LMFDB - Embedded newform 475.2.j.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(49,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("475.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.j (of order $6$, degree $2$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	475.49
Dual form			475.2.j.a.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 - 1.00000i) q^{3} +(-1.00000 - 1.73205i) q^{4} -4.00000i q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.73205 - 1.00000i) q^{3} +(-1.00000 - 1.73205i) q^{4} -4.00000i q^{7} +(0.500000 + 0.866025i) q^{9} +3.00000 q^{11} +4.00000i q^{12} +(-1.73205 + 1.00000i) q^{13} +(-2.00000 + 3.46410i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(3.50000 + 2.59808i) q^{19} +(-4.00000 + 6.92820i) q^{21} +4.00000i q^{27} +(-6.92820 + 4.00000i) q^{28} +(-1.50000 - 2.59808i) q^{29} -7.00000 q^{31} +(-5.19615 - 3.00000i) q^{33} +(1.00000 - 1.73205i) q^{36} +8.00000i q^{37} +4.00000 q^{39} +(3.00000 - 5.19615i) q^{41} +(-3.46410 - 2.00000i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(5.19615 - 3.00000i) q^{47} +(6.92820 - 4.00000i) q^{48} -9.00000 q^{49} +(6.00000 + 10.3923i) q^{51} +(3.46410 + 2.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(-3.46410 - 8.00000i) q^{57} +(-7.50000 + 12.9904i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(3.46410 - 2.00000i) q^{63} +8.00000 q^{64} +(1.73205 - 1.00000i) q^{67} +12.0000i q^{68} +(1.50000 - 2.59808i) q^{71} +(6.92820 + 4.00000i) q^{73} +(1.00000 - 8.66025i) q^{76} -12.0000i q^{77} +(2.50000 - 4.33013i) q^{79} +(5.50000 - 9.52628i) q^{81} -12.0000i q^{83} +16.0000 q^{84} +6.00000i q^{87} +(-7.50000 - 12.9904i) q^{89} +(4.00000 + 6.92820i) q^{91} +(12.1244 + 7.00000i) q^{93} +(-6.92820 - 4.00000i) q^{97} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 2 * q^9	$ 4 q - 4 q^{4} + 2 q^{9} + 12 q^{11} - 8 q^{16} + 14 q^{19} - 16 q^{21} - 6 q^{29} - 28 q^{31} + 4 q^{36} + 16 q^{39} + 12 q^{41} - 12 q^{44} - 36 q^{49} + 24 q^{51} - 30 q^{59} - 10 q^{61} + 32 q^{64} + 6 q^{71} + 4 q^{76} + 10 q^{79} + 22 q^{81} + 64 q^{84} - 30 q^{89} + 16 q^{91} + 6 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 2 * q^9 + 12 * q^11 - 8 * q^16 + 14 * q^19 - 16 * q^21 - 6 * q^29 - 28 * q^31 + 4 * q^36 + 16 * q^39 + 12 * q^41 - 12 * q^44 - 36 * q^49 + 24 * q^51 - 30 * q^59 - 10 * q^61 + 32 * q^64 + 6 * q^71 + 4 * q^76 + 10 * q^79 + 22 * q^81 + 64 * q^84 - 30 * q^89 + 16 * q^91 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$2$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$3$	−1.73205	−	1.00000i	−1.00000	−	0.577350i	−0.0917517	−	0.995782i	$-0.529247\pi$
$3$	−1.73205	−	1.00000i	−1.00000	−	0.577350i	−0.908248	+	0.418432i	$0.862580\pi$
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	4.00000i		−	1.51186i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$		−	4.00000i		−	1.51186i	0.654654	−	0.755929i	$-0.272814\pi$
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$			4.00000i			1.15470i
$13$	−1.73205	+	1.00000i	−0.480384	+	0.277350i	−0.720577	−	0.693375i	$-0.756123\pi$
$13$	−1.73205	+	1.00000i	−0.480384	+	0.277350i	0.240192	+	0.970725i	$0.422790\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	−5.19615	−	3.00000i	−1.26025	−	0.727607i	−0.287129	−	0.957892i	$-0.592701\pi$
$17$	−5.19615	−	3.00000i	−1.26025	−	0.727607i	−0.973123	+	0.230285i	$0.926034\pi$
$18$		0			0
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$20$		0			0
$21$	−4.00000	+	6.92820i	−0.872872	+	1.51186i
$22$		0			0
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			4.00000i			0.769800i
$28$	−6.92820	+	4.00000i	−1.30931	+	0.755929i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	−7.00000			−1.25724			−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000			−1.25724			−0.628619	+	0.777714i	$0.716379\pi$
$32$		0			0
$33$	−5.19615	−	3.00000i	−0.904534	−	0.522233i
$34$		0			0
$35$		0			0
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$			8.00000i			1.31519i	0.753371	+	0.657596i	$0.228427\pi$
$37$			8.00000i			1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$		0			0
$39$	4.00000			0.640513
$40$		0			0
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$		0			0
$43$	−3.46410	−	2.00000i	−0.528271	−	0.304997i	0.212041	−	0.977261i	$-0.431989\pi$
$43$	−3.46410	−	2.00000i	−0.528271	−	0.304997i	−0.740312	+	0.672264i	$0.765322\pi$
$44$	−3.00000	−	5.19615i	−0.452267	−	0.783349i
$45$		0			0
$46$		0			0
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	−0.0706177	−	0.997503i	$-0.522497\pi$
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	0.828554	+	0.559908i	$0.189164\pi$
$48$	6.92820	−	4.00000i	1.00000	−	0.577350i
$49$	−9.00000			−1.28571
$50$		0			0
$51$	6.00000	+	10.3923i	0.840168	+	1.45521i
$52$	3.46410	+	2.00000i	0.480384	+	0.277350i
$53$	5.19615	−	3.00000i	0.713746	−	0.412082i	−0.0987002	−	0.995117i	$-0.531468\pi$
$53$	5.19615	−	3.00000i	0.713746	−	0.412082i	0.812447	+	0.583036i	$0.198135\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.46410	−	8.00000i	−0.458831	−	1.05963i
$58$		0			0
$59$	−7.50000	+	12.9904i	−0.976417	+	1.69120i	−0.301239	+	0.953549i	$0.597400\pi$
$59$	−7.50000	+	12.9904i	−0.976417	+	1.69120i	−0.675178	+	0.737655i	$0.735933\pi$
$60$		0			0
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$		0			0
$63$	3.46410	−	2.00000i	0.436436	−	0.251976i
$64$	8.00000			1.00000
$65$		0			0
$66$		0			0
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	−0.390453	−	0.920623i	$-0.627682\pi$
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	0.602056	+	0.798454i	$0.294348\pi$
$68$			12.0000i			1.45521i
$69$		0			0
$70$		0			0
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	−0.763184	−	0.646181i	$-0.776365\pi$
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	0.941201	+	0.337846i	$0.109698\pi$
$72$		0			0
$73$	6.92820	+	4.00000i	0.810885	+	0.468165i	0.847263	−	0.531174i	$-0.178249\pi$
$73$	6.92820	+	4.00000i	0.810885	+	0.468165i	−0.0363782	+	0.999338i	$0.511582\pi$
$74$		0			0
$75$		0			0
$76$	1.00000	−	8.66025i	0.114708	−	0.993399i
$77$		−	12.0000i		−	1.36753i
$78$		0			0
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	−0.690426	−	0.723403i	$-0.742577\pi$
