LMFDB - Embedded newform 882.3.s.h.557.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,3,Mod(557,882)]

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, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("882.557");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	882.s (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:	$24.0327593166$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.621801639936.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 34x^{6} + 116x^{5} + 413x^{4} - 1024x^{3} - 1664x^{2} + 2196x + 4467 $ x^8 - 4x^7 - 34x^6 + 116x^5 + 413x^4 - 1024x^3 - 1664x^2 + 2196*x + 4467
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			557.2
Root			$2.31664 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	882.557
Dual form			882.3.s.h.863.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.44983 - 4.30116i) q^{5} +2.82843i q^{8} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.44983 - 4.30116i) q^{5} +2.82843i q^{8} +(-6.08276 + 10.5357i) q^{10} +(-2.44949 - 1.41421i) q^{11} -12.1655 q^{13} +(-2.00000 - 3.46410i) q^{16} +(-22.3495 - 12.9035i) q^{17} +(-12.1655 - 21.0713i) q^{19} -17.2047i q^{20} +4.00000 q^{22} +(-36.7423 + 21.2132i) q^{23} +(24.5000 - 42.4352i) q^{25} +(14.8997 - 8.60233i) q^{26} +15.5563i q^{29} +(12.1655 - 21.0713i) q^{31} +(4.89898 + 2.82843i) q^{32} +36.4966 q^{34} +(3.00000 + 5.19615i) q^{37} +(29.7993 + 17.2047i) q^{38} +(12.1655 + 21.0713i) q^{40} +25.8070i q^{41} -68.0000 q^{43} +(-4.89898 + 2.82843i) q^{44} +(30.0000 - 51.9615i) q^{46} +(-59.5987 + 34.4093i) q^{47} +69.2965i q^{50} +(-12.1655 + 21.0713i) q^{52} +(-35.5176 - 20.5061i) q^{53} -24.3311 q^{55} +(-11.0000 - 19.0526i) q^{58} +(59.5987 + 34.4093i) q^{59} +(48.6621 + 84.2852i) q^{61} +34.4093i q^{62} -8.00000 q^{64} +(-90.6311 + 52.3259i) q^{65} +(52.0000 - 90.0666i) q^{67} +(-44.6990 + 25.8070i) q^{68} +70.7107i q^{71} +(30.4138 - 52.6783i) q^{73} +(-7.34847 - 4.24264i) q^{74} -48.6621 q^{76} +(10.0000 + 17.3205i) q^{79} +(-29.7993 - 17.2047i) q^{80} +(-18.2483 - 31.6070i) q^{82} -222.000 q^{85} +(83.2827 - 48.0833i) q^{86} +(4.00000 - 6.92820i) q^{88} +(81.9482 - 47.3128i) q^{89} +84.8528i q^{92} +(48.6621 - 84.2852i) q^{94} +(-181.262 - 104.652i) q^{95} +158.152 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4}+O(q^{10}) $ 8 * q + 8 * q^4	$ 8 q + 8 q^{4} - 16 q^{16} + 32 q^{22} + 196 q^{25} + 24 q^{37} - 544 q^{43} + 240 q^{46} - 88 q^{58} - 64 q^{64} + 416 q^{67} + 80 q^{79} - 1776 q^{85} + 32 q^{88}+O(q^{100}) $ 8 * q + 8 * q^4 - 16 * q^16 + 32 * q^22 + 196 * q^25 + 24 * q^37 - 544 * q^43 + 240 * q^46 - 88 * q^58 - 64 * q^64 + 416 * q^67 + 80 * q^79 - 1776 * q^85 + 32 * q^88

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	7.44983	−	4.30116i	1.48997	−	0.860233i	0.490032	−	0.871704i	$-0.336985\pi$
$5$	7.44983	−	4.30116i	1.48997	−	0.860233i	0.999934	+	0.0114718i	$0.00365166\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			2.82843i			0.353553i
$9$		0			0
$10$	−6.08276	+	10.5357i	−0.608276	+	1.05357i
$11$	−2.44949	−	1.41421i	−0.222681	−	0.128565i	0.384510	−	0.923121i	$-0.374370\pi$
$11$	−2.44949	−	1.41421i	−0.222681	−	0.128565i	−0.607191	+	0.794556i	$0.707704\pi$
$12$		0			0
$13$	−12.1655			−0.935810			−0.467905	−	0.883779i	$-0.654991\pi$
$13$	−12.1655			−0.935810			−0.467905	+	0.883779i	$0.654991\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−22.3495	−	12.9035i	−1.31468	−	0.759029i	−0.331810	−	0.943346i	$-0.607659\pi$
$17$	−22.3495	−	12.9035i	−1.31468	−	0.759029i	−0.982867	+	0.184318i	$0.940992\pi$
$18$		0			0
$19$	−12.1655	−	21.0713i	−0.640291	−	1.10902i	−0.985368	−	0.170442i	$-0.945481\pi$
$19$	−12.1655	−	21.0713i	−0.640291	−	1.10902i	0.345077	−	0.938574i	$-0.387853\pi$
$20$		−	17.2047i		−	0.860233i
$21$		0			0
$22$	4.00000			0.181818
$23$	−36.7423	+	21.2132i	−1.59749	+	0.922313i	−0.605525	+	0.795826i	$0.707037\pi$
$23$	−36.7423	+	21.2132i	−1.59749	+	0.922313i	−0.991968	+	0.126487i	$0.959630\pi$
$24$		0			0
$25$	24.5000	−	42.4352i	0.980000	−	1.69741i
$26$	14.8997	−	8.60233i	0.573064	−	0.330859i
$27$		0			0
$28$		0			0
$29$			15.5563i			0.536426i	0.963360	+	0.268213i	$0.0864331\pi$
$29$			15.5563i			0.536426i	−0.963360	+	0.268213i	$0.913567\pi$
$30$		0			0
$31$	12.1655	−	21.0713i	0.392436	−	0.679720i	−0.600334	−	0.799749i	$-0.704966\pi$
$31$	12.1655	−	21.0713i	0.392436	−	0.679720i	0.992770	+	0.120030i	$0.0382990\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$		0			0
$34$	36.4966			1.07343
$35$		0			0
$36$		0			0
$37$	3.00000	+	5.19615i	0.0810811	+	0.140437i	0.903715	−	0.428135i	$-0.140829\pi$
$37$	3.00000	+	5.19615i	0.0810811	+	0.140437i	−0.822633	+	0.568572i	$0.807496\pi$
$38$	29.7993	+	17.2047i	0.784193	+	0.452754i
$39$		0			0
$40$	12.1655	+	21.0713i	0.304138	+	0.526783i
$41$			25.8070i			0.629438i	0.949185	+	0.314719i	$0.101910\pi$
$41$			25.8070i			0.629438i	−0.949185	+	0.314719i	$0.898090\pi$
$42$		0			0
$43$	−68.0000			−1.58140			−0.790698	−	0.612207i	$-0.790282\pi$
$43$	−68.0000			−1.58140			−0.790698	+	0.612207i	$0.790282\pi$
$44$	−4.89898	+	2.82843i	−0.111340	+	0.0642824i
$45$		0			0
$46$	30.0000	−	51.9615i	0.652174	−	1.12960i
$47$	−59.5987	+	34.4093i	−1.26806	+	0.732113i	−0.974620	−	0.223866i	$-0.928132\pi$
$47$	−59.5987	+	34.4093i	−1.26806	+	0.732113i	−0.293437	+	0.955979i	$0.594799\pi$
$48$		0			0
$49$		0			0
$50$			69.2965i			1.38593i
$51$		0			0
$52$	−12.1655	+	21.0713i	−0.233952	+	0.405217i
$53$	−35.5176	−	20.5061i	−0.670143	−	0.386907i	0.125988	−	0.992032i	$-0.459790\pi$
$53$	−35.5176	−	20.5061i	−0.670143	−	0.386907i	−0.796131	+	0.605124i	$0.793123\pi$
$54$		0			0
$55$	−24.3311			−0.442383
$56$		0			0
$57$		0			0
$58$	−11.0000	−	19.0526i	−0.189655	−	0.328492i
$59$	59.5987	+	34.4093i	1.01015	+	0.583208i	0.911235	−	0.411888i	$-0.135130\pi$
$59$	59.5987	+	34.4093i	1.01015	+	0.583208i	0.0989121	+	0.995096i	$0.468464\pi$
$60$		0			0
$61$	48.6621	+	84.2852i	0.797739	+	1.38173i	0.921085	+	0.389361i	$0.127304\pi$
$61$	48.6621	+	84.2852i	0.797739	+	1.38173i	−0.123346	+	0.992364i	$0.539362\pi$
$62$			34.4093i			0.554989i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−90.6311	+	52.3259i	−1.39432	+	0.805014i
$66$		0			0
$67$	52.0000	−	90.0666i	0.776119	−	1.34428i	−0.158044	−	0.987432i	$-0.550519\pi$
$67$	52.0000	−	90.0666i	0.776119	−	1.34428i	0.934163	−	0.356846i	$-0.116148\pi$
$68$	−44.6990	+	25.8070i	−0.657338	+	0.379514i
$69$		0			0
$70$		0			0
$71$			70.7107i			0.995925i	0.867199	+	0.497963i	$0.165918\pi$
$71$			70.7107i			0.995925i	−0.867199	+	0.497963i	$0.834082\pi$
$72$		0			0
$73$	30.4138	−	52.6783i	0.416628	−	0.721620i	−0.578970	−	0.815349i	$-0.696545\pi$
