LMFDB - Embedded newform 882.4.k.b.521.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(215,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("882.215");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$52.0396846251$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{48})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{8} + 1 $ x^16 - x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.7
Root			$-0.991445 + 0.130526i$ of defining polynomial
Character	$\chi$	$=$	882.521
Dual form			882.4.k.b.215.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(1.24090 + 2.14931i) q^{5} -8.00000i q^{8} +O(q^{10})$	\(q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(1.24090 + 2.14931i) q^{5} -8.00000i q^{8} +(4.29862 + 2.48181i) q^{10} +(1.73205 + 1.00000i) q^{11} +4.90923i q^{13} +(-8.00000 - 13.8564i) q^{16} +(1.70518 - 2.95345i) q^{17} +(5.71849 - 3.30157i) q^{19} +9.92724 q^{20} +4.00000 q^{22} +(39.5611 - 22.8406i) q^{23} +(59.4203 - 102.919i) q^{25} +(4.90923 + 8.50303i) q^{26} -139.054i q^{29} +(157.142 + 90.7259i) q^{31} +(-27.7128 - 16.0000i) q^{32} -6.82071i q^{34} +(-72.3051 - 125.236i) q^{37} +(6.60314 - 11.4370i) q^{38} +(17.1945 - 9.92724i) q^{40} +359.077 q^{41} +4.26999 q^{43} +(6.92820 - 4.00000i) q^{44} +(45.6812 - 79.1222i) q^{46} +(-126.042 - 218.310i) q^{47} -237.681i q^{50} +(17.0061 + 9.81845i) q^{52} +(-114.016 - 65.8269i) q^{53} +4.96362i q^{55} +(-139.054 - 240.848i) q^{58} +(-176.076 + 304.972i) q^{59} +(473.846 - 273.575i) q^{61} +362.904 q^{62} -64.0000 q^{64} +(-10.5515 + 6.09188i) q^{65} +(301.286 - 521.843i) q^{67} +(-6.82071 - 11.8138i) q^{68} -206.833i q^{71} +(354.330 + 204.572i) q^{73} +(-250.472 - 144.610i) q^{74} -26.4126i q^{76} +(-491.137 - 850.674i) q^{79} +(19.8545 - 34.3890i) q^{80} +(621.939 - 359.077i) q^{82} +1008.80 q^{83} +8.46385 q^{85} +(7.39583 - 4.26999i) q^{86} +(8.00000 - 13.8564i) q^{88} +(-535.695 - 927.852i) q^{89} -182.725i q^{92} +(-436.621 - 252.083i) q^{94} +(14.1922 + 8.19387i) q^{95} +675.605i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4}+O(q^{10}) $ 16 * q + 32 * q^4	$ 16 q + 32 q^{4} - 128 q^{16} + 64 q^{22} + 600 q^{25} - 512 q^{37} + 4096 q^{43} - 672 q^{46} - 1184 q^{58} - 1024 q^{64} + 544 q^{67} - 6048 q^{79} + 6720 q^{85} + 128 q^{88}+O(q^{100}) $ 16 * q + 32 * q^4 - 128 * q^16 + 64 * q^22 + 600 * q^25 - 512 * q^37 + 4096 * q^43 - 672 * q^46 - 1184 * q^58 - 1024 * q^64 + 544 * q^67 - 6048 * q^79 + 6720 * q^85 + 128 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	1.24090	+	2.14931i	0.110990	+	0.192240i	0.916170	−	0.400791i	$-0.131265\pi$
$5$	1.24090	+	2.14931i	0.110990	+	0.192240i	−0.805180	+	0.593031i	$0.797931\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	8.00000i		−	0.353553i
$9$		0			0
$10$	4.29862	+	2.48181i	0.135934	+	0.0784817i
$11$	1.73205	+	1.00000i	0.0474757	+	0.0274101i	0.523550	−	0.851995i	$-0.324607\pi$
$11$	1.73205	+	1.00000i	0.0474757	+	0.0274101i	−0.476074	+	0.879405i	$0.657941\pi$
$12$		0			0
$13$			4.90923i			0.104736i	0.998628	+	0.0523682i	$0.0166770\pi$
$13$			4.90923i			0.104736i	−0.998628	+	0.0523682i	$0.983323\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	1.70518	−	2.95345i	0.0243274	−	0.0421363i	−0.853605	−	0.520920i	$-0.825589\pi$
$17$	1.70518	−	2.95345i	0.0243274	−	0.0421363i	0.877933	+	0.478784i	$0.158922\pi$
$18$		0			0
$19$	5.71849	−	3.30157i	0.0690479	−	0.0398648i	−0.465079	−	0.885269i	$-0.653974\pi$
$19$	5.71849	−	3.30157i	0.0690479	−	0.0398648i	0.534127	+	0.845405i	$0.320641\pi$
$20$	9.92724			0.110990
$21$		0			0
$22$	4.00000			0.0387638
$23$	39.5611	−	22.8406i	0.358655	−	0.207070i	−0.309836	−	0.950790i	$-0.600274\pi$
$23$	39.5611	−	22.8406i	0.358655	−	0.207070i	0.668491	+	0.743721i	$0.266941\pi$
$24$		0			0
$25$	59.4203	−	102.919i	0.475362	−	0.823352i
$26$	4.90923	+	8.50303i	0.0370299	+	0.0641377i
$27$		0			0
$28$		0			0
$29$		−	139.054i		−	0.890402i	−0.895431	−	0.445201i	$-0.853132\pi$
$29$		−	139.054i		−	0.890402i	0.895431	−	0.445201i	$-0.146868\pi$
$30$		0			0
$31$	157.142	+	90.7259i	0.910436	+	0.525640i	0.880571	−	0.473914i	$-0.157159\pi$
$31$	157.142	+	90.7259i	0.910436	+	0.525640i	0.0298645	+	0.999554i	$0.490492\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	6.82071i		−	0.0344042i
$35$		0			0
$36$		0			0
$37$	−72.3051	−	125.236i	−0.321267	−	0.556451i	0.659483	−	0.751720i	$-0.270775\pi$
$37$	−72.3051	−	125.236i	−0.321267	−	0.556451i	−0.980750	+	0.195269i	$0.937442\pi$
$38$	6.60314	−	11.4370i	0.0281887	−	0.0488243i
$39$		0			0
$40$	17.1945	−	9.92724i	0.0679672	−	0.0392409i
$41$	359.077			1.36777			0.683883	−	0.729592i	$-0.260290\pi$
$41$	359.077			1.36777			0.683883	+	0.729592i	$0.260290\pi$
$42$		0			0
$43$	4.26999			0.0151434			0.00757171	−	0.999971i	$-0.497590\pi$
$43$	4.26999			0.0151434			0.00757171	+	0.999971i	$0.497590\pi$
$44$	6.92820	−	4.00000i	0.0237379	−	0.0137051i
$45$		0			0
$46$	45.6812	−	79.1222i	0.146420	−	0.253607i
$47$	−126.042	−	218.310i	−0.391171	−	0.677529i	0.601433	−	0.798923i	$-0.294597\pi$
$47$	−126.042	−	218.310i	−0.391171	−	0.677529i	−0.992604	+	0.121395i	$0.961263\pi$
$48$		0			0
$49$		0			0
$50$		−	237.681i		−	0.672264i
$51$		0			0
$52$	17.0061	+	9.81845i	0.0453522	+	0.0261841i
$53$	−114.016	−	65.8269i	−0.295495	−	0.170604i	0.344922	−	0.938631i	$-0.387905\pi$
$53$	−114.016	−	65.8269i	−0.295495	−	0.170604i	−0.640417	+	0.768027i	$0.721239\pi$
$54$		0			0
$55$			4.96362i			0.0121690i
$56$		0			0
$57$		0			0
$58$	−139.054	−	240.848i	−0.314805	−	0.545257i
$59$	−176.076	+	304.972i	−0.388527	+	0.672948i	−0.992252	−	0.124245i	$-0.960349\pi$
$59$	−176.076	+	304.972i	−0.388527	+	0.672948i	0.603725	+	0.797193i	$0.293683\pi$
$60$		0			0
$61$	473.846	−	273.575i	0.994587	−	0.574225i	0.0879445	−	0.996125i	$-0.471970\pi$
$61$	473.846	−	273.575i	0.994587	−	0.574225i	0.906642	+	0.421901i	$0.138637\pi$
$62$	362.904			0.743368
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−10.5515	+	6.09188i	−0.0201346	+	0.0116247i
$66$		0			0
$67$	301.286	−	521.843i	0.549373	−	0.951542i	−0.448945	−	0.893560i	$-0.648200\pi$
$67$	301.286	−	521.843i	0.549373	−	0.951542i	0.998318	−	0.0579823i	$-0.0184667\pi$
$68$	−6.82071	−	11.8138i	−0.0121637	−	0.0210682i
$69$		0			0
$70$		0			0
$71$		−	206.833i		−	0.345726i	−0.984946	−	0.172863i	$-0.944698\pi$
$71$		−	206.833i		−	0.345726i	0.984946	−	0.172863i	$-0.0553017\pi$
$72$		0			0
$73$	354.330	+	204.572i	0.568098	+	0.327992i	0.756389	−	0.654122i	$-0.226962\pi$
$73$	354.330	+	204.572i	0.568098	+	0.327992i	−0.188291	+	0.982113i	$0.560295\pi$
$74$	−250.472	−	144.610i	−0.393470	−	0.227170i
$75$		0			0
$76$		−	26.4126i		−	0.0398648i
$77$		0			0
$78$		0			0
$79$	−491.137	−	850.674i	−0.699459	−	1.21150i	−0.968654	−	0.248413i	$-0.920091\pi$
