LMFDB - Embedded newform 882.4.g.bg.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(361,882)]

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([0, 4]))

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

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

chi := DirichletCharacter("882.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.g (of order $3$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.4.g.bg.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.53553 - 6.12372i) q^{5} -8.00000 q^{8} +(7.07107 - 12.2474i) q^{10} +(-20.0000 + 34.6410i) q^{11} +63.6396 q^{13} +(-8.00000 - 13.8564i) q^{16} +(0.707107 - 1.22474i) q^{17} +(5.65685 + 9.79796i) q^{19} +28.2843 q^{20} -80.0000 q^{22} +(-34.0000 - 58.8897i) q^{23} +(37.5000 - 64.9519i) q^{25} +(63.6396 + 110.227i) q^{26} +110.000 q^{29} +(-59.3970 + 102.879i) q^{31} +(16.0000 - 27.7128i) q^{32} +2.82843 q^{34} +(10.0000 + 17.3205i) q^{37} +(-11.3137 + 19.5959i) q^{38} +(28.2843 + 48.9898i) q^{40} +49.4975 q^{41} -340.000 q^{43} +(-80.0000 - 138.564i) q^{44} +(68.0000 - 117.779i) q^{46} +(45.2548 + 78.3837i) q^{47} +150.000 q^{50} +(-127.279 + 220.454i) q^{52} +(-314.000 + 543.864i) q^{53} +282.843 q^{55} +(110.000 + 190.526i) q^{58} +(-438.406 + 759.342i) q^{59} +(458.912 + 794.859i) q^{61} -237.588 q^{62} +64.0000 q^{64} +(-225.000 - 389.711i) q^{65} +(-270.000 + 467.654i) q^{67} +(2.82843 + 4.89898i) q^{68} -420.000 q^{71} +(144.957 - 251.073i) q^{73} +(-20.0000 + 34.6410i) q^{74} -45.2548 q^{76} +(380.000 + 658.179i) q^{79} +(-56.5685 + 97.9796i) q^{80} +(49.4975 + 85.7321i) q^{82} -944.695 q^{83} -10.0000 q^{85} +(-340.000 - 588.897i) q^{86} +(160.000 - 277.128i) q^{88} +(576.292 + 998.167i) q^{89} +272.000 q^{92} +(-90.5097 + 156.767i) q^{94} +(40.0000 - 69.2820i) q^{95} +502.046 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8} - 80 q^{11} - 32 q^{16} - 320 q^{22} - 136 q^{23} + 150 q^{25} + 440 q^{29} + 64 q^{32} + 40 q^{37} - 1360 q^{43} - 320 q^{44} + 272 q^{46} + 600 q^{50} - 1256 q^{53}+ \cdots + 160 q^{95}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8 - 80 * q^11 - 32 * q^16 - 320 * q^22 - 136 * q^23 + 150 * q^25 + 440 * q^29 + 64 * q^32 + 40 * q^37 - 1360 * q^43 - 320 * q^44 + 272 * q^46 + 600 * q^50 - 1256 * q^53 + 440 * q^58 + 256 * q^64 - 900 * q^65 - 1080 * q^67 - 1680 * q^71 - 80 * q^74 + 1520 * q^79 - 40 * q^85 - 1360 * q^86 + 640 * q^88 + 1088 * q^92 + 160 * q^95

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−3.53553	−	6.12372i	−0.316228	−	0.547723i	0.663470	−	0.748203i	$-0.269083\pi$
$5$	−3.53553	−	6.12372i	−0.316228	−	0.547723i	−0.979698	+	0.200480i	$0.935750\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$		0			0
$10$	7.07107	−	12.2474i	0.223607	−	0.387298i
$11$	−20.0000	+	34.6410i	−0.548202	+	0.949514i	0.450195	+	0.892930i	$0.351354\pi$
$11$	−20.0000	+	34.6410i	−0.548202	+	0.949514i	−0.998398	+	0.0565844i	$0.981979\pi$
$12$		0			0
$13$	63.6396			1.35773			0.678864	−	0.734264i	$-0.262473\pi$
$13$	63.6396			1.35773			0.678864	+	0.734264i	$0.262473\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	0.707107	−	1.22474i	0.0100882	−	0.0174732i	−0.860937	−	0.508711i	$-0.830122\pi$
$17$	0.707107	−	1.22474i	0.0100882	−	0.0174732i	0.871025	+	0.491238i	$0.163455\pi$
$18$		0			0
$19$	5.65685	+	9.79796i	0.0683038	+	0.118306i	0.898155	−	0.439679i	$-0.144908\pi$
$19$	5.65685	+	9.79796i	0.0683038	+	0.118306i	−0.829851	+	0.557985i	$0.811575\pi$
$20$	28.2843			0.316228
$21$		0			0
$22$	−80.0000			−0.775275
$23$	−34.0000	−	58.8897i	−0.308239	−	0.533885i	0.669738	−	0.742597i	$-0.266406\pi$
$23$	−34.0000	−	58.8897i	−0.308239	−	0.533885i	−0.977977	+	0.208712i	$0.933073\pi$
$24$		0			0
$25$	37.5000	−	64.9519i	0.300000	−	0.519615i
$26$	63.6396	+	110.227i	0.480029	+	0.831435i
$27$		0			0
$28$		0			0
$29$	110.000			0.704362			0.352181	−	0.935932i	$-0.385440\pi$
$29$	110.000			0.704362			0.352181	+	0.935932i	$0.385440\pi$
$30$		0			0
$31$	−59.3970	+	102.879i	−0.344129	+	0.596050i	−0.985195	−	0.171436i	$-0.945159\pi$
$31$	−59.3970	+	102.879i	−0.344129	+	0.596050i	0.641066	+	0.767486i	$0.278493\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	2.82843			0.0142668
$35$		0			0
$36$		0			0
$37$	10.0000	+	17.3205i	0.0444322	+	0.0769588i	0.887386	−	0.461027i	$-0.152519\pi$
$37$	10.0000	+	17.3205i	0.0444322	+	0.0769588i	−0.842954	+	0.537986i	$0.819185\pi$
$38$	−11.3137	+	19.5959i	−0.0482980	+	0.0836547i
$39$		0			0
$40$	28.2843	+	48.9898i	0.111803	+	0.193649i
$41$	49.4975			0.188542			0.0942708	−	0.995547i	$-0.469948\pi$
$41$	49.4975			0.188542			0.0942708	+	0.995547i	$0.469948\pi$
$42$		0			0
$43$	−340.000			−1.20580			−0.602901	−	0.797816i	$-0.705989\pi$
$43$	−340.000			−1.20580			−0.602901	+	0.797816i	$0.705989\pi$
$44$	−80.0000	−	138.564i	−0.274101	−	0.474757i
$45$		0			0
$46$	68.0000	−	117.779i	0.217958	−	0.377514i
$47$	45.2548	+	78.3837i	0.140449	+	0.243265i	0.927666	−	0.373412i	$-0.121812\pi$
$47$	45.2548	+	78.3837i	0.140449	+	0.243265i	−0.787217	+	0.616676i	$0.788479\pi$
$48$		0			0
$49$		0			0
$50$	150.000			0.424264
$51$		0			0
$52$	−127.279	+	220.454i	−0.339432	+	0.587913i
$53$	−314.000	+	543.864i	−0.813797	+	1.40954i	0.0963923	+	0.995343i	$0.469270\pi$
$53$	−314.000	+	543.864i	−0.813797	+	1.40954i	−0.910189	+	0.414194i	$0.864064\pi$
$54$		0			0
$55$	282.843			0.693427
$56$		0			0
$57$		0			0
$58$	110.000	+	190.526i	0.249029	+	0.431332i
$59$	−438.406	+	759.342i	−0.967383	+	1.67556i	−0.264313	+	0.964437i	$0.585145\pi$
$59$	−438.406	+	759.342i	−0.967383	+	1.67556i	−0.703070	+	0.711121i	$0.748188\pi$
$60$		0			0
$61$	458.912	+	794.859i	0.963241	+	1.66838i	0.714269	+	0.699872i	$0.246760\pi$
$61$	458.912	+	794.859i	0.963241	+	1.66838i	0.248972	+	0.968511i	$0.419907\pi$
$62$	−237.588			−0.486672
$63$		0			0
$64$	64.0000			0.125000
$65$	−225.000	−	389.711i	−0.429351	−	0.743658i
$66$		0			0
$67$	−270.000	+	467.654i	−0.492325	+	0.852731i	−0.999961	−	0.00884020i	$-0.997186\pi$
$67$	−270.000	+	467.654i	−0.492325	+	0.852731i	0.507636	+	0.861571i	$0.330519\pi$
$68$	2.82843	+	4.89898i	0.00504408	+	0.00873660i
$69$		0			0
$70$		0			0
$71$	−420.000			−0.702040			−0.351020	−	0.936368i	$-0.614165\pi$
$71$	−420.000			−0.702040			−0.351020	+	0.936368i	$0.614165\pi$
$72$		0			0
$73$	144.957	−	251.073i	0.232410	−	0.402546i	−0.726107	−	0.687582i	$-0.758672\pi$
$73$	144.957	−	251.073i	0.232410	−	0.402546i	0.958517	+	0.285036i	$0.0920056\pi$
$74$	−20.0000	+	34.6410i	−0.0314183	+	0.0544181i
$75$		0			0
$76$	−45.2548			−0.0683038
$77$		0			0
$78$		0			0
$79$	380.000	+	658.179i	0.541182	+	0.937354i	0.998837	+	0.0482240i	$0.0153561\pi$
