LMFDB - Embedded newform 224.2.p.a.159.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(31,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("224.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.p (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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.2353561680715186176.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 2 x^{14} + 41 x^{12} - 92 x^{11} + 66 x^{10} - 104 x^{9} + 291 x^{8} - 388 x^{7} + \cdots + 4 $ x^16 - 4x^15 + 2x^14 + 41x^12 - 92x^11 + 66x^10 - 104x^9 + 291x^8 - 388x^7 + 366x^6 - 344x^5 + 286x^4 - 184x^3 + 84x^2 - 24x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			159.8
Root			$0.849168 + 0.0870829i$ of defining polynomial
Character	$\chi$	$=$	224.159
Dual form			224.2.p.a.31.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60159 + 2.77404i) q^{3} +(-1.00367 - 0.579471i) q^{5} +(-1.44550 + 2.21597i) q^{7} +(-3.63019 + 6.28767i) q^{9} +O(q^{10})$	\(q+(1.60159 + 2.77404i) q^{3} +(-1.00367 - 0.579471i) q^{5} +(-1.44550 + 2.21597i) q^{7} +(-3.63019 + 6.28767i) q^{9} +(3.93239 - 2.27036i) q^{11} -2.08049i q^{13} -3.71230i q^{15} +(-0.301760 + 0.174221i) q^{17} +(-0.156095 + 0.270364i) q^{19} +(-8.46229 - 0.460776i) q^{21} +(4.08733 + 2.35982i) q^{23} +(-1.82843 - 3.16693i) q^{25} -13.6468 q^{27} +7.26038 q^{29} +(1.13445 + 1.96493i) q^{31} +(12.5961 + 7.27239i) q^{33} +(2.73490 - 1.38649i) q^{35} +(3.63386 - 6.29403i) q^{37} +(5.77137 - 3.33210i) q^{39} -2.08049i q^{41} -1.43929i q^{43} +(7.28704 - 4.20718i) q^{45} +(-4.02545 + 6.97228i) q^{47} +(-2.82108 - 6.40636i) q^{49} +(-0.966594 - 0.558063i) q^{51} +(0.805433 + 1.39505i) q^{53} -5.26244 q^{55} -1.00000 q^{57} +(-0.478903 - 0.829484i) q^{59} +(-9.88689 - 5.70820i) q^{61} +(-8.68589 - 17.1332i) q^{63} +(-1.20559 + 2.08814i) q^{65} +(0.592516 - 0.342089i) q^{67} +15.1179i q^{69} -4.57540i q^{71} +(7.58880 - 4.38140i) q^{73} +(5.85678 - 10.1442i) q^{75} +(-0.653181 + 11.9959i) q^{77} +(-13.6969 - 7.90790i) q^{79} +(-10.9660 - 18.9936i) q^{81} +10.0455 q^{83} +0.403825 q^{85} +(11.6282 + 20.1405i) q^{87} +(-7.11087 - 4.10546i) q^{89} +(4.61032 + 3.00735i) q^{91} +(-3.63386 + 6.29403i) q^{93} +(0.313336 - 0.180905i) q^{95} +13.0247i q^{97} +32.9674i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^9	$ 16 q - 8 q^{9} - 24 q^{21} + 16 q^{25} + 16 q^{29} + 24 q^{33} - 8 q^{37} - 24 q^{45} - 32 q^{49} - 8 q^{53} - 16 q^{57} - 24 q^{61} + 8 q^{65} - 24 q^{73} + 64 q^{77} - 48 q^{81} - 16 q^{85} - 72 q^{89} + 8 q^{93}+O(q^{100}) $ 16 * q - 8 * q^9 - 24 * q^21 + 16 * q^25 + 16 * q^29 + 24 * q^33 - 8 * q^37 - 24 * q^45 - 32 * q^49 - 8 * q^53 - 16 * q^57 - 24 * q^61 + 8 * q^65 - 24 * q^73 + 64 * q^77 - 48 * q^81 - 16 * q^85 - 72 * q^89 + 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

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

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
$3$	1.60159	+	2.77404i	0.924679	+	1.60159i	0.792077	+	0.610422i	$0.209000\pi$
$3$	1.60159	+	2.77404i	0.924679	+	1.60159i	0.132602	+	0.991169i	$0.457667\pi$
$4$		0			0
$5$	−1.00367	−	0.579471i	−0.448856	−	0.259147i	0.258491	−	0.966014i	$-0.416775\pi$
$5$	−1.00367	−	0.579471i	−0.448856	−	0.259147i	−0.707347	+	0.706866i	$0.750108\pi$
$6$		0			0
$7$	−1.44550	+	2.21597i	−0.546346	+	0.837559i
$7$	−1.44550	+	2.21597i	−0.546346	+	0.837559i
$8$		0			0
$9$	−3.63019	+	6.28767i	−1.21006	+	2.09589i
$10$		0			0
$11$	3.93239	−	2.27036i	1.18566	−	0.684541i	0.228342	−	0.973581i	$-0.426670\pi$
$11$	3.93239	−	2.27036i	1.18566	−	0.684541i	0.957317	+	0.289040i	$0.0933362\pi$
$12$		0			0
$13$		−	2.08049i		−	0.577025i	−0.957476	−	0.288513i	$-0.906839\pi$
$13$		−	2.08049i		−	0.577025i	0.957476	−	0.288513i	$-0.0931607\pi$
$14$		0			0
$15$		−	3.71230i		−	0.958512i
$16$		0			0
$17$	−0.301760	+	0.174221i	−0.0731876	+	0.0422549i	−0.536147	−	0.844124i	$-0.680121\pi$
$17$	−0.301760	+	0.174221i	−0.0731876	+	0.0422549i	0.462960	+	0.886379i	$0.346787\pi$
$18$		0			0
$19$	−0.156095	+	0.270364i	−0.0358106	+	0.0620258i	−0.883375	−	0.468666i	$-0.844735\pi$
$19$	−0.156095	+	0.270364i	−0.0358106	+	0.0620258i	0.847565	+	0.530692i	$0.178068\pi$
$20$		0			0
$21$	−8.46229	−	0.460776i	−1.84662	−	0.100550i
$22$		0			0
$23$	4.08733	+	2.35982i	0.852268	+	0.492057i	0.861415	−	0.507901i	$-0.169578\pi$
$23$	4.08733	+	2.35982i	0.852268	+	0.492057i	−0.00914740	+	0.999958i	$0.502912\pi$
$24$		0			0
$25$	−1.82843	−	3.16693i	−0.365685	−	0.633386i
$26$		0			0
$27$	−13.6468			−2.62632
$28$		0			0
$29$	7.26038			1.34822			0.674109	−	0.738632i	$-0.264528\pi$
$29$	7.26038			1.34822			0.674109	+	0.738632i	$0.264528\pi$
$30$		0			0
$31$	1.13445	+	1.96493i	0.203754	+	0.352912i	0.949735	−	0.313055i	$-0.101352\pi$
$31$	1.13445	+	1.96493i	0.203754	+	0.352912i	−0.745981	+	0.665967i	$0.768019\pi$
$32$		0			0
$33$	12.5961	+	7.27239i	2.19271	+	1.26596i
$34$		0			0
$35$	2.73490	−	1.38649i	0.462282	−	0.234360i
$36$		0			0
$37$	3.63386	−	6.29403i	0.597403	−	1.03473i	−0.395800	−	0.918337i	$-0.629533\pi$
$37$	3.63386	−	6.29403i	0.597403	−	1.03473i	0.993203	−	0.116396i	$-0.0371340\pi$
$38$		0			0
$39$	5.77137	−	3.33210i	0.924158	−	0.533563i
$40$		0			0
$41$		−	2.08049i		−	0.324919i	−0.986715	−	0.162459i	$-0.948057\pi$
$41$		−	2.08049i		−	0.324919i	0.986715	−	0.162459i	$-0.0519426\pi$
$42$		0			0
$43$		−	1.43929i		−	0.219490i	−0.993960	−	0.109745i	$-0.964997\pi$
$43$		−	1.43929i		−	0.219490i	0.993960	−	0.109745i	$-0.0350035\pi$
$44$		0			0
$45$	7.28704	−	4.20718i	1.08629	−	0.627169i
$46$		0			0
$47$	−4.02545	+	6.97228i	−0.587172	+	1.01701i	0.407429	+	0.913237i	$0.366425\pi$
$47$	−4.02545	+	6.97228i	−0.587172	+	1.01701i	−0.994601	+	0.103774i	$0.966908\pi$
$48$		0			0
$49$	−2.82108	−	6.40636i	−0.403012	−	0.915195i
$50$		0			0
$51$	−0.966594	−	0.558063i	−0.135350	−	0.0781445i
$52$		0			0
$53$	0.805433	+	1.39505i	0.110635	+	0.191625i	0.916026	−	0.401118i	$-0.131378\pi$
$53$	0.805433	+	1.39505i	0.110635	+	0.191625i	−0.805392	+	0.592743i	$0.798045\pi$
$54$		0			0
$55$	−5.26244			−0.709587
$56$		0			0
$57$	−1.00000			−0.132453
$58$		0			0
$59$	−0.478903	−	0.829484i	−0.0623478	−	0.107990i	0.833167	−	0.553022i	$-0.186525\pi$
$59$	−0.478903	−	0.829484i	−0.0623478	−	0.107990i	−0.895514	+	0.445032i	$0.853192\pi$
$60$		0			0
$61$	−9.88689	−	5.70820i	−1.26589	−	0.730860i	−0.291680	−	0.956516i	$-0.594214\pi$
$61$	−9.88689	−	5.70820i	−1.26589	−	0.730860i	−0.974207	+	0.225656i	$0.927547\pi$
$62$		0			0
$63$	−8.68589	−	17.1332i	−1.09432	−	2.15858i
$64$		0			0
$65$	−1.20559	+	2.08814i	−0.149534	+	0.259001i
$66$		0			0
$67$	0.592516	−	0.342089i	0.0723873	−	0.0417928i	−0.463369	−	0.886165i	$-0.653360\pi$