$79$	−491.137	−	850.674i	−0.699459	−	1.21150i	0.269196	−	0.963086i	$-0.413242\pi$
$80$	19.8545	−	34.3890i	0.0277475	−	0.0480600i
$81$		0			0
$82$	621.939	−	359.077i	0.837582	−	0.483578i
$83$	1008.80			1.33411			0.667053	−	0.745011i	$-0.267556\pi$
$83$	1008.80			1.33411			0.667053	+	0.745011i	$0.267556\pi$
$84$		0			0
$85$	8.46385			0.0108004
$86$	7.39583	−	4.26999i	0.00927341	−	0.00535400i
$87$		0			0
$88$	8.00000	−	13.8564i	0.00969094	−	0.0167852i
$89$	−535.695	−	927.852i	−0.638018	−	1.10508i	−0.985867	−	0.167529i	$-0.946421\pi$
$89$	−535.695	−	927.852i	−0.638018	−	1.10508i	0.347849	−	0.937551i	$-0.386912\pi$
$90$		0			0
$91$		0			0
$92$		−	182.725i		−	0.207070i
$93$		0			0
$94$	−436.621	−	252.083i	−0.479085	−	0.276600i
$95$	14.1922	+	8.19387i	0.0153272	+	0.00884919i
$96$		0			0
$97$			675.605i			0.707188i	0.935399	+	0.353594i	$0.115041\pi$
$97$			675.605i			0.707188i	−0.935399	+	0.353594i	$0.884959\pi$
$98$		0			0
$99$		0			0
$100$	−237.681	−	411.676i	−0.237681	−	0.411676i
$101$	−542.828	+	940.205i	−0.534786	+	0.926276i	0.464388	+	0.885632i	$0.346274\pi$
$101$	−542.828	+	940.205i	−0.534786	+	0.926276i	−0.999174	+	0.0406444i	$0.987059\pi$
$102$		0			0
$103$	1699.20	−	981.033i	1.62550	−	0.938486i	0.640093	−	0.768297i	$-0.278896\pi$
$103$	1699.20	−	981.033i	1.62550	−	0.938486i	0.985412	−	0.170188i	$-0.0544376\pi$
$104$	39.2738			0.0370299
$105$		0			0
$106$	−263.308			−0.241271
$107$	−686.880	+	396.571i	−0.620591	+	0.358298i	−0.777099	−	0.629378i	$-0.783310\pi$
$107$	−686.880	+	396.571i	−0.620591	+	0.358298i	0.156508	+	0.987677i	$0.449976\pi$
$108$		0			0
$109$	669.145	−	1158.99i	0.588004	−	1.01845i	−0.406489	−	0.913655i	$-0.633247\pi$
$109$	669.145	−	1158.99i	0.588004	−	1.01845i	0.994494	−	0.104798i	$-0.0334195\pi$
$110$	4.96362	+	8.59724i	0.00430239	+	0.00745195i
$111$		0			0
$112$		0			0
$113$			408.395i			0.339987i	0.985445	+	0.169994i	$0.0543747\pi$
$113$			408.395i			0.339987i	−0.985445	+	0.169994i	$0.945625\pi$
$114$		0			0
$115$	98.1832	+	56.6861i	0.0796141	+	0.0459652i
$116$	−481.697	−	278.108i	−0.385555	−	0.222600i
$117$		0			0
$118$			704.302i			0.549460i
$119$		0			0
$120$		0			0
$121$	−663.500	−	1149.22i	−0.498497	−	0.863423i
$122$	547.150	−	947.692i	0.406038	−	0.703279i
$123$		0			0
$124$	628.567	−	362.904i	0.455218	−	0.262820i
$125$	605.166			0.433022
$126$		0			0
$127$	1176.17			0.821799			0.410899	−	0.911681i	$-0.365215\pi$
$127$	1176.17			0.821799			0.410899	+	0.911681i	$0.365215\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−12.1838	+	21.1029i	−0.00821990	+	0.0142373i
$131$	−1103.76	−	1911.76i	−0.736151	−	1.27505i	−0.954217	−	0.299117i	$-0.903308\pi$
$131$	−1103.76	−	1911.76i	−0.736151	−	1.27505i	0.218066	−	0.975934i	$-0.430025\pi$
$132$		0			0
$133$		0			0
$134$		−	1205.15i		−	0.776931i
$135$		0			0
$136$	−23.6276	−	13.6414i	−0.0148974	−	0.00860105i
$137$	−465.740	−	268.895i	−0.290444	−	0.167688i	0.347698	−	0.937607i	$-0.386964\pi$
$137$	−465.740	−	268.895i	−0.290444	−	0.167688i	−0.638142	+	0.769918i	$0.720297\pi$
$138$		0			0
$139$			2107.99i			1.28631i	0.765736	+	0.643156i	$0.222375\pi$
$139$			2107.99i			1.28631i	−0.765736	+	0.643156i	$0.777625\pi$
$140$		0			0
$141$		0			0
$142$	−206.833	−	358.245i	−0.122232	−	0.211713i
$143$	−4.90923	+	8.50303i	−0.00287084	+	0.00497244i
$144$		0			0
$145$	298.870	−	172.553i	0.171171	−	0.0988256i
$146$	818.290			0.463850
$147$		0			0
$148$	−578.441			−0.321267
$149$	−2381.50	+	1374.96i	−1.30939	+	0.755979i	−0.981995	−	0.188907i	$-0.939505\pi$
$149$	−2381.50	+	1374.96i	−1.30939	+	0.755979i	−0.327399	+	0.944886i	$0.606172\pi$
$150$		0			0
$151$	968.811	−	1678.03i	0.522124	−	0.904345i	−0.477545	−	0.878607i	$-0.658473\pi$
$151$	968.811	−	1678.03i	0.522124	−	0.904345i	0.999669	−	0.0257379i	$-0.00819355\pi$
$152$	−26.4126	−	45.7479i	−0.0140944	−	0.0244121i
$153$		0			0
$154$		0			0
$155$			450.329i			0.233363i
$156$		0			0
$157$	701.036	+	404.743i	0.356361	+	0.205745i	0.667483	−	0.744625i	$-0.267371\pi$
$157$	701.036	+	404.743i	0.356361	+	0.205745i	−0.311122	+	0.950370i	$0.600705\pi$
$158$	−1701.35	−	982.274i	−0.856658	−	0.494592i
$159$		0			0
$160$		−	79.4179i		−	0.0392409i
$161$		0			0
$162$		0			0
$163$	−56.4008	−	97.6890i	−0.0271022	−	0.0469423i	0.852156	−	0.523287i	$-0.175295\pi$
$163$	−56.4008	−	97.6890i	−0.0271022	−	0.0469423i	−0.879258	+	0.476345i	$0.841961\pi$
$164$	718.154	−	1243.88i	0.341941	−	0.592260i
$165$		0			0
$166$	1747.30	−	1008.80i	0.816969	−	0.471677i
$167$	−1430.72			−0.662950			−0.331475	−	0.943464i	$-0.607546\pi$
$167$	−1430.72			−0.662950			−0.331475	+	0.943464i	$0.607546\pi$
$168$		0			0
$169$	2172.90			0.989030
$170$	14.6598	−	8.46385i	0.00661387	−	0.00381852i
$171$		0			0
$172$	8.53997	−	14.7917i	0.00378585	−	0.00655729i
$173$	−1391.75	−	2410.58i	−0.611635	−	1.05938i	−0.990965	−	0.134121i	$-0.957179\pi$
$173$	−1391.75	−	2410.58i	−0.611635	−	1.05938i	0.379330	−	0.925261i	$-0.376154\pi$
$174$		0			0
$175$		0			0
$176$		−	32.0000i		−	0.0137051i
$177$		0			0
$178$	−1855.70	−	1071.39i	−0.781409	−	0.451147i
$179$	−576.815	−	333.024i	−0.240856	−	0.139058i	0.374714	−	0.927140i	$-0.377741\pi$
$179$	−576.815	−	333.024i	−0.240856	−	0.139058i	−0.615570	+	0.788082i	$0.711074\pi$
$180$		0			0
$181$			2275.59i			0.934491i	0.884128	+	0.467246i	$0.154754\pi$
$181$			2275.59i			0.934491i	−0.884128	+	0.467246i	$0.845246\pi$
$182$		0			0
$183$		0			0
$184$	−182.725	−	316.489i	−0.0732101	−	0.126804i
$185$	179.447	−	310.812i	0.0713148	−	0.123521i
$186$		0			0
$187$	5.90691	−	3.41036i	0.00230992	−	0.00133364i
$188$	−1008.33			−0.391171
$189$		0			0
$190$	32.7755			0.0125146
$191$	−1289.50	+	744.495i	−0.488508	+	0.282040i	−0.723955	−	0.689847i	$-0.757678\pi$
$191$	−1289.50	+	744.495i	−0.488508	+	0.282040i	0.235447	+	0.971887i	$0.424345\pi$
$192$		0			0
$193$	1433.97	−	2483.72i	0.534817	−	0.926330i	−0.464355	−	0.885649i	$-0.653714\pi$
$193$	1433.97	−	2483.72i	0.534817	−	0.926330i	0.999172	−	0.0406813i	$-0.0129528\pi$
$194$	675.605	+	1170.18i	0.250029	+	0.433063i
$195$		0			0
$196$		0			0
$197$			1720.75i			0.622327i	0.950356	+	0.311163i	$0.100719\pi$
$197$			1720.75i			0.622327i	−0.950356	+	0.311163i	$0.899281\pi$
$198$		0			0
$199$	1855.58	+	1071.32i	0.660997	+	0.381627i	0.792657	−	0.609668i	$-0.208697\pi$
$199$	1855.58	+	1071.32i	0.660997	+	0.381627i	−0.131660	+	0.991295i	$0.542031\pi$
$200$	−823.352	−	475.362i	−0.291099	−	0.168066i
$201$		0			0
$202$			2171.31i			0.756302i
$203$		0			0
$204$		0			0
$205$	445.580	+	771.767i	0.151808	+	0.262939i
$206$	1962.07	−	3398.40i	0.663610	−	1.14941i
$207$		0			0
$208$	68.0242	−	39.2738i	0.0226761	−	0.0130921i
$209$	13.2063			0.00437080
$210$		0			0