$79$	380.000	+	658.179i	0.541182	+	0.937354i	−0.457655	+	0.889130i	$0.651311\pi$
$80$	−56.5685	+	97.9796i	−0.0790569	+	0.136931i
$81$		0			0
$82$	49.4975	+	85.7321i	0.0666595	+	0.115458i
$83$	−944.695			−1.24932			−0.624661	−	0.780896i	$-0.714763\pi$
$83$	−944.695			−1.24932			−0.624661	+	0.780896i	$0.714763\pi$
$84$		0			0
$85$	−10.0000			−0.0127606
$86$	−340.000	−	588.897i	−0.426316	−	0.738400i
$87$		0			0
$88$	160.000	−	277.128i	0.193819	−	0.335704i
$89$	576.292	+	998.167i	0.686369	+	1.18883i	0.973005	+	0.230786i	$0.0741298\pi$
$89$	576.292	+	998.167i	0.686369	+	1.18883i	−0.286636	+	0.958040i	$0.592537\pi$
$90$		0			0
$91$		0			0
$92$	272.000			0.308239
$93$		0			0
$94$	−90.5097	+	156.767i	−0.0993123	+	0.172014i
$95$	40.0000	−	69.2820i	0.0431991	−	0.0748230i
$96$		0			0
$97$	502.046			0.525516			0.262758	−	0.964862i	$-0.415368\pi$
$97$	502.046			0.525516			0.262758	+	0.964862i	$0.415368\pi$
$98$		0			0
$99$		0			0
$100$	150.000	+	259.808i	0.150000	+	0.259808i
$101$	−880.348	+	1524.81i	−0.867306	+	1.50222i	−0.00256667	+	0.999997i	$0.500817\pi$
$101$	−880.348	+	1524.81i	−0.867306	+	1.50222i	−0.864739	+	0.502221i	$0.832516\pi$
$102$		0			0
$103$	113.137	+	195.959i	0.108230	+	0.187461i	0.915053	−	0.403333i	$-0.132148\pi$
$103$	113.137	+	195.959i	0.108230	+	0.187461i	−0.806823	+	0.590793i	$0.798815\pi$
$104$	−509.117			−0.480029
$105$		0			0
$106$	−1256.00			−1.15088
$107$	−1012.00	−	1752.84i	−0.914334	−	1.58367i	−0.807874	−	0.589356i	$-0.799382\pi$
$107$	−1012.00	−	1752.84i	−0.914334	−	1.58367i	−0.106460	−	0.994317i	$-0.533952\pi$
$108$		0			0
$109$	202.000	−	349.874i	0.177505	−	0.307448i	−0.763520	−	0.645784i	$-0.776531\pi$
$109$	202.000	−	349.874i	0.177505	−	0.307448i	0.941025	+	0.338336i	$0.109864\pi$
$110$	282.843	+	489.898i	0.245164	+	0.424636i
$111$		0			0
$112$		0			0
$113$	1008.00			0.839156			0.419578	−	0.907719i	$-0.362178\pi$
$113$	1008.00			0.839156			0.419578	+	0.907719i	$0.362178\pi$
$114$		0			0
$115$	−240.416	+	416.413i	−0.194947	+	0.337659i
$116$	−220.000	+	381.051i	−0.176090	+	0.304998i
$117$		0			0
$118$	−1753.62			−1.36809
$119$		0			0
$120$		0			0
$121$	−134.500	−	232.961i	−0.101052	−	0.175027i
$122$	−917.825	+	1589.72i	−0.681114	+	1.17972i
$123$		0			0
$124$	−237.588	−	411.514i	−0.172065	−	0.298025i
$125$	−1414.21			−1.01193
$126$		0			0
$127$	1000.00			0.698706			0.349353	−	0.936991i	$-0.386401\pi$
$127$	1000.00			0.698706			0.349353	+	0.936991i	$0.386401\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	450.000	−	779.423i	0.303597	−	0.525845i
$131$	42.4264	+	73.4847i	0.0282963	+	0.0490106i	0.879827	−	0.475294i	$-0.157658\pi$
$131$	42.4264	+	73.4847i	0.0282963	+	0.0490106i	−0.851530	+	0.524305i	$0.824325\pi$
$132$		0			0
$133$		0			0
$134$	−1080.00			−0.696252
$135$		0			0
$136$	−5.65685	+	9.79796i	−0.00356670	+	0.00617771i
$137$	−1017.00	+	1761.50i	−0.634220	+	1.09850i	0.352460	+	0.935827i	$0.385345\pi$
$137$	−1017.00	+	1761.50i	−0.634220	+	1.09850i	−0.986680	+	0.162675i	$0.947988\pi$
$138$		0			0
$139$	1736.65			1.05972			0.529860	−	0.848085i	$-0.322244\pi$
$139$	1736.65			1.05972			0.529860	+	0.848085i	$0.322244\pi$
$140$		0			0
$141$		0			0
$142$	−420.000	−	727.461i	−0.248209	−	0.429910i
$143$	−1272.79	+	2204.54i	−0.744309	+	1.28918i
$144$		0			0
$145$	−388.909	−	673.610i	−0.222739	−	0.385795i
$146$	579.828			0.328677
$147$		0			0
$148$	−80.0000			−0.0444322
$149$	−1070.00	−	1853.29i	−0.588307	−	1.01898i	−0.994454	−	0.105171i	$-0.966461\pi$
$149$	−1070.00	−	1853.29i	−0.588307	−	1.01898i	0.406147	−	0.913808i	$-0.366872\pi$
$150$		0			0
$151$	−1060.00	+	1835.97i	−0.571269	+	0.989466i	0.425167	+	0.905115i	$0.360215\pi$
$151$	−1060.00	+	1835.97i	−0.571269	+	0.989466i	−0.996436	+	0.0843517i	$0.973118\pi$
$152$	−45.2548	−	78.3837i	−0.0241490	−	0.0418273i
$153$		0			0
$154$		0			0
$155$	840.000			0.435293
$156$		0			0
$157$	873.277	−	1512.56i	0.443918	−	0.768888i	−0.554058	−	0.832478i	$-0.686922\pi$
$157$	873.277	−	1512.56i	0.443918	−	0.768888i	0.997976	+	0.0635898i	$0.0202549\pi$
$158$	−760.000	+	1316.36i	−0.382673	+	0.662809i
$159$		0			0
$160$	−226.274			−0.111803
$161$		0			0
$162$		0			0
$163$	−1670.00	−	2892.52i	−0.802482	−	1.38994i	−0.917978	−	0.396631i	$-0.870179\pi$
$163$	−1670.00	−	2892.52i	−0.802482	−	1.38994i	0.115497	−	0.993308i	$-0.463154\pi$
$164$	−98.9949	+	171.464i	−0.0471354	+	0.0816409i
$165$		0			0
$166$	−944.695	−	1636.26i	−0.441702	−	0.765050i
$167$	−367.696			−0.170378			−0.0851890	−	0.996365i	$-0.527149\pi$
$167$	−367.696			−0.170378			−0.0851890	+	0.996365i	$0.527149\pi$
$168$		0			0
$169$	1853.00			0.843423
$170$	−10.0000	−	17.3205i	−0.00451156	−	0.00781425i
$171$		0			0
$172$	680.000	−	1177.79i	0.301451	−	0.522128i
$173$	1694.93	+	2935.71i	0.744876	+	1.29016i	0.950253	+	0.311480i	$0.100825\pi$
$173$	1694.93	+	2935.71i	0.744876	+	1.29016i	−0.205377	+	0.978683i	$0.565842\pi$
$174$		0			0
$175$		0			0
$176$	640.000			0.274101
$177$		0			0
$178$	−1152.58	+	1996.33i	−0.485336	+	0.840627i
$179$	−360.000	+	623.538i	−0.150322	+	0.260366i	−0.931346	−	0.364136i	$-0.881364\pi$
$179$	−360.000	+	623.538i	−0.150322	+	0.260366i	0.781024	+	0.624501i	$0.214698\pi$
$180$		0			0
$181$	1854.03			0.761377			0.380689	−	0.924703i	$-0.375687\pi$
$181$	1854.03			0.761377			0.380689	+	0.924703i	$0.375687\pi$
$182$		0			0
$183$		0			0
$184$	272.000	+	471.118i	0.108979	+	0.188757i
$185$	70.7107	−	122.474i	0.0281014	−	0.0486730i
$186$		0			0
$187$	28.2843	+	48.9898i	0.0110607	+	0.0191577i
$188$	−362.039			−0.140449
$189$		0			0
$190$	160.000			0.0610927
$191$	−1990.00	−	3446.78i	−0.753881	−	1.30576i	−0.945929	−	0.324375i	$-0.894846\pi$
$191$	−1990.00	−	3446.78i	−0.753881	−	1.30576i	0.192047	−	0.981386i	$-0.438487\pi$
$192$		0			0
$193$	−1855.00	+	3212.95i	−0.691844	+	1.19831i	0.279390	+	0.960178i	$0.409868\pi$
$193$	−1855.00	+	3212.95i	−0.691844	+	1.19831i	−0.971233	+	0.238130i	$0.923465\pi$
$194$	502.046	+	869.569i	0.185798	+	0.321811i
$195$		0			0
$196$		0			0
$197$	956.000			0.345747			0.172874	−	0.984944i	$-0.444695\pi$
$197$	956.000			0.345747			0.172874	+	0.984944i	$0.444695\pi$
$198$		0			0
$199$	2044.95	−	3541.96i	0.728457	−	1.26172i	−0.229079	−	0.973408i	$-0.573571\pi$
$199$	2044.95	−	3541.96i	0.728457	−	1.26172i	0.957535	−	0.288316i	$-0.0930953\pi$
$200$	−300.000	+	519.615i	−0.106066	+	0.183712i
$201$		0			0
$202$	−3521.39			−1.22656
$203$		0			0
$204$		0			0
$205$	−175.000	−	303.109i	−0.0596221	−	0.103269i
$206$	−226.274	+	391.918i	−0.0765304	+	0.132555i
$207$		0			0
$208$	−509.117	−	881.816i	−0.169716	−	0.293957i
$209$	−452.548			−0.149777
$210$		0			0
$211$	2868.00			0.935741			0.467870	−	0.883797i	$-0.345021\pi$
