LMFDB - Embedded newform 722.2.e.i.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			99.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	722.99
Dual form			722.2.e.i.423.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.173648 + 0.984808i) q^{6} +(2.00000 - 3.46410i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.87939 - 0.684040i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.173648 + 0.984808i) q^{6} +(2.00000 - 3.46410i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.87939 - 0.684040i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.347296 + 1.96962i) q^{13} +(-3.06418 + 2.57115i) q^{14} +(0.173648 + 0.984808i) q^{16} +(5.63816 + 2.05212i) q^{17} -2.00000 q^{18} +(-3.75877 - 1.36808i) q^{21} +(0.520945 + 2.95442i) q^{22} +(-4.59627 - 3.85673i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(-0.868241 + 4.92404i) q^{25} +(1.00000 - 1.73205i) q^{26} +(-2.50000 - 4.33013i) q^{27} +(3.75877 - 1.36808i) q^{28} +(1.00000 - 1.73205i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-2.29813 + 1.92836i) q^{33} +(-4.59627 - 3.85673i) q^{34} +(1.87939 + 0.684040i) q^{36} +10.0000 q^{37} +2.00000 q^{39} +(-1.56283 - 8.86327i) q^{41} +(3.06418 + 2.57115i) q^{42} +(-3.06418 + 2.57115i) q^{43} +(0.520945 - 2.95442i) q^{44} +(3.00000 + 5.19615i) q^{46} +(0.939693 - 0.342020i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(2.50000 - 4.33013i) q^{50} +(1.04189 - 5.90885i) q^{51} +(-1.53209 + 1.28558i) q^{52} +(-4.59627 - 3.85673i) q^{53} +(0.868241 + 4.92404i) q^{54} -4.00000 q^{56} +(-8.45723 - 3.07818i) q^{59} +(-3.06418 - 2.57115i) q^{61} +(-1.53209 + 1.28558i) q^{62} +(1.38919 - 7.87846i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.81908 - 1.02606i) q^{66} +(-6.57785 + 2.39414i) q^{67} +(3.00000 + 5.19615i) q^{68} +(-3.00000 + 5.19615i) q^{69} +(4.59627 - 3.85673i) q^{71} +(-1.53209 - 1.28558i) q^{72} +(-0.173648 - 0.984808i) q^{73} +(-9.39693 - 3.42020i) q^{74} +5.00000 q^{75} -12.0000 q^{77} +(-1.87939 - 0.684040i) q^{78} +(0.694593 + 3.93923i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-1.56283 + 8.86327i) q^{82} +(-1.50000 + 2.59808i) q^{83} +(-2.00000 - 3.46410i) q^{84} +(3.75877 - 1.36808i) q^{86} +(-1.50000 + 2.59808i) q^{88} +(-1.04189 + 5.90885i) q^{89} +(6.12836 + 5.14230i) q^{91} +(-1.04189 - 5.90885i) q^{92} +(-1.87939 - 0.684040i) q^{93} -1.00000 q^{96} +(15.9748 + 5.81434i) q^{97} +(1.56283 + 8.86327i) q^{98} +(-4.59627 - 3.85673i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q + 12 * q^7 - 3 * q^8	$ 6 q + 12 q^{7} - 3 q^{8} - 9 q^{11} + 3 q^{12} - 12 q^{18} + 6 q^{26} - 15 q^{27} + 6 q^{31} + 60 q^{37} + 12 q^{39} + 18 q^{46} - 27 q^{49} + 15 q^{50} - 24 q^{56} - 3 q^{64} + 18 q^{68} - 18 q^{69} + 30 q^{75} - 72 q^{77} - 9 q^{83} - 12 q^{84} - 9 q^{88} - 6 q^{96}+O(q^{100}) $ 6 * q + 12 * q^7 - 3 * q^8 - 9 * q^11 + 3 * q^12 - 12 * q^18 + 6 * q^26 - 15 * q^27 + 6 * q^31 + 60 * q^37 + 12 * q^39 + 18 * q^46 - 27 * q^49 + 15 * q^50 - 24 * q^56 - 3 * q^64 + 18 * q^68 - 18 * q^69 + 30 * q^75 - 72 * q^77 - 9 * q^83 - 12 * q^84 - 9 * q^88 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$363$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i	−0.993010	−	0.118034i	$-0.962341\pi$
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i	0.892754	−	0.450545i	$-0.148770\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$5$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$6$	−0.173648	+	0.984808i	−0.0708916	+	0.402046i
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	0.944911	−	0.327327i	$-0.106148\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	1.87939	−	0.684040i	0.626462	−	0.228013i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−0.347296	+	1.96962i	−0.0963227	+	0.546273i	0.898011	+	0.439972i	$0.145012\pi$
$13$	−0.347296	+	1.96962i	−0.0963227	+	0.546273i	−0.994334	+	0.106301i	$0.966099\pi$
$14$	−3.06418	+	2.57115i	−0.818936	+	0.687169i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	5.63816	+	2.05212i	1.36745	+	0.497712i	0.918351	−	0.395768i	$-0.129521\pi$
$17$	5.63816	+	2.05212i	1.36745	+	0.497712i	0.449103	+	0.893480i	$0.351744\pi$
$18$	−2.00000			−0.471405
$19$		0			0
$19$		0			0
$20$		0			0
$21$	−3.75877	−	1.36808i	−0.820231	−	0.298540i
$22$	0.520945	+	2.95442i	0.111066	+	0.629885i
$23$	−4.59627	−	3.85673i	−0.958388	−	0.804183i	0.0223022	−	0.999751i	$-0.492900\pi$
$23$	−4.59627	−	3.85673i	−0.958388	−	0.804183i	−0.980690	+	0.195568i	$0.937345\pi$
$24$	−0.766044	+	0.642788i	−0.156368	+	0.131208i
$25$	−0.868241	+	4.92404i	−0.173648	+	0.984808i
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$	−2.50000	−	4.33013i	−0.481125	−	0.833333i
$28$	3.75877	−	1.36808i	0.710341	−	0.258543i
$29$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$29$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$30$		0			0
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	−2.29813	+	1.92836i	−0.400054	+	0.335685i
$34$	−4.59627	−	3.85673i	−0.788253	−	0.661423i
$35$		0			0
$36$	1.87939	+	0.684040i	0.313231	+	0.114007i
$37$	10.0000			1.64399			0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000			1.64399			0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$	2.00000			0.320256
$40$		0			0
$41$	−1.56283	−	8.86327i	−0.244074	−	1.38421i	−0.822634	−	0.568571i	$-0.807497\pi$
$41$	−1.56283	−	8.86327i	−0.244074	−	1.38421i	0.578561	−	0.815639i	$-0.303615\pi$
$42$	3.06418	+	2.57115i	0.472813	+	0.396737i
$43$	−3.06418	+	2.57115i	−0.467283	+	0.392097i	−0.845802	−	0.533497i	$-0.820878\pi$
$43$	−3.06418	+	2.57115i	−0.467283	+	0.392097i	0.378520	+	0.925593i	$0.376433\pi$
$44$	0.520945	−	2.95442i	0.0785353	−	0.445396i
$45$		0			0
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$47$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$48$	0.939693	−	0.342020i	0.135633	−	0.0493664i
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	2.50000	−	4.33013i	0.353553	−	0.612372i
$51$	1.04189	−	5.90885i	0.145894	−	0.827404i
$52$	−1.53209	+	1.28558i	−0.212463	+	0.178277i
$53$	−4.59627	−	3.85673i	−0.631346	−	0.529762i	0.270001	−	0.962860i	$-0.412976\pi$
$53$	−4.59627	−	3.85673i	−0.631346	−	0.529762i	−0.901347	+	0.433098i	$0.857420\pi$
$54$	0.868241	+	4.92404i	0.118153	+	0.670077i
$55$		0			0
$56$	−4.00000			−0.534522
$57$		0			0
$58$		0			0
$59$	−8.45723	−	3.07818i	−1.10104	−	0.400745i	−0.273339	−	0.961918i	$-0.588128\pi$
$59$	−8.45723	−	3.07818i	−1.10104	−	0.400745i	−0.827699	+	0.561173i	$0.810350\pi$
$60$		0			0
$61$	−3.06418	−	2.57115i	−0.392328	−	0.329202i	0.425191	−	0.905103i	$-0.360207\pi$
$61$	−3.06418	−	2.57115i	−0.392328	−	0.329202i	−0.817519	+	0.575901i	$0.804651\pi$
$62$	−1.53209	+	1.28558i	−0.194575	+	0.163268i
$63$	1.38919	−	7.87846i	0.175021	−	0.992593i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	2.81908	−	1.02606i	0.347004	−	0.126299i
$67$	−6.57785	+	2.39414i	−0.803612	+	0.292491i	−0.710982	−	0.703210i	$-0.751749\pi$
$67$	−6.57785	+	2.39414i	−0.803612	+	0.292491i	−0.0926296	+	0.995701i	$0.529527\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$	−3.00000	+	5.19615i	−0.361158	+	0.625543i
$70$		0			0
$71$	4.59627	−	3.85673i	0.545476	−	0.457709i	−0.327929	−	0.944702i	$-0.606351\pi$
$71$	4.59627	−	3.85673i	0.545476	−	0.457709i	0.873406	+	0.486993i	$0.161906\pi$
$72$	−1.53209	−	1.28558i	−0.180558	−	0.151506i
$73$	−0.173648	−	0.984808i	−0.0203240	−	0.115263i	0.972958	−	0.230982i	$-0.0741939\pi$
$73$	−0.173648	−	0.984808i	−0.0203240	−	0.115263i	−0.993282	+	0.115719i	$0.963083\pi$
$74$	−9.39693	−	3.42020i	−1.09237	−	0.397590i
$75$	5.00000			0.577350
$76$		0			0
$77$	−12.0000			−1.36753
$78$	−1.87939	−	0.684040i	−0.212798	−	0.0774523i
$79$	0.694593	+	3.93923i	0.0781478	+	0.443198i	0.998626	+	0.0524041i	$0.0166884\pi$
$79$	0.694593	+	3.93923i	0.0781478	+	0.443198i	−0.920478	+	0.390794i	$0.872200\pi$
$80$		0			0
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−1.56283	+	8.86327i	−0.172586	+	0.978784i