$211$	3641.90			1.18824			0.594120	−	0.804377i	$-0.297501\pi$
$211$	3641.90			1.18824			0.594120	+	0.804377i	$0.297501\pi$
$212$	−456.062	+	263.308i	−0.147748	+	0.0853021i
$213$		0			0
$214$	−793.141	+	1373.76i	−0.253355	+	0.438824i
$215$	5.29865	+	9.17752i	0.00168077	+	0.00291117i
$216$		0			0
$217$		0			0
$218$		−	2676.58i		−	0.831563i
$219$		0			0
$220$	17.1945	+	9.92724i	0.00526933	+	0.00304225i
$221$	14.4992	+	8.37110i	0.00441321	+	0.00254797i
$222$		0			0
$223$			1337.74i			0.401710i	0.979621	+	0.200855i	$0.0643721\pi$
$223$			1337.74i			0.401710i	−0.979621	+	0.200855i	$0.935628\pi$
$224$		0			0
$225$		0			0
$226$	408.395	+	707.361i	0.120204	+	0.208199i
$227$	−1343.59	+	2327.16i	−0.392850	+	0.680436i	−0.992824	−	0.119583i	$-0.961844\pi$
$227$	−1343.59	+	2327.16i	−0.392850	+	0.680436i	0.599974	+	0.800019i	$0.295178\pi$
$228$		0			0
$229$	−184.746	+	106.663i	−0.0533116	+	0.0307795i	−0.526419	−	0.850225i	$-0.676466\pi$
$229$	−184.746	+	106.663i	−0.0533116	+	0.0307795i	0.473107	+	0.881005i	$0.343132\pi$
$230$	226.744			0.0650047
$231$		0			0
$232$	−1112.43			−0.314805
$233$	−1407.98	+	812.900i	−0.395880	+	0.228562i	−0.684705	−	0.728820i	$-0.740069\pi$
$233$	−1407.98	+	812.900i	−0.395880	+	0.228562i	0.288824	+	0.957382i	$0.406736\pi$
$234$		0			0
$235$	312.811	−	541.805i	0.0868321	−	0.150398i
$236$	704.302	+	1219.89i	0.194263	+	0.336474i
$237$		0			0
$238$		0			0
$239$			4477.61i			1.21185i	0.795521	+	0.605926i	$0.207197\pi$
$239$			4477.61i			1.21185i	−0.795521	+	0.605926i	$0.792803\pi$
$240$		0			0
$241$	296.586	+	171.234i	0.0792729	+	0.0457682i	0.539112	−	0.842234i	$-0.318760\pi$
$241$	296.586	+	171.234i	0.0792729	+	0.0457682i	−0.459840	+	0.888002i	$0.652093\pi$
$242$	−2298.43	−	1327.00i	−0.610532	−	0.352491i
$243$		0			0
$244$		−	2188.60i		−	0.574225i
$245$		0			0
$246$		0			0
$247$	16.2082	+	28.0733i	0.00417530	+	0.00723184i
$248$	725.807	−	1257.13i	0.185842	−	0.321888i
$249$		0			0
$250$	1048.18	−	605.166i	0.265170	−	0.153096i
$251$	−3228.23			−0.811810			−0.405905	−	0.913915i	$-0.633044\pi$
$251$	−3228.23			−0.811810			−0.405905	+	0.913915i	$0.633044\pi$
$252$		0			0
$253$	91.3625			0.0227032
$254$	2037.19	−	1176.17i	0.503247	−	0.290550i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−889.723	−	1541.05i	−0.215951	−	0.374038i	0.737615	−	0.675221i	$-0.235952\pi$
$257$	−889.723	−	1541.05i	−0.215951	−	0.374038i	−0.953566	+	0.301183i	$0.902618\pi$
$258$		0			0
$259$		0			0
$260$			48.7351i			0.0116247i
$261$		0			0
$262$	−3823.53	−	2207.52i	−0.901597	−	0.520537i
$263$	4943.57	+	2854.17i	1.15906	+	0.669185i	0.951079	−	0.308947i	$-0.0999767\pi$
$263$	4943.57	+	2854.17i	1.15906	+	0.669185i	0.207983	+	0.978132i	$0.433310\pi$
$264$		0			0
$265$		−	326.740i		−	0.0757414i
$266$		0			0
$267$		0			0
$268$	−1205.15	−	2087.37i	−0.274686	−	0.475771i
$269$	−673.034	+	1165.73i	−0.152549	+	0.264222i	−0.932164	−	0.362037i	$-0.882081\pi$
$269$	−673.034	+	1165.73i	−0.152549	+	0.264222i	0.779615	+	0.626259i	$0.215415\pi$
$270$		0			0
$271$	−2216.03	+	1279.43i	−0.496732	+	0.286788i	−0.727363	−	0.686253i	$-0.759254\pi$
$271$	−2216.03	+	1279.43i	−0.496732	+	0.286788i	0.230631	+	0.973041i	$0.425921\pi$
$272$	−54.5657			−0.0121637
$273$		0			0
$274$	−1075.58			−0.237147
$275$	205.838	−	118.841i	0.0451364	−	0.0260595i
$276$		0			0
$277$	−1725.09	+	2987.94i	−0.374189	+	0.648115i	−0.990205	−	0.139619i	$-0.955412\pi$
$277$	−1725.09	+	2987.94i	−0.374189	+	0.648115i	0.616016	+	0.787734i	$0.288746\pi$
$278$	2107.99	+	3651.14i	0.454780	+	0.787701i
$279$		0			0
$280$		0			0
$281$			2714.07i			0.576184i	0.957603	+	0.288092i	$0.0930210\pi$
$281$			2714.07i			0.576184i	−0.957603	+	0.288092i	$0.906979\pi$
$282$		0			0
$283$	1594.72	+	920.714i	0.334970	+	0.193395i	0.658045	−	0.752978i	$-0.271383\pi$
$283$	1594.72	+	920.714i	0.334970	+	0.193395i	−0.323076	+	0.946373i	$0.604717\pi$
$284$	−716.489	−	413.665i	−0.149704	−	0.0864314i
$285$		0			0
$286$			19.6369i			0.00405998i
$287$		0			0
$288$		0			0
$289$	2450.68	+	4244.71i	0.498816	+	0.863975i
$290$	345.105	−	597.740i	0.0698802	−	0.121036i
$291$		0			0
$292$	1417.32	−	818.290i	0.284049	−	0.163996i
$293$	244.833			0.0488168			0.0244084	−	0.999702i	$-0.492230\pi$
$293$	244.833			0.0488168			0.0244084	+	0.999702i	$0.492230\pi$
$294$		0			0
$295$	−873.972			−0.172490
$296$	−1001.89	+	578.441i	−0.196735	+	0.113585i
$297$		0			0
$298$	−2749.91	+	4762.99i	−0.534558	+	0.925881i
$299$	112.130	+	194.214i	0.0216877	+	0.0375643i
$300$		0			0
$301$		0			0
$302$		−	3875.24i		−	0.738395i
$303$		0			0
$304$	−91.4958	−	52.8251i	−0.0172620	−	0.00996621i
$305$	1176.00	+	678.962i	0.220778	+	0.127466i
$306$		0			0
$307$		−	5646.40i		−	1.04970i	−0.851195	−	0.524849i	$-0.824122\pi$
$307$		−	5646.40i		−	1.04970i	0.851195	−	0.524849i	$-0.175878\pi$
$308$		0			0
$309$		0			0
$310$	450.329	+	779.992i	0.0825063	+	0.142905i
$311$	−2604.95	+	4511.90i	−0.474962	+	0.822658i	−0.999589	−	0.0286744i	$-0.990871\pi$
$311$	−2604.95	+	4511.90i	−0.474962	+	0.822658i	0.524627	+	0.851332i	$0.324205\pi$
$312$		0			0
$313$	−7612.72	+	4395.21i	−1.37475	+	0.793712i	−0.991522	−	0.129942i	$-0.958521\pi$
$313$	−7612.72	+	4395.21i	−1.37475	+	0.793712i	−0.383228	+	0.923654i	$0.625188\pi$
$314$	1618.97			0.290968
$315$		0			0
$316$	−3929.10			−0.699459
$317$	2876.47	−	1660.73i	0.509648	−	0.294246i	−0.223041	−	0.974809i	$-0.571598\pi$
$317$	2876.47	−	1660.73i	0.509648	−	0.294246i	0.732689	+	0.680563i	$0.238265\pi$
$318$		0			0
$319$	139.054	−	240.848i	0.0244060	−	0.0422725i
$320$	−79.4179	−	137.556i	−0.0138737	−	0.0240300i
$321$		0			0
$322$		0			0
$323$		−	22.5191i		−	0.00387924i
$324$		0			0
$325$	505.253	+	291.708i	0.0862350	+	0.0497878i
$326$	−195.378	−	112.802i	−0.0331932	−	0.0191641i
$327$		0			0
$328$		−	2872.61i		−	0.483578i
$329$		0			0
$330$		0			0
$331$	1508.77	+	2613.27i	0.250543	+	0.433953i	0.963675	−	0.267077i	$-0.0860576\pi$
$331$	1508.77	+	2613.27i	0.250543	+	0.433953i	−0.713133	+	0.701029i	$0.752724\pi$
$332$	2017.61	−	3494.60i	0.333526	−	0.577685i
$333$		0			0
$334$	−2478.08	+	1430.72i	−0.405972	+	0.234388i
$335$	1495.47			0.243899
$336$		0			0
$337$	−4293.62			−0.694031			−0.347015	−	0.937859i	$-0.612805\pi$
$337$	−4293.62			−0.694031			−0.347015	+	0.937859i	$0.612805\pi$
$338$	3763.57	−	2172.90i	0.605655	−	0.349675i
$339$		0			0
$340$	16.9277	−	29.3196i	0.00270010	−	0.00467671i
$341$	181.452	+	314.284i	0.0288157	+	0.0499103i
$342$		0			0
$343$		0			0
$344$		−	34.1599i		−	0.00535400i
$345$		0			0
$346$	−4821.16	−	2783.50i	−0.749096	−	0.432491i
$347$	8182.17	+	4723.98i	1.26583	+	0.730826i	0.974196	−	0.225705i	$-0.0724685\pi$
$347$	8182.17	+	4723.98i	1.26583	+	0.730826i	0.291632	+	0.956531i	$0.405802\pi$
$348$		0			0
