$		0			0
$891$	−19.4438	+	44.3370i	−0.651391	+	1.48535i
$892$		0			0
$893$	1.01986	+	5.78393i	0.0341284	+	0.193552i
$894$		0			0
$895$	17.9868	−	6.54665i	0.601232	−	0.218830i
$896$		0			0
$897$	−17.7091	+	5.27262i	−0.591290	+	0.176048i
$898$		0			0
$899$	−26.8755	−	46.5497i	−0.896347	−	1.55252i
$900$		0			0
$901$	11.8599	−	20.5419i	0.395110	−	0.684351i
$902$		0			0
$903$	0.616616	+	1.23242i	0.0205197	+	0.0410124i
$904$		0			0
$905$	−16.3538	+	92.7472i	−0.543620	+	3.08302i
$906$		0			0
$907$	−3.91098	+	3.28170i	−0.129862	+	0.108967i	−0.705405	−	0.708804i	$-0.749235\pi$
$907$	−3.91098	+	3.28170i	−0.129862	+	0.108967i	0.575543	+	0.817771i	$0.304791\pi$
$908$		0			0
$909$	−24.3053	−	2.91536i	−0.806155	−	0.0966963i
$910$		0			0
$911$	−31.5094	−	11.4685i	−1.04395	−	0.379968i	−0.237575	−	0.971369i	$-0.576353\pi$
$911$	−31.5094	−	11.4685i	−1.04395	−	0.379968i	−0.806377	+	0.591401i	$0.798575\pi$
$912$		0			0
$913$	34.8775	+	29.2657i	1.15428	+	0.968553i
$914$		0			0
$915$	−30.0271	+	22.2839i	−0.992665	+	0.736683i
$916$		0			0
$917$	2.33469			0.0770984
$918$		0			0
$919$	2.97857			0.0982540			0.0491270	−	0.998793i	$-0.484356\pi$
$919$	2.97857			0.0982540			0.0491270	+	0.998793i	$0.484356\pi$
$920$		0			0
$921$	40.7156	+	17.6360i	1.34162	+	0.581126i
$922$		0			0
$923$	4.56121	+	3.82731i	0.150134	+	0.125978i
$924$		0			0
$925$	13.4030	+	4.87828i	0.440687	+	0.160397i
$926$		0			0
$927$	41.4060	+	20.9518i	1.35995	+	0.688147i
$928$		0			0
$929$	27.8662	−	23.3825i	0.914259	−	0.767154i	−0.0586655	−	0.998278i	$-0.518685\pi$
$929$	27.8662	−	23.3825i	0.914259	−	0.767154i	0.972924	+	0.231123i	$0.0742401\pi$
$930$		0			0
$931$	−2.67073	+	15.1465i	−0.0875297	+	0.496405i
$932$		0			0
$933$	−2.50116	−	0.149468i	−0.0818843	−	0.00489337i
$934$		0			0
$935$	59.3066	−	102.722i	1.93953	−	3.35937i
$936$		0			0
$937$	17.3840	+	30.1099i	0.567909	+	0.983647i	0.996773	+	0.0802780i	$0.0255808\pi$
$937$	17.3840	+	30.1099i	0.567909	+	0.983647i	−0.428863	+	0.903369i	$0.641086\pi$
$938$		0			0
$939$	−30.3242	−	28.6961i	−0.989592	−	0.936462i
$940$		0			0
$941$	15.1471	−	5.51309i	0.493781	−	0.179722i	−0.0831138	−	0.996540i	$-0.526486\pi$
$941$	15.1471	−	5.51309i	0.493781	−	0.179722i	0.576895	+	0.816818i	$0.304264\pi$
$942$		0			0
$943$	2.53548	+	14.3794i	0.0825665	+	0.468258i
$944$		0			0
$945$	11.0089	−	12.9998i	0.358121	−	0.422884i
$946$		0			0
$947$	1.76894	+	10.0322i	0.0574829	+	0.326002i	0.999966	−	0.00825215i	$-0.00262677\pi$
$947$	1.76894	+	10.0322i	0.0574829	+	0.326002i	−0.942483	+	0.334254i	$0.891516\pi$
$948$		0			0
$949$	8.39952	−	3.05717i	0.272660	−	0.0992401i
$950$		0			0
$951$	−2.72737	+	11.4307i	−0.0884409	+	0.370665i
$952$		0			0
$953$	3.32082	+	5.75183i	0.107572	+	0.186320i	0.914786	−	0.403939i	$-0.132359\pi$
$953$	3.32082	+	5.75183i	0.107572	+	0.186320i	−0.807214	+	0.590259i	$0.799026\pi$