$73$	30.4138	−	52.6783i	0.416628	−	0.721620i	0.995598	+	0.0937286i	$0.0298786\pi$
$74$	−7.34847	−	4.24264i	−0.0993036	−	0.0573330i
$75$		0			0
$76$	−48.6621			−0.640291
$77$		0			0
$78$		0			0
$79$	10.0000	+	17.3205i	0.126582	+	0.219247i	0.922350	−	0.386355i	$-0.126266\pi$
$79$	10.0000	+	17.3205i	0.126582	+	0.219247i	−0.795768	+	0.605602i	$0.792933\pi$
$80$	−29.7993	−	17.2047i	−0.372492	−	0.215058i
$81$		0			0
$82$	−18.2483	−	31.6070i	−0.222540	−	0.385451i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$	−222.000			−2.61176
$86$	83.2827	−	48.0833i	0.968403	−	0.559108i
$87$		0			0
$88$	4.00000	−	6.92820i	0.0454545	−	0.0787296i
$89$	81.9482	−	47.3128i	0.920766	−	0.531604i	0.0368865	−	0.999319i	$-0.488256\pi$
$89$	81.9482	−	47.3128i	0.920766	−	0.531604i	0.883879	+	0.467715i	$0.154923\pi$
$90$		0			0
$91$		0			0
$92$			84.8528i			0.922313i
$93$		0			0
$94$	48.6621	−	84.2852i	0.517682	−	0.896651i
$95$	−181.262	−	104.652i	−1.90802	−	1.10160i
$96$		0			0
$97$	158.152			1.63043			0.815216	−	0.579158i	$-0.196618\pi$
$97$	158.152			1.63043			0.815216	+	0.579158i	$0.196618\pi$
$98$		0			0
$99$		0			0
$100$	−49.0000	−	84.8705i	−0.490000	−	0.848705i
$101$	−52.1488	−	30.1081i	−0.516325	−	0.298100i	0.219105	−	0.975701i	$-0.429686\pi$
$101$	−52.1488	−	30.1081i	−0.516325	−	0.298100i	−0.735430	+	0.677601i	$0.763020\pi$
$102$		0			0
$103$	−85.1587	−	147.499i	−0.826783	−	1.43203i	−0.900549	−	0.434755i	$-0.856835\pi$
$103$	−85.1587	−	147.499i	−0.826783	−	1.43203i	0.0737655	−	0.997276i	$-0.476498\pi$
$104$		−	34.4093i		−	0.330859i
$105$		0			0
$106$	58.0000			0.547170
$107$	−17.1464	+	9.89949i	−0.160247	+	0.0925186i	−0.577979	−	0.816052i	$-0.696158\pi$
$107$	−17.1464	+	9.89949i	−0.160247	+	0.0925186i	0.417732	+	0.908570i	$0.362825\pi$
$108$		0			0
$109$	28.0000	−	48.4974i	0.256881	−	0.444930i	−0.708524	−	0.705687i	$-0.750639\pi$
$109$	28.0000	−	48.4974i	0.256881	−	0.444930i	0.965405	+	0.260756i	$0.0839719\pi$
$110$	29.7993	−	17.2047i	0.270903	−	0.156406i
$111$		0			0
$112$		0			0
$113$		−	159.806i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$113$		−	159.806i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$114$		0			0
$115$	−182.483	+	316.070i	−1.58681	+	2.74843i
$116$	26.9444	+	15.5563i	0.232279	+	0.134106i
$117$		0			0
$118$	−97.3242			−0.824781
$119$		0			0
$120$		0			0
$121$	−56.5000	−	97.8609i	−0.466942	−	0.808768i
$122$	−119.197	−	68.8186i	−0.977027	−	0.564087i
$123$		0			0
$124$	−24.3311	−	42.1426i	−0.196218	−	0.339860i
$125$		−	206.456i		−	1.65165i
$126$		0			0
$127$	−76.0000			−0.598425			−0.299213	−	0.954186i	$-0.596724\pi$
$127$	−76.0000			−0.598425			−0.299213	+	0.954186i	$0.596724\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$		0			0
$130$	74.0000	−	128.172i	0.569231	−	0.985937i
$131$	89.3980	−	51.6140i	0.682427	−	0.394000i	−0.118342	−	0.992973i	$-0.537758\pi$
$131$	89.3980	−	51.6140i	0.682427	−	0.394000i	0.800769	+	0.598973i	$0.204424\pi$
$132$		0			0
$133$		0			0
$134$			147.078i			1.09760i
$135$		0			0
$136$	36.4966	−	63.2139i	0.268357	−	0.464808i
$137$	−86.9569	−	50.2046i	−0.634722	−	0.366457i	0.147857	−	0.989009i	$-0.452763\pi$
$137$	−86.9569	−	50.2046i	−0.634722	−	0.366457i	−0.782578	+	0.622552i	$0.786096\pi$
$138$		0			0
$139$	−145.986			−1.05026			−0.525131	−	0.851022i	$-0.675984\pi$
$139$	−145.986			−1.05026			−0.525131	+	0.851022i	$0.675984\pi$
$140$		0			0
$141$		0			0
$142$	−50.0000	−	86.6025i	−0.352113	−	0.609877i
$143$	29.7993	+	17.2047i	0.208387	+	0.120312i
$144$		0			0
$145$	66.9104	+	115.892i	0.461451	+	0.799256i
$146$			86.0233i			0.589200i
$147$		0			0
$148$	12.0000			0.0810811
$149$	35.5176	−	20.5061i	0.238373	−	0.137625i	−0.376056	−	0.926597i	$-0.622720\pi$
$149$	35.5176	−	20.5061i	0.238373	−	0.137625i	0.614429	+	0.788972i	$0.289387\pi$
$150$		0			0
$151$	−80.0000	+	138.564i	−0.529801	+	0.917643i	0.469594	+	0.882882i	$0.344400\pi$
$151$	−80.0000	+	138.564i	−0.529801	+	0.917643i	−0.999396	+	0.0347605i	$0.988933\pi$
$152$	59.5987	−	34.4093i	0.392096	−	0.226377i
$153$		0			0
$154$		0			0
$155$		−	209.304i		−	1.35035i
$156$		0			0
$157$	97.3242	−	168.570i	0.619899	−	1.07370i	−0.369604	−	0.929189i	$-0.620507\pi$
$157$	97.3242	−	168.570i	0.619899	−	1.07370i	0.989504	−	0.144508i	$-0.0461599\pi$
$158$	−24.4949	−	14.1421i	−0.155031	−	0.0895072i
$159$		0			0
$160$	48.6621			0.304138
$161$		0			0
$162$		0			0
$163$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$163$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$164$	44.6990	+	25.8070i	0.272555	+	0.157360i
$165$		0			0
$166$		0			0
$167$			172.047i			1.03022i	0.857125	+	0.515109i	$0.172249\pi$
$167$			172.047i			1.03022i	−0.857125	+	0.515109i	$0.827751\pi$
$168$		0			0
$169$	−21.0000			−0.124260
$170$	271.893	−	156.978i	1.59937	−	0.923398i
$171$		0			0
$172$	−68.0000	+	117.779i	−0.395349	+	0.684764i
$173$	−7.44983	+	4.30116i	−0.0430626	+	0.0248622i	−0.521377	−	0.853327i	$-0.674581\pi$
$173$	−7.44983	+	4.30116i	−0.0430626	+	0.0248622i	0.478314	+	0.878189i	$0.341248\pi$
$174$		0			0
$175$		0			0
$176$			11.3137i			0.0642824i
$177$		0			0
$178$	−66.9104	+	115.892i	−0.375901	+	0.651080i
$179$	−124.924	−	72.1249i	−0.697899	−	0.402932i	0.108665	−	0.994078i	$-0.465342\pi$
$179$	−124.924	−	72.1249i	−0.697899	−	0.402932i	−0.806565	+	0.591146i	$0.798676\pi$
$180$		0			0
$181$	12.1655			0.0672128			0.0336064	−	0.999435i	$-0.489301\pi$
$181$	12.1655			0.0672128			0.0336064	+	0.999435i	$0.489301\pi$
$182$		0			0
$183$		0			0
$184$	−60.0000	−	103.923i	−0.326087	−	0.564799i
$185$	44.6990	+	25.8070i	0.241616	+	0.139497i
$186$		0			0
$187$	36.4966	+	63.2139i	0.195169	+	0.338042i
$188$			137.637i			0.732113i
$189$		0			0
$190$	296.000			1.55789
$191$	−227.803	+	131.522i	−1.19268	+	0.688596i	−0.958914	−	0.283696i	$-0.908439\pi$
$191$	−227.803	+	131.522i	−1.19268	+	0.688596i	−0.233769	+	0.972292i	$0.575106\pi$
$192$		0			0
$193$	−19.0000	+	32.9090i	−0.0984456	+	0.170513i	−0.911041	−	0.412315i	$-0.864720\pi$
$193$	−19.0000	+	32.9090i	−0.0984456	+	0.170513i	0.812596	+	0.582828i	$0.198054\pi$
$194$	−193.696	+	111.830i	−0.998431	+	0.576444i
$195$		0			0
$196$		0			0
$197$		−	165.463i		−	0.839914i	−0.907544	−	0.419957i	$-0.862045\pi$
$197$		−	165.463i		−	0.839914i	0.907544	−	0.419957i	$-0.137955\pi$
$198$		0			0
$199$	121.655	−	210.713i	0.611333	−	1.05886i	−0.379683	−	0.925117i	$-0.623967\pi$
$199$	121.655	−	210.713i	0.611333	−	1.05886i	0.991016	−	0.133743i	$-0.0426997\pi$
$200$	120.025	+	69.2965i	0.600125	+	0.346482i
$201$		0			0
$202$	85.1587			0.421578
$203$		0			0
$204$		0			0
$205$	111.000	+	192.258i	0.541463	+	0.937842i