$349$		−	8845.25i		−	1.35666i	−0.734756	−	0.678331i	$-0.762704\pi$
$349$		−	8845.25i		−	1.35666i	0.734756	−	0.678331i	$-0.237296\pi$
$350$		0			0
$351$		0			0
$352$	−32.0000	−	55.4256i	−0.00484547	−	0.00839260i
$353$	−5601.62	+	9702.29i	−0.844601	+	1.46289i	0.0413665	+	0.999144i	$0.486829\pi$
$353$	−5601.62	+	9702.29i	−0.844601	+	1.46289i	−0.885967	+	0.463748i	$0.846504\pi$
$354$		0			0
$355$	444.547	−	256.660i	0.0664623	−	0.0383720i
$356$	−4285.56			−0.638018
$357$		0			0
$358$	−1332.10			−0.196658
$359$	7454.44	−	4303.82i	1.09591	−	0.632722i	0.160763	−	0.986993i	$-0.448604\pi$
$359$	7454.44	−	4303.82i	1.09591	−	0.632722i	0.935143	+	0.354271i	$0.115271\pi$
$360$		0			0
$361$	−3407.70	+	5902.31i	−0.496822	+	0.860520i
$362$	2275.59	+	3941.43i	0.330393	+	0.572257i
$363$		0			0
$364$		0			0
$365$			1015.42i			0.145615i
$366$		0			0
$367$	1407.28	+	812.493i	0.200162	+	0.115563i	0.596731	−	0.802441i	$-0.296466\pi$
$367$	1407.28	+	812.493i	0.200162	+	0.115563i	−0.396569	+	0.918005i	$0.629799\pi$
$368$	−632.978	−	365.450i	−0.0896637	−	0.0517674i
$369$		0			0
$370$		−	717.790i		−	0.100854i
$371$		0			0
$372$		0			0
$373$	508.611	+	880.941i	0.0706029	+	0.122288i	0.899166	−	0.437608i	$-0.144174\pi$
$373$	508.611	+	880.941i	0.0706029	+	0.122288i	−0.828563	+	0.559896i	$0.810841\pi$
$374$	6.82071	−	11.8138i	0.000943023	−	0.00163336i
$375$		0			0
$376$	−1746.48	+	1008.33i	−0.239543	+	0.138300i
$377$	682.647			0.0932575
$378$		0			0
$379$	−4328.58			−0.586660			−0.293330	−	0.956011i	$-0.594764\pi$
$379$	−4328.58			−0.586660			−0.293330	+	0.956011i	$0.594764\pi$
$380$	56.7688	−	32.7755i	0.00766362	−	0.00442460i
$381$		0			0
$382$	−1488.99	+	2579.00i	−0.199433	+	0.345428i
$383$	3538.04	+	6128.06i	0.472024	+	0.817570i	0.999488	−	0.0320077i	$-0.0101901\pi$
$383$	3538.04	+	6128.06i	0.472024	+	0.817570i	−0.527463	+	0.849578i	$0.676857\pi$
$384$		0			0
$385$		0			0
$386$		−	5735.90i		−	0.756346i
$387$		0			0
$388$	2340.36	+	1351.21i	0.306221	+	0.176797i
$389$	6287.55	+	3630.12i	0.819515	+	0.473147i	0.850249	−	0.526380i	$-0.176451\pi$
$389$	6287.55	+	3630.12i	0.819515	+	0.473147i	−0.0307341	+	0.999528i	$0.509785\pi$
$390$		0			0
$391$		−	155.789i		−	0.0201499i
$392$		0			0
$393$		0			0
$394$	1720.75	+	2980.43i	0.220026	+	0.381096i
$395$	1218.91	−	2111.21i	0.155266	−	0.268928i
$396$		0			0
$397$	−12955.5	+	7479.84i	−1.63782	+	0.945599i	−0.656245	+	0.754548i	$0.727856\pi$
$397$	−12955.5	+	7479.84i	−1.63782	+	0.945599i	−0.981580	+	0.191050i	$0.938811\pi$
$398$	4285.27			0.539702
$399$		0			0
$400$	−1901.45			−0.237681
$401$	585.084	−	337.798i	0.0728621	−	0.0420670i	−0.463126	−	0.886292i	$-0.653272\pi$
$401$	585.084	−	337.798i	0.0728621	−	0.0420670i	0.535988	+	0.844225i	$0.319939\pi$
$402$		0			0
$403$	−445.394	+	771.445i	−0.0550537	+	0.0953559i
$404$	2171.31	+	3760.82i	0.267393	+	0.463138i
$405$		0			0
$406$		0			0
$407$		−	289.220i		−	0.0352239i
$408$		0			0
$409$	5784.92	+	3339.93i	0.699379	+	0.403787i	0.807116	−	0.590393i	$-0.201027\pi$
$409$	5784.92	+	3339.93i	0.699379	+	0.403787i	−0.107737	+	0.994179i	$0.534360\pi$
$410$	1543.53	+	891.160i	0.185926	+	0.107345i
$411$		0			0
$412$		−	7848.26i		−	0.938486i
$413$		0			0
$414$		0			0
$415$	1251.83	+	2168.23i	0.148072	+	0.256469i
$416$	78.5476	−	136.048i	0.00925749	−	0.0160344i
$417$		0			0
$418$	22.8739	−	13.2063i	0.00267656	−	0.00154531i
$419$	−7351.89			−0.857192			−0.428596	−	0.903496i	$-0.640992\pi$
$419$	−7351.89			−0.857192			−0.428596	+	0.903496i	$0.640992\pi$
$420$		0			0
$421$	602.461			0.0697438			0.0348719	−	0.999392i	$-0.488898\pi$
$421$	602.461			0.0697438			0.0348719	+	0.999392i	$0.488898\pi$
$422$	6307.95	−	3641.90i	0.727645	−	0.420106i
$423$		0			0
$424$	−526.616	+	912.125i	−0.0603177	+	0.104473i
$425$	−202.644	−	350.990i	−0.0231287	−	0.0400601i
$426$		0			0
$427$		0			0
$428$			3172.57i			0.358298i
$429$		0			0
$430$	18.3550	+	10.5973i	0.00205851	+	0.00118848i
$431$	793.977	+	458.403i	0.0887344	+	0.0512308i	0.543711	−	0.839273i	$-0.317019\pi$
$431$	793.977	+	458.403i	0.0887344	+	0.0512308i	−0.454976	+	0.890504i	$0.650352\pi$
$432$		0			0
$433$		−	11960.5i		−	1.32745i	−0.747976	−	0.663726i	$-0.768974\pi$
$433$		−	11960.5i		−	1.32745i	0.747976	−	0.663726i	$-0.231026\pi$
$434$		0			0
$435$		0			0
$436$	−2676.58	−	4635.97i	−0.294002	−	0.509227i
$437$	150.820	−	261.228i	0.0165096	−	0.0285954i
$438$		0			0
$439$	−8517.65	+	4917.67i	−0.926025	+	0.534641i	−0.885552	−	0.464540i	$-0.846220\pi$
$439$	−8517.65	+	4917.67i	−0.926025	+	0.534641i	−0.0404731	+	0.999181i	$0.512886\pi$
$440$	39.7090			0.00430239
$441$		0			0
$442$	33.4844			0.00360337
$443$	9269.39	−	5351.68i	0.994135	−	0.573964i	0.0876276	−	0.996153i	$-0.472071\pi$
$443$	9269.39	−	5351.68i	0.994135	−	0.573964i	0.906508	+	0.422189i	$0.138738\pi$
$444$		0			0
$445$	1329.49	−	2302.75i	0.141627	−	0.245305i
$446$	1337.74	+	2317.03i	0.142026	+	0.245996i
$447$		0			0
$448$		0			0
$449$		−	6205.55i		−	0.652245i	−0.945328	−	0.326122i	$-0.894258\pi$
$449$		−	6205.55i		−	0.652245i	0.945328	−	0.326122i	$-0.105742\pi$
$450$		0			0
$451$	621.939	+	359.077i	0.0649356	+	0.0374906i
$452$	1414.72	+	816.790i	0.147219	+	0.0849968i
$453$		0			0
$454$			5374.35i			0.555574i
$455$		0			0
$456$		0			0
$457$	5143.29	+	8908.44i	0.526462	+	0.911858i	0.999525	+	0.0308298i	$0.00981498\pi$
$457$	5143.29	+	8908.44i	0.526462	+	0.911858i	−0.473063	+	0.881029i	$0.656852\pi$
$458$	−213.326	+	369.492i	−0.0217644	+	0.0376970i
$459$		0			0
$460$	392.733	−	226.744i	0.0398071	−	0.0229826i
$461$	4023.34			0.406477			0.203238	−	0.979129i	$-0.434853\pi$
$461$	4023.34			0.406477			0.203238	+	0.979129i	$0.434853\pi$
$462$		0			0
$463$	3812.77			0.382710			0.191355	−	0.981521i	$-0.438712\pi$
$463$	3812.77			0.382710			0.191355	+	0.981521i	$0.438712\pi$
$464$	−1926.79	+	1112.43i	−0.192778	+	0.111300i
$465$		0			0
$466$	−1625.80	+	2815.97i	−0.161618	+	0.279930i
$467$	10003.2	+	17326.0i	0.991203	+	1.71681i	0.610218	+	0.792234i	$0.291082\pi$
$467$	10003.2	+	17326.0i	0.991203	+	1.71681i	0.380985	+	0.924581i	$0.375585\pi$
$468$		0			0
$469$		0			0
$470$		−	1251.24i		−	0.122799i
$471$		0			0
$472$	2439.77	+	1408.60i	0.237923	+	0.137365i
$473$	7.39583	+	4.26999i	0.000718944	+	0.000415083i
$474$		0			0
$475$		−	784.721i		−	0.0758010i
$476$		0			0
$477$		0			0
$478$	4477.61	+	7755.45i	0.428454	+	0.742105i
$479$	−3643.69	+	6311.05i	−0.347567	+	0.602003i	−0.985817	−	0.167826i	$-0.946325\pi$
$479$	−3643.69	+	6311.05i	−0.347567	+	0.602003i	0.638250	+	0.769829i	$0.279659\pi$
$480$		0			0
$481$	614.812	−	354.962i	0.0582807	−	0.0336484i
$482$	684.935			0.0647260
$483$		0			0
$484$	−5308.00			−0.498497
$485$	−1452.08	+	838.361i	−0.135950	+	0.0784907i
$486$		0			0