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	0.971698	+	0.236225i	$0.0759104\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$	16.0000			1.74574
$85$		0			0
$86$		0			0
$87$			6.00000i			0.643268i
$88$		0			0
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	−0.922840	−	0.385183i	$-0.874138\pi$
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	0.127842	−	0.991795i	$-0.459195\pi$
$90$		0			0
$91$	4.00000	+	6.92820i	0.419314	+	0.726273i
$92$		0			0
$93$	12.1244	+	7.00000i	1.25724	+	0.725866i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.92820	−	4.00000i	−0.703452	−	0.406138i	0.105180	−	0.994453i	$-0.466458\pi$
$97$	−6.92820	−	4.00000i	−0.703452	−	0.406138i	−0.808632	+	0.588315i	$0.799792\pi$
$98$		0			0
$99$	1.50000	+	2.59808i	0.150756	+	0.261116i
$100$		0			0
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	−0.949595	−	0.313478i	$-0.898506\pi$
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	0.203317	−	0.979113i	$-0.434828\pi$
$102$		0			0
$103$			16.0000i			1.57653i	0.615338	+	0.788263i	$0.289020\pi$
$103$			16.0000i			1.57653i	−0.615338	+	0.788263i	$0.710980\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	6.92820	−	4.00000i	0.666667	−	0.384900i
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	−0.472708	−	0.881219i	$-0.656723\pi$
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	0.999512	−	0.0312328i	$-0.00994332\pi$
$110$		0			0
$111$	8.00000	−	13.8564i	0.759326	−	1.31519i
$112$	13.8564	+	8.00000i	1.30931	+	0.755929i
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$		0			0
$115$		0			0
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	−1.73205	−	1.00000i	−0.160128	−	0.0924500i
$118$		0			0
$119$	−12.0000	+	20.7846i	−1.10004	+	1.90532i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$	−10.3923	+	6.00000i	−0.937043	+	0.541002i
$124$	7.00000	+	12.1244i	0.628619	+	1.08880i
$125$		0			0
$126$		0			0
$127$	1.73205	−	1.00000i	0.153695	−	0.0887357i	−0.421180	−	0.906977i	$-0.638384\pi$
$127$	1.73205	−	1.00000i	0.153695	−	0.0887357i	0.574875	+	0.818241i	$0.305051\pi$
$128$		0			0
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$		0			0
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$			12.0000i			1.04447i
$133$	10.3923	−	14.0000i	0.901127	−	1.21395i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.873247	−	0.487278i	$-0.837990\pi$
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.0146279	+	0.999893i	$0.504656\pi$
$138$		0			0
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	0.296866	−	0.954919i	$-0.404058\pi$
$140$		0			0
$141$	−12.0000			−1.01058
$142$		0			0
$143$	−5.19615	+	3.00000i	−0.434524	+	0.250873i
$144$	−4.00000			−0.333333
$145$		0			0
$146$		0			0
$147$	15.5885	+	9.00000i	1.28571	+	0.742307i
$148$	13.8564	−	8.00000i	1.13899	−	0.657596i
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$	17.0000			1.38344			0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000			1.38344			0.691720	+	0.722166i	$0.256853\pi$
$152$		0			0
$153$		−	6.00000i		−	0.485071i
$154$		0			0
$155$		0			0
$156$	−4.00000	−	6.92820i	−0.320256	−	0.554700i
$157$	−1.73205	−	1.00000i	−0.138233	−	0.0798087i	0.429289	−	0.903167i	$-0.358764\pi$
$157$	−1.73205	−	1.00000i	−0.138233	−	0.0798087i	−0.567521	+	0.823359i	$0.692098\pi$
$158$		0			0
$159$	−12.0000			−0.951662
$160$		0			0
$161$		0			0
$162$		0			0
$163$			10.0000i			0.783260i	0.920123	+	0.391630i	$0.128089\pi$
$163$			10.0000i			0.783260i	−0.920123	+	0.391630i	$0.871911\pi$
$164$	−12.0000			−0.937043
$165$		0			0
$166$		0			0
$167$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$167$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$168$		0			0
$169$	−4.50000	+	7.79423i	−0.346154	+	0.599556i
$170$		0			0
$171$	−0.500000	+	4.33013i	−0.0382360	+	0.331133i
$172$			8.00000i			0.609994i
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$		0			0
$175$		0			0
$176$	−6.00000	+	10.3923i	−0.452267	+	0.783349i
$177$	25.9808	−	15.0000i	1.95283	−	1.12747i
$178$		0			0
$179$	9.00000			0.672692			0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000			0.672692			0.336346	+	0.941739i	$0.390809\pi$
$180$		0			0
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	0.826465	−	0.562988i	$-0.190348\pi$
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	−0.900794	+	0.434246i	$0.857015\pi$
$182$		0			0
$183$			10.0000i			0.739221i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−15.5885	−	9.00000i	−1.13994	−	0.658145i
$188$	−10.3923	−	6.00000i	−0.757937	−	0.437595i
$189$	16.0000			1.16383
$190$		0			0
$191$	−15.0000			−1.08536			−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000			−1.08536			−0.542681	+	0.839939i	$0.682591\pi$
$192$	−13.8564	−	8.00000i	−1.00000	−	0.577350i
$193$	−13.8564	−	8.00000i	−0.997406	−	0.575853i	−0.0899262	−	0.995948i	$-0.528663\pi$
$193$	−13.8564	−	8.00000i	−0.997406	−	0.575853i	−0.907480	+	0.420096i	$0.861996\pi$
$194$		0			0
$195$		0			0
$196$	9.00000	+	15.5885i	0.642857	+	1.11346i
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		0			0
$199$	−9.50000	−	16.4545i	−0.673437	−	1.16643i	−0.976923	−	0.213591i	$-0.931484\pi$
$199$	−9.50000	−	16.4545i	−0.673437	−	1.16643i	0.303486	−	0.952836i	$-0.401849\pi$
$200$		0			0
$201$	−4.00000			−0.282138
$202$		0			0
$203$	−10.3923	+	6.00000i	−0.729397	+	0.421117i
$204$	12.0000	−	20.7846i	0.840168	−	1.45521i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		−	8.00000i		−	0.554700i
$209$	10.5000	+	7.79423i	0.726300	+	0.539138i
$210$		0			0
$211$	3.50000	−	6.06218i	0.240950	−	0.417338i	−0.720035	−	0.693938i	$-0.755874\pi$
$211$	3.50000	−	6.06218i	0.240950	−	0.417338i	0.960985	+	0.276600i	$0.0892077\pi$
$212$	−10.3923	−	6.00000i	−0.713746	−	0.412082i
$213$	−5.19615	+	3.00000i	−0.356034	+	0.205557i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			28.0000i			1.90076i
$218$		0			0
$219$	−8.00000	−	13.8564i	−0.540590	−	0.936329i
$220$		0			0
$221$	12.0000			0.807207
$222$		0			0
$223$	−3.46410	−	2.00000i	−0.231973	−	0.133930i	0.379509	−	0.925188i	$-0.376093\pi$
$223$	−3.46410	−	2.00000i	−0.231973	−	0.133930i	−0.611482	+	0.791258i	$0.709426\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	24.0000i		−	1.59294i	−0.604681	−	0.796468i	$-0.706699\pi$
