LMFDB - Embedded newform 441.4.p.d.215.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(80,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("441.80");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.p (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:	$26.0198423125$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			215.24
Character	$\chi$	$=$	441.215
Dual form			441.4.p.d.80.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.66169 + 2.69143i) q^{2} +(10.4876 + 18.1650i) q^{4} +(9.16288 - 15.8706i) q^{5} +69.8432i q^{8} +O(q^{10})$	\(q+(4.66169 + 2.69143i) q^{2} +(10.4876 + 18.1650i) q^{4} +(9.16288 - 15.8706i) q^{5} +69.8432i q^{8} +(85.4290 - 49.3225i) q^{10} +(20.5857 - 11.8852i) q^{11} -11.7971i q^{13} +(-104.077 + 180.267i) q^{16} +(48.2099 + 83.5020i) q^{17} +(-18.1933 - 10.5039i) q^{19} +384.385 q^{20} +127.952 q^{22} +(132.203 + 76.3277i) q^{23} +(-105.417 - 182.587i) q^{25} +(31.7509 - 54.9943i) q^{26} -77.5438i q^{29} +(172.974 - 99.8667i) q^{31} +(-486.465 + 280.861i) q^{32} +519.014i q^{34} +(-82.1957 + 142.367i) q^{37} +(-56.5410 - 97.9319i) q^{38} +(1108.45 + 639.965i) q^{40} -435.473 q^{41} -106.148 q^{43} +(431.787 + 249.293i) q^{44} +(410.861 + 711.632i) q^{46} +(-5.52293 + 9.56599i) q^{47} -1134.89i q^{50} +(214.294 - 123.722i) q^{52} +(-96.0735 + 55.4681i) q^{53} -435.609i q^{55} +(208.703 - 361.485i) q^{58} +(-414.518 - 717.966i) q^{59} +(-19.5452 - 11.2845i) q^{61} +1075.14 q^{62} -1358.43 q^{64} +(-187.226 - 108.095i) q^{65} +(-199.265 - 345.137i) q^{67} +(-1011.21 + 1751.47i) q^{68} +228.153i q^{71} +(-231.194 + 133.480i) q^{73} +(-766.341 + 442.447i) q^{74} -440.641i q^{76} +(-460.333 + 797.321i) q^{79} +(1907.30 + 3303.54i) q^{80} +(-2030.04 - 1172.04i) q^{82} -642.787 q^{83} +1766.97 q^{85} +(-494.828 - 285.689i) q^{86} +(830.097 + 1437.77i) q^{88} +(-222.627 + 385.601i) q^{89} +3201.97i q^{92} +(-51.4923 + 29.7291i) q^{94} +(-333.406 + 192.492i) q^{95} -1617.57i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4}+O(q^{10}) $ 48 * q + 96 * q^4	$ 48 q + 96 q^{4} - 144 q^{16} + 1248 q^{22} - 312 q^{25} + 864 q^{37} + 2496 q^{43} + 3888 q^{46} + 7440 q^{58} - 6720 q^{64} + 2688 q^{67} - 480 q^{79} + 26496 q^{85} + 7248 q^{88}+O(q^{100}) $ 48 * q + 96 * q^4 - 144 * q^16 + 1248 * q^22 - 312 * q^25 + 864 * q^37 + 2496 * q^43 + 3888 * q^46 + 7440 * q^58 - 6720 * q^64 + 2688 * q^67 - 480 * q^79 + 26496 * q^85 + 7248 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	4.66169	+	2.69143i	1.64816	+	0.951563i	0.977804	+	0.209519i	$0.0671900\pi$
$2$	4.66169	+	2.69143i	1.64816	+	0.951563i	0.670351	+	0.742044i	$0.266143\pi$
$3$		0			0
$3$		0			0
$4$	10.4876	+	18.1650i	1.31095	+	2.27062i
$5$	9.16288	−	15.8706i	0.819553	−	1.41951i	−0.0864589	−	0.996255i	$-0.527555\pi$
$5$	9.16288	−	15.8706i	0.819553	−	1.41951i	0.906012	−	0.423252i	$-0.139112\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			69.8432i			3.08666i
$9$		0			0
$10$	85.4290	−	49.3225i	2.70150	−	1.55971i
$11$	20.5857	−	11.8852i	0.564256	−	0.325773i	−0.190596	−	0.981669i	$-0.561042\pi$
$11$	20.5857	−	11.8852i	0.564256	−	0.325773i	0.754852	+	0.655895i	$0.227709\pi$
$12$		0			0
$13$		−	11.7971i		−	0.251686i	−0.992050	−	0.125843i	$-0.959836\pi$
$13$		−	11.7971i		−	0.251686i	0.992050	−	0.125843i	$-0.0401636\pi$
$14$		0			0
$15$		0			0
$16$	−104.077	+	180.267i	−1.62621	+	2.81668i
$17$	48.2099	+	83.5020i	0.687801	+	1.19131i	0.972548	+	0.232704i	$0.0747573\pi$
$17$	48.2099	+	83.5020i	0.687801	+	1.19131i	−0.284746	+	0.958603i	$0.591909\pi$
$18$		0			0
$19$	−18.1933	−	10.5039i	−0.219675	−	0.126830i	0.386125	−	0.922447i	$-0.373813\pi$
$19$	−18.1933	−	10.5039i	−0.219675	−	0.126830i	−0.605800	+	0.795617i	$0.707147\pi$
$20$	384.385			4.29756
$21$		0			0
$22$	127.952			1.23998
$23$	132.203	+	76.3277i	1.19854	+	0.691975i	0.960229	−	0.279215i	$-0.0900742\pi$
$23$	132.203	+	76.3277i	1.19854	+	0.691975i	0.238307	+	0.971190i	$0.423408\pi$
$24$		0			0
$25$	−105.417	−	182.587i	−0.843334	−	1.46070i
$26$	31.7509	−	54.9943i	0.239495	−	0.414818i
$27$		0			0
$28$		0			0
$29$		−	77.5438i		−	0.496535i	−0.968691	−	0.248268i	$-0.920139\pi$
$29$		−	77.5438i		−	0.496535i	0.968691	−	0.248268i	$-0.0798612\pi$
$30$		0			0
$31$	172.974	−	99.8667i	1.00216	−	0.578600i	0.0932764	−	0.995640i	$-0.470266\pi$
$31$	172.974	−	99.8667i	1.00216	−	0.578600i	0.908888	+	0.417040i	$0.136933\pi$
$32$	−486.465	+	280.861i	−2.68737	+	1.55155i
$33$		0			0
$34$			519.014i			2.61795i
$35$		0			0
$36$		0			0
$37$	−82.1957	+	142.367i	−0.365213	+	0.632568i	−0.988810	−	0.149178i	$-0.952337\pi$
$37$	−82.1957	+	142.367i	−0.365213	+	0.632568i	0.623597	+	0.781746i	$0.285671\pi$
$38$	−56.5410	−	97.9319i	−0.241373	−	0.418070i
$39$		0			0
$40$	1108.45	+	639.965i	4.38154	+	2.52968i
$41$	−435.473			−1.65877			−0.829384	−	0.558679i	$-0.811308\pi$
$41$	−435.473			−1.65877			−0.829384	+	0.558679i	$0.811308\pi$
$42$		0			0
$43$	−106.148			−0.376451			−0.188226	−	0.982126i	$-0.560274\pi$
$43$	−106.148			−0.376451			−0.188226	+	0.982126i	$0.560274\pi$
$44$	431.787	+	249.293i	1.47942	+	0.854142i
$45$		0			0
$46$	410.861	+	711.632i	1.31692	+	2.28097i
$47$	−5.52293	+	9.56599i	−0.0171405	+	0.0296882i	−0.874468	−	0.485082i	$-0.838790\pi$
$47$	−5.52293	+	9.56599i	−0.0171405	+	0.0296882i	0.857328	+	0.514771i	$0.172123\pi$
$48$		0			0
$49$		0			0
$50$		−	1134.89i		−	3.20994i
$51$		0			0
$52$	214.294	−	123.722i	0.571484	−	0.329947i
$53$	−96.0735	+	55.4681i	−0.248995	+	0.143757i	−0.619304	−	0.785151i	$-0.712585\pi$
$53$	−96.0735	+	55.4681i	−0.248995	+	0.143757i	0.370309	+	0.928909i	$0.379252\pi$
$54$		0			0
$55$		−	435.609i		−	1.06795i
$56$		0			0
$57$		0			0
$58$	208.703	−	361.485i	0.472485	−	0.818367i
$59$	−414.518	−	717.966i	−0.914672	−	1.58426i	−0.807381	−	0.590031i	$-0.799116\pi$
$59$	−414.518	−	717.966i	−0.914672	−	1.58426i	−0.107291	−	0.994228i	$-0.534218\pi$
$60$		0			0
$61$	−19.5452	−	11.2845i	−0.0410248	−	0.0236857i	0.479347	−	0.877625i	$-0.340873\pi$
$61$	−19.5452	−	11.2845i	−0.0410248	−	0.0236857i	−0.520372	+	0.853940i	$0.674207\pi$
$62$	1075.14			2.20230
$63$		0			0
$64$	−1358.43			−2.65318
$65$	−187.226	−	108.095i	−0.357270	−	0.206270i
$66$		0			0
$67$	−199.265	−	345.137i	−0.363345	−	0.629331i	0.625164	−	0.780493i	$-0.285032\pi$
$67$	−199.265	−	345.137i	−0.363345	−	0.629331i	−0.988509	+	0.151162i	$0.951699\pi$
$68$	−1011.21	+	1751.47i	−1.80334	+	3.12348i
$69$		0			0
$70$		0			0
$71$			228.153i			0.381363i	0.981652	+	0.190682i	$0.0610698\pi$
$71$			228.153i			0.381363i	−0.981652	+	0.190682i	$0.938930\pi$
$72$		0			0
$73$	−231.194	+	133.480i	−0.370674	+	0.214009i	−0.673753	−	0.738957i	$-0.735319\pi$
$73$	−231.194	+	133.480i	−0.370674	+	0.214009i	0.303079	+	0.952966i	$0.401986\pi$
