LMFDB - Embedded newform 448.2.j.d.111.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(111,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("448.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.j (of order $4$, 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:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			111.1
Root			$-1.40927 - 0.118126i$ of defining polynomial
Character	$\chi$	$=$	448.111
Dual form			448.2.j.d.335.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23450 - 2.23450i) q^{3} +(0.584038 + 0.584038i) q^{5} +(1.82596 + 1.91465i) q^{7} +6.98602i q^{9} +O(q^{10})$	\(q+(-2.23450 - 2.23450i) q^{3} +(0.584038 + 0.584038i) q^{5} +(1.82596 + 1.91465i) q^{7} +6.98602i q^{9} +(2.00000 + 2.00000i) q^{11} +(2.91203 - 2.91203i) q^{13} -2.61007i q^{15} +2.66123i q^{17} +(-0.319854 - 0.319854i) q^{19} +(0.198191 - 8.35840i) q^{21} +3.27830 q^{23} -4.31780i q^{25} +(8.90678 - 8.90678i) q^{27} +(-2.04184 - 2.04184i) q^{29} -2.52312 q^{31} -8.93802i q^{33} +(-0.0518018 + 2.18466i) q^{35} +(1.70773 - 1.70773i) q^{37} -13.0139 q^{39} +11.9895 q^{41} +(3.27830 + 3.27830i) q^{43} +(-4.08010 + 4.08010i) q^{45} +9.96799 q^{47} +(-0.331777 + 6.99213i) q^{49} +(5.94652 - 5.94652i) q^{51} +(-2.37595 + 2.37595i) q^{53} +2.33615i q^{55} +1.42943i q^{57} +(-4.14916 + 4.14916i) q^{59} +(-4.52468 + 4.52468i) q^{61} +(-13.3758 + 12.7562i) q^{63} +3.40147 q^{65} +(4.37361 - 4.37361i) q^{67} +(-7.32537 - 7.32537i) q^{69} -5.14114 q^{71} -6.99213 q^{73} +(-9.64814 + 9.64814i) q^{75} +(-0.177392 + 7.48121i) q^{77} -11.2248i q^{79} -18.8464 q^{81} +(5.39734 + 5.39734i) q^{83} +(-1.55426 + 1.55426i) q^{85} +9.12499i q^{87} -1.05674 q^{89} +(10.8927 + 0.258285i) q^{91} +(5.63793 + 5.63793i) q^{93} -0.373614i q^{95} +13.2689i q^{97} +(-13.9720 + 13.9720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 32 q^{11} + 16 q^{21} - 8 q^{35} - 16 q^{39} - 16 q^{49} + 32 q^{51} - 80 q^{65} + 48 q^{67} - 32 q^{71} - 16 q^{77} + 32 q^{81} + 64 q^{85} - 8 q^{91} - 64 q^{93} - 64 q^{99}+O(q^{100}) $ 16 * q - 8 * q^7 + 32 * q^11 + 16 * q^21 - 8 * q^35 - 16 * q^39 - 16 * q^49 + 32 * q^51 - 80 * q^65 + 48 * q^67 - 32 * q^71 - 16 * q^77 + 32 * q^81 + 64 * q^85 - 8 * q^91 - 64 * q^93 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.23450	−	2.23450i	−1.29009	−	1.29009i	−0.934728	−	0.355364i	$-0.884357\pi$
$3$	−2.23450	−	2.23450i	−1.29009	−	1.29009i	−0.355364	−	0.934728i	$-0.615643\pi$
$4$		0			0
$5$	0.584038	+	0.584038i	0.261190	+	0.261190i	0.825537	−	0.564347i	$-0.190872\pi$
$5$	0.584038	+	0.584038i	0.261190	+	0.261190i	−0.564347	+	0.825537i	$0.690872\pi$
$6$		0			0
$7$	1.82596	+	1.91465i	0.690146	+	0.723670i
$7$	1.82596	+	1.91465i	0.690146	+	0.723670i
$8$		0			0
$9$			6.98602i			2.32867i
$10$		0			0
$11$	2.00000	+	2.00000i	0.603023	+	0.603023i	0.941113	−	0.338091i	$-0.109781\pi$
$11$	2.00000	+	2.00000i	0.603023	+	0.603023i	−0.338091	+	0.941113i	$0.609781\pi$
$12$		0			0
$13$	2.91203	−	2.91203i	0.807651	−	0.807651i	−0.176627	−	0.984278i	$-0.556519\pi$
$13$	2.91203	−	2.91203i	0.807651	−	0.807651i	0.984278	+	0.176627i	$0.0565185\pi$
$14$		0			0
$15$		−	2.61007i		−	0.673918i
$16$		0			0
$17$			2.66123i			0.645442i	0.946494	+	0.322721i	$0.104598\pi$
$17$			2.66123i			0.645442i	−0.946494	+	0.322721i	$0.895402\pi$
$18$		0			0
$19$	−0.319854	−	0.319854i	−0.0733795	−	0.0733795i	0.669465	−	0.742844i	$-0.266524\pi$
$19$	−0.319854	−	0.319854i	−0.0733795	−	0.0733795i	−0.742844	+	0.669465i	$0.766524\pi$
$20$		0			0
$21$	0.198191	−	8.35840i	0.0432489	−	1.82395i
$22$		0			0
$23$	3.27830			0.683572			0.341786	−	0.939778i	$-0.388968\pi$
$23$	3.27830			0.683572			0.341786	+	0.939778i	$0.388968\pi$
$24$		0			0
$25$		−	4.31780i		−	0.863560i
$26$		0			0
$27$	8.90678	−	8.90678i	1.71411	−	1.71411i
$28$		0			0
$29$	−2.04184	−	2.04184i	−0.379160	−	0.379160i	0.491639	−	0.870799i	$-0.336398\pi$
$29$	−2.04184	−	2.04184i	−0.379160	−	0.379160i	−0.870799	+	0.491639i	$0.836398\pi$
$30$		0			0
$31$	−2.52312			−0.453166			−0.226583	−	0.973992i	$-0.572756\pi$
$31$	−2.52312			−0.453166			−0.226583	+	0.973992i	$0.572756\pi$
$32$		0			0
$33$		−	8.93802i		−	1.55591i
$34$		0			0
$35$	−0.0518018	+	2.18466i	−0.00875611	+	0.369275i
$36$		0			0
$37$	1.70773	−	1.70773i	0.280748	−	0.280748i	−0.552659	−	0.833407i	$-0.686387\pi$
$37$	1.70773	−	1.70773i	0.280748	−	0.280748i	0.833407	+	0.552659i	$0.186387\pi$
$38$		0			0
$39$	−13.0139			−2.08389
$40$		0			0
$41$	11.9895			1.87245			0.936224	−	0.351405i	$-0.114296\pi$
$41$	11.9895			1.87245			0.936224	+	0.351405i	$0.114296\pi$
$42$		0			0
$43$	3.27830	+	3.27830i	0.499936	+	0.499936i	0.911418	−	0.411482i	$-0.134989\pi$
$43$	3.27830	+	3.27830i	0.499936	+	0.499936i	−0.411482	+	0.911418i	$0.634989\pi$
$44$		0			0
$45$	−4.08010	+	4.08010i	−0.608226	+	0.608226i
$46$		0			0
$47$	9.96799			1.45398			0.726991	−	0.686647i	$-0.240918\pi$
$47$	9.96799			1.45398			0.726991	+	0.686647i	$0.240918\pi$
$48$		0			0
$49$	−0.331777	+	6.99213i	−0.0473967	+	0.998876i
$50$		0			0
$51$	5.94652	−	5.94652i	0.832679	−	0.832679i
$52$		0			0
$53$	−2.37595	+	2.37595i	−0.326362	+	0.326362i	−0.851201	−	0.524840i	$-0.824125\pi$
$53$	−2.37595	+	2.37595i	−0.326362	+	0.326362i	0.524840	+	0.851201i	$0.324125\pi$
$54$		0			0
$55$			2.33615i			0.315007i
$56$		0			0
$57$			1.42943i			0.189332i
$58$		0			0
$59$	−4.14916	+	4.14916i	−0.540174	+	0.540174i	−0.923580	−	0.383406i	$-0.874751\pi$
$59$	−4.14916	+	4.14916i	−0.540174	+	0.540174i	0.383406	+	0.923580i	$0.374751\pi$
$60$		0			0
$61$	−4.52468	+	4.52468i	−0.579326	+	0.579326i	−0.934717	−	0.355392i	$-0.884347\pi$
$61$	−4.52468	+	4.52468i	−0.579326	+	0.579326i	0.355392	+	0.934717i	$0.384347\pi$
$62$		0			0
$63$	−13.3758	+	12.7562i	−1.68519	+	1.60713i
$64$		0			0
$65$	3.40147			0.421901
$66$		0			0
$67$	4.37361	−	4.37361i	0.534322	−	0.534322i	−0.387534	−	0.921856i	$-0.626673\pi$
$67$	4.37361	−	4.37361i	0.534322	−	0.534322i	0.921856	+	0.387534i	$0.126673\pi$
$68$		0			0
$69$	−7.32537	−	7.32537i	−0.881871	−	0.881871i
$70$		0			0
$71$	−5.14114			−0.610141			−0.305071	−	0.952330i	$-0.598680\pi$
$71$	−5.14114			−0.610141			−0.305071	+	0.952330i	$0.598680\pi$
$72$		0			0
$73$	−6.99213			−0.818367			−0.409184	−	0.912452i	$-0.634186\pi$
$73$	−6.99213			−0.818367			−0.409184	+	0.912452i	$0.634186\pi$
$74$		0			0
$75$	−9.64814	+	9.64814i	−1.11407	+	1.11407i
