LMFDB - Embedded newform 882.4.k.b.521.2

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			521.2
Root			$-0.608761 + 0.793353i$ of defining polynomial
Character	$\chi$	$=$	882.521
Dual form			882.4.k.b.215.2

$q$-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	0.805180	−	0.593031i	$-0.202069\pi$
$5$	−1.24090	−	2.14931i	−0.110990	−	0.192240i	−0.916170	+	0.400791i	$0.868735\pi$
$6$		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	0.476074	−	0.879405i	$-0.342059\pi$
$11$	−1.73205	−	1.00000i	−0.0474757	−	0.0274101i	−0.523550	+	0.851995i	$0.675393\pi$
$12$		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	−0.877933	−	0.478784i	$-0.841078\pi$
$17$	−1.70518	+	2.95345i	−0.0243274	+	0.0421363i	0.853605	+	0.520920i	$0.174411\pi$
$18$		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	−0.668491	−	0.743721i	$-0.733059\pi$
$23$	−39.5611	+	22.8406i	−0.358655	+	0.207070i	0.309836	+	0.950790i	$0.399726\pi$
$24$		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	$0.146868\pi$
$29$			139.054i			0.890402i	−0.895431	+	0.445201i	$0.853132\pi$
$30$		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	$-0.739710\pi$
$41$	−359.077			−1.36777			−0.683883	+	0.729592i	$0.739710\pi$
$42$		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	0.992604	−	0.121395i	$-0.0387367\pi$
$47$	126.042	+	218.310i	0.391171	+	0.677529i	−0.601433	+	0.798923i	$0.705403\pi$
$48$		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	0.640417	−	0.768027i	$-0.278761\pi$
$53$	114.016	+	65.8269i	0.295495	+	0.170604i	−0.344922	+	0.938631i	$0.612095\pi$
$54$		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	−0.603725	−	0.797193i	$-0.706317\pi$
$59$	176.076	−	304.972i	0.388527	−	0.672948i	0.992252	+	0.124245i	$0.0396507\pi$
$60$		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	$0.0553017\pi$
$71$			206.833i			0.345726i	−0.984946	+	0.172863i	$0.944698\pi$
$72$		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	$-0.732444\pi$
$83$	−1008.80			−1.33411			−0.667053	+	0.745011i	$0.732444\pi$
$84$		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	$0.0535788\pi$
$89$	535.695	+	927.852i	0.638018	+	1.10508i	−0.347849	+	0.937551i	$0.613088\pi$
$90$		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	$-0.653726\pi$
$101$	542.828	−	940.205i	0.534786	−	0.926276i	0.999174	−	0.0406444i	$-0.0129411\pi$
$102$		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	−0.156508	−	0.987677i	$-0.550024\pi$
$107$	686.880	−	396.571i	0.620591	−	0.358298i	0.777099	+	0.629378i	$0.216690\pi$
$108$		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	$-0.945625\pi$
$113$		−	408.395i		−	0.339987i	0.985445	−	0.169994i	$-0.0543747\pi$
$114$		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	$0.0966920\pi$
$131$	1103.76	+	1911.76i	0.736151	+	1.27505i	−0.218066	+	0.975934i	$0.569975\pi$
$132$		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	0.638142	−	0.769918i	$-0.279703\pi$
$137$	465.740	+	268.895i	0.290444	+	0.167688i	−0.347698	+	0.937607i	$0.613036\pi$
$138$		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	0.327399	−	0.944886i	$-0.393828\pi$
$149$	2381.50	−	1374.96i	1.30939	−	0.755979i	0.981995	+	0.188907i	$0.0604946\pi$
$150$		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	$-0.392454\pi$
$167$	1430.72			0.662950			0.331475	+	0.943464i	$0.392454\pi$
$168$		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	$0.0428210\pi$
$173$	1391.75	+	2410.58i	0.611635	+	1.05938i	−0.379330	+	0.925261i	$0.623846\pi$
$174$		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	0.615570	−	0.788082i	$-0.288926\pi$
$179$	576.815	+	333.024i	0.240856	+	0.139058i	−0.374714	+	0.927140i	$0.622259\pi$
$180$		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	−0.235447	−	0.971887i	$-0.575655\pi$
$191$	1289.50	−	744.495i	0.488508	−	0.282040i	0.723955	+	0.689847i	$0.242322\pi$