$74$	−766.341	+	442.447i	−1.20386	+	0.695047i
$75$		0			0
$76$		−	440.641i		−	0.665066i
$77$		0			0
$78$		0			0
$79$	−460.333	+	797.321i	−0.655589	+	1.13551i	0.326156	+	0.945316i	$0.394246\pi$
$79$	−460.333	+	797.321i	−0.655589	+	1.13551i	−0.981746	+	0.190198i	$0.939087\pi$
$80$	1907.30	+	3303.54i	2.66553	+	4.61683i
$81$		0			0
$82$	−2030.04	−	1172.04i	−2.73391	−	1.57842i
$83$	−642.787			−0.850061			−0.425031	−	0.905179i	$-0.639737\pi$
$83$	−642.787			−0.850061			−0.425031	+	0.905179i	$0.639737\pi$
$84$		0			0
$85$	1766.97			2.25476
$86$	−494.828	−	285.689i	−0.620450	−	0.358217i
$87$		0			0
$88$	830.097	+	1437.77i	1.00555	+	1.74167i
$89$	−222.627	+	385.601i	−0.265150	+	0.459254i	−0.967603	−	0.252476i	$-0.918755\pi$
$89$	−222.627	+	385.601i	−0.265150	+	0.459254i	0.702453	+	0.711731i	$0.252088\pi$
$90$		0			0
$91$		0			0
$92$			3201.97i			3.62856i
$93$		0			0
$94$	−51.4923	+	29.7291i	−0.0565003	+	0.0326205i
$95$	−333.406	+	192.492i	−0.360071	+	0.207887i
$96$		0			0
$97$		−	1617.57i		−	1.69319i	−0.532236	−	0.846596i	$-0.678648\pi$
$97$		−	1617.57i		−	1.69319i	0.532236	−	0.846596i	$-0.321352\pi$
$98$		0			0
$99$		0			0
$100$	2211.13	−	3829.79i	2.21113	−	3.82979i
$101$	−37.5166	−	64.9806i	−0.0369608	−	0.0640180i	0.846953	−	0.531667i	$-0.178434\pi$
$101$	−37.5166	−	64.9806i	−0.0369608	−	0.0640180i	−0.883914	+	0.467649i	$0.845101\pi$
$102$		0			0
$103$	−834.971	−	482.071i	−0.798759	−	0.461164i	0.0442780	−	0.999019i	$-0.485901\pi$
$103$	−834.971	−	482.071i	−0.798759	−	0.461164i	−0.843037	+	0.537856i	$0.819235\pi$
$104$	823.945			0.776870
$105$		0			0
$106$	−597.153			−0.547176
$107$	−1153.79	−	666.138i	−1.04244	−	0.601851i	−0.121914	−	0.992541i	$-0.538903\pi$
$107$	−1153.79	−	666.138i	−1.04244	−	0.601851i	−0.920522	+	0.390690i	$0.872236\pi$
$108$		0			0
$109$	445.080	+	770.901i	0.391110	+	0.677422i	0.992596	−	0.121461i	$-0.0387580\pi$
$109$	445.080	+	770.901i	0.391110	+	0.677422i	−0.601487	+	0.798883i	$0.705425\pi$
$110$	1172.41	−	2030.67i	1.01623	−	1.76016i
$111$		0			0
$112$		0			0
$113$		−	1240.25i		−	1.03251i	−0.856436	−	0.516253i	$-0.827326\pi$
$113$		−	1240.25i		−	1.03251i	0.856436	−	0.516253i	$-0.172674\pi$
$114$		0			0
$115$	2422.73	−	1398.76i	1.96453	−	1.13422i
$116$	1408.58	−	813.245i	1.12744	−	0.650930i
$117$		0			0
$118$		−	4462.58i		−	3.48147i
$119$		0			0
$120$		0			0
$121$	−382.986	+	663.352i	−0.287743	+	0.498386i
$122$	−60.7426	−	105.209i	−0.0450768	−	0.0780754i
$123$		0			0
$124$	3628.16	+	2094.72i	2.62756	+	1.51703i
$125$	−1572.97			−1.12552
$126$		0			0
$127$	1338.38			0.935137			0.467569	−	0.883957i	$-0.345130\pi$
$127$	1338.38			0.935137			0.467569	+	0.883957i	$0.345130\pi$
$128$	−2440.84	−	1409.22i	−1.68548	−	0.973114i
$129$		0			0
$130$	−581.860	−	1007.81i	−0.392558	−	0.679930i
$131$	−1156.91	+	2003.82i	−0.771597	+	1.33645i	0.165090	+	0.986279i	$0.447209\pi$
$131$	−1156.91	+	2003.82i	−0.771597	+	1.33645i	−0.936687	+	0.350167i	$0.886125\pi$
$132$		0			0
$133$		0			0
$134$		−	2145.23i		−	1.38298i
$135$		0			0
$136$	−5832.05	+	3367.13i	−3.67716	+	2.12301i
$137$	1915.10	−	1105.68i	1.19429	−	0.689524i	0.235014	−	0.971992i	$-0.424486\pi$
$137$	1915.10	−	1105.68i	1.19429	−	0.689524i	0.959277	+	0.282468i	$0.0911531\pi$
$138$		0			0
$139$			2718.66i			1.65895i	0.558545	+	0.829474i	$0.311360\pi$
$139$			2718.66i			1.65895i	−0.558545	+	0.829474i	$0.688640\pi$
$140$		0			0
$141$		0			0
$142$	−614.058	+	1063.58i	−0.362891	+	0.628546i
$143$	−140.210	−	242.851i	−0.0819926	−	0.142015i
$144$		0			0
$145$	−1230.66	−	710.524i	−0.704835	−	0.406937i
$146$	−1437.01			−0.814572
$147$		0			0
$148$	−3448.13			−1.91510
$149$	1589.86	+	917.904i	0.874135	+	0.504682i	0.868720	−	0.495303i	$-0.164943\pi$
$149$	1589.86	+	917.904i	0.874135	+	0.504682i	0.00541480	+	0.999985i	$0.498276\pi$
$150$		0			0
$151$	−1446.78	−	2505.90i	−0.779718	−	1.35051i	−0.932104	−	0.362190i	$-0.882029\pi$
$151$	−1446.78	−	2505.90i	−0.779718	−	1.35051i	0.152386	−	0.988321i	$-0.451304\pi$
$152$	733.626	−	1270.68i	0.391480	−	0.678063i
$153$		0			0
$154$		0			0
$155$		−	3660.27i		−	1.89677i
$156$		0			0
$157$	1479.73	−	854.325i	0.752201	−	0.434284i	−0.0742874	−	0.997237i	$-0.523668\pi$
$157$	1479.73	−	854.325i	0.752201	−	0.434284i	0.826489	+	0.562953i	$0.190335\pi$
$158$	−4291.86	+	2477.91i	−2.16103	+	1.24767i
$159$		0			0
$160$			10294.0i			5.08631i
$161$		0			0
$162$		0			0
$163$	1519.04	−	2631.05i	0.729941	−	1.26429i	−0.226967	−	0.973903i	$-0.572881\pi$
$163$	1519.04	−	2631.05i	0.729941	−	1.26429i	0.956908	−	0.290392i	$-0.0937858\pi$
$164$	−4567.05	−	7910.36i	−2.17455	−	3.76644i
$165$		0			0
$166$	−2996.47	−	1730.02i	−1.40103	−	0.808887i
$167$	−702.416			−0.325477			−0.162738	−	0.986669i	$-0.552033\pi$
$167$	−702.416			−0.325477			−0.162738	+	0.986669i	$0.552033\pi$
$168$		0			0
$169$	2057.83			0.936654
$170$	8237.05	+	4755.66i	3.71619	+	2.14555i
$171$		0			0
$172$	−1113.23	−	1928.17i	−0.493507	−	0.854779i
$173$	−740.395	+	1282.40i	−0.325383	+	0.563579i	−0.981590	−	0.191002i	$-0.938826\pi$
$173$	−740.395	+	1282.40i	−0.325383	+	0.563579i	0.656207	+	0.754581i	$0.272160\pi$
$174$		0			0
$175$		0			0
$176$			4947.90i			2.11910i
$177$		0			0
$178$	−2075.63	+	1198.37i	−0.874019	+	0.504615i
$179$	−829.096	+	478.679i	−0.346199	+	0.199878i	−0.663010	−	0.748611i	$-0.730721\pi$
$179$	−829.096	+	478.679i	−0.346199	+	0.199878i	0.316811	+	0.948489i	$0.397388\pi$
$180$		0			0
$181$			505.013i			0.207389i	0.994609	+	0.103694i	$0.0330664\pi$
$181$			505.013i			0.207389i	−0.994609	+	0.103694i	$0.966934\pi$
$182$		0			0
$183$		0			0
$184$	−5330.97	+	9233.51i	−2.13589	+	3.69948i
$185$	1506.30	+	2608.99i	0.598623	+	1.03685i
$186$		0			0
$187$	1984.87	+	1145.96i	0.776192	+	0.448135i
$188$	−231.688			−0.0898808
$189$		0			0
$190$	−2072.31			−0.791271
$191$	−2019.91	−	1166.20i	−0.765214	−	0.441796i	0.0659508	−	0.997823i	$-0.478992\pi$
$191$	−2019.91	−	1166.20i	−0.765214	−	0.441796i	−0.831165	+	0.556027i	$0.812325\pi$
$192$		0			0
$193$	1962.92	+	3399.89i	0.732095	+	1.26803i	0.955986	+	0.293412i	$0.0947908\pi$
$193$	1962.92	+	3399.89i	0.732095	+	1.26803i	−0.223891	+	0.974614i	$0.571876\pi$
$194$	4353.58	−	7540.62i	1.61118	−	2.79064i
$195$		0			0
$196$		0			0
$197$		−	1429.05i		−	0.516831i	−0.966034	−	0.258416i	$-0.916800\pi$
$197$		−	1429.05i		−	0.516831i	0.966034	−	0.258416i	$-0.0832004\pi$
$198$		0			0
$199$	4276.35	−	2468.95i	1.52333	−	0.879494i	0.523709	−	0.851897i	$-0.324548\pi$
$199$	4276.35	−	2468.95i	1.52333	−	0.879494i	0.999619	−	0.0275964i	$-0.00878533\pi$
$200$	12752.5	−	7362.65i	4.50868	−	2.60309i
$201$		0			0
$202$		−	403.893i		−	0.140682i
$203$		0			0
$204$		0			0
