LMFDB - Embedded newform 896.2.q.d.831.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(703,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, 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("896.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 24x^{14} + 226x^{12} - 972x^{10} + 1575x^{8} + 252x^{6} + 550x^{4} + 156x^{2} + 49 $ x^16 - 24x^14 + 226x^12 - 972x^10 + 1575x^8 + 252x^6 + 550x^4 + 156*x^2 + 49
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			831.3
Root			$-0.245327 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	896.831
Dual form			896.2.q.d.703.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.537541 - 0.310349i) q^{3} +(-0.0337794 + 0.0585076i) q^{5} +(1.98532 + 1.74886i) q^{7} +(-1.30737 + 2.26443i) q^{9} +O(q^{10})$	\(q+(0.537541 - 0.310349i) q^{3} +(-0.0337794 + 0.0585076i) q^{5} +(1.98532 + 1.74886i) q^{7} +(-1.30737 + 2.26443i) q^{9} +(1.28640 + 2.22811i) q^{11} +5.63513 q^{13} +0.0419337i q^{15} +(-4.45525 + 2.57224i) q^{17} +(-5.90113 - 3.40702i) q^{19} +(1.60995 + 0.323941i) q^{21} +(-4.92752 - 2.84491i) q^{23} +(2.49772 + 4.32617i) q^{25} +3.48506i q^{27} +2.76490i q^{29} +(1.14260 + 1.97903i) q^{31} +(1.38298 + 0.798467i) q^{33} +(-0.169384 + 0.0570809i) q^{35} +(6.82198 + 3.93867i) q^{37} +(3.02911 - 1.74886i) q^{39} +4.39373i q^{41} +6.99544 q^{43} +(-0.0883241 - 0.152982i) q^{45} +(2.32151 - 4.02097i) q^{47} +(0.882985 + 6.94409i) q^{49} +(-1.59658 + 2.76537i) q^{51} +(7.48928 - 4.32394i) q^{53} -0.173815 q^{55} -4.22947 q^{57} +(4.38738 - 2.53305i) q^{59} +(3.34200 - 5.78851i) q^{61} +(-6.55570 + 2.20921i) q^{63} +(-0.190351 + 0.329698i) q^{65} +(-5.72507 - 9.91612i) q^{67} -3.53166 q^{69} +9.52979i q^{71} +(-0.767178 + 0.442931i) q^{73} +(2.68525 + 1.55033i) q^{75} +(-1.34274 + 6.67324i) q^{77} +(-2.07331 - 1.19703i) q^{79} +(-2.84051 - 4.91992i) q^{81} -11.2703i q^{83} -0.347555i q^{85} +(0.858084 + 1.48624i) q^{87} +(1.73403 + 1.00114i) q^{89} +(11.1875 + 9.85505i) q^{91} +(1.22838 + 0.709207i) q^{93} +(0.398673 - 0.230174i) q^{95} +4.52885i q^{97} -6.72718 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{3} + 8 q^{9}+O(q^{10}) $ 16 * q + 12 * q^3 + 8 * q^9	$ 16 q + 12 q^{3} + 8 q^{9} - 4 q^{11} - 12 q^{19} - 16 q^{25} + 24 q^{33} + 20 q^{35} + 16 q^{49} - 52 q^{51} + 48 q^{57} + 60 q^{59} + 24 q^{65} + 12 q^{67} - 24 q^{73} - 120 q^{75} - 32 q^{81} + 24 q^{89} + 72 q^{91} + 64 q^{99}+O(q^{100}) $ 16 * q + 12 * q^3 + 8 * q^9 - 4 * q^11 - 12 * q^19 - 16 * q^25 + 24 * q^33 + 20 * q^35 + 16 * q^49 - 52 * q^51 + 48 * q^57 + 60 * q^59 + 24 * q^65 + 12 * q^67 - 24 * q^73 - 120 * q^75 - 32 * q^81 + 24 * q^89 + 72 * q^91 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	0.537541	−	0.310349i	0.310349	−	0.179180i	−0.336733	−	0.941600i	$-0.609322\pi$
$3$	0.537541	−	0.310349i	0.310349	−	0.179180i	0.647083	+	0.762420i	$0.275989\pi$
$4$		0			0
$5$	−0.0337794	+	0.0585076i	−0.0151066	+	0.0261654i	−0.873480	−	0.486860i	$-0.838142\pi$
$5$	−0.0337794	+	0.0585076i	−0.0151066	+	0.0261654i	0.858373	+	0.513026i	$0.171475\pi$
$6$		0			0
$7$	1.98532	+	1.74886i	0.750380	+	0.661007i
$7$	1.98532	+	1.74886i	0.750380	+	0.661007i
$8$		0			0
$9$	−1.30737	+	2.26443i	−0.435789	+	0.754808i
$10$		0			0
$11$	1.28640	+	2.22811i	0.387864	+	0.671800i	0.992162	−	0.124958i	$-0.0398796\pi$
$11$	1.28640	+	2.22811i	0.387864	+	0.671800i	−0.604298	+	0.796758i	$0.706546\pi$
$12$		0			0
$13$	5.63513			1.56290			0.781452	−	0.623965i	$-0.214479\pi$
$13$	5.63513			1.56290			0.781452	+	0.623965i	$0.214479\pi$
$14$		0			0
$15$			0.0419337i			0.0108272i
$16$		0			0
$17$	−4.45525	+	2.57224i	−1.08056	+	0.623859i	−0.931046	−	0.364901i	$-0.881103\pi$
$17$	−4.45525	+	2.57224i	−1.08056	+	0.623859i	−0.149510	+	0.988760i	$0.547770\pi$
$18$		0			0
$19$	−5.90113	−	3.40702i	−1.35381	−	0.781624i	−0.365032	−	0.930995i	$-0.618942\pi$
$19$	−5.90113	−	3.40702i	−1.35381	−	0.781624i	−0.988781	+	0.149371i	$0.952275\pi$
$20$		0			0
$21$	1.60995	+	0.323941i	0.351319	+	0.0706896i
$22$		0			0
$23$	−4.92752	−	2.84491i	−1.02746	−	0.593204i	−0.111204	−	0.993798i	$-0.535471\pi$
$23$	−4.92752	−	2.84491i	−1.02746	−	0.593204i	−0.916256	+	0.400593i	$0.868804\pi$
$24$		0			0
$25$	2.49772	+	4.32617i	0.499544	+	0.865235i
$26$		0			0
$27$			3.48506i			0.670700i
$28$		0			0
$29$			2.76490i			0.513428i	0.966487	+	0.256714i	$0.0826399\pi$
$29$			2.76490i			0.513428i	−0.966487	+	0.256714i	$0.917360\pi$
$30$		0			0
$31$	1.14260	+	1.97903i	0.205216	+	0.355445i	0.950202	−	0.311636i	$-0.100877\pi$
$31$	1.14260	+	1.97903i	0.205216	+	0.355445i	−0.744985	+	0.667081i	$0.767544\pi$
$32$		0			0
$33$	1.38298	+	0.798467i	0.240747	+	0.138995i
$34$		0			0
$35$	−0.169384	+	0.0570809i	−0.0286312	+	0.00964844i
$36$		0			0
$37$	6.82198	+	3.93867i	1.12153	+	0.647514i	0.941790	−	0.336201i	$-0.109142\pi$
$37$	6.82198	+	3.93867i	1.12153	+	0.647514i	0.179737	+	0.983715i	$0.442475\pi$
$38$		0			0
$39$	3.02911	−	1.74886i	0.485046	−	0.280042i
$40$		0			0
$41$			4.39373i			0.686186i	0.939301	+	0.343093i	$0.111475\pi$
$41$			4.39373i			0.686186i	−0.939301	+	0.343093i	$0.888525\pi$
$42$		0			0
$43$	6.99544			1.06679			0.533397	−	0.845865i	$-0.320915\pi$
$43$	6.99544			1.06679			0.533397	+	0.845865i	$0.320915\pi$
$44$		0			0
$45$	−0.0883241	−	0.152982i	−0.0131666	−	0.0228052i
$46$		0			0
$47$	2.32151	−	4.02097i	0.338626	−	0.586518i	−0.645548	−	0.763720i	$-0.723371\pi$
$47$	2.32151	−	4.02097i	0.338626	−	0.586518i	0.984175	+	0.177201i	$0.0567044\pi$
$48$		0			0
$49$	0.882985	+	6.94409i	0.126141	+	0.992012i
$50$		0			0
$51$	−1.59658	+	2.76537i	−0.223567	+	0.387229i
$52$		0			0
$53$	7.48928	−	4.32394i	1.02873	−	0.593939i	0.112111	−	0.993696i	$-0.464239\pi$
$53$	7.48928	−	4.32394i	1.02873	−	0.593939i	0.916621	+	0.399757i	$0.130905\pi$
$54$		0			0
$55$	−0.173815			−0.0234372
$56$		0			0
$57$	−4.22947			−0.560207
$58$		0			0
$59$	4.38738	−	2.53305i	0.571188	−	0.329775i	−0.186436	−	0.982467i	$-0.559694\pi$
$59$	4.38738	−	2.53305i	0.571188	−	0.329775i	0.757624	+	0.652692i	$0.226360\pi$
$60$		0			0
$61$	3.34200	−	5.78851i	0.427899	−	0.741143i	−0.568787	−	0.822485i	$-0.692587\pi$
$61$	3.34200	−	5.78851i	0.427899	−	0.741143i	0.996686	+	0.0813419i	$0.0259206\pi$
$62$		0			0
$63$	−6.55570	+	2.20921i	−0.825941	+	0.278334i
$64$		0			0
$65$	−0.190351	+	0.329698i	−0.0236102	+	0.0408940i
$66$		0			0
$67$	−5.72507	−	9.91612i	−0.699429	−	1.21145i	−0.968665	−	0.248372i	$-0.920104\pi$
$67$	−5.72507	−	9.91612i	−0.699429	−	1.21145i	0.269236	−	0.963074i	$-0.413229\pi$
$68$		0			0
$69$	−3.53166			−0.425162
$70$		0			0