$211$	2868.00			0.935741			0.467870	+	0.883797i	$0.345021\pi$
$212$	−1256.00	−	2175.46i	−0.406898	−	0.704768i
$213$		0			0
$214$	2024.00	−	3505.67i	0.646532	−	1.11983i
$215$	1202.08	+	2082.07i	0.381308	+	0.660445i
$216$		0			0
$217$		0			0
$218$	808.000			0.251031
$219$		0			0
$220$	−565.685	+	979.796i	−0.173357	+	0.300263i
$221$	45.0000	−	77.9423i	0.0136970	−	0.0237238i
$222$		0			0
$223$	−2630.44			−0.789897			−0.394949	−	0.918703i	$-0.629238\pi$
$223$	−2630.44			−0.789897			−0.394949	+	0.918703i	$0.629238\pi$
$224$		0			0
$225$		0			0
$226$	1008.00	+	1745.91i	0.296687	+	0.513876i
$227$	−84.8528	+	146.969i	−0.0248100	+	0.0429722i	−0.878164	−	0.478360i	$-0.841231\pi$
$227$	−84.8528	+	146.969i	−0.0248100	+	0.0429722i	0.853354	+	0.521332i	$0.174565\pi$
$228$		0			0
$229$	−1571.90	−	2722.61i	−0.453598	−	0.785655i	0.545008	−	0.838431i	$-0.316527\pi$
$229$	−1571.90	−	2722.61i	−0.453598	−	0.785655i	−0.998606	+	0.0527757i	$0.983193\pi$
$230$	−961.665			−0.275697
$231$		0			0
$232$	−880.000			−0.249029
$233$	2241.00	+	3881.53i	0.630098	+	1.09136i	0.987531	+	0.157423i	$0.0503186\pi$
$233$	2241.00	+	3881.53i	0.630098	+	1.09136i	−0.357433	+	0.933939i	$0.616348\pi$
$234$		0			0
$235$	320.000	−	554.256i	0.0888277	−	0.153854i
$236$	−1753.62	−	3037.37i	−0.483692	−	0.837779i
$237$		0			0
$238$		0			0
$239$	−1740.00			−0.470926			−0.235463	−	0.971883i	$-0.575661\pi$
$239$	−1740.00			−0.470926			−0.235463	+	0.971883i	$0.575661\pi$
$240$		0			0
$241$	630.032	−	1091.25i	0.168398	−	0.291674i	−0.769459	−	0.638697i	$-0.779474\pi$
$241$	630.032	−	1091.25i	0.168398	−	0.291674i	0.937857	+	0.347023i	$0.112807\pi$
$242$	269.000	−	465.922i	0.0714544	−	0.123763i
$243$		0			0
$244$	−3671.30			−0.963241
$245$		0			0
$246$		0			0
$247$	360.000	+	623.538i	0.0927379	+	0.160627i
$248$	475.176	−	823.029i	0.121668	−	0.210735i
$249$		0			0
$250$	−1414.21	−	2449.49i	−0.357771	−	0.619677i
$251$	5826.56			1.46522			0.732608	−	0.680651i	$-0.238303\pi$
$251$	5826.56			1.46522			0.732608	+	0.680651i	$0.238303\pi$
$252$		0			0
$253$	2720.00			0.675909
$254$	1000.00	+	1732.05i	0.247030	+	0.427868i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−2344.06	−	4060.03i	−0.568943	−	0.985438i	−0.996671	−	0.0815308i	$-0.974019\pi$
$257$	−2344.06	−	4060.03i	−0.568943	−	0.985438i	0.427728	−	0.903908i	$-0.359314\pi$
$258$		0			0
$259$		0			0
$260$	1800.00			0.429351
$261$		0			0
$262$	−84.8528	+	146.969i	−0.0200085	+	0.0346557i
$263$	−1086.00	+	1881.01i	−0.254622	+	0.441019i	−0.964793	−	0.263011i	$-0.915284\pi$
$263$	−1086.00	+	1881.01i	−0.254622	+	0.441019i	0.710171	+	0.704030i	$0.248618\pi$
$264$		0			0
$265$	4440.63			1.02938
$266$		0			0
$267$		0			0
$268$	−1080.00	−	1870.61i	−0.246162	−	0.426366i
$269$	−1354.11	+	2345.39i	−0.306920	+	0.531601i	−0.977687	−	0.210067i	$-0.932632\pi$
$269$	−1354.11	+	2345.39i	−0.306920	+	0.531601i	0.670767	+	0.741668i	$0.265965\pi$
$270$		0			0
$271$	3094.30	+	5359.48i	0.693599	+	1.20135i	0.970651	+	0.240494i	$0.0773093\pi$
$271$	3094.30	+	5359.48i	0.693599	+	1.20135i	−0.277052	+	0.960855i	$0.589357\pi$
$272$	−22.6274			−0.00504408
$273$		0			0
$274$	−4068.00			−0.896923
$275$	1500.00	+	2598.08i	0.328921	+	0.569709i
$276$		0			0
$277$	−3065.00	+	5308.74i	−0.664830	+	1.15152i	0.314501	+	0.949257i	$0.398163\pi$
$277$	−3065.00	+	5308.74i	−0.664830	+	1.15152i	−0.979331	+	0.202263i	$0.935170\pi$
$278$	1736.65	+	3007.97i	0.374668	+	0.648943i
$279$		0			0
$280$		0			0
$281$	−1970.00			−0.418222			−0.209111	−	0.977892i	$-0.567057\pi$
$281$	−1970.00			−0.418222			−0.209111	+	0.977892i	$0.567057\pi$
$282$		0			0
$283$	−777.817	+	1347.22i	−0.163380	+	0.282982i	−0.936079	−	0.351791i	$-0.885573\pi$
$283$	−777.817	+	1347.22i	−0.163380	+	0.282982i	0.772699	+	0.634773i	$0.218906\pi$
$284$	840.000	−	1454.92i	0.175510	−	0.303992i
$285$		0			0
$286$	−5091.17			−1.05261
$287$		0			0
$288$		0			0
$289$	2455.50	+	4253.05i	0.499796	+	0.865673i
$290$	777.817	−	1347.22i	0.157500	−	0.272798i
$291$		0			0
$292$	579.828	+	1004.29i	0.116205	+	0.201273i
$293$	−7686.25			−1.53254			−0.766272	−	0.642516i	$-0.777891\pi$
$293$	−7686.25			−1.53254			−0.766272	+	0.642516i	$0.777891\pi$
$294$		0			0
$295$	6200.00			1.22365
$296$	−80.0000	−	138.564i	−0.0157091	−	0.0272090i
$297$		0			0
$298$	2140.00	−	3706.59i	0.415996	−	0.720527i
$299$	−2163.75	−	3747.72i	−0.418504	−	0.724870i
$300$		0			0
$301$		0			0
$302$	−4240.00			−0.807896
$303$		0			0
$304$	90.5097	−	156.767i	0.0170759	−	0.0295764i
$305$	3245.00	−	5620.50i	0.609207	−	1.05518i
$306$		0			0
$307$	8598.42			1.59849			0.799247	−	0.601003i	$-0.205232\pi$
$307$	8598.42			1.59849			0.799247	+	0.601003i	$0.205232\pi$
$308$		0			0
$309$		0			0
$310$	840.000	+	1454.92i	0.153899	+	0.266561i
$311$	3790.09	−	6564.63i	0.691050	−	1.19693i	−0.280445	−	0.959870i	$-0.590482\pi$
$311$	3790.09	−	6564.63i	0.691050	−	1.19693i	0.971494	−	0.237063i	$-0.0761847\pi$
$312$		0			0
$313$	1537.96	+	2663.82i	0.277733	+	0.481048i	0.970821	−	0.239805i	$-0.0770836\pi$
$313$	1537.96	+	2663.82i	0.277733	+	0.481048i	−0.693088	+	0.720853i	$0.743750\pi$
$314$	3493.11			0.627794
$315$		0			0
$316$	−3040.00			−0.541182
$317$	1162.00	+	2012.64i	0.205881	+	0.356597i	0.950413	−	0.310990i	$-0.100661\pi$
$317$	1162.00	+	2012.64i	0.205881	+	0.356597i	−0.744532	+	0.667587i	$0.767327\pi$
$318$		0			0
$319$	−2200.00	+	3810.51i	−0.386133	+	0.668802i
$320$	−226.274	−	391.918i	−0.0395285	−	0.0684653i
$321$		0			0
$322$		0			0
$323$	16.0000			0.00275623
$324$		0			0
$325$	2386.49	−	4133.51i	0.407318	−	0.705496i
$326$	3340.00	−	5785.05i	0.567440	−	0.982835i
$327$		0			0
$328$	−395.980			−0.0666595
$329$		0			0
$330$		0			0
$331$	−4754.00	−	8234.17i	−0.789436	−	1.36734i	−0.926313	−	0.376756i	$-0.877040\pi$
$331$	−4754.00	−	8234.17i	−0.789436	−	1.36734i	0.136876	−	0.990588i	$-0.456294\pi$
$332$	1889.39	−	3272.52i	0.312330	−	0.540972i
$333$		0			0
$334$	−367.696	−	636.867i	−0.0602377	−	0.104335i
$335$	3818.38			0.622747
$336$		0			0
$337$	−4720.00			−0.762952			−0.381476	−	0.924379i	$-0.624584\pi$
$337$	−4720.00			−0.762952			−0.381476	+	0.924379i	$0.624584\pi$
$338$	1853.00	+	3209.49i	0.298195	+	0.516489i
$339$		0			0
$340$	20.0000	−	34.6410i	0.00319015	−	0.00552551i
$341$	−2375.88	−	4115.14i	−0.377305	−	0.653512i
$342$		0			0
$343$		0			0
$344$	2720.00			0.426316
$345$		0			0
$346$	−3389.87	+	5871.43i	−0.526707	+	0.912283i
$347$	3252.00	−	5632.63i	0.503102	−	0.871399i	−0.496891	−	0.867813i	$-0.665525\pi$
$347$	3252.00	−	5632.63i	0.503102	−	0.871399i	0.999994	−	0.00358597i	$-0.00114145\pi$
$348$		0			0
$349$	5256.63			0.806249			0.403125	−	0.915145i	$-0.367924\pi$