$205$	−3990.19	+	6911.21i	−1.35945	+	2.35463i
$206$	−2594.92	−	4494.53i	−0.877653	−	1.52014i
$207$		0			0
$208$	2126.63	+	1227.81i	0.708918	+	0.409294i
$209$	−499.362			−0.165271
$210$		0			0
$211$	1803.90			0.588557			0.294279	−	0.955720i	$-0.404921\pi$
$211$	1803.90			0.588557			0.294279	+	0.955720i	$0.404921\pi$
$212$	−2015.15	−	1163.45i	−0.652836	−	0.376915i
$213$		0			0
$214$	−3585.73	−	6210.66i	−1.14540	−	1.98389i
$215$	−972.620	+	1684.63i	−0.308522	+	0.534375i
$216$		0			0
$217$		0			0
$218$			4791.60i			1.48866i
$219$		0			0
$220$	7912.83	−	4568.48i	2.42492	−	1.40003i
$221$	985.079	−	568.736i	0.299835	−	0.173110i
$222$		0			0
$223$		−	2540.18i		−	0.762795i	−0.924411	−	0.381397i	$-0.875443\pi$
$223$		−	2540.18i		−	0.762795i	0.924411	−	0.381397i	$-0.124557\pi$
$224$		0			0
$225$		0			0
$226$	3338.05	−	5781.67i	0.982495	−	1.70173i
$227$	−1989.54	−	3445.98i	−0.581719	−	1.00757i	−0.995276	−	0.0970885i	$-0.969047\pi$
$227$	−1989.54	−	3445.98i	−0.581719	−	1.00757i	0.413557	−	0.910478i	$-0.364286\pi$
$228$		0			0
$229$	1917.78	+	1107.23i	0.553407	+	0.319510i	0.750495	−	0.660876i	$-0.229815\pi$
$229$	1917.78	+	1107.23i	0.553407	+	0.319510i	−0.197088	+	0.980386i	$0.563148\pi$
$230$	15058.7			4.31713
$231$		0			0
$232$	5415.91			1.53264
$233$	−4060.10	−	2344.10i	−1.14157	−	0.659087i	−0.194752	−	0.980852i	$-0.562390\pi$
$233$	−4060.10	−	2344.10i	−1.14157	−	0.659087i	−0.946819	+	0.321766i	$0.895724\pi$
$234$		0			0
$235$	101.212	+	175.304i	0.0280950	+	0.0486620i
$236$	8694.57	−	15059.4i	2.39817	−	4.15375i
$237$		0			0
$238$		0			0
$239$			6575.90i			1.77975i	0.456207	+	0.889874i	$0.349208\pi$
$239$			6575.90i			1.77975i	−0.456207	+	0.889874i	$0.650792\pi$
$240$		0			0
$241$	−3358.45	+	1939.00i	−0.897662	+	0.518265i	−0.876441	−	0.481510i	$-0.840089\pi$
$241$	−3358.45	+	1939.00i	−0.897662	+	0.518265i	−0.0212209	+	0.999775i	$0.506755\pi$
$242$	−3570.73	+	2061.56i	−0.948492	+	0.547612i
$243$		0			0
$244$		−	473.386i		−	0.124202i
$245$		0			0
$246$		0			0
$247$	−123.915	+	214.628i	−0.0319212	+	0.0552892i
$248$	6975.01	+	12081.1i	1.78594	+	3.09334i
$249$		0			0
$250$	−7332.68	−	4233.53i	−1.85504	−	1.07101i
$251$	−2789.25			−0.701418			−0.350709	−	0.936484i	$-0.614059\pi$
$251$	−2789.25			−0.701418			−0.350709	+	0.936484i	$0.614059\pi$
$252$		0			0
$253$	3628.66			0.901708
$254$	6239.13	+	3602.16i	1.54125	+	0.889842i
$255$		0			0
$256$	−2151.92	−	3727.24i	−0.525371	−	0.909970i
$257$	−1502.32	+	2602.09i	−0.364638	+	0.631572i	−0.988718	−	0.149789i	$-0.952141\pi$
$257$	−1502.32	+	2602.09i	−0.364638	+	0.631572i	0.624080	+	0.781361i	$0.285474\pi$
$258$		0			0
$259$		0			0
$260$		−	4534.62i		−	1.08163i
$261$		0			0
$262$	−10786.3	+	6227.45i	−2.54343	+	1.46845i
$263$	−3452.66	+	1993.39i	−0.809506	+	0.467368i	−0.846784	−	0.531937i	$-0.821464\pi$
$263$	−3452.66	+	1993.39i	−0.809506	+	0.467368i	0.0372784	+	0.999305i	$0.488131\pi$
$264$		0			0
$265$			2032.99i			0.471266i
$266$		0			0
$267$		0			0
$268$	4179.61	−	7239.29i	0.952650	−	1.65004i
$269$	2608.45	+	4517.97i	0.591227	+	1.02403i	0.994068	+	0.108765i	$0.0346895\pi$
$269$	2608.45	+	4517.97i	0.591227	+	1.02403i	−0.402841	+	0.915270i	$0.631977\pi$
$270$		0			0
$271$	−232.269	−	134.101i	−0.0520640	−	0.0300591i	0.473742	−	0.880664i	$-0.342903\pi$
$271$	−232.269	−	134.101i	−0.0520640	−	0.0300591i	−0.525806	+	0.850604i	$0.676236\pi$
$272$	−20070.3			−4.47404
$273$		0			0
$274$	11903.5			2.62450
$275$	−4340.16	−	2505.79i	−0.951713	−	0.549472i
$276$		0			0
$277$	−1859.88	−	3221.41i	−0.403427	−	0.698756i	0.590710	−	0.806884i	$-0.298848\pi$
$277$	−1859.88	−	3221.41i	−0.403427	−	0.698756i	−0.994137	+	0.108128i	$0.965514\pi$
$278$	−7317.08	+	12673.6i	−1.57859	+	2.73421i
$279$		0			0
$280$		0			0
$281$			4360.92i			0.925802i	0.886410	+	0.462901i	$0.153191\pi$
$281$			4360.92i			0.925802i	−0.886410	+	0.462901i	$0.846809\pi$
$282$		0			0
$283$	−2540.70	+	1466.87i	−0.533671	+	0.308115i	−0.742510	−	0.669835i	$-0.766365\pi$
$283$	−2540.70	+	1466.87i	−0.533671	+	0.308115i	0.208839	+	0.977950i	$0.433032\pi$
$284$	−4144.40	+	2392.77i	−0.865933	+	0.499946i
$285$		0			0
$286$		−	1509.46i		−	0.312085i
$287$		0			0
$288$		0			0
$289$	−2191.89	+	3796.47i	−0.446141	+	0.772739i
$290$	−3824.65	−	6624.49i	−0.774452	−	1.34139i
$291$		0			0
$292$	−4849.33	−	2799.76i	−0.971868	−	0.561108i
$293$	−1081.19			−0.215577			−0.107789	−	0.994174i	$-0.534377\pi$
$293$	−1081.19			−0.215577			−0.107789	+	0.994174i	$0.534377\pi$
$294$		0			0
$295$	−15192.7			−2.99849
$296$	−9943.37	−	5740.81i	−1.95252	−	1.12729i
$297$		0			0
$298$	4940.94	+	8557.97i	0.960474	+	1.66359i
$299$	900.443	−	1559.61i	0.174160	−	0.301655i
$300$		0			0
$301$		0			0
$302$		−	15575.6i		−	2.96780i
$303$		0			0
$304$	3787.02	−	2186.44i	0.714476	−	0.412503i
$305$	−358.182	+	206.796i	−0.0672440	+	0.0388233i
$306$		0			0
$307$			4327.83i			0.804567i	0.915515	+	0.402284i	$0.131783\pi$
$307$			4327.83i			0.804567i	−0.915515	+	0.402284i	$0.868217\pi$
$308$		0			0
$309$		0			0
$310$	9851.35	−	17063.0i	1.80490	−	3.12618i
$311$	−762.084	−	1319.97i	−0.138951	−	0.240671i	0.788149	−	0.615485i	$-0.211040\pi$
$311$	−762.084	−	1319.97i	−0.138951	−	0.240671i	−0.927100	+	0.374814i	$0.877706\pi$
$312$		0			0
$313$	5520.33	+	3187.16i	0.996893	+	0.575556i	0.907327	−	0.420425i	$-0.138119\pi$
$313$	5520.33	+	3187.16i	0.996893	+	0.575556i	0.0895652	+	0.995981i	$0.471452\pi$
$314$	9197.41			1.65299
$315$		0			0
$316$	−19311.1			−3.43777
$317$	809.520	+	467.377i	0.143430	+	0.0828091i	0.569998	−	0.821646i	$-0.306944\pi$
$317$	809.520	+	467.377i	0.143430	+	0.0828091i	−0.426568	+	0.904456i	$0.640277\pi$
$318$		0			0
$319$	−921.620	−	1596.29i	−0.161758	−	0.280173i
$320$	−12447.1	+	21559.0i	−2.17442	+	3.76620i
$321$		0			0
$322$		0			0
$323$		−	2025.57i		−	0.348934i
$324$		0			0
$325$	−2153.99	+	1243.61i	−0.367637	+	0.212255i
$326$	14162.6	−	8176.77i	2.40611	−	1.38917i
$327$		0			0
$328$		−	30414.8i		−	5.12006i
$329$		0			0
$330$		0			0
$331$	2488.04	−	4309.41i	0.413157	−	0.715609i	−0.582076	−	0.813134i	$-0.697759\pi$
$331$	2488.04	−	4309.41i	0.413157	−	0.715609i	0.995233	+	0.0975255i	$0.0310928\pi$
$332$	−6741.27	−	11676.2i	−1.11438	−	1.93017i
$333$		0			0
$334$	−3274.45	−	1890.50i	−0.536436	−	0.309712i
$335$	−7303.37			−1.19112
$336$		0			0
$337$	−5127.06			−0.828750			−0.414375	−	0.910106i	$-0.636000\pi$
$337$	−5127.06			−0.828750			−0.414375	+	0.910106i	$0.636000\pi$
$338$	9592.96	+	5538.50i	1.54375	+	0.891286i
$339$		0			0
$340$	18531.2	+	32096.9i	2.95587	+	5.11971i
$341$	2373.86	−	4111.65i	0.376985	−	0.652957i
$342$		0			0
$343$		0			0
$344$		−	7413.71i		−	1.16198i
$345$		0			0
$346$	−6902.98	+	3985.44i	−1.07256	+	0.619244i