$71$			9.52979i			1.13098i	0.824756	+	0.565489i	$0.191313\pi$
$71$			9.52979i			1.13098i	−0.824756	+	0.565489i	$0.808687\pi$
$72$		0			0
$73$	−0.767178	+	0.442931i	−0.0897915	+	0.0518411i	−0.544223	−	0.838940i	$-0.683176\pi$
$73$	−0.767178	+	0.442931i	−0.0897915	+	0.0518411i	0.454432	+	0.890781i	$0.349842\pi$
$74$		0			0
$75$	2.68525	+	1.55033i	0.310066	+	0.179017i
$76$		0			0
$77$	−1.34274	+	6.67324i	−0.153019	+	0.760486i
$78$		0			0
$79$	−2.07331	−	1.19703i	−0.233266	−	0.134676i	0.378812	−	0.925474i	$-0.376333\pi$
$79$	−2.07331	−	1.19703i	−0.233266	−	0.134676i	−0.612078	+	0.790798i	$0.709666\pi$
$80$		0			0
$81$	−2.84051	−	4.91992i	−0.315613	−	0.546657i
$82$		0			0
$83$		−	11.2703i		−	1.23707i	−0.785757	−	0.618536i	$-0.787726\pi$
$83$		−	11.2703i		−	1.23707i	0.785757	−	0.618536i	$-0.212274\pi$
$84$		0			0
$85$		−	0.347555i		−	0.0376976i
$86$		0			0
$87$	0.858084	+	1.48624i	0.0919962	+	0.159342i
$88$		0			0
$89$	1.73403	+	1.00114i	0.183807	+	0.106121i	0.589080	−	0.808075i	$-0.299490\pi$
$89$	1.73403	+	1.00114i	0.183807	+	0.106121i	−0.405273	+	0.914196i	$0.632824\pi$
$90$		0			0
$91$	11.1875	+	9.85505i	1.17277	+	1.03309i
$92$		0			0
$93$	1.22838	+	0.709207i	0.127377	+	0.0735414i
$94$		0			0
$95$	0.398673	−	0.230174i	0.0409030	−	0.0236154i
$96$		0			0
$97$			4.52885i			0.459835i	0.973210	+	0.229918i	$0.0738457\pi$
$97$			4.52885i			0.459835i	−0.973210	+	0.229918i	$0.926154\pi$
$98$		0			0
$99$	−6.72718			−0.676107
$100$		0			0
$101$	2.18892	+	3.79133i	0.217806	+	0.377251i	0.954137	−	0.299370i	$-0.0967766\pi$
$101$	2.18892	+	3.79133i	0.217806	+	0.377251i	−0.736331	+	0.676622i	$0.763443\pi$
$102$		0			0
$103$	7.63581	−	13.2256i	0.752379	−	1.30316i	−0.194288	−	0.980944i	$-0.562240\pi$
$103$	7.63581	−	13.2256i	0.752379	−	1.30316i	0.946667	−	0.322214i	$-0.104427\pi$
$104$		0			0
$105$	−0.0733360	+	0.0832517i	−0.00715687	+	0.00812453i
$106$		0			0
$107$	−8.97621	+	15.5473i	−0.867763	+	1.50301i	−0.00348655	+	0.999994i	$0.501110\pi$
$107$	−8.97621	+	15.5473i	−0.867763	+	1.50301i	−0.864277	+	0.503016i	$0.832224\pi$
$108$		0			0
$109$	−0.508550	+	0.293611i	−0.0487102	+	0.0281229i	−0.524157	−	0.851621i	$-0.675620\pi$
$109$	−0.508550	+	0.293611i	−0.0487102	+	0.0281229i	0.475447	+	0.879744i	$0.342286\pi$
$110$		0			0
$111$	4.88946			0.464087
$112$		0			0
$113$	4.91506			0.462370			0.231185	−	0.972910i	$-0.425740\pi$
$113$	4.91506			0.462370			0.231185	+	0.972910i	$0.425740\pi$
$114$		0			0
$115$	0.332898	−	0.192199i	0.0310429	−	0.0179226i
$116$		0			0
$117$	−7.36718	+	12.7603i	−0.681096	+	1.17969i
$118$		0			0
$119$	−13.3436	−	2.68489i	−1.22320	−	0.246123i
$120$		0			0
$121$	2.19035	−	3.79380i	0.199123	−	0.344891i
$122$		0			0
$123$	1.36359	+	2.36181i	0.122951	+	0.212957i
$124$		0			0
$125$	−0.675280			−0.0603988
$126$		0			0
$127$		−	5.52979i		−	0.490690i	−0.969436	−	0.245345i	$-0.921099\pi$
$127$		−	5.52979i		−	0.490690i	0.969436	−	0.245345i	$-0.0789012\pi$
$128$		0			0
$129$	3.76033	−	2.17103i	0.331079	−	0.191148i
$130$		0			0
$131$	−8.34544	−	4.81824i	−0.729145	−	0.420972i	0.0889644	−	0.996035i	$-0.471644\pi$
$131$	−8.34544	−	4.81824i	−0.729145	−	0.420972i	−0.818109	+	0.575063i	$0.804978\pi$
$132$		0			0
$133$	−5.75723	−	17.0843i	−0.499215	−	1.48139i
$134$		0			0
$135$	−0.203902	−	0.117723i	−0.0175491	−	0.0101320i
$136$		0			0
$137$	−8.06998	−	13.9776i	−0.689465	−	1.19419i	−0.972011	−	0.234935i	$-0.924512\pi$
$137$	−8.06998	−	13.9776i	−0.689465	−	1.19419i	0.282546	−	0.959254i	$-0.408821\pi$
$138$		0			0
$139$		−	8.04463i		−	0.682336i	−0.940002	−	0.341168i	$-0.889177\pi$
$139$		−	8.04463i		−	0.682336i	0.940002	−	0.341168i	$-0.110823\pi$
$140$		0			0
$141$		−	2.88191i		−	0.242701i
$142$		0			0
$143$	7.24903	+	12.5557i	0.606194	+	1.04996i
$144$		0			0
$145$	−0.161768	−	0.0933965i	−0.0134341	−	0.00775616i
$146$		0			0
$147$	2.62973	+	3.45870i	0.216897	+	0.285268i
$148$		0			0
$149$	−17.0067	−	9.81884i	−1.39325	−	0.804391i	−0.399572	−	0.916702i	$-0.630841\pi$
$149$	−17.0067	−	9.81884i	−1.39325	−	0.804391i	−0.993673	+	0.112311i	$0.964175\pi$
$150$		0			0
$151$	−12.4129	+	7.16657i	−1.01014	+	0.583207i	−0.911234	−	0.411890i	$-0.864869\pi$
$151$	−12.4129	+	7.16657i	−1.01014	+	0.583207i	−0.0989101	+	0.995096i	$0.531536\pi$
$152$		0			0
$153$		−	13.4514i		−	1.08748i
$154$		0			0
$155$	−0.154385			−0.0124005
$156$		0			0
$157$	−8.11506	−	14.0557i	−0.647652	−	1.12177i	−0.983682	−	0.179915i	$-0.942418\pi$
$157$	−8.11506	−	14.0557i	−0.647652	−	1.12177i	0.336030	−	0.941851i	$-0.390916\pi$
$158$		0			0
$159$	2.68386	−	4.64859i	0.212844	−	0.368657i
$160$		0			0
$161$	−4.80737	−	14.2656i	−0.378874	−	1.12429i
$162$		0			0
$163$	−5.46246	+	9.46126i	−0.427853	+	0.741063i	−0.996682	−	0.0813928i	$-0.974063\pi$
$163$	−5.46246	+	9.46126i	−0.427853	+	0.741063i	0.568829	+	0.822456i	$0.307397\pi$
$164$		0			0
$165$	−0.0934328	+	0.0539434i	−0.00727373	+	0.00419949i
$166$		0			0
$167$	21.0527			1.62911			0.814553	−	0.580090i	$-0.196983\pi$
$167$	21.0527			1.62911			0.814553	+	0.580090i	$0.196983\pi$
$168$		0			0
$169$	18.7547			1.44267
$170$		0			0
$171$	15.4299	−	8.90845i	1.17995	−	0.681246i
$172$		0			0
$173$	−1.54239	+	2.67150i	−0.117266	+	0.203110i	−0.918683	−	0.394995i	$-0.870746\pi$
$173$	−1.54239	+	2.67150i	−0.117266	+	0.203110i	0.801418	+	0.598105i	$0.204080\pi$
$174$		0			0
$175$	−2.60710	+	12.9570i	−0.197078	+	0.979457i
$176$		0			0
$177$	1.57226	−	2.72324i	0.118179	−	0.204691i
$178$		0			0
$179$	2.93428	+	5.08232i	0.219318	+	0.379871i	0.954600	−	0.297891i	$-0.0962833\pi$
$179$	2.93428	+	5.08232i	0.219318	+	0.379871i	−0.735281	+	0.677762i	$0.762950\pi$
$180$		0			0
$181$	−7.77439			−0.577866			−0.288933	−	0.957349i	$-0.593300\pi$
$181$	−7.77439			−0.577866			−0.288933	+	0.957349i	$0.593300\pi$
$182$		0			0
$183$		−	4.14875i		−	0.306684i
$184$		0			0
$185$	−0.460885	+	0.266092i	−0.0338849	+	0.0195635i
$186$		0			0
$187$	−11.4625	−	6.61785i	−0.838218	−	0.483945i
$188$		0			0
$189$	−6.09487	+	6.91895i	−0.443337	+	0.503280i
$190$		0			0
$191$	−19.0083	−	10.9745i	−1.37540	−	0.794085i	−0.383794	−	0.923419i	$-0.625383\pi$
$191$	−19.0083	−	10.9745i	−1.37540	−	0.794085i	−0.991601	+	0.129334i	$0.958716\pi$
$192$		0			0
$193$	4.57226	+	7.91939i	0.329119	+	0.570050i	0.982337	−	0.187119i	$-0.0599150\pi$
$193$	4.57226	+	7.91939i	0.329119	+	0.570050i	−0.653219	+	0.757169i	$0.726582\pi$
$194$		0			0
$195$			0.236302i			0.0169219i
$196$		0			0
$197$			15.5263i			1.10620i	0.833114	+	0.553102i	$0.186556\pi$
$197$			15.5263i			1.10620i	−0.833114	+	0.553102i	$0.813444\pi$
$198$		0			0
$199$	11.9273	+	20.6586i	0.845502	+	1.46445i	0.885184	+	0.465240i	$0.154032\pi$
