LMFDB - Embedded newform 448.2.q.c.159.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(31,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("448.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 16x^{8} + 8x^{7} + 8x^{6} + 32x^{5} + 240x^{4} + 120x^{3} + 32x^{2} + 16x + 4 $ x^12 - 4x^9 - 16x^8 + 8x^7 + 8x^6 + 32x^5 + 240x^4 + 120x^3 + 32x^2 + 16*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			159.5
Root			$2.08413 - 0.558440i$ of defining polynomial
Character	$\chi$	$=$	448.159
Dual form			448.2.q.c.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43366 - 0.827721i) q^{3} +(2.02569 - 3.50859i) q^{5} +(2.64257 + 0.129755i) q^{7} +(-0.129755 + 0.224743i) q^{9} +O(q^{10})$	\(q+(1.43366 - 0.827721i) q^{3} +(2.02569 - 3.50859i) q^{5} +(2.64257 + 0.129755i) q^{7} +(-0.129755 + 0.224743i) q^{9} +(1.20891 + 2.09390i) q^{11} -2.25951 q^{13} -6.70682i q^{15} +(-6.07706 + 3.50859i) q^{17} +(2.34417 + 1.35341i) q^{19} +(3.89593 - 2.00128i) q^{21} +(-4.30097 - 2.48316i) q^{23} +(-5.70682 - 9.88450i) q^{25} +5.39593i q^{27} -1.82103i q^{29} +(2.94096 + 5.09390i) q^{31} +(3.46633 + 2.00128i) q^{33} +(5.80827 - 9.00885i) q^{35} +(-1.50000 - 0.866025i) q^{37} +(-3.23936 + 1.87024i) q^{39} -1.82103i q^{41} +6.92820 q^{43} +(0.525687 + 0.910517i) q^{45} +(-3.39045 + 5.87243i) q^{47} +(6.96633 + 0.685774i) q^{49} +(-5.80827 + 10.0602i) q^{51} +(-3.46633 + 2.00128i) q^{53} +9.79551 q^{55} +4.48098 q^{57} +(-2.47993 + 1.43179i) q^{59} +(3.75951 - 6.51166i) q^{61} +(-0.372049 + 0.577061i) q^{63} +(-4.57706 + 7.92770i) q^{65} +(-5.58353 - 9.67096i) q^{67} -8.22147 q^{69} -6.00000i q^{71} +(2.68780 - 1.55180i) q^{73} +(-16.3632 - 9.44731i) q^{75} +(2.92294 + 5.69013i) q^{77} +(-3.85148 - 2.22365i) q^{79} +(4.07706 + 7.06168i) q^{81} +3.89725i q^{83} +28.4292i q^{85} +(-1.50731 - 2.61073i) q^{87} +(-4.50000 - 2.59808i) q^{89} +(-5.97091 - 0.293183i) q^{91} +(8.43265 + 4.86860i) q^{93} +(9.49712 - 5.48316i) q^{95} +17.0490i q^{97} -0.627451 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} + 4 q^{9}+O(q^{10}) $ 12 * q + 6 * q^5 + 4 * q^9	$ 12 q + 6 q^{5} + 4 q^{9} - 16 q^{13} - 18 q^{17} + 34 q^{21} - 8 q^{25} - 30 q^{33} - 18 q^{37} - 12 q^{45} + 12 q^{49} + 30 q^{53} + 76 q^{57} + 34 q^{61} - 132 q^{69} - 6 q^{73} + 90 q^{77} - 6 q^{81} - 54 q^{89} - 42 q^{93}+O(q^{100}) $ 12 * q + 6 * q^5 + 4 * q^9 - 16 * q^13 - 18 * q^17 + 34 * q^21 - 8 * q^25 - 30 * q^33 - 18 * q^37 - 12 * q^45 + 12 * q^49 + 30 * q^53 + 76 * q^57 + 34 * q^61 - 132 * q^69 - 6 * q^73 + 90 * q^77 - 6 * q^81 - 54 * q^89 - 42 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.43366	−	0.827721i	0.827721	−	0.477885i	−0.0253506	−	0.999679i	$-0.508070\pi$
$3$	1.43366	−	0.827721i	0.827721	−	0.477885i	0.853072	+	0.521794i	$0.174737\pi$
$4$		0			0
$5$	2.02569	−	3.50859i	0.905915	−	1.56909i	0.0862303	−	0.996275i	$-0.472518\pi$
$5$	2.02569	−	3.50859i	0.905915	−	1.56909i	0.819684	−	0.572815i	$-0.194149\pi$
$6$		0			0
$7$	2.64257	+	0.129755i	0.998797	+	0.0490429i
$7$	2.64257	+	0.129755i	0.998797	+	0.0490429i
$8$		0			0
$9$	−0.129755	+	0.224743i	−0.0432518	+	0.0749142i
$10$		0			0
$11$	1.20891	+	2.09390i	0.364501	+	0.631334i	0.988696	−	0.149935i	$-0.0479063\pi$
$11$	1.20891	+	2.09390i	0.364501	+	0.631334i	−0.624195	+	0.781269i	$0.714573\pi$
$12$		0			0
$13$	−2.25951			−0.626675			−0.313338	−	0.949642i	$-0.601447\pi$
$13$	−2.25951			−0.626675			−0.313338	+	0.949642i	$0.601447\pi$
$14$		0			0
$15$		−	6.70682i		−	1.73169i
$16$		0			0
$17$	−6.07706	+	3.50859i	−1.47390	+	0.850959i	−0.999568	−	0.0293852i	$-0.990645\pi$
$17$	−6.07706	+	3.50859i	−1.47390	+	0.850959i	−0.474336	+	0.880344i	$0.657312\pi$
$18$		0			0
$19$	2.34417	+	1.35341i	0.537790	+	0.310493i	0.744183	−	0.667976i	$-0.232839\pi$
$19$	2.34417	+	1.35341i	0.537790	+	0.310493i	−0.206393	+	0.978469i	$0.566172\pi$
$20$		0			0
$21$	3.89593	−	2.00128i	0.850162	−	0.436716i
$22$		0			0
$23$	−4.30097	−	2.48316i	−0.896813	−	0.517775i	−0.0206484	−	0.999787i	$-0.506573\pi$
$23$	−4.30097	−	2.48316i	−0.896813	−	0.517775i	−0.876165	+	0.482011i	$0.839906\pi$
$24$		0			0
$25$	−5.70682	−	9.88450i	−1.14136	−	1.97690i
$26$		0			0
$27$			5.39593i			1.03845i
$28$		0			0
$29$		−	1.82103i		−	0.338157i	−0.985603	−	0.169079i	$-0.945921\pi$
$29$		−	1.82103i		−	0.338157i	0.985603	−	0.169079i	$-0.0540792\pi$
$30$		0			0
$31$	2.94096	+	5.09390i	0.528213	+	0.914891i	0.999459	+	0.0328894i	$0.0104709\pi$
$31$	2.94096	+	5.09390i	0.528213	+	0.914891i	−0.471246	+	0.882002i	$0.656196\pi$
$32$		0			0
$33$	3.46633	+	2.00128i	0.603410	+	0.348379i
$34$		0			0
$35$	5.80827	−	9.00885i	0.981777	−	1.52277i
$36$		0			0
$37$	−1.50000	−	0.866025i	−0.246598	−	0.142374i	0.371607	−	0.928390i	$-0.378807\pi$
$37$	−1.50000	−	0.866025i	−0.246598	−	0.142374i	−0.618206	+	0.786016i	$0.712140\pi$
$38$		0			0
$39$	−3.23936	+	1.87024i	−0.518713	+	0.299479i
$40$		0			0
$41$		−	1.82103i		−	0.284398i	−0.989838	−	0.142199i	$-0.954583\pi$
$41$		−	1.82103i		−	0.284398i	0.989838	−	0.142199i	$-0.0454172\pi$
$42$		0			0
$43$	6.92820			1.05654			0.528271	−	0.849076i	$-0.322841\pi$
$43$	6.92820			1.05654			0.528271	+	0.849076i	$0.322841\pi$
$44$		0			0
$45$	0.525687	+	0.910517i	0.0783648	+	0.135732i
$46$		0			0
$47$	−3.39045	+	5.87243i	−0.494548	+	0.856582i	−0.999980	−	0.00628430i	$-0.998000\pi$
$47$	−3.39045	+	5.87243i	−0.494548	+	0.856582i	0.505432	+	0.862866i	$0.331333\pi$
$48$		0			0
$49$	6.96633	+	0.685774i	0.995190	+	0.0979677i
$50$		0			0
$51$	−5.80827	+	10.0602i	−0.813321	+	1.40871i
$52$		0			0
$53$	−3.46633	+	2.00128i	−0.476137	+	0.274898i	−0.718805	−	0.695212i	$-0.755311\pi$
$53$	−3.46633	+	2.00128i	−0.476137	+	0.274898i	0.242668	+	0.970109i	$0.421977\pi$
$54$		0			0
$55$	9.79551			1.32083
$56$		0			0
$57$	4.48098			0.593520
$58$		0			0
$59$	−2.47993	+	1.43179i	−0.322860	+	0.186403i	−0.652666	−	0.757645i	$-0.726350\pi$
$59$	−2.47993	+	1.43179i	−0.322860	+	0.186403i	0.329807	+	0.944048i	$0.393016\pi$
$60$		0			0
$61$	3.75951	−	6.51166i	0.481356	−	0.833733i	−0.518415	−	0.855129i	$-0.673478\pi$
$61$	3.75951	−	6.51166i	0.481356	−	0.833733i	0.999771	+	0.0213961i	$0.00681110\pi$
$62$		0			0
$63$	−0.372049	+	0.577061i	−0.0468737	+	0.0727029i
$64$		0			0
$65$	−4.57706	+	7.92770i	−0.567715	+	0.983311i
$66$		0			0
$67$	−5.58353	−	9.67096i	−0.682137	−	1.18150i	−0.974327	−	0.225136i	$-0.927717\pi$
$67$	−5.58353	−	9.67096i	−0.682137	−	1.18150i	0.292191	−	0.956360i	$-0.405616\pi$
$68$		0			0
$69$	−8.22147			−0.989748
$70$		0			0
$71$		−	6.00000i		−	0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$		−	6.00000i		−	0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$		0			0