$76$		0			0
$77$	−0.177392	+	7.48121i	−0.0202157	+	0.852563i
$78$		0			0
$79$		−	11.2248i		−	1.26289i	−0.775420	−	0.631445i	$-0.782462\pi$
$79$		−	11.2248i		−	1.26289i	0.775420	−	0.631445i	$-0.217538\pi$
$80$		0			0
$81$	−18.8464			−2.09405
$82$		0			0
$83$	5.39734	+	5.39734i	0.592435	+	0.592435i	0.938288	−	0.345854i	$-0.112411\pi$
$83$	5.39734	+	5.39734i	0.592435	+	0.592435i	−0.345854	+	0.938288i	$0.612411\pi$
$84$		0			0
$85$	−1.55426	+	1.55426i	−0.168583	+	0.168583i
$86$		0			0
$87$			9.12499i			0.978301i
$88$		0			0
$89$	−1.05674			−0.112014			−0.0560071	−	0.998430i	$-0.517837\pi$
$89$	−1.05674			−0.112014			−0.0560071	+	0.998430i	$0.517837\pi$
$90$		0			0
$91$	10.8927	+	0.258285i	1.14187	+	0.0270756i
$92$		0			0
$93$	5.63793	+	5.63793i	0.584626	+	0.584626i
$94$		0			0
$95$		−	0.373614i		−	0.0383319i
$96$		0			0
$97$			13.2689i			1.34726i	0.739071	+	0.673628i	$0.235265\pi$
$97$			13.2689i			1.34726i	−0.739071	+	0.673628i	$0.764735\pi$
$98$		0			0
$99$	−13.9720	+	13.9720i	−1.40424	+	1.40424i
$100$		0			0
$101$	0.250803	+	0.250803i	0.0249558	+	0.0249558i	0.719475	−	0.694519i	$-0.244383\pi$
$101$	0.250803	+	0.250803i	0.0249558	+	0.0249558i	−0.694519	+	0.719475i	$0.744383\pi$
$102$		0			0
$103$		−	12.5179i		−	1.23342i	−0.787189	−	0.616712i	$-0.788464\pi$
$103$		−	12.5179i		−	1.23342i	0.787189	−	0.616712i	$-0.211536\pi$
$104$		0			0
$105$	4.99738	−	4.76588i	0.487694	−	0.465102i
$106$		0			0
$107$	3.88837	+	3.88837i	0.375903	+	0.375903i	0.869622	−	0.493719i	$-0.164363\pi$
$107$	3.88837	+	3.88837i	0.375903	+	0.375903i	−0.493719	+	0.869622i	$0.664363\pi$
$108$		0			0
$109$	−4.26432	−	4.26432i	−0.408448	−	0.408448i	0.472749	−	0.881197i	$-0.343262\pi$
$109$	−4.26432	−	4.26432i	−0.408448	−	0.408448i	−0.881197	+	0.472749i	$0.843262\pi$
$110$		0			0
$111$	−7.63184			−0.724382
$112$		0			0
$113$	7.79072			0.732889			0.366445	−	0.930440i	$-0.380575\pi$
$113$	7.79072			0.732889			0.366445	+	0.930440i	$0.380575\pi$
$114$		0			0
$115$	1.91465	+	1.91465i	0.178542	+	0.178542i
$116$		0			0
$117$	20.3435	+	20.3435i	1.88076	+	1.88076i
$118$		0			0
$119$	−5.09532	+	4.85928i	−0.467087	+	0.445449i
$120$		0			0
$121$		−	3.00000i		−	0.272727i
$122$		0			0
$123$	−26.7906	−	26.7906i	−2.41563	−	2.41563i
$124$		0			0
$125$	5.44195	−	5.44195i	0.486743	−	0.486743i
$126$		0			0
$127$		−	8.02552i		−	0.712150i	−0.934457	−	0.356075i	$-0.884115\pi$
$127$		−	8.02552i		−	0.712150i	0.934457	−	0.356075i	$-0.115885\pi$
$128$		0			0
$129$		−	14.6507i		−	1.28993i
$130$		0			0
$131$	−9.22664	−	9.22664i	−0.806135	−	0.806135i	0.177911	−	0.984047i	$-0.443066\pi$
$131$	−9.22664	−	9.22664i	−0.806135	−	0.806135i	−0.984047	+	0.177911i	$0.943066\pi$
$132$		0			0
$133$	0.0283697	−	1.19645i	0.00245997	−	0.103745i
$134$		0			0
$135$	10.4038			0.895417
$136$		0			0
$137$			9.02951i			0.771443i	0.922615	+	0.385722i	$0.126047\pi$
$137$			9.02951i			0.771443i	−0.922615	+	0.385722i	$0.873953\pi$
$138$		0			0
$139$	−4.33613	+	4.33613i	−0.367785	+	0.367785i	−0.866669	−	0.498884i	$-0.833744\pi$
$139$	−4.33613	+	4.33613i	−0.367785	+	0.367785i	0.498884	+	0.866669i	$0.333744\pi$
$140$		0			0
$141$	−22.2735	−	22.2735i	−1.87577	−	1.87577i
$142$		0			0
$143$	11.6481			0.974064
$144$		0			0
$145$		−	2.38502i		−	0.198065i
$146$		0			0
$147$	16.3653	−	14.8826i	1.34979	−	1.22750i
$148$		0			0
$149$	−13.2620	+	13.2620i	−1.08646	+	1.08646i	−0.0905743	+	0.995890i	$0.528870\pi$
$149$	−13.2620	+	13.2620i	−1.08646	+	1.08646i	−0.995890	+	0.0905743i	$0.971130\pi$
$150$		0			0
$151$	11.7512			0.956300			0.478150	−	0.878278i	$-0.341307\pi$
$151$	11.7512			0.956300			0.478150	+	0.878278i	$0.341307\pi$
$152$		0			0
$153$	−18.5914			−1.50302
$154$		0			0
$155$	−1.47360	−	1.47360i	−0.118362	−	0.118362i
$156$		0			0
$157$	7.90941	−	7.90941i	0.631239	−	0.631239i	−0.317140	−	0.948379i	$-0.602722\pi$
$157$	7.90941	−	7.90941i	0.631239	−	0.631239i	0.948379	+	0.317140i	$0.102722\pi$
$158$		0			0
$159$	10.6181			0.842073
$160$		0			0
$161$	5.98602	+	6.27679i	0.471765	+	0.494681i
$162$		0			0
$163$	−9.65191	+	9.65191i	−0.755996	+	0.755996i	−0.975591	−	0.219595i	$-0.929526\pi$
$163$	−9.65191	+	9.65191i	−0.755996	+	0.755996i	0.219595	+	0.975591i	$0.429526\pi$
$164$		0			0
$165$	5.22015	−	5.22015i	0.406388	−	0.406388i
$166$		0			0
$167$			7.84557i			0.607109i	0.952814	+	0.303554i	$0.0981734\pi$
$167$			7.84557i			0.607109i	−0.952814	+	0.303554i	$0.901827\pi$
$168$		0			0
$169$		−	3.95982i		−	0.304601i
$170$		0			0
$171$	2.23450	−	2.23450i	0.170877	−	0.170877i
$172$		0			0
$173$	2.19669	−	2.19669i	0.167011	−	0.167011i	−0.618653	−	0.785664i	$-0.712321\pi$
$173$	2.19669	−	2.19669i	0.167011	−	0.167011i	0.785664	+	0.618653i	$0.212321\pi$
$174$		0			0
$175$	8.26708	−	7.88411i	0.624932	−	0.595982i
$176$		0			0
$177$	18.5426			1.39375
$178$		0			0
$179$	−10.0302	+	10.0302i	−0.749692	+	0.749692i	−0.974421	−	0.224729i	$-0.927850\pi$
$179$	−10.0302	+	10.0302i	−0.749692	+	0.749692i	0.224729	+	0.974421i	$0.427850\pi$
$180$		0			0
$181$	−3.03153	−	3.03153i	−0.225332	−	0.225332i	0.585407	−	0.810739i	$-0.300935\pi$
$181$	−3.03153	−	3.03153i	−0.225332	−	0.225332i	−0.810739	+	0.585407i	$0.800935\pi$
$182$		0			0
$183$	20.2208			1.49477
$184$		0			0
$185$	1.99475			0.146657
$186$		0			0
$187$	−5.32245	+	5.32245i	−0.389216	+	0.389216i
$188$		0			0
$189$	33.3168	+	0.789996i	2.42344	+	0.0574637i
$190$		0			0
$191$			14.2085i			1.02809i	0.857763	+	0.514046i	$0.171854\pi$
$191$			14.2085i			1.02809i	−0.857763	+	0.514046i	$0.828146\pi$
$192$		0			0
$193$	−19.2945			−1.38885			−0.694425	−	0.719565i	$-0.744341\pi$
$193$	−19.2945			−1.38885			−0.694425	+	0.719565i	$0.744341\pi$
$194$		0			0
$195$	−7.60061	−	7.60061i	−0.544291	−	0.544291i
$196$		0			0
$197$	0.454953	−	0.454953i	0.0324140	−	0.0324140i	−0.690714	−	0.723128i	$-0.742704\pi$
$197$	0.454953	−	0.454953i	0.0324140	−	0.0324140i	0.723128	+	0.690714i	$0.242704\pi$
$198$		0			0
$199$		−	24.6024i		−	1.74402i	−0.489490	−	0.872009i	$-0.662817\pi$
$199$		−	24.6024i		−	1.74402i	0.489490	−	0.872009i	$-0.337183\pi$
$200$		0			0
$201$	−19.5457			−1.37865
$202$		0			0
$203$	0.181103	−	7.63771i	0.0127109	−	0.536062i
$204$		0			0
$205$	7.00234	+	7.00234i	0.489064	+	0.489064i
$206$		0			0
$207$			22.9022i			1.59182i
$208$		0			0
$209$		−	1.27941i		−	0.0884990i
$210$		0			0