$199$	11.9273	+	20.6586i	0.845502	+	1.46445i	−0.0396823	+	0.999212i	$0.512635\pi$
$200$		0			0
$201$	−6.15492	−	3.55355i	−0.434135	−	0.250648i
$202$		0			0
$203$	−4.83541	+	5.48920i	−0.339380	+	0.385266i
$204$		0			0
$205$	−0.257067	−	0.148418i	−0.0179543	−	0.0103659i
$206$		0			0
$207$	12.8842	−	7.43867i	0.895511	−	0.517024i
$208$		0			0
$209$		−	17.5312i		−	1.21266i
$210$		0			0
$211$	4.08387			0.281145			0.140573	−	0.990070i	$-0.455106\pi$
$211$	4.08387			0.281145			0.140573	+	0.990070i	$0.455106\pi$
$212$		0			0
$213$	2.95756	+	5.12265i	0.202649	+	0.350998i
$214$		0			0
$215$	−0.236302	+	0.409286i	−0.0161156	+	0.0279131i
$216$		0			0
$217$	−1.19263	+	5.92725i	−0.0809612	+	0.402368i
$218$		0			0
$219$	−0.274926	+	0.476187i	−0.0185778	+	0.0321777i
$220$		0			0
$221$	−25.1059	+	14.4949i	−1.68881	+	0.975032i
$222$		0			0
$223$	−4.73727			−0.317231			−0.158615	−	0.987340i	$-0.550703\pi$
$223$	−4.73727			−0.317231			−0.158615	+	0.987340i	$0.550703\pi$
$224$		0			0
$225$	−13.0617			−0.870782
$226$		0			0
$227$	22.3943	−	12.9293i	1.48636	−	0.858151i	0.486482	−	0.873691i	$-0.338280\pi$
$227$	22.3943	−	12.9293i	1.48636	−	0.858151i	0.999879	+	0.0155398i	$0.00494667\pi$
$228$		0			0
$229$	6.17545	−	10.6962i	0.408085	−	0.706824i	−0.586590	−	0.809884i	$-0.699530\pi$
$229$	6.17545	−	10.6962i	0.408085	−	0.706824i	0.994675	+	0.103060i	$0.0328634\pi$
$230$		0			0
$231$	1.34926	+	4.00386i	0.0887748	+	0.263434i
$232$		0			0
$233$	4.95297	−	8.57879i	0.324480	−	0.562015i	−0.656927	−	0.753954i	$-0.728144\pi$
$233$	4.95297	−	8.57879i	0.324480	−	0.562015i	0.981407	+	0.191939i	$0.0614775\pi$
$234$		0			0
$235$	0.156838	+	0.271652i	0.0102310	+	0.0177206i
$236$		0			0
$237$	−1.48599			−0.0965251
$238$		0			0
$239$			6.49315i			0.420007i	0.977701	+	0.210004i	$0.0673476\pi$
$239$			6.49315i			0.420007i	−0.977701	+	0.210004i	$0.932652\pi$
$240$		0			0
$241$	15.3442	−	8.85898i	0.988407	−	0.570657i	0.0836091	−	0.996499i	$-0.473355\pi$
$241$	15.3442	−	8.85898i	0.988407	−	0.570657i	0.904798	+	0.425842i	$0.140022\pi$
$242$		0			0
$243$	−12.1082	−	6.99069i	−0.776743	−	0.448453i
$244$		0			0
$245$	−0.436109	−	0.182906i	−0.0278620	−	0.0116854i
$246$		0			0
$247$	−33.2537	−	19.1990i	−2.11588	−	1.22160i
$248$		0			0
$249$	−3.49772	−	6.05823i	−0.221659	−	0.383924i
$250$		0			0
$251$		−	5.61739i		−	0.354566i	−0.984160	−	0.177283i	$-0.943269\pi$
$251$		−	5.61739i		−	0.354566i	0.984160	−	0.177283i	$-0.0567309\pi$
$252$		0			0
$253$		−	14.6388i		−	0.920331i
$254$		0			0
$255$	−0.107863	−	0.186825i	−0.00675467	−	0.0116994i
$256$		0			0
$257$	−6.06542	−	3.50187i	−0.378350	−	0.218441i	0.298750	−	0.954331i	$-0.403430\pi$
$257$	−6.06542	−	3.50187i	−0.378350	−	0.218441i	−0.677100	+	0.735891i	$0.736764\pi$
$258$		0			0
$259$	6.65563	+	19.7502i	0.413561	+	1.22722i
$260$		0			0
$261$	−6.26090	−	3.61473i	−0.387540	−	0.223746i
$262$		0			0
$263$	18.6460	−	10.7653i	1.14976	−	0.663814i	0.200932	−	0.979605i	$-0.435603\pi$
$263$	18.6460	−	10.7653i	1.14976	−	0.663814i	0.948829	+	0.315791i	$0.102270\pi$
$264$		0			0
$265$			0.584240i			0.0358896i
$266$		0			0
$267$	1.24282			0.0760591
$268$		0			0
$269$	−12.5088	−	21.6659i	−0.762674	−	1.32099i	−0.941467	−	0.337104i	$-0.890553\pi$
$269$	−12.5088	−	21.6659i	−0.762674	−	1.32099i	0.178793	−	0.983887i	$-0.442781\pi$
$270$		0			0
$271$	9.99363	−	17.3095i	0.607070	−	1.05148i	−0.384651	−	0.923062i	$-0.625678\pi$
$271$	9.99363	−	17.3095i	0.607070	−	1.05148i	0.991721	−	0.128414i	$-0.0409885\pi$
$272$		0			0
$273$	9.07226	+	1.82545i	0.549078	+	0.110481i
$274$		0			0
$275$	−6.42613	+	11.1304i	−0.387510	+	0.671187i
$276$		0			0
$277$	18.6862	−	10.7885i	1.12275	−	0.648219i	0.180647	−	0.983548i	$-0.442181\pi$
$277$	18.6862	−	10.7885i	1.12275	−	0.648219i	0.942101	+	0.335329i	$0.108848\pi$
$278$		0			0
$279$	−5.97516			−0.357724
$280$		0			0
$281$	−13.8442			−0.825876			−0.412938	−	0.910759i	$-0.635497\pi$
$281$	−13.8442			−0.825876			−0.412938	+	0.910759i	$0.635497\pi$
$282$		0			0
$283$	−7.08444	+	4.09021i	−0.421126	+	0.243137i	−0.695559	−	0.718469i	$-0.744843\pi$
$283$	−7.08444	+	4.09021i	−0.421126	+	0.243137i	0.274433	+	0.961606i	$0.411510\pi$
$284$		0			0
$285$	0.142869	−	0.247456i	0.00846282	−	0.0146580i
$286$		0			0
$287$	−7.68402	+	8.72296i	−0.453573	+	0.514900i
$288$		0			0
$289$	4.73282	−	8.19749i	0.278401	−	0.482205i
$290$		0			0
$291$	1.40553	+	2.43444i	0.0823934	+	0.142710i
$292$		0			0
$293$	−25.2618			−1.47581			−0.737905	−	0.674905i	$-0.764185\pi$
$293$	−25.2618			−1.47581			−0.737905	+	0.674905i	$0.764185\pi$
$294$		0			0
$295$			0.342260i			0.0199272i
$296$		0			0
$297$	−7.76509	+	4.48318i	−0.450576	+	0.260140i
$298$		0			0
$299$	−27.7672	−	16.0314i	−1.60582	−	0.927121i
$300$		0			0
$301$	13.8882	+	12.2340i	0.800501	+	0.705158i
$302$		0			0
$303$	2.35327	+	1.35866i	0.135192	+	0.0780531i
$304$		0			0
$305$	0.225781	+	0.391065i	0.0129282	+	0.0223923i
$306$		0			0
$307$		−	0.228324i		−	0.0130311i	−0.999979	−	0.00651556i	$-0.997926\pi$
$307$		−	0.228324i		−	0.0130311i	0.999979	−	0.00651556i	$-0.00207398\pi$
$308$		0			0
$309$		−	9.47907i		−	0.539246i
$310$		0			0
$311$	−5.80548	−	10.0554i	−0.329199	−	0.570189i	0.653154	−	0.757225i	$-0.273445\pi$
$311$	−5.80548	−	10.0554i	−0.329199	−	0.570189i	−0.982353	+	0.187036i	$0.940112\pi$
$312$		0			0
$313$	16.8374	+	9.72105i	0.951703	+	0.549466i	0.893610	−	0.448845i	$-0.148164\pi$
$313$	16.8374	+	9.72105i	0.951703	+	0.549466i	0.0580938	+	0.998311i	$0.481498\pi$
$314$		0			0
$315$	0.0921921	−	0.458184i	0.00519444	−	0.0258158i
$316$		0			0
$317$	15.8815	+	9.16921i	0.891996	+	0.514994i	0.874595	−	0.484854i	$-0.161127\pi$
$317$	15.8815	+	9.16921i	0.891996	+	0.514994i	0.0174014	+	0.999849i	$0.494461\pi$
$318$		0			0
$319$	−6.16049	+	3.55676i	−0.344921	+	0.199140i
$320$		0			0
$321$			11.1430i			0.621944i
$322$		0			0
$323$	35.0547			1.95049
$324$		0			0
$325$	14.0750	+	24.3786i	0.780739	+	1.35228i
$326$		0			0
$327$	−0.182244	+	0.315656i	−0.0100781	+	0.0174558i
$328$		0			0
$329$	11.6410	−	3.92292i	0.641791	−	0.216277i
$330$		0			0
$331$	−0.274926	+	0.476187i	−0.0151113	+	0.0261736i	−0.873482	−	0.486856i	$-0.838144\pi$
$331$	−0.274926	+	0.476187i	−0.0151113	+	0.0261736i	0.858371	+	0.513030i	$0.171477\pi$
$332$		0			0
$333$	−17.8377	+	10.2986i	−0.977498	+	0.564359i
$334$		0			0
$335$	0.773558			0.0422640
$336$		0			0
$337$	−2.37856			−0.129568			−0.0647841	−	0.997899i	$-0.520636\pi$
$337$	−2.37856			−0.129568			−0.0647841	+	0.997899i	$0.520636\pi$
$338$		0			0
$339$	2.64205	−	1.52539i	0.143496	−	0.0828476i
$340$		0			0