$73$	2.68780	−	1.55180i	0.314583	−	0.181624i	−0.334393	−	0.942434i	$-0.608531\pi$
$73$	2.68780	−	1.55180i	0.314583	−	0.181624i	0.648975	+	0.760809i	$0.275198\pi$
$74$		0			0
$75$	−16.3632	−	9.44731i	−1.88946	−	1.09088i
$76$		0			0
$77$	2.92294	+	5.69013i	0.333100	+	0.648450i
$78$		0			0
$79$	−3.85148	−	2.22365i	−0.433325	−	0.250181i	0.267437	−	0.963575i	$-0.413823\pi$
$79$	−3.85148	−	2.22365i	−0.433325	−	0.250181i	−0.700762	+	0.713395i	$0.747157\pi$
$80$		0			0
$81$	4.07706	+	7.06168i	0.453007	+	0.784631i
$82$		0			0
$83$			3.89725i			0.427779i	0.976858	+	0.213889i	$0.0686132\pi$
$83$			3.89725i			0.427779i	−0.976858	+	0.213889i	$0.931387\pi$
$84$		0			0
$85$			28.4292i			3.08358i
$86$		0			0
$87$	−1.50731	−	2.61073i	−0.161600	−	0.279900i
$88$		0			0
$89$	−4.50000	−	2.59808i	−0.476999	−	0.275396i	0.242166	−	0.970235i	$-0.422142\pi$
$89$	−4.50000	−	2.59808i	−0.476999	−	0.275396i	−0.719165	+	0.694839i	$0.755475\pi$
$90$		0			0
$91$	−5.97091	−	0.293183i	−0.625921	−	0.0307340i
$92$		0			0
$93$	8.43265	+	4.86860i	0.874426	+	0.504850i
$94$		0			0
$95$	9.49712	−	5.48316i	0.974384	−	0.562561i
$96$		0			0
$97$			17.0490i			1.73106i	0.500855	+	0.865531i	$0.333019\pi$
$97$			17.0490i			1.73106i	−0.500855	+	0.865531i	$0.666981\pi$
$98$		0			0
$99$	−0.627451			−0.0630612
$100$		0			0
$101$	−5.02569	−	8.70475i	−0.500075	−	0.866155i	−1.00000		8.60956e-5i	$-0.999973\pi$
$101$	−5.02569	−	8.70475i	−0.500075	−	0.866155i	0.499925	−	0.866068i	$-0.333361\pi$
$102$		0			0
$103$	−5.58353	+	9.67096i	−0.550162	+	0.952908i	0.448101	+	0.893983i	$0.352101\pi$
$103$	−5.58353	+	9.67096i	−0.550162	+	0.952908i	−0.998262	+	0.0589249i	$0.981233\pi$
$104$		0			0
$105$	0.870245	−	17.7232i	0.0849272	−	1.72961i
$106$		0			0
$107$	8.22610	−	14.2480i	0.795247	−	1.37741i	−0.127435	−	0.991847i	$-0.540675\pi$
$107$	8.22610	−	14.2480i	0.795247	−	1.37741i	0.922682	−	0.385561i	$-0.125992\pi$
$108$		0			0
$109$	4.88927	−	2.82282i	0.468307	−	0.270377i	−0.247224	−	0.968958i	$-0.579518\pi$
$109$	4.88927	−	2.82282i	0.468307	−	0.270377i	0.715531	+	0.698581i	$0.246185\pi$
$110$		0			0
$111$	−2.86731			−0.272153
$112$		0			0
$113$	6.77853			0.637671			0.318835	−	0.947810i	$-0.396708\pi$
$113$	6.77853			0.637671			0.318835	+	0.947810i	$0.396708\pi$
$114$		0			0
$115$	−17.4248	+	10.0602i	−1.62487	+	0.938121i
$116$		0			0
$117$	0.293183	−	0.507809i	0.0271048	−	0.0469469i
$118$		0			0
$119$	−16.5143	+	8.48316i	−1.51386	+	0.777650i
$120$		0			0
$121$	2.57706	−	4.46360i	0.234278	−	0.405782i
$122$		0			0
$123$	−1.50731	−	2.61073i	−0.135909	−	0.235402i
$124$		0			0
$125$	−25.9840			−2.32408
$126$		0			0
$127$			16.3082i			1.44712i	0.690260	+	0.723561i	$0.257496\pi$
$127$			16.3082i			1.44712i	−0.690260	+	0.723561i	$0.742504\pi$
$128$		0			0
$129$	9.93265	−	5.73462i	0.874521	−	0.504905i
$130$		0			0
$131$	4.53725	+	2.61958i	0.396422	+	0.228874i	0.684939	−	0.728601i	$-0.259829\pi$
$131$	4.53725	+	2.61958i	0.396422	+	0.228874i	−0.288517	+	0.957475i	$0.593162\pi$
$132$		0			0
$133$	6.01902	+	3.88064i	0.521915	+	0.336494i
$134$		0			0
$135$	18.9321	+	10.9305i	1.62942	+	0.940745i
$136$		0			0
$137$	6.07706	+	10.5258i	0.519198	+	0.899278i	0.999751	+	0.0223121i	$0.00710276\pi$
$137$	6.07706	+	10.5258i	0.519198	+	0.899278i	−0.480553	+	0.876966i	$0.659564\pi$
$138$		0			0
$139$			10.5190i			0.892212i	0.894980	+	0.446106i	$0.147190\pi$
$139$			10.5190i			0.892212i	−0.894980	+	0.446106i	$0.852810\pi$
$140$		0			0
$141$			11.2254i			0.945348i
$142$		0			0
$143$	−2.73155	−	4.73118i	−0.228424	−	0.395641i
$144$		0			0
$145$	−6.38927	−	3.68884i	−0.530600	−	0.306342i
$146$		0			0
$147$	10.5549	−	4.78301i	0.870557	−	0.394496i
$148$		0			0
$149$	−13.0097	−	7.51116i	−1.06580	−	0.615338i	−0.138767	−	0.990325i	$-0.544314\pi$
$149$	−13.0097	−	7.51116i	−1.06580	−	0.615338i	−0.927030	+	0.374987i	$0.877647\pi$
$150$		0			0
$151$	−5.03352	+	2.90610i	−0.409622	+	0.236495i	−0.690627	−	0.723211i	$-0.742665\pi$
$151$	−5.03352	+	2.90610i	−0.409622	+	0.236495i	0.281005	+	0.959706i	$0.409332\pi$
$152$		0			0
$153$		−	1.82103i		−	0.147222i
$154$		0			0
$155$	23.8299			1.91406
$156$		0			0
$157$	−2.24049	−	3.88064i	−0.178811	−	0.309709i	0.762663	−	0.646796i	$-0.223892\pi$
$157$	−2.24049	−	3.88064i	−0.178811	−	0.309709i	−0.941473	+	0.337087i	$0.890558\pi$
$158$		0			0
$159$	−3.31301	+	5.73830i	−0.262739	+	0.455077i
$160$		0			0
$161$	−11.0434	−	7.12000i	−0.870341	−	0.561135i
$162$		0			0
$163$	−7.31558	+	12.6710i	−0.573001	+	0.992466i	0.423255	+	0.906011i	$0.360887\pi$
$163$	−7.31558	+	12.6710i	−0.573001	+	0.992466i	−0.996256	+	0.0864556i	$0.972446\pi$
$164$		0			0
$165$	14.0434	−	8.10795i	1.09328	−	0.631203i
$166$		0			0
$167$	8.57127			0.663265			0.331632	−	0.943409i	$-0.392401\pi$
$167$	8.57127			0.663265			0.331632	+	0.943409i	$0.392401\pi$
$168$		0			0
$169$	−7.89461			−0.607278
$170$		0			0
$171$	−0.608337	+	0.351224i	−0.0465207	+	0.0268587i
$172$		0			0
$173$	1.63642	−	2.83436i	0.124415	−	0.215493i	−0.797089	−	0.603862i	$-0.793628\pi$
$173$	1.63642	−	2.83436i	0.124415	−	0.215493i	0.921504	+	0.388369i	$0.126961\pi$
$174$		0			0
$175$	−13.7981	−	26.8609i	−1.04304	−	2.03050i
$176$		0			0
$177$	−2.37024	+	4.10538i	−0.178159	+	0.308580i
$178$		0			0
$179$	−7.98981	−	13.8388i	−0.597186	−	1.03436i	−0.993234	−	0.116127i	$-0.962952\pi$
$179$	−7.98981	−	13.8388i	−0.597186	−	1.03436i	0.396048	−	0.918230i	$-0.370381\pi$
$180$		0			0
$181$	23.7219			1.76323			0.881617	−	0.471966i	$-0.156456\pi$
$181$	23.7219			1.76323			0.881617	+	0.471966i	$0.156456\pi$
$182$		0			0
$183$		−	12.4473i		−	0.920131i
$184$		0			0
$185$	−6.07706	+	3.50859i	−0.446794	+	0.257957i
$186$		0			0
$187$	−14.6933	−	8.48316i	−1.07448	−	0.620350i
$188$		0			0
$189$	−0.700151	+	14.2591i	−0.0509285	+	1.03720i
$190$		0			0
$191$	7.03252	+	4.06022i	0.508855	+	0.293788i	0.732363	−	0.680915i	$-0.238418\pi$
$191$	7.03252	+	4.06022i	0.508855	+	0.293788i	−0.223508	+	0.974702i	$0.571751\pi$
$192$		0			0
$193$	−1.37024	−	2.37333i	−0.0986324	−	0.170836i	0.812486	−	0.582980i	$-0.198113\pi$
$193$	−1.37024	−	2.37333i	−0.0986324	−	0.170836i	−0.911119	+	0.412144i	$0.864780\pi$
$194$		0			0
$195$			15.1541i			1.08521i
$196$		0			0
$197$		−	11.4923i		−	0.818795i	−0.912356	−	0.409397i	$-0.865739\pi$
$197$		−	11.4923i		−	0.818795i	0.912356	−	0.409397i	$-0.134261\pi$
$198$		0			0
$199$	−8.58660	−	14.8724i	−0.608688	−	1.05428i	−0.991457	−	0.130434i	$-0.958363\pi$
$199$	−8.58660	−	14.8724i	−0.608688	−	1.05428i	0.382769	−	0.923844i	$-0.374971\pi$
$200$		0			0
$201$	−16.0097	−	9.24321i	−1.12924	−	0.651966i
