LMFDB - Embedded newform 882.3.s.h.863.1

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			863.1
Root			$-3.76613 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	882.863
Dual form			882.3.s.h.557.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-7.44983 - 4.30116i) q^{5} -2.82843i q^{8} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-7.44983 - 4.30116i) q^{5} -2.82843i q^{8} +(6.08276 + 10.5357i) q^{10} +(-2.44949 + 1.41421i) q^{11} +12.1655 q^{13} +(-2.00000 + 3.46410i) q^{16} +(22.3495 - 12.9035i) q^{17} +(12.1655 - 21.0713i) q^{19} -17.2047i q^{20} +4.00000 q^{22} +(-36.7423 - 21.2132i) q^{23} +(24.5000 + 42.4352i) q^{25} +(-14.8997 - 8.60233i) q^{26} -15.5563i q^{29} +(-12.1655 - 21.0713i) q^{31} +(4.89898 - 2.82843i) q^{32} -36.4966 q^{34} +(3.00000 - 5.19615i) q^{37} +(-29.7993 + 17.2047i) q^{38} +(-12.1655 + 21.0713i) q^{40} +25.8070i q^{41} -68.0000 q^{43} +(-4.89898 - 2.82843i) q^{44} +(30.0000 + 51.9615i) q^{46} +(59.5987 + 34.4093i) q^{47} -69.2965i q^{50} +(12.1655 + 21.0713i) q^{52} +(-35.5176 + 20.5061i) q^{53} +24.3311 q^{55} +(-11.0000 + 19.0526i) q^{58} +(-59.5987 + 34.4093i) q^{59} +(-48.6621 + 84.2852i) q^{61} +34.4093i q^{62} -8.00000 q^{64} +(-90.6311 - 52.3259i) q^{65} +(52.0000 + 90.0666i) q^{67} +(44.6990 + 25.8070i) q^{68} -70.7107i q^{71} +(-30.4138 - 52.6783i) q^{73} +(-7.34847 + 4.24264i) q^{74} +48.6621 q^{76} +(10.0000 - 17.3205i) q^{79} +(29.7993 - 17.2047i) q^{80} +(18.2483 - 31.6070i) q^{82} -222.000 q^{85} +(83.2827 + 48.0833i) q^{86} +(4.00000 + 6.92820i) q^{88} +(-81.9482 - 47.3128i) q^{89} -84.8528i q^{92} +(-48.6621 - 84.2852i) q^{94} +(-181.262 + 104.652i) q^{95} -158.152 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

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

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	$-0.663015\pi$
$5$	−7.44983	−	4.30116i	−1.48997	−	0.860233i	−0.999934	+	0.0114718i	$0.996348\pi$
$6$		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	−0.607191	−	0.794556i	$-0.707704\pi$
$11$	−2.44949	+	1.41421i	−0.222681	+	0.128565i	0.384510	+	0.923121i	$0.374370\pi$
$12$		0			0
$13$	12.1655			0.935810			0.467905	−	0.883779i	$-0.345009\pi$
$13$	12.1655			0.935810			0.467905	+	0.883779i	$0.345009\pi$
$14$		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	$-0.392341\pi$
$17$	22.3495	−	12.9035i	1.31468	−	0.759029i	0.982867	+	0.184318i	$0.0590075\pi$
$18$		0			0
$19$	12.1655	−	21.0713i	0.640291	−	1.10902i	−0.345077	−	0.938574i	$-0.612147\pi$
$19$	12.1655	−	21.0713i	0.640291	−	1.10902i	0.985368	−	0.170442i	$-0.0545195\pi$
$20$		−	17.2047i		−	0.860233i
$21$		0			0
$22$	4.00000			0.181818
$23$	−36.7423	−	21.2132i	−1.59749	−	0.922313i	−0.991968	−	0.126487i	$-0.959630\pi$
$23$	−36.7423	−	21.2132i	−1.59749	−	0.922313i	−0.605525	−	0.795826i	$-0.707037\pi$
$24$		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	$-0.913567\pi$
$29$		−	15.5563i		−	0.536426i	0.963360	−	0.268213i	$-0.0864331\pi$
$30$		0			0
$31$	−12.1655	−	21.0713i	−0.392436	−	0.679720i	0.600334	−	0.799749i	$-0.295034\pi$
$31$	−12.1655	−	21.0713i	−0.392436	−	0.679720i	−0.992770	+	0.120030i	$0.961701\pi$
$32$	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	−0.822633	−	0.568572i	$-0.807496\pi$
$37$	3.00000	−	5.19615i	0.0810811	−	0.140437i	0.903715	+	0.428135i	$0.140829\pi$