$206$	208.595	+	120.433i	1.01260	+	0.584624i
$207$		0			0
$208$	24.3311	+	42.1426i	0.116976	+	0.202609i
$209$			68.8186i			0.329276i
$210$		0			0
$211$	44.0000			0.208531			0.104265	−	0.994550i	$-0.466751\pi$
$211$	44.0000			0.208531			0.104265	+	0.994550i	$0.466751\pi$
$212$	−71.0352	+	41.0122i	−0.335072	+	0.193454i
$213$		0			0
$214$	14.0000	−	24.2487i	0.0654206	−	0.113312i
$215$	−506.589	+	292.479i	−2.35623	+	1.36037i
$216$		0			0
$217$		0			0
$218$			79.1960i			0.363284i
$219$		0			0
$220$	−24.3311	+	42.1426i	−0.110596	+	0.191557i
$221$	271.893	+	156.978i	1.23029	+	0.710306i
$222$		0			0
$223$	194.648			0.872863			0.436431	−	0.899738i	$-0.356242\pi$
$223$	194.648			0.872863			0.436431	+	0.899738i	$0.356242\pi$
$224$		0			0
$225$		0			0
$226$	113.000	+	195.722i	0.500000	+	0.866025i
$227$	29.7993	+	17.2047i	0.131275	+	0.0757914i	0.564199	−	0.825639i	$-0.309185\pi$
$227$	29.7993	+	17.2047i	0.131275	+	0.0757914i	−0.432925	+	0.901430i	$0.642518\pi$
$228$		0			0
$229$	6.08276	+	10.5357i	0.0265623	+	0.0460072i	0.879001	−	0.476820i	$-0.158211\pi$
$229$	6.08276	+	10.5357i	0.0265623	+	0.0460072i	−0.852439	+	0.522827i	$0.824877\pi$
$230$		−	516.140i		−	2.24408i
$231$		0			0
$232$	−44.0000			−0.189655
$233$	233.926	−	135.057i	1.00398	−	0.579645i	0.0945533	−	0.995520i	$-0.469858\pi$
$233$	233.926	−	135.057i	1.00398	−	0.579645i	0.909422	+	0.415874i	$0.136524\pi$
$234$		0			0
$235$	−296.000	+	512.687i	−1.25957	+	2.18165i
$236$	119.197	−	68.8186i	0.505073	−	0.291604i
$237$		0			0
$238$		0			0
$239$		−	76.3675i		−	0.319529i	−0.987155	−	0.159765i	$-0.948926\pi$
$239$		−	76.3675i		−	0.319529i	0.987155	−	0.159765i	$-0.0510736\pi$
$240$		0			0
$241$	66.9104	−	115.892i	0.277636	−	0.480880i	−0.693160	−	0.720783i	$-0.743782\pi$
$241$	66.9104	−	115.892i	0.277636	−	0.480880i	0.970797	+	0.239903i	$0.0771156\pi$
$242$	138.396	+	79.9031i	0.571885	+	0.330178i
$243$		0			0
$244$	194.648			0.797739
$245$		0			0
$246$		0			0
$247$	148.000	+	256.344i	0.599190	+	1.03783i
$248$	59.5987	+	34.4093i	0.240317	+	0.138747i
$249$		0			0
$250$	145.986	+	252.856i	0.583945	+	1.01142i
$251$			137.637i			0.548355i	0.961679	+	0.274178i	$0.0884056\pi$
$251$			137.637i			0.548355i	−0.961679	+	0.274178i	$0.911594\pi$
$252$		0			0
$253$	120.000			0.474308
$254$	93.0806	−	53.7401i	0.366459	−	0.211575i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	216.045	−	124.734i	0.840643	−	0.485345i	−0.0168400	−	0.999858i	$-0.505361\pi$
$257$	216.045	−	124.734i	0.840643	−	0.485345i	0.857483	+	0.514513i	$0.172027\pi$
$258$		0			0
$259$		0			0
$260$			209.304i			0.805014i
$261$		0			0
$262$	−72.9932	+	126.428i	−0.278600	+	0.482549i
$263$	203.308	+	117.380i	0.773033	+	0.446311i	0.833955	−	0.551832i	$-0.186071\pi$
$263$	203.308	+	117.380i	0.773033	+	0.446311i	−0.0609226	+	0.998142i	$0.519404\pi$
$264$		0			0
$265$	−352.800			−1.33132
$266$		0			0
$267$		0			0
$268$	−104.000	−	180.133i	−0.388060	−	0.672139i
$269$	−186.246	−	107.529i	−0.692364	−	0.399736i	0.112133	−	0.993693i	$-0.464232\pi$
$269$	−186.246	−	107.529i	−0.692364	−	0.399736i	−0.804497	+	0.593957i	$0.797565\pi$
$270$		0			0
$271$	−158.152	−	273.927i	−0.583586	−	1.01080i	−0.995050	−	0.0993747i	$-0.968316\pi$
$271$	−158.152	−	273.927i	−0.583586	−	1.01080i	0.411464	−	0.911426i	$-0.365018\pi$
$272$			103.228i			0.379514i
$273$		0			0
$274$	142.000			0.518248
$275$	−120.025	+	69.2965i	−0.436455	+	0.251987i
$276$		0			0
$277$	−32.0000	+	55.4256i	−0.115523	+	0.200093i	−0.917989	−	0.396606i	$-0.870188\pi$
$277$	−32.0000	+	55.4256i	−0.115523	+	0.200093i	0.802465	+	0.596699i	$0.203521\pi$
$278$	178.796	−	103.228i	0.643151	−	0.371323i
$279$		0			0
$280$		0			0
$281$		−	462.448i		−	1.64572i	−0.568243	−	0.822861i	$-0.692377\pi$
$281$		−	462.448i		−	1.64572i	0.568243	−	0.822861i	$-0.307623\pi$
$282$		0			0
$283$	12.1655	−	21.0713i	0.0429877	−	0.0744569i	−0.843731	−	0.536766i	$-0.819646\pi$
$283$	12.1655	−	21.0713i	0.0429877	−	0.0744569i	0.886719	+	0.462309i	$0.152979\pi$
$284$	122.474	+	70.7107i	0.431248	+	0.248981i
$285$		0			0
$286$	−48.6621			−0.170147
$287$		0			0
$288$		0			0
$289$	188.500	+	326.492i	0.652249	+	1.12973i
$290$	−163.896	−	94.6256i	−0.565160	−	0.326295i
$291$		0			0
$292$	−60.8276	−	105.357i	−0.208314	−	0.360810i
$293$			283.877i			0.968863i	0.874829	+	0.484431i	$0.160973\pi$
$293$			283.877i			0.968863i	−0.874829	+	0.484431i	$0.839027\pi$
$294$		0			0
$295$	592.000			2.00678
$296$	−14.6969	+	8.48528i	−0.0496518	+	0.0286665i
$297$		0			0
$298$	−29.0000	+	50.2295i	−0.0973154	+	0.168555i
$299$	446.990	−	258.070i	1.49495	−	0.863110i
$300$		0			0
$301$		0			0
$302$		−	226.274i		−	0.749252i
$303$		0			0
$304$	−48.6621	+	84.2852i	−0.160073	+	0.277254i
$305$	725.049	+	418.607i	2.37721	+	1.37248i
$306$		0			0
$307$	−316.304			−1.03031			−0.515153	−	0.857099i	$-0.672265\pi$
$307$	−316.304			−1.03031			−0.515153	+	0.857099i	$0.672265\pi$
$308$		0			0
$309$		0			0
$310$	148.000	+	256.344i	0.477419	+	0.826915i
$311$	−238.395	−	137.637i	−0.766542	−	0.442563i	0.0650975	−	0.997879i	$-0.479264\pi$
$311$	−238.395	−	137.637i	−0.766542	−	0.442563i	−0.831640	+	0.555316i	$0.812597\pi$
$312$		0			0
$313$	−145.986	−	252.856i	−0.466410	−	0.807846i	0.532854	−	0.846207i	$-0.321119\pi$
$313$	−145.986	−	252.856i	−0.466410	−	0.807846i	−0.999264	+	0.0383615i	$0.987786\pi$
$314$			275.274i			0.876670i
$315$		0			0
$316$	40.0000			0.126582
$317$	−290.265	+	167.584i	−0.915661	+	0.528657i	−0.882248	−	0.470785i	$-0.843971\pi$
$317$	−290.265	+	167.584i	−0.915661	+	0.528657i	−0.0334128	+	0.999442i	$0.510638\pi$
$318$		0			0
$319$	22.0000	−	38.1051i	0.0689655	−	0.119452i
$320$	−59.5987	+	34.4093i	−0.186246	+	0.107529i
$321$		0			0
$322$		0			0
$323$			627.911i			1.94400i
$324$		0			0
$325$	−298.055	+	516.247i	−0.917093	+	1.58845i
$326$		0			0
$327$		0			0
$328$	−72.9932			−0.222540
$329$		0			0
$330$		0			0
$331$	194.000	+	336.018i	0.586103	+	1.01516i	0.994737	+	0.102461i	$0.0326718\pi$
$331$	194.000	+	336.018i	0.586103	+	1.01516i	−0.408634	+	0.912698i	$0.633995\pi$
$332$		0			0
$333$		0			0
$334$	−121.655	−	210.713i	−0.364237	−	0.630877i
$335$		−	894.642i		−	2.67057i
$336$		0			0
$337$	−208.000			−0.617211			−0.308605	−	0.951190i	$-0.599862\pi$
$337$	−208.000			−0.617211			−0.308605	+	0.951190i	$0.599862\pi$
$338$	25.7196	−	14.8492i	0.0760936	−	0.0439327i
$339$		0			0
$340$	−222.000	+	384.515i	−0.652941	+	1.13093i
$341$	−59.5987	+	34.4093i	−0.174776	+	0.100907i
$342$		0			0
$343$		0			0
$344$		−	192.333i		−	0.559108i
$345$		0			0
$346$	6.08276	−	10.5357i	0.0175802	−	0.0304499i
$347$	−315.984	−	182.434i	−0.910617	−	0.525745i	−0.0299875	−	0.999550i	$-0.509547\pi$