$67$	0.592516	−	0.342089i	0.0723873	−	0.0417928i	0.535757	+	0.844372i	$0.320026\pi$
$68$		0			0
$69$			15.1179i			1.81998i
$70$		0			0
$71$		−	4.57540i		−	0.543000i	−0.962438	−	0.271500i	$-0.912480\pi$
$71$		−	4.57540i		−	0.543000i	0.962438	−	0.271500i	$-0.0875197\pi$
$72$		0			0
$73$	7.58880	−	4.38140i	0.888202	−	0.512804i	0.0148481	−	0.999890i	$-0.495274\pi$
$73$	7.58880	−	4.38140i	0.888202	−	0.512804i	0.873354	+	0.487086i	$0.161940\pi$
$74$		0			0
$75$	5.85678	−	10.1442i	0.676283	−	1.17136i
$76$		0			0
$77$	−0.653181	+	11.9959i	−0.0744369	+	1.36706i
$78$		0			0
$79$	−13.6969	−	7.90790i	−1.54102	−	0.889708i	−0.998775	−	0.0494873i	$-0.984241\pi$
$79$	−13.6969	−	7.90790i	−1.54102	−	0.889708i	−0.542245	−	0.840221i	$-0.682425\pi$
$80$		0			0
$81$	−10.9660	−	18.9936i	−1.21844	−	2.11040i
$82$		0			0
$83$	10.0455			1.10264			0.551319	−	0.834294i	$-0.314125\pi$
$83$	10.0455			1.10264			0.551319	+	0.834294i	$0.314125\pi$
$84$		0			0
$85$	0.403825			0.0438010
$86$		0			0
$87$	11.6282	+	20.1405i	1.24667	+	2.15929i
$88$		0			0
$89$	−7.11087	−	4.10546i	−0.753750	−	0.435178i	0.0732970	−	0.997310i	$-0.476648\pi$
$89$	−7.11087	−	4.10546i	−0.753750	−	0.435178i	−0.827047	+	0.562132i	$0.809981\pi$
$90$		0			0
$91$	4.61032	+	3.00735i	0.483293	+	0.315256i
$92$		0			0
$93$	−3.63386	+	6.29403i	−0.376814	+	0.652661i
$94$		0			0
$95$	0.313336	−	0.180905i	0.0321476	−	0.0185604i
$96$		0			0
$97$			13.0247i			1.32245i	0.750185	+	0.661227i	$0.229964\pi$
$97$			13.0247i			1.32245i	−0.750185	+	0.661227i	$0.770036\pi$
$98$		0			0
$99$			32.9674i			3.31335i
$100$		0			0
$101$	6.40015	−	3.69513i	0.636839	−	0.367679i	−0.146557	−	0.989202i	$-0.546819\pi$
$101$	6.40015	−	3.69513i	0.636839	−	0.367679i	0.783396	+	0.621523i	$0.213486\pi$
$102$		0			0
$103$	−4.66044	+	8.07212i	−0.459207	+	0.795370i	−0.998919	−	0.0464796i	$-0.985200\pi$
$103$	−4.66044	+	8.07212i	−0.459207	+	0.795370i	0.539712	+	0.841850i	$0.318533\pi$
$104$		0			0
$105$	8.22636	+	5.36612i	0.802811	+	0.523679i
$106$		0			0
$107$	−5.96161	−	3.44194i	−0.576331	−	0.332745i	0.183343	−	0.983049i	$-0.441308\pi$
$107$	−5.96161	−	3.44194i	−0.576331	−	0.332745i	−0.759674	+	0.650304i	$0.774641\pi$
$108$		0			0
$109$	−0.832100	−	1.44124i	−0.0797007	−	0.138046i	0.823420	−	0.567432i	$-0.192063\pi$
$109$	−0.832100	−	1.44124i	−0.0797007	−	0.138046i	−0.903121	+	0.429387i	$0.858730\pi$
$110$		0			0
$111$	23.2798			2.20962
$112$		0			0
$113$	−13.2751			−1.24881			−0.624407	−	0.781099i	$-0.714659\pi$
$113$	−13.2751			−1.24881			−0.624407	+	0.781099i	$0.714659\pi$
$114$		0			0
$115$	−2.73490	−	4.73698i	−0.255031	−	0.441726i
$116$		0			0
$117$	13.0815	+	7.55258i	1.20938	+	0.698236i
$118$		0			0
$119$	0.0501233	−	0.920530i	0.00459480	−	0.0843848i
$120$		0			0
$121$	4.80911	−	8.32962i	0.437191	−	0.757238i
$122$		0			0
$123$	5.77137	−	3.33210i	0.520387	−	0.300445i
$124$		0			0
$125$			10.0328i			0.897360i
$126$		0			0
$127$			8.75300i			0.776703i	0.921511	+	0.388352i	$0.126955\pi$
$127$			8.75300i			0.776703i	−0.921511	+	0.388352i	$0.873045\pi$
$128$		0			0
$129$	3.99265	−	2.30516i	0.351534	−	0.202958i
$130$		0			0
$131$	−3.73335	+	6.46636i	−0.326185	+	0.564968i	−0.981751	−	0.190169i	$-0.939096\pi$
$131$	−3.73335	+	6.46636i	−0.326185	+	0.564968i	0.655567	+	0.755137i	$0.272430\pi$
$132$		0			0
$133$	−0.373485	−	0.736712i	−0.0323853	−	0.0638811i
$134$		0			0
$135$	13.6969	+	7.90790i	1.17884	+	0.680603i
$136$		0			0
$137$	3.70559	+	6.41826i	0.316590	+	0.548349i	0.979774	−	0.200107i	$-0.0641289\pi$
$137$	3.70559	+	6.41826i	0.316590	+	0.548349i	−0.663185	+	0.748456i	$0.730796\pi$
$138$		0			0
$139$	−21.3619			−1.81190			−0.905948	−	0.423390i	$-0.860840\pi$
$139$	−21.3619			−1.81190			−0.905948	+	0.423390i	$0.860840\pi$
$140$		0			0
$141$	−25.7885			−2.17178
$142$		0			0
$143$	−4.72348	−	8.18130i	−0.394997	−	0.684155i
$144$		0			0
$145$	−7.28704	−	4.20718i	−0.605156	−	0.349387i
$146$		0			0
$147$	13.2533	−	18.0862i	1.09311	−	1.49172i
$148$		0			0
$149$	3.00367	−	5.20251i	0.246070	−	0.426207i	−0.716362	−	0.697729i	$-0.754194\pi$
$149$	3.00367	−	5.20251i	0.246070	−	0.426207i	0.962432	+	0.271523i	$0.0875272\pi$
$150$		0			0
$151$	−4.95972	+	2.86350i	−0.403616	+	0.233028i	−0.688043	−	0.725670i	$-0.741530\pi$
$151$	−4.95972	+	2.86350i	−0.403616	+	0.233028i	0.284427	+	0.958698i	$0.408197\pi$
$152$		0			0
$153$		−	2.52983i		−	0.204524i
$154$		0			0
$155$		−	2.62953i		−	0.211209i
$156$		0			0
$157$	−17.2907	+	9.98280i	−1.37995	+	0.796714i	−0.992153	−	0.125031i	$-0.960097\pi$
$157$	−17.2907	+	9.98280i	−1.37995	+	0.796714i	−0.387796	+	0.921745i	$0.626764\pi$
$158$		0			0
$159$	−2.57995	+	4.46860i	−0.204603	+	0.354383i
$160$		0			0
$161$	−11.1375	+	5.64631i	−0.877761	+	0.444992i
$162$		0			0
$163$	−12.1712	−	7.02707i	−0.953325	−	0.550402i	−0.0592126	−	0.998245i	$-0.518859\pi$
$163$	−12.1712	−	7.02707i	−0.953325	−	0.550402i	−0.894112	+	0.447843i	$0.852192\pi$
$164$		0			0
$165$	−8.42828	−	14.5982i	−0.656140	−	1.13647i
$166$		0			0
$167$	5.18343			0.401106			0.200553	−	0.979683i	$-0.435726\pi$
$167$	5.18343			0.401106			0.200553	+	0.979683i	$0.435726\pi$
$168$		0			0
$169$	8.67155			0.667042
$170$		0			0
$171$	−1.13331	−	1.96294i	−0.0866661	−	0.150110i
$172$		0			0
$173$	16.9904	+	9.80940i	1.29175	+	0.745795i	0.978965	−	0.204027i	$-0.0654031\pi$
$173$	16.9904	+	9.80940i	1.29175	+	0.745795i	0.312790	+	0.949822i	$0.398736\pi$
$174$		0			0
$175$	9.66082	+	0.526037i	0.730289	+	0.0397646i
$176$		0			0
$177$	1.53401	−	2.65699i	0.115303	−	0.199711i
$178$		0			0
$179$	10.1739	−	5.87388i	0.760431	−	0.439035i	−0.0690198	−	0.997615i	$-0.521987\pi$
$179$	10.1739	−	5.87388i	0.760431	−	0.439035i	0.829450	+	0.558581i	$0.188654\pi$
$180$		0			0
$181$		−	4.26353i		−	0.316905i	−0.987367	−	0.158453i	$-0.949349\pi$
$181$		−	4.26353i		−	0.316905i	0.987367	−	0.158453i	$-0.0506506\pi$
$182$		0			0
$183$		−	36.5688i		−	2.70324i
$184$		0			0
$185$	−7.29441	+	4.21143i	−0.536296	+	0.309631i
$186$		0			0
$187$	−0.791092	+	1.37021i	−0.0578504	+	0.100200i
$188$		0			0
$189$	19.7263	−	30.2409i	1.43488	−	2.19970i
$190$		0			0
$191$	−5.89629	−	3.40422i	−0.426641	−	0.246321i	0.271274	−	0.962502i	$-0.412555\pi$
$191$	−5.89629	−	3.40422i	−0.426641	−	0.246321i	−0.697914	+	0.716181i	$0.745888\pi$
$192$		0			0
$193$	9.39791	+	16.2777i	0.676476	+	1.17169i	0.976035	+	0.217613i	$0.0698272\pi$
$193$	9.39791	+	16.2777i	0.676476	+	1.17169i	−0.299559	+	0.954078i	$0.596839\pi$
$194$		0			0
$195$	−7.72342			−0.553086
$196$		0			0
$197$	14.4674			1.03076			0.515380	−	0.856962i	$-0.327651\pi$
$197$	14.4674			1.03076			0.515380	+	0.856962i	$0.327651\pi$
$198$		0			0
$199$	−7.27990	−	12.6092i	−0.516058	−	0.893839i	−0.999826	−	0.0186428i	$-0.994065\pi$
