LMFDB - Embedded newform 400.2.j.d.43.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(43,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("400.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.j (of order $4$, degree $2$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.8
Root			$1.41323 + 0.0526497i$ of defining polynomial
Character	$\chi$	$=$	400.43
Dual form			400.2.j.d.307.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31641 - 0.516777i) q^{2} -1.28110i q^{3} +(1.46588 - 1.36058i) q^{4} +(-0.662041 - 1.68645i) q^{6} +(1.13975 - 1.13975i) q^{7} +(1.22659 - 2.54862i) q^{8} +1.35879 q^{9} +O(q^{10})$	\(q+(1.31641 - 0.516777i) q^{2} -1.28110i q^{3} +(1.46588 - 1.36058i) q^{4} +(-0.662041 - 1.68645i) q^{6} +(1.13975 - 1.13975i) q^{7} +(1.22659 - 2.54862i) q^{8} +1.35879 q^{9} +(-2.32204 + 2.32204i) q^{11} +(-1.74304 - 1.87794i) q^{12} -1.36502 q^{13} +(0.911384 - 2.08938i) q^{14} +(0.297625 - 3.98891i) q^{16} +(-5.25380 + 5.25380i) q^{17} +(1.78873 - 0.702192i) q^{18} +(3.69752 - 3.69752i) q^{19} +(-1.46013 - 1.46013i) q^{21} +(-1.85678 + 4.25673i) q^{22} +(0.911118 + 0.911118i) q^{23} +(-3.26503 - 1.57138i) q^{24} +(-1.79693 + 0.705412i) q^{26} -5.58403i q^{27} +(0.120015 - 3.22146i) q^{28} +(2.37343 + 2.37343i) q^{29} +0.242577i q^{31} +(-1.66958 - 5.40486i) q^{32} +(2.97475 + 2.97475i) q^{33} +(-4.20112 + 9.63121i) q^{34} +(1.99183 - 1.84875i) q^{36} +3.34494 q^{37} +(2.95666 - 6.77825i) q^{38} +1.74872i q^{39} +2.66956i q^{41} +(-2.67669 - 1.16757i) q^{42} -9.04874 q^{43} +(-0.244509 + 6.56316i) q^{44} +(1.67025 + 0.728562i) q^{46} +(7.87820 + 7.87820i) q^{47} +(-5.11018 - 0.381287i) q^{48} +4.40194i q^{49} +(6.73063 + 6.73063i) q^{51} +(-2.00096 + 1.85723i) q^{52} +5.80113i q^{53} +(-2.88570 - 7.35089i) q^{54} +(-1.50679 - 4.30279i) q^{56} +(-4.73688 - 4.73688i) q^{57} +(4.35095 + 1.89788i) q^{58} +(-5.91474 - 5.91474i) q^{59} +(-6.67404 + 6.67404i) q^{61} +(0.125358 + 0.319332i) q^{62} +(1.54868 - 1.54868i) q^{63} +(-4.99096 - 6.25222i) q^{64} +(5.45328 + 2.37872i) q^{66} +4.54673 q^{67} +(-0.553222 + 14.8497i) q^{68} +(1.16723 - 1.16723i) q^{69} +15.4389 q^{71} +(1.66668 - 3.46305i) q^{72} +(-1.49307 + 1.49307i) q^{73} +(4.40332 - 1.72859i) q^{74} +(0.389347 - 10.4509i) q^{76} +5.29308i q^{77} +(0.903701 + 2.30204i) q^{78} +10.3024 q^{79} -3.07731 q^{81} +(1.37957 + 3.51424i) q^{82} -3.26589i q^{83} +(-4.12701 - 0.153751i) q^{84} +(-11.9119 + 4.67618i) q^{86} +(3.04060 - 3.04060i) q^{87} +(3.06981 + 8.76618i) q^{88} -9.77206 q^{89} +(-1.55578 + 1.55578i) q^{91} +(2.57524 + 0.0959403i) q^{92} +0.310765 q^{93} +(14.4422 + 6.29969i) q^{94} +(-6.92415 + 2.13889i) q^{96} +(1.63587 - 1.63587i) q^{97} +(2.27482 + 5.79477i) q^{98} +(-3.15516 + 3.15516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9	$ 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9} - 2 q^{11} - 4 q^{12} + 12 q^{14} + 6 q^{17} - 16 q^{18} + 2 q^{19} - 16 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 16 q^{26} + 4 q^{28} - 14 q^{29} + 4 q^{32} + 8 q^{33} - 28 q^{34} - 4 q^{36} - 8 q^{37} - 16 q^{38} - 28 q^{42} + 44 q^{43} + 44 q^{44} + 12 q^{46} + 38 q^{47} - 60 q^{48} + 8 q^{51} + 40 q^{52} - 4 q^{54} + 20 q^{56} - 24 q^{57} + 20 q^{58} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 16 q^{64} + 4 q^{66} - 12 q^{67} - 36 q^{68} + 32 q^{69} + 24 q^{71} + 36 q^{72} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 84 q^{78} + 16 q^{79} + 2 q^{81} + 28 q^{82} - 24 q^{84} - 36 q^{86} - 24 q^{87} + 96 q^{88} - 12 q^{89} - 52 q^{92} - 16 q^{93} + 28 q^{94} - 40 q^{96} - 18 q^{97} - 32 q^{98} - 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9 - 2 * q^11 - 4 * q^12 + 12 * q^14 + 6 * q^17 - 16 * q^18 + 2 * q^19 - 16 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 16 * q^26 + 4 * q^28 - 14 * q^29 + 4 * q^32 + 8 * q^33 - 28 * q^34 - 4 * q^36 - 8 * q^37 - 16 * q^38 - 28 * q^42 + 44 * q^43 + 44 * q^44 + 12 * q^46 + 38 * q^47 - 60 * q^48 + 8 * q^51 + 40 * q^52 - 4 * q^54 + 20 * q^56 - 24 * q^57 + 20 * q^58 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 16 * q^64 + 4 * q^66 - 12 * q^67 - 36 * q^68 + 32 * q^69 + 24 * q^71 + 36 * q^72 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 84 * q^78 + 16 * q^79 + 2 * q^81 + 28 * q^82 - 24 * q^84 - 36 * q^86 - 24 * q^87 + 96 * q^88 - 12 * q^89 - 52 * q^92 - 16 * q^93 + 28 * q^94 - 40 * q^96 - 18 * q^97 - 32 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.31641	−	0.516777i	0.930844	−	0.365417i
$2$	1.31641	−	0.516777i	0.930844	−	0.365417i
$3$		−	1.28110i		−	0.739642i	−0.929103	−	0.369821i	$-0.879419\pi$
$3$		−	1.28110i		−	0.739642i	0.929103	−	0.369821i	$-0.120581\pi$
$4$	1.46588	−	1.36058i	0.732941	−	0.680292i
$5$		0			0
$5$		0			0
$6$	−0.662041	−	1.68645i	−0.270277	−	0.688491i
$7$	1.13975	−	1.13975i	0.430785	−	0.430785i	−0.458111	−	0.888895i	$-0.651474\pi$
$7$	1.13975	−	1.13975i	0.430785	−	0.430785i	0.888895	+	0.458111i	$0.151474\pi$
$8$	1.22659	−	2.54862i	0.433664	−	0.901074i
$9$	1.35879			0.452930
$10$		0			0
$11$	−2.32204	+	2.32204i	−0.700120	+	0.700120i	−0.964436	−	0.264316i	$-0.914854\pi$
$11$	−2.32204	+	2.32204i	−0.700120	+	0.700120i	0.264316	+	0.964436i	$0.414854\pi$
$12$	−1.74304	−	1.87794i	−0.503172	−	0.542114i
$13$	−1.36502			−0.378589			−0.189294	−	0.981920i	$-0.560620\pi$
$13$	−1.36502			−0.378589			−0.189294	+	0.981920i	$0.560620\pi$
$14$	0.911384	−	2.08938i	0.243578	−	0.558409i
$15$		0			0
$16$	0.297625	−	3.98891i	0.0744064	−	0.997228i
$17$	−5.25380	+	5.25380i	−1.27423	+	1.27423i	−0.330389	+	0.943845i	$0.607180\pi$
$17$	−5.25380	+	5.25380i	−1.27423	+	1.27423i	−0.943845	+	0.330389i	$0.892820\pi$
$18$	1.78873	−	0.702192i	0.421608	−	0.165508i
$19$	3.69752	−	3.69752i	0.848269	−	0.848269i	−0.141648	−	0.989917i	$-0.545240\pi$
$19$	3.69752	−	3.69752i	0.848269	−	0.848269i	0.989917	+	0.141648i	$0.0452403\pi$
$20$		0			0
$21$	−1.46013	−	1.46013i	−0.318626	−	0.318626i
$22$	−1.85678	+	4.25673i	−0.395867	+	0.907538i
$23$	0.911118	+	0.911118i	0.189981	+	0.189981i	0.795688	−	0.605707i	$-0.207110\pi$
$23$	0.911118	+	0.911118i	0.189981	+	0.189981i	−0.605707	+	0.795688i	$0.707110\pi$
$24$	−3.26503	−	1.57138i	−0.666472	−	0.320756i
$25$		0			0
$26$	−1.79693	+	0.705412i	−0.352407	+	0.138343i
$27$		−	5.58403i		−	1.07465i
$28$	0.120015	−	3.22146i	0.0226807	−	0.608799i
$29$	2.37343	+	2.37343i	0.440736	+	0.440736i	0.892259	−	0.451524i	$-0.149119\pi$
$29$	2.37343	+	2.37343i	0.440736	+	0.440736i	−0.451524	+	0.892259i	$0.649119\pi$
$30$		0			0
$31$			0.242577i			0.0435681i	0.999763	+	0.0217841i	$0.00693463\pi$
$31$			0.242577i			0.0435681i	−0.999763	+	0.0217841i	$0.993065\pi$
$32$	−1.66958	−	5.40486i	−0.295143	−	0.955453i
$33$	2.97475	+	2.97475i	0.517838	+	0.517838i
$34$	−4.20112	+	9.63121i	−0.720487	+	1.65174i
$35$		0			0
$36$	1.99183	−	1.84875i	0.331971	−	0.308125i
$37$	3.34494			0.549905			0.274953	−	0.961458i	$-0.411338\pi$
$37$	3.34494			0.549905			0.274953	+	0.961458i	$0.411338\pi$
$38$	2.95666	−	6.77825i	0.479634	−	1.09958i
$39$			1.74872i			0.280020i
$40$		0			0
$41$			2.66956i			0.416915i	0.978031	+	0.208457i	$0.0668442\pi$
$41$			2.66956i			0.416915i	−0.978031	+	0.208457i	$0.933156\pi$
$42$	−2.67669	−	1.16757i	−0.413023	−	0.180160i
$43$	−9.04874			−1.37992			−0.689960	−	0.723847i	$-0.742372\pi$
$43$	−9.04874			−1.37992			−0.689960	+	0.723847i	$0.742372\pi$
$44$	−0.244509	+	6.56316i	−0.0368611	+	0.989433i
$45$		0			0
$46$	1.67025	+	0.728562i	0.246265	+	0.107421i
$47$	7.87820	+	7.87820i	1.14915	+	1.14915i	0.986719	+	0.162435i	$0.0519348\pi$
$47$	7.87820	+	7.87820i	1.14915	+	1.14915i	0.162435	+	0.986719i	$0.448065\pi$
$48$	−5.11018	−	0.381287i	−0.737591	−	0.0550340i
$49$			4.40194i			0.628849i
$50$		0			0
$51$	6.73063	+	6.73063i	0.942476	+	0.942476i
$52$	−2.00096	+	1.85723i	−0.277483	+	0.257551i
$53$			5.80113i			0.796846i	0.917202	+	0.398423i	$0.130442\pi$
$53$			5.80113i			0.796846i	−0.917202	+	0.398423i	$0.869558\pi$
$54$	−2.88570	−	7.35089i	−0.392694	−	1.00033i
$55$		0			0
$56$	−1.50679	−	4.30279i	−0.201353	−	0.574985i
$57$	−4.73688	−	4.73688i	−0.627415	−	0.627415i
$58$	4.35095	+	1.89788i	0.571308	+	0.249204i
$59$	−5.91474	−	5.91474i	−0.770033	−	0.770033i	0.208079	−	0.978112i	$-0.433279\pi$
$59$	−5.91474	−	5.91474i	−0.770033	−	0.770033i	−0.978112	+	0.208079i	$0.933279\pi$