$954$		0			0
$955$	38.3289	−	66.3877i	1.24030	−	2.14825i
$956$		0			0
$957$	43.1344	−	65.3673i	1.39434	−	2.11302i
$958$		0			0
$959$	−1.40791	+	7.98464i	−0.0454637	+	0.257837i
$960$		0			0
$961$	7.57710	−	6.35794i	0.244423	−	0.205095i
$962$		0			0
$963$	−3.76332	+	0.879920i	−0.121271	+	0.0283550i
$964$		0			0
$965$	−88.0467	−	32.0464i	−2.83432	−	1.03161i
$966$		0			0
$967$	−24.4648	−	20.5284i	−0.786735	−	0.660149i	0.158200	−	0.987407i	$-0.449431\pi$
$967$	−24.4648	−	20.5284i	−0.786735	−	0.660149i	−0.944935	+	0.327258i	$0.893875\pi$
$968$		0			0
$969$	2.97412	+	25.7831i	0.0955426	+	0.828271i
$970$		0			0
$971$	−17.7010			−0.568052			−0.284026	−	0.958817i	$-0.591670\pi$
$971$	−17.7010			−0.568052			−0.284026	+	0.958817i	$0.591670\pi$
$972$		0			0
$973$	−5.09160			−0.163229
$974$		0			0
$975$	−5.34579	−	46.3433i	−0.171202	−	1.48417i
$976$		0			0
$977$	3.33720	+	2.80024i	0.106766	+	0.0895877i	0.694608	−	0.719388i	$-0.255578\pi$
$977$	3.33720	+	2.80024i	0.106766	+	0.0895877i	−0.587842	+	0.808976i	$0.700022\pi$
$978$		0			0
$979$	69.3016	+	25.2237i	2.21489	+	0.806154i
$980$		0			0
$981$	−16.1836	+	3.78396i	−0.516702	+	0.120813i
$982$		0			0
$983$	−33.4479	+	28.0661i	−1.06682	+	0.895171i	−0.994761	−	0.102229i	$-0.967402\pi$
$983$	−33.4479	+	28.0661i	−1.06682	+	0.895171i	−0.0720622	+	0.997400i	$0.522958\pi$
$984$		0			0
$985$	11.4105	−	64.7123i	0.363569	−	2.06190i
$986$		0			0
$987$	−2.02501	+	3.06877i	−0.0644568	+	0.0976800i
$988$		0			0
$989$	−1.46578	+	2.53881i	−0.0466091	+	0.0807293i
$990$		0			0
$991$	6.03137	+	10.4466i	0.191593	+	0.331848i	0.945778	−	0.324813i	$-0.105301\pi$
$991$	6.03137	+	10.4466i	0.191593	+	0.331848i	−0.754186	+	0.656661i	$0.771968\pi$
$992$		0			0
$993$	−11.4888	+	48.1505i	−0.364585	+	1.52801i
$994$		0			0
$995$	−23.0759	+	8.39893i	−0.731554	+	0.266264i
$996$		0			0
$997$	1.78576	+	10.1275i	0.0565555	+	0.320742i	0.999940	−	0.0109591i	$-0.00348845\pi$
$997$	1.78576	+	10.1275i	0.0565555	+	0.320742i	−0.943384	+	0.331701i	$0.892377\pi$
$998$		0			0
$999$	8.73641	+	1.58133i	0.276408	+	0.0500311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.b.121.3	yes	30
3.2	odd	2		648.2.q.b.577.5		30
4.3	odd	2		432.2.u.f.337.3		30
27.2	odd	18		648.2.q.b.73.5		30
27.5	odd	18		5832.2.a.l.1.13		15
27.22	even	9		5832.2.a.k.1.3		15
27.25	even	9	inner	216.2.q.b.25.3	✓	30
108.79	odd	18		432.2.u.f.241.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.25.3	✓	30	27.25	even	9	inner
216.2.q.b.121.3	yes	30	1.1	even	1	trivial
432.2.u.f.241.3		30	108.79	odd	18
432.2.u.f.337.3		30	4.3	odd	2
648.2.q.b.73.5		30	27.2	odd	18
648.2.q.b.577.5		30	3.2	odd	2
5832.2.a.k.1.3		15	27.22	even	9