$202$		0			0
$203$	0.236289	−	4.81220i	0.0165842	−	0.337751i
$204$		0			0
$205$	−6.38927	−	3.68884i	−0.446246	−	0.257640i
$206$		0			0
$207$	1.11615	−	0.644407i	0.0775775	−	0.0447894i
$208$		0			0
$209$			6.54461i			0.452700i
$210$		0			0
$211$	27.5962			1.89980			0.949899	−	0.312556i	$-0.101185\pi$
$211$	27.5962			1.89980			0.949899	+	0.312556i	$0.101185\pi$
$212$		0			0
$213$	−4.96633	−	8.60193i	−0.340287	−	0.589395i
$214$		0			0
$215$	14.0344	−	24.3082i	0.957136	−	1.65781i
$216$		0			0
$217$	7.11073	+	13.8426i	0.482708	+	0.939695i
$218$		0			0
$219$	2.56891	−	4.44949i	0.173591	−	0.300669i
$220$		0			0
$221$	13.7312	−	7.92770i	0.923659	−	0.533275i
$222$		0			0
$223$	12.8408			0.859883			0.429941	−	0.902857i	$-0.358534\pi$
$223$	12.8408			0.859883			0.429941	+	0.902857i	$0.358534\pi$
$224$		0			0
$225$	2.96196			0.197464
$226$		0			0
$227$	8.85355	−	5.11160i	0.587631	−	0.339269i	−0.176529	−	0.984295i	$-0.556487\pi$
$227$	8.85355	−	5.11160i	0.587631	−	0.339269i	0.764160	+	0.645027i	$0.223154\pi$
$228$		0			0
$229$	3.37024	−	5.83744i	0.222712	−	0.385749i	−0.732919	−	0.680316i	$-0.761842\pi$
$229$	3.37024	−	5.83744i	0.222712	−	0.385749i	0.955631	+	0.294568i	$0.0951757\pi$
$230$		0			0
$231$	8.90033	+	5.73830i	0.585598	+	0.377553i
$232$		0			0
$233$	4.88927	−	8.46846i	0.320306	−	0.554787i	−0.660245	−	0.751051i	$-0.729547\pi$
$233$	4.88927	−	8.46846i	0.320306	−	0.554787i	0.980551	+	0.196263i	$0.0628808\pi$
$234$		0			0
$235$	13.7360	+	23.7914i	0.896036	+	1.55198i
$236$		0			0
$237$	−7.36226			−0.478230
$238$		0			0
$239$		−	17.5297i		−	1.13390i	−0.823751	−	0.566951i	$-0.808123\pi$
$239$		−	17.5297i		−	1.13390i	0.823751	−	0.566951i	$-0.191877\pi$
$240$		0			0
$241$	0.721468	−	0.416540i	0.0464739	−	0.0268317i	−0.476583	−	0.879129i	$-0.658125\pi$
$241$	0.721468	−	0.416540i	0.0464739	−	0.0268317i	0.523057	+	0.852298i	$0.324792\pi$
$242$		0			0
$243$	−2.32884	−	1.34456i	−0.149395	−	0.0862534i
$244$		0			0
$245$	16.5177	−	23.0528i	1.05528	−	1.47279i
$246$		0			0
$247$	−5.29668	−	3.05804i	−0.337020	−	0.194578i
$248$		0			0
$249$	3.22584	+	5.58731i	0.204429	+	0.354082i
$250$		0			0
$251$			13.3242i			0.841017i	0.907289	+	0.420509i	$0.138148\pi$
$251$			13.3242i			0.841017i	−0.907289	+	0.420509i	$0.861852\pi$
$252$		0			0
$253$		−	12.0077i		−	0.754918i
$254$		0			0
$255$	23.5315	+	40.7577i	1.47360	+	2.55235i
$256$		0			0
$257$	−9.23118	−	5.32963i	−0.575825	−	0.332453i	0.183647	−	0.982992i	$-0.441210\pi$
$257$	−9.23118	−	5.32963i	−0.575825	−	0.332453i	−0.759473	+	0.650539i	$0.774543\pi$
$258$		0			0
$259$	−3.85148	−	2.48316i	−0.239319	−	0.154296i
$260$		0			0
$261$	0.409264	+	0.236289i	0.0253328	+	0.0146259i
$262$		0			0
$263$	−19.8894	+	11.4832i	−1.22643	+	0.708082i	−0.966282	−	0.257485i	$-0.917106\pi$
$263$	−19.8894	+	11.4832i	−1.22643	+	0.708082i	−0.260152	+	0.965568i	$0.583773\pi$
$264$		0			0
$265$			16.2159i			0.996135i
$266$		0			0
$267$	−8.60193			−0.526430
$268$		0			0
$269$	−5.55137	−	9.61526i	−0.338473	−	0.586253i	0.645672	−	0.763614i	$-0.276577\pi$
$269$	−5.55137	−	9.61526i	−0.338473	−	0.586253i	−0.984146	+	0.177362i	$0.943244\pi$
$270$		0			0
$271$	1.52264	−	2.63729i	0.0924937	−	0.160204i	−0.816066	−	0.577959i	$-0.803850\pi$
$271$	1.52264	−	2.63729i	0.0924937	−	0.160204i	0.908560	+	0.417755i	$0.137183\pi$
$272$		0			0
$273$	−8.80290	+	4.52192i	−0.532776	+	0.273679i
$274$		0			0
$275$	13.7981	−	23.8990i	0.832056	−	1.44116i
$276$		0			0
$277$	−18.6204	+	10.7505i	−1.11879	+	0.645936i	−0.941093	−	0.338148i	$-0.890199\pi$
$277$	−18.6204	+	10.7505i	−1.11879	+	0.645936i	−0.177702	+	0.984084i	$0.556866\pi$
$278$		0			0
$279$	−1.52642			−0.0913845
$280$		0			0
$281$	25.0868			1.49655			0.748276	−	0.663388i	$-0.230882\pi$
$281$	25.0868			1.49655			0.748276	+	0.663388i	$0.230882\pi$
$282$		0			0
$283$	10.1055	−	5.83439i	0.600707	−	0.346818i	−0.168613	−	0.985682i	$-0.553929\pi$
$283$	10.1055	−	5.83439i	0.600707	−	0.346818i	0.769320	+	0.638864i	$0.220595\pi$
$284$		0			0
$285$	9.07706	−	15.7219i	0.537679	−	0.931287i
$286$		0			0
$287$	0.236289	−	4.81220i	0.0139477	−	0.284055i
$288$		0			0
$289$	16.1204	−	27.9214i	0.948262	−	1.64244i
$290$		0			0
$291$	14.1118	+	24.4424i	0.827249	+	1.43284i
$292$		0			0
$293$	−22.2055			−1.29726			−0.648629	−	0.761104i	$-0.724658\pi$
$293$	−22.2055			−1.29726			−0.648629	+	0.761104i	$0.724658\pi$
$294$		0			0
$295$			11.6014i			0.675461i
$296$		0			0
$297$	−11.2985	+	6.52321i	−0.655607	+	0.378515i
$298$		0			0
$299$	9.71808	+	5.61073i	0.562011	+	0.324477i
$300$		0			0
$301$	18.3082	+	0.898971i	1.05527	+	0.0518158i
$302$		0			0
$303$	−14.4102	−	8.31974i	−0.827845	−	0.477956i
$304$		0			0
$305$	−15.2312	−	26.3812i	−0.872135	−	1.51058i
$306$		0			0
$307$		−	17.4136i		−	0.993849i	−0.867794	−	0.496924i	$-0.834463\pi$
$307$		−	17.4136i		−	0.993849i	0.867794	−	0.496924i	$-0.165537\pi$
$308$		0			0
$309$			18.4864i			1.05166i
$310$		0			0
$311$	−2.47993	−	4.29537i	−0.140624	−	0.243568i	0.787108	−	0.616816i	$-0.211578\pi$
$311$	−2.47993	−	4.29537i	−0.140624	−	0.243568i	−0.927732	+	0.373248i	$0.878244\pi$
$312$		0			0
$313$	−2.53367	−	1.46282i	−0.143212	−	0.0826833i	0.426682	−	0.904402i	$-0.359682\pi$
$313$	−2.53367	−	1.46282i	−0.143212	−	0.0826833i	−0.569894	+	0.821718i	$0.693016\pi$
$314$		0			0
$315$	1.27102	+	2.47431i	0.0716138	+	0.139412i
$316$		0			0
$317$	9.31220	+	5.37640i	0.523026	+	0.301969i	0.738172	−	0.674613i	$-0.235689\pi$
$317$	9.31220	+	5.37640i	0.523026	+	0.301969i	−0.215146	+	0.976582i	$0.569023\pi$
$318$		0			0
$319$	3.81306	−	2.20147i	0.213490	−	0.123259i
$320$		0			0
$321$		−	27.2357i		−	1.52015i
$322$		0			0
$323$	−18.9942			−1.05687
$324$		0			0
$325$	12.8946	+	22.3341i	0.715264	+	1.23887i
$326$		0			0
$327$	4.67301	−	8.09390i	0.258418	−	0.447594i
$328$		0			0
$329$	−9.72147	+	15.0784i	−0.535962	+	0.831297i
$330$		0			0
$331$	−17.2001	+	29.7914i	−0.945402	+	1.63748i	−0.190457	+	0.981696i	$0.560997\pi$
$331$	−17.2001	+	29.7914i	−0.945402	+	1.63748i	−0.754945	+	0.655788i	$0.772336\pi$
$332$		0			0
$333$	0.389266	−	0.224743i	0.0213316	−	0.0123158i
$334$		0			0
$335$	−45.2419			−2.47183
$336$		0			0
$337$	9.67314			0.526930			0.263465	−	0.964669i	$-0.415135\pi$
$337$	9.67314			0.526930			0.263465	+	0.964669i	$0.415135\pi$
$338$		0			0
$339$	9.71808	−	5.61073i	0.527813	−	0.304733i
$340$		0			0
$341$	−7.11073	+	12.3162i	−0.385068	+	0.666957i
$342$		0			0
$343$	18.3200	+	2.71612i	0.989187	+	0.146657i
$344$		0			0
$345$	−16.6541	+	28.8458i	−0.896628	+	1.55300i
$346$		0			0
$347$	−8.53982	−	14.7914i	−0.458442	−	0.794044i	0.540437	−	0.841384i	$-0.318259\pi$