$227$		−	24.0000i		−	1.59294i	0.604681	−	0.796468i	$-0.293301\pi$
$228$	−10.3923	+	14.0000i	−0.688247	+	0.927173i
$229$	7.00000			0.462573			0.231287	−	0.972886i	$-0.425707\pi$
$229$	7.00000			0.462573			0.231287	+	0.972886i	$0.425707\pi$
$230$		0			0
$231$	−12.0000	+	20.7846i	−0.789542	+	1.36753i
$232$		0			0
$233$	5.19615	+	3.00000i	0.340411	+	0.196537i	0.660454	−	0.750867i	$-0.270364\pi$
$233$	5.19615	+	3.00000i	0.340411	+	0.196537i	−0.320043	+	0.947403i	$0.603697\pi$
$234$		0			0
$235$		0			0
$236$	30.0000			1.95283
$237$	−8.66025	+	5.00000i	−0.562544	+	0.324785i
$238$		0			0
$239$	3.00000			0.194054			0.0970269	−	0.995282i	$-0.469067\pi$
$239$	3.00000			0.194054			0.0970269	+	0.995282i	$0.469067\pi$
$240$		0			0
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	0.774202	−	0.632938i	$-0.218151\pi$
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	−0.935242	+	0.354010i	$0.884818\pi$
$242$		0			0
$243$	−8.66025	+	5.00000i	−0.555556	+	0.320750i
$244$	−5.00000	+	8.66025i	−0.320092	+	0.554416i
$245$		0			0
$246$		0			0
$247$	−8.66025	−	1.00000i	−0.551039	−	0.0636285i
$248$		0			0
$249$	−12.0000	+	20.7846i	−0.760469	+	1.31717i
$250$		0			0
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	0.999536	−	0.0304521i	$-0.00969471\pi$
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	−0.526140	+	0.850398i	$0.676361\pi$
$252$	−6.92820	−	4.00000i	−0.436436	−	0.251976i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.899961	−	0.435970i	$-0.856405\pi$
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.0724199	+	0.997374i	$0.523072\pi$
$258$		0			0
$259$	32.0000			1.98838
$260$		0			0
$261$	1.50000	−	2.59808i	0.0928477	−	0.160817i
$262$		0			0
$263$	−15.5885	−	9.00000i	−0.961225	−	0.554964i	−0.0646755	−	0.997906i	$-0.520601\pi$
$263$	−15.5885	−	9.00000i	−0.961225	−	0.554964i	−0.896550	+	0.442943i	$0.853935\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			30.0000i			1.83597i
$268$	−3.46410	−	2.00000i	−0.211604	−	0.122169i
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	0.345192	+	0.938532i	$0.387814\pi$
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	−0.985389	+	0.170321i	$0.945520\pi$
$270$		0			0
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	−0.983312	−	0.181928i	$-0.941766\pi$
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	0.649211	+	0.760609i	$0.275099\pi$
$272$	20.7846	−	12.0000i	1.26025	−	0.727607i
$273$		−	16.0000i		−	0.968364i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			8.00000i			0.480673i	0.970690	+	0.240337i	$0.0772579\pi$
$277$			8.00000i			0.480673i	−0.970690	+	0.240337i	$0.922742\pi$
$278$		0			0
$279$	−3.50000	−	6.06218i	−0.209540	−	0.362933i
$280$		0			0
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	0.762561	−	0.646916i	$-0.223942\pi$
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	−0.941526	+	0.336939i	$0.890608\pi$
$282$		0			0
$283$	12.1244	+	7.00000i	0.720718	+	0.416107i	0.815017	−	0.579437i	$-0.196728\pi$
$283$	12.1244	+	7.00000i	0.720718	+	0.416107i	−0.0942988	+	0.995544i	$0.530061\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$		0			0
$287$	−20.7846	−	12.0000i	−1.22688	−	0.708338i
$288$		0			0
$289$	9.50000	+	16.4545i	0.558824	+	0.967911i
$290$		0			0
$291$	8.00000	+	13.8564i	0.468968	+	0.812277i
$292$		−	16.0000i		−	0.936329i
$293$		−	24.0000i		−	1.40209i	−0.713115	−	0.701047i	$-0.752716\pi$
$293$		−	24.0000i		−	1.40209i	0.713115	−	0.701047i	$-0.247284\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$			12.0000i			0.696311i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−8.00000	+	13.8564i	−0.461112	+	0.798670i
$302$		0			0
$303$			30.0000i			1.72345i
$304$	−16.0000	+	6.92820i	−0.917663	+	0.397360i
$305$		0			0
$306$		0			0
$307$	29.4449	+	17.0000i	1.68051	+	0.970241i	0.961324	+	0.275421i	$0.0888172\pi$
$307$	29.4449	+	17.0000i	1.68051	+	0.970241i	0.719183	+	0.694820i	$0.244516\pi$
$308$	−20.7846	+	12.0000i	−1.18431	+	0.683763i
$309$	16.0000	−	27.7128i	0.910208	−	1.57653i
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	8.66025	−	5.00000i	0.489506	−	0.282617i	−0.234863	−	0.972028i	$-0.575464\pi$
$313$	8.66025	−	5.00000i	0.489506	−	0.282617i	0.724370	+	0.689412i	$0.242131\pi$
$314$		0			0
$315$		0			0
$316$	−10.0000			−0.562544
$317$	20.7846	−	12.0000i	1.16738	−	0.673987i	0.214318	−	0.976764i	$-0.431247\pi$
$317$	20.7846	−	12.0000i	1.16738	−	0.673987i	0.953062	+	0.302777i	$0.0979136\pi$
$318$		0			0
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−10.3923	−	24.0000i	−0.578243	−	1.33540i
$324$	−22.0000			−1.22222
$325$		0			0
$326$		0			0
$327$	−19.0526	+	11.0000i	−1.05361	+	0.608301i
$328$		0			0
$329$	−12.0000	−	20.7846i	−0.661581	−	1.14589i
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$	−20.7846	+	12.0000i	−1.14070	+	0.658586i
$333$	−6.92820	+	4.00000i	−0.379663	+	0.219199i
$334$		0			0
$335$		0			0
$336$	−16.0000	−	27.7128i	−0.872872	−	1.51186i
$337$	13.8564	+	8.00000i	0.754807	+	0.435788i	0.827428	−	0.561572i	$-0.189803\pi$
$337$	13.8564	+	8.00000i	0.754807	+	0.435788i	−0.0726214	+	0.997360i	$0.523136\pi$
$338$		0			0
$339$	−6.00000	+	10.3923i	−0.325875	+	0.564433i
$340$		0			0
$341$	−21.0000			−1.13721
$342$		0			0
$343$			8.00000i			0.431959i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	0.194409	−	0.980921i	$-0.437721\pi$
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	−0.752297	+	0.658824i	$0.771054\pi$
$348$	10.3923	−	6.00000i	0.557086	−	0.321634i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	−4.00000	−	6.92820i	−0.213504	−	0.369800i
$352$		0			0
$353$		−	12.0000i		−	0.638696i	−0.947638	−	0.319348i	$-0.896536\pi$
$353$		−	12.0000i		−	0.638696i	0.947638	−	0.319348i	$-0.103464\pi$
$354$		0			0
$355$		0			0
$356$	−15.0000	+	25.9808i	−0.794998	+	1.37698i
$357$	41.5692	−	24.0000i	2.20008	−	1.27021i
$358$		0			0
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$		0			0
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$		0			0
$363$	3.46410	+	2.00000i	0.181818	+	0.104973i
$364$	8.00000	−	13.8564i	0.419314	−	0.726273i
$365$		0			0
$366$		0			0
$367$	−3.46410	+	2.00000i	−0.180825	+	0.104399i	−0.587680	−	0.809093i	$-0.699959\pi$
$367$	−3.46410	+	2.00000i	−0.180825	+	0.104399i	0.406855	+	0.913493i	$0.366625\pi$