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	−0.936530	−	0.350588i	$-0.885982\pi$
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	0.771883	+	0.635764i	$0.219315\pi$
$84$	−2.00000	−	3.46410i	−0.218218	−	0.377964i
$85$		0			0
$86$	3.75877	−	1.36808i	0.405319	−	0.147524i
$87$		0			0
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	−1.04189	+	5.90885i	−0.110440	+	0.626336i	0.878467	+	0.477803i	$0.158567\pi$
$89$	−1.04189	+	5.90885i	−0.110440	+	0.626336i	−0.988907	+	0.148534i	$0.952545\pi$
$90$		0			0
$91$	6.12836	+	5.14230i	0.642426	+	0.539060i
$92$	−1.04189	−	5.90885i	−0.108624	−	0.616040i
$93$	−1.87939	−	0.684040i	−0.194883	−	0.0709317i
$94$		0			0
$95$		0			0
$96$	−1.00000			−0.102062
$97$	15.9748	+	5.81434i	1.62199	+	0.590357i	0.983760	−	0.179487i	$-0.0574437\pi$
$97$	15.9748	+	5.81434i	1.62199	+	0.590357i	0.638232	+	0.769844i	$0.279666\pi$
$98$	1.56283	+	8.86327i	0.157870	+	0.895325i
$99$	−4.59627	−	3.85673i	−0.461942	−	0.387616i
$100$	−3.83022	+	3.21394i	−0.383022	+	0.321394i
$101$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$101$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$102$	−3.00000	+	5.19615i	−0.297044	+	0.514496i
$103$	1.00000	+	1.73205i	0.0985329	+	0.170664i	0.911078	−	0.412235i	$-0.135252\pi$
$103$	1.00000	+	1.73205i	0.0985329	+	0.170664i	−0.812545	+	0.582899i	$0.801918\pi$
$104$	1.87939	−	0.684040i	0.184289	−	0.0670757i
$105$		0			0
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$	0.868241	−	4.92404i	0.0835465	−	0.473816i
$109$	12.2567	−	10.2846i	1.17398	−	0.985086i	0.173980	−	0.984749i	$-0.444337\pi$
$109$	12.2567	−	10.2846i	1.17398	−	0.985086i	1.00000		0.000337014i	$-0.000107275\pi$
$110$		0			0
$111$	−1.73648	−	9.84808i	−0.164820	−	0.934738i
$112$	3.75877	+	1.36808i	0.355170	+	0.129271i
$113$	−15.0000			−1.41108			−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000			−1.41108			−0.705541	+	0.708669i	$0.749296\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.694593	+	3.93923i	0.0642151	+	0.364182i
$118$	6.89440	+	5.78509i	0.634681	+	0.532561i
$119$	18.3851	−	15.4269i	1.68536	−	1.41418i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	2.00000	+	3.46410i	0.181071	+	0.313625i
$123$	−8.45723	+	3.07818i	−0.762563	+	0.277550i
$124$	1.87939	−	0.684040i	0.168774	−	0.0614286i
$125$		0			0
$126$	−4.00000	+	6.92820i	−0.356348	+	0.617213i
$127$	−0.347296	+	1.96962i	−0.0308176	+	0.174775i	−0.996332	−	0.0855756i	$-0.972727\pi$
$127$	−0.347296	+	1.96962i	−0.0308176	+	0.174775i	0.965514	+	0.260351i	$0.0838382\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	3.06418	+	2.57115i	0.269786	+	0.226377i
$130$		0			0
$131$	−8.45723	−	3.07818i	−0.738912	−	0.268942i	−0.0549797	−	0.998487i	$-0.517509\pi$
$131$	−8.45723	−	3.07818i	−0.738912	−	0.268942i	−0.683932	+	0.729546i	$0.739732\pi$
$132$	−3.00000			−0.261116
$133$		0			0
$134$	7.00000			0.604708
$135$		0			0
$136$	−1.04189	−	5.90885i	−0.0893413	−	0.506679i
$137$	6.89440	+	5.78509i	0.589028	+	0.494253i	0.887898	−	0.460040i	$-0.152165\pi$
$137$	6.89440	+	5.78509i	0.589028	+	0.494253i	−0.298870	+	0.954294i	$0.596610\pi$
$138$	4.59627	−	3.85673i	0.391260	−	0.328306i
$139$	1.91013	−	10.8329i	0.162015	−	0.918833i	−0.790074	−	0.613012i	$-0.789958\pi$
$139$	1.91013	−	10.8329i	0.162015	−	0.918833i	0.952089	−	0.305822i	$-0.0989311\pi$
$140$		0			0
$141$		0			0
$142$	−5.63816	+	2.05212i	−0.473144	+	0.172210i
$143$	5.63816	−	2.05212i	0.471486	−	0.171607i
$144$	1.00000	+	1.73205i	0.0833333	+	0.144338i
$145$		0			0
$146$	−0.173648	+	0.984808i	−0.0143712	+	0.0815033i
$147$	−6.89440	+	5.78509i	−0.568641	+	0.477146i
$148$	7.66044	+	6.42788i	0.629685	+	0.528368i
$149$	3.12567	+	17.7265i	0.256065	+	1.45221i	0.793325	+	0.608798i	$0.208348\pi$
$149$	3.12567	+	17.7265i	0.256065	+	1.45221i	−0.537260	+	0.843416i	$0.680541\pi$
$150$	−4.69846	−	1.71010i	−0.383628	−	0.139629i
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$	11.2763	+	4.10424i	0.908671	+	0.330729i
$155$		0			0
$156$	1.53209	+	1.28558i	0.122665	+	0.102928i
$157$	−12.2567	+	10.2846i	−0.978192	+	0.820801i	−0.983816	−	0.179184i	$-0.942654\pi$
$157$	−12.2567	+	10.2846i	−0.978192	+	0.820801i	0.00562361	+	0.999984i	$0.498210\pi$
$158$	0.694593	−	3.93923i	0.0552588	−	0.313388i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$		0			0
$161$	−22.5526	+	8.20848i	−1.77740	+	0.646919i
$162$	−0.939693	+	0.342020i	−0.0738292	+	0.0268716i
$163$	9.50000	+	16.4545i	0.744097	+	1.28881i	0.950615	+	0.310372i	$0.100454\pi$
$163$	9.50000	+	16.4545i	0.744097	+	1.28881i	−0.206518	+	0.978443i	$0.566213\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$	2.29813	−	1.92836i	0.178370	−	0.149670i
$167$	18.3851	+	15.4269i	1.42268	+	1.19377i	0.949886	+	0.312596i	$0.101199\pi$
$167$	18.3851	+	15.4269i	1.42268	+	1.19377i	0.472793	+	0.881174i	$0.343246\pi$
$168$	0.694593	+	3.93923i	0.0535890	+	0.303918i
$169$	8.45723	+	3.07818i	0.650556	+	0.236783i
$170$		0			0
$171$		0			0
$172$	−4.00000			−0.304997
$173$	5.63816	+	2.05212i	0.428661	+	0.156020i	0.547335	−	0.836913i	$-0.315642\pi$
$173$	5.63816	+	2.05212i	0.428661	+	0.156020i	−0.118674	+	0.992933i	$0.537864\pi$
$174$		0			0
$175$	15.3209	+	12.8558i	1.15815	+	0.971804i
$176$	2.29813	−	1.92836i	0.173228	−	0.145356i
$177$	−1.56283	+	8.86327i	−0.117470	+	0.666204i
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	0.983742	−	0.179585i	$-0.0574756\pi$
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	−0.647397	+	0.762153i	$0.724142\pi$
$180$		0			0
$181$	1.87939	−	0.684040i	0.139694	−	0.0508443i	−0.271227	−	0.962515i	$-0.587429\pi$
$181$	1.87939	−	0.684040i	0.139694	−	0.0508443i	0.410921	+	0.911671i	$0.365207\pi$
$182$	−4.00000	−	6.92820i	−0.296500	−	0.513553i
$183$	−2.00000	+	3.46410i	−0.147844	+	0.256074i
$184$	−1.04189	+	5.90885i	−0.0768091	+	0.435606i
$185$		0			0
$186$	1.53209	+	1.28558i	0.112338	+	0.0942629i
$187$	−3.12567	−	17.7265i	−0.228571	−	1.29629i
$188$		0			0
$189$	−20.0000			−1.45479
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$	0.939693	+	0.342020i	0.0678165	+	0.0246832i
$193$	−0.347296	−	1.96962i	−0.0249989	−	0.141776i	0.969754	−	0.244086i	$-0.0784878\pi$
$193$	−0.347296	−	1.96962i	−0.0249989	−	0.141776i	−0.994753	+	0.102310i	$0.967377\pi$
$194$	−13.0228	−	10.9274i	−0.934979	−	0.784541i
$195$		0			0
$196$	1.56283	−	8.86327i	0.111631	−	0.633091i
$197$	−9.00000	+	15.5885i	−0.641223	+	1.11063i	0.343937	+	0.938993i	$0.388239\pi$
$197$	−9.00000	+	15.5885i	−0.641223	+	1.11063i	−0.985160	+	0.171639i	$0.945094\pi$
$198$	3.00000	+	5.19615i	0.213201	+	0.369274i
$199$	9.39693	−	3.42020i	0.666130	−	0.242452i	0.0132495	−	0.999912i	$-0.495782\pi$
$199$	9.39693	−	3.42020i	0.666130	−	0.242452i	0.652881	+	0.757461i	$0.273560\pi$
$200$	4.69846	−	1.71010i	0.332232	−	0.120922i
$201$	3.50000	+	6.06218i	0.246871	+	0.427593i
$202$		0			0
$203$		0			0
$204$	4.59627	−	3.85673i	0.321803	−	0.270025i
$205$		0			0
$206$	−0.347296	−	1.96962i	−0.0241973	−	0.137230i
$207$	−11.2763	−	4.10424i	−0.783758	−	0.285265i
$208$	−2.00000			−0.138675
$209$		0			0
$210$		0			0
$211$	18.7939	+	6.84040i	1.29382	+	0.470913i	0.894980	−	0.446107i	$-0.147190\pi$
$211$	18.7939	+	6.84040i	1.29382	+	0.470913i	0.398842	+	0.917019i	$0.369412\pi$
$212$	−1.04189	−	5.90885i	−0.0715572	−	0.405821i
$213$	−4.59627	−	3.85673i	−0.314931	−	0.264258i
$214$		0			0
$215$		0			0
$216$	−2.50000	+	4.33013i	−0.170103	+	0.294628i
$217$	−4.00000	−	6.92820i	−0.271538	−	0.470317i
$218$	−15.0351	+	5.47232i	−1.01830	+	0.370632i
$219$	−0.939693	+	0.342020i	−0.0634985	+	0.0231116i
$220$		0			0
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$	−1.73648	+	9.84808i	−0.116545	+	0.660960i
$223$	−10.7246	+	8.99903i	−0.718174	+	0.602619i	−0.926879	−	0.375359i	$-0.877519\pi$
$223$	−10.7246	+	8.99903i	−0.718174	+	0.602619i	0.208706	+	0.977979i	$0.433075\pi$
$224$	−3.06418	−	2.57115i	−0.204734	−	0.171792i
$225$	1.73648	+	9.84808i	0.115765	+	0.656539i
$226$	14.0954	+	5.13030i	0.937611	+	0.341263i