$349$	5256.63			0.806249			0.403125	+	0.915145i	$0.367924\pi$
$350$		0			0
$351$		0			0
$352$	640.000	+	1108.51i	0.0969094	+	0.167852i
$353$	6105.87	−	10575.7i	0.920630	−	1.59458i	0.122188	−	0.992507i	$-0.461009\pi$
$353$	6105.87	−	10575.7i	0.920630	−	1.59458i	0.798442	−	0.602072i	$-0.205658\pi$
$354$		0			0
$355$	1484.92	+	2571.96i	0.222004	+	0.384523i
$356$	−4610.34			−0.686369
$357$		0			0
$358$	−1440.00			−0.212588
$359$	3670.00	+	6356.63i	0.539541	+	0.934512i	0.998929	+	0.0462765i	$0.0147355\pi$
$359$	3670.00	+	6356.63i	0.539541	+	0.934512i	−0.459388	+	0.888236i	$0.651931\pi$
$360$		0			0
$361$	3365.50	−	5829.22i	0.490669	−	0.849864i
$362$	1854.03	+	3211.28i	0.269187	+	0.466246i
$363$		0			0
$364$		0			0
$365$	−2050.00			−0.293978
$366$		0			0
$367$	−3832.52	+	6638.12i	−0.545111	+	0.944160i	0.453489	+	0.891262i	$0.350179\pi$
$367$	−3832.52	+	6638.12i	−0.545111	+	0.944160i	−0.998600	+	0.0528984i	$0.983154\pi$
$368$	−544.000	+	942.236i	−0.0770597	+	0.133471i
$369$		0			0
$370$	282.843			0.0397413
$371$		0			0
$372$		0			0
$373$	1495.00	+	2589.42i	0.207529	+	0.359450i	0.950935	−	0.309389i	$-0.100125\pi$
$373$	1495.00	+	2589.42i	0.207529	+	0.359450i	−0.743407	+	0.668840i	$0.766791\pi$
$374$	−56.5685	+	97.9796i	−0.00782110	+	0.0135465i
$375$		0			0
$376$	−362.039	−	627.069i	−0.0496562	−	0.0860070i
$377$	7000.36			0.956331
$378$		0			0
$379$	−11900.0			−1.61283			−0.806414	−	0.591351i	$-0.798595\pi$
$379$	−11900.0			−1.61283			−0.806414	+	0.591351i	$0.798595\pi$
$380$	160.000	+	277.128i	0.0215995	+	0.0374115i
$381$		0			0
$382$	3980.00	−	6893.56i	0.533075	−	0.923312i
$383$	−4856.41	−	8411.55i	−0.647914	−	1.12222i	−0.983620	−	0.180253i	$-0.942308\pi$
$383$	−4856.41	−	8411.55i	−0.647914	−	1.12222i	0.335707	−	0.941967i	$-0.391025\pi$
$384$		0			0
$385$		0			0
$386$	−7420.00			−0.978415
$387$		0			0
$388$	−1004.09	+	1739.14i	−0.131379	+	0.227555i
$389$	−1075.00	+	1861.95i	−0.140115	+	0.242686i	−0.927540	−	0.373725i	$-0.878081\pi$
$389$	−1075.00	+	1861.95i	−0.140115	+	0.242686i	0.787425	+	0.616411i	$0.211414\pi$
$390$		0			0
$391$	−96.1665			−0.0124382
$392$		0			0
$393$		0			0
$394$	956.000	+	1655.84i	0.122240	+	0.211726i
$395$	2687.01	−	4654.03i	0.342273	−	0.592835i
$396$		0			0
$397$	1700.59	+	2945.51i	0.214988	+	0.372370i	0.953269	−	0.302123i	$-0.0976954\pi$
$397$	1700.59	+	2945.51i	0.214988	+	0.372370i	−0.738281	+	0.674493i	$0.764362\pi$
$398$	8179.81			1.03019
$399$		0			0
$400$	−1200.00			−0.150000
$401$	6045.00	+	10470.2i	0.752800	+	1.30389i	0.946461	+	0.322820i	$0.104631\pi$
$401$	6045.00	+	10470.2i	0.752800	+	1.30389i	−0.193660	+	0.981069i	$0.562036\pi$
$402$		0			0
$403$	−3780.00	+	6547.15i	−0.467234	+	0.809273i
$404$	−3521.39	−	6099.23i	−0.433653	−	0.751109i
$405$		0			0
$406$		0			0
$407$	−800.000			−0.0974313
$408$		0			0
$409$	4096.27	−	7094.95i	0.495226	−	0.857757i	−0.504759	−	0.863260i	$-0.668419\pi$
$409$	4096.27	−	7094.95i	0.495226	−	0.857757i	0.999985	+	0.00550362i	$0.00175187\pi$
$410$	350.000	−	606.218i	0.0421592	−	0.0730219i
$411$		0			0
$412$	−905.097			−0.108230
$413$		0			0
$414$		0			0
$415$	3340.00	+	5785.05i	0.395070	+	0.684282i
$416$	1018.23	−	1763.63i	0.120007	−	0.207859i
$417$		0			0
$418$	−452.548	−	783.837i	−0.0529542	−	0.0917194i
$419$	1046.52			0.122019			0.0610093	−	0.998137i	$-0.480568\pi$
$419$	1046.52			0.122019			0.0610093	+	0.998137i	$0.480568\pi$
$420$		0			0
$421$	−3870.00			−0.448010			−0.224005	−	0.974588i	$-0.571913\pi$
$421$	−3870.00			−0.448010			−0.224005	+	0.974588i	$0.571913\pi$
$422$	2868.00	+	4967.52i	0.330834	+	0.573022i
$423$		0			0
$424$	2512.00	−	4350.91i	0.287721	−	0.498347i
$425$	−53.0330	−	91.8559i	−0.00605289	−	0.0104839i
$426$		0			0
$427$		0			0
$428$	8096.00			0.914334
$429$		0			0
$430$	−2404.16	+	4164.13i	−0.269626	+	0.467005i
$431$	1350.00	−	2338.27i	0.150875	−	0.261324i	−0.780674	−	0.624938i	$-0.785124\pi$
$431$	1350.00	−	2338.27i	0.150875	−	0.261324i	0.931549	+	0.363615i	$0.118458\pi$
$432$		0			0
$433$	5876.06			0.652160			0.326080	−	0.945342i	$-0.394272\pi$
$433$	5876.06			0.652160			0.326080	+	0.945342i	$0.394272\pi$
$434$		0			0
$435$		0			0
$436$	808.000	+	1399.50i	0.0887527	+	0.153724i
$437$	384.666	−	666.261i	0.0421077	−	0.0729327i
$438$		0			0
$439$	3173.50	+	5496.65i	0.345017	+	0.597588i	0.985357	−	0.170504i	$-0.0545397\pi$
$439$	3173.50	+	5496.65i	0.345017	+	0.597588i	−0.640339	+	0.768092i	$0.721206\pi$
$440$	−2262.74			−0.245164
$441$		0			0
$442$	180.000			0.0193704
$443$	3464.00	+	5999.82i	0.371512	+	0.643477i	0.989798	−	0.142476i	$-0.0455063\pi$
$443$	3464.00	+	5999.82i	0.371512	+	0.643477i	−0.618287	+	0.785953i	$0.712173\pi$
$444$		0			0
$445$	4075.00	−	7058.11i	0.434098	−	0.751879i
$446$	−2630.44	−	4556.05i	−0.279271	−	0.483711i
$447$		0			0
$448$		0			0
$449$	−1320.00			−0.138741			−0.0693704	−	0.997591i	$-0.522099\pi$
$449$	−1320.00			−0.138741			−0.0693704	+	0.997591i	$0.522099\pi$
$450$		0			0
$451$	−989.949	+	1714.64i	−0.103359	+	0.179023i
$452$	−2016.00	+	3491.81i	−0.209789	+	0.363365i
$453$		0			0
$454$	−339.411			−0.0350867
$455$		0			0
$456$		0			0
$457$	−645.000	−	1117.17i	−0.0660215	−	0.114353i	0.831125	−	0.556085i	$-0.187697\pi$
$457$	−645.000	−	1117.17i	−0.0660215	−	0.114353i	−0.897147	+	0.441733i	$0.854364\pi$
$458$	3143.80	−	5445.22i	0.320742	−	0.555542i
$459$		0			0
$460$	−961.665	−	1665.65i	−0.0974736	−	0.168829i
$461$	17642.3			1.78240			0.891198	−	0.453615i	$-0.149866\pi$
$461$	17642.3			1.78240			0.891198	+	0.453615i	$0.149866\pi$
$462$		0			0
$463$	5680.00			0.570134			0.285067	−	0.958508i	$-0.407984\pi$
$463$	5680.00			0.570134			0.285067	+	0.958508i	$0.407984\pi$
$464$	−880.000	−	1524.20i	−0.0880452	−	0.152499i
$465$		0			0
$466$	−4482.00	+	7763.05i	−0.445546	+	0.771709i
$467$	3846.66	+	6662.61i	0.381161	+	0.660190i	0.991229	−	0.132159i	$-0.0421910\pi$
$467$	3846.66	+	6662.61i	0.381161	+	0.660190i	−0.610067	+	0.792350i	$0.708858\pi$
$468$		0			0
$469$		0			0
$470$	1280.00			0.125621
$471$		0			0
$472$	3507.25	−	6074.73i	0.342022	−	0.592399i
$473$	6800.00	−	11777.9i	0.661024	−	1.14493i
$474$		0			0
$475$	848.528			0.0819645
$476$		0			0
$477$		0			0
$478$	−1740.00	−	3013.77i	−0.166497	−	0.288382i
$479$	8259.01	−	14305.0i	0.787816	−	1.36454i	−0.139487	−	0.990224i	$-0.544545\pi$
$479$	8259.01	−	14305.0i	0.787816	−	1.36454i	0.927303	−	0.374313i	$-0.122121\pi$
$480$		0			0
$481$	636.396	+	1102.27i	0.0603267	+	0.104489i
$482$	2520.13			0.238151
$483$		0			0
$484$	1076.00			0.101052
$485$	−1775.00	−	3074.39i	−0.166183	−	0.287837i
$486$		0			0
$487$	−6840.00	+	11847.2i	−0.636448	+	1.10236i	0.349759	+	0.936840i	$0.386264\pi$