$38$	−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	$-0.0718677\pi$
$47$	59.5987	+	34.4093i	1.26806	+	0.732113i	0.293437	+	0.955979i	$0.405201\pi$
$48$		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	−0.796131	−	0.605124i	$-0.793123\pi$
$53$	−35.5176	+	20.5061i	−0.670143	+	0.386907i	0.125988	+	0.992032i	$0.459790\pi$
$54$		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	$-0.864870\pi$
$59$	−59.5987	+	34.4093i	−1.01015	+	0.583208i	−0.0989121	+	0.995096i	$0.531536\pi$
$60$		0			0
$61$	−48.6621	+	84.2852i	−0.797739	+	1.38173i	0.123346	+	0.992364i	$0.460638\pi$
$61$	−48.6621	+	84.2852i	−0.797739	+	1.38173i	−0.921085	+	0.389361i	$0.872696\pi$
$62$			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	0.934163	+	0.356846i	$0.116148\pi$
$67$	52.0000	+	90.0666i	0.776119	+	1.34428i	−0.158044	+	0.987432i	$0.550519\pi$
$68$	44.6990	+	25.8070i	0.657338	+	0.379514i
$69$		0			0
$70$		0			0
$71$		−	70.7107i		−	0.995925i	−0.867199	−	0.497963i	$-0.834082\pi$
$71$		−	70.7107i		−	0.995925i	0.867199	−	0.497963i	$-0.165918\pi$
$72$		0			0
$73$	−30.4138	−	52.6783i	−0.416628	−	0.721620i	0.578970	−	0.815349i	$-0.303455\pi$
$73$	−30.4138	−	52.6783i	−0.416628	−	0.721620i	−0.995598	+	0.0937286i	$0.970121\pi$
$74$	−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	−0.795768	−	0.605602i	$-0.792933\pi$
$79$	10.0000	−	17.3205i	0.126582	−	0.219247i	0.922350	+	0.386355i	$0.126266\pi$
$80$	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	$-0.511744\pi$
$89$	−81.9482	−	47.3128i	−0.920766	−	0.531604i	−0.883879	+	0.467715i	$0.845077\pi$
$90$		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	$-0.803382\pi$
$97$	−158.152			−1.63043			−0.815216	+	0.579158i	$0.803382\pi$
$98$		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	$-0.570314\pi$
$101$	52.1488	−	30.1081i	0.516325	−	0.298100i	0.735430	+	0.677601i	$0.236980\pi$
$102$		0			0
$103$	85.1587	−	147.499i	0.826783	−	1.43203i	−0.0737655	−	0.997276i	$-0.523502\pi$
$103$	85.1587	−	147.499i	0.826783	−	1.43203i	0.900549	−	0.434755i	$-0.143165\pi$
$104$		−	34.4093i		−	0.330859i
$105$		0			0
$106$	58.0000			0.547170
$107$	−17.1464	−	9.89949i	−0.160247	−	0.0925186i	0.417732	−	0.908570i	$-0.362825\pi$
$107$	−17.1464	−	9.89949i	−0.160247	−	0.0925186i	−0.577979	+	0.816052i	$0.696158\pi$
$108$		0			0
$109$	28.0000	+	48.4974i	0.256881	+	0.444930i	0.965405	−	0.260756i	$-0.0839719\pi$
$109$	28.0000	+	48.4974i	0.256881	+	0.444930i	−0.708524	+	0.705687i	$0.750639\pi$
$110$	−29.7993	−	17.2047i	−0.270903	−	0.156406i
$111$		0			0
$112$		0			0
$113$			159.806i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$113$			159.806i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$114$		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	$-0.462242\pi$
$131$	−89.3980	−	51.6140i	−0.682427	−	0.394000i	−0.800769	+	0.598973i	$0.795576\pi$
$132$		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	−0.782578	−	0.622552i	$-0.786096\pi$
$137$	−86.9569	+	50.2046i	−0.634722	+	0.366457i	0.147857	+	0.989009i	$0.452763\pi$
$138$		0			0
$139$	145.986			1.05026			0.525131	−	0.851022i	$-0.324016\pi$
$139$	145.986			1.05026			0.525131	+	0.851022i	$0.324016\pi$
$140$		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	0.614429	−	0.788972i	$-0.289387\pi$
$149$	35.5176	+	20.5061i	0.238373	+	0.137625i	−0.376056	+	0.926597i	$0.622720\pi$