$227$	−3.00000			−0.199117			−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000			−0.199117			−0.0995585	+	0.995032i	$0.531743\pi$
$228$		0			0
$229$	−16.0000			−1.05731			−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000			−1.05731			−0.528655	+	0.848837i	$0.677303\pi$
$230$		0			0
$231$	2.08378	+	11.8177i	0.137103	+	0.777547i
$232$		0			0
$233$	2.29813	−	1.92836i	0.150556	−	0.126331i	−0.564399	−	0.825502i	$-0.690892\pi$
$233$	2.29813	−	1.92836i	0.150556	−	0.126331i	0.714954	+	0.699171i	$0.246447\pi$
$234$	0.694593	−	3.93923i	0.0454069	−	0.257516i
$235$		0			0
$236$	−4.50000	−	7.79423i	−0.292925	−	0.507361i
$237$	3.75877	−	1.36808i	0.244158	−	0.0888664i
$238$	−22.5526	+	8.20848i	−1.46187	+	0.532077i
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	0.992195	−	0.124696i	$-0.0397955\pi$
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	−0.604087	+	0.796918i	$0.706462\pi$
$240$		0			0
$241$	−0.868241	+	4.92404i	−0.0559283	+	0.317185i	−0.999918	−	0.0127891i	$-0.995929\pi$
$241$	−0.868241	+	4.92404i	−0.0559283	+	0.317185i	0.943990	+	0.329974i	$0.107040\pi$
$242$	−1.53209	+	1.28558i	−0.0984864	+	0.0826399i
$243$	−12.2567	−	10.2846i	−0.786268	−	0.659758i
$244$	−0.694593	−	3.93923i	−0.0444667	−	0.252183i
$245$		0			0
$246$	9.00000			0.573819
$247$		0			0
$248$	−2.00000			−0.127000
$249$	2.81908	+	1.02606i	0.178652	+	0.0650239i
$250$		0			0
$251$	−2.29813	−	1.92836i	−0.145057	−	0.121717i	0.567372	−	0.823462i	$-0.307960\pi$
$251$	−2.29813	−	1.92836i	−0.145057	−	0.121717i	−0.712429	+	0.701745i	$0.752405\pi$
$252$	6.12836	−	5.14230i	0.386050	−	0.323935i
$253$	−3.12567	+	17.7265i	−0.196509	+	1.11446i
$254$	1.00000	−	1.73205i	0.0627456	−	0.108679i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	2.81908	−	1.02606i	0.175849	−	0.0640039i	−0.252595	−	0.967572i	$-0.581284\pi$
$257$	2.81908	−	1.02606i	0.175849	−	0.0640039i	0.428444	+	0.903568i	$0.359062\pi$
$258$	−2.00000	−	3.46410i	−0.124515	−	0.215666i
$259$	20.0000	−	34.6410i	1.24274	−	2.15249i
$260$		0			0
$261$		0			0
$262$	6.89440	+	5.78509i	0.425937	+	0.357404i
$263$	−2.08378	−	11.8177i	−0.128491	−	0.728710i	−0.979173	−	0.203029i	$-0.934922\pi$
$263$	−2.08378	−	11.8177i	−0.128491	−	0.728710i	0.850682	−	0.525681i	$-0.176190\pi$
$264$	2.81908	+	1.02606i	0.173502	+	0.0631497i
$265$		0			0
$266$		0			0
$267$	6.00000			0.367194
$268$	−6.57785	−	2.39414i	−0.401806	−	0.146245i
$269$	−2.08378	−	11.8177i	−0.127050	−	0.720537i	−0.980069	−	0.198657i	$-0.936342\pi$
$269$	−2.08378	−	11.8177i	−0.127050	−	0.720537i	0.853019	−	0.521880i	$-0.174769\pi$
$270$		0			0
$271$	−12.2567	+	10.2846i	−0.744542	+	0.624745i	−0.934053	−	0.357133i	$-0.883754\pi$
$271$	−12.2567	+	10.2846i	−0.744542	+	0.624745i	0.189511	+	0.981879i	$0.439310\pi$
$272$	−1.04189	+	5.90885i	−0.0631738	+	0.358276i
$273$	4.00000	−	6.92820i	0.242091	−	0.419314i
$274$	−4.50000	−	7.79423i	−0.271855	−	0.470867i
$275$	14.0954	−	5.13030i	0.849984	−	0.309369i
$276$	−5.63816	+	2.05212i	−0.339377	+	0.123523i
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	0.720473	−	0.693482i	$-0.243925\pi$
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	−0.960810	+	0.277207i	$0.910591\pi$
$278$	−5.50000	+	9.52628i	−0.329868	+	0.571348i
$279$	0.694593	−	3.93923i	0.0415842	−	0.235836i
$280$		0			0
$281$	−20.6832	−	17.3553i	−1.23386	−	1.03533i	−0.997979	−	0.0635455i	$-0.979759\pi$
$281$	−20.6832	−	17.3553i	−1.23386	−	1.03533i	−0.235877	−	0.971783i	$-0.575796\pi$
$282$		0			0
$283$	−4.69846	−	1.71010i	−0.279295	−	0.101655i	0.198575	−	0.980086i	$-0.436369\pi$
$283$	−4.69846	−	1.71010i	−0.279295	−	0.101655i	−0.477870	+	0.878431i	$0.658591\pi$
$284$	6.00000			0.356034
$285$		0			0
$286$	−6.00000			−0.354787
$287$	−33.8289	−	12.3127i	−1.99686	−	0.726797i
$288$	−0.347296	−	1.96962i	−0.0204646	−	0.116061i
$289$	14.5548	+	12.2130i	0.856167	+	0.718410i
$290$		0			0
$291$	2.95202	−	16.7417i	0.173050	−	0.981418i
$292$	0.500000	−	0.866025i	0.0292603	−	0.0506803i
$293$	12.0000	+	20.7846i	0.701047	+	1.21425i	0.968099	+	0.250568i	$0.0806172\pi$
$293$	12.0000	+	20.7846i	0.701047	+	1.21425i	−0.267052	+	0.963682i	$0.586049\pi$
$294$	8.45723	−	3.07818i	0.493236	−	0.179523i
$295$		0			0
$296$	−5.00000	−	8.66025i	−0.290619	−	0.503367i
$297$	−7.50000	+	12.9904i	−0.435194	+	0.753778i
$298$	3.12567	−	17.7265i	0.181065	−	1.02687i
$299$	9.19253	−	7.71345i	0.531618	−	0.446080i
$300$	3.83022	+	3.21394i	0.221138	+	0.185557i
$301$	2.77837	+	15.7569i	0.160143	+	0.908214i
$302$	−9.39693	−	3.42020i	−0.540732	−	0.196810i
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−11.2763	−	4.10424i	−0.644624	−	0.234624i
$307$	1.21554	+	6.89365i	0.0693744	+	0.393442i	0.999647	+	0.0265724i	$0.00845925\pi$
$307$	1.21554	+	6.89365i	0.0693744	+	0.393442i	−0.930273	+	0.366869i	$0.880430\pi$
$308$	−9.19253	−	7.71345i	−0.523793	−	0.439515i
$309$	1.53209	−	1.28558i	0.0871575	−	0.0731338i
$310$		0			0
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	−0.0301210	−	0.999546i	$-0.509589\pi$
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	0.880693	−	0.473688i	$-0.157077\pi$
$312$	−1.00000	−	1.73205i	−0.0566139	−	0.0980581i
$313$	17.8542	−	6.49838i	1.00918	−	0.367310i	0.216060	−	0.976380i	$-0.430679\pi$
$313$	17.8542	−	6.49838i	1.00918	−	0.367310i	0.793117	+	0.609070i	$0.208457\pi$
$314$	15.0351	−	5.47232i	0.848479	−	0.308821i
$315$		0			0
$316$	−2.00000	+	3.46410i	−0.112509	+	0.194871i
$317$	3.12567	−	17.7265i	0.175555	−	0.995622i	−0.761946	−	0.647640i	$-0.775756\pi$
$317$	3.12567	−	17.7265i	0.175555	−	0.995622i	0.937501	−	0.347982i	$-0.113133\pi$
$318$	4.59627	−	3.85673i	0.257746	−	0.216274i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	24.0000			1.33747
$323$		0			0
$324$	1.00000			0.0555556
$325$	−9.39693	−	3.42020i	−0.521248	−	0.189719i
$326$	−3.29932	−	18.7113i	−0.182732	−	1.03633i
$327$	−12.2567	−	10.2846i	−0.677798	−	0.568740i
$328$	−6.89440	+	5.78509i	−0.380680	+	0.319428i
$329$		0			0
$330$		0			0
$331$	2.50000	+	4.33013i	0.137412	+	0.238005i	0.926516	−	0.376254i	$-0.122788\pi$
$331$	2.50000	+	4.33013i	0.137412	+	0.238005i	−0.789104	+	0.614260i	$0.789455\pi$
$332$	−2.81908	+	1.02606i	−0.154717	+	0.0563124i
$333$	18.7939	−	6.84040i	1.02990	−	0.374852i
$334$	−12.0000	−	20.7846i	−0.656611	−	1.13728i
$335$		0			0
$336$	0.694593	−	3.93923i	0.0378931	−	0.214903i
$337$	−8.42649	+	7.07066i	−0.459020	+	0.385164i	−0.842770	−	0.538273i	$-0.819077\pi$
$337$	−8.42649	+	7.07066i	−0.459020	+	0.385164i	0.383750	+	0.923437i	$0.374632\pi$
$338$	−6.89440	−	5.78509i	−0.375006	−	0.314667i
$339$	2.60472	+	14.7721i	0.141469	+	0.802311i
$340$		0			0
$341$	−6.00000			−0.324918
$342$		0			0
$343$	−8.00000			−0.431959
$344$	3.75877	+	1.36808i	0.202659	+	0.0737620i
$345$		0			0
$346$	−4.59627	−	3.85673i	−0.247097	−	0.207339i
$347$	−6.89440	+	5.78509i	−0.370111	+	0.310560i	−0.808805	−	0.588076i	$-0.799885\pi$
$347$	−6.89440	+	5.78509i	−0.370111	+	0.310560i	0.438695	+	0.898636i	$0.355441\pi$
$348$		0			0
$349$	2.00000	−	3.46410i	0.107058	−	0.185429i	−0.807519	−	0.589841i	$-0.799190\pi$
$349$	2.00000	−	3.46410i	0.107058	−	0.185429i	0.914577	+	0.404412i	$0.132524\pi$
$350$	−10.0000	−	17.3205i	−0.534522	−	0.925820i
$351$	9.39693	−	3.42020i	0.501571	−	0.182557i
$352$	−2.81908	+	1.02606i	−0.150257	+	0.0546892i
$353$	−1.50000	−	2.59808i	−0.0798369	−	0.138282i	0.823343	−	0.567545i	$-0.192107\pi$
$353$	−1.50000	−	2.59808i	−0.0798369	−	0.138282i	−0.903179	+	0.429263i	$0.858773\pi$
$354$	4.50000	−	7.79423i	0.239172	−	0.414259i
$355$		0			0
$356$	−4.59627	+	3.85673i	−0.243602	+	0.204406i
$357$	−18.3851	−	15.4269i	−0.973041	−	0.816478i
$358$	−1.56283	−	8.86327i	−0.0825983	−	0.468438i
$359$	5.63816	+	2.05212i	0.297570	+	0.108307i	0.486491	−	0.873686i	$-0.338277\pi$
$359$	5.63816	+	2.05212i	0.297570	+	0.108307i	−0.188921	+	0.981992i	$0.560499\pi$
$360$		0			0
$361$		0			0
$362$	−2.00000			−0.105118
$363$	−1.87939	−	0.684040i	−0.0986421	−	0.0359028i