$347$	4466.14	−	2578.52i	0.690936	−	0.398912i	−0.113027	−	0.993592i	$-0.536055\pi$
$347$	4466.14	−	2578.52i	0.690936	−	0.398912i	0.803963	+	0.594680i	$0.202721\pi$
$348$		0			0
$349$		−	2961.44i		−	0.454218i	−0.973869	−	0.227109i	$-0.927073\pi$
$349$		−	2961.44i		−	0.454218i	0.973869	−	0.227109i	$-0.0729274\pi$
$350$		0			0
$351$		0			0
$352$	−6676.15	+	11563.4i	−1.01091	+	1.75094i
$353$	5649.11	+	9784.54i	0.851761	+	1.47529i	0.879618	+	0.475681i	$0.157798\pi$
$353$	5649.11	+	9784.54i	0.851761	+	1.47529i	−0.0278569	+	0.999612i	$0.508868\pi$
$354$		0			0
$355$	3620.92	+	2090.54i	0.541348	+	0.312547i
$356$	−9339.25			−1.39039
$357$		0			0
$358$	−5153.32			−0.760786
$359$	−2275.44	−	1313.72i	−0.334521	−	0.193136i	0.323326	−	0.946288i	$-0.395199\pi$
$359$	−2275.44	−	1313.72i	−0.334521	−	0.193136i	−0.657847	+	0.753152i	$0.728532\pi$
$360$		0			0
$361$	−3208.84	−	5557.87i	−0.467829	−	0.810303i
$362$	−1359.21	+	2354.21i	−0.197343	+	0.341809i
$363$		0			0
$364$		0			0
$365$			4892.25i			0.701567i
$366$		0			0
$367$	−2320.20	+	1339.57i	−0.330009	+	0.190531i	−0.655845	−	0.754895i	$-0.727688\pi$
$367$	−2320.20	+	1339.57i	−0.330009	+	0.190531i	0.325836	+	0.945426i	$0.394354\pi$
$368$	−27518.8	+	15888.0i	−3.89814	+	2.25059i
$369$		0			0
$370$			16216.4i			2.27851i
$371$		0			0
$372$		0			0
$373$	2593.86	−	4492.70i	0.360068	−	0.623655i	−0.627904	−	0.778291i	$-0.716087\pi$
$373$	2593.86	−	4492.70i	0.360068	−	0.623655i	0.987972	+	0.154636i	$0.0494203\pi$
$374$	6168.56	+	10684.3i	0.852857	+	1.47719i
$375$		0			0
$376$	−668.119	−	385.739i	−0.0916373	−	0.0529068i
$377$	−914.789			−0.124971
$378$		0			0
$379$	−2469.97			−0.334760			−0.167380	−	0.985892i	$-0.553531\pi$
$379$	−2469.97			−0.334760			−0.167380	+	0.985892i	$0.553531\pi$
$380$	−6993.23	−	4037.54i	−0.944067	−	0.545057i
$381$		0			0
$382$	−6277.47	−	10872.9i	−0.840794	−	1.45630i
$383$	−5632.62	+	9755.99i	−0.751472	+	1.30159i	0.195638	+	0.980676i	$0.437322\pi$
$383$	−5632.62	+	9755.99i	−0.751472	+	1.30159i	−0.947109	+	0.320911i	$0.896011\pi$
$384$		0			0
$385$		0			0
$386$			21132.3i			2.78654i
$387$		0			0
$388$	29383.2	−	16964.4i	3.84460	−	2.21968i
$389$	6658.54	−	3844.31i	0.867870	−	0.501065i	0.00122995	−	0.999999i	$-0.499608\pi$
$389$	6658.54	−	3844.31i	0.867870	−	0.501065i	0.866640	+	0.498934i	$0.166275\pi$
$390$		0			0
$391$			14719.0i			1.90376i
$392$		0			0
$393$		0			0
$394$	3846.19	−	6661.80i	0.491798	−	0.851819i
$395$	8435.96	+	14611.5i	1.07458	+	1.86123i
$396$		0			0
$397$	700.905	+	404.668i	0.0886081	+	0.0511579i	0.543649	−	0.839312i	$-0.317042\pi$
$397$	700.905	+	404.668i	0.0886081	+	0.0511579i	−0.455041	+	0.890470i	$0.650375\pi$
$398$	26580.0			3.34758
$399$		0			0
$400$	43886.0			5.48575
$401$	3813.91	+	2201.96i	0.474956	+	0.274216i	0.718312	−	0.695721i	$-0.244915\pi$
$401$	3813.91	+	2201.96i	0.474956	+	0.274216i	−0.243356	+	0.969937i	$0.578248\pi$
$402$		0			0
$403$	−1178.13	−	2040.59i	−0.145625	−	0.252231i
$404$	786.915	−	1362.98i	0.0969072	−	0.167848i
$405$		0			0
$406$		0			0
$407$			3907.63i			0.475907i
$408$		0			0
$409$	50.4345	−	29.1184i	0.00609737	−	0.00352032i	−0.496948	−	0.867780i	$-0.665546\pi$
$409$	50.4345	−	29.1184i	0.00609737	−	0.00352032i	0.503046	+	0.864260i	$0.332213\pi$
$410$	−37202.0	+	21478.6i	−4.48116	+	2.58720i
$411$		0			0
$412$		−	20223.0i		−	2.41824i
$413$		0			0
$414$		0			0
$415$	−5889.78	+	10201.4i	−0.696670	+	1.20667i
$416$	3313.33	+	5738.86i	0.390504	+	0.676372i
$417$		0			0
$418$	−2327.87	−	1344.00i	−0.272392	−	0.157266i
$419$	6309.98			0.735711			0.367855	−	0.929883i	$-0.380092\pi$
$419$	6309.98			0.735711			0.367855	+	0.929883i	$0.380092\pi$
$420$		0			0
$421$	939.246			0.108732			0.0543658	−	0.998521i	$-0.482686\pi$
$421$	939.246			0.108732			0.0543658	+	0.998521i	$0.482686\pi$
$422$	8409.22	+	4855.07i	0.970034	+	0.560050i
$423$		0			0
$424$	−3874.07	−	6710.08i	−0.443730	−	0.768562i
$425$	10164.3	−	17605.0i	1.16009	−	2.00934i
$426$		0			0
$427$		0			0
$428$		−	27944.7i		−	3.15597i
$429$		0			0
$430$	−9068.11	+	5235.47i	−1.01698	+	0.587156i
$431$	8233.84	−	4753.81i	0.920209	−	0.531283i	0.0365070	−	0.999333i	$-0.488377\pi$
$431$	8233.84	−	4753.81i	0.920209	−	0.531283i	0.883702	+	0.468051i	$0.155044\pi$
$432$		0			0
$433$			9603.12i			1.06581i	0.846175	+	0.532906i	$0.178900\pi$
$433$			9603.12i			1.06581i	−0.846175	+	0.532906i	$0.821100\pi$
$434$		0			0
$435$		0			0
$436$	−9335.61	+	16169.8i	−1.02545	+	1.77613i
$437$	−1603.48	−	2777.30i	−0.175526	−	0.304019i
$438$		0			0
$439$	−756.045	−	436.503i	−0.0821960	−	0.0474559i	0.458339	−	0.888778i	$-0.348445\pi$
$439$	−756.045	−	436.503i	−0.0821960	−	0.0474559i	−0.540535	+	0.841322i	$0.681778\pi$
$440$	30424.3			3.29642
$441$		0			0
$442$	6122.84			0.658900
$443$	−696.335	−	402.029i	−0.0746815	−	0.0431174i	0.462194	−	0.886779i	$-0.347062\pi$
$443$	−696.335	−	402.029i	−0.0746815	−	0.0431174i	−0.536876	+	0.843661i	$0.680396\pi$
$444$		0			0
$445$	4079.81	+	7066.43i	0.434610	+	0.752766i
$446$	6836.72	−	11841.5i	0.725847	−	1.25720i
$447$		0			0
$448$		0			0
$449$			12649.5i			1.32955i	0.747046	+	0.664773i	$0.231472\pi$
$449$			12649.5i			1.32955i	−0.747046	+	0.664773i	$0.768528\pi$
$450$		0			0
$451$	−8964.51	+	5175.66i	−0.935970	+	0.540383i
$452$	22529.2	−	13007.2i	2.34443	−	1.35356i
$453$		0			0
$454$		−	21418.8i		−	2.21417i
$455$		0			0
$456$		0			0
$457$	3813.36	−	6604.93i	0.390331	−	0.676073i	−0.602162	−	0.798374i	$-0.705694\pi$
$457$	3813.36	−	6604.93i	0.390331	−	0.676073i	0.992493	+	0.122301i	$0.0390272\pi$
$458$	5960.05	+	10323.1i	0.608067	+	1.05320i
$459$		0			0
$460$	50817.0	+	29339.2i	5.15078	+	2.97380i
$461$	15305.4			1.54630			0.773148	−	0.634226i	$-0.218681\pi$
$461$	15305.4			1.54630			0.773148	+	0.634226i	$0.218681\pi$
$462$		0			0
$463$	−9675.77			−0.971212			−0.485606	−	0.874178i	$-0.661401\pi$
$463$	−9675.77			−0.971212			−0.485606	+	0.874178i	$0.661401\pi$
$464$	13978.6	+	8070.56i	1.39858	+	0.807470i
$465$		0			0
$466$	−12618.0	−	21854.9i	−1.25433	−	2.17256i
$467$	1743.83	−	3020.40i	0.172794	−	0.299288i	−0.766602	−	0.642123i	$-0.778054\pi$
$467$	1743.83	−	3020.40i	0.172794	−	0.299288i	0.939396	+	0.342835i	$0.111387\pi$
$468$		0			0
$469$		0			0
$470$			1089.62i			0.106937i
$471$		0			0
$472$	50145.1	−	28951.3i	4.89007	−	2.82328i
$473$	−2185.13	+	1261.58i	−0.212415	+	0.122638i
$474$		0			0
$475$			4429.15i			0.427839i
$476$		0			0
$477$		0			0
$478$	−17698.6	+	30654.8i	−1.69354	+	2.93330i
$479$	−9087.22	−	15739.5i	−0.866818	−	1.50137i	−0.865231	−	0.501373i	$-0.832828\pi$
$479$	−9087.22	−	15739.5i	−0.866818	−	1.50137i	−0.00158646	−	0.999999i	$-0.500505\pi$
$480$		0			0
$481$	1679.51	+	969.668i	0.159208	+	0.0919190i
$482$	−20874.7			−1.97265
$483$		0			0