$487$	−6840.00	+	11847.2i	−0.636448	+	1.10236i	−0.986206	+	0.165520i	$0.947070\pi$
$488$	−3671.30	−	6358.88i	−0.340557	−	0.589862i
$489$		0			0
$490$		0			0
$491$	2280.00			0.209562			0.104781	−	0.994495i	$-0.466586\pi$
$491$	2280.00			0.209562			0.104781	+	0.994495i	$0.466586\pi$
$492$		0			0
$493$	77.7817	−	134.722i	0.00710571	−	0.0123074i
$494$	−720.000	+	1247.08i	−0.0655756	+	0.113580i
$495$		0			0
$496$	1900.70			0.172065
$497$		0			0
$498$		0			0
$499$	−430.000	−	744.782i	−0.0385760	−	0.0668157i	0.846093	−	0.533036i	$-0.178949\pi$
$499$	−430.000	−	744.782i	−0.0385760	−	0.0668157i	−0.884669	+	0.466220i	$0.845616\pi$
$500$	2828.43	−	4898.98i	0.252982	−	0.438178i
$501$		0			0
$502$	5826.56	+	10091.9i	0.518032	+	0.897258i
$503$	−5730.39			−0.507963			−0.253982	−	0.967209i	$-0.581740\pi$
$503$	−5730.39			−0.507963			−0.253982	+	0.967209i	$0.581740\pi$
$504$		0			0
$505$	12450.0			1.09706
$506$	2720.00	+	4711.18i	0.238970	+	0.413908i
$507$		0			0
$508$	−2000.00	+	3464.10i	−0.174676	+	0.302549i
$509$	2294.56	+	3974.30i	0.199813	+	0.346086i	0.948468	−	0.316874i	$-0.102633\pi$
$509$	2294.56	+	3974.30i	0.199813	+	0.346086i	−0.748655	+	0.662960i	$0.769300\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−0.0441942
$513$		0			0
$514$	4688.12	−	8120.06i	0.402304	−	0.696810i
$515$	800.000	−	1385.64i	0.0684509	−	0.118560i
$516$		0			0
$517$	−3620.39			−0.307978
$518$		0			0
$519$		0			0
$520$	1800.00	+	3117.69i	0.151799	+	0.262923i
$521$	7293.81	−	12633.2i	0.613335	−	1.06233i	−0.377339	−	0.926075i	$-0.623161\pi$
$521$	7293.81	−	12633.2i	0.613335	−	1.06233i	0.990674	−	0.136252i	$-0.0435057\pi$
$522$		0			0
$523$	−3054.70	−	5290.90i	−0.255397	−	0.442361i	0.709606	−	0.704599i	$-0.248873\pi$
$523$	−3054.70	−	5290.90i	−0.255397	−	0.442361i	−0.965003	+	0.262238i	$0.915540\pi$
$524$	−339.411			−0.0282963
$525$		0			0
$526$	−4344.00			−0.360090
$527$	84.0000	+	145.492i	0.00694326	+	0.0120261i
$528$		0			0
$529$	3771.50	−	6532.43i	0.309978	−	0.536897i
$530$	4440.63	+	7691.40i	0.363941	+	0.630364i
$531$		0			0
$532$		0			0
$533$	3150.00			0.255988
$534$		0			0
$535$	−7155.92	+	12394.4i	−0.578276	+	1.00160i
$536$	2160.00	−	3741.23i	0.174063	−	0.301486i
$537$		0			0
$538$	−5416.44			−0.434051
$539$		0			0
$540$		0			0
$541$	8605.00	+	14904.3i	0.683841	+	1.18445i	0.973800	+	0.227408i	$0.0730250\pi$
$541$	8605.00	+	14904.3i	0.683841	+	1.18445i	−0.289959	+	0.957039i	$0.593642\pi$
$542$	−6188.60	+	10719.0i	−0.490448	+	0.849482i
$543$		0			0
$544$	−22.6274	−	39.1918i	−0.00178335	−	0.00308885i
$545$	−2856.71			−0.224529
$546$		0			0
$547$	4060.00			0.317355			0.158677	−	0.987330i	$-0.449277\pi$
$547$	4060.00			0.317355			0.158677	+	0.987330i	$0.449277\pi$
$548$	−4068.00	−	7045.98i	−0.317110	−	0.549251i
$549$		0			0
$550$	−3000.00	+	5196.15i	−0.232583	+	0.402845i
$551$	622.254	+	1077.78i	0.0481105	+	0.0833299i
$552$		0			0
$553$		0			0
$554$	−12260.0			−0.940212
$555$		0			0
$556$	−3473.31	+	6015.95i	−0.264930	+	0.458872i
$557$	−5178.00	+	8968.56i	−0.393894	+	0.682244i	−0.992959	−	0.118456i	$-0.962206\pi$
$557$	−5178.00	+	8968.56i	−0.393894	+	0.682244i	0.599065	+	0.800700i	$0.295539\pi$
$558$		0			0
$559$	−21637.5			−1.63715
$560$		0			0
$561$		0			0
$562$	−1970.00	−	3412.14i	−0.147864	−	0.256108i
$563$	−11605.0	+	20100.5i	−0.868728	+	1.50468i	−0.00543113	+	0.999985i	$0.501729\pi$
$563$	−11605.0	+	20100.5i	−0.868728	+	1.50468i	−0.863297	+	0.504696i	$0.831605\pi$
$564$		0			0
$565$	−3563.82	−	6172.71i	−0.265365	−	0.459625i
$566$	−3111.27			−0.231054
$567$		0			0
$568$	3360.00			0.248209
$569$	−2945.00	−	5100.89i	−0.216979	−	0.375818i	0.736904	−	0.675997i	$-0.236287\pi$
$569$	−2945.00	−	5100.89i	−0.216979	−	0.375818i	−0.953883	+	0.300179i	$0.902954\pi$
$570$		0			0
$571$	2806.00	−	4860.13i	0.205652	−	0.356200i	−0.744688	−	0.667413i	$-0.767402\pi$
$571$	2806.00	−	4860.13i	0.205652	−	0.356200i	0.950340	+	0.311212i	$0.100735\pi$
$572$	−5091.17	−	8818.16i	−0.372155	−	0.644591i
$573$		0			0
$574$		0			0
$575$	−5100.00			−0.369886
$576$		0			0
$577$	8898.94	−	15413.4i	0.642058	−	1.11208i	−0.342914	−	0.939367i	$-0.611414\pi$
$577$	8898.94	−	15413.4i	0.642058	−	1.11208i	0.984973	−	0.172711i	$-0.0552527\pi$
$578$	−4911.00	+	8506.10i	−0.353409	+	0.612123i
$579$		0			0
$580$	3111.27			0.222739
$581$		0			0
$582$		0			0
$583$	−12560.0	−	21754.6i	−0.892251	−	1.54542i
$584$	−1159.66	+	2008.58i	−0.0821693	+	0.142321i
$585$		0			0
$586$	−7686.25	−	13313.0i	−0.541836	−	0.938488i
$587$	−7942.22			−0.558451			−0.279225	−	0.960226i	$-0.590078\pi$
$587$	−7942.22			−0.558451			−0.279225	+	0.960226i	$0.590078\pi$
$588$		0			0
$589$	−1344.00			−0.0940213
$590$	6200.00	+	10738.7i	0.432627	+	0.749332i
$591$		0			0
$592$	160.000	−	277.128i	0.0111080	−	0.0192397i
$593$	−7039.25	−	12192.3i	−0.487466	−	0.844316i	0.512430	−	0.858729i	$-0.328745\pi$
$593$	−7039.25	−	12192.3i	−0.487466	−	0.844316i	−0.999896	+	0.0144132i	$0.995412\pi$
$594$		0			0
$595$		0			0
$596$	8560.00			0.588307
$597$		0			0
$598$	4327.49	−	7495.44i	0.295927	−	0.512561i
$599$	3650.00	−	6321.99i	0.248973	−	0.431234i	−0.714268	−	0.699872i	$-0.753240\pi$
$599$	3650.00	−	6321.99i	0.248973	−	0.431234i	0.963241	+	0.268638i	$0.0865736\pi$
$600$		0			0
$601$	−8727.11			−0.592323			−0.296162	−	0.955138i	$-0.595707\pi$
$601$	−8727.11			−0.592323			−0.296162	+	0.955138i	$0.595707\pi$
$602$		0			0
$603$		0			0
$604$	−4240.00	−	7343.90i	−0.285634	−	0.494733i
$605$	−951.059	+	1647.28i	−0.0639108	+	0.110697i
$606$		0			0
$607$	−5303.30	−	9185.59i	−0.354620	−	0.614220i	0.632433	−	0.774615i	$-0.282056\pi$
$607$	−5303.30	−	9185.59i	−0.354620	−	0.614220i	−0.987053	+	0.160395i	$0.948723\pi$
$608$	362.039			0.0241490
$609$		0			0
$610$	12980.0			0.861549
$611$	2880.00	+	4988.31i	0.190691	+	0.330287i
$612$		0			0
$613$	6990.00	−	12107.0i	0.460560	−	0.797714i	−0.538429	−	0.842671i	$-0.680982\pi$
$613$	6990.00	−	12107.0i	0.460560	−	0.797714i	0.998989	+	0.0449573i	$0.0143152\pi$
$614$	8598.42	+	14892.9i	0.565153	+	0.978874i
$615$		0			0
$616$		0			0
$617$	−2654.00			−0.173170			−0.0865851	−	0.996244i	$-0.527595\pi$
$617$	−2654.00			−0.173170			−0.0865851	+	0.996244i	$0.527595\pi$
$618$		0			0
$619$	−11941.6	+	20683.5i	−0.775403	+	1.34304i	0.159165	+	0.987252i	$0.449120\pi$
$619$	−11941.6	+	20683.5i	−0.775403	+	1.34304i	−0.934568	+	0.355785i	$0.884214\pi$
$620$	−1680.00	+	2909.85i	−0.108823	+	0.188487i
$621$		0			0
$622$	15160.4			0.977292
$623$		0			0
$624$		0			0
$625$	312.500	+	541.266i	0.0200000	+	0.0346410i
$626$	−3075.91	+	5327.64i	−0.196387	+	0.340152i
$627$		0			0
$628$	3493.11	+	6050.24i	0.221959	+	0.384444i
$629$	28.2843			0.00179295