$60$		0			0
$61$	−6.67404	+	6.67404i	−0.854523	+	0.854523i	−0.990686	−	0.136163i	$-0.956523\pi$
$61$	−6.67404	+	6.67404i	−0.854523	+	0.854523i	0.136163	+	0.990686i	$0.456523\pi$
$62$	0.125358	+	0.319332i	0.0159205	+	0.0405551i
$63$	1.54868	−	1.54868i	0.195116	−	0.195116i
$64$	−4.99096	−	6.25222i	−0.623870	−	0.781528i
$65$		0			0
$66$	5.45328	+	2.37872i	0.671253	+	0.292800i
$67$	4.54673			0.555471			0.277736	−	0.960658i	$-0.410416\pi$
$67$	4.54673			0.555471			0.277736	+	0.960658i	$0.410416\pi$
$68$	−0.553222	+	14.8497i	−0.0670881	+	1.80079i
$69$	1.16723	−	1.16723i	0.140518	−	0.140518i
$70$		0			0
$71$	15.4389			1.83226			0.916128	−	0.400885i	$-0.131297\pi$
$71$	15.4389			1.83226			0.916128	+	0.400885i	$0.131297\pi$
$72$	1.66668	−	3.46305i	0.196420	−	0.408124i
$73$	−1.49307	+	1.49307i	−0.174750	+	0.174750i	−0.789063	−	0.614313i	$-0.789433\pi$
$73$	−1.49307	+	1.49307i	−0.174750	+	0.174750i	0.614313	+	0.789063i	$0.289433\pi$
$74$	4.40332	−	1.72859i	0.511876	−	0.200944i
$75$		0			0
$76$	0.389347	−	10.4509i	0.0446611	−	1.19880i
$77$			5.29308i			0.603202i
$78$	0.903701	+	2.30204i	0.102324	+	0.260655i
$79$	10.3024			1.15911			0.579556	−	0.814932i	$-0.303226\pi$
$79$	10.3024			1.15911			0.579556	+	0.814932i	$0.303226\pi$
$80$		0			0
$81$	−3.07731			−0.341924
$82$	1.37957	+	3.51424i	0.152348	+	0.388083i
$83$		−	3.26589i		−	0.358478i	−0.983806	−	0.179239i	$-0.942636\pi$
$83$		−	3.26589i		−	0.358478i	0.983806	−	0.179239i	$-0.0573636\pi$
$84$	−4.12701	−	0.153751i	−0.450293	−	0.0167756i
$85$		0			0
$86$	−11.9119	+	4.67618i	−1.28449	+	0.504246i
$87$	3.04060	−	3.04060i	0.325986	−	0.325986i
$88$	3.06981	+	8.76618i	0.327243	+	0.934477i
$89$	−9.77206			−1.03584			−0.517918	−	0.855430i	$-0.673293\pi$
$89$	−9.77206			−1.03584			−0.517918	+	0.855430i	$0.673293\pi$
$90$		0			0
$91$	−1.55578	+	1.55578i	−0.163090	+	0.163090i
$92$	2.57524	+	0.0959403i	0.268488	+	0.0100025i
$93$	0.310765			0.0322248
$94$	14.4422	+	6.29969i	1.48960	+	0.649763i
$95$		0			0
$96$	−6.92415	+	2.13889i	−0.706693	+	0.218300i
$97$	1.63587	−	1.63587i	0.166097	−	0.166097i	−0.619164	−	0.785262i	$-0.712528\pi$
$97$	1.63587	−	1.63587i	0.166097	−	0.166097i	0.785262	+	0.619164i	$0.212528\pi$
$98$	2.27482	+	5.79477i	0.229792	+	0.585360i
$99$	−3.15516	+	3.15516i	−0.317106	+	0.317106i
$100$		0			0
$101$	−6.63953	−	6.63953i	−0.660658	−	0.660658i	0.294877	−	0.955535i	$-0.404721\pi$
$101$	−6.63953	−	6.63953i	−0.660658	−	0.660658i	−0.955535	+	0.294877i	$0.904721\pi$
$102$	12.3385	+	5.38205i	1.22170	+	0.532902i
$103$	−1.62219	−	1.62219i	−0.159839	−	0.159839i	0.622656	−	0.782496i	$-0.286054\pi$
$103$	−1.62219	−	1.62219i	−0.159839	−	0.159839i	−0.782496	+	0.622656i	$0.786054\pi$
$104$	−1.67432	+	3.47893i	−0.164180	+	0.341137i
$105$		0			0
$106$	2.99789	+	7.63667i	0.291181	+	0.741739i
$107$			3.65206i			0.353058i	0.984295	+	0.176529i	$0.0564869\pi$
$107$			3.65206i			0.353058i	−0.984295	+	0.176529i	$0.943513\pi$
$108$	−7.59754	−	8.18554i	−0.731074	−	0.787654i
$109$	−5.20757	−	5.20757i	−0.498795	−	0.498795i	0.412268	−	0.911063i	$-0.364737\pi$
$109$	−5.20757	−	5.20757i	−0.498795	−	0.498795i	−0.911063	+	0.412268i	$0.864737\pi$
$110$		0			0
$111$		−	4.28519i		−	0.406733i
$112$	−4.20714	−	4.88558i	−0.397537	−	0.461644i
$113$	4.27905	+	4.27905i	0.402539	+	0.402539i	0.879127	−	0.476588i	$-0.158127\pi$
$113$	4.27905	+	4.27905i	0.402539	+	0.402539i	−0.476588	+	0.879127i	$0.658127\pi$
$114$	−8.68359	−	3.78777i	−0.813293	−	0.354757i
$115$		0			0
$116$	6.70843	+	0.249921i	0.622862	+	0.0232046i
$117$	−1.85478			−0.171474
$118$	−10.8428	−	4.72963i	−0.998164	−	0.435398i
$119$			11.9760i			1.09784i
$120$		0			0
$121$			0.216302i			0.0196639i
$122$	−5.33680	+	12.2348i	−0.483171	+	1.10768i
$123$	3.41996			0.308367
$124$	0.330046	+	0.355590i	0.0296390	+	0.0319329i
$125$		0			0
$126$	1.23838	−	2.83903i	0.110324	−	0.252921i
$127$	−7.29257	−	7.29257i	−0.647111	−	0.647111i	0.305183	−	0.952294i	$-0.401282\pi$
$127$	−7.29257	−	7.29257i	−0.647111	−	0.647111i	−0.952294	+	0.305183i	$0.901282\pi$
$128$	−9.80117	−	5.65129i	−0.866309	−	0.499508i
$129$			11.5923i			1.02065i
$130$		0			0
$131$	−11.9793	−	11.9793i	−1.04664	−	1.04664i	−0.998858	−	0.0477778i	$-0.984786\pi$
$131$	−11.9793	−	11.9793i	−1.04664	−	1.04664i	−0.0477778	−	0.998858i	$-0.515214\pi$
$132$	8.40804	+	0.313240i	0.731826	+	0.0272640i
$133$		−	8.42848i		−	0.730842i
$134$	5.98537	−	2.34965i	0.517057	−	0.202978i
$135$		0			0
$136$	6.94571	+	19.8342i	0.595590	+	1.70077i
$137$	−4.92762	−	4.92762i	−0.420995	−	0.420995i	0.464551	−	0.885546i	$-0.346216\pi$
$137$	−4.92762	−	4.92762i	−0.420995	−	0.420995i	−0.885546	+	0.464551i	$0.846216\pi$
$138$	0.933359	−	2.13975i	0.0794528	−	0.182148i
$139$	−10.3015	−	10.3015i	−0.873761	−	0.873761i	0.119119	−	0.992880i	$-0.461993\pi$
$139$	−10.3015	−	10.3015i	−0.873761	−	0.873761i	−0.992880	+	0.119119i	$0.961993\pi$
$140$		0			0
$141$	10.0927	−	10.0927i	0.849962	−	0.849962i
$142$	20.3239	−	7.97845i	1.70555	−	0.669537i
$143$	3.16963	−	3.16963i	0.265058	−	0.265058i
$144$	0.404411	−	5.42010i	0.0337009	−	0.451675i
$145$		0			0
$146$	−1.19391	+	2.73707i	−0.0988086	+	0.226522i
$147$	5.63931			0.465123
$148$	4.90329	−	4.55107i	0.403048	−	0.374096i
$149$	15.2040	−	15.2040i	1.24556	−	1.24556i	0.287896	−	0.957662i	$-0.407044\pi$
$149$	15.2040	−	15.2040i	1.24556	−	1.24556i	0.957662	−	0.287896i	$-0.0929557\pi$
$150$		0			0
$151$	−10.7055			−0.871204			−0.435602	−	0.900139i	$-0.643464\pi$
$151$	−10.7055			−0.871204			−0.435602	+	0.900139i	$0.643464\pi$
$152$	−4.88825	−	13.9589i	−0.396489	−	1.13222i
$153$	−7.13882	+	7.13882i	−0.577139	+	0.577139i
$154$	2.73534	+	6.96787i	0.220420	+	0.561487i
$155$		0			0
$156$	2.37929	+	2.56343i	0.190495	+	0.205238i
$157$			2.34588i			0.187222i	0.995609	+	0.0936108i	$0.0298409\pi$
$157$			2.34588i			0.187222i	−0.995609	+	0.0936108i	$0.970159\pi$
$158$	13.5622	−	5.32405i	1.07895	−	0.423559i
$159$	7.43180			0.589380
$160$		0			0
$161$	2.07689			0.163682
$162$	−4.05101	+	1.59028i	−0.318278	+	0.124945i
$163$			2.73625i			0.214319i	0.994242	+	0.107160i	$0.0341756\pi$
$163$			2.73625i			0.214319i	−0.994242	+	0.107160i	$0.965824\pi$
$164$	3.63215	+	3.91326i	0.283624	+	0.305574i
$165$		0			0
$166$	−1.68774	−	4.29926i	−0.130994	−	0.333687i
$167$	−10.1328	+	10.1328i	−0.784097	+	0.784097i	−0.980519	−	0.196423i	$-0.937068\pi$
$167$	−10.1328	+	10.1328i	−0.784097	+	0.784097i	0.196423	+	0.980519i	$0.437068\pi$
$168$	−5.51230	+	1.93034i	−0.425283	+	0.148929i
$169$	−11.1367			−0.856670
$170$		0			0
$171$	5.02415	−	5.02415i	0.384207	−	0.384207i
$172$	−13.2644	+	12.3116i	−1.01140	+	0.938748i
$173$	8.79590			0.668740			0.334370	−	0.942442i	$-0.391477\pi$
$173$	8.79590			0.668740			0.334370	+	0.942442i	$0.391477\pi$
$174$	2.43137	−	5.57399i	0.184322	−	0.422563i
$175$		0			0
$176$	8.57130	+	9.95349i	0.646086	+	0.750273i
$177$	−7.57735	+	7.57735i	−0.569549	+	0.569549i
$178$	−12.8641	+	5.04998i	−0.964202	+	0.378512i
$179$	−6.62071	+	6.62071i	−0.494855	+	0.494855i	−0.909832	−	0.414977i	$-0.863790\pi$
$179$	−6.62071	+	6.62071i	−0.494855	+	0.494855i	0.414977	+	0.909832i	$0.363790\pi$
$180$		0			0
$181$	−5.84339	−	5.84339i	−0.434336	−	0.434336i	0.455765	−	0.890100i	$-0.349366\pi$
$181$	−5.84339	−	5.84339i	−0.434336	−	0.434336i	−0.890100	+	0.455765i	$0.849366\pi$
$182$	−1.24406	+	2.85204i	−0.0922157	+	0.211408i
$183$	8.55009	+	8.55009i	0.632041	+	0.632041i
$184$	3.43966	−	1.20453i	0.253575	−	0.0887992i
$185$		0			0
$186$	0.409095	−	0.160596i	0.0299963	−	0.0117755i
$187$		−	24.3990i		−	1.78423i
$188$	22.2675	+	0.829571i	1.62402	+	0.0605027i
$189$	−6.36440	−	6.36440i	−0.462942	−	0.462942i
$190$		0			0
$191$			1.83906i			0.133070i	0.997784	+	0.0665349i	$0.0211944\pi$
$191$			1.83906i			0.133070i	−0.997784	+	0.0665349i	$0.978806\pi$
$192$	−8.00970	+	6.39391i	−0.578050	+	0.461440i
$193$	−6.18343	−	6.18343i	−0.445093	−	0.445093i	0.448626	−	0.893719i	$-0.351913\pi$
$193$	−6.18343	−	6.18343i	−0.445093	−	0.445093i	−0.893719	+	0.448626i	$0.851913\pi$
$194$	1.30810	−	2.99886i	0.0939160	−	0.215305i
$195$		0			0
$196$	5.98921	+	6.45273i	0.427801	+	0.460910i
$197$	−5.55669			−0.395898			−0.197949	−	0.980212i	$-0.563428\pi$
$197$	−5.55669			−0.395898			−0.197949	+	0.980212i	$0.563428\pi$