$487$	−3820.05	+	6616.51i	−0.355447	+	0.615653i	−0.987194	−	0.159522i	$-0.949005\pi$
$487$	−3820.05	+	6616.51i	−0.355447	+	0.615653i	0.631747	+	0.775175i	$0.282338\pi$
$488$	−2188.60	−	3790.77i	−0.203019	−	0.351639i
$489$		0			0
$490$		0			0
$491$			6954.84i			0.639241i	0.947546	+	0.319621i	$0.103555\pi$
$491$			6954.84i			0.639241i	−0.947546	+	0.319621i	$0.896445\pi$
$492$		0			0
$493$	−410.689	−	237.111i	−0.0375183	−	0.0216612i
$494$	56.1467	+	32.4163i	0.00511368	+	0.00295239i
$495$		0			0
$496$		−	2903.23i		−	0.262820i
$497$		0			0
$498$		0			0
$499$	−3579.48	−	6199.84i	−0.321121	−	0.556198i	0.659599	−	0.751618i	$-0.270726\pi$
$499$	−3579.48	−	6199.84i	−0.321121	−	0.556198i	−0.980720	+	0.195420i	$0.937393\pi$
$500$	1210.33	−	2096.36i	0.108255	−	0.187504i
$501$		0			0
$502$	−5591.46	+	3228.23i	−0.497130	+	0.287018i
$503$	−2400.81			−0.212817			−0.106408	−	0.994323i	$-0.533935\pi$
$503$	−2400.81			−0.212817			−0.106408	+	0.994323i	$0.533935\pi$
$504$		0			0
$505$	−2694.39			−0.237423
$506$	158.244	−	91.3625i	0.0139028	−	0.00802679i
$507$		0			0
$508$	2352.34	−	4074.38i	0.205450	−	0.355849i
$509$	−3506.44	−	6073.33i	−0.305344	−	0.528872i	0.671994	−	0.740557i	$-0.265438\pi$
$509$	−3506.44	−	6073.33i	−0.305344	−	0.528872i	−0.977338	+	0.211685i	$0.932105\pi$
$510$		0			0
$511$		0			0
$512$			512.000i			0.0441942i
$513$		0			0
$514$	−3082.09	−	1779.45i	−0.264485	−	0.152700i
$515$	4217.09	+	2434.74i	0.360829	+	0.208325i
$516$		0			0
$517$		−	504.166i		−	0.0428882i
$518$		0			0
$519$		0			0
$520$	48.7351	+	84.4116i	0.00410995	+	0.00711864i
$521$	8177.82	−	14164.4i	0.687672	−	1.19108i	−0.284917	−	0.958552i	$-0.591966\pi$
$521$	8177.82	−	14164.4i	0.687672	−	1.19108i	0.972589	−	0.232530i	$-0.0747005\pi$
$522$		0			0
$523$	−2439.53	+	1408.47i	−0.203964	+	0.117759i	−0.598503	−	0.801120i	$-0.704238\pi$
$523$	−2439.53	+	1408.47i	−0.203964	+	0.117759i	0.394539	+	0.918879i	$0.370904\pi$
$524$	−8830.06			−0.736151
$525$		0			0
$526$	11416.7			0.946370
$527$	535.910	−	309.408i	0.0442971	−	0.0255750i
$528$		0			0
$529$	−5040.11	+	8729.73i	−0.414244	+	0.717492i
$530$	−326.740	−	565.930i	−0.0267786	−	0.0463820i
$531$		0			0
$532$		0			0
$533$			1762.79i			0.143255i
$534$		0			0
$535$	−1704.71	−	984.213i	−0.137759	−	0.0795350i
$536$	−4174.75	−	2410.29i	−0.336421	−	0.194233i
$537$		0			0
$538$			2692.14i			0.215736i
$539$		0			0
$540$		0			0
$541$	4192.35	+	7261.37i	0.333167	+	0.577062i	0.983131	−	0.182903i	$-0.0585494\pi$
$541$	4192.35	+	7261.37i	0.333167	+	0.577062i	−0.649964	+	0.759965i	$0.725216\pi$
$542$	−2558.85	+	4432.06i	−0.202790	+	0.351242i
$543$		0			0
$544$	−94.5105	+	54.5657i	−0.00744872	+	0.00430052i
$545$	3321.38			0.261050
$546$		0			0
$547$	1942.57			0.151843			0.0759216	−	0.997114i	$-0.475810\pi$
$547$	1942.57			0.151843			0.0759216	+	0.997114i	$0.475810\pi$
$548$	−1862.96	+	1075.58i	−0.145222	+	0.0838441i
$549$		0			0
$550$	237.681	−	411.676i	0.0184268	−	0.0319162i
$551$	−459.096	−	795.177i	−0.0354957	−	0.0614804i
$552$		0			0
$553$		0			0
$554$			6900.35i			0.529183i
$555$		0			0
$556$	7302.29	+	4215.98i	0.556989	+	0.321578i
$557$	−20669.4	−	11933.5i	−1.57233	−	0.907787i	−0.995882	−	0.0906555i	$-0.971104\pi$
$557$	−20669.4	−	11933.5i	−1.57233	−	0.907787i	−0.576451	−	0.817132i	$-0.695563\pi$
$558$		0			0
$559$			20.9623i			0.00158607i
$560$		0			0
$561$		0			0
$562$	2714.07	+	4700.91i	0.203712	+	0.352839i
$563$	−768.172	+	1330.51i	−0.0575037	+	0.0995993i	−0.893344	−	0.449373i	$-0.851647\pi$
$563$	−768.172	+	1330.51i	−0.0575037	+	0.0995993i	0.835841	+	0.548972i	$0.184981\pi$
$564$		0			0
$565$	−877.767	+	506.779i	−0.0653592	+	0.0377352i
$566$	3682.86			0.273502
$567$		0			0
$568$	−1654.66			−0.122232
$569$	−14218.9	+	8209.29i	−1.04761	+	0.604835i	−0.921978	−	0.387242i	$-0.873428\pi$
$569$	−14218.9	+	8209.29i	−1.04761	+	0.604835i	−0.125628	+	0.992077i	$0.540094\pi$
$570$		0			0
$571$	7813.62	−	13533.6i	0.572662	−	0.991879i	−0.423630	−	0.905835i	$-0.639244\pi$
$571$	7813.62	−	13533.6i	0.572662	−	0.991879i	0.996291	−	0.0860436i	$-0.0274224\pi$
$572$	19.6369	+	34.0121i	0.00143542	+	0.00248622i
$573$		0			0
$574$		0			0
$575$		−	5428.79i		−	0.393732i
$576$		0			0
$577$	−12649.8	−	7303.38i	−0.912685	−	0.526939i	−0.0313910	−	0.999507i	$-0.509994\pi$
$577$	−12649.8	−	7303.38i	−0.912685	−	0.526939i	−0.881294	+	0.472568i	$0.843327\pi$
$578$	8489.42	+	4901.37i	0.610923	+	0.352716i
$579$		0			0
$580$		−	1380.42i		−	0.0988256i
$581$		0			0
$582$		0			0
$583$	−131.654	−	228.031i	−0.00935257	−	0.0161991i
$584$	1636.58	−	2834.64i	0.115963	−	0.200853i
$585$		0			0
$586$	424.064	−	244.833i	0.0298941	−	0.0172593i
$587$	−16836.8			−1.18386			−0.591931	−	0.805988i	$-0.701634\pi$
$587$	−16836.8			−1.18386			−0.591931	+	0.805988i	$0.701634\pi$
$588$		0			0
$589$	1198.15			0.0838183
$590$	−1513.76	+	873.972i	−0.105628	+	0.0609845i
$591$		0			0
$592$	−1156.88	+	2003.78i	−0.0803168	+	0.139113i
$593$	−1945.17	−	3369.14i	−0.134703	−	0.233312i	0.790781	−	0.612099i	$-0.209675\pi$
$593$	−1945.17	−	3369.14i	−0.134703	−	0.233312i	−0.925484	+	0.378787i	$0.876341\pi$
$594$		0			0
$595$		0			0
$596$			10999.7i			0.755979i
$597$		0			0
$598$	388.429	+	224.260i	0.0265619	+	0.0153355i
$599$	7954.06	+	4592.28i	0.542561	+	0.313248i	0.746116	−	0.665816i	$-0.231916\pi$
$599$	7954.06	+	4592.28i	0.542561	+	0.313248i	−0.203555	+	0.979063i	$0.565250\pi$
$600$		0			0
$601$			11221.8i			0.761643i	0.924649	+	0.380821i	$0.124359\pi$
$601$			11221.8i			0.761643i	−0.924649	+	0.380821i	$0.875641\pi$
$602$		0			0
$603$		0			0
$604$	−3875.24	−	6712.12i	−0.261062	−	0.452173i
$605$	1646.68	−	2852.13i	0.110656	−	0.191662i
$606$		0			0
$607$	24021.8	−	13869.0i	1.60628	−	0.927388i	0.616092	−	0.787674i	$-0.288715\pi$
$607$	24021.8	−	13869.0i	1.60628	−	0.927388i	0.990192	−	0.139714i	$-0.0446183\pi$
$608$	−211.300			−0.0140944
$609$		0			0
$610$	2715.85			0.180265
$611$	1071.74	−	618.767i	0.0709620	−	0.0409699i
$612$		0			0
$613$	−7340.75	+	12714.6i	−0.483671	+	0.837742i	−0.999824	−	0.0187538i	$-0.994030\pi$
$613$	−7340.75	+	12714.6i	−0.483671	+	0.837742i	0.516153	+	0.856496i	$0.327363\pi$
$614$	−5646.40	−	9779.85i	−0.371124	−	0.642806i
$615$		0			0
$616$		0			0
$617$		−	2168.39i		−	0.141485i	−0.997495	−	0.0707424i	$-0.977463\pi$
$617$		−	2168.39i		−	0.141485i	0.997495	−	0.0707424i	$-0.0225368\pi$
$618$		0			0
$619$	−9041.52	−	5220.12i	−0.587091	−	0.338957i	0.176855	−	0.984237i	$-0.443408\pi$
$619$	−9041.52	−	5220.12i	−0.587091	−	0.338957i	−0.763946	+	0.645280i	$0.776741\pi$
$620$	1559.98	+	900.658i	0.101049	+	0.0583408i
$621$		0			0
$622$			10419.8i			0.671697i
$623$		0			0
$624$		0			0
$625$	−6676.59	−	11564.2i	−0.427301	−	0.740108i
$626$	−8790.42	+	15225.4i	−0.561239	+	0.972095i
$627$		0			0