$199$	−7.27990	−	12.6092i	−0.516058	−	0.893839i	0.483768	−	0.875196i	$-0.339268\pi$
$200$		0			0
$201$	1.89794	+	1.09577i	0.133870	+	0.0772899i
$202$		0			0
$203$	−10.4948	+	16.0888i	−0.736594	+	1.12921i
$204$		0			0
$205$	−1.20559	+	2.08814i	−0.0842017	+	0.145842i
$206$		0			0
$207$	−29.6756	+	17.1332i	−2.06260	+	1.19084i
$208$		0			0
$209$			1.41757i			0.0980552i
$210$		0			0
$211$			5.87441i			0.404411i	0.979343	+	0.202206i	$0.0648110\pi$
$211$			5.87441i			0.404411i	−0.979343	+	0.202206i	$0.935189\pi$
$212$		0			0
$213$	12.6923	−	7.32792i	0.869664	−	0.502101i
$214$		0			0
$215$	−0.834029	+	1.44458i	−0.0568803	+	0.0985195i
$216$		0			0
$217$	−5.99408	−	0.326381i	−0.406905	−	0.0221562i
$218$		0			0
$219$	24.3083	+	14.0344i	1.64260	+	0.948358i
$220$		0			0
$221$	0.362467	+	0.627811i	0.0243821	+	0.0422311i
$222$		0			0
$223$	10.4178			0.697624			0.348812	−	0.937193i	$-0.386585\pi$
$223$	10.4178			0.697624			0.348812	+	0.937193i	$0.386585\pi$
$224$		0			0
$225$	26.5501			1.77001
$226$		0			0
$227$	1.61221	+	2.79243i	0.107006	+	0.185340i	0.914556	−	0.404459i	$-0.132540\pi$
$227$	1.61221	+	2.79243i	0.107006	+	0.185340i	−0.807550	+	0.589799i	$0.799207\pi$
$228$		0			0
$229$	−14.0851	−	8.13205i	−0.930772	−	0.537381i	−0.0437160	−	0.999044i	$-0.513920\pi$
$229$	−14.0851	−	8.13205i	−0.930772	−	0.537381i	−0.887056	+	0.461663i	$0.847253\pi$
$230$		0			0
$231$	−34.3231	+	17.4005i	−2.25829	+	1.14487i
$232$		0			0
$233$	8.78704	−	15.2196i	0.575658	−	0.997069i	−0.420312	−	0.907380i	$-0.638079\pi$
$233$	8.78704	−	15.2196i	0.575658	−	0.997069i	0.995970	−	0.0896895i	$-0.0285875\pi$
$234$		0			0
$235$	8.08046	−	4.66526i	0.527111	−	0.304328i
$236$		0			0
$237$		−	50.6609i		−	3.29078i
$238$		0			0
$239$		−	3.56805i		−	0.230798i	−0.993319	−	0.115399i	$-0.963185\pi$
$239$		−	3.56805i		−	0.230798i	0.993319	−	0.115399i	$-0.0368147\pi$
$240$		0			0
$241$	15.1182	−	8.72850i	0.973850	−	0.562252i	0.0734420	−	0.997299i	$-0.476602\pi$
$241$	15.1182	−	8.72850i	0.973850	−	0.562252i	0.900408	+	0.435047i	$0.143268\pi$
$242$		0			0
$243$	14.6558	−	25.3846i	0.940172	−	1.62843i
$244$		0			0
$245$	−0.880858	+	8.06463i	−0.0562760	+	0.515230i
$246$		0			0
$247$	0.562491	+	0.324754i	0.0357904	+	0.0206636i
$248$		0			0
$249$	16.0888	+	27.8666i	1.01959	+	1.76598i
$250$		0			0
$251$	−4.28476			−0.270452			−0.135226	−	0.990815i	$-0.543176\pi$
$251$	−4.28476			−0.270452			−0.135226	+	0.990815i	$0.543176\pi$
$252$		0			0
$253$	21.4306			1.34733
$254$		0			0
$255$	0.646762	+	1.12023i	0.0405018	+	0.0701512i
$256$		0			0
$257$	−16.0829	−	9.28546i	−1.00322	−	0.579211i	−0.0940226	−	0.995570i	$-0.529973\pi$
$257$	−16.0829	−	9.28546i	−1.00322	−	0.579211i	−0.909200	+	0.416359i	$0.863306\pi$
$258$		0			0
$259$	8.69468	+	17.1505i	0.540261	+	1.06568i
$260$		0			0
$261$	−26.3565	+	45.6508i	−1.63143	+	2.82572i
$262$		0			0
$263$	18.2190	−	10.5188i	1.12343	−	0.648615i	0.181158	−	0.983454i	$-0.442015\pi$
$263$	18.2190	−	10.5188i	1.12343	−	0.648615i	0.942275	+	0.334839i	$0.108682\pi$
$264$		0			0
$265$		−	1.86690i		−	0.114683i
$266$		0			0
$267$		−	26.3011i		−	1.60960i
$268$		0			0
$269$	−13.6872	+	7.90231i	−0.834523	+	0.481812i	−0.855399	−	0.517970i	$-0.826688\pi$
$269$	−13.6872	+	7.90231i	−0.834523	+	0.481812i	0.0208758	+	0.999782i	$0.493355\pi$
$270$		0			0
$271$	8.36423	−	14.4873i	0.508091	−	0.880039i	−0.491865	−	0.870671i	$-0.663685\pi$
$271$	8.36423	−	14.4873i	0.508091	−	0.880039i	0.999956	−	0.00936761i	$-0.00298185\pi$
$272$		0			0
$273$	−0.958642	+	17.6057i	−0.0580196	+	1.06555i
$274$		0			0
$275$	−14.3802	−	8.30239i	−0.867156	−	0.500653i
$276$		0			0
$277$	−8.81278	−	15.2642i	−0.529509	−	0.917136i	−0.999408	−	0.0344156i	$-0.989043\pi$
$277$	−8.81278	−	15.2642i	−0.529509	−	0.917136i	0.469899	−	0.882720i	$-0.344290\pi$
$278$		0			0
$279$	−16.4731			−0.986219
$280$		0			0
$281$	−6.06803			−0.361988			−0.180994	−	0.983484i	$-0.557931\pi$
$281$	−6.06803			−0.361988			−0.180994	+	0.983484i	$0.557931\pi$
$282$		0			0
$283$	−0.917617	−	1.58936i	−0.0545467	−	0.0944776i	0.837463	−	0.546494i	$-0.184038\pi$
$283$	−0.917617	−	1.58936i	−0.0545467	−	0.0944776i	−0.892009	+	0.452017i	$0.850705\pi$
$284$		0			0
$285$	1.00367	+	0.579471i	0.0594525	+	0.0343249i
$286$		0			0
$287$	4.61032	+	3.00735i	0.272139	+	0.177518i
$288$		0			0
$289$	−8.43929	+	14.6173i	−0.496429	+	0.859840i
$290$		0			0
$291$	−36.1309	+	20.8602i	−2.11803	+	1.22285i
$292$		0			0
$293$		−	22.6107i		−	1.32093i	−0.750857	−	0.660465i	$-0.770359\pi$
$293$		−	22.6107i		−	1.32093i	0.750857	−	0.660465i	$-0.229641\pi$
$294$		0			0
$295$			1.11004i			0.0646291i
$296$		0			0
$297$	−53.6643	+	30.9831i	−3.11392	+	1.79782i
$298$		0			0
$299$	4.90960	−	8.50367i	0.283929	−	0.491780i
$300$		0			0
$301$	3.18944	+	2.08049i	0.183836	+	0.119918i
$302$		0			0
$303$	20.5009	+	11.8362i	1.17774	+	0.679970i
$304$		0			0
$305$	6.61547	+	11.4583i	0.378801	+	0.656102i
$306$		0			0
$307$	−0.372239			−0.0212448			−0.0106224	−	0.999944i	$-0.503381\pi$
$307$	−0.372239			−0.0212448			−0.0106224	+	0.999944i	$0.503381\pi$
$308$		0			0
$309$	−29.8565			−1.69848
$310$		0			0
$311$	8.22708	+	14.2497i	0.466515	+	0.808028i	0.999268	−	0.0382426i	$-0.0121760\pi$
$311$	8.22708	+	14.2497i	0.466515	+	0.808028i	−0.532753	+	0.846271i	$0.678843\pi$
$312$		0			0
$313$	−12.9853	−	7.49706i	−0.733971	−	0.423759i	0.0859018	−	0.996304i	$-0.472623\pi$
$313$	−12.9853	−	7.49706i	−0.733971	−	0.423759i	−0.819873	+	0.572545i	$0.805956\pi$
$314$		0			0
$315$	−1.21040	+	22.2294i	−0.0681983	+	1.25248i
$316$		0			0
$317$	12.4623	−	21.5853i	0.699952	−	1.21235i	−0.268531	−	0.963271i	$-0.586538\pi$
$317$	12.4623	−	21.5853i	0.699952	−	1.21235i	0.968483	−	0.249081i	$-0.0801285\pi$
$318$		0			0
$319$	28.5506	−	16.4837i	1.59853	−	0.922910i
$320$		0			0
$321$		−	22.0503i		−	1.23073i
$322$		0			0
$323$		−	0.108780i		−	0.00605269i
$324$		0			0
$325$	−6.58878	+	3.80403i	−0.365479	+	0.211010i
$326$		0			0
$327$	2.66537	−	4.61655i	0.147395	−	0.255296i
$328$		0			0
$329$	−9.63162	−	18.9987i	−0.531008	−	1.04743i
$330$		0			0
$331$	25.5548	+	14.7541i	1.40462	+	0.810956i	0.994862	−	0.101239i	$-0.0322807\pi$
$331$	25.5548	+	14.7541i	1.40462	+	0.810956i	0.409756	+	0.912195i	$0.365614\pi$
$332$		0			0
$333$	26.3832	+	45.6970i	1.44579	+	2.50418i
$334$		0			0
$335$	−0.792923			−0.0433220
$336$		0			0
$337$	12.8878			0.702046			0.351023	−	0.936367i	$-0.385834\pi$
$337$	12.8878			0.702046			0.351023	+	0.936367i	$0.385834\pi$
$338$		0			0
$339$	−21.2612	−	36.8255i	−1.15475	−	2.00009i
$340$		0			0
$341$	8.92222	+	5.15124i	0.483165	+	0.278956i
$342$		0			0
$343$	18.2742	+	3.00893i	0.986714	+	0.162467i
$344$		0			0
$345$	8.76038	−	15.1734i	0.471643	−	0.816909i