$630$		0			0
$631$	−6400.00			−0.403772			−0.201886	−	0.979409i	$-0.564707\pi$
$631$	−6400.00			−0.403772			−0.201886	+	0.979409i	$0.564707\pi$
$632$	−3040.00	−	5265.43i	−0.191337	−	0.331405i
$633$		0			0
$634$	−2324.00	+	4025.29i	−0.145580	+	0.252152i
$635$	−3535.53	−	6123.72i	−0.220950	−	0.382697i
$636$		0			0
$637$		0			0
$638$	−8800.00			−0.546074
$639$		0			0
$640$	452.548	−	783.837i	0.0279508	−	0.0484123i
$641$	−7675.00	+	13293.5i	−0.472924	+	0.819128i	−0.999520	−	0.0309874i	$-0.990135\pi$
$641$	−7675.00	+	13293.5i	−0.472924	+	0.819128i	0.526596	+	0.850116i	$0.323468\pi$
$642$		0			0
$643$	−17847.4			−1.09461			−0.547303	−	0.836934i	$-0.684345\pi$
$643$	−17847.4			−1.09461			−0.547303	+	0.836934i	$0.684345\pi$
$644$		0			0
$645$		0			0
$646$	16.0000	+	27.7128i	0.000974476	+	0.00168784i
$647$	−7000.36	+	12125.0i	−0.425367	+	0.736757i	−0.996455	−	0.0841319i	$-0.973188\pi$
$647$	−7000.36	+	12125.0i	−0.425367	+	0.736757i	0.571088	+	0.820889i	$0.306522\pi$
$648$		0			0
$649$	−17536.2	−	30373.7i	−1.06064	−	1.83709i
$650$	9545.94			0.576035
$651$		0			0
$652$	13360.0			0.802482
$653$	−13191.0	−	22847.5i	−0.790511	−	1.36921i	−0.925651	−	0.378379i	$-0.876482\pi$
$653$	−13191.0	−	22847.5i	−0.790511	−	1.36921i	0.135140	−	0.990827i	$-0.456852\pi$
$654$		0			0
$655$	300.000	−	519.615i	0.0178961	−	0.0309970i
$656$	−395.980	−	685.857i	−0.0235677	−	0.0408205i
$657$		0			0
$658$		0			0
$659$	14400.0			0.851205			0.425603	−	0.904910i	$-0.360062\pi$
$659$	14400.0			0.851205			0.425603	+	0.904910i	$0.360062\pi$
$660$		0			0
$661$	14291.3	−	24753.3i	0.840951	−	1.45657i	−0.0481409	−	0.998841i	$-0.515330\pi$
$661$	14291.3	−	24753.3i	0.840951	−	1.45657i	0.889092	−	0.457729i	$-0.151337\pi$
$662$	9508.00	−	16468.3i	0.558216	−	0.966858i
$663$		0			0
$664$	7557.56			0.441702
$665$		0			0
$666$		0			0
$667$	−3740.00	−	6477.87i	−0.217112	−	0.376048i
$668$	735.391	−	1273.73i	0.0425945	−	0.0737759i
$669$		0			0
$670$	3818.38	+	6613.62i	0.220174	+	0.381353i
$671$	−36713.0			−2.11220
$672$		0			0
$673$	−18120.0			−1.03785			−0.518926	−	0.854819i	$-0.673668\pi$
$673$	−18120.0			−1.03785			−0.518926	+	0.854819i	$0.673668\pi$
$674$	−4720.00	−	8175.28i	−0.269744	−	0.467211i
$675$		0			0
$676$	−3706.00	+	6418.98i	−0.210856	+	0.365213i
$677$	8898.94	+	15413.4i	0.505191	+	0.875016i	0.999982	+	0.00600394i	$0.00191112\pi$
$677$	8898.94	+	15413.4i	0.505191	+	0.875016i	−0.494791	+	0.869012i	$0.664756\pi$
$678$		0			0
$679$		0			0
$680$	80.0000			0.00451156
$681$		0			0
$682$	4751.76	−	8230.29i	0.266795	−	0.462103i
$683$	−864.000	+	1496.49i	−0.0484042	+	0.0838385i	−0.889212	−	0.457495i	$-0.848747\pi$
$683$	−864.000	+	1496.49i	−0.0484042	+	0.0838385i	0.840808	+	0.541333i	$0.182080\pi$
$684$		0			0
$685$	14382.6			0.802232
$686$		0			0
$687$		0			0
$688$	2720.00	+	4711.18i	0.150725	+	0.261064i
$689$	−19982.8	+	34611.3i	−1.10491	+	1.91377i
$690$		0			0
$691$	8544.68	+	14799.8i	0.470412	+	0.814778i	0.999427	−	0.0338344i	$-0.0107719\pi$
$691$	8544.68	+	14799.8i	0.470412	+	0.814778i	−0.529015	+	0.848612i	$0.677439\pi$
$692$	−13559.5			−0.744876
$693$		0			0
$694$	13008.0			0.711494
$695$	−6140.00	−	10634.8i	−0.335113	−	0.580433i
$696$		0			0
$697$	35.0000	−	60.6218i	0.00190204	−	0.00329442i
$698$	5256.63	+	9104.75i	0.285052	+	0.493725i
$699$		0			0
$700$		0			0
$701$	13410.0			0.722523			0.361262	−	0.932465i	$-0.382346\pi$
$701$	13410.0			0.722523			0.361262	+	0.932465i	$0.382346\pi$
$702$		0			0
$703$	−113.137	+	195.959i	−0.00606977	+	0.0105131i
$704$	−1280.00	+	2217.03i	−0.0685253	+	0.118689i
$705$		0			0
$706$	24423.5			1.30197
$707$		0			0
$708$		0			0
$709$	70.0000	+	121.244i	0.00370791	+	0.00642228i	0.867873	−	0.496785i	$-0.165486\pi$
$709$	70.0000	+	121.244i	0.00370791	+	0.00642228i	−0.864165	+	0.503208i	$0.832153\pi$
$710$	−2969.85	+	5143.93i	−0.156981	+	0.271899i
$711$		0			0
$712$	−4610.34	−	7985.34i	−0.242668	−	0.420313i
$713$	8077.99			0.424296
$714$		0			0
$715$	18000.0			0.941485
$716$	−1440.00	−	2494.15i	−0.0751611	−	0.130183i
$717$		0			0
$718$	−7340.00	+	12713.3i	−0.381513	+	0.660800i
$719$	12968.3	+	22461.8i	0.672653	+	1.16507i	0.977149	+	0.212555i	$0.0681786\pi$
$719$	12968.3	+	22461.8i	0.672653	+	1.16507i	−0.304496	+	0.952514i	$0.598488\pi$
$720$		0			0
$721$		0			0
$722$	13462.0			0.693911
$723$		0			0
$724$	−3708.07	+	6422.56i	−0.190344	+	0.329686i
$725$	4125.00	−	7144.71i	0.211308	−	0.365997i
$726$		0			0
$727$	−9277.24			−0.473279			−0.236639	−	0.971598i	$-0.576046\pi$
$727$	−9277.24			−0.473279			−0.236639	+	0.971598i	$0.576046\pi$
$728$		0			0
$729$		0			0
$730$	−2050.00	−	3550.70i	−0.103937	−	0.180024i
$731$	−240.416	+	416.413i	−0.0121643	+	0.0210692i
$732$		0			0
$733$	−12738.5	−	22063.8i	−0.641894	−	1.11179i	−0.985010	−	0.172500i	$-0.944816\pi$
$733$	−12738.5	−	22063.8i	−0.641894	−	1.11179i	0.343116	−	0.939293i	$-0.388518\pi$
$734$	−15330.1			−0.770904
$735$		0			0
$736$	−2176.00			−0.108979
$737$	−10800.0	−	18706.1i	−0.539787	−	0.934939i
$738$		0			0
$739$	3462.00	−	5996.36i	0.172330	−	0.298484i	−0.766904	−	0.641762i	$-0.778204\pi$
$739$	3462.00	−	5996.36i	0.172330	−	0.298484i	0.939234	+	0.343278i	$0.111537\pi$
$740$	282.843	+	489.898i	0.0140507	+	0.0243365i
$741$		0			0
$742$		0			0
$743$	−29108.0			−1.43724			−0.718620	−	0.695403i	$-0.755226\pi$
$743$	−29108.0			−1.43724			−0.718620	+	0.695403i	$0.755226\pi$
$744$		0			0
$745$	−7566.04	+	13104.8i	−0.372078	+	0.644459i
$746$	−2990.00	+	5178.83i	−0.146745	+	0.254170i
$747$		0			0
$748$	−226.274			−0.0110607
$749$		0			0
$750$		0			0
$751$	−15724.0	−	27234.8i	−0.764017	−	1.32332i	−0.940765	−	0.339060i	$-0.889891\pi$
$751$	−15724.0	−	27234.8i	−0.764017	−	1.32332i	0.176747	−	0.984256i	$-0.443442\pi$
$752$	724.077	−	1254.14i	0.0351122	−	0.0608161i
$753$		0			0
$754$	7000.36	+	12125.0i	0.338114	+	0.585631i
$755$	14990.7			0.722604
$756$		0			0
$757$	−13300.0			−0.638569			−0.319284	−	0.947659i	$-0.603443\pi$
$757$	−13300.0			−0.638569			−0.319284	+	0.947659i	$0.603443\pi$
$758$	−11900.0	−	20611.4i	−0.570221	−	0.987652i
$759$		0			0
$760$	−320.000	+	554.256i	−0.0152732	+	0.0264539i
$761$	2400.63	+	4158.01i	0.114353	+	0.198065i	0.917521	−	0.397687i	$-0.130187\pi$
$761$	2400.63	+	4158.01i	0.114353	+	0.198065i	−0.803168	+	0.595753i	$0.796854\pi$
$762$		0			0
$763$		0			0
$764$	15920.0			0.753881
$765$		0			0
$766$	9712.82	−	16823.1i	0.458144	−	0.793529i
$767$	−27900.0	+	48324.2i	−1.31344	+	2.27495i
$768$		0			0
$769$	−16932.4			−0.794015			−0.397007	−	0.917815i	$-0.629951\pi$
$769$	−16932.4			−0.794015			−0.397007	+	0.917815i	$0.629951\pi$
$770$		0			0
$771$		0			0