$628$	2804.14	−	1618.97i	0.178181	−	0.102873i
$629$	−493.172			−0.0312624
$630$		0			0
$631$	−2976.73			−0.187800			−0.0939000	−	0.995582i	$-0.529933\pi$
$631$	−2976.73			−0.187800			−0.0939000	+	0.995582i	$0.529933\pi$
$632$	−6805.40	+	3929.10i	−0.428329	+	0.247296i
$633$		0			0
$634$	3321.46	−	5752.94i	0.208063	−	0.360376i
$635$	1459.52	+	2527.96i	0.0912114	+	0.157983i
$636$		0			0
$637$		0			0
$638$		−	556.215i		−	0.0345153i
$639$		0			0
$640$	−275.112	−	158.836i	−0.0169918	−	0.00981021i
$641$	−8351.25	−	4821.60i	−0.514594	−	0.297101i	0.220126	−	0.975471i	$-0.429353\pi$
$641$	−8351.25	−	4821.60i	−0.514594	−	0.297101i	−0.734720	+	0.678371i	$0.762686\pi$
$642$		0			0
$643$			28235.9i			1.73175i	0.500260	+	0.865875i	$0.333238\pi$
$643$			28235.9i			1.73175i	−0.500260	+	0.865875i	$0.666762\pi$
$644$		0			0
$645$		0			0
$646$	−22.5191	−	39.0041i	−0.00137152	−	0.00237554i
$647$	14710.9	−	25480.0i	0.893886	−	1.54826i	0.0587083	−	0.998275i	$-0.481302\pi$
$647$	14710.9	−	25480.0i	0.893886	−	1.54826i	0.835178	−	0.549980i	$-0.185365\pi$
$648$		0			0
$649$	−609.944	+	352.151i	−0.0368912	+	0.0212991i
$650$	1166.83			0.0704106
$651$		0			0
$652$	−451.206			−0.0271022
$653$	−10023.3	+	5786.98i	−0.600679	+	0.346802i	−0.769309	−	0.638877i	$-0.779399\pi$
$653$	−10023.3	+	5786.98i	−0.600679	+	0.346802i	0.168629	+	0.985680i	$0.446066\pi$
$654$		0			0
$655$	2739.32	−	4744.64i	0.163411	−	0.283036i
$656$	−2872.61	−	4975.51i	−0.170971	−	0.296130i
$657$		0			0
$658$		0			0
$659$			21336.2i			1.26122i	0.776101	+	0.630608i	$0.217194\pi$
$659$			21336.2i			1.26122i	−0.776101	+	0.630608i	$0.782806\pi$
$660$		0			0
$661$	−7537.07	−	4351.53i	−0.443507	−	0.256059i	0.261577	−	0.965183i	$-0.415757\pi$
$661$	−7537.07	−	4351.53i	−0.443507	−	0.256059i	−0.705084	+	0.709124i	$0.749091\pi$
$662$	5226.54	+	3017.54i	0.306851	+	0.177160i
$663$		0			0
$664$		−	8070.44i		−	0.471677i
$665$		0			0
$666$		0			0
$667$	−3176.08	−	5501.12i	−0.184375	−	0.319347i
$668$	−2861.44	+	4956.17i	−0.165737	+	0.287066i
$669$		0			0
$670$	2590.23	−	1495.47i	0.149357	−	0.0862315i
$671$	1094.30			0.0629583
$672$		0			0
$673$	1332.12			0.0762993			0.0381497	−	0.999272i	$-0.487854\pi$
$673$	1332.12			0.0762993			0.0381497	+	0.999272i	$0.487854\pi$
$674$	−7436.77	+	4293.62i	−0.425005	+	0.245377i
$675$		0			0
$676$	4345.80	−	7527.14i	0.247258	−	0.428263i
$677$	−10211.2	−	17686.3i	−0.579688	−	1.00405i	−0.995515	−	0.0946052i	$-0.969841\pi$
$677$	−10211.2	−	17686.3i	−0.579688	−	1.00405i	0.415827	−	0.909444i	$-0.363492\pi$
$678$		0			0
$679$		0			0
$680$		−	67.7108i		−	0.00381852i
$681$		0			0
$682$	628.567	+	362.904i	0.0352919	+	0.0203758i
$683$	−13720.5	−	7921.51i	−0.768666	−	0.443790i	0.0637324	−	0.997967i	$-0.479700\pi$
$683$	−13720.5	−	7921.51i	−0.768666	−	0.443790i	−0.832399	+	0.554177i	$0.813033\pi$
$684$		0			0
$685$		−	1334.69i		−	0.0744468i
$686$		0			0
$687$		0			0
$688$	−34.1599	−	59.1667i	−0.00189293	−	0.00327865i
$689$	323.159	−	559.728i	0.0178685	−	0.0309491i
$690$		0			0
$691$	27531.7	−	15895.5i	1.51571	−	0.875096i	0.515881	−	0.856660i	$-0.327464\pi$
$691$	27531.7	−	15895.5i	1.51571	−	0.875096i	0.999830	−	0.0184365i	$-0.00586885\pi$
$692$	−11134.0			−0.611635
$693$		0			0
$694$	18895.9			1.03354
$695$	−4530.72	+	2615.81i	−0.247281	+	0.142768i
$696$		0			0
$697$	612.290	−	1060.52i	0.0332742	−	0.0576326i
$698$	−8845.25	−	15320.4i	−0.479653	−	0.830783i
$699$		0			0
$700$		0			0
$701$		−	31077.5i		−	1.67444i	−0.546866	−	0.837220i	$-0.684179\pi$
$701$		−	31077.5i		−	1.67444i	0.546866	−	0.837220i	$-0.315821\pi$
$702$		0			0
$703$	−826.951	−	477.441i	−0.0443657	−	0.0256145i
$704$	−110.851	−	64.0000i	−0.00593447	−	0.00342627i
$705$		0			0
$706$			22406.5i			1.19445i
$707$		0			0
$708$		0			0
$709$	2530.96	+	4383.76i	0.134065	+	0.232208i	0.925240	−	0.379382i	$-0.123863\pi$
$709$	2530.96	+	4383.76i	0.134065	+	0.232208i	−0.791175	+	0.611590i	$0.790530\pi$
$710$	513.319	−	889.095i	0.0271331	−	0.0469960i
$711$		0			0
$712$	−7422.81	+	4285.56i	−0.390705	+	0.225573i
$713$	8288.94			0.435376
$714$		0			0
$715$	−24.3675			−0.00127454
$716$	−2307.26	+	1332.10i	−0.120428	+	0.0695291i
$717$		0			0
$718$	8607.65	−	14908.9i	0.447402	−	0.774923i
$719$	10268.6	+	17785.8i	0.532622	+	0.922528i	0.999274	+	0.0380871i	$0.0121264\pi$
$719$	10268.6	+	17785.8i	0.532622	+	0.922528i	−0.466653	+	0.884441i	$0.654540\pi$
$720$		0			0
$721$		0			0
$722$			13630.8i			0.702612i
$723$		0			0
$724$	7882.86	+	4551.17i	0.404647	+	0.233623i
$725$	−14311.3	−	8262.62i	−0.733114	−	0.423264i
$726$		0			0
$727$			18303.0i			0.933728i	0.884329	+	0.466864i	$0.154616\pi$
$727$			18303.0i			0.933728i	−0.884329	+	0.466864i	$0.845384\pi$
$728$		0			0
$729$		0			0
$730$	1015.42	+	1758.76i	0.0514827	+	0.0891707i
$731$	7.28108	−	12.6112i	0.000368400	−	0.000638088i
$732$		0			0
$733$	17466.8	−	10084.4i	0.880150	−	0.508155i	0.00944201	−	0.999955i	$-0.496994\pi$
$733$	17466.8	−	10084.4i	0.880150	−	0.508155i	0.870708	+	0.491801i	$0.163661\pi$
$734$	3249.97			0.163431
$735$		0			0
$736$	−1461.80			−0.0732101
$737$	1043.69	−	602.573i	0.0521638	−	0.0301168i
$738$		0			0
$739$	8962.50	−	15523.5i	0.446131	−	0.772721i	−0.551999	−	0.833845i	$-0.686135\pi$
$739$	8962.50	−	15523.5i	0.446131	−	0.772721i	0.998130	+	0.0611232i	$0.0194682\pi$
$740$	−717.790	−	1243.25i	−0.0356574	−	0.0617604i
$741$		0			0
$742$		0			0
$743$		−	9644.16i		−	0.476191i	−0.971242	−	0.238096i	$-0.923477\pi$
$743$		−	9644.16i		−	0.476191i	0.971242	−	0.238096i	$-0.0765231\pi$
$744$		0			0
$745$	−5910.42	−	3412.38i	−0.290659	−	0.167812i
$746$	1761.88	+	1017.22i	0.0864706	+	0.0499238i
$747$		0			0
$748$		−	27.2828i		−	0.00133364i
$749$		0			0
$750$		0			0
$751$	−20432.8	−	35390.6i	−0.992814	−	1.71960i	−0.600044	−	0.799967i	$-0.704850\pi$
$751$	−20432.8	−	35390.6i	−0.992814	−	1.71960i	−0.392770	−	0.919637i	$-0.628483\pi$
$752$	−2016.67	+	3492.97i	−0.0977928	+	0.169382i
$753$		0			0
$754$	1182.38	−	682.647i	0.0571084	−	0.0329715i
$755$	4808.81			0.231802
$756$		0			0
$757$	−7510.00			−0.360576			−0.180288	−	0.983614i	$-0.557703\pi$
$757$	−7510.00			−0.360576			−0.180288	+	0.983614i	$0.557703\pi$
$758$	−7497.32	+	4328.58i	−0.359255	+	0.207416i
$759$		0			0
$760$	65.5509	−	113.538i	0.00312866	−	0.00541900i
$761$	−17072.4	−	29570.3i	−0.813238	−	1.40857i	−0.910586	−	0.413319i	$-0.864369\pi$
$761$	−17072.4	−	29570.3i	−0.813238	−	1.40857i	0.0973479	−	0.995250i	$-0.468964\pi$
$762$		0			0
$763$		0			0
$764$			5955.96i			0.282040i
$765$		0			0
$766$	12256.1	+	7076.08i	0.578109	+	0.333772i
$767$	−1497.18	−	864.395i	−0.0704823	−	0.0406929i
$768$		0			0
$769$		−	8264.90i		−	0.387568i	−0.981044	−	0.193784i	$-0.937924\pi$
$769$		−	8264.90i		−	0.387568i	0.981044	−	0.193784i	$-0.0620762\pi$