$364$	1.38919	+	7.87846i	0.0728131	+	0.412944i
$365$		0			0
$366$	3.06418	−	2.57115i	0.160167	−	0.134396i
$367$	−3.82026	+	21.6658i	−0.199416	+	1.13094i	0.706572	+	0.707641i	$0.250241\pi$
$367$	−3.82026	+	21.6658i	−0.199416	+	1.13094i	−0.905988	+	0.423303i	$0.860871\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$	−9.00000	−	15.5885i	−0.468521	−	0.811503i
$370$		0			0
$371$	−22.5526	+	8.20848i	−1.17087	+	0.426163i
$372$	−1.00000	−	1.73205i	−0.0518476	−	0.0898027i
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	−0.913147	−	0.407630i	$-0.866355\pi$
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	0.809591	+	0.586994i	$0.199689\pi$
$374$	−3.12567	+	17.7265i	−0.161624	+	0.916618i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	18.7939	+	6.84040i	0.966651	+	0.351832i
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$		0			0
$381$	2.00000			0.102463
$382$	−11.2763	−	4.10424i	−0.576946	−	0.209991i
$383$	6.25133	+	35.4531i	0.319428	+	1.81157i	0.546240	+	0.837629i	$0.316059\pi$
$383$	6.25133	+	35.4531i	0.319428	+	1.81157i	−0.226811	+	0.973939i	$0.572830\pi$
$384$	−0.766044	−	0.642788i	−0.0390920	−	0.0328021i
$385$		0			0
$386$	−0.347296	+	1.96962i	−0.0176769	+	0.100251i
$387$	−4.00000	+	6.92820i	−0.203331	+	0.352180i
$388$	8.50000	+	14.7224i	0.431522	+	0.747418i
$389$	33.8289	−	12.3127i	1.71520	−	0.624280i	0.717789	−	0.696261i	$-0.245154\pi$
$389$	33.8289	−	12.3127i	1.71520	−	0.624280i	0.997406	+	0.0719807i	$0.0229320\pi$
$390$		0			0
$391$	−18.0000	−	31.1769i	−0.910299	−	1.57668i
$392$	−4.50000	+	7.79423i	−0.227284	+	0.393668i
$393$	−1.56283	+	8.86327i	−0.0788345	+	0.447093i
$394$	13.7888	−	11.5702i	0.694670	−	0.582897i
$395$		0			0
$396$	−1.04189	−	5.90885i	−0.0523569	−	0.296931i
$397$	9.39693	+	3.42020i	0.471618	+	0.171655i	0.566885	−	0.823797i	$-0.308148\pi$
$397$	9.39693	+	3.42020i	0.471618	+	0.171655i	−0.0952671	+	0.995452i	$0.530371\pi$
$398$	−10.0000			−0.501255
$399$		0			0
$400$	−5.00000			−0.250000
$401$	−25.3717	−	9.23454i	−1.26700	−	0.461151i	−0.380889	−	0.924621i	$-0.624382\pi$
$401$	−25.3717	−	9.23454i	−1.26700	−	0.461151i	−0.886113	+	0.463469i	$0.846604\pi$
$402$	−1.21554	−	6.89365i	−0.0606255	−	0.343824i
$403$	3.06418	+	2.57115i	0.152638	+	0.128078i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−15.0000	−	25.9808i	−0.743522	−	1.28782i
$408$	−5.63816	+	2.05212i	−0.279130	+	0.101595i
$409$	4.69846	−	1.71010i	0.232324	−	0.0845590i	−0.223235	−	0.974765i	$-0.571662\pi$
$409$	4.69846	−	1.71010i	0.232324	−	0.0845590i	0.455559	+	0.890206i	$0.349439\pi$
$410$		0			0
$411$	4.50000	−	7.79423i	0.221969	−	0.384461i
$412$	−0.347296	+	1.96962i	−0.0171101	+	0.0970360i
$413$	−27.5776	+	23.1404i	−1.35700	+	1.13866i
$414$	9.19253	+	7.71345i	0.451788	+	0.379095i
$415$		0			0
$416$	1.87939	+	0.684040i	0.0921444	+	0.0335378i
$417$	−11.0000			−0.538672
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	1.73648	+	9.84808i	0.0846309	+	0.479966i	0.997436	+	0.0715695i	$0.0228008\pi$
$421$	1.73648	+	9.84808i	0.0846309	+	0.479966i	−0.912805	+	0.408396i	$0.866088\pi$
$422$	−15.3209	−	12.8558i	−0.745809	−	0.625808i
$423$		0			0
$424$	−1.04189	+	5.90885i	−0.0505986	+	0.286959i
$425$	−15.0000	+	25.9808i	−0.727607	+	1.26025i
$426$	3.00000	+	5.19615i	0.145350	+	0.251754i
$427$	−15.0351	+	5.47232i	−0.727599	+	0.264824i
$428$		0			0
$429$	−3.00000	−	5.19615i	−0.144841	−	0.250873i
$430$		0			0
$431$	5.20945	−	29.5442i	0.250930	−	1.42310i	−0.555377	−	0.831599i	$-0.687426\pi$
$431$	5.20945	−	29.5442i	0.250930	−	1.42310i	0.806307	−	0.591497i	$-0.201463\pi$
$432$	3.83022	−	3.21394i	0.184282	−	0.154631i
$433$	−19.9172	−	16.7125i	−0.957157	−	0.803150i	0.0233309	−	0.999728i	$-0.492573\pi$
$433$	−19.9172	−	16.7125i	−0.957157	−	0.803150i	−0.980488	+	0.196577i	$0.937017\pi$
$434$	1.38919	+	7.87846i	0.0666830	+	0.378178i
$435$		0			0
$436$	16.0000			0.766261
$437$		0			0
$438$	1.00000			0.0477818
$439$	13.1557	+	4.78828i	0.627887	+	0.228532i	0.636311	−	0.771432i	$-0.280459\pi$
$439$	13.1557	+	4.78828i	0.627887	+	0.228532i	−0.00842428	+	0.999965i	$0.502682\pi$
$440$		0			0
$441$	−13.7888	−	11.5702i	−0.656610	−	0.550961i
$442$	9.19253	−	7.71345i	0.437244	−	0.366891i
$443$	1.56283	−	8.86327i	0.0742525	−	0.421107i	−0.924910	−	0.380186i	$-0.875860\pi$
$443$	1.56283	−	8.86327i	0.0742525	−	0.421107i	0.999162	−	0.0409204i	$-0.0130290\pi$
$444$	5.00000	−	8.66025i	0.237289	−	0.410997i
$445$		0			0
$446$	13.1557	−	4.78828i	0.622940	−	0.226732i
$447$	16.9145	−	6.15636i	0.800027	−	0.291186i
$448$	2.00000	+	3.46410i	0.0944911	+	0.163663i
$449$	4.50000	−	7.79423i	0.212368	−	0.367832i	−0.740087	−	0.672511i	$-0.765216\pi$
$449$	4.50000	−	7.79423i	0.212368	−	0.367832i	0.952455	+	0.304679i	$0.0985491\pi$
$450$	1.73648	−	9.84808i	0.0818585	−	0.464243i
$451$	−20.6832	+	17.3553i	−0.973934	+	0.817228i
$452$	−11.4907	−	9.64181i	−0.540475	−	0.453513i
$453$	−1.73648	−	9.84808i	−0.0815870	−	0.462703i
$454$	2.81908	+	1.02606i	0.132306	+	0.0481554i
$455$		0			0
$456$		0			0
$457$	5.00000			0.233890			0.116945	−	0.993138i	$-0.462690\pi$
$457$	5.00000			0.233890			0.116945	+	0.993138i	$0.462690\pi$
$458$	15.0351	+	5.47232i	0.702543	+	0.255705i
$459$	−5.20945	−	29.5442i	−0.243156	−	1.37901i
$460$		0			0
$461$	4.59627	−	3.85673i	0.214069	−	0.179626i	−0.529447	−	0.848343i	$-0.677601\pi$
$461$	4.59627	−	3.85673i	0.214069	−	0.179626i	0.743517	+	0.668717i	$0.233156\pi$
$462$	2.08378	−	11.8177i	0.0969461	−	0.549809i
$463$	17.0000	−	29.4449i	0.790057	−	1.36842i	−0.135874	−	0.990726i	$-0.543384\pi$
$463$	17.0000	−	29.4449i	0.790057	−	1.36842i	0.925931	−	0.377693i	$-0.123282\pi$
$464$		0			0
$465$		0			0
$466$	−2.81908	+	1.02606i	−0.130591	+	0.0475313i
$467$	13.5000	+	23.3827i	0.624705	+	1.08202i	0.988598	+	0.150581i	$0.0481143\pi$
$467$	13.5000	+	23.3827i	0.624705	+	1.08202i	−0.363892	+	0.931441i	$0.618552\pi$
$468$	−2.00000	+	3.46410i	−0.0924500	+	0.160128i
$469$	−4.86215	+	27.5746i	−0.224513	+	1.27328i
$470$		0			0
$471$	12.2567	+	10.2846i	0.564759	+	0.473889i
$472$	1.56283	+	8.86327i	0.0719352	+	0.407965i
$473$	11.2763	+	4.10424i	0.518485	+	0.188713i
$474$	−4.00000			−0.183726
$475$		0			0
$476$	24.0000			1.10004
$477$	−11.2763	−	4.10424i	−0.516307	−	0.187920i
$478$	−2.08378	−	11.8177i	−0.0953098	−	0.540529i
$479$	27.5776	+	23.1404i	1.26005	+	1.05731i	0.995676	+	0.0928902i	$0.0296105\pi$
$479$	27.5776	+	23.1404i	1.26005	+	1.05731i	0.264376	+	0.964420i	$0.414834\pi$
$480$		0			0
$481$	−3.47296	+	19.6962i	−0.158354	+	0.898067i
$482$	2.50000	−	4.33013i	0.113872	−	0.197232i
$483$	12.0000	+	20.7846i	0.546019	+	0.945732i
$484$	1.87939	−	0.684040i	0.0854266	−	0.0310927i
$485$		0			0
$486$	8.00000	+	13.8564i	0.362887	+	0.628539i
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	−0.842479	−	0.538730i	$-0.818904\pi$
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	0.887793	+	0.460243i	$0.152238\pi$
$488$	−0.694593	+	3.93923i	−0.0314427	+	0.178321i
$489$	14.5548	−	12.2130i	0.658193	−	0.552289i
$490$		0			0
$491$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$491$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$492$	−8.45723	−	3.07818i	−0.381282	−	0.138775i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	1.87939	+	0.684040i	0.0843869	+	0.0307143i
$497$	−4.16756	−	23.6354i	−0.186940	−	1.06019i
$498$	−2.29813	−	1.92836i	−0.102982	−	0.0864120i
$499$	−19.1511	+	16.0697i	−0.857321	+	0.719378i	−0.961389	−	0.275192i	$-0.911259\pi$
$499$	−19.1511	+	16.0697i	−0.857321	+	0.719378i	0.104068	+	0.994570i	$0.466814\pi$
$500$		0			0
$501$	12.0000	−	20.7846i	0.536120	−	0.928588i
$502$	1.50000	+	2.59808i	0.0669483	+	0.115958i
$503$	−5.63816	+	2.05212i	−0.251393	+	0.0914995i	−0.464643	−	0.885498i	$-0.653817\pi$
$503$	−5.63816	+	2.05212i	−0.251393	+	0.0914995i	0.213250	+	0.976998i	$0.431595\pi$
$504$	−7.51754	+	2.73616i	−0.334858	+	0.121878i
$505$		0			0
$506$	9.00000	−	15.5885i	0.400099	−	0.692991i
$507$	1.56283	−	8.86327i	0.0694079	−	0.393632i