$346$		0			0
$347$	−23.5256	+	13.5825i	−1.26292	+	0.729146i	−0.973638	−	0.228098i	$-0.926749\pi$
$347$	−23.5256	+	13.5825i	−1.26292	+	0.729146i	−0.289280	+	0.957245i	$0.593416\pi$
$348$		0			0
$349$			28.9547i			1.54991i	0.632016	+	0.774955i	$0.282228\pi$
$349$			28.9547i			1.54991i	−0.632016	+	0.774955i	$0.717772\pi$
$350$		0			0
$351$			28.3920i			1.51545i
$352$		0			0
$353$	19.9867	−	11.5393i	1.06379	−	0.614178i	0.137309	−	0.990528i	$-0.456155\pi$
$353$	19.9867	−	11.5393i	1.06379	−	0.614178i	0.926477	+	0.376351i	$0.122821\pi$
$354$		0			0
$355$	−2.65131	+	4.59220i	−0.140717	+	0.243729i
$356$		0			0
$357$	2.63386	−	1.33527i	0.139399	−	0.0706699i
$358$		0			0
$359$	18.2218	+	10.5204i	0.961709	+	0.555243i	0.896699	−	0.442642i	$-0.145959\pi$
$359$	18.2218	+	10.5204i	0.961709	+	0.555243i	0.0650103	+	0.997885i	$0.479292\pi$
$360$		0			0
$361$	9.45127	+	16.3701i	0.497435	+	0.861583i
$362$		0			0
$363$	30.8089			1.61705
$364$		0			0
$365$	−10.1556			−0.531567
$366$		0			0
$367$	3.97372	+	6.88269i	0.207427	+	0.359273i	0.950903	−	0.309489i	$-0.100158\pi$
$367$	3.97372	+	6.88269i	0.207427	+	0.359273i	−0.743477	+	0.668762i	$0.766825\pi$
$368$		0			0
$369$	13.0815	+	7.55258i	0.680993	+	0.393172i
$370$		0			0
$371$	−4.25565	−	0.231722i	−0.220942	−	0.0120304i
$372$		0			0
$373$	2.19457	−	3.80110i	0.113630	−	0.196814i	−0.803601	−	0.595168i	$-0.797085\pi$
$373$	2.19457	−	3.80110i	0.113630	−	0.196814i	0.917231	+	0.398355i	$0.130419\pi$
$374$		0			0
$375$	−27.8313	+	16.0684i	−1.43720	+	0.829770i
$376$		0			0
$377$		−	15.1052i		−	0.777956i
$378$		0			0
$379$			8.93801i			0.459115i	0.973295	+	0.229557i	$0.0737278\pi$
$379$			8.93801i			0.459115i	−0.973295	+	0.229557i	$0.926272\pi$
$380$		0			0
$381$	−24.2812	+	14.0187i	−1.24396	+	0.718201i
$382$		0			0
$383$	−18.6813	+	32.3569i	−0.954569	+	1.65336i	−0.219217	+	0.975676i	$0.570350\pi$
$383$	−18.6813	+	32.3569i	−0.954569	+	1.65336i	−0.735352	+	0.677685i	$0.762983\pi$
$384$		0			0
$385$	7.60684	−	11.6614i	0.387680	−	0.594321i
$386$		0			0
$387$	9.04980	+	5.22491i	0.460027	+	0.265597i
$388$		0			0
$389$	1.25670	+	2.17667i	0.0637173	+	0.110362i	0.896124	−	0.443803i	$-0.146371\pi$
$389$	1.25670	+	2.17667i	0.0637173	+	0.110362i	−0.832407	+	0.554165i	$0.813038\pi$
$390$		0			0
$391$	−1.64453			−0.0831673
$392$		0			0
$393$	−23.9172			−1.20646
$394$		0			0
$395$	9.16479	+	15.8739i	0.461131	+	0.798702i
$396$		0			0
$397$	2.27748	+	1.31490i	0.114303	+	0.0659931i	0.556062	−	0.831141i	$-0.312312\pi$
$397$	2.27748	+	1.31490i	0.114303	+	0.0659931i	−0.441758	+	0.897134i	$0.645645\pi$
$398$		0			0
$399$	1.44550	−	2.21597i	0.0723653	−	0.110937i
$400$		0			0
$401$	−1.34040	+	2.32164i	−0.0669365	+	0.115937i	−0.897551	−	0.440910i	$-0.854656\pi$
$401$	−1.34040	+	2.32164i	−0.0669365	+	0.115937i	0.830615	+	0.556847i	$0.187989\pi$
$402$		0			0
$403$	4.08803	−	2.36022i	0.203639	−	0.117571i
$404$		0			0
$405$			25.4178i			1.26302i
$406$		0			0
$407$		−	33.0007i		−	1.63579i
$408$		0			0
$409$	−6.49854	+	3.75194i	−0.321332	+	0.185521i	−0.651986	−	0.758231i	$-0.726064\pi$
$409$	−6.49854	+	3.75194i	−0.321332	+	0.185521i	0.330654	+	0.943752i	$0.392731\pi$
$410$		0			0
$411$	−11.8697	+	20.5589i	−0.585487	+	1.01409i
$412$		0			0
$413$	2.53037	+	0.137780i	0.124511	+	0.00677970i
$414$		0			0
$415$	−10.0824	−	5.82108i	−0.494926	−	0.285746i
$416$		0			0
$417$	−34.2131	−	59.2588i	−1.67542	−	2.90191i
$418$		0			0
$419$	30.5826			1.49406			0.747028	−	0.664792i	$-0.231480\pi$
$419$	30.5826			1.49406			0.747028	+	0.664792i	$0.231480\pi$
$420$		0			0
$421$	31.0386			1.51273			0.756364	−	0.654151i	$-0.226974\pi$
$421$	31.0386			1.51273			0.756364	+	0.654151i	$0.226974\pi$
$422$		0			0
$423$	−29.2262	−	50.6213i	−1.42103	−	2.46129i
$424$		0			0
$425$	1.10349	+	0.637102i	0.0535273	+	0.0309040i
$426$		0			0
$427$	26.9407	−	13.6579i	1.30375	−	0.660953i
$428$		0			0
$429$	15.1302	−	26.2062i	0.730491	−	1.26525i
$430$		0			0
$431$	−18.6600	+	10.7734i	−0.898823	+	0.518935i	−0.876818	−	0.480822i	$-0.840338\pi$
$431$	−18.6600	+	10.7734i	−0.898823	+	0.518935i	−0.0220046	+	0.999758i	$0.507005\pi$
$432$		0			0
$433$			29.6992i			1.42725i	0.700527	+	0.713626i	$0.252948\pi$
$433$			29.6992i			1.42725i	−0.700527	+	0.713626i	$0.747052\pi$
$434$		0			0
$435$		−	26.9527i		−	1.29228i
$436$		0			0
$437$	−1.27602	+	0.736712i	−0.0610405	+	0.0352417i
$438$		0			0
$439$	14.2081	−	24.6092i	0.678116	−	1.17453i	−0.297432	−	0.954743i	$-0.596130\pi$
$439$	14.2081	−	24.6092i	0.678116	−	1.17453i	0.975548	−	0.219788i	$-0.0705365\pi$
$440$		0			0
$441$	50.5222	+	5.51828i	2.40582	+	0.262775i
$442$		0			0
$443$	−25.9034	−	14.9553i	−1.23071	−	0.710550i	−0.263531	−	0.964651i	$-0.584887\pi$
$443$	−25.9034	−	14.9553i	−1.23071	−	0.710550i	−0.967178	+	0.254101i	$0.918220\pi$
$444$		0			0
$445$	4.75799	+	8.24108i	0.225550	+	0.390665i
$446$		0			0
$447$	19.2426			0.910145
$448$		0			0
$449$	−27.4086			−1.29349			−0.646746	−	0.762706i	$-0.723871\pi$
$449$	−27.4086			−1.29349			−0.646746	+	0.762706i	$0.723871\pi$
$450$		0			0
$451$	−4.72348	−	8.18130i	−0.222420	−	0.385243i
$452$		0			0
$453$	−15.8869	−	9.17230i	−0.746431	−	0.430952i
$454$		0			0
$455$	−2.88458	−	5.68994i	−0.135231	−	0.266748i
$456$		0			0
$457$	−2.34312	+	4.05840i	−0.109606	+	0.189844i	−0.915611	−	0.402066i	$-0.868292\pi$
$457$	−2.34312	+	4.05840i	−0.109606	+	0.189844i	0.806004	+	0.591910i	$0.201626\pi$
$458$		0			0
$459$	4.11805	−	2.37756i	0.192214	−	0.110975i
$460$		0			0
$461$		−	4.70270i		−	0.219026i	−0.993985	−	0.109513i	$-0.965071\pi$
$461$		−	4.70270i		−	0.219026i	0.993985	−	0.109513i	$-0.0349292\pi$
$462$		0			0
$463$			23.4246i			1.08863i	0.838880	+	0.544317i	$0.183211\pi$
$463$			23.4246i			1.08863i	−0.838880	+	0.544317i	$0.816789\pi$
$464$		0			0
$465$	7.29441	−	4.21143i	0.338270	−	0.195300i
$466$		0			0
$467$	−0.0216998	+	0.0375851i	−0.00100415	+	0.00173923i	−0.866527	−	0.499130i	$-0.833653\pi$
$467$	−0.0216998	+	0.0375851i	−0.00100415	+	0.00173923i	0.865523	+	0.500869i	$0.166986\pi$
$468$		0			0
$469$	−0.0984187	+	1.80749i	−0.00454455	+	0.0834620i
$470$		0			0
$471$	−55.3853	−	31.9767i	−2.55202	−	1.47341i
$472$		0			0
$473$	−3.26772	−	5.65986i	−0.150250	−	0.260241i
$474$		0			0
$475$	1.14163			0.0523817
$476$		0			0
$477$	−11.6955			−0.535500
$478$		0			0
$479$	−14.8431	−	25.7090i	−0.678198	−	1.17467i	−0.975523	−	0.219898i	$-0.929428\pi$
$479$	−14.8431	−	25.7090i	−0.678198	−	1.17467i	0.297324	−	0.954777i	$-0.403906\pi$
$480$		0			0
$481$	−13.0947	−	7.56022i	−0.597067	−	0.344717i
$482$		0			0
$483$	−33.5008	−	21.8529i	−1.52434	−	0.994339i
$484$		0			0
$485$	7.54742	−	13.0725i	0.342711	−	0.593592i
$486$		0			0