5832.2.a.l.1.13		15	27.5	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.198479 - 1.72064i) q^{3} +(-2.79870 - 2.34839i) q^{5} +(0.843226 + 0.306909i) q^{7} +(-2.92121 + 0.683023i) q^{9} +O(q^{10})\)	\(q+(-0.198479 - 1.72064i) q^{3} +(-2.79870 - 2.34839i) q^{5} +(0.843226 + 0.306909i) q^{7} +(-2.92121 + 0.683023i) q^{9} +(-4.12074 + 3.45771i) q^{11} +(0.560278 - 3.17749i) q^{13} +(-3.48525 + 5.28166i) q^{15} +(3.01773 - 5.22685i) q^{17} +(-1.24138 - 2.15013i) q^{19} +(0.360718 - 1.51180i) q^{21} +(3.10693 - 1.13083i) q^{23} +(1.44955 + 8.22082i) q^{25} +(1.75504 + 4.89079i) q^{27} +(-1.45963 - 8.27795i) q^{29} +(6.00898 - 2.18709i) q^{31} +(6.76735 + 6.40402i) q^{33} +(-1.63919 - 2.83917i) q^{35} +(0.854321 - 1.47973i) q^{37} +(-5.57853 - 0.333371i) q^{39} +(-0.766855 + 4.34905i) q^{41} +(-0.679214 + 0.569928i) q^{43} +(9.77960 + 4.94856i) q^{45} +(-2.22292 - 0.809076i) q^{47} +(-4.74547 - 3.98193i) q^{49} +(-9.59250 - 4.15500i) q^{51} +3.93007 q^{53} +19.6527 q^{55} +(-3.45322 + 2.56272i) q^{57} +(9.65346 + 8.10021i) q^{59} +(5.55274 + 2.02103i) q^{61} +(-2.67287 - 0.320604i) q^{63} +(-9.03003 + 7.57710i) q^{65} +(-1.25539 + 7.11964i) q^{67} +(-2.56242 - 5.12147i) q^{69} +(-0.922706 + 1.59817i) q^{71} +(1.38518 + 2.39920i) q^{73} +(13.8574 - 4.12582i) q^{75} +(-4.53591 + 1.65094i) q^{77} +(-0.942692 - 5.34627i) q^{79} +(8.06696 - 3.99051i) q^{81} +(-1.46974 - 8.33532i) q^{83} +(-20.7204 + 7.54160i) q^{85} +(-13.9537 + 4.15449i) q^{87} +(-6.85499 - 11.8732i) q^{89} +(1.44764 - 2.50739i) q^{91} +(-4.95585 - 9.90521i) q^{93} +(-1.57509 + 8.93281i) q^{95} +(-8.16171 + 6.84849i) q^{97} +(9.67585 - 12.9153i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) \) 30 * q + 3 * q^7 - 6 * q^9	\( 30 q + 3 q^{7} - 6 q^{9} - 3 q^{11} - 12 q^{13} + 15 q^{15} + 6 q^{17} - 9 q^{19} + 30 q^{21} - 12 q^{23} + 24 q^{25} - 15 q^{27} - 9 q^{29} + 27 q^{31} - 30 q^{33} - 18 q^{35} - 15 q^{37} - 21 q^{39} - 15 q^{41} - 30 q^{43} + 15 q^{45} - 18 q^{47} + 15 q^{49} - 6 q^{51} - 18 q^{53} + 54 q^{55} - 72 q^{57} - 12 q^{59} + 6 q^{61} - 54 q^{63} - 54 q^{65} - 45 q^{67} + 9 q^{69} - 36 q^{73} + 69 q^{75} + 12 q^{77} + 45 q^{79} - 30 q^{81} - 3 q^{83} + 57 q^{85} - 60 q^{87} + 36 q^{89} - 39 q^{91} + 30 q^{93} + 51 q^{95} - 84 q^{97} + 162 q^{99}+O(q^{100}) \) 30 * q + 3 * q^7 - 6 * q^9 - 3 * q^11 - 12 * q^13 + 15 * q^15 + 6 * q^17 - 9 * q^19 + 30 * q^21 - 12 * q^23 + 24 * q^25 - 15 * q^27 - 9 * q^29 + 27 * q^31 - 30 * q^33 - 18 * q^35 - 15 * q^37 - 21 * q^39 - 15 * q^41 - 30 * q^43 + 15 * q^45 - 18 * q^47 + 15 * q^49 - 6 * q^51 - 18 * q^53 + 54 * q^55 - 72 * q^57 - 12 * q^59 + 6 * q^61 - 54 * q^63 - 54 * q^65 - 45 * q^67 + 9 * q^69 - 36 * q^73 + 69 * q^75 + 12 * q^77 + 45 * q^79 - 30 * q^81 - 3 * q^83 + 57 * q^85 - 60 * q^87 + 36 * q^89 - 39 * q^91 + 30 * q^93 + 51 * q^95 - 84 * q^97 + 162 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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