$341$	−2.93967	+	5.09166i	−0.159192	+	0.275729i
$342$		0			0
$343$	−10.3912	+	15.3304i	−0.561073	+	0.827766i
$344$		0			0
$345$	0.119297	−	0.206629i	0.00642275	−	0.0111245i
$346$		0			0
$347$	−15.2968	−	26.4948i	−0.821175	−	1.42232i	−0.904808	−	0.425821i	$-0.859985\pi$
$347$	−15.2968	−	26.4948i	−0.821175	−	1.42232i	0.0836324	−	0.996497i	$-0.473348\pi$
$348$		0			0
$349$	34.6630			1.85547			0.927734	−	0.373241i	$-0.121754\pi$
$349$	34.6630			1.85547			0.927734	+	0.373241i	$0.121754\pi$
$350$		0			0
$351$			19.6388i			1.04824i
$352$		0			0
$353$	−16.0323	+	9.25623i	−0.853312	+	0.492660i	−0.861767	−	0.507305i	$-0.830642\pi$
$353$	−16.0323	+	9.25623i	−0.853312	+	0.492660i	0.00845525	+	0.999964i	$0.497309\pi$
$354$		0			0
$355$	−0.557566	−	0.321911i	−0.0295925	−	0.0170852i
$356$		0			0
$357$	−8.00597	+	2.69793i	−0.423721	+	0.142790i
$358$		0			0
$359$	3.41802	+	1.97340i	0.180396	+	0.104152i	0.587479	−	0.809240i	$-0.300121\pi$
$359$	3.41802	+	1.97340i	0.180396	+	0.104152i	−0.407083	+	0.913391i	$0.633454\pi$
$360$		0			0
$361$	13.7156	+	23.7561i	0.721873	+	1.25032i
$362$		0			0
$363$		−	2.71910i		−	0.142716i
$364$		0			0
$365$		−	0.0598477i		−	0.00313257i
$366$		0			0
$367$	2.02163	+	3.50157i	0.105528	+	0.182781i	0.913954	−	0.405818i	$-0.133013\pi$
$367$	2.02163	+	3.50157i	0.105528	+	0.182781i	−0.808426	+	0.588598i	$0.799680\pi$
$368$		0			0
$369$	−9.94928	−	5.74422i	−0.517939	−	0.299032i
$370$		0			0
$371$	22.4306	+	4.51330i	1.16454	+	0.234319i
$372$		0			0
$373$	2.54532	+	1.46954i	0.131792	+	0.0760899i	0.564446	−	0.825470i	$-0.309090\pi$
$373$	2.54532	+	1.46954i	0.131792	+	0.0760899i	−0.432655	+	0.901560i	$0.642423\pi$
$374$		0			0
$375$	−0.362990	+	0.209573i	−0.0187447	+	0.0108223i
$376$		0			0
$377$			15.5806i			0.802439i
$378$		0			0
$379$	4.41627			0.226848			0.113424	−	0.993547i	$-0.463818\pi$
$379$	4.41627			0.226848			0.113424	+	0.993547i	$0.463818\pi$
$380$		0			0
$381$	−1.71617	−	2.97249i	−0.0879219	−	0.152285i
$382$		0			0
$383$	13.2413	−	22.9346i	0.676599	−	1.17190i	−0.299400	−	0.954128i	$-0.596786\pi$
$383$	13.2413	−	22.9346i	0.676599	−	1.17190i	0.975999	−	0.217776i	$-0.0698803\pi$
$384$		0			0
$385$	−0.345079	−	0.303978i	−0.0175868	−	0.0154922i
$386$		0			0
$387$	−9.14560	+	15.8406i	−0.464897	+	0.805225i
$388$		0			0
$389$	18.0238	−	10.4061i	0.913844	−	0.527608i	0.0321783	−	0.999482i	$-0.489756\pi$
$389$	18.0238	−	10.4061i	0.913844	−	0.527608i	0.881666	+	0.471874i	$0.156422\pi$
$390$		0			0
$391$	29.2711			1.48030
$392$		0			0
$393$	−5.98136			−0.301719
$394$		0			0
$395$	0.140070	−	0.0808697i	0.00704770	−	0.00406899i
$396$		0			0
$397$	6.14368	−	10.6412i	0.308342	−	0.534065i	−0.669657	−	0.742670i	$-0.733559\pi$
$397$	6.14368	−	10.6412i	0.308342	−	0.534065i	0.978000	+	0.208605i	$0.0668924\pi$
$398$		0			0
$399$	−8.39684	−	7.39674i	−0.420368	−	0.370300i
$400$		0			0
$401$	−16.2201	+	28.0941i	−0.809995	+	1.40295i	0.102871	+	0.994695i	$0.467197\pi$
$401$	−16.2201	+	28.0941i	−0.809995	+	1.40295i	−0.912866	+	0.408258i	$0.866136\pi$
$402$		0			0
$403$	6.43867	+	11.1521i	0.320733	+	0.555526i
$404$		0			0
$405$	0.383803			0.0190713
$406$		0			0
$407$			20.2668i			1.00459i
$408$		0			0
$409$	6.98719	−	4.03405i	0.345494	−	0.199471i	−0.317205	−	0.948357i	$-0.602744\pi$
$409$	6.98719	−	4.03405i	0.345494	−	0.199471i	0.662699	+	0.748886i	$0.269411\pi$
$410$		0			0
$411$	−8.67589	−	5.00903i	−0.427950	−	0.247077i
$412$		0			0
$413$	13.1403	+	2.64398i	0.646592	+	0.130102i
$414$		0			0
$415$	0.659396	+	0.380703i	0.0323685	+	0.0186880i
$416$		0			0
$417$	−2.49664	−	4.32432i	−0.122261	−	0.211763i
$418$		0			0
$419$			10.1957i			0.498095i	0.968491	+	0.249047i	$0.0801175\pi$
$419$			10.1957i			0.498095i	−0.968491	+	0.249047i	$0.919882\pi$
$420$		0			0
$421$		−	13.5263i		−	0.659232i	−0.944115	−	0.329616i	$-0.893081\pi$
$421$		−	13.5263i		−	0.659232i	0.944115	−	0.329616i	$-0.106919\pi$
$422$		0			0
$423$	6.07012	+	10.5138i	0.295139	+	0.511196i
$424$		0			0
$425$	−22.2559	−	12.8495i	−1.07957	−	0.623290i
$426$		0			0
$427$	16.7582	−	5.64736i	0.810987	−	0.273295i
$428$		0			0
$429$	7.79330	+	4.49946i	0.376264	+	0.217236i
$430$		0			0
$431$	−1.43379	+	0.827797i	−0.0690631	+	0.0398736i	−0.534134	−	0.845400i	$-0.679362\pi$
$431$	−1.43379	+	0.827797i	−0.0690631	+	0.0398736i	0.465071	+	0.885273i	$0.346029\pi$
$432$		0			0
$433$			13.2130i			0.634975i	0.948263	+	0.317487i	$0.102839\pi$
$433$			13.2130i			0.634975i	−0.948263	+	0.317487i	$0.897161\pi$
$434$		0			0
$435$	−0.115942			−0.00555900
$436$		0			0
$437$	19.3853	+	33.5764i	0.927325	+	1.60617i
$438$		0			0
$439$	13.2312	−	22.9170i	0.631489	−	1.09377i	−0.355759	−	0.934578i	$-0.615778\pi$
$439$	13.2312	−	22.9170i	0.631489	−	1.09377i	0.987248	−	0.159193i	$-0.0508891\pi$
$440$		0			0
$441$	−16.8788	−	7.07901i	−0.803750	−	0.337096i
$442$		0			0
$443$	−15.8634	+	27.4763i	−0.753694	+	1.30544i	0.192327	+	0.981331i	$0.438397\pi$
$443$	−15.8634	+	27.4763i	−0.753694	+	1.30544i	−0.946021	+	0.324105i	$0.894937\pi$
$444$		0			0
$445$	−0.117149	+	0.0676360i	−0.00555340	+	0.00320625i
$446$		0			0
$447$	−12.1891			−0.576524
$448$		0			0
$449$	19.9014			0.939204			0.469602	−	0.882878i	$-0.344397\pi$
$449$	19.9014			0.939204			0.469602	+	0.882878i	$0.344397\pi$
$450$		0			0
$451$	−9.78972	+	5.65210i	−0.460980	+	0.266147i
$452$		0			0
$453$	−4.44828	+	7.70464i	−0.208998	+	0.361996i
$454$		0			0
$455$	−0.954504	+	0.321658i	−0.0447478	+	0.0150796i
$456$		0			0
$457$	−21.0538	+	36.4663i	−0.984856	+	1.70582i	−0.342280	+	0.939598i	$0.611199\pi$
$457$	−21.0538	+	36.4663i	−0.984856	+	1.70582i	−0.642575	+	0.766222i	$0.722134\pi$
$458$		0			0
$459$	−8.96440	−	15.5268i	−0.418422	−	0.724729i
$460$		0			0
$461$	29.6136			1.37924			0.689622	−	0.724170i	$-0.257777\pi$
$461$	29.6136			1.37924			0.689622	+	0.724170i	$0.257777\pi$
$462$		0			0
$463$		−	2.91157i		−	0.135312i	−0.997709	−	0.0676560i	$-0.978448\pi$
$463$		−	2.91157i		−	0.135312i	0.997709	−	0.0676560i	$-0.0215520\pi$
$464$		0			0
$465$	−0.0829881	+	0.0479132i	−0.00384848	+	0.00222192i
$466$		0			0
$467$	22.2447	+	12.8430i	1.02936	+	0.594301i	0.916801	−	0.399344i	$-0.130762\pi$
$467$	22.2447	+	12.8430i	1.02936	+	0.594301i	0.112559	+	0.993645i	$0.464095\pi$
$468$		0			0
$469$	5.97579	−	29.6990i	0.275937	−	1.37137i
$470$		0			0
$471$	−8.72435	−	5.03700i	−0.401997	−	0.232093i
$472$		0			0
$473$	8.99893	+	15.5866i	0.413771	+	0.716673i
$474$		0			0
$475$		−	34.0391i		−	1.56182i
$476$		0			0
$477$			22.6119i			1.03533i
$478$		0			0
$479$	12.1647	+	21.0698i	0.555818	+	0.962704i	0.997839	+	0.0656999i	$0.0209280\pi$