$211$	−10.1092	+	10.1092i	−0.695946	+	0.695946i	−0.963534	−	0.267588i	$-0.913774\pi$
$211$	−10.1092	+	10.1092i	−0.695946	+	0.695946i	0.267588	+	0.963534i	$0.413774\pi$
$212$		0			0
$213$	11.4879	+	11.4879i	0.787138	+	0.787138i
$214$		0			0
$215$			3.82930i			0.261156i
$216$		0			0
$217$	−4.60711	−	4.83090i	−0.312751	−	0.327943i
$218$		0			0
$219$	15.6240	+	15.6240i	1.05577	+	1.05577i
$220$		0			0
$221$	7.74956	+	7.74956i	0.521292	+	0.521292i
$222$		0			0
$223$	−15.1035			−1.01140			−0.505702	−	0.862708i	$-0.668766\pi$
$223$	−15.1035			−1.01140			−0.505702	+	0.862708i	$0.668766\pi$
$224$		0			0
$225$	30.1642			2.01095
$226$		0			0
$227$	7.12502	+	7.12502i	0.472904	+	0.472904i	0.902853	−	0.429949i	$-0.141469\pi$
$227$	7.12502	+	7.12502i	0.472904	+	0.472904i	−0.429949	+	0.902853i	$0.641469\pi$
$228$		0			0
$229$	−18.7933	−	18.7933i	−1.24190	−	1.24190i	−0.959213	−	0.282684i	$-0.908775\pi$
$229$	−18.7933	−	18.7933i	−1.24190	−	1.24190i	−0.282684	−	0.959213i	$-0.591225\pi$
$230$		0			0
$231$	17.1132	−	16.3204i	1.12596	−	1.07380i
$232$		0			0
$233$		−	4.47759i		−	0.293337i	−0.989186	−	0.146668i	$-0.953145\pi$
$233$		−	4.47759i		−	0.293337i	0.989186	−	0.146668i	$-0.0468550\pi$
$234$		0			0
$235$	5.82169	+	5.82169i	0.379765	+	0.379765i
$236$		0			0
$237$	−25.0819	+	25.0819i	−1.62924	+	1.62924i
$238$		0			0
$239$		−	9.13871i		−	0.591134i	−0.955322	−	0.295567i	$-0.904491\pi$
$239$		−	9.13871i		−	0.591134i	0.955322	−	0.295567i	$-0.0955086\pi$
$240$		0			0
$241$			9.66969i			0.622879i	0.950266	+	0.311440i	$0.100811\pi$
$241$			9.66969i			0.622879i	−0.950266	+	0.311440i	$0.899189\pi$
$242$		0			0
$243$	15.3921	+	15.3921i	0.987403	+	0.987403i
$244$		0			0
$245$	−4.27744	+	3.88990i	−0.273276	+	0.248517i
$246$		0			0
$247$	−1.86285			−0.118530
$248$		0			0
$249$		−	24.1207i		−	1.52859i
$250$		0			0
$251$	−10.9231	+	10.9231i	−0.689459	+	0.689459i	−0.962112	−	0.272653i	$-0.912099\pi$
$251$	−10.9231	+	10.9231i	−0.689459	+	0.689459i	0.272653	+	0.962112i	$0.412099\pi$
$252$		0			0
$253$	6.55659	+	6.55659i	0.412209	+	0.412209i
$254$		0			0
$255$	6.94599			0.434975
$256$		0			0
$257$		−	23.5888i		−	1.47143i	−0.677293	−	0.735713i	$-0.736847\pi$
$257$		−	23.5888i		−	1.47143i	0.677293	−	0.735713i	$-0.263153\pi$
$258$		0			0
$259$	6.38793	+	0.151468i	0.396927	+	0.00941178i
$260$		0			0
$261$	14.2643	−	14.2643i	0.882939	−	0.882939i
$262$		0			0
$263$	−25.3595			−1.56374			−0.781868	−	0.623444i	$-0.785733\pi$
$263$	−25.3595			−1.56374			−0.781868	+	0.623444i	$0.785733\pi$
$264$		0			0
$265$	−2.77529			−0.170485
$266$		0			0
$267$	2.36129	+	2.36129i	0.144508	+	0.144508i
$268$		0			0
$269$	5.74979	−	5.74979i	0.350571	−	0.350571i	−0.509751	−	0.860322i	$-0.670263\pi$
$269$	5.74979	−	5.74979i	0.350571	−	0.350571i	0.860322	+	0.509751i	$0.170263\pi$
$270$		0			0
$271$	−16.7568			−1.01790			−0.508952	−	0.860795i	$-0.669967\pi$
$271$	−16.7568			−1.01790			−0.508952	+	0.860795i	$0.669967\pi$
$272$		0			0
$273$	−23.7628	−	24.9170i	−1.43819	−	1.50805i
$274$		0			0
$275$	8.63560	−	8.63560i	0.520746	−	0.520746i
$276$		0			0
$277$	−5.45729	+	5.45729i	−0.327897	+	0.327897i	−0.851786	−	0.523890i	$-0.824480\pi$
$277$	−5.45729	+	5.45729i	−0.327897	+	0.327897i	0.523890	+	0.851786i	$0.324480\pi$
$278$		0			0
$279$		−	17.6266i		−	1.05528i
$280$		0			0
$281$			6.11163i			0.364589i	0.983244	+	0.182295i	$0.0583525\pi$
$281$			6.11163i			0.364589i	−0.983244	+	0.182295i	$0.941648\pi$
$282$		0			0
$283$	5.03383	−	5.03383i	0.299230	−	0.299230i	−0.541482	−	0.840712i	$-0.682137\pi$
$283$	5.03383	−	5.03383i	0.299230	−	0.299230i	0.840712	+	0.541482i	$0.182137\pi$
$284$		0			0
$285$	−0.834841	+	0.834841i	−0.0494517	+	0.0494517i
$286$		0			0
$287$	21.8923	+	22.9557i	1.29226	+	1.35503i
$288$		0			0
$289$	9.91788			0.583405
$290$		0			0
$291$	29.6495	−	29.6495i	1.73808	−	1.73808i
$292$		0			0
$293$	19.6200	+	19.6200i	1.14621	+	1.14621i	0.987291	+	0.158921i	$0.0508014\pi$
$293$	19.6200	+	19.6200i	1.14621	+	1.14621i	0.158921	+	0.987291i	$0.449199\pi$
$294$		0			0
$295$	−4.84653			−0.282176
$296$		0			0
$297$	35.6271			2.06730
$298$		0			0
$299$	9.54649	−	9.54649i	0.552088	−	0.552088i
$300$		0			0
$301$	−0.290772	+	12.2628i	−0.0167598	+	0.706817i
$302$		0			0
$303$		−	1.12084i		−	0.0643906i
$304$		0			0
$305$	−5.28517			−0.302628
$306$		0			0
$307$	3.08795	+	3.08795i	0.176238	+	0.176238i	0.789714	−	0.613475i	$-0.210229\pi$
$307$	3.08795	+	3.08795i	0.176238	+	0.176238i	−0.613475	+	0.789714i	$0.710229\pi$
$308$		0			0
$309$	−27.9713	+	27.9713i	−1.59123	+	1.59123i
$310$		0			0
$311$		−	20.2122i		−	1.14613i	−0.819511	−	0.573064i	$-0.805755\pi$
$311$		−	20.2122i		−	1.14613i	0.819511	−	0.573064i	$-0.194245\pi$
$312$		0			0
$313$	15.2311			0.860915			0.430457	−	0.902611i	$-0.358352\pi$
$313$	15.2311			0.860915			0.430457	+	0.902611i	$0.358352\pi$
$314$		0			0
$315$	−15.2621	−	0.361889i	−0.859920	−	0.0203901i
$316$		0			0
$317$	−20.3480	−	20.3480i	−1.14286	−	1.14286i	−0.987925	−	0.154932i	$-0.950484\pi$
$317$	−20.3480	−	20.3480i	−1.14286	−	1.14286i	−0.154932	−	0.987925i	$-0.549516\pi$
$318$		0			0
$319$		−	8.16735i		−	0.457284i
$320$		0			0
$321$		−	17.3772i		−	0.969898i
$322$		0			0
$323$	0.851203	−	0.851203i	0.0473622	−	0.0473622i
$324$		0			0
$325$	−12.5736	−	12.5736i	−0.697455	−	0.697455i
$326$		0			0
$327$			19.0573i			1.05387i
$328$		0			0
$329$	18.2011	+	19.0852i	1.00346	+	1.05220i
$330$		0			0
$331$	−20.8186	−	20.8186i	−1.14429	−	1.14429i	−0.987656	−	0.156636i	$-0.949935\pi$
$331$	−20.8186	−	20.8186i	−1.14429	−	1.14429i	−0.156636	−	0.987656i	$-0.550065\pi$
$332$		0			0
$333$	11.9302	+	11.9302i	0.653771	+	0.653771i
$334$		0			0
$335$	5.10872			0.279119
$336$		0			0
$337$	−13.7954			−0.751483			−0.375741	−	0.926725i	$-0.622612\pi$
$337$	−13.7954			−0.751483			−0.375741	+	0.926725i	$0.622612\pi$
$338$		0			0
$339$	−17.4084	−	17.4084i	−0.945494	−	0.945494i
$340$		0			0
$341$	−5.04625	−	5.04625i	−0.273270	−	0.273270i
$342$		0			0
$343$	−13.9933	+	12.1321i	−0.755567	+	0.655071i
$344$		0			0
$345$		−	8.55659i		−	0.460671i
$346$		0			0
$347$	3.67743	+	3.67743i	0.197415	+	0.197415i	0.798891	−	0.601476i	$-0.205420\pi$
$347$	3.67743	+	3.67743i	0.197415	+	0.197415i	−0.601476	+	0.798891i	$0.705420\pi$
$348$		0			0
$349$	17.8960	−	17.8960i	0.957951	−	0.957951i	−0.0412000	−	0.999151i	$-0.513118\pi$