$484$	−16066.4			−1.50886
$485$	−25671.8	−	14821.6i	−2.40350	−	1.38766i
$486$		0			0
$487$	7405.34	+	12826.4i	0.689052	+	1.19347i	0.972145	+	0.234380i	$0.0753060\pi$
$487$	7405.34	+	12826.4i	0.689052	+	1.19347i	−0.283094	+	0.959092i	$0.591361\pi$
$488$	788.142	−	1365.10i	0.0731097	−	0.126630i
$489$		0			0
$490$		0			0
$491$		−	5187.59i		−	0.476808i	−0.971166	−	0.238404i	$-0.923376\pi$
$491$		−	5187.59i		−	0.476808i	0.971166	−	0.238404i	$-0.0766242\pi$
$492$		0			0
$493$	6475.06	−	3738.38i	0.591526	−	0.341517i
$494$	−1155.31	+	667.018i	−0.105222	+	0.0607501i
$495$		0			0
$496$			41575.5i			3.76370i
$497$		0			0
$498$		0			0
$499$	2292.61	−	3970.91i	0.205674	−	0.356238i	−0.744673	−	0.667429i	$-0.767395\pi$
$499$	2292.61	−	3970.91i	0.205674	−	0.356238i	0.950347	+	0.311192i	$0.100728\pi$
$500$	−16496.6	−	28572.9i	−1.47550	−	2.55564i
$501$		0			0
$502$	−13002.6	−	7507.06i	−1.15605	−	0.667444i
$503$	−2600.54			−0.230521			−0.115261	−	0.993335i	$-0.536770\pi$
$503$	−2600.54			−0.230521			−0.115261	+	0.993335i	$0.536770\pi$
$504$		0			0
$505$	−1375.04			−0.121165
$506$	16915.7	+	9766.29i	1.48616	+	0.858032i
$507$		0			0
$508$	14036.4	+	24311.7i	1.22591	+	2.12334i
$509$	−5759.80	+	9976.27i	−0.501569	+	0.868743i	0.498429	+	0.866930i	$0.333910\pi$
$509$	−5759.80	+	9976.27i	−0.501569	+	0.868743i	−0.999998	+	0.00181295i	$0.999423\pi$
$510$		0			0
$511$		0			0
$512$		−	619.438i		−	0.0534678i
$513$		0			0
$514$	−14006.7	+	8086.76i	−1.20196	+	0.693953i
$515$	−15301.5	+	8834.32i	−1.30925	+	0.755896i
$516$		0			0
$517$			262.563i			0.0223356i
$518$		0			0
$519$		0			0
$520$	7549.71	−	13076.5i	0.636686	−	1.10277i
$521$	−3361.14	−	5821.67i	−0.282638	−	0.489543i	0.689396	−	0.724385i	$-0.257876\pi$
$521$	−3361.14	−	5821.67i	−0.282638	−	0.489543i	−0.972034	+	0.234842i	$0.924543\pi$
$522$		0			0
$523$	19252.8	+	11115.6i	1.60969	+	0.929352i	0.989440	+	0.144945i	$0.0463005\pi$
$523$	19252.8	+	11115.6i	1.60969	+	0.929352i	0.620246	+	0.784407i	$0.287033\pi$
$524$	−48532.5			−4.04609
$525$		0			0
$526$	−21460.3			−1.77892
$527$	16678.1	+	9629.13i	1.37858	+	0.795923i
$528$		0			0
$529$	5568.33	+	9644.63i	0.457659	+	0.792688i
$530$	−5471.64	+	9477.16i	−0.448440	+	0.776720i
$531$		0			0
$532$		0			0
$533$			5137.31i			0.417489i
$534$		0			0
$535$	−21144.0	+	12207.5i	−1.70866	+	0.986497i
$536$	24105.5	−	13917.3i	1.94253	−	1.12152i
$537$		0			0
$538$			28081.8i			2.25036i
$539$		0			0
$540$		0			0
$541$	2578.35	−	4465.84i	0.204902	−	0.354901i	−0.745199	−	0.666842i	$-0.767646\pi$
$541$	2578.35	−	4465.84i	0.204902	−	0.354901i	0.950102	+	0.311941i	$0.100979\pi$
$542$	−721.844	−	1250.27i	−0.0572064	−	0.0990843i
$543$		0			0
$544$	−46904.9	−	27080.5i	−3.69675	−	2.13432i
$545$	16312.9			1.28214
$546$		0			0
$547$	22545.5			1.76230			0.881149	−	0.472839i	$-0.156771\pi$
$547$	22545.5			1.76230			0.881149	+	0.472839i	$0.156771\pi$
$548$	40169.4	+	23191.8i	3.13130	+	1.80786i
$549$		0			0
$550$	−13488.3	−	23362.4i	−1.04571	−	1.81123i
$551$	−814.512	+	1410.78i	−0.0629753	+	0.109076i
$552$		0			0
$553$		0			0
$554$		−	20022.9i		−	1.53555i
$555$		0			0
$556$	−49384.5	+	28512.1i	−3.76685	+	2.17479i
$557$	−8246.05	+	4760.86i	−0.627282	+	0.362162i	−0.779699	−	0.626155i	$-0.784628\pi$
$557$	−8246.05	+	4760.86i	−0.627282	+	0.362162i	0.152417	+	0.988316i	$0.451294\pi$
$558$		0			0
$559$			1252.23i			0.0947475i
$560$		0			0
$561$		0			0
$562$	−11737.1	+	20329.2i	−0.880959	+	1.52587i
$563$	−2761.09	−	4782.34i	−0.206689	−	0.357996i	0.743981	−	0.668201i	$-0.232935\pi$
$563$	−2761.09	−	4782.34i	−0.206689	−	0.357996i	−0.950670	+	0.310205i	$0.899602\pi$
$564$		0			0
$565$	−19683.5	−	11364.3i	−1.46565	−	0.846194i
$566$	−15791.9			−1.17276
$567$		0			0
$568$	−15934.9			−1.17714
$569$	−2537.61	−	1465.09i	−0.186963	−	0.107943i	0.403597	−	0.914937i	$-0.367760\pi$
$569$	−2537.61	−	1465.09i	−0.186963	−	0.107943i	−0.590560	+	0.806994i	$0.701093\pi$
$570$		0			0
$571$	−4359.17	−	7550.30i	−0.319484	−	0.553363i	0.660896	−	0.750477i	$-0.270176\pi$
$571$	−4359.17	−	7550.30i	−0.319484	−	0.553363i	−0.980381	+	0.197114i	$0.936843\pi$
$572$	2940.92	−	5093.82i	0.214976	−	0.372349i
$573$		0			0
$574$		0			0
$575$		−	32184.9i		−	2.33427i
$576$		0			0
$577$	14243.4	−	8223.43i	1.02766	−	0.593320i	0.111347	−	0.993782i	$-0.464483\pi$
$577$	14243.4	−	8223.43i	1.02766	−	0.593320i	0.916314	+	0.400461i	$0.131150\pi$
$578$	−20435.8	+	11798.6i	−1.47062	+	0.849063i
$579$		0			0
$580$		−	29806.7i		−	2.13389i
$581$		0			0
$582$		0			0
$583$	−1318.49	+	2283.70i	−0.0936645	+	0.162232i
$584$	−9322.67	−	16147.3i	−0.660574	−	1.14415i
$585$		0			0
$586$	−5040.19	−	2909.96i	−0.355305	−	0.205135i
$587$	−2346.72			−0.165008			−0.0825040	−	0.996591i	$-0.526292\pi$
$587$	−2346.72			−0.165008			−0.0825040	+	0.996591i	$0.526292\pi$
$588$		0			0
$589$	−4195.96			−0.293534
$590$	−70823.7	−	40890.1i	−4.94198	−	2.85325i
$591$		0			0
$592$	−17109.4	−	29634.4i	−1.18783	−	2.05738i
$593$	−7971.40	+	13806.9i	−0.552017	+	0.956122i	0.446112	+	0.894977i	$0.352808\pi$
$593$	−7971.40	+	13806.9i	−0.552017	+	0.956122i	−0.998129	+	0.0611443i	$0.980525\pi$
$594$		0			0
$595$		0			0
$596$			38506.3i			2.64644i
$597$		0			0
$598$	8395.17	−	4846.95i	0.574087	−	0.331449i
$599$	17836.6	−	10298.0i	1.21667	−	0.702445i	0.252466	−	0.967606i	$-0.418758\pi$
$599$	17836.6	−	10298.0i	1.21667	−	0.702445i	0.964204	+	0.265161i	$0.0854251\pi$
$600$		0			0
$601$			662.921i			0.0449935i	0.999747	+	0.0224968i	$0.00716154\pi$
$601$			662.921i			0.0449935i	−0.999747	+	0.0224968i	$0.992838\pi$
$602$		0			0
$603$		0			0
$604$	30346.4	−	52561.5i	2.04434	−	3.54089i
$605$	7018.52	+	12156.4i	0.471642	+	0.816908i
$606$		0			0
$607$	−11688.2	−	6748.21i	−0.781567	−	0.451238i	0.0554186	−	0.998463i	$-0.482351\pi$
$607$	−11688.2	−	6748.21i	−0.781567	−	0.451238i	−0.836985	+	0.547226i	$0.815684\pi$
$608$	11800.5			0.787130
$609$		0			0
$610$	−2226.31			−0.147771
$611$	112.851	+	65.1543i	0.00747209	+	0.00431401i
$612$		0			0
$613$	−10037.0	−	17384.6i	−0.661322	−	1.14544i	−0.980268	−	0.197671i	$-0.936662\pi$
$613$	−10037.0	−	17384.6i	−0.661322	−	1.14544i	0.318946	−	0.947773i	$-0.396671\pi$
$614$	−11648.0	+	20175.0i	−0.765597	+	1.32605i
$615$		0			0
$616$		0			0
$617$			21664.4i			1.41358i	0.707425	+	0.706788i	$0.249857\pi$
$617$			21664.4i			1.41358i	−0.707425	+	0.706788i	$0.750143\pi$
$618$		0			0
$619$	−1881.89	+	1086.51i	−0.122196	+	0.0705501i	−0.559852	−	0.828592i	$-0.689142\pi$
$619$	−1881.89	+	1086.51i	−0.122196	+	0.0705501i	0.437656	+	0.899143i	$0.355809\pi$
$620$	66488.7	−	38387.3i	4.30686	−	2.48657i
$621$		0			0
$622$		−	8204.38i		−	0.528884i
$623$		0			0
$624$		0			0
$625$	−1235.81	+	2140.48i	−0.0790916	+	0.136991i