$150$		0			0
$151$	−80.0000	−	138.564i	−0.529801	−	0.917643i	−0.999396	−	0.0347605i	$-0.988933\pi$
$151$	−80.0000	−	138.564i	−0.529801	−	0.917643i	0.469594	−	0.882882i	$-0.344400\pi$
$152$	−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	−0.989504	−	0.144508i	$-0.953840\pi$
$157$	−97.3242	−	168.570i	−0.619899	−	1.07370i	0.369604	−	0.929189i	$-0.379493\pi$
$158$	−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	$-0.833333\pi$
$163$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$164$	−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	$-0.325419\pi$
$173$	7.44983	+	4.30116i	0.0430626	+	0.0248622i	−0.478314	+	0.878189i	$0.658752\pi$
$174$		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	−0.806565	−	0.591146i	$-0.798676\pi$
$179$	−124.924	+	72.1249i	−0.697899	+	0.402932i	0.108665	+	0.994078i	$0.465342\pi$
$180$		0			0
$181$	−12.1655			−0.0672128			−0.0336064	−	0.999435i	$-0.510699\pi$
$181$	−12.1655			−0.0672128			−0.0336064	+	0.999435i	$0.510699\pi$
$182$		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	−0.233769	−	0.972292i	$-0.575106\pi$
$191$	−227.803	−	131.522i	−1.19268	−	0.688596i	−0.958914	+	0.283696i	$0.908439\pi$
$192$		0			0
$193$	−19.0000	−	32.9090i	−0.0984456	−	0.170513i	0.812596	−	0.582828i	$-0.198054\pi$
$193$	−19.0000	−	32.9090i	−0.0984456	−	0.170513i	−0.911041	+	0.412315i	$0.864720\pi$
$194$	193.696	+	111.830i	0.998431	+	0.576444i
$195$		0			0
$196$		0			0
$197$			165.463i			0.839914i	0.907544	+	0.419957i	$0.137955\pi$
$197$			165.463i			0.839914i	−0.907544	+	0.419957i	$0.862045\pi$
$198$		0			0
$199$	−121.655	−	210.713i	−0.611333	−	1.05886i	−0.991016	−	0.133743i	$-0.957300\pi$
$199$	−121.655	−	210.713i	−0.611333	−	1.05886i	0.379683	−	0.925117i	$-0.376033\pi$
$200$	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	$-0.643758\pi$
$223$	−194.648			−0.872863			−0.436431	+	0.899738i	$0.643758\pi$
$224$		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	$-0.690815\pi$
$227$	−29.7993	+	17.2047i	−0.131275	+	0.0757914i	0.432925	+	0.901430i	$0.357482\pi$
$228$		0			0
$229$	−6.08276	+	10.5357i	−0.0265623	+	0.0460072i	−0.879001	−	0.476820i	$-0.841789\pi$
$229$	−6.08276	+	10.5357i	−0.0265623	+	0.0460072i	0.852439	+	0.522827i	$0.175123\pi$
$230$		−	516.140i		−	2.24408i
$231$		0			0
$232$	−44.0000			−0.189655
$233$	233.926	+	135.057i	1.00398	+	0.579645i	0.909422	−	0.415874i	$-0.136524\pi$
$233$	233.926	+	135.057i	1.00398	+	0.579645i	0.0945533	+	0.995520i	$0.469858\pi$
$234$		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	$0.0510736\pi$
$239$			76.3675i			0.319529i	−0.987155	+	0.159765i	$0.948926\pi$
$240$		0			0
$241$	−66.9104	−	115.892i	−0.277636	−	0.480880i	0.693160	−	0.720783i	$-0.256218\pi$
$241$	−66.9104	−	115.892i	−0.277636	−	0.480880i	−0.970797	+	0.239903i	$0.922884\pi$
$242$	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	$-0.494639\pi$
$257$	−216.045	−	124.734i	−0.840643	−	0.485345i	−0.857483	+	0.514513i	$0.827973\pi$
$258$		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	−0.0609226	−	0.998142i	$-0.519404\pi$
$263$	203.308	−	117.380i	0.773033	−	0.446311i	0.833955	+	0.551832i	$0.186071\pi$
$264$		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	$-0.535768\pi$
$269$	186.246	−	107.529i	0.692364	−	0.399736i	0.804497	+	0.593957i	$0.202435\pi$
$270$		0			0