$487$	−4.68168	+	2.70297i	−0.212147	+	0.122483i	−0.602309	−	0.798263i	$-0.705752\pi$
$487$	−4.68168	+	2.70297i	−0.212147	+	0.122483i	0.390162	+	0.920746i	$0.372419\pi$
$488$		0			0
$489$		−	45.0179i		−	2.03578i
$490$		0			0
$491$			20.9674i			0.946245i	0.880997	+	0.473123i	$0.156873\pi$
$491$			20.9674i			0.946245i	−0.880997	+	0.473123i	$0.843127\pi$
$492$		0			0
$493$	−2.19089	+	1.26491i	−0.0986729	+	0.0569688i
$494$		0			0
$495$	19.1036	−	33.0885i	0.858645	−	1.48722i
$496$		0			0
$497$	10.1390	+	6.61372i	0.454795	+	0.296666i
$498$		0			0
$499$	−12.1712	−	7.02707i	−0.544859	−	0.314575i	0.202187	−	0.979347i	$-0.435195\pi$
$499$	−12.1712	−	7.02707i	−0.544859	−	0.314575i	−0.747046	+	0.664772i	$0.768529\pi$
$500$		0			0
$501$	8.30173	+	14.3790i	0.370894	+	0.642407i
$502$		0			0
$503$	9.67327			0.431310			0.215655	−	0.976470i	$-0.430811\pi$
$503$	9.67327			0.431310			0.215655	+	0.976470i	$0.430811\pi$
$504$		0			0
$505$	−8.56488			−0.381132
$506$		0			0
$507$	13.8883	+	24.0552i	0.616800	+	1.06833i
$508$		0			0
$509$	−31.8068	−	18.3637i	−1.40981	−	0.813956i	−0.414443	−	0.910075i	$-0.636024\pi$
$509$	−31.8068	−	18.3637i	−1.40981	−	0.813956i	−0.995370	+	0.0961191i	$0.969357\pi$
$510$		0			0
$511$	−1.26052	+	23.1499i	−0.0557623	+	1.02409i
$512$		0			0
$513$	2.13019	−	3.68959i	0.0940501	−	0.162900i
$514$		0			0
$515$	9.35512	−	5.40118i	0.412236	−	0.238005i
$516$		0			0
$517$			36.5569i			1.60777i
$518$		0			0
$519$			62.8426i			2.75848i
$520$		0			0
$521$	34.4661	−	19.8990i	1.50999	−	0.871791i	0.510054	−	0.860142i	$-0.329625\pi$
$521$	34.4661	−	19.8990i	1.50999	−	0.871791i	0.999932	−	0.0116486i	$-0.00370794\pi$
$522$		0			0
$523$	3.64794	−	6.31841i	0.159513	−	0.276285i	−0.775180	−	0.631740i	$-0.782341\pi$
$523$	3.64794	−	6.31841i	0.159513	−	0.276285i	0.934693	+	0.355455i	$0.115674\pi$
$524$		0			0
$525$	14.0134	+	27.6420i	0.611596	+	1.20639i
$526$		0			0
$527$	−0.684666	−	0.395292i	−0.0298245	−	0.0172192i
$528$		0			0
$529$	−0.362467	−	0.627811i	−0.0157594	−	0.0272961i
$530$		0			0
$531$	6.95403			0.301779
$532$		0			0
$533$	−4.32845			−0.187486
$534$		0			0
$535$	3.98900	+	6.90916i	0.172460	+	0.298709i
$536$		0			0
$537$	32.5887	+	18.8151i	1.40631	+	0.811932i
$538$		0			0
$539$	−25.6384	−	18.7874i	−1.10432	−	0.809231i
$540$		0			0
$541$	2.35416	−	4.07753i	0.101213	−	0.175307i	−0.810971	−	0.585086i	$-0.801061\pi$
$541$	2.35416	−	4.07753i	0.101213	−	0.175307i	0.912185	+	0.409779i	$0.134394\pi$
$542$		0			0
$543$	11.8272	−	6.82843i	0.507553	−	0.293036i
$544$		0			0
$545$			1.92871i			0.0826169i
$546$		0			0
$547$		−	4.76040i		−	0.203540i	−0.994808	−	0.101770i	$-0.967549\pi$
$547$		−	4.76040i		−	0.203540i	0.994808	−	0.101770i	$-0.0324506\pi$
$548$		0			0
$549$	71.7825	−	41.4437i	3.06360	−	1.76877i
$550$		0			0
$551$	−1.13331	+	1.96294i	−0.0482805	+	0.0836243i
$552$		0			0
$553$	37.3225	−	18.9211i	1.58711	−	0.804607i
$554$		0			0
$555$	−23.3653	−	13.4900i	−0.991803	−	0.572618i
$556$		0			0
$557$	−4.43562	−	7.68272i	−0.187943	−	0.325527i	0.756621	−	0.653854i	$-0.226849\pi$
$557$	−4.43562	−	7.68272i	−0.187943	−	0.325527i	−0.944564	+	0.328326i	$0.893515\pi$
$558$		0			0
$559$	−2.99444			−0.126651
$560$		0			0
$561$	−5.06803			−0.213972
$562$		0			0
$563$	11.4979	+	19.9149i	0.484578	+	0.839313i	0.999843	−	0.0177173i	$-0.00563989\pi$
$563$	11.4979	+	19.9149i	0.484578	+	0.839313i	−0.515265	+	0.857031i	$0.672307\pi$
$564$		0			0
$565$	13.3238	+	7.69251i	0.560538	+	0.323626i
$566$		0			0
$567$	57.9406	+	3.15490i	2.43328	+	0.132493i
$568$		0			0
$569$	−20.4674	+	35.4506i	−0.858038	+	1.48616i	0.0157605	+	0.999876i	$0.494983\pi$
$569$	−20.4674	+	35.4506i	−0.858038	+	1.48616i	−0.873798	+	0.486289i	$0.838350\pi$
$570$		0			0
$571$	15.4751	−	8.93456i	0.647614	−	0.373900i	−0.139928	−	0.990162i	$-0.544687\pi$
$571$	15.4751	−	8.93456i	0.647614	−	0.373900i	0.787541	+	0.616262i	$0.211354\pi$
$572$		0			0
$573$		−	21.8087i		−	0.911072i
$574$		0			0
$575$		−	17.2591i		−	0.719753i
$576$		0			0
$577$	−35.6511	+	20.5832i	−1.48417	+	0.856888i	−0.999838	−	0.0179940i	$-0.994272\pi$
$577$	−35.6511	+	20.5832i	−1.48417	+	0.856888i	−0.484336	+	0.874882i	$0.660939\pi$
$578$		0			0
$579$	−30.1032	+	52.1403i	−1.25105	+	2.16688i
$580$		0			0
$581$	−14.5208	+	22.2606i	−0.602422	+	0.923525i
$582$		0			0
$583$	6.33455	+	3.65725i	0.262350	+	0.151468i
$584$		0			0
$585$	−8.75300	−	15.1606i	−0.361892	−	0.626816i
$586$		0			0
$587$	0.372239			0.0153640			0.00768198	−	0.999970i	$-0.497555\pi$
$587$	0.372239			0.0153640			0.00768198	+	0.999970i	$0.497555\pi$
$588$		0			0
$589$	−0.708329			−0.0291862
$590$		0			0
$591$	23.1709	+	40.1331i	0.953123	+	1.65086i
$592$		0			0
$593$	36.9573	+	21.3373i	1.51765	+	0.876218i	0.999785	+	0.0207588i	$0.00660821\pi$
$593$	36.9573	+	21.3373i	1.51765	+	0.876218i	0.517870	+	0.855459i	$0.326725\pi$
$594$		0			0
$595$	−0.583728	+	0.894866i	−0.0239305	+	0.0366859i
$596$		0			0
$597$	23.3188	−	40.3894i	0.954376	−	1.65303i
$598$		0			0
$599$	−28.6691	+	16.5521i	−1.17139	+	0.676301i	−0.954007	−	0.299785i	$-0.903085\pi$
$599$	−28.6691	+	16.5521i	−1.17139	+	0.676301i	−0.217382	+	0.976087i	$0.569752\pi$
$600$		0			0
$601$			24.7937i			1.01136i	0.862722	+	0.505678i	$0.168758\pi$
$601$			24.7937i			1.01136i	−0.862722	+	0.505678i	$0.831242\pi$
$602$		0			0
$603$			4.96739i			0.202288i
$604$		0			0
$605$	−9.65354	+	5.57347i	−0.392472	+	0.226594i
$606$		0			0
$607$	10.4041	−	18.0204i	0.422288	−	0.731425i	−0.573875	−	0.818943i	$-0.694560\pi$
$607$	10.4041	−	18.0204i	0.422288	−	0.731425i	0.996163	+	0.0875185i	$0.0278937\pi$
$608$		0			0
$609$	−61.4394	−	3.34541i	−2.48965	−	0.135563i
$610$		0			0
$611$	14.5058	+	8.37491i	0.586841	+	0.338813i
$612$		0			0
$613$	−14.2359	−	24.6573i	−0.574984	−	0.995901i	−0.996043	−	0.0888679i	$-0.971675\pi$
$613$	−14.2359	−	24.6573i	−0.574984	−	0.995901i	0.421060	−	0.907033i	$-0.361658\pi$
$614$		0			0
$615$	−7.72342			−0.311438
$616$		0			0
$617$	3.08277			0.124108			0.0620538	−	0.998073i	$-0.480235\pi$
$617$	3.08277			0.124108			0.0620538	+	0.998073i	$0.480235\pi$
$618$		0			0
$619$	−20.7929	−	36.0144i	−0.835739	−	1.44754i	−0.893427	−	0.449208i	$-0.851706\pi$
$619$	−20.7929	−	36.0144i	−0.835739	−	1.44754i	0.0576884	−	0.998335i	$-0.481627\pi$
$620$		0			0
$621$	−55.7789	−	32.2039i	−2.23833	−	1.29230i
$622$		0			0
$623$	19.3763	−	9.82307i	0.776296	−	0.393553i
$624$		0			0
$625$	−3.32843	+	5.76500i	−0.133137	+	0.230600i
$626$		0			0
$627$	−3.93239	+	2.27036i	−0.157044	+	0.0906696i
$628$		0			0
$629$			2.53239i			0.100973i
$630$		0			0
$631$			32.0373i			1.27539i	0.770291	+	0.637693i	$0.220111\pi$
$631$			32.0373i			1.27539i	−0.770291	+	0.637693i	$0.779889\pi$
$632$		0			0
$633$	−16.2958	+	9.40841i	−0.647702	+	0.373951i