$772$	−7420.00	−	12851.8i	−0.345922	−	0.599154i
$773$	−9720.60	+	16836.6i	−0.452297	+	0.783401i	−0.998528	−	0.0542330i	$-0.982729\pi$
$773$	−9720.60	+	16836.6i	−0.452297	+	0.783401i	0.546231	+	0.837634i	$0.316062\pi$
$774$		0			0
$775$	4454.77	+	7715.89i	0.206478	+	0.357630i
$776$	−4016.37			−0.185798
$777$		0			0
$778$	−4300.00			−0.198152
$779$	280.000	+	484.974i	0.0128781	+	0.0223055i
$780$		0			0
$781$	8400.00	−	14549.2i	0.384860	−	0.666597i
$782$	−96.1665	−	166.565i	−0.00439758	−	0.00761683i
$783$		0			0
$784$		0			0
$785$	−12350.0			−0.561516
$786$		0			0
$787$	−10366.2	+	17954.8i	−0.469523	+	0.813238i	−0.999393	−	0.0348413i	$-0.988907\pi$
$787$	−10366.2	+	17954.8i	−0.469523	+	0.813238i	0.529870	+	0.848079i	$0.322241\pi$
$788$	−1912.00	+	3311.68i	−0.0864368	+	0.149713i
$789$		0			0
$790$	10748.0			0.484047
$791$		0			0
$792$		0			0
$793$	29205.0	+	50584.5i	1.30782	+	2.26521i
$794$	−3401.18	+	5891.02i	−0.152020	+	0.263306i
$795$		0			0
$796$	8179.81	+	14167.8i	0.364228	+	0.630862i
$797$	−28582.7			−1.27033			−0.635163	−	0.772378i	$-0.719067\pi$
$797$	−28582.7			−1.27033			−0.635163	+	0.772378i	$0.719067\pi$
$798$		0			0
$799$	128.000			0.00566748
$800$	−1200.00	−	2078.46i	−0.0530330	−	0.0918559i
$801$		0			0
$802$	−12090.0	+	20940.5i	−0.532310	+	0.921988i
$803$	5798.28	+	10042.9i	0.254815	+	0.441353i
$804$		0			0
$805$		0			0
$806$	−15120.0			−0.660768
$807$		0			0
$808$	7042.78	−	12198.5i	0.306639	−	0.531114i
$809$	−11140.0	+	19295.0i	−0.484130	+	0.838539i	−0.999834	−	0.0182286i	$-0.994197\pi$
$809$	−11140.0	+	19295.0i	−0.484130	+	0.838539i	0.515703	+	0.856767i	$0.327531\pi$
$810$		0			0
$811$	−26100.7			−1.13011			−0.565056	−	0.825053i	$-0.691145\pi$
$811$	−26100.7			−1.13011			−0.565056	+	0.825053i	$0.691145\pi$
$812$		0			0
$813$		0			0
$814$	−800.000	−	1385.64i	−0.0344472	−	0.0596642i
$815$	−11808.7	+	20453.2i	−0.507534	+	0.879075i
$816$		0			0
$817$	−1923.33	−	3331.31i	−0.0823609	−	0.142653i
$818$	16385.1			0.700356
$819$		0			0
$820$	1400.00			0.0596221
$821$	1770.00	+	3065.73i	0.0752417	+	0.130322i	0.901191	−	0.433421i	$-0.142694\pi$
$821$	1770.00	+	3065.73i	0.0752417	+	0.130322i	−0.825950	+	0.563744i	$0.809361\pi$
$822$		0			0
$823$	14200.0	−	24595.1i	0.601435	−	1.04172i	−0.391169	−	0.920319i	$-0.627929\pi$
$823$	14200.0	−	24595.1i	0.601435	−	1.04172i	0.992604	−	0.121397i	$-0.0387374\pi$
$824$	−905.097	−	1567.67i	−0.0382652	−	0.0662773i
$825$		0			0
$826$		0			0
$827$	38736.0			1.62876			0.814379	−	0.580334i	$-0.197078\pi$
$827$	38736.0			1.62876			0.814379	+	0.580334i	$0.197078\pi$
$828$		0			0
$829$	−11704.7	+	20273.2i	−0.490377	+	0.849358i	−0.999939	−	0.0110765i	$-0.996474\pi$
$829$	−11704.7	+	20273.2i	−0.490377	+	0.849358i	0.509562	+	0.860434i	$0.329808\pi$
$830$	−6680.00	+	11570.1i	−0.279357	+	0.483860i
$831$		0			0
$832$	4072.94			0.169716
$833$		0			0
$834$		0			0
$835$	1300.00	+	2251.67i	0.0538783	+	0.0933199i
$836$	905.097	−	1567.67i	0.0374443	−	0.0648554i
$837$		0			0
$838$	1046.52	+	1812.62i	0.0431401	+	0.0747208i
$839$	29387.4			1.20925			0.604627	−	0.796509i	$-0.293322\pi$
$839$	29387.4			1.20925			0.604627	+	0.796509i	$0.293322\pi$
$840$		0			0
$841$	−12289.0			−0.503875
$842$	−3870.00	−	6703.04i	−0.158395	−	0.274349i
$843$		0			0
$844$	−5736.00	+	9935.04i	−0.233935	+	0.405188i
$845$	−6551.34	−	11347.3i	−0.266714	−	0.461962i
$846$		0			0
$847$		0			0
$848$	10048.0			0.406898
$849$		0			0
$850$	106.066	−	183.712i	0.00428004	−	0.00741325i
$851$	680.000	−	1177.79i	0.0273914	−	0.0474433i
$852$		0			0
$853$	−22252.7			−0.893220			−0.446610	−	0.894729i	$-0.647369\pi$
$853$	−22252.7			−0.893220			−0.446610	+	0.894729i	$0.647369\pi$
$854$		0			0
$855$		0			0
$856$	8096.00	+	14022.7i	0.323266	+	0.559913i
$857$	−6916.21	+	11979.2i	−0.275675	+	0.477483i	−0.970305	−	0.241884i	$-0.922235\pi$
$857$	−6916.21	+	11979.2i	−0.275675	+	0.477483i	0.694630	+	0.719367i	$0.255568\pi$
$858$		0			0
$859$	19832.9	+	34351.6i	0.787766	+	1.36445i	0.927333	+	0.374238i	$0.122096\pi$
$859$	19832.9	+	34351.6i	0.787766	+	1.36445i	−0.139567	+	0.990213i	$0.544571\pi$
$860$	−9616.65			−0.381308
$861$		0			0
$862$	5400.00			0.213370
$863$	−15994.0	−	27702.4i	−0.630871	−	1.09270i	−0.987374	−	0.158407i	$-0.949364\pi$
$863$	−15994.0	−	27702.4i	−0.630871	−	1.09270i	0.356502	−	0.934294i	$-0.383969\pi$
$864$		0			0
$865$	11985.0	−	20758.6i	0.471101	−	0.815971i
$866$	5876.06	+	10177.6i	0.230573	+	0.399365i
$867$		0			0
$868$		0			0
$869$	−30400.0			−1.18671
$870$		0			0
$871$	−17182.7	+	29761.3i	−0.668442	+	1.15778i
$872$	−1616.00	+	2798.99i	−0.0627576	+	0.108699i
$873$		0			0
$874$	1538.66			0.0595493
$875$		0			0
$876$		0			0
$877$	16730.0	+	28977.2i	0.644164	+	1.11573i	0.984494	+	0.175419i	$0.0561280\pi$
$877$	16730.0	+	28977.2i	0.644164	+	1.11573i	−0.340330	+	0.940306i	$0.610539\pi$
$878$	−6346.99	+	10993.3i	−0.243964	+	0.422558i
$879$		0			0
$880$	−2262.74	−	3919.18i	−0.0866784	−	0.150131i
$881$	−12791.6			−0.489170			−0.244585	−	0.969628i	$-0.578652\pi$
$881$	−12791.6			−0.489170			−0.244585	+	0.969628i	$0.578652\pi$
$882$		0			0
$883$	−35260.0			−1.34382			−0.671910	−	0.740633i	$-0.734526\pi$
$883$	−35260.0			−1.34382			−0.671910	+	0.740633i	$0.734526\pi$
$884$	180.000	+	311.769i	0.00684848	+	0.0118619i
$885$		0			0
$886$	−6928.00	+	11999.6i	−0.262698	+	0.455007i
$887$	7718.78	+	13369.3i	0.292188	+	0.506085i	0.974327	−	0.225138i	$-0.0722832\pi$
$887$	7718.78	+	13369.3i	0.292188	+	0.506085i	−0.682138	+	0.731223i	$0.738950\pi$
$888$		0			0
$889$		0			0
$890$	16300.0			0.613907
$891$		0			0
$892$	5260.87	−	9112.10i	0.197474	−	0.342036i
$893$	−512.000	+	886.810i	−0.0191864	+	0.0332318i
$894$		0			0
$895$	5091.17			0.190144
$896$		0			0
$897$		0			0
$898$	−1320.00	−	2286.31i	−0.0490523	−	0.0849611i
$899$	−6533.67	+	11316.6i	−0.242392	+	0.419834i
$900$		0			0
$901$	444.063	+	769.140i	0.0164194	+	0.0284392i
$902$	−3959.80			−0.146172
$903$		0			0
$904$	−8064.00			−0.296687
$905$	−6555.00	−	11353.6i	−0.240769	−	0.417023i
$906$		0			0
$907$	−16550.0	+	28665.4i	−0.605881	+	1.04942i	0.386031	+	0.922486i	$0.373846\pi$
$907$	−16550.0	+	28665.4i	−0.605881	+	1.04942i	−0.991912	+	0.126930i	$0.959488\pi$
$908$	−339.411	−	587.878i	−0.0124050	−	0.0214861i
$909$		0			0
$910$		0			0
$911$	39620.0			1.44091			0.720455	−	0.693502i	$-0.243933\pi$
$911$	39620.0			1.44091			0.720455	+	0.693502i	$0.243933\pi$
$912$		0			0
$913$	18893.9	−	32725.2i	0.684881	−	1.18625i
$914$	1290.00	−	2234.35i	0.0466843	−	0.0808595i
$915$		0			0
$916$	12575.2			0.453598
$917$		0			0
$918$		0			0
$919$	−10472.0	−	18138.0i	−0.375886	−	0.651054i	0.614573	−	0.788860i	$-0.289328\pi$