$271$	158.152	−	273.927i	0.583586	−	1.01080i	−0.411464	−	0.911426i	$-0.634982\pi$
$271$	158.152	−	273.927i	0.583586	−	1.01080i	0.995050	−	0.0993747i	$-0.0316843\pi$
$272$			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	0.802465	−	0.596699i	$-0.203521\pi$
$277$	−32.0000	−	55.4256i	−0.115523	−	0.200093i	−0.917989	+	0.396606i	$0.870188\pi$
$278$	−178.796	−	103.228i	−0.643151	−	0.371323i
$279$		0			0
$280$		0			0
$281$			462.448i			1.64572i	0.568243	+	0.822861i	$0.307623\pi$
$281$			462.448i			1.64572i	−0.568243	+	0.822861i	$0.692377\pi$
$282$		0			0
$283$	−12.1655	−	21.0713i	−0.0429877	−	0.0744569i	0.843731	−	0.536766i	$-0.180354\pi$
$283$	−12.1655	−	21.0713i	−0.0429877	−	0.0744569i	−0.886719	+	0.462309i	$0.847021\pi$
$284$	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	$-0.327735\pi$
$307$	316.304			1.03031			0.515153	+	0.857099i	$0.327735\pi$
$308$		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	$-0.520736\pi$
$311$	238.395	−	137.637i	0.766542	−	0.442563i	0.831640	+	0.555316i	$0.187403\pi$
$312$		0			0
$313$	145.986	−	252.856i	0.466410	−	0.807846i	−0.532854	−	0.846207i	$-0.678881\pi$
$313$	145.986	−	252.856i	0.466410	−	0.807846i	0.999264	+	0.0383615i	$0.0122139\pi$
$314$			275.274i			0.876670i
$315$		0			0
$316$	40.0000			0.126582
$317$	−290.265	−	167.584i	−0.915661	−	0.528657i	−0.0334128	−	0.999442i	$-0.510638\pi$
$317$	−290.265	−	167.584i	−0.915661	−	0.528657i	−0.882248	+	0.470785i	$0.843971\pi$
$318$		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	−0.408634	−	0.912698i	$-0.633995\pi$
$331$	194.000	−	336.018i	0.586103	−	1.01516i	0.994737	−	0.102461i	$-0.0326718\pi$
$332$		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	−0.880630	−	0.473805i	$-0.842880\pi$
$347$	−315.984	+	182.434i	−0.910617	+	0.525745i	−0.0299875	+	0.999550i	$0.509547\pi$
$348$		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	$-0.678305\pi$
$353$	−22.3495	+	12.9035i	−0.0633130	+	0.0365538i	0.468009	+	0.883724i	$0.344971\pi$
$354$		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	0.818448	−	0.574581i	$-0.194835\pi$
$359$	262.095	+	151.321i	0.730071	+	0.421507i	−0.0883773	+	0.996087i	$0.528168\pi$
$360$		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	−0.999372	−	0.0354391i	$-0.988717\pi$
$367$	−194.648	−	337.141i	−0.530377	−	0.918640i	0.468995	−	0.883201i	$-0.344616\pi$
$368$	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	−0.193418	+	0.981116i	$0.561957\pi$
$373$	−353.000	+	611.414i	−0.946381	+	1.63918i	−0.752963	+	0.658063i	$0.771376\pi$
$374$	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	$-0.465814\pi$
$383$	−268.194	−	154.842i	−0.700245	−	0.404287i	−0.807439	+	0.589951i	$0.799147\pi$
$384$		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	−0.346401	−	0.938087i	$-0.612596\pi$
$389$	113.901	−	65.7609i	0.292805	−	0.169051i	0.639206	+	0.769035i	$0.279263\pi$
$390$		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	$-0.794218\pi$
$397$	48.6621	−	84.2852i	0.122575	−	0.212305i	0.920782	+	0.390077i	$0.127552\pi$
$398$			344.093i			0.864555i
$399$		0			0
$400$	−196.000			−0.490000
$401$	77.1589	+	44.5477i	0.192416	+	0.111092i	0.593113	−	0.805119i	$-0.297899\pi$
$401$	77.1589	+	44.5477i	0.192416	+	0.111092i	−0.400697	+	0.916211i	$0.631232\pi$
$402$		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	0.978113	+	0.208072i	$0.0667189\pi$