$192$		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	$-0.899281\pi$
$197$		−	1720.75i		−	0.622327i	0.950356	−	0.311163i	$-0.100719\pi$
$198$		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	−0.599974	−	0.800019i	$-0.704822\pi$
$227$	1343.59	−	2327.16i	0.392850	−	0.680436i	0.992824	+	0.119583i	$0.0381558\pi$
$228$		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	−0.288824	−	0.957382i	$-0.593264\pi$
$233$	1407.98	−	812.900i	0.395880	−	0.228562i	0.684705	+	0.728820i	$0.259931\pi$
$234$		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	$-0.792803\pi$
$239$		−	4477.61i		−	1.21185i	0.795521	−	0.605926i	$-0.207197\pi$
$240$		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	$-0.366956\pi$
$251$	3228.23			0.811810			0.405905	+	0.913915i	$0.366956\pi$
$252$		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	0.953566	−	0.301183i	$-0.0973815\pi$
$257$	889.723	+	1541.05i	0.215951	+	0.374038i	−0.737615	+	0.675221i	$0.764048\pi$
$258$		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	−0.207983	−	0.978132i	$-0.566690\pi$
$263$	−4943.57	−	2854.17i	−1.15906	−	0.669185i	−0.951079	+	0.308947i	$0.900023\pi$
$264$		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	−0.779615	−	0.626259i	$-0.784585\pi$
$269$	673.034	−	1165.73i	0.152549	−	0.264222i	0.932164	+	0.362037i	$0.117919\pi$
$270$		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	$-0.906979\pi$
$281$		−	2714.07i		−	0.576184i	0.957603	−	0.288092i	$-0.0930210\pi$
$282$		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	$-0.507770\pi$
$293$	−244.833			−0.0488168			−0.0244084	+	0.999702i	$0.507770\pi$
$294$		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	−0.524627	−	0.851332i	$-0.675795\pi$
$311$	2604.95	−	4511.90i	0.474962	−	0.822658i	0.999589	+	0.0286744i	$0.00912858\pi$
$312$		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	−0.732689	−	0.680563i	$-0.761735\pi$
$317$	−2876.47	+	1660.73i	−0.509648	+	0.294246i	0.223041	+	0.974809i	$0.428402\pi$
$318$		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	−0.291632	−	0.956531i	$-0.594198\pi$
$347$	−8182.17	−	4723.98i	−1.26583	−	0.730826i	−0.974196	+	0.225705i	$0.927531\pi$
$348$		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	$-0.513171\pi$
$353$	5601.62	−	9702.29i	0.844601	−	1.46289i	0.885967	−	0.463748i	$-0.153496\pi$
$354$		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	−0.935143	−	0.354271i	$-0.884729\pi$
$359$	−7454.44	+	4303.82i	−1.09591	+	0.632722i	−0.160763	+	0.986993i	$0.551396\pi$
$360$		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	0.527463	−	0.849578i	$-0.323143\pi$
$383$	−3538.04	−	6128.06i	−0.472024	−	0.817570i	−0.999488	+	0.0320077i	$0.989810\pi$
$384$		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	0.0307341	−	0.999528i	$-0.490215\pi$
$389$	−6287.55	−	3630.12i	−0.819515	−	0.473147i	−0.850249	+	0.526380i	$0.823549\pi$
$390$		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	−0.535988	−	0.844225i	$-0.680061\pi$
$401$	−585.084	+	337.798i	−0.0728621	+	0.0420670i	0.463126	+	0.886292i	$0.346728\pi$
$402$		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	$-0.359008\pi$
$419$	7351.89			0.857192			0.428596	+	0.903496i	$0.359008\pi$
$420$		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	0.454976	−	0.890504i	$-0.349648\pi$
$431$	−793.977	−	458.403i	−0.0887344	−	0.0512308i	−0.543711	+	0.839273i	$0.682981\pi$
$432$		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	−0.906508	−	0.422189i	$-0.861262\pi$
$443$	−9269.39	+	5351.68i	−0.994135	+	0.573964i	−0.0876276	+	0.996153i	$0.527929\pi$
$444$		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	$0.105742\pi$
$449$			6205.55i			0.652245i	−0.945328	+	0.326122i	$0.894258\pi$
$450$		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	$-0.565147\pi$
$461$	−4023.34			−0.406477			−0.203238	+	0.979129i	$0.565147\pi$