$368$		0			0
$369$	6.00000			0.312348
$370$		0			0
$371$	−12.0000	−	20.7846i	−0.623009	−	1.07908i
$372$		−	28.0000i		−	1.45173i
$373$			4.00000i			0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$			4.00000i			0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	5.19615	+	3.00000i	0.267615	+	0.154508i
$378$		0			0
$379$	37.0000			1.90056			0.950281	−	0.311393i	$-0.100796\pi$
$379$	37.0000			1.90056			0.950281	+	0.311393i	$0.100796\pi$
$380$		0			0
$381$	−4.00000			−0.204926
$382$		0			0
$383$	25.9808	+	15.0000i	1.32755	+	0.766464i	0.984921	−	0.173005i	$-0.0553476\pi$
$383$	25.9808	+	15.0000i	1.32755	+	0.766464i	0.342634	+	0.939469i	$0.388681\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	4.00000i		−	0.203331i
$388$			16.0000i			0.812277i
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	0.991100	−	0.133120i	$-0.0424994\pi$
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	−0.610835	+	0.791758i	$0.709166\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	20.7846	−	12.0000i	1.04844	−	0.605320i
$394$		0			0
$395$		0			0
$396$	3.00000	−	5.19615i	0.150756	−	0.261116i
$397$	−6.92820	−	4.00000i	−0.347717	−	0.200754i	0.315963	−	0.948772i	$-0.397673\pi$
$397$	−6.92820	−	4.00000i	−0.347717	−	0.200754i	−0.663679	+	0.748017i	$0.731006\pi$
$398$		0			0
$399$	−32.0000	+	13.8564i	−1.60200	+	0.693688i
$400$		0			0
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	−0.0787327	−	0.996896i	$-0.525087\pi$
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	0.902703	−	0.430263i	$-0.141579\pi$
$402$		0			0
$403$	12.1244	−	7.00000i	0.603957	−	0.348695i
$404$	−15.0000	+	25.9808i	−0.746278	+	1.29259i
$405$		0			0
$406$		0			0
$407$			24.0000i			1.18964i
$408$		0			0
$409$	11.5000	+	19.9186i	0.568638	+	0.984911i	0.996701	+	0.0811615i	$0.0258630\pi$
$409$	11.5000	+	19.9186i	0.568638	+	0.984911i	−0.428063	+	0.903749i	$0.640804\pi$
$410$		0			0
$411$	24.0000			1.18383
$412$	27.7128	−	16.0000i	1.36531	−	0.788263i
$413$	51.9615	+	30.0000i	2.55686	+	1.47620i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			32.0000i			1.56705i
$418$		0			0
$419$	3.00000			0.146560			0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000			0.146560			0.0732798	+	0.997311i	$0.476653\pi$
$420$		0			0
$421$	9.50000	−	16.4545i	0.463002	−	0.801942i	−0.536107	−	0.844150i	$-0.680106\pi$
$421$	9.50000	−	16.4545i	0.463002	−	0.801942i	0.999109	+	0.0422075i	$0.0134391\pi$
$422$		0			0
$423$	5.19615	+	3.00000i	0.252646	+	0.145865i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−17.3205	+	10.0000i	−0.838198	+	0.483934i
$428$		0			0
$429$	12.0000			0.579365
$430$		0			0
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	0.988169	−	0.153370i	$-0.0490126\pi$
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	−0.626907	+	0.779094i	$0.715679\pi$
$432$	−13.8564	−	8.00000i	−0.666667	−	0.384900i
$433$	−6.92820	+	4.00000i	−0.332948	+	0.192228i	−0.657149	−	0.753760i	$-0.728238\pi$
$433$	−6.92820	+	4.00000i	−0.332948	+	0.192228i	0.324201	+	0.945988i	$0.394905\pi$
$434$		0			0
$435$		0			0
$436$	−22.0000			−1.05361
$437$		0			0
$438$		0			0
$439$	−6.50000	+	11.2583i	−0.310228	+	0.537331i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−6.50000	+	11.2583i	−0.310228	+	0.537331i	0.668184	+	0.743996i	$0.267072\pi$
$440$		0			0
$441$	−4.50000	−	7.79423i	−0.214286	−	0.371154i
$442$		0			0
$443$	10.3923	−	6.00000i	0.493753	−	0.285069i	−0.232377	−	0.972626i	$-0.574650\pi$
$443$	10.3923	−	6.00000i	0.493753	−	0.285069i	0.726130	+	0.687557i	$0.241317\pi$
$444$	−32.0000			−1.51865
$445$		0			0
$446$		0			0
$447$	−5.19615	+	3.00000i	−0.245770	+	0.141895i
$448$		−	32.0000i		−	1.51186i
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$		0			0
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	−10.3923	+	6.00000i	−0.488813	+	0.282216i
$453$	−29.4449	−	17.0000i	−1.38344	−	0.798730i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	22.0000i		−	1.02912i	−0.857455	−	0.514558i	$-0.827956\pi$
$457$		−	22.0000i		−	1.02912i	0.857455	−	0.514558i	$-0.172044\pi$
$458$		0			0
$459$	12.0000	−	20.7846i	0.560112	−	0.970143i
$460$		0			0
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	−0.741998	−	0.670402i	$-0.766122\pi$
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	0.951584	+	0.307388i	$0.0994551\pi$
$462$		0			0
$463$			16.0000i			0.743583i	0.928316	+	0.371792i	$0.121256\pi$
$463$			16.0000i			0.743583i	−0.928316	+	0.371792i	$0.878744\pi$
$464$	12.0000			0.557086
$465$		0			0
$466$		0			0
$467$		0			0		1.00000			$0$
$467$		0			0		−1.00000			$\pi$
$468$			4.00000i			0.184900i
$469$	−4.00000	−	6.92820i	−0.184703	−	0.319915i
$470$		0			0
$471$	2.00000	+	3.46410i	0.0921551	+	0.159617i
$472$		0			0
$473$	−10.3923	−	6.00000i	−0.477839	−	0.275880i
$474$		0			0
$475$		0			0
$476$	48.0000			2.20008
$477$	5.19615	+	3.00000i	0.237915	+	0.137361i
$478$		0			0
$479$	7.50000	+	12.9904i	0.342684	+	0.593546i	0.984930	−	0.172953i	$-0.0553307\pi$
$479$	7.50000	+	12.9904i	0.342684	+	0.593546i	−0.642246	+	0.766498i	$0.721997\pi$
$480$		0			0
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$		0			0
$483$		0			0
$484$	2.00000	+	3.46410i	0.0909091	+	0.157459i
$485$		0			0
$486$		0			0
$487$			2.00000i			0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$			2.00000i			0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$		0			0
$489$	10.0000	−	17.3205i	0.452216	−	0.783260i
$490$		0			0
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	−0.645675	−	0.763612i	$-0.723424\pi$
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	0.984145	+	0.177365i	$0.0567572\pi$
$492$	20.7846	+	12.0000i	0.937043	+	0.541002i
$493$			18.0000i			0.810679i
$494$		0			0
$495$		0			0
$496$	14.0000	−	24.2487i	0.628619	−	1.08880i
$497$	−10.3923	−	6.00000i	−0.466159	−	0.269137i
$498$		0			0
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	−0.550572	−	0.834788i	$-0.685590\pi$
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	0.998233	+	0.0594153i	$0.0189236\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	36.3731	−	21.0000i	1.62179	−	0.936344i	0.635355	−	0.772220i	$-0.280854\pi$