$626$	17156.0	+	29715.1i	1.09536	+	1.89721i
$627$		0			0
$628$	31037.6	+	17919.6i	1.97219	+	1.13864i
$629$	−15850.6			−1.00478
$630$		0			0
$631$	−7823.69			−0.493591			−0.246796	−	0.969068i	$-0.579378\pi$
$631$	−7823.69			−0.493591			−0.246796	+	0.969068i	$0.579378\pi$
$632$	−55687.5	−	32151.2i	−3.50495	−	2.02358i
$633$		0			0
$634$	2515.82	+	4357.53i	0.157596	+	0.272965i
$635$	12263.5	−	21240.9i	0.766395	−	1.32743i
$636$		0			0
$637$		0			0
$638$		−	9921.89i		−	0.615692i
$639$		0			0
$640$	−44730.3	+	25825.0i	−2.76269	+	1.59504i
$641$	268.735	−	155.154i	0.0165591	−	0.00956040i	−0.491698	−	0.870766i	$-0.663623\pi$
$641$	268.735	−	155.154i	0.0165591	−	0.00956040i	0.508257	+	0.861206i	$0.330290\pi$
$642$		0			0
$643$		−	28064.5i		−	1.72124i	−0.509250	−	0.860618i	$-0.670077\pi$
$643$		−	28064.5i		−	1.72124i	0.509250	−	0.860618i	$-0.329923\pi$
$644$		0			0
$645$		0			0
$646$	5451.67	−	9442.57i	0.332033	−	0.575098i
$647$	4219.67	+	7308.68i	0.256402	+	0.444101i	0.965275	−	0.261234i	$-0.0841295\pi$
$647$	4219.67	+	7308.68i	0.256402	+	0.444101i	−0.708873	+	0.705336i	$0.750796\pi$
$648$		0			0
$649$	−17066.3	−	9853.22i	−1.03222	−	0.595952i
$650$	−13388.3			−0.807898
$651$		0			0
$652$	63724.1			3.82765
$653$	22966.4	+	13259.6i	1.37633	+	0.794624i	0.991716	−	0.128453i	$-0.0410012\pi$
$653$	22966.4	+	13259.6i	1.37633	+	0.794624i	0.384614	+	0.923077i	$0.374335\pi$
$654$		0			0
$655$	21201.2	+	36721.5i	1.26473	+	2.19058i
$656$	45322.9	−	78501.6i	2.69750	−	4.67221i
$657$		0			0
$658$		0			0
$659$		−	29625.1i		−	1.75118i	−0.483054	−	0.875591i	$-0.660473\pi$
$659$		−	29625.1i		−	1.75118i	0.483054	−	0.875591i	$-0.339527\pi$
$660$		0			0
$661$	18868.3	−	10893.6i	1.11027	−	0.641018i	0.171374	−	0.985206i	$-0.445179\pi$
$661$	18868.3	−	10893.6i	1.11027	−	0.641018i	0.938901	+	0.344188i	$0.111846\pi$
$662$	23196.9	−	13392.7i	1.36189	−	0.786290i
$663$		0			0
$664$		−	44894.3i		−	2.62385i
$665$		0			0
$666$		0			0
$667$	5918.74	−	10251.6i	0.343590	−	0.595115i
$668$	−7366.63	−	12759.4i	−0.426682	−	0.739035i
$669$		0			0
$670$	−34046.0	−	19656.5i	−1.96315	−	1.13343i
$671$	−536.470			−0.0308647
$672$		0			0
$673$	14551.5			0.833462			0.416731	−	0.909030i	$-0.363176\pi$
$673$	14551.5			0.833462			0.416731	+	0.909030i	$0.363176\pi$
$674$	−23900.8	−	13799.1i	−1.36591	−	0.788608i
$675$		0			0
$676$	21581.6	+	37380.4i	1.22790	+	2.12679i
$677$	6158.05	−	10666.0i	0.349591	−	0.605509i	−0.636586	−	0.771206i	$-0.719654\pi$
$677$	6158.05	−	10666.0i	0.349591	−	0.605509i	0.986177	+	0.165697i	$0.0529873\pi$
$678$		0			0
$679$		0			0
$680$			123411.i			6.95968i
$681$		0			0
$682$	22132.4	−	12778.2i	1.24266	−	0.717450i
$683$	−9488.46	+	5478.16i	−0.531575	+	0.306905i	−0.741658	−	0.670779i	$-0.765960\pi$
$683$	−9488.46	+	5478.16i	−0.531575	+	0.306905i	0.210083	+	0.977684i	$0.432627\pi$
$684$		0			0
$685$		−	40524.9i		−	2.26041i
$686$		0			0
$687$		0			0
$688$	11047.6	−	19135.0i	0.612188	−	1.06034i
$689$	654.361	+	1133.39i	0.0361816	+	0.0626684i
$690$		0			0
$691$	20240.0	+	11685.6i	1.11428	+	0.643328i	0.939934	−	0.341357i	$-0.110887\pi$
$691$	20240.0	+	11685.6i	1.11428	+	0.643328i	0.174343	+	0.984685i	$0.444220\pi$
$692$	−31059.7			−1.70623
$693$		0			0
$694$	27759.6			1.51836
$695$	43146.7	+	24910.8i	2.35489	+	1.35960i
$696$		0			0
$697$	−20994.1	−	36362.9i	−1.14090	−	1.97610i
$698$	7970.49	−	13805.3i	0.432217	−	0.748622i
$699$		0			0
$700$		0			0
$701$			13644.5i			0.735160i	0.929992	+	0.367580i	$0.119814\pi$
$701$			13644.5i			0.735160i	−0.929992	+	0.367580i	$0.880186\pi$
$702$		0			0
$703$	2990.82	−	1726.75i	0.160457	−	0.0926396i
$704$	−27964.1	+	16145.1i	−1.49707	+	0.864335i
$705$		0			0
$706$			60816.6i			3.24202i
$707$		0			0
$708$		0			0
$709$	11964.6	−	20723.3i	0.633767	−	1.09772i	−0.353008	−	0.935620i	$-0.614841\pi$
$709$	11964.6	−	20723.3i	0.633767	−	1.09772i	0.986775	−	0.162096i	$-0.0518256\pi$
$710$	11253.1	+	19490.9i	0.594817	+	1.03025i
$711$		0			0
$712$	−26931.6	−	15549.0i	−1.41756	−	0.818430i
$713$	30490.4			1.60151
$714$		0			0
$715$	−5138.91			−0.268789
$716$	−17390.4	−	10040.3i	−0.907695	−	0.524058i
$717$		0			0
$718$	−7071.59	−	12248.4i	−0.367562	−	0.636636i
$719$	−14781.6	+	25602.4i	−0.766703	+	1.32797i	0.172638	+	0.984985i	$0.444771\pi$
$719$	−14781.6	+	25602.4i	−0.766703	+	1.32797i	−0.939341	+	0.342984i	$0.888562\pi$
$720$		0			0
$721$		0			0
$722$		−	34545.4i		−	1.78067i
$723$		0			0
$724$	−9173.56	+	5296.36i	−0.470902	+	0.271875i
$725$	−14158.5	+	8174.42i	−0.725288	+	0.418745i
$726$		0			0
$727$			3335.51i			0.170161i	0.996374	+	0.0850805i	$0.0271148\pi$
$727$			3335.51i			0.170161i	−0.996374	+	0.0850805i	$0.972885\pi$
$728$		0			0
$729$		0			0
$730$	−13167.1	+	22806.1i	−0.667585	+	1.15629i
$731$	−5117.38	−	8863.56i	−0.258924	−	0.448469i
$732$		0			0
$733$	−10582.6	−	6109.89i	−0.533258	−	0.307877i	0.209084	−	0.977898i	$-0.432952\pi$
$733$	−10582.6	−	6109.89i	−0.533258	−	0.307877i	−0.742342	+	0.670021i	$0.766285\pi$
$734$	−14421.4			−0.725209
$735$		0			0
$736$	−85749.8			−4.29454
$737$	−8204.01	−	4736.59i	−0.410039	−	0.236736i
$738$		0			0
$739$	−8879.68	−	15380.1i	−0.442009	−	0.765581i	0.555830	−	0.831296i	$-0.312401\pi$
$739$	−8879.68	−	15380.1i	−0.442009	−	0.765581i	−0.997838	+	0.0657148i	$0.979067\pi$
$740$	−31594.8	+	54723.8i	−1.56952	+	2.71850i
$741$		0			0
$742$		0			0
$743$		−	5371.15i		−	0.265207i	−0.991169	−	0.132603i	$-0.957666\pi$
$743$		−	5371.15i		−	0.265207i	0.991169	−	0.132603i	$-0.0423336\pi$
$744$		0			0
$745$	29135.3	−	16821.3i	1.43280	−	0.827227i
$746$	24183.6	−	13962.4i	1.18689	−	0.685254i
$747$		0			0
$748$			48073.5i			2.34992i
$749$		0			0
$750$		0			0
$751$	−11636.4	+	20154.8i	−0.565403	+	0.979306i	0.431609	+	0.902061i	$0.357946\pi$
$751$	−11636.4	+	20154.8i	−0.565403	+	0.979306i	−0.997012	+	0.0772457i	$0.975387\pi$
$752$	−1149.62	−	1991.21i	−0.0557480	−	0.0965583i
$753$		0			0
$754$	−4264.46	−	2462.09i	−0.205972	−	0.118918i
$755$	−53026.8			−2.55608
$756$		0			0
$757$	16172.1			0.776465			0.388233	−	0.921561i	$-0.373086\pi$
$757$	16172.1			0.776465			0.388233	+	0.921561i	$0.373086\pi$
$758$	−11514.2	−	6647.76i	−0.551737	−	0.318545i
$759$		0			0
$760$	−13444.3	−	23286.1i	−0.641677	−	1.11142i
$761$	9460.31	−	16385.7i	0.450639	−	0.780529i	−0.547787	−	0.836618i	$-0.684530\pi$
$761$	9460.31	−	16385.7i	0.450639	−	0.780529i	0.998426	+	0.0560887i	$0.0178630\pi$
$762$		0			0
$763$		0			0
$764$		−	48922.3i		−	2.31668i
$765$		0			0
$766$	−52515.1	+	30319.6i	−2.47709	+	1.43015i
$767$	−8469.90	+	4890.10i	−0.398736	+	0.230210i
$768$		0			0
$769$		−	33747.4i		−	1.58253i	−0.611475	−	0.791264i	$-0.709423\pi$
$769$		−	33747.4i		−	1.58253i	0.611475	−	0.791264i	$-0.290577\pi$
$770$		0			0
$771$		0			0