$349$	17.8960	−	17.8960i	0.957951	−	0.957951i	0.999151	+	0.0412000i	$0.0131181\pi$
$350$		0			0
$351$		−	51.8736i		−	2.76881i
$352$		0			0
$353$			4.37978i			0.233112i	0.993184	+	0.116556i	$0.0371854\pi$
$353$			4.37978i			0.233112i	−0.993184	+	0.116556i	$0.962815\pi$
$354$		0			0
$355$	−3.00262	−	3.00262i	−0.159363	−	0.159363i
$356$		0			0
$357$	22.2436	+	0.527432i	1.17726	+	0.0279147i
$358$		0			0
$359$	15.3293			0.809052			0.404526	−	0.914527i	$-0.367437\pi$
$359$	15.3293			0.809052			0.404526	+	0.914527i	$0.367437\pi$
$360$		0			0
$361$		−	18.7954i		−	0.989231i
$362$		0			0
$363$	−6.70351	+	6.70351i	−0.351843	+	0.351843i
$364$		0			0
$365$	−4.08367	−	4.08367i	−0.213749	−	0.213749i
$366$		0			0
$367$	−26.3152			−1.37364			−0.686821	−	0.726827i	$-0.740994\pi$
$367$	−26.3152			−1.37364			−0.686821	+	0.726827i	$0.740994\pi$
$368$		0			0
$369$			83.7590i			4.36032i
$370$		0			0
$371$	−8.88749	−	0.210737i	−0.461415	−	0.0109409i
$372$		0			0
$373$	24.6821	−	24.6821i	1.27799	−	1.27799i	0.336200	−	0.941790i	$-0.390858\pi$
$373$	24.6821	−	24.6821i	1.27799	−	1.27799i	0.941790	−	0.336200i	$-0.109142\pi$
$374$		0			0
$375$	−24.3201			−1.25589
$376$		0			0
$377$	−11.8918			−0.612458
$378$		0			0
$379$	14.8512	+	14.8512i	0.762855	+	0.762855i	0.976838	−	0.213982i	$-0.0686435\pi$
$379$	14.8512	+	14.8512i	0.762855	+	0.762855i	−0.213982	+	0.976838i	$0.568644\pi$
$380$		0			0
$381$	−17.9331	+	17.9331i	−0.918739	+	0.918739i
$382$		0			0
$383$	−25.4454			−1.30020			−0.650100	−	0.759849i	$-0.725273\pi$
$383$	−25.4454			−1.30020			−0.650100	+	0.759849i	$0.725273\pi$
$384$		0			0
$385$	−4.47292	+	4.26571i	−0.227961	+	0.217401i
$386$		0			0
$387$	−22.9022	+	22.9022i	−1.16419	+	1.16419i
$388$		0			0
$389$	0.848867	−	0.848867i	0.0430393	−	0.0430393i	−0.685260	−	0.728299i	$-0.740311\pi$
$389$	0.848867	−	0.848867i	0.0430393	−	0.0430393i	0.728299	+	0.685260i	$0.240311\pi$
$390$		0			0
$391$			8.72428i			0.441206i
$392$		0			0
$393$			41.2339i			2.07998i
$394$		0			0
$395$	6.55572	−	6.55572i	0.329854	−	0.329854i
$396$		0			0
$397$	15.4575	−	15.4575i	0.775787	−	0.775787i	−0.203324	−	0.979111i	$-0.565175\pi$
$397$	15.4575	−	15.4575i	0.775787	−	0.775787i	0.979111	+	0.203324i	$0.0651746\pi$
$398$		0			0
$399$	−2.73686	+	2.61007i	−0.137014	+	0.130667i
$400$		0			0
$401$	−21.7348			−1.08538			−0.542692	−	0.839932i	$-0.682595\pi$
$401$	−21.7348			−1.08538			−0.542692	+	0.839932i	$0.682595\pi$
$402$		0			0
$403$	−7.34741	+	7.34741i	−0.366000	+	0.366000i
$404$		0			0
$405$	−11.0070	−	11.0070i	−0.546944	−	0.546944i
$406$		0			0
$407$	6.83090			0.338595
$408$		0			0
$409$	−27.0142			−1.33577			−0.667883	−	0.744266i	$-0.732799\pi$
$409$	−27.0142			−1.33577			−0.667883	+	0.744266i	$0.732799\pi$
$410$		0			0
$411$	20.1765	−	20.1765i	0.995233	−	0.995233i
$412$		0			0
$413$	−15.5204	−	0.368013i	−0.763707	−	0.0181087i
$414$		0			0
$415$			6.30450i			0.309476i
$416$		0			0
$417$	19.3782			0.948954
$418$		0			0
$419$	1.31859	+	1.31859i	0.0644176	+	0.0644176i	0.738582	−	0.674164i	$-0.235496\pi$
$419$	1.31859	+	1.31859i	0.0644176	+	0.0644176i	−0.674164	+	0.738582i	$0.735496\pi$
$420$		0			0
$421$	−9.73490	+	9.73490i	−0.474450	+	0.474450i	−0.903351	−	0.428901i	$-0.858901\pi$
$421$	−9.73490	+	9.73490i	−0.474450	+	0.474450i	0.428901	+	0.903351i	$0.358901\pi$
$422$		0			0
$423$			69.6366i			3.38585i
$424$		0			0
$425$	11.4906			0.557378
$426$		0			0
$427$	−16.9250	−	0.401321i	−0.819060	−	0.0194213i
$428$		0			0
$429$	−26.0278	−	26.0278i	−1.25663	−	1.25663i
$430$		0			0
$431$			22.5262i			1.08505i	0.840040	+	0.542525i	$0.182531\pi$
$431$			22.5262i			1.08505i	−0.840040	+	0.542525i	$0.817469\pi$
$432$		0			0
$433$		−	7.16594i		−	0.344373i	−0.985064	−	0.172187i	$-0.944917\pi$
$433$		−	7.16594i		−	0.344373i	0.985064	−	0.172187i	$-0.0550832\pi$
$434$		0			0
$435$	−5.32934	+	5.32934i	−0.255522	+	0.255522i
$436$		0			0
$437$	−1.04858	−	1.04858i	−0.0501601	−	0.0501601i
$438$		0			0
$439$			14.4533i			0.689820i	0.938636	+	0.344910i	$0.112091\pi$
$439$			14.4533i			0.689820i	−0.938636	+	0.344910i	$0.887909\pi$
$440$		0			0
$441$	−48.8472	−	2.31780i	−2.32606	−	0.110371i
$442$		0			0
$443$	13.5148	+	13.5148i	0.642105	+	0.642105i	0.951073	−	0.308967i	$-0.0999834\pi$
$443$	13.5148	+	13.5148i	0.642105	+	0.642105i	−0.308967	+	0.951073i	$0.599983\pi$
$444$		0			0
$445$	−0.617176	−	0.617176i	−0.0292570	−	0.0292570i
$446$		0			0
$447$	59.2679			2.80328
$448$		0			0
$449$	13.2712			0.626306			0.313153	−	0.949703i	$-0.398615\pi$
$449$	13.2712			0.626306			0.313153	+	0.949703i	$0.398615\pi$
$450$		0			0
$451$	23.9790	+	23.9790i	1.12913	+	1.12913i
$452$		0			0
$453$	−26.2581	−	26.2581i	−1.23372	−	1.23372i
$454$		0			0
$455$	6.21094	+	6.51263i	0.291173	+	0.305317i
$456$		0			0
$457$			35.0713i			1.64056i	0.571959	+	0.820282i	$0.306183\pi$
$457$			35.0713i			1.64056i	−0.571959	+	0.820282i	$0.693817\pi$
$458$		0			0
$459$	23.7030	+	23.7030i	1.10636	+	1.10636i
$460$		0			0
$461$	−16.3005	+	16.3005i	−0.759188	+	0.759188i	−0.976175	−	0.216987i	$-0.930377\pi$
$461$	−16.3005	+	16.3005i	−0.759188	+	0.759188i	0.216987	+	0.976175i	$0.430377\pi$
$462$		0			0
$463$		−	1.09532i		−	0.0509037i	−0.999676	−	0.0254519i	$-0.991898\pi$
$463$		−	1.09532i		−	0.0509037i	0.999676	−	0.0254519i	$-0.00810245\pi$
$464$		0			0
$465$			6.58554i			0.305397i
$466$		0			0
$467$	−17.5205	−	17.5205i	−0.810751	−	0.810751i	0.173995	−	0.984746i	$-0.444332\pi$
$467$	−17.5205	−	17.5205i	−0.810751	−	0.810751i	−0.984746	+	0.173995i	$0.944332\pi$
$468$		0			0
$469$	16.3600	+	0.387922i	0.755433	+	0.0179126i
$470$		0			0
$471$	−35.3472			−1.62871
$472$		0			0
$473$			13.1132i			0.602945i
$474$		0			0
$475$	−1.38106	+	1.38106i	−0.0633675	+	0.0633675i
$476$		0			0
$477$	−16.5984	−	16.5984i	−0.759990	−	0.759990i
$478$		0			0
$479$	−7.78311			−0.355619			−0.177810	−	0.984065i	$-0.556901\pi$
$479$	−7.78311			−0.355619			−0.177810	+	0.984065i	$0.556901\pi$
$480$		0			0
$481$		−	9.94589i		−	0.453493i
$482$		0			0
$483$	0.649730	−	27.4013i	0.0295638	−	1.24680i
$484$		0			0
$485$	−7.74956	+	7.74956i	−0.351890	+	0.351890i
$486$		0			0
$487$	27.6953			1.25499			0.627497	−	0.778619i	$-0.284079\pi$
$487$	27.6953			1.25499			0.627497	+	0.778619i	$0.284079\pi$
$488$		0			0
$489$	43.1345			1.95061
$490$		0			0
$491$	−20.2667	−	20.2667i	−0.914621	−	0.914621i	0.0820102	−	0.996631i	$-0.473866\pi$