$503$	36.3731	−	21.0000i	1.62179	−	0.936344i	0.986440	−	0.164124i	$-0.0524796\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	15.5885	−	9.00000i	0.692308	−	0.399704i
$508$	−3.46410	−	2.00000i	−0.153695	−	0.0887357i
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	0.594675	−	0.803966i	$-0.297281\pi$
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	−0.993593	+	0.113020i	$0.963948\pi$
$510$		0			0
$511$	16.0000	−	27.7128i	0.707798	−	1.22594i
$512$		0			0
$513$	−10.3923	+	14.0000i	−0.458831	+	0.618115i
$514$		0			0
$515$		0			0
$516$	8.00000	−	13.8564i	0.352180	−	0.609994i
$517$	15.5885	−	9.00000i	0.685580	−	0.395820i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−45.0000			−1.97149			−0.985743	−	0.168259i	$-0.946186\pi$
$521$	−45.0000			−1.97149			−0.985743	+	0.168259i	$0.946186\pi$
$522$		0			0
$523$	−22.5167	+	13.0000i	−0.984585	+	0.568450i	−0.903651	−	0.428269i	$-0.859124\pi$
$523$	−22.5167	+	13.0000i	−0.984585	+	0.568450i	−0.0809336	+	0.996719i	$0.525790\pi$
$524$	24.0000			1.04844
$525$		0			0
$526$		0			0
$527$	36.3731	+	21.0000i	1.58444	+	0.914774i
$528$	20.7846	−	12.0000i	0.904534	−	0.522233i
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$		0			0
$531$	−15.0000			−0.650945
$532$	−34.6410	−	4.00000i	−1.50188	−	0.173422i
$533$			12.0000i			0.519778i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−15.5885	−	9.00000i	−0.672692	−	0.388379i
$538$		0			0
$539$	−27.0000			−1.16297
$540$		0			0
$541$	18.5000	+	32.0429i	0.795377	+	1.37763i	0.922599	+	0.385759i	$0.126061\pi$
$541$	18.5000	+	32.0429i	0.795377	+	1.37763i	−0.127222	+	0.991874i	$0.540606\pi$
$542$		0			0
$543$			4.00000i			0.171656i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−3.46410	+	2.00000i	−0.148114	+	0.0855138i	−0.572226	−	0.820096i	$-0.693920\pi$
$547$	−3.46410	+	2.00000i	−0.148114	+	0.0855138i	0.424111	+	0.905610i	$0.360587\pi$
$548$	20.7846	+	12.0000i	0.887875	+	0.512615i
$549$	2.50000	−	4.33013i	0.106697	−	0.184805i
$550$		0			0
$551$	1.50000	−	12.9904i	0.0639021	−	0.553409i
$552$		0			0
$553$	−17.3205	−	10.0000i	−0.736543	−	0.425243i
$554$		0			0
$555$		0			0
$556$	−16.0000	+	27.7128i	−0.678551	+	1.17529i
$557$	10.3923	−	6.00000i	0.440336	−	0.254228i	−0.263404	−	0.964686i	$-0.584845\pi$
$557$	10.3923	−	6.00000i	0.440336	−	0.254228i	0.703740	+	0.710457i	$0.251512\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$	18.0000	+	31.1769i	0.759961	+	1.31629i
$562$		0			0
$563$		−	6.00000i		−	0.252870i	−0.991975	−	0.126435i	$-0.959647\pi$
$563$		−	6.00000i		−	0.252870i	0.991975	−	0.126435i	$-0.0403535\pi$
$564$	12.0000	+	20.7846i	0.505291	+	0.875190i
$565$		0			0
$566$		0			0
$567$	−38.1051	−	22.0000i	−1.60026	−	0.923913i
$568$		0			0
$569$	−39.0000			−1.63497			−0.817483	−	0.575953i	$-0.804631\pi$
$569$	−39.0000			−1.63497			−0.817483	+	0.575953i	$0.804631\pi$
$570$		0			0
$571$	−7.00000			−0.292941			−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000			−0.292941			−0.146470	+	0.989215i	$0.546791\pi$
$572$	10.3923	+	6.00000i	0.434524	+	0.250873i
$573$	25.9808	+	15.0000i	1.08536	+	0.626634i
$574$		0			0
$575$		0			0
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$		−	16.0000i		−	0.666089i	−0.942911	−	0.333044i	$-0.891924\pi$
$577$		−	16.0000i		−	0.666089i	0.942911	−	0.333044i	$-0.108076\pi$
$578$		0			0
$579$	16.0000	+	27.7128i	0.664937	+	1.15171i
$580$		0			0
$581$	−48.0000			−1.99138
$582$		0			0
$583$	15.5885	−	9.00000i	0.645608	−	0.372742i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	31.1769	+	18.0000i	1.28681	+	0.742940i	0.978084	−	0.208212i	$-0.0667643\pi$
$587$	31.1769	+	18.0000i	1.28681	+	0.742940i	0.308725	+	0.951151i	$0.400098\pi$
$588$		−	36.0000i		−	1.48461i
$589$	−24.5000	−	18.1865i	−1.00950	−	0.749363i
$590$		0			0
$591$	−18.0000	+	31.1769i	−0.740421	+	1.28245i
$592$	−27.7128	−	16.0000i	−1.13899	−	0.657596i
$593$	−10.3923	+	6.00000i	−0.426761	+	0.246390i	−0.697966	−	0.716131i	$-0.745911\pi$
$593$	−10.3923	+	6.00000i	−0.426761	+	0.246390i	0.271205	+	0.962522i	$0.412578\pi$
$594$		0			0
$595$		0			0
$596$	−6.00000			−0.245770
$597$			38.0000i			1.55524i
$598$		0			0
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	−31.0000			−1.26452			−0.632258	−	0.774758i	$-0.717872\pi$
$601$	−31.0000			−1.26452			−0.632258	+	0.774758i	$0.717872\pi$
$602$		0			0
$603$	1.73205	+	1.00000i	0.0705346	+	0.0407231i
$604$	−17.0000	−	29.4449i	−0.691720	−	1.19809i
$605$		0			0
$606$		0			0
$607$			2.00000i			0.0811775i	0.999176	+	0.0405887i	$0.0129233\pi$
$607$			2.00000i			0.0811775i	−0.999176	+	0.0405887i	$0.987077\pi$
$608$		0			0
$609$	24.0000			0.972529
$610$		0			0
$611$	−6.00000	+	10.3923i	−0.242734	+	0.420428i
$612$	−10.3923	+	6.00000i	−0.420084	+	0.242536i
$613$	1.73205	+	1.00000i	0.0699569	+	0.0403896i	0.534570	−	0.845124i	$-0.320473\pi$
$613$	1.73205	+	1.00000i	0.0699569	+	0.0403896i	−0.464614	+	0.885514i	$0.653807\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	31.1769	−	18.0000i	1.25514	−	0.724653i	0.283011	−	0.959117i	$-0.408667\pi$
$617$	31.1769	−	18.0000i	1.25514	−	0.724653i	0.972125	+	0.234464i	$0.0753335\pi$
$618$		0			0
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−51.9615	+	30.0000i	−2.08179	+	1.20192i
$624$	−8.00000	+	13.8564i	−0.320256	+	0.554700i
$625$		0			0
$626$		0			0
$627$	−10.3923	−	24.0000i	−0.415029	−	0.958468i
$628$			4.00000i			0.159617i
$629$	24.0000	−	41.5692i	0.956943	−	1.65747i
$630$		0			0
$631$	9.50000	+	16.4545i	0.378189	+	0.655043i	0.990799	−	0.135343i	$-0.0432136\pi$
$631$	9.50000	+	16.4545i	0.378189	+	0.655043i	−0.612610	+	0.790386i	$0.709880\pi$
$632$		0			0
$633$	−12.1244	+	7.00000i	−0.481900	+	0.278225i
$634$		0			0
$635$		0			0
$636$	12.0000	+	20.7846i	0.475831	+	0.824163i
$637$	15.5885	−	9.00000i	0.617637	−	0.356593i
$638$		0			0
$639$	3.00000			0.118678
$640$		0			0
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	−0.941106	−	0.338112i	$-0.890212\pi$
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	0.763367	+	0.645966i	$0.223545\pi$
$642$		0			0
$643$	−29.4449	−	17.0000i	−1.16119	−	0.670415i	−0.209603	−	0.977787i	$-0.567217\pi$
$643$	−29.4449	−	17.0000i	−1.16119	−	0.670415i	−0.951589	+	0.307372i	$0.900550\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			18.0000i			0.707653i	0.935311	+	0.353827i	$0.115120\pi$
