LMFDB - Embedded newform 1456.2.cc.f.673.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1456,2,Mod(225,1456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1456, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1456.225"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 $ x^16 + 38x^14 + 587x^12 + 4762x^10 + 21849x^8 + 56552x^6 + 76456x^4 + 42624*x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.8
Root			$3.23100i$ of defining polynomial
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.f.225.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.61550 + 2.79813i) q^{3} +3.14769i q^{5} +(-0.866025 - 0.500000i) q^{7} +(-3.71968 + 6.44268i) q^{9} +(3.33264 - 1.92410i) q^{11} +(1.38576 + 3.32861i) q^{13} +(-8.80765 + 5.08510i) q^{15} +(0.0971843 - 0.168328i) q^{17} +(-5.33141 - 3.07809i) q^{19} -3.23100i q^{21} +(4.01081 + 6.94693i) q^{23} -4.90796 q^{25} -14.3436 q^{27} +(1.35952 + 2.35475i) q^{29} -8.51671i q^{31} +(10.7678 + 6.21677i) q^{33} +(1.57385 - 2.72598i) q^{35} +(3.10928 - 1.79515i) q^{37} +(-7.07520 + 9.25491i) q^{39} +(-3.44934 + 1.99148i) q^{41} +(5.74755 - 9.95506i) q^{43} +(-20.2796 - 11.7084i) q^{45} +4.35126i q^{47} +(0.500000 + 0.866025i) q^{49} +0.628005 q^{51} -0.576803 q^{53} +(6.05647 + 10.4901i) q^{55} -19.8906i q^{57} +(-1.80715 - 1.04336i) q^{59} +(-1.70255 + 2.94891i) q^{61} +(6.44268 - 3.71968i) q^{63} +(-10.4775 + 4.36194i) q^{65} +(-4.69408 + 2.71013i) q^{67} +(-12.9589 + 22.4456i) q^{69} +(7.92574 + 4.57593i) q^{71} -3.31209i q^{73} +(-7.92882 - 13.7331i) q^{75} -3.84820 q^{77} +8.98752 q^{79} +(-12.0130 - 20.8072i) q^{81} -7.66353i q^{83} +(0.529845 + 0.305906i) q^{85} +(-4.39260 + 7.60821i) q^{87} +(4.42996 - 2.55764i) q^{89} +(0.464204 - 3.57554i) q^{91} +(23.8309 - 13.7588i) q^{93} +(9.68888 - 16.7816i) q^{95} +(8.33696 + 4.81334i) q^{97} +28.6282i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{9} - 6 q^{11} + 10 q^{13} - 6 q^{15} + 2 q^{17} - 44 q^{25} + 12 q^{27} - 22 q^{29} + 42 q^{33} + 6 q^{35} + 12 q^{37} - 24 q^{39} + 36 q^{41} - 6 q^{43} - 30 q^{45} + 8 q^{49} + 4 q^{51} + 8 q^{53}+ \cdots - 42 q^{97}+O(q^{100}) $ 16 * q - 14 * q^9 - 6 * q^11 + 10 * q^13 - 6 * q^15 + 2 * q^17 - 44 * q^25 + 12 * q^27 - 22 * q^29 + 42 * q^33 + 6 * q^35 + 12 * q^37 - 24 * q^39 + 36 * q^41 - 6 * q^43 - 30 * q^45 + 8 * q^49 + 4 * q^51 + 8 * q^53 - 2 * q^55 + 18 * q^59 + 4 * q^61 + 12 * q^63 - 30 * q^65 - 24 * q^67 - 52 * q^69 - 36 * q^71 + 10 * q^75 - 24 * q^77 - 8 * q^79 + 42 * q^85 - 26 * q^87 - 36 * q^89 + 2 * q^91 - 42 * q^93 + 30 * q^95 - 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.61550	+	2.79813i	0.932710	+	1.61550i	0.778668	+	0.627436i	$0.215896\pi$
$3$	1.61550	+	2.79813i	0.932710	+	1.61550i	0.154042	+	0.988064i	$0.450771\pi$
$4$		0			0
$5$			3.14769i			1.40769i	0.710353	+	0.703845i	$0.248535\pi$
$5$			3.14769i			1.40769i	−0.710353	+	0.703845i	$0.751465\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		0			0
$9$	−3.71968	+	6.44268i	−1.23989	+	2.14756i
$10$		0			0
$11$	3.33264	−	1.92410i	1.00483	−	0.580138i	0.0951552	−	0.995462i	$-0.469665\pi$
$11$	3.33264	−	1.92410i	1.00483	−	0.580138i	0.909673	+	0.415324i	$0.136332\pi$
$12$		0			0
$13$	1.38576	+	3.32861i	0.384340	+	0.923191i
$13$	1.38576	+	3.32861i	0.384340	+	0.923191i
$14$		0			0
$15$	−8.80765	+	5.08510i	−2.27412	+	1.31297i
$16$		0			0
$17$	0.0971843	−	0.168328i	0.0235707	−	0.0408256i	−0.853999	−	0.520274i	$-0.825830\pi$
$17$	0.0971843	−	0.168328i	0.0235707	−	0.0408256i	0.877570	+	0.479448i	$0.159163\pi$
$18$		0			0
$19$	−5.33141	−	3.07809i	−1.22311	−	0.706162i	−0.257529	−	0.966271i	$-0.582908\pi$
$19$	−5.33141	−	3.07809i	−1.22311	−	0.706162i	−0.965579	+	0.260108i	$0.916242\pi$
$20$		0			0
$21$		−	3.23100i		−	0.705062i
$22$		0			0
$23$	4.01081	+	6.94693i	0.836313	+	1.44854i	0.892957	+	0.450141i	$0.148626\pi$
$23$	4.01081	+	6.94693i	0.836313	+	1.44854i	−0.0566448	+	0.998394i	$0.518040\pi$
$24$		0			0
$25$	−4.90796			−0.981593
$26$		0			0
$27$	−14.3436			−2.76043
$28$		0			0
$29$	1.35952	+	2.35475i	0.252456	+	0.437267i	0.964201	−	0.265171i	$-0.0854283\pi$
$29$	1.35952	+	2.35475i	0.252456	+	0.437267i	−0.711745	+	0.702438i	$0.752095\pi$
$30$		0			0
$31$		−	8.51671i		−	1.52965i	−0.644240	−	0.764823i	$-0.722826\pi$
$31$		−	8.51671i		−	1.52965i	0.644240	−	0.764823i	$-0.277174\pi$
$32$		0			0
$33$	10.7678	+	6.21677i	1.87443	+	1.08220i
$34$		0			0
$35$	1.57385	−	2.72598i	0.266029	−	0.460775i
$36$		0			0
$37$	3.10928	−	1.79515i	0.511163	−	0.295120i	−0.222149	−	0.975013i	$-0.571307\pi$
$37$	3.10928	−	1.79515i	0.511163	−	0.295120i	0.733312	+	0.679893i	$0.237974\pi$
$38$		0			0
$39$	−7.07520	+	9.25491i	−1.13294	+	1.48197i
$40$		0			0
$41$	−3.44934	+	1.99148i	−0.538696	+	0.311016i	−0.744550	−	0.667566i	$-0.767336\pi$
$41$	−3.44934	+	1.99148i	−0.538696	+	0.311016i	0.205854	+	0.978583i	$0.434003\pi$
$42$		0			0
$43$	5.74755	−	9.95506i	0.876494	−	1.51813i	0.0213310	−	0.999772i	$-0.493210\pi$
$43$	5.74755	−	9.95506i	0.876494	−	1.51813i	0.855163	−	0.518359i	$-0.173457\pi$
$44$		0			0
$45$	−20.2796	−	11.7084i	−3.02310	−	1.74539i
$46$		0			0
$47$			4.35126i			0.634696i	0.948309	+	0.317348i	$0.102792\pi$
$47$			4.35126i			0.634696i	−0.948309	+	0.317348i	$0.897208\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	0.628005			0.0879383
$52$		0			0
$53$	−0.576803			−0.0792300			−0.0396150	−	0.999215i	$-0.512613\pi$
$53$	−0.576803			−0.0792300			−0.0396150	+	0.999215i	$0.512613\pi$
$54$		0			0
$55$	6.05647	+	10.4901i	0.816655	+	1.41449i
$56$		0			0
$57$		−	19.8906i		−	2.63458i
$58$		0			0
$59$	−1.80715	−	1.04336i	−0.235271	−	0.135834i	0.377730	−	0.925916i	$-0.376705\pi$
$59$	−1.80715	−	1.04336i	−0.235271	−	0.135834i	−0.613002	+	0.790082i	$0.710038\pi$
$60$		0			0
$61$	−1.70255	+	2.94891i	−0.217989	+	0.377569i	−0.954193	−	0.299191i	$-0.903283\pi$
$61$	−1.70255	+	2.94891i	−0.217989	+	0.377569i	0.736204	+	0.676760i	$0.236617\pi$
$62$		0			0
$63$	6.44268	−	3.71968i	0.811702	−	0.468636i
$64$		0			0
$65$	−10.4775	+	4.36194i	−1.29957	+	0.541032i
$66$		0			0
$67$	−4.69408	+	2.71013i	−0.573474	+	0.331095i	−0.758535	−	0.651632i	$-0.774085\pi$
$67$	−4.69408	+	2.71013i	−0.573474	+	0.331095i	0.185062	+	0.982727i	$0.440751\pi$
$68$		0			0
$69$	−12.9589	+	22.4456i	−1.56007	+	2.70213i
$70$		0			0
$71$	7.92574	+	4.57593i	0.940612	+	0.543063i	0.890152	−	0.455663i	$-0.150598\pi$
$71$	7.92574	+	4.57593i	0.940612	+	0.543063i	0.0504599	+	0.998726i	$0.483931\pi$
$72$		0			0
$73$		−	3.31209i		−	0.387650i	−0.981036	−	0.193825i	$-0.937911\pi$
$73$		−	3.31209i		−	0.387650i	0.981036	−	0.193825i	$-0.0620894\pi$