$409$	273.724	+	474.104i	0.669253	+	1.15918i	−0.308861	+	0.951107i	$0.599948\pi$
$410$	−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	−0.514141	−	0.857706i	$-0.671889\pi$
$431$	−12.2474	+	7.07107i	−0.0284164	+	0.0164062i	0.485725	+	0.874112i	$0.338556\pi$
$432$		0			0
$433$	−389.297			−0.899069			−0.449534	−	0.893263i	$-0.648410\pi$
$433$	−389.297			−0.899069			−0.449534	+	0.893263i	$0.648410\pi$
$434$		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	$-0.941240\pi$
$439$	−145.986	+	252.856i	−0.332543	+	0.575981i	0.650467	+	0.759535i	$0.274573\pi$
$440$		−	68.8186i		−	0.156406i
$441$		0			0
$442$	−444.000			−1.00452
$443$	−22.0454	−	12.7279i	−0.0497639	−	0.0287312i	0.474912	−	0.880033i	$-0.342480\pi$
$443$	−22.0454	−	12.7279i	−0.0497639	−	0.0287312i	−0.524676	+	0.851302i	$0.675813\pi$
$444$		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	$-0.695444\pi$
$449$		−	733.977i		−	1.63469i	0.576147	−	0.817346i	$-0.304556\pi$
$450$		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	−0.975585	−	0.219623i	$-0.929517\pi$
$457$	−136.000	+	235.559i	−0.297593	+	0.515446i	0.677992	+	0.735070i	$0.262851\pi$
$458$	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	$-0.505828\pi$
$467$	−417.191	−	240.865i	−0.893342	−	0.515771i	−0.875034	+	0.484061i	$0.839161\pi$
$468$		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	$-0.701032\pi$
$479$	−89.3980	+	51.6140i	−0.186635	+	0.107754i	0.403772	+	0.914860i	$0.367699\pi$
$480$		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	0.722003	−	0.691890i	$-0.243222\pi$
$487$	−116.000	−	200.918i	−0.238193	−	0.412562i	−0.960196	+	0.279328i	$0.909888\pi$
$488$	238.395	+	137.637i	0.488514	+	0.282043i
$489$		0			0
$490$		0			0
$491$		−	449.720i		−	0.915927i	−0.888971	−	0.457963i	$-0.848579\pi$
$491$		−	449.720i		−	0.915927i	0.888971	−	0.457963i	$-0.151421\pi$
$492$		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	0.186599	+	0.982436i	$0.440253\pi$
$499$	−378.000	+	654.715i	−0.757515	+	1.31205i	−0.944114	+	0.329618i	$0.893080\pi$
$500$	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	$-0.330644\pi$
$509$	7.44983	+	4.30116i	0.0146362	+	0.00845022i	−0.492664	+	0.870220i	$0.663977\pi$
$510$		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	$-0.637721\pi$
$521$	81.9482	−	47.3128i	0.157290	−	0.0908115i	0.576579	+	0.817041i	$0.304387\pi$
$522$		0			0
$523$	−462.290	+	800.710i	−0.883920	+	1.53099i	−0.0369726	+	0.999316i	$0.511771\pi$
$523$	−462.290	+	800.710i	−0.883920	+	1.53099i	−0.846947	+	0.531677i	$0.821562\pi$
$524$		−	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	0.451334	+	0.892355i	$0.350948\pi$
$541$	−296.000	+	512.687i	−0.547135	+	0.947666i	−0.998469	+	0.0553105i	$0.982385\pi$
$542$	−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	−0.239517	−	0.970892i	$-0.576989\pi$
$557$	268.219	−	154.856i	0.481542	−	0.278019i	0.721059	+	0.692874i	$0.243656\pi$
$558$		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	$-0.374383\pi$
$563$	774.783	−	447.321i	1.37617	−	0.794531i	0.991696	+	0.128606i	$0.0410501\pi$
$564$		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	0.940665	−	0.339337i	$-0.110203\pi$
$569$	635.643	+	366.988i	1.11712	+	0.644971i	0.176458	+	0.984308i	$0.443536\pi$
$570$		0			0
$571$	−156.000	−	270.200i	−0.273205	−	0.473205i	0.696476	−	0.717580i	$-0.254750\pi$