$647$			18.0000i			0.707653i	−0.935311	+	0.353827i	$0.884880\pi$
$648$		0			0
$649$	−22.5000	+	38.9711i	−0.883202	+	1.52975i
$650$		0			0
$651$	28.0000	−	48.4974i	1.09741	−	1.90076i
$652$	17.3205	−	10.0000i	0.678323	−	0.391630i
$653$		−	24.0000i		−	0.939193i	−0.882881	−	0.469596i	$-0.844399\pi$
$653$		−	24.0000i		−	0.939193i	0.882881	−	0.469596i	$-0.155601\pi$
$654$		0			0
$655$		0			0
$656$	12.0000	+	20.7846i	0.468521	+	0.811503i
$657$			8.00000i			0.312110i
$658$		0			0
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	0.725175	−	0.688565i	$-0.241759\pi$
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	−0.958902	+	0.283738i	$0.908425\pi$
$660$		0			0
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	0.813302	−	0.581842i	$-0.197668\pi$
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	−0.910541	+	0.413419i	$0.864334\pi$
$662$		0			0
$663$	−20.7846	−	12.0000i	−0.807207	−	0.466041i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	4.00000	+	6.92820i	0.154649	+	0.267860i
$670$		0			0
$671$	−7.50000	−	12.9904i	−0.289534	−	0.501488i
$672$		0			0
$673$			4.00000i			0.154189i	0.997024	+	0.0770943i	$0.0245643\pi$
$673$			4.00000i			0.154189i	−0.997024	+	0.0770943i	$0.975436\pi$
$674$		0			0
$675$		0			0
$676$	18.0000			0.692308
$677$			48.0000i			1.84479i	0.386248	+	0.922395i	$0.373771\pi$
$677$			48.0000i			1.84479i	−0.386248	+	0.922395i	$0.626229\pi$
$678$		0			0
$679$	−16.0000	+	27.7128i	−0.614024	+	1.06352i
$680$		0			0
$681$	−24.0000	+	41.5692i	−0.919682	+	1.59294i
$682$		0			0
$683$			18.0000i			0.688751i	0.938832	+	0.344375i	$0.111909\pi$
$683$			18.0000i			0.688751i	−0.938832	+	0.344375i	$0.888091\pi$
$684$	8.00000	−	3.46410i	0.305888	−	0.132453i
$685$		0			0
$686$		0			0
$687$	−12.1244	−	7.00000i	−0.462573	−	0.267067i
$688$	13.8564	−	8.00000i	0.528271	−	0.304997i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	−37.0000			−1.40755			−0.703773	−	0.710425i	$-0.748503\pi$
$691$	−37.0000			−1.40755			−0.703773	+	0.710425i	$0.748503\pi$
$692$		0			0
$693$	10.3923	−	6.00000i	0.394771	−	0.227921i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−31.1769	+	18.0000i	−1.18091	+	0.681799i
$698$		0			0
$699$	−6.00000	−	10.3923i	−0.226941	−	0.393073i
$700$		0			0
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	−0.917102	−	0.398652i	$-0.869478\pi$
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	0.803794	+	0.594908i	$0.202811\pi$
$702$		0			0
$703$	−20.7846	+	28.0000i	−0.783906	+	1.05604i
$704$	24.0000			0.904534
$705$		0			0
$706$		0			0
$707$	−51.9615	+	30.0000i	−1.95421	+	1.12827i
$708$	−51.9615	−	30.0000i	−1.95283	−	1.12747i
$709$	−15.5000	−	26.8468i	−0.582115	−	1.00825i	−0.995228	−	0.0975728i	$-0.968892\pi$
$709$	−15.5000	−	26.8468i	−0.582115	−	1.00825i	0.413114	−	0.910679i	$-0.364441\pi$
$710$		0			0
$711$	5.00000			0.187515
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−9.00000	−	15.5885i	−0.336346	−	0.582568i
$717$	−5.19615	−	3.00000i	−0.194054	−	0.112037i
$718$		0			0
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	−0.691608	−	0.722273i	$-0.743097\pi$
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	0.971311	+	0.237814i	$0.0764307\pi$
$720$		0			0
$721$	64.0000			2.38348
$722$		0			0
$723$			10.0000i			0.371904i
$724$	−2.00000	+	3.46410i	−0.0743294	+	0.128742i
$725$		0			0
$726$		0			0
$727$	−12.1244	−	7.00000i	−0.449667	−	0.259616i	0.258022	−	0.966139i	$-0.416929\pi$
$727$	−12.1244	−	7.00000i	−0.449667	−	0.259616i	−0.707690	+	0.706523i	$0.750263\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	17.3205	−	10.0000i	0.640184	−	0.369611i
$733$		−	32.0000i		−	1.18195i	−0.806691	−	0.590973i	$-0.798744\pi$
$733$		−	32.0000i		−	1.18195i	0.806691	−	0.590973i	$-0.201256\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.19615	−	3.00000i	0.191403	−	0.110506i
$738$		0			0
$739$	17.5000	−	30.3109i	0.643748	−	1.11500i	−0.340841	−	0.940121i	$-0.610712\pi$
$739$	17.5000	−	30.3109i	0.643748	−	1.11500i	0.984589	−	0.174883i	$-0.0559548\pi$
$740$		0			0
$741$	14.0000	+	10.3923i	0.514303	+	0.381771i
$742$		0			0
$743$	−20.7846	−	12.0000i	−0.762513	−	0.440237i	0.0676840	−	0.997707i	$-0.478439\pi$
$743$	−20.7846	−	12.0000i	−0.762513	−	0.440237i	−0.830197	+	0.557470i	$0.811772\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	10.3923	−	6.00000i	0.380235	−	0.219529i
$748$			36.0000i			1.31629i
$749$		0			0
$750$		0			0
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	0.922792	−	0.385299i	$-0.125902\pi$
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	−0.795075	+	0.606511i	$0.792568\pi$
$752$			24.0000i			0.875190i
$753$		−	30.0000i		−	1.09326i
$754$		0			0
$755$		0			0
$756$	−16.0000	−	27.7128i	−0.581914	−	1.00791i
$757$	8.66025	+	5.00000i	0.314762	+	0.181728i	0.649056	−	0.760741i	$-0.275164\pi$
$757$	8.66025	+	5.00000i	0.314762	+	0.181728i	−0.334293	+	0.942469i	$0.608498\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.00000			0.217500			0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000			0.217500			0.108750	+	0.994069i	$0.465315\pi$
$762$		0			0
$763$	−38.1051	−	22.0000i	−1.37950	−	0.796453i
$764$	15.0000	+	25.9808i	0.542681	+	0.939951i
$765$		0			0
$766$		0			0
$767$		−	30.0000i		−	1.08324i
$768$			32.0000i			1.15470i
$769$	14.5000	+	25.1147i	0.522883	+	0.905661i	0.999645	+	0.0266282i	$0.00847701\pi$
$769$	14.5000	+	25.1147i	0.522883	+	0.905661i	−0.476762	+	0.879032i	$0.658190\pi$
$770$		0			0
$771$	36.0000			1.29651
$772$			32.0000i			1.15171i
$773$	−25.9808	+	15.0000i	−0.934463	+	0.539513i	−0.888220	−	0.459418i	$-0.848058\pi$
$773$	−25.9808	+	15.0000i	−0.934463	+	0.539513i	−0.0462427	+	0.998930i	$0.514725\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−55.4256	−	32.0000i	−1.98838	−	1.14799i
$778$		0			0
$779$	24.0000	−	10.3923i	0.859889	−	0.372343i
$780$		0			0
$781$	4.50000	−	7.79423i	0.161023	−	0.278899i
$782$		0			0
$783$	10.3923	−	6.00000i	0.371391	−	0.214423i
$784$	18.0000	−	31.1769i	0.642857	−	1.11346i
$785$		0			0
$786$		0			0
$787$		−	34.0000i		−	1.21197i	−0.795476	−	0.605985i	$-0.792779\pi$
$787$		−	34.0000i		−	1.21197i	0.795476	−	0.605985i	$-0.207221\pi$
$788$	−31.1769	+	18.0000i	−1.11063	+	0.641223i
$789$	18.0000	+	31.1769i	0.640817	+	1.10993i