$74$		0			0
$75$	−7.92882	−	13.7331i	−0.915541	−	1.58576i
$76$		0			0
$77$	−3.84820			−0.438543
$78$		0			0
$79$	8.98752			1.01117			0.505587	−	0.862775i	$-0.331276\pi$
$79$	8.98752			1.01117			0.505587	+	0.862775i	$0.331276\pi$
$80$		0			0
$81$	−12.0130	−	20.8072i	−1.33478	−	2.31191i
$82$		0			0
$83$		−	7.66353i		−	0.841181i	−0.907251	−	0.420591i	$-0.861823\pi$
$83$		−	7.66353i		−	0.841181i	0.907251	−	0.420591i	$-0.138177\pi$
$84$		0			0
$85$	0.529845	+	0.305906i	0.0574698	+	0.0331802i
$86$		0			0
$87$	−4.39260	+	7.60821i	−0.470936	+	0.815686i
$88$		0			0
$89$	4.42996	−	2.55764i	0.469574	−	0.271109i	−0.246487	−	0.969146i	$-0.579276\pi$
$89$	4.42996	−	2.55764i	0.469574	−	0.271109i	0.716062	+	0.698037i	$0.245943\pi$
$90$		0			0
$91$	0.464204	−	3.57554i	0.0486618	−	0.374819i
$92$		0			0
$93$	23.8309	−	13.7588i	2.47114	−	1.42672i
$94$		0			0
$95$	9.68888	−	16.7816i	0.994058	−	1.72176i
$96$		0			0
$97$	8.33696	+	4.81334i	0.846490	+	0.488721i	0.859465	−	0.511195i	$-0.170797\pi$
$97$	8.33696	+	4.81334i	0.846490	+	0.488721i	−0.0129752	+	0.999916i	$0.504130\pi$
$98$		0			0
$99$			28.6282i			2.87724i
$100$		0			0
$101$	−1.27079	−	2.20107i	−0.126448	−	0.219015i	0.795850	−	0.605494i	$-0.207024\pi$
$101$	−1.27079	−	2.20107i	−0.126448	−	0.219015i	−0.922298	+	0.386479i	$0.873691\pi$
$102$		0			0
$103$	−3.35392			−0.330471			−0.165236	−	0.986254i	$-0.552838\pi$
$103$	−3.35392			−0.330471			−0.165236	+	0.986254i	$0.552838\pi$
$104$		0			0
$105$	10.1702			0.992510
$106$		0			0
$107$	−6.45650	−	11.1830i	−0.624174	−	1.08110i	−0.988700	−	0.149907i	$-0.952102\pi$
$107$	−6.45650	−	11.1830i	−0.624174	−	1.08110i	0.364526	−	0.931193i	$-0.381231\pi$
$108$		0			0
$109$		−	8.04268i		−	0.770349i	−0.922844	−	0.385174i	$-0.874141\pi$
$109$		−	8.04268i		−	0.770349i	0.922844	−	0.385174i	$-0.125859\pi$
$110$		0			0
$111$	10.0461	+	5.80012i	0.953534	+	0.550523i
$112$		0			0
$113$	4.00235	−	6.93227i	0.376509	−	0.652133i	−0.614043	−	0.789273i	$-0.710458\pi$
$113$	4.00235	−	6.93227i	0.376509	−	0.652133i	0.990552	+	0.137140i	$0.0437910\pi$
$114$		0			0
$115$	−21.8668	+	12.6248i	−2.03909	+	1.17727i
$116$		0			0
$117$	−26.5998	−	3.45339i	−2.45915	−	0.319266i
$118$		0			0
$119$	−0.168328	+	0.0971843i	−0.0154306	+	0.00890887i
$120$		0			0
$121$	1.90432	−	3.29839i	0.173120	−	0.299853i
$122$		0			0
$123$	−11.1448	−	6.43446i	−1.00489	−	0.580176i
$124$		0			0
$125$			0.289701i			0.0259116i
$126$		0			0
$127$	−0.664383	−	1.15075i	−0.0589545	−	0.102112i	0.835042	−	0.550186i	$-0.185443\pi$
$127$	−0.664383	−	1.15075i	−0.0589545	−	0.102112i	−0.893996	+	0.448074i	$0.852110\pi$
$128$		0			0
$129$	37.1407			3.27006
$130$		0			0
$131$	0.592761			0.0517897			0.0258949	−	0.999665i	$-0.491756\pi$
$131$	0.592761			0.0517897			0.0258949	+	0.999665i	$0.491756\pi$
$132$		0			0
$133$	3.07809	+	5.33141i	0.266904	+	0.462292i
$134$		0			0
$135$		−	45.1492i		−	3.88583i
$136$		0			0
$137$	−2.21732	−	1.28017i	−0.189439	−	0.109372i	0.402281	−	0.915516i	$-0.368217\pi$
$137$	−2.21732	−	1.28017i	−0.189439	−	0.109372i	−0.591720	+	0.806144i	$0.701551\pi$
$138$		0			0
$139$	−9.01150	+	15.6084i	−0.764345	+	1.32388i	0.176247	+	0.984346i	$0.443604\pi$
$139$	−9.01150	+	15.6084i	−0.764345	+	1.32388i	−0.940592	+	0.339538i	$0.889729\pi$
$140$		0			0
$141$	−12.1754	+	7.02946i	−1.02535	+	0.591987i
$142$		0			0
$143$	11.0228	+	8.42673i	0.921775	+	0.704679i
$144$		0			0
$145$	−7.41204	+	4.27934i	−0.615536	+	0.355380i
$146$		0			0
$147$	−1.61550	+	2.79813i	−0.133244	+	0.230786i
$148$		0			0
$149$	7.02164	+	4.05394i	0.575235	+	0.332112i	0.759237	−	0.650814i	$-0.225572\pi$
$149$	7.02164	+	4.05394i	0.575235	+	0.332112i	−0.184002	+	0.982926i	$0.558905\pi$
$150$		0			0
$151$			3.58804i			0.291991i	0.989285	+	0.145995i	$0.0466385\pi$
$151$			3.58804i			0.291991i	−0.989285	+	0.145995i	$0.953362\pi$
$152$		0			0
$153$	0.722990	+	1.25226i	0.0584503	+	0.101239i
$154$		0			0
$155$	26.8080			2.15327
$156$		0			0
$157$	14.3447			1.14483			0.572417	−	0.819963i	$-0.306006\pi$
$157$	14.3447			1.14483			0.572417	+	0.819963i	$0.306006\pi$
$158$		0			0
$159$	−0.931826	−	1.61397i	−0.0738986	−	0.127996i
$160$		0			0
$161$		−	8.02163i		−	0.632193i
$162$		0			0
$163$	−0.213164	−	0.123070i	−0.0166963	−	0.00963961i	0.491629	−	0.870805i	$-0.336402\pi$
$163$	−0.213164	−	0.123070i	−0.0166963	−	0.00963961i	−0.508325	+	0.861165i	$0.669735\pi$
$164$		0			0
$165$	−19.5685	+	33.8936i	−1.52340	+	2.63861i
$166$		0			0
$167$	−1.56604	+	0.904156i	−0.121184	+	0.0699657i	−0.559367	−	0.828920i	$-0.688956\pi$
$167$	−1.56604	+	0.904156i	−0.121184	+	0.0699657i	0.438183	+	0.898886i	$0.355622\pi$
$168$		0			0
$169$	−9.15934	+	9.22532i	−0.704565	+	0.709640i
$170$		0			0
$171$	39.6623	−	22.8990i	3.03305	−	1.75113i
$172$		0			0
$173$	−5.39981	+	9.35275i	−0.410540	+	0.711076i	−0.994949	−	0.100383i	$-0.967993\pi$
$173$	−5.39981	+	9.35275i	−0.410540	+	0.711076i	0.584409	+	0.811459i	$0.301326\pi$
$174$		0			0
$175$	4.25042	+	2.45398i	0.321302	+	0.185504i
$176$		0			0
$177$		−	6.74220i		−	0.506775i
$178$		0			0
$179$	−4.33823	−	7.51404i	−0.324255	−	0.561626i	0.657106	−	0.753798i	$-0.271780\pi$
$179$	−4.33823	−	7.51404i	−0.324255	−	0.561626i	−0.981361	+	0.192172i	$0.938447\pi$
$180$		0			0
$181$	−10.0087			−0.743940			−0.371970	−	0.928245i	$-0.621318\pi$
$181$	−10.0087			−0.743940			−0.371970	+	0.928245i	$0.621318\pi$
$182$		0			0
$183$	−11.0019			−0.813283
$184$		0			0
$185$	5.65057	+	9.78707i	0.415438	+	0.719559i
$186$		0			0
$187$		−	0.747970i		−	0.0546970i
$188$		0			0
$189$	12.4219	+	7.17180i	0.903562	+	0.521672i
$190$		0			0
$191$	−12.0156	+	20.8117i	−0.869420	+	1.50588i	−0.00682903	+	0.999977i	$0.502174\pi$
$191$	−12.0156	+	20.8117i	−0.869420	+	1.50588i	−0.862591	+	0.505902i	$0.831160\pi$
$192$		0			0
$193$	−2.83457	+	1.63654i	−0.204037	+	0.117801i	−0.598537	−	0.801095i	$-0.704251\pi$
$193$	−2.83457	+	1.63654i	−0.204037	+	0.117801i	0.394500	+	0.918896i	$0.370918\pi$
$194$		0			0
$195$	−29.1316	−	22.2705i	−2.08616	−	1.59483i
$196$		0			0
$197$	11.0439	−	6.37619i	0.786844	−	0.454285i	−0.0520061	−	0.998647i	$-0.516562\pi$
$197$	11.0439	−	6.37619i	0.786844	−	0.454285i	0.838850	+	0.544362i	$0.183228\pi$
$198$		0			0
$199$	−13.6616	+	23.6625i	−0.968442	+	1.67739i	−0.268373	+	0.963315i	$0.586486\pi$
$199$	−13.6616	+	23.6625i	−0.968442	+	1.67739i	−0.700069	+	0.714076i	$0.746847\pi$
$200$		0			0
$201$	−15.1666	−	8.75643i	−1.06977	−	0.617631i
$202$		0			0
$203$		−	2.71904i		−	0.190839i
$204$		0			0
$205$	−6.26855	−	10.8575i	−0.437815	−	0.758317i
$206$		0			0
$207$	−59.6758			−4.14776