$508$	−1.53209	+	1.28558i	−0.0679755	+	0.0570382i
$509$	18.3851	+	15.4269i	0.814904	+	0.683785i	0.951773	−	0.306804i	$-0.0992595\pi$
$509$	18.3851	+	15.4269i	0.814904	+	0.683785i	−0.136869	+	0.990589i	$0.543704\pi$
$510$		0			0
$511$	−3.75877	−	1.36808i	−0.166278	−	0.0605203i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−3.00000			−0.132324
$515$		0			0
$516$	0.694593	+	3.93923i	0.0305777	+	0.173415i
$517$		0			0
$518$	−30.6418	+	25.7115i	−1.34632	+	1.12970i
$519$	1.04189	−	5.90885i	0.0457339	−	0.259370i
$520$		0			0
$521$	4.50000	+	7.79423i	0.197149	+	0.341471i	0.947603	−	0.319451i	$-0.103499\pi$
$521$	4.50000	+	7.79423i	0.197149	+	0.341471i	−0.750454	+	0.660922i	$0.770165\pi$
$522$		0			0
$523$	−26.3114	+	9.57656i	−1.15052	+	0.418754i	−0.845701	−	0.533657i	$-0.820817\pi$
$523$	−26.3114	+	9.57656i	−1.15052	+	0.418754i	−0.304816	+	0.952411i	$0.598595\pi$
$524$	−4.50000	−	7.79423i	−0.196583	−	0.340492i
$525$	10.0000	−	17.3205i	0.436436	−	0.755929i
$526$	−2.08378	+	11.8177i	−0.0908570	+	0.515276i
$527$	9.19253	−	7.71345i	0.400433	−	0.336003i
$528$	−2.29813	−	1.92836i	−0.100013	−	0.0839212i
$529$	2.25743	+	12.8025i	0.0981490	+	0.556630i
$530$		0			0
$531$	−18.0000			−0.781133
$532$		0			0
$533$	18.0000			0.779667
$534$	−5.63816	−	2.05212i	−0.243987	−	0.0888040i
$535$		0			0
$536$	5.36231	+	4.49951i	0.231617	+	0.194349i
$537$	6.89440	−	5.78509i	0.297515	−	0.249645i
$538$	−2.08378	+	11.8177i	−0.0898381	+	0.509497i
$539$	−13.5000	+	23.3827i	−0.581486	+	1.00716i
$540$		0			0
$541$	−41.3465	+	15.0489i	−1.77762	+	0.647002i	−0.777795	+	0.628518i	$0.783662\pi$
$541$	−41.3465	+	15.0489i	−1.77762	+	0.647002i	−0.999829	+	0.0184837i	$0.994116\pi$
$542$	15.0351	−	5.47232i	0.645812	−	0.235056i
$543$	−1.00000	−	1.73205i	−0.0429141	−	0.0743294i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$		0			0
$546$	−6.12836	+	5.14230i	−0.262269	+	0.220070i
$547$	3.06418	+	2.57115i	0.131015	+	0.109934i	0.705940	−	0.708271i	$-0.250525\pi$
$547$	3.06418	+	2.57115i	0.131015	+	0.109934i	−0.574926	+	0.818206i	$0.694969\pi$
$548$	1.56283	+	8.86327i	0.0667609	+	0.378620i
$549$	−7.51754	−	2.73616i	−0.320841	−	0.116777i
$550$	−15.0000			−0.639602
$551$		0			0
$552$	6.00000			0.255377
$553$	15.0351	+	5.47232i	0.639357	+	0.232707i
$554$	1.38919	+	7.87846i	0.0590208	+	0.334724i
$555$		0			0
$556$	8.42649	−	7.07066i	0.357363	−	0.299863i
$557$	4.16756	−	23.6354i	0.176585	−	1.00146i	−0.759713	−	0.650258i	$-0.774661\pi$
$557$	4.16756	−	23.6354i	0.176585	−	1.00146i	0.936298	−	0.351205i	$-0.114228\pi$
$558$	−2.00000	+	3.46410i	−0.0846668	+	0.146647i
$559$	−4.00000	−	6.92820i	−0.169182	−	0.293032i
$560$		0			0
$561$	−16.9145	+	6.15636i	−0.714129	+	0.259922i
$562$	13.5000	+	23.3827i	0.569463	+	0.986339i
$563$	−10.5000	+	18.1865i	−0.442522	+	0.766471i	−0.997876	−	0.0651433i	$-0.979250\pi$
$563$	−10.5000	+	18.1865i	−0.442522	+	0.766471i	0.555354	+	0.831614i	$0.312583\pi$
$564$		0			0
$565$		0			0
$566$	3.83022	+	3.21394i	0.160996	+	0.135092i
$567$	−0.694593	−	3.93923i	−0.0291702	−	0.165432i
$568$	−5.63816	−	2.05212i	−0.236572	−	0.0861051i
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$		0			0
$571$	−7.00000			−0.292941			−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000			−0.292941			−0.146470	+	0.989215i	$0.546791\pi$
$572$	5.63816	+	2.05212i	0.235743	+	0.0858035i
$573$	−2.08378	−	11.8177i	−0.0870511	−	0.493691i
$574$	27.5776	+	23.1404i	1.15107	+	0.965860i
$575$	22.9813	−	19.2836i	0.958388	−	0.804183i
$576$	−0.347296	+	1.96962i	−0.0144707	+	0.0820673i
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	0.728535	+	0.685009i	$0.240202\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$	−1.87939	+	0.684040i	−0.0781046	+	0.0284277i
$580$		0			0
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$	−8.50000	+	14.7224i	−0.352336	+	0.610264i
$583$	−3.12567	+	17.7265i	−0.129452	+	0.734158i
$584$	−0.766044	+	0.642788i	−0.0316991	+	0.0265987i
$585$		0			0
$586$	−4.16756	−	23.6354i	−0.172160	−	0.976369i
$587$	11.2763	+	4.10424i	0.465423	+	0.169400i	0.564078	−	0.825722i	$-0.309232\pi$
$587$	11.2763	+	4.10424i	0.465423	+	0.169400i	−0.0986548	+	0.995122i	$0.531454\pi$
$588$	−9.00000			−0.371154
$589$		0			0
$590$		0			0
$591$	16.9145	+	6.15636i	0.695768	+	0.253239i
$592$	1.73648	+	9.84808i	0.0713690	+	0.404753i
$593$	−16.0869	−	13.4985i	−0.660611	−	0.554319i	0.249659	−	0.968334i	$-0.419682\pi$
$593$	−16.0869	−	13.4985i	−0.660611	−	0.554319i	−0.910270	+	0.414015i	$0.864126\pi$
$594$	11.4907	−	9.64181i	0.471468	−	0.395608i
$595$		0			0
$596$	−9.00000	+	15.5885i	−0.368654	+	0.638528i
$597$	−5.00000	−	8.66025i	−0.204636	−	0.354441i
$598$	−11.2763	+	4.10424i	−0.461123	+	0.167835i
$599$	−5.63816	+	2.05212i	−0.230369	+	0.0838474i	−0.454625	−	0.890683i	$-0.650227\pi$
$599$	−5.63816	+	2.05212i	−0.230369	+	0.0838474i	0.224257	+	0.974530i	$0.428005\pi$
$600$	−2.50000	−	4.33013i	−0.102062	−	0.176777i
$601$	−6.50000	+	11.2583i	−0.265141	+	0.459237i	−0.967600	−	0.252486i	$-0.918752\pi$
$601$	−6.50000	+	11.2583i	−0.265141	+	0.459237i	0.702460	+	0.711723i	$0.252085\pi$
$602$	2.77837	−	15.7569i	0.113238	−	0.642204i
$603$	−10.7246	+	8.99903i	−0.436740	+	0.366469i
$604$	7.66044	+	6.42788i	0.311699	+	0.261547i
$605$		0			0
$606$		0			0
$607$	−20.0000			−0.811775			−0.405887	−	0.913923i	$-0.633038\pi$
$607$	−20.0000			−0.811775			−0.405887	+	0.913923i	$0.633038\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	9.19253	+	7.71345i	0.371586	+	0.311798i
$613$	1.53209	−	1.28558i	0.0618805	−	0.0519239i	−0.611323	−	0.791381i	$-0.709362\pi$
$613$	1.53209	−	1.28558i	0.0618805	−	0.0519239i	0.673203	+	0.739457i	$0.264918\pi$
$614$	1.21554	−	6.89365i	0.0490551	−	0.278205i
$615$		0			0
$616$	6.00000	+	10.3923i	0.241747	+	0.418718i
$617$	−2.81908	+	1.02606i	−0.113492	+	0.0413076i	−0.398142	−	0.917324i	$-0.630345\pi$
$617$	−2.81908	+	1.02606i	−0.113492	+	0.0413076i	0.284650	+	0.958631i	$0.408123\pi$
$618$	−1.87939	+	0.684040i	−0.0756000	+	0.0275161i
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	0.903416	−	0.428765i	$-0.141051\pi$
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	−0.823029	+	0.567999i	$0.807718\pi$
$620$		0			0
$621$	−5.20945	+	29.5442i	−0.209048	+	1.18557i
$622$	−22.9813	+	19.2836i	−0.921468	+	0.773203i
$623$	18.3851	+	15.4269i	0.736582	+	0.618066i
$624$	0.347296	+	1.96962i	0.0139030	+	0.0788477i
$625$	−23.4923	−	8.55050i	−0.939693	−	0.342020i
$626$	−19.0000			−0.759393
$627$		0			0
$628$	−16.0000			−0.638470
$629$	56.3816	+	20.5212i	2.24808	+	0.818234i
$630$		0			0
$631$	−21.4492	−	17.9981i	−0.853881	−	0.716491i	0.106760	−	0.994285i	$-0.465952\pi$
$631$	−21.4492	−	17.9981i	−0.853881	−	0.716491i	−0.960641	+	0.277794i	$0.910397\pi$
$632$	3.06418	−	2.57115i	0.121886	−	0.102275i
$633$	3.47296	−	19.6962i	0.138038	−	0.782852i
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$		0			0
$636$	−5.63816	+	2.05212i	−0.223567	+	0.0813719i
$637$	16.9145	−	6.15636i	0.670176	−	0.243924i
$638$		0			0
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$		0			0
$641$	29.8757	−	25.0687i	1.18002	−	0.990155i	0.180042	−	0.983659i	$-0.442377\pi$
$641$	29.8757	−	25.0687i	1.18002	−	0.990155i	0.999979	−	0.00649579i	$-0.00206769\pi$
$642$		0			0
$643$	−7.46687	−	42.3467i	−0.294465	−	1.66999i	−0.669370	−	0.742929i	$-0.733436\pi$
$643$	−7.46687	−	42.3467i	−0.294465	−	1.66999i	0.374905	−	0.927063i	$-0.377675\pi$
$644$	−22.5526	−	8.20848i	−0.888698	−	0.323460i
$645$		0			0
$646$		0			0
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$	−0.939693	−	0.342020i	−0.0369146	−	0.0134358i
$649$	4.68850	+	26.5898i	0.184040	+	1.04374i
$650$	7.66044	+	6.42788i	0.300467	+	0.252122i
$651$	−6.12836	+	5.14230i	−0.240189	+	0.201543i
$652$	−3.29932	+	18.7113i	−0.129211	+	0.732793i
$653$	6.00000	−	10.3923i	0.234798	−	0.406682i	−0.724416	−	0.689363i	$-0.757890\pi$
$653$	6.00000	−	10.3923i	0.234798	−	0.406682i	0.959214	+	0.282681i	$0.0912238\pi$
$654$	8.00000	+	13.8564i	0.312825	+	0.541828i