$770$		0			0
$771$		0			0
$772$	−5735.90	−	9934.86i	−0.267409	−	0.463165i
$773$	14935.7	−	25869.4i	0.694955	−	1.20370i	−0.275241	−	0.961375i	$-0.588758\pi$
$773$	14935.7	−	25869.4i	0.694955	−	1.20370i	0.970196	−	0.242322i	$-0.0779089\pi$
$774$		0			0
$775$	18674.8	−	10781.9i	0.865574	−	0.499739i
$776$	5404.84			0.250029
$777$		0			0
$778$	14520.5			0.669131
$779$	2053.38	−	1185.52i	0.0944414	−	0.0545257i
$780$		0			0
$781$	206.833	−	358.245i	0.00947638	−	0.0164136i
$782$	−155.789	−	269.835i	−0.00712406	−	0.0123392i
$783$		0			0
$784$		0			0
$785$			2008.99i			0.0913426i
$786$		0			0
$787$	−5366.00	−	3098.06i	−0.243046	−	0.140323i	0.373530	−	0.927618i	$-0.378147\pi$
$787$	−5366.00	−	3098.06i	−0.243046	−	0.140323i	−0.616576	+	0.787296i	$0.711481\pi$
$788$	5960.85	+	3441.50i	0.269475	+	0.155582i
$789$		0			0
$790$		−	4875.64i		−	0.219579i
$791$		0			0
$792$		0			0
$793$	1343.04	+	2326.22i	0.0601423	+	0.104170i
$794$	−14959.7	+	25910.9i	−0.668639	+	1.15812i
$795$		0			0
$796$	7422.31	−	4285.27i	0.330498	−	0.190813i
$797$	31854.7			1.41575			0.707874	−	0.706338i	$-0.249654\pi$
$797$	31854.7			1.41575			0.707874	+	0.706338i	$0.249654\pi$
$798$		0			0
$799$	−859.693			−0.0380648
$800$	−3293.41	+	1901.45i	−0.145549	+	0.0840330i
$801$		0			0
$802$	675.597	−	1170.17i	0.0297458	−	0.0515213i
$803$	409.145	+	708.660i	0.0179806	+	0.0311433i
$804$		0			0
$805$		0			0
$806$			1781.58i			0.0778577i
$807$		0			0
$808$	7521.64	+	4342.62i	0.327488	+	0.189075i
$809$	−37054.1	−	21393.2i	−1.61032	−	0.929721i	−0.989294	−	0.145934i	$-0.953381\pi$
$809$	−37054.1	−	21393.2i	−1.61032	−	0.929721i	−0.621030	−	0.783787i	$-0.713285\pi$
$810$		0			0
$811$			13685.6i			0.592559i	0.955101	+	0.296279i	$0.0957460\pi$
$811$			13685.6i			0.592559i	−0.955101	+	0.296279i	$0.904254\pi$
$812$		0			0
$813$		0			0
$814$	−289.220	−	500.944i	−0.0124535	−	0.0215701i
$815$	139.976	−	242.446i	0.00601613	−	0.0104202i
$816$		0			0
$817$	24.4179	−	14.0977i	0.00104562	−	0.000603690i
$818$	13359.7			0.571041
$819$		0			0
$820$	3564.64			0.151808
$821$	−26993.7	+	15584.8i	−1.14749	+	0.662501i	−0.948273	−	0.317455i	$-0.897172\pi$
$821$	−26993.7	+	15584.8i	−1.14749	+	0.662501i	−0.199212	+	0.979956i	$0.563838\pi$
$822$		0			0
$823$	11417.9	−	19776.4i	0.483600	−	0.837620i	−0.516222	−	0.856455i	$-0.672662\pi$
$823$	11417.9	−	19776.4i	0.483600	−	0.837620i	0.999823	+	0.0188343i	$0.00599549\pi$
$824$	−7848.26	−	13593.6i	−0.331805	−	0.574703i
$825$		0			0
$826$		0			0
$827$		−	43776.3i		−	1.84069i	−0.391106	−	0.920346i	$-0.627907\pi$
$827$		−	43776.3i		−	1.84069i	0.391106	−	0.920346i	$-0.372093\pi$
$828$		0			0
$829$	18169.5	+	10490.2i	0.761222	+	0.439491i	0.829734	−	0.558159i	$-0.188492\pi$
$829$	18169.5	+	10490.2i	0.761222	+	0.439491i	−0.0685126	+	0.997650i	$0.521825\pi$
$830$	4336.47	+	2503.66i	0.181351	+	0.104703i
$831$		0			0
$832$		−	314.190i		−	0.0130921i
$833$		0			0
$834$		0			0
$835$	−1775.39	−	3075.06i	−0.0735807	−	0.127446i
$836$	26.4126	−	45.7479i	0.00109270	−	0.00189261i
$837$		0			0
$838$	−12733.8	+	7351.89i	−0.524921	+	0.303063i
$839$	−5328.94			−0.219279			−0.109640	−	0.993971i	$-0.534970\pi$
$839$	−5328.94			−0.219279			−0.109640	+	0.993971i	$0.534970\pi$
$840$		0			0
$841$	5053.03			0.207185
$842$	1043.49	−	602.461i	0.0427092	−	0.0246582i
$843$		0			0
$844$	7283.79	−	12615.9i	0.297060	−	0.514523i
$845$	2696.36	+	4670.24i	0.109772	+	0.190131i
$846$		0			0
$847$		0			0
$848$			2106.46i			0.0853021i
$849$		0			0
$850$	−701.981	−	405.289i	−0.0283268	−	0.0163545i
$851$	−5720.94	−	3302.99i	−0.230448	−	0.133049i
$852$		0			0
$853$			5328.47i			0.213884i	0.994265	+	0.106942i	$0.0341060\pi$
$853$			5328.47i			0.213884i	−0.994265	+	0.106942i	$0.965894\pi$
$854$		0			0
$855$		0			0
$856$	3172.57	+	5495.04i	0.126678	+	0.219412i
$857$	2685.74	−	4651.84i	0.107052	−	0.185419i	−0.807523	−	0.589836i	$-0.799192\pi$
$857$	2685.74	−	4651.84i	0.107052	−	0.185419i	0.914575	+	0.404417i	$0.132526\pi$
$858$		0			0
$859$	22862.8	−	13199.9i	0.908114	−	0.524300i	0.0282905	−	0.999600i	$-0.490994\pi$
$859$	22862.8	−	13199.9i	0.908114	−	0.524300i	0.879824	+	0.475300i	$0.157660\pi$
$860$	42.3892			0.00168077
$861$		0			0
$862$	1833.61			0.0724513
$863$	33233.4	−	19187.3i	1.31087	−	0.756830i	0.328628	−	0.944460i	$-0.393414\pi$
$863$	33233.4	−	19187.3i	1.31087	−	0.756830i	0.982240	+	0.187630i	$0.0600805\pi$
$864$		0			0
$865$	3454.06	−	5982.60i	0.135771	−	0.235161i
$866$	−11960.5	−	20716.2i	−0.469325	−	0.812894i
$867$		0			0
$868$		0			0
$869$		−	1964.55i		−	0.0766890i
$870$		0			0
$871$	2561.85	+	1479.08i	0.0996612	+	0.0575394i
$872$	−9271.94	−	5353.16i	−0.360078	−	0.207891i
$873$		0			0
$874$		−	603.279i		−	0.0233481i
$875$		0			0
$876$		0			0
$877$	−6382.41	−	11054.7i	−0.245745	−	0.425643i	0.716596	−	0.697489i	$-0.245699\pi$
$877$	−6382.41	−	11054.7i	−0.245745	−	0.425643i	−0.962341	+	0.271846i	$0.912366\pi$
$878$	−9835.33	+	17035.3i	−0.378048	+	0.654799i
$879$		0			0
$880$	68.7779	−	39.7090i	0.00263466	−	0.00152112i
$881$	45192.3			1.72823			0.864114	−	0.503296i	$-0.167880\pi$
$881$	45192.3			1.72823			0.864114	+	0.503296i	$0.167880\pi$
$882$		0			0
$883$	15308.3			0.583426			0.291713	−	0.956506i	$-0.405775\pi$
$883$	15308.3			0.583426			0.291713	+	0.956506i	$0.405775\pi$
$884$	57.9967	−	33.4844i	0.00220661	−	0.00127399i
$885$		0			0
$886$	10703.4	−	18538.8i	0.405854	−	0.702960i
$887$	17580.9	+	30451.0i	0.665511	+	1.15270i	0.979147	+	0.203155i	$0.0651196\pi$
$887$	17580.9	+	30451.0i	0.665511	+	1.15270i	−0.313636	+	0.949543i	$0.601547\pi$
$888$		0			0
$889$		0			0
$890$		−	5317.98i		−	0.200291i
$891$		0			0
$892$	4634.05	+	2675.47i	0.173946	+	0.100428i
$893$	−1441.53	−	832.270i	−0.0540191	−	0.0311880i
$894$		0			0
$895$		−	1653.01i		−	0.0617362i
$896$		0			0
$897$		0			0
$898$	−6205.55	−	10748.3i	−0.230603	−	0.399417i
$899$	12615.8	−	21851.2i	0.468031	−	0.810654i
$900$		0			0
$901$	−388.834	+	224.493i	−0.0143773	+	0.00830073i
$902$	1436.31			0.0530197
$903$		0			0
$904$	3267.16			0.120204
$905$	−4890.94	+	2823.78i	−0.179647	+	0.103719i
$906$		0			0
$907$	−7343.88	+	12720.0i	−0.268853	+	0.465667i	−0.968566	−	0.248757i	$-0.919978\pi$
$907$	−7343.88	+	12720.0i	−0.268853	+	0.465667i	0.699713	+	0.714424i	$0.253311\pi$
$908$	5374.35	+	9308.64i	0.196425	+	0.340218i
$909$		0			0
$910$		0			0
$911$			6922.25i			0.251750i	0.992046	+	0.125875i	$0.0401739\pi$
$911$			6922.25i			0.251750i	−0.992046	+	0.125875i	$0.959826\pi$
$912$		0			0
$913$	1747.30	+	1008.80i	0.0633376	+	0.0365680i
$914$	17816.9	+	10286.6i	0.644781	+	0.372265i
$915$		0			0
$916$			853.305i			0.0307795i
$917$		0			0
$918$		0			0
$919$	−17306.8	−	29976.2i	−0.621216	−	1.07598i	−0.989260	−	0.146169i	$-0.953306\pi$