$347$	−315.984	−	182.434i	−0.910617	−	0.525745i	−0.880630	+	0.473805i	$0.842880\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$		0			0
$351$		0			0
$352$	−8.00000	−	13.8564i	−0.0227273	−	0.0393648i
$353$	22.3495	+	12.9035i	0.0633130	+	0.0365538i	0.531322	−	0.847170i	$-0.321695\pi$
$353$	22.3495	+	12.9035i	0.0633130	+	0.0365538i	−0.468009	+	0.883724i	$0.655029\pi$
$354$		0			0
$355$	304.138	+	526.783i	0.856727	+	1.48389i
$356$		−	189.251i		−	0.531604i
$357$		0			0
$358$	204.000			0.569832
$359$	262.095	−	151.321i	0.730071	−	0.421507i	−0.0883773	−	0.996087i	$-0.528168\pi$
$359$	262.095	−	151.321i	0.730071	−	0.421507i	0.818448	+	0.574581i	$0.194835\pi$
$360$		0			0
$361$	−115.500	+	200.052i	−0.319945	+	0.554160i
$362$	−14.8997	+	8.60233i	−0.0411593	+	0.0237633i
$363$		0			0
$364$		0			0
$365$		−	523.259i		−	1.43359i
$366$		0			0
$367$	194.648	−	337.141i	0.530377	−	0.918640i	−0.468995	−	0.883201i	$-0.655384\pi$
$367$	194.648	−	337.141i	0.530377	−	0.918640i	0.999372	−	0.0354391i	$-0.0112830\pi$
$368$	146.969	+	84.8528i	0.399373	+	0.230578i
$369$		0			0
$370$	−72.9932			−0.197279
$371$		0			0
$372$		0			0
$373$	−353.000	−	611.414i	−0.946381	−	1.63918i	−0.752963	−	0.658063i	$-0.771376\pi$
$373$	−353.000	−	611.414i	−0.946381	−	1.63918i	−0.193418	−	0.981116i	$-0.561957\pi$
$374$	−89.3980	−	51.6140i	−0.239032	−	0.138005i
$375$		0			0
$376$	−97.3242	−	168.570i	−0.258841	−	0.448326i
$377$		−	189.251i		−	0.501992i
$378$		0			0
$379$	708.000			1.86807			0.934037	−	0.357176i	$-0.116261\pi$
$379$	708.000			1.86807			0.934037	+	0.357176i	$0.116261\pi$
$380$	−362.524	+	209.304i	−0.954012	+	0.550799i
$381$		0			0
$382$	186.000	−	322.161i	0.486911	−	0.843355i
$383$	268.194	−	154.842i	0.700245	−	0.404287i	−0.107193	−	0.994238i	$-0.534186\pi$
$383$	268.194	−	154.842i	0.700245	−	0.404287i	0.807439	+	0.589951i	$0.200853\pi$
$384$		0			0
$385$		0			0
$386$		−	53.7401i		−	0.139223i
$387$		0			0
$388$	158.152	−	273.927i	0.407608	−	0.705997i
$389$	113.901	+	65.7609i	0.292805	+	0.169051i	0.639206	−	0.769035i	$-0.279263\pi$
$389$	113.901	+	65.7609i	0.292805	+	0.169051i	−0.346401	+	0.938087i	$0.612596\pi$
$390$		0			0
$391$	1094.90			2.80025
$392$		0			0
$393$		0			0
$394$	117.000	+	202.650i	0.296954	+	0.514340i
$395$	148.997	+	86.0233i	0.377207	+	0.217780i
$396$		0			0
$397$	−48.6621	−	84.2852i	−0.122575	−	0.212305i	0.798208	−	0.602382i	$-0.205782\pi$
$397$	−48.6621	−	84.2852i	−0.122575	−	0.212305i	−0.920782	+	0.390077i	$0.872448\pi$
$398$			344.093i			0.864555i
$399$		0			0
$400$	−196.000			−0.490000
$401$	77.1589	−	44.5477i	0.192416	−	0.111092i	−0.400697	−	0.916211i	$-0.631232\pi$
$401$	77.1589	−	44.5477i	0.192416	−	0.111092i	0.593113	+	0.805119i	$0.297899\pi$
$402$		0			0
$403$	−148.000	+	256.344i	−0.367246	+	0.636088i
$404$	−104.298	+	60.2163i	−0.258163	+	0.149050i
$405$		0			0
$406$		0			0
$407$		−	16.9706i		−	0.0416967i
$408$		0			0
$409$	−273.724	+	474.104i	−0.669253	+	1.15918i	0.308861	+	0.951107i	$0.400052\pi$
$409$	−273.724	+	474.104i	−0.669253	+	1.15918i	−0.978113	+	0.208072i	$0.933281\pi$
$410$	−271.893	−	156.978i	−0.663155	−	0.382872i
$411$		0			0
$412$	−340.635			−0.826783
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−59.5987	−	34.4093i	−0.143266	−	0.0827147i
$417$		0			0
$418$	−48.6621	−	84.2852i	−0.116417	−	0.201639i
$419$			653.777i			1.56033i	0.625576	+	0.780163i	$0.284864\pi$
$419$			653.777i			1.56033i	−0.625576	+	0.780163i	$0.715136\pi$
$420$		0			0
$421$	240.000			0.570071			0.285036	−	0.958517i	$-0.407995\pi$
$421$	240.000			0.570071			0.285036	+	0.958517i	$0.407995\pi$
$422$	−53.8888	+	31.1127i	−0.127699	+	0.0737268i
$423$		0			0
$424$	58.0000	−	100.459i	0.136792	−	0.236931i
$425$	−1095.13	+	632.271i	−2.57677	+	1.48770i
$426$		0			0
$427$		0			0
$428$			39.5980i			0.0925186i
$429$		0			0
$430$	413.628	−	716.424i	0.961925	−	1.66610i
$431$	−12.2474	−	7.07107i	−0.0284164	−	0.0164062i	0.485725	−	0.874112i	$-0.338556\pi$
$431$	−12.2474	−	7.07107i	−0.0284164	−	0.0164062i	−0.514141	+	0.857706i	$0.671889\pi$
$432$		0			0
$433$	389.297			0.899069			0.449534	−	0.893263i	$-0.351590\pi$
$433$	389.297			0.899069			0.449534	+	0.893263i	$0.351590\pi$
$434$		0			0
$435$		0			0
$436$	−56.0000	−	96.9948i	−0.128440	−	0.222465i
$437$	893.980	+	516.140i	2.04572	+	1.18110i
$438$		0			0
$439$	145.986	+	252.856i	0.332543	+	0.575981i	0.983010	−	0.183554i	$-0.0587601\pi$
$439$	145.986	+	252.856i	0.332543	+	0.575981i	−0.650467	+	0.759535i	$0.725427\pi$
$440$		−	68.8186i		−	0.156406i
$441$		0			0
$442$	−444.000			−1.00452
$443$	−22.0454	+	12.7279i	−0.0497639	+	0.0287312i	−0.524676	−	0.851302i	$-0.675813\pi$
$443$	−22.0454	+	12.7279i	−0.0497639	+	0.0287312i	0.474912	+	0.880033i	$0.342480\pi$
$444$		0			0
$445$	407.000	−	704.945i	0.914607	−	1.58415i
$446$	−238.395	+	137.637i	−0.534517	+	0.308604i
$447$		0			0
$448$		0			0
$449$			733.977i			1.63469i	0.576147	+	0.817346i	$0.304556\pi$
$449$			733.977i			1.63469i	−0.576147	+	0.817346i	$0.695444\pi$
$450$		0			0
$451$	36.4966	−	63.2139i	0.0809237	−	0.140164i
$452$	−276.792	−	159.806i	−0.612372	−	0.353553i
$453$		0			0
$454$	−48.6621			−0.107185
$455$		0			0
$456$		0			0
$457$	−136.000	−	235.559i	−0.297593	−	0.515446i	0.677992	−	0.735070i	$-0.262851\pi$
$457$	−136.000	−	235.559i	−0.297593	−	0.515446i	−0.975585	+	0.219623i	$0.929517\pi$
$458$	−14.8997	−	8.60233i	−0.0325320	−	0.0187824i
$459$		0			0
$460$	364.966	+	632.139i	0.793404	+	1.37422i
$461$			490.333i			1.06363i	0.846861	+	0.531814i	$0.178489\pi$
$461$			490.333i			1.06363i	−0.846861	+	0.531814i	$0.821511\pi$
$462$		0			0
$463$	−436.000			−0.941685			−0.470842	−	0.882217i	$-0.656050\pi$
$463$	−436.000			−0.941685			−0.470842	+	0.882217i	$0.656050\pi$
$464$	53.8888	−	31.1127i	0.116140	−	0.0670532i
$465$		0			0
$466$	−191.000	+	330.822i	−0.409871	+	0.709918i
$467$	417.191	−	240.865i	0.893342	−	0.515771i	0.0183077	−	0.999832i	$-0.494172\pi$
$467$	417.191	−	240.865i	0.893342	−	0.515771i	0.875034	+	0.484061i	$0.160839\pi$
$468$		0			0
$469$		0			0
$470$		−	837.214i		−	1.78131i
$471$		0			0
$472$	−97.3242	+	168.570i	−0.206195	+	0.357141i
$473$	166.565	+	96.1665i	0.352147	+	0.203312i
$474$		0			0
$475$	−1192.22			−2.50994
$476$		0			0
$477$		0			0
$478$	54.0000	+	93.5307i	0.112971	+	0.195671i
$479$	89.3980	+	51.6140i	0.186635	+	0.107754i	0.590406	−	0.807106i	$-0.298968\pi$
$479$	89.3980	+	51.6140i	0.186635	+	0.107754i	−0.403772	+	0.914860i	$0.632301\pi$
$480$		0			0
$481$	−36.4966	−	63.2139i	−0.0758765	−	0.131422i
$482$			189.251i			0.392637i
$483$		0			0
$484$	−226.000			−0.466942
$485$	1178.20	−	680.237i	2.42929	−	1.40255i
$486$		0			0