$479$	12.1647	+	21.0698i	0.555818	+	0.962704i	−0.442022	+	0.897004i	$0.645739\pi$
$480$		0			0
$481$	38.4428	+	22.1949i	1.75284	+	1.01200i
$482$		0			0
$483$	−7.01147	−	6.17638i	−0.319033	−	0.281035i
$484$		0			0
$485$	−0.264972	−	0.152982i	−0.0120318	−	0.00694655i
$486$		0			0
$487$	−4.73275	+	2.73246i	−0.214462	+	0.123819i	−0.603383	−	0.797451i	$-0.706181\pi$
$487$	−4.73275	+	2.73246i	−0.214462	+	0.123819i	0.388922	+	0.921271i	$0.372848\pi$
$488$		0			0
$489$			6.78108i			0.306651i
$490$		0			0
$491$	−36.1618			−1.63196			−0.815980	−	0.578080i	$-0.803802\pi$
$491$	−36.1618			−1.63196			−0.815980	+	0.578080i	$0.803802\pi$
$492$		0			0
$493$	−7.11197	−	12.3183i	−0.320307	−	0.554788i
$494$		0			0
$495$	0.227240	−	0.393592i	0.0102137	−	0.0176906i
$496$		0			0
$497$	−16.6663	+	18.9197i	−0.747584	+	0.848664i
$498$		0			0
$499$	−6.10578	+	10.5755i	−0.273332	+	0.473425i	−0.969713	−	0.244247i	$-0.921459\pi$
$499$	−6.10578	+	10.5755i	−0.273332	+	0.473425i	0.696381	+	0.717672i	$0.254792\pi$
$500$		0			0
$501$	11.3167	−	6.53368i	0.505592	−	0.291903i
$502$		0			0
$503$	−40.5937			−1.80998			−0.904992	−	0.425428i	$-0.860124\pi$
$503$	−40.5937			−1.80998			−0.904992	+	0.425428i	$0.860124\pi$
$504$		0			0
$505$	−0.295762			−0.0131612
$506$		0			0
$507$	10.0814	−	5.82051i	0.447731	−	0.258498i
$508$		0			0
$509$	5.60135	−	9.70182i	0.248276	−	0.430026i	−0.714772	−	0.699358i	$-0.753470\pi$
$509$	5.60135	−	9.70182i	0.248276	−	0.430026i	0.963047	+	0.269332i	$0.0868028\pi$
$510$		0			0
$511$	−2.29772	−	0.462328i	−0.101645	−	0.0204522i
$512$		0			0
$513$	11.8737	−	20.5658i	0.524235	−	0.908002i
$514$		0			0
$515$	0.515866	+	0.893506i	0.0227318	+	0.0393726i
$516$		0			0
$517$	11.9455			0.525364
$518$		0			0
$519$			1.91472i			0.0840467i
$520$		0			0
$521$	19.6445	−	11.3418i	0.860642	−	0.496892i	−0.00358502	−	0.999994i	$-0.501141\pi$
$521$	19.6445	−	11.3418i	0.860642	−	0.496892i	0.864227	+	0.503102i	$0.167808\pi$
$522$		0			0
$523$	−9.55814	−	5.51840i	−0.417948	−	0.241303i	0.276251	−	0.961086i	$-0.410908\pi$
$523$	−9.55814	−	5.51840i	−0.417948	−	0.241303i	−0.694199	+	0.719783i	$0.744241\pi$
$524$		0			0
$525$	2.61977	+	7.77402i	0.114336	+	0.339286i
$526$		0			0
$527$	−10.1811	−	5.87806i	−0.443495	−	0.256052i
$528$		0			0
$529$	4.68700	+	8.11812i	0.203782	+	0.352962i
$530$		0			0
$531$			13.2465i			0.574850i
$532$		0			0
$533$			24.7593i			1.07244i
$534$		0			0
$535$	−0.606422	−	1.05035i	−0.0262179	−	0.0454108i
$536$		0			0
$537$	3.15459	+	1.82130i	0.136131	+	0.0785951i
$538$		0			0
$539$	−14.3363	+	10.9003i	−0.617509	+	0.469507i
$540$		0			0
$541$	−7.28963	−	4.20867i	−0.313406	−	0.180945i	0.335044	−	0.942203i	$-0.391249\pi$
$541$	−7.28963	−	4.20867i	−0.313406	−	0.180945i	−0.648449	+	0.761258i	$0.724582\pi$
$542$		0			0
$543$	−4.17905	+	2.41278i	−0.179340	+	0.103542i
$544$		0			0
$545$		−	0.0396720i		−	0.00169936i
$546$		0			0
$547$	−14.1068			−0.603164			−0.301582	−	0.953440i	$-0.597515\pi$
$547$	−14.1068			−0.603164			−0.301582	+	0.953440i	$0.597515\pi$
$548$		0			0
$549$	8.73843	+	15.1354i	0.372947	+	0.645964i
$550$		0			0
$551$	9.42006	−	16.3160i	0.401308	−	0.695086i
$552$		0			0
$553$	−2.02275	−	6.00241i	−0.0860162	−	0.255248i
$554$		0			0
$555$	−0.165163	+	0.286071i	−0.00701078	+	0.0121430i
$556$		0			0
$557$	−20.4787	+	11.8234i	−0.867712	+	0.500974i	−0.866587	−	0.499026i	$-0.833691\pi$
$557$	−20.4787	+	11.8234i	−0.867712	+	0.500974i	−0.00112471	+	0.999999i	$0.500358\pi$
$558$		0			0
$559$	39.4202			1.66730
$560$		0			0
$561$	−8.21539			−0.346854
$562$		0			0
$563$	30.8936	−	17.8364i	1.30201	−	0.751716i	0.321262	−	0.946990i	$-0.395893\pi$
$563$	30.8936	−	17.8364i	1.30201	−	0.751716i	0.980749	+	0.195274i	$0.0625596\pi$
$564$		0			0
$565$	−0.166028	+	0.287569i	−0.00698484	+	0.0120981i
$566$		0			0
$567$	2.96491	−	14.7353i	0.124515	−	0.618823i
$568$		0			0
$569$	2.46685	−	4.27271i	0.103416	−	0.179121i	−0.809674	−	0.586880i	$-0.800356\pi$
$569$	2.46685	−	4.27271i	0.103416	−	0.179121i	0.913090	+	0.407758i	$0.133689\pi$
$570$		0			0
$571$	10.3657	+	17.9539i	0.433791	+	0.751348i	0.997196	−	0.0748326i	$-0.0238422\pi$
$571$	10.3657	+	17.9539i	0.433791	+	0.751348i	−0.563405	+	0.826181i	$0.690509\pi$
$572$		0			0
$573$	−13.6237			−0.569137
$574$		0			0
$575$		−	28.4231i		−	1.18533i
$576$		0			0
$577$	−30.0207	+	17.3324i	−1.24978	+	0.721559i	−0.971065	−	0.238816i	$-0.923241\pi$
$577$	−30.0207	+	17.3324i	−1.24978	+	0.721559i	−0.278712	+	0.960375i	$0.589907\pi$
$578$		0			0
$579$	4.91556	+	2.83800i	0.204284	+	0.117943i
$580$		0			0
$581$	19.7101	−	22.3751i	0.817713	−	0.928274i
$582$		0			0
$583$	19.2684	+	11.1246i	0.798017	+	0.460735i
$584$		0			0
$585$	−0.497718	−	0.862073i	−0.0205781	−	0.0356423i
$586$		0			0
$587$			22.7688i			0.939771i	0.882727	+	0.469885i	$0.155705\pi$
$587$			22.7688i			0.939771i	−0.882727	+	0.469885i	$0.844295\pi$
$588$		0			0
$589$		−	15.5714i		−	0.641608i
$590$		0			0
$591$	4.81858	+	8.34602i	0.198210	+	0.343309i
$592$		0			0
$593$	−16.4277	−	9.48456i	−0.674606	−	0.389484i	0.123213	−	0.992380i	$-0.460680\pi$
$593$	−16.4277	−	9.48456i	−0.674606	−	0.389484i	−0.797820	+	0.602896i	$0.794013\pi$
$594$		0			0
$595$	0.607824	−	0.690007i	0.0249184	−	0.0282875i
$596$		0			0
$597$	12.8228	+	7.40324i	0.524802	+	0.302995i
$598$		0			0
$599$	−7.38974	+	4.26647i	−0.301937	+	0.174323i	−0.643313	−	0.765604i	$-0.722440\pi$
$599$	−7.38974	+	4.26647i	−0.301937	+	0.174323i	0.341376	+	0.939927i	$0.389107\pi$
$600$		0			0
$601$		−	0.186793i		−	0.00761945i	−0.999993	−	0.00380972i	$-0.998787\pi$
$601$		−	0.186793i		−	0.00761945i	0.999993	−	0.00380972i	$-0.00121268\pi$
$602$		0			0
$603$	29.9391			1.21921
$604$		0			0
$605$	0.147978	+	0.256305i	0.00601614	+	0.0104203i
$606$		0			0
$607$	−18.7521	+	32.4796i	−0.761125	+	1.31831i	0.181146	+	0.983456i	$0.442019\pi$
$607$	−18.7521	+	32.4796i	−0.761125	+	1.31831i	−0.942271	+	0.334852i	$0.891314\pi$
$608$		0			0
$609$	−0.895662	+	4.45134i	−0.0362941	+	0.180377i
$610$		0			0
$611$	13.0820	−	22.6587i	0.529241	−	0.916672i
$612$		0			0
$613$	30.1384	−	17.4004i	1.21728	−	0.702797i	0.252944	−	0.967481i	$-0.418601\pi$
$613$	30.1384	−	17.4004i	1.21728	−	0.702797i	0.964335	+	0.264684i	$0.0852678\pi$
$614$		0			0
$615$	−0.184245			−0.00742949
$616$		0			0
$617$	−21.1308			−0.850695			−0.425348	−	0.905030i	$-0.639848\pi$
$617$	−21.1308			−0.850695			−0.425348	+	0.905030i	$0.639848\pi$
$618$		0			0
$619$	21.2778	−	12.2848i	0.855228	−	0.493766i	−0.00718370	−	0.999974i	$-0.502287\pi$
$619$	21.2778	−	12.2848i	0.855228	−	0.493766i	0.862411	+	0.506208i	$0.168953\pi$
$620$		0			0