$198$	−2.52298	+	5.78401i	−0.179300	+	0.411052i
$199$		−	6.96413i		−	0.493674i	−0.969057	−	0.246837i	$-0.920609\pi$
$199$		−	6.96413i		−	0.493674i	0.969057	−	0.246837i	$-0.0793912\pi$
$200$		0			0
$201$		−	5.82480i		−	0.410850i
$202$	−12.1715	−	5.30920i	−0.856385	−	0.373554i
$203$	5.41024			0.379724
$204$	19.0239	+	0.708731i	1.33194	+	0.0496211i
$205$		0			0
$206$	−2.97379	−	1.29716i	−0.207194	−	0.0903776i
$207$	1.23802	+	1.23802i	0.0860483	+	0.0860483i
$208$	−0.406265	+	5.44495i	−0.0281694	+	0.377539i
$209$			17.1715i			1.18778i
$210$		0			0
$211$	5.43389	+	5.43389i	0.374084	+	0.374084i	0.868962	−	0.494878i	$-0.164787\pi$
$211$	5.43389	+	5.43389i	0.374084	+	0.374084i	−0.494878	+	0.868962i	$0.664787\pi$
$212$	7.89291	+	8.50377i	0.542088	+	0.584041i
$213$		−	19.7787i		−	1.35521i
$214$	1.88730	+	4.80761i	0.129013	+	0.328642i
$215$		0			0
$216$	−14.2316	−	6.84931i	−0.968338	−	0.466036i
$217$	0.276477	+	0.276477i	0.0187685	+	0.0187685i
$218$	−9.54647	−	4.16416i	−0.646568	−	0.282032i
$219$	1.91276	+	1.91276i	0.129253	+	0.129253i
$220$		0			0
$221$	7.17155	−	7.17155i	0.482411	−	0.482411i
$222$	−2.21449	−	5.64108i	−0.148627	−	0.378605i
$223$	8.61776	−	8.61776i	0.577088	−	0.577088i	−0.357012	−	0.934100i	$-0.616204\pi$
$223$	8.61776	−	8.61776i	0.577088	−	0.577088i	0.934100	+	0.357012i	$0.116204\pi$
$224$	−8.06309	−	4.25728i	−0.538738	−	0.284452i
$225$		0			0
$226$	7.84431	+	3.42168i	0.521796	+	0.227607i
$227$	−6.01977			−0.399546			−0.199773	−	0.979842i	$-0.564020\pi$
$227$	−6.01977			−0.399546			−0.199773	+	0.979842i	$0.564020\pi$
$228$	−13.3886	−	0.498791i	−0.886683	−	0.0330332i
$229$	0.568504	−	0.568504i	0.0375678	−	0.0375678i	−0.688073	−	0.725641i	$-0.741543\pi$
$229$	0.568504	−	0.568504i	0.0375678	−	0.0375678i	0.725641	+	0.688073i	$0.241543\pi$
$230$		0			0
$231$	6.78094			0.446153
$232$	8.96022	−	3.13776i	0.588267	−	0.206004i
$233$	12.6979	−	12.6979i	0.831869	−	0.831869i	−0.155904	−	0.987772i	$-0.549829\pi$
$233$	12.6979	−	12.6979i	0.831869	−	0.831869i	0.987772	+	0.155904i	$0.0498289\pi$
$234$	−2.44165	+	0.958508i	−0.159616	+	0.0626596i
$235$		0			0
$236$	−16.7178	−	0.622819i	−1.08824	−	0.0405421i
$237$		−	13.1984i		−	0.857327i
$238$	6.18894	+	15.7654i	0.401169	+	1.02192i
$239$	−1.78306			−0.115336			−0.0576682	−	0.998336i	$-0.518367\pi$
$239$	−1.78306			−0.115336			−0.0576682	+	0.998336i	$0.518367\pi$
$240$		0			0
$241$	10.4440			0.672754			0.336377	−	0.941727i	$-0.390798\pi$
$241$	10.4440			0.672754			0.336377	+	0.941727i	$0.390798\pi$
$242$	0.111780	+	0.284743i	0.00718550	+	0.0183040i
$243$		−	12.8098i		−	0.821747i
$244$	−0.702773	+	18.8639i	−0.0449904	+	1.20764i
$245$		0			0
$246$	4.50208	−	1.76736i	0.287042	−	0.112683i
$247$	−5.04719	+	5.04719i	−0.321145	+	0.321145i
$248$	0.618238	+	0.297542i	0.0392581	+	0.0188939i
$249$	−4.18392			−0.265145
$250$		0			0
$251$	−12.6497	+	12.6497i	−0.798445	+	0.798445i	−0.982850	−	0.184406i	$-0.940964\pi$
$251$	−12.6497	+	12.6497i	−0.798445	+	0.798445i	0.184406	+	0.982850i	$0.440964\pi$
$252$	0.163075	−	4.37730i	0.0102728	−	0.275744i
$253$	−4.23130			−0.266019
$254$	−13.3687	−	5.83140i	−0.838825	−	0.365894i
$255$		0			0
$256$	−15.8228	−	2.37440i	−0.988927	−	0.148400i
$257$	4.13062	−	4.13062i	0.257661	−	0.257661i	−0.566441	−	0.824102i	$-0.691680\pi$
$257$	4.13062	−	4.13062i	0.257661	−	0.257661i	0.824102	+	0.566441i	$0.191680\pi$
$258$	5.99064	+	15.2603i	0.372961	+	0.950063i
$259$	3.81240	−	3.81240i	0.236891	−	0.236891i
$260$		0			0
$261$	3.22500	+	3.22500i	0.199623	+	0.199623i
$262$	−21.9603	−	9.57907i	−1.35671	−	0.591797i
$263$	−17.1303	−	17.1303i	−1.05630	−	1.05630i	−0.998318	−	0.0579798i	$-0.981534\pi$
$263$	−17.1303	−	17.1303i	−1.05630	−	1.05630i	−0.0579798	−	0.998318i	$-0.518466\pi$
$264$	11.2303	−	3.93273i	0.691178	−	0.242043i
$265$		0			0
$266$	−4.35565	−	11.0954i	−0.267062	−	0.680300i
$267$			12.5190i			0.766147i
$268$	6.66497	−	6.18620i	0.407128	−	0.377883i
$269$	19.8075	+	19.8075i	1.20768	+	1.20768i	0.971775	+	0.235910i	$0.0758070\pi$
$269$	19.8075	+	19.8075i	1.20768	+	1.20768i	0.235910	+	0.971775i	$0.424193\pi$
$270$		0			0
$271$		−	27.9542i		−	1.69810i	−0.528316	−	0.849048i	$-0.677176\pi$
$271$		−	27.9542i		−	1.69810i	0.528316	−	0.849048i	$-0.322824\pi$
$272$	19.3933	+	22.5206i	1.17589	+	1.36551i
$273$	1.99311	+	1.99311i	0.120628	+	0.120628i
$274$	−9.03326	−	3.94030i	−0.545719	−	0.238042i
$275$		0			0
$276$	0.122909	−	3.29914i	0.00739824	−	0.198585i
$277$	26.0257			1.56373			0.781866	−	0.623447i	$-0.214268\pi$
$277$	26.0257			1.56373			0.781866	+	0.623447i	$0.214268\pi$
$278$	−18.8846	−	8.23743i	−1.13262	−	0.494048i
$279$			0.329612i			0.0197333i
$280$		0			0
$281$			24.1001i			1.43769i	0.695170	+	0.718846i	$0.255329\pi$
$281$			24.1001i			1.43769i	−0.695170	+	0.718846i	$0.744671\pi$
$282$	8.07051	−	18.5019i	0.480592	−	1.10177i
$283$	−4.73708			−0.281590			−0.140795	−	0.990039i	$-0.544966\pi$
$283$	−4.73708			−0.281590			−0.140795	+	0.990039i	$0.544966\pi$
$284$	22.6316	−	21.0059i	1.34294	−	1.24647i
$285$		0			0
$286$	2.53455	−	5.81053i	0.149871	−	0.343584i
$287$	3.04262	+	3.04262i	0.179600	+	0.179600i
$288$	−2.26861	−	7.34408i	−0.133679	−	0.432754i
$289$		−	38.2049i		−	2.24734i
$290$		0			0
$291$	−2.09571	−	2.09571i	−0.122852	−	0.122852i
$292$	−0.157219	+	4.22010i	−0.00920056	+	0.246963i
$293$			3.11001i			0.181689i	0.995865	+	0.0908445i	$0.0289566\pi$
$293$			3.11001i			0.181689i	−0.995865	+	0.0908445i	$0.971043\pi$
$294$	7.42366	−	2.91427i	0.432957	−	0.169964i
$295$		0			0
$296$	4.10287	−	8.52500i	0.238474	−	0.495505i
$297$	12.9663	+	12.9663i	0.752382	+	0.752382i
$298$	12.1576	−	27.8718i	0.704273	−	1.61457i
$299$	−1.24370	−	1.24370i	−0.0719248	−	0.0719248i
$300$		0			0
$301$	−10.3133	+	10.3133i	−0.594449	+	0.594449i
$302$	−14.0929	+	5.53238i	−0.810955	+	0.318352i
$303$	−8.50588	+	8.50588i	−0.488650	+	0.488650i
$304$	−13.6486	−	15.8495i	−0.782801	−	0.909034i
$305$		0			0
$306$	−5.70845	+	13.0868i	−0.326330	+	0.748123i
$307$	−14.5670			−0.831382			−0.415691	−	0.909506i	$-0.636460\pi$
$307$	−14.5670			−0.831382			−0.415691	+	0.909506i	$0.636460\pi$
$308$	7.20167	+	7.75903i	0.410353	+	0.442112i
$309$	−2.07819	+	2.07819i	−0.118224	+	0.118224i
$310$		0			0
$311$	−14.4572			−0.819791			−0.409896	−	0.912132i	$-0.634435\pi$
$311$	−14.4572			−0.819791			−0.409896	+	0.912132i	$0.634435\pi$
$312$	4.45684	+	2.14496i	0.252319	+	0.121435i
$313$	−10.1273	+	10.1273i	−0.572429	+	0.572429i	−0.932807	−	0.360377i	$-0.882648\pi$
$313$	−10.1273	+	10.1273i	−0.572429	+	0.572429i	0.360377	+	0.932807i	$0.382648\pi$
$314$	1.21230	+	3.08815i	0.0684139	+	0.174274i
$315$		0			0
$316$	15.1021	−	14.0173i	0.849561	−	0.788534i
$317$		−	13.8750i		−	0.779295i	−0.920964	−	0.389648i	$-0.872597\pi$
$317$		−	13.8750i		−	0.779295i	0.920964	−	0.389648i	$-0.127403\pi$
$318$	9.78332	−	3.84058i	0.548621	−	0.215369i
$319$	−11.0224			−0.617136
$320$		0			0
$321$	4.67864			0.261136
$322$	2.73405	−	1.07329i	0.152362	−	0.0598121i
$323$			38.8520i			2.16179i
$324$	−4.51098	+	4.18694i	−0.250610	+	0.232608i
$325$		0			0
$326$	1.41403	+	3.60203i	0.0783158	+	0.199498i
$327$	−6.67140	+	6.67140i	−0.368930	+	0.368930i
$328$	6.80369	+	3.27445i	0.375671	+	0.180801i
$329$	17.9584			0.990076
$330$		0			0
$331$	1.69458	−	1.69458i	0.0931425	−	0.0931425i	−0.659000	−	0.752143i	$-0.729020\pi$
$331$	1.69458	−	1.69458i	0.0931425	−	0.0931425i	0.752143	+	0.659000i	$0.229020\pi$
$332$	−4.44352	−	4.78741i	−0.243870	−	0.262743i
$333$	4.54508			0.249069
$334$	−8.10251	+	18.5753i	−0.443350	+	1.01639i
$335$		0			0
$336$	−6.25890	+	5.38975i	−0.341451	+	0.294035i
$337$	9.53338	−	9.53338i	0.519316	−	0.519316i	−0.398048	−	0.917364i	$-0.630312\pi$
$337$	9.53338	−	9.53338i	0.519316	−	0.519316i	0.917364	+	0.398048i	$0.130312\pi$
$338$	−14.6605	+	5.75520i	−0.797427	+	0.313042i
$339$	5.48188	−	5.48188i	0.297735	−	0.297735i
$340$		0			0
$341$	−0.563273	−	0.563273i	−0.0305029	−	0.0305029i
$342$	4.01749	−	9.21023i	0.217241	−	0.498032i
$343$	12.9954	+	12.9954i	0.701683	+	0.701683i
$344$	−11.0991	+	23.0618i	−0.598422	+	1.24341i
$345$		0			0
$346$	11.5790	−	4.54552i	0.622492	−	0.244369i
$347$		−	6.67273i		−	0.358211i	−0.983830	−	0.179105i	$-0.942680\pi$
$347$		−	6.67273i		−	0.358211i	0.983830	−	0.179105i	$-0.0573203\pi$
$348$	0.320173	−	8.59415i	0.0171631	−	0.460695i