$491$	−20.2667	−	20.2667i	−0.914621	−	0.914621i	−0.996631	+	0.0820102i	$0.973866\pi$
$492$		0			0
$493$	5.43379	−	5.43379i	0.244726	−	0.244726i
$494$		0			0
$495$	−16.3204			−0.733548
$496$		0			0
$497$	−9.38749	−	9.84349i	−0.421087	−	0.441541i
$498$		0			0
$499$	−19.9852	+	19.9852i	−0.894662	+	0.894662i	−0.994958	−	0.100295i	$-0.968021\pi$
$499$	−19.9852	+	19.9852i	−0.894662	+	0.894662i	0.100295	+	0.994958i	$0.468021\pi$
$500$		0			0
$501$	17.5310	−	17.5310i	0.783226	−	0.783226i
$502$		0			0
$503$			3.04877i			0.135938i	0.997687	+	0.0679689i	$0.0216519\pi$
$503$			3.04877i			0.135938i	−0.997687	+	0.0679689i	$0.978348\pi$
$504$		0			0
$505$			0.292957i			0.0130364i
$506$		0			0
$507$	−8.84823	+	8.84823i	−0.392964	+	0.392964i
$508$		0			0
$509$	−16.4653	+	16.4653i	−0.729813	+	0.729813i	−0.970582	−	0.240770i	$-0.922600\pi$
$509$	−16.4653	+	16.4653i	−0.729813	+	0.729813i	0.240770	+	0.970582i	$0.422600\pi$
$510$		0			0
$511$	−12.7673	−	13.3875i	−0.564793	−	0.592228i
$512$		0			0
$513$	−5.69773			−0.251561
$514$		0			0
$515$	7.31092	−	7.31092i	0.322158	−	0.322158i
$516$		0			0
$517$	19.9360	+	19.9360i	0.876784	+	0.876784i
$518$		0			0
$519$	−9.81702			−0.430919
$520$		0			0
$521$	−34.8583			−1.52717			−0.763584	−	0.645708i	$-0.776562\pi$
$521$	−34.8583			−1.52717			−0.763584	+	0.645708i	$0.776562\pi$
$522$		0			0
$523$	31.9307	−	31.9307i	1.39623	−	1.39623i	0.585718	−	0.810515i	$-0.300813\pi$
$523$	31.9307	−	31.9307i	1.39623	−	1.39623i	0.810515	−	0.585718i	$-0.199187\pi$
$524$		0			0
$525$	−36.0899	−	0.855751i	−1.57509	−	0.0373480i
$526$		0			0
$527$		−	6.71460i		−	0.292493i
$528$		0			0
$529$	−12.2528			−0.532729
$530$		0			0
$531$	−28.9861	−	28.9861i	−1.25789	−	1.25789i
$532$		0			0
$533$	34.9138	−	34.9138i	1.51228	−	1.51228i
$534$		0			0
$535$			4.54191i			0.196364i
$536$		0			0
$537$	44.8250			1.93434
$538$		0			0
$539$	−14.6478	+	13.3207i	−0.630926	+	0.573764i
$540$		0			0
$541$	28.5705	+	28.5705i	1.22834	+	1.22834i	0.964591	+	0.263749i	$0.0849592\pi$
$541$	28.5705	+	28.5705i	1.22834	+	1.22834i	0.263749	+	0.964591i	$0.415041\pi$
$542$		0			0
$543$			13.5479i			0.581398i
$544$		0			0
$545$		−	4.98105i		−	0.213365i
$546$		0			0
$547$	7.86041	−	7.86041i	0.336087	−	0.336087i	−0.518805	−	0.854892i	$-0.673623\pi$
$547$	7.86041	−	7.86041i	0.336087	−	0.336087i	0.854892	+	0.518805i	$0.173623\pi$
$548$		0			0
$549$	−31.6095	−	31.6095i	−1.34906	−	1.34906i
$550$		0			0
$551$			1.30618i			0.0556451i
$552$		0			0
$553$	21.4916	−	20.4960i	0.913916	−	0.871579i
$554$		0			0
$555$	−4.45729	−	4.45729i	−0.189201	−	0.189201i
$556$		0			0
$557$	5.60077	+	5.60077i	0.237312	+	0.237312i	0.815736	−	0.578424i	$-0.196332\pi$
$557$	5.60077	+	5.60077i	0.237312	+	0.237312i	−0.578424	+	0.815736i	$0.696332\pi$
$558$		0			0
$559$	19.0930			0.807547
$560$		0			0
$561$	23.7861			1.00425
$562$		0			0
$563$	2.66644	+	2.66644i	0.112377	+	0.112377i	0.761059	−	0.648682i	$-0.224680\pi$
$563$	2.66644	+	2.66644i	0.112377	+	0.112377i	−0.648682	+	0.761059i	$0.724680\pi$
$564$		0			0
$565$	4.55008	+	4.55008i	0.191423	+	0.191423i
$566$		0			0
$567$	−34.4127	−	36.0843i	−1.44520	−	1.51540i
$568$		0			0
$569$		−	28.3704i		−	1.18935i	−0.803967	−	0.594675i	$-0.797281\pi$
$569$		−	28.3704i		−	1.18935i	0.803967	−	0.594675i	$-0.202719\pi$
$570$		0			0
$571$	−0.132484	−	0.132484i	−0.00554428	−	0.00554428i	0.704329	−	0.709873i	$-0.251248\pi$
$571$	−0.132484	−	0.132484i	−0.00554428	−	0.00554428i	−0.709873	+	0.704329i	$0.751248\pi$
$572$		0			0
$573$	31.7490	−	31.7490i	1.32633	−	1.32633i
$574$		0			0
$575$		−	14.1550i		−	0.590305i
$576$		0			0
$577$		−	0.612944i		−	0.0255172i	−0.999919	−	0.0127586i	$-0.995939\pi$
$577$		−	0.612944i		−	0.0255172i	0.999919	−	0.0127586i	$-0.00406130\pi$
$578$		0			0
$579$	43.1137	+	43.1137i	1.79174	+	1.79174i
$580$		0			0
$581$	−0.478722	+	20.1893i	−0.0198607	+	0.837594i
$582$		0			0
$583$	−9.50380			−0.393607
$584$		0			0
$585$			23.7628i			0.982469i
$586$		0			0
$587$	21.1197	−	21.1197i	0.871704	−	0.871704i	−0.120954	−	0.992658i	$-0.538595\pi$
$587$	21.1197	−	21.1197i	0.871704	−	0.871704i	0.992658	+	0.120954i	$0.0385954\pi$
$588$		0			0
$589$	0.807030	+	0.807030i	0.0332531	+	0.0332531i
$590$		0			0
$591$	−2.03319			−0.0836342
$592$		0			0
$593$			3.50150i			0.143789i	0.997412	+	0.0718947i	$0.0229046\pi$
$593$			3.50150i			0.143789i	−0.997412	+	0.0718947i	$0.977095\pi$
$594$		0			0
$595$	−5.81387	−	0.137856i	−0.238345	−	0.00565156i
$596$		0			0
$597$	−54.9742	+	54.9742i	−2.24994	+	2.24994i
$598$		0			0
$599$	14.3759			0.587381			0.293691	−	0.955901i	$-0.405116\pi$
$599$	14.3759			0.587381			0.293691	+	0.955901i	$0.405116\pi$
$600$		0			0
$601$	−4.26571			−0.174002			−0.0870010	−	0.996208i	$-0.527728\pi$
$601$	−4.26571			−0.174002			−0.0870010	+	0.996208i	$0.527728\pi$
$602$		0			0
$603$	30.5542	+	30.5542i	1.24426	+	1.24426i
$604$		0			0
$605$	1.75212	−	1.75212i	0.0712336	−	0.0712336i
$606$		0			0
$607$	−13.0435			−0.529420			−0.264710	−	0.964328i	$-0.585276\pi$
$607$	−13.0435			−0.529420			−0.264710	+	0.964328i	$0.585276\pi$
$608$		0			0
$609$	−17.4712	+	16.6618i	−0.707967	+	0.675171i
$610$		0			0
$611$	29.0271	−	29.0271i	1.17431	−	1.17431i
$612$		0			0
$613$	29.3177	−	29.3177i	1.18413	−	1.18413i	0.205467	−	0.978664i	$-0.434129\pi$
$613$	29.3177	−	29.3177i	1.18413	−	1.18413i	0.978664	−	0.205467i	$-0.0658712\pi$
$614$		0			0
$615$		−	31.2935i		−	1.26188i
$616$		0			0
$617$		−	19.2992i		−	0.776956i	−0.921458	−	0.388478i	$-0.873001\pi$
$617$		−	19.2992i		−	0.776956i	0.921458	−	0.388478i	$-0.126999\pi$
$618$		0			0
$619$	1.58436	−	1.58436i	0.0636809	−	0.0636809i	−0.674549	−	0.738230i	$-0.735662\pi$
$619$	1.58436	−	1.58436i	0.0636809	−	0.0636809i	0.738230	+	0.674549i	$0.235662\pi$
$620$		0			0
$621$	29.1991	−	29.1991i	1.17172	−	1.17172i
$622$		0			0
$623$	−1.92956	−	2.02329i	−0.0773061	−	0.0810613i
$624$		0			0
$625$	−15.2324			−0.609295
$626$		0			0
$627$	−2.85886	+	2.85886i	−0.114172	+	0.114172i
$628$		0			0
$629$	4.54464	+	4.54464i	0.181207	+	0.181207i
$630$		0			0
$631$	13.7915			0.549031			0.274515	−	0.961583i	$-0.411483\pi$
$631$	13.7915			0.549031			0.274515	+	0.961583i	$0.411483\pi$
$632$		0			0
$633$	45.1781			1.79567
$634$		0			0
$635$	4.68721	−	4.68721i	0.186006	−	0.186006i
$636$		0			0
$637$	19.3951	+	21.3274i	0.768464	+	0.845024i
$638$		0			0
$639$		−	35.9161i		−	1.42082i