$621$	9.91467	−	17.1727i	0.397862	−	0.689117i
$622$		0			0
$623$	1.69175	+	5.02016i	0.0677784	+	0.201129i
$624$		0			0
$625$	−12.4658	+	21.5914i	−0.498631	+	0.863655i
$626$		0			0
$627$	−5.44078	−	9.42372i	−0.217284	−	0.376347i
$628$		0			0
$629$	−40.5248			−1.61583
$630$		0			0
$631$		−	8.69296i		−	0.346061i	−0.984916	−	0.173031i	$-0.944644\pi$
$631$		−	8.69296i		−	0.346061i	0.984916	−	0.173031i	$-0.0553560\pi$
$632$		0			0
$633$	2.19525	−	1.26743i	0.0872532	−	0.0503756i
$634$		0			0
$635$	0.323535	+	0.186793i	0.0128391	+	0.00741266i
$636$		0			0
$637$	4.97573	+	39.1308i	0.197146	+	1.55042i
$638$		0			0
$639$	−21.5795	−	12.4589i	−0.853672	−	0.492868i
$640$		0			0
$641$	−4.87963	−	8.45177i	−0.192734	−	0.333825i	0.753421	−	0.657538i	$-0.228402\pi$
$641$	−4.87963	−	8.45177i	−0.192734	−	0.333825i	−0.946155	+	0.323713i	$0.895069\pi$
$642$		0			0
$643$		−	31.4530i		−	1.24038i	−0.784450	−	0.620192i	$-0.787055\pi$
$643$		−	31.4530i		−	1.24038i	0.784450	−	0.620192i	$-0.212945\pi$
$644$		0			0
$645$			0.293344i			0.0115504i
$646$		0			0
$647$	10.2122	+	17.6880i	0.401483	+	0.695388i	0.993905	−	0.110239i	$-0.0351617\pi$
$647$	10.2122	+	17.6880i	0.401483	+	0.695388i	−0.592422	+	0.805627i	$0.701828\pi$
$648$		0			0
$649$	11.2878	+	6.51704i	0.443087	+	0.255816i
$650$		0			0
$651$	1.19843	+	3.55627i	0.0469701	+	0.139381i
$652$		0			0
$653$	5.76514	+	3.32850i	0.225607	+	0.130254i	0.608544	−	0.793520i	$-0.291754\pi$
$653$	5.76514	+	3.32850i	0.225607	+	0.130254i	−0.382937	+	0.923775i	$0.625087\pi$
$654$		0			0
$655$	0.563808	−	0.325515i	0.0220298	−	0.0127189i
$656$		0			0
$657$		−	2.31629i		−	0.0903671i
$658$		0			0
$659$	−5.38876			−0.209916			−0.104958	−	0.994477i	$-0.533471\pi$
$659$	−5.38876			−0.209916			−0.104958	+	0.994477i	$0.533471\pi$
$660$		0			0
$661$	0.106220	+	0.183979i	0.00413149	+	0.00715595i	0.868084	−	0.496418i	$-0.165352\pi$
$661$	0.106220	+	0.183979i	0.00413149	+	0.00715595i	−0.863952	+	0.503574i	$0.832018\pi$
$662$		0			0
$663$	−8.99696	+	15.5832i	−0.349413	+	0.605201i
$664$		0			0
$665$	1.19404	+	0.240254i	0.0463027	+	0.00931666i
$666$		0			0
$667$	7.86587	−	13.6241i	0.304568	−	0.527527i
$668$		0			0
$669$	−2.54647	+	1.47021i	−0.0984524	+	0.0568415i
$670$		0			0
$671$	17.1966			0.663867
$672$		0			0
$673$	−2.25724			−0.0870102			−0.0435051	−	0.999053i	$-0.513852\pi$
$673$	−2.25724			−0.0870102			−0.0435051	+	0.999053i	$0.513852\pi$
$674$		0			0
$675$	−15.0770	+	8.70469i	−0.580313	+	0.335044i
$676$		0			0
$677$	−19.8711	+	34.4177i	−0.763708	+	1.32278i	0.177219	+	0.984171i	$0.443290\pi$
$677$	−19.8711	+	34.4177i	−0.763708	+	1.32278i	−0.940927	+	0.338610i	$0.890043\pi$
$678$		0			0
$679$	−7.92032	+	8.99121i	−0.303954	+	0.345051i
$680$		0			0
$681$	8.02523	−	13.9001i	0.307527	−	0.532653i
$682$		0			0
$683$	8.23990	+	14.2719i	0.315291	+	0.546100i	0.979499	−	0.201447i	$-0.0645645\pi$
$683$	8.23990	+	14.2719i	0.315291	+	0.546100i	−0.664208	+	0.747548i	$0.731231\pi$
$684$		0			0
$685$	1.09040			0.0416619
$686$		0			0
$687$		−	7.66618i		−	0.292483i
$688$		0			0
$689$	42.2031	−	24.3660i	1.60781	−	0.928269i
$690$		0			0
$691$	−33.2778	−	19.2130i	−1.26595	−	0.730895i	−0.291729	−	0.956501i	$-0.594231\pi$
$691$	−33.2778	−	19.2130i	−1.26595	−	0.730895i	−0.974219	+	0.225606i	$0.927564\pi$
$692$		0			0
$693$	−13.3556	−	11.7649i	−0.507338	−	0.446911i
$694$		0			0
$695$	0.470672	+	0.271743i	0.0178536	+	0.0103078i
$696$		0			0
$697$	−11.3017	−	19.5752i	−0.428084	−	0.741462i
$698$		0			0
$699$		−	6.14860i		−	0.232561i
$700$		0			0
$701$		−	37.8119i		−	1.42813i	−0.700077	−	0.714067i	$-0.746851\pi$
$701$		−	37.8119i		−	1.42813i	0.700077	−	0.714067i	$-0.253149\pi$
$702$		0			0
$703$	−26.8383	−	46.4853i	−1.01223	−	1.75323i
$704$		0			0
$705$	0.168614	+	0.0973492i	0.00635036	+	0.00366638i
$706$		0			0
$707$	−2.28479	+	11.3551i	−0.0859282	+	0.427053i
$708$		0			0
$709$	−34.8365	−	20.1129i	−1.30831	−	0.755354i	−0.326498	−	0.945198i	$-0.605868\pi$
$709$	−34.8365	−	20.1129i	−1.30831	−	0.755354i	−0.981814	+	0.189844i	$0.939202\pi$
$710$		0			0
$711$	5.42115	−	3.12990i	0.203309	−	0.117381i
$712$		0			0
$713$		−	13.0023i		−	0.486940i
$714$		0			0
$715$	−0.979472			−0.0366302
$716$		0			0
$717$	2.01515	+	3.49034i	0.0752570	+	0.130349i
$718$		0			0
$719$	−17.4909	+	30.2951i	−0.652299	+	1.12981i	0.330265	+	0.943888i	$0.392862\pi$
$719$	−17.4909	+	30.2951i	−0.652299	+	1.12981i	−0.982564	+	0.185927i	$0.940471\pi$
$720$		0			0
$721$	38.2892	−	12.9031i	1.42597	−	0.480537i
$722$		0			0
$723$	5.49876	−	9.52412i	0.204501	−	0.354206i
$724$		0			0
$725$	−11.9614	+	6.90593i	−0.444236	+	0.256480i
$726$		0			0
$727$	15.3205			0.568204			0.284102	−	0.958794i	$-0.408304\pi$
$727$	15.3205			0.568204			0.284102	+	0.958794i	$0.408304\pi$
$728$		0			0
$729$	8.36486			0.309810
$730$		0			0
$731$	−31.1664	+	17.9939i	−1.15273	+	0.665530i
$732$		0			0
$733$	4.22786	−	7.32287i	0.156160	−	0.270476i	−0.777321	−	0.629104i	$-0.783422\pi$
$733$	4.22786	−	7.32287i	0.156160	−	0.270476i	0.933481	+	0.358628i	$0.116755\pi$
$734$		0			0
$735$	−0.291191	+	0.0370268i	−0.0107407	+	0.00136575i
$736$		0			0
$737$	14.7295	−	25.5122i	0.542567	−	0.939753i
$738$		0			0
$739$	12.8603	+	22.2746i	0.473073	+	0.819386i	0.999525	−	0.0308186i	$-0.00981143\pi$
$739$	12.8603	+	22.2746i	0.473073	+	0.819386i	−0.526452	+	0.850205i	$0.676478\pi$
$740$		0			0
$741$	−23.8336			−0.875549
$742$		0			0
$743$		−	22.8164i		−	0.837054i	−0.908204	−	0.418527i	$-0.862547\pi$
$743$		−	22.8164i		−	0.837054i	0.908204	−	0.418527i	$-0.137453\pi$
$744$		0			0
$745$	1.14895	−	0.663349i	0.0420944	−	0.0243032i
$746$		0			0
$747$	25.5207	+	14.7344i	0.933752	+	0.539102i
$748$		0			0
$749$	−45.0106	+	15.1681i	−1.64465	+	0.554232i
$750$		0			0
$751$	5.57436	+	3.21836i	0.203411	+	0.117440i	0.598246	−	0.801313i	$-0.295865\pi$
$751$	5.57436	+	3.21836i	0.203411	+	0.117440i	−0.394834	+	0.918752i	$0.629198\pi$
$752$		0			0
$753$	−1.74335	−	3.01958i	−0.0635313	−	0.110039i
$754$		0			0
$755$		−	0.968329i		−	0.0352411i
$756$		0			0
$757$			7.82663i			0.284464i	0.989833	+	0.142232i	$0.0454278\pi$
$757$			7.82663i			0.284464i	−0.989833	+	0.142232i	$0.954572\pi$
$758$		0			0
$759$	−4.54313	−	7.86893i	−0.164905	−	0.285624i
$760$		0			0
$761$	−4.00476	−	2.31215i	−0.145172	−	0.0838153i	0.425654	−	0.904886i	$-0.360044\pi$
$761$	−4.00476	−	2.31215i	−0.145172	−	0.0838153i	−0.570827	+	0.821070i	$0.693377\pi$
$762$		0			0
$763$	−1.52312	−	0.306469i	−0.0551406	−	0.0110949i
$764$		0			0
$765$	0.787012	+	0.454381i	0.0284545	+	0.0164282i
$766$		0			0
$767$	24.7234	−	14.2741i	0.892712	−	0.515407i