$347$	−8.53982	−	14.7914i	−0.458442	−	0.794044i	−0.998879	+	0.0473400i	$0.984926\pi$
$348$		0			0
$349$	−4.63510			−0.248111			−0.124056	−	0.992275i	$-0.539590\pi$
$349$	−4.63510			−0.248111			−0.124056	+	0.992275i	$0.539590\pi$
$350$		0			0
$351$		−	12.1922i		−	0.650770i
$352$		0			0
$353$	−29.9760	+	17.3067i	−1.59546	+	0.921141i	−0.603118	+	0.797652i	$0.706075\pi$
$353$	−29.9760	+	17.3067i	−1.59546	+	0.921141i	−0.992346	+	0.123489i	$0.960592\pi$
$354$		0			0
$355$	−21.0516	−	12.1541i	−1.11730	−	0.645074i
$356$		0			0
$357$	−16.6541	+	25.8312i	−0.881430	+	1.36713i
$358$		0			0
$359$	4.97519	+	2.87243i	0.262581	+	0.151601i	0.625511	−	0.780215i	$-0.284890\pi$
$359$	4.97519	+	2.87243i	0.262581	+	0.151601i	−0.362931	+	0.931816i	$0.618224\pi$
$360$		0			0
$361$	−5.83657	−	10.1092i	−0.307188	−	0.532065i
$362$		0			0
$363$		−	8.53235i		−	0.447832i
$364$		0			0
$365$		−	12.5738i		−	0.658145i
$366$		0			0
$367$	2.39095	+	4.14125i	0.124807	+	0.216171i	0.921657	−	0.388005i	$-0.126836\pi$
$367$	2.39095	+	4.14125i	0.124807	+	0.216171i	−0.796851	+	0.604176i	$0.793502\pi$
$368$		0			0
$369$	0.409264	+	0.236289i	0.0213054	+	0.0123007i
$370$		0			0
$371$	−9.41968	+	4.83876i	−0.489045	+	0.251216i
$372$		0			0
$373$	−23.0634	−	13.3157i	−1.19418	−	0.689458i	−0.234926	−	0.972013i	$-0.575485\pi$
$373$	−23.0634	−	13.3157i	−1.19418	−	0.689458i	−0.959251	+	0.282555i	$0.908818\pi$
$374$		0			0
$375$	−37.2521	+	21.5075i	−1.92369	+	1.11064i
$376$		0			0
$377$			4.11464i			0.211915i
$378$		0			0
$379$	−22.7836			−1.17032			−0.585158	−	0.810920i	$-0.698967\pi$
$379$	−22.7836			−1.17032			−0.585158	+	0.810920i	$0.698967\pi$
$380$		0			0
$381$	13.4987	+	23.3804i	0.691558	+	1.19781i
$382$		0			0
$383$	−5.44777	+	9.43582i	−0.278368	+	0.482148i	−0.970979	−	0.239163i	$-0.923127\pi$
$383$	−5.44777	+	9.43582i	−0.278368	+	0.482148i	0.692611	+	0.721311i	$0.256460\pi$
$384$		0			0
$385$	25.8853	+	1.27102i	1.31924	+	0.0647771i
$386$		0			0
$387$	−0.898971	+	1.55706i	−0.0456973	+	0.0791500i
$388$		0			0
$389$	−13.0097	+	7.51116i	−0.659619	+	0.380831i	−0.792132	−	0.610350i	$-0.791029\pi$
$389$	−13.0097	+	7.51116i	−0.659619	+	0.380831i	0.132513	+	0.991181i	$0.457695\pi$
$390$		0			0
$391$	34.8496			1.76242
$392$		0			0
$393$	8.67314			0.437502
$394$		0			0
$395$	−15.6038	+	9.00885i	−0.785112	+	0.453284i
$396$		0			0
$397$	−9.52437	+	16.4967i	−0.478014	+	0.827945i	−0.999682	−	0.0252035i	$-0.991977\pi$
$397$	−9.52437	+	16.4967i	−0.478014	+	0.827945i	0.521668	+	0.853149i	$0.325310\pi$
$398$		0			0
$399$	11.8413	+	0.581431i	0.592806	+	0.0291079i
$400$		0			0
$401$	5.29853	−	9.17732i	0.264596	−	0.458294i	−0.702862	−	0.711326i	$-0.748095\pi$
$401$	5.29853	−	9.17732i	0.264596	−	0.458294i	0.967458	+	0.253033i	$0.0814281\pi$
$402$		0			0
$403$	−6.64514	−	11.5097i	−0.331018	−	0.573340i
$404$		0			0
$405$	33.0354			1.64154
$406$		0			0
$407$		−	4.18780i		−	0.207581i
$408$		0			0
$409$	12.7015	−	7.33320i	0.628047	−	0.362603i	−0.151948	−	0.988388i	$-0.548555\pi$
$409$	12.7015	−	7.33320i	0.628047	−	0.362603i	0.779995	+	0.625785i	$0.215221\pi$
$410$		0			0
$411$	17.4248	+	10.0602i	0.859503	+	0.496234i
$412$		0			0
$413$	−6.73917	+	3.46182i	−0.331613	+	0.170345i
$414$		0			0
$415$	13.6739	+	7.89461i	0.671224	+	0.387531i
$416$		0			0
$417$	8.70682	+	15.0806i	0.426375	+	0.738503i
$418$		0			0
$419$			7.82991i			0.382516i	0.981540	+	0.191258i	$0.0612567\pi$
$419$			7.82991i			0.382516i	−0.981540	+	0.191258i	$0.938743\pi$
$420$		0			0
$421$		−	14.3059i		−	0.697227i	−0.937267	−	0.348613i	$-0.886653\pi$
$421$		−	14.3059i		−	0.697227i	0.937267	−	0.348613i	$-0.113347\pi$
$422$		0			0
$423$	−0.879857	−	1.52396i	−0.0427801	−	0.0740973i
$424$		0			0
$425$	69.3613	+	40.0458i	3.36452	+	1.94251i
$426$		0			0
$427$	10.7797	−	16.7197i	0.521665	−	0.809123i
$428$		0			0
$429$	−7.83220	−	4.52192i	−0.378142	−	0.218321i
$430$		0			0
$431$	33.0133	−	19.0602i	1.59019	−	0.918099i	0.596921	−	0.802300i	$-0.296391\pi$
$431$	33.0133	−	19.0602i	1.59019	−	0.918099i	0.993273	−	0.115799i	$-0.0369427\pi$
$432$		0			0
$433$		−	17.9480i		−	0.862524i	−0.902227	−	0.431262i	$-0.858068\pi$
$433$		−	17.9480i		−	0.862524i	0.902227	−	0.431262i	$-0.141932\pi$
$434$		0			0
$435$	−12.2133			−0.585585
$436$		0			0
$437$	−6.72147	−	11.6419i	−0.321531	−	0.556909i
$438$		0			0
$439$	−11.6319	+	20.1470i	−0.555159	+	0.961564i	0.442732	+	0.896654i	$0.354009\pi$
$439$	−11.6319	+	20.1470i	−0.555159	+	0.961564i	−0.997891	+	0.0649099i	$0.979324\pi$
$440$		0			0
$441$	−1.05804	+	1.47665i	−0.0503829	+	0.0703166i
$442$		0			0
$443$	−0.0153299	+	0.0265521i	−0.000728343	+	0.00126153i	−0.866389	−	0.499369i	$-0.833565\pi$
$443$	−0.0153299	+	0.0265521i	−0.000728343	+	0.00126153i	0.865661	+	0.500631i	$0.166899\pi$
$444$		0			0
$445$	−18.2312	+	10.5258i	−0.864241	+	0.498970i
$446$		0			0
$447$	−24.8686			−1.17624
$448$		0			0
$449$	−22.7112			−1.07181			−0.535904	−	0.844279i	$-0.680029\pi$
$449$	−22.7112			−1.07181			−0.535904	+	0.844279i	$0.680029\pi$
$450$		0			0
$451$	3.81306	−	2.20147i	0.179550	−	0.103663i
$452$		0			0
$453$	−4.81088	+	8.33270i	−0.226035	+	0.391504i
$454$		0			0
$455$	−13.1239	+	20.3556i	−0.615256	+	0.954285i
$456$		0			0
$457$	2.79318	−	4.83794i	0.130660	−	0.226309i	−0.793271	−	0.608868i	$-0.791624\pi$
$457$	2.79318	−	4.83794i	0.130660	−	0.226309i	0.923931	+	0.382559i	$0.124957\pi$
$458$		0			0
$459$	−18.9321	−	32.7914i	−0.883676	−	1.53057i
$460$		0			0
$461$	23.2569			1.08318			0.541590	−	0.840643i	$-0.317822\pi$
$461$	23.2569			1.08318			0.541590	+	0.840643i	$0.317822\pi$
$462$		0			0
$463$			22.4517i			1.04342i	0.853124	+	0.521709i	$0.174705\pi$
$463$			22.4517i			1.04342i	−0.853124	+	0.521709i	$0.825295\pi$
$464$		0			0
$465$	34.1638	−	19.7245i	1.58431	−	0.914702i
$466$		0			0
$467$	−2.98317	−	1.72233i	−0.138045	−	0.0797001i	0.429387	−	0.903121i	$-0.358730\pi$
$467$	−2.98317	−	1.72233i	−0.138045	−	0.0797001i	−0.567432	+	0.823420i	$0.692063\pi$
$468$		0			0
$469$	−13.5000	−	26.2807i	−0.623372	−	1.21353i
$470$		0			0
$471$	−6.42418	−	3.70900i	−0.296011	−	0.170902i
$472$		0			0
$473$	8.37559	+	14.5069i	0.385110	+	0.667030i
$474$		0			0
$475$		−	30.8946i		−	1.41754i
$476$		0			0
$477$		−	1.03871i		−	0.0475592i
$478$		0			0
$479$	7.91237	+	13.7046i	0.361526	+	0.626181i	0.988212	−	0.153091i	$-0.0489227\pi$
$479$	7.91237	+	13.7046i	0.361526	+	0.626181i	−0.626687	+	0.779271i	$0.715589\pi$
$480$		0			0
$481$	3.38927	+	1.95679i	0.154537	+	0.0892221i
$482$		0			0
$483$	−21.7258	−	1.06678i	−0.988558	−	0.0485401i
$484$		0			0
$485$	59.8180	+	34.5359i	2.71619	+	1.56820i