$655$		0			0
$656$	8.45723	−	3.07818i	0.330199	−	0.120183i
$657$	−1.00000	−	1.73205i	−0.0390137	−	0.0675737i
$658$		0			0
$659$	−6.25133	+	35.4531i	−0.243517	+	1.38106i	0.580393	+	0.814336i	$0.302899\pi$
$659$	−6.25133	+	35.4531i	−0.243517	+	1.38106i	−0.823911	+	0.566720i	$0.808212\pi$
$660$		0			0
$661$	30.6418	+	25.7115i	1.19183	+	1.00006i	0.999826	+	0.0186669i	$0.00594222\pi$
$661$	30.6418	+	25.7115i	1.19183	+	1.00006i	0.192001	+	0.981395i	$0.438502\pi$
$662$	−0.868241	−	4.92404i	−0.0337451	−	0.191378i
$663$	11.2763	+	4.10424i	0.437936	+	0.159396i
$664$	3.00000			0.116423
$665$		0			0
$666$	−20.0000			−0.774984
$667$		0			0
$668$	4.16756	+	23.6354i	0.161248	+	0.914481i
$669$	10.7246	+	8.99903i	0.414638	+	0.347922i
$670$		0			0
$671$	−2.08378	+	11.8177i	−0.0804434	+	0.456217i
$672$	−2.00000	+	3.46410i	−0.0771517	+	0.133631i
$673$	7.00000	+	12.1244i	0.269830	+	0.467360i	0.968818	−	0.247774i	$-0.0796991\pi$
$673$	7.00000	+	12.1244i	0.269830	+	0.467360i	−0.698988	+	0.715134i	$0.746366\pi$
$674$	10.3366	−	3.76222i	0.398152	−	0.144915i
$675$	23.4923	−	8.55050i	0.904220	−	0.329109i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	0.107772	+	0.994176i	$0.465628\pi$
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	−0.914867	+	0.403755i	$0.867705\pi$
$678$	2.60472	−	14.7721i	0.100034	−	0.567320i
$679$	52.0910	−	43.7096i	1.99907	−	1.67742i
$680$		0			0
$681$	0.520945	+	2.95442i	0.0199626	+	0.113214i
$682$	5.63816	+	2.05212i	0.215896	+	0.0785798i
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$		0			0
$686$	7.51754	+	2.73616i	0.287021	+	0.104467i
$687$	2.77837	+	15.7569i	0.106001	+	0.601164i
$688$	−3.06418	−	2.57115i	−0.116821	−	0.0980242i
$689$	9.19253	−	7.71345i	0.350208	−	0.293859i
$690$		0			0
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	0.0555386	+	0.998457i	$0.482312\pi$
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	−0.892458	+	0.451130i	$0.851021\pi$
$692$	3.00000	+	5.19615i	0.114043	+	0.197528i
$693$	−22.5526	+	8.20848i	−0.856703	+	0.311815i
$694$	8.45723	−	3.07818i	0.321032	−	0.116846i
$695$		0			0
$696$		0			0
$697$	9.37700	−	53.1796i	0.355179	−	2.01432i
$698$	−3.06418	+	2.57115i	−0.115981	+	0.0973195i
$699$	−2.29813	−	1.92836i	−0.0869234	−	0.0729374i
$700$	3.47296	+	19.6962i	0.131266	+	0.744445i
$701$	22.5526	+	8.20848i	0.851801	+	0.310030i	0.730774	−	0.682619i	$-0.239159\pi$
$701$	22.5526	+	8.20848i	0.851801	+	0.310030i	0.121026	+	0.992649i	$0.461381\pi$
$702$	−10.0000			−0.377426
$703$		0			0
$704$	3.00000			0.113067
$705$		0			0
$706$	0.520945	+	2.95442i	0.0196060	+	0.111191i
$707$		0			0
$708$	−6.89440	+	5.78509i	−0.259107	+	0.217417i
$709$	2.43107	−	13.7873i	0.0913009	−	0.517793i	−0.904517	−	0.426437i	$-0.859769\pi$
$709$	2.43107	−	13.7873i	0.0913009	−	0.517793i	0.995818	−	0.0913564i	$-0.0291202\pi$
$710$		0			0
$711$	4.00000	+	6.92820i	0.150012	+	0.259828i
$712$	5.63816	−	2.05212i	0.211299	−	0.0769065i
$713$	−11.2763	+	4.10424i	−0.422301	+	0.153705i
$714$	12.0000	+	20.7846i	0.449089	+	0.777844i
$715$		0			0
$716$	−1.56283	+	8.86327i	−0.0584058	+	0.331236i
$717$	9.19253	−	7.71345i	0.343301	−	0.288064i
$718$	−4.59627	−	3.85673i	−0.171531	−	0.143932i
$719$	5.20945	+	29.5442i	0.194280	+	1.10181i	0.913441	+	0.406971i	$0.133415\pi$
$719$	5.20945	+	29.5442i	0.194280	+	1.10181i	−0.719162	+	0.694843i	$0.755474\pi$
$720$		0			0
$721$	8.00000			0.297936
$722$		0			0
$723$	5.00000			0.185952
$724$	1.87939	+	0.684040i	0.0698468	+	0.0254222i
$725$		0			0
$726$	1.53209	+	1.28558i	0.0568612	+	0.0477122i
$727$	24.5134	−	20.5692i	0.909153	−	0.762870i	−0.0628051	−	0.998026i	$-0.520005\pi$
$727$	24.5134	−	20.5692i	0.909153	−	0.762870i	0.971958	+	0.235156i	$0.0755602\pi$
$728$	1.38919	−	7.87846i	0.0514866	−	0.291995i
$729$	−6.50000	+	11.2583i	−0.240741	+	0.416975i
$730$		0			0
$731$	−22.5526	+	8.20848i	−0.834139	+	0.303602i
$732$	−3.75877	+	1.36808i	−0.138928	+	0.0505657i
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$	11.0000	−	19.0526i	0.406017	−	0.703243i
$735$		0			0
$736$	−4.59627	+	3.85673i	−0.169421	+	0.142161i
$737$	16.0869	+	13.4985i	0.592570	+	0.497225i
$738$	3.12567	+	17.7265i	0.115057	+	0.652523i
$739$	−32.8892	−	11.9707i	−1.20985	−	0.440350i	−0.343198	−	0.939263i	$-0.611510\pi$
$739$	−32.8892	−	11.9707i	−1.20985	−	0.440350i	−0.866652	+	0.498913i	$0.833733\pi$
$740$		0			0
$741$		0			0
$742$	24.0000			0.881068
$743$	−16.9145	−	6.15636i	−0.620532	−	0.225855i	0.0125734	−	0.999921i	$-0.495998\pi$
$743$	−16.9145	−	6.15636i	−0.620532	−	0.225855i	−0.633105	+	0.774066i	$0.718220\pi$
$744$	0.347296	+	1.96962i	0.0127325	+	0.0722096i
$745$		0			0
$746$	3.06418	−	2.57115i	0.112188	−	0.0941365i
$747$	−1.04189	+	5.90885i	−0.0381207	+	0.216193i
$748$	9.00000	−	15.5885i	0.329073	−	0.569970i
$749$		0			0
$750$		0			0
$751$	35.7083	−	12.9968i	1.30302	−	0.474259i	0.405038	−	0.914300i	$-0.367258\pi$
$751$	35.7083	−	12.9968i	1.30302	−	0.474259i	0.897978	+	0.440041i	$0.145036\pi$
$752$		0			0
$753$	−1.50000	+	2.59808i	−0.0546630	+	0.0946792i
$754$		0			0
$755$		0			0
$756$	−15.3209	−	12.8558i	−0.557215	−	0.467559i
$757$	−1.73648	−	9.84808i	−0.0631135	−	0.357934i	−0.999966	−	0.00821050i	$-0.997386\pi$
$757$	−1.73648	−	9.84808i	−0.0631135	−	0.357934i	0.936853	−	0.349724i	$-0.113725\pi$
$758$	−26.3114	−	9.57656i	−0.955673	−	0.347836i
$759$	18.0000			0.653359
$760$		0			0
$761$	−39.0000			−1.41375			−0.706874	−	0.707339i	$-0.749895\pi$
$761$	−39.0000			−1.41375			−0.706874	+	0.707339i	$0.749895\pi$
$762$	−1.87939	−	0.684040i	−0.0680829	−	0.0247802i
$763$	−11.1135	−	63.0277i	−0.402335	−	2.28176i
$764$	9.19253	+	7.71345i	0.332574	+	0.279063i
$765$		0			0
$766$	6.25133	−	35.4531i	0.225870	−	1.28097i
$767$	9.00000	−	15.5885i	0.324971	−	0.562867i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−1.87939	+	0.684040i	−0.0677724	+	0.0246671i	−0.375684	−	0.926748i	$-0.622592\pi$
$769$	−1.87939	+	0.684040i	−0.0677724	+	0.0246671i	0.307912	+	0.951415i	$0.400370\pi$
$770$		0			0
$771$	−1.50000	−	2.59808i	−0.0540212	−	0.0935674i
$772$	1.00000	−	1.73205i	0.0359908	−	0.0623379i
$773$	8.33511	−	47.2708i	0.299793	−	1.70021i	−0.347262	−	0.937768i	$-0.612888\pi$
$773$	8.33511	−	47.2708i	0.299793	−	1.70021i	0.647055	−	0.762443i	$-0.276000\pi$
$774$	6.12836	−	5.14230i	0.220279	−	0.184836i
$775$	7.66044	+	6.42788i	0.275171	+	0.230896i
$776$	−2.95202	−	16.7417i	−0.105971	−	0.600993i
$777$	−37.5877	−	13.6808i	−1.34845	−	0.490796i
$778$	−36.0000			−1.29066
$779$		0			0
$780$		0			0
$781$	−16.9145	−	6.15636i	−0.605247	−	0.220292i
$782$	6.25133	+	35.4531i	0.223547	+	1.26780i
$783$		0			0
$784$	6.89440	−	5.78509i	0.246229	−	0.206610i
$785$		0			0
$786$	4.50000	−	7.79423i	0.160510	−	0.278011i
$787$	−3.50000	−	6.06218i	−0.124762	−	0.216093i	0.796878	−	0.604140i	$-0.206483\pi$
$787$	−3.50000	−	6.06218i	−0.124762	−	0.216093i	−0.921640	+	0.388047i	$0.873150\pi$
$788$	−16.9145	+	6.15636i	−0.602553	+	0.219311i
$789$	−11.2763	+	4.10424i	−0.401447	+	0.146115i
$790$		0			0
$791$	−30.0000	+	51.9615i	−1.06668	+	1.84754i
$792$	−1.04189	+	5.90885i	−0.0370219	+	0.209962i
$793$	6.12836	−	5.14230i	0.217624	−	0.182608i
$794$	−7.66044	−	6.42788i	−0.271859	−	0.228117i
$795$		0			0
$796$	9.39693	+	3.42020i	0.333065	+	0.121226i
$797$	−6.00000			−0.212531			−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000			−0.212531			−0.106265	+	0.994338i	$0.533889\pi$
$798$		0			0
$799$		0			0
$800$	4.69846	+	1.71010i	0.166116	+	0.0604612i
$801$	2.08378	+	11.8177i	0.0736267	+	0.417558i
$802$	20.6832	+	17.3553i	0.730349	+	0.612836i
$803$	−2.29813	+	1.92836i	−0.0810994	+	0.0680504i
$804$	−1.21554	+	6.89365i	−0.0428687	+	0.243120i
$805$		0			0
$806$	−2.00000	−	3.46410i	−0.0704470	−	0.122018i
$807$	−11.2763	+	4.10424i	−0.396945	+	0.144476i
$808$		0			0
$809$	−22.5000	−	38.9711i	−0.791058	−	1.37015i	−0.925312	−	0.379206i	$-0.876197\pi$
$809$	−22.5000	−	38.9711i	−0.791058	−	1.37015i	0.134255	−	0.990947i	$-0.457136\pi$