$790$		0			0
$791$	−24.0000			−0.853342
$792$		0			0
$793$	8.66025	+	5.00000i	0.307535	+	0.177555i
$794$		0			0
$795$		0			0
$796$	−19.0000	+	32.9090i	−0.673437	+	1.16643i
$797$		−	30.0000i		−	1.06265i	−0.847167	−	0.531327i	$-0.821693\pi$
$797$		−	30.0000i		−	1.06265i	0.847167	−	0.531327i	$-0.178307\pi$
$798$		0			0
$799$	−36.0000			−1.27359
$800$		0			0
$801$	7.50000	−	12.9904i	0.264999	−	0.458993i
$802$		0			0
$803$	20.7846	+	12.0000i	0.733473	+	0.423471i
$804$	4.00000	+	6.92820i	0.141069	+	0.244339i
$805$		0			0
$806$		0			0
$807$	36.3731	−	21.0000i	1.28039	−	0.739235i
$808$		0			0
$809$	27.0000			0.949269			0.474635	−	0.880183i	$-0.342580\pi$
$809$	27.0000			0.949269			0.474635	+	0.880183i	$0.342580\pi$
$810$		0			0
$811$	21.5000	+	37.2391i	0.754967	+	1.30764i	0.945391	+	0.325939i	$0.105681\pi$
$811$	21.5000	+	37.2391i	0.754967	+	1.30764i	−0.190424	+	0.981702i	$0.560986\pi$
$812$	20.7846	+	12.0000i	0.729397	+	0.421117i
$813$	19.0526	−	11.0000i	0.668202	−	0.385787i
$814$		0			0
$815$		0			0
$816$	−48.0000			−1.68034
$817$	−6.92820	−	16.0000i	−0.242387	−	0.559769i
$818$		0			0
$819$	−4.00000	+	6.92820i	−0.139771	+	0.242091i
$820$		0			0
$821$	1.50000	+	2.59808i	0.0523504	+	0.0906735i	0.891013	−	0.453978i	$-0.149995\pi$
$821$	1.50000	+	2.59808i	0.0523504	+	0.0906735i	−0.838663	+	0.544651i	$0.816662\pi$
$822$		0			0
$823$	19.0526	−	11.0000i	0.664130	−	0.383436i	−0.129719	−	0.991551i	$-0.541407\pi$
$823$	19.0526	−	11.0000i	0.664130	−	0.383436i	0.793849	+	0.608115i	$0.208074\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−36.3731	+	21.0000i	−1.26482	+	0.730242i	−0.974002	−	0.226538i	$-0.927259\pi$
$827$	−36.3731	+	21.0000i	−1.26482	+	0.730242i	−0.290813	+	0.956780i	$0.593926\pi$
$828$		0			0
$829$	−26.0000			−0.903017			−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000			−0.903017			−0.451509	+	0.892267i	$0.649114\pi$
$830$		0			0
$831$	8.00000	−	13.8564i	0.277517	−	0.480673i
$832$	−13.8564	+	8.00000i	−0.480384	+	0.277350i
$833$	46.7654	+	27.0000i	1.62032	+	0.935495i
$834$		0			0
$835$		0			0
$836$	3.00000	−	25.9808i	0.103757	−	0.898563i
$837$		−	28.0000i		−	0.967822i
$838$		0			0
$839$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$839$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$			12.0000i			0.413302i
$844$	−14.0000			−0.481900
$845$		0			0
$846$		0			0
$847$			8.00000i			0.274883i
$848$			24.0000i			0.824163i
$849$	−14.0000	−	24.2487i	−0.480479	−	0.832214i
$850$		0			0
$851$		0			0
$852$	10.3923	+	6.00000i	0.356034	+	0.205557i
$853$	12.1244	+	7.00000i	0.415130	+	0.239675i	0.692992	−	0.720946i	$-0.256292\pi$
$853$	12.1244	+	7.00000i	0.415130	+	0.239675i	−0.277862	+	0.960621i	$0.589626\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−31.1769	−	18.0000i	−1.06498	−	0.614868i	−0.138177	−	0.990408i	$-0.544124\pi$
$857$	−31.1769	−	18.0000i	−1.06498	−	0.614868i	−0.926806	+	0.375539i	$0.877458\pi$
$858$		0			0
$859$	−3.50000	−	6.06218i	−0.119418	−	0.206839i	0.800119	−	0.599841i	$-0.204770\pi$
$859$	−3.50000	−	6.06218i	−0.119418	−	0.206839i	−0.919537	+	0.393003i	$0.871436\pi$
$860$		0			0
$861$	24.0000	+	41.5692i	0.817918	+	1.41668i
$862$		0			0
$863$		−	18.0000i		−	0.612727i	−0.951915	−	0.306364i	$-0.900888\pi$
$863$		−	18.0000i		−	0.612727i	0.951915	−	0.306364i	$-0.0991123\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	38.0000i		−	1.29055i
$868$	48.4974	−	28.0000i	1.64611	−	0.950382i
$869$	7.50000	−	12.9904i	0.254420	−	0.440668i
$870$		0			0
$871$	−2.00000	+	3.46410i	−0.0677674	+	0.117377i
$872$		0			0
$873$		−	8.00000i		−	0.270759i
$874$		0			0
$875$		0			0
$876$	−16.0000	+	27.7128i	−0.540590	+	0.936329i
$877$	45.0333	+	26.0000i	1.52067	+	0.877958i	0.999703	+	0.0243792i	$0.00776092\pi$
$877$	45.0333	+	26.0000i	1.52067	+	0.877958i	0.520964	+	0.853578i	$0.325572\pi$
$878$		0			0
$879$	−24.0000	+	41.5692i	−0.809500	+	1.40209i
$880$		0			0
$881$	9.00000			0.303218			0.151609	−	0.988441i	$-0.451555\pi$
$881$	9.00000			0.303218			0.151609	+	0.988441i	$0.451555\pi$
$882$		0			0
$883$	−6.92820	+	4.00000i	−0.233153	+	0.134611i	−0.612026	−	0.790838i	$-0.709645\pi$
$883$	−6.92820	+	4.00000i	−0.233153	+	0.134611i	0.378873	+	0.925449i	$0.376312\pi$
$884$	−12.0000	−	20.7846i	−0.403604	−	0.699062i
$885$		0			0
$886$		0			0
$887$	31.1769	−	18.0000i	1.04682	−	0.604381i	0.125061	−	0.992149i	$-0.460087\pi$
$887$	31.1769	−	18.0000i	1.04682	−	0.604381i	0.921757	+	0.387768i	$0.126754\pi$
$888$		0			0
$889$	−4.00000	−	6.92820i	−0.134156	−	0.232364i
$890$		0			0
$891$	16.5000	−	28.5788i	0.552771	−	0.957427i
$892$			8.00000i			0.267860i
$893$	25.9808	+	3.00000i	0.869413	+	0.100391i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$	10.5000	+	18.1865i	0.350195	+	0.606555i
$900$		0			0
$901$	−36.0000			−1.19933
$902$		0			0
$903$	27.7128	−	16.0000i	0.922225	−	0.532447i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−6.92820	−	4.00000i	−0.230047	−	0.132818i	0.380547	−	0.924762i	$-0.375736\pi$
$907$	−6.92820	−	4.00000i	−0.230047	−	0.132818i	−0.610594	+	0.791944i	$0.709069\pi$
$908$	−41.5692	+	24.0000i	−1.37952	+	0.796468i
$909$	7.50000	−	12.9904i	0.248759	−	0.430864i
$910$		0			0
$911$	21.0000			0.695761			0.347881	−	0.937539i	$-0.386901\pi$
$911$	21.0000			0.695761			0.347881	+	0.937539i	$0.386901\pi$
$912$	34.6410	+	4.00000i	1.14708	+	0.132453i
$913$		−	36.0000i		−	1.19143i
$914$		0			0
$915$		0			0
$916$	−7.00000	−	12.1244i	−0.231287	−	0.400600i
$917$	41.5692	+	24.0000i	1.37274	+	0.792550i
$918$		0			0
$919$	−8.00000			−0.263896			−0.131948	−	0.991257i	$-0.542123\pi$
$919$	−8.00000			−0.263896			−0.131948	+	0.991257i	$0.542123\pi$
$920$		0			0
$921$	−34.0000	−	58.8897i	−1.12034	−	1.94048i
$922$		0			0
$923$			6.00000i			0.197492i
$924$	48.0000			1.57908
$925$		0			0
$926$		0			0
$927$	−13.8564	+	8.00000i	−0.455104	+	0.262754i
$928$		0			0
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	−0.554984	−	0.831861i	$-0.687276\pi$
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	0.997905	+	0.0646999i	$0.0206090\pi$
$930$		0			0
$931$	−31.5000	−	23.3827i	−1.03237	−	0.766337i
$932$		−	12.0000i		−	0.393073i
$933$	−41.5692	−	24.0000i	−1.36092	−	0.785725i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−39.8372	+	23.0000i	−1.30142	+	0.751377i	−0.980648	−	0.195778i	$-0.937277\pi$