$486$		0			0
$487$	4.24264	−	2.44949i	0.192252	−	0.110997i	−0.400784	−	0.916173i	$-0.631262\pi$
$487$	4.24264	−	2.44949i	0.192252	−	0.110997i	0.593037	+	0.805175i	$0.297929\pi$
$488$		0			0
$489$			24.2210i			1.09531i
$490$		0			0
$491$	−18.2426			−0.823276			−0.411638	−	0.911348i	$-0.635043\pi$
$491$	−18.2426			−0.823276			−0.411638	+	0.911348i	$0.635043\pi$
$492$		0			0
$493$	6.38927	+	11.0665i	0.287758	+	0.498412i
$494$		0			0
$495$	−1.27102	+	2.20147i	−0.0571281	+	0.0989487i
$496$		0			0
$497$	0.778532	−	15.8554i	0.0349219	−	0.711212i
$498$		0			0
$499$	8.09034	−	14.0129i	0.362173	−	0.627303i	−0.626145	−	0.779707i	$-0.715368\pi$
$499$	8.09034	−	14.0129i	0.362173	−	0.627303i	0.988318	+	0.152404i	$0.0487015\pi$
$500$		0			0
$501$	12.2882	−	7.09462i	0.548998	−	0.316964i
$502$		0			0
$503$	23.9541			1.06806			0.534030	−	0.845465i	$-0.320677\pi$
$503$	23.9541			1.06806			0.534030	+	0.845465i	$0.320677\pi$
$504$		0			0
$505$	−40.7219			−1.81210
$506$		0			0
$507$	−11.3182	+	6.53454i	−0.502657	+	0.290209i
$508$		0			0
$509$	−17.0257	+	29.4894i	−0.754650	+	1.30709i	0.190898	+	0.981610i	$0.438860\pi$
$509$	−17.0257	+	29.4894i	−0.754650	+	1.30709i	−0.945548	+	0.325483i	$0.894473\pi$
$510$		0			0
$511$	7.30404	−	3.75198i	0.323112	−	0.165978i
$512$		0			0
$513$	−7.30290	+	12.6490i	−0.322431	+	0.558467i
$514$		0			0
$515$	22.6210	+	39.1807i	0.996799	+	1.72651i
$516$		0			0
$517$	−16.3950			−0.721052
$518$		0			0
$519$		−	5.41800i		−	0.237824i
$520$		0			0
$521$	−1.34588	+	0.777043i	−0.0589640	+	0.0340429i	−0.529192	−	0.848502i	$-0.677505\pi$
$521$	−1.34588	+	0.777043i	−0.0589640	+	0.0340429i	0.470228	+	0.882545i	$0.344172\pi$
$522$		0			0
$523$	29.9403	+	17.2861i	1.30920	+	0.755867i	0.981963	−	0.189076i	$-0.0605491\pi$
$523$	29.9403	+	17.2861i	1.30920	+	0.755867i	0.327237	+	0.944942i	$0.393882\pi$
$524$		0			0
$525$	−42.0151	−	27.0884i	−1.83369	−	1.18223i
$526$		0			0
$527$	−35.7448	−	20.6373i	−1.55707	−	0.898974i
$528$		0			0
$529$	0.832203	+	1.44142i	0.0361827	+	0.0626703i
$530$		0			0
$531$		−	0.743129i		−	0.0322490i
$532$		0			0
$533$			4.11464i			0.178225i
$534$		0			0
$535$	−33.3270	−	57.7241i	−1.44085	−	2.49563i
$536$		0			0
$537$	−22.9093	−	13.2267i	−0.988608	−	0.570773i
$538$		0			0
$539$	6.98574	+	15.4158i	0.300897	+	0.664006i
$540$		0			0
$541$	7.67412	+	4.43066i	0.329936	+	0.190489i	0.655813	−	0.754924i	$-0.272326\pi$
$541$	7.67412	+	4.43066i	0.329936	+	0.190489i	−0.325877	+	0.945412i	$0.605659\pi$
$542$		0			0
$543$	34.0090	−	19.6351i	1.45947	−	0.842623i
$544$		0			0
$545$		−	22.8726i		−	0.979754i
$546$		0			0
$547$	7.12926			0.304825			0.152413	−	0.988317i	$-0.451296\pi$
$547$	7.12926			0.304825			0.152413	+	0.988317i	$0.451296\pi$
$548$		0			0
$549$	0.975633	+	1.68985i	0.0416390	+	0.0721208i
$550$		0			0
$551$	2.46460	−	4.26882i	0.104996	−	0.181858i
$552$		0			0
$553$	−9.88927	−	6.37590i	−0.420534	−	0.271131i
$554$		0			0
$555$	−5.80827	+	10.0602i	−0.246547	+	0.427033i
$556$		0			0
$557$	−23.0434	+	13.3041i	−0.976380	+	0.563713i	−0.901175	−	0.433455i	$-0.857294\pi$
$557$	−23.0434	+	13.3041i	−0.976380	+	0.563713i	−0.0752045	+	0.997168i	$0.523961\pi$
$558$		0			0
$559$	−15.6543			−0.662108
$560$		0			0
$561$	−28.0868			−1.18582
$562$		0			0
$563$	−19.9201	+	11.5009i	−0.839531	+	0.484704i	−0.857105	−	0.515142i	$-0.827739\pi$
$563$	−19.9201	+	11.5009i	−0.839531	+	0.484704i	0.0175735	+	0.999846i	$0.494406\pi$
$564$		0			0
$565$	13.7312	−	23.7831i	0.577675	−	1.00056i
$566$		0			0
$567$	9.85762	+	19.1900i	0.413981	+	0.805903i
$568$		0			0
$569$	−8.68780	+	15.0477i	−0.364211	+	0.630833i	−0.988649	−	0.150242i	$-0.951995\pi$
$569$	−8.68780	+	15.0477i	−0.364211	+	0.630833i	0.624438	+	0.781074i	$0.285328\pi$
$570$		0			0
$571$	−8.43930	−	14.6173i	−0.353174	−	0.611714i	0.633630	−	0.773636i	$-0.281564\pi$
$571$	−8.43930	−	14.6173i	−0.353174	−	0.611714i	−0.986804	+	0.161922i	$0.948231\pi$
$572$		0			0
$573$	13.4429			0.561587
$574$		0			0
$575$			56.6838i			2.36388i
$576$		0			0
$577$	1.50000	−	0.866025i	0.0624458	−	0.0360531i	−0.468452	−	0.883489i	$-0.655188\pi$
$577$	1.50000	−	0.866025i	0.0624458	−	0.0360531i	0.530898	+	0.847436i	$0.321855\pi$
$578$		0			0
$579$	−3.92892	−	2.26836i	−0.163280	−	0.0942699i
$580$		0			0
$581$	−0.505689	+	10.2988i	−0.0209795	+	0.427264i
$582$		0			0
$583$	−8.38097	−	4.83876i	−0.347104	−	0.200401i
$584$		0			0
$585$	−1.18780	−	2.05732i	−0.0491093	−	0.0850598i
$586$		0			0
$587$		−	36.0354i		−	1.48734i	−0.668547	−	0.743670i	$-0.733083\pi$
$587$		−	36.0354i		−	1.48734i	0.668547	−	0.743670i	$-0.266917\pi$
$588$		0			0
$589$			15.9213i			0.656026i
$590$		0			0
$591$	−9.51245	−	16.4760i	−0.391290	−	0.677734i
$592$		0			0
$593$	−9.64045	−	5.56592i	−0.395886	−	0.228565i	0.288821	−	0.957383i	$-0.406737\pi$
$593$	−9.64045	−	5.56592i	−0.395886	−	0.228565i	−0.684707	+	0.728818i	$0.740070\pi$
$594$		0			0
$595$	−3.68884	+	75.1262i	−0.151228	+	3.07987i
$596$		0			0
$597$	−24.6204	−	14.2146i	−1.00765	−	0.581766i
$598$		0			0
$599$	25.6195	−	14.7914i	1.04678	−	0.604361i	0.125036	−	0.992152i	$-0.460095\pi$
$599$	25.6195	−	14.7914i	1.04678	−	0.604361i	0.921747	+	0.387792i	$0.126762\pi$
$600$		0			0
$601$		−	23.9772i		−	0.978050i	−0.872270	−	0.489025i	$-0.837353\pi$
$601$		−	23.9772i		−	0.978050i	0.872270	−	0.489025i	$-0.162647\pi$
$602$		0			0
$603$	2.89797			0.118014
$604$		0			0
$605$	−10.4406	−	18.0837i	−0.424472	−	0.735208i
$606$		0			0
$607$	−11.9034	+	20.6173i	−0.483144	+	0.836830i	−0.999813	−	0.0193555i	$-0.993839\pi$
$607$	−11.9034	+	20.6173i	−0.483144	+	0.836830i	0.516669	+	0.856185i	$0.327172\pi$
$608$		0			0
$609$	−3.64441	−	7.09462i	−0.147679	−	0.287489i
$610$		0			0
$611$	7.66075	−	13.2688i	0.309921	−	0.536799i
$612$		0			0
$613$	30.7946	−	17.7793i	1.24378	−	0.718097i	0.273919	−	0.961753i	$-0.411680\pi$
$613$	30.7946	−	17.7793i	1.24378	−	0.718097i	0.969862	+	0.243655i	$0.0783466\pi$
$614$		0			0
$615$	−12.2133			−0.492489
$616$		0			0
$617$	−14.8459			−0.597673			−0.298836	−	0.954304i	$-0.596598\pi$
$617$	−14.8459			−0.597673			−0.298836	+	0.954304i	$0.596598\pi$
$618$		0			0
$619$	39.6584	−	22.8968i	1.59401	−	0.920300i	0.601396	−	0.798951i	$-0.294611\pi$
$619$	39.6584	−	22.8968i	1.59401	−	0.920300i	0.992610	−	0.121349i	$-0.0387221\pi$
$620$		0			0
$621$	13.3990	−	23.2077i	0.537683	−	0.931294i
$622$		0			0
$623$	−11.5544	−	7.44949i	−0.462919	−	0.298458i
$624$		0			0
$625$	−24.1014	+	41.7449i	−0.964057	+	1.66980i
$626$		0			0
$627$	5.41711	+	9.38271i	0.216339	+	0.374709i
$628$		0			0
$629$	12.1541			0.484617
$630$		0			0