$487$	−116.000	+	200.918i	−0.238193	+	0.412562i	−0.960196	−	0.279328i	$-0.909888\pi$
$487$	−116.000	+	200.918i	−0.238193	+	0.412562i	0.722003	+	0.691890i	$0.243222\pi$
$488$	−238.395	+	137.637i	−0.488514	+	0.282043i
$489$		0			0
$490$		0			0
$491$			449.720i			0.915927i	0.888971	+	0.457963i	$0.151421\pi$
$491$			449.720i			0.915927i	−0.888971	+	0.457963i	$0.848579\pi$
$492$		0			0
$493$	200.731	−	347.677i	0.407163	−	0.705226i
$494$	−362.524	−	209.304i	−0.733855	−	0.423692i
$495$		0			0
$496$	−97.3242			−0.196218
$497$		0			0
$498$		0			0
$499$	−378.000	−	654.715i	−0.757515	−	1.31205i	−0.944114	−	0.329618i	$-0.893080\pi$
$499$	−378.000	−	654.715i	−0.757515	−	1.31205i	0.186599	−	0.982436i	$-0.440253\pi$
$500$	−357.592	−	206.456i	−0.715184	−	0.412912i
$501$		0			0
$502$	−97.3242	−	168.570i	−0.193873	−	0.335798i
$503$		−	550.549i		−	1.09453i	−0.836959	−	0.547265i	$-0.815669\pi$
$503$		−	550.549i		−	1.09453i	0.836959	−	0.547265i	$-0.184331\pi$
$504$		0			0
$505$	−518.000			−1.02574
$506$	−146.969	+	84.8528i	−0.290453	+	0.167693i
$507$		0			0
$508$	−76.0000	+	131.636i	−0.149606	+	0.259126i
$509$	−7.44983	+	4.30116i	−0.0146362	+	0.00845022i	−0.507300	−	0.861769i	$-0.669356\pi$
$509$	−7.44983	+	4.30116i	−0.0146362	+	0.00845022i	0.492664	+	0.870220i	$0.336023\pi$
$510$		0			0
$511$		0			0
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	−176.400	+	305.534i	−0.343191	+	0.594424i
$515$	−1268.84	−	732.563i	−2.46376	−	1.42245i
$516$		0			0
$517$	194.648			0.376496
$518$		0			0
$519$		0			0
$520$	−148.000	−	256.344i	−0.284615	−	0.492968i
$521$	−81.9482	−	47.3128i	−0.157290	−	0.0908115i	0.419289	−	0.907853i	$-0.362279\pi$
$521$	−81.9482	−	47.3128i	−0.157290	−	0.0908115i	−0.576579	+	0.817041i	$0.695613\pi$
$522$		0			0
$523$	462.290	+	800.710i	0.883920	+	1.53099i	0.846947	+	0.531677i	$0.178438\pi$
$523$	462.290	+	800.710i	0.883920	+	1.53099i	0.0369726	+	0.999316i	$0.488229\pi$
$524$		−	206.456i		−	0.394000i
$525$		0			0
$526$	−332.000			−0.631179
$527$	−543.787	+	313.955i	−1.03185	+	0.595741i
$528$		0			0
$529$	635.500	−	1100.72i	1.20132	−	2.08075i
$530$	432.090	−	249.467i	0.815265	−	0.470693i
$531$		0			0
$532$		0			0
$533$		−	313.955i		−	0.589035i
$534$		0			0
$535$	−85.1587	+	147.499i	−0.159175	+	0.275699i
$536$	254.747	+	147.078i	0.475274	+	0.274400i
$537$		0			0
$538$	304.138			0.565313
$539$		0			0
$540$		0			0
$541$	−296.000	−	512.687i	−0.547135	−	0.947666i	−0.998469	−	0.0553105i	$-0.982385\pi$
$541$	−296.000	−	512.687i	−0.547135	−	0.947666i	0.451334	−	0.892355i	$-0.350948\pi$
$542$	387.391	+	223.660i	0.714744	+	0.412658i
$543$		0			0
$544$	−72.9932	−	126.428i	−0.134179	−	0.232404i
$545$		−	481.730i		−	0.883909i
$546$		0			0
$547$	−416.000			−0.760512			−0.380256	−	0.924881i	$-0.624164\pi$
$547$	−416.000			−0.760512			−0.380256	+	0.924881i	$0.624164\pi$
$548$	−173.914	+	100.409i	−0.317361	+	0.183228i
$549$		0			0
$550$	98.0000	−	169.741i	0.178182	−	0.308620i
$551$	327.793	−	189.251i	0.594905	−	0.343469i
$552$		0			0
$553$		0			0
$554$		−	90.5097i		−	0.163375i
$555$		0			0
$556$	−145.986	+	252.856i	−0.262565	+	0.454776i
$557$	268.219	+	154.856i	0.481542	+	0.278019i	0.721059	−	0.692874i	$-0.243656\pi$
$557$	268.219	+	154.856i	0.481542	+	0.278019i	−0.239517	+	0.970892i	$0.576989\pi$
$558$		0			0
$559$	827.256			1.47988
$560$		0			0
$561$		0			0
$562$	327.000	+	566.381i	0.581851	+	1.00779i
$563$	−774.783	−	447.321i	−1.37617	−	0.794531i	−0.384472	−	0.923137i	$-0.625617\pi$
$563$	−774.783	−	447.321i	−1.37617	−	0.794531i	−0.991696	+	0.128606i	$0.958950\pi$
$564$		0			0
$565$	−687.352	−	1190.53i	−1.21655	−	2.10713i
$566$			34.4093i			0.0607938i
$567$		0			0
$568$	−200.000			−0.352113
$569$	635.643	−	366.988i	1.11712	−	0.644971i	0.176458	−	0.984308i	$-0.443536\pi$
$569$	635.643	−	366.988i	1.11712	−	0.644971i	0.940665	+	0.339337i	$0.110203\pi$
$570$		0			0
$571$	−156.000	+	270.200i	−0.273205	+	0.473205i	−0.969681	−	0.244376i	$-0.921417\pi$
$571$	−156.000	+	270.200i	−0.273205	+	0.473205i	0.696476	+	0.717580i	$0.254750\pi$
$572$	59.5987	−	34.4093i	0.104193	−	0.0601561i
$573$		0			0
$574$		0			0
$575$			2078.89i			3.61547i
$576$		0			0
$577$	−97.3242	+	168.570i	−0.168673	+	0.292150i	−0.937953	−	0.346761i	$-0.887281\pi$
$577$	−97.3242	+	168.570i	−0.168673	+	0.292150i	0.769281	+	0.638911i	$0.220615\pi$
$578$	−461.729	−	266.579i	−0.798839	−	0.461210i
$579$		0			0
$580$	267.642			0.461451
$581$		0			0
$582$		0			0
$583$	58.0000	+	100.459i	0.0994854	+	0.172314i
$584$	148.997	+	86.0233i	0.255131	+	0.147300i
$585$		0			0
$586$	−200.731	−	347.677i	−0.342545	−	0.593305i
$587$			447.321i			0.762046i	0.924566	+	0.381023i	$0.124428\pi$
$587$			447.321i			0.762046i	−0.924566	+	0.381023i	$0.875572\pi$
$588$		0			0
$589$	−592.000			−1.00509
$590$	−725.049	+	418.607i	−1.22890	+	0.709504i
$591$		0			0
$592$	12.0000	−	20.7846i	0.0202703	−	0.0351091i
$593$	558.737	−	322.587i	0.942222	−	0.543992i	0.0515656	−	0.998670i	$-0.483579\pi$
$593$	558.737	−	322.587i	0.942222	−	0.543992i	0.890656	+	0.454678i	$0.150246\pi$
$594$		0			0
$595$		0			0
$596$		−	82.0244i		−	0.137625i
$597$		0			0
$598$	−364.966	+	632.139i	−0.610311	+	1.05709i
$599$	−595.226	−	343.654i	−0.993700	−	0.573713i	−0.0873214	−	0.996180i	$-0.527831\pi$
$599$	−595.226	−	343.654i	−0.993700	−	0.573713i	−0.906378	+	0.422468i	$0.861164\pi$
$600$		0			0
$601$	−1070.57			−1.78131			−0.890654	−	0.454682i	$-0.849753\pi$
$601$	−1070.57			−1.78131			−0.890654	+	0.454682i	$0.849753\pi$
$602$		0			0
$603$		0			0
$604$	160.000	+	277.128i	0.264901	+	0.458821i
$605$	−841.831	−	486.031i	−1.39146	−	0.803358i
$606$		0			0
$607$	−364.966	−	632.139i	−0.601262	−	1.04142i	−0.992630	−	0.121182i	$-0.961332\pi$
$607$	−364.966	−	632.139i	−0.601262	−	1.04142i	0.391369	−	0.920234i	$-0.372002\pi$
$608$		−	137.637i		−	0.226377i
$609$		0			0
$610$	−1184.00			−1.94098
$611$	725.049	−	418.607i	1.18666	−	0.685118i
$612$		0			0
$613$	257.000	−	445.137i	0.419250	−	0.726162i	−0.576615	−	0.817016i	$-0.695627\pi$
$613$	257.000	−	445.137i	0.419250	−	0.726162i	0.995864	+	0.0908547i	$0.0289599\pi$
$614$	387.391	−	223.660i	0.630930	−	0.364268i
$615$		0			0
$616$		0			0
$617$		−	202.233i		−	0.327767i	−0.986480	−	0.163884i	$-0.947598\pi$
$617$		−	202.233i		−	0.327767i	0.986480	−	0.163884i	$-0.0524022\pi$
$618$		0			0
$619$	340.635	−	589.997i	0.550298	−	0.953145i	−0.447954	−	0.894056i	$-0.647847\pi$
$619$	340.635	−	589.997i	0.550298	−	0.953145i	0.998253	−	0.0590883i	$-0.0188194\pi$
$620$	−362.524	−	209.304i	−0.584717	−	0.337586i
$621$		0			0
$622$	389.297			0.625879
$623$		0			0
$624$		0			0
$625$	−275.500	−	477.180i	−0.440800	−	0.763488i