$571$	−156.000	−	270.200i	−0.273205	−	0.473205i	−0.969681	+	0.244376i	$0.921417\pi$
$572$	−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	$-0.112719\pi$
$577$	97.3242	+	168.570i	0.168673	+	0.292150i	−0.769281	+	0.638911i	$0.779385\pi$
$578$	−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	$-0.516421\pi$
$593$	−558.737	−	322.587i	−0.942222	−	0.543992i	−0.890656	+	0.454678i	$0.849754\pi$
$594$		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	−0.906378	−	0.422468i	$-0.861164\pi$
$599$	−595.226	+	343.654i	−0.993700	+	0.573713i	−0.0873214	+	0.996180i	$0.527831\pi$
$600$		0			0
$601$	1070.57			1.78131			0.890654	−	0.454682i	$-0.150247\pi$
$601$	1070.57			1.78131			0.890654	+	0.454682i	$0.150247\pi$
$602$		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	−0.391369	−	0.920234i	$-0.627998\pi$
$607$	364.966	−	632.139i	0.601262	−	1.04142i	0.992630	−	0.121182i	$-0.0386683\pi$
$608$		−	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	0.995864	−	0.0908547i	$-0.0289599\pi$
$613$	257.000	+	445.137i	0.419250	+	0.726162i	−0.576615	+	0.817016i	$0.695627\pi$
$614$	−387.391	−	223.660i	−0.630930	−	0.364268i
$615$		0			0
$616$		0			0
$617$			202.233i			0.327767i	0.986480	+	0.163884i	$0.0524022\pi$
$617$			202.233i			0.327767i	−0.986480	+	0.163884i	$0.947598\pi$
$618$		0			0
$619$	−340.635	−	589.997i	−0.550298	−	0.953145i	−0.998253	−	0.0590883i	$-0.981181\pi$
$619$	−340.635	−	589.997i	−0.550298	−	0.953145i	0.447954	−	0.894056i	$-0.352153\pi$
$620$	−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	−0.551623	−	0.834094i	$-0.685991\pi$
$641$	−67.3610	+	38.8909i	−0.105087	+	0.0606722i	0.446535	+	0.894766i	$0.352658\pi$
$642$		0			0
$643$	510.952			0.794638			0.397319	−	0.917681i	$-0.369941\pi$
$643$	510.952			0.794638			0.397319	+	0.917681i	$0.369941\pi$
$644$		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	$-0.411739\pi$
$647$	804.582	−	464.526i	1.24356	−	0.717968i	0.969817	+	0.243835i	$0.0784055\pi$
$648$		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	0.0133783	−	0.999911i	$-0.495741\pi$
$653$	−552.360	−	318.905i	−0.845880	−	0.488369i	−0.859259	+	0.511541i	$0.829075\pi$
$654$		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	$-0.951311\pi$
$659$		−	200.818i		−	0.304732i	0.988324	−	0.152366i	$-0.0486892\pi$
$660$		0			0
$661$	48.6621	+	84.2852i	0.0736189	+	0.127512i	0.900485	−	0.434887i	$-0.143212\pi$
$661$	48.6621	+	84.2852i	0.0736189	+	0.127512i	−0.826866	+	0.562399i	$0.809878\pi$
$662$	−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	$-0.413034\pi$
$677$	−290.543	−	167.745i	−0.429163	−	0.247777i	−0.698990	+	0.715131i	$0.746367\pi$
$678$		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	−0.303799	−	0.952736i	$-0.598255\pi$
$683$	252.297	−	145.664i	0.369396	−	0.213271i	0.673195	+	0.739465i	$0.264922\pi$
$684$		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	$-0.959934\pi$
$691$	−267.642	+	463.569i	−0.387325	+	0.670867i	0.604764	+	0.796405i	$0.293268\pi$
$692$			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	$-0.732240\pi$
$701$		−	1045.10i		−	1.49088i	0.666575	−	0.745438i	$-0.267760\pi$
$702$		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	−0.641052	−	0.767498i	$-0.721502\pi$
$709$	244.000	−	422.620i	0.344147	−	0.596080i	0.985198	+	0.171418i	$0.0548349\pi$