$631$			6.51902i			0.259518i	0.991546	+	0.129759i	$0.0414204\pi$
$631$			6.51902i			0.259518i	−0.991546	+	0.129759i	$0.958580\pi$
$632$		0			0
$633$	39.5634	−	22.8419i	1.57250	−	0.907885i
$634$		0			0
$635$	57.2190	+	33.0354i	2.27067	+	1.31097i
$636$		0			0
$637$	−15.7405	−	1.54951i	−0.623661	−	0.0613940i
$638$		0			0
$639$	1.34846	+	0.778532i	0.0533441	+	0.0307982i
$640$		0			0
$641$	−4.65412	−	8.06118i	−0.183827	−	0.318397i	0.759354	−	0.650678i	$-0.225515\pi$
$641$	−4.65412	−	8.06118i	−0.183827	−	0.318397i	−0.943181	+	0.332281i	$0.892182\pi$
$642$		0			0
$643$		−	26.4517i		−	1.04315i	−0.853205	−	0.521576i	$-0.825344\pi$
$643$		−	26.4517i		−	1.04315i	0.853205	−	0.521576i	$-0.174656\pi$
$644$		0			0
$645$		−	46.4662i		−	1.82960i
$646$		0			0
$647$	−4.30097	−	7.44949i	−0.169088	−	0.292870i	0.769011	−	0.639235i	$-0.220749\pi$
$647$	−4.30097	−	7.44949i	−0.169088	−	0.292870i	−0.938100	+	0.346366i	$0.887416\pi$
$648$		0			0
$649$	−5.99604	−	3.46182i	−0.235365	−	0.135888i
$650$		0			0
$651$	21.6521	+	13.9598i	0.848614	+	0.547127i
$652$		0			0
$653$	14.5337	+	8.39102i	0.568747	+	0.328366i	0.756649	−	0.653822i	$-0.226835\pi$
$653$	14.5337	+	8.39102i	0.568747	+	0.328366i	−0.187902	+	0.982188i	$0.560169\pi$
$654$		0			0
$655$	18.3821	−	10.6129i	0.718249	−	0.414681i
$656$		0			0
$657$			0.805417i			0.0314223i
$658$		0			0
$659$	−7.94382			−0.309447			−0.154724	−	0.987958i	$-0.549449\pi$
$659$	−7.94382			−0.309447			−0.154724	+	0.987958i	$0.549449\pi$
$660$		0			0
$661$	−3.91363	−	6.77861i	−0.152223	−	0.263657i	0.779822	−	0.626002i	$-0.215310\pi$
$661$	−3.91363	−	6.77861i	−0.152223	−	0.263657i	−0.932044	+	0.362344i	$0.881976\pi$
$662$		0			0
$663$	13.1239	−	22.7312i	0.509688	−	0.882806i
$664$		0			0
$665$	25.8082	−	13.2573i	1.00080	−	0.514097i
$666$		0			0
$667$	−4.52192	+	7.83220i	−0.175090	+	0.303264i
$668$		0			0
$669$	18.4093	−	10.6286i	0.711743	−	0.410925i
$670$		0			0
$671$	18.1797			0.701819
$672$		0			0
$673$	6.71119			0.258697			0.129349	−	0.991599i	$-0.458711\pi$
$673$	6.71119			0.258697			0.129349	+	0.991599i	$0.458711\pi$
$674$		0			0
$675$	53.3361	−	30.7936i	2.05291	−	1.18525i
$676$		0			0
$677$	−9.05936	+	15.6913i	−0.348179	+	0.603065i	−0.985926	−	0.167182i	$-0.946533\pi$
$677$	−9.05936	+	15.6913i	−0.348179	+	0.603065i	0.637747	+	0.770246i	$0.279867\pi$
$678$		0			0
$679$	−2.21220	+	45.0531i	−0.0848963	+	1.72898i
$680$		0			0
$681$	8.46196	−	14.6565i	0.324263	−	0.561640i
$682$		0			0
$683$	−2.04199	−	3.53683i	−0.0781347	−	0.135333i	0.824310	−	0.566138i	$-0.191563\pi$
$683$	−2.04199	−	3.53683i	−0.0781347	−	0.135333i	−0.902445	+	0.430805i	$0.858230\pi$
$684$		0			0
$685$	49.2409			1.88140
$686$		0			0
$687$		−	11.1585i		−	0.425723i
$688$		0			0
$689$	7.83220	−	4.52192i	0.298383	−	0.172272i
$690$		0			0
$691$	30.0409	+	17.3441i	1.14281	+	0.659801i	0.947125	−	0.320866i	$-0.103974\pi$
$691$	30.0409	+	17.3441i	1.14281	+	0.659801i	0.195684	+	0.980667i	$0.437307\pi$
$692$		0			0
$693$	−1.65808	−	0.0814151i	−0.0629853	−	0.00309270i
$694$		0			0
$695$	36.9070	+	21.3082i	1.39996	+	0.808268i
$696$		0			0
$697$	6.38927	+	11.0665i	0.242011	+	0.419175i
$698$		0			0
$699$		−	16.1878i		−	0.612279i
$700$		0			0
$701$		−	39.1821i		−	1.47989i	−0.672670	−	0.739943i	$-0.734852\pi$
$701$		−	39.1821i		−	1.47989i	0.672670	−	0.739943i	$-0.265148\pi$
$702$		0			0
$703$	−2.34417	−	4.06022i	−0.0884121	−	0.153134i
$704$		0			0
$705$	39.3853	+	22.7391i	1.48334	+	0.856405i
$706$		0			0
$707$	−12.1512	−	23.6550i	−0.456994	−	0.889637i
$708$		0			0
$709$	−0.721468	−	0.416540i	−0.0270953	−	0.0156435i	0.486391	−	0.873741i	$-0.338313\pi$
$709$	−0.721468	−	0.416540i	−0.0270953	−	0.0156435i	−0.513486	+	0.858098i	$0.671646\pi$
$710$		0			0
$711$	0.999500	−	0.577061i	0.0374842	−	0.0216415i
$712$		0			0
$713$		−	29.2116i		−	1.09398i
$714$		0			0
$715$	−22.1331			−0.827730
$716$		0			0
$717$	−14.5097	−	25.1316i	−0.541875	−	0.938555i
$718$		0			0
$719$	13.1085	−	22.7046i	0.488866	−	0.846740i	−0.511052	−	0.859550i	$-0.670744\pi$
$719$	13.1085	−	22.7046i	0.488866	−	0.846740i	0.999918	+	0.0128096i	$0.00407755\pi$
$720$		0			0
$721$	−16.0097	+	24.8317i	−0.596233	+	0.924780i
$722$		0			0
$723$	0.689558	−	1.19435i	0.0256449	−	0.0444183i
$724$		0			0
$725$	−18.0000	+	10.3923i	−0.668503	+	0.385961i
$726$		0			0
$727$	−45.0946			−1.67247			−0.836234	−	0.548373i	$-0.815247\pi$
$727$	−45.0946			−1.67247			−0.836234	+	0.548373i	$0.815247\pi$
$728$		0			0
$729$	−28.9140			−1.07089
$730$		0			0
$731$	−42.1031	+	24.3082i	−1.55724	+	0.899073i
$732$		0			0
$733$	−8.72584	+	15.1136i	−0.322296	+	0.558233i	−0.980961	−	0.194203i	$-0.937788\pi$
$733$	−8.72584	+	15.1136i	−0.322296	+	0.558233i	0.658665	+	0.752436i	$0.271121\pi$
$734$		0			0
$735$	4.59936	−	46.7219i	0.169650	−	1.72336i
$736$		0			0
$737$	13.5000	−	23.3827i	0.497279	−	0.861312i
$738$		0			0
$739$	−4.13455	−	7.16124i	−0.152092	−	0.263431i	0.779905	−	0.625898i	$-0.215268\pi$
$739$	−4.13455	−	7.16124i	−0.152092	−	0.263431i	−0.931996	+	0.362468i	$0.881934\pi$
$740$		0			0
$741$	−10.1248			−0.371945
$742$		0			0
$743$			13.8653i			0.508669i	0.967116	+	0.254334i	$0.0818564\pi$
$743$			13.8653i			0.508669i	−0.967116	+	0.254334i	$0.918144\pi$
$744$		0			0
$745$	−52.7072	+	30.4305i	−1.93104	+	1.11489i
$746$		0			0
$747$	−0.875879	−	0.505689i	−0.0320467	−	0.0185022i
$748$		0			0
$749$	23.5868	−	36.5840i	0.861842	−	1.33675i
$750$		0			0
$751$	−1.89469	−	1.09390i	−0.0691381	−	0.0399169i	0.465032	−	0.885294i	$-0.346043\pi$
$751$	−1.89469	−	1.09390i	−0.0691381	−	0.0399169i	−0.534171	+	0.845377i	$0.679376\pi$
$752$		0			0
$753$	11.0287	+	19.1023i	0.401910	+	0.696128i
$754$		0			0
$755$			23.5474i			0.856978i
$756$		0			0
$757$		−	34.9739i		−	1.27115i	−0.772041	−	0.635573i	$-0.780764\pi$
$757$		−	34.9739i		−	1.27115i	0.772041	−	0.635573i	$-0.219236\pi$
$758$		0			0
$759$	−9.93904	−	17.2149i	−0.360764	−	0.624862i
$760$		0			0
$761$	−8.41266	−	4.85705i	−0.304959	−	0.176068i	0.339710	−	0.940530i	$-0.389671\pi$
$761$	−8.41266	−	4.85705i	−0.304959	−	0.176068i	−0.644668	+	0.764462i	$0.723004\pi$
$762$		0			0
$763$	13.2865	−	6.82508i	0.481003	−	0.247085i
$764$		0			0
$765$	−6.38927	−	3.68884i	−0.231004	−	0.133370i
$766$		0			0
$767$	5.60343	−	3.23514i	0.202328	−	0.116814i
$768$		0			0
$769$			34.4308i			1.24161i	0.783966	+	0.620803i	$0.213194\pi$
$769$			34.4308i			1.24161i	−0.783966	+	0.620803i	$0.786806\pi$
$770$		0			0
$771$	−17.6458			−0.635497
$772$		0			0
$773$	20.3339	+	35.2194i	0.731361	+	1.26675i	0.956302	+	0.292382i	$0.0944477\pi$
$773$	20.3339	+	35.2194i	0.731361	+	1.26675i	−0.224941	+	0.974372i	$0.572219\pi$