$626$	357.592	+	206.456i	0.571233	+	0.329802i
$627$		0			0
$628$	−194.648	−	337.141i	−0.309950	−	0.536849i
$629$		−	154.842i		−	0.246171i
$630$		0			0
$631$	636.000			1.00792			0.503962	−	0.863726i	$-0.331875\pi$
$631$	636.000			1.00792			0.503962	+	0.863726i	$0.331875\pi$
$632$	−48.9898	+	28.2843i	−0.0775155	+	0.0447536i
$633$		0			0
$634$	237.000	−	410.496i	0.373817	−	0.647470i
$635$	−566.187	+	326.888i	−0.891633	+	0.514785i
$636$		0			0
$637$		0			0
$638$			62.2254i			0.0975320i
$639$		0			0
$640$	48.6621	−	84.2852i	0.0760345	−	0.131696i
$641$	−67.3610	−	38.8909i	−0.105087	−	0.0606722i	0.446535	−	0.894766i	$-0.352658\pi$
$641$	−67.3610	−	38.8909i	−0.105087	−	0.0606722i	−0.551623	+	0.834094i	$0.685991\pi$
$642$		0			0
$643$	−510.952			−0.794638			−0.397319	−	0.917681i	$-0.630059\pi$
$643$	−510.952			−0.794638			−0.397319	+	0.917681i	$0.630059\pi$
$644$		0			0
$645$		0			0
$646$	−444.000	−	769.031i	−0.687307	−	1.19045i
$647$	−804.582	−	464.526i	−1.24356	−	0.717968i	−0.273741	−	0.961803i	$-0.588261\pi$
$647$	−804.582	−	464.526i	−1.24356	−	0.717968i	−0.969817	+	0.243835i	$0.921594\pi$
$648$		0			0
$649$	−97.3242	−	168.570i	−0.149960	−	0.259739i
$650$		−	843.028i		−	1.29697i
$651$		0			0
$652$		0			0
$653$	−552.360	+	318.905i	−0.845880	+	0.488369i	−0.859259	−	0.511541i	$-0.829075\pi$
$653$	−552.360	+	318.905i	−0.845880	+	0.488369i	0.0133783	+	0.999911i	$0.495741\pi$
$654$		0			0
$655$	444.000	−	769.031i	0.677863	−	1.17409i
$656$	89.3980	−	51.6140i	0.136277	−	0.0786798i
$657$		0			0
$658$		0			0
$659$			200.818i			0.304732i	0.988324	+	0.152366i	$0.0486892\pi$
$659$			200.818i			0.304732i	−0.988324	+	0.152366i	$0.951311\pi$
$660$		0			0
$661$	−48.6621	+	84.2852i	−0.0736189	+	0.127512i	−0.900485	−	0.434887i	$-0.856788\pi$
$661$	−48.6621	+	84.2852i	−0.0736189	+	0.127512i	0.826866	+	0.562399i	$0.190122\pi$
$662$	−475.201	−	274.357i	−0.717826	−	0.414437i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−330.000	−	571.577i	−0.494753	−	0.856937i
$668$	297.993	+	172.047i	0.446098	+	0.257555i
$669$		0			0
$670$	632.607	+	1095.71i	0.944190	+	1.63539i
$671$		−	275.274i		−	0.410245i
$672$		0			0
$673$	−250.000			−0.371471			−0.185736	−	0.982600i	$-0.559467\pi$
$673$	−250.000			−0.371471			−0.185736	+	0.982600i	$0.559467\pi$
$674$	254.747	−	147.078i	0.377963	−	0.218217i
$675$		0			0
$676$	−21.0000	+	36.3731i	−0.0310651	+	0.0538063i
$677$	290.543	−	167.745i	0.429163	−	0.247777i	−0.269827	−	0.962909i	$-0.586966\pi$
$677$	290.543	−	167.745i	0.429163	−	0.247777i	0.698990	+	0.715131i	$0.253633\pi$
$678$		0			0
$679$		0			0
$680$		−	627.911i		−	0.923398i
$681$		0			0
$682$	48.6621	−	84.2852i	0.0713521	−	0.123585i
$683$	252.297	+	145.664i	0.369396	+	0.213271i	0.673195	−	0.739465i	$-0.264922\pi$
$683$	252.297	+	145.664i	0.369396	+	0.213271i	−0.303799	+	0.952736i	$0.598255\pi$
$684$		0			0
$685$	−863.752			−1.26095
$686$		0			0
$687$		0			0
$688$	136.000	+	235.559i	0.197674	+	0.342382i
$689$	432.090	+	249.467i	0.627127	+	0.362072i
$690$		0			0
$691$	267.642	+	463.569i	0.387325	+	0.670867i	0.992089	−	0.125538i	$-0.0400658\pi$
$691$	267.642	+	463.569i	0.387325	+	0.670867i	−0.604764	+	0.796405i	$0.706732\pi$
$692$			17.2047i			0.0248622i
$693$		0			0
$694$	516.000			0.743516
$695$	−1087.57	+	627.911i	−1.56485	+	0.903469i
$696$		0			0
$697$	333.000	−	576.773i	0.477762	−	0.827508i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			1045.10i			1.49088i	0.666575	+	0.745438i	$0.267760\pi$
$701$			1045.10i			1.49088i	−0.666575	+	0.745438i	$0.732240\pi$
$702$		0			0
$703$	72.9932	−	126.428i	0.103831	−	0.179840i
$704$	19.5959	+	11.3137i	0.0278351	+	0.0160706i
$705$		0			0
$706$	−36.4966			−0.0516949
$707$		0			0
$708$		0			0
$709$	244.000	+	422.620i	0.344147	+	0.596080i	0.985198	−	0.171418i	$-0.0548349\pi$
$709$	244.000	+	422.620i	0.344147	+	0.596080i	−0.641052	+	0.767498i	$0.721502\pi$
$710$	−744.983	−	430.116i	−1.04927	−	0.605798i
$711$		0			0
$712$	133.821	+	231.784i	0.187951	+	0.325540i
$713$			1032.28i			1.44780i
$714$		0			0
$715$	296.000			0.413986
$716$	−249.848	+	144.250i	−0.348950	+	0.201466i
$717$		0			0
$718$	−214.000	+	370.659i	−0.298050	+	0.516238i
$719$	−804.582	+	464.526i	−1.11903	+	0.646072i	−0.941153	−	0.337981i	$-0.890256\pi$
$719$	−804.582	+	464.526i	−1.11903	+	0.646072i	−0.177876	+	0.984053i	$0.556923\pi$
$720$		0			0
$721$		0			0
$722$		−	326.683i		−	0.452470i
$723$		0			0
$724$	12.1655	−	21.0713i	0.0168032	−	0.0291040i
$725$	660.137	+	381.131i	0.910534	+	0.525697i
$726$		0			0
$727$	900.249			1.23831			0.619153	−	0.785270i	$-0.287476\pi$
$727$	900.249			1.23831			0.619153	+	0.785270i	$0.287476\pi$
$728$		0			0
$729$		0			0
$730$	370.000	+	640.859i	0.506849	+	0.877889i
$731$	1519.77	+	877.437i	2.07902	+	1.20032i
$732$		0			0
$733$	577.862	+	1000.89i	0.788353	+	1.36547i	0.926976	+	0.375122i	$0.122399\pi$
$733$	577.862	+	1000.89i	0.788353	+	1.36547i	−0.138623	+	0.990345i	$0.544268\pi$
$734$			550.549i			0.750067i
$735$		0			0
$736$	−240.000			−0.326087
$737$	−254.747	+	147.078i	−0.345654	+	0.199563i
$738$		0			0
$739$	460.000	−	796.743i	0.622463	−	1.07814i	−0.366563	−	0.930393i	$-0.619466\pi$
$739$	460.000	−	796.743i	0.622463	−	1.07814i	0.989026	−	0.147744i	$-0.0472011\pi$
$740$	89.3980	−	51.6140i	0.120808	−	0.0697486i
$741$		0			0
$742$		0			0
$743$			755.190i			1.01641i	0.861237	+	0.508203i	$0.169690\pi$
$743$			755.190i			1.01641i	−0.861237	+	0.508203i	$0.830310\pi$
$744$		0			0
$745$	176.400	−	305.534i	0.236779	−	0.410113i
$746$	864.670	+	499.217i	1.15907	+	0.669192i
$747$		0			0
$748$	145.986			0.195169
$749$		0			0
$750$		0			0
$751$	60.0000	+	103.923i	0.0798935	+	0.138380i	0.903204	−	0.429212i	$-0.141209\pi$
$751$	60.0000	+	103.923i	0.0798935	+	0.138380i	−0.823310	+	0.567591i	$0.807875\pi$
$752$	238.395	+	137.637i	0.317014	+	0.183028i
$753$		0			0
$754$	133.821	+	231.784i	0.177481	+	0.307406i
$755$			1376.37i			1.82301i
$756$		0			0
$757$	−1016.00			−1.34214			−0.671070	−	0.741394i	$-0.734165\pi$
$757$	−1016.00			−1.34214			−0.671070	+	0.741394i	$0.734165\pi$
$758$	−867.119	+	500.632i	−1.14396	+	0.660464i
$759$		0			0
$760$	296.000	−	512.687i	0.389474	−	0.674588i
$761$	−37.2492	+	21.5058i	−0.0489476	+	0.0282599i	−0.524274	−	0.851550i	$-0.675663\pi$
$761$	−37.2492	+	21.5058i	−0.0489476	+	0.0282599i	0.475326	+	0.879809i	$0.342330\pi$
$762$		0			0
$763$		0			0
$764$			526.087i			0.688596i
$765$		0			0
$766$	−218.979	+	379.284i	−0.285874	+	0.495148i
$767$	−725.049	−	418.607i	−0.945305	−	0.545772i
$768$		0			0
$769$	681.269			0.885916			0.442958	−	0.896542i	$-0.353929\pi$
$769$	681.269			0.885916			0.442958	+	0.896542i	$0.353929\pi$