$710$	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	$-0.109744\pi$
$719$	804.582	+	464.526i	1.11903	+	0.646072i	0.177876	+	0.984053i	$0.443077\pi$
$720$		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	$-0.712524\pi$
$727$	−900.249			−1.23831			−0.619153	+	0.785270i	$0.712524\pi$
$728$		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	0.138623	+	0.990345i	$0.455732\pi$
$733$	−577.862	+	1000.89i	−0.788353	+	1.36547i	−0.926976	+	0.375122i	$0.877601\pi$
$734$			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	0.989026	+	0.147744i	$0.0472011\pi$
$739$	460.000	+	796.743i	0.622463	+	1.07814i	−0.366563	+	0.930393i	$0.619466\pi$
$740$	−89.3980	−	51.6140i	−0.120808	−	0.0697486i
$741$		0			0
$742$		0			0
$743$		−	755.190i		−	1.01641i	−0.861237	−	0.508203i	$-0.830310\pi$
$743$		−	755.190i		−	1.01641i	0.861237	−	0.508203i	$-0.169690\pi$
$744$		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	−0.823310	−	0.567591i	$-0.807875\pi$
$751$	60.0000	−	103.923i	0.0798935	−	0.138380i	0.903204	+	0.429212i	$0.141209\pi$
$752$	−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	$-0.324337\pi$
$761$	37.2492	+	21.5058i	0.0489476	+	0.0282599i	−0.475326	+	0.879809i	$0.657670\pi$
$762$		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	$-0.646071\pi$
$769$	−681.269			−0.885916			−0.442958	+	0.896542i	$0.646071\pi$
$770$		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	$-0.937178\pi$
$773$	−1005.73	+	580.657i	−1.30107	+	0.751173i	−0.320483	+	0.947254i	$0.603845\pi$
$774$		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	$-0.127202\pi$
$787$	97.3242	+	168.570i	0.123665	+	0.214194i	−0.797545	+	0.603259i	$0.793869\pi$
$788$	−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	0.166460	−	0.986048i	$-0.446766\pi$
$809$	892.839	−	515.481i	1.10363	−	0.637183i	0.937173	+	0.348865i	$0.113433\pi$
$810$		0			0
$811$	−243.311			−0.300013			−0.150006	−	0.988685i	$-0.547929\pi$
$811$	−243.311			−0.300013			−0.150006	+	0.988685i	$0.547929\pi$
$812$		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	0.299276	−	0.954167i	$-0.403255\pi$
$821$	−309.860	−	178.898i	−0.377418	−	0.217903i	−0.676694	+	0.736264i	$0.736588\pi$
$822$		0			0
$823$	−614.000	−	1063.48i	−0.746051	−	1.29220i	−0.949702	−	0.313155i	$-0.898614\pi$
$823$	−614.000	−	1063.48i	−0.746051	−	1.29220i	0.203651	−	0.979044i	$-0.434719\pi$
$824$	−417.191	−	240.865i	−0.506299	−	0.292312i
$825$		0			0
$826$		0			0
$827$		−	195.161i		−	0.235987i	−0.993014	−	0.117994i	$-0.962354\pi$
$827$		−	195.161i		−	0.235987i	0.993014	−	0.117994i	$-0.0376462\pi$
$828$		0			0
$829$	−395.380	−	684.817i	−0.476936	−	0.826077i	0.522715	−	0.852507i	$-0.324919\pi$
$829$	−395.380	−	684.817i	−0.476936	−	0.826077i	−0.999651	+	0.0264308i	$0.991586\pi$
$830$		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	$-0.866062\pi$
$853$	−1557.19			−1.82554			−0.912771	+	0.408472i	$0.866062\pi$
$854$		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	$-0.338234\pi$
$857$	1273.92	−	735.499i	1.48649	−	0.858225i	0.999881	+	0.0153956i	$0.00490075\pi$
$858$		0			0
$859$	255.476	−	442.497i	0.297411	−	0.515131i	−0.678132	−	0.734940i	$-0.737210\pi$
$859$	255.476	−	442.497i	0.297411	−	0.515131i	0.975543	+	0.219809i	$0.0705435\pi$
$860$			1169.92i			1.36037i
$861$		0			0
$862$	20.0000			0.0232019