$774$		0			0
$775$	33.5671	−	58.1399i	1.20576	−	2.08845i
$776$		0			0
$777$	−7.57706	−	0.372049i	−0.271826	−	0.0133472i
$778$		0			0
$779$	2.46460	−	4.26882i	0.0883035	−	0.152946i
$780$		0			0
$781$	12.5634	−	7.25347i	0.449553	−	0.259550i
$782$		0			0
$783$	9.82617			0.351159
$784$		0			0
$785$	−18.1541			−0.647948
$786$		0			0
$787$	−29.3320	+	16.9348i	−1.04557	+	0.603662i	−0.921407	−	0.388600i	$-0.872959\pi$
$787$	−29.3320	+	16.9348i	−1.04557	+	0.603662i	−0.124166	+	0.992261i	$0.539626\pi$
$788$		0			0
$789$	−19.0097	+	32.9258i	−0.676764	+	1.17219i
$790$		0			0
$791$	17.9127	+	0.879550i	0.636903	+	0.0312732i
$792$		0			0
$793$	−8.49465	+	14.7132i	−0.301654	+	0.522480i
$794$		0			0
$795$	13.4223	+	23.2480i	0.476038	+	0.824522i
$796$		0			0
$797$	40.4737			1.43365			0.716827	−	0.697251i	$-0.245594\pi$
$797$	40.4737			1.43365			0.716827	+	0.697251i	$0.245594\pi$
$798$		0			0
$799$		−	47.5828i		−	1.68336i
$800$		0			0
$801$	1.16780	−	0.674228i	0.0412621	−	0.0238227i
$802$		0			0
$803$	6.49862	+	3.75198i	0.229331	+	0.132404i
$804$		0			0
$805$	−47.3516	+	24.3239i	−1.66893	+	0.857304i
$806$		0			0
$807$	−15.9175	−	9.18998i	−0.560323	−	0.323503i
$808$		0			0
$809$	−3.46633	−	6.00385i	−0.121870	−	0.211084i	0.798635	−	0.601815i	$-0.205556\pi$
$809$	−3.46633	−	6.00385i	−0.121870	−	0.211084i	−0.920505	+	0.390731i	$0.872222\pi$
$810$		0			0
$811$			22.1648i			0.778312i	0.921172	+	0.389156i	$0.127233\pi$
$811$			22.1648i			0.778312i	−0.921172	+	0.389156i	$0.872767\pi$
$812$		0			0
$813$		−	5.04128i		−	0.176805i
$814$		0			0
$815$	29.6382	+	51.3348i	1.03818	+	1.79818i
$816$		0			0
$817$	16.2409	+	9.37669i	0.568197	+	0.328049i
$818$		0			0
$819$	0.840648	−	1.30388i	0.0293746	−	0.0455611i
$820$		0			0
$821$	29.9760	+	17.3067i	1.04617	+	0.604007i	0.921575	−	0.388200i	$-0.126903\pi$
$821$	29.9760	+	17.3067i	1.04617	+	0.604007i	0.124596	+	0.992208i	$0.460236\pi$
$822$		0			0
$823$	−38.7011	+	22.3441i	−1.34904	+	0.778866i	−0.988113	−	0.153729i	$-0.950872\pi$
$823$	−38.7011	+	22.3441i	−1.34904	+	0.778866i	−0.360923	+	0.932596i	$0.617538\pi$
$824$		0			0
$825$		−	45.6839i		−	1.59051i
$826$		0			0
$827$	−24.4267			−0.849399			−0.424699	−	0.905334i	$-0.639620\pi$
$827$	−24.4267			−0.849399			−0.424699	+	0.905334i	$0.639620\pi$
$828$		0			0
$829$	15.3702	+	26.6220i	0.533831	+	0.924622i	0.999219	+	0.0395152i	$0.0125814\pi$
$829$	15.3702	+	26.6220i	0.533831	+	0.924622i	−0.465388	+	0.885107i	$0.654085\pi$
$830$		0			0
$831$	−17.7969	+	30.8251i	−0.617367	+	1.06931i
$832$		0			0
$833$	−44.7409	+	20.2745i	−1.55018	+	0.702470i
$834$		0			0
$835$	17.3627	−	30.0731i	0.600861	−	1.04072i
$836$		0			0
$837$	−27.4863	+	15.8692i	−0.950066	+	0.548521i
$838$		0			0
$839$	17.1425			0.591826			0.295913	−	0.955215i	$-0.404376\pi$
$839$	17.1425			0.591826			0.295913	+	0.955215i	$0.404376\pi$
$840$		0			0
$841$	25.6838			0.885650
$842$		0			0
$843$	35.9658	−	20.7649i	1.23873	−	0.715180i
$844$		0			0
$845$	−15.9920	+	27.6990i	−0.550142	+	0.952874i
$846$		0			0
$847$	7.38923	−	11.4610i	0.253897	−	0.393804i
$848$		0			0
$849$	9.65849	−	16.7290i	0.331479	−	0.574138i
$850$		0			0
$851$	4.30097	+	7.44949i	0.147435	+	0.255365i
$852$		0			0
$853$	−5.60580			−0.191939			−0.0959694	−	0.995384i	$-0.530595\pi$
$853$	−5.60580			−0.191939			−0.0959694	+	0.995384i	$0.530595\pi$
$854$		0			0
$855$			2.84588i			0.0973269i
$856$		0			0
$857$	22.5531	−	13.0210i	0.770399	−	0.444790i	−0.0626177	−	0.998038i	$-0.519945\pi$
$857$	22.5531	−	13.0210i	0.770399	−	0.444790i	0.833017	+	0.553247i	$0.186612\pi$
$858$		0			0
$859$	−40.5996	−	23.4402i	−1.38524	−	0.799769i	−0.392466	−	0.919767i	$-0.628378\pi$
$859$	−40.5996	−	23.4402i	−1.38524	−	0.799769i	−0.992774	+	0.119998i	$0.961711\pi$
$860$		0			0
$861$	−3.64441	−	7.09462i	−0.124201	−	0.241784i
$862$		0			0
$863$	−25.0856	−	14.4832i	−0.853923	−	0.493013i	0.00804962	−	0.999968i	$-0.497438\pi$
$863$	−25.0856	−	14.4832i	−0.853923	−	0.493013i	−0.861973	+	0.506955i	$0.830771\pi$
$864$		0			0
$865$	−6.62976	−	11.4831i	−0.225418	−	0.390436i
$866$		0			0
$867$		−	53.3730i		−	1.81264i
$868$		0			0
$869$		−	10.7528i		−	0.364764i
$870$		0			0
$871$	12.6160	+	21.8516i	0.427478	+	0.740414i
$872$		0			0
$873$	−3.83164	−	2.21220i	−0.129681	−	0.0748715i
$874$		0			0
$875$	−68.6646	−	3.37156i	−2.32129	−	0.113980i
$876$		0			0
$877$	−40.4721	−	23.3666i	−1.36665	−	0.789033i	−0.376147	−	0.926560i	$-0.622751\pi$
$877$	−40.4721	−	23.3666i	−1.36665	−	0.789033i	−0.990498	+	0.137527i	$0.956085\pi$
$878$		0			0
$879$	−31.8350	+	18.3800i	−1.07377	+	0.619941i
$880$		0			0
$881$			24.8993i			0.838877i	0.907784	+	0.419439i	$0.137773\pi$
$881$			24.8993i			0.838877i	−0.907784	+	0.419439i	$0.862227\pi$
$882$		0			0
$883$	28.4951			0.958938			0.479469	−	0.877559i	$-0.340829\pi$
$883$	28.4951			0.958938			0.479469	+	0.877559i	$0.340829\pi$
$884$		0			0
$885$	9.60275	+	16.6324i	0.322793	+	0.559094i
$886$		0			0
$887$	−17.8974	+	30.9992i	−0.600936	+	1.04085i	0.391744	+	0.920074i	$0.371872\pi$
$887$	−17.8974	+	30.9992i	−0.600936	+	1.04085i	−0.992680	+	0.120777i	$0.961461\pi$
$888$		0			0
$889$	−2.11608	+	43.0956i	−0.0709711	+	1.44538i
$890$		0			0
$891$	−9.85762	+	17.0739i	−0.330243	+	0.571997i
$892$		0			0
$893$	−15.8956	+	9.17732i	−0.531926	+	0.307107i
$894$		0			0
$895$	−64.7394			−2.16400
$896$		0			0
$897$	18.5765			0.620251
$898$		0			0
$899$	9.27616	−	5.35559i	0.309377	−	0.178619i
$900$		0			0
$901$	14.0434	−	24.3239i	0.467853	−	0.810345i
$902$		0			0
$903$	26.9918	−	13.8653i	0.898231	−	0.461409i
$904$		0			0
$905$	48.0531	−	83.2304i	1.59734	−	2.76667i
$906$		0			0
$907$	25.5351	+	44.2280i	0.847878	+	1.46857i	0.883098	+	0.469188i	$0.155453\pi$
$907$	25.5351	+	44.2280i	0.847878	+	1.46857i	−0.0352206	+	0.999380i	$0.511213\pi$
$908$		0			0
$909$	2.60844			0.0865164
$910$		0			0
$911$			52.2409i			1.73082i	0.501066	+	0.865409i	$0.332941\pi$
$911$			52.2409i			1.73082i	−0.501066	+	0.865409i	$0.667059\pi$
$912$		0			0
$913$	−8.16045	+	4.71144i	−0.270071	+	0.155926i
$914$		0			0
$915$	−43.6725	−	25.2143i	−1.44377	−	0.833561i
$916$		0			0
$917$	11.6501	+	7.51116i	0.384720	+	0.248040i
$918$		0			0
$919$	31.6724	+	18.2861i	1.04478	+	0.603202i	0.921182	−	0.389131i	$-0.127225\pi$
$919$	31.6724	+	18.2861i	1.04478	+	0.603202i	0.123593	+	0.992333i	$0.460558\pi$
$920$		0			0
$921$	−14.4136	−	24.9651i	−0.474945	−	0.822630i
$922$		0			0
$923$			13.5571i			0.446236i
$924$		0			0
$925$			19.7690i			0.650000i
$926$		0			0
$927$	−1.44899	−	2.50972i	−0.0475909	−	0.0824299i
$928$		0			0
$929$	10.7551	+	6.20948i	0.352865	+	0.203727i	0.665946	−	0.746000i	$-0.268028\pi$