$768$		0			0
$769$		−	1.53735i		−	0.0554383i	−0.999616	−	0.0277192i	$-0.991176\pi$
$769$		−	1.53735i		−	0.0554383i	0.999616	−	0.0277192i	$-0.00882442\pi$
$770$		0			0
$771$	−4.34721			−0.156561
$772$		0			0
$773$	−14.5297	−	25.1661i	−0.522596	−	0.905163i	−0.999654	−	0.0262912i	$-0.991630\pi$
$773$	−14.5297	−	25.1661i	−0.522596	−	0.905163i	0.477058	−	0.878872i	$-0.341703\pi$
$774$		0			0
$775$	−5.70776	+	9.88613i	−0.205029	+	0.355120i
$776$		0			0
$777$	9.70714	+	8.55097i	0.348242	+	0.306764i
$778$		0			0
$779$	14.9695	−	25.9280i	0.536339	−	0.928967i
$780$		0			0
$781$	−21.2334	+	12.2591i	−0.759792	+	0.438666i
$782$		0			0
$783$	−9.63582			−0.344356
$784$		0			0
$785$	1.09649			0.0391353
$786$		0			0
$787$	−20.8442	+	12.0344i	−0.743017	+	0.428981i	−0.823165	−	0.567802i	$-0.807794\pi$
$787$	−20.8442	+	12.0344i	−0.743017	+	0.428981i	0.0801484	+	0.996783i	$0.474461\pi$
$788$		0			0
$789$	6.68198	−	11.5735i	0.237885	−	0.412029i
$790$		0			0
$791$	9.75796	+	8.59575i	0.346953	+	0.305630i
$792$		0			0
$793$	18.8326	−	32.6190i	0.668765	−	1.15834i
$794$		0			0
$795$	0.181319	+	0.314053i	0.00643071	+	0.0111383i
$796$		0			0
$797$	32.3666			1.14649			0.573243	−	0.819386i	$-0.305685\pi$
$797$	32.3666			1.14649			0.573243	+	0.819386i	$0.305685\pi$
$798$		0			0
$799$			23.8859i			0.845021i
$800$		0			0
$801$	−4.53403	+	2.61772i	−0.160202	+	0.0924927i
$802$		0			0
$803$	−1.97380	−	1.13957i	−0.0696538	−	0.0402146i
$804$		0			0
$805$	0.997036	+	0.200616i	0.0351409	+	0.00707077i
$806$		0			0
$807$	−13.4480	−	7.76419i	−0.473391	−	0.273312i
$808$		0			0
$809$	−7.14895	−	12.3824i	−0.251344	−	0.435340i	0.712552	−	0.701619i	$-0.247539\pi$
$809$	−7.14895	−	12.3824i	−0.251344	−	0.435340i	−0.963896	+	0.266279i	$0.914206\pi$
$810$		0			0
$811$			12.6785i			0.445204i	0.974909	+	0.222602i	$0.0714550\pi$
$811$			12.6785i			0.445204i	−0.974909	+	0.222602i	$0.928545\pi$
$812$		0			0
$813$		−	12.4061i		−	0.435100i
$814$		0			0
$815$	−0.369037	−	0.639191i	−0.0129268	−	0.0223899i
$816$		0			0
$817$	−41.2810	−	23.8336i	−1.44424	−	0.833832i
$818$		0			0
$819$	−36.9422	+	12.4492i	−1.29087	+	0.435009i
$820$		0			0
$821$	6.81896	+	3.93693i	0.237983	+	0.137400i	0.614250	−	0.789112i	$-0.289459\pi$
$821$	6.81896	+	3.93693i	0.237983	+	0.137400i	−0.376266	+	0.926512i	$0.622792\pi$
$822$		0			0
$823$	8.43137	−	4.86785i	0.293899	−	0.169683i	−0.345800	−	0.938308i	$-0.612392\pi$
$823$	8.43137	−	4.86785i	0.293899	−	0.169683i	0.639699	+	0.768626i	$0.279059\pi$
$824$		0			0
$825$			7.97738i			0.277737i
$826$		0			0
$827$	4.83683			0.168193			0.0840965	−	0.996458i	$-0.473200\pi$
$827$	4.83683			0.168193			0.0840965	+	0.996458i	$0.473200\pi$
$828$		0			0
$829$	−22.2603	−	38.5560i	−0.773132	−	1.33910i	−0.935838	−	0.352429i	$-0.885356\pi$
$829$	−22.2603	−	38.5560i	−0.773132	−	1.33910i	0.162706	−	0.986675i	$-0.447978\pi$
$830$		0			0
$831$	6.69641	−	11.5985i	0.232296	−	0.402349i
$832$		0			0
$833$	−21.7958	−	28.6664i	−0.755178	−	0.993231i
$834$		0			0
$835$	−0.711147	+	1.23174i	−0.0246102	+	0.0426262i
$836$		0			0
$837$	−6.89704	+	3.98201i	−0.238397	+	0.137638i
$838$		0			0
$839$	−22.5881			−0.779828			−0.389914	−	0.920851i	$-0.627495\pi$
$839$	−22.5881			−0.779828			−0.389914	+	0.920851i	$0.627495\pi$
$840$		0			0
$841$	21.3553			0.736391
$842$		0			0
$843$	−7.44182	+	4.29654i	−0.256310	+	0.147981i
$844$		0			0
$845$	−0.633522	+	1.09729i	−0.0217938	+	0.0377480i
$846$		0			0
$847$	10.9834	−	3.70129i	0.377393	−	0.127178i
$848$		0			0
$849$	−2.53879	+	4.39730i	−0.0871309	+	0.150915i
$850$		0			0
$851$	−22.4103	−	38.8158i	−0.768216	−	1.33059i
$852$		0			0
$853$	−9.45701			−0.323802			−0.161901	−	0.986807i	$-0.551762\pi$
$853$	−9.45701			−0.323802			−0.161901	+	0.986807i	$0.551762\pi$
$854$		0			0
$855$			1.20369i			0.0411653i
$856$		0			0
$857$	−47.5082	+	27.4289i	−1.62285	+	0.936952i	−0.636695	+	0.771115i	$0.719699\pi$
$857$	−47.5082	+	27.4289i	−1.62285	+	0.936952i	−0.986153	+	0.165837i	$0.946968\pi$
$858$		0			0
$859$	41.6326	+	24.0366i	1.42049	+	0.820118i	0.996340	−	0.0854753i	$-0.0272409\pi$
$859$	41.6326	+	24.0366i	1.42049	+	0.820118i	0.424146	+	0.905594i	$0.360574\pi$
$860$		0			0
$861$	−1.42331	+	7.07368i	−0.0485062	+	0.241070i
$862$		0			0
$863$	25.7690	+	14.8777i	0.877185	+	0.506443i	0.869729	−	0.493529i	$-0.164293\pi$
$863$	25.7690	+	14.8777i	0.877185	+	0.506443i	0.00745605	+	0.999972i	$0.497627\pi$
$864$		0			0
$865$	−0.104202	−	0.180483i	−0.00354297	−	0.00613661i
$866$		0			0
$867$		−	5.87531i		−	0.199536i
$868$		0			0
$869$		−	6.15942i		−	0.208944i
$870$		0			0
$871$	−32.2615	−	55.8786i	−1.09314	−	1.89337i
$872$		0			0
$873$	−10.2552	−	5.92087i	−0.347087	−	0.200391i
$874$		0			0
$875$	−1.34065	−	1.18097i	−0.0453221	−	0.0399240i
$876$		0			0
$877$	−0.506691	−	0.292538i	−0.0171097	−	0.00987831i	0.491421	−	0.870922i	$-0.336478\pi$
$877$	−0.506691	−	0.292538i	−0.0171097	−	0.00987831i	−0.508530	+	0.861044i	$0.669811\pi$
$878$		0			0
$879$	−13.5792	+	7.83998i	−0.458016	+	0.264436i
$880$		0			0
$881$		−	38.4744i		−	1.29623i	−0.761541	−	0.648117i	$-0.775557\pi$
$881$		−	38.4744i		−	1.29623i	0.761541	−	0.648117i	$-0.224443\pi$
$882$		0			0
$883$	−17.6067			−0.592512			−0.296256	−	0.955109i	$-0.595738\pi$
$883$	−17.6067			−0.592512			−0.296256	+	0.955109i	$0.595738\pi$
$884$		0			0
$885$	0.106220	+	0.183979i	0.00357055	+	0.00618438i
$886$		0			0
$887$	−7.81071	+	13.5285i	−0.262258	+	0.454244i	−0.966842	−	0.255377i	$-0.917800\pi$
$887$	−7.81071	+	13.5285i	−0.262258	+	0.454244i	0.704584	+	0.709621i	$0.251134\pi$
$888$		0			0
$889$	9.67083	−	10.9784i	0.324349	−	0.368204i
$890$		0			0
$891$	7.30807	−	12.6580i	0.244830	−	0.424057i
$892$		0			0
$893$	−27.3990	+	15.8188i	−0.916874	+	0.529357i
$894$		0			0
$895$	−0.396473			−0.0132526
$896$		0			0
$897$	−19.9014			−0.664487
$898$		0			0
$899$	−5.47182	+	3.15916i	−0.182495	+	0.105364i
$900$		0			0
$901$	−22.2444	+	38.5285i	−0.741069	+	1.28357i
$902$		0			0
$903$	11.2623	+	2.26611i	0.374785	+	0.0754113i
$904$		0			0
$905$	0.262614	−	0.454861i	0.00872959	−	0.0151201i
$906$		0			0
$907$	22.2880	+	38.6040i	0.740061	+	1.28182i	0.952467	+	0.304642i	$0.0985369\pi$
$907$	22.2880	+	38.6040i	0.740061	+	1.28182i	−0.212405	+	0.977182i	$0.568130\pi$
$908$		0			0
$909$	−11.4469			−0.379670
$910$		0			0
$911$			21.3705i			0.708036i	0.935239	+	0.354018i	$0.115185\pi$
$911$			21.3705i			0.708036i	−0.935239	+	0.354018i	$0.884815\pi$
$912$		0			0
$913$	25.1114	−	14.4981i	0.831065	−	0.479816i
$914$		0			0
$915$	0.242733	+	0.140142i	0.00802452	+	0.00463296i
$916$		0			0
$917$	−8.14194	−	24.1608i	−0.268871	−	0.797858i