$863$	−492.347	−	284.257i	−0.570507	−	0.329382i	0.186845	−	0.982389i	$-0.440174\pi$
$863$	−492.347	−	284.257i	−0.570507	−	0.329382i	−0.757352	+	0.653007i	$0.773507\pi$
$864$		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	−0.497144	−	0.867668i	$-0.665618\pi$
$877$	441.000	−	763.834i	0.502851	−	0.870963i	0.999995	−	0.00329475i	$-0.00104875\pi$
$878$	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	$-0.277480\pi$
$887$	268.194	+	154.842i	0.302361	+	0.174568i	−0.341142	+	0.940012i	$0.610814\pi$
$888$		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	−0.975893	−	0.218251i	$-0.929965\pi$
$907$	−614.000	−	1063.48i	−0.676957	−	1.17252i	0.298936	−	0.954273i	$-0.403368\pi$
$908$	−59.5987	−	34.4093i	−0.0656373	−	0.0378957i
$909$		0			0
$910$		0			0
$911$			138.593i			0.152133i	0.997103	+	0.0760664i	$0.0242361\pi$
$911$			138.593i			0.152133i	−0.997103	+	0.0760664i	$0.975764\pi$
$912$		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	0.0179564	−	0.999839i	$-0.494284\pi$
$919$	804.000	−	1392.57i	0.874864	−	1.51531i	0.856908	−	0.515470i	$-0.172383\pi$
$920$	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	$-0.610067\pi$
$929$	−1229.22	−	709.692i	−1.32317	−	0.763931i	−0.984233	+	0.176879i	$0.943400\pi$
$930$		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	$-0.549796\pi$
$937$	−291.973			−0.311604			−0.155802	+	0.987788i	$0.549796\pi$
$938$		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	$-0.407690\pi$
$941$	1184.52	−	683.885i	1.25879	−	0.726764i	0.972840	+	0.231480i	$0.0743568\pi$
$942$		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	0.204725	−	0.978820i	$-0.434370\pi$
$947$	−511.943	−	295.571i	−0.540595	−	0.312113i	−0.745320	+	0.666707i	$0.767703\pi$
$948$		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	$-0.940851\pi$
$953$		−	352.139i		−	0.369506i	0.982785	−	0.184753i	$-0.0591485\pi$
$954$		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	$-0.609064\pi$
$971$	−1281.37	−	739.800i	−1.31964	−	0.761895i	−0.983671	+	0.179978i	$0.942397\pi$
$972$		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	−0.638881	−	0.769306i	$-0.720602\pi$
$977$	−285.366	+	164.756i	−0.292083	+	0.168634i	0.346798	+	0.937940i	$0.387269\pi$
$978$		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	$-0.836120\pi$
$983$	−864.181	+	498.935i	−0.879126	+	0.507563i	−0.00875564	+	0.999962i	$0.502787\pi$
$984$		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	−0.945477	−	0.325689i	$-0.894404\pi$
$991$	−748.000	−	1295.57i	−0.754793	−	1.30734i	0.190684	−	0.981651i	$-0.438929\pi$
$992$	−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	0.931397	+	0.364006i	$0.118591\pi$
$997$	778.594	+	1348.56i	0.780936	+	1.35262i	−0.150460	+	0.988616i	$0.548076\pi$
$998$	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.863.1		8
3.2	odd	2	inner	882.3.s.h.863.4		8
7.2	even	3		882.3.b.g.197.4	yes	4
7.3	odd	6	inner	882.3.s.h.557.3		8
7.4	even	3	inner	882.3.s.h.557.4		8
7.5	odd	6		882.3.b.g.197.3	yes	4
7.6	odd	2	inner	882.3.s.h.863.2		8
21.2	odd	6		882.3.b.g.197.1	✓	4
21.5	even	6		882.3.b.g.197.2	yes	4
21.11	odd	6	inner	882.3.s.h.557.1		8
21.17	even	6	inner	882.3.s.h.557.2		8
21.20	even	2	inner	882.3.s.h.863.3		8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
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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