$640$		0			0
$641$	6.82159			0.269437			0.134718	−	0.990884i	$-0.456987\pi$
$641$	6.82159			0.269437			0.134718	+	0.990884i	$0.456987\pi$
$642$		0			0
$643$	32.9875	+	32.9875i	1.30090	+	1.30090i	0.927786	+	0.373112i	$0.121709\pi$
$643$	32.9875	+	32.9875i	1.30090	+	1.30090i	0.373112	+	0.927786i	$0.378291\pi$
$644$		0			0
$645$	8.55659	−	8.55659i	0.336916	−	0.336916i
$646$		0			0
$647$		−	20.4616i		−	0.804430i	−0.915545	−	0.402215i	$-0.868240\pi$
$647$		−	20.4616i		−	0.804430i	0.915545	−	0.402215i	$-0.131760\pi$
$648$		0			0
$649$	−16.5966			−0.651474
$650$		0			0
$651$	−0.500062	+	21.0893i	−0.0195990	+	0.826554i
$652$		0			0
$653$	3.37361	+	3.37361i	0.132020	+	0.132020i	0.770029	−	0.638009i	$-0.220242\pi$
$653$	3.37361	+	3.37361i	0.132020	+	0.132020i	−0.638009	+	0.770029i	$0.720242\pi$
$654$		0			0
$655$		−	10.7774i		−	0.421109i
$656$		0			0
$657$		−	48.8472i		−	1.90571i
$658$		0			0
$659$	17.8983	−	17.8983i	0.697217	−	0.697217i	−0.266592	−	0.963809i	$-0.585898\pi$
$659$	17.8983	−	17.8983i	0.697217	−	0.697217i	0.963809	+	0.266592i	$0.0858977\pi$
$660$		0			0
$661$	15.3379	+	15.3379i	0.596577	+	0.596577i	0.939400	−	0.342823i	$-0.111383\pi$
$661$	15.3379	+	15.3379i	0.596577	+	0.596577i	−0.342823	+	0.939400i	$0.611383\pi$
$662$		0			0
$663$		−	34.6329i		−	1.34503i
$664$		0			0
$665$	0.715340	−	0.682202i	0.0277397	−	0.0264546i
$666$		0			0
$667$	−6.69375	−	6.69375i	−0.259183	−	0.259183i
$668$		0			0
$669$	33.7488	+	33.7488i	1.30480	+	1.30480i
$670$		0			0
$671$	−18.0987			−0.698693
$672$		0			0
$673$	−6.74723			−0.260086			−0.130043	−	0.991508i	$-0.541512\pi$
$673$	−6.74723			−0.260086			−0.130043	+	0.991508i	$0.541512\pi$
$674$		0			0
$675$	−38.4577	−	38.4577i	−1.48024	−	1.48024i
$676$		0			0
$677$	−27.4470	−	27.4470i	−1.05487	−	1.05487i	−0.998404	−	0.0564681i	$-0.982016\pi$
$677$	−27.4470	−	27.4470i	−1.05487	−	1.05487i	−0.0564681	−	0.998404i	$-0.517984\pi$
$678$		0			0
$679$	−25.4054	+	24.2285i	−0.974968	+	0.929803i
$680$		0			0
$681$		−	31.8418i		−	1.22018i
$682$		0			0
$683$	−17.1085	−	17.1085i	−0.654639	−	0.654639i	0.299467	−	0.954107i	$-0.403191\pi$
$683$	−17.1085	−	17.1085i	−0.654639	−	0.654639i	−0.954107	+	0.299467i	$0.903191\pi$
$684$		0			0
$685$	−5.27358	+	5.27358i	−0.201493	+	0.201493i
$686$		0			0
$687$			83.9875i			3.20432i
$688$		0			0
$689$			13.8377i			0.527173i
$690$		0			0
$691$	−11.0833	−	11.0833i	−0.421628	−	0.421628i	0.464136	−	0.885764i	$-0.346365\pi$
$691$	−11.0833	−	11.0833i	−0.421628	−	0.421628i	−0.885764	+	0.464136i	$0.846365\pi$
$692$		0			0
$693$	−52.2639	−	1.23926i	−1.98534	−	0.0470757i
$694$		0			0
$695$	−5.06493			−0.192124
$696$		0			0
$697$			31.9068i			1.20856i
$698$		0			0
$699$	−10.0052	+	10.0052i	−0.378431	+	0.378431i
$700$		0			0
$701$	0.821691	+	0.821691i	0.0310348	+	0.0310348i	0.722454	−	0.691419i	$-0.243014\pi$
$701$	0.821691	+	0.821691i	0.0310348	+	0.0310348i	−0.691419	+	0.722454i	$0.743014\pi$
$702$		0			0
$703$	−1.09244			−0.0412023
$704$		0			0
$705$		−	26.0172i		−	0.979864i
$706$		0			0
$707$	−0.0222452	+	0.938155i	−0.000836617	+	0.0352830i
$708$		0			0
$709$	8.61763	−	8.61763i	0.323642	−	0.323642i	−0.526521	−	0.850162i	$-0.676504\pi$
$709$	8.61763	−	8.61763i	0.323642	−	0.323642i	0.850162	+	0.526521i	$0.176504\pi$
$710$		0			0
$711$	78.4168			2.94086
$712$		0			0
$713$	−8.27155			−0.309772
$714$		0			0
$715$	6.80294	+	6.80294i	0.254416	+	0.254416i
$716$		0			0
$717$	−20.4205	+	20.4205i	−0.762617	+	0.762617i
$718$		0			0
$719$	22.8866			0.853525			0.426763	−	0.904364i	$-0.359654\pi$
$719$	22.8866			0.853525			0.426763	+	0.904364i	$0.359654\pi$
$720$		0			0
$721$	23.9674	−	22.8571i	0.892592	−	0.851242i
$722$		0			0
$723$	21.6070	−	21.6070i	0.803571	−	0.803571i
$724$		0			0
$725$	−8.81624	+	8.81624i	−0.327427	+	0.327427i
$726$		0			0
$727$		−	12.6428i		−	0.468896i	−0.972129	−	0.234448i	$-0.924672\pi$
$727$		−	12.6428i		−	0.468896i	0.972129	−	0.234448i	$-0.0753283\pi$
$728$		0			0
$729$		−	12.2481i		−	0.453633i
$730$		0			0
$731$	−8.72428	+	8.72428i	−0.322679	+	0.322679i
$732$		0			0
$733$	−16.9017	+	16.9017i	−0.624280	+	0.624280i	−0.946623	−	0.322343i	$-0.895529\pi$
$733$	−16.9017	+	16.9017i	−0.624280	+	0.624280i	0.322343	+	0.946623i	$0.395529\pi$
$734$		0			0
$735$	18.2500	+	0.865961i	0.673161	+	0.0319415i
$736$		0			0
$737$	17.4945			0.644417
$738$		0			0
$739$	14.7651	−	14.7651i	0.543143	−	0.543143i	−0.381306	−	0.924449i	$-0.624526\pi$
$739$	14.7651	−	14.7651i	0.543143	−	0.543143i	0.924449	+	0.381306i	$0.124526\pi$
$740$		0			0
$741$	4.16254	+	4.16254i	0.152915	+	0.152915i
$742$		0			0
$743$	10.6332			0.390093			0.195046	−	0.980794i	$-0.437514\pi$
$743$	10.6332			0.390093			0.195046	+	0.980794i	$0.437514\pi$
$744$		0			0
$745$	−15.4910			−0.567547
$746$		0			0
$747$	−37.7059	+	37.7059i	−1.37959	+	1.37959i
$748$		0			0
$749$	−0.344883	+	14.5449i	−0.0126017	+	0.531458i
$750$		0			0
$751$			10.9634i			0.400060i	0.979790	+	0.200030i	$0.0641039\pi$
$751$			10.9634i			0.400060i	−0.979790	+	0.200030i	$0.935896\pi$
$752$		0			0
$753$	48.8154			1.77893
$754$		0			0
$755$	6.86316	+	6.86316i	0.249776	+	0.249776i
$756$		0			0
$757$	−21.8153	+	21.8153i	−0.792889	+	0.792889i	−0.981963	−	0.189073i	$-0.939452\pi$
$757$	−21.8153	+	21.8153i	−0.792889	+	0.792889i	0.189073	+	0.981963i	$0.439452\pi$
$758$		0			0
$759$		−	29.3015i		−	1.06358i
$760$		0			0
$761$	9.51842			0.345042			0.172521	−	0.985006i	$-0.444809\pi$
$761$	9.51842			0.345042			0.172521	+	0.985006i	$0.444809\pi$
$762$		0			0
$763$	0.378228	−	15.9511i	0.0136928	−	0.577470i
$764$		0			0
$765$	−10.8581	−	10.8581i	−0.392575	−	0.392575i
$766$		0			0
$767$			24.1649i			0.872545i
$768$		0			0
$769$			36.0771i			1.30098i	0.759517	+	0.650488i	$0.225435\pi$
$769$			36.0771i			1.30098i	−0.759517	+	0.650488i	$0.774565\pi$
$770$		0			0
$771$	−52.7092	+	52.7092i	−1.89827	+	1.89827i
$772$		0			0
$773$	24.1103	+	24.1103i	0.867188	+	0.867188i	0.992160	−	0.124972i	$-0.0398842\pi$
$773$	24.1103	+	24.1103i	0.867188	+	0.867188i	−0.124972	+	0.992160i	$0.539884\pi$
$774$		0			0
$775$			10.8943i			0.391336i
$776$		0			0
$777$	−13.9354	−	14.6123i	−0.499930	−	0.524214i
$778$		0			0
$779$	−3.83489	−	3.83489i	−0.137399	−	0.137399i
$780$		0			0
$781$	−10.2823	−	10.2823i	−0.367929	−	0.367929i
$782$		0			0
$783$	−36.3724			−1.29984
$784$		0			0
$785$	9.23879			0.329747