$349$	−2.02618	−	2.02618i	−0.108459	−	0.108459i	0.650795	−	0.759254i	$-0.274436\pi$
$349$	−2.02618	−	2.02618i	−0.108459	−	0.108459i	−0.759254	+	0.650795i	$0.774436\pi$
$350$		0			0
$351$			7.62233i			0.406850i
$352$	16.4271	+	8.67345i	0.875567	+	0.462296i
$353$	5.36542	+	5.36542i	0.285572	+	0.285572i	0.835327	−	0.549754i	$-0.185279\pi$
$353$	5.36542	+	5.36542i	0.285572	+	0.285572i	−0.549754	+	0.835327i	$0.685279\pi$
$354$	−6.05912	+	13.8907i	−0.322039	+	0.738284i
$355$		0			0
$356$	−14.3247	+	13.2957i	−0.759207	+	0.704671i
$357$	15.3425			0.812009
$358$	−5.29416	+	12.1370i	−0.279805	+	0.641462i
$359$			7.76117i			0.409619i	0.978802	+	0.204809i	$0.0656574\pi$
$359$			7.76117i			0.409619i	−0.978802	+	0.204809i	$0.934343\pi$
$360$		0			0
$361$		−	8.34326i		−	0.439119i
$362$	−10.7120	−	4.67258i	−0.563012	−	0.245585i
$363$	0.277104			0.0145442
$364$	−0.163823	+	4.39737i	−0.00858666	+	0.230485i
$365$		0			0
$366$	15.6739	+	6.83695i	0.819290	+	0.357373i
$367$	18.0536	+	18.0536i	0.942389	+	0.942389i	0.998429	−	0.0560392i	$-0.0178472\pi$
$367$	18.0536	+	18.0536i	0.942389	+	0.942389i	−0.0560392	+	0.998429i	$0.517847\pi$
$368$	3.90554	−	3.36320i	0.203590	−	0.175319i
$369$			3.62737i			0.188833i
$370$		0			0
$371$	6.61183	+	6.61183i	0.343269	+	0.343269i
$372$	0.455545	−	0.422821i	0.0236189	−	0.0219223i
$373$			4.36197i			0.225854i	0.993603	+	0.112927i	$0.0360226\pi$
$373$			4.36197i			0.225854i	−0.993603	+	0.112927i	$0.963977\pi$
$374$	−12.6089	−	32.1192i	−0.651988	−	1.66084i
$375$		0			0
$376$	29.7419	−	10.4153i	1.53382	−	0.537126i
$377$	−3.23979	−	3.23979i	−0.166858	−	0.166858i
$378$	−11.6671	−	5.08920i	−0.600093	−	0.261760i
$379$	5.93072	+	5.93072i	0.304641	+	0.304641i	0.842826	−	0.538186i	$-0.180890\pi$
$379$	5.93072	+	5.93072i	0.304641	+	0.304641i	−0.538186	+	0.842826i	$0.680890\pi$
$380$		0			0
$381$	−9.34249	+	9.34249i	−0.478630	+	0.478630i
$382$	0.950385	+	2.42096i	0.0486259	+	0.123867i
$383$	−19.3340	+	19.3340i	−0.987922	+	0.987922i	−0.999928	−	0.0120057i	$-0.996178\pi$
$383$	−19.3340	+	19.3340i	−0.987922	+	0.987922i	0.0120057	+	0.999928i	$0.496178\pi$
$384$	−7.23984	+	12.5562i	−0.369457	+	0.640758i
$385$		0			0
$386$	−11.3354	−	4.94449i	−0.576957	−	0.251668i
$387$	−12.2954			−0.625008
$388$	0.172256	−	4.62373i	0.00874498	−	0.234734i
$389$	−6.28607	+	6.28607i	−0.318716	+	0.318716i	−0.848274	−	0.529558i	$-0.822358\pi$
$389$	−6.28607	+	6.28607i	−0.318716	+	0.318716i	0.529558	+	0.848274i	$0.322358\pi$
$390$		0			0
$391$	−9.57367			−0.484161
$392$	11.2189	+	5.39937i	0.566640	+	0.272709i
$393$	−15.3466	+	15.3466i	−0.774135	+	0.774135i
$394$	−7.31489	+	2.87157i	−0.368519	+	0.144668i
$395$		0			0
$396$	−0.332237	+	8.91796i	−0.0166955	+	0.448144i
$397$			6.58413i			0.330448i	0.986256	+	0.165224i	$0.0528347\pi$
$397$			6.58413i			0.330448i	−0.986256	+	0.165224i	$0.947165\pi$
$398$	−3.59890	−	9.16767i	−0.180397	−	0.459534i
$399$	−10.7977			−0.540561
$400$		0			0
$401$	19.7951			0.988522			0.494261	−	0.869313i	$-0.335439\pi$
$401$	19.7951			0.988522			0.494261	+	0.869313i	$0.335439\pi$
$402$	−3.01012	−	7.66784i	−0.150131	−	0.382437i
$403$		−	0.331123i		−	0.0164944i
$404$	−18.7664	−	0.699139i	−0.933664	−	0.0347835i
$405$		0			0
$406$	7.12211	−	2.79589i	0.353464	−	0.138758i
$407$	−7.76707	+	7.76707i	−0.385000	+	0.385000i
$408$	25.4095	−	8.89813i	1.25796	−	0.440523i
$409$	−5.76937			−0.285277			−0.142638	−	0.989775i	$-0.545559\pi$
$409$	−5.76937			−0.285277			−0.142638	+	0.989775i	$0.545559\pi$
$410$		0			0
$411$	−6.31276	+	6.31276i	−0.311385	+	0.311385i
$412$	−4.58507	−	0.170816i	−0.225890	−	0.00841550i
$413$	−13.4826			−0.663437
$414$	2.26952	+	0.989964i	0.111541	+	0.0486541i
$415$		0			0
$416$	2.27901	+	7.37775i	0.111738	+	0.361724i
$417$	−13.1972	+	13.1972i	−0.646270	+	0.646270i
$418$	8.87385	+	22.6048i	0.434034	+	1.10564i
$419$	−8.68932	+	8.68932i	−0.424501	+	0.424501i	−0.886750	−	0.462249i	$-0.847043\pi$
$419$	−8.68932	+	8.68932i	−0.424501	+	0.424501i	0.462249	+	0.886750i	$0.347043\pi$
$420$		0			0
$421$	20.1193	+	20.1193i	0.980555	+	0.980555i	0.999815	−	0.0192594i	$-0.00613083\pi$
$421$	20.1193	+	20.1193i	0.980555	+	0.980555i	−0.0192594	+	0.999815i	$0.506131\pi$
$422$	9.96134	+	4.34513i	0.484911	+	0.211517i
$423$	10.7048	+	10.7048i	0.520487	+	0.520487i
$424$	14.7849	+	7.11559i	0.718017	+	0.345564i
$425$		0			0
$426$	−10.2212	−	26.0369i	−0.495217	−	1.26149i
$427$			15.2135i			0.736231i
$428$	4.96893	+	5.35349i	0.240182	+	0.258770i
$429$	−4.06060	−	4.06060i	−0.196048	−	0.196048i
$430$		0			0
$431$			33.6247i			1.61965i	0.586675	+	0.809823i	$0.300437\pi$
$431$			33.6247i			1.61965i	−0.586675	+	0.809823i	$0.699563\pi$
$432$	−22.2742	−	1.66195i	−1.07167	−	0.0799606i
$433$	−7.46558	−	7.46558i	−0.358773	−	0.358773i	0.504588	−	0.863361i	$-0.331645\pi$
$433$	−7.46558	−	7.46558i	−0.358773	−	0.358773i	−0.863361	+	0.504588i	$0.831645\pi$
$434$	0.506835	+	0.221081i	0.0243289	+	0.0106122i
$435$		0			0
$436$	−14.7190	−	0.548355i	−0.704914	−	0.0262614i
$437$	6.73775			0.322310
$438$	3.50646	+	1.52951i	0.167545	+	0.0730829i
$439$			7.91929i			0.377967i	0.981980	+	0.188984i	$0.0605193\pi$
$439$			7.91929i			0.377967i	−0.981980	+	0.188984i	$0.939481\pi$
$440$		0			0
$441$			5.98132i			0.284825i
$442$	5.73463	−	13.1468i	0.272768	−	0.625330i
$443$	−10.6463			−0.505823			−0.252911	−	0.967489i	$-0.581388\pi$
$443$	−10.6463			−0.505823			−0.252911	+	0.967489i	$0.581388\pi$
$444$	−5.83036	−	6.28159i	−0.276697	−	0.298111i
$445$		0			0
$446$	6.89106	−	15.7980i	0.326301	−	0.748056i
$447$	−19.4778	−	19.4778i	−0.921266	−	0.921266i
$448$	−12.8144	−	1.43752i	−0.605424	−	0.0679164i
$449$			6.08115i			0.286987i	0.989651	+	0.143494i	$0.0458336\pi$
$449$			6.08115i			0.286987i	−0.989651	+	0.143494i	$0.954166\pi$
$450$		0			0
$451$	−6.19880	−	6.19880i	−0.291890	−	0.291890i
$452$	12.0946	+	0.450582i	0.568882	+	0.0211936i
$453$			13.7148i			0.644379i
$454$	−7.92450	+	3.11088i	−0.371915	+	0.146001i
$455$		0			0
$456$	−17.8827	+	6.26232i	−0.837435	+	0.293260i
$457$	0.313815	+	0.313815i	0.0146796	+	0.0146796i	0.714409	−	0.699729i	$-0.246696\pi$
$457$	0.313815	+	0.313815i	0.0146796	+	0.0146796i	−0.699729	+	0.714409i	$0.746696\pi$
$458$	0.454596	−	1.04218i	0.0212419	−	0.0486977i
$459$	29.3374	+	29.3374i	1.36935	+	1.36935i
$460$		0			0
$461$	9.90949	−	9.90949i	0.461531	−	0.461531i	−0.437626	−	0.899157i	$-0.644181\pi$
$461$	9.90949	−	9.90949i	0.461531	−	0.461531i	0.899157	+	0.437626i	$0.144181\pi$
$462$	8.92652	−	3.50424i	0.415299	−	0.163032i
$463$	17.3430	−	17.3430i	0.805999	−	0.805999i	−0.178027	−	0.984026i	$-0.556971\pi$
$463$	17.3430	−	17.3430i	0.805999	−	0.805999i	0.984026	+	0.178027i	$0.0569714\pi$
$464$	10.1738	−	8.76103i	0.472307	−	0.406720i
$465$		0			0
$466$	10.1537	−	23.2777i	0.470361	−	1.07832i
$467$	−1.52267			−0.0704606			−0.0352303	−	0.999379i	$-0.511216\pi$
$467$	−1.52267			−0.0704606			−0.0352303	+	0.999379i	$0.511216\pi$
$468$	−2.71889	+	2.52358i	−0.125681	+	0.116653i
$469$	5.18213	−	5.18213i	0.239289	−	0.239289i
$470$		0			0
$471$	3.00530			0.138477
$472$	−22.3294	+	7.81950i	−1.02779	+	0.359921i
$473$	21.0115	−	21.0115i	0.966110	−	0.966110i
$474$	−6.82062	−	17.3745i	−0.313282	−	0.798038i
$475$		0			0
$476$	16.2944	+	17.5555i	0.746852	+	0.804653i
$477$			7.88252i			0.360916i
$478$	−2.34724	+	0.921443i	−0.107360	+	0.0421458i
$479$	−0.507657			−0.0231955			−0.0115977	−	0.999933i	$-0.503692\pi$
$479$	−0.507657			−0.0231955			−0.0115977	+	0.999933i	$0.503692\pi$
$480$		0			0
$481$	−4.56592			−0.208188
$482$	13.7486	−	5.39720i	0.626229	−	0.245836i
$483$		−	2.66070i		−	0.121066i
$484$	0.294297	+	0.317074i	0.0133772	+	0.0144125i
$485$		0			0
$486$	−6.61979	−	16.8629i	−0.300280	−	0.764918i
$487$	25.9809	−	25.9809i	1.17730	−	1.17730i	0.196876	−	0.980428i	$-0.436920\pi$
$487$	25.9809	−	25.9809i	1.17730	−	1.17730i	0.980428	−	0.196876i	$-0.0630798\pi$
$488$	8.82332	+	25.1959i	0.399413	+	1.14057i
$489$	3.50539			0.158519
$490$		0			0
$491$	−3.28208	+	3.28208i	−0.148118	+	0.148118i	−0.777277	−	0.629159i	$-0.783400\pi$
$491$	−3.28208	+	3.28208i	−0.148118	+	0.148118i	0.629159	+	0.777277i	$0.283400\pi$
$492$	5.01326	−	4.65314i	0.226015	−	0.209780i
$493$	−24.9391			−1.12320
$494$	−4.03591	+	9.25246i	−0.181584	+	0.416288i
$495$		0			0
$496$	0.967619	+	0.0721971i	0.0434474	+	0.00324175i