$937$	−39.8372	+	23.0000i	−1.30142	+	0.751377i	−0.320775	+	0.947155i	$0.603943\pi$
$938$		0			0
$939$	−20.0000			−0.652675
$940$		0			0
$941$	4.50000	+	7.79423i	0.146696	+	0.254085i	0.930004	−	0.367549i	$-0.119803\pi$
$941$	4.50000	+	7.79423i	0.146696	+	0.254085i	−0.783309	+	0.621633i	$0.786469\pi$
$942$		0			0
$943$		0			0
$944$	−30.0000	−	51.9615i	−0.976417	−	1.69120i
$945$		0			0
$946$		0			0
$947$	15.5885	+	9.00000i	0.506557	+	0.292461i	0.731417	−	0.681930i	$-0.238859\pi$
$947$	15.5885	+	9.00000i	0.506557	+	0.292461i	−0.224860	+	0.974391i	$0.572193\pi$
$948$	17.3205	+	10.0000i	0.562544	+	0.324785i
$949$	−16.0000			−0.519382
$950$		0			0
$951$	−48.0000			−1.55651
$952$		0			0
$953$	−10.3923	−	6.00000i	−0.336640	−	0.194359i	0.322145	−	0.946690i	$-0.395596\pi$
$953$	−10.3923	−	6.00000i	−0.336640	−	0.194359i	−0.658785	+	0.752331i	$0.728929\pi$
$954$		0			0
$955$		0			0
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$			18.0000i			0.581857i
$958$		0			0
$959$	24.0000	+	41.5692i	0.775000	+	1.34234i
$960$		0			0
$961$	18.0000			0.580645
$962$		0			0
$963$		0			0
$964$	−5.00000	+	8.66025i	−0.161039	+	0.278928i
$965$		0			0
$966$		0			0
$967$	13.8564	+	8.00000i	0.445592	+	0.257263i	0.705967	−	0.708245i	$-0.250513\pi$
$967$	13.8564	+	8.00000i	0.445592	+	0.257263i	−0.260375	+	0.965508i	$0.583846\pi$
$968$		0			0
$969$	−6.00000	+	51.9615i	−0.192748	+	1.66924i
$970$		0			0
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	−0.753545	−	0.657396i	$-0.771658\pi$
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	0.946094	+	0.323891i	$0.104991\pi$
$972$	17.3205	+	10.0000i	0.555556	+	0.320750i
$973$	−55.4256	+	32.0000i	−1.77686	+	1.02587i
$974$		0			0
$975$		0			0
$976$	20.0000			0.640184
$977$		−	12.0000i		−	0.383914i	−0.981403	−	0.191957i	$-0.938517\pi$
$977$		−	12.0000i		−	0.383914i	0.981403	−	0.191957i	$-0.0614834\pi$
$978$		0			0
$979$	−22.5000	−	38.9711i	−0.719103	−	1.24552i
$980$		0			0
$981$	11.0000			0.351203
$982$		0			0
$983$	−31.1769	−	18.0000i	−0.994389	−	0.574111i	−0.0878058	−	0.996138i	$-0.527985\pi$
$983$	−31.1769	−	18.0000i	−0.994389	−	0.574111i	−0.906583	+	0.422027i	$0.861319\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			48.0000i			1.52786i
$988$	6.92820	+	16.0000i	0.220416	+	0.509028i
$989$		0			0
$990$		0			0
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	−0.922538	−	0.385906i	$-0.873889\pi$
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	0.795474	+	0.605988i	$0.207222\pi$
$992$		0			0
$993$	6.92820	+	4.00000i	0.219860	+	0.126936i
$994$		0			0
$995$		0			0
$996$	48.0000			1.52094
$997$	−19.0526	+	11.0000i	−0.603401	+	0.348373i	−0.770378	−	0.637587i	$-0.779933\pi$
$997$	−19.0526	+	11.0000i	−0.603401	+	0.348373i	0.166978	+	0.985961i	$0.446599\pi$
$998$		0			0
$999$	−32.0000			−1.01244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.j.a.49.1		4
5.2	odd	4		475.2.e.b.201.1		2
5.3	odd	4		95.2.e.a.11.1	✓	2
5.4	even	2	inner	475.2.j.a.49.2		4
15.8	even	4		855.2.k.b.676.1		2
19.7	even	3	inner	475.2.j.a.349.2		4
20.3	even	4		1520.2.q.c.961.1		2
95.7	odd	12		475.2.e.b.26.1		2
95.8	even	12		1805.2.a.b.1.1		1
95.27	even	12		9025.2.a.e.1.1		1
95.64	even	6	inner	475.2.j.a.349.1		4
95.68	odd	12		1805.2.a.a.1.1		1
95.83	odd	12		95.2.e.a.26.1	yes	2
95.87	odd	12		9025.2.a.g.1.1		1
285.83	even	12		855.2.k.b.406.1		2
380.83	even	12		1520.2.q.c.881.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.a.11.1	✓	2	5.3	odd	4
95.2.e.a.26.1	yes	2	95.83	odd	12
475.2.e.b.26.1		2	95.7	odd	12
475.2.e.b.201.1		2	5.2	odd	4
475.2.j.a.49.1		4	1.1	even	1	trivial
475.2.j.a.49.2		4	5.4	even	2	inner
475.2.j.a.349.1		4	95.64	even	6	inner
475.2.j.a.349.2		4	19.7	even	3	inner
855.2.k.b.406.1		2	285.83	even	12
855.2.k.b.676.1		2	15.8	even	4
1520.2.q.c.881.1		2	380.83	even	12
1520.2.q.c.961.1		2	20.3	even	4
1805.2.a.a.1.1		1	95.68	odd	12
1805.2.a.b.1.1		1	95.8	even	12
9025.2.a.e.1.1		1	95.27	even	12
9025.2.a.g.1.1		1	95.87	odd	12

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{3} +(-1.00000 - 1.73205i) q^{4} -4.00000i q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.73205 - 1.00000i) q^{3} +(-1.00000 - 1.73205i) q^{4} -4.00000i q^{7} +(0.500000 + 0.866025i) q^{9} +3.00000 q^{11} +4.00000i q^{12} +(-1.73205 + 1.00000i) q^{13} +(-2.00000 + 3.46410i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(3.50000 + 2.59808i) q^{19} +(-4.00000 + 6.92820i) q^{21} +4.00000i q^{27} +(-6.92820 + 4.00000i) q^{28} +(-1.50000 - 2.59808i) q^{29} -7.00000 q^{31} +(-5.19615 - 3.00000i) q^{33} +(1.00000 - 1.73205i) q^{36} +8.00000i q^{37} +4.00000 q^{39} +(3.00000 - 5.19615i) q^{41} +(-3.46410 - 2.00000i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(5.19615 - 3.00000i) q^{47} +(6.92820 - 4.00000i) q^{48} -9.00000 q^{49} +(6.00000 + 10.3923i) q^{51} +(3.46410 + 2.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(-3.46410 - 8.00000i) q^{57} +(-7.50000 + 12.9904i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(3.46410 - 2.00000i) q^{63} +8.00000 q^{64} +(1.73205 - 1.00000i) q^{67} +12.0000i q^{68} +(1.50000 - 2.59808i) q^{71} +(6.92820 + 4.00000i) q^{73} +(1.00000 - 8.66025i) q^{76} -12.0000i q^{77} +(2.50000 - 4.33013i) q^{79} +(5.50000 - 9.52628i) q^{81} -12.0000i q^{83} +16.0000 q^{84} +6.00000i q^{87} +(-7.50000 - 12.9904i) q^{89} +(4.00000 + 6.92820i) q^{91} +(12.1244 + 7.00000i) q^{93} +(-6.92820 - 4.00000i) q^{97} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 2 * q^9	\( 4 q - 4 q^{4} + 2 q^{9} + 12 q^{11} - 8 q^{16} + 14 q^{19} - 16 q^{21} - 6 q^{29} - 28 q^{31} + 4 q^{36} + 16 q^{39} + 12 q^{41} - 12 q^{44} - 36 q^{49} + 24 q^{51} - 30 q^{59} - 10 q^{61} + 32 q^{64} + 6 q^{71} + 4 q^{76} + 10 q^{79} + 22 q^{81} + 64 q^{84} - 30 q^{89} + 16 q^{91} + 6 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 2 * q^9 + 12 * q^11 - 8 * q^16 + 14 * q^19 - 16 * q^21 - 6 * q^29 - 28 * q^31 + 4 * q^36 + 16 * q^39 + 12 * q^41 - 12 * q^44 - 36 * q^49 + 24 * q^51 - 30 * q^59 - 10 * q^61 + 32 * q^64 + 6 * q^71 + 4 * q^76 + 10 * q^79 + 22 * q^81 + 64 * q^84 - 30 * q^89 + 16 * q^91 + 6 * q^99

Introduction

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