$208$		0			0
$209$	−23.6902			−1.63869
$210$		0			0
$211$	13.2929	+	23.0239i	0.915118	+	1.58503i	0.806728	+	0.590923i	$0.201236\pi$
$211$	13.2929	+	23.0239i	0.915118	+	1.58503i	0.108390	+	0.994108i	$0.465430\pi$
$212$		0			0
$213$			29.5696i			2.02608i
$214$		0			0
$215$	31.3355	+	18.0915i	2.13706	+	1.23383i
$216$		0			0
$217$	−4.25836	+	7.37569i	−0.289076	+	0.500694i
$218$		0			0
$219$	9.26764	−	5.35068i	0.626249	−	0.361565i
$220$		0			0
$221$	0.694974	+	0.0902268i	0.0467490	+	0.00606931i
$222$		0			0
$223$	−13.1063	+	7.56691i	−0.877661	+	0.506718i	−0.869887	−	0.493252i	$-0.835808\pi$
$223$	−13.1063	+	7.56691i	−0.877661	+	0.506718i	−0.00777474	+	0.999970i	$0.502475\pi$
$224$		0			0
$225$	18.2561	−	31.6205i	1.21707	−	2.10803i
$226$		0			0
$227$	18.5376	+	10.7027i	1.23038	+	0.710362i	0.967110	−	0.254359i	$-0.0818644\pi$
$227$	18.5376	+	10.7027i	1.23038	+	0.710362i	0.263274	+	0.964721i	$0.415198\pi$
$228$		0			0
$229$		−	8.36123i		−	0.552526i	−0.961082	−	0.276263i	$-0.910904\pi$
$229$		−	8.36123i		−	0.552526i	0.961082	−	0.276263i	$-0.0890961\pi$
$230$		0			0
$231$	−6.21677	−	10.7678i	−0.409033	−	0.708467i
$232$		0			0
$233$	26.1663			1.71421			0.857107	−	0.515138i	$-0.172260\pi$
$233$	26.1663			1.71421			0.857107	+	0.515138i	$0.172260\pi$
$234$		0			0
$235$	−13.6964			−0.893456
$236$		0			0
$237$	14.5193	+	25.1482i	0.943132	+	1.63355i
$238$		0			0
$239$		−	18.3562i		−	1.18736i	−0.804700	−	0.593682i	$-0.797674\pi$
$239$		−	18.3562i		−	1.18736i	0.804700	−	0.593682i	$-0.202326\pi$
$240$		0			0
$241$	−2.88804	−	1.66741i	−0.186035	−	0.107407i	0.404090	−	0.914719i	$-0.367588\pi$
$241$	−2.88804	−	1.66741i	−0.186035	−	0.107407i	−0.590125	+	0.807312i	$0.700922\pi$
$242$		0			0
$243$	17.2988	−	29.9623i	1.10972	−	1.92209i
$244$		0			0
$245$	−2.72598	+	1.57385i	−0.174157	+	0.100549i
$246$		0			0
$247$	2.85772	−	22.0117i	0.181833	−	1.40057i
$248$		0			0
$249$	21.4435	−	12.3804i	1.35893	−	0.784578i
$250$		0			0
$251$	6.09884	−	10.5635i	0.384956	−	0.666763i	−0.606807	−	0.794849i	$-0.707550\pi$
$251$	6.09884	−	10.5635i	0.384956	−	0.666763i	0.991763	+	0.128086i	$0.0408834\pi$
$252$		0			0
$253$	26.7332	+	15.4344i	1.68070	+	0.970353i
$254$		0			0
$255$			1.97677i			0.123790i
$256$		0			0
$257$	7.63648	+	13.2268i	0.476350	+	0.825063i	0.999633	−	0.0270962i	$-0.00862605\pi$
$257$	7.63648	+	13.2268i	0.476350	+	0.825063i	−0.523282	+	0.852159i	$0.675293\pi$
$258$		0			0
$259$	−3.59029			−0.223090
$260$		0			0
$261$	−20.2279			−1.25208
$262$		0			0
$263$	12.4495	+	21.5631i	0.767666	+	1.32964i	0.938825	+	0.344394i	$0.111915\pi$
$263$	12.4495	+	21.5631i	0.767666	+	1.32964i	−0.171159	+	0.985243i	$0.554751\pi$
$264$		0			0
$265$		−	1.81560i		−	0.111531i
$266$		0			0
$267$	14.3132	+	8.26373i	0.875953	+	0.505732i
$268$		0			0
$269$	3.92836	−	6.80413i	0.239517	−	0.414855i	−0.721059	−	0.692874i	$-0.756344\pi$
$269$	3.92836	−	6.80413i	0.239517	−	0.414855i	0.960576	+	0.278019i	$0.0896777\pi$
$270$		0			0
$271$	−2.28514	+	1.31933i	−0.138812	+	0.0801433i	−0.567798	−	0.823168i	$-0.692204\pi$
$271$	−2.28514	+	1.31933i	−0.138812	+	0.0801433i	0.428986	+	0.903311i	$0.358871\pi$
$272$		0			0
$273$	10.7548	−	4.47739i	0.650907	−	0.270984i
$274$		0			0
$275$	−16.3565	+	9.44342i	−0.986333	+	0.569459i
$276$		0			0
$277$	5.82743	−	10.0934i	0.350136	−	0.606454i	−0.636137	−	0.771576i	$-0.719469\pi$
$277$	5.82743	−	10.0934i	0.350136	−	0.606454i	0.986273	+	0.165122i	$0.0528019\pi$
$278$		0			0
$279$	54.8705	+	31.6795i	3.28501	+	1.89660i
$280$		0			0
$281$			3.86501i			0.230567i	0.993333	+	0.115283i	$0.0367776\pi$
$281$			3.86501i			0.230567i	−0.993333	+	0.115283i	$0.963222\pi$
$282$		0			0
$283$	−3.42431	−	5.93109i	−0.203554	−	0.352566i	0.746117	−	0.665815i	$-0.231916\pi$
$283$	−3.42431	−	5.93109i	−0.203554	−	0.352566i	−0.949671	+	0.313249i	$0.898583\pi$
$284$		0			0
$285$	62.6095			3.70867
$286$		0			0
$287$	3.98295			0.235106
$288$		0			0
$289$	8.48111	+	14.6897i	0.498889	+	0.864101i
$290$		0			0
$291$			31.1038i			1.82334i
$292$		0			0
$293$	1.28946	+	0.744468i	0.0753309	+	0.0434923i	0.537192	−	0.843460i	$-0.319485\pi$
$293$	1.28946	+	0.744468i	0.0753309	+	0.0434923i	−0.461861	+	0.886952i	$0.652818\pi$
$294$		0			0
$295$	3.28418	−	5.68836i	0.191212	−	0.331189i
$296$		0			0
$297$	−47.8021	+	27.5985i	−2.77376	+	1.60143i
$298$		0			0
$299$	−17.5656	+	22.9772i	−1.01585	+	1.32881i
$300$		0			0
$301$	−9.95506	+	5.74755i	−0.573800	+	0.331284i
$302$		0			0
$303$	4.10592	−	7.11166i	0.235879	−	0.408554i
$304$		0			0
$305$	−9.28225	−	5.35911i	−0.531500	−	0.306862i
$306$		0			0
$307$		−	2.33128i		−	0.133053i	−0.997785	−	0.0665265i	$-0.978808\pi$
$307$		−	2.33128i		−	0.133053i	0.997785	−	0.0665265i	$-0.0211917\pi$
$308$		0			0
$309$	−5.41826	−	9.38470i	−0.308234	−	0.533877i
$310$		0			0
$311$	−11.8244			−0.670502			−0.335251	−	0.942129i	$-0.608821\pi$
$311$	−11.8244			−0.670502			−0.335251	+	0.942129i	$0.608821\pi$
$312$		0			0
$313$	−18.4087			−1.04052			−0.520260	−	0.854008i	$-0.674165\pi$
$313$	−18.4087			−1.04052			−0.520260	+	0.854008i	$0.674165\pi$
$314$		0			0
$315$	11.7084	+	20.2796i	0.659695	+	1.14262i
$316$		0			0
$317$		−	8.42274i		−	0.473068i	−0.971623	−	0.236534i	$-0.923988\pi$
$317$		−	8.42274i		−	0.473068i	0.971623	−	0.236534i	$-0.0760115\pi$
$318$		0			0
$319$	9.06156	+	5.23170i	0.507350	+	0.292919i
$320$		0			0
$321$	20.8610	−	36.1323i	1.16435	−	2.01671i
$322$		0			0
$323$	−1.03626	+	0.598284i	−0.0576590	+	0.0332894i
$324$		0			0
$325$	−6.80126	−	16.3367i	−0.377266	−	0.906198i
$326$		0			0
$327$	22.5044	−	12.9929i	1.24450	−	0.718512i
$328$		0			0
$329$	2.17563	−	3.76830i	0.119946	−	0.207753i
$330$		0			0
$331$	−15.6375	−	9.02830i	−0.859513	−	0.496240i	0.00433587	−	0.999991i	$-0.498620\pi$
$331$	−15.6375	−	9.02830i	−0.859513	−	0.496240i	−0.863849	+	0.503750i	$0.831953\pi$
$332$		0			0
$333$			26.7095i			1.46367i
$334$		0			0
$335$	−8.53065	−	14.7755i	−0.466079	−	0.807273i
$336$		0			0
$337$	−3.64765			−0.198700			−0.0993500	−	0.995053i	$-0.531676\pi$
$337$	−3.64765			−0.198700			−0.0993500	+	0.995053i	$0.531676\pi$
$338$		0			0
$339$	25.8632			1.40469
$340$		0			0
$341$	−16.3870	−	28.3831i	−0.887406	−	1.53703i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	−70.6517	−	40.7908i	−3.80376	−	2.19610i
$346$		0			0
$347$	7.29727	−	12.6392i	0.391738	−	0.678510i	−0.600941	−	0.799294i	$-0.705207\pi$
$347$	7.29727	−	12.6392i	0.391738	−	0.678510i	0.992679	+	0.120783i	$0.0385406\pi$
$348$		0			0
$349$	−15.4877	+	8.94182i	−0.829037	+	0.478645i	−0.853523	−	0.521056i	$-0.825538\pi$