$634$		0			0
$635$	5.07211	−	8.78515i	0.201281	−	0.348628i
$636$		0			0
$637$	−13.3284	+	5.86924i	−0.528090	+	0.232548i
$638$		0			0
$639$	28.7686	+	16.6096i	1.13807	+	0.657064i
$640$		0			0
$641$	4.96742	+	8.60382i	0.196201	+	0.339830i	0.947294	−	0.320367i	$-0.103806\pi$
$641$	4.96742	+	8.60382i	0.196201	+	0.339830i	−0.751092	+	0.660197i	$0.770473\pi$
$642$		0			0
$643$	−22.7132			−0.895722			−0.447861	−	0.894103i	$-0.647814\pi$
$643$	−22.7132			−0.895722			−0.447861	+	0.894103i	$0.647814\pi$
$644$		0			0
$645$	−5.34309			−0.210384
$646$		0			0
$647$	−13.1348	−	22.7502i	−0.516384	−	0.894403i	−0.999819	−	0.0190231i	$-0.993944\pi$
$647$	−13.1348	−	22.7502i	−0.516384	−	0.894403i	0.483435	−	0.875380i	$-0.339389\pi$
$648$		0			0
$649$	−3.76646	−	2.17457i	−0.147847	−	0.0853592i
$650$		0			0
$651$	−8.69468	−	17.1505i	−0.340771	−	0.672183i
$652$		0			0
$653$	−16.1118	+	27.9064i	−0.630503	+	1.09206i	0.356946	+	0.934125i	$0.383818\pi$
$653$	−16.1118	+	27.9064i	−0.630503	+	1.09206i	−0.987449	+	0.157939i	$0.949515\pi$
$654$		0			0
$655$	7.49413	−	4.32674i	0.292820	−	0.169060i
$656$		0			0
$657$			63.6212i			2.48210i
$658$		0			0
$659$		−	44.0667i		−	1.71660i	−0.513152	−	0.858298i	$-0.671522\pi$
$659$		−	44.0667i		−	1.71660i	0.513152	−	0.858298i	$-0.328478\pi$
$660$		0			0
$661$	−29.1380	+	16.8228i	−1.13334	+	0.654332i	−0.944772	−	0.327728i	$-0.893717\pi$
$661$	−29.1380	+	16.8228i	−1.13334	+	0.654332i	−0.188565	+	0.982061i	$0.560384\pi$
$662$		0			0
$663$	−1.16105	+	2.01099i	−0.0450913	+	0.0781004i
$664$		0			0
$665$	−0.0520461	+	0.955842i	−0.00201826	+	0.0370660i
$666$		0			0
$667$	29.6756	+	17.1332i	1.14904	+	0.663400i
$668$		0			0
$669$	16.6850	+	28.8992i	0.645078	+	1.11731i
$670$		0			0
$671$	−51.8388			−2.00121
$672$		0			0
$673$	−4.12427			−0.158979			−0.0794895	−	0.996836i	$-0.525329\pi$
$673$	−4.12427			−0.158979			−0.0794895	+	0.996836i	$0.525329\pi$
$674$		0			0
$675$	24.9521	+	43.2183i	0.960407	+	1.66347i
$676$		0			0
$677$	15.0630	+	8.69665i	0.578920	+	0.334239i	0.760704	−	0.649099i	$-0.224854\pi$
$677$	15.0630	+	8.69665i	0.578920	+	0.334239i	−0.181784	+	0.983338i	$0.558187\pi$
$678$		0			0
$679$	−28.8623	−	18.8271i	−1.10763	−	0.722518i
$680$		0			0
$681$	−5.16420	+	8.94466i	−0.197893	+	0.342760i
$682$		0			0
$683$	−14.8844	+	8.59353i	−0.569537	+	0.328822i	−0.756964	−	0.653456i	$-0.773318\pi$
$683$	−14.8844	+	8.59353i	−0.569537	+	0.328822i	0.187427	+	0.982278i	$0.439985\pi$
$684$		0			0
$685$		−	8.58911i		−	0.328173i
$686$		0			0
$687$		−	52.0969i		−	1.98762i
$688$		0			0
$689$	2.90240	−	1.67570i	0.110572	−	0.0638390i
$690$		0			0
$691$	7.43714	−	12.8815i	0.282922	−	0.490035i	−0.689181	−	0.724589i	$-0.742030\pi$
$691$	7.43714	−	12.8815i	0.282922	−	0.490035i	0.972103	+	0.234554i	$0.0753629\pi$
$692$		0			0
$693$	−73.0549	−	47.6542i	−2.77513	−	1.81023i
$694$		0			0
$695$	21.4404	+	12.3786i	0.813280	+	0.469548i
$696$		0			0
$697$	0.362467	+	0.627811i	0.0137294	+	0.0237800i
$698$		0			0
$699$	56.2930			2.12920
$700$		0			0
$701$	9.31371			0.351774			0.175887	−	0.984410i	$-0.443721\pi$
$701$	9.31371			0.351774			0.175887	+	0.984410i	$0.443721\pi$
$702$		0			0
$703$	1.13445	+	1.96493i	0.0427867	+	0.0741088i
$704$		0			0
$705$	25.8832	+	14.9437i	0.974817	+	0.562811i
$706$		0			0
$707$	−1.06308	+	19.5239i	−0.0399814	+	0.734271i
$708$		0			0
$709$	−3.10576	+	5.37934i	−0.116639	+	0.202025i	−0.918434	−	0.395574i	$-0.870546\pi$
$709$	−3.10576	+	5.37934i	−0.116639	+	0.202025i	0.801794	+	0.597600i	$0.203879\pi$
$710$		0			0
$711$	99.4445	−	57.4143i	3.72946	−	2.15320i
$712$		0			0
$713$			10.7084i			0.401034i
$714$		0			0
$715$			10.9485i			0.409450i
$716$		0			0
$717$	9.89791	−	5.71456i	0.369644	−	0.213414i
$718$		0			0
$719$	−23.9419	+	41.4685i	−0.892881	+	1.54652i	−0.0564765	+	0.998404i	$0.517987\pi$
$719$	−23.9419	+	41.4685i	−0.892881	+	1.54652i	−0.836405	+	0.548112i	$0.815347\pi$
$720$		0			0
$721$	−11.1510	−	21.9956i	−0.415284	−	0.819161i
$722$		0			0
$723$	48.4264	+	27.9590i	1.80100	+	1.03981i
$724$		0			0
$725$	−13.2751	−	22.9931i	−0.493024	−	0.853942i
$726$		0			0
$727$	−51.2000			−1.89890			−0.949452	−	0.313913i	$-0.898360\pi$
$727$	−51.2000			−1.89890			−0.949452	+	0.313913i	$0.898360\pi$
$728$		0			0
$729$	28.0948			1.04055
$730$		0			0
$731$	0.250756	+	0.434322i	0.00927454	+	0.0160640i
$732$		0			0
$733$	6.79809	+	3.92488i	0.251093	+	0.144969i	0.620265	−	0.784393i	$-0.287025\pi$
$733$	6.79809	+	3.92488i	0.251093	+	0.144969i	−0.369172	+	0.929361i	$0.620359\pi$
$734$		0			0
$735$	−23.7824	+	10.4727i	−0.877225	+	0.386291i
$736$		0			0
$737$	1.55333	−	2.69045i	0.0572178	−	0.0991041i
$738$		0			0
$739$	4.02476	−	2.32370i	0.148053	−	0.0854786i	−0.424143	−	0.905595i	$-0.639425\pi$
$739$	4.02476	−	2.32370i	0.148053	−	0.0854786i	0.572197	+	0.820116i	$0.306091\pi$
$740$		0			0
$741$			2.08049i			0.0764288i
$742$		0			0
$743$			49.8239i			1.82786i	0.405871	+	0.913931i	$0.366968\pi$
$743$			49.8239i			1.82786i	−0.405871	+	0.913931i	$0.633032\pi$
$744$		0			0
$745$	−6.02941	+	3.48108i	−0.220901	+	0.127537i
$746$		0			0
$747$	−36.4671	+	63.1629i	−1.33426	+	2.31101i
$748$		0			0
$749$	16.2447	−	8.23547i	0.593569	−	0.300917i
$750$		0			0
$751$	−23.9959	−	13.8540i	−0.875623	−	0.505541i	−0.00641005	−	0.999979i	$-0.502040\pi$
$751$	−23.9959	−	13.8540i	−0.875623	−	0.505541i	−0.869213	+	0.494438i	$0.835374\pi$
$752$		0			0
$753$	−6.86244	−	11.8861i	−0.250081	−	0.433153i
$754$		0			0
$755$	6.63725			0.241554
$756$		0			0
$757$	43.5089			1.58136			0.790679	−	0.612231i	$-0.209728\pi$
$757$	43.5089			1.58136			0.790679	+	0.612231i	$0.209728\pi$
$758$		0			0
$759$	34.3231	+	59.4494i	1.24585	+	2.15788i
$760$		0			0
$761$	−15.0726	−	8.70219i	−0.546382	−	0.315454i	0.201279	−	0.979534i	$-0.435490\pi$
$761$	−15.0726	−	8.70219i	−0.546382	−	0.315454i	−0.747662	+	0.664080i	$0.768823\pi$
$762$		0			0
$763$	4.39655	+	0.239394i	0.159166	+	0.00866666i
$764$		0			0
$765$	−1.46596	+	2.53912i	−0.0530019	+	0.0918020i
$766$		0			0
$767$	−1.72574	+	0.996354i	−0.0623127	+	0.0359763i
$768$		0			0
$769$		−	30.4935i		−	1.09962i	−0.835289	−	0.549812i	$-0.814699\pi$
$769$		−	30.4935i		−	1.09962i	0.835289	−	0.549812i	$-0.185301\pi$
$770$		0			0
$771$		−	59.4860i		−	2.14234i
$772$		0			0
$773$	−7.39566	+	4.26989i	−0.266004	+	0.153577i	−0.627070	−	0.778963i	$-0.715746\pi$
$773$	−7.39566	+	4.26989i	−0.266004	+	0.153577i	0.361067	+	0.932540i	$0.382413\pi$
$774$		0			0
$775$	4.14853	−	7.18547i	0.149020	−	0.258110i
$776$		0			0
$777$	−33.6509	+	51.5875i	−1.20722	+	1.85069i
$778$		0			0
$779$	0.562491	+	0.324754i	0.0201533	+	0.0116355i
$780$		0			0
$781$	−10.3878	−	17.9922i	−0.371705	−	0.643813i
$782$		0			0