$786$		0			0
$787$	3.65922	+	3.65922i	0.130437	+	0.130437i	0.769311	−	0.638874i	$-0.220600\pi$
$787$	3.65922	+	3.65922i	0.130437	+	0.130437i	−0.638874	+	0.769311i	$0.720600\pi$
$788$		0			0
$789$	56.6660	+	56.6660i	2.01736	+	2.01736i
$790$		0			0
$791$	14.2255	+	14.9165i	0.505801	+	0.530370i
$792$		0			0
$793$			26.3520i			0.935786i
$794$		0			0
$795$	6.20140	+	6.20140i	0.219941	+	0.219941i
$796$		0			0
$797$	−8.56228	+	8.56228i	−0.303291	+	0.303291i	−0.842300	−	0.539009i	$-0.818799\pi$
$797$	−8.56228	+	8.56228i	−0.303291	+	0.303291i	0.539009	+	0.842300i	$0.318799\pi$
$798$		0			0
$799$			26.5271i			0.938460i
$800$		0			0
$801$		−	7.38240i		−	0.260844i
$802$		0			0
$803$	−13.9843	−	13.9843i	−0.493494	−	0.493494i
$804$		0			0
$805$	−0.169822	+	7.16195i	−0.00598543	+	0.252426i
$806$		0			0
$807$	−25.6959			−0.904537
$808$		0			0
$809$			9.48515i			0.333480i	0.986001	+	0.166740i	$0.0533241\pi$
$809$			9.48515i			0.333480i	−0.986001	+	0.166740i	$0.946676\pi$
$810$		0			0
$811$	8.37320	−	8.37320i	0.294023	−	0.294023i	−0.544644	−	0.838667i	$-0.683335\pi$
$811$	8.37320	−	8.37320i	0.294023	−	0.294023i	0.838667	+	0.544644i	$0.183335\pi$
$812$		0			0
$813$	37.4432	+	37.4432i	1.31319	+	1.31319i
$814$		0			0
$815$	−11.2742			−0.394917
$816$		0			0
$817$		−	2.09715i		−	0.0733700i
$818$		0			0
$819$	−1.80439	+	76.0970i	−0.0630503	+	2.65904i
$820$		0			0
$821$	29.9813	−	29.9813i	1.04635	−	1.04635i	0.0474808	−	0.998872i	$-0.484881\pi$
$821$	29.9813	−	29.9813i	1.04635	−	1.04635i	0.998872	−	0.0474808i	$-0.0151193\pi$
$822$		0			0
$823$	9.25258			0.322525			0.161262	−	0.986912i	$-0.448443\pi$
$823$	9.25258			0.322525			0.161262	+	0.986912i	$0.448443\pi$
$824$		0			0
$825$	−38.5926			−1.34362
$826$		0			0
$827$	−18.2363	−	18.2363i	−0.634137	−	0.634137i	0.314966	−	0.949103i	$-0.398007\pi$
$827$	−18.2363	−	18.2363i	−0.634137	−	0.634137i	−0.949103	+	0.314966i	$0.898007\pi$
$828$		0			0
$829$	32.7233	−	32.7233i	1.13653	−	1.13653i	0.147458	−	0.989068i	$-0.452891\pi$
$829$	32.7233	−	32.7233i	1.13653	−	1.13653i	0.989068	−	0.147458i	$-0.0471091\pi$
$830$		0			0
$831$	24.3887			0.846034
$832$		0			0
$833$	−18.6076	−	0.882932i	−0.644717	−	0.0305918i
$834$		0			0
$835$	−4.58212	+	4.58212i	−0.158571	+	0.158571i
$836$		0			0
$837$	−22.4729	+	22.4729i	−0.776778	+	0.776778i
$838$		0			0
$839$			14.1360i			0.488028i	0.969772	+	0.244014i	$0.0784643\pi$
$839$			14.1360i			0.488028i	−0.969772	+	0.244014i	$0.921536\pi$
$840$		0			0
$841$		−	20.6618i		−	0.712476i
$842$		0			0
$843$	13.6565	−	13.6565i	0.470354	−	0.470354i
$844$		0			0
$845$	2.31268	−	2.31268i	0.0795588	−	0.0795588i
$846$		0			0
$847$	5.74395	−	5.47787i	0.197365	−	0.188222i
$848$		0			0
$849$	−22.4962			−0.772069
$850$		0			0
$851$	5.59843	−	5.59843i	0.191912	−	0.191912i
$852$		0			0
$853$	−11.3648	−	11.3648i	−0.389122	−	0.389122i	0.485252	−	0.874374i	$-0.338728\pi$
$853$	−11.3648	−	11.3648i	−0.389122	−	0.389122i	−0.874374	+	0.485252i	$0.838728\pi$
$854$		0			0
$855$	2.61007			0.0892626
$856$		0			0
$857$	−15.3289			−0.523624			−0.261812	−	0.965119i	$-0.584320\pi$
$857$	−15.3289			−0.523624			−0.261812	+	0.965119i	$0.584320\pi$
$858$		0			0
$859$	−12.9667	+	12.9667i	−0.442418	+	0.442418i	−0.892824	−	0.450406i	$-0.851279\pi$
$859$	−12.9667	+	12.9667i	−0.442418	+	0.442418i	0.450406	+	0.892824i	$0.351279\pi$
$860$		0			0
$861$	2.37622	−	100.213i	0.0809813	−	3.41526i
$862$		0			0
$863$		−	42.8175i		−	1.45752i	−0.684767	−	0.728762i	$-0.740096\pi$
$863$		−	42.8175i		−	1.45752i	0.684767	−	0.728762i	$-0.259904\pi$
$864$		0			0
$865$	2.56590			0.0872432
$866$		0			0
$867$	−22.1616	−	22.1616i	−0.752646	−	0.752646i
$868$		0			0
$869$	22.4496	−	22.4496i	0.761552	−	0.761552i
$870$		0			0
$871$		−	25.4722i		−	0.863092i
$872$		0			0
$873$	−92.6970			−3.13732
$874$		0			0
$875$	20.3562	+	0.482679i	0.688165	+	0.0163175i
$876$		0			0
$877$	−28.6209	−	28.6209i	−0.966460	−	0.966460i	0.0329952	−	0.999456i	$-0.489495\pi$
$877$	−28.6209	−	28.6209i	−0.966460	−	0.966460i	−0.999456	+	0.0329952i	$0.989495\pi$
$878$		0			0
$879$		−	87.6819i		−	2.95744i
$880$		0			0
$881$			5.93539i			0.199969i	0.994989	+	0.0999843i	$0.0318792\pi$
$881$			5.93539i			0.199969i	−0.994989	+	0.0999843i	$0.968121\pi$
$882$		0			0
$883$	−2.96040	+	2.96040i	−0.0996254	+	0.0996254i	−0.755163	−	0.655537i	$-0.772442\pi$
$883$	−2.96040	+	2.96040i	−0.0996254	+	0.0996254i	0.655537	+	0.755163i	$0.272442\pi$
$884$		0			0
$885$	10.8296	+	10.8296i	0.364033	+	0.364033i
$886$		0			0
$887$			12.0578i			0.404860i	0.979297	+	0.202430i	$0.0648838\pi$
$887$			12.0578i			0.404860i	−0.979297	+	0.202430i	$0.935116\pi$
$888$		0			0
$889$	15.3661	−	14.6542i	0.515362	−	0.491488i
$890$		0			0
$891$	−37.6929	−	37.6929i	−1.26276	−	1.26276i
$892$		0			0
$893$	−3.18830	−	3.18830i	−0.106692	−	0.106692i
$894$		0			0
$895$	−11.7160			−0.391624
$896$		0			0
$897$	−42.6634			−1.42449
$898$		0			0
$899$	5.15181	+	5.15181i	0.171822	+	0.171822i
$900$		0			0
$901$	−6.32293	−	6.32293i	−0.210647	−	0.210647i
$902$		0			0
$903$	28.0510	−	26.7516i	0.933480	−	0.890237i
$904$		0			0
$905$		−	3.54106i		−	0.117709i
$906$		0			0
$907$	6.21946	+	6.21946i	0.206514	+	0.206514i	0.802784	−	0.596270i	$-0.203351\pi$
$907$	6.21946	+	6.21946i	0.206514	+	0.206514i	−0.596270	+	0.802784i	$0.703351\pi$
$908$		0			0
$909$	−1.75212	+	1.75212i	−0.0581140	+	0.0581140i
$910$		0			0
$911$		−	26.3682i		−	0.873617i	−0.899554	−	0.436809i	$-0.856109\pi$
$911$		−	26.3682i		−	0.873617i	0.899554	−	0.436809i	$-0.143891\pi$
$912$		0			0
$913$			21.5893i			0.714503i
$914$		0			0
$915$	11.8097	+	11.8097i	0.390418	+	0.390418i
$916$		0			0
$917$	0.818365	−	34.5132i	0.0270248	−	1.13973i
$918$		0			0
$919$	60.0495			1.98085			0.990425	−	0.138053i	$-0.0440843\pi$
$919$	60.0495			1.98085			0.990425	+	0.138053i	$0.0440843\pi$
$920$		0			0
$921$		−	13.8001i		−	0.454727i
$922$		0			0
$923$	−14.9712	+	14.9712i	−0.492781	+	0.492781i
$924$		0			0
$925$	−7.37361	−	7.37361i	−0.242443	−	0.242443i
$926$		0			0
$927$	87.4502			2.87224
$928$		0			0
$929$		−	38.1534i		−	1.25177i	−0.779914	−	0.625887i	$-0.784737\pi$
$929$		−	38.1534i		−	1.25177i	0.779914	−	0.625887i	$-0.215263\pi$
$930$		0			0
$931$	2.34258	−	2.13034i	0.0767749	−	0.0698191i
$932$		0			0
$933$	−45.1642	+	45.1642i	−1.47861	+	1.47861i
$934$		0			0
$935$	−6.21703			−0.203319
$936$		0			0