$349$	−15.4877	+	8.94182i	−0.829037	+	0.478645i	0.0244861	+	0.999700i	$0.492205\pi$
$350$		0			0
$351$	−19.8768	−	47.7443i	−1.06094	−	2.54840i
$352$		0			0
$353$	5.52760	−	3.19136i	0.294204	−	0.169859i	−0.345632	−	0.938370i	$-0.612335\pi$
$353$	5.52760	−	3.19136i	0.294204	−	0.169859i	0.639836	+	0.768511i	$0.279002\pi$
$354$		0			0
$355$	−14.4036	+	24.9478i	−0.764464	+	1.32409i
$356$		0			0
$357$	−0.543869	−	0.314003i	−0.0287846	−	0.0166188i
$358$		0			0
$359$		−	30.4944i		−	1.60943i	−0.593659	−	0.804717i	$-0.702317\pi$
$359$		−	30.4944i		−	1.60943i	0.593659	−	0.804717i	$-0.297683\pi$
$360$		0			0
$361$	9.44927	+	16.3666i	0.497330	+	0.861400i
$362$		0			0
$363$	12.3057			0.645884
$364$		0			0
$365$	10.4254			0.545692
$366$		0			0
$367$	−3.58169	−	6.20366i	−0.186962	−	0.323829i	0.757274	−	0.653098i	$-0.226531\pi$
$367$	−3.58169	−	6.20366i	−0.186962	−	0.323829i	−0.944236	+	0.329269i	$0.893198\pi$
$368$		0			0
$369$		−	29.6306i		−	1.54251i
$370$		0			0
$371$	0.499526	+	0.288402i	0.0259341	+	0.0149731i
$372$		0			0
$373$	0.582337	−	1.00864i	0.0301523	−	0.0522252i	−0.850556	−	0.525885i	$-0.823734\pi$
$373$	0.582337	−	1.00864i	0.0301523	−	0.0522252i	0.880708	+	0.473660i	$0.157067\pi$
$374$		0			0
$375$	−0.810620	+	0.468011i	−0.0418602	+	0.0241680i
$376$		0			0
$377$	−5.95410	+	7.78843i	−0.306652	+	0.401125i
$378$		0			0
$379$	25.1318	−	14.5099i	1.29093	−	0.745322i	0.312115	−	0.950044i	$-0.398963\pi$
$379$	25.1318	−	14.5099i	1.29093	−	0.745322i	0.978820	+	0.204723i	$0.0656293\pi$
$380$		0			0
$381$	2.14662	−	3.71806i	0.109975	−	0.190482i
$382$		0			0
$383$	−19.0154	−	10.9786i	−0.971642	−	0.560978i	−0.0719059	−	0.997411i	$-0.522908\pi$
$383$	−19.0154	−	10.9786i	−0.971642	−	0.560978i	−0.899737	+	0.436433i	$0.856241\pi$
$384$		0			0
$385$		−	12.1129i		−	0.617333i
$386$		0			0
$387$	42.7582	+	74.0593i	2.17352	+	3.76465i
$388$		0			0
$389$	−29.1973			−1.48036			−0.740180	−	0.672409i	$-0.765260\pi$
$389$	−29.1973			−1.48036			−0.740180	+	0.672409i	$0.765260\pi$
$390$		0			0
$391$	1.55915			0.0788498
$392$		0			0
$393$	0.957605	+	1.65862i	0.0483048	+	0.0836664i
$394$		0			0
$395$			28.2899i			1.42342i
$396$		0			0
$397$	27.6698	+	15.9752i	1.38871	+	0.801771i	0.993170	−	0.116679i	$-0.0372248\pi$
$397$	27.6698	+	15.9752i	1.38871	+	0.801771i	0.395538	+	0.918450i	$0.370558\pi$
$398$		0			0
$399$	−9.94531	+	17.2258i	−0.497888	+	0.862368i
$400$		0			0
$401$	31.9176	−	18.4276i	1.59389	−	0.920232i	0.601257	−	0.799056i	$-0.294667\pi$
$401$	31.9176	−	18.4276i	1.59389	−	0.920232i	0.992631	−	0.121176i	$-0.0386664\pi$
$402$		0			0
$403$	28.3488	−	11.8021i	1.41216	−	0.587905i
$404$		0			0
$405$	65.4947	−	37.8134i	3.25446	−	1.87896i
$406$		0			0
$407$	6.90808	−	11.9651i	0.342421	−	0.593090i
$408$		0			0
$409$	4.89732	+	2.82747i	0.242157	+	0.139809i	0.616168	−	0.787615i	$-0.288684\pi$
$409$	4.89732	+	2.82747i	0.242157	+	0.139809i	−0.374011	+	0.927424i	$0.622018\pi$
$410$		0			0
$411$		−	8.27247i		−	0.408051i
$412$		0			0
$413$	1.04336	+	1.80715i	0.0513404	+	0.0889242i
$414$		0			0
$415$	24.1224			1.18412
$416$		0			0
$417$	−58.2323			−2.85165
$418$		0			0
$419$	−12.9031	−	22.3488i	−0.630358	−	1.09181i	−0.987478	−	0.157754i	$-0.949575\pi$
$419$	−12.9031	−	22.3488i	−0.630358	−	1.09181i	0.357120	−	0.934059i	$-0.383759\pi$
$420$		0			0
$421$			28.8606i			1.40658i	0.710903	+	0.703290i	$0.248286\pi$
$421$			28.8606i			1.40658i	−0.710903	+	0.703290i	$0.751714\pi$
$422$		0			0
$423$	−28.0338	−	16.1853i	−1.36305	−	0.786957i
$424$		0			0
$425$	−0.476977	+	0.826149i	−0.0231368	+	0.0400741i
$426$		0			0
$427$	2.94891	−	1.70255i	0.142708	−	0.0823923i
$428$		0			0
$429$	−5.77170	+	44.4567i	−0.278660	+	2.14639i
$430$		0			0
$431$	27.4281	−	15.8356i	1.32116	−	0.762774i	0.337249	−	0.941415i	$-0.390504\pi$
$431$	27.4281	−	15.8356i	1.32116	−	0.762774i	0.983914	+	0.178641i	$0.0571702\pi$
$432$		0			0
$433$	15.6517	−	27.1095i	0.752172	−	1.30280i	−0.194597	−	0.980883i	$-0.562340\pi$
$433$	15.6517	−	27.1095i	0.752172	−	1.30280i	0.946768	−	0.321916i	$-0.104327\pi$
$434$		0			0
$435$	−23.9483	−	13.8266i	−1.14823	−	0.662933i
$436$		0			0
$437$		−	49.3826i		−	2.36229i
$438$		0			0
$439$	−18.4786	−	32.0059i	−0.881935	−	1.52756i	−0.849187	−	0.528092i	$-0.822907\pi$
$439$	−18.4786	−	32.0059i	−0.881935	−	1.52756i	−0.0327479	−	0.999464i	$-0.510426\pi$
$440$		0			0
$441$	−7.43937			−0.354256
$442$		0			0
$443$	−28.2871			−1.34396			−0.671981	−	0.740568i	$-0.734556\pi$
$443$	−28.2871			−1.34396			−0.671981	+	0.740568i	$0.734556\pi$
$444$		0			0
$445$	8.05065	+	13.9441i	0.381638	+	0.661016i
$446$		0			0
$447$			26.1966i			1.23906i
$448$		0			0
$449$	21.0690	+	12.1642i	0.994308	+	0.574064i	0.906559	−	0.422079i	$-0.138699\pi$
$449$	21.0690	+	12.1642i	0.994308	+	0.574064i	0.0877485	+	0.996143i	$0.472033\pi$
$450$		0			0
$451$	−7.66360	+	13.2737i	−0.360865	+	0.625036i
$452$		0			0
$453$	−10.0398	+	5.79649i	−0.471712	+	0.272343i
$454$		0			0
$455$	11.2547	+	1.46117i	0.527629	+	0.0685008i
$456$		0			0
$457$	−1.34199	+	0.774798i	−0.0627756	+	0.0362435i	−0.531059	−	0.847335i	$-0.678206\pi$
$457$	−1.34199	+	0.774798i	−0.0627756	+	0.0362435i	0.468284	+	0.883578i	$0.344873\pi$
$458$		0			0
$459$	−1.39397	+	2.41443i	−0.0650651	+	0.112696i
$460$		0			0
$461$	11.2195	+	6.47760i	0.522545	+	0.301692i	0.737975	−	0.674828i	$-0.235782\pi$
$461$	11.2195	+	6.47760i	0.522545	+	0.301692i	−0.215430	+	0.976519i	$0.569115\pi$
$462$		0			0
$463$			28.1690i			1.30912i	0.756008	+	0.654562i	$0.227147\pi$
$463$			28.1690i			1.30912i	−0.756008	+	0.654562i	$0.772853\pi$
$464$		0			0
$465$	43.3083	+	75.0122i	2.00837	+	3.47861i
$466$		0			0
$467$	29.2908			1.35542			0.677709	−	0.735330i	$-0.262973\pi$
$467$	29.2908			1.35542			0.677709	+	0.735330i	$0.262973\pi$
$468$		0			0
$469$	5.42026			0.250284
$470$		0			0
$471$	23.1739	+	40.1384i	1.06780	+	1.84948i
$472$		0			0
$473$		−	44.2355i		−	2.03395i
$474$		0			0
$475$	26.1664	+	15.1072i	1.20059	+	0.693164i
$476$		0			0
$477$	2.14553	−	3.71616i	0.0982369	−	0.170151i
$478$		0			0
$479$	16.8625	−	9.73555i	0.770466	−	0.444829i	−0.0625747	−	0.998040i	$-0.519931\pi$
$479$	16.8625	−	9.73555i	0.770466	−	0.444829i	0.833041	+	0.553211i	$0.186598\pi$
$480$		0			0
$481$	10.2841	+	7.86197i	0.468913	+	0.358475i
$482$		0			0
$483$	22.4456	−	12.9589i	1.02131	−	0.589652i
$484$		0			0
$485$	−15.1509	+	26.2422i	−0.687968	+	1.19160i
$486$		0			0
$487$	−3.92783	−	2.26773i	−0.177987	−	0.102761i	0.408360	−	0.912821i	$-0.366101\pi$
$487$	−3.92783	−	2.26773i	−0.177987	−	0.102761i	−0.586346	+	0.810060i	$0.699434\pi$
$488$		0			0
$489$		−	0.795281i		−	0.0359638i