$929$	10.7551	+	6.20948i	0.352865	+	0.203727i	−0.313082	+	0.949726i	$0.601361\pi$
$930$		0			0
$931$	15.4021	+	11.0359i	0.504785	+	0.361686i
$932$		0			0
$933$	−7.11073	−	4.10538i	−0.232795	−	0.134404i
$934$		0			0
$935$	−59.5279	+	34.3685i	−1.94677	+	1.12397i
$936$		0			0
$937$		−	49.2093i		−	1.60760i	−0.594901	−	0.803799i	$-0.702809\pi$
$937$		−	49.2093i		−	1.60760i	0.594901	−	0.803799i	$-0.297191\pi$
$938$		0			0
$939$	−4.84322			−0.158052
$940$		0			0
$941$	22.8259	+	39.5357i	0.744105	+	1.28883i	0.950612	+	0.310382i	$0.100457\pi$
$941$	22.8259	+	39.5357i	0.744105	+	1.28883i	−0.206507	+	0.978445i	$0.566210\pi$
$942$		0			0
$943$	−4.52192	+	7.83220i	−0.147254	+	0.255052i
$944$		0			0
$945$	48.6111	+	31.3410i	1.58132	+	1.01952i
$946$		0			0
$947$	−0.329055	+	0.569941i	−0.0106929	+	0.0185206i	−0.871322	−	0.490711i	$-0.836737\pi$
$947$	−0.329055	+	0.569941i	−0.0106929	+	0.0185206i	0.860629	+	0.509232i	$0.170070\pi$
$948$		0			0
$949$	−6.07310	+	3.50631i	−0.197141	+	0.113820i
$950$		0			0
$951$	17.8007			0.577226
$952$		0			0
$953$	49.7033			1.61005			0.805023	−	0.593243i	$-0.202153\pi$
$953$	49.7033			1.61005			0.805023	+	0.593243i	$0.202153\pi$
$954$		0			0
$955$	28.4914	−	16.4495i	0.921959	−	0.532293i
$956$		0			0
$957$	3.64441	−	6.31230i	0.117807	−	0.204048i
$958$		0			0
$959$	14.6933	+	28.6036i	0.474470	+	0.923659i
$960$		0			0
$961$	−1.79853	+	3.11514i	−0.0580171	+	0.100489i
$962$		0			0
$963$	2.13476	+	3.69751i	0.0687917	+	0.119151i
$964$		0			0
$965$	−11.1027			−0.357410
$966$		0			0
$967$		−	14.7512i		−	0.474366i	−0.971465	−	0.237183i	$-0.923776\pi$
$967$		−	14.7512i		−	0.474366i	0.971465	−	0.237183i	$-0.0762241\pi$
$968$		0			0
$969$	−27.2312	+	15.7219i	−0.874792	+	0.505061i
$970$		0			0
$971$	−5.04049	−	2.91013i	−0.161757	−	0.0933905i	0.416936	−	0.908936i	$-0.363104\pi$
$971$	−5.04049	−	2.91013i	−0.161757	−	0.0933905i	−0.578693	+	0.815545i	$0.696437\pi$
$972$		0			0
$973$	−1.36490	+	27.7972i	−0.0437566	+	0.891138i
$974$		0			0
$975$	36.9729	+	21.3463i	1.18408	+	0.683628i
$976$		0			0
$977$	14.0434	+	24.3239i	0.449288	+	0.778189i	0.998340	−	0.0575989i	$-0.0183444\pi$
$977$	14.0434	+	24.3239i	0.449288	+	0.778189i	−0.549052	+	0.835788i	$0.685011\pi$
$978$		0			0
$979$		−	12.5634i		−	0.401528i
$980$		0			0
$981$			1.46510i			0.0467771i
$982$		0			0
$983$	2.04199	+	3.53683i	0.0651294	+	0.112808i	0.896751	−	0.442535i	$-0.145921\pi$
$983$	2.04199	+	3.53683i	0.0651294	+	0.112808i	−0.831622	+	0.555342i	$0.812587\pi$
$984$		0			0
$985$	−40.3219	−	23.2799i	−1.28476	−	0.741758i
$986$		0			0
$987$	−1.45655	+	29.6638i	−0.0463626	+	0.944210i
$988$		0			0
$989$	−29.7980	−	17.2039i	−0.947520	−	0.547051i
$990$		0			0
$991$	2.05354	−	1.18561i	0.0652328	−	0.0376622i	−0.467029	−	0.884242i	$-0.654676\pi$
$991$	2.05354	−	1.18561i	0.0652328	−	0.0376622i	0.532262	+	0.846580i	$0.321342\pi$
$992$		0			0
$993$			56.9475i			1.80717i
$994$		0			0
$995$	−69.5751			−2.20568
$996$		0			0
$997$	−7.46196	−	12.9245i	−0.236323	−	0.409323i	0.723334	−	0.690499i	$-0.242609\pi$
$997$	−7.46196	−	12.9245i	−0.236323	−	0.409323i	−0.959656	+	0.281176i	$0.909276\pi$
$998$		0			0
$999$	4.67301	−	8.09390i	0.147848	−	0.256080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.q.c.159.5	yes	12
4.3	odd	2	inner	448.2.q.c.159.2	yes	12
7.2	even	3		3136.2.e.d.1567.9		12
7.3	odd	6		448.2.q.b.31.5	yes	12
7.5	odd	6		3136.2.e.e.1567.3		12
8.3	odd	2		448.2.q.b.159.5	yes	12
8.5	even	2		448.2.q.b.159.2	yes	12
28.3	even	6		448.2.q.b.31.2	✓	12
28.19	even	6		3136.2.e.e.1567.10		12
28.23	odd	6		3136.2.e.d.1567.4		12
56.3	even	6	inner	448.2.q.c.31.5	yes	12
56.5	odd	6		3136.2.e.d.1567.10		12
56.19	even	6		3136.2.e.d.1567.3		12
56.37	even	6		3136.2.e.e.1567.4		12
56.45	odd	6	inner	448.2.q.c.31.2	yes	12
56.51	odd	6		3136.2.e.e.1567.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
448.2.q.b.31.2	✓	12	28.3	even	6
448.2.q.b.31.5	yes	12	7.3	odd	6
448.2.q.b.159.2	yes	12	8.5	even	2
448.2.q.b.159.5	yes	12	8.3	odd	2
448.2.q.c.31.2	yes	12	56.45	odd	6	inner
448.2.q.c.31.5	yes	12	56.3	even	6	inner
448.2.q.c.159.2	yes	12	4.3	odd	2	inner
448.2.q.c.159.5	yes	12	1.1	even	1	trivial
3136.2.e.d.1567.3		12	56.19	even	6
3136.2.e.d.1567.4		12	28.23	odd	6
3136.2.e.d.1567.9		12	7.2	even	3
3136.2.e.d.1567.10		12	56.5	odd	6
3136.2.e.e.1567.3		12	7.5	odd	6
3136.2.e.e.1567.4		12	56.37	even	6
3136.2.e.e.1567.9		12	56.51	odd	6
3136.2.e.e.1567.10		12	28.19	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43366 - 0.827721i) q^{3} +(2.02569 - 3.50859i) q^{5} +(2.64257 + 0.129755i) q^{7} +(-0.129755 + 0.224743i) q^{9} +O(q^{10})\)	\(q+(1.43366 - 0.827721i) q^{3} +(2.02569 - 3.50859i) q^{5} +(2.64257 + 0.129755i) q^{7} +(-0.129755 + 0.224743i) q^{9} +(1.20891 + 2.09390i) q^{11} -2.25951 q^{13} -6.70682i q^{15} +(-6.07706 + 3.50859i) q^{17} +(2.34417 + 1.35341i) q^{19} +(3.89593 - 2.00128i) q^{21} +(-4.30097 - 2.48316i) q^{23} +(-5.70682 - 9.88450i) q^{25} +5.39593i q^{27} -1.82103i q^{29} +(2.94096 + 5.09390i) q^{31} +(3.46633 + 2.00128i) q^{33} +(5.80827 - 9.00885i) q^{35} +(-1.50000 - 0.866025i) q^{37} +(-3.23936 + 1.87024i) q^{39} -1.82103i q^{41} +6.92820 q^{43} +(0.525687 + 0.910517i) q^{45} +(-3.39045 + 5.87243i) q^{47} +(6.96633 + 0.685774i) q^{49} +(-5.80827 + 10.0602i) q^{51} +(-3.46633 + 2.00128i) q^{53} +9.79551 q^{55} +4.48098 q^{57} +(-2.47993 + 1.43179i) q^{59} +(3.75951 - 6.51166i) q^{61} +(-0.372049 + 0.577061i) q^{63} +(-4.57706 + 7.92770i) q^{65} +(-5.58353 - 9.67096i) q^{67} -8.22147 q^{69} -6.00000i q^{71} +(2.68780 - 1.55180i) q^{73} +(-16.3632 - 9.44731i) q^{75} +(2.92294 + 5.69013i) q^{77} +(-3.85148 - 2.22365i) q^{79} +(4.07706 + 7.06168i) q^{81} +3.89725i q^{83} +28.4292i q^{85} +(-1.50731 - 2.61073i) q^{87} +(-4.50000 - 2.59808i) q^{89} +(-5.97091 - 0.293183i) q^{91} +(8.43265 + 4.86860i) q^{93} +(9.49712 - 5.48316i) q^{95} +17.0490i q^{97} -0.627451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} + 4 q^{9}+O(q^{10}) \) 12 * q + 6 * q^5 + 4 * q^9	\( 12 q + 6 q^{5} + 4 q^{9} - 16 q^{13} - 18 q^{17} + 34 q^{21} - 8 q^{25} - 30 q^{33} - 18 q^{37} - 12 q^{45} + 12 q^{49} + 30 q^{53} + 76 q^{57} + 34 q^{61} - 132 q^{69} - 6 q^{73} + 90 q^{77} - 6 q^{81} - 54 q^{89} - 42 q^{93}+O(q^{100}) \) 12 * q + 6 * q^5 + 4 * q^9 - 16 * q^13 - 18 * q^17 + 34 * q^21 - 8 * q^25 - 30 * q^33 - 18 * q^37 - 12 * q^45 + 12 * q^49 + 30 * q^53 + 76 * q^57 + 34 * q^61 - 132 * q^69 - 6 * q^73 + 90 * q^77 - 6 * q^81 - 54 * q^89 - 42 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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