$918$		0			0
$919$	46.9715	+	27.1190i	1.54945	+	0.894573i	0.998184	+	0.0602410i	$0.0191869\pi$
$919$	46.9715	+	27.1190i	1.54945	+	0.894573i	0.551262	+	0.834332i	$0.314146\pi$
$920$		0			0
$921$	−0.0708601	−	0.122733i	−0.00233492	−	0.00404420i
$922$		0			0
$923$			53.7016i			1.76761i
$924$		0			0
$925$			39.3508i			1.29385i
$926$		0			0
$927$	19.9656	+	34.5814i	0.655756	+	1.13580i
$928$		0			0
$929$	37.7615	+	21.8016i	1.23892	+	0.715288i	0.968873	−	0.247560i	$-0.0796286\pi$
$929$	37.7615	+	21.8016i	1.23892	+	0.715288i	0.270043	+	0.962848i	$0.412962\pi$
$930$		0			0
$931$	18.4480	−	43.9863i	0.604610	−	1.44159i
$932$		0			0
$933$	−6.24136	−	3.60345i	−0.204333	−	0.117972i
$934$		0			0
$935$	0.774390	−	0.447094i	0.0253253	−	0.0146215i
$936$		0			0
$937$		−	39.8573i		−	1.30208i	−0.759043	−	0.651041i	$-0.774333\pi$
$937$		−	39.8573i		−	1.30208i	0.759043	−	0.651041i	$-0.225667\pi$
$938$		0			0
$939$	12.0677			0.393814
$940$		0			0
$941$	−8.54389	−	14.7984i	−0.278523	−	0.482416i	0.692495	−	0.721423i	$-0.256511\pi$
$941$	−8.54389	−	14.7984i	−0.278523	−	0.482416i	−0.971018	+	0.239007i	$0.923178\pi$
$942$		0			0
$943$	12.4998	−	21.6502i	0.407048	−	0.705028i
$944$		0			0
$945$	−0.198930	−	0.590315i	−0.00647120	−	0.0192029i
$946$		0			0
$947$	9.72507	−	16.8443i	0.316022	−	0.547367i	−0.663632	−	0.748059i	$-0.730986\pi$
$947$	9.72507	−	16.8443i	0.316022	−	0.547367i	0.979654	+	0.200692i	$0.0643192\pi$
$948$		0			0
$949$	−4.32315	+	2.49597i	−0.140335	+	0.0810227i
$950$		0			0
$951$	11.3826			0.369107
$952$		0			0
$953$	43.1950			1.39922			0.699611	−	0.714524i	$-0.253356\pi$
$953$	43.1950			1.39922			0.699611	+	0.714524i	$0.253356\pi$
$954$		0			0
$955$	1.28418	−	0.741422i	0.0415551	−	0.0239919i
$956$		0			0
$957$	−2.20768	+	3.82381i	−0.0713641	+	0.123606i
$958$		0			0
$959$	8.42339	−	41.8633i	0.272006	−	1.35184i
$960$		0			0
$961$	12.8890	−	22.3243i	0.415773	−	0.720139i
$962$		0			0
$963$	−23.4704	−	40.6519i	−0.756323	−	1.30999i
$964$		0			0
$965$	−0.617793			−0.0198875
$966$		0			0
$967$			17.9154i			0.576122i	0.957612	+	0.288061i	$0.0930106\pi$
$967$			17.9154i			0.576122i	−0.957612	+	0.288061i	$0.906989\pi$
$968$		0			0
$969$	18.8433	−	10.8792i	0.605335	−	0.349490i
$970$		0			0
$971$	21.6134	+	12.4785i	0.693605	+	0.400453i	0.804961	−	0.593327i	$-0.202186\pi$
$971$	21.6134	+	12.4785i	0.693605	+	0.400453i	−0.111356	+	0.993781i	$0.535519\pi$
$972$		0			0
$973$	14.0689	−	15.9712i	0.451029	−	0.512012i
$974$		0			0
$975$	15.1317	+	8.73631i	0.484603	+	0.279786i
$976$		0			0
$977$	7.26737	+	12.5875i	0.232504	+	0.402708i	0.958544	−	0.284944i	$-0.0919748\pi$
$977$	7.26737	+	12.5875i	0.232504	+	0.402708i	−0.726040	+	0.687652i	$0.758642\pi$
$978$		0			0
$979$			5.15148i			0.164642i
$980$		0			0
$981$		−	1.53543i		−	0.0490225i
$982$		0			0
$983$	23.0732	+	39.9640i	0.735922	+	1.27465i	0.954318	+	0.298794i	$0.0965842\pi$
$983$	23.0732	+	39.9640i	0.735922	+	1.27465i	−0.218396	+	0.975860i	$0.570082\pi$
$984$		0			0
$985$	−0.908407	−	0.524469i	−0.0289443	−	0.0167110i
$986$		0			0
$987$	5.04006	−	5.72151i	0.160427	−	0.182118i
$988$		0			0
$989$	−34.4702	−	19.9014i	−1.09609	−	0.632827i
$990$		0			0
$991$	−37.4921	+	21.6461i	−1.19098	+	0.687611i	−0.958528	−	0.284998i	$-0.908007\pi$
$991$	−37.4921	+	21.6461i	−1.19098	+	0.687611i	−0.232449	+	0.972609i	$0.574674\pi$
$992$		0			0
$993$			0.341293i			0.0108306i
$994$		0			0
$995$	−1.61158			−0.0510907
$996$		0			0
$997$	11.7343	+	20.3243i	0.371628	+	0.643678i	0.989816	−	0.142352i	$-0.0454665\pi$
$997$	11.7343	+	20.3243i	0.371628	+	0.643678i	−0.618188	+	0.786030i	$0.712133\pi$
$998$		0			0
$999$	−13.7265	+	23.7750i	−0.434287	+	0.752208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.q.d.831.3	yes	16
4.3	odd	2		896.2.q.a.831.5	yes	16
7.3	odd	6	inner	896.2.q.d.703.4	yes	16
8.3	odd	2	inner	896.2.q.d.831.4	yes	16
8.5	even	2		896.2.q.a.831.6	yes	16
28.3	even	6		896.2.q.a.703.6	yes	16
56.3	even	6	inner	896.2.q.d.703.3	yes	16
56.45	odd	6		896.2.q.a.703.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.q.a.703.5	✓	16	56.45	odd	6
896.2.q.a.703.6	yes	16	28.3	even	6
896.2.q.a.831.5	yes	16	4.3	odd	2
896.2.q.a.831.6	yes	16	8.5	even	2
896.2.q.d.703.3	yes	16	56.3	even	6	inner
896.2.q.d.703.4	yes	16	7.3	odd	6	inner
896.2.q.d.831.3	yes	16	1.1	even	1	trivial
896.2.q.d.831.4	yes	16	8.3	odd	2	inner

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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.537541 - 0.310349i) q^{3} +(-0.0337794 + 0.0585076i) q^{5} +(1.98532 + 1.74886i) q^{7} +(-1.30737 + 2.26443i) q^{9} +O(q^{10})\)	\(q+(0.537541 - 0.310349i) q^{3} +(-0.0337794 + 0.0585076i) q^{5} +(1.98532 + 1.74886i) q^{7} +(-1.30737 + 2.26443i) q^{9} +(1.28640 + 2.22811i) q^{11} +5.63513 q^{13} +0.0419337i q^{15} +(-4.45525 + 2.57224i) q^{17} +(-5.90113 - 3.40702i) q^{19} +(1.60995 + 0.323941i) q^{21} +(-4.92752 - 2.84491i) q^{23} +(2.49772 + 4.32617i) q^{25} +3.48506i q^{27} +2.76490i q^{29} +(1.14260 + 1.97903i) q^{31} +(1.38298 + 0.798467i) q^{33} +(-0.169384 + 0.0570809i) q^{35} +(6.82198 + 3.93867i) q^{37} +(3.02911 - 1.74886i) q^{39} +4.39373i q^{41} +6.99544 q^{43} +(-0.0883241 - 0.152982i) q^{45} +(2.32151 - 4.02097i) q^{47} +(0.882985 + 6.94409i) q^{49} +(-1.59658 + 2.76537i) q^{51} +(7.48928 - 4.32394i) q^{53} -0.173815 q^{55} -4.22947 q^{57} +(4.38738 - 2.53305i) q^{59} +(3.34200 - 5.78851i) q^{61} +(-6.55570 + 2.20921i) q^{63} +(-0.190351 + 0.329698i) q^{65} +(-5.72507 - 9.91612i) q^{67} -3.53166 q^{69} +9.52979i q^{71} +(-0.767178 + 0.442931i) q^{73} +(2.68525 + 1.55033i) q^{75} +(-1.34274 + 6.67324i) q^{77} +(-2.07331 - 1.19703i) q^{79} +(-2.84051 - 4.91992i) q^{81} -11.2703i q^{83} -0.347555i q^{85} +(0.858084 + 1.48624i) q^{87} +(1.73403 + 1.00114i) q^{89} +(11.1875 + 9.85505i) q^{91} +(1.22838 + 0.709207i) q^{93} +(0.398673 - 0.230174i) q^{95} +4.52885i q^{97} -6.72718 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{3} + 8 q^{9}+O(q^{10}) \) 16 * q + 12 * q^3 + 8 * q^9	\( 16 q + 12 q^{3} + 8 q^{9} - 4 q^{11} - 12 q^{19} - 16 q^{25} + 24 q^{33} + 20 q^{35} + 16 q^{49} - 52 q^{51} + 48 q^{57} + 60 q^{59} + 24 q^{65} + 12 q^{67} - 24 q^{73} - 120 q^{75} - 32 q^{81} + 24 q^{89} + 72 q^{91} + 64 q^{99}+O(q^{100}) \) 16 * q + 12 * q^3 + 8 * q^9 - 4 * q^11 - 12 * q^19 - 16 * q^25 + 24 * q^33 + 20 * q^35 + 16 * q^49 - 52 * q^51 + 48 * q^57 + 60 * q^59 + 24 * q^65 + 12 * q^67 - 24 * q^73 - 120 * q^75 - 32 * q^81 + 24 * q^89 + 72 * q^91 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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