$783$	−99.0806			−3.54085
$784$		0			0
$785$	23.1390			0.825865
$786$		0			0
$787$	15.5818	+	26.9884i	0.555430	+	0.962033i	0.997870	+	0.0652352i	$0.0207798\pi$
$787$	15.5818	+	26.9884i	0.555430	+	0.962033i	−0.442440	+	0.896798i	$0.645887\pi$
$788$		0			0
$789$	58.3589	+	33.6935i	2.07763	+	1.19952i
$790$		0			0
$791$	19.1891	−	29.4172i	0.682284	−	1.04596i
$792$		0			0
$793$	−11.8759	+	20.5696i	−0.421725	+	0.730448i
$794$		0			0
$795$	5.17885	−	2.99001i	0.183675	−	0.106045i
$796$		0			0
$797$		−	37.2767i		−	1.32041i	−0.751086	−	0.660204i	$-0.770470\pi$
$797$		−	37.2767i		−	1.32041i	0.751086	−	0.660204i	$-0.229530\pi$
$798$		0			0
$799$		−	2.80528i		−	0.0992435i
$800$		0			0
$801$	51.6276	−	29.8072i	1.82417	−	1.05319i
$802$		0			0
$803$	19.8947	−	34.4587i	0.702070	−	1.21602i
$804$		0			0
$805$	14.4503	+	0.786827i	0.509307	+	0.0277320i
$806$		0			0
$807$	−43.8426	−	25.3125i	−1.54333	−	0.891043i
$808$		0			0
$809$	19.8105	+	34.3129i	0.696501	+	1.20638i	0.969672	+	0.244410i	$0.0785943\pi$
$809$	19.8105	+	34.3129i	0.696501	+	1.20638i	−0.273171	+	0.961966i	$0.588072\pi$
$810$		0			0
$811$	−10.9442			−0.384302			−0.192151	−	0.981365i	$-0.561546\pi$
$811$	−10.9442			−0.384302			−0.192151	+	0.981365i	$0.561546\pi$
$812$		0			0
$813$	53.5843			1.87928
$814$		0			0
$815$	8.14396	+	14.1058i	0.285270	+	0.494103i
$816$		0			0
$817$	0.389133	+	0.224666i	0.0136141	+	0.00786008i
$818$		0			0
$819$	−35.6455	+	18.0709i	−1.24556	+	0.631450i
$820$		0			0
$821$	−15.3675	+	26.6174i	−0.536331	+	0.928952i	0.462767	+	0.886480i	$0.346857\pi$
$821$	−15.3675	+	26.6174i	−0.536331	+	0.928952i	−0.999098	+	0.0424723i	$0.986477\pi$
$822$		0			0
$823$	−18.2514	+	10.5374i	−0.636202	+	0.367312i	−0.783150	−	0.621833i	$-0.786388\pi$
$823$	−18.2514	+	10.5374i	−0.636202	+	0.367312i	0.146948	+	0.989144i	$0.453055\pi$
$824$		0			0
$825$		−	53.1881i		−	1.85177i
$826$		0			0
$827$		−	17.1524i		−	0.596447i	−0.954496	−	0.298224i	$-0.903606\pi$
$827$		−	17.1524i		−	0.596447i	0.954496	−	0.298224i	$-0.0963941\pi$
$828$		0			0
$829$	41.5212	−	23.9723i	1.44209	−	0.832591i	0.444102	−	0.895976i	$-0.353523\pi$
$829$	41.5212	−	23.9723i	1.44209	−	0.832591i	0.997989	+	0.0633850i	$0.0201896\pi$
$830$		0			0
$831$	28.2289	−	48.8940i	0.979251	−	1.69611i
$832$		0			0
$833$	1.96742	+	1.44169i	0.0681669	+	0.0499517i
$834$		0			0
$835$	−5.20247	−	3.00365i	−0.180039	−	0.103945i
$836$		0			0
$837$	−15.4816	−	26.8149i	−0.535123	−	0.926860i
$838$		0			0
$839$	21.2881			0.734948			0.367474	−	0.930034i	$-0.380223\pi$
$839$	21.2881			0.734948			0.367474	+	0.930034i	$0.380223\pi$
$840$		0			0
$841$	23.7130			0.817691
$842$		0			0
$843$	−9.71849	−	16.8329i	−0.334723	−	0.579757i
$844$		0			0
$845$	−8.70340	−	5.02491i	−0.299406	−	0.172862i
$846$		0			0
$847$	11.5067	+	22.6973i	0.395374	+	0.779888i
$848$		0			0
$849$	2.93929	−	5.09101i	0.100876	−	0.174723i
$850$		0			0
$851$	29.7056	−	17.1505i	1.01829	−	0.587913i
$852$		0			0
$853$			16.3608i			0.560183i	0.959973	+	0.280091i	$0.0903648\pi$
$853$			16.3608i			0.560183i	−0.959973	+	0.280091i	$0.909635\pi$
$854$		0			0
$855$			2.62687i			0.0898371i
$856$		0			0
$857$	14.1776	−	8.18543i	0.484297	−	0.279609i	−0.237909	−	0.971288i	$-0.576462\pi$
$857$	14.1776	−	8.18543i	0.484297	−	0.279609i	0.722205	+	0.691679i	$0.243129\pi$
$858$		0			0
$859$	17.1788	−	29.7545i	0.586133	−	1.01521i	−0.408601	−	0.912713i	$-0.633983\pi$
$859$	17.1788	−	29.7545i	0.586133	−	1.01521i	0.994733	−	0.102498i	$-0.0326836\pi$
$860$		0			0
$861$	−0.958642	+	17.6057i	−0.0326704	+	0.600002i
$862$		0			0
$863$	28.4284	+	16.4132i	0.967715	+	0.558710i	0.898539	−	0.438894i	$-0.144630\pi$
$863$	28.4284	+	16.4132i	0.967715	+	0.558710i	0.0691759	+	0.997604i	$0.477963\pi$
$864$		0			0
$865$	−11.3685	−	19.6909i	−0.386541	−	0.669509i
$866$		0			0
$867$	−54.0652			−1.83615
$868$		0			0
$869$	−71.8152			−2.43616
$870$		0			0
$871$	−0.711714	−	1.23273i	−0.0241155	−	0.0417693i
$872$		0			0
$873$	−81.8948	−	47.2820i	−2.77172	−	1.60025i
$874$		0			0
$875$	−22.2324	−	14.5024i	−0.751592	−	0.490269i
$876$		0			0
$877$	−14.4711	+	25.0647i	−0.488654	+	0.846374i	−0.999915	−	0.0130521i	$-0.995845\pi$
$877$	−14.4711	+	25.0647i	−0.488654	+	0.846374i	0.511261	+	0.859426i	$0.329179\pi$
$878$		0			0
$879$	62.7229	−	36.2131i	2.11559	−	1.22144i
$880$		0			0
$881$		−	28.9616i		−	0.975740i	−0.872916	−	0.487870i	$-0.837774\pi$
$881$		−	28.9616i		−	0.975740i	0.872916	−	0.487870i	$-0.162226\pi$
$882$		0			0
$883$			21.5875i			0.726478i	0.931696	+	0.363239i	$0.118329\pi$
$883$			21.5875i			0.726478i	−0.931696	+	0.363239i	$0.881671\pi$
$884$		0			0
$885$	−3.07929	+	1.77783i	−0.103509	+	0.0597611i
$886$		0			0
$887$	8.47280	−	14.6753i	0.284489	−	0.492749i	−0.687996	−	0.725714i	$-0.741509\pi$
$887$	8.47280	−	14.6753i	0.284489	−	0.492749i	0.972485	+	0.232965i	$0.0748428\pi$
$888$		0			0
$889$	−19.3964	−	12.6524i	−0.650535	−	0.424349i
$890$		0			0
$891$	−86.2448	−	49.7934i	−2.88931	−	1.66814i
$892$		0			0
$893$	−1.25670	−	2.17667i	−0.0420539	−	0.0728396i
$894$		0			0
$895$	−13.6150			−0.455099
$896$		0			0
$897$	31.4527			1.05017
$898$		0			0
$899$	8.23656	+	14.2661i	0.274705	+	0.475802i
$900$		0			0
$901$	−0.486096	−	0.280648i	−0.0161942	−	0.00934972i
$902$		0			0
$903$	−0.663192	+	12.1797i	−0.0220697	+	0.405316i
$904$		0			0
$905$	−2.47059	+	4.27919i	−0.0821252	+	0.142245i
$906$		0			0
$907$	−32.8183	+	18.9477i	−1.08971	+	0.629147i	−0.933500	−	0.358576i	$-0.883262\pi$
$907$	−32.8183	+	18.9477i	−1.08971	+	0.629147i	−0.156214	+	0.987723i	$0.549929\pi$
$908$		0			0
$909$			53.6561i			1.77966i
$910$		0			0
$911$		−	21.3300i		−	0.706694i	−0.935492	−	0.353347i	$-0.885043\pi$
$911$		−	21.3300i		−	0.706694i	0.935492	−	0.353347i	$-0.114957\pi$
$912$		0			0
$913$	39.5028	−	22.8070i	1.30735	−	0.754801i
$914$		0			0
$915$	−21.1906	+	36.7031i	−0.700538	+	1.21337i
$916$		0			0
$917$	−8.93274	−	17.6201i	−0.294985	−	0.581867i
$918$		0			0
$919$	−6.92890	−	4.00040i	−0.228563	−	0.131961i	0.381346	−	0.924432i	$-0.375461\pi$
$919$	−6.92890	−	4.00040i	−0.228563	−	0.131961i	−0.609909	+	0.792471i	$0.708794\pi$
$920$		0			0
$921$	−0.596175	−	1.03261i	−0.0196446	−	0.0340255i
$922$		0			0
$923$	−9.51909			−0.313325
$924$		0			0
$925$	−26.5770			−0.873846
$926$		0			0
$927$	−33.8366	−	58.6067i	−1.11134	−	1.92489i
$928$		0			0
$929$	40.3773	+	23.3118i	1.32474	+	0.764836i	0.984480	−	0.175497i	$-0.0561532\pi$
$929$	40.3773	+	23.3118i	1.32474	+	0.764836i	0.340255	+	0.940333i	$0.389486\pi$
$930$		0			0
$931$	2.17241	+	0.237281i	0.0711978	+	0.00777657i
$932$		0			0
$933$	−26.3529	+	45.6445i	−0.862754	+	1.49433i
$934$		0			0
$935$	1.58800	−	0.916830i	0.0519330	−	0.0299835i
$936$		0			0