$497$	17.5964	−	17.5964i	0.789308	−	0.789308i
$498$	−5.50777	+	2.16215i	−0.246809	+	0.0968885i
$499$	6.73907	−	6.73907i	0.301682	−	0.301682i	−0.539990	−	0.841672i	$-0.681572\pi$
$499$	6.73907	−	6.73907i	0.301682	−	0.301682i	0.841672	+	0.539990i	$0.181572\pi$
$500$		0			0
$501$	12.9810	+	12.9810i	0.579950	+	0.579950i
$502$	−10.1152	+	23.1894i	−0.451463	+	1.03499i
$503$	6.12090	+	6.12090i	0.272918	+	0.272918i	0.830274	−	0.557356i	$-0.188184\pi$
$503$	6.12090	+	6.12090i	0.272918	+	0.272918i	−0.557356	+	0.830274i	$0.688184\pi$
$504$	−2.04741	−	5.84660i	−0.0911990	−	0.260428i
$505$		0			0
$506$	−5.57013	+	2.18664i	−0.247623	+	0.0972079i
$507$			14.2672i			0.633629i
$508$	−20.6122	−	0.767904i	−0.914519	−	0.0340702i
$509$	−13.8727	−	13.8727i	−0.614894	−	0.614894i	0.329323	−	0.944217i	$-0.393180\pi$
$509$	−13.8727	−	13.8727i	−0.614894	−	0.614894i	−0.944217	+	0.329323i	$0.893180\pi$
$510$		0			0
$511$			3.40344i			0.150559i
$512$	−22.0564	+	5.05119i	−0.974765	+	0.223233i
$513$	−20.6471	−	20.6471i	−0.911590	−	0.911590i
$514$	3.30299	−	7.57221i	0.145689	−	0.333996i
$515$		0			0
$516$	15.7723	+	16.9930i	0.694337	+	0.748074i
$517$	−36.5869			−1.60909
$518$	3.04853	−	6.98884i	0.133945	−	0.307072i
$519$		−	11.2684i		−	0.494628i
$520$		0			0
$521$		−	5.87686i		−	0.257470i	−0.991679	−	0.128735i	$-0.958908\pi$
$521$		−	5.87686i		−	0.257470i	0.991679	−	0.128735i	$-0.0410917\pi$
$522$	5.91204	+	2.57883i	0.258763	+	0.112872i
$523$	26.0176			1.13767			0.568834	−	0.822452i	$-0.307395\pi$
$523$	26.0176			1.13767			0.568834	+	0.822452i	$0.307395\pi$
$524$	−33.8591	−	1.26141i	−1.47914	−	0.0551051i
$525$		0			0
$526$	−31.4030	−	13.6980i	−1.36924	−	0.597260i
$527$	−1.27445	−	1.27445i	−0.0555160	−	0.0555160i
$528$	12.7514	−	10.9807i	0.554933	−	0.477872i
$529$		−	21.3397i		−	0.927814i
$530$		0			0
$531$	−8.03690	−	8.03690i	−0.348772	−	0.348772i
$532$	−11.4677	−	12.3552i	−0.497186	−	0.535665i
$533$		−	3.64400i		−	0.157839i
$534$	6.46951	+	16.4801i	0.279963	+	0.713164i
$535$		0			0
$536$	5.57696	−	11.5879i	0.240888	−	0.500521i
$537$	8.48177	+	8.48177i	0.366016	+	0.366016i
$538$	36.3109	+	15.8388i	1.56547	+	0.682858i
$539$	−10.2215	−	10.2215i	−0.440270	−	0.440270i
$540$		0			0
$541$	−6.57691	+	6.57691i	−0.282764	+	0.282764i	−0.834210	−	0.551447i	$-0.814076\pi$
$541$	−6.57691	+	6.57691i	−0.282764	+	0.282764i	0.551447	+	0.834210i	$0.314076\pi$
$542$	−14.4461	−	36.7992i	−0.620513	−	1.58066i
$543$	−7.48594	+	7.48594i	−0.321253	+	0.321253i
$544$	37.1677	+	19.6244i	1.59355	+	0.841390i
$545$		0			0
$546$	3.65374	+	1.59376i	0.156366	+	0.0682066i
$547$	10.6170			0.453951			0.226976	−	0.973900i	$-0.427116\pi$
$547$	10.6170			0.453951			0.226976	+	0.973900i	$0.427116\pi$
$548$	−13.9277	−	0.518876i	−0.594964	−	0.0221653i
$549$	−9.06863	+	9.06863i	−0.387040	+	0.387040i
$550$		0			0
$551$	17.5516			0.747724
$552$	−1.54312	−	4.40654i	−0.0656796	−	0.187555i
$553$	11.7422	−	11.7422i	0.499328	−	0.499328i
$554$	34.2605	−	13.4495i	1.45559	−	0.571414i
$555$		0			0
$556$	−29.1168	−	1.08474i	−1.23483	−	0.0460033i
$557$			20.9610i			0.888146i	0.895991	+	0.444073i	$0.146467\pi$
$557$			20.9610i			0.888146i	−0.895991	+	0.444073i	$0.853533\pi$
$558$	0.170336	+	0.433905i	0.00721089	+	0.0183687i
$559$	12.3517			0.522422
$560$		0			0
$561$	−31.2575			−1.31969
$562$	12.4544	+	31.7257i	0.525356	+	1.33827i
$563$		−	16.5598i		−	0.697911i	−0.937139	−	0.348955i	$-0.886536\pi$
$563$		−	16.5598i		−	0.697911i	0.937139	−	0.348955i	$-0.113464\pi$
$564$	1.06276	−	28.5268i	0.0447503	−	1.20119i
$565$		0			0
$566$	−6.23594	+	2.44801i	−0.262116	+	0.102898i
$567$	−3.50736	+	3.50736i	−0.147295	+	0.147295i
$568$	18.9371	−	39.3479i	0.794584	−	1.65100i
$569$	39.6751			1.66327			0.831634	−	0.555325i	$-0.187406\pi$
$569$	39.6751			1.66327			0.831634	+	0.555325i	$0.187406\pi$
$570$		0			0
$571$	24.0292	−	24.0292i	1.00559	−	1.00559i	0.00560819	−	0.999984i	$-0.498215\pi$
$571$	24.0292	−	24.0292i	1.00559	−	1.00559i	0.999984	−	0.00560819i	$-0.00178515\pi$
$572$	0.333760	−	8.95885i	0.0139552	−	0.374588i
$573$	2.35602			0.0984240
$574$	5.57771	+	2.43299i	0.232809	+	0.101551i
$575$		0			0
$576$	−6.78168	−	8.49547i	−0.282570	−	0.353978i
$577$	28.7705	−	28.7705i	1.19773	−	1.19773i	0.222888	−	0.974844i	$-0.428451\pi$
$577$	28.7705	−	28.7705i	1.19773	−	1.19773i	0.974844	−	0.222888i	$-0.0715485\pi$
$578$	−19.7434	−	50.2933i	−0.821217	−	2.09193i
$579$	−7.92157	+	7.92157i	−0.329209	+	0.329209i
$580$		0			0
$581$	−3.72230	−	3.72230i	−0.154427	−	0.154427i
$582$	−3.84182	−	1.67580i	−0.159249	−	0.0694641i
$583$	−13.4704	−	13.4704i	−0.557888	−	0.557888i
$584$	1.97389	+	5.63664i	0.0816800	+	0.233246i
$585$		0			0
$586$	1.60718	+	4.09406i	0.0663922	+	0.169124i
$587$			33.4854i			1.38209i	0.722811	+	0.691046i	$0.242850\pi$
$587$			33.4854i			1.38209i	−0.722811	+	0.691046i	$0.757150\pi$
$588$	8.26657	−	7.67276i	0.340908	−	0.316419i
$589$	0.896933	+	0.896933i	0.0369575	+	0.0369575i
$590$		0			0
$591$			7.11866i			0.292822i
$592$	0.995540	−	13.3427i	0.0409164	−	0.548381i
$593$	−11.5298	−	11.5298i	−0.473472	−	0.473472i	0.429564	−	0.903036i	$-0.358667\pi$
$593$	−11.5298	−	11.5298i	−0.473472	−	0.473472i	−0.903036	+	0.429564i	$0.858667\pi$
$594$	23.7697	+	10.3683i	0.975284	+	0.425418i
$595$		0			0
$596$	1.60097	−	42.9735i	0.0655783	−	1.76026i
$597$	−8.92172			−0.365142
$598$	−2.27993	−	0.994503i	−0.0932333	−	0.0406683i
$599$		−	20.0148i		−	0.817781i	−0.912583	−	0.408891i	$-0.865916\pi$
$599$		−	20.0148i		−	0.817781i	0.912583	−	0.408891i	$-0.134084\pi$
$600$		0			0
$601$		−	27.5924i		−	1.12552i	−0.826621	−	0.562759i	$-0.809740\pi$
$601$		−	27.5924i		−	1.12552i	0.826621	−	0.562759i	$-0.190260\pi$
$602$	−8.24688	+	18.9062i	−0.336118	+	0.770560i
$603$	6.17806			0.251590
$604$	−15.6931	+	14.5658i	−0.638542	+	0.592673i
$605$		0			0
$606$	−6.80160	+	15.5929i	−0.276296	+	0.633418i
$607$	−30.4850	−	30.4850i	−1.23735	−	1.23735i	−0.961081	−	0.276265i	$-0.910903\pi$
$607$	−30.4850	−	30.4850i	−1.23735	−	1.23735i	−0.276265	−	0.961081i	$-0.589097\pi$
$608$	−26.1579	−	13.8113i	−1.06084	−	0.560120i
$609$		−	6.93104i		−	0.280860i
$610$		0			0
$611$	−10.7539	−	10.7539i	−0.435057	−	0.435057i
$612$	−0.751714	+	20.1776i	−0.0303862	+	0.815632i
$613$			20.2657i			0.818523i	0.912417	+	0.409261i	$0.134214\pi$
$613$			20.2657i			0.818523i	−0.912417	+	0.409261i	$0.865786\pi$
$614$	−19.1762	+	7.52788i	−0.773887	+	0.303801i
$615$		0			0
$616$	13.4901	+	6.49242i	0.543530	+	0.261587i
$617$	1.61302	+	1.61302i	0.0649378	+	0.0649378i	0.738830	−	0.673892i	$-0.235379\pi$
$617$	1.61302	+	1.61302i	0.0649378	+	0.0649378i	−0.673892	+	0.738830i	$0.735379\pi$
$618$	−1.66179	+	3.80971i	−0.0668470	+	0.153249i
$619$	2.46756	+	2.46756i	0.0991797	+	0.0991797i	0.754956	−	0.655776i	$-0.227658\pi$
$619$	2.46756	+	2.46756i	0.0991797	+	0.0991797i	−0.655776	+	0.754956i	$0.727658\pi$
$620$		0			0
$621$	5.08771	−	5.08771i	0.204163	−	0.204163i
$622$	−19.0316	+	7.47114i	−0.763098	+	0.299565i
$623$	−11.1377	+	11.1377i	−0.446222	+	0.446222i
$624$	6.97551	+	0.520465i	0.279244	+	0.0208353i
$625$		0			0
$626$	−8.09815	+	18.5653i	−0.323667	+	0.742017i
$627$	21.9984			0.878531
$628$	3.19177	+	3.43879i	0.127365	+	0.137222i
$629$	−17.5737	+	17.5737i	−0.700708	+	0.700708i
$630$		0			0
$631$	−29.9602			−1.19270			−0.596348	−	0.802726i	$-0.703382\pi$
$631$	−29.9602			−1.19270			−0.596348	+	0.802726i	$0.703382\pi$
$632$	12.6368	−	26.2570i	0.502666	−	1.04445i
$633$	6.96133	−	6.96133i	0.276688	−	0.276688i
$634$	−7.17026	−	18.2652i	−0.284767	−	0.725402i
$635$		0			0
$636$	10.8942	−	10.1116i	0.431981	−	0.400950i
$637$		−	6.00875i		−	0.238075i
$638$	−14.5100	+	5.69612i	−0.574457	+	0.225512i
$639$	20.9782			0.829885
$640$		0			0
$641$	−37.3386			−1.47478			−0.737392	−	0.675465i	$-0.763943\pi$
$641$	−37.3386			−1.47478			−0.737392	+	0.675465i	$0.763943\pi$
$642$	6.15901	−	2.41781i	0.243077	−	0.0954234i
$643$		−	24.5635i		−	0.968691i	−0.874877	−	0.484345i	$-0.839058\pi$
$643$		−	24.5635i		−	0.968691i	0.874877	−	0.484345i	$-0.160942\pi$
$644$	3.04448	−	2.82579i	0.119969	−	0.111352i
$645$		0			0
$646$	20.0778	+	51.1453i	0.789952	+	2.01229i
$647$	23.1347	−	23.1347i	0.909519	−	0.909519i	−0.0867142	−	0.996233i	$-0.527637\pi$
$647$	23.1347	−	23.1347i	0.909519	−	0.909519i	0.996233	+	0.0867142i	$0.0276367\pi$