$772$	−41172.6	+	71313.0i	−1.91947	+	3.32463i
$773$	−10806.4	−	18717.2i	−0.502817	−	0.870905i	−0.999995	−	0.00325584i	$-0.998964\pi$
$773$	−10806.4	−	18717.2i	−0.502817	−	0.870905i	0.497178	−	0.867649i	$-0.334370\pi$
$774$		0			0
$775$	−36468.8	−	21055.3i	−1.69032	−	0.975906i
$776$	112976.			5.22631
$777$		0			0
$778$	41386.7			1.90718
$779$	7922.69	+	4574.17i	0.364390	+	0.210381i
$780$		0			0
$781$	2711.63	+	4696.69i	0.124238	+	0.215187i
$782$	−39615.1	+	68615.4i	−1.81155	+	3.13770i
$783$		0			0
$784$		0			0
$785$		−	31312.3i		−	1.42367i
$786$		0			0
$787$	−21260.3	+	12274.6i	−0.962957	+	0.555963i	−0.897082	−	0.441865i	$-0.854317\pi$
$787$	−21260.3	+	12274.6i	−0.962957	+	0.555963i	−0.0658748	+	0.997828i	$0.520984\pi$
$788$	25958.7	−	14987.3i	1.17353	−	0.677538i
$789$		0			0
$790$			90819.1i			4.09013i
$791$		0			0
$792$		0			0
$793$	−133.123	+	230.577i	−0.00596135	+	0.0103254i
$794$	2178.27	+	3772.87i	0.0973600	+	0.168632i
$795$		0			0
$796$	89696.9	+	51786.5i	3.99400	+	2.30594i
$797$	12323.1			0.547687			0.273844	−	0.961774i	$-0.411705\pi$
$797$	12323.1			0.547687			0.273844	+	0.961774i	$0.411705\pi$
$798$		0			0
$799$	−1065.04			−0.0471569
$800$	102563.	+	59214.9i	4.53270	+	2.61695i
$801$		0			0
$802$	11852.8	+	20529.7i	0.521868	+	0.903901i
$803$	−3172.86	+	5495.56i	−0.139437	+	0.241512i
$804$		0			0
$805$		0			0
$806$		−	12683.5i		−	0.554287i
$807$		0			0
$808$	4538.46	−	2620.28i	0.197602	−	0.114086i
$809$	−3177.11	+	1834.31i	−0.138073	+	0.0797167i	−0.567445	−	0.823411i	$-0.692068\pi$
$809$	−3177.11	+	1834.31i	−0.138073	+	0.0797167i	0.429372	+	0.903128i	$0.358735\pi$
$810$		0			0
$811$		−	24967.7i		−	1.08105i	−0.841327	−	0.540527i	$-0.818225\pi$
$811$		−	24967.7i		−	1.08105i	0.841327	−	0.540527i	$-0.181775\pi$
$812$		0			0
$813$		0			0
$814$	−10517.1	+	18216.2i	−0.452856	+	0.784369i
$815$	−27837.6	−	48216.1i	−1.19645	−	2.07231i
$816$		0			0
$817$	1931.18	+	1114.97i	0.0826970	+	0.0477451i
$818$	313.480			0.0133992
$819$		0			0
$820$	−167389.			−7.12865
$821$	5425.51	+	3132.42i	0.230635	+	0.133157i	0.610865	−	0.791735i	$-0.290822\pi$
$821$	5425.51	+	3132.42i	0.230635	+	0.133157i	−0.380230	+	0.924892i	$0.624155\pi$
$822$		0			0
$823$	−1666.86	−	2887.08i	−0.0705990	−	0.122281i	0.828565	−	0.559893i	$-0.189158\pi$
$823$	−1666.86	−	2887.08i	−0.0705990	−	0.122281i	−0.899164	+	0.437612i	$0.855824\pi$
$824$	33669.4	−	58317.1i	1.42346	−	2.46550i
$825$		0			0
$826$		0			0
$827$		−	27785.4i		−	1.16831i	−0.811643	−	0.584154i	$-0.801426\pi$
$827$		−	27785.4i		−	1.16831i	0.811643	−	0.584154i	$-0.198574\pi$
$828$		0			0
$829$	7667.54	−	4426.86i	0.321236	−	0.185466i	−0.330707	−	0.943733i	$-0.607287\pi$
$829$	7667.54	−	4426.86i	0.321236	−	0.185466i	0.651943	+	0.758268i	$0.273954\pi$
$830$	−54912.7	+	31703.8i	−2.29644	+	1.32585i
$831$		0			0
$832$			16025.4i			0.667767i
$833$		0			0
$834$		0			0
$835$	−6436.16	+	11147.8i	−0.266745	+	0.462017i
$836$	−5237.09	−	9070.91i	−0.216661	−	0.375268i
$837$		0			0
$838$	29415.2	+	16982.9i	1.21257	+	0.700075i
$839$	92.8332			0.00381997			0.00190999	−	0.999998i	$-0.499392\pi$
$839$	92.8332			0.00381997			0.00190999	+	0.999998i	$0.499392\pi$
$840$		0			0
$841$	18376.0			0.753453
$842$	4378.47	+	2527.91i	0.179207	+	0.103465i
$843$		0			0
$844$	18918.5	+	32767.8i	0.771566	+	1.33639i
$845$	18855.6	−	32658.9i	0.767638	−	1.32959i
$846$		0			0
$847$		0			0
$848$		−	23091.9i		−	0.935116i
$849$		0			0
$850$	94765.3	−	54712.8i	3.82403	−	2.20780i
$851$	−21733.1	+	12547.6i	−0.875442	+	0.505437i
$852$		0			0
$853$			8509.71i			0.341579i	0.985308	+	0.170790i	$0.0546318\pi$
$853$			8509.71i			0.341579i	−0.985308	+	0.170790i	$0.945368\pi$
$854$		0			0
$855$		0			0
$856$	46525.2	−	80584.1i	1.85771	−	3.21765i
$857$	−19517.2	−	33804.9i	−0.777942	−	1.34744i	−0.933126	−	0.359550i	$-0.882930\pi$
$857$	−19517.2	−	33804.9i	−0.777942	−	1.34744i	0.155184	−	0.987886i	$-0.450403\pi$
$858$		0			0
$859$	30440.2	+	17574.7i	1.20909	+	0.698067i	0.962560	−	0.271069i	$-0.0873771\pi$
$859$	30440.2	+	17574.7i	1.20909	+	0.698067i	0.246527	+	0.969136i	$0.420710\pi$
$860$	−40801.7			−1.61782
$861$		0			0
$862$	51178.1			2.02220
$863$	−13889.2	−	8018.96i	−0.547851	−	0.316302i	0.200404	−	0.979713i	$-0.435775\pi$
$863$	−13889.2	−	8018.96i	−0.547851	−	0.316302i	−0.748255	+	0.663411i	$0.769108\pi$
$864$		0			0
$865$	13568.3	+	23501.0i	0.533336	+	0.923766i
$866$	−25846.1	+	44766.7i	−1.01419	+	1.75662i
$867$		0			0
$868$		0			0
$869$			21884.5i			0.854295i
$870$		0			0
$871$	−4071.60	+	2350.74i	−0.158394	+	0.0914488i
$872$	−53842.2	+	31085.8i	−2.09097	+	1.20722i
$873$		0			0
$874$		−	17262.6i		−	0.668095i
$875$		0			0
$876$		0			0
$877$	−11223.0	+	19438.8i	−0.432126	+	0.748464i	−0.997056	−	0.0766749i	$-0.975570\pi$
$877$	−11223.0	+	19438.8i	−0.432126	+	0.748464i	0.564930	+	0.825139i	$0.308903\pi$
$878$	−2349.63	−	4069.68i	−0.0903146	−	0.156429i
$879$		0			0
$880$	78526.1	+	45337.1i	3.00808	+	1.73672i
$881$	4544.20			0.173778			0.0868888	−	0.996218i	$-0.472308\pi$
$881$	4544.20			0.173778			0.0868888	+	0.996218i	$0.472308\pi$
$882$		0			0
$883$	18749.1			0.714561			0.357280	−	0.933997i	$-0.383704\pi$
$883$	18749.1			0.714561			0.357280	+	0.933997i	$0.383704\pi$
$884$	20662.2	+	11929.3i	0.786135	+	0.453875i
$885$		0			0
$886$	−2164.07	−	3748.27i	−0.0820578	−	0.142128i
$887$	−12553.5	+	21743.4i	−0.475205	+	0.823079i	−0.999597	−	0.0283981i	$-0.990959\pi$
$887$	−12553.5	+	21743.4i	−0.475205	+	0.823079i	0.524392	+	0.851477i	$0.324293\pi$
$888$		0			0
$889$		0			0
$890$			43922.0i			1.65423i
$891$		0			0
$892$	46142.4	−	26640.3i	1.73202	−	0.999982i
$893$	200.960	−	116.025i	0.00753067	−	0.00434783i
$894$		0			0
$895$			17544.3i			0.655242i
$896$		0			0
$897$		0			0
$898$	−34045.1	+	58967.9i	−1.26515	+	2.19130i
$899$	−7744.04	−	13413.1i	−0.287295	−	0.497610i
$900$		0			0
$901$	−9263.39	−	5348.22i	−0.342518	−	0.197753i
$902$	−55719.7			−2.05683
$903$		0			0
$904$	86623.3			3.18700
$905$	8014.85	+	4627.38i	0.294390	+	0.169966i
$906$		0			0
$907$	5098.56	+	8830.96i	0.186654	+	0.323293i	0.944132	−	0.329566i	$-0.106902\pi$
$907$	5098.56	+	8830.96i	0.186654	+	0.323293i	−0.757479	+	0.652860i	$0.773569\pi$
$908$	41730.8	−	72279.8i	1.52520	−	2.64173i
$909$		0			0
$910$		0			0
$911$			27309.8i			0.993208i	0.867977	+	0.496604i	$0.165420\pi$
$911$			27309.8i			0.993208i	−0.867977	+	0.496604i	$0.834580\pi$
$912$		0			0
$913$	−13232.2	+	7639.62i	−0.479652	+	0.276927i
$914$	35553.4	−	20526.7i	1.28665	−	0.742849i
$915$		0			0
$916$			46448.5i			1.67544i
$917$		0			0
$918$		0			0
$919$	117.243	−	203.071i	0.00420837	−	0.00728911i	−0.863914	−	0.503640i	$-0.831994\pi$
$919$	117.243	−	203.071i	0.00420837	−	0.00728911i	0.868122	+	0.496351i	$0.165327\pi$