$490$		0			0
$491$	−9.07433	−	15.7172i	−0.409519	−	0.709307i	0.585317	−	0.810804i	$-0.300970\pi$
$491$	−9.07433	−	15.7172i	−0.409519	−	0.709307i	−0.994836	+	0.101497i	$0.967637\pi$
$492$		0			0
$493$	0.528495			0.0238022
$494$		0			0
$495$	−90.1127			−4.05026
$496$		0			0
$497$	−4.57593	−	7.92574i	−0.205258	−	0.355518i
$498$		0			0
$499$			6.65532i			0.297933i	0.988842	+	0.148967i	$0.0475947\pi$
$499$			6.65532i			0.297933i	−0.988842	+	0.148967i	$0.952405\pi$
$500$		0			0
$501$	−5.05989	−	2.92133i	−0.226059	−	0.130515i
$502$		0			0
$503$	7.45978	−	12.9207i	0.332615	−	0.576106i	−0.650409	−	0.759584i	$-0.725402\pi$
$503$	7.45978	−	12.9207i	0.332615	−	0.576106i	0.983024	+	0.183478i	$0.0587357\pi$
$504$		0			0
$505$	6.92829	−	4.00005i	0.308305	−	0.178000i
$506$		0			0
$507$	−40.6105	−	10.7255i	−1.80358	−	0.476337i
$508$		0			0
$509$	−15.3869	+	8.88365i	−0.682014	+	0.393761i	−0.800613	−	0.599181i	$-0.795493\pi$
$509$	−15.3869	+	8.88365i	−0.682014	+	0.393761i	0.118599	+	0.992942i	$0.462160\pi$
$510$		0			0
$511$	−1.65604	+	2.86835i	−0.0732590	+	0.126888i
$512$		0			0
$513$	76.4716	+	44.1509i	3.37630	+	1.94931i
$514$		0			0
$515$		−	10.5571i		−	0.465201i
$516$		0			0
$517$	8.37226	+	14.5012i	0.368211	+	0.637761i
$518$		0			0
$519$	−34.8936			−1.53166
$520$		0			0
$521$	38.0579			1.66735			0.833673	−	0.552258i	$-0.186234\pi$
$521$	38.0579			1.66735			0.833673	+	0.552258i	$0.186234\pi$
$522$		0			0
$523$	6.94526	+	12.0295i	0.303695	+	0.526015i	0.976970	−	0.213377i	$-0.0684463\pi$
$523$	6.94526	+	12.0295i	0.303695	+	0.526015i	−0.673275	+	0.739392i	$0.735113\pi$
$524$		0			0
$525$			15.8576i			0.692084i
$526$		0			0
$527$	−1.43360	−	0.827691i	−0.0624487	−	0.0360548i
$528$		0			0
$529$	−20.6733	+	35.8071i	−0.898837	+	1.55683i
$530$		0			0
$531$	13.4441	−	7.76195i	0.583424	−	0.336840i
$532$		0			0
$533$	−11.4088	−	8.72181i	−0.494170	−	0.377783i
$534$		0			0
$535$	35.2006	−	20.3231i	1.52185	−	0.878643i
$536$		0			0
$537$	14.0168	−	24.2779i	0.604871	−	1.04767i
$538$		0			0
$539$	3.33264	+	1.92410i	0.143547	+	0.0828769i
$540$		0			0
$541$		−	41.8453i		−	1.79907i	−0.436850	−	0.899535i	$-0.643906\pi$
$541$		−	41.8453i		−	1.79907i	0.436850	−	0.899535i	$-0.356094\pi$
$542$		0			0
$543$	−16.1690	−	28.0056i	−0.693880	−	1.20184i
$544$		0			0
$545$	25.3159			1.08441
$546$		0			0
$547$	22.3475			0.955509			0.477754	−	0.878493i	$-0.341451\pi$
$547$	22.3475			0.955509			0.477754	+	0.878493i	$0.341451\pi$
$548$		0			0
$549$	−12.6659	−	21.9380i	−0.540568	−	0.936291i
$550$		0			0
$551$		−	16.7389i		−	0.713100i
$552$		0			0
$553$	−7.78342	−	4.49376i	−0.330985	−	0.191094i
$554$		0			0
$555$	−18.2570	+	31.6220i	−0.774966	+	1.34228i
$556$		0			0
$557$	26.5499	−	15.3286i	1.12495	−	0.649493i	0.182293	−	0.983244i	$-0.441648\pi$
$557$	26.5499	−	15.3286i	1.12495	−	0.649493i	0.942661	+	0.333752i	$0.108315\pi$
$558$		0			0
$559$	41.1013	+	5.33608i	1.73840	+	0.225692i
$560$		0			0
$561$	2.09292	−	1.20835i	0.0883630	−	0.0510164i
$562$		0			0
$563$	16.6237	−	28.7930i	0.700604	−	1.21348i	−0.267651	−	0.963516i	$-0.586247\pi$
$563$	16.6237	−	28.7930i	0.700604	−	1.21348i	0.968255	−	0.249966i	$-0.0804193\pi$
$564$		0			0
$565$	21.8206	+	12.5982i	0.918001	+	0.530008i
$566$		0			0
$567$			24.0261i			1.00900i
$568$		0			0
$569$	5.80511	+	10.0547i	0.243363	+	0.421517i	0.961670	−	0.274209i	$-0.0884161\pi$
$569$	5.80511	+	10.0547i	0.243363	+	0.421517i	−0.718307	+	0.695726i	$0.755083\pi$
$570$		0			0
$571$	−16.6994			−0.698847			−0.349423	−	0.936965i	$-0.613623\pi$
$571$	−16.6994			−0.698847			−0.349423	+	0.936965i	$0.613623\pi$
$572$		0			0
$573$	−77.6450			−3.24366
$574$		0			0
$575$	−19.6849	−	34.0953i	−0.820918	−	1.42187i
$576$		0			0
$577$		−	37.2583i		−	1.55108i	−0.631297	−	0.775541i	$-0.717477\pi$
$577$		−	37.2583i		−	1.55108i	0.631297	−	0.775541i	$-0.282523\pi$
$578$		0			0
$579$	−9.15849	−	5.28765i	−0.380614	−	0.219747i
$580$		0			0
$581$	−3.83176	+	6.63681i	−0.158968	+	0.275341i
$582$		0			0
$583$	−1.92228	+	1.10983i	−0.0796126	+	0.0459643i
$584$		0			0
$585$	10.8702	−	83.7279i	0.449427	−	3.46172i
$586$		0			0
$587$	−36.1912	+	20.8950i	−1.49377	+	0.862429i	−0.999974	−	0.00714861i	$-0.997725\pi$
$587$	−36.1912	+	20.8950i	−1.49377	+	0.862429i	−0.493796	+	0.869578i	$0.664391\pi$
$588$		0			0
$589$	−26.2152	+	45.4061i	−1.08018	+	1.87092i
$590$		0			0
$591$	35.6828	+	20.6015i	1.46779	+	0.847432i
$592$		0			0
$593$		−	4.33672i		−	0.178088i	−0.996028	−	0.0890438i	$-0.971619\pi$
$593$		−	4.33672i		−	0.178088i	0.996028	−	0.0890438i	$-0.0283811\pi$
$594$		0			0
$595$	−0.305906	−	0.529845i	−0.0125409	−	0.0217215i
$596$		0			0
$597$	−88.2810			−3.61310
$598$		0			0
$599$	−22.7578			−0.929858			−0.464929	−	0.885348i	$-0.653920\pi$
$599$	−22.7578			−0.929858			−0.464929	+	0.885348i	$0.653920\pi$
$600$		0			0
$601$	13.7634	+	23.8389i	0.561421	+	0.972410i	0.997373	+	0.0724402i	$0.0230786\pi$
$601$	13.7634	+	23.8389i	0.561421	+	0.972410i	−0.435951	+	0.899970i	$0.643588\pi$
$602$		0			0
$603$		−	40.3233i		−	1.64209i
$604$		0			0
$605$	10.3823	+	5.99423i	0.422101	+	0.243700i
$606$		0			0
$607$	−4.53483	+	7.85456i	−0.184063	+	0.318807i	−0.943260	−	0.332054i	$-0.892258\pi$
$607$	−4.53483	+	7.85456i	−0.184063	+	0.318807i	0.759197	+	0.650861i	$0.225592\pi$
$608$		0			0
$609$	7.60821	−	4.39260i	0.308300	−	0.177997i
$610$		0			0
$611$	−14.4837	+	6.02980i	−0.585946	+	0.243939i
$612$		0			0
$613$	−8.12241	+	4.68947i	−0.328061	+	0.189406i	−0.654980	−	0.755646i	$-0.727323\pi$
$613$	−8.12241	+	4.68947i	−0.328061	+	0.189406i	0.326919	+	0.945052i	$0.393990\pi$
$614$		0			0
$615$	20.2537	−	35.0804i	0.816708	−	1.41458i
$616$		0			0
$617$	−26.0786	−	15.0565i	−1.04988	−	0.606151i	−0.127267	−	0.991869i	$-0.540620\pi$
$617$	−26.0786	−	15.0565i	−1.04988	−	0.606151i	−0.922617	+	0.385718i	$0.873954\pi$
$618$		0			0
$619$		−	39.8942i		−	1.60348i	−0.597671	−	0.801742i	$-0.703907\pi$
$619$		−	39.8942i		−	1.60348i	0.597671	−	0.801742i	$-0.296093\pi$
$620$		0			0
$621$	−57.5295	−	99.6441i	−2.30858	−	3.99858i
$622$		0			0
$623$	−5.11527			−0.204939
$624$		0			0
$625$	−25.4517			−1.01807
$626$		0			0
$627$	−38.2715	−	66.2883i	−1.52842	−	2.64730i
$628$		0			0
$629$		−	0.697840i		−	0.0278247i
$630$		0			0
$631$	21.3804	+	12.3440i	0.851140	+	0.491406i	0.861035	−	0.508545i	$-0.169816\pi$
$631$	21.3804	+	12.3440i	0.851140	+	0.491406i	−0.00989522	+	0.999951i	$0.503150\pi$
$632$		0			0
$633$	−42.9492	+	74.3903i	−1.70708	+	2.95675i
$634$		0			0
$635$	3.62219	−	2.09127i	0.143742	−	0.0829896i
$636$		0			0
$637$	−2.18978	+	2.86441i	−0.0867624	+	0.113492i
$638$		0			0