$648$	−3.77459	+	7.84291i	−0.148280	+	0.308099i
$649$	27.4685			1.07823
$650$		0			0
$651$	0.354194	−	0.354194i	0.0138820	−	0.0138820i
$652$	3.72289	+	4.01101i	0.145800	+	0.157083i
$653$	50.8060			1.98819			0.994097	−	0.108496i	$-0.0346033\pi$
$653$	50.8060			1.98819			0.994097	+	0.108496i	$0.0346033\pi$
$654$	−5.33469	+	12.2299i	−0.208603	+	0.478229i
$655$		0			0
$656$	10.6486	+	0.794528i	0.415759	+	0.0310211i
$657$	−2.02877	+	2.02877i	−0.0791497	+	0.0791497i
$658$	23.6406	−	9.28047i	0.921607	−	0.361790i
$659$	9.97780	−	9.97780i	0.388680	−	0.388680i	−0.485537	−	0.874216i	$-0.661376\pi$
$659$	9.97780	−	9.97780i	0.388680	−	0.388680i	0.874216	+	0.485537i	$0.161376\pi$
$660$		0			0
$661$	−5.09643	−	5.09643i	−0.198228	−	0.198228i	0.601012	−	0.799240i	$-0.294764\pi$
$661$	−5.09643	−	5.09643i	−0.198228	−	0.198228i	−0.799240	+	0.601012i	$0.794764\pi$
$662$	1.35505	−	3.10648i	0.0526653	−	0.120737i
$663$	−9.18745	−	9.18745i	−0.356811	−	0.356811i
$664$	−8.32353	−	4.00590i	−0.323015	−	0.155459i
$665$		0			0
$666$	5.98320	−	2.34879i	0.231844	−	0.0910139i
$667$			4.32496i			0.167463i
$668$	−1.06697	+	28.6399i	−0.0412825	+	1.10811i
$669$	−11.0402	−	11.0402i	−0.426838	−	0.426838i
$670$		0			0
$671$		−	30.9947i		−	1.19654i
$672$	−5.45399	+	10.3296i	−0.210392	+	0.398473i
$673$	31.6322	+	31.6322i	1.21933	+	1.21933i	0.967867	+	0.251464i	$0.0809121\pi$
$673$	31.6322	+	31.6322i	1.21933	+	1.21933i	0.251464	+	0.967867i	$0.419088\pi$
$674$	7.62323	−	17.4765i	0.293636	−	0.673169i
$675$		0			0
$676$	−16.3251	+	15.1524i	−0.627889	+	0.582786i
$677$	−25.6600			−0.986196			−0.493098	−	0.869974i	$-0.664136\pi$
$677$	−25.6600			−0.986196			−0.493098	+	0.869974i	$0.664136\pi$
$678$	4.38350	−	10.0493i	0.168347	−	0.385942i
$679$		−	3.72896i		−	0.143104i
$680$		0			0
$681$			7.71190i			0.295521i
$682$	−1.03259	−	0.450413i	−0.0395397	−	0.0172472i
$683$	−12.3536			−0.472698			−0.236349	−	0.971668i	$-0.575951\pi$
$683$	−12.3536			−0.472698			−0.236349	+	0.971668i	$0.575951\pi$
$684$	0.529041	−	14.2006i	0.0202284	−	0.542974i
$685$		0			0
$686$	23.8230	+	10.3915i	0.909564	+	0.396751i
$687$	−0.728309	−	0.728309i	−0.0277867	−	0.0277867i
$688$	−2.69314	+	36.0946i	−0.102675	+	1.37610i
$689$		−	7.91866i		−	0.301677i
$690$		0			0
$691$	22.5426	+	22.5426i	0.857561	+	0.857561i	0.991050	−	0.133489i	$-0.0426180\pi$
$691$	22.5426	+	22.5426i	0.857561	+	0.857561i	−0.133489	+	0.991050i	$0.542618\pi$
$692$	12.8938	−	11.9676i	0.490147	−	0.454938i
$693$			7.19219i			0.273209i
$694$	−3.44831	−	8.78406i	−0.130896	−	0.333438i
$695$		0			0
$696$	−4.01978	−	11.4789i	−0.152369	−	0.435107i
$697$	−14.0253	−	14.0253i	−0.531247	−	0.531247i
$698$	−3.71438	−	1.62021i	−0.140591	−	0.0613258i
$699$	−16.2673	−	16.2673i	−0.615285	−	0.615285i
$700$		0			0
$701$	26.9530	−	26.9530i	1.01800	−	1.01800i	0.0181663	−	0.999835i	$-0.494217\pi$
$701$	26.9530	−	26.9530i	1.01800	−	1.01800i	0.999835	−	0.0181663i	$-0.00578284\pi$
$702$	3.93904	+	10.0341i	0.148670	+	0.378714i
$703$	12.3680	−	12.3680i	0.466467	−	0.466467i
$704$	26.1071	+	2.92869i	0.983947	+	0.110379i
$705$		0			0
$706$	9.83583	+	4.29038i	0.370176	+	0.161471i
$707$	−15.1348			−0.569203
$708$	−0.797891	+	21.4171i	−0.0299866	+	0.804905i
$709$	−7.78615	+	7.78615i	−0.292415	+	0.292415i	−0.838034	−	0.545619i	$-0.816295\pi$
$709$	−7.78615	+	7.78615i	−0.292415	+	0.292415i	0.545619	+	0.838034i	$0.316295\pi$
$710$		0			0
$711$	13.9988			0.524997
$712$	−11.9863	+	24.9053i	−0.449205	+	0.933365i
$713$	−0.221016	+	0.221016i	−0.00827713	+	0.00827713i
$714$	20.1970	−	7.92863i	0.755854	−	0.296721i
$715$		0			0
$716$	−0.697158	+	18.7132i	−0.0260540	+	0.699346i
$717$			2.28427i			0.0853076i
$718$	4.01079	+	10.2169i	0.149681	+	0.381291i
$719$	−20.6777			−0.771150			−0.385575	−	0.922677i	$-0.625997\pi$
$719$	−20.6777			−0.771150			−0.385575	+	0.922677i	$0.625997\pi$
$720$		0			0
$721$	−3.69779			−0.137713
$722$	−4.31161	−	10.9832i	−0.160461	−	0.408751i
$723$		−	13.3797i		−	0.497597i
$724$	−16.5161	−	0.615306i	−0.613817	−	0.0228677i
$725$		0			0
$726$	0.364783	−	0.143201i	0.0135384	−	0.00531469i
$727$	−20.4994	+	20.4994i	−0.760280	+	0.760280i	−0.976373	−	0.216093i	$-0.930669\pi$
$727$	−20.4994	+	20.4994i	−0.760280	+	0.760280i	0.216093	+	0.976373i	$0.430669\pi$
$728$	2.05680	+	5.87341i	0.0762301	+	0.217683i
$729$	−25.6425			−0.949722
$730$		0			0
$731$	47.5403	−	47.5403i	1.75834	−	1.75834i
$732$	24.1665	+	0.900320i	0.893221	+	0.0332768i
$733$	−10.7306			−0.396344			−0.198172	−	0.980167i	$-0.563500\pi$
$733$	−10.7306			−0.396344			−0.198172	+	0.980167i	$0.563500\pi$
$734$	33.0956	+	14.4363i	1.22158	+	0.532853i
$735$		0			0
$736$	3.40328	−	6.44565i	0.125447	−	0.237590i
$737$	−10.5577	+	10.5577i	−0.388897	+	0.388897i
$738$	1.87454	+	4.77511i	0.0690028	+	0.175774i
$739$	−2.93837	+	2.93837i	−0.108090	+	0.108090i	−0.759083	−	0.650994i	$-0.774352\pi$
$739$	−2.93837	+	2.93837i	−0.108090	+	0.108090i	0.650994	+	0.759083i	$0.274352\pi$
$740$		0			0
$741$	6.46594	+	6.46594i	0.237532	+	0.237532i
$742$	12.1207	+	5.28705i	0.444966	+	0.194094i
$743$	0.223404	+	0.223404i	0.00819590	+	0.00819590i	0.711193	−	0.702997i	$-0.248155\pi$
$743$	0.223404	+	0.223404i	0.00819590	+	0.00819590i	−0.702997	+	0.711193i	$0.748155\pi$
$744$	0.381180	−	0.792022i	0.0139747	−	0.0290369i
$745$		0			0
$746$	2.25416	+	5.74215i	0.0825308	+	0.210235i
$747$		−	4.43766i		−	0.162366i
$748$	−33.1969	−	35.7661i	−1.21380	−	1.30774i
$749$	4.16243	+	4.16243i	0.152092	+	0.152092i
$750$		0			0
$751$			39.9939i			1.45940i	0.683769	+	0.729699i	$0.260340\pi$
$751$			39.9939i			1.45940i	−0.683769	+	0.729699i	$0.739660\pi$
$752$	33.7702	−	29.0807i	1.23147	−	1.06046i
$753$	16.2055	+	16.2055i	0.590563	+	0.590563i
$754$	−5.93915	−	2.59065i	−0.216291	−	0.0943459i
$755$		0			0
$756$	−17.9888	−	0.670168i	−0.654245	−	0.0243738i
$757$	−32.9120			−1.19621			−0.598103	−	0.801419i	$-0.704079\pi$
$757$	−32.9120			−1.19621			−0.598103	+	0.801419i	$0.704079\pi$
$758$	10.8721	+	4.74241i	0.394894	+	0.172252i
$759$			5.42070i			0.196759i
$760$		0			0
$761$		−	33.9591i		−	1.23102i	−0.788130	−	0.615509i	$-0.788951\pi$
$761$		−	33.9591i		−	1.23102i	0.788130	−	0.615509i	$-0.211049\pi$
$762$	−7.47058	+	17.1266i	−0.270631	+	0.620430i
$763$	−11.8707			−0.429747
$764$	2.50220	+	2.69585i	0.0905263	+	0.0975324i
$765$		0			0
$766$	−15.4602	+	35.4429i	−0.558598	+	1.28060i
$767$	8.07375	+	8.07375i	0.291526	+	0.291526i
$768$	−3.04184	+	20.2706i	−0.109763	+	0.731452i
$769$			40.2535i			1.45158i	0.687917	+	0.725789i	$0.258525\pi$
$769$			40.2535i			1.45158i	−0.687917	+	0.725789i	$0.741475\pi$
$770$		0			0
$771$	−5.29172	−	5.29172i	−0.190577	−	0.190577i
$772$	−17.4773	−	0.651112i	−0.629020	−	0.0234340i
$773$		−	9.47175i		−	0.340675i	−0.985386	−	0.170338i	$-0.945514\pi$
$773$		−	9.47175i		−	0.340675i	0.985386	−	0.170338i	$-0.0544858\pi$
$774$	−16.1858	+	6.35396i	−0.581785	+	0.228388i
$775$		0			0
$776$	−2.16268	−	6.17575i	−0.0776355	−	0.221696i
$777$	−4.88405	−	4.88405i	−0.175214	−	0.175214i
$778$	−5.02656	+	11.5236i	−0.180211	+	0.413139i
$779$	9.87073	+	9.87073i	0.353656	+	0.353656i
$780$		0			0
$781$	−35.8496	+	35.8496i	−1.28280	+	1.28280i
$782$	−12.6029	+	4.94745i	−0.450679	+	0.176921i
$783$	13.2533	−	13.2533i	0.473636	−	0.473636i
$784$	17.5590	+	1.31013i	0.627106	+	0.0467904i
$785$		0			0
$786$	−12.2717	+	28.1333i	−0.437717	+	1.00348i
$787$	48.1367			1.71589			0.857945	−	0.513742i	$-0.171741\pi$
$787$	48.1367			1.71589			0.857945	+	0.513742i	$0.171741\pi$
$788$	−8.14546	+	7.56034i	−0.290170	+	0.269326i
$789$	−21.9455	+	21.9455i	−0.781282	+	0.781282i
$790$		0			0
$791$	9.75409			0.346815
$792$	4.17124	+	11.9114i	0.148218	+	0.423253i
$793$	9.11021	−	9.11021i	0.323513	−	0.323513i
$794$	3.40253	+	8.66743i	0.120751	+	0.307596i
$795$		0			0
$796$	−9.47528	−	10.2086i	−0.335842	−	0.361834i
$797$		−	33.8962i		−	1.20066i	−0.799751	−	0.600332i	$-0.795035\pi$
$797$		−	33.8962i		−	1.20066i	0.799751	−	0.600332i	$-0.204965\pi$
$798$	−14.2142	+	5.58001i	−0.503178	+	0.197530i
$799$	−82.7810			−2.92858
$800$		0			0
$801$	−13.2782			−0.469162
$802$	26.0586	−	10.2297i	0.920160	−	0.361222i
$803$		−	6.93391i		−	0.244692i
$804$	−7.92513	−	8.53847i	−0.279498	−	0.301129i
$805$		0			0
$806$	−0.171117	−	0.435894i	−0.00602733	−	0.0153537i