$462$		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	$-0.708918\pi$
$467$	−10003.2	−	17326.0i	−0.991203	−	1.71681i	−0.380985	−	0.924581i	$-0.624415\pi$
$468$		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	−0.638250	−	0.769829i	$-0.720341\pi$
$479$	3643.69	−	6311.05i	0.347567	−	0.602003i	0.985817	+	0.167826i	$0.0536747\pi$
$480$		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	$-0.896445\pi$
$491$		−	6954.84i		−	0.639241i	0.947546	−	0.319621i	$-0.103555\pi$
$492$		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	$-0.466065\pi$
$503$	2400.81			0.212817			0.106408	+	0.994323i	$0.466065\pi$
$504$		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	0.977338	−	0.211685i	$-0.0678951\pi$
$509$	3506.44	+	6073.33i	0.305344	+	0.528872i	−0.671994	+	0.740557i	$0.734562\pi$
$510$		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	$0.408034\pi$
$521$	−8177.82	+	14164.4i	−0.687672	+	1.19108i	−0.972589	+	0.232530i	$0.925300\pi$
$522$		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	$0.0288962\pi$
$557$	20669.4	+	11933.5i	1.57233	+	0.907787i	0.576451	+	0.817132i	$0.304437\pi$
$558$		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	−0.835841	−	0.548972i	$-0.815019\pi$
$563$	768.172	−	1330.51i	0.0575037	−	0.0995993i	0.893344	+	0.449373i	$0.148353\pi$
$564$		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	0.125628	−	0.992077i	$-0.459906\pi$
$569$	14218.9	−	8209.29i	1.04761	−	0.604835i	0.921978	+	0.387242i	$0.126572\pi$
$570$		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	$-0.298366\pi$
$587$	16836.8			1.18386			0.591931	+	0.805988i	$0.298366\pi$
$588$		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	0.925484	−	0.378787i	$-0.123659\pi$
$593$	1945.17	+	3369.14i	0.134703	+	0.233312i	−0.790781	+	0.612099i	$0.790325\pi$
$594$		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	0.203555	−	0.979063i	$-0.434750\pi$
$599$	−7954.06	−	4592.28i	−0.542561	−	0.313248i	−0.746116	+	0.665816i	$0.768084\pi$
$600$		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	$0.0225368\pi$
$617$			2168.39i			0.141485i	−0.997495	+	0.0707424i	$0.977463\pi$
$618$		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	0.734720	−	0.678371i	$-0.237314\pi$
$641$	8351.25	+	4821.60i	0.514594	+	0.297101i	−0.220126	+	0.975471i	$0.570647\pi$
$642$		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	$0.518698\pi$
$647$	−14710.9	+	25480.0i	−0.893886	+	1.54826i	−0.835178	+	0.549980i	$0.814635\pi$
$648$		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	−0.168629	−	0.985680i	$-0.553934\pi$
$653$	10023.3	−	5786.98i	0.600679	−	0.346802i	0.769309	+	0.638877i	$0.220601\pi$
$654$		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	$-0.782806\pi$
$659$		−	21336.2i		−	1.26122i	0.776101	−	0.630608i	$-0.217194\pi$
$660$		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	$0.0301589\pi$
$677$	10211.2	+	17686.3i	0.579688	+	1.00405i	−0.415827	+	0.909444i	$0.636508\pi$
$678$		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	0.832399	−	0.554177i	$-0.186967\pi$
$683$	13720.5	+	7921.51i	0.768666	+	0.443790i	−0.0637324	+	0.997967i	$0.520300\pi$
$684$		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	$0.315821\pi$
$701$			31077.5i			1.67444i	−0.546866	+	0.837220i	$0.684179\pi$
$702$		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	$-0.987874\pi$
$719$	−10268.6	−	17785.8i	−0.532622	−	0.922528i	0.466653	−	0.884441i	$-0.345460\pi$
$720$		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	$0.0765231\pi$
$743$			9644.16i			0.476191i	−0.971242	+	0.238096i	$0.923477\pi$
$744$		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	$0.135631\pi$
$761$	17072.4	+	29570.3i	0.813238	+	1.40857i	−0.0973479	+	0.995250i	$0.531036\pi$
$762$		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	$0.411242\pi$
$773$	−14935.7	+	25869.4i	−0.694955	+	1.20370i	−0.970196	+	0.242322i	$0.922091\pi$