$810$		0			0
$811$	2.77837	−	15.7569i	0.0975618	−	0.553300i	−0.896370	−	0.443306i	$-0.853806\pi$
$811$	2.77837	−	15.7569i	0.0975618	−	0.553300i	0.993932	−	0.109995i	$-0.0350833\pi$
$812$		0			0
$813$	12.2567	+	10.2846i	0.429862	+	0.360697i
$814$	5.20945	+	29.5442i	0.182591	+	1.03552i
$815$		0			0
$816$	6.00000			0.210042
$817$		0			0
$818$	−5.00000			−0.174821
$819$	15.0351	+	5.47232i	0.525368	+	0.191218i
$820$		0			0
$821$	13.7888	+	11.5702i	0.481232	+	0.403802i	0.850872	−	0.525373i	$-0.176074\pi$
$821$	13.7888	+	11.5702i	0.481232	+	0.403802i	−0.369639	+	0.929175i	$0.620519\pi$
$822$	−6.89440	+	5.78509i	−0.240470	+	0.201778i
$823$	2.43107	−	13.7873i	0.0847419	−	0.480595i	−0.912670	−	0.408697i	$-0.865983\pi$
$823$	2.43107	−	13.7873i	0.0847419	−	0.480595i	0.997412	−	0.0718982i	$-0.0229057\pi$
$824$	1.00000	−	1.73205i	0.0348367	−	0.0603388i
$825$	−7.50000	−	12.9904i	−0.261116	−	0.452267i
$826$	33.8289	−	12.3127i	1.17706	−	0.428415i
$827$	−36.6480	+	13.3388i	−1.27438	+	0.463835i	−0.888568	−	0.458744i	$-0.848299\pi$
$827$	−36.6480	+	13.3388i	−1.27438	+	0.463835i	−0.385808	+	0.922579i	$0.626077\pi$
$828$	−6.00000	−	10.3923i	−0.208514	−	0.361158i
$829$	22.0000	−	38.1051i	0.764092	−	1.32345i	−0.176634	−	0.984277i	$-0.556521\pi$
$829$	22.0000	−	38.1051i	0.764092	−	1.32345i	0.940726	−	0.339169i	$-0.110146\pi$
$830$		0			0
$831$	−6.12836	+	5.14230i	−0.212590	+	0.178384i
$832$	−1.53209	−	1.28558i	−0.0531156	−	0.0445693i
$833$	−9.37700	−	53.1796i	−0.324894	−	1.84256i
$834$	10.3366	+	3.76222i	0.357928	+	0.130275i
$835$		0			0
$836$		0			0
$837$	−10.0000			−0.345651
$838$	11.2763	+	4.10424i	0.389534	+	0.141779i
$839$	2.08378	+	11.8177i	0.0719400	+	0.407992i	0.999418	+	0.0341142i	$0.0108610\pi$
$839$	2.08378	+	11.8177i	0.0719400	+	0.407992i	−0.927478	+	0.373878i	$0.878028\pi$
$840$		0			0
$841$	−22.2153	+	18.6408i	−0.766044	+	0.642788i
$842$	1.73648	−	9.84808i	0.0598431	−	0.339387i
$843$	−13.5000	+	23.3827i	−0.464965	+	0.805342i
$844$	10.0000	+	17.3205i	0.344214	+	0.596196i
$845$		0			0
$846$		0			0
$847$	−4.00000	−	6.92820i	−0.137442	−	0.238056i
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$	−0.868241	+	4.92404i	−0.0297980	+	0.168993i
$850$	22.9813	−	19.2836i	0.788253	−	0.661423i
$851$	−45.9627	−	38.5673i	−1.57558	−	1.32207i
$852$	−1.04189	−	5.90885i	−0.0356945	−	0.202434i
$853$	20.6732	+	7.52444i	0.707838	+	0.257632i	0.670754	−	0.741680i	$-0.265971\pi$
$853$	20.6732	+	7.52444i	0.707838	+	0.257632i	0.0370844	+	0.999312i	$0.488193\pi$
$854$	16.0000			0.547509
$855$		0			0
$856$		0			0
$857$	−2.81908	−	1.02606i	−0.0962979	−	0.0350496i	0.293422	−	0.955983i	$-0.405206\pi$
$857$	−2.81908	−	1.02606i	−0.0962979	−	0.0350496i	−0.389720	+	0.920933i	$0.627428\pi$
$858$	1.04189	+	5.90885i	0.0355695	+	0.201725i
$859$	−32.9399	−	27.6399i	−1.12390	−	0.943060i	−0.125101	−	0.992144i	$-0.539925\pi$
$859$	−32.9399	−	27.6399i	−1.12390	−	0.943060i	−0.998795	+	0.0490840i	$0.984370\pi$
$860$		0			0
$861$	−6.25133	+	35.4531i	−0.213045	+	1.20824i
$862$	−15.0000	+	25.9808i	−0.510902	+	0.884908i
$863$	9.00000	+	15.5885i	0.306364	+	0.530637i	0.977564	−	0.210639i	$-0.0675543\pi$
$863$	9.00000	+	15.5885i	0.306364	+	0.530637i	−0.671200	+	0.741276i	$0.734221\pi$
$864$	−4.69846	+	1.71010i	−0.159845	+	0.0581788i
$865$		0			0
$866$	13.0000	+	22.5167i	0.441758	+	0.765147i
$867$	9.50000	−	16.4545i	0.322637	−	0.558824i
$868$	1.38919	−	7.87846i	0.0471520	−	0.267412i
$869$	9.19253	−	7.71345i	0.311835	−	0.261661i
$870$		0			0
$871$	−2.43107	−	13.7873i	−0.0823738	−	0.467165i
$872$	−15.0351	−	5.47232i	−0.509152	−	0.185316i
$873$	34.0000			1.15073
$874$		0			0
$875$		0			0
$876$	−0.939693	−	0.342020i	−0.0317493	−	0.0115558i
$877$	−3.47296	−	19.6962i	−0.117274	−	0.665092i	−0.985599	−	0.169097i	$-0.945915\pi$
$877$	−3.47296	−	19.6962i	−0.117274	−	0.665092i	0.868326	−	0.495994i	$-0.165196\pi$
$878$	−10.7246	−	8.99903i	−0.361938	−	0.303702i
$879$	18.3851	−	15.4269i	0.620113	−	0.520337i
$880$		0			0
$881$	4.50000	−	7.79423i	0.151609	−	0.262594i	−0.780210	−	0.625517i	$-0.784888\pi$
$881$	4.50000	−	7.79423i	0.151609	−	0.262594i	0.931819	+	0.362923i	$0.118221\pi$
$882$	9.00000	+	15.5885i	0.303046	+	0.524891i
$883$	17.8542	−	6.49838i	0.600840	−	0.218688i	−0.0236503	−	0.999720i	$-0.507529\pi$
$883$	17.8542	−	6.49838i	0.600840	−	0.218688i	0.624491	+	0.781032i	$0.285307\pi$
$884$	−11.2763	+	4.10424i	−0.379263	+	0.138041i
$885$		0			0
$886$	−4.50000	+	7.79423i	−0.151180	+	0.261852i
$887$	−8.33511	+	47.2708i	−0.279866	+	1.58720i	0.443203	+	0.896421i	$0.353842\pi$
$887$	−8.33511	+	47.2708i	−0.279866	+	1.58720i	−0.723069	+	0.690776i	$0.757269\pi$
$888$	−7.66044	+	6.42788i	−0.257068	+	0.215705i
$889$	6.12836	+	5.14230i	0.205538	+	0.172467i
$890$		0			0
$891$	−2.81908	−	1.02606i	−0.0944427	−	0.0343743i
$892$	−14.0000			−0.468755
$893$		0			0
$894$	−18.0000			−0.602010
$895$		0			0
$896$	−0.694593	−	3.93923i	−0.0232047	−	0.131600i
$897$	−9.19253	−	7.71345i	−0.306930	−	0.257545i
$898$	−6.89440	+	5.78509i	−0.230069	+	0.193051i
$899$		0			0
$900$	−5.00000	+	8.66025i	−0.166667	+	0.288675i
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$	25.3717	−	9.23454i	0.844785	−	0.307477i
$903$	15.0351	−	5.47232i	0.500336	−	0.182107i
$904$	7.50000	+	12.9904i	0.249446	+	0.432054i
$905$		0			0
$906$	−1.73648	+	9.84808i	−0.0576907	+	0.327180i
$907$	−13.0228	+	10.9274i	−0.432414	+	0.362838i	−0.832861	−	0.553481i	$-0.813299\pi$
$907$	−13.0228	+	10.9274i	−0.432414	+	0.362838i	0.400448	+	0.916319i	$0.368855\pi$
$908$	−2.29813	−	1.92836i	−0.0762662	−	0.0639950i
$909$		0			0
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	9.00000			0.297857
$914$	−4.69846	−	1.71010i	−0.155411	−	0.0565651i
$915$		0			0
$916$	−12.2567	−	10.2846i	−0.404973	−	0.339813i
$917$	−27.5776	+	23.1404i	−0.910693	+	0.764162i
$918$	−5.20945	+	29.5442i	−0.171937	+	0.975105i
$919$	5.00000	−	8.66025i	0.164935	−	0.285675i	−0.771697	−	0.635990i	$-0.780592\pi$
$919$	5.00000	−	8.66025i	0.164935	−	0.285675i	0.936632	+	0.350315i	$0.113925\pi$
$920$		0			0
$921$	6.57785	−	2.39414i	0.216747	−	0.0788896i
$922$	−5.63816	+	2.05212i	−0.185683	+	0.0675830i
$923$	6.00000	+	10.3923i	0.197492	+	0.342067i
$924$	−6.00000	+	10.3923i	−0.197386	+	0.341882i
$925$	−8.68241	+	49.2404i	−0.285476	+	1.61901i
$926$	−26.0455	+	21.8548i	−0.855909	+	0.718193i
$927$	3.06418	+	2.57115i	0.100641	+	0.0844477i
$928$		0			0
$929$	2.81908	+	1.02606i	0.0924909	+	0.0336640i	0.387851	−	0.921722i	$-0.373217\pi$
$929$	2.81908	+	1.02606i	0.0924909	+	0.0336640i	−0.295360	+	0.955386i	$0.595440\pi$
$930$		0			0
$931$		0			0
$932$	3.00000			0.0982683
$933$	−28.1908	−	10.2606i	−0.922925	−	0.335917i
$934$	−4.68850	−	26.5898i	−0.153412	−	0.870045i
$935$		0			0
$936$	3.06418	−	2.57115i	0.100156	−	0.0840407i
$937$	6.07769	−	34.4683i	0.198549	−	1.12603i	−0.708723	−	0.705487i	$-0.750729\pi$
$937$	6.07769	−	34.4683i	0.198549	−	1.12603i	0.907273	−	0.420543i	$-0.138160\pi$
$938$	14.0000	−	24.2487i	0.457116	−	0.791748i
$939$	−9.50000	−	16.4545i	−0.310021	−	0.536972i
$940$		0			0
$941$	−39.4671	+	14.3648i	−1.28659	+	0.468281i	−0.892606	−	0.450837i	$-0.851126\pi$
$941$	−39.4671	+	14.3648i	−1.28659	+	0.468281i	−0.393984	+	0.919117i	$0.628903\pi$
$942$	−8.00000	−	13.8564i	−0.260654	−	0.451466i
$943$	−27.0000	+	46.7654i	−0.879241	+	1.52289i
$944$	1.56283	−	8.86327i	0.0508659	−	0.288475i
$945$		0			0
$946$	−9.19253	−	7.71345i	−0.298875	−	0.250786i
$947$	10.4189	+	59.0885i	0.338568	+	1.92012i	0.388679	+	0.921373i	$0.372932\pi$
$947$	10.4189	+	59.0885i	0.338568	+	1.92012i	−0.0501101	+	0.998744i	$0.515957\pi$
$948$	3.75877	+	1.36808i	0.122079	+	0.0444332i
$949$	2.00000			0.0649227
$950$		0			0
$951$	−18.0000			−0.583690
$952$	−22.5526	−	8.20848i	−0.730935	−	0.266038i
$953$	2.60472	+	14.7721i	0.0843752	+	0.478516i	0.997490	+	0.0708124i	$0.0225592\pi$
$953$	2.60472	+	14.7721i	0.0843752	+	0.478516i	−0.913114	+	0.407703i	$0.866330\pi$
$954$	9.19253	+	7.71345i	0.297619	+	0.249732i