$770$		0			0
$771$		0			0
$772$	38.0000	+	65.8179i	0.0492228	+	0.0852564i
$773$	1005.73	+	580.657i	1.30107	+	0.751173i	0.980588	−	0.196081i	$-0.0628216\pi$
$773$	1005.73	+	580.657i	1.30107	+	0.751173i	0.320483	+	0.947254i	$0.396155\pi$
$774$		0			0
$775$	−596.111	−	1032.49i	−0.769175	−	1.33225i
$776$			447.321i			0.576444i
$777$		0			0
$778$	−186.000			−0.239075
$779$	543.787	−	313.955i	0.698057	−	0.403024i
$780$		0			0
$781$	100.000	−	173.205i	0.128041	−	0.221773i
$782$	−1340.97	+	774.209i	−1.71480	+	0.990037i
$783$		0			0
$784$		0			0
$785$		−	1674.43i		−	2.13303i
$786$		0			0
$787$	−97.3242	+	168.570i	−0.123665	+	0.214194i	−0.921210	−	0.389065i	$-0.872798\pi$
$787$	−97.3242	+	168.570i	−0.123665	+	0.214194i	0.797545	+	0.603259i	$0.206131\pi$
$788$	−286.590	−	165.463i	−0.363693	−	0.209978i
$789$		0			0
$790$	−243.311			−0.307988
$791$		0			0
$792$		0			0
$793$	−592.000	−	1025.37i	−0.746532	−	1.29303i
$794$	119.197	+	68.8186i	0.150123	+	0.0866733i
$795$		0			0
$796$	−243.311	−	421.426i	−0.305666	−	0.529430i
$797$		−	1109.70i		−	1.39235i	−0.717874	−	0.696173i	$-0.754885\pi$
$797$		−	1109.70i		−	1.39235i	0.717874	−	0.696173i	$-0.245115\pi$
$798$		0			0
$799$	1776.00			2.22278
$800$	240.050	−	138.593i	0.300062	−	0.173241i
$801$		0			0
$802$	−63.0000	+	109.119i	−0.0785536	+	0.136059i
$803$	−148.997	+	86.0233i	−0.185550	+	0.107127i
$804$		0			0
$805$		0			0
$806$		−	418.607i		−	0.519364i
$807$		0			0
$808$	85.1587	−	147.499i	0.105394	−	0.182548i
$809$	892.839	+	515.481i	1.10363	+	0.637183i	0.937173	−	0.348865i	$-0.113433\pi$
$809$	892.839	+	515.481i	1.10363	+	0.637183i	0.166460	+	0.986048i	$0.446766\pi$
$810$		0			0
$811$	243.311			0.300013			0.150006	−	0.988685i	$-0.452071\pi$
$811$	243.311			0.300013			0.150006	+	0.988685i	$0.452071\pi$
$812$		0			0
$813$		0			0
$814$	12.0000	+	20.7846i	0.0147420	+	0.0255339i
$815$		0			0
$816$		0			0
$817$	827.256	+	1432.85i	1.01255	+	1.75379i
$818$		−	774.209i		−	0.946466i
$819$		0			0
$820$	444.000			0.541463
$821$	−309.860	+	178.898i	−0.377418	+	0.217903i	−0.676694	−	0.736264i	$-0.736588\pi$
$821$	−309.860	+	178.898i	−0.377418	+	0.217903i	0.299276	+	0.954167i	$0.403255\pi$
$822$		0			0
$823$	−614.000	+	1063.48i	−0.746051	+	1.29220i	0.203651	+	0.979044i	$0.434719\pi$
$823$	−614.000	+	1063.48i	−0.746051	+	1.29220i	−0.949702	+	0.313155i	$0.898614\pi$
$824$	417.191	−	240.865i	0.506299	−	0.292312i
$825$		0			0
$826$		0			0
$827$			195.161i			0.235987i	0.993014	+	0.117994i	$0.0376462\pi$
$827$			195.161i			0.235987i	−0.993014	+	0.117994i	$0.962354\pi$
$828$		0			0
$829$	395.380	−	684.817i	0.476936	−	0.826077i	−0.522715	−	0.852507i	$-0.675081\pi$
$829$	395.380	−	684.817i	0.476936	−	0.826077i	0.999651	+	0.0264308i	$0.00841418\pi$
$830$		0			0
$831$		0			0
$832$	97.3242			0.116976
$833$		0			0
$834$		0			0
$835$	740.000	+	1281.72i	0.886228	+	1.53499i
$836$	119.197	+	68.8186i	0.142581	+	0.0823189i
$837$		0			0
$838$	−462.290	−	800.710i	−0.551659	−	0.955501i
$839$		−	1238.73i		−	1.47644i	−0.674559	−	0.738221i	$-0.735666\pi$
$839$		−	1238.73i		−	1.47644i	0.674559	−	0.738221i	$-0.264334\pi$
$840$		0			0
$841$	599.000			0.712247
$842$	−293.939	+	169.706i	−0.349096	+	0.201551i
$843$		0			0
$844$	44.0000	−	76.2102i	0.0521327	−	0.0902965i
$845$	−156.446	+	90.3244i	−0.185144	+	0.106893i
$846$		0			0
$847$		0			0
$848$			164.049i			0.193454i
$849$		0			0
$850$	894.166	−	1548.74i	1.05196	−	1.82205i
$851$	−220.454	−	127.279i	−0.259053	−	0.149564i
$852$		0			0
$853$	1557.19			1.82554			0.912771	−	0.408472i	$-0.133938\pi$
$853$	1557.19			1.82554			0.912771	+	0.408472i	$0.133938\pi$
$854$		0			0
$855$		0			0
$856$	−28.0000	−	48.4974i	−0.0327103	−	0.0566559i
$857$	−1273.92	−	735.499i	−1.48649	−	0.858225i	−0.486608	−	0.873621i	$-0.661766\pi$
$857$	−1273.92	−	735.499i	−1.48649	−	0.858225i	−0.999881	+	0.0153956i	$0.995099\pi$
$858$		0			0
$859$	−255.476	−	442.497i	−0.297411	−	0.515131i	0.678132	−	0.734940i	$-0.262790\pi$
$859$	−255.476	−	442.497i	−0.297411	−	0.515131i	−0.975543	+	0.219809i	$0.929456\pi$
$860$			1169.92i			1.36037i
$861$		0			0
$862$	20.0000			0.0232019
$863$	−492.347	+	284.257i	−0.570507	+	0.329382i	−0.757352	−	0.653007i	$-0.773507\pi$
$863$	−492.347	+	284.257i	−0.570507	+	0.329382i	0.186845	+	0.982389i	$0.440174\pi$
$864$		0			0
$865$	−37.0000	+	64.0859i	−0.0427746	+	0.0740877i
$866$	−476.789	+	275.274i	−0.550565	+	0.317869i
$867$		0			0
$868$		0			0
$869$		−	56.5685i		−	0.0650961i
$870$		0			0
$871$	−632.607	+	1095.71i	−0.726300	+	1.25799i
$872$	137.171	+	79.1960i	0.157307	+	0.0908211i
$873$		0			0
$874$	−1459.86			−1.67032
$875$		0			0
$876$		0			0
$877$	441.000	+	763.834i	0.502851	+	0.870963i	0.999995	+	0.00329475i	$0.00104875\pi$
$877$	441.000	+	763.834i	0.502851	+	0.870963i	−0.497144	+	0.867668i	$0.665618\pi$
$878$	−357.592	−	206.456i	−0.407280	−	0.235143i
$879$		0			0
$880$	48.6621	+	84.2852i	0.0552978	+	0.0957787i
$881$		−	43.0116i		−	0.0488214i	−0.999702	−	0.0244107i	$-0.992229\pi$
$881$		−	43.0116i		−	0.0488214i	0.999702	−	0.0244107i	$-0.00777093\pi$
$882$		0			0
$883$	−140.000			−0.158550			−0.0792752	−	0.996853i	$-0.525261\pi$
$883$	−140.000			−0.158550			−0.0792752	+	0.996853i	$0.525261\pi$
$884$	543.787	−	313.955i	0.615143	−	0.355153i
$885$		0			0
$886$	18.0000	−	31.1769i	0.0203160	−	0.0351884i
$887$	−268.194	+	154.842i	−0.302361	+	0.174568i	−0.643503	−	0.765444i	$-0.722520\pi$
$887$	−268.194	+	154.842i	−0.302361	+	0.174568i	0.341142	+	0.940012i	$0.389186\pi$
$888$		0			0
$889$		0			0
$890$			1151.17i			1.29345i
$891$		0			0
$892$	194.648	−	337.141i	0.218216	−	0.377961i
$893$	1450.10	+	837.214i	1.62385	+	0.937530i
$894$		0			0
$895$	−1240.88			−1.38646
$896$		0			0
$897$		0			0
$898$	−519.000	−	898.934i	−0.577951	−	1.00104i
$899$	327.793	+	189.251i	0.364619	+	0.210513i
$900$		0			0
$901$	529.200	+	916.602i	0.587348	+	1.01732i
$902$			103.228i			0.114443i
$903$		0			0
$904$	452.000			0.500000
$905$	90.6311	−	52.3259i	0.100145	−	0.0578187i
$906$		0			0
$907$	−614.000	+	1063.48i	−0.676957	+	1.17252i	0.298936	+	0.954273i	$0.403368\pi$
$907$	−614.000	+	1063.48i	−0.676957	+	1.17252i	−0.975893	+	0.218251i	$0.929965\pi$
$908$	59.5987	−	34.4093i	0.0656373	−	0.0378957i
$909$		0			0
$910$		0			0
$911$		−	138.593i		−	0.152133i	−0.997103	−	0.0760664i	$-0.975764\pi$
$911$		−	138.593i		−	0.152133i	0.997103	−	0.0760664i	$-0.0242361\pi$
$912$		0			0
$913$		0			0
$914$	333.131	+	192.333i	0.364475	+	0.210430i
$915$		0			0
$916$	24.3311			0.0265623
$917$		0			0
$918$		0			0
$919$	804.000	+	1392.57i	0.874864	+	1.51531i	0.856908	+	0.515470i	$0.172383\pi$