$774$		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	$-0.750346\pi$
$797$	−31854.7			−1.41575			−0.707874	+	0.706338i	$0.750346\pi$
$798$		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	$0.0466187\pi$
$809$	37054.1	+	21393.2i	1.61032	+	0.929721i	0.621030	+	0.783787i	$0.286715\pi$
$810$		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	0.199212	−	0.979956i	$-0.436162\pi$
$821$	26993.7	−	15584.8i	1.14749	−	0.662501i	0.948273	+	0.317455i	$0.102828\pi$
$822$		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	$0.372093\pi$
$827$			43776.3i			1.84069i	−0.391106	+	0.920346i	$0.627907\pi$
$828$		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	$-0.465030\pi$
$839$	5328.94			0.219279			0.109640	+	0.993971i	$0.465030\pi$
$840$		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	−0.914575	−	0.404417i	$-0.867474\pi$
$857$	−2685.74	+	4651.84i	−0.107052	+	0.185419i	0.807523	+	0.589836i	$0.200808\pi$
$858$		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	−0.982240	−	0.187630i	$-0.939920\pi$
$863$	−33233.4	+	19187.3i	−1.31087	+	0.756830i	−0.328628	+	0.944460i	$0.606586\pi$
$864$		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	$-0.832120\pi$
$881$	−45192.3			−1.72823			−0.864114	+	0.503296i	$0.832120\pi$
$882$		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	$-0.934880\pi$
$887$	−17580.9	−	30451.0i	−0.665511	−	1.15270i	0.313636	−	0.949543i	$-0.398453\pi$
$888$		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	$-0.959826\pi$
$911$		−	6922.25i		−	0.251750i	0.992046	−	0.125875i	$-0.0401739\pi$
$912$		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	$0.0344843\pi$
$929$	16726.1	+	28970.5i	0.590707	+	1.02313i	−0.403431	+	0.915010i	$0.632182\pi$
$930$		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	−0.580950	−	0.813939i	$-0.697319\pi$
$941$	11962.5	−	20719.7i	0.414417	−	0.717792i	0.995367	+	0.0961475i	$0.0306521\pi$
$942$		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	−0.764969	−	0.644067i	$-0.777246\pi$
$947$	−17184.6	+	9921.51i	−0.589676	+	0.340450i	0.175293	+	0.984516i	$0.443913\pi$
$948$		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	$0.270348\pi$
$953$			44178.8i			1.50167i	−0.660490	+	0.750834i	$0.729652\pi$
$954$		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	$-0.948773\pi$
$971$	−19132.0	−	33137.5i	−0.632311	−	1.09519i	0.354767	−	0.934955i	$-0.384560\pi$
$972$		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	0.589464	−	0.807795i	$-0.299339\pi$
$977$	5638.08	+	3255.14i	0.184624	+	0.106593i	−0.404839	+	0.914388i	$0.632673\pi$
$978$		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	$-0.596018\pi$
$983$	20907.4	−	36212.7i	0.678375	−	1.17498i	0.975470	−	0.220132i	$-0.0706488\pi$
$984$		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.521.2		16
3.2	odd	2	inner	882.4.k.b.521.7		16
7.2	even	3	inner	882.4.k.b.215.6		16
7.3	odd	6		882.4.d.a.881.2	✓	8
7.4	even	3		882.4.d.a.881.3	yes	8
7.5	odd	6	inner	882.4.k.b.215.7		16
7.6	odd	2	inner	882.4.k.b.521.3		16
21.2	odd	6	inner	882.4.k.b.215.3		16
21.5	even	6	inner	882.4.k.b.215.2		16
21.11	odd	6		882.4.d.a.881.6	yes	8
21.17	even	6		882.4.d.a.881.7	yes	8
21.20	even	2	inner	882.4.k.b.521.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.4.d.a.881.2	✓	8	7.3	odd	6
882.4.d.a.881.3	yes	8	7.4	even	3
882.4.d.a.881.6	yes	8	21.11	odd	6
882.4.d.a.881.7	yes	8	21.17	even	6
882.4.k.b.215.2		16	21.5	even	6	inner
882.4.k.b.215.3		16	21.2	odd	6	inner
882.4.k.b.215.6		16	7.2	even	3	inner
882.4.k.b.215.7		16	7.5	odd	6	inner
882.4.k.b.521.2		16	1.1	even	1	trivial
882.4.k.b.521.3		16	7.6	odd	2	inner
882.4.k.b.521.6		16	21.20	even	2	inner
882.4.k.b.521.7		16	3.2	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
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

Related objects

Downloads

Learn more