$920$	97694.1	+	169211.i	3.50096	+	6.06383i
$921$		0			0
$922$	71348.9	+	41193.3i	2.54854	+	1.47140i
$923$	2691.54			0.0959838
$924$		0			0
$925$	34659.2			1.23199
$926$	−45105.4	−	26041.6i	−1.60071	−	0.924169i
$927$		0			0
$928$	21779.0	+	37722.3i	0.770400	+	1.33437i
$929$	12740.7	−	22067.6i	0.449956	−	0.779347i	−0.548426	−	0.836199i	$-0.684773\pi$
$929$	12740.7	−	22067.6i	0.449956	−	0.779347i	0.998383	+	0.0568516i	$0.0181062\pi$
$930$		0			0
$931$		0			0
$932$		−	98335.6i		−	3.45611i
$933$		0			0
$934$	16258.4	−	9386.76i	0.569582	−	0.328848i
$935$	36374.2	−	21000.7i	1.27226	−	0.734541i
$936$		0			0
$937$		−	36561.0i		−	1.27470i	−0.770574	−	0.637350i	$-0.780031\pi$
$937$		−	36561.0i		−	1.27470i	0.770574	−	0.637350i	$-0.219969\pi$
$938$		0			0
$939$		0			0
$940$	−2122.93	+	3677.02i	−0.0736621	+	0.127587i
$941$	17521.1	+	30347.4i	0.606984	+	1.05133i	0.991735	+	0.128306i	$0.0409540\pi$
$941$	17521.1	+	30347.4i	0.606984	+	1.05133i	−0.384751	+	0.923020i	$0.625713\pi$
$942$		0			0
$943$	−57571.0	−	33238.7i	−1.98809	−	1.14783i
$944$	172568.			5.94979
$945$		0			0
$946$	−13581.8			−0.466790
$947$	30868.9	+	17822.1i	1.05924	+	0.611554i	0.925223	−	0.379424i	$-0.123878\pi$
$947$	30868.9	+	17822.1i	1.05924	+	0.611554i	0.134020	+	0.990979i	$0.457211\pi$
$948$		0			0
$949$	1574.67	+	2727.41i	0.0538631	+	0.0932936i
$950$	−11920.7	+	20647.3i	−0.407116	+	0.705145i
$951$		0			0
$952$		0			0
$953$			35376.7i			1.20248i	0.799068	+	0.601240i	$0.205327\pi$
$953$			35376.7i			1.20248i	−0.799068	+	0.601240i	$0.794673\pi$
$954$		0			0
$955$	−37016.5	+	21371.5i	−1.25427	+	0.724151i
$956$	−119451.	+	68965.2i	−4.04114	+	2.33315i
$957$		0			0
$958$		−	97830.3i		−	3.29933i
$959$		0			0
$960$		0			0
$961$	5051.23	−	8748.98i	0.169556	−	0.293679i
$962$	5219.58	+	9040.58i	0.174934	+	0.302994i
$963$		0			0
$964$	−70443.8	−	40670.8i	−2.35357	−	1.35883i
$965$	71944.2			2.39996
$966$		0			0
$967$	−27697.2			−0.921078			−0.460539	−	0.887640i	$-0.652344\pi$
$967$	−27697.2			−0.921078			−0.460539	+	0.887640i	$0.652344\pi$
$968$	−46330.6	−	26749.0i	−1.53835	−	0.888166i
$969$		0			0
$970$	−79782.7	−	138188.i	−2.64089	−	4.57416i
$971$	−15880.0	+	27505.0i	−0.524834	+	0.909040i	0.474747	+	0.880122i	$0.342539\pi$
$971$	−15880.0	+	27505.0i	−0.524834	+	0.909040i	−0.999582	+	0.0289176i	$0.990794\pi$
$972$		0			0
$973$		0			0
$974$			79723.8i			2.62270i
$975$		0			0
$976$	4068.44	−	2348.91i	0.133430	−	0.0770357i
$977$	989.925	−	571.533i	0.0324161	−	0.0187154i	−0.483704	−	0.875231i	$-0.660709\pi$
$977$	989.925	−	571.533i	0.0324161	−	0.0187154i	0.516120	+	0.856516i	$0.327376\pi$
$978$		0			0
$979$			10583.8i			0.345516i
$980$		0			0
$981$		0			0
$982$	13962.0	−	24182.9i	0.453713	−	0.785853i
$983$	−6695.23	−	11596.5i	−0.217238	−	0.376267i	0.736725	−	0.676193i	$-0.236371\pi$
$983$	−6695.23	−	11596.5i	−0.217238	−	0.376267i	−0.953962	+	0.299926i	$0.903038\pi$
$984$		0			0
$985$	−22679.9	−	13094.2i	−0.733646	−	0.423571i
$986$	40246.3			1.29990
$987$		0			0
$988$	−5198.28			−0.167388
$989$	−14033.1	−	8102.02i	−0.451190	−	0.260495i
$990$		0			0
$991$	−8007.84	−	13870.0i	−0.256688	−	0.444596i	0.708665	−	0.705545i	$-0.249298\pi$
$991$	−8007.84	−	13870.0i	−0.256688	−	0.444596i	−0.965353	+	0.260949i	$0.915964\pi$
$992$	−56097.3	+	97163.4i	−1.79545	+	3.10982i
$993$		0			0
$994$		0			0
$995$		−	90490.8i		−	2.88317i
$996$		0			0
$997$	25588.5	−	14773.6i	0.812836	−	0.469291i	−0.0351038	−	0.999384i	$-0.511176\pi$
$997$	25588.5	−	14773.6i	0.812836	−	0.469291i	0.847940	+	0.530093i	$0.177843\pi$
$998$	21374.9	−	12340.8i	0.677965	−	0.391423i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.p.d.215.24		48
3.2	odd	2	inner	441.4.p.d.215.1		48
7.2	even	3		441.4.c.b.440.23	yes	24
7.3	odd	6	inner	441.4.p.d.80.1		48
7.4	even	3	inner	441.4.p.d.80.2		48
7.5	odd	6		441.4.c.b.440.1	✓	24
7.6	odd	2	inner	441.4.p.d.215.23		48
21.2	odd	6		441.4.c.b.440.2	yes	24
21.5	even	6		441.4.c.b.440.24	yes	24
21.11	odd	6	inner	441.4.p.d.80.23		48
21.17	even	6	inner	441.4.p.d.80.24		48
21.20	even	2	inner	441.4.p.d.215.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.4.c.b.440.1	✓	24	7.5	odd	6
441.4.c.b.440.2	yes	24	21.2	odd	6
441.4.c.b.440.23	yes	24	7.2	even	3
441.4.c.b.440.24	yes	24	21.5	even	6
441.4.p.d.80.1		48	7.3	odd	6	inner
441.4.p.d.80.2		48	7.4	even	3	inner
441.4.p.d.80.23		48	21.11	odd	6	inner
441.4.p.d.80.24		48	21.17	even	6	inner
441.4.p.d.215.1		48	3.2	odd	2	inner
441.4.p.d.215.2		48	21.20	even	2	inner
441.4.p.d.215.23		48	7.6	odd	2	inner
441.4.p.d.215.24		48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.66169 + 2.69143i) q^{2} +(10.4876 + 18.1650i) q^{4} +(9.16288 - 15.8706i) q^{5} +69.8432i q^{8} +O(q^{10})\)	\(q+(4.66169 + 2.69143i) q^{2} +(10.4876 + 18.1650i) q^{4} +(9.16288 - 15.8706i) q^{5} +69.8432i q^{8} +(85.4290 - 49.3225i) q^{10} +(20.5857 - 11.8852i) q^{11} -11.7971i q^{13} +(-104.077 + 180.267i) q^{16} +(48.2099 + 83.5020i) q^{17} +(-18.1933 - 10.5039i) q^{19} +384.385 q^{20} +127.952 q^{22} +(132.203 + 76.3277i) q^{23} +(-105.417 - 182.587i) q^{25} +(31.7509 - 54.9943i) q^{26} -77.5438i q^{29} +(172.974 - 99.8667i) q^{31} +(-486.465 + 280.861i) q^{32} +519.014i q^{34} +(-82.1957 + 142.367i) q^{37} +(-56.5410 - 97.9319i) q^{38} +(1108.45 + 639.965i) q^{40} -435.473 q^{41} -106.148 q^{43} +(431.787 + 249.293i) q^{44} +(410.861 + 711.632i) q^{46} +(-5.52293 + 9.56599i) q^{47} -1134.89i q^{50} +(214.294 - 123.722i) q^{52} +(-96.0735 + 55.4681i) q^{53} -435.609i q^{55} +(208.703 - 361.485i) q^{58} +(-414.518 - 717.966i) q^{59} +(-19.5452 - 11.2845i) q^{61} +1075.14 q^{62} -1358.43 q^{64} +(-187.226 - 108.095i) q^{65} +(-199.265 - 345.137i) q^{67} +(-1011.21 + 1751.47i) q^{68} +228.153i q^{71} +(-231.194 + 133.480i) q^{73} +(-766.341 + 442.447i) q^{74} -440.641i q^{76} +(-460.333 + 797.321i) q^{79} +(1907.30 + 3303.54i) q^{80} +(-2030.04 - 1172.04i) q^{82} -642.787 q^{83} +1766.97 q^{85} +(-494.828 - 285.689i) q^{86} +(830.097 + 1437.77i) q^{88} +(-222.627 + 385.601i) q^{89} +3201.97i q^{92} +(-51.4923 + 29.7291i) q^{94} +(-333.406 + 192.492i) q^{95} -1617.57i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4}+O(q^{10}) \) 48 * q + 96 * q^4	\( 48 q + 96 q^{4} - 144 q^{16} + 1248 q^{22} - 312 q^{25} + 864 q^{37} + 2496 q^{43} + 3888 q^{46} + 7440 q^{58} - 6720 q^{64} + 2688 q^{67} - 480 q^{79} + 26496 q^{85} + 7248 q^{88}+O(q^{100}) \) 48 * q + 96 * q^4 - 144 * q^16 + 1248 * q^22 - 312 * q^25 + 864 * q^37 + 2496 * q^43 + 3888 * q^46 + 7440 * q^58 - 6720 * q^64 + 2688 * q^67 - 480 * q^79 + 26496 * q^85 + 7248 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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