$639$	−58.9625	+	34.0420i	−2.33252	+	1.34668i
$640$		0			0
$641$	−9.30883	+	16.1234i	−0.367677	+	0.636834i	−0.989202	−	0.146560i	$-0.953180\pi$
$641$	−9.30883	+	16.1234i	−0.367677	+	0.636834i	0.621525	+	0.783394i	$0.286513\pi$
$642$		0			0
$643$	27.4384	+	15.8415i	1.08206	+	0.624729i	0.931452	−	0.363864i	$-0.118543\pi$
$643$	27.4384	+	15.8415i	1.08206	+	0.624729i	0.150611	+	0.988593i	$0.451876\pi$
$644$		0			0
$645$			116.908i			4.60323i
$646$		0			0
$647$	−14.8291	−	25.6848i	−0.582994	−	1.00977i	−0.995122	−	0.0986488i	$-0.968548\pi$
$647$	−14.8291	−	25.6848i	−0.582994	−	1.00977i	0.412129	−	0.911126i	$-0.364785\pi$
$648$		0			0
$649$	−8.03013			−0.315210
$650$		0			0
$651$	−27.5175			−1.07850
$652$		0			0
$653$	−6.34483	−	10.9896i	−0.248292	−	0.430055i	0.714760	−	0.699370i	$-0.246536\pi$
$653$	−6.34483	−	10.9896i	−0.248292	−	0.430055i	−0.963052	+	0.269315i	$0.913203\pi$
$654$		0			0
$655$			1.86583i			0.0729039i
$656$		0			0
$657$	21.3387	+	12.3199i	0.832502	+	0.480645i
$658$		0			0
$659$	−12.2763	+	21.2632i	−0.478217	+	0.828296i	−0.999688	−	0.0249730i	$-0.992050\pi$
$659$	−12.2763	+	21.2632i	−0.478217	+	0.828296i	0.521471	+	0.853269i	$0.325383\pi$
$660$		0			0
$661$	22.1333	−	12.7787i	0.860887	−	0.497033i	−0.00342228	−	0.999994i	$-0.501089\pi$
$661$	22.1333	−	12.7787i	0.860887	−	0.497033i	0.864309	+	0.502961i	$0.167756\pi$
$662$		0			0
$663$	0.870264	+	2.09039i	0.0337983	+	0.0811839i
$664$		0			0
$665$	−16.7816	+	9.68888i	−0.650764	+	0.375719i
$666$		0			0
$667$	−10.9055	+	18.8890i	−0.422264	+	0.731383i
$668$		0			0
$669$	−42.3464	−	24.4487i	−1.63721	−	0.945242i
$670$		0			0
$671$			13.1035i			0.505856i
$672$		0			0
$673$	−3.39829	−	5.88601i	−0.130994	−	0.226889i	0.793066	−	0.609136i	$-0.208484\pi$
$673$	−3.39829	−	5.88601i	−0.130994	−	0.226889i	−0.924060	+	0.382247i	$0.875150\pi$
$674$		0			0
$675$	70.3979			2.70962
$676$		0			0
$677$	−26.0956			−1.00294			−0.501468	−	0.865176i	$-0.667207\pi$
$677$	−26.0956			−1.00294			−0.501468	+	0.865176i	$0.667207\pi$
$678$		0			0
$679$	−4.81334	−	8.33696i	−0.184719	−	0.319943i
$680$		0			0
$681$			69.1608i			2.65025i
$682$		0			0
$683$	−42.1666	−	24.3449i	−1.61346	−	0.931532i	−0.988560	−	0.150827i	$-0.951806\pi$
$683$	−42.1666	−	24.3449i	−1.61346	−	0.931532i	−0.624900	−	0.780705i	$-0.714860\pi$
$684$		0			0
$685$	4.02958	−	6.97944i	0.153962	−	0.266671i
$686$		0			0
$687$	23.3958	−	13.5076i	0.892606	−	0.515346i
$688$		0			0
$689$	−0.799310	−	1.91995i	−0.0304513	−	0.0731445i
$690$		0			0
$691$	3.10942	−	1.79522i	0.118288	−	0.0682935i	−0.439689	−	0.898150i	$-0.644911\pi$
$691$	3.10942	−	1.79522i	0.118288	−	0.0682935i	0.557977	+	0.829857i	$0.311578\pi$
$692$		0			0
$693$	14.3141	−	24.7927i	0.543747	−	0.941798i
$694$		0			0
$695$	−49.1303	−	28.3654i	−1.86362	−	1.07596i
$696$		0			0
$697$			0.774161i			0.0293234i
$698$		0			0
$699$	42.2717	+	73.2168i	1.59886	+	2.76931i
$700$		0			0
$701$	−15.8746			−0.599575			−0.299787	−	0.954006i	$-0.596916\pi$
$701$	−15.8746			−0.599575			−0.299787	+	0.954006i	$0.596916\pi$
$702$		0			0
$703$	−22.1025			−0.833611
$704$		0			0
$705$	−22.1266	−	38.3244i	−0.833335	−	1.44338i
$706$		0			0
$707$			2.54158i			0.0955858i
$708$		0			0
$709$	−19.6154	−	11.3250i	−0.736673	−	0.425318i	0.0841852	−	0.996450i	$-0.473171\pi$
$709$	−19.6154	−	11.3250i	−0.736673	−	0.425318i	−0.820858	+	0.571132i	$0.806505\pi$
$710$		0			0
$711$	−33.4307	+	57.9037i	−1.25375	+	2.17156i
$712$		0			0
$713$	59.1650	−	34.1589i	2.21575	−	1.27926i
$714$		0			0
$715$	−26.5248	+	34.6965i	−0.991969	+	1.29757i
$716$		0			0
$717$	51.3630	−	29.6544i	1.91819	−	1.10747i
$718$		0			0
$719$	−5.12631	+	8.87903i	−0.191179	+	0.331132i	−0.945641	−	0.325212i	$-0.894564\pi$
$719$	−5.12631	+	8.87903i	−0.191179	+	0.331132i	0.754462	+	0.656344i	$0.227898\pi$
$720$		0			0
$721$	2.90458	+	1.67696i	0.108172	+	0.0624532i
$722$		0			0
$723$		−	10.7748i		−	0.400719i
$724$		0			0
$725$	−6.67246	−	11.5570i	−0.247809	−	0.429218i
$726$		0			0
$727$	5.60059			0.207715			0.103857	−	0.994592i	$-0.466881\pi$
$727$	5.60059			0.207715			0.103857	+	0.994592i	$0.466881\pi$
$728$		0			0
$729$	39.7064			1.47061
$730$		0			0
$731$	−1.11714	−	1.93495i	−0.0413191	−	0.0715667i
$732$		0			0
$733$		−	41.1556i		−	1.52012i	−0.649855	−	0.760058i	$-0.725170\pi$
$733$		−	41.1556i		−	1.52012i	0.649855	−	0.760058i	$-0.274830\pi$
$734$		0			0
$735$	−8.80765	−	5.08510i	−0.324875	−	0.187567i
$736$		0			0
$737$	−10.4291	+	18.0638i	−0.384162	+	0.665388i
$738$		0			0
$739$	−10.5196	+	6.07347i	−0.386968	+	0.223416i	−0.680846	−	0.732427i	$-0.738388\pi$
$739$	−10.5196	+	6.07347i	−0.386968	+	0.223416i	0.293877	+	0.955843i	$0.405054\pi$
$740$		0			0
$741$	66.2082	−	27.5636i	2.43222	−	1.01257i
$742$		0			0
$743$	−0.486744	+	0.281022i	−0.0178569	+	0.0103097i	−0.508902	−	0.860825i	$-0.669948\pi$
$743$	−0.486744	+	0.281022i	−0.0178569	+	0.0103097i	0.491045	+	0.871134i	$0.336615\pi$
$744$		0			0
$745$	−12.7606	+	22.1020i	−0.467511	+	0.809753i
$746$		0			0
$747$	49.3737	+	28.5059i	1.80649	+	1.04298i
$748$		0			0
$749$			12.9130i			0.471831i
$750$		0			0
$751$	11.3569	+	19.6707i	0.414418	+	0.717794i	0.995367	−	0.0961463i	$-0.0306517\pi$
$751$	11.3569	+	19.6707i	0.414418	+	0.717794i	−0.580949	+	0.813940i	$0.697318\pi$
$752$		0			0
$753$	39.4107			1.43621
$754$		0			0
$755$	−11.2941			−0.411033
$756$		0			0
$757$	−9.74099	−	16.8719i	−0.354042	−	0.613219i	0.632911	−	0.774224i	$-0.281860\pi$
$757$	−9.74099	−	16.8719i	−0.354042	−	0.613219i	−0.986954	+	0.161005i	$0.948526\pi$
$758$		0			0
$759$			99.7372i			3.62023i
$760$		0			0
$761$	37.0082	+	21.3667i	1.34155	+	0.774543i	0.987034	−	0.160509i	$-0.0513135\pi$
$761$	37.0082	+	21.3667i	1.34155	+	0.774543i	0.354513	+	0.935051i	$0.384647\pi$
$762$		0			0
$763$	−4.02134	+	6.96516i	−0.145582	+	0.252156i
$764$		0			0
$765$	−3.94171	+	2.27575i	−0.142513	+	0.0822799i
$766$		0			0
$767$	0.968665	−	7.46117i	0.0349765	−	0.269407i
$768$		0			0
$769$	−29.5477	+	17.0593i	−1.06552	+	0.615176i	−0.926953	−	0.375178i	$-0.877582\pi$
$769$	−29.5477	+	17.0593i	−1.06552	+	0.615176i	−0.138563	+	0.990354i	$0.544248\pi$
$770$		0			0
$771$	−24.6735	+	42.7357i	−0.888593	+	1.53909i
$772$		0			0
$773$	−25.0026	−	14.4353i	−0.899281	−	0.519200i	−0.0223144	−	0.999751i	$-0.507103\pi$
$773$	−25.0026	−	14.4353i	−0.899281	−	0.519200i	−0.876967	+	0.480551i	$0.840437\pi$
$774$		0			0
$775$			41.7997i			1.50149i
$776$		0			0
$777$	−5.80012	−	10.0461i	−0.208078	−	0.360402i
$778$		0			0
$779$	24.5198			0.878512
$780$		0			0
$781$	35.2182			1.26021
$782$		0			0
$783$	−19.5004	−	33.7757i	−0.696887	−	1.20704i