$937$		−	2.78754i		−	0.0910651i	−0.998963	−	0.0455325i	$-0.985502\pi$
$937$		−	2.78754i		−	0.0910651i	0.998963	−	0.0455325i	$-0.0144985\pi$
$938$		0			0
$939$		−	48.0289i		−	1.56736i
$940$		0			0
$941$	7.53957	−	4.35297i	0.245783	−	0.141903i	−0.372049	−	0.928213i	$-0.621345\pi$
$941$	7.53957	−	4.35297i	0.245783	−	0.141903i	0.617832	+	0.786310i	$0.288011\pi$
$942$		0			0
$943$	4.90960	−	8.50367i	0.159879	−	0.276918i
$944$		0			0
$945$	−37.3225	+	18.9211i	−1.21410	+	0.615503i
$946$		0			0
$947$	−0.851519	−	0.491624i	−0.0276706	−	0.0159756i	0.486101	−	0.873903i	$-0.338419\pi$
$947$	−0.851519	−	0.491624i	−0.0276706	−	0.0159756i	−0.513772	+	0.857927i	$0.671752\pi$
$948$		0			0
$949$	−9.11547	−	15.7885i	−0.295901	−	0.512515i
$950$		0			0
$951$	79.8380			2.58892
$952$		0			0
$953$	−27.9025			−0.903850			−0.451925	−	0.892056i	$-0.649263\pi$
$953$	−27.9025			−0.903850			−0.451925	+	0.892056i	$0.649263\pi$
$954$		0			0
$955$	3.94530	+	6.83346i	0.127667	+	0.221125i
$956$		0			0
$957$	91.4528	+	52.8003i	2.95625	+	1.70679i
$958$		0			0
$959$	−19.5791	−	1.06609i	−0.632242	−	0.0344259i
$960$		0			0
$961$	12.9260	−	22.3885i	0.416969	−	0.722211i
$962$		0			0
$963$	43.2835	−	24.9898i	1.39479	−	0.805284i
$964$		0			0
$965$		−	21.7833i		−	0.701228i
$966$		0			0
$967$			36.4955i			1.17362i	0.809726	+	0.586808i	$0.199616\pi$
$967$			36.4955i			1.17362i	−0.809726	+	0.586808i	$0.800384\pi$
$968$		0			0
$969$	0.301760	−	0.174221i	0.00969394	−	0.00559680i
$970$		0			0
$971$	9.88987	−	17.1298i	0.317381	−	0.549720i	−0.662560	−	0.749009i	$-0.730530\pi$
$971$	9.88987	−	17.1298i	0.317381	−	0.549720i	0.979941	+	0.199289i	$0.0638632\pi$
$972$		0			0
$973$	30.8786	−	47.3375i	0.989922	−	1.51757i
$974$		0			0
$975$	−21.1050	−	12.1850i	−0.675902	−	0.390232i
$976$		0			0
$977$	−11.1375	−	19.2908i	−0.356321	−	0.617167i	0.631022	−	0.775765i	$-0.282636\pi$
$977$	−11.1375	−	19.2908i	−0.356321	−	0.617167i	−0.987343	+	0.158598i	$0.949302\pi$
$978$		0			0
$979$	−37.2836			−1.19159
$980$		0			0
$981$	12.0827			0.385771
$982$		0			0
$983$	9.09947	+	15.7607i	0.290228	+	0.502690i	0.973864	−	0.227134i	$-0.0729355\pi$
$983$	9.09947	+	15.7607i	0.290228	+	0.502690i	−0.683635	+	0.729824i	$0.739602\pi$
$984$		0			0
$985$	−14.5206	−	8.38345i	−0.462663	−	0.267119i
$986$		0			0
$987$	37.2771	−	57.1466i	1.18654	−	1.81900i
$988$		0			0
$989$	3.39648	−	5.88287i	0.108002	−	0.187065i
$990$		0			0
$991$	−7.96425	+	4.59816i	−0.252993	+	0.146065i	−0.621134	−	0.783705i	$-0.713328\pi$
$991$	−7.96425	+	4.59816i	−0.252993	+	0.146065i	0.368141	+	0.929770i	$0.379994\pi$
$992$		0			0
$993$			94.5199i			2.99950i
$994$		0			0
$995$			16.8740i			0.534940i
$996$		0			0
$997$	−10.4757	+	6.04813i	−0.331768	+	0.191546i	−0.656626	−	0.754217i	$-0.728017\pi$
$997$	−10.4757	+	6.04813i	−0.331768	+	0.191546i	0.324858	+	0.945763i	$0.394683\pi$
$998$		0			0
$999$	−49.5904	+	85.8931i	−1.56897	+	2.71754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.p.a.159.8	yes	16
3.2	odd	2		2016.2.cs.b.1279.5		16
4.3	odd	2	inner	224.2.p.a.159.1	yes	16
7.2	even	3		1568.2.f.b.1567.2		16
7.3	odd	6	inner	224.2.p.a.31.1	✓	16
7.4	even	3		1568.2.p.b.31.8		16
7.5	odd	6		1568.2.f.b.1567.15		16
7.6	odd	2		1568.2.p.b.607.1		16
8.3	odd	2		448.2.p.e.383.8		16
8.5	even	2		448.2.p.e.383.1		16
12.11	even	2		2016.2.cs.b.1279.6		16
21.17	even	6		2016.2.cs.b.703.6		16
28.3	even	6	inner	224.2.p.a.31.8	yes	16
28.11	odd	6		1568.2.p.b.31.1		16
28.19	even	6		1568.2.f.b.1567.1		16
28.23	odd	6		1568.2.f.b.1567.16		16
28.27	even	2		1568.2.p.b.607.8		16
56.3	even	6		448.2.p.e.255.1		16
56.5	odd	6		3136.2.f.j.3135.2		16
56.19	even	6		3136.2.f.j.3135.16		16
56.37	even	6		3136.2.f.j.3135.15		16
56.45	odd	6		448.2.p.e.255.8		16
56.51	odd	6		3136.2.f.j.3135.1		16
84.59	odd	6		2016.2.cs.b.703.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.p.a.31.1	✓	16	7.3	odd	6	inner
224.2.p.a.31.8	yes	16	28.3	even	6	inner
224.2.p.a.159.1	yes	16	4.3	odd	2	inner
224.2.p.a.159.8	yes	16	1.1	even	1	trivial
448.2.p.e.255.1		16	56.3	even	6
448.2.p.e.255.8		16	56.45	odd	6
448.2.p.e.383.1		16	8.5	even	2
448.2.p.e.383.8		16	8.3	odd	2
1568.2.f.b.1567.1		16	28.19	even	6
1568.2.f.b.1567.2		16	7.2	even	3
1568.2.f.b.1567.15		16	7.5	odd	6
1568.2.f.b.1567.16		16	28.23	odd	6
1568.2.p.b.31.1		16	28.11	odd	6
1568.2.p.b.31.8		16	7.4	even	3
1568.2.p.b.607.1		16	7.6	odd	2
1568.2.p.b.607.8		16	28.27	even	2
2016.2.cs.b.703.5		16	84.59	odd	6
2016.2.cs.b.703.6		16	21.17	even	6
2016.2.cs.b.1279.5		16	3.2	odd	2
2016.2.cs.b.1279.6		16	12.11	even	2
3136.2.f.j.3135.1		16	56.51	odd	6
3136.2.f.j.3135.2		16	56.5	odd	6
3136.2.f.j.3135.15		16	56.37	even	6
3136.2.f.j.3135.16		16	56.19	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60159 + 2.77404i) q^{3} +(-1.00367 - 0.579471i) q^{5} +(-1.44550 + 2.21597i) q^{7} +(-3.63019 + 6.28767i) q^{9} +O(q^{10})\)	\(q+(1.60159 + 2.77404i) q^{3} +(-1.00367 - 0.579471i) q^{5} +(-1.44550 + 2.21597i) q^{7} +(-3.63019 + 6.28767i) q^{9} +(3.93239 - 2.27036i) q^{11} -2.08049i q^{13} -3.71230i q^{15} +(-0.301760 + 0.174221i) q^{17} +(-0.156095 + 0.270364i) q^{19} +(-8.46229 - 0.460776i) q^{21} +(4.08733 + 2.35982i) q^{23} +(-1.82843 - 3.16693i) q^{25} -13.6468 q^{27} +7.26038 q^{29} +(1.13445 + 1.96493i) q^{31} +(12.5961 + 7.27239i) q^{33} +(2.73490 - 1.38649i) q^{35} +(3.63386 - 6.29403i) q^{37} +(5.77137 - 3.33210i) q^{39} -2.08049i q^{41} -1.43929i q^{43} +(7.28704 - 4.20718i) q^{45} +(-4.02545 + 6.97228i) q^{47} +(-2.82108 - 6.40636i) q^{49} +(-0.966594 - 0.558063i) q^{51} +(0.805433 + 1.39505i) q^{53} -5.26244 q^{55} -1.00000 q^{57} +(-0.478903 - 0.829484i) q^{59} +(-9.88689 - 5.70820i) q^{61} +(-8.68589 - 17.1332i) q^{63} +(-1.20559 + 2.08814i) q^{65} +(0.592516 - 0.342089i) q^{67} +15.1179i q^{69} -4.57540i q^{71} +(7.58880 - 4.38140i) q^{73} +(5.85678 - 10.1442i) q^{75} +(-0.653181 + 11.9959i) q^{77} +(-13.6969 - 7.90790i) q^{79} +(-10.9660 - 18.9936i) q^{81} +10.0455 q^{83} +0.403825 q^{85} +(11.6282 + 20.1405i) q^{87} +(-7.11087 - 4.10546i) q^{89} +(4.61032 + 3.00735i) q^{91} +(-3.63386 + 6.29403i) q^{93} +(0.313336 - 0.180905i) q^{95} +13.0247i q^{97} +32.9674i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^9	\( 16 q - 8 q^{9} - 24 q^{21} + 16 q^{25} + 16 q^{29} + 24 q^{33} - 8 q^{37} - 24 q^{45} - 32 q^{49} - 8 q^{53} - 16 q^{57} - 24 q^{61} + 8 q^{65} - 24 q^{73} + 64 q^{77} - 48 q^{81} - 16 q^{85} - 72 q^{89} + 8 q^{93}+O(q^{100}) \) 16 * q - 8 * q^9 - 24 * q^21 + 16 * q^25 + 16 * q^29 + 24 * q^33 - 8 * q^37 - 24 * q^45 - 32 * q^49 - 8 * q^53 - 16 * q^57 - 24 * q^61 + 8 * q^65 - 24 * q^73 + 64 * q^77 - 48 * q^81 - 16 * q^85 - 72 * q^89 + 8 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more