$807$	25.3753	−	25.3753i	0.893254	−	0.893254i
$808$	−25.0656	+	8.77770i	−0.881806	+	0.308798i
$809$	−27.5625			−0.969047			−0.484523	−	0.874778i	$-0.661007\pi$
$809$	−27.5625			−0.969047			−0.484523	+	0.874778i	$0.661007\pi$
$810$		0			0
$811$	−24.1817	+	24.1817i	−0.849133	+	0.849133i	−0.990025	−	0.140892i	$-0.955003\pi$
$811$	−24.1817	+	24.1817i	−0.849133	+	0.849133i	0.140892	+	0.990025i	$0.455003\pi$
$812$	7.93078	−	7.36108i	0.278316	−	0.258323i
$813$	−35.8120			−1.25598
$814$	−6.21083	+	14.2385i	−0.217689	+	0.499060i
$815$		0			0
$816$	28.8511	−	24.8447i	1.00999	−	0.869738i
$817$	−33.4579	+	33.4579i	−1.17054	+	1.17054i
$818$	−7.59486	+	2.98148i	−0.265548	+	0.104245i
$819$	−2.11398	+	2.11398i	−0.0738686	+	0.0738686i
$820$		0			0
$821$	0.0575735	+	0.0575735i	0.00200933	+	0.00200933i	0.708111	−	0.706101i	$-0.249548\pi$
$821$	0.0575735	+	0.0575735i	0.00200933	+	0.00200933i	−0.706101	+	0.708111i	$0.749548\pi$
$822$	−5.04790	+	11.5725i	−0.176066	+	0.403636i
$823$	−28.5594	−	28.5594i	−0.995518	−	0.995518i	0.00447159	−	0.999990i	$-0.498577\pi$
$823$	−28.5594	−	28.5594i	−0.995518	−	0.995518i	−0.999990	+	0.00447159i	$0.998577\pi$
$824$	−6.12412	+	2.14460i	−0.213344	+	0.0747106i
$825$		0			0
$826$	−17.7487	+	6.96752i	−0.617557	+	0.242431i
$827$		−	23.0863i		−	0.802788i	−0.915905	−	0.401394i	$-0.868526\pi$
$827$		−	23.0863i		−	0.802788i	0.915905	−	0.401394i	$-0.131474\pi$
$828$	3.49922	+	0.130363i	0.121606	+	0.00453042i
$829$	33.3543	+	33.3543i	1.15844	+	1.15844i	0.984811	+	0.173631i	$0.0555499\pi$
$829$	33.3543	+	33.3543i	1.15844	+	1.15844i	0.173631	+	0.984811i	$0.444450\pi$
$830$		0			0
$831$		−	33.3414i		−	1.15660i
$832$	6.81277	+	8.53442i	0.236190	+	0.295878i
$833$	−23.1269	−	23.1269i	−0.801301	−	0.801301i
$834$	−10.5529	+	24.1930i	−0.365419	+	0.837734i
$835$		0			0
$836$	23.3633	+	25.1715i	0.808037	+	0.870573i
$837$	1.35456			0.0468204
$838$	−6.94829	+	15.9292i	−0.240025	+	0.550264i
$839$		−	49.4524i		−	1.70729i	−0.520859	−	0.853643i	$-0.674388\pi$
$839$		−	49.4524i		−	1.70729i	0.520859	−	0.853643i	$-0.325612\pi$
$840$		0			0
$841$		−	17.7336i		−	0.611504i
$842$	36.8825	+	16.0881i	1.27106	+	0.554433i
$843$	30.8746			1.06338
$844$	15.3587	+	0.572185i	0.528668	+	0.0196954i
$845$		0			0
$846$	19.6240	+	8.55996i	0.674687	+	0.294298i
$847$	0.246530	+	0.246530i	0.00847089	+	0.00847089i
$848$	23.1402	+	1.72656i	0.794637	+	0.0592904i
$849$			6.06865i			0.208276i
$850$		0			0
$851$	3.04764	+	3.04764i	0.104472	+	0.104472i
$852$	−26.9105	−	28.9932i	−0.921940	−	0.993292i
$853$			31.3639i			1.07388i	0.843621	+	0.536939i	$0.180419\pi$
$853$			31.3639i			1.07388i	−0.843621	+	0.536939i	$0.819581\pi$
$854$	7.86197	+	20.0272i	0.269031	+	0.685316i
$855$		0			0
$856$	9.30771	+	4.47957i	0.318131	+	0.153108i
$857$	16.1594	+	16.1594i	0.551996	+	0.551996i	0.927016	−	0.375021i	$-0.122364\pi$
$857$	16.1594	+	16.1594i	0.551996	+	0.551996i	−0.375021	+	0.927016i	$0.622364\pi$
$858$	−7.44385	−	3.24700i	−0.254129	−	0.110851i
$859$	30.7369	+	30.7369i	1.04873	+	1.04873i	0.998750	+	0.0499792i	$0.0159155\pi$
$859$	30.7369	+	30.7369i	1.04873	+	1.04873i	0.0499792	+	0.998750i	$0.484085\pi$
$860$		0			0
$861$	3.89790	−	3.89790i	0.132840	−	0.132840i
$862$	17.3765	+	44.2640i	0.591845	+	1.50764i
$863$	−18.9353	+	18.9353i	−0.644565	+	0.644565i	−0.951674	−	0.307109i	$-0.900638\pi$
$863$	−18.9353	+	18.9353i	−0.644565	+	0.644565i	0.307109	+	0.951674i	$0.400638\pi$
$864$	−30.1809	+	9.32299i	−1.02678	+	0.317175i
$865$		0			0
$866$	−13.6858	−	5.96974i	−0.465063	−	0.202860i
$867$	−48.9441			−1.66223
$868$	0.781453	+	0.0291129i	0.0265242	+	0.000988156i
$869$	−23.9226	+	23.9226i	−0.811517	+	0.811517i
$870$		0			0
$871$	−6.20638			−0.210295
$872$	−19.6597	+	6.88460i	−0.665761	+	0.233142i
$873$	2.22280	−	2.22280i	0.0752305	−	0.0752305i
$874$	8.86966	−	3.48191i	0.300021	−	0.117778i
$875$		0			0
$876$	5.40636	+	0.201413i	0.182664	+	0.00680511i
$877$			49.7461i			1.67981i	0.542737	+	0.839903i	$0.317388\pi$
$877$			49.7461i			1.67981i	−0.542737	+	0.839903i	$0.682612\pi$
$878$	4.09251	+	10.4250i	0.138115	+	0.351828i
$879$	3.98423			0.134385
$880$		0			0
$881$	27.7694			0.935574			0.467787	−	0.883841i	$-0.345051\pi$
$881$	27.7694			0.935574			0.467787	+	0.883841i	$0.345051\pi$
$882$	3.09101	+	7.87389i	0.104080	+	0.265128i
$883$			42.4602i			1.42890i	0.699686	+	0.714450i	$0.253323\pi$
$883$			42.4602i			1.42890i	−0.699686	+	0.714450i	$0.746677\pi$
$884$	0.755161	−	20.2702i	0.0253988	−	0.681759i
$885$		0			0
$886$	−14.0150	+	5.50178i	−0.470842	+	0.184836i
$887$	16.1076	−	16.1076i	0.540842	−	0.540842i	−0.382934	−	0.923776i	$-0.625086\pi$
$887$	16.1076	−	16.1076i	0.540842	−	0.540842i	0.923776	+	0.382934i	$0.125086\pi$
$888$	−10.9213	−	5.25617i	−0.366496	−	0.176385i
$889$	−16.6234			−0.557531
$890$		0			0
$891$	7.14563	−	7.14563i	0.239388	−	0.239388i
$892$	0.907445	−	24.3578i	0.0303835	−	0.815560i
$893$	58.2596			1.94958
$894$	−35.7064	−	15.5751i	−1.19420	−	0.520909i
$895$		0			0
$896$	−17.6119	+	4.72983i	−0.588373	+	0.158012i
$897$	−1.59329	+	1.59329i	−0.0531986	+	0.0531986i
$898$	3.14260	+	8.00530i	0.104870	+	0.267140i
$899$	−0.575741	+	0.575741i	−0.0192020	+	0.0192020i
$900$		0			0
$901$	−30.4780	−	30.4780i	−1.01537	−	1.01537i
$902$	−11.3636	−	4.95678i	−0.378366	−	0.165043i
$903$	13.2123	+	13.2123i	0.439679	+	0.439679i
$904$	16.1543	−	5.65706i	0.537285	−	0.188151i
$905$		0			0
$906$	7.08751	+	18.0544i	0.235467	+	0.599816i
$907$		−	9.20991i		−	0.305810i	−0.988241	−	0.152905i	$-0.951137\pi$
$907$		−	9.20991i		−	0.305810i	0.988241	−	0.152905i	$-0.0488628\pi$
$908$	−8.82427	+	8.19040i	−0.292844	+	0.271808i
$909$	−9.02174	−	9.02174i	−0.299232	−	0.299232i
$910$		0			0
$911$			45.8065i			1.51764i	0.651302	+	0.758819i	$0.274223\pi$
$911$			45.8065i			1.51764i	−0.651302	+	0.758819i	$0.725777\pi$
$912$	−20.3048	+	17.4852i	−0.672359	+	0.578992i
$913$	7.58351	+	7.58351i	0.250978	+	0.250978i
$914$	0.575282	+	0.250938i	0.0190286	+	0.00830028i
$915$		0			0
$916$	0.0598632	−	1.60686i	0.00197794	−	0.0530921i
$917$	−27.3068			−0.901749
$918$	53.7810	+	23.4592i	1.77504	+	0.774270i
$919$		−	5.52468i		−	0.182242i	−0.995840	−	0.0911211i	$-0.970955\pi$
$919$		−	5.52468i		−	0.182242i	0.995840	−	0.0911211i	$-0.0290450\pi$
$920$		0			0
$921$			18.6617i			0.614924i
$922$	7.92398	−	18.1660i	0.260962	−	0.598264i
$923$	−21.0744			−0.693672
$924$	9.94007	−	9.22604i	0.327004	−	0.303514i
$925$		0			0
$926$	13.8681	−	31.7930i	0.455734	−	1.04478i
$927$	−2.20422	−	2.20422i	−0.0723961	−	0.0723961i
$928$	8.86544	−	16.7907i	0.291022	−	0.551182i
$929$		−	43.4288i		−	1.42485i	−0.701746	−	0.712427i	$-0.747596\pi$
$929$		−	43.4288i		−	1.42485i	0.701746	−	0.712427i	$-0.252404\pi$
$930$		0			0
$931$	16.2763	+	16.2763i	0.533433	+	0.533433i
$932$	1.33708	−	35.8903i	0.0437977	−	1.17562i
$933$			18.5210i			0.606352i
$934$	−2.00446	+	0.786879i	−0.0655878	+	0.0257475i
$935$		0			0
$936$	−2.27505	+	4.72713i	−0.0743623	+	0.154511i
$937$	20.7275	+	20.7275i	0.677138	+	0.677138i	0.959352	−	0.282213i	$-0.0910686\pi$
$937$	20.7275	+	20.7275i	0.677138	+	0.677138i	−0.282213	+	0.959352i	$0.591069\pi$
$938$	4.14381	−	9.49983i	0.135300	−	0.310180i
$939$	12.9741	+	12.9741i	0.423392	+	0.423392i
$940$		0			0
$941$	12.3393	−	12.3393i	0.402251	−	0.402251i	−0.476775	−	0.879026i	$-0.658194\pi$
$941$	12.3393	−	12.3393i	0.402251	−	0.402251i	0.879026	+	0.476775i	$0.158194\pi$
$942$	3.95621	−	1.55307i	0.128900	−	0.0506017i
$943$	−2.43228	+	2.43228i	−0.0792060	+	0.0792060i
$944$	−25.3538	+	21.8330i	−0.825194	+	0.710604i
$945$		0			0
$946$	16.8015	−	38.5181i	0.546265	−	1.25233i
$947$	48.3611			1.57152			0.785762	−	0.618529i	$-0.212271\pi$
$947$	48.3611			1.57152			0.785762	+	0.618529i	$0.212271\pi$
$948$	−17.9575	−	19.3473i	−0.583233	−	0.628371i
$949$	2.03807	−	2.03807i	0.0661585	−	0.0661585i
$950$		0			0
$951$	−17.7752			−0.576399
$952$	30.5224	+	14.6897i	0.989237	+	0.476095i
$953$	−34.0371	+	34.0371i	−1.10257	+	1.10257i	−0.108471	+	0.994100i	$0.534595\pi$
$953$	−34.0371	+	34.0371i	−1.10257	+	1.10257i	−0.994100	+	0.108471i	$0.965405\pi$
$954$	4.07350	+	10.3766i	0.131885	+	0.335956i
$955$		0			0
$956$	−2.61375	+	2.42600i	−0.0845348	+	0.0784624i
$957$			14.1208i			0.456459i
$958$	−0.668286	+	0.262346i	−0.0215913	+	0.00847600i
$959$	−11.2325			−0.362716