$784$		0			0
$785$			45.1528i			1.61157i
$786$		0			0
$787$	−38.9448	−	22.4848i	−1.38823	−	0.801497i	−0.395117	−	0.918631i	$-0.629296\pi$
$787$	−38.9448	−	22.4848i	−1.38823	−	0.801497i	−0.993116	+	0.117134i	$0.962629\pi$
$788$		0			0
$789$	−40.2242	+	69.6704i	−1.43202	+	2.48033i
$790$		0			0
$791$	−6.93227	+	4.00235i	−0.246483	+	0.142307i
$792$		0			0
$793$	−12.1751	−	1.58066i	−0.432350	−	0.0561310i
$794$		0			0
$795$	5.08028	−	2.93310i	0.180179	−	0.104026i
$796$		0			0
$797$	−10.7092	+	18.5489i	−0.379340	+	0.657036i	−0.990966	−	0.134111i	$-0.957182\pi$
$797$	−10.7092	+	18.5489i	−0.379340	+	0.657036i	0.611627	+	0.791147i	$0.290515\pi$
$798$		0			0
$799$	0.732440	+	0.422874i	0.0259118	+	0.0149602i
$800$		0			0
$801$			38.0544i			1.34459i
$802$		0			0
$803$	−6.37278	−	11.0380i	−0.224891	−	0.389522i
$804$		0			0
$805$	25.2496			0.889932
$806$		0			0
$807$	25.3851			0.893598
$808$		0			0
$809$	4.12749	+	7.14902i	0.145115	+	0.251346i	0.929416	−	0.369034i	$-0.120312\pi$
$809$	4.12749	+	7.14902i	0.145115	+	0.251346i	−0.784301	+	0.620381i	$0.786978\pi$
$810$		0			0
$811$		−	43.7679i		−	1.53690i	−0.639910	−	0.768450i	$-0.721029\pi$
$811$		−	43.7679i		−	1.53690i	0.639910	−	0.768450i	$-0.278971\pi$
$812$		0			0
$813$	−7.38329	−	4.26274i	−0.258943	−	0.149501i
$814$		0			0
$815$	0.387387	−	0.670975i	0.0135696	−	0.0235032i
$816$		0			0
$817$	−61.2851	+	35.3830i	−2.14409	+	1.23789i
$818$		0			0
$819$	21.3094	+	16.2906i	0.744611	+	0.569240i
$820$		0			0
$821$	19.1465	−	11.0542i	0.668216	−	0.385795i	−0.127184	−	0.991879i	$-0.540594\pi$
$821$	19.1465	−	11.0542i	0.668216	−	0.385795i	0.795400	+	0.606084i	$0.207261\pi$
$822$		0			0
$823$	21.0355	−	36.4346i	0.733252	−	1.27003i	−0.222234	−	0.974993i	$-0.571335\pi$
$823$	21.0355	−	36.4346i	0.733252	−	1.27003i	0.955486	−	0.295037i	$-0.0953319\pi$
$824$		0			0
$825$	−52.8478	−	30.5117i	−1.83992	−	1.06228i
$826$		0			0
$827$			44.4242i			1.54478i	0.635148	+	0.772390i	$0.280939\pi$
$827$			44.4242i			1.54478i	−0.635148	+	0.772390i	$0.719061\pi$
$828$		0			0
$829$	−8.97394	−	15.5433i	−0.311678	−	0.539842i	0.667048	−	0.745015i	$-0.267558\pi$
$829$	−8.97394	−	15.5433i	−0.311678	−	0.539842i	−0.978726	+	0.205173i	$0.934224\pi$
$830$		0			0
$831$	37.6569			1.30630
$832$		0			0
$833$	0.194369			0.00673448
$834$		0			0
$835$	−2.84600	−	4.92942i	−0.0984900	−	0.170590i
$836$		0			0
$837$			122.160i			4.22248i
$838$		0			0
$839$	−3.09534	−	1.78709i	−0.106863	−	0.0616973i	0.445616	−	0.895224i	$-0.352985\pi$
$839$	−3.09534	−	1.78709i	−0.106863	−	0.0616973i	−0.552479	+	0.833527i	$0.686318\pi$
$840$		0			0
$841$	10.8034	−	18.7121i	0.372532	−	0.645244i
$842$		0			0
$843$	−10.8148	+	6.24392i	−0.372481	+	0.215052i
$844$		0			0
$845$	−29.0385	−	28.8308i	−0.998953	−	0.991809i
$846$		0			0
$847$	−3.29839	+	1.90432i	−0.113334	+	0.0654334i
$848$		0			0
$849$	11.0640	−	19.1633i	0.379714	−	0.657684i
$850$		0			0
$851$	24.9415	+	14.4000i	0.854984	+	0.493625i
$852$		0			0
$853$			24.4780i			0.838111i	0.907961	+	0.419055i	$0.137639\pi$
$853$			24.4780i			0.838111i	−0.907961	+	0.419055i	$0.862361\pi$
$854$		0			0
$855$	72.0791	+	124.845i	2.46505	+	4.26960i
$856$		0			0
$857$	−26.9438			−0.920384			−0.460192	−	0.887820i	$-0.652219\pi$
$857$	−26.9438			−0.920384			−0.460192	+	0.887820i	$0.652219\pi$
$858$		0			0
$859$	17.9537			0.612573			0.306287	−	0.951939i	$-0.400913\pi$
$859$	17.9537			0.612573			0.306287	+	0.951939i	$0.400913\pi$
$860$		0			0
$861$	6.43446	+	11.1448i	0.219286	+	0.379814i
$862$		0			0
$863$		−	11.0841i		−	0.377308i	−0.982044	−	0.188654i	$-0.939588\pi$
$863$		−	11.0841i		−	0.377308i	0.982044	−	0.188654i	$-0.0604125\pi$
$864$		0			0
$865$	−29.4396	−	16.9969i	−1.00098	−	0.577913i
$866$		0			0
$867$	−27.4025	+	47.4625i	−0.930637	+	1.61191i
$868$		0			0
$869$	29.9521	−	17.2929i	1.01606	−	0.586621i
$870$		0			0
$871$	−15.5258	−	11.8692i	−0.526073	−	0.402173i
$872$		0			0
$873$	−62.0217	+	35.8082i	−2.09912	+	1.21193i
$874$		0			0
$875$	0.144850	−	0.250888i	0.00489683	−	0.00848156i
$876$		0			0
$877$	−3.99010	−	2.30368i	−0.134736	−	0.0777899i	0.431117	−	0.902296i	$-0.358120\pi$
$877$	−3.99010	−	2.30368i	−0.134736	−	0.0777899i	−0.565853	+	0.824506i	$0.691453\pi$
$878$		0			0
$879$			4.81075i			0.162263i
$880$		0			0
$881$	−17.1554	−	29.7140i	−0.577979	−	1.00109i	−0.995711	−	0.0925186i	$-0.970508\pi$
$881$	−17.1554	−	29.7140i	−0.577979	−	1.00109i	0.417732	−	0.908570i	$-0.362825\pi$
$882$		0			0
$883$	−42.5926			−1.43336			−0.716678	−	0.697404i	$-0.754338\pi$
$883$	−42.5926			−1.43336			−0.716678	+	0.697404i	$0.754338\pi$
$884$		0			0
$885$	21.2224			0.713382
$886$		0			0
$887$	20.8026	+	36.0312i	0.698483	+	1.20981i	0.968992	+	0.247091i	$0.0794745\pi$
$887$	20.8026	+	36.0312i	0.698483	+	1.20981i	−0.270509	+	0.962717i	$0.587192\pi$
$888$		0			0
$889$			1.32877i			0.0445654i
$890$		0			0
$891$	−80.0703	−	46.2286i	−2.68246	−	1.54872i
$892$		0			0
$893$	13.3936	−	23.1983i	0.448198	−	0.776302i
$894$		0			0
$895$	23.6519	−	13.6554i	0.790595	−	0.456450i
$896$		0			0
$897$	−92.6706	−	12.0312i	−3.09418	−	0.401710i
$898$		0			0
$899$	20.0548	−	11.5786i	0.668864	−	0.386169i
$900$		0			0
$901$	−0.0560562	+	0.0970922i	−0.00186750	+	0.00323461i
$902$		0			0
$903$	−32.1648	−	18.5704i	−1.07038	−	0.617983i
$904$		0			0
$905$		−	31.5043i		−	1.04724i
$906$		0			0
$907$	−7.83580	−	13.5720i	−0.260183	−	0.450651i	0.706107	−	0.708105i	$-0.250450\pi$
$907$	−7.83580	−	13.5720i	−0.260183	−	0.450651i	−0.966290	+	0.257454i	$0.917116\pi$
$908$		0			0
$909$	18.9077			0.627129
$910$		0			0
$911$	33.5478			1.11149			0.555743	−	0.831354i	$-0.312434\pi$
$911$	33.5478			1.11149			0.555743	+	0.831354i	$0.312434\pi$
$912$		0			0
$913$	−14.7454	−	25.5398i	−0.488001	−	0.845243i
$914$		0			0
$915$		−	34.6306i		−	1.14485i
$916$		0			0
$917$	−0.513346	−	0.296380i	−0.0169522	−	0.00978734i
$918$		0			0
$919$	1.66880	−	2.89045i	0.0550488	−	0.0953473i	−0.837188	−	0.546915i	$-0.815802\pi$
$919$	1.66880	−	2.89045i	0.0550488	−	0.0953473i	0.892237	+	0.451568i	$0.149135\pi$
$920$		0			0
$921$	6.52321	−	3.76618i	0.214947	−	0.124100i
$922$		0			0
$923$	−4.24833	+	32.7229i	−0.139835	+	1.07709i
$924$		0			0
$925$	−15.2603	+	8.81051i	−0.501754	+	0.289688i
$926$		0			0
$927$	12.4755	−	21.6082i	0.409750	−	0.709707i
$928$		0			0
$929$	7.87813	+	4.54844i	0.258473	+	0.149230i	0.623638	−	0.781713i	$-0.285654\pi$
$929$	7.87813	+	4.54844i	0.258473	+	0.149230i	−0.365165	+	0.930943i	$0.618987\pi$
$930$		0			0
$931$		−	6.15618i		−	0.201761i
$932$		0			0
$933$	−19.1024	−	33.0863i	−0.625384	−	1.08320i