$919$	−10472.0	−	18138.0i	−0.375886	−	0.651054i	−0.990459	+	0.137806i	$0.955995\pi$
$920$	1923.33	−	3331.31i	0.0689243	−	0.119380i
$921$		0			0
$922$	17642.3	+	30557.4i	0.630172	+	1.09149i
$923$	−26728.6			−0.953179
$924$		0			0
$925$	1500.00			0.0533186
$926$	5680.00	+	9838.05i	0.201573	+	0.349134i
$927$		0			0
$928$	1760.00	−	3048.41i	0.0622574	−	0.107833i
$929$	23118.9	+	40043.0i	0.816475	+	1.41418i	0.908264	+	0.418397i	$0.137408\pi$
$929$	23118.9	+	40043.0i	0.816475	+	1.41418i	−0.0917893	+	0.995778i	$0.529259\pi$
$930$		0			0
$931$		0			0
$932$	−17928.0			−0.630098
$933$		0			0
$934$	−7693.32	+	13325.2i	−0.269522	+	0.466825i
$935$	200.000	−	346.410i	0.00699540	−	0.0121164i
$936$		0			0
$937$	50522.8			1.76148			0.880740	−	0.473600i	$-0.157046\pi$
$937$	50522.8			1.76148			0.880740	+	0.473600i	$0.157046\pi$
$938$		0			0
$939$		0			0
$940$	1280.00	+	2217.03i	0.0444138	+	0.0769270i
$941$	4939.14	−	8554.84i	0.171107	−	0.296365i	−0.767700	−	0.640809i	$-0.778599\pi$
$941$	4939.14	−	8554.84i	0.171107	−	0.296365i	0.938807	+	0.344444i	$0.111932\pi$
$942$		0			0
$943$	−1682.91	−	2914.89i	−0.0581158	−	0.100660i
$944$	14029.0			0.483692
$945$		0			0
$946$	27200.0			0.934829
$947$	−15108.0	−	26167.8i	−0.518420	−	0.897930i	−0.999771	−	0.0214022i	$-0.993187\pi$
$947$	−15108.0	−	26167.8i	−0.518420	−	0.897930i	0.481351	−	0.876528i	$-0.340146\pi$
$948$		0			0
$949$	9225.00	−	15978.2i	0.315549	−	0.546547i
$950$	848.528	+	1469.69i	0.0289788	+	0.0501928i
$951$		0			0
$952$		0			0
$953$	35512.0			1.20708			0.603540	−	0.797333i	$-0.293757\pi$
$953$	35512.0			1.20708			0.603540	+	0.797333i	$0.293757\pi$
$954$		0			0
$955$	−14071.4	+	24372.4i	−0.476796	+	0.825836i
$956$	3480.00	−	6027.54i	0.117731	−	0.203917i
$957$		0			0
$958$	33036.0			1.11414
$959$		0			0
$960$		0			0
$961$	7839.50	+	13578.4i	0.263150	+	0.455789i
$962$	−1272.79	+	2204.54i	−0.0426575	+	0.0738849i
$963$		0			0
$964$	2520.13	+	4364.99i	0.0841990	+	0.145837i
$965$	26233.7			0.875121
$966$		0			0
$967$	−720.000			−0.0239438			−0.0119719	−	0.999928i	$-0.503811\pi$
$967$	−720.000			−0.0239438			−0.0119719	+	0.999928i	$0.503811\pi$
$968$	1076.00	+	1863.69i	0.0357272	+	0.0618814i
$969$		0			0
$970$	3550.00	−	6148.78i	0.117509	−	0.203531i
$971$	−7693.32	−	13325.2i	−0.254264	−	0.440398i	0.710431	−	0.703767i	$-0.248500\pi$
$971$	−7693.32	−	13325.2i	−0.254264	−	0.440398i	−0.964695	+	0.263368i	$0.915167\pi$
$972$		0			0
$973$		0			0
$974$	−27360.0			−0.900073
$975$		0			0
$976$	7342.60	−	12717.8i	0.240810	−	0.417096i
$977$	20787.0	−	36004.1i	0.680691	−	1.17899i	−0.294079	−	0.955781i	$-0.595013\pi$
$977$	20787.0	−	36004.1i	0.680691	−	1.17899i	0.974770	−	0.223210i	$-0.0716537\pi$
$978$		0			0
$979$	−46103.4			−1.50508
$980$		0			0
$981$		0			0
$982$	2280.00	+	3949.08i	0.0740914	+	0.128330i
$983$	22118.3	−	38310.0i	0.717665	−	1.24303i	−0.244258	−	0.969710i	$-0.578544\pi$
$983$	22118.3	−	38310.0i	0.717665	−	1.24303i	0.961923	−	0.273321i	$-0.0881222\pi$
$984$		0			0
$985$	−3379.97	−	5854.28i	−0.109335	−	0.189373i
$986$	311.127			0.0100490
$987$		0			0
$988$	−2880.00			−0.0927379
$989$	11560.0	+	20022.5i	0.371675	+	0.643760i
$990$		0			0
$991$	−6136.00	+	10627.9i	−0.196687	+	0.340671i	−0.947452	−	0.319898i	$-0.896351\pi$
$991$	−6136.00	+	10627.9i	−0.196687	+	0.340671i	0.750765	+	0.660569i	$0.229685\pi$
$992$	1900.70	+	3292.11i	0.0608341	+	0.105368i
$993$		0			0
$994$		0			0
$995$	−28920.0			−0.921433
$996$		0			0
$997$	28846.4	−	49963.5i	0.916324	−	1.58712i	0.111374	−	0.993779i	$-0.464475\pi$
$997$	28846.4	−	49963.5i	0.916324	−	1.58712i	0.804951	−	0.593342i	$-0.202192\pi$
$998$	860.000	−	1489.56i	0.0272774	−	0.0472458i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.bg.361.1		4
3.2	odd	2		882.4.g.bc.361.2		4
7.2	even	3	inner	882.4.g.bg.667.1		4
7.3	odd	6		882.4.a.y.1.1	✓	2
7.4	even	3		882.4.a.y.1.2	yes	2
7.5	odd	6	inner	882.4.g.bg.667.2		4
7.6	odd	2	inner	882.4.g.bg.361.2		4
21.2	odd	6		882.4.g.bc.667.2		4
21.5	even	6		882.4.g.bc.667.1		4
21.11	odd	6		882.4.a.be.1.1	yes	2
21.17	even	6		882.4.a.be.1.2	yes	2
21.20	even	2		882.4.g.bc.361.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.4.a.y.1.1	✓	2	7.3	odd	6
882.4.a.y.1.2	yes	2	7.4	even	3
882.4.a.be.1.1	yes	2	21.11	odd	6
882.4.a.be.1.2	yes	2	21.17	even	6
882.4.g.bc.361.1		4	21.20	even	2
882.4.g.bc.361.2		4	3.2	odd	2
882.4.g.bc.667.1		4	21.5	even	6
882.4.g.bc.667.2		4	21.2	odd	6
882.4.g.bg.361.1		4	1.1	even	1	trivial
882.4.g.bg.361.2		4	7.6	odd	2	inner
882.4.g.bg.667.1		4	7.2	even	3	inner
882.4.g.bg.667.2		4	7.5	odd	6	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.53553 - 6.12372i) q^{5} -8.00000 q^{8} +(7.07107 - 12.2474i) q^{10} +(-20.0000 + 34.6410i) q^{11} +63.6396 q^{13} +(-8.00000 - 13.8564i) q^{16} +(0.707107 - 1.22474i) q^{17} +(5.65685 + 9.79796i) q^{19} +28.2843 q^{20} -80.0000 q^{22} +(-34.0000 - 58.8897i) q^{23} +(37.5000 - 64.9519i) q^{25} +(63.6396 + 110.227i) q^{26} +110.000 q^{29} +(-59.3970 + 102.879i) q^{31} +(16.0000 - 27.7128i) q^{32} +2.82843 q^{34} +(10.0000 + 17.3205i) q^{37} +(-11.3137 + 19.5959i) q^{38} +(28.2843 + 48.9898i) q^{40} +49.4975 q^{41} -340.000 q^{43} +(-80.0000 - 138.564i) q^{44} +(68.0000 - 117.779i) q^{46} +(45.2548 + 78.3837i) q^{47} +150.000 q^{50} +(-127.279 + 220.454i) q^{52} +(-314.000 + 543.864i) q^{53} +282.843 q^{55} +(110.000 + 190.526i) q^{58} +(-438.406 + 759.342i) q^{59} +(458.912 + 794.859i) q^{61} -237.588 q^{62} +64.0000 q^{64} +(-225.000 - 389.711i) q^{65} +(-270.000 + 467.654i) q^{67} +(2.82843 + 4.89898i) q^{68} -420.000 q^{71} +(144.957 - 251.073i) q^{73} +(-20.0000 + 34.6410i) q^{74} -45.2548 q^{76} +(380.000 + 658.179i) q^{79} +(-56.5685 + 97.9796i) q^{80} +(49.4975 + 85.7321i) q^{82} -944.695 q^{83} -10.0000 q^{85} +(-340.000 - 588.897i) q^{86} +(160.000 - 277.128i) q^{88} +(576.292 + 998.167i) q^{89} +272.000 q^{92} +(-90.5097 + 156.767i) q^{94} +(40.0000 - 69.2820i) q^{95} +502.046 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8} - 80 q^{11} - 32 q^{16} - 320 q^{22} - 136 q^{23} + 150 q^{25} + 440 q^{29} + 64 q^{32} + 40 q^{37} - 1360 q^{43} - 320 q^{44} + 272 q^{46} + 600 q^{50} - 1256 q^{53}+ \cdots + 160 q^{95}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8 - 80 * q^11 - 32 * q^16 - 320 * q^22 - 136 * q^23 + 150 * q^25 + 440 * q^29 + 64 * q^32 + 40 * q^37 - 1360 * q^43 - 320 * q^44 + 272 * q^46 + 600 * q^50 - 1256 * q^53 + 440 * q^58 + 256 * q^64 - 900 * q^65 - 1080 * q^67 - 1680 * q^71 - 80 * q^74 + 1520 * q^79 - 40 * q^85 - 1360 * q^86 + 640 * q^88 + 1088 * q^92 + 160 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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