$960$		0			0
$961$	30.9412			0.998102
$962$	−6.01063	+	2.35956i	−0.193791	+	0.0760753i
$963$			4.96238i			0.159911i
$964$	15.3096	−	14.2099i	0.493090	−	0.457669i
$965$		0			0
$966$	−1.37499	−	3.50258i	−0.0442395	−	0.112694i
$967$	18.9307	−	18.9307i	0.608770	−	0.608770i	−0.333855	−	0.942625i	$-0.608349\pi$
$967$	18.9307	−	18.9307i	0.608770	−	0.608770i	0.942625	+	0.333855i	$0.108349\pi$
$968$	0.551273	+	0.265314i	0.0177186	+	0.00852751i
$969$	49.7732			1.59895
$970$		0			0
$971$	−21.2698	+	21.2698i	−0.682580	+	0.682580i	−0.960581	−	0.278001i	$-0.910328\pi$
$971$	−21.2698	+	21.2698i	−0.682580	+	0.682580i	0.278001	+	0.960581i	$0.410328\pi$
$972$	−17.4288	−	18.7776i	−0.559028	−	0.602292i
$973$	−23.4822			−0.752805
$974$	20.7752	−	47.6278i	0.665681	−	1.52609i
$975$		0			0
$976$	24.6358	+	28.6085i	0.788573	+	0.915736i
$977$	−2.13884	+	2.13884i	−0.0684275	+	0.0684275i	−0.740492	−	0.672065i	$-0.765408\pi$
$977$	−2.13884	+	2.13884i	−0.0684275	+	0.0684275i	0.672065	+	0.740492i	$0.265408\pi$
$978$	4.61454	−	1.81151i	0.147557	−	0.0579256i
$979$	22.6911	−	22.6911i	0.725210	−	0.725210i
$980$		0			0
$981$	−7.07601	−	7.07601i	−0.225919	−	0.225919i
$982$	−2.62447	+	6.01667i	−0.0837501	+	0.192000i
$983$	6.18193	+	6.18193i	0.197173	+	0.197173i	0.798787	−	0.601614i	$-0.205475\pi$
$983$	6.18193	+	6.18193i	0.197173	+	0.197173i	−0.601614	+	0.798787i	$0.705475\pi$
$984$	4.19488	−	8.71619i	0.133728	−	0.277862i
$985$		0			0
$986$	−32.8301	+	12.8880i	−1.04552	+	0.410436i
$987$		−	23.0064i		−	0.732302i
$988$	−0.531466	+	14.2657i	−0.0169082	+	0.453853i
$989$	−8.24447	−	8.24447i	−0.262159	−	0.262159i
$990$		0			0
$991$		−	43.4847i		−	1.38134i	−0.723172	−	0.690668i	$-0.757317\pi$
$991$		−	43.4847i		−	1.38134i	0.723172	−	0.690668i	$-0.242683\pi$
$992$	1.31110	−	0.405002i	0.0416273	−	0.0128588i
$993$	−2.17092	−	2.17092i	−0.0688921	−	0.0688921i
$994$	14.0707	−	32.2576i	0.446297	−	1.02315i
$995$		0			0
$996$	−6.13314	+	5.69257i	−0.194336	+	0.180376i
$997$	33.4043			1.05793			0.528963	−	0.848645i	$-0.322581\pi$
$997$	33.4043			1.05793			0.528963	+	0.848645i	$0.322581\pi$
$998$	5.38879	−	12.3540i	0.170579	−	0.391059i
$999$		−	18.6783i		−	0.590954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.j.d.43.8		18
4.3	odd	2		1600.2.j.d.143.7		18
5.2	odd	4		400.2.s.d.107.6		18
5.3	odd	4		80.2.s.b.27.4	yes	18
5.4	even	2		80.2.j.b.43.2	✓	18
15.8	even	4		720.2.z.g.667.6		18
15.14	odd	2		720.2.bd.g.523.8		18
16.3	odd	4		400.2.s.d.243.6		18
16.13	even	4		1600.2.s.d.943.7		18
20.3	even	4		320.2.s.b.207.3		18
20.7	even	4		1600.2.s.d.207.7		18
20.19	odd	2		320.2.j.b.143.3		18
40.3	even	4		640.2.s.c.287.7		18
40.13	odd	4		640.2.s.d.287.3		18
40.19	odd	2		640.2.j.c.543.7		18
40.29	even	2		640.2.j.d.543.3		18
80.3	even	4		80.2.j.b.67.2	yes	18
80.13	odd	4		320.2.j.b.47.7		18
80.19	odd	4		80.2.s.b.3.4	yes	18
80.29	even	4		320.2.s.b.303.3		18
80.43	even	4		640.2.j.d.607.7		18
80.53	odd	4		640.2.j.c.607.3		18
80.59	odd	4		640.2.s.d.223.3		18
80.67	even	4	inner	400.2.j.d.307.8		18
80.69	even	4		640.2.s.c.223.7		18
80.77	odd	4		1600.2.j.d.1007.3		18
240.83	odd	4		720.2.bd.g.307.8		18
240.179	even	4		720.2.z.g.163.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.2	✓	18	5.4	even	2
80.2.j.b.67.2	yes	18	80.3	even	4
80.2.s.b.3.4	yes	18	80.19	odd	4
80.2.s.b.27.4	yes	18	5.3	odd	4
320.2.j.b.47.7		18	80.13	odd	4
320.2.j.b.143.3		18	20.19	odd	2
320.2.s.b.207.3		18	20.3	even	4
320.2.s.b.303.3		18	80.29	even	4
400.2.j.d.43.8		18	1.1	even	1	trivial
400.2.j.d.307.8		18	80.67	even	4	inner
400.2.s.d.107.6		18	5.2	odd	4
400.2.s.d.243.6		18	16.3	odd	4
640.2.j.c.543.7		18	40.19	odd	2
640.2.j.c.607.3		18	80.53	odd	4
640.2.j.d.543.3		18	40.29	even	2
640.2.j.d.607.7		18	80.43	even	4
640.2.s.c.223.7		18	80.69	even	4
640.2.s.c.287.7		18	40.3	even	4
640.2.s.d.223.3		18	80.59	odd	4
640.2.s.d.287.3		18	40.13	odd	4
720.2.z.g.163.6		18	240.179	even	4
720.2.z.g.667.6		18	15.8	even	4
720.2.bd.g.307.8		18	240.83	odd	4
720.2.bd.g.523.8		18	15.14	odd	2
1600.2.j.d.143.7		18	4.3	odd	2
1600.2.j.d.1007.3		18	80.77	odd	4
1600.2.s.d.207.7		18	20.7	even	4
1600.2.s.d.943.7		18	16.13	even	4

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31641 - 0.516777i) q^{2} -1.28110i q^{3} +(1.46588 - 1.36058i) q^{4} +(-0.662041 - 1.68645i) q^{6} +(1.13975 - 1.13975i) q^{7} +(1.22659 - 2.54862i) q^{8} +1.35879 q^{9} +O(q^{10})\)	\(q+(1.31641 - 0.516777i) q^{2} -1.28110i q^{3} +(1.46588 - 1.36058i) q^{4} +(-0.662041 - 1.68645i) q^{6} +(1.13975 - 1.13975i) q^{7} +(1.22659 - 2.54862i) q^{8} +1.35879 q^{9} +(-2.32204 + 2.32204i) q^{11} +(-1.74304 - 1.87794i) q^{12} -1.36502 q^{13} +(0.911384 - 2.08938i) q^{14} +(0.297625 - 3.98891i) q^{16} +(-5.25380 + 5.25380i) q^{17} +(1.78873 - 0.702192i) q^{18} +(3.69752 - 3.69752i) q^{19} +(-1.46013 - 1.46013i) q^{21} +(-1.85678 + 4.25673i) q^{22} +(0.911118 + 0.911118i) q^{23} +(-3.26503 - 1.57138i) q^{24} +(-1.79693 + 0.705412i) q^{26} -5.58403i q^{27} +(0.120015 - 3.22146i) q^{28} +(2.37343 + 2.37343i) q^{29} +0.242577i q^{31} +(-1.66958 - 5.40486i) q^{32} +(2.97475 + 2.97475i) q^{33} +(-4.20112 + 9.63121i) q^{34} +(1.99183 - 1.84875i) q^{36} +3.34494 q^{37} +(2.95666 - 6.77825i) q^{38} +1.74872i q^{39} +2.66956i q^{41} +(-2.67669 - 1.16757i) q^{42} -9.04874 q^{43} +(-0.244509 + 6.56316i) q^{44} +(1.67025 + 0.728562i) q^{46} +(7.87820 + 7.87820i) q^{47} +(-5.11018 - 0.381287i) q^{48} +4.40194i q^{49} +(6.73063 + 6.73063i) q^{51} +(-2.00096 + 1.85723i) q^{52} +5.80113i q^{53} +(-2.88570 - 7.35089i) q^{54} +(-1.50679 - 4.30279i) q^{56} +(-4.73688 - 4.73688i) q^{57} +(4.35095 + 1.89788i) q^{58} +(-5.91474 - 5.91474i) q^{59} +(-6.67404 + 6.67404i) q^{61} +(0.125358 + 0.319332i) q^{62} +(1.54868 - 1.54868i) q^{63} +(-4.99096 - 6.25222i) q^{64} +(5.45328 + 2.37872i) q^{66} +4.54673 q^{67} +(-0.553222 + 14.8497i) q^{68} +(1.16723 - 1.16723i) q^{69} +15.4389 q^{71} +(1.66668 - 3.46305i) q^{72} +(-1.49307 + 1.49307i) q^{73} +(4.40332 - 1.72859i) q^{74} +(0.389347 - 10.4509i) q^{76} +5.29308i q^{77} +(0.903701 + 2.30204i) q^{78} +10.3024 q^{79} -3.07731 q^{81} +(1.37957 + 3.51424i) q^{82} -3.26589i q^{83} +(-4.12701 - 0.153751i) q^{84} +(-11.9119 + 4.67618i) q^{86} +(3.04060 - 3.04060i) q^{87} +(3.06981 + 8.76618i) q^{88} -9.77206 q^{89} +(-1.55578 + 1.55578i) q^{91} +(2.57524 + 0.0959403i) q^{92} +0.310765 q^{93} +(14.4422 + 6.29969i) q^{94} +(-6.92415 + 2.13889i) q^{96} +(1.63587 - 1.63587i) q^{97} +(2.27482 + 5.79477i) q^{98} +(-3.15516 + 3.15516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9}+O(q^{10}) \) 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9	\( 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9} - 2 q^{11} - 4 q^{12} + 12 q^{14} + 6 q^{17} - 16 q^{18} + 2 q^{19} - 16 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 16 q^{26} + 4 q^{28} - 14 q^{29} + 4 q^{32} + 8 q^{33} - 28 q^{34} - 4 q^{36} - 8 q^{37} - 16 q^{38} - 28 q^{42} + 44 q^{43} + 44 q^{44} + 12 q^{46} + 38 q^{47} - 60 q^{48} + 8 q^{51} + 40 q^{52} - 4 q^{54} + 20 q^{56} - 24 q^{57} + 20 q^{58} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 16 q^{64} + 4 q^{66} - 12 q^{67} - 36 q^{68} + 32 q^{69} + 24 q^{71} + 36 q^{72} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 84 q^{78} + 16 q^{79} + 2 q^{81} + 28 q^{82} - 24 q^{84} - 36 q^{86} - 24 q^{87} + 96 q^{88} - 12 q^{89} - 52 q^{92} - 16 q^{93} + 28 q^{94} - 40 q^{96} - 18 q^{97} - 32 q^{98} - 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9 - 2 * q^11 - 4 * q^12 + 12 * q^14 + 6 * q^17 - 16 * q^18 + 2 * q^19 - 16 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 16 * q^26 + 4 * q^28 - 14 * q^29 + 4 * q^32 + 8 * q^33 - 28 * q^34 - 4 * q^36 - 8 * q^37 - 16 * q^38 - 28 * q^42 + 44 * q^43 + 44 * q^44 + 12 * q^46 + 38 * q^47 - 60 * q^48 + 8 * q^51 + 40 * q^52 - 4 * q^54 + 20 * q^56 - 24 * q^57 + 20 * q^58 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 16 * q^64 + 4 * q^66 - 12 * q^67 - 36 * q^68 + 32 * q^69 + 24 * q^71 + 36 * q^72 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 84 * q^78 + 16 * q^79 + 2 * q^81 + 28 * q^82 - 24 * q^84 - 36 * q^86 - 24 * q^87 + 96 * q^88 - 12 * q^89 - 52 * q^92 - 16 * q^93 + 28 * q^94 - 40 * q^96 - 18 * q^97 - 32 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more