$955$		0			0
$956$	−2.08378	+	11.8177i	−0.0673942	+	0.382212i
$957$		0			0
$958$	−18.0000	−	31.1769i	−0.581554	−	1.00728i
$959$	33.8289	−	12.3127i	1.09239	−	0.397599i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	10.0000	−	17.3205i	0.322413	−	0.558436i
$963$		0			0
$964$	−3.83022	+	3.21394i	−0.123363	+	0.103514i
$965$		0			0
$966$	−4.16756	−	23.6354i	−0.134089	−	0.760456i
$967$	31.9495	+	11.6287i	1.02743	+	0.373953i	0.800101	−	0.599865i	$-0.204779\pi$
$967$	31.9495	+	11.6287i	1.02743	+	0.373953i	0.227327	+	0.973818i	$0.427001\pi$
$968$	−2.00000			−0.0642824
$969$		0			0
$970$		0			0
$971$	19.7335	+	7.18242i	0.633280	+	0.230495i	0.638658	−	0.769491i	$-0.279490\pi$
$971$	19.7335	+	7.18242i	0.633280	+	0.230495i	−0.00537853	+	0.999986i	$0.501712\pi$
$972$	−2.77837	−	15.7569i	−0.0891163	−	0.505404i
$973$	−33.7060	−	28.2827i	−1.08056	−	0.906700i
$974$	−1.53209	+	1.28558i	−0.0490913	+	0.0411925i
$975$	−1.73648	+	9.84808i	−0.0556119	+	0.315391i
$976$	2.00000	−	3.46410i	0.0640184	−	0.110883i
$977$	16.5000	+	28.5788i	0.527882	+	0.914318i	0.999472	+	0.0325001i	$0.0103469\pi$
$977$	16.5000	+	28.5788i	0.527882	+	0.914318i	−0.471590	+	0.881818i	$0.656320\pi$
$978$	−17.8542	+	6.49838i	−0.570913	+	0.207795i
$979$	16.9145	−	6.15636i	0.540589	−	0.196758i
$980$		0			0
$981$	16.0000	−	27.7128i	0.510841	−	0.884802i
$982$		0			0
$983$	−18.3851	+	15.4269i	−0.586393	+	0.492042i	−0.887039	−	0.461694i	$-0.847242\pi$
$983$	−18.3851	+	15.4269i	−0.586393	+	0.492042i	0.300647	+	0.953736i	$0.402797\pi$
$984$	6.89440	+	5.78509i	0.219785	+	0.184422i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	24.0000			0.763156
$990$		0			0
$991$	−1.38919	−	7.87846i	−0.0441289	−	0.250268i	0.954761	−	0.297374i	$-0.0961110\pi$
$991$	−1.38919	−	7.87846i	−0.0441289	−	0.250268i	−0.998890	+	0.0471069i	$0.985000\pi$
$992$	−1.53209	−	1.28558i	−0.0486439	−	0.0408171i
$993$	3.83022	−	3.21394i	0.121548	−	0.101991i
$994$	−4.16756	+	23.6354i	−0.132187	+	0.749669i
$995$		0			0
$996$	1.50000	+	2.59808i	0.0475293	+	0.0823232i
$997$	3.75877	−	1.36808i	0.119041	−	0.0433275i	−0.281813	−	0.959469i	$-0.590936\pi$
$997$	3.75877	−	1.36808i	0.119041	−	0.0433275i	0.400854	+	0.916142i	$0.368713\pi$
$998$	23.4923	−	8.55050i	0.743636	−	0.270661i
$999$	−25.0000	−	43.3013i	−0.790965	−	1.36999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.i.99.1		6
19.2	odd	18		722.2.e.j.415.1		6
19.3	odd	18		722.2.e.j.245.1		6
19.4	even	9		722.2.c.b.653.1		2
19.5	even	9	inner	722.2.e.i.423.1		6
19.6	even	9		722.2.c.b.429.1		2
19.7	even	3	inner	722.2.e.i.595.1		6
19.8	odd	6		722.2.e.j.389.1		6
19.9	even	9		722.2.a.d.1.1		1
19.10	odd	18		722.2.a.c.1.1		1
19.11	even	3	inner	722.2.e.i.389.1		6
19.12	odd	6		722.2.e.j.595.1		6
19.13	odd	18		38.2.c.a.11.1	yes	2
19.14	odd	18		722.2.e.j.423.1		6
19.15	odd	18		38.2.c.a.7.1	✓	2
19.16	even	9	inner	722.2.e.i.245.1		6
19.17	even	9	inner	722.2.e.i.415.1		6
19.18	odd	2		722.2.e.j.99.1		6
57.29	even	18		6498.2.a.s.1.1		1
57.32	even	18		342.2.g.b.163.1		2
57.47	odd	18		6498.2.a.e.1.1		1
57.53	even	18		342.2.g.b.235.1		2
76.15	even	18		304.2.i.c.273.1		2
76.47	odd	18		5776.2.a.n.1.1		1
76.51	even	18		304.2.i.c.49.1		2
76.67	even	18		5776.2.a.g.1.1		1
95.13	even	36		950.2.j.e.49.1		4
95.32	even	36		950.2.j.e.49.2		4
95.34	odd	18		950.2.e.d.501.1		2
95.53	even	36		950.2.j.e.349.2		4
95.72	even	36		950.2.j.e.349.1		4
95.89	odd	18		950.2.e.d.201.1		2
152.13	odd	18		1216.2.i.h.961.1		2
152.51	even	18		1216.2.i.d.961.1		2
152.53	odd	18		1216.2.i.h.577.1		2
152.91	even	18		1216.2.i.d.577.1		2
228.167	odd	18		2736.2.s.m.577.1		2
228.203	odd	18		2736.2.s.m.1873.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.a.7.1	✓	2	19.15	odd	18
38.2.c.a.11.1	yes	2	19.13	odd	18
304.2.i.c.49.1		2	76.51	even	18
304.2.i.c.273.1		2	76.15	even	18
342.2.g.b.163.1		2	57.32	even	18
342.2.g.b.235.1		2	57.53	even	18
722.2.a.c.1.1		1	19.10	odd	18
722.2.a.d.1.1		1	19.9	even	9
722.2.c.b.429.1		2	19.6	even	9
722.2.c.b.653.1		2	19.4	even	9
722.2.e.i.99.1		6	1.1	even	1	trivial
722.2.e.i.245.1		6	19.16	even	9	inner
722.2.e.i.389.1		6	19.11	even	3	inner
722.2.e.i.415.1		6	19.17	even	9	inner
722.2.e.i.423.1		6	19.5	even	9	inner
722.2.e.i.595.1		6	19.7	even	3	inner
722.2.e.j.99.1		6	19.18	odd	2
722.2.e.j.245.1		6	19.3	odd	18
722.2.e.j.389.1		6	19.8	odd	6
722.2.e.j.415.1		6	19.2	odd	18
722.2.e.j.423.1		6	19.14	odd	18
722.2.e.j.595.1		6	19.12	odd	6
950.2.e.d.201.1		2	95.89	odd	18
950.2.e.d.501.1		2	95.34	odd	18
950.2.j.e.49.1		4	95.13	even	36
950.2.j.e.49.2		4	95.32	even	36
950.2.j.e.349.1		4	95.72	even	36
950.2.j.e.349.2		4	95.53	even	36
1216.2.i.d.577.1		2	152.91	even	18
1216.2.i.d.961.1		2	152.51	even	18
1216.2.i.h.577.1		2	152.53	odd	18
1216.2.i.h.961.1		2	152.13	odd	18
2736.2.s.m.577.1		2	228.167	odd	18
2736.2.s.m.1873.1		2	228.203	odd	18
5776.2.a.g.1.1		1	76.67	even	18
5776.2.a.n.1.1		1	76.47	odd	18
6498.2.a.e.1.1		1	57.47	odd	18
6498.2.a.s.1.1		1	57.29	even	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.173648 + 0.984808i) q^{6} +(2.00000 - 3.46410i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.87939 - 0.684040i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.173648 + 0.984808i) q^{6} +(2.00000 - 3.46410i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.87939 - 0.684040i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.347296 + 1.96962i) q^{13} +(-3.06418 + 2.57115i) q^{14} +(0.173648 + 0.984808i) q^{16} +(5.63816 + 2.05212i) q^{17} -2.00000 q^{18} +(-3.75877 - 1.36808i) q^{21} +(0.520945 + 2.95442i) q^{22} +(-4.59627 - 3.85673i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(-0.868241 + 4.92404i) q^{25} +(1.00000 - 1.73205i) q^{26} +(-2.50000 - 4.33013i) q^{27} +(3.75877 - 1.36808i) q^{28} +(1.00000 - 1.73205i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-2.29813 + 1.92836i) q^{33} +(-4.59627 - 3.85673i) q^{34} +(1.87939 + 0.684040i) q^{36} +10.0000 q^{37} +2.00000 q^{39} +(-1.56283 - 8.86327i) q^{41} +(3.06418 + 2.57115i) q^{42} +(-3.06418 + 2.57115i) q^{43} +(0.520945 - 2.95442i) q^{44} +(3.00000 + 5.19615i) q^{46} +(0.939693 - 0.342020i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(2.50000 - 4.33013i) q^{50} +(1.04189 - 5.90885i) q^{51} +(-1.53209 + 1.28558i) q^{52} +(-4.59627 - 3.85673i) q^{53} +(0.868241 + 4.92404i) q^{54} -4.00000 q^{56} +(-8.45723 - 3.07818i) q^{59} +(-3.06418 - 2.57115i) q^{61} +(-1.53209 + 1.28558i) q^{62} +(1.38919 - 7.87846i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.81908 - 1.02606i) q^{66} +(-6.57785 + 2.39414i) q^{67} +(3.00000 + 5.19615i) q^{68} +(-3.00000 + 5.19615i) q^{69} +(4.59627 - 3.85673i) q^{71} +(-1.53209 - 1.28558i) q^{72} +(-0.173648 - 0.984808i) q^{73} +(-9.39693 - 3.42020i) q^{74} +5.00000 q^{75} -12.0000 q^{77} +(-1.87939 - 0.684040i) q^{78} +(0.694593 + 3.93923i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-1.56283 + 8.86327i) q^{82} +(-1.50000 + 2.59808i) q^{83} +(-2.00000 - 3.46410i) q^{84} +(3.75877 - 1.36808i) q^{86} +(-1.50000 + 2.59808i) q^{88} +(-1.04189 + 5.90885i) q^{89} +(6.12836 + 5.14230i) q^{91} +(-1.04189 - 5.90885i) q^{92} +(-1.87939 - 0.684040i) q^{93} -1.00000 q^{96} +(15.9748 + 5.81434i) q^{97} +(1.56283 + 8.86327i) q^{98} +(-4.59627 - 3.85673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q + 12 * q^7 - 3 * q^8	\( 6 q + 12 q^{7} - 3 q^{8} - 9 q^{11} + 3 q^{12} - 12 q^{18} + 6 q^{26} - 15 q^{27} + 6 q^{31} + 60 q^{37} + 12 q^{39} + 18 q^{46} - 27 q^{49} + 15 q^{50} - 24 q^{56} - 3 q^{64} + 18 q^{68} - 18 q^{69} + 30 q^{75} - 72 q^{77} - 9 q^{83} - 12 q^{84} - 9 q^{88} - 6 q^{96}+O(q^{100}) \) 6 * q + 12 * q^7 - 3 * q^8 - 9 * q^11 + 3 * q^12 - 12 * q^18 + 6 * q^26 - 15 * q^27 + 6 * q^31 + 60 * q^37 + 12 * q^39 + 18 * q^46 - 27 * q^49 + 15 * q^50 - 24 * q^56 - 3 * q^64 + 18 * q^68 - 18 * q^69 + 30 * q^75 - 72 * q^77 - 9 * q^83 - 12 * q^84 - 9 * q^88 - 6 * q^96

Introduction

L-functions

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