$919$	804.000	+	1392.57i	0.874864	+	1.51531i	0.0179564	+	0.999839i	$0.494284\pi$
$920$	−893.980	−	516.140i	−0.971717	−	0.561021i
$921$		0			0
$922$	−346.717	−	600.532i	−0.376049	−	0.651337i
$923$		−	860.233i		−	0.931996i
$924$		0			0
$925$	294.000			0.317838
$926$	533.989	−	308.299i	0.576662	−	0.332936i
$927$		0			0
$928$	−44.0000	+	76.2102i	−0.0474138	+	0.0821231i
$929$	1229.22	−	709.692i	1.32317	−	0.763931i	0.338935	−	0.940810i	$-0.389933\pi$
$929$	1229.22	−	709.692i	1.32317	−	0.763931i	0.984233	+	0.176879i	$0.0566001\pi$
$930$		0			0
$931$		0			0
$932$		−	540.230i		−	0.579645i
$933$		0			0
$934$	−340.635	+	589.997i	−0.364705	+	0.631688i
$935$	543.787	+	313.955i	0.581590	+	0.335781i
$936$		0			0
$937$	291.973			0.311604			0.155802	−	0.987788i	$-0.450204\pi$
$937$	291.973			0.311604			0.155802	+	0.987788i	$0.450204\pi$
$938$		0			0
$939$		0			0
$940$	592.000	+	1025.37i	0.629787	+	1.09082i
$941$	−1184.52	−	683.885i	−1.25879	−	0.726764i	−0.285952	−	0.958244i	$-0.592310\pi$
$941$	−1184.52	−	683.885i	−1.25879	−	0.726764i	−0.972840	+	0.231480i	$0.925643\pi$
$942$		0			0
$943$	−547.449	−	948.209i	−0.580539	−	1.00552i
$944$		−	275.274i		−	0.291604i
$945$		0			0
$946$	−272.000			−0.287526
$947$	−511.943	+	295.571i	−0.540595	+	0.312113i	−0.745320	−	0.666707i	$-0.767703\pi$
$947$	−511.943	+	295.571i	−0.540595	+	0.312113i	0.204725	+	0.978820i	$0.434370\pi$
$948$		0			0
$949$	−370.000	+	640.859i	−0.389884	+	0.675299i
$950$	1460.17	−	843.028i	1.53702	−	0.887398i
$951$		0			0
$952$		0			0
$953$			352.139i			0.369506i	0.982785	+	0.184753i	$0.0591485\pi$
$953$			352.139i			0.369506i	−0.982785	+	0.184753i	$0.940851\pi$
$954$		0			0
$955$	−1131.39	+	1959.63i	−1.18471	+	2.05197i
$956$	−132.272	−	76.3675i	−0.138360	−	0.0798824i
$957$		0			0
$958$	−145.986			−0.152387
$959$		0			0
$960$		0			0
$961$	184.500	+	319.563i	0.191988	+	0.332532i
$962$	89.3980	+	51.6140i	0.0929293	+	0.0536528i
$963$		0			0
$964$	−133.821	−	231.784i	−0.138818	−	0.240440i
$965$			326.888i			0.338744i
$966$		0			0
$967$	−260.000			−0.268873			−0.134436	−	0.990922i	$-0.542922\pi$
$967$	−260.000			−0.268873			−0.134436	+	0.990922i	$0.542922\pi$
$968$	276.792	−	159.806i	0.285943	−	0.165089i
$969$		0			0
$970$	−962.000	+	1666.23i	−0.991753	+	1.71777i
$971$	1281.37	−	739.800i	1.31964	−	0.761895i	0.335970	−	0.941873i	$-0.390936\pi$
$971$	1281.37	−	739.800i	1.31964	−	0.761895i	0.983671	+	0.179978i	$0.0576026\pi$
$972$		0			0
$973$		0			0
$974$		−	328.098i		−	0.336856i
$975$		0			0
$976$	194.648	−	337.141i	0.199435	−	0.345431i
$977$	−285.366	−	164.756i	−0.292083	−	0.168634i	0.346798	−	0.937940i	$-0.387269\pi$
$977$	−285.366	−	164.756i	−0.292083	−	0.168634i	−0.638881	+	0.769306i	$0.720602\pi$
$978$		0			0
$979$	−267.642			−0.273383
$980$		0			0
$981$		0			0
$982$	−318.000	−	550.792i	−0.323829	−	0.560888i
$983$	864.181	+	498.935i	0.879126	+	0.507563i	0.870370	−	0.492398i	$-0.163880\pi$
$983$	864.181	+	498.935i	0.879126	+	0.507563i	0.00875564	+	0.999962i	$0.497213\pi$
$984$		0			0
$985$	−711.683	−	1232.67i	−0.722521	−	1.25144i
$986$			567.753i			0.575815i
$987$		0			0
$988$	592.000			0.599190
$989$	2498.48	−	1442.50i	2.52627	−	1.45854i
$990$		0			0
$991$	−748.000	+	1295.57i	−0.754793	+	1.30734i	0.190684	+	0.981651i	$0.438929\pi$
$991$	−748.000	+	1295.57i	−0.754793	+	1.30734i	−0.945477	+	0.325689i	$0.894404\pi$
$992$	119.197	−	68.8186i	0.120159	−	0.0693736i
$993$		0			0
$994$		0			0
$995$		−	2093.04i		−	2.10355i
$996$		0			0
$997$	−778.594	+	1348.56i	−0.780936	+	1.35262i	0.150460	+	0.988616i	$0.451924\pi$
$997$	−778.594	+	1348.56i	−0.780936	+	1.35262i	−0.931397	+	0.364006i	$0.881409\pi$
$998$	925.907	+	534.573i	0.927763	+	0.535644i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.3.s.h.557.2		8
3.2	odd	2	inner	882.3.s.h.557.3		8
7.2	even	3	inner	882.3.s.h.863.3		8
7.3	odd	6		882.3.b.g.197.1	✓	4
7.4	even	3		882.3.b.g.197.2	yes	4
7.5	odd	6	inner	882.3.s.h.863.4		8
7.6	odd	2	inner	882.3.s.h.557.1		8
21.2	odd	6	inner	882.3.s.h.863.2		8
21.5	even	6	inner	882.3.s.h.863.1		8
21.11	odd	6		882.3.b.g.197.3	yes	4
21.17	even	6		882.3.b.g.197.4	yes	4
21.20	even	2	inner	882.3.s.h.557.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.3.b.g.197.1	✓	4	7.3	odd	6
882.3.b.g.197.2	yes	4	7.4	even	3
882.3.b.g.197.3	yes	4	21.11	odd	6
882.3.b.g.197.4	yes	4	21.17	even	6
882.3.s.h.557.1		8	7.6	odd	2	inner
882.3.s.h.557.2		8	1.1	even	1	trivial
882.3.s.h.557.3		8	3.2	odd	2	inner
882.3.s.h.557.4		8	21.20	even	2	inner
882.3.s.h.863.1		8	21.5	even	6	inner
882.3.s.h.863.2		8	21.2	odd	6	inner
882.3.s.h.863.3		8	7.2	even	3	inner
882.3.s.h.863.4		8	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	882.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.44983 - 4.30116i) q^{5} +2.82843i q^{8} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.44983 - 4.30116i) q^{5} +2.82843i q^{8} +(-6.08276 + 10.5357i) q^{10} +(-2.44949 - 1.41421i) q^{11} -12.1655 q^{13} +(-2.00000 - 3.46410i) q^{16} +(-22.3495 - 12.9035i) q^{17} +(-12.1655 - 21.0713i) q^{19} -17.2047i q^{20} +4.00000 q^{22} +(-36.7423 + 21.2132i) q^{23} +(24.5000 - 42.4352i) q^{25} +(14.8997 - 8.60233i) q^{26} +15.5563i q^{29} +(12.1655 - 21.0713i) q^{31} +(4.89898 + 2.82843i) q^{32} +36.4966 q^{34} +(3.00000 + 5.19615i) q^{37} +(29.7993 + 17.2047i) q^{38} +(12.1655 + 21.0713i) q^{40} +25.8070i q^{41} -68.0000 q^{43} +(-4.89898 + 2.82843i) q^{44} +(30.0000 - 51.9615i) q^{46} +(-59.5987 + 34.4093i) q^{47} +69.2965i q^{50} +(-12.1655 + 21.0713i) q^{52} +(-35.5176 - 20.5061i) q^{53} -24.3311 q^{55} +(-11.0000 - 19.0526i) q^{58} +(59.5987 + 34.4093i) q^{59} +(48.6621 + 84.2852i) q^{61} +34.4093i q^{62} -8.00000 q^{64} +(-90.6311 + 52.3259i) q^{65} +(52.0000 - 90.0666i) q^{67} +(-44.6990 + 25.8070i) q^{68} +70.7107i q^{71} +(30.4138 - 52.6783i) q^{73} +(-7.34847 - 4.24264i) q^{74} -48.6621 q^{76} +(10.0000 + 17.3205i) q^{79} +(-29.7993 - 17.2047i) q^{80} +(-18.2483 - 31.6070i) q^{82} -222.000 q^{85} +(83.2827 - 48.0833i) q^{86} +(4.00000 - 6.92820i) q^{88} +(81.9482 - 47.3128i) q^{89} +84.8528i q^{92} +(48.6621 - 84.2852i) q^{94} +(-181.262 - 104.652i) q^{95} +158.152 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4}+O(q^{10}) \) 8 * q + 8 * q^4	\( 8 q + 8 q^{4} - 16 q^{16} + 32 q^{22} + 196 q^{25} + 24 q^{37} - 544 q^{43} + 240 q^{46} - 88 q^{58} - 64 q^{64} + 416 q^{67} + 80 q^{79} - 1776 q^{85} + 32 q^{88}+O(q^{100}) \) 8 * q + 8 * q^4 - 16 * q^16 + 32 * q^22 + 196 * q^25 + 24 * q^37 - 544 * q^43 + 240 * q^46 - 88 * q^58 - 64 * q^64 + 416 * q^67 + 80 * q^79 - 1776 * q^85 + 32 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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