$937$	15.2637			0.498643			0.249321	−	0.968421i	$-0.419792\pi$
$937$	15.2637			0.498643			0.249321	+	0.968421i	$0.419792\pi$
$938$		0			0
$939$	−34.0341	−	34.0341i	−1.11066	−	1.11066i
$940$		0			0
$941$	35.7177	−	35.7177i	1.16436	−	1.16436i	0.180855	−	0.983510i	$-0.442114\pi$
$941$	35.7177	−	35.7177i	1.16436	−	1.16436i	0.983510	−	0.180855i	$-0.0578865\pi$
$942$		0			0
$943$	39.3052			1.27995
$944$		0			0
$945$	18.9969	+	19.9197i	0.617969	+	0.647987i
$946$		0			0
$947$	−26.4222	+	26.4222i	−0.858607	+	0.858607i	−0.991174	−	0.132567i	$-0.957678\pi$
$947$	−26.4222	+	26.4222i	−0.858607	+	0.858607i	0.132567	+	0.991174i	$0.457678\pi$
$948$		0			0
$949$	−20.3613	+	20.3613i	−0.660955	+	0.660955i
$950$		0			0
$951$			90.9354i			2.94878i
$952$		0			0
$953$		−	52.2788i		−	1.69348i	−0.532010	−	0.846738i	$-0.678563\pi$
$953$		−	52.2788i		−	1.69348i	0.532010	−	0.846738i	$-0.321437\pi$
$954$		0			0
$955$	−8.29831	+	8.29831i	−0.268527	+	0.268527i
$956$		0			0
$957$	−18.2500	+	18.2500i	−0.589938	+	0.589938i
$958$		0			0
$959$	−17.2884	+	16.4875i	−0.558270	+	0.532409i
$960$		0			0
$961$	−24.6338			−0.794640
$962$		0			0
$963$	−27.1642	+	27.1642i	−0.875355	+	0.875355i
$964$		0			0
$965$	−11.2687	−	11.2687i	−0.362753	−	0.362753i
$966$		0			0
$967$	−28.6054			−0.919888			−0.459944	−	0.887948i	$-0.652130\pi$
$967$	−28.6054			−0.919888			−0.459944	+	0.887948i	$0.652130\pi$
$968$		0			0
$969$	−3.80403			−0.122203
$970$		0			0
$971$	−32.7842	+	32.7842i	−1.05209	+	1.05209i	−0.0535273	+	0.998566i	$0.517046\pi$
$971$	−32.7842	+	32.7842i	−1.05209	+	1.05209i	−0.998566	+	0.0535273i	$0.982954\pi$
$972$		0			0
$973$	−16.2197	−	0.384597i	−0.519981	−	0.0123296i
$974$		0			0
$975$			56.1913i			1.79956i
$976$		0			0
$977$	33.2805			1.06474			0.532369	−	0.846512i	$-0.321302\pi$
$977$	33.2805			1.06474			0.532369	+	0.846512i	$0.321302\pi$
$978$		0			0
$979$	−2.11348	−	2.11348i	−0.0675470	−	0.0675470i
$980$		0			0
$981$	29.7906	−	29.7906i	0.951141	−	0.951141i
$982$		0			0
$983$			27.1939i			0.867350i	0.901069	+	0.433675i	$0.142783\pi$
$983$			27.1939i			0.867350i	−0.901069	+	0.433675i	$0.857217\pi$
$984$		0			0
$985$	0.531420			0.0169324
$986$		0			0
$987$	1.97557	−	83.3165i	0.0628831	−	2.65199i
$988$		0			0
$989$	10.7472	+	10.7472i	0.341742	+	0.341742i
$990$		0			0
$991$			42.4776i			1.34935i	0.738117	+	0.674673i	$0.235715\pi$
$991$			42.4776i			1.34935i	−0.738117	+	0.674673i	$0.764285\pi$
$992$		0			0
$993$			93.0384i			2.95248i
$994$		0			0
$995$	14.3687	−	14.3687i	0.455520	−	0.455520i
$996$		0			0
$997$	30.9512	+	30.9512i	0.980234	+	0.980234i	0.999808	−	0.0195743i	$-0.00623109\pi$
$997$	30.9512	+	30.9512i	0.980234	+	0.980234i	−0.0195743	+	0.999808i	$0.506231\pi$
$998$		0			0
$999$		−	30.4207i		−	0.962468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.j.d.111.1		16
4.3	odd	2		112.2.j.d.83.2	yes	16
7.6	odd	2	inner	448.2.j.d.111.8		16
8.3	odd	2		896.2.j.h.223.1		16
8.5	even	2		896.2.j.g.223.8		16
16.3	odd	4		896.2.j.g.671.1		16
16.5	even	4		112.2.j.d.27.1	✓	16
16.11	odd	4	inner	448.2.j.d.335.8		16
16.13	even	4		896.2.j.h.671.8		16
28.3	even	6		784.2.w.e.19.5		32
28.11	odd	6		784.2.w.e.19.6		32
28.19	even	6		784.2.w.e.227.6		32
28.23	odd	6		784.2.w.e.227.5		32
28.27	even	2		112.2.j.d.83.1	yes	16
56.13	odd	2		896.2.j.g.223.1		16
56.27	even	2		896.2.j.h.223.8		16
112.5	odd	12		784.2.w.e.619.6		32
112.13	odd	4		896.2.j.h.671.1		16
112.27	even	4	inner	448.2.j.d.335.1		16
112.37	even	12		784.2.w.e.619.5		32
112.53	even	12		784.2.w.e.411.6		32
112.69	odd	4		112.2.j.d.27.2	yes	16
112.83	even	4		896.2.j.g.671.8		16
112.101	odd	12		784.2.w.e.411.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.j.d.27.1	✓	16	16.5	even	4
112.2.j.d.27.2	yes	16	112.69	odd	4
112.2.j.d.83.1	yes	16	28.27	even	2
112.2.j.d.83.2	yes	16	4.3	odd	2
448.2.j.d.111.1		16	1.1	even	1	trivial
448.2.j.d.111.8		16	7.6	odd	2	inner
448.2.j.d.335.1		16	112.27	even	4	inner
448.2.j.d.335.8		16	16.11	odd	4	inner
784.2.w.e.19.5		32	28.3	even	6
784.2.w.e.19.6		32	28.11	odd	6
784.2.w.e.227.5		32	28.23	odd	6
784.2.w.e.227.6		32	28.19	even	6
784.2.w.e.411.5		32	112.101	odd	12
784.2.w.e.411.6		32	112.53	even	12
784.2.w.e.619.5		32	112.37	even	12
784.2.w.e.619.6		32	112.5	odd	12
896.2.j.g.223.1		16	56.13	odd	2
896.2.j.g.223.8		16	8.5	even	2
896.2.j.g.671.1		16	16.3	odd	4
896.2.j.g.671.8		16	112.83	even	4
896.2.j.h.223.1		16	8.3	odd	2
896.2.j.h.223.8		16	56.27	even	2
896.2.j.h.671.1		16	112.13	odd	4
896.2.j.h.671.8		16	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.23450 - 2.23450i) q^{3} +(0.584038 + 0.584038i) q^{5} +(1.82596 + 1.91465i) q^{7} +6.98602i q^{9} +O(q^{10})\)	\(q+(-2.23450 - 2.23450i) q^{3} +(0.584038 + 0.584038i) q^{5} +(1.82596 + 1.91465i) q^{7} +6.98602i q^{9} +(2.00000 + 2.00000i) q^{11} +(2.91203 - 2.91203i) q^{13} -2.61007i q^{15} +2.66123i q^{17} +(-0.319854 - 0.319854i) q^{19} +(0.198191 - 8.35840i) q^{21} +3.27830 q^{23} -4.31780i q^{25} +(8.90678 - 8.90678i) q^{27} +(-2.04184 - 2.04184i) q^{29} -2.52312 q^{31} -8.93802i q^{33} +(-0.0518018 + 2.18466i) q^{35} +(1.70773 - 1.70773i) q^{37} -13.0139 q^{39} +11.9895 q^{41} +(3.27830 + 3.27830i) q^{43} +(-4.08010 + 4.08010i) q^{45} +9.96799 q^{47} +(-0.331777 + 6.99213i) q^{49} +(5.94652 - 5.94652i) q^{51} +(-2.37595 + 2.37595i) q^{53} +2.33615i q^{55} +1.42943i q^{57} +(-4.14916 + 4.14916i) q^{59} +(-4.52468 + 4.52468i) q^{61} +(-13.3758 + 12.7562i) q^{63} +3.40147 q^{65} +(4.37361 - 4.37361i) q^{67} +(-7.32537 - 7.32537i) q^{69} -5.14114 q^{71} -6.99213 q^{73} +(-9.64814 + 9.64814i) q^{75} +(-0.177392 + 7.48121i) q^{77} -11.2248i q^{79} -18.8464 q^{81} +(5.39734 + 5.39734i) q^{83} +(-1.55426 + 1.55426i) q^{85} +9.12499i q^{87} -1.05674 q^{89} +(10.8927 + 0.258285i) q^{91} +(5.63793 + 5.63793i) q^{93} -0.373614i q^{95} +13.2689i q^{97} +(-13.9720 + 13.9720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 32 q^{11} + 16 q^{21} - 8 q^{35} - 16 q^{39} - 16 q^{49} + 32 q^{51} - 80 q^{65} + 48 q^{67} - 32 q^{71} - 16 q^{77} + 32 q^{81} + 64 q^{85} - 8 q^{91} - 64 q^{93} - 64 q^{99}+O(q^{100}) \) 16 * q - 8 * q^7 + 32 * q^11 + 16 * q^21 - 8 * q^35 - 16 * q^39 - 16 * q^49 + 32 * q^51 - 80 * q^65 + 48 * q^67 - 32 * q^71 - 16 * q^77 + 32 * q^81 + 64 * q^85 - 8 * q^91 - 64 * q^93 - 64 * q^99

Introduction

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