$934$		0			0
$935$	2.35438			0.0769964
$936$		0			0
$937$	9.08442			0.296775			0.148388	−	0.988929i	$-0.452592\pi$
$937$	9.08442			0.296775			0.148388	+	0.988929i	$0.452592\pi$
$938$		0			0
$939$	−29.7392	−	51.5099i	−0.970504	−	1.68096i
$940$		0			0
$941$			8.23345i			0.268403i	0.990954	+	0.134201i	$0.0428469\pi$
$941$			8.23345i			0.268403i	−0.990954	+	0.134201i	$0.957153\pi$
$942$		0			0
$943$	−27.6693	−	15.9749i	−0.901036	−	0.520214i
$944$		0			0
$945$	−22.5746	+	39.1004i	−0.734353	+	1.27194i
$946$		0			0
$947$	−4.37804	+	2.52766i	−0.142267	+	0.0821380i	−0.569444	−	0.822030i	$-0.692841\pi$
$947$	−4.37804	+	2.52766i	−0.142267	+	0.0821380i	0.427177	+	0.904168i	$0.359508\pi$
$948$		0			0
$949$	11.0247	−	4.58975i	0.357875	−	0.148990i
$950$		0			0
$951$	23.5679	−	13.6069i	0.764242	−	0.441235i
$952$		0			0
$953$	19.6579	−	34.0485i	0.636782	−	1.10294i	−0.349352	−	0.936992i	$-0.613598\pi$
$953$	19.6579	−	34.0485i	0.636782	−	1.10294i	0.986135	−	0.165948i	$-0.0530684\pi$
$954$		0			0
$955$	−65.5087	−	37.8215i	−2.11981	−	1.22387i
$956$		0			0
$957$			33.8072i			1.09283i
$958$		0			0
$959$	1.28017	+	2.21732i	0.0413389	+	0.0716010i
$960$		0			0
$961$	−41.5344			−1.33982
$962$		0			0
$963$	96.0646			3.09564
$964$		0			0
$965$	−5.15132	−	8.92234i	−0.165827	−	0.287220i
$966$		0			0
$967$		−	21.2101i		−	0.682071i	−0.940050	−	0.341036i	$-0.889222\pi$
$967$		−	21.2101i		−	0.682071i	0.940050	−	0.341036i	$-0.110778\pi$
$968$		0			0
$969$	−3.34815	−	1.93306i	−0.107558	−	0.0620987i
$970$		0			0
$971$	−11.7705	+	20.3871i	−0.377733	+	0.654252i	−0.990732	−	0.135831i	$-0.956630\pi$
$971$	−11.7705	+	20.3871i	−0.377733	+	0.654252i	0.612999	+	0.790084i	$0.289963\pi$
$972$		0			0
$973$	15.6084	−	9.01150i	0.500381	−	0.288895i
$974$		0			0
$975$	34.7248	−	45.4228i	1.11208	−	1.45469i
$976$		0			0
$977$	−10.7380	+	6.19958i	−0.343539	+	0.198342i	−0.661836	−	0.749649i	$-0.730222\pi$
$977$	−10.7380	+	6.19958i	−0.343539	+	0.198342i	0.318297	+	0.947991i	$0.396889\pi$
$978$		0			0
$979$	9.84230	−	17.0474i	0.314561	−	0.544836i
$980$		0			0
$981$	51.8164	+	29.9162i	1.65437	+	0.955151i
$982$		0			0
$983$			36.0862i			1.15097i	0.817812	+	0.575486i	$0.195187\pi$
$983$			36.0862i			1.15097i	−0.817812	+	0.575486i	$0.804813\pi$
$984$		0			0
$985$	20.0703	+	34.7628i	0.639492	+	1.10763i
$986$		0			0
$987$	14.0589			0.447500
$988$		0			0
$989$	92.2095			2.93209
$990$		0			0
$991$	26.4245	+	45.7686i	0.839403	+	1.45389i	0.890395	+	0.455189i	$0.150428\pi$
$991$	26.4245	+	45.7686i	0.839403	+	1.45389i	−0.0509920	+	0.998699i	$0.516238\pi$
$992$		0			0
$993$		−	58.3409i		−	1.85139i
$994$		0			0
$995$	−74.4823	−	43.0024i	−2.36125	−	1.36327i
$996$		0			0
$997$	−0.704139	+	1.21960i	−0.0223003	+	0.0386252i	−0.876960	−	0.480563i	$-0.840432\pi$
$997$	−0.704139	+	1.21960i	−0.0223003	+	0.0386252i	0.854660	+	0.519188i	$0.173766\pi$
$998$		0			0
$999$	−44.5983	+	25.7489i	−1.41103	+	0.814658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.f.673.8		16
4.3	odd	2		364.2.u.a.309.1	yes	16
12.11	even	2		3276.2.cf.c.1765.2		16
13.4	even	6	inner	1456.2.cc.f.225.8		16
28.3	even	6		2548.2.bb.c.569.8		16
28.11	odd	6		2548.2.bb.d.569.1		16
28.19	even	6		2548.2.bq.c.361.1		16
28.23	odd	6		2548.2.bq.e.361.8		16
28.27	even	2		2548.2.u.c.1765.8		16
52.3	odd	6		4732.2.g.k.337.16		16
52.11	even	12		4732.2.a.s.1.8		8
52.15	even	12		4732.2.a.t.1.8		8
52.23	odd	6		4732.2.g.k.337.15		16
52.43	odd	6		364.2.u.a.225.1	✓	16
156.95	even	6		3276.2.cf.c.2773.7		16
364.95	odd	6		2548.2.bq.e.1941.8		16
364.199	even	6		2548.2.bq.c.1941.1		16
364.251	even	6		2548.2.u.c.589.8		16
364.303	odd	6		2548.2.bb.d.1733.1		16
364.355	even	6		2548.2.bb.c.1733.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.1	✓	16	52.43	odd	6
364.2.u.a.309.1	yes	16	4.3	odd	2
1456.2.cc.f.225.8		16	13.4	even	6	inner
1456.2.cc.f.673.8		16	1.1	even	1	trivial
2548.2.u.c.589.8		16	364.251	even	6
2548.2.u.c.1765.8		16	28.27	even	2
2548.2.bb.c.569.8		16	28.3	even	6
2548.2.bb.c.1733.8		16	364.355	even	6
2548.2.bb.d.569.1		16	28.11	odd	6
2548.2.bb.d.1733.1		16	364.303	odd	6
2548.2.bq.c.361.1		16	28.19	even	6
2548.2.bq.c.1941.1		16	364.199	even	6
2548.2.bq.e.361.8		16	28.23	odd	6
2548.2.bq.e.1941.8		16	364.95	odd	6
3276.2.cf.c.1765.2		16	12.11	even	2
3276.2.cf.c.2773.7		16	156.95	even	6
4732.2.a.s.1.8		8	52.11	even	12
4732.2.a.t.1.8		8	52.15	even	12
4732.2.g.k.337.15		16	52.23	odd	6
4732.2.g.k.337.16		16	52.3	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.61550 + 2.79813i) q^{3} +3.14769i q^{5} +(-0.866025 - 0.500000i) q^{7} +(-3.71968 + 6.44268i) q^{9} +(3.33264 - 1.92410i) q^{11} +(1.38576 + 3.32861i) q^{13} +(-8.80765 + 5.08510i) q^{15} +(0.0971843 - 0.168328i) q^{17} +(-5.33141 - 3.07809i) q^{19} -3.23100i q^{21} +(4.01081 + 6.94693i) q^{23} -4.90796 q^{25} -14.3436 q^{27} +(1.35952 + 2.35475i) q^{29} -8.51671i q^{31} +(10.7678 + 6.21677i) q^{33} +(1.57385 - 2.72598i) q^{35} +(3.10928 - 1.79515i) q^{37} +(-7.07520 + 9.25491i) q^{39} +(-3.44934 + 1.99148i) q^{41} +(5.74755 - 9.95506i) q^{43} +(-20.2796 - 11.7084i) q^{45} +4.35126i q^{47} +(0.500000 + 0.866025i) q^{49} +0.628005 q^{51} -0.576803 q^{53} +(6.05647 + 10.4901i) q^{55} -19.8906i q^{57} +(-1.80715 - 1.04336i) q^{59} +(-1.70255 + 2.94891i) q^{61} +(6.44268 - 3.71968i) q^{63} +(-10.4775 + 4.36194i) q^{65} +(-4.69408 + 2.71013i) q^{67} +(-12.9589 + 22.4456i) q^{69} +(7.92574 + 4.57593i) q^{71} -3.31209i q^{73} +(-7.92882 - 13.7331i) q^{75} -3.84820 q^{77} +8.98752 q^{79} +(-12.0130 - 20.8072i) q^{81} -7.66353i q^{83} +(0.529845 + 0.305906i) q^{85} +(-4.39260 + 7.60821i) q^{87} +(4.42996 - 2.55764i) q^{89} +(0.464204 - 3.57554i) q^{91} +(23.8309 - 13.7588i) q^{93} +(9.68888 - 16.7816i) q^{95} +(8.33696 + 4.81334i) q^{97} +28.6282i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{9} - 6 q^{11} + 10 q^{13} - 6 q^{15} + 2 q^{17} - 44 q^{25} + 12 q^{27} - 22 q^{29} + 42 q^{33} + 6 q^{35} + 12 q^{37} - 24 q^{39} + 36 q^{41} - 6 q^{43} - 30 q^{45} + 8 q^{49} + 4 q^{51} + 8 q^{53}+ \cdots - 42 q^{97}+O(q^{100}) \) 16 * q - 14 * q^9 - 6 * q^11 + 10 * q^13 - 6 * q^15 + 2 * q^17 - 44 * q^25 + 12 * q^27 - 22 * q^29 + 42 * q^33 + 6 * q^35 + 12 * q^37 - 24 * q^39 + 36 * q^41 - 6 * q^43 - 30 * q^45 + 8 * q^49 + 4 * q^51 + 8 * q^53 - 2 * q^55 + 18 * q^59 + 4 * q^61 + 12 * q^63 - 30 * q^65 - 24 * q^67 - 52 * q^69 - 36 * q^71 + 10 * q^75 - 24 * q^77 - 8 * q^79 + 42 * q^85 - 26 * q^87 - 36 * q^89 + 2 * q^91 - 42 * q^93 + 30 * q^95 - 42 * q^97

Introduction

L-functions

Modular forms

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