$919$	−17306.8	−	29976.2i	−0.621216	−	1.07598i	0.368044	−	0.929808i	$-0.380028\pi$
$920$	453.489	−	785.465i	0.0162512	−	0.0281479i
$921$		0			0
$922$	6968.63	−	4023.34i	0.248915	−	0.143711i
$923$	1015.39			0.0362101
$924$		0			0
$925$	−17185.6			−0.610873
$926$	6603.92	−	3812.77i	0.234361	−	0.135308i
$927$		0			0
$928$	−2224.86	+	3853.57i	−0.0787011	+	0.136314i
$929$	−16726.1	−	28970.5i	−0.590707	−	1.02313i	−0.994137	−	0.108124i	$-0.965516\pi$
$929$	−16726.1	−	28970.5i	−0.590707	−	1.02313i	0.403431	−	0.915010i	$-0.367818\pi$
$930$		0			0
$931$		0			0
$932$			6503.20i			0.228562i
$933$		0			0
$934$	34652.0	+	20006.4i	1.21397	+	0.700887i
$935$	14.6598	+	8.46385i	0.000512757	+	0.000296040i
$936$		0			0
$937$		−	25914.8i		−	0.903522i	−0.892139	−	0.451761i	$-0.850796\pi$
$937$		−	25914.8i		−	0.903522i	0.892139	−	0.451761i	$-0.149204\pi$
$938$		0			0
$939$		0			0
$940$	−1251.24	−	2167.22i	−0.0434161	−	0.0751988i
$941$	−11962.5	+	20719.7i	−0.414417	+	0.717792i	−0.995367	−	0.0961475i	$-0.969348\pi$
$941$	−11962.5	+	20719.7i	−0.414417	+	0.717792i	0.580950	+	0.813939i	$0.302681\pi$
$942$		0			0
$943$	14205.5	−	8201.54i	0.490556	−	0.283222i
$944$	5634.42			0.194263
$945$		0			0
$946$	17.0799			0.000587016
$947$	17184.6	−	9921.51i	0.589676	−	0.340450i	−0.175293	−	0.984516i	$-0.556087\pi$
$947$	17184.6	−	9921.51i	0.589676	−	0.340450i	0.764969	+	0.644067i	$0.222754\pi$
$948$		0			0
$949$	−1004.29	+	1739.49i	−0.0343527	+	0.0595006i
$950$	−784.721	−	1359.18i	−0.0267997	−	0.0464184i
$951$		0			0
$952$		0			0
$953$		−	44178.8i		−	1.50167i	−0.660490	−	0.750834i	$-0.729652\pi$
$953$		−	44178.8i		−	1.50167i	0.660490	−	0.750834i	$-0.270348\pi$
$954$		0			0
$955$	−3200.30	−	1847.69i	−0.108439	−	0.0626073i
$956$	15510.9	+	8955.22i	0.524747	+	0.302963i
$957$		0			0
$958$			14574.8i			0.491533i
$959$		0			0
$960$		0			0
$961$	1566.88	+	2713.91i	0.0525957	+	0.0910985i
$962$	709.924	−	1229.62i	0.0237930	−	0.0412107i
$963$		0			0
$964$	1186.34	−	684.935i	0.0396364	−	0.0228841i
$965$	7117.70			0.237437
$966$		0			0
$967$	−30120.1			−1.00165			−0.500827	−	0.865548i	$-0.666971\pi$
$967$	−30120.1			−1.00165			−0.500827	+	0.865548i	$0.666971\pi$
$968$	−9193.73	+	5308.00i	−0.305266	+	0.176245i
$969$		0			0
$970$	−1676.72	+	2904.17i	−0.0555013	+	0.0961311i
$971$	19132.0	+	33137.5i	0.632311	+	1.09519i	0.987078	+	0.160240i	$0.0512267\pi$
$971$	19132.0	+	33137.5i	0.632311	+	1.09519i	−0.354767	+	0.934955i	$0.615440\pi$
$972$		0			0
$973$		0			0
$974$			15280.2i			0.502678i
$975$		0			0
$976$	−7581.54	−	4377.20i	−0.248647	−	0.143556i
$977$	−5638.08	−	3255.14i	−0.184624	−	0.106593i	0.404839	−	0.914388i	$-0.367327\pi$
$977$	−5638.08	−	3255.14i	−0.184624	−	0.106593i	−0.589464	+	0.807795i	$0.700661\pi$
$978$		0			0
$979$		−	2142.78i		−	0.0699526i
$980$		0			0
$981$		0			0
$982$	6954.84	+	12046.1i	0.226006	+	0.391454i
$983$	−20907.4	+	36212.7i	−0.678375	+	1.17498i	0.297095	+	0.954848i	$0.403982\pi$
$983$	−20907.4	+	36212.7i	−0.678375	+	1.17498i	−0.975470	+	0.220132i	$0.929351\pi$
$984$		0			0
$985$	−3698.43	+	2135.29i	−0.119636	+	0.0690720i
$986$	−948.446			−0.0306335
$987$		0			0
$988$	129.665			0.00417530
$989$	168.925	−	97.5291i	0.00543126	−	0.00313574i
$990$		0			0
$991$	7382.90	−	12787.6i	0.236655	−	0.409899i	−0.723097	−	0.690746i	$-0.757282\pi$
$991$	7382.90	−	12787.6i	0.236655	−	0.409899i	0.959752	+	0.280847i	$0.0906154\pi$
$992$	−2903.23	−	5028.54i	−0.0929210	−	0.160944i
$993$		0			0
$994$		0			0
$995$			5317.61i			0.169427i
$996$		0			0
$997$	−32290.0	−	18642.7i	−1.02571	−	0.592196i	−0.109960	−	0.993936i	$-0.535072\pi$
$997$	−32290.0	−	18642.7i	−1.02571	−	0.592196i	−0.915754	+	0.401740i	$0.868405\pi$
$998$	−12399.7	−	7158.96i	−0.393291	−	0.227067i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.k.b.521.7		16
3.2	odd	2	inner	882.4.k.b.521.2		16
7.2	even	3	inner	882.4.k.b.215.3		16
7.3	odd	6		882.4.d.a.881.7	yes	8
7.4	even	3		882.4.d.a.881.6	yes	8
7.5	odd	6	inner	882.4.k.b.215.2		16
7.6	odd	2	inner	882.4.k.b.521.6		16
21.2	odd	6	inner	882.4.k.b.215.6		16
21.5	even	6	inner	882.4.k.b.215.7		16
21.11	odd	6		882.4.d.a.881.3	yes	8
21.17	even	6		882.4.d.a.881.2	✓	8
21.20	even	2	inner	882.4.k.b.521.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.4.d.a.881.2	✓	8	21.17	even	6
882.4.d.a.881.3	yes	8	21.11	odd	6
882.4.d.a.881.6	yes	8	7.4	even	3
882.4.d.a.881.7	yes	8	7.3	odd	6
882.4.k.b.215.2		16	7.5	odd	6	inner
882.4.k.b.215.3		16	7.2	even	3	inner
882.4.k.b.215.6		16	21.2	odd	6	inner
882.4.k.b.215.7		16	21.5	even	6	inner
882.4.k.b.521.2		16	3.2	odd	2	inner
882.4.k.b.521.3		16	21.20	even	2	inner
882.4.k.b.521.6		16	7.6	odd	2	inner
882.4.k.b.521.7		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(1.24090 + 2.14931i) q^{5} -8.00000i q^{8} +O(q^{10})\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(1.24090 + 2.14931i) q^{5} -8.00000i q^{8} +(4.29862 + 2.48181i) q^{10} +(1.73205 + 1.00000i) q^{11} +4.90923i q^{13} +(-8.00000 - 13.8564i) q^{16} +(1.70518 - 2.95345i) q^{17} +(5.71849 - 3.30157i) q^{19} +9.92724 q^{20} +4.00000 q^{22} +(39.5611 - 22.8406i) q^{23} +(59.4203 - 102.919i) q^{25} +(4.90923 + 8.50303i) q^{26} -139.054i q^{29} +(157.142 + 90.7259i) q^{31} +(-27.7128 - 16.0000i) q^{32} -6.82071i q^{34} +(-72.3051 - 125.236i) q^{37} +(6.60314 - 11.4370i) q^{38} +(17.1945 - 9.92724i) q^{40} +359.077 q^{41} +4.26999 q^{43} +(6.92820 - 4.00000i) q^{44} +(45.6812 - 79.1222i) q^{46} +(-126.042 - 218.310i) q^{47} -237.681i q^{50} +(17.0061 + 9.81845i) q^{52} +(-114.016 - 65.8269i) q^{53} +4.96362i q^{55} +(-139.054 - 240.848i) q^{58} +(-176.076 + 304.972i) q^{59} +(473.846 - 273.575i) q^{61} +362.904 q^{62} -64.0000 q^{64} +(-10.5515 + 6.09188i) q^{65} +(301.286 - 521.843i) q^{67} +(-6.82071 - 11.8138i) q^{68} -206.833i q^{71} +(354.330 + 204.572i) q^{73} +(-250.472 - 144.610i) q^{74} -26.4126i q^{76} +(-491.137 - 850.674i) q^{79} +(19.8545 - 34.3890i) q^{80} +(621.939 - 359.077i) q^{82} +1008.80 q^{83} +8.46385 q^{85} +(7.39583 - 4.26999i) q^{86} +(8.00000 - 13.8564i) q^{88} +(-535.695 - 927.852i) q^{89} -182.725i q^{92} +(-436.621 - 252.083i) q^{94} +(14.1922 + 8.19387i) q^{95} +675.605i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4}+O(q^{10}) \) 16 * q + 32 * q^4	\( 16 q + 32 q^{4} - 128 q^{16} + 64 q^{22} + 600 q^{25} - 512 q^{37} + 4096 q^{43} - 672 q^{46} - 1184 q^{58} - 1024 q^{64} + 544 q^{67} - 6048 q^{79} + 6720 q^{85} + 128 q^{88}+O(q^{100}) \) 16 * q + 32 * q^4 - 128 * q^16 + 64 * q^22 + 600 * q^25 - 512 * q^37 + 4096 * q^43 - 672 * q^46 - 1184 * q^58 - 1024 * q^64 + 544 * q^67 - 6048 * q^79 + 